LMFDB - Group of Dirichlet Characters of Modulus 6001

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(6001)

pari: g = idealstar(,6001,2)

Character group

sage: G.order() pari: g.no
Order	=	5632
sage: H.invariants() pari: g.cyc
Structure	=	$C_{352}\times C_{16}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6001}(3180,\cdot)$, $\chi_{6001}(2825,\cdot)$

First 32 of 5632 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.

	orbit label	order	primitive	-1	1	2	3	4	5	6	7	8	9	10	11
$\chi_{6001}(1,\cdot)$	6001.a	1	No	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6001}(2,\cdot)$	6001.dc	88	Yes	$1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{44}\right)$	$1$	$-i$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{15}{22}\right)$	$1$	$e\left(\frac{7}{88}\right)$
$\chi_{6001}(3,\cdot)$	6001.er	352	Yes	$1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{23}{352}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{67}{352}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{23}{176}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{107}{176}\right)$
$\chi_{6001}(4,\cdot)$	6001.ct	44	Yes	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{15}{22}\right)$	$1$	$-1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{4}{11}\right)$	$1$	$e\left(\frac{7}{44}\right)$
$\chi_{6001}(5,\cdot)$	6001.er	352	Yes	$1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{67}{352}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{287}{352}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{67}{176}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{151}{176}\right)$
$\chi_{6001}(6,\cdot)$	6001.cm	32	Yes	$1$	$1$	$1$	$e\left(\frac{13}{32}\right)$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{23}{32}\right)$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{6001}(7,\cdot)$	6001.cd	32	Yes	$1$	$1$	$-i$	$e\left(\frac{31}{32}\right)$	$-1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{13}{32}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{6001}(8,\cdot)$	6001.dc	88	Yes	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{44}\right)$	$1$	$i$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{1}{22}\right)$	$1$	$e\left(\frac{21}{88}\right)$
$\chi_{6001}(9,\cdot)$	6001.ec	176	Yes	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{23}{176}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{67}{176}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{19}{88}\right)$
$\chi_{6001}(10,\cdot)$	6001.cn	32	Yes	$1$	$1$	$1$	$e\left(\frac{17}{32}\right)$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{3}{32}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{6001}(11,\cdot)$	6001.do	176	Yes	$-1$	$1$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{107}{176}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{151}{176}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{51}{176}\right)$
$\chi_{6001}(12,\cdot)$	6001.ep	352	Yes	$1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{263}{352}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{307}{352}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{135}{176}\right)$
$\chi_{6001}(13,\cdot)$	6001.ej	352	Yes	$-1$	$1$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{73}{352}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{29}{352}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{73}{176}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{17}{88}\right)$
$\chi_{6001}(14,\cdot)$	6001.es	352	Yes	$1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{109}{352}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{241}{352}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{109}{176}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{135}{176}\right)$
$\chi_{6001}(15,\cdot)$	6001.ec	176	Yes	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{45}{176}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{176}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{41}{88}\right)$
$\chi_{6001}(16,\cdot)$	6001.bv	22	Yes	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{11}\right)$	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{8}{11}\right)$	$1$	$e\left(\frac{7}{22}\right)$
$\chi_{6001}(18,\cdot)$	6001.dy	176	No	$1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{83}{176}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{127}{176}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{6001}(19,\cdot)$	6001.ed	176	Yes	$1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{13}{176}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{145}{176}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{88}\right)$
$\chi_{6001}(20,\cdot)$	6001.ep	352	Yes	$1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{307}{352}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{175}{352}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{131}{176}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{176}\right)$
$\chi_{6001}(21,\cdot)$	6001.cv	88	Yes	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{6001}(22,\cdot)$	6001.dn	176	Yes	$-1$	$1$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{167}{176}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{35}{176}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{65}{176}\right)$
$\chi_{6001}(23,\cdot)$	6001.eb	176	Yes	$-1$	$1$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{103}{176}\right)$
$\chi_{6001}(24,\cdot)$	6001.et	352	Yes	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{31}{352}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{75}{352}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{31}{176}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{149}{176}\right)$
$\chi_{6001}(25,\cdot)$	6001.ec	176	Yes	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{67}{176}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{111}{176}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{63}{88}\right)$
$\chi_{6001}(26,\cdot)$	6001.eg	352	Yes	$-1$	$1$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{193}{352}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{149}{352}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{17}{176}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{6001}(27,\cdot)$	6001.er	352	Yes	$1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{69}{352}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{201}{352}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{69}{176}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{145}{176}\right)$
$\chi_{6001}(28,\cdot)$	6001.ep	352	Yes	$1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{229}{352}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{352}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{53}{176}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{149}{176}\right)$
$\chi_{6001}(29,\cdot)$	6001.dq	176	Yes	$-1$	$1$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{45}{176}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{1}{176}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{49}{176}\right)$
$\chi_{6001}(30,\cdot)$	6001.dx	176	Yes	$1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{105}{176}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{61}{176}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{6001}(31,\cdot)$	6001.eq	352	Yes	$1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{291}{352}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{159}{352}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{115}{176}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{139}{176}\right)$
$\chi_{6001}(32,\cdot)$	6001.dc	88	Yes	$1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{31}{44}\right)$	$1$	$-i$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{9}{22}\right)$	$1$	$e\left(\frac{35}{88}\right)$
$\chi_{6001}(33,\cdot)$	6001.em	352	Yes	$-1$	$1$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{237}{352}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{17}{352}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{61}{176}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{79}{88}\right)$

Introduction	Features
Universe	News

	orbit label	order	primitive	-1	1	2	3	4	5	6	7	8	9	10	11
\(\chi_{6001}(1,\cdot)\)	6001.a	1	No	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6001}(2,\cdot)\)	6001.dc	88	Yes	\(1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(1\)	\(e\left(\frac{7}{88}\right)\)
\(\chi_{6001}(3,\cdot)\)	6001.er	352	Yes	\(1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{23}{352}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{67}{352}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{23}{176}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{107}{176}\right)\)
\(\chi_{6001}(4,\cdot)\)	6001.ct	44	Yes	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(1\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{6001}(5,\cdot)\)	6001.er	352	Yes	\(1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{67}{352}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{287}{352}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{67}{176}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{151}{176}\right)\)
\(\chi_{6001}(6,\cdot)\)	6001.cm	32	Yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{6001}(7,\cdot)\)	6001.cd	32	Yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{31}{32}\right)\)	\(-1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{6001}(8,\cdot)\)	6001.dc	88	Yes	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(1\)	\(i\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(1\)	\(e\left(\frac{21}{88}\right)\)
\(\chi_{6001}(9,\cdot)\)	6001.ec	176	Yes	\(1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{23}{176}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{67}{176}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{19}{88}\right)\)
\(\chi_{6001}(10,\cdot)\)	6001.cn	32	Yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{6001}(11,\cdot)\)	6001.do	176	Yes	\(-1\)	\(1\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{107}{176}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{151}{176}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{51}{176}\right)\)
\(\chi_{6001}(12,\cdot)\)	6001.ep	352	Yes	\(1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{263}{352}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{307}{352}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{135}{176}\right)\)
\(\chi_{6001}(13,\cdot)\)	6001.ej	352	Yes	\(-1\)	\(1\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{73}{352}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{29}{352}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{73}{176}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{17}{88}\right)\)
\(\chi_{6001}(14,\cdot)\)	6001.es	352	Yes	\(1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{109}{352}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{241}{352}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{109}{176}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{135}{176}\right)\)
\(\chi_{6001}(15,\cdot)\)	6001.ec	176	Yes	\(1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{45}{176}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{176}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{41}{88}\right)\)
\(\chi_{6001}(16,\cdot)\)	6001.bv	22	Yes	\(1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(1\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{6001}(18,\cdot)\)	6001.dy	176	No	\(1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{83}{176}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{127}{176}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{6001}(19,\cdot)\)	6001.ed	176	Yes	\(1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{13}{176}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{145}{176}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{88}\right)\)
\(\chi_{6001}(20,\cdot)\)	6001.ep	352	Yes	\(1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{307}{352}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{175}{352}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{131}{176}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{176}\right)\)
\(\chi_{6001}(21,\cdot)\)	6001.cv	88	Yes	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{6001}(22,\cdot)\)	6001.dn	176	Yes	\(-1\)	\(1\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{167}{176}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{35}{176}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{65}{176}\right)\)
\(\chi_{6001}(23,\cdot)\)	6001.eb	176	Yes	\(-1\)	\(1\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{103}{176}\right)\)
\(\chi_{6001}(24,\cdot)\)	6001.et	352	Yes	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{31}{352}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{75}{352}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{31}{176}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{149}{176}\right)\)
\(\chi_{6001}(25,\cdot)\)	6001.ec	176	Yes	\(1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{67}{176}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{111}{176}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{63}{88}\right)\)
\(\chi_{6001}(26,\cdot)\)	6001.eg	352	Yes	\(-1\)	\(1\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{193}{352}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{149}{352}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{17}{176}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{6001}(27,\cdot)\)	6001.er	352	Yes	\(1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{69}{352}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{201}{352}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{69}{176}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{145}{176}\right)\)
\(\chi_{6001}(28,\cdot)\)	6001.ep	352	Yes	\(1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{229}{352}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{352}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{53}{176}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{149}{176}\right)\)
\(\chi_{6001}(29,\cdot)\)	6001.dq	176	Yes	\(-1\)	\(1\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{45}{176}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{1}{176}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{49}{176}\right)\)
\(\chi_{6001}(30,\cdot)\)	6001.dx	176	Yes	\(1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{105}{176}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{61}{176}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{6001}(31,\cdot)\)	6001.eq	352	Yes	\(1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{291}{352}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{159}{352}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{115}{176}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{139}{176}\right)\)
\(\chi_{6001}(32,\cdot)\)	6001.dc	88	Yes	\(1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(1\)	\(e\left(\frac{35}{88}\right)\)
\(\chi_{6001}(33,\cdot)\)	6001.em	352	Yes	\(-1\)	\(1\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{237}{352}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{17}{352}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{61}{176}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{79}{88}\right)\)

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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.