LMFDB - Dirichlet character orbit 1450.bn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1450, base_ring=CyclotomicField(140)) M = H._module chi = DirichletCharacter(H, M([49,25])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(3,1450)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1450$
Conductor:	$725$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$140$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 725.bi	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:	$\Q(\zeta_{140})$
Fixed field:	Number field defined by a degree 140 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{1450}(3,\cdot)$	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{1450}(27,\cdot)$	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{1450}(37,\cdot)$	$1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{1450}(47,\cdot)$	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{1450}(97,\cdot)$	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{1450}(247,\cdot)$	$1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{1450}(253,\cdot)$	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{1450}(263,\cdot)$	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{1450}(287,\cdot)$	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{1450}(317,\cdot)$	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{1450}(327,\cdot)$	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{1450}(333,\cdot)$	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{1450}(337,\cdot)$	$1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{1450}(387,\cdot)$	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{1450}(483,\cdot)$	$1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{1450}(533,\cdot)$	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{1450}(537,\cdot)$	$1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{1450}(553,\cdot)$	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{1450}(577,\cdot)$	$1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{1450}(583,\cdot)$	$1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{1450}(617,\cdot)$	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{1450}(623,\cdot)$	$1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{1450}(627,\cdot)$	$1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{1450}(677,\cdot)$	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{1450}(773,\cdot)$	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{1450}(823,\cdot)$	$1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{1450}(827,\cdot)$	$1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{1450}(833,\cdot)$	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{1450}(867,\cdot)$	$1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{1450}(873,\cdot)$	$1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{1450}(897,\cdot)$	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{31}{35}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{1450}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{1450}(27,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{1450}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{1450}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{1450}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{1450}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{1450}(253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{1450}(263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{1450}(287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{1450}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{1450}(327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{1450}(333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{1450}(337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{1450}(387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{1450}(483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{1450}(533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{1450}(537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{1450}(553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{1450}(577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{1450}(583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{1450}(617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{1450}(623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{1450}(627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{1450}(677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{1450}(773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{1450}(823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{1450}(827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{1450}(833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{1450}(867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{1450}(873,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{1450}(897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{31}{35}\right)\)

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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	1450.bn
Modulus	$1450$
Conductor	$725$
Order	$140$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(1450\)
Conductor:	\(725\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(140\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 725.bi	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)