LMFDB - Dirichlet character orbit 6427.bc

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6427, base_ring=CyclotomicField(2142)) M = H._module chi = DirichletCharacter(H, M([1472])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(4, 6427)) 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("6427.4"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$6427$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$6427$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$1071$	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:	$\Q(\zeta_{1071})$
Fixed field:	Number field defined by a degree 1071 polynomial (not computed)

First 31 of 576 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{6427}(4,\cdot)$	$1$	$1$	$e\left(\frac{127}{357}\right)$	$e\left(\frac{736}{1071}\right)$	$e\left(\frac{254}{357}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{46}{1071}\right)$	$e\left(\frac{26}{153}\right)$	$e\left(\frac{8}{119}\right)$	$e\left(\frac{401}{1071}\right)$	$e\left(\frac{344}{357}\right)$	$e\left(\frac{55}{63}\right)$
$\chi_{6427}(10,\cdot)$	$1$	$1$	$e\left(\frac{172}{357}\right)$	$e\left(\frac{235}{1071}\right)$	$e\left(\frac{344}{357}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{751}{1071}\right)$	$e\left(\frac{32}{153}\right)$	$e\left(\frac{53}{119}\right)$	$e\left(\frac{470}{1071}\right)$	$e\left(\frac{137}{357}\right)$	$e\left(\frac{31}{63}\right)$
$\chi_{6427}(16,\cdot)$	$1$	$1$	$e\left(\frac{254}{357}\right)$	$e\left(\frac{401}{1071}\right)$	$e\left(\frac{151}{357}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{92}{1071}\right)$	$e\left(\frac{52}{153}\right)$	$e\left(\frac{16}{119}\right)$	$e\left(\frac{802}{1071}\right)$	$e\left(\frac{331}{357}\right)$	$e\left(\frac{47}{63}\right)$
$\chi_{6427}(23,\cdot)$	$1$	$1$	$e\left(\frac{244}{357}\right)$	$e\left(\frac{790}{1071}\right)$	$e\left(\frac{131}{357}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{451}{1071}\right)$	$e\left(\frac{62}{153}\right)$	$e\left(\frac{6}{119}\right)$	$e\left(\frac{509}{1071}\right)$	$e\left(\frac{20}{357}\right)$	$e\left(\frac{1}{63}\right)$
$\chi_{6427}(33,\cdot)$	$1$	$1$	$e\left(\frac{100}{357}\right)$	$e\left(\frac{37}{1071}\right)$	$e\left(\frac{200}{357}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{337}{1071}\right)$	$e\left(\frac{104}{153}\right)$	$e\left(\frac{100}{119}\right)$	$e\left(\frac{74}{1071}\right)$	$e\left(\frac{254}{357}\right)$	$e\left(\frac{40}{63}\right)$
$\chi_{6427}(40,\cdot)$	$1$	$1$	$e\left(\frac{299}{357}\right)$	$e\left(\frac{971}{1071}\right)$	$e\left(\frac{241}{357}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{797}{1071}\right)$	$e\left(\frac{58}{153}\right)$	$e\left(\frac{61}{119}\right)$	$e\left(\frac{871}{1071}\right)$	$e\left(\frac{124}{357}\right)$	$e\left(\frac{23}{63}\right)$
$\chi_{6427}(54,\cdot)$	$1$	$1$	$e\left(\frac{253}{357}\right)$	$e\left(\frac{904}{1071}\right)$	$e\left(\frac{149}{357}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{592}{1071}\right)$	$e\left(\frac{2}{153}\right)$	$e\left(\frac{15}{119}\right)$	$e\left(\frac{737}{1071}\right)$	$e\left(\frac{50}{357}\right)$	$e\left(\frac{34}{63}\right)$
$\chi_{6427}(57,\cdot)$	$1$	$1$	$e\left(\frac{92}{357}\right)$	$e\left(\frac{848}{1071}\right)$	$e\left(\frac{184}{357}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{53}{1071}\right)$	$e\left(\frac{10}{153}\right)$	$e\left(\frac{92}{119}\right)$	$e\left(\frac{625}{1071}\right)$	$e\left(\frac{148}{357}\right)$	$e\left(\frac{62}{63}\right)$
$\chi_{6427}(87,\cdot)$	$1$	$1$	$e\left(\frac{320}{357}\right)$	$e\left(\frac{47}{1071}\right)$	$e\left(\frac{283}{357}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{1007}{1071}\right)$	$e\left(\frac{37}{153}\right)$	$e\left(\frac{82}{119}\right)$	$e\left(\frac{94}{1071}\right)$	$e\left(\frac{313}{357}\right)$	$e\left(\frac{44}{63}\right)$
$\chi_{6427}(97,\cdot)$	$1$	$1$	$e\left(\frac{232}{357}\right)$	$e\left(\frac{400}{1071}\right)$	$e\left(\frac{107}{357}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{25}{1071}\right)$	$e\left(\frac{74}{153}\right)$	$e\left(\frac{113}{119}\right)$	$e\left(\frac{800}{1071}\right)$	$e\left(\frac{218}{357}\right)$	$e\left(\frac{34}{63}\right)$
$\chi_{6427}(100,\cdot)$	$1$	$1$	$e\left(\frac{344}{357}\right)$	$e\left(\frac{470}{1071}\right)$	$e\left(\frac{331}{357}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{431}{1071}\right)$	$e\left(\frac{64}{153}\right)$	$e\left(\frac{106}{119}\right)$	$e\left(\frac{940}{1071}\right)$	$e\left(\frac{274}{357}\right)$	$e\left(\frac{62}{63}\right)$
$\chi_{6427}(132,\cdot)$	$1$	$1$	$e\left(\frac{227}{357}\right)$	$e\left(\frac{773}{1071}\right)$	$e\left(\frac{97}{357}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{383}{1071}\right)$	$e\left(\frac{130}{153}\right)$	$e\left(\frac{108}{119}\right)$	$e\left(\frac{475}{1071}\right)$	$e\left(\frac{241}{357}\right)$	$e\left(\frac{32}{63}\right)$
$\chi_{6427}(135,\cdot)$	$1$	$1$	$e\left(\frac{298}{357}\right)$	$e\left(\frac{403}{1071}\right)$	$e\left(\frac{239}{357}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{226}{1071}\right)$	$e\left(\frac{8}{153}\right)$	$e\left(\frac{60}{119}\right)$	$e\left(\frac{806}{1071}\right)$	$e\left(\frac{200}{357}\right)$	$e\left(\frac{10}{63}\right)$
$\chi_{6427}(139,\cdot)$	$1$	$1$	$e\left(\frac{328}{357}\right)$	$e\left(\frac{1021}{1071}\right)$	$e\left(\frac{299}{357}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{934}{1071}\right)$	$e\left(\frac{29}{153}\right)$	$e\left(\frac{90}{119}\right)$	$e\left(\frac{971}{1071}\right)$	$e\left(\frac{62}{357}\right)$	$e\left(\frac{43}{63}\right)$
$\chi_{6427}(142,\cdot)$	$1$	$1$	$e\left(\frac{311}{357}\right)$	$e\left(\frac{290}{1071}\right)$	$e\left(\frac{265}{357}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{152}{1071}\right)$	$e\left(\frac{46}{153}\right)$	$e\left(\frac{73}{119}\right)$	$e\left(\frac{580}{1071}\right)$	$e\left(\frac{283}{357}\right)$	$e\left(\frac{53}{63}\right)$
$\chi_{6427}(153,\cdot)$	$1$	$1$	$e\left(\frac{319}{357}\right)$	$e\left(\frac{193}{1071}\right)$	$e\left(\frac{281}{357}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{79}{1071}\right)$	$e\left(\frac{38}{153}\right)$	$e\left(\frac{81}{119}\right)$	$e\left(\frac{386}{1071}\right)$	$e\left(\frac{32}{357}\right)$	$e\left(\frac{52}{63}\right)$
$\chi_{6427}(156,\cdot)$	$1$	$1$	$e\left(\frac{109}{357}\right)$	$e\left(\frac{865}{1071}\right)$	$e\left(\frac{218}{357}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{121}{1071}\right)$	$e\left(\frac{95}{153}\right)$	$e\left(\frac{109}{119}\right)$	$e\left(\frac{659}{1071}\right)$	$e\left(\frac{284}{357}\right)$	$e\left(\frac{31}{63}\right)$
$\chi_{6427}(178,\cdot)$	$1$	$1$	$e\left(\frac{311}{357}\right)$	$e\left(\frac{647}{1071}\right)$	$e\left(\frac{265}{357}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{509}{1071}\right)$	$e\left(\frac{148}{153}\right)$	$e\left(\frac{73}{119}\right)$	$e\left(\frac{223}{1071}\right)$	$e\left(\frac{283}{357}\right)$	$e\left(\frac{32}{63}\right)$
$\chi_{6427}(201,\cdot)$	$1$	$1$	$e\left(\frac{148}{357}\right)$	$e\left(\frac{169}{1071}\right)$	$e\left(\frac{296}{357}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{613}{1071}\right)$	$e\left(\frac{107}{153}\right)$	$e\left(\frac{29}{119}\right)$	$e\left(\frac{338}{1071}\right)$	$e\left(\frac{176}{357}\right)$	$e\left(\frac{55}{63}\right)$
$\chi_{6427}(206,\cdot)$	$1$	$1$	$e\left(\frac{248}{357}\right)$	$e\left(\frac{206}{1071}\right)$	$e\left(\frac{139}{357}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{950}{1071}\right)$	$e\left(\frac{58}{153}\right)$	$e\left(\frac{10}{119}\right)$	$e\left(\frac{412}{1071}\right)$	$e\left(\frac{73}{357}\right)$	$e\left(\frac{32}{63}\right)$
$\chi_{6427}(210,\cdot)$	$1$	$1$	$e\left(\frac{325}{357}\right)$	$e\left(\frac{745}{1071}\right)$	$e\left(\frac{293}{357}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{649}{1071}\right)$	$e\left(\frac{134}{153}\right)$	$e\left(\frac{87}{119}\right)$	$e\left(\frac{419}{1071}\right)$	$e\left(\frac{290}{357}\right)$	$e\left(\frac{46}{63}\right)$
$\chi_{6427}(216,\cdot)$	$1$	$1$	$e\left(\frac{23}{357}\right)$	$e\left(\frac{569}{1071}\right)$	$e\left(\frac{46}{357}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{638}{1071}\right)$	$e\left(\frac{28}{153}\right)$	$e\left(\frac{23}{119}\right)$	$e\left(\frac{67}{1071}\right)$	$e\left(\frac{37}{357}\right)$	$e\left(\frac{26}{63}\right)$
$\chi_{6427}(222,\cdot)$	$1$	$1$	$e\left(\frac{137}{357}\right)$	$e\left(\frac{1061}{1071}\right)$	$e\left(\frac{274}{357}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{401}{1071}\right)$	$e\left(\frac{67}{153}\right)$	$e\left(\frac{18}{119}\right)$	$e\left(\frac{1051}{1071}\right)$	$e\left(\frac{298}{357}\right)$	$e\left(\frac{59}{63}\right)$
$\chi_{6427}(230,\cdot)$	$1$	$1$	$e\left(\frac{59}{357}\right)$	$e\left(\frac{1025}{1071}\right)$	$e\left(\frac{118}{357}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{131}{1071}\right)$	$e\left(\frac{94}{153}\right)$	$e\left(\frac{59}{119}\right)$	$e\left(\frac{979}{1071}\right)$	$e\left(\frac{157}{357}\right)$	$e\left(\frac{32}{63}\right)$
$\chi_{6427}(238,\cdot)$	$1$	$1$	$e\left(\frac{346}{357}\right)$	$e\left(\frac{535}{1071}\right)$	$e\left(\frac{335}{357}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{502}{1071}\right)$	$e\left(\frac{11}{153}\right)$	$e\left(\frac{108}{119}\right)$	$e\left(\frac{1070}{1071}\right)$	$e\left(\frac{122}{357}\right)$	$e\left(\frac{25}{63}\right)$
$\chi_{6427}(241,\cdot)$	$1$	$1$	$e\left(\frac{173}{357}\right)$	$e\left(\frac{803}{1071}\right)$	$e\left(\frac{346}{357}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{251}{1071}\right)$	$e\left(\frac{82}{153}\right)$	$e\left(\frac{54}{119}\right)$	$e\left(\frac{535}{1071}\right)$	$e\left(\frac{61}{357}\right)$	$e\left(\frac{44}{63}\right)$
$\chi_{6427}(250,\cdot)$	$1$	$1$	$e\left(\frac{32}{357}\right)$	$e\left(\frac{1040}{1071}\right)$	$e\left(\frac{64}{357}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{65}{1071}\right)$	$e\left(\frac{70}{153}\right)$	$e\left(\frac{32}{119}\right)$	$e\left(\frac{1009}{1071}\right)$	$e\left(\frac{67}{357}\right)$	$e\left(\frac{38}{63}\right)$
$\chi_{6427}(256,\cdot)$	$1$	$1$	$e\left(\frac{151}{357}\right)$	$e\left(\frac{802}{1071}\right)$	$e\left(\frac{302}{357}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{184}{1071}\right)$	$e\left(\frac{104}{153}\right)$	$e\left(\frac{32}{119}\right)$	$e\left(\frac{533}{1071}\right)$	$e\left(\frac{305}{357}\right)$	$e\left(\frac{31}{63}\right)$
$\chi_{6427}(257,\cdot)$	$1$	$1$	$e\left(\frac{25}{357}\right)$	$e\left(\frac{634}{1071}\right)$	$e\left(\frac{50}{357}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{709}{1071}\right)$	$e\left(\frac{128}{153}\right)$	$e\left(\frac{25}{119}\right)$	$e\left(\frac{197}{1071}\right)$	$e\left(\frac{242}{357}\right)$	$e\left(\frac{52}{63}\right)$
$\chi_{6427}(271,\cdot)$	$1$	$1$	$e\left(\frac{230}{357}\right)$	$e\left(\frac{1049}{1071}\right)$	$e\left(\frac{103}{357}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{668}{1071}\right)$	$e\left(\frac{25}{153}\right)$	$e\left(\frac{111}{119}\right)$	$e\left(\frac{1027}{1071}\right)$	$e\left(\frac{13}{357}\right)$	$e\left(\frac{29}{63}\right)$
$\chi_{6427}(274,\cdot)$	$1$	$1$	$e\left(\frac{260}{357}\right)$	$e\left(\frac{953}{1071}\right)$	$e\left(\frac{163}{357}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{662}{1071}\right)$	$e\left(\frac{148}{153}\right)$	$e\left(\frac{22}{119}\right)$	$e\left(\frac{835}{1071}\right)$	$e\left(\frac{232}{357}\right)$	$e\left(\frac{41}{63}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{6427}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{357}\right)\)	\(e\left(\frac{736}{1071}\right)\)	\(e\left(\frac{254}{357}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{46}{1071}\right)\)	\(e\left(\frac{26}{153}\right)\)	\(e\left(\frac{8}{119}\right)\)	\(e\left(\frac{401}{1071}\right)\)	\(e\left(\frac{344}{357}\right)\)	\(e\left(\frac{55}{63}\right)\)
\(\chi_{6427}(10,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{172}{357}\right)\)	\(e\left(\frac{235}{1071}\right)\)	\(e\left(\frac{344}{357}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{751}{1071}\right)\)	\(e\left(\frac{32}{153}\right)\)	\(e\left(\frac{53}{119}\right)\)	\(e\left(\frac{470}{1071}\right)\)	\(e\left(\frac{137}{357}\right)\)	\(e\left(\frac{31}{63}\right)\)
\(\chi_{6427}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{254}{357}\right)\)	\(e\left(\frac{401}{1071}\right)\)	\(e\left(\frac{151}{357}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{92}{1071}\right)\)	\(e\left(\frac{52}{153}\right)\)	\(e\left(\frac{16}{119}\right)\)	\(e\left(\frac{802}{1071}\right)\)	\(e\left(\frac{331}{357}\right)\)	\(e\left(\frac{47}{63}\right)\)
\(\chi_{6427}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{244}{357}\right)\)	\(e\left(\frac{790}{1071}\right)\)	\(e\left(\frac{131}{357}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{451}{1071}\right)\)	\(e\left(\frac{62}{153}\right)\)	\(e\left(\frac{6}{119}\right)\)	\(e\left(\frac{509}{1071}\right)\)	\(e\left(\frac{20}{357}\right)\)	\(e\left(\frac{1}{63}\right)\)
\(\chi_{6427}(33,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{100}{357}\right)\)	\(e\left(\frac{37}{1071}\right)\)	\(e\left(\frac{200}{357}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{337}{1071}\right)\)	\(e\left(\frac{104}{153}\right)\)	\(e\left(\frac{100}{119}\right)\)	\(e\left(\frac{74}{1071}\right)\)	\(e\left(\frac{254}{357}\right)\)	\(e\left(\frac{40}{63}\right)\)
\(\chi_{6427}(40,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{299}{357}\right)\)	\(e\left(\frac{971}{1071}\right)\)	\(e\left(\frac{241}{357}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{797}{1071}\right)\)	\(e\left(\frac{58}{153}\right)\)	\(e\left(\frac{61}{119}\right)\)	\(e\left(\frac{871}{1071}\right)\)	\(e\left(\frac{124}{357}\right)\)	\(e\left(\frac{23}{63}\right)\)
\(\chi_{6427}(54,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{357}\right)\)	\(e\left(\frac{904}{1071}\right)\)	\(e\left(\frac{149}{357}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{592}{1071}\right)\)	\(e\left(\frac{2}{153}\right)\)	\(e\left(\frac{15}{119}\right)\)	\(e\left(\frac{737}{1071}\right)\)	\(e\left(\frac{50}{357}\right)\)	\(e\left(\frac{34}{63}\right)\)
\(\chi_{6427}(57,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{357}\right)\)	\(e\left(\frac{848}{1071}\right)\)	\(e\left(\frac{184}{357}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{53}{1071}\right)\)	\(e\left(\frac{10}{153}\right)\)	\(e\left(\frac{92}{119}\right)\)	\(e\left(\frac{625}{1071}\right)\)	\(e\left(\frac{148}{357}\right)\)	\(e\left(\frac{62}{63}\right)\)
\(\chi_{6427}(87,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{320}{357}\right)\)	\(e\left(\frac{47}{1071}\right)\)	\(e\left(\frac{283}{357}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{1007}{1071}\right)\)	\(e\left(\frac{37}{153}\right)\)	\(e\left(\frac{82}{119}\right)\)	\(e\left(\frac{94}{1071}\right)\)	\(e\left(\frac{313}{357}\right)\)	\(e\left(\frac{44}{63}\right)\)
\(\chi_{6427}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{232}{357}\right)\)	\(e\left(\frac{400}{1071}\right)\)	\(e\left(\frac{107}{357}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{25}{1071}\right)\)	\(e\left(\frac{74}{153}\right)\)	\(e\left(\frac{113}{119}\right)\)	\(e\left(\frac{800}{1071}\right)\)	\(e\left(\frac{218}{357}\right)\)	\(e\left(\frac{34}{63}\right)\)
\(\chi_{6427}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{344}{357}\right)\)	\(e\left(\frac{470}{1071}\right)\)	\(e\left(\frac{331}{357}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{431}{1071}\right)\)	\(e\left(\frac{64}{153}\right)\)	\(e\left(\frac{106}{119}\right)\)	\(e\left(\frac{940}{1071}\right)\)	\(e\left(\frac{274}{357}\right)\)	\(e\left(\frac{62}{63}\right)\)
\(\chi_{6427}(132,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{357}\right)\)	\(e\left(\frac{773}{1071}\right)\)	\(e\left(\frac{97}{357}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{383}{1071}\right)\)	\(e\left(\frac{130}{153}\right)\)	\(e\left(\frac{108}{119}\right)\)	\(e\left(\frac{475}{1071}\right)\)	\(e\left(\frac{241}{357}\right)\)	\(e\left(\frac{32}{63}\right)\)
\(\chi_{6427}(135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{298}{357}\right)\)	\(e\left(\frac{403}{1071}\right)\)	\(e\left(\frac{239}{357}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{226}{1071}\right)\)	\(e\left(\frac{8}{153}\right)\)	\(e\left(\frac{60}{119}\right)\)	\(e\left(\frac{806}{1071}\right)\)	\(e\left(\frac{200}{357}\right)\)	\(e\left(\frac{10}{63}\right)\)
\(\chi_{6427}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{328}{357}\right)\)	\(e\left(\frac{1021}{1071}\right)\)	\(e\left(\frac{299}{357}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{934}{1071}\right)\)	\(e\left(\frac{29}{153}\right)\)	\(e\left(\frac{90}{119}\right)\)	\(e\left(\frac{971}{1071}\right)\)	\(e\left(\frac{62}{357}\right)\)	\(e\left(\frac{43}{63}\right)\)
\(\chi_{6427}(142,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{357}\right)\)	\(e\left(\frac{290}{1071}\right)\)	\(e\left(\frac{265}{357}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{152}{1071}\right)\)	\(e\left(\frac{46}{153}\right)\)	\(e\left(\frac{73}{119}\right)\)	\(e\left(\frac{580}{1071}\right)\)	\(e\left(\frac{283}{357}\right)\)	\(e\left(\frac{53}{63}\right)\)
\(\chi_{6427}(153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{319}{357}\right)\)	\(e\left(\frac{193}{1071}\right)\)	\(e\left(\frac{281}{357}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{79}{1071}\right)\)	\(e\left(\frac{38}{153}\right)\)	\(e\left(\frac{81}{119}\right)\)	\(e\left(\frac{386}{1071}\right)\)	\(e\left(\frac{32}{357}\right)\)	\(e\left(\frac{52}{63}\right)\)
\(\chi_{6427}(156,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{357}\right)\)	\(e\left(\frac{865}{1071}\right)\)	\(e\left(\frac{218}{357}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{121}{1071}\right)\)	\(e\left(\frac{95}{153}\right)\)	\(e\left(\frac{109}{119}\right)\)	\(e\left(\frac{659}{1071}\right)\)	\(e\left(\frac{284}{357}\right)\)	\(e\left(\frac{31}{63}\right)\)
\(\chi_{6427}(178,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{357}\right)\)	\(e\left(\frac{647}{1071}\right)\)	\(e\left(\frac{265}{357}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{509}{1071}\right)\)	\(e\left(\frac{148}{153}\right)\)	\(e\left(\frac{73}{119}\right)\)	\(e\left(\frac{223}{1071}\right)\)	\(e\left(\frac{283}{357}\right)\)	\(e\left(\frac{32}{63}\right)\)
\(\chi_{6427}(201,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{357}\right)\)	\(e\left(\frac{169}{1071}\right)\)	\(e\left(\frac{296}{357}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{613}{1071}\right)\)	\(e\left(\frac{107}{153}\right)\)	\(e\left(\frac{29}{119}\right)\)	\(e\left(\frac{338}{1071}\right)\)	\(e\left(\frac{176}{357}\right)\)	\(e\left(\frac{55}{63}\right)\)
\(\chi_{6427}(206,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{248}{357}\right)\)	\(e\left(\frac{206}{1071}\right)\)	\(e\left(\frac{139}{357}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{950}{1071}\right)\)	\(e\left(\frac{58}{153}\right)\)	\(e\left(\frac{10}{119}\right)\)	\(e\left(\frac{412}{1071}\right)\)	\(e\left(\frac{73}{357}\right)\)	\(e\left(\frac{32}{63}\right)\)
\(\chi_{6427}(210,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{325}{357}\right)\)	\(e\left(\frac{745}{1071}\right)\)	\(e\left(\frac{293}{357}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{649}{1071}\right)\)	\(e\left(\frac{134}{153}\right)\)	\(e\left(\frac{87}{119}\right)\)	\(e\left(\frac{419}{1071}\right)\)	\(e\left(\frac{290}{357}\right)\)	\(e\left(\frac{46}{63}\right)\)
\(\chi_{6427}(216,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{357}\right)\)	\(e\left(\frac{569}{1071}\right)\)	\(e\left(\frac{46}{357}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{638}{1071}\right)\)	\(e\left(\frac{28}{153}\right)\)	\(e\left(\frac{23}{119}\right)\)	\(e\left(\frac{67}{1071}\right)\)	\(e\left(\frac{37}{357}\right)\)	\(e\left(\frac{26}{63}\right)\)
\(\chi_{6427}(222,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{357}\right)\)	\(e\left(\frac{1061}{1071}\right)\)	\(e\left(\frac{274}{357}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{401}{1071}\right)\)	\(e\left(\frac{67}{153}\right)\)	\(e\left(\frac{18}{119}\right)\)	\(e\left(\frac{1051}{1071}\right)\)	\(e\left(\frac{298}{357}\right)\)	\(e\left(\frac{59}{63}\right)\)
\(\chi_{6427}(230,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{357}\right)\)	\(e\left(\frac{1025}{1071}\right)\)	\(e\left(\frac{118}{357}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{131}{1071}\right)\)	\(e\left(\frac{94}{153}\right)\)	\(e\left(\frac{59}{119}\right)\)	\(e\left(\frac{979}{1071}\right)\)	\(e\left(\frac{157}{357}\right)\)	\(e\left(\frac{32}{63}\right)\)
\(\chi_{6427}(238,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{346}{357}\right)\)	\(e\left(\frac{535}{1071}\right)\)	\(e\left(\frac{335}{357}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{502}{1071}\right)\)	\(e\left(\frac{11}{153}\right)\)	\(e\left(\frac{108}{119}\right)\)	\(e\left(\frac{1070}{1071}\right)\)	\(e\left(\frac{122}{357}\right)\)	\(e\left(\frac{25}{63}\right)\)
\(\chi_{6427}(241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{357}\right)\)	\(e\left(\frac{803}{1071}\right)\)	\(e\left(\frac{346}{357}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{251}{1071}\right)\)	\(e\left(\frac{82}{153}\right)\)	\(e\left(\frac{54}{119}\right)\)	\(e\left(\frac{535}{1071}\right)\)	\(e\left(\frac{61}{357}\right)\)	\(e\left(\frac{44}{63}\right)\)
\(\chi_{6427}(250,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{357}\right)\)	\(e\left(\frac{1040}{1071}\right)\)	\(e\left(\frac{64}{357}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{65}{1071}\right)\)	\(e\left(\frac{70}{153}\right)\)	\(e\left(\frac{32}{119}\right)\)	\(e\left(\frac{1009}{1071}\right)\)	\(e\left(\frac{67}{357}\right)\)	\(e\left(\frac{38}{63}\right)\)
\(\chi_{6427}(256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{357}\right)\)	\(e\left(\frac{802}{1071}\right)\)	\(e\left(\frac{302}{357}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{184}{1071}\right)\)	\(e\left(\frac{104}{153}\right)\)	\(e\left(\frac{32}{119}\right)\)	\(e\left(\frac{533}{1071}\right)\)	\(e\left(\frac{305}{357}\right)\)	\(e\left(\frac{31}{63}\right)\)
\(\chi_{6427}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{357}\right)\)	\(e\left(\frac{634}{1071}\right)\)	\(e\left(\frac{50}{357}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{709}{1071}\right)\)	\(e\left(\frac{128}{153}\right)\)	\(e\left(\frac{25}{119}\right)\)	\(e\left(\frac{197}{1071}\right)\)	\(e\left(\frac{242}{357}\right)\)	\(e\left(\frac{52}{63}\right)\)
\(\chi_{6427}(271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{230}{357}\right)\)	\(e\left(\frac{1049}{1071}\right)\)	\(e\left(\frac{103}{357}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{668}{1071}\right)\)	\(e\left(\frac{25}{153}\right)\)	\(e\left(\frac{111}{119}\right)\)	\(e\left(\frac{1027}{1071}\right)\)	\(e\left(\frac{13}{357}\right)\)	\(e\left(\frac{29}{63}\right)\)
\(\chi_{6427}(274,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{260}{357}\right)\)	\(e\left(\frac{953}{1071}\right)\)	\(e\left(\frac{163}{357}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{662}{1071}\right)\)	\(e\left(\frac{148}{153}\right)\)	\(e\left(\frac{22}{119}\right)\)	\(e\left(\frac{835}{1071}\right)\)	\(e\left(\frac{232}{357}\right)\)	\(e\left(\frac{41}{63}\right)\)

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First 31 of 576 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	6427.bc
Modulus	$6427$
Conductor	$6427$
Order	$1071$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(6427\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(6427\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(1071\)	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);