from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4050, base_ring=CyclotomicField(540))
M = H._module
chi = DirichletCharacter(H, M([110,297]))
chi.galois_orbit()
[g,chi] = znchar(Mod(23,4050))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(4050\) | |
| Conductor: | \(2025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(540\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 2025.bv | 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: | $\Q(\zeta_{540})$ |
| Fixed field: | Number field defined by a degree 540 polynomial (not computed) |
First 31 of 144 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4050}(23,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{121}{270}\right)\) | \(e\left(\frac{43}{540}\right)\) | \(e\left(\frac{157}{180}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{157}{540}\right)\) | \(e\left(\frac{86}{135}\right)\) | \(e\left(\frac{64}{135}\right)\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{269}{270}\right)\) |
| \(\chi_{4050}(47,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{108}\right)\) | \(e\left(\frac{77}{270}\right)\) | \(e\left(\frac{101}{540}\right)\) | \(e\left(\frac{59}{180}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{419}{540}\right)\) | \(e\left(\frac{67}{135}\right)\) | \(e\left(\frac{53}{135}\right)\) | \(e\left(\frac{17}{180}\right)\) | \(e\left(\frac{73}{270}\right)\) |
| \(\chi_{4050}(77,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{91}{108}\right)\) | \(e\left(\frac{211}{270}\right)\) | \(e\left(\frac{133}{540}\right)\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{247}{540}\right)\) | \(e\left(\frac{131}{135}\right)\) | \(e\left(\frac{19}{135}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{179}{270}\right)\) |
| \(\chi_{4050}(83,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{108}\right)\) | \(e\left(\frac{173}{270}\right)\) | \(e\left(\frac{539}{540}\right)\) | \(e\left(\frac{101}{180}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{461}{540}\right)\) | \(e\left(\frac{133}{135}\right)\) | \(e\left(\frac{77}{135}\right)\) | \(e\left(\frac{23}{180}\right)\) | \(e\left(\frac{157}{270}\right)\) |
| \(\chi_{4050}(113,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{108}\right)\) | \(e\left(\frac{109}{270}\right)\) | \(e\left(\frac{427}{540}\right)\) | \(e\left(\frac{73}{180}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{253}{540}\right)\) | \(e\left(\frac{44}{135}\right)\) | \(e\left(\frac{61}{135}\right)\) | \(e\left(\frac{79}{180}\right)\) | \(e\left(\frac{191}{270}\right)\) |
| \(\chi_{4050}(137,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{95}{108}\right)\) | \(e\left(\frac{209}{270}\right)\) | \(e\left(\frac{197}{540}\right)\) | \(e\left(\frac{83}{180}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{443}{540}\right)\) | \(e\left(\frac{124}{135}\right)\) | \(e\left(\frac{86}{135}\right)\) | \(e\left(\frac{149}{180}\right)\) | \(e\left(\frac{121}{270}\right)\) |
| \(\chi_{4050}(167,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{108}\right)\) | \(e\left(\frac{253}{270}\right)\) | \(e\left(\frac{409}{540}\right)\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{451}{540}\right)\) | \(e\left(\frac{8}{135}\right)\) | \(e\left(\frac{97}{135}\right)\) | \(e\left(\frac{133}{180}\right)\) | \(e\left(\frac{47}{270}\right)\) |
| \(\chi_{4050}(173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{108}\right)\) | \(e\left(\frac{251}{270}\right)\) | \(e\left(\frac{203}{540}\right)\) | \(e\left(\frac{17}{180}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{377}{540}\right)\) | \(e\left(\frac{1}{135}\right)\) | \(e\left(\frac{29}{135}\right)\) | \(e\left(\frac{11}{180}\right)\) | \(e\left(\frac{259}{270}\right)\) |
| \(\chi_{4050}(203,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{108}\right)\) | \(e\left(\frac{97}{270}\right)\) | \(e\left(\frac{271}{540}\right)\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{349}{540}\right)\) | \(e\left(\frac{2}{135}\right)\) | \(e\left(\frac{58}{135}\right)\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{113}{270}\right)\) |
| \(\chi_{4050}(227,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{108}\right)\) | \(e\left(\frac{71}{270}\right)\) | \(e\left(\frac{293}{540}\right)\) | \(e\left(\frac{107}{180}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{467}{540}\right)\) | \(e\left(\frac{46}{135}\right)\) | \(e\left(\frac{119}{135}\right)\) | \(e\left(\frac{101}{180}\right)\) | \(e\left(\frac{169}{270}\right)\) |
| \(\chi_{4050}(263,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{108}\right)\) | \(e\left(\frac{59}{270}\right)\) | \(e\left(\frac{407}{540}\right)\) | \(e\left(\frac{113}{180}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{293}{540}\right)\) | \(e\left(\frac{4}{135}\right)\) | \(e\left(\frac{116}{135}\right)\) | \(e\left(\frac{179}{180}\right)\) | \(e\left(\frac{91}{270}\right)\) |
| \(\chi_{4050}(317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{203}{270}\right)\) | \(e\left(\frac{389}{540}\right)\) | \(e\left(\frac{131}{180}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{491}{540}\right)\) | \(e\left(\frac{103}{135}\right)\) | \(e\left(\frac{17}{135}\right)\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{217}{270}\right)\) |
| \(\chi_{4050}(347,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{108}\right)\) | \(e\left(\frac{67}{270}\right)\) | \(e\left(\frac{421}{540}\right)\) | \(e\left(\frac{139}{180}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{319}{540}\right)\) | \(e\left(\frac{32}{135}\right)\) | \(e\left(\frac{118}{135}\right)\) | \(e\left(\frac{37}{180}\right)\) | \(e\left(\frac{53}{270}\right)\) |
| \(\chi_{4050}(353,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{108}\right)\) | \(e\left(\frac{137}{270}\right)\) | \(e\left(\frac{71}{540}\right)\) | \(e\left(\frac{29}{180}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{209}{540}\right)\) | \(e\left(\frac{7}{135}\right)\) | \(e\left(\frac{68}{135}\right)\) | \(e\left(\frac{167}{180}\right)\) | \(e\left(\frac{193}{270}\right)\) |
| \(\chi_{4050}(383,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{108}\right)\) | \(e\left(\frac{73}{270}\right)\) | \(e\left(\frac{499}{540}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{1}{540}\right)\) | \(e\left(\frac{53}{135}\right)\) | \(e\left(\frac{52}{135}\right)\) | \(e\left(\frac{43}{180}\right)\) | \(e\left(\frac{227}{270}\right)\) |
| \(\chi_{4050}(437,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{108}\right)\) | \(e\left(\frac{109}{270}\right)\) | \(e\left(\frac{157}{540}\right)\) | \(e\left(\frac{163}{180}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{523}{540}\right)\) | \(e\left(\frac{44}{135}\right)\) | \(e\left(\frac{61}{135}\right)\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{191}{270}\right)\) |
| \(\chi_{4050}(473,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{61}{270}\right)\) | \(e\left(\frac{343}{540}\right)\) | \(e\left(\frac{97}{180}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{97}{540}\right)\) | \(e\left(\frac{11}{135}\right)\) | \(e\left(\frac{49}{135}\right)\) | \(e\left(\frac{31}{180}\right)\) | \(e\left(\frac{149}{270}\right)\) |
| \(\chi_{4050}(497,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{108}\right)\) | \(e\left(\frac{197}{270}\right)\) | \(e\left(\frac{41}{540}\right)\) | \(e\left(\frac{179}{180}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{539}{540}\right)\) | \(e\left(\frac{82}{135}\right)\) | \(e\left(\frac{83}{135}\right)\) | \(e\left(\frac{137}{180}\right)\) | \(e\left(\frac{43}{270}\right)\) |
| \(\chi_{4050}(527,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{151}{270}\right)\) | \(e\left(\frac{433}{540}\right)\) | \(e\left(\frac{7}{180}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{187}{540}\right)\) | \(e\left(\frac{56}{135}\right)\) | \(e\left(\frac{4}{135}\right)\) | \(e\left(\frac{121}{180}\right)\) | \(e\left(\frac{59}{270}\right)\) |
| \(\chi_{4050}(533,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{108}\right)\) | \(e\left(\frac{23}{270}\right)\) | \(e\left(\frac{479}{540}\right)\) | \(e\left(\frac{41}{180}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{41}{540}\right)\) | \(e\left(\frac{13}{135}\right)\) | \(e\left(\frac{107}{135}\right)\) | \(e\left(\frac{143}{180}\right)\) | \(e\left(\frac{127}{270}\right)\) |
| \(\chi_{4050}(563,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{108}\right)\) | \(e\left(\frac{49}{270}\right)\) | \(e\left(\frac{187}{540}\right)\) | \(e\left(\frac{13}{180}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{193}{540}\right)\) | \(e\left(\frac{104}{135}\right)\) | \(e\left(\frac{46}{135}\right)\) | \(e\left(\frac{19}{180}\right)\) | \(e\left(\frac{71}{270}\right)\) |
| \(\chi_{4050}(587,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{59}{270}\right)\) | \(e\left(\frac{137}{540}\right)\) | \(e\left(\frac{23}{180}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{23}{540}\right)\) | \(e\left(\frac{4}{135}\right)\) | \(e\left(\frac{116}{135}\right)\) | \(e\left(\frac{89}{180}\right)\) | \(e\left(\frac{91}{270}\right)\) |
| \(\chi_{4050}(617,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{108}\right)\) | \(e\left(\frac{193}{270}\right)\) | \(e\left(\frac{169}{540}\right)\) | \(e\left(\frac{31}{180}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{391}{540}\right)\) | \(e\left(\frac{68}{135}\right)\) | \(e\left(\frac{82}{135}\right)\) | \(e\left(\frac{73}{180}\right)\) | \(e\left(\frac{197}{270}\right)\) |
| \(\chi_{4050}(623,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{101}{270}\right)\) | \(e\left(\frac{143}{540}\right)\) | \(e\left(\frac{137}{180}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{497}{540}\right)\) | \(e\left(\frac{16}{135}\right)\) | \(e\left(\frac{59}{135}\right)\) | \(e\left(\frac{131}{180}\right)\) | \(e\left(\frac{229}{270}\right)\) |
| \(\chi_{4050}(653,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{37}{270}\right)\) | \(e\left(\frac{31}{540}\right)\) | \(e\left(\frac{109}{180}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{289}{540}\right)\) | \(e\left(\frac{62}{135}\right)\) | \(e\left(\frac{43}{135}\right)\) | \(e\left(\frac{7}{180}\right)\) | \(e\left(\frac{263}{270}\right)\) |
| \(\chi_{4050}(677,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{108}\right)\) | \(e\left(\frac{191}{270}\right)\) | \(e\left(\frac{233}{540}\right)\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{47}{540}\right)\) | \(e\left(\frac{61}{135}\right)\) | \(e\left(\frac{14}{135}\right)\) | \(e\left(\frac{41}{180}\right)\) | \(e\left(\frac{139}{270}\right)\) |
| \(\chi_{4050}(713,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{108}\right)\) | \(e\left(\frac{179}{270}\right)\) | \(e\left(\frac{347}{540}\right)\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{413}{540}\right)\) | \(e\left(\frac{19}{135}\right)\) | \(e\left(\frac{11}{135}\right)\) | \(e\left(\frac{119}{180}\right)\) | \(e\left(\frac{61}{270}\right)\) |
| \(\chi_{4050}(767,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{108}\right)\) | \(e\left(\frac{53}{270}\right)\) | \(e\left(\frac{329}{540}\right)\) | \(e\left(\frac{71}{180}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{71}{540}\right)\) | \(e\left(\frac{118}{135}\right)\) | \(e\left(\frac{47}{135}\right)\) | \(e\left(\frac{173}{180}\right)\) | \(e\left(\frac{187}{270}\right)\) |
| \(\chi_{4050}(797,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{108}\right)\) | \(e\left(\frac{7}{270}\right)\) | \(e\left(\frac{181}{540}\right)\) | \(e\left(\frac{79}{180}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{259}{540}\right)\) | \(e\left(\frac{92}{135}\right)\) | \(e\left(\frac{103}{135}\right)\) | \(e\left(\frac{157}{180}\right)\) | \(e\left(\frac{203}{270}\right)\) |
| \(\chi_{4050}(803,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{108}\right)\) | \(e\left(\frac{257}{270}\right)\) | \(e\left(\frac{11}{540}\right)\) | \(e\left(\frac{149}{180}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{329}{540}\right)\) | \(e\left(\frac{22}{135}\right)\) | \(e\left(\frac{98}{135}\right)\) | \(e\left(\frac{107}{180}\right)\) | \(e\left(\frac{163}{270}\right)\) |
| \(\chi_{4050}(833,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{13}{270}\right)\) | \(e\left(\frac{259}{540}\right)\) | \(e\left(\frac{121}{180}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{481}{540}\right)\) | \(e\left(\frac{113}{135}\right)\) | \(e\left(\frac{37}{135}\right)\) | \(e\left(\frac{163}{180}\right)\) | \(e\left(\frac{107}{270}\right)\) |