LMFDB - Dirichlet character orbit 164025.dl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(164025, base_ring=CyclotomicField(14580)) M = H._module chi = DirichletCharacter(H, M([7340,6561])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(37,164025)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$164025$
Conductor:	$54675$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$14580$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 54675.de	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{14580})$
Fixed field:	Number field defined by a degree 14580 polynomial (not computed)

First 31 of 3888 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{164025}(37,\cdot)$	$-1$	$1$	$e\left(\frac{13901}{14580}\right)$	$e\left(\frac{6611}{7290}\right)$	$e\left(\frac{1753}{2916}\right)$	$e\left(\frac{4181}{4860}\right)$	$e\left(\frac{1229}{3645}\right)$	$e\left(\frac{319}{14580}\right)$	$e\left(\frac{4043}{7290}\right)$	$e\left(\frac{2966}{3645}\right)$	$e\left(\frac{2251}{4860}\right)$	$e\left(\frac{463}{2430}\right)$
$\chi_{164025}(73,\cdot)$	$-1$	$1$	$e\left(\frac{6319}{14580}\right)$	$e\left(\frac{6319}{7290}\right)$	$e\left(\frac{2363}{2916}\right)$	$e\left(\frac{1459}{4860}\right)$	$e\left(\frac{496}{3645}\right)$	$e\left(\frac{5921}{14580}\right)$	$e\left(\frac{1777}{7290}\right)$	$e\left(\frac{2674}{3645}\right)$	$e\left(\frac{1469}{4860}\right)$	$e\left(\frac{1997}{2430}\right)$
$\chi_{164025}(127,\cdot)$	$-1$	$1$	$e\left(\frac{14089}{14580}\right)$	$e\left(\frac{6799}{7290}\right)$	$e\left(\frac{821}{2916}\right)$	$e\left(\frac{4369}{4860}\right)$	$e\left(\frac{1651}{3645}\right)$	$e\left(\frac{12191}{14580}\right)$	$e\left(\frac{1807}{7290}\right)$	$e\left(\frac{3154}{3645}\right)$	$e\left(\frac{4319}{4860}\right)$	$e\left(\frac{707}{2430}\right)$
$\chi_{164025}(172,\cdot)$	$-1$	$1$	$e\left(\frac{5813}{14580}\right)$	$e\left(\frac{5813}{7290}\right)$	$e\left(\frac{1273}{2916}\right)$	$e\left(\frac{953}{4860}\right)$	$e\left(\frac{1997}{3645}\right)$	$e\left(\frac{9487}{14580}\right)$	$e\left(\frac{6089}{7290}\right)$	$e\left(\frac{2168}{3645}\right)$	$e\left(\frac{763}{4860}\right)$	$e\left(\frac{1909}{2430}\right)$
$\chi_{164025}(208,\cdot)$	$-1$	$1$	$e\left(\frac{11407}{14580}\right)$	$e\left(\frac{4117}{7290}\right)$	$e\left(\frac{2639}{2916}\right)$	$e\left(\frac{1687}{4860}\right)$	$e\left(\frac{2533}{3645}\right)$	$e\left(\frac{6773}{14580}\right)$	$e\left(\frac{5011}{7290}\right)$	$e\left(\frac{472}{3645}\right)$	$e\left(\frac{3977}{4860}\right)$	$e\left(\frac{1931}{2430}\right)$
$\chi_{164025}(253,\cdot)$	$-1$	$1$	$e\left(\frac{5723}{14580}\right)$	$e\left(\frac{5723}{7290}\right)$	$e\left(\frac{1471}{2916}\right)$	$e\left(\frac{863}{4860}\right)$	$e\left(\frac{1097}{3645}\right)$	$e\left(\frac{1477}{14580}\right)$	$e\left(\frac{6539}{7290}\right)$	$e\left(\frac{2078}{3645}\right)$	$e\left(\frac{4633}{4860}\right)$	$e\left(\frac{1999}{2430}\right)$
$\chi_{164025}(262,\cdot)$	$-1$	$1$	$e\left(\frac{9781}{14580}\right)$	$e\left(\frac{2491}{7290}\right)$	$e\left(\frac{773}{2916}\right)$	$e\left(\frac{61}{4860}\right)$	$e\left(\frac{124}{3645}\right)$	$e\left(\frac{7859}{14580}\right)$	$e\left(\frac{6823}{7290}\right)$	$e\left(\frac{2491}{3645}\right)$	$e\left(\frac{671}{4860}\right)$	$e\left(\frac{803}{2430}\right)$
$\chi_{164025}(388,\cdot)$	$-1$	$1$	$e\left(\frac{3791}{14580}\right)$	$e\left(\frac{3791}{7290}\right)$	$e\left(\frac{2611}{2916}\right)$	$e\left(\frac{3791}{4860}\right)$	$e\left(\frac{2189}{3645}\right)$	$e\left(\frac{4489}{14580}\right)$	$e\left(\frac{1133}{7290}\right)$	$e\left(\frac{146}{3645}\right)$	$e\left(\frac{2821}{4860}\right)$	$e\left(\frac{1663}{2430}\right)$
$\chi_{164025}(397,\cdot)$	$-1$	$1$	$e\left(\frac{3853}{14580}\right)$	$e\left(\frac{3853}{7290}\right)$	$e\left(\frac{1373}{2916}\right)$	$e\left(\frac{3853}{4860}\right)$	$e\left(\frac{622}{3645}\right)$	$e\left(\frac{5147}{14580}\right)$	$e\left(\frac{5359}{7290}\right)$	$e\left(\frac{208}{3645}\right)$	$e\left(\frac{3503}{4860}\right)$	$e\left(\frac{89}{2430}\right)$
$\chi_{164025}(442,\cdot)$	$-1$	$1$	$e\left(\frac{13937}{14580}\right)$	$e\left(\frac{6647}{7290}\right)$	$e\left(\frac{2257}{2916}\right)$	$e\left(\frac{4217}{4860}\right)$	$e\left(\frac{2318}{3645}\right)$	$e\left(\frac{3523}{14580}\right)$	$e\left(\frac{5321}{7290}\right)$	$e\left(\frac{3002}{3645}\right)$	$e\left(\frac{2647}{4860}\right)$	$e\left(\frac{2371}{2430}\right)$
$\chi_{164025}(478,\cdot)$	$-1$	$1$	$e\left(\frac{2143}{14580}\right)$	$e\left(\frac{2143}{7290}\right)$	$e\left(\frac{2219}{2916}\right)$	$e\left(\frac{2143}{4860}\right)$	$e\left(\frac{1747}{3645}\right)$	$e\left(\frac{13337}{14580}\right)$	$e\left(\frac{6619}{7290}\right)$	$e\left(\frac{2143}{3645}\right)$	$e\left(\frac{4133}{4860}\right)$	$e\left(\frac{1799}{2430}\right)$
$\chi_{164025}(523,\cdot)$	$-1$	$1$	$e\left(\frac{239}{14580}\right)$	$e\left(\frac{239}{7290}\right)$	$e\left(\frac{1483}{2916}\right)$	$e\left(\frac{239}{4860}\right)$	$e\left(\frac{1661}{3645}\right)$	$e\left(\frac{9121}{14580}\right)$	$e\left(\frac{3827}{7290}\right)$	$e\left(\frac{239}{3645}\right)$	$e\left(\frac{2629}{4860}\right)$	$e\left(\frac{517}{2430}\right)$
$\chi_{164025}(577,\cdot)$	$-1$	$1$	$e\left(\frac{989}{14580}\right)$	$e\left(\frac{989}{7290}\right)$	$e\left(\frac{805}{2916}\right)$	$e\left(\frac{989}{4860}\right)$	$e\left(\frac{1871}{3645}\right)$	$e\left(\frac{2971}{14580}\right)$	$e\left(\frac{2507}{7290}\right)$	$e\left(\frac{989}{3645}\right)$	$e\left(\frac{1159}{4860}\right)$	$e\left(\frac{1387}{2430}\right)$
$\chi_{164025}(613,\cdot)$	$-1$	$1$	$e\left(\frac{2371}{14580}\right)$	$e\left(\frac{2371}{7290}\right)$	$e\left(\frac{1523}{2916}\right)$	$e\left(\frac{2371}{4860}\right)$	$e\left(\frac{2569}{3645}\right)$	$e\left(\frac{4469}{14580}\right)$	$e\left(\frac{4993}{7290}\right)$	$e\left(\frac{2371}{3645}\right)$	$e\left(\frac{1781}{4860}\right)$	$e\left(\frac{1733}{2430}\right)$
$\chi_{164025}(658,\cdot)$	$-1$	$1$	$e\left(\frac{9647}{14580}\right)$	$e\left(\frac{2357}{7290}\right)$	$e\left(\frac{1003}{2916}\right)$	$e\left(\frac{4787}{4860}\right)$	$e\left(\frac{3158}{3645}\right)$	$e\left(\frac{793}{14580}\right)$	$e\left(\frac{41}{7290}\right)$	$e\left(\frac{2357}{3645}\right)$	$e\left(\frac{4057}{4860}\right)$	$e\left(\frac{991}{2430}\right)$
$\chi_{164025}(667,\cdot)$	$-1$	$1$	$e\left(\frac{1717}{14580}\right)$	$e\left(\frac{1717}{7290}\right)$	$e\left(\frac{1601}{2916}\right)$	$e\left(\frac{1717}{4860}\right)$	$e\left(\frac{403}{3645}\right)$	$e\left(\frac{4583}{14580}\right)$	$e\left(\frac{4861}{7290}\right)$	$e\left(\frac{1717}{3645}\right)$	$e\left(\frac{4307}{4860}\right)$	$e\left(\frac{1091}{2430}\right)$
$\chi_{164025}(712,\cdot)$	$-1$	$1$	$e\left(\frac{1001}{14580}\right)$	$e\left(\frac{1001}{7290}\right)$	$e\left(\frac{1}{2916}\right)$	$e\left(\frac{1001}{4860}\right)$	$e\left(\frac{3449}{3645}\right)$	$e\left(\frac{4039}{14580}\right)$	$e\left(\frac{503}{7290}\right)$	$e\left(\frac{1001}{3645}\right)$	$e\left(\frac{1291}{4860}\right)$	$e\left(\frac{2023}{2430}\right)$
$\chi_{164025}(748,\cdot)$	$-1$	$1$	$e\left(\frac{979}{14580}\right)$	$e\left(\frac{979}{7290}\right)$	$e\left(\frac{1475}{2916}\right)$	$e\left(\frac{979}{4860}\right)$	$e\left(\frac{1771}{3645}\right)$	$e\left(\frac{11801}{14580}\right)$	$e\left(\frac{4177}{7290}\right)$	$e\left(\frac{979}{3645}\right)$	$e\left(\frac{1049}{4860}\right)$	$e\left(\frac{857}{2430}\right)$
$\chi_{164025}(802,\cdot)$	$-1$	$1$	$e\left(\frac{5509}{14580}\right)$	$e\left(\frac{5509}{7290}\right)$	$e\left(\frac{1229}{2916}\right)$	$e\left(\frac{649}{4860}\right)$	$e\left(\frac{3331}{3645}\right)$	$e\left(\frac{6731}{14580}\right)$	$e\left(\frac{5827}{7290}\right)$	$e\left(\frac{1864}{3645}\right)$	$e\left(\frac{2279}{4860}\right)$	$e\left(\frac{377}{2430}\right)$
$\chi_{164025}(847,\cdot)$	$-1$	$1$	$e\left(\frac{13973}{14580}\right)$	$e\left(\frac{6683}{7290}\right)$	$e\left(\frac{2761}{2916}\right)$	$e\left(\frac{4253}{4860}\right)$	$e\left(\frac{3407}{3645}\right)$	$e\left(\frac{6727}{14580}\right)$	$e\left(\frac{6599}{7290}\right)$	$e\left(\frac{3038}{3645}\right)$	$e\left(\frac{3043}{4860}\right)$	$e\left(\frac{1849}{2430}\right)$
$\chi_{164025}(883,\cdot)$	$-1$	$1$	$e\left(\frac{12547}{14580}\right)$	$e\left(\frac{5257}{7290}\right)$	$e\left(\frac{2075}{2916}\right)$	$e\left(\frac{2827}{4860}\right)$	$e\left(\frac{2998}{3645}\right)$	$e\left(\frac{6173}{14580}\right)$	$e\left(\frac{4171}{7290}\right)$	$e\left(\frac{1612}{3645}\right)$	$e\left(\frac{1937}{4860}\right)$	$e\left(\frac{1601}{2430}\right)$
$\chi_{164025}(928,\cdot)$	$-1$	$1$	$e\left(\frac{9023}{14580}\right)$	$e\left(\frac{1733}{7290}\right)$	$e\left(\frac{1987}{2916}\right)$	$e\left(\frac{4163}{4860}\right)$	$e\left(\frac{1292}{3645}\right)$	$e\left(\frac{3577}{14580}\right)$	$e\left(\frac{2189}{7290}\right)$	$e\left(\frac{1733}{3645}\right)$	$e\left(\frac{2053}{4860}\right)$	$e\left(\frac{1939}{2430}\right)$
$\chi_{164025}(937,\cdot)$	$-1$	$1$	$e\left(\frac{7681}{14580}\right)$	$e\left(\frac{391}{7290}\right)$	$e\left(\frac{1505}{2916}\right)$	$e\left(\frac{2821}{4860}\right)$	$e\left(\frac{994}{3645}\right)$	$e\left(\frac{10499}{14580}\right)$	$e\left(\frac{313}{7290}\right)$	$e\left(\frac{391}{3645}\right)$	$e\left(\frac{1871}{4860}\right)$	$e\left(\frac{1283}{2430}\right)$
$\chi_{164025}(1063,\cdot)$	$-1$	$1$	$e\left(\frac{13571}{14580}\right)$	$e\left(\frac{6281}{7290}\right)$	$e\left(\frac{535}{2916}\right)$	$e\left(\frac{3851}{4860}\right)$	$e\left(\frac{1574}{3645}\right)$	$e\left(\frac{109}{14580}\right)$	$e\left(\frac{833}{7290}\right)$	$e\left(\frac{2636}{3645}\right)$	$e\left(\frac{3481}{4860}\right)$	$e\left(\frac{2413}{2430}\right)$
$\chi_{164025}(1072,\cdot)$	$-1$	$1$	$e\left(\frac{8233}{14580}\right)$	$e\left(\frac{943}{7290}\right)$	$e\left(\frac{2429}{2916}\right)$	$e\left(\frac{3373}{4860}\right)$	$e\left(\frac{682}{3645}\right)$	$e\left(\frac{1307}{14580}\right)$	$e\left(\frac{2899}{7290}\right)$	$e\left(\frac{943}{3645}\right)$	$e\left(\frac{3083}{4860}\right)$	$e\left(\frac{1379}{2430}\right)$
$\chi_{164025}(1117,\cdot)$	$-1$	$1$	$e\left(\frac{5897}{14580}\right)$	$e\left(\frac{5897}{7290}\right)$	$e\left(\frac{1477}{2916}\right)$	$e\left(\frac{1037}{4860}\right)$	$e\left(\frac{2108}{3645}\right)$	$e\left(\frac{2383}{14580}\right)$	$e\left(\frac{6641}{7290}\right)$	$e\left(\frac{2252}{3645}\right)$	$e\left(\frac{1687}{4860}\right)$	$e\left(\frac{1501}{2430}\right)$
$\chi_{164025}(1153,\cdot)$	$-1$	$1$	$e\left(\frac{1663}{14580}\right)$	$e\left(\frac{1663}{7290}\right)$	$e\left(\frac{2303}{2916}\right)$	$e\left(\frac{1663}{4860}\right)$	$e\left(\frac{592}{3645}\right)$	$e\left(\frac{14357}{14580}\right)$	$e\left(\frac{6589}{7290}\right)$	$e\left(\frac{1663}{3645}\right)$	$e\left(\frac{3713}{4860}\right)$	$e\left(\frac{659}{2430}\right)$
$\chi_{164025}(1198,\cdot)$	$-1$	$1$	$e\left(\frac{1919}{14580}\right)$	$e\left(\frac{1919}{7290}\right)$	$e\left(\frac{2647}{2916}\right)$	$e\left(\frac{1919}{4860}\right)$	$e\left(\frac{236}{3645}\right)$	$e\left(\frac{12841}{14580}\right)$	$e\left(\frac{287}{7290}\right)$	$e\left(\frac{1919}{3645}\right)$	$e\left(\frac{1669}{4860}\right)$	$e\left(\frac{2077}{2430}\right)$
$\chi_{164025}(1252,\cdot)$	$-1$	$1$	$e\left(\frac{14009}{14580}\right)$	$e\left(\frac{6719}{7290}\right)$	$e\left(\frac{349}{2916}\right)$	$e\left(\frac{4289}{4860}\right)$	$e\left(\frac{851}{3645}\right)$	$e\left(\frac{9931}{14580}\right)$	$e\left(\frac{587}{7290}\right)$	$e\left(\frac{3074}{3645}\right)$	$e\left(\frac{3439}{4860}\right)$	$e\left(\frac{1327}{2430}\right)$
$\chi_{164025}(1288,\cdot)$	$-1$	$1$	$e\left(\frac{8371}{14580}\right)$	$e\left(\frac{1081}{7290}\right)$	$e\left(\frac{1931}{2916}\right)$	$e\left(\frac{3511}{4860}\right)$	$e\left(\frac{604}{3645}\right)$	$e\left(\frac{13589}{14580}\right)$	$e\left(\frac{1723}{7290}\right)$	$e\left(\frac{1081}{3645}\right)$	$e\left(\frac{4601}{4860}\right)$	$e\left(\frac{1403}{2430}\right)$
$\chi_{164025}(1333,\cdot)$	$-1$	$1$	$e\left(\frac{3227}{14580}\right)$	$e\left(\frac{3227}{7290}\right)$	$e\left(\frac{2491}{2916}\right)$	$e\left(\frac{3227}{4860}\right)$	$e\left(\frac{923}{3645}\right)$	$e\left(\frac{12613}{14580}\right)$	$e\left(\frac{551}{7290}\right)$	$e\left(\frac{3227}{3645}\right)$	$e\left(\frac{1477}{4860}\right)$	$e\left(\frac{931}{2430}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{164025}(37,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13901}{14580}\right)\)	\(e\left(\frac{6611}{7290}\right)\)	\(e\left(\frac{1753}{2916}\right)\)	\(e\left(\frac{4181}{4860}\right)\)	\(e\left(\frac{1229}{3645}\right)\)	\(e\left(\frac{319}{14580}\right)\)	\(e\left(\frac{4043}{7290}\right)\)	\(e\left(\frac{2966}{3645}\right)\)	\(e\left(\frac{2251}{4860}\right)\)	\(e\left(\frac{463}{2430}\right)\)
\(\chi_{164025}(73,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6319}{14580}\right)\)	\(e\left(\frac{6319}{7290}\right)\)	\(e\left(\frac{2363}{2916}\right)\)	\(e\left(\frac{1459}{4860}\right)\)	\(e\left(\frac{496}{3645}\right)\)	\(e\left(\frac{5921}{14580}\right)\)	\(e\left(\frac{1777}{7290}\right)\)	\(e\left(\frac{2674}{3645}\right)\)	\(e\left(\frac{1469}{4860}\right)\)	\(e\left(\frac{1997}{2430}\right)\)
\(\chi_{164025}(127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14089}{14580}\right)\)	\(e\left(\frac{6799}{7290}\right)\)	\(e\left(\frac{821}{2916}\right)\)	\(e\left(\frac{4369}{4860}\right)\)	\(e\left(\frac{1651}{3645}\right)\)	\(e\left(\frac{12191}{14580}\right)\)	\(e\left(\frac{1807}{7290}\right)\)	\(e\left(\frac{3154}{3645}\right)\)	\(e\left(\frac{4319}{4860}\right)\)	\(e\left(\frac{707}{2430}\right)\)
\(\chi_{164025}(172,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5813}{14580}\right)\)	\(e\left(\frac{5813}{7290}\right)\)	\(e\left(\frac{1273}{2916}\right)\)	\(e\left(\frac{953}{4860}\right)\)	\(e\left(\frac{1997}{3645}\right)\)	\(e\left(\frac{9487}{14580}\right)\)	\(e\left(\frac{6089}{7290}\right)\)	\(e\left(\frac{2168}{3645}\right)\)	\(e\left(\frac{763}{4860}\right)\)	\(e\left(\frac{1909}{2430}\right)\)
\(\chi_{164025}(208,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11407}{14580}\right)\)	\(e\left(\frac{4117}{7290}\right)\)	\(e\left(\frac{2639}{2916}\right)\)	\(e\left(\frac{1687}{4860}\right)\)	\(e\left(\frac{2533}{3645}\right)\)	\(e\left(\frac{6773}{14580}\right)\)	\(e\left(\frac{5011}{7290}\right)\)	\(e\left(\frac{472}{3645}\right)\)	\(e\left(\frac{3977}{4860}\right)\)	\(e\left(\frac{1931}{2430}\right)\)
\(\chi_{164025}(253,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5723}{14580}\right)\)	\(e\left(\frac{5723}{7290}\right)\)	\(e\left(\frac{1471}{2916}\right)\)	\(e\left(\frac{863}{4860}\right)\)	\(e\left(\frac{1097}{3645}\right)\)	\(e\left(\frac{1477}{14580}\right)\)	\(e\left(\frac{6539}{7290}\right)\)	\(e\left(\frac{2078}{3645}\right)\)	\(e\left(\frac{4633}{4860}\right)\)	\(e\left(\frac{1999}{2430}\right)\)
\(\chi_{164025}(262,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9781}{14580}\right)\)	\(e\left(\frac{2491}{7290}\right)\)	\(e\left(\frac{773}{2916}\right)\)	\(e\left(\frac{61}{4860}\right)\)	\(e\left(\frac{124}{3645}\right)\)	\(e\left(\frac{7859}{14580}\right)\)	\(e\left(\frac{6823}{7290}\right)\)	\(e\left(\frac{2491}{3645}\right)\)	\(e\left(\frac{671}{4860}\right)\)	\(e\left(\frac{803}{2430}\right)\)
\(\chi_{164025}(388,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3791}{14580}\right)\)	\(e\left(\frac{3791}{7290}\right)\)	\(e\left(\frac{2611}{2916}\right)\)	\(e\left(\frac{3791}{4860}\right)\)	\(e\left(\frac{2189}{3645}\right)\)	\(e\left(\frac{4489}{14580}\right)\)	\(e\left(\frac{1133}{7290}\right)\)	\(e\left(\frac{146}{3645}\right)\)	\(e\left(\frac{2821}{4860}\right)\)	\(e\left(\frac{1663}{2430}\right)\)
\(\chi_{164025}(397,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3853}{14580}\right)\)	\(e\left(\frac{3853}{7290}\right)\)	\(e\left(\frac{1373}{2916}\right)\)	\(e\left(\frac{3853}{4860}\right)\)	\(e\left(\frac{622}{3645}\right)\)	\(e\left(\frac{5147}{14580}\right)\)	\(e\left(\frac{5359}{7290}\right)\)	\(e\left(\frac{208}{3645}\right)\)	\(e\left(\frac{3503}{4860}\right)\)	\(e\left(\frac{89}{2430}\right)\)
\(\chi_{164025}(442,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13937}{14580}\right)\)	\(e\left(\frac{6647}{7290}\right)\)	\(e\left(\frac{2257}{2916}\right)\)	\(e\left(\frac{4217}{4860}\right)\)	\(e\left(\frac{2318}{3645}\right)\)	\(e\left(\frac{3523}{14580}\right)\)	\(e\left(\frac{5321}{7290}\right)\)	\(e\left(\frac{3002}{3645}\right)\)	\(e\left(\frac{2647}{4860}\right)\)	\(e\left(\frac{2371}{2430}\right)\)
\(\chi_{164025}(478,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2143}{14580}\right)\)	\(e\left(\frac{2143}{7290}\right)\)	\(e\left(\frac{2219}{2916}\right)\)	\(e\left(\frac{2143}{4860}\right)\)	\(e\left(\frac{1747}{3645}\right)\)	\(e\left(\frac{13337}{14580}\right)\)	\(e\left(\frac{6619}{7290}\right)\)	\(e\left(\frac{2143}{3645}\right)\)	\(e\left(\frac{4133}{4860}\right)\)	\(e\left(\frac{1799}{2430}\right)\)
\(\chi_{164025}(523,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{239}{14580}\right)\)	\(e\left(\frac{239}{7290}\right)\)	\(e\left(\frac{1483}{2916}\right)\)	\(e\left(\frac{239}{4860}\right)\)	\(e\left(\frac{1661}{3645}\right)\)	\(e\left(\frac{9121}{14580}\right)\)	\(e\left(\frac{3827}{7290}\right)\)	\(e\left(\frac{239}{3645}\right)\)	\(e\left(\frac{2629}{4860}\right)\)	\(e\left(\frac{517}{2430}\right)\)
\(\chi_{164025}(577,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{989}{14580}\right)\)	\(e\left(\frac{989}{7290}\right)\)	\(e\left(\frac{805}{2916}\right)\)	\(e\left(\frac{989}{4860}\right)\)	\(e\left(\frac{1871}{3645}\right)\)	\(e\left(\frac{2971}{14580}\right)\)	\(e\left(\frac{2507}{7290}\right)\)	\(e\left(\frac{989}{3645}\right)\)	\(e\left(\frac{1159}{4860}\right)\)	\(e\left(\frac{1387}{2430}\right)\)
\(\chi_{164025}(613,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2371}{14580}\right)\)	\(e\left(\frac{2371}{7290}\right)\)	\(e\left(\frac{1523}{2916}\right)\)	\(e\left(\frac{2371}{4860}\right)\)	\(e\left(\frac{2569}{3645}\right)\)	\(e\left(\frac{4469}{14580}\right)\)	\(e\left(\frac{4993}{7290}\right)\)	\(e\left(\frac{2371}{3645}\right)\)	\(e\left(\frac{1781}{4860}\right)\)	\(e\left(\frac{1733}{2430}\right)\)
\(\chi_{164025}(658,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9647}{14580}\right)\)	\(e\left(\frac{2357}{7290}\right)\)	\(e\left(\frac{1003}{2916}\right)\)	\(e\left(\frac{4787}{4860}\right)\)	\(e\left(\frac{3158}{3645}\right)\)	\(e\left(\frac{793}{14580}\right)\)	\(e\left(\frac{41}{7290}\right)\)	\(e\left(\frac{2357}{3645}\right)\)	\(e\left(\frac{4057}{4860}\right)\)	\(e\left(\frac{991}{2430}\right)\)
\(\chi_{164025}(667,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1717}{14580}\right)\)	\(e\left(\frac{1717}{7290}\right)\)	\(e\left(\frac{1601}{2916}\right)\)	\(e\left(\frac{1717}{4860}\right)\)	\(e\left(\frac{403}{3645}\right)\)	\(e\left(\frac{4583}{14580}\right)\)	\(e\left(\frac{4861}{7290}\right)\)	\(e\left(\frac{1717}{3645}\right)\)	\(e\left(\frac{4307}{4860}\right)\)	\(e\left(\frac{1091}{2430}\right)\)
\(\chi_{164025}(712,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1001}{14580}\right)\)	\(e\left(\frac{1001}{7290}\right)\)	\(e\left(\frac{1}{2916}\right)\)	\(e\left(\frac{1001}{4860}\right)\)	\(e\left(\frac{3449}{3645}\right)\)	\(e\left(\frac{4039}{14580}\right)\)	\(e\left(\frac{503}{7290}\right)\)	\(e\left(\frac{1001}{3645}\right)\)	\(e\left(\frac{1291}{4860}\right)\)	\(e\left(\frac{2023}{2430}\right)\)
\(\chi_{164025}(748,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{979}{14580}\right)\)	\(e\left(\frac{979}{7290}\right)\)	\(e\left(\frac{1475}{2916}\right)\)	\(e\left(\frac{979}{4860}\right)\)	\(e\left(\frac{1771}{3645}\right)\)	\(e\left(\frac{11801}{14580}\right)\)	\(e\left(\frac{4177}{7290}\right)\)	\(e\left(\frac{979}{3645}\right)\)	\(e\left(\frac{1049}{4860}\right)\)	\(e\left(\frac{857}{2430}\right)\)
\(\chi_{164025}(802,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5509}{14580}\right)\)	\(e\left(\frac{5509}{7290}\right)\)	\(e\left(\frac{1229}{2916}\right)\)	\(e\left(\frac{649}{4860}\right)\)	\(e\left(\frac{3331}{3645}\right)\)	\(e\left(\frac{6731}{14580}\right)\)	\(e\left(\frac{5827}{7290}\right)\)	\(e\left(\frac{1864}{3645}\right)\)	\(e\left(\frac{2279}{4860}\right)\)	\(e\left(\frac{377}{2430}\right)\)
\(\chi_{164025}(847,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13973}{14580}\right)\)	\(e\left(\frac{6683}{7290}\right)\)	\(e\left(\frac{2761}{2916}\right)\)	\(e\left(\frac{4253}{4860}\right)\)	\(e\left(\frac{3407}{3645}\right)\)	\(e\left(\frac{6727}{14580}\right)\)	\(e\left(\frac{6599}{7290}\right)\)	\(e\left(\frac{3038}{3645}\right)\)	\(e\left(\frac{3043}{4860}\right)\)	\(e\left(\frac{1849}{2430}\right)\)
\(\chi_{164025}(883,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{12547}{14580}\right)\)	\(e\left(\frac{5257}{7290}\right)\)	\(e\left(\frac{2075}{2916}\right)\)	\(e\left(\frac{2827}{4860}\right)\)	\(e\left(\frac{2998}{3645}\right)\)	\(e\left(\frac{6173}{14580}\right)\)	\(e\left(\frac{4171}{7290}\right)\)	\(e\left(\frac{1612}{3645}\right)\)	\(e\left(\frac{1937}{4860}\right)\)	\(e\left(\frac{1601}{2430}\right)\)
\(\chi_{164025}(928,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9023}{14580}\right)\)	\(e\left(\frac{1733}{7290}\right)\)	\(e\left(\frac{1987}{2916}\right)\)	\(e\left(\frac{4163}{4860}\right)\)	\(e\left(\frac{1292}{3645}\right)\)	\(e\left(\frac{3577}{14580}\right)\)	\(e\left(\frac{2189}{7290}\right)\)	\(e\left(\frac{1733}{3645}\right)\)	\(e\left(\frac{2053}{4860}\right)\)	\(e\left(\frac{1939}{2430}\right)\)
\(\chi_{164025}(937,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7681}{14580}\right)\)	\(e\left(\frac{391}{7290}\right)\)	\(e\left(\frac{1505}{2916}\right)\)	\(e\left(\frac{2821}{4860}\right)\)	\(e\left(\frac{994}{3645}\right)\)	\(e\left(\frac{10499}{14580}\right)\)	\(e\left(\frac{313}{7290}\right)\)	\(e\left(\frac{391}{3645}\right)\)	\(e\left(\frac{1871}{4860}\right)\)	\(e\left(\frac{1283}{2430}\right)\)
\(\chi_{164025}(1063,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13571}{14580}\right)\)	\(e\left(\frac{6281}{7290}\right)\)	\(e\left(\frac{535}{2916}\right)\)	\(e\left(\frac{3851}{4860}\right)\)	\(e\left(\frac{1574}{3645}\right)\)	\(e\left(\frac{109}{14580}\right)\)	\(e\left(\frac{833}{7290}\right)\)	\(e\left(\frac{2636}{3645}\right)\)	\(e\left(\frac{3481}{4860}\right)\)	\(e\left(\frac{2413}{2430}\right)\)
\(\chi_{164025}(1072,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8233}{14580}\right)\)	\(e\left(\frac{943}{7290}\right)\)	\(e\left(\frac{2429}{2916}\right)\)	\(e\left(\frac{3373}{4860}\right)\)	\(e\left(\frac{682}{3645}\right)\)	\(e\left(\frac{1307}{14580}\right)\)	\(e\left(\frac{2899}{7290}\right)\)	\(e\left(\frac{943}{3645}\right)\)	\(e\left(\frac{3083}{4860}\right)\)	\(e\left(\frac{1379}{2430}\right)\)
\(\chi_{164025}(1117,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5897}{14580}\right)\)	\(e\left(\frac{5897}{7290}\right)\)	\(e\left(\frac{1477}{2916}\right)\)	\(e\left(\frac{1037}{4860}\right)\)	\(e\left(\frac{2108}{3645}\right)\)	\(e\left(\frac{2383}{14580}\right)\)	\(e\left(\frac{6641}{7290}\right)\)	\(e\left(\frac{2252}{3645}\right)\)	\(e\left(\frac{1687}{4860}\right)\)	\(e\left(\frac{1501}{2430}\right)\)
\(\chi_{164025}(1153,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1663}{14580}\right)\)	\(e\left(\frac{1663}{7290}\right)\)	\(e\left(\frac{2303}{2916}\right)\)	\(e\left(\frac{1663}{4860}\right)\)	\(e\left(\frac{592}{3645}\right)\)	\(e\left(\frac{14357}{14580}\right)\)	\(e\left(\frac{6589}{7290}\right)\)	\(e\left(\frac{1663}{3645}\right)\)	\(e\left(\frac{3713}{4860}\right)\)	\(e\left(\frac{659}{2430}\right)\)
\(\chi_{164025}(1198,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1919}{14580}\right)\)	\(e\left(\frac{1919}{7290}\right)\)	\(e\left(\frac{2647}{2916}\right)\)	\(e\left(\frac{1919}{4860}\right)\)	\(e\left(\frac{236}{3645}\right)\)	\(e\left(\frac{12841}{14580}\right)\)	\(e\left(\frac{287}{7290}\right)\)	\(e\left(\frac{1919}{3645}\right)\)	\(e\left(\frac{1669}{4860}\right)\)	\(e\left(\frac{2077}{2430}\right)\)
\(\chi_{164025}(1252,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14009}{14580}\right)\)	\(e\left(\frac{6719}{7290}\right)\)	\(e\left(\frac{349}{2916}\right)\)	\(e\left(\frac{4289}{4860}\right)\)	\(e\left(\frac{851}{3645}\right)\)	\(e\left(\frac{9931}{14580}\right)\)	\(e\left(\frac{587}{7290}\right)\)	\(e\left(\frac{3074}{3645}\right)\)	\(e\left(\frac{3439}{4860}\right)\)	\(e\left(\frac{1327}{2430}\right)\)
\(\chi_{164025}(1288,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8371}{14580}\right)\)	\(e\left(\frac{1081}{7290}\right)\)	\(e\left(\frac{1931}{2916}\right)\)	\(e\left(\frac{3511}{4860}\right)\)	\(e\left(\frac{604}{3645}\right)\)	\(e\left(\frac{13589}{14580}\right)\)	\(e\left(\frac{1723}{7290}\right)\)	\(e\left(\frac{1081}{3645}\right)\)	\(e\left(\frac{4601}{4860}\right)\)	\(e\left(\frac{1403}{2430}\right)\)
\(\chi_{164025}(1333,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3227}{14580}\right)\)	\(e\left(\frac{3227}{7290}\right)\)	\(e\left(\frac{2491}{2916}\right)\)	\(e\left(\frac{3227}{4860}\right)\)	\(e\left(\frac{923}{3645}\right)\)	\(e\left(\frac{12613}{14580}\right)\)	\(e\left(\frac{551}{7290}\right)\)	\(e\left(\frac{3227}{3645}\right)\)	\(e\left(\frac{1477}{4860}\right)\)	\(e\left(\frac{931}{2430}\right)\)

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First 31 of 3888 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	164025.dl
Modulus	$164025$
Conductor	$54675$
Order	$14580$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(164025\)
Conductor:	\(54675\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(14580\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 54675.de	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)