LMFDB - Dirichlet character orbit 836352.xl

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(836352, base_ring=CyclotomicField(3520)) M = H._module chi = DirichletCharacter(H, M([0,275,1760,3392])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(53, 836352)) 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("836352.53"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$836352$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$92928$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$3520$	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 92928.ij	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:	$\Q(\zeta_{3520})$	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 3520 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 1280 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{836352}(53,\cdot)$	$-1$	$1$	$e\left(\frac{3123}{3520}\right)$	$e\left(\frac{927}{1760}\right)$	$e\left(\frac{3517}{3520}\right)$	$e\left(\frac{797}{880}\right)$	$e\left(\frac{2741}{3520}\right)$	$e\left(\frac{17}{352}\right)$	$e\left(\frac{1363}{1760}\right)$	$e\left(\frac{1729}{3520}\right)$	$e\left(\frac{219}{440}\right)$	$e\left(\frac{1457}{3520}\right)$
$\chi_{836352}(917,\cdot)$	$-1$	$1$	$e\left(\frac{3051}{3520}\right)$	$e\left(\frac{439}{1760}\right)$	$e\left(\frac{2949}{3520}\right)$	$e\left(\frac{629}{880}\right)$	$e\left(\frac{1917}{3520}\right)$	$e\left(\frac{185}{352}\right)$	$e\left(\frac{1291}{1760}\right)$	$e\left(\frac{553}{3520}\right)$	$e\left(\frac{323}{440}\right)$	$e\left(\frac{409}{3520}\right)$
$\chi_{836352}(1565,\cdot)$	$-1$	$1$	$e\left(\frac{1549}{3520}\right)$	$e\left(\frac{1601}{1760}\right)$	$e\left(\frac{2051}{3520}\right)$	$e\left(\frac{131}{880}\right)$	$e\left(\frac{3403}{3520}\right)$	$e\left(\frac{111}{352}\right)$	$e\left(\frac{1549}{1760}\right)$	$e\left(\frac{3007}{3520}\right)$	$e\left(\frac{317}{440}\right)$	$e\left(\frac{1231}{3520}\right)$
$\chi_{836352}(2645,\cdot)$	$-1$	$1$	$e\left(\frac{3227}{3520}\right)$	$e\left(\frac{263}{1760}\right)$	$e\left(\frac{2773}{3520}\right)$	$e\left(\frac{453}{880}\right)$	$e\left(\frac{3149}{3520}\right)$	$e\left(\frac{9}{352}\right)$	$e\left(\frac{1467}{1760}\right)$	$e\left(\frac{1081}{3520}\right)$	$e\left(\frac{411}{440}\right)$	$e\left(\frac{233}{3520}\right)$
$\chi_{836352}(3293,\cdot)$	$-1$	$1$	$e\left(\frac{1021}{3520}\right)$	$e\left(\frac{369}{1760}\right)$	$e\left(\frac{2579}{3520}\right)$	$e\left(\frac{659}{880}\right)$	$e\left(\frac{3227}{3520}\right)$	$e\left(\frac{287}{352}\right)$	$e\left(\frac{1021}{1760}\right)$	$e\left(\frac{1423}{3520}\right)$	$e\left(\frac{53}{440}\right)$	$e\left(\frac{1759}{3520}\right)$
$\chi_{836352}(3941,\cdot)$	$-1$	$1$	$e\left(\frac{3279}{3520}\right)$	$e\left(\frac{811}{1760}\right)$	$e\left(\frac{2401}{3520}\right)$	$e\left(\frac{721}{880}\right)$	$e\left(\frac{1593}{3520}\right)$	$e\left(\frac{5}{352}\right)$	$e\left(\frac{1519}{1760}\right)$	$e\left(\frac{757}{3520}\right)$	$e\left(\frac{287}{440}\right)$	$e\left(\frac{1381}{3520}\right)$
$\chi_{836352}(4805,\cdot)$	$-1$	$1$	$e\left(\frac{903}{3520}\right)$	$e\left(\frac{547}{1760}\right)$	$e\left(\frac{1257}{3520}\right)$	$e\left(\frac{457}{880}\right)$	$e\left(\frac{2561}{3520}\right)$	$e\left(\frac{269}{352}\right)$	$e\left(\frac{903}{1760}\right)$	$e\left(\frac{669}{3520}\right)$	$e\left(\frac{199}{440}\right)$	$e\left(\frac{1997}{3520}\right)$
$\chi_{836352}(5021,\cdot)$	$-1$	$1$	$e\left(\frac{877}{3520}\right)$	$e\left(\frac{1153}{1760}\right)$	$e\left(\frac{1443}{3520}\right)$	$e\left(\frac{323}{880}\right)$	$e\left(\frac{1579}{3520}\right)$	$e\left(\frac{271}{352}\right)$	$e\left(\frac{877}{1760}\right)$	$e\left(\frac{2591}{3520}\right)$	$e\left(\frac{261}{440}\right)$	$e\left(\frac{3183}{3520}\right)$
$\chi_{836352}(5669,\cdot)$	$-1$	$1$	$e\left(\frac{3391}{3520}\right)$	$e\left(\frac{1179}{1760}\right)$	$e\left(\frac{1329}{3520}\right)$	$e\left(\frac{689}{880}\right)$	$e\left(\frac{137}{3520}\right)$	$e\left(\frac{213}{352}\right)$	$e\left(\frac{1631}{1760}\right)$	$e\left(\frac{1413}{3520}\right)$	$e\left(\frac{223}{440}\right)$	$e\left(\frac{2229}{3520}\right)$
$\chi_{836352}(6317,\cdot)$	$-1$	$1$	$e\left(\frac{2369}{3520}\right)$	$e\left(\frac{901}{1760}\right)$	$e\left(\frac{1871}{3520}\right)$	$e\left(\frac{431}{880}\right)$	$e\left(\frac{2423}{3520}\right)$	$e\left(\frac{75}{352}\right)$	$e\left(\frac{609}{1760}\right)$	$e\left(\frac{1147}{3520}\right)$	$e\left(\frac{257}{440}\right)$	$e\left(\frac{651}{3520}\right)$
$\chi_{836352}(7181,\cdot)$	$-1$	$1$	$e\left(\frac{2873}{3520}\right)$	$e\left(\frac{797}{1760}\right)$	$e\left(\frac{2327}{3520}\right)$	$e\left(\frac{727}{880}\right)$	$e\left(\frac{1151}{3520}\right)$	$e\left(\frac{307}{352}\right)$	$e\left(\frac{1113}{1760}\right)$	$e\left(\frac{2339}{3520}\right)$	$e\left(\frac{409}{440}\right)$	$e\left(\frac{947}{3520}\right)$
$\chi_{836352}(7397,\cdot)$	$-1$	$1$	$e\left(\frac{2927}{3520}\right)$	$e\left(\frac{1163}{1760}\right)$	$e\left(\frac{2753}{3520}\right)$	$e\left(\frac{193}{880}\right)$	$e\left(\frac{2649}{3520}\right)$	$e\left(\frac{5}{352}\right)$	$e\left(\frac{1167}{1760}\right)$	$e\left(\frac{3221}{3520}\right)$	$e\left(\frac{111}{440}\right)$	$e\left(\frac{1733}{3520}\right)$
$\chi_{836352}(8045,\cdot)$	$-1$	$1$	$e\left(\frac{3121}{3520}\right)$	$e\left(\frac{1109}{1760}\right)$	$e\left(\frac{2719}{3520}\right)$	$e\left(\frac{719}{880}\right)$	$e\left(\frac{3207}{3520}\right)$	$e\left(\frac{315}{352}\right)$	$e\left(\frac{1361}{1760}\right)$	$e\left(\frac{523}{3520}\right)$	$e\left(\frac{393}{440}\right)$	$e\left(\frac{1819}{3520}\right)$
$\chi_{836352}(8693,\cdot)$	$-1$	$1$	$e\left(\frac{2339}{3520}\right)$	$e\left(\frac{111}{1760}\right)$	$e\left(\frac{461}{3520}\right)$	$e\left(\frac{141}{880}\right)$	$e\left(\frac{2373}{3520}\right)$	$e\left(\frac{321}{352}\right)$	$e\left(\frac{579}{1760}\right)$	$e\left(\frac{657}{3520}\right)$	$e\left(\frac{227}{440}\right)$	$e\left(\frac{2561}{3520}\right)$
$\chi_{836352}(9557,\cdot)$	$-1$	$1$	$e\left(\frac{2203}{3520}\right)$	$e\left(\frac{167}{1760}\right)$	$e\left(\frac{2517}{3520}\right)$	$e\left(\frac{117}{880}\right)$	$e\left(\frac{2381}{3520}\right)$	$e\left(\frac{169}{352}\right)$	$e\left(\frac{443}{1760}\right)$	$e\left(\frac{3129}{3520}\right)$	$e\left(\frac{179}{440}\right)$	$e\left(\frac{2537}{3520}\right)$
$\chi_{836352}(9773,\cdot)$	$-1$	$1$	$e\left(\frac{2337}{3520}\right)$	$e\left(\frac{293}{1760}\right)$	$e\left(\frac{3183}{3520}\right)$	$e\left(\frac{63}{880}\right)$	$e\left(\frac{2839}{3520}\right)$	$e\left(\frac{267}{352}\right)$	$e\left(\frac{577}{1760}\right)$	$e\left(\frac{2971}{3520}\right)$	$e\left(\frac{401}{440}\right)$	$e\left(\frac{2923}{3520}\right)$
$\chi_{836352}(10421,\cdot)$	$-1$	$1$	$e\left(\frac{211}{3520}\right)$	$e\left(\frac{159}{1760}\right)$	$e\left(\frac{3229}{3520}\right)$	$e\left(\frac{749}{880}\right)$	$e\left(\frac{1877}{3520}\right)$	$e\left(\frac{241}{352}\right)$	$e\left(\frac{211}{1760}\right)$	$e\left(\frac{2273}{3520}\right)$	$e\left(\frac{123}{440}\right)$	$e\left(\frac{529}{3520}\right)$
$\chi_{836352}(11069,\cdot)$	$-1$	$1$	$e\left(\frac{3189}{3520}\right)$	$e\left(\frac{201}{1760}\right)$	$e\left(\frac{1691}{3520}\right)$	$e\left(\frac{731}{880}\right)$	$e\left(\frac{1443}{3520}\right)$	$e\left(\frac{39}{352}\right)$	$e\left(\frac{1429}{1760}\right)$	$e\left(\frac{2807}{3520}\right)$	$e\left(\frac{197}{440}\right)$	$e\left(\frac{71}{3520}\right)$
$\chi_{836352}(11933,\cdot)$	$-1$	$1$	$e\left(\frac{2413}{3520}\right)$	$e\left(\frac{417}{1760}\right)$	$e\left(\frac{1827}{3520}\right)$	$e\left(\frac{387}{880}\right)$	$e\left(\frac{2731}{3520}\right)$	$e\left(\frac{207}{352}\right)$	$e\left(\frac{653}{1760}\right)$	$e\left(\frac{3039}{3520}\right)$	$e\left(\frac{389}{440}\right)$	$e\left(\frac{3247}{3520}\right)$
$\chi_{836352}(12149,\cdot)$	$-1$	$1$	$e\left(\frac{2627}{3520}\right)$	$e\left(\frac{303}{1760}\right)$	$e\left(\frac{2733}{3520}\right)$	$e\left(\frac{813}{880}\right)$	$e\left(\frac{2149}{3520}\right)$	$e\left(\frac{1}{352}\right)$	$e\left(\frac{867}{1760}\right)$	$e\left(\frac{1841}{3520}\right)$	$e\left(\frac{251}{440}\right)$	$e\left(\frac{3233}{3520}\right)$
$\chi_{836352}(12797,\cdot)$	$-1$	$1$	$e\left(\frac{1701}{3520}\right)$	$e\left(\frac{89}{1760}\right)$	$e\left(\frac{2859}{3520}\right)$	$e\left(\frac{779}{880}\right)$	$e\left(\frac{3187}{3520}\right)$	$e\left(\frac{343}{352}\right)$	$e\left(\frac{1701}{1760}\right)$	$e\left(\frac{3143}{3520}\right)$	$e\left(\frac{293}{440}\right)$	$e\left(\frac{1879}{3520}\right)$
$\chi_{836352}(13445,\cdot)$	$-1$	$1$	$e\left(\frac{1399}{3520}\right)$	$e\left(\frac{1171}{1760}\right)$	$e\left(\frac{2041}{3520}\right)$	$e\left(\frac{441}{880}\right)$	$e\left(\frac{3153}{3520}\right)$	$e\left(\frac{285}{352}\right)$	$e\left(\frac{1399}{1760}\right)$	$e\left(\frac{557}{3520}\right)$	$e\left(\frac{167}{440}\right)$	$e\left(\frac{221}{3520}\right)$
$\chi_{836352}(14309,\cdot)$	$-1$	$1$	$e\left(\frac{3503}{3520}\right)$	$e\left(\frac{1547}{1760}\right)$	$e\left(\frac{257}{3520}\right)$	$e\left(\frac{657}{880}\right)$	$e\left(\frac{2201}{3520}\right)$	$e\left(\frac{69}{352}\right)$	$e\left(\frac{1743}{1760}\right)$	$e\left(\frac{2069}{3520}\right)$	$e\left(\frac{159}{440}\right)$	$e\left(\frac{3077}{3520}\right)$
$\chi_{836352}(14525,\cdot)$	$-1$	$1$	$e\left(\frac{277}{3520}\right)$	$e\left(\frac{1193}{1760}\right)$	$e\left(\frac{1403}{3520}\right)$	$e\left(\frac{683}{880}\right)$	$e\left(\frac{579}{3520}\right)$	$e\left(\frac{263}{352}\right)$	$e\left(\frac{277}{1760}\right)$	$e\left(\frac{3351}{3520}\right)$	$e\left(\frac{101}{440}\right)$	$e\left(\frac{2663}{3520}\right)$
$\chi_{836352}(15173,\cdot)$	$-1$	$1$	$e\left(\frac{551}{3520}\right)$	$e\left(\frac{899}{1760}\right)$	$e\left(\frac{1609}{3520}\right)$	$e\left(\frac{809}{880}\right)$	$e\left(\frac{97}{3520}\right)$	$e\left(\frac{269}{352}\right)$	$e\left(\frac{551}{1760}\right)$	$e\left(\frac{3133}{3520}\right)$	$e\left(\frac{23}{440}\right)$	$e\left(\frac{2349}{3520}\right)$
$\chi_{836352}(15821,\cdot)$	$-1$	$1$	$e\left(\frac{489}{3520}\right)$	$e\left(\frac{1261}{1760}\right)$	$e\left(\frac{1511}{3520}\right)$	$e\left(\frac{151}{880}\right)$	$e\left(\frac{463}{3520}\right)$	$e\left(\frac{3}{352}\right)$	$e\left(\frac{489}{1760}\right)$	$e\left(\frac{947}{3520}\right)$	$e\left(\frac{137}{440}\right)$	$e\left(\frac{3011}{3520}\right)$
$\chi_{836352}(16685,\cdot)$	$-1$	$1$	$e\left(\frac{1953}{3520}\right)$	$e\left(\frac{37}{1760}\right)$	$e\left(\frac{1327}{3520}\right)$	$e\left(\frac{47}{880}\right)$	$e\left(\frac{791}{3520}\right)$	$e\left(\frac{107}{352}\right)$	$e\left(\frac{193}{1760}\right)$	$e\left(\frac{219}{3520}\right)$	$e\left(\frac{369}{440}\right)$	$e\left(\frac{2027}{3520}\right)$
$\chi_{836352}(16901,\cdot)$	$-1$	$1$	$e\left(\frac{2327}{3520}\right)$	$e\left(\frac{1203}{1760}\right)$	$e\left(\frac{2713}{3520}\right)$	$e\left(\frac{553}{880}\right)$	$e\left(\frac{1649}{3520}\right)$	$e\left(\frac{349}{352}\right)$	$e\left(\frac{567}{1760}\right)$	$e\left(\frac{461}{3520}\right)$	$e\left(\frac{391}{440}\right)$	$e\left(\frac{1213}{3520}\right)$
$\chi_{836352}(17549,\cdot)$	$-1$	$1$	$e\left(\frac{281}{3520}\right)$	$e\left(\frac{829}{1760}\right)$	$e\left(\frac{2999}{3520}\right)$	$e\left(\frac{839}{880}\right)$	$e\left(\frac{3167}{3520}\right)$	$e\left(\frac{19}{352}\right)$	$e\left(\frac{281}{1760}\right)$	$e\left(\frac{2243}{3520}\right)$	$e\left(\frac{193}{440}\right)$	$e\left(\frac{1939}{3520}\right)$
$\chi_{836352}(18197,\cdot)$	$-1$	$1$	$e\left(\frac{459}{3520}\right)$	$e\left(\frac{471}{1760}\right)$	$e\left(\frac{101}{3520}\right)$	$e\left(\frac{741}{880}\right)$	$e\left(\frac{413}{3520}\right)$	$e\left(\frac{249}{352}\right)$	$e\left(\frac{459}{1760}\right)$	$e\left(\frac{457}{3520}\right)$	$e\left(\frac{107}{440}\right)$	$e\left(\frac{1401}{3520}\right)$
$\chi_{836352}(19061,\cdot)$	$-1$	$1$	$e\left(\frac{1283}{3520}\right)$	$e\left(\frac{1167}{1760}\right)$	$e\left(\frac{1517}{3520}\right)$	$e\left(\frac{317}{880}\right)$	$e\left(\frac{2021}{3520}\right)$	$e\left(\frac{321}{352}\right)$	$e\left(\frac{1283}{1760}\right)$	$e\left(\frac{1009}{3520}\right)$	$e\left(\frac{139}{440}\right)$	$e\left(\frac{97}{3520}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{836352}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3123}{3520}\right)\)	\(e\left(\frac{927}{1760}\right)\)	\(e\left(\frac{3517}{3520}\right)\)	\(e\left(\frac{797}{880}\right)\)	\(e\left(\frac{2741}{3520}\right)\)	\(e\left(\frac{17}{352}\right)\)	\(e\left(\frac{1363}{1760}\right)\)	\(e\left(\frac{1729}{3520}\right)\)	\(e\left(\frac{219}{440}\right)\)	\(e\left(\frac{1457}{3520}\right)\)
\(\chi_{836352}(917,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3051}{3520}\right)\)	\(e\left(\frac{439}{1760}\right)\)	\(e\left(\frac{2949}{3520}\right)\)	\(e\left(\frac{629}{880}\right)\)	\(e\left(\frac{1917}{3520}\right)\)	\(e\left(\frac{185}{352}\right)\)	\(e\left(\frac{1291}{1760}\right)\)	\(e\left(\frac{553}{3520}\right)\)	\(e\left(\frac{323}{440}\right)\)	\(e\left(\frac{409}{3520}\right)\)
\(\chi_{836352}(1565,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1549}{3520}\right)\)	\(e\left(\frac{1601}{1760}\right)\)	\(e\left(\frac{2051}{3520}\right)\)	\(e\left(\frac{131}{880}\right)\)	\(e\left(\frac{3403}{3520}\right)\)	\(e\left(\frac{111}{352}\right)\)	\(e\left(\frac{1549}{1760}\right)\)	\(e\left(\frac{3007}{3520}\right)\)	\(e\left(\frac{317}{440}\right)\)	\(e\left(\frac{1231}{3520}\right)\)
\(\chi_{836352}(2645,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3227}{3520}\right)\)	\(e\left(\frac{263}{1760}\right)\)	\(e\left(\frac{2773}{3520}\right)\)	\(e\left(\frac{453}{880}\right)\)	\(e\left(\frac{3149}{3520}\right)\)	\(e\left(\frac{9}{352}\right)\)	\(e\left(\frac{1467}{1760}\right)\)	\(e\left(\frac{1081}{3520}\right)\)	\(e\left(\frac{411}{440}\right)\)	\(e\left(\frac{233}{3520}\right)\)
\(\chi_{836352}(3293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1021}{3520}\right)\)	\(e\left(\frac{369}{1760}\right)\)	\(e\left(\frac{2579}{3520}\right)\)	\(e\left(\frac{659}{880}\right)\)	\(e\left(\frac{3227}{3520}\right)\)	\(e\left(\frac{287}{352}\right)\)	\(e\left(\frac{1021}{1760}\right)\)	\(e\left(\frac{1423}{3520}\right)\)	\(e\left(\frac{53}{440}\right)\)	\(e\left(\frac{1759}{3520}\right)\)
\(\chi_{836352}(3941,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3279}{3520}\right)\)	\(e\left(\frac{811}{1760}\right)\)	\(e\left(\frac{2401}{3520}\right)\)	\(e\left(\frac{721}{880}\right)\)	\(e\left(\frac{1593}{3520}\right)\)	\(e\left(\frac{5}{352}\right)\)	\(e\left(\frac{1519}{1760}\right)\)	\(e\left(\frac{757}{3520}\right)\)	\(e\left(\frac{287}{440}\right)\)	\(e\left(\frac{1381}{3520}\right)\)
\(\chi_{836352}(4805,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{903}{3520}\right)\)	\(e\left(\frac{547}{1760}\right)\)	\(e\left(\frac{1257}{3520}\right)\)	\(e\left(\frac{457}{880}\right)\)	\(e\left(\frac{2561}{3520}\right)\)	\(e\left(\frac{269}{352}\right)\)	\(e\left(\frac{903}{1760}\right)\)	\(e\left(\frac{669}{3520}\right)\)	\(e\left(\frac{199}{440}\right)\)	\(e\left(\frac{1997}{3520}\right)\)
\(\chi_{836352}(5021,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{877}{3520}\right)\)	\(e\left(\frac{1153}{1760}\right)\)	\(e\left(\frac{1443}{3520}\right)\)	\(e\left(\frac{323}{880}\right)\)	\(e\left(\frac{1579}{3520}\right)\)	\(e\left(\frac{271}{352}\right)\)	\(e\left(\frac{877}{1760}\right)\)	\(e\left(\frac{2591}{3520}\right)\)	\(e\left(\frac{261}{440}\right)\)	\(e\left(\frac{3183}{3520}\right)\)
\(\chi_{836352}(5669,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3391}{3520}\right)\)	\(e\left(\frac{1179}{1760}\right)\)	\(e\left(\frac{1329}{3520}\right)\)	\(e\left(\frac{689}{880}\right)\)	\(e\left(\frac{137}{3520}\right)\)	\(e\left(\frac{213}{352}\right)\)	\(e\left(\frac{1631}{1760}\right)\)	\(e\left(\frac{1413}{3520}\right)\)	\(e\left(\frac{223}{440}\right)\)	\(e\left(\frac{2229}{3520}\right)\)
\(\chi_{836352}(6317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2369}{3520}\right)\)	\(e\left(\frac{901}{1760}\right)\)	\(e\left(\frac{1871}{3520}\right)\)	\(e\left(\frac{431}{880}\right)\)	\(e\left(\frac{2423}{3520}\right)\)	\(e\left(\frac{75}{352}\right)\)	\(e\left(\frac{609}{1760}\right)\)	\(e\left(\frac{1147}{3520}\right)\)	\(e\left(\frac{257}{440}\right)\)	\(e\left(\frac{651}{3520}\right)\)
\(\chi_{836352}(7181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2873}{3520}\right)\)	\(e\left(\frac{797}{1760}\right)\)	\(e\left(\frac{2327}{3520}\right)\)	\(e\left(\frac{727}{880}\right)\)	\(e\left(\frac{1151}{3520}\right)\)	\(e\left(\frac{307}{352}\right)\)	\(e\left(\frac{1113}{1760}\right)\)	\(e\left(\frac{2339}{3520}\right)\)	\(e\left(\frac{409}{440}\right)\)	\(e\left(\frac{947}{3520}\right)\)
\(\chi_{836352}(7397,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2927}{3520}\right)\)	\(e\left(\frac{1163}{1760}\right)\)	\(e\left(\frac{2753}{3520}\right)\)	\(e\left(\frac{193}{880}\right)\)	\(e\left(\frac{2649}{3520}\right)\)	\(e\left(\frac{5}{352}\right)\)	\(e\left(\frac{1167}{1760}\right)\)	\(e\left(\frac{3221}{3520}\right)\)	\(e\left(\frac{111}{440}\right)\)	\(e\left(\frac{1733}{3520}\right)\)
\(\chi_{836352}(8045,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3121}{3520}\right)\)	\(e\left(\frac{1109}{1760}\right)\)	\(e\left(\frac{2719}{3520}\right)\)	\(e\left(\frac{719}{880}\right)\)	\(e\left(\frac{3207}{3520}\right)\)	\(e\left(\frac{315}{352}\right)\)	\(e\left(\frac{1361}{1760}\right)\)	\(e\left(\frac{523}{3520}\right)\)	\(e\left(\frac{393}{440}\right)\)	\(e\left(\frac{1819}{3520}\right)\)
\(\chi_{836352}(8693,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2339}{3520}\right)\)	\(e\left(\frac{111}{1760}\right)\)	\(e\left(\frac{461}{3520}\right)\)	\(e\left(\frac{141}{880}\right)\)	\(e\left(\frac{2373}{3520}\right)\)	\(e\left(\frac{321}{352}\right)\)	\(e\left(\frac{579}{1760}\right)\)	\(e\left(\frac{657}{3520}\right)\)	\(e\left(\frac{227}{440}\right)\)	\(e\left(\frac{2561}{3520}\right)\)
\(\chi_{836352}(9557,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2203}{3520}\right)\)	\(e\left(\frac{167}{1760}\right)\)	\(e\left(\frac{2517}{3520}\right)\)	\(e\left(\frac{117}{880}\right)\)	\(e\left(\frac{2381}{3520}\right)\)	\(e\left(\frac{169}{352}\right)\)	\(e\left(\frac{443}{1760}\right)\)	\(e\left(\frac{3129}{3520}\right)\)	\(e\left(\frac{179}{440}\right)\)	\(e\left(\frac{2537}{3520}\right)\)
\(\chi_{836352}(9773,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2337}{3520}\right)\)	\(e\left(\frac{293}{1760}\right)\)	\(e\left(\frac{3183}{3520}\right)\)	\(e\left(\frac{63}{880}\right)\)	\(e\left(\frac{2839}{3520}\right)\)	\(e\left(\frac{267}{352}\right)\)	\(e\left(\frac{577}{1760}\right)\)	\(e\left(\frac{2971}{3520}\right)\)	\(e\left(\frac{401}{440}\right)\)	\(e\left(\frac{2923}{3520}\right)\)
\(\chi_{836352}(10421,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{211}{3520}\right)\)	\(e\left(\frac{159}{1760}\right)\)	\(e\left(\frac{3229}{3520}\right)\)	\(e\left(\frac{749}{880}\right)\)	\(e\left(\frac{1877}{3520}\right)\)	\(e\left(\frac{241}{352}\right)\)	\(e\left(\frac{211}{1760}\right)\)	\(e\left(\frac{2273}{3520}\right)\)	\(e\left(\frac{123}{440}\right)\)	\(e\left(\frac{529}{3520}\right)\)
\(\chi_{836352}(11069,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3189}{3520}\right)\)	\(e\left(\frac{201}{1760}\right)\)	\(e\left(\frac{1691}{3520}\right)\)	\(e\left(\frac{731}{880}\right)\)	\(e\left(\frac{1443}{3520}\right)\)	\(e\left(\frac{39}{352}\right)\)	\(e\left(\frac{1429}{1760}\right)\)	\(e\left(\frac{2807}{3520}\right)\)	\(e\left(\frac{197}{440}\right)\)	\(e\left(\frac{71}{3520}\right)\)
\(\chi_{836352}(11933,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2413}{3520}\right)\)	\(e\left(\frac{417}{1760}\right)\)	\(e\left(\frac{1827}{3520}\right)\)	\(e\left(\frac{387}{880}\right)\)	\(e\left(\frac{2731}{3520}\right)\)	\(e\left(\frac{207}{352}\right)\)	\(e\left(\frac{653}{1760}\right)\)	\(e\left(\frac{3039}{3520}\right)\)	\(e\left(\frac{389}{440}\right)\)	\(e\left(\frac{3247}{3520}\right)\)
\(\chi_{836352}(12149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2627}{3520}\right)\)	\(e\left(\frac{303}{1760}\right)\)	\(e\left(\frac{2733}{3520}\right)\)	\(e\left(\frac{813}{880}\right)\)	\(e\left(\frac{2149}{3520}\right)\)	\(e\left(\frac{1}{352}\right)\)	\(e\left(\frac{867}{1760}\right)\)	\(e\left(\frac{1841}{3520}\right)\)	\(e\left(\frac{251}{440}\right)\)	\(e\left(\frac{3233}{3520}\right)\)
\(\chi_{836352}(12797,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1701}{3520}\right)\)	\(e\left(\frac{89}{1760}\right)\)	\(e\left(\frac{2859}{3520}\right)\)	\(e\left(\frac{779}{880}\right)\)	\(e\left(\frac{3187}{3520}\right)\)	\(e\left(\frac{343}{352}\right)\)	\(e\left(\frac{1701}{1760}\right)\)	\(e\left(\frac{3143}{3520}\right)\)	\(e\left(\frac{293}{440}\right)\)	\(e\left(\frac{1879}{3520}\right)\)
\(\chi_{836352}(13445,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1399}{3520}\right)\)	\(e\left(\frac{1171}{1760}\right)\)	\(e\left(\frac{2041}{3520}\right)\)	\(e\left(\frac{441}{880}\right)\)	\(e\left(\frac{3153}{3520}\right)\)	\(e\left(\frac{285}{352}\right)\)	\(e\left(\frac{1399}{1760}\right)\)	\(e\left(\frac{557}{3520}\right)\)	\(e\left(\frac{167}{440}\right)\)	\(e\left(\frac{221}{3520}\right)\)
\(\chi_{836352}(14309,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3503}{3520}\right)\)	\(e\left(\frac{1547}{1760}\right)\)	\(e\left(\frac{257}{3520}\right)\)	\(e\left(\frac{657}{880}\right)\)	\(e\left(\frac{2201}{3520}\right)\)	\(e\left(\frac{69}{352}\right)\)	\(e\left(\frac{1743}{1760}\right)\)	\(e\left(\frac{2069}{3520}\right)\)	\(e\left(\frac{159}{440}\right)\)	\(e\left(\frac{3077}{3520}\right)\)
\(\chi_{836352}(14525,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{277}{3520}\right)\)	\(e\left(\frac{1193}{1760}\right)\)	\(e\left(\frac{1403}{3520}\right)\)	\(e\left(\frac{683}{880}\right)\)	\(e\left(\frac{579}{3520}\right)\)	\(e\left(\frac{263}{352}\right)\)	\(e\left(\frac{277}{1760}\right)\)	\(e\left(\frac{3351}{3520}\right)\)	\(e\left(\frac{101}{440}\right)\)	\(e\left(\frac{2663}{3520}\right)\)
\(\chi_{836352}(15173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{551}{3520}\right)\)	\(e\left(\frac{899}{1760}\right)\)	\(e\left(\frac{1609}{3520}\right)\)	\(e\left(\frac{809}{880}\right)\)	\(e\left(\frac{97}{3520}\right)\)	\(e\left(\frac{269}{352}\right)\)	\(e\left(\frac{551}{1760}\right)\)	\(e\left(\frac{3133}{3520}\right)\)	\(e\left(\frac{23}{440}\right)\)	\(e\left(\frac{2349}{3520}\right)\)
\(\chi_{836352}(15821,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{489}{3520}\right)\)	\(e\left(\frac{1261}{1760}\right)\)	\(e\left(\frac{1511}{3520}\right)\)	\(e\left(\frac{151}{880}\right)\)	\(e\left(\frac{463}{3520}\right)\)	\(e\left(\frac{3}{352}\right)\)	\(e\left(\frac{489}{1760}\right)\)	\(e\left(\frac{947}{3520}\right)\)	\(e\left(\frac{137}{440}\right)\)	\(e\left(\frac{3011}{3520}\right)\)
\(\chi_{836352}(16685,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1953}{3520}\right)\)	\(e\left(\frac{37}{1760}\right)\)	\(e\left(\frac{1327}{3520}\right)\)	\(e\left(\frac{47}{880}\right)\)	\(e\left(\frac{791}{3520}\right)\)	\(e\left(\frac{107}{352}\right)\)	\(e\left(\frac{193}{1760}\right)\)	\(e\left(\frac{219}{3520}\right)\)	\(e\left(\frac{369}{440}\right)\)	\(e\left(\frac{2027}{3520}\right)\)
\(\chi_{836352}(16901,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2327}{3520}\right)\)	\(e\left(\frac{1203}{1760}\right)\)	\(e\left(\frac{2713}{3520}\right)\)	\(e\left(\frac{553}{880}\right)\)	\(e\left(\frac{1649}{3520}\right)\)	\(e\left(\frac{349}{352}\right)\)	\(e\left(\frac{567}{1760}\right)\)	\(e\left(\frac{461}{3520}\right)\)	\(e\left(\frac{391}{440}\right)\)	\(e\left(\frac{1213}{3520}\right)\)
\(\chi_{836352}(17549,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{281}{3520}\right)\)	\(e\left(\frac{829}{1760}\right)\)	\(e\left(\frac{2999}{3520}\right)\)	\(e\left(\frac{839}{880}\right)\)	\(e\left(\frac{3167}{3520}\right)\)	\(e\left(\frac{19}{352}\right)\)	\(e\left(\frac{281}{1760}\right)\)	\(e\left(\frac{2243}{3520}\right)\)	\(e\left(\frac{193}{440}\right)\)	\(e\left(\frac{1939}{3520}\right)\)
\(\chi_{836352}(18197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{459}{3520}\right)\)	\(e\left(\frac{471}{1760}\right)\)	\(e\left(\frac{101}{3520}\right)\)	\(e\left(\frac{741}{880}\right)\)	\(e\left(\frac{413}{3520}\right)\)	\(e\left(\frac{249}{352}\right)\)	\(e\left(\frac{459}{1760}\right)\)	\(e\left(\frac{457}{3520}\right)\)	\(e\left(\frac{107}{440}\right)\)	\(e\left(\frac{1401}{3520}\right)\)
\(\chi_{836352}(19061,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1283}{3520}\right)\)	\(e\left(\frac{1167}{1760}\right)\)	\(e\left(\frac{1517}{3520}\right)\)	\(e\left(\frac{317}{880}\right)\)	\(e\left(\frac{2021}{3520}\right)\)	\(e\left(\frac{321}{352}\right)\)	\(e\left(\frac{1283}{1760}\right)\)	\(e\left(\frac{1009}{3520}\right)\)	\(e\left(\frac{139}{440}\right)\)	\(e\left(\frac{97}{3520}\right)\)

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First 31 of 1280 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	836352.xl
Modulus	$836352$
Conductor	$92928$
Order	$3520$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(836352\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(92928\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(3520\)	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 92928.ij	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);