from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(460))
M = H._module
chi = DirichletCharacter(H, M([230,253,50]))
chi.galois_orbit()
[g,chi] = znchar(Mod(23,3525))
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: | 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3525}(23,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{460}\right)\) | \(e\left(\frac{3}{230}\right)\) | \(e\left(\frac{21}{92}\right)\) | \(e\left(\frac{9}{460}\right)\) | \(e\left(\frac{7}{115}\right)\) | \(e\left(\frac{297}{460}\right)\) | \(e\left(\frac{27}{115}\right)\) | \(e\left(\frac{3}{115}\right)\) | \(e\left(\frac{179}{460}\right)\) | \(e\left(\frac{91}{115}\right)\) |
\(\chi_{3525}(38,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{460}\right)\) | \(e\left(\frac{47}{230}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{141}{460}\right)\) | \(e\left(\frac{33}{115}\right)\) | \(e\left(\frac{53}{460}\right)\) | \(e\left(\frac{78}{115}\right)\) | \(e\left(\frac{47}{115}\right)\) | \(e\left(\frac{351}{460}\right)\) | \(e\left(\frac{84}{115}\right)\) |
\(\chi_{3525}(62,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{77}{460}\right)\) | \(e\left(\frac{77}{230}\right)\) | \(e\left(\frac{79}{92}\right)\) | \(e\left(\frac{231}{460}\right)\) | \(e\left(\frac{103}{115}\right)\) | \(e\left(\frac{263}{460}\right)\) | \(e\left(\frac{3}{115}\right)\) | \(e\left(\frac{77}{115}\right)\) | \(e\left(\frac{301}{460}\right)\) | \(e\left(\frac{74}{115}\right)\) |
\(\chi_{3525}(77,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{373}{460}\right)\) | \(e\left(\frac{143}{230}\right)\) | \(e\left(\frac{35}{92}\right)\) | \(e\left(\frac{199}{460}\right)\) | \(e\left(\frac{27}{115}\right)\) | \(e\left(\frac{127}{460}\right)\) | \(e\left(\frac{22}{115}\right)\) | \(e\left(\frac{28}{115}\right)\) | \(e\left(\frac{329}{460}\right)\) | \(e\left(\frac{6}{115}\right)\) |
\(\chi_{3525}(92,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{89}{460}\right)\) | \(e\left(\frac{89}{230}\right)\) | \(e\left(\frac{71}{92}\right)\) | \(e\left(\frac{267}{460}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{71}{460}\right)\) | \(e\left(\frac{111}{115}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{97}{460}\right)\) | \(e\left(\frac{93}{115}\right)\) |
\(\chi_{3525}(113,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{27}{460}\right)\) | \(e\left(\frac{27}{230}\right)\) | \(e\left(\frac{5}{92}\right)\) | \(e\left(\frac{81}{460}\right)\) | \(e\left(\frac{63}{115}\right)\) | \(e\left(\frac{373}{460}\right)\) | \(e\left(\frac{13}{115}\right)\) | \(e\left(\frac{27}{115}\right)\) | \(e\left(\frac{231}{460}\right)\) | \(e\left(\frac{14}{115}\right)\) |
\(\chi_{3525}(137,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{460}\right)\) | \(e\left(\frac{17}{230}\right)\) | \(e\left(\frac{27}{92}\right)\) | \(e\left(\frac{51}{460}\right)\) | \(e\left(\frac{78}{115}\right)\) | \(e\left(\frac{303}{460}\right)\) | \(e\left(\frac{38}{115}\right)\) | \(e\left(\frac{17}{115}\right)\) | \(e\left(\frac{401}{460}\right)\) | \(e\left(\frac{94}{115}\right)\) |
\(\chi_{3525}(152,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{133}{460}\right)\) | \(e\left(\frac{133}{230}\right)\) | \(e\left(\frac{11}{92}\right)\) | \(e\left(\frac{399}{460}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{287}{460}\right)\) | \(e\left(\frac{47}{115}\right)\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{269}{460}\right)\) | \(e\left(\frac{86}{115}\right)\) |
\(\chi_{3525}(167,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{229}{460}\right)\) | \(e\left(\frac{229}{230}\right)\) | \(e\left(\frac{39}{92}\right)\) | \(e\left(\frac{227}{460}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{131}{460}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{114}{115}\right)\) | \(e\left(\frac{17}{460}\right)\) | \(e\left(\frac{8}{115}\right)\) |
\(\chi_{3525}(203,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{460}\right)\) | \(e\left(\frac{31}{230}\right)\) | \(e\left(\frac{33}{92}\right)\) | \(e\left(\frac{93}{460}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{309}{460}\right)\) | \(e\left(\frac{49}{115}\right)\) | \(e\left(\frac{31}{115}\right)\) | \(e\left(\frac{163}{460}\right)\) | \(e\left(\frac{97}{115}\right)\) |
\(\chi_{3525}(227,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{313}{460}\right)\) | \(e\left(\frac{83}{230}\right)\) | \(e\left(\frac{75}{92}\right)\) | \(e\left(\frac{19}{460}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{167}{460}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{83}{115}\right)\) | \(e\left(\frac{429}{460}\right)\) | \(e\left(\frac{26}{115}\right)\) |
\(\chi_{3525}(233,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{319}{460}\right)\) | \(e\left(\frac{89}{230}\right)\) | \(e\left(\frac{25}{92}\right)\) | \(e\left(\frac{37}{460}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{301}{460}\right)\) | \(e\left(\frac{111}{115}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{327}{460}\right)\) | \(e\left(\frac{93}{115}\right)\) |
\(\chi_{3525}(248,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{163}{460}\right)\) | \(e\left(\frac{163}{230}\right)\) | \(e\left(\frac{37}{92}\right)\) | \(e\left(\frac{29}{460}\right)\) | \(e\left(\frac{112}{115}\right)\) | \(e\left(\frac{37}{460}\right)\) | \(e\left(\frac{87}{115}\right)\) | \(e\left(\frac{48}{115}\right)\) | \(e\left(\frac{219}{460}\right)\) | \(e\left(\frac{76}{115}\right)\) |
\(\chi_{3525}(278,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{431}{460}\right)\) | \(e\left(\frac{201}{230}\right)\) | \(e\left(\frac{73}{92}\right)\) | \(e\left(\frac{373}{460}\right)\) | \(e\left(\frac{9}{115}\right)\) | \(e\left(\frac{349}{460}\right)\) | \(e\left(\frac{84}{115}\right)\) | \(e\left(\frac{86}{115}\right)\) | \(e\left(\frac{263}{460}\right)\) | \(e\left(\frac{2}{115}\right)\) |
\(\chi_{3525}(287,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{157}{460}\right)\) | \(e\left(\frac{157}{230}\right)\) | \(e\left(\frac{87}{92}\right)\) | \(e\left(\frac{11}{460}\right)\) | \(e\left(\frac{98}{115}\right)\) | \(e\left(\frac{363}{460}\right)\) | \(e\left(\frac{33}{115}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{321}{460}\right)\) | \(e\left(\frac{9}{115}\right)\) |
\(\chi_{3525}(302,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{460}\right)\) | \(e\left(\frac{13}{230}\right)\) | \(e\left(\frac{91}{92}\right)\) | \(e\left(\frac{39}{460}\right)\) | \(e\left(\frac{107}{115}\right)\) | \(e\left(\frac{367}{460}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{13}{115}\right)\) | \(e\left(\frac{9}{460}\right)\) | \(e\left(\frac{11}{115}\right)\) |
\(\chi_{3525}(308,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{459}{460}\right)\) | \(e\left(\frac{229}{230}\right)\) | \(e\left(\frac{85}{92}\right)\) | \(e\left(\frac{457}{460}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{361}{460}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{114}{115}\right)\) | \(e\left(\frac{247}{460}\right)\) | \(e\left(\frac{8}{115}\right)\) |
\(\chi_{3525}(317,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{460}\right)\) | \(e\left(\frac{29}{230}\right)\) | \(e\left(\frac{19}{92}\right)\) | \(e\left(\frac{87}{460}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{111}{460}\right)\) | \(e\left(\frac{31}{115}\right)\) | \(e\left(\frac{29}{115}\right)\) | \(e\left(\frac{197}{460}\right)\) | \(e\left(\frac{113}{115}\right)\) |
\(\chi_{3525}(323,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{423}{460}\right)\) | \(e\left(\frac{193}{230}\right)\) | \(e\left(\frac{17}{92}\right)\) | \(e\left(\frac{349}{460}\right)\) | \(e\left(\frac{67}{115}\right)\) | \(e\left(\frac{17}{460}\right)\) | \(e\left(\frac{12}{115}\right)\) | \(e\left(\frac{78}{115}\right)\) | \(e\left(\frac{399}{460}\right)\) | \(e\left(\frac{66}{115}\right)\) |
\(\chi_{3525}(362,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{237}{460}\right)\) | \(e\left(\frac{7}{230}\right)\) | \(e\left(\frac{3}{92}\right)\) | \(e\left(\frac{251}{460}\right)\) | \(e\left(\frac{93}{115}\right)\) | \(e\left(\frac{3}{460}\right)\) | \(e\left(\frac{63}{115}\right)\) | \(e\left(\frac{7}{115}\right)\) | \(e\left(\frac{341}{460}\right)\) | \(e\left(\frac{59}{115}\right)\) |
\(\chi_{3525}(398,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{383}{460}\right)\) | \(e\left(\frac{153}{230}\right)\) | \(e\left(\frac{13}{92}\right)\) | \(e\left(\frac{229}{460}\right)\) | \(e\left(\frac{12}{115}\right)\) | \(e\left(\frac{197}{460}\right)\) | \(e\left(\frac{112}{115}\right)\) | \(e\left(\frac{38}{115}\right)\) | \(e\left(\frac{159}{460}\right)\) | \(e\left(\frac{41}{115}\right)\) |
\(\chi_{3525}(428,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{111}{460}\right)\) | \(e\left(\frac{111}{230}\right)\) | \(e\left(\frac{41}{92}\right)\) | \(e\left(\frac{333}{460}\right)\) | \(e\left(\frac{29}{115}\right)\) | \(e\left(\frac{409}{460}\right)\) | \(e\left(\frac{79}{115}\right)\) | \(e\left(\frac{111}{115}\right)\) | \(e\left(\frac{183}{460}\right)\) | \(e\left(\frac{32}{115}\right)\) |
\(\chi_{3525}(452,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{113}{460}\right)\) | \(e\left(\frac{113}{230}\right)\) | \(e\left(\frac{55}{92}\right)\) | \(e\left(\frac{339}{460}\right)\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{147}{460}\right)\) | \(e\left(\frac{97}{115}\right)\) | \(e\left(\frac{113}{115}\right)\) | \(e\left(\frac{149}{460}\right)\) | \(e\left(\frac{16}{115}\right)\) |
\(\chi_{3525}(458,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{259}{460}\right)\) | \(e\left(\frac{29}{230}\right)\) | \(e\left(\frac{65}{92}\right)\) | \(e\left(\frac{317}{460}\right)\) | \(e\left(\frac{106}{115}\right)\) | \(e\left(\frac{341}{460}\right)\) | \(e\left(\frac{31}{115}\right)\) | \(e\left(\frac{29}{115}\right)\) | \(e\left(\frac{427}{460}\right)\) | \(e\left(\frac{113}{115}\right)\) |
\(\chi_{3525}(467,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{449}{460}\right)\) | \(e\left(\frac{219}{230}\right)\) | \(e\left(\frac{15}{92}\right)\) | \(e\left(\frac{427}{460}\right)\) | \(e\left(\frac{51}{115}\right)\) | \(e\left(\frac{291}{460}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{417}{460}\right)\) | \(e\left(\frac{88}{115}\right)\) |
\(\chi_{3525}(503,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{191}{460}\right)\) | \(e\left(\frac{191}{230}\right)\) | \(e\left(\frac{49}{92}\right)\) | \(e\left(\frac{113}{460}\right)\) | \(e\left(\frac{24}{115}\right)\) | \(e\left(\frac{49}{460}\right)\) | \(e\left(\frac{109}{115}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{203}{460}\right)\) | \(e\left(\frac{82}{115}\right)\) |
\(\chi_{3525}(527,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{453}{460}\right)\) | \(e\left(\frac{223}{230}\right)\) | \(e\left(\frac{43}{92}\right)\) | \(e\left(\frac{439}{460}\right)\) | \(e\left(\frac{22}{115}\right)\) | \(e\left(\frac{227}{460}\right)\) | \(e\left(\frac{52}{115}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{349}{460}\right)\) | \(e\left(\frac{56}{115}\right)\) |
\(\chi_{3525}(548,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{103}{460}\right)\) | \(e\left(\frac{103}{230}\right)\) | \(e\left(\frac{77}{92}\right)\) | \(e\left(\frac{309}{460}\right)\) | \(e\left(\frac{87}{115}\right)\) | \(e\left(\frac{77}{460}\right)\) | \(e\left(\frac{7}{115}\right)\) | \(e\left(\frac{103}{115}\right)\) | \(e\left(\frac{319}{460}\right)\) | \(e\left(\frac{96}{115}\right)\) |
\(\chi_{3525}(587,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{417}{460}\right)\) | \(e\left(\frac{187}{230}\right)\) | \(e\left(\frac{67}{92}\right)\) | \(e\left(\frac{331}{460}\right)\) | \(e\left(\frac{53}{115}\right)\) | \(e\left(\frac{343}{460}\right)\) | \(e\left(\frac{73}{115}\right)\) | \(e\left(\frac{72}{115}\right)\) | \(e\left(\frac{41}{460}\right)\) | \(e\left(\frac{114}{115}\right)\) |
\(\chi_{3525}(602,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{93}{460}\right)\) | \(e\left(\frac{93}{230}\right)\) | \(e\left(\frac{7}{92}\right)\) | \(e\left(\frac{279}{460}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{7}{460}\right)\) | \(e\left(\frac{32}{115}\right)\) | \(e\left(\frac{93}{115}\right)\) | \(e\left(\frac{29}{460}\right)\) | \(e\left(\frac{61}{115}\right)\) |
\(\chi_{3525}(608,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{219}{460}\right)\) | \(e\left(\frac{219}{230}\right)\) | \(e\left(\frac{61}{92}\right)\) | \(e\left(\frac{197}{460}\right)\) | \(e\left(\frac{51}{115}\right)\) | \(e\left(\frac{61}{460}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{187}{460}\right)\) | \(e\left(\frac{88}{115}\right)\) |