LMFDB - Group of Dirichlet characters of modulus 103488

Show commands: PariGP / SageMath

sage: H = DirichletGroup(103488)

pari: g = idealstar(,103488,2)

Character group

sage: G.order() pari: g.no
Order	=	26880
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{1680}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{103488}(48511,\cdot)$, $\chi_{103488}(6469,\cdot)$, $\chi_{103488}(68993,\cdot)$, $\chi_{103488}(42241,\cdot)$, $\chi_{103488}(37633,\cdot)$

First 32 of 26880 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	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{103488}(1,\cdot)$	103488.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{103488}(5,\cdot)$	103488.yj	1680	yes	$1$	$1$	$e\left(\frac{313}{1680}\right)$	$e\left(\frac{69}{560}\right)$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{313}{840}\right)$	$e\left(\frac{233}{560}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{769}{1680}\right)$	$e\left(\frac{261}{280}\right)$
$\chi_{103488}(13,\cdot)$	103488.xa	560	no	$1$	$1$	$e\left(\frac{69}{560}\right)$	$e\left(\frac{51}{560}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{69}{280}\right)$	$e\left(\frac{87}{560}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{437}{560}\right)$	$e\left(\frac{59}{280}\right)$
$\chi_{103488}(17,\cdot)$	103488.wq	420	no	$-1$	$1$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{103488}(19,\cdot)$	103488.um	240	no	$-1$	$1$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{103488}(23,\cdot)$	103488.sz	168	no	$1$	$1$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{103488}(25,\cdot)$	103488.xz	840	no	$1$	$1$	$e\left(\frac{313}{840}\right)$	$e\left(\frac{69}{280}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{233}{280}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{769}{840}\right)$	$e\left(\frac{121}{140}\right)$
$\chi_{103488}(29,\cdot)$	103488.xc	560	yes	$1$	$1$	$e\left(\frac{233}{560}\right)$	$e\left(\frac{87}{560}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{233}{280}\right)$	$e\left(\frac{379}{560}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{169}{560}\right)$	$e\left(\frac{183}{280}\right)$
$\chi_{103488}(31,\cdot)$	103488.jz	30	no	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{103488}(37,\cdot)$	103488.yh	1680	no	$1$	$1$	$e\left(\frac{769}{1680}\right)$	$e\left(\frac{437}{560}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{769}{840}\right)$	$e\left(\frac{169}{560}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1417}{1680}\right)$	$e\left(\frac{253}{280}\right)$
$\chi_{103488}(41,\cdot)$	103488.vk	280	no	$-1$	$1$	$e\left(\frac{261}{280}\right)$	$e\left(\frac{59}{280}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{183}{280}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{253}{280}\right)$	$e\left(\frac{1}{140}\right)$
$\chi_{103488}(43,\cdot)$	103488.rf	112	no	$1$	$1$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{1}{112}\right)$	$1$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{1}{56}\right)$
$\chi_{103488}(47,\cdot)$	103488.wh	420	no	$-1$	$1$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{67}{420}\right)$	$e\left(\frac{13}{70}\right)$
$\chi_{103488}(53,\cdot)$	103488.yb	1680	yes	$-1$	$1$	$e\left(\frac{197}{1680}\right)$	$e\left(\frac{81}{560}\right)$	$e\left(\frac{253}{420}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{197}{840}\right)$	$e\left(\frac{237}{560}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1061}{1680}\right)$	$e\left(\frac{69}{280}\right)$
$\chi_{103488}(59,\cdot)$	103488.yc	1680	yes	$-1$	$1$	$e\left(\frac{569}{1680}\right)$	$e\left(\frac{197}{560}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{569}{840}\right)$	$e\left(\frac{89}{560}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1457}{1680}\right)$	$e\left(\frac{173}{280}\right)$
$\chi_{103488}(61,\cdot)$	103488.yi	1680	no	$1$	$1$	$e\left(\frac{643}{1680}\right)$	$e\left(\frac{199}{560}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{643}{840}\right)$	$e\left(\frac{43}{560}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1459}{1680}\right)$	$e\left(\frac{71}{280}\right)$
$\chi_{103488}(65,\cdot)$	103488.ls	42	no	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{103488}(67,\cdot)$	103488.mj	48	no	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{103488}(71,\cdot)$	103488.vl	280	no	$1$	$1$	$e\left(\frac{83}{280}\right)$	$e\left(\frac{177}{280}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{129}{280}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{199}{280}\right)$	$e\left(\frac{3}{140}\right)$
$\chi_{103488}(73,\cdot)$	103488.xs	840	no	$1$	$1$	$e\left(\frac{607}{840}\right)$	$e\left(\frac{111}{280}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{187}{420}\right)$	$e\left(\frac{247}{280}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{811}{840}\right)$	$e\left(\frac{79}{140}\right)$
$\chi_{103488}(79,\cdot)$	103488.np	60	no	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{103488}(83,\cdot)$	103488.xf	560	yes	$1$	$1$	$e\left(\frac{421}{560}\right)$	$e\left(\frac{299}{560}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{141}{280}\right)$	$e\left(\frac{263}{560}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{333}{560}\right)$	$e\left(\frac{151}{280}\right)$
$\chi_{103488}(85,\cdot)$	103488.xi	560	no	$-1$	$1$	$e\left(\frac{167}{560}\right)$	$e\left(\frac{513}{560}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{167}{280}\right)$	$e\left(\frac{101}{560}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{560}\right)$	$e\left(\frac{157}{280}\right)$
$\chi_{103488}(89,\cdot)$	103488.sr	168	no	$1$	$1$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{103488}(95,\cdot)$	103488.tm	210	no	$-1$	$1$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{103488}(97,\cdot)$	103488.dy	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{103488}(101,\cdot)$	103488.yo	1680	yes	$-1$	$1$	$e\left(\frac{257}{1680}\right)$	$e\left(\frac{181}{560}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{257}{840}\right)$	$e\left(\frac{457}{560}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{41}{1680}\right)$	$e\left(\frac{9}{280}\right)$
$\chi_{103488}(103,\cdot)$	103488.xr	840	no	$1$	$1$	$e\left(\frac{797}{840}\right)$	$e\left(\frac{241}{280}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{57}{280}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{521}{840}\right)$	$e\left(\frac{99}{140}\right)$
$\chi_{103488}(107,\cdot)$	103488.yn	1680	yes	$-1$	$1$	$e\left(\frac{1501}{1680}\right)$	$e\left(\frac{33}{560}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{661}{840}\right)$	$e\left(\frac{221}{560}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{733}{1680}\right)$	$e\left(\frac{137}{280}\right)$
$\chi_{103488}(109,\cdot)$	103488.vz	336	no	$-1$	$1$	$e\left(\frac{19}{336}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{51}{56}\right)$
$\chi_{103488}(113,\cdot)$	103488.rx	140	no	$-1$	$1$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{103488}(115,\cdot)$	103488.ye	1680	no	$1$	$1$	$e\left(\frac{1343}{1680}\right)$	$e\left(\frac{59}{560}\right)$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{503}{840}\right)$	$e\left(\frac{463}{560}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{479}{1680}\right)$	$e\left(\frac{71}{280}\right)$

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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	$103488$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{1680}\)
Order	$26880$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{103488}(1,\cdot)\)	103488.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{103488}(5,\cdot)\)	103488.yj	1680	yes	\(1\)	\(1\)	\(e\left(\frac{313}{1680}\right)\)	\(e\left(\frac{69}{560}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{313}{840}\right)\)	\(e\left(\frac{233}{560}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{769}{1680}\right)\)	\(e\left(\frac{261}{280}\right)\)
\(\chi_{103488}(13,\cdot)\)	103488.xa	560	no	\(1\)	\(1\)	\(e\left(\frac{69}{560}\right)\)	\(e\left(\frac{51}{560}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{69}{280}\right)\)	\(e\left(\frac{87}{560}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{437}{560}\right)\)	\(e\left(\frac{59}{280}\right)\)
\(\chi_{103488}(17,\cdot)\)	103488.wq	420	no	\(-1\)	\(1\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{103488}(19,\cdot)\)	103488.um	240	no	\(-1\)	\(1\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{103488}(23,\cdot)\)	103488.sz	168	no	\(1\)	\(1\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{103488}(25,\cdot)\)	103488.xz	840	no	\(1\)	\(1\)	\(e\left(\frac{313}{840}\right)\)	\(e\left(\frac{69}{280}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{233}{280}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{769}{840}\right)\)	\(e\left(\frac{121}{140}\right)\)
\(\chi_{103488}(29,\cdot)\)	103488.xc	560	yes	\(1\)	\(1\)	\(e\left(\frac{233}{560}\right)\)	\(e\left(\frac{87}{560}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{233}{280}\right)\)	\(e\left(\frac{379}{560}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{169}{560}\right)\)	\(e\left(\frac{183}{280}\right)\)
\(\chi_{103488}(31,\cdot)\)	103488.jz	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{103488}(37,\cdot)\)	103488.yh	1680	no	\(1\)	\(1\)	\(e\left(\frac{769}{1680}\right)\)	\(e\left(\frac{437}{560}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{769}{840}\right)\)	\(e\left(\frac{169}{560}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1417}{1680}\right)\)	\(e\left(\frac{253}{280}\right)\)
\(\chi_{103488}(41,\cdot)\)	103488.vk	280	no	\(-1\)	\(1\)	\(e\left(\frac{261}{280}\right)\)	\(e\left(\frac{59}{280}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{183}{280}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{253}{280}\right)\)	\(e\left(\frac{1}{140}\right)\)
\(\chi_{103488}(43,\cdot)\)	103488.rf	112	no	\(1\)	\(1\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(1\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)
\(\chi_{103488}(47,\cdot)\)	103488.wh	420	no	\(-1\)	\(1\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{67}{420}\right)\)	\(e\left(\frac{13}{70}\right)\)
\(\chi_{103488}(53,\cdot)\)	103488.yb	1680	yes	\(-1\)	\(1\)	\(e\left(\frac{197}{1680}\right)\)	\(e\left(\frac{81}{560}\right)\)	\(e\left(\frac{253}{420}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{197}{840}\right)\)	\(e\left(\frac{237}{560}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1061}{1680}\right)\)	\(e\left(\frac{69}{280}\right)\)
\(\chi_{103488}(59,\cdot)\)	103488.yc	1680	yes	\(-1\)	\(1\)	\(e\left(\frac{569}{1680}\right)\)	\(e\left(\frac{197}{560}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{569}{840}\right)\)	\(e\left(\frac{89}{560}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1457}{1680}\right)\)	\(e\left(\frac{173}{280}\right)\)
\(\chi_{103488}(61,\cdot)\)	103488.yi	1680	no	\(1\)	\(1\)	\(e\left(\frac{643}{1680}\right)\)	\(e\left(\frac{199}{560}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{643}{840}\right)\)	\(e\left(\frac{43}{560}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1459}{1680}\right)\)	\(e\left(\frac{71}{280}\right)\)
\(\chi_{103488}(65,\cdot)\)	103488.ls	42	no	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{103488}(67,\cdot)\)	103488.mj	48	no	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{103488}(71,\cdot)\)	103488.vl	280	no	\(1\)	\(1\)	\(e\left(\frac{83}{280}\right)\)	\(e\left(\frac{177}{280}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{129}{280}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{199}{280}\right)\)	\(e\left(\frac{3}{140}\right)\)
\(\chi_{103488}(73,\cdot)\)	103488.xs	840	no	\(1\)	\(1\)	\(e\left(\frac{607}{840}\right)\)	\(e\left(\frac{111}{280}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{187}{420}\right)\)	\(e\left(\frac{247}{280}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{811}{840}\right)\)	\(e\left(\frac{79}{140}\right)\)
\(\chi_{103488}(79,\cdot)\)	103488.np	60	no	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{103488}(83,\cdot)\)	103488.xf	560	yes	\(1\)	\(1\)	\(e\left(\frac{421}{560}\right)\)	\(e\left(\frac{299}{560}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{141}{280}\right)\)	\(e\left(\frac{263}{560}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{333}{560}\right)\)	\(e\left(\frac{151}{280}\right)\)
\(\chi_{103488}(85,\cdot)\)	103488.xi	560	no	\(-1\)	\(1\)	\(e\left(\frac{167}{560}\right)\)	\(e\left(\frac{513}{560}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{167}{280}\right)\)	\(e\left(\frac{101}{560}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{560}\right)\)	\(e\left(\frac{157}{280}\right)\)
\(\chi_{103488}(89,\cdot)\)	103488.sr	168	no	\(1\)	\(1\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{103488}(95,\cdot)\)	103488.tm	210	no	\(-1\)	\(1\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{103488}(97,\cdot)\)	103488.dy	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{103488}(101,\cdot)\)	103488.yo	1680	yes	\(-1\)	\(1\)	\(e\left(\frac{257}{1680}\right)\)	\(e\left(\frac{181}{560}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{257}{840}\right)\)	\(e\left(\frac{457}{560}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{41}{1680}\right)\)	\(e\left(\frac{9}{280}\right)\)
\(\chi_{103488}(103,\cdot)\)	103488.xr	840	no	\(1\)	\(1\)	\(e\left(\frac{797}{840}\right)\)	\(e\left(\frac{241}{280}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{57}{280}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{521}{840}\right)\)	\(e\left(\frac{99}{140}\right)\)
\(\chi_{103488}(107,\cdot)\)	103488.yn	1680	yes	\(-1\)	\(1\)	\(e\left(\frac{1501}{1680}\right)\)	\(e\left(\frac{33}{560}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{661}{840}\right)\)	\(e\left(\frac{221}{560}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{733}{1680}\right)\)	\(e\left(\frac{137}{280}\right)\)
\(\chi_{103488}(109,\cdot)\)	103488.vz	336	no	\(-1\)	\(1\)	\(e\left(\frac{19}{336}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{51}{56}\right)\)
\(\chi_{103488}(113,\cdot)\)	103488.rx	140	no	\(-1\)	\(1\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{103488}(115,\cdot)\)	103488.ye	1680	no	\(1\)	\(1\)	\(e\left(\frac{1343}{1680}\right)\)	\(e\left(\frac{59}{560}\right)\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{503}{840}\right)\)	\(e\left(\frac{463}{560}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{479}{1680}\right)\)	\(e\left(\frac{71}{280}\right)\)

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L-functions

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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.