LMFDB - Dirichlet character orbit 9280.jw

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9280, base_ring=CyclotomicField(112)) M = H._module chi = DirichletCharacter(H, M([0,35,28,4])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(437,9280)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9280$
Conductor:	$9280$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$112$	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:	$\Q(\zeta_{112})$
Fixed field:	Number field defined by a degree 112 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{9280}(437,\cdot)$	$1$	$1$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{9}{112}\right)$	$-i$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{67}{112}\right)$
$\chi_{9280}(653,\cdot)$	$1$	$1$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{75}{112}\right)$	$i$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{73}{112}\right)$
$\chi_{9280}(733,\cdot)$	$1$	$1$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{55}{112}\right)$	$i$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{61}{112}\right)$
$\chi_{9280}(757,\cdot)$	$1$	$1$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{73}{112}\right)$	$-i$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{83}{112}\right)$
$\chi_{9280}(997,\cdot)$	$1$	$1$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{29}{112}\right)$	$-i$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{79}{112}\right)$
$\chi_{9280}(1237,\cdot)$	$1$	$1$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{81}{112}\right)$	$-i$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{43}{112}\right)$
$\chi_{9280}(1373,\cdot)$	$1$	$1$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{39}{112}\right)$	$i$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{29}{112}\right)$
$\chi_{9280}(1613,\cdot)$	$1$	$1$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{43}{112}\right)$	$i$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{9}{112}\right)$
$\chi_{9280}(1853,\cdot)$	$1$	$1$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{31}{112}\right)$	$i$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{69}{112}\right)$
$\chi_{9280}(1877,\cdot)$	$1$	$1$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{97}{112}\right)$	$-i$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{75}{112}\right)$
$\chi_{9280}(1957,\cdot)$	$1$	$1$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{61}{112}\right)$	$-i$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{31}{112}\right)$
$\chi_{9280}(2173,\cdot)$	$1$	$1$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{79}{112}\right)$	$i$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{53}{112}\right)$
$\chi_{9280}(2757,\cdot)$	$1$	$1$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{37}{112}\right)$	$-i$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{39}{112}\right)$
$\chi_{9280}(2973,\cdot)$	$1$	$1$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{103}{112}\right)$	$i$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{45}{112}\right)$
$\chi_{9280}(3053,\cdot)$	$1$	$1$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{83}{112}\right)$	$i$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{33}{112}\right)$
$\chi_{9280}(3077,\cdot)$	$1$	$1$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{101}{112}\right)$	$-i$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{55}{112}\right)$
$\chi_{9280}(3317,\cdot)$	$1$	$1$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{57}{112}\right)$	$-i$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{51}{112}\right)$
$\chi_{9280}(3557,\cdot)$	$1$	$1$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{109}{112}\right)$	$-i$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{15}{112}\right)$
$\chi_{9280}(3693,\cdot)$	$1$	$1$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{67}{112}\right)$	$i$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{1}{112}\right)$
$\chi_{9280}(3933,\cdot)$	$1$	$1$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{71}{112}\right)$	$i$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{93}{112}\right)$
$\chi_{9280}(4173,\cdot)$	$1$	$1$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{59}{112}\right)$	$i$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{41}{112}\right)$
$\chi_{9280}(4197,\cdot)$	$1$	$1$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{13}{112}\right)$	$-i$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{47}{112}\right)$
$\chi_{9280}(4277,\cdot)$	$1$	$1$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{89}{112}\right)$	$-i$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{3}{112}\right)$
$\chi_{9280}(4493,\cdot)$	$1$	$1$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{107}{112}\right)$	$i$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{25}{112}\right)$
$\chi_{9280}(5077,\cdot)$	$1$	$1$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{65}{112}\right)$	$-i$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{11}{112}\right)$
$\chi_{9280}(5293,\cdot)$	$1$	$1$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{19}{112}\right)$	$i$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{17}{112}\right)$
$\chi_{9280}(5373,\cdot)$	$1$	$1$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{111}{112}\right)$	$i$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{5}{112}\right)$
$\chi_{9280}(5397,\cdot)$	$1$	$1$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{17}{112}\right)$	$-i$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{27}{112}\right)$
$\chi_{9280}(5637,\cdot)$	$1$	$1$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{85}{112}\right)$	$-i$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{23}{112}\right)$
$\chi_{9280}(5877,\cdot)$	$1$	$1$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{25}{112}\right)$	$-i$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{99}{112}\right)$
$\chi_{9280}(6013,\cdot)$	$1$	$1$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{95}{112}\right)$	$i$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{85}{112}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{9280}(437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(-i\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{67}{112}\right)\)
\(\chi_{9280}(653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(i\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{73}{112}\right)\)
\(\chi_{9280}(733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(i\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{61}{112}\right)\)
\(\chi_{9280}(757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(-i\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{83}{112}\right)\)
\(\chi_{9280}(997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(-i\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{79}{112}\right)\)
\(\chi_{9280}(1237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(-i\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{43}{112}\right)\)
\(\chi_{9280}(1373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(i\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{29}{112}\right)\)
\(\chi_{9280}(1613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(i\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{9}{112}\right)\)
\(\chi_{9280}(1853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(i\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{69}{112}\right)\)
\(\chi_{9280}(1877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(-i\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{75}{112}\right)\)
\(\chi_{9280}(1957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(-i\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{31}{112}\right)\)
\(\chi_{9280}(2173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(i\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{53}{112}\right)\)
\(\chi_{9280}(2757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(-i\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{39}{112}\right)\)
\(\chi_{9280}(2973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(i\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{45}{112}\right)\)
\(\chi_{9280}(3053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(i\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{33}{112}\right)\)
\(\chi_{9280}(3077,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(-i\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{55}{112}\right)\)
\(\chi_{9280}(3317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(-i\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{51}{112}\right)\)
\(\chi_{9280}(3557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(-i\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{15}{112}\right)\)
\(\chi_{9280}(3693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(i\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)
\(\chi_{9280}(3933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(i\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{93}{112}\right)\)
\(\chi_{9280}(4173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(i\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{41}{112}\right)\)
\(\chi_{9280}(4197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(-i\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{47}{112}\right)\)
\(\chi_{9280}(4277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(-i\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{3}{112}\right)\)
\(\chi_{9280}(4493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(i\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{25}{112}\right)\)
\(\chi_{9280}(5077,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(-i\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{11}{112}\right)\)
\(\chi_{9280}(5293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(i\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{17}{112}\right)\)
\(\chi_{9280}(5373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(i\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{5}{112}\right)\)
\(\chi_{9280}(5397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(-i\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{27}{112}\right)\)
\(\chi_{9280}(5637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(-i\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{23}{112}\right)\)
\(\chi_{9280}(5877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(-i\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{99}{112}\right)\)
\(\chi_{9280}(6013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(i\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{85}{112}\right)\)

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First 31 of 48 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	9280.jw
Modulus	$9280$
Conductor	$9280$
Order	$112$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(9280\)
Conductor:	\(9280\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(112\)	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)