LMFDB - Group of Dirichlet characters of modulus 1225

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1225)

pari: g = idealstar(,1225,2)

Character group

sage: G.order() pari: g.no
Order	=	840
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{420}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1225}(1177,\cdot)$, $\chi_{1225}(101,\cdot)$

First 32 of 840 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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{1225}(1,\cdot)$	1225.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1225}(2,\cdot)$	1225.bv	420	yes	$-1$	$1$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{61}{105}\right)$
$\chi_{1225}(3,\cdot)$	1225.bu	420	yes	$1$	$1$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{199}{420}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{92}{105}\right)$
$\chi_{1225}(4,\cdot)$	1225.bt	210	yes	$1$	$1$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{17}{105}\right)$
$\chi_{1225}(6,\cdot)$	1225.bl	70	yes	$-1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{1225}(8,\cdot)$	1225.bq	140	yes	$-1$	$1$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{1225}(9,\cdot)$	1225.bt	210	yes	$1$	$1$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{79}{105}\right)$
$\chi_{1225}(11,\cdot)$	1225.bo	105	yes	$1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{26}{105}\right)$
$\chi_{1225}(12,\cdot)$	1225.bu	420	yes	$1$	$1$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{391}{420}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{4}{105}\right)$
$\chi_{1225}(13,\cdot)$	1225.bp	140	yes	$1$	$1$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{1225}(16,\cdot)$	1225.bo	105	yes	$1$	$1$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{34}{105}\right)$
$\chi_{1225}(17,\cdot)$	1225.bu	420	yes	$1$	$1$	$e\left(\frac{53}{420}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{53}{105}\right)$
$\chi_{1225}(18,\cdot)$	1225.q	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{1225}(19,\cdot)$	1225.bb	30	no	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1225}(22,\cdot)$	1225.bq	140	yes	$-1$	$1$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{1225}(23,\cdot)$	1225.bv	420	yes	$-1$	$1$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{317}{420}\right)$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{31}{105}\right)$
$\chi_{1225}(24,\cdot)$	1225.bf	42	no	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{1225}(26,\cdot)$	1225.bg	42	no	$-1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{1225}(27,\cdot)$	1225.bp	140	yes	$1$	$1$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{1225}(29,\cdot)$	1225.bj	70	yes	$1$	$1$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{1225}(31,\cdot)$	1225.bc	30	no	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1225}(32,\cdot)$	1225.bm	84	no	$-1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{1225}(33,\cdot)$	1225.bu	420	yes	$1$	$1$	$e\left(\frac{223}{420}\right)$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{13}{105}\right)$
$\chi_{1225}(34,\cdot)$	1225.bk	70	yes	$-1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{1225}(36,\cdot)$	1225.bd	35	yes	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{1225}(37,\cdot)$	1225.bv	420	yes	$-1$	$1$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{4}{105}\right)$
$\chi_{1225}(38,\cdot)$	1225.bu	420	yes	$1$	$1$	$e\left(\frac{299}{420}\right)$	$e\left(\frac{43}{420}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{89}{105}\right)$
$\chi_{1225}(39,\cdot)$	1225.bt	210	yes	$1$	$1$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{41}{105}\right)$
$\chi_{1225}(41,\cdot)$	1225.bl	70	yes	$-1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{1225}(43,\cdot)$	1225.y	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{1225}(44,\cdot)$	1225.bt	210	yes	$1$	$1$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{43}{105}\right)$
$\chi_{1225}(46,\cdot)$	1225.bo	105	yes	$1$	$1$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{92}{105}\right)$

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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	$1225$
Structure	\(C_{2}\times C_{420}\)
Order	$840$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{1225}(1,\cdot)\)	1225.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1225}(2,\cdot)\)	1225.bv	420	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{61}{105}\right)\)
\(\chi_{1225}(3,\cdot)\)	1225.bu	420	yes	\(1\)	\(1\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{199}{420}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{92}{105}\right)\)
\(\chi_{1225}(4,\cdot)\)	1225.bt	210	yes	\(1\)	\(1\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{17}{105}\right)\)
\(\chi_{1225}(6,\cdot)\)	1225.bl	70	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{1225}(8,\cdot)\)	1225.bq	140	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{1225}(9,\cdot)\)	1225.bt	210	yes	\(1\)	\(1\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{79}{105}\right)\)
\(\chi_{1225}(11,\cdot)\)	1225.bo	105	yes	\(1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{26}{105}\right)\)
\(\chi_{1225}(12,\cdot)\)	1225.bu	420	yes	\(1\)	\(1\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{391}{420}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{4}{105}\right)\)
\(\chi_{1225}(13,\cdot)\)	1225.bp	140	yes	\(1\)	\(1\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{1225}(16,\cdot)\)	1225.bo	105	yes	\(1\)	\(1\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)
\(\chi_{1225}(17,\cdot)\)	1225.bu	420	yes	\(1\)	\(1\)	\(e\left(\frac{53}{420}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{53}{105}\right)\)
\(\chi_{1225}(18,\cdot)\)	1225.q	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1225}(19,\cdot)\)	1225.bb	30	no	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1225}(22,\cdot)\)	1225.bq	140	yes	\(-1\)	\(1\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{1225}(23,\cdot)\)	1225.bv	420	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{317}{420}\right)\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{31}{105}\right)\)
\(\chi_{1225}(24,\cdot)\)	1225.bf	42	no	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{1225}(26,\cdot)\)	1225.bg	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{1225}(27,\cdot)\)	1225.bp	140	yes	\(1\)	\(1\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{1225}(29,\cdot)\)	1225.bj	70	yes	\(1\)	\(1\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{1225}(31,\cdot)\)	1225.bc	30	no	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1225}(32,\cdot)\)	1225.bm	84	no	\(-1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{1225}(33,\cdot)\)	1225.bu	420	yes	\(1\)	\(1\)	\(e\left(\frac{223}{420}\right)\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{13}{105}\right)\)
\(\chi_{1225}(34,\cdot)\)	1225.bk	70	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{1225}(36,\cdot)\)	1225.bd	35	yes	\(1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{1225}(37,\cdot)\)	1225.bv	420	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{4}{105}\right)\)
\(\chi_{1225}(38,\cdot)\)	1225.bu	420	yes	\(1\)	\(1\)	\(e\left(\frac{299}{420}\right)\)	\(e\left(\frac{43}{420}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{89}{105}\right)\)
\(\chi_{1225}(39,\cdot)\)	1225.bt	210	yes	\(1\)	\(1\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{41}{105}\right)\)
\(\chi_{1225}(41,\cdot)\)	1225.bl	70	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{1225}(43,\cdot)\)	1225.y	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{1225}(44,\cdot)\)	1225.bt	210	yes	\(1\)	\(1\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{43}{105}\right)\)
\(\chi_{1225}(46,\cdot)\)	1225.bo	105	yes	\(1\)	\(1\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{92}{105}\right)\)

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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.