LMFDB - Group of Dirichlet characters of modulus 21675

Show commands: PariGP / SageMath

sage: H = DirichletGroup(21675)

pari: g = idealstar(,21675,2)

Character group

sage: G.order() pari: g.no
Order	=	10880
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{1360}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{21675}(7226,\cdot)$, $\chi_{21675}(2602,\cdot)$, $\chi_{21675}(2026,\cdot)$

First 32 of 10880 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$19$	$22$
$\chi_{21675}(1,\cdot)$	21675.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{21675}(2,\cdot)$	21675.ff	680	yes	$1$	$1$	$e\left(\frac{23}{85}\right)$	$e\left(\frac{46}{85}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{69}{85}\right)$	$e\left(\frac{249}{680}\right)$	$e\left(\frac{293}{340}\right)$	$e\left(\frac{539}{680}\right)$	$e\left(\frac{7}{85}\right)$	$e\left(\frac{231}{340}\right)$	$e\left(\frac{433}{680}\right)$
$\chi_{21675}(4,\cdot)$	21675.ew	340	no	$1$	$1$	$e\left(\frac{46}{85}\right)$	$e\left(\frac{7}{85}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{53}{85}\right)$	$e\left(\frac{249}{340}\right)$	$e\left(\frac{123}{170}\right)$	$e\left(\frac{199}{340}\right)$	$e\left(\frac{14}{85}\right)$	$e\left(\frac{61}{170}\right)$	$e\left(\frac{93}{340}\right)$
$\chi_{21675}(7,\cdot)$	21675.el	272	no	$1$	$1$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{157}{272}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{29}{272}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{27}{272}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{171}{272}\right)$
$\chi_{21675}(8,\cdot)$	21675.ff	680	yes	$1$	$1$	$e\left(\frac{69}{85}\right)$	$e\left(\frac{53}{85}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{37}{85}\right)$	$e\left(\frac{67}{680}\right)$	$e\left(\frac{199}{340}\right)$	$e\left(\frac{257}{680}\right)$	$e\left(\frac{21}{85}\right)$	$e\left(\frac{13}{340}\right)$	$e\left(\frac{619}{680}\right)$
$\chi_{21675}(11,\cdot)$	21675.fk	1360	yes	$1$	$1$	$e\left(\frac{249}{680}\right)$	$e\left(\frac{249}{340}\right)$	$e\left(\frac{29}{272}\right)$	$e\left(\frac{67}{680}\right)$	$e\left(\frac{333}{1360}\right)$	$e\left(\frac{263}{340}\right)$	$e\left(\frac{643}{1360}\right)$	$e\left(\frac{79}{170}\right)$	$e\left(\frac{397}{680}\right)$	$e\left(\frac{831}{1360}\right)$
$\chi_{21675}(13,\cdot)$	21675.ev	340	no	$-1$	$1$	$e\left(\frac{293}{340}\right)$	$e\left(\frac{123}{170}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{199}{340}\right)$	$e\left(\frac{263}{340}\right)$	$e\left(\frac{97}{340}\right)$	$e\left(\frac{103}{340}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{54}{85}\right)$
$\chi_{21675}(14,\cdot)$	21675.fi	1360	yes	$1$	$1$	$e\left(\frac{539}{680}\right)$	$e\left(\frac{199}{340}\right)$	$e\left(\frac{27}{272}\right)$	$e\left(\frac{257}{680}\right)$	$e\left(\frac{643}{1360}\right)$	$e\left(\frac{103}{340}\right)$	$e\left(\frac{1213}{1360}\right)$	$e\left(\frac{29}{170}\right)$	$e\left(\frac{107}{680}\right)$	$e\left(\frac{361}{1360}\right)$
$\chi_{21675}(16,\cdot)$	21675.ed	170	no	$1$	$1$	$e\left(\frac{7}{85}\right)$	$e\left(\frac{14}{85}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{21}{85}\right)$	$e\left(\frac{79}{170}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{29}{170}\right)$	$e\left(\frac{28}{85}\right)$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{93}{170}\right)$
$\chi_{21675}(19,\cdot)$	21675.fc	680	no	$1$	$1$	$e\left(\frac{231}{340}\right)$	$e\left(\frac{61}{170}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{13}{340}\right)$	$e\left(\frac{397}{680}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{107}{680}\right)$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{313}{340}\right)$	$e\left(\frac{179}{680}\right)$
$\chi_{21675}(22,\cdot)$	21675.fn	1360	no	$1$	$1$	$e\left(\frac{433}{680}\right)$	$e\left(\frac{93}{340}\right)$	$e\left(\frac{171}{272}\right)$	$e\left(\frac{619}{680}\right)$	$e\left(\frac{831}{1360}\right)$	$e\left(\frac{54}{85}\right)$	$e\left(\frac{361}{1360}\right)$	$e\left(\frac{93}{170}\right)$	$e\left(\frac{179}{680}\right)$	$e\left(\frac{337}{1360}\right)$
$\chi_{21675}(23,\cdot)$	21675.fm	1360	yes	$-1$	$1$	$e\left(\frac{559}{680}\right)$	$e\left(\frac{219}{340}\right)$	$e\left(\frac{225}{272}\right)$	$e\left(\frac{317}{680}\right)$	$e\left(\frac{213}{1360}\right)$	$e\left(\frac{12}{85}\right)$	$e\left(\frac{883}{1360}\right)$	$e\left(\frac{49}{170}\right)$	$e\left(\frac{257}{680}\right)$	$e\left(\frac{1331}{1360}\right)$
$\chi_{21675}(26,\cdot)$	21675.du	136	no	$-1$	$1$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{37}{136}\right)$
$\chi_{21675}(28,\cdot)$	21675.fn	1360	no	$1$	$1$	$e\left(\frac{43}{680}\right)$	$e\left(\frac{43}{340}\right)$	$e\left(\frac{169}{272}\right)$	$e\left(\frac{129}{680}\right)$	$e\left(\frac{1141}{1360}\right)$	$e\left(\frac{14}{85}\right)$	$e\left(\frac{931}{1360}\right)$	$e\left(\frac{43}{170}\right)$	$e\left(\frac{569}{680}\right)$	$e\left(\frac{1227}{1360}\right)$
$\chi_{21675}(29,\cdot)$	21675.fi	1360	yes	$1$	$1$	$e\left(\frac{623}{680}\right)$	$e\left(\frac{283}{340}\right)$	$e\left(\frac{199}{272}\right)$	$e\left(\frac{509}{680}\right)$	$e\left(\frac{911}{1360}\right)$	$e\left(\frac{331}{340}\right)$	$e\left(\frac{881}{1360}\right)$	$e\left(\frac{113}{170}\right)$	$e\left(\frac{159}{680}\right)$	$e\left(\frac{797}{1360}\right)$
$\chi_{21675}(31,\cdot)$	21675.fl	1360	no	$-1$	$1$	$e\left(\frac{467}{680}\right)$	$e\left(\frac{127}{340}\right)$	$e\left(\frac{35}{272}\right)$	$e\left(\frac{41}{680}\right)$	$e\left(\frac{219}{1360}\right)$	$e\left(\frac{29}{340}\right)$	$e\left(\frac{1109}{1360}\right)$	$e\left(\frac{127}{170}\right)$	$e\left(\frac{451}{680}\right)$	$e\left(\frac{1153}{1360}\right)$
$\chi_{21675}(32,\cdot)$	21675.dq	136	no	$1$	$1$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{25}{136}\right)$
$\chi_{21675}(37,\cdot)$	21675.fn	1360	no	$1$	$1$	$e\left(\frac{381}{680}\right)$	$e\left(\frac{41}{340}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{463}{680}\right)$	$e\left(\frac{147}{1360}\right)$	$e\left(\frac{43}{85}\right)$	$e\left(\frac{437}{1360}\right)$	$e\left(\frac{41}{170}\right)$	$e\left(\frac{503}{680}\right)$	$e\left(\frac{909}{1360}\right)$
$\chi_{21675}(38,\cdot)$	21675.cb	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{21675}(41,\cdot)$	21675.fk	1360	yes	$1$	$1$	$e\left(\frac{101}{680}\right)$	$e\left(\frac{101}{340}\right)$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{303}{680}\right)$	$e\left(\frac{217}{1360}\right)$	$e\left(\frac{7}{340}\right)$	$e\left(\frac{807}{1360}\right)$	$e\left(\frac{101}{170}\right)$	$e\left(\frac{273}{680}\right)$	$e\left(\frac{419}{1360}\right)$
$\chi_{21675}(43,\cdot)$	21675.dw	136	no	$-1$	$1$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{99}{136}\right)$
$\chi_{21675}(44,\cdot)$	21675.fi	1360	yes	$1$	$1$	$e\left(\frac{617}{680}\right)$	$e\left(\frac{277}{340}\right)$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{491}{680}\right)$	$e\left(\frac{1329}{1360}\right)$	$e\left(\frac{169}{340}\right)$	$e\left(\frac{79}{1360}\right)$	$e\left(\frac{107}{170}\right)$	$e\left(\frac{641}{680}\right)$	$e\left(\frac{1203}{1360}\right)$
$\chi_{21675}(46,\cdot)$	21675.fl	1360	no	$-1$	$1$	$e\left(\frac{63}{680}\right)$	$e\left(\frac{63}{340}\right)$	$e\left(\frac{95}{272}\right)$	$e\left(\frac{189}{680}\right)$	$e\left(\frac{711}{1360}\right)$	$e\left(\frac{1}{340}\right)$	$e\left(\frac{601}{1360}\right)$	$e\left(\frac{63}{170}\right)$	$e\left(\frac{39}{680}\right)$	$e\left(\frac{837}{1360}\right)$
$\chi_{21675}(47,\cdot)$	21675.ep	340	yes	$1$	$1$	$e\left(\frac{69}{340}\right)$	$e\left(\frac{69}{170}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{207}{340}\right)$	$e\left(\frac{189}{340}\right)$	$e\left(\frac{71}{340}\right)$	$e\left(\frac{149}{340}\right)$	$e\left(\frac{69}{85}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{129}{170}\right)$
$\chi_{21675}(49,\cdot)$	21675.ds	136	no	$1$	$1$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{35}{136}\right)$
$\chi_{21675}(52,\cdot)$	21675.es	340	no	$-1$	$1$	$e\left(\frac{137}{340}\right)$	$e\left(\frac{137}{170}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{71}{340}\right)$	$e\left(\frac{43}{85}\right)$	$e\left(\frac{3}{340}\right)$	$e\left(\frac{151}{170}\right)$	$e\left(\frac{52}{85}\right)$	$e\left(\frac{93}{170}\right)$	$e\left(\frac{309}{340}\right)$
$\chi_{21675}(53,\cdot)$	21675.ey	680	yes	$1$	$1$	$e\left(\frac{127}{170}\right)$	$e\left(\frac{42}{85}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{41}{170}\right)$	$e\left(\frac{353}{680}\right)$	$e\left(\frac{31}{340}\right)$	$e\left(\frac{603}{680}\right)$	$e\left(\frac{84}{85}\right)$	$e\left(\frac{307}{340}\right)$	$e\left(\frac{181}{680}\right)$
$\chi_{21675}(56,\cdot)$	21675.fk	1360	yes	$1$	$1$	$e\left(\frac{227}{680}\right)$	$e\left(\frac{227}{340}\right)$	$e\left(\frac{39}{272}\right)$	$e\left(\frac{1}{680}\right)$	$e\left(\frac{279}{1360}\right)$	$e\left(\frac{9}{340}\right)$	$e\left(\frac{649}{1360}\right)$	$e\left(\frac{57}{170}\right)$	$e\left(\frac{351}{680}\right)$	$e\left(\frac{733}{1360}\right)$
$\chi_{21675}(58,\cdot)$	21675.fn	1360	no	$1$	$1$	$e\left(\frac{127}{680}\right)$	$e\left(\frac{127}{340}\right)$	$e\left(\frac{69}{272}\right)$	$e\left(\frac{381}{680}\right)$	$e\left(\frac{49}{1360}\right)$	$e\left(\frac{71}{85}\right)$	$e\left(\frac{599}{1360}\right)$	$e\left(\frac{127}{170}\right)$	$e\left(\frac{621}{680}\right)$	$e\left(\frac{303}{1360}\right)$
$\chi_{21675}(59,\cdot)$	21675.fd	680	yes	$-1$	$1$	$e\left(\frac{223}{340}\right)$	$e\left(\frac{53}{170}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{329}{340}\right)$	$e\left(\frac{331}{680}\right)$	$e\left(\frac{78}{85}\right)$	$e\left(\frac{341}{680}\right)$	$e\left(\frac{53}{85}\right)$	$e\left(\frac{219}{340}\right)$	$e\left(\frac{97}{680}\right)$
$\chi_{21675}(61,\cdot)$	21675.fl	1360	no	$-1$	$1$	$e\left(\frac{489}{680}\right)$	$e\left(\frac{149}{340}\right)$	$e\left(\frac{161}{272}\right)$	$e\left(\frac{107}{680}\right)$	$e\left(\frac{953}{1360}\right)$	$e\left(\frac{283}{340}\right)$	$e\left(\frac{423}{1360}\right)$	$e\left(\frac{149}{170}\right)$	$e\left(\frac{497}{680}\right)$	$e\left(\frac{571}{1360}\right)$
$\chi_{21675}(62,\cdot)$	21675.fh	1360	yes	$-1$	$1$	$e\left(\frac{651}{680}\right)$	$e\left(\frac{311}{340}\right)$	$e\left(\frac{177}{272}\right)$	$e\left(\frac{593}{680}\right)$	$e\left(\frac{717}{1360}\right)$	$e\left(\frac{161}{170}\right)$	$e\left(\frac{827}{1360}\right)$	$e\left(\frac{141}{170}\right)$	$e\left(\frac{233}{680}\right)$	$e\left(\frac{659}{1360}\right)$

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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	$21675$
Structure	\(C_{2}\times C_{4}\times C_{1360}\)
Order	$10880$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(19\)	\(22\)
\(\chi_{21675}(1,\cdot)\)	21675.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{21675}(2,\cdot)\)	21675.ff	680	yes	\(1\)	\(1\)	\(e\left(\frac{23}{85}\right)\)	\(e\left(\frac{46}{85}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{69}{85}\right)\)	\(e\left(\frac{249}{680}\right)\)	\(e\left(\frac{293}{340}\right)\)	\(e\left(\frac{539}{680}\right)\)	\(e\left(\frac{7}{85}\right)\)	\(e\left(\frac{231}{340}\right)\)	\(e\left(\frac{433}{680}\right)\)
\(\chi_{21675}(4,\cdot)\)	21675.ew	340	no	\(1\)	\(1\)	\(e\left(\frac{46}{85}\right)\)	\(e\left(\frac{7}{85}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{53}{85}\right)\)	\(e\left(\frac{249}{340}\right)\)	\(e\left(\frac{123}{170}\right)\)	\(e\left(\frac{199}{340}\right)\)	\(e\left(\frac{14}{85}\right)\)	\(e\left(\frac{61}{170}\right)\)	\(e\left(\frac{93}{340}\right)\)
\(\chi_{21675}(7,\cdot)\)	21675.el	272	no	\(1\)	\(1\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{157}{272}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{29}{272}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{27}{272}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{171}{272}\right)\)
\(\chi_{21675}(8,\cdot)\)	21675.ff	680	yes	\(1\)	\(1\)	\(e\left(\frac{69}{85}\right)\)	\(e\left(\frac{53}{85}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{37}{85}\right)\)	\(e\left(\frac{67}{680}\right)\)	\(e\left(\frac{199}{340}\right)\)	\(e\left(\frac{257}{680}\right)\)	\(e\left(\frac{21}{85}\right)\)	\(e\left(\frac{13}{340}\right)\)	\(e\left(\frac{619}{680}\right)\)
\(\chi_{21675}(11,\cdot)\)	21675.fk	1360	yes	\(1\)	\(1\)	\(e\left(\frac{249}{680}\right)\)	\(e\left(\frac{249}{340}\right)\)	\(e\left(\frac{29}{272}\right)\)	\(e\left(\frac{67}{680}\right)\)	\(e\left(\frac{333}{1360}\right)\)	\(e\left(\frac{263}{340}\right)\)	\(e\left(\frac{643}{1360}\right)\)	\(e\left(\frac{79}{170}\right)\)	\(e\left(\frac{397}{680}\right)\)	\(e\left(\frac{831}{1360}\right)\)
\(\chi_{21675}(13,\cdot)\)	21675.ev	340	no	\(-1\)	\(1\)	\(e\left(\frac{293}{340}\right)\)	\(e\left(\frac{123}{170}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{199}{340}\right)\)	\(e\left(\frac{263}{340}\right)\)	\(e\left(\frac{97}{340}\right)\)	\(e\left(\frac{103}{340}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{54}{85}\right)\)
\(\chi_{21675}(14,\cdot)\)	21675.fi	1360	yes	\(1\)	\(1\)	\(e\left(\frac{539}{680}\right)\)	\(e\left(\frac{199}{340}\right)\)	\(e\left(\frac{27}{272}\right)\)	\(e\left(\frac{257}{680}\right)\)	\(e\left(\frac{643}{1360}\right)\)	\(e\left(\frac{103}{340}\right)\)	\(e\left(\frac{1213}{1360}\right)\)	\(e\left(\frac{29}{170}\right)\)	\(e\left(\frac{107}{680}\right)\)	\(e\left(\frac{361}{1360}\right)\)
\(\chi_{21675}(16,\cdot)\)	21675.ed	170	no	\(1\)	\(1\)	\(e\left(\frac{7}{85}\right)\)	\(e\left(\frac{14}{85}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{21}{85}\right)\)	\(e\left(\frac{79}{170}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{29}{170}\right)\)	\(e\left(\frac{28}{85}\right)\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{93}{170}\right)\)
\(\chi_{21675}(19,\cdot)\)	21675.fc	680	no	\(1\)	\(1\)	\(e\left(\frac{231}{340}\right)\)	\(e\left(\frac{61}{170}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{13}{340}\right)\)	\(e\left(\frac{397}{680}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{107}{680}\right)\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{313}{340}\right)\)	\(e\left(\frac{179}{680}\right)\)
\(\chi_{21675}(22,\cdot)\)	21675.fn	1360	no	\(1\)	\(1\)	\(e\left(\frac{433}{680}\right)\)	\(e\left(\frac{93}{340}\right)\)	\(e\left(\frac{171}{272}\right)\)	\(e\left(\frac{619}{680}\right)\)	\(e\left(\frac{831}{1360}\right)\)	\(e\left(\frac{54}{85}\right)\)	\(e\left(\frac{361}{1360}\right)\)	\(e\left(\frac{93}{170}\right)\)	\(e\left(\frac{179}{680}\right)\)	\(e\left(\frac{337}{1360}\right)\)
\(\chi_{21675}(23,\cdot)\)	21675.fm	1360	yes	\(-1\)	\(1\)	\(e\left(\frac{559}{680}\right)\)	\(e\left(\frac{219}{340}\right)\)	\(e\left(\frac{225}{272}\right)\)	\(e\left(\frac{317}{680}\right)\)	\(e\left(\frac{213}{1360}\right)\)	\(e\left(\frac{12}{85}\right)\)	\(e\left(\frac{883}{1360}\right)\)	\(e\left(\frac{49}{170}\right)\)	\(e\left(\frac{257}{680}\right)\)	\(e\left(\frac{1331}{1360}\right)\)
\(\chi_{21675}(26,\cdot)\)	21675.du	136	no	\(-1\)	\(1\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{37}{136}\right)\)
\(\chi_{21675}(28,\cdot)\)	21675.fn	1360	no	\(1\)	\(1\)	\(e\left(\frac{43}{680}\right)\)	\(e\left(\frac{43}{340}\right)\)	\(e\left(\frac{169}{272}\right)\)	\(e\left(\frac{129}{680}\right)\)	\(e\left(\frac{1141}{1360}\right)\)	\(e\left(\frac{14}{85}\right)\)	\(e\left(\frac{931}{1360}\right)\)	\(e\left(\frac{43}{170}\right)\)	\(e\left(\frac{569}{680}\right)\)	\(e\left(\frac{1227}{1360}\right)\)
\(\chi_{21675}(29,\cdot)\)	21675.fi	1360	yes	\(1\)	\(1\)	\(e\left(\frac{623}{680}\right)\)	\(e\left(\frac{283}{340}\right)\)	\(e\left(\frac{199}{272}\right)\)	\(e\left(\frac{509}{680}\right)\)	\(e\left(\frac{911}{1360}\right)\)	\(e\left(\frac{331}{340}\right)\)	\(e\left(\frac{881}{1360}\right)\)	\(e\left(\frac{113}{170}\right)\)	\(e\left(\frac{159}{680}\right)\)	\(e\left(\frac{797}{1360}\right)\)
\(\chi_{21675}(31,\cdot)\)	21675.fl	1360	no	\(-1\)	\(1\)	\(e\left(\frac{467}{680}\right)\)	\(e\left(\frac{127}{340}\right)\)	\(e\left(\frac{35}{272}\right)\)	\(e\left(\frac{41}{680}\right)\)	\(e\left(\frac{219}{1360}\right)\)	\(e\left(\frac{29}{340}\right)\)	\(e\left(\frac{1109}{1360}\right)\)	\(e\left(\frac{127}{170}\right)\)	\(e\left(\frac{451}{680}\right)\)	\(e\left(\frac{1153}{1360}\right)\)
\(\chi_{21675}(32,\cdot)\)	21675.dq	136	no	\(1\)	\(1\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{25}{136}\right)\)
\(\chi_{21675}(37,\cdot)\)	21675.fn	1360	no	\(1\)	\(1\)	\(e\left(\frac{381}{680}\right)\)	\(e\left(\frac{41}{340}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{463}{680}\right)\)	\(e\left(\frac{147}{1360}\right)\)	\(e\left(\frac{43}{85}\right)\)	\(e\left(\frac{437}{1360}\right)\)	\(e\left(\frac{41}{170}\right)\)	\(e\left(\frac{503}{680}\right)\)	\(e\left(\frac{909}{1360}\right)\)
\(\chi_{21675}(38,\cdot)\)	21675.cb	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{21675}(41,\cdot)\)	21675.fk	1360	yes	\(1\)	\(1\)	\(e\left(\frac{101}{680}\right)\)	\(e\left(\frac{101}{340}\right)\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{303}{680}\right)\)	\(e\left(\frac{217}{1360}\right)\)	\(e\left(\frac{7}{340}\right)\)	\(e\left(\frac{807}{1360}\right)\)	\(e\left(\frac{101}{170}\right)\)	\(e\left(\frac{273}{680}\right)\)	\(e\left(\frac{419}{1360}\right)\)
\(\chi_{21675}(43,\cdot)\)	21675.dw	136	no	\(-1\)	\(1\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{99}{136}\right)\)
\(\chi_{21675}(44,\cdot)\)	21675.fi	1360	yes	\(1\)	\(1\)	\(e\left(\frac{617}{680}\right)\)	\(e\left(\frac{277}{340}\right)\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{491}{680}\right)\)	\(e\left(\frac{1329}{1360}\right)\)	\(e\left(\frac{169}{340}\right)\)	\(e\left(\frac{79}{1360}\right)\)	\(e\left(\frac{107}{170}\right)\)	\(e\left(\frac{641}{680}\right)\)	\(e\left(\frac{1203}{1360}\right)\)
\(\chi_{21675}(46,\cdot)\)	21675.fl	1360	no	\(-1\)	\(1\)	\(e\left(\frac{63}{680}\right)\)	\(e\left(\frac{63}{340}\right)\)	\(e\left(\frac{95}{272}\right)\)	\(e\left(\frac{189}{680}\right)\)	\(e\left(\frac{711}{1360}\right)\)	\(e\left(\frac{1}{340}\right)\)	\(e\left(\frac{601}{1360}\right)\)	\(e\left(\frac{63}{170}\right)\)	\(e\left(\frac{39}{680}\right)\)	\(e\left(\frac{837}{1360}\right)\)
\(\chi_{21675}(47,\cdot)\)	21675.ep	340	yes	\(1\)	\(1\)	\(e\left(\frac{69}{340}\right)\)	\(e\left(\frac{69}{170}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{207}{340}\right)\)	\(e\left(\frac{189}{340}\right)\)	\(e\left(\frac{71}{340}\right)\)	\(e\left(\frac{149}{340}\right)\)	\(e\left(\frac{69}{85}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{129}{170}\right)\)
\(\chi_{21675}(49,\cdot)\)	21675.ds	136	no	\(1\)	\(1\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{35}{136}\right)\)
\(\chi_{21675}(52,\cdot)\)	21675.es	340	no	\(-1\)	\(1\)	\(e\left(\frac{137}{340}\right)\)	\(e\left(\frac{137}{170}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{71}{340}\right)\)	\(e\left(\frac{43}{85}\right)\)	\(e\left(\frac{3}{340}\right)\)	\(e\left(\frac{151}{170}\right)\)	\(e\left(\frac{52}{85}\right)\)	\(e\left(\frac{93}{170}\right)\)	\(e\left(\frac{309}{340}\right)\)
\(\chi_{21675}(53,\cdot)\)	21675.ey	680	yes	\(1\)	\(1\)	\(e\left(\frac{127}{170}\right)\)	\(e\left(\frac{42}{85}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{41}{170}\right)\)	\(e\left(\frac{353}{680}\right)\)	\(e\left(\frac{31}{340}\right)\)	\(e\left(\frac{603}{680}\right)\)	\(e\left(\frac{84}{85}\right)\)	\(e\left(\frac{307}{340}\right)\)	\(e\left(\frac{181}{680}\right)\)
\(\chi_{21675}(56,\cdot)\)	21675.fk	1360	yes	\(1\)	\(1\)	\(e\left(\frac{227}{680}\right)\)	\(e\left(\frac{227}{340}\right)\)	\(e\left(\frac{39}{272}\right)\)	\(e\left(\frac{1}{680}\right)\)	\(e\left(\frac{279}{1360}\right)\)	\(e\left(\frac{9}{340}\right)\)	\(e\left(\frac{649}{1360}\right)\)	\(e\left(\frac{57}{170}\right)\)	\(e\left(\frac{351}{680}\right)\)	\(e\left(\frac{733}{1360}\right)\)
\(\chi_{21675}(58,\cdot)\)	21675.fn	1360	no	\(1\)	\(1\)	\(e\left(\frac{127}{680}\right)\)	\(e\left(\frac{127}{340}\right)\)	\(e\left(\frac{69}{272}\right)\)	\(e\left(\frac{381}{680}\right)\)	\(e\left(\frac{49}{1360}\right)\)	\(e\left(\frac{71}{85}\right)\)	\(e\left(\frac{599}{1360}\right)\)	\(e\left(\frac{127}{170}\right)\)	\(e\left(\frac{621}{680}\right)\)	\(e\left(\frac{303}{1360}\right)\)
\(\chi_{21675}(59,\cdot)\)	21675.fd	680	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{340}\right)\)	\(e\left(\frac{53}{170}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{329}{340}\right)\)	\(e\left(\frac{331}{680}\right)\)	\(e\left(\frac{78}{85}\right)\)	\(e\left(\frac{341}{680}\right)\)	\(e\left(\frac{53}{85}\right)\)	\(e\left(\frac{219}{340}\right)\)	\(e\left(\frac{97}{680}\right)\)
\(\chi_{21675}(61,\cdot)\)	21675.fl	1360	no	\(-1\)	\(1\)	\(e\left(\frac{489}{680}\right)\)	\(e\left(\frac{149}{340}\right)\)	\(e\left(\frac{161}{272}\right)\)	\(e\left(\frac{107}{680}\right)\)	\(e\left(\frac{953}{1360}\right)\)	\(e\left(\frac{283}{340}\right)\)	\(e\left(\frac{423}{1360}\right)\)	\(e\left(\frac{149}{170}\right)\)	\(e\left(\frac{497}{680}\right)\)	\(e\left(\frac{571}{1360}\right)\)
\(\chi_{21675}(62,\cdot)\)	21675.fh	1360	yes	\(-1\)	\(1\)	\(e\left(\frac{651}{680}\right)\)	\(e\left(\frac{311}{340}\right)\)	\(e\left(\frac{177}{272}\right)\)	\(e\left(\frac{593}{680}\right)\)	\(e\left(\frac{717}{1360}\right)\)	\(e\left(\frac{161}{170}\right)\)	\(e\left(\frac{827}{1360}\right)\)	\(e\left(\frac{141}{170}\right)\)	\(e\left(\frac{233}{680}\right)\)	\(e\left(\frac{659}{1360}\right)\)

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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.