LMFDB - Group of Dirichlet characters of modulus 41600

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(41600)

gp:g = idealstar(,41600,2)

magma:G = FullDirichletGroup(41600);

Character group

Order	=	15360	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{4}\times C_{480}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{41600}(33151,\cdot)$, $\chi_{41600}(16901,\cdot)$, $\chi_{41600}(14977,\cdot)$, $\chi_{41600}(22401,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 15360 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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{41600}(1,\cdot)$	41600.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{41600}(3,\cdot)$	41600.za	480	yes	$1$	$1$	$e\left(\frac{271}{480}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{193}{480}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{299}{480}\right)$	$e\left(\frac{67}{160}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{111}{160}\right)$	$e\left(\frac{271}{480}\right)$
$\chi_{41600}(7,\cdot)$	41600.qc	48	no	$-1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{29}{48}\right)$
$\chi_{41600}(9,\cdot)$	41600.yg	240	no	$1$	$1$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{31}{240}\right)$
$\chi_{41600}(11,\cdot)$	41600.yq	480	yes	$1$	$1$	$e\left(\frac{193}{480}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{79}{480}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{437}{480}\right)$	$e\left(\frac{141}{160}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{313}{480}\right)$
$\chi_{41600}(17,\cdot)$	41600.wb	120	no	$-1$	$1$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{71}{120}\right)$
$\chi_{41600}(19,\cdot)$	41600.yw	480	yes	$1$	$1$	$e\left(\frac{299}{480}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{437}{480}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{151}{480}\right)$	$e\left(\frac{63}{160}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{139}{160}\right)$	$e\left(\frac{419}{480}\right)$
$\chi_{41600}(21,\cdot)$	41600.xi	160	yes	$-1$	$1$	$e\left(\frac{67}{160}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{141}{160}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{63}{160}\right)$	$e\left(\frac{37}{160}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{27}{160}\right)$
$\chi_{41600}(23,\cdot)$	41600.yo	240	no	$1$	$1$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{59}{240}\right)$
$\chi_{41600}(27,\cdot)$	41600.wy	160	no	$1$	$1$	$e\left(\frac{111}{160}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{139}{160}\right)$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{111}{160}\right)$
$\chi_{41600}(29,\cdot)$	41600.zg	480	yes	$1$	$1$	$e\left(\frac{271}{480}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{313}{480}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{419}{480}\right)$	$e\left(\frac{27}{160}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{111}{160}\right)$	$e\left(\frac{151}{480}\right)$
$\chi_{41600}(31,\cdot)$	41600.js	20	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{41600}(33,\cdot)$	41600.qi	60	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{60}\right)$
$\chi_{41600}(37,\cdot)$	41600.zs	480	yes	$1$	$1$	$e\left(\frac{397}{480}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{331}{480}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{473}{480}\right)$	$e\left(\frac{49}{160}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{77}{160}\right)$	$e\left(\frac{157}{480}\right)$
$\chi_{41600}(41,\cdot)$	41600.ya	240	no	$-1$	$1$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{11}{240}\right)$
$\chi_{41600}(43,\cdot)$	41600.um	96	no	$1$	$1$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{61}{96}\right)$
$\chi_{41600}(47,\cdot)$	41600.ol	40	no	$-1$	$1$	$e\left(\frac{23}{40}\right)$	$i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{33}{40}\right)$
$\chi_{41600}(49,\cdot)$	41600.ld	24	no	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{41600}(51,\cdot)$	41600.nd	32	no	$-1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{41600}(53,\cdot)$	41600.wo	160	no	$-1$	$1$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{141}{160}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{37}{160}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{147}{160}\right)$
$\chi_{41600}(57,\cdot)$	41600.ho	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{41600}(59,\cdot)$	41600.yw	480	yes	$1$	$1$	$e\left(\frac{317}{480}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{131}{480}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{433}{480}\right)$	$e\left(\frac{9}{160}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{157}{160}\right)$	$e\left(\frac{197}{480}\right)$
$\chi_{41600}(61,\cdot)$	41600.ze	480	yes	$1$	$1$	$e\left(\frac{23}{480}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{449}{480}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{187}{480}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{23}{160}\right)$	$e\left(\frac{143}{480}\right)$
$\chi_{41600}(63,\cdot)$	41600.qz	60	no	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{41600}(67,\cdot)$	41600.yu	480	yes	$-1$	$1$	$e\left(\frac{79}{480}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{457}{480}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{131}{480}\right)$	$e\left(\frac{123}{160}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{79}{160}\right)$	$e\left(\frac{319}{480}\right)$
$\chi_{41600}(69,\cdot)$	41600.zc	480	yes	$1$	$1$	$e\left(\frac{269}{480}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{347}{480}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{121}{480}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{109}{160}\right)$	$e\left(\frac{389}{480}\right)$
$\chi_{41600}(71,\cdot)$	41600.yb	240	no	$1$	$1$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{193}{240}\right)$
$\chi_{41600}(73,\cdot)$	41600.to	80	no	$1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{53}{80}\right)$
$\chi_{41600}(77,\cdot)$	41600.xa	160	yes	$-1$	$1$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{103}{160}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{109}{160}\right)$	$e\left(\frac{111}{160}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{123}{160}\right)$	$e\left(\frac{41}{160}\right)$
$\chi_{41600}(79,\cdot)$	41600.oh	40	no	$-1$	$1$	$e\left(\frac{3}{40}\right)$	$i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{40}\right)$
$\chi_{41600}(81,\cdot)$	41600.vh	120	no	$1$	$1$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{31}{120}\right)$
$\chi_{41600}(83,\cdot)$	41600.wi	160	yes	$-1$	$1$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{119}{160}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{157}{160}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{99}{160}\right)$	$e\left(\frac{33}{160}\right)$

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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	$41600$
Structure	\(C_{2}\times C_{4}\times C_{4}\times C_{480}\)
Order	$15360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{41600}(1,\cdot)\)	41600.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{41600}(3,\cdot)\)	41600.za	480	yes	\(1\)	\(1\)	\(e\left(\frac{271}{480}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{193}{480}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{299}{480}\right)\)	\(e\left(\frac{67}{160}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{111}{160}\right)\)	\(e\left(\frac{271}{480}\right)\)
\(\chi_{41600}(7,\cdot)\)	41600.qc	48	no	\(-1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{29}{48}\right)\)
\(\chi_{41600}(9,\cdot)\)	41600.yg	240	no	\(1\)	\(1\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{31}{240}\right)\)
\(\chi_{41600}(11,\cdot)\)	41600.yq	480	yes	\(1\)	\(1\)	\(e\left(\frac{193}{480}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{79}{480}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{437}{480}\right)\)	\(e\left(\frac{141}{160}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{313}{480}\right)\)
\(\chi_{41600}(17,\cdot)\)	41600.wb	120	no	\(-1\)	\(1\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{71}{120}\right)\)
\(\chi_{41600}(19,\cdot)\)	41600.yw	480	yes	\(1\)	\(1\)	\(e\left(\frac{299}{480}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{437}{480}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{151}{480}\right)\)	\(e\left(\frac{63}{160}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{139}{160}\right)\)	\(e\left(\frac{419}{480}\right)\)
\(\chi_{41600}(21,\cdot)\)	41600.xi	160	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{160}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{141}{160}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{63}{160}\right)\)	\(e\left(\frac{37}{160}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{27}{160}\right)\)
\(\chi_{41600}(23,\cdot)\)	41600.yo	240	no	\(1\)	\(1\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{59}{240}\right)\)
\(\chi_{41600}(27,\cdot)\)	41600.wy	160	no	\(1\)	\(1\)	\(e\left(\frac{111}{160}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{139}{160}\right)\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{111}{160}\right)\)
\(\chi_{41600}(29,\cdot)\)	41600.zg	480	yes	\(1\)	\(1\)	\(e\left(\frac{271}{480}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{313}{480}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{419}{480}\right)\)	\(e\left(\frac{27}{160}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{111}{160}\right)\)	\(e\left(\frac{151}{480}\right)\)
\(\chi_{41600}(31,\cdot)\)	41600.js	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{41600}(33,\cdot)\)	41600.qi	60	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{60}\right)\)
\(\chi_{41600}(37,\cdot)\)	41600.zs	480	yes	\(1\)	\(1\)	\(e\left(\frac{397}{480}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{331}{480}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{473}{480}\right)\)	\(e\left(\frac{49}{160}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{77}{160}\right)\)	\(e\left(\frac{157}{480}\right)\)
\(\chi_{41600}(41,\cdot)\)	41600.ya	240	no	\(-1\)	\(1\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{11}{240}\right)\)
\(\chi_{41600}(43,\cdot)\)	41600.um	96	no	\(1\)	\(1\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{61}{96}\right)\)
\(\chi_{41600}(47,\cdot)\)	41600.ol	40	no	\(-1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)
\(\chi_{41600}(49,\cdot)\)	41600.ld	24	no	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{41600}(51,\cdot)\)	41600.nd	32	no	\(-1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{41600}(53,\cdot)\)	41600.wo	160	no	\(-1\)	\(1\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{141}{160}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{37}{160}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{147}{160}\right)\)
\(\chi_{41600}(57,\cdot)\)	41600.ho	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{41600}(59,\cdot)\)	41600.yw	480	yes	\(1\)	\(1\)	\(e\left(\frac{317}{480}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{131}{480}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{433}{480}\right)\)	\(e\left(\frac{9}{160}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{157}{160}\right)\)	\(e\left(\frac{197}{480}\right)\)
\(\chi_{41600}(61,\cdot)\)	41600.ze	480	yes	\(1\)	\(1\)	\(e\left(\frac{23}{480}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{449}{480}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{187}{480}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{23}{160}\right)\)	\(e\left(\frac{143}{480}\right)\)
\(\chi_{41600}(63,\cdot)\)	41600.qz	60	no	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{41600}(67,\cdot)\)	41600.yu	480	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{480}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{457}{480}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{131}{480}\right)\)	\(e\left(\frac{123}{160}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{79}{160}\right)\)	\(e\left(\frac{319}{480}\right)\)
\(\chi_{41600}(69,\cdot)\)	41600.zc	480	yes	\(1\)	\(1\)	\(e\left(\frac{269}{480}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{347}{480}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{121}{480}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{109}{160}\right)\)	\(e\left(\frac{389}{480}\right)\)
\(\chi_{41600}(71,\cdot)\)	41600.yb	240	no	\(1\)	\(1\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{193}{240}\right)\)
\(\chi_{41600}(73,\cdot)\)	41600.to	80	no	\(1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)
\(\chi_{41600}(77,\cdot)\)	41600.xa	160	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{103}{160}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{109}{160}\right)\)	\(e\left(\frac{111}{160}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{123}{160}\right)\)	\(e\left(\frac{41}{160}\right)\)
\(\chi_{41600}(79,\cdot)\)	41600.oh	40	no	\(-1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)
\(\chi_{41600}(81,\cdot)\)	41600.vh	120	no	\(1\)	\(1\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{31}{120}\right)\)
\(\chi_{41600}(83,\cdot)\)	41600.wi	160	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{119}{160}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{157}{160}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{99}{160}\right)\)	\(e\left(\frac{33}{160}\right)\)

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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.