LMFDB - Dirichlet character orbit 4219.m

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4219, base_ring=CyclotomicField(1406)) M = H._module chi = DirichletCharacter(H, M([84])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(5, 4219)) 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("4219.5"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$4219$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$4219$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$703$	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:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{703})$
Fixed field:	Number field defined by a degree 703 polynomial (not computed)

First 31 of 648 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{4219}(5,\cdot)$	$1$	$1$	$e\left(\frac{42}{703}\right)$	$e\left(\frac{651}{703}\right)$	$e\left(\frac{84}{703}\right)$	$e\left(\frac{39}{703}\right)$	$e\left(\frac{693}{703}\right)$	$e\left(\frac{535}{703}\right)$	$e\left(\frac{126}{703}\right)$	$e\left(\frac{599}{703}\right)$	$e\left(\frac{81}{703}\right)$	$e\left(\frac{500}{703}\right)$
$\chi_{4219}(6,\cdot)$	$1$	$1$	$e\left(\frac{530}{703}\right)$	$e\left(\frac{482}{703}\right)$	$e\left(\frac{357}{703}\right)$	$e\left(\frac{693}{703}\right)$	$e\left(\frac{309}{703}\right)$	$e\left(\frac{692}{703}\right)$	$e\left(\frac{184}{703}\right)$	$e\left(\frac{261}{703}\right)$	$e\left(\frac{520}{703}\right)$	$e\left(\frac{16}{703}\right)$
$\chi_{4219}(11,\cdot)$	$1$	$1$	$e\left(\frac{214}{703}\right)$	$e\left(\frac{505}{703}\right)$	$e\left(\frac{428}{703}\right)$	$e\left(\frac{500}{703}\right)$	$e\left(\frac{16}{703}\right)$	$e\left(\frac{550}{703}\right)$	$e\left(\frac{642}{703}\right)$	$e\left(\frac{307}{703}\right)$	$e\left(\frac{11}{703}\right)$	$e\left(\frac{606}{703}\right)$
$\chi_{4219}(23,\cdot)$	$1$	$1$	$e\left(\frac{287}{703}\right)$	$e\left(\frac{582}{703}\right)$	$e\left(\frac{574}{703}\right)$	$e\left(\frac{618}{703}\right)$	$e\left(\frac{166}{703}\right)$	$e\left(\frac{258}{703}\right)$	$e\left(\frac{158}{703}\right)$	$e\left(\frac{461}{703}\right)$	$e\left(\frac{202}{703}\right)$	$e\left(\frac{136}{703}\right)$
$\chi_{4219}(25,\cdot)$	$1$	$1$	$e\left(\frac{84}{703}\right)$	$e\left(\frac{599}{703}\right)$	$e\left(\frac{168}{703}\right)$	$e\left(\frac{78}{703}\right)$	$e\left(\frac{683}{703}\right)$	$e\left(\frac{367}{703}\right)$	$e\left(\frac{252}{703}\right)$	$e\left(\frac{495}{703}\right)$	$e\left(\frac{162}{703}\right)$	$e\left(\frac{297}{703}\right)$
$\chi_{4219}(28,\cdot)$	$1$	$1$	$e\left(\frac{234}{703}\right)$	$e\left(\frac{112}{703}\right)$	$e\left(\frac{468}{703}\right)$	$e\left(\frac{619}{703}\right)$	$e\left(\frac{346}{703}\right)$	$e\left(\frac{470}{703}\right)$	$e\left(\frac{702}{703}\right)$	$e\left(\frac{224}{703}\right)$	$e\left(\frac{150}{703}\right)$	$e\left(\frac{275}{703}\right)$
$\chi_{4219}(30,\cdot)$	$1$	$1$	$e\left(\frac{572}{703}\right)$	$e\left(\frac{430}{703}\right)$	$e\left(\frac{441}{703}\right)$	$e\left(\frac{29}{703}\right)$	$e\left(\frac{299}{703}\right)$	$e\left(\frac{524}{703}\right)$	$e\left(\frac{310}{703}\right)$	$e\left(\frac{157}{703}\right)$	$e\left(\frac{601}{703}\right)$	$e\left(\frac{516}{703}\right)$
$\chi_{4219}(34,\cdot)$	$1$	$1$	$e\left(\frac{26}{703}\right)$	$e\left(\frac{403}{703}\right)$	$e\left(\frac{52}{703}\right)$	$e\left(\frac{225}{703}\right)$	$e\left(\frac{429}{703}\right)$	$e\left(\frac{599}{703}\right)$	$e\left(\frac{78}{703}\right)$	$e\left(\frac{103}{703}\right)$	$e\left(\frac{251}{703}\right)$	$e\left(\frac{343}{703}\right)$
$\chi_{4219}(36,\cdot)$	$1$	$1$	$e\left(\frac{357}{703}\right)$	$e\left(\frac{261}{703}\right)$	$e\left(\frac{11}{703}\right)$	$e\left(\frac{683}{703}\right)$	$e\left(\frac{618}{703}\right)$	$e\left(\frac{681}{703}\right)$	$e\left(\frac{368}{703}\right)$	$e\left(\frac{522}{703}\right)$	$e\left(\frac{337}{703}\right)$	$e\left(\frac{32}{703}\right)$
$\chi_{4219}(37,\cdot)$	$1$	$1$	$e\left(\frac{28}{703}\right)$	$e\left(\frac{434}{703}\right)$	$e\left(\frac{56}{703}\right)$	$e\left(\frac{26}{703}\right)$	$e\left(\frac{462}{703}\right)$	$e\left(\frac{591}{703}\right)$	$e\left(\frac{84}{703}\right)$	$e\left(\frac{165}{703}\right)$	$e\left(\frac{54}{703}\right)$	$e\left(\frac{99}{703}\right)$
$\chi_{4219}(55,\cdot)$	$1$	$1$	$e\left(\frac{256}{703}\right)$	$e\left(\frac{453}{703}\right)$	$e\left(\frac{512}{703}\right)$	$e\left(\frac{539}{703}\right)$	$e\left(\frac{6}{703}\right)$	$e\left(\frac{382}{703}\right)$	$e\left(\frac{65}{703}\right)$	$e\left(\frac{203}{703}\right)$	$e\left(\frac{92}{703}\right)$	$e\left(\frac{403}{703}\right)$
$\chi_{4219}(64,\cdot)$	$1$	$1$	$e\left(\frac{1}{703}\right)$	$e\left(\frac{367}{703}\right)$	$e\left(\frac{2}{703}\right)$	$e\left(\frac{252}{703}\right)$	$e\left(\frac{368}{703}\right)$	$e\left(\frac{699}{703}\right)$	$e\left(\frac{3}{703}\right)$	$e\left(\frac{31}{703}\right)$	$e\left(\frac{253}{703}\right)$	$e\left(\frac{581}{703}\right)$
$\chi_{4219}(66,\cdot)$	$1$	$1$	$e\left(\frac{41}{703}\right)$	$e\left(\frac{284}{703}\right)$	$e\left(\frac{82}{703}\right)$	$e\left(\frac{490}{703}\right)$	$e\left(\frac{325}{703}\right)$	$e\left(\frac{539}{703}\right)$	$e\left(\frac{123}{703}\right)$	$e\left(\frac{568}{703}\right)$	$e\left(\frac{531}{703}\right)$	$e\left(\frac{622}{703}\right)$
$\chi_{4219}(87,\cdot)$	$1$	$1$	$e\left(\frac{450}{703}\right)$	$e\left(\frac{648}{703}\right)$	$e\left(\frac{197}{703}\right)$	$e\left(\frac{217}{703}\right)$	$e\left(\frac{395}{703}\right)$	$e\left(\frac{309}{703}\right)$	$e\left(\frac{647}{703}\right)$	$e\left(\frac{593}{703}\right)$	$e\left(\frac{667}{703}\right)$	$e\left(\frac{637}{703}\right)$
$\chi_{4219}(97,\cdot)$	$1$	$1$	$e\left(\frac{253}{703}\right)$	$e\left(\frac{55}{703}\right)$	$e\left(\frac{506}{703}\right)$	$e\left(\frac{486}{703}\right)$	$e\left(\frac{308}{703}\right)$	$e\left(\frac{394}{703}\right)$	$e\left(\frac{56}{703}\right)$	$e\left(\frac{110}{703}\right)$	$e\left(\frac{36}{703}\right)$	$e\left(\frac{66}{703}\right)$
$\chi_{4219}(104,\cdot)$	$1$	$1$	$e\left(\frac{575}{703}\right)$	$e\left(\frac{125}{703}\right)$	$e\left(\frac{447}{703}\right)$	$e\left(\frac{82}{703}\right)$	$e\left(\frac{700}{703}\right)$	$e\left(\frac{512}{703}\right)$	$e\left(\frac{319}{703}\right)$	$e\left(\frac{250}{703}\right)$	$e\left(\frac{657}{703}\right)$	$e\left(\frac{150}{703}\right)$
$\chi_{4219}(106,\cdot)$	$1$	$1$	$e\left(\frac{18}{703}\right)$	$e\left(\frac{279}{703}\right)$	$e\left(\frac{36}{703}\right)$	$e\left(\frac{318}{703}\right)$	$e\left(\frac{297}{703}\right)$	$e\left(\frac{631}{703}\right)$	$e\left(\frac{54}{703}\right)$	$e\left(\frac{558}{703}\right)$	$e\left(\frac{336}{703}\right)$	$e\left(\frac{616}{703}\right)$
$\chi_{4219}(115,\cdot)$	$1$	$1$	$e\left(\frac{329}{703}\right)$	$e\left(\frac{530}{703}\right)$	$e\left(\frac{658}{703}\right)$	$e\left(\frac{657}{703}\right)$	$e\left(\frac{156}{703}\right)$	$e\left(\frac{90}{703}\right)$	$e\left(\frac{284}{703}\right)$	$e\left(\frac{357}{703}\right)$	$e\left(\frac{283}{703}\right)$	$e\left(\frac{636}{703}\right)$
$\chi_{4219}(121,\cdot)$	$1$	$1$	$e\left(\frac{428}{703}\right)$	$e\left(\frac{307}{703}\right)$	$e\left(\frac{153}{703}\right)$	$e\left(\frac{297}{703}\right)$	$e\left(\frac{32}{703}\right)$	$e\left(\frac{397}{703}\right)$	$e\left(\frac{581}{703}\right)$	$e\left(\frac{614}{703}\right)$	$e\left(\frac{22}{703}\right)$	$e\left(\frac{509}{703}\right)$
$\chi_{4219}(122,\cdot)$	$1$	$1$	$e\left(\frac{280}{703}\right)$	$e\left(\frac{122}{703}\right)$	$e\left(\frac{560}{703}\right)$	$e\left(\frac{260}{703}\right)$	$e\left(\frac{402}{703}\right)$	$e\left(\frac{286}{703}\right)$	$e\left(\frac{137}{703}\right)$	$e\left(\frac{244}{703}\right)$	$e\left(\frac{540}{703}\right)$	$e\left(\frac{287}{703}\right)$
$\chi_{4219}(125,\cdot)$	$1$	$1$	$e\left(\frac{126}{703}\right)$	$e\left(\frac{547}{703}\right)$	$e\left(\frac{252}{703}\right)$	$e\left(\frac{117}{703}\right)$	$e\left(\frac{673}{703}\right)$	$e\left(\frac{199}{703}\right)$	$e\left(\frac{378}{703}\right)$	$e\left(\frac{391}{703}\right)$	$e\left(\frac{243}{703}\right)$	$e\left(\frac{94}{703}\right)$
$\chi_{4219}(134,\cdot)$	$1$	$1$	$e\left(\frac{113}{703}\right)$	$e\left(\frac{697}{703}\right)$	$e\left(\frac{226}{703}\right)$	$e\left(\frac{356}{703}\right)$	$e\left(\frac{107}{703}\right)$	$e\left(\frac{251}{703}\right)$	$e\left(\frac{339}{703}\right)$	$e\left(\frac{691}{703}\right)$	$e\left(\frac{469}{703}\right)$	$e\left(\frac{274}{703}\right)$
$\chi_{4219}(137,\cdot)$	$1$	$1$	$e\left(\frac{82}{703}\right)$	$e\left(\frac{568}{703}\right)$	$e\left(\frac{164}{703}\right)$	$e\left(\frac{277}{703}\right)$	$e\left(\frac{650}{703}\right)$	$e\left(\frac{375}{703}\right)$	$e\left(\frac{246}{703}\right)$	$e\left(\frac{433}{703}\right)$	$e\left(\frac{359}{703}\right)$	$e\left(\frac{541}{703}\right)$
$\chi_{4219}(140,\cdot)$	$1$	$1$	$e\left(\frac{276}{703}\right)$	$e\left(\frac{60}{703}\right)$	$e\left(\frac{552}{703}\right)$	$e\left(\frac{658}{703}\right)$	$e\left(\frac{336}{703}\right)$	$e\left(\frac{302}{703}\right)$	$e\left(\frac{125}{703}\right)$	$e\left(\frac{120}{703}\right)$	$e\left(\frac{231}{703}\right)$	$e\left(\frac{72}{703}\right)$
$\chi_{4219}(141,\cdot)$	$1$	$1$	$e\left(\frac{345}{703}\right)$	$e\left(\frac{75}{703}\right)$	$e\left(\frac{690}{703}\right)$	$e\left(\frac{471}{703}\right)$	$e\left(\frac{420}{703}\right)$	$e\left(\frac{26}{703}\right)$	$e\left(\frac{332}{703}\right)$	$e\left(\frac{150}{703}\right)$	$e\left(\frac{113}{703}\right)$	$e\left(\frac{90}{703}\right)$
$\chi_{4219}(150,\cdot)$	$1$	$1$	$e\left(\frac{614}{703}\right)$	$e\left(\frac{378}{703}\right)$	$e\left(\frac{525}{703}\right)$	$e\left(\frac{68}{703}\right)$	$e\left(\frac{289}{703}\right)$	$e\left(\frac{356}{703}\right)$	$e\left(\frac{436}{703}\right)$	$e\left(\frac{53}{703}\right)$	$e\left(\frac{682}{703}\right)$	$e\left(\frac{313}{703}\right)$
$\chi_{4219}(152,\cdot)$	$1$	$1$	$e\left(\frac{497}{703}\right)$	$e\left(\frac{322}{703}\right)$	$e\left(\frac{291}{703}\right)$	$e\left(\frac{110}{703}\right)$	$e\left(\frac{116}{703}\right)$	$e\left(\frac{121}{703}\right)$	$e\left(\frac{85}{703}\right)$	$e\left(\frac{644}{703}\right)$	$e\left(\frac{607}{703}\right)$	$e\left(\frac{527}{703}\right)$
$\chi_{4219}(155,\cdot)$	$1$	$1$	$e\left(\frac{194}{703}\right)$	$e\left(\frac{195}{703}\right)$	$e\left(\frac{388}{703}\right)$	$e\left(\frac{381}{703}\right)$	$e\left(\frac{389}{703}\right)$	$e\left(\frac{630}{703}\right)$	$e\left(\frac{582}{703}\right)$	$e\left(\frac{390}{703}\right)$	$e\left(\frac{575}{703}\right)$	$e\left(\frac{234}{703}\right)$
$\chi_{4219}(164,\cdot)$	$1$	$1$	$e\left(\frac{527}{703}\right)$	$e\left(\frac{84}{703}\right)$	$e\left(\frac{351}{703}\right)$	$e\left(\frac{640}{703}\right)$	$e\left(\frac{611}{703}\right)$	$e\left(\frac{1}{703}\right)$	$e\left(\frac{175}{703}\right)$	$e\left(\frac{168}{703}\right)$	$e\left(\frac{464}{703}\right)$	$e\left(\frac{382}{703}\right)$
$\chi_{4219}(168,\cdot)$	$1$	$1$	$e\left(\frac{61}{703}\right)$	$e\left(\frac{594}{703}\right)$	$e\left(\frac{122}{703}\right)$	$e\left(\frac{609}{703}\right)$	$e\left(\frac{655}{703}\right)$	$e\left(\frac{459}{703}\right)$	$e\left(\frac{183}{703}\right)$	$e\left(\frac{485}{703}\right)$	$e\left(\frac{670}{703}\right)$	$e\left(\frac{291}{703}\right)$
$\chi_{4219}(169,\cdot)$	$1$	$1$	$e\left(\frac{446}{703}\right)$	$e\left(\frac{586}{703}\right)$	$e\left(\frac{189}{703}\right)$	$e\left(\frac{615}{703}\right)$	$e\left(\frac{329}{703}\right)$	$e\left(\frac{325}{703}\right)$	$e\left(\frac{635}{703}\right)$	$e\left(\frac{469}{703}\right)$	$e\left(\frac{358}{703}\right)$	$e\left(\frac{422}{703}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{4219}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{42}{703}\right)\)	\(e\left(\frac{651}{703}\right)\)	\(e\left(\frac{84}{703}\right)\)	\(e\left(\frac{39}{703}\right)\)	\(e\left(\frac{693}{703}\right)\)	\(e\left(\frac{535}{703}\right)\)	\(e\left(\frac{126}{703}\right)\)	\(e\left(\frac{599}{703}\right)\)	\(e\left(\frac{81}{703}\right)\)	\(e\left(\frac{500}{703}\right)\)
\(\chi_{4219}(6,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{530}{703}\right)\)	\(e\left(\frac{482}{703}\right)\)	\(e\left(\frac{357}{703}\right)\)	\(e\left(\frac{693}{703}\right)\)	\(e\left(\frac{309}{703}\right)\)	\(e\left(\frac{692}{703}\right)\)	\(e\left(\frac{184}{703}\right)\)	\(e\left(\frac{261}{703}\right)\)	\(e\left(\frac{520}{703}\right)\)	\(e\left(\frac{16}{703}\right)\)
\(\chi_{4219}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{214}{703}\right)\)	\(e\left(\frac{505}{703}\right)\)	\(e\left(\frac{428}{703}\right)\)	\(e\left(\frac{500}{703}\right)\)	\(e\left(\frac{16}{703}\right)\)	\(e\left(\frac{550}{703}\right)\)	\(e\left(\frac{642}{703}\right)\)	\(e\left(\frac{307}{703}\right)\)	\(e\left(\frac{11}{703}\right)\)	\(e\left(\frac{606}{703}\right)\)
\(\chi_{4219}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{703}\right)\)	\(e\left(\frac{582}{703}\right)\)	\(e\left(\frac{574}{703}\right)\)	\(e\left(\frac{618}{703}\right)\)	\(e\left(\frac{166}{703}\right)\)	\(e\left(\frac{258}{703}\right)\)	\(e\left(\frac{158}{703}\right)\)	\(e\left(\frac{461}{703}\right)\)	\(e\left(\frac{202}{703}\right)\)	\(e\left(\frac{136}{703}\right)\)
\(\chi_{4219}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{84}{703}\right)\)	\(e\left(\frac{599}{703}\right)\)	\(e\left(\frac{168}{703}\right)\)	\(e\left(\frac{78}{703}\right)\)	\(e\left(\frac{683}{703}\right)\)	\(e\left(\frac{367}{703}\right)\)	\(e\left(\frac{252}{703}\right)\)	\(e\left(\frac{495}{703}\right)\)	\(e\left(\frac{162}{703}\right)\)	\(e\left(\frac{297}{703}\right)\)
\(\chi_{4219}(28,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{234}{703}\right)\)	\(e\left(\frac{112}{703}\right)\)	\(e\left(\frac{468}{703}\right)\)	\(e\left(\frac{619}{703}\right)\)	\(e\left(\frac{346}{703}\right)\)	\(e\left(\frac{470}{703}\right)\)	\(e\left(\frac{702}{703}\right)\)	\(e\left(\frac{224}{703}\right)\)	\(e\left(\frac{150}{703}\right)\)	\(e\left(\frac{275}{703}\right)\)
\(\chi_{4219}(30,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{572}{703}\right)\)	\(e\left(\frac{430}{703}\right)\)	\(e\left(\frac{441}{703}\right)\)	\(e\left(\frac{29}{703}\right)\)	\(e\left(\frac{299}{703}\right)\)	\(e\left(\frac{524}{703}\right)\)	\(e\left(\frac{310}{703}\right)\)	\(e\left(\frac{157}{703}\right)\)	\(e\left(\frac{601}{703}\right)\)	\(e\left(\frac{516}{703}\right)\)
\(\chi_{4219}(34,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{703}\right)\)	\(e\left(\frac{403}{703}\right)\)	\(e\left(\frac{52}{703}\right)\)	\(e\left(\frac{225}{703}\right)\)	\(e\left(\frac{429}{703}\right)\)	\(e\left(\frac{599}{703}\right)\)	\(e\left(\frac{78}{703}\right)\)	\(e\left(\frac{103}{703}\right)\)	\(e\left(\frac{251}{703}\right)\)	\(e\left(\frac{343}{703}\right)\)
\(\chi_{4219}(36,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{357}{703}\right)\)	\(e\left(\frac{261}{703}\right)\)	\(e\left(\frac{11}{703}\right)\)	\(e\left(\frac{683}{703}\right)\)	\(e\left(\frac{618}{703}\right)\)	\(e\left(\frac{681}{703}\right)\)	\(e\left(\frac{368}{703}\right)\)	\(e\left(\frac{522}{703}\right)\)	\(e\left(\frac{337}{703}\right)\)	\(e\left(\frac{32}{703}\right)\)
\(\chi_{4219}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{703}\right)\)	\(e\left(\frac{434}{703}\right)\)	\(e\left(\frac{56}{703}\right)\)	\(e\left(\frac{26}{703}\right)\)	\(e\left(\frac{462}{703}\right)\)	\(e\left(\frac{591}{703}\right)\)	\(e\left(\frac{84}{703}\right)\)	\(e\left(\frac{165}{703}\right)\)	\(e\left(\frac{54}{703}\right)\)	\(e\left(\frac{99}{703}\right)\)
\(\chi_{4219}(55,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{256}{703}\right)\)	\(e\left(\frac{453}{703}\right)\)	\(e\left(\frac{512}{703}\right)\)	\(e\left(\frac{539}{703}\right)\)	\(e\left(\frac{6}{703}\right)\)	\(e\left(\frac{382}{703}\right)\)	\(e\left(\frac{65}{703}\right)\)	\(e\left(\frac{203}{703}\right)\)	\(e\left(\frac{92}{703}\right)\)	\(e\left(\frac{403}{703}\right)\)
\(\chi_{4219}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{703}\right)\)	\(e\left(\frac{367}{703}\right)\)	\(e\left(\frac{2}{703}\right)\)	\(e\left(\frac{252}{703}\right)\)	\(e\left(\frac{368}{703}\right)\)	\(e\left(\frac{699}{703}\right)\)	\(e\left(\frac{3}{703}\right)\)	\(e\left(\frac{31}{703}\right)\)	\(e\left(\frac{253}{703}\right)\)	\(e\left(\frac{581}{703}\right)\)
\(\chi_{4219}(66,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{703}\right)\)	\(e\left(\frac{284}{703}\right)\)	\(e\left(\frac{82}{703}\right)\)	\(e\left(\frac{490}{703}\right)\)	\(e\left(\frac{325}{703}\right)\)	\(e\left(\frac{539}{703}\right)\)	\(e\left(\frac{123}{703}\right)\)	\(e\left(\frac{568}{703}\right)\)	\(e\left(\frac{531}{703}\right)\)	\(e\left(\frac{622}{703}\right)\)
\(\chi_{4219}(87,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{450}{703}\right)\)	\(e\left(\frac{648}{703}\right)\)	\(e\left(\frac{197}{703}\right)\)	\(e\left(\frac{217}{703}\right)\)	\(e\left(\frac{395}{703}\right)\)	\(e\left(\frac{309}{703}\right)\)	\(e\left(\frac{647}{703}\right)\)	\(e\left(\frac{593}{703}\right)\)	\(e\left(\frac{667}{703}\right)\)	\(e\left(\frac{637}{703}\right)\)
\(\chi_{4219}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{703}\right)\)	\(e\left(\frac{55}{703}\right)\)	\(e\left(\frac{506}{703}\right)\)	\(e\left(\frac{486}{703}\right)\)	\(e\left(\frac{308}{703}\right)\)	\(e\left(\frac{394}{703}\right)\)	\(e\left(\frac{56}{703}\right)\)	\(e\left(\frac{110}{703}\right)\)	\(e\left(\frac{36}{703}\right)\)	\(e\left(\frac{66}{703}\right)\)
\(\chi_{4219}(104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{575}{703}\right)\)	\(e\left(\frac{125}{703}\right)\)	\(e\left(\frac{447}{703}\right)\)	\(e\left(\frac{82}{703}\right)\)	\(e\left(\frac{700}{703}\right)\)	\(e\left(\frac{512}{703}\right)\)	\(e\left(\frac{319}{703}\right)\)	\(e\left(\frac{250}{703}\right)\)	\(e\left(\frac{657}{703}\right)\)	\(e\left(\frac{150}{703}\right)\)
\(\chi_{4219}(106,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{703}\right)\)	\(e\left(\frac{279}{703}\right)\)	\(e\left(\frac{36}{703}\right)\)	\(e\left(\frac{318}{703}\right)\)	\(e\left(\frac{297}{703}\right)\)	\(e\left(\frac{631}{703}\right)\)	\(e\left(\frac{54}{703}\right)\)	\(e\left(\frac{558}{703}\right)\)	\(e\left(\frac{336}{703}\right)\)	\(e\left(\frac{616}{703}\right)\)
\(\chi_{4219}(115,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{329}{703}\right)\)	\(e\left(\frac{530}{703}\right)\)	\(e\left(\frac{658}{703}\right)\)	\(e\left(\frac{657}{703}\right)\)	\(e\left(\frac{156}{703}\right)\)	\(e\left(\frac{90}{703}\right)\)	\(e\left(\frac{284}{703}\right)\)	\(e\left(\frac{357}{703}\right)\)	\(e\left(\frac{283}{703}\right)\)	\(e\left(\frac{636}{703}\right)\)
\(\chi_{4219}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{428}{703}\right)\)	\(e\left(\frac{307}{703}\right)\)	\(e\left(\frac{153}{703}\right)\)	\(e\left(\frac{297}{703}\right)\)	\(e\left(\frac{32}{703}\right)\)	\(e\left(\frac{397}{703}\right)\)	\(e\left(\frac{581}{703}\right)\)	\(e\left(\frac{614}{703}\right)\)	\(e\left(\frac{22}{703}\right)\)	\(e\left(\frac{509}{703}\right)\)
\(\chi_{4219}(122,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{280}{703}\right)\)	\(e\left(\frac{122}{703}\right)\)	\(e\left(\frac{560}{703}\right)\)	\(e\left(\frac{260}{703}\right)\)	\(e\left(\frac{402}{703}\right)\)	\(e\left(\frac{286}{703}\right)\)	\(e\left(\frac{137}{703}\right)\)	\(e\left(\frac{244}{703}\right)\)	\(e\left(\frac{540}{703}\right)\)	\(e\left(\frac{287}{703}\right)\)
\(\chi_{4219}(125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{126}{703}\right)\)	\(e\left(\frac{547}{703}\right)\)	\(e\left(\frac{252}{703}\right)\)	\(e\left(\frac{117}{703}\right)\)	\(e\left(\frac{673}{703}\right)\)	\(e\left(\frac{199}{703}\right)\)	\(e\left(\frac{378}{703}\right)\)	\(e\left(\frac{391}{703}\right)\)	\(e\left(\frac{243}{703}\right)\)	\(e\left(\frac{94}{703}\right)\)
\(\chi_{4219}(134,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{703}\right)\)	\(e\left(\frac{697}{703}\right)\)	\(e\left(\frac{226}{703}\right)\)	\(e\left(\frac{356}{703}\right)\)	\(e\left(\frac{107}{703}\right)\)	\(e\left(\frac{251}{703}\right)\)	\(e\left(\frac{339}{703}\right)\)	\(e\left(\frac{691}{703}\right)\)	\(e\left(\frac{469}{703}\right)\)	\(e\left(\frac{274}{703}\right)\)
\(\chi_{4219}(137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{703}\right)\)	\(e\left(\frac{568}{703}\right)\)	\(e\left(\frac{164}{703}\right)\)	\(e\left(\frac{277}{703}\right)\)	\(e\left(\frac{650}{703}\right)\)	\(e\left(\frac{375}{703}\right)\)	\(e\left(\frac{246}{703}\right)\)	\(e\left(\frac{433}{703}\right)\)	\(e\left(\frac{359}{703}\right)\)	\(e\left(\frac{541}{703}\right)\)
\(\chi_{4219}(140,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{276}{703}\right)\)	\(e\left(\frac{60}{703}\right)\)	\(e\left(\frac{552}{703}\right)\)	\(e\left(\frac{658}{703}\right)\)	\(e\left(\frac{336}{703}\right)\)	\(e\left(\frac{302}{703}\right)\)	\(e\left(\frac{125}{703}\right)\)	\(e\left(\frac{120}{703}\right)\)	\(e\left(\frac{231}{703}\right)\)	\(e\left(\frac{72}{703}\right)\)
\(\chi_{4219}(141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{345}{703}\right)\)	\(e\left(\frac{75}{703}\right)\)	\(e\left(\frac{690}{703}\right)\)	\(e\left(\frac{471}{703}\right)\)	\(e\left(\frac{420}{703}\right)\)	\(e\left(\frac{26}{703}\right)\)	\(e\left(\frac{332}{703}\right)\)	\(e\left(\frac{150}{703}\right)\)	\(e\left(\frac{113}{703}\right)\)	\(e\left(\frac{90}{703}\right)\)
\(\chi_{4219}(150,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{614}{703}\right)\)	\(e\left(\frac{378}{703}\right)\)	\(e\left(\frac{525}{703}\right)\)	\(e\left(\frac{68}{703}\right)\)	\(e\left(\frac{289}{703}\right)\)	\(e\left(\frac{356}{703}\right)\)	\(e\left(\frac{436}{703}\right)\)	\(e\left(\frac{53}{703}\right)\)	\(e\left(\frac{682}{703}\right)\)	\(e\left(\frac{313}{703}\right)\)
\(\chi_{4219}(152,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{497}{703}\right)\)	\(e\left(\frac{322}{703}\right)\)	\(e\left(\frac{291}{703}\right)\)	\(e\left(\frac{110}{703}\right)\)	\(e\left(\frac{116}{703}\right)\)	\(e\left(\frac{121}{703}\right)\)	\(e\left(\frac{85}{703}\right)\)	\(e\left(\frac{644}{703}\right)\)	\(e\left(\frac{607}{703}\right)\)	\(e\left(\frac{527}{703}\right)\)
\(\chi_{4219}(155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{194}{703}\right)\)	\(e\left(\frac{195}{703}\right)\)	\(e\left(\frac{388}{703}\right)\)	\(e\left(\frac{381}{703}\right)\)	\(e\left(\frac{389}{703}\right)\)	\(e\left(\frac{630}{703}\right)\)	\(e\left(\frac{582}{703}\right)\)	\(e\left(\frac{390}{703}\right)\)	\(e\left(\frac{575}{703}\right)\)	\(e\left(\frac{234}{703}\right)\)
\(\chi_{4219}(164,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{527}{703}\right)\)	\(e\left(\frac{84}{703}\right)\)	\(e\left(\frac{351}{703}\right)\)	\(e\left(\frac{640}{703}\right)\)	\(e\left(\frac{611}{703}\right)\)	\(e\left(\frac{1}{703}\right)\)	\(e\left(\frac{175}{703}\right)\)	\(e\left(\frac{168}{703}\right)\)	\(e\left(\frac{464}{703}\right)\)	\(e\left(\frac{382}{703}\right)\)
\(\chi_{4219}(168,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{703}\right)\)	\(e\left(\frac{594}{703}\right)\)	\(e\left(\frac{122}{703}\right)\)	\(e\left(\frac{609}{703}\right)\)	\(e\left(\frac{655}{703}\right)\)	\(e\left(\frac{459}{703}\right)\)	\(e\left(\frac{183}{703}\right)\)	\(e\left(\frac{485}{703}\right)\)	\(e\left(\frac{670}{703}\right)\)	\(e\left(\frac{291}{703}\right)\)
\(\chi_{4219}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{446}{703}\right)\)	\(e\left(\frac{586}{703}\right)\)	\(e\left(\frac{189}{703}\right)\)	\(e\left(\frac{615}{703}\right)\)	\(e\left(\frac{329}{703}\right)\)	\(e\left(\frac{325}{703}\right)\)	\(e\left(\frac{635}{703}\right)\)	\(e\left(\frac{469}{703}\right)\)	\(e\left(\frac{358}{703}\right)\)	\(e\left(\frac{422}{703}\right)\)

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First 31 of 648 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	4219.m
Modulus	$4219$
Conductor	$4219$
Order	$703$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(4219\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(4219\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(703\)	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:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);