LMFDB - Group of Dirichlet characters of modulus 10005

Show commands: PariGP / SageMath

sage: H = DirichletGroup(10005)

pari: g = idealstar(,10005,2)

Character group

sage: G.order() pari: g.no
Order	=	4928
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{308}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{10005}(6671,\cdot)$, $\chi_{10005}(2002,\cdot)$, $\chi_{10005}(9136,\cdot)$, $\chi_{10005}(6556,\cdot)$

First 32 of 4928 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{10005}(1,\cdot)$	10005.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{10005}(2,\cdot)$	10005.fi	308	yes	$-1$	$1$	$e\left(\frac{149}{154}\right)$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{125}{308}\right)$	$e\left(\frac{139}{154}\right)$	$e\left(\frac{65}{308}\right)$	$e\left(\frac{205}{308}\right)$	$e\left(\frac{115}{308}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{57}{308}\right)$
$\chi_{10005}(4,\cdot)$	10005.ez	154	no	$1$	$1$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{57}{154}\right)$
$\chi_{10005}(7,\cdot)$	10005.fr	308	no	$1$	$1$	$e\left(\frac{125}{308}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{247}{308}\right)$	$e\left(\frac{67}{308}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{171}{308}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{24}{77}\right)$
$\chi_{10005}(8,\cdot)$	10005.fi	308	yes	$-1$	$1$	$e\left(\frac{139}{154}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{67}{308}\right)$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{195}{308}\right)$	$e\left(\frac{307}{308}\right)$	$e\left(\frac{37}{308}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{171}{308}\right)$
$\chi_{10005}(11,\cdot)$	10005.fk	308	no	$-1$	$1$	$e\left(\frac{65}{308}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{195}{308}\right)$	$e\left(\frac{155}{308}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{215}{308}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{53}{308}\right)$
$\chi_{10005}(13,\cdot)$	10005.fq	308	no	$-1$	$1$	$e\left(\frac{205}{308}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{171}{308}\right)$	$e\left(\frac{307}{308}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{225}{308}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{64}{77}\right)$
$\chi_{10005}(14,\cdot)$	10005.fz	308	yes	$-1$	$1$	$e\left(\frac{115}{308}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{37}{308}\right)$	$e\left(\frac{215}{308}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{179}{308}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{153}{308}\right)$
$\chi_{10005}(16,\cdot)$	10005.eq	77	no	$1$	$1$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{57}{77}\right)$
$\chi_{10005}(17,\cdot)$	10005.em	44	yes	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{10005}(19,\cdot)$	10005.fy	308	no	$1$	$1$	$e\left(\frac{57}{308}\right)$	$e\left(\frac{57}{154}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{171}{308}\right)$	$e\left(\frac{53}{308}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{153}{308}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{37}{308}\right)$
$\chi_{10005}(22,\cdot)$	10005.df	28	no	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$i$	$e\left(\frac{5}{14}\right)$
$\chi_{10005}(26,\cdot)$	10005.fx	308	no	$1$	$1$	$e\left(\frac{195}{308}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{277}{308}\right)$	$e\left(\frac{3}{308}\right)$	$e\left(\frac{61}{154}\right)$	$e\left(\frac{183}{308}\right)$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{5}{308}\right)$
$\chi_{10005}(28,\cdot)$	10005.ed	44	no	$1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{10005}(31,\cdot)$	10005.fw	308	no	$-1$	$1$	$e\left(\frac{179}{308}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{229}{308}\right)$	$e\left(\frac{107}{308}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{59}{308}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{127}{308}\right)$
$\chi_{10005}(32,\cdot)$	10005.fi	308	yes	$-1$	$1$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{9}{308}\right)$	$e\left(\frac{79}{154}\right)$	$e\left(\frac{17}{308}\right)$	$e\left(\frac{101}{308}\right)$	$e\left(\frac{267}{308}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{285}{308}\right)$
$\chi_{10005}(34,\cdot)$	10005.fe	154	no	$-1$	$1$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{57}{154}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{16}{77}\right)$
$\chi_{10005}(37,\cdot)$	10005.fg	308	no	$-1$	$1$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{207}{308}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{83}{308}\right)$	$e\left(\frac{13}{308}\right)$	$e\left(\frac{289}{308}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{241}{308}\right)$
$\chi_{10005}(38,\cdot)$	10005.fp	308	yes	$-1$	$1$	$e\left(\frac{47}{308}\right)$	$e\left(\frac{47}{154}\right)$	$e\left(\frac{221}{308}\right)$	$e\left(\frac{141}{308}\right)$	$e\left(\frac{59}{154}\right)$	$e\left(\frac{153}{308}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{47}{154}\right)$
$\chi_{10005}(41,\cdot)$	10005.dy	44	no	$1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{10005}(43,\cdot)$	10005.fg	308	no	$-1$	$1$	$e\left(\frac{103}{154}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{197}{308}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{201}{308}\right)$	$e\left(\frac{243}{308}\right)$	$e\left(\frac{95}{308}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{27}{308}\right)$
$\chi_{10005}(44,\cdot)$	10005.fz	308	yes	$-1$	$1$	$e\left(\frac{45}{308}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{135}{308}\right)$	$e\left(\frac{285}{308}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{137}{308}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{167}{308}\right)$
$\chi_{10005}(47,\cdot)$	10005.cw	28	no	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{1}{28}\right)$
$\chi_{10005}(49,\cdot)$	10005.es	154	no	$1$	$1$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{67}{154}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{17}{154}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{48}{77}\right)$
$\chi_{10005}(52,\cdot)$	10005.ft	308	no	$-1$	$1$	$e\left(\frac{185}{308}\right)$	$e\left(\frac{31}{154}\right)$	$e\left(\frac{113}{308}\right)$	$e\left(\frac{247}{308}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{19}{308}\right)$	$e\left(\frac{149}{154}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{31}{154}\right)$
$\chi_{10005}(53,\cdot)$	10005.fu	308	yes	$-1$	$1$	$e\left(\frac{81}{308}\right)$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{181}{308}\right)$	$e\left(\frac{243}{308}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{149}{308}\right)$	$e\left(\frac{131}{154}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{2}{77}\right)$
$\chi_{10005}(56,\cdot)$	10005.fk	308	no	$-1$	$1$	$e\left(\frac{95}{308}\right)$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{3}{154}\right)$	$e\left(\frac{285}{308}\right)$	$e\left(\frac{37}{308}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{101}{308}\right)$	$e\left(\frac{18}{77}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{267}{308}\right)$
$\chi_{10005}(59,\cdot)$	10005.ck	22	no	$-1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{10005}(61,\cdot)$	10005.fl	308	no	$1$	$1$	$e\left(\frac{223}{308}\right)$	$e\left(\frac{69}{154}\right)$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{53}{308}\right)$	$e\left(\frac{129}{308}\right)$	$e\left(\frac{5}{154}\right)$	$e\left(\frac{169}{308}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{61}{308}\right)$
$\chi_{10005}(62,\cdot)$	10005.fv	308	yes	$1$	$1$	$e\left(\frac{169}{308}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{5}{308}\right)$	$e\left(\frac{199}{308}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{39}{308}\right)$	$e\left(\frac{87}{154}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{46}{77}\right)$
$\chi_{10005}(64,\cdot)$	10005.ez	154	no	$1$	$1$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{67}{154}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{153}{154}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{154}\right)$
$\chi_{10005}(67,\cdot)$	10005.fs	308	no	$1$	$1$	$e\left(\frac{243}{308}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{235}{308}\right)$	$e\left(\frac{113}{308}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{139}{308}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{89}{154}\right)$

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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	$10005$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{308}\)
Order	$4928$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{10005}(1,\cdot)\)	10005.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{10005}(2,\cdot)\)	10005.fi	308	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{154}\right)\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{125}{308}\right)\)	\(e\left(\frac{139}{154}\right)\)	\(e\left(\frac{65}{308}\right)\)	\(e\left(\frac{205}{308}\right)\)	\(e\left(\frac{115}{308}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{57}{308}\right)\)
\(\chi_{10005}(4,\cdot)\)	10005.ez	154	no	\(1\)	\(1\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{57}{154}\right)\)
\(\chi_{10005}(7,\cdot)\)	10005.fr	308	no	\(1\)	\(1\)	\(e\left(\frac{125}{308}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{247}{308}\right)\)	\(e\left(\frac{67}{308}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{171}{308}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{24}{77}\right)\)
\(\chi_{10005}(8,\cdot)\)	10005.fi	308	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{154}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{67}{308}\right)\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{195}{308}\right)\)	\(e\left(\frac{307}{308}\right)\)	\(e\left(\frac{37}{308}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{171}{308}\right)\)
\(\chi_{10005}(11,\cdot)\)	10005.fk	308	no	\(-1\)	\(1\)	\(e\left(\frac{65}{308}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{195}{308}\right)\)	\(e\left(\frac{155}{308}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{215}{308}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{53}{308}\right)\)
\(\chi_{10005}(13,\cdot)\)	10005.fq	308	no	\(-1\)	\(1\)	\(e\left(\frac{205}{308}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{171}{308}\right)\)	\(e\left(\frac{307}{308}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{225}{308}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{64}{77}\right)\)
\(\chi_{10005}(14,\cdot)\)	10005.fz	308	yes	\(-1\)	\(1\)	\(e\left(\frac{115}{308}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{37}{308}\right)\)	\(e\left(\frac{215}{308}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{179}{308}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{153}{308}\right)\)
\(\chi_{10005}(16,\cdot)\)	10005.eq	77	no	\(1\)	\(1\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{57}{77}\right)\)
\(\chi_{10005}(17,\cdot)\)	10005.em	44	yes	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{44}\right)\)
\(\chi_{10005}(19,\cdot)\)	10005.fy	308	no	\(1\)	\(1\)	\(e\left(\frac{57}{308}\right)\)	\(e\left(\frac{57}{154}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{171}{308}\right)\)	\(e\left(\frac{53}{308}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{153}{308}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{37}{308}\right)\)
\(\chi_{10005}(22,\cdot)\)	10005.df	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(i\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{10005}(26,\cdot)\)	10005.fx	308	no	\(1\)	\(1\)	\(e\left(\frac{195}{308}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{277}{308}\right)\)	\(e\left(\frac{3}{308}\right)\)	\(e\left(\frac{61}{154}\right)\)	\(e\left(\frac{183}{308}\right)\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{5}{308}\right)\)
\(\chi_{10005}(28,\cdot)\)	10005.ed	44	no	\(1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{10005}(31,\cdot)\)	10005.fw	308	no	\(-1\)	\(1\)	\(e\left(\frac{179}{308}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{229}{308}\right)\)	\(e\left(\frac{107}{308}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{59}{308}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{127}{308}\right)\)
\(\chi_{10005}(32,\cdot)\)	10005.fi	308	yes	\(-1\)	\(1\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{9}{308}\right)\)	\(e\left(\frac{79}{154}\right)\)	\(e\left(\frac{17}{308}\right)\)	\(e\left(\frac{101}{308}\right)\)	\(e\left(\frac{267}{308}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{285}{308}\right)\)
\(\chi_{10005}(34,\cdot)\)	10005.fe	154	no	\(-1\)	\(1\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{57}{154}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{16}{77}\right)\)
\(\chi_{10005}(37,\cdot)\)	10005.fg	308	no	\(-1\)	\(1\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{207}{308}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{83}{308}\right)\)	\(e\left(\frac{13}{308}\right)\)	\(e\left(\frac{289}{308}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{241}{308}\right)\)
\(\chi_{10005}(38,\cdot)\)	10005.fp	308	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{308}\right)\)	\(e\left(\frac{47}{154}\right)\)	\(e\left(\frac{221}{308}\right)\)	\(e\left(\frac{141}{308}\right)\)	\(e\left(\frac{59}{154}\right)\)	\(e\left(\frac{153}{308}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{47}{154}\right)\)
\(\chi_{10005}(41,\cdot)\)	10005.dy	44	no	\(1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{10005}(43,\cdot)\)	10005.fg	308	no	\(-1\)	\(1\)	\(e\left(\frac{103}{154}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{197}{308}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{201}{308}\right)\)	\(e\left(\frac{243}{308}\right)\)	\(e\left(\frac{95}{308}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{27}{308}\right)\)
\(\chi_{10005}(44,\cdot)\)	10005.fz	308	yes	\(-1\)	\(1\)	\(e\left(\frac{45}{308}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{135}{308}\right)\)	\(e\left(\frac{285}{308}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{137}{308}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{167}{308}\right)\)
\(\chi_{10005}(47,\cdot)\)	10005.cw	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{10005}(49,\cdot)\)	10005.es	154	no	\(1\)	\(1\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{67}{154}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{17}{154}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{48}{77}\right)\)
\(\chi_{10005}(52,\cdot)\)	10005.ft	308	no	\(-1\)	\(1\)	\(e\left(\frac{185}{308}\right)\)	\(e\left(\frac{31}{154}\right)\)	\(e\left(\frac{113}{308}\right)\)	\(e\left(\frac{247}{308}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{19}{308}\right)\)	\(e\left(\frac{149}{154}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{31}{154}\right)\)
\(\chi_{10005}(53,\cdot)\)	10005.fu	308	yes	\(-1\)	\(1\)	\(e\left(\frac{81}{308}\right)\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{181}{308}\right)\)	\(e\left(\frac{243}{308}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{149}{308}\right)\)	\(e\left(\frac{131}{154}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{2}{77}\right)\)
\(\chi_{10005}(56,\cdot)\)	10005.fk	308	no	\(-1\)	\(1\)	\(e\left(\frac{95}{308}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{3}{154}\right)\)	\(e\left(\frac{285}{308}\right)\)	\(e\left(\frac{37}{308}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{101}{308}\right)\)	\(e\left(\frac{18}{77}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{267}{308}\right)\)
\(\chi_{10005}(59,\cdot)\)	10005.ck	22	no	\(-1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{10005}(61,\cdot)\)	10005.fl	308	no	\(1\)	\(1\)	\(e\left(\frac{223}{308}\right)\)	\(e\left(\frac{69}{154}\right)\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{53}{308}\right)\)	\(e\left(\frac{129}{308}\right)\)	\(e\left(\frac{5}{154}\right)\)	\(e\left(\frac{169}{308}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{61}{308}\right)\)
\(\chi_{10005}(62,\cdot)\)	10005.fv	308	yes	\(1\)	\(1\)	\(e\left(\frac{169}{308}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{5}{308}\right)\)	\(e\left(\frac{199}{308}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{39}{308}\right)\)	\(e\left(\frac{87}{154}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{46}{77}\right)\)
\(\chi_{10005}(64,\cdot)\)	10005.ez	154	no	\(1\)	\(1\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{67}{154}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{153}{154}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{17}{154}\right)\)
\(\chi_{10005}(67,\cdot)\)	10005.fs	308	no	\(1\)	\(1\)	\(e\left(\frac{243}{308}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{235}{308}\right)\)	\(e\left(\frac{113}{308}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{139}{308}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{89}{154}\right)\)

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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.