LMFDB - Group of Dirichlet characters of modulus 4015

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4015)

pari: g = idealstar(,4015,2)

Character group

sage: G.order() pari: g.no
Order	=	2880
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{360}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4015}(1607,\cdot)$, $\chi_{4015}(2191,\cdot)$, $\chi_{4015}(881,\cdot)$

First 32 of 2880 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{4015}(1,\cdot)$	4015.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4015}(2,\cdot)$	4015.fz	180	yes	$1$	$1$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{4015}(3,\cdot)$	4015.eo	60	yes	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{60}\right)$
$\chi_{4015}(4,\cdot)$	4015.fd	90	yes	$1$	$1$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{4015}(6,\cdot)$	4015.fs	180	no	$-1$	$1$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{31}{180}\right)$
$\chi_{4015}(7,\cdot)$	4015.fp	120	yes	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{107}{120}\right)$
$\chi_{4015}(8,\cdot)$	4015.em	60	yes	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{4015}(9,\cdot)$	4015.dj	30	yes	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{4015}(12,\cdot)$	4015.dq	36	no	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{4015}(13,\cdot)$	4015.ge	360	yes	$-1$	$1$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{251}{360}\right)$	$e\left(\frac{323}{360}\right)$
$\chi_{4015}(14,\cdot)$	4015.gg	360	yes	$-1$	$1$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{323}{360}\right)$	$e\left(\frac{269}{360}\right)$
$\chi_{4015}(16,\cdot)$	4015.ei	45	no	$1$	$1$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{4015}(17,\cdot)$	4015.fp	120	yes	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{79}{120}\right)$
$\chi_{4015}(18,\cdot)$	4015.fx	180	yes	$1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{4015}(19,\cdot)$	4015.gd	180	yes	$-1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{127}{180}\right)$
$\chi_{4015}(21,\cdot)$	4015.df	24	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{4015}(23,\cdot)$	4015.dw	36	no	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{4015}(24,\cdot)$	4015.et	60	yes	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{53}{60}\right)$
$\chi_{4015}(26,\cdot)$	4015.gi	360	no	$-1$	$1$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{37}{360}\right)$	$e\left(\frac{271}{360}\right)$
$\chi_{4015}(27,\cdot)$	4015.cw	20	yes	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{4015}(28,\cdot)$	4015.gk	360	yes	$-1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{109}{360}\right)$	$e\left(\frac{217}{360}\right)$
$\chi_{4015}(29,\cdot)$	4015.gj	360	yes	$1$	$1$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{317}{360}\right)$	$e\left(\frac{191}{360}\right)$
$\chi_{4015}(31,\cdot)$	4015.gi	360	no	$-1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{221}{360}\right)$	$e\left(\frac{23}{360}\right)$
$\chi_{4015}(32,\cdot)$	4015.du	36	yes	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{4015}(34,\cdot)$	4015.fa	72	no	$-1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{37}{72}\right)$
$\chi_{4015}(36,\cdot)$	4015.fi	90	no	$1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{4015}(37,\cdot)$	4015.fw	180	yes	$-1$	$1$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{49}{90}\right)$
$\chi_{4015}(38,\cdot)$	4015.fv	180	yes	$-1$	$1$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{101}{180}\right)$
$\chi_{4015}(39,\cdot)$	4015.gj	360	yes	$1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{239}{360}\right)$	$e\left(\frac{77}{360}\right)$
$\chi_{4015}(41,\cdot)$	4015.fj	90	no	$-1$	$1$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{61}{90}\right)$
$\chi_{4015}(42,\cdot)$	4015.gl	360	yes	$1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{311}{360}\right)$	$e\left(\frac{23}{360}\right)$
$\chi_{4015}(43,\cdot)$	4015.db	24	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{24}\right)$

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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	$4015$
Structure	\(C_{2}\times C_{4}\times C_{360}\)
Order	$2880$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{4015}(1,\cdot)\)	4015.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4015}(2,\cdot)\)	4015.fz	180	yes	\(1\)	\(1\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)
\(\chi_{4015}(3,\cdot)\)	4015.eo	60	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{4015}(4,\cdot)\)	4015.fd	90	yes	\(1\)	\(1\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{4015}(6,\cdot)\)	4015.fs	180	no	\(-1\)	\(1\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{31}{180}\right)\)
\(\chi_{4015}(7,\cdot)\)	4015.fp	120	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{107}{120}\right)\)
\(\chi_{4015}(8,\cdot)\)	4015.em	60	yes	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{4015}(9,\cdot)\)	4015.dj	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{4015}(12,\cdot)\)	4015.dq	36	no	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{4015}(13,\cdot)\)	4015.ge	360	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{251}{360}\right)\)	\(e\left(\frac{323}{360}\right)\)
\(\chi_{4015}(14,\cdot)\)	4015.gg	360	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{323}{360}\right)\)	\(e\left(\frac{269}{360}\right)\)
\(\chi_{4015}(16,\cdot)\)	4015.ei	45	no	\(1\)	\(1\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{4015}(17,\cdot)\)	4015.fp	120	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{79}{120}\right)\)
\(\chi_{4015}(18,\cdot)\)	4015.fx	180	yes	\(1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{4015}(19,\cdot)\)	4015.gd	180	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{127}{180}\right)\)
\(\chi_{4015}(21,\cdot)\)	4015.df	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{4015}(23,\cdot)\)	4015.dw	36	no	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{4015}(24,\cdot)\)	4015.et	60	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)
\(\chi_{4015}(26,\cdot)\)	4015.gi	360	no	\(-1\)	\(1\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{37}{360}\right)\)	\(e\left(\frac{271}{360}\right)\)
\(\chi_{4015}(27,\cdot)\)	4015.cw	20	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{4015}(28,\cdot)\)	4015.gk	360	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{109}{360}\right)\)	\(e\left(\frac{217}{360}\right)\)
\(\chi_{4015}(29,\cdot)\)	4015.gj	360	yes	\(1\)	\(1\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{317}{360}\right)\)	\(e\left(\frac{191}{360}\right)\)
\(\chi_{4015}(31,\cdot)\)	4015.gi	360	no	\(-1\)	\(1\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{221}{360}\right)\)	\(e\left(\frac{23}{360}\right)\)
\(\chi_{4015}(32,\cdot)\)	4015.du	36	yes	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{4015}(34,\cdot)\)	4015.fa	72	no	\(-1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)
\(\chi_{4015}(36,\cdot)\)	4015.fi	90	no	\(1\)	\(1\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{4015}(37,\cdot)\)	4015.fw	180	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)
\(\chi_{4015}(38,\cdot)\)	4015.fv	180	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{101}{180}\right)\)
\(\chi_{4015}(39,\cdot)\)	4015.gj	360	yes	\(1\)	\(1\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{239}{360}\right)\)	\(e\left(\frac{77}{360}\right)\)
\(\chi_{4015}(41,\cdot)\)	4015.fj	90	no	\(-1\)	\(1\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{61}{90}\right)\)
\(\chi_{4015}(42,\cdot)\)	4015.gl	360	yes	\(1\)	\(1\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{311}{360}\right)\)	\(e\left(\frac{23}{360}\right)\)
\(\chi_{4015}(43,\cdot)\)	4015.db	24	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)

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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.