LMFDB - Group of Dirichlet characters of modulus 206400

Show commands: PariGP / SageMath

sage: H = DirichletGroup(206400)

pari: g = idealstar(,206400,2)

Character group

sage: G.order() pari: g.no
Order	=	53760
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{1680}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{206400}(148351,\cdot)$, $\chi_{206400}(116101,\cdot)$, $\chi_{206400}(68801,\cdot)$, $\chi_{206400}(173377,\cdot)$, $\chi_{206400}(76801,\cdot)$

First 32 of 53760 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{206400}(1,\cdot)$	206400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{206400}(7,\cdot)$	206400.ob	24	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$-i$
$\chi_{206400}(11,\cdot)$	206400.bpj	560	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{443}{560}\right)$	$e\left(\frac{417}{560}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{369}{560}\right)$	$e\left(\frac{169}{280}\right)$	$e\left(\frac{461}{560}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{101}{280}\right)$
$\chi_{206400}(13,\cdot)$	206400.bri	1680	no	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{417}{560}\right)$	$e\left(\frac{829}{1680}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{233}{1680}\right)$	$e\left(\frac{643}{840}\right)$	$e\left(\frac{757}{1680}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{139}{280}\right)$
$\chi_{206400}(17,\cdot)$	206400.bnn	420	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{263}{420}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{206400}(19,\cdot)$	206400.brr	1680	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{369}{560}\right)$	$e\left(\frac{233}{1680}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{601}{1680}\right)$	$e\left(\frac{641}{840}\right)$	$e\left(\frac{269}{1680}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{123}{280}\right)$
$\chi_{206400}(23,\cdot)$	206400.bqd	840	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{169}{280}\right)$	$e\left(\frac{643}{840}\right)$	$e\left(\frac{263}{420}\right)$	$e\left(\frac{641}{840}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{709}{840}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{33}{140}\right)$
$\chi_{206400}(29,\cdot)$	206400.brw	1680	yes	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{461}{560}\right)$	$e\left(\frac{757}{1680}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{269}{1680}\right)$	$e\left(\frac{709}{840}\right)$	$e\left(\frac{481}{1680}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{107}{280}\right)$
$\chi_{206400}(31,\cdot)$	206400.biz	210	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{206400}(37,\cdot)$	206400.bkc	240	no	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{206400}(41,\cdot)$	206400.blf	280	no	$-1$	$1$	$-i$	$e\left(\frac{101}{280}\right)$	$e\left(\frac{139}{280}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{123}{280}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{107}{280}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{57}{140}\right)$
$\chi_{206400}(47,\cdot)$	206400.bfu	140	no	$-1$	$1$	$i$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{206400}(49,\cdot)$	206400.gz	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-1$
$\chi_{206400}(53,\cdot)$	206400.brj	1680	yes	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{451}{560}\right)$	$e\left(\frac{1607}{1680}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{19}{1680}\right)$	$e\left(\frac{449}{840}\right)$	$e\left(\frac{671}{1680}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{197}{280}\right)$
$\chi_{206400}(59,\cdot)$	206400.bpm	560	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{367}{560}\right)$	$e\left(\frac{293}{560}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{221}{560}\right)$	$e\left(\frac{201}{280}\right)$	$e\left(\frac{9}{560}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{169}{280}\right)$
$\chi_{206400}(61,\cdot)$	206400.brv	1680	no	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{253}{560}\right)$	$e\left(\frac{181}{1680}\right)$	$e\left(\frac{373}{420}\right)$	$e\left(\frac{1397}{1680}\right)$	$e\left(\frac{397}{840}\right)$	$e\left(\frac{1633}{1680}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{271}{280}\right)$
$\chi_{206400}(67,\cdot)$	206400.bsa	1680	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{229}{560}\right)$	$e\left(\frac{1073}{1680}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{1021}{1680}\right)$	$e\left(\frac{431}{840}\right)$	$e\left(\frac{689}{1680}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{263}{280}\right)$
$\chi_{206400}(71,\cdot)$	206400.bqk	840	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{83}{280}\right)$	$e\left(\frac{491}{840}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{787}{840}\right)$	$e\left(\frac{107}{420}\right)$	$e\left(\frac{383}{840}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{51}{140}\right)$
$\chi_{206400}(73,\cdot)$	206400.bqa	840	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{149}{280}\right)$	$e\left(\frac{383}{840}\right)$	$e\left(\frac{253}{420}\right)$	$e\left(\frac{421}{840}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{809}{840}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{3}{140}\right)$
$\chi_{206400}(77,\cdot)$	206400.brg	1680	yes	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{233}{560}\right)$	$e\left(\frac{901}{1680}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{1457}{1680}\right)$	$e\left(\frac{787}{840}\right)$	$e\left(\frac{613}{1680}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{31}{280}\right)$
$\chi_{206400}(79,\cdot)$	206400.xu	60	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{206400}(83,\cdot)$	206400.bsb	1680	yes	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{169}{560}\right)$	$e\left(\frac{293}{1680}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{361}{1680}\right)$	$e\left(\frac{131}{840}\right)$	$e\left(\frac{149}{1680}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{103}{280}\right)$
$\chi_{206400}(89,\cdot)$	206400.bqn	840	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{179}{280}\right)$	$e\left(\frac{283}{840}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{611}{840}\right)$	$e\left(\frac{391}{420}\right)$	$e\left(\frac{379}{840}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{83}{140}\right)$
$\chi_{206400}(91,\cdot)$	206400.brm	1680	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{207}{560}\right)$	$e\left(\frac{479}{1680}\right)$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{583}{1680}\right)$	$e\left(\frac{83}{840}\right)$	$e\left(\frac{1667}{1680}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{69}{280}\right)$
$\chi_{206400}(97,\cdot)$	206400.bfk	140	no	$-1$	$1$	$i$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{206400}(101,\cdot)$	206400.bmb	336	no	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{83}{336}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{235}{336}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{56}\right)$
$\chi_{206400}(103,\cdot)$	206400.bra	840	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{243}{280}\right)$	$e\left(\frac{401}{840}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{727}{840}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{143}{840}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{81}{140}\right)$
$\chi_{206400}(107,\cdot)$	206400.bdj	112	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{56}\right)$
$\chi_{206400}(109,\cdot)$	206400.brx	1680	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{457}{560}\right)$	$e\left(\frac{89}{1680}\right)$	$e\left(\frac{347}{420}\right)$	$e\left(\frac{1513}{1680}\right)$	$e\left(\frac{773}{840}\right)$	$e\left(\frac{1397}{1680}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{59}{280}\right)$
$\chi_{206400}(113,\cdot)$	206400.bga	140	no	$-1$	$1$	$-i$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{206400}(119,\cdot)$	206400.bqr	840	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{117}{280}\right)$	$e\left(\frac{289}{840}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{293}{840}\right)$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{577}{840}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{109}{140}\right)$
$\chi_{206400}(121,\cdot)$	206400.bkw	280	no	$1$	$1$	$i$	$e\left(\frac{163}{280}\right)$	$e\left(\frac{137}{280}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{89}{280}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{181}{280}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{101}{140}\right)$

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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	$206400$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{1680}\)
Order	$53760$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{206400}(1,\cdot)\)	206400.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{206400}(7,\cdot)\)	206400.ob	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(-i\)
\(\chi_{206400}(11,\cdot)\)	206400.bpj	560	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{443}{560}\right)\)	\(e\left(\frac{417}{560}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{369}{560}\right)\)	\(e\left(\frac{169}{280}\right)\)	\(e\left(\frac{461}{560}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{101}{280}\right)\)
\(\chi_{206400}(13,\cdot)\)	206400.bri	1680	no	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{417}{560}\right)\)	\(e\left(\frac{829}{1680}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{233}{1680}\right)\)	\(e\left(\frac{643}{840}\right)\)	\(e\left(\frac{757}{1680}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{139}{280}\right)\)
\(\chi_{206400}(17,\cdot)\)	206400.bnn	420	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{206400}(19,\cdot)\)	206400.brr	1680	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{369}{560}\right)\)	\(e\left(\frac{233}{1680}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{601}{1680}\right)\)	\(e\left(\frac{641}{840}\right)\)	\(e\left(\frac{269}{1680}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{123}{280}\right)\)
\(\chi_{206400}(23,\cdot)\)	206400.bqd	840	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{169}{280}\right)\)	\(e\left(\frac{643}{840}\right)\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{641}{840}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{709}{840}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{33}{140}\right)\)
\(\chi_{206400}(29,\cdot)\)	206400.brw	1680	yes	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{461}{560}\right)\)	\(e\left(\frac{757}{1680}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{269}{1680}\right)\)	\(e\left(\frac{709}{840}\right)\)	\(e\left(\frac{481}{1680}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{107}{280}\right)\)
\(\chi_{206400}(31,\cdot)\)	206400.biz	210	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{206400}(37,\cdot)\)	206400.bkc	240	no	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{206400}(41,\cdot)\)	206400.blf	280	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{101}{280}\right)\)	\(e\left(\frac{139}{280}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{123}{280}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{107}{280}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{57}{140}\right)\)
\(\chi_{206400}(47,\cdot)\)	206400.bfu	140	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{206400}(49,\cdot)\)	206400.gz	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)
\(\chi_{206400}(53,\cdot)\)	206400.brj	1680	yes	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{451}{560}\right)\)	\(e\left(\frac{1607}{1680}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{19}{1680}\right)\)	\(e\left(\frac{449}{840}\right)\)	\(e\left(\frac{671}{1680}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{197}{280}\right)\)
\(\chi_{206400}(59,\cdot)\)	206400.bpm	560	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{367}{560}\right)\)	\(e\left(\frac{293}{560}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{221}{560}\right)\)	\(e\left(\frac{201}{280}\right)\)	\(e\left(\frac{9}{560}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{169}{280}\right)\)
\(\chi_{206400}(61,\cdot)\)	206400.brv	1680	no	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{253}{560}\right)\)	\(e\left(\frac{181}{1680}\right)\)	\(e\left(\frac{373}{420}\right)\)	\(e\left(\frac{1397}{1680}\right)\)	\(e\left(\frac{397}{840}\right)\)	\(e\left(\frac{1633}{1680}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{271}{280}\right)\)
\(\chi_{206400}(67,\cdot)\)	206400.bsa	1680	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{229}{560}\right)\)	\(e\left(\frac{1073}{1680}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{1021}{1680}\right)\)	\(e\left(\frac{431}{840}\right)\)	\(e\left(\frac{689}{1680}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{263}{280}\right)\)
\(\chi_{206400}(71,\cdot)\)	206400.bqk	840	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{83}{280}\right)\)	\(e\left(\frac{491}{840}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{787}{840}\right)\)	\(e\left(\frac{107}{420}\right)\)	\(e\left(\frac{383}{840}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{51}{140}\right)\)
\(\chi_{206400}(73,\cdot)\)	206400.bqa	840	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{149}{280}\right)\)	\(e\left(\frac{383}{840}\right)\)	\(e\left(\frac{253}{420}\right)\)	\(e\left(\frac{421}{840}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{809}{840}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{3}{140}\right)\)
\(\chi_{206400}(77,\cdot)\)	206400.brg	1680	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{233}{560}\right)\)	\(e\left(\frac{901}{1680}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{1457}{1680}\right)\)	\(e\left(\frac{787}{840}\right)\)	\(e\left(\frac{613}{1680}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{31}{280}\right)\)
\(\chi_{206400}(79,\cdot)\)	206400.xu	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{206400}(83,\cdot)\)	206400.bsb	1680	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{169}{560}\right)\)	\(e\left(\frac{293}{1680}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{361}{1680}\right)\)	\(e\left(\frac{131}{840}\right)\)	\(e\left(\frac{149}{1680}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{103}{280}\right)\)
\(\chi_{206400}(89,\cdot)\)	206400.bqn	840	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{179}{280}\right)\)	\(e\left(\frac{283}{840}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{611}{840}\right)\)	\(e\left(\frac{391}{420}\right)\)	\(e\left(\frac{379}{840}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{83}{140}\right)\)
\(\chi_{206400}(91,\cdot)\)	206400.brm	1680	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{207}{560}\right)\)	\(e\left(\frac{479}{1680}\right)\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{583}{1680}\right)\)	\(e\left(\frac{83}{840}\right)\)	\(e\left(\frac{1667}{1680}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{69}{280}\right)\)
\(\chi_{206400}(97,\cdot)\)	206400.bfk	140	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{206400}(101,\cdot)\)	206400.bmb	336	no	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{83}{336}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{235}{336}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{56}\right)\)
\(\chi_{206400}(103,\cdot)\)	206400.bra	840	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{243}{280}\right)\)	\(e\left(\frac{401}{840}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{727}{840}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{143}{840}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{81}{140}\right)\)
\(\chi_{206400}(107,\cdot)\)	206400.bdj	112	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{56}\right)\)
\(\chi_{206400}(109,\cdot)\)	206400.brx	1680	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{457}{560}\right)\)	\(e\left(\frac{89}{1680}\right)\)	\(e\left(\frac{347}{420}\right)\)	\(e\left(\frac{1513}{1680}\right)\)	\(e\left(\frac{773}{840}\right)\)	\(e\left(\frac{1397}{1680}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{59}{280}\right)\)
\(\chi_{206400}(113,\cdot)\)	206400.bga	140	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{206400}(119,\cdot)\)	206400.bqr	840	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{117}{280}\right)\)	\(e\left(\frac{289}{840}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{293}{840}\right)\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{577}{840}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{109}{140}\right)\)
\(\chi_{206400}(121,\cdot)\)	206400.bkw	280	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{163}{280}\right)\)	\(e\left(\frac{137}{280}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{89}{280}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{181}{280}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{101}{140}\right)\)

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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.