LMFDB - Group of Dirichlet characters of modulus 187200

Show commands: PariGP / SageMath

sage: H = DirichletGroup(187200)

pari: g = idealstar(,187200,2)

Character group

sage: G.order() pari: g.no
Order	=	46080
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{12}\times C_{240}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{187200}(157951,\cdot)$, $\chi_{187200}(58501,\cdot)$, $\chi_{187200}(20801,\cdot)$, $\chi_{187200}(14977,\cdot)$, $\chi_{187200}(43201,\cdot)$

First 32 of 46080 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	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{187200}(1,\cdot)$	187200.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{187200}(7,\cdot)$	187200.bqe	24	no	$-1$	$1$	$-i$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{24}\right)$	$-1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$1$	$e\left(\frac{7}{8}\right)$
$\chi_{187200}(11,\cdot)$	187200.dvl	240	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{187200}(17,\cdot)$	187200.cwv	60	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{187200}(19,\cdot)$	187200.dwr	240	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{187200}(23,\cdot)$	187200.dhi	120	no	$-1$	$1$	$-1$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{187200}(29,\cdot)$	187200.dua	240	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{187200}(31,\cdot)$	187200.cyf	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{187200}(37,\cdot)$	187200.dso	240	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{187200}(41,\cdot)$	187200.dqg	120	no	$1$	$1$	$1$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{187200}(43,\cdot)$	187200.cml	48	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{187200}(47,\cdot)$	187200.cop	60	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{187200}(49,\cdot)$	187200.ox	12	no	$1$	$1$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$-i$
$\chi_{187200}(53,\cdot)$	187200.dez	80	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{187200}(59,\cdot)$	187200.dwb	240	yes	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{187200}(61,\cdot)$	187200.duk	240	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{187200}(67,\cdot)$	187200.dzm	240	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{187200}(71,\cdot)$	187200.dhx	120	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{187200}(73,\cdot)$	187200.cca	40	no	$1$	$1$	$i$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{187200}(77,\cdot)$	187200.dri	240	yes	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{13}{48}\right)$
$\chi_{187200}(79,\cdot)$	187200.dcy	60	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{187200}(83,\cdot)$	187200.drf	240	yes	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{29}{48}\right)$
$\chi_{187200}(89,\cdot)$	187200.dpv	120	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{187200}(97,\cdot)$	187200.cnu	60	no	$1$	$1$	$-1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{20}\right)$	$-i$
$\chi_{187200}(101,\cdot)$	187200.cgj	48	no	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{187200}(103,\cdot)$	187200.dii	120	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{187200}(107,\cdot)$	187200.cmp	48	no	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{48}\right)$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{23}{48}\right)$
$\chi_{187200}(109,\cdot)$	187200.dfk	80	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{187200}(113,\cdot)$	187200.cwm	60	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{187200}(119,\cdot)$	187200.dja	120	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{187200}(121,\cdot)$	187200.dka	120	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{187200}(127,\cdot)$	187200.cyy	60	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{12}\right)$

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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	$187200$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{12}\times C_{240}\)
Order	$46080$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{187200}(1,\cdot)\)	187200.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{187200}(7,\cdot)\)	187200.bqe	24	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(-1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{187200}(11,\cdot)\)	187200.dvl	240	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{187200}(17,\cdot)\)	187200.cwv	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{187200}(19,\cdot)\)	187200.dwr	240	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{187200}(23,\cdot)\)	187200.dhi	120	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{187200}(29,\cdot)\)	187200.dua	240	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{187200}(31,\cdot)\)	187200.cyf	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{187200}(37,\cdot)\)	187200.dso	240	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{187200}(41,\cdot)\)	187200.dqg	120	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{187200}(43,\cdot)\)	187200.cml	48	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{187200}(47,\cdot)\)	187200.cop	60	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{187200}(49,\cdot)\)	187200.ox	12	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(-i\)
\(\chi_{187200}(53,\cdot)\)	187200.dez	80	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{187200}(59,\cdot)\)	187200.dwb	240	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{187200}(61,\cdot)\)	187200.duk	240	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{187200}(67,\cdot)\)	187200.dzm	240	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{187200}(71,\cdot)\)	187200.dhx	120	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{187200}(73,\cdot)\)	187200.cca	40	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{187200}(77,\cdot)\)	187200.dri	240	yes	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{13}{48}\right)\)
\(\chi_{187200}(79,\cdot)\)	187200.dcy	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{187200}(83,\cdot)\)	187200.drf	240	yes	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{29}{48}\right)\)
\(\chi_{187200}(89,\cdot)\)	187200.dpv	120	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{187200}(97,\cdot)\)	187200.cnu	60	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-i\)
\(\chi_{187200}(101,\cdot)\)	187200.cgj	48	no	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{187200}(103,\cdot)\)	187200.dii	120	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{187200}(107,\cdot)\)	187200.cmp	48	no	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)
\(\chi_{187200}(109,\cdot)\)	187200.dfk	80	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{187200}(113,\cdot)\)	187200.cwm	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{187200}(119,\cdot)\)	187200.dja	120	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{187200}(121,\cdot)\)	187200.dka	120	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{187200}(127,\cdot)\)	187200.cyy	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)

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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.