LMFDB - Group of Dirichlet characters of modulus 450468

Show commands: PariGP / SageMath

sage: H = DirichletGroup(450468)

pari: g = idealstar(,450468,2)

Character group

sage: G.order() pari: g.no
Order	=	145152
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{6}\times C_{2016}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{450468}(225235,\cdot)$, $\chi_{450468}(216893,\cdot)$, $\chi_{450468}(167617,\cdot)$, $\chi_{450468}(148609,\cdot)$

First 32 of 145152 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{450468}(1,\cdot)$	450468.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{450468}(5,\cdot)$	450468.des	2016	no	$-1$	$1$	$e\left(\frac{565}{2016}\right)$	$e\left(\frac{173}{288}\right)$	$e\left(\frac{367}{1008}\right)$	$e\left(\frac{1069}{2016}\right)$	$e\left(\frac{479}{672}\right)$	$e\left(\frac{109}{224}\right)$	$e\left(\frac{769}{2016}\right)$	$e\left(\frac{565}{1008}\right)$	$e\left(\frac{1649}{2016}\right)$	$e\left(\frac{275}{1008}\right)$
$\chi_{450468}(7,\cdot)$	450468.coc	288	yes	$-1$	$1$	$e\left(\frac{173}{288}\right)$	$e\left(\frac{259}{288}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{245}{288}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{137}{288}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{73}{288}\right)$	$e\left(\frac{67}{144}\right)$
$\chi_{450468}(11,\cdot)$	450468.dcu	1008	yes	$1$	$1$	$e\left(\frac{367}{1008}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{181}{504}\right)$	$e\left(\frac{31}{1008}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{101}{336}\right)$	$e\left(\frac{859}{1008}\right)$	$e\left(\frac{367}{504}\right)$	$e\left(\frac{659}{1008}\right)$	$e\left(\frac{221}{504}\right)$
$\chi_{450468}(13,\cdot)$	450468.dgc	2016	no	$-1$	$1$	$e\left(\frac{1069}{2016}\right)$	$e\left(\frac{245}{288}\right)$	$e\left(\frac{31}{1008}\right)$	$e\left(\frac{901}{2016}\right)$	$e\left(\frac{535}{672}\right)$	$e\left(\frac{607}{672}\right)$	$e\left(\frac{265}{2016}\right)$	$e\left(\frac{61}{1008}\right)$	$e\left(\frac{137}{2016}\right)$	$e\left(\frac{779}{1008}\right)$
$\chi_{450468}(17,\cdot)$	450468.cyt	672	no	$1$	$1$	$e\left(\frac{479}{672}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{535}{672}\right)$	$e\left(\frac{263}{672}\right)$	$e\left(\frac{191}{672}\right)$	$e\left(\frac{19}{672}\right)$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{659}{672}\right)$	$e\left(\frac{25}{336}\right)$
$\chi_{450468}(19,\cdot)$	450468.dbj	672	no	$-1$	$1$	$e\left(\frac{109}{224}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{101}{336}\right)$	$e\left(\frac{607}{672}\right)$	$e\left(\frac{191}{672}\right)$	$e\left(\frac{295}{672}\right)$	$e\left(\frac{9}{224}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{41}{224}\right)$	$e\left(\frac{3}{112}\right)$
$\chi_{450468}(23,\cdot)$	450468.dei	2016	yes	$-1$	$1$	$e\left(\frac{769}{2016}\right)$	$e\left(\frac{137}{288}\right)$	$e\left(\frac{859}{1008}\right)$	$e\left(\frac{265}{2016}\right)$	$e\left(\frac{19}{672}\right)$	$e\left(\frac{9}{224}\right)$	$e\left(\frac{157}{2016}\right)$	$e\left(\frac{769}{1008}\right)$	$e\left(\frac{1325}{2016}\right)$	$e\left(\frac{575}{1008}\right)$
$\chi_{450468}(25,\cdot)$	450468.ddc	1008	no	$1$	$1$	$e\left(\frac{565}{1008}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{367}{504}\right)$	$e\left(\frac{61}{1008}\right)$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{769}{1008}\right)$	$e\left(\frac{61}{504}\right)$	$e\left(\frac{641}{1008}\right)$	$e\left(\frac{275}{504}\right)$
$\chi_{450468}(29,\cdot)$	450468.dgt	2016	no	$-1$	$1$	$e\left(\frac{1649}{2016}\right)$	$e\left(\frac{73}{288}\right)$	$e\left(\frac{659}{1008}\right)$	$e\left(\frac{137}{2016}\right)$	$e\left(\frac{659}{672}\right)$	$e\left(\frac{41}{224}\right)$	$e\left(\frac{1325}{2016}\right)$	$e\left(\frac{641}{1008}\right)$	$e\left(\frac{1693}{2016}\right)$	$e\left(\frac{535}{1008}\right)$
$\chi_{450468}(31,\cdot)$	450468.dcp	1008	yes	$-1$	$1$	$e\left(\frac{275}{1008}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{221}{504}\right)$	$e\left(\frac{779}{1008}\right)$	$e\left(\frac{25}{336}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{575}{1008}\right)$	$e\left(\frac{275}{504}\right)$	$e\left(\frac{535}{1008}\right)$	$e\left(\frac{145}{504}\right)$
$\chi_{450468}(35,\cdot)$	450468.bcz	42	no	$1$	$1$	$e\left(\frac{37}{42}\right)$	$-1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{450468}(37,\cdot)$	450468.bvv	96	no	$1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{450468}(41,\cdot)$	450468.dew	2016	no	$1$	$1$	$e\left(\frac{361}{2016}\right)$	$e\left(\frac{161}{288}\right)$	$e\left(\frac{715}{1008}\right)$	$e\left(\frac{529}{2016}\right)$	$e\left(\frac{89}{224}\right)$	$e\left(\frac{515}{672}\right)$	$e\left(\frac{1717}{2016}\right)$	$e\left(\frac{361}{1008}\right)$	$e\left(\frac{629}{2016}\right)$	$e\left(\frac{479}{1008}\right)$
$\chi_{450468}(47,\cdot)$	450468.cwg	504	yes	$1$	$1$	$e\left(\frac{485}{504}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{95}{252}\right)$	$e\left(\frac{65}{504}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{79}{168}\right)$	$e\left(\frac{365}{504}\right)$	$e\left(\frac{233}{252}\right)$	$e\left(\frac{241}{504}\right)$	$e\left(\frac{61}{252}\right)$
$\chi_{450468}(49,\cdot)$	450468.cgi	144	no	$1$	$1$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{67}{72}\right)$
$\chi_{450468}(53,\cdot)$	450468.crl	336	no	$-1$	$1$	$e\left(\frac{187}{336}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{275}{336}\right)$	$e\left(\frac{323}{336}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{149}{168}\right)$
$\chi_{450468}(55,\cdot)$	450468.dba	672	no	$-1$	$1$	$e\left(\frac{433}{672}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{377}{672}\right)$	$e\left(\frac{281}{672}\right)$	$e\left(\frac{529}{672}\right)$	$e\left(\frac{157}{672}\right)$	$e\left(\frac{97}{336}\right)$	$e\left(\frac{317}{672}\right)$	$e\left(\frac{239}{336}\right)$
$\chi_{450468}(59,\cdot)$	450468.dft	2016	yes	$-1$	$1$	$e\left(\frac{751}{2016}\right)$	$e\left(\frac{167}{288}\right)$	$e\left(\frac{277}{1008}\right)$	$e\left(\frac{1927}{2016}\right)$	$e\left(\frac{223}{224}\right)$	$e\left(\frac{149}{672}\right)$	$e\left(\frac{883}{2016}\right)$	$e\left(\frac{751}{1008}\right)$	$e\left(\frac{1571}{2016}\right)$	$e\left(\frac{593}{1008}\right)$
$\chi_{450468}(61,\cdot)$	450468.ccv	126	no	$-1$	$1$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{58}{63}\right)$
$\chi_{450468}(65,\cdot)$	450468.dbx	1008	no	$1$	$1$	$e\left(\frac{817}{1008}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{199}{504}\right)$	$e\left(\frac{985}{1008}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{517}{1008}\right)$	$e\left(\frac{313}{504}\right)$	$e\left(\frac{893}{1008}\right)$	$e\left(\frac{23}{504}\right)$
$\chi_{450468}(67,\cdot)$	450468.dfh	2016	yes	$1$	$1$	$e\left(\frac{1261}{2016}\right)$	$e\left(\frac{101}{288}\right)$	$e\left(\frac{919}{1008}\right)$	$e\left(\frac{1765}{2016}\right)$	$e\left(\frac{157}{224}\right)$	$e\left(\frac{5}{224}\right)$	$e\left(\frac{697}{2016}\right)$	$e\left(\frac{253}{1008}\right)$	$e\left(\frac{425}{2016}\right)$	$e\left(\frac{83}{1008}\right)$
$\chi_{450468}(71,\cdot)$	450468.czr	672	no	$1$	$1$	$e\left(\frac{173}{672}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{229}{672}\right)$	$e\left(\frac{149}{672}\right)$	$e\left(\frac{29}{672}\right)$	$e\left(\frac{265}{672}\right)$	$e\left(\frac{173}{336}\right)$	$e\left(\frac{137}{672}\right)$	$e\left(\frac{163}{336}\right)$
$\chi_{450468}(73,\cdot)$	450468.cjp	168	no	$-1$	$1$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{450468}(77,\cdot)$	450468.det	2016	no	$-1$	$1$	$e\left(\frac{1945}{2016}\right)$	$e\left(\frac{209}{288}\right)$	$e\left(\frac{187}{1008}\right)$	$e\left(\frac{1777}{2016}\right)$	$e\left(\frac{299}{672}\right)$	$e\left(\frac{307}{672}\right)$	$e\left(\frac{661}{2016}\right)$	$e\left(\frac{937}{1008}\right)$	$e\left(\frac{1829}{2016}\right)$	$e\left(\frac{911}{1008}\right)$
$\chi_{450468}(79,\cdot)$	450468.cfq	144	yes	$-1$	$1$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{23}{72}\right)$
$\chi_{450468}(83,\cdot)$	450468.dfx	2016	yes	$-1$	$1$	$e\left(\frac{1109}{2016}\right)$	$e\left(\frac{61}{288}\right)$	$e\left(\frac{167}{1008}\right)$	$e\left(\frac{1277}{2016}\right)$	$e\left(\frac{335}{672}\right)$	$e\left(\frac{311}{672}\right)$	$e\left(\frac{257}{2016}\right)$	$e\left(\frac{101}{1008}\right)$	$e\left(\frac{1681}{2016}\right)$	$e\left(\frac{571}{1008}\right)$
$\chi_{450468}(85,\cdot)$	450468.ces	144	no	$-1$	$1$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{25}{72}\right)$
$\chi_{450468}(89,\cdot)$	450468.cup	336	no	$1$	$1$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{53}{336}\right)$	$e\left(\frac{157}{336}\right)$	$e\left(\frac{5}{336}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{1}{56}\right)$
$\chi_{450468}(91,\cdot)$	450468.bqu	84	no	$1$	$1$	$e\left(\frac{11}{84}\right)$	$-i$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{450468}(95,\cdot)$	450468.ddh	1008	yes	$1$	$1$	$e\left(\frac{773}{1008}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{335}{504}\right)$	$e\left(\frac{437}{1008}\right)$	$e\left(\frac{335}{336}\right)$	$e\left(\frac{311}{336}\right)$	$e\left(\frac{425}{1008}\right)$	$e\left(\frac{269}{504}\right)$	$e\left(\frac{1}{1008}\right)$	$e\left(\frac{151}{504}\right)$
$\chi_{450468}(101,\cdot)$	450468.cvn	504	no	$-1$	$1$	$e\left(\frac{65}{504}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{137}{252}\right)$	$e\left(\frac{317}{504}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{365}{504}\right)$	$e\left(\frac{65}{252}\right)$	$e\left(\frac{493}{504}\right)$	$e\left(\frac{103}{252}\right)$

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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	$450468$
Structure	\(C_{2}\times C_{6}\times C_{6}\times C_{2016}\)
Order	$145152$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{450468}(1,\cdot)\)	450468.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{450468}(5,\cdot)\)	450468.des	2016	no	\(-1\)	\(1\)	\(e\left(\frac{565}{2016}\right)\)	\(e\left(\frac{173}{288}\right)\)	\(e\left(\frac{367}{1008}\right)\)	\(e\left(\frac{1069}{2016}\right)\)	\(e\left(\frac{479}{672}\right)\)	\(e\left(\frac{109}{224}\right)\)	\(e\left(\frac{769}{2016}\right)\)	\(e\left(\frac{565}{1008}\right)\)	\(e\left(\frac{1649}{2016}\right)\)	\(e\left(\frac{275}{1008}\right)\)
\(\chi_{450468}(7,\cdot)\)	450468.coc	288	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{288}\right)\)	\(e\left(\frac{259}{288}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{245}{288}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{137}{288}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{73}{288}\right)\)	\(e\left(\frac{67}{144}\right)\)
\(\chi_{450468}(11,\cdot)\)	450468.dcu	1008	yes	\(1\)	\(1\)	\(e\left(\frac{367}{1008}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{181}{504}\right)\)	\(e\left(\frac{31}{1008}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{101}{336}\right)\)	\(e\left(\frac{859}{1008}\right)\)	\(e\left(\frac{367}{504}\right)\)	\(e\left(\frac{659}{1008}\right)\)	\(e\left(\frac{221}{504}\right)\)
\(\chi_{450468}(13,\cdot)\)	450468.dgc	2016	no	\(-1\)	\(1\)	\(e\left(\frac{1069}{2016}\right)\)	\(e\left(\frac{245}{288}\right)\)	\(e\left(\frac{31}{1008}\right)\)	\(e\left(\frac{901}{2016}\right)\)	\(e\left(\frac{535}{672}\right)\)	\(e\left(\frac{607}{672}\right)\)	\(e\left(\frac{265}{2016}\right)\)	\(e\left(\frac{61}{1008}\right)\)	\(e\left(\frac{137}{2016}\right)\)	\(e\left(\frac{779}{1008}\right)\)
\(\chi_{450468}(17,\cdot)\)	450468.cyt	672	no	\(1\)	\(1\)	\(e\left(\frac{479}{672}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{535}{672}\right)\)	\(e\left(\frac{263}{672}\right)\)	\(e\left(\frac{191}{672}\right)\)	\(e\left(\frac{19}{672}\right)\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{659}{672}\right)\)	\(e\left(\frac{25}{336}\right)\)
\(\chi_{450468}(19,\cdot)\)	450468.dbj	672	no	\(-1\)	\(1\)	\(e\left(\frac{109}{224}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{101}{336}\right)\)	\(e\left(\frac{607}{672}\right)\)	\(e\left(\frac{191}{672}\right)\)	\(e\left(\frac{295}{672}\right)\)	\(e\left(\frac{9}{224}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{41}{224}\right)\)	\(e\left(\frac{3}{112}\right)\)
\(\chi_{450468}(23,\cdot)\)	450468.dei	2016	yes	\(-1\)	\(1\)	\(e\left(\frac{769}{2016}\right)\)	\(e\left(\frac{137}{288}\right)\)	\(e\left(\frac{859}{1008}\right)\)	\(e\left(\frac{265}{2016}\right)\)	\(e\left(\frac{19}{672}\right)\)	\(e\left(\frac{9}{224}\right)\)	\(e\left(\frac{157}{2016}\right)\)	\(e\left(\frac{769}{1008}\right)\)	\(e\left(\frac{1325}{2016}\right)\)	\(e\left(\frac{575}{1008}\right)\)
\(\chi_{450468}(25,\cdot)\)	450468.ddc	1008	no	\(1\)	\(1\)	\(e\left(\frac{565}{1008}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{367}{504}\right)\)	\(e\left(\frac{61}{1008}\right)\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{769}{1008}\right)\)	\(e\left(\frac{61}{504}\right)\)	\(e\left(\frac{641}{1008}\right)\)	\(e\left(\frac{275}{504}\right)\)
\(\chi_{450468}(29,\cdot)\)	450468.dgt	2016	no	\(-1\)	\(1\)	\(e\left(\frac{1649}{2016}\right)\)	\(e\left(\frac{73}{288}\right)\)	\(e\left(\frac{659}{1008}\right)\)	\(e\left(\frac{137}{2016}\right)\)	\(e\left(\frac{659}{672}\right)\)	\(e\left(\frac{41}{224}\right)\)	\(e\left(\frac{1325}{2016}\right)\)	\(e\left(\frac{641}{1008}\right)\)	\(e\left(\frac{1693}{2016}\right)\)	\(e\left(\frac{535}{1008}\right)\)
\(\chi_{450468}(31,\cdot)\)	450468.dcp	1008	yes	\(-1\)	\(1\)	\(e\left(\frac{275}{1008}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{221}{504}\right)\)	\(e\left(\frac{779}{1008}\right)\)	\(e\left(\frac{25}{336}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{575}{1008}\right)\)	\(e\left(\frac{275}{504}\right)\)	\(e\left(\frac{535}{1008}\right)\)	\(e\left(\frac{145}{504}\right)\)
\(\chi_{450468}(35,\cdot)\)	450468.bcz	42	no	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(-1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{450468}(37,\cdot)\)	450468.bvv	96	no	\(1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{450468}(41,\cdot)\)	450468.dew	2016	no	\(1\)	\(1\)	\(e\left(\frac{361}{2016}\right)\)	\(e\left(\frac{161}{288}\right)\)	\(e\left(\frac{715}{1008}\right)\)	\(e\left(\frac{529}{2016}\right)\)	\(e\left(\frac{89}{224}\right)\)	\(e\left(\frac{515}{672}\right)\)	\(e\left(\frac{1717}{2016}\right)\)	\(e\left(\frac{361}{1008}\right)\)	\(e\left(\frac{629}{2016}\right)\)	\(e\left(\frac{479}{1008}\right)\)
\(\chi_{450468}(47,\cdot)\)	450468.cwg	504	yes	\(1\)	\(1\)	\(e\left(\frac{485}{504}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{95}{252}\right)\)	\(e\left(\frac{65}{504}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{79}{168}\right)\)	\(e\left(\frac{365}{504}\right)\)	\(e\left(\frac{233}{252}\right)\)	\(e\left(\frac{241}{504}\right)\)	\(e\left(\frac{61}{252}\right)\)
\(\chi_{450468}(49,\cdot)\)	450468.cgi	144	no	\(1\)	\(1\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{67}{72}\right)\)
\(\chi_{450468}(53,\cdot)\)	450468.crl	336	no	\(-1\)	\(1\)	\(e\left(\frac{187}{336}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{275}{336}\right)\)	\(e\left(\frac{323}{336}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{149}{168}\right)\)
\(\chi_{450468}(55,\cdot)\)	450468.dba	672	no	\(-1\)	\(1\)	\(e\left(\frac{433}{672}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{377}{672}\right)\)	\(e\left(\frac{281}{672}\right)\)	\(e\left(\frac{529}{672}\right)\)	\(e\left(\frac{157}{672}\right)\)	\(e\left(\frac{97}{336}\right)\)	\(e\left(\frac{317}{672}\right)\)	\(e\left(\frac{239}{336}\right)\)
\(\chi_{450468}(59,\cdot)\)	450468.dft	2016	yes	\(-1\)	\(1\)	\(e\left(\frac{751}{2016}\right)\)	\(e\left(\frac{167}{288}\right)\)	\(e\left(\frac{277}{1008}\right)\)	\(e\left(\frac{1927}{2016}\right)\)	\(e\left(\frac{223}{224}\right)\)	\(e\left(\frac{149}{672}\right)\)	\(e\left(\frac{883}{2016}\right)\)	\(e\left(\frac{751}{1008}\right)\)	\(e\left(\frac{1571}{2016}\right)\)	\(e\left(\frac{593}{1008}\right)\)
\(\chi_{450468}(61,\cdot)\)	450468.ccv	126	no	\(-1\)	\(1\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)
\(\chi_{450468}(65,\cdot)\)	450468.dbx	1008	no	\(1\)	\(1\)	\(e\left(\frac{817}{1008}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{199}{504}\right)\)	\(e\left(\frac{985}{1008}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{517}{1008}\right)\)	\(e\left(\frac{313}{504}\right)\)	\(e\left(\frac{893}{1008}\right)\)	\(e\left(\frac{23}{504}\right)\)
\(\chi_{450468}(67,\cdot)\)	450468.dfh	2016	yes	\(1\)	\(1\)	\(e\left(\frac{1261}{2016}\right)\)	\(e\left(\frac{101}{288}\right)\)	\(e\left(\frac{919}{1008}\right)\)	\(e\left(\frac{1765}{2016}\right)\)	\(e\left(\frac{157}{224}\right)\)	\(e\left(\frac{5}{224}\right)\)	\(e\left(\frac{697}{2016}\right)\)	\(e\left(\frac{253}{1008}\right)\)	\(e\left(\frac{425}{2016}\right)\)	\(e\left(\frac{83}{1008}\right)\)
\(\chi_{450468}(71,\cdot)\)	450468.czr	672	no	\(1\)	\(1\)	\(e\left(\frac{173}{672}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{229}{672}\right)\)	\(e\left(\frac{149}{672}\right)\)	\(e\left(\frac{29}{672}\right)\)	\(e\left(\frac{265}{672}\right)\)	\(e\left(\frac{173}{336}\right)\)	\(e\left(\frac{137}{672}\right)\)	\(e\left(\frac{163}{336}\right)\)
\(\chi_{450468}(73,\cdot)\)	450468.cjp	168	no	\(-1\)	\(1\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{450468}(77,\cdot)\)	450468.det	2016	no	\(-1\)	\(1\)	\(e\left(\frac{1945}{2016}\right)\)	\(e\left(\frac{209}{288}\right)\)	\(e\left(\frac{187}{1008}\right)\)	\(e\left(\frac{1777}{2016}\right)\)	\(e\left(\frac{299}{672}\right)\)	\(e\left(\frac{307}{672}\right)\)	\(e\left(\frac{661}{2016}\right)\)	\(e\left(\frac{937}{1008}\right)\)	\(e\left(\frac{1829}{2016}\right)\)	\(e\left(\frac{911}{1008}\right)\)
\(\chi_{450468}(79,\cdot)\)	450468.cfq	144	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{23}{72}\right)\)
\(\chi_{450468}(83,\cdot)\)	450468.dfx	2016	yes	\(-1\)	\(1\)	\(e\left(\frac{1109}{2016}\right)\)	\(e\left(\frac{61}{288}\right)\)	\(e\left(\frac{167}{1008}\right)\)	\(e\left(\frac{1277}{2016}\right)\)	\(e\left(\frac{335}{672}\right)\)	\(e\left(\frac{311}{672}\right)\)	\(e\left(\frac{257}{2016}\right)\)	\(e\left(\frac{101}{1008}\right)\)	\(e\left(\frac{1681}{2016}\right)\)	\(e\left(\frac{571}{1008}\right)\)
\(\chi_{450468}(85,\cdot)\)	450468.ces	144	no	\(-1\)	\(1\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{25}{72}\right)\)
\(\chi_{450468}(89,\cdot)\)	450468.cup	336	no	\(1\)	\(1\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{53}{336}\right)\)	\(e\left(\frac{157}{336}\right)\)	\(e\left(\frac{5}{336}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)
\(\chi_{450468}(91,\cdot)\)	450468.bqu	84	no	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(-i\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{450468}(95,\cdot)\)	450468.ddh	1008	yes	\(1\)	\(1\)	\(e\left(\frac{773}{1008}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{335}{504}\right)\)	\(e\left(\frac{437}{1008}\right)\)	\(e\left(\frac{335}{336}\right)\)	\(e\left(\frac{311}{336}\right)\)	\(e\left(\frac{425}{1008}\right)\)	\(e\left(\frac{269}{504}\right)\)	\(e\left(\frac{1}{1008}\right)\)	\(e\left(\frac{151}{504}\right)\)
\(\chi_{450468}(101,\cdot)\)	450468.cvn	504	no	\(-1\)	\(1\)	\(e\left(\frac{65}{504}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{137}{252}\right)\)	\(e\left(\frac{317}{504}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{365}{504}\right)\)	\(e\left(\frac{65}{252}\right)\)	\(e\left(\frac{493}{504}\right)\)	\(e\left(\frac{103}{252}\right)\)

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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.