LMFDB - Dirichlet character orbit 242.g

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(242, base_ring=CyclotomicField(110)) M = H._module chi = DirichletCharacter(H, M([74])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,242)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$242$
Conductor:	$121$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$55$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 121.g	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:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 55 polynomial

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{242}(5,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{242}(15,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{242}(25,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{242}(31,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{242}(37,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{242}(47,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{242}(49,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{242}(53,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{242}(59,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{242}(69,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{242}(71,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{242}(75,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{242}(91,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{242}(93,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{242}(97,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{242}(103,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{242}(113,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{242}(115,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{242}(119,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{242}(125,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{242}(135,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{242}(137,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{242}(141,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{242}(147,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{242}(157,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{242}(159,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{242}(163,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{242}(169,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{242}(179,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{242}(181,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{242}(185,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{242}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{242}(15,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{242}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{242}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{242}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{242}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{242}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{242}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{242}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{242}(69,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{242}(71,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{242}(75,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{242}(91,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{242}(93,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{242}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{242}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{242}(113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{242}(115,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{242}(119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{242}(125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{242}(135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{242}(137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{242}(141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{242}(147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{242}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{242}(159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{242}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{242}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{242}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{242}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{242}(185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)

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First 31 of 40 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	242.g
Modulus	$242$
Conductor	$121$
Order	$55$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(242\)
Conductor:	\(121\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(55\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 121.g	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)