LMFDB - Dirichlet character orbit 3234.cf

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3234, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([105,145,84])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,3234)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3234$
Conductor:	$1617$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$210$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1617.ci	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	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{3234}(5,\cdot)$	$1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{3234}(47,\cdot)$	$1$	$1$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{3234}(59,\cdot)$	$1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{3234}(185,\cdot)$	$1$	$1$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{3234}(257,\cdot)$	$1$	$1$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{3234}(269,\cdot)$	$1$	$1$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{3234}(311,\cdot)$	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{3234}(383,\cdot)$	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{3234}(467,\cdot)$	$1$	$1$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{3234}(647,\cdot)$	$1$	$1$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{3234}(719,\cdot)$	$1$	$1$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{3234}(731,\cdot)$	$1$	$1$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{3234}(773,\cdot)$	$1$	$1$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{3234}(845,\cdot)$	$1$	$1$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{3234}(929,\cdot)$	$1$	$1$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{3234}(971,\cdot)$	$1$	$1$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{3234}(983,\cdot)$	$1$	$1$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{3234}(1181,\cdot)$	$1$	$1$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{3234}(1193,\cdot)$	$1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{3234}(1235,\cdot)$	$1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{3234}(1307,\cdot)$	$1$	$1$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{3234}(1433,\cdot)$	$1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{3234}(1445,\cdot)$	$1$	$1$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{3234}(1571,\cdot)$	$1$	$1$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{3234}(1643,\cdot)$	$1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{3234}(1655,\cdot)$	$1$	$1$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{3234}(1769,\cdot)$	$1$	$1$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{3234}(1853,\cdot)$	$1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{3234}(1895,\cdot)$	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{3234}(1907,\cdot)$	$1$	$1$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{3234}(2033,\cdot)$	$1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{18}{35}\right)$

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	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{3234}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{3234}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{3234}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{3234}(185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{3234}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{3234}(269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{3234}(311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{3234}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{3234}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{3234}(647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{3234}(719,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{3234}(731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{3234}(773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{3234}(845,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{3234}(929,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{3234}(971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{3234}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{3234}(1181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{3234}(1193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{3234}(1235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{3234}(1307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{3234}(1433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{3234}(1445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{3234}(1571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{3234}(1643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{3234}(1655,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{3234}(1769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{3234}(1853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{3234}(1895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{3234}(1907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{3234}(2033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)

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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	3234.cf
Modulus	$3234$
Conductor	$1617$
Order	$210$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(3234\)
Conductor:	\(1617\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(210\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1617.ci	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)