from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(764, base_ring=CyclotomicField(190))
M = H._module
chi = DirichletCharacter(H, M([0,42]))
chi.galois_orbit()
[g,chi] = znchar(Mod(9,764))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(764\) | |
| Conductor: | \(191\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(95\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 191.g | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | 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 95 polynomial |
First 31 of 72 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{764}(9,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{95}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{27}{95}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{72}{95}\right)\) | \(e\left(\frac{66}{95}\right)\) | \(e\left(\frac{63}{95}\right)\) | \(e\left(\frac{21}{95}\right)\) | \(e\left(\frac{42}{95}\right)\) |
| \(\chi_{764}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{36}{95}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{72}{95}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{2}{95}\right)\) | \(e\left(\frac{81}{95}\right)\) | \(e\left(\frac{73}{95}\right)\) | \(e\left(\frac{56}{95}\right)\) | \(e\left(\frac{17}{95}\right)\) |
| \(\chi_{764}(17,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{95}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{63}{95}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{73}{95}\right)\) | \(e\left(\frac{59}{95}\right)\) | \(e\left(\frac{52}{95}\right)\) | \(e\left(\frac{49}{95}\right)\) | \(e\left(\frac{3}{95}\right)\) |
| \(\chi_{764}(45,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{95}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{32}{95}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{22}{95}\right)\) | \(e\left(\frac{36}{95}\right)\) | \(e\left(\frac{43}{95}\right)\) | \(e\left(\frac{46}{95}\right)\) | \(e\left(\frac{92}{95}\right)\) |
| \(\chi_{764}(65,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{86}{95}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{77}{95}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{47}{95}\right)\) | \(e\left(\frac{51}{95}\right)\) | \(e\left(\frac{53}{95}\right)\) | \(e\left(\frac{81}{95}\right)\) | \(e\left(\frac{67}{95}\right)\) |
| \(\chi_{764}(77,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{95}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{56}{95}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{86}{95}\right)\) | \(e\left(\frac{63}{95}\right)\) | \(e\left(\frac{4}{95}\right)\) | \(e\left(\frac{33}{95}\right)\) | \(e\left(\frac{66}{95}\right)\) |
| \(\chi_{764}(81,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{95}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{54}{95}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{49}{95}\right)\) | \(e\left(\frac{37}{95}\right)\) | \(e\left(\frac{31}{95}\right)\) | \(e\left(\frac{42}{95}\right)\) | \(e\left(\frac{84}{95}\right)\) |
| \(\chi_{764}(85,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{95}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{68}{95}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{23}{95}\right)\) | \(e\left(\frac{29}{95}\right)\) | \(e\left(\frac{32}{95}\right)\) | \(e\left(\frac{74}{95}\right)\) | \(e\left(\frac{53}{95}\right)\) |
| \(\chi_{764}(97,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{91}{95}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{87}{95}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{42}{95}\right)\) | \(e\left(\frac{86}{95}\right)\) | \(e\left(\frac{13}{95}\right)\) | \(e\left(\frac{36}{95}\right)\) | \(e\left(\frac{72}{95}\right)\) |
| \(\chi_{764}(117,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{95}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{95}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{74}{95}\right)\) | \(e\left(\frac{52}{95}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{77}{95}\right)\) | \(e\left(\frac{59}{95}\right)\) |
| \(\chi_{764}(129,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{95}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{39}{95}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{9}{95}\right)\) | \(e\left(\frac{32}{95}\right)\) | \(e\left(\frac{91}{95}\right)\) | \(e\left(\frac{62}{95}\right)\) | \(e\left(\frac{29}{95}\right)\) |
| \(\chi_{764}(133,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{95}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{95}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{37}{95}\right)\) | \(e\left(\frac{26}{95}\right)\) | \(e\left(\frac{68}{95}\right)\) | \(e\left(\frac{86}{95}\right)\) | \(e\left(\frac{77}{95}\right)\) |
| \(\chi_{764}(149,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{95}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{16}{95}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{11}{95}\right)\) | \(e\left(\frac{18}{95}\right)\) | \(e\left(\frac{69}{95}\right)\) | \(e\left(\frac{23}{95}\right)\) | \(e\left(\frac{46}{95}\right)\) |
| \(\chi_{764}(169,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{72}{95}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{49}{95}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{4}{95}\right)\) | \(e\left(\frac{67}{95}\right)\) | \(e\left(\frac{51}{95}\right)\) | \(e\left(\frac{17}{95}\right)\) | \(e\left(\frac{34}{95}\right)\) |
| \(\chi_{764}(193,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{82}{95}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{69}{95}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{89}{95}\right)\) | \(e\left(\frac{42}{95}\right)\) | \(e\left(\frac{66}{95}\right)\) | \(e\left(\frac{22}{95}\right)\) | \(e\left(\frac{44}{95}\right)\) |
| \(\chi_{764}(201,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{95}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{74}{95}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{39}{95}\right)\) | \(e\left(\frac{12}{95}\right)\) | \(e\left(\frac{46}{95}\right)\) | \(e\left(\frac{47}{95}\right)\) | \(e\left(\frac{94}{95}\right)\) |
| \(\chi_{764}(209,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{48}{95}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{95}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{66}{95}\right)\) | \(e\left(\frac{13}{95}\right)\) | \(e\left(\frac{34}{95}\right)\) | \(e\left(\frac{43}{95}\right)\) | \(e\left(\frac{86}{95}\right)\) |
| \(\chi_{764}(217,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{95}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{46}{95}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{91}{95}\right)\) | \(e\left(\frac{28}{95}\right)\) | \(e\left(\frac{44}{95}\right)\) | \(e\left(\frac{78}{95}\right)\) | \(e\left(\frac{61}{95}\right)\) |
| \(\chi_{764}(225,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{66}{95}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{37}{95}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{67}{95}\right)\) | \(e\left(\frac{6}{95}\right)\) | \(e\left(\frac{23}{95}\right)\) | \(e\left(\frac{71}{95}\right)\) | \(e\left(\frac{47}{95}\right)\) |
| \(\chi_{764}(237,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{95}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{33}{95}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{88}{95}\right)\) | \(e\left(\frac{49}{95}\right)\) | \(e\left(\frac{77}{95}\right)\) | \(e\left(\frac{89}{95}\right)\) | \(e\left(\frac{83}{95}\right)\) |
| \(\chi_{764}(241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{87}{95}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{79}{95}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{84}{95}\right)\) | \(e\left(\frac{77}{95}\right)\) | \(e\left(\frac{26}{95}\right)\) | \(e\left(\frac{72}{95}\right)\) | \(e\left(\frac{49}{95}\right)\) |
| \(\chi_{764}(245,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{95}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{62}{95}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{7}{95}\right)\) | \(e\left(\frac{46}{95}\right)\) | \(e\left(\frac{18}{95}\right)\) | \(e\left(\frac{6}{95}\right)\) | \(e\left(\frac{12}{95}\right)\) |
| \(\chi_{764}(269,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{95}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{12}{95}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{32}{95}\right)\) | \(e\left(\frac{61}{95}\right)\) | \(e\left(\frac{28}{95}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{82}{95}\right)\) |
| \(\chi_{764}(277,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{95}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{47}{95}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{62}{95}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{78}{95}\right)\) | \(e\left(\frac{26}{95}\right)\) | \(e\left(\frac{52}{95}\right)\) |
| \(\chi_{764}(281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{95}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{6}{95}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{16}{95}\right)\) | \(e\left(\frac{78}{95}\right)\) | \(e\left(\frac{14}{95}\right)\) | \(e\left(\frac{68}{95}\right)\) | \(e\left(\frac{41}{95}\right)\) |
| \(\chi_{764}(289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{95}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{31}{95}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{51}{95}\right)\) | \(e\left(\frac{23}{95}\right)\) | \(e\left(\frac{9}{95}\right)\) | \(e\left(\frac{3}{95}\right)\) | \(e\left(\frac{6}{95}\right)\) |
| \(\chi_{764}(293,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{95}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{95}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{8}{95}\right)\) | \(e\left(\frac{39}{95}\right)\) | \(e\left(\frac{7}{95}\right)\) | \(e\left(\frac{34}{95}\right)\) | \(e\left(\frac{68}{95}\right)\) |
| \(\chi_{764}(309,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{95}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{58}{95}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{28}{95}\right)\) | \(e\left(\frac{89}{95}\right)\) | \(e\left(\frac{72}{95}\right)\) | \(e\left(\frac{24}{95}\right)\) | \(e\left(\frac{48}{95}\right)\) |
| \(\chi_{764}(321,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{95}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{51}{95}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{93}{95}\right)\) | \(e\left(\frac{24}{95}\right)\) | \(e\left(\frac{8}{95}\right)\) | \(e\left(\frac{16}{95}\right)\) |
| \(\chi_{764}(325,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{82}{95}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{92}{95}\right)\) | \(e\left(\frac{21}{95}\right)\) | \(e\left(\frac{33}{95}\right)\) | \(e\left(\frac{11}{95}\right)\) | \(e\left(\frac{22}{95}\right)\) |
| \(\chi_{764}(329,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{95}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{94}{95}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{29}{95}\right)\) | \(e\left(\frac{82}{95}\right)\) | \(e\left(\frac{61}{95}\right)\) | \(e\left(\frac{52}{95}\right)\) | \(e\left(\frac{9}{95}\right)\) |