LMFDB - Dirichlet character orbit 4225.cm

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4225, base_ring=CyclotomicField(390)) M = H._module chi = DirichletCharacter(H, M([78,10])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(16,4225)) 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:	$195$	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 195 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{4225}(16,\cdot)$	$1$	$1$	$e\left(\frac{44}{195}\right)$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{88}{195}\right)$	$e\left(\frac{157}{195}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{31}{195}\right)$	$e\left(\frac{164}{195}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{63}{65}\right)$
$\chi_{4225}(61,\cdot)$	$1$	$1$	$e\left(\frac{136}{195}\right)$	$e\left(\frac{172}{195}\right)$	$e\left(\frac{77}{195}\right)$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{149}{195}\right)$	$e\left(\frac{46}{195}\right)$	$e\left(\frac{18}{65}\right)$	$e\left(\frac{47}{65}\right)$
$\chi_{4225}(81,\cdot)$	$1$	$1$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{31}{195}\right)$	$e\left(\frac{124}{195}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{173}{195}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{51}{65}\right)$
$\chi_{4225}(211,\cdot)$	$1$	$1$	$e\left(\frac{56}{195}\right)$	$e\left(\frac{2}{195}\right)$	$e\left(\frac{112}{195}\right)$	$e\left(\frac{58}{195}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{4}{195}\right)$	$e\left(\frac{191}{195}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{27}{65}\right)$
$\chi_{4225}(256,\cdot)$	$1$	$1$	$e\left(\frac{88}{195}\right)$	$e\left(\frac{31}{195}\right)$	$e\left(\frac{176}{195}\right)$	$e\left(\frac{119}{195}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{62}{195}\right)$	$e\left(\frac{133}{195}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{61}{65}\right)$
$\chi_{4225}(321,\cdot)$	$1$	$1$	$e\left(\frac{7}{195}\right)$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{14}{195}\right)$	$e\left(\frac{56}{195}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{98}{195}\right)$	$e\left(\frac{97}{195}\right)$	$e\left(\frac{21}{65}\right)$	$e\left(\frac{44}{65}\right)$
$\chi_{4225}(341,\cdot)$	$1$	$1$	$e\left(\frac{194}{195}\right)$	$e\left(\frac{188}{195}\right)$	$e\left(\frac{193}{195}\right)$	$e\left(\frac{187}{195}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{14}{195}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{3}{65}\right)$
$\chi_{4225}(386,\cdot)$	$1$	$1$	$e\left(\frac{121}{195}\right)$	$e\left(\frac{67}{195}\right)$	$e\left(\frac{47}{195}\right)$	$e\left(\frac{188}{195}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{134}{195}\right)$	$e\left(\frac{61}{195}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{27}{65}\right)$
$\chi_{4225}(406,\cdot)$	$1$	$1$	$e\left(\frac{68}{195}\right)$	$e\left(\frac{86}{195}\right)$	$e\left(\frac{136}{195}\right)$	$e\left(\frac{154}{195}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{3}{65}\right)$	$e\left(\frac{172}{195}\right)$	$e\left(\frac{23}{195}\right)$	$e\left(\frac{9}{65}\right)$	$e\left(\frac{56}{65}\right)$
$\chi_{4225}(471,\cdot)$	$1$	$1$	$e\left(\frac{137}{195}\right)$	$e\left(\frac{179}{195}\right)$	$e\left(\frac{79}{195}\right)$	$e\left(\frac{121}{195}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{163}{195}\right)$	$e\left(\frac{32}{195}\right)$	$e\left(\frac{21}{65}\right)$	$e\left(\frac{44}{65}\right)$
$\chi_{4225}(516,\cdot)$	$1$	$1$	$e\left(\frac{154}{195}\right)$	$e\left(\frac{103}{195}\right)$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{62}{195}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{58}{65}\right)$
$\chi_{4225}(536,\cdot)$	$1$	$1$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{77}{195}\right)$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{88}{195}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{154}{195}\right)$	$e\left(\frac{41}{195}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{32}{65}\right)$
$\chi_{4225}(581,\cdot)$	$1$	$1$	$e\left(\frac{73}{195}\right)$	$e\left(\frac{121}{195}\right)$	$e\left(\frac{146}{195}\right)$	$e\left(\frac{194}{195}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{47}{195}\right)$	$e\left(\frac{148}{195}\right)$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{41}{65}\right)$
$\chi_{4225}(646,\cdot)$	$1$	$1$	$e\left(\frac{187}{195}\right)$	$e\left(\frac{139}{195}\right)$	$e\left(\frac{179}{195}\right)$	$e\left(\frac{131}{195}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{83}{195}\right)$	$e\left(\frac{112}{195}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{24}{65}\right)$
$\chi_{4225}(666,\cdot)$	$1$	$1$	$e\left(\frac{149}{195}\right)$	$e\left(\frac{68}{195}\right)$	$e\left(\frac{103}{195}\right)$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{136}{195}\right)$	$e\left(\frac{59}{195}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{8}{65}\right)$
$\chi_{4225}(711,\cdot)$	$1$	$1$	$e\left(\frac{106}{195}\right)$	$e\left(\frac{157}{195}\right)$	$e\left(\frac{17}{195}\right)$	$e\left(\frac{68}{195}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{119}{195}\right)$	$e\left(\frac{76}{195}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{7}{65}\right)$
$\chi_{4225}(731,\cdot)$	$1$	$1$	$e\left(\frac{23}{195}\right)$	$e\left(\frac{161}{195}\right)$	$e\left(\frac{46}{195}\right)$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{127}{195}\right)$	$e\left(\frac{68}{195}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{61}{65}\right)$
$\chi_{4225}(796,\cdot)$	$1$	$1$	$e\left(\frac{92}{195}\right)$	$e\left(\frac{59}{195}\right)$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{151}{195}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{118}{195}\right)$	$e\left(\frac{77}{195}\right)$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{49}{65}\right)$
$\chi_{4225}(841,\cdot)$	$1$	$1$	$e\left(\frac{139}{195}\right)$	$e\left(\frac{193}{195}\right)$	$e\left(\frac{83}{195}\right)$	$e\left(\frac{137}{195}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{9}{65}\right)$	$e\left(\frac{191}{195}\right)$	$e\left(\frac{4}{195}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{38}{65}\right)$
$\chi_{4225}(861,\cdot)$	$1$	$1$	$e\left(\frac{161}{195}\right)$	$e\left(\frac{152}{195}\right)$	$e\left(\frac{127}{195}\right)$	$e\left(\frac{118}{195}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{109}{195}\right)$	$e\left(\frac{86}{195}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{37}{65}\right)$
$\chi_{4225}(906,\cdot)$	$1$	$1$	$e\left(\frac{58}{195}\right)$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{116}{195}\right)$	$e\left(\frac{74}{195}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{32}{195}\right)$	$e\left(\frac{163}{195}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{21}{65}\right)$
$\chi_{4225}(971,\cdot)$	$1$	$1$	$e\left(\frac{172}{195}\right)$	$e\left(\frac{34}{195}\right)$	$e\left(\frac{149}{195}\right)$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{68}{195}\right)$	$e\left(\frac{127}{195}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{4}{65}\right)$
$\chi_{4225}(1056,\cdot)$	$1$	$1$	$e\left(\frac{173}{195}\right)$	$e\left(\frac{41}{195}\right)$	$e\left(\frac{151}{195}\right)$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{43}{65}\right)$	$e\left(\frac{82}{195}\right)$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{1}{65}\right)$
$\chi_{4225}(1121,\cdot)$	$1$	$1$	$e\left(\frac{47}{195}\right)$	$e\left(\frac{134}{195}\right)$	$e\left(\frac{94}{195}\right)$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{47}{65}\right)$	$e\left(\frac{73}{195}\right)$	$e\left(\frac{122}{195}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{54}{65}\right)$
$\chi_{4225}(1166,\cdot)$	$1$	$1$	$e\left(\frac{124}{195}\right)$	$e\left(\frac{88}{195}\right)$	$e\left(\frac{53}{195}\right)$	$e\left(\frac{17}{195}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{176}{195}\right)$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{47}{65}\right)$	$e\left(\frac{18}{65}\right)$
$\chi_{4225}(1186,\cdot)$	$1$	$1$	$e\left(\frac{116}{195}\right)$	$e\left(\frac{32}{195}\right)$	$e\left(\frac{37}{195}\right)$	$e\left(\frac{148}{195}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{64}{195}\right)$	$e\left(\frac{131}{195}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{42}{65}\right)$
$\chi_{4225}(1231,\cdot)$	$1$	$1$	$e\left(\frac{43}{195}\right)$	$e\left(\frac{106}{195}\right)$	$e\left(\frac{86}{195}\right)$	$e\left(\frac{149}{195}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{43}{65}\right)$	$e\left(\frac{17}{195}\right)$	$e\left(\frac{178}{195}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{1}{65}\right)$
$\chi_{4225}(1296,\cdot)$	$1$	$1$	$e\left(\frac{157}{195}\right)$	$e\left(\frac{124}{195}\right)$	$e\left(\frac{119}{195}\right)$	$e\left(\frac{86}{195}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{53}{195}\right)$	$e\left(\frac{142}{195}\right)$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{49}{65}\right)$
$\chi_{4225}(1316,\cdot)$	$1$	$1$	$e\left(\frac{59}{195}\right)$	$e\left(\frac{23}{195}\right)$	$e\left(\frac{118}{195}\right)$	$e\left(\frac{82}{195}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{46}{195}\right)$	$e\left(\frac{149}{195}\right)$	$e\left(\frac{47}{65}\right)$	$e\left(\frac{18}{65}\right)$
$\chi_{4225}(1361,\cdot)$	$1$	$1$	$e\left(\frac{76}{195}\right)$	$e\left(\frac{142}{195}\right)$	$e\left(\frac{152}{195}\right)$	$e\left(\frac{23}{195}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{89}{195}\right)$	$e\left(\frac{106}{195}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{32}{65}\right)$
$\chi_{4225}(1381,\cdot)$	$1$	$1$	$e\left(\frac{128}{195}\right)$	$e\left(\frac{116}{195}\right)$	$e\left(\frac{61}{195}\right)$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{37}{195}\right)$	$e\left(\frac{158}{195}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{6}{65}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{4225}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{195}\right)\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{88}{195}\right)\)	\(e\left(\frac{157}{195}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{31}{195}\right)\)	\(e\left(\frac{164}{195}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{63}{65}\right)\)
\(\chi_{4225}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{136}{195}\right)\)	\(e\left(\frac{172}{195}\right)\)	\(e\left(\frac{77}{195}\right)\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{149}{195}\right)\)	\(e\left(\frac{46}{195}\right)\)	\(e\left(\frac{18}{65}\right)\)	\(e\left(\frac{47}{65}\right)\)
\(\chi_{4225}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{31}{195}\right)\)	\(e\left(\frac{124}{195}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{173}{195}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{51}{65}\right)\)
\(\chi_{4225}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{195}\right)\)	\(e\left(\frac{2}{195}\right)\)	\(e\left(\frac{112}{195}\right)\)	\(e\left(\frac{58}{195}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{4}{195}\right)\)	\(e\left(\frac{191}{195}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{27}{65}\right)\)
\(\chi_{4225}(256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{88}{195}\right)\)	\(e\left(\frac{31}{195}\right)\)	\(e\left(\frac{176}{195}\right)\)	\(e\left(\frac{119}{195}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{62}{195}\right)\)	\(e\left(\frac{133}{195}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{61}{65}\right)\)
\(\chi_{4225}(321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{195}\right)\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{14}{195}\right)\)	\(e\left(\frac{56}{195}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{98}{195}\right)\)	\(e\left(\frac{97}{195}\right)\)	\(e\left(\frac{21}{65}\right)\)	\(e\left(\frac{44}{65}\right)\)
\(\chi_{4225}(341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{194}{195}\right)\)	\(e\left(\frac{188}{195}\right)\)	\(e\left(\frac{193}{195}\right)\)	\(e\left(\frac{187}{195}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{14}{195}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{3}{65}\right)\)
\(\chi_{4225}(386,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{195}\right)\)	\(e\left(\frac{67}{195}\right)\)	\(e\left(\frac{47}{195}\right)\)	\(e\left(\frac{188}{195}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{134}{195}\right)\)	\(e\left(\frac{61}{195}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{27}{65}\right)\)
\(\chi_{4225}(406,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{195}\right)\)	\(e\left(\frac{86}{195}\right)\)	\(e\left(\frac{136}{195}\right)\)	\(e\left(\frac{154}{195}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{3}{65}\right)\)	\(e\left(\frac{172}{195}\right)\)	\(e\left(\frac{23}{195}\right)\)	\(e\left(\frac{9}{65}\right)\)	\(e\left(\frac{56}{65}\right)\)
\(\chi_{4225}(471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{195}\right)\)	\(e\left(\frac{179}{195}\right)\)	\(e\left(\frac{79}{195}\right)\)	\(e\left(\frac{121}{195}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{163}{195}\right)\)	\(e\left(\frac{32}{195}\right)\)	\(e\left(\frac{21}{65}\right)\)	\(e\left(\frac{44}{65}\right)\)
\(\chi_{4225}(516,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{154}{195}\right)\)	\(e\left(\frac{103}{195}\right)\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{62}{195}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{58}{65}\right)\)
\(\chi_{4225}(536,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{77}{195}\right)\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{88}{195}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{154}{195}\right)\)	\(e\left(\frac{41}{195}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{32}{65}\right)\)
\(\chi_{4225}(581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{195}\right)\)	\(e\left(\frac{121}{195}\right)\)	\(e\left(\frac{146}{195}\right)\)	\(e\left(\frac{194}{195}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{47}{195}\right)\)	\(e\left(\frac{148}{195}\right)\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{41}{65}\right)\)
\(\chi_{4225}(646,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{195}\right)\)	\(e\left(\frac{139}{195}\right)\)	\(e\left(\frac{179}{195}\right)\)	\(e\left(\frac{131}{195}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{83}{195}\right)\)	\(e\left(\frac{112}{195}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{24}{65}\right)\)
\(\chi_{4225}(666,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{195}\right)\)	\(e\left(\frac{68}{195}\right)\)	\(e\left(\frac{103}{195}\right)\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{136}{195}\right)\)	\(e\left(\frac{59}{195}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{8}{65}\right)\)
\(\chi_{4225}(711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{106}{195}\right)\)	\(e\left(\frac{157}{195}\right)\)	\(e\left(\frac{17}{195}\right)\)	\(e\left(\frac{68}{195}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{119}{195}\right)\)	\(e\left(\frac{76}{195}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{7}{65}\right)\)
\(\chi_{4225}(731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{195}\right)\)	\(e\left(\frac{161}{195}\right)\)	\(e\left(\frac{46}{195}\right)\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{127}{195}\right)\)	\(e\left(\frac{68}{195}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{61}{65}\right)\)
\(\chi_{4225}(796,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{195}\right)\)	\(e\left(\frac{59}{195}\right)\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{151}{195}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{77}{195}\right)\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{49}{65}\right)\)
\(\chi_{4225}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{195}\right)\)	\(e\left(\frac{193}{195}\right)\)	\(e\left(\frac{83}{195}\right)\)	\(e\left(\frac{137}{195}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{9}{65}\right)\)	\(e\left(\frac{191}{195}\right)\)	\(e\left(\frac{4}{195}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{38}{65}\right)\)
\(\chi_{4225}(861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{195}\right)\)	\(e\left(\frac{152}{195}\right)\)	\(e\left(\frac{127}{195}\right)\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{109}{195}\right)\)	\(e\left(\frac{86}{195}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{37}{65}\right)\)
\(\chi_{4225}(906,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{195}\right)\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{116}{195}\right)\)	\(e\left(\frac{74}{195}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{32}{195}\right)\)	\(e\left(\frac{163}{195}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{21}{65}\right)\)
\(\chi_{4225}(971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{172}{195}\right)\)	\(e\left(\frac{34}{195}\right)\)	\(e\left(\frac{149}{195}\right)\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{42}{65}\right)\)	\(e\left(\frac{68}{195}\right)\)	\(e\left(\frac{127}{195}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{4}{65}\right)\)
\(\chi_{4225}(1056,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{195}\right)\)	\(e\left(\frac{41}{195}\right)\)	\(e\left(\frac{151}{195}\right)\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{43}{65}\right)\)	\(e\left(\frac{82}{195}\right)\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{1}{65}\right)\)
\(\chi_{4225}(1121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{195}\right)\)	\(e\left(\frac{134}{195}\right)\)	\(e\left(\frac{94}{195}\right)\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{47}{65}\right)\)	\(e\left(\frac{73}{195}\right)\)	\(e\left(\frac{122}{195}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{54}{65}\right)\)
\(\chi_{4225}(1166,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{124}{195}\right)\)	\(e\left(\frac{88}{195}\right)\)	\(e\left(\frac{53}{195}\right)\)	\(e\left(\frac{17}{195}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{176}{195}\right)\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{47}{65}\right)\)	\(e\left(\frac{18}{65}\right)\)
\(\chi_{4225}(1186,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{116}{195}\right)\)	\(e\left(\frac{32}{195}\right)\)	\(e\left(\frac{37}{195}\right)\)	\(e\left(\frac{148}{195}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{64}{195}\right)\)	\(e\left(\frac{131}{195}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{42}{65}\right)\)
\(\chi_{4225}(1231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{195}\right)\)	\(e\left(\frac{106}{195}\right)\)	\(e\left(\frac{86}{195}\right)\)	\(e\left(\frac{149}{195}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{43}{65}\right)\)	\(e\left(\frac{17}{195}\right)\)	\(e\left(\frac{178}{195}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{1}{65}\right)\)
\(\chi_{4225}(1296,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{195}\right)\)	\(e\left(\frac{124}{195}\right)\)	\(e\left(\frac{119}{195}\right)\)	\(e\left(\frac{86}{195}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{53}{195}\right)\)	\(e\left(\frac{142}{195}\right)\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{49}{65}\right)\)
\(\chi_{4225}(1316,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{195}\right)\)	\(e\left(\frac{23}{195}\right)\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{82}{195}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{46}{195}\right)\)	\(e\left(\frac{149}{195}\right)\)	\(e\left(\frac{47}{65}\right)\)	\(e\left(\frac{18}{65}\right)\)
\(\chi_{4225}(1361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{195}\right)\)	\(e\left(\frac{142}{195}\right)\)	\(e\left(\frac{152}{195}\right)\)	\(e\left(\frac{23}{195}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{89}{195}\right)\)	\(e\left(\frac{106}{195}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{32}{65}\right)\)
\(\chi_{4225}(1381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{128}{195}\right)\)	\(e\left(\frac{116}{195}\right)\)	\(e\left(\frac{61}{195}\right)\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{37}{195}\right)\)	\(e\left(\frac{158}{195}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{6}{65}\right)\)

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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.cm
Modulus	$4225$
Conductor	$4225$
Order	$195$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(4225\)
Conductor:	\(4225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(195\)	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)