LMFDB - Dirichlet character orbit 417.p

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(417, base_ring=CyclotomicField(138)) M = H._module chi = DirichletCharacter(H, M([69,1])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,417)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$417$
Conductor:	$417$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$138$	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:	$\Q(\zeta_{69})$
Fixed field:	Number field defined by a degree 138 polynomial (not computed)

First 31 of 44 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{417}(2,\cdot)$	$1$	$1$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{2}{69}\right)$
$\chi_{417}(17,\cdot)$	$1$	$1$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{7}{69}\right)$
$\chi_{417}(26,\cdot)$	$1$	$1$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{61}{69}\right)$
$\chi_{417}(32,\cdot)$	$1$	$1$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{10}{69}\right)$
$\chi_{417}(50,\cdot)$	$1$	$1$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{1}{69}\right)$
$\chi_{417}(53,\cdot)$	$1$	$1$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{25}{69}\right)$
$\chi_{417}(56,\cdot)$	$1$	$1$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{37}{69}\right)$
$\chi_{417}(68,\cdot)$	$1$	$1$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{11}{69}\right)$
$\chi_{417}(92,\cdot)$	$1$	$1$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{58}{69}\right)$
$\chi_{417}(98,\cdot)$	$1$	$1$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{64}{69}\right)$
$\chi_{417}(101,\cdot)$	$1$	$1$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{55}{69}\right)$
$\chi_{417}(104,\cdot)$	$1$	$1$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{65}{69}\right)$
$\chi_{417}(110,\cdot)$	$1$	$1$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{50}{69}\right)$
$\chi_{417}(119,\cdot)$	$1$	$1$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{38}{69}\right)$
$\chi_{417}(128,\cdot)$	$1$	$1$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{14}{69}\right)$
$\chi_{417}(134,\cdot)$	$1$	$1$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{34}{69}\right)$
$\chi_{417}(158,\cdot)$	$1$	$1$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{53}{69}\right)$
$\chi_{417}(161,\cdot)$	$1$	$1$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{16}{69}\right)$
$\chi_{417}(179,\cdot)$	$1$	$1$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{40}{69}\right)$
$\chi_{417}(197,\cdot)$	$1$	$1$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{52}{69}\right)$
$\chi_{417}(200,\cdot)$	$1$	$1$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{121}{138}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{5}{69}\right)$
$\chi_{417}(209,\cdot)$	$1$	$1$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{121}{138}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{67}{69}\right)$
$\chi_{417}(212,\cdot)$	$1$	$1$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{29}{69}\right)$
$\chi_{417}(224,\cdot)$	$1$	$1$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{41}{69}\right)$
$\chi_{417}(227,\cdot)$	$1$	$1$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{20}{69}\right)$
$\chi_{417}(248,\cdot)$	$1$	$1$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{49}{69}\right)$
$\chi_{417}(254,\cdot)$	$1$	$1$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{127}{138}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{19}{69}\right)$
$\chi_{417}(269,\cdot)$	$1$	$1$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{26}{69}\right)$
$\chi_{417}(281,\cdot)$	$1$	$1$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{13}{69}\right)$
$\chi_{417}(290,\cdot)$	$1$	$1$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{17}{69}\right)$
$\chi_{417}(293,\cdot)$	$1$	$1$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{47}{69}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{417}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{2}{69}\right)\)
\(\chi_{417}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{7}{69}\right)\)
\(\chi_{417}(26,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{61}{69}\right)\)
\(\chi_{417}(32,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{10}{69}\right)\)
\(\chi_{417}(50,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{1}{69}\right)\)
\(\chi_{417}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{25}{69}\right)\)
\(\chi_{417}(56,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{37}{69}\right)\)
\(\chi_{417}(68,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{11}{69}\right)\)
\(\chi_{417}(92,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{58}{69}\right)\)
\(\chi_{417}(98,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{64}{69}\right)\)
\(\chi_{417}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{55}{69}\right)\)
\(\chi_{417}(104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{65}{69}\right)\)
\(\chi_{417}(110,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{50}{69}\right)\)
\(\chi_{417}(119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{38}{69}\right)\)
\(\chi_{417}(128,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{14}{69}\right)\)
\(\chi_{417}(134,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{34}{69}\right)\)
\(\chi_{417}(158,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{53}{69}\right)\)
\(\chi_{417}(161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{16}{69}\right)\)
\(\chi_{417}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{40}{69}\right)\)
\(\chi_{417}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{52}{69}\right)\)
\(\chi_{417}(200,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{121}{138}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{5}{69}\right)\)
\(\chi_{417}(209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{121}{138}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{67}{69}\right)\)
\(\chi_{417}(212,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{29}{69}\right)\)
\(\chi_{417}(224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{41}{69}\right)\)
\(\chi_{417}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{20}{69}\right)\)
\(\chi_{417}(248,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{49}{69}\right)\)
\(\chi_{417}(254,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{127}{138}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{19}{69}\right)\)
\(\chi_{417}(269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{26}{69}\right)\)
\(\chi_{417}(281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{13}{69}\right)\)
\(\chi_{417}(290,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{17}{69}\right)\)
\(\chi_{417}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{47}{69}\right)\)

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First 31 of 44 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	417.p
Modulus	$417$
Conductor	$417$
Order	$138$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(417\)
Conductor:	\(417\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(138\)	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)