LMFDB - Group of Dirichlet characters of modulus 2700

sage:H = DirichletGroup(2700)

pari:g = idealstar(,2700,2)

Character group

sage:G.order() pari:g.no
Order	=	720
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{180}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{2700}(1351,\cdot)$, $\chi_{2700}(1001,\cdot)$, $\chi_{2700}(2377,\cdot)$

First 32 of 720 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{2700}(1,\cdot)$	2700.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2700}(7,\cdot)$	2700.cb	36	no	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{2700}(11,\cdot)$	2700.ck	90	yes	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{43}{90}\right)$
$\chi_{2700}(13,\cdot)$	2700.cr	180	no	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{2700}(17,\cdot)$	2700.cg	60	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{2700}(19,\cdot)$	2700.bt	30	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{2700}(23,\cdot)$	2700.ct	180	yes	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{2700}(29,\cdot)$	2700.cp	90	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{2700}(31,\cdot)$	2700.co	90	yes	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{2700}(37,\cdot)$	2700.ci	60	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{2700}(41,\cdot)$	2700.cm	90	no	$-1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{2700}(43,\cdot)$	2700.cb	36	no	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{2700}(47,\cdot)$	2700.ct	180	yes	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{90}\right)$
$\chi_{2700}(49,\cdot)$	2700.bm	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{2700}(53,\cdot)$	2700.bs	20	no	$1$	$1$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{2700}(59,\cdot)$	2700.cn	90	yes	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{2700}(61,\cdot)$	2700.ce	45	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{2700}(67,\cdot)$	2700.cs	180	yes	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{2700}(71,\cdot)$	2700.bz	30	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{2700}(73,\cdot)$	2700.ci	60	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{2700}(77,\cdot)$	2700.cq	180	no	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{2700}(79,\cdot)$	2700.cj	90	yes	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{2700}(83,\cdot)$	2700.ct	180	yes	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{49}{90}\right)$
$\chi_{2700}(89,\cdot)$	2700.bw	30	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{2700}(91,\cdot)$	2700.bx	30	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{2700}(97,\cdot)$	2700.cr	180	no	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{2700}(101,\cdot)$	2700.bl	18	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{2700}(103,\cdot)$	2700.cs	180	yes	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{2700}(107,\cdot)$	2700.m	4	no	$-1$	$1$	$-i$	$1$	$-i$	$-i$	$1$	$-i$	$1$	$-1$	$i$	$-1$
$\chi_{2700}(109,\cdot)$	2700.x	10	no	$1$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{2700}(113,\cdot)$	2700.cq	180	no	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{2700}(119,\cdot)$	2700.cn	90	yes	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{79}{90}\right)$

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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	$2700$
Structure	\(C_{2}\times C_{2}\times C_{180}\)
Order	$720$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{2700}(1,\cdot)\)	2700.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2700}(7,\cdot)\)	2700.cb	36	no	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{2700}(11,\cdot)\)	2700.ck	90	yes	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{43}{90}\right)\)
\(\chi_{2700}(13,\cdot)\)	2700.cr	180	no	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{2700}(17,\cdot)\)	2700.cg	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{2700}(19,\cdot)\)	2700.bt	30	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{2700}(23,\cdot)\)	2700.ct	180	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)
\(\chi_{2700}(29,\cdot)\)	2700.cp	90	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{2700}(31,\cdot)\)	2700.co	90	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{2700}(37,\cdot)\)	2700.ci	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{2700}(41,\cdot)\)	2700.cm	90	no	\(-1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{77}{90}\right)\)
\(\chi_{2700}(43,\cdot)\)	2700.cb	36	no	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{2700}(47,\cdot)\)	2700.ct	180	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)
\(\chi_{2700}(49,\cdot)\)	2700.bm	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{2700}(53,\cdot)\)	2700.bs	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{2700}(59,\cdot)\)	2700.cn	90	yes	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{47}{90}\right)\)
\(\chi_{2700}(61,\cdot)\)	2700.ce	45	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{2700}(67,\cdot)\)	2700.cs	180	yes	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{2700}(71,\cdot)\)	2700.bz	30	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{2700}(73,\cdot)\)	2700.ci	60	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{2700}(77,\cdot)\)	2700.cq	180	no	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)
\(\chi_{2700}(79,\cdot)\)	2700.cj	90	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{2700}(83,\cdot)\)	2700.ct	180	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{49}{90}\right)\)
\(\chi_{2700}(89,\cdot)\)	2700.bw	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{2700}(91,\cdot)\)	2700.bx	30	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{2700}(97,\cdot)\)	2700.cr	180	no	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{2700}(101,\cdot)\)	2700.bl	18	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{2700}(103,\cdot)\)	2700.cs	180	yes	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{2700}(107,\cdot)\)	2700.m	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{2700}(109,\cdot)\)	2700.x	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{2700}(113,\cdot)\)	2700.cq	180	no	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)
\(\chi_{2700}(119,\cdot)\)	2700.cn	90	yes	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{79}{90}\right)\)

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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.