LMFDB - Dirichlet character orbit 3298.ek

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3298, base_ring=CyclotomicField(96)) M = H._module chi = DirichletCharacter(H, M([24,25])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(13, 3298)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3298.13"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3298$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1649$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$96$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 1649.es	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{96})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 96 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$19$	$21$	$23$
$\chi_{3298}(13,\cdot)$	$-1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{77}{96}\right)$
$\chi_{3298}(123,\cdot)$	$-1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{55}{96}\right)$
$\chi_{3298}(157,\cdot)$	$-1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{71}{96}\right)$
$\chi_{3298}(217,\cdot)$	$-1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{49}{96}\right)$
$\chi_{3298}(395,\cdot)$	$-1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{11}{96}\right)$
$\chi_{3298}(693,\cdot)$	$-1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{85}{96}\right)$
$\chi_{3298}(769,\cdot)$	$-1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{59}{96}\right)$
$\chi_{3298}(965,\cdot)$	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{5}{96}\right)$
$\chi_{3298}(999,\cdot)$	$-1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{17}{96}\right)$
$\chi_{3298}(1007,\cdot)$	$-1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{23}{96}\right)$
$\chi_{3298}(1041,\cdot)$	$-1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{7}{96}\right)$
$\chi_{3298}(1135,\cdot)$	$-1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{65}{96}\right)$
$\chi_{3298}(1169,\cdot)$	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{53}{96}\right)$
$\chi_{3298}(1415,\cdot)$	$-1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{35}{96}\right)$
$\chi_{3298}(1441,\cdot)$	$-1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{37}{96}\right)$
$\chi_{3298}(1687,\cdot)$	$-1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{47}{96}\right)$
$\chi_{3298}(1917,\cdot)$	$-1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{1}{96}\right)$
$\chi_{3298}(1925,\cdot)$	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{67}{96}\right)$
$\chi_{3298}(2027,\cdot)$	$-1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{79}{96}\right)$
$\chi_{3298}(2095,\cdot)$	$-1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{91}{96}\right)$
$\chi_{3298}(2121,\cdot)$	$-1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{29}{96}\right)$
$\chi_{3298}(2155,\cdot)$	$-1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{73}{96}\right)$
$\chi_{3298}(2367,\cdot)$	$-1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{43}{96}\right)$
$\chi_{3298}(2435,\cdot)$	$-1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{31}{96}\right)$
$\chi_{3298}(2537,\cdot)$	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{19}{96}\right)$
$\chi_{3298}(2563,\cdot)$	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{89}{96}\right)$
$\chi_{3298}(2699,\cdot)$	$-1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{61}{96}\right)$
$\chi_{3298}(2733,\cdot)$	$-1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{13}{96}\right)$
$\chi_{3298}(2775,\cdot)$	$-1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{95}{96}\right)$
$\chi_{3298}(2869,\cdot)$	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{41}{96}\right)$
$\chi_{3298}(3047,\cdot)$	$-1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{83}{96}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(21\)	\(23\)
\(\chi_{3298}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{77}{96}\right)\)
\(\chi_{3298}(123,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{55}{96}\right)\)
\(\chi_{3298}(157,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{71}{96}\right)\)
\(\chi_{3298}(217,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)
\(\chi_{3298}(395,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{11}{96}\right)\)
\(\chi_{3298}(693,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{85}{96}\right)\)
\(\chi_{3298}(769,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{59}{96}\right)\)
\(\chi_{3298}(965,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)
\(\chi_{3298}(999,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{17}{96}\right)\)
\(\chi_{3298}(1007,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{23}{96}\right)\)
\(\chi_{3298}(1041,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{7}{96}\right)\)
\(\chi_{3298}(1135,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{65}{96}\right)\)
\(\chi_{3298}(1169,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{53}{96}\right)\)
\(\chi_{3298}(1415,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{35}{96}\right)\)
\(\chi_{3298}(1441,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{37}{96}\right)\)
\(\chi_{3298}(1687,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)
\(\chi_{3298}(1917,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{1}{96}\right)\)
\(\chi_{3298}(1925,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{67}{96}\right)\)
\(\chi_{3298}(2027,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{79}{96}\right)\)
\(\chi_{3298}(2095,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{91}{96}\right)\)
\(\chi_{3298}(2121,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{29}{96}\right)\)
\(\chi_{3298}(2155,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{73}{96}\right)\)
\(\chi_{3298}(2367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{43}{96}\right)\)
\(\chi_{3298}(2435,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{31}{96}\right)\)
\(\chi_{3298}(2537,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{19}{96}\right)\)
\(\chi_{3298}(2563,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)
\(\chi_{3298}(2699,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{61}{96}\right)\)
\(\chi_{3298}(2733,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{13}{96}\right)\)
\(\chi_{3298}(2775,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{95}{96}\right)\)
\(\chi_{3298}(2869,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{41}{96}\right)\)
\(\chi_{3298}(3047,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{83}{96}\right)\)

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First 31 of 32 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	3298.ek
Modulus	$3298$
Conductor	$1649$
Order	$96$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(3298\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1649\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(96\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 1649.es	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);