LMFDB - Dirichlet character orbit 4225.ct

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4225, base_ring=CyclotomicField(390)) M = H._module chi = DirichletCharacter(H, M([39,5])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(4,4225)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4225$
Conductor:	$4225$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$390$	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:	$\Q(\zeta_{195})$
Fixed field:	Number field defined by a degree 390 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{4225}(4,\cdot)$	$1$	$1$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{113}{390}\right)$	$e\left(\frac{44}{195}\right)$	$e\left(\frac{157}{390}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{359}{390}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{64}{65}\right)$
$\chi_{4225}(69,\cdot)$	$1$	$1$	$e\left(\frac{103}{195}\right)$	$e\left(\frac{77}{390}\right)$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{283}{390}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{77}{195}\right)$	$e\left(\frac{41}{390}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{16}{65}\right)$
$\chi_{4225}(114,\cdot)$	$1$	$1$	$e\left(\frac{101}{195}\right)$	$e\left(\frac{49}{390}\right)$	$e\left(\frac{7}{195}\right)$	$e\left(\frac{251}{390}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{97}{390}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{22}{65}\right)$
$\chi_{4225}(134,\cdot)$	$1$	$1$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{41}{390}\right)$	$e\left(\frac{173}{195}\right)$	$e\left(\frac{19}{390}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{41}{195}\right)$	$e\left(\frac{113}{390}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{33}{65}\right)$
$\chi_{4225}(179,\cdot)$	$1$	$1$	$e\left(\frac{32}{195}\right)$	$e\left(\frac{253}{390}\right)$	$e\left(\frac{64}{195}\right)$	$e\left(\frac{317}{390}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{58}{195}\right)$	$e\left(\frac{79}{390}\right)$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{34}{65}\right)$
$\chi_{4225}(244,\cdot)$	$1$	$1$	$e\left(\frac{158}{195}\right)$	$e\left(\frac{67}{390}\right)$	$e\left(\frac{121}{195}\right)$	$e\left(\frac{383}{390}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{67}{195}\right)$	$e\left(\frac{61}{390}\right)$	$e\left(\frac{103}{130}\right)$	$e\left(\frac{46}{65}\right)$
$\chi_{4225}(264,\cdot)$	$1$	$1$	$e\left(\frac{151}{195}\right)$	$e\left(\frac{359}{390}\right)$	$e\left(\frac{107}{195}\right)$	$e\left(\frac{271}{390}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{21}{65}\right)$	$e\left(\frac{164}{195}\right)$	$e\left(\frac{257}{390}\right)$	$e\left(\frac{61}{130}\right)$	$e\left(\frac{2}{65}\right)$
$\chi_{4225}(309,\cdot)$	$1$	$1$	$e\left(\frac{89}{195}\right)$	$e\left(\frac{271}{390}\right)$	$e\left(\frac{178}{195}\right)$	$e\left(\frac{59}{390}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{76}{195}\right)$	$e\left(\frac{43}{390}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{58}{65}\right)$
$\chi_{4225}(329,\cdot)$	$1$	$1$	$e\left(\frac{37}{195}\right)$	$e\left(\frac{323}{390}\right)$	$e\left(\frac{74}{195}\right)$	$e\left(\frac{7}{390}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{128}{195}\right)$	$e\left(\frac{329}{390}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{19}{65}\right)$
$\chi_{4225}(394,\cdot)$	$1$	$1$	$e\left(\frac{118}{195}\right)$	$e\left(\frac{287}{390}\right)$	$e\left(\frac{41}{195}\right)$	$e\left(\frac{133}{390}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{92}{195}\right)$	$e\left(\frac{11}{390}\right)$	$e\left(\frac{123}{130}\right)$	$e\left(\frac{36}{65}\right)$
$\chi_{4225}(439,\cdot)$	$1$	$1$	$e\left(\frac{146}{195}\right)$	$e\left(\frac{289}{390}\right)$	$e\left(\frac{97}{195}\right)$	$e\left(\frac{191}{390}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{94}{195}\right)$	$e\left(\frac{7}{390}\right)$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{17}{65}\right)$
$\chi_{4225}(459,\cdot)$	$1$	$1$	$e\left(\frac{4}{195}\right)$	$e\left(\frac{251}{390}\right)$	$e\left(\frac{8}{195}\right)$	$e\left(\frac{259}{390}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{56}{195}\right)$	$e\left(\frac{83}{390}\right)$	$e\left(\frac{89}{130}\right)$	$e\left(\frac{53}{65}\right)$
$\chi_{4225}(504,\cdot)$	$1$	$1$	$e\left(\frac{77}{195}\right)$	$e\left(\frac{103}{390}\right)$	$e\left(\frac{154}{195}\right)$	$e\left(\frac{257}{390}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{12}{65}\right)$	$e\left(\frac{103}{195}\right)$	$e\left(\frac{379}{390}\right)$	$e\left(\frac{7}{130}\right)$	$e\left(\frac{29}{65}\right)$
$\chi_{4225}(569,\cdot)$	$1$	$1$	$e\left(\frac{8}{195}\right)$	$e\left(\frac{307}{390}\right)$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{323}{390}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{112}{195}\right)$	$e\left(\frac{361}{390}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{41}{65}\right)$
$\chi_{4225}(589,\cdot)$	$1$	$1$	$e\left(\frac{166}{195}\right)$	$e\left(\frac{179}{390}\right)$	$e\left(\frac{137}{195}\right)$	$e\left(\frac{121}{390}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{179}{195}\right)$	$e\left(\frac{227}{390}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{22}{65}\right)$
$\chi_{4225}(634,\cdot)$	$1$	$1$	$e\left(\frac{134}{195}\right)$	$e\left(\frac{121}{390}\right)$	$e\left(\frac{73}{195}\right)$	$e\left(\frac{389}{390}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{121}{195}\right)$	$e\left(\frac{343}{390}\right)$	$e\left(\frac{89}{130}\right)$	$e\left(\frac{53}{65}\right)$
$\chi_{4225}(719,\cdot)$	$1$	$1$	$e\left(\frac{133}{195}\right)$	$e\left(\frac{107}{390}\right)$	$e\left(\frac{71}{195}\right)$	$e\left(\frac{373}{390}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{3}{65}\right)$	$e\left(\frac{107}{195}\right)$	$e\left(\frac{371}{390}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{56}{65}\right)$
$\chi_{4225}(764,\cdot)$	$1$	$1$	$e\left(\frac{191}{195}\right)$	$e\left(\frac{139}{390}\right)$	$e\left(\frac{187}{195}\right)$	$e\left(\frac{131}{390}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{139}{195}\right)$	$e\left(\frac{307}{390}\right)$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{12}{65}\right)$
$\chi_{4225}(784,\cdot)$	$1$	$1$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{71}{390}\right)$	$e\left(\frac{38}{195}\right)$	$e\left(\frac{109}{390}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{71}{195}\right)$	$e\left(\frac{53}{390}\right)$	$e\left(\frac{49}{130}\right)$	$e\left(\frac{8}{65}\right)$
$\chi_{4225}(829,\cdot)$	$1$	$1$	$e\left(\frac{122}{195}\right)$	$e\left(\frac{343}{390}\right)$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{197}{390}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{148}{195}\right)$	$e\left(\frac{289}{390}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{24}{65}\right)$
$\chi_{4225}(894,\cdot)$	$1$	$1$	$e\left(\frac{53}{195}\right)$	$e\left(\frac{157}{390}\right)$	$e\left(\frac{106}{195}\right)$	$e\left(\frac{263}{390}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{157}{195}\right)$	$e\left(\frac{271}{390}\right)$	$e\left(\frac{123}{130}\right)$	$e\left(\frac{36}{65}\right)$
$\chi_{4225}(914,\cdot)$	$1$	$1$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{389}{390}\right)$	$e\left(\frac{167}{195}\right)$	$e\left(\frac{361}{390}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{194}{195}\right)$	$e\left(\frac{197}{390}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{42}{65}\right)$
$\chi_{4225}(959,\cdot)$	$1$	$1$	$e\left(\frac{179}{195}\right)$	$e\left(\frac{361}{390}\right)$	$e\left(\frac{163}{195}\right)$	$e\left(\frac{329}{390}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{166}{195}\right)$	$e\left(\frac{253}{390}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{48}{65}\right)$
$\chi_{4225}(979,\cdot)$	$1$	$1$	$e\left(\frac{67}{195}\right)$	$e\left(\frac{353}{390}\right)$	$e\left(\frac{134}{195}\right)$	$e\left(\frac{97}{390}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{158}{195}\right)$	$e\left(\frac{269}{390}\right)$	$e\left(\frac{77}{130}\right)$	$e\left(\frac{59}{65}\right)$
$\chi_{4225}(1044,\cdot)$	$1$	$1$	$e\left(\frac{148}{195}\right)$	$e\left(\frac{317}{390}\right)$	$e\left(\frac{101}{195}\right)$	$e\left(\frac{223}{390}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{18}{65}\right)$	$e\left(\frac{122}{195}\right)$	$e\left(\frac{341}{390}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{11}{65}\right)$
$\chi_{4225}(1089,\cdot)$	$1$	$1$	$e\left(\frac{41}{195}\right)$	$e\left(\frac{379}{390}\right)$	$e\left(\frac{82}{195}\right)$	$e\left(\frac{71}{390}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{217}{390}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{7}{65}\right)$
$\chi_{4225}(1109,\cdot)$	$1$	$1$	$e\left(\frac{34}{195}\right)$	$e\left(\frac{281}{390}\right)$	$e\left(\frac{68}{195}\right)$	$e\left(\frac{349}{390}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{34}{65}\right)$	$e\left(\frac{86}{195}\right)$	$e\left(\frac{23}{390}\right)$	$e\left(\frac{9}{130}\right)$	$e\left(\frac{28}{65}\right)$
$\chi_{4225}(1154,\cdot)$	$1$	$1$	$e\left(\frac{167}{195}\right)$	$e\left(\frac{193}{390}\right)$	$e\left(\frac{139}{195}\right)$	$e\left(\frac{137}{390}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{193}{195}\right)$	$e\left(\frac{199}{390}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{19}{65}\right)$
$\chi_{4225}(1219,\cdot)$	$1$	$1$	$e\left(\frac{98}{195}\right)$	$e\left(\frac{7}{390}\right)$	$e\left(\frac{1}{195}\right)$	$e\left(\frac{203}{390}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{7}{195}\right)$	$e\left(\frac{181}{390}\right)$	$e\left(\frac{3}{130}\right)$	$e\left(\frac{31}{65}\right)$
$\chi_{4225}(1239,\cdot)$	$1$	$1$	$e\left(\frac{1}{195}\right)$	$e\left(\frac{209}{390}\right)$	$e\left(\frac{2}{195}\right)$	$e\left(\frac{211}{390}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{14}{195}\right)$	$e\left(\frac{167}{390}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{62}{65}\right)$
$\chi_{4225}(1284,\cdot)$	$1$	$1$	$e\left(\frac{29}{195}\right)$	$e\left(\frac{211}{390}\right)$	$e\left(\frac{58}{195}\right)$	$e\left(\frac{269}{390}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{163}{390}\right)$	$e\left(\frac{109}{130}\right)$	$e\left(\frac{43}{65}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{4225}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{113}{390}\right)\)	\(e\left(\frac{44}{195}\right)\)	\(e\left(\frac{157}{390}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{359}{390}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{64}{65}\right)\)
\(\chi_{4225}(69,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{195}\right)\)	\(e\left(\frac{77}{390}\right)\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{283}{390}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{77}{195}\right)\)	\(e\left(\frac{41}{390}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{16}{65}\right)\)
\(\chi_{4225}(114,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{195}\right)\)	\(e\left(\frac{49}{390}\right)\)	\(e\left(\frac{7}{195}\right)\)	\(e\left(\frac{251}{390}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{97}{390}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{22}{65}\right)\)
\(\chi_{4225}(134,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{41}{390}\right)\)	\(e\left(\frac{173}{195}\right)\)	\(e\left(\frac{19}{390}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{41}{195}\right)\)	\(e\left(\frac{113}{390}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{33}{65}\right)\)
\(\chi_{4225}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{195}\right)\)	\(e\left(\frac{253}{390}\right)\)	\(e\left(\frac{64}{195}\right)\)	\(e\left(\frac{317}{390}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{58}{195}\right)\)	\(e\left(\frac{79}{390}\right)\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{34}{65}\right)\)
\(\chi_{4225}(244,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{158}{195}\right)\)	\(e\left(\frac{67}{390}\right)\)	\(e\left(\frac{121}{195}\right)\)	\(e\left(\frac{383}{390}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{67}{195}\right)\)	\(e\left(\frac{61}{390}\right)\)	\(e\left(\frac{103}{130}\right)\)	\(e\left(\frac{46}{65}\right)\)
\(\chi_{4225}(264,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{195}\right)\)	\(e\left(\frac{359}{390}\right)\)	\(e\left(\frac{107}{195}\right)\)	\(e\left(\frac{271}{390}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{21}{65}\right)\)	\(e\left(\frac{164}{195}\right)\)	\(e\left(\frac{257}{390}\right)\)	\(e\left(\frac{61}{130}\right)\)	\(e\left(\frac{2}{65}\right)\)
\(\chi_{4225}(309,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{195}\right)\)	\(e\left(\frac{271}{390}\right)\)	\(e\left(\frac{178}{195}\right)\)	\(e\left(\frac{59}{390}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{76}{195}\right)\)	\(e\left(\frac{43}{390}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{58}{65}\right)\)
\(\chi_{4225}(329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{195}\right)\)	\(e\left(\frac{323}{390}\right)\)	\(e\left(\frac{74}{195}\right)\)	\(e\left(\frac{7}{390}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{128}{195}\right)\)	\(e\left(\frac{329}{390}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{19}{65}\right)\)
\(\chi_{4225}(394,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{287}{390}\right)\)	\(e\left(\frac{41}{195}\right)\)	\(e\left(\frac{133}{390}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{92}{195}\right)\)	\(e\left(\frac{11}{390}\right)\)	\(e\left(\frac{123}{130}\right)\)	\(e\left(\frac{36}{65}\right)\)
\(\chi_{4225}(439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{146}{195}\right)\)	\(e\left(\frac{289}{390}\right)\)	\(e\left(\frac{97}{195}\right)\)	\(e\left(\frac{191}{390}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{94}{195}\right)\)	\(e\left(\frac{7}{390}\right)\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{17}{65}\right)\)
\(\chi_{4225}(459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{195}\right)\)	\(e\left(\frac{251}{390}\right)\)	\(e\left(\frac{8}{195}\right)\)	\(e\left(\frac{259}{390}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{56}{195}\right)\)	\(e\left(\frac{83}{390}\right)\)	\(e\left(\frac{89}{130}\right)\)	\(e\left(\frac{53}{65}\right)\)
\(\chi_{4225}(504,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{195}\right)\)	\(e\left(\frac{103}{390}\right)\)	\(e\left(\frac{154}{195}\right)\)	\(e\left(\frac{257}{390}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{12}{65}\right)\)	\(e\left(\frac{103}{195}\right)\)	\(e\left(\frac{379}{390}\right)\)	\(e\left(\frac{7}{130}\right)\)	\(e\left(\frac{29}{65}\right)\)
\(\chi_{4225}(569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{195}\right)\)	\(e\left(\frac{307}{390}\right)\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{323}{390}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{112}{195}\right)\)	\(e\left(\frac{361}{390}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{41}{65}\right)\)
\(\chi_{4225}(589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{166}{195}\right)\)	\(e\left(\frac{179}{390}\right)\)	\(e\left(\frac{137}{195}\right)\)	\(e\left(\frac{121}{390}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{179}{195}\right)\)	\(e\left(\frac{227}{390}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{22}{65}\right)\)
\(\chi_{4225}(634,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{134}{195}\right)\)	\(e\left(\frac{121}{390}\right)\)	\(e\left(\frac{73}{195}\right)\)	\(e\left(\frac{389}{390}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{121}{195}\right)\)	\(e\left(\frac{343}{390}\right)\)	\(e\left(\frac{89}{130}\right)\)	\(e\left(\frac{53}{65}\right)\)
\(\chi_{4225}(719,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{195}\right)\)	\(e\left(\frac{107}{390}\right)\)	\(e\left(\frac{71}{195}\right)\)	\(e\left(\frac{373}{390}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{3}{65}\right)\)	\(e\left(\frac{107}{195}\right)\)	\(e\left(\frac{371}{390}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{56}{65}\right)\)
\(\chi_{4225}(764,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{195}\right)\)	\(e\left(\frac{139}{390}\right)\)	\(e\left(\frac{187}{195}\right)\)	\(e\left(\frac{131}{390}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{139}{195}\right)\)	\(e\left(\frac{307}{390}\right)\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{12}{65}\right)\)
\(\chi_{4225}(784,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{71}{390}\right)\)	\(e\left(\frac{38}{195}\right)\)	\(e\left(\frac{109}{390}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{71}{195}\right)\)	\(e\left(\frac{53}{390}\right)\)	\(e\left(\frac{49}{130}\right)\)	\(e\left(\frac{8}{65}\right)\)
\(\chi_{4225}(829,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{122}{195}\right)\)	\(e\left(\frac{343}{390}\right)\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{197}{390}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{148}{195}\right)\)	\(e\left(\frac{289}{390}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{24}{65}\right)\)
\(\chi_{4225}(894,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{195}\right)\)	\(e\left(\frac{157}{390}\right)\)	\(e\left(\frac{106}{195}\right)\)	\(e\left(\frac{263}{390}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{157}{195}\right)\)	\(e\left(\frac{271}{390}\right)\)	\(e\left(\frac{123}{130}\right)\)	\(e\left(\frac{36}{65}\right)\)
\(\chi_{4225}(914,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{389}{390}\right)\)	\(e\left(\frac{167}{195}\right)\)	\(e\left(\frac{361}{390}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{194}{195}\right)\)	\(e\left(\frac{197}{390}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{42}{65}\right)\)
\(\chi_{4225}(959,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{195}\right)\)	\(e\left(\frac{361}{390}\right)\)	\(e\left(\frac{163}{195}\right)\)	\(e\left(\frac{329}{390}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{166}{195}\right)\)	\(e\left(\frac{253}{390}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{48}{65}\right)\)
\(\chi_{4225}(979,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{195}\right)\)	\(e\left(\frac{353}{390}\right)\)	\(e\left(\frac{134}{195}\right)\)	\(e\left(\frac{97}{390}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{158}{195}\right)\)	\(e\left(\frac{269}{390}\right)\)	\(e\left(\frac{77}{130}\right)\)	\(e\left(\frac{59}{65}\right)\)
\(\chi_{4225}(1044,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{195}\right)\)	\(e\left(\frac{317}{390}\right)\)	\(e\left(\frac{101}{195}\right)\)	\(e\left(\frac{223}{390}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{18}{65}\right)\)	\(e\left(\frac{122}{195}\right)\)	\(e\left(\frac{341}{390}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{11}{65}\right)\)
\(\chi_{4225}(1089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{195}\right)\)	\(e\left(\frac{379}{390}\right)\)	\(e\left(\frac{82}{195}\right)\)	\(e\left(\frac{71}{390}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{217}{390}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{7}{65}\right)\)
\(\chi_{4225}(1109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{195}\right)\)	\(e\left(\frac{281}{390}\right)\)	\(e\left(\frac{68}{195}\right)\)	\(e\left(\frac{349}{390}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{34}{65}\right)\)	\(e\left(\frac{86}{195}\right)\)	\(e\left(\frac{23}{390}\right)\)	\(e\left(\frac{9}{130}\right)\)	\(e\left(\frac{28}{65}\right)\)
\(\chi_{4225}(1154,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{195}\right)\)	\(e\left(\frac{193}{390}\right)\)	\(e\left(\frac{139}{195}\right)\)	\(e\left(\frac{137}{390}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{193}{195}\right)\)	\(e\left(\frac{199}{390}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{19}{65}\right)\)
\(\chi_{4225}(1219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{98}{195}\right)\)	\(e\left(\frac{7}{390}\right)\)	\(e\left(\frac{1}{195}\right)\)	\(e\left(\frac{203}{390}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{7}{195}\right)\)	\(e\left(\frac{181}{390}\right)\)	\(e\left(\frac{3}{130}\right)\)	\(e\left(\frac{31}{65}\right)\)
\(\chi_{4225}(1239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{195}\right)\)	\(e\left(\frac{209}{390}\right)\)	\(e\left(\frac{2}{195}\right)\)	\(e\left(\frac{211}{390}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{14}{195}\right)\)	\(e\left(\frac{167}{390}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{62}{65}\right)\)
\(\chi_{4225}(1284,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{195}\right)\)	\(e\left(\frac{211}{390}\right)\)	\(e\left(\frac{58}{195}\right)\)	\(e\left(\frac{269}{390}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{163}{390}\right)\)	\(e\left(\frac{109}{130}\right)\)	\(e\left(\frac{43}{65}\right)\)

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First 31 of 96 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	4225.ct
Modulus	$4225$
Conductor	$4225$
Order	$390$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(4225\)
Conductor:	\(4225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(390\)	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)