LMFDB - Dirichlet character orbit 7098.cu

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from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, base_ring=CyclotomicField(52))

M = H._module

chi = DirichletCharacter(H, M([0,26,43]))

chi.galois_orbit()

[g,chi] = znchar(Mod(265,7098))

order = charorder(g,chi)

[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$7098$
Conductor:	$1183$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$52$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 1183.bn	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:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{7098}(265,\cdot)$	$1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{3}{13}\right)$	$i$	$-1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{41}{52}\right)$
$\chi_{7098}(307,\cdot)$	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{2}{13}\right)$	$-i$	$-1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{23}{52}\right)$
$\chi_{7098}(811,\cdot)$	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{13}\right)$	$i$	$-1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{52}\right)$
$\chi_{7098}(853,\cdot)$	$1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{4}{13}\right)$	$-i$	$-1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{7}{52}\right)$
$\chi_{7098}(1357,\cdot)$	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{12}{13}\right)$	$i$	$-1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{21}{52}\right)$
$\chi_{7098}(1399,\cdot)$	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{6}{13}\right)$	$-i$	$-1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{43}{52}\right)$
$\chi_{7098}(1903,\cdot)$	$1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{10}{13}\right)$	$i$	$-1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{37}{52}\right)$
$\chi_{7098}(1945,\cdot)$	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{8}{13}\right)$	$-i$	$-1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{27}{52}\right)$
$\chi_{7098}(2449,\cdot)$	$1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{8}{13}\right)$	$i$	$-1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{52}\right)$
$\chi_{7098}(2491,\cdot)$	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{10}{13}\right)$	$-i$	$-1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{11}{52}\right)$
$\chi_{7098}(2995,\cdot)$	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{6}{13}\right)$	$i$	$-1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{17}{52}\right)$
$\chi_{7098}(3037,\cdot)$	$1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{12}{13}\right)$	$-i$	$-1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{47}{52}\right)$
$\chi_{7098}(3541,\cdot)$	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{4}{13}\right)$	$i$	$-1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{33}{52}\right)$
$\chi_{7098}(3583,\cdot)$	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{13}\right)$	$-i$	$-1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{31}{52}\right)$
$\chi_{7098}(4087,\cdot)$	$1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{2}{13}\right)$	$i$	$-1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{49}{52}\right)$
$\chi_{7098}(4129,\cdot)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{13}\right)$	$-i$	$-1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{15}{52}\right)$
$\chi_{7098}(4675,\cdot)$	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{5}{13}\right)$	$-i$	$-1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{51}{52}\right)$
$\chi_{7098}(5179,\cdot)$	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{11}{13}\right)$	$i$	$-1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{29}{52}\right)$
$\chi_{7098}(5221,\cdot)$	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{7}{13}\right)$	$-i$	$-1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{35}{52}\right)$
$\chi_{7098}(5725,\cdot)$	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{13}\right)$	$i$	$-1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{45}{52}\right)$
$\chi_{7098}(5767,\cdot)$	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{13}\right)$	$-i$	$-1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{19}{52}\right)$
$\chi_{7098}(6271,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{7}{13}\right)$	$i$	$-1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{52}\right)$
$\chi_{7098}(6313,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{11}{13}\right)$	$-i$	$-1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{52}\right)$
$\chi_{7098}(6817,\cdot)$	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{13}\right)$	$i$	$-1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{25}{52}\right)$

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 $\F_{q}$

Character	\(-1\)	\(1\)	\(5\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{7098}(265,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)
\(\chi_{7098}(307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)
\(\chi_{7098}(811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)
\(\chi_{7098}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)
\(\chi_{7098}(1357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)
\(\chi_{7098}(1399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)
\(\chi_{7098}(1903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)
\(\chi_{7098}(1945,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)
\(\chi_{7098}(2449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)
\(\chi_{7098}(2491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)
\(\chi_{7098}(2995,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)
\(\chi_{7098}(3037,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)
\(\chi_{7098}(3541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)
\(\chi_{7098}(3583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)
\(\chi_{7098}(4087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)
\(\chi_{7098}(4129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)
\(\chi_{7098}(4675,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)
\(\chi_{7098}(5179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)
\(\chi_{7098}(5221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)
\(\chi_{7098}(5725,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)
\(\chi_{7098}(5767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)
\(\chi_{7098}(6271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)
\(\chi_{7098}(6313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)
\(\chi_{7098}(6817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)

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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	7098.cu
Modulus	$7098$
Conductor	$1183$
Order	$52$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(7098\)
Conductor:	\(1183\)	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	\(52\)	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 1183.bn	sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage: chi.is_odd() pari: zncharisodd(g,chi)