LMFDB - Group of Dirichlet characters of modulus 3307

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3307)

pari: g = idealstar(,3307,2)

Character group

sage: G.order() pari: g.no
Order	=	3306
sage: H.invariants() pari: g.cyc
Structure	=	$C_{3306}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3307}(2,\cdot)$

First 32 of 3306 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{3307}(1,\cdot)$	3307.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3307}(2,\cdot)$	3307.p	3306	yes	$-1$	$1$	$e\left(\frac{1}{3306}\right)$	$e\left(\frac{1129}{3306}\right)$	$e\left(\frac{1}{1653}\right)$	$e\left(\frac{2653}{3306}\right)$	$e\left(\frac{565}{1653}\right)$	$e\left(\frac{143}{1653}\right)$	$e\left(\frac{1}{1102}\right)$	$e\left(\frac{1129}{1653}\right)$	$e\left(\frac{1327}{1653}\right)$	$e\left(\frac{1057}{1653}\right)$
$\chi_{3307}(3,\cdot)$	3307.p	3306	yes	$-1$	$1$	$e\left(\frac{1129}{3306}\right)$	$e\left(\frac{1831}{3306}\right)$	$e\left(\frac{1129}{1653}\right)$	$e\left(\frac{1}{3306}\right)$	$e\left(\frac{1480}{1653}\right)$	$e\left(\frac{1106}{1653}\right)$	$e\left(\frac{27}{1102}\right)$	$e\left(\frac{178}{1653}\right)$	$e\left(\frac{565}{1653}\right)$	$e\left(\frac{1540}{1653}\right)$
$\chi_{3307}(4,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{1}{1653}\right)$	$e\left(\frac{1129}{1653}\right)$	$e\left(\frac{2}{1653}\right)$	$e\left(\frac{1000}{1653}\right)$	$e\left(\frac{1130}{1653}\right)$	$e\left(\frac{286}{1653}\right)$	$e\left(\frac{1}{551}\right)$	$e\left(\frac{605}{1653}\right)$	$e\left(\frac{1001}{1653}\right)$	$e\left(\frac{461}{1653}\right)$
$\chi_{3307}(5,\cdot)$	3307.p	3306	yes	$-1$	$1$	$e\left(\frac{2653}{3306}\right)$	$e\left(\frac{1}{3306}\right)$	$e\left(\frac{1000}{1653}\right)$	$e\left(\frac{3241}{3306}\right)$	$e\left(\frac{1327}{1653}\right)$	$e\left(\frac{842}{1653}\right)$	$e\left(\frac{449}{1102}\right)$	$e\left(\frac{1}{1653}\right)$	$e\left(\frac{1294}{1653}\right)$	$e\left(\frac{733}{1653}\right)$
$\chi_{3307}(6,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{565}{1653}\right)$	$e\left(\frac{1480}{1653}\right)$	$e\left(\frac{1130}{1653}\right)$	$e\left(\frac{1327}{1653}\right)$	$e\left(\frac{392}{1653}\right)$	$e\left(\frac{1249}{1653}\right)$	$e\left(\frac{14}{551}\right)$	$e\left(\frac{1307}{1653}\right)$	$e\left(\frac{239}{1653}\right)$	$e\left(\frac{944}{1653}\right)$
$\chi_{3307}(7,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{143}{1653}\right)$	$e\left(\frac{1106}{1653}\right)$	$e\left(\frac{286}{1653}\right)$	$e\left(\frac{842}{1653}\right)$	$e\left(\frac{1249}{1653}\right)$	$e\left(\frac{1226}{1653}\right)$	$e\left(\frac{143}{551}\right)$	$e\left(\frac{559}{1653}\right)$	$e\left(\frac{985}{1653}\right)$	$e\left(\frac{1456}{1653}\right)$
$\chi_{3307}(8,\cdot)$	3307.n	1102	yes	$-1$	$1$	$e\left(\frac{1}{1102}\right)$	$e\left(\frac{27}{1102}\right)$	$e\left(\frac{1}{551}\right)$	$e\left(\frac{449}{1102}\right)$	$e\left(\frac{14}{551}\right)$	$e\left(\frac{143}{551}\right)$	$e\left(\frac{3}{1102}\right)$	$e\left(\frac{27}{551}\right)$	$e\left(\frac{225}{551}\right)$	$e\left(\frac{506}{551}\right)$
$\chi_{3307}(9,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{1129}{1653}\right)$	$e\left(\frac{178}{1653}\right)$	$e\left(\frac{605}{1653}\right)$	$e\left(\frac{1}{1653}\right)$	$e\left(\frac{1307}{1653}\right)$	$e\left(\frac{559}{1653}\right)$	$e\left(\frac{27}{551}\right)$	$e\left(\frac{356}{1653}\right)$	$e\left(\frac{1130}{1653}\right)$	$e\left(\frac{1427}{1653}\right)$
$\chi_{3307}(10,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{1327}{1653}\right)$	$e\left(\frac{565}{1653}\right)$	$e\left(\frac{1001}{1653}\right)$	$e\left(\frac{1294}{1653}\right)$	$e\left(\frac{239}{1653}\right)$	$e\left(\frac{985}{1653}\right)$	$e\left(\frac{225}{551}\right)$	$e\left(\frac{1130}{1653}\right)$	$e\left(\frac{968}{1653}\right)$	$e\left(\frac{137}{1653}\right)$
$\chi_{3307}(11,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{1057}{1653}\right)$	$e\left(\frac{1540}{1653}\right)$	$e\left(\frac{461}{1653}\right)$	$e\left(\frac{733}{1653}\right)$	$e\left(\frac{944}{1653}\right)$	$e\left(\frac{1456}{1653}\right)$	$e\left(\frac{506}{551}\right)$	$e\left(\frac{1427}{1653}\right)$	$e\left(\frac{137}{1653}\right)$	$e\left(\frac{1295}{1653}\right)$
$\chi_{3307}(12,\cdot)$	3307.g	38	yes	$-1$	$1$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{4}{19}\right)$
$\chi_{3307}(13,\cdot)$	3307.n	1102	yes	$-1$	$1$	$e\left(\frac{469}{1102}\right)$	$e\left(\frac{541}{1102}\right)$	$e\left(\frac{469}{551}\right)$	$e\left(\frac{99}{1102}\right)$	$e\left(\frac{505}{551}\right)$	$e\left(\frac{396}{551}\right)$	$e\left(\frac{305}{1102}\right)$	$e\left(\frac{541}{551}\right)$	$e\left(\frac{284}{551}\right)$	$e\left(\frac{384}{551}\right)$
$\chi_{3307}(14,\cdot)$	3307.p	3306	yes	$-1$	$1$	$e\left(\frac{287}{3306}\right)$	$e\left(\frac{35}{3306}\right)$	$e\left(\frac{287}{1653}\right)$	$e\left(\frac{1031}{3306}\right)$	$e\left(\frac{161}{1653}\right)$	$e\left(\frac{1369}{1653}\right)$	$e\left(\frac{287}{1102}\right)$	$e\left(\frac{35}{1653}\right)$	$e\left(\frac{659}{1653}\right)$	$e\left(\frac{860}{1653}\right)$
$\chi_{3307}(15,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{238}{1653}\right)$	$e\left(\frac{916}{1653}\right)$	$e\left(\frac{476}{1653}\right)$	$e\left(\frac{1621}{1653}\right)$	$e\left(\frac{1154}{1653}\right)$	$e\left(\frac{295}{1653}\right)$	$e\left(\frac{238}{551}\right)$	$e\left(\frac{179}{1653}\right)$	$e\left(\frac{206}{1653}\right)$	$e\left(\frac{620}{1653}\right)$
$\chi_{3307}(16,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{2}{1653}\right)$	$e\left(\frac{605}{1653}\right)$	$e\left(\frac{4}{1653}\right)$	$e\left(\frac{347}{1653}\right)$	$e\left(\frac{607}{1653}\right)$	$e\left(\frac{572}{1653}\right)$	$e\left(\frac{2}{551}\right)$	$e\left(\frac{1210}{1653}\right)$	$e\left(\frac{349}{1653}\right)$	$e\left(\frac{922}{1653}\right)$
$\chi_{3307}(17,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{713}{1653}\right)$	$e\left(\frac{1619}{1653}\right)$	$e\left(\frac{1426}{1653}\right)$	$e\left(\frac{557}{1653}\right)$	$e\left(\frac{679}{1653}\right)$	$e\left(\frac{599}{1653}\right)$	$e\left(\frac{162}{551}\right)$	$e\left(\frac{1585}{1653}\right)$	$e\left(\frac{1270}{1653}\right)$	$e\left(\frac{1399}{1653}\right)$
$\chi_{3307}(18,\cdot)$	3307.n	1102	yes	$-1$	$1$	$e\left(\frac{753}{1102}\right)$	$e\left(\frac{495}{1102}\right)$	$e\left(\frac{202}{551}\right)$	$e\left(\frac{885}{1102}\right)$	$e\left(\frac{73}{551}\right)$	$e\left(\frac{234}{551}\right)$	$e\left(\frac{55}{1102}\right)$	$e\left(\frac{495}{551}\right)$	$e\left(\frac{268}{551}\right)$	$e\left(\frac{277}{551}\right)$
$\chi_{3307}(19,\cdot)$	3307.n	1102	yes	$-1$	$1$	$e\left(\frac{1093}{1102}\right)$	$e\left(\frac{859}{1102}\right)$	$e\left(\frac{542}{551}\right)$	$e\left(\frac{367}{1102}\right)$	$e\left(\frac{425}{551}\right)$	$e\left(\frac{366}{551}\right)$	$e\left(\frac{1075}{1102}\right)$	$e\left(\frac{308}{551}\right)$	$e\left(\frac{179}{551}\right)$	$e\left(\frac{405}{551}\right)$
$\chi_{3307}(20,\cdot)$	3307.n	1102	yes	$-1$	$1$	$e\left(\frac{885}{1102}\right)$	$e\left(\frac{753}{1102}\right)$	$e\left(\frac{334}{551}\right)$	$e\left(\frac{645}{1102}\right)$	$e\left(\frac{268}{551}\right)$	$e\left(\frac{376}{551}\right)$	$e\left(\frac{451}{1102}\right)$	$e\left(\frac{202}{551}\right)$	$e\left(\frac{214}{551}\right)$	$e\left(\frac{398}{551}\right)$
$\chi_{3307}(21,\cdot)$	3307.p	3306	yes	$-1$	$1$	$e\left(\frac{1415}{3306}\right)$	$e\left(\frac{737}{3306}\right)$	$e\left(\frac{1415}{1653}\right)$	$e\left(\frac{1685}{3306}\right)$	$e\left(\frac{1076}{1653}\right)$	$e\left(\frac{679}{1653}\right)$	$e\left(\frac{313}{1102}\right)$	$e\left(\frac{737}{1653}\right)$	$e\left(\frac{1550}{1653}\right)$	$e\left(\frac{1343}{1653}\right)$
$\chi_{3307}(22,\cdot)$	3307.n	1102	yes	$-1$	$1$	$e\left(\frac{705}{1102}\right)$	$e\left(\frac{301}{1102}\right)$	$e\left(\frac{154}{551}\right)$	$e\left(\frac{271}{1102}\right)$	$e\left(\frac{503}{551}\right)$	$e\left(\frac{533}{551}\right)$	$e\left(\frac{1013}{1102}\right)$	$e\left(\frac{301}{551}\right)$	$e\left(\frac{488}{551}\right)$	$e\left(\frac{233}{551}\right)$
$\chi_{3307}(23,\cdot)$	3307.p	3306	yes	$-1$	$1$	$e\left(\frac{391}{3306}\right)$	$e\left(\frac{1741}{3306}\right)$	$e\left(\frac{391}{1653}\right)$	$e\left(\frac{2545}{3306}\right)$	$e\left(\frac{1066}{1653}\right)$	$e\left(\frac{1364}{1653}\right)$	$e\left(\frac{391}{1102}\right)$	$e\left(\frac{88}{1653}\right)$	$e\left(\frac{1468}{1653}\right)$	$e\left(\frac{37}{1653}\right)$
$\chi_{3307}(24,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{566}{1653}\right)$	$e\left(\frac{956}{1653}\right)$	$e\left(\frac{1132}{1653}\right)$	$e\left(\frac{674}{1653}\right)$	$e\left(\frac{1522}{1653}\right)$	$e\left(\frac{1535}{1653}\right)$	$e\left(\frac{15}{551}\right)$	$e\left(\frac{259}{1653}\right)$	$e\left(\frac{1240}{1653}\right)$	$e\left(\frac{1405}{1653}\right)$
$\chi_{3307}(25,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{1000}{1653}\right)$	$e\left(\frac{1}{1653}\right)$	$e\left(\frac{347}{1653}\right)$	$e\left(\frac{1588}{1653}\right)$	$e\left(\frac{1001}{1653}\right)$	$e\left(\frac{31}{1653}\right)$	$e\left(\frac{449}{551}\right)$	$e\left(\frac{2}{1653}\right)$	$e\left(\frac{935}{1653}\right)$	$e\left(\frac{1466}{1653}\right)$
$\chi_{3307}(26,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{704}{1653}\right)$	$e\left(\frac{1376}{1653}\right)$	$e\left(\frac{1408}{1653}\right)$	$e\left(\frac{1475}{1653}\right)$	$e\left(\frac{427}{1653}\right)$	$e\left(\frac{1331}{1653}\right)$	$e\left(\frac{153}{551}\right)$	$e\left(\frac{1099}{1653}\right)$	$e\left(\frac{526}{1653}\right)$	$e\left(\frac{556}{1653}\right)$
$\chi_{3307}(27,\cdot)$	3307.n	1102	yes	$-1$	$1$	$e\left(\frac{27}{1102}\right)$	$e\left(\frac{729}{1102}\right)$	$e\left(\frac{27}{551}\right)$	$e\left(\frac{1}{1102}\right)$	$e\left(\frac{378}{551}\right)$	$e\left(\frac{4}{551}\right)$	$e\left(\frac{81}{1102}\right)$	$e\left(\frac{178}{551}\right)$	$e\left(\frac{14}{551}\right)$	$e\left(\frac{438}{551}\right)$
$\chi_{3307}(28,\cdot)$	3307.m	551	yes	$1$	$1$	$e\left(\frac{48}{551}\right)$	$e\left(\frac{194}{551}\right)$	$e\left(\frac{96}{551}\right)$	$e\left(\frac{63}{551}\right)$	$e\left(\frac{242}{551}\right)$	$e\left(\frac{504}{551}\right)$	$e\left(\frac{144}{551}\right)$	$e\left(\frac{388}{551}\right)$	$e\left(\frac{111}{551}\right)$	$e\left(\frac{88}{551}\right)$
$\chi_{3307}(29,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{275}{1653}\right)$	$e\left(\frac{1364}{1653}\right)$	$e\left(\frac{550}{1653}\right)$	$e\left(\frac{602}{1653}\right)$	$e\left(\frac{1639}{1653}\right)$	$e\left(\frac{959}{1653}\right)$	$e\left(\frac{275}{551}\right)$	$e\left(\frac{1075}{1653}\right)$	$e\left(\frac{877}{1653}\right)$	$e\left(\frac{1147}{1653}\right)$
$\chi_{3307}(30,\cdot)$	3307.n	1102	yes	$-1$	$1$	$e\left(\frac{159}{1102}\right)$	$e\left(\frac{987}{1102}\right)$	$e\left(\frac{159}{551}\right)$	$e\left(\frac{863}{1102}\right)$	$e\left(\frac{22}{551}\right)$	$e\left(\frac{146}{551}\right)$	$e\left(\frac{477}{1102}\right)$	$e\left(\frac{436}{551}\right)$	$e\left(\frac{511}{551}\right)$	$e\left(\frac{8}{551}\right)$
$\chi_{3307}(31,\cdot)$	3307.o	1653	yes	$1$	$1$	$e\left(\frac{1150}{1653}\right)$	$e\left(\frac{745}{1653}\right)$	$e\left(\frac{647}{1653}\right)$	$e\left(\frac{1165}{1653}\right)$	$e\left(\frac{242}{1653}\right)$	$e\left(\frac{1606}{1653}\right)$	$e\left(\frac{48}{551}\right)$	$e\left(\frac{1490}{1653}\right)$	$e\left(\frac{662}{1653}\right)$	$e\left(\frac{1190}{1653}\right)$
$\chi_{3307}(32,\cdot)$	3307.p	3306	yes	$-1$	$1$	$e\left(\frac{5}{3306}\right)$	$e\left(\frac{2339}{3306}\right)$	$e\left(\frac{5}{1653}\right)$	$e\left(\frac{41}{3306}\right)$	$e\left(\frac{1172}{1653}\right)$	$e\left(\frac{715}{1653}\right)$	$e\left(\frac{5}{1102}\right)$	$e\left(\frac{686}{1653}\right)$	$e\left(\frac{23}{1653}\right)$	$e\left(\frac{326}{1653}\right)$

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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	$3307$
Structure	\(C_{3306}\)
Order	$3306$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{3307}(1,\cdot)\)	3307.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3307}(2,\cdot)\)	3307.p	3306	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3306}\right)\)	\(e\left(\frac{1129}{3306}\right)\)	\(e\left(\frac{1}{1653}\right)\)	\(e\left(\frac{2653}{3306}\right)\)	\(e\left(\frac{565}{1653}\right)\)	\(e\left(\frac{143}{1653}\right)\)	\(e\left(\frac{1}{1102}\right)\)	\(e\left(\frac{1129}{1653}\right)\)	\(e\left(\frac{1327}{1653}\right)\)	\(e\left(\frac{1057}{1653}\right)\)
\(\chi_{3307}(3,\cdot)\)	3307.p	3306	yes	\(-1\)	\(1\)	\(e\left(\frac{1129}{3306}\right)\)	\(e\left(\frac{1831}{3306}\right)\)	\(e\left(\frac{1129}{1653}\right)\)	\(e\left(\frac{1}{3306}\right)\)	\(e\left(\frac{1480}{1653}\right)\)	\(e\left(\frac{1106}{1653}\right)\)	\(e\left(\frac{27}{1102}\right)\)	\(e\left(\frac{178}{1653}\right)\)	\(e\left(\frac{565}{1653}\right)\)	\(e\left(\frac{1540}{1653}\right)\)
\(\chi_{3307}(4,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{1}{1653}\right)\)	\(e\left(\frac{1129}{1653}\right)\)	\(e\left(\frac{2}{1653}\right)\)	\(e\left(\frac{1000}{1653}\right)\)	\(e\left(\frac{1130}{1653}\right)\)	\(e\left(\frac{286}{1653}\right)\)	\(e\left(\frac{1}{551}\right)\)	\(e\left(\frac{605}{1653}\right)\)	\(e\left(\frac{1001}{1653}\right)\)	\(e\left(\frac{461}{1653}\right)\)
\(\chi_{3307}(5,\cdot)\)	3307.p	3306	yes	\(-1\)	\(1\)	\(e\left(\frac{2653}{3306}\right)\)	\(e\left(\frac{1}{3306}\right)\)	\(e\left(\frac{1000}{1653}\right)\)	\(e\left(\frac{3241}{3306}\right)\)	\(e\left(\frac{1327}{1653}\right)\)	\(e\left(\frac{842}{1653}\right)\)	\(e\left(\frac{449}{1102}\right)\)	\(e\left(\frac{1}{1653}\right)\)	\(e\left(\frac{1294}{1653}\right)\)	\(e\left(\frac{733}{1653}\right)\)
\(\chi_{3307}(6,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{565}{1653}\right)\)	\(e\left(\frac{1480}{1653}\right)\)	\(e\left(\frac{1130}{1653}\right)\)	\(e\left(\frac{1327}{1653}\right)\)	\(e\left(\frac{392}{1653}\right)\)	\(e\left(\frac{1249}{1653}\right)\)	\(e\left(\frac{14}{551}\right)\)	\(e\left(\frac{1307}{1653}\right)\)	\(e\left(\frac{239}{1653}\right)\)	\(e\left(\frac{944}{1653}\right)\)
\(\chi_{3307}(7,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{143}{1653}\right)\)	\(e\left(\frac{1106}{1653}\right)\)	\(e\left(\frac{286}{1653}\right)\)	\(e\left(\frac{842}{1653}\right)\)	\(e\left(\frac{1249}{1653}\right)\)	\(e\left(\frac{1226}{1653}\right)\)	\(e\left(\frac{143}{551}\right)\)	\(e\left(\frac{559}{1653}\right)\)	\(e\left(\frac{985}{1653}\right)\)	\(e\left(\frac{1456}{1653}\right)\)
\(\chi_{3307}(8,\cdot)\)	3307.n	1102	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{1102}\right)\)	\(e\left(\frac{27}{1102}\right)\)	\(e\left(\frac{1}{551}\right)\)	\(e\left(\frac{449}{1102}\right)\)	\(e\left(\frac{14}{551}\right)\)	\(e\left(\frac{143}{551}\right)\)	\(e\left(\frac{3}{1102}\right)\)	\(e\left(\frac{27}{551}\right)\)	\(e\left(\frac{225}{551}\right)\)	\(e\left(\frac{506}{551}\right)\)
\(\chi_{3307}(9,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{1129}{1653}\right)\)	\(e\left(\frac{178}{1653}\right)\)	\(e\left(\frac{605}{1653}\right)\)	\(e\left(\frac{1}{1653}\right)\)	\(e\left(\frac{1307}{1653}\right)\)	\(e\left(\frac{559}{1653}\right)\)	\(e\left(\frac{27}{551}\right)\)	\(e\left(\frac{356}{1653}\right)\)	\(e\left(\frac{1130}{1653}\right)\)	\(e\left(\frac{1427}{1653}\right)\)
\(\chi_{3307}(10,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{1327}{1653}\right)\)	\(e\left(\frac{565}{1653}\right)\)	\(e\left(\frac{1001}{1653}\right)\)	\(e\left(\frac{1294}{1653}\right)\)	\(e\left(\frac{239}{1653}\right)\)	\(e\left(\frac{985}{1653}\right)\)	\(e\left(\frac{225}{551}\right)\)	\(e\left(\frac{1130}{1653}\right)\)	\(e\left(\frac{968}{1653}\right)\)	\(e\left(\frac{137}{1653}\right)\)
\(\chi_{3307}(11,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{1057}{1653}\right)\)	\(e\left(\frac{1540}{1653}\right)\)	\(e\left(\frac{461}{1653}\right)\)	\(e\left(\frac{733}{1653}\right)\)	\(e\left(\frac{944}{1653}\right)\)	\(e\left(\frac{1456}{1653}\right)\)	\(e\left(\frac{506}{551}\right)\)	\(e\left(\frac{1427}{1653}\right)\)	\(e\left(\frac{137}{1653}\right)\)	\(e\left(\frac{1295}{1653}\right)\)
\(\chi_{3307}(12,\cdot)\)	3307.g	38	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)
\(\chi_{3307}(13,\cdot)\)	3307.n	1102	yes	\(-1\)	\(1\)	\(e\left(\frac{469}{1102}\right)\)	\(e\left(\frac{541}{1102}\right)\)	\(e\left(\frac{469}{551}\right)\)	\(e\left(\frac{99}{1102}\right)\)	\(e\left(\frac{505}{551}\right)\)	\(e\left(\frac{396}{551}\right)\)	\(e\left(\frac{305}{1102}\right)\)	\(e\left(\frac{541}{551}\right)\)	\(e\left(\frac{284}{551}\right)\)	\(e\left(\frac{384}{551}\right)\)
\(\chi_{3307}(14,\cdot)\)	3307.p	3306	yes	\(-1\)	\(1\)	\(e\left(\frac{287}{3306}\right)\)	\(e\left(\frac{35}{3306}\right)\)	\(e\left(\frac{287}{1653}\right)\)	\(e\left(\frac{1031}{3306}\right)\)	\(e\left(\frac{161}{1653}\right)\)	\(e\left(\frac{1369}{1653}\right)\)	\(e\left(\frac{287}{1102}\right)\)	\(e\left(\frac{35}{1653}\right)\)	\(e\left(\frac{659}{1653}\right)\)	\(e\left(\frac{860}{1653}\right)\)
\(\chi_{3307}(15,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{238}{1653}\right)\)	\(e\left(\frac{916}{1653}\right)\)	\(e\left(\frac{476}{1653}\right)\)	\(e\left(\frac{1621}{1653}\right)\)	\(e\left(\frac{1154}{1653}\right)\)	\(e\left(\frac{295}{1653}\right)\)	\(e\left(\frac{238}{551}\right)\)	\(e\left(\frac{179}{1653}\right)\)	\(e\left(\frac{206}{1653}\right)\)	\(e\left(\frac{620}{1653}\right)\)
\(\chi_{3307}(16,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{2}{1653}\right)\)	\(e\left(\frac{605}{1653}\right)\)	\(e\left(\frac{4}{1653}\right)\)	\(e\left(\frac{347}{1653}\right)\)	\(e\left(\frac{607}{1653}\right)\)	\(e\left(\frac{572}{1653}\right)\)	\(e\left(\frac{2}{551}\right)\)	\(e\left(\frac{1210}{1653}\right)\)	\(e\left(\frac{349}{1653}\right)\)	\(e\left(\frac{922}{1653}\right)\)
\(\chi_{3307}(17,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{713}{1653}\right)\)	\(e\left(\frac{1619}{1653}\right)\)	\(e\left(\frac{1426}{1653}\right)\)	\(e\left(\frac{557}{1653}\right)\)	\(e\left(\frac{679}{1653}\right)\)	\(e\left(\frac{599}{1653}\right)\)	\(e\left(\frac{162}{551}\right)\)	\(e\left(\frac{1585}{1653}\right)\)	\(e\left(\frac{1270}{1653}\right)\)	\(e\left(\frac{1399}{1653}\right)\)
\(\chi_{3307}(18,\cdot)\)	3307.n	1102	yes	\(-1\)	\(1\)	\(e\left(\frac{753}{1102}\right)\)	\(e\left(\frac{495}{1102}\right)\)	\(e\left(\frac{202}{551}\right)\)	\(e\left(\frac{885}{1102}\right)\)	\(e\left(\frac{73}{551}\right)\)	\(e\left(\frac{234}{551}\right)\)	\(e\left(\frac{55}{1102}\right)\)	\(e\left(\frac{495}{551}\right)\)	\(e\left(\frac{268}{551}\right)\)	\(e\left(\frac{277}{551}\right)\)
\(\chi_{3307}(19,\cdot)\)	3307.n	1102	yes	\(-1\)	\(1\)	\(e\left(\frac{1093}{1102}\right)\)	\(e\left(\frac{859}{1102}\right)\)	\(e\left(\frac{542}{551}\right)\)	\(e\left(\frac{367}{1102}\right)\)	\(e\left(\frac{425}{551}\right)\)	\(e\left(\frac{366}{551}\right)\)	\(e\left(\frac{1075}{1102}\right)\)	\(e\left(\frac{308}{551}\right)\)	\(e\left(\frac{179}{551}\right)\)	\(e\left(\frac{405}{551}\right)\)
\(\chi_{3307}(20,\cdot)\)	3307.n	1102	yes	\(-1\)	\(1\)	\(e\left(\frac{885}{1102}\right)\)	\(e\left(\frac{753}{1102}\right)\)	\(e\left(\frac{334}{551}\right)\)	\(e\left(\frac{645}{1102}\right)\)	\(e\left(\frac{268}{551}\right)\)	\(e\left(\frac{376}{551}\right)\)	\(e\left(\frac{451}{1102}\right)\)	\(e\left(\frac{202}{551}\right)\)	\(e\left(\frac{214}{551}\right)\)	\(e\left(\frac{398}{551}\right)\)
\(\chi_{3307}(21,\cdot)\)	3307.p	3306	yes	\(-1\)	\(1\)	\(e\left(\frac{1415}{3306}\right)\)	\(e\left(\frac{737}{3306}\right)\)	\(e\left(\frac{1415}{1653}\right)\)	\(e\left(\frac{1685}{3306}\right)\)	\(e\left(\frac{1076}{1653}\right)\)	\(e\left(\frac{679}{1653}\right)\)	\(e\left(\frac{313}{1102}\right)\)	\(e\left(\frac{737}{1653}\right)\)	\(e\left(\frac{1550}{1653}\right)\)	\(e\left(\frac{1343}{1653}\right)\)
\(\chi_{3307}(22,\cdot)\)	3307.n	1102	yes	\(-1\)	\(1\)	\(e\left(\frac{705}{1102}\right)\)	\(e\left(\frac{301}{1102}\right)\)	\(e\left(\frac{154}{551}\right)\)	\(e\left(\frac{271}{1102}\right)\)	\(e\left(\frac{503}{551}\right)\)	\(e\left(\frac{533}{551}\right)\)	\(e\left(\frac{1013}{1102}\right)\)	\(e\left(\frac{301}{551}\right)\)	\(e\left(\frac{488}{551}\right)\)	\(e\left(\frac{233}{551}\right)\)
\(\chi_{3307}(23,\cdot)\)	3307.p	3306	yes	\(-1\)	\(1\)	\(e\left(\frac{391}{3306}\right)\)	\(e\left(\frac{1741}{3306}\right)\)	\(e\left(\frac{391}{1653}\right)\)	\(e\left(\frac{2545}{3306}\right)\)	\(e\left(\frac{1066}{1653}\right)\)	\(e\left(\frac{1364}{1653}\right)\)	\(e\left(\frac{391}{1102}\right)\)	\(e\left(\frac{88}{1653}\right)\)	\(e\left(\frac{1468}{1653}\right)\)	\(e\left(\frac{37}{1653}\right)\)
\(\chi_{3307}(24,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{566}{1653}\right)\)	\(e\left(\frac{956}{1653}\right)\)	\(e\left(\frac{1132}{1653}\right)\)	\(e\left(\frac{674}{1653}\right)\)	\(e\left(\frac{1522}{1653}\right)\)	\(e\left(\frac{1535}{1653}\right)\)	\(e\left(\frac{15}{551}\right)\)	\(e\left(\frac{259}{1653}\right)\)	\(e\left(\frac{1240}{1653}\right)\)	\(e\left(\frac{1405}{1653}\right)\)
\(\chi_{3307}(25,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{1000}{1653}\right)\)	\(e\left(\frac{1}{1653}\right)\)	\(e\left(\frac{347}{1653}\right)\)	\(e\left(\frac{1588}{1653}\right)\)	\(e\left(\frac{1001}{1653}\right)\)	\(e\left(\frac{31}{1653}\right)\)	\(e\left(\frac{449}{551}\right)\)	\(e\left(\frac{2}{1653}\right)\)	\(e\left(\frac{935}{1653}\right)\)	\(e\left(\frac{1466}{1653}\right)\)
\(\chi_{3307}(26,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{704}{1653}\right)\)	\(e\left(\frac{1376}{1653}\right)\)	\(e\left(\frac{1408}{1653}\right)\)	\(e\left(\frac{1475}{1653}\right)\)	\(e\left(\frac{427}{1653}\right)\)	\(e\left(\frac{1331}{1653}\right)\)	\(e\left(\frac{153}{551}\right)\)	\(e\left(\frac{1099}{1653}\right)\)	\(e\left(\frac{526}{1653}\right)\)	\(e\left(\frac{556}{1653}\right)\)
\(\chi_{3307}(27,\cdot)\)	3307.n	1102	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{1102}\right)\)	\(e\left(\frac{729}{1102}\right)\)	\(e\left(\frac{27}{551}\right)\)	\(e\left(\frac{1}{1102}\right)\)	\(e\left(\frac{378}{551}\right)\)	\(e\left(\frac{4}{551}\right)\)	\(e\left(\frac{81}{1102}\right)\)	\(e\left(\frac{178}{551}\right)\)	\(e\left(\frac{14}{551}\right)\)	\(e\left(\frac{438}{551}\right)\)
\(\chi_{3307}(28,\cdot)\)	3307.m	551	yes	\(1\)	\(1\)	\(e\left(\frac{48}{551}\right)\)	\(e\left(\frac{194}{551}\right)\)	\(e\left(\frac{96}{551}\right)\)	\(e\left(\frac{63}{551}\right)\)	\(e\left(\frac{242}{551}\right)\)	\(e\left(\frac{504}{551}\right)\)	\(e\left(\frac{144}{551}\right)\)	\(e\left(\frac{388}{551}\right)\)	\(e\left(\frac{111}{551}\right)\)	\(e\left(\frac{88}{551}\right)\)
\(\chi_{3307}(29,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{275}{1653}\right)\)	\(e\left(\frac{1364}{1653}\right)\)	\(e\left(\frac{550}{1653}\right)\)	\(e\left(\frac{602}{1653}\right)\)	\(e\left(\frac{1639}{1653}\right)\)	\(e\left(\frac{959}{1653}\right)\)	\(e\left(\frac{275}{551}\right)\)	\(e\left(\frac{1075}{1653}\right)\)	\(e\left(\frac{877}{1653}\right)\)	\(e\left(\frac{1147}{1653}\right)\)
\(\chi_{3307}(30,\cdot)\)	3307.n	1102	yes	\(-1\)	\(1\)	\(e\left(\frac{159}{1102}\right)\)	\(e\left(\frac{987}{1102}\right)\)	\(e\left(\frac{159}{551}\right)\)	\(e\left(\frac{863}{1102}\right)\)	\(e\left(\frac{22}{551}\right)\)	\(e\left(\frac{146}{551}\right)\)	\(e\left(\frac{477}{1102}\right)\)	\(e\left(\frac{436}{551}\right)\)	\(e\left(\frac{511}{551}\right)\)	\(e\left(\frac{8}{551}\right)\)
\(\chi_{3307}(31,\cdot)\)	3307.o	1653	yes	\(1\)	\(1\)	\(e\left(\frac{1150}{1653}\right)\)	\(e\left(\frac{745}{1653}\right)\)	\(e\left(\frac{647}{1653}\right)\)	\(e\left(\frac{1165}{1653}\right)\)	\(e\left(\frac{242}{1653}\right)\)	\(e\left(\frac{1606}{1653}\right)\)	\(e\left(\frac{48}{551}\right)\)	\(e\left(\frac{1490}{1653}\right)\)	\(e\left(\frac{662}{1653}\right)\)	\(e\left(\frac{1190}{1653}\right)\)
\(\chi_{3307}(32,\cdot)\)	3307.p	3306	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{3306}\right)\)	\(e\left(\frac{2339}{3306}\right)\)	\(e\left(\frac{5}{1653}\right)\)	\(e\left(\frac{41}{3306}\right)\)	\(e\left(\frac{1172}{1653}\right)\)	\(e\left(\frac{715}{1653}\right)\)	\(e\left(\frac{5}{1102}\right)\)	\(e\left(\frac{686}{1653}\right)\)	\(e\left(\frac{23}{1653}\right)\)	\(e\left(\frac{326}{1653}\right)\)

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Character group

First 32 of 3306 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.