LMFDB - Group of Dirichlet characters of modulus 209952

Show commands: PariGP / SageMath

sage: H = DirichletGroup(209952)

pari: g = idealstar(,209952,2)

Character group

sage: G.order() pari: g.no
Order	=	69984
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{17496}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{209952}(196831,\cdot)$, $\chi_{209952}(26245,\cdot)$, $\chi_{209952}(203393,\cdot)$

First 32 of 69984 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{209952}(1,\cdot)$	209952.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{209952}(5,\cdot)$	209952.ev	17496	yes	$-1$	$1$	$e\left(\frac{14023}{17496}\right)$	$e\left(\frac{7675}{8748}\right)$	$e\left(\frac{3923}{17496}\right)$	$e\left(\frac{14749}{17496}\right)$	$e\left(\frac{248}{729}\right)$	$e\left(\frac{1247}{5832}\right)$	$e\left(\frac{4043}{8748}\right)$	$e\left(\frac{5275}{8748}\right)$	$e\left(\frac{1541}{17496}\right)$	$e\left(\frac{311}{2187}\right)$
$\chi_{209952}(7,\cdot)$	209952.er	8748	no	$-1$	$1$	$e\left(\frac{7675}{8748}\right)$	$e\left(\frac{344}{2187}\right)$	$e\left(\frac{173}{8748}\right)$	$e\left(\frac{1849}{8748}\right)$	$e\left(\frac{466}{729}\right)$	$e\left(\frac{2609}{2916}\right)$	$e\left(\frac{1060}{2187}\right)$	$e\left(\frac{3301}{4374}\right)$	$e\left(\frac{4937}{8748}\right)$	$e\left(\frac{1157}{4374}\right)$
$\chi_{209952}(11,\cdot)$	209952.eu	17496	yes	$1$	$1$	$e\left(\frac{3923}{17496}\right)$	$e\left(\frac{173}{8748}\right)$	$e\left(\frac{2755}{17496}\right)$	$e\left(\frac{5249}{17496}\right)$	$e\left(\frac{706}{729}\right)$	$e\left(\frac{4567}{5832}\right)$	$e\left(\frac{3661}{8748}\right)$	$e\left(\frac{3923}{8748}\right)$	$e\left(\frac{7297}{17496}\right)$	$e\left(\frac{395}{4374}\right)$
$\chi_{209952}(13,\cdot)$	209952.ex	17496	yes	$1$	$1$	$e\left(\frac{14749}{17496}\right)$	$e\left(\frac{1849}{8748}\right)$	$e\left(\frac{5249}{17496}\right)$	$e\left(\frac{3739}{17496}\right)$	$e\left(\frac{979}{1458}\right)$	$e\left(\frac{5417}{5832}\right)$	$e\left(\frac{6791}{8748}\right)$	$e\left(\frac{6001}{8748}\right)$	$e\left(\frac{1103}{17496}\right)$	$e\left(\frac{1700}{2187}\right)$
$\chi_{209952}(17,\cdot)$	209952.dv	1458	no	$-1$	$1$	$e\left(\frac{248}{729}\right)$	$e\left(\frac{466}{729}\right)$	$e\left(\frac{706}{729}\right)$	$e\left(\frac{979}{1458}\right)$	$e\left(\frac{121}{486}\right)$	$e\left(\frac{437}{486}\right)$	$e\left(\frac{1363}{1458}\right)$	$e\left(\frac{496}{729}\right)$	$e\left(\frac{1}{729}\right)$	$e\left(\frac{434}{729}\right)$
$\chi_{209952}(19,\cdot)$	209952.ep	5832	no	$-1$	$1$	$e\left(\frac{1247}{5832}\right)$	$e\left(\frac{2609}{2916}\right)$	$e\left(\frac{4567}{5832}\right)$	$e\left(\frac{5417}{5832}\right)$	$e\left(\frac{437}{486}\right)$	$e\left(\frac{1447}{1944}\right)$	$e\left(\frac{1063}{2916}\right)$	$e\left(\frac{1247}{2916}\right)$	$e\left(\frac{4429}{5832}\right)$	$e\left(\frac{1229}{1458}\right)$
$\chi_{209952}(23,\cdot)$	209952.eq	8748	no	$1$	$1$	$e\left(\frac{4043}{8748}\right)$	$e\left(\frac{1060}{2187}\right)$	$e\left(\frac{3661}{8748}\right)$	$e\left(\frac{6791}{8748}\right)$	$e\left(\frac{1363}{1458}\right)$	$e\left(\frac{1063}{2916}\right)$	$e\left(\frac{175}{4374}\right)$	$e\left(\frac{4043}{4374}\right)$	$e\left(\frac{4405}{8748}\right)$	$e\left(\frac{895}{4374}\right)$
$\chi_{209952}(25,\cdot)$	209952.et	8748	no	$1$	$1$	$e\left(\frac{5275}{8748}\right)$	$e\left(\frac{3301}{4374}\right)$	$e\left(\frac{3923}{8748}\right)$	$e\left(\frac{6001}{8748}\right)$	$e\left(\frac{496}{729}\right)$	$e\left(\frac{1247}{2916}\right)$	$e\left(\frac{4043}{4374}\right)$	$e\left(\frac{901}{4374}\right)$	$e\left(\frac{1541}{8748}\right)$	$e\left(\frac{622}{2187}\right)$
$\chi_{209952}(29,\cdot)$	209952.ev	17496	yes	$-1$	$1$	$e\left(\frac{1541}{17496}\right)$	$e\left(\frac{4937}{8748}\right)$	$e\left(\frac{7297}{17496}\right)$	$e\left(\frac{1103}{17496}\right)$	$e\left(\frac{1}{729}\right)$	$e\left(\frac{4429}{5832}\right)$	$e\left(\frac{4405}{8748}\right)$	$e\left(\frac{1541}{8748}\right)$	$e\left(\frac{10903}{17496}\right)$	$e\left(\frac{1180}{2187}\right)$
$\chi_{209952}(31,\cdot)$	209952.eg	4374	no	$-1$	$1$	$e\left(\frac{311}{2187}\right)$	$e\left(\frac{1157}{4374}\right)$	$e\left(\frac{395}{4374}\right)$	$e\left(\frac{1700}{2187}\right)$	$e\left(\frac{434}{729}\right)$	$e\left(\frac{1229}{1458}\right)$	$e\left(\frac{895}{4374}\right)$	$e\left(\frac{622}{2187}\right)$	$e\left(\frac{1180}{2187}\right)$	$e\left(\frac{1453}{4374}\right)$
$\chi_{209952}(35,\cdot)$	209952.en	5832	no	$1$	$1$	$e\left(\frac{3959}{5832}\right)$	$e\left(\frac{101}{2916}\right)$	$e\left(\frac{1423}{5832}\right)$	$e\left(\frac{317}{5832}\right)$	$e\left(\frac{238}{243}\right)$	$e\left(\frac{211}{1944}\right)$	$e\left(\frac{2761}{2916}\right)$	$e\left(\frac{1043}{2916}\right)$	$e\left(\frac{3805}{5832}\right)$	$e\left(\frac{593}{1458}\right)$
$\chi_{209952}(37,\cdot)$	209952.eo	5832	no	$1$	$1$	$e\left(\frac{217}{5832}\right)$	$e\left(\frac{1753}{2916}\right)$	$e\left(\frac{4445}{5832}\right)$	$e\left(\frac{2023}{5832}\right)$	$e\left(\frac{55}{486}\right)$	$e\left(\frac{1877}{1944}\right)$	$e\left(\frac{731}{2916}\right)$	$e\left(\frac{217}{2916}\right)$	$e\left(\frac{5195}{5832}\right)$	$e\left(\frac{617}{729}\right)$
$\chi_{209952}(41,\cdot)$	209952.es	8748	no	$-1$	$1$	$e\left(\frac{6731}{8748}\right)$	$e\left(\frac{3305}{4374}\right)$	$e\left(\frac{3835}{8748}\right)$	$e\left(\frac{1091}{8748}\right)$	$e\left(\frac{421}{1458}\right)$	$e\left(\frac{1597}{2916}\right)$	$e\left(\frac{629}{2187}\right)$	$e\left(\frac{2357}{4374}\right)$	$e\left(\frac{6109}{8748}\right)$	$e\left(\frac{530}{2187}\right)$
$\chi_{209952}(43,\cdot)$	209952.ew	17496	yes	$-1$	$1$	$e\left(\frac{7991}{17496}\right)$	$e\left(\frac{785}{8748}\right)$	$e\left(\frac{15535}{17496}\right)$	$e\left(\frac{10721}{17496}\right)$	$e\left(\frac{377}{1458}\right)$	$e\left(\frac{1255}{5832}\right)$	$e\left(\frac{8395}{8748}\right)$	$e\left(\frac{7991}{8748}\right)$	$e\left(\frac{15109}{17496}\right)$	$e\left(\frac{3815}{4374}\right)$
$\chi_{209952}(47,\cdot)$	209952.eh	4374	no	$1$	$1$	$e\left(\frac{904}{2187}\right)$	$e\left(\frac{2245}{4374}\right)$	$e\left(\frac{1549}{4374}\right)$	$e\left(\frac{2675}{4374}\right)$	$e\left(\frac{833}{1458}\right)$	$e\left(\frac{722}{729}\right)$	$e\left(\frac{1132}{2187}\right)$	$e\left(\frac{1808}{2187}\right)$	$e\left(\frac{1250}{2187}\right)$	$e\left(\frac{3893}{4374}\right)$
$\chi_{209952}(49,\cdot)$	209952.ej	4374	no	$1$	$1$	$e\left(\frac{3301}{4374}\right)$	$e\left(\frac{688}{2187}\right)$	$e\left(\frac{173}{4374}\right)$	$e\left(\frac{1849}{4374}\right)$	$e\left(\frac{203}{729}\right)$	$e\left(\frac{1151}{1458}\right)$	$e\left(\frac{2120}{2187}\right)$	$e\left(\frac{1114}{2187}\right)$	$e\left(\frac{563}{4374}\right)$	$e\left(\frac{1157}{2187}\right)$
$\chi_{209952}(53,\cdot)$	209952.dy	1944	no	$-1$	$1$	$e\left(\frac{1867}{1944}\right)$	$e\left(\frac{883}{972}\right)$	$e\left(\frac{743}{1944}\right)$	$e\left(\frac{505}{1944}\right)$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{515}{648}\right)$	$e\left(\frac{791}{972}\right)$	$e\left(\frac{895}{972}\right)$	$e\left(\frac{665}{1944}\right)$	$e\left(\frac{173}{243}\right)$
$\chi_{209952}(55,\cdot)$	209952.dm	972	no	$-1$	$1$	$e\left(\frac{25}{972}\right)$	$e\left(\frac{218}{243}\right)$	$e\left(\frac{371}{972}\right)$	$e\left(\frac{139}{972}\right)$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{323}{324}\right)$	$e\left(\frac{214}{243}\right)$	$e\left(\frac{25}{486}\right)$	$e\left(\frac{491}{972}\right)$	$e\left(\frac{113}{486}\right)$
$\chi_{209952}(59,\cdot)$	209952.eu	17496	yes	$1$	$1$	$e\left(\frac{2935}{17496}\right)$	$e\left(\frac{7981}{8748}\right)$	$e\left(\frac{14687}{17496}\right)$	$e\left(\frac{17485}{17496}\right)$	$e\left(\frac{536}{729}\right)$	$e\left(\frac{2507}{5832}\right)$	$e\left(\frac{8597}{8748}\right)$	$e\left(\frac{2935}{8748}\right)$	$e\left(\frac{9821}{17496}\right)$	$e\left(\frac{145}{4374}\right)$
$\chi_{209952}(61,\cdot)$	209952.ex	17496	yes	$1$	$1$	$e\left(\frac{17393}{17496}\right)$	$e\left(\frac{8225}{8748}\right)$	$e\left(\frac{13693}{17496}\right)$	$e\left(\frac{15407}{17496}\right)$	$e\left(\frac{59}{1458}\right)$	$e\left(\frac{3445}{5832}\right)$	$e\left(\frac{7111}{8748}\right)$	$e\left(\frac{8645}{8748}\right)$	$e\left(\frac{12907}{17496}\right)$	$e\left(\frac{547}{2187}\right)$
$\chi_{209952}(65,\cdot)$	209952.ei	4374	no	$-1$	$1$	$e\left(\frac{2819}{4374}\right)$	$e\left(\frac{194}{2187}\right)$	$e\left(\frac{2293}{4374}\right)$	$e\left(\frac{124}{2187}\right)$	$e\left(\frac{17}{1458}\right)$	$e\left(\frac{104}{729}\right)$	$e\left(\frac{1043}{4374}\right)$	$e\left(\frac{632}{2187}\right)$	$e\left(\frac{661}{4374}\right)$	$e\left(\frac{2011}{2187}\right)$
$\chi_{209952}(67,\cdot)$	209952.ew	17496	yes	$-1$	$1$	$e\left(\frac{4129}{17496}\right)$	$e\left(\frac{1219}{8748}\right)$	$e\left(\frac{10361}{17496}\right)$	$e\left(\frac{679}{17496}\right)$	$e\left(\frac{565}{1458}\right)$	$e\left(\frac{593}{5832}\right)$	$e\left(\frac{2561}{8748}\right)$	$e\left(\frac{4129}{8748}\right)$	$e\left(\frac{16475}{17496}\right)$	$e\left(\frac{2581}{4374}\right)$
$\chi_{209952}(71,\cdot)$	209952.ee	2916	no	$1$	$1$	$e\left(\frac{1835}{2916}\right)$	$e\left(\frac{352}{729}\right)$	$e\left(\frac{2737}{2916}\right)$	$e\left(\frac{1163}{2916}\right)$	$e\left(\frac{349}{486}\right)$	$e\left(\frac{607}{972}\right)$	$e\left(\frac{457}{1458}\right)$	$e\left(\frac{377}{1458}\right)$	$e\left(\frac{2797}{2916}\right)$	$e\left(\frac{421}{1458}\right)$
$\chi_{209952}(73,\cdot)$	209952.eb	2916	no	$1$	$1$	$e\left(\frac{2143}{2916}\right)$	$e\left(\frac{817}{1458}\right)$	$e\left(\frac{251}{2916}\right)$	$e\left(\frac{601}{2916}\right)$	$e\left(\frac{37}{243}\right)$	$e\left(\frac{167}{972}\right)$	$e\left(\frac{695}{1458}\right)$	$e\left(\frac{685}{1458}\right)$	$e\left(\frac{2081}{2916}\right)$	$e\left(\frac{163}{729}\right)$
$\chi_{209952}(77,\cdot)$	209952.ev	17496	yes	$-1$	$1$	$e\left(\frac{1777}{17496}\right)$	$e\left(\frac{1549}{8748}\right)$	$e\left(\frac{3101}{17496}\right)$	$e\left(\frac{8947}{17496}\right)$	$e\left(\frac{443}{729}\right)$	$e\left(\frac{3953}{5832}\right)$	$e\left(\frac{7901}{8748}\right)$	$e\left(\frac{1777}{8748}\right)$	$e\left(\frac{17171}{17496}\right)$	$e\left(\frac{776}{2187}\right)$
$\chi_{209952}(79,\cdot)$	209952.el	4374	no	$-1$	$1$	$e\left(\frac{3371}{4374}\right)$	$e\left(\frac{367}{4374}\right)$	$e\left(\frac{1262}{2187}\right)$	$e\left(\frac{1655}{4374}\right)$	$e\left(\frac{505}{729}\right)$	$e\left(\frac{647}{729}\right)$	$e\left(\frac{3089}{4374}\right)$	$e\left(\frac{1184}{2187}\right)$	$e\left(\frac{3979}{4374}\right)$	$e\left(\frac{2801}{4374}\right)$
$\chi_{209952}(83,\cdot)$	209952.eu	17496	yes	$1$	$1$	$e\left(\frac{3953}{17496}\right)$	$e\left(\frac{4487}{8748}\right)$	$e\left(\frac{8449}{17496}\right)$	$e\left(\frac{8915}{17496}\right)$	$e\left(\frac{478}{729}\right)$	$e\left(\frac{5149}{5832}\right)$	$e\left(\frac{3883}{8748}\right)$	$e\left(\frac{3953}{8748}\right)$	$e\left(\frac{4387}{17496}\right)$	$e\left(\frac{1775}{4374}\right)$
$\chi_{209952}(85,\cdot)$	209952.ex	17496	yes	$1$	$1$	$e\left(\frac{2479}{17496}\right)$	$e\left(\frac{4519}{8748}\right)$	$e\left(\frac{3371}{17496}\right)$	$e\left(\frac{9001}{17496}\right)$	$e\left(\frac{859}{1458}\right)$	$e\left(\frac{659}{5832}\right)$	$e\left(\frac{3473}{8748}\right)$	$e\left(\frac{2479}{8748}\right)$	$e\left(\frac{1565}{17496}\right)$	$e\left(\frac{1613}{2187}\right)$
$\chi_{209952}(89,\cdot)$	209952.ed	2916	no	$-1$	$1$	$e\left(\frac{379}{2916}\right)$	$e\left(\frac{1429}{1458}\right)$	$e\left(\frac{1367}{2916}\right)$	$e\left(\frac{1699}{2916}\right)$	$e\left(\frac{191}{486}\right)$	$e\left(\frac{257}{972}\right)$	$e\left(\frac{163}{729}\right)$	$e\left(\frac{379}{1458}\right)$	$e\left(\frac{1145}{2916}\right)$	$e\left(\frac{667}{729}\right)$
$\chi_{209952}(91,\cdot)$	209952.ep	5832	no	$-1$	$1$	$e\left(\frac{4201}{5832}\right)$	$e\left(\frac{1075}{2916}\right)$	$e\left(\frac{1865}{5832}\right)$	$e\left(\frac{2479}{5832}\right)$	$e\left(\frac{151}{486}\right)$	$e\left(\frac{1601}{1944}\right)$	$e\left(\frac{761}{2916}\right)$	$e\left(\frac{1285}{2916}\right)$	$e\left(\frac{3659}{5832}\right)$	$e\left(\frac{61}{1458}\right)$
$\chi_{209952}(95,\cdot)$	209952.ek	4374	no	$1$	$1$	$e\left(\frac{67}{4374}\right)$	$e\left(\frac{3377}{4374}\right)$	$e\left(\frac{16}{2187}\right)$	$e\left(\frac{1688}{2187}\right)$	$e\left(\frac{349}{1458}\right)$	$e\left(\frac{1397}{1458}\right)$	$e\left(\frac{1808}{2187}\right)$	$e\left(\frac{67}{2187}\right)$	$e\left(\frac{3707}{4374}\right)$	$e\left(\frac{4309}{4374}\right)$

Click here to search among the remaining 69952 characters.

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	$209952$
Structure	\(C_{2}\times C_{2}\times C_{17496}\)
Order	$69984$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{209952}(1,\cdot)\)	209952.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{209952}(5,\cdot)\)	209952.ev	17496	yes	\(-1\)	\(1\)	\(e\left(\frac{14023}{17496}\right)\)	\(e\left(\frac{7675}{8748}\right)\)	\(e\left(\frac{3923}{17496}\right)\)	\(e\left(\frac{14749}{17496}\right)\)	\(e\left(\frac{248}{729}\right)\)	\(e\left(\frac{1247}{5832}\right)\)	\(e\left(\frac{4043}{8748}\right)\)	\(e\left(\frac{5275}{8748}\right)\)	\(e\left(\frac{1541}{17496}\right)\)	\(e\left(\frac{311}{2187}\right)\)
\(\chi_{209952}(7,\cdot)\)	209952.er	8748	no	\(-1\)	\(1\)	\(e\left(\frac{7675}{8748}\right)\)	\(e\left(\frac{344}{2187}\right)\)	\(e\left(\frac{173}{8748}\right)\)	\(e\left(\frac{1849}{8748}\right)\)	\(e\left(\frac{466}{729}\right)\)	\(e\left(\frac{2609}{2916}\right)\)	\(e\left(\frac{1060}{2187}\right)\)	\(e\left(\frac{3301}{4374}\right)\)	\(e\left(\frac{4937}{8748}\right)\)	\(e\left(\frac{1157}{4374}\right)\)
\(\chi_{209952}(11,\cdot)\)	209952.eu	17496	yes	\(1\)	\(1\)	\(e\left(\frac{3923}{17496}\right)\)	\(e\left(\frac{173}{8748}\right)\)	\(e\left(\frac{2755}{17496}\right)\)	\(e\left(\frac{5249}{17496}\right)\)	\(e\left(\frac{706}{729}\right)\)	\(e\left(\frac{4567}{5832}\right)\)	\(e\left(\frac{3661}{8748}\right)\)	\(e\left(\frac{3923}{8748}\right)\)	\(e\left(\frac{7297}{17496}\right)\)	\(e\left(\frac{395}{4374}\right)\)
\(\chi_{209952}(13,\cdot)\)	209952.ex	17496	yes	\(1\)	\(1\)	\(e\left(\frac{14749}{17496}\right)\)	\(e\left(\frac{1849}{8748}\right)\)	\(e\left(\frac{5249}{17496}\right)\)	\(e\left(\frac{3739}{17496}\right)\)	\(e\left(\frac{979}{1458}\right)\)	\(e\left(\frac{5417}{5832}\right)\)	\(e\left(\frac{6791}{8748}\right)\)	\(e\left(\frac{6001}{8748}\right)\)	\(e\left(\frac{1103}{17496}\right)\)	\(e\left(\frac{1700}{2187}\right)\)
\(\chi_{209952}(17,\cdot)\)	209952.dv	1458	no	\(-1\)	\(1\)	\(e\left(\frac{248}{729}\right)\)	\(e\left(\frac{466}{729}\right)\)	\(e\left(\frac{706}{729}\right)\)	\(e\left(\frac{979}{1458}\right)\)	\(e\left(\frac{121}{486}\right)\)	\(e\left(\frac{437}{486}\right)\)	\(e\left(\frac{1363}{1458}\right)\)	\(e\left(\frac{496}{729}\right)\)	\(e\left(\frac{1}{729}\right)\)	\(e\left(\frac{434}{729}\right)\)
\(\chi_{209952}(19,\cdot)\)	209952.ep	5832	no	\(-1\)	\(1\)	\(e\left(\frac{1247}{5832}\right)\)	\(e\left(\frac{2609}{2916}\right)\)	\(e\left(\frac{4567}{5832}\right)\)	\(e\left(\frac{5417}{5832}\right)\)	\(e\left(\frac{437}{486}\right)\)	\(e\left(\frac{1447}{1944}\right)\)	\(e\left(\frac{1063}{2916}\right)\)	\(e\left(\frac{1247}{2916}\right)\)	\(e\left(\frac{4429}{5832}\right)\)	\(e\left(\frac{1229}{1458}\right)\)
\(\chi_{209952}(23,\cdot)\)	209952.eq	8748	no	\(1\)	\(1\)	\(e\left(\frac{4043}{8748}\right)\)	\(e\left(\frac{1060}{2187}\right)\)	\(e\left(\frac{3661}{8748}\right)\)	\(e\left(\frac{6791}{8748}\right)\)	\(e\left(\frac{1363}{1458}\right)\)	\(e\left(\frac{1063}{2916}\right)\)	\(e\left(\frac{175}{4374}\right)\)	\(e\left(\frac{4043}{4374}\right)\)	\(e\left(\frac{4405}{8748}\right)\)	\(e\left(\frac{895}{4374}\right)\)
\(\chi_{209952}(25,\cdot)\)	209952.et	8748	no	\(1\)	\(1\)	\(e\left(\frac{5275}{8748}\right)\)	\(e\left(\frac{3301}{4374}\right)\)	\(e\left(\frac{3923}{8748}\right)\)	\(e\left(\frac{6001}{8748}\right)\)	\(e\left(\frac{496}{729}\right)\)	\(e\left(\frac{1247}{2916}\right)\)	\(e\left(\frac{4043}{4374}\right)\)	\(e\left(\frac{901}{4374}\right)\)	\(e\left(\frac{1541}{8748}\right)\)	\(e\left(\frac{622}{2187}\right)\)
\(\chi_{209952}(29,\cdot)\)	209952.ev	17496	yes	\(-1\)	\(1\)	\(e\left(\frac{1541}{17496}\right)\)	\(e\left(\frac{4937}{8748}\right)\)	\(e\left(\frac{7297}{17496}\right)\)	\(e\left(\frac{1103}{17496}\right)\)	\(e\left(\frac{1}{729}\right)\)	\(e\left(\frac{4429}{5832}\right)\)	\(e\left(\frac{4405}{8748}\right)\)	\(e\left(\frac{1541}{8748}\right)\)	\(e\left(\frac{10903}{17496}\right)\)	\(e\left(\frac{1180}{2187}\right)\)
\(\chi_{209952}(31,\cdot)\)	209952.eg	4374	no	\(-1\)	\(1\)	\(e\left(\frac{311}{2187}\right)\)	\(e\left(\frac{1157}{4374}\right)\)	\(e\left(\frac{395}{4374}\right)\)	\(e\left(\frac{1700}{2187}\right)\)	\(e\left(\frac{434}{729}\right)\)	\(e\left(\frac{1229}{1458}\right)\)	\(e\left(\frac{895}{4374}\right)\)	\(e\left(\frac{622}{2187}\right)\)	\(e\left(\frac{1180}{2187}\right)\)	\(e\left(\frac{1453}{4374}\right)\)
\(\chi_{209952}(35,\cdot)\)	209952.en	5832	no	\(1\)	\(1\)	\(e\left(\frac{3959}{5832}\right)\)	\(e\left(\frac{101}{2916}\right)\)	\(e\left(\frac{1423}{5832}\right)\)	\(e\left(\frac{317}{5832}\right)\)	\(e\left(\frac{238}{243}\right)\)	\(e\left(\frac{211}{1944}\right)\)	\(e\left(\frac{2761}{2916}\right)\)	\(e\left(\frac{1043}{2916}\right)\)	\(e\left(\frac{3805}{5832}\right)\)	\(e\left(\frac{593}{1458}\right)\)
\(\chi_{209952}(37,\cdot)\)	209952.eo	5832	no	\(1\)	\(1\)	\(e\left(\frac{217}{5832}\right)\)	\(e\left(\frac{1753}{2916}\right)\)	\(e\left(\frac{4445}{5832}\right)\)	\(e\left(\frac{2023}{5832}\right)\)	\(e\left(\frac{55}{486}\right)\)	\(e\left(\frac{1877}{1944}\right)\)	\(e\left(\frac{731}{2916}\right)\)	\(e\left(\frac{217}{2916}\right)\)	\(e\left(\frac{5195}{5832}\right)\)	\(e\left(\frac{617}{729}\right)\)
\(\chi_{209952}(41,\cdot)\)	209952.es	8748	no	\(-1\)	\(1\)	\(e\left(\frac{6731}{8748}\right)\)	\(e\left(\frac{3305}{4374}\right)\)	\(e\left(\frac{3835}{8748}\right)\)	\(e\left(\frac{1091}{8748}\right)\)	\(e\left(\frac{421}{1458}\right)\)	\(e\left(\frac{1597}{2916}\right)\)	\(e\left(\frac{629}{2187}\right)\)	\(e\left(\frac{2357}{4374}\right)\)	\(e\left(\frac{6109}{8748}\right)\)	\(e\left(\frac{530}{2187}\right)\)
\(\chi_{209952}(43,\cdot)\)	209952.ew	17496	yes	\(-1\)	\(1\)	\(e\left(\frac{7991}{17496}\right)\)	\(e\left(\frac{785}{8748}\right)\)	\(e\left(\frac{15535}{17496}\right)\)	\(e\left(\frac{10721}{17496}\right)\)	\(e\left(\frac{377}{1458}\right)\)	\(e\left(\frac{1255}{5832}\right)\)	\(e\left(\frac{8395}{8748}\right)\)	\(e\left(\frac{7991}{8748}\right)\)	\(e\left(\frac{15109}{17496}\right)\)	\(e\left(\frac{3815}{4374}\right)\)
\(\chi_{209952}(47,\cdot)\)	209952.eh	4374	no	\(1\)	\(1\)	\(e\left(\frac{904}{2187}\right)\)	\(e\left(\frac{2245}{4374}\right)\)	\(e\left(\frac{1549}{4374}\right)\)	\(e\left(\frac{2675}{4374}\right)\)	\(e\left(\frac{833}{1458}\right)\)	\(e\left(\frac{722}{729}\right)\)	\(e\left(\frac{1132}{2187}\right)\)	\(e\left(\frac{1808}{2187}\right)\)	\(e\left(\frac{1250}{2187}\right)\)	\(e\left(\frac{3893}{4374}\right)\)
\(\chi_{209952}(49,\cdot)\)	209952.ej	4374	no	\(1\)	\(1\)	\(e\left(\frac{3301}{4374}\right)\)	\(e\left(\frac{688}{2187}\right)\)	\(e\left(\frac{173}{4374}\right)\)	\(e\left(\frac{1849}{4374}\right)\)	\(e\left(\frac{203}{729}\right)\)	\(e\left(\frac{1151}{1458}\right)\)	\(e\left(\frac{2120}{2187}\right)\)	\(e\left(\frac{1114}{2187}\right)\)	\(e\left(\frac{563}{4374}\right)\)	\(e\left(\frac{1157}{2187}\right)\)
\(\chi_{209952}(53,\cdot)\)	209952.dy	1944	no	\(-1\)	\(1\)	\(e\left(\frac{1867}{1944}\right)\)	\(e\left(\frac{883}{972}\right)\)	\(e\left(\frac{743}{1944}\right)\)	\(e\left(\frac{505}{1944}\right)\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{515}{648}\right)\)	\(e\left(\frac{791}{972}\right)\)	\(e\left(\frac{895}{972}\right)\)	\(e\left(\frac{665}{1944}\right)\)	\(e\left(\frac{173}{243}\right)\)
\(\chi_{209952}(55,\cdot)\)	209952.dm	972	no	\(-1\)	\(1\)	\(e\left(\frac{25}{972}\right)\)	\(e\left(\frac{218}{243}\right)\)	\(e\left(\frac{371}{972}\right)\)	\(e\left(\frac{139}{972}\right)\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{323}{324}\right)\)	\(e\left(\frac{214}{243}\right)\)	\(e\left(\frac{25}{486}\right)\)	\(e\left(\frac{491}{972}\right)\)	\(e\left(\frac{113}{486}\right)\)
\(\chi_{209952}(59,\cdot)\)	209952.eu	17496	yes	\(1\)	\(1\)	\(e\left(\frac{2935}{17496}\right)\)	\(e\left(\frac{7981}{8748}\right)\)	\(e\left(\frac{14687}{17496}\right)\)	\(e\left(\frac{17485}{17496}\right)\)	\(e\left(\frac{536}{729}\right)\)	\(e\left(\frac{2507}{5832}\right)\)	\(e\left(\frac{8597}{8748}\right)\)	\(e\left(\frac{2935}{8748}\right)\)	\(e\left(\frac{9821}{17496}\right)\)	\(e\left(\frac{145}{4374}\right)\)
\(\chi_{209952}(61,\cdot)\)	209952.ex	17496	yes	\(1\)	\(1\)	\(e\left(\frac{17393}{17496}\right)\)	\(e\left(\frac{8225}{8748}\right)\)	\(e\left(\frac{13693}{17496}\right)\)	\(e\left(\frac{15407}{17496}\right)\)	\(e\left(\frac{59}{1458}\right)\)	\(e\left(\frac{3445}{5832}\right)\)	\(e\left(\frac{7111}{8748}\right)\)	\(e\left(\frac{8645}{8748}\right)\)	\(e\left(\frac{12907}{17496}\right)\)	\(e\left(\frac{547}{2187}\right)\)
\(\chi_{209952}(65,\cdot)\)	209952.ei	4374	no	\(-1\)	\(1\)	\(e\left(\frac{2819}{4374}\right)\)	\(e\left(\frac{194}{2187}\right)\)	\(e\left(\frac{2293}{4374}\right)\)	\(e\left(\frac{124}{2187}\right)\)	\(e\left(\frac{17}{1458}\right)\)	\(e\left(\frac{104}{729}\right)\)	\(e\left(\frac{1043}{4374}\right)\)	\(e\left(\frac{632}{2187}\right)\)	\(e\left(\frac{661}{4374}\right)\)	\(e\left(\frac{2011}{2187}\right)\)
\(\chi_{209952}(67,\cdot)\)	209952.ew	17496	yes	\(-1\)	\(1\)	\(e\left(\frac{4129}{17496}\right)\)	\(e\left(\frac{1219}{8748}\right)\)	\(e\left(\frac{10361}{17496}\right)\)	\(e\left(\frac{679}{17496}\right)\)	\(e\left(\frac{565}{1458}\right)\)	\(e\left(\frac{593}{5832}\right)\)	\(e\left(\frac{2561}{8748}\right)\)	\(e\left(\frac{4129}{8748}\right)\)	\(e\left(\frac{16475}{17496}\right)\)	\(e\left(\frac{2581}{4374}\right)\)
\(\chi_{209952}(71,\cdot)\)	209952.ee	2916	no	\(1\)	\(1\)	\(e\left(\frac{1835}{2916}\right)\)	\(e\left(\frac{352}{729}\right)\)	\(e\left(\frac{2737}{2916}\right)\)	\(e\left(\frac{1163}{2916}\right)\)	\(e\left(\frac{349}{486}\right)\)	\(e\left(\frac{607}{972}\right)\)	\(e\left(\frac{457}{1458}\right)\)	\(e\left(\frac{377}{1458}\right)\)	\(e\left(\frac{2797}{2916}\right)\)	\(e\left(\frac{421}{1458}\right)\)
\(\chi_{209952}(73,\cdot)\)	209952.eb	2916	no	\(1\)	\(1\)	\(e\left(\frac{2143}{2916}\right)\)	\(e\left(\frac{817}{1458}\right)\)	\(e\left(\frac{251}{2916}\right)\)	\(e\left(\frac{601}{2916}\right)\)	\(e\left(\frac{37}{243}\right)\)	\(e\left(\frac{167}{972}\right)\)	\(e\left(\frac{695}{1458}\right)\)	\(e\left(\frac{685}{1458}\right)\)	\(e\left(\frac{2081}{2916}\right)\)	\(e\left(\frac{163}{729}\right)\)
\(\chi_{209952}(77,\cdot)\)	209952.ev	17496	yes	\(-1\)	\(1\)	\(e\left(\frac{1777}{17496}\right)\)	\(e\left(\frac{1549}{8748}\right)\)	\(e\left(\frac{3101}{17496}\right)\)	\(e\left(\frac{8947}{17496}\right)\)	\(e\left(\frac{443}{729}\right)\)	\(e\left(\frac{3953}{5832}\right)\)	\(e\left(\frac{7901}{8748}\right)\)	\(e\left(\frac{1777}{8748}\right)\)	\(e\left(\frac{17171}{17496}\right)\)	\(e\left(\frac{776}{2187}\right)\)
\(\chi_{209952}(79,\cdot)\)	209952.el	4374	no	\(-1\)	\(1\)	\(e\left(\frac{3371}{4374}\right)\)	\(e\left(\frac{367}{4374}\right)\)	\(e\left(\frac{1262}{2187}\right)\)	\(e\left(\frac{1655}{4374}\right)\)	\(e\left(\frac{505}{729}\right)\)	\(e\left(\frac{647}{729}\right)\)	\(e\left(\frac{3089}{4374}\right)\)	\(e\left(\frac{1184}{2187}\right)\)	\(e\left(\frac{3979}{4374}\right)\)	\(e\left(\frac{2801}{4374}\right)\)
\(\chi_{209952}(83,\cdot)\)	209952.eu	17496	yes	\(1\)	\(1\)	\(e\left(\frac{3953}{17496}\right)\)	\(e\left(\frac{4487}{8748}\right)\)	\(e\left(\frac{8449}{17496}\right)\)	\(e\left(\frac{8915}{17496}\right)\)	\(e\left(\frac{478}{729}\right)\)	\(e\left(\frac{5149}{5832}\right)\)	\(e\left(\frac{3883}{8748}\right)\)	\(e\left(\frac{3953}{8748}\right)\)	\(e\left(\frac{4387}{17496}\right)\)	\(e\left(\frac{1775}{4374}\right)\)
\(\chi_{209952}(85,\cdot)\)	209952.ex	17496	yes	\(1\)	\(1\)	\(e\left(\frac{2479}{17496}\right)\)	\(e\left(\frac{4519}{8748}\right)\)	\(e\left(\frac{3371}{17496}\right)\)	\(e\left(\frac{9001}{17496}\right)\)	\(e\left(\frac{859}{1458}\right)\)	\(e\left(\frac{659}{5832}\right)\)	\(e\left(\frac{3473}{8748}\right)\)	\(e\left(\frac{2479}{8748}\right)\)	\(e\left(\frac{1565}{17496}\right)\)	\(e\left(\frac{1613}{2187}\right)\)
\(\chi_{209952}(89,\cdot)\)	209952.ed	2916	no	\(-1\)	\(1\)	\(e\left(\frac{379}{2916}\right)\)	\(e\left(\frac{1429}{1458}\right)\)	\(e\left(\frac{1367}{2916}\right)\)	\(e\left(\frac{1699}{2916}\right)\)	\(e\left(\frac{191}{486}\right)\)	\(e\left(\frac{257}{972}\right)\)	\(e\left(\frac{163}{729}\right)\)	\(e\left(\frac{379}{1458}\right)\)	\(e\left(\frac{1145}{2916}\right)\)	\(e\left(\frac{667}{729}\right)\)
\(\chi_{209952}(91,\cdot)\)	209952.ep	5832	no	\(-1\)	\(1\)	\(e\left(\frac{4201}{5832}\right)\)	\(e\left(\frac{1075}{2916}\right)\)	\(e\left(\frac{1865}{5832}\right)\)	\(e\left(\frac{2479}{5832}\right)\)	\(e\left(\frac{151}{486}\right)\)	\(e\left(\frac{1601}{1944}\right)\)	\(e\left(\frac{761}{2916}\right)\)	\(e\left(\frac{1285}{2916}\right)\)	\(e\left(\frac{3659}{5832}\right)\)	\(e\left(\frac{61}{1458}\right)\)
\(\chi_{209952}(95,\cdot)\)	209952.ek	4374	no	\(1\)	\(1\)	\(e\left(\frac{67}{4374}\right)\)	\(e\left(\frac{3377}{4374}\right)\)	\(e\left(\frac{16}{2187}\right)\)	\(e\left(\frac{1688}{2187}\right)\)	\(e\left(\frac{349}{1458}\right)\)	\(e\left(\frac{1397}{1458}\right)\)	\(e\left(\frac{1808}{2187}\right)\)	\(e\left(\frac{67}{2187}\right)\)	\(e\left(\frac{3707}{4374}\right)\)	\(e\left(\frac{4309}{4374}\right)\)

Introduction

L-functions

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Character group

First 32 of 69984 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.