LMFDB - Dirichlet character orbit 45738.gp

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45738, base_ring=CyclotomicField(198)) M = H._module chi = DirichletCharacter(H, M([22,0,72])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(463, 45738)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45738.463"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$45738$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3267$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$99$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 3267.bh	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{99})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 99 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 60 characters in Galois orbit

Character	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{45738}(463,\cdot)$	$1$	$1$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{25}{99}\right)$
$\chi_{45738}(925,\cdot)$	$1$	$1$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{56}{99}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{83}{99}\right)$
$\chi_{45738}(1849,\cdot)$	$1$	$1$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{70}{99}\right)$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{1}{99}\right)$
$\chi_{45738}(2311,\cdot)$	$1$	$1$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{41}{99}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{59}{99}\right)$
$\chi_{45738}(3235,\cdot)$	$1$	$1$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{73}{99}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{76}{99}\right)$
$\chi_{45738}(3697,\cdot)$	$1$	$1$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{10}{99}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{35}{99}\right)$
$\chi_{45738}(4621,\cdot)$	$1$	$1$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{94}{99}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{52}{99}\right)$
$\chi_{45738}(6007,\cdot)$	$1$	$1$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{28}{99}\right)$
$\chi_{45738}(6469,\cdot)$	$1$	$1$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{86}{99}\right)$
$\chi_{45738}(7393,\cdot)$	$1$	$1$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{4}{99}\right)$
$\chi_{45738}(7855,\cdot)$	$1$	$1$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{62}{99}\right)$
$\chi_{45738}(8779,\cdot)$	$1$	$1$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{70}{99}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{56}{99}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{79}{99}\right)$
$\chi_{45738}(9241,\cdot)$	$1$	$1$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{38}{99}\right)$
$\chi_{45738}(10627,\cdot)$	$1$	$1$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{14}{99}\right)$
$\chi_{45738}(11551,\cdot)$	$1$	$1$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{31}{99}\right)$
$\chi_{45738}(12013,\cdot)$	$1$	$1$	$e\left(\frac{41}{99}\right)$	$e\left(\frac{35}{99}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{28}{99}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{89}{99}\right)$
$\chi_{45738}(12937,\cdot)$	$1$	$1$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{94}{99}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{7}{99}\right)$
$\chi_{45738}(13399,\cdot)$	$1$	$1$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{65}{99}\right)$
$\chi_{45738}(14323,\cdot)$	$1$	$1$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{10}{99}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{82}{99}\right)$
$\chi_{45738}(14785,\cdot)$	$1$	$1$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{98}{99}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{41}{99}\right)$
$\chi_{45738}(15709,\cdot)$	$1$	$1$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{94}{99}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{58}{99}\right)$
$\chi_{45738}(16171,\cdot)$	$1$	$1$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{17}{99}\right)$
$\chi_{45738}(17095,\cdot)$	$1$	$1$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{38}{99}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{34}{99}\right)$
$\chi_{45738}(17557,\cdot)$	$1$	$1$	$e\left(\frac{98}{99}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{14}{99}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{92}{99}\right)$
$\chi_{45738}(18481,\cdot)$	$1$	$1$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{7}{99}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{10}{99}\right)$
$\chi_{45738}(18943,\cdot)$	$1$	$1$	$e\left(\frac{38}{99}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{68}{99}\right)$
$\chi_{45738}(19867,\cdot)$	$1$	$1$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{99}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{28}{99}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{85}{99}\right)$
$\chi_{45738}(21253,\cdot)$	$1$	$1$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{61}{99}\right)$
$\chi_{45738}(21715,\cdot)$	$1$	$1$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{14}{99}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{20}{99}\right)$
$\chi_{45738}(22639,\cdot)$	$1$	$1$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{53}{99}\right)$	$e\left(\frac{35}{99}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{37}{99}\right)$
$\chi_{45738}(23101,\cdot)$	$1$	$1$	$e\left(\frac{56}{99}\right)$	$e\left(\frac{14}{99}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{95}{99}\right)$

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	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{45738}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{25}{99}\right)\)
\(\chi_{45738}(925,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{56}{99}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{83}{99}\right)\)
\(\chi_{45738}(1849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{70}{99}\right)\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{1}{99}\right)\)
\(\chi_{45738}(2311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{41}{99}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{59}{99}\right)\)
\(\chi_{45738}(3235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{73}{99}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{76}{99}\right)\)
\(\chi_{45738}(3697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{10}{99}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{35}{99}\right)\)
\(\chi_{45738}(4621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{94}{99}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{52}{99}\right)\)
\(\chi_{45738}(6007,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{28}{99}\right)\)
\(\chi_{45738}(6469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{86}{99}\right)\)
\(\chi_{45738}(7393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{4}{99}\right)\)
\(\chi_{45738}(7855,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{62}{99}\right)\)
\(\chi_{45738}(8779,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{70}{99}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{56}{99}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{79}{99}\right)\)
\(\chi_{45738}(9241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{38}{99}\right)\)
\(\chi_{45738}(10627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{14}{99}\right)\)
\(\chi_{45738}(11551,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{31}{99}\right)\)
\(\chi_{45738}(12013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{99}\right)\)	\(e\left(\frac{35}{99}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{28}{99}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{89}{99}\right)\)
\(\chi_{45738}(12937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{94}{99}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{7}{99}\right)\)
\(\chi_{45738}(13399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{65}{99}\right)\)
\(\chi_{45738}(14323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{10}{99}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{82}{99}\right)\)
\(\chi_{45738}(14785,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{98}{99}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{41}{99}\right)\)
\(\chi_{45738}(15709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{94}{99}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{58}{99}\right)\)
\(\chi_{45738}(16171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{17}{99}\right)\)
\(\chi_{45738}(17095,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{38}{99}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{34}{99}\right)\)
\(\chi_{45738}(17557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{98}{99}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{14}{99}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{92}{99}\right)\)
\(\chi_{45738}(18481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{7}{99}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{10}{99}\right)\)
\(\chi_{45738}(18943,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{99}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{68}{99}\right)\)
\(\chi_{45738}(19867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{99}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{28}{99}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{85}{99}\right)\)
\(\chi_{45738}(21253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{61}{99}\right)\)
\(\chi_{45738}(21715,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{14}{99}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{20}{99}\right)\)
\(\chi_{45738}(22639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{53}{99}\right)\)	\(e\left(\frac{35}{99}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{37}{99}\right)\)
\(\chi_{45738}(23101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{99}\right)\)	\(e\left(\frac{14}{99}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{95}{99}\right)\)

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Basic properties

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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	45738.gp
Modulus	$45738$
Conductor	$3267$
Order	$99$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(45738\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3267\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(99\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 3267.bh	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);