LMFDB - Dirichlet character orbit 8007.eq

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8007, base_ring=CyclotomicField(208)) M = H._module chi = DirichletCharacter(H, M([0,39,188])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(316,8007)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8007$
Conductor:	$2669$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$208$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2669.cj	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:	$\Q(\zeta_{208})$
Fixed field:	Number field defined by a degree 208 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{8007}(316,\cdot)$	$1$	$1$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{175}{208}\right)$	$e\left(\frac{193}{208}\right)$	$e\left(\frac{21}{104}\right)$	$e\left(\frac{189}{208}\right)$	$e\left(\frac{129}{208}\right)$	$i$	$e\left(\frac{207}{208}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{8007}(337,\cdot)$	$1$	$1$	$e\left(\frac{93}{104}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{141}{208}\right)$	$e\left(\frac{83}{208}\right)$	$e\left(\frac{71}{104}\right)$	$e\left(\frac{119}{208}\right)$	$e\left(\frac{35}{208}\right)$	$-i$	$e\left(\frac{61}{208}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{8007}(346,\cdot)$	$1$	$1$	$e\left(\frac{35}{104}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{43}{208}\right)$	$e\left(\frac{133}{208}\right)$	$e\left(\frac{1}{104}\right)$	$e\left(\frac{113}{208}\right)$	$e\left(\frac{21}{208}\right)$	$i$	$e\left(\frac{203}{208}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8007}(379,\cdot)$	$1$	$1$	$e\left(\frac{81}{104}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{153}{208}\right)$	$e\left(\frac{183}{208}\right)$	$e\left(\frac{35}{104}\right)$	$e\left(\frac{107}{208}\right)$	$e\left(\frac{7}{208}\right)$	$-i$	$e\left(\frac{137}{208}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{8007}(430,\cdot)$	$1$	$1$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{41}{208}\right)$	$e\left(\frac{151}{208}\right)$	$e\left(\frac{59}{104}\right)$	$e\left(\frac{11}{208}\right)$	$e\left(\frac{199}{208}\right)$	$-i$	$e\left(\frac{121}{208}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{8007}(439,\cdot)$	$1$	$1$	$e\left(\frac{61}{104}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{173}{208}\right)$	$e\left(\frac{3}{208}\right)$	$e\left(\frac{79}{104}\right)$	$e\left(\frac{87}{208}\right)$	$e\left(\frac{99}{208}\right)$	$-i$	$e\left(\frac{125}{208}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8007}(448,\cdot)$	$1$	$1$	$e\left(\frac{67}{104}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{11}{208}\right)$	$e\left(\frac{5}{208}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{145}{208}\right)$	$e\left(\frac{165}{208}\right)$	$i$	$e\left(\frac{139}{208}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{8007}(583,\cdot)$	$1$	$1$	$e\left(\frac{1}{104}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{25}{208}\right)$	$e\left(\frac{87}{208}\right)$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{27}{208}\right)$	$e\left(\frac{167}{208}\right)$	$-i$	$e\left(\frac{89}{208}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{8007}(673,\cdot)$	$1$	$1$	$e\left(\frac{79}{104}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{207}{208}\right)$	$e\left(\frac{113}{208}\right)$	$e\left(\frac{29}{104}\right)$	$e\left(\frac{157}{208}\right)$	$e\left(\frac{193}{208}\right)$	$i$	$e\left(\frac{63}{208}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{8007}(826,\cdot)$	$1$	$1$	$e\left(\frac{63}{104}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{15}{208}\right)$	$e\left(\frac{177}{208}\right)$	$e\left(\frac{85}{104}\right)$	$e\left(\frac{141}{208}\right)$	$e\left(\frac{17}{208}\right)$	$i$	$e\left(\frac{95}{208}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{8007}(844,\cdot)$	$1$	$1$	$e\left(\frac{83}{104}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{99}{208}\right)$	$e\left(\frac{45}{208}\right)$	$e\left(\frac{41}{104}\right)$	$e\left(\frac{57}{208}\right)$	$e\left(\frac{29}{208}\right)$	$i$	$e\left(\frac{3}{208}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{8007}(877,\cdot)$	$1$	$1$	$e\left(\frac{55}{104}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{127}{208}\right)$	$e\left(\frac{1}{208}\right)$	$e\left(\frac{61}{104}\right)$	$e\left(\frac{29}{208}\right)$	$e\left(\frac{33}{208}\right)$	$i$	$e\left(\frac{111}{208}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{8007}(913,\cdot)$	$1$	$1$	$e\left(\frac{49}{104}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{81}{208}\right)$	$e\left(\frac{207}{208}\right)$	$e\left(\frac{43}{104}\right)$	$e\left(\frac{179}{208}\right)$	$e\left(\frac{175}{208}\right)$	$-i$	$e\left(\frac{97}{208}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{8007}(940,\cdot)$	$1$	$1$	$e\left(\frac{33}{104}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{201}{208}\right)$	$e\left(\frac{167}{208}\right)$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{59}{208}\right)$	$e\left(\frac{103}{208}\right)$	$-i$	$e\left(\frac{25}{208}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{8007}(949,\cdot)$	$1$	$1$	$e\left(\frac{77}{104}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{157}{208}\right)$	$e\left(\frac{147}{208}\right)$	$e\left(\frac{23}{104}\right)$	$e\left(\frac{103}{208}\right)$	$e\left(\frac{67}{208}\right)$	$-i$	$e\left(\frac{93}{208}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8007}(1153,\cdot)$	$1$	$1$	$e\left(\frac{69}{104}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{61}{208}\right)$	$e\left(\frac{179}{208}\right)$	$e\left(\frac{103}{104}\right)$	$e\left(\frac{199}{208}\right)$	$e\left(\frac{83}{208}\right)$	$-i$	$e\left(\frac{109}{208}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{8007}(1285,\cdot)$	$1$	$1$	$e\left(\frac{23}{104}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{159}{208}\right)$	$e\left(\frac{129}{208}\right)$	$e\left(\frac{69}{104}\right)$	$e\left(\frac{205}{208}\right)$	$e\left(\frac{97}{208}\right)$	$i$	$e\left(\frac{175}{208}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{8007}(1315,\cdot)$	$1$	$1$	$e\left(\frac{83}{104}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{203}{208}\right)$	$e\left(\frac{149}{208}\right)$	$e\left(\frac{41}{104}\right)$	$e\left(\frac{161}{208}\right)$	$e\left(\frac{133}{208}\right)$	$i$	$e\left(\frac{107}{208}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{8007}(1321,\cdot)$	$1$	$1$	$e\left(\frac{81}{104}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{49}{208}\right)$	$e\left(\frac{79}{208}\right)$	$e\left(\frac{35}{104}\right)$	$e\left(\frac{3}{208}\right)$	$e\left(\frac{111}{208}\right)$	$-i$	$e\left(\frac{33}{208}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{8007}(1372,\cdot)$	$1$	$1$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{145}{208}\right)$	$e\left(\frac{47}{208}\right)$	$e\left(\frac{59}{104}\right)$	$e\left(\frac{115}{208}\right)$	$e\left(\frac{95}{208}\right)$	$-i$	$e\left(\frac{17}{208}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{8007}(1405,\cdot)$	$1$	$1$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{83}{208}\right)$	$e\left(\frac{189}{208}\right)$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{73}{208}\right)$	$e\left(\frac{205}{208}\right)$	$i$	$e\left(\frac{179}{208}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{8007}(1525,\cdot)$	$1$	$1$	$e\left(\frac{1}{104}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{129}{208}\right)$	$e\left(\frac{191}{208}\right)$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{131}{208}\right)$	$e\left(\frac{63}{208}\right)$	$-i$	$e\left(\frac{193}{208}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{8007}(1876,\cdot)$	$1$	$1$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{187}{208}\right)$	$e\left(\frac{85}{208}\right)$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{177}{208}\right)$	$e\left(\frac{101}{208}\right)$	$i$	$e\left(\frac{75}{208}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{8007}(1882,\cdot)$	$1$	$1$	$e\left(\frac{33}{104}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{97}{208}\right)$	$e\left(\frac{63}{208}\right)$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{163}{208}\right)$	$e\left(\frac{207}{208}\right)$	$-i$	$e\left(\frac{129}{208}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{8007}(2119,\cdot)$	$1$	$1$	$e\left(\frac{19}{104}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{163}{208}\right)$	$e\left(\frac{93}{208}\right)$	$e\left(\frac{57}{104}\right)$	$e\left(\frac{201}{208}\right)$	$e\left(\frac{157}{208}\right)$	$i$	$e\left(\frac{131}{208}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{8007}(2200,\cdot)$	$1$	$1$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{71}{208}\right)$	$e\left(\frac{89}{208}\right)$	$e\left(\frac{21}{104}\right)$	$e\left(\frac{85}{208}\right)$	$e\left(\frac{25}{208}\right)$	$i$	$e\left(\frac{103}{208}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{8007}(2326,\cdot)$	$1$	$1$	$e\left(\frac{101}{104}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{29}{208}\right)$	$e\left(\frac{51}{208}\right)$	$e\left(\frac{95}{104}\right)$	$e\left(\frac{23}{208}\right)$	$e\left(\frac{19}{208}\right)$	$-i$	$e\left(\frac{45}{208}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{8007}(2434,\cdot)$	$1$	$1$	$e\left(\frac{45}{104}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{85}{208}\right)$	$e\left(\frac{171}{208}\right)$	$e\left(\frac{31}{104}\right)$	$e\left(\frac{175}{208}\right)$	$e\left(\frac{27}{208}\right)$	$-i$	$e\left(\frac{53}{208}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{8007}(2458,\cdot)$	$1$	$1$	$e\left(\frac{95}{104}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{191}{208}\right)$	$e\left(\frac{49}{208}\right)$	$e\left(\frac{77}{104}\right)$	$e\left(\frac{173}{208}\right)$	$e\left(\frac{161}{208}\right)$	$i$	$e\left(\frac{31}{208}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{8007}(2557,\cdot)$	$1$	$1$	$e\left(\frac{79}{104}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{103}{208}\right)$	$e\left(\frac{9}{208}\right)$	$e\left(\frac{29}{104}\right)$	$e\left(\frac{53}{208}\right)$	$e\left(\frac{89}{208}\right)$	$i$	$e\left(\frac{167}{208}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{8007}(2590,\cdot)$	$1$	$1$	$e\left(\frac{19}{104}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{59}{208}\right)$	$e\left(\frac{197}{208}\right)$	$e\left(\frac{57}{104}\right)$	$e\left(\frac{97}{208}\right)$	$e\left(\frac{53}{208}\right)$	$i$	$e\left(\frac{27}{208}\right)$	$e\left(\frac{19}{26}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{8007}(316,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{175}{208}\right)\)	\(e\left(\frac{193}{208}\right)\)	\(e\left(\frac{21}{104}\right)\)	\(e\left(\frac{189}{208}\right)\)	\(e\left(\frac{129}{208}\right)\)	\(i\)	\(e\left(\frac{207}{208}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{8007}(337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{104}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{141}{208}\right)\)	\(e\left(\frac{83}{208}\right)\)	\(e\left(\frac{71}{104}\right)\)	\(e\left(\frac{119}{208}\right)\)	\(e\left(\frac{35}{208}\right)\)	\(-i\)	\(e\left(\frac{61}{208}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{8007}(346,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{104}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{43}{208}\right)\)	\(e\left(\frac{133}{208}\right)\)	\(e\left(\frac{1}{104}\right)\)	\(e\left(\frac{113}{208}\right)\)	\(e\left(\frac{21}{208}\right)\)	\(i\)	\(e\left(\frac{203}{208}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{8007}(379,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{104}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{153}{208}\right)\)	\(e\left(\frac{183}{208}\right)\)	\(e\left(\frac{35}{104}\right)\)	\(e\left(\frac{107}{208}\right)\)	\(e\left(\frac{7}{208}\right)\)	\(-i\)	\(e\left(\frac{137}{208}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{8007}(430,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{41}{208}\right)\)	\(e\left(\frac{151}{208}\right)\)	\(e\left(\frac{59}{104}\right)\)	\(e\left(\frac{11}{208}\right)\)	\(e\left(\frac{199}{208}\right)\)	\(-i\)	\(e\left(\frac{121}{208}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{8007}(439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{104}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{173}{208}\right)\)	\(e\left(\frac{3}{208}\right)\)	\(e\left(\frac{79}{104}\right)\)	\(e\left(\frac{87}{208}\right)\)	\(e\left(\frac{99}{208}\right)\)	\(-i\)	\(e\left(\frac{125}{208}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{8007}(448,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{104}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{11}{208}\right)\)	\(e\left(\frac{5}{208}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{145}{208}\right)\)	\(e\left(\frac{165}{208}\right)\)	\(i\)	\(e\left(\frac{139}{208}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{8007}(583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{104}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{25}{208}\right)\)	\(e\left(\frac{87}{208}\right)\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{27}{208}\right)\)	\(e\left(\frac{167}{208}\right)\)	\(-i\)	\(e\left(\frac{89}{208}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{8007}(673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{104}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{207}{208}\right)\)	\(e\left(\frac{113}{208}\right)\)	\(e\left(\frac{29}{104}\right)\)	\(e\left(\frac{157}{208}\right)\)	\(e\left(\frac{193}{208}\right)\)	\(i\)	\(e\left(\frac{63}{208}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{8007}(826,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{104}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{15}{208}\right)\)	\(e\left(\frac{177}{208}\right)\)	\(e\left(\frac{85}{104}\right)\)	\(e\left(\frac{141}{208}\right)\)	\(e\left(\frac{17}{208}\right)\)	\(i\)	\(e\left(\frac{95}{208}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{8007}(844,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{104}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{99}{208}\right)\)	\(e\left(\frac{45}{208}\right)\)	\(e\left(\frac{41}{104}\right)\)	\(e\left(\frac{57}{208}\right)\)	\(e\left(\frac{29}{208}\right)\)	\(i\)	\(e\left(\frac{3}{208}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{8007}(877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{104}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{127}{208}\right)\)	\(e\left(\frac{1}{208}\right)\)	\(e\left(\frac{61}{104}\right)\)	\(e\left(\frac{29}{208}\right)\)	\(e\left(\frac{33}{208}\right)\)	\(i\)	\(e\left(\frac{111}{208}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{8007}(913,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{104}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{81}{208}\right)\)	\(e\left(\frac{207}{208}\right)\)	\(e\left(\frac{43}{104}\right)\)	\(e\left(\frac{179}{208}\right)\)	\(e\left(\frac{175}{208}\right)\)	\(-i\)	\(e\left(\frac{97}{208}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{8007}(940,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{104}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{201}{208}\right)\)	\(e\left(\frac{167}{208}\right)\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{59}{208}\right)\)	\(e\left(\frac{103}{208}\right)\)	\(-i\)	\(e\left(\frac{25}{208}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{8007}(949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{104}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{157}{208}\right)\)	\(e\left(\frac{147}{208}\right)\)	\(e\left(\frac{23}{104}\right)\)	\(e\left(\frac{103}{208}\right)\)	\(e\left(\frac{67}{208}\right)\)	\(-i\)	\(e\left(\frac{93}{208}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{8007}(1153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{104}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{61}{208}\right)\)	\(e\left(\frac{179}{208}\right)\)	\(e\left(\frac{103}{104}\right)\)	\(e\left(\frac{199}{208}\right)\)	\(e\left(\frac{83}{208}\right)\)	\(-i\)	\(e\left(\frac{109}{208}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{8007}(1285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{104}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{159}{208}\right)\)	\(e\left(\frac{129}{208}\right)\)	\(e\left(\frac{69}{104}\right)\)	\(e\left(\frac{205}{208}\right)\)	\(e\left(\frac{97}{208}\right)\)	\(i\)	\(e\left(\frac{175}{208}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{8007}(1315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{104}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{203}{208}\right)\)	\(e\left(\frac{149}{208}\right)\)	\(e\left(\frac{41}{104}\right)\)	\(e\left(\frac{161}{208}\right)\)	\(e\left(\frac{133}{208}\right)\)	\(i\)	\(e\left(\frac{107}{208}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{8007}(1321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{104}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{49}{208}\right)\)	\(e\left(\frac{79}{208}\right)\)	\(e\left(\frac{35}{104}\right)\)	\(e\left(\frac{3}{208}\right)\)	\(e\left(\frac{111}{208}\right)\)	\(-i\)	\(e\left(\frac{33}{208}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{8007}(1372,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{145}{208}\right)\)	\(e\left(\frac{47}{208}\right)\)	\(e\left(\frac{59}{104}\right)\)	\(e\left(\frac{115}{208}\right)\)	\(e\left(\frac{95}{208}\right)\)	\(-i\)	\(e\left(\frac{17}{208}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{8007}(1405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{83}{208}\right)\)	\(e\left(\frac{189}{208}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{73}{208}\right)\)	\(e\left(\frac{205}{208}\right)\)	\(i\)	\(e\left(\frac{179}{208}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{8007}(1525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{104}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{129}{208}\right)\)	\(e\left(\frac{191}{208}\right)\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{131}{208}\right)\)	\(e\left(\frac{63}{208}\right)\)	\(-i\)	\(e\left(\frac{193}{208}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{8007}(1876,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{187}{208}\right)\)	\(e\left(\frac{85}{208}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{177}{208}\right)\)	\(e\left(\frac{101}{208}\right)\)	\(i\)	\(e\left(\frac{75}{208}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{8007}(1882,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{104}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{97}{208}\right)\)	\(e\left(\frac{63}{208}\right)\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{163}{208}\right)\)	\(e\left(\frac{207}{208}\right)\)	\(-i\)	\(e\left(\frac{129}{208}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{8007}(2119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{104}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{163}{208}\right)\)	\(e\left(\frac{93}{208}\right)\)	\(e\left(\frac{57}{104}\right)\)	\(e\left(\frac{201}{208}\right)\)	\(e\left(\frac{157}{208}\right)\)	\(i\)	\(e\left(\frac{131}{208}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{8007}(2200,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{71}{208}\right)\)	\(e\left(\frac{89}{208}\right)\)	\(e\left(\frac{21}{104}\right)\)	\(e\left(\frac{85}{208}\right)\)	\(e\left(\frac{25}{208}\right)\)	\(i\)	\(e\left(\frac{103}{208}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{8007}(2326,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{104}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{29}{208}\right)\)	\(e\left(\frac{51}{208}\right)\)	\(e\left(\frac{95}{104}\right)\)	\(e\left(\frac{23}{208}\right)\)	\(e\left(\frac{19}{208}\right)\)	\(-i\)	\(e\left(\frac{45}{208}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{8007}(2434,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{104}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{85}{208}\right)\)	\(e\left(\frac{171}{208}\right)\)	\(e\left(\frac{31}{104}\right)\)	\(e\left(\frac{175}{208}\right)\)	\(e\left(\frac{27}{208}\right)\)	\(-i\)	\(e\left(\frac{53}{208}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{8007}(2458,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{104}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{191}{208}\right)\)	\(e\left(\frac{49}{208}\right)\)	\(e\left(\frac{77}{104}\right)\)	\(e\left(\frac{173}{208}\right)\)	\(e\left(\frac{161}{208}\right)\)	\(i\)	\(e\left(\frac{31}{208}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{8007}(2557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{104}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{103}{208}\right)\)	\(e\left(\frac{9}{208}\right)\)	\(e\left(\frac{29}{104}\right)\)	\(e\left(\frac{53}{208}\right)\)	\(e\left(\frac{89}{208}\right)\)	\(i\)	\(e\left(\frac{167}{208}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{8007}(2590,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{104}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{59}{208}\right)\)	\(e\left(\frac{197}{208}\right)\)	\(e\left(\frac{57}{104}\right)\)	\(e\left(\frac{97}{208}\right)\)	\(e\left(\frac{53}{208}\right)\)	\(i\)	\(e\left(\frac{27}{208}\right)\)	\(e\left(\frac{19}{26}\right)\)

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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.eq
Modulus	$8007$
Conductor	$2669$
Order	$208$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8007\)
Conductor:	\(2669\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(208\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2669.cj	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)