LMFDB - Dirichlet character orbit 355008.ji

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(355008, base_ring=CyclotomicField(1032)) M = H._module chi = DirichletCharacter(H, M([516,645,0,140])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(7, 355008)) 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("355008.7"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$355008$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$59168$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$1032$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 59168.dz	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{1032})$	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 1032 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 336 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{355008}(7,\cdot)$	$1$	$1$	$e\left(\frac{833}{1032}\right)$	$e\left(\frac{509}{516}\right)$	$e\left(\frac{143}{344}\right)$	$e\left(\frac{475}{1032}\right)$	$e\left(\frac{31}{258}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{373}{516}\right)$	$e\left(\frac{317}{516}\right)$	$e\left(\frac{451}{1032}\right)$	$e\left(\frac{107}{258}\right)$
$\chi_{355008}(295,\cdot)$	$1$	$1$	$e\left(\frac{685}{1032}\right)$	$e\left(\frac{133}{516}\right)$	$e\left(\frac{35}{344}\right)$	$e\left(\frac{263}{1032}\right)$	$e\left(\frac{185}{258}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{137}{516}\right)$	$e\left(\frac{169}{516}\right)$	$e\left(\frac{719}{1032}\right)$	$e\left(\frac{31}{258}\right)$
$\chi_{355008}(2071,\cdot)$	$1$	$1$	$e\left(\frac{755}{1032}\right)$	$e\left(\frac{11}{516}\right)$	$e\left(\frac{21}{344}\right)$	$e\left(\frac{433}{1032}\right)$	$e\left(\frac{25}{258}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{151}{516}\right)$	$e\left(\frac{239}{516}\right)$	$e\left(\frac{913}{1032}\right)$	$e\left(\frac{53}{258}\right)$
$\chi_{355008}(2359,\cdot)$	$1$	$1$	$e\left(\frac{991}{1032}\right)$	$e\left(\frac{499}{516}\right)$	$e\left(\frac{249}{344}\right)$	$e\left(\frac{269}{1032}\right)$	$e\left(\frac{149}{258}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{95}{516}\right)$	$e\left(\frac{475}{516}\right)$	$e\left(\frac{653}{1032}\right)$	$e\left(\frac{223}{258}\right)$
$\chi_{355008}(4135,\cdot)$	$1$	$1$	$e\left(\frac{677}{1032}\right)$	$e\left(\frac{29}{516}\right)$	$e\left(\frac{243}{344}\right)$	$e\left(\frac{391}{1032}\right)$	$e\left(\frac{19}{258}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{445}{516}\right)$	$e\left(\frac{161}{516}\right)$	$e\left(\frac{343}{1032}\right)$	$e\left(\frac{257}{258}\right)$
$\chi_{355008}(4423,\cdot)$	$1$	$1$	$e\left(\frac{265}{1032}\right)$	$e\left(\frac{349}{516}\right)$	$e\left(\frac{119}{344}\right)$	$e\left(\frac{275}{1032}\right)$	$e\left(\frac{113}{258}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{53}{516}\right)$	$e\left(\frac{265}{516}\right)$	$e\left(\frac{587}{1032}\right)$	$e\left(\frac{157}{258}\right)$
$\chi_{355008}(6199,\cdot)$	$1$	$1$	$e\left(\frac{599}{1032}\right)$	$e\left(\frac{47}{516}\right)$	$e\left(\frac{121}{344}\right)$	$e\left(\frac{349}{1032}\right)$	$e\left(\frac{13}{258}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{223}{516}\right)$	$e\left(\frac{83}{516}\right)$	$e\left(\frac{805}{1032}\right)$	$e\left(\frac{203}{258}\right)$
$\chi_{355008}(6487,\cdot)$	$1$	$1$	$e\left(\frac{571}{1032}\right)$	$e\left(\frac{199}{516}\right)$	$e\left(\frac{333}{344}\right)$	$e\left(\frac{281}{1032}\right)$	$e\left(\frac{77}{258}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{516}\right)$	$e\left(\frac{55}{516}\right)$	$e\left(\frac{521}{1032}\right)$	$e\left(\frac{91}{258}\right)$
$\chi_{355008}(8263,\cdot)$	$1$	$1$	$e\left(\frac{521}{1032}\right)$	$e\left(\frac{65}{516}\right)$	$e\left(\frac{343}{344}\right)$	$e\left(\frac{307}{1032}\right)$	$e\left(\frac{7}{258}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{516}\right)$	$e\left(\frac{5}{516}\right)$	$e\left(\frac{235}{1032}\right)$	$e\left(\frac{149}{258}\right)$
$\chi_{355008}(8551,\cdot)$	$1$	$1$	$e\left(\frac{877}{1032}\right)$	$e\left(\frac{49}{516}\right)$	$e\left(\frac{203}{344}\right)$	$e\left(\frac{287}{1032}\right)$	$e\left(\frac{41}{258}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{485}{516}\right)$	$e\left(\frac{361}{516}\right)$	$e\left(\frac{455}{1032}\right)$	$e\left(\frac{25}{258}\right)$
$\chi_{355008}(10327,\cdot)$	$1$	$1$	$e\left(\frac{443}{1032}\right)$	$e\left(\frac{83}{516}\right)$	$e\left(\frac{221}{344}\right)$	$e\left(\frac{265}{1032}\right)$	$e\left(\frac{1}{258}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{295}{516}\right)$	$e\left(\frac{443}{516}\right)$	$e\left(\frac{697}{1032}\right)$	$e\left(\frac{95}{258}\right)$
$\chi_{355008}(10615,\cdot)$	$1$	$1$	$e\left(\frac{151}{1032}\right)$	$e\left(\frac{415}{516}\right)$	$e\left(\frac{73}{344}\right)$	$e\left(\frac{293}{1032}\right)$	$e\left(\frac{5}{258}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{443}{516}\right)$	$e\left(\frac{151}{516}\right)$	$e\left(\frac{389}{1032}\right)$	$e\left(\frac{217}{258}\right)$
$\chi_{355008}(12391,\cdot)$	$1$	$1$	$e\left(\frac{365}{1032}\right)$	$e\left(\frac{101}{516}\right)$	$e\left(\frac{99}{344}\right)$	$e\left(\frac{223}{1032}\right)$	$e\left(\frac{253}{258}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{73}{516}\right)$	$e\left(\frac{365}{516}\right)$	$e\left(\frac{127}{1032}\right)$	$e\left(\frac{41}{258}\right)$
$\chi_{355008}(12679,\cdot)$	$1$	$1$	$e\left(\frac{457}{1032}\right)$	$e\left(\frac{265}{516}\right)$	$e\left(\frac{287}{344}\right)$	$e\left(\frac{299}{1032}\right)$	$e\left(\frac{227}{258}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{401}{516}\right)$	$e\left(\frac{457}{516}\right)$	$e\left(\frac{323}{1032}\right)$	$e\left(\frac{151}{258}\right)$
$\chi_{355008}(14455,\cdot)$	$1$	$1$	$e\left(\frac{287}{1032}\right)$	$e\left(\frac{119}{516}\right)$	$e\left(\frac{321}{344}\right)$	$e\left(\frac{181}{1032}\right)$	$e\left(\frac{247}{258}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{367}{516}\right)$	$e\left(\frac{287}{516}\right)$	$e\left(\frac{589}{1032}\right)$	$e\left(\frac{245}{258}\right)$
$\chi_{355008}(14743,\cdot)$	$1$	$1$	$e\left(\frac{763}{1032}\right)$	$e\left(\frac{115}{516}\right)$	$e\left(\frac{157}{344}\right)$	$e\left(\frac{305}{1032}\right)$	$e\left(\frac{191}{258}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{359}{516}\right)$	$e\left(\frac{247}{516}\right)$	$e\left(\frac{257}{1032}\right)$	$e\left(\frac{85}{258}\right)$
$\chi_{355008}(16519,\cdot)$	$1$	$1$	$e\left(\frac{209}{1032}\right)$	$e\left(\frac{137}{516}\right)$	$e\left(\frac{199}{344}\right)$	$e\left(\frac{139}{1032}\right)$	$e\left(\frac{241}{258}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{145}{516}\right)$	$e\left(\frac{209}{516}\right)$	$e\left(\frac{19}{1032}\right)$	$e\left(\frac{191}{258}\right)$
$\chi_{355008}(16807,\cdot)$	$1$	$1$	$e\left(\frac{37}{1032}\right)$	$e\left(\frac{481}{516}\right)$	$e\left(\frac{27}{344}\right)$	$e\left(\frac{311}{1032}\right)$	$e\left(\frac{155}{258}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{317}{516}\right)$	$e\left(\frac{37}{516}\right)$	$e\left(\frac{191}{1032}\right)$	$e\left(\frac{19}{258}\right)$
$\chi_{355008}(18583,\cdot)$	$1$	$1$	$e\left(\frac{131}{1032}\right)$	$e\left(\frac{155}{516}\right)$	$e\left(\frac{77}{344}\right)$	$e\left(\frac{97}{1032}\right)$	$e\left(\frac{235}{258}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{439}{516}\right)$	$e\left(\frac{131}{516}\right)$	$e\left(\frac{481}{1032}\right)$	$e\left(\frac{137}{258}\right)$
$\chi_{355008}(18871,\cdot)$	$1$	$1$	$e\left(\frac{343}{1032}\right)$	$e\left(\frac{331}{516}\right)$	$e\left(\frac{241}{344}\right)$	$e\left(\frac{317}{1032}\right)$	$e\left(\frac{119}{258}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{275}{516}\right)$	$e\left(\frac{343}{516}\right)$	$e\left(\frac{125}{1032}\right)$	$e\left(\frac{211}{258}\right)$
$\chi_{355008}(20647,\cdot)$	$1$	$1$	$e\left(\frac{53}{1032}\right)$	$e\left(\frac{173}{516}\right)$	$e\left(\frac{299}{344}\right)$	$e\left(\frac{55}{1032}\right)$	$e\left(\frac{229}{258}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{217}{516}\right)$	$e\left(\frac{53}{516}\right)$	$e\left(\frac{943}{1032}\right)$	$e\left(\frac{83}{258}\right)$
$\chi_{355008}(20935,\cdot)$	$1$	$1$	$e\left(\frac{649}{1032}\right)$	$e\left(\frac{181}{516}\right)$	$e\left(\frac{111}{344}\right)$	$e\left(\frac{323}{1032}\right)$	$e\left(\frac{83}{258}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{233}{516}\right)$	$e\left(\frac{133}{516}\right)$	$e\left(\frac{59}{1032}\right)$	$e\left(\frac{145}{258}\right)$
$\chi_{355008}(22711,\cdot)$	$1$	$1$	$e\left(\frac{1007}{1032}\right)$	$e\left(\frac{191}{516}\right)$	$e\left(\frac{177}{344}\right)$	$e\left(\frac{13}{1032}\right)$	$e\left(\frac{223}{258}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{511}{516}\right)$	$e\left(\frac{491}{516}\right)$	$e\left(\frac{373}{1032}\right)$	$e\left(\frac{29}{258}\right)$
$\chi_{355008}(22999,\cdot)$	$1$	$1$	$e\left(\frac{955}{1032}\right)$	$e\left(\frac{31}{516}\right)$	$e\left(\frac{325}{344}\right)$	$e\left(\frac{329}{1032}\right)$	$e\left(\frac{47}{258}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{191}{516}\right)$	$e\left(\frac{439}{516}\right)$	$e\left(\frac{1025}{1032}\right)$	$e\left(\frac{79}{258}\right)$
$\chi_{355008}(24775,\cdot)$	$1$	$1$	$e\left(\frac{929}{1032}\right)$	$e\left(\frac{209}{516}\right)$	$e\left(\frac{55}{344}\right)$	$e\left(\frac{1003}{1032}\right)$	$e\left(\frac{217}{258}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{289}{516}\right)$	$e\left(\frac{413}{516}\right)$	$e\left(\frac{835}{1032}\right)$	$e\left(\frac{233}{258}\right)$
$\chi_{355008}(25063,\cdot)$	$1$	$1$	$e\left(\frac{229}{1032}\right)$	$e\left(\frac{397}{516}\right)$	$e\left(\frac{195}{344}\right)$	$e\left(\frac{335}{1032}\right)$	$e\left(\frac{11}{258}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{149}{516}\right)$	$e\left(\frac{229}{516}\right)$	$e\left(\frac{959}{1032}\right)$	$e\left(\frac{13}{258}\right)$
$\chi_{355008}(26839,\cdot)$	$1$	$1$	$e\left(\frac{851}{1032}\right)$	$e\left(\frac{227}{516}\right)$	$e\left(\frac{277}{344}\right)$	$e\left(\frac{961}{1032}\right)$	$e\left(\frac{211}{258}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{67}{516}\right)$	$e\left(\frac{335}{516}\right)$	$e\left(\frac{265}{1032}\right)$	$e\left(\frac{179}{258}\right)$
$\chi_{355008}(27127,\cdot)$	$1$	$1$	$e\left(\frac{535}{1032}\right)$	$e\left(\frac{247}{516}\right)$	$e\left(\frac{65}{344}\right)$	$e\left(\frac{341}{1032}\right)$	$e\left(\frac{233}{258}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{107}{516}\right)$	$e\left(\frac{19}{516}\right)$	$e\left(\frac{893}{1032}\right)$	$e\left(\frac{205}{258}\right)$
$\chi_{355008}(28903,\cdot)$	$1$	$1$	$e\left(\frac{773}{1032}\right)$	$e\left(\frac{245}{516}\right)$	$e\left(\frac{155}{344}\right)$	$e\left(\frac{919}{1032}\right)$	$e\left(\frac{205}{258}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{361}{516}\right)$	$e\left(\frac{257}{516}\right)$	$e\left(\frac{727}{1032}\right)$	$e\left(\frac{125}{258}\right)$
$\chi_{355008}(29191,\cdot)$	$1$	$1$	$e\left(\frac{841}{1032}\right)$	$e\left(\frac{97}{516}\right)$	$e\left(\frac{279}{344}\right)$	$e\left(\frac{347}{1032}\right)$	$e\left(\frac{197}{258}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{65}{516}\right)$	$e\left(\frac{325}{516}\right)$	$e\left(\frac{827}{1032}\right)$	$e\left(\frac{139}{258}\right)$
$\chi_{355008}(30967,\cdot)$	$1$	$1$	$e\left(\frac{695}{1032}\right)$	$e\left(\frac{263}{516}\right)$	$e\left(\frac{33}{344}\right)$	$e\left(\frac{877}{1032}\right)$	$e\left(\frac{199}{258}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{139}{516}\right)$	$e\left(\frac{179}{516}\right)$	$e\left(\frac{157}{1032}\right)$	$e\left(\frac{71}{258}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{355008}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{833}{1032}\right)\)	\(e\left(\frac{509}{516}\right)\)	\(e\left(\frac{143}{344}\right)\)	\(e\left(\frac{475}{1032}\right)\)	\(e\left(\frac{31}{258}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{373}{516}\right)\)	\(e\left(\frac{317}{516}\right)\)	\(e\left(\frac{451}{1032}\right)\)	\(e\left(\frac{107}{258}\right)\)
\(\chi_{355008}(295,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{685}{1032}\right)\)	\(e\left(\frac{133}{516}\right)\)	\(e\left(\frac{35}{344}\right)\)	\(e\left(\frac{263}{1032}\right)\)	\(e\left(\frac{185}{258}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{137}{516}\right)\)	\(e\left(\frac{169}{516}\right)\)	\(e\left(\frac{719}{1032}\right)\)	\(e\left(\frac{31}{258}\right)\)
\(\chi_{355008}(2071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{755}{1032}\right)\)	\(e\left(\frac{11}{516}\right)\)	\(e\left(\frac{21}{344}\right)\)	\(e\left(\frac{433}{1032}\right)\)	\(e\left(\frac{25}{258}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{151}{516}\right)\)	\(e\left(\frac{239}{516}\right)\)	\(e\left(\frac{913}{1032}\right)\)	\(e\left(\frac{53}{258}\right)\)
\(\chi_{355008}(2359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{991}{1032}\right)\)	\(e\left(\frac{499}{516}\right)\)	\(e\left(\frac{249}{344}\right)\)	\(e\left(\frac{269}{1032}\right)\)	\(e\left(\frac{149}{258}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{95}{516}\right)\)	\(e\left(\frac{475}{516}\right)\)	\(e\left(\frac{653}{1032}\right)\)	\(e\left(\frac{223}{258}\right)\)
\(\chi_{355008}(4135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{677}{1032}\right)\)	\(e\left(\frac{29}{516}\right)\)	\(e\left(\frac{243}{344}\right)\)	\(e\left(\frac{391}{1032}\right)\)	\(e\left(\frac{19}{258}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{445}{516}\right)\)	\(e\left(\frac{161}{516}\right)\)	\(e\left(\frac{343}{1032}\right)\)	\(e\left(\frac{257}{258}\right)\)
\(\chi_{355008}(4423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{265}{1032}\right)\)	\(e\left(\frac{349}{516}\right)\)	\(e\left(\frac{119}{344}\right)\)	\(e\left(\frac{275}{1032}\right)\)	\(e\left(\frac{113}{258}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{53}{516}\right)\)	\(e\left(\frac{265}{516}\right)\)	\(e\left(\frac{587}{1032}\right)\)	\(e\left(\frac{157}{258}\right)\)
\(\chi_{355008}(6199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{599}{1032}\right)\)	\(e\left(\frac{47}{516}\right)\)	\(e\left(\frac{121}{344}\right)\)	\(e\left(\frac{349}{1032}\right)\)	\(e\left(\frac{13}{258}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{223}{516}\right)\)	\(e\left(\frac{83}{516}\right)\)	\(e\left(\frac{805}{1032}\right)\)	\(e\left(\frac{203}{258}\right)\)
\(\chi_{355008}(6487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{571}{1032}\right)\)	\(e\left(\frac{199}{516}\right)\)	\(e\left(\frac{333}{344}\right)\)	\(e\left(\frac{281}{1032}\right)\)	\(e\left(\frac{77}{258}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{516}\right)\)	\(e\left(\frac{55}{516}\right)\)	\(e\left(\frac{521}{1032}\right)\)	\(e\left(\frac{91}{258}\right)\)
\(\chi_{355008}(8263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{521}{1032}\right)\)	\(e\left(\frac{65}{516}\right)\)	\(e\left(\frac{343}{344}\right)\)	\(e\left(\frac{307}{1032}\right)\)	\(e\left(\frac{7}{258}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{516}\right)\)	\(e\left(\frac{5}{516}\right)\)	\(e\left(\frac{235}{1032}\right)\)	\(e\left(\frac{149}{258}\right)\)
\(\chi_{355008}(8551,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{877}{1032}\right)\)	\(e\left(\frac{49}{516}\right)\)	\(e\left(\frac{203}{344}\right)\)	\(e\left(\frac{287}{1032}\right)\)	\(e\left(\frac{41}{258}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{485}{516}\right)\)	\(e\left(\frac{361}{516}\right)\)	\(e\left(\frac{455}{1032}\right)\)	\(e\left(\frac{25}{258}\right)\)
\(\chi_{355008}(10327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{443}{1032}\right)\)	\(e\left(\frac{83}{516}\right)\)	\(e\left(\frac{221}{344}\right)\)	\(e\left(\frac{265}{1032}\right)\)	\(e\left(\frac{1}{258}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{295}{516}\right)\)	\(e\left(\frac{443}{516}\right)\)	\(e\left(\frac{697}{1032}\right)\)	\(e\left(\frac{95}{258}\right)\)
\(\chi_{355008}(10615,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{1032}\right)\)	\(e\left(\frac{415}{516}\right)\)	\(e\left(\frac{73}{344}\right)\)	\(e\left(\frac{293}{1032}\right)\)	\(e\left(\frac{5}{258}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{443}{516}\right)\)	\(e\left(\frac{151}{516}\right)\)	\(e\left(\frac{389}{1032}\right)\)	\(e\left(\frac{217}{258}\right)\)
\(\chi_{355008}(12391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{365}{1032}\right)\)	\(e\left(\frac{101}{516}\right)\)	\(e\left(\frac{99}{344}\right)\)	\(e\left(\frac{223}{1032}\right)\)	\(e\left(\frac{253}{258}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{73}{516}\right)\)	\(e\left(\frac{365}{516}\right)\)	\(e\left(\frac{127}{1032}\right)\)	\(e\left(\frac{41}{258}\right)\)
\(\chi_{355008}(12679,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{457}{1032}\right)\)	\(e\left(\frac{265}{516}\right)\)	\(e\left(\frac{287}{344}\right)\)	\(e\left(\frac{299}{1032}\right)\)	\(e\left(\frac{227}{258}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{401}{516}\right)\)	\(e\left(\frac{457}{516}\right)\)	\(e\left(\frac{323}{1032}\right)\)	\(e\left(\frac{151}{258}\right)\)
\(\chi_{355008}(14455,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{1032}\right)\)	\(e\left(\frac{119}{516}\right)\)	\(e\left(\frac{321}{344}\right)\)	\(e\left(\frac{181}{1032}\right)\)	\(e\left(\frac{247}{258}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{367}{516}\right)\)	\(e\left(\frac{287}{516}\right)\)	\(e\left(\frac{589}{1032}\right)\)	\(e\left(\frac{245}{258}\right)\)
\(\chi_{355008}(14743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{763}{1032}\right)\)	\(e\left(\frac{115}{516}\right)\)	\(e\left(\frac{157}{344}\right)\)	\(e\left(\frac{305}{1032}\right)\)	\(e\left(\frac{191}{258}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{359}{516}\right)\)	\(e\left(\frac{247}{516}\right)\)	\(e\left(\frac{257}{1032}\right)\)	\(e\left(\frac{85}{258}\right)\)
\(\chi_{355008}(16519,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{209}{1032}\right)\)	\(e\left(\frac{137}{516}\right)\)	\(e\left(\frac{199}{344}\right)\)	\(e\left(\frac{139}{1032}\right)\)	\(e\left(\frac{241}{258}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{145}{516}\right)\)	\(e\left(\frac{209}{516}\right)\)	\(e\left(\frac{19}{1032}\right)\)	\(e\left(\frac{191}{258}\right)\)
\(\chi_{355008}(16807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{1032}\right)\)	\(e\left(\frac{481}{516}\right)\)	\(e\left(\frac{27}{344}\right)\)	\(e\left(\frac{311}{1032}\right)\)	\(e\left(\frac{155}{258}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{317}{516}\right)\)	\(e\left(\frac{37}{516}\right)\)	\(e\left(\frac{191}{1032}\right)\)	\(e\left(\frac{19}{258}\right)\)
\(\chi_{355008}(18583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{1032}\right)\)	\(e\left(\frac{155}{516}\right)\)	\(e\left(\frac{77}{344}\right)\)	\(e\left(\frac{97}{1032}\right)\)	\(e\left(\frac{235}{258}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{439}{516}\right)\)	\(e\left(\frac{131}{516}\right)\)	\(e\left(\frac{481}{1032}\right)\)	\(e\left(\frac{137}{258}\right)\)
\(\chi_{355008}(18871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{343}{1032}\right)\)	\(e\left(\frac{331}{516}\right)\)	\(e\left(\frac{241}{344}\right)\)	\(e\left(\frac{317}{1032}\right)\)	\(e\left(\frac{119}{258}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{275}{516}\right)\)	\(e\left(\frac{343}{516}\right)\)	\(e\left(\frac{125}{1032}\right)\)	\(e\left(\frac{211}{258}\right)\)
\(\chi_{355008}(20647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{1032}\right)\)	\(e\left(\frac{173}{516}\right)\)	\(e\left(\frac{299}{344}\right)\)	\(e\left(\frac{55}{1032}\right)\)	\(e\left(\frac{229}{258}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{217}{516}\right)\)	\(e\left(\frac{53}{516}\right)\)	\(e\left(\frac{943}{1032}\right)\)	\(e\left(\frac{83}{258}\right)\)
\(\chi_{355008}(20935,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{649}{1032}\right)\)	\(e\left(\frac{181}{516}\right)\)	\(e\left(\frac{111}{344}\right)\)	\(e\left(\frac{323}{1032}\right)\)	\(e\left(\frac{83}{258}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{233}{516}\right)\)	\(e\left(\frac{133}{516}\right)\)	\(e\left(\frac{59}{1032}\right)\)	\(e\left(\frac{145}{258}\right)\)
\(\chi_{355008}(22711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1007}{1032}\right)\)	\(e\left(\frac{191}{516}\right)\)	\(e\left(\frac{177}{344}\right)\)	\(e\left(\frac{13}{1032}\right)\)	\(e\left(\frac{223}{258}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{511}{516}\right)\)	\(e\left(\frac{491}{516}\right)\)	\(e\left(\frac{373}{1032}\right)\)	\(e\left(\frac{29}{258}\right)\)
\(\chi_{355008}(22999,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{955}{1032}\right)\)	\(e\left(\frac{31}{516}\right)\)	\(e\left(\frac{325}{344}\right)\)	\(e\left(\frac{329}{1032}\right)\)	\(e\left(\frac{47}{258}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{191}{516}\right)\)	\(e\left(\frac{439}{516}\right)\)	\(e\left(\frac{1025}{1032}\right)\)	\(e\left(\frac{79}{258}\right)\)
\(\chi_{355008}(24775,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{929}{1032}\right)\)	\(e\left(\frac{209}{516}\right)\)	\(e\left(\frac{55}{344}\right)\)	\(e\left(\frac{1003}{1032}\right)\)	\(e\left(\frac{217}{258}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{289}{516}\right)\)	\(e\left(\frac{413}{516}\right)\)	\(e\left(\frac{835}{1032}\right)\)	\(e\left(\frac{233}{258}\right)\)
\(\chi_{355008}(25063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{229}{1032}\right)\)	\(e\left(\frac{397}{516}\right)\)	\(e\left(\frac{195}{344}\right)\)	\(e\left(\frac{335}{1032}\right)\)	\(e\left(\frac{11}{258}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{149}{516}\right)\)	\(e\left(\frac{229}{516}\right)\)	\(e\left(\frac{959}{1032}\right)\)	\(e\left(\frac{13}{258}\right)\)
\(\chi_{355008}(26839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{851}{1032}\right)\)	\(e\left(\frac{227}{516}\right)\)	\(e\left(\frac{277}{344}\right)\)	\(e\left(\frac{961}{1032}\right)\)	\(e\left(\frac{211}{258}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{67}{516}\right)\)	\(e\left(\frac{335}{516}\right)\)	\(e\left(\frac{265}{1032}\right)\)	\(e\left(\frac{179}{258}\right)\)
\(\chi_{355008}(27127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{535}{1032}\right)\)	\(e\left(\frac{247}{516}\right)\)	\(e\left(\frac{65}{344}\right)\)	\(e\left(\frac{341}{1032}\right)\)	\(e\left(\frac{233}{258}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{107}{516}\right)\)	\(e\left(\frac{19}{516}\right)\)	\(e\left(\frac{893}{1032}\right)\)	\(e\left(\frac{205}{258}\right)\)
\(\chi_{355008}(28903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{773}{1032}\right)\)	\(e\left(\frac{245}{516}\right)\)	\(e\left(\frac{155}{344}\right)\)	\(e\left(\frac{919}{1032}\right)\)	\(e\left(\frac{205}{258}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{361}{516}\right)\)	\(e\left(\frac{257}{516}\right)\)	\(e\left(\frac{727}{1032}\right)\)	\(e\left(\frac{125}{258}\right)\)
\(\chi_{355008}(29191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{841}{1032}\right)\)	\(e\left(\frac{97}{516}\right)\)	\(e\left(\frac{279}{344}\right)\)	\(e\left(\frac{347}{1032}\right)\)	\(e\left(\frac{197}{258}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{65}{516}\right)\)	\(e\left(\frac{325}{516}\right)\)	\(e\left(\frac{827}{1032}\right)\)	\(e\left(\frac{139}{258}\right)\)
\(\chi_{355008}(30967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{695}{1032}\right)\)	\(e\left(\frac{263}{516}\right)\)	\(e\left(\frac{33}{344}\right)\)	\(e\left(\frac{877}{1032}\right)\)	\(e\left(\frac{199}{258}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{139}{516}\right)\)	\(e\left(\frac{179}{516}\right)\)	\(e\left(\frac{157}{1032}\right)\)	\(e\left(\frac{71}{258}\right)\)

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First 31 of 336 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	355008.ji
Modulus	$355008$
Conductor	$59168$
Order	$1032$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(355008\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(59168\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(1032\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 59168.dz	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);