LMFDB - Dirichlet character orbit 8450.cd

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8450, base_ring=CyclotomicField(130)) M = H._module chi = DirichletCharacter(H, M([13,75])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(129,8450)) 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:	$130$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4225.cf	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:	$\Q(\zeta_{65})$
Fixed field:	Number field defined by a degree 130 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{8450}(129,\cdot)$	$1$	$1$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{3}{130}\right)$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{61}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{93}{130}\right)$	$e\left(\frac{18}{65}\right)$
$\chi_{8450}(259,\cdot)$	$1$	$1$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{57}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{121}{130}\right)$	$e\left(\frac{36}{65}\right)$
$\chi_{8450}(389,\cdot)$	$1$	$1$	$e\left(\frac{93}{130}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{9}{130}\right)$	$e\left(\frac{77}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{53}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{130}\right)$	$e\left(\frac{54}{65}\right)$
$\chi_{8450}(519,\cdot)$	$1$	$1$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{77}{130}\right)$	$e\left(\frac{81}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{49}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{47}{130}\right)$	$e\left(\frac{7}{65}\right)$
$\chi_{8450}(779,\cdot)$	$1$	$1$	$e\left(\frac{121}{130}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{89}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{103}{130}\right)$	$e\left(\frac{43}{65}\right)$
$\chi_{8450}(909,\cdot)$	$1$	$1$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{93}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{61}{65}\right)$
$\chi_{8450}(1039,\cdot)$	$1$	$1$	$e\left(\frac{53}{130}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{89}{130}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{14}{65}\right)$
$\chi_{8450}(1169,\cdot)$	$1$	$1$	$e\left(\frac{19}{130}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{57}{130}\right)$	$e\left(\frac{32}{65}\right)$
$\chi_{8450}(1429,\cdot)$	$1$	$1$	$e\left(\frac{81}{130}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{109}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{3}{65}\right)$
$\chi_{8450}(1559,\cdot)$	$1$	$1$	$e\left(\frac{47}{130}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{47}{65}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{21}{65}\right)$
$\chi_{8450}(1819,\cdot)$	$1$	$1$	$e\left(\frac{109}{130}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{121}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{57}{65}\right)$
$\chi_{8450}(2079,\cdot)$	$1$	$1$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{123}{130}\right)$	$e\left(\frac{28}{65}\right)$
$\chi_{8450}(2209,\cdot)$	$1$	$1$	$e\left(\frac{7}{130}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{3}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{46}{65}\right)$
$\chi_{8450}(2339,\cdot)$	$1$	$1$	$e\left(\frac{103}{130}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{119}{130}\right)$	$e\left(\frac{7}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{123}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{49}{130}\right)$	$e\left(\frac{64}{65}\right)$
$\chi_{8450}(2469,\cdot)$	$1$	$1$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{57}{130}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{119}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{77}{130}\right)$	$e\left(\frac{17}{65}\right)$
$\chi_{8450}(2729,\cdot)$	$1$	$1$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{63}{130}\right)$	$e\left(\frac{19}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{130}\right)$	$e\left(\frac{53}{65}\right)$
$\chi_{8450}(2859,\cdot)$	$1$	$1$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{6}{65}\right)$
$\chi_{8450}(2989,\cdot)$	$1$	$1$	$e\left(\frac{63}{130}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{103}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{24}{65}\right)$
$\chi_{8450}(3119,\cdot)$	$1$	$1$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{7}{130}\right)$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{42}{65}\right)$
$\chi_{8450}(3509,\cdot)$	$1$	$1$	$e\left(\frac{57}{130}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{81}{130}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{31}{65}\right)$
$\chi_{8450}(3639,\cdot)$	$1$	$1$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{19}{130}\right)$	$e\left(\frac{47}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{49}{65}\right)$
$\chi_{8450}(3769,\cdot)$	$1$	$1$	$e\left(\frac{119}{130}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{2}{65}\right)$
$\chi_{8450}(4029,\cdot)$	$1$	$1$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{93}{130}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{38}{65}\right)$
$\chi_{8450}(4159,\cdot)$	$1$	$1$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{65}\right)$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{63}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{56}{65}\right)$
$\chi_{8450}(4289,\cdot)$	$1$	$1$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{63}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{9}{65}\right)$
$\chi_{8450}(4419,\cdot)$	$1$	$1$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{27}{65}\right)$
$\chi_{8450}(4679,\cdot)$	$1$	$1$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{63}{65}\right)$
$\chi_{8450}(4809,\cdot)$	$1$	$1$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{47}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{61}{130}\right)$	$e\left(\frac{16}{65}\right)$
$\chi_{8450}(4939,\cdot)$	$1$	$1$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{49}{130}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{89}{130}\right)$	$e\left(\frac{34}{65}\right)$
$\chi_{8450}(5329,\cdot)$	$1$	$1$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{123}{130}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{23}{65}\right)$
$\chi_{8450}(5459,\cdot)$	$1$	$1$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{61}{130}\right)$	$e\left(\frac{103}{130}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{41}{65}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{8450}(129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{3}{130}\right)\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{61}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{93}{130}\right)\)	\(e\left(\frac{18}{65}\right)\)
\(\chi_{8450}(259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{57}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{121}{130}\right)\)	\(e\left(\frac{36}{65}\right)\)
\(\chi_{8450}(389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{130}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{9}{130}\right)\)	\(e\left(\frac{77}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{53}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{130}\right)\)	\(e\left(\frac{54}{65}\right)\)
\(\chi_{8450}(519,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{77}{130}\right)\)	\(e\left(\frac{81}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{49}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{47}{130}\right)\)	\(e\left(\frac{7}{65}\right)\)
\(\chi_{8450}(779,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{130}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{89}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{103}{130}\right)\)	\(e\left(\frac{43}{65}\right)\)
\(\chi_{8450}(909,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{93}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{61}{65}\right)\)
\(\chi_{8450}(1039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{130}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{89}{130}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{14}{65}\right)\)
\(\chi_{8450}(1169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{130}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{57}{130}\right)\)	\(e\left(\frac{32}{65}\right)\)
\(\chi_{8450}(1429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{130}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{109}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{3}{65}\right)\)
\(\chi_{8450}(1559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{130}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{47}{65}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{21}{65}\right)\)
\(\chi_{8450}(1819,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{130}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{121}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{57}{65}\right)\)
\(\chi_{8450}(2079,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{123}{130}\right)\)	\(e\left(\frac{28}{65}\right)\)
\(\chi_{8450}(2209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{130}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{3}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{46}{65}\right)\)
\(\chi_{8450}(2339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{130}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{119}{130}\right)\)	\(e\left(\frac{7}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{123}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{49}{130}\right)\)	\(e\left(\frac{64}{65}\right)\)
\(\chi_{8450}(2469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{57}{130}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{119}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{77}{130}\right)\)	\(e\left(\frac{17}{65}\right)\)
\(\chi_{8450}(2729,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{63}{130}\right)\)	\(e\left(\frac{19}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{130}\right)\)	\(e\left(\frac{53}{65}\right)\)
\(\chi_{8450}(2859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{6}{65}\right)\)
\(\chi_{8450}(2989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{130}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{103}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{24}{65}\right)\)
\(\chi_{8450}(3119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{7}{130}\right)\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{42}{65}\right)\)
\(\chi_{8450}(3509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{130}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{81}{130}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{31}{65}\right)\)
\(\chi_{8450}(3639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{19}{130}\right)\)	\(e\left(\frac{47}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{49}{65}\right)\)
\(\chi_{8450}(3769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{130}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{2}{65}\right)\)
\(\chi_{8450}(4029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{93}{130}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{38}{65}\right)\)
\(\chi_{8450}(4159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{65}\right)\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{63}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{56}{65}\right)\)
\(\chi_{8450}(4289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{63}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{9}{65}\right)\)
\(\chi_{8450}(4419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{27}{65}\right)\)
\(\chi_{8450}(4679,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{63}{65}\right)\)
\(\chi_{8450}(4809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{42}{65}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{47}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{61}{130}\right)\)	\(e\left(\frac{16}{65}\right)\)
\(\chi_{8450}(4939,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{49}{130}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{89}{130}\right)\)	\(e\left(\frac{34}{65}\right)\)
\(\chi_{8450}(5329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{123}{130}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{23}{65}\right)\)
\(\chi_{8450}(5459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{61}{130}\right)\)	\(e\left(\frac{103}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{41}{65}\right)\)

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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	8450.cd
Modulus	$8450$
Conductor	$4225$
Order	$130$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8450\)
Conductor:	\(4225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(130\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4225.cf	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)