LMFDB - Group of Dirichlet characters of modulus 216000

Show commands: PariGP / SageMath

sage: H = DirichletGroup(216000)

pari: g = idealstar(,216000,2)

Character group

sage: G.order() pari: g.no
Order	=	57600
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{3600}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{216000}(114751,\cdot)$, $\chi_{216000}(202501,\cdot)$, $\chi_{216000}(136001,\cdot)$, $\chi_{216000}(29377,\cdot)$

First 32 of 57600 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{216000}(1,\cdot)$	216000.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{216000}(7,\cdot)$	216000.th	360	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{281}{360}\right)$	$e\left(\frac{229}{360}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{167}{360}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{47}{180}\right)$
$\chi_{216000}(11,\cdot)$	216000.yp	3600	yes	$1$	$1$	$e\left(\frac{281}{360}\right)$	$e\left(\frac{761}{3600}\right)$	$e\left(\frac{379}{3600}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{41}{1200}\right)$	$e\left(\frac{683}{1800}\right)$	$e\left(\frac{1007}{3600}\right)$	$e\left(\frac{208}{225}\right)$	$e\left(\frac{223}{1200}\right)$	$e\left(\frac{167}{1800}\right)$
$\chi_{216000}(13,\cdot)$	216000.yv	3600	yes	$-1$	$1$	$e\left(\frac{229}{360}\right)$	$e\left(\frac{379}{3600}\right)$	$e\left(\frac{2981}{3600}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{1099}{1200}\right)$	$e\left(\frac{187}{1800}\right)$	$e\left(\frac{3373}{3600}\right)$	$e\left(\frac{49}{450}\right)$	$e\left(\frac{497}{1200}\right)$	$e\left(\frac{1513}{1800}\right)$
$\chi_{216000}(17,\cdot)$	216000.sl	300	no	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{59}{75}\right)$
$\chi_{216000}(19,\cdot)$	216000.xk	1200	no	$-1$	$1$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{41}{1200}\right)$	$e\left(\frac{1099}{1200}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{321}{400}\right)$	$e\left(\frac{323}{600}\right)$	$e\left(\frac{767}{1200}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{63}{400}\right)$	$e\left(\frac{227}{600}\right)$
$\chi_{216000}(23,\cdot)$	216000.yd	1800	no	$-1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{683}{1800}\right)$	$e\left(\frac{187}{1800}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{323}{600}\right)$	$e\left(\frac{37}{450}\right)$	$e\left(\frac{821}{1800}\right)$	$e\left(\frac{271}{450}\right)$	$e\left(\frac{319}{600}\right)$	$e\left(\frac{251}{900}\right)$
$\chi_{216000}(29,\cdot)$	216000.yn	3600	yes	$-1$	$1$	$e\left(\frac{167}{360}\right)$	$e\left(\frac{1007}{3600}\right)$	$e\left(\frac{3373}{3600}\right)$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{767}{1200}\right)$	$e\left(\frac{821}{1800}\right)$	$e\left(\frac{209}{3600}\right)$	$e\left(\frac{167}{450}\right)$	$e\left(\frac{601}{1200}\right)$	$e\left(\frac{1529}{1800}\right)$
$\chi_{216000}(31,\cdot)$	216000.uj	450	no	$-1$	$1$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{208}{225}\right)$	$e\left(\frac{49}{450}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{271}{450}\right)$	$e\left(\frac{167}{450}\right)$	$e\left(\frac{343}{450}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{2}{225}\right)$
$\chi_{216000}(37,\cdot)$	216000.xf	1200	no	$-1$	$1$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{223}{1200}\right)$	$e\left(\frac{497}{1200}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{63}{400}\right)$	$e\left(\frac{319}{600}\right)$	$e\left(\frac{601}{1200}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{189}{400}\right)$	$e\left(\frac{181}{600}\right)$
$\chi_{216000}(41,\cdot)$	216000.ye	1800	no	$-1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{167}{1800}\right)$	$e\left(\frac{1513}{1800}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{227}{600}\right)$	$e\left(\frac{251}{900}\right)$	$e\left(\frac{1529}{1800}\right)$	$e\left(\frac{2}{225}\right)$	$e\left(\frac{181}{600}\right)$	$e\left(\frac{599}{900}\right)$
$\chi_{216000}(43,\cdot)$	216000.vp	720	no	$1$	$1$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{469}{720}\right)$	$e\left(\frac{11}{720}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{277}{360}\right)$	$e\left(\frac{43}{720}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{343}{360}\right)$
$\chi_{216000}(47,\cdot)$	216000.we	900	no	$-1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{23}{900}\right)$	$e\left(\frac{43}{225}\right)$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{313}{900}\right)$	$e\left(\frac{701}{900}\right)$	$e\left(\frac{377}{450}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{178}{225}\right)$
$\chi_{216000}(49,\cdot)$	216000.qb	180	no	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{216000}(53,\cdot)$	216000.tu	400	no	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{393}{400}\right)$	$e\left(\frac{327}{400}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{99}{400}\right)$	$e\left(\frac{129}{200}\right)$	$e\left(\frac{191}{400}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{97}{400}\right)$	$e\left(\frac{71}{200}\right)$
$\chi_{216000}(59,\cdot)$	216000.yo	3600	yes	$1$	$1$	$e\left(\frac{169}{360}\right)$	$e\left(\frac{949}{3600}\right)$	$e\left(\frac{1511}{3600}\right)$	$e\left(\frac{221}{300}\right)$	$e\left(\frac{469}{1200}\right)$	$e\left(\frac{1747}{1800}\right)$	$e\left(\frac{163}{3600}\right)$	$e\left(\frac{197}{225}\right)$	$e\left(\frac{107}{1200}\right)$	$e\left(\frac{1003}{1800}\right)$
$\chi_{216000}(61,\cdot)$	216000.ys	3600	yes	$1$	$1$	$e\left(\frac{251}{360}\right)$	$e\left(\frac{191}{3600}\right)$	$e\left(\frac{2749}{3600}\right)$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{71}{1200}\right)$	$e\left(\frac{1373}{1800}\right)$	$e\left(\frac{2417}{3600}\right)$	$e\left(\frac{71}{450}\right)$	$e\left(\frac{313}{1200}\right)$	$e\left(\frac{677}{1800}\right)$
$\chi_{216000}(67,\cdot)$	216000.yu	3600	yes	$1$	$1$	$e\left(\frac{193}{360}\right)$	$e\left(\frac{343}{3600}\right)$	$e\left(\frac{1577}{3600}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{583}{1200}\right)$	$e\left(\frac{79}{1800}\right)$	$e\left(\frac{2041}{3600}\right)$	$e\left(\frac{29}{225}\right)$	$e\left(\frac{149}{1200}\right)$	$e\left(\frac{1621}{1800}\right)$
$\chi_{216000}(71,\cdot)$	216000.vg	600	no	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{107}{600}\right)$	$e\left(\frac{73}{600}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{167}{200}\right)$	$e\left(\frac{221}{300}\right)$	$e\left(\frac{209}{600}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{101}{200}\right)$	$e\left(\frac{179}{300}\right)$
$\chi_{216000}(73,\cdot)$	216000.uz	600	no	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{421}{600}\right)$	$e\left(\frac{269}{600}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{1}{200}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{127}{600}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{187}{300}\right)$
$\chi_{216000}(77,\cdot)$	216000.yx	3600	yes	$1$	$1$	$e\left(\frac{1}{360}\right)$	$e\left(\frac{3571}{3600}\right)$	$e\left(\frac{2669}{3600}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{1051}{1200}\right)$	$e\left(\frac{1363}{1800}\right)$	$e\left(\frac{2677}{3600}\right)$	$e\left(\frac{1}{450}\right)$	$e\left(\frac{953}{1200}\right)$	$e\left(\frac{637}{1800}\right)$
$\chi_{216000}(79,\cdot)$	216000.ww	900	no	$-1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{263}{900}\right)$	$e\left(\frac{157}{900}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{239}{450}\right)$	$e\left(\frac{131}{900}\right)$	$e\left(\frac{437}{450}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{11}{450}\right)$
$\chi_{216000}(83,\cdot)$	216000.yw	3600	yes	$-1$	$1$	$e\left(\frac{113}{360}\right)$	$e\left(\frac{323}{3600}\right)$	$e\left(\frac{2797}{3600}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{1163}{1200}\right)$	$e\left(\frac{1019}{1800}\right)$	$e\left(\frac{1901}{3600}\right)$	$e\left(\frac{169}{225}\right)$	$e\left(\frac{889}{1200}\right)$	$e\left(\frac{1781}{1800}\right)$
$\chi_{216000}(89,\cdot)$	216000.vj	600	no	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{571}{600}\right)$	$e\left(\frac{569}{600}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{277}{600}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{187}{300}\right)$
$\chi_{216000}(91,\cdot)$	216000.xj	1200	no	$-1$	$1$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{1063}{1200}\right)$	$e\left(\frac{557}{1200}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{303}{400}\right)$	$e\left(\frac{289}{600}\right)$	$e\left(\frac{481}{1200}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{9}{400}\right)$	$e\left(\frac{61}{600}\right)$
$\chi_{216000}(97,\cdot)$	216000.wo	900	no	$-1$	$1$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{229}{450}\right)$	$e\left(\frac{637}{900}\right)$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{823}{900}\right)$	$e\left(\frac{149}{225}\right)$	$e\left(\frac{46}{225}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{13}{225}\right)$
$\chi_{216000}(101,\cdot)$	216000.vx	720	no	$-1$	$1$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{337}{720}\right)$	$e\left(\frac{683}{720}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{271}{360}\right)$	$e\left(\frac{559}{720}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{319}{360}\right)$
$\chi_{216000}(103,\cdot)$	216000.xw	1800	no	$1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1361}{1800}\right)$	$e\left(\frac{1129}{1800}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{341}{600}\right)$	$e\left(\frac{79}{450}\right)$	$e\left(\frac{1607}{1800}\right)$	$e\left(\frac{7}{450}\right)$	$e\left(\frac{373}{600}\right)$	$e\left(\frac{767}{900}\right)$
$\chi_{216000}(107,\cdot)$	216000.mo	80	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{19}{40}\right)$
$\chi_{216000}(109,\cdot)$	216000.tz	400	no	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{91}{400}\right)$	$e\left(\frac{249}{400}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{313}{400}\right)$	$e\left(\frac{173}{200}\right)$	$e\left(\frac{117}{400}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{239}{400}\right)$	$e\left(\frac{177}{200}\right)$
$\chi_{216000}(113,\cdot)$	216000.xb	900	no	$1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{631}{900}\right)$	$e\left(\frac{221}{225}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{211}{300}\right)$	$e\left(\frac{761}{900}\right)$	$e\left(\frac{547}{900}\right)$	$e\left(\frac{197}{225}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{41}{225}\right)$
$\chi_{216000}(119,\cdot)$	216000.yf	1800	no	$1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{1519}{1800}\right)$	$e\left(\frac{41}{1800}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{139}{600}\right)$	$e\left(\frac{607}{900}\right)$	$e\left(\frac{1453}{1800}\right)$	$e\left(\frac{353}{450}\right)$	$e\left(\frac{317}{600}\right)$	$e\left(\frac{43}{900}\right)$

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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	$216000$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{3600}\)
Order	$57600$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{216000}(1,\cdot)\)	216000.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{216000}(7,\cdot)\)	216000.th	360	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{281}{360}\right)\)	\(e\left(\frac{229}{360}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{167}{360}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{47}{180}\right)\)
\(\chi_{216000}(11,\cdot)\)	216000.yp	3600	yes	\(1\)	\(1\)	\(e\left(\frac{281}{360}\right)\)	\(e\left(\frac{761}{3600}\right)\)	\(e\left(\frac{379}{3600}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{41}{1200}\right)\)	\(e\left(\frac{683}{1800}\right)\)	\(e\left(\frac{1007}{3600}\right)\)	\(e\left(\frac{208}{225}\right)\)	\(e\left(\frac{223}{1200}\right)\)	\(e\left(\frac{167}{1800}\right)\)
\(\chi_{216000}(13,\cdot)\)	216000.yv	3600	yes	\(-1\)	\(1\)	\(e\left(\frac{229}{360}\right)\)	\(e\left(\frac{379}{3600}\right)\)	\(e\left(\frac{2981}{3600}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{1099}{1200}\right)\)	\(e\left(\frac{187}{1800}\right)\)	\(e\left(\frac{3373}{3600}\right)\)	\(e\left(\frac{49}{450}\right)\)	\(e\left(\frac{497}{1200}\right)\)	\(e\left(\frac{1513}{1800}\right)\)
\(\chi_{216000}(17,\cdot)\)	216000.sl	300	no	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{59}{75}\right)\)
\(\chi_{216000}(19,\cdot)\)	216000.xk	1200	no	\(-1\)	\(1\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{41}{1200}\right)\)	\(e\left(\frac{1099}{1200}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{321}{400}\right)\)	\(e\left(\frac{323}{600}\right)\)	\(e\left(\frac{767}{1200}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{63}{400}\right)\)	\(e\left(\frac{227}{600}\right)\)
\(\chi_{216000}(23,\cdot)\)	216000.yd	1800	no	\(-1\)	\(1\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{683}{1800}\right)\)	\(e\left(\frac{187}{1800}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{323}{600}\right)\)	\(e\left(\frac{37}{450}\right)\)	\(e\left(\frac{821}{1800}\right)\)	\(e\left(\frac{271}{450}\right)\)	\(e\left(\frac{319}{600}\right)\)	\(e\left(\frac{251}{900}\right)\)
\(\chi_{216000}(29,\cdot)\)	216000.yn	3600	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{360}\right)\)	\(e\left(\frac{1007}{3600}\right)\)	\(e\left(\frac{3373}{3600}\right)\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{767}{1200}\right)\)	\(e\left(\frac{821}{1800}\right)\)	\(e\left(\frac{209}{3600}\right)\)	\(e\left(\frac{167}{450}\right)\)	\(e\left(\frac{601}{1200}\right)\)	\(e\left(\frac{1529}{1800}\right)\)
\(\chi_{216000}(31,\cdot)\)	216000.uj	450	no	\(-1\)	\(1\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{208}{225}\right)\)	\(e\left(\frac{49}{450}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{271}{450}\right)\)	\(e\left(\frac{167}{450}\right)\)	\(e\left(\frac{343}{450}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{2}{225}\right)\)
\(\chi_{216000}(37,\cdot)\)	216000.xf	1200	no	\(-1\)	\(1\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{223}{1200}\right)\)	\(e\left(\frac{497}{1200}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{63}{400}\right)\)	\(e\left(\frac{319}{600}\right)\)	\(e\left(\frac{601}{1200}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{189}{400}\right)\)	\(e\left(\frac{181}{600}\right)\)
\(\chi_{216000}(41,\cdot)\)	216000.ye	1800	no	\(-1\)	\(1\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{167}{1800}\right)\)	\(e\left(\frac{1513}{1800}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{227}{600}\right)\)	\(e\left(\frac{251}{900}\right)\)	\(e\left(\frac{1529}{1800}\right)\)	\(e\left(\frac{2}{225}\right)\)	\(e\left(\frac{181}{600}\right)\)	\(e\left(\frac{599}{900}\right)\)
\(\chi_{216000}(43,\cdot)\)	216000.vp	720	no	\(1\)	\(1\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{469}{720}\right)\)	\(e\left(\frac{11}{720}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{277}{360}\right)\)	\(e\left(\frac{43}{720}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{343}{360}\right)\)
\(\chi_{216000}(47,\cdot)\)	216000.we	900	no	\(-1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{23}{900}\right)\)	\(e\left(\frac{43}{225}\right)\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{313}{900}\right)\)	\(e\left(\frac{701}{900}\right)\)	\(e\left(\frac{377}{450}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{178}{225}\right)\)
\(\chi_{216000}(49,\cdot)\)	216000.qb	180	no	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)
\(\chi_{216000}(53,\cdot)\)	216000.tu	400	no	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{393}{400}\right)\)	\(e\left(\frac{327}{400}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{99}{400}\right)\)	\(e\left(\frac{129}{200}\right)\)	\(e\left(\frac{191}{400}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{97}{400}\right)\)	\(e\left(\frac{71}{200}\right)\)
\(\chi_{216000}(59,\cdot)\)	216000.yo	3600	yes	\(1\)	\(1\)	\(e\left(\frac{169}{360}\right)\)	\(e\left(\frac{949}{3600}\right)\)	\(e\left(\frac{1511}{3600}\right)\)	\(e\left(\frac{221}{300}\right)\)	\(e\left(\frac{469}{1200}\right)\)	\(e\left(\frac{1747}{1800}\right)\)	\(e\left(\frac{163}{3600}\right)\)	\(e\left(\frac{197}{225}\right)\)	\(e\left(\frac{107}{1200}\right)\)	\(e\left(\frac{1003}{1800}\right)\)
\(\chi_{216000}(61,\cdot)\)	216000.ys	3600	yes	\(1\)	\(1\)	\(e\left(\frac{251}{360}\right)\)	\(e\left(\frac{191}{3600}\right)\)	\(e\left(\frac{2749}{3600}\right)\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{71}{1200}\right)\)	\(e\left(\frac{1373}{1800}\right)\)	\(e\left(\frac{2417}{3600}\right)\)	\(e\left(\frac{71}{450}\right)\)	\(e\left(\frac{313}{1200}\right)\)	\(e\left(\frac{677}{1800}\right)\)
\(\chi_{216000}(67,\cdot)\)	216000.yu	3600	yes	\(1\)	\(1\)	\(e\left(\frac{193}{360}\right)\)	\(e\left(\frac{343}{3600}\right)\)	\(e\left(\frac{1577}{3600}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{583}{1200}\right)\)	\(e\left(\frac{79}{1800}\right)\)	\(e\left(\frac{2041}{3600}\right)\)	\(e\left(\frac{29}{225}\right)\)	\(e\left(\frac{149}{1200}\right)\)	\(e\left(\frac{1621}{1800}\right)\)
\(\chi_{216000}(71,\cdot)\)	216000.vg	600	no	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{107}{600}\right)\)	\(e\left(\frac{73}{600}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{167}{200}\right)\)	\(e\left(\frac{221}{300}\right)\)	\(e\left(\frac{209}{600}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{101}{200}\right)\)	\(e\left(\frac{179}{300}\right)\)
\(\chi_{216000}(73,\cdot)\)	216000.uz	600	no	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{421}{600}\right)\)	\(e\left(\frac{269}{600}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{1}{200}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{127}{600}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{153}{200}\right)\)	\(e\left(\frac{187}{300}\right)\)
\(\chi_{216000}(77,\cdot)\)	216000.yx	3600	yes	\(1\)	\(1\)	\(e\left(\frac{1}{360}\right)\)	\(e\left(\frac{3571}{3600}\right)\)	\(e\left(\frac{2669}{3600}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{1051}{1200}\right)\)	\(e\left(\frac{1363}{1800}\right)\)	\(e\left(\frac{2677}{3600}\right)\)	\(e\left(\frac{1}{450}\right)\)	\(e\left(\frac{953}{1200}\right)\)	\(e\left(\frac{637}{1800}\right)\)
\(\chi_{216000}(79,\cdot)\)	216000.ww	900	no	\(-1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{263}{900}\right)\)	\(e\left(\frac{157}{900}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{239}{450}\right)\)	\(e\left(\frac{131}{900}\right)\)	\(e\left(\frac{437}{450}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{11}{450}\right)\)
\(\chi_{216000}(83,\cdot)\)	216000.yw	3600	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{360}\right)\)	\(e\left(\frac{323}{3600}\right)\)	\(e\left(\frac{2797}{3600}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{1163}{1200}\right)\)	\(e\left(\frac{1019}{1800}\right)\)	\(e\left(\frac{1901}{3600}\right)\)	\(e\left(\frac{169}{225}\right)\)	\(e\left(\frac{889}{1200}\right)\)	\(e\left(\frac{1781}{1800}\right)\)
\(\chi_{216000}(89,\cdot)\)	216000.vj	600	no	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{571}{600}\right)\)	\(e\left(\frac{569}{600}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{151}{200}\right)\)	\(e\left(\frac{13}{300}\right)\)	\(e\left(\frac{277}{600}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{53}{200}\right)\)	\(e\left(\frac{187}{300}\right)\)
\(\chi_{216000}(91,\cdot)\)	216000.xj	1200	no	\(-1\)	\(1\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{1063}{1200}\right)\)	\(e\left(\frac{557}{1200}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{303}{400}\right)\)	\(e\left(\frac{289}{600}\right)\)	\(e\left(\frac{481}{1200}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{9}{400}\right)\)	\(e\left(\frac{61}{600}\right)\)
\(\chi_{216000}(97,\cdot)\)	216000.wo	900	no	\(-1\)	\(1\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{229}{450}\right)\)	\(e\left(\frac{637}{900}\right)\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{823}{900}\right)\)	\(e\left(\frac{149}{225}\right)\)	\(e\left(\frac{46}{225}\right)\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{13}{225}\right)\)
\(\chi_{216000}(101,\cdot)\)	216000.vx	720	no	\(-1\)	\(1\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{337}{720}\right)\)	\(e\left(\frac{683}{720}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{271}{360}\right)\)	\(e\left(\frac{559}{720}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{319}{360}\right)\)
\(\chi_{216000}(103,\cdot)\)	216000.xw	1800	no	\(1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1361}{1800}\right)\)	\(e\left(\frac{1129}{1800}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{341}{600}\right)\)	\(e\left(\frac{79}{450}\right)\)	\(e\left(\frac{1607}{1800}\right)\)	\(e\left(\frac{7}{450}\right)\)	\(e\left(\frac{373}{600}\right)\)	\(e\left(\frac{767}{900}\right)\)
\(\chi_{216000}(107,\cdot)\)	216000.mo	80	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)
\(\chi_{216000}(109,\cdot)\)	216000.tz	400	no	\(1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{91}{400}\right)\)	\(e\left(\frac{249}{400}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{313}{400}\right)\)	\(e\left(\frac{173}{200}\right)\)	\(e\left(\frac{117}{400}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{239}{400}\right)\)	\(e\left(\frac{177}{200}\right)\)
\(\chi_{216000}(113,\cdot)\)	216000.xb	900	no	\(1\)	\(1\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{631}{900}\right)\)	\(e\left(\frac{221}{225}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{211}{300}\right)\)	\(e\left(\frac{761}{900}\right)\)	\(e\left(\frac{547}{900}\right)\)	\(e\left(\frac{197}{225}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{41}{225}\right)\)
\(\chi_{216000}(119,\cdot)\)	216000.yf	1800	no	\(1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{1519}{1800}\right)\)	\(e\left(\frac{41}{1800}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{139}{600}\right)\)	\(e\left(\frac{607}{900}\right)\)	\(e\left(\frac{1453}{1800}\right)\)	\(e\left(\frac{353}{450}\right)\)	\(e\left(\frac{317}{600}\right)\)	\(e\left(\frac{43}{900}\right)\)

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.