LMFDB - Dirichlet character orbit 8007.fe

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8007, base_ring=CyclotomicField(312)) M = H._module chi = DirichletCharacter(H, M([156,39,22])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(26,8007)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8007$
Conductor:	$8007$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$312$	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:	$\Q(\zeta_{312})$
Fixed field:	Number field defined by a degree 312 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{8007}(26,\cdot)$	$1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{61}{312}\right)$	$e\left(\frac{77}{104}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{121}{312}\right)$	$e\left(\frac{109}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{8007}(77,\cdot)$	$1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{77}{312}\right)$	$e\left(\frac{29}{104}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{209}{312}\right)$	$e\left(\frac{245}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{73}{104}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{8007}(104,\cdot)$	$1$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{235}{312}\right)$	$e\left(\frac{75}{104}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{103}{312}\right)$	$e\left(\frac{67}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{104}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{8007}(308,\cdot)$	$1$	$1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{251}{312}\right)$	$e\left(\frac{27}{104}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{191}{312}\right)$	$e\left(\frac{203}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{8007}(338,\cdot)$	$1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{191}{312}\right)$	$e\left(\frac{103}{104}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{251}{312}\right)$	$e\left(\frac{239}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{104}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{8007}(416,\cdot)$	$1$	$1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{97}{312}\right)$	$e\left(\frac{73}{104}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{85}{312}\right)$	$e\left(\frac{25}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{69}{104}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{8007}(791,\cdot)$	$1$	$1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{173}{312}\right)$	$e\left(\frac{53}{104}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{113}{312}\right)$	$e\left(\frac{125}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{33}{104}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{8007}(995,\cdot)$	$1$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{157}{312}\right)$	$e\left(\frac{101}{104}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{25}{312}\right)$	$e\left(\frac{301}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{57}{104}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{8007}(1022,\cdot)$	$1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{155}{312}\right)$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{287}{312}\right)$	$e\left(\frac{11}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{104}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{8007}(1073,\cdot)$	$1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{139}{312}\right)$	$e\left(\frac{51}{104}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{199}{312}\right)$	$e\left(\frac{187}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{71}{104}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{8007}(1154,\cdot)$	$1$	$1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{175}{312}\right)$	$e\left(\frac{47}{104}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{163}{312}\right)$	$e\left(\frac{103}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{43}{104}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{8007}(1232,\cdot)$	$1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{113}{312}\right)$	$e\left(\frac{25}{104}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{173}{312}\right)$	$e\left(\frac{161}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{45}{104}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{8007}(1277,\cdot)$	$1$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{107}{312}\right)$	$e\left(\frac{43}{104}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{23}{312}\right)$	$e\left(\frac{227}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{15}{104}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{8007}(1352,\cdot)$	$1$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{53}{312}\right)$	$e\left(\frac{101}{104}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{233}{312}\right)$	$e\left(\frac{197}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{57}{104}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{8007}(1613,\cdot)$	$1$	$1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{31}{312}\right)$	$e\left(\frac{63}{104}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{307}{312}\right)$	$e\left(\frac{127}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{51}{104}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{8007}(1658,\cdot)$	$1$	$1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{5}{312}\right)$	$e\left(\frac{37}{104}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{281}{312}\right)$	$e\left(\frac{101}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{104}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{8007}(1664,\cdot)$	$1$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{271}{312}\right)$	$e\left(\frac{71}{104}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{67}{312}\right)$	$e\left(\frac{295}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{8007}(1709,\cdot)$	$1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{181}{312}\right)$	$e\left(\frac{29}{104}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{1}{312}\right)$	$e\left(\frac{37}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{73}{104}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{8007}(1742,\cdot)$	$1$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{49}{312}\right)$	$e\left(\frac{9}{104}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{133}{312}\right)$	$e\left(\frac{241}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{104}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{8007}(1787,\cdot)$	$1$	$1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{67}{312}\right)$	$e\left(\frac{59}{104}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{271}{312}\right)$	$e\left(\frac{43}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{104}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{8007}(1793,\cdot)$	$1$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{73}{312}\right)$	$e\left(\frac{41}{104}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{109}{312}\right)$	$e\left(\frac{289}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{104}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{8007}(1811,\cdot)$	$1$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{125}{312}\right)$	$e\left(\frac{93}{104}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{161}{312}\right)$	$e\left(\frac{29}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{104}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{8007}(1889,\cdot)$	$1$	$1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{275}{312}\right)$	$e\left(\frac{59}{104}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{167}{312}\right)$	$e\left(\frac{251}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{104}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{8007}(1946,\cdot)$	$1$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{289}{312}\right)$	$e\left(\frac{17}{104}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{205}{312}\right)$	$e\left(\frac{97}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{93}{104}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{8007}(2021,\cdot)$	$1$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{215}{312}\right)$	$e\left(\frac{31}{104}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{227}{312}\right)$	$e\left(\frac{287}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{35}{104}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{8007}(2270,\cdot)$	$1$	$1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{277}{312}\right)$	$e\left(\frac{53}{104}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{217}{312}\right)$	$e\left(\frac{229}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{33}{104}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{8007}(2321,\cdot)$	$1$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{245}{312}\right)$	$e\left(\frac{45}{104}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{41}{312}\right)$	$e\left(\frac{269}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{81}{104}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{8007}(2429,\cdot)$	$1$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{7}{312}\right)$	$e\left(\frac{31}{104}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{19}{312}\right)$	$e\left(\frac{79}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{35}{104}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{8007}(2450,\cdot)$	$1$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{211}{312}\right)$	$e\left(\frac{43}{104}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{127}{312}\right)$	$e\left(\frac{19}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{15}{104}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{8007}(2474,\cdot)$	$1$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{101}{312}\right)$	$e\left(\frac{61}{104}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{185}{312}\right)$	$e\left(\frac{293}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{8007}(2507,\cdot)$	$1$	$1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{41}{312}\right)$	$e\left(\frac{33}{104}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{245}{312}\right)$	$e\left(\frac{17}{312}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{101}{104}\right)$	$e\left(\frac{8}{13}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{8007}(26,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{61}{312}\right)\)	\(e\left(\frac{77}{104}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{121}{312}\right)\)	\(e\left(\frac{109}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{8007}(77,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{77}{312}\right)\)	\(e\left(\frac{29}{104}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{209}{312}\right)\)	\(e\left(\frac{245}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{73}{104}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{8007}(104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{235}{312}\right)\)	\(e\left(\frac{75}{104}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{103}{312}\right)\)	\(e\left(\frac{67}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{104}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{8007}(308,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{251}{312}\right)\)	\(e\left(\frac{27}{104}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{191}{312}\right)\)	\(e\left(\frac{203}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{8007}(338,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{191}{312}\right)\)	\(e\left(\frac{103}{104}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{251}{312}\right)\)	\(e\left(\frac{239}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{104}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{8007}(416,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{97}{312}\right)\)	\(e\left(\frac{73}{104}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{85}{312}\right)\)	\(e\left(\frac{25}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{69}{104}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{8007}(791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{173}{312}\right)\)	\(e\left(\frac{53}{104}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{113}{312}\right)\)	\(e\left(\frac{125}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{33}{104}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{8007}(995,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{157}{312}\right)\)	\(e\left(\frac{101}{104}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{25}{312}\right)\)	\(e\left(\frac{301}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{57}{104}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{8007}(1022,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{155}{312}\right)\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{287}{312}\right)\)	\(e\left(\frac{11}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{104}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{8007}(1073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{139}{312}\right)\)	\(e\left(\frac{51}{104}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{199}{312}\right)\)	\(e\left(\frac{187}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{71}{104}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{8007}(1154,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{175}{312}\right)\)	\(e\left(\frac{47}{104}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{163}{312}\right)\)	\(e\left(\frac{103}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{43}{104}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{8007}(1232,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{113}{312}\right)\)	\(e\left(\frac{25}{104}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{173}{312}\right)\)	\(e\left(\frac{161}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{45}{104}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{8007}(1277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{107}{312}\right)\)	\(e\left(\frac{43}{104}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{23}{312}\right)\)	\(e\left(\frac{227}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{15}{104}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{8007}(1352,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{53}{312}\right)\)	\(e\left(\frac{101}{104}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{233}{312}\right)\)	\(e\left(\frac{197}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{57}{104}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{8007}(1613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{31}{312}\right)\)	\(e\left(\frac{63}{104}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{307}{312}\right)\)	\(e\left(\frac{127}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{51}{104}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{8007}(1658,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{5}{312}\right)\)	\(e\left(\frac{37}{104}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{281}{312}\right)\)	\(e\left(\frac{101}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{104}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{8007}(1664,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{271}{312}\right)\)	\(e\left(\frac{71}{104}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{67}{312}\right)\)	\(e\left(\frac{295}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{8007}(1709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{181}{312}\right)\)	\(e\left(\frac{29}{104}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{1}{312}\right)\)	\(e\left(\frac{37}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{73}{104}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{8007}(1742,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{49}{312}\right)\)	\(e\left(\frac{9}{104}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{133}{312}\right)\)	\(e\left(\frac{241}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{104}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{8007}(1787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{67}{312}\right)\)	\(e\left(\frac{59}{104}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{271}{312}\right)\)	\(e\left(\frac{43}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{104}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{8007}(1793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{73}{312}\right)\)	\(e\left(\frac{41}{104}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{109}{312}\right)\)	\(e\left(\frac{289}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{104}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{8007}(1811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{125}{312}\right)\)	\(e\left(\frac{93}{104}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{161}{312}\right)\)	\(e\left(\frac{29}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{104}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{8007}(1889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{275}{312}\right)\)	\(e\left(\frac{59}{104}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{167}{312}\right)\)	\(e\left(\frac{251}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{104}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{8007}(1946,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{289}{312}\right)\)	\(e\left(\frac{17}{104}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{205}{312}\right)\)	\(e\left(\frac{97}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{93}{104}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{8007}(2021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{215}{312}\right)\)	\(e\left(\frac{31}{104}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{227}{312}\right)\)	\(e\left(\frac{287}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{35}{104}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{8007}(2270,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{277}{312}\right)\)	\(e\left(\frac{53}{104}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{217}{312}\right)\)	\(e\left(\frac{229}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{33}{104}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{8007}(2321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{245}{312}\right)\)	\(e\left(\frac{45}{104}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{41}{312}\right)\)	\(e\left(\frac{269}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{81}{104}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{8007}(2429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{7}{312}\right)\)	\(e\left(\frac{31}{104}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{19}{312}\right)\)	\(e\left(\frac{79}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{35}{104}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{8007}(2450,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{211}{312}\right)\)	\(e\left(\frac{43}{104}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{127}{312}\right)\)	\(e\left(\frac{19}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{15}{104}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{8007}(2474,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{101}{312}\right)\)	\(e\left(\frac{61}{104}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{185}{312}\right)\)	\(e\left(\frac{293}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{8007}(2507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{41}{312}\right)\)	\(e\left(\frac{33}{104}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{245}{312}\right)\)	\(e\left(\frac{17}{312}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{101}{104}\right)\)	\(e\left(\frac{8}{13}\right)\)

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First 31 of 96 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	8007.fe
Modulus	$8007$
Conductor	$8007$
Order	$312$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8007\)
Conductor:	\(8007\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(312\)	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)