LMFDB - Group of Dirichlet characters of modulus 2401

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(2401)

gp:g = idealstar(,2401,2)

magma:G = FullDirichletGroup(2401);

Character group

Order	=	2058	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2058}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{2401}(3,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 2058 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{2401}(1,\cdot)$	2401.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2401}(2,\cdot)$	2401.o	1029	yes	$1$	$1$	$e\left(\frac{590}{1029}\right)$	$e\left(\frac{538}{1029}\right)$	$e\left(\frac{151}{1029}\right)$	$e\left(\frac{314}{1029}\right)$	$e\left(\frac{33}{343}\right)$	$e\left(\frac{247}{343}\right)$	$e\left(\frac{47}{1029}\right)$	$e\left(\frac{904}{1029}\right)$	$e\left(\frac{331}{1029}\right)$	$e\left(\frac{689}{1029}\right)$
$\chi_{2401}(3,\cdot)$	2401.p	2058	yes	$-1$	$1$	$e\left(\frac{538}{1029}\right)$	$e\left(\frac{1}{2058}\right)$	$e\left(\frac{47}{1029}\right)$	$e\left(\frac{911}{2058}\right)$	$e\left(\frac{359}{686}\right)$	$e\left(\frac{195}{343}\right)$	$e\left(\frac{1}{1029}\right)$	$e\left(\frac{1987}{2058}\right)$	$e\left(\frac{839}{1029}\right)$	$e\left(\frac{95}{2058}\right)$
$\chi_{2401}(4,\cdot)$	2401.o	1029	yes	$1$	$1$	$e\left(\frac{151}{1029}\right)$	$e\left(\frac{47}{1029}\right)$	$e\left(\frac{302}{1029}\right)$	$e\left(\frac{628}{1029}\right)$	$e\left(\frac{66}{343}\right)$	$e\left(\frac{151}{343}\right)$	$e\left(\frac{94}{1029}\right)$	$e\left(\frac{779}{1029}\right)$	$e\left(\frac{662}{1029}\right)$	$e\left(\frac{349}{1029}\right)$
$\chi_{2401}(5,\cdot)$	2401.p	2058	yes	$-1$	$1$	$e\left(\frac{314}{1029}\right)$	$e\left(\frac{911}{2058}\right)$	$e\left(\frac{628}{1029}\right)$	$e\left(\frac{547}{2058}\right)$	$e\left(\frac{513}{686}\right)$	$e\left(\frac{314}{343}\right)$	$e\left(\frac{911}{1029}\right)$	$e\left(\frac{1175}{2058}\right)$	$e\left(\frac{811}{1029}\right)$	$e\left(\frac{109}{2058}\right)$
$\chi_{2401}(6,\cdot)$	2401.n	686	yes	$-1$	$1$	$e\left(\frac{33}{343}\right)$	$e\left(\frac{359}{686}\right)$	$e\left(\frac{66}{343}\right)$	$e\left(\frac{513}{686}\right)$	$e\left(\frac{425}{686}\right)$	$e\left(\frac{99}{343}\right)$	$e\left(\frac{16}{343}\right)$	$e\left(\frac{579}{686}\right)$	$e\left(\frac{47}{343}\right)$	$e\left(\frac{491}{686}\right)$
$\chi_{2401}(8,\cdot)$	2401.m	343	yes	$1$	$1$	$e\left(\frac{247}{343}\right)$	$e\left(\frac{195}{343}\right)$	$e\left(\frac{151}{343}\right)$	$e\left(\frac{314}{343}\right)$	$e\left(\frac{99}{343}\right)$	$e\left(\frac{55}{343}\right)$	$e\left(\frac{47}{343}\right)$	$e\left(\frac{218}{343}\right)$	$e\left(\frac{331}{343}\right)$	$e\left(\frac{3}{343}\right)$
$\chi_{2401}(9,\cdot)$	2401.o	1029	yes	$1$	$1$	$e\left(\frac{47}{1029}\right)$	$e\left(\frac{1}{1029}\right)$	$e\left(\frac{94}{1029}\right)$	$e\left(\frac{911}{1029}\right)$	$e\left(\frac{16}{343}\right)$	$e\left(\frac{47}{343}\right)$	$e\left(\frac{2}{1029}\right)$	$e\left(\frac{958}{1029}\right)$	$e\left(\frac{649}{1029}\right)$	$e\left(\frac{95}{1029}\right)$
$\chi_{2401}(10,\cdot)$	2401.p	2058	yes	$-1$	$1$	$e\left(\frac{904}{1029}\right)$	$e\left(\frac{1987}{2058}\right)$	$e\left(\frac{779}{1029}\right)$	$e\left(\frac{1175}{2058}\right)$	$e\left(\frac{579}{686}\right)$	$e\left(\frac{218}{343}\right)$	$e\left(\frac{958}{1029}\right)$	$e\left(\frac{925}{2058}\right)$	$e\left(\frac{113}{1029}\right)$	$e\left(\frac{1487}{2058}\right)$
$\chi_{2401}(11,\cdot)$	2401.o	1029	yes	$1$	$1$	$e\left(\frac{331}{1029}\right)$	$e\left(\frac{839}{1029}\right)$	$e\left(\frac{662}{1029}\right)$	$e\left(\frac{811}{1029}\right)$	$e\left(\frac{47}{343}\right)$	$e\left(\frac{331}{343}\right)$	$e\left(\frac{649}{1029}\right)$	$e\left(\frac{113}{1029}\right)$	$e\left(\frac{170}{1029}\right)$	$e\left(\frac{472}{1029}\right)$
$\chi_{2401}(12,\cdot)$	2401.p	2058	yes	$-1$	$1$	$e\left(\frac{689}{1029}\right)$	$e\left(\frac{95}{2058}\right)$	$e\left(\frac{349}{1029}\right)$	$e\left(\frac{109}{2058}\right)$	$e\left(\frac{491}{686}\right)$	$e\left(\frac{3}{343}\right)$	$e\left(\frac{95}{1029}\right)$	$e\left(\frac{1487}{2058}\right)$	$e\left(\frac{472}{1029}\right)$	$e\left(\frac{793}{2058}\right)$
$\chi_{2401}(13,\cdot)$	2401.n	686	yes	$-1$	$1$	$e\left(\frac{150}{343}\right)$	$e\left(\frac{291}{686}\right)$	$e\left(\frac{300}{343}\right)$	$e\left(\frac{305}{686}\right)$	$e\left(\frac{591}{686}\right)$	$e\left(\frac{107}{343}\right)$	$e\left(\frac{291}{343}\right)$	$e\left(\frac{605}{686}\right)$	$e\left(\frac{276}{343}\right)$	$e\left(\frac{205}{686}\right)$
$\chi_{2401}(15,\cdot)$	2401.m	343	yes	$1$	$1$	$e\left(\frac{284}{343}\right)$	$e\left(\frac{152}{343}\right)$	$e\left(\frac{225}{343}\right)$	$e\left(\frac{243}{343}\right)$	$e\left(\frac{93}{343}\right)$	$e\left(\frac{166}{343}\right)$	$e\left(\frac{304}{343}\right)$	$e\left(\frac{184}{343}\right)$	$e\left(\frac{207}{343}\right)$	$e\left(\frac{34}{343}\right)$
$\chi_{2401}(16,\cdot)$	2401.o	1029	yes	$1$	$1$	$e\left(\frac{302}{1029}\right)$	$e\left(\frac{94}{1029}\right)$	$e\left(\frac{604}{1029}\right)$	$e\left(\frac{227}{1029}\right)$	$e\left(\frac{132}{343}\right)$	$e\left(\frac{302}{343}\right)$	$e\left(\frac{188}{1029}\right)$	$e\left(\frac{529}{1029}\right)$	$e\left(\frac{295}{1029}\right)$	$e\left(\frac{698}{1029}\right)$
$\chi_{2401}(17,\cdot)$	2401.p	2058	yes	$-1$	$1$	$e\left(\frac{661}{1029}\right)$	$e\left(\frac{1495}{2058}\right)$	$e\left(\frac{293}{1029}\right)$	$e\left(\frac{1607}{2058}\right)$	$e\left(\frac{253}{686}\right)$	$e\left(\frac{318}{343}\right)$	$e\left(\frac{466}{1029}\right)$	$e\left(\frac{871}{2058}\right)$	$e\left(\frac{983}{1029}\right)$	$e\left(\frac{23}{2058}\right)$
$\chi_{2401}(18,\cdot)$	2401.g	21	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{2401}(19,\cdot)$	2401.h	42	no	$-1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{42}\right)$
$\chi_{2401}(20,\cdot)$	2401.n	686	yes	$-1$	$1$	$e\left(\frac{155}{343}\right)$	$e\left(\frac{335}{686}\right)$	$e\left(\frac{310}{343}\right)$	$e\left(\frac{601}{686}\right)$	$e\left(\frac{645}{686}\right)$	$e\left(\frac{122}{343}\right)$	$e\left(\frac{335}{343}\right)$	$e\left(\frac{225}{686}\right)$	$e\left(\frac{148}{343}\right)$	$e\left(\frac{269}{686}\right)$
$\chi_{2401}(22,\cdot)$	2401.m	343	yes	$1$	$1$	$e\left(\frac{307}{343}\right)$	$e\left(\frac{116}{343}\right)$	$e\left(\frac{271}{343}\right)$	$e\left(\frac{32}{343}\right)$	$e\left(\frac{80}{343}\right)$	$e\left(\frac{235}{343}\right)$	$e\left(\frac{232}{343}\right)$	$e\left(\frac{339}{343}\right)$	$e\left(\frac{167}{343}\right)$	$e\left(\frac{44}{343}\right)$
$\chi_{2401}(23,\cdot)$	2401.o	1029	yes	$1$	$1$	$e\left(\frac{914}{1029}\right)$	$e\left(\frac{523}{1029}\right)$	$e\left(\frac{799}{1029}\right)$	$e\left(\frac{26}{1029}\right)$	$e\left(\frac{136}{343}\right)$	$e\left(\frac{228}{343}\right)$	$e\left(\frac{17}{1029}\right)$	$e\left(\frac{940}{1029}\right)$	$e\left(\frac{886}{1029}\right)$	$e\left(\frac{293}{1029}\right)$
$\chi_{2401}(24,\cdot)$	2401.p	2058	yes	$-1$	$1$	$e\left(\frac{250}{1029}\right)$	$e\left(\frac{1171}{2058}\right)$	$e\left(\frac{500}{1029}\right)$	$e\left(\frac{737}{2058}\right)$	$e\left(\frac{557}{686}\right)$	$e\left(\frac{250}{343}\right)$	$e\left(\frac{142}{1029}\right)$	$e\left(\frac{1237}{2058}\right)$	$e\left(\frac{803}{1029}\right)$	$e\left(\frac{113}{2058}\right)$
$\chi_{2401}(25,\cdot)$	2401.o	1029	yes	$1$	$1$	$e\left(\frac{628}{1029}\right)$	$e\left(\frac{911}{1029}\right)$	$e\left(\frac{227}{1029}\right)$	$e\left(\frac{547}{1029}\right)$	$e\left(\frac{170}{343}\right)$	$e\left(\frac{285}{343}\right)$	$e\left(\frac{793}{1029}\right)$	$e\left(\frac{146}{1029}\right)$	$e\left(\frac{593}{1029}\right)$	$e\left(\frac{109}{1029}\right)$
$\chi_{2401}(26,\cdot)$	2401.p	2058	yes	$-1$	$1$	$e\left(\frac{11}{1029}\right)$	$e\left(\frac{1949}{2058}\right)$	$e\left(\frac{22}{1029}\right)$	$e\left(\frac{1543}{2058}\right)$	$e\left(\frac{657}{686}\right)$	$e\left(\frac{11}{343}\right)$	$e\left(\frac{920}{1029}\right)$	$e\left(\frac{1565}{2058}\right)$	$e\left(\frac{130}{1029}\right)$	$e\left(\frac{1993}{2058}\right)$
$\chi_{2401}(27,\cdot)$	2401.n	686	yes	$-1$	$1$	$e\left(\frac{195}{343}\right)$	$e\left(\frac{1}{686}\right)$	$e\left(\frac{47}{343}\right)$	$e\left(\frac{225}{686}\right)$	$e\left(\frac{391}{686}\right)$	$e\left(\frac{242}{343}\right)$	$e\left(\frac{1}{343}\right)$	$e\left(\frac{615}{686}\right)$	$e\left(\frac{153}{343}\right)$	$e\left(\frac{95}{686}\right)$
$\chi_{2401}(29,\cdot)$	2401.m	343	yes	$1$	$1$	$e\left(\frac{169}{343}\right)$	$e\left(\frac{332}{343}\right)$	$e\left(\frac{338}{343}\right)$	$e\left(\frac{269}{343}\right)$	$e\left(\frac{158}{343}\right)$	$e\left(\frac{164}{343}\right)$	$e\left(\frac{321}{343}\right)$	$e\left(\frac{95}{343}\right)$	$e\left(\frac{64}{343}\right)$	$e\left(\frac{327}{343}\right)$
$\chi_{2401}(30,\cdot)$	2401.k	147	no	$1$	$1$	$e\left(\frac{59}{147}\right)$	$e\left(\frac{142}{147}\right)$	$e\left(\frac{118}{147}\right)$	$e\left(\frac{2}{147}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{137}{147}\right)$	$e\left(\frac{61}{147}\right)$	$e\left(\frac{136}{147}\right)$	$e\left(\frac{113}{147}\right)$
$\chi_{2401}(31,\cdot)$	2401.l	294	no	$-1$	$1$	$e\left(\frac{16}{147}\right)$	$e\left(\frac{229}{294}\right)$	$e\left(\frac{32}{147}\right)$	$e\left(\frac{173}{294}\right)$	$e\left(\frac{87}{98}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{82}{147}\right)$	$e\left(\frac{205}{294}\right)$	$e\left(\frac{2}{147}\right)$	$e\left(\frac{293}{294}\right)$
$\chi_{2401}(32,\cdot)$	2401.o	1029	yes	$1$	$1$	$e\left(\frac{892}{1029}\right)$	$e\left(\frac{632}{1029}\right)$	$e\left(\frac{755}{1029}\right)$	$e\left(\frac{541}{1029}\right)$	$e\left(\frac{165}{343}\right)$	$e\left(\frac{206}{343}\right)$	$e\left(\frac{235}{1029}\right)$	$e\left(\frac{404}{1029}\right)$	$e\left(\frac{626}{1029}\right)$	$e\left(\frac{358}{1029}\right)$
$\chi_{2401}(33,\cdot)$	2401.p	2058	yes	$-1$	$1$	$e\left(\frac{869}{1029}\right)$	$e\left(\frac{1679}{2058}\right)$	$e\left(\frac{709}{1029}\right)$	$e\left(\frac{475}{2058}\right)$	$e\left(\frac{453}{686}\right)$	$e\left(\frac{183}{343}\right)$	$e\left(\frac{650}{1029}\right)$	$e\left(\frac{155}{2058}\right)$	$e\left(\frac{1009}{1029}\right)$	$e\left(\frac{1039}{2058}\right)$
$\chi_{2401}(34,\cdot)$	2401.n	686	yes	$-1$	$1$	$e\left(\frac{74}{343}\right)$	$e\left(\frac{171}{686}\right)$	$e\left(\frac{148}{343}\right)$	$e\left(\frac{59}{686}\right)$	$e\left(\frac{319}{686}\right)$	$e\left(\frac{222}{343}\right)$	$e\left(\frac{171}{343}\right)$	$e\left(\frac{207}{686}\right)$	$e\left(\frac{95}{343}\right)$	$e\left(\frac{467}{686}\right)$
$\chi_{2401}(36,\cdot)$	2401.m	343	yes	$1$	$1$	$e\left(\frac{66}{343}\right)$	$e\left(\frac{16}{343}\right)$	$e\left(\frac{132}{343}\right)$	$e\left(\frac{170}{343}\right)$	$e\left(\frac{82}{343}\right)$	$e\left(\frac{198}{343}\right)$	$e\left(\frac{32}{343}\right)$	$e\left(\frac{236}{343}\right)$	$e\left(\frac{94}{343}\right)$	$e\left(\frac{148}{343}\right)$
$\chi_{2401}(37,\cdot)$	2401.o	1029	yes	$1$	$1$	$e\left(\frac{416}{1029}\right)$	$e\left(\frac{184}{1029}\right)$	$e\left(\frac{832}{1029}\right)$	$e\left(\frac{926}{1029}\right)$	$e\left(\frac{200}{343}\right)$	$e\left(\frac{73}{343}\right)$	$e\left(\frac{368}{1029}\right)$	$e\left(\frac{313}{1029}\right)$	$e\left(\frac{52}{1029}\right)$	$e\left(\frac{1016}{1029}\right)$

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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	$2401$
Structure	\(C_{2058}\)
Order	$2058$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{2401}(1,\cdot)\)	2401.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2401}(2,\cdot)\)	2401.o	1029	yes	\(1\)	\(1\)	\(e\left(\frac{590}{1029}\right)\)	\(e\left(\frac{538}{1029}\right)\)	\(e\left(\frac{151}{1029}\right)\)	\(e\left(\frac{314}{1029}\right)\)	\(e\left(\frac{33}{343}\right)\)	\(e\left(\frac{247}{343}\right)\)	\(e\left(\frac{47}{1029}\right)\)	\(e\left(\frac{904}{1029}\right)\)	\(e\left(\frac{331}{1029}\right)\)	\(e\left(\frac{689}{1029}\right)\)
\(\chi_{2401}(3,\cdot)\)	2401.p	2058	yes	\(-1\)	\(1\)	\(e\left(\frac{538}{1029}\right)\)	\(e\left(\frac{1}{2058}\right)\)	\(e\left(\frac{47}{1029}\right)\)	\(e\left(\frac{911}{2058}\right)\)	\(e\left(\frac{359}{686}\right)\)	\(e\left(\frac{195}{343}\right)\)	\(e\left(\frac{1}{1029}\right)\)	\(e\left(\frac{1987}{2058}\right)\)	\(e\left(\frac{839}{1029}\right)\)	\(e\left(\frac{95}{2058}\right)\)
\(\chi_{2401}(4,\cdot)\)	2401.o	1029	yes	\(1\)	\(1\)	\(e\left(\frac{151}{1029}\right)\)	\(e\left(\frac{47}{1029}\right)\)	\(e\left(\frac{302}{1029}\right)\)	\(e\left(\frac{628}{1029}\right)\)	\(e\left(\frac{66}{343}\right)\)	\(e\left(\frac{151}{343}\right)\)	\(e\left(\frac{94}{1029}\right)\)	\(e\left(\frac{779}{1029}\right)\)	\(e\left(\frac{662}{1029}\right)\)	\(e\left(\frac{349}{1029}\right)\)
\(\chi_{2401}(5,\cdot)\)	2401.p	2058	yes	\(-1\)	\(1\)	\(e\left(\frac{314}{1029}\right)\)	\(e\left(\frac{911}{2058}\right)\)	\(e\left(\frac{628}{1029}\right)\)	\(e\left(\frac{547}{2058}\right)\)	\(e\left(\frac{513}{686}\right)\)	\(e\left(\frac{314}{343}\right)\)	\(e\left(\frac{911}{1029}\right)\)	\(e\left(\frac{1175}{2058}\right)\)	\(e\left(\frac{811}{1029}\right)\)	\(e\left(\frac{109}{2058}\right)\)
\(\chi_{2401}(6,\cdot)\)	2401.n	686	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{343}\right)\)	\(e\left(\frac{359}{686}\right)\)	\(e\left(\frac{66}{343}\right)\)	\(e\left(\frac{513}{686}\right)\)	\(e\left(\frac{425}{686}\right)\)	\(e\left(\frac{99}{343}\right)\)	\(e\left(\frac{16}{343}\right)\)	\(e\left(\frac{579}{686}\right)\)	\(e\left(\frac{47}{343}\right)\)	\(e\left(\frac{491}{686}\right)\)
\(\chi_{2401}(8,\cdot)\)	2401.m	343	yes	\(1\)	\(1\)	\(e\left(\frac{247}{343}\right)\)	\(e\left(\frac{195}{343}\right)\)	\(e\left(\frac{151}{343}\right)\)	\(e\left(\frac{314}{343}\right)\)	\(e\left(\frac{99}{343}\right)\)	\(e\left(\frac{55}{343}\right)\)	\(e\left(\frac{47}{343}\right)\)	\(e\left(\frac{218}{343}\right)\)	\(e\left(\frac{331}{343}\right)\)	\(e\left(\frac{3}{343}\right)\)
\(\chi_{2401}(9,\cdot)\)	2401.o	1029	yes	\(1\)	\(1\)	\(e\left(\frac{47}{1029}\right)\)	\(e\left(\frac{1}{1029}\right)\)	\(e\left(\frac{94}{1029}\right)\)	\(e\left(\frac{911}{1029}\right)\)	\(e\left(\frac{16}{343}\right)\)	\(e\left(\frac{47}{343}\right)\)	\(e\left(\frac{2}{1029}\right)\)	\(e\left(\frac{958}{1029}\right)\)	\(e\left(\frac{649}{1029}\right)\)	\(e\left(\frac{95}{1029}\right)\)
\(\chi_{2401}(10,\cdot)\)	2401.p	2058	yes	\(-1\)	\(1\)	\(e\left(\frac{904}{1029}\right)\)	\(e\left(\frac{1987}{2058}\right)\)	\(e\left(\frac{779}{1029}\right)\)	\(e\left(\frac{1175}{2058}\right)\)	\(e\left(\frac{579}{686}\right)\)	\(e\left(\frac{218}{343}\right)\)	\(e\left(\frac{958}{1029}\right)\)	\(e\left(\frac{925}{2058}\right)\)	\(e\left(\frac{113}{1029}\right)\)	\(e\left(\frac{1487}{2058}\right)\)
\(\chi_{2401}(11,\cdot)\)	2401.o	1029	yes	\(1\)	\(1\)	\(e\left(\frac{331}{1029}\right)\)	\(e\left(\frac{839}{1029}\right)\)	\(e\left(\frac{662}{1029}\right)\)	\(e\left(\frac{811}{1029}\right)\)	\(e\left(\frac{47}{343}\right)\)	\(e\left(\frac{331}{343}\right)\)	\(e\left(\frac{649}{1029}\right)\)	\(e\left(\frac{113}{1029}\right)\)	\(e\left(\frac{170}{1029}\right)\)	\(e\left(\frac{472}{1029}\right)\)
\(\chi_{2401}(12,\cdot)\)	2401.p	2058	yes	\(-1\)	\(1\)	\(e\left(\frac{689}{1029}\right)\)	\(e\left(\frac{95}{2058}\right)\)	\(e\left(\frac{349}{1029}\right)\)	\(e\left(\frac{109}{2058}\right)\)	\(e\left(\frac{491}{686}\right)\)	\(e\left(\frac{3}{343}\right)\)	\(e\left(\frac{95}{1029}\right)\)	\(e\left(\frac{1487}{2058}\right)\)	\(e\left(\frac{472}{1029}\right)\)	\(e\left(\frac{793}{2058}\right)\)
\(\chi_{2401}(13,\cdot)\)	2401.n	686	yes	\(-1\)	\(1\)	\(e\left(\frac{150}{343}\right)\)	\(e\left(\frac{291}{686}\right)\)	\(e\left(\frac{300}{343}\right)\)	\(e\left(\frac{305}{686}\right)\)	\(e\left(\frac{591}{686}\right)\)	\(e\left(\frac{107}{343}\right)\)	\(e\left(\frac{291}{343}\right)\)	\(e\left(\frac{605}{686}\right)\)	\(e\left(\frac{276}{343}\right)\)	\(e\left(\frac{205}{686}\right)\)
\(\chi_{2401}(15,\cdot)\)	2401.m	343	yes	\(1\)	\(1\)	\(e\left(\frac{284}{343}\right)\)	\(e\left(\frac{152}{343}\right)\)	\(e\left(\frac{225}{343}\right)\)	\(e\left(\frac{243}{343}\right)\)	\(e\left(\frac{93}{343}\right)\)	\(e\left(\frac{166}{343}\right)\)	\(e\left(\frac{304}{343}\right)\)	\(e\left(\frac{184}{343}\right)\)	\(e\left(\frac{207}{343}\right)\)	\(e\left(\frac{34}{343}\right)\)
\(\chi_{2401}(16,\cdot)\)	2401.o	1029	yes	\(1\)	\(1\)	\(e\left(\frac{302}{1029}\right)\)	\(e\left(\frac{94}{1029}\right)\)	\(e\left(\frac{604}{1029}\right)\)	\(e\left(\frac{227}{1029}\right)\)	\(e\left(\frac{132}{343}\right)\)	\(e\left(\frac{302}{343}\right)\)	\(e\left(\frac{188}{1029}\right)\)	\(e\left(\frac{529}{1029}\right)\)	\(e\left(\frac{295}{1029}\right)\)	\(e\left(\frac{698}{1029}\right)\)
\(\chi_{2401}(17,\cdot)\)	2401.p	2058	yes	\(-1\)	\(1\)	\(e\left(\frac{661}{1029}\right)\)	\(e\left(\frac{1495}{2058}\right)\)	\(e\left(\frac{293}{1029}\right)\)	\(e\left(\frac{1607}{2058}\right)\)	\(e\left(\frac{253}{686}\right)\)	\(e\left(\frac{318}{343}\right)\)	\(e\left(\frac{466}{1029}\right)\)	\(e\left(\frac{871}{2058}\right)\)	\(e\left(\frac{983}{1029}\right)\)	\(e\left(\frac{23}{2058}\right)\)
\(\chi_{2401}(18,\cdot)\)	2401.g	21	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{2401}(19,\cdot)\)	2401.h	42	no	\(-1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)
\(\chi_{2401}(20,\cdot)\)	2401.n	686	yes	\(-1\)	\(1\)	\(e\left(\frac{155}{343}\right)\)	\(e\left(\frac{335}{686}\right)\)	\(e\left(\frac{310}{343}\right)\)	\(e\left(\frac{601}{686}\right)\)	\(e\left(\frac{645}{686}\right)\)	\(e\left(\frac{122}{343}\right)\)	\(e\left(\frac{335}{343}\right)\)	\(e\left(\frac{225}{686}\right)\)	\(e\left(\frac{148}{343}\right)\)	\(e\left(\frac{269}{686}\right)\)
\(\chi_{2401}(22,\cdot)\)	2401.m	343	yes	\(1\)	\(1\)	\(e\left(\frac{307}{343}\right)\)	\(e\left(\frac{116}{343}\right)\)	\(e\left(\frac{271}{343}\right)\)	\(e\left(\frac{32}{343}\right)\)	\(e\left(\frac{80}{343}\right)\)	\(e\left(\frac{235}{343}\right)\)	\(e\left(\frac{232}{343}\right)\)	\(e\left(\frac{339}{343}\right)\)	\(e\left(\frac{167}{343}\right)\)	\(e\left(\frac{44}{343}\right)\)
\(\chi_{2401}(23,\cdot)\)	2401.o	1029	yes	\(1\)	\(1\)	\(e\left(\frac{914}{1029}\right)\)	\(e\left(\frac{523}{1029}\right)\)	\(e\left(\frac{799}{1029}\right)\)	\(e\left(\frac{26}{1029}\right)\)	\(e\left(\frac{136}{343}\right)\)	\(e\left(\frac{228}{343}\right)\)	\(e\left(\frac{17}{1029}\right)\)	\(e\left(\frac{940}{1029}\right)\)	\(e\left(\frac{886}{1029}\right)\)	\(e\left(\frac{293}{1029}\right)\)
\(\chi_{2401}(24,\cdot)\)	2401.p	2058	yes	\(-1\)	\(1\)	\(e\left(\frac{250}{1029}\right)\)	\(e\left(\frac{1171}{2058}\right)\)	\(e\left(\frac{500}{1029}\right)\)	\(e\left(\frac{737}{2058}\right)\)	\(e\left(\frac{557}{686}\right)\)	\(e\left(\frac{250}{343}\right)\)	\(e\left(\frac{142}{1029}\right)\)	\(e\left(\frac{1237}{2058}\right)\)	\(e\left(\frac{803}{1029}\right)\)	\(e\left(\frac{113}{2058}\right)\)
\(\chi_{2401}(25,\cdot)\)	2401.o	1029	yes	\(1\)	\(1\)	\(e\left(\frac{628}{1029}\right)\)	\(e\left(\frac{911}{1029}\right)\)	\(e\left(\frac{227}{1029}\right)\)	\(e\left(\frac{547}{1029}\right)\)	\(e\left(\frac{170}{343}\right)\)	\(e\left(\frac{285}{343}\right)\)	\(e\left(\frac{793}{1029}\right)\)	\(e\left(\frac{146}{1029}\right)\)	\(e\left(\frac{593}{1029}\right)\)	\(e\left(\frac{109}{1029}\right)\)
\(\chi_{2401}(26,\cdot)\)	2401.p	2058	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{1029}\right)\)	\(e\left(\frac{1949}{2058}\right)\)	\(e\left(\frac{22}{1029}\right)\)	\(e\left(\frac{1543}{2058}\right)\)	\(e\left(\frac{657}{686}\right)\)	\(e\left(\frac{11}{343}\right)\)	\(e\left(\frac{920}{1029}\right)\)	\(e\left(\frac{1565}{2058}\right)\)	\(e\left(\frac{130}{1029}\right)\)	\(e\left(\frac{1993}{2058}\right)\)
\(\chi_{2401}(27,\cdot)\)	2401.n	686	yes	\(-1\)	\(1\)	\(e\left(\frac{195}{343}\right)\)	\(e\left(\frac{1}{686}\right)\)	\(e\left(\frac{47}{343}\right)\)	\(e\left(\frac{225}{686}\right)\)	\(e\left(\frac{391}{686}\right)\)	\(e\left(\frac{242}{343}\right)\)	\(e\left(\frac{1}{343}\right)\)	\(e\left(\frac{615}{686}\right)\)	\(e\left(\frac{153}{343}\right)\)	\(e\left(\frac{95}{686}\right)\)
\(\chi_{2401}(29,\cdot)\)	2401.m	343	yes	\(1\)	\(1\)	\(e\left(\frac{169}{343}\right)\)	\(e\left(\frac{332}{343}\right)\)	\(e\left(\frac{338}{343}\right)\)	\(e\left(\frac{269}{343}\right)\)	\(e\left(\frac{158}{343}\right)\)	\(e\left(\frac{164}{343}\right)\)	\(e\left(\frac{321}{343}\right)\)	\(e\left(\frac{95}{343}\right)\)	\(e\left(\frac{64}{343}\right)\)	\(e\left(\frac{327}{343}\right)\)
\(\chi_{2401}(30,\cdot)\)	2401.k	147	no	\(1\)	\(1\)	\(e\left(\frac{59}{147}\right)\)	\(e\left(\frac{142}{147}\right)\)	\(e\left(\frac{118}{147}\right)\)	\(e\left(\frac{2}{147}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{137}{147}\right)\)	\(e\left(\frac{61}{147}\right)\)	\(e\left(\frac{136}{147}\right)\)	\(e\left(\frac{113}{147}\right)\)
\(\chi_{2401}(31,\cdot)\)	2401.l	294	no	\(-1\)	\(1\)	\(e\left(\frac{16}{147}\right)\)	\(e\left(\frac{229}{294}\right)\)	\(e\left(\frac{32}{147}\right)\)	\(e\left(\frac{173}{294}\right)\)	\(e\left(\frac{87}{98}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{82}{147}\right)\)	\(e\left(\frac{205}{294}\right)\)	\(e\left(\frac{2}{147}\right)\)	\(e\left(\frac{293}{294}\right)\)
\(\chi_{2401}(32,\cdot)\)	2401.o	1029	yes	\(1\)	\(1\)	\(e\left(\frac{892}{1029}\right)\)	\(e\left(\frac{632}{1029}\right)\)	\(e\left(\frac{755}{1029}\right)\)	\(e\left(\frac{541}{1029}\right)\)	\(e\left(\frac{165}{343}\right)\)	\(e\left(\frac{206}{343}\right)\)	\(e\left(\frac{235}{1029}\right)\)	\(e\left(\frac{404}{1029}\right)\)	\(e\left(\frac{626}{1029}\right)\)	\(e\left(\frac{358}{1029}\right)\)
\(\chi_{2401}(33,\cdot)\)	2401.p	2058	yes	\(-1\)	\(1\)	\(e\left(\frac{869}{1029}\right)\)	\(e\left(\frac{1679}{2058}\right)\)	\(e\left(\frac{709}{1029}\right)\)	\(e\left(\frac{475}{2058}\right)\)	\(e\left(\frac{453}{686}\right)\)	\(e\left(\frac{183}{343}\right)\)	\(e\left(\frac{650}{1029}\right)\)	\(e\left(\frac{155}{2058}\right)\)	\(e\left(\frac{1009}{1029}\right)\)	\(e\left(\frac{1039}{2058}\right)\)
\(\chi_{2401}(34,\cdot)\)	2401.n	686	yes	\(-1\)	\(1\)	\(e\left(\frac{74}{343}\right)\)	\(e\left(\frac{171}{686}\right)\)	\(e\left(\frac{148}{343}\right)\)	\(e\left(\frac{59}{686}\right)\)	\(e\left(\frac{319}{686}\right)\)	\(e\left(\frac{222}{343}\right)\)	\(e\left(\frac{171}{343}\right)\)	\(e\left(\frac{207}{686}\right)\)	\(e\left(\frac{95}{343}\right)\)	\(e\left(\frac{467}{686}\right)\)
\(\chi_{2401}(36,\cdot)\)	2401.m	343	yes	\(1\)	\(1\)	\(e\left(\frac{66}{343}\right)\)	\(e\left(\frac{16}{343}\right)\)	\(e\left(\frac{132}{343}\right)\)	\(e\left(\frac{170}{343}\right)\)	\(e\left(\frac{82}{343}\right)\)	\(e\left(\frac{198}{343}\right)\)	\(e\left(\frac{32}{343}\right)\)	\(e\left(\frac{236}{343}\right)\)	\(e\left(\frac{94}{343}\right)\)	\(e\left(\frac{148}{343}\right)\)
\(\chi_{2401}(37,\cdot)\)	2401.o	1029	yes	\(1\)	\(1\)	\(e\left(\frac{416}{1029}\right)\)	\(e\left(\frac{184}{1029}\right)\)	\(e\left(\frac{832}{1029}\right)\)	\(e\left(\frac{926}{1029}\right)\)	\(e\left(\frac{200}{343}\right)\)	\(e\left(\frac{73}{343}\right)\)	\(e\left(\frac{368}{1029}\right)\)	\(e\left(\frac{313}{1029}\right)\)	\(e\left(\frac{52}{1029}\right)\)	\(e\left(\frac{1016}{1029}\right)\)

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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.