LMFDB - Dirichlet character orbit 8954.bt

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8954, base_ring=CyclotomicField(198)) M = H._module chi = DirichletCharacter(H, M([90,176])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(155,8954)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8954$
Conductor:	$4477$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$99$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4477.bt	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:	$\Q(\zeta_{99})$
Fixed field:	Number field defined by a degree 99 polynomial

First 31 of 60 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{8954}(155,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{73}{99}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{8954}(419,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{73}{99}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{8954}(441,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{70}{99}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{14}{99}\right)$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{8}{33}\right)$
$\chi_{8954}(551,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{14}{99}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{8954}(749,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{7}{33}\right)$
$\chi_{8954}(793,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{10}{33}\right)$
$\chi_{8954}(1233,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{56}{99}\right)$	$e\left(\frac{7}{33}\right)$
$\chi_{8954}(1255,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{98}{99}\right)$	$e\left(\frac{7}{99}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{41}{99}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{14}{33}\right)$
$\chi_{8954}(1365,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{41}{99}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{8954}(1563,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{13}{33}\right)$
$\chi_{8954}(1607,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{73}{99}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{16}{33}\right)$
$\chi_{8954}(1783,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{94}{99}\right)$	$e\left(\frac{38}{99}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{17}{33}\right)$
$\chi_{8954}(2047,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{56}{99}\right)$	$e\left(\frac{35}{99}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{38}{99}\right)$	$e\left(\frac{13}{33}\right)$
$\chi_{8954}(2069,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{20}{33}\right)$
$\chi_{8954}(2377,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{19}{33}\right)$
$\chi_{8954}(2597,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{28}{99}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{23}{33}\right)$
$\chi_{8954}(2861,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{70}{99}\right)$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{19}{33}\right)$
$\chi_{8954}(2883,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{26}{33}\right)$
$\chi_{8954}(2993,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{14}{99}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{17}{33}\right)$
$\chi_{8954}(3191,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{8954}(3235,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{28}{33}\right)$
$\chi_{8954}(3411,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{53}{99}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{8954}(3675,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{99}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{10}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{8954}(3697,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{38}{99}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{10}{99}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{8954}(3807,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{41}{99}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{94}{99}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{98}{99}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{23}{33}\right)$
$\chi_{8954}(4005,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{94}{99}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{8954}(4049,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{28}{99}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{8954}(4225,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{14}{99}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{2}{33}\right)$
$\chi_{8954}(4489,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{53}{99}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{8954}(4511,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{35}{99}\right)$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{7}{99}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{8954}(4621,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{38}{99}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{7}{99}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{29}{33}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{8954}(155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{73}{99}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{8954}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{73}{99}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{8954}(441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{70}{99}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{14}{99}\right)\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{8}{33}\right)\)
\(\chi_{8954}(551,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{14}{99}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{8954}(749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{7}{33}\right)\)
\(\chi_{8954}(793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{10}{33}\right)\)
\(\chi_{8954}(1233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{56}{99}\right)\)	\(e\left(\frac{7}{33}\right)\)
\(\chi_{8954}(1255,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{98}{99}\right)\)	\(e\left(\frac{7}{99}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{41}{99}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{14}{33}\right)\)
\(\chi_{8954}(1365,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{41}{99}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{8954}(1563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{13}{33}\right)\)
\(\chi_{8954}(1607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{73}{99}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{16}{33}\right)\)
\(\chi_{8954}(1783,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{94}{99}\right)\)	\(e\left(\frac{38}{99}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{17}{33}\right)\)
\(\chi_{8954}(2047,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{56}{99}\right)\)	\(e\left(\frac{35}{99}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{38}{99}\right)\)	\(e\left(\frac{13}{33}\right)\)
\(\chi_{8954}(2069,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{20}{33}\right)\)
\(\chi_{8954}(2377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{19}{33}\right)\)
\(\chi_{8954}(2597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{28}{99}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{23}{33}\right)\)
\(\chi_{8954}(2861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{70}{99}\right)\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{19}{33}\right)\)
\(\chi_{8954}(2883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{8954}(2993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{14}{99}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{17}{33}\right)\)
\(\chi_{8954}(3191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{8954}(3235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{28}{33}\right)\)
\(\chi_{8954}(3411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{53}{99}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{8954}(3675,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{99}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{10}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{8954}(3697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{38}{99}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{10}{99}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{8954}(3807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{41}{99}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{94}{99}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{98}{99}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{23}{33}\right)\)
\(\chi_{8954}(4005,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{94}{99}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{8954}(4049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{28}{99}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{8954}(4225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{14}{99}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{2}{33}\right)\)
\(\chi_{8954}(4489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{53}{99}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{8954}(4511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{35}{99}\right)\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{7}{99}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{8954}(4621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{38}{99}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{7}{99}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{29}{33}\right)\)

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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	8954.bt
Modulus	$8954$
Conductor	$4477$
Order	$99$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8954\)
Conductor:	\(4477\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(99\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4477.bt	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)