LMFDB - Dirichlet character orbit 925056.gvu

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925056, base_ring=CyclotomicField(720)) M = H._module chi = DirichletCharacter(H, M([360,45,480,72,370])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(871, 925056)) 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("925056.871"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$925056$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$462528$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$720$	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 462528.fpu	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{720})$	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 720 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 192 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{925056}(871,\cdot)$	$-1$	$1$	$e\left(\frac{223}{720}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{497}{720}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{71}{720}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{223}{360}\right)$	$e\left(\frac{29}{720}\right)$	$e\left(\frac{211}{360}\right)$	$e\left(\frac{547}{720}\right)$
$\chi_{925056}(7783,\cdot)$	$-1$	$1$	$e\left(\frac{127}{720}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{593}{720}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{599}{720}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{127}{360}\right)$	$e\left(\frac{701}{720}\right)$	$e\left(\frac{259}{360}\right)$	$e\left(\frac{163}{720}\right)$
$\chi_{925056}(24295,\cdot)$	$-1$	$1$	$e\left(\frac{431}{720}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{289}{720}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{247}{720}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{71}{360}\right)$	$e\left(\frac{253}{720}\right)$	$e\left(\frac{227}{360}\right)$	$e\left(\frac{179}{720}\right)$
$\chi_{925056}(25735,\cdot)$	$-1$	$1$	$e\left(\frac{347}{720}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{373}{720}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{259}{720}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{347}{360}\right)$	$e\left(\frac{481}{720}\right)$	$e\left(\frac{359}{360}\right)$	$e\left(\frac{383}{720}\right)$
$\chi_{925056}(27607,\cdot)$	$-1$	$1$	$e\left(\frac{449}{720}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{271}{720}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{553}{720}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{89}{360}\right)$	$e\left(\frac{307}{720}\right)$	$e\left(\frac{173}{360}\right)$	$e\left(\frac{701}{720}\right)$
$\chi_{925056}(28663,\cdot)$	$-1$	$1$	$e\left(\frac{109}{720}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{611}{720}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{293}{720}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{109}{360}\right)$	$e\left(\frac{647}{720}\right)$	$e\left(\frac{313}{360}\right)$	$e\left(\frac{361}{720}\right)$
$\chi_{925056}(30775,\cdot)$	$-1$	$1$	$e\left(\frac{149}{720}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{571}{720}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{493}{720}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{149}{360}\right)$	$e\left(\frac{607}{720}\right)$	$e\left(\frac{233}{360}\right)$	$e\left(\frac{401}{720}\right)$
$\chi_{925056}(30967,\cdot)$	$-1$	$1$	$e\left(\frac{13}{720}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{707}{720}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{101}{720}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{13}{360}\right)$	$e\left(\frac{599}{720}\right)$	$e\left(\frac{1}{360}\right)$	$e\left(\frac{697}{720}\right)$
$\chi_{925056}(31687,\cdot)$	$-1$	$1$	$e\left(\frac{691}{720}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{29}{720}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{107}{720}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{331}{360}\right)$	$e\left(\frac{713}{720}\right)$	$e\left(\frac{247}{360}\right)$	$e\left(\frac{439}{720}\right)$
$\chi_{925056}(35239,\cdot)$	$-1$	$1$	$e\left(\frac{407}{720}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{313}{720}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{559}{720}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{47}{360}\right)$	$e\left(\frac{421}{720}\right)$	$e\left(\frac{59}{360}\right)$	$e\left(\frac{443}{720}\right)$
$\chi_{925056}(36823,\cdot)$	$-1$	$1$	$e\left(\frac{257}{720}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{463}{720}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{169}{720}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{257}{360}\right)$	$e\left(\frac{211}{720}\right)$	$e\left(\frac{269}{360}\right)$	$e\left(\frac{653}{720}\right)$
$\chi_{925056}(39991,\cdot)$	$-1$	$1$	$e\left(\frac{197}{720}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{523}{720}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{589}{720}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{197}{360}\right)$	$e\left(\frac{271}{720}\right)$	$e\left(\frac{209}{360}\right)$	$e\left(\frac{593}{720}\right)$
$\chi_{925056}(42919,\cdot)$	$-1$	$1$	$e\left(\frac{439}{720}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{281}{720}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{143}{720}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{79}{360}\right)$	$e\left(\frac{677}{720}\right)$	$e\left(\frac{283}{360}\right)$	$e\left(\frac{331}{720}\right)$
$\chi_{925056}(52279,\cdot)$	$-1$	$1$	$e\left(\frac{421}{720}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{299}{720}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{557}{720}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{61}{360}\right)$	$e\left(\frac{623}{720}\right)$	$e\left(\frac{337}{360}\right)$	$e\left(\frac{529}{720}\right)$
$\chi_{925056}(66343,\cdot)$	$-1$	$1$	$e\left(\frac{503}{720}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{217}{720}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{31}{720}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{143}{360}\right)$	$e\left(\frac{469}{720}\right)$	$e\left(\frac{11}{360}\right)$	$e\left(\frac{107}{720}\right)$
$\chi_{925056}(68503,\cdot)$	$-1$	$1$	$e\left(\frac{137}{720}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{583}{720}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{289}{720}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{137}{360}\right)$	$e\left(\frac{331}{720}\right)$	$e\left(\frac{149}{360}\right)$	$e\left(\frac{533}{720}\right)$
$\chi_{925056}(73015,\cdot)$	$-1$	$1$	$e\left(\frac{229}{720}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{491}{720}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{173}{720}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{229}{360}\right)$	$e\left(\frac{527}{720}\right)$	$e\left(\frac{73}{360}\right)$	$e\left(\frac{481}{720}\right)$
$\chi_{925056}(73735,\cdot)$	$-1$	$1$	$e\left(\frac{43}{720}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{677}{720}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{611}{720}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{43}{360}\right)$	$e\left(\frac{209}{720}\right)$	$e\left(\frac{31}{360}\right)$	$e\left(\frac{367}{720}\right)$
$\chi_{925056}(85399,\cdot)$	$-1$	$1$	$e\left(\frac{457}{720}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{263}{720}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{449}{720}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{97}{360}\right)$	$e\left(\frac{11}{720}\right)$	$e\left(\frac{229}{360}\right)$	$e\left(\frac{133}{720}\right)$
$\chi_{925056}(86983,\cdot)$	$-1$	$1$	$e\left(\frac{67}{720}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{653}{720}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{299}{720}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{67}{360}\right)$	$e\left(\frac{41}{720}\right)$	$e\left(\frac{199}{360}\right)$	$e\left(\frac{103}{720}\right)$
$\chi_{925056}(91879,\cdot)$	$-1$	$1$	$e\left(\frac{271}{720}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{449}{720}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{167}{720}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{271}{360}\right)$	$e\left(\frac{413}{720}\right)$	$e\left(\frac{187}{360}\right)$	$e\left(\frac{19}{720}\right)$
$\chi_{925056}(94327,\cdot)$	$-1$	$1$	$e\left(\frac{493}{720}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{227}{720}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{341}{720}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{133}{360}\right)$	$e\left(\frac{119}{720}\right)$	$e\left(\frac{121}{360}\right)$	$e\left(\frac{457}{720}\right)$
$\chi_{925056}(95431,\cdot)$	$-1$	$1$	$e\left(\frac{227}{720}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{493}{720}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{379}{720}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{227}{360}\right)$	$e\left(\frac{601}{720}\right)$	$e\left(\frac{239}{360}\right)$	$e\left(\frac{263}{720}\right)$
$\chi_{925056}(104935,\cdot)$	$-1$	$1$	$e\left(\frac{527}{720}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{193}{720}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{439}{720}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{167}{360}\right)$	$e\left(\frac{301}{720}\right)$	$e\left(\frac{179}{360}\right)$	$e\left(\frac{563}{720}\right)$
$\chi_{925056}(108391,\cdot)$	$-1$	$1$	$e\left(\frac{719}{720}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{720}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{103}{720}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{359}{360}\right)$	$e\left(\frac{397}{720}\right)$	$e\left(\frac{83}{360}\right)$	$e\left(\frac{611}{720}\right)$
$\chi_{925056}(109831,\cdot)$	$-1$	$1$	$e\left(\frac{491}{720}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{229}{720}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{547}{720}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{131}{360}\right)$	$e\left(\frac{193}{720}\right)$	$e\left(\frac{287}{360}\right)$	$e\left(\frac{239}{720}\right)$
$\chi_{925056}(115783,\cdot)$	$-1$	$1$	$e\left(\frac{259}{720}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{461}{720}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{683}{720}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{259}{360}\right)$	$e\left(\frac{137}{720}\right)$	$e\left(\frac{103}{360}\right)$	$e\left(\frac{151}{720}\right)$
$\chi_{925056}(119335,\cdot)$	$-1$	$1$	$e\left(\frac{551}{720}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{169}{720}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{127}{720}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{191}{360}\right)$	$e\left(\frac{133}{720}\right)$	$e\left(\frac{347}{360}\right)$	$e\left(\frac{299}{720}\right)$
$\chi_{925056}(120919,\cdot)$	$-1$	$1$	$e\left(\frac{401}{720}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{319}{720}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{457}{720}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{41}{360}\right)$	$e\left(\frac{643}{720}\right)$	$e\left(\frac{197}{360}\right)$	$e\left(\frac{509}{720}\right)$
$\chi_{925056}(124087,\cdot)$	$-1$	$1$	$e\left(\frac{341}{720}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{379}{720}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{157}{720}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{341}{360}\right)$	$e\left(\frac{703}{720}\right)$	$e\left(\frac{137}{360}\right)$	$e\left(\frac{449}{720}\right)$
$\chi_{925056}(133927,\cdot)$	$-1$	$1$	$e\left(\frac{343}{720}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{377}{720}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{671}{720}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{343}{360}\right)$	$e\left(\frac{629}{720}\right)$	$e\left(\frac{331}{360}\right)$	$e\left(\frac{667}{720}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{925056}(871,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{223}{720}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{497}{720}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{71}{720}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{223}{360}\right)\)	\(e\left(\frac{29}{720}\right)\)	\(e\left(\frac{211}{360}\right)\)	\(e\left(\frac{547}{720}\right)\)
\(\chi_{925056}(7783,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{720}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{593}{720}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{599}{720}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{127}{360}\right)\)	\(e\left(\frac{701}{720}\right)\)	\(e\left(\frac{259}{360}\right)\)	\(e\left(\frac{163}{720}\right)\)
\(\chi_{925056}(24295,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{431}{720}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{289}{720}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{247}{720}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{71}{360}\right)\)	\(e\left(\frac{253}{720}\right)\)	\(e\left(\frac{227}{360}\right)\)	\(e\left(\frac{179}{720}\right)\)
\(\chi_{925056}(25735,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{347}{720}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{373}{720}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{259}{720}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{347}{360}\right)\)	\(e\left(\frac{481}{720}\right)\)	\(e\left(\frac{359}{360}\right)\)	\(e\left(\frac{383}{720}\right)\)
\(\chi_{925056}(27607,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{449}{720}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{271}{720}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{553}{720}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{89}{360}\right)\)	\(e\left(\frac{307}{720}\right)\)	\(e\left(\frac{173}{360}\right)\)	\(e\left(\frac{701}{720}\right)\)
\(\chi_{925056}(28663,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{720}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{611}{720}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{293}{720}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{109}{360}\right)\)	\(e\left(\frac{647}{720}\right)\)	\(e\left(\frac{313}{360}\right)\)	\(e\left(\frac{361}{720}\right)\)
\(\chi_{925056}(30775,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{720}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{571}{720}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{493}{720}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{149}{360}\right)\)	\(e\left(\frac{607}{720}\right)\)	\(e\left(\frac{233}{360}\right)\)	\(e\left(\frac{401}{720}\right)\)
\(\chi_{925056}(30967,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{720}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{707}{720}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{101}{720}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{13}{360}\right)\)	\(e\left(\frac{599}{720}\right)\)	\(e\left(\frac{1}{360}\right)\)	\(e\left(\frac{697}{720}\right)\)
\(\chi_{925056}(31687,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{691}{720}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{29}{720}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{107}{720}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{331}{360}\right)\)	\(e\left(\frac{713}{720}\right)\)	\(e\left(\frac{247}{360}\right)\)	\(e\left(\frac{439}{720}\right)\)
\(\chi_{925056}(35239,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{407}{720}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{313}{720}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{559}{720}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{47}{360}\right)\)	\(e\left(\frac{421}{720}\right)\)	\(e\left(\frac{59}{360}\right)\)	\(e\left(\frac{443}{720}\right)\)
\(\chi_{925056}(36823,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{257}{720}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{463}{720}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{169}{720}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{257}{360}\right)\)	\(e\left(\frac{211}{720}\right)\)	\(e\left(\frac{269}{360}\right)\)	\(e\left(\frac{653}{720}\right)\)
\(\chi_{925056}(39991,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{197}{720}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{523}{720}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{589}{720}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{197}{360}\right)\)	\(e\left(\frac{271}{720}\right)\)	\(e\left(\frac{209}{360}\right)\)	\(e\left(\frac{593}{720}\right)\)
\(\chi_{925056}(42919,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{439}{720}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{281}{720}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{143}{720}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{79}{360}\right)\)	\(e\left(\frac{677}{720}\right)\)	\(e\left(\frac{283}{360}\right)\)	\(e\left(\frac{331}{720}\right)\)
\(\chi_{925056}(52279,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{421}{720}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{299}{720}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{557}{720}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{61}{360}\right)\)	\(e\left(\frac{623}{720}\right)\)	\(e\left(\frac{337}{360}\right)\)	\(e\left(\frac{529}{720}\right)\)
\(\chi_{925056}(66343,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{503}{720}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{217}{720}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{31}{720}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{143}{360}\right)\)	\(e\left(\frac{469}{720}\right)\)	\(e\left(\frac{11}{360}\right)\)	\(e\left(\frac{107}{720}\right)\)
\(\chi_{925056}(68503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{720}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{583}{720}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{289}{720}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{137}{360}\right)\)	\(e\left(\frac{331}{720}\right)\)	\(e\left(\frac{149}{360}\right)\)	\(e\left(\frac{533}{720}\right)\)
\(\chi_{925056}(73015,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{229}{720}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{491}{720}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{173}{720}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{229}{360}\right)\)	\(e\left(\frac{527}{720}\right)\)	\(e\left(\frac{73}{360}\right)\)	\(e\left(\frac{481}{720}\right)\)
\(\chi_{925056}(73735,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{720}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{677}{720}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{611}{720}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{43}{360}\right)\)	\(e\left(\frac{209}{720}\right)\)	\(e\left(\frac{31}{360}\right)\)	\(e\left(\frac{367}{720}\right)\)
\(\chi_{925056}(85399,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{457}{720}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{263}{720}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{449}{720}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{97}{360}\right)\)	\(e\left(\frac{11}{720}\right)\)	\(e\left(\frac{229}{360}\right)\)	\(e\left(\frac{133}{720}\right)\)
\(\chi_{925056}(86983,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{720}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{653}{720}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{299}{720}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{67}{360}\right)\)	\(e\left(\frac{41}{720}\right)\)	\(e\left(\frac{199}{360}\right)\)	\(e\left(\frac{103}{720}\right)\)
\(\chi_{925056}(91879,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{271}{720}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{449}{720}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{167}{720}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{271}{360}\right)\)	\(e\left(\frac{413}{720}\right)\)	\(e\left(\frac{187}{360}\right)\)	\(e\left(\frac{19}{720}\right)\)
\(\chi_{925056}(94327,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{493}{720}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{227}{720}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{341}{720}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{133}{360}\right)\)	\(e\left(\frac{119}{720}\right)\)	\(e\left(\frac{121}{360}\right)\)	\(e\left(\frac{457}{720}\right)\)
\(\chi_{925056}(95431,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{227}{720}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{493}{720}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{379}{720}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{227}{360}\right)\)	\(e\left(\frac{601}{720}\right)\)	\(e\left(\frac{239}{360}\right)\)	\(e\left(\frac{263}{720}\right)\)
\(\chi_{925056}(104935,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{527}{720}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{193}{720}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{439}{720}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{167}{360}\right)\)	\(e\left(\frac{301}{720}\right)\)	\(e\left(\frac{179}{360}\right)\)	\(e\left(\frac{563}{720}\right)\)
\(\chi_{925056}(108391,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{719}{720}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{720}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{103}{720}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{359}{360}\right)\)	\(e\left(\frac{397}{720}\right)\)	\(e\left(\frac{83}{360}\right)\)	\(e\left(\frac{611}{720}\right)\)
\(\chi_{925056}(109831,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{491}{720}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{229}{720}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{547}{720}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{131}{360}\right)\)	\(e\left(\frac{193}{720}\right)\)	\(e\left(\frac{287}{360}\right)\)	\(e\left(\frac{239}{720}\right)\)
\(\chi_{925056}(115783,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{259}{720}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{461}{720}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{683}{720}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{259}{360}\right)\)	\(e\left(\frac{137}{720}\right)\)	\(e\left(\frac{103}{360}\right)\)	\(e\left(\frac{151}{720}\right)\)
\(\chi_{925056}(119335,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{551}{720}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{169}{720}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{127}{720}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{191}{360}\right)\)	\(e\left(\frac{133}{720}\right)\)	\(e\left(\frac{347}{360}\right)\)	\(e\left(\frac{299}{720}\right)\)
\(\chi_{925056}(120919,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{401}{720}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{319}{720}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{457}{720}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{41}{360}\right)\)	\(e\left(\frac{643}{720}\right)\)	\(e\left(\frac{197}{360}\right)\)	\(e\left(\frac{509}{720}\right)\)
\(\chi_{925056}(124087,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{341}{720}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{379}{720}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{157}{720}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{341}{360}\right)\)	\(e\left(\frac{703}{720}\right)\)	\(e\left(\frac{137}{360}\right)\)	\(e\left(\frac{449}{720}\right)\)
\(\chi_{925056}(133927,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{343}{720}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{377}{720}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{671}{720}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{343}{360}\right)\)	\(e\left(\frac{629}{720}\right)\)	\(e\left(\frac{331}{360}\right)\)	\(e\left(\frac{667}{720}\right)\)

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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	925056.gvu
Modulus	$925056$
Conductor	$462528$
Order	$720$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(925056\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(462528\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(720\)	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 462528.fpu	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);