LMFDB - Dirichlet character orbit 1576.bj

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1576, base_ring=CyclotomicField(196)) M = H._module chi = DirichletCharacter(H, M([0,0,159])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(17,1576)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1576$
Conductor:	$197$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$196$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 197.i	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{196})$
Fixed field:	Number field defined by a degree 196 polynomial (not computed)

First 31 of 84 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{1576}(17,\cdot)$	$-1$	$1$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{53}{196}\right)$
$\chi_{1576}(57,\cdot)$	$-1$	$1$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{23}{196}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{143}{196}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{149}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{177}{196}\right)$
$\chi_{1576}(73,\cdot)$	$-1$	$1$	$e\left(\frac{109}{196}\right)$	$e\left(\frac{85}{196}\right)$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{145}{196}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{99}{196}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{15}{196}\right)$
$\chi_{1576}(89,\cdot)$	$-1$	$1$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{191}{196}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{27}{196}\right)$	$e\left(\frac{3}{196}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{121}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{149}{196}\right)$
$\chi_{1576}(145,\cdot)$	$-1$	$1$	$e\left(\frac{85}{196}\right)$	$e\left(\frac{149}{196}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{85}{98}\right)$	$e\left(\frac{97}{196}\right)$	$e\left(\frac{185}{196}\right)$	$e\left(\frac{19}{98}\right)$	$e\left(\frac{79}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{107}{196}\right)$
$\chi_{1576}(153,\cdot)$	$-1$	$1$	$e\left(\frac{25}{196}\right)$	$e\left(\frac{113}{196}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{17}{196}\right)$	$e\left(\frac{89}{196}\right)$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{127}{196}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{43}{196}\right)$
$\chi_{1576}(185,\cdot)$	$-1$	$1$	$e\left(\frac{97}{196}\right)$	$e\left(\frac{117}{196}\right)$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{113}{196}\right)$	$e\left(\frac{165}{196}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{187}{196}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{159}{196}\right)$
$\chi_{1576}(209,\cdot)$	$-1$	$1$	$e\left(\frac{195}{196}\right)$	$e\left(\frac{19}{196}\right)$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{15}{196}\right)$	$e\left(\frac{67}{196}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{89}{196}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{61}{196}\right)$
$\chi_{1576}(241,\cdot)$	$-1$	$1$	$e\left(\frac{123}{196}\right)$	$e\left(\frac{15}{196}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{115}{196}\right)$	$e\left(\frac{187}{196}\right)$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{29}{196}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{141}{196}\right)$
$\chi_{1576}(249,\cdot)$	$-1$	$1$	$e\left(\frac{183}{196}\right)$	$e\left(\frac{51}{196}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{85}{98}\right)$	$e\left(\frac{195}{196}\right)$	$e\left(\frac{87}{196}\right)$	$e\left(\frac{19}{98}\right)$	$e\left(\frac{177}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{196}\right)$
$\chi_{1576}(305,\cdot)$	$-1$	$1$	$e\left(\frac{57}{196}\right)$	$e\left(\frac{93}{196}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{125}{196}\right)$	$e\left(\frac{101}{196}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{23}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{51}{196}\right)$
$\chi_{1576}(321,\cdot)$	$-1$	$1$	$e\left(\frac{11}{196}\right)$	$e\left(\frac{183}{196}\right)$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{31}{196}\right)$	$e\left(\frac{47}{196}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{1}{196}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{113}{196}\right)$
$\chi_{1576}(337,\cdot)$	$-1$	$1$	$e\left(\frac{169}{196}\right)$	$e\left(\frac{121}{196}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{13}{196}\right)$	$e\left(\frac{45}{196}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{51}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{79}{196}\right)$
$\chi_{1576}(377,\cdot)$	$-1$	$1$	$e\left(\frac{65}{196}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{153}{196}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{151}{196}\right)$
$\chi_{1576}(425,\cdot)$	$-1$	$1$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{169}{196}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{47}{196}\right)$
$\chi_{1576}(465,\cdot)$	$-1$	$1$	$e\left(\frac{107}{196}\right)$	$e\left(\frac{123}{196}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{159}{196}\right)$	$e\left(\frac{83}{196}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{81}{196}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{137}{196}\right)$
$\chi_{1576}(473,\cdot)$	$-1$	$1$	$e\left(\frac{159}{196}\right)$	$e\left(\frac{115}{196}\right)$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{127}{196}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{157}{196}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{101}{196}\right)$
$\chi_{1576}(489,\cdot)$	$-1$	$1$	$e\left(\frac{79}{196}\right)$	$e\left(\frac{67}{196}\right)$	$e\left(\frac{1}{98}\right)$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{187}{196}\right)$	$e\left(\frac{195}{196}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{25}{196}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{81}{196}\right)$
$\chi_{1576}(497,\cdot)$	$-1$	$1$	$e\left(\frac{73}{196}\right)$	$e\left(\frac{181}{196}\right)$	$e\left(\frac{89}{98}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{81}{196}\right)$	$e\left(\frac{9}{196}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{167}{196}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{55}{196}\right)$
$\chi_{1576}(505,\cdot)$	$-1$	$1$	$e\left(\frac{89}{196}\right)$	$e\left(\frac{73}{196}\right)$	$e\left(\frac{83}{98}\right)$	$e\left(\frac{89}{98}\right)$	$e\left(\frac{37}{196}\right)$	$e\left(\frac{113}{196}\right)$	$e\left(\frac{81}{98}\right)$	$e\left(\frac{115}{196}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{59}{196}\right)$
$\chi_{1576}(513,\cdot)$	$-1$	$1$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{97}{196}\right)$	$e\left(\frac{19}{98}\right)$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{25}{196}\right)$	$e\left(\frac{177}{196}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{83}{196}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{167}{196}\right)$
$\chi_{1576}(545,\cdot)$	$-1$	$1$	$e\left(\frac{47}{196}\right)$	$e\left(\frac{87}{196}\right)$	$e\left(\frac{13}{98}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{79}{196}\right)$	$e\left(\frac{183}{196}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{73}{196}\right)$
$\chi_{1576}(553,\cdot)$	$-1$	$1$	$e\left(\frac{125}{196}\right)$	$e\left(\frac{173}{196}\right)$	$e\left(\frac{45}{98}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{85}{196}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{47}{196}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{196}\right)$
$\chi_{1576}(561,\cdot)$	$-1$	$1$	$e\left(\frac{149}{196}\right)$	$e\left(\frac{109}{196}\right)$	$e\left(\frac{85}{98}\right)$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{117}{196}\right)$	$e\left(\frac{13}{196}\right)$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{67}{196}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{123}{196}\right)$
$\chi_{1576}(593,\cdot)$	$-1$	$1$	$e\left(\frac{181}{196}\right)$	$e\left(\frac{89}{196}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{83}{98}\right)$	$e\left(\frac{29}{196}\right)$	$e\left(\frac{25}{196}\right)$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{159}{196}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{131}{196}\right)$
$\chi_{1576}(609,\cdot)$	$-1$	$1$	$e\left(\frac{43}{196}\right)$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{59}{196}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{93}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{121}{196}\right)$
$\chi_{1576}(641,\cdot)$	$-1$	$1$	$e\left(\frac{59}{196}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{125}{196}\right)$
$\chi_{1576}(649,\cdot)$	$-1$	$1$	$e\left(\frac{33}{196}\right)$	$e\left(\frac{157}{196}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{93}{196}\right)$	$e\left(\frac{141}{196}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{3}{196}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{143}{196}\right)$
$\chi_{1576}(657,\cdot)$	$-1$	$1$	$e\left(\frac{167}{196}\right)$	$e\left(\frac{159}{196}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{43}{196}\right)$	$e\left(\frac{179}{196}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{33}{196}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{196}\right)$
$\chi_{1576}(665,\cdot)$	$-1$	$1$	$e\left(\frac{45}{196}\right)$	$e\left(\frac{125}{196}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{45}{98}\right)$	$e\left(\frac{109}{196}\right)$	$e\left(\frac{121}{196}\right)$	$e\left(\frac{85}{98}\right)$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{195}{196}\right)$
$\chi_{1576}(673,\cdot)$	$-1$	$1$	$e\left(\frac{99}{196}\right)$	$e\left(\frac{79}{196}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{1}{98}\right)$	$e\left(\frac{83}{196}\right)$	$e\left(\frac{31}{196}\right)$	$e\left(\frac{89}{98}\right)$	$e\left(\frac{9}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{37}{196}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{1576}(17,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{53}{196}\right)\)
\(\chi_{1576}(57,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{23}{196}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{143}{196}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{149}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{177}{196}\right)\)
\(\chi_{1576}(73,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{196}\right)\)	\(e\left(\frac{85}{196}\right)\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{145}{196}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{99}{196}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{15}{196}\right)\)
\(\chi_{1576}(89,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{155}{196}\right)\)	\(e\left(\frac{191}{196}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{27}{196}\right)\)	\(e\left(\frac{3}{196}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{121}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{149}{196}\right)\)
\(\chi_{1576}(145,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{196}\right)\)	\(e\left(\frac{149}{196}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{85}{98}\right)\)	\(e\left(\frac{97}{196}\right)\)	\(e\left(\frac{185}{196}\right)\)	\(e\left(\frac{19}{98}\right)\)	\(e\left(\frac{79}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{107}{196}\right)\)
\(\chi_{1576}(153,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{196}\right)\)	\(e\left(\frac{113}{196}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{17}{196}\right)\)	\(e\left(\frac{89}{196}\right)\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{127}{196}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{43}{196}\right)\)
\(\chi_{1576}(185,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{196}\right)\)	\(e\left(\frac{117}{196}\right)\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{113}{196}\right)\)	\(e\left(\frac{165}{196}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{187}{196}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{159}{196}\right)\)
\(\chi_{1576}(209,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{195}{196}\right)\)	\(e\left(\frac{19}{196}\right)\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{15}{196}\right)\)	\(e\left(\frac{67}{196}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{89}{196}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{61}{196}\right)\)
\(\chi_{1576}(241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{123}{196}\right)\)	\(e\left(\frac{15}{196}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{115}{196}\right)\)	\(e\left(\frac{187}{196}\right)\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{29}{196}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{141}{196}\right)\)
\(\chi_{1576}(249,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{183}{196}\right)\)	\(e\left(\frac{51}{196}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{85}{98}\right)\)	\(e\left(\frac{195}{196}\right)\)	\(e\left(\frac{87}{196}\right)\)	\(e\left(\frac{19}{98}\right)\)	\(e\left(\frac{177}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{196}\right)\)
\(\chi_{1576}(305,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{196}\right)\)	\(e\left(\frac{93}{196}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{101}{196}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{23}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{51}{196}\right)\)
\(\chi_{1576}(321,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{196}\right)\)	\(e\left(\frac{183}{196}\right)\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{31}{196}\right)\)	\(e\left(\frac{47}{196}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{1}{196}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{113}{196}\right)\)
\(\chi_{1576}(337,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{196}\right)\)	\(e\left(\frac{121}{196}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{13}{196}\right)\)	\(e\left(\frac{45}{196}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{51}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{79}{196}\right)\)
\(\chi_{1576}(377,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{196}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{153}{196}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{95}{196}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{151}{196}\right)\)
\(\chi_{1576}(425,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{169}{196}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{47}{196}\right)\)
\(\chi_{1576}(465,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{196}\right)\)	\(e\left(\frac{123}{196}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{159}{196}\right)\)	\(e\left(\frac{83}{196}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{81}{196}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{137}{196}\right)\)
\(\chi_{1576}(473,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{159}{196}\right)\)	\(e\left(\frac{115}{196}\right)\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{127}{196}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{157}{196}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{101}{196}\right)\)
\(\chi_{1576}(489,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{196}\right)\)	\(e\left(\frac{67}{196}\right)\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{187}{196}\right)\)	\(e\left(\frac{195}{196}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{25}{196}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{81}{196}\right)\)
\(\chi_{1576}(497,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{196}\right)\)	\(e\left(\frac{181}{196}\right)\)	\(e\left(\frac{89}{98}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{81}{196}\right)\)	\(e\left(\frac{9}{196}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{167}{196}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{55}{196}\right)\)
\(\chi_{1576}(505,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{196}\right)\)	\(e\left(\frac{73}{196}\right)\)	\(e\left(\frac{83}{98}\right)\)	\(e\left(\frac{89}{98}\right)\)	\(e\left(\frac{37}{196}\right)\)	\(e\left(\frac{113}{196}\right)\)	\(e\left(\frac{81}{98}\right)\)	\(e\left(\frac{115}{196}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{59}{196}\right)\)
\(\chi_{1576}(513,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{97}{196}\right)\)	\(e\left(\frac{19}{98}\right)\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{25}{196}\right)\)	\(e\left(\frac{177}{196}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{83}{196}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{167}{196}\right)\)
\(\chi_{1576}(545,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{196}\right)\)	\(e\left(\frac{87}{196}\right)\)	\(e\left(\frac{13}{98}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{79}{196}\right)\)	\(e\left(\frac{183}{196}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{73}{196}\right)\)
\(\chi_{1576}(553,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{173}{196}\right)\)	\(e\left(\frac{45}{98}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{85}{196}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{47}{196}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{196}\right)\)
\(\chi_{1576}(561,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{196}\right)\)	\(e\left(\frac{109}{196}\right)\)	\(e\left(\frac{85}{98}\right)\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{117}{196}\right)\)	\(e\left(\frac{13}{196}\right)\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{67}{196}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{123}{196}\right)\)
\(\chi_{1576}(593,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{181}{196}\right)\)	\(e\left(\frac{89}{196}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{83}{98}\right)\)	\(e\left(\frac{29}{196}\right)\)	\(e\left(\frac{25}{196}\right)\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{159}{196}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{131}{196}\right)\)
\(\chi_{1576}(609,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{196}\right)\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{59}{196}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{93}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{121}{196}\right)\)
\(\chi_{1576}(641,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{196}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{95}{196}\right)\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{125}{196}\right)\)
\(\chi_{1576}(649,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{196}\right)\)	\(e\left(\frac{157}{196}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{93}{196}\right)\)	\(e\left(\frac{141}{196}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{3}{196}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{143}{196}\right)\)
\(\chi_{1576}(657,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{196}\right)\)	\(e\left(\frac{159}{196}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{43}{196}\right)\)	\(e\left(\frac{179}{196}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{33}{196}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{196}\right)\)
\(\chi_{1576}(665,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{196}\right)\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{45}{98}\right)\)	\(e\left(\frac{109}{196}\right)\)	\(e\left(\frac{121}{196}\right)\)	\(e\left(\frac{85}{98}\right)\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{195}{196}\right)\)
\(\chi_{1576}(673,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{99}{196}\right)\)	\(e\left(\frac{79}{196}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{83}{196}\right)\)	\(e\left(\frac{31}{196}\right)\)	\(e\left(\frac{89}{98}\right)\)	\(e\left(\frac{9}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{37}{196}\right)\)

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First 31 of 84 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	1576.bj
Modulus	$1576$
Conductor	$197$
Order	$196$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(1576\)
Conductor:	\(197\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(196\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 197.i	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)