from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(79350, base_ring=CyclotomicField(230))
M = H._module
chi = DirichletCharacter(H, M([0,46,145]))
chi.galois_orbit()
[g,chi] = znchar(Mod(91,79350))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(79350\) | |
| Conductor: | \(13225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(230\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 13225.bh | 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: | $\Q(\zeta_{115})$ |
| Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
First 31 of 88 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{79350}(91,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{61}{230}\right)\) | \(e\left(\frac{67}{115}\right)\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{43}{230}\right)\) | \(e\left(\frac{111}{115}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{219}{230}\right)\) | \(e\left(\frac{22}{115}\right)\) | \(e\left(\frac{1}{46}\right)\) |
| \(\chi_{79350}(781,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{47}{230}\right)\) | \(e\left(\frac{29}{115}\right)\) | \(e\left(\frac{81}{230}\right)\) | \(e\left(\frac{101}{230}\right)\) | \(e\left(\frac{12}{115}\right)\) | \(e\left(\frac{33}{115}\right)\) | \(e\left(\frac{33}{230}\right)\) | \(e\left(\frac{49}{115}\right)\) | \(e\left(\frac{43}{46}\right)\) |
| \(\chi_{79350}(1471,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{33}{230}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{189}{230}\right)\) | \(e\left(\frac{159}{230}\right)\) | \(e\left(\frac{28}{115}\right)\) | \(e\left(\frac{77}{115}\right)\) | \(e\left(\frac{77}{230}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{39}{46}\right)\) |
| \(\chi_{79350}(2161,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{19}{230}\right)\) | \(e\left(\frac{68}{115}\right)\) | \(e\left(\frac{67}{230}\right)\) | \(e\left(\frac{217}{230}\right)\) | \(e\left(\frac{44}{115}\right)\) | \(e\left(\frac{6}{115}\right)\) | \(e\left(\frac{121}{230}\right)\) | \(e\left(\frac{103}{115}\right)\) | \(e\left(\frac{35}{46}\right)\) |
| \(\chi_{79350}(3541,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{221}{230}\right)\) | \(e\left(\frac{107}{115}\right)\) | \(e\left(\frac{53}{230}\right)\) | \(e\left(\frac{103}{230}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{94}{115}\right)\) | \(e\left(\frac{209}{230}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{27}{46}\right)\) |
| \(\chi_{79350}(4921,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{193}{230}\right)\) | \(e\left(\frac{31}{115}\right)\) | \(e\left(\frac{39}{230}\right)\) | \(e\left(\frac{219}{230}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{67}{115}\right)\) | \(e\left(\frac{67}{230}\right)\) | \(e\left(\frac{96}{115}\right)\) | \(e\left(\frac{19}{46}\right)\) |
| \(\chi_{79350}(5611,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{179}{230}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{147}{230}\right)\) | \(e\left(\frac{47}{230}\right)\) | \(e\left(\frac{9}{115}\right)\) | \(e\left(\frac{111}{115}\right)\) | \(e\left(\frac{111}{230}\right)\) | \(e\left(\frac{8}{115}\right)\) | \(e\left(\frac{15}{46}\right)\) |
| \(\chi_{79350}(6991,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{151}{230}\right)\) | \(e\left(\frac{32}{115}\right)\) | \(e\left(\frac{133}{230}\right)\) | \(e\left(\frac{163}{230}\right)\) | \(e\left(\frac{41}{115}\right)\) | \(e\left(\frac{84}{115}\right)\) | \(e\left(\frac{199}{230}\right)\) | \(e\left(\frac{62}{115}\right)\) | \(e\left(\frac{7}{46}\right)\) |
| \(\chi_{79350}(7681,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{137}{230}\right)\) | \(e\left(\frac{109}{115}\right)\) | \(e\left(\frac{11}{230}\right)\) | \(e\left(\frac{221}{230}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{13}{115}\right)\) | \(e\left(\frac{13}{230}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{3}{46}\right)\) |
| \(\chi_{79350}(8371,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{123}{230}\right)\) | \(e\left(\frac{71}{115}\right)\) | \(e\left(\frac{119}{230}\right)\) | \(e\left(\frac{49}{230}\right)\) | \(e\left(\frac{73}{115}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{57}{230}\right)\) | \(e\left(\frac{1}{115}\right)\) | \(e\left(\frac{45}{46}\right)\) |
| \(\chi_{79350}(9061,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{109}{230}\right)\) | \(e\left(\frac{33}{115}\right)\) | \(e\left(\frac{227}{230}\right)\) | \(e\left(\frac{107}{230}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{101}{115}\right)\) | \(e\left(\frac{101}{230}\right)\) | \(e\left(\frac{28}{115}\right)\) | \(e\left(\frac{41}{46}\right)\) |
| \(\chi_{79350}(10441,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{81}{230}\right)\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{213}{230}\right)\) | \(e\left(\frac{223}{230}\right)\) | \(e\left(\frac{6}{115}\right)\) | \(e\left(\frac{74}{115}\right)\) | \(e\left(\frac{189}{230}\right)\) | \(e\left(\frac{82}{115}\right)\) | \(e\left(\frac{33}{46}\right)\) |
| \(\chi_{79350}(11131,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{67}{230}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{91}{230}\right)\) | \(e\left(\frac{51}{230}\right)\) | \(e\left(\frac{22}{115}\right)\) | \(e\left(\frac{3}{115}\right)\) | \(e\left(\frac{3}{230}\right)\) | \(e\left(\frac{109}{115}\right)\) | \(e\left(\frac{29}{46}\right)\) |
| \(\chi_{79350}(11821,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{53}{230}\right)\) | \(e\left(\frac{111}{115}\right)\) | \(e\left(\frac{199}{230}\right)\) | \(e\left(\frac{109}{230}\right)\) | \(e\left(\frac{38}{115}\right)\) | \(e\left(\frac{47}{115}\right)\) | \(e\left(\frac{47}{230}\right)\) | \(e\left(\frac{21}{115}\right)\) | \(e\left(\frac{25}{46}\right)\) |
| \(\chi_{79350}(12511,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{39}{230}\right)\) | \(e\left(\frac{73}{115}\right)\) | \(e\left(\frac{77}{230}\right)\) | \(e\left(\frac{167}{230}\right)\) | \(e\left(\frac{54}{115}\right)\) | \(e\left(\frac{91}{115}\right)\) | \(e\left(\frac{91}{230}\right)\) | \(e\left(\frac{48}{115}\right)\) | \(e\left(\frac{21}{46}\right)\) |
| \(\chi_{79350}(13891,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{11}{230}\right)\) | \(e\left(\frac{112}{115}\right)\) | \(e\left(\frac{63}{230}\right)\) | \(e\left(\frac{53}{230}\right)\) | \(e\left(\frac{86}{115}\right)\) | \(e\left(\frac{64}{115}\right)\) | \(e\left(\frac{179}{230}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{13}{46}\right)\) |
| \(\chi_{79350}(14581,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{227}{230}\right)\) | \(e\left(\frac{74}{115}\right)\) | \(e\left(\frac{171}{230}\right)\) | \(e\left(\frac{111}{230}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{223}{230}\right)\) | \(e\left(\frac{14}{115}\right)\) | \(e\left(\frac{9}{46}\right)\) |
| \(\chi_{79350}(15271,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{213}{230}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{49}{230}\right)\) | \(e\left(\frac{169}{230}\right)\) | \(e\left(\frac{3}{115}\right)\) | \(e\left(\frac{37}{115}\right)\) | \(e\left(\frac{37}{230}\right)\) | \(e\left(\frac{41}{115}\right)\) | \(e\left(\frac{5}{46}\right)\) |
| \(\chi_{79350}(15961,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{199}{230}\right)\) | \(e\left(\frac{113}{115}\right)\) | \(e\left(\frac{157}{230}\right)\) | \(e\left(\frac{227}{230}\right)\) | \(e\left(\frac{19}{115}\right)\) | \(e\left(\frac{81}{115}\right)\) | \(e\left(\frac{81}{230}\right)\) | \(e\left(\frac{68}{115}\right)\) | \(e\left(\frac{1}{46}\right)\) |
| \(\chi_{79350}(17341,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{171}{230}\right)\) | \(e\left(\frac{37}{115}\right)\) | \(e\left(\frac{143}{230}\right)\) | \(e\left(\frac{113}{230}\right)\) | \(e\left(\frac{51}{115}\right)\) | \(e\left(\frac{54}{115}\right)\) | \(e\left(\frac{169}{230}\right)\) | \(e\left(\frac{7}{115}\right)\) | \(e\left(\frac{39}{46}\right)\) |
| \(\chi_{79350}(18031,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{157}{230}\right)\) | \(e\left(\frac{114}{115}\right)\) | \(e\left(\frac{21}{230}\right)\) | \(e\left(\frac{171}{230}\right)\) | \(e\left(\frac{67}{115}\right)\) | \(e\left(\frac{98}{115}\right)\) | \(e\left(\frac{213}{230}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{35}{46}\right)\) |
| \(\chi_{79350}(18721,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{143}{230}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{129}{230}\right)\) | \(e\left(\frac{229}{230}\right)\) | \(e\left(\frac{83}{115}\right)\) | \(e\left(\frac{27}{115}\right)\) | \(e\left(\frac{27}{230}\right)\) | \(e\left(\frac{61}{115}\right)\) | \(e\left(\frac{31}{46}\right)\) |
| \(\chi_{79350}(19411,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{129}{230}\right)\) | \(e\left(\frac{38}{115}\right)\) | \(e\left(\frac{7}{230}\right)\) | \(e\left(\frac{57}{230}\right)\) | \(e\left(\frac{99}{115}\right)\) | \(e\left(\frac{71}{115}\right)\) | \(e\left(\frac{71}{230}\right)\) | \(e\left(\frac{88}{115}\right)\) | \(e\left(\frac{27}{46}\right)\) |
| \(\chi_{79350}(20791,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{101}{230}\right)\) | \(e\left(\frac{77}{115}\right)\) | \(e\left(\frac{223}{230}\right)\) | \(e\left(\frac{173}{230}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{44}{115}\right)\) | \(e\left(\frac{159}{230}\right)\) | \(e\left(\frac{27}{115}\right)\) | \(e\left(\frac{19}{46}\right)\) |
| \(\chi_{79350}(21481,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{87}{230}\right)\) | \(e\left(\frac{39}{115}\right)\) | \(e\left(\frac{101}{230}\right)\) | \(e\left(\frac{1}{230}\right)\) | \(e\left(\frac{32}{115}\right)\) | \(e\left(\frac{88}{115}\right)\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{54}{115}\right)\) | \(e\left(\frac{15}{46}\right)\) |
| \(\chi_{79350}(22171,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{73}{230}\right)\) | \(e\left(\frac{1}{115}\right)\) | \(e\left(\frac{209}{230}\right)\) | \(e\left(\frac{59}{230}\right)\) | \(e\left(\frac{48}{115}\right)\) | \(e\left(\frac{17}{115}\right)\) | \(e\left(\frac{17}{230}\right)\) | \(e\left(\frac{81}{115}\right)\) | \(e\left(\frac{11}{46}\right)\) |
| \(\chi_{79350}(22861,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{59}{230}\right)\) | \(e\left(\frac{78}{115}\right)\) | \(e\left(\frac{87}{230}\right)\) | \(e\left(\frac{117}{230}\right)\) | \(e\left(\frac{64}{115}\right)\) | \(e\left(\frac{61}{115}\right)\) | \(e\left(\frac{61}{230}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{7}{46}\right)\) |
| \(\chi_{79350}(24241,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{31}{230}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{73}{230}\right)\) | \(e\left(\frac{3}{230}\right)\) | \(e\left(\frac{96}{115}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{149}{230}\right)\) | \(e\left(\frac{47}{115}\right)\) | \(e\left(\frac{45}{46}\right)\) |
| \(\chi_{79350}(24931,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{17}{230}\right)\) | \(e\left(\frac{79}{115}\right)\) | \(e\left(\frac{181}{230}\right)\) | \(e\left(\frac{61}{230}\right)\) | \(e\left(\frac{112}{115}\right)\) | \(e\left(\frac{78}{115}\right)\) | \(e\left(\frac{193}{230}\right)\) | \(e\left(\frac{74}{115}\right)\) | \(e\left(\frac{41}{46}\right)\) |
| \(\chi_{79350}(25621,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{3}{230}\right)\) | \(e\left(\frac{41}{115}\right)\) | \(e\left(\frac{59}{230}\right)\) | \(e\left(\frac{119}{230}\right)\) | \(e\left(\frac{13}{115}\right)\) | \(e\left(\frac{7}{115}\right)\) | \(e\left(\frac{7}{230}\right)\) | \(e\left(\frac{101}{115}\right)\) | \(e\left(\frac{37}{46}\right)\) |
| \(\chi_{79350}(26311,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{219}{230}\right)\) | \(e\left(\frac{3}{115}\right)\) | \(e\left(\frac{167}{230}\right)\) | \(e\left(\frac{177}{230}\right)\) | \(e\left(\frac{29}{115}\right)\) | \(e\left(\frac{51}{115}\right)\) | \(e\left(\frac{51}{230}\right)\) | \(e\left(\frac{13}{115}\right)\) | \(e\left(\frac{33}{46}\right)\) |