from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(790142, base_ring=CyclotomicField(2112))
M = H._module
chi = DirichletCharacter(H, M([0,1296,319]))
chi.galois_orbit()
[g,chi] = znchar(Mod(47,790142))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(790142\) | |
| Conductor: | \(17177\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 17177.gw | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{2112})$ |
| Fixed field: | Number field defined by a degree 2112 polynomial (not computed) |
First 31 of 640 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{790142}(47,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{176}\right)\) | \(e\left(\frac{223}{2112}\right)\) | \(e\left(\frac{109}{264}\right)\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{131}{704}\right)\) | \(e\left(\frac{289}{704}\right)\) | \(e\left(\frac{859}{2112}\right)\) | \(e\left(\frac{769}{2112}\right)\) | \(e\left(\frac{799}{2112}\right)\) | \(e\left(\frac{377}{528}\right)\) |
| \(\chi_{790142}(2393,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{176}\right)\) | \(e\left(\frac{1909}{2112}\right)\) | \(e\left(\frac{31}{264}\right)\) | \(e\left(\frac{7}{88}\right)\) | \(e\left(\frac{449}{704}\right)\) | \(e\left(\frac{523}{704}\right)\) | \(e\left(\frac{1993}{2112}\right)\) | \(e\left(\frac{427}{2112}\right)\) | \(e\left(\frac{949}{2112}\right)\) | \(e\left(\frac{83}{528}\right)\) |
| \(\chi_{790142}(2439,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{35}{176}\right)\) | \(e\left(\frac{569}{2112}\right)\) | \(e\left(\frac{155}{264}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{309}{704}\right)\) | \(e\left(\frac{327}{704}\right)\) | \(e\left(\frac{989}{2112}\right)\) | \(e\left(\frac{551}{2112}\right)\) | \(e\left(\frac{2105}{2112}\right)\) | \(e\left(\frac{415}{528}\right)\) |
| \(\chi_{790142}(2623,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{176}\right)\) | \(e\left(\frac{685}{2112}\right)\) | \(e\left(\frac{175}{264}\right)\) | \(e\left(\frac{31}{88}\right)\) | \(e\left(\frac{153}{704}\right)\) | \(e\left(\frac{531}{704}\right)\) | \(e\left(\frac{1057}{2112}\right)\) | \(e\left(\frac{307}{2112}\right)\) | \(e\left(\frac{1261}{2112}\right)\) | \(e\left(\frac{443}{528}\right)\) |
| \(\chi_{790142}(3911,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{107}{176}\right)\) | \(e\left(\frac{593}{2112}\right)\) | \(e\left(\frac{59}{264}\right)\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{301}{704}\right)\) | \(e\left(\frac{175}{704}\right)\) | \(e\left(\frac{1877}{2112}\right)\) | \(e\left(\frac{719}{2112}\right)\) | \(e\left(\frac{401}{2112}\right)\) | \(e\left(\frac{439}{528}\right)\) |
| \(\chi_{790142}(4877,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{25}{176}\right)\) | \(e\left(\frac{859}{2112}\right)\) | \(e\left(\frac{73}{264}\right)\) | \(e\left(\frac{25}{88}\right)\) | \(e\left(\frac{271}{704}\right)\) | \(e\left(\frac{485}{704}\right)\) | \(e\left(\frac{1159}{2112}\right)\) | \(e\left(\frac{2053}{2112}\right)\) | \(e\left(\frac{1051}{2112}\right)\) | \(e\left(\frac{221}{528}\right)\) |
| \(\chi_{790142}(5153,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{176}\right)\) | \(e\left(\frac{1919}{2112}\right)\) | \(e\left(\frac{101}{264}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{35}{704}\right)\) | \(e\left(\frac{577}{704}\right)\) | \(e\left(\frac{251}{2112}\right)\) | \(e\left(\frac{2081}{2112}\right)\) | \(e\left(\frac{767}{2112}\right)\) | \(e\left(\frac{313}{528}\right)\) |
| \(\chi_{790142}(5291,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{49}{176}\right)\) | \(e\left(\frac{1219}{2112}\right)\) | \(e\left(\frac{217}{264}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{151}{704}\right)\) | \(e\left(\frac{317}{704}\right)\) | \(e\left(\frac{1807}{2112}\right)\) | \(e\left(\frac{349}{2112}\right)\) | \(e\left(\frac{835}{2112}\right)\) | \(e\left(\frac{53}{528}\right)\) |
| \(\chi_{790142}(5567,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{159}{176}\right)\) | \(e\left(\frac{2077}{2112}\right)\) | \(e\left(\frac{151}{264}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{393}{704}\right)\) | \(e\left(\frac{163}{704}\right)\) | \(e\left(\frac{1873}{2112}\right)\) | \(e\left(\frac{1603}{2112}\right)\) | \(e\left(\frac{1693}{2112}\right)\) | \(e\left(\frac{251}{528}\right)\) |
| \(\chi_{790142}(6073,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{131}{176}\right)\) | \(e\left(\frac{601}{2112}\right)\) | \(e\left(\frac{115}{264}\right)\) | \(e\left(\frac{43}{88}\right)\) | \(e\left(\frac{533}{704}\right)\) | \(e\left(\frac{359}{704}\right)\) | \(e\left(\frac{61}{2112}\right)\) | \(e\left(\frac{775}{2112}\right)\) | \(e\left(\frac{1945}{2112}\right)\) | \(e\left(\frac{95}{528}\right)\) |
| \(\chi_{790142}(6717,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{75}{176}\right)\) | \(e\left(\frac{817}{2112}\right)\) | \(e\left(\frac{43}{264}\right)\) | \(e\left(\frac{75}{88}\right)\) | \(e\left(\frac{461}{704}\right)\) | \(e\left(\frac{399}{704}\right)\) | \(e\left(\frac{1717}{2112}\right)\) | \(e\left(\frac{175}{2112}\right)\) | \(e\left(\frac{1393}{2112}\right)\) | \(e\left(\frac{311}{528}\right)\) |
| \(\chi_{790142}(7315,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{89}{176}\right)\) | \(e\left(\frac{59}{2112}\right)\) | \(e\left(\frac{17}{264}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{303}{704}\right)\) | \(e\left(\frac{389}{704}\right)\) | \(e\left(\frac{1127}{2112}\right)\) | \(e\left(\frac{677}{2112}\right)\) | \(e\left(\frac{827}{2112}\right)\) | \(e\left(\frac{301}{528}\right)\) |
| \(\chi_{790142}(9799,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{147}{176}\right)\) | \(e\left(\frac{841}{2112}\right)\) | \(e\left(\frac{211}{264}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{453}{704}\right)\) | \(e\left(\frac{247}{704}\right)\) | \(e\left(\frac{493}{2112}\right)\) | \(e\left(\frac{343}{2112}\right)\) | \(e\left(\frac{1801}{2112}\right)\) | \(e\left(\frac{335}{528}\right)\) |
| \(\chi_{790142}(11409,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{176}\right)\) | \(e\left(\frac{1907}{2112}\right)\) | \(e\left(\frac{17}{264}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{391}{704}\right)\) | \(e\left(\frac{653}{704}\right)\) | \(e\left(\frac{1919}{2112}\right)\) | \(e\left(\frac{941}{2112}\right)\) | \(e\left(\frac{563}{2112}\right)\) | \(e\left(\frac{37}{528}\right)\) |
| \(\chi_{790142}(14905,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{163}{176}\right)\) | \(e\left(\frac{553}{2112}\right)\) | \(e\left(\frac{43}{264}\right)\) | \(e\left(\frac{75}{88}\right)\) | \(e\left(\frac{549}{704}\right)\) | \(e\left(\frac{663}{704}\right)\) | \(e\left(\frac{397}{2112}\right)\) | \(e\left(\frac{439}{2112}\right)\) | \(e\left(\frac{1129}{2112}\right)\) | \(e\left(\frac{47}{528}\right)\) |
| \(\chi_{790142}(17987,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{59}{176}\right)\) | \(e\left(\frac{1105}{2112}\right)\) | \(e\left(\frac{211}{264}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{365}{704}\right)\) | \(e\left(\frac{687}{704}\right)\) | \(e\left(\frac{1813}{2112}\right)\) | \(e\left(\frac{79}{2112}\right)\) | \(e\left(\frac{2065}{2112}\right)\) | \(e\left(\frac{71}{528}\right)\) |
| \(\chi_{790142}(19919,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{111}{176}\right)\) | \(e\left(\frac{653}{2112}\right)\) | \(e\left(\frac{215}{264}\right)\) | \(e\left(\frac{23}{88}\right)\) | \(e\left(\frac{633}{704}\right)\) | \(e\left(\frac{499}{704}\right)\) | \(e\left(\frac{1985}{2112}\right)\) | \(e\left(\frac{83}{2112}\right)\) | \(e\left(\frac{1421}{2112}\right)\) | \(e\left(\frac{235}{528}\right)\) |
| \(\chi_{790142}(22081,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{15}{176}\right)\) | \(e\left(\frac{973}{2112}\right)\) | \(e\left(\frac{79}{264}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{57}{704}\right)\) | \(e\left(\frac{115}{704}\right)\) | \(e\left(\frac{1153}{2112}\right)\) | \(e\left(\frac{211}{2112}\right)\) | \(e\left(\frac{1933}{2112}\right)\) | \(e\left(\frac{203}{528}\right)\) |
| \(\chi_{790142}(22449,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{87}{176}\right)\) | \(e\left(\frac{997}{2112}\right)\) | \(e\left(\frac{247}{264}\right)\) | \(e\left(\frac{87}{88}\right)\) | \(e\left(\frac{49}{704}\right)\) | \(e\left(\frac{667}{704}\right)\) | \(e\left(\frac{2041}{2112}\right)\) | \(e\left(\frac{379}{2112}\right)\) | \(e\left(\frac{229}{2112}\right)\) | \(e\left(\frac{227}{528}\right)\) |
| \(\chi_{790142}(24795,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{176}\right)\) | \(e\left(\frac{679}{2112}\right)\) | \(e\left(\frac{133}{264}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{683}{704}\right)\) | \(e\left(\frac{217}{704}\right)\) | \(e\left(\frac{835}{2112}\right)\) | \(e\left(\frac{1849}{2112}\right)\) | \(e\left(\frac{103}{2112}\right)\) | \(e\left(\frac{305}{528}\right)\) |
| \(\chi_{790142}(26175,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{147}{176}\right)\) | \(e\left(\frac{1193}{2112}\right)\) | \(e\left(\frac{35}{264}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{101}{704}\right)\) | \(e\left(\frac{599}{704}\right)\) | \(e\left(\frac{845}{2112}\right)\) | \(e\left(\frac{695}{2112}\right)\) | \(e\left(\frac{41}{2112}\right)\) | \(e\left(\frac{511}{528}\right)\) |
| \(\chi_{790142}(26451,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{91}{176}\right)\) | \(e\left(\frac{1057}{2112}\right)\) | \(e\left(\frac{139}{264}\right)\) | \(e\left(\frac{3}{88}\right)\) | \(e\left(\frac{381}{704}\right)\) | \(e\left(\frac{287}{704}\right)\) | \(e\left(\frac{37}{2112}\right)\) | \(e\left(\frac{1855}{2112}\right)\) | \(e\left(\frac{1249}{2112}\right)\) | \(e\left(\frac{23}{528}\right)\) |
| \(\chi_{790142}(27003,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{167}{176}\right)\) | \(e\left(\frac{1493}{2112}\right)\) | \(e\left(\frac{23}{264}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{353}{704}\right)\) | \(e\left(\frac{107}{704}\right)\) | \(e\left(\frac{1385}{2112}\right)\) | \(e\left(\frac{1739}{2112}\right)\) | \(e\left(\frac{917}{2112}\right)\) | \(e\left(\frac{19}{528}\right)\) |
| \(\chi_{790142}(27187,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{119}{176}\right)\) | \(e\left(\frac{773}{2112}\right)\) | \(e\left(\frac{263}{264}\right)\) | \(e\left(\frac{31}{88}\right)\) | \(e\left(\frac{593}{704}\right)\) | \(e\left(\frac{443}{704}\right)\) | \(e\left(\frac{89}{2112}\right)\) | \(e\left(\frac{923}{2112}\right)\) | \(e\left(\frac{1349}{2112}\right)\) | \(e\left(\frac{355}{528}\right)\) |
| \(\chi_{790142}(28015,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{127}{176}\right)\) | \(e\left(\frac{1597}{2112}\right)\) | \(e\left(\frac{223}{264}\right)\) | \(e\left(\frac{39}{88}\right)\) | \(e\left(\frac{553}{704}\right)\) | \(e\left(\frac{387}{704}\right)\) | \(e\left(\frac{1009}{2112}\right)\) | \(e\left(\frac{355}{2112}\right)\) | \(e\left(\frac{1981}{2112}\right)\) | \(e\left(\frac{299}{528}\right)\) |
| \(\chi_{790142}(28705,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{176}\right)\) | \(e\left(\frac{1147}{2112}\right)\) | \(e\left(\frac{241}{264}\right)\) | \(e\left(\frac{9}{88}\right)\) | \(e\left(\frac{175}{704}\right)\) | \(e\left(\frac{69}{704}\right)\) | \(e\left(\frac{1255}{2112}\right)\) | \(e\left(\frac{1957}{2112}\right)\) | \(e\left(\frac{1723}{2112}\right)\) | \(e\left(\frac{509}{528}\right)\) |
| \(\chi_{790142}(28935,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{176}\right)\) | \(e\left(\frac{743}{2112}\right)\) | \(e\left(\frac{53}{264}\right)\) | \(e\left(\frac{29}{88}\right)\) | \(e\left(\frac{427}{704}\right)\) | \(e\left(\frac{281}{704}\right)\) | \(e\left(\frac{1091}{2112}\right)\) | \(e\left(\frac{185}{2112}\right)\) | \(e\left(\frac{1895}{2112}\right)\) | \(e\left(\frac{193}{528}\right)\) |
| \(\chi_{790142}(29717,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{169}{176}\right)\) | \(e\left(\frac{203}{2112}\right)\) | \(e\left(\frac{233}{264}\right)\) | \(e\left(\frac{81}{88}\right)\) | \(e\left(\frac{255}{704}\right)\) | \(e\left(\frac{181}{704}\right)\) | \(e\left(\frac{119}{2112}\right)\) | \(e\left(\frac{1685}{2112}\right)\) | \(e\left(\frac{1163}{2112}\right)\) | \(e\left(\frac{445}{528}\right)\) |
| \(\chi_{790142}(30545,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{91}{176}\right)\) | \(e\left(\frac{1937}{2112}\right)\) | \(e\left(\frac{227}{264}\right)\) | \(e\left(\frac{3}{88}\right)\) | \(e\left(\frac{557}{704}\right)\) | \(e\left(\frac{111}{704}\right)\) | \(e\left(\frac{917}{2112}\right)\) | \(e\left(\frac{1679}{2112}\right)\) | \(e\left(\frac{17}{2112}\right)\) | \(e\left(\frac{199}{528}\right)\) |
| \(\chi_{790142}(31511,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{176}\right)\) | \(e\left(\frac{1627}{2112}\right)\) | \(e\left(\frac{169}{264}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{15}{704}\right)\) | \(e\left(\frac{549}{704}\right)\) | \(e\left(\frac{7}{2112}\right)\) | \(e\left(\frac{1093}{2112}\right)\) | \(e\left(\frac{1435}{2112}\right)\) | \(e\left(\frac{461}{528}\right)\) |
| \(\chi_{790142}(31879,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{89}{176}\right)\) | \(e\left(\frac{235}{2112}\right)\) | \(e\left(\frac{193}{264}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{479}{704}\right)\) | \(e\left(\frac{213}{704}\right)\) | \(e\left(\frac{1303}{2112}\right)\) | \(e\left(\frac{1909}{2112}\right)\) | \(e\left(\frac{1003}{2112}\right)\) | \(e\left(\frac{125}{528}\right)\) |