LMFDB - Dirichlet character orbit 8450.cr

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8450, base_ring=CyclotomicField(260)) M = H._module chi = DirichletCharacter(H, M([143,85])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(73,8450)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8450$
Conductor:	$4225$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$260$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4225.cs	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:	$\Q(\zeta_{260})$
Fixed field:	Number field defined by a degree 260 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{8450}(73,\cdot)$	$1$	$1$	$e\left(\frac{101}{260}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{123}{260}\right)$	$e\left(\frac{229}{260}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{23}{130}\right)$
$\chi_{8450}(187,\cdot)$	$1$	$1$	$e\left(\frac{19}{260}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{19}{130}\right)$	$e\left(\frac{157}{260}\right)$	$e\left(\frac{231}{260}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{260}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{57}{260}\right)$	$e\left(\frac{97}{130}\right)$
$\chi_{8450}(203,\cdot)$	$1$	$1$	$e\left(\frac{77}{260}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{77}{130}\right)$	$e\left(\frac{171}{260}\right)$	$e\left(\frac{33}{260}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{227}{260}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{231}{260}\right)$	$e\left(\frac{51}{130}\right)$
$\chi_{8450}(317,\cdot)$	$1$	$1$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{109}{260}\right)$	$e\left(\frac{167}{260}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{93}{260}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{129}{260}\right)$	$e\left(\frac{69}{130}\right)$
$\chi_{8450}(333,\cdot)$	$1$	$1$	$e\left(\frac{53}{260}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{53}{130}\right)$	$e\left(\frac{219}{260}\right)$	$e\left(\frac{97}{260}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{163}{260}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{159}{260}\right)$	$e\left(\frac{79}{130}\right)$
$\chi_{8450}(447,\cdot)$	$1$	$1$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{61}{260}\right)$	$e\left(\frac{103}{260}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{157}{260}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{41}{130}\right)$
$\chi_{8450}(463,\cdot)$	$1$	$1$	$e\left(\frac{29}{260}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{161}{260}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{99}{260}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{87}{260}\right)$	$e\left(\frac{107}{130}\right)$
$\chi_{8450}(723,\cdot)$	$1$	$1$	$e\left(\frac{241}{260}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{103}{260}\right)$	$e\left(\frac{29}{260}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{231}{260}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{203}{260}\right)$	$e\left(\frac{33}{130}\right)$
$\chi_{8450}(837,\cdot)$	$1$	$1$	$e\left(\frac{139}{260}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{9}{130}\right)$	$e\left(\frac{177}{260}\right)$	$e\left(\frac{171}{260}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{89}{260}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{157}{260}\right)$	$e\left(\frac{87}{130}\right)$
$\chi_{8450}(853,\cdot)$	$1$	$1$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{151}{260}\right)$	$e\left(\frac{93}{260}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{167}{260}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{131}{260}\right)$	$e\left(\frac{61}{130}\right)$
$\chi_{8450}(967,\cdot)$	$1$	$1$	$e\left(\frac{163}{260}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{129}{260}\right)$	$e\left(\frac{107}{260}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{229}{260}\right)$	$e\left(\frac{59}{130}\right)$
$\chi_{8450}(983,\cdot)$	$1$	$1$	$e\left(\frac{193}{260}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{63}{130}\right)$	$e\left(\frac{199}{260}\right)$	$e\left(\frac{157}{260}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{103}{260}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{59}{260}\right)$	$e\left(\frac{89}{130}\right)$
$\chi_{8450}(1097,\cdot)$	$1$	$1$	$e\left(\frac{187}{260}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{57}{130}\right)$	$e\left(\frac{81}{260}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{41}{260}\right)$	$e\left(\frac{31}{130}\right)$
$\chi_{8450}(1227,\cdot)$	$1$	$1$	$e\left(\frac{211}{260}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{81}{130}\right)$	$e\left(\frac{33}{260}\right)$	$e\left(\frac{239}{260}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{21}{260}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{113}{260}\right)$	$e\left(\frac{3}{130}\right)$
$\chi_{8450}(1373,\cdot)$	$1$	$1$	$e\left(\frac{121}{260}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{121}{130}\right)$	$e\left(\frac{83}{260}\right)$	$e\left(\frac{89}{260}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{171}{260}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{103}{260}\right)$	$e\left(\frac{43}{130}\right)$
$\chi_{8450}(1487,\cdot)$	$1$	$1$	$e\left(\frac{259}{260}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{197}{260}\right)$	$e\left(\frac{111}{260}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{149}{260}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{257}{260}\right)$	$e\left(\frac{77}{130}\right)$
$\chi_{8450}(1503,\cdot)$	$1$	$1$	$e\left(\frac{97}{260}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{131}{260}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{107}{260}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{71}{130}\right)$
$\chi_{8450}(1617,\cdot)$	$1$	$1$	$e\left(\frac{23}{260}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{149}{260}\right)$	$e\left(\frac{47}{260}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{49}{130}\right)$
$\chi_{8450}(1633,\cdot)$	$1$	$1$	$e\left(\frac{73}{260}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{179}{260}\right)$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{219}{260}\right)$	$e\left(\frac{99}{130}\right)$
$\chi_{8450}(1747,\cdot)$	$1$	$1$	$e\left(\frac{47}{260}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{47}{130}\right)$	$e\left(\frac{101}{260}\right)$	$e\left(\frac{243}{260}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{260}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{141}{260}\right)$	$e\left(\frac{21}{130}\right)$
$\chi_{8450}(1763,\cdot)$	$1$	$1$	$e\left(\frac{49}{260}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{49}{130}\right)$	$e\left(\frac{227}{260}\right)$	$e\left(\frac{21}{260}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{239}{260}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{147}{260}\right)$	$e\left(\frac{127}{130}\right)$
$\chi_{8450}(1877,\cdot)$	$1$	$1$	$e\left(\frac{71}{260}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{53}{260}\right)$	$e\left(\frac{179}{260}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{81}{260}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{123}{130}\right)$
$\chi_{8450}(2023,\cdot)$	$1$	$1$	$e\left(\frac{1}{260}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{63}{260}\right)$	$e\left(\frac{149}{260}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{111}{260}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{260}\right)$	$e\left(\frac{53}{130}\right)$
$\chi_{8450}(2137,\cdot)$	$1$	$1$	$e\left(\frac{119}{260}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{119}{130}\right)$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{51}{260}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{209}{260}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{97}{260}\right)$	$e\left(\frac{67}{130}\right)$
$\chi_{8450}(2153,\cdot)$	$1$	$1$	$e\left(\frac{237}{260}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{111}{260}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{47}{260}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{191}{260}\right)$	$e\left(\frac{81}{130}\right)$
$\chi_{8450}(2283,\cdot)$	$1$	$1$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{159}{260}\right)$	$e\left(\frac{17}{260}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{243}{260}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{119}{260}\right)$	$e\left(\frac{109}{130}\right)$
$\chi_{8450}(2397,\cdot)$	$1$	$1$	$e\left(\frac{167}{260}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{121}{260}\right)$	$e\left(\frac{183}{260}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{77}{260}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{241}{260}\right)$	$e\left(\frac{11}{130}\right)$
$\chi_{8450}(2413,\cdot)$	$1$	$1$	$e\left(\frac{189}{260}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{207}{260}\right)$	$e\left(\frac{81}{260}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{179}{260}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{47}{260}\right)$	$e\left(\frac{7}{130}\right)$
$\chi_{8450}(2527,\cdot)$	$1$	$1$	$e\left(\frac{191}{260}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{61}{130}\right)$	$e\left(\frac{73}{260}\right)$	$e\left(\frac{119}{260}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{141}{260}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{53}{260}\right)$	$e\left(\frac{113}{130}\right)$
$\chi_{8450}(2673,\cdot)$	$1$	$1$	$e\left(\frac{141}{260}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{209}{260}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{51}{260}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{163}{260}\right)$	$e\left(\frac{63}{130}\right)$
$\chi_{8450}(2787,\cdot)$	$1$	$1$	$e\left(\frac{239}{260}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{109}{130}\right)$	$e\left(\frac{237}{260}\right)$	$e\left(\frac{251}{260}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{260}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{197}{260}\right)$	$e\left(\frac{57}{130}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{8450}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{260}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{123}{260}\right)\)	\(e\left(\frac{229}{260}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{23}{130}\right)\)
\(\chi_{8450}(187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{260}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{19}{130}\right)\)	\(e\left(\frac{157}{260}\right)\)	\(e\left(\frac{231}{260}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{260}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{57}{260}\right)\)	\(e\left(\frac{97}{130}\right)\)
\(\chi_{8450}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{260}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{77}{130}\right)\)	\(e\left(\frac{171}{260}\right)\)	\(e\left(\frac{33}{260}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{227}{260}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{231}{260}\right)\)	\(e\left(\frac{51}{130}\right)\)
\(\chi_{8450}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{109}{260}\right)\)	\(e\left(\frac{167}{260}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{93}{260}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{129}{260}\right)\)	\(e\left(\frac{69}{130}\right)\)
\(\chi_{8450}(333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{260}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{53}{130}\right)\)	\(e\left(\frac{219}{260}\right)\)	\(e\left(\frac{97}{260}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{163}{260}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{159}{260}\right)\)	\(e\left(\frac{79}{130}\right)\)
\(\chi_{8450}(447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{61}{260}\right)\)	\(e\left(\frac{103}{260}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{157}{260}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{41}{130}\right)\)
\(\chi_{8450}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{260}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{161}{260}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{99}{260}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{87}{260}\right)\)	\(e\left(\frac{107}{130}\right)\)
\(\chi_{8450}(723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{241}{260}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{103}{260}\right)\)	\(e\left(\frac{29}{260}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{231}{260}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{203}{260}\right)\)	\(e\left(\frac{33}{130}\right)\)
\(\chi_{8450}(837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{260}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{9}{130}\right)\)	\(e\left(\frac{177}{260}\right)\)	\(e\left(\frac{171}{260}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{89}{260}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{157}{260}\right)\)	\(e\left(\frac{87}{130}\right)\)
\(\chi_{8450}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{151}{260}\right)\)	\(e\left(\frac{93}{260}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{167}{260}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{131}{260}\right)\)	\(e\left(\frac{61}{130}\right)\)
\(\chi_{8450}(967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{260}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{129}{260}\right)\)	\(e\left(\frac{107}{260}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{229}{260}\right)\)	\(e\left(\frac{59}{130}\right)\)
\(\chi_{8450}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{260}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{63}{130}\right)\)	\(e\left(\frac{199}{260}\right)\)	\(e\left(\frac{157}{260}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{103}{260}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{59}{260}\right)\)	\(e\left(\frac{89}{130}\right)\)
\(\chi_{8450}(1097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{260}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{57}{130}\right)\)	\(e\left(\frac{81}{260}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{41}{260}\right)\)	\(e\left(\frac{31}{130}\right)\)
\(\chi_{8450}(1227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{260}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{81}{130}\right)\)	\(e\left(\frac{33}{260}\right)\)	\(e\left(\frac{239}{260}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{21}{260}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{113}{260}\right)\)	\(e\left(\frac{3}{130}\right)\)
\(\chi_{8450}(1373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{260}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{121}{130}\right)\)	\(e\left(\frac{83}{260}\right)\)	\(e\left(\frac{89}{260}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{171}{260}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{103}{260}\right)\)	\(e\left(\frac{43}{130}\right)\)
\(\chi_{8450}(1487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{260}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{197}{260}\right)\)	\(e\left(\frac{111}{260}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{149}{260}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{257}{260}\right)\)	\(e\left(\frac{77}{130}\right)\)
\(\chi_{8450}(1503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{260}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{131}{260}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{107}{260}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{71}{130}\right)\)
\(\chi_{8450}(1617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{260}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{149}{260}\right)\)	\(e\left(\frac{47}{260}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{49}{130}\right)\)
\(\chi_{8450}(1633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{260}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{179}{260}\right)\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{219}{260}\right)\)	\(e\left(\frac{99}{130}\right)\)
\(\chi_{8450}(1747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{260}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{47}{130}\right)\)	\(e\left(\frac{101}{260}\right)\)	\(e\left(\frac{243}{260}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{260}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{141}{260}\right)\)	\(e\left(\frac{21}{130}\right)\)
\(\chi_{8450}(1763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{260}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{49}{130}\right)\)	\(e\left(\frac{227}{260}\right)\)	\(e\left(\frac{21}{260}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{239}{260}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{147}{260}\right)\)	\(e\left(\frac{127}{130}\right)\)
\(\chi_{8450}(1877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{260}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{53}{260}\right)\)	\(e\left(\frac{179}{260}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{81}{260}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{123}{130}\right)\)
\(\chi_{8450}(2023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{260}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{63}{260}\right)\)	\(e\left(\frac{149}{260}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{111}{260}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{260}\right)\)	\(e\left(\frac{53}{130}\right)\)
\(\chi_{8450}(2137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{260}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{119}{130}\right)\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{51}{260}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{209}{260}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{97}{260}\right)\)	\(e\left(\frac{67}{130}\right)\)
\(\chi_{8450}(2153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{237}{260}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{111}{260}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{47}{260}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{191}{260}\right)\)	\(e\left(\frac{81}{130}\right)\)
\(\chi_{8450}(2283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{159}{260}\right)\)	\(e\left(\frac{17}{260}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{243}{260}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{119}{260}\right)\)	\(e\left(\frac{109}{130}\right)\)
\(\chi_{8450}(2397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{260}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{121}{260}\right)\)	\(e\left(\frac{183}{260}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{77}{260}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{241}{260}\right)\)	\(e\left(\frac{11}{130}\right)\)
\(\chi_{8450}(2413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{189}{260}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{207}{260}\right)\)	\(e\left(\frac{81}{260}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{179}{260}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{47}{260}\right)\)	\(e\left(\frac{7}{130}\right)\)
\(\chi_{8450}(2527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{260}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{61}{130}\right)\)	\(e\left(\frac{73}{260}\right)\)	\(e\left(\frac{119}{260}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{141}{260}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{53}{260}\right)\)	\(e\left(\frac{113}{130}\right)\)
\(\chi_{8450}(2673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{141}{260}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{209}{260}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{51}{260}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{163}{260}\right)\)	\(e\left(\frac{63}{130}\right)\)
\(\chi_{8450}(2787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{260}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{109}{130}\right)\)	\(e\left(\frac{237}{260}\right)\)	\(e\left(\frac{251}{260}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{260}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{197}{260}\right)\)	\(e\left(\frac{57}{130}\right)\)

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First 31 of 96 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	8450.cr
Modulus	$8450$
Conductor	$4225$
Order	$260$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8450\)
Conductor:	\(4225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(260\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4225.cs	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)