LMFDB - Dirichlet character orbit 9702.fb

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9702, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([70,50,84])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(445, 9702)) 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("9702.445"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$9702$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$4851$	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 4851.fa	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	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{9702}(445,\cdot)$	$1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{46}{105}\right)$
$\chi_{9702}(697,\cdot)$	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{58}{105}\right)$
$\chi_{9702}(709,\cdot)$	$1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{11}{105}\right)$
$\chi_{9702}(823,\cdot)$	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{64}{105}\right)$
$\chi_{9702}(1087,\cdot)$	$1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{89}{105}\right)$
$\chi_{9702}(1213,\cdot)$	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{17}{105}\right)$
$\chi_{9702}(2083,\cdot)$	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{103}{105}\right)$
$\chi_{9702}(2095,\cdot)$	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{101}{105}\right)$
$\chi_{9702}(2209,\cdot)$	$1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{4}{105}\right)$
$\chi_{9702}(2335,\cdot)$	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{52}{105}\right)$
$\chi_{9702}(2347,\cdot)$	$1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{83}{105}\right)$
$\chi_{9702}(2473,\cdot)$	$1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{74}{105}\right)$
$\chi_{9702}(2599,\cdot)$	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{2}{105}\right)$
$\chi_{9702}(3217,\cdot)$	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{31}{105}\right)$
$\chi_{9702}(3469,\cdot)$	$1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{43}{105}\right)$
$\chi_{9702}(3481,\cdot)$	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{86}{105}\right)$
$\chi_{9702}(3721,\cdot)$	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{97}{105}\right)$
$\chi_{9702}(3733,\cdot)$	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{68}{105}\right)$
$\chi_{9702}(3859,\cdot)$	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{59}{105}\right)$
$\chi_{9702}(3985,\cdot)$	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{92}{105}\right)$
$\chi_{9702}(4603,\cdot)$	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{76}{105}\right)$
$\chi_{9702}(4855,\cdot)$	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{88}{105}\right)$
$\chi_{9702}(4867,\cdot)$	$1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{71}{105}\right)$
$\chi_{9702}(4981,\cdot)$	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{94}{105}\right)$
$\chi_{9702}(5107,\cdot)$	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{37}{105}\right)$
$\chi_{9702}(5119,\cdot)$	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{53}{105}\right)$
$\chi_{9702}(5245,\cdot)$	$1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{44}{105}\right)$
$\chi_{9702}(5989,\cdot)$	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{16}{105}\right)$
$\chi_{9702}(6367,\cdot)$	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{34}{105}\right)$
$\chi_{9702}(6493,\cdot)$	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{82}{105}\right)$
$\chi_{9702}(6505,\cdot)$	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{38}{105}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{9702}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)
\(\chi_{9702}(697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)
\(\chi_{9702}(709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)
\(\chi_{9702}(823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)
\(\chi_{9702}(1087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)
\(\chi_{9702}(1213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)
\(\chi_{9702}(2083,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)
\(\chi_{9702}(2095,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)
\(\chi_{9702}(2209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)
\(\chi_{9702}(2335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)
\(\chi_{9702}(2347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)
\(\chi_{9702}(2473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)
\(\chi_{9702}(2599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)
\(\chi_{9702}(3217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)
\(\chi_{9702}(3469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)
\(\chi_{9702}(3481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)
\(\chi_{9702}(3721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)
\(\chi_{9702}(3733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)
\(\chi_{9702}(3859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)
\(\chi_{9702}(3985,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)
\(\chi_{9702}(4603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)
\(\chi_{9702}(4855,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)
\(\chi_{9702}(4867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)
\(\chi_{9702}(4981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)
\(\chi_{9702}(5107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)
\(\chi_{9702}(5119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)
\(\chi_{9702}(5245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)
\(\chi_{9702}(5989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{16}{105}\right)\)
\(\chi_{9702}(6367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)
\(\chi_{9702}(6493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)
\(\chi_{9702}(6505,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)

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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	9702.fb
Modulus	$9702$
Conductor	$4851$
Order	$105$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(9702\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(4851\)	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 4851.fa	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);