LMFDB - Group of Dirichlet characters of modulus 14700

sage:H = DirichletGroup(14700)

pari:g = idealstar(,14700,2)

Character group

sage:G.order() pari:g.no
Order	=	3360
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{420}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{14700}(7351,\cdot)$, $\chi_{14700}(4901,\cdot)$, $\chi_{14700}(1177,\cdot)$, $\chi_{14700}(9901,\cdot)$

First 32 of 3360 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{14700}(1,\cdot)$	14700.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{14700}(11,\cdot)$	14700.gs	210	yes	$1$	$1$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{14700}(13,\cdot)$	14700.gj	140	no	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{14700}(17,\cdot)$	14700.hj	420	no	$-1$	$1$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{349}{420}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{14700}(19,\cdot)$	14700.dx	30	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$	$1$
$\chi_{14700}(23,\cdot)$	14700.hf	420	yes	$-1$	$1$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{14700}(29,\cdot)$	14700.fj	70	no	$-1$	$1$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{14700}(31,\cdot)$	14700.dz	30	no	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$-1$
$\chi_{14700}(37,\cdot)$	14700.hc	420	no	$-1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{14700}(41,\cdot)$	14700.fk	70	no	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{14700}(43,\cdot)$	14700.dt	28	no	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{28}\right)$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{14}\right)$	$-1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{14700}(47,\cdot)$	14700.hd	420	yes	$1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{367}{420}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{14700}(53,\cdot)$	14700.hh	420	no	$1$	$1$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{14700}(59,\cdot)$	14700.gt	210	yes	$-1$	$1$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{14700}(61,\cdot)$	14700.gp	210	no	$-1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{14700}(67,\cdot)$	14700.fc	60	no	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{3}{5}\right)$	$i$
$\chi_{14700}(71,\cdot)$	14700.fu	70	yes	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{14700}(73,\cdot)$	14700.he	420	no	$1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{14700}(79,\cdot)$	14700.dy	30	no	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{5}\right)$	$1$
$\chi_{14700}(83,\cdot)$	14700.gm	140	yes	$1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{14700}(89,\cdot)$	14700.ha	210	no	$1$	$1$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{14700}(97,\cdot)$	14700.de	20	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$
$\chi_{14700}(101,\cdot)$	14700.er	42	no	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{14700}(103,\cdot)$	14700.hg	420	no	$-1$	$1$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{341}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{14700}(107,\cdot)$	14700.ga	84	no	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{14700}(109,\cdot)$	14700.gq	210	no	$1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{14700}(113,\cdot)$	14700.gi	140	no	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{14700}(121,\cdot)$	14700.ge	105	no	$1$	$1$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{14700}(127,\cdot)$	14700.gf	140	no	$1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{14700}(131,\cdot)$	14700.go	210	yes	$-1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{14700}(137,\cdot)$	14700.hh	420	no	$1$	$1$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{89}{420}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{14700}(139,\cdot)$	14700.fn	70	no	$1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{1}{7}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$14700$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{420}\)
Order	$3360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{14700}(1,\cdot)\)	14700.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{14700}(11,\cdot)\)	14700.gs	210	yes	\(1\)	\(1\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{14700}(13,\cdot)\)	14700.gj	140	no	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{14700}(17,\cdot)\)	14700.hj	420	no	\(-1\)	\(1\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{349}{420}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{14700}(19,\cdot)\)	14700.dx	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)
\(\chi_{14700}(23,\cdot)\)	14700.hf	420	yes	\(-1\)	\(1\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{14700}(29,\cdot)\)	14700.fj	70	no	\(-1\)	\(1\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{14700}(31,\cdot)\)	14700.dz	30	no	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)
\(\chi_{14700}(37,\cdot)\)	14700.hc	420	no	\(-1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{14700}(41,\cdot)\)	14700.fk	70	no	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{14700}(43,\cdot)\)	14700.dt	28	no	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{14700}(47,\cdot)\)	14700.hd	420	yes	\(1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{367}{420}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{14700}(53,\cdot)\)	14700.hh	420	no	\(1\)	\(1\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{14700}(59,\cdot)\)	14700.gt	210	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{14700}(61,\cdot)\)	14700.gp	210	no	\(-1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{14700}(67,\cdot)\)	14700.fc	60	no	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(i\)
\(\chi_{14700}(71,\cdot)\)	14700.fu	70	yes	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{14700}(73,\cdot)\)	14700.he	420	no	\(1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{14700}(79,\cdot)\)	14700.dy	30	no	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)
\(\chi_{14700}(83,\cdot)\)	14700.gm	140	yes	\(1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{14700}(89,\cdot)\)	14700.ha	210	no	\(1\)	\(1\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{14700}(97,\cdot)\)	14700.de	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)
\(\chi_{14700}(101,\cdot)\)	14700.er	42	no	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{14700}(103,\cdot)\)	14700.hg	420	no	\(-1\)	\(1\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{341}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{14700}(107,\cdot)\)	14700.ga	84	no	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{14700}(109,\cdot)\)	14700.gq	210	no	\(1\)	\(1\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{14700}(113,\cdot)\)	14700.gi	140	no	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{14700}(121,\cdot)\)	14700.ge	105	no	\(1\)	\(1\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{14700}(127,\cdot)\)	14700.gf	140	no	\(1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{14700}(131,\cdot)\)	14700.go	210	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{14700}(137,\cdot)\)	14700.hh	420	no	\(1\)	\(1\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{89}{420}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{14700}(139,\cdot)\)	14700.fn	70	no	\(1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{1}{7}\right)\)

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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.