from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(1290))
M = H._module
chi = DirichletCharacter(H, M([430,921]))
chi.galois_orbit()
[g,chi] = znchar(Mod(37,6034))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6034\) | |
| Conductor: | \(3017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1290\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 3017.bf | 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: | $\Q(\zeta_{645})$ |
| Fixed field: | Number field defined by a degree 1290 polynomial (not computed) |
First 31 of 336 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6034}(37,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{129}\right)\) | \(e\left(\frac{541}{645}\right)\) | \(e\left(\frac{62}{129}\right)\) | \(e\left(\frac{494}{645}\right)\) | \(e\left(\frac{99}{430}\right)\) | \(e\left(\frac{17}{215}\right)\) | \(e\left(\frac{601}{1290}\right)\) | \(e\left(\frac{577}{645}\right)\) | \(e\left(\frac{268}{645}\right)\) | \(e\left(\frac{437}{645}\right)\) |
| \(\chi_{6034}(39,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{95}{129}\right)\) | \(e\left(\frac{551}{645}\right)\) | \(e\left(\frac{61}{129}\right)\) | \(e\left(\frac{124}{645}\right)\) | \(e\left(\frac{259}{430}\right)\) | \(e\left(\frac{127}{215}\right)\) | \(e\left(\frac{1151}{1290}\right)\) | \(e\left(\frac{137}{645}\right)\) | \(e\left(\frac{143}{645}\right)\) | \(e\left(\frac{457}{645}\right)\) |
| \(\chi_{6034}(51,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{109}{129}\right)\) | \(e\left(\frac{13}{645}\right)\) | \(e\left(\frac{89}{129}\right)\) | \(e\left(\frac{422}{645}\right)\) | \(e\left(\frac{337}{430}\right)\) | \(e\left(\frac{186}{215}\right)\) | \(e\left(\frac{973}{1290}\right)\) | \(e\left(\frac{331}{645}\right)\) | \(e\left(\frac{289}{645}\right)\) | \(e\left(\frac{26}{645}\right)\) |
| \(\chi_{6034}(65,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{100}{129}\right)\) | \(e\left(\frac{322}{645}\right)\) | \(e\left(\frac{71}{129}\right)\) | \(e\left(\frac{83}{645}\right)\) | \(e\left(\frac{293}{430}\right)\) | \(e\left(\frac{59}{215}\right)\) | \(e\left(\frac{37}{1290}\right)\) | \(e\left(\frac{409}{645}\right)\) | \(e\left(\frac{361}{645}\right)\) | \(e\left(\frac{644}{645}\right)\) |
| \(\chi_{6034}(67,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{74}{129}\right)\) | \(e\left(\frac{584}{645}\right)\) | \(e\left(\frac{19}{129}\right)\) | \(e\left(\frac{451}{645}\right)\) | \(e\left(\frac{271}{430}\right)\) | \(e\left(\frac{103}{215}\right)\) | \(e\left(\frac{1289}{1290}\right)\) | \(e\left(\frac{233}{645}\right)\) | \(e\left(\frac{182}{645}\right)\) | \(e\left(\frac{523}{645}\right)\) |
| \(\chi_{6034}(79,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{103}{129}\right)\) | \(e\left(\frac{4}{645}\right)\) | \(e\left(\frac{77}{129}\right)\) | \(e\left(\frac{626}{645}\right)\) | \(e\left(\frac{21}{430}\right)\) | \(e\left(\frac{173}{215}\right)\) | \(e\left(\frac{349}{1290}\right)\) | \(e\left(\frac{598}{645}\right)\) | \(e\left(\frac{337}{645}\right)\) | \(e\left(\frac{8}{645}\right)\) |
| \(\chi_{6034}(93,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{10}{129}\right)\) | \(e\left(\frac{187}{645}\right)\) | \(e\left(\frac{20}{129}\right)\) | \(e\left(\frac{563}{645}\right)\) | \(e\left(\frac{283}{430}\right)\) | \(e\left(\frac{79}{215}\right)\) | \(e\left(\frac{997}{1290}\right)\) | \(e\left(\frac{544}{645}\right)\) | \(e\left(\frac{436}{645}\right)\) | \(e\left(\frac{374}{645}\right)\) |
| \(\chi_{6034}(137,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{71}{129}\right)\) | \(e\left(\frac{386}{645}\right)\) | \(e\left(\frac{13}{129}\right)\) | \(e\left(\frac{424}{645}\right)\) | \(e\left(\frac{199}{430}\right)\) | \(e\left(\frac{32}{215}\right)\) | \(e\left(\frac{461}{1290}\right)\) | \(e\left(\frac{302}{645}\right)\) | \(e\left(\frac{593}{645}\right)\) | \(e\left(\frac{127}{645}\right)\) |
| \(\chi_{6034}(191,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{49}{129}\right)\) | \(e\left(\frac{181}{645}\right)\) | \(e\left(\frac{98}{129}\right)\) | \(e\left(\frac{269}{645}\right)\) | \(e\left(\frac{359}{430}\right)\) | \(e\left(\frac{142}{215}\right)\) | \(e\left(\frac{151}{1290}\right)\) | \(e\left(\frac{292}{645}\right)\) | \(e\left(\frac{253}{645}\right)\) | \(e\left(\frac{362}{645}\right)\) |
| \(\chi_{6034}(193,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{98}{129}\right)\) | \(e\left(\frac{491}{645}\right)\) | \(e\left(\frac{67}{129}\right)\) | \(e\left(\frac{409}{645}\right)\) | \(e\left(\frac{159}{430}\right)\) | \(e\left(\frac{112}{215}\right)\) | \(e\left(\frac{431}{1290}\right)\) | \(e\left(\frac{197}{645}\right)\) | \(e\left(\frac{248}{645}\right)\) | \(e\left(\frac{337}{645}\right)\) |
| \(\chi_{6034}(219,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{94}{129}\right)\) | \(e\left(\frac{313}{645}\right)\) | \(e\left(\frac{59}{129}\right)\) | \(e\left(\frac{287}{645}\right)\) | \(e\left(\frac{407}{430}\right)\) | \(e\left(\frac{46}{215}\right)\) | \(e\left(\frac{703}{1290}\right)\) | \(e\left(\frac{31}{645}\right)\) | \(e\left(\frac{409}{645}\right)\) | \(e\left(\frac{626}{645}\right)\) |
| \(\chi_{6034}(233,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{55}{129}\right)\) | \(e\left(\frac{319}{645}\right)\) | \(e\left(\frac{110}{129}\right)\) | \(e\left(\frac{581}{645}\right)\) | \(e\left(\frac{331}{430}\right)\) | \(e\left(\frac{198}{215}\right)\) | \(e\left(\frac{259}{1290}\right)\) | \(e\left(\frac{283}{645}\right)\) | \(e\left(\frac{592}{645}\right)\) | \(e\left(\frac{638}{645}\right)\) |
| \(\chi_{6034}(235,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{62}{129}\right)\) | \(e\left(\frac{566}{645}\right)\) | \(e\left(\frac{124}{129}\right)\) | \(e\left(\frac{214}{645}\right)\) | \(e\left(\frac{69}{430}\right)\) | \(e\left(\frac{77}{215}\right)\) | \(e\left(\frac{41}{1290}\right)\) | \(e\left(\frac{122}{645}\right)\) | \(e\left(\frac{278}{645}\right)\) | \(e\left(\frac{487}{645}\right)\) |
| \(\chi_{6034}(247,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{49}{129}\right)\) | \(e\left(\frac{568}{645}\right)\) | \(e\left(\frac{98}{129}\right)\) | \(e\left(\frac{527}{645}\right)\) | \(e\left(\frac{187}{430}\right)\) | \(e\left(\frac{56}{215}\right)\) | \(e\left(\frac{1183}{1290}\right)\) | \(e\left(\frac{421}{645}\right)\) | \(e\left(\frac{124}{645}\right)\) | \(e\left(\frac{491}{645}\right)\) |
| \(\chi_{6034}(249,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{129}\right)\) | \(e\left(\frac{599}{645}\right)\) | \(e\left(\frac{82}{129}\right)\) | \(e\left(\frac{541}{645}\right)\) | \(e\left(\frac{81}{430}\right)\) | \(e\left(\frac{53}{215}\right)\) | \(e\left(\frac{179}{1290}\right)\) | \(e\left(\frac{218}{645}\right)\) | \(e\left(\frac{317}{645}\right)\) | \(e\left(\frac{553}{645}\right)\) |
| \(\chi_{6034}(317,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{28}{129}\right)\) | \(e\left(\frac{472}{645}\right)\) | \(e\left(\frac{56}{129}\right)\) | \(e\left(\frac{338}{645}\right)\) | \(e\left(\frac{113}{430}\right)\) | \(e\left(\frac{204}{215}\right)\) | \(e\left(\frac{547}{1290}\right)\) | \(e\left(\frac{259}{645}\right)\) | \(e\left(\frac{421}{645}\right)\) | \(e\left(\frac{299}{645}\right)\) |
| \(\chi_{6034}(331,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{129}\right)\) | \(e\left(\frac{412}{645}\right)\) | \(e\left(\frac{62}{129}\right)\) | \(e\left(\frac{623}{645}\right)\) | \(e\left(\frac{13}{430}\right)\) | \(e\left(\frac{189}{215}\right)\) | \(e\left(\frac{1117}{1290}\right)\) | \(e\left(\frac{319}{645}\right)\) | \(e\left(\frac{526}{645}\right)\) | \(e\left(\frac{179}{645}\right)\) |
| \(\chi_{6034}(333,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{129}\right)\) | \(e\left(\frac{581}{645}\right)\) | \(e\left(\frac{58}{129}\right)\) | \(e\left(\frac{304}{645}\right)\) | \(e\left(\frac{309}{430}\right)\) | \(e\left(\frac{27}{215}\right)\) | \(e\left(\frac{221}{1290}\right)\) | \(e\left(\frac{107}{645}\right)\) | \(e\left(\frac{413}{645}\right)\) | \(e\left(\frac{517}{645}\right)\) |
| \(\chi_{6034}(373,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{10}{129}\right)\) | \(e\left(\frac{574}{645}\right)\) | \(e\left(\frac{20}{129}\right)\) | \(e\left(\frac{176}{645}\right)\) | \(e\left(\frac{111}{430}\right)\) | \(e\left(\frac{208}{215}\right)\) | \(e\left(\frac{739}{1290}\right)\) | \(e\left(\frac{28}{645}\right)\) | \(e\left(\frac{307}{645}\right)\) | \(e\left(\frac{503}{645}\right)\) |
| \(\chi_{6034}(387,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{129}\right)\) | \(e\left(\frac{49}{645}\right)\) | \(e\left(\frac{8}{129}\right)\) | \(e\left(\frac{251}{645}\right)\) | \(e\left(\frac{311}{430}\right)\) | \(e\left(\frac{23}{215}\right)\) | \(e\left(\frac{889}{1290}\right)\) | \(e\left(\frac{553}{645}\right)\) | \(e\left(\frac{97}{645}\right)\) | \(e\left(\frac{98}{645}\right)\) |
| \(\chi_{6034}(401,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{129}\right)\) | \(e\left(\frac{226}{645}\right)\) | \(e\left(\frac{29}{129}\right)\) | \(e\left(\frac{539}{645}\right)\) | \(e\left(\frac{219}{430}\right)\) | \(e\left(\frac{207}{215}\right)\) | \(e\left(\frac{691}{1290}\right)\) | \(e\left(\frac{247}{645}\right)\) | \(e\left(\frac{13}{645}\right)\) | \(e\left(\frac{452}{645}\right)\) |
| \(\chi_{6034}(445,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{74}{129}\right)\) | \(e\left(\frac{68}{645}\right)\) | \(e\left(\frac{19}{129}\right)\) | \(e\left(\frac{322}{645}\right)\) | \(e\left(\frac{357}{430}\right)\) | \(e\left(\frac{146}{215}\right)\) | \(e\left(\frac{773}{1290}\right)\) | \(e\left(\frac{491}{645}\right)\) | \(e\left(\frac{569}{645}\right)\) | \(e\left(\frac{136}{645}\right)\) |
| \(\chi_{6034}(459,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{107}{129}\right)\) | \(e\left(\frac{53}{645}\right)\) | \(e\left(\frac{85}{129}\right)\) | \(e\left(\frac{232}{645}\right)\) | \(e\left(\frac{117}{430}\right)\) | \(e\left(\frac{196}{215}\right)\) | \(e\left(\frac{593}{1290}\right)\) | \(e\left(\frac{506}{645}\right)\) | \(e\left(\frac{434}{645}\right)\) | \(e\left(\frac{106}{645}\right)\) |
| \(\chi_{6034}(473,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{116}{129}\right)\) | \(e\left(\frac{518}{645}\right)\) | \(e\left(\frac{103}{129}\right)\) | \(e\left(\frac{442}{645}\right)\) | \(e\left(\frac{247}{430}\right)\) | \(e\left(\frac{151}{215}\right)\) | \(e\left(\frac{1013}{1290}\right)\) | \(e\left(\frac{41}{645}\right)\) | \(e\left(\frac{104}{645}\right)\) | \(e\left(\frac{391}{645}\right)\) |
| \(\chi_{6034}(487,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{129}\right)\) | \(e\left(\frac{38}{645}\right)\) | \(e\left(\frac{22}{129}\right)\) | \(e\left(\frac{142}{645}\right)\) | \(e\left(\frac{307}{430}\right)\) | \(e\left(\frac{31}{215}\right)\) | \(e\left(\frac{413}{1290}\right)\) | \(e\left(\frac{521}{645}\right)\) | \(e\left(\frac{299}{645}\right)\) | \(e\left(\frac{76}{645}\right)\) |
| \(\chi_{6034}(499,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{129}\right)\) | \(e\left(\frac{178}{645}\right)\) | \(e\left(\frac{8}{129}\right)\) | \(e\left(\frac{122}{645}\right)\) | \(e\left(\frac{397}{430}\right)\) | \(e\left(\frac{66}{215}\right)\) | \(e\left(\frac{373}{1290}\right)\) | \(e\left(\frac{166}{645}\right)\) | \(e\left(\frac{484}{645}\right)\) | \(e\left(\frac{356}{645}\right)\) |
| \(\chi_{6034}(501,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{35}{129}\right)\) | \(e\left(\frac{74}{645}\right)\) | \(e\left(\frac{70}{129}\right)\) | \(e\left(\frac{616}{645}\right)\) | \(e\left(\frac{281}{430}\right)\) | \(e\left(\frac{83}{215}\right)\) | \(e\left(\frac{329}{1290}\right)\) | \(e\left(\frac{98}{645}\right)\) | \(e\left(\frac{107}{645}\right)\) | \(e\left(\frac{148}{645}\right)\) |
| \(\chi_{6034}(515,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{20}{129}\right)\) | \(e\left(\frac{503}{645}\right)\) | \(e\left(\frac{40}{129}\right)\) | \(e\left(\frac{352}{645}\right)\) | \(e\left(\frac{7}{430}\right)\) | \(e\left(\frac{201}{215}\right)\) | \(e\left(\frac{833}{1290}\right)\) | \(e\left(\frac{56}{645}\right)\) | \(e\left(\frac{614}{645}\right)\) | \(e\left(\frac{361}{645}\right)\) |
| \(\chi_{6034}(543,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{44}{129}\right)\) | \(e\left(\frac{23}{645}\right)\) | \(e\left(\frac{88}{129}\right)\) | \(e\left(\frac{52}{645}\right)\) | \(e\left(\frac{67}{430}\right)\) | \(e\left(\frac{81}{215}\right)\) | \(e\left(\frac{233}{1290}\right)\) | \(e\left(\frac{536}{645}\right)\) | \(e\left(\frac{164}{645}\right)\) | \(e\left(\frac{46}{645}\right)\) |
| \(\chi_{6034}(555,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{34}{129}\right)\) | \(e\left(\frac{352}{645}\right)\) | \(e\left(\frac{68}{129}\right)\) | \(e\left(\frac{263}{645}\right)\) | \(e\left(\frac{343}{430}\right)\) | \(e\left(\frac{174}{215}\right)\) | \(e\left(\frac{397}{1290}\right)\) | \(e\left(\frac{379}{645}\right)\) | \(e\left(\frac{631}{645}\right)\) | \(e\left(\frac{59}{645}\right)\) |
| \(\chi_{6034}(557,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{129}\right)\) | \(e\left(\frac{323}{645}\right)\) | \(e\left(\frac{58}{129}\right)\) | \(e\left(\frac{562}{645}\right)\) | \(e\left(\frac{137}{430}\right)\) | \(e\left(\frac{156}{215}\right)\) | \(e\left(\frac{1253}{1290}\right)\) | \(e\left(\frac{236}{645}\right)\) | \(e\left(\frac{284}{645}\right)\) | \(e\left(\frac{1}{645}\right)\) |