LMFDB - Group of Dirichlet characters of modulus 101478

Show commands: PariGP / SageMath

sage: H = DirichletGroup(101478)

pari: g = idealstar(,101478,2)

Character group

sage: G.order() pari: g.no
Order	=	31200
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{3900}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{101478}(33827,\cdot)$, $\chi_{101478}(85867,\cdot)$, $\chi_{101478}(32527,\cdot)$

First 32 of 31200 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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{101478}(1,\cdot)$	101478.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{101478}(5,\cdot)$	101478.ie	1300	no	$1$	$1$	$e\left(\frac{61}{1300}\right)$	$e\left(\frac{531}{1300}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{118}{325}\right)$	$e\left(\frac{47}{1300}\right)$	$e\left(\frac{223}{325}\right)$	$e\left(\frac{61}{650}\right)$	$e\left(\frac{7}{130}\right)$	$e\left(\frac{37}{260}\right)$	$e\left(\frac{148}{325}\right)$
$\chi_{101478}(7,\cdot)$	101478.jd	3900	no	$1$	$1$	$e\left(\frac{531}{1300}\right)$	$e\left(\frac{607}{975}\right)$	$e\left(\frac{19}{780}\right)$	$e\left(\frac{1043}{1950}\right)$	$e\left(\frac{961}{3900}\right)$	$e\left(\frac{224}{975}\right)$	$e\left(\frac{531}{650}\right)$	$e\left(\frac{251}{390}\right)$	$e\left(\frac{3}{65}\right)$	$e\left(\frac{121}{3900}\right)$
$\chi_{101478}(11,\cdot)$	101478.hs	780	no	$1$	$1$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{19}{780}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{127}{195}\right)$	$e\left(\frac{223}{780}\right)$	$e\left(\frac{137}{195}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{37}{195}\right)$
$\chi_{101478}(17,\cdot)$	101478.io	1950	no	$-1$	$1$	$e\left(\frac{118}{325}\right)$	$e\left(\frac{1043}{1950}\right)$	$e\left(\frac{127}{195}\right)$	$e\left(\frac{1541}{1950}\right)$	$e\left(\frac{1691}{1950}\right)$	$e\left(\frac{1}{1950}\right)$	$e\left(\frac{236}{325}\right)$	$e\left(\frac{317}{390}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{1751}{1950}\right)$
$\chi_{101478}(19,\cdot)$	101478.ix	3900	no	$-1$	$1$	$e\left(\frac{47}{1300}\right)$	$e\left(\frac{961}{3900}\right)$	$e\left(\frac{223}{780}\right)$	$e\left(\frac{1691}{1950}\right)$	$e\left(\frac{1057}{3900}\right)$	$e\left(\frac{301}{1950}\right)$	$e\left(\frac{47}{650}\right)$	$e\left(\frac{31}{195}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{551}{1950}\right)$
$\chi_{101478}(23,\cdot)$	101478.ip	1950	no	$-1$	$1$	$e\left(\frac{223}{325}\right)$	$e\left(\frac{224}{975}\right)$	$e\left(\frac{137}{195}\right)$	$e\left(\frac{1}{1950}\right)$	$e\left(\frac{301}{1950}\right)$	$e\left(\frac{1211}{1950}\right)$	$e\left(\frac{121}{325}\right)$	$e\left(\frac{127}{390}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{893}{975}\right)$
$\chi_{101478}(25,\cdot)$	101478.hj	650	no	$1$	$1$	$e\left(\frac{61}{650}\right)$	$e\left(\frac{531}{650}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{236}{325}\right)$	$e\left(\frac{47}{650}\right)$	$e\left(\frac{121}{325}\right)$	$e\left(\frac{61}{325}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{296}{325}\right)$
$\chi_{101478}(29,\cdot)$	101478.hd	390	no	$-1$	$1$	$e\left(\frac{7}{130}\right)$	$e\left(\frac{251}{390}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{317}{390}\right)$	$e\left(\frac{31}{195}\right)$	$e\left(\frac{127}{390}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{136}{195}\right)$
$\chi_{101478}(31,\cdot)$	101478.gj	260	no	$1$	$1$	$e\left(\frac{37}{260}\right)$	$e\left(\frac{3}{65}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{49}{260}\right)$
$\chi_{101478}(35,\cdot)$	101478.iu	3900	no	$1$	$1$	$e\left(\frac{148}{325}\right)$	$e\left(\frac{121}{3900}\right)$	$e\left(\frac{37}{195}\right)$	$e\left(\frac{1751}{1950}\right)$	$e\left(\frac{551}{1950}\right)$	$e\left(\frac{893}{975}\right)$	$e\left(\frac{296}{325}\right)$	$e\left(\frac{136}{195}\right)$	$e\left(\frac{49}{260}\right)$	$e\left(\frac{1897}{3900}\right)$
$\chi_{101478}(37,\cdot)$	101478.ja	3900	no	$1$	$1$	$e\left(\frac{967}{1300}\right)$	$e\left(\frac{1723}{1950}\right)$	$e\left(\frac{323}{780}\right)$	$e\left(\frac{1351}{1950}\right)$	$e\left(\frac{3077}{3900}\right)$	$e\left(\frac{493}{975}\right)$	$e\left(\frac{317}{650}\right)$	$e\left(\frac{367}{390}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{2447}{3900}\right)$
$\chi_{101478}(41,\cdot)$	101478.hw	780	no	$-1$	$1$	$e\left(\frac{27}{260}\right)$	$e\left(\frac{173}{390}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{178}{195}\right)$	$e\left(\frac{7}{780}\right)$	$e\left(\frac{361}{390}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{427}{780}\right)$
$\chi_{101478}(43,\cdot)$	101478.ha	390	no	$1$	$1$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{23}{195}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{71}{195}\right)$	$e\left(\frac{37}{390}\right)$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{307}{390}\right)$
$\chi_{101478}(47,\cdot)$	101478.ie	1300	no	$1$	$1$	$e\left(\frac{1171}{1300}\right)$	$e\left(\frac{241}{1300}\right)$	$e\left(\frac{233}{260}\right)$	$e\left(\frac{198}{325}\right)$	$e\left(\frac{817}{1300}\right)$	$e\left(\frac{253}{325}\right)$	$e\left(\frac{521}{650}\right)$	$e\left(\frac{47}{130}\right)$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{28}{325}\right)$
$\chi_{101478}(49,\cdot)$	101478.ir	1950	no	$1$	$1$	$e\left(\frac{531}{650}\right)$	$e\left(\frac{239}{975}\right)$	$e\left(\frac{19}{390}\right)$	$e\left(\frac{68}{975}\right)$	$e\left(\frac{961}{1950}\right)$	$e\left(\frac{448}{975}\right)$	$e\left(\frac{206}{325}\right)$	$e\left(\frac{56}{195}\right)$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{121}{1950}\right)$
$\chi_{101478}(53,\cdot)$	101478.dg	50	no	$-1$	$1$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{14}{25}\right)$
$\chi_{101478}(55,\cdot)$	101478.ia	975	no	$1$	$1$	$e\left(\frac{69}{325}\right)$	$e\left(\frac{422}{975}\right)$	$e\left(\frac{131}{195}\right)$	$e\left(\frac{14}{975}\right)$	$e\left(\frac{314}{975}\right)$	$e\left(\frac{379}{975}\right)$	$e\left(\frac{138}{325}\right)$	$e\left(\frac{23}{195}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{629}{975}\right)$
$\chi_{101478}(59,\cdot)$	101478.jc	3900	no	$1$	$1$	$e\left(\frac{207}{1300}\right)$	$e\left(\frac{1591}{3900}\right)$	$e\left(\frac{523}{780}\right)$	$e\left(\frac{823}{975}\right)$	$e\left(\frac{1267}{3900}\right)$	$e\left(\frac{203}{975}\right)$	$e\left(\frac{207}{650}\right)$	$e\left(\frac{197}{390}\right)$	$e\left(\frac{19}{260}\right)$	$e\left(\frac{553}{975}\right)$
$\chi_{101478}(61,\cdot)$	101478.in	1950	no	$1$	$1$	$e\left(\frac{41}{325}\right)$	$e\left(\frac{1241}{1950}\right)$	$e\left(\frac{124}{195}\right)$	$e\left(\frac{46}{975}\right)$	$e\left(\frac{196}{975}\right)$	$e\left(\frac{131}{975}\right)$	$e\left(\frac{82}{325}\right)$	$e\left(\frac{187}{195}\right)$	$e\left(\frac{119}{130}\right)$	$e\left(\frac{1487}{1950}\right)$
$\chi_{101478}(67,\cdot)$	101478.jd	3900	no	$1$	$1$	$e\left(\frac{321}{1300}\right)$	$e\left(\frac{512}{975}\right)$	$e\left(\frac{389}{780}\right)$	$e\left(\frac{1813}{1950}\right)$	$e\left(\frac{2351}{3900}\right)$	$e\left(\frac{409}{975}\right)$	$e\left(\frac{321}{650}\right)$	$e\left(\frac{151}{390}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{3011}{3900}\right)$
$\chi_{101478}(71,\cdot)$	101478.dw	60	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{47}{60}\right)$
$\chi_{101478}(73,\cdot)$	101478.ig	1300	no	$1$	$1$	$e\left(\frac{579}{1300}\right)$	$e\left(\frac{321}{325}\right)$	$e\left(\frac{97}{260}\right)$	$e\left(\frac{29}{650}\right)$	$e\left(\frac{883}{1300}\right)$	$e\left(\frac{172}{325}\right)$	$e\left(\frac{579}{650}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{563}{1300}\right)$
$\chi_{101478}(77,\cdot)$	101478.ic	1300	no	$1$	$1$	$e\left(\frac{373}{650}\right)$	$e\left(\frac{841}{1300}\right)$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{121}{650}\right)$	$e\left(\frac{173}{325}\right)$	$e\left(\frac{303}{325}\right)$	$e\left(\frac{48}{325}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{87}{260}\right)$	$e\left(\frac{287}{1300}\right)$
$\chi_{101478}(79,\cdot)$	101478.ib	1300	no	$-1$	$1$	$e\left(\frac{159}{650}\right)$	$e\left(\frac{653}{1300}\right)$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{109}{325}\right)$	$e\left(\frac{293}{650}\right)$	$e\left(\frac{423}{650}\right)$	$e\left(\frac{159}{325}\right)$	$e\left(\frac{61}{130}\right)$	$e\left(\frac{211}{260}\right)$	$e\left(\frac{971}{1300}\right)$
$\chi_{101478}(83,\cdot)$	101478.ge	260	no	$-1$	$1$	$e\left(\frac{107}{260}\right)$	$e\left(\frac{121}{130}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{189}{260}\right)$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{89}{260}\right)$
$\chi_{101478}(85,\cdot)$	101478.gv	300	no	$-1$	$1$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{271}{300}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{53}{150}\right)$
$\chi_{101478}(89,\cdot)$	101478.jb	3900	no	$1$	$1$	$e\left(\frac{639}{1300}\right)$	$e\left(\frac{2057}{3900}\right)$	$e\left(\frac{371}{780}\right)$	$e\left(\frac{746}{975}\right)$	$e\left(\frac{2159}{3900}\right)$	$e\left(\frac{556}{975}\right)$	$e\left(\frac{639}{650}\right)$	$e\left(\frac{139}{390}\right)$	$e\left(\frac{53}{260}\right)$	$e\left(\frac{37}{1950}\right)$
$\chi_{101478}(95,\cdot)$	101478.io	1950	no	$-1$	$1$	$e\left(\frac{27}{325}\right)$	$e\left(\frac{1277}{1950}\right)$	$e\left(\frac{88}{195}\right)$	$e\left(\frac{449}{1950}\right)$	$e\left(\frac{599}{1950}\right)$	$e\left(\frac{1639}{1950}\right)$	$e\left(\frac{54}{325}\right)$	$e\left(\frac{83}{390}\right)$	$e\left(\frac{53}{130}\right)$	$e\left(\frac{1439}{1950}\right)$
$\chi_{101478}(97,\cdot)$	101478.jd	3900	no	$1$	$1$	$e\left(\frac{913}{1300}\right)$	$e\left(\frac{136}{975}\right)$	$e\left(\frac{277}{780}\right)$	$e\left(\frac{1289}{1950}\right)$	$e\left(\frac{2803}{3900}\right)$	$e\left(\frac{2}{975}\right)$	$e\left(\frac{263}{650}\right)$	$e\left(\frac{293}{390}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{3283}{3900}\right)$
$\chi_{101478}(101,\cdot)$	101478.go	300	no	$1$	$1$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{143}{300}\right)$
$\chi_{101478}(103,\cdot)$	101478.il	1300	no	$-1$	$1$	$e\left(\frac{103}{325}\right)$	$e\left(\frac{1077}{1300}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{131}{325}\right)$	$e\left(\frac{106}{325}\right)$	$e\left(\frac{407}{650}\right)$	$e\left(\frac{206}{325}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{219}{260}\right)$	$e\left(\frac{189}{1300}\right)$

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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	$101478$
Structure	\(C_{2}\times C_{4}\times C_{3900}\)
Order	$31200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{101478}(1,\cdot)\)	101478.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{101478}(5,\cdot)\)	101478.ie	1300	no	\(1\)	\(1\)	\(e\left(\frac{61}{1300}\right)\)	\(e\left(\frac{531}{1300}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{118}{325}\right)\)	\(e\left(\frac{47}{1300}\right)\)	\(e\left(\frac{223}{325}\right)\)	\(e\left(\frac{61}{650}\right)\)	\(e\left(\frac{7}{130}\right)\)	\(e\left(\frac{37}{260}\right)\)	\(e\left(\frac{148}{325}\right)\)
\(\chi_{101478}(7,\cdot)\)	101478.jd	3900	no	\(1\)	\(1\)	\(e\left(\frac{531}{1300}\right)\)	\(e\left(\frac{607}{975}\right)\)	\(e\left(\frac{19}{780}\right)\)	\(e\left(\frac{1043}{1950}\right)\)	\(e\left(\frac{961}{3900}\right)\)	\(e\left(\frac{224}{975}\right)\)	\(e\left(\frac{531}{650}\right)\)	\(e\left(\frac{251}{390}\right)\)	\(e\left(\frac{3}{65}\right)\)	\(e\left(\frac{121}{3900}\right)\)
\(\chi_{101478}(11,\cdot)\)	101478.hs	780	no	\(1\)	\(1\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{19}{780}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{127}{195}\right)\)	\(e\left(\frac{223}{780}\right)\)	\(e\left(\frac{137}{195}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{37}{195}\right)\)
\(\chi_{101478}(17,\cdot)\)	101478.io	1950	no	\(-1\)	\(1\)	\(e\left(\frac{118}{325}\right)\)	\(e\left(\frac{1043}{1950}\right)\)	\(e\left(\frac{127}{195}\right)\)	\(e\left(\frac{1541}{1950}\right)\)	\(e\left(\frac{1691}{1950}\right)\)	\(e\left(\frac{1}{1950}\right)\)	\(e\left(\frac{236}{325}\right)\)	\(e\left(\frac{317}{390}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{1751}{1950}\right)\)
\(\chi_{101478}(19,\cdot)\)	101478.ix	3900	no	\(-1\)	\(1\)	\(e\left(\frac{47}{1300}\right)\)	\(e\left(\frac{961}{3900}\right)\)	\(e\left(\frac{223}{780}\right)\)	\(e\left(\frac{1691}{1950}\right)\)	\(e\left(\frac{1057}{3900}\right)\)	\(e\left(\frac{301}{1950}\right)\)	\(e\left(\frac{47}{650}\right)\)	\(e\left(\frac{31}{195}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{551}{1950}\right)\)
\(\chi_{101478}(23,\cdot)\)	101478.ip	1950	no	\(-1\)	\(1\)	\(e\left(\frac{223}{325}\right)\)	\(e\left(\frac{224}{975}\right)\)	\(e\left(\frac{137}{195}\right)\)	\(e\left(\frac{1}{1950}\right)\)	\(e\left(\frac{301}{1950}\right)\)	\(e\left(\frac{1211}{1950}\right)\)	\(e\left(\frac{121}{325}\right)\)	\(e\left(\frac{127}{390}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{893}{975}\right)\)
\(\chi_{101478}(25,\cdot)\)	101478.hj	650	no	\(1\)	\(1\)	\(e\left(\frac{61}{650}\right)\)	\(e\left(\frac{531}{650}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{236}{325}\right)\)	\(e\left(\frac{47}{650}\right)\)	\(e\left(\frac{121}{325}\right)\)	\(e\left(\frac{61}{325}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{296}{325}\right)\)
\(\chi_{101478}(29,\cdot)\)	101478.hd	390	no	\(-1\)	\(1\)	\(e\left(\frac{7}{130}\right)\)	\(e\left(\frac{251}{390}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{317}{390}\right)\)	\(e\left(\frac{31}{195}\right)\)	\(e\left(\frac{127}{390}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{136}{195}\right)\)
\(\chi_{101478}(31,\cdot)\)	101478.gj	260	no	\(1\)	\(1\)	\(e\left(\frac{37}{260}\right)\)	\(e\left(\frac{3}{65}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{49}{260}\right)\)
\(\chi_{101478}(35,\cdot)\)	101478.iu	3900	no	\(1\)	\(1\)	\(e\left(\frac{148}{325}\right)\)	\(e\left(\frac{121}{3900}\right)\)	\(e\left(\frac{37}{195}\right)\)	\(e\left(\frac{1751}{1950}\right)\)	\(e\left(\frac{551}{1950}\right)\)	\(e\left(\frac{893}{975}\right)\)	\(e\left(\frac{296}{325}\right)\)	\(e\left(\frac{136}{195}\right)\)	\(e\left(\frac{49}{260}\right)\)	\(e\left(\frac{1897}{3900}\right)\)
\(\chi_{101478}(37,\cdot)\)	101478.ja	3900	no	\(1\)	\(1\)	\(e\left(\frac{967}{1300}\right)\)	\(e\left(\frac{1723}{1950}\right)\)	\(e\left(\frac{323}{780}\right)\)	\(e\left(\frac{1351}{1950}\right)\)	\(e\left(\frac{3077}{3900}\right)\)	\(e\left(\frac{493}{975}\right)\)	\(e\left(\frac{317}{650}\right)\)	\(e\left(\frac{367}{390}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{2447}{3900}\right)\)
\(\chi_{101478}(41,\cdot)\)	101478.hw	780	no	\(-1\)	\(1\)	\(e\left(\frac{27}{260}\right)\)	\(e\left(\frac{173}{390}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{178}{195}\right)\)	\(e\left(\frac{7}{780}\right)\)	\(e\left(\frac{361}{390}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{427}{780}\right)\)
\(\chi_{101478}(43,\cdot)\)	101478.ha	390	no	\(1\)	\(1\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{23}{195}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{71}{195}\right)\)	\(e\left(\frac{37}{390}\right)\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{307}{390}\right)\)
\(\chi_{101478}(47,\cdot)\)	101478.ie	1300	no	\(1\)	\(1\)	\(e\left(\frac{1171}{1300}\right)\)	\(e\left(\frac{241}{1300}\right)\)	\(e\left(\frac{233}{260}\right)\)	\(e\left(\frac{198}{325}\right)\)	\(e\left(\frac{817}{1300}\right)\)	\(e\left(\frac{253}{325}\right)\)	\(e\left(\frac{521}{650}\right)\)	\(e\left(\frac{47}{130}\right)\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{28}{325}\right)\)
\(\chi_{101478}(49,\cdot)\)	101478.ir	1950	no	\(1\)	\(1\)	\(e\left(\frac{531}{650}\right)\)	\(e\left(\frac{239}{975}\right)\)	\(e\left(\frac{19}{390}\right)\)	\(e\left(\frac{68}{975}\right)\)	\(e\left(\frac{961}{1950}\right)\)	\(e\left(\frac{448}{975}\right)\)	\(e\left(\frac{206}{325}\right)\)	\(e\left(\frac{56}{195}\right)\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{121}{1950}\right)\)
\(\chi_{101478}(53,\cdot)\)	101478.dg	50	no	\(-1\)	\(1\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{14}{25}\right)\)
\(\chi_{101478}(55,\cdot)\)	101478.ia	975	no	\(1\)	\(1\)	\(e\left(\frac{69}{325}\right)\)	\(e\left(\frac{422}{975}\right)\)	\(e\left(\frac{131}{195}\right)\)	\(e\left(\frac{14}{975}\right)\)	\(e\left(\frac{314}{975}\right)\)	\(e\left(\frac{379}{975}\right)\)	\(e\left(\frac{138}{325}\right)\)	\(e\left(\frac{23}{195}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{629}{975}\right)\)
\(\chi_{101478}(59,\cdot)\)	101478.jc	3900	no	\(1\)	\(1\)	\(e\left(\frac{207}{1300}\right)\)	\(e\left(\frac{1591}{3900}\right)\)	\(e\left(\frac{523}{780}\right)\)	\(e\left(\frac{823}{975}\right)\)	\(e\left(\frac{1267}{3900}\right)\)	\(e\left(\frac{203}{975}\right)\)	\(e\left(\frac{207}{650}\right)\)	\(e\left(\frac{197}{390}\right)\)	\(e\left(\frac{19}{260}\right)\)	\(e\left(\frac{553}{975}\right)\)
\(\chi_{101478}(61,\cdot)\)	101478.in	1950	no	\(1\)	\(1\)	\(e\left(\frac{41}{325}\right)\)	\(e\left(\frac{1241}{1950}\right)\)	\(e\left(\frac{124}{195}\right)\)	\(e\left(\frac{46}{975}\right)\)	\(e\left(\frac{196}{975}\right)\)	\(e\left(\frac{131}{975}\right)\)	\(e\left(\frac{82}{325}\right)\)	\(e\left(\frac{187}{195}\right)\)	\(e\left(\frac{119}{130}\right)\)	\(e\left(\frac{1487}{1950}\right)\)
\(\chi_{101478}(67,\cdot)\)	101478.jd	3900	no	\(1\)	\(1\)	\(e\left(\frac{321}{1300}\right)\)	\(e\left(\frac{512}{975}\right)\)	\(e\left(\frac{389}{780}\right)\)	\(e\left(\frac{1813}{1950}\right)\)	\(e\left(\frac{2351}{3900}\right)\)	\(e\left(\frac{409}{975}\right)\)	\(e\left(\frac{321}{650}\right)\)	\(e\left(\frac{151}{390}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{3011}{3900}\right)\)
\(\chi_{101478}(71,\cdot)\)	101478.dw	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{101478}(73,\cdot)\)	101478.ig	1300	no	\(1\)	\(1\)	\(e\left(\frac{579}{1300}\right)\)	\(e\left(\frac{321}{325}\right)\)	\(e\left(\frac{97}{260}\right)\)	\(e\left(\frac{29}{650}\right)\)	\(e\left(\frac{883}{1300}\right)\)	\(e\left(\frac{172}{325}\right)\)	\(e\left(\frac{579}{650}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{563}{1300}\right)\)
\(\chi_{101478}(77,\cdot)\)	101478.ic	1300	no	\(1\)	\(1\)	\(e\left(\frac{373}{650}\right)\)	\(e\left(\frac{841}{1300}\right)\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{121}{650}\right)\)	\(e\left(\frac{173}{325}\right)\)	\(e\left(\frac{303}{325}\right)\)	\(e\left(\frac{48}{325}\right)\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{87}{260}\right)\)	\(e\left(\frac{287}{1300}\right)\)
\(\chi_{101478}(79,\cdot)\)	101478.ib	1300	no	\(-1\)	\(1\)	\(e\left(\frac{159}{650}\right)\)	\(e\left(\frac{653}{1300}\right)\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{109}{325}\right)\)	\(e\left(\frac{293}{650}\right)\)	\(e\left(\frac{423}{650}\right)\)	\(e\left(\frac{159}{325}\right)\)	\(e\left(\frac{61}{130}\right)\)	\(e\left(\frac{211}{260}\right)\)	\(e\left(\frac{971}{1300}\right)\)
\(\chi_{101478}(83,\cdot)\)	101478.ge	260	no	\(-1\)	\(1\)	\(e\left(\frac{107}{260}\right)\)	\(e\left(\frac{121}{130}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{189}{260}\right)\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{89}{260}\right)\)
\(\chi_{101478}(85,\cdot)\)	101478.gv	300	no	\(-1\)	\(1\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{271}{300}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{53}{150}\right)\)
\(\chi_{101478}(89,\cdot)\)	101478.jb	3900	no	\(1\)	\(1\)	\(e\left(\frac{639}{1300}\right)\)	\(e\left(\frac{2057}{3900}\right)\)	\(e\left(\frac{371}{780}\right)\)	\(e\left(\frac{746}{975}\right)\)	\(e\left(\frac{2159}{3900}\right)\)	\(e\left(\frac{556}{975}\right)\)	\(e\left(\frac{639}{650}\right)\)	\(e\left(\frac{139}{390}\right)\)	\(e\left(\frac{53}{260}\right)\)	\(e\left(\frac{37}{1950}\right)\)
\(\chi_{101478}(95,\cdot)\)	101478.io	1950	no	\(-1\)	\(1\)	\(e\left(\frac{27}{325}\right)\)	\(e\left(\frac{1277}{1950}\right)\)	\(e\left(\frac{88}{195}\right)\)	\(e\left(\frac{449}{1950}\right)\)	\(e\left(\frac{599}{1950}\right)\)	\(e\left(\frac{1639}{1950}\right)\)	\(e\left(\frac{54}{325}\right)\)	\(e\left(\frac{83}{390}\right)\)	\(e\left(\frac{53}{130}\right)\)	\(e\left(\frac{1439}{1950}\right)\)
\(\chi_{101478}(97,\cdot)\)	101478.jd	3900	no	\(1\)	\(1\)	\(e\left(\frac{913}{1300}\right)\)	\(e\left(\frac{136}{975}\right)\)	\(e\left(\frac{277}{780}\right)\)	\(e\left(\frac{1289}{1950}\right)\)	\(e\left(\frac{2803}{3900}\right)\)	\(e\left(\frac{2}{975}\right)\)	\(e\left(\frac{263}{650}\right)\)	\(e\left(\frac{293}{390}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{3283}{3900}\right)\)
\(\chi_{101478}(101,\cdot)\)	101478.go	300	no	\(1\)	\(1\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{143}{300}\right)\)
\(\chi_{101478}(103,\cdot)\)	101478.il	1300	no	\(-1\)	\(1\)	\(e\left(\frac{103}{325}\right)\)	\(e\left(\frac{1077}{1300}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{131}{325}\right)\)	\(e\left(\frac{106}{325}\right)\)	\(e\left(\frac{407}{650}\right)\)	\(e\left(\frac{206}{325}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{219}{260}\right)\)	\(e\left(\frac{189}{1300}\right)\)

Introduction

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.