LMFDB - Dirichlet character orbit 8624.ha

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8624, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([0,0,125,189])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(17, 8624)) 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("8624.17"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8624$	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:	$210$	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.bf	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
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 210 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$13$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{8624}(17,\cdot)$	$1$	$1$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{8624}(145,\cdot)$	$1$	$1$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{53}{70}\right)$
$\chi_{8624}(369,\cdot)$	$1$	$1$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{57}{70}\right)$
$\chi_{8624}(481,\cdot)$	$1$	$1$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{59}{70}\right)$
$\chi_{8624}(689,\cdot)$	$1$	$1$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{61}{70}\right)$
$\chi_{8624}(1025,\cdot)$	$1$	$1$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{43}{70}\right)$
$\chi_{8624}(1041,\cdot)$	$1$	$1$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{41}{70}\right)$
$\chi_{8624}(1249,\cdot)$	$1$	$1$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{17}{70}\right)$
$\chi_{8624}(1361,\cdot)$	$1$	$1$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{39}{70}\right)$
$\chi_{8624}(1377,\cdot)$	$1$	$1$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{33}{70}\right)$
$\chi_{8624}(1601,\cdot)$	$1$	$1$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{37}{70}\right)$
$\chi_{8624}(1713,\cdot)$	$1$	$1$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{39}{70}\right)$
$\chi_{8624}(1921,\cdot)$	$1$	$1$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{51}{70}\right)$
$\chi_{8624}(2257,\cdot)$	$1$	$1$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{33}{70}\right)$
$\chi_{8624}(2593,\cdot)$	$1$	$1$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{29}{70}\right)$
$\chi_{8624}(2609,\cdot)$	$1$	$1$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{13}{70}\right)$
$\chi_{8624}(2833,\cdot)$	$1$	$1$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{17}{70}\right)$
$\chi_{8624}(2945,\cdot)$	$1$	$1$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{8624}(3153,\cdot)$	$1$	$1$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{41}{70}\right)$
$\chi_{8624}(3489,\cdot)$	$1$	$1$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{23}{70}\right)$
$\chi_{8624}(3505,\cdot)$	$1$	$1$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{1}{70}\right)$
$\chi_{8624}(3713,\cdot)$	$1$	$1$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{67}{70}\right)$
$\chi_{8624}(3825,\cdot)$	$1$	$1$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{8624}(4065,\cdot)$	$1$	$1$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{67}{70}\right)$
$\chi_{8624}(4177,\cdot)$	$1$	$1$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{69}{70}\right)$
$\chi_{8624}(4385,\cdot)$	$1$	$1$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{8624}(4721,\cdot)$	$1$	$1$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{13}{70}\right)$
$\chi_{8624}(4737,\cdot)$	$1$	$1$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{51}{70}\right)$
$\chi_{8624}(4945,\cdot)$	$1$	$1$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{57}{70}\right)$
$\chi_{8624}(5057,\cdot)$	$1$	$1$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{9}{70}\right)$
$\chi_{8624}(5073,\cdot)$	$1$	$1$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{43}{70}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{8624}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)
\(\chi_{8624}(145,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{53}{70}\right)\)
\(\chi_{8624}(369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{57}{70}\right)\)
\(\chi_{8624}(481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)
\(\chi_{8624}(689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{61}{70}\right)\)
\(\chi_{8624}(1025,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)
\(\chi_{8624}(1041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{41}{70}\right)\)
\(\chi_{8624}(1249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{17}{70}\right)\)
\(\chi_{8624}(1361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)
\(\chi_{8624}(1377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)
\(\chi_{8624}(1601,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{37}{70}\right)\)
\(\chi_{8624}(1713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)
\(\chi_{8624}(1921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)
\(\chi_{8624}(2257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)
\(\chi_{8624}(2593,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)
\(\chi_{8624}(2609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)
\(\chi_{8624}(2833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{17}{70}\right)\)
\(\chi_{8624}(2945,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{8624}(3153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{41}{70}\right)\)
\(\chi_{8624}(3489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{23}{70}\right)\)
\(\chi_{8624}(3505,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{1}{70}\right)\)
\(\chi_{8624}(3713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)
\(\chi_{8624}(3825,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{8624}(4065,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)
\(\chi_{8624}(4177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)
\(\chi_{8624}(4385,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{31}{70}\right)\)
\(\chi_{8624}(4721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)
\(\chi_{8624}(4737,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)
\(\chi_{8624}(4945,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{57}{70}\right)\)
\(\chi_{8624}(5057,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)
\(\chi_{8624}(5073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)

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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	8624.ha
Modulus	$8624$
Conductor	$539$
Order	$210$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(8624\)	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:	\(210\)	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.bf	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);