LMFDB - Dirichlet character orbit 50423.g

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(50423, base_ring=CyclotomicField(50422)) M = H._module chi = DirichletCharacter(H, M([36814])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,50423)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$50423$
Conductor:	$50423$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$25211$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{25211})$
Fixed field:	Number field defined by a degree 25211 polynomial (not computed)

First 31 of 23712 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{50423}(2,\cdot)$	$1$	$1$	$e\left(\frac{14040}{25211}\right)$	$e\left(\frac{14293}{25211}\right)$	$e\left(\frac{2869}{25211}\right)$	$e\left(\frac{18407}{25211}\right)$	$e\left(\frac{3122}{25211}\right)$	$e\left(\frac{15076}{25211}\right)$	$e\left(\frac{16909}{25211}\right)$	$e\left(\frac{3375}{25211}\right)$	$e\left(\frac{7236}{25211}\right)$	$e\left(\frac{8508}{25211}\right)$
$\chi_{50423}(3,\cdot)$	$1$	$1$	$e\left(\frac{14293}{25211}\right)$	$e\left(\frac{10566}{25211}\right)$	$e\left(\frac{3375}{25211}\right)$	$e\left(\frac{2576}{25211}\right)$	$e\left(\frac{24859}{25211}\right)$	$e\left(\frac{15872}{25211}\right)$	$e\left(\frac{17668}{25211}\right)$	$e\left(\frac{21132}{25211}\right)$	$e\left(\frac{16869}{25211}\right)$	$e\left(\frac{8295}{25211}\right)$
$\chi_{50423}(4,\cdot)$	$1$	$1$	$e\left(\frac{2869}{25211}\right)$	$e\left(\frac{3375}{25211}\right)$	$e\left(\frac{5738}{25211}\right)$	$e\left(\frac{11603}{25211}\right)$	$e\left(\frac{6244}{25211}\right)$	$e\left(\frac{4941}{25211}\right)$	$e\left(\frac{8607}{25211}\right)$	$e\left(\frac{6750}{25211}\right)$	$e\left(\frac{14472}{25211}\right)$	$e\left(\frac{17016}{25211}\right)$
$\chi_{50423}(6,\cdot)$	$1$	$1$	$e\left(\frac{3122}{25211}\right)$	$e\left(\frac{24859}{25211}\right)$	$e\left(\frac{6244}{25211}\right)$	$e\left(\frac{20983}{25211}\right)$	$e\left(\frac{2770}{25211}\right)$	$e\left(\frac{5737}{25211}\right)$	$e\left(\frac{9366}{25211}\right)$	$e\left(\frac{24507}{25211}\right)$	$e\left(\frac{24105}{25211}\right)$	$e\left(\frac{16803}{25211}\right)$
$\chi_{50423}(8,\cdot)$	$1$	$1$	$e\left(\frac{16909}{25211}\right)$	$e\left(\frac{17668}{25211}\right)$	$e\left(\frac{8607}{25211}\right)$	$e\left(\frac{4799}{25211}\right)$	$e\left(\frac{9366}{25211}\right)$	$e\left(\frac{20017}{25211}\right)$	$e\left(\frac{305}{25211}\right)$	$e\left(\frac{10125}{25211}\right)$	$e\left(\frac{21708}{25211}\right)$	$e\left(\frac{313}{25211}\right)$
$\chi_{50423}(9,\cdot)$	$1$	$1$	$e\left(\frac{3375}{25211}\right)$	$e\left(\frac{21132}{25211}\right)$	$e\left(\frac{6750}{25211}\right)$	$e\left(\frac{5152}{25211}\right)$	$e\left(\frac{24507}{25211}\right)$	$e\left(\frac{6533}{25211}\right)$	$e\left(\frac{10125}{25211}\right)$	$e\left(\frac{17053}{25211}\right)$	$e\left(\frac{8527}{25211}\right)$	$e\left(\frac{16590}{25211}\right)$
$\chi_{50423}(11,\cdot)$	$1$	$1$	$e\left(\frac{8508}{25211}\right)$	$e\left(\frac{8295}{25211}\right)$	$e\left(\frac{17016}{25211}\right)$	$e\left(\frac{17985}{25211}\right)$	$e\left(\frac{16803}{25211}\right)$	$e\left(\frac{10127}{25211}\right)$	$e\left(\frac{313}{25211}\right)$	$e\left(\frac{16590}{25211}\right)$	$e\left(\frac{1282}{25211}\right)$	$e\left(\frac{6190}{25211}\right)$
$\chi_{50423}(12,\cdot)$	$1$	$1$	$e\left(\frac{17162}{25211}\right)$	$e\left(\frac{13941}{25211}\right)$	$e\left(\frac{9113}{25211}\right)$	$e\left(\frac{14179}{25211}\right)$	$e\left(\frac{5892}{25211}\right)$	$e\left(\frac{20813}{25211}\right)$	$e\left(\frac{1064}{25211}\right)$	$e\left(\frac{2671}{25211}\right)$	$e\left(\frac{6130}{25211}\right)$	$e\left(\frac{100}{25211}\right)$
$\chi_{50423}(13,\cdot)$	$1$	$1$	$e\left(\frac{15446}{25211}\right)$	$e\left(\frac{7432}{25211}\right)$	$e\left(\frac{5681}{25211}\right)$	$e\left(\frac{25095}{25211}\right)$	$e\left(\frac{22878}{25211}\right)$	$e\left(\frac{6645}{25211}\right)$	$e\left(\frac{21127}{25211}\right)$	$e\left(\frac{14864}{25211}\right)$	$e\left(\frac{15330}{25211}\right)$	$e\left(\frac{12506}{25211}\right)$
$\chi_{50423}(16,\cdot)$	$1$	$1$	$e\left(\frac{5738}{25211}\right)$	$e\left(\frac{6750}{25211}\right)$	$e\left(\frac{11476}{25211}\right)$	$e\left(\frac{23206}{25211}\right)$	$e\left(\frac{12488}{25211}\right)$	$e\left(\frac{9882}{25211}\right)$	$e\left(\frac{17214}{25211}\right)$	$e\left(\frac{13500}{25211}\right)$	$e\left(\frac{3733}{25211}\right)$	$e\left(\frac{8821}{25211}\right)$
$\chi_{50423}(17,\cdot)$	$1$	$1$	$e\left(\frac{22246}{25211}\right)$	$e\left(\frac{6310}{25211}\right)$	$e\left(\frac{19281}{25211}\right)$	$e\left(\frac{17921}{25211}\right)$	$e\left(\frac{3345}{25211}\right)$	$e\left(\frac{23356}{25211}\right)$	$e\left(\frac{16316}{25211}\right)$	$e\left(\frac{12620}{25211}\right)$	$e\left(\frac{14956}{25211}\right)$	$e\left(\frac{23522}{25211}\right)$
$\chi_{50423}(18,\cdot)$	$1$	$1$	$e\left(\frac{17415}{25211}\right)$	$e\left(\frac{10214}{25211}\right)$	$e\left(\frac{9619}{25211}\right)$	$e\left(\frac{23559}{25211}\right)$	$e\left(\frac{2418}{25211}\right)$	$e\left(\frac{21609}{25211}\right)$	$e\left(\frac{1823}{25211}\right)$	$e\left(\frac{20428}{25211}\right)$	$e\left(\frac{15763}{25211}\right)$	$e\left(\frac{25098}{25211}\right)$
$\chi_{50423}(22,\cdot)$	$1$	$1$	$e\left(\frac{22548}{25211}\right)$	$e\left(\frac{22588}{25211}\right)$	$e\left(\frac{19885}{25211}\right)$	$e\left(\frac{11181}{25211}\right)$	$e\left(\frac{19925}{25211}\right)$	$e\left(\frac{25203}{25211}\right)$	$e\left(\frac{17222}{25211}\right)$	$e\left(\frac{19965}{25211}\right)$	$e\left(\frac{8518}{25211}\right)$	$e\left(\frac{14698}{25211}\right)$
$\chi_{50423}(23,\cdot)$	$1$	$1$	$e\left(\frac{24621}{25211}\right)$	$e\left(\frac{12777}{25211}\right)$	$e\left(\frac{24031}{25211}\right)$	$e\left(\frac{19679}{25211}\right)$	$e\left(\frac{12187}{25211}\right)$	$e\left(\frac{7411}{25211}\right)$	$e\left(\frac{23441}{25211}\right)$	$e\left(\frac{343}{25211}\right)$	$e\left(\frac{19089}{25211}\right)$	$e\left(\frac{4383}{25211}\right)$
$\chi_{50423}(24,\cdot)$	$1$	$1$	$e\left(\frac{5991}{25211}\right)$	$e\left(\frac{3023}{25211}\right)$	$e\left(\frac{11982}{25211}\right)$	$e\left(\frac{7375}{25211}\right)$	$e\left(\frac{9014}{25211}\right)$	$e\left(\frac{10678}{25211}\right)$	$e\left(\frac{17973}{25211}\right)$	$e\left(\frac{6046}{25211}\right)$	$e\left(\frac{13366}{25211}\right)$	$e\left(\frac{8608}{25211}\right)$
$\chi_{50423}(25,\cdot)$	$1$	$1$	$e\left(\frac{11603}{25211}\right)$	$e\left(\frac{5152}{25211}\right)$	$e\left(\frac{23206}{25211}\right)$	$e\left(\frac{1}{25211}\right)$	$e\left(\frac{16755}{25211}\right)$	$e\left(\frac{21459}{25211}\right)$	$e\left(\frac{9598}{25211}\right)$	$e\left(\frac{10304}{25211}\right)$	$e\left(\frac{11604}{25211}\right)$	$e\left(\frac{10759}{25211}\right)$
$\chi_{50423}(26,\cdot)$	$1$	$1$	$e\left(\frac{4275}{25211}\right)$	$e\left(\frac{21725}{25211}\right)$	$e\left(\frac{8550}{25211}\right)$	$e\left(\frac{18291}{25211}\right)$	$e\left(\frac{789}{25211}\right)$	$e\left(\frac{21721}{25211}\right)$	$e\left(\frac{12825}{25211}\right)$	$e\left(\frac{18239}{25211}\right)$	$e\left(\frac{22566}{25211}\right)$	$e\left(\frac{21014}{25211}\right)$
$\chi_{50423}(27,\cdot)$	$1$	$1$	$e\left(\frac{17668}{25211}\right)$	$e\left(\frac{6487}{25211}\right)$	$e\left(\frac{10125}{25211}\right)$	$e\left(\frac{7728}{25211}\right)$	$e\left(\frac{24155}{25211}\right)$	$e\left(\frac{22405}{25211}\right)$	$e\left(\frac{2582}{25211}\right)$	$e\left(\frac{12974}{25211}\right)$	$e\left(\frac{185}{25211}\right)$	$e\left(\frac{24885}{25211}\right)$
$\chi_{50423}(31,\cdot)$	$1$	$1$	$e\left(\frac{24997}{25211}\right)$	$e\left(\frac{2156}{25211}\right)$	$e\left(\frac{24783}{25211}\right)$	$e\left(\frac{13291}{25211}\right)$	$e\left(\frac{1942}{25211}\right)$	$e\left(\frac{24737}{25211}\right)$	$e\left(\frac{24569}{25211}\right)$	$e\left(\frac{4312}{25211}\right)$	$e\left(\frac{13077}{25211}\right)$	$e\left(\frac{1077}{25211}\right)$
$\chi_{50423}(32,\cdot)$	$1$	$1$	$e\left(\frac{19778}{25211}\right)$	$e\left(\frac{21043}{25211}\right)$	$e\left(\frac{14345}{25211}\right)$	$e\left(\frac{16402}{25211}\right)$	$e\left(\frac{15610}{25211}\right)$	$e\left(\frac{24958}{25211}\right)$	$e\left(\frac{8912}{25211}\right)$	$e\left(\frac{16875}{25211}\right)$	$e\left(\frac{10969}{25211}\right)$	$e\left(\frac{17329}{25211}\right)$
$\chi_{50423}(33,\cdot)$	$1$	$1$	$e\left(\frac{22801}{25211}\right)$	$e\left(\frac{18861}{25211}\right)$	$e\left(\frac{20391}{25211}\right)$	$e\left(\frac{20561}{25211}\right)$	$e\left(\frac{16451}{25211}\right)$	$e\left(\frac{788}{25211}\right)$	$e\left(\frac{17981}{25211}\right)$	$e\left(\frac{12511}{25211}\right)$	$e\left(\frac{18151}{25211}\right)$	$e\left(\frac{14485}{25211}\right)$
$\chi_{50423}(34,\cdot)$	$1$	$1$	$e\left(\frac{11075}{25211}\right)$	$e\left(\frac{20603}{25211}\right)$	$e\left(\frac{22150}{25211}\right)$	$e\left(\frac{11117}{25211}\right)$	$e\left(\frac{6467}{25211}\right)$	$e\left(\frac{13221}{25211}\right)$	$e\left(\frac{8014}{25211}\right)$	$e\left(\frac{15995}{25211}\right)$	$e\left(\frac{22192}{25211}\right)$	$e\left(\frac{6819}{25211}\right)$
$\chi_{50423}(35,\cdot)$	$1$	$1$	$e\left(\frac{8272}{25211}\right)$	$e\left(\frac{18448}{25211}\right)$	$e\left(\frac{16544}{25211}\right)$	$e\left(\frac{10730}{25211}\right)$	$e\left(\frac{1509}{25211}\right)$	$e\left(\frac{3007}{25211}\right)$	$e\left(\frac{24816}{25211}\right)$	$e\left(\frac{11685}{25211}\right)$	$e\left(\frac{19002}{25211}\right)$	$e\left(\frac{2901}{25211}\right)$
$\chi_{50423}(36,\cdot)$	$1$	$1$	$e\left(\frac{6244}{25211}\right)$	$e\left(\frac{24507}{25211}\right)$	$e\left(\frac{12488}{25211}\right)$	$e\left(\frac{16755}{25211}\right)$	$e\left(\frac{5540}{25211}\right)$	$e\left(\frac{11474}{25211}\right)$	$e\left(\frac{18732}{25211}\right)$	$e\left(\frac{23803}{25211}\right)$	$e\left(\frac{22999}{25211}\right)$	$e\left(\frac{8395}{25211}\right)$
$\chi_{50423}(39,\cdot)$	$1$	$1$	$e\left(\frac{4528}{25211}\right)$	$e\left(\frac{17998}{25211}\right)$	$e\left(\frac{9056}{25211}\right)$	$e\left(\frac{2460}{25211}\right)$	$e\left(\frac{22526}{25211}\right)$	$e\left(\frac{22517}{25211}\right)$	$e\left(\frac{13584}{25211}\right)$	$e\left(\frac{10785}{25211}\right)$	$e\left(\frac{6988}{25211}\right)$	$e\left(\frac{20801}{25211}\right)$
$\chi_{50423}(43,\cdot)$	$1$	$1$	$e\left(\frac{20211}{25211}\right)$	$e\left(\frac{2308}{25211}\right)$	$e\left(\frac{15211}{25211}\right)$	$e\left(\frac{8241}{25211}\right)$	$e\left(\frac{22519}{25211}\right)$	$e\left(\frac{13665}{25211}\right)$	$e\left(\frac{10211}{25211}\right)$	$e\left(\frac{4616}{25211}\right)$	$e\left(\frac{3241}{25211}\right)$	$e\left(\frac{23043}{25211}\right)$
$\chi_{50423}(44,\cdot)$	$1$	$1$	$e\left(\frac{11377}{25211}\right)$	$e\left(\frac{11670}{25211}\right)$	$e\left(\frac{22754}{25211}\right)$	$e\left(\frac{4377}{25211}\right)$	$e\left(\frac{23047}{25211}\right)$	$e\left(\frac{15068}{25211}\right)$	$e\left(\frac{8920}{25211}\right)$	$e\left(\frac{23340}{25211}\right)$	$e\left(\frac{15754}{25211}\right)$	$e\left(\frac{23206}{25211}\right)$
$\chi_{50423}(46,\cdot)$	$1$	$1$	$e\left(\frac{13450}{25211}\right)$	$e\left(\frac{1859}{25211}\right)$	$e\left(\frac{1689}{25211}\right)$	$e\left(\frac{12875}{25211}\right)$	$e\left(\frac{15309}{25211}\right)$	$e\left(\frac{22487}{25211}\right)$	$e\left(\frac{15139}{25211}\right)$	$e\left(\frac{3718}{25211}\right)$	$e\left(\frac{1114}{25211}\right)$	$e\left(\frac{12891}{25211}\right)$
$\chi_{50423}(47,\cdot)$	$1$	$1$	$e\left(\frac{18765}{25211}\right)$	$e\left(\frac{23709}{25211}\right)$	$e\left(\frac{12319}{25211}\right)$	$e\left(\frac{5451}{25211}\right)$	$e\left(\frac{17263}{25211}\right)$	$e\left(\frac{19180}{25211}\right)$	$e\left(\frac{5873}{25211}\right)$	$e\left(\frac{22207}{25211}\right)$	$e\left(\frac{24216}{25211}\right)$	$e\left(\frac{6523}{25211}\right)$
$\chi_{50423}(48,\cdot)$	$1$	$1$	$e\left(\frac{20031}{25211}\right)$	$e\left(\frac{17316}{25211}\right)$	$e\left(\frac{14851}{25211}\right)$	$e\left(\frac{571}{25211}\right)$	$e\left(\frac{12136}{25211}\right)$	$e\left(\frac{543}{25211}\right)$	$e\left(\frac{9671}{25211}\right)$	$e\left(\frac{9421}{25211}\right)$	$e\left(\frac{20602}{25211}\right)$	$e\left(\frac{17116}{25211}\right)$
$\chi_{50423}(49,\cdot)$	$1$	$1$	$e\left(\frac{4941}{25211}\right)$	$e\left(\frac{6533}{25211}\right)$	$e\left(\frac{9882}{25211}\right)$	$e\left(\frac{21459}{25211}\right)$	$e\left(\frac{11474}{25211}\right)$	$e\left(\frac{9766}{25211}\right)$	$e\left(\frac{14823}{25211}\right)$	$e\left(\frac{13066}{25211}\right)$	$e\left(\frac{1189}{25211}\right)$	$e\left(\frac{20254}{25211}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{50423}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14040}{25211}\right)\)	\(e\left(\frac{14293}{25211}\right)\)	\(e\left(\frac{2869}{25211}\right)\)	\(e\left(\frac{18407}{25211}\right)\)	\(e\left(\frac{3122}{25211}\right)\)	\(e\left(\frac{15076}{25211}\right)\)	\(e\left(\frac{16909}{25211}\right)\)	\(e\left(\frac{3375}{25211}\right)\)	\(e\left(\frac{7236}{25211}\right)\)	\(e\left(\frac{8508}{25211}\right)\)
\(\chi_{50423}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14293}{25211}\right)\)	\(e\left(\frac{10566}{25211}\right)\)	\(e\left(\frac{3375}{25211}\right)\)	\(e\left(\frac{2576}{25211}\right)\)	\(e\left(\frac{24859}{25211}\right)\)	\(e\left(\frac{15872}{25211}\right)\)	\(e\left(\frac{17668}{25211}\right)\)	\(e\left(\frac{21132}{25211}\right)\)	\(e\left(\frac{16869}{25211}\right)\)	\(e\left(\frac{8295}{25211}\right)\)
\(\chi_{50423}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2869}{25211}\right)\)	\(e\left(\frac{3375}{25211}\right)\)	\(e\left(\frac{5738}{25211}\right)\)	\(e\left(\frac{11603}{25211}\right)\)	\(e\left(\frac{6244}{25211}\right)\)	\(e\left(\frac{4941}{25211}\right)\)	\(e\left(\frac{8607}{25211}\right)\)	\(e\left(\frac{6750}{25211}\right)\)	\(e\left(\frac{14472}{25211}\right)\)	\(e\left(\frac{17016}{25211}\right)\)
\(\chi_{50423}(6,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3122}{25211}\right)\)	\(e\left(\frac{24859}{25211}\right)\)	\(e\left(\frac{6244}{25211}\right)\)	\(e\left(\frac{20983}{25211}\right)\)	\(e\left(\frac{2770}{25211}\right)\)	\(e\left(\frac{5737}{25211}\right)\)	\(e\left(\frac{9366}{25211}\right)\)	\(e\left(\frac{24507}{25211}\right)\)	\(e\left(\frac{24105}{25211}\right)\)	\(e\left(\frac{16803}{25211}\right)\)
\(\chi_{50423}(8,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16909}{25211}\right)\)	\(e\left(\frac{17668}{25211}\right)\)	\(e\left(\frac{8607}{25211}\right)\)	\(e\left(\frac{4799}{25211}\right)\)	\(e\left(\frac{9366}{25211}\right)\)	\(e\left(\frac{20017}{25211}\right)\)	\(e\left(\frac{305}{25211}\right)\)	\(e\left(\frac{10125}{25211}\right)\)	\(e\left(\frac{21708}{25211}\right)\)	\(e\left(\frac{313}{25211}\right)\)
\(\chi_{50423}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3375}{25211}\right)\)	\(e\left(\frac{21132}{25211}\right)\)	\(e\left(\frac{6750}{25211}\right)\)	\(e\left(\frac{5152}{25211}\right)\)	\(e\left(\frac{24507}{25211}\right)\)	\(e\left(\frac{6533}{25211}\right)\)	\(e\left(\frac{10125}{25211}\right)\)	\(e\left(\frac{17053}{25211}\right)\)	\(e\left(\frac{8527}{25211}\right)\)	\(e\left(\frac{16590}{25211}\right)\)
\(\chi_{50423}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8508}{25211}\right)\)	\(e\left(\frac{8295}{25211}\right)\)	\(e\left(\frac{17016}{25211}\right)\)	\(e\left(\frac{17985}{25211}\right)\)	\(e\left(\frac{16803}{25211}\right)\)	\(e\left(\frac{10127}{25211}\right)\)	\(e\left(\frac{313}{25211}\right)\)	\(e\left(\frac{16590}{25211}\right)\)	\(e\left(\frac{1282}{25211}\right)\)	\(e\left(\frac{6190}{25211}\right)\)
\(\chi_{50423}(12,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17162}{25211}\right)\)	\(e\left(\frac{13941}{25211}\right)\)	\(e\left(\frac{9113}{25211}\right)\)	\(e\left(\frac{14179}{25211}\right)\)	\(e\left(\frac{5892}{25211}\right)\)	\(e\left(\frac{20813}{25211}\right)\)	\(e\left(\frac{1064}{25211}\right)\)	\(e\left(\frac{2671}{25211}\right)\)	\(e\left(\frac{6130}{25211}\right)\)	\(e\left(\frac{100}{25211}\right)\)
\(\chi_{50423}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15446}{25211}\right)\)	\(e\left(\frac{7432}{25211}\right)\)	\(e\left(\frac{5681}{25211}\right)\)	\(e\left(\frac{25095}{25211}\right)\)	\(e\left(\frac{22878}{25211}\right)\)	\(e\left(\frac{6645}{25211}\right)\)	\(e\left(\frac{21127}{25211}\right)\)	\(e\left(\frac{14864}{25211}\right)\)	\(e\left(\frac{15330}{25211}\right)\)	\(e\left(\frac{12506}{25211}\right)\)
\(\chi_{50423}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5738}{25211}\right)\)	\(e\left(\frac{6750}{25211}\right)\)	\(e\left(\frac{11476}{25211}\right)\)	\(e\left(\frac{23206}{25211}\right)\)	\(e\left(\frac{12488}{25211}\right)\)	\(e\left(\frac{9882}{25211}\right)\)	\(e\left(\frac{17214}{25211}\right)\)	\(e\left(\frac{13500}{25211}\right)\)	\(e\left(\frac{3733}{25211}\right)\)	\(e\left(\frac{8821}{25211}\right)\)
\(\chi_{50423}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22246}{25211}\right)\)	\(e\left(\frac{6310}{25211}\right)\)	\(e\left(\frac{19281}{25211}\right)\)	\(e\left(\frac{17921}{25211}\right)\)	\(e\left(\frac{3345}{25211}\right)\)	\(e\left(\frac{23356}{25211}\right)\)	\(e\left(\frac{16316}{25211}\right)\)	\(e\left(\frac{12620}{25211}\right)\)	\(e\left(\frac{14956}{25211}\right)\)	\(e\left(\frac{23522}{25211}\right)\)
\(\chi_{50423}(18,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17415}{25211}\right)\)	\(e\left(\frac{10214}{25211}\right)\)	\(e\left(\frac{9619}{25211}\right)\)	\(e\left(\frac{23559}{25211}\right)\)	\(e\left(\frac{2418}{25211}\right)\)	\(e\left(\frac{21609}{25211}\right)\)	\(e\left(\frac{1823}{25211}\right)\)	\(e\left(\frac{20428}{25211}\right)\)	\(e\left(\frac{15763}{25211}\right)\)	\(e\left(\frac{25098}{25211}\right)\)
\(\chi_{50423}(22,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22548}{25211}\right)\)	\(e\left(\frac{22588}{25211}\right)\)	\(e\left(\frac{19885}{25211}\right)\)	\(e\left(\frac{11181}{25211}\right)\)	\(e\left(\frac{19925}{25211}\right)\)	\(e\left(\frac{25203}{25211}\right)\)	\(e\left(\frac{17222}{25211}\right)\)	\(e\left(\frac{19965}{25211}\right)\)	\(e\left(\frac{8518}{25211}\right)\)	\(e\left(\frac{14698}{25211}\right)\)
\(\chi_{50423}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24621}{25211}\right)\)	\(e\left(\frac{12777}{25211}\right)\)	\(e\left(\frac{24031}{25211}\right)\)	\(e\left(\frac{19679}{25211}\right)\)	\(e\left(\frac{12187}{25211}\right)\)	\(e\left(\frac{7411}{25211}\right)\)	\(e\left(\frac{23441}{25211}\right)\)	\(e\left(\frac{343}{25211}\right)\)	\(e\left(\frac{19089}{25211}\right)\)	\(e\left(\frac{4383}{25211}\right)\)
\(\chi_{50423}(24,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5991}{25211}\right)\)	\(e\left(\frac{3023}{25211}\right)\)	\(e\left(\frac{11982}{25211}\right)\)	\(e\left(\frac{7375}{25211}\right)\)	\(e\left(\frac{9014}{25211}\right)\)	\(e\left(\frac{10678}{25211}\right)\)	\(e\left(\frac{17973}{25211}\right)\)	\(e\left(\frac{6046}{25211}\right)\)	\(e\left(\frac{13366}{25211}\right)\)	\(e\left(\frac{8608}{25211}\right)\)
\(\chi_{50423}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11603}{25211}\right)\)	\(e\left(\frac{5152}{25211}\right)\)	\(e\left(\frac{23206}{25211}\right)\)	\(e\left(\frac{1}{25211}\right)\)	\(e\left(\frac{16755}{25211}\right)\)	\(e\left(\frac{21459}{25211}\right)\)	\(e\left(\frac{9598}{25211}\right)\)	\(e\left(\frac{10304}{25211}\right)\)	\(e\left(\frac{11604}{25211}\right)\)	\(e\left(\frac{10759}{25211}\right)\)
\(\chi_{50423}(26,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4275}{25211}\right)\)	\(e\left(\frac{21725}{25211}\right)\)	\(e\left(\frac{8550}{25211}\right)\)	\(e\left(\frac{18291}{25211}\right)\)	\(e\left(\frac{789}{25211}\right)\)	\(e\left(\frac{21721}{25211}\right)\)	\(e\left(\frac{12825}{25211}\right)\)	\(e\left(\frac{18239}{25211}\right)\)	\(e\left(\frac{22566}{25211}\right)\)	\(e\left(\frac{21014}{25211}\right)\)
\(\chi_{50423}(27,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17668}{25211}\right)\)	\(e\left(\frac{6487}{25211}\right)\)	\(e\left(\frac{10125}{25211}\right)\)	\(e\left(\frac{7728}{25211}\right)\)	\(e\left(\frac{24155}{25211}\right)\)	\(e\left(\frac{22405}{25211}\right)\)	\(e\left(\frac{2582}{25211}\right)\)	\(e\left(\frac{12974}{25211}\right)\)	\(e\left(\frac{185}{25211}\right)\)	\(e\left(\frac{24885}{25211}\right)\)
\(\chi_{50423}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24997}{25211}\right)\)	\(e\left(\frac{2156}{25211}\right)\)	\(e\left(\frac{24783}{25211}\right)\)	\(e\left(\frac{13291}{25211}\right)\)	\(e\left(\frac{1942}{25211}\right)\)	\(e\left(\frac{24737}{25211}\right)\)	\(e\left(\frac{24569}{25211}\right)\)	\(e\left(\frac{4312}{25211}\right)\)	\(e\left(\frac{13077}{25211}\right)\)	\(e\left(\frac{1077}{25211}\right)\)
\(\chi_{50423}(32,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19778}{25211}\right)\)	\(e\left(\frac{21043}{25211}\right)\)	\(e\left(\frac{14345}{25211}\right)\)	\(e\left(\frac{16402}{25211}\right)\)	\(e\left(\frac{15610}{25211}\right)\)	\(e\left(\frac{24958}{25211}\right)\)	\(e\left(\frac{8912}{25211}\right)\)	\(e\left(\frac{16875}{25211}\right)\)	\(e\left(\frac{10969}{25211}\right)\)	\(e\left(\frac{17329}{25211}\right)\)
\(\chi_{50423}(33,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22801}{25211}\right)\)	\(e\left(\frac{18861}{25211}\right)\)	\(e\left(\frac{20391}{25211}\right)\)	\(e\left(\frac{20561}{25211}\right)\)	\(e\left(\frac{16451}{25211}\right)\)	\(e\left(\frac{788}{25211}\right)\)	\(e\left(\frac{17981}{25211}\right)\)	\(e\left(\frac{12511}{25211}\right)\)	\(e\left(\frac{18151}{25211}\right)\)	\(e\left(\frac{14485}{25211}\right)\)
\(\chi_{50423}(34,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11075}{25211}\right)\)	\(e\left(\frac{20603}{25211}\right)\)	\(e\left(\frac{22150}{25211}\right)\)	\(e\left(\frac{11117}{25211}\right)\)	\(e\left(\frac{6467}{25211}\right)\)	\(e\left(\frac{13221}{25211}\right)\)	\(e\left(\frac{8014}{25211}\right)\)	\(e\left(\frac{15995}{25211}\right)\)	\(e\left(\frac{22192}{25211}\right)\)	\(e\left(\frac{6819}{25211}\right)\)
\(\chi_{50423}(35,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8272}{25211}\right)\)	\(e\left(\frac{18448}{25211}\right)\)	\(e\left(\frac{16544}{25211}\right)\)	\(e\left(\frac{10730}{25211}\right)\)	\(e\left(\frac{1509}{25211}\right)\)	\(e\left(\frac{3007}{25211}\right)\)	\(e\left(\frac{24816}{25211}\right)\)	\(e\left(\frac{11685}{25211}\right)\)	\(e\left(\frac{19002}{25211}\right)\)	\(e\left(\frac{2901}{25211}\right)\)
\(\chi_{50423}(36,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6244}{25211}\right)\)	\(e\left(\frac{24507}{25211}\right)\)	\(e\left(\frac{12488}{25211}\right)\)	\(e\left(\frac{16755}{25211}\right)\)	\(e\left(\frac{5540}{25211}\right)\)	\(e\left(\frac{11474}{25211}\right)\)	\(e\left(\frac{18732}{25211}\right)\)	\(e\left(\frac{23803}{25211}\right)\)	\(e\left(\frac{22999}{25211}\right)\)	\(e\left(\frac{8395}{25211}\right)\)
\(\chi_{50423}(39,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4528}{25211}\right)\)	\(e\left(\frac{17998}{25211}\right)\)	\(e\left(\frac{9056}{25211}\right)\)	\(e\left(\frac{2460}{25211}\right)\)	\(e\left(\frac{22526}{25211}\right)\)	\(e\left(\frac{22517}{25211}\right)\)	\(e\left(\frac{13584}{25211}\right)\)	\(e\left(\frac{10785}{25211}\right)\)	\(e\left(\frac{6988}{25211}\right)\)	\(e\left(\frac{20801}{25211}\right)\)
\(\chi_{50423}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20211}{25211}\right)\)	\(e\left(\frac{2308}{25211}\right)\)	\(e\left(\frac{15211}{25211}\right)\)	\(e\left(\frac{8241}{25211}\right)\)	\(e\left(\frac{22519}{25211}\right)\)	\(e\left(\frac{13665}{25211}\right)\)	\(e\left(\frac{10211}{25211}\right)\)	\(e\left(\frac{4616}{25211}\right)\)	\(e\left(\frac{3241}{25211}\right)\)	\(e\left(\frac{23043}{25211}\right)\)
\(\chi_{50423}(44,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11377}{25211}\right)\)	\(e\left(\frac{11670}{25211}\right)\)	\(e\left(\frac{22754}{25211}\right)\)	\(e\left(\frac{4377}{25211}\right)\)	\(e\left(\frac{23047}{25211}\right)\)	\(e\left(\frac{15068}{25211}\right)\)	\(e\left(\frac{8920}{25211}\right)\)	\(e\left(\frac{23340}{25211}\right)\)	\(e\left(\frac{15754}{25211}\right)\)	\(e\left(\frac{23206}{25211}\right)\)
\(\chi_{50423}(46,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13450}{25211}\right)\)	\(e\left(\frac{1859}{25211}\right)\)	\(e\left(\frac{1689}{25211}\right)\)	\(e\left(\frac{12875}{25211}\right)\)	\(e\left(\frac{15309}{25211}\right)\)	\(e\left(\frac{22487}{25211}\right)\)	\(e\left(\frac{15139}{25211}\right)\)	\(e\left(\frac{3718}{25211}\right)\)	\(e\left(\frac{1114}{25211}\right)\)	\(e\left(\frac{12891}{25211}\right)\)
\(\chi_{50423}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18765}{25211}\right)\)	\(e\left(\frac{23709}{25211}\right)\)	\(e\left(\frac{12319}{25211}\right)\)	\(e\left(\frac{5451}{25211}\right)\)	\(e\left(\frac{17263}{25211}\right)\)	\(e\left(\frac{19180}{25211}\right)\)	\(e\left(\frac{5873}{25211}\right)\)	\(e\left(\frac{22207}{25211}\right)\)	\(e\left(\frac{24216}{25211}\right)\)	\(e\left(\frac{6523}{25211}\right)\)
\(\chi_{50423}(48,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20031}{25211}\right)\)	\(e\left(\frac{17316}{25211}\right)\)	\(e\left(\frac{14851}{25211}\right)\)	\(e\left(\frac{571}{25211}\right)\)	\(e\left(\frac{12136}{25211}\right)\)	\(e\left(\frac{543}{25211}\right)\)	\(e\left(\frac{9671}{25211}\right)\)	\(e\left(\frac{9421}{25211}\right)\)	\(e\left(\frac{20602}{25211}\right)\)	\(e\left(\frac{17116}{25211}\right)\)
\(\chi_{50423}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4941}{25211}\right)\)	\(e\left(\frac{6533}{25211}\right)\)	\(e\left(\frac{9882}{25211}\right)\)	\(e\left(\frac{21459}{25211}\right)\)	\(e\left(\frac{11474}{25211}\right)\)	\(e\left(\frac{9766}{25211}\right)\)	\(e\left(\frac{14823}{25211}\right)\)	\(e\left(\frac{13066}{25211}\right)\)	\(e\left(\frac{1189}{25211}\right)\)	\(e\left(\frac{20254}{25211}\right)\)

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Basic properties

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First 31 of 23712 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	50423.g
Modulus	$50423$
Conductor	$50423$
Order	$25211$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(50423\)
Conductor:	\(50423\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(25211\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)