from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(460))
M = H._module
chi = DirichletCharacter(H, M([230,23,180]))
chi.galois_orbit()
[g,chi] = znchar(Mod(2,3525))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3525\) | |
| Conductor: | \(3525\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(460\) | 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: | $\Q(\zeta_{460})$ |
| Fixed field: | Number field defined by a degree 460 polynomial (not computed) |
First 31 of 176 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3525}(2,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{273}{460}\right)\) | \(e\left(\frac{43}{230}\right)\) | \(e\left(\frac{71}{92}\right)\) | \(e\left(\frac{359}{460}\right)\) | \(e\left(\frac{9}{230}\right)\) | \(e\left(\frac{117}{460}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{43}{115}\right)\) | \(e\left(\frac{189}{460}\right)\) | \(e\left(\frac{117}{230}\right)\) |
| \(\chi_{3525}(8,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{359}{460}\right)\) | \(e\left(\frac{129}{230}\right)\) | \(e\left(\frac{29}{92}\right)\) | \(e\left(\frac{157}{460}\right)\) | \(e\left(\frac{27}{230}\right)\) | \(e\left(\frac{351}{460}\right)\) | \(e\left(\frac{11}{115}\right)\) | \(e\left(\frac{14}{115}\right)\) | \(e\left(\frac{107}{460}\right)\) | \(e\left(\frac{121}{230}\right)\) |
| \(\chi_{3525}(17,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{189}{460}\right)\) | \(e\left(\frac{189}{230}\right)\) | \(e\left(\frac{35}{92}\right)\) | \(e\left(\frac{107}{460}\right)\) | \(e\left(\frac{77}{230}\right)\) | \(e\left(\frac{81}{460}\right)\) | \(e\left(\frac{91}{115}\right)\) | \(e\left(\frac{74}{115}\right)\) | \(e\left(\frac{237}{460}\right)\) | \(e\left(\frac{81}{230}\right)\) |
| \(\chi_{3525}(53,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{331}{460}\right)\) | \(e\left(\frac{101}{230}\right)\) | \(e\left(\frac{17}{92}\right)\) | \(e\left(\frac{73}{460}\right)\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{339}{460}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{101}{115}\right)\) | \(e\left(\frac{123}{460}\right)\) | \(e\left(\frac{109}{230}\right)\) |
| \(\chi_{3525}(83,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{460}\right)\) | \(e\left(\frac{179}{230}\right)\) | \(e\left(\frac{57}{92}\right)\) | \(e\left(\frac{77}{460}\right)\) | \(e\left(\frac{107}{230}\right)\) | \(e\left(\frac{11}{460}\right)\) | \(e\left(\frac{1}{115}\right)\) | \(e\left(\frac{64}{115}\right)\) | \(e\left(\frac{407}{460}\right)\) | \(e\left(\frac{11}{230}\right)\) |
| \(\chi_{3525}(98,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{460}\right)\) | \(e\left(\frac{63}{230}\right)\) | \(e\left(\frac{73}{92}\right)\) | \(e\left(\frac{189}{460}\right)\) | \(e\left(\frac{179}{230}\right)\) | \(e\left(\frac{27}{460}\right)\) | \(e\left(\frac{107}{115}\right)\) | \(e\left(\frac{63}{115}\right)\) | \(e\left(\frac{79}{460}\right)\) | \(e\left(\frac{27}{230}\right)\) |
| \(\chi_{3525}(122,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{441}{460}\right)\) | \(e\left(\frac{211}{230}\right)\) | \(e\left(\frac{51}{92}\right)\) | \(e\left(\frac{403}{460}\right)\) | \(e\left(\frac{103}{230}\right)\) | \(e\left(\frac{189}{460}\right)\) | \(e\left(\frac{59}{115}\right)\) | \(e\left(\frac{96}{115}\right)\) | \(e\left(\frac{93}{460}\right)\) | \(e\left(\frac{189}{230}\right)\) |
| \(\chi_{3525}(128,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{460}\right)\) | \(e\left(\frac{71}{230}\right)\) | \(e\left(\frac{37}{92}\right)\) | \(e\left(\frac{213}{460}\right)\) | \(e\left(\frac{63}{230}\right)\) | \(e\left(\frac{359}{460}\right)\) | \(e\left(\frac{64}{115}\right)\) | \(e\left(\frac{71}{115}\right)\) | \(e\left(\frac{403}{460}\right)\) | \(e\left(\frac{129}{230}\right)\) |
| \(\chi_{3525}(158,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{419}{460}\right)\) | \(e\left(\frac{189}{230}\right)\) | \(e\left(\frac{81}{92}\right)\) | \(e\left(\frac{337}{460}\right)\) | \(e\left(\frac{77}{230}\right)\) | \(e\left(\frac{311}{460}\right)\) | \(e\left(\frac{91}{115}\right)\) | \(e\left(\frac{74}{115}\right)\) | \(e\left(\frac{7}{460}\right)\) | \(e\left(\frac{81}{230}\right)\) |
| \(\chi_{3525}(173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{123}{460}\right)\) | \(e\left(\frac{123}{230}\right)\) | \(e\left(\frac{33}{92}\right)\) | \(e\left(\frac{369}{460}\right)\) | \(e\left(\frac{229}{230}\right)\) | \(e\left(\frac{447}{460}\right)\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{8}{115}\right)\) | \(e\left(\frac{439}{460}\right)\) | \(e\left(\frac{217}{230}\right)\) |
| \(\chi_{3525}(197,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{460}\right)\) | \(e\left(\frac{1}{230}\right)\) | \(e\left(\frac{7}{92}\right)\) | \(e\left(\frac{3}{460}\right)\) | \(e\left(\frac{43}{230}\right)\) | \(e\left(\frac{329}{460}\right)\) | \(e\left(\frac{9}{115}\right)\) | \(e\left(\frac{1}{115}\right)\) | \(e\left(\frac{213}{460}\right)\) | \(e\left(\frac{99}{230}\right)\) |
| \(\chi_{3525}(212,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{417}{460}\right)\) | \(e\left(\frac{187}{230}\right)\) | \(e\left(\frac{67}{92}\right)\) | \(e\left(\frac{331}{460}\right)\) | \(e\left(\frac{221}{230}\right)\) | \(e\left(\frac{113}{460}\right)\) | \(e\left(\frac{73}{115}\right)\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{41}{460}\right)\) | \(e\left(\frac{113}{230}\right)\) |
| \(\chi_{3525}(242,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{309}{460}\right)\) | \(e\left(\frac{79}{230}\right)\) | \(e\left(\frac{47}{92}\right)\) | \(e\left(\frac{7}{460}\right)\) | \(e\left(\frac{177}{230}\right)\) | \(e\left(\frac{1}{460}\right)\) | \(e\left(\frac{21}{115}\right)\) | \(e\left(\frac{79}{115}\right)\) | \(e\left(\frac{37}{460}\right)\) | \(e\left(\frac{1}{230}\right)\) |
| \(\chi_{3525}(263,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{460}\right)\) | \(e\left(\frac{27}{230}\right)\) | \(e\left(\frac{5}{92}\right)\) | \(e\left(\frac{81}{460}\right)\) | \(e\left(\frac{11}{230}\right)\) | \(e\left(\frac{143}{460}\right)\) | \(e\left(\frac{13}{115}\right)\) | \(e\left(\frac{27}{115}\right)\) | \(e\left(\frac{231}{460}\right)\) | \(e\left(\frac{143}{230}\right)\) |
| \(\chi_{3525}(272,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{361}{460}\right)\) | \(e\left(\frac{131}{230}\right)\) | \(e\left(\frac{43}{92}\right)\) | \(e\left(\frac{163}{460}\right)\) | \(e\left(\frac{113}{230}\right)\) | \(e\left(\frac{89}{460}\right)\) | \(e\left(\frac{29}{115}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{73}{460}\right)\) | \(e\left(\frac{89}{230}\right)\) |
| \(\chi_{3525}(338,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{460}\right)\) | \(e\left(\frac{47}{230}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{141}{460}\right)\) | \(e\left(\frac{181}{230}\right)\) | \(e\left(\frac{283}{460}\right)\) | \(e\left(\frac{78}{115}\right)\) | \(e\left(\frac{47}{115}\right)\) | \(e\left(\frac{351}{460}\right)\) | \(e\left(\frac{53}{230}\right)\) |
| \(\chi_{3525}(347,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{460}\right)\) | \(e\left(\frac{21}{230}\right)\) | \(e\left(\frac{55}{92}\right)\) | \(e\left(\frac{63}{460}\right)\) | \(e\left(\frac{213}{230}\right)\) | \(e\left(\frac{9}{460}\right)\) | \(e\left(\frac{74}{115}\right)\) | \(e\left(\frac{21}{115}\right)\) | \(e\left(\frac{333}{460}\right)\) | \(e\left(\frac{9}{230}\right)\) |
| \(\chi_{3525}(353,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{371}{460}\right)\) | \(e\left(\frac{141}{230}\right)\) | \(e\left(\frac{21}{92}\right)\) | \(e\left(\frac{193}{460}\right)\) | \(e\left(\frac{83}{230}\right)\) | \(e\left(\frac{159}{460}\right)\) | \(e\left(\frac{4}{115}\right)\) | \(e\left(\frac{26}{115}\right)\) | \(e\left(\frac{363}{460}\right)\) | \(e\left(\frac{159}{230}\right)\) |
| \(\chi_{3525}(383,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{460}\right)\) | \(e\left(\frac{79}{230}\right)\) | \(e\left(\frac{1}{92}\right)\) | \(e\left(\frac{237}{460}\right)\) | \(e\left(\frac{177}{230}\right)\) | \(e\left(\frac{231}{460}\right)\) | \(e\left(\frac{21}{115}\right)\) | \(e\left(\frac{79}{115}\right)\) | \(e\left(\frac{267}{460}\right)\) | \(e\left(\frac{1}{230}\right)\) |
| \(\chi_{3525}(392,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{460}\right)\) | \(e\left(\frac{149}{230}\right)\) | \(e\left(\frac{31}{92}\right)\) | \(e\left(\frac{447}{460}\right)\) | \(e\left(\frac{197}{230}\right)\) | \(e\left(\frac{261}{460}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{457}{460}\right)\) | \(e\left(\frac{31}{230}\right)\) |
| \(\chi_{3525}(413,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{407}{460}\right)\) | \(e\left(\frac{177}{230}\right)\) | \(e\left(\frac{89}{92}\right)\) | \(e\left(\frac{301}{460}\right)\) | \(e\left(\frac{21}{230}\right)\) | \(e\left(\frac{43}{460}\right)\) | \(e\left(\frac{98}{115}\right)\) | \(e\left(\frac{62}{115}\right)\) | \(e\left(\frac{211}{460}\right)\) | \(e\left(\frac{43}{230}\right)\) |
| \(\chi_{3525}(437,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{237}{460}\right)\) | \(e\left(\frac{7}{230}\right)\) | \(e\left(\frac{3}{92}\right)\) | \(e\left(\frac{251}{460}\right)\) | \(e\left(\frac{71}{230}\right)\) | \(e\left(\frac{233}{460}\right)\) | \(e\left(\frac{63}{115}\right)\) | \(e\left(\frac{7}{115}\right)\) | \(e\left(\frac{341}{460}\right)\) | \(e\left(\frac{3}{230}\right)\) |
| \(\chi_{3525}(473,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{403}{460}\right)\) | \(e\left(\frac{173}{230}\right)\) | \(e\left(\frac{61}{92}\right)\) | \(e\left(\frac{289}{460}\right)\) | \(e\left(\frac{79}{230}\right)\) | \(e\left(\frac{107}{460}\right)\) | \(e\left(\frac{62}{115}\right)\) | \(e\left(\frac{58}{115}\right)\) | \(e\left(\frac{279}{460}\right)\) | \(e\left(\frac{107}{230}\right)\) |
| \(\chi_{3525}(488,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{460}\right)\) | \(e\left(\frac{67}{230}\right)\) | \(e\left(\frac{9}{92}\right)\) | \(e\left(\frac{201}{460}\right)\) | \(e\left(\frac{121}{230}\right)\) | \(e\left(\frac{423}{460}\right)\) | \(e\left(\frac{28}{115}\right)\) | \(e\left(\frac{67}{115}\right)\) | \(e\left(\frac{11}{460}\right)\) | \(e\left(\frac{193}{230}\right)\) |
| \(\chi_{3525}(497,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{381}{460}\right)\) | \(e\left(\frac{151}{230}\right)\) | \(e\left(\frac{91}{92}\right)\) | \(e\left(\frac{223}{460}\right)\) | \(e\left(\frac{53}{230}\right)\) | \(e\left(\frac{229}{460}\right)\) | \(e\left(\frac{94}{115}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{193}{460}\right)\) | \(e\left(\frac{229}{230}\right)\) |
| \(\chi_{3525}(512,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{460}\right)\) | \(e\left(\frac{157}{230}\right)\) | \(e\left(\frac{87}{92}\right)\) | \(e\left(\frac{11}{460}\right)\) | \(e\left(\frac{81}{230}\right)\) | \(e\left(\frac{133}{460}\right)\) | \(e\left(\frac{33}{115}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{321}{460}\right)\) | \(e\left(\frac{133}{230}\right)\) |
| \(\chi_{3525}(533,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{379}{460}\right)\) | \(e\left(\frac{149}{230}\right)\) | \(e\left(\frac{77}{92}\right)\) | \(e\left(\frac{217}{460}\right)\) | \(e\left(\frac{197}{230}\right)\) | \(e\left(\frac{31}{460}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{227}{460}\right)\) | \(e\left(\frac{31}{230}\right)\) |
| \(\chi_{3525}(542,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{429}{460}\right)\) | \(e\left(\frac{199}{230}\right)\) | \(e\left(\frac{59}{92}\right)\) | \(e\left(\frac{367}{460}\right)\) | \(e\left(\frac{47}{230}\right)\) | \(e\left(\frac{381}{460}\right)\) | \(e\left(\frac{66}{115}\right)\) | \(e\left(\frac{84}{115}\right)\) | \(e\left(\frac{297}{460}\right)\) | \(e\left(\frac{151}{230}\right)\) |
| \(\chi_{3525}(572,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{221}{460}\right)\) | \(e\left(\frac{221}{230}\right)\) | \(e\left(\frac{75}{92}\right)\) | \(e\left(\frac{203}{460}\right)\) | \(e\left(\frac{73}{230}\right)\) | \(e\left(\frac{29}{460}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{153}{460}\right)\) | \(e\left(\frac{29}{230}\right)\) |
| \(\chi_{3525}(578,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{460}\right)\) | \(e\left(\frac{191}{230}\right)\) | \(e\left(\frac{49}{92}\right)\) | \(e\left(\frac{113}{460}\right)\) | \(e\left(\frac{163}{230}\right)\) | \(e\left(\frac{279}{460}\right)\) | \(e\left(\frac{109}{115}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{203}{460}\right)\) | \(e\left(\frac{49}{230}\right)\) |
| \(\chi_{3525}(617,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{460}\right)\) | \(e\left(\frac{9}{230}\right)\) | \(e\left(\frac{63}{92}\right)\) | \(e\left(\frac{27}{460}\right)\) | \(e\left(\frac{157}{230}\right)\) | \(e\left(\frac{201}{460}\right)\) | \(e\left(\frac{81}{115}\right)\) | \(e\left(\frac{9}{115}\right)\) | \(e\left(\frac{77}{460}\right)\) | \(e\left(\frac{201}{230}\right)\) |