from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4425, base_ring=CyclotomicField(580))
M = H._module
chi = DirichletCharacter(H, M([0,551,450]))
chi.galois_orbit()
[g,chi] = znchar(Mod(13,4425))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(4425\) | |
| Conductor: | \(1475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(580\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 1475.w | 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: | $\Q(\zeta_{580})$ |
| Fixed field: | Number field defined by a degree 580 polynomial (not computed) |
First 31 of 224 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4425}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{421}{580}\right)\) | \(e\left(\frac{131}{290}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{103}{580}\right)\) | \(e\left(\frac{173}{290}\right)\) | \(e\left(\frac{559}{580}\right)\) | \(e\left(\frac{64}{145}\right)\) | \(e\left(\frac{131}{145}\right)\) | \(e\left(\frac{223}{580}\right)\) | \(e\left(\frac{169}{290}\right)\) |
| \(\chi_{4425}(37,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{231}{580}\right)\) | \(e\left(\frac{231}{290}\right)\) | \(e\left(\frac{37}{116}\right)\) | \(e\left(\frac{113}{580}\right)\) | \(e\left(\frac{263}{290}\right)\) | \(e\left(\frac{129}{580}\right)\) | \(e\left(\frac{104}{145}\right)\) | \(e\left(\frac{86}{145}\right)\) | \(e\left(\frac{453}{580}\right)\) | \(e\left(\frac{39}{290}\right)\) |
| \(\chi_{4425}(52,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{499}{580}\right)\) | \(e\left(\frac{209}{290}\right)\) | \(e\left(\frac{97}{116}\right)\) | \(e\left(\frac{337}{580}\right)\) | \(e\left(\frac{17}{290}\right)\) | \(e\left(\frac{241}{580}\right)\) | \(e\left(\frac{101}{145}\right)\) | \(e\left(\frac{64}{145}\right)\) | \(e\left(\frac{37}{580}\right)\) | \(e\left(\frac{201}{290}\right)\) |
| \(\chi_{4425}(67,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{407}{580}\right)\) | \(e\left(\frac{117}{290}\right)\) | \(e\left(\frac{21}{116}\right)\) | \(e\left(\frac{61}{580}\right)\) | \(e\left(\frac{201}{290}\right)\) | \(e\left(\frac{393}{580}\right)\) | \(e\left(\frac{128}{145}\right)\) | \(e\left(\frac{117}{145}\right)\) | \(e\left(\frac{301}{580}\right)\) | \(e\left(\frac{193}{290}\right)\) |
| \(\chi_{4425}(73,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{509}{580}\right)\) | \(e\left(\frac{219}{290}\right)\) | \(e\left(\frac{75}{116}\right)\) | \(e\left(\frac{367}{580}\right)\) | \(e\left(\frac{287}{290}\right)\) | \(e\left(\frac{111}{580}\right)\) | \(e\left(\frac{76}{145}\right)\) | \(e\left(\frac{74}{145}\right)\) | \(e\left(\frac{147}{580}\right)\) | \(e\left(\frac{101}{290}\right)\) |
| \(\chi_{4425}(97,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{303}{580}\right)\) | \(e\left(\frac{13}{290}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{329}{580}\right)\) | \(e\left(\frac{119}{290}\right)\) | \(e\left(\frac{237}{580}\right)\) | \(e\left(\frac{127}{145}\right)\) | \(e\left(\frac{13}{145}\right)\) | \(e\left(\frac{549}{580}\right)\) | \(e\left(\frac{247}{290}\right)\) |
| \(\chi_{4425}(103,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{473}{580}\right)\) | \(e\left(\frac{183}{290}\right)\) | \(e\left(\frac{15}{116}\right)\) | \(e\left(\frac{259}{580}\right)\) | \(e\left(\frac{69}{290}\right)\) | \(e\left(\frac{347}{580}\right)\) | \(e\left(\frac{137}{145}\right)\) | \(e\left(\frac{38}{145}\right)\) | \(e\left(\frac{99}{580}\right)\) | \(e\left(\frac{287}{290}\right)\) |
| \(\chi_{4425}(142,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{327}{580}\right)\) | \(e\left(\frac{37}{290}\right)\) | \(e\left(\frac{81}{116}\right)\) | \(e\left(\frac{401}{580}\right)\) | \(e\left(\frac{71}{290}\right)\) | \(e\left(\frac{273}{580}\right)\) | \(e\left(\frac{38}{145}\right)\) | \(e\left(\frac{37}{145}\right)\) | \(e\left(\frac{1}{580}\right)\) | \(e\left(\frac{123}{290}\right)\) |
| \(\chi_{4425}(148,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{309}{580}\right)\) | \(e\left(\frac{19}{290}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{347}{580}\right)\) | \(e\left(\frac{107}{290}\right)\) | \(e\left(\frac{391}{580}\right)\) | \(e\left(\frac{141}{145}\right)\) | \(e\left(\frac{19}{145}\right)\) | \(e\left(\frac{267}{580}\right)\) | \(e\left(\frac{71}{290}\right)\) |
| \(\chi_{4425}(172,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{263}{580}\right)\) | \(e\left(\frac{263}{290}\right)\) | \(e\left(\frac{13}{116}\right)\) | \(e\left(\frac{209}{580}\right)\) | \(e\left(\frac{199}{290}\right)\) | \(e\left(\frac{177}{580}\right)\) | \(e\left(\frac{82}{145}\right)\) | \(e\left(\frac{118}{145}\right)\) | \(e\left(\frac{109}{580}\right)\) | \(e\left(\frac{67}{290}\right)\) |
| \(\chi_{4425}(187,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{331}{580}\right)\) | \(e\left(\frac{41}{290}\right)\) | \(e\left(\frac{49}{116}\right)\) | \(e\left(\frac{413}{580}\right)\) | \(e\left(\frac{63}{290}\right)\) | \(e\left(\frac{569}{580}\right)\) | \(e\left(\frac{144}{145}\right)\) | \(e\left(\frac{41}{145}\right)\) | \(e\left(\frac{393}{580}\right)\) | \(e\left(\frac{199}{290}\right)\) |
| \(\chi_{4425}(208,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{577}{580}\right)\) | \(e\left(\frac{287}{290}\right)\) | \(e\left(\frac{111}{116}\right)\) | \(e\left(\frac{571}{580}\right)\) | \(e\left(\frac{151}{290}\right)\) | \(e\left(\frac{503}{580}\right)\) | \(e\left(\frac{138}{145}\right)\) | \(e\left(\frac{142}{145}\right)\) | \(e\left(\frac{431}{580}\right)\) | \(e\left(\frac{233}{290}\right)\) |
| \(\chi_{4425}(217,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{467}{580}\right)\) | \(e\left(\frac{177}{290}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{241}{580}\right)\) | \(e\left(\frac{81}{290}\right)\) | \(e\left(\frac{193}{580}\right)\) | \(e\left(\frac{123}{145}\right)\) | \(e\left(\frac{32}{145}\right)\) | \(e\left(\frac{381}{580}\right)\) | \(e\left(\frac{173}{290}\right)\) |
| \(\chi_{4425}(238,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{561}{580}\right)\) | \(e\left(\frac{271}{290}\right)\) | \(e\left(\frac{7}{116}\right)\) | \(e\left(\frac{523}{580}\right)\) | \(e\left(\frac{183}{290}\right)\) | \(e\left(\frac{479}{580}\right)\) | \(e\left(\frac{4}{145}\right)\) | \(e\left(\frac{126}{145}\right)\) | \(e\left(\frac{23}{580}\right)\) | \(e\left(\frac{219}{290}\right)\) |
| \(\chi_{4425}(247,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{163}{580}\right)\) | \(e\left(\frac{163}{290}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{489}{580}\right)\) | \(e\left(\frac{109}{290}\right)\) | \(e\left(\frac{317}{580}\right)\) | \(e\left(\frac{42}{145}\right)\) | \(e\left(\frac{18}{145}\right)\) | \(e\left(\frac{169}{580}\right)\) | \(e\left(\frac{197}{290}\right)\) |
| \(\chi_{4425}(283,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{317}{580}\right)\) | \(e\left(\frac{27}{290}\right)\) | \(e\left(\frac{103}{116}\right)\) | \(e\left(\frac{371}{580}\right)\) | \(e\left(\frac{91}{290}\right)\) | \(e\left(\frac{403}{580}\right)\) | \(e\left(\frac{63}{145}\right)\) | \(e\left(\frac{27}{145}\right)\) | \(e\left(\frac{471}{580}\right)\) | \(e\left(\frac{223}{290}\right)\) |
| \(\chi_{4425}(292,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{580}\right)\) | \(e\left(\frac{7}{290}\right)\) | \(e\left(\frac{89}{116}\right)\) | \(e\left(\frac{21}{580}\right)\) | \(e\left(\frac{131}{290}\right)\) | \(e\left(\frac{373}{580}\right)\) | \(e\left(\frac{113}{145}\right)\) | \(e\left(\frac{7}{145}\right)\) | \(e\left(\frac{541}{580}\right)\) | \(e\left(\frac{133}{290}\right)\) |
| \(\chi_{4425}(313,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{401}{580}\right)\) | \(e\left(\frac{111}{290}\right)\) | \(e\left(\frac{11}{116}\right)\) | \(e\left(\frac{43}{580}\right)\) | \(e\left(\frac{213}{290}\right)\) | \(e\left(\frac{239}{580}\right)\) | \(e\left(\frac{114}{145}\right)\) | \(e\left(\frac{111}{145}\right)\) | \(e\left(\frac{3}{580}\right)\) | \(e\left(\frac{79}{290}\right)\) |
| \(\chi_{4425}(328,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{373}{580}\right)\) | \(e\left(\frac{83}{290}\right)\) | \(e\left(\frac{3}{116}\right)\) | \(e\left(\frac{539}{580}\right)\) | \(e\left(\frac{269}{290}\right)\) | \(e\left(\frac{487}{580}\right)\) | \(e\left(\frac{97}{145}\right)\) | \(e\left(\frac{83}{145}\right)\) | \(e\left(\frac{159}{580}\right)\) | \(e\left(\frac{127}{290}\right)\) |
| \(\chi_{4425}(337,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{371}{580}\right)\) | \(e\left(\frac{81}{290}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{533}{580}\right)\) | \(e\left(\frac{273}{290}\right)\) | \(e\left(\frac{49}{580}\right)\) | \(e\left(\frac{44}{145}\right)\) | \(e\left(\frac{81}{145}\right)\) | \(e\left(\frac{253}{580}\right)\) | \(e\left(\frac{89}{290}\right)\) |
| \(\chi_{4425}(367,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{247}{580}\right)\) | \(e\left(\frac{247}{290}\right)\) | \(e\left(\frac{25}{116}\right)\) | \(e\left(\frac{161}{580}\right)\) | \(e\left(\frac{231}{290}\right)\) | \(e\left(\frac{153}{580}\right)\) | \(e\left(\frac{93}{145}\right)\) | \(e\left(\frac{102}{145}\right)\) | \(e\left(\frac{281}{580}\right)\) | \(e\left(\frac{53}{290}\right)\) |
| \(\chi_{4425}(388,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{381}{580}\right)\) | \(e\left(\frac{91}{290}\right)\) | \(e\left(\frac{55}{116}\right)\) | \(e\left(\frac{563}{580}\right)\) | \(e\left(\frac{253}{290}\right)\) | \(e\left(\frac{499}{580}\right)\) | \(e\left(\frac{19}{145}\right)\) | \(e\left(\frac{91}{145}\right)\) | \(e\left(\frac{363}{580}\right)\) | \(e\left(\frac{279}{290}\right)\) |
| \(\chi_{4425}(397,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{243}{580}\right)\) | \(e\left(\frac{243}{290}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{149}{580}\right)\) | \(e\left(\frac{239}{290}\right)\) | \(e\left(\frac{437}{580}\right)\) | \(e\left(\frac{132}{145}\right)\) | \(e\left(\frac{98}{145}\right)\) | \(e\left(\frac{469}{580}\right)\) | \(e\left(\frac{267}{290}\right)\) |
| \(\chi_{4425}(427,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{219}{580}\right)\) | \(e\left(\frac{219}{290}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{77}{580}\right)\) | \(e\left(\frac{287}{290}\right)\) | \(e\left(\frac{401}{580}\right)\) | \(e\left(\frac{76}{145}\right)\) | \(e\left(\frac{74}{145}\right)\) | \(e\left(\frac{437}{580}\right)\) | \(e\left(\frac{101}{290}\right)\) |
| \(\chi_{4425}(463,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{580}\right)\) | \(e\left(\frac{101}{290}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{303}{580}\right)\) | \(e\left(\frac{233}{290}\right)\) | \(e\left(\frac{79}{580}\right)\) | \(e\left(\frac{139}{145}\right)\) | \(e\left(\frac{101}{145}\right)\) | \(e\left(\frac{183}{580}\right)\) | \(e\left(\frac{179}{290}\right)\) |
| \(\chi_{4425}(478,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{133}{580}\right)\) | \(e\left(\frac{133}{290}\right)\) | \(e\left(\frac{67}{116}\right)\) | \(e\left(\frac{399}{580}\right)\) | \(e\left(\frac{169}{290}\right)\) | \(e\left(\frac{127}{580}\right)\) | \(e\left(\frac{117}{145}\right)\) | \(e\left(\frac{133}{145}\right)\) | \(e\left(\frac{419}{580}\right)\) | \(e\left(\frac{207}{290}\right)\) |
| \(\chi_{4425}(502,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{580}\right)\) | \(e\left(\frac{19}{290}\right)\) | \(e\left(\frac{109}{116}\right)\) | \(e\left(\frac{57}{580}\right)\) | \(e\left(\frac{107}{290}\right)\) | \(e\left(\frac{101}{580}\right)\) | \(e\left(\frac{141}{145}\right)\) | \(e\left(\frac{19}{145}\right)\) | \(e\left(\frac{557}{580}\right)\) | \(e\left(\frac{71}{290}\right)\) |
| \(\chi_{4425}(562,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{171}{580}\right)\) | \(e\left(\frac{171}{290}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{513}{580}\right)\) | \(e\left(\frac{93}{290}\right)\) | \(e\left(\frac{329}{580}\right)\) | \(e\left(\frac{109}{145}\right)\) | \(e\left(\frac{26}{145}\right)\) | \(e\left(\frac{373}{580}\right)\) | \(e\left(\frac{59}{290}\right)\) |
| \(\chi_{4425}(583,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{557}{580}\right)\) | \(e\left(\frac{267}{290}\right)\) | \(e\left(\frac{39}{116}\right)\) | \(e\left(\frac{511}{580}\right)\) | \(e\left(\frac{191}{290}\right)\) | \(e\left(\frac{183}{580}\right)\) | \(e\left(\frac{43}{145}\right)\) | \(e\left(\frac{122}{145}\right)\) | \(e\left(\frac{211}{580}\right)\) | \(e\left(\frac{143}{290}\right)\) |
| \(\chi_{4425}(592,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{387}{580}\right)\) | \(e\left(\frac{97}{290}\right)\) | \(e\left(\frac{65}{116}\right)\) | \(e\left(\frac{1}{580}\right)\) | \(e\left(\frac{241}{290}\right)\) | \(e\left(\frac{73}{580}\right)\) | \(e\left(\frac{33}{145}\right)\) | \(e\left(\frac{97}{145}\right)\) | \(e\left(\frac{81}{580}\right)\) | \(e\left(\frac{103}{290}\right)\) |
| \(\chi_{4425}(598,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{349}{580}\right)\) | \(e\left(\frac{59}{290}\right)\) | \(e\left(\frac{79}{116}\right)\) | \(e\left(\frac{467}{580}\right)\) | \(e\left(\frac{27}{290}\right)\) | \(e\left(\frac{451}{580}\right)\) | \(e\left(\frac{41}{145}\right)\) | \(e\left(\frac{59}{145}\right)\) | \(e\left(\frac{127}{580}\right)\) | \(e\left(\frac{251}{290}\right)\) |