from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(946, base_ring=CyclotomicField(210))
M = H._module
chi = DirichletCharacter(H, M([126,10]))
chi.galois_orbit()
[g,chi] = znchar(Mod(9,946))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(946\) | |
| Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 473.bc | 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: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
First 31 of 48 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{946}(9,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) |
| \(\chi_{946}(15,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) |
| \(\chi_{946}(25,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) |
| \(\chi_{946}(31,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) |
| \(\chi_{946}(53,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) |
| \(\chi_{946}(81,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) |
| \(\chi_{946}(103,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) |
| \(\chi_{946}(169,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) |
| \(\chi_{946}(181,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) |
| \(\chi_{946}(185,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{4}{21}\right)\) |
| \(\chi_{946}(203,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) |
| \(\chi_{946}(225,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) |
| \(\chi_{946}(229,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) |
| \(\chi_{946}(267,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) |
| \(\chi_{946}(273,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) |
| \(\chi_{946}(289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) |
| \(\chi_{946}(311,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) |
| \(\chi_{946}(339,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) |
| \(\chi_{946}(357,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{4}{21}\right)\) |
| \(\chi_{946}(361,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) |
| \(\chi_{946}(367,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{21}\right)\) |
| \(\chi_{946}(401,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) |
| \(\chi_{946}(411,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) |
| \(\chi_{946}(427,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) |
| \(\chi_{946}(443,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{4}{21}\right)\) |
| \(\chi_{946}(445,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) |
| \(\chi_{946}(455,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) |
| \(\chi_{946}(487,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) |
| \(\chi_{946}(511,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) |
| \(\chi_{946}(531,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) |
| \(\chi_{946}(533,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) |