LMFDB - Dirichlet character orbit 3392.cr

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3392, base_ring=CyclotomicField(208)) M = H._module chi = DirichletCharacter(H, M([104,39,68])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(3, 3392)) 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("3392.3"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3392$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3392$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$208$	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:	$\Q(\zeta_{208})$
Fixed field:	Number field defined by a degree 208 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{3392}(3,\cdot)$	$1$	$1$	$e\left(\frac{129}{208}\right)$	$e\left(\frac{115}{208}\right)$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{25}{104}\right)$	$e\left(\frac{83}{208}\right)$	$e\left(\frac{137}{208}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{189}{208}\right)$	$e\left(\frac{119}{208}\right)$
$\chi_{3392}(19,\cdot)$	$1$	$1$	$e\left(\frac{189}{208}\right)$	$e\left(\frac{183}{208}\right)$	$e\left(\frac{87}{104}\right)$	$e\left(\frac{85}{104}\right)$	$e\left(\frac{199}{208}\right)$	$e\left(\frac{133}{208}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{185}{208}\right)$	$e\left(\frac{155}{208}\right)$
$\chi_{3392}(27,\cdot)$	$1$	$1$	$e\left(\frac{179}{208}\right)$	$e\left(\frac{137}{208}\right)$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{75}{104}\right)$	$e\left(\frac{41}{208}\right)$	$e\left(\frac{203}{208}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{151}{208}\right)$	$e\left(\frac{149}{208}\right)$
$\chi_{3392}(35,\cdot)$	$1$	$1$	$e\left(\frac{105}{208}\right)$	$e\left(\frac{171}{208}\right)$	$e\left(\frac{83}{104}\right)$	$e\left(\frac{1}{104}\right)$	$e\left(\frac{203}{208}\right)$	$e\left(\frac{97}{208}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{149}{208}\right)$	$e\left(\frac{63}{208}\right)$
$\chi_{3392}(75,\cdot)$	$1$	$1$	$e\left(\frac{151}{208}\right)$	$e\left(\frac{133}{208}\right)$	$e\left(\frac{53}{104}\right)$	$e\left(\frac{47}{104}\right)$	$e\left(\frac{181}{208}\right)$	$e\left(\frac{191}{208}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{139}{208}\right)$	$e\left(\frac{49}{208}\right)$
$\chi_{3392}(139,\cdot)$	$1$	$1$	$e\left(\frac{199}{208}\right)$	$e\left(\frac{21}{208}\right)$	$e\left(\frac{85}{104}\right)$	$e\left(\frac{95}{104}\right)$	$e\left(\frac{149}{208}\right)$	$e\left(\frac{63}{208}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{11}{208}\right)$	$e\left(\frac{161}{208}\right)$
$\chi_{3392}(147,\cdot)$	$1$	$1$	$e\left(\frac{109}{208}\right)$	$e\left(\frac{23}{208}\right)$	$e\left(\frac{103}{104}\right)$	$e\left(\frac{5}{104}\right)$	$e\left(\frac{183}{208}\right)$	$e\left(\frac{69}{208}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{121}{208}\right)$	$e\left(\frac{107}{208}\right)$
$\chi_{3392}(171,\cdot)$	$1$	$1$	$e\left(\frac{31}{208}\right)$	$e\left(\frac{205}{208}\right)$	$e\left(\frac{77}{104}\right)$	$e\left(\frac{31}{104}\right)$	$e\left(\frac{157}{208}\right)$	$e\left(\frac{199}{208}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{147}{208}\right)$	$e\left(\frac{185}{208}\right)$
$\chi_{3392}(179,\cdot)$	$1$	$1$	$e\left(\frac{69}{208}\right)$	$e\left(\frac{47}{208}\right)$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{69}{104}\right)$	$e\left(\frac{175}{208}\right)$	$e\left(\frac{141}{208}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{193}{208}\right)$	$e\left(\frac{83}{208}\right)$
$\chi_{3392}(243,\cdot)$	$1$	$1$	$e\left(\frac{21}{208}\right)$	$e\left(\frac{159}{208}\right)$	$e\left(\frac{79}{104}\right)$	$e\left(\frac{21}{104}\right)$	$e\left(\frac{207}{208}\right)$	$e\left(\frac{61}{208}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{113}{208}\right)$	$e\left(\frac{179}{208}\right)$
$\chi_{3392}(283,\cdot)$	$1$	$1$	$e\left(\frac{131}{208}\right)$	$e\left(\frac{41}{208}\right)$	$e\left(\frac{57}{104}\right)$	$e\left(\frac{27}{104}\right)$	$e\left(\frac{73}{208}\right)$	$e\left(\frac{123}{208}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{71}{208}\right)$	$e\left(\frac{37}{208}\right)$
$\chi_{3392}(291,\cdot)$	$1$	$1$	$e\left(\frac{153}{208}\right)$	$e\left(\frac{59}{208}\right)$	$e\left(\frac{11}{104}\right)$	$e\left(\frac{49}{104}\right)$	$e\left(\frac{171}{208}\right)$	$e\left(\frac{177}{208}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{21}{208}\right)$	$e\left(\frac{175}{208}\right)$
$\chi_{3392}(299,\cdot)$	$1$	$1$	$e\left(\frac{111}{208}\right)$	$e\left(\frac{157}{208}\right)$	$e\left(\frac{61}{104}\right)$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{173}{208}\right)$	$e\left(\frac{55}{208}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{3}{208}\right)$	$e\left(\frac{25}{208}\right)$
$\chi_{3392}(315,\cdot)$	$1$	$1$	$e\left(\frac{155}{208}\right)$	$e\left(\frac{193}{208}\right)$	$e\left(\frac{73}{104}\right)$	$e\left(\frac{51}{104}\right)$	$e\left(\frac{161}{208}\right)$	$e\left(\frac{163}{208}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{111}{208}\right)$	$e\left(\frac{93}{208}\right)$
$\chi_{3392}(379,\cdot)$	$1$	$1$	$e\left(\frac{139}{208}\right)$	$e\left(\frac{161}{208}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{35}{104}\right)$	$e\left(\frac{33}{208}\right)$	$e\left(\frac{67}{208}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{15}{208}\right)$	$e\left(\frac{125}{208}\right)$
$\chi_{3392}(403,\cdot)$	$1$	$1$	$e\left(\frac{93}{208}\right)$	$e\left(\frac{199}{208}\right)$	$e\left(\frac{23}{104}\right)$	$e\left(\frac{93}{104}\right)$	$e\left(\frac{55}{208}\right)$	$e\left(\frac{181}{208}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{25}{208}\right)$	$e\left(\frac{139}{208}\right)$
$\chi_{3392}(419,\cdot)$	$1$	$1$	$e\left(\frac{89}{208}\right)$	$e\left(\frac{139}{208}\right)$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{75}{208}\right)$	$e\left(\frac{1}{208}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{53}{208}\right)$	$e\left(\frac{95}{208}\right)$
$\chi_{3392}(475,\cdot)$	$1$	$1$	$e\left(\frac{3}{208}\right)$	$e\left(\frac{201}{208}\right)$	$e\left(\frac{41}{104}\right)$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{89}{208}\right)$	$e\left(\frac{187}{208}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{135}{208}\right)$	$e\left(\frac{85}{208}\right)$
$\chi_{3392}(491,\cdot)$	$1$	$1$	$e\left(\frac{175}{208}\right)$	$e\left(\frac{77}{208}\right)$	$e\left(\frac{69}{104}\right)$	$e\left(\frac{71}{104}\right)$	$e\left(\frac{61}{208}\right)$	$e\left(\frac{23}{208}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{179}{208}\right)$	$e\left(\frac{105}{208}\right)$
$\chi_{3392}(675,\cdot)$	$1$	$1$	$e\left(\frac{201}{208}\right)$	$e\left(\frac{155}{208}\right)$	$e\left(\frac{43}{104}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{139}{208}\right)$	$e\left(\frac{49}{208}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{101}{208}\right)$	$e\left(\frac{79}{208}\right)$
$\chi_{3392}(691,\cdot)$	$1$	$1$	$e\left(\frac{133}{208}\right)$	$e\left(\frac{175}{208}\right)$	$e\left(\frac{15}{104}\right)$	$e\left(\frac{29}{104}\right)$	$e\left(\frac{63}{208}\right)$	$e\left(\frac{109}{208}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{161}{208}\right)$	$e\left(\frac{163}{208}\right)$
$\chi_{3392}(747,\cdot)$	$1$	$1$	$e\left(\frac{63}{208}\right)$	$e\left(\frac{61}{208}\right)$	$e\left(\frac{29}{104}\right)$	$e\left(\frac{63}{104}\right)$	$e\left(\frac{205}{208}\right)$	$e\left(\frac{183}{208}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{131}{208}\right)$	$e\left(\frac{121}{208}\right)$
$\chi_{3392}(763,\cdot)$	$1$	$1$	$e\left(\frac{171}{208}\right)$	$e\left(\frac{17}{208}\right)$	$e\left(\frac{49}{104}\right)$	$e\left(\frac{67}{104}\right)$	$e\left(\frac{81}{208}\right)$	$e\left(\frac{51}{208}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{207}{208}\right)$	$e\left(\frac{61}{208}\right)$
$\chi_{3392}(787,\cdot)$	$1$	$1$	$e\left(\frac{61}{208}\right)$	$e\left(\frac{135}{208}\right)$	$e\left(\frac{71}{104}\right)$	$e\left(\frac{61}{104}\right)$	$e\left(\frac{7}{208}\right)$	$e\left(\frac{197}{208}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{41}{208}\right)$	$e\left(\frac{203}{208}\right)$
$\chi_{3392}(851,\cdot)$	$1$	$1$	$e\left(\frac{77}{208}\right)$	$e\left(\frac{167}{208}\right)$	$e\left(\frac{47}{104}\right)$	$e\left(\frac{77}{104}\right)$	$e\left(\frac{135}{208}\right)$	$e\left(\frac{85}{208}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{137}{208}\right)$	$e\left(\frac{171}{208}\right)$
$\chi_{3392}(867,\cdot)$	$1$	$1$	$e\left(\frac{137}{208}\right)$	$e\left(\frac{27}{208}\right)$	$e\left(\frac{35}{104}\right)$	$e\left(\frac{33}{104}\right)$	$e\left(\frac{43}{208}\right)$	$e\left(\frac{81}{208}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{133}{208}\right)$	$e\left(\frac{207}{208}\right)$
$\chi_{3392}(875,\cdot)$	$1$	$1$	$e\left(\frac{127}{208}\right)$	$e\left(\frac{189}{208}\right)$	$e\left(\frac{37}{104}\right)$	$e\left(\frac{23}{104}\right)$	$e\left(\frac{93}{208}\right)$	$e\left(\frac{151}{208}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{99}{208}\right)$	$e\left(\frac{201}{208}\right)$
$\chi_{3392}(883,\cdot)$	$1$	$1$	$e\left(\frac{53}{208}\right)$	$e\left(\frac{15}{208}\right)$	$e\left(\frac{31}{104}\right)$	$e\left(\frac{53}{104}\right)$	$e\left(\frac{47}{208}\right)$	$e\left(\frac{45}{208}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{97}{208}\right)$	$e\left(\frac{115}{208}\right)$
$\chi_{3392}(923,\cdot)$	$1$	$1$	$e\left(\frac{99}{208}\right)$	$e\left(\frac{185}{208}\right)$	$e\left(\frac{1}{104}\right)$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{25}{208}\right)$	$e\left(\frac{139}{208}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{87}{208}\right)$	$e\left(\frac{101}{208}\right)$
$\chi_{3392}(987,\cdot)$	$1$	$1$	$e\left(\frac{147}{208}\right)$	$e\left(\frac{73}{208}\right)$	$e\left(\frac{33}{104}\right)$	$e\left(\frac{43}{104}\right)$	$e\left(\frac{201}{208}\right)$	$e\left(\frac{11}{208}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{167}{208}\right)$	$e\left(\frac{5}{208}\right)$
$\chi_{3392}(995,\cdot)$	$1$	$1$	$e\left(\frac{57}{208}\right)$	$e\left(\frac{75}{208}\right)$	$e\left(\frac{51}{104}\right)$	$e\left(\frac{57}{104}\right)$	$e\left(\frac{27}{208}\right)$	$e\left(\frac{17}{208}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{69}{208}\right)$	$e\left(\frac{159}{208}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{3392}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{129}{208}\right)\)	\(e\left(\frac{115}{208}\right)\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{25}{104}\right)\)	\(e\left(\frac{83}{208}\right)\)	\(e\left(\frac{137}{208}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{189}{208}\right)\)	\(e\left(\frac{119}{208}\right)\)
\(\chi_{3392}(19,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{189}{208}\right)\)	\(e\left(\frac{183}{208}\right)\)	\(e\left(\frac{87}{104}\right)\)	\(e\left(\frac{85}{104}\right)\)	\(e\left(\frac{199}{208}\right)\)	\(e\left(\frac{133}{208}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{185}{208}\right)\)	\(e\left(\frac{155}{208}\right)\)
\(\chi_{3392}(27,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{208}\right)\)	\(e\left(\frac{137}{208}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{75}{104}\right)\)	\(e\left(\frac{41}{208}\right)\)	\(e\left(\frac{203}{208}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{151}{208}\right)\)	\(e\left(\frac{149}{208}\right)\)
\(\chi_{3392}(35,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{105}{208}\right)\)	\(e\left(\frac{171}{208}\right)\)	\(e\left(\frac{83}{104}\right)\)	\(e\left(\frac{1}{104}\right)\)	\(e\left(\frac{203}{208}\right)\)	\(e\left(\frac{97}{208}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{149}{208}\right)\)	\(e\left(\frac{63}{208}\right)\)
\(\chi_{3392}(75,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{208}\right)\)	\(e\left(\frac{133}{208}\right)\)	\(e\left(\frac{53}{104}\right)\)	\(e\left(\frac{47}{104}\right)\)	\(e\left(\frac{181}{208}\right)\)	\(e\left(\frac{191}{208}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{139}{208}\right)\)	\(e\left(\frac{49}{208}\right)\)
\(\chi_{3392}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{208}\right)\)	\(e\left(\frac{21}{208}\right)\)	\(e\left(\frac{85}{104}\right)\)	\(e\left(\frac{95}{104}\right)\)	\(e\left(\frac{149}{208}\right)\)	\(e\left(\frac{63}{208}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{11}{208}\right)\)	\(e\left(\frac{161}{208}\right)\)
\(\chi_{3392}(147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{208}\right)\)	\(e\left(\frac{23}{208}\right)\)	\(e\left(\frac{103}{104}\right)\)	\(e\left(\frac{5}{104}\right)\)	\(e\left(\frac{183}{208}\right)\)	\(e\left(\frac{69}{208}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{121}{208}\right)\)	\(e\left(\frac{107}{208}\right)\)
\(\chi_{3392}(171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{208}\right)\)	\(e\left(\frac{205}{208}\right)\)	\(e\left(\frac{77}{104}\right)\)	\(e\left(\frac{31}{104}\right)\)	\(e\left(\frac{157}{208}\right)\)	\(e\left(\frac{199}{208}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{147}{208}\right)\)	\(e\left(\frac{185}{208}\right)\)
\(\chi_{3392}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{208}\right)\)	\(e\left(\frac{47}{208}\right)\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{69}{104}\right)\)	\(e\left(\frac{175}{208}\right)\)	\(e\left(\frac{141}{208}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{193}{208}\right)\)	\(e\left(\frac{83}{208}\right)\)
\(\chi_{3392}(243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{208}\right)\)	\(e\left(\frac{159}{208}\right)\)	\(e\left(\frac{79}{104}\right)\)	\(e\left(\frac{21}{104}\right)\)	\(e\left(\frac{207}{208}\right)\)	\(e\left(\frac{61}{208}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{113}{208}\right)\)	\(e\left(\frac{179}{208}\right)\)
\(\chi_{3392}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{208}\right)\)	\(e\left(\frac{41}{208}\right)\)	\(e\left(\frac{57}{104}\right)\)	\(e\left(\frac{27}{104}\right)\)	\(e\left(\frac{73}{208}\right)\)	\(e\left(\frac{123}{208}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{71}{208}\right)\)	\(e\left(\frac{37}{208}\right)\)
\(\chi_{3392}(291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{208}\right)\)	\(e\left(\frac{59}{208}\right)\)	\(e\left(\frac{11}{104}\right)\)	\(e\left(\frac{49}{104}\right)\)	\(e\left(\frac{171}{208}\right)\)	\(e\left(\frac{177}{208}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{21}{208}\right)\)	\(e\left(\frac{175}{208}\right)\)
\(\chi_{3392}(299,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{208}\right)\)	\(e\left(\frac{157}{208}\right)\)	\(e\left(\frac{61}{104}\right)\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{173}{208}\right)\)	\(e\left(\frac{55}{208}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{3}{208}\right)\)	\(e\left(\frac{25}{208}\right)\)
\(\chi_{3392}(315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{208}\right)\)	\(e\left(\frac{193}{208}\right)\)	\(e\left(\frac{73}{104}\right)\)	\(e\left(\frac{51}{104}\right)\)	\(e\left(\frac{161}{208}\right)\)	\(e\left(\frac{163}{208}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{111}{208}\right)\)	\(e\left(\frac{93}{208}\right)\)
\(\chi_{3392}(379,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{208}\right)\)	\(e\left(\frac{161}{208}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{35}{104}\right)\)	\(e\left(\frac{33}{208}\right)\)	\(e\left(\frac{67}{208}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{15}{208}\right)\)	\(e\left(\frac{125}{208}\right)\)
\(\chi_{3392}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{208}\right)\)	\(e\left(\frac{199}{208}\right)\)	\(e\left(\frac{23}{104}\right)\)	\(e\left(\frac{93}{104}\right)\)	\(e\left(\frac{55}{208}\right)\)	\(e\left(\frac{181}{208}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{25}{208}\right)\)	\(e\left(\frac{139}{208}\right)\)
\(\chi_{3392}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{208}\right)\)	\(e\left(\frac{139}{208}\right)\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{75}{208}\right)\)	\(e\left(\frac{1}{208}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{53}{208}\right)\)	\(e\left(\frac{95}{208}\right)\)
\(\chi_{3392}(475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{208}\right)\)	\(e\left(\frac{201}{208}\right)\)	\(e\left(\frac{41}{104}\right)\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{89}{208}\right)\)	\(e\left(\frac{187}{208}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{135}{208}\right)\)	\(e\left(\frac{85}{208}\right)\)
\(\chi_{3392}(491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{208}\right)\)	\(e\left(\frac{77}{208}\right)\)	\(e\left(\frac{69}{104}\right)\)	\(e\left(\frac{71}{104}\right)\)	\(e\left(\frac{61}{208}\right)\)	\(e\left(\frac{23}{208}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{179}{208}\right)\)	\(e\left(\frac{105}{208}\right)\)
\(\chi_{3392}(675,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{201}{208}\right)\)	\(e\left(\frac{155}{208}\right)\)	\(e\left(\frac{43}{104}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{139}{208}\right)\)	\(e\left(\frac{49}{208}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{101}{208}\right)\)	\(e\left(\frac{79}{208}\right)\)
\(\chi_{3392}(691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{208}\right)\)	\(e\left(\frac{175}{208}\right)\)	\(e\left(\frac{15}{104}\right)\)	\(e\left(\frac{29}{104}\right)\)	\(e\left(\frac{63}{208}\right)\)	\(e\left(\frac{109}{208}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{161}{208}\right)\)	\(e\left(\frac{163}{208}\right)\)
\(\chi_{3392}(747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{208}\right)\)	\(e\left(\frac{61}{208}\right)\)	\(e\left(\frac{29}{104}\right)\)	\(e\left(\frac{63}{104}\right)\)	\(e\left(\frac{205}{208}\right)\)	\(e\left(\frac{183}{208}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{131}{208}\right)\)	\(e\left(\frac{121}{208}\right)\)
\(\chi_{3392}(763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{171}{208}\right)\)	\(e\left(\frac{17}{208}\right)\)	\(e\left(\frac{49}{104}\right)\)	\(e\left(\frac{67}{104}\right)\)	\(e\left(\frac{81}{208}\right)\)	\(e\left(\frac{51}{208}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{207}{208}\right)\)	\(e\left(\frac{61}{208}\right)\)
\(\chi_{3392}(787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{208}\right)\)	\(e\left(\frac{135}{208}\right)\)	\(e\left(\frac{71}{104}\right)\)	\(e\left(\frac{61}{104}\right)\)	\(e\left(\frac{7}{208}\right)\)	\(e\left(\frac{197}{208}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{41}{208}\right)\)	\(e\left(\frac{203}{208}\right)\)
\(\chi_{3392}(851,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{208}\right)\)	\(e\left(\frac{167}{208}\right)\)	\(e\left(\frac{47}{104}\right)\)	\(e\left(\frac{77}{104}\right)\)	\(e\left(\frac{135}{208}\right)\)	\(e\left(\frac{85}{208}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{137}{208}\right)\)	\(e\left(\frac{171}{208}\right)\)
\(\chi_{3392}(867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{208}\right)\)	\(e\left(\frac{27}{208}\right)\)	\(e\left(\frac{35}{104}\right)\)	\(e\left(\frac{33}{104}\right)\)	\(e\left(\frac{43}{208}\right)\)	\(e\left(\frac{81}{208}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{133}{208}\right)\)	\(e\left(\frac{207}{208}\right)\)
\(\chi_{3392}(875,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{208}\right)\)	\(e\left(\frac{189}{208}\right)\)	\(e\left(\frac{37}{104}\right)\)	\(e\left(\frac{23}{104}\right)\)	\(e\left(\frac{93}{208}\right)\)	\(e\left(\frac{151}{208}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{99}{208}\right)\)	\(e\left(\frac{201}{208}\right)\)
\(\chi_{3392}(883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{208}\right)\)	\(e\left(\frac{15}{208}\right)\)	\(e\left(\frac{31}{104}\right)\)	\(e\left(\frac{53}{104}\right)\)	\(e\left(\frac{47}{208}\right)\)	\(e\left(\frac{45}{208}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{97}{208}\right)\)	\(e\left(\frac{115}{208}\right)\)
\(\chi_{3392}(923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{208}\right)\)	\(e\left(\frac{185}{208}\right)\)	\(e\left(\frac{1}{104}\right)\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{25}{208}\right)\)	\(e\left(\frac{139}{208}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{87}{208}\right)\)	\(e\left(\frac{101}{208}\right)\)
\(\chi_{3392}(987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{147}{208}\right)\)	\(e\left(\frac{73}{208}\right)\)	\(e\left(\frac{33}{104}\right)\)	\(e\left(\frac{43}{104}\right)\)	\(e\left(\frac{201}{208}\right)\)	\(e\left(\frac{11}{208}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{167}{208}\right)\)	\(e\left(\frac{5}{208}\right)\)
\(\chi_{3392}(995,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{208}\right)\)	\(e\left(\frac{75}{208}\right)\)	\(e\left(\frac{51}{104}\right)\)	\(e\left(\frac{57}{104}\right)\)	\(e\left(\frac{27}{208}\right)\)	\(e\left(\frac{17}{208}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{69}{208}\right)\)	\(e\left(\frac{159}{208}\right)\)

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First 31 of 96 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	3392.cr
Modulus	$3392$
Conductor	$3392$
Order	$208$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3392\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3392\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(208\)	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);