LMFDB - Dirichlet character orbit 9800.gi

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9800, base_ring=CyclotomicField(140)) M = H._module chi = DirichletCharacter(H, M([0,70,133,110])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,9800)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9800$
Conductor:	$9800$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$140$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{9800}(13,\cdot)$	$1$	$1$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{9800}(237,\cdot)$	$1$	$1$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{9800}(517,\cdot)$	$1$	$1$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{9800}(573,\cdot)$	$1$	$1$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{9800}(797,\cdot)$	$1$	$1$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{9800}(853,\cdot)$	$1$	$1$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{9800}(1133,\cdot)$	$1$	$1$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{9800}(1413,\cdot)$	$1$	$1$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{9800}(1637,\cdot)$	$1$	$1$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{9800}(1917,\cdot)$	$1$	$1$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{9800}(1973,\cdot)$	$1$	$1$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{9800}(2197,\cdot)$	$1$	$1$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{9800}(2477,\cdot)$	$1$	$1$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{9800}(2533,\cdot)$	$1$	$1$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{9800}(2813,\cdot)$	$1$	$1$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{9800}(3317,\cdot)$	$1$	$1$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{9800}(3373,\cdot)$	$1$	$1$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{9800}(3597,\cdot)$	$1$	$1$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{9800}(3653,\cdot)$	$1$	$1$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{9800}(3877,\cdot)$	$1$	$1$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{9800}(3933,\cdot)$	$1$	$1$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{9800}(4437,\cdot)$	$1$	$1$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{9800}(4717,\cdot)$	$1$	$1$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{9800}(4773,\cdot)$	$1$	$1$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{9800}(5053,\cdot)$	$1$	$1$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{9800}(5277,\cdot)$	$1$	$1$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{9800}(5333,\cdot)$	$1$	$1$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{9800}(5613,\cdot)$	$1$	$1$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{9800}(5837,\cdot)$	$1$	$1$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{9800}(6117,\cdot)$	$1$	$1$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{9800}(6397,\cdot)$	$1$	$1$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{10}\right)$

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	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{9800}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{9800}(237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{9800}(517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{9800}(573,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{9800}(797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{9800}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{9800}(1133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{9800}(1413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{9800}(1637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{9800}(1917,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{9800}(1973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{9800}(2197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{9800}(2477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{9800}(2533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{9800}(2813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{9800}(3317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{9800}(3373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{9800}(3597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{9800}(3653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{9800}(3877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{9800}(3933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{9800}(4437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{9800}(4717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{9800}(4773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{9800}(5053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{9800}(5277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{9800}(5333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{9800}(5613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{9800}(5837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{9800}(6117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{9800}(6397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)

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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	9800.gi
Modulus	$9800$
Conductor	$9800$
Order	$140$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(9800\)
Conductor:	\(9800\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(140\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)