LMFDB - Group of Dirichlet characters of modulus 4016

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4016)

pari: g = idealstar(,4016,2)

Character group

sage: G.order() pari: g.no
Order	=	2000
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{500}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4016}(2511,\cdot)$, $\chi_{4016}(3013,\cdot)$, $\chi_{4016}(257,\cdot)$

First 32 of 2000 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{4016}(1,\cdot)$	4016.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4016}(3,\cdot)$	4016.bt	500	yes	$-1$	$1$	$e\left(\frac{387}{500}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{109}{125}\right)$	$e\left(\frac{137}{250}\right)$	$e\left(\frac{377}{500}\right)$	$e\left(\frac{449}{500}\right)$	$e\left(\frac{211}{250}\right)$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{91}{500}\right)$	$e\left(\frac{323}{500}\right)$
$\chi_{4016}(5,\cdot)$	4016.bg	100	yes	$1$	$1$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{53}{100}\right)$
$\chi_{4016}(7,\cdot)$	4016.bp	250	no	$-1$	$1$	$e\left(\frac{109}{125}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{129}{250}\right)$	$e\left(\frac{93}{125}\right)$	$e\left(\frac{39}{125}\right)$	$e\left(\frac{11}{250}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{87}{125}\right)$	$e\left(\frac{97}{250}\right)$
$\chi_{4016}(9,\cdot)$	4016.bq	250	no	$1$	$1$	$e\left(\frac{137}{250}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{93}{125}\right)$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{127}{250}\right)$	$e\left(\frac{199}{250}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{91}{250}\right)$	$e\left(\frac{73}{250}\right)$
$\chi_{4016}(11,\cdot)$	4016.bv	500	yes	$1$	$1$	$e\left(\frac{377}{500}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{39}{125}\right)$	$e\left(\frac{127}{250}\right)$	$e\left(\frac{417}{500}\right)$	$e\left(\frac{179}{500}\right)$	$e\left(\frac{181}{250}\right)$	$e\left(\frac{57}{125}\right)$	$e\left(\frac{411}{500}\right)$	$e\left(\frac{33}{500}\right)$
$\chi_{4016}(13,\cdot)$	4016.bu	500	yes	$1$	$1$	$e\left(\frac{449}{500}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{11}{250}\right)$	$e\left(\frac{199}{250}\right)$	$e\left(\frac{179}{500}\right)$	$e\left(\frac{373}{500}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{109}{125}\right)$	$e\left(\frac{457}{500}\right)$	$e\left(\frac{471}{500}\right)$
$\chi_{4016}(15,\cdot)$	4016.bn	250	no	$-1$	$1$	$e\left(\frac{211}{250}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{181}{250}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{191}{250}\right)$	$e\left(\frac{27}{125}\right)$	$e\left(\frac{173}{250}\right)$	$e\left(\frac{22}{125}\right)$
$\chi_{4016}(17,\cdot)$	4016.bk	125	no	$1$	$1$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{57}{125}\right)$	$e\left(\frac{109}{125}\right)$	$e\left(\frac{27}{125}\right)$	$e\left(\frac{113}{125}\right)$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{18}{125}\right)$
$\chi_{4016}(19,\cdot)$	4016.bv	500	yes	$1$	$1$	$e\left(\frac{91}{500}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{87}{125}\right)$	$e\left(\frac{91}{250}\right)$	$e\left(\frac{411}{500}\right)$	$e\left(\frac{457}{500}\right)$	$e\left(\frac{173}{250}\right)$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{13}{500}\right)$	$e\left(\frac{439}{500}\right)$
$\chi_{4016}(21,\cdot)$	4016.bu	500	yes	$1$	$1$	$e\left(\frac{323}{500}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{97}{250}\right)$	$e\left(\frac{73}{250}\right)$	$e\left(\frac{33}{500}\right)$	$e\left(\frac{471}{500}\right)$	$e\left(\frac{22}{125}\right)$	$e\left(\frac{18}{125}\right)$	$e\left(\frac{439}{500}\right)$	$e\left(\frac{17}{500}\right)$
$\chi_{4016}(23,\cdot)$	4016.bp	250	no	$-1$	$1$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{77}{250}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{32}{125}\right)$	$e\left(\frac{243}{250}\right)$	$e\left(\frac{129}{250}\right)$	$e\left(\frac{13}{125}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{211}{250}\right)$
$\chi_{4016}(25,\cdot)$	4016.bd	50	no	$1$	$1$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{3}{50}\right)$
$\chi_{4016}(27,\cdot)$	4016.bt	500	yes	$-1$	$1$	$e\left(\frac{161}{500}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{77}{125}\right)$	$e\left(\frac{161}{250}\right)$	$e\left(\frac{131}{500}\right)$	$e\left(\frac{347}{500}\right)$	$e\left(\frac{133}{250}\right)$	$e\left(\frac{26}{125}\right)$	$e\left(\frac{273}{500}\right)$	$e\left(\frac{469}{500}\right)$
$\chi_{4016}(29,\cdot)$	4016.bs	500	yes	$-1$	$1$	$e\left(\frac{281}{500}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{209}{250}\right)$	$e\left(\frac{31}{250}\right)$	$e\left(\frac{401}{500}\right)$	$e\left(\frac{337}{500}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{71}{125}\right)$	$e\left(\frac{183}{500}\right)$	$e\left(\frac{199}{500}\right)$
$\chi_{4016}(31,\cdot)$	4016.bn	250	no	$-1$	$1$	$e\left(\frac{101}{250}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{3}{250}\right)$	$e\left(\frac{101}{125}\right)$	$e\left(\frac{121}{250}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{31}{250}\right)$	$e\left(\frac{7}{125}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{52}{125}\right)$
$\chi_{4016}(33,\cdot)$	4016.bl	250	no	$-1$	$1$	$e\left(\frac{66}{125}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{7}{125}\right)$	$e\left(\frac{147}{250}\right)$	$e\left(\frac{32}{125}\right)$	$e\left(\frac{71}{125}\right)$	$e\left(\frac{24}{125}\right)$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{89}{125}\right)$
$\chi_{4016}(35,\cdot)$	4016.bt	500	yes	$-1$	$1$	$e\left(\frac{471}{500}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{122}{125}\right)$	$e\left(\frac{221}{250}\right)$	$e\left(\frac{141}{500}\right)$	$e\left(\frac{217}{500}\right)$	$e\left(\frac{63}{250}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{103}{500}\right)$	$e\left(\frac{459}{500}\right)$
$\chi_{4016}(37,\cdot)$	4016.bs	500	yes	$-1$	$1$	$e\left(\frac{499}{500}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{211}{250}\right)$	$e\left(\frac{249}{250}\right)$	$e\left(\frac{479}{500}\right)$	$e\left(\frac{223}{500}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{34}{125}\right)$	$e\left(\frac{357}{500}\right)$	$e\left(\frac{421}{500}\right)$
$\chi_{4016}(39,\cdot)$	4016.bp	250	no	$-1$	$1$	$e\left(\frac{84}{125}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{229}{250}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{161}{250}\right)$	$e\left(\frac{33}{250}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{147}{250}\right)$
$\chi_{4016}(41,\cdot)$	4016.bq	250	no	$1$	$1$	$e\left(\frac{189}{250}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{121}{125}\right)$	$e\left(\frac{64}{125}\right)$	$e\left(\frac{219}{250}\right)$	$e\left(\frac{103}{250}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{27}{250}\right)$	$e\left(\frac{181}{250}\right)$
$\chi_{4016}(43,\cdot)$	4016.bv	500	yes	$1$	$1$	$e\left(\frac{29}{500}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{3}{125}\right)$	$e\left(\frac{29}{250}\right)$	$e\left(\frac{109}{500}\right)$	$e\left(\frac{283}{500}\right)$	$e\left(\frac{187}{250}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{147}{500}\right)$	$e\left(\frac{41}{500}\right)$
$\chi_{4016}(45,\cdot)$	4016.bu	500	yes	$1$	$1$	$e\left(\frac{309}{500}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{51}{250}\right)$	$e\left(\frac{59}{250}\right)$	$e\left(\frac{239}{500}\right)$	$e\left(\frac{93}{500}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{119}{125}\right)$	$e\left(\frac{437}{500}\right)$	$e\left(\frac{411}{500}\right)$
$\chi_{4016}(47,\cdot)$	4016.z	50	no	$1$	$1$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{9}{25}\right)$
$\chi_{4016}(49,\cdot)$	4016.bk	125	no	$1$	$1$	$e\left(\frac{93}{125}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{4}{125}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{11}{125}\right)$	$e\left(\frac{83}{125}\right)$	$e\left(\frac{102}{125}\right)$	$e\left(\frac{49}{125}\right)$	$e\left(\frac{97}{125}\right)$
$\chi_{4016}(51,\cdot)$	4016.bj	100	yes	$-1$	$1$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{79}{100}\right)$
$\chi_{4016}(53,\cdot)$	4016.bs	500	yes	$-1$	$1$	$e\left(\frac{171}{500}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{169}{250}\right)$	$e\left(\frac{171}{250}\right)$	$e\left(\frac{91}{500}\right)$	$e\left(\frac{367}{500}\right)$	$e\left(\frac{19}{125}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{453}{500}\right)$	$e\left(\frac{9}{500}\right)$
$\chi_{4016}(55,\cdot)$	4016.bo	250	no	$1$	$1$	$e\left(\frac{103}{125}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{201}{250}\right)$	$e\left(\frac{187}{250}\right)$	$e\left(\frac{161}{250}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{149}{250}\right)$
$\chi_{4016}(57,\cdot)$	4016.br	250	no	$-1$	$1$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{71}{125}\right)$	$e\left(\frac{114}{125}\right)$	$e\left(\frac{72}{125}\right)$	$e\left(\frac{203}{250}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{26}{125}\right)$	$e\left(\frac{131}{250}\right)$
$\chi_{4016}(59,\cdot)$	4016.bv	500	yes	$1$	$1$	$e\left(\frac{257}{500}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{74}{125}\right)$	$e\left(\frac{7}{250}\right)$	$e\left(\frac{397}{500}\right)$	$e\left(\frac{439}{500}\right)$	$e\left(\frac{71}{250}\right)$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{251}{500}\right)$	$e\left(\frac{53}{500}\right)$
$\chi_{4016}(61,\cdot)$	4016.bs	500	yes	$-1$	$1$	$e\left(\frac{21}{500}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{69}{250}\right)$	$e\left(\frac{21}{250}\right)$	$e\left(\frac{441}{500}\right)$	$e\left(\frac{317}{500}\right)$	$e\left(\frac{44}{125}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{3}{500}\right)$	$e\left(\frac{159}{500}\right)$
$\chi_{4016}(63,\cdot)$	4016.bb	50	no	$-1$	$1$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{17}{25}\right)$

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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	$4016$
Structure	\(C_{2}\times C_{2}\times C_{500}\)
Order	$2000$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{4016}(1,\cdot)\)	4016.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4016}(3,\cdot)\)	4016.bt	500	yes	\(-1\)	\(1\)	\(e\left(\frac{387}{500}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{109}{125}\right)\)	\(e\left(\frac{137}{250}\right)\)	\(e\left(\frac{377}{500}\right)\)	\(e\left(\frac{449}{500}\right)\)	\(e\left(\frac{211}{250}\right)\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{91}{500}\right)\)	\(e\left(\frac{323}{500}\right)\)
\(\chi_{4016}(5,\cdot)\)	4016.bg	100	yes	\(1\)	\(1\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)
\(\chi_{4016}(7,\cdot)\)	4016.bp	250	no	\(-1\)	\(1\)	\(e\left(\frac{109}{125}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{129}{250}\right)\)	\(e\left(\frac{93}{125}\right)\)	\(e\left(\frac{39}{125}\right)\)	\(e\left(\frac{11}{250}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{87}{125}\right)\)	\(e\left(\frac{97}{250}\right)\)
\(\chi_{4016}(9,\cdot)\)	4016.bq	250	no	\(1\)	\(1\)	\(e\left(\frac{137}{250}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{93}{125}\right)\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{127}{250}\right)\)	\(e\left(\frac{199}{250}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{91}{250}\right)\)	\(e\left(\frac{73}{250}\right)\)
\(\chi_{4016}(11,\cdot)\)	4016.bv	500	yes	\(1\)	\(1\)	\(e\left(\frac{377}{500}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{39}{125}\right)\)	\(e\left(\frac{127}{250}\right)\)	\(e\left(\frac{417}{500}\right)\)	\(e\left(\frac{179}{500}\right)\)	\(e\left(\frac{181}{250}\right)\)	\(e\left(\frac{57}{125}\right)\)	\(e\left(\frac{411}{500}\right)\)	\(e\left(\frac{33}{500}\right)\)
\(\chi_{4016}(13,\cdot)\)	4016.bu	500	yes	\(1\)	\(1\)	\(e\left(\frac{449}{500}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{11}{250}\right)\)	\(e\left(\frac{199}{250}\right)\)	\(e\left(\frac{179}{500}\right)\)	\(e\left(\frac{373}{500}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{109}{125}\right)\)	\(e\left(\frac{457}{500}\right)\)	\(e\left(\frac{471}{500}\right)\)
\(\chi_{4016}(15,\cdot)\)	4016.bn	250	no	\(-1\)	\(1\)	\(e\left(\frac{211}{250}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{181}{250}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{191}{250}\right)\)	\(e\left(\frac{27}{125}\right)\)	\(e\left(\frac{173}{250}\right)\)	\(e\left(\frac{22}{125}\right)\)
\(\chi_{4016}(17,\cdot)\)	4016.bk	125	no	\(1\)	\(1\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{57}{125}\right)\)	\(e\left(\frac{109}{125}\right)\)	\(e\left(\frac{27}{125}\right)\)	\(e\left(\frac{113}{125}\right)\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{18}{125}\right)\)
\(\chi_{4016}(19,\cdot)\)	4016.bv	500	yes	\(1\)	\(1\)	\(e\left(\frac{91}{500}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{87}{125}\right)\)	\(e\left(\frac{91}{250}\right)\)	\(e\left(\frac{411}{500}\right)\)	\(e\left(\frac{457}{500}\right)\)	\(e\left(\frac{173}{250}\right)\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{13}{500}\right)\)	\(e\left(\frac{439}{500}\right)\)
\(\chi_{4016}(21,\cdot)\)	4016.bu	500	yes	\(1\)	\(1\)	\(e\left(\frac{323}{500}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{97}{250}\right)\)	\(e\left(\frac{73}{250}\right)\)	\(e\left(\frac{33}{500}\right)\)	\(e\left(\frac{471}{500}\right)\)	\(e\left(\frac{22}{125}\right)\)	\(e\left(\frac{18}{125}\right)\)	\(e\left(\frac{439}{500}\right)\)	\(e\left(\frac{17}{500}\right)\)
\(\chi_{4016}(23,\cdot)\)	4016.bp	250	no	\(-1\)	\(1\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{77}{250}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{32}{125}\right)\)	\(e\left(\frac{243}{250}\right)\)	\(e\left(\frac{129}{250}\right)\)	\(e\left(\frac{13}{125}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{211}{250}\right)\)
\(\chi_{4016}(25,\cdot)\)	4016.bd	50	no	\(1\)	\(1\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{3}{50}\right)\)
\(\chi_{4016}(27,\cdot)\)	4016.bt	500	yes	\(-1\)	\(1\)	\(e\left(\frac{161}{500}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{77}{125}\right)\)	\(e\left(\frac{161}{250}\right)\)	\(e\left(\frac{131}{500}\right)\)	\(e\left(\frac{347}{500}\right)\)	\(e\left(\frac{133}{250}\right)\)	\(e\left(\frac{26}{125}\right)\)	\(e\left(\frac{273}{500}\right)\)	\(e\left(\frac{469}{500}\right)\)
\(\chi_{4016}(29,\cdot)\)	4016.bs	500	yes	\(-1\)	\(1\)	\(e\left(\frac{281}{500}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{209}{250}\right)\)	\(e\left(\frac{31}{250}\right)\)	\(e\left(\frac{401}{500}\right)\)	\(e\left(\frac{337}{500}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{71}{125}\right)\)	\(e\left(\frac{183}{500}\right)\)	\(e\left(\frac{199}{500}\right)\)
\(\chi_{4016}(31,\cdot)\)	4016.bn	250	no	\(-1\)	\(1\)	\(e\left(\frac{101}{250}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{3}{250}\right)\)	\(e\left(\frac{101}{125}\right)\)	\(e\left(\frac{121}{250}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{31}{250}\right)\)	\(e\left(\frac{7}{125}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{52}{125}\right)\)
\(\chi_{4016}(33,\cdot)\)	4016.bl	250	no	\(-1\)	\(1\)	\(e\left(\frac{66}{125}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{7}{125}\right)\)	\(e\left(\frac{147}{250}\right)\)	\(e\left(\frac{32}{125}\right)\)	\(e\left(\frac{71}{125}\right)\)	\(e\left(\frac{24}{125}\right)\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{89}{125}\right)\)
\(\chi_{4016}(35,\cdot)\)	4016.bt	500	yes	\(-1\)	\(1\)	\(e\left(\frac{471}{500}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{122}{125}\right)\)	\(e\left(\frac{221}{250}\right)\)	\(e\left(\frac{141}{500}\right)\)	\(e\left(\frac{217}{500}\right)\)	\(e\left(\frac{63}{250}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{103}{500}\right)\)	\(e\left(\frac{459}{500}\right)\)
\(\chi_{4016}(37,\cdot)\)	4016.bs	500	yes	\(-1\)	\(1\)	\(e\left(\frac{499}{500}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{211}{250}\right)\)	\(e\left(\frac{249}{250}\right)\)	\(e\left(\frac{479}{500}\right)\)	\(e\left(\frac{223}{500}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{34}{125}\right)\)	\(e\left(\frac{357}{500}\right)\)	\(e\left(\frac{421}{500}\right)\)
\(\chi_{4016}(39,\cdot)\)	4016.bp	250	no	\(-1\)	\(1\)	\(e\left(\frac{84}{125}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{229}{250}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{161}{250}\right)\)	\(e\left(\frac{33}{250}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{147}{250}\right)\)
\(\chi_{4016}(41,\cdot)\)	4016.bq	250	no	\(1\)	\(1\)	\(e\left(\frac{189}{250}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{121}{125}\right)\)	\(e\left(\frac{64}{125}\right)\)	\(e\left(\frac{219}{250}\right)\)	\(e\left(\frac{103}{250}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{27}{250}\right)\)	\(e\left(\frac{181}{250}\right)\)
\(\chi_{4016}(43,\cdot)\)	4016.bv	500	yes	\(1\)	\(1\)	\(e\left(\frac{29}{500}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{3}{125}\right)\)	\(e\left(\frac{29}{250}\right)\)	\(e\left(\frac{109}{500}\right)\)	\(e\left(\frac{283}{500}\right)\)	\(e\left(\frac{187}{250}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{147}{500}\right)\)	\(e\left(\frac{41}{500}\right)\)
\(\chi_{4016}(45,\cdot)\)	4016.bu	500	yes	\(1\)	\(1\)	\(e\left(\frac{309}{500}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{51}{250}\right)\)	\(e\left(\frac{59}{250}\right)\)	\(e\left(\frac{239}{500}\right)\)	\(e\left(\frac{93}{500}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{119}{125}\right)\)	\(e\left(\frac{437}{500}\right)\)	\(e\left(\frac{411}{500}\right)\)
\(\chi_{4016}(47,\cdot)\)	4016.z	50	no	\(1\)	\(1\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)
\(\chi_{4016}(49,\cdot)\)	4016.bk	125	no	\(1\)	\(1\)	\(e\left(\frac{93}{125}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{4}{125}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{11}{125}\right)\)	\(e\left(\frac{83}{125}\right)\)	\(e\left(\frac{102}{125}\right)\)	\(e\left(\frac{49}{125}\right)\)	\(e\left(\frac{97}{125}\right)\)
\(\chi_{4016}(51,\cdot)\)	4016.bj	100	yes	\(-1\)	\(1\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{79}{100}\right)\)
\(\chi_{4016}(53,\cdot)\)	4016.bs	500	yes	\(-1\)	\(1\)	\(e\left(\frac{171}{500}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{169}{250}\right)\)	\(e\left(\frac{171}{250}\right)\)	\(e\left(\frac{91}{500}\right)\)	\(e\left(\frac{367}{500}\right)\)	\(e\left(\frac{19}{125}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{453}{500}\right)\)	\(e\left(\frac{9}{500}\right)\)
\(\chi_{4016}(55,\cdot)\)	4016.bo	250	no	\(1\)	\(1\)	\(e\left(\frac{103}{125}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{201}{250}\right)\)	\(e\left(\frac{187}{250}\right)\)	\(e\left(\frac{161}{250}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{149}{250}\right)\)
\(\chi_{4016}(57,\cdot)\)	4016.br	250	no	\(-1\)	\(1\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{71}{125}\right)\)	\(e\left(\frac{114}{125}\right)\)	\(e\left(\frac{72}{125}\right)\)	\(e\left(\frac{203}{250}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{26}{125}\right)\)	\(e\left(\frac{131}{250}\right)\)
\(\chi_{4016}(59,\cdot)\)	4016.bv	500	yes	\(1\)	\(1\)	\(e\left(\frac{257}{500}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{74}{125}\right)\)	\(e\left(\frac{7}{250}\right)\)	\(e\left(\frac{397}{500}\right)\)	\(e\left(\frac{439}{500}\right)\)	\(e\left(\frac{71}{250}\right)\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{251}{500}\right)\)	\(e\left(\frac{53}{500}\right)\)
\(\chi_{4016}(61,\cdot)\)	4016.bs	500	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{500}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{69}{250}\right)\)	\(e\left(\frac{21}{250}\right)\)	\(e\left(\frac{441}{500}\right)\)	\(e\left(\frac{317}{500}\right)\)	\(e\left(\frac{44}{125}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{3}{500}\right)\)	\(e\left(\frac{159}{500}\right)\)
\(\chi_{4016}(63,\cdot)\)	4016.bb	50	no	\(-1\)	\(1\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)

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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.