LMFDB - Group of Dirichlet characters of modulus 221067

Show commands: PariGP / SageMath

sage: H = DirichletGroup(221067)

pari: g = idealstar(,221067,2)

Character group

sage: G.order() pari: g.no
Order	=	110880
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{4620}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{221067}(122816,\cdot)$, $\chi_{221067}(126325,\cdot)$, $\chi_{221067}(202798,\cdot)$, $\chi_{221067}(53362,\cdot)$

First 32 of 110880 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{221067}(1,\cdot)$	221067.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{221067}(2,\cdot)$	221067.bju	4620	yes	$-1$	$1$	$e\left(\frac{4057}{4620}\right)$	$e\left(\frac{1747}{2310}\right)$	$e\left(\frac{369}{385}\right)$	$e\left(\frac{977}{1540}\right)$	$e\left(\frac{773}{924}\right)$	$e\left(\frac{1033}{1155}\right)$	$e\left(\frac{592}{1155}\right)$	$e\left(\frac{19}{660}\right)$	$e\left(\frac{3431}{4620}\right)$	$e\left(\frac{1651}{2310}\right)$
$\chi_{221067}(4,\cdot)$	221067.bhu	2310	yes	$1$	$1$	$e\left(\frac{1747}{2310}\right)$	$e\left(\frac{592}{1155}\right)$	$e\left(\frac{353}{385}\right)$	$e\left(\frac{207}{770}\right)$	$e\left(\frac{311}{462}\right)$	$e\left(\frac{911}{1155}\right)$	$e\left(\frac{29}{1155}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{1121}{2310}\right)$	$e\left(\frac{496}{1155}\right)$
$\chi_{221067}(5,\cdot)$	221067.bhp	2310	yes	$1$	$1$	$e\left(\frac{369}{385}\right)$	$e\left(\frac{353}{385}\right)$	$e\left(\frac{463}{1155}\right)$	$e\left(\frac{337}{385}\right)$	$e\left(\frac{83}{231}\right)$	$e\left(\frac{589}{2310}\right)$	$e\left(\frac{321}{385}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{86}{1155}\right)$	$e\left(\frac{367}{1155}\right)$
$\chi_{221067}(8,\cdot)$	221067.bhc	1540	no	$-1$	$1$	$e\left(\frac{977}{1540}\right)$	$e\left(\frac{207}{770}\right)$	$e\left(\frac{337}{385}\right)$	$e\left(\frac{1391}{1540}\right)$	$e\left(\frac{157}{308}\right)$	$e\left(\frac{263}{385}\right)$	$e\left(\frac{207}{385}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{351}{1540}\right)$	$e\left(\frac{111}{770}\right)$
$\chi_{221067}(10,\cdot)$	221067.bge	924	no	$-1$	$1$	$e\left(\frac{773}{924}\right)$	$e\left(\frac{311}{462}\right)$	$e\left(\frac{83}{231}\right)$	$e\left(\frac{157}{308}\right)$	$e\left(\frac{181}{924}\right)$	$e\left(\frac{23}{154}\right)$	$e\left(\frac{80}{231}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{755}{924}\right)$	$e\left(\frac{5}{154}\right)$
$\chi_{221067}(13,\cdot)$	221067.biu	2310	yes	$1$	$1$	$e\left(\frac{1033}{1155}\right)$	$e\left(\frac{911}{1155}\right)$	$e\left(\frac{589}{2310}\right)$	$e\left(\frac{263}{385}\right)$	$e\left(\frac{23}{154}\right)$	$e\left(\frac{548}{1155}\right)$	$e\left(\frac{667}{1155}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{381}{770}\right)$	$e\left(\frac{101}{2310}\right)$
$\chi_{221067}(16,\cdot)$	221067.bgz	1155	yes	$1$	$1$	$e\left(\frac{592}{1155}\right)$	$e\left(\frac{29}{1155}\right)$	$e\left(\frac{321}{385}\right)$	$e\left(\frac{207}{385}\right)$	$e\left(\frac{80}{231}\right)$	$e\left(\frac{667}{1155}\right)$	$e\left(\frac{58}{1155}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{1121}{1155}\right)$	$e\left(\frac{992}{1155}\right)$
$\chi_{221067}(17,\cdot)$	221067.ber	660	no	$1$	$1$	$e\left(\frac{19}{660}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{161}{660}\right)$	$e\left(\frac{367}{660}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{221067}(19,\cdot)$	221067.bkk	4620	no	$-1$	$1$	$e\left(\frac{3431}{4620}\right)$	$e\left(\frac{1121}{2310}\right)$	$e\left(\frac{86}{1155}\right)$	$e\left(\frac{351}{1540}\right)$	$e\left(\frac{755}{924}\right)$	$e\left(\frac{381}{770}\right)$	$e\left(\frac{1121}{1155}\right)$	$e\left(\frac{367}{660}\right)$	$e\left(\frac{3173}{4620}\right)$	$e\left(\frac{431}{770}\right)$
$\chi_{221067}(20,\cdot)$	221067.bie	2310	yes	$1$	$1$	$e\left(\frac{1651}{2310}\right)$	$e\left(\frac{496}{1155}\right)$	$e\left(\frac{367}{1155}\right)$	$e\left(\frac{111}{770}\right)$	$e\left(\frac{5}{154}\right)$	$e\left(\frac{101}{2310}\right)$	$e\left(\frac{992}{1155}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{431}{770}\right)$	$e\left(\frac{863}{1155}\right)$
$\chi_{221067}(23,\cdot)$	221067.bbt	462	yes	$-1$	$1$	$e\left(\frac{131}{154}\right)$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{295}{462}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{113}{231}\right)$	$e\left(\frac{184}{231}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{211}{231}\right)$	$e\left(\frac{157}{462}\right)$
$\chi_{221067}(25,\cdot)$	221067.bgy	1155	yes	$1$	$1$	$e\left(\frac{353}{385}\right)$	$e\left(\frac{321}{385}\right)$	$e\left(\frac{926}{1155}\right)$	$e\left(\frac{289}{385}\right)$	$e\left(\frac{166}{231}\right)$	$e\left(\frac{589}{1155}\right)$	$e\left(\frac{257}{385}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{172}{1155}\right)$	$e\left(\frac{734}{1155}\right)$
$\chi_{221067}(26,\cdot)$	221067.bjx	4620	no	$-1$	$1$	$e\left(\frac{3569}{4620}\right)$	$e\left(\frac{1259}{2310}\right)$	$e\left(\frac{493}{2310}\right)$	$e\left(\frac{489}{1540}\right)$	$e\left(\frac{911}{924}\right)$	$e\left(\frac{142}{385}\right)$	$e\left(\frac{104}{1155}\right)$	$e\left(\frac{13}{660}\right)$	$e\left(\frac{1097}{4620}\right)$	$e\left(\frac{292}{385}\right)$
$\chi_{221067}(31,\cdot)$	221067.bjv	4620	yes	$1$	$1$	$e\left(\frac{2237}{4620}\right)$	$e\left(\frac{2237}{2310}\right)$	$e\left(\frac{54}{385}\right)$	$e\left(\frac{697}{1540}\right)$	$e\left(\frac{577}{924}\right)$	$e\left(\frac{893}{1155}\right)$	$e\left(\frac{1082}{1155}\right)$	$e\left(\frac{149}{660}\right)$	$e\left(\frac{211}{4620}\right)$	$e\left(\frac{251}{2310}\right)$
$\chi_{221067}(32,\cdot)$	221067.bgu	924	yes	$-1$	$1$	$e\left(\frac{361}{924}\right)$	$e\left(\frac{361}{462}\right)$	$e\left(\frac{61}{77}\right)$	$e\left(\frac{53}{308}\right)$	$e\left(\frac{169}{924}\right)$	$e\left(\frac{109}{231}\right)$	$e\left(\frac{130}{231}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{659}{924}\right)$	$e\left(\frac{265}{462}\right)$
$\chi_{221067}(34,\cdot)$	221067.bdk	462	yes	$-1$	$1$	$e\left(\frac{419}{462}\right)$	$e\left(\frac{188}{231}\right)$	$e\left(\frac{349}{462}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{409}{462}\right)$	$e\left(\frac{145}{231}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{263}{462}\right)$
$\chi_{221067}(37,\cdot)$	221067.bkc	4620	no	$-1$	$1$	$e\left(\frac{719}{4620}\right)$	$e\left(\frac{719}{2310}\right)$	$e\left(\frac{643}{2310}\right)$	$e\left(\frac{719}{1540}\right)$	$e\left(\frac{401}{924}\right)$	$e\left(\frac{379}{770}\right)$	$e\left(\frac{719}{1155}\right)$	$e\left(\frac{193}{660}\right)$	$e\left(\frac{1487}{4620}\right)$	$e\left(\frac{227}{385}\right)$
$\chi_{221067}(38,\cdot)$	221067.bhp	2310	yes	$1$	$1$	$e\left(\frac{239}{385}\right)$	$e\left(\frac{93}{385}\right)$	$e\left(\frac{38}{1155}\right)$	$e\left(\frac{332}{385}\right)$	$e\left(\frac{151}{231}\right)$	$e\left(\frac{899}{2310}\right)$	$e\left(\frac{186}{385}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{496}{1155}\right)$	$e\left(\frac{317}{1155}\right)$
$\chi_{221067}(40,\cdot)$	221067.bam	420	no	$-1$	$1$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{127}{420}\right)$	$e\left(\frac{97}{210}\right)$
$\chi_{221067}(41,\cdot)$	221067.bev	660	yes	$1$	$1$	$e\left(\frac{193}{660}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{37}{165}\right)$
$\chi_{221067}(43,\cdot)$	221067.bgo	924	no	$1$	$1$	$e\left(\frac{331}{924}\right)$	$e\left(\frac{331}{462}\right)$	$e\left(\frac{169}{462}\right)$	$e\left(\frac{23}{308}\right)$	$e\left(\frac{223}{308}\right)$	$e\left(\frac{149}{231}\right)$	$e\left(\frac{100}{231}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{13}{308}\right)$	$e\left(\frac{19}{231}\right)$
$\chi_{221067}(46,\cdot)$	221067.bey	660	no	$1$	$1$	$e\left(\frac{481}{660}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{29}{660}\right)$	$e\left(\frac{433}{660}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{221067}(47,\cdot)$	221067.bko	4620	yes	$-1$	$1$	$e\left(\frac{541}{4620}\right)$	$e\left(\frac{541}{2310}\right)$	$e\left(\frac{439}{770}\right)$	$e\left(\frac{541}{1540}\right)$	$e\left(\frac{635}{924}\right)$	$e\left(\frac{1024}{1155}\right)$	$e\left(\frac{541}{1155}\right)$	$e\left(\frac{157}{660}\right)$	$e\left(\frac{2993}{4620}\right)$	$e\left(\frac{929}{1155}\right)$
$\chi_{221067}(50,\cdot)$	221067.bkj	4620	no	$-1$	$1$	$e\left(\frac{3673}{4620}\right)$	$e\left(\frac{1363}{2310}\right)$	$e\left(\frac{878}{1155}\right)$	$e\left(\frac{593}{1540}\right)$	$e\left(\frac{171}{308}\right)$	$e\left(\frac{467}{1155}\right)$	$e\left(\frac{208}{1155}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{1373}{1540}\right)$	$e\left(\frac{809}{2310}\right)$
$\chi_{221067}(52,\cdot)$	221067.bjm	2310	yes	$1$	$1$	$e\left(\frac{501}{770}\right)$	$e\left(\frac{116}{385}\right)$	$e\left(\frac{397}{2310}\right)$	$e\left(\frac{733}{770}\right)$	$e\left(\frac{190}{231}\right)$	$e\left(\frac{304}{1155}\right)$	$e\left(\frac{232}{385}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{1132}{1155}\right)$	$e\left(\frac{1093}{2310}\right)$
$\chi_{221067}(53,\cdot)$	221067.bhw	2310	no	$-1$	$1$	$e\left(\frac{191}{2310}\right)$	$e\left(\frac{191}{1155}\right)$	$e\left(\frac{989}{2310}\right)$	$e\left(\frac{191}{770}\right)$	$e\left(\frac{118}{231}\right)$	$e\left(\frac{181}{385}\right)$	$e\left(\frac{382}{1155}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{1024}{1155}\right)$	$e\left(\frac{457}{770}\right)$
$\chi_{221067}(59,\cdot)$	221067.zz	330	no	$1$	$1$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{73}{165}\right)$
$\chi_{221067}(61,\cdot)$	221067.bjt	4620	yes	$-1$	$1$	$e\left(\frac{2323}{4620}\right)$	$e\left(\frac{13}{2310}\right)$	$e\left(\frac{291}{385}\right)$	$e\left(\frac{783}{1540}\right)$	$e\left(\frac{239}{924}\right)$	$e\left(\frac{299}{2310}\right)$	$e\left(\frac{13}{1155}\right)$	$e\left(\frac{91}{660}\right)$	$e\left(\frac{89}{4620}\right)$	$e\left(\frac{1759}{2310}\right)$
$\chi_{221067}(62,\cdot)$	221067.bfl	770	no	$-1$	$1$	$e\left(\frac{279}{770}\right)$	$e\left(\frac{279}{385}\right)$	$e\left(\frac{38}{385}\right)$	$e\left(\frac{67}{770}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{257}{385}\right)$	$e\left(\frac{173}{385}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{607}{770}\right)$	$e\left(\frac{317}{385}\right)$
$\chi_{221067}(64,\cdot)$	221067.bfk	770	no	$1$	$1$	$e\left(\frac{207}{770}\right)$	$e\left(\frac{207}{385}\right)$	$e\left(\frac{289}{385}\right)$	$e\left(\frac{621}{770}\right)$	$e\left(\frac{3}{154}\right)$	$e\left(\frac{141}{385}\right)$	$e\left(\frac{29}{385}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{351}{770}\right)$	$e\left(\frac{111}{385}\right)$
$\chi_{221067}(65,\cdot)$	221067.bca	462	yes	$1$	$1$	$e\left(\frac{197}{231}\right)$	$e\left(\frac{163}{231}\right)$	$e\left(\frac{101}{154}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{235}{462}\right)$	$e\left(\frac{337}{462}\right)$	$e\left(\frac{95}{231}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{263}{462}\right)$	$e\left(\frac{167}{462}\right)$

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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	$221067$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{4620}\)
Order	$110880$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{221067}(1,\cdot)\)	221067.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{221067}(2,\cdot)\)	221067.bju	4620	yes	\(-1\)	\(1\)	\(e\left(\frac{4057}{4620}\right)\)	\(e\left(\frac{1747}{2310}\right)\)	\(e\left(\frac{369}{385}\right)\)	\(e\left(\frac{977}{1540}\right)\)	\(e\left(\frac{773}{924}\right)\)	\(e\left(\frac{1033}{1155}\right)\)	\(e\left(\frac{592}{1155}\right)\)	\(e\left(\frac{19}{660}\right)\)	\(e\left(\frac{3431}{4620}\right)\)	\(e\left(\frac{1651}{2310}\right)\)
\(\chi_{221067}(4,\cdot)\)	221067.bhu	2310	yes	\(1\)	\(1\)	\(e\left(\frac{1747}{2310}\right)\)	\(e\left(\frac{592}{1155}\right)\)	\(e\left(\frac{353}{385}\right)\)	\(e\left(\frac{207}{770}\right)\)	\(e\left(\frac{311}{462}\right)\)	\(e\left(\frac{911}{1155}\right)\)	\(e\left(\frac{29}{1155}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{1121}{2310}\right)\)	\(e\left(\frac{496}{1155}\right)\)
\(\chi_{221067}(5,\cdot)\)	221067.bhp	2310	yes	\(1\)	\(1\)	\(e\left(\frac{369}{385}\right)\)	\(e\left(\frac{353}{385}\right)\)	\(e\left(\frac{463}{1155}\right)\)	\(e\left(\frac{337}{385}\right)\)	\(e\left(\frac{83}{231}\right)\)	\(e\left(\frac{589}{2310}\right)\)	\(e\left(\frac{321}{385}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{86}{1155}\right)\)	\(e\left(\frac{367}{1155}\right)\)
\(\chi_{221067}(8,\cdot)\)	221067.bhc	1540	no	\(-1\)	\(1\)	\(e\left(\frac{977}{1540}\right)\)	\(e\left(\frac{207}{770}\right)\)	\(e\left(\frac{337}{385}\right)\)	\(e\left(\frac{1391}{1540}\right)\)	\(e\left(\frac{157}{308}\right)\)	\(e\left(\frac{263}{385}\right)\)	\(e\left(\frac{207}{385}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{351}{1540}\right)\)	\(e\left(\frac{111}{770}\right)\)
\(\chi_{221067}(10,\cdot)\)	221067.bge	924	no	\(-1\)	\(1\)	\(e\left(\frac{773}{924}\right)\)	\(e\left(\frac{311}{462}\right)\)	\(e\left(\frac{83}{231}\right)\)	\(e\left(\frac{157}{308}\right)\)	\(e\left(\frac{181}{924}\right)\)	\(e\left(\frac{23}{154}\right)\)	\(e\left(\frac{80}{231}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{755}{924}\right)\)	\(e\left(\frac{5}{154}\right)\)
\(\chi_{221067}(13,\cdot)\)	221067.biu	2310	yes	\(1\)	\(1\)	\(e\left(\frac{1033}{1155}\right)\)	\(e\left(\frac{911}{1155}\right)\)	\(e\left(\frac{589}{2310}\right)\)	\(e\left(\frac{263}{385}\right)\)	\(e\left(\frac{23}{154}\right)\)	\(e\left(\frac{548}{1155}\right)\)	\(e\left(\frac{667}{1155}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{381}{770}\right)\)	\(e\left(\frac{101}{2310}\right)\)
\(\chi_{221067}(16,\cdot)\)	221067.bgz	1155	yes	\(1\)	\(1\)	\(e\left(\frac{592}{1155}\right)\)	\(e\left(\frac{29}{1155}\right)\)	\(e\left(\frac{321}{385}\right)\)	\(e\left(\frac{207}{385}\right)\)	\(e\left(\frac{80}{231}\right)\)	\(e\left(\frac{667}{1155}\right)\)	\(e\left(\frac{58}{1155}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{1121}{1155}\right)\)	\(e\left(\frac{992}{1155}\right)\)
\(\chi_{221067}(17,\cdot)\)	221067.ber	660	no	\(1\)	\(1\)	\(e\left(\frac{19}{660}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{161}{660}\right)\)	\(e\left(\frac{367}{660}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{221067}(19,\cdot)\)	221067.bkk	4620	no	\(-1\)	\(1\)	\(e\left(\frac{3431}{4620}\right)\)	\(e\left(\frac{1121}{2310}\right)\)	\(e\left(\frac{86}{1155}\right)\)	\(e\left(\frac{351}{1540}\right)\)	\(e\left(\frac{755}{924}\right)\)	\(e\left(\frac{381}{770}\right)\)	\(e\left(\frac{1121}{1155}\right)\)	\(e\left(\frac{367}{660}\right)\)	\(e\left(\frac{3173}{4620}\right)\)	\(e\left(\frac{431}{770}\right)\)
\(\chi_{221067}(20,\cdot)\)	221067.bie	2310	yes	\(1\)	\(1\)	\(e\left(\frac{1651}{2310}\right)\)	\(e\left(\frac{496}{1155}\right)\)	\(e\left(\frac{367}{1155}\right)\)	\(e\left(\frac{111}{770}\right)\)	\(e\left(\frac{5}{154}\right)\)	\(e\left(\frac{101}{2310}\right)\)	\(e\left(\frac{992}{1155}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{431}{770}\right)\)	\(e\left(\frac{863}{1155}\right)\)
\(\chi_{221067}(23,\cdot)\)	221067.bbt	462	yes	\(-1\)	\(1\)	\(e\left(\frac{131}{154}\right)\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{295}{462}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{113}{231}\right)\)	\(e\left(\frac{184}{231}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{211}{231}\right)\)	\(e\left(\frac{157}{462}\right)\)
\(\chi_{221067}(25,\cdot)\)	221067.bgy	1155	yes	\(1\)	\(1\)	\(e\left(\frac{353}{385}\right)\)	\(e\left(\frac{321}{385}\right)\)	\(e\left(\frac{926}{1155}\right)\)	\(e\left(\frac{289}{385}\right)\)	\(e\left(\frac{166}{231}\right)\)	\(e\left(\frac{589}{1155}\right)\)	\(e\left(\frac{257}{385}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{172}{1155}\right)\)	\(e\left(\frac{734}{1155}\right)\)
\(\chi_{221067}(26,\cdot)\)	221067.bjx	4620	no	\(-1\)	\(1\)	\(e\left(\frac{3569}{4620}\right)\)	\(e\left(\frac{1259}{2310}\right)\)	\(e\left(\frac{493}{2310}\right)\)	\(e\left(\frac{489}{1540}\right)\)	\(e\left(\frac{911}{924}\right)\)	\(e\left(\frac{142}{385}\right)\)	\(e\left(\frac{104}{1155}\right)\)	\(e\left(\frac{13}{660}\right)\)	\(e\left(\frac{1097}{4620}\right)\)	\(e\left(\frac{292}{385}\right)\)
\(\chi_{221067}(31,\cdot)\)	221067.bjv	4620	yes	\(1\)	\(1\)	\(e\left(\frac{2237}{4620}\right)\)	\(e\left(\frac{2237}{2310}\right)\)	\(e\left(\frac{54}{385}\right)\)	\(e\left(\frac{697}{1540}\right)\)	\(e\left(\frac{577}{924}\right)\)	\(e\left(\frac{893}{1155}\right)\)	\(e\left(\frac{1082}{1155}\right)\)	\(e\left(\frac{149}{660}\right)\)	\(e\left(\frac{211}{4620}\right)\)	\(e\left(\frac{251}{2310}\right)\)
\(\chi_{221067}(32,\cdot)\)	221067.bgu	924	yes	\(-1\)	\(1\)	\(e\left(\frac{361}{924}\right)\)	\(e\left(\frac{361}{462}\right)\)	\(e\left(\frac{61}{77}\right)\)	\(e\left(\frac{53}{308}\right)\)	\(e\left(\frac{169}{924}\right)\)	\(e\left(\frac{109}{231}\right)\)	\(e\left(\frac{130}{231}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{659}{924}\right)\)	\(e\left(\frac{265}{462}\right)\)
\(\chi_{221067}(34,\cdot)\)	221067.bdk	462	yes	\(-1\)	\(1\)	\(e\left(\frac{419}{462}\right)\)	\(e\left(\frac{188}{231}\right)\)	\(e\left(\frac{349}{462}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{409}{462}\right)\)	\(e\left(\frac{145}{231}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{263}{462}\right)\)
\(\chi_{221067}(37,\cdot)\)	221067.bkc	4620	no	\(-1\)	\(1\)	\(e\left(\frac{719}{4620}\right)\)	\(e\left(\frac{719}{2310}\right)\)	\(e\left(\frac{643}{2310}\right)\)	\(e\left(\frac{719}{1540}\right)\)	\(e\left(\frac{401}{924}\right)\)	\(e\left(\frac{379}{770}\right)\)	\(e\left(\frac{719}{1155}\right)\)	\(e\left(\frac{193}{660}\right)\)	\(e\left(\frac{1487}{4620}\right)\)	\(e\left(\frac{227}{385}\right)\)
\(\chi_{221067}(38,\cdot)\)	221067.bhp	2310	yes	\(1\)	\(1\)	\(e\left(\frac{239}{385}\right)\)	\(e\left(\frac{93}{385}\right)\)	\(e\left(\frac{38}{1155}\right)\)	\(e\left(\frac{332}{385}\right)\)	\(e\left(\frac{151}{231}\right)\)	\(e\left(\frac{899}{2310}\right)\)	\(e\left(\frac{186}{385}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{496}{1155}\right)\)	\(e\left(\frac{317}{1155}\right)\)
\(\chi_{221067}(40,\cdot)\)	221067.bam	420	no	\(-1\)	\(1\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{127}{420}\right)\)	\(e\left(\frac{97}{210}\right)\)
\(\chi_{221067}(41,\cdot)\)	221067.bev	660	yes	\(1\)	\(1\)	\(e\left(\frac{193}{660}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{37}{165}\right)\)
\(\chi_{221067}(43,\cdot)\)	221067.bgo	924	no	\(1\)	\(1\)	\(e\left(\frac{331}{924}\right)\)	\(e\left(\frac{331}{462}\right)\)	\(e\left(\frac{169}{462}\right)\)	\(e\left(\frac{23}{308}\right)\)	\(e\left(\frac{223}{308}\right)\)	\(e\left(\frac{149}{231}\right)\)	\(e\left(\frac{100}{231}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{13}{308}\right)\)	\(e\left(\frac{19}{231}\right)\)
\(\chi_{221067}(46,\cdot)\)	221067.bey	660	no	\(1\)	\(1\)	\(e\left(\frac{481}{660}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{29}{660}\right)\)	\(e\left(\frac{433}{660}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{221067}(47,\cdot)\)	221067.bko	4620	yes	\(-1\)	\(1\)	\(e\left(\frac{541}{4620}\right)\)	\(e\left(\frac{541}{2310}\right)\)	\(e\left(\frac{439}{770}\right)\)	\(e\left(\frac{541}{1540}\right)\)	\(e\left(\frac{635}{924}\right)\)	\(e\left(\frac{1024}{1155}\right)\)	\(e\left(\frac{541}{1155}\right)\)	\(e\left(\frac{157}{660}\right)\)	\(e\left(\frac{2993}{4620}\right)\)	\(e\left(\frac{929}{1155}\right)\)
\(\chi_{221067}(50,\cdot)\)	221067.bkj	4620	no	\(-1\)	\(1\)	\(e\left(\frac{3673}{4620}\right)\)	\(e\left(\frac{1363}{2310}\right)\)	\(e\left(\frac{878}{1155}\right)\)	\(e\left(\frac{593}{1540}\right)\)	\(e\left(\frac{171}{308}\right)\)	\(e\left(\frac{467}{1155}\right)\)	\(e\left(\frac{208}{1155}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{1373}{1540}\right)\)	\(e\left(\frac{809}{2310}\right)\)
\(\chi_{221067}(52,\cdot)\)	221067.bjm	2310	yes	\(1\)	\(1\)	\(e\left(\frac{501}{770}\right)\)	\(e\left(\frac{116}{385}\right)\)	\(e\left(\frac{397}{2310}\right)\)	\(e\left(\frac{733}{770}\right)\)	\(e\left(\frac{190}{231}\right)\)	\(e\left(\frac{304}{1155}\right)\)	\(e\left(\frac{232}{385}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{1132}{1155}\right)\)	\(e\left(\frac{1093}{2310}\right)\)
\(\chi_{221067}(53,\cdot)\)	221067.bhw	2310	no	\(-1\)	\(1\)	\(e\left(\frac{191}{2310}\right)\)	\(e\left(\frac{191}{1155}\right)\)	\(e\left(\frac{989}{2310}\right)\)	\(e\left(\frac{191}{770}\right)\)	\(e\left(\frac{118}{231}\right)\)	\(e\left(\frac{181}{385}\right)\)	\(e\left(\frac{382}{1155}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{1024}{1155}\right)\)	\(e\left(\frac{457}{770}\right)\)
\(\chi_{221067}(59,\cdot)\)	221067.zz	330	no	\(1\)	\(1\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{73}{165}\right)\)
\(\chi_{221067}(61,\cdot)\)	221067.bjt	4620	yes	\(-1\)	\(1\)	\(e\left(\frac{2323}{4620}\right)\)	\(e\left(\frac{13}{2310}\right)\)	\(e\left(\frac{291}{385}\right)\)	\(e\left(\frac{783}{1540}\right)\)	\(e\left(\frac{239}{924}\right)\)	\(e\left(\frac{299}{2310}\right)\)	\(e\left(\frac{13}{1155}\right)\)	\(e\left(\frac{91}{660}\right)\)	\(e\left(\frac{89}{4620}\right)\)	\(e\left(\frac{1759}{2310}\right)\)
\(\chi_{221067}(62,\cdot)\)	221067.bfl	770	no	\(-1\)	\(1\)	\(e\left(\frac{279}{770}\right)\)	\(e\left(\frac{279}{385}\right)\)	\(e\left(\frac{38}{385}\right)\)	\(e\left(\frac{67}{770}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{257}{385}\right)\)	\(e\left(\frac{173}{385}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{607}{770}\right)\)	\(e\left(\frac{317}{385}\right)\)
\(\chi_{221067}(64,\cdot)\)	221067.bfk	770	no	\(1\)	\(1\)	\(e\left(\frac{207}{770}\right)\)	\(e\left(\frac{207}{385}\right)\)	\(e\left(\frac{289}{385}\right)\)	\(e\left(\frac{621}{770}\right)\)	\(e\left(\frac{3}{154}\right)\)	\(e\left(\frac{141}{385}\right)\)	\(e\left(\frac{29}{385}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{351}{770}\right)\)	\(e\left(\frac{111}{385}\right)\)
\(\chi_{221067}(65,\cdot)\)	221067.bca	462	yes	\(1\)	\(1\)	\(e\left(\frac{197}{231}\right)\)	\(e\left(\frac{163}{231}\right)\)	\(e\left(\frac{101}{154}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{235}{462}\right)\)	\(e\left(\frac{337}{462}\right)\)	\(e\left(\frac{95}{231}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{263}{462}\right)\)	\(e\left(\frac{167}{462}\right)\)

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L-functions

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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.