from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(290145, base_ring=CyclotomicField(812))
M = H._module
chi = DirichletCharacter(H, M([0,203,406,82]))
chi.galois_orbit()
[g,chi] = znchar(Mod(22,290145))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(290145\) | |
| Conductor: | \(96715\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(812\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 96715.eu | 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: | $\Q(\zeta_{812})$ |
| Fixed field: | Number field defined by a degree 812 polynomial (not computed) |
First 31 of 336 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{290145}(22,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{285}{812}\right)\) | \(e\left(\frac{285}{406}\right)\) | \(e\left(\frac{585}{812}\right)\) | \(e\left(\frac{43}{812}\right)\) | \(e\left(\frac{138}{203}\right)\) | \(e\left(\frac{489}{812}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{82}{203}\right)\) | \(e\left(\frac{13}{116}\right)\) | \(e\left(\frac{47}{406}\right)\) |
| \(\chi_{290145}(643,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{547}{812}\right)\) | \(e\left(\frac{141}{406}\right)\) | \(e\left(\frac{439}{812}\right)\) | \(e\left(\frac{17}{812}\right)\) | \(e\left(\frac{64}{203}\right)\) | \(e\left(\frac{571}{812}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{141}{203}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{113}{406}\right)\) |
| \(\chi_{290145}(1057,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{812}\right)\) | \(e\left(\frac{193}{406}\right)\) | \(e\left(\frac{97}{812}\right)\) | \(e\left(\frac{579}{812}\right)\) | \(e\left(\frac{102}{203}\right)\) | \(e\left(\frac{485}{812}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{193}{203}\right)\) | \(e\left(\frac{113}{116}\right)\) | \(e\left(\frac{123}{406}\right)\) |
| \(\chi_{290145}(2023,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{299}{812}\right)\) | \(e\left(\frac{299}{406}\right)\) | \(e\left(\frac{571}{812}\right)\) | \(e\left(\frac{85}{812}\right)\) | \(e\left(\frac{117}{203}\right)\) | \(e\left(\frac{419}{812}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{96}{203}\right)\) | \(e\left(\frac{23}{116}\right)\) | \(e\left(\frac{159}{406}\right)\) |
| \(\chi_{290145}(2092,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{709}{812}\right)\) | \(e\left(\frac{303}{406}\right)\) | \(e\left(\frac{45}{812}\right)\) | \(e\left(\frac{503}{812}\right)\) | \(e\left(\frac{198}{203}\right)\) | \(e\left(\frac{225}{812}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{100}{203}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{191}{406}\right)\) |
| \(\chi_{290145}(3058,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{123}{812}\right)\) | \(e\left(\frac{123}{406}\right)\) | \(e\left(\frac{167}{812}\right)\) | \(e\left(\frac{369}{812}\right)\) | \(e\left(\frac{4}{203}\right)\) | \(e\left(\frac{23}{812}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{123}{203}\right)\) | \(e\left(\frac{63}{116}\right)\) | \(e\left(\frac{375}{406}\right)\) |
| \(\chi_{290145}(4093,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{583}{812}\right)\) | \(e\left(\frac{177}{406}\right)\) | \(e\left(\frac{171}{812}\right)\) | \(e\left(\frac{125}{812}\right)\) | \(e\left(\frac{184}{203}\right)\) | \(e\left(\frac{43}{812}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{177}{203}\right)\) | \(e\left(\frac{27}{116}\right)\) | \(e\left(\frac{401}{406}\right)\) |
| \(\chi_{290145}(4852,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{353}{812}\right)\) | \(e\left(\frac{353}{406}\right)\) | \(e\left(\frac{169}{812}\right)\) | \(e\left(\frac{247}{812}\right)\) | \(e\left(\frac{94}{203}\right)\) | \(e\left(\frac{33}{812}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{150}{203}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{185}{406}\right)\) |
| \(\chi_{290145}(5197,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{629}{812}\right)\) | \(e\left(\frac{223}{406}\right)\) | \(e\left(\frac{9}{812}\right)\) | \(e\left(\frac{263}{812}\right)\) | \(e\left(\frac{202}{203}\right)\) | \(e\left(\frac{45}{812}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{20}{203}\right)\) | \(e\left(\frac{93}{116}\right)\) | \(e\left(\frac{363}{406}\right)\) |
| \(\chi_{290145}(6853,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{703}{812}\right)\) | \(e\left(\frac{297}{406}\right)\) | \(e\left(\frac{631}{812}\right)\) | \(e\left(\frac{485}{812}\right)\) | \(e\left(\frac{178}{203}\right)\) | \(e\left(\frac{719}{812}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{94}{203}\right)\) | \(e\left(\frac{63}{116}\right)\) | \(e\left(\frac{143}{406}\right)\) |
| \(\chi_{290145}(7198,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{812}\right)\) | \(e\left(\frac{139}{406}\right)\) | \(e\left(\frac{499}{812}\right)\) | \(e\left(\frac{417}{812}\right)\) | \(e\left(\frac{125}{203}\right)\) | \(e\left(\frac{59}{812}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{139}{203}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{97}{406}\right)\) |
| \(\chi_{290145}(8647,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{225}{812}\right)\) | \(e\left(\frac{225}{406}\right)\) | \(e\left(\frac{761}{812}\right)\) | \(e\left(\frac{675}{812}\right)\) | \(e\left(\frac{141}{203}\right)\) | \(e\left(\frac{557}{812}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{22}{203}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{379}{406}\right)\) |
| \(\chi_{290145}(10027,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{761}{812}\right)\) | \(e\left(\frac{355}{406}\right)\) | \(e\left(\frac{109}{812}\right)\) | \(e\left(\frac{659}{812}\right)\) | \(e\left(\frac{33}{203}\right)\) | \(e\left(\frac{545}{812}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{152}{203}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{201}{406}\right)\) |
| \(\chi_{290145}(10648,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{812}\right)\) | \(e\left(\frac{43}{406}\right)\) | \(e\left(\frac{131}{812}\right)\) | \(e\left(\frac{129}{812}\right)\) | \(e\left(\frac{8}{203}\right)\) | \(e\left(\frac{655}{812}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{43}{203}\right)\) | \(e\left(\frac{39}{116}\right)\) | \(e\left(\frac{141}{406}\right)\) |
| \(\chi_{290145}(11062,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{249}{812}\right)\) | \(e\left(\frac{249}{406}\right)\) | \(e\left(\frac{41}{812}\right)\) | \(e\left(\frac{747}{812}\right)\) | \(e\left(\frac{18}{203}\right)\) | \(e\left(\frac{205}{812}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{46}{203}\right)\) | \(e\left(\frac{37}{116}\right)\) | \(e\left(\frac{165}{406}\right)\) |
| \(\chi_{290145}(12028,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{775}{812}\right)\) | \(e\left(\frac{369}{406}\right)\) | \(e\left(\frac{95}{812}\right)\) | \(e\left(\frac{701}{812}\right)\) | \(e\left(\frac{12}{203}\right)\) | \(e\left(\frac{475}{812}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{166}{203}\right)\) | \(e\left(\frac{15}{116}\right)\) | \(e\left(\frac{313}{406}\right)\) |
| \(\chi_{290145}(12097,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{485}{812}\right)\) | \(e\left(\frac{79}{406}\right)\) | \(e\left(\frac{269}{812}\right)\) | \(e\left(\frac{643}{812}\right)\) | \(e\left(\frac{128}{203}\right)\) | \(e\left(\frac{533}{812}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{79}{203}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{23}{406}\right)\) |
| \(\chi_{290145}(13063,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{812}\right)\) | \(e\left(\frac{179}{406}\right)\) | \(e\left(\frac{111}{812}\right)\) | \(e\left(\frac{537}{812}\right)\) | \(e\left(\frac{123}{203}\right)\) | \(e\left(\frac{555}{812}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{179}{203}\right)\) | \(e\left(\frac{103}{116}\right)\) | \(e\left(\frac{11}{406}\right)\) |
| \(\chi_{290145}(14098,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{359}{812}\right)\) | \(e\left(\frac{359}{406}\right)\) | \(e\left(\frac{395}{812}\right)\) | \(e\left(\frac{265}{812}\right)\) | \(e\left(\frac{114}{203}\right)\) | \(e\left(\frac{351}{812}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{156}{203}\right)\) | \(e\left(\frac{99}{116}\right)\) | \(e\left(\frac{233}{406}\right)\) |
| \(\chi_{290145}(14857,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{812}\right)\) | \(e\left(\frac{73}{406}\right)\) | \(e\left(\frac{449}{812}\right)\) | \(e\left(\frac{219}{812}\right)\) | \(e\left(\frac{108}{203}\right)\) | \(e\left(\frac{621}{812}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{73}{203}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{381}{406}\right)\) |
| \(\chi_{290145}(15202,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{209}{812}\right)\) | \(e\left(\frac{209}{406}\right)\) | \(e\left(\frac{429}{812}\right)\) | \(e\left(\frac{627}{812}\right)\) | \(e\left(\frac{20}{203}\right)\) | \(e\left(\frac{521}{812}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{6}{203}\right)\) | \(e\left(\frac{25}{116}\right)\) | \(e\left(\frac{251}{406}\right)\) |
| \(\chi_{290145}(16858,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{423}{812}\right)\) | \(e\left(\frac{17}{406}\right)\) | \(e\left(\frac{99}{812}\right)\) | \(e\left(\frac{457}{812}\right)\) | \(e\left(\frac{192}{203}\right)\) | \(e\left(\frac{495}{812}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{17}{203}\right)\) | \(e\left(\frac{95}{116}\right)\) | \(e\left(\frac{339}{406}\right)\) |
| \(\chi_{290145}(17203,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{531}{812}\right)\) | \(e\left(\frac{125}{406}\right)\) | \(e\left(\frac{107}{812}\right)\) | \(e\left(\frac{781}{812}\right)\) | \(e\left(\frac{146}{203}\right)\) | \(e\left(\frac{535}{812}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{125}{203}\right)\) | \(e\left(\frac{23}{116}\right)\) | \(e\left(\frac{391}{406}\right)\) |
| \(\chi_{290145}(18652,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{533}{812}\right)\) | \(e\left(\frac{127}{406}\right)\) | \(e\left(\frac{453}{812}\right)\) | \(e\left(\frac{787}{812}\right)\) | \(e\left(\frac{85}{203}\right)\) | \(e\left(\frac{641}{812}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{127}{203}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{1}{406}\right)\) |
| \(\chi_{290145}(20032,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{425}{812}\right)\) | \(e\left(\frac{19}{406}\right)\) | \(e\left(\frac{445}{812}\right)\) | \(e\left(\frac{463}{812}\right)\) | \(e\left(\frac{131}{203}\right)\) | \(e\left(\frac{601}{812}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{19}{203}\right)\) | \(e\left(\frac{113}{116}\right)\) | \(e\left(\frac{355}{406}\right)\) |
| \(\chi_{290145}(20653,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{351}{812}\right)\) | \(e\left(\frac{351}{406}\right)\) | \(e\left(\frac{635}{812}\right)\) | \(e\left(\frac{241}{812}\right)\) | \(e\left(\frac{155}{203}\right)\) | \(e\left(\frac{739}{812}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{148}{203}\right)\) | \(e\left(\frac{27}{116}\right)\) | \(e\left(\frac{169}{406}\right)\) |
| \(\chi_{290145}(21067,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{305}{812}\right)\) | \(e\left(\frac{305}{406}\right)\) | \(e\left(\frac{797}{812}\right)\) | \(e\left(\frac{103}{812}\right)\) | \(e\left(\frac{137}{203}\right)\) | \(e\left(\frac{737}{812}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{102}{203}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{207}{406}\right)\) |
| \(\chi_{290145}(22033,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{439}{812}\right)\) | \(e\left(\frac{33}{406}\right)\) | \(e\left(\frac{431}{812}\right)\) | \(e\left(\frac{505}{812}\right)\) | \(e\left(\frac{110}{203}\right)\) | \(e\left(\frac{531}{812}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{33}{203}\right)\) | \(e\left(\frac{7}{116}\right)\) | \(e\left(\frac{61}{406}\right)\) |
| \(\chi_{290145}(23068,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{235}{812}\right)\) | \(e\left(\frac{235}{406}\right)\) | \(e\left(\frac{55}{812}\right)\) | \(e\left(\frac{705}{812}\right)\) | \(e\left(\frac{39}{203}\right)\) | \(e\left(\frac{275}{812}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{32}{203}\right)\) | \(e\left(\frac{27}{116}\right)\) | \(e\left(\frac{53}{406}\right)\) |
| \(\chi_{290145}(24103,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{135}{812}\right)\) | \(e\left(\frac{135}{406}\right)\) | \(e\left(\frac{619}{812}\right)\) | \(e\left(\frac{405}{812}\right)\) | \(e\left(\frac{44}{203}\right)\) | \(e\left(\frac{659}{812}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{135}{203}\right)\) | \(e\left(\frac{55}{116}\right)\) | \(e\left(\frac{65}{406}\right)\) |
| \(\chi_{290145}(24862,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{605}{812}\right)\) | \(e\left(\frac{199}{406}\right)\) | \(e\left(\frac{729}{812}\right)\) | \(e\left(\frac{191}{812}\right)\) | \(e\left(\frac{122}{203}\right)\) | \(e\left(\frac{397}{812}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{199}{203}\right)\) | \(e\left(\frac{109}{116}\right)\) | \(e\left(\frac{171}{406}\right)\) |