LMFDB - Group of Dirichlet characters of modulus 4165

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(4165)

gp:g = idealstar(,4165,2)

magma:G = FullDirichletGroup(4165);

Character group

Order	=	2688	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{336}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{4165}(1667,\cdot)$, $\chi_{4165}(2551,\cdot)$, $\chi_{4165}(2451,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 2688 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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{4165}(1,\cdot)$	4165.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4165}(2,\cdot)$	4165.ez	168	yes	$-1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{4165}(3,\cdot)$	4165.fg	336	yes	$-1$	$1$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{113}{336}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{277}{336}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{4165}(4,\cdot)$	4165.ep	84	yes	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{4165}(6,\cdot)$	4165.eu	112	no	$1$	$1$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{4165}(8,\cdot)$	4165.ed	56	yes	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{4165}(9,\cdot)$	4165.fb	168	yes	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{4165}(11,\cdot)$	4165.fi	336	no	$-1$	$1$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{53}{336}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{4165}(12,\cdot)$	4165.fm	336	yes	$-1$	$1$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{277}{336}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{4165}(13,\cdot)$	4165.cx	28	yes	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{4165}(16,\cdot)$	4165.dl	42	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{4165}(18,\cdot)$	4165.br	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{4165}(19,\cdot)$	4165.cq	24	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{4165}(22,\cdot)$	4165.er	112	yes	$1$	$1$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{4165}(23,\cdot)$	4165.fh	336	yes	$1$	$1$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{253}{336}\right)$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{4165}(24,\cdot)$	4165.fk	336	yes	$1$	$1$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{43}{336}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{4165}(26,\cdot)$	4165.fa	168	no	$-1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{4165}(27,\cdot)$	4165.eq	112	yes	$-1$	$1$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{4165}(29,\cdot)$	4165.es	112	yes	$-1$	$1$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{4165}(31,\cdot)$	4165.dq	48	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{7}{48}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{4165}(32,\cdot)$	4165.ez	168	yes	$-1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{4165}(33,\cdot)$	4165.ei	84	yes	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{4165}(36,\cdot)$	4165.eb	56	no	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{4165}(37,\cdot)$	4165.fh	336	yes	$1$	$1$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{193}{336}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{149}{336}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{4165}(38,\cdot)$	4165.eh	84	yes	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{4165}(39,\cdot)$	4165.fl	336	yes	$-1$	$1$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{157}{336}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{4165}(41,\cdot)$	4165.eu	112	no	$1$	$1$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{4165}(43,\cdot)$	4165.ed	56	yes	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{4165}(44,\cdot)$	4165.fl	336	yes	$-1$	$1$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{295}{336}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{11}{336}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{42}\right)$
$\chi_{4165}(46,\cdot)$	4165.fi	336	no	$-1$	$1$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{113}{336}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{215}{336}\right)$	$e\left(\frac{109}{336}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{4165}(47,\cdot)$	4165.eh	84	yes	$1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{4165}(48,\cdot)$	4165.cl	16	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$-1$

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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	$4165$
Structure	\(C_{2}\times C_{4}\times C_{336}\)
Order	$2688$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{4165}(1,\cdot)\)	4165.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4165}(2,\cdot)\)	4165.ez	168	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{4165}(3,\cdot)\)	4165.fg	336	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{113}{336}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{277}{336}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{4165}(4,\cdot)\)	4165.ep	84	yes	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{4165}(6,\cdot)\)	4165.eu	112	no	\(1\)	\(1\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{4165}(8,\cdot)\)	4165.ed	56	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{4165}(9,\cdot)\)	4165.fb	168	yes	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{4165}(11,\cdot)\)	4165.fi	336	no	\(-1\)	\(1\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{53}{336}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{4165}(12,\cdot)\)	4165.fm	336	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{277}{336}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{4165}(13,\cdot)\)	4165.cx	28	yes	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{4165}(16,\cdot)\)	4165.dl	42	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{4165}(18,\cdot)\)	4165.br	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4165}(19,\cdot)\)	4165.cq	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4165}(22,\cdot)\)	4165.er	112	yes	\(1\)	\(1\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{4165}(23,\cdot)\)	4165.fh	336	yes	\(1\)	\(1\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{253}{336}\right)\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{4165}(24,\cdot)\)	4165.fk	336	yes	\(1\)	\(1\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{43}{336}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{4165}(26,\cdot)\)	4165.fa	168	no	\(-1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{4165}(27,\cdot)\)	4165.eq	112	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{4165}(29,\cdot)\)	4165.es	112	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{4165}(31,\cdot)\)	4165.dq	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4165}(32,\cdot)\)	4165.ez	168	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{4165}(33,\cdot)\)	4165.ei	84	yes	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{4165}(36,\cdot)\)	4165.eb	56	no	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{4165}(37,\cdot)\)	4165.fh	336	yes	\(1\)	\(1\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{193}{336}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{149}{336}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{4165}(38,\cdot)\)	4165.eh	84	yes	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{4165}(39,\cdot)\)	4165.fl	336	yes	\(-1\)	\(1\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{157}{336}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{4165}(41,\cdot)\)	4165.eu	112	no	\(1\)	\(1\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{4165}(43,\cdot)\)	4165.ed	56	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{4165}(44,\cdot)\)	4165.fl	336	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{295}{336}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{11}{336}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)
\(\chi_{4165}(46,\cdot)\)	4165.fi	336	no	\(-1\)	\(1\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{113}{336}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{215}{336}\right)\)	\(e\left(\frac{109}{336}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{4165}(47,\cdot)\)	4165.eh	84	yes	\(1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{4165}(48,\cdot)\)	4165.cl	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(-1\)

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