LMFDB - Group of Dirichlet characters of modulus 105222

Show commands: PariGP / SageMath

sage: H = DirichletGroup(105222)

pari: g = idealstar(,105222,2)

Character group

sage: G.order() pari: g.no
Order	=	30240
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{1260}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{105222}(35075,\cdot)$, $\chi_{105222}(40471,\cdot)$, $\chi_{105222}(94147,\cdot)$, $\chi_{105222}(34087,\cdot)$

First 32 of 30240 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	$-1$	$1$	$5$	$7$	$11$	$17$	$23$	$25$	$29$	$31$	$35$	$37$
$\chi_{105222}(1,\cdot)$	105222.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{105222}(5,\cdot)$	105222.vp	180	no	$1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{59}{90}\right)$	$i$
$\chi_{105222}(7,\cdot)$	105222.bak	420	no	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{361}{420}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{105222}(11,\cdot)$	105222.bab	420	no	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{361}{420}\right)$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{105222}(17,\cdot)$	105222.sp	90	no	$1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{105222}(23,\cdot)$	105222.ul	126	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{105222}(25,\cdot)$	105222.rt	90	no	$1$	$1$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{45}\right)$	$-1$
$\chi_{105222}(29,\cdot)$	105222.bbq	630	no	$1$	$1$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{298}{315}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{73}{630}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{105222}(31,\cdot)$	105222.bal	420	no	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{105222}(35,\cdot)$	105222.bbz	630	no	$1$	$1$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{73}{630}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{232}{315}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{105222}(37,\cdot)$	105222.qx	84	no	$1$	$1$	$i$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{42}\right)$	$-1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{105222}(41,\cdot)$	105222.zi	252	no	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{105222}(43,\cdot)$	105222.bcg	630	no	$1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{128}{315}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{244}{315}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{105222}(47,\cdot)$	105222.bdj	1260	no	$-1$	$1$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{239}{420}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{503}{630}\right)$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{2}{315}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{105222}(49,\cdot)$	105222.xh	210	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{105222}(53,\cdot)$	105222.bbw	630	no	$-1$	$1$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{73}{315}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{149}{315}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{105222}(55,\cdot)$	105222.bba	630	no	$-1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{29}{315}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{209}{630}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{105222}(59,\cdot)$	105222.bdn	1260	no	$1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{8}{315}\right)$	$e\left(\frac{233}{420}\right)$	$e\left(\frac{94}{315}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{105222}(61,\cdot)$	105222.bba	630	no	$-1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{184}{315}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{229}{630}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{105222}(67,\cdot)$	105222.bdc	1260	no	$-1$	$1$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{107}{420}\right)$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{29}{630}\right)$	$e\left(\frac{127}{420}\right)$	$e\left(\frac{577}{630}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{105222}(73,\cdot)$	105222.bcz	1260	no	$-1$	$1$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{71}{420}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{191}{315}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{118}{315}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{105222}(77,\cdot)$	105222.pt	70	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{105222}(79,\cdot)$	105222.bbk	630	no	$-1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{481}{630}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{109}{315}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{105222}(83,\cdot)$	105222.bam	420	no	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{105222}(85,\cdot)$	105222.wg	180	no	$1$	$1$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{105222}(89,\cdot)$	105222.bdm	1260	no	$-1$	$1$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{253}{420}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{283}{315}\right)$	$e\left(\frac{223}{420}\right)$	$e\left(\frac{193}{630}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{105222}(97,\cdot)$	105222.zf	252	no	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{105222}(101,\cdot)$	105222.tz	126	no	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{105222}(103,\cdot)$	105222.nw	42	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{105222}(107,\cdot)$	105222.xa	210	no	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{105222}(109,\cdot)$	105222.bde	1260	no	$1$	$1$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{619}{630}\right)$	$e\left(\frac{17}{420}\right)$	$e\left(\frac{211}{315}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{105222}(113,\cdot)$	105222.ym	210	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{25}{42}\right)$

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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	$105222$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{1260}\)
Order	$30240$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)	\(37\)
\(\chi_{105222}(1,\cdot)\)	105222.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{105222}(5,\cdot)\)	105222.vp	180	no	\(1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(i\)
\(\chi_{105222}(7,\cdot)\)	105222.bak	420	no	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{361}{420}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{105222}(11,\cdot)\)	105222.bab	420	no	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{361}{420}\right)\)	\(e\left(\frac{131}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{105222}(17,\cdot)\)	105222.sp	90	no	\(1\)	\(1\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{105222}(23,\cdot)\)	105222.ul	126	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{105222}(25,\cdot)\)	105222.rt	90	no	\(1\)	\(1\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(-1\)
\(\chi_{105222}(29,\cdot)\)	105222.bbq	630	no	\(1\)	\(1\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{298}{315}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{73}{630}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{105222}(31,\cdot)\)	105222.bal	420	no	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{105222}(35,\cdot)\)	105222.bbz	630	no	\(1\)	\(1\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{73}{630}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{232}{315}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{105222}(37,\cdot)\)	105222.qx	84	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(-1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{105222}(41,\cdot)\)	105222.zi	252	no	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{105222}(43,\cdot)\)	105222.bcg	630	no	\(1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{128}{315}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{244}{315}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{105222}(47,\cdot)\)	105222.bdj	1260	no	\(-1\)	\(1\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{239}{420}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{503}{630}\right)\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{2}{315}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{105222}(49,\cdot)\)	105222.xh	210	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{105222}(53,\cdot)\)	105222.bbw	630	no	\(-1\)	\(1\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{73}{315}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{149}{315}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{105222}(55,\cdot)\)	105222.bba	630	no	\(-1\)	\(1\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{29}{315}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{209}{630}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{105222}(59,\cdot)\)	105222.bdn	1260	no	\(1\)	\(1\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{8}{315}\right)\)	\(e\left(\frac{233}{420}\right)\)	\(e\left(\frac{94}{315}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{105222}(61,\cdot)\)	105222.bba	630	no	\(-1\)	\(1\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{184}{315}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{229}{630}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{105222}(67,\cdot)\)	105222.bdc	1260	no	\(-1\)	\(1\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{107}{420}\right)\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{29}{630}\right)\)	\(e\left(\frac{127}{420}\right)\)	\(e\left(\frac{577}{630}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{105222}(73,\cdot)\)	105222.bcz	1260	no	\(-1\)	\(1\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{71}{420}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{191}{315}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{118}{315}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{105222}(77,\cdot)\)	105222.pt	70	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{105222}(79,\cdot)\)	105222.bbk	630	no	\(-1\)	\(1\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{481}{630}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{109}{315}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{105222}(83,\cdot)\)	105222.bam	420	no	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{105222}(85,\cdot)\)	105222.wg	180	no	\(1\)	\(1\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{105222}(89,\cdot)\)	105222.bdm	1260	no	\(-1\)	\(1\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{253}{420}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{283}{315}\right)\)	\(e\left(\frac{223}{420}\right)\)	\(e\left(\frac{193}{630}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{105222}(97,\cdot)\)	105222.zf	252	no	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{105222}(101,\cdot)\)	105222.tz	126	no	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{105222}(103,\cdot)\)	105222.nw	42	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{105222}(107,\cdot)\)	105222.xa	210	no	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{105222}(109,\cdot)\)	105222.bde	1260	no	\(1\)	\(1\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{277}{420}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{619}{630}\right)\)	\(e\left(\frac{17}{420}\right)\)	\(e\left(\frac{211}{315}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{105222}(113,\cdot)\)	105222.ym	210	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{25}{42}\right)\)

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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.