LMFDB - Group of Dirichlet characters of modulus 8048

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8048)

pari: g = idealstar(,8048,2)

Character group

sage: G.order() pari: g.no
Order	=	4016
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{1004}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8048}(1007,\cdot)$, $\chi_{8048}(6037,\cdot)$, $\chi_{8048}(2017,\cdot)$

First 32 of 4016 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8048}(1,\cdot)$	8048.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8048}(3,\cdot)$	8048.v	1004	yes	$-1$	$1$	$e\left(\frac{229}{1004}\right)$	$e\left(\frac{61}{1004}\right)$	$e\left(\frac{182}{251}\right)$	$e\left(\frac{229}{502}\right)$	$e\left(\frac{303}{1004}\right)$	$e\left(\frac{787}{1004}\right)$	$e\left(\frac{145}{502}\right)$	$e\left(\frac{41}{251}\right)$	$e\left(\frac{401}{1004}\right)$	$e\left(\frac{957}{1004}\right)$
$\chi_{8048}(5,\cdot)$	8048.x	1004	yes	$-1$	$1$	$e\left(\frac{61}{1004}\right)$	$e\left(\frac{253}{1004}\right)$	$e\left(\frac{337}{502}\right)$	$e\left(\frac{61}{502}\right)$	$e\left(\frac{335}{1004}\right)$	$e\left(\frac{1001}{1004}\right)$	$e\left(\frac{157}{502}\right)$	$e\left(\frac{229}{502}\right)$	$e\left(\frac{223}{1004}\right)$	$e\left(\frac{735}{1004}\right)$
$\chi_{8048}(7,\cdot)$	8048.p	502	no	$-1$	$1$	$e\left(\frac{182}{251}\right)$	$e\left(\frac{337}{502}\right)$	$e\left(\frac{117}{502}\right)$	$e\left(\frac{113}{251}\right)$	$e\left(\frac{49}{251}\right)$	$e\left(\frac{373}{502}\right)$	$e\left(\frac{199}{502}\right)$	$e\left(\frac{58}{251}\right)$	$e\left(\frac{151}{251}\right)$	$e\left(\frac{481}{502}\right)$
$\chi_{8048}(9,\cdot)$	8048.s	502	no	$1$	$1$	$e\left(\frac{229}{502}\right)$	$e\left(\frac{61}{502}\right)$	$e\left(\frac{113}{251}\right)$	$e\left(\frac{229}{251}\right)$	$e\left(\frac{303}{502}\right)$	$e\left(\frac{285}{502}\right)$	$e\left(\frac{145}{251}\right)$	$e\left(\frac{82}{251}\right)$	$e\left(\frac{401}{502}\right)$	$e\left(\frac{455}{502}\right)$
$\chi_{8048}(11,\cdot)$	8048.v	1004	yes	$-1$	$1$	$e\left(\frac{303}{1004}\right)$	$e\left(\frac{335}{1004}\right)$	$e\left(\frac{49}{251}\right)$	$e\left(\frac{303}{502}\right)$	$e\left(\frac{265}{1004}\right)$	$e\left(\frac{125}{1004}\right)$	$e\left(\frac{319}{502}\right)$	$e\left(\frac{40}{251}\right)$	$e\left(\frac{79}{1004}\right)$	$e\left(\frac{499}{1004}\right)$
$\chi_{8048}(13,\cdot)$	8048.w	1004	yes	$1$	$1$	$e\left(\frac{787}{1004}\right)$	$e\left(\frac{1001}{1004}\right)$	$e\left(\frac{373}{502}\right)$	$e\left(\frac{285}{502}\right)$	$e\left(\frac{125}{1004}\right)$	$e\left(\frac{883}{1004}\right)$	$e\left(\frac{196}{251}\right)$	$e\left(\frac{142}{251}\right)$	$e\left(\frac{795}{1004}\right)$	$e\left(\frac{529}{1004}\right)$
$\chi_{8048}(15,\cdot)$	8048.t	502	no	$1$	$1$	$e\left(\frac{145}{502}\right)$	$e\left(\frac{157}{502}\right)$	$e\left(\frac{199}{502}\right)$	$e\left(\frac{145}{251}\right)$	$e\left(\frac{319}{502}\right)$	$e\left(\frac{196}{251}\right)$	$e\left(\frac{151}{251}\right)$	$e\left(\frac{311}{502}\right)$	$e\left(\frac{156}{251}\right)$	$e\left(\frac{172}{251}\right)$
$\chi_{8048}(17,\cdot)$	8048.o	502	no	$-1$	$1$	$e\left(\frac{41}{251}\right)$	$e\left(\frac{229}{502}\right)$	$e\left(\frac{58}{251}\right)$	$e\left(\frac{82}{251}\right)$	$e\left(\frac{40}{251}\right)$	$e\left(\frac{142}{251}\right)$	$e\left(\frac{311}{502}\right)$	$e\left(\frac{233}{502}\right)$	$e\left(\frac{57}{502}\right)$	$e\left(\frac{99}{251}\right)$
$\chi_{8048}(19,\cdot)$	8048.u	1004	yes	$1$	$1$	$e\left(\frac{401}{1004}\right)$	$e\left(\frac{223}{1004}\right)$	$e\left(\frac{151}{251}\right)$	$e\left(\frac{401}{502}\right)$	$e\left(\frac{79}{1004}\right)$	$e\left(\frac{795}{1004}\right)$	$e\left(\frac{156}{251}\right)$	$e\left(\frac{57}{502}\right)$	$e\left(\frac{643}{1004}\right)$	$e\left(\frac{1}{1004}\right)$
$\chi_{8048}(21,\cdot)$	8048.w	1004	yes	$1$	$1$	$e\left(\frac{957}{1004}\right)$	$e\left(\frac{735}{1004}\right)$	$e\left(\frac{481}{502}\right)$	$e\left(\frac{455}{502}\right)$	$e\left(\frac{499}{1004}\right)$	$e\left(\frac{529}{1004}\right)$	$e\left(\frac{172}{251}\right)$	$e\left(\frac{99}{251}\right)$	$e\left(\frac{1}{1004}\right)$	$e\left(\frac{915}{1004}\right)$
$\chi_{8048}(23,\cdot)$	8048.p	502	no	$-1$	$1$	$e\left(\frac{164}{251}\right)$	$e\left(\frac{163}{502}\right)$	$e\left(\frac{213}{502}\right)$	$e\left(\frac{77}{251}\right)$	$e\left(\frac{160}{251}\right)$	$e\left(\frac{383}{502}\right)$	$e\left(\frac{491}{502}\right)$	$e\left(\frac{215}{251}\right)$	$e\left(\frac{114}{251}\right)$	$e\left(\frac{39}{502}\right)$
$\chi_{8048}(25,\cdot)$	8048.s	502	no	$1$	$1$	$e\left(\frac{61}{502}\right)$	$e\left(\frac{253}{502}\right)$	$e\left(\frac{86}{251}\right)$	$e\left(\frac{61}{251}\right)$	$e\left(\frac{335}{502}\right)$	$e\left(\frac{499}{502}\right)$	$e\left(\frac{157}{251}\right)$	$e\left(\frac{229}{251}\right)$	$e\left(\frac{223}{502}\right)$	$e\left(\frac{233}{502}\right)$
$\chi_{8048}(27,\cdot)$	8048.v	1004	yes	$-1$	$1$	$e\left(\frac{687}{1004}\right)$	$e\left(\frac{183}{1004}\right)$	$e\left(\frac{44}{251}\right)$	$e\left(\frac{185}{502}\right)$	$e\left(\frac{909}{1004}\right)$	$e\left(\frac{353}{1004}\right)$	$e\left(\frac{435}{502}\right)$	$e\left(\frac{123}{251}\right)$	$e\left(\frac{199}{1004}\right)$	$e\left(\frac{863}{1004}\right)$
$\chi_{8048}(29,\cdot)$	8048.x	1004	yes	$-1$	$1$	$e\left(\frac{171}{1004}\right)$	$e\left(\frac{199}{1004}\right)$	$e\left(\frac{23}{502}\right)$	$e\left(\frac{171}{502}\right)$	$e\left(\frac{577}{1004}\right)$	$e\left(\frac{831}{1004}\right)$	$e\left(\frac{185}{502}\right)$	$e\left(\frac{321}{502}\right)$	$e\left(\frac{477}{1004}\right)$	$e\left(\frac{217}{1004}\right)$
$\chi_{8048}(31,\cdot)$	8048.t	502	no	$1$	$1$	$e\left(\frac{67}{502}\right)$	$e\left(\frac{31}{502}\right)$	$e\left(\frac{407}{502}\right)$	$e\left(\frac{67}{251}\right)$	$e\left(\frac{47}{502}\right)$	$e\left(\frac{165}{251}\right)$	$e\left(\frac{49}{251}\right)$	$e\left(\frac{71}{502}\right)$	$e\left(\frac{34}{251}\right)$	$e\left(\frac{237}{251}\right)$
$\chi_{8048}(33,\cdot)$	8048.m	251	no	$1$	$1$	$e\left(\frac{133}{251}\right)$	$e\left(\frac{99}{251}\right)$	$e\left(\frac{231}{251}\right)$	$e\left(\frac{15}{251}\right)$	$e\left(\frac{142}{251}\right)$	$e\left(\frac{228}{251}\right)$	$e\left(\frac{232}{251}\right)$	$e\left(\frac{81}{251}\right)$	$e\left(\frac{120}{251}\right)$	$e\left(\frac{113}{251}\right)$
$\chi_{8048}(35,\cdot)$	8048.u	1004	yes	$1$	$1$	$e\left(\frac{789}{1004}\right)$	$e\left(\frac{927}{1004}\right)$	$e\left(\frac{227}{251}\right)$	$e\left(\frac{287}{502}\right)$	$e\left(\frac{531}{1004}\right)$	$e\left(\frac{743}{1004}\right)$	$e\left(\frac{178}{251}\right)$	$e\left(\frac{345}{502}\right)$	$e\left(\frac{827}{1004}\right)$	$e\left(\frac{693}{1004}\right)$
$\chi_{8048}(37,\cdot)$	8048.x	1004	yes	$-1$	$1$	$e\left(\frac{41}{1004}\right)$	$e\left(\frac{993}{1004}\right)$	$e\left(\frac{29}{502}\right)$	$e\left(\frac{41}{502}\right)$	$e\left(\frac{291}{1004}\right)$	$e\left(\frac{393}{1004}\right)$	$e\left(\frac{15}{502}\right)$	$e\left(\frac{121}{502}\right)$	$e\left(\frac{907}{1004}\right)$	$e\left(\frac{99}{1004}\right)$
$\chi_{8048}(39,\cdot)$	8048.p	502	no	$-1$	$1$	$e\left(\frac{3}{251}\right)$	$e\left(\frac{29}{502}\right)$	$e\left(\frac{235}{502}\right)$	$e\left(\frac{6}{251}\right)$	$e\left(\frac{107}{251}\right)$	$e\left(\frac{333}{502}\right)$	$e\left(\frac{35}{502}\right)$	$e\left(\frac{183}{251}\right)$	$e\left(\frac{48}{251}\right)$	$e\left(\frac{241}{502}\right)$
$\chi_{8048}(41,\cdot)$	8048.q	502	no	$-1$	$1$	$e\left(\frac{265}{502}\right)$	$e\left(\frac{243}{251}\right)$	$e\left(\frac{65}{251}\right)$	$e\left(\frac{14}{251}\right)$	$e\left(\frac{81}{502}\right)$	$e\left(\frac{275}{502}\right)$	$e\left(\frac{249}{502}\right)$	$e\left(\frac{101}{502}\right)$	$e\left(\frac{112}{251}\right)$	$e\left(\frac{395}{502}\right)$
$\chi_{8048}(43,\cdot)$	8048.v	1004	yes	$-1$	$1$	$e\left(\frac{763}{1004}\right)$	$e\left(\frac{383}{1004}\right)$	$e\left(\frac{77}{251}\right)$	$e\left(\frac{261}{502}\right)$	$e\left(\frac{273}{1004}\right)$	$e\left(\frac{53}{1004}\right)$	$e\left(\frac{71}{502}\right)$	$e\left(\frac{27}{251}\right)$	$e\left(\frac{411}{1004}\right)$	$e\left(\frac{67}{1004}\right)$
$\chi_{8048}(45,\cdot)$	8048.x	1004	yes	$-1$	$1$	$e\left(\frac{519}{1004}\right)$	$e\left(\frac{375}{1004}\right)$	$e\left(\frac{61}{502}\right)$	$e\left(\frac{17}{502}\right)$	$e\left(\frac{941}{1004}\right)$	$e\left(\frac{567}{1004}\right)$	$e\left(\frac{447}{502}\right)$	$e\left(\frac{393}{502}\right)$	$e\left(\frac{21}{1004}\right)$	$e\left(\frac{641}{1004}\right)$
$\chi_{8048}(47,\cdot)$	8048.r	502	no	$-1$	$1$	$e\left(\frac{475}{502}\right)$	$e\left(\frac{123}{251}\right)$	$e\left(\frac{323}{502}\right)$	$e\left(\frac{224}{251}\right)$	$e\left(\frac{41}{502}\right)$	$e\left(\frac{192}{251}\right)$	$e\left(\frac{219}{502}\right)$	$e\left(\frac{55}{251}\right)$	$e\left(\frac{321}{502}\right)$	$e\left(\frac{148}{251}\right)$
$\chi_{8048}(49,\cdot)$	8048.m	251	no	$1$	$1$	$e\left(\frac{113}{251}\right)$	$e\left(\frac{86}{251}\right)$	$e\left(\frac{117}{251}\right)$	$e\left(\frac{226}{251}\right)$	$e\left(\frac{98}{251}\right)$	$e\left(\frac{122}{251}\right)$	$e\left(\frac{199}{251}\right)$	$e\left(\frac{116}{251}\right)$	$e\left(\frac{51}{251}\right)$	$e\left(\frac{230}{251}\right)$
$\chi_{8048}(51,\cdot)$	8048.u	1004	yes	$1$	$1$	$e\left(\frac{393}{1004}\right)$	$e\left(\frac{519}{1004}\right)$	$e\left(\frac{240}{251}\right)$	$e\left(\frac{393}{502}\right)$	$e\left(\frac{463}{1004}\right)$	$e\left(\frac{351}{1004}\right)$	$e\left(\frac{228}{251}\right)$	$e\left(\frac{315}{502}\right)$	$e\left(\frac{515}{1004}\right)$	$e\left(\frac{349}{1004}\right)$
$\chi_{8048}(53,\cdot)$	8048.x	1004	yes	$-1$	$1$	$e\left(\frac{101}{1004}\right)$	$e\left(\frac{781}{1004}\right)$	$e\left(\frac{451}{502}\right)$	$e\left(\frac{101}{502}\right)$	$e\left(\frac{423}{1004}\right)$	$e\left(\frac{209}{1004}\right)$	$e\left(\frac{441}{502}\right)$	$e\left(\frac{445}{502}\right)$	$e\left(\frac{863}{1004}\right)$	$e\left(\frac{1003}{1004}\right)$
$\chi_{8048}(55,\cdot)$	8048.n	502	no	$1$	$1$	$e\left(\frac{91}{251}\right)$	$e\left(\frac{147}{251}\right)$	$e\left(\frac{435}{502}\right)$	$e\left(\frac{182}{251}\right)$	$e\left(\frac{150}{251}\right)$	$e\left(\frac{61}{502}\right)$	$e\left(\frac{238}{251}\right)$	$e\left(\frac{309}{502}\right)$	$e\left(\frac{151}{502}\right)$	$e\left(\frac{115}{502}\right)$
$\chi_{8048}(57,\cdot)$	8048.q	502	no	$-1$	$1$	$e\left(\frac{315}{502}\right)$	$e\left(\frac{71}{251}\right)$	$e\left(\frac{82}{251}\right)$	$e\left(\frac{64}{251}\right)$	$e\left(\frac{191}{502}\right)$	$e\left(\frac{289}{502}\right)$	$e\left(\frac{457}{502}\right)$	$e\left(\frac{139}{502}\right)$	$e\left(\frac{10}{251}\right)$	$e\left(\frac{479}{502}\right)$
$\chi_{8048}(59,\cdot)$	8048.v	1004	yes	$-1$	$1$	$e\left(\frac{567}{1004}\right)$	$e\left(\frac{607}{1004}\right)$	$e\left(\frac{124}{251}\right)$	$e\left(\frac{65}{502}\right)$	$e\left(\frac{645}{1004}\right)$	$e\left(\frac{721}{1004}\right)$	$e\left(\frac{85}{502}\right)$	$e\left(\frac{50}{251}\right)$	$e\left(\frac{287}{1004}\right)$	$e\left(\frac{59}{1004}\right)$
$\chi_{8048}(61,\cdot)$	8048.w	1004	yes	$1$	$1$	$e\left(\frac{723}{1004}\right)$	$e\left(\frac{357}{1004}\right)$	$e\left(\frac{291}{502}\right)$	$e\left(\frac{221}{502}\right)$	$e\left(\frac{185}{1004}\right)$	$e\left(\frac{343}{1004}\right)$	$e\left(\frac{19}{251}\right)$	$e\left(\frac{170}{251}\right)$	$e\left(\frac{775}{1004}\right)$	$e\left(\frac{301}{1004}\right)$
$\chi_{8048}(63,\cdot)$	8048.r	502	no	$-1$	$1$	$e\left(\frac{91}{502}\right)$	$e\left(\frac{199}{251}\right)$	$e\left(\frac{343}{502}\right)$	$e\left(\frac{91}{251}\right)$	$e\left(\frac{401}{502}\right)$	$e\left(\frac{78}{251}\right)$	$e\left(\frac{489}{502}\right)$	$e\left(\frac{140}{251}\right)$	$e\left(\frac{201}{502}\right)$	$e\left(\frac{217}{251}\right)$

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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	$8048$
Structure	\(C_{2}\times C_{2}\times C_{1004}\)
Order	$4016$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8048}(1,\cdot)\)	8048.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8048}(3,\cdot)\)	8048.v	1004	yes	\(-1\)	\(1\)	\(e\left(\frac{229}{1004}\right)\)	\(e\left(\frac{61}{1004}\right)\)	\(e\left(\frac{182}{251}\right)\)	\(e\left(\frac{229}{502}\right)\)	\(e\left(\frac{303}{1004}\right)\)	\(e\left(\frac{787}{1004}\right)\)	\(e\left(\frac{145}{502}\right)\)	\(e\left(\frac{41}{251}\right)\)	\(e\left(\frac{401}{1004}\right)\)	\(e\left(\frac{957}{1004}\right)\)
\(\chi_{8048}(5,\cdot)\)	8048.x	1004	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{1004}\right)\)	\(e\left(\frac{253}{1004}\right)\)	\(e\left(\frac{337}{502}\right)\)	\(e\left(\frac{61}{502}\right)\)	\(e\left(\frac{335}{1004}\right)\)	\(e\left(\frac{1001}{1004}\right)\)	\(e\left(\frac{157}{502}\right)\)	\(e\left(\frac{229}{502}\right)\)	\(e\left(\frac{223}{1004}\right)\)	\(e\left(\frac{735}{1004}\right)\)
\(\chi_{8048}(7,\cdot)\)	8048.p	502	no	\(-1\)	\(1\)	\(e\left(\frac{182}{251}\right)\)	\(e\left(\frac{337}{502}\right)\)	\(e\left(\frac{117}{502}\right)\)	\(e\left(\frac{113}{251}\right)\)	\(e\left(\frac{49}{251}\right)\)	\(e\left(\frac{373}{502}\right)\)	\(e\left(\frac{199}{502}\right)\)	\(e\left(\frac{58}{251}\right)\)	\(e\left(\frac{151}{251}\right)\)	\(e\left(\frac{481}{502}\right)\)
\(\chi_{8048}(9,\cdot)\)	8048.s	502	no	\(1\)	\(1\)	\(e\left(\frac{229}{502}\right)\)	\(e\left(\frac{61}{502}\right)\)	\(e\left(\frac{113}{251}\right)\)	\(e\left(\frac{229}{251}\right)\)	\(e\left(\frac{303}{502}\right)\)	\(e\left(\frac{285}{502}\right)\)	\(e\left(\frac{145}{251}\right)\)	\(e\left(\frac{82}{251}\right)\)	\(e\left(\frac{401}{502}\right)\)	\(e\left(\frac{455}{502}\right)\)
\(\chi_{8048}(11,\cdot)\)	8048.v	1004	yes	\(-1\)	\(1\)	\(e\left(\frac{303}{1004}\right)\)	\(e\left(\frac{335}{1004}\right)\)	\(e\left(\frac{49}{251}\right)\)	\(e\left(\frac{303}{502}\right)\)	\(e\left(\frac{265}{1004}\right)\)	\(e\left(\frac{125}{1004}\right)\)	\(e\left(\frac{319}{502}\right)\)	\(e\left(\frac{40}{251}\right)\)	\(e\left(\frac{79}{1004}\right)\)	\(e\left(\frac{499}{1004}\right)\)
\(\chi_{8048}(13,\cdot)\)	8048.w	1004	yes	\(1\)	\(1\)	\(e\left(\frac{787}{1004}\right)\)	\(e\left(\frac{1001}{1004}\right)\)	\(e\left(\frac{373}{502}\right)\)	\(e\left(\frac{285}{502}\right)\)	\(e\left(\frac{125}{1004}\right)\)	\(e\left(\frac{883}{1004}\right)\)	\(e\left(\frac{196}{251}\right)\)	\(e\left(\frac{142}{251}\right)\)	\(e\left(\frac{795}{1004}\right)\)	\(e\left(\frac{529}{1004}\right)\)
\(\chi_{8048}(15,\cdot)\)	8048.t	502	no	\(1\)	\(1\)	\(e\left(\frac{145}{502}\right)\)	\(e\left(\frac{157}{502}\right)\)	\(e\left(\frac{199}{502}\right)\)	\(e\left(\frac{145}{251}\right)\)	\(e\left(\frac{319}{502}\right)\)	\(e\left(\frac{196}{251}\right)\)	\(e\left(\frac{151}{251}\right)\)	\(e\left(\frac{311}{502}\right)\)	\(e\left(\frac{156}{251}\right)\)	\(e\left(\frac{172}{251}\right)\)
\(\chi_{8048}(17,\cdot)\)	8048.o	502	no	\(-1\)	\(1\)	\(e\left(\frac{41}{251}\right)\)	\(e\left(\frac{229}{502}\right)\)	\(e\left(\frac{58}{251}\right)\)	\(e\left(\frac{82}{251}\right)\)	\(e\left(\frac{40}{251}\right)\)	\(e\left(\frac{142}{251}\right)\)	\(e\left(\frac{311}{502}\right)\)	\(e\left(\frac{233}{502}\right)\)	\(e\left(\frac{57}{502}\right)\)	\(e\left(\frac{99}{251}\right)\)
\(\chi_{8048}(19,\cdot)\)	8048.u	1004	yes	\(1\)	\(1\)	\(e\left(\frac{401}{1004}\right)\)	\(e\left(\frac{223}{1004}\right)\)	\(e\left(\frac{151}{251}\right)\)	\(e\left(\frac{401}{502}\right)\)	\(e\left(\frac{79}{1004}\right)\)	\(e\left(\frac{795}{1004}\right)\)	\(e\left(\frac{156}{251}\right)\)	\(e\left(\frac{57}{502}\right)\)	\(e\left(\frac{643}{1004}\right)\)	\(e\left(\frac{1}{1004}\right)\)
\(\chi_{8048}(21,\cdot)\)	8048.w	1004	yes	\(1\)	\(1\)	\(e\left(\frac{957}{1004}\right)\)	\(e\left(\frac{735}{1004}\right)\)	\(e\left(\frac{481}{502}\right)\)	\(e\left(\frac{455}{502}\right)\)	\(e\left(\frac{499}{1004}\right)\)	\(e\left(\frac{529}{1004}\right)\)	\(e\left(\frac{172}{251}\right)\)	\(e\left(\frac{99}{251}\right)\)	\(e\left(\frac{1}{1004}\right)\)	\(e\left(\frac{915}{1004}\right)\)
\(\chi_{8048}(23,\cdot)\)	8048.p	502	no	\(-1\)	\(1\)	\(e\left(\frac{164}{251}\right)\)	\(e\left(\frac{163}{502}\right)\)	\(e\left(\frac{213}{502}\right)\)	\(e\left(\frac{77}{251}\right)\)	\(e\left(\frac{160}{251}\right)\)	\(e\left(\frac{383}{502}\right)\)	\(e\left(\frac{491}{502}\right)\)	\(e\left(\frac{215}{251}\right)\)	\(e\left(\frac{114}{251}\right)\)	\(e\left(\frac{39}{502}\right)\)
\(\chi_{8048}(25,\cdot)\)	8048.s	502	no	\(1\)	\(1\)	\(e\left(\frac{61}{502}\right)\)	\(e\left(\frac{253}{502}\right)\)	\(e\left(\frac{86}{251}\right)\)	\(e\left(\frac{61}{251}\right)\)	\(e\left(\frac{335}{502}\right)\)	\(e\left(\frac{499}{502}\right)\)	\(e\left(\frac{157}{251}\right)\)	\(e\left(\frac{229}{251}\right)\)	\(e\left(\frac{223}{502}\right)\)	\(e\left(\frac{233}{502}\right)\)
\(\chi_{8048}(27,\cdot)\)	8048.v	1004	yes	\(-1\)	\(1\)	\(e\left(\frac{687}{1004}\right)\)	\(e\left(\frac{183}{1004}\right)\)	\(e\left(\frac{44}{251}\right)\)	\(e\left(\frac{185}{502}\right)\)	\(e\left(\frac{909}{1004}\right)\)	\(e\left(\frac{353}{1004}\right)\)	\(e\left(\frac{435}{502}\right)\)	\(e\left(\frac{123}{251}\right)\)	\(e\left(\frac{199}{1004}\right)\)	\(e\left(\frac{863}{1004}\right)\)
\(\chi_{8048}(29,\cdot)\)	8048.x	1004	yes	\(-1\)	\(1\)	\(e\left(\frac{171}{1004}\right)\)	\(e\left(\frac{199}{1004}\right)\)	\(e\left(\frac{23}{502}\right)\)	\(e\left(\frac{171}{502}\right)\)	\(e\left(\frac{577}{1004}\right)\)	\(e\left(\frac{831}{1004}\right)\)	\(e\left(\frac{185}{502}\right)\)	\(e\left(\frac{321}{502}\right)\)	\(e\left(\frac{477}{1004}\right)\)	\(e\left(\frac{217}{1004}\right)\)
\(\chi_{8048}(31,\cdot)\)	8048.t	502	no	\(1\)	\(1\)	\(e\left(\frac{67}{502}\right)\)	\(e\left(\frac{31}{502}\right)\)	\(e\left(\frac{407}{502}\right)\)	\(e\left(\frac{67}{251}\right)\)	\(e\left(\frac{47}{502}\right)\)	\(e\left(\frac{165}{251}\right)\)	\(e\left(\frac{49}{251}\right)\)	\(e\left(\frac{71}{502}\right)\)	\(e\left(\frac{34}{251}\right)\)	\(e\left(\frac{237}{251}\right)\)
\(\chi_{8048}(33,\cdot)\)	8048.m	251	no	\(1\)	\(1\)	\(e\left(\frac{133}{251}\right)\)	\(e\left(\frac{99}{251}\right)\)	\(e\left(\frac{231}{251}\right)\)	\(e\left(\frac{15}{251}\right)\)	\(e\left(\frac{142}{251}\right)\)	\(e\left(\frac{228}{251}\right)\)	\(e\left(\frac{232}{251}\right)\)	\(e\left(\frac{81}{251}\right)\)	\(e\left(\frac{120}{251}\right)\)	\(e\left(\frac{113}{251}\right)\)
\(\chi_{8048}(35,\cdot)\)	8048.u	1004	yes	\(1\)	\(1\)	\(e\left(\frac{789}{1004}\right)\)	\(e\left(\frac{927}{1004}\right)\)	\(e\left(\frac{227}{251}\right)\)	\(e\left(\frac{287}{502}\right)\)	\(e\left(\frac{531}{1004}\right)\)	\(e\left(\frac{743}{1004}\right)\)	\(e\left(\frac{178}{251}\right)\)	\(e\left(\frac{345}{502}\right)\)	\(e\left(\frac{827}{1004}\right)\)	\(e\left(\frac{693}{1004}\right)\)
\(\chi_{8048}(37,\cdot)\)	8048.x	1004	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{1004}\right)\)	\(e\left(\frac{993}{1004}\right)\)	\(e\left(\frac{29}{502}\right)\)	\(e\left(\frac{41}{502}\right)\)	\(e\left(\frac{291}{1004}\right)\)	\(e\left(\frac{393}{1004}\right)\)	\(e\left(\frac{15}{502}\right)\)	\(e\left(\frac{121}{502}\right)\)	\(e\left(\frac{907}{1004}\right)\)	\(e\left(\frac{99}{1004}\right)\)
\(\chi_{8048}(39,\cdot)\)	8048.p	502	no	\(-1\)	\(1\)	\(e\left(\frac{3}{251}\right)\)	\(e\left(\frac{29}{502}\right)\)	\(e\left(\frac{235}{502}\right)\)	\(e\left(\frac{6}{251}\right)\)	\(e\left(\frac{107}{251}\right)\)	\(e\left(\frac{333}{502}\right)\)	\(e\left(\frac{35}{502}\right)\)	\(e\left(\frac{183}{251}\right)\)	\(e\left(\frac{48}{251}\right)\)	\(e\left(\frac{241}{502}\right)\)
\(\chi_{8048}(41,\cdot)\)	8048.q	502	no	\(-1\)	\(1\)	\(e\left(\frac{265}{502}\right)\)	\(e\left(\frac{243}{251}\right)\)	\(e\left(\frac{65}{251}\right)\)	\(e\left(\frac{14}{251}\right)\)	\(e\left(\frac{81}{502}\right)\)	\(e\left(\frac{275}{502}\right)\)	\(e\left(\frac{249}{502}\right)\)	\(e\left(\frac{101}{502}\right)\)	\(e\left(\frac{112}{251}\right)\)	\(e\left(\frac{395}{502}\right)\)
\(\chi_{8048}(43,\cdot)\)	8048.v	1004	yes	\(-1\)	\(1\)	\(e\left(\frac{763}{1004}\right)\)	\(e\left(\frac{383}{1004}\right)\)	\(e\left(\frac{77}{251}\right)\)	\(e\left(\frac{261}{502}\right)\)	\(e\left(\frac{273}{1004}\right)\)	\(e\left(\frac{53}{1004}\right)\)	\(e\left(\frac{71}{502}\right)\)	\(e\left(\frac{27}{251}\right)\)	\(e\left(\frac{411}{1004}\right)\)	\(e\left(\frac{67}{1004}\right)\)
\(\chi_{8048}(45,\cdot)\)	8048.x	1004	yes	\(-1\)	\(1\)	\(e\left(\frac{519}{1004}\right)\)	\(e\left(\frac{375}{1004}\right)\)	\(e\left(\frac{61}{502}\right)\)	\(e\left(\frac{17}{502}\right)\)	\(e\left(\frac{941}{1004}\right)\)	\(e\left(\frac{567}{1004}\right)\)	\(e\left(\frac{447}{502}\right)\)	\(e\left(\frac{393}{502}\right)\)	\(e\left(\frac{21}{1004}\right)\)	\(e\left(\frac{641}{1004}\right)\)
\(\chi_{8048}(47,\cdot)\)	8048.r	502	no	\(-1\)	\(1\)	\(e\left(\frac{475}{502}\right)\)	\(e\left(\frac{123}{251}\right)\)	\(e\left(\frac{323}{502}\right)\)	\(e\left(\frac{224}{251}\right)\)	\(e\left(\frac{41}{502}\right)\)	\(e\left(\frac{192}{251}\right)\)	\(e\left(\frac{219}{502}\right)\)	\(e\left(\frac{55}{251}\right)\)	\(e\left(\frac{321}{502}\right)\)	\(e\left(\frac{148}{251}\right)\)
\(\chi_{8048}(49,\cdot)\)	8048.m	251	no	\(1\)	\(1\)	\(e\left(\frac{113}{251}\right)\)	\(e\left(\frac{86}{251}\right)\)	\(e\left(\frac{117}{251}\right)\)	\(e\left(\frac{226}{251}\right)\)	\(e\left(\frac{98}{251}\right)\)	\(e\left(\frac{122}{251}\right)\)	\(e\left(\frac{199}{251}\right)\)	\(e\left(\frac{116}{251}\right)\)	\(e\left(\frac{51}{251}\right)\)	\(e\left(\frac{230}{251}\right)\)
\(\chi_{8048}(51,\cdot)\)	8048.u	1004	yes	\(1\)	\(1\)	\(e\left(\frac{393}{1004}\right)\)	\(e\left(\frac{519}{1004}\right)\)	\(e\left(\frac{240}{251}\right)\)	\(e\left(\frac{393}{502}\right)\)	\(e\left(\frac{463}{1004}\right)\)	\(e\left(\frac{351}{1004}\right)\)	\(e\left(\frac{228}{251}\right)\)	\(e\left(\frac{315}{502}\right)\)	\(e\left(\frac{515}{1004}\right)\)	\(e\left(\frac{349}{1004}\right)\)
\(\chi_{8048}(53,\cdot)\)	8048.x	1004	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{1004}\right)\)	\(e\left(\frac{781}{1004}\right)\)	\(e\left(\frac{451}{502}\right)\)	\(e\left(\frac{101}{502}\right)\)	\(e\left(\frac{423}{1004}\right)\)	\(e\left(\frac{209}{1004}\right)\)	\(e\left(\frac{441}{502}\right)\)	\(e\left(\frac{445}{502}\right)\)	\(e\left(\frac{863}{1004}\right)\)	\(e\left(\frac{1003}{1004}\right)\)
\(\chi_{8048}(55,\cdot)\)	8048.n	502	no	\(1\)	\(1\)	\(e\left(\frac{91}{251}\right)\)	\(e\left(\frac{147}{251}\right)\)	\(e\left(\frac{435}{502}\right)\)	\(e\left(\frac{182}{251}\right)\)	\(e\left(\frac{150}{251}\right)\)	\(e\left(\frac{61}{502}\right)\)	\(e\left(\frac{238}{251}\right)\)	\(e\left(\frac{309}{502}\right)\)	\(e\left(\frac{151}{502}\right)\)	\(e\left(\frac{115}{502}\right)\)
\(\chi_{8048}(57,\cdot)\)	8048.q	502	no	\(-1\)	\(1\)	\(e\left(\frac{315}{502}\right)\)	\(e\left(\frac{71}{251}\right)\)	\(e\left(\frac{82}{251}\right)\)	\(e\left(\frac{64}{251}\right)\)	\(e\left(\frac{191}{502}\right)\)	\(e\left(\frac{289}{502}\right)\)	\(e\left(\frac{457}{502}\right)\)	\(e\left(\frac{139}{502}\right)\)	\(e\left(\frac{10}{251}\right)\)	\(e\left(\frac{479}{502}\right)\)
\(\chi_{8048}(59,\cdot)\)	8048.v	1004	yes	\(-1\)	\(1\)	\(e\left(\frac{567}{1004}\right)\)	\(e\left(\frac{607}{1004}\right)\)	\(e\left(\frac{124}{251}\right)\)	\(e\left(\frac{65}{502}\right)\)	\(e\left(\frac{645}{1004}\right)\)	\(e\left(\frac{721}{1004}\right)\)	\(e\left(\frac{85}{502}\right)\)	\(e\left(\frac{50}{251}\right)\)	\(e\left(\frac{287}{1004}\right)\)	\(e\left(\frac{59}{1004}\right)\)
\(\chi_{8048}(61,\cdot)\)	8048.w	1004	yes	\(1\)	\(1\)	\(e\left(\frac{723}{1004}\right)\)	\(e\left(\frac{357}{1004}\right)\)	\(e\left(\frac{291}{502}\right)\)	\(e\left(\frac{221}{502}\right)\)	\(e\left(\frac{185}{1004}\right)\)	\(e\left(\frac{343}{1004}\right)\)	\(e\left(\frac{19}{251}\right)\)	\(e\left(\frac{170}{251}\right)\)	\(e\left(\frac{775}{1004}\right)\)	\(e\left(\frac{301}{1004}\right)\)
\(\chi_{8048}(63,\cdot)\)	8048.r	502	no	\(-1\)	\(1\)	\(e\left(\frac{91}{502}\right)\)	\(e\left(\frac{199}{251}\right)\)	\(e\left(\frac{343}{502}\right)\)	\(e\left(\frac{91}{251}\right)\)	\(e\left(\frac{401}{502}\right)\)	\(e\left(\frac{78}{251}\right)\)	\(e\left(\frac{489}{502}\right)\)	\(e\left(\frac{140}{251}\right)\)	\(e\left(\frac{201}{502}\right)\)	\(e\left(\frac{217}{251}\right)\)

Introduction

L-functions

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Character group

First 32 of 4016 characters

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