LMFDB - Group of Dirichlet characters of modulus 11200

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(11200)

gp:g = idealstar(,11200,2)

magma:G = FullDirichletGroup(11200);

Character group

Order	=	3840	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{240}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{11200}(5951,\cdot)$, $\chi_{11200}(10501,\cdot)$, $\chi_{11200}(5377,\cdot)$, $\chi_{11200}(6401,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 3840 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{11200}(1,\cdot)$	11200.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{11200}(3,\cdot)$	11200.kn	240	yes	$-1$	$1$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{11200}(9,\cdot)$	11200.kl	120	no	$1$	$1$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{11200}(11,\cdot)$	11200.kv	240	yes	$-1$	$1$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{11200}(13,\cdot)$	11200.jt	80	yes	$1$	$1$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{11200}(17,\cdot)$	11200.ik	60	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{11200}(19,\cdot)$	11200.kq	240	yes	$1$	$1$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{11200}(23,\cdot)$	11200.ke	120	no	$1$	$1$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{11200}(27,\cdot)$	11200.ju	80	yes	$-1$	$1$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{11200}(29,\cdot)$	11200.jo	80	no	$1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{11200}(31,\cdot)$	11200.gr	30	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{11200}(33,\cdot)$	11200.im	60	no	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{11200}(37,\cdot)$	11200.kz	240	yes	$-1$	$1$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{11200}(39,\cdot)$	11200.ki	120	no	$-1$	$1$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{11200}(41,\cdot)$	11200.he	40	no	$-1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{11200}(43,\cdot)$	11200.em	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$1$
$\chi_{11200}(47,\cdot)$	11200.jf	60	no	$-1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{11200}(51,\cdot)$	11200.hy	48	no	$-1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{11200}(53,\cdot)$	11200.km	240	yes	$-1$	$1$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{11200}(57,\cdot)$	11200.cl	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{11200}(59,\cdot)$	11200.kq	240	yes	$1$	$1$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{11200}(61,\cdot)$	11200.kw	240	yes	$-1$	$1$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{11200}(67,\cdot)$	11200.kp	240	yes	$1$	$1$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{11200}(69,\cdot)$	11200.jn	80	yes	$-1$	$1$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{11200}(71,\cdot)$	11200.hq	40	no	$-1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{11200}(73,\cdot)$	11200.ka	120	no	$1$	$1$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{11200}(79,\cdot)$	11200.ir	60	no	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{11200}(81,\cdot)$	11200.iu	60	no	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{11200}(83,\cdot)$	11200.ju	80	yes	$-1$	$1$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{11200}(87,\cdot)$	11200.kd	120	no	$-1$	$1$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{11200}(89,\cdot)$	11200.jw	120	no	$-1$	$1$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{11200}(93,\cdot)$	11200.hu	48	no	$-1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{6}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$11200$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{240}\)
Order	$3840$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{11200}(1,\cdot)\)	11200.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{11200}(3,\cdot)\)	11200.kn	240	yes	\(-1\)	\(1\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{11200}(9,\cdot)\)	11200.kl	120	no	\(1\)	\(1\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{11200}(11,\cdot)\)	11200.kv	240	yes	\(-1\)	\(1\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{11200}(13,\cdot)\)	11200.jt	80	yes	\(1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{11200}(17,\cdot)\)	11200.ik	60	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{11200}(19,\cdot)\)	11200.kq	240	yes	\(1\)	\(1\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{11200}(23,\cdot)\)	11200.ke	120	no	\(1\)	\(1\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{11200}(27,\cdot)\)	11200.ju	80	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{11200}(29,\cdot)\)	11200.jo	80	no	\(1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{11200}(31,\cdot)\)	11200.gr	30	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{11200}(33,\cdot)\)	11200.im	60	no	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{11200}(37,\cdot)\)	11200.kz	240	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{11200}(39,\cdot)\)	11200.ki	120	no	\(-1\)	\(1\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{11200}(41,\cdot)\)	11200.he	40	no	\(-1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{11200}(43,\cdot)\)	11200.em	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)
\(\chi_{11200}(47,\cdot)\)	11200.jf	60	no	\(-1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{11200}(51,\cdot)\)	11200.hy	48	no	\(-1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{11200}(53,\cdot)\)	11200.km	240	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{11200}(57,\cdot)\)	11200.cl	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{11200}(59,\cdot)\)	11200.kq	240	yes	\(1\)	\(1\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{11200}(61,\cdot)\)	11200.kw	240	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{11200}(67,\cdot)\)	11200.kp	240	yes	\(1\)	\(1\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{11200}(69,\cdot)\)	11200.jn	80	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{11200}(71,\cdot)\)	11200.hq	40	no	\(-1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{11200}(73,\cdot)\)	11200.ka	120	no	\(1\)	\(1\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{11200}(79,\cdot)\)	11200.ir	60	no	\(-1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{11200}(81,\cdot)\)	11200.iu	60	no	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{11200}(83,\cdot)\)	11200.ju	80	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{11200}(87,\cdot)\)	11200.kd	120	no	\(-1\)	\(1\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{11200}(89,\cdot)\)	11200.jw	120	no	\(-1\)	\(1\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{11200}(93,\cdot)\)	11200.hu	48	no	\(-1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{6}\right)\)

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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.