LMFDB - Dirichlet character orbit 8004.dk

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8004, base_ring=CyclotomicField(308)) M = H._module chi = DirichletCharacter(H, M([154,0,84,11])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(31,8004)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8004$
Conductor:	$2668$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$308$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2668.bs	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:	$\Q(\zeta_{308})$
Fixed field:	Number field defined by a degree 308 polynomial (not computed)

First 31 of 120 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$25$	$31$	$35$	$37$
$\chi_{8004}(31,\cdot)$	$1$	$1$	$e\left(\frac{9}{154}\right)$	$e\left(\frac{17}{154}\right)$	$e\left(\frac{261}{308}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{281}{308}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{53}{308}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{257}{308}\right)$
$\chi_{8004}(55,\cdot)$	$1$	$1$	$e\left(\frac{59}{154}\right)$	$e\left(\frac{43}{154}\right)$	$e\left(\frac{171}{308}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{131}{308}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{279}{308}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{179}{308}\right)$
$\chi_{8004}(127,\cdot)$	$1$	$1$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{1}{308}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{53}{308}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{261}{308}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{237}{308}\right)$
$\chi_{8004}(163,\cdot)$	$1$	$1$	$e\left(\frac{113}{154}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{43}{308}\right)$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{123}{308}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{135}{308}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{27}{308}\right)$
$\chi_{8004}(211,\cdot)$	$1$	$1$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{251}{308}\right)$	$e\left(\frac{73}{154}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{59}{308}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{215}{308}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{43}{308}\right)$
$\chi_{8004}(259,\cdot)$	$1$	$1$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{73}{154}\right)$	$e\left(\frac{79}{308}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{183}{308}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{291}{308}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{243}{308}\right)$
$\chi_{8004}(271,\cdot)$	$1$	$1$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{291}{308}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{23}{308}\right)$	$e\left(\frac{18}{77}\right)$	$e\left(\frac{183}{308}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{283}{308}\right)$
$\chi_{8004}(403,\cdot)$	$1$	$1$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{141}{154}\right)$	$e\left(\frac{199}{308}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{75}{308}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{195}{308}\right)$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{39}{308}\right)$
$\chi_{8004}(427,\cdot)$	$1$	$1$	$e\left(\frac{153}{154}\right)$	$e\left(\frac{135}{154}\right)$	$e\left(\frac{125}{308}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{157}{308}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{285}{308}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{57}{308}\right)$
$\chi_{8004}(583,\cdot)$	$1$	$1$	$e\left(\frac{31}{154}\right)$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{129}{308}\right)$	$e\left(\frac{5}{154}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{61}{308}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{97}{308}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{81}{308}\right)$
$\chi_{8004}(607,\cdot)$	$1$	$1$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{87}{154}\right)$	$e\left(\frac{303}{308}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{43}{308}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{235}{308}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{47}{308}\right)$
$\chi_{8004}(715,\cdot)$	$1$	$1$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{13}{154}\right)$	$e\left(\frac{109}{308}\right)$	$e\left(\frac{9}{154}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{233}{308}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{113}{308}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{269}{308}\right)$
$\chi_{8004}(739,\cdot)$	$1$	$1$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{137}{154}\right)$	$e\left(\frac{201}{308}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{181}{308}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{101}{308}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{205}{308}\right)$
$\chi_{8004}(775,\cdot)$	$1$	$1$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{293}{308}\right)$	$e\left(\frac{3}{154}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{129}{308}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{89}{308}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{141}{308}\right)$
$\chi_{8004}(823,\cdot)$	$1$	$1$	$e\left(\frac{29}{154}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{225}{308}\right)$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{221}{308}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{205}{308}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{41}{308}\right)$
$\chi_{8004}(859,\cdot)$	$1$	$1$	$e\left(\frac{141}{154}\right)$	$e\left(\frac{61}{154}\right)$	$e\left(\frac{239}{308}\right)$	$e\left(\frac{137}{154}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{39}{308}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{163}{308}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{279}{308}\right)$
$\chi_{8004}(955,\cdot)$	$1$	$1$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{31}{154}\right)$	$e\left(\frac{23}{308}\right)$	$e\left(\frac{57}{154}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{295}{308}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{151}{308}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{215}{308}\right)$
$\chi_{8004}(1087,\cdot)$	$1$	$1$	$e\left(\frac{5}{154}\right)$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{145}{308}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{293}{308}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{269}{308}\right)$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{177}{308}\right)$
$\chi_{8004}(1099,\cdot)$	$1$	$1$	$e\left(\frac{73}{154}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{115}{308}\right)$	$e\left(\frac{131}{154}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{243}{308}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{139}{308}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{151}{308}\right)$
$\chi_{8004}(1255,\cdot)$	$1$	$1$	$e\left(\frac{153}{154}\right)$	$e\left(\frac{135}{154}\right)$	$e\left(\frac{279}{308}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{3}{308}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{131}{308}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{211}{308}\right)$
$\chi_{8004}(1291,\cdot)$	$1$	$1$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{137}{154}\right)$	$e\left(\frac{47}{308}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{27}{308}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{255}{308}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{51}{308}\right)$
$\chi_{8004}(1315,\cdot)$	$1$	$1$	$e\left(\frac{39}{154}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{207}{308}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{191}{308}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{127}{308}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{87}{308}\right)$
$\chi_{8004}(1411,\cdot)$	$1$	$1$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{305}{308}\right)$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{149}{308}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{141}{308}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{213}{308}\right)$
$\chi_{8004}(1435,\cdot)$	$1$	$1$	$e\left(\frac{103}{154}\right)$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{61}{308}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{153}{308}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{213}{308}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{289}{308}\right)$
$\chi_{8004}(1603,\cdot)$	$1$	$1$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{139}{308}\right)$	$e\left(\frac{3}{154}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{283}{308}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{243}{308}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{295}{308}\right)$
$\chi_{8004}(1639,\cdot)$	$1$	$1$	$e\left(\frac{5}{154}\right)$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{299}{308}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{139}{308}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{115}{308}\right)$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{23}{308}\right)$
$\chi_{8004}(1651,\cdot)$	$1$	$1$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{247}{308}\right)$	$e\left(\frac{43}{154}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{155}{308}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{95}{308}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{19}{308}\right)$
$\chi_{8004}(1783,\cdot)$	$1$	$1$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{89}{308}\right)$	$e\left(\frac{13}{154}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{97}{308}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{129}{308}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{149}{308}\right)$
$\chi_{8004}(1819,\cdot)$	$1$	$1$	$e\left(\frac{69}{154}\right)$	$e\left(\frac{79}{154}\right)$	$e\left(\frac{153}{308}\right)$	$e\left(\frac{31}{154}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{101}{308}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{201}{308}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{225}{308}\right)$
$\chi_{8004}(1867,\cdot)$	$1$	$1$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{103}{154}\right)$	$e\left(\frac{141}{308}\right)$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{81}{308}\right)$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{149}{308}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{153}{308}\right)$
$\chi_{8004}(1987,\cdot)$	$1$	$1$	$e\left(\frac{103}{154}\right)$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{215}{308}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{307}{308}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{59}{308}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{135}{308}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(31\)	\(35\)	\(37\)
\(\chi_{8004}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{154}\right)\)	\(e\left(\frac{17}{154}\right)\)	\(e\left(\frac{261}{308}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{281}{308}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{53}{308}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{257}{308}\right)\)
\(\chi_{8004}(55,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{154}\right)\)	\(e\left(\frac{43}{154}\right)\)	\(e\left(\frac{171}{308}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{131}{308}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{279}{308}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{179}{308}\right)\)
\(\chi_{8004}(127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{1}{308}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{53}{308}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{261}{308}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{237}{308}\right)\)
\(\chi_{8004}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{154}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{43}{308}\right)\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{123}{308}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{135}{308}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{27}{308}\right)\)
\(\chi_{8004}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{251}{308}\right)\)	\(e\left(\frac{73}{154}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{59}{308}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{215}{308}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{43}{308}\right)\)
\(\chi_{8004}(259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{73}{154}\right)\)	\(e\left(\frac{79}{308}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{183}{308}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{291}{308}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{243}{308}\right)\)
\(\chi_{8004}(271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{291}{308}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{23}{308}\right)\)	\(e\left(\frac{18}{77}\right)\)	\(e\left(\frac{183}{308}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{283}{308}\right)\)
\(\chi_{8004}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{141}{154}\right)\)	\(e\left(\frac{199}{308}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{75}{308}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{195}{308}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{39}{308}\right)\)
\(\chi_{8004}(427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{154}\right)\)	\(e\left(\frac{135}{154}\right)\)	\(e\left(\frac{125}{308}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{157}{308}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{285}{308}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{57}{308}\right)\)
\(\chi_{8004}(583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{154}\right)\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{129}{308}\right)\)	\(e\left(\frac{5}{154}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{61}{308}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{97}{308}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{81}{308}\right)\)
\(\chi_{8004}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{87}{154}\right)\)	\(e\left(\frac{303}{308}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{43}{308}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{235}{308}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{47}{308}\right)\)
\(\chi_{8004}(715,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{13}{154}\right)\)	\(e\left(\frac{109}{308}\right)\)	\(e\left(\frac{9}{154}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{233}{308}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{113}{308}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{269}{308}\right)\)
\(\chi_{8004}(739,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{137}{154}\right)\)	\(e\left(\frac{201}{308}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{181}{308}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{101}{308}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{205}{308}\right)\)
\(\chi_{8004}(775,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{293}{308}\right)\)	\(e\left(\frac{3}{154}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{129}{308}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{89}{308}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{141}{308}\right)\)
\(\chi_{8004}(823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{154}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{225}{308}\right)\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{221}{308}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{205}{308}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{41}{308}\right)\)
\(\chi_{8004}(859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{141}{154}\right)\)	\(e\left(\frac{61}{154}\right)\)	\(e\left(\frac{239}{308}\right)\)	\(e\left(\frac{137}{154}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{39}{308}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{163}{308}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{279}{308}\right)\)
\(\chi_{8004}(955,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{31}{154}\right)\)	\(e\left(\frac{23}{308}\right)\)	\(e\left(\frac{57}{154}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{295}{308}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{151}{308}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{215}{308}\right)\)
\(\chi_{8004}(1087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{154}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{145}{308}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{293}{308}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{269}{308}\right)\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{177}{308}\right)\)
\(\chi_{8004}(1099,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{154}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{115}{308}\right)\)	\(e\left(\frac{131}{154}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{243}{308}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{139}{308}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{151}{308}\right)\)
\(\chi_{8004}(1255,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{154}\right)\)	\(e\left(\frac{135}{154}\right)\)	\(e\left(\frac{279}{308}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{3}{308}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{131}{308}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{211}{308}\right)\)
\(\chi_{8004}(1291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{137}{154}\right)\)	\(e\left(\frac{47}{308}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{27}{308}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{255}{308}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{51}{308}\right)\)
\(\chi_{8004}(1315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{154}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{207}{308}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{191}{308}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{127}{308}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{87}{308}\right)\)
\(\chi_{8004}(1411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{305}{308}\right)\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{149}{308}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{141}{308}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{213}{308}\right)\)
\(\chi_{8004}(1435,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{154}\right)\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{61}{308}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{153}{308}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{213}{308}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{289}{308}\right)\)
\(\chi_{8004}(1603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{139}{308}\right)\)	\(e\left(\frac{3}{154}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{283}{308}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{243}{308}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{295}{308}\right)\)
\(\chi_{8004}(1639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{154}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{299}{308}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{139}{308}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{115}{308}\right)\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{23}{308}\right)\)
\(\chi_{8004}(1651,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{247}{308}\right)\)	\(e\left(\frac{43}{154}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{155}{308}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{95}{308}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{19}{308}\right)\)
\(\chi_{8004}(1783,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{89}{308}\right)\)	\(e\left(\frac{13}{154}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{97}{308}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{129}{308}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{149}{308}\right)\)
\(\chi_{8004}(1819,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{154}\right)\)	\(e\left(\frac{79}{154}\right)\)	\(e\left(\frac{153}{308}\right)\)	\(e\left(\frac{31}{154}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{101}{308}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{201}{308}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{225}{308}\right)\)
\(\chi_{8004}(1867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{103}{154}\right)\)	\(e\left(\frac{141}{308}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{81}{308}\right)\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{149}{308}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{153}{308}\right)\)
\(\chi_{8004}(1987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{154}\right)\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{215}{308}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{307}{308}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{59}{308}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{135}{308}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 120 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	8004.dk
Modulus	$8004$
Conductor	$2668$
Order	$308$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8004\)
Conductor:	\(2668\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(308\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2668.bs	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)