LMFDB - Group of Dirichlet characters of modulus 1004

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1004)

pari: g = idealstar(,1004,2)

Character group

sage: G.order() pari: g.no
Order	=	500
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{250}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1004}(503,\cdot)$, $\chi_{1004}(257,\cdot)$

First 32 of 500 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{1004}(1,\cdot)$	1004.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1004}(3,\cdot)$	1004.p	250	yes	$-1$	$1$	$e\left(\frac{131}{250}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{93}{250}\right)$	$e\left(\frac{6}{125}\right)$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{211}{250}\right)$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{233}{250}\right)$	$e\left(\frac{112}{125}\right)$
$\chi_{1004}(5,\cdot)$	1004.i	25	no	$1$	$1$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{7}{25}\right)$
$\chi_{1004}(7,\cdot)$	1004.p	250	yes	$-1$	$1$	$e\left(\frac{93}{250}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{129}{250}\right)$	$e\left(\frac{93}{125}\right)$	$e\left(\frac{203}{250}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{111}{125}\right)$
$\chi_{1004}(9,\cdot)$	1004.m	125	no	$1$	$1$	$e\left(\frac{6}{125}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{93}{125}\right)$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{1}{125}\right)$	$e\left(\frac{37}{125}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{108}{125}\right)$	$e\left(\frac{99}{125}\right)$
$\chi_{1004}(11,\cdot)$	1004.o	250	yes	$1$	$1$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{203}{250}\right)$	$e\left(\frac{1}{125}\right)$	$e\left(\frac{73}{125}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{181}{250}\right)$	$e\left(\frac{57}{125}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{102}{125}\right)$
$\chi_{1004}(13,\cdot)$	1004.m	125	no	$1$	$1$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{37}{125}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{62}{125}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{109}{125}\right)$	$e\left(\frac{83}{125}\right)$	$e\left(\frac{24}{125}\right)$
$\chi_{1004}(15,\cdot)$	1004.p	250	yes	$-1$	$1$	$e\left(\frac{211}{250}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{181}{250}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{191}{250}\right)$	$e\left(\frac{27}{125}\right)$	$e\left(\frac{173}{250}\right)$	$e\left(\frac{22}{125}\right)$
$\chi_{1004}(17,\cdot)$	1004.m	125	no	$1$	$1$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{57}{125}\right)$	$e\left(\frac{109}{125}\right)$	$e\left(\frac{27}{125}\right)$	$e\left(\frac{113}{125}\right)$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{18}{125}\right)$
$\chi_{1004}(19,\cdot)$	1004.o	250	yes	$1$	$1$	$e\left(\frac{233}{250}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{108}{125}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{83}{125}\right)$	$e\left(\frac{173}{250}\right)$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{16}{125}\right)$
$\chi_{1004}(21,\cdot)$	1004.m	125	no	$1$	$1$	$e\left(\frac{112}{125}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{99}{125}\right)$	$e\left(\frac{102}{125}\right)$	$e\left(\frac{24}{125}\right)$	$e\left(\frac{22}{125}\right)$	$e\left(\frac{18}{125}\right)$	$e\left(\frac{16}{125}\right)$	$e\left(\frac{98}{125}\right)$
$\chi_{1004}(23,\cdot)$	1004.p	250	yes	$-1$	$1$	$e\left(\frac{9}{250}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{77}{250}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{189}{250}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{129}{250}\right)$	$e\left(\frac{13}{125}\right)$	$e\left(\frac{37}{250}\right)$	$e\left(\frac{43}{125}\right)$
$\chi_{1004}(25,\cdot)$	1004.i	25	no	$1$	$1$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{14}{25}\right)$
$\chi_{1004}(27,\cdot)$	1004.p	250	yes	$-1$	$1$	$e\left(\frac{143}{250}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{29}{250}\right)$	$e\left(\frac{18}{125}\right)$	$e\left(\frac{3}{250}\right)$	$e\left(\frac{118}{125}\right)$	$e\left(\frac{133}{250}\right)$	$e\left(\frac{26}{125}\right)$	$e\left(\frac{199}{250}\right)$	$e\left(\frac{86}{125}\right)$
$\chi_{1004}(29,\cdot)$	1004.n	250	no	$-1$	$1$	$e\left(\frac{39}{125}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{13}{250}\right)$	$e\left(\frac{53}{125}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{71}{125}\right)$	$e\left(\frac{29}{250}\right)$	$e\left(\frac{81}{125}\right)$
$\chi_{1004}(31,\cdot)$	1004.p	250	yes	$-1$	$1$	$e\left(\frac{101}{250}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{3}{250}\right)$	$e\left(\frac{101}{125}\right)$	$e\left(\frac{121}{250}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{31}{250}\right)$	$e\left(\frac{7}{125}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{52}{125}\right)$
$\chi_{1004}(33,\cdot)$	1004.n	250	no	$-1$	$1$	$e\left(\frac{66}{125}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{7}{125}\right)$	$e\left(\frac{147}{250}\right)$	$e\left(\frac{32}{125}\right)$	$e\left(\frac{71}{125}\right)$	$e\left(\frac{24}{125}\right)$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{89}{125}\right)$
$\chi_{1004}(35,\cdot)$	1004.p	250	yes	$-1$	$1$	$e\left(\frac{173}{250}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{119}{250}\right)$	$e\left(\frac{48}{125}\right)$	$e\left(\frac{133}{250}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{63}{250}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{21}{125}\right)$
$\chi_{1004}(37,\cdot)$	1004.n	250	no	$-1$	$1$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{62}{125}\right)$	$e\left(\frac{177}{250}\right)$	$e\left(\frac{87}{125}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{34}{125}\right)$	$e\left(\frac{241}{250}\right)$	$e\left(\frac{74}{125}\right)$
$\chi_{1004}(39,\cdot)$	1004.p	250	yes	$-1$	$1$	$e\left(\frac{43}{250}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{229}{250}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{153}{250}\right)$	$e\left(\frac{18}{125}\right)$	$e\left(\frac{33}{250}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{149}{250}\right)$	$e\left(\frac{11}{125}\right)$
$\chi_{1004}(41,\cdot)$	1004.m	125	no	$1$	$1$	$e\left(\frac{32}{125}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{121}{125}\right)$	$e\left(\frac{64}{125}\right)$	$e\left(\frac{47}{125}\right)$	$e\left(\frac{114}{125}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{28}{125}\right)$
$\chi_{1004}(43,\cdot)$	1004.o	250	yes	$1$	$1$	$e\left(\frac{77}{250}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{131}{250}\right)$	$e\left(\frac{77}{125}\right)$	$e\left(\frac{121}{125}\right)$	$e\left(\frac{102}{125}\right)$	$e\left(\frac{187}{250}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{104}{125}\right)$
$\chi_{1004}(45,\cdot)$	1004.m	125	no	$1$	$1$	$e\left(\frac{46}{125}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{88}{125}\right)$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{91}{125}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{119}{125}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{9}{125}\right)$
$\chi_{1004}(47,\cdot)$	1004.j	50	yes	$1$	$1$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{9}{25}\right)$
$\chi_{1004}(49,\cdot)$	1004.m	125	no	$1$	$1$	$e\left(\frac{93}{125}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{4}{125}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{11}{125}\right)$	$e\left(\frac{83}{125}\right)$	$e\left(\frac{102}{125}\right)$	$e\left(\frac{49}{125}\right)$	$e\left(\frac{97}{125}\right)$
$\chi_{1004}(51,\cdot)$	1004.l	50	yes	$-1$	$1$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{1}{25}\right)$
$\chi_{1004}(53,\cdot)$	1004.n	250	no	$-1$	$1$	$e\left(\frac{74}{125}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{22}{125}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{233}{250}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{19}{125}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{39}{250}\right)$	$e\left(\frac{96}{125}\right)$
$\chi_{1004}(55,\cdot)$	1004.o	250	yes	$1$	$1$	$e\left(\frac{81}{250}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{38}{125}\right)$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{161}{250}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{104}{125}\right)$	$e\left(\frac{12}{125}\right)$
$\chi_{1004}(57,\cdot)$	1004.n	250	no	$-1$	$1$	$e\left(\frac{57}{125}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{71}{125}\right)$	$e\left(\frac{114}{125}\right)$	$e\left(\frac{19}{250}\right)$	$e\left(\frac{39}{125}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{177}{250}\right)$	$e\left(\frac{3}{125}\right)$
$\chi_{1004}(59,\cdot)$	1004.o	250	yes	$1$	$1$	$e\left(\frac{191}{250}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{23}{250}\right)$	$e\left(\frac{66}{125}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{16}{125}\right)$	$e\left(\frac{71}{250}\right)$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{94}{125}\right)$	$e\left(\frac{107}{125}\right)$
$\chi_{1004}(61,\cdot)$	1004.n	250	no	$-1$	$1$	$e\left(\frac{99}{125}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{73}{125}\right)$	$e\left(\frac{33}{250}\right)$	$e\left(\frac{48}{125}\right)$	$e\left(\frac{44}{125}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{189}{250}\right)$	$e\left(\frac{71}{125}\right)$
$\chi_{1004}(63,\cdot)$	1004.l	50	yes	$-1$	$1$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{17}{25}\right)$

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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 $\F_{q}$

Modulus	$1004$
Structure	\(C_{2}\times C_{250}\)
Order	$500$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{1004}(1,\cdot)\)	1004.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1004}(3,\cdot)\)	1004.p	250	yes	\(-1\)	\(1\)	\(e\left(\frac{131}{250}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{93}{250}\right)\)	\(e\left(\frac{6}{125}\right)\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{211}{250}\right)\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{233}{250}\right)\)	\(e\left(\frac{112}{125}\right)\)
\(\chi_{1004}(5,\cdot)\)	1004.i	25	no	\(1\)	\(1\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)
\(\chi_{1004}(7,\cdot)\)	1004.p	250	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{250}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{129}{250}\right)\)	\(e\left(\frac{93}{125}\right)\)	\(e\left(\frac{203}{250}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{111}{125}\right)\)
\(\chi_{1004}(9,\cdot)\)	1004.m	125	no	\(1\)	\(1\)	\(e\left(\frac{6}{125}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{93}{125}\right)\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{1}{125}\right)\)	\(e\left(\frac{37}{125}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{108}{125}\right)\)	\(e\left(\frac{99}{125}\right)\)
\(\chi_{1004}(11,\cdot)\)	1004.o	250	yes	\(1\)	\(1\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{203}{250}\right)\)	\(e\left(\frac{1}{125}\right)\)	\(e\left(\frac{73}{125}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{181}{250}\right)\)	\(e\left(\frac{57}{125}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{102}{125}\right)\)
\(\chi_{1004}(13,\cdot)\)	1004.m	125	no	\(1\)	\(1\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{37}{125}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{62}{125}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{109}{125}\right)\)	\(e\left(\frac{83}{125}\right)\)	\(e\left(\frac{24}{125}\right)\)
\(\chi_{1004}(15,\cdot)\)	1004.p	250	yes	\(-1\)	\(1\)	\(e\left(\frac{211}{250}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{181}{250}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{191}{250}\right)\)	\(e\left(\frac{27}{125}\right)\)	\(e\left(\frac{173}{250}\right)\)	\(e\left(\frac{22}{125}\right)\)
\(\chi_{1004}(17,\cdot)\)	1004.m	125	no	\(1\)	\(1\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{57}{125}\right)\)	\(e\left(\frac{109}{125}\right)\)	\(e\left(\frac{27}{125}\right)\)	\(e\left(\frac{113}{125}\right)\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{18}{125}\right)\)
\(\chi_{1004}(19,\cdot)\)	1004.o	250	yes	\(1\)	\(1\)	\(e\left(\frac{233}{250}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{108}{125}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{83}{125}\right)\)	\(e\left(\frac{173}{250}\right)\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{16}{125}\right)\)
\(\chi_{1004}(21,\cdot)\)	1004.m	125	no	\(1\)	\(1\)	\(e\left(\frac{112}{125}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{99}{125}\right)\)	\(e\left(\frac{102}{125}\right)\)	\(e\left(\frac{24}{125}\right)\)	\(e\left(\frac{22}{125}\right)\)	\(e\left(\frac{18}{125}\right)\)	\(e\left(\frac{16}{125}\right)\)	\(e\left(\frac{98}{125}\right)\)
\(\chi_{1004}(23,\cdot)\)	1004.p	250	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{250}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{77}{250}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{189}{250}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{129}{250}\right)\)	\(e\left(\frac{13}{125}\right)\)	\(e\left(\frac{37}{250}\right)\)	\(e\left(\frac{43}{125}\right)\)
\(\chi_{1004}(25,\cdot)\)	1004.i	25	no	\(1\)	\(1\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)
\(\chi_{1004}(27,\cdot)\)	1004.p	250	yes	\(-1\)	\(1\)	\(e\left(\frac{143}{250}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{29}{250}\right)\)	\(e\left(\frac{18}{125}\right)\)	\(e\left(\frac{3}{250}\right)\)	\(e\left(\frac{118}{125}\right)\)	\(e\left(\frac{133}{250}\right)\)	\(e\left(\frac{26}{125}\right)\)	\(e\left(\frac{199}{250}\right)\)	\(e\left(\frac{86}{125}\right)\)
\(\chi_{1004}(29,\cdot)\)	1004.n	250	no	\(-1\)	\(1\)	\(e\left(\frac{39}{125}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{13}{250}\right)\)	\(e\left(\frac{53}{125}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{71}{125}\right)\)	\(e\left(\frac{29}{250}\right)\)	\(e\left(\frac{81}{125}\right)\)
\(\chi_{1004}(31,\cdot)\)	1004.p	250	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{250}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{3}{250}\right)\)	\(e\left(\frac{101}{125}\right)\)	\(e\left(\frac{121}{250}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{31}{250}\right)\)	\(e\left(\frac{7}{125}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{52}{125}\right)\)
\(\chi_{1004}(33,\cdot)\)	1004.n	250	no	\(-1\)	\(1\)	\(e\left(\frac{66}{125}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{7}{125}\right)\)	\(e\left(\frac{147}{250}\right)\)	\(e\left(\frac{32}{125}\right)\)	\(e\left(\frac{71}{125}\right)\)	\(e\left(\frac{24}{125}\right)\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{89}{125}\right)\)
\(\chi_{1004}(35,\cdot)\)	1004.p	250	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{250}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{119}{250}\right)\)	\(e\left(\frac{48}{125}\right)\)	\(e\left(\frac{133}{250}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{63}{250}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{21}{125}\right)\)
\(\chi_{1004}(37,\cdot)\)	1004.n	250	no	\(-1\)	\(1\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{62}{125}\right)\)	\(e\left(\frac{177}{250}\right)\)	\(e\left(\frac{87}{125}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{34}{125}\right)\)	\(e\left(\frac{241}{250}\right)\)	\(e\left(\frac{74}{125}\right)\)
\(\chi_{1004}(39,\cdot)\)	1004.p	250	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{250}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{229}{250}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{153}{250}\right)\)	\(e\left(\frac{18}{125}\right)\)	\(e\left(\frac{33}{250}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{149}{250}\right)\)	\(e\left(\frac{11}{125}\right)\)
\(\chi_{1004}(41,\cdot)\)	1004.m	125	no	\(1\)	\(1\)	\(e\left(\frac{32}{125}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{121}{125}\right)\)	\(e\left(\frac{64}{125}\right)\)	\(e\left(\frac{47}{125}\right)\)	\(e\left(\frac{114}{125}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{28}{125}\right)\)
\(\chi_{1004}(43,\cdot)\)	1004.o	250	yes	\(1\)	\(1\)	\(e\left(\frac{77}{250}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{131}{250}\right)\)	\(e\left(\frac{77}{125}\right)\)	\(e\left(\frac{121}{125}\right)\)	\(e\left(\frac{102}{125}\right)\)	\(e\left(\frac{187}{250}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{104}{125}\right)\)
\(\chi_{1004}(45,\cdot)\)	1004.m	125	no	\(1\)	\(1\)	\(e\left(\frac{46}{125}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{88}{125}\right)\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{91}{125}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{119}{125}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{9}{125}\right)\)
\(\chi_{1004}(47,\cdot)\)	1004.j	50	yes	\(1\)	\(1\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)
\(\chi_{1004}(49,\cdot)\)	1004.m	125	no	\(1\)	\(1\)	\(e\left(\frac{93}{125}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{4}{125}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{11}{125}\right)\)	\(e\left(\frac{83}{125}\right)\)	\(e\left(\frac{102}{125}\right)\)	\(e\left(\frac{49}{125}\right)\)	\(e\left(\frac{97}{125}\right)\)
\(\chi_{1004}(51,\cdot)\)	1004.l	50	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{1}{25}\right)\)
\(\chi_{1004}(53,\cdot)\)	1004.n	250	no	\(-1\)	\(1\)	\(e\left(\frac{74}{125}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{22}{125}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{233}{250}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{19}{125}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{39}{250}\right)\)	\(e\left(\frac{96}{125}\right)\)
\(\chi_{1004}(55,\cdot)\)	1004.o	250	yes	\(1\)	\(1\)	\(e\left(\frac{81}{250}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{38}{125}\right)\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{161}{250}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{104}{125}\right)\)	\(e\left(\frac{12}{125}\right)\)
\(\chi_{1004}(57,\cdot)\)	1004.n	250	no	\(-1\)	\(1\)	\(e\left(\frac{57}{125}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{71}{125}\right)\)	\(e\left(\frac{114}{125}\right)\)	\(e\left(\frac{19}{250}\right)\)	\(e\left(\frac{39}{125}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{177}{250}\right)\)	\(e\left(\frac{3}{125}\right)\)
\(\chi_{1004}(59,\cdot)\)	1004.o	250	yes	\(1\)	\(1\)	\(e\left(\frac{191}{250}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{23}{250}\right)\)	\(e\left(\frac{66}{125}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{16}{125}\right)\)	\(e\left(\frac{71}{250}\right)\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{94}{125}\right)\)	\(e\left(\frac{107}{125}\right)\)
\(\chi_{1004}(61,\cdot)\)	1004.n	250	no	\(-1\)	\(1\)	\(e\left(\frac{99}{125}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{73}{125}\right)\)	\(e\left(\frac{33}{250}\right)\)	\(e\left(\frac{48}{125}\right)\)	\(e\left(\frac{44}{125}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{189}{250}\right)\)	\(e\left(\frac{71}{125}\right)\)
\(\chi_{1004}(63,\cdot)\)	1004.l	50	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.