LMFDB - Group of Dirichlet characters of modulus 9016

Show commands: PariGP / SageMath

sage: H = DirichletGroup(9016)

pari: g = idealstar(,9016,2)

Character group

sage: G.order() pari: g.no
Order	=	3696
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{462}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{9016}(2255,\cdot)$, $\chi_{9016}(4509,\cdot)$, $\chi_{9016}(1473,\cdot)$, $\chi_{9016}(1569,\cdot)$

First 32 of 3696 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$25$	$27$
$\chi_{9016}(1,\cdot)$	9016.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9016}(3,\cdot)$	9016.er	462	yes	$1$	$1$	$e\left(\frac{305}{462}\right)$	$e\left(\frac{212}{231}\right)$	$e\left(\frac{74}{231}\right)$	$e\left(\frac{115}{231}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{317}{462}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{193}{231}\right)$	$e\left(\frac{151}{154}\right)$
$\chi_{9016}(5,\cdot)$	9016.en	462	yes	$1$	$1$	$e\left(\frac{212}{231}\right)$	$e\left(\frac{263}{462}\right)$	$e\left(\frac{193}{231}\right)$	$e\left(\frac{122}{231}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{134}{231}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{32}{231}\right)$	$e\left(\frac{58}{77}\right)$
$\chi_{9016}(9,\cdot)$	9016.ei	231	no	$1$	$1$	$e\left(\frac{74}{231}\right)$	$e\left(\frac{193}{231}\right)$	$e\left(\frac{148}{231}\right)$	$e\left(\frac{230}{231}\right)$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{86}{231}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{155}{231}\right)$	$e\left(\frac{74}{77}\right)$
$\chi_{9016}(11,\cdot)$	9016.ek	462	yes	$1$	$1$	$e\left(\frac{115}{231}\right)$	$e\left(\frac{122}{231}\right)$	$e\left(\frac{230}{231}\right)$	$e\left(\frac{359}{462}\right)$	$e\left(\frac{101}{154}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{311}{462}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{38}{77}\right)$
$\chi_{9016}(13,\cdot)$	9016.eg	154	yes	$-1$	$1$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{101}{154}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{31}{77}\right)$
$\chi_{9016}(15,\cdot)$	9016.dw	154	no	$1$	$1$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{113}{154}\right)$
$\chi_{9016}(17,\cdot)$	9016.es	462	no	$1$	$1$	$e\left(\frac{317}{462}\right)$	$e\left(\frac{134}{231}\right)$	$e\left(\frac{86}{231}\right)$	$e\left(\frac{311}{462}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{25}{231}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{37}{231}\right)$	$e\left(\frac{9}{154}\right)$
$\chi_{9016}(19,\cdot)$	9016.dd	66	no	$-1$	$1$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{9016}(25,\cdot)$	9016.ei	231	no	$1$	$1$	$e\left(\frac{193}{231}\right)$	$e\left(\frac{32}{231}\right)$	$e\left(\frac{155}{231}\right)$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{37}{231}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{64}{231}\right)$	$e\left(\frac{39}{77}\right)$
$\chi_{9016}(27,\cdot)$	9016.ea	154	yes	$1$	$1$	$e\left(\frac{151}{154}\right)$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{113}{154}\right)$	$e\left(\frac{9}{154}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{145}{154}\right)$
$\chi_{9016}(29,\cdot)$	9016.dt	154	yes	$1$	$1$	$e\left(\frac{3}{154}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{9}{154}\right)$
$\chi_{9016}(31,\cdot)$	9016.dm	66	no	$1$	$1$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{9016}(33,\cdot)$	9016.es	462	no	$1$	$1$	$e\left(\frac{73}{462}\right)$	$e\left(\frac{103}{231}\right)$	$e\left(\frac{73}{231}\right)$	$e\left(\frac{127}{462}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{83}{231}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{206}{231}\right)$	$e\left(\frac{73}{154}\right)$
$\chi_{9016}(37,\cdot)$	9016.eq	462	yes	$-1$	$1$	$e\left(\frac{247}{462}\right)$	$e\left(\frac{127}{231}\right)$	$e\left(\frac{16}{231}\right)$	$e\left(\frac{131}{231}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{13}{154}\right)$	$e\left(\frac{337}{462}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{23}{231}\right)$	$e\left(\frac{93}{154}\right)$
$\chi_{9016}(39,\cdot)$	9016.et	462	no	$-1$	$1$	$e\left(\frac{59}{462}\right)$	$e\left(\frac{194}{231}\right)$	$e\left(\frac{59}{231}\right)$	$e\left(\frac{71}{462}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{149}{154}\right)$	$e\left(\frac{181}{231}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{157}{231}\right)$	$e\left(\frac{59}{154}\right)$
$\chi_{9016}(41,\cdot)$	9016.dv	154	no	$-1$	$1$	$e\left(\frac{13}{154}\right)$	$e\left(\frac{139}{154}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{39}{154}\right)$
$\chi_{9016}(43,\cdot)$	9016.ef	154	yes	$1$	$1$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{117}{154}\right)$	$e\left(\frac{61}{154}\right)$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{26}{77}\right)$
$\chi_{9016}(45,\cdot)$	9016.cy	42	yes	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{9016}(47,\cdot)$	9016.cx	42	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{9016}(51,\cdot)$	9016.ek	462	yes	$1$	$1$	$e\left(\frac{80}{231}\right)$	$e\left(\frac{115}{231}\right)$	$e\left(\frac{160}{231}\right)$	$e\left(\frac{79}{462}\right)$	$e\left(\frac{87}{154}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{367}{462}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{230}{231}\right)$	$e\left(\frac{3}{77}\right)$
$\chi_{9016}(53,\cdot)$	9016.eq	462	yes	$-1$	$1$	$e\left(\frac{257}{462}\right)$	$e\left(\frac{62}{231}\right)$	$e\left(\frac{26}{231}\right)$	$e\left(\frac{184}{231}\right)$	$e\left(\frac{69}{154}\right)$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{461}{462}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{124}{231}\right)$	$e\left(\frac{103}{154}\right)$
$\chi_{9016}(55,\cdot)$	9016.eb	154	no	$1$	$1$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{47}{154}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{79}{154}\right)$	$e\left(\frac{39}{154}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{19}{77}\right)$
$\chi_{9016}(57,\cdot)$	9016.ec	154	no	$-1$	$1$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{149}{154}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{103}{154}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{16}{77}\right)$
$\chi_{9016}(59,\cdot)$	9016.er	462	yes	$1$	$1$	$e\left(\frac{227}{462}\right)$	$e\left(\frac{26}{231}\right)$	$e\left(\frac{227}{231}\right)$	$e\left(\frac{25}{231}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{89}{462}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{52}{231}\right)$	$e\left(\frac{73}{154}\right)$
$\chi_{9016}(61,\cdot)$	9016.en	462	yes	$1$	$1$	$e\left(\frac{29}{231}\right)$	$e\left(\frac{401}{462}\right)$	$e\left(\frac{58}{231}\right)$	$e\left(\frac{215}{231}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{153}{154}\right)$	$e\left(\frac{221}{231}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{170}{231}\right)$	$e\left(\frac{29}{77}\right)$
$\chi_{9016}(65,\cdot)$	9016.ep	462	no	$-1$	$1$	$e\left(\frac{89}{231}\right)$	$e\left(\frac{227}{462}\right)$	$e\left(\frac{178}{231}\right)$	$e\left(\frac{85}{462}\right)$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{135}{154}\right)$	$e\left(\frac{313}{462}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{227}{231}\right)$	$e\left(\frac{12}{77}\right)$
$\chi_{9016}(67,\cdot)$	9016.dq	66	no	$1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{9016}(71,\cdot)$	9016.dy	154	no	$-1$	$1$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{27}{154}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{29}{154}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{89}{154}\right)$
$\chi_{9016}(73,\cdot)$	9016.eu	462	no	$-1$	$1$	$e\left(\frac{365}{462}\right)$	$e\left(\frac{337}{462}\right)$	$e\left(\frac{134}{231}\right)$	$e\left(\frac{202}{231}\right)$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{137}{462}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{106}{231}\right)$	$e\left(\frac{57}{154}\right)$
$\chi_{9016}(75,\cdot)$	9016.er	462	yes	$1$	$1$	$e\left(\frac{229}{462}\right)$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{229}{231}\right)$	$e\left(\frac{128}{231}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{391}{462}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{26}{231}\right)$	$e\left(\frac{75}{154}\right)$
$\chi_{9016}(79,\cdot)$	9016.df	66	no	$1$	$1$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{1}{22}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$9016$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{462}\)
Order	$3696$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(25\)	\(27\)
\(\chi_{9016}(1,\cdot)\)	9016.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9016}(3,\cdot)\)	9016.er	462	yes	\(1\)	\(1\)	\(e\left(\frac{305}{462}\right)\)	\(e\left(\frac{212}{231}\right)\)	\(e\left(\frac{74}{231}\right)\)	\(e\left(\frac{115}{231}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{317}{462}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{193}{231}\right)\)	\(e\left(\frac{151}{154}\right)\)
\(\chi_{9016}(5,\cdot)\)	9016.en	462	yes	\(1\)	\(1\)	\(e\left(\frac{212}{231}\right)\)	\(e\left(\frac{263}{462}\right)\)	\(e\left(\frac{193}{231}\right)\)	\(e\left(\frac{122}{231}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{134}{231}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{32}{231}\right)\)	\(e\left(\frac{58}{77}\right)\)
\(\chi_{9016}(9,\cdot)\)	9016.ei	231	no	\(1\)	\(1\)	\(e\left(\frac{74}{231}\right)\)	\(e\left(\frac{193}{231}\right)\)	\(e\left(\frac{148}{231}\right)\)	\(e\left(\frac{230}{231}\right)\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{86}{231}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{155}{231}\right)\)	\(e\left(\frac{74}{77}\right)\)
\(\chi_{9016}(11,\cdot)\)	9016.ek	462	yes	\(1\)	\(1\)	\(e\left(\frac{115}{231}\right)\)	\(e\left(\frac{122}{231}\right)\)	\(e\left(\frac{230}{231}\right)\)	\(e\left(\frac{359}{462}\right)\)	\(e\left(\frac{101}{154}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{311}{462}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{38}{77}\right)\)
\(\chi_{9016}(13,\cdot)\)	9016.eg	154	yes	\(-1\)	\(1\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{101}{154}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)
\(\chi_{9016}(15,\cdot)\)	9016.dw	154	no	\(1\)	\(1\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{113}{154}\right)\)
\(\chi_{9016}(17,\cdot)\)	9016.es	462	no	\(1\)	\(1\)	\(e\left(\frac{317}{462}\right)\)	\(e\left(\frac{134}{231}\right)\)	\(e\left(\frac{86}{231}\right)\)	\(e\left(\frac{311}{462}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{25}{231}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{37}{231}\right)\)	\(e\left(\frac{9}{154}\right)\)
\(\chi_{9016}(19,\cdot)\)	9016.dd	66	no	\(-1\)	\(1\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{9016}(25,\cdot)\)	9016.ei	231	no	\(1\)	\(1\)	\(e\left(\frac{193}{231}\right)\)	\(e\left(\frac{32}{231}\right)\)	\(e\left(\frac{155}{231}\right)\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{37}{231}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{64}{231}\right)\)	\(e\left(\frac{39}{77}\right)\)
\(\chi_{9016}(27,\cdot)\)	9016.ea	154	yes	\(1\)	\(1\)	\(e\left(\frac{151}{154}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{113}{154}\right)\)	\(e\left(\frac{9}{154}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{145}{154}\right)\)
\(\chi_{9016}(29,\cdot)\)	9016.dt	154	yes	\(1\)	\(1\)	\(e\left(\frac{3}{154}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{9}{154}\right)\)
\(\chi_{9016}(31,\cdot)\)	9016.dm	66	no	\(1\)	\(1\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{9016}(33,\cdot)\)	9016.es	462	no	\(1\)	\(1\)	\(e\left(\frac{73}{462}\right)\)	\(e\left(\frac{103}{231}\right)\)	\(e\left(\frac{73}{231}\right)\)	\(e\left(\frac{127}{462}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{83}{231}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{206}{231}\right)\)	\(e\left(\frac{73}{154}\right)\)
\(\chi_{9016}(37,\cdot)\)	9016.eq	462	yes	\(-1\)	\(1\)	\(e\left(\frac{247}{462}\right)\)	\(e\left(\frac{127}{231}\right)\)	\(e\left(\frac{16}{231}\right)\)	\(e\left(\frac{131}{231}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{13}{154}\right)\)	\(e\left(\frac{337}{462}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{23}{231}\right)\)	\(e\left(\frac{93}{154}\right)\)
\(\chi_{9016}(39,\cdot)\)	9016.et	462	no	\(-1\)	\(1\)	\(e\left(\frac{59}{462}\right)\)	\(e\left(\frac{194}{231}\right)\)	\(e\left(\frac{59}{231}\right)\)	\(e\left(\frac{71}{462}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{149}{154}\right)\)	\(e\left(\frac{181}{231}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{157}{231}\right)\)	\(e\left(\frac{59}{154}\right)\)
\(\chi_{9016}(41,\cdot)\)	9016.dv	154	no	\(-1\)	\(1\)	\(e\left(\frac{13}{154}\right)\)	\(e\left(\frac{139}{154}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{39}{154}\right)\)
\(\chi_{9016}(43,\cdot)\)	9016.ef	154	yes	\(1\)	\(1\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{117}{154}\right)\)	\(e\left(\frac{61}{154}\right)\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{26}{77}\right)\)
\(\chi_{9016}(45,\cdot)\)	9016.cy	42	yes	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{9016}(47,\cdot)\)	9016.cx	42	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{9016}(51,\cdot)\)	9016.ek	462	yes	\(1\)	\(1\)	\(e\left(\frac{80}{231}\right)\)	\(e\left(\frac{115}{231}\right)\)	\(e\left(\frac{160}{231}\right)\)	\(e\left(\frac{79}{462}\right)\)	\(e\left(\frac{87}{154}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{367}{462}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{230}{231}\right)\)	\(e\left(\frac{3}{77}\right)\)
\(\chi_{9016}(53,\cdot)\)	9016.eq	462	yes	\(-1\)	\(1\)	\(e\left(\frac{257}{462}\right)\)	\(e\left(\frac{62}{231}\right)\)	\(e\left(\frac{26}{231}\right)\)	\(e\left(\frac{184}{231}\right)\)	\(e\left(\frac{69}{154}\right)\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{461}{462}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{124}{231}\right)\)	\(e\left(\frac{103}{154}\right)\)
\(\chi_{9016}(55,\cdot)\)	9016.eb	154	no	\(1\)	\(1\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{47}{154}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{79}{154}\right)\)	\(e\left(\frac{39}{154}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)
\(\chi_{9016}(57,\cdot)\)	9016.ec	154	no	\(-1\)	\(1\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{149}{154}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{103}{154}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{16}{77}\right)\)
\(\chi_{9016}(59,\cdot)\)	9016.er	462	yes	\(1\)	\(1\)	\(e\left(\frac{227}{462}\right)\)	\(e\left(\frac{26}{231}\right)\)	\(e\left(\frac{227}{231}\right)\)	\(e\left(\frac{25}{231}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{89}{462}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{52}{231}\right)\)	\(e\left(\frac{73}{154}\right)\)
\(\chi_{9016}(61,\cdot)\)	9016.en	462	yes	\(1\)	\(1\)	\(e\left(\frac{29}{231}\right)\)	\(e\left(\frac{401}{462}\right)\)	\(e\left(\frac{58}{231}\right)\)	\(e\left(\frac{215}{231}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{153}{154}\right)\)	\(e\left(\frac{221}{231}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{170}{231}\right)\)	\(e\left(\frac{29}{77}\right)\)
\(\chi_{9016}(65,\cdot)\)	9016.ep	462	no	\(-1\)	\(1\)	\(e\left(\frac{89}{231}\right)\)	\(e\left(\frac{227}{462}\right)\)	\(e\left(\frac{178}{231}\right)\)	\(e\left(\frac{85}{462}\right)\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{135}{154}\right)\)	\(e\left(\frac{313}{462}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{227}{231}\right)\)	\(e\left(\frac{12}{77}\right)\)
\(\chi_{9016}(67,\cdot)\)	9016.dq	66	no	\(1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{9016}(71,\cdot)\)	9016.dy	154	no	\(-1\)	\(1\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{27}{154}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{29}{154}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{89}{154}\right)\)
\(\chi_{9016}(73,\cdot)\)	9016.eu	462	no	\(-1\)	\(1\)	\(e\left(\frac{365}{462}\right)\)	\(e\left(\frac{337}{462}\right)\)	\(e\left(\frac{134}{231}\right)\)	\(e\left(\frac{202}{231}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{137}{462}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{106}{231}\right)\)	\(e\left(\frac{57}{154}\right)\)
\(\chi_{9016}(75,\cdot)\)	9016.er	462	yes	\(1\)	\(1\)	\(e\left(\frac{229}{462}\right)\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{229}{231}\right)\)	\(e\left(\frac{128}{231}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{391}{462}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{26}{231}\right)\)	\(e\left(\frac{75}{154}\right)\)
\(\chi_{9016}(79,\cdot)\)	9016.df	66	no	\(1\)	\(1\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)

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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.