LMFDB - Dirichlet character orbit 8007.fi

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8007, base_ring=CyclotomicField(624)) M = H._module chi = DirichletCharacter(H, M([312,117,616])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(44,8007)) 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:	$624$	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:	$\Q(\zeta_{624})$
Fixed field:	Number field defined by a degree 624 polynomial (not computed)

First 31 of 192 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{8007}(44,\cdot)$	$1$	$1$	$e\left(\frac{33}{104}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{265}{624}\right)$	$e\left(\frac{37}{208}\right)$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{463}{624}\right)$	$e\left(\frac{283}{624}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{103}{208}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{8007}(122,\cdot)$	$1$	$1$	$e\left(\frac{67}{104}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{163}{624}\right)$	$e\left(\frac{135}{208}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{565}{624}\right)$	$e\left(\frac{313}{624}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{61}{208}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{8007}(146,\cdot)$	$1$	$1$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{73}{624}\right)$	$e\left(\frac{197}{208}\right)$	$e\left(\frac{83}{104}\right)$	$e\left(\frac{31}{624}\right)$	$e\left(\frac{523}{624}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{183}{208}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{8007}(167,\cdot)$	$1$	$1$	$e\left(\frac{75}{104}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{139}{624}\right)$	$e\left(\frac{207}{208}\right)$	$e\left(\frac{17}{104}\right)$	$e\left(\frac{589}{624}\right)$	$e\left(\frac{577}{624}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{149}{208}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{8007}(182,\cdot)$	$1$	$1$	$e\left(\frac{71}{104}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{359}{624}\right)$	$e\left(\frac{171}{208}\right)$	$e\left(\frac{5}{104}\right)$	$e\left(\frac{161}{624}\right)$	$e\left(\frac{341}{624}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{105}{208}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{8007}(233,\cdot)$	$1$	$1$	$e\left(\frac{87}{104}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{103}{624}\right)$	$e\left(\frac{107}{208}\right)$	$e\left(\frac{53}{104}\right)$	$e\left(\frac{1}{624}\right)$	$e\left(\frac{37}{624}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{73}{208}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8007}(284,\cdot)$	$1$	$1$	$e\left(\frac{87}{104}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{311}{624}\right)$	$e\left(\frac{107}{208}\right)$	$e\left(\frac{53}{104}\right)$	$e\left(\frac{209}{624}\right)$	$e\left(\frac{245}{624}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{73}{208}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8007}(317,\cdot)$	$1$	$1$	$e\left(\frac{77}{104}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{133}{624}\right)$	$e\left(\frac{17}{208}\right)$	$e\left(\frac{23}{104}\right)$	$e\left(\frac{595}{624}\right)$	$e\left(\frac{175}{624}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{171}{208}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8007}(347,\cdot)$	$1$	$1$	$e\left(\frac{57}{104}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{401}{624}\right)$	$e\left(\frac{45}{208}\right)$	$e\left(\frac{67}{104}\right)$	$e\left(\frac{119}{624}\right)$	$e\left(\frac{35}{624}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{159}{208}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{8007}(350,\cdot)$	$1$	$1$	$e\left(\frac{25}{104}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{185}{624}\right)$	$e\left(\frac{69}{208}\right)$	$e\left(\frac{75}{104}\right)$	$e\left(\frac{335}{624}\right)$	$e\left(\frac{539}{624}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{119}{208}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8007}(362,\cdot)$	$1$	$1$	$e\left(\frac{79}{104}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{127}{624}\right)$	$e\left(\frac{35}{208}\right)$	$e\left(\frac{29}{104}\right)$	$e\left(\frac{601}{624}\right)$	$e\left(\frac{397}{624}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{193}{208}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{8007}(371,\cdot)$	$1$	$1$	$e\left(\frac{59}{104}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{395}{624}\right)$	$e\left(\frac{63}{208}\right)$	$e\left(\frac{73}{104}\right)$	$e\left(\frac{125}{624}\right)$	$e\left(\frac{257}{624}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{181}{208}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{8007}(419,\cdot)$	$1$	$1$	$e\left(\frac{53}{104}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{101}{624}\right)$	$e\left(\frac{113}{208}\right)$	$e\left(\frac{55}{104}\right)$	$e\left(\frac{419}{624}\right)$	$e\left(\frac{527}{624}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{208}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{8007}(431,\cdot)$	$1$	$1$	$e\left(\frac{37}{104}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{253}{624}\right)$	$e\left(\frac{73}{208}\right)$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{475}{624}\right)$	$e\left(\frac{103}{624}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{147}{208}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{8007}(452,\cdot)$	$1$	$1$	$e\left(\frac{73}{104}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{457}{624}\right)$	$e\left(\frac{85}{208}\right)$	$e\left(\frac{11}{104}\right)$	$e\left(\frac{271}{624}\right)$	$e\left(\frac{43}{624}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{208}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{8007}(515,\cdot)$	$1$	$1$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{31}{624}\right)$	$e\left(\frac{115}{208}\right)$	$e\left(\frac{21}{104}\right)$	$e\left(\frac{73}{624}\right)$	$e\left(\frac{205}{624}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{129}{208}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{8007}(539,\cdot)$	$1$	$1$	$e\left(\frac{95}{104}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{391}{624}\right)$	$e\left(\frac{75}{208}\right)$	$e\left(\frac{77}{104}\right)$	$e\left(\frac{337}{624}\right)$	$e\left(\frac{613}{624}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{57}{208}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{8007}(581,\cdot)$	$1$	$1$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{563}{624}\right)$	$e\left(\frac{183}{208}\right)$	$e\left(\frac{9}{104}\right)$	$e\left(\frac{581}{624}\right)$	$e\left(\frac{281}{624}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{189}{208}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{8007}(617,\cdot)$	$1$	$1$	$e\left(\frac{71}{104}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{463}{624}\right)$	$e\left(\frac{67}{208}\right)$	$e\left(\frac{5}{104}\right)$	$e\left(\frac{265}{624}\right)$	$e\left(\frac{445}{624}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{208}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{8007}(653,\cdot)$	$1$	$1$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{593}{624}\right)$	$e\left(\frac{93}{208}\right)$	$e\left(\frac{83}{104}\right)$	$e\left(\frac{551}{624}\right)$	$e\left(\frac{419}{624}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{79}{208}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{8007}(704,\cdot)$	$1$	$1$	$e\left(\frac{9}{104}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{337}{624}\right)$	$e\left(\frac{29}{208}\right)$	$e\left(\frac{27}{104}\right)$	$e\left(\frac{391}{624}\right)$	$e\left(\frac{115}{624}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{47}{208}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8007}(755,\cdot)$	$1$	$1$	$e\left(\frac{9}{104}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{545}{624}\right)$	$e\left(\frac{29}{208}\right)$	$e\left(\frac{27}{104}\right)$	$e\left(\frac{599}{624}\right)$	$e\left(\frac{323}{624}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{208}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8007}(776,\cdot)$	$1$	$1$	$e\left(\frac{37}{104}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{149}{624}\right)$	$e\left(\frac{177}{208}\right)$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{371}{624}\right)$	$e\left(\frac{623}{624}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{43}{208}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{8007}(788,\cdot)$	$1$	$1$	$e\left(\frac{77}{104}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{445}{624}\right)$	$e\left(\frac{121}{208}\right)$	$e\left(\frac{23}{104}\right)$	$e\left(\frac{283}{624}\right)$	$e\left(\frac{487}{624}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{67}{208}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8007}(821,\cdot)$	$1$	$1$	$e\left(\frac{103}{104}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{575}{624}\right)$	$e\left(\frac{147}{208}\right)$	$e\left(\frac{101}{104}\right)$	$e\left(\frac{569}{624}\right)$	$e\left(\frac{461}{624}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{145}{208}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8007}(827,\cdot)$	$1$	$1$	$e\left(\frac{5}{104}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{37}{624}\right)$	$e\left(\frac{97}{208}\right)$	$e\left(\frac{15}{104}\right)$	$e\left(\frac{67}{624}\right)$	$e\left(\frac{607}{624}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{107}{208}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{8007}(836,\cdot)$	$1$	$1$	$e\left(\frac{67}{104}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{371}{624}\right)$	$e\left(\frac{135}{208}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{149}{624}\right)$	$e\left(\frac{521}{624}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{61}{208}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{8007}(890,\cdot)$	$1$	$1$	$e\left(\frac{53}{104}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{413}{624}\right)$	$e\left(\frac{9}{208}\right)$	$e\left(\frac{55}{104}\right)$	$e\left(\frac{107}{624}\right)$	$e\left(\frac{215}{624}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{115}{208}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{8007}(923,\cdot)$	$1$	$1$	$e\left(\frac{47}{104}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{223}{624}\right)$	$e\left(\frac{163}{208}\right)$	$e\left(\frac{37}{104}\right)$	$e\left(\frac{505}{624}\right)$	$e\left(\frac{589}{624}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{49}{208}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{8007}(1010,\cdot)$	$1$	$1$	$e\left(\frac{17}{104}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{1}{624}\right)$	$e\left(\frac{205}{208}\right)$	$e\left(\frac{51}{104}\right)$	$e\left(\frac{103}{624}\right)$	$e\left(\frac{67}{624}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{208}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{8007}(1064,\cdot)$	$1$	$1$	$e\left(\frac{41}{104}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{553}{624}\right)$	$e\left(\frac{5}{208}\right)$	$e\left(\frac{19}{104}\right)$	$e\left(\frac{175}{624}\right)$	$e\left(\frac{235}{624}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{87}{208}\right)$	$e\left(\frac{15}{26}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{8007}(44,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{104}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{265}{624}\right)\)	\(e\left(\frac{37}{208}\right)\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{463}{624}\right)\)	\(e\left(\frac{283}{624}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{103}{208}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{8007}(122,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{104}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{163}{624}\right)\)	\(e\left(\frac{135}{208}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{565}{624}\right)\)	\(e\left(\frac{313}{624}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{61}{208}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{8007}(146,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{73}{624}\right)\)	\(e\left(\frac{197}{208}\right)\)	\(e\left(\frac{83}{104}\right)\)	\(e\left(\frac{31}{624}\right)\)	\(e\left(\frac{523}{624}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{183}{208}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{8007}(167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{104}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{139}{624}\right)\)	\(e\left(\frac{207}{208}\right)\)	\(e\left(\frac{17}{104}\right)\)	\(e\left(\frac{589}{624}\right)\)	\(e\left(\frac{577}{624}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{149}{208}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{8007}(182,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{104}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{359}{624}\right)\)	\(e\left(\frac{171}{208}\right)\)	\(e\left(\frac{5}{104}\right)\)	\(e\left(\frac{161}{624}\right)\)	\(e\left(\frac{341}{624}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{105}{208}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{8007}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{104}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{103}{624}\right)\)	\(e\left(\frac{107}{208}\right)\)	\(e\left(\frac{53}{104}\right)\)	\(e\left(\frac{1}{624}\right)\)	\(e\left(\frac{37}{624}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{73}{208}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{8007}(284,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{104}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{311}{624}\right)\)	\(e\left(\frac{107}{208}\right)\)	\(e\left(\frac{53}{104}\right)\)	\(e\left(\frac{209}{624}\right)\)	\(e\left(\frac{245}{624}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{73}{208}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{8007}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{104}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{133}{624}\right)\)	\(e\left(\frac{17}{208}\right)\)	\(e\left(\frac{23}{104}\right)\)	\(e\left(\frac{595}{624}\right)\)	\(e\left(\frac{175}{624}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{171}{208}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{8007}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{104}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{401}{624}\right)\)	\(e\left(\frac{45}{208}\right)\)	\(e\left(\frac{67}{104}\right)\)	\(e\left(\frac{119}{624}\right)\)	\(e\left(\frac{35}{624}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{159}{208}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{8007}(350,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{104}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{185}{624}\right)\)	\(e\left(\frac{69}{208}\right)\)	\(e\left(\frac{75}{104}\right)\)	\(e\left(\frac{335}{624}\right)\)	\(e\left(\frac{539}{624}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{119}{208}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{8007}(362,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{104}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{127}{624}\right)\)	\(e\left(\frac{35}{208}\right)\)	\(e\left(\frac{29}{104}\right)\)	\(e\left(\frac{601}{624}\right)\)	\(e\left(\frac{397}{624}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{193}{208}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{8007}(371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{104}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{395}{624}\right)\)	\(e\left(\frac{63}{208}\right)\)	\(e\left(\frac{73}{104}\right)\)	\(e\left(\frac{125}{624}\right)\)	\(e\left(\frac{257}{624}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{181}{208}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{8007}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{104}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{101}{624}\right)\)	\(e\left(\frac{113}{208}\right)\)	\(e\left(\frac{55}{104}\right)\)	\(e\left(\frac{419}{624}\right)\)	\(e\left(\frac{527}{624}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{208}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{8007}(431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{104}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{253}{624}\right)\)	\(e\left(\frac{73}{208}\right)\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{475}{624}\right)\)	\(e\left(\frac{103}{624}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{147}{208}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{8007}(452,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{104}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{457}{624}\right)\)	\(e\left(\frac{85}{208}\right)\)	\(e\left(\frac{11}{104}\right)\)	\(e\left(\frac{271}{624}\right)\)	\(e\left(\frac{43}{624}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{208}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{8007}(515,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{31}{624}\right)\)	\(e\left(\frac{115}{208}\right)\)	\(e\left(\frac{21}{104}\right)\)	\(e\left(\frac{73}{624}\right)\)	\(e\left(\frac{205}{624}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{129}{208}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{8007}(539,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{104}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{391}{624}\right)\)	\(e\left(\frac{75}{208}\right)\)	\(e\left(\frac{77}{104}\right)\)	\(e\left(\frac{337}{624}\right)\)	\(e\left(\frac{613}{624}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{57}{208}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{8007}(581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{563}{624}\right)\)	\(e\left(\frac{183}{208}\right)\)	\(e\left(\frac{9}{104}\right)\)	\(e\left(\frac{581}{624}\right)\)	\(e\left(\frac{281}{624}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{189}{208}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{8007}(617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{104}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{463}{624}\right)\)	\(e\left(\frac{67}{208}\right)\)	\(e\left(\frac{5}{104}\right)\)	\(e\left(\frac{265}{624}\right)\)	\(e\left(\frac{445}{624}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{208}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{8007}(653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{593}{624}\right)\)	\(e\left(\frac{93}{208}\right)\)	\(e\left(\frac{83}{104}\right)\)	\(e\left(\frac{551}{624}\right)\)	\(e\left(\frac{419}{624}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{79}{208}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{8007}(704,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{104}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{337}{624}\right)\)	\(e\left(\frac{29}{208}\right)\)	\(e\left(\frac{27}{104}\right)\)	\(e\left(\frac{391}{624}\right)\)	\(e\left(\frac{115}{624}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{47}{208}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{8007}(755,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{104}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{545}{624}\right)\)	\(e\left(\frac{29}{208}\right)\)	\(e\left(\frac{27}{104}\right)\)	\(e\left(\frac{599}{624}\right)\)	\(e\left(\frac{323}{624}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{208}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{8007}(776,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{104}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{149}{624}\right)\)	\(e\left(\frac{177}{208}\right)\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{371}{624}\right)\)	\(e\left(\frac{623}{624}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{43}{208}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{8007}(788,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{104}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{445}{624}\right)\)	\(e\left(\frac{121}{208}\right)\)	\(e\left(\frac{23}{104}\right)\)	\(e\left(\frac{283}{624}\right)\)	\(e\left(\frac{487}{624}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{67}{208}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{8007}(821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{104}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{575}{624}\right)\)	\(e\left(\frac{147}{208}\right)\)	\(e\left(\frac{101}{104}\right)\)	\(e\left(\frac{569}{624}\right)\)	\(e\left(\frac{461}{624}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{145}{208}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{8007}(827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{104}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{37}{624}\right)\)	\(e\left(\frac{97}{208}\right)\)	\(e\left(\frac{15}{104}\right)\)	\(e\left(\frac{67}{624}\right)\)	\(e\left(\frac{607}{624}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{107}{208}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{8007}(836,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{104}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{371}{624}\right)\)	\(e\left(\frac{135}{208}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{149}{624}\right)\)	\(e\left(\frac{521}{624}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{61}{208}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{8007}(890,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{104}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{413}{624}\right)\)	\(e\left(\frac{9}{208}\right)\)	\(e\left(\frac{55}{104}\right)\)	\(e\left(\frac{107}{624}\right)\)	\(e\left(\frac{215}{624}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{115}{208}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{8007}(923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{104}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{223}{624}\right)\)	\(e\left(\frac{163}{208}\right)\)	\(e\left(\frac{37}{104}\right)\)	\(e\left(\frac{505}{624}\right)\)	\(e\left(\frac{589}{624}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{49}{208}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{8007}(1010,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{104}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{1}{624}\right)\)	\(e\left(\frac{205}{208}\right)\)	\(e\left(\frac{51}{104}\right)\)	\(e\left(\frac{103}{624}\right)\)	\(e\left(\frac{67}{624}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{208}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{8007}(1064,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{104}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{553}{624}\right)\)	\(e\left(\frac{5}{208}\right)\)	\(e\left(\frac{19}{104}\right)\)	\(e\left(\frac{175}{624}\right)\)	\(e\left(\frac{235}{624}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{87}{208}\right)\)	\(e\left(\frac{15}{26}\right)\)

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First 31 of 192 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.fi
Modulus	$8007$
Conductor	$8007$
Order	$624$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8007\)
Conductor:	\(8007\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(624\)	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)