LMFDB - Group of Dirichlet characters of modulus 2304

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2304)

pari: g = idealstar(,2304,2)

Character group

sage: G.order() pari: g.no
Order	=	768
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{192}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2304}(1279,\cdot)$, $\chi_{2304}(2053,\cdot)$, $\chi_{2304}(1793,\cdot)$

First 32 of 768 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{2304}(1,\cdot)$	2304.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2304}(5,\cdot)$	2304.cb	192	yes	$-1$	$1$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{31}{192}\right)$	$e\left(\frac{77}{192}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{145}{192}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{2304}(7,\cdot)$	2304.by	96	no	$-1$	$1$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2304}(11,\cdot)$	2304.cd	192	yes	$1$	$1$	$e\left(\frac{31}{192}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{107}{192}\right)$	$e\left(\frac{145}{192}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{2304}(13,\cdot)$	2304.ca	192	yes	$1$	$1$	$e\left(\frac{77}{192}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{145}{192}\right)$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{127}{192}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{2304}(17,\cdot)$	2304.bc	16	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-1$
$\chi_{2304}(19,\cdot)$	2304.bv	64	no	$-1$	$1$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2304}(23,\cdot)$	2304.bw	96	no	$1$	$1$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{2304}(25,\cdot)$	2304.bz	96	no	$1$	$1$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{2304}(29,\cdot)$	2304.cb	192	yes	$-1$	$1$	$e\left(\frac{145}{192}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{127}{192}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{107}{192}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{2304}(31,\cdot)$	2304.bh	24	no	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{24}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2304}(35,\cdot)$	2304.bu	64	no	$1$	$1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2304}(37,\cdot)$	2304.bt	64	no	$1$	$1$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2304}(41,\cdot)$	2304.bx	96	no	$-1$	$1$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2304}(43,\cdot)$	2304.cc	192	yes	$-1$	$1$	$e\left(\frac{55}{192}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{25}{192}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{2304}(47,\cdot)$	2304.bp	48	no	$1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{31}{48}\right)$	$-i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2304}(49,\cdot)$	2304.bq	48	no	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{48}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2304}(53,\cdot)$	2304.bs	64	no	$-1$	$1$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{2304}(55,\cdot)$	2304.bk	32	no	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{32}\right)$	$i$
$\chi_{2304}(59,\cdot)$	2304.cd	192	yes	$1$	$1$	$e\left(\frac{83}{192}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{175}{192}\right)$	$e\left(\frac{29}{192}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{97}{192}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{2304}(61,\cdot)$	2304.ca	192	yes	$1$	$1$	$e\left(\frac{121}{192}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{55}{192}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{2304}(65,\cdot)$	2304.ba	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2304}(67,\cdot)$	2304.cc	192	yes	$-1$	$1$	$e\left(\frac{89}{192}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{109}{192}\right)$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{67}{192}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{2304}(71,\cdot)$	2304.bm	32	no	$1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{32}\right)$	$-i$
$\chi_{2304}(73,\cdot)$	2304.bl	32	no	$1$	$1$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{25}{32}\right)$	$-i$
$\chi_{2304}(77,\cdot)$	2304.cb	192	yes	$-1$	$1$	$e\left(\frac{125}{192}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{1}{192}\right)$	$e\left(\frac{83}{192}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{79}{192}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{2304}(79,\cdot)$	2304.bo	48	no	$-1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{25}{48}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2304}(83,\cdot)$	2304.cd	192	yes	$1$	$1$	$e\left(\frac{85}{192}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{89}{192}\right)$	$e\left(\frac{187}{192}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{2304}(85,\cdot)$	2304.ca	192	yes	$1$	$1$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{185}{192}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{13}{192}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{2304}(89,\cdot)$	2304.bn	32	no	$-1$	$1$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{19}{32}\right)$	$i$
$\chi_{2304}(91,\cdot)$	2304.bv	64	no	$-1$	$1$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{2304}(95,\cdot)$	2304.bj	24	no	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{6}\right)$

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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	$2304$
Structure	\(C_{2}\times C_{2}\times C_{192}\)
Order	$768$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{2304}(1,\cdot)\)	2304.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2304}(5,\cdot)\)	2304.cb	192	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{31}{192}\right)\)	\(e\left(\frac{77}{192}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{145}{192}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{2304}(7,\cdot)\)	2304.by	96	no	\(-1\)	\(1\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2304}(11,\cdot)\)	2304.cd	192	yes	\(1\)	\(1\)	\(e\left(\frac{31}{192}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{107}{192}\right)\)	\(e\left(\frac{145}{192}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{2304}(13,\cdot)\)	2304.ca	192	yes	\(1\)	\(1\)	\(e\left(\frac{77}{192}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{145}{192}\right)\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{127}{192}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{2304}(17,\cdot)\)	2304.bc	16	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)
\(\chi_{2304}(19,\cdot)\)	2304.bv	64	no	\(-1\)	\(1\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2304}(23,\cdot)\)	2304.bw	96	no	\(1\)	\(1\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2304}(25,\cdot)\)	2304.bz	96	no	\(1\)	\(1\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2304}(29,\cdot)\)	2304.cb	192	yes	\(-1\)	\(1\)	\(e\left(\frac{145}{192}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{127}{192}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{107}{192}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{2304}(31,\cdot)\)	2304.bh	24	no	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2304}(35,\cdot)\)	2304.bu	64	no	\(1\)	\(1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2304}(37,\cdot)\)	2304.bt	64	no	\(1\)	\(1\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2304}(41,\cdot)\)	2304.bx	96	no	\(-1\)	\(1\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2304}(43,\cdot)\)	2304.cc	192	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{192}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{25}{192}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{2304}(47,\cdot)\)	2304.bp	48	no	\(1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2304}(49,\cdot)\)	2304.bq	48	no	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2304}(53,\cdot)\)	2304.bs	64	no	\(-1\)	\(1\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{2304}(55,\cdot)\)	2304.bk	32	no	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(i\)
\(\chi_{2304}(59,\cdot)\)	2304.cd	192	yes	\(1\)	\(1\)	\(e\left(\frac{83}{192}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{175}{192}\right)\)	\(e\left(\frac{29}{192}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{97}{192}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{2304}(61,\cdot)\)	2304.ca	192	yes	\(1\)	\(1\)	\(e\left(\frac{121}{192}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{55}{192}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{2304}(65,\cdot)\)	2304.ba	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2304}(67,\cdot)\)	2304.cc	192	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{192}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{109}{192}\right)\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{67}{192}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{2304}(71,\cdot)\)	2304.bm	32	no	\(1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(-i\)
\(\chi_{2304}(73,\cdot)\)	2304.bl	32	no	\(1\)	\(1\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(-i\)
\(\chi_{2304}(77,\cdot)\)	2304.cb	192	yes	\(-1\)	\(1\)	\(e\left(\frac{125}{192}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{1}{192}\right)\)	\(e\left(\frac{83}{192}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{79}{192}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{2304}(79,\cdot)\)	2304.bo	48	no	\(-1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2304}(83,\cdot)\)	2304.cd	192	yes	\(1\)	\(1\)	\(e\left(\frac{85}{192}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{89}{192}\right)\)	\(e\left(\frac{187}{192}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{2304}(85,\cdot)\)	2304.ca	192	yes	\(1\)	\(1\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{185}{192}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{13}{192}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{2304}(89,\cdot)\)	2304.bn	32	no	\(-1\)	\(1\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(i\)
\(\chi_{2304}(91,\cdot)\)	2304.bv	64	no	\(-1\)	\(1\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{2304}(95,\cdot)\)	2304.bj	24	no	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)

Introduction

L-functions

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First 32 of 768 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.