LMFDB - Group of Dirichlet characters of modulus 917415

Show commands: PariGP / SageMath

sage: H = DirichletGroup(917415)

pari: g = idealstar(,917415,2)

Character group

sage: G.order() pari: g.no
Order	=	435456
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{12}\times C_{36}\times C_{252}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{917415}(101936,\cdot)$, $\chi_{917415}(366967,\cdot)$, $\chi_{917415}(772561,\cdot)$, $\chi_{917415}(221446,\cdot)$, $\chi_{917415}(371926,\cdot)$

First 32 of 435456 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$22$
$\chi_{917415}(1,\cdot)$	917415.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{917415}(2,\cdot)$	917415.uvf	252	yes	$-1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{143}{252}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{1}{7}\right)$	$i$	$e\left(\frac{2}{21}\right)$
$\chi_{917415}(4,\cdot)$	917415.phi	126	yes	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{2}{7}\right)$	$-1$	$e\left(\frac{4}{21}\right)$
$\chi_{917415}(7,\cdot)$	917415.tiy	252	yes	$-1$	$1$	$e\left(\frac{143}{252}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{127}{252}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{61}{252}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{155}{252}\right)$
$\chi_{917415}(8,\cdot)$	917415.nbf	84	no	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{3}{7}\right)$	$-i$	$e\left(\frac{2}{7}\right)$
$\chi_{917415}(11,\cdot)$	917415.mtc	84	no	$1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{21}\right)$	$-i$	$e\left(\frac{1}{21}\right)$
$\chi_{917415}(13,\cdot)$	917415.pqs	252	yes	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{61}{252}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{139}{252}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{917415}(14,\cdot)$	917415.upu	252	yes	$1$	$1$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{139}{252}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{179}{252}\right)$
$\chi_{917415}(16,\cdot)$	917415.lmo	63	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{8}{21}\right)$
$\chi_{917415}(17,\cdot)$	917415.flq	36	no	$1$	$1$	$i$	$-1$	$e\left(\frac{29}{36}\right)$	$-i$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{18}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$1$
$\chi_{917415}(22,\cdot)$	917415.ves	252	yes	$-1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{155}{252}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{179}{252}\right)$	$e\left(\frac{8}{21}\right)$	$1$	$e\left(\frac{1}{7}\right)$
$\chi_{917415}(23,\cdot)$	917415.ugz	252	yes	$-1$	$1$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{121}{252}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{22}{63}\right)$
$\chi_{917415}(26,\cdot)$	917415.mrn	84	no	$1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{42}\right)$
$\chi_{917415}(28,\cdot)$	917415.ijf	36	no	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{917415}(31,\cdot)$	917415.lzf	84	no	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{917415}(32,\cdot)$	917415.uvf	252	yes	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{211}{252}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{5}{7}\right)$	$i$	$e\left(\frac{10}{21}\right)$
$\chi_{917415}(34,\cdot)$	917415.phl	126	yes	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{917415}(41,\cdot)$	917415.hzj	36	no	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{917415}(43,\cdot)$	917415.slq	252	yes	$-1$	$1$	$e\left(\frac{131}{252}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{121}{126}\right)$
$\chi_{917415}(44,\cdot)$	917415.pzr	252	no	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{205}{252}\right)$	$e\left(\frac{11}{21}\right)$	$i$	$e\left(\frac{5}{21}\right)$
$\chi_{917415}(46,\cdot)$	917415.ieg	36	no	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{917415}(47,\cdot)$	917415.txl	252	yes	$-1$	$1$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{179}{252}\right)$	$e\left(\frac{139}{252}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{61}{252}\right)$
$\chi_{917415}(49,\cdot)$	917415.oii	126	yes	$1$	$1$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{29}{126}\right)$
$\chi_{917415}(52,\cdot)$	917415.uzz	252	yes	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{95}{252}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{191}{252}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{917415}(53,\cdot)$	917415.rwa	252	no	$-1$	$1$	$e\left(\frac{65}{252}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{101}{252}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{169}{252}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{143}{252}\right)$
$\chi_{917415}(56,\cdot)$	917415.uep	252	no	$1$	$1$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{43}{252}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{227}{252}\right)$
$\chi_{917415}(59,\cdot)$	917415.fhu	36	no	$-1$	$1$	$i$	$-1$	$e\left(\frac{13}{18}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{36}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{917415}(61,\cdot)$	917415.vam	252	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{1}{21}\right)$	$-1$	$e\left(\frac{11}{28}\right)$
$\chi_{917415}(62,\cdot)$	917415.psg	252	no	$1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{83}{252}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{917415}(64,\cdot)$	917415.lld	42	no	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{4}{7}\right)$
$\chi_{917415}(67,\cdot)$	917415.psx	252	yes	$1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{247}{252}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{917415}(68,\cdot)$	917415.nbm	84	yes	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{21}\right)$

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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	$917415$
Structure	\(C_{2}\times C_{2}\times C_{12}\times C_{36}\times C_{252}\)
Order	$435456$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(22\)
\(\chi_{917415}(1,\cdot)\)	917415.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{917415}(2,\cdot)\)	917415.uvf	252	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{143}{252}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(i\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{917415}(4,\cdot)\)	917415.phi	126	yes	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-1\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{917415}(7,\cdot)\)	917415.tiy	252	yes	\(-1\)	\(1\)	\(e\left(\frac{143}{252}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{127}{252}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{61}{252}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{155}{252}\right)\)
\(\chi_{917415}(8,\cdot)\)	917415.nbf	84	no	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-i\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{917415}(11,\cdot)\)	917415.mtc	84	no	\(1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(-i\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{917415}(13,\cdot)\)	917415.pqs	252	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{61}{252}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{139}{252}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{917415}(14,\cdot)\)	917415.upu	252	yes	\(1\)	\(1\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{139}{252}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{179}{252}\right)\)
\(\chi_{917415}(16,\cdot)\)	917415.lmo	63	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{917415}(17,\cdot)\)	917415.flq	36	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{29}{36}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(1\)
\(\chi_{917415}(22,\cdot)\)	917415.ves	252	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{155}{252}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{179}{252}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(1\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{917415}(23,\cdot)\)	917415.ugz	252	yes	\(-1\)	\(1\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{121}{252}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{22}{63}\right)\)
\(\chi_{917415}(26,\cdot)\)	917415.mrn	84	no	\(1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{42}\right)\)
\(\chi_{917415}(28,\cdot)\)	917415.ijf	36	no	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{917415}(31,\cdot)\)	917415.lzf	84	no	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{917415}(32,\cdot)\)	917415.uvf	252	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{211}{252}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(i\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{917415}(34,\cdot)\)	917415.phl	126	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{917415}(41,\cdot)\)	917415.hzj	36	no	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{917415}(43,\cdot)\)	917415.slq	252	yes	\(-1\)	\(1\)	\(e\left(\frac{131}{252}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{121}{126}\right)\)
\(\chi_{917415}(44,\cdot)\)	917415.pzr	252	no	\(1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{205}{252}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(i\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{917415}(46,\cdot)\)	917415.ieg	36	no	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{917415}(47,\cdot)\)	917415.txl	252	yes	\(-1\)	\(1\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{179}{252}\right)\)	\(e\left(\frac{139}{252}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{61}{252}\right)\)
\(\chi_{917415}(49,\cdot)\)	917415.oii	126	yes	\(1\)	\(1\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{29}{126}\right)\)
\(\chi_{917415}(52,\cdot)\)	917415.uzz	252	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{95}{252}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{191}{252}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{917415}(53,\cdot)\)	917415.rwa	252	no	\(-1\)	\(1\)	\(e\left(\frac{65}{252}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{101}{252}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{169}{252}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{143}{252}\right)\)
\(\chi_{917415}(56,\cdot)\)	917415.uep	252	no	\(1\)	\(1\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{43}{252}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{227}{252}\right)\)
\(\chi_{917415}(59,\cdot)\)	917415.fhu	36	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{13}{18}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{917415}(61,\cdot)\)	917415.vam	252	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(-1\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{917415}(62,\cdot)\)	917415.psg	252	no	\(1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{83}{252}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{917415}(64,\cdot)\)	917415.lld	42	no	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{917415}(67,\cdot)\)	917415.psx	252	yes	\(1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{247}{252}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{917415}(68,\cdot)\)	917415.nbm	84	yes	\(1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{21}\right)\)

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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.