from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(374790, base_ring=CyclotomicField(1860))
M = H._module
chi = DirichletCharacter(H, M([930,0,775,1804]))
chi.galois_orbit()
[g,chi] = znchar(Mod(71,374790))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(374790\) | |
| Conductor: | \(37479\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1860\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 37479.ix | 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: | $\Q(\zeta_{1860})$ |
| Fixed field: | Number field defined by a degree 1860 polynomial (not computed) |
First 31 of 480 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(37\) | \(41\) | \(43\) | \(47\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{374790}(71,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{479}{620}\right)\) | \(e\left(\frac{429}{620}\right)\) | \(e\left(\frac{69}{155}\right)\) | \(e\left(\frac{397}{620}\right)\) | \(e\left(\frac{22}{465}\right)\) | \(e\left(\frac{323}{930}\right)\) | \(e\left(\frac{289}{372}\right)\) | \(e\left(\frac{427}{620}\right)\) | \(e\left(\frac{21}{310}\right)\) | \(e\left(\frac{453}{620}\right)\) |
| \(\chi_{374790}(431,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{227}{620}\right)\) | \(e\left(\frac{457}{620}\right)\) | \(e\left(\frac{67}{155}\right)\) | \(e\left(\frac{381}{620}\right)\) | \(e\left(\frac{401}{465}\right)\) | \(e\left(\frac{709}{930}\right)\) | \(e\left(\frac{233}{372}\right)\) | \(e\left(\frac{491}{620}\right)\) | \(e\left(\frac{263}{310}\right)\) | \(e\left(\frac{49}{620}\right)\) |
| \(\chi_{374790}(1931,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{309}{620}\right)\) | \(e\left(\frac{379}{620}\right)\) | \(e\left(\frac{139}{155}\right)\) | \(e\left(\frac{27}{620}\right)\) | \(e\left(\frac{397}{465}\right)\) | \(e\left(\frac{143}{930}\right)\) | \(e\left(\frac{79}{372}\right)\) | \(e\left(\frac{357}{620}\right)\) | \(e\left(\frac{231}{310}\right)\) | \(e\left(\frac{23}{620}\right)\) |
| \(\chi_{374790}(1991,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{111}{620}\right)\) | \(e\left(\frac{401}{620}\right)\) | \(e\left(\frac{71}{155}\right)\) | \(e\left(\frac{413}{620}\right)\) | \(e\left(\frac{263}{465}\right)\) | \(e\left(\frac{247}{930}\right)\) | \(e\left(\frac{221}{372}\right)\) | \(e\left(\frac{363}{620}\right)\) | \(e\left(\frac{89}{310}\right)\) | \(e\left(\frac{237}{620}\right)\) |
| \(\chi_{374790}(5081,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{417}{620}\right)\) | \(e\left(\frac{367}{620}\right)\) | \(e\left(\frac{7}{155}\right)\) | \(e\left(\frac{211}{620}\right)\) | \(e\left(\frac{146}{465}\right)\) | \(e\left(\frac{199}{930}\right)\) | \(e\left(\frac{227}{372}\right)\) | \(e\left(\frac{241}{620}\right)\) | \(e\left(\frac{83}{310}\right)\) | \(e\left(\frac{19}{620}\right)\) |
| \(\chi_{374790}(5501,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{539}{620}\right)\) | \(e\left(\frac{9}{620}\right)\) | \(e\left(\frac{99}{155}\right)\) | \(e\left(\frac{17}{620}\right)\) | \(e\left(\frac{227}{465}\right)\) | \(e\left(\frac{733}{930}\right)\) | \(e\left(\frac{137}{372}\right)\) | \(e\left(\frac{87}{620}\right)\) | \(e\left(\frac{111}{310}\right)\) | \(e\left(\frac{313}{620}\right)\) |
| \(\chi_{374790}(6281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{423}{620}\right)\) | \(e\left(\frac{573}{620}\right)\) | \(e\left(\frac{103}{155}\right)\) | \(e\left(\frac{49}{620}\right)\) | \(e\left(\frac{89}{465}\right)\) | \(e\left(\frac{271}{930}\right)\) | \(e\left(\frac{125}{372}\right)\) | \(e\left(\frac{579}{620}\right)\) | \(e\left(\frac{247}{310}\right)\) | \(e\left(\frac{501}{620}\right)\) |
| \(\chi_{374790}(6311,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{487}{620}\right)\) | \(e\left(\frac{497}{620}\right)\) | \(e\left(\frac{42}{155}\right)\) | \(e\left(\frac{181}{620}\right)\) | \(e\left(\frac{256}{465}\right)\) | \(e\left(\frac{419}{930}\right)\) | \(e\left(\frac{277}{372}\right)\) | \(e\left(\frac{51}{620}\right)\) | \(e\left(\frac{33}{310}\right)\) | \(e\left(\frac{269}{620}\right)\) |
| \(\chi_{374790}(6641,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{561}{620}\right)\) | \(e\left(\frac{351}{620}\right)\) | \(e\left(\frac{141}{155}\right)\) | \(e\left(\frac{43}{620}\right)\) | \(e\left(\frac{173}{465}\right)\) | \(e\left(\frac{67}{930}\right)\) | \(e\left(\frac{11}{372}\right)\) | \(e\left(\frac{293}{620}\right)\) | \(e\left(\frac{299}{310}\right)\) | \(e\left(\frac{427}{620}\right)\) |
| \(\chi_{374790}(7481,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{343}{620}\right)\) | \(e\left(\frac{513}{620}\right)\) | \(e\left(\frac{63}{155}\right)\) | \(e\left(\frac{349}{620}\right)\) | \(e\left(\frac{229}{465}\right)\) | \(e\left(\frac{551}{930}\right)\) | \(e\left(\frac{121}{372}\right)\) | \(e\left(\frac{619}{620}\right)\) | \(e\left(\frac{127}{310}\right)\) | \(e\left(\frac{481}{620}\right)\) |
| \(\chi_{374790}(8171,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{557}{620}\right)\) | \(e\left(\frac{7}{620}\right)\) | \(e\left(\frac{77}{155}\right)\) | \(e\left(\frac{151}{620}\right)\) | \(e\left(\frac{211}{465}\right)\) | \(e\left(\frac{329}{930}\right)\) | \(e\left(\frac{79}{372}\right)\) | \(e\left(\frac{481}{620}\right)\) | \(e\left(\frac{293}{310}\right)\) | \(e\left(\frac{519}{620}\right)\) |
| \(\chi_{374790}(9041,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{111}{620}\right)\) | \(e\left(\frac{401}{620}\right)\) | \(e\left(\frac{71}{155}\right)\) | \(e\left(\frac{413}{620}\right)\) | \(e\left(\frac{418}{465}\right)\) | \(e\left(\frac{557}{930}\right)\) | \(e\left(\frac{97}{372}\right)\) | \(e\left(\frac{363}{620}\right)\) | \(e\left(\frac{89}{310}\right)\) | \(e\left(\frac{237}{620}\right)\) |
| \(\chi_{374790}(9341,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{593}{620}\right)\) | \(e\left(\frac{3}{620}\right)\) | \(e\left(\frac{33}{155}\right)\) | \(e\left(\frac{419}{620}\right)\) | \(e\left(\frac{334}{465}\right)\) | \(e\left(\frac{761}{930}\right)\) | \(e\left(\frac{211}{372}\right)\) | \(e\left(\frac{29}{620}\right)\) | \(e\left(\frac{37}{310}\right)\) | \(e\left(\frac{311}{620}\right)\) |
| \(\chi_{374790}(10151,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{609}{620}\right)\) | \(e\left(\frac{139}{620}\right)\) | \(e\left(\frac{134}{155}\right)\) | \(e\left(\frac{607}{620}\right)\) | \(e\left(\frac{182}{465}\right)\) | \(e\left(\frac{643}{930}\right)\) | \(e\left(\frac{311}{372}\right)\) | \(e\left(\frac{517}{620}\right)\) | \(e\left(\frac{61}{310}\right)\) | \(e\left(\frac{563}{620}\right)\) |
| \(\chi_{374790}(10901,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{81}{620}\right)\) | \(e\left(\frac{611}{620}\right)\) | \(e\left(\frac{56}{155}\right)\) | \(e\left(\frac{603}{620}\right)\) | \(e\left(\frac{238}{465}\right)\) | \(e\left(\frac{197}{930}\right)\) | \(e\left(\frac{235}{372}\right)\) | \(e\left(\frac{533}{620}\right)\) | \(e\left(\frac{199}{310}\right)\) | \(e\left(\frac{307}{620}\right)\) |
| \(\chi_{374790}(10931,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{393}{620}\right)\) | \(e\left(\frac{163}{620}\right)\) | \(e\left(\frac{88}{155}\right)\) | \(e\left(\frac{239}{620}\right)\) | \(e\left(\frac{374}{465}\right)\) | \(e\left(\frac{841}{930}\right)\) | \(e\left(\frac{263}{372}\right)\) | \(e\left(\frac{129}{620}\right)\) | \(e\left(\frac{47}{310}\right)\) | \(e\left(\frac{571}{620}\right)\) |
| \(\chi_{374790}(12161,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{459}{620}\right)\) | \(e\left(\frac{569}{620}\right)\) | \(e\left(\frac{59}{155}\right)\) | \(e\left(\frac{317}{620}\right)\) | \(e\left(\frac{367}{465}\right)\) | \(e\left(\frac{83}{930}\right)\) | \(e\left(\frac{133}{372}\right)\) | \(e\left(\frac{127}{620}\right)\) | \(e\left(\frac{301}{310}\right)\) | \(e\left(\frac{293}{620}\right)\) |
| \(\chi_{374790}(12521,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{287}{620}\right)\) | \(e\left(\frac{37}{620}\right)\) | \(e\left(\frac{97}{155}\right)\) | \(e\left(\frac{1}{620}\right)\) | \(e\left(\frac{296}{465}\right)\) | \(e\left(\frac{499}{930}\right)\) | \(e\left(\frac{329}{372}\right)\) | \(e\left(\frac{151}{620}\right)\) | \(e\left(\frac{43}{310}\right)\) | \(e\left(\frac{529}{620}\right)\) |
| \(\chi_{374790}(14021,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{289}{620}\right)\) | \(e\left(\frac{519}{620}\right)\) | \(e\left(\frac{129}{155}\right)\) | \(e\left(\frac{567}{620}\right)\) | \(e\left(\frac{277}{465}\right)\) | \(e\left(\frac{833}{930}\right)\) | \(e\left(\frac{295}{372}\right)\) | \(e\left(\frac{57}{620}\right)\) | \(e\left(\frac{201}{310}\right)\) | \(e\left(\frac{483}{620}\right)\) |
| \(\chi_{374790}(14081,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{351}{620}\right)\) | \(e\left(\frac{581}{620}\right)\) | \(e\left(\frac{36}{155}\right)\) | \(e\left(\frac{133}{620}\right)\) | \(e\left(\frac{308}{465}\right)\) | \(e\left(\frac{337}{930}\right)\) | \(e\left(\frac{233}{372}\right)\) | \(e\left(\frac{243}{620}\right)\) | \(e\left(\frac{139}{310}\right)\) | \(e\left(\frac{297}{620}\right)\) |
| \(\chi_{374790}(17171,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{477}{620}\right)\) | \(e\left(\frac{567}{620}\right)\) | \(e\left(\frac{37}{155}\right)\) | \(e\left(\frac{451}{620}\right)\) | \(e\left(\frac{41}{465}\right)\) | \(e\left(\frac{919}{930}\right)\) | \(e\left(\frac{323}{372}\right)\) | \(e\left(\frac{521}{620}\right)\) | \(e\left(\frac{173}{310}\right)\) | \(e\left(\frac{499}{620}\right)\) |
| \(\chi_{374790}(17591,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{620}\right)\) | \(e\left(\frac{409}{620}\right)\) | \(e\left(\frac{4}{155}\right)\) | \(e\left(\frac{497}{620}\right)\) | \(e\left(\frac{17}{465}\right)\) | \(e\left(\frac{313}{930}\right)\) | \(e\left(\frac{329}{372}\right)\) | \(e\left(\frac{27}{620}\right)\) | \(e\left(\frac{291}{310}\right)\) | \(e\left(\frac{33}{620}\right)\) |
| \(\chi_{374790}(18371,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{283}{620}\right)\) | \(e\left(\frac{313}{620}\right)\) | \(e\left(\frac{33}{155}\right)\) | \(e\left(\frac{109}{620}\right)\) | \(e\left(\frac{179}{465}\right)\) | \(e\left(\frac{451}{930}\right)\) | \(e\left(\frac{149}{372}\right)\) | \(e\left(\frac{339}{620}\right)\) | \(e\left(\frac{37}{310}\right)\) | \(e\left(\frac{1}{620}\right)\) |
| \(\chi_{374790}(18401,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{620}\right)\) | \(e\left(\frac{257}{620}\right)\) | \(e\left(\frac{37}{155}\right)\) | \(e\left(\frac{141}{620}\right)\) | \(e\left(\frac{196}{465}\right)\) | \(e\left(\frac{299}{930}\right)\) | \(e\left(\frac{13}{372}\right)\) | \(e\left(\frac{211}{620}\right)\) | \(e\left(\frac{173}{310}\right)\) | \(e\left(\frac{189}{620}\right)\) |
| \(\chi_{374790}(18731,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{181}{620}\right)\) | \(e\left(\frac{531}{620}\right)\) | \(e\left(\frac{106}{155}\right)\) | \(e\left(\frac{383}{620}\right)\) | \(e\left(\frac{218}{465}\right)\) | \(e\left(\frac{157}{930}\right)\) | \(e\left(\frac{23}{372}\right)\) | \(e\left(\frac{173}{620}\right)\) | \(e\left(\frac{39}{310}\right)\) | \(e\left(\frac{487}{620}\right)\) |
| \(\chi_{374790}(19571,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{263}{620}\right)\) | \(e\left(\frac{453}{620}\right)\) | \(e\left(\frac{23}{155}\right)\) | \(e\left(\frac{29}{620}\right)\) | \(e\left(\frac{214}{465}\right)\) | \(e\left(\frac{521}{930}\right)\) | \(e\left(\frac{241}{372}\right)\) | \(e\left(\frac{39}{620}\right)\) | \(e\left(\frac{7}{310}\right)\) | \(e\left(\frac{461}{620}\right)\) |
| \(\chi_{374790}(20261,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{237}{620}\right)\) | \(e\left(\frac{387}{620}\right)\) | \(e\left(\frac{72}{155}\right)\) | \(e\left(\frac{111}{620}\right)\) | \(e\left(\frac{151}{465}\right)\) | \(e\left(\frac{209}{930}\right)\) | \(e\left(\frac{187}{372}\right)\) | \(e\left(\frac{21}{620}\right)\) | \(e\left(\frac{123}{310}\right)\) | \(e\left(\frac{439}{620}\right)\) |
| \(\chi_{374790}(21131,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{620}\right)\) | \(e\left(\frac{61}{620}\right)\) | \(e\left(\frac{51}{155}\right)\) | \(e\left(\frac{253}{620}\right)\) | \(e\left(\frac{178}{465}\right)\) | \(e\left(\frac{77}{930}\right)\) | \(e\left(\frac{157}{372}\right)\) | \(e\left(\frac{383}{620}\right)\) | \(e\left(\frac{29}{310}\right)\) | \(e\left(\frac{537}{620}\right)\) |
| \(\chi_{374790}(21431,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{513}{620}\right)\) | \(e\left(\frac{563}{620}\right)\) | \(e\left(\frac{148}{155}\right)\) | \(e\left(\frac{99}{620}\right)\) | \(e\left(\frac{319}{465}\right)\) | \(e\left(\frac{731}{930}\right)\) | \(e\left(\frac{331}{372}\right)\) | \(e\left(\frac{69}{620}\right)\) | \(e\left(\frac{227}{310}\right)\) | \(e\left(\frac{291}{620}\right)\) |
| \(\chi_{374790}(22241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{620}\right)\) | \(e\left(\frac{539}{620}\right)\) | \(e\left(\frac{39}{155}\right)\) | \(e\left(\frac{467}{620}\right)\) | \(e\left(\frac{437}{465}\right)\) | \(e\left(\frac{223}{930}\right)\) | \(e\left(\frac{131}{372}\right)\) | \(e\left(\frac{457}{620}\right)\) | \(e\left(\frac{241}{310}\right)\) | \(e\left(\frac{283}{620}\right)\) |
| \(\chi_{374790}(22991,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{620}\right)\) | \(e\left(\frac{271}{620}\right)\) | \(e\left(\frac{36}{155}\right)\) | \(e\left(\frac{443}{620}\right)\) | \(e\left(\frac{463}{465}\right)\) | \(e\left(\frac{647}{930}\right)\) | \(e\left(\frac{295}{372}\right)\) | \(e\left(\frac{553}{620}\right)\) | \(e\left(\frac{139}{310}\right)\) | \(e\left(\frac{607}{620}\right)\) |