LMFDB - Dirichlet character orbit 1617.ce

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1617, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([0,50,42])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(4, 1617)) 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("1617.4"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1617$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$539$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$105$	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 539.bc	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:	$\Q(\zeta_{105})$	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 105 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{1617}(4,\cdot)$	$1$	$1$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{1617}(16,\cdot)$	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{1617}(25,\cdot)$	$1$	$1$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{1617}(37,\cdot)$	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{1617}(58,\cdot)$	$1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{1617}(130,\cdot)$	$1$	$1$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{1617}(163,\cdot)$	$1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{1617}(235,\cdot)$	$1$	$1$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{1617}(247,\cdot)$	$1$	$1$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{1617}(256,\cdot)$	$1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{1617}(268,\cdot)$	$1$	$1$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{1617}(289,\cdot)$	$1$	$1$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{1617}(394,\cdot)$	$1$	$1$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{1617}(445,\cdot)$	$1$	$1$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{1617}(466,\cdot)$	$1$	$1$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{1617}(478,\cdot)$	$1$	$1$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{1617}(487,\cdot)$	$1$	$1$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{1617}(499,\cdot)$	$1$	$1$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{1617}(592,\cdot)$	$1$	$1$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{1617}(625,\cdot)$	$1$	$1$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{1617}(676,\cdot)$	$1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{1617}(697,\cdot)$	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{1617}(709,\cdot)$	$1$	$1$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{1617}(718,\cdot)$	$1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{1617}(730,\cdot)$	$1$	$1$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{1617}(751,\cdot)$	$1$	$1$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{1617}(823,\cdot)$	$1$	$1$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{1617}(856,\cdot)$	$1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{1617}(907,\cdot)$	$1$	$1$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{1617}(928,\cdot)$	$1$	$1$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{1617}(940,\cdot)$	$1$	$1$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{9}{35}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{1617}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{1617}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{1617}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{1617}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{1617}(58,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{1617}(130,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{1617}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{1617}(235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{1617}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{1617}(256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{1617}(268,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{1617}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{1617}(394,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{1617}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{1617}(466,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{1617}(478,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{1617}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{1617}(499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{1617}(592,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{1617}(625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{1617}(676,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{1617}(697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{1617}(709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{1617}(718,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{1617}(730,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{1617}(751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{1617}(823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{1617}(856,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{1617}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{1617}(928,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{1617}(940,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{9}{35}\right)\)

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First 31 of 48 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	1617.ce
Modulus	$1617$
Conductor	$539$
Order	$105$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(1617\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(539\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(105\)	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 539.bc	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);