LMFDB - Group of Dirichlet characters of modulus 114075

Show commands: PariGP / SageMath

sage: H = DirichletGroup(114075)

pari: g = idealstar(,114075,2)

Character group

sage: G.order() pari: g.no
Order	=	56160
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{12}\times C_{2340}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{114075}(105626,\cdot)$, $\chi_{114075}(9127,\cdot)$, $\chi_{114075}(113401,\cdot)$

First 32 of 56160 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$14$	$16$	$17$	$19$	$22$
$\chi_{114075}(1,\cdot)$	114075.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{114075}(2,\cdot)$	114075.yo	2340	yes	$-1$	$1$	$e\left(\frac{131}{1170}\right)$	$e\left(\frac{131}{585}\right)$	$e\left(\frac{193}{234}\right)$	$e\left(\frac{131}{390}\right)$	$e\left(\frac{427}{2340}\right)$	$e\left(\frac{548}{585}\right)$	$e\left(\frac{262}{585}\right)$	$e\left(\frac{109}{260}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{53}{180}\right)$
$\chi_{114075}(4,\cdot)$	114075.wl	1170	yes	$1$	$1$	$e\left(\frac{131}{585}\right)$	$e\left(\frac{262}{585}\right)$	$e\left(\frac{76}{117}\right)$	$e\left(\frac{131}{195}\right)$	$e\left(\frac{427}{1170}\right)$	$e\left(\frac{511}{585}\right)$	$e\left(\frac{524}{585}\right)$	$e\left(\frac{109}{130}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{114075}(7,\cdot)$	114075.tf	468	no	$1$	$1$	$e\left(\frac{193}{234}\right)$	$e\left(\frac{76}{117}\right)$	$e\left(\frac{101}{117}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{95}{468}\right)$	$e\left(\frac{161}{234}\right)$	$e\left(\frac{35}{117}\right)$	$e\left(\frac{113}{156}\right)$	$-i$	$e\left(\frac{1}{36}\right)$
$\chi_{114075}(8,\cdot)$	114075.we	780	no	$-1$	$1$	$e\left(\frac{131}{390}\right)$	$e\left(\frac{131}{195}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{427}{780}\right)$	$e\left(\frac{158}{195}\right)$	$e\left(\frac{67}{195}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{53}{60}\right)$
$\chi_{114075}(11,\cdot)$	114075.yi	2340	yes	$1$	$1$	$e\left(\frac{427}{2340}\right)$	$e\left(\frac{427}{1170}\right)$	$e\left(\frac{95}{468}\right)$	$e\left(\frac{427}{780}\right)$	$e\left(\frac{457}{2340}\right)$	$e\left(\frac{451}{1170}\right)$	$e\left(\frac{427}{585}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{114075}(14,\cdot)$	114075.wo	1170	yes	$-1$	$1$	$e\left(\frac{548}{585}\right)$	$e\left(\frac{511}{585}\right)$	$e\left(\frac{161}{234}\right)$	$e\left(\frac{158}{195}\right)$	$e\left(\frac{451}{1170}\right)$	$e\left(\frac{731}{1170}\right)$	$e\left(\frac{437}{585}\right)$	$e\left(\frac{28}{195}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{90}\right)$
$\chi_{114075}(16,\cdot)$	114075.uo	585	yes	$1$	$1$	$e\left(\frac{262}{585}\right)$	$e\left(\frac{524}{585}\right)$	$e\left(\frac{35}{117}\right)$	$e\left(\frac{67}{195}\right)$	$e\left(\frac{427}{585}\right)$	$e\left(\frac{437}{585}\right)$	$e\left(\frac{463}{585}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{114075}(17,\cdot)$	114075.vd	780	no	$1$	$1$	$e\left(\frac{109}{260}\right)$	$e\left(\frac{109}{130}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{28}{195}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{461}{780}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{114075}(19,\cdot)$	114075.kb	60	no	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{114075}(22,\cdot)$	114075.pt	180	no	$-1$	$1$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{121}{180}\right)$
$\chi_{114075}(23,\cdot)$	114075.pr	180	no	$1$	$1$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{103}{180}\right)$
$\chi_{114075}(28,\cdot)$	114075.wg	780	no	$1$	$1$	$e\left(\frac{19}{390}\right)$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{19}{130}\right)$	$e\left(\frac{443}{780}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{38}{195}\right)$	$e\left(\frac{439}{780}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{114075}(29,\cdot)$	114075.wt	1170	yes	$-1$	$1$	$e\left(\frac{241}{585}\right)$	$e\left(\frac{482}{585}\right)$	$e\left(\frac{193}{234}\right)$	$e\left(\frac{46}{195}\right)$	$e\left(\frac{857}{1170}\right)$	$e\left(\frac{277}{1170}\right)$	$e\left(\frac{379}{585}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{90}\right)$
$\chi_{114075}(31,\cdot)$	114075.yh	2340	yes	$-1$	$1$	$e\left(\frac{1511}{2340}\right)$	$e\left(\frac{341}{1170}\right)$	$e\left(\frac{85}{468}\right)$	$e\left(\frac{731}{780}\right)$	$e\left(\frac{1661}{2340}\right)$	$e\left(\frac{484}{585}\right)$	$e\left(\frac{341}{585}\right)$	$e\left(\frac{203}{390}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{114075}(32,\cdot)$	114075.td	468	no	$-1$	$1$	$e\left(\frac{131}{234}\right)$	$e\left(\frac{14}{117}\right)$	$e\left(\frac{29}{234}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{427}{468}\right)$	$e\left(\frac{80}{117}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{114075}(34,\cdot)$	114075.xo	2340	yes	$-1$	$1$	$e\left(\frac{1243}{2340}\right)$	$e\left(\frac{73}{1170}\right)$	$e\left(\frac{257}{468}\right)$	$e\left(\frac{463}{780}\right)$	$e\left(\frac{1903}{2340}\right)$	$e\left(\frac{47}{585}\right)$	$e\left(\frac{73}{585}\right)$	$e\left(\frac{2}{195}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{114075}(37,\cdot)$	114075.wd	780	no	$1$	$1$	$e\left(\frac{293}{390}\right)$	$e\left(\frac{98}{195}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{181}{780}\right)$	$e\left(\frac{353}{390}\right)$	$e\left(\frac{1}{195}\right)$	$e\left(\frac{133}{780}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{114075}(38,\cdot)$	114075.ya	2340	yes	$1$	$1$	$e\left(\frac{223}{2340}\right)$	$e\left(\frac{223}{1170}\right)$	$e\left(\frac{269}{468}\right)$	$e\left(\frac{223}{780}\right)$	$e\left(\frac{97}{585}\right)$	$e\left(\frac{392}{585}\right)$	$e\left(\frac{223}{585}\right)$	$e\left(\frac{743}{780}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{47}{180}\right)$
$\chi_{114075}(41,\cdot)$	114075.xp	2340	yes	$1$	$1$	$e\left(\frac{1613}{2340}\right)$	$e\left(\frac{443}{1170}\right)$	$e\left(\frac{193}{468}\right)$	$e\left(\frac{53}{780}\right)$	$e\left(\frac{1403}{2340}\right)$	$e\left(\frac{119}{1170}\right)$	$e\left(\frac{443}{585}\right)$	$e\left(\frac{62}{195}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{114075}(43,\cdot)$	114075.tz	468	no	$-1$	$1$	$e\left(\frac{353}{468}\right)$	$e\left(\frac{119}{234}\right)$	$e\left(\frac{461}{468}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{103}{234}\right)$	$e\left(\frac{173}{234}\right)$	$e\left(\frac{2}{117}\right)$	$e\left(\frac{41}{156}\right)$	$1$	$e\left(\frac{7}{36}\right)$
$\chi_{114075}(44,\cdot)$	114075.vr	780	no	$1$	$1$	$e\left(\frac{317}{780}\right)$	$e\left(\frac{317}{390}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{57}{260}\right)$	$e\left(\frac{437}{780}\right)$	$e\left(\frac{101}{390}\right)$	$e\left(\frac{122}{195}\right)$	$e\left(\frac{61}{130}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{114075}(46,\cdot)$	114075.vp	780	no	$-1$	$1$	$e\left(\frac{83}{780}\right)$	$e\left(\frac{83}{390}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{83}{260}\right)$	$e\left(\frac{593}{780}\right)$	$e\left(\frac{122}{195}\right)$	$e\left(\frac{83}{195}\right)$	$e\left(\frac{157}{390}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{114075}(47,\cdot)$	114075.xl	2340	yes	$-1$	$1$	$e\left(\frac{376}{585}\right)$	$e\left(\frac{167}{585}\right)$	$e\left(\frac{80}{117}\right)$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{589}{2340}\right)$	$e\left(\frac{191}{585}\right)$	$e\left(\frac{334}{585}\right)$	$e\left(\frac{659}{780}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{161}{180}\right)$
$\chi_{114075}(49,\cdot)$	114075.rh	234	no	$1$	$1$	$e\left(\frac{76}{117}\right)$	$e\left(\frac{35}{117}\right)$	$e\left(\frac{85}{117}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{44}{117}\right)$	$e\left(\frac{70}{117}\right)$	$e\left(\frac{35}{78}\right)$	$-1$	$e\left(\frac{1}{18}\right)$
$\chi_{114075}(53,\cdot)$	114075.rr	260	no	$1$	$1$	$e\left(\frac{161}{260}\right)$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{223}{260}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{93}{260}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{114075}(56,\cdot)$	114075.ws	1170	yes	$-1$	$1$	$e\left(\frac{94}{585}\right)$	$e\left(\frac{188}{585}\right)$	$e\left(\frac{79}{234}\right)$	$e\left(\frac{94}{195}\right)$	$e\left(\frac{439}{585}\right)$	$e\left(\frac{583}{1170}\right)$	$e\left(\frac{376}{585}\right)$	$e\left(\frac{383}{390}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{114075}(58,\cdot)$	114075.yl	2340	yes	$1$	$1$	$e\left(\frac{613}{1170}\right)$	$e\left(\frac{28}{585}\right)$	$e\left(\frac{76}{117}\right)$	$e\left(\frac{223}{390}\right)$	$e\left(\frac{2141}{2340}\right)$	$e\left(\frac{203}{1170}\right)$	$e\left(\frac{56}{585}\right)$	$e\left(\frac{257}{260}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{79}{180}\right)$
$\chi_{114075}(59,\cdot)$	114075.xn	2340	yes	$1$	$1$	$e\left(\frac{473}{2340}\right)$	$e\left(\frac{473}{1170}\right)$	$e\left(\frac{445}{468}\right)$	$e\left(\frac{473}{780}\right)$	$e\left(\frac{2153}{2340}\right)$	$e\left(\frac{179}{1170}\right)$	$e\left(\frac{473}{585}\right)$	$e\left(\frac{3}{130}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{90}\right)$
$\chi_{114075}(61,\cdot)$	114075.um	585	yes	$1$	$1$	$e\left(\frac{343}{585}\right)$	$e\left(\frac{101}{585}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{148}{195}\right)$	$e\left(\frac{463}{585}\right)$	$e\left(\frac{488}{585}\right)$	$e\left(\frac{202}{585}\right)$	$e\left(\frac{148}{195}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{114075}(62,\cdot)$	114075.vd	780	no	$1$	$1$	$e\left(\frac{197}{260}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{71}{260}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{149}{195}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{733}{780}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{114075}(64,\cdot)$	114075.sj	390	no	$1$	$1$	$e\left(\frac{131}{195}\right)$	$e\left(\frac{67}{195}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{37}{390}\right)$	$e\left(\frac{121}{195}\right)$	$e\left(\frac{134}{195}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{30}\right)$

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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	$114075$
Structure	\(C_{2}\times C_{12}\times C_{2340}\)
Order	$56160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(14\)	\(16\)	\(17\)	\(19\)	\(22\)
\(\chi_{114075}(1,\cdot)\)	114075.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{114075}(2,\cdot)\)	114075.yo	2340	yes	\(-1\)	\(1\)	\(e\left(\frac{131}{1170}\right)\)	\(e\left(\frac{131}{585}\right)\)	\(e\left(\frac{193}{234}\right)\)	\(e\left(\frac{131}{390}\right)\)	\(e\left(\frac{427}{2340}\right)\)	\(e\left(\frac{548}{585}\right)\)	\(e\left(\frac{262}{585}\right)\)	\(e\left(\frac{109}{260}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{53}{180}\right)\)
\(\chi_{114075}(4,\cdot)\)	114075.wl	1170	yes	\(1\)	\(1\)	\(e\left(\frac{131}{585}\right)\)	\(e\left(\frac{262}{585}\right)\)	\(e\left(\frac{76}{117}\right)\)	\(e\left(\frac{131}{195}\right)\)	\(e\left(\frac{427}{1170}\right)\)	\(e\left(\frac{511}{585}\right)\)	\(e\left(\frac{524}{585}\right)\)	\(e\left(\frac{109}{130}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{90}\right)\)
\(\chi_{114075}(7,\cdot)\)	114075.tf	468	no	\(1\)	\(1\)	\(e\left(\frac{193}{234}\right)\)	\(e\left(\frac{76}{117}\right)\)	\(e\left(\frac{101}{117}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{95}{468}\right)\)	\(e\left(\frac{161}{234}\right)\)	\(e\left(\frac{35}{117}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(-i\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{114075}(8,\cdot)\)	114075.we	780	no	\(-1\)	\(1\)	\(e\left(\frac{131}{390}\right)\)	\(e\left(\frac{131}{195}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{427}{780}\right)\)	\(e\left(\frac{158}{195}\right)\)	\(e\left(\frac{67}{195}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{53}{60}\right)\)
\(\chi_{114075}(11,\cdot)\)	114075.yi	2340	yes	\(1\)	\(1\)	\(e\left(\frac{427}{2340}\right)\)	\(e\left(\frac{427}{1170}\right)\)	\(e\left(\frac{95}{468}\right)\)	\(e\left(\frac{427}{780}\right)\)	\(e\left(\frac{457}{2340}\right)\)	\(e\left(\frac{451}{1170}\right)\)	\(e\left(\frac{427}{585}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{114075}(14,\cdot)\)	114075.wo	1170	yes	\(-1\)	\(1\)	\(e\left(\frac{548}{585}\right)\)	\(e\left(\frac{511}{585}\right)\)	\(e\left(\frac{161}{234}\right)\)	\(e\left(\frac{158}{195}\right)\)	\(e\left(\frac{451}{1170}\right)\)	\(e\left(\frac{731}{1170}\right)\)	\(e\left(\frac{437}{585}\right)\)	\(e\left(\frac{28}{195}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{90}\right)\)
\(\chi_{114075}(16,\cdot)\)	114075.uo	585	yes	\(1\)	\(1\)	\(e\left(\frac{262}{585}\right)\)	\(e\left(\frac{524}{585}\right)\)	\(e\left(\frac{35}{117}\right)\)	\(e\left(\frac{67}{195}\right)\)	\(e\left(\frac{427}{585}\right)\)	\(e\left(\frac{437}{585}\right)\)	\(e\left(\frac{463}{585}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{114075}(17,\cdot)\)	114075.vd	780	no	\(1\)	\(1\)	\(e\left(\frac{109}{260}\right)\)	\(e\left(\frac{109}{130}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{28}{195}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{461}{780}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{114075}(19,\cdot)\)	114075.kb	60	no	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{114075}(22,\cdot)\)	114075.pt	180	no	\(-1\)	\(1\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{121}{180}\right)\)
\(\chi_{114075}(23,\cdot)\)	114075.pr	180	no	\(1\)	\(1\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{103}{180}\right)\)
\(\chi_{114075}(28,\cdot)\)	114075.wg	780	no	\(1\)	\(1\)	\(e\left(\frac{19}{390}\right)\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{19}{130}\right)\)	\(e\left(\frac{443}{780}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{38}{195}\right)\)	\(e\left(\frac{439}{780}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{114075}(29,\cdot)\)	114075.wt	1170	yes	\(-1\)	\(1\)	\(e\left(\frac{241}{585}\right)\)	\(e\left(\frac{482}{585}\right)\)	\(e\left(\frac{193}{234}\right)\)	\(e\left(\frac{46}{195}\right)\)	\(e\left(\frac{857}{1170}\right)\)	\(e\left(\frac{277}{1170}\right)\)	\(e\left(\frac{379}{585}\right)\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{90}\right)\)
\(\chi_{114075}(31,\cdot)\)	114075.yh	2340	yes	\(-1\)	\(1\)	\(e\left(\frac{1511}{2340}\right)\)	\(e\left(\frac{341}{1170}\right)\)	\(e\left(\frac{85}{468}\right)\)	\(e\left(\frac{731}{780}\right)\)	\(e\left(\frac{1661}{2340}\right)\)	\(e\left(\frac{484}{585}\right)\)	\(e\left(\frac{341}{585}\right)\)	\(e\left(\frac{203}{390}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{114075}(32,\cdot)\)	114075.td	468	no	\(-1\)	\(1\)	\(e\left(\frac{131}{234}\right)\)	\(e\left(\frac{14}{117}\right)\)	\(e\left(\frac{29}{234}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{427}{468}\right)\)	\(e\left(\frac{80}{117}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{114075}(34,\cdot)\)	114075.xo	2340	yes	\(-1\)	\(1\)	\(e\left(\frac{1243}{2340}\right)\)	\(e\left(\frac{73}{1170}\right)\)	\(e\left(\frac{257}{468}\right)\)	\(e\left(\frac{463}{780}\right)\)	\(e\left(\frac{1903}{2340}\right)\)	\(e\left(\frac{47}{585}\right)\)	\(e\left(\frac{73}{585}\right)\)	\(e\left(\frac{2}{195}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{114075}(37,\cdot)\)	114075.wd	780	no	\(1\)	\(1\)	\(e\left(\frac{293}{390}\right)\)	\(e\left(\frac{98}{195}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{181}{780}\right)\)	\(e\left(\frac{353}{390}\right)\)	\(e\left(\frac{1}{195}\right)\)	\(e\left(\frac{133}{780}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{114075}(38,\cdot)\)	114075.ya	2340	yes	\(1\)	\(1\)	\(e\left(\frac{223}{2340}\right)\)	\(e\left(\frac{223}{1170}\right)\)	\(e\left(\frac{269}{468}\right)\)	\(e\left(\frac{223}{780}\right)\)	\(e\left(\frac{97}{585}\right)\)	\(e\left(\frac{392}{585}\right)\)	\(e\left(\frac{223}{585}\right)\)	\(e\left(\frac{743}{780}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{47}{180}\right)\)
\(\chi_{114075}(41,\cdot)\)	114075.xp	2340	yes	\(1\)	\(1\)	\(e\left(\frac{1613}{2340}\right)\)	\(e\left(\frac{443}{1170}\right)\)	\(e\left(\frac{193}{468}\right)\)	\(e\left(\frac{53}{780}\right)\)	\(e\left(\frac{1403}{2340}\right)\)	\(e\left(\frac{119}{1170}\right)\)	\(e\left(\frac{443}{585}\right)\)	\(e\left(\frac{62}{195}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{114075}(43,\cdot)\)	114075.tz	468	no	\(-1\)	\(1\)	\(e\left(\frac{353}{468}\right)\)	\(e\left(\frac{119}{234}\right)\)	\(e\left(\frac{461}{468}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{103}{234}\right)\)	\(e\left(\frac{173}{234}\right)\)	\(e\left(\frac{2}{117}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(1\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{114075}(44,\cdot)\)	114075.vr	780	no	\(1\)	\(1\)	\(e\left(\frac{317}{780}\right)\)	\(e\left(\frac{317}{390}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{57}{260}\right)\)	\(e\left(\frac{437}{780}\right)\)	\(e\left(\frac{101}{390}\right)\)	\(e\left(\frac{122}{195}\right)\)	\(e\left(\frac{61}{130}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{114075}(46,\cdot)\)	114075.vp	780	no	\(-1\)	\(1\)	\(e\left(\frac{83}{780}\right)\)	\(e\left(\frac{83}{390}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{83}{260}\right)\)	\(e\left(\frac{593}{780}\right)\)	\(e\left(\frac{122}{195}\right)\)	\(e\left(\frac{83}{195}\right)\)	\(e\left(\frac{157}{390}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{114075}(47,\cdot)\)	114075.xl	2340	yes	\(-1\)	\(1\)	\(e\left(\frac{376}{585}\right)\)	\(e\left(\frac{167}{585}\right)\)	\(e\left(\frac{80}{117}\right)\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{589}{2340}\right)\)	\(e\left(\frac{191}{585}\right)\)	\(e\left(\frac{334}{585}\right)\)	\(e\left(\frac{659}{780}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{161}{180}\right)\)
\(\chi_{114075}(49,\cdot)\)	114075.rh	234	no	\(1\)	\(1\)	\(e\left(\frac{76}{117}\right)\)	\(e\left(\frac{35}{117}\right)\)	\(e\left(\frac{85}{117}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{44}{117}\right)\)	\(e\left(\frac{70}{117}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(-1\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{114075}(53,\cdot)\)	114075.rr	260	no	\(1\)	\(1\)	\(e\left(\frac{161}{260}\right)\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{223}{260}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{93}{260}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{114075}(56,\cdot)\)	114075.ws	1170	yes	\(-1\)	\(1\)	\(e\left(\frac{94}{585}\right)\)	\(e\left(\frac{188}{585}\right)\)	\(e\left(\frac{79}{234}\right)\)	\(e\left(\frac{94}{195}\right)\)	\(e\left(\frac{439}{585}\right)\)	\(e\left(\frac{583}{1170}\right)\)	\(e\left(\frac{376}{585}\right)\)	\(e\left(\frac{383}{390}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{114075}(58,\cdot)\)	114075.yl	2340	yes	\(1\)	\(1\)	\(e\left(\frac{613}{1170}\right)\)	\(e\left(\frac{28}{585}\right)\)	\(e\left(\frac{76}{117}\right)\)	\(e\left(\frac{223}{390}\right)\)	\(e\left(\frac{2141}{2340}\right)\)	\(e\left(\frac{203}{1170}\right)\)	\(e\left(\frac{56}{585}\right)\)	\(e\left(\frac{257}{260}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{79}{180}\right)\)
\(\chi_{114075}(59,\cdot)\)	114075.xn	2340	yes	\(1\)	\(1\)	\(e\left(\frac{473}{2340}\right)\)	\(e\left(\frac{473}{1170}\right)\)	\(e\left(\frac{445}{468}\right)\)	\(e\left(\frac{473}{780}\right)\)	\(e\left(\frac{2153}{2340}\right)\)	\(e\left(\frac{179}{1170}\right)\)	\(e\left(\frac{473}{585}\right)\)	\(e\left(\frac{3}{130}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)
\(\chi_{114075}(61,\cdot)\)	114075.um	585	yes	\(1\)	\(1\)	\(e\left(\frac{343}{585}\right)\)	\(e\left(\frac{101}{585}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{148}{195}\right)\)	\(e\left(\frac{463}{585}\right)\)	\(e\left(\frac{488}{585}\right)\)	\(e\left(\frac{202}{585}\right)\)	\(e\left(\frac{148}{195}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{114075}(62,\cdot)\)	114075.vd	780	no	\(1\)	\(1\)	\(e\left(\frac{197}{260}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{71}{260}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{149}{195}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{733}{780}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{114075}(64,\cdot)\)	114075.sj	390	no	\(1\)	\(1\)	\(e\left(\frac{131}{195}\right)\)	\(e\left(\frac{67}{195}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{37}{390}\right)\)	\(e\left(\frac{121}{195}\right)\)	\(e\left(\frac{134}{195}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)

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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.