LMFDB - Dirichlet character orbit 31734.lw

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31734, base_ring=CyclotomicField(840)) M = H._module chi = DirichletCharacter(H, M([140,147,820])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(29, 31734)) 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("31734.29"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$31734$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$15867$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$840$	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 15867.ly	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{840})$	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 840 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 192 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{31734}(29,\cdot)$	$-1$	$1$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{821}{840}\right)$	$e\left(\frac{279}{280}\right)$	$e\left(\frac{311}{840}\right)$	$e\left(\frac{103}{840}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{349}{840}\right)$	$e\left(\frac{89}{210}\right)$
$\chi_{31734}(149,\cdot)$	$-1$	$1$	$e\left(\frac{227}{420}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{451}{840}\right)$	$e\left(\frac{9}{280}\right)$	$e\left(\frac{1}{840}\right)$	$e\left(\frac{473}{840}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{779}{840}\right)$	$e\left(\frac{109}{210}\right)$
$\chi_{31734}(335,\cdot)$	$-1$	$1$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{437}{840}\right)$	$e\left(\frac{23}{280}\right)$	$e\left(\frac{407}{840}\right)$	$e\left(\frac{151}{840}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{373}{840}\right)$	$e\left(\frac{53}{210}\right)$
$\chi_{31734}(347,\cdot)$	$-1$	$1$	$e\left(\frac{299}{420}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{187}{840}\right)$	$e\left(\frac{113}{280}\right)$	$e\left(\frac{697}{840}\right)$	$e\left(\frac{401}{840}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{323}{840}\right)$	$e\left(\frac{163}{210}\right)$
$\chi_{31734}(587,\cdot)$	$-1$	$1$	$e\left(\frac{361}{420}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{53}{840}\right)$	$e\left(\frac{47}{280}\right)$	$e\left(\frac{503}{840}\right)$	$e\left(\frac{199}{840}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{397}{840}\right)$	$e\left(\frac{17}{210}\right)$
$\chi_{31734}(749,\cdot)$	$-1$	$1$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{89}{840}\right)$	$e\left(\frac{211}{280}\right)$	$e\left(\frac{179}{840}\right)$	$e\left(\frac{667}{840}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{1}{840}\right)$	$e\left(\frac{191}{210}\right)$
$\chi_{31734}(803,\cdot)$	$-1$	$1$	$e\left(\frac{163}{420}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{359}{840}\right)$	$e\left(\frac{181}{280}\right)$	$e\left(\frac{269}{840}\right)$	$e\left(\frac{397}{840}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{391}{840}\right)$	$e\left(\frac{131}{210}\right)$
$\chi_{31734}(1019,\cdot)$	$-1$	$1$	$e\left(\frac{391}{420}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{503}{840}\right)$	$e\left(\frac{277}{280}\right)$	$e\left(\frac{653}{840}\right)$	$e\left(\frac{589}{840}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{487}{840}\right)$	$e\left(\frac{197}{210}\right)$
$\chi_{31734}(1409,\cdot)$	$-1$	$1$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{631}{840}\right)$	$e\left(\frac{269}{280}\right)$	$e\left(\frac{61}{840}\right)$	$e\left(\frac{293}{840}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{479}{840}\right)$	$e\left(\frac{139}{210}\right)$
$\chi_{31734}(1523,\cdot)$	$-1$	$1$	$e\left(\frac{271}{420}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{803}{840}\right)$	$e\left(\frac{57}{280}\right)$	$e\left(\frac{473}{840}\right)$	$e\left(\frac{289}{840}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{547}{840}\right)$	$e\left(\frac{107}{210}\right)$
$\chi_{31734}(1577,\cdot)$	$-1$	$1$	$e\left(\frac{79}{420}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{107}{840}\right)$	$e\left(\frac{153}{280}\right)$	$e\left(\frac{17}{840}\right)$	$e\left(\frac{481}{840}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{643}{840}\right)$	$e\left(\frac{173}{210}\right)$
$\chi_{31734}(1703,\cdot)$	$-1$	$1$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{407}{840}\right)$	$e\left(\frac{213}{280}\right)$	$e\left(\frac{677}{840}\right)$	$e\left(\frac{181}{840}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{703}{840}\right)$	$e\left(\frac{83}{210}\right)$
$\chi_{31734}(1793,\cdot)$	$-1$	$1$	$e\left(\frac{13}{420}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{629}{840}\right)$	$e\left(\frac{151}{280}\right)$	$e\left(\frac{359}{840}\right)$	$e\left(\frac{127}{840}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{781}{840}\right)$	$e\left(\frac{71}{210}\right)$
$\chi_{31734}(2471,\cdot)$	$-1$	$1$	$e\left(\frac{353}{420}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{409}{840}\right)$	$e\left(\frac{51}{280}\right)$	$e\left(\frac{379}{840}\right)$	$e\left(\frac{347}{840}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{401}{840}\right)$	$e\left(\frac{151}{210}\right)$
$\chi_{31734}(2477,\cdot)$	$-1$	$1$	$e\left(\frac{43}{420}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{659}{840}\right)$	$e\left(\frac{241}{280}\right)$	$e\left(\frac{89}{840}\right)$	$e\left(\frac{97}{840}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{451}{840}\right)$	$e\left(\frac{41}{210}\right)$
$\chi_{31734}(3101,\cdot)$	$-1$	$1$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{811}{840}\right)$	$e\left(\frac{249}{280}\right)$	$e\left(\frac{121}{840}\right)$	$e\left(\frac{113}{840}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{179}{840}\right)$	$e\left(\frac{169}{210}\right)$
$\chi_{31734}(3245,\cdot)$	$-1$	$1$	$e\left(\frac{311}{420}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{283}{840}\right)$	$e\left(\frac{177}{280}\right)$	$e\left(\frac{673}{840}\right)$	$e\left(\frac{809}{840}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{107}{840}\right)$	$e\left(\frac{67}{210}\right)$
$\chi_{31734}(3251,\cdot)$	$-1$	$1$	$e\left(\frac{337}{420}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{281}{840}\right)$	$e\left(\frac{59}{280}\right)$	$e\left(\frac{131}{840}\right)$	$e\left(\frac{643}{840}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{409}{840}\right)$	$e\left(\frac{209}{210}\right)$
$\chi_{31734}(3431,\cdot)$	$-1$	$1$	$e\left(\frac{241}{420}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{353}{840}\right)$	$e\left(\frac{107}{280}\right)$	$e\left(\frac{323}{840}\right)$	$e\left(\frac{739}{840}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{457}{840}\right)$	$e\left(\frac{137}{210}\right)$
$\chi_{31734}(3683,\cdot)$	$-1$	$1$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{137}{840}\right)$	$e\left(\frac{243}{280}\right)$	$e\left(\frac{587}{840}\right)$	$e\left(\frac{451}{840}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{313}{840}\right)$	$e\left(\frac{143}{210}\right)$
$\chi_{31734}(3839,\cdot)$	$-1$	$1$	$e\left(\frac{107}{420}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{331}{840}\right)$	$e\left(\frac{209}{280}\right)$	$e\left(\frac{241}{840}\right)$	$e\left(\frac{593}{840}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{419}{840}\right)$	$e\left(\frac{19}{210}\right)$
$\chi_{31734}(4025,\cdot)$	$-1$	$1$	$e\left(\frac{169}{420}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{197}{840}\right)$	$e\left(\frac{143}{280}\right)$	$e\left(\frac{47}{840}\right)$	$e\left(\frac{391}{840}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{493}{840}\right)$	$e\left(\frac{83}{210}\right)$
$\chi_{31734}(4115,\cdot)$	$-1$	$1$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{671}{840}\right)$	$e\left(\frac{109}{280}\right)$	$e\left(\frac{821}{840}\right)$	$e\left(\frac{253}{840}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{319}{840}\right)$	$e\left(\frac{29}{210}\right)$
$\chi_{31734}(4217,\cdot)$	$-1$	$1$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{103}{840}\right)$	$e\left(\frac{197}{280}\right)$	$e\left(\frac{613}{840}\right)$	$e\left(\frac{149}{840}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{407}{840}\right)$	$e\left(\frac{37}{210}\right)$
$\chi_{31734}(4457,\cdot)$	$-1$	$1$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{221}{840}\right)$	$e\left(\frac{159}{280}\right)$	$e\left(\frac{671}{840}\right)$	$e\left(\frac{703}{840}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{229}{840}\right)$	$e\left(\frac{59}{210}\right)$
$\chi_{31734}(4577,\cdot)$	$-1$	$1$	$e\left(\frac{347}{420}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{571}{840}\right)$	$e\left(\frac{89}{280}\right)$	$e\left(\frac{601}{840}\right)$	$e\left(\frac{353}{840}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{299}{840}\right)$	$e\left(\frac{199}{210}\right)$
$\chi_{31734}(4991,\cdot)$	$-1$	$1$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{229}{840}\right)$	$e\left(\frac{71}{280}\right)$	$e\left(\frac{319}{840}\right)$	$e\left(\frac{527}{840}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{701}{840}\right)$	$e\left(\frac{121}{210}\right)$
$\chi_{31734}(5231,\cdot)$	$-1$	$1$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{599}{840}\right)$	$e\left(\frac{61}{280}\right)$	$e\left(\frac{629}{840}\right)$	$e\left(\frac{157}{840}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{271}{840}\right)$	$e\left(\frac{101}{210}\right)$
$\chi_{31734}(5393,\cdot)$	$-1$	$1$	$e\left(\frac{19}{420}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{47}{840}\right)$	$e\left(\frac{253}{280}\right)$	$e\left(\frac{557}{840}\right)$	$e\left(\frac{541}{840}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{463}{840}\right)$	$e\left(\frac{23}{210}\right)$
$\chi_{31734}(5423,\cdot)$	$-1$	$1$	$e\left(\frac{293}{420}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{769}{840}\right)$	$e\left(\frac{11}{280}\right)$	$e\left(\frac{499}{840}\right)$	$e\left(\frac{827}{840}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{641}{840}\right)$	$e\left(\frac{1}{210}\right)$
$\chi_{31734}(5447,\cdot)$	$-1$	$1$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{23}{840}\right)$	$e\left(\frac{237}{280}\right)$	$e\left(\frac{773}{840}\right)$	$e\left(\frac{229}{840}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{727}{840}\right)$	$e\left(\frac{47}{210}\right)$

Overview	Random
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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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{31734}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{821}{840}\right)\)	\(e\left(\frac{279}{280}\right)\)	\(e\left(\frac{311}{840}\right)\)	\(e\left(\frac{103}{840}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{349}{840}\right)\)	\(e\left(\frac{89}{210}\right)\)
\(\chi_{31734}(149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{227}{420}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{451}{840}\right)\)	\(e\left(\frac{9}{280}\right)\)	\(e\left(\frac{1}{840}\right)\)	\(e\left(\frac{473}{840}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{779}{840}\right)\)	\(e\left(\frac{109}{210}\right)\)
\(\chi_{31734}(335,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{437}{840}\right)\)	\(e\left(\frac{23}{280}\right)\)	\(e\left(\frac{407}{840}\right)\)	\(e\left(\frac{151}{840}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{373}{840}\right)\)	\(e\left(\frac{53}{210}\right)\)
\(\chi_{31734}(347,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{299}{420}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{187}{840}\right)\)	\(e\left(\frac{113}{280}\right)\)	\(e\left(\frac{697}{840}\right)\)	\(e\left(\frac{401}{840}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{323}{840}\right)\)	\(e\left(\frac{163}{210}\right)\)
\(\chi_{31734}(587,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{361}{420}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{53}{840}\right)\)	\(e\left(\frac{47}{280}\right)\)	\(e\left(\frac{503}{840}\right)\)	\(e\left(\frac{199}{840}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{397}{840}\right)\)	\(e\left(\frac{17}{210}\right)\)
\(\chi_{31734}(749,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{89}{840}\right)\)	\(e\left(\frac{211}{280}\right)\)	\(e\left(\frac{179}{840}\right)\)	\(e\left(\frac{667}{840}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{1}{840}\right)\)	\(e\left(\frac{191}{210}\right)\)
\(\chi_{31734}(803,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{420}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{359}{840}\right)\)	\(e\left(\frac{181}{280}\right)\)	\(e\left(\frac{269}{840}\right)\)	\(e\left(\frac{397}{840}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{391}{840}\right)\)	\(e\left(\frac{131}{210}\right)\)
\(\chi_{31734}(1019,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{391}{420}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{503}{840}\right)\)	\(e\left(\frac{277}{280}\right)\)	\(e\left(\frac{653}{840}\right)\)	\(e\left(\frac{589}{840}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{487}{840}\right)\)	\(e\left(\frac{197}{210}\right)\)
\(\chi_{31734}(1409,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{631}{840}\right)\)	\(e\left(\frac{269}{280}\right)\)	\(e\left(\frac{61}{840}\right)\)	\(e\left(\frac{293}{840}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{479}{840}\right)\)	\(e\left(\frac{139}{210}\right)\)
\(\chi_{31734}(1523,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{271}{420}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{803}{840}\right)\)	\(e\left(\frac{57}{280}\right)\)	\(e\left(\frac{473}{840}\right)\)	\(e\left(\frac{289}{840}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{547}{840}\right)\)	\(e\left(\frac{107}{210}\right)\)
\(\chi_{31734}(1577,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{420}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{107}{840}\right)\)	\(e\left(\frac{153}{280}\right)\)	\(e\left(\frac{17}{840}\right)\)	\(e\left(\frac{481}{840}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{643}{840}\right)\)	\(e\left(\frac{173}{210}\right)\)
\(\chi_{31734}(1703,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{407}{840}\right)\)	\(e\left(\frac{213}{280}\right)\)	\(e\left(\frac{677}{840}\right)\)	\(e\left(\frac{181}{840}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{703}{840}\right)\)	\(e\left(\frac{83}{210}\right)\)
\(\chi_{31734}(1793,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{420}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{629}{840}\right)\)	\(e\left(\frac{151}{280}\right)\)	\(e\left(\frac{359}{840}\right)\)	\(e\left(\frac{127}{840}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{781}{840}\right)\)	\(e\left(\frac{71}{210}\right)\)
\(\chi_{31734}(2471,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{353}{420}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{409}{840}\right)\)	\(e\left(\frac{51}{280}\right)\)	\(e\left(\frac{379}{840}\right)\)	\(e\left(\frac{347}{840}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{401}{840}\right)\)	\(e\left(\frac{151}{210}\right)\)
\(\chi_{31734}(2477,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{420}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{659}{840}\right)\)	\(e\left(\frac{241}{280}\right)\)	\(e\left(\frac{89}{840}\right)\)	\(e\left(\frac{97}{840}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{451}{840}\right)\)	\(e\left(\frac{41}{210}\right)\)
\(\chi_{31734}(3101,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{811}{840}\right)\)	\(e\left(\frac{249}{280}\right)\)	\(e\left(\frac{121}{840}\right)\)	\(e\left(\frac{113}{840}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{179}{840}\right)\)	\(e\left(\frac{169}{210}\right)\)
\(\chi_{31734}(3245,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{311}{420}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{283}{840}\right)\)	\(e\left(\frac{177}{280}\right)\)	\(e\left(\frac{673}{840}\right)\)	\(e\left(\frac{809}{840}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{107}{840}\right)\)	\(e\left(\frac{67}{210}\right)\)
\(\chi_{31734}(3251,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{337}{420}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{281}{840}\right)\)	\(e\left(\frac{59}{280}\right)\)	\(e\left(\frac{131}{840}\right)\)	\(e\left(\frac{643}{840}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{409}{840}\right)\)	\(e\left(\frac{209}{210}\right)\)
\(\chi_{31734}(3431,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{241}{420}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{353}{840}\right)\)	\(e\left(\frac{107}{280}\right)\)	\(e\left(\frac{323}{840}\right)\)	\(e\left(\frac{739}{840}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{457}{840}\right)\)	\(e\left(\frac{137}{210}\right)\)
\(\chi_{31734}(3683,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{137}{840}\right)\)	\(e\left(\frac{243}{280}\right)\)	\(e\left(\frac{587}{840}\right)\)	\(e\left(\frac{451}{840}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{313}{840}\right)\)	\(e\left(\frac{143}{210}\right)\)
\(\chi_{31734}(3839,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{420}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{331}{840}\right)\)	\(e\left(\frac{209}{280}\right)\)	\(e\left(\frac{241}{840}\right)\)	\(e\left(\frac{593}{840}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{419}{840}\right)\)	\(e\left(\frac{19}{210}\right)\)
\(\chi_{31734}(4025,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{420}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{197}{840}\right)\)	\(e\left(\frac{143}{280}\right)\)	\(e\left(\frac{47}{840}\right)\)	\(e\left(\frac{391}{840}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{493}{840}\right)\)	\(e\left(\frac{83}{210}\right)\)
\(\chi_{31734}(4115,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{671}{840}\right)\)	\(e\left(\frac{109}{280}\right)\)	\(e\left(\frac{821}{840}\right)\)	\(e\left(\frac{253}{840}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{319}{840}\right)\)	\(e\left(\frac{29}{210}\right)\)
\(\chi_{31734}(4217,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{420}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{103}{840}\right)\)	\(e\left(\frac{197}{280}\right)\)	\(e\left(\frac{613}{840}\right)\)	\(e\left(\frac{149}{840}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{407}{840}\right)\)	\(e\left(\frac{37}{210}\right)\)
\(\chi_{31734}(4457,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{277}{420}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{221}{840}\right)\)	\(e\left(\frac{159}{280}\right)\)	\(e\left(\frac{671}{840}\right)\)	\(e\left(\frac{703}{840}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{229}{840}\right)\)	\(e\left(\frac{59}{210}\right)\)
\(\chi_{31734}(4577,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{347}{420}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{571}{840}\right)\)	\(e\left(\frac{89}{280}\right)\)	\(e\left(\frac{601}{840}\right)\)	\(e\left(\frac{353}{840}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{299}{840}\right)\)	\(e\left(\frac{199}{210}\right)\)
\(\chi_{31734}(4991,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{229}{840}\right)\)	\(e\left(\frac{71}{280}\right)\)	\(e\left(\frac{319}{840}\right)\)	\(e\left(\frac{527}{840}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{701}{840}\right)\)	\(e\left(\frac{121}{210}\right)\)
\(\chi_{31734}(5231,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{599}{840}\right)\)	\(e\left(\frac{61}{280}\right)\)	\(e\left(\frac{629}{840}\right)\)	\(e\left(\frac{157}{840}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{271}{840}\right)\)	\(e\left(\frac{101}{210}\right)\)
\(\chi_{31734}(5393,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{420}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{47}{840}\right)\)	\(e\left(\frac{253}{280}\right)\)	\(e\left(\frac{557}{840}\right)\)	\(e\left(\frac{541}{840}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{463}{840}\right)\)	\(e\left(\frac{23}{210}\right)\)
\(\chi_{31734}(5423,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{293}{420}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{769}{840}\right)\)	\(e\left(\frac{11}{280}\right)\)	\(e\left(\frac{499}{840}\right)\)	\(e\left(\frac{827}{840}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{641}{840}\right)\)	\(e\left(\frac{1}{210}\right)\)
\(\chi_{31734}(5447,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{23}{840}\right)\)	\(e\left(\frac{237}{280}\right)\)	\(e\left(\frac{773}{840}\right)\)	\(e\left(\frac{229}{840}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{727}{840}\right)\)	\(e\left(\frac{47}{210}\right)\)

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First 31 of 192 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	31734.lw
Modulus	$31734$
Conductor	$15867$
Order	$840$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(31734\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(15867\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(840\)	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 15867.ly	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);