LMFDB - Dirichlet character orbit 8450.bo

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8450, base_ring=CyclotomicField(52)) M = H._module chi = DirichletCharacter(H, M([13,33])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(307,8450)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8450$
Conductor:	$845$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$52$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 845.be	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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{8450}(307,\cdot)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{47}{52}\right)$	$-i$	$e\left(\frac{31}{52}\right)$	$i$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{8450}(343,\cdot)$	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{9}{52}\right)$	$i$	$e\left(\frac{17}{52}\right)$	$-i$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{8450}(957,\cdot)$	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{7}{52}\right)$	$-i$	$e\left(\frac{19}{52}\right)$	$i$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8450}(993,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{49}{52}\right)$	$i$	$e\left(\frac{29}{52}\right)$	$-i$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{8450}(1607,\cdot)$	$1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{19}{52}\right)$	$-i$	$e\left(\frac{7}{52}\right)$	$i$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{8450}(1643,\cdot)$	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{37}{52}\right)$	$i$	$e\left(\frac{41}{52}\right)$	$-i$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{8450}(2257,\cdot)$	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{31}{52}\right)$	$-i$	$e\left(\frac{47}{52}\right)$	$i$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{8450}(2293,\cdot)$	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{25}{52}\right)$	$i$	$e\left(\frac{1}{52}\right)$	$-i$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{8450}(2907,\cdot)$	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{43}{52}\right)$	$-i$	$e\left(\frac{35}{52}\right)$	$i$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{8450}(3557,\cdot)$	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{3}{52}\right)$	$-i$	$e\left(\frac{23}{52}\right)$	$i$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{8450}(3593,\cdot)$	$1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{1}{52}\right)$	$i$	$e\left(\frac{25}{52}\right)$	$-i$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{8450}(4207,\cdot)$	$1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{15}{52}\right)$	$-i$	$e\left(\frac{11}{52}\right)$	$i$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8450}(4243,\cdot)$	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{41}{52}\right)$	$i$	$e\left(\frac{37}{52}\right)$	$-i$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8450}(4857,\cdot)$	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{27}{52}\right)$	$-i$	$e\left(\frac{51}{52}\right)$	$i$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{8450}(4893,\cdot)$	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{29}{52}\right)$	$i$	$e\left(\frac{49}{52}\right)$	$-i$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{8450}(5543,\cdot)$	$1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{17}{52}\right)$	$i$	$e\left(\frac{9}{52}\right)$	$-i$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{8450}(6157,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{51}{52}\right)$	$-i$	$e\left(\frac{27}{52}\right)$	$i$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{8450}(6193,\cdot)$	$1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{5}{52}\right)$	$i$	$e\left(\frac{21}{52}\right)$	$-i$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{8450}(6807,\cdot)$	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{11}{52}\right)$	$-i$	$e\left(\frac{15}{52}\right)$	$i$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{8450}(6843,\cdot)$	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{45}{52}\right)$	$i$	$e\left(\frac{33}{52}\right)$	$-i$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{8450}(7457,\cdot)$	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{23}{52}\right)$	$-i$	$e\left(\frac{3}{52}\right)$	$i$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{8450}(7493,\cdot)$	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{33}{52}\right)$	$i$	$e\left(\frac{45}{52}\right)$	$-i$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8450}(8107,\cdot)$	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{35}{52}\right)$	$-i$	$e\left(\frac{43}{52}\right)$	$i$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{8450}(8143,\cdot)$	$1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{21}{52}\right)$	$i$	$e\left(\frac{5}{52}\right)$	$-i$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{23}{26}\right)$

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Character	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{8450}(307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(-i\)	\(e\left(\frac{31}{52}\right)\)	\(i\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{8450}(343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(i\)	\(e\left(\frac{17}{52}\right)\)	\(-i\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{8450}(957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(-i\)	\(e\left(\frac{19}{52}\right)\)	\(i\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{8450}(993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(i\)	\(e\left(\frac{29}{52}\right)\)	\(-i\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{8450}(1607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(-i\)	\(e\left(\frac{7}{52}\right)\)	\(i\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{8450}(1643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(i\)	\(e\left(\frac{41}{52}\right)\)	\(-i\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{8450}(2257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(-i\)	\(e\left(\frac{47}{52}\right)\)	\(i\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{8450}(2293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(i\)	\(e\left(\frac{1}{52}\right)\)	\(-i\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{8450}(2907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(-i\)	\(e\left(\frac{35}{52}\right)\)	\(i\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{8450}(3557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(-i\)	\(e\left(\frac{23}{52}\right)\)	\(i\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{8450}(3593,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(i\)	\(e\left(\frac{25}{52}\right)\)	\(-i\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{8450}(4207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(-i\)	\(e\left(\frac{11}{52}\right)\)	\(i\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{8450}(4243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(i\)	\(e\left(\frac{37}{52}\right)\)	\(-i\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{8450}(4857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(-i\)	\(e\left(\frac{51}{52}\right)\)	\(i\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{8450}(4893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(i\)	\(e\left(\frac{49}{52}\right)\)	\(-i\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{8450}(5543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(i\)	\(e\left(\frac{9}{52}\right)\)	\(-i\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{8450}(6157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(-i\)	\(e\left(\frac{27}{52}\right)\)	\(i\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{8450}(6193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(i\)	\(e\left(\frac{21}{52}\right)\)	\(-i\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{8450}(6807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(-i\)	\(e\left(\frac{15}{52}\right)\)	\(i\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{8450}(6843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(i\)	\(e\left(\frac{33}{52}\right)\)	\(-i\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{8450}(7457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(-i\)	\(e\left(\frac{3}{52}\right)\)	\(i\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{8450}(7493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(i\)	\(e\left(\frac{45}{52}\right)\)	\(-i\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{8450}(8107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(-i\)	\(e\left(\frac{43}{52}\right)\)	\(i\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{8450}(8143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(i\)	\(e\left(\frac{5}{52}\right)\)	\(-i\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)

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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	8450.bo
Modulus	$8450$
Conductor	$845$
Order	$52$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8450\)
Conductor:	\(845\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(52\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 845.be	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)