LMFDB - Group of Dirichlet characters of modulus 397800

Show commands: PariGP / SageMath

sage: H = DirichletGroup(397800)

pari: g = idealstar(,397800,2)

Character group

sage: G.order() pari: g.no
Order	=	92160
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{12}\times C_{240}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{397800}(298351,\cdot)$, $\chi_{397800}(198901,\cdot)$, $\chi_{397800}(44201,\cdot)$, $\chi_{397800}(365977,\cdot)$, $\chi_{397800}(183601,\cdot)$, $\chi_{397800}(304201,\cdot)$

First 32 of 92160 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	$-1$	$1$	$7$	$11$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{397800}(1,\cdot)$	397800.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{397800}(7,\cdot)$	397800.emt	48	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{397800}(11,\cdot)$	397800.hjr	240	yes	$1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{397800}(19,\cdot)$	397800.hez	120	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{397800}(23,\cdot)$	397800.hxr	240	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{397800}(29,\cdot)$	397800.hot	240	yes	$1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{60}\right)$
$\chi_{397800}(31,\cdot)$	397800.hwi	240	no	$-1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{397800}(37,\cdot)$	397800.hqx	240	no	$-1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{397800}(41,\cdot)$	397800.hlw	240	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{397800}(43,\cdot)$	397800.ddr	24	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{11}{12}\right)$
$\chi_{397800}(47,\cdot)$	397800.flh	60	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{397800}(49,\cdot)$	397800.djy	24	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{397800}(53,\cdot)$	397800.edr	40	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{21}{40}\right)$	$-1$	$e\left(\frac{19}{20}\right)$
$\chi_{397800}(59,\cdot)$	397800.hfg	120	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{60}\right)$
$\chi_{397800}(61,\cdot)$	397800.hmz	240	yes	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{60}\right)$
$\chi_{397800}(67,\cdot)$	397800.fbe	60	yes	$-1$	$1$	$-1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{20}\right)$	$i$	$e\left(\frac{2}{15}\right)$
$\chi_{397800}(71,\cdot)$	397800.iah	240	no	$1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{397800}(73,\cdot)$	397800.glr	80	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{397800}(77,\cdot)$	397800.hbl	120	yes	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{397800}(79,\cdot)$	397800.hpw	240	no	$1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{397800}(83,\cdot)$	397800.hhi	120	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{397800}(89,\cdot)$	397800.gby	60	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{397800}(97,\cdot)$	397800.hvf	240	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{397800}(101,\cdot)$	397800.pn	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{397800}(103,\cdot)$	397800.gac	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{60}\right)$
$\chi_{397800}(107,\cdot)$	397800.ehn	48	no	$1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{1}{24}\right)$	$-1$
$\chi_{397800}(109,\cdot)$	397800.gnq	80	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{397800}(113,\cdot)$	397800.hyv	240	no	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{397800}(121,\cdot)$	397800.gyj	120	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{397800}(127,\cdot)$	397800.hbx	120	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{397800}(131,\cdot)$	397800.hpt	240	no	$-1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{23}{60}\right)$
$\chi_{397800}(133,\cdot)$	397800.hyw	240	yes	$1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{15}\right)$

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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	$397800$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{12}\times C_{240}\)
Order	$92160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{397800}(1,\cdot)\)	397800.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{397800}(7,\cdot)\)	397800.emt	48	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{397800}(11,\cdot)\)	397800.hjr	240	yes	\(1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{397800}(19,\cdot)\)	397800.hez	120	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{397800}(23,\cdot)\)	397800.hxr	240	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{397800}(29,\cdot)\)	397800.hot	240	yes	\(1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{60}\right)\)
\(\chi_{397800}(31,\cdot)\)	397800.hwi	240	no	\(-1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{397800}(37,\cdot)\)	397800.hqx	240	no	\(-1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{397800}(41,\cdot)\)	397800.hlw	240	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{397800}(43,\cdot)\)	397800.ddr	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{397800}(47,\cdot)\)	397800.flh	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{397800}(49,\cdot)\)	397800.djy	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{397800}(53,\cdot)\)	397800.edr	40	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(-1\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{397800}(59,\cdot)\)	397800.hfg	120	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{60}\right)\)
\(\chi_{397800}(61,\cdot)\)	397800.hmz	240	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{397800}(67,\cdot)\)	397800.fbe	60	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(i\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{397800}(71,\cdot)\)	397800.iah	240	no	\(1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{397800}(73,\cdot)\)	397800.glr	80	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{397800}(77,\cdot)\)	397800.hbl	120	yes	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{397800}(79,\cdot)\)	397800.hpw	240	no	\(1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{397800}(83,\cdot)\)	397800.hhi	120	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{397800}(89,\cdot)\)	397800.gby	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{397800}(97,\cdot)\)	397800.hvf	240	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{397800}(101,\cdot)\)	397800.pn	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{397800}(103,\cdot)\)	397800.gac	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{60}\right)\)
\(\chi_{397800}(107,\cdot)\)	397800.ehn	48	no	\(1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-1\)
\(\chi_{397800}(109,\cdot)\)	397800.gnq	80	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{397800}(113,\cdot)\)	397800.hyv	240	no	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{397800}(121,\cdot)\)	397800.gyj	120	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{397800}(127,\cdot)\)	397800.hbx	120	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{397800}(131,\cdot)\)	397800.hpt	240	no	\(-1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{23}{60}\right)\)
\(\chi_{397800}(133,\cdot)\)	397800.hyw	240	yes	\(1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{15}\right)\)

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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.