LMFDB - Dirichlet character orbit 961.k

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(186)) M = H._module chi = DirichletCharacter(H, M([88])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,961)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$961$
Conductor:	$961$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$93$	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:	$\Q(\zeta_{93})$
Fixed field:	Number field defined by a degree 93 polynomial

First 31 of 60 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{961}(5,\cdot)$	$1$	$1$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{44}{93}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{29}{93}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{76}{93}\right)$
$\chi_{961}(25,\cdot)$	$1$	$1$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{74}{93}\right)$	$e\left(\frac{59}{93}\right)$
$\chi_{961}(36,\cdot)$	$1$	$1$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{5}{93}\right)$	$e\left(\frac{38}{93}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{64}{93}\right)$	$e\left(\frac{10}{93}\right)$	$e\left(\frac{13}{93}\right)$
$\chi_{961}(56,\cdot)$	$1$	$1$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{67}{93}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{92}{93}\right)$	$e\left(\frac{25}{93}\right)$	$e\left(\frac{4}{93}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{41}{93}\right)$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{65}{93}\right)$
$\chi_{961}(67,\cdot)$	$1$	$1$	$e\left(\frac{6}{31}\right)$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{12}{31}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{38}{93}\right)$	$e\left(\frac{47}{93}\right)$	$e\left(\frac{18}{31}\right)$	$e\left(\frac{40}{93}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{43}{93}\right)$
$\chi_{961}(87,\cdot)$	$1$	$1$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{59}{93}\right)$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{43}{93}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{92}{93}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{71}{93}\right)$
$\chi_{961}(98,\cdot)$	$1$	$1$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{8}{93}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{79}{93}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{56}{93}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{49}{93}\right)$	$e\left(\frac{73}{93}\right)$
$\chi_{961}(118,\cdot)$	$1$	$1$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{25}{93}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{82}{93}\right)$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{77}{93}\right)$
$\chi_{961}(129,\cdot)$	$1$	$1$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{11}{93}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{22}{93}\right)$	$e\left(\frac{10}{93}\right)$
$\chi_{961}(149,\cdot)$	$1$	$1$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{4}{93}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{86}{93}\right)$	$e\left(\frac{82}{93}\right)$	$e\left(\frac{28}{93}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{8}{93}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{83}{93}\right)$
$\chi_{961}(160,\cdot)$	$1$	$1$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{77}{93}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{28}{93}\right)$	$e\left(\frac{44}{93}\right)$	$e\left(\frac{74}{93}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{61}{93}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{40}{93}\right)$
$\chi_{961}(180,\cdot)$	$1$	$1$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{53}{93}\right)$	$e\left(\frac{70}{93}\right)$	$e\left(\frac{67}{93}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{59}{93}\right)$	$e\left(\frac{47}{93}\right)$	$e\left(\frac{89}{93}\right)$
$\chi_{961}(191,\cdot)$	$1$	$1$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{49}{93}\right)$	$e\left(\frac{77}{93}\right)$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{12}{31}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{61}{93}\right)$	$e\left(\frac{70}{93}\right)$
$\chi_{961}(211,\cdot)$	$1$	$1$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{55}{93}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{2}{93}\right)$
$\chi_{961}(222,\cdot)$	$1$	$1$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{53}{93}\right)$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{70}{93}\right)$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{92}{93}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{7}{93}\right)$
$\chi_{961}(242,\cdot)$	$1$	$1$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{80}{93}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{12}{31}\right)$	$e\left(\frac{68}{93}\right)$	$e\left(\frac{92}{93}\right)$	$e\left(\frac{8}{93}\right)$
$\chi_{961}(253,\cdot)$	$1$	$1$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{41}{93}\right)$	$e\left(\frac{6}{31}\right)$	$e\left(\frac{91}{93}\right)$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{8}{93}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{82}{93}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{37}{93}\right)$
$\chi_{961}(273,\cdot)$	$1$	$1$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{47}{93}\right)$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{91}{93}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{68}{93}\right)$	$e\left(\frac{14}{93}\right)$
$\chi_{961}(284,\cdot)$	$1$	$1$	$e\left(\frac{18}{31}\right)$	$e\left(\frac{29}{93}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{67}{93}\right)$
$\chi_{961}(304,\cdot)$	$1$	$1$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{14}{93}\right)$	$e\left(\frac{22}{93}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{30}{31}\right)$	$e\left(\frac{77}{93}\right)$	$e\left(\frac{44}{93}\right)$	$e\left(\frac{20}{93}\right)$
$\chi_{961}(315,\cdot)$	$1$	$1$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{40}{93}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{6}{31}\right)$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{4}{93}\right)$
$\chi_{961}(335,\cdot)$	$1$	$1$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{64}{93}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{74}{93}\right)$	$e\left(\frac{10}{93}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{26}{93}\right)$
$\chi_{961}(346,\cdot)$	$1$	$1$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{5}{93}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{61}{93}\right)$	$e\left(\frac{56}{93}\right)$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{10}{93}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{34}{93}\right)$
$\chi_{961}(366,\cdot)$	$1$	$1$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{43}{93}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{41}{93}\right)$	$e\left(\frac{91}{93}\right)$	$e\left(\frac{22}{93}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{86}{93}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{32}{93}\right)$
$\chi_{961}(377,\cdot)$	$1$	$1$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{86}{93}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{82}{93}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{44}{93}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{79}{93}\right)$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{64}{93}\right)$
$\chi_{961}(397,\cdot)$	$1$	$1$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{22}{93}\right)$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{8}{93}\right)$	$e\left(\frac{79}{93}\right)$	$e\left(\frac{61}{93}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{44}{93}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{38}{93}\right)$
$\chi_{961}(408,\cdot)$	$1$	$1$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{74}{93}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{10}{93}\right)$	$e\left(\frac{29}{93}\right)$	$e\left(\frac{53}{93}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{55}{93}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{1}{93}\right)$
$\chi_{961}(428,\cdot)$	$1$	$1$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{68}{93}\right)$	$e\left(\frac{67}{93}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{41}{93}\right)$	$e\left(\frac{44}{93}\right)$
$\chi_{961}(459,\cdot)$	$1$	$1$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{55}{93}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{53}{93}\right)$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{50}{93}\right)$
$\chi_{961}(470,\cdot)$	$1$	$1$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{30}{31}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{4}{93}\right)$	$e\left(\frac{61}{93}\right)$
$\chi_{961}(490,\cdot)$	$1$	$1$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{43}{93}\right)$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{11}{93}\right)$	$e\left(\frac{86}{93}\right)$	$e\left(\frac{56}{93}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{961}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{44}{93}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{29}{93}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{76}{93}\right)\)
\(\chi_{961}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{74}{93}\right)\)	\(e\left(\frac{59}{93}\right)\)
\(\chi_{961}(36,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{5}{93}\right)\)	\(e\left(\frac{38}{93}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{64}{93}\right)\)	\(e\left(\frac{10}{93}\right)\)	\(e\left(\frac{13}{93}\right)\)
\(\chi_{961}(56,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{67}{93}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{92}{93}\right)\)	\(e\left(\frac{25}{93}\right)\)	\(e\left(\frac{4}{93}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{41}{93}\right)\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{65}{93}\right)\)
\(\chi_{961}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{31}\right)\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{12}{31}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{38}{93}\right)\)	\(e\left(\frac{47}{93}\right)\)	\(e\left(\frac{18}{31}\right)\)	\(e\left(\frac{40}{93}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{43}{93}\right)\)
\(\chi_{961}(87,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{59}{93}\right)\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{43}{93}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{92}{93}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{71}{93}\right)\)
\(\chi_{961}(98,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{8}{93}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{79}{93}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{56}{93}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{49}{93}\right)\)	\(e\left(\frac{73}{93}\right)\)
\(\chi_{961}(118,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{25}{93}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{82}{93}\right)\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{77}{93}\right)\)
\(\chi_{961}(129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{11}{93}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{22}{93}\right)\)	\(e\left(\frac{10}{93}\right)\)
\(\chi_{961}(149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{4}{93}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{86}{93}\right)\)	\(e\left(\frac{82}{93}\right)\)	\(e\left(\frac{28}{93}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{8}{93}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{83}{93}\right)\)
\(\chi_{961}(160,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{77}{93}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{28}{93}\right)\)	\(e\left(\frac{44}{93}\right)\)	\(e\left(\frac{74}{93}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{61}{93}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{40}{93}\right)\)
\(\chi_{961}(180,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{53}{93}\right)\)	\(e\left(\frac{70}{93}\right)\)	\(e\left(\frac{67}{93}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{59}{93}\right)\)	\(e\left(\frac{47}{93}\right)\)	\(e\left(\frac{89}{93}\right)\)
\(\chi_{961}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{49}{93}\right)\)	\(e\left(\frac{77}{93}\right)\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{12}{31}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{61}{93}\right)\)	\(e\left(\frac{70}{93}\right)\)
\(\chi_{961}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{55}{93}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{2}{93}\right)\)
\(\chi_{961}(222,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{53}{93}\right)\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{70}{93}\right)\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{92}{93}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{7}{93}\right)\)
\(\chi_{961}(242,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{80}{93}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{12}{31}\right)\)	\(e\left(\frac{68}{93}\right)\)	\(e\left(\frac{92}{93}\right)\)	\(e\left(\frac{8}{93}\right)\)
\(\chi_{961}(253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{41}{93}\right)\)	\(e\left(\frac{6}{31}\right)\)	\(e\left(\frac{91}{93}\right)\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{8}{93}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{82}{93}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{37}{93}\right)\)
\(\chi_{961}(273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{47}{93}\right)\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{91}{93}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{68}{93}\right)\)	\(e\left(\frac{14}{93}\right)\)
\(\chi_{961}(284,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{31}\right)\)	\(e\left(\frac{29}{93}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{67}{93}\right)\)
\(\chi_{961}(304,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{14}{93}\right)\)	\(e\left(\frac{22}{93}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{30}{31}\right)\)	\(e\left(\frac{77}{93}\right)\)	\(e\left(\frac{44}{93}\right)\)	\(e\left(\frac{20}{93}\right)\)
\(\chi_{961}(315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{40}{93}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{6}{31}\right)\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{4}{93}\right)\)
\(\chi_{961}(335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{64}{93}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{74}{93}\right)\)	\(e\left(\frac{10}{93}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{26}{93}\right)\)
\(\chi_{961}(346,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{5}{93}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{61}{93}\right)\)	\(e\left(\frac{56}{93}\right)\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{10}{93}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{34}{93}\right)\)
\(\chi_{961}(366,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{43}{93}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{41}{93}\right)\)	\(e\left(\frac{91}{93}\right)\)	\(e\left(\frac{22}{93}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{86}{93}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{32}{93}\right)\)
\(\chi_{961}(377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{86}{93}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{82}{93}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{44}{93}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{79}{93}\right)\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{64}{93}\right)\)
\(\chi_{961}(397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{22}{93}\right)\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{8}{93}\right)\)	\(e\left(\frac{79}{93}\right)\)	\(e\left(\frac{61}{93}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{44}{93}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{38}{93}\right)\)
\(\chi_{961}(408,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{74}{93}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{10}{93}\right)\)	\(e\left(\frac{29}{93}\right)\)	\(e\left(\frac{53}{93}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{55}{93}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{1}{93}\right)\)
\(\chi_{961}(428,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{68}{93}\right)\)	\(e\left(\frac{67}{93}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{41}{93}\right)\)	\(e\left(\frac{44}{93}\right)\)
\(\chi_{961}(459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{55}{93}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{53}{93}\right)\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{50}{93}\right)\)
\(\chi_{961}(470,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{30}{31}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{4}{93}\right)\)	\(e\left(\frac{61}{93}\right)\)
\(\chi_{961}(490,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{43}{93}\right)\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{11}{93}\right)\)	\(e\left(\frac{86}{93}\right)\)	\(e\left(\frac{56}{93}\right)\)

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First 31 of 60 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	961.k
Modulus	$961$
Conductor	$961$
Order	$93$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(961\)
Conductor:	\(961\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(93\)	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)