LMFDB - Group of Dirichlet characters of modulus 3800

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3800)

pari: g = idealstar(,3800,2)

Character group

sage: G.order() pari: g.no
Order	=	1440
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{180}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3800}(951,\cdot)$, $\chi_{3800}(1901,\cdot)$, $\chi_{3800}(1977,\cdot)$, $\chi_{3800}(401,\cdot)$

First 32 of 1440 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{3800}(1,\cdot)$	3800.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3800}(3,\cdot)$	3800.fm	180	yes	$-1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{43}{90}\right)$
$\chi_{3800}(7,\cdot)$	3800.cg	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{3800}(9,\cdot)$	3800.fd	90	no	$1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{3800}(11,\cdot)$	3800.dt	30	yes	$-1$	$1$	$e\left(\frac{4}{15}\right)$	$-1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{3800}(13,\cdot)$	3800.fh	180	yes	$1$	$1$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{90}\right)$
$\chi_{3800}(17,\cdot)$	3800.fn	180	no	$-1$	$1$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{67}{90}\right)$
$\chi_{3800}(21,\cdot)$	3800.et	90	yes	$-1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{3800}(23,\cdot)$	3800.fg	180	no	$1$	$1$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{3800}(27,\cdot)$	3800.el	60	yes	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$-i$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{3800}(29,\cdot)$	3800.ez	90	yes	$-1$	$1$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{3800}(31,\cdot)$	3800.dv	30	no	$1$	$1$	$e\left(\frac{2}{15}\right)$	$-1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{3800}(33,\cdot)$	3800.fl	180	no	$1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{3800}(37,\cdot)$	3800.di	20	yes	$1$	$1$	$e\left(\frac{3}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{3800}(39,\cdot)$	3800.bw	10	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3800}(41,\cdot)$	3800.ew	90	no	$-1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{61}{90}\right)$
$\chi_{3800}(43,\cdot)$	3800.ed	36	no	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{3800}(47,\cdot)$	3800.fg	180	no	$1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{90}\right)$
$\chi_{3800}(49,\cdot)$	3800.bk	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{3800}(51,\cdot)$	3800.cy	18	no	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{3800}(53,\cdot)$	3800.fh	180	yes	$1$	$1$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{3800}(59,\cdot)$	3800.ex	90	yes	$1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{3800}(61,\cdot)$	3800.es	90	yes	$1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{3800}(63,\cdot)$	3800.fg	180	no	$1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{90}\right)$
$\chi_{3800}(67,\cdot)$	3800.fm	180	yes	$-1$	$1$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{3800}(69,\cdot)$	3800.dn	30	yes	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$-1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{3800}(71,\cdot)$	3800.fb	90	no	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{73}{90}\right)$
$\chi_{3800}(73,\cdot)$	3800.fn	180	no	$-1$	$1$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{79}{90}\right)$
$\chi_{3800}(77,\cdot)$	3800.dk	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3800}(79,\cdot)$	3800.er	90	no	$1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{43}{90}\right)$
$\chi_{3800}(81,\cdot)$	3800.ei	45	no	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{3800}(83,\cdot)$	3800.ej	60	yes	$1$	$1$	$e\left(\frac{23}{60}\right)$	$i$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{15}\right)$

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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	$3800$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{180}\)
Order	$1440$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{3800}(1,\cdot)\)	3800.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3800}(3,\cdot)\)	3800.fm	180	yes	\(-1\)	\(1\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{43}{90}\right)\)
\(\chi_{3800}(7,\cdot)\)	3800.cg	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{3800}(9,\cdot)\)	3800.fd	90	no	\(1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{3800}(11,\cdot)\)	3800.dt	30	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(-1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{3800}(13,\cdot)\)	3800.fh	180	yes	\(1\)	\(1\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)
\(\chi_{3800}(17,\cdot)\)	3800.fn	180	no	\(-1\)	\(1\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{67}{90}\right)\)
\(\chi_{3800}(21,\cdot)\)	3800.et	90	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{3800}(23,\cdot)\)	3800.fg	180	no	\(1\)	\(1\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{3800}(27,\cdot)\)	3800.el	60	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(-i\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{3800}(29,\cdot)\)	3800.ez	90	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{3800}(31,\cdot)\)	3800.dv	30	no	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(-1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{3800}(33,\cdot)\)	3800.fl	180	no	\(1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{3800}(37,\cdot)\)	3800.di	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{3800}(39,\cdot)\)	3800.bw	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3800}(41,\cdot)\)	3800.ew	90	no	\(-1\)	\(1\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{61}{90}\right)\)
\(\chi_{3800}(43,\cdot)\)	3800.ed	36	no	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{3800}(47,\cdot)\)	3800.fg	180	no	\(1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{90}\right)\)
\(\chi_{3800}(49,\cdot)\)	3800.bk	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{3800}(51,\cdot)\)	3800.cy	18	no	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{3800}(53,\cdot)\)	3800.fh	180	yes	\(1\)	\(1\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)
\(\chi_{3800}(59,\cdot)\)	3800.ex	90	yes	\(1\)	\(1\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{3800}(61,\cdot)\)	3800.es	90	yes	\(1\)	\(1\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{3800}(63,\cdot)\)	3800.fg	180	no	\(1\)	\(1\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)
\(\chi_{3800}(67,\cdot)\)	3800.fm	180	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{77}{90}\right)\)
\(\chi_{3800}(69,\cdot)\)	3800.dn	30	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(-1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{3800}(71,\cdot)\)	3800.fb	90	no	\(1\)	\(1\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{73}{90}\right)\)
\(\chi_{3800}(73,\cdot)\)	3800.fn	180	no	\(-1\)	\(1\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{79}{90}\right)\)
\(\chi_{3800}(77,\cdot)\)	3800.dk	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3800}(79,\cdot)\)	3800.er	90	no	\(1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{43}{90}\right)\)
\(\chi_{3800}(81,\cdot)\)	3800.ei	45	no	\(1\)	\(1\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{3800}(83,\cdot)\)	3800.ej	60	yes	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(i\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)

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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.