LMFDB - Dirichlet character orbit 2116.n

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2116, base_ring=CyclotomicField(506)) M = H._module chi = DirichletCharacter(H, M([253,129])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(7, 2116)) 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("2116.7"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$2116$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$2116$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$506$	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:	$\Q(\zeta_{253})$
Fixed field:	Number field defined by a degree 506 polynomial (not computed)

First 31 of 220 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{2116}(7,\cdot)$	$1$	$1$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{129}{506}\right)$	$e\left(\frac{98}{253}\right)$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{245}{253}\right)$	$e\left(\frac{111}{253}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{199}{506}\right)$	$e\left(\frac{181}{253}\right)$	$e\left(\frac{489}{506}\right)$
$\chi_{2116}(11,\cdot)$	$1$	$1$	$e\left(\frac{353}{506}\right)$	$e\left(\frac{449}{506}\right)$	$e\left(\frac{245}{253}\right)$	$e\left(\frac{100}{253}\right)$	$e\left(\frac{233}{253}\right)$	$e\left(\frac{151}{253}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{371}{506}\right)$	$e\left(\frac{73}{253}\right)$	$e\left(\frac{337}{506}\right)$
$\chi_{2116}(15,\cdot)$	$1$	$1$	$e\left(\frac{19}{506}\right)$	$e\left(\frac{17}{506}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{19}{253}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{97}{253}\right)$	$e\left(\frac{18}{253}\right)$	$e\left(\frac{493}{506}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{441}{506}\right)$
$\chi_{2116}(19,\cdot)$	$1$	$1$	$e\left(\frac{141}{506}\right)$	$e\left(\frac{499}{506}\right)$	$e\left(\frac{181}{253}\right)$	$e\left(\frac{141}{253}\right)$	$e\left(\frac{73}{253}\right)$	$e\left(\frac{94}{253}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{303}{506}\right)$	$e\left(\frac{151}{253}\right)$	$e\left(\frac{503}{506}\right)$
$\chi_{2116}(43,\cdot)$	$1$	$1$	$e\left(\frac{179}{506}\right)$	$e\left(\frac{27}{506}\right)$	$e\left(\frac{97}{253}\right)$	$e\left(\frac{179}{253}\right)$	$e\left(\frac{116}{253}\right)$	$e\left(\frac{35}{253}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{277}{506}\right)$	$e\left(\frac{32}{253}\right)$	$e\left(\frac{373}{506}\right)$
$\chi_{2116}(51,\cdot)$	$1$	$1$	$e\left(\frac{467}{506}\right)$	$e\left(\frac{45}{506}\right)$	$e\left(\frac{246}{253}\right)$	$e\left(\frac{214}{253}\right)$	$e\left(\frac{109}{253}\right)$	$e\left(\frac{227}{253}\right)$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{222}{253}\right)$	$e\left(\frac{453}{506}\right)$
$\chi_{2116}(67,\cdot)$	$1$	$1$	$e\left(\frac{307}{506}\right)$	$e\left(\frac{35}{506}\right)$	$e\left(\frac{107}{253}\right)$	$e\left(\frac{54}{253}\right)$	$e\left(\frac{141}{253}\right)$	$e\left(\frac{36}{253}\right)$	$e\left(\frac{171}{253}\right)$	$e\left(\frac{3}{506}\right)$	$e\left(\frac{4}{253}\right)$	$e\left(\frac{15}{506}\right)$
$\chi_{2116}(79,\cdot)$	$1$	$1$	$e\left(\frac{455}{506}\right)$	$e\left(\frac{487}{506}\right)$	$e\left(\frac{166}{253}\right)$	$e\left(\frac{202}{253}\right)$	$e\left(\frac{162}{253}\right)$	$e\left(\frac{219}{253}\right)$	$e\left(\frac{218}{253}\right)$	$e\left(\frac{461}{506}\right)$	$e\left(\frac{193}{253}\right)$	$e\left(\frac{281}{506}\right)$
$\chi_{2116}(83,\cdot)$	$1$	$1$	$e\left(\frac{39}{506}\right)$	$e\left(\frac{461}{506}\right)$	$e\left(\frac{7}{253}\right)$	$e\left(\frac{39}{253}\right)$	$e\left(\frac{144}{253}\right)$	$e\left(\frac{26}{253}\right)$	$e\left(\frac{250}{253}\right)$	$e\left(\frac{213}{506}\right)$	$e\left(\frac{31}{253}\right)$	$e\left(\frac{53}{506}\right)$
$\chi_{2116}(99,\cdot)$	$1$	$1$	$e\left(\frac{359}{506}\right)$	$e\left(\frac{481}{506}\right)$	$e\left(\frac{32}{253}\right)$	$e\left(\frac{106}{253}\right)$	$e\left(\frac{80}{253}\right)$	$e\left(\frac{155}{253}\right)$	$e\left(\frac{167}{253}\right)$	$e\left(\frac{287}{506}\right)$	$e\left(\frac{214}{253}\right)$	$e\left(\frac{423}{506}\right)$
$\chi_{2116}(103,\cdot)$	$1$	$1$	$e\left(\frac{441}{506}\right)$	$e\left(\frac{75}{506}\right)$	$e\left(\frac{157}{253}\right)$	$e\left(\frac{188}{253}\right)$	$e\left(\frac{13}{253}\right)$	$e\left(\frac{41}{253}\right)$	$e\left(\frac{5}{253}\right)$	$e\left(\frac{151}{506}\right)$	$e\left(\frac{117}{253}\right)$	$e\left(\frac{249}{506}\right)$
$\chi_{2116}(107,\cdot)$	$1$	$1$	$e\left(\frac{151}{506}\right)$	$e\left(\frac{215}{506}\right)$	$e\left(\frac{79}{253}\right)$	$e\left(\frac{151}{253}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{185}{253}\right)$	$e\left(\frac{183}{253}\right)$	$e\left(\frac{163}{506}\right)$	$e\left(\frac{133}{253}\right)$	$e\left(\frac{309}{506}\right)$
$\chi_{2116}(111,\cdot)$	$1$	$1$	$e\left(\frac{405}{506}\right)$	$e\left(\frac{389}{506}\right)$	$e\left(\frac{170}{253}\right)$	$e\left(\frac{152}{253}\right)$	$e\left(\frac{172}{253}\right)$	$e\left(\frac{17}{253}\right)$	$e\left(\frac{144}{253}\right)$	$e\left(\frac{149}{506}\right)$	$e\left(\frac{30}{253}\right)$	$e\left(\frac{239}{506}\right)$
$\chi_{2116}(135,\cdot)$	$1$	$1$	$e\left(\frac{25}{506}\right)$	$e\left(\frac{49}{506}\right)$	$e\left(\frac{251}{253}\right)$	$e\left(\frac{25}{253}\right)$	$e\left(\frac{248}{253}\right)$	$e\left(\frac{101}{253}\right)$	$e\left(\frac{37}{253}\right)$	$e\left(\frac{409}{506}\right)$	$e\left(\frac{208}{253}\right)$	$e\left(\frac{21}{506}\right)$
$\chi_{2116}(143,\cdot)$	$1$	$1$	$e\left(\frac{357}{506}\right)$	$e\left(\frac{133}{506}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{104}{253}\right)$	$e\left(\frac{131}{253}\right)$	$e\left(\frac{238}{253}\right)$	$e\left(\frac{245}{253}\right)$	$e\left(\frac{315}{506}\right)$	$e\left(\frac{167}{253}\right)$	$e\left(\frac{57}{506}\right)$
$\chi_{2116}(155,\cdot)$	$1$	$1$	$e\left(\frac{475}{506}\right)$	$e\left(\frac{425}{506}\right)$	$e\left(\frac{215}{253}\right)$	$e\left(\frac{222}{253}\right)$	$e\left(\frac{158}{253}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{197}{253}\right)$	$e\left(\frac{181}{506}\right)$	$e\left(\frac{157}{253}\right)$	$e\left(\frac{399}{506}\right)$
$\chi_{2116}(159,\cdot)$	$1$	$1$	$e\left(\frac{329}{506}\right)$	$e\left(\frac{321}{506}\right)$	$e\left(\frac{85}{253}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{86}{253}\right)$	$e\left(\frac{135}{253}\right)$	$e\left(\frac{72}{253}\right)$	$e\left(\frac{201}{506}\right)$	$e\left(\frac{15}{253}\right)$	$e\left(\frac{499}{506}\right)$
$\chi_{2116}(171,\cdot)$	$1$	$1$	$e\left(\frac{147}{506}\right)$	$e\left(\frac{25}{506}\right)$	$e\left(\frac{221}{253}\right)$	$e\left(\frac{147}{253}\right)$	$e\left(\frac{173}{253}\right)$	$e\left(\frac{98}{253}\right)$	$e\left(\frac{86}{253}\right)$	$e\left(\frac{219}{506}\right)$	$e\left(\frac{39}{253}\right)$	$e\left(\frac{83}{506}\right)$
$\chi_{2116}(175,\cdot)$	$1$	$1$	$e\left(\frac{325}{506}\right)$	$e\left(\frac{131}{506}\right)$	$e\left(\frac{227}{253}\right)$	$e\left(\frac{72}{253}\right)$	$e\left(\frac{188}{253}\right)$	$e\left(\frac{48}{253}\right)$	$e\left(\frac{228}{253}\right)$	$e\left(\frac{257}{506}\right)$	$e\left(\frac{174}{253}\right)$	$e\left(\frac{273}{506}\right)$
$\chi_{2116}(191,\cdot)$	$1$	$1$	$e\left(\frac{425}{506}\right)$	$e\left(\frac{327}{506}\right)$	$e\left(\frac{219}{253}\right)$	$e\left(\frac{172}{253}\right)$	$e\left(\frac{168}{253}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{123}{253}\right)$	$e\left(\frac{375}{506}\right)$	$e\left(\frac{247}{253}\right)$	$e\left(\frac{357}{506}\right)$
$\chi_{2116}(199,\cdot)$	$1$	$1$	$e\left(\frac{283}{506}\right)$	$e\left(\frac{413}{506}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{30}{253}\right)$	$e\left(\frac{247}{253}\right)$	$e\left(\frac{20}{253}\right)$	$e\left(\frac{95}{253}\right)$	$e\left(\frac{339}{506}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{177}{506}\right)$
$\chi_{2116}(203,\cdot)$	$1$	$1$	$e\left(\frac{163}{506}\right)$	$e\left(\frac{279}{506}\right)$	$e\left(\frac{159}{253}\right)$	$e\left(\frac{163}{253}\right)$	$e\left(\frac{18}{253}\right)$	$e\left(\frac{193}{253}\right)$	$e\left(\frac{221}{253}\right)$	$e\left(\frac{501}{506}\right)$	$e\left(\frac{162}{253}\right)$	$e\left(\frac{481}{506}\right)$
$\chi_{2116}(227,\cdot)$	$1$	$1$	$e\left(\frac{377}{506}\right)$	$e\left(\frac{71}{506}\right)$	$e\left(\frac{152}{253}\right)$	$e\left(\frac{124}{253}\right)$	$e\left(\frac{127}{253}\right)$	$e\left(\frac{167}{253}\right)$	$e\left(\frac{224}{253}\right)$	$e\left(\frac{35}{506}\right)$	$e\left(\frac{131}{253}\right)$	$e\left(\frac{175}{506}\right)$
$\chi_{2116}(235,\cdot)$	$1$	$1$	$e\left(\frac{247}{506}\right)$	$e\left(\frac{221}{506}\right)$	$e\left(\frac{213}{253}\right)$	$e\left(\frac{247}{253}\right)$	$e\left(\frac{153}{253}\right)$	$e\left(\frac{249}{253}\right)$	$e\left(\frac{234}{253}\right)$	$e\left(\frac{337}{506}\right)$	$e\left(\frac{112}{253}\right)$	$e\left(\frac{167}{506}\right)$
$\chi_{2116}(247,\cdot)$	$1$	$1$	$e\left(\frac{145}{506}\right)$	$e\left(\frac{183}{506}\right)$	$e\left(\frac{39}{253}\right)$	$e\left(\frac{145}{253}\right)$	$e\left(\frac{224}{253}\right)$	$e\left(\frac{181}{253}\right)$	$e\left(\frac{164}{253}\right)$	$e\left(\frac{247}{506}\right)$	$e\left(\frac{245}{253}\right)$	$e\left(\frac{223}{506}\right)$
$\chi_{2116}(251,\cdot)$	$1$	$1$	$e\left(\frac{351}{506}\right)$	$e\left(\frac{101}{506}\right)$	$e\left(\frac{63}{253}\right)$	$e\left(\frac{98}{253}\right)$	$e\left(\frac{31}{253}\right)$	$e\left(\frac{234}{253}\right)$	$e\left(\frac{226}{253}\right)$	$e\left(\frac{399}{506}\right)$	$e\left(\frac{26}{253}\right)$	$e\left(\frac{477}{506}\right)$
$\chi_{2116}(267,\cdot)$	$1$	$1$	$e\left(\frac{105}{506}\right)$	$e\left(\frac{307}{506}\right)$	$e\left(\frac{194}{253}\right)$	$e\left(\frac{105}{253}\right)$	$e\left(\frac{232}{253}\right)$	$e\left(\frac{70}{253}\right)$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{301}{506}\right)$	$e\left(\frac{64}{253}\right)$	$e\left(\frac{493}{506}\right)$
$\chi_{2116}(283,\cdot)$	$1$	$1$	$e\left(\frac{491}{506}\right)$	$e\left(\frac{173}{506}\right)$	$e\left(\frac{153}{253}\right)$	$e\left(\frac{238}{253}\right)$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{243}{253}\right)$	$e\left(\frac{79}{253}\right)$	$e\left(\frac{463}{506}\right)$	$e\left(\frac{27}{253}\right)$	$e\left(\frac{291}{506}\right)$
$\chi_{2116}(287,\cdot)$	$1$	$1$	$e\left(\frac{111}{506}\right)$	$e\left(\frac{339}{506}\right)$	$e\left(\frac{234}{253}\right)$	$e\left(\frac{111}{253}\right)$	$e\left(\frac{79}{253}\right)$	$e\left(\frac{74}{253}\right)$	$e\left(\frac{225}{253}\right)$	$e\left(\frac{217}{506}\right)$	$e\left(\frac{205}{253}\right)$	$e\left(\frac{73}{506}\right)$
$\chi_{2116}(291,\cdot)$	$1$	$1$	$e\left(\frac{415}{506}\right)$	$e\left(\frac{105}{506}\right)$	$e\left(\frac{68}{253}\right)$	$e\left(\frac{162}{253}\right)$	$e\left(\frac{170}{253}\right)$	$e\left(\frac{108}{253}\right)$	$e\left(\frac{7}{253}\right)$	$e\left(\frac{9}{506}\right)$	$e\left(\frac{12}{253}\right)$	$e\left(\frac{45}{506}\right)$
$\chi_{2116}(295,\cdot)$	$1$	$1$	$e\left(\frac{427}{506}\right)$	$e\left(\frac{169}{506}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{174}{253}\right)$	$e\left(\frac{117}{253}\right)$	$e\left(\frac{116}{253}\right)$	$e\left(\frac{45}{253}\right)$	$e\left(\frac{347}{506}\right)$	$e\left(\frac{41}{253}\right)$	$e\left(\frac{217}{506}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{2116}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{129}{506}\right)\)	\(e\left(\frac{98}{253}\right)\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{245}{253}\right)\)	\(e\left(\frac{111}{253}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{199}{506}\right)\)	\(e\left(\frac{181}{253}\right)\)	\(e\left(\frac{489}{506}\right)\)
\(\chi_{2116}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{506}\right)\)	\(e\left(\frac{449}{506}\right)\)	\(e\left(\frac{245}{253}\right)\)	\(e\left(\frac{100}{253}\right)\)	\(e\left(\frac{233}{253}\right)\)	\(e\left(\frac{151}{253}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{371}{506}\right)\)	\(e\left(\frac{73}{253}\right)\)	\(e\left(\frac{337}{506}\right)\)
\(\chi_{2116}(15,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{506}\right)\)	\(e\left(\frac{17}{506}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{19}{253}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{97}{253}\right)\)	\(e\left(\frac{18}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{441}{506}\right)\)
\(\chi_{2116}(19,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{141}{506}\right)\)	\(e\left(\frac{499}{506}\right)\)	\(e\left(\frac{181}{253}\right)\)	\(e\left(\frac{141}{253}\right)\)	\(e\left(\frac{73}{253}\right)\)	\(e\left(\frac{94}{253}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{303}{506}\right)\)	\(e\left(\frac{151}{253}\right)\)	\(e\left(\frac{503}{506}\right)\)
\(\chi_{2116}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{506}\right)\)	\(e\left(\frac{27}{506}\right)\)	\(e\left(\frac{97}{253}\right)\)	\(e\left(\frac{179}{253}\right)\)	\(e\left(\frac{116}{253}\right)\)	\(e\left(\frac{35}{253}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{277}{506}\right)\)	\(e\left(\frac{32}{253}\right)\)	\(e\left(\frac{373}{506}\right)\)
\(\chi_{2116}(51,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{467}{506}\right)\)	\(e\left(\frac{45}{506}\right)\)	\(e\left(\frac{246}{253}\right)\)	\(e\left(\frac{214}{253}\right)\)	\(e\left(\frac{109}{253}\right)\)	\(e\left(\frac{227}{253}\right)\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{222}{253}\right)\)	\(e\left(\frac{453}{506}\right)\)
\(\chi_{2116}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{506}\right)\)	\(e\left(\frac{35}{506}\right)\)	\(e\left(\frac{107}{253}\right)\)	\(e\left(\frac{54}{253}\right)\)	\(e\left(\frac{141}{253}\right)\)	\(e\left(\frac{36}{253}\right)\)	\(e\left(\frac{171}{253}\right)\)	\(e\left(\frac{3}{506}\right)\)	\(e\left(\frac{4}{253}\right)\)	\(e\left(\frac{15}{506}\right)\)
\(\chi_{2116}(79,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{455}{506}\right)\)	\(e\left(\frac{487}{506}\right)\)	\(e\left(\frac{166}{253}\right)\)	\(e\left(\frac{202}{253}\right)\)	\(e\left(\frac{162}{253}\right)\)	\(e\left(\frac{219}{253}\right)\)	\(e\left(\frac{218}{253}\right)\)	\(e\left(\frac{461}{506}\right)\)	\(e\left(\frac{193}{253}\right)\)	\(e\left(\frac{281}{506}\right)\)
\(\chi_{2116}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{506}\right)\)	\(e\left(\frac{461}{506}\right)\)	\(e\left(\frac{7}{253}\right)\)	\(e\left(\frac{39}{253}\right)\)	\(e\left(\frac{144}{253}\right)\)	\(e\left(\frac{26}{253}\right)\)	\(e\left(\frac{250}{253}\right)\)	\(e\left(\frac{213}{506}\right)\)	\(e\left(\frac{31}{253}\right)\)	\(e\left(\frac{53}{506}\right)\)
\(\chi_{2116}(99,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{359}{506}\right)\)	\(e\left(\frac{481}{506}\right)\)	\(e\left(\frac{32}{253}\right)\)	\(e\left(\frac{106}{253}\right)\)	\(e\left(\frac{80}{253}\right)\)	\(e\left(\frac{155}{253}\right)\)	\(e\left(\frac{167}{253}\right)\)	\(e\left(\frac{287}{506}\right)\)	\(e\left(\frac{214}{253}\right)\)	\(e\left(\frac{423}{506}\right)\)
\(\chi_{2116}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{441}{506}\right)\)	\(e\left(\frac{75}{506}\right)\)	\(e\left(\frac{157}{253}\right)\)	\(e\left(\frac{188}{253}\right)\)	\(e\left(\frac{13}{253}\right)\)	\(e\left(\frac{41}{253}\right)\)	\(e\left(\frac{5}{253}\right)\)	\(e\left(\frac{151}{506}\right)\)	\(e\left(\frac{117}{253}\right)\)	\(e\left(\frac{249}{506}\right)\)
\(\chi_{2116}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{506}\right)\)	\(e\left(\frac{215}{506}\right)\)	\(e\left(\frac{79}{253}\right)\)	\(e\left(\frac{151}{253}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{185}{253}\right)\)	\(e\left(\frac{183}{253}\right)\)	\(e\left(\frac{163}{506}\right)\)	\(e\left(\frac{133}{253}\right)\)	\(e\left(\frac{309}{506}\right)\)
\(\chi_{2116}(111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{405}{506}\right)\)	\(e\left(\frac{389}{506}\right)\)	\(e\left(\frac{170}{253}\right)\)	\(e\left(\frac{152}{253}\right)\)	\(e\left(\frac{172}{253}\right)\)	\(e\left(\frac{17}{253}\right)\)	\(e\left(\frac{144}{253}\right)\)	\(e\left(\frac{149}{506}\right)\)	\(e\left(\frac{30}{253}\right)\)	\(e\left(\frac{239}{506}\right)\)
\(\chi_{2116}(135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{506}\right)\)	\(e\left(\frac{49}{506}\right)\)	\(e\left(\frac{251}{253}\right)\)	\(e\left(\frac{25}{253}\right)\)	\(e\left(\frac{248}{253}\right)\)	\(e\left(\frac{101}{253}\right)\)	\(e\left(\frac{37}{253}\right)\)	\(e\left(\frac{409}{506}\right)\)	\(e\left(\frac{208}{253}\right)\)	\(e\left(\frac{21}{506}\right)\)
\(\chi_{2116}(143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{357}{506}\right)\)	\(e\left(\frac{133}{506}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{104}{253}\right)\)	\(e\left(\frac{131}{253}\right)\)	\(e\left(\frac{238}{253}\right)\)	\(e\left(\frac{245}{253}\right)\)	\(e\left(\frac{315}{506}\right)\)	\(e\left(\frac{167}{253}\right)\)	\(e\left(\frac{57}{506}\right)\)
\(\chi_{2116}(155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{475}{506}\right)\)	\(e\left(\frac{425}{506}\right)\)	\(e\left(\frac{215}{253}\right)\)	\(e\left(\frac{222}{253}\right)\)	\(e\left(\frac{158}{253}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{197}{253}\right)\)	\(e\left(\frac{181}{506}\right)\)	\(e\left(\frac{157}{253}\right)\)	\(e\left(\frac{399}{506}\right)\)
\(\chi_{2116}(159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{329}{506}\right)\)	\(e\left(\frac{321}{506}\right)\)	\(e\left(\frac{85}{253}\right)\)	\(e\left(\frac{76}{253}\right)\)	\(e\left(\frac{86}{253}\right)\)	\(e\left(\frac{135}{253}\right)\)	\(e\left(\frac{72}{253}\right)\)	\(e\left(\frac{201}{506}\right)\)	\(e\left(\frac{15}{253}\right)\)	\(e\left(\frac{499}{506}\right)\)
\(\chi_{2116}(171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{147}{506}\right)\)	\(e\left(\frac{25}{506}\right)\)	\(e\left(\frac{221}{253}\right)\)	\(e\left(\frac{147}{253}\right)\)	\(e\left(\frac{173}{253}\right)\)	\(e\left(\frac{98}{253}\right)\)	\(e\left(\frac{86}{253}\right)\)	\(e\left(\frac{219}{506}\right)\)	\(e\left(\frac{39}{253}\right)\)	\(e\left(\frac{83}{506}\right)\)
\(\chi_{2116}(175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{325}{506}\right)\)	\(e\left(\frac{131}{506}\right)\)	\(e\left(\frac{227}{253}\right)\)	\(e\left(\frac{72}{253}\right)\)	\(e\left(\frac{188}{253}\right)\)	\(e\left(\frac{48}{253}\right)\)	\(e\left(\frac{228}{253}\right)\)	\(e\left(\frac{257}{506}\right)\)	\(e\left(\frac{174}{253}\right)\)	\(e\left(\frac{273}{506}\right)\)
\(\chi_{2116}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{425}{506}\right)\)	\(e\left(\frac{327}{506}\right)\)	\(e\left(\frac{219}{253}\right)\)	\(e\left(\frac{172}{253}\right)\)	\(e\left(\frac{168}{253}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{123}{253}\right)\)	\(e\left(\frac{375}{506}\right)\)	\(e\left(\frac{247}{253}\right)\)	\(e\left(\frac{357}{506}\right)\)
\(\chi_{2116}(199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{506}\right)\)	\(e\left(\frac{413}{506}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{30}{253}\right)\)	\(e\left(\frac{247}{253}\right)\)	\(e\left(\frac{20}{253}\right)\)	\(e\left(\frac{95}{253}\right)\)	\(e\left(\frac{339}{506}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{177}{506}\right)\)
\(\chi_{2116}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{506}\right)\)	\(e\left(\frac{279}{506}\right)\)	\(e\left(\frac{159}{253}\right)\)	\(e\left(\frac{163}{253}\right)\)	\(e\left(\frac{18}{253}\right)\)	\(e\left(\frac{193}{253}\right)\)	\(e\left(\frac{221}{253}\right)\)	\(e\left(\frac{501}{506}\right)\)	\(e\left(\frac{162}{253}\right)\)	\(e\left(\frac{481}{506}\right)\)
\(\chi_{2116}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{377}{506}\right)\)	\(e\left(\frac{71}{506}\right)\)	\(e\left(\frac{152}{253}\right)\)	\(e\left(\frac{124}{253}\right)\)	\(e\left(\frac{127}{253}\right)\)	\(e\left(\frac{167}{253}\right)\)	\(e\left(\frac{224}{253}\right)\)	\(e\left(\frac{35}{506}\right)\)	\(e\left(\frac{131}{253}\right)\)	\(e\left(\frac{175}{506}\right)\)
\(\chi_{2116}(235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{506}\right)\)	\(e\left(\frac{221}{506}\right)\)	\(e\left(\frac{213}{253}\right)\)	\(e\left(\frac{247}{253}\right)\)	\(e\left(\frac{153}{253}\right)\)	\(e\left(\frac{249}{253}\right)\)	\(e\left(\frac{234}{253}\right)\)	\(e\left(\frac{337}{506}\right)\)	\(e\left(\frac{112}{253}\right)\)	\(e\left(\frac{167}{506}\right)\)
\(\chi_{2116}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{506}\right)\)	\(e\left(\frac{183}{506}\right)\)	\(e\left(\frac{39}{253}\right)\)	\(e\left(\frac{145}{253}\right)\)	\(e\left(\frac{224}{253}\right)\)	\(e\left(\frac{181}{253}\right)\)	\(e\left(\frac{164}{253}\right)\)	\(e\left(\frac{247}{506}\right)\)	\(e\left(\frac{245}{253}\right)\)	\(e\left(\frac{223}{506}\right)\)
\(\chi_{2116}(251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{351}{506}\right)\)	\(e\left(\frac{101}{506}\right)\)	\(e\left(\frac{63}{253}\right)\)	\(e\left(\frac{98}{253}\right)\)	\(e\left(\frac{31}{253}\right)\)	\(e\left(\frac{234}{253}\right)\)	\(e\left(\frac{226}{253}\right)\)	\(e\left(\frac{399}{506}\right)\)	\(e\left(\frac{26}{253}\right)\)	\(e\left(\frac{477}{506}\right)\)
\(\chi_{2116}(267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{105}{506}\right)\)	\(e\left(\frac{307}{506}\right)\)	\(e\left(\frac{194}{253}\right)\)	\(e\left(\frac{105}{253}\right)\)	\(e\left(\frac{232}{253}\right)\)	\(e\left(\frac{70}{253}\right)\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{301}{506}\right)\)	\(e\left(\frac{64}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)
\(\chi_{2116}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{491}{506}\right)\)	\(e\left(\frac{173}{506}\right)\)	\(e\left(\frac{153}{253}\right)\)	\(e\left(\frac{238}{253}\right)\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{243}{253}\right)\)	\(e\left(\frac{79}{253}\right)\)	\(e\left(\frac{463}{506}\right)\)	\(e\left(\frac{27}{253}\right)\)	\(e\left(\frac{291}{506}\right)\)
\(\chi_{2116}(287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{506}\right)\)	\(e\left(\frac{339}{506}\right)\)	\(e\left(\frac{234}{253}\right)\)	\(e\left(\frac{111}{253}\right)\)	\(e\left(\frac{79}{253}\right)\)	\(e\left(\frac{74}{253}\right)\)	\(e\left(\frac{225}{253}\right)\)	\(e\left(\frac{217}{506}\right)\)	\(e\left(\frac{205}{253}\right)\)	\(e\left(\frac{73}{506}\right)\)
\(\chi_{2116}(291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{415}{506}\right)\)	\(e\left(\frac{105}{506}\right)\)	\(e\left(\frac{68}{253}\right)\)	\(e\left(\frac{162}{253}\right)\)	\(e\left(\frac{170}{253}\right)\)	\(e\left(\frac{108}{253}\right)\)	\(e\left(\frac{7}{253}\right)\)	\(e\left(\frac{9}{506}\right)\)	\(e\left(\frac{12}{253}\right)\)	\(e\left(\frac{45}{506}\right)\)
\(\chi_{2116}(295,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{427}{506}\right)\)	\(e\left(\frac{169}{506}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{174}{253}\right)\)	\(e\left(\frac{117}{253}\right)\)	\(e\left(\frac{116}{253}\right)\)	\(e\left(\frac{45}{253}\right)\)	\(e\left(\frac{347}{506}\right)\)	\(e\left(\frac{41}{253}\right)\)	\(e\left(\frac{217}{506}\right)\)

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First 31 of 220 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	2116.n
Modulus	$2116$
Conductor	$2116$
Order	$506$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(2116\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(2116\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(506\)	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);