LMFDB - Dirichlet character orbit 8004.df

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8004, base_ring=CyclotomicField(154)) M = H._module chi = DirichletCharacter(H, M([0,77,133,44])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(53,8004)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8004$
Conductor:	$2001$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$154$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2001.bn	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:	$\Q(\zeta_{77})$
Fixed field:	Number field defined by a degree 154 polynomial (not computed)

First 31 of 60 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$25$	$31$	$35$	$37$
$\chi_{8004}(53,\cdot)$	$1$	$1$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{18}{77}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{153}{154}\right)$
$\chi_{8004}(65,\cdot)$	$1$	$1$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{154}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{93}{154}\right)$
$\chi_{8004}(281,\cdot)$	$1$	$1$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{23}{154}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{61}{154}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{81}{154}\right)$
$\chi_{8004}(401,\cdot)$	$1$	$1$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{3}{154}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{111}{154}\right)$
$\chi_{8004}(605,\cdot)$	$1$	$1$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{31}{154}\right)$	$e\left(\frac{131}{154}\right)$
$\chi_{8004}(893,\cdot)$	$1$	$1$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{101}{154}\right)$	$e\left(\frac{61}{77}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{71}{154}\right)$
$\chi_{8004}(953,\cdot)$	$1$	$1$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{69}{154}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{29}{154}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{101}{154}\right)$	$e\left(\frac{89}{154}\right)$
$\chi_{8004}(977,\cdot)$	$1$	$1$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{9}{154}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{131}{154}\right)$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{25}{154}\right)$
$\chi_{8004}(1109,\cdot)$	$1$	$1$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{151}{154}\right)$	$e\left(\frac{37}{154}\right)$
$\chi_{8004}(1325,\cdot)$	$1$	$1$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{61}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{154}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{113}{154}\right)$	$e\left(\frac{95}{154}\right)$
$\chi_{8004}(1445,\cdot)$	$1$	$1$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{59}{154}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{131}{154}\right)$	$e\left(\frac{27}{154}\right)$
$\chi_{8004}(1673,\cdot)$	$1$	$1$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{61}{77}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{39}{154}\right)$
$\chi_{8004}(1805,\cdot)$	$1$	$1$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{141}{154}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{153}{154}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{39}{154}\right)$	$e\left(\frac{135}{154}\right)$
$\chi_{8004}(1901,\cdot)$	$1$	$1$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{61}{154}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{135}{154}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{101}{154}\right)$
$\chi_{8004}(1937,\cdot)$	$1$	$1$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{67}{154}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{154}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{15}{154}\right)$
$\chi_{8004}(1997,\cdot)$	$1$	$1$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{57}{154}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{87}{154}\right)$	$e\left(\frac{5}{154}\right)$
$\chi_{8004}(2021,\cdot)$	$1$	$1$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{29}{154}\right)$	$e\left(\frac{53}{154}\right)$
$\chi_{8004}(2153,\cdot)$	$1$	$1$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{43}{154}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{27}{154}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{51}{154}\right)$
$\chi_{8004}(2489,\cdot)$	$1$	$1$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{39}{154}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{125}{154}\right)$
$\chi_{8004}(2501,\cdot)$	$1$	$1$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{29}{154}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{97}{154}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{67}{154}\right)$	$e\left(\frac{149}{154}\right)$
$\chi_{8004}(2597,\cdot)$	$1$	$1$	$e\left(\frac{18}{77}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{23}{154}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{27}{154}\right)$	$e\left(\frac{129}{154}\right)$
$\chi_{8004}(2633,\cdot)$	$1$	$1$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{87}{154}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{149}{154}\right)$	$e\left(\frac{113}{154}\right)$
$\chi_{8004}(2849,\cdot)$	$1$	$1$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{61}{77}\right)$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{9}{154}\right)$
$\chi_{8004}(2981,\cdot)$	$1$	$1$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{135}{154}\right)$	$e\left(\frac{29}{154}\right)$
$\chi_{8004}(3041,\cdot)$	$1$	$1$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{18}{77}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{103}{154}\right)$
$\chi_{8004}(3185,\cdot)$	$1$	$1$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{31}{154}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{61}{154}\right)$	$e\left(\frac{69}{154}\right)$
$\chi_{8004}(3329,\cdot)$	$1$	$1$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{31}{154}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{23}{154}\right)$	$e\left(\frac{127}{154}\right)$
$\chi_{8004}(3533,\cdot)$	$1$	$1$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{87}{154}\right)$	$e\left(\frac{18}{77}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{137}{154}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{47}{154}\right)$	$e\left(\frac{139}{154}\right)$
$\chi_{8004}(3641,\cdot)$	$1$	$1$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{97}{154}\right)$	$e\left(\frac{87}{154}\right)$
$\chi_{8004}(3677,\cdot)$	$1$	$1$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{137}{154}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{141}{154}\right)$
$\chi_{8004}(3737,\cdot)$	$1$	$1$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{97}{154}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{43}{154}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{17}{154}\right)$	$e\left(\frac{47}{154}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(31\)	\(35\)	\(37\)
\(\chi_{8004}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{18}{77}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{153}{154}\right)\)
\(\chi_{8004}(65,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{154}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{93}{154}\right)\)
\(\chi_{8004}(281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{23}{154}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{61}{154}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{81}{154}\right)\)
\(\chi_{8004}(401,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{3}{154}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{111}{154}\right)\)
\(\chi_{8004}(605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{31}{154}\right)\)	\(e\left(\frac{131}{154}\right)\)
\(\chi_{8004}(893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{101}{154}\right)\)	\(e\left(\frac{61}{77}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{71}{154}\right)\)
\(\chi_{8004}(953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{69}{154}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{29}{154}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{101}{154}\right)\)	\(e\left(\frac{89}{154}\right)\)
\(\chi_{8004}(977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{9}{154}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{131}{154}\right)\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{25}{154}\right)\)
\(\chi_{8004}(1109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{151}{154}\right)\)	\(e\left(\frac{37}{154}\right)\)
\(\chi_{8004}(1325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{61}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{154}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{113}{154}\right)\)	\(e\left(\frac{95}{154}\right)\)
\(\chi_{8004}(1445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{59}{154}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{131}{154}\right)\)	\(e\left(\frac{27}{154}\right)\)
\(\chi_{8004}(1673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{61}{77}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{39}{154}\right)\)
\(\chi_{8004}(1805,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{141}{154}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{153}{154}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{39}{154}\right)\)	\(e\left(\frac{135}{154}\right)\)
\(\chi_{8004}(1901,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{61}{154}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{135}{154}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{101}{154}\right)\)
\(\chi_{8004}(1937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{67}{154}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{17}{154}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{15}{154}\right)\)
\(\chi_{8004}(1997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{57}{154}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{87}{154}\right)\)	\(e\left(\frac{5}{154}\right)\)
\(\chi_{8004}(2021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{29}{154}\right)\)	\(e\left(\frac{53}{154}\right)\)
\(\chi_{8004}(2153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{43}{154}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{27}{154}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{51}{154}\right)\)
\(\chi_{8004}(2489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{39}{154}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{125}{154}\right)\)
\(\chi_{8004}(2501,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{29}{154}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{97}{154}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{67}{154}\right)\)	\(e\left(\frac{149}{154}\right)\)
\(\chi_{8004}(2597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{77}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{23}{154}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{27}{154}\right)\)	\(e\left(\frac{129}{154}\right)\)
\(\chi_{8004}(2633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{87}{154}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{149}{154}\right)\)	\(e\left(\frac{113}{154}\right)\)
\(\chi_{8004}(2849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{61}{77}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{9}{154}\right)\)
\(\chi_{8004}(2981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{135}{154}\right)\)	\(e\left(\frac{29}{154}\right)\)
\(\chi_{8004}(3041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{18}{77}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{103}{154}\right)\)
\(\chi_{8004}(3185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{31}{154}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{61}{154}\right)\)	\(e\left(\frac{69}{154}\right)\)
\(\chi_{8004}(3329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{31}{154}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{23}{154}\right)\)	\(e\left(\frac{127}{154}\right)\)
\(\chi_{8004}(3533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{87}{154}\right)\)	\(e\left(\frac{18}{77}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{137}{154}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{47}{154}\right)\)	\(e\left(\frac{139}{154}\right)\)
\(\chi_{8004}(3641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{97}{154}\right)\)	\(e\left(\frac{87}{154}\right)\)
\(\chi_{8004}(3677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{137}{154}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{141}{154}\right)\)
\(\chi_{8004}(3737,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{97}{154}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{43}{154}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{17}{154}\right)\)	\(e\left(\frac{47}{154}\right)\)

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First 31 of 60 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.df
Modulus	$8004$
Conductor	$2001$
Order	$154$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8004\)
Conductor:	\(2001\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(154\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2001.bn	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)