LMFDB - Dirichlet character orbit 8450.cs

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8450, base_ring=CyclotomicField(260)) M = H._module chi = DirichletCharacter(H, M([156,125])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(21,8450)) 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.cr	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:	$\Q(\zeta_{260})$
Fixed field:	Number field defined by a degree 260 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{8450}(21,\cdot)$	$-1$	$1$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{28}{65}\right)$
$\chi_{8450}(31,\cdot)$	$-1$	$1$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{233}{260}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{12}{65}\right)$
$\chi_{8450}(161,\cdot)$	$-1$	$1$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{73}{260}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{141}{260}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{24}{65}\right)$
$\chi_{8450}(281,\cdot)$	$-1$	$1$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{179}{260}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{17}{65}\right)$
$\chi_{8450}(291,\cdot)$	$-1$	$1$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{77}{260}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{49}{260}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{36}{65}\right)$
$\chi_{8450}(411,\cdot)$	$-1$	$1$	$e\left(\frac{9}{65}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{18}{65}\right)$	$e\left(\frac{123}{260}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{44}{65}\right)$
$\chi_{8450}(421,\cdot)$	$-1$	$1$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{81}{260}\right)$	$e\left(\frac{119}{130}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{48}{65}\right)$
$\chi_{8450}(541,\cdot)$	$-1$	$1$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{260}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{6}{65}\right)$
$\chi_{8450}(671,\cdot)$	$-1$	$1$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{11}{260}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{33}{65}\right)$
$\chi_{8450}(681,\cdot)$	$-1$	$1$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{89}{260}\right)$	$e\left(\frac{81}{130}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{33}{260}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{7}{65}\right)$
$\chi_{8450}(811,\cdot)$	$-1$	$1$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{93}{260}\right)$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{19}{65}\right)$
$\chi_{8450}(931,\cdot)$	$-1$	$1$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{9}{65}\right)$	$e\left(\frac{159}{260}\right)$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{243}{260}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{22}{65}\right)$
$\chi_{8450}(941,\cdot)$	$-1$	$1$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{97}{260}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{109}{260}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{31}{65}\right)$
$\chi_{8450}(1061,\cdot)$	$-1$	$1$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{103}{260}\right)$	$e\left(\frac{47}{130}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{231}{260}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{49}{65}\right)$
$\chi_{8450}(1071,\cdot)$	$-1$	$1$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{101}{260}\right)$	$e\left(\frac{89}{130}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{260}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{43}{65}\right)$
$\chi_{8450}(1191,\cdot)$	$-1$	$1$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{47}{260}\right)$	$e\left(\frac{53}{130}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{219}{260}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{11}{65}\right)$
$\chi_{8450}(1321,\cdot)$	$-1$	$1$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{251}{260}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{207}{260}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{38}{65}\right)$
$\chi_{8450}(1331,\cdot)$	$-1$	$1$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{109}{260}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{93}{260}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{2}{65}\right)$
$\chi_{8450}(1461,\cdot)$	$-1$	$1$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{113}{260}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{260}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{47}{65}\right)$	$e\left(\frac{14}{65}\right)$
$\chi_{8450}(1581,\cdot)$	$-1$	$1$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{139}{260}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{183}{260}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{21}{65}\right)$	$e\left(\frac{27}{65}\right)$
$\chi_{8450}(1711,\cdot)$	$-1$	$1$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{83}{260}\right)$	$e\left(\frac{77}{130}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{171}{260}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{54}{65}\right)$
$\chi_{8450}(1721,\cdot)$	$-1$	$1$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{121}{260}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{77}{260}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{38}{65}\right)$
$\chi_{8450}(1841,\cdot)$	$-1$	$1$	$e\left(\frac{21}{65}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{27}{260}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{159}{260}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{16}{65}\right)$
$\chi_{8450}(1971,\cdot)$	$-1$	$1$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{231}{260}\right)$	$e\left(\frac{89}{130}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{147}{260}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{43}{65}\right)$
$\chi_{8450}(1981,\cdot)$	$-1$	$1$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{129}{260}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{62}{65}\right)$
$\chi_{8450}(2111,\cdot)$	$-1$	$1$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{133}{260}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{61}{260}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{9}{65}\right)$
$\chi_{8450}(2231,\cdot)$	$-1$	$1$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{119}{260}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{123}{260}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{32}{65}\right)$
$\chi_{8450}(2241,\cdot)$	$-1$	$1$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{47}{65}\right)$	$e\left(\frac{137}{260}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{229}{260}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{21}{65}\right)$
$\chi_{8450}(2361,\cdot)$	$-1$	$1$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{63}{260}\right)$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{111}{260}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{65}\right)$	$e\left(\frac{59}{65}\right)$
$\chi_{8450}(2371,\cdot)$	$-1$	$1$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{141}{260}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{137}{260}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{33}{65}\right)$
$\chi_{8450}(2491,\cdot)$	$-1$	$1$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{47}{65}\right)$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{99}{260}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{21}{65}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{8450}(21,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{28}{65}\right)\)
\(\chi_{8450}(31,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{233}{260}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{12}{65}\right)\)
\(\chi_{8450}(161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{73}{260}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{141}{260}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{24}{65}\right)\)
\(\chi_{8450}(281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{179}{260}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{17}{65}\right)\)
\(\chi_{8450}(291,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{77}{260}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{49}{260}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{36}{65}\right)\)
\(\chi_{8450}(411,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{65}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{18}{65}\right)\)	\(e\left(\frac{123}{260}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{44}{65}\right)\)
\(\chi_{8450}(421,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{81}{260}\right)\)	\(e\left(\frac{119}{130}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{48}{65}\right)\)
\(\chi_{8450}(541,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{260}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{6}{65}\right)\)
\(\chi_{8450}(671,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{11}{260}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{33}{65}\right)\)
\(\chi_{8450}(681,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{89}{260}\right)\)	\(e\left(\frac{81}{130}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{33}{260}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{7}{65}\right)\)
\(\chi_{8450}(811,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{93}{260}\right)\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{19}{65}\right)\)
\(\chi_{8450}(931,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{9}{65}\right)\)	\(e\left(\frac{159}{260}\right)\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{243}{260}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{22}{65}\right)\)
\(\chi_{8450}(941,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{97}{260}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{109}{260}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{31}{65}\right)\)
\(\chi_{8450}(1061,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{103}{260}\right)\)	\(e\left(\frac{47}{130}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{231}{260}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{49}{65}\right)\)
\(\chi_{8450}(1071,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{101}{260}\right)\)	\(e\left(\frac{89}{130}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{260}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{43}{65}\right)\)
\(\chi_{8450}(1191,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{47}{260}\right)\)	\(e\left(\frac{53}{130}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{219}{260}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{11}{65}\right)\)
\(\chi_{8450}(1321,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{251}{260}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{207}{260}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{38}{65}\right)\)
\(\chi_{8450}(1331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{109}{260}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{93}{260}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{2}{65}\right)\)
\(\chi_{8450}(1461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{113}{260}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{260}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{47}{65}\right)\)	\(e\left(\frac{14}{65}\right)\)
\(\chi_{8450}(1581,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{139}{260}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{183}{260}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{21}{65}\right)\)	\(e\left(\frac{27}{65}\right)\)
\(\chi_{8450}(1711,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{83}{260}\right)\)	\(e\left(\frac{77}{130}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{171}{260}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{42}{65}\right)\)	\(e\left(\frac{54}{65}\right)\)
\(\chi_{8450}(1721,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{121}{260}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{77}{260}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{38}{65}\right)\)
\(\chi_{8450}(1841,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{65}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{42}{65}\right)\)	\(e\left(\frac{27}{260}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{159}{260}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{16}{65}\right)\)
\(\chi_{8450}(1971,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{231}{260}\right)\)	\(e\left(\frac{89}{130}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{147}{260}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{43}{65}\right)\)
\(\chi_{8450}(1981,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{129}{260}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{62}{65}\right)\)
\(\chi_{8450}(2111,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{133}{260}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{61}{260}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{9}{65}\right)\)
\(\chi_{8450}(2231,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{42}{65}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{119}{260}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{123}{260}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{32}{65}\right)\)
\(\chi_{8450}(2241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{47}{65}\right)\)	\(e\left(\frac{137}{260}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{229}{260}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{21}{65}\right)\)
\(\chi_{8450}(2361,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{63}{260}\right)\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{111}{260}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{65}\right)\)	\(e\left(\frac{59}{65}\right)\)
\(\chi_{8450}(2371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{141}{260}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{137}{260}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{33}{65}\right)\)
\(\chi_{8450}(2491,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{47}{65}\right)\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{99}{260}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{21}{65}\right)\)

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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.cs
Modulus	$8450$
Conductor	$4225$
Order	$260$
Real	no
Primitive	no
Minimal	yes
Parity	odd

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.cr	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)