LMFDB - Group of Dirichlet characters of modulus 1061

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1061)

pari: g = idealstar(,1061,2)

Character group

sage: G.order() pari: g.no
Order	=	1060
sage: H.invariants() pari: g.cyc
Structure	=	$C_{1060}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1061}(2,\cdot)$

First 32 of 1060 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1061}(1,\cdot)$	1061.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1061}(2,\cdot)$	1061.l	1060	yes	$-1$	$1$	$e\left(\frac{1}{1060}\right)$	$e\left(\frac{167}{1060}\right)$	$e\left(\frac{1}{530}\right)$	$e\left(\frac{61}{265}\right)$	$e\left(\frac{42}{265}\right)$	$e\left(\frac{119}{265}\right)$	$e\left(\frac{3}{1060}\right)$	$e\left(\frac{167}{530}\right)$	$e\left(\frac{49}{212}\right)$	$e\left(\frac{301}{530}\right)$
$\chi_{1061}(3,\cdot)$	1061.l	1060	yes	$-1$	$1$	$e\left(\frac{167}{1060}\right)$	$e\left(\frac{329}{1060}\right)$	$e\left(\frac{167}{530}\right)$	$e\left(\frac{117}{265}\right)$	$e\left(\frac{124}{265}\right)$	$e\left(\frac{263}{265}\right)$	$e\left(\frac{501}{1060}\right)$	$e\left(\frac{329}{530}\right)$	$e\left(\frac{127}{212}\right)$	$e\left(\frac{447}{530}\right)$
$\chi_{1061}(4,\cdot)$	1061.k	530	yes	$1$	$1$	$e\left(\frac{1}{530}\right)$	$e\left(\frac{167}{530}\right)$	$e\left(\frac{1}{265}\right)$	$e\left(\frac{122}{265}\right)$	$e\left(\frac{84}{265}\right)$	$e\left(\frac{238}{265}\right)$	$e\left(\frac{3}{530}\right)$	$e\left(\frac{167}{265}\right)$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{36}{265}\right)$
$\chi_{1061}(5,\cdot)$	1061.j	265	yes	$1$	$1$	$e\left(\frac{61}{265}\right)$	$e\left(\frac{117}{265}\right)$	$e\left(\frac{122}{265}\right)$	$e\left(\frac{44}{265}\right)$	$e\left(\frac{178}{265}\right)$	$e\left(\frac{151}{265}\right)$	$e\left(\frac{183}{265}\right)$	$e\left(\frac{234}{265}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{152}{265}\right)$
$\chi_{1061}(6,\cdot)$	1061.j	265	yes	$1$	$1$	$e\left(\frac{42}{265}\right)$	$e\left(\frac{124}{265}\right)$	$e\left(\frac{84}{265}\right)$	$e\left(\frac{178}{265}\right)$	$e\left(\frac{166}{265}\right)$	$e\left(\frac{117}{265}\right)$	$e\left(\frac{126}{265}\right)$	$e\left(\frac{248}{265}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{109}{265}\right)$
$\chi_{1061}(7,\cdot)$	1061.j	265	yes	$1$	$1$	$e\left(\frac{119}{265}\right)$	$e\left(\frac{263}{265}\right)$	$e\left(\frac{238}{265}\right)$	$e\left(\frac{151}{265}\right)$	$e\left(\frac{117}{265}\right)$	$e\left(\frac{199}{265}\right)$	$e\left(\frac{92}{265}\right)$	$e\left(\frac{261}{265}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{88}{265}\right)$
$\chi_{1061}(8,\cdot)$	1061.l	1060	yes	$-1$	$1$	$e\left(\frac{3}{1060}\right)$	$e\left(\frac{501}{1060}\right)$	$e\left(\frac{3}{530}\right)$	$e\left(\frac{183}{265}\right)$	$e\left(\frac{126}{265}\right)$	$e\left(\frac{92}{265}\right)$	$e\left(\frac{9}{1060}\right)$	$e\left(\frac{501}{530}\right)$	$e\left(\frac{147}{212}\right)$	$e\left(\frac{373}{530}\right)$
$\chi_{1061}(9,\cdot)$	1061.k	530	yes	$1$	$1$	$e\left(\frac{167}{530}\right)$	$e\left(\frac{329}{530}\right)$	$e\left(\frac{167}{265}\right)$	$e\left(\frac{234}{265}\right)$	$e\left(\frac{248}{265}\right)$	$e\left(\frac{261}{265}\right)$	$e\left(\frac{501}{530}\right)$	$e\left(\frac{64}{265}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{182}{265}\right)$
$\chi_{1061}(10,\cdot)$	1061.i	212	yes	$-1$	$1$	$e\left(\frac{49}{212}\right)$	$e\left(\frac{127}{212}\right)$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{147}{212}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{133}{212}\right)$	$e\left(\frac{15}{106}\right)$
$\chi_{1061}(11,\cdot)$	1061.k	530	yes	$1$	$1$	$e\left(\frac{301}{530}\right)$	$e\left(\frac{447}{530}\right)$	$e\left(\frac{36}{265}\right)$	$e\left(\frac{152}{265}\right)$	$e\left(\frac{109}{265}\right)$	$e\left(\frac{88}{265}\right)$	$e\left(\frac{373}{530}\right)$	$e\left(\frac{182}{265}\right)$	$e\left(\frac{15}{106}\right)$	$e\left(\frac{236}{265}\right)$
$\chi_{1061}(12,\cdot)$	1061.l	1060	yes	$-1$	$1$	$e\left(\frac{169}{1060}\right)$	$e\left(\frac{663}{1060}\right)$	$e\left(\frac{169}{530}\right)$	$e\left(\frac{239}{265}\right)$	$e\left(\frac{208}{265}\right)$	$e\left(\frac{236}{265}\right)$	$e\left(\frac{507}{1060}\right)$	$e\left(\frac{133}{530}\right)$	$e\left(\frac{13}{212}\right)$	$e\left(\frac{519}{530}\right)$
$\chi_{1061}(13,\cdot)$	1061.i	212	yes	$-1$	$1$	$e\left(\frac{185}{212}\right)$	$e\left(\frac{155}{212}\right)$	$e\left(\frac{79}{106}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{131}{212}\right)$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{169}{212}\right)$	$e\left(\frac{35}{106}\right)$
$\chi_{1061}(14,\cdot)$	1061.f	20	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{9}{10}\right)$
$\chi_{1061}(15,\cdot)$	1061.l	1060	yes	$-1$	$1$	$e\left(\frac{411}{1060}\right)$	$e\left(\frac{797}{1060}\right)$	$e\left(\frac{411}{530}\right)$	$e\left(\frac{161}{265}\right)$	$e\left(\frac{37}{265}\right)$	$e\left(\frac{149}{265}\right)$	$e\left(\frac{173}{1060}\right)$	$e\left(\frac{267}{530}\right)$	$e\left(\frac{211}{212}\right)$	$e\left(\frac{221}{530}\right)$
$\chi_{1061}(16,\cdot)$	1061.j	265	yes	$1$	$1$	$e\left(\frac{1}{265}\right)$	$e\left(\frac{167}{265}\right)$	$e\left(\frac{2}{265}\right)$	$e\left(\frac{244}{265}\right)$	$e\left(\frac{168}{265}\right)$	$e\left(\frac{211}{265}\right)$	$e\left(\frac{3}{265}\right)$	$e\left(\frac{69}{265}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{72}{265}\right)$
$\chi_{1061}(17,\cdot)$	1061.i	212	yes	$-1$	$1$	$e\left(\frac{99}{212}\right)$	$e\left(\frac{209}{212}\right)$	$e\left(\frac{99}{106}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{85}{212}\right)$	$e\left(\frac{103}{106}\right)$	$e\left(\frac{87}{212}\right)$	$e\left(\frac{13}{106}\right)$
$\chi_{1061}(18,\cdot)$	1061.i	212	yes	$-1$	$1$	$e\left(\frac{67}{212}\right)$	$e\left(\frac{165}{212}\right)$	$e\left(\frac{67}{106}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{201}{212}\right)$	$e\left(\frac{59}{106}\right)$	$e\left(\frac{91}{212}\right)$	$e\left(\frac{27}{106}\right)$
$\chi_{1061}(19,\cdot)$	1061.j	265	yes	$1$	$1$	$e\left(\frac{187}{265}\right)$	$e\left(\frac{224}{265}\right)$	$e\left(\frac{109}{265}\right)$	$e\left(\frac{48}{265}\right)$	$e\left(\frac{146}{265}\right)$	$e\left(\frac{237}{265}\right)$	$e\left(\frac{31}{265}\right)$	$e\left(\frac{183}{265}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{214}{265}\right)$
$\chi_{1061}(20,\cdot)$	1061.k	530	yes	$1$	$1$	$e\left(\frac{123}{530}\right)$	$e\left(\frac{401}{530}\right)$	$e\left(\frac{123}{265}\right)$	$e\left(\frac{166}{265}\right)$	$e\left(\frac{262}{265}\right)$	$e\left(\frac{124}{265}\right)$	$e\left(\frac{369}{530}\right)$	$e\left(\frac{136}{265}\right)$	$e\left(\frac{91}{106}\right)$	$e\left(\frac{188}{265}\right)$
$\chi_{1061}(21,\cdot)$	1061.l	1060	yes	$-1$	$1$	$e\left(\frac{643}{1060}\right)$	$e\left(\frac{321}{1060}\right)$	$e\left(\frac{113}{530}\right)$	$e\left(\frac{3}{265}\right)$	$e\left(\frac{241}{265}\right)$	$e\left(\frac{197}{265}\right)$	$e\left(\frac{869}{1060}\right)$	$e\left(\frac{321}{530}\right)$	$e\left(\frac{131}{212}\right)$	$e\left(\frac{93}{530}\right)$
$\chi_{1061}(22,\cdot)$	1061.l	1060	yes	$-1$	$1$	$e\left(\frac{603}{1060}\right)$	$e\left(\frac{1}{1060}\right)$	$e\left(\frac{73}{530}\right)$	$e\left(\frac{213}{265}\right)$	$e\left(\frac{151}{265}\right)$	$e\left(\frac{207}{265}\right)$	$e\left(\frac{749}{1060}\right)$	$e\left(\frac{1}{530}\right)$	$e\left(\frac{79}{212}\right)$	$e\left(\frac{243}{530}\right)$
$\chi_{1061}(23,\cdot)$	1061.k	530	yes	$1$	$1$	$e\left(\frac{439}{530}\right)$	$e\left(\frac{173}{530}\right)$	$e\left(\frac{174}{265}\right)$	$e\left(\frac{28}{265}\right)$	$e\left(\frac{41}{265}\right)$	$e\left(\frac{72}{265}\right)$	$e\left(\frac{257}{530}\right)$	$e\left(\frac{173}{265}\right)$	$e\left(\frac{99}{106}\right)$	$e\left(\frac{169}{265}\right)$
$\chi_{1061}(24,\cdot)$	1061.h	106	yes	$1$	$1$	$e\left(\frac{17}{106}\right)$	$e\left(\frac{83}{106}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{51}{106}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{31}{106}\right)$	$e\left(\frac{29}{53}\right)$
$\chi_{1061}(25,\cdot)$	1061.j	265	yes	$1$	$1$	$e\left(\frac{122}{265}\right)$	$e\left(\frac{234}{265}\right)$	$e\left(\frac{244}{265}\right)$	$e\left(\frac{88}{265}\right)$	$e\left(\frac{91}{265}\right)$	$e\left(\frac{37}{265}\right)$	$e\left(\frac{101}{265}\right)$	$e\left(\frac{203}{265}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{39}{265}\right)$
$\chi_{1061}(26,\cdot)$	1061.k	530	yes	$1$	$1$	$e\left(\frac{463}{530}\right)$	$e\left(\frac{471}{530}\right)$	$e\left(\frac{198}{265}\right)$	$e\left(\frac{41}{265}\right)$	$e\left(\frac{202}{265}\right)$	$e\left(\frac{219}{265}\right)$	$e\left(\frac{329}{530}\right)$	$e\left(\frac{206}{265}\right)$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{238}{265}\right)$
$\chi_{1061}(27,\cdot)$	1061.l	1060	yes	$-1$	$1$	$e\left(\frac{501}{1060}\right)$	$e\left(\frac{987}{1060}\right)$	$e\left(\frac{501}{530}\right)$	$e\left(\frac{86}{265}\right)$	$e\left(\frac{107}{265}\right)$	$e\left(\frac{259}{265}\right)$	$e\left(\frac{443}{1060}\right)$	$e\left(\frac{457}{530}\right)$	$e\left(\frac{169}{212}\right)$	$e\left(\frac{281}{530}\right)$
$\chi_{1061}(28,\cdot)$	1061.k	530	yes	$1$	$1$	$e\left(\frac{239}{530}\right)$	$e\left(\frac{163}{530}\right)$	$e\left(\frac{239}{265}\right)$	$e\left(\frac{8}{265}\right)$	$e\left(\frac{201}{265}\right)$	$e\left(\frac{172}{265}\right)$	$e\left(\frac{187}{530}\right)$	$e\left(\frac{163}{265}\right)$	$e\left(\frac{51}{106}\right)$	$e\left(\frac{124}{265}\right)$
$\chi_{1061}(29,\cdot)$	1061.f	20	yes	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{3}{10}\right)$
$\chi_{1061}(30,\cdot)$	1061.j	265	yes	$1$	$1$	$e\left(\frac{103}{265}\right)$	$e\left(\frac{241}{265}\right)$	$e\left(\frac{206}{265}\right)$	$e\left(\frac{222}{265}\right)$	$e\left(\frac{79}{265}\right)$	$e\left(\frac{3}{265}\right)$	$e\left(\frac{44}{265}\right)$	$e\left(\frac{217}{265}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{261}{265}\right)$
$\chi_{1061}(31,\cdot)$	1061.h	106	yes	$1$	$1$	$e\left(\frac{51}{106}\right)$	$e\left(\frac{37}{106}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{93}{106}\right)$	$e\left(\frac{34}{53}\right)$
$\chi_{1061}(32,\cdot)$	1061.i	212	yes	$-1$	$1$	$e\left(\frac{1}{212}\right)$	$e\left(\frac{167}{212}\right)$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{3}{212}\right)$	$e\left(\frac{61}{106}\right)$	$e\left(\frac{33}{212}\right)$	$e\left(\frac{89}{106}\right)$

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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	$1061$
Structure	\(C_{1060}\)
Order	$1060$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1061}(1,\cdot)\)	1061.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1061}(2,\cdot)\)	1061.l	1060	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{1060}\right)\)	\(e\left(\frac{167}{1060}\right)\)	\(e\left(\frac{1}{530}\right)\)	\(e\left(\frac{61}{265}\right)\)	\(e\left(\frac{42}{265}\right)\)	\(e\left(\frac{119}{265}\right)\)	\(e\left(\frac{3}{1060}\right)\)	\(e\left(\frac{167}{530}\right)\)	\(e\left(\frac{49}{212}\right)\)	\(e\left(\frac{301}{530}\right)\)
\(\chi_{1061}(3,\cdot)\)	1061.l	1060	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{1060}\right)\)	\(e\left(\frac{329}{1060}\right)\)	\(e\left(\frac{167}{530}\right)\)	\(e\left(\frac{117}{265}\right)\)	\(e\left(\frac{124}{265}\right)\)	\(e\left(\frac{263}{265}\right)\)	\(e\left(\frac{501}{1060}\right)\)	\(e\left(\frac{329}{530}\right)\)	\(e\left(\frac{127}{212}\right)\)	\(e\left(\frac{447}{530}\right)\)
\(\chi_{1061}(4,\cdot)\)	1061.k	530	yes	\(1\)	\(1\)	\(e\left(\frac{1}{530}\right)\)	\(e\left(\frac{167}{530}\right)\)	\(e\left(\frac{1}{265}\right)\)	\(e\left(\frac{122}{265}\right)\)	\(e\left(\frac{84}{265}\right)\)	\(e\left(\frac{238}{265}\right)\)	\(e\left(\frac{3}{530}\right)\)	\(e\left(\frac{167}{265}\right)\)	\(e\left(\frac{49}{106}\right)\)	\(e\left(\frac{36}{265}\right)\)
\(\chi_{1061}(5,\cdot)\)	1061.j	265	yes	\(1\)	\(1\)	\(e\left(\frac{61}{265}\right)\)	\(e\left(\frac{117}{265}\right)\)	\(e\left(\frac{122}{265}\right)\)	\(e\left(\frac{44}{265}\right)\)	\(e\left(\frac{178}{265}\right)\)	\(e\left(\frac{151}{265}\right)\)	\(e\left(\frac{183}{265}\right)\)	\(e\left(\frac{234}{265}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{152}{265}\right)\)
\(\chi_{1061}(6,\cdot)\)	1061.j	265	yes	\(1\)	\(1\)	\(e\left(\frac{42}{265}\right)\)	\(e\left(\frac{124}{265}\right)\)	\(e\left(\frac{84}{265}\right)\)	\(e\left(\frac{178}{265}\right)\)	\(e\left(\frac{166}{265}\right)\)	\(e\left(\frac{117}{265}\right)\)	\(e\left(\frac{126}{265}\right)\)	\(e\left(\frac{248}{265}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{109}{265}\right)\)
\(\chi_{1061}(7,\cdot)\)	1061.j	265	yes	\(1\)	\(1\)	\(e\left(\frac{119}{265}\right)\)	\(e\left(\frac{263}{265}\right)\)	\(e\left(\frac{238}{265}\right)\)	\(e\left(\frac{151}{265}\right)\)	\(e\left(\frac{117}{265}\right)\)	\(e\left(\frac{199}{265}\right)\)	\(e\left(\frac{92}{265}\right)\)	\(e\left(\frac{261}{265}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{88}{265}\right)\)
\(\chi_{1061}(8,\cdot)\)	1061.l	1060	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{1060}\right)\)	\(e\left(\frac{501}{1060}\right)\)	\(e\left(\frac{3}{530}\right)\)	\(e\left(\frac{183}{265}\right)\)	\(e\left(\frac{126}{265}\right)\)	\(e\left(\frac{92}{265}\right)\)	\(e\left(\frac{9}{1060}\right)\)	\(e\left(\frac{501}{530}\right)\)	\(e\left(\frac{147}{212}\right)\)	\(e\left(\frac{373}{530}\right)\)
\(\chi_{1061}(9,\cdot)\)	1061.k	530	yes	\(1\)	\(1\)	\(e\left(\frac{167}{530}\right)\)	\(e\left(\frac{329}{530}\right)\)	\(e\left(\frac{167}{265}\right)\)	\(e\left(\frac{234}{265}\right)\)	\(e\left(\frac{248}{265}\right)\)	\(e\left(\frac{261}{265}\right)\)	\(e\left(\frac{501}{530}\right)\)	\(e\left(\frac{64}{265}\right)\)	\(e\left(\frac{21}{106}\right)\)	\(e\left(\frac{182}{265}\right)\)
\(\chi_{1061}(10,\cdot)\)	1061.i	212	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{212}\right)\)	\(e\left(\frac{127}{212}\right)\)	\(e\left(\frac{49}{106}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{147}{212}\right)\)	\(e\left(\frac{21}{106}\right)\)	\(e\left(\frac{133}{212}\right)\)	\(e\left(\frac{15}{106}\right)\)
\(\chi_{1061}(11,\cdot)\)	1061.k	530	yes	\(1\)	\(1\)	\(e\left(\frac{301}{530}\right)\)	\(e\left(\frac{447}{530}\right)\)	\(e\left(\frac{36}{265}\right)\)	\(e\left(\frac{152}{265}\right)\)	\(e\left(\frac{109}{265}\right)\)	\(e\left(\frac{88}{265}\right)\)	\(e\left(\frac{373}{530}\right)\)	\(e\left(\frac{182}{265}\right)\)	\(e\left(\frac{15}{106}\right)\)	\(e\left(\frac{236}{265}\right)\)
\(\chi_{1061}(12,\cdot)\)	1061.l	1060	yes	\(-1\)	\(1\)	\(e\left(\frac{169}{1060}\right)\)	\(e\left(\frac{663}{1060}\right)\)	\(e\left(\frac{169}{530}\right)\)	\(e\left(\frac{239}{265}\right)\)	\(e\left(\frac{208}{265}\right)\)	\(e\left(\frac{236}{265}\right)\)	\(e\left(\frac{507}{1060}\right)\)	\(e\left(\frac{133}{530}\right)\)	\(e\left(\frac{13}{212}\right)\)	\(e\left(\frac{519}{530}\right)\)
\(\chi_{1061}(13,\cdot)\)	1061.i	212	yes	\(-1\)	\(1\)	\(e\left(\frac{185}{212}\right)\)	\(e\left(\frac{155}{212}\right)\)	\(e\left(\frac{79}{106}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{131}{212}\right)\)	\(e\left(\frac{49}{106}\right)\)	\(e\left(\frac{169}{212}\right)\)	\(e\left(\frac{35}{106}\right)\)
\(\chi_{1061}(14,\cdot)\)	1061.f	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1061}(15,\cdot)\)	1061.l	1060	yes	\(-1\)	\(1\)	\(e\left(\frac{411}{1060}\right)\)	\(e\left(\frac{797}{1060}\right)\)	\(e\left(\frac{411}{530}\right)\)	\(e\left(\frac{161}{265}\right)\)	\(e\left(\frac{37}{265}\right)\)	\(e\left(\frac{149}{265}\right)\)	\(e\left(\frac{173}{1060}\right)\)	\(e\left(\frac{267}{530}\right)\)	\(e\left(\frac{211}{212}\right)\)	\(e\left(\frac{221}{530}\right)\)
\(\chi_{1061}(16,\cdot)\)	1061.j	265	yes	\(1\)	\(1\)	\(e\left(\frac{1}{265}\right)\)	\(e\left(\frac{167}{265}\right)\)	\(e\left(\frac{2}{265}\right)\)	\(e\left(\frac{244}{265}\right)\)	\(e\left(\frac{168}{265}\right)\)	\(e\left(\frac{211}{265}\right)\)	\(e\left(\frac{3}{265}\right)\)	\(e\left(\frac{69}{265}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{72}{265}\right)\)
\(\chi_{1061}(17,\cdot)\)	1061.i	212	yes	\(-1\)	\(1\)	\(e\left(\frac{99}{212}\right)\)	\(e\left(\frac{209}{212}\right)\)	\(e\left(\frac{99}{106}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{85}{212}\right)\)	\(e\left(\frac{103}{106}\right)\)	\(e\left(\frac{87}{212}\right)\)	\(e\left(\frac{13}{106}\right)\)
\(\chi_{1061}(18,\cdot)\)	1061.i	212	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{212}\right)\)	\(e\left(\frac{165}{212}\right)\)	\(e\left(\frac{67}{106}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{201}{212}\right)\)	\(e\left(\frac{59}{106}\right)\)	\(e\left(\frac{91}{212}\right)\)	\(e\left(\frac{27}{106}\right)\)
\(\chi_{1061}(19,\cdot)\)	1061.j	265	yes	\(1\)	\(1\)	\(e\left(\frac{187}{265}\right)\)	\(e\left(\frac{224}{265}\right)\)	\(e\left(\frac{109}{265}\right)\)	\(e\left(\frac{48}{265}\right)\)	\(e\left(\frac{146}{265}\right)\)	\(e\left(\frac{237}{265}\right)\)	\(e\left(\frac{31}{265}\right)\)	\(e\left(\frac{183}{265}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{214}{265}\right)\)
\(\chi_{1061}(20,\cdot)\)	1061.k	530	yes	\(1\)	\(1\)	\(e\left(\frac{123}{530}\right)\)	\(e\left(\frac{401}{530}\right)\)	\(e\left(\frac{123}{265}\right)\)	\(e\left(\frac{166}{265}\right)\)	\(e\left(\frac{262}{265}\right)\)	\(e\left(\frac{124}{265}\right)\)	\(e\left(\frac{369}{530}\right)\)	\(e\left(\frac{136}{265}\right)\)	\(e\left(\frac{91}{106}\right)\)	\(e\left(\frac{188}{265}\right)\)
\(\chi_{1061}(21,\cdot)\)	1061.l	1060	yes	\(-1\)	\(1\)	\(e\left(\frac{643}{1060}\right)\)	\(e\left(\frac{321}{1060}\right)\)	\(e\left(\frac{113}{530}\right)\)	\(e\left(\frac{3}{265}\right)\)	\(e\left(\frac{241}{265}\right)\)	\(e\left(\frac{197}{265}\right)\)	\(e\left(\frac{869}{1060}\right)\)	\(e\left(\frac{321}{530}\right)\)	\(e\left(\frac{131}{212}\right)\)	\(e\left(\frac{93}{530}\right)\)
\(\chi_{1061}(22,\cdot)\)	1061.l	1060	yes	\(-1\)	\(1\)	\(e\left(\frac{603}{1060}\right)\)	\(e\left(\frac{1}{1060}\right)\)	\(e\left(\frac{73}{530}\right)\)	\(e\left(\frac{213}{265}\right)\)	\(e\left(\frac{151}{265}\right)\)	\(e\left(\frac{207}{265}\right)\)	\(e\left(\frac{749}{1060}\right)\)	\(e\left(\frac{1}{530}\right)\)	\(e\left(\frac{79}{212}\right)\)	\(e\left(\frac{243}{530}\right)\)
\(\chi_{1061}(23,\cdot)\)	1061.k	530	yes	\(1\)	\(1\)	\(e\left(\frac{439}{530}\right)\)	\(e\left(\frac{173}{530}\right)\)	\(e\left(\frac{174}{265}\right)\)	\(e\left(\frac{28}{265}\right)\)	\(e\left(\frac{41}{265}\right)\)	\(e\left(\frac{72}{265}\right)\)	\(e\left(\frac{257}{530}\right)\)	\(e\left(\frac{173}{265}\right)\)	\(e\left(\frac{99}{106}\right)\)	\(e\left(\frac{169}{265}\right)\)
\(\chi_{1061}(24,\cdot)\)	1061.h	106	yes	\(1\)	\(1\)	\(e\left(\frac{17}{106}\right)\)	\(e\left(\frac{83}{106}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{51}{106}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{31}{106}\right)\)	\(e\left(\frac{29}{53}\right)\)
\(\chi_{1061}(25,\cdot)\)	1061.j	265	yes	\(1\)	\(1\)	\(e\left(\frac{122}{265}\right)\)	\(e\left(\frac{234}{265}\right)\)	\(e\left(\frac{244}{265}\right)\)	\(e\left(\frac{88}{265}\right)\)	\(e\left(\frac{91}{265}\right)\)	\(e\left(\frac{37}{265}\right)\)	\(e\left(\frac{101}{265}\right)\)	\(e\left(\frac{203}{265}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{39}{265}\right)\)
\(\chi_{1061}(26,\cdot)\)	1061.k	530	yes	\(1\)	\(1\)	\(e\left(\frac{463}{530}\right)\)	\(e\left(\frac{471}{530}\right)\)	\(e\left(\frac{198}{265}\right)\)	\(e\left(\frac{41}{265}\right)\)	\(e\left(\frac{202}{265}\right)\)	\(e\left(\frac{219}{265}\right)\)	\(e\left(\frac{329}{530}\right)\)	\(e\left(\frac{206}{265}\right)\)	\(e\left(\frac{3}{106}\right)\)	\(e\left(\frac{238}{265}\right)\)
\(\chi_{1061}(27,\cdot)\)	1061.l	1060	yes	\(-1\)	\(1\)	\(e\left(\frac{501}{1060}\right)\)	\(e\left(\frac{987}{1060}\right)\)	\(e\left(\frac{501}{530}\right)\)	\(e\left(\frac{86}{265}\right)\)	\(e\left(\frac{107}{265}\right)\)	\(e\left(\frac{259}{265}\right)\)	\(e\left(\frac{443}{1060}\right)\)	\(e\left(\frac{457}{530}\right)\)	\(e\left(\frac{169}{212}\right)\)	\(e\left(\frac{281}{530}\right)\)
\(\chi_{1061}(28,\cdot)\)	1061.k	530	yes	\(1\)	\(1\)	\(e\left(\frac{239}{530}\right)\)	\(e\left(\frac{163}{530}\right)\)	\(e\left(\frac{239}{265}\right)\)	\(e\left(\frac{8}{265}\right)\)	\(e\left(\frac{201}{265}\right)\)	\(e\left(\frac{172}{265}\right)\)	\(e\left(\frac{187}{530}\right)\)	\(e\left(\frac{163}{265}\right)\)	\(e\left(\frac{51}{106}\right)\)	\(e\left(\frac{124}{265}\right)\)
\(\chi_{1061}(29,\cdot)\)	1061.f	20	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1061}(30,\cdot)\)	1061.j	265	yes	\(1\)	\(1\)	\(e\left(\frac{103}{265}\right)\)	\(e\left(\frac{241}{265}\right)\)	\(e\left(\frac{206}{265}\right)\)	\(e\left(\frac{222}{265}\right)\)	\(e\left(\frac{79}{265}\right)\)	\(e\left(\frac{3}{265}\right)\)	\(e\left(\frac{44}{265}\right)\)	\(e\left(\frac{217}{265}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{261}{265}\right)\)
\(\chi_{1061}(31,\cdot)\)	1061.h	106	yes	\(1\)	\(1\)	\(e\left(\frac{51}{106}\right)\)	\(e\left(\frac{37}{106}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{47}{106}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{93}{106}\right)\)	\(e\left(\frac{34}{53}\right)\)
\(\chi_{1061}(32,\cdot)\)	1061.i	212	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{212}\right)\)	\(e\left(\frac{167}{212}\right)\)	\(e\left(\frac{1}{106}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{3}{212}\right)\)	\(e\left(\frac{61}{106}\right)\)	\(e\left(\frac{33}{212}\right)\)	\(e\left(\frac{89}{106}\right)\)

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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.