LMFDB - Group of Dirichlet characters of modulus 41650

Show commands: PariGP / SageMath

sage: H = DirichletGroup(41650)

pari: g = idealstar(,41650,2)

Character group

sage: G.order() pari: g.no
Order	=	13440
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{1680}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{41650}(18327,\cdot)$, $\chi_{41650}(2551,\cdot)$, $\chi_{41650}(2451,\cdot)$

First 32 of 13440 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	$-1$	$1$	$3$	$9$	$11$	$13$	$19$	$23$	$27$	$29$	$31$	$33$
$\chi_{41650}(1,\cdot)$	41650.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{41650}(3,\cdot)$	41650.lb	1680	no	$-1$	$1$	$e\left(\frac{901}{1680}\right)$	$e\left(\frac{61}{840}\right)$	$e\left(\frac{1663}{1680}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1163}{1680}\right)$	$e\left(\frac{341}{560}\right)$	$e\left(\frac{527}{560}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{221}{420}\right)$
$\chi_{41650}(9,\cdot)$	41650.ks	840	no	$1$	$1$	$e\left(\frac{61}{840}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{823}{840}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{323}{840}\right)$	$e\left(\frac{61}{280}\right)$	$e\left(\frac{247}{280}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{11}{210}\right)$
$\chi_{41650}(11,\cdot)$	41650.ky	1680	no	$-1$	$1$	$e\left(\frac{1663}{1680}\right)$	$e\left(\frac{823}{840}\right)$	$e\left(\frac{1609}{1680}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{929}{1680}\right)$	$e\left(\frac{543}{560}\right)$	$e\left(\frac{241}{560}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{199}{210}\right)$
$\chi_{41650}(13,\cdot)$	41650.ie	140	no	$1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{140}\right)$
$\chi_{41650}(19,\cdot)$	41650.hr	120	no	$-1$	$1$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{41650}(23,\cdot)$	41650.la	1680	no	$1$	$1$	$e\left(\frac{1163}{1680}\right)$	$e\left(\frac{323}{840}\right)$	$e\left(\frac{929}{1680}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{829}{1680}\right)$	$e\left(\frac{43}{560}\right)$	$e\left(\frac{321}{560}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{103}{420}\right)$
$\chi_{41650}(27,\cdot)$	41650.kl	560	no	$-1$	$1$	$e\left(\frac{341}{560}\right)$	$e\left(\frac{61}{280}\right)$	$e\left(\frac{543}{560}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{43}{560}\right)$	$e\left(\frac{463}{560}\right)$	$e\left(\frac{461}{560}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{81}{140}\right)$
$\chi_{41650}(29,\cdot)$	41650.ki	560	no	$-1$	$1$	$e\left(\frac{527}{560}\right)$	$e\left(\frac{247}{280}\right)$	$e\left(\frac{241}{560}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{321}{560}\right)$	$e\left(\frac{461}{560}\right)$	$e\left(\frac{267}{560}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{41650}(31,\cdot)$	41650.iy	240	no	$1$	$1$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{41650}(33,\cdot)$	41650.kb	420	no	$1$	$1$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{199}{420}\right)$
$\chi_{41650}(37,\cdot)$	41650.la	1680	no	$1$	$1$	$e\left(\frac{1637}{1680}\right)$	$e\left(\frac{797}{840}\right)$	$e\left(\frac{191}{1680}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{1411}{1680}\right)$	$e\left(\frac{517}{560}\right)$	$e\left(\frac{239}{560}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{37}{420}\right)$
$\chi_{41650}(39,\cdot)$	41650.kx	1680	no	$-1$	$1$	$e\left(\frac{373}{1680}\right)$	$e\left(\frac{373}{840}\right)$	$e\left(\frac{619}{1680}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{1259}{1680}\right)$	$e\left(\frac{373}{560}\right)$	$e\left(\frac{131}{560}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{62}{105}\right)$
$\chi_{41650}(41,\cdot)$	41650.kj	560	no	$1$	$1$	$e\left(\frac{249}{560}\right)$	$e\left(\frac{249}{280}\right)$	$e\left(\frac{167}{560}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{47}{560}\right)$	$e\left(\frac{187}{560}\right)$	$e\left(\frac{429}{560}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{41650}(43,\cdot)$	41650.fm	56	no	$-1$	$1$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{13}{28}\right)$	$i$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{41650}(47,\cdot)$	41650.kc	420	no	$1$	$1$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{181}{420}\right)$
$\chi_{41650}(53,\cdot)$	41650.ko	840	no	$-1$	$1$	$e\left(\frac{473}{840}\right)$	$e\left(\frac{53}{420}\right)$	$e\left(\frac{209}{840}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{840}\right)$	$e\left(\frac{193}{280}\right)$	$e\left(\frac{101}{280}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{341}{420}\right)$
$\chi_{41650}(57,\cdot)$	41650.hk	112	no	$1$	$1$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{41650}(59,\cdot)$	41650.km	840	no	$-1$	$1$	$e\left(\frac{701}{840}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{803}{840}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{703}{840}\right)$	$e\left(\frac{141}{280}\right)$	$e\left(\frac{27}{280}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{83}{105}\right)$
$\chi_{41650}(61,\cdot)$	41650.kw	1680	no	$1$	$1$	$e\left(\frac{83}{1680}\right)$	$e\left(\frac{83}{840}\right)$	$e\left(\frac{989}{1680}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{949}{1680}\right)$	$e\left(\frac{83}{560}\right)$	$e\left(\frac{421}{560}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{67}{105}\right)$
$\chi_{41650}(67,\cdot)$	41650.fr	60	no	$-1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{60}\right)$
$\chi_{41650}(69,\cdot)$	41650.gh	70	no	$-1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{41650}(71,\cdot)$	41650.kh	560	no	$-1$	$1$	$e\left(\frac{467}{560}\right)$	$e\left(\frac{187}{280}\right)$	$e\left(\frac{501}{560}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{141}{560}\right)$	$e\left(\frac{281}{560}\right)$	$e\left(\frac{167}{560}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{51}{70}\right)$
$\chi_{41650}(73,\cdot)$	41650.lb	1680	no	$-1$	$1$	$e\left(\frac{73}{1680}\right)$	$e\left(\frac{73}{840}\right)$	$e\left(\frac{379}{1680}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{359}{1680}\right)$	$e\left(\frac{73}{560}\right)$	$e\left(\frac{11}{560}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{113}{420}\right)$
$\chi_{41650}(79,\cdot)$	41650.iz	240	no	$-1$	$1$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{41650}(81,\cdot)$	41650.jy	420	no	$1$	$1$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{105}\right)$
$\chi_{41650}(83,\cdot)$	41650.jf	280	no	$1$	$1$	$e\left(\frac{179}{280}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{167}{280}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{117}{280}\right)$	$e\left(\frac{257}{280}\right)$	$e\left(\frac{9}{280}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{33}{140}\right)$
$\chi_{41650}(87,\cdot)$	41650.kr	840	no	$1$	$1$	$e\left(\frac{401}{840}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{353}{840}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{223}{840}\right)$	$e\left(\frac{121}{280}\right)$	$e\left(\frac{117}{280}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{377}{420}\right)$
$\chi_{41650}(89,\cdot)$	41650.jz	420	no	$-1$	$1$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{37}{105}\right)$
$\chi_{41650}(93,\cdot)$	41650.ik	168	no	$-1$	$1$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{41650}(97,\cdot)$	41650.go	80	no	$-1$	$1$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{41650}(99,\cdot)$	41650.cs	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$1$

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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	$41650$
Structure	\(C_{2}\times C_{4}\times C_{1680}\)
Order	$13440$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)	\(33\)
\(\chi_{41650}(1,\cdot)\)	41650.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{41650}(3,\cdot)\)	41650.lb	1680	no	\(-1\)	\(1\)	\(e\left(\frac{901}{1680}\right)\)	\(e\left(\frac{61}{840}\right)\)	\(e\left(\frac{1663}{1680}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1163}{1680}\right)\)	\(e\left(\frac{341}{560}\right)\)	\(e\left(\frac{527}{560}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{221}{420}\right)\)
\(\chi_{41650}(9,\cdot)\)	41650.ks	840	no	\(1\)	\(1\)	\(e\left(\frac{61}{840}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{823}{840}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{323}{840}\right)\)	\(e\left(\frac{61}{280}\right)\)	\(e\left(\frac{247}{280}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{11}{210}\right)\)
\(\chi_{41650}(11,\cdot)\)	41650.ky	1680	no	\(-1\)	\(1\)	\(e\left(\frac{1663}{1680}\right)\)	\(e\left(\frac{823}{840}\right)\)	\(e\left(\frac{1609}{1680}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{929}{1680}\right)\)	\(e\left(\frac{543}{560}\right)\)	\(e\left(\frac{241}{560}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{199}{210}\right)\)
\(\chi_{41650}(13,\cdot)\)	41650.ie	140	no	\(1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{140}\right)\)
\(\chi_{41650}(19,\cdot)\)	41650.hr	120	no	\(-1\)	\(1\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{41650}(23,\cdot)\)	41650.la	1680	no	\(1\)	\(1\)	\(e\left(\frac{1163}{1680}\right)\)	\(e\left(\frac{323}{840}\right)\)	\(e\left(\frac{929}{1680}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{829}{1680}\right)\)	\(e\left(\frac{43}{560}\right)\)	\(e\left(\frac{321}{560}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{103}{420}\right)\)
\(\chi_{41650}(27,\cdot)\)	41650.kl	560	no	\(-1\)	\(1\)	\(e\left(\frac{341}{560}\right)\)	\(e\left(\frac{61}{280}\right)\)	\(e\left(\frac{543}{560}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{43}{560}\right)\)	\(e\left(\frac{463}{560}\right)\)	\(e\left(\frac{461}{560}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{81}{140}\right)\)
\(\chi_{41650}(29,\cdot)\)	41650.ki	560	no	\(-1\)	\(1\)	\(e\left(\frac{527}{560}\right)\)	\(e\left(\frac{247}{280}\right)\)	\(e\left(\frac{241}{560}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{321}{560}\right)\)	\(e\left(\frac{461}{560}\right)\)	\(e\left(\frac{267}{560}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{41650}(31,\cdot)\)	41650.iy	240	no	\(1\)	\(1\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{41650}(33,\cdot)\)	41650.kb	420	no	\(1\)	\(1\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{199}{420}\right)\)
\(\chi_{41650}(37,\cdot)\)	41650.la	1680	no	\(1\)	\(1\)	\(e\left(\frac{1637}{1680}\right)\)	\(e\left(\frac{797}{840}\right)\)	\(e\left(\frac{191}{1680}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{1411}{1680}\right)\)	\(e\left(\frac{517}{560}\right)\)	\(e\left(\frac{239}{560}\right)\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{37}{420}\right)\)
\(\chi_{41650}(39,\cdot)\)	41650.kx	1680	no	\(-1\)	\(1\)	\(e\left(\frac{373}{1680}\right)\)	\(e\left(\frac{373}{840}\right)\)	\(e\left(\frac{619}{1680}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{1259}{1680}\right)\)	\(e\left(\frac{373}{560}\right)\)	\(e\left(\frac{131}{560}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{62}{105}\right)\)
\(\chi_{41650}(41,\cdot)\)	41650.kj	560	no	\(1\)	\(1\)	\(e\left(\frac{249}{560}\right)\)	\(e\left(\frac{249}{280}\right)\)	\(e\left(\frac{167}{560}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{47}{560}\right)\)	\(e\left(\frac{187}{560}\right)\)	\(e\left(\frac{429}{560}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{41650}(43,\cdot)\)	41650.fm	56	no	\(-1\)	\(1\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(i\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{41650}(47,\cdot)\)	41650.kc	420	no	\(1\)	\(1\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{181}{420}\right)\)
\(\chi_{41650}(53,\cdot)\)	41650.ko	840	no	\(-1\)	\(1\)	\(e\left(\frac{473}{840}\right)\)	\(e\left(\frac{53}{420}\right)\)	\(e\left(\frac{209}{840}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{840}\right)\)	\(e\left(\frac{193}{280}\right)\)	\(e\left(\frac{101}{280}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{341}{420}\right)\)
\(\chi_{41650}(57,\cdot)\)	41650.hk	112	no	\(1\)	\(1\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{41650}(59,\cdot)\)	41650.km	840	no	\(-1\)	\(1\)	\(e\left(\frac{701}{840}\right)\)	\(e\left(\frac{281}{420}\right)\)	\(e\left(\frac{803}{840}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{703}{840}\right)\)	\(e\left(\frac{141}{280}\right)\)	\(e\left(\frac{27}{280}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{83}{105}\right)\)
\(\chi_{41650}(61,\cdot)\)	41650.kw	1680	no	\(1\)	\(1\)	\(e\left(\frac{83}{1680}\right)\)	\(e\left(\frac{83}{840}\right)\)	\(e\left(\frac{989}{1680}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{949}{1680}\right)\)	\(e\left(\frac{83}{560}\right)\)	\(e\left(\frac{421}{560}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{67}{105}\right)\)
\(\chi_{41650}(67,\cdot)\)	41650.fr	60	no	\(-1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)
\(\chi_{41650}(69,\cdot)\)	41650.gh	70	no	\(-1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{41650}(71,\cdot)\)	41650.kh	560	no	\(-1\)	\(1\)	\(e\left(\frac{467}{560}\right)\)	\(e\left(\frac{187}{280}\right)\)	\(e\left(\frac{501}{560}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{141}{560}\right)\)	\(e\left(\frac{281}{560}\right)\)	\(e\left(\frac{167}{560}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{51}{70}\right)\)
\(\chi_{41650}(73,\cdot)\)	41650.lb	1680	no	\(-1\)	\(1\)	\(e\left(\frac{73}{1680}\right)\)	\(e\left(\frac{73}{840}\right)\)	\(e\left(\frac{379}{1680}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{359}{1680}\right)\)	\(e\left(\frac{73}{560}\right)\)	\(e\left(\frac{11}{560}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{113}{420}\right)\)
\(\chi_{41650}(79,\cdot)\)	41650.iz	240	no	\(-1\)	\(1\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{41650}(81,\cdot)\)	41650.jy	420	no	\(1\)	\(1\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{105}\right)\)
\(\chi_{41650}(83,\cdot)\)	41650.jf	280	no	\(1\)	\(1\)	\(e\left(\frac{179}{280}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{167}{280}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{117}{280}\right)\)	\(e\left(\frac{257}{280}\right)\)	\(e\left(\frac{9}{280}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{33}{140}\right)\)
\(\chi_{41650}(87,\cdot)\)	41650.kr	840	no	\(1\)	\(1\)	\(e\left(\frac{401}{840}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{353}{840}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{223}{840}\right)\)	\(e\left(\frac{121}{280}\right)\)	\(e\left(\frac{117}{280}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{377}{420}\right)\)
\(\chi_{41650}(89,\cdot)\)	41650.jz	420	no	\(-1\)	\(1\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{37}{105}\right)\)
\(\chi_{41650}(93,\cdot)\)	41650.ik	168	no	\(-1\)	\(1\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{41650}(97,\cdot)\)	41650.go	80	no	\(-1\)	\(1\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{41650}(99,\cdot)\)	41650.cs	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)

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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.