LMFDB - Dirichlet character orbit 6256.fa

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6256, base_ring=CyclotomicField(176)) M = H._module chi = DirichletCharacter(H, M([0,44,55,8])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(5, 6256)) 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("6256.5"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$6256$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$6256$	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:	$\Q(\zeta_{176})$
Fixed field:	Number field defined by a degree 176 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$19$	$21$	$25$
$\chi_{6256}(5,\cdot)$	$1$	$1$	$e\left(\frac{139}{176}\right)$	$e\left(\frac{151}{176}\right)$	$e\left(\frac{141}{176}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{149}{176}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{63}{88}\right)$
$\chi_{6256}(37,\cdot)$	$1$	$1$	$e\left(\frac{15}{176}\right)$	$e\left(\frac{91}{176}\right)$	$e\left(\frac{57}{176}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{49}{176}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{88}\right)$
$\chi_{6256}(61,\cdot)$	$1$	$1$	$e\left(\frac{141}{176}\right)$	$e\left(\frac{81}{176}\right)$	$e\left(\frac{43}{176}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{3}{176}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{81}{88}\right)$
$\chi_{6256}(109,\cdot)$	$1$	$1$	$e\left(\frac{5}{176}\right)$	$e\left(\frac{89}{176}\right)$	$e\left(\frac{19}{176}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{75}{176}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{88}\right)$
$\chi_{6256}(125,\cdot)$	$1$	$1$	$e\left(\frac{65}{176}\right)$	$e\left(\frac{101}{176}\right)$	$e\left(\frac{71}{176}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{95}{176}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{13}{88}\right)$
$\chi_{6256}(309,\cdot)$	$1$	$1$	$e\left(\frac{175}{176}\right)$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{137}{176}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{35}{88}\right)$
$\chi_{6256}(333,\cdot)$	$1$	$1$	$e\left(\frac{173}{176}\right)$	$e\left(\frac{17}{176}\right)$	$e\left(\frac{59}{176}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{131}{176}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{88}\right)$
$\chi_{6256}(405,\cdot)$	$1$	$1$	$e\left(\frac{103}{176}\right)$	$e\left(\frac{3}{176}\right)$	$e\left(\frac{145}{176}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{137}{176}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{88}\right)$
$\chi_{6256}(549,\cdot)$	$1$	$1$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{7}{176}\right)$	$e\left(\frac{45}{176}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{85}{176}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{88}\right)$
$\chi_{6256}(589,\cdot)$	$1$	$1$	$e\left(\frac{169}{176}\right)$	$e\left(\frac{157}{176}\right)$	$e\left(\frac{79}{176}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{71}{176}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{69}{88}\right)$
$\chi_{6256}(605,\cdot)$	$1$	$1$	$e\left(\frac{45}{176}\right)$	$e\left(\frac{97}{176}\right)$	$e\left(\frac{171}{176}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{147}{176}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{88}\right)$
$\chi_{6256}(677,\cdot)$	$1$	$1$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{35}{176}\right)$	$e\left(\frac{49}{176}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{73}{176}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{35}{88}\right)$
$\chi_{6256}(709,\cdot)$	$1$	$1$	$e\left(\frac{83}{176}\right)$	$e\left(\frac{175}{176}\right)$	$e\left(\frac{69}{176}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{13}{176}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{87}{88}\right)$
$\chi_{6256}(861,\cdot)$	$1$	$1$	$e\left(\frac{153}{176}\right)$	$e\left(\frac{13}{176}\right)$	$e\left(\frac{159}{176}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{7}{176}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{13}{88}\right)$
$\chi_{6256}(925,\cdot)$	$1$	$1$	$e\left(\frac{117}{176}\right)$	$e\left(\frac{41}{176}\right)$	$e\left(\frac{163}{176}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{171}{176}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{41}{88}\right)$
$\chi_{6256}(941,\cdot)$	$1$	$1$	$e\left(\frac{113}{176}\right)$	$e\left(\frac{5}{176}\right)$	$e\left(\frac{7}{176}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{111}{176}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{5}{88}\right)$
$\chi_{6256}(981,\cdot)$	$1$	$1$	$e\left(\frac{163}{176}\right)$	$e\left(\frac{15}{176}\right)$	$e\left(\frac{21}{176}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{157}{176}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{15}{88}\right)$
$\chi_{6256}(1125,\cdot)$	$1$	$1$	$e\left(\frac{47}{176}\right)$	$e\left(\frac{27}{176}\right)$	$e\left(\frac{73}{176}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{1}{176}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{27}{88}\right)$
$\chi_{6256}(1213,\cdot)$	$1$	$1$	$e\left(\frac{49}{176}\right)$	$e\left(\frac{133}{176}\right)$	$e\left(\frac{151}{176}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{31}{176}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{45}{88}\right)$
$\chi_{6256}(1253,\cdot)$	$1$	$1$	$e\left(\frac{19}{176}\right)$	$e\left(\frac{127}{176}\right)$	$e\left(\frac{37}{176}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{109}{176}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{39}{88}\right)$
$\chi_{6256}(1397,\cdot)$	$1$	$1$	$e\left(\frac{159}{176}\right)$	$e\left(\frac{155}{176}\right)$	$e\left(\frac{41}{176}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{97}{176}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{67}{88}\right)$
$\chi_{6256}(1469,\cdot)$	$1$	$1$	$e\left(\frac{101}{176}\right)$	$e\left(\frac{73}{176}\right)$	$e\left(\frac{67}{176}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{107}{176}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{73}{88}\right)$
$\chi_{6256}(1493,\cdot)$	$1$	$1$	$e\left(\frac{135}{176}\right)$	$e\left(\frac{115}{176}\right)$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{89}{176}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{27}{88}\right)$
$\chi_{6256}(1525,\cdot)$	$1$	$1$	$e\left(\frac{67}{176}\right)$	$e\left(\frac{31}{176}\right)$	$e\left(\frac{149}{176}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{125}{176}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{31}{88}\right)$
$\chi_{6256}(1677,\cdot)$	$1$	$1$	$e\left(\frac{25}{176}\right)$	$e\left(\frac{93}{176}\right)$	$e\left(\frac{95}{176}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{23}{176}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{5}{88}\right)$
$\chi_{6256}(1693,\cdot)$	$1$	$1$	$e\left(\frac{125}{176}\right)$	$e\left(\frac{113}{176}\right)$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{115}{176}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{25}{88}\right)$
$\chi_{6256}(1765,\cdot)$	$1$	$1$	$e\left(\frac{71}{176}\right)$	$e\left(\frac{67}{176}\right)$	$e\left(\frac{129}{176}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{9}{176}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{67}{88}\right)$
$\chi_{6256}(1949,\cdot)$	$1$	$1$	$e\left(\frac{137}{176}\right)$	$e\left(\frac{45}{176}\right)$	$e\left(\frac{63}{176}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{119}{176}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{45}{88}\right)$
$\chi_{6256}(1965,\cdot)$	$1$	$1$	$e\left(\frac{109}{176}\right)$	$e\left(\frac{145}{176}\right)$	$e\left(\frac{27}{176}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{51}{176}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{57}{88}\right)$
$\chi_{6256}(2029,\cdot)$	$1$	$1$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{85}{176}\right)$	$e\left(\frac{119}{176}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{127}{176}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{85}{88}\right)$
$\chi_{6256}(2181,\cdot)$	$1$	$1$	$e\left(\frac{171}{176}\right)$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{157}{176}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{101}{176}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{87}{88}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(21\)	\(25\)
\(\chi_{6256}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{176}\right)\)	\(e\left(\frac{151}{176}\right)\)	\(e\left(\frac{141}{176}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{149}{176}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{63}{88}\right)\)
\(\chi_{6256}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{176}\right)\)	\(e\left(\frac{91}{176}\right)\)	\(e\left(\frac{57}{176}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{49}{176}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{88}\right)\)
\(\chi_{6256}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{141}{176}\right)\)	\(e\left(\frac{81}{176}\right)\)	\(e\left(\frac{43}{176}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{3}{176}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{81}{88}\right)\)
\(\chi_{6256}(109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{176}\right)\)	\(e\left(\frac{89}{176}\right)\)	\(e\left(\frac{19}{176}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{75}{176}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{88}\right)\)
\(\chi_{6256}(125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{176}\right)\)	\(e\left(\frac{101}{176}\right)\)	\(e\left(\frac{71}{176}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{95}{176}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{13}{88}\right)\)
\(\chi_{6256}(309,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{176}\right)\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{137}{176}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{35}{88}\right)\)
\(\chi_{6256}(333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{176}\right)\)	\(e\left(\frac{17}{176}\right)\)	\(e\left(\frac{59}{176}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{131}{176}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{88}\right)\)
\(\chi_{6256}(405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{176}\right)\)	\(e\left(\frac{3}{176}\right)\)	\(e\left(\frac{145}{176}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{137}{176}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{88}\right)\)
\(\chi_{6256}(549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{7}{176}\right)\)	\(e\left(\frac{45}{176}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{85}{176}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{88}\right)\)
\(\chi_{6256}(589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{176}\right)\)	\(e\left(\frac{157}{176}\right)\)	\(e\left(\frac{79}{176}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{71}{176}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{69}{88}\right)\)
\(\chi_{6256}(605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{176}\right)\)	\(e\left(\frac{97}{176}\right)\)	\(e\left(\frac{171}{176}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{147}{176}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{88}\right)\)
\(\chi_{6256}(677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{35}{176}\right)\)	\(e\left(\frac{49}{176}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{73}{176}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{35}{88}\right)\)
\(\chi_{6256}(709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{176}\right)\)	\(e\left(\frac{175}{176}\right)\)	\(e\left(\frac{69}{176}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{13}{176}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{87}{88}\right)\)
\(\chi_{6256}(861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{176}\right)\)	\(e\left(\frac{13}{176}\right)\)	\(e\left(\frac{159}{176}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{7}{176}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{13}{88}\right)\)
\(\chi_{6256}(925,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{176}\right)\)	\(e\left(\frac{41}{176}\right)\)	\(e\left(\frac{163}{176}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{171}{176}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{41}{88}\right)\)
\(\chi_{6256}(941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{176}\right)\)	\(e\left(\frac{5}{176}\right)\)	\(e\left(\frac{7}{176}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{111}{176}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{5}{88}\right)\)
\(\chi_{6256}(981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{176}\right)\)	\(e\left(\frac{15}{176}\right)\)	\(e\left(\frac{21}{176}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{157}{176}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{15}{88}\right)\)
\(\chi_{6256}(1125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{176}\right)\)	\(e\left(\frac{27}{176}\right)\)	\(e\left(\frac{73}{176}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{1}{176}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{27}{88}\right)\)
\(\chi_{6256}(1213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{176}\right)\)	\(e\left(\frac{133}{176}\right)\)	\(e\left(\frac{151}{176}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{31}{176}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{45}{88}\right)\)
\(\chi_{6256}(1253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{176}\right)\)	\(e\left(\frac{127}{176}\right)\)	\(e\left(\frac{37}{176}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{109}{176}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{39}{88}\right)\)
\(\chi_{6256}(1397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{159}{176}\right)\)	\(e\left(\frac{155}{176}\right)\)	\(e\left(\frac{41}{176}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{97}{176}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{67}{88}\right)\)
\(\chi_{6256}(1469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{176}\right)\)	\(e\left(\frac{73}{176}\right)\)	\(e\left(\frac{67}{176}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{107}{176}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{73}{88}\right)\)
\(\chi_{6256}(1493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{135}{176}\right)\)	\(e\left(\frac{115}{176}\right)\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{89}{176}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{27}{88}\right)\)
\(\chi_{6256}(1525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{176}\right)\)	\(e\left(\frac{31}{176}\right)\)	\(e\left(\frac{149}{176}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{125}{176}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{31}{88}\right)\)
\(\chi_{6256}(1677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{176}\right)\)	\(e\left(\frac{93}{176}\right)\)	\(e\left(\frac{95}{176}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{23}{176}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{5}{88}\right)\)
\(\chi_{6256}(1693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{176}\right)\)	\(e\left(\frac{113}{176}\right)\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{115}{176}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{25}{88}\right)\)
\(\chi_{6256}(1765,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{176}\right)\)	\(e\left(\frac{67}{176}\right)\)	\(e\left(\frac{129}{176}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{9}{176}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{67}{88}\right)\)
\(\chi_{6256}(1949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{176}\right)\)	\(e\left(\frac{45}{176}\right)\)	\(e\left(\frac{63}{176}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{119}{176}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{45}{88}\right)\)
\(\chi_{6256}(1965,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{176}\right)\)	\(e\left(\frac{145}{176}\right)\)	\(e\left(\frac{27}{176}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{51}{176}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{57}{88}\right)\)
\(\chi_{6256}(2029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{85}{176}\right)\)	\(e\left(\frac{119}{176}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{127}{176}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{85}{88}\right)\)
\(\chi_{6256}(2181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{171}{176}\right)\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{157}{176}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{101}{176}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{87}{88}\right)\)

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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	6256.fa
Modulus	$6256$
Conductor	$6256$
Order	$176$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(6256\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(6256\)	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);