from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(460))
M = H._module
chi = DirichletCharacter(H, M([0,437,110]))
chi.galois_orbit()
[g,chi] = znchar(Mod(13,3525))
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.w | 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3525}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{117}{460}\right)\) | \(e\left(\frac{117}{230}\right)\) | \(e\left(\frac{37}{92}\right)\) | \(e\left(\frac{351}{460}\right)\) | \(e\left(\frac{201}{230}\right)\) | \(e\left(\frac{313}{460}\right)\) | \(e\left(\frac{151}{230}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{81}{460}\right)\) | \(e\left(\frac{99}{115}\right)\) |
\(\chi_{3525}(22,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{291}{460}\right)\) | \(e\left(\frac{61}{230}\right)\) | \(e\left(\frac{59}{92}\right)\) | \(e\left(\frac{413}{460}\right)\) | \(e\left(\frac{93}{230}\right)\) | \(e\left(\frac{59}{460}\right)\) | \(e\left(\frac{63}{230}\right)\) | \(e\left(\frac{61}{115}\right)\) | \(e\left(\frac{343}{460}\right)\) | \(e\left(\frac{87}{115}\right)\) |
\(\chi_{3525}(52,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{203}{460}\right)\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{87}{92}\right)\) | \(e\left(\frac{149}{460}\right)\) | \(e\left(\frac{219}{230}\right)\) | \(e\left(\frac{87}{460}\right)\) | \(e\left(\frac{89}{230}\right)\) | \(e\left(\frac{88}{115}\right)\) | \(e\left(\frac{459}{460}\right)\) | \(e\left(\frac{101}{115}\right)\) |
\(\chi_{3525}(58,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{409}{460}\right)\) | \(e\left(\frac{179}{230}\right)\) | \(e\left(\frac{57}{92}\right)\) | \(e\left(\frac{307}{460}\right)\) | \(e\left(\frac{107}{230}\right)\) | \(e\left(\frac{241}{460}\right)\) | \(e\left(\frac{117}{230}\right)\) | \(e\left(\frac{64}{115}\right)\) | \(e\left(\frac{177}{460}\right)\) | \(e\left(\frac{63}{115}\right)\) |
\(\chi_{3525}(67,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{460}\right)\) | \(e\left(\frac{59}{230}\right)\) | \(e\left(\frac{91}{92}\right)\) | \(e\left(\frac{177}{460}\right)\) | \(e\left(\frac{7}{230}\right)\) | \(e\left(\frac{91}{460}\right)\) | \(e\left(\frac{27}{230}\right)\) | \(e\left(\frac{59}{115}\right)\) | \(e\left(\frac{147}{460}\right)\) | \(e\left(\frac{103}{115}\right)\) |
\(\chi_{3525}(73,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{413}{460}\right)\) | \(e\left(\frac{183}{230}\right)\) | \(e\left(\frac{85}{92}\right)\) | \(e\left(\frac{319}{460}\right)\) | \(e\left(\frac{49}{230}\right)\) | \(e\left(\frac{177}{460}\right)\) | \(e\left(\frac{189}{230}\right)\) | \(e\left(\frac{68}{115}\right)\) | \(e\left(\frac{109}{460}\right)\) | \(e\left(\frac{31}{115}\right)\) |
\(\chi_{3525}(88,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{377}{460}\right)\) | \(e\left(\frac{147}{230}\right)\) | \(e\left(\frac{17}{92}\right)\) | \(e\left(\frac{211}{460}\right)\) | \(e\left(\frac{111}{230}\right)\) | \(e\left(\frac{293}{460}\right)\) | \(e\left(\frac{1}{230}\right)\) | \(e\left(\frac{32}{115}\right)\) | \(e\left(\frac{261}{460}\right)\) | \(e\left(\frac{89}{115}\right)\) |
\(\chi_{3525}(127,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{283}{460}\right)\) | \(e\left(\frac{53}{230}\right)\) | \(e\left(\frac{3}{92}\right)\) | \(e\left(\frac{389}{460}\right)\) | \(e\left(\frac{209}{230}\right)\) | \(e\left(\frac{187}{460}\right)\) | \(e\left(\frac{149}{230}\right)\) | \(e\left(\frac{53}{115}\right)\) | \(e\left(\frac{19}{460}\right)\) | \(e\left(\frac{36}{115}\right)\) |
\(\chi_{3525}(133,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{129}{460}\right)\) | \(e\left(\frac{129}{230}\right)\) | \(e\left(\frac{29}{92}\right)\) | \(e\left(\frac{387}{460}\right)\) | \(e\left(\frac{27}{230}\right)\) | \(e\left(\frac{121}{460}\right)\) | \(e\left(\frac{137}{230}\right)\) | \(e\left(\frac{14}{115}\right)\) | \(e\left(\frac{337}{460}\right)\) | \(e\left(\frac{3}{115}\right)\) |
\(\chi_{3525}(163,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{337}{460}\right)\) | \(e\left(\frac{107}{230}\right)\) | \(e\left(\frac{13}{92}\right)\) | \(e\left(\frac{91}{460}\right)\) | \(e\left(\frac{1}{230}\right)\) | \(e\left(\frac{13}{460}\right)\) | \(e\left(\frac{201}{230}\right)\) | \(e\left(\frac{107}{115}\right)\) | \(e\left(\frac{21}{460}\right)\) | \(e\left(\frac{64}{115}\right)\) |
\(\chi_{3525}(172,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{460}\right)\) | \(e\left(\frac{11}{230}\right)\) | \(e\left(\frac{31}{92}\right)\) | \(e\left(\frac{33}{460}\right)\) | \(e\left(\frac{13}{230}\right)\) | \(e\left(\frac{399}{460}\right)\) | \(e\left(\frac{83}{230}\right)\) | \(e\left(\frac{11}{115}\right)\) | \(e\left(\frac{43}{460}\right)\) | \(e\left(\frac{27}{115}\right)\) |
\(\chi_{3525}(208,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{289}{460}\right)\) | \(e\left(\frac{59}{230}\right)\) | \(e\left(\frac{45}{92}\right)\) | \(e\left(\frac{407}{460}\right)\) | \(e\left(\frac{7}{230}\right)\) | \(e\left(\frac{321}{460}\right)\) | \(e\left(\frac{27}{230}\right)\) | \(e\left(\frac{59}{115}\right)\) | \(e\left(\frac{377}{460}\right)\) | \(e\left(\frac{103}{115}\right)\) |
\(\chi_{3525}(217,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{159}{460}\right)\) | \(e\left(\frac{159}{230}\right)\) | \(e\left(\frac{55}{92}\right)\) | \(e\left(\frac{17}{460}\right)\) | \(e\left(\frac{167}{230}\right)\) | \(e\left(\frac{331}{460}\right)\) | \(e\left(\frac{217}{230}\right)\) | \(e\left(\frac{44}{115}\right)\) | \(e\left(\frac{287}{460}\right)\) | \(e\left(\frac{108}{115}\right)\) |
\(\chi_{3525}(223,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{213}{460}\right)\) | \(e\left(\frac{213}{230}\right)\) | \(e\left(\frac{65}{92}\right)\) | \(e\left(\frac{179}{460}\right)\) | \(e\left(\frac{189}{230}\right)\) | \(e\left(\frac{157}{460}\right)\) | \(e\left(\frac{39}{230}\right)\) | \(e\left(\frac{98}{115}\right)\) | \(e\left(\frac{289}{460}\right)\) | \(e\left(\frac{21}{115}\right)\) |
\(\chi_{3525}(292,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{460}\right)\) | \(e\left(\frac{39}{230}\right)\) | \(e\left(\frac{43}{92}\right)\) | \(e\left(\frac{117}{460}\right)\) | \(e\left(\frac{67}{230}\right)\) | \(e\left(\frac{411}{460}\right)\) | \(e\left(\frac{127}{230}\right)\) | \(e\left(\frac{39}{115}\right)\) | \(e\left(\frac{27}{460}\right)\) | \(e\left(\frac{33}{115}\right)\) |
\(\chi_{3525}(313,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{460}\right)\) | \(e\left(\frac{57}{230}\right)\) | \(e\left(\frac{77}{92}\right)\) | \(e\left(\frac{171}{460}\right)\) | \(e\left(\frac{151}{230}\right)\) | \(e\left(\frac{353}{460}\right)\) | \(e\left(\frac{221}{230}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{181}{460}\right)\) | \(e\left(\frac{4}{115}\right)\) |
\(\chi_{3525}(322,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{171}{460}\right)\) | \(e\left(\frac{171}{230}\right)\) | \(e\left(\frac{47}{92}\right)\) | \(e\left(\frac{53}{460}\right)\) | \(e\left(\frac{223}{230}\right)\) | \(e\left(\frac{139}{460}\right)\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{56}{115}\right)\) | \(e\left(\frac{83}{460}\right)\) | \(e\left(\frac{12}{115}\right)\) |
\(\chi_{3525}(352,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{460}\right)\) | \(e\left(\frac{3}{230}\right)\) | \(e\left(\frac{67}{92}\right)\) | \(e\left(\frac{9}{460}\right)\) | \(e\left(\frac{129}{230}\right)\) | \(e\left(\frac{67}{460}\right)\) | \(e\left(\frac{169}{230}\right)\) | \(e\left(\frac{3}{115}\right)\) | \(e\left(\frac{179}{460}\right)\) | \(e\left(\frac{91}{115}\right)\) |
\(\chi_{3525}(358,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{389}{460}\right)\) | \(e\left(\frac{159}{230}\right)\) | \(e\left(\frac{9}{92}\right)\) | \(e\left(\frac{247}{460}\right)\) | \(e\left(\frac{167}{230}\right)\) | \(e\left(\frac{101}{460}\right)\) | \(e\left(\frac{217}{230}\right)\) | \(e\left(\frac{44}{115}\right)\) | \(e\left(\frac{57}{460}\right)\) | \(e\left(\frac{108}{115}\right)\) |
\(\chi_{3525}(367,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{460}\right)\) | \(e\left(\frac{139}{230}\right)\) | \(e\left(\frac{7}{92}\right)\) | \(e\left(\frac{417}{460}\right)\) | \(e\left(\frac{227}{230}\right)\) | \(e\left(\frac{191}{460}\right)\) | \(e\left(\frac{87}{230}\right)\) | \(e\left(\frac{24}{115}\right)\) | \(e\left(\frac{167}{460}\right)\) | \(e\left(\frac{38}{115}\right)\) |
\(\chi_{3525}(373,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{460}\right)\) | \(e\left(\frac{173}{230}\right)\) | \(e\left(\frac{61}{92}\right)\) | \(e\left(\frac{59}{460}\right)\) | \(e\left(\frac{79}{230}\right)\) | \(e\left(\frac{337}{460}\right)\) | \(e\left(\frac{9}{230}\right)\) | \(e\left(\frac{58}{115}\right)\) | \(e\left(\frac{49}{460}\right)\) | \(e\left(\frac{111}{115}\right)\) |
\(\chi_{3525}(433,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{269}{460}\right)\) | \(e\left(\frac{39}{230}\right)\) | \(e\left(\frac{89}{92}\right)\) | \(e\left(\frac{347}{460}\right)\) | \(e\left(\frac{67}{230}\right)\) | \(e\left(\frac{181}{460}\right)\) | \(e\left(\frac{127}{230}\right)\) | \(e\left(\frac{39}{115}\right)\) | \(e\left(\frac{257}{460}\right)\) | \(e\left(\frac{33}{115}\right)\) |
\(\chi_{3525}(442,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{460}\right)\) | \(e\left(\frac{119}{230}\right)\) | \(e\left(\frac{51}{92}\right)\) | \(e\left(\frac{357}{460}\right)\) | \(e\left(\frac{57}{230}\right)\) | \(e\left(\frac{51}{460}\right)\) | \(e\left(\frac{187}{230}\right)\) | \(e\left(\frac{4}{115}\right)\) | \(e\left(\frac{47}{460}\right)\) | \(e\left(\frac{83}{115}\right)\) |
\(\chi_{3525}(463,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{217}{460}\right)\) | \(e\left(\frac{217}{230}\right)\) | \(e\left(\frac{1}{92}\right)\) | \(e\left(\frac{191}{460}\right)\) | \(e\left(\frac{131}{230}\right)\) | \(e\left(\frac{93}{460}\right)\) | \(e\left(\frac{111}{230}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{221}{460}\right)\) | \(e\left(\frac{104}{115}\right)\) |
\(\chi_{3525}(508,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{369}{460}\right)\) | \(e\left(\frac{139}{230}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{187}{460}\right)\) | \(e\left(\frac{227}{230}\right)\) | \(e\left(\frac{421}{460}\right)\) | \(e\left(\frac{87}{230}\right)\) | \(e\left(\frac{24}{115}\right)\) | \(e\left(\frac{397}{460}\right)\) | \(e\left(\frac{38}{115}\right)\) |
\(\chi_{3525}(547,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{460}\right)\) | \(e\left(\frac{51}{230}\right)\) | \(e\left(\frac{35}{92}\right)\) | \(e\left(\frac{153}{460}\right)\) | \(e\left(\frac{123}{230}\right)\) | \(e\left(\frac{219}{460}\right)\) | \(e\left(\frac{113}{230}\right)\) | \(e\left(\frac{51}{115}\right)\) | \(e\left(\frac{283}{460}\right)\) | \(e\left(\frac{52}{115}\right)\) |
\(\chi_{3525}(562,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{227}{460}\right)\) | \(e\left(\frac{227}{230}\right)\) | \(e\left(\frac{71}{92}\right)\) | \(e\left(\frac{221}{460}\right)\) | \(e\left(\frac{101}{230}\right)\) | \(e\left(\frac{163}{460}\right)\) | \(e\left(\frac{61}{230}\right)\) | \(e\left(\frac{112}{115}\right)\) | \(e\left(\frac{51}{460}\right)\) | \(e\left(\frac{24}{115}\right)\) |
\(\chi_{3525}(577,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{163}{460}\right)\) | \(e\left(\frac{163}{230}\right)\) | \(e\left(\frac{83}{92}\right)\) | \(e\left(\frac{29}{460}\right)\) | \(e\left(\frac{109}{230}\right)\) | \(e\left(\frac{267}{460}\right)\) | \(e\left(\frac{59}{230}\right)\) | \(e\left(\frac{48}{115}\right)\) | \(e\left(\frac{219}{460}\right)\) | \(e\left(\frac{76}{115}\right)\) |
\(\chi_{3525}(583,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{349}{460}\right)\) | \(e\left(\frac{119}{230}\right)\) | \(e\left(\frac{5}{92}\right)\) | \(e\left(\frac{127}{460}\right)\) | \(e\left(\frac{57}{230}\right)\) | \(e\left(\frac{281}{460}\right)\) | \(e\left(\frac{187}{230}\right)\) | \(e\left(\frac{4}{115}\right)\) | \(e\left(\frac{277}{460}\right)\) | \(e\left(\frac{83}{115}\right)\) |
\(\chi_{3525}(622,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{271}{460}\right)\) | \(e\left(\frac{41}{230}\right)\) | \(e\left(\frac{11}{92}\right)\) | \(e\left(\frac{353}{460}\right)\) | \(e\left(\frac{153}{230}\right)\) | \(e\left(\frac{379}{460}\right)\) | \(e\left(\frac{163}{230}\right)\) | \(e\left(\frac{41}{115}\right)\) | \(e\left(\frac{223}{460}\right)\) | \(e\left(\frac{17}{115}\right)\) |
\(\chi_{3525}(637,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{367}{460}\right)\) | \(e\left(\frac{137}{230}\right)\) | \(e\left(\frac{39}{92}\right)\) | \(e\left(\frac{181}{460}\right)\) | \(e\left(\frac{141}{230}\right)\) | \(e\left(\frac{223}{460}\right)\) | \(e\left(\frac{51}{230}\right)\) | \(e\left(\frac{22}{115}\right)\) | \(e\left(\frac{431}{460}\right)\) | \(e\left(\frac{54}{115}\right)\) |