LMFDB - Group of Dirichlet characters of modulus 28900

Show commands: PariGP / SageMath

sage: H = DirichletGroup(28900)

pari: g = idealstar(,28900,2)

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	=	$\chi_{28900}(14451,\cdot)$, $\chi_{28900}(24277,\cdot)$, $\chi_{28900}(23701,\cdot)$

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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{28900}(1,\cdot)$	28900.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{28900}(3,\cdot)$	28900.fg	1360	yes	$-1$	$1$	$e\left(\frac{1297}{1360}\right)$	$e\left(\frac{223}{272}\right)$	$e\left(\frac{617}{680}\right)$	$e\left(\frac{251}{1360}\right)$	$e\left(\frac{63}{170}\right)$	$e\left(\frac{579}{680}\right)$	$e\left(\frac{263}{340}\right)$	$e\left(\frac{231}{1360}\right)$	$e\left(\frac{1171}{1360}\right)$	$e\left(\frac{217}{1360}\right)$
$\chi_{28900}(7,\cdot)$	28900.el	272	no	$-1$	$1$	$e\left(\frac{223}{272}\right)$	$e\left(\frac{21}{272}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{165}{272}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{89}{272}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{199}{272}\right)$
$\chi_{28900}(9,\cdot)$	28900.ff	680	no	$1$	$1$	$e\left(\frac{617}{680}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{277}{340}\right)$	$e\left(\frac{251}{680}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{239}{340}\right)$	$e\left(\frac{93}{170}\right)$	$e\left(\frac{231}{680}\right)$	$e\left(\frac{491}{680}\right)$	$e\left(\frac{217}{680}\right)$
$\chi_{28900}(11,\cdot)$	28900.fj	1360	yes	$1$	$1$	$e\left(\frac{251}{1360}\right)$	$e\left(\frac{165}{272}\right)$	$e\left(\frac{251}{680}\right)$	$e\left(\frac{333}{1360}\right)$	$e\left(\frac{263}{340}\right)$	$e\left(\frac{57}{680}\right)$	$e\left(\frac{269}{340}\right)$	$e\left(\frac{213}{1360}\right)$	$e\left(\frac{753}{1360}\right)$	$e\left(\frac{231}{1360}\right)$
$\chi_{28900}(13,\cdot)$	28900.en	340	no	$-1$	$1$	$e\left(\frac{63}{170}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{263}{340}\right)$	$e\left(\frac{97}{340}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{69}{85}\right)$	$e\left(\frac{12}{85}\right)$	$e\left(\frac{19}{170}\right)$	$e\left(\frac{331}{340}\right)$
$\chi_{28900}(19,\cdot)$	28900.fe	680	yes	$-1$	$1$	$e\left(\frac{579}{680}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{239}{340}\right)$	$e\left(\frac{57}{680}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{143}{340}\right)$	$e\left(\frac{141}{170}\right)$	$e\left(\frac{597}{680}\right)$	$e\left(\frac{377}{680}\right)$	$e\left(\frac{159}{680}\right)$
$\chi_{28900}(21,\cdot)$	28900.es	340	no	$1$	$1$	$e\left(\frac{263}{340}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{93}{170}\right)$	$e\left(\frac{269}{340}\right)$	$e\left(\frac{69}{85}\right)$	$e\left(\frac{141}{170}\right)$	$e\left(\frac{57}{85}\right)$	$e\left(\frac{169}{340}\right)$	$e\left(\frac{109}{340}\right)$	$e\left(\frac{303}{340}\right)$
$\chi_{28900}(23,\cdot)$	28900.fn	1360	yes	$-1$	$1$	$e\left(\frac{231}{1360}\right)$	$e\left(\frac{89}{272}\right)$	$e\left(\frac{231}{680}\right)$	$e\left(\frac{213}{1360}\right)$	$e\left(\frac{12}{85}\right)$	$e\left(\frac{597}{680}\right)$	$e\left(\frac{169}{340}\right)$	$e\left(\frac{513}{1360}\right)$	$e\left(\frac{693}{1360}\right)$	$e\left(\frac{791}{1360}\right)$
$\chi_{28900}(27,\cdot)$	28900.fg	1360	yes	$-1$	$1$	$e\left(\frac{1171}{1360}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{491}{680}\right)$	$e\left(\frac{753}{1360}\right)$	$e\left(\frac{19}{170}\right)$	$e\left(\frac{377}{680}\right)$	$e\left(\frac{109}{340}\right)$	$e\left(\frac{693}{1360}\right)$	$e\left(\frac{793}{1360}\right)$	$e\left(\frac{651}{1360}\right)$
$\chi_{28900}(29,\cdot)$	28900.fl	1360	no	$-1$	$1$	$e\left(\frac{217}{1360}\right)$	$e\left(\frac{199}{272}\right)$	$e\left(\frac{217}{680}\right)$	$e\left(\frac{231}{1360}\right)$	$e\left(\frac{331}{340}\right)$	$e\left(\frac{159}{680}\right)$	$e\left(\frac{303}{340}\right)$	$e\left(\frac{791}{1360}\right)$	$e\left(\frac{651}{1360}\right)$	$e\left(\frac{877}{1360}\right)$
$\chi_{28900}(31,\cdot)$	28900.fj	1360	yes	$1$	$1$	$e\left(\frac{453}{1360}\right)$	$e\left(\frac{171}{272}\right)$	$e\left(\frac{453}{680}\right)$	$e\left(\frac{899}{1360}\right)$	$e\left(\frac{29}{340}\right)$	$e\left(\frac{111}{680}\right)$	$e\left(\frac{327}{340}\right)$	$e\left(\frac{379}{1360}\right)$	$e\left(\frac{1359}{1360}\right)$	$e\left(\frac{1273}{1360}\right)$
$\chi_{28900}(33,\cdot)$	28900.eo	340	no	$-1$	$1$	$e\left(\frac{47}{340}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{47}{170}\right)$	$e\left(\frac{73}{170}\right)$	$e\left(\frac{49}{340}\right)$	$e\left(\frac{159}{170}\right)$	$e\left(\frac{48}{85}\right)$	$e\left(\frac{111}{340}\right)$	$e\left(\frac{141}{340}\right)$	$e\left(\frac{28}{85}\right)$
$\chi_{28900}(37,\cdot)$	28900.fm	1360	no	$1$	$1$	$e\left(\frac{849}{1360}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{169}{680}\right)$	$e\left(\frac{147}{1360}\right)$	$e\left(\frac{43}{85}\right)$	$e\left(\frac{503}{680}\right)$	$e\left(\frac{131}{340}\right)$	$e\left(\frac{967}{1360}\right)$	$e\left(\frac{1187}{1360}\right)$	$e\left(\frac{249}{1360}\right)$
$\chi_{28900}(39,\cdot)$	28900.fk	1360	yes	$1$	$1$	$e\left(\frac{441}{1360}\right)$	$e\left(\frac{71}{272}\right)$	$e\left(\frac{441}{680}\right)$	$e\left(\frac{1303}{1360}\right)$	$e\left(\frac{223}{340}\right)$	$e\left(\frac{27}{680}\right)$	$e\left(\frac{199}{340}\right)$	$e\left(\frac{423}{1360}\right)$	$e\left(\frac{1323}{1360}\right)$	$e\left(\frac{181}{1360}\right)$
$\chi_{28900}(41,\cdot)$	28900.fi	1360	no	$-1$	$1$	$e\left(\frac{39}{1360}\right)$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{39}{680}\right)$	$e\left(\frac{897}{1360}\right)$	$e\left(\frac{7}{340}\right)$	$e\left(\frac{273}{680}\right)$	$e\left(\frac{161}{340}\right)$	$e\left(\frac{537}{1360}\right)$	$e\left(\frac{117}{1360}\right)$	$e\left(\frac{1339}{1360}\right)$
$\chi_{28900}(43,\cdot)$	28900.dr	136	no	$1$	$1$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{49}{136}\right)$
$\chi_{28900}(47,\cdot)$	28900.em	340	yes	$1$	$1$	$e\left(\frac{139}{170}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{54}{85}\right)$	$e\left(\frac{189}{340}\right)$	$e\left(\frac{71}{340}\right)$	$e\left(\frac{161}{170}\right)$	$e\left(\frac{47}{85}\right)$	$e\left(\frac{71}{85}\right)$	$e\left(\frac{77}{170}\right)$	$e\left(\frac{223}{340}\right)$
$\chi_{28900}(49,\cdot)$	28900.dp	136	no	$1$	$1$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{63}{136}\right)$
$\chi_{28900}(53,\cdot)$	28900.fa	680	no	$-1$	$1$	$e\left(\frac{141}{680}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{141}{340}\right)$	$e\left(\frac{13}{680}\right)$	$e\left(\frac{31}{340}\right)$	$e\left(\frac{307}{340}\right)$	$e\left(\frac{59}{170}\right)$	$e\left(\frac{503}{680}\right)$	$e\left(\frac{423}{680}\right)$	$e\left(\frac{251}{680}\right)$
$\chi_{28900}(57,\cdot)$	28900.ek	272	no	$1$	$1$	$e\left(\frac{219}{272}\right)$	$e\left(\frac{217}{272}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{73}{272}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{13}{272}\right)$	$e\left(\frac{113}{272}\right)$	$e\left(\frac{107}{272}\right)$
$\chi_{28900}(59,\cdot)$	28900.fe	680	yes	$-1$	$1$	$e\left(\frac{177}{680}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{177}{340}\right)$	$e\left(\frac{331}{680}\right)$	$e\left(\frac{78}{85}\right)$	$e\left(\frac{49}{340}\right)$	$e\left(\frac{103}{170}\right)$	$e\left(\frac{31}{680}\right)$	$e\left(\frac{531}{680}\right)$	$e\left(\frac{637}{680}\right)$
$\chi_{28900}(61,\cdot)$	28900.fi	1360	no	$-1$	$1$	$e\left(\frac{751}{1360}\right)$	$e\left(\frac{161}{272}\right)$	$e\left(\frac{71}{680}\right)$	$e\left(\frac{953}{1360}\right)$	$e\left(\frac{283}{340}\right)$	$e\left(\frac{497}{680}\right)$	$e\left(\frac{49}{340}\right)$	$e\left(\frac{193}{1360}\right)$	$e\left(\frac{893}{1360}\right)$	$e\left(\frac{851}{1360}\right)$
$\chi_{28900}(63,\cdot)$	28900.fg	1360	yes	$-1$	$1$	$e\left(\frac{989}{1360}\right)$	$e\left(\frac{195}{272}\right)$	$e\left(\frac{309}{680}\right)$	$e\left(\frac{1327}{1360}\right)$	$e\left(\frac{31}{170}\right)$	$e\left(\frac{463}{680}\right)$	$e\left(\frac{151}{340}\right)$	$e\left(\frac{907}{1360}\right)$	$e\left(\frac{247}{1360}\right)$	$e\left(\frac{69}{1360}\right)$
$\chi_{28900}(67,\cdot)$	28900.ev	340	yes	$1$	$1$	$e\left(\frac{247}{340}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{77}{170}\right)$	$e\left(\frac{39}{85}\right)$	$e\left(\frac{319}{340}\right)$	$e\left(\frac{57}{85}\right)$	$e\left(\frac{28}{85}\right)$	$e\left(\frac{171}{340}\right)$	$e\left(\frac{61}{340}\right)$	$e\left(\frac{73}{85}\right)$
$\chi_{28900}(69,\cdot)$	28900.ea	170	no	$1$	$1$	$e\left(\frac{21}{170}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{21}{85}\right)$	$e\left(\frac{29}{85}\right)$	$e\left(\frac{87}{170}\right)$	$e\left(\frac{62}{85}\right)$	$e\left(\frac{23}{85}\right)$	$e\left(\frac{93}{170}\right)$	$e\left(\frac{63}{170}\right)$	$e\left(\frac{63}{85}\right)$
$\chi_{28900}(71,\cdot)$	28900.fj	1360	yes	$1$	$1$	$e\left(\frac{877}{1360}\right)$	$e\left(\frac{259}{272}\right)$	$e\left(\frac{197}{680}\right)$	$e\left(\frac{1131}{1360}\right)$	$e\left(\frac{201}{340}\right)$	$e\left(\frac{359}{680}\right)$	$e\left(\frac{203}{340}\right)$	$e\left(\frac{1091}{1360}\right)$	$e\left(\frac{1271}{1360}\right)$	$e\left(\frac{417}{1360}\right)$
$\chi_{28900}(73,\cdot)$	28900.fh	1360	no	$1$	$1$	$e\left(\frac{621}{1360}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{621}{680}\right)$	$e\left(\frac{1023}{1360}\right)$	$e\left(\frac{59}{170}\right)$	$e\left(\frac{267}{680}\right)$	$e\left(\frac{79}{340}\right)$	$e\left(\frac{443}{1360}\right)$	$e\left(\frac{503}{1360}\right)$	$e\left(\frac{1261}{1360}\right)$
$\chi_{28900}(77,\cdot)$	28900.fa	680	no	$-1$	$1$	$e\left(\frac{3}{680}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{3}{340}\right)$	$e\left(\frac{579}{680}\right)$	$e\left(\frac{73}{340}\right)$	$e\left(\frac{21}{340}\right)$	$e\left(\frac{117}{170}\right)$	$e\left(\frac{329}{680}\right)$	$e\left(\frac{9}{680}\right)$	$e\left(\frac{613}{680}\right)$
$\chi_{28900}(79,\cdot)$	28900.fk	1360	yes	$1$	$1$	$e\left(\frac{1107}{1360}\right)$	$e\left(\frac{45}{272}\right)$	$e\left(\frac{427}{680}\right)$	$e\left(\frac{301}{1360}\right)$	$e\left(\frac{81}{340}\right)$	$e\left(\frac{609}{680}\right)$	$e\left(\frac{333}{340}\right)$	$e\left(\frac{701}{1360}\right)$	$e\left(\frac{601}{1360}\right)$	$e\left(\frac{1287}{1360}\right)$
$\chi_{28900}(81,\cdot)$	28900.es	340	no	$1$	$1$	$e\left(\frac{277}{340}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{107}{170}\right)$	$e\left(\frac{251}{340}\right)$	$e\left(\frac{41}{85}\right)$	$e\left(\frac{69}{170}\right)$	$e\left(\frac{8}{85}\right)$	$e\left(\frac{231}{340}\right)$	$e\left(\frac{151}{340}\right)$	$e\left(\frac{217}{340}\right)$
$\chi_{28900}(83,\cdot)$	28900.fc	680	yes	$1$	$1$	$e\left(\frac{669}{680}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{329}{340}\right)$	$e\left(\frac{597}{680}\right)$	$e\left(\frac{299}{340}\right)$	$e\left(\frac{93}{340}\right)$	$e\left(\frac{81}{170}\right)$	$e\left(\frac{607}{680}\right)$	$e\left(\frac{647}{680}\right)$	$e\left(\frac{359}{680}\right)$

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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	$28900$
Structure	\(C_{2}\times C_{4}\times C_{1360}\)
Order	$10880$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{28900}(1,\cdot)\)	28900.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{28900}(3,\cdot)\)	28900.fg	1360	yes	\(-1\)	\(1\)	\(e\left(\frac{1297}{1360}\right)\)	\(e\left(\frac{223}{272}\right)\)	\(e\left(\frac{617}{680}\right)\)	\(e\left(\frac{251}{1360}\right)\)	\(e\left(\frac{63}{170}\right)\)	\(e\left(\frac{579}{680}\right)\)	\(e\left(\frac{263}{340}\right)\)	\(e\left(\frac{231}{1360}\right)\)	\(e\left(\frac{1171}{1360}\right)\)	\(e\left(\frac{217}{1360}\right)\)
\(\chi_{28900}(7,\cdot)\)	28900.el	272	no	\(-1\)	\(1\)	\(e\left(\frac{223}{272}\right)\)	\(e\left(\frac{21}{272}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{165}{272}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{89}{272}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{199}{272}\right)\)
\(\chi_{28900}(9,\cdot)\)	28900.ff	680	no	\(1\)	\(1\)	\(e\left(\frac{617}{680}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{277}{340}\right)\)	\(e\left(\frac{251}{680}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{239}{340}\right)\)	\(e\left(\frac{93}{170}\right)\)	\(e\left(\frac{231}{680}\right)\)	\(e\left(\frac{491}{680}\right)\)	\(e\left(\frac{217}{680}\right)\)
\(\chi_{28900}(11,\cdot)\)	28900.fj	1360	yes	\(1\)	\(1\)	\(e\left(\frac{251}{1360}\right)\)	\(e\left(\frac{165}{272}\right)\)	\(e\left(\frac{251}{680}\right)\)	\(e\left(\frac{333}{1360}\right)\)	\(e\left(\frac{263}{340}\right)\)	\(e\left(\frac{57}{680}\right)\)	\(e\left(\frac{269}{340}\right)\)	\(e\left(\frac{213}{1360}\right)\)	\(e\left(\frac{753}{1360}\right)\)	\(e\left(\frac{231}{1360}\right)\)
\(\chi_{28900}(13,\cdot)\)	28900.en	340	no	\(-1\)	\(1\)	\(e\left(\frac{63}{170}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{263}{340}\right)\)	\(e\left(\frac{97}{340}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{69}{85}\right)\)	\(e\left(\frac{12}{85}\right)\)	\(e\left(\frac{19}{170}\right)\)	\(e\left(\frac{331}{340}\right)\)
\(\chi_{28900}(19,\cdot)\)	28900.fe	680	yes	\(-1\)	\(1\)	\(e\left(\frac{579}{680}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{239}{340}\right)\)	\(e\left(\frac{57}{680}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{143}{340}\right)\)	\(e\left(\frac{141}{170}\right)\)	\(e\left(\frac{597}{680}\right)\)	\(e\left(\frac{377}{680}\right)\)	\(e\left(\frac{159}{680}\right)\)
\(\chi_{28900}(21,\cdot)\)	28900.es	340	no	\(1\)	\(1\)	\(e\left(\frac{263}{340}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{93}{170}\right)\)	\(e\left(\frac{269}{340}\right)\)	\(e\left(\frac{69}{85}\right)\)	\(e\left(\frac{141}{170}\right)\)	\(e\left(\frac{57}{85}\right)\)	\(e\left(\frac{169}{340}\right)\)	\(e\left(\frac{109}{340}\right)\)	\(e\left(\frac{303}{340}\right)\)
\(\chi_{28900}(23,\cdot)\)	28900.fn	1360	yes	\(-1\)	\(1\)	\(e\left(\frac{231}{1360}\right)\)	\(e\left(\frac{89}{272}\right)\)	\(e\left(\frac{231}{680}\right)\)	\(e\left(\frac{213}{1360}\right)\)	\(e\left(\frac{12}{85}\right)\)	\(e\left(\frac{597}{680}\right)\)	\(e\left(\frac{169}{340}\right)\)	\(e\left(\frac{513}{1360}\right)\)	\(e\left(\frac{693}{1360}\right)\)	\(e\left(\frac{791}{1360}\right)\)
\(\chi_{28900}(27,\cdot)\)	28900.fg	1360	yes	\(-1\)	\(1\)	\(e\left(\frac{1171}{1360}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{491}{680}\right)\)	\(e\left(\frac{753}{1360}\right)\)	\(e\left(\frac{19}{170}\right)\)	\(e\left(\frac{377}{680}\right)\)	\(e\left(\frac{109}{340}\right)\)	\(e\left(\frac{693}{1360}\right)\)	\(e\left(\frac{793}{1360}\right)\)	\(e\left(\frac{651}{1360}\right)\)
\(\chi_{28900}(29,\cdot)\)	28900.fl	1360	no	\(-1\)	\(1\)	\(e\left(\frac{217}{1360}\right)\)	\(e\left(\frac{199}{272}\right)\)	\(e\left(\frac{217}{680}\right)\)	\(e\left(\frac{231}{1360}\right)\)	\(e\left(\frac{331}{340}\right)\)	\(e\left(\frac{159}{680}\right)\)	\(e\left(\frac{303}{340}\right)\)	\(e\left(\frac{791}{1360}\right)\)	\(e\left(\frac{651}{1360}\right)\)	\(e\left(\frac{877}{1360}\right)\)
\(\chi_{28900}(31,\cdot)\)	28900.fj	1360	yes	\(1\)	\(1\)	\(e\left(\frac{453}{1360}\right)\)	\(e\left(\frac{171}{272}\right)\)	\(e\left(\frac{453}{680}\right)\)	\(e\left(\frac{899}{1360}\right)\)	\(e\left(\frac{29}{340}\right)\)	\(e\left(\frac{111}{680}\right)\)	\(e\left(\frac{327}{340}\right)\)	\(e\left(\frac{379}{1360}\right)\)	\(e\left(\frac{1359}{1360}\right)\)	\(e\left(\frac{1273}{1360}\right)\)
\(\chi_{28900}(33,\cdot)\)	28900.eo	340	no	\(-1\)	\(1\)	\(e\left(\frac{47}{340}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{47}{170}\right)\)	\(e\left(\frac{73}{170}\right)\)	\(e\left(\frac{49}{340}\right)\)	\(e\left(\frac{159}{170}\right)\)	\(e\left(\frac{48}{85}\right)\)	\(e\left(\frac{111}{340}\right)\)	\(e\left(\frac{141}{340}\right)\)	\(e\left(\frac{28}{85}\right)\)
\(\chi_{28900}(37,\cdot)\)	28900.fm	1360	no	\(1\)	\(1\)	\(e\left(\frac{849}{1360}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{169}{680}\right)\)	\(e\left(\frac{147}{1360}\right)\)	\(e\left(\frac{43}{85}\right)\)	\(e\left(\frac{503}{680}\right)\)	\(e\left(\frac{131}{340}\right)\)	\(e\left(\frac{967}{1360}\right)\)	\(e\left(\frac{1187}{1360}\right)\)	\(e\left(\frac{249}{1360}\right)\)
\(\chi_{28900}(39,\cdot)\)	28900.fk	1360	yes	\(1\)	\(1\)	\(e\left(\frac{441}{1360}\right)\)	\(e\left(\frac{71}{272}\right)\)	\(e\left(\frac{441}{680}\right)\)	\(e\left(\frac{1303}{1360}\right)\)	\(e\left(\frac{223}{340}\right)\)	\(e\left(\frac{27}{680}\right)\)	\(e\left(\frac{199}{340}\right)\)	\(e\left(\frac{423}{1360}\right)\)	\(e\left(\frac{1323}{1360}\right)\)	\(e\left(\frac{181}{1360}\right)\)
\(\chi_{28900}(41,\cdot)\)	28900.fi	1360	no	\(-1\)	\(1\)	\(e\left(\frac{39}{1360}\right)\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{39}{680}\right)\)	\(e\left(\frac{897}{1360}\right)\)	\(e\left(\frac{7}{340}\right)\)	\(e\left(\frac{273}{680}\right)\)	\(e\left(\frac{161}{340}\right)\)	\(e\left(\frac{537}{1360}\right)\)	\(e\left(\frac{117}{1360}\right)\)	\(e\left(\frac{1339}{1360}\right)\)
\(\chi_{28900}(43,\cdot)\)	28900.dr	136	no	\(1\)	\(1\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{49}{136}\right)\)
\(\chi_{28900}(47,\cdot)\)	28900.em	340	yes	\(1\)	\(1\)	\(e\left(\frac{139}{170}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{54}{85}\right)\)	\(e\left(\frac{189}{340}\right)\)	\(e\left(\frac{71}{340}\right)\)	\(e\left(\frac{161}{170}\right)\)	\(e\left(\frac{47}{85}\right)\)	\(e\left(\frac{71}{85}\right)\)	\(e\left(\frac{77}{170}\right)\)	\(e\left(\frac{223}{340}\right)\)
\(\chi_{28900}(49,\cdot)\)	28900.dp	136	no	\(1\)	\(1\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{63}{136}\right)\)
\(\chi_{28900}(53,\cdot)\)	28900.fa	680	no	\(-1\)	\(1\)	\(e\left(\frac{141}{680}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{141}{340}\right)\)	\(e\left(\frac{13}{680}\right)\)	\(e\left(\frac{31}{340}\right)\)	\(e\left(\frac{307}{340}\right)\)	\(e\left(\frac{59}{170}\right)\)	\(e\left(\frac{503}{680}\right)\)	\(e\left(\frac{423}{680}\right)\)	\(e\left(\frac{251}{680}\right)\)
\(\chi_{28900}(57,\cdot)\)	28900.ek	272	no	\(1\)	\(1\)	\(e\left(\frac{219}{272}\right)\)	\(e\left(\frac{217}{272}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{73}{272}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{13}{272}\right)\)	\(e\left(\frac{113}{272}\right)\)	\(e\left(\frac{107}{272}\right)\)
\(\chi_{28900}(59,\cdot)\)	28900.fe	680	yes	\(-1\)	\(1\)	\(e\left(\frac{177}{680}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{177}{340}\right)\)	\(e\left(\frac{331}{680}\right)\)	\(e\left(\frac{78}{85}\right)\)	\(e\left(\frac{49}{340}\right)\)	\(e\left(\frac{103}{170}\right)\)	\(e\left(\frac{31}{680}\right)\)	\(e\left(\frac{531}{680}\right)\)	\(e\left(\frac{637}{680}\right)\)
\(\chi_{28900}(61,\cdot)\)	28900.fi	1360	no	\(-1\)	\(1\)	\(e\left(\frac{751}{1360}\right)\)	\(e\left(\frac{161}{272}\right)\)	\(e\left(\frac{71}{680}\right)\)	\(e\left(\frac{953}{1360}\right)\)	\(e\left(\frac{283}{340}\right)\)	\(e\left(\frac{497}{680}\right)\)	\(e\left(\frac{49}{340}\right)\)	\(e\left(\frac{193}{1360}\right)\)	\(e\left(\frac{893}{1360}\right)\)	\(e\left(\frac{851}{1360}\right)\)
\(\chi_{28900}(63,\cdot)\)	28900.fg	1360	yes	\(-1\)	\(1\)	\(e\left(\frac{989}{1360}\right)\)	\(e\left(\frac{195}{272}\right)\)	\(e\left(\frac{309}{680}\right)\)	\(e\left(\frac{1327}{1360}\right)\)	\(e\left(\frac{31}{170}\right)\)	\(e\left(\frac{463}{680}\right)\)	\(e\left(\frac{151}{340}\right)\)	\(e\left(\frac{907}{1360}\right)\)	\(e\left(\frac{247}{1360}\right)\)	\(e\left(\frac{69}{1360}\right)\)
\(\chi_{28900}(67,\cdot)\)	28900.ev	340	yes	\(1\)	\(1\)	\(e\left(\frac{247}{340}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{77}{170}\right)\)	\(e\left(\frac{39}{85}\right)\)	\(e\left(\frac{319}{340}\right)\)	\(e\left(\frac{57}{85}\right)\)	\(e\left(\frac{28}{85}\right)\)	\(e\left(\frac{171}{340}\right)\)	\(e\left(\frac{61}{340}\right)\)	\(e\left(\frac{73}{85}\right)\)
\(\chi_{28900}(69,\cdot)\)	28900.ea	170	no	\(1\)	\(1\)	\(e\left(\frac{21}{170}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{21}{85}\right)\)	\(e\left(\frac{29}{85}\right)\)	\(e\left(\frac{87}{170}\right)\)	\(e\left(\frac{62}{85}\right)\)	\(e\left(\frac{23}{85}\right)\)	\(e\left(\frac{93}{170}\right)\)	\(e\left(\frac{63}{170}\right)\)	\(e\left(\frac{63}{85}\right)\)
\(\chi_{28900}(71,\cdot)\)	28900.fj	1360	yes	\(1\)	\(1\)	\(e\left(\frac{877}{1360}\right)\)	\(e\left(\frac{259}{272}\right)\)	\(e\left(\frac{197}{680}\right)\)	\(e\left(\frac{1131}{1360}\right)\)	\(e\left(\frac{201}{340}\right)\)	\(e\left(\frac{359}{680}\right)\)	\(e\left(\frac{203}{340}\right)\)	\(e\left(\frac{1091}{1360}\right)\)	\(e\left(\frac{1271}{1360}\right)\)	\(e\left(\frac{417}{1360}\right)\)
\(\chi_{28900}(73,\cdot)\)	28900.fh	1360	no	\(1\)	\(1\)	\(e\left(\frac{621}{1360}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{621}{680}\right)\)	\(e\left(\frac{1023}{1360}\right)\)	\(e\left(\frac{59}{170}\right)\)	\(e\left(\frac{267}{680}\right)\)	\(e\left(\frac{79}{340}\right)\)	\(e\left(\frac{443}{1360}\right)\)	\(e\left(\frac{503}{1360}\right)\)	\(e\left(\frac{1261}{1360}\right)\)
\(\chi_{28900}(77,\cdot)\)	28900.fa	680	no	\(-1\)	\(1\)	\(e\left(\frac{3}{680}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{3}{340}\right)\)	\(e\left(\frac{579}{680}\right)\)	\(e\left(\frac{73}{340}\right)\)	\(e\left(\frac{21}{340}\right)\)	\(e\left(\frac{117}{170}\right)\)	\(e\left(\frac{329}{680}\right)\)	\(e\left(\frac{9}{680}\right)\)	\(e\left(\frac{613}{680}\right)\)
\(\chi_{28900}(79,\cdot)\)	28900.fk	1360	yes	\(1\)	\(1\)	\(e\left(\frac{1107}{1360}\right)\)	\(e\left(\frac{45}{272}\right)\)	\(e\left(\frac{427}{680}\right)\)	\(e\left(\frac{301}{1360}\right)\)	\(e\left(\frac{81}{340}\right)\)	\(e\left(\frac{609}{680}\right)\)	\(e\left(\frac{333}{340}\right)\)	\(e\left(\frac{701}{1360}\right)\)	\(e\left(\frac{601}{1360}\right)\)	\(e\left(\frac{1287}{1360}\right)\)
\(\chi_{28900}(81,\cdot)\)	28900.es	340	no	\(1\)	\(1\)	\(e\left(\frac{277}{340}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{107}{170}\right)\)	\(e\left(\frac{251}{340}\right)\)	\(e\left(\frac{41}{85}\right)\)	\(e\left(\frac{69}{170}\right)\)	\(e\left(\frac{8}{85}\right)\)	\(e\left(\frac{231}{340}\right)\)	\(e\left(\frac{151}{340}\right)\)	\(e\left(\frac{217}{340}\right)\)
\(\chi_{28900}(83,\cdot)\)	28900.fc	680	yes	\(1\)	\(1\)	\(e\left(\frac{669}{680}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{329}{340}\right)\)	\(e\left(\frac{597}{680}\right)\)	\(e\left(\frac{299}{340}\right)\)	\(e\left(\frac{93}{340}\right)\)	\(e\left(\frac{81}{170}\right)\)	\(e\left(\frac{607}{680}\right)\)	\(e\left(\frac{647}{680}\right)\)	\(e\left(\frac{359}{680}\right)\)

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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.