from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(191, base_ring=CyclotomicField(190))
M = H._module
chi = DirichletCharacter(H, M([1]))
chi.galois_orbit()
[g,chi] = znchar(Mod(19,191))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(191\) | |
| Conductor: | \(191\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(190\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | 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: | $\Q(\zeta_{95})$ |
| Fixed field: | Number field defined by a degree 190 polynomial (not computed) |
First 31 of 72 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{191}(19,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{22}{95}\right)\) | \(e\left(\frac{58}{95}\right)\) | \(e\left(\frac{44}{95}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{66}{95}\right)\) | \(e\left(\frac{21}{95}\right)\) | \(e\left(\frac{47}{95}\right)\) | \(e\left(\frac{17}{38}\right)\) |
| \(\chi_{191}(21,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{44}{95}\right)\) | \(e\left(\frac{21}{95}\right)\) | \(e\left(\frac{88}{95}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{37}{95}\right)\) | \(e\left(\frac{42}{95}\right)\) | \(e\left(\frac{94}{95}\right)\) | \(e\left(\frac{15}{38}\right)\) |
| \(\chi_{191}(22,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{83}{95}\right)\) | \(e\left(\frac{72}{95}\right)\) | \(e\left(\frac{71}{95}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{59}{95}\right)\) | \(e\left(\frac{49}{95}\right)\) | \(e\left(\frac{78}{95}\right)\) | \(e\left(\frac{27}{38}\right)\) |
| \(\chi_{191}(28,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{93}{95}\right)\) | \(e\left(\frac{12}{95}\right)\) | \(e\left(\frac{91}{95}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{89}{95}\right)\) | \(e\left(\frac{24}{95}\right)\) | \(e\left(\frac{13}{95}\right)\) | \(e\left(\frac{33}{38}\right)\) |
| \(\chi_{191}(29,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{61}{95}\right)\) | \(e\left(\frac{14}{95}\right)\) | \(e\left(\frac{27}{95}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{88}{95}\right)\) | \(e\left(\frac{28}{95}\right)\) | \(e\left(\frac{31}{95}\right)\) | \(e\left(\frac{29}{38}\right)\) |
| \(\chi_{191}(33,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{52}{95}\right)\) | \(e\left(\frac{68}{95}\right)\) | \(e\left(\frac{9}{95}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{61}{95}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{42}{95}\right)\) | \(e\left(\frac{35}{38}\right)\) |
| \(\chi_{191}(35,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{95}\right)\) | \(e\left(\frac{88}{95}\right)\) | \(e\left(\frac{34}{95}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{51}{95}\right)\) | \(e\left(\frac{81}{95}\right)\) | \(e\left(\frac{32}{95}\right)\) | \(e\left(\frac{33}{38}\right)\) |
| \(\chi_{191}(42,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{62}{95}\right)\) | \(e\left(\frac{8}{95}\right)\) | \(e\left(\frac{29}{95}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{91}{95}\right)\) | \(e\left(\frac{16}{95}\right)\) | \(e\left(\frac{72}{95}\right)\) | \(e\left(\frac{3}{38}\right)\) |
| \(\chi_{191}(44,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{6}{95}\right)\) | \(e\left(\frac{59}{95}\right)\) | \(e\left(\frac{12}{95}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{18}{95}\right)\) | \(e\left(\frac{23}{95}\right)\) | \(e\left(\frac{56}{95}\right)\) | \(e\left(\frac{15}{38}\right)\) |
| \(\chi_{191}(47,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{46}{95}\right)\) | \(e\left(\frac{9}{95}\right)\) | \(e\left(\frac{92}{95}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{43}{95}\right)\) | \(e\left(\frac{18}{95}\right)\) | \(e\left(\frac{81}{95}\right)\) | \(e\left(\frac{1}{38}\right)\) |
| \(\chi_{191}(53,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{95}\right)\) | \(e\left(\frac{47}{95}\right)\) | \(e\left(\frac{16}{95}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{24}{95}\right)\) | \(e\left(\frac{94}{95}\right)\) | \(e\left(\frac{43}{95}\right)\) | \(e\left(\frac{1}{38}\right)\) |
| \(\chi_{191}(56,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{16}{95}\right)\) | \(e\left(\frac{94}{95}\right)\) | \(e\left(\frac{32}{95}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{48}{95}\right)\) | \(e\left(\frac{93}{95}\right)\) | \(e\left(\frac{86}{95}\right)\) | \(e\left(\frac{21}{38}\right)\) |
| \(\chi_{191}(57,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{95}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{18}{95}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{27}{95}\right)\) | \(e\left(\frac{82}{95}\right)\) | \(e\left(\frac{84}{95}\right)\) | \(e\left(\frac{13}{38}\right)\) |
| \(\chi_{191}(58,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{95}\right)\) | \(e\left(\frac{1}{95}\right)\) | \(e\left(\frac{63}{95}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{47}{95}\right)\) | \(e\left(\frac{2}{95}\right)\) | \(e\left(\frac{9}{95}\right)\) | \(e\left(\frac{17}{38}\right)\) |
| \(\chi_{191}(61,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{67}{95}\right)\) | \(e\left(\frac{73}{95}\right)\) | \(e\left(\frac{39}{95}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{11}{95}\right)\) | \(e\left(\frac{51}{95}\right)\) | \(e\left(\frac{87}{95}\right)\) | \(e\left(\frac{25}{38}\right)\) |
| \(\chi_{191}(62,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{68}{95}\right)\) | \(e\left(\frac{67}{95}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{14}{95}\right)\) | \(e\left(\frac{39}{95}\right)\) | \(e\left(\frac{33}{95}\right)\) | \(e\left(\frac{37}{38}\right)\) |
| \(\chi_{191}(63,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{95}\right)\) | \(e\left(\frac{4}{95}\right)\) | \(e\left(\frac{62}{95}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{93}{95}\right)\) | \(e\left(\frac{8}{95}\right)\) | \(e\left(\frac{36}{95}\right)\) | \(e\left(\frac{11}{38}\right)\) |
| \(\chi_{191}(71,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{95}\right)\) | \(e\left(\frac{89}{95}\right)\) | \(e\left(\frac{2}{95}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{95}\right)\) | \(e\left(\frac{83}{95}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{31}{38}\right)\) |
| \(\chi_{191}(73,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{95}\right)\) | \(e\left(\frac{29}{95}\right)\) | \(e\left(\frac{22}{95}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{33}{95}\right)\) | \(e\left(\frac{58}{95}\right)\) | \(e\left(\frac{71}{95}\right)\) | \(e\left(\frac{37}{38}\right)\) |
| \(\chi_{191}(74,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{63}{95}\right)\) | \(e\left(\frac{2}{95}\right)\) | \(e\left(\frac{31}{95}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{94}{95}\right)\) | \(e\left(\frac{4}{95}\right)\) | \(e\left(\frac{18}{95}\right)\) | \(e\left(\frac{15}{38}\right)\) |
| \(\chi_{191}(76,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{58}{95}\right)\) | \(e\left(\frac{32}{95}\right)\) | \(e\left(\frac{21}{95}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{79}{95}\right)\) | \(e\left(\frac{64}{95}\right)\) | \(e\left(\frac{3}{95}\right)\) | \(e\left(\frac{31}{38}\right)\) |
| \(\chi_{191}(83,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{92}{95}\right)\) | \(e\left(\frac{18}{95}\right)\) | \(e\left(\frac{89}{95}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{86}{95}\right)\) | \(e\left(\frac{36}{95}\right)\) | \(e\left(\frac{67}{95}\right)\) | \(e\left(\frac{21}{38}\right)\) |
| \(\chi_{191}(87,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{48}{95}\right)\) | \(e\left(\frac{92}{95}\right)\) | \(e\left(\frac{1}{95}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{49}{95}\right)\) | \(e\left(\frac{89}{95}\right)\) | \(e\left(\frac{68}{95}\right)\) | \(e\left(\frac{25}{38}\right)\) |
| \(\chi_{191}(88,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{24}{95}\right)\) | \(e\left(\frac{46}{95}\right)\) | \(e\left(\frac{48}{95}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{72}{95}\right)\) | \(e\left(\frac{92}{95}\right)\) | \(e\left(\frac{34}{95}\right)\) | \(e\left(\frac{3}{38}\right)\) |
| \(\chi_{191}(89,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{71}{95}\right)\) | \(e\left(\frac{49}{95}\right)\) | \(e\left(\frac{47}{95}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{23}{95}\right)\) | \(e\left(\frac{3}{95}\right)\) | \(e\left(\frac{61}{95}\right)\) | \(e\left(\frac{35}{38}\right)\) |
| \(\chi_{191}(91,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{51}{95}\right)\) | \(e\left(\frac{74}{95}\right)\) | \(e\left(\frac{7}{95}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{58}{95}\right)\) | \(e\left(\frac{53}{95}\right)\) | \(e\left(\frac{1}{95}\right)\) | \(e\left(\frac{23}{38}\right)\) |
| \(\chi_{191}(93,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{95}\right)\) | \(e\left(\frac{63}{95}\right)\) | \(e\left(\frac{74}{95}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{16}{95}\right)\) | \(e\left(\frac{31}{95}\right)\) | \(e\left(\frac{92}{95}\right)\) | \(e\left(\frac{7}{38}\right)\) |
| \(\chi_{191}(94,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{64}{95}\right)\) | \(e\left(\frac{91}{95}\right)\) | \(e\left(\frac{33}{95}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{95}\right)\) | \(e\left(\frac{87}{95}\right)\) | \(e\left(\frac{59}{95}\right)\) | \(e\left(\frac{27}{38}\right)\) |
| \(\chi_{191}(95,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{77}{95}\right)\) | \(e\left(\frac{13}{95}\right)\) | \(e\left(\frac{59}{95}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{26}{95}\right)\) | \(e\left(\frac{22}{95}\right)\) | \(e\left(\frac{31}{38}\right)\) |
| \(\chi_{191}(99,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{39}{95}\right)\) | \(e\left(\frac{51}{95}\right)\) | \(e\left(\frac{78}{95}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{22}{95}\right)\) | \(e\left(\frac{7}{95}\right)\) | \(e\left(\frac{79}{95}\right)\) | \(e\left(\frac{31}{38}\right)\) |
| \(\chi_{191}(101,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{95}\right)\) | \(e\left(\frac{3}{95}\right)\) | \(e\left(\frac{94}{95}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{46}{95}\right)\) | \(e\left(\frac{6}{95}\right)\) | \(e\left(\frac{27}{95}\right)\) | \(e\left(\frac{13}{38}\right)\) |