LMFDB - Dirichlet character orbit 2304.bz

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2304, base_ring=CyclotomicField(96)) M = H._module chi = DirichletCharacter(H, M([0,3,64])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(25, 2304)) 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("2304.25"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$2304$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1152$	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 1152.bv	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{2304}(25,\cdot)$	$1$	$1$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{2304}(121,\cdot)$	$1$	$1$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{2304}(169,\cdot)$	$1$	$1$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2304}(265,\cdot)$	$1$	$1$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2304}(313,\cdot)$	$1$	$1$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{2304}(409,\cdot)$	$1$	$1$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{2304}(457,\cdot)$	$1$	$1$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2304}(553,\cdot)$	$1$	$1$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2304}(601,\cdot)$	$1$	$1$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{2304}(697,\cdot)$	$1$	$1$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{2304}(745,\cdot)$	$1$	$1$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2304}(841,\cdot)$	$1$	$1$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2304}(889,\cdot)$	$1$	$1$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{2304}(985,\cdot)$	$1$	$1$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{2304}(1033,\cdot)$	$1$	$1$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2304}(1129,\cdot)$	$1$	$1$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2304}(1177,\cdot)$	$1$	$1$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{2304}(1273,\cdot)$	$1$	$1$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{2304}(1321,\cdot)$	$1$	$1$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2304}(1417,\cdot)$	$1$	$1$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2304}(1465,\cdot)$	$1$	$1$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{2304}(1561,\cdot)$	$1$	$1$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{2304}(1609,\cdot)$	$1$	$1$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2304}(1705,\cdot)$	$1$	$1$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2304}(1753,\cdot)$	$1$	$1$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{2304}(1849,\cdot)$	$1$	$1$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{2304}(1897,\cdot)$	$1$	$1$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2304}(1993,\cdot)$	$1$	$1$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2304}(2041,\cdot)$	$1$	$1$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{2304}(2137,\cdot)$	$1$	$1$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{2304}(2185,\cdot)$	$1$	$1$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{1}{12}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{2304}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2304}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2304}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2304}(265,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2304}(313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2304}(409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2304}(457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2304}(553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2304}(601,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2304}(697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2304}(745,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2304}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2304}(889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2304}(985,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2304}(1033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2304}(1129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2304}(1177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2304}(1273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2304}(1321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2304}(1417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2304}(1465,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2304}(1561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2304}(1609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2304}(1705,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2304}(1753,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2304}(1849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2304}(1897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2304}(1993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2304}(2041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2304}(2137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2304}(2185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)

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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	2304.bz
Modulus	$2304$
Conductor	$1152$
Order	$96$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(2304\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1152\)	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 1152.bv	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);