from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(230))
M = H._module
chi = DirichletCharacter(H, M([0,46,130]))
chi.galois_orbit()
[g,chi] = znchar(Mod(16,3525))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(3525\) | |
Conductor: | \(1175\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(115\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 1175.s | 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: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 115 polynomial (not computed) |
First 31 of 88 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3525}(16,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{115}\right)\) | \(e\left(\frac{86}{115}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{14}{115}\right)\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{53}{115}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{74}{115}\right)\) | \(e\left(\frac{4}{115}\right)\) |
\(\chi_{3525}(61,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{84}{115}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{11}{115}\right)\) | \(e\left(\frac{47}{115}\right)\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{17}{115}\right)\) | \(e\left(\frac{53}{115}\right)\) | \(e\left(\frac{91}{115}\right)\) | \(e\left(\frac{36}{115}\right)\) |
\(\chi_{3525}(106,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{114}{115}\right)\) | \(e\left(\frac{31}{115}\right)\) | \(e\left(\frac{29}{115}\right)\) | \(e\left(\frac{78}{115}\right)\) | \(e\left(\frac{113}{115}\right)\) |
\(\chi_{3525}(121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{115}\right)\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{27}{115}\right)\) | \(e\left(\frac{84}{115}\right)\) | \(e\left(\frac{86}{115}\right)\) | \(e\left(\frac{94}{115}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{77}{115}\right)\) | \(e\left(\frac{57}{115}\right)\) |
\(\chi_{3525}(136,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{115}\right)\) | \(e\left(\frac{44}{115}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{66}{115}\right)\) | \(e\left(\frac{52}{115}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{88}{115}\right)\) | \(e\left(\frac{86}{115}\right)\) | \(e\left(\frac{101}{115}\right)\) |
\(\chi_{3525}(166,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{115}\right)\) | \(e\left(\frac{111}{115}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{109}{115}\right)\) | \(e\left(\frac{58}{115}\right)\) | \(e\left(\frac{32}{115}\right)\) | \(e\left(\frac{43}{115}\right)\) | \(e\left(\frac{107}{115}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{64}{115}\right)\) |
\(\chi_{3525}(196,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{84}{115}\right)\) | \(e\left(\frac{53}{115}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{22}{115}\right)\) | \(e\left(\frac{94}{115}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{67}{115}\right)\) | \(e\left(\frac{72}{115}\right)\) |
\(\chi_{3525}(241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{115}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{24}{115}\right)\) | \(e\left(\frac{113}{115}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{58}{115}\right)\) | \(e\left(\frac{32}{115}\right)\) | \(e\left(\frac{94}{115}\right)\) | \(e\left(\frac{89}{115}\right)\) |
\(\chi_{3525}(256,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{86}{115}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{28}{115}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{4}{115}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{114}{115}\right)\) | \(e\left(\frac{33}{115}\right)\) | \(e\left(\frac{8}{115}\right)\) |
\(\chi_{3525}(271,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{115}\right)\) | \(e\left(\frac{78}{115}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{19}{115}\right)\) | \(e\left(\frac{66}{115}\right)\) | \(e\left(\frac{24}{115}\right)\) | \(e\left(\frac{41}{115}\right)\) | \(e\left(\frac{27}{115}\right)\) | \(e\left(\frac{17}{115}\right)\) |
\(\chi_{3525}(286,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{32}{115}\right)\) | \(e\left(\frac{93}{115}\right)\) | \(e\left(\frac{107}{115}\right)\) | \(e\left(\frac{63}{115}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{71}{115}\right)\) |
\(\chi_{3525}(316,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{58}{115}\right)\) | \(e\left(\frac{1}{115}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{59}{115}\right)\) | \(e\left(\frac{43}{115}\right)\) | \(e\left(\frac{107}{115}\right)\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{49}{115}\right)\) | \(e\left(\frac{99}{115}\right)\) |
\(\chi_{3525}(331,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{115}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{38}{115}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{111}{115}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{53}{115}\right)\) | \(e\left(\frac{93}{115}\right)\) |
\(\chi_{3525}(346,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{99}{115}\right)\) | \(e\left(\frac{83}{115}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{67}{115}\right)\) | \(e\left(\frac{4}{115}\right)\) | \(e\left(\frac{26}{115}\right)\) | \(e\left(\frac{114}{115}\right)\) | \(e\left(\frac{51}{115}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{52}{115}\right)\) |
\(\chi_{3525}(361,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{4}{115}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{6}{115}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{83}{115}\right)\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{8}{115}\right)\) | \(e\left(\frac{81}{115}\right)\) | \(e\left(\frac{51}{115}\right)\) |
\(\chi_{3525}(541,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{54}{115}\right)\) | \(e\left(\frac{53}{115}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{73}{115}\right)\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{39}{115}\right)\) | \(e\left(\frac{114}{115}\right)\) |
\(\chi_{3525}(571,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{115}\right)\) | \(e\left(\frac{28}{115}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{54}{115}\right)\) | \(e\left(\frac{6}{115}\right)\) | \(e\left(\frac{44}{115}\right)\) | \(e\left(\frac{56}{115}\right)\) | \(e\left(\frac{107}{115}\right)\) | \(e\left(\frac{12}{115}\right)\) |
\(\chi_{3525}(661,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{29}{115}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{101}{115}\right)\) | \(e\left(\frac{97}{115}\right)\) | \(e\left(\frac{113}{115}\right)\) | \(e\left(\frac{62}{115}\right)\) | \(e\left(\frac{58}{115}\right)\) | \(e\left(\frac{41}{115}\right)\) | \(e\left(\frac{111}{115}\right)\) |
\(\chi_{3525}(721,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{63}{115}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{37}{115}\right)\) | \(e\left(\frac{64}{115}\right)\) | \(e\left(\frac{71}{115}\right)\) | \(e\left(\frac{99}{115}\right)\) | \(e\left(\frac{11}{115}\right)\) | \(e\left(\frac{97}{115}\right)\) | \(e\left(\frac{27}{115}\right)\) |
\(\chi_{3525}(766,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{88}{115}\right)\) | \(e\left(\frac{61}{115}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{93}{115}\right)\) | \(e\left(\frac{87}{115}\right)\) | \(e\left(\frac{63}{115}\right)\) | \(e\left(\frac{7}{115}\right)\) | \(e\left(\frac{114}{115}\right)\) | \(e\left(\frac{59}{115}\right)\) |
\(\chi_{3525}(811,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{82}{115}\right)\) | \(e\left(\frac{49}{115}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{37}{115}\right)\) | \(e\left(\frac{68}{115}\right)\) | \(e\left(\frac{77}{115}\right)\) | \(e\left(\frac{98}{115}\right)\) | \(e\left(\frac{101}{115}\right)\) | \(e\left(\frac{21}{115}\right)\) |
\(\chi_{3525}(841,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{68}{115}\right)\) | \(e\left(\frac{21}{115}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{98}{115}\right)\) | \(e\left(\frac{62}{115}\right)\) | \(e\left(\frac{33}{115}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{109}{115}\right)\) | \(e\left(\frac{9}{115}\right)\) |
\(\chi_{3525}(871,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{44}{115}\right)\) | \(e\left(\frac{88}{115}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{17}{115}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{101}{115}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{61}{115}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{87}{115}\right)\) |
\(\chi_{3525}(946,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{54}{115}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{47}{115}\right)\) | \(e\left(\frac{44}{115}\right)\) | \(e\left(\frac{56}{115}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{101}{115}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{112}{115}\right)\) |
\(\chi_{3525}(961,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{115}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{51}{115}\right)\) | \(e\left(\frac{82}{115}\right)\) | \(e\left(\frac{73}{115}\right)\) | \(e\left(\frac{37}{115}\right)\) | \(e\left(\frac{68}{115}\right)\) | \(e\left(\frac{56}{115}\right)\) | \(e\left(\frac{31}{115}\right)\) |
\(\chi_{3525}(991,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{115}\right)\) | \(e\left(\frac{66}{115}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{99}{115}\right)\) | \(e\left(\frac{78}{115}\right)\) | \(e\left(\frac{47}{115}\right)\) | \(e\left(\frac{38}{115}\right)\) | \(e\left(\frac{17}{115}\right)\) | \(e\left(\frac{14}{115}\right)\) | \(e\left(\frac{94}{115}\right)\) |
\(\chi_{3525}(1021,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{93}{115}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{82}{115}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{61}{115}\right)\) | \(e\left(\frac{64}{115}\right)\) | \(e\left(\frac{71}{115}\right)\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{7}{115}\right)\) |
\(\chi_{3525}(1036,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{115}\right)\) | \(e\left(\frac{79}{115}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{61}{115}\right)\) | \(e\left(\frac{62}{115}\right)\) | \(e\left(\frac{58}{115}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{43}{115}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{1}{115}\right)\) |
\(\chi_{3525}(1066,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{48}{115}\right)\) | \(e\left(\frac{96}{115}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{29}{115}\right)\) | \(e\left(\frac{103}{115}\right)\) | \(e\left(\frac{37}{115}\right)\) | \(e\left(\frac{3}{115}\right)\) | \(e\left(\frac{77}{115}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{74}{115}\right)\) |
\(\chi_{3525}(1156,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{115}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{3}{115}\right)\) | \(e\left(\frac{86}{115}\right)\) | \(e\left(\frac{99}{115}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{4}{115}\right)\) | \(e\left(\frac{98}{115}\right)\) | \(e\left(\frac{83}{115}\right)\) |
\(\chi_{3525}(1231,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{115}\right)\) | \(e\left(\frac{12}{115}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{56}{115}\right)\) | \(e\left(\frac{19}{115}\right)\) | \(e\left(\frac{101}{115}\right)\) | \(e\left(\frac{24}{115}\right)\) | \(e\left(\frac{13}{115}\right)\) | \(e\left(\frac{38}{115}\right)\) |