LMFDB - Group of Dirichlet characters of modulus 2153

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2153)

pari: g = idealstar(,2153,2)

Character group

sage: G.order() pari: g.no
Order	=	2152
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2152}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2153}(3,\cdot)$

First 32 of 2152 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{2153}(1,\cdot)$	2153.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2153}(2,\cdot)$	2153.g	1076	yes	$1$	$1$	$e\left(\frac{115}{538}\right)$	$e\left(\frac{955}{1076}\right)$	$e\left(\frac{115}{269}\right)$	$e\left(\frac{1047}{1076}\right)$	$e\left(\frac{109}{1076}\right)$	$e\left(\frac{132}{269}\right)$	$e\left(\frac{345}{538}\right)$	$e\left(\frac{417}{538}\right)$	$e\left(\frac{201}{1076}\right)$	$e\left(\frac{515}{1076}\right)$
$\chi_{2153}(3,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{955}{1076}\right)$	$e\left(\frac{1}{2152}\right)$	$e\left(\frac{417}{538}\right)$	$e\left(\frac{765}{2152}\right)$	$e\left(\frac{1911}{2152}\right)$	$e\left(\frac{244}{269}\right)$	$e\left(\frac{713}{1076}\right)$	$e\left(\frac{1}{1076}\right)$	$e\left(\frac{523}{2152}\right)$	$e\left(\frac{885}{2152}\right)$
$\chi_{2153}(4,\cdot)$	2153.f	538	yes	$1$	$1$	$e\left(\frac{115}{269}\right)$	$e\left(\frac{417}{538}\right)$	$e\left(\frac{230}{269}\right)$	$e\left(\frac{509}{538}\right)$	$e\left(\frac{109}{538}\right)$	$e\left(\frac{264}{269}\right)$	$e\left(\frac{76}{269}\right)$	$e\left(\frac{148}{269}\right)$	$e\left(\frac{201}{538}\right)$	$e\left(\frac{515}{538}\right)$
$\chi_{2153}(5,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{1047}{1076}\right)$	$e\left(\frac{765}{2152}\right)$	$e\left(\frac{509}{538}\right)$	$e\left(\frac{2033}{2152}\right)$	$e\left(\frac{707}{2152}\right)$	$e\left(\frac{243}{269}\right)$	$e\left(\frac{989}{1076}\right)$	$e\left(\frac{765}{1076}\right)$	$e\left(\frac{1975}{2152}\right)$	$e\left(\frac{1297}{2152}\right)$
$\chi_{2153}(6,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{109}{1076}\right)$	$e\left(\frac{1911}{2152}\right)$	$e\left(\frac{109}{538}\right)$	$e\left(\frac{707}{2152}\right)$	$e\left(\frac{2129}{2152}\right)$	$e\left(\frac{107}{269}\right)$	$e\left(\frac{327}{1076}\right)$	$e\left(\frac{835}{1076}\right)$	$e\left(\frac{925}{2152}\right)$	$e\left(\frac{1915}{2152}\right)$
$\chi_{2153}(7,\cdot)$	2153.e	269	yes	$1$	$1$	$e\left(\frac{132}{269}\right)$	$e\left(\frac{244}{269}\right)$	$e\left(\frac{264}{269}\right)$	$e\left(\frac{243}{269}\right)$	$e\left(\frac{107}{269}\right)$	$e\left(\frac{158}{269}\right)$	$e\left(\frac{127}{269}\right)$	$e\left(\frac{219}{269}\right)$	$e\left(\frac{106}{269}\right)$	$e\left(\frac{202}{269}\right)$
$\chi_{2153}(8,\cdot)$	2153.g	1076	yes	$1$	$1$	$e\left(\frac{345}{538}\right)$	$e\left(\frac{713}{1076}\right)$	$e\left(\frac{76}{269}\right)$	$e\left(\frac{989}{1076}\right)$	$e\left(\frac{327}{1076}\right)$	$e\left(\frac{127}{269}\right)$	$e\left(\frac{497}{538}\right)$	$e\left(\frac{175}{538}\right)$	$e\left(\frac{603}{1076}\right)$	$e\left(\frac{469}{1076}\right)$
$\chi_{2153}(9,\cdot)$	2153.g	1076	yes	$1$	$1$	$e\left(\frac{417}{538}\right)$	$e\left(\frac{1}{1076}\right)$	$e\left(\frac{148}{269}\right)$	$e\left(\frac{765}{1076}\right)$	$e\left(\frac{835}{1076}\right)$	$e\left(\frac{219}{269}\right)$	$e\left(\frac{175}{538}\right)$	$e\left(\frac{1}{538}\right)$	$e\left(\frac{523}{1076}\right)$	$e\left(\frac{885}{1076}\right)$
$\chi_{2153}(10,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{201}{1076}\right)$	$e\left(\frac{523}{2152}\right)$	$e\left(\frac{201}{538}\right)$	$e\left(\frac{1975}{2152}\right)$	$e\left(\frac{925}{2152}\right)$	$e\left(\frac{106}{269}\right)$	$e\left(\frac{603}{1076}\right)$	$e\left(\frac{523}{1076}\right)$	$e\left(\frac{225}{2152}\right)$	$e\left(\frac{175}{2152}\right)$
$\chi_{2153}(11,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{515}{1076}\right)$	$e\left(\frac{885}{2152}\right)$	$e\left(\frac{515}{538}\right)$	$e\left(\frac{1297}{2152}\right)$	$e\left(\frac{1915}{2152}\right)$	$e\left(\frac{202}{269}\right)$	$e\left(\frac{469}{1076}\right)$	$e\left(\frac{885}{1076}\right)$	$e\left(\frac{175}{2152}\right)$	$e\left(\frac{2049}{2152}\right)$
$\chi_{2153}(12,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{339}{1076}\right)$	$e\left(\frac{1669}{2152}\right)$	$e\left(\frac{339}{538}\right)$	$e\left(\frac{649}{2152}\right)$	$e\left(\frac{195}{2152}\right)$	$e\left(\frac{239}{269}\right)$	$e\left(\frac{1017}{1076}\right)$	$e\left(\frac{593}{1076}\right)$	$e\left(\frac{1327}{2152}\right)$	$e\left(\frac{793}{2152}\right)$
$\chi_{2153}(13,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{325}{1076}\right)$	$e\left(\frac{851}{2152}\right)$	$e\left(\frac{325}{538}\right)$	$e\left(\frac{1111}{2152}\right)$	$e\left(\frac{1501}{2152}\right)$	$e\left(\frac{245}{269}\right)$	$e\left(\frac{975}{1076}\right)$	$e\left(\frac{851}{1076}\right)$	$e\left(\frac{1761}{2152}\right)$	$e\left(\frac{2087}{2152}\right)$
$\chi_{2153}(14,\cdot)$	2153.g	1076	yes	$1$	$1$	$e\left(\frac{379}{538}\right)$	$e\left(\frac{855}{1076}\right)$	$e\left(\frac{110}{269}\right)$	$e\left(\frac{943}{1076}\right)$	$e\left(\frac{537}{1076}\right)$	$e\left(\frac{21}{269}\right)$	$e\left(\frac{61}{538}\right)$	$e\left(\frac{317}{538}\right)$	$e\left(\frac{625}{1076}\right)$	$e\left(\frac{247}{1076}\right)$
$\chi_{2153}(15,\cdot)$	2153.g	1076	yes	$1$	$1$	$e\left(\frac{463}{538}\right)$	$e\left(\frac{383}{1076}\right)$	$e\left(\frac{194}{269}\right)$	$e\left(\frac{323}{1076}\right)$	$e\left(\frac{233}{1076}\right)$	$e\left(\frac{218}{269}\right)$	$e\left(\frac{313}{538}\right)$	$e\left(\frac{383}{538}\right)$	$e\left(\frac{173}{1076}\right)$	$e\left(\frac{15}{1076}\right)$
$\chi_{2153}(16,\cdot)$	2153.e	269	yes	$1$	$1$	$e\left(\frac{230}{269}\right)$	$e\left(\frac{148}{269}\right)$	$e\left(\frac{191}{269}\right)$	$e\left(\frac{240}{269}\right)$	$e\left(\frac{109}{269}\right)$	$e\left(\frac{259}{269}\right)$	$e\left(\frac{152}{269}\right)$	$e\left(\frac{27}{269}\right)$	$e\left(\frac{201}{269}\right)$	$e\left(\frac{246}{269}\right)$
$\chi_{2153}(17,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{1075}{1076}\right)$	$e\left(\frac{249}{2152}\right)$	$e\left(\frac{537}{538}\right)$	$e\left(\frac{1109}{2152}\right)$	$e\left(\frac{247}{2152}\right)$	$e\left(\frac{231}{269}\right)$	$e\left(\frac{1073}{1076}\right)$	$e\left(\frac{249}{1076}\right)$	$e\left(\frac{1107}{2152}\right)$	$e\left(\frac{861}{2152}\right)$
$\chi_{2153}(18,\cdot)$	2153.e	269	yes	$1$	$1$	$e\left(\frac{266}{269}\right)$	$e\left(\frac{239}{269}\right)$	$e\left(\frac{263}{269}\right)$	$e\left(\frac{184}{269}\right)$	$e\left(\frac{236}{269}\right)$	$e\left(\frac{82}{269}\right)$	$e\left(\frac{260}{269}\right)$	$e\left(\frac{209}{269}\right)$	$e\left(\frac{181}{269}\right)$	$e\left(\frac{81}{269}\right)$
$\chi_{2153}(19,\cdot)$	2153.g	1076	yes	$1$	$1$	$e\left(\frac{323}{538}\right)$	$e\left(\frac{811}{1076}\right)$	$e\left(\frac{54}{269}\right)$	$e\left(\frac{639}{1076}\right)$	$e\left(\frac{381}{1076}\right)$	$e\left(\frac{69}{269}\right)$	$e\left(\frac{431}{538}\right)$	$e\left(\frac{273}{538}\right)$	$e\left(\frac{209}{1076}\right)$	$e\left(\frac{43}{1076}\right)$
$\chi_{2153}(20,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{431}{1076}\right)$	$e\left(\frac{281}{2152}\right)$	$e\left(\frac{431}{538}\right)$	$e\left(\frac{1917}{2152}\right)$	$e\left(\frac{1143}{2152}\right)$	$e\left(\frac{238}{269}\right)$	$e\left(\frac{217}{1076}\right)$	$e\left(\frac{281}{1076}\right)$	$e\left(\frac{627}{2152}\right)$	$e\left(\frac{1205}{2152}\right)$
$\chi_{2153}(21,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{407}{1076}\right)$	$e\left(\frac{1953}{2152}\right)$	$e\left(\frac{407}{538}\right)$	$e\left(\frac{557}{2152}\right)$	$e\left(\frac{615}{2152}\right)$	$e\left(\frac{133}{269}\right)$	$e\left(\frac{145}{1076}\right)$	$e\left(\frac{877}{1076}\right)$	$e\left(\frac{1371}{2152}\right)$	$e\left(\frac{349}{2152}\right)$
$\chi_{2153}(22,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{745}{1076}\right)$	$e\left(\frac{643}{2152}\right)$	$e\left(\frac{207}{538}\right)$	$e\left(\frac{1239}{2152}\right)$	$e\left(\frac{2133}{2152}\right)$	$e\left(\frac{65}{269}\right)$	$e\left(\frac{83}{1076}\right)$	$e\left(\frac{643}{1076}\right)$	$e\left(\frac{577}{2152}\right)$	$e\left(\frac{927}{2152}\right)$
$\chi_{2153}(23,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{533}{1076}\right)$	$e\left(\frac{707}{2152}\right)$	$e\left(\frac{533}{538}\right)$	$e\left(\frac{703}{2152}\right)$	$e\left(\frac{1773}{2152}\right)$	$e\left(\frac{79}{269}\right)$	$e\left(\frac{523}{1076}\right)$	$e\left(\frac{707}{1076}\right)$	$e\left(\frac{1769}{2152}\right)$	$e\left(\frac{1615}{2152}\right)$
$\chi_{2153}(24,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{569}{1076}\right)$	$e\left(\frac{1427}{2152}\right)$	$e\left(\frac{31}{538}\right)$	$e\left(\frac{591}{2152}\right)$	$e\left(\frac{413}{2152}\right)$	$e\left(\frac{102}{269}\right)$	$e\left(\frac{631}{1076}\right)$	$e\left(\frac{351}{1076}\right)$	$e\left(\frac{1729}{2152}\right)$	$e\left(\frac{1823}{2152}\right)$
$\chi_{2153}(25,\cdot)$	2153.g	1076	yes	$1$	$1$	$e\left(\frac{509}{538}\right)$	$e\left(\frac{765}{1076}\right)$	$e\left(\frac{240}{269}\right)$	$e\left(\frac{957}{1076}\right)$	$e\left(\frac{707}{1076}\right)$	$e\left(\frac{217}{269}\right)$	$e\left(\frac{451}{538}\right)$	$e\left(\frac{227}{538}\right)$	$e\left(\frac{899}{1076}\right)$	$e\left(\frac{221}{1076}\right)$
$\chi_{2153}(26,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{555}{1076}\right)$	$e\left(\frac{609}{2152}\right)$	$e\left(\frac{17}{538}\right)$	$e\left(\frac{1053}{2152}\right)$	$e\left(\frac{1719}{2152}\right)$	$e\left(\frac{108}{269}\right)$	$e\left(\frac{589}{1076}\right)$	$e\left(\frac{609}{1076}\right)$	$e\left(\frac{11}{2152}\right)$	$e\left(\frac{965}{2152}\right)$
$\chi_{2153}(27,\cdot)$	2153.h	2152	yes	$-1$	$1$	$e\left(\frac{713}{1076}\right)$	$e\left(\frac{3}{2152}\right)$	$e\left(\frac{175}{538}\right)$	$e\left(\frac{143}{2152}\right)$	$e\left(\frac{1429}{2152}\right)$	$e\left(\frac{194}{269}\right)$	$e\left(\frac{1063}{1076}\right)$	$e\left(\frac{3}{1076}\right)$	$e\left(\frac{1569}{2152}\right)$	$e\left(\frac{503}{2152}\right)$
$\chi_{2153}(28,\cdot)$	2153.f	538	yes	$1$	$1$	$e\left(\frac{247}{269}\right)$	$e\left(\frac{367}{538}\right)$	$e\left(\frac{225}{269}\right)$	$e\left(\frac{457}{538}\right)$	$e\left(\frac{323}{538}\right)$	$e\left(\frac{153}{269}\right)$	$e\left(\frac{203}{269}\right)$	$e\left(\frac{98}{269}\right)$	$e\left(\frac{413}{538}\right)$	$e\left(\frac{381}{538}\right)$
$\chi_{2153}(29,\cdot)$	2153.e	269	yes	$1$	$1$	$e\left(\frac{231}{269}\right)$	$e\left(\frac{158}{269}\right)$	$e\left(\frac{193}{269}\right)$	$e\left(\frac{89}{269}\right)$	$e\left(\frac{120}{269}\right)$	$e\left(\frac{142}{269}\right)$	$e\left(\frac{155}{269}\right)$	$e\left(\frac{47}{269}\right)$	$e\left(\frac{51}{269}\right)$	$e\left(\frac{219}{269}\right)$
$\chi_{2153}(30,\cdot)$	2153.f	538	yes	$1$	$1$	$e\left(\frac{20}{269}\right)$	$e\left(\frac{131}{538}\right)$	$e\left(\frac{40}{269}\right)$	$e\left(\frac{147}{538}\right)$	$e\left(\frac{171}{538}\right)$	$e\left(\frac{81}{269}\right)$	$e\left(\frac{60}{269}\right)$	$e\left(\frac{131}{269}\right)$	$e\left(\frac{187}{538}\right)$	$e\left(\frac{265}{538}\right)$
$\chi_{2153}(31,\cdot)$	2153.g	1076	yes	$1$	$1$	$e\left(\frac{173}{538}\right)$	$e\left(\frac{1039}{1076}\right)$	$e\left(\frac{173}{269}\right)$	$e\left(\frac{747}{1076}\right)$	$e\left(\frac{309}{1076}\right)$	$e\left(\frac{236}{269}\right)$	$e\left(\frac{519}{538}\right)$	$e\left(\frac{501}{538}\right)$	$e\left(\frac{17}{1076}\right)$	$e\left(\frac{611}{1076}\right)$
$\chi_{2153}(32,\cdot)$	2153.g	1076	yes	$1$	$1$	$e\left(\frac{37}{538}\right)$	$e\left(\frac{471}{1076}\right)$	$e\left(\frac{37}{269}\right)$	$e\left(\frac{931}{1076}\right)$	$e\left(\frac{545}{1076}\right)$	$e\left(\frac{122}{269}\right)$	$e\left(\frac{111}{538}\right)$	$e\left(\frac{471}{538}\right)$	$e\left(\frac{1005}{1076}\right)$	$e\left(\frac{423}{1076}\right)$

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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	$2153$
Structure	\(C_{2152}\)
Order	$2152$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{2153}(1,\cdot)\)	2153.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2153}(2,\cdot)\)	2153.g	1076	yes	\(1\)	\(1\)	\(e\left(\frac{115}{538}\right)\)	\(e\left(\frac{955}{1076}\right)\)	\(e\left(\frac{115}{269}\right)\)	\(e\left(\frac{1047}{1076}\right)\)	\(e\left(\frac{109}{1076}\right)\)	\(e\left(\frac{132}{269}\right)\)	\(e\left(\frac{345}{538}\right)\)	\(e\left(\frac{417}{538}\right)\)	\(e\left(\frac{201}{1076}\right)\)	\(e\left(\frac{515}{1076}\right)\)
\(\chi_{2153}(3,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{955}{1076}\right)\)	\(e\left(\frac{1}{2152}\right)\)	\(e\left(\frac{417}{538}\right)\)	\(e\left(\frac{765}{2152}\right)\)	\(e\left(\frac{1911}{2152}\right)\)	\(e\left(\frac{244}{269}\right)\)	\(e\left(\frac{713}{1076}\right)\)	\(e\left(\frac{1}{1076}\right)\)	\(e\left(\frac{523}{2152}\right)\)	\(e\left(\frac{885}{2152}\right)\)
\(\chi_{2153}(4,\cdot)\)	2153.f	538	yes	\(1\)	\(1\)	\(e\left(\frac{115}{269}\right)\)	\(e\left(\frac{417}{538}\right)\)	\(e\left(\frac{230}{269}\right)\)	\(e\left(\frac{509}{538}\right)\)	\(e\left(\frac{109}{538}\right)\)	\(e\left(\frac{264}{269}\right)\)	\(e\left(\frac{76}{269}\right)\)	\(e\left(\frac{148}{269}\right)\)	\(e\left(\frac{201}{538}\right)\)	\(e\left(\frac{515}{538}\right)\)
\(\chi_{2153}(5,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{1047}{1076}\right)\)	\(e\left(\frac{765}{2152}\right)\)	\(e\left(\frac{509}{538}\right)\)	\(e\left(\frac{2033}{2152}\right)\)	\(e\left(\frac{707}{2152}\right)\)	\(e\left(\frac{243}{269}\right)\)	\(e\left(\frac{989}{1076}\right)\)	\(e\left(\frac{765}{1076}\right)\)	\(e\left(\frac{1975}{2152}\right)\)	\(e\left(\frac{1297}{2152}\right)\)
\(\chi_{2153}(6,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{1076}\right)\)	\(e\left(\frac{1911}{2152}\right)\)	\(e\left(\frac{109}{538}\right)\)	\(e\left(\frac{707}{2152}\right)\)	\(e\left(\frac{2129}{2152}\right)\)	\(e\left(\frac{107}{269}\right)\)	\(e\left(\frac{327}{1076}\right)\)	\(e\left(\frac{835}{1076}\right)\)	\(e\left(\frac{925}{2152}\right)\)	\(e\left(\frac{1915}{2152}\right)\)
\(\chi_{2153}(7,\cdot)\)	2153.e	269	yes	\(1\)	\(1\)	\(e\left(\frac{132}{269}\right)\)	\(e\left(\frac{244}{269}\right)\)	\(e\left(\frac{264}{269}\right)\)	\(e\left(\frac{243}{269}\right)\)	\(e\left(\frac{107}{269}\right)\)	\(e\left(\frac{158}{269}\right)\)	\(e\left(\frac{127}{269}\right)\)	\(e\left(\frac{219}{269}\right)\)	\(e\left(\frac{106}{269}\right)\)	\(e\left(\frac{202}{269}\right)\)
\(\chi_{2153}(8,\cdot)\)	2153.g	1076	yes	\(1\)	\(1\)	\(e\left(\frac{345}{538}\right)\)	\(e\left(\frac{713}{1076}\right)\)	\(e\left(\frac{76}{269}\right)\)	\(e\left(\frac{989}{1076}\right)\)	\(e\left(\frac{327}{1076}\right)\)	\(e\left(\frac{127}{269}\right)\)	\(e\left(\frac{497}{538}\right)\)	\(e\left(\frac{175}{538}\right)\)	\(e\left(\frac{603}{1076}\right)\)	\(e\left(\frac{469}{1076}\right)\)
\(\chi_{2153}(9,\cdot)\)	2153.g	1076	yes	\(1\)	\(1\)	\(e\left(\frac{417}{538}\right)\)	\(e\left(\frac{1}{1076}\right)\)	\(e\left(\frac{148}{269}\right)\)	\(e\left(\frac{765}{1076}\right)\)	\(e\left(\frac{835}{1076}\right)\)	\(e\left(\frac{219}{269}\right)\)	\(e\left(\frac{175}{538}\right)\)	\(e\left(\frac{1}{538}\right)\)	\(e\left(\frac{523}{1076}\right)\)	\(e\left(\frac{885}{1076}\right)\)
\(\chi_{2153}(10,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{201}{1076}\right)\)	\(e\left(\frac{523}{2152}\right)\)	\(e\left(\frac{201}{538}\right)\)	\(e\left(\frac{1975}{2152}\right)\)	\(e\left(\frac{925}{2152}\right)\)	\(e\left(\frac{106}{269}\right)\)	\(e\left(\frac{603}{1076}\right)\)	\(e\left(\frac{523}{1076}\right)\)	\(e\left(\frac{225}{2152}\right)\)	\(e\left(\frac{175}{2152}\right)\)
\(\chi_{2153}(11,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{515}{1076}\right)\)	\(e\left(\frac{885}{2152}\right)\)	\(e\left(\frac{515}{538}\right)\)	\(e\left(\frac{1297}{2152}\right)\)	\(e\left(\frac{1915}{2152}\right)\)	\(e\left(\frac{202}{269}\right)\)	\(e\left(\frac{469}{1076}\right)\)	\(e\left(\frac{885}{1076}\right)\)	\(e\left(\frac{175}{2152}\right)\)	\(e\left(\frac{2049}{2152}\right)\)
\(\chi_{2153}(12,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{339}{1076}\right)\)	\(e\left(\frac{1669}{2152}\right)\)	\(e\left(\frac{339}{538}\right)\)	\(e\left(\frac{649}{2152}\right)\)	\(e\left(\frac{195}{2152}\right)\)	\(e\left(\frac{239}{269}\right)\)	\(e\left(\frac{1017}{1076}\right)\)	\(e\left(\frac{593}{1076}\right)\)	\(e\left(\frac{1327}{2152}\right)\)	\(e\left(\frac{793}{2152}\right)\)
\(\chi_{2153}(13,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{325}{1076}\right)\)	\(e\left(\frac{851}{2152}\right)\)	\(e\left(\frac{325}{538}\right)\)	\(e\left(\frac{1111}{2152}\right)\)	\(e\left(\frac{1501}{2152}\right)\)	\(e\left(\frac{245}{269}\right)\)	\(e\left(\frac{975}{1076}\right)\)	\(e\left(\frac{851}{1076}\right)\)	\(e\left(\frac{1761}{2152}\right)\)	\(e\left(\frac{2087}{2152}\right)\)
\(\chi_{2153}(14,\cdot)\)	2153.g	1076	yes	\(1\)	\(1\)	\(e\left(\frac{379}{538}\right)\)	\(e\left(\frac{855}{1076}\right)\)	\(e\left(\frac{110}{269}\right)\)	\(e\left(\frac{943}{1076}\right)\)	\(e\left(\frac{537}{1076}\right)\)	\(e\left(\frac{21}{269}\right)\)	\(e\left(\frac{61}{538}\right)\)	\(e\left(\frac{317}{538}\right)\)	\(e\left(\frac{625}{1076}\right)\)	\(e\left(\frac{247}{1076}\right)\)
\(\chi_{2153}(15,\cdot)\)	2153.g	1076	yes	\(1\)	\(1\)	\(e\left(\frac{463}{538}\right)\)	\(e\left(\frac{383}{1076}\right)\)	\(e\left(\frac{194}{269}\right)\)	\(e\left(\frac{323}{1076}\right)\)	\(e\left(\frac{233}{1076}\right)\)	\(e\left(\frac{218}{269}\right)\)	\(e\left(\frac{313}{538}\right)\)	\(e\left(\frac{383}{538}\right)\)	\(e\left(\frac{173}{1076}\right)\)	\(e\left(\frac{15}{1076}\right)\)
\(\chi_{2153}(16,\cdot)\)	2153.e	269	yes	\(1\)	\(1\)	\(e\left(\frac{230}{269}\right)\)	\(e\left(\frac{148}{269}\right)\)	\(e\left(\frac{191}{269}\right)\)	\(e\left(\frac{240}{269}\right)\)	\(e\left(\frac{109}{269}\right)\)	\(e\left(\frac{259}{269}\right)\)	\(e\left(\frac{152}{269}\right)\)	\(e\left(\frac{27}{269}\right)\)	\(e\left(\frac{201}{269}\right)\)	\(e\left(\frac{246}{269}\right)\)
\(\chi_{2153}(17,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{1075}{1076}\right)\)	\(e\left(\frac{249}{2152}\right)\)	\(e\left(\frac{537}{538}\right)\)	\(e\left(\frac{1109}{2152}\right)\)	\(e\left(\frac{247}{2152}\right)\)	\(e\left(\frac{231}{269}\right)\)	\(e\left(\frac{1073}{1076}\right)\)	\(e\left(\frac{249}{1076}\right)\)	\(e\left(\frac{1107}{2152}\right)\)	\(e\left(\frac{861}{2152}\right)\)
\(\chi_{2153}(18,\cdot)\)	2153.e	269	yes	\(1\)	\(1\)	\(e\left(\frac{266}{269}\right)\)	\(e\left(\frac{239}{269}\right)\)	\(e\left(\frac{263}{269}\right)\)	\(e\left(\frac{184}{269}\right)\)	\(e\left(\frac{236}{269}\right)\)	\(e\left(\frac{82}{269}\right)\)	\(e\left(\frac{260}{269}\right)\)	\(e\left(\frac{209}{269}\right)\)	\(e\left(\frac{181}{269}\right)\)	\(e\left(\frac{81}{269}\right)\)
\(\chi_{2153}(19,\cdot)\)	2153.g	1076	yes	\(1\)	\(1\)	\(e\left(\frac{323}{538}\right)\)	\(e\left(\frac{811}{1076}\right)\)	\(e\left(\frac{54}{269}\right)\)	\(e\left(\frac{639}{1076}\right)\)	\(e\left(\frac{381}{1076}\right)\)	\(e\left(\frac{69}{269}\right)\)	\(e\left(\frac{431}{538}\right)\)	\(e\left(\frac{273}{538}\right)\)	\(e\left(\frac{209}{1076}\right)\)	\(e\left(\frac{43}{1076}\right)\)
\(\chi_{2153}(20,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{431}{1076}\right)\)	\(e\left(\frac{281}{2152}\right)\)	\(e\left(\frac{431}{538}\right)\)	\(e\left(\frac{1917}{2152}\right)\)	\(e\left(\frac{1143}{2152}\right)\)	\(e\left(\frac{238}{269}\right)\)	\(e\left(\frac{217}{1076}\right)\)	\(e\left(\frac{281}{1076}\right)\)	\(e\left(\frac{627}{2152}\right)\)	\(e\left(\frac{1205}{2152}\right)\)
\(\chi_{2153}(21,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{407}{1076}\right)\)	\(e\left(\frac{1953}{2152}\right)\)	\(e\left(\frac{407}{538}\right)\)	\(e\left(\frac{557}{2152}\right)\)	\(e\left(\frac{615}{2152}\right)\)	\(e\left(\frac{133}{269}\right)\)	\(e\left(\frac{145}{1076}\right)\)	\(e\left(\frac{877}{1076}\right)\)	\(e\left(\frac{1371}{2152}\right)\)	\(e\left(\frac{349}{2152}\right)\)
\(\chi_{2153}(22,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{745}{1076}\right)\)	\(e\left(\frac{643}{2152}\right)\)	\(e\left(\frac{207}{538}\right)\)	\(e\left(\frac{1239}{2152}\right)\)	\(e\left(\frac{2133}{2152}\right)\)	\(e\left(\frac{65}{269}\right)\)	\(e\left(\frac{83}{1076}\right)\)	\(e\left(\frac{643}{1076}\right)\)	\(e\left(\frac{577}{2152}\right)\)	\(e\left(\frac{927}{2152}\right)\)
\(\chi_{2153}(23,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{533}{1076}\right)\)	\(e\left(\frac{707}{2152}\right)\)	\(e\left(\frac{533}{538}\right)\)	\(e\left(\frac{703}{2152}\right)\)	\(e\left(\frac{1773}{2152}\right)\)	\(e\left(\frac{79}{269}\right)\)	\(e\left(\frac{523}{1076}\right)\)	\(e\left(\frac{707}{1076}\right)\)	\(e\left(\frac{1769}{2152}\right)\)	\(e\left(\frac{1615}{2152}\right)\)
\(\chi_{2153}(24,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{569}{1076}\right)\)	\(e\left(\frac{1427}{2152}\right)\)	\(e\left(\frac{31}{538}\right)\)	\(e\left(\frac{591}{2152}\right)\)	\(e\left(\frac{413}{2152}\right)\)	\(e\left(\frac{102}{269}\right)\)	\(e\left(\frac{631}{1076}\right)\)	\(e\left(\frac{351}{1076}\right)\)	\(e\left(\frac{1729}{2152}\right)\)	\(e\left(\frac{1823}{2152}\right)\)
\(\chi_{2153}(25,\cdot)\)	2153.g	1076	yes	\(1\)	\(1\)	\(e\left(\frac{509}{538}\right)\)	\(e\left(\frac{765}{1076}\right)\)	\(e\left(\frac{240}{269}\right)\)	\(e\left(\frac{957}{1076}\right)\)	\(e\left(\frac{707}{1076}\right)\)	\(e\left(\frac{217}{269}\right)\)	\(e\left(\frac{451}{538}\right)\)	\(e\left(\frac{227}{538}\right)\)	\(e\left(\frac{899}{1076}\right)\)	\(e\left(\frac{221}{1076}\right)\)
\(\chi_{2153}(26,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{555}{1076}\right)\)	\(e\left(\frac{609}{2152}\right)\)	\(e\left(\frac{17}{538}\right)\)	\(e\left(\frac{1053}{2152}\right)\)	\(e\left(\frac{1719}{2152}\right)\)	\(e\left(\frac{108}{269}\right)\)	\(e\left(\frac{589}{1076}\right)\)	\(e\left(\frac{609}{1076}\right)\)	\(e\left(\frac{11}{2152}\right)\)	\(e\left(\frac{965}{2152}\right)\)
\(\chi_{2153}(27,\cdot)\)	2153.h	2152	yes	\(-1\)	\(1\)	\(e\left(\frac{713}{1076}\right)\)	\(e\left(\frac{3}{2152}\right)\)	\(e\left(\frac{175}{538}\right)\)	\(e\left(\frac{143}{2152}\right)\)	\(e\left(\frac{1429}{2152}\right)\)	\(e\left(\frac{194}{269}\right)\)	\(e\left(\frac{1063}{1076}\right)\)	\(e\left(\frac{3}{1076}\right)\)	\(e\left(\frac{1569}{2152}\right)\)	\(e\left(\frac{503}{2152}\right)\)
\(\chi_{2153}(28,\cdot)\)	2153.f	538	yes	\(1\)	\(1\)	\(e\left(\frac{247}{269}\right)\)	\(e\left(\frac{367}{538}\right)\)	\(e\left(\frac{225}{269}\right)\)	\(e\left(\frac{457}{538}\right)\)	\(e\left(\frac{323}{538}\right)\)	\(e\left(\frac{153}{269}\right)\)	\(e\left(\frac{203}{269}\right)\)	\(e\left(\frac{98}{269}\right)\)	\(e\left(\frac{413}{538}\right)\)	\(e\left(\frac{381}{538}\right)\)
\(\chi_{2153}(29,\cdot)\)	2153.e	269	yes	\(1\)	\(1\)	\(e\left(\frac{231}{269}\right)\)	\(e\left(\frac{158}{269}\right)\)	\(e\left(\frac{193}{269}\right)\)	\(e\left(\frac{89}{269}\right)\)	\(e\left(\frac{120}{269}\right)\)	\(e\left(\frac{142}{269}\right)\)	\(e\left(\frac{155}{269}\right)\)	\(e\left(\frac{47}{269}\right)\)	\(e\left(\frac{51}{269}\right)\)	\(e\left(\frac{219}{269}\right)\)
\(\chi_{2153}(30,\cdot)\)	2153.f	538	yes	\(1\)	\(1\)	\(e\left(\frac{20}{269}\right)\)	\(e\left(\frac{131}{538}\right)\)	\(e\left(\frac{40}{269}\right)\)	\(e\left(\frac{147}{538}\right)\)	\(e\left(\frac{171}{538}\right)\)	\(e\left(\frac{81}{269}\right)\)	\(e\left(\frac{60}{269}\right)\)	\(e\left(\frac{131}{269}\right)\)	\(e\left(\frac{187}{538}\right)\)	\(e\left(\frac{265}{538}\right)\)
\(\chi_{2153}(31,\cdot)\)	2153.g	1076	yes	\(1\)	\(1\)	\(e\left(\frac{173}{538}\right)\)	\(e\left(\frac{1039}{1076}\right)\)	\(e\left(\frac{173}{269}\right)\)	\(e\left(\frac{747}{1076}\right)\)	\(e\left(\frac{309}{1076}\right)\)	\(e\left(\frac{236}{269}\right)\)	\(e\left(\frac{519}{538}\right)\)	\(e\left(\frac{501}{538}\right)\)	\(e\left(\frac{17}{1076}\right)\)	\(e\left(\frac{611}{1076}\right)\)
\(\chi_{2153}(32,\cdot)\)	2153.g	1076	yes	\(1\)	\(1\)	\(e\left(\frac{37}{538}\right)\)	\(e\left(\frac{471}{1076}\right)\)	\(e\left(\frac{37}{269}\right)\)	\(e\left(\frac{931}{1076}\right)\)	\(e\left(\frac{545}{1076}\right)\)	\(e\left(\frac{122}{269}\right)\)	\(e\left(\frac{111}{538}\right)\)	\(e\left(\frac{471}{538}\right)\)	\(e\left(\frac{1005}{1076}\right)\)	\(e\left(\frac{423}{1076}\right)\)

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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.