LMFDB - Dirichlet character orbit 10304.fj

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10304, base_ring=CyclotomicField(176)) M = H._module chi = DirichletCharacter(H, M([0,33,88,24])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(125, 10304)) 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("10304.125"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$10304$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$10304$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$176$	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:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{176})$	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 176 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$25$	$27$
$\chi_{10304}(125,\cdot)$	$1$	$1$	$e\left(\frac{43}{176}\right)$	$e\left(\frac{145}{176}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{29}{176}\right)$	$e\left(\frac{39}{176}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{151}{176}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{129}{176}\right)$
$\chi_{10304}(181,\cdot)$	$1$	$1$	$e\left(\frac{13}{176}\right)$	$e\left(\frac{7}{176}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{107}{176}\right)$	$e\left(\frac{65}{176}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{17}{176}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{39}{176}\right)$
$\chi_{10304}(237,\cdot)$	$1$	$1$	$e\left(\frac{111}{176}\right)$	$e\left(\frac{141}{176}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{169}{176}\right)$	$e\left(\frac{27}{176}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{91}{176}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{157}{176}\right)$
$\chi_{10304}(293,\cdot)$	$1$	$1$	$e\left(\frac{49}{176}\right)$	$e\left(\frac{67}{176}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{119}{176}\right)$	$e\left(\frac{69}{176}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{37}{176}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{147}{176}\right)$
$\chi_{10304}(405,\cdot)$	$1$	$1$	$e\left(\frac{37}{176}\right)$	$e\left(\frac{47}{176}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{115}{176}\right)$	$e\left(\frac{9}{176}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{89}{176}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{111}{176}\right)$
$\chi_{10304}(517,\cdot)$	$1$	$1$	$e\left(\frac{41}{176}\right)$	$e\left(\frac{171}{176}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{175}{176}\right)$	$e\left(\frac{29}{176}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{13}{176}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{123}{176}\right)$
$\chi_{10304}(573,\cdot)$	$1$	$1$	$e\left(\frac{91}{176}\right)$	$e\left(\frac{49}{176}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{45}{176}\right)$	$e\left(\frac{103}{176}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{119}{176}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{97}{176}\right)$
$\chi_{10304}(741,\cdot)$	$1$	$1$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{19}{176}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{39}{176}\right)$	$e\left(\frac{101}{176}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{21}{176}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{131}{176}\right)$
$\chi_{10304}(797,\cdot)$	$1$	$1$	$e\left(\frac{163}{176}\right)$	$e\left(\frac{169}{176}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{69}{176}\right)$	$e\left(\frac{111}{176}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{159}{176}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{137}{176}\right)$
$\chi_{10304}(1077,\cdot)$	$1$	$1$	$e\left(\frac{61}{176}\right)$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{129}{176}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{7}{176}\right)$
$\chi_{10304}(1413,\cdot)$	$1$	$1$	$e\left(\frac{153}{176}\right)$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{95}{176}\right)$	$e\left(\frac{61}{176}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{173}{176}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{107}{176}\right)$
$\chi_{10304}(1469,\cdot)$	$1$	$1$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{173}{176}\right)$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{39}{176}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{17}{176}\right)$
$\chi_{10304}(1525,\cdot)$	$1$	$1$	$e\left(\frac{45}{176}\right)$	$e\left(\frac{119}{176}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{59}{176}\right)$	$e\left(\frac{49}{176}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{113}{176}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{135}{176}\right)$
$\chi_{10304}(1581,\cdot)$	$1$	$1$	$e\left(\frac{159}{176}\right)$	$e\left(\frac{45}{176}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{9}{176}\right)$	$e\left(\frac{91}{176}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{59}{176}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{125}{176}\right)$
$\chi_{10304}(1693,\cdot)$	$1$	$1$	$e\left(\frac{147}{176}\right)$	$e\left(\frac{25}{176}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{5}{176}\right)$	$e\left(\frac{31}{176}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{111}{176}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{89}{176}\right)$
$\chi_{10304}(1805,\cdot)$	$1$	$1$	$e\left(\frac{151}{176}\right)$	$e\left(\frac{149}{176}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{65}{176}\right)$	$e\left(\frac{51}{176}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{35}{176}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{101}{176}\right)$
$\chi_{10304}(1861,\cdot)$	$1$	$1$	$e\left(\frac{25}{176}\right)$	$e\left(\frac{27}{176}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{111}{176}\right)$	$e\left(\frac{125}{176}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{141}{176}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{75}{176}\right)$
$\chi_{10304}(2029,\cdot)$	$1$	$1$	$e\left(\frac{95}{176}\right)$	$e\left(\frac{173}{176}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{105}{176}\right)$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{43}{176}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{109}{176}\right)$
$\chi_{10304}(2085,\cdot)$	$1$	$1$	$e\left(\frac{97}{176}\right)$	$e\left(\frac{147}{176}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{135}{176}\right)$	$e\left(\frac{133}{176}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{5}{176}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{115}{176}\right)$
$\chi_{10304}(2365,\cdot)$	$1$	$1$	$e\left(\frac{171}{176}\right)$	$e\left(\frac{65}{176}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{13}{176}\right)$	$e\left(\frac{151}{176}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{7}{176}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{161}{176}\right)$
$\chi_{10304}(2701,\cdot)$	$1$	$1$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{101}{176}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{83}{176}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{19}{176}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{85}{176}\right)$
$\chi_{10304}(2757,\cdot)$	$1$	$1$	$e\left(\frac{57}{176}\right)$	$e\left(\frac{139}{176}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{63}{176}\right)$	$e\left(\frac{109}{176}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{61}{176}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{171}{176}\right)$
$\chi_{10304}(2813,\cdot)$	$1$	$1$	$e\left(\frac{155}{176}\right)$	$e\left(\frac{97}{176}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{125}{176}\right)$	$e\left(\frac{71}{176}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{135}{176}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{113}{176}\right)$
$\chi_{10304}(2869,\cdot)$	$1$	$1$	$e\left(\frac{93}{176}\right)$	$e\left(\frac{23}{176}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{75}{176}\right)$	$e\left(\frac{113}{176}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{81}{176}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{103}{176}\right)$
$\chi_{10304}(2981,\cdot)$	$1$	$1$	$e\left(\frac{81}{176}\right)$	$e\left(\frac{3}{176}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{71}{176}\right)$	$e\left(\frac{53}{176}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{133}{176}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{67}{176}\right)$
$\chi_{10304}(3093,\cdot)$	$1$	$1$	$e\left(\frac{85}{176}\right)$	$e\left(\frac{127}{176}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{131}{176}\right)$	$e\left(\frac{73}{176}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{57}{176}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{79}{176}\right)$
$\chi_{10304}(3149,\cdot)$	$1$	$1$	$e\left(\frac{135}{176}\right)$	$e\left(\frac{5}{176}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{1}{176}\right)$	$e\left(\frac{147}{176}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{163}{176}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{53}{176}\right)$
$\chi_{10304}(3317,\cdot)$	$1$	$1$	$e\left(\frac{29}{176}\right)$	$e\left(\frac{151}{176}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{171}{176}\right)$	$e\left(\frac{145}{176}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{65}{176}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{87}{176}\right)$
$\chi_{10304}(3373,\cdot)$	$1$	$1$	$e\left(\frac{31}{176}\right)$	$e\left(\frac{125}{176}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{25}{176}\right)$	$e\left(\frac{155}{176}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{27}{176}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{93}{176}\right)$
$\chi_{10304}(3653,\cdot)$	$1$	$1$	$e\left(\frac{105}{176}\right)$	$e\left(\frac{43}{176}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{79}{176}\right)$	$e\left(\frac{173}{176}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{29}{176}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{139}{176}\right)$
$\chi_{10304}(3989,\cdot)$	$1$	$1$	$e\left(\frac{21}{176}\right)$	$e\left(\frac{79}{176}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{51}{176}\right)$	$e\left(\frac{105}{176}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{41}{176}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{63}{176}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(25\)	\(27\)
\(\chi_{10304}(125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{176}\right)\)	\(e\left(\frac{145}{176}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{29}{176}\right)\)	\(e\left(\frac{39}{176}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{151}{176}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{129}{176}\right)\)
\(\chi_{10304}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{176}\right)\)	\(e\left(\frac{7}{176}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{107}{176}\right)\)	\(e\left(\frac{65}{176}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{17}{176}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{39}{176}\right)\)
\(\chi_{10304}(237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{176}\right)\)	\(e\left(\frac{141}{176}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{169}{176}\right)\)	\(e\left(\frac{27}{176}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{91}{176}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{157}{176}\right)\)
\(\chi_{10304}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{176}\right)\)	\(e\left(\frac{67}{176}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{119}{176}\right)\)	\(e\left(\frac{69}{176}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{37}{176}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{147}{176}\right)\)
\(\chi_{10304}(405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{176}\right)\)	\(e\left(\frac{47}{176}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{115}{176}\right)\)	\(e\left(\frac{9}{176}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{89}{176}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{111}{176}\right)\)
\(\chi_{10304}(517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{176}\right)\)	\(e\left(\frac{171}{176}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{175}{176}\right)\)	\(e\left(\frac{29}{176}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{13}{176}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{123}{176}\right)\)
\(\chi_{10304}(573,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{176}\right)\)	\(e\left(\frac{49}{176}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{45}{176}\right)\)	\(e\left(\frac{103}{176}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{119}{176}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{97}{176}\right)\)
\(\chi_{10304}(741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{19}{176}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{39}{176}\right)\)	\(e\left(\frac{101}{176}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{21}{176}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{131}{176}\right)\)
\(\chi_{10304}(797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{176}\right)\)	\(e\left(\frac{169}{176}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{69}{176}\right)\)	\(e\left(\frac{111}{176}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{159}{176}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{137}{176}\right)\)
\(\chi_{10304}(1077,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{176}\right)\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{129}{176}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{7}{176}\right)\)
\(\chi_{10304}(1413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{176}\right)\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{95}{176}\right)\)	\(e\left(\frac{61}{176}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{173}{176}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{107}{176}\right)\)
\(\chi_{10304}(1469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{173}{176}\right)\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{39}{176}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{17}{176}\right)\)
\(\chi_{10304}(1525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{176}\right)\)	\(e\left(\frac{119}{176}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{59}{176}\right)\)	\(e\left(\frac{49}{176}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{113}{176}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{135}{176}\right)\)
\(\chi_{10304}(1581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{159}{176}\right)\)	\(e\left(\frac{45}{176}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{9}{176}\right)\)	\(e\left(\frac{91}{176}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{59}{176}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{125}{176}\right)\)
\(\chi_{10304}(1693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{147}{176}\right)\)	\(e\left(\frac{25}{176}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{5}{176}\right)\)	\(e\left(\frac{31}{176}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{111}{176}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{89}{176}\right)\)
\(\chi_{10304}(1805,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{176}\right)\)	\(e\left(\frac{149}{176}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{65}{176}\right)\)	\(e\left(\frac{51}{176}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{35}{176}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{101}{176}\right)\)
\(\chi_{10304}(1861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{176}\right)\)	\(e\left(\frac{27}{176}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{111}{176}\right)\)	\(e\left(\frac{125}{176}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{141}{176}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{75}{176}\right)\)
\(\chi_{10304}(2029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{176}\right)\)	\(e\left(\frac{173}{176}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{105}{176}\right)\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{43}{176}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{109}{176}\right)\)
\(\chi_{10304}(2085,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{176}\right)\)	\(e\left(\frac{147}{176}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{135}{176}\right)\)	\(e\left(\frac{133}{176}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{5}{176}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{115}{176}\right)\)
\(\chi_{10304}(2365,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{171}{176}\right)\)	\(e\left(\frac{65}{176}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{13}{176}\right)\)	\(e\left(\frac{151}{176}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{7}{176}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{161}{176}\right)\)
\(\chi_{10304}(2701,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{101}{176}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{83}{176}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{19}{176}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{85}{176}\right)\)
\(\chi_{10304}(2757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{176}\right)\)	\(e\left(\frac{139}{176}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{63}{176}\right)\)	\(e\left(\frac{109}{176}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{61}{176}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{171}{176}\right)\)
\(\chi_{10304}(2813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{176}\right)\)	\(e\left(\frac{97}{176}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{125}{176}\right)\)	\(e\left(\frac{71}{176}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{135}{176}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{113}{176}\right)\)
\(\chi_{10304}(2869,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{176}\right)\)	\(e\left(\frac{23}{176}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{75}{176}\right)\)	\(e\left(\frac{113}{176}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{81}{176}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{103}{176}\right)\)
\(\chi_{10304}(2981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{176}\right)\)	\(e\left(\frac{3}{176}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{71}{176}\right)\)	\(e\left(\frac{53}{176}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{133}{176}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{67}{176}\right)\)
\(\chi_{10304}(3093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{176}\right)\)	\(e\left(\frac{127}{176}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{131}{176}\right)\)	\(e\left(\frac{73}{176}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{57}{176}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{79}{176}\right)\)
\(\chi_{10304}(3149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{135}{176}\right)\)	\(e\left(\frac{5}{176}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{1}{176}\right)\)	\(e\left(\frac{147}{176}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{163}{176}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{53}{176}\right)\)
\(\chi_{10304}(3317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{176}\right)\)	\(e\left(\frac{151}{176}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{171}{176}\right)\)	\(e\left(\frac{145}{176}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{65}{176}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{87}{176}\right)\)
\(\chi_{10304}(3373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{176}\right)\)	\(e\left(\frac{125}{176}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{25}{176}\right)\)	\(e\left(\frac{155}{176}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{27}{176}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{93}{176}\right)\)
\(\chi_{10304}(3653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{105}{176}\right)\)	\(e\left(\frac{43}{176}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{79}{176}\right)\)	\(e\left(\frac{173}{176}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{29}{176}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{139}{176}\right)\)
\(\chi_{10304}(3989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{176}\right)\)	\(e\left(\frac{79}{176}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{51}{176}\right)\)	\(e\left(\frac{105}{176}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{41}{176}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{63}{176}\right)\)

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First 31 of 80 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	10304.fj
Modulus	$10304$
Conductor	$10304$
Order	$176$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(10304\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(10304\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(176\)	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:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);