from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, base_ring=CyclotomicField(660))
M = H._module
chi = DirichletCharacter(H, M([440,165,42]))
chi.galois_orbit()
[g,chi] = znchar(Mod(7,5445))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(5445\) | |
| Conductor: | \(5445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(660\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | 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: | $\Q(\zeta_{660})$ |
| Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
First 31 of 160 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{5445}(7,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{647}{660}\right)\) | \(e\left(\frac{317}{330}\right)\) | \(e\left(\frac{239}{660}\right)\) | \(e\left(\frac{207}{220}\right)\) | \(e\left(\frac{337}{660}\right)\) | \(e\left(\frac{113}{330}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{81}{220}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{71}{132}\right)\) |
| \(\chi_{5445}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{660}\right)\) | \(e\left(\frac{1}{330}\right)\) | \(e\left(\frac{337}{660}\right)\) | \(e\left(\frac{1}{220}\right)\) | \(e\left(\frac{431}{660}\right)\) | \(e\left(\frac{169}{330}\right)\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{25}{132}\right)\) |
| \(\chi_{5445}(52,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{563}{660}\right)\) | \(e\left(\frac{233}{330}\right)\) | \(e\left(\frac{311}{660}\right)\) | \(e\left(\frac{123}{220}\right)\) | \(e\left(\frac{433}{660}\right)\) | \(e\left(\frac{107}{330}\right)\) | \(e\left(\frac{68}{165}\right)\) | \(e\left(\frac{29}{220}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{83}{132}\right)\) |
| \(\chi_{5445}(178,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{641}{660}\right)\) | \(e\left(\frac{311}{330}\right)\) | \(e\left(\frac{197}{660}\right)\) | \(e\left(\frac{201}{220}\right)\) | \(e\left(\frac{391}{660}\right)\) | \(e\left(\frac{89}{330}\right)\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{53}{132}\right)\) |
| \(\chi_{5445}(193,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{469}{660}\right)\) | \(e\left(\frac{139}{330}\right)\) | \(e\left(\frac{313}{660}\right)\) | \(e\left(\frac{29}{220}\right)\) | \(e\left(\frac{179}{660}\right)\) | \(e\left(\frac{61}{330}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{107}{220}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{109}{132}\right)\) |
| \(\chi_{5445}(238,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{397}{660}\right)\) | \(e\left(\frac{67}{330}\right)\) | \(e\left(\frac{469}{660}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{167}{660}\right)\) | \(e\left(\frac{103}{330}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{31}{220}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{25}{132}\right)\) |
| \(\chi_{5445}(277,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{431}{660}\right)\) | \(e\left(\frac{101}{330}\right)\) | \(e\left(\frac{47}{660}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{301}{660}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{101}{165}\right)\) | \(e\left(\frac{73}{220}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{83}{132}\right)\) |
| \(\chi_{5445}(283,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{660}\right)\) | \(e\left(\frac{193}{330}\right)\) | \(e\left(\frac{361}{660}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{23}{660}\right)\) | \(e\left(\frac{277}{330}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{219}{220}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{73}{132}\right)\) |
| \(\chi_{5445}(292,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{619}{660}\right)\) | \(e\left(\frac{289}{330}\right)\) | \(e\left(\frac{43}{660}\right)\) | \(e\left(\frac{179}{220}\right)\) | \(e\left(\frac{149}{660}\right)\) | \(e\left(\frac{1}{330}\right)\) | \(e\left(\frac{124}{165}\right)\) | \(e\left(\frac{137}{220}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{31}{132}\right)\) |
| \(\chi_{5445}(337,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{660}\right)\) | \(e\left(\frac{7}{330}\right)\) | \(e\left(\frac{379}{660}\right)\) | \(e\left(\frac{7}{220}\right)\) | \(e\left(\frac{377}{660}\right)\) | \(e\left(\frac{193}{330}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{41}{220}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{43}{132}\right)\) |
| \(\chi_{5445}(358,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{389}{660}\right)\) | \(e\left(\frac{59}{330}\right)\) | \(e\left(\frac{413}{660}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{19}{660}\right)\) | \(e\left(\frac{71}{330}\right)\) | \(e\left(\frac{59}{165}\right)\) | \(e\left(\frac{47}{220}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{89}{132}\right)\) |
| \(\chi_{5445}(382,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{660}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{571}{660}\right)\) | \(e\left(\frac{3}{220}\right)\) | \(e\left(\frac{413}{660}\right)\) | \(e\left(\frac{67}{330}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{49}{220}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{31}{132}\right)\) |
| \(\chi_{5445}(448,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{353}{660}\right)\) | \(e\left(\frac{23}{330}\right)\) | \(e\left(\frac{161}{660}\right)\) | \(e\left(\frac{133}{220}\right)\) | \(e\left(\frac{343}{660}\right)\) | \(e\left(\frac{257}{330}\right)\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{119}{220}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{113}{132}\right)\) |
| \(\chi_{5445}(502,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{347}{660}\right)\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{119}{660}\right)\) | \(e\left(\frac{127}{220}\right)\) | \(e\left(\frac{397}{660}\right)\) | \(e\left(\frac{233}{330}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{95}{132}\right)\) |
| \(\chi_{5445}(508,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{601}{660}\right)\) | \(e\left(\frac{271}{330}\right)\) | \(e\left(\frac{577}{660}\right)\) | \(e\left(\frac{161}{220}\right)\) | \(e\left(\frac{311}{660}\right)\) | \(e\left(\frac{259}{330}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{109}{132}\right)\) |
| \(\chi_{5445}(547,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{383}{660}\right)\) | \(e\left(\frac{53}{330}\right)\) | \(e\left(\frac{371}{660}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{73}{660}\right)\) | \(e\left(\frac{47}{330}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{71}{132}\right)\) |
| \(\chi_{5445}(607,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{391}{660}\right)\) | \(e\left(\frac{61}{330}\right)\) | \(e\left(\frac{427}{660}\right)\) | \(e\left(\frac{171}{220}\right)\) | \(e\left(\frac{221}{660}\right)\) | \(e\left(\frac{79}{330}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{153}{220}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{7}{132}\right)\) |
| \(\chi_{5445}(673,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{581}{660}\right)\) | \(e\left(\frac{251}{330}\right)\) | \(e\left(\frac{437}{660}\right)\) | \(e\left(\frac{141}{220}\right)\) | \(e\left(\frac{271}{660}\right)\) | \(e\left(\frac{179}{330}\right)\) | \(e\left(\frac{86}{165}\right)\) | \(e\left(\frac{103}{220}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{5}{132}\right)\) |
| \(\chi_{5445}(688,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{229}{660}\right)\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{613}{660}\right)\) | \(e\left(\frac{9}{220}\right)\) | \(e\left(\frac{359}{660}\right)\) | \(e\left(\frac{91}{330}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{147}{220}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{49}{132}\right)\) |
| \(\chi_{5445}(733,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{660}\right)\) | \(e\left(\frac{97}{330}\right)\) | \(e\left(\frac{349}{660}\right)\) | \(e\left(\frac{97}{220}\right)\) | \(e\left(\frac{227}{660}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{97}{165}\right)\) | \(e\left(\frac{191}{220}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{49}{132}\right)\) |
| \(\chi_{5445}(772,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{371}{660}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{287}{660}\right)\) | \(e\left(\frac{151}{220}\right)\) | \(e\left(\frac{181}{660}\right)\) | \(e\left(\frac{329}{330}\right)\) | \(e\left(\frac{41}{165}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{35}{132}\right)\) |
| \(\chi_{5445}(778,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{660}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{421}{660}\right)\) | \(e\left(\frac{13}{220}\right)\) | \(e\left(\frac{323}{660}\right)\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{139}{220}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{61}{132}\right)\) |
| \(\chi_{5445}(787,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{379}{660}\right)\) | \(e\left(\frac{49}{330}\right)\) | \(e\left(\frac{343}{660}\right)\) | \(e\left(\frac{159}{220}\right)\) | \(e\left(\frac{329}{660}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{49}{165}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{103}{132}\right)\) |
| \(\chi_{5445}(832,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{367}{660}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{259}{660}\right)\) | \(e\left(\frac{147}{220}\right)\) | \(e\left(\frac{437}{660}\right)\) | \(e\left(\frac{313}{330}\right)\) | \(e\left(\frac{37}{165}\right)\) | \(e\left(\frac{201}{220}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{67}{132}\right)\) |
| \(\chi_{5445}(853,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{660}\right)\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{53}{660}\right)\) | \(e\left(\frac{149}{220}\right)\) | \(e\left(\frac{199}{660}\right)\) | \(e\left(\frac{101}{330}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{87}{220}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{29}{132}\right)\) |
| \(\chi_{5445}(877,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{660}\right)\) | \(e\left(\frac{43}{330}\right)\) | \(e\left(\frac{631}{660}\right)\) | \(e\left(\frac{43}{220}\right)\) | \(e\left(\frac{53}{660}\right)\) | \(e\left(\frac{7}{330}\right)\) | \(e\left(\frac{43}{165}\right)\) | \(e\left(\frac{189}{220}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{19}{132}\right)\) |
| \(\chi_{5445}(898,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{437}{660}\right)\) | \(e\left(\frac{107}{330}\right)\) | \(e\left(\frac{89}{660}\right)\) | \(e\left(\frac{217}{220}\right)\) | \(e\left(\frac{247}{660}\right)\) | \(e\left(\frac{263}{330}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{171}{220}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{101}{132}\right)\) |
| \(\chi_{5445}(943,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{660}\right)\) | \(e\left(\frac{173}{330}\right)\) | \(e\left(\frac{221}{660}\right)\) | \(e\left(\frac{173}{220}\right)\) | \(e\left(\frac{643}{660}\right)\) | \(e\left(\frac{197}{330}\right)\) | \(e\left(\frac{8}{165}\right)\) | \(e\left(\frac{39}{220}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{101}{132}\right)\) |
| \(\chi_{5445}(952,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{299}{660}\right)\) | \(e\left(\frac{299}{330}\right)\) | \(e\left(\frac{443}{660}\right)\) | \(e\left(\frac{79}{220}\right)\) | \(e\left(\frac{169}{660}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{134}{165}\right)\) | \(e\left(\frac{117}{220}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{83}{132}\right)\) |
| \(\chi_{5445}(997,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{660}\right)\) | \(e\left(\frac{47}{330}\right)\) | \(e\left(\frac{659}{660}\right)\) | \(e\left(\frac{47}{220}\right)\) | \(e\left(\frac{457}{660}\right)\) | \(e\left(\frac{23}{330}\right)\) | \(e\left(\frac{47}{165}\right)\) | \(e\left(\frac{181}{220}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{119}{132}\right)\) |
| \(\chi_{5445}(1003,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{541}{660}\right)\) | \(e\left(\frac{211}{330}\right)\) | \(e\left(\frac{157}{660}\right)\) | \(e\left(\frac{101}{220}\right)\) | \(e\left(\frac{191}{660}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{183}{220}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{61}{132}\right)\) |