LMFDB - Group of Dirichlet characters of modulus 360000

Show commands: PariGP / SageMath

sage: H = DirichletGroup(360000)

pari: g = idealstar(,360000,2)

Character group

sage: G.order() pari: g.no
Order	=	96000
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{6000}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{360000}(258751,\cdot)$, $\chi_{360000}(202501,\cdot)$, $\chi_{360000}(280001,\cdot)$, $\chi_{360000}(29377,\cdot)$

First 32 of 96000 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{360000}(1,\cdot)$	360000.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{360000}(7,\cdot)$	360000.rm	600	no	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{600}\right)$	$e\left(\frac{323}{600}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{67}{200}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{409}{600}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{229}{300}\right)$
$\chi_{360000}(11,\cdot)$	360000.wc	6000	yes	$1$	$1$	$e\left(\frac{7}{600}\right)$	$e\left(\frac{2287}{6000}\right)$	$e\left(\frac{2093}{6000}\right)$	$e\left(\frac{473}{500}\right)$	$e\left(\frac{1247}{2000}\right)$	$e\left(\frac{61}{3000}\right)$	$e\left(\frac{4969}{6000}\right)$	$e\left(\frac{11}{375}\right)$	$e\left(\frac{41}{2000}\right)$	$e\left(\frac{289}{3000}\right)$
$\chi_{360000}(13,\cdot)$	360000.vs	6000	yes	$-1$	$1$	$e\left(\frac{323}{600}\right)$	$e\left(\frac{2093}{6000}\right)$	$e\left(\frac{2227}{6000}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{1533}{2000}\right)$	$e\left(\frac{1829}{3000}\right)$	$e\left(\frac{4091}{6000}\right)$	$e\left(\frac{383}{750}\right)$	$e\left(\frac{1799}{2000}\right)$	$e\left(\frac{71}{3000}\right)$
$\chi_{360000}(17,\cdot)$	360000.qp	500	no	$1$	$1$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{473}{500}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{179}{500}\right)$	$e\left(\frac{439}{500}\right)$	$e\left(\frac{63}{500}\right)$	$e\left(\frac{401}{500}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{73}{125}\right)$	$e\left(\frac{28}{125}\right)$
$\chi_{360000}(19,\cdot)$	360000.uw	2000	no	$-1$	$1$	$e\left(\frac{67}{200}\right)$	$e\left(\frac{1247}{2000}\right)$	$e\left(\frac{1533}{2000}\right)$	$e\left(\frac{439}{500}\right)$	$e\left(\frac{21}{2000}\right)$	$e\left(\frac{941}{1000}\right)$	$e\left(\frac{489}{2000}\right)$	$e\left(\frac{16}{125}\right)$	$e\left(\frac{1963}{2000}\right)$	$e\left(\frac{909}{1000}\right)$
$\chi_{360000}(23,\cdot)$	360000.vj	3000	no	$-1$	$1$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{61}{3000}\right)$	$e\left(\frac{1829}{3000}\right)$	$e\left(\frac{63}{500}\right)$	$e\left(\frac{941}{1000}\right)$	$e\left(\frac{329}{750}\right)$	$e\left(\frac{307}{3000}\right)$	$e\left(\frac{407}{750}\right)$	$e\left(\frac{473}{1000}\right)$	$e\left(\frac{517}{1500}\right)$
$\chi_{360000}(29,\cdot)$	360000.vr	6000	yes	$-1$	$1$	$e\left(\frac{409}{600}\right)$	$e\left(\frac{4969}{6000}\right)$	$e\left(\frac{4091}{6000}\right)$	$e\left(\frac{401}{500}\right)$	$e\left(\frac{489}{2000}\right)$	$e\left(\frac{307}{3000}\right)$	$e\left(\frac{1303}{6000}\right)$	$e\left(\frac{289}{750}\right)$	$e\left(\frac{1567}{2000}\right)$	$e\left(\frac{2143}{3000}\right)$
$\chi_{360000}(31,\cdot)$	360000.rx	750	no	$-1$	$1$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{11}{375}\right)$	$e\left(\frac{383}{750}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{16}{125}\right)$	$e\left(\frac{407}{750}\right)$	$e\left(\frac{289}{750}\right)$	$e\left(\frac{581}{750}\right)$	$e\left(\frac{21}{250}\right)$	$e\left(\frac{334}{375}\right)$
$\chi_{360000}(37,\cdot)$	360000.us	2000	no	$-1$	$1$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{41}{2000}\right)$	$e\left(\frac{1799}{2000}\right)$	$e\left(\frac{73}{125}\right)$	$e\left(\frac{1963}{2000}\right)$	$e\left(\frac{473}{1000}\right)$	$e\left(\frac{1567}{2000}\right)$	$e\left(\frac{21}{250}\right)$	$e\left(\frac{1089}{2000}\right)$	$e\left(\frac{827}{1000}\right)$
$\chi_{360000}(41,\cdot)$	360000.vk	3000	no	$-1$	$1$	$e\left(\frac{229}{300}\right)$	$e\left(\frac{289}{3000}\right)$	$e\left(\frac{71}{3000}\right)$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{909}{1000}\right)$	$e\left(\frac{517}{1500}\right)$	$e\left(\frac{2143}{3000}\right)$	$e\left(\frac{334}{375}\right)$	$e\left(\frac{827}{1000}\right)$	$e\left(\frac{433}{1500}\right)$
$\chi_{360000}(43,\cdot)$	360000.sw	1200	no	$1$	$1$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{1043}{1200}\right)$	$e\left(\frac{877}{1200}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{83}{400}\right)$	$e\left(\frac{179}{600}\right)$	$e\left(\frac{941}{1200}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{249}{400}\right)$	$e\left(\frac{521}{600}\right)$
$\chi_{360000}(47,\cdot)$	360000.tu	1500	no	$-1$	$1$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{1141}{1500}\right)$	$e\left(\frac{206}{375}\right)$	$e\left(\frac{31}{500}\right)$	$e\left(\frac{421}{500}\right)$	$e\left(\frac{671}{1500}\right)$	$e\left(\frac{1267}{1500}\right)$	$e\left(\frac{109}{750}\right)$	$e\left(\frac{72}{125}\right)$	$e\left(\frac{326}{375}\right)$
$\chi_{360000}(49,\cdot)$	360000.pi	300	no	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{23}{300}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{79}{150}\right)$
$\chi_{360000}(53,\cdot)$	360000.un	2000	no	$1$	$1$	$e\left(\frac{23}{200}\right)$	$e\left(\frac{893}{2000}\right)$	$e\left(\frac{1427}{2000}\right)$	$e\left(\frac{29}{125}\right)$	$e\left(\frac{1999}{2000}\right)$	$e\left(\frac{229}{1000}\right)$	$e\left(\frac{1691}{2000}\right)$	$e\left(\frac{183}{250}\right)$	$e\left(\frac{597}{2000}\right)$	$e\left(\frac{171}{1000}\right)$
$\chi_{360000}(59,\cdot)$	360000.vq	6000	yes	$1$	$1$	$e\left(\frac{263}{600}\right)$	$e\left(\frac{1283}{6000}\right)$	$e\left(\frac{5137}{6000}\right)$	$e\left(\frac{307}{500}\right)$	$e\left(\frac{1923}{2000}\right)$	$e\left(\frac{149}{3000}\right)$	$e\left(\frac{5621}{6000}\right)$	$e\left(\frac{199}{375}\right)$	$e\left(\frac{1469}{2000}\right)$	$e\left(\frac{2501}{3000}\right)$
$\chi_{360000}(61,\cdot)$	360000.wb	6000	yes	$1$	$1$	$e\left(\frac{517}{600}\right)$	$e\left(\frac{4297}{6000}\right)$	$e\left(\frac{5483}{6000}\right)$	$e\left(\frac{13}{500}\right)$	$e\left(\frac{1057}{2000}\right)$	$e\left(\frac{91}{3000}\right)$	$e\left(\frac{2839}{6000}\right)$	$e\left(\frac{457}{750}\right)$	$e\left(\frac{1471}{2000}\right)$	$e\left(\frac{259}{3000}\right)$
$\chi_{360000}(67,\cdot)$	360000.vt	6000	yes	$1$	$1$	$e\left(\frac{191}{600}\right)$	$e\left(\frac{881}{6000}\right)$	$e\left(\frac{559}{6000}\right)$	$e\left(\frac{187}{250}\right)$	$e\left(\frac{1361}{2000}\right)$	$e\left(\frac{2993}{3000}\right)$	$e\left(\frac{3647}{6000}\right)$	$e\left(\frac{343}{375}\right)$	$e\left(\frac{483}{2000}\right)$	$e\left(\frac{1307}{3000}\right)$
$\chi_{360000}(71,\cdot)$	360000.sf	1000	no	$1$	$1$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{69}{1000}\right)$	$e\left(\frac{991}{1000}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{267}{1000}\right)$	$e\left(\frac{107}{500}\right)$	$e\left(\frac{503}{1000}\right)$	$e\left(\frac{153}{250}\right)$	$e\left(\frac{601}{1000}\right)$	$e\left(\frac{93}{500}\right)$
$\chi_{360000}(73,\cdot)$	360000.so	1000	no	$-1$	$1$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{907}{1000}\right)$	$e\left(\frac{523}{1000}\right)$	$e\left(\frac{93}{500}\right)$	$e\left(\frac{901}{1000}\right)$	$e\left(\frac{23}{250}\right)$	$e\left(\frac{409}{1000}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{853}{1000}\right)$	$e\left(\frac{429}{500}\right)$
$\chi_{360000}(77,\cdot)$	360000.vz	6000	yes	$1$	$1$	$e\left(\frac{527}{600}\right)$	$e\left(\frac{2357}{6000}\right)$	$e\left(\frac{5323}{6000}\right)$	$e\left(\frac{32}{125}\right)$	$e\left(\frac{1917}{2000}\right)$	$e\left(\frac{2021}{3000}\right)$	$e\left(\frac{3059}{6000}\right)$	$e\left(\frac{317}{750}\right)$	$e\left(\frac{1551}{2000}\right)$	$e\left(\frac{2579}{3000}\right)$
$\chi_{360000}(79,\cdot)$	360000.tk	1500	no	$-1$	$1$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{421}{1500}\right)$	$e\left(\frac{119}{1500}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{101}{500}\right)$	$e\left(\frac{613}{750}\right)$	$e\left(\frac{877}{1500}\right)$	$e\left(\frac{79}{750}\right)$	$e\left(\frac{203}{500}\right)$	$e\left(\frac{187}{750}\right)$
$\chi_{360000}(83,\cdot)$	360000.vy	6000	yes	$-1$	$1$	$e\left(\frac{151}{600}\right)$	$e\left(\frac{1141}{6000}\right)$	$e\left(\frac{2699}{6000}\right)$	$e\left(\frac{207}{250}\right)$	$e\left(\frac{1421}{2000}\right)$	$e\left(\frac{2773}{3000}\right)$	$e\left(\frac{4267}{6000}\right)$	$e\left(\frac{248}{375}\right)$	$e\left(\frac{1663}{2000}\right)$	$e\left(\frac{1027}{3000}\right)$
$\chi_{360000}(89,\cdot)$	360000.st	1000	no	$-1$	$1$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{357}{1000}\right)$	$e\left(\frac{823}{1000}\right)$	$e\left(\frac{9}{250}\right)$	$e\left(\frac{251}{1000}\right)$	$e\left(\frac{271}{500}\right)$	$e\left(\frac{59}{1000}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{153}{1000}\right)$	$e\left(\frac{329}{500}\right)$
$\chi_{360000}(91,\cdot)$	360000.uk	2000	no	$-1$	$1$	$e\left(\frac{81}{200}\right)$	$e\left(\frac{721}{2000}\right)$	$e\left(\frac{1819}{2000}\right)$	$e\left(\frac{327}{500}\right)$	$e\left(\frac{203}{2000}\right)$	$e\left(\frac{263}{1000}\right)$	$e\left(\frac{727}{2000}\right)$	$e\left(\frac{113}{125}\right)$	$e\left(\frac{1309}{2000}\right)$	$e\left(\frac{787}{1000}\right)$
$\chi_{360000}(97,\cdot)$	360000.ud	1500	no	$-1$	$1$	$e\left(\frac{167}{300}\right)$	$e\left(\frac{743}{750}\right)$	$e\left(\frac{779}{1500}\right)$	$e\left(\frac{301}{500}\right)$	$e\left(\frac{29}{125}\right)$	$e\left(\frac{1241}{1500}\right)$	$e\left(\frac{133}{375}\right)$	$e\left(\frac{257}{375}\right)$	$e\left(\frac{123}{500}\right)$	$e\left(\frac{371}{375}\right)$
$\chi_{360000}(101,\cdot)$	360000.sy	1200	no	$-1$	$1$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{119}{1200}\right)$	$e\left(\frac{541}{1200}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{39}{400}\right)$	$e\left(\frac{257}{600}\right)$	$e\left(\frac{953}{1200}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{217}{400}\right)$	$e\left(\frac{593}{600}\right)$
$\chi_{360000}(103,\cdot)$	360000.vi	3000	no	$1$	$1$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{1087}{3000}\right)$	$e\left(\frac{2543}{3000}\right)$	$e\left(\frac{221}{500}\right)$	$e\left(\frac{547}{1000}\right)$	$e\left(\frac{293}{750}\right)$	$e\left(\frac{2569}{3000}\right)$	$e\left(\frac{269}{750}\right)$	$e\left(\frac{691}{1000}\right)$	$e\left(\frac{889}{1500}\right)$
$\chi_{360000}(107,\cdot)$	360000.pl	400	no	$-1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{377}{400}\right)$	$e\left(\frac{103}{400}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{211}{400}\right)$	$e\left(\frac{81}{200}\right)$	$e\left(\frac{199}{400}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{33}{400}\right)$	$e\left(\frac{119}{200}\right)$
$\chi_{360000}(109,\cdot)$	360000.ux	2000	no	$1$	$1$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{1191}{2000}\right)$	$e\left(\frac{1149}{2000}\right)$	$e\left(\frac{467}{500}\right)$	$e\left(\frac{413}{2000}\right)$	$e\left(\frac{673}{1000}\right)$	$e\left(\frac{617}{2000}\right)$	$e\left(\frac{171}{250}\right)$	$e\left(\frac{939}{2000}\right)$	$e\left(\frac{877}{1000}\right)$
$\chi_{360000}(113,\cdot)$	360000.tw	1500	no	$1$	$1$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{977}{1500}\right)$	$e\left(\frac{157}{375}\right)$	$e\left(\frac{57}{500}\right)$	$e\left(\frac{137}{500}\right)$	$e\left(\frac{1387}{1500}\right)$	$e\left(\frac{749}{1500}\right)$	$e\left(\frac{199}{375}\right)$	$e\left(\frac{84}{125}\right)$	$e\left(\frac{172}{375}\right)$
$\chi_{360000}(119,\cdot)$	360000.va	3000	no	$1$	$1$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{2873}{3000}\right)$	$e\left(\frac{2647}{3000}\right)$	$e\left(\frac{167}{250}\right)$	$e\left(\frac{213}{1000}\right)$	$e\left(\frac{1169}{1500}\right)$	$e\left(\frac{1451}{3000}\right)$	$e\left(\frac{1}{750}\right)$	$e\left(\frac{339}{1000}\right)$	$e\left(\frac{1481}{1500}\right)$

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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	$360000$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{6000}\)
Order	$96000$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{360000}(1,\cdot)\)	360000.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{360000}(7,\cdot)\)	360000.rm	600	no	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{600}\right)\)	\(e\left(\frac{323}{600}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{67}{200}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{409}{600}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{151}{200}\right)\)	\(e\left(\frac{229}{300}\right)\)
\(\chi_{360000}(11,\cdot)\)	360000.wc	6000	yes	\(1\)	\(1\)	\(e\left(\frac{7}{600}\right)\)	\(e\left(\frac{2287}{6000}\right)\)	\(e\left(\frac{2093}{6000}\right)\)	\(e\left(\frac{473}{500}\right)\)	\(e\left(\frac{1247}{2000}\right)\)	\(e\left(\frac{61}{3000}\right)\)	\(e\left(\frac{4969}{6000}\right)\)	\(e\left(\frac{11}{375}\right)\)	\(e\left(\frac{41}{2000}\right)\)	\(e\left(\frac{289}{3000}\right)\)
\(\chi_{360000}(13,\cdot)\)	360000.vs	6000	yes	\(-1\)	\(1\)	\(e\left(\frac{323}{600}\right)\)	\(e\left(\frac{2093}{6000}\right)\)	\(e\left(\frac{2227}{6000}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{1533}{2000}\right)\)	\(e\left(\frac{1829}{3000}\right)\)	\(e\left(\frac{4091}{6000}\right)\)	\(e\left(\frac{383}{750}\right)\)	\(e\left(\frac{1799}{2000}\right)\)	\(e\left(\frac{71}{3000}\right)\)
\(\chi_{360000}(17,\cdot)\)	360000.qp	500	no	\(1\)	\(1\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{473}{500}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{179}{500}\right)\)	\(e\left(\frac{439}{500}\right)\)	\(e\left(\frac{63}{500}\right)\)	\(e\left(\frac{401}{500}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{73}{125}\right)\)	\(e\left(\frac{28}{125}\right)\)
\(\chi_{360000}(19,\cdot)\)	360000.uw	2000	no	\(-1\)	\(1\)	\(e\left(\frac{67}{200}\right)\)	\(e\left(\frac{1247}{2000}\right)\)	\(e\left(\frac{1533}{2000}\right)\)	\(e\left(\frac{439}{500}\right)\)	\(e\left(\frac{21}{2000}\right)\)	\(e\left(\frac{941}{1000}\right)\)	\(e\left(\frac{489}{2000}\right)\)	\(e\left(\frac{16}{125}\right)\)	\(e\left(\frac{1963}{2000}\right)\)	\(e\left(\frac{909}{1000}\right)\)
\(\chi_{360000}(23,\cdot)\)	360000.vj	3000	no	\(-1\)	\(1\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{61}{3000}\right)\)	\(e\left(\frac{1829}{3000}\right)\)	\(e\left(\frac{63}{500}\right)\)	\(e\left(\frac{941}{1000}\right)\)	\(e\left(\frac{329}{750}\right)\)	\(e\left(\frac{307}{3000}\right)\)	\(e\left(\frac{407}{750}\right)\)	\(e\left(\frac{473}{1000}\right)\)	\(e\left(\frac{517}{1500}\right)\)
\(\chi_{360000}(29,\cdot)\)	360000.vr	6000	yes	\(-1\)	\(1\)	\(e\left(\frac{409}{600}\right)\)	\(e\left(\frac{4969}{6000}\right)\)	\(e\left(\frac{4091}{6000}\right)\)	\(e\left(\frac{401}{500}\right)\)	\(e\left(\frac{489}{2000}\right)\)	\(e\left(\frac{307}{3000}\right)\)	\(e\left(\frac{1303}{6000}\right)\)	\(e\left(\frac{289}{750}\right)\)	\(e\left(\frac{1567}{2000}\right)\)	\(e\left(\frac{2143}{3000}\right)\)
\(\chi_{360000}(31,\cdot)\)	360000.rx	750	no	\(-1\)	\(1\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{11}{375}\right)\)	\(e\left(\frac{383}{750}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{16}{125}\right)\)	\(e\left(\frac{407}{750}\right)\)	\(e\left(\frac{289}{750}\right)\)	\(e\left(\frac{581}{750}\right)\)	\(e\left(\frac{21}{250}\right)\)	\(e\left(\frac{334}{375}\right)\)
\(\chi_{360000}(37,\cdot)\)	360000.us	2000	no	\(-1\)	\(1\)	\(e\left(\frac{151}{200}\right)\)	\(e\left(\frac{41}{2000}\right)\)	\(e\left(\frac{1799}{2000}\right)\)	\(e\left(\frac{73}{125}\right)\)	\(e\left(\frac{1963}{2000}\right)\)	\(e\left(\frac{473}{1000}\right)\)	\(e\left(\frac{1567}{2000}\right)\)	\(e\left(\frac{21}{250}\right)\)	\(e\left(\frac{1089}{2000}\right)\)	\(e\left(\frac{827}{1000}\right)\)
\(\chi_{360000}(41,\cdot)\)	360000.vk	3000	no	\(-1\)	\(1\)	\(e\left(\frac{229}{300}\right)\)	\(e\left(\frac{289}{3000}\right)\)	\(e\left(\frac{71}{3000}\right)\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{909}{1000}\right)\)	\(e\left(\frac{517}{1500}\right)\)	\(e\left(\frac{2143}{3000}\right)\)	\(e\left(\frac{334}{375}\right)\)	\(e\left(\frac{827}{1000}\right)\)	\(e\left(\frac{433}{1500}\right)\)
\(\chi_{360000}(43,\cdot)\)	360000.sw	1200	no	\(1\)	\(1\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{1043}{1200}\right)\)	\(e\left(\frac{877}{1200}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{83}{400}\right)\)	\(e\left(\frac{179}{600}\right)\)	\(e\left(\frac{941}{1200}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{249}{400}\right)\)	\(e\left(\frac{521}{600}\right)\)
\(\chi_{360000}(47,\cdot)\)	360000.tu	1500	no	\(-1\)	\(1\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{1141}{1500}\right)\)	\(e\left(\frac{206}{375}\right)\)	\(e\left(\frac{31}{500}\right)\)	\(e\left(\frac{421}{500}\right)\)	\(e\left(\frac{671}{1500}\right)\)	\(e\left(\frac{1267}{1500}\right)\)	\(e\left(\frac{109}{750}\right)\)	\(e\left(\frac{72}{125}\right)\)	\(e\left(\frac{326}{375}\right)\)
\(\chi_{360000}(49,\cdot)\)	360000.pi	300	no	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{23}{300}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{79}{150}\right)\)
\(\chi_{360000}(53,\cdot)\)	360000.un	2000	no	\(1\)	\(1\)	\(e\left(\frac{23}{200}\right)\)	\(e\left(\frac{893}{2000}\right)\)	\(e\left(\frac{1427}{2000}\right)\)	\(e\left(\frac{29}{125}\right)\)	\(e\left(\frac{1999}{2000}\right)\)	\(e\left(\frac{229}{1000}\right)\)	\(e\left(\frac{1691}{2000}\right)\)	\(e\left(\frac{183}{250}\right)\)	\(e\left(\frac{597}{2000}\right)\)	\(e\left(\frac{171}{1000}\right)\)
\(\chi_{360000}(59,\cdot)\)	360000.vq	6000	yes	\(1\)	\(1\)	\(e\left(\frac{263}{600}\right)\)	\(e\left(\frac{1283}{6000}\right)\)	\(e\left(\frac{5137}{6000}\right)\)	\(e\left(\frac{307}{500}\right)\)	\(e\left(\frac{1923}{2000}\right)\)	\(e\left(\frac{149}{3000}\right)\)	\(e\left(\frac{5621}{6000}\right)\)	\(e\left(\frac{199}{375}\right)\)	\(e\left(\frac{1469}{2000}\right)\)	\(e\left(\frac{2501}{3000}\right)\)
\(\chi_{360000}(61,\cdot)\)	360000.wb	6000	yes	\(1\)	\(1\)	\(e\left(\frac{517}{600}\right)\)	\(e\left(\frac{4297}{6000}\right)\)	\(e\left(\frac{5483}{6000}\right)\)	\(e\left(\frac{13}{500}\right)\)	\(e\left(\frac{1057}{2000}\right)\)	\(e\left(\frac{91}{3000}\right)\)	\(e\left(\frac{2839}{6000}\right)\)	\(e\left(\frac{457}{750}\right)\)	\(e\left(\frac{1471}{2000}\right)\)	\(e\left(\frac{259}{3000}\right)\)
\(\chi_{360000}(67,\cdot)\)	360000.vt	6000	yes	\(1\)	\(1\)	\(e\left(\frac{191}{600}\right)\)	\(e\left(\frac{881}{6000}\right)\)	\(e\left(\frac{559}{6000}\right)\)	\(e\left(\frac{187}{250}\right)\)	\(e\left(\frac{1361}{2000}\right)\)	\(e\left(\frac{2993}{3000}\right)\)	\(e\left(\frac{3647}{6000}\right)\)	\(e\left(\frac{343}{375}\right)\)	\(e\left(\frac{483}{2000}\right)\)	\(e\left(\frac{1307}{3000}\right)\)
\(\chi_{360000}(71,\cdot)\)	360000.sf	1000	no	\(1\)	\(1\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{69}{1000}\right)\)	\(e\left(\frac{991}{1000}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{267}{1000}\right)\)	\(e\left(\frac{107}{500}\right)\)	\(e\left(\frac{503}{1000}\right)\)	\(e\left(\frac{153}{250}\right)\)	\(e\left(\frac{601}{1000}\right)\)	\(e\left(\frac{93}{500}\right)\)
\(\chi_{360000}(73,\cdot)\)	360000.so	1000	no	\(-1\)	\(1\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{907}{1000}\right)\)	\(e\left(\frac{523}{1000}\right)\)	\(e\left(\frac{93}{500}\right)\)	\(e\left(\frac{901}{1000}\right)\)	\(e\left(\frac{23}{250}\right)\)	\(e\left(\frac{409}{1000}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{853}{1000}\right)\)	\(e\left(\frac{429}{500}\right)\)
\(\chi_{360000}(77,\cdot)\)	360000.vz	6000	yes	\(1\)	\(1\)	\(e\left(\frac{527}{600}\right)\)	\(e\left(\frac{2357}{6000}\right)\)	\(e\left(\frac{5323}{6000}\right)\)	\(e\left(\frac{32}{125}\right)\)	\(e\left(\frac{1917}{2000}\right)\)	\(e\left(\frac{2021}{3000}\right)\)	\(e\left(\frac{3059}{6000}\right)\)	\(e\left(\frac{317}{750}\right)\)	\(e\left(\frac{1551}{2000}\right)\)	\(e\left(\frac{2579}{3000}\right)\)
\(\chi_{360000}(79,\cdot)\)	360000.tk	1500	no	\(-1\)	\(1\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{421}{1500}\right)\)	\(e\left(\frac{119}{1500}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{101}{500}\right)\)	\(e\left(\frac{613}{750}\right)\)	\(e\left(\frac{877}{1500}\right)\)	\(e\left(\frac{79}{750}\right)\)	\(e\left(\frac{203}{500}\right)\)	\(e\left(\frac{187}{750}\right)\)
\(\chi_{360000}(83,\cdot)\)	360000.vy	6000	yes	\(-1\)	\(1\)	\(e\left(\frac{151}{600}\right)\)	\(e\left(\frac{1141}{6000}\right)\)	\(e\left(\frac{2699}{6000}\right)\)	\(e\left(\frac{207}{250}\right)\)	\(e\left(\frac{1421}{2000}\right)\)	\(e\left(\frac{2773}{3000}\right)\)	\(e\left(\frac{4267}{6000}\right)\)	\(e\left(\frac{248}{375}\right)\)	\(e\left(\frac{1663}{2000}\right)\)	\(e\left(\frac{1027}{3000}\right)\)
\(\chi_{360000}(89,\cdot)\)	360000.st	1000	no	\(-1\)	\(1\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{357}{1000}\right)\)	\(e\left(\frac{823}{1000}\right)\)	\(e\left(\frac{9}{250}\right)\)	\(e\left(\frac{251}{1000}\right)\)	\(e\left(\frac{271}{500}\right)\)	\(e\left(\frac{59}{1000}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{153}{1000}\right)\)	\(e\left(\frac{329}{500}\right)\)
\(\chi_{360000}(91,\cdot)\)	360000.uk	2000	no	\(-1\)	\(1\)	\(e\left(\frac{81}{200}\right)\)	\(e\left(\frac{721}{2000}\right)\)	\(e\left(\frac{1819}{2000}\right)\)	\(e\left(\frac{327}{500}\right)\)	\(e\left(\frac{203}{2000}\right)\)	\(e\left(\frac{263}{1000}\right)\)	\(e\left(\frac{727}{2000}\right)\)	\(e\left(\frac{113}{125}\right)\)	\(e\left(\frac{1309}{2000}\right)\)	\(e\left(\frac{787}{1000}\right)\)
\(\chi_{360000}(97,\cdot)\)	360000.ud	1500	no	\(-1\)	\(1\)	\(e\left(\frac{167}{300}\right)\)	\(e\left(\frac{743}{750}\right)\)	\(e\left(\frac{779}{1500}\right)\)	\(e\left(\frac{301}{500}\right)\)	\(e\left(\frac{29}{125}\right)\)	\(e\left(\frac{1241}{1500}\right)\)	\(e\left(\frac{133}{375}\right)\)	\(e\left(\frac{257}{375}\right)\)	\(e\left(\frac{123}{500}\right)\)	\(e\left(\frac{371}{375}\right)\)
\(\chi_{360000}(101,\cdot)\)	360000.sy	1200	no	\(-1\)	\(1\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{119}{1200}\right)\)	\(e\left(\frac{541}{1200}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{39}{400}\right)\)	\(e\left(\frac{257}{600}\right)\)	\(e\left(\frac{953}{1200}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{217}{400}\right)\)	\(e\left(\frac{593}{600}\right)\)
\(\chi_{360000}(103,\cdot)\)	360000.vi	3000	no	\(1\)	\(1\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{1087}{3000}\right)\)	\(e\left(\frac{2543}{3000}\right)\)	\(e\left(\frac{221}{500}\right)\)	\(e\left(\frac{547}{1000}\right)\)	\(e\left(\frac{293}{750}\right)\)	\(e\left(\frac{2569}{3000}\right)\)	\(e\left(\frac{269}{750}\right)\)	\(e\left(\frac{691}{1000}\right)\)	\(e\left(\frac{889}{1500}\right)\)
\(\chi_{360000}(107,\cdot)\)	360000.pl	400	no	\(-1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{377}{400}\right)\)	\(e\left(\frac{103}{400}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{211}{400}\right)\)	\(e\left(\frac{81}{200}\right)\)	\(e\left(\frac{199}{400}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{33}{400}\right)\)	\(e\left(\frac{119}{200}\right)\)
\(\chi_{360000}(109,\cdot)\)	360000.ux	2000	no	\(1\)	\(1\)	\(e\left(\frac{151}{200}\right)\)	\(e\left(\frac{1191}{2000}\right)\)	\(e\left(\frac{1149}{2000}\right)\)	\(e\left(\frac{467}{500}\right)\)	\(e\left(\frac{413}{2000}\right)\)	\(e\left(\frac{673}{1000}\right)\)	\(e\left(\frac{617}{2000}\right)\)	\(e\left(\frac{171}{250}\right)\)	\(e\left(\frac{939}{2000}\right)\)	\(e\left(\frac{877}{1000}\right)\)
\(\chi_{360000}(113,\cdot)\)	360000.tw	1500	no	\(1\)	\(1\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{977}{1500}\right)\)	\(e\left(\frac{157}{375}\right)\)	\(e\left(\frac{57}{500}\right)\)	\(e\left(\frac{137}{500}\right)\)	\(e\left(\frac{1387}{1500}\right)\)	\(e\left(\frac{749}{1500}\right)\)	\(e\left(\frac{199}{375}\right)\)	\(e\left(\frac{84}{125}\right)\)	\(e\left(\frac{172}{375}\right)\)
\(\chi_{360000}(119,\cdot)\)	360000.va	3000	no	\(1\)	\(1\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{2873}{3000}\right)\)	\(e\left(\frac{2647}{3000}\right)\)	\(e\left(\frac{167}{250}\right)\)	\(e\left(\frac{213}{1000}\right)\)	\(e\left(\frac{1169}{1500}\right)\)	\(e\left(\frac{1451}{3000}\right)\)	\(e\left(\frac{1}{750}\right)\)	\(e\left(\frac{339}{1000}\right)\)	\(e\left(\frac{1481}{1500}\right)\)

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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.