from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(460))
M = H._module
chi = DirichletCharacter(H, M([0,161,220]))
chi.galois_orbit()
[g,chi] = znchar(Mod(28,3525))
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: | \(460\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 1175.x | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3525}(28,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{441}{460}\right)\) | \(e\left(\frac{211}{230}\right)\) | \(e\left(\frac{5}{92}\right)\) | \(e\left(\frac{403}{460}\right)\) | \(e\left(\frac{109}{115}\right)\) | \(e\left(\frac{419}{460}\right)\) | \(e\left(\frac{3}{230}\right)\) | \(e\left(\frac{96}{115}\right)\) | \(e\left(\frac{93}{460}\right)\) | \(e\left(\frac{189}{230}\right)\) |
\(\chi_{3525}(37,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{407}{460}\right)\) | \(e\left(\frac{177}{230}\right)\) | \(e\left(\frac{43}{92}\right)\) | \(e\left(\frac{301}{460}\right)\) | \(e\left(\frac{68}{115}\right)\) | \(e\left(\frac{273}{460}\right)\) | \(e\left(\frac{81}{230}\right)\) | \(e\left(\frac{62}{115}\right)\) | \(e\left(\frac{211}{460}\right)\) | \(e\left(\frac{43}{230}\right)\) |
\(\chi_{3525}(97,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{311}{460}\right)\) | \(e\left(\frac{81}{230}\right)\) | \(e\left(\frac{15}{92}\right)\) | \(e\left(\frac{13}{460}\right)\) | \(e\left(\frac{74}{115}\right)\) | \(e\left(\frac{429}{460}\right)\) | \(e\left(\frac{193}{230}\right)\) | \(e\left(\frac{81}{115}\right)\) | \(e\left(\frac{3}{460}\right)\) | \(e\left(\frac{199}{230}\right)\) |
\(\chi_{3525}(103,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{460}\right)\) | \(e\left(\frac{1}{230}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{3}{460}\right)\) | \(e\left(\frac{79}{115}\right)\) | \(e\left(\frac{99}{460}\right)\) | \(e\left(\frac{133}{230}\right)\) | \(e\left(\frac{1}{115}\right)\) | \(e\left(\frac{213}{460}\right)\) | \(e\left(\frac{99}{230}\right)\) |
\(\chi_{3525}(112,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{67}{460}\right)\) | \(e\left(\frac{67}{230}\right)\) | \(e\left(\frac{55}{92}\right)\) | \(e\left(\frac{201}{460}\right)\) | \(e\left(\frac{3}{115}\right)\) | \(e\left(\frac{193}{460}\right)\) | \(e\left(\frac{171}{230}\right)\) | \(e\left(\frac{67}{115}\right)\) | \(e\left(\frac{11}{460}\right)\) | \(e\left(\frac{193}{230}\right)\) |
\(\chi_{3525}(148,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{33}{460}\right)\) | \(e\left(\frac{33}{230}\right)\) | \(e\left(\frac{1}{92}\right)\) | \(e\left(\frac{99}{460}\right)\) | \(e\left(\frac{77}{115}\right)\) | \(e\left(\frac{47}{460}\right)\) | \(e\left(\frac{19}{230}\right)\) | \(e\left(\frac{33}{115}\right)\) | \(e\left(\frac{129}{460}\right)\) | \(e\left(\frac{47}{230}\right)\) |
\(\chi_{3525}(178,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{361}{460}\right)\) | \(e\left(\frac{131}{230}\right)\) | \(e\left(\frac{89}{92}\right)\) | \(e\left(\frac{163}{460}\right)\) | \(e\left(\frac{114}{115}\right)\) | \(e\left(\frac{319}{460}\right)\) | \(e\left(\frac{173}{230}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{73}{460}\right)\) | \(e\left(\frac{89}{230}\right)\) |
\(\chi_{3525}(202,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{283}{460}\right)\) | \(e\left(\frac{53}{230}\right)\) | \(e\left(\frac{3}{92}\right)\) | \(e\left(\frac{389}{460}\right)\) | \(e\left(\frac{47}{115}\right)\) | \(e\left(\frac{417}{460}\right)\) | \(e\left(\frac{149}{230}\right)\) | \(e\left(\frac{53}{115}\right)\) | \(e\left(\frac{19}{460}\right)\) | \(e\left(\frac{187}{230}\right)\) |
\(\chi_{3525}(238,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{357}{460}\right)\) | \(e\left(\frac{127}{230}\right)\) | \(e\left(\frac{61}{92}\right)\) | \(e\left(\frac{151}{460}\right)\) | \(e\left(\frac{28}{115}\right)\) | \(e\left(\frac{383}{460}\right)\) | \(e\left(\frac{101}{230}\right)\) | \(e\left(\frac{12}{115}\right)\) | \(e\left(\frac{141}{460}\right)\) | \(e\left(\frac{153}{230}\right)\) |
\(\chi_{3525}(247,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{351}{460}\right)\) | \(e\left(\frac{121}{230}\right)\) | \(e\left(\frac{19}{92}\right)\) | \(e\left(\frac{133}{460}\right)\) | \(e\left(\frac{14}{115}\right)\) | \(e\left(\frac{249}{460}\right)\) | \(e\left(\frac{223}{230}\right)\) | \(e\left(\frac{6}{115}\right)\) | \(e\left(\frac{243}{460}\right)\) | \(e\left(\frac{19}{230}\right)\) |
\(\chi_{3525}(253,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{21}{460}\right)\) | \(e\left(\frac{21}{230}\right)\) | \(e\left(\frac{9}{92}\right)\) | \(e\left(\frac{63}{460}\right)\) | \(e\left(\frac{49}{115}\right)\) | \(e\left(\frac{239}{460}\right)\) | \(e\left(\frac{33}{230}\right)\) | \(e\left(\frac{21}{115}\right)\) | \(e\left(\frac{333}{460}\right)\) | \(e\left(\frac{9}{230}\right)\) |
\(\chi_{3525}(262,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{427}{460}\right)\) | \(e\left(\frac{197}{230}\right)\) | \(e\left(\frac{91}{92}\right)\) | \(e\left(\frac{361}{460}\right)\) | \(e\left(\frac{38}{115}\right)\) | \(e\left(\frac{413}{460}\right)\) | \(e\left(\frac{211}{230}\right)\) | \(e\left(\frac{82}{115}\right)\) | \(e\left(\frac{331}{460}\right)\) | \(e\left(\frac{183}{230}\right)\) |
\(\chi_{3525}(277,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{203}{460}\right)\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{87}{92}\right)\) | \(e\left(\frac{149}{460}\right)\) | \(e\left(\frac{52}{115}\right)\) | \(e\left(\frac{317}{460}\right)\) | \(e\left(\frac{89}{230}\right)\) | \(e\left(\frac{88}{115}\right)\) | \(e\left(\frac{459}{460}\right)\) | \(e\left(\frac{87}{230}\right)\) |
\(\chi_{3525}(298,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{333}{460}\right)\) | \(e\left(\frac{103}{230}\right)\) | \(e\left(\frac{77}{92}\right)\) | \(e\left(\frac{79}{460}\right)\) | \(e\left(\frac{87}{115}\right)\) | \(e\left(\frac{307}{460}\right)\) | \(e\left(\frac{129}{230}\right)\) | \(e\left(\frac{103}{115}\right)\) | \(e\left(\frac{89}{460}\right)\) | \(e\left(\frac{77}{230}\right)\) |
\(\chi_{3525}(337,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{267}{460}\right)\) | \(e\left(\frac{37}{230}\right)\) | \(e\left(\frac{75}{92}\right)\) | \(e\left(\frac{341}{460}\right)\) | \(e\left(\frac{48}{115}\right)\) | \(e\left(\frac{213}{460}\right)\) | \(e\left(\frac{91}{230}\right)\) | \(e\left(\frac{37}{115}\right)\) | \(e\left(\frac{291}{460}\right)\) | \(e\left(\frac{213}{230}\right)\) |
\(\chi_{3525}(388,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{397}{460}\right)\) | \(e\left(\frac{167}{230}\right)\) | \(e\left(\frac{65}{92}\right)\) | \(e\left(\frac{271}{460}\right)\) | \(e\left(\frac{83}{115}\right)\) | \(e\left(\frac{203}{460}\right)\) | \(e\left(\frac{131}{230}\right)\) | \(e\left(\frac{52}{115}\right)\) | \(e\left(\frac{381}{460}\right)\) | \(e\left(\frac{203}{230}\right)\) |
\(\chi_{3525}(397,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{91}{460}\right)\) | \(e\left(\frac{91}{230}\right)\) | \(e\left(\frac{39}{92}\right)\) | \(e\left(\frac{273}{460}\right)\) | \(e\left(\frac{59}{115}\right)\) | \(e\left(\frac{269}{460}\right)\) | \(e\left(\frac{143}{230}\right)\) | \(e\left(\frac{91}{115}\right)\) | \(e\left(\frac{63}{460}\right)\) | \(e\left(\frac{39}{230}\right)\) |
\(\chi_{3525}(403,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{381}{460}\right)\) | \(e\left(\frac{151}{230}\right)\) | \(e\left(\frac{45}{92}\right)\) | \(e\left(\frac{223}{460}\right)\) | \(e\left(\frac{84}{115}\right)\) | \(e\left(\frac{459}{460}\right)\) | \(e\left(\frac{73}{230}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{193}{460}\right)\) | \(e\left(\frac{229}{230}\right)\) |
\(\chi_{3525}(412,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{87}{460}\right)\) | \(e\left(\frac{87}{230}\right)\) | \(e\left(\frac{11}{92}\right)\) | \(e\left(\frac{261}{460}\right)\) | \(e\left(\frac{88}{115}\right)\) | \(e\left(\frac{333}{460}\right)\) | \(e\left(\frac{71}{230}\right)\) | \(e\left(\frac{87}{115}\right)\) | \(e\left(\frac{131}{460}\right)\) | \(e\left(\frac{103}{230}\right)\) |
\(\chi_{3525}(427,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{63}{460}\right)\) | \(e\left(\frac{63}{230}\right)\) | \(e\left(\frac{27}{92}\right)\) | \(e\left(\frac{189}{460}\right)\) | \(e\left(\frac{32}{115}\right)\) | \(e\left(\frac{257}{460}\right)\) | \(e\left(\frac{99}{230}\right)\) | \(e\left(\frac{63}{115}\right)\) | \(e\left(\frac{79}{460}\right)\) | \(e\left(\frac{27}{230}\right)\) |
\(\chi_{3525}(448,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{153}{460}\right)\) | \(e\left(\frac{153}{230}\right)\) | \(e\left(\frac{13}{92}\right)\) | \(e\left(\frac{459}{460}\right)\) | \(e\left(\frac{12}{115}\right)\) | \(e\left(\frac{427}{460}\right)\) | \(e\left(\frac{109}{230}\right)\) | \(e\left(\frac{38}{115}\right)\) | \(e\left(\frac{389}{460}\right)\) | \(e\left(\frac{197}{230}\right)\) |
\(\chi_{3525}(472,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{411}{460}\right)\) | \(e\left(\frac{181}{230}\right)\) | \(e\left(\frac{71}{92}\right)\) | \(e\left(\frac{313}{460}\right)\) | \(e\left(\frac{39}{115}\right)\) | \(e\left(\frac{209}{460}\right)\) | \(e\left(\frac{153}{230}\right)\) | \(e\left(\frac{66}{115}\right)\) | \(e\left(\frac{143}{460}\right)\) | \(e\left(\frac{209}{230}\right)\) |
\(\chi_{3525}(478,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{221}{460}\right)\) | \(e\left(\frac{221}{230}\right)\) | \(e\left(\frac{29}{92}\right)\) | \(e\left(\frac{203}{460}\right)\) | \(e\left(\frac{94}{115}\right)\) | \(e\left(\frac{259}{460}\right)\) | \(e\left(\frac{183}{230}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{153}{460}\right)\) | \(e\left(\frac{29}{230}\right)\) |
\(\chi_{3525}(487,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{327}{460}\right)\) | \(e\left(\frac{97}{230}\right)\) | \(e\left(\frac{35}{92}\right)\) | \(e\left(\frac{61}{460}\right)\) | \(e\left(\frac{73}{115}\right)\) | \(e\left(\frac{173}{460}\right)\) | \(e\left(\frac{21}{230}\right)\) | \(e\left(\frac{97}{115}\right)\) | \(e\left(\frac{191}{460}\right)\) | \(e\left(\frac{173}{230}\right)\) |
\(\chi_{3525}(502,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{123}{460}\right)\) | \(e\left(\frac{123}{230}\right)\) | \(e\left(\frac{79}{92}\right)\) | \(e\left(\frac{369}{460}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{217}{460}\right)\) | \(e\left(\frac{29}{230}\right)\) | \(e\left(\frac{8}{115}\right)\) | \(e\left(\frac{439}{460}\right)\) | \(e\left(\frac{217}{230}\right)\) |
\(\chi_{3525}(523,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{193}{460}\right)\) | \(e\left(\frac{193}{230}\right)\) | \(e\left(\frac{17}{92}\right)\) | \(e\left(\frac{119}{460}\right)\) | \(e\left(\frac{67}{115}\right)\) | \(e\left(\frac{247}{460}\right)\) | \(e\left(\frac{139}{230}\right)\) | \(e\left(\frac{78}{115}\right)\) | \(e\left(\frac{169}{460}\right)\) | \(e\left(\frac{17}{230}\right)\) |
\(\chi_{3525}(538,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{137}{460}\right)\) | \(e\left(\frac{137}{230}\right)\) | \(e\left(\frac{85}{92}\right)\) | \(e\left(\frac{411}{460}\right)\) | \(e\left(\frac{13}{115}\right)\) | \(e\left(\frac{223}{460}\right)\) | \(e\left(\frac{51}{230}\right)\) | \(e\left(\frac{22}{115}\right)\) | \(e\left(\frac{201}{460}\right)\) | \(e\left(\frac{223}{230}\right)\) |
\(\chi_{3525}(553,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{460}\right)\) | \(e\left(\frac{41}{230}\right)\) | \(e\left(\frac{57}{92}\right)\) | \(e\left(\frac{123}{460}\right)\) | \(e\left(\frac{19}{115}\right)\) | \(e\left(\frac{379}{460}\right)\) | \(e\left(\frac{163}{230}\right)\) | \(e\left(\frac{41}{115}\right)\) | \(e\left(\frac{453}{460}\right)\) | \(e\left(\frac{149}{230}\right)\) |
\(\chi_{3525}(592,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{119}{460}\right)\) | \(e\left(\frac{119}{230}\right)\) | \(e\left(\frac{51}{92}\right)\) | \(e\left(\frac{357}{460}\right)\) | \(e\left(\frac{86}{115}\right)\) | \(e\left(\frac{281}{460}\right)\) | \(e\left(\frac{187}{230}\right)\) | \(e\left(\frac{4}{115}\right)\) | \(e\left(\frac{47}{460}\right)\) | \(e\left(\frac{51}{230}\right)\) |
\(\chi_{3525}(598,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{393}{460}\right)\) | \(e\left(\frac{163}{230}\right)\) | \(e\left(\frac{37}{92}\right)\) | \(e\left(\frac{259}{460}\right)\) | \(e\left(\frac{112}{115}\right)\) | \(e\left(\frac{267}{460}\right)\) | \(e\left(\frac{59}{230}\right)\) | \(e\left(\frac{48}{115}\right)\) | \(e\left(\frac{449}{460}\right)\) | \(e\left(\frac{37}{230}\right)\) |
\(\chi_{3525}(613,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{457}{460}\right)\) | \(e\left(\frac{227}{230}\right)\) | \(e\left(\frac{25}{92}\right)\) | \(e\left(\frac{451}{460}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{163}{460}\right)\) | \(e\left(\frac{61}{230}\right)\) | \(e\left(\frac{112}{115}\right)\) | \(e\left(\frac{281}{460}\right)\) | \(e\left(\frac{163}{230}\right)\) |