LMFDB - Dirichlet character orbit 9702.fl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9702, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([175,145,84])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,9702)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9702$
Conductor:	$4851$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$210$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4851.fc	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:	$\Q(\zeta_{105})$
Fixed field:	Number field defined by a degree 210 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{9702}(5,\cdot)$	$1$	$1$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{76}{105}\right)$
$\chi_{9702}(257,\cdot)$	$1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{73}{105}\right)$
$\chi_{9702}(383,\cdot)$	$1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{19}{105}\right)$
$\chi_{9702}(731,\cdot)$	$1$	$1$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{11}{105}\right)$
$\chi_{9702}(983,\cdot)$	$1$	$1$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{83}{105}\right)$
$\chi_{9702}(1235,\cdot)$	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{92}{105}\right)$
$\chi_{9702}(1643,\cdot)$	$1$	$1$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{88}{105}\right)$
$\chi_{9702}(1769,\cdot)$	$1$	$1$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{34}{105}\right)$
$\chi_{9702}(1895,\cdot)$	$1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{22}{105}\right)$
$\chi_{9702}(2117,\cdot)$	$1$	$1$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{71}{105}\right)$
$\chi_{9702}(2369,\cdot)$	$1$	$1$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{38}{105}\right)$
$\chi_{9702}(2495,\cdot)$	$1$	$1$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{74}{105}\right)$
$\chi_{9702}(2621,\cdot)$	$1$	$1$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{47}{105}\right)$
$\chi_{9702}(2777,\cdot)$	$1$	$1$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{1}{105}\right)$
$\chi_{9702}(3029,\cdot)$	$1$	$1$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{103}{105}\right)$
$\chi_{9702}(3281,\cdot)$	$1$	$1$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{37}{105}\right)$
$\chi_{9702}(3503,\cdot)$	$1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{26}{105}\right)$
$\chi_{9702}(3881,\cdot)$	$1$	$1$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{29}{105}\right)$
$\chi_{9702}(4007,\cdot)$	$1$	$1$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{2}{105}\right)$
$\chi_{9702}(4163,\cdot)$	$1$	$1$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{16}{105}\right)$
$\chi_{9702}(4415,\cdot)$	$1$	$1$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{13}{105}\right)$
$\chi_{9702}(4541,\cdot)$	$1$	$1$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{64}{105}\right)$
$\chi_{9702}(4667,\cdot)$	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{52}{105}\right)$
$\chi_{9702}(4889,\cdot)$	$1$	$1$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{86}{105}\right)$
$\chi_{9702}(5141,\cdot)$	$1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{53}{105}\right)$
$\chi_{9702}(5267,\cdot)$	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{89}{105}\right)$
$\chi_{9702}(5393,\cdot)$	$1$	$1$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{62}{105}\right)$
$\chi_{9702}(5549,\cdot)$	$1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{31}{105}\right)$
$\chi_{9702}(5927,\cdot)$	$1$	$1$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{79}{105}\right)$
$\chi_{9702}(6053,\cdot)$	$1$	$1$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{67}{105}\right)$
$\chi_{9702}(6275,\cdot)$	$1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{41}{105}\right)$

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	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{9702}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)
\(\chi_{9702}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)
\(\chi_{9702}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)
\(\chi_{9702}(731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)
\(\chi_{9702}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)
\(\chi_{9702}(1235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)
\(\chi_{9702}(1643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)
\(\chi_{9702}(1769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)
\(\chi_{9702}(1895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)
\(\chi_{9702}(2117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)
\(\chi_{9702}(2369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)
\(\chi_{9702}(2495,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)
\(\chi_{9702}(2621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)
\(\chi_{9702}(2777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)
\(\chi_{9702}(3029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)
\(\chi_{9702}(3281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)
\(\chi_{9702}(3503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)
\(\chi_{9702}(3881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)
\(\chi_{9702}(4007,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)
\(\chi_{9702}(4163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{16}{105}\right)\)
\(\chi_{9702}(4415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)
\(\chi_{9702}(4541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)
\(\chi_{9702}(4667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)
\(\chi_{9702}(4889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)
\(\chi_{9702}(5141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)
\(\chi_{9702}(5267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)
\(\chi_{9702}(5393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)
\(\chi_{9702}(5549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)
\(\chi_{9702}(5927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)
\(\chi_{9702}(6053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)
\(\chi_{9702}(6275,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)

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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.fl
Modulus	$9702$
Conductor	$4851$
Order	$210$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(9702\)
Conductor:	\(4851\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(210\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4851.fc	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)