LMFDB - Group of Dirichlet characters of modulus 311

Show commands: PariGP / SageMath

sage: H = DirichletGroup(311)

pari: g = idealstar(,311,2)

Character group

sage: G.order() pari: g.no
Order	=	310
sage: H.invariants() pari: g.cyc
Structure	=	$C_{310}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{311}(17,\cdot)$

First 32 of 310 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{311}(1,\cdot)$	311.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{311}(2,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{87}{155}\right)$	$e\left(\frac{99}{155}\right)$	$e\left(\frac{19}{155}\right)$	$e\left(\frac{141}{155}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{43}{155}\right)$	$e\left(\frac{73}{155}\right)$	$e\left(\frac{18}{31}\right)$
$\chi_{311}(3,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{99}{155}\right)$	$e\left(\frac{118}{155}\right)$	$e\left(\frac{43}{155}\right)$	$e\left(\frac{107}{155}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{142}{155}\right)$	$e\left(\frac{81}{155}\right)$	$e\left(\frac{51}{155}\right)$	$e\left(\frac{13}{31}\right)$
$\chi_{311}(4,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{19}{155}\right)$	$e\left(\frac{43}{155}\right)$	$e\left(\frac{38}{155}\right)$	$e\left(\frac{127}{155}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{57}{155}\right)$	$e\left(\frac{86}{155}\right)$	$e\left(\frac{146}{155}\right)$	$e\left(\frac{5}{31}\right)$
$\chi_{311}(5,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{141}{155}\right)$	$e\left(\frac{107}{155}\right)$	$e\left(\frac{127}{155}\right)$	$e\left(\frac{143}{155}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{113}{155}\right)$	$e\left(\frac{59}{155}\right)$	$e\left(\frac{129}{155}\right)$	$e\left(\frac{11}{31}\right)$
$\chi_{311}(6,\cdot)$	311.c	5	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$
$\chi_{311}(7,\cdot)$	311.e	31	yes	$1$	$1$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{16}{31}\right)$	$1$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{30}{31}\right)$
$\chi_{311}(8,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{142}{155}\right)$	$e\left(\frac{57}{155}\right)$	$e\left(\frac{113}{155}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{8}{155}\right)$	$e\left(\frac{129}{155}\right)$	$e\left(\frac{64}{155}\right)$	$e\left(\frac{23}{31}\right)$
$\chi_{311}(9,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{43}{155}\right)$	$e\left(\frac{81}{155}\right)$	$e\left(\frac{86}{155}\right)$	$e\left(\frac{59}{155}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{129}{155}\right)$	$e\left(\frac{7}{155}\right)$	$e\left(\frac{102}{155}\right)$	$e\left(\frac{26}{31}\right)$
$\chi_{311}(10,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{73}{155}\right)$	$e\left(\frac{51}{155}\right)$	$e\left(\frac{146}{155}\right)$	$e\left(\frac{129}{155}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{64}{155}\right)$	$e\left(\frac{102}{155}\right)$	$e\left(\frac{47}{155}\right)$	$e\left(\frac{29}{31}\right)$
$\chi_{311}(11,\cdot)$	311.f	62	yes	$-1$	$1$	$e\left(\frac{18}{31}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{11}{31}\right)$	$1$	$e\left(\frac{30}{31}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{49}{62}\right)$
$\chi_{311}(12,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{118}{155}\right)$	$e\left(\frac{6}{155}\right)$	$e\left(\frac{81}{155}\right)$	$e\left(\frac{79}{155}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{44}{155}\right)$	$e\left(\frac{12}{155}\right)$	$e\left(\frac{42}{155}\right)$	$e\left(\frac{18}{31}\right)$
$\chi_{311}(13,\cdot)$	311.e	31	yes	$1$	$1$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{18}{31}\right)$	$1$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{26}{31}\right)$
$\chi_{311}(14,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{77}{155}\right)$	$e\left(\frac{109}{155}\right)$	$e\left(\frac{154}{155}\right)$	$e\left(\frac{66}{155}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{76}{155}\right)$	$e\left(\frac{63}{155}\right)$	$e\left(\frac{143}{155}\right)$	$e\left(\frac{17}{31}\right)$
$\chi_{311}(15,\cdot)$	311.e	31	yes	$1$	$1$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{19}{31}\right)$	$1$	$e\left(\frac{18}{31}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{24}{31}\right)$
$\chi_{311}(16,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{38}{155}\right)$	$e\left(\frac{86}{155}\right)$	$e\left(\frac{76}{155}\right)$	$e\left(\frac{99}{155}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{114}{155}\right)$	$e\left(\frac{17}{155}\right)$	$e\left(\frac{137}{155}\right)$	$e\left(\frac{10}{31}\right)$
$\chi_{311}(17,\cdot)$	311.h	310	yes	$-1$	$1$	$e\left(\frac{11}{155}\right)$	$e\left(\frac{82}{155}\right)$	$e\left(\frac{22}{155}\right)$	$e\left(\frac{98}{155}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{33}{155}\right)$	$e\left(\frac{9}{155}\right)$	$e\left(\frac{109}{155}\right)$	$e\left(\frac{27}{62}\right)$
$\chi_{311}(18,\cdot)$	311.e	31	yes	$1$	$1$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{9}{31}\right)$	$1$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{13}{31}\right)$
$\chi_{311}(19,\cdot)$	311.h	310	yes	$-1$	$1$	$e\left(\frac{107}{155}\right)$	$e\left(\frac{79}{155}\right)$	$e\left(\frac{59}{155}\right)$	$e\left(\frac{136}{155}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{11}{155}\right)$	$e\left(\frac{3}{155}\right)$	$e\left(\frac{88}{155}\right)$	$e\left(\frac{9}{62}\right)$
$\chi_{311}(20,\cdot)$	311.e	31	yes	$1$	$1$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{30}{31}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{23}{31}\right)$	$1$	$e\left(\frac{12}{31}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{24}{31}\right)$	$e\left(\frac{16}{31}\right)$
$\chi_{311}(21,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{89}{155}\right)$	$e\left(\frac{128}{155}\right)$	$e\left(\frac{23}{155}\right)$	$e\left(\frac{32}{155}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{112}{155}\right)$	$e\left(\frac{101}{155}\right)$	$e\left(\frac{121}{155}\right)$	$e\left(\frac{12}{31}\right)$
$\chi_{311}(22,\cdot)$	311.h	310	yes	$-1$	$1$	$e\left(\frac{22}{155}\right)$	$e\left(\frac{9}{155}\right)$	$e\left(\frac{44}{155}\right)$	$e\left(\frac{41}{155}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{66}{155}\right)$	$e\left(\frac{18}{155}\right)$	$e\left(\frac{63}{155}\right)$	$e\left(\frac{23}{62}\right)$
$\chi_{311}(23,\cdot)$	311.h	310	yes	$-1$	$1$	$e\left(\frac{13}{155}\right)$	$e\left(\frac{111}{155}\right)$	$e\left(\frac{26}{155}\right)$	$e\left(\frac{144}{155}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{39}{155}\right)$	$e\left(\frac{67}{155}\right)$	$e\left(\frac{2}{155}\right)$	$e\left(\frac{15}{62}\right)$
$\chi_{311}(24,\cdot)$	311.e	31	yes	$1$	$1$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{13}{31}\right)$	$1$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{30}{31}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{5}{31}\right)$
$\chi_{311}(25,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{127}{155}\right)$	$e\left(\frac{59}{155}\right)$	$e\left(\frac{99}{155}\right)$	$e\left(\frac{131}{155}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{71}{155}\right)$	$e\left(\frac{118}{155}\right)$	$e\left(\frac{103}{155}\right)$	$e\left(\frac{22}{31}\right)$
$\chi_{311}(26,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{37}{155}\right)$	$e\left(\frac{149}{155}\right)$	$e\left(\frac{74}{155}\right)$	$e\left(\frac{76}{155}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{111}{155}\right)$	$e\left(\frac{143}{155}\right)$	$e\left(\frac{113}{155}\right)$	$e\left(\frac{13}{31}\right)$
$\chi_{311}(27,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{142}{155}\right)$	$e\left(\frac{44}{155}\right)$	$e\left(\frac{129}{155}\right)$	$e\left(\frac{11}{155}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{6}{31}\right)$	$e\left(\frac{116}{155}\right)$	$e\left(\frac{88}{155}\right)$	$e\left(\frac{153}{155}\right)$	$e\left(\frac{8}{31}\right)$
$\chi_{311}(28,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{9}{155}\right)$	$e\left(\frac{53}{155}\right)$	$e\left(\frac{18}{155}\right)$	$e\left(\frac{52}{155}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{27}{155}\right)$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{61}{155}\right)$	$e\left(\frac{4}{31}\right)$
$\chi_{311}(29,\cdot)$	311.h	310	yes	$-1$	$1$	$e\left(\frac{16}{155}\right)$	$e\left(\frac{77}{155}\right)$	$e\left(\frac{32}{155}\right)$	$e\left(\frac{58}{155}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{48}{155}\right)$	$e\left(\frac{154}{155}\right)$	$e\left(\frac{74}{155}\right)$	$e\left(\frac{59}{62}\right)$
$\chi_{311}(30,\cdot)$	311.g	155	yes	$1$	$1$	$e\left(\frac{17}{155}\right)$	$e\left(\frac{14}{155}\right)$	$e\left(\frac{34}{155}\right)$	$e\left(\frac{81}{155}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{51}{155}\right)$	$e\left(\frac{28}{155}\right)$	$e\left(\frac{98}{155}\right)$	$e\left(\frac{11}{31}\right)$
$\chi_{311}(31,\cdot)$	311.h	310	yes	$-1$	$1$	$e\left(\frac{82}{155}\right)$	$e\left(\frac{104}{155}\right)$	$e\left(\frac{9}{155}\right)$	$e\left(\frac{26}{155}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{91}{155}\right)$	$e\left(\frac{53}{155}\right)$	$e\left(\frac{108}{155}\right)$	$e\left(\frac{35}{62}\right)$
$\chi_{311}(32,\cdot)$	311.e	31	yes	$1$	$1$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{6}{31}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{17}{31}\right)$	$1$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{12}{31}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{28}{31}\right)$

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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	$311$
Structure	\(C_{310}\)
Order	$310$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{311}(1,\cdot)\)	311.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{311}(2,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{87}{155}\right)\)	\(e\left(\frac{99}{155}\right)\)	\(e\left(\frac{19}{155}\right)\)	\(e\left(\frac{141}{155}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{43}{155}\right)\)	\(e\left(\frac{73}{155}\right)\)	\(e\left(\frac{18}{31}\right)\)
\(\chi_{311}(3,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{99}{155}\right)\)	\(e\left(\frac{118}{155}\right)\)	\(e\left(\frac{43}{155}\right)\)	\(e\left(\frac{107}{155}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{142}{155}\right)\)	\(e\left(\frac{81}{155}\right)\)	\(e\left(\frac{51}{155}\right)\)	\(e\left(\frac{13}{31}\right)\)
\(\chi_{311}(4,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{19}{155}\right)\)	\(e\left(\frac{43}{155}\right)\)	\(e\left(\frac{38}{155}\right)\)	\(e\left(\frac{127}{155}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{57}{155}\right)\)	\(e\left(\frac{86}{155}\right)\)	\(e\left(\frac{146}{155}\right)\)	\(e\left(\frac{5}{31}\right)\)
\(\chi_{311}(5,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{141}{155}\right)\)	\(e\left(\frac{107}{155}\right)\)	\(e\left(\frac{127}{155}\right)\)	\(e\left(\frac{143}{155}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{113}{155}\right)\)	\(e\left(\frac{59}{155}\right)\)	\(e\left(\frac{129}{155}\right)\)	\(e\left(\frac{11}{31}\right)\)
\(\chi_{311}(6,\cdot)\)	311.c	5	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)
\(\chi_{311}(7,\cdot)\)	311.e	31	yes	\(1\)	\(1\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(1\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{30}{31}\right)\)
\(\chi_{311}(8,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{142}{155}\right)\)	\(e\left(\frac{57}{155}\right)\)	\(e\left(\frac{113}{155}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{8}{155}\right)\)	\(e\left(\frac{129}{155}\right)\)	\(e\left(\frac{64}{155}\right)\)	\(e\left(\frac{23}{31}\right)\)
\(\chi_{311}(9,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{43}{155}\right)\)	\(e\left(\frac{81}{155}\right)\)	\(e\left(\frac{86}{155}\right)\)	\(e\left(\frac{59}{155}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{129}{155}\right)\)	\(e\left(\frac{7}{155}\right)\)	\(e\left(\frac{102}{155}\right)\)	\(e\left(\frac{26}{31}\right)\)
\(\chi_{311}(10,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{73}{155}\right)\)	\(e\left(\frac{51}{155}\right)\)	\(e\left(\frac{146}{155}\right)\)	\(e\left(\frac{129}{155}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{64}{155}\right)\)	\(e\left(\frac{102}{155}\right)\)	\(e\left(\frac{47}{155}\right)\)	\(e\left(\frac{29}{31}\right)\)
\(\chi_{311}(11,\cdot)\)	311.f	62	yes	\(-1\)	\(1\)	\(e\left(\frac{18}{31}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(1\)	\(e\left(\frac{30}{31}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{49}{62}\right)\)
\(\chi_{311}(12,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{118}{155}\right)\)	\(e\left(\frac{6}{155}\right)\)	\(e\left(\frac{81}{155}\right)\)	\(e\left(\frac{79}{155}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{44}{155}\right)\)	\(e\left(\frac{12}{155}\right)\)	\(e\left(\frac{42}{155}\right)\)	\(e\left(\frac{18}{31}\right)\)
\(\chi_{311}(13,\cdot)\)	311.e	31	yes	\(1\)	\(1\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{18}{31}\right)\)	\(1\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{26}{31}\right)\)
\(\chi_{311}(14,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{77}{155}\right)\)	\(e\left(\frac{109}{155}\right)\)	\(e\left(\frac{154}{155}\right)\)	\(e\left(\frac{66}{155}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{76}{155}\right)\)	\(e\left(\frac{63}{155}\right)\)	\(e\left(\frac{143}{155}\right)\)	\(e\left(\frac{17}{31}\right)\)
\(\chi_{311}(15,\cdot)\)	311.e	31	yes	\(1\)	\(1\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(1\)	\(e\left(\frac{18}{31}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{24}{31}\right)\)
\(\chi_{311}(16,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{38}{155}\right)\)	\(e\left(\frac{86}{155}\right)\)	\(e\left(\frac{76}{155}\right)\)	\(e\left(\frac{99}{155}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{114}{155}\right)\)	\(e\left(\frac{17}{155}\right)\)	\(e\left(\frac{137}{155}\right)\)	\(e\left(\frac{10}{31}\right)\)
\(\chi_{311}(17,\cdot)\)	311.h	310	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{155}\right)\)	\(e\left(\frac{82}{155}\right)\)	\(e\left(\frac{22}{155}\right)\)	\(e\left(\frac{98}{155}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{33}{155}\right)\)	\(e\left(\frac{9}{155}\right)\)	\(e\left(\frac{109}{155}\right)\)	\(e\left(\frac{27}{62}\right)\)
\(\chi_{311}(18,\cdot)\)	311.e	31	yes	\(1\)	\(1\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(1\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{13}{31}\right)\)
\(\chi_{311}(19,\cdot)\)	311.h	310	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{155}\right)\)	\(e\left(\frac{79}{155}\right)\)	\(e\left(\frac{59}{155}\right)\)	\(e\left(\frac{136}{155}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{11}{155}\right)\)	\(e\left(\frac{3}{155}\right)\)	\(e\left(\frac{88}{155}\right)\)	\(e\left(\frac{9}{62}\right)\)
\(\chi_{311}(20,\cdot)\)	311.e	31	yes	\(1\)	\(1\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{30}{31}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(1\)	\(e\left(\frac{12}{31}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{24}{31}\right)\)	\(e\left(\frac{16}{31}\right)\)
\(\chi_{311}(21,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{89}{155}\right)\)	\(e\left(\frac{128}{155}\right)\)	\(e\left(\frac{23}{155}\right)\)	\(e\left(\frac{32}{155}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{112}{155}\right)\)	\(e\left(\frac{101}{155}\right)\)	\(e\left(\frac{121}{155}\right)\)	\(e\left(\frac{12}{31}\right)\)
\(\chi_{311}(22,\cdot)\)	311.h	310	yes	\(-1\)	\(1\)	\(e\left(\frac{22}{155}\right)\)	\(e\left(\frac{9}{155}\right)\)	\(e\left(\frac{44}{155}\right)\)	\(e\left(\frac{41}{155}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{66}{155}\right)\)	\(e\left(\frac{18}{155}\right)\)	\(e\left(\frac{63}{155}\right)\)	\(e\left(\frac{23}{62}\right)\)
\(\chi_{311}(23,\cdot)\)	311.h	310	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{155}\right)\)	\(e\left(\frac{111}{155}\right)\)	\(e\left(\frac{26}{155}\right)\)	\(e\left(\frac{144}{155}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{39}{155}\right)\)	\(e\left(\frac{67}{155}\right)\)	\(e\left(\frac{2}{155}\right)\)	\(e\left(\frac{15}{62}\right)\)
\(\chi_{311}(24,\cdot)\)	311.e	31	yes	\(1\)	\(1\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(1\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{30}{31}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{5}{31}\right)\)
\(\chi_{311}(25,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{127}{155}\right)\)	\(e\left(\frac{59}{155}\right)\)	\(e\left(\frac{99}{155}\right)\)	\(e\left(\frac{131}{155}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{71}{155}\right)\)	\(e\left(\frac{118}{155}\right)\)	\(e\left(\frac{103}{155}\right)\)	\(e\left(\frac{22}{31}\right)\)
\(\chi_{311}(26,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{37}{155}\right)\)	\(e\left(\frac{149}{155}\right)\)	\(e\left(\frac{74}{155}\right)\)	\(e\left(\frac{76}{155}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{111}{155}\right)\)	\(e\left(\frac{143}{155}\right)\)	\(e\left(\frac{113}{155}\right)\)	\(e\left(\frac{13}{31}\right)\)
\(\chi_{311}(27,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{142}{155}\right)\)	\(e\left(\frac{44}{155}\right)\)	\(e\left(\frac{129}{155}\right)\)	\(e\left(\frac{11}{155}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{6}{31}\right)\)	\(e\left(\frac{116}{155}\right)\)	\(e\left(\frac{88}{155}\right)\)	\(e\left(\frac{153}{155}\right)\)	\(e\left(\frac{8}{31}\right)\)
\(\chi_{311}(28,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{9}{155}\right)\)	\(e\left(\frac{53}{155}\right)\)	\(e\left(\frac{18}{155}\right)\)	\(e\left(\frac{52}{155}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{27}{155}\right)\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{61}{155}\right)\)	\(e\left(\frac{4}{31}\right)\)
\(\chi_{311}(29,\cdot)\)	311.h	310	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{155}\right)\)	\(e\left(\frac{77}{155}\right)\)	\(e\left(\frac{32}{155}\right)\)	\(e\left(\frac{58}{155}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{48}{155}\right)\)	\(e\left(\frac{154}{155}\right)\)	\(e\left(\frac{74}{155}\right)\)	\(e\left(\frac{59}{62}\right)\)
\(\chi_{311}(30,\cdot)\)	311.g	155	yes	\(1\)	\(1\)	\(e\left(\frac{17}{155}\right)\)	\(e\left(\frac{14}{155}\right)\)	\(e\left(\frac{34}{155}\right)\)	\(e\left(\frac{81}{155}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{51}{155}\right)\)	\(e\left(\frac{28}{155}\right)\)	\(e\left(\frac{98}{155}\right)\)	\(e\left(\frac{11}{31}\right)\)
\(\chi_{311}(31,\cdot)\)	311.h	310	yes	\(-1\)	\(1\)	\(e\left(\frac{82}{155}\right)\)	\(e\left(\frac{104}{155}\right)\)	\(e\left(\frac{9}{155}\right)\)	\(e\left(\frac{26}{155}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{91}{155}\right)\)	\(e\left(\frac{53}{155}\right)\)	\(e\left(\frac{108}{155}\right)\)	\(e\left(\frac{35}{62}\right)\)
\(\chi_{311}(32,\cdot)\)	311.e	31	yes	\(1\)	\(1\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{6}{31}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(1\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{12}{31}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{28}{31}\right)\)

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First 32 of 310 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.