LMFDB - Group of Dirichlet characters of modulus 2300

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2300)

pari: g = idealstar(,2300,2)

Character group

sage: G.order() pari: g.no
Order	=	880
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{220}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2300}(1151,\cdot)$, $\chi_{2300}(277,\cdot)$, $\chi_{2300}(1201,\cdot)$

First 32 of 880 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$27$	$29$
$\chi_{2300}(1,\cdot)$	2300.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2300}(3,\cdot)$	2300.bt	220	yes	$1$	$1$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{87}{110}\right)$
$\chi_{2300}(7,\cdot)$	2300.bh	44	no	$-1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{2300}(9,\cdot)$	2300.bo	110	no	$1$	$1$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{2300}(11,\cdot)$	2300.bm	110	yes	$1$	$1$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{2300}(13,\cdot)$	2300.bv	220	no	$-1$	$1$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{39}{110}\right)$
$\chi_{2300}(17,\cdot)$	2300.bs	220	no	$1$	$1$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{2300}(19,\cdot)$	2300.br	110	yes	$1$	$1$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{2300}(21,\cdot)$	2300.bq	110	no	$-1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{2300}(27,\cdot)$	2300.bt	220	yes	$1$	$1$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{41}{110}\right)$
$\chi_{2300}(29,\cdot)$	2300.bo	110	no	$1$	$1$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{2300}(31,\cdot)$	2300.bn	110	yes	$-1$	$1$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{2300}(33,\cdot)$	2300.bs	220	no	$1$	$1$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{83}{110}\right)$
$\chi_{2300}(37,\cdot)$	2300.bs	220	no	$1$	$1$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{9}{110}\right)$
$\chi_{2300}(39,\cdot)$	2300.bp	110	yes	$-1$	$1$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{2300}(41,\cdot)$	2300.bk	55	no	$1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{2300}(43,\cdot)$	2300.bh	44	no	$-1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{2300}(47,\cdot)$	2300.x	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{2300}(49,\cdot)$	2300.be	22	no	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{2300}(51,\cdot)$	2300.bc	22	no	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{2300}(53,\cdot)$	2300.bs	220	no	$1$	$1$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{27}{110}\right)$
$\chi_{2300}(57,\cdot)$	2300.bj	44	no	$1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{2300}(59,\cdot)$	2300.bp	110	yes	$-1$	$1$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{2300}(61,\cdot)$	2300.bq	110	no	$-1$	$1$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{2300}(63,\cdot)$	2300.bu	220	yes	$-1$	$1$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{2300}(67,\cdot)$	2300.bu	220	yes	$-1$	$1$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{103}{110}\right)$
$\chi_{2300}(71,\cdot)$	2300.bn	110	yes	$-1$	$1$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{2300}(73,\cdot)$	2300.bv	220	no	$-1$	$1$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{41}{110}\right)$
$\chi_{2300}(77,\cdot)$	2300.bv	220	no	$-1$	$1$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{1}{110}\right)$
$\chi_{2300}(79,\cdot)$	2300.br	110	yes	$1$	$1$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{2300}(81,\cdot)$	2300.bk	55	no	$1$	$1$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{2300}(83,\cdot)$	2300.bu	220	yes	$-1$	$1$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{53}{110}\right)$

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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	$2300$
Structure	\(C_{2}\times C_{2}\times C_{220}\)
Order	$880$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(27\)	\(29\)
\(\chi_{2300}(1,\cdot)\)	2300.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2300}(3,\cdot)\)	2300.bt	220	yes	\(1\)	\(1\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{87}{110}\right)\)
\(\chi_{2300}(7,\cdot)\)	2300.bh	44	no	\(-1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{2300}(9,\cdot)\)	2300.bo	110	no	\(1\)	\(1\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{2300}(11,\cdot)\)	2300.bm	110	yes	\(1\)	\(1\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{2300}(13,\cdot)\)	2300.bv	220	no	\(-1\)	\(1\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{39}{110}\right)\)
\(\chi_{2300}(17,\cdot)\)	2300.bs	220	no	\(1\)	\(1\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{2300}(19,\cdot)\)	2300.br	110	yes	\(1\)	\(1\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{2300}(21,\cdot)\)	2300.bq	110	no	\(-1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{2300}(27,\cdot)\)	2300.bt	220	yes	\(1\)	\(1\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)
\(\chi_{2300}(29,\cdot)\)	2300.bo	110	no	\(1\)	\(1\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{2300}(31,\cdot)\)	2300.bn	110	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{2300}(33,\cdot)\)	2300.bs	220	no	\(1\)	\(1\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)
\(\chi_{2300}(37,\cdot)\)	2300.bs	220	no	\(1\)	\(1\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)
\(\chi_{2300}(39,\cdot)\)	2300.bp	110	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{2300}(41,\cdot)\)	2300.bk	55	no	\(1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{2300}(43,\cdot)\)	2300.bh	44	no	\(-1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{2300}(47,\cdot)\)	2300.x	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{2300}(49,\cdot)\)	2300.be	22	no	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{2300}(51,\cdot)\)	2300.bc	22	no	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{2300}(53,\cdot)\)	2300.bs	220	no	\(1\)	\(1\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{27}{110}\right)\)
\(\chi_{2300}(57,\cdot)\)	2300.bj	44	no	\(1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{2300}(59,\cdot)\)	2300.bp	110	yes	\(-1\)	\(1\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{2300}(61,\cdot)\)	2300.bq	110	no	\(-1\)	\(1\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{2300}(63,\cdot)\)	2300.bu	220	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{2300}(67,\cdot)\)	2300.bu	220	yes	\(-1\)	\(1\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{103}{110}\right)\)
\(\chi_{2300}(71,\cdot)\)	2300.bn	110	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{2300}(73,\cdot)\)	2300.bv	220	no	\(-1\)	\(1\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)
\(\chi_{2300}(77,\cdot)\)	2300.bv	220	no	\(-1\)	\(1\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{1}{110}\right)\)
\(\chi_{2300}(79,\cdot)\)	2300.br	110	yes	\(1\)	\(1\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)
\(\chi_{2300}(81,\cdot)\)	2300.bk	55	no	\(1\)	\(1\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{2300}(83,\cdot)\)	2300.bu	220	yes	\(-1\)	\(1\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)

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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.