from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40310, base_ring=CyclotomicField(966))
M = H._module
chi = DirichletCharacter(H, M([0,690,182]))
chi.galois_orbit()
[g,chi] = znchar(Mod(81,40310))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(40310\) | |
| Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(483\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 4031.bo | 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: | $\Q(\zeta_{483})$ |
| Fixed field: | Number field defined by a degree 483 polynomial (not computed) |
First 31 of 264 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{40310}(81,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{143}{483}\right)\) | \(e\left(\frac{479}{483}\right)\) | \(e\left(\frac{286}{483}\right)\) | \(e\left(\frac{85}{483}\right)\) | \(e\left(\frac{442}{483}\right)\) | \(e\left(\frac{11}{69}\right)\) | \(e\left(\frac{445}{483}\right)\) | \(e\left(\frac{139}{483}\right)\) | \(e\left(\frac{60}{161}\right)\) | \(e\left(\frac{143}{161}\right)\) |
| \(\chi_{40310}(471,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{475}{483}\right)\) | \(e\left(\frac{34}{483}\right)\) | \(e\left(\frac{467}{483}\right)\) | \(e\left(\frac{2}{483}\right)\) | \(e\left(\frac{107}{483}\right)\) | \(e\left(\frac{10}{69}\right)\) | \(e\left(\frac{323}{483}\right)\) | \(e\left(\frac{26}{483}\right)\) | \(e\left(\frac{134}{161}\right)\) | \(e\left(\frac{153}{161}\right)\) |
| \(\chi_{40310}(741,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{483}\right)\) | \(e\left(\frac{415}{483}\right)\) | \(e\left(\frac{32}{483}\right)\) | \(e\left(\frac{479}{483}\right)\) | \(e\left(\frac{269}{483}\right)\) | \(e\left(\frac{49}{69}\right)\) | \(e\left(\frac{320}{483}\right)\) | \(e\left(\frac{431}{483}\right)\) | \(e\left(\frac{54}{161}\right)\) | \(e\left(\frac{16}{161}\right)\) |
| \(\chi_{40310}(761,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{483}\right)\) | \(e\left(\frac{433}{483}\right)\) | \(e\left(\frac{194}{483}\right)\) | \(e\left(\frac{338}{483}\right)\) | \(e\left(\frac{212}{483}\right)\) | \(e\left(\frac{34}{69}\right)\) | \(e\left(\frac{8}{483}\right)\) | \(e\left(\frac{47}{483}\right)\) | \(e\left(\frac{106}{161}\right)\) | \(e\left(\frac{97}{161}\right)\) |
| \(\chi_{40310}(951,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{458}{483}\right)\) | \(e\left(\frac{227}{483}\right)\) | \(e\left(\frac{433}{483}\right)\) | \(e\left(\frac{127}{483}\right)\) | \(e\left(\frac{274}{483}\right)\) | \(e\left(\frac{14}{69}\right)\) | \(e\left(\frac{466}{483}\right)\) | \(e\left(\frac{202}{483}\right)\) | \(e\left(\frac{137}{161}\right)\) | \(e\left(\frac{136}{161}\right)\) |
| \(\chi_{40310}(1011,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{134}{483}\right)\) | \(e\left(\frac{155}{483}\right)\) | \(e\left(\frac{268}{483}\right)\) | \(e\left(\frac{208}{483}\right)\) | \(e\left(\frac{19}{483}\right)\) | \(e\left(\frac{5}{69}\right)\) | \(e\left(\frac{265}{483}\right)\) | \(e\left(\frac{289}{483}\right)\) | \(e\left(\frac{90}{161}\right)\) | \(e\left(\frac{134}{161}\right)\) |
| \(\chi_{40310}(1051,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{307}{483}\right)\) | \(e\left(\frac{265}{483}\right)\) | \(e\left(\frac{131}{483}\right)\) | \(e\left(\frac{44}{483}\right)\) | \(e\left(\frac{422}{483}\right)\) | \(e\left(\frac{13}{69}\right)\) | \(e\left(\frac{344}{483}\right)\) | \(e\left(\frac{89}{483}\right)\) | \(e\left(\frac{50}{161}\right)\) | \(e\left(\frac{146}{161}\right)\) |
| \(\chi_{40310}(1271,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{277}{483}\right)\) | \(e\left(\frac{151}{483}\right)\) | \(e\left(\frac{71}{483}\right)\) | \(e\left(\frac{293}{483}\right)\) | \(e\left(\frac{461}{483}\right)\) | \(e\left(\frac{16}{69}\right)\) | \(e\left(\frac{227}{483}\right)\) | \(e\left(\frac{428}{483}\right)\) | \(e\left(\frac{150}{161}\right)\) | \(e\left(\frac{116}{161}\right)\) |
| \(\chi_{40310}(1441,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{124}{483}\right)\) | \(e\left(\frac{439}{483}\right)\) | \(e\left(\frac{248}{483}\right)\) | \(e\left(\frac{452}{483}\right)\) | \(e\left(\frac{32}{483}\right)\) | \(e\left(\frac{52}{69}\right)\) | \(e\left(\frac{65}{483}\right)\) | \(e\left(\frac{80}{483}\right)\) | \(e\left(\frac{16}{161}\right)\) | \(e\left(\frac{124}{161}\right)\) |
| \(\chi_{40310}(2171,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{155}{483}\right)\) | \(e\left(\frac{428}{483}\right)\) | \(e\left(\frac{310}{483}\right)\) | \(e\left(\frac{82}{483}\right)\) | \(e\left(\frac{40}{483}\right)\) | \(e\left(\frac{65}{69}\right)\) | \(e\left(\frac{202}{483}\right)\) | \(e\left(\frac{100}{483}\right)\) | \(e\left(\frac{20}{161}\right)\) | \(e\left(\frac{155}{161}\right)\) |
| \(\chi_{40310}(2401,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{479}{483}\right)\) | \(e\left(\frac{17}{483}\right)\) | \(e\left(\frac{475}{483}\right)\) | \(e\left(\frac{1}{483}\right)\) | \(e\left(\frac{295}{483}\right)\) | \(e\left(\frac{5}{69}\right)\) | \(e\left(\frac{403}{483}\right)\) | \(e\left(\frac{13}{483}\right)\) | \(e\left(\frac{67}{161}\right)\) | \(e\left(\frac{157}{161}\right)\) |
| \(\chi_{40310}(2481,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{483}\right)\) | \(e\left(\frac{331}{483}\right)\) | \(e\left(\frac{242}{483}\right)\) | \(e\left(\frac{332}{483}\right)\) | \(e\left(\frac{374}{483}\right)\) | \(e\left(\frac{4}{69}\right)\) | \(e\left(\frac{5}{483}\right)\) | \(e\left(\frac{452}{483}\right)\) | \(e\left(\frac{26}{161}\right)\) | \(e\left(\frac{121}{161}\right)\) |
| \(\chi_{40310}(2601,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{110}{483}\right)\) | \(e\left(\frac{257}{483}\right)\) | \(e\left(\frac{220}{483}\right)\) | \(e\left(\frac{214}{483}\right)\) | \(e\left(\frac{340}{483}\right)\) | \(e\left(\frac{35}{69}\right)\) | \(e\left(\frac{268}{483}\right)\) | \(e\left(\frac{367}{483}\right)\) | \(e\left(\frac{9}{161}\right)\) | \(e\left(\frac{110}{161}\right)\) |
| \(\chi_{40310}(2791,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{349}{483}\right)\) | \(e\left(\frac{328}{483}\right)\) | \(e\left(\frac{215}{483}\right)\) | \(e\left(\frac{275}{483}\right)\) | \(e\left(\frac{464}{483}\right)\) | \(e\left(\frac{64}{69}\right)\) | \(e\left(\frac{218}{483}\right)\) | \(e\left(\frac{194}{483}\right)\) | \(e\left(\frac{71}{161}\right)\) | \(e\left(\frac{27}{161}\right)\) |
| \(\chi_{40310}(3041,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{483}\right)\) | \(e\left(\frac{302}{483}\right)\) | \(e\left(\frac{142}{483}\right)\) | \(e\left(\frac{103}{483}\right)\) | \(e\left(\frac{439}{483}\right)\) | \(e\left(\frac{32}{69}\right)\) | \(e\left(\frac{454}{483}\right)\) | \(e\left(\frac{373}{483}\right)\) | \(e\left(\frac{139}{161}\right)\) | \(e\left(\frac{71}{161}\right)\) |
| \(\chi_{40310}(3371,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{265}{483}\right)\) | \(e\left(\frac{202}{483}\right)\) | \(e\left(\frac{47}{483}\right)\) | \(e\left(\frac{296}{483}\right)\) | \(e\left(\frac{380}{483}\right)\) | \(e\left(\frac{31}{69}\right)\) | \(e\left(\frac{470}{483}\right)\) | \(e\left(\frac{467}{483}\right)\) | \(e\left(\frac{29}{161}\right)\) | \(e\left(\frac{104}{161}\right)\) |
| \(\chi_{40310}(3561,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{483}\right)\) | \(e\left(\frac{290}{483}\right)\) | \(e\left(\frac{34}{483}\right)\) | \(e\left(\frac{358}{483}\right)\) | \(e\left(\frac{316}{483}\right)\) | \(e\left(\frac{65}{69}\right)\) | \(e\left(\frac{340}{483}\right)\) | \(e\left(\frac{307}{483}\right)\) | \(e\left(\frac{158}{161}\right)\) | \(e\left(\frac{17}{161}\right)\) |
| \(\chi_{40310}(3621,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{344}{483}\right)\) | \(e\left(\frac{470}{483}\right)\) | \(e\left(\frac{205}{483}\right)\) | \(e\left(\frac{397}{483}\right)\) | \(e\left(\frac{229}{483}\right)\) | \(e\left(\frac{53}{69}\right)\) | \(e\left(\frac{118}{483}\right)\) | \(e\left(\frac{331}{483}\right)\) | \(e\left(\frac{34}{161}\right)\) | \(e\left(\frac{22}{161}\right)\) |
| \(\chi_{40310}(3661,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{125}{483}\right)\) | \(e\left(\frac{314}{483}\right)\) | \(e\left(\frac{250}{483}\right)\) | \(e\left(\frac{331}{483}\right)\) | \(e\left(\frac{79}{483}\right)\) | \(e\left(\frac{68}{69}\right)\) | \(e\left(\frac{85}{483}\right)\) | \(e\left(\frac{439}{483}\right)\) | \(e\left(\frac{120}{161}\right)\) | \(e\left(\frac{125}{161}\right)\) |
| \(\chi_{40310}(4051,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{208}{483}\right)\) | \(e\left(\frac{82}{483}\right)\) | \(e\left(\frac{416}{483}\right)\) | \(e\left(\frac{431}{483}\right)\) | \(e\left(\frac{116}{483}\right)\) | \(e\left(\frac{16}{69}\right)\) | \(e\left(\frac{296}{483}\right)\) | \(e\left(\frac{290}{483}\right)\) | \(e\left(\frac{58}{161}\right)\) | \(e\left(\frac{47}{161}\right)\) |
| \(\chi_{40310}(4201,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{239}{483}\right)\) | \(e\left(\frac{71}{483}\right)\) | \(e\left(\frac{478}{483}\right)\) | \(e\left(\frac{61}{483}\right)\) | \(e\left(\frac{124}{483}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{433}{483}\right)\) | \(e\left(\frac{310}{483}\right)\) | \(e\left(\frac{62}{161}\right)\) | \(e\left(\frac{78}{161}\right)\) |
| \(\chi_{40310}(4221,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{331}{483}\right)\) | \(e\left(\frac{163}{483}\right)\) | \(e\left(\frac{179}{483}\right)\) | \(e\left(\frac{38}{483}\right)\) | \(e\left(\frac{101}{483}\right)\) | \(e\left(\frac{52}{69}\right)\) | \(e\left(\frac{341}{483}\right)\) | \(e\left(\frac{11}{483}\right)\) | \(e\left(\frac{131}{161}\right)\) | \(e\left(\frac{9}{161}\right)\) |
| \(\chi_{40310}(4241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{483}\right)\) | \(e\left(\frac{307}{483}\right)\) | \(e\left(\frac{26}{483}\right)\) | \(e\left(\frac{359}{483}\right)\) | \(e\left(\frac{128}{483}\right)\) | \(e\left(\frac{1}{69}\right)\) | \(e\left(\frac{260}{483}\right)\) | \(e\left(\frac{320}{483}\right)\) | \(e\left(\frac{64}{161}\right)\) | \(e\left(\frac{13}{161}\right)\) |
| \(\chi_{40310}(4431,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{416}{483}\right)\) | \(e\left(\frac{164}{483}\right)\) | \(e\left(\frac{349}{483}\right)\) | \(e\left(\frac{379}{483}\right)\) | \(e\left(\frac{232}{483}\right)\) | \(e\left(\frac{32}{69}\right)\) | \(e\left(\frac{109}{483}\right)\) | \(e\left(\frac{97}{483}\right)\) | \(e\left(\frac{116}{161}\right)\) | \(e\left(\frac{94}{161}\right)\) |
| \(\chi_{40310}(4461,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{214}{483}\right)\) | \(e\left(\frac{298}{483}\right)\) | \(e\left(\frac{428}{483}\right)\) | \(e\left(\frac{188}{483}\right)\) | \(e\left(\frac{398}{483}\right)\) | \(e\left(\frac{43}{69}\right)\) | \(e\left(\frac{416}{483}\right)\) | \(e\left(\frac{29}{483}\right)\) | \(e\left(\frac{38}{161}\right)\) | \(e\left(\frac{53}{161}\right)\) |
| \(\chi_{40310}(4531,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{188}{483}\right)\) | \(e\left(\frac{167}{483}\right)\) | \(e\left(\frac{376}{483}\right)\) | \(e\left(\frac{436}{483}\right)\) | \(e\left(\frac{142}{483}\right)\) | \(e\left(\frac{41}{69}\right)\) | \(e\left(\frac{379}{483}\right)\) | \(e\left(\frac{355}{483}\right)\) | \(e\left(\frac{71}{161}\right)\) | \(e\left(\frac{27}{161}\right)\) |
| \(\chi_{40310}(4751,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{256}{483}\right)\) | \(e\left(\frac{361}{483}\right)\) | \(e\left(\frac{29}{483}\right)\) | \(e\left(\frac{419}{483}\right)\) | \(e\left(\frac{440}{483}\right)\) | \(e\left(\frac{25}{69}\right)\) | \(e\left(\frac{290}{483}\right)\) | \(e\left(\frac{134}{483}\right)\) | \(e\left(\frac{59}{161}\right)\) | \(e\left(\frac{95}{161}\right)\) |
| \(\chi_{40310}(5011,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{206}{483}\right)\) | \(e\left(\frac{332}{483}\right)\) | \(e\left(\frac{412}{483}\right)\) | \(e\left(\frac{190}{483}\right)\) | \(e\left(\frac{22}{483}\right)\) | \(e\left(\frac{53}{69}\right)\) | \(e\left(\frac{256}{483}\right)\) | \(e\left(\frac{55}{483}\right)\) | \(e\left(\frac{11}{161}\right)\) | \(e\left(\frac{45}{161}\right)\) |
| \(\chi_{40310}(5041,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{95}{483}\right)\) | \(e\left(\frac{200}{483}\right)\) | \(e\left(\frac{190}{483}\right)\) | \(e\left(\frac{97}{483}\right)\) | \(e\left(\frac{118}{483}\right)\) | \(e\left(\frac{2}{69}\right)\) | \(e\left(\frac{451}{483}\right)\) | \(e\left(\frac{295}{483}\right)\) | \(e\left(\frac{59}{161}\right)\) | \(e\left(\frac{95}{161}\right)\) |
| \(\chi_{40310}(5071,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{295}{483}\right)\) | \(e\left(\frac{316}{483}\right)\) | \(e\left(\frac{107}{483}\right)\) | \(e\left(\frac{47}{483}\right)\) | \(e\left(\frac{341}{483}\right)\) | \(e\left(\frac{28}{69}\right)\) | \(e\left(\frac{104}{483}\right)\) | \(e\left(\frac{128}{483}\right)\) | \(e\left(\frac{90}{161}\right)\) | \(e\left(\frac{134}{161}\right)\) |
| \(\chi_{40310}(5111,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{62}{483}\right)\) | \(e\left(\frac{461}{483}\right)\) | \(e\left(\frac{124}{483}\right)\) | \(e\left(\frac{226}{483}\right)\) | \(e\left(\frac{16}{483}\right)\) | \(e\left(\frac{26}{69}\right)\) | \(e\left(\frac{274}{483}\right)\) | \(e\left(\frac{40}{483}\right)\) | \(e\left(\frac{8}{161}\right)\) | \(e\left(\frac{62}{161}\right)\) |