LMFDB - Group of Dirichlet characters of modulus 5225

Show commands: PariGP / SageMath

sage: H = DirichletGroup(5225)

pari: g = idealstar(,5225,2)

Character group

sage: G.order() pari: g.no
Order	=	3600
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{10}\times C_{180}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{5225}(2927,\cdot)$, $\chi_{5225}(2851,\cdot)$, $\chi_{5225}(4676,\cdot)$

First 32 of 3600 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{5225}(1,\cdot)$	5225.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{5225}(2,\cdot)$	5225.jq	180	yes	$-1$	$1$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{5225}(3,\cdot)$	5225.jg	180	yes	$1$	$1$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{5225}(4,\cdot)$	5225.hk	90	yes	$1$	$1$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{5225}(6,\cdot)$	5225.hn	90	yes	$-1$	$1$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{5225}(7,\cdot)$	5225.gk	60	no	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{30}\right)$	$i$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{5225}(8,\cdot)$	5225.gn	60	yes	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{5225}(9,\cdot)$	5225.hl	90	yes	$1$	$1$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{5225}(12,\cdot)$	5225.gu	60	no	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{15}\right)$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{5225}(13,\cdot)$	5225.jb	180	yes	$-1$	$1$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{5225}(14,\cdot)$	5225.hv	90	yes	$-1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{83}{90}\right)$
$\chi_{5225}(16,\cdot)$	5225.ge	45	yes	$1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{5225}(17,\cdot)$	5225.jp	180	yes	$1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{5225}(18,\cdot)$	5225.ea	20	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{5225}(21,\cdot)$	5225.is	90	yes	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{5225}(23,\cdot)$	5225.ix	180	no	$-1$	$1$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{7}{90}\right)$
$\chi_{5225}(24,\cdot)$	5225.in	90	no	$-1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{5225}(26,\cdot)$	5225.cz	15	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{5225}(27,\cdot)$	5225.gg	60	yes	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5225}(28,\cdot)$	5225.jj	180	yes	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{5225}(29,\cdot)$	5225.ii	90	yes	$1$	$1$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{73}{90}\right)$
$\chi_{5225}(31,\cdot)$	5225.fs	30	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{5225}(32,\cdot)$	5225.fz	36	no	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{5225}(34,\cdot)$	5225.it	90	no	$-1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{43}{90}\right)$
$\chi_{5225}(36,\cdot)$	5225.gd	45	yes	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{5225}(37,\cdot)$	5225.do	20	yes	$1$	$1$	$e\left(\frac{3}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$-1$	$e\left(\frac{11}{20}\right)$	$i$	$e\left(\frac{4}{5}\right)$
$\chi_{5225}(39,\cdot)$	5225.bl	10	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$
$\chi_{5225}(41,\cdot)$	5225.hh	90	yes	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{59}{90}\right)$
$\chi_{5225}(42,\cdot)$	5225.jn	180	yes	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{43}{90}\right)$
$\chi_{5225}(43,\cdot)$	5225.fx	36	no	$1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{5225}(46,\cdot)$	5225.fr	30	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{5225}(47,\cdot)$	5225.jm	180	yes	$-1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{11}{18}\right)$

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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	$5225$
Structure	\(C_{2}\times C_{10}\times C_{180}\)
Order	$3600$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{5225}(1,\cdot)\)	5225.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{5225}(2,\cdot)\)	5225.jq	180	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{5225}(3,\cdot)\)	5225.jg	180	yes	\(1\)	\(1\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{5225}(4,\cdot)\)	5225.hk	90	yes	\(1\)	\(1\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{5225}(6,\cdot)\)	5225.hn	90	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{5225}(7,\cdot)\)	5225.gk	60	no	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(i\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{5225}(8,\cdot)\)	5225.gn	60	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{5225}(9,\cdot)\)	5225.hl	90	yes	\(1\)	\(1\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{5225}(12,\cdot)\)	5225.gu	60	no	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{5225}(13,\cdot)\)	5225.jb	180	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{5225}(14,\cdot)\)	5225.hv	90	yes	\(-1\)	\(1\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{83}{90}\right)\)
\(\chi_{5225}(16,\cdot)\)	5225.ge	45	yes	\(1\)	\(1\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{5225}(17,\cdot)\)	5225.jp	180	yes	\(1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{5225}(18,\cdot)\)	5225.ea	20	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{5225}(21,\cdot)\)	5225.is	90	yes	\(1\)	\(1\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{5225}(23,\cdot)\)	5225.ix	180	no	\(-1\)	\(1\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)
\(\chi_{5225}(24,\cdot)\)	5225.in	90	no	\(-1\)	\(1\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{5225}(26,\cdot)\)	5225.cz	15	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{5225}(27,\cdot)\)	5225.gg	60	yes	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5225}(28,\cdot)\)	5225.jj	180	yes	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)
\(\chi_{5225}(29,\cdot)\)	5225.ii	90	yes	\(1\)	\(1\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{73}{90}\right)\)
\(\chi_{5225}(31,\cdot)\)	5225.fs	30	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{5225}(32,\cdot)\)	5225.fz	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{5225}(34,\cdot)\)	5225.it	90	no	\(-1\)	\(1\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)
\(\chi_{5225}(36,\cdot)\)	5225.gd	45	yes	\(1\)	\(1\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{5225}(37,\cdot)\)	5225.do	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(-1\)	\(e\left(\frac{11}{20}\right)\)	\(i\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{5225}(39,\cdot)\)	5225.bl	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)
\(\chi_{5225}(41,\cdot)\)	5225.hh	90	yes	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)
\(\chi_{5225}(42,\cdot)\)	5225.jn	180	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)
\(\chi_{5225}(43,\cdot)\)	5225.fx	36	no	\(1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{5225}(46,\cdot)\)	5225.fr	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{5225}(47,\cdot)\)	5225.jm	180	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{11}{18}\right)\)

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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.