from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(230))
M = H._module
chi = DirichletCharacter(H, M([115,184,35]))
chi.galois_orbit()
[g,chi] = znchar(Mod(11,3525))
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: | \(230\) | 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: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
First 31 of 88 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3525}(11,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{230}\right)\) | \(e\left(\frac{9}{115}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{27}{230}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{201}{230}\right)\) | \(e\left(\frac{209}{230}\right)\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{77}{230}\right)\) | \(e\left(\frac{57}{230}\right)\) |
\(\chi_{3525}(41,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{230}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{163}{230}\right)\) | \(e\left(\frac{113}{115}\right)\) | \(e\left(\frac{89}{230}\right)\) | \(e\left(\frac{1}{230}\right)\) | \(e\left(\frac{32}{115}\right)\) | \(e\left(\frac{73}{230}\right)\) | \(e\left(\frac{63}{230}\right)\) |
\(\chi_{3525}(86,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{99}{230}\right)\) | \(e\left(\frac{99}{115}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{67}{230}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{141}{230}\right)\) | \(e\left(\frac{229}{230}\right)\) | \(e\left(\frac{83}{115}\right)\) | \(e\left(\frac{157}{230}\right)\) | \(e\left(\frac{167}{230}\right)\) |
\(\chi_{3525}(116,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{111}{230}\right)\) | \(e\left(\frac{111}{115}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{103}{230}\right)\) | \(e\left(\frac{58}{115}\right)\) | \(e\left(\frac{179}{230}\right)\) | \(e\left(\frac{201}{230}\right)\) | \(e\left(\frac{107}{115}\right)\) | \(e\left(\frac{183}{230}\right)\) | \(e\left(\frac{13}{230}\right)\) |
\(\chi_{3525}(146,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{230}\right)\) | \(e\left(\frac{113}{115}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{109}{230}\right)\) | \(e\left(\frac{29}{115}\right)\) | \(e\left(\frac{147}{230}\right)\) | \(e\left(\frac{43}{230}\right)\) | \(e\left(\frac{111}{115}\right)\) | \(e\left(\frac{149}{230}\right)\) | \(e\left(\frac{179}{230}\right)\) |
\(\chi_{3525}(161,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{230}\right)\) | \(e\left(\frac{64}{115}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{77}{230}\right)\) | \(e\left(\frac{107}{115}\right)\) | \(e\left(\frac{11}{230}\right)\) | \(e\left(\frac{119}{230}\right)\) | \(e\left(\frac{13}{115}\right)\) | \(e\left(\frac{177}{230}\right)\) | \(e\left(\frac{137}{230}\right)\) |
\(\chi_{3525}(221,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{153}{230}\right)\) | \(e\left(\frac{38}{115}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{229}{230}\right)\) | \(e\left(\frac{24}{115}\right)\) | \(e\left(\frac{197}{230}\right)\) | \(e\left(\frac{103}{230}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{159}{230}\right)\) | \(e\left(\frac{49}{230}\right)\) |
\(\chi_{3525}(266,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{201}{230}\right)\) | \(e\left(\frac{86}{115}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{143}{230}\right)\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{119}{230}\right)\) | \(e\left(\frac{221}{230}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{33}{230}\right)\) | \(e\left(\frac{123}{230}\right)\) |
\(\chi_{3525}(311,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{229}{230}\right)\) | \(e\left(\frac{114}{115}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{227}{230}\right)\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{131}{230}\right)\) | \(e\left(\frac{79}{230}\right)\) | \(e\left(\frac{113}{115}\right)\) | \(e\left(\frac{17}{230}\right)\) | \(e\left(\frac{147}{230}\right)\) |
\(\chi_{3525}(386,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{230}\right)\) | \(e\left(\frac{54}{115}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{47}{230}\right)\) | \(e\left(\frac{22}{115}\right)\) | \(e\left(\frac{171}{230}\right)\) | \(e\left(\frac{219}{230}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{117}{230}\right)\) | \(e\left(\frac{227}{230}\right)\) |
\(\chi_{3525}(416,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{230}\right)\) | \(e\left(\frac{51}{115}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{153}{230}\right)\) | \(e\left(\frac{8}{115}\right)\) | \(e\left(\frac{219}{230}\right)\) | \(e\left(\frac{111}{230}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{53}{230}\right)\) | \(e\left(\frac{93}{230}\right)\) |
\(\chi_{3525}(446,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{230}\right)\) | \(e\left(\frac{13}{115}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{39}{230}\right)\) | \(e\left(\frac{99}{115}\right)\) | \(e\left(\frac{137}{230}\right)\) | \(e\left(\frac{123}{230}\right)\) | \(e\left(\frac{26}{115}\right)\) | \(e\left(\frac{9}{230}\right)\) | \(e\left(\frac{159}{230}\right)\) |
\(\chi_{3525}(461,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{219}{230}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{197}{230}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{61}{230}\right)\) | \(e\left(\frac{179}{230}\right)\) | \(e\left(\frac{93}{115}\right)\) | \(e\left(\frac{187}{230}\right)\) | \(e\left(\frac{7}{230}\right)\) |
\(\chi_{3525}(536,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{209}{230}\right)\) | \(e\left(\frac{94}{115}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{167}{230}\right)\) | \(e\left(\frac{17}{115}\right)\) | \(e\left(\frac{221}{230}\right)\) | \(e\left(\frac{49}{230}\right)\) | \(e\left(\frac{73}{115}\right)\) | \(e\left(\frac{127}{230}\right)\) | \(e\left(\frac{97}{230}\right)\) |
\(\chi_{3525}(641,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{221}{230}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{73}{115}\right)\) | \(e\left(\frac{29}{230}\right)\) | \(e\left(\frac{21}{230}\right)\) | \(e\left(\frac{97}{115}\right)\) | \(e\left(\frac{153}{230}\right)\) | \(e\left(\frac{173}{230}\right)\) |
\(\chi_{3525}(656,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{217}{230}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{191}{230}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{93}{230}\right)\) | \(e\left(\frac{107}{230}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{221}{230}\right)\) | \(e\left(\frac{71}{230}\right)\) |
\(\chi_{3525}(671,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{93}{230}\right)\) | \(e\left(\frac{93}{115}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{49}{230}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{7}{230}\right)\) | \(e\left(\frac{13}{230}\right)\) | \(e\left(\frac{71}{115}\right)\) | \(e\left(\frac{29}{230}\right)\) | \(e\left(\frac{129}{230}\right)\) |
\(\chi_{3525}(716,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{230}\right)\) | \(e\left(\frac{101}{115}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{73}{230}\right)\) | \(e\left(\frac{88}{115}\right)\) | \(e\left(\frac{109}{230}\right)\) | \(e\left(\frac{71}{230}\right)\) | \(e\left(\frac{87}{115}\right)\) | \(e\left(\frac{123}{230}\right)\) | \(e\left(\frac{103}{230}\right)\) |
\(\chi_{3525}(731,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{230}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{171}{230}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{123}{230}\right)\) | \(e\left(\frac{97}{230}\right)\) | \(e\left(\frac{114}{115}\right)\) | \(e\left(\frac{181}{230}\right)\) | \(e\left(\frac{131}{230}\right)\) |
\(\chi_{3525}(746,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{230}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{209}{230}\right)\) | \(e\left(\frac{44}{115}\right)\) | \(e\left(\frac{227}{230}\right)\) | \(e\left(\frac{93}{230}\right)\) | \(e\left(\frac{101}{115}\right)\) | \(e\left(\frac{119}{230}\right)\) | \(e\left(\frac{109}{230}\right)\) |
\(\chi_{3525}(791,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{230}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{113}{230}\right)\) | \(e\left(\frac{48}{115}\right)\) | \(e\left(\frac{49}{230}\right)\) | \(e\left(\frac{91}{230}\right)\) | \(e\left(\frac{37}{115}\right)\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{213}{230}\right)\) |
\(\chi_{3525}(821,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{88}{115}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{149}{230}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{87}{230}\right)\) | \(e\left(\frac{63}{230}\right)\) | \(e\left(\frac{61}{115}\right)\) | \(e\left(\frac{229}{230}\right)\) | \(e\left(\frac{59}{230}\right)\) |
\(\chi_{3525}(866,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{230}\right)\) | \(e\left(\frac{41}{115}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{123}{230}\right)\) | \(e\left(\frac{38}{115}\right)\) | \(e\left(\frac{149}{230}\right)\) | \(e\left(\frac{211}{230}\right)\) | \(e\left(\frac{82}{115}\right)\) | \(e\left(\frac{223}{230}\right)\) | \(e\left(\frac{183}{230}\right)\) |
\(\chi_{3525}(881,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{230}\right)\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{101}{230}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{113}{230}\right)\) | \(e\left(\frac{177}{230}\right)\) | \(e\left(\frac{29}{115}\right)\) | \(e\left(\frac{41}{230}\right)\) | \(e\left(\frac{111}{230}\right)\) |
\(\chi_{3525}(971,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{230}\right)\) | \(e\left(\frac{63}{115}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{189}{230}\right)\) | \(e\left(\frac{64}{115}\right)\) | \(e\left(\frac{27}{230}\right)\) | \(e\left(\frac{83}{230}\right)\) | \(e\left(\frac{11}{115}\right)\) | \(e\left(\frac{79}{230}\right)\) | \(e\left(\frac{169}{230}\right)\) |
\(\chi_{3525}(1016,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{91}{230}\right)\) | \(e\left(\frac{91}{115}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{43}{230}\right)\) | \(e\left(\frac{3}{115}\right)\) | \(e\left(\frac{39}{230}\right)\) | \(e\left(\frac{171}{230}\right)\) | \(e\left(\frac{67}{115}\right)\) | \(e\left(\frac{63}{230}\right)\) | \(e\left(\frac{193}{230}\right)\) |
\(\chi_{3525}(1031,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{230}\right)\) | \(e\left(\frac{52}{115}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{41}{230}\right)\) | \(e\left(\frac{51}{115}\right)\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{147}{230}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{151}{230}\right)\) | \(e\left(\frac{61}{230}\right)\) |
\(\chi_{3525}(1091,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{230}\right)\) | \(e\left(\frac{31}{115}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{93}{230}\right)\) | \(e\left(\frac{68}{115}\right)\) | \(e\left(\frac{79}{230}\right)\) | \(e\left(\frac{81}{230}\right)\) | \(e\left(\frac{62}{115}\right)\) | \(e\left(\frac{163}{230}\right)\) | \(e\left(\frac{43}{230}\right)\) |
\(\chi_{3525}(1121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{143}{230}\right)\) | \(e\left(\frac{28}{115}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{199}{230}\right)\) | \(e\left(\frac{54}{115}\right)\) | \(e\left(\frac{127}{230}\right)\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{56}{115}\right)\) | \(e\left(\frac{99}{230}\right)\) | \(e\left(\frac{139}{230}\right)\) |
\(\chi_{3525}(1166,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{81}{230}\right)\) | \(e\left(\frac{81}{115}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{13}{230}\right)\) | \(e\left(\frac{33}{115}\right)\) | \(e\left(\frac{199}{230}\right)\) | \(e\left(\frac{41}{230}\right)\) | \(e\left(\frac{47}{115}\right)\) | \(e\left(\frac{3}{230}\right)\) | \(e\left(\frac{53}{230}\right)\) |
\(\chi_{3525}(1241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{230}\right)\) | \(e\left(\frac{71}{115}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{213}{230}\right)\) | \(e\left(\frac{63}{115}\right)\) | \(e\left(\frac{129}{230}\right)\) | \(e\left(\frac{141}{230}\right)\) | \(e\left(\frac{27}{115}\right)\) | \(e\left(\frac{173}{230}\right)\) | \(e\left(\frac{143}{230}\right)\) |