LMFDB - Dirichlet character orbit 269.e

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(269, base_ring=CyclotomicField(134)) M = H._module chi = DirichletCharacter(H, M([1])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(4,269)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$269$
Conductor:	$269$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$134$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{67})$
Fixed field:	Number field defined by a degree 134 polynomial (not computed)

First 31 of 66 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{269}(4,\cdot)$	$1$	$1$	$e\left(\frac{1}{134}\right)$	$e\left(\frac{109}{134}\right)$	$e\left(\frac{1}{67}\right)$	$e\left(\frac{37}{67}\right)$	$e\left(\frac{55}{67}\right)$	$e\left(\frac{19}{134}\right)$	$e\left(\frac{3}{134}\right)$	$e\left(\frac{42}{67}\right)$	$e\left(\frac{75}{134}\right)$	$e\left(\frac{48}{67}\right)$
$\chi_{269}(6,\cdot)$	$1$	$1$	$e\left(\frac{55}{134}\right)$	$e\left(\frac{99}{134}\right)$	$e\left(\frac{55}{67}\right)$	$e\left(\frac{25}{67}\right)$	$e\left(\frac{10}{67}\right)$	$e\left(\frac{107}{134}\right)$	$e\left(\frac{31}{134}\right)$	$e\left(\frac{32}{67}\right)$	$e\left(\frac{105}{134}\right)$	$e\left(\frac{27}{67}\right)$
$\chi_{269}(9,\cdot)$	$1$	$1$	$e\left(\frac{109}{134}\right)$	$e\left(\frac{89}{134}\right)$	$e\left(\frac{42}{67}\right)$	$e\left(\frac{13}{67}\right)$	$e\left(\frac{32}{67}\right)$	$e\left(\frac{61}{134}\right)$	$e\left(\frac{59}{134}\right)$	$e\left(\frac{22}{67}\right)$	$e\left(\frac{1}{134}\right)$	$e\left(\frac{6}{67}\right)$
$\chi_{269}(11,\cdot)$	$1$	$1$	$e\left(\frac{115}{134}\right)$	$e\left(\frac{73}{134}\right)$	$e\left(\frac{48}{67}\right)$	$e\left(\frac{34}{67}\right)$	$e\left(\frac{27}{67}\right)$	$e\left(\frac{41}{134}\right)$	$e\left(\frac{77}{134}\right)$	$e\left(\frac{6}{67}\right)$	$e\left(\frac{49}{134}\right)$	$e\left(\frac{26}{67}\right)$
$\chi_{269}(13,\cdot)$	$1$	$1$	$e\left(\frac{71}{134}\right)$	$e\left(\frac{101}{134}\right)$	$e\left(\frac{4}{67}\right)$	$e\left(\frac{14}{67}\right)$	$e\left(\frac{19}{67}\right)$	$e\left(\frac{9}{134}\right)$	$e\left(\frac{79}{134}\right)$	$e\left(\frac{34}{67}\right)$	$e\left(\frac{99}{134}\right)$	$e\left(\frac{58}{67}\right)$
$\chi_{269}(20,\cdot)$	$1$	$1$	$e\left(\frac{105}{134}\right)$	$e\left(\frac{55}{134}\right)$	$e\left(\frac{38}{67}\right)$	$e\left(\frac{66}{67}\right)$	$e\left(\frac{13}{67}\right)$	$e\left(\frac{119}{134}\right)$	$e\left(\frac{47}{134}\right)$	$e\left(\frac{55}{67}\right)$	$e\left(\frac{103}{134}\right)$	$e\left(\frac{15}{67}\right)$
$\chi_{269}(30,\cdot)$	$1$	$1$	$e\left(\frac{25}{134}\right)$	$e\left(\frac{45}{134}\right)$	$e\left(\frac{25}{67}\right)$	$e\left(\frac{54}{67}\right)$	$e\left(\frac{35}{67}\right)$	$e\left(\frac{73}{134}\right)$	$e\left(\frac{75}{134}\right)$	$e\left(\frac{45}{67}\right)$	$e\left(\frac{133}{134}\right)$	$e\left(\frac{61}{67}\right)$
$\chi_{269}(34,\cdot)$	$1$	$1$	$e\left(\frac{53}{134}\right)$	$e\left(\frac{15}{134}\right)$	$e\left(\frac{53}{67}\right)$	$e\left(\frac{18}{67}\right)$	$e\left(\frac{34}{67}\right)$	$e\left(\frac{69}{134}\right)$	$e\left(\frac{25}{134}\right)$	$e\left(\frac{15}{67}\right)$	$e\left(\frac{89}{134}\right)$	$e\left(\frac{65}{67}\right)$
$\chi_{269}(43,\cdot)$	$1$	$1$	$e\left(\frac{127}{134}\right)$	$e\left(\frac{41}{134}\right)$	$e\left(\frac{60}{67}\right)$	$e\left(\frac{9}{67}\right)$	$e\left(\frac{17}{67}\right)$	$e\left(\frac{1}{134}\right)$	$e\left(\frac{113}{134}\right)$	$e\left(\frac{41}{67}\right)$	$e\left(\frac{11}{134}\right)$	$e\left(\frac{66}{67}\right)$
$\chi_{269}(45,\cdot)$	$1$	$1$	$e\left(\frac{79}{134}\right)$	$e\left(\frac{35}{134}\right)$	$e\left(\frac{12}{67}\right)$	$e\left(\frac{42}{67}\right)$	$e\left(\frac{57}{67}\right)$	$e\left(\frac{27}{134}\right)$	$e\left(\frac{103}{134}\right)$	$e\left(\frac{35}{67}\right)$	$e\left(\frac{29}{134}\right)$	$e\left(\frac{40}{67}\right)$
$\chi_{269}(49,\cdot)$	$1$	$1$	$e\left(\frac{19}{134}\right)$	$e\left(\frac{61}{134}\right)$	$e\left(\frac{19}{67}\right)$	$e\left(\frac{33}{67}\right)$	$e\left(\frac{40}{67}\right)$	$e\left(\frac{93}{134}\right)$	$e\left(\frac{57}{134}\right)$	$e\left(\frac{61}{67}\right)$	$e\left(\frac{85}{134}\right)$	$e\left(\frac{41}{67}\right)$
$\chi_{269}(51,\cdot)$	$1$	$1$	$e\left(\frac{107}{134}\right)$	$e\left(\frac{5}{134}\right)$	$e\left(\frac{40}{67}\right)$	$e\left(\frac{6}{67}\right)$	$e\left(\frac{56}{67}\right)$	$e\left(\frac{23}{134}\right)$	$e\left(\frac{53}{134}\right)$	$e\left(\frac{5}{67}\right)$	$e\left(\frac{119}{134}\right)$	$e\left(\frac{44}{67}\right)$
$\chi_{269}(55,\cdot)$	$1$	$1$	$e\left(\frac{85}{134}\right)$	$e\left(\frac{19}{134}\right)$	$e\left(\frac{18}{67}\right)$	$e\left(\frac{63}{67}\right)$	$e\left(\frac{52}{67}\right)$	$e\left(\frac{7}{134}\right)$	$e\left(\frac{121}{134}\right)$	$e\left(\frac{19}{67}\right)$	$e\left(\frac{77}{134}\right)$	$e\left(\frac{60}{67}\right)$
$\chi_{269}(56,\cdot)$	$1$	$1$	$e\left(\frac{11}{134}\right)$	$e\left(\frac{127}{134}\right)$	$e\left(\frac{11}{67}\right)$	$e\left(\frac{5}{67}\right)$	$e\left(\frac{2}{67}\right)$	$e\left(\frac{75}{134}\right)$	$e\left(\frac{33}{134}\right)$	$e\left(\frac{60}{67}\right)$	$e\left(\frac{21}{134}\right)$	$e\left(\frac{59}{67}\right)$
$\chi_{269}(64,\cdot)$	$1$	$1$	$e\left(\frac{3}{134}\right)$	$e\left(\frac{59}{134}\right)$	$e\left(\frac{3}{67}\right)$	$e\left(\frac{44}{67}\right)$	$e\left(\frac{31}{67}\right)$	$e\left(\frac{57}{134}\right)$	$e\left(\frac{9}{134}\right)$	$e\left(\frac{59}{67}\right)$	$e\left(\frac{91}{134}\right)$	$e\left(\frac{10}{67}\right)$
$\chi_{269}(65,\cdot)$	$1$	$1$	$e\left(\frac{41}{134}\right)$	$e\left(\frac{47}{134}\right)$	$e\left(\frac{41}{67}\right)$	$e\left(\frac{43}{67}\right)$	$e\left(\frac{44}{67}\right)$	$e\left(\frac{109}{134}\right)$	$e\left(\frac{123}{134}\right)$	$e\left(\frac{47}{67}\right)$	$e\left(\frac{127}{134}\right)$	$e\left(\frac{25}{67}\right)$
$\chi_{269}(73,\cdot)$	$1$	$1$	$e\left(\frac{87}{134}\right)$	$e\left(\frac{103}{134}\right)$	$e\left(\frac{20}{67}\right)$	$e\left(\frac{3}{67}\right)$	$e\left(\frac{28}{67}\right)$	$e\left(\frac{45}{134}\right)$	$e\left(\frac{127}{134}\right)$	$e\left(\frac{36}{67}\right)$	$e\left(\frac{93}{134}\right)$	$e\left(\frac{22}{67}\right)$
$\chi_{269}(79,\cdot)$	$1$	$1$	$e\left(\frac{15}{134}\right)$	$e\left(\frac{27}{134}\right)$	$e\left(\frac{15}{67}\right)$	$e\left(\frac{19}{67}\right)$	$e\left(\frac{21}{67}\right)$	$e\left(\frac{17}{134}\right)$	$e\left(\frac{45}{134}\right)$	$e\left(\frac{27}{67}\right)$	$e\left(\frac{53}{134}\right)$	$e\left(\frac{50}{67}\right)$
$\chi_{269}(84,\cdot)$	$1$	$1$	$e\left(\frac{65}{134}\right)$	$e\left(\frac{117}{134}\right)$	$e\left(\frac{65}{67}\right)$	$e\left(\frac{60}{67}\right)$	$e\left(\frac{24}{67}\right)$	$e\left(\frac{29}{134}\right)$	$e\left(\frac{61}{134}\right)$	$e\left(\frac{50}{67}\right)$	$e\left(\frac{51}{134}\right)$	$e\left(\frac{38}{67}\right)$
$\chi_{269}(89,\cdot)$	$1$	$1$	$e\left(\frac{13}{134}\right)$	$e\left(\frac{77}{134}\right)$	$e\left(\frac{13}{67}\right)$	$e\left(\frac{12}{67}\right)$	$e\left(\frac{45}{67}\right)$	$e\left(\frac{113}{134}\right)$	$e\left(\frac{39}{134}\right)$	$e\left(\frac{10}{67}\right)$	$e\left(\frac{37}{134}\right)$	$e\left(\frac{21}{67}\right)$
$\chi_{269}(92,\cdot)$	$1$	$1$	$e\left(\frac{89}{134}\right)$	$e\left(\frac{53}{134}\right)$	$e\left(\frac{22}{67}\right)$	$e\left(\frac{10}{67}\right)$	$e\left(\frac{4}{67}\right)$	$e\left(\frac{83}{134}\right)$	$e\left(\frac{133}{134}\right)$	$e\left(\frac{53}{67}\right)$	$e\left(\frac{109}{134}\right)$	$e\left(\frac{51}{67}\right)$
$\chi_{269}(96,\cdot)$	$1$	$1$	$e\left(\frac{57}{134}\right)$	$e\left(\frac{49}{134}\right)$	$e\left(\frac{57}{67}\right)$	$e\left(\frac{32}{67}\right)$	$e\left(\frac{53}{67}\right)$	$e\left(\frac{11}{134}\right)$	$e\left(\frac{37}{134}\right)$	$e\left(\frac{49}{67}\right)$	$e\left(\frac{121}{134}\right)$	$e\left(\frac{56}{67}\right)$
$\chi_{269}(97,\cdot)$	$1$	$1$	$e\left(\frac{61}{134}\right)$	$e\left(\frac{83}{134}\right)$	$e\left(\frac{61}{67}\right)$	$e\left(\frac{46}{67}\right)$	$e\left(\frac{5}{67}\right)$	$e\left(\frac{87}{134}\right)$	$e\left(\frac{49}{134}\right)$	$e\left(\frac{16}{67}\right)$	$e\left(\frac{19}{134}\right)$	$e\left(\frac{47}{67}\right)$
$\chi_{269}(100,\cdot)$	$1$	$1$	$e\left(\frac{75}{134}\right)$	$e\left(\frac{1}{134}\right)$	$e\left(\frac{8}{67}\right)$	$e\left(\frac{28}{67}\right)$	$e\left(\frac{38}{67}\right)$	$e\left(\frac{85}{134}\right)$	$e\left(\frac{91}{134}\right)$	$e\left(\frac{1}{67}\right)$	$e\left(\frac{131}{134}\right)$	$e\left(\frac{49}{67}\right)$
$\chi_{269}(103,\cdot)$	$1$	$1$	$e\left(\frac{51}{134}\right)$	$e\left(\frac{65}{134}\right)$	$e\left(\frac{51}{67}\right)$	$e\left(\frac{11}{67}\right)$	$e\left(\frac{58}{67}\right)$	$e\left(\frac{31}{134}\right)$	$e\left(\frac{19}{134}\right)$	$e\left(\frac{65}{67}\right)$	$e\left(\frac{73}{134}\right)$	$e\left(\frac{36}{67}\right)$
$\chi_{269}(126,\cdot)$	$1$	$1$	$e\left(\frac{119}{134}\right)$	$e\left(\frac{107}{134}\right)$	$e\left(\frac{52}{67}\right)$	$e\left(\frac{48}{67}\right)$	$e\left(\frac{46}{67}\right)$	$e\left(\frac{117}{134}\right)$	$e\left(\frac{89}{134}\right)$	$e\left(\frac{40}{67}\right)$	$e\left(\frac{81}{134}\right)$	$e\left(\frac{17}{67}\right)$
$\chi_{269}(127,\cdot)$	$1$	$1$	$e\left(\frac{91}{134}\right)$	$e\left(\frac{3}{134}\right)$	$e\left(\frac{24}{67}\right)$	$e\left(\frac{17}{67}\right)$	$e\left(\frac{47}{67}\right)$	$e\left(\frac{121}{134}\right)$	$e\left(\frac{5}{134}\right)$	$e\left(\frac{3}{67}\right)$	$e\left(\frac{125}{134}\right)$	$e\left(\frac{13}{67}\right)$
$\chi_{269}(133,\cdot)$	$1$	$1$	$e\left(\frac{121}{134}\right)$	$e\left(\frac{57}{134}\right)$	$e\left(\frac{54}{67}\right)$	$e\left(\frac{55}{67}\right)$	$e\left(\frac{22}{67}\right)$	$e\left(\frac{21}{134}\right)$	$e\left(\frac{95}{134}\right)$	$e\left(\frac{57}{67}\right)$	$e\left(\frac{97}{134}\right)$	$e\left(\frac{46}{67}\right)$
$\chi_{269}(138,\cdot)$	$1$	$1$	$e\left(\frac{9}{134}\right)$	$e\left(\frac{43}{134}\right)$	$e\left(\frac{9}{67}\right)$	$e\left(\frac{65}{67}\right)$	$e\left(\frac{26}{67}\right)$	$e\left(\frac{37}{134}\right)$	$e\left(\frac{27}{134}\right)$	$e\left(\frac{43}{67}\right)$	$e\left(\frac{5}{134}\right)$	$e\left(\frac{30}{67}\right)$
$\chi_{269}(144,\cdot)$	$1$	$1$	$e\left(\frac{111}{134}\right)$	$e\left(\frac{39}{134}\right)$	$e\left(\frac{44}{67}\right)$	$e\left(\frac{20}{67}\right)$	$e\left(\frac{8}{67}\right)$	$e\left(\frac{99}{134}\right)$	$e\left(\frac{65}{134}\right)$	$e\left(\frac{39}{67}\right)$	$e\left(\frac{17}{134}\right)$	$e\left(\frac{35}{67}\right)$
$\chi_{269}(148,\cdot)$	$1$	$1$	$e\left(\frac{29}{134}\right)$	$e\left(\frac{79}{134}\right)$	$e\left(\frac{29}{67}\right)$	$e\left(\frac{1}{67}\right)$	$e\left(\frac{54}{67}\right)$	$e\left(\frac{15}{134}\right)$	$e\left(\frac{87}{134}\right)$	$e\left(\frac{12}{67}\right)$	$e\left(\frac{31}{134}\right)$	$e\left(\frac{52}{67}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{269}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{134}\right)\)	\(e\left(\frac{109}{134}\right)\)	\(e\left(\frac{1}{67}\right)\)	\(e\left(\frac{37}{67}\right)\)	\(e\left(\frac{55}{67}\right)\)	\(e\left(\frac{19}{134}\right)\)	\(e\left(\frac{3}{134}\right)\)	\(e\left(\frac{42}{67}\right)\)	\(e\left(\frac{75}{134}\right)\)	\(e\left(\frac{48}{67}\right)\)
\(\chi_{269}(6,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{134}\right)\)	\(e\left(\frac{99}{134}\right)\)	\(e\left(\frac{55}{67}\right)\)	\(e\left(\frac{25}{67}\right)\)	\(e\left(\frac{10}{67}\right)\)	\(e\left(\frac{107}{134}\right)\)	\(e\left(\frac{31}{134}\right)\)	\(e\left(\frac{32}{67}\right)\)	\(e\left(\frac{105}{134}\right)\)	\(e\left(\frac{27}{67}\right)\)
\(\chi_{269}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{134}\right)\)	\(e\left(\frac{89}{134}\right)\)	\(e\left(\frac{42}{67}\right)\)	\(e\left(\frac{13}{67}\right)\)	\(e\left(\frac{32}{67}\right)\)	\(e\left(\frac{61}{134}\right)\)	\(e\left(\frac{59}{134}\right)\)	\(e\left(\frac{22}{67}\right)\)	\(e\left(\frac{1}{134}\right)\)	\(e\left(\frac{6}{67}\right)\)
\(\chi_{269}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{134}\right)\)	\(e\left(\frac{73}{134}\right)\)	\(e\left(\frac{48}{67}\right)\)	\(e\left(\frac{34}{67}\right)\)	\(e\left(\frac{27}{67}\right)\)	\(e\left(\frac{41}{134}\right)\)	\(e\left(\frac{77}{134}\right)\)	\(e\left(\frac{6}{67}\right)\)	\(e\left(\frac{49}{134}\right)\)	\(e\left(\frac{26}{67}\right)\)
\(\chi_{269}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{134}\right)\)	\(e\left(\frac{101}{134}\right)\)	\(e\left(\frac{4}{67}\right)\)	\(e\left(\frac{14}{67}\right)\)	\(e\left(\frac{19}{67}\right)\)	\(e\left(\frac{9}{134}\right)\)	\(e\left(\frac{79}{134}\right)\)	\(e\left(\frac{34}{67}\right)\)	\(e\left(\frac{99}{134}\right)\)	\(e\left(\frac{58}{67}\right)\)
\(\chi_{269}(20,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{105}{134}\right)\)	\(e\left(\frac{55}{134}\right)\)	\(e\left(\frac{38}{67}\right)\)	\(e\left(\frac{66}{67}\right)\)	\(e\left(\frac{13}{67}\right)\)	\(e\left(\frac{119}{134}\right)\)	\(e\left(\frac{47}{134}\right)\)	\(e\left(\frac{55}{67}\right)\)	\(e\left(\frac{103}{134}\right)\)	\(e\left(\frac{15}{67}\right)\)
\(\chi_{269}(30,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{134}\right)\)	\(e\left(\frac{45}{134}\right)\)	\(e\left(\frac{25}{67}\right)\)	\(e\left(\frac{54}{67}\right)\)	\(e\left(\frac{35}{67}\right)\)	\(e\left(\frac{73}{134}\right)\)	\(e\left(\frac{75}{134}\right)\)	\(e\left(\frac{45}{67}\right)\)	\(e\left(\frac{133}{134}\right)\)	\(e\left(\frac{61}{67}\right)\)
\(\chi_{269}(34,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{134}\right)\)	\(e\left(\frac{15}{134}\right)\)	\(e\left(\frac{53}{67}\right)\)	\(e\left(\frac{18}{67}\right)\)	\(e\left(\frac{34}{67}\right)\)	\(e\left(\frac{69}{134}\right)\)	\(e\left(\frac{25}{134}\right)\)	\(e\left(\frac{15}{67}\right)\)	\(e\left(\frac{89}{134}\right)\)	\(e\left(\frac{65}{67}\right)\)
\(\chi_{269}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{134}\right)\)	\(e\left(\frac{41}{134}\right)\)	\(e\left(\frac{60}{67}\right)\)	\(e\left(\frac{9}{67}\right)\)	\(e\left(\frac{17}{67}\right)\)	\(e\left(\frac{1}{134}\right)\)	\(e\left(\frac{113}{134}\right)\)	\(e\left(\frac{41}{67}\right)\)	\(e\left(\frac{11}{134}\right)\)	\(e\left(\frac{66}{67}\right)\)
\(\chi_{269}(45,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{134}\right)\)	\(e\left(\frac{35}{134}\right)\)	\(e\left(\frac{12}{67}\right)\)	\(e\left(\frac{42}{67}\right)\)	\(e\left(\frac{57}{67}\right)\)	\(e\left(\frac{27}{134}\right)\)	\(e\left(\frac{103}{134}\right)\)	\(e\left(\frac{35}{67}\right)\)	\(e\left(\frac{29}{134}\right)\)	\(e\left(\frac{40}{67}\right)\)
\(\chi_{269}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{134}\right)\)	\(e\left(\frac{61}{134}\right)\)	\(e\left(\frac{19}{67}\right)\)	\(e\left(\frac{33}{67}\right)\)	\(e\left(\frac{40}{67}\right)\)	\(e\left(\frac{93}{134}\right)\)	\(e\left(\frac{57}{134}\right)\)	\(e\left(\frac{61}{67}\right)\)	\(e\left(\frac{85}{134}\right)\)	\(e\left(\frac{41}{67}\right)\)
\(\chi_{269}(51,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{134}\right)\)	\(e\left(\frac{5}{134}\right)\)	\(e\left(\frac{40}{67}\right)\)	\(e\left(\frac{6}{67}\right)\)	\(e\left(\frac{56}{67}\right)\)	\(e\left(\frac{23}{134}\right)\)	\(e\left(\frac{53}{134}\right)\)	\(e\left(\frac{5}{67}\right)\)	\(e\left(\frac{119}{134}\right)\)	\(e\left(\frac{44}{67}\right)\)
\(\chi_{269}(55,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{134}\right)\)	\(e\left(\frac{19}{134}\right)\)	\(e\left(\frac{18}{67}\right)\)	\(e\left(\frac{63}{67}\right)\)	\(e\left(\frac{52}{67}\right)\)	\(e\left(\frac{7}{134}\right)\)	\(e\left(\frac{121}{134}\right)\)	\(e\left(\frac{19}{67}\right)\)	\(e\left(\frac{77}{134}\right)\)	\(e\left(\frac{60}{67}\right)\)
\(\chi_{269}(56,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{134}\right)\)	\(e\left(\frac{127}{134}\right)\)	\(e\left(\frac{11}{67}\right)\)	\(e\left(\frac{5}{67}\right)\)	\(e\left(\frac{2}{67}\right)\)	\(e\left(\frac{75}{134}\right)\)	\(e\left(\frac{33}{134}\right)\)	\(e\left(\frac{60}{67}\right)\)	\(e\left(\frac{21}{134}\right)\)	\(e\left(\frac{59}{67}\right)\)
\(\chi_{269}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{134}\right)\)	\(e\left(\frac{59}{134}\right)\)	\(e\left(\frac{3}{67}\right)\)	\(e\left(\frac{44}{67}\right)\)	\(e\left(\frac{31}{67}\right)\)	\(e\left(\frac{57}{134}\right)\)	\(e\left(\frac{9}{134}\right)\)	\(e\left(\frac{59}{67}\right)\)	\(e\left(\frac{91}{134}\right)\)	\(e\left(\frac{10}{67}\right)\)
\(\chi_{269}(65,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{134}\right)\)	\(e\left(\frac{47}{134}\right)\)	\(e\left(\frac{41}{67}\right)\)	\(e\left(\frac{43}{67}\right)\)	\(e\left(\frac{44}{67}\right)\)	\(e\left(\frac{109}{134}\right)\)	\(e\left(\frac{123}{134}\right)\)	\(e\left(\frac{47}{67}\right)\)	\(e\left(\frac{127}{134}\right)\)	\(e\left(\frac{25}{67}\right)\)
\(\chi_{269}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{134}\right)\)	\(e\left(\frac{103}{134}\right)\)	\(e\left(\frac{20}{67}\right)\)	\(e\left(\frac{3}{67}\right)\)	\(e\left(\frac{28}{67}\right)\)	\(e\left(\frac{45}{134}\right)\)	\(e\left(\frac{127}{134}\right)\)	\(e\left(\frac{36}{67}\right)\)	\(e\left(\frac{93}{134}\right)\)	\(e\left(\frac{22}{67}\right)\)
\(\chi_{269}(79,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{134}\right)\)	\(e\left(\frac{27}{134}\right)\)	\(e\left(\frac{15}{67}\right)\)	\(e\left(\frac{19}{67}\right)\)	\(e\left(\frac{21}{67}\right)\)	\(e\left(\frac{17}{134}\right)\)	\(e\left(\frac{45}{134}\right)\)	\(e\left(\frac{27}{67}\right)\)	\(e\left(\frac{53}{134}\right)\)	\(e\left(\frac{50}{67}\right)\)
\(\chi_{269}(84,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{134}\right)\)	\(e\left(\frac{117}{134}\right)\)	\(e\left(\frac{65}{67}\right)\)	\(e\left(\frac{60}{67}\right)\)	\(e\left(\frac{24}{67}\right)\)	\(e\left(\frac{29}{134}\right)\)	\(e\left(\frac{61}{134}\right)\)	\(e\left(\frac{50}{67}\right)\)	\(e\left(\frac{51}{134}\right)\)	\(e\left(\frac{38}{67}\right)\)
\(\chi_{269}(89,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{134}\right)\)	\(e\left(\frac{77}{134}\right)\)	\(e\left(\frac{13}{67}\right)\)	\(e\left(\frac{12}{67}\right)\)	\(e\left(\frac{45}{67}\right)\)	\(e\left(\frac{113}{134}\right)\)	\(e\left(\frac{39}{134}\right)\)	\(e\left(\frac{10}{67}\right)\)	\(e\left(\frac{37}{134}\right)\)	\(e\left(\frac{21}{67}\right)\)
\(\chi_{269}(92,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{134}\right)\)	\(e\left(\frac{53}{134}\right)\)	\(e\left(\frac{22}{67}\right)\)	\(e\left(\frac{10}{67}\right)\)	\(e\left(\frac{4}{67}\right)\)	\(e\left(\frac{83}{134}\right)\)	\(e\left(\frac{133}{134}\right)\)	\(e\left(\frac{53}{67}\right)\)	\(e\left(\frac{109}{134}\right)\)	\(e\left(\frac{51}{67}\right)\)
\(\chi_{269}(96,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{134}\right)\)	\(e\left(\frac{49}{134}\right)\)	\(e\left(\frac{57}{67}\right)\)	\(e\left(\frac{32}{67}\right)\)	\(e\left(\frac{53}{67}\right)\)	\(e\left(\frac{11}{134}\right)\)	\(e\left(\frac{37}{134}\right)\)	\(e\left(\frac{49}{67}\right)\)	\(e\left(\frac{121}{134}\right)\)	\(e\left(\frac{56}{67}\right)\)
\(\chi_{269}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{134}\right)\)	\(e\left(\frac{83}{134}\right)\)	\(e\left(\frac{61}{67}\right)\)	\(e\left(\frac{46}{67}\right)\)	\(e\left(\frac{5}{67}\right)\)	\(e\left(\frac{87}{134}\right)\)	\(e\left(\frac{49}{134}\right)\)	\(e\left(\frac{16}{67}\right)\)	\(e\left(\frac{19}{134}\right)\)	\(e\left(\frac{47}{67}\right)\)
\(\chi_{269}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{134}\right)\)	\(e\left(\frac{1}{134}\right)\)	\(e\left(\frac{8}{67}\right)\)	\(e\left(\frac{28}{67}\right)\)	\(e\left(\frac{38}{67}\right)\)	\(e\left(\frac{85}{134}\right)\)	\(e\left(\frac{91}{134}\right)\)	\(e\left(\frac{1}{67}\right)\)	\(e\left(\frac{131}{134}\right)\)	\(e\left(\frac{49}{67}\right)\)
\(\chi_{269}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{134}\right)\)	\(e\left(\frac{65}{134}\right)\)	\(e\left(\frac{51}{67}\right)\)	\(e\left(\frac{11}{67}\right)\)	\(e\left(\frac{58}{67}\right)\)	\(e\left(\frac{31}{134}\right)\)	\(e\left(\frac{19}{134}\right)\)	\(e\left(\frac{65}{67}\right)\)	\(e\left(\frac{73}{134}\right)\)	\(e\left(\frac{36}{67}\right)\)
\(\chi_{269}(126,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{134}\right)\)	\(e\left(\frac{107}{134}\right)\)	\(e\left(\frac{52}{67}\right)\)	\(e\left(\frac{48}{67}\right)\)	\(e\left(\frac{46}{67}\right)\)	\(e\left(\frac{117}{134}\right)\)	\(e\left(\frac{89}{134}\right)\)	\(e\left(\frac{40}{67}\right)\)	\(e\left(\frac{81}{134}\right)\)	\(e\left(\frac{17}{67}\right)\)
\(\chi_{269}(127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{134}\right)\)	\(e\left(\frac{3}{134}\right)\)	\(e\left(\frac{24}{67}\right)\)	\(e\left(\frac{17}{67}\right)\)	\(e\left(\frac{47}{67}\right)\)	\(e\left(\frac{121}{134}\right)\)	\(e\left(\frac{5}{134}\right)\)	\(e\left(\frac{3}{67}\right)\)	\(e\left(\frac{125}{134}\right)\)	\(e\left(\frac{13}{67}\right)\)
\(\chi_{269}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{134}\right)\)	\(e\left(\frac{57}{134}\right)\)	\(e\left(\frac{54}{67}\right)\)	\(e\left(\frac{55}{67}\right)\)	\(e\left(\frac{22}{67}\right)\)	\(e\left(\frac{21}{134}\right)\)	\(e\left(\frac{95}{134}\right)\)	\(e\left(\frac{57}{67}\right)\)	\(e\left(\frac{97}{134}\right)\)	\(e\left(\frac{46}{67}\right)\)
\(\chi_{269}(138,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{134}\right)\)	\(e\left(\frac{43}{134}\right)\)	\(e\left(\frac{9}{67}\right)\)	\(e\left(\frac{65}{67}\right)\)	\(e\left(\frac{26}{67}\right)\)	\(e\left(\frac{37}{134}\right)\)	\(e\left(\frac{27}{134}\right)\)	\(e\left(\frac{43}{67}\right)\)	\(e\left(\frac{5}{134}\right)\)	\(e\left(\frac{30}{67}\right)\)
\(\chi_{269}(144,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{134}\right)\)	\(e\left(\frac{39}{134}\right)\)	\(e\left(\frac{44}{67}\right)\)	\(e\left(\frac{20}{67}\right)\)	\(e\left(\frac{8}{67}\right)\)	\(e\left(\frac{99}{134}\right)\)	\(e\left(\frac{65}{134}\right)\)	\(e\left(\frac{39}{67}\right)\)	\(e\left(\frac{17}{134}\right)\)	\(e\left(\frac{35}{67}\right)\)
\(\chi_{269}(148,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{134}\right)\)	\(e\left(\frac{79}{134}\right)\)	\(e\left(\frac{29}{67}\right)\)	\(e\left(\frac{1}{67}\right)\)	\(e\left(\frac{54}{67}\right)\)	\(e\left(\frac{15}{134}\right)\)	\(e\left(\frac{87}{134}\right)\)	\(e\left(\frac{12}{67}\right)\)	\(e\left(\frac{31}{134}\right)\)	\(e\left(\frac{52}{67}\right)\)

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First 31 of 66 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	269.e
Modulus	$269$
Conductor	$269$
Order	$134$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(269\)
Conductor:	\(269\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(134\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)