LMFDB - Dirichlet character orbit 8007.dh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8007, base_ring=CyclotomicField(52)) M = H._module chi = DirichletCharacter(H, M([26,26,17])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(1070,8007)) 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:	$52$	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:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{8007}(1070,\cdot)$	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{2}{13}\right)$	$-1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{8007}(1478,\cdot)$	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{11}{13}\right)$	$-1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{8007}(1529,\cdot)$	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{10}{13}\right)$	$-1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{8007}(1682,\cdot)$	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{8}{13}\right)$	$-1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{8007}(1886,\cdot)$	$1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{4}{13}\right)$	$-1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{8007}(2039,\cdot)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{4}{13}\right)$	$-1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{8007}(2243,\cdot)$	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{8}{13}\right)$	$-1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{8007}(2396,\cdot)$	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{10}{13}\right)$	$-1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{8007}(2447,\cdot)$	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{11}{13}\right)$	$-1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{8007}(2855,\cdot)$	$1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{2}{13}\right)$	$-1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{8007}(4028,\cdot)$	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{6}{13}\right)$	$-1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{8007}(4232,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{5}{13}\right)$	$-1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{8007}(4742,\cdot)$	$1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{13}\right)$	$-1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{8007}(4844,\cdot)$	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{3}{13}\right)$	$-1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{8007}(4946,\cdot)$	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{9}{13}\right)$	$-1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{8007}(5660,\cdot)$	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{12}{13}\right)$	$-1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{8007}(5711,\cdot)$	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{13}\right)$	$-1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{8007}(6221,\cdot)$	$1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{13}\right)$	$-1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{8007}(6272,\cdot)$	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{12}{13}\right)$	$-1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{8007}(6986,\cdot)$	$1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{9}{13}\right)$	$-1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{8007}(7088,\cdot)$	$1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{3}{13}\right)$	$-1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{8007}(7190,\cdot)$	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{13}\right)$	$-1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{8007}(7700,\cdot)$	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{5}{13}\right)$	$-1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{8007}(7904,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{6}{13}\right)$	$-1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{13}\right)$

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Elliptic curves over $\Q$
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Higher genus families
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Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{8007}(1070,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(-1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{8007}(1478,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{8007}(1529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(-1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{8007}(1682,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(-1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{8007}(1886,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(-1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{8007}(2039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(-1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{8007}(2243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(-1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{8007}(2396,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(-1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{8007}(2447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{8007}(2855,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(-1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{8007}(4028,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{8007}(4232,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(-1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{8007}(4742,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(-1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{8007}(4844,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(-1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{8007}(4946,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(-1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{8007}(5660,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(-1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{8007}(5711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(-1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{8007}(6221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(-1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{8007}(6272,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(-1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{8007}(6986,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(-1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{8007}(7088,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(-1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{8007}(7190,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(-1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{8007}(7700,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(-1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{8007}(7904,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)

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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.dh
Modulus	$8007$
Conductor	$8007$
Order	$52$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8007\)
Conductor:	\(8007\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(52\)	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)