LMFDB - Group of Dirichlet characters of modulus 3400

sage:H = DirichletGroup(3400)

pari:g = idealstar(,3400,2)

Character group

sage:G.order() pari:g.no
Order	=	1280
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{80}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{3400}(2551,\cdot)$, $\chi_{3400}(1701,\cdot)$, $\chi_{3400}(2177,\cdot)$, $\chi_{3400}(1601,\cdot)$

First 32 of 1280 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{3400}(1,\cdot)$	3400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3400}(3,\cdot)$	3400.fa	80	yes	$-1$	$1$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{1}{80}\right)$
$\chi_{3400}(7,\cdot)$	3400.cu	16	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{3400}(9,\cdot)$	3400.ek	40	no	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{3400}(11,\cdot)$	3400.fj	80	yes	$1$	$1$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{63}{80}\right)$
$\chi_{3400}(13,\cdot)$	3400.dl	20	yes	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{3400}(19,\cdot)$	3400.ev	40	yes	$-1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{3400}(21,\cdot)$	3400.dx	20	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{3400}(23,\cdot)$	3400.ez	80	no	$-1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{3400}(27,\cdot)$	3400.fa	80	yes	$-1$	$1$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{3}{80}\right)$
$\chi_{3400}(29,\cdot)$	3400.ff	80	yes	$-1$	$1$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{21}{80}\right)$
$\chi_{3400}(31,\cdot)$	3400.fg	80	no	$1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{9}{80}\right)$
$\chi_{3400}(33,\cdot)$	3400.ec	20	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3400}(37,\cdot)$	3400.fm	80	yes	$1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{17}{80}\right)$
$\chi_{3400}(39,\cdot)$	3400.fe	80	no	$1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{53}{80}\right)$
$\chi_{3400}(41,\cdot)$	3400.fi	80	no	$-1$	$1$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{27}{80}\right)$
$\chi_{3400}(43,\cdot)$	3400.bx	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$i$	$i$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{3400}(47,\cdot)$	3400.ef	20	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{3400}(49,\cdot)$	3400.cc	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{3400}(53,\cdot)$	3400.em	40	yes	$-1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{23}{40}\right)$
$\chi_{3400}(57,\cdot)$	3400.cw	16	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{3400}(59,\cdot)$	3400.ev	40	yes	$-1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{3400}(61,\cdot)$	3400.fh	80	yes	$-1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{43}{80}\right)$
$\chi_{3400}(63,\cdot)$	3400.fn	80	no	$-1$	$1$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{37}{80}\right)$
$\chi_{3400}(67,\cdot)$	3400.ed	20	yes	$1$	$1$	$e\left(\frac{1}{20}\right)$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{3400}(69,\cdot)$	3400.ci	10	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{3400}(71,\cdot)$	3400.fg	80	no	$1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{1}{80}\right)$
$\chi_{3400}(73,\cdot)$	3400.fl	80	no	$1$	$1$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{13}{80}\right)$
$\chi_{3400}(77,\cdot)$	3400.em	40	yes	$-1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{3400}(79,\cdot)$	3400.fe	80	no	$1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{71}{80}\right)$
$\chi_{3400}(81,\cdot)$	3400.du	20	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{3400}(83,\cdot)$	3400.eo	40	yes	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{27}{40}\right)$

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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	$3400$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{80}\)
Order	$1280$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{3400}(1,\cdot)\)	3400.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3400}(3,\cdot)\)	3400.fa	80	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)
\(\chi_{3400}(7,\cdot)\)	3400.cu	16	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{3400}(9,\cdot)\)	3400.ek	40	no	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{3400}(11,\cdot)\)	3400.fj	80	yes	\(1\)	\(1\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)
\(\chi_{3400}(13,\cdot)\)	3400.dl	20	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{3400}(19,\cdot)\)	3400.ev	40	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{3400}(21,\cdot)\)	3400.dx	20	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{3400}(23,\cdot)\)	3400.ez	80	no	\(-1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)
\(\chi_{3400}(27,\cdot)\)	3400.fa	80	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)
\(\chi_{3400}(29,\cdot)\)	3400.ff	80	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)
\(\chi_{3400}(31,\cdot)\)	3400.fg	80	no	\(1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)
\(\chi_{3400}(33,\cdot)\)	3400.ec	20	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3400}(37,\cdot)\)	3400.fm	80	yes	\(1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)
\(\chi_{3400}(39,\cdot)\)	3400.fe	80	no	\(1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)
\(\chi_{3400}(41,\cdot)\)	3400.fi	80	no	\(-1\)	\(1\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)
\(\chi_{3400}(43,\cdot)\)	3400.bx	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(i\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{3400}(47,\cdot)\)	3400.ef	20	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{3400}(49,\cdot)\)	3400.cc	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{3400}(53,\cdot)\)	3400.em	40	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)
\(\chi_{3400}(57,\cdot)\)	3400.cw	16	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{3400}(59,\cdot)\)	3400.ev	40	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{3400}(61,\cdot)\)	3400.fh	80	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)
\(\chi_{3400}(63,\cdot)\)	3400.fn	80	no	\(-1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)
\(\chi_{3400}(67,\cdot)\)	3400.ed	20	yes	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{3400}(69,\cdot)\)	3400.ci	10	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{3400}(71,\cdot)\)	3400.fg	80	no	\(1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)
\(\chi_{3400}(73,\cdot)\)	3400.fl	80	no	\(1\)	\(1\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)
\(\chi_{3400}(77,\cdot)\)	3400.em	40	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{3400}(79,\cdot)\)	3400.fe	80	no	\(1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)
\(\chi_{3400}(81,\cdot)\)	3400.du	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{3400}(83,\cdot)\)	3400.eo	40	yes	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)

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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.