LMFDB - Group of Dirichlet characters of modulus 30148

Show commands: PariGP / SageMath

sage: H = DirichletGroup(30148)

pari: g = idealstar(,30148,2)

Character group

sage: G.order() pari: g.no
Order	=	15072
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{7536}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{30148}(15075,\cdot)$, $\chi_{30148}(15081,\cdot)$

First 32 of 15072 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{30148}(1,\cdot)$	30148.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{30148}(3,\cdot)$	30148.bg	1884	yes	$-1$	$1$	$e\left(\frac{689}{942}\right)$	$e\left(\frac{67}{628}\right)$	$e\left(\frac{1313}{1884}\right)$	$e\left(\frac{218}{471}\right)$	$e\left(\frac{1235}{1884}\right)$	$e\left(\frac{595}{942}\right)$	$e\left(\frac{1579}{1884}\right)$	$e\left(\frac{251}{628}\right)$	$e\left(\frac{151}{1884}\right)$	$e\left(\frac{269}{628}\right)$
$\chi_{30148}(5,\cdot)$	30148.bj	2512	no	$-1$	$1$	$e\left(\frac{67}{628}\right)$	$e\left(\frac{1731}{2512}\right)$	$e\left(\frac{2089}{2512}\right)$	$e\left(\frac{67}{314}\right)$	$e\left(\frac{255}{2512}\right)$	$e\left(\frac{311}{1256}\right)$	$e\left(\frac{1999}{2512}\right)$	$e\left(\frac{411}{2512}\right)$	$e\left(\frac{499}{2512}\right)$	$e\left(\frac{2357}{2512}\right)$
$\chi_{30148}(7,\cdot)$	30148.bn	7536	yes	$1$	$1$	$e\left(\frac{1313}{1884}\right)$	$e\left(\frac{2089}{2512}\right)$	$e\left(\frac{3769}{7536}\right)$	$e\left(\frac{371}{942}\right)$	$e\left(\frac{6511}{7536}\right)$	$e\left(\frac{3503}{3768}\right)$	$e\left(\frac{3983}{7536}\right)$	$e\left(\frac{65}{2512}\right)$	$e\left(\frac{851}{7536}\right)$	$e\left(\frac{495}{2512}\right)$
$\chi_{30148}(9,\cdot)$	30148.bd	942	no	$1$	$1$	$e\left(\frac{218}{471}\right)$	$e\left(\frac{67}{314}\right)$	$e\left(\frac{371}{942}\right)$	$e\left(\frac{436}{471}\right)$	$e\left(\frac{293}{942}\right)$	$e\left(\frac{124}{471}\right)$	$e\left(\frac{637}{942}\right)$	$e\left(\frac{251}{314}\right)$	$e\left(\frac{151}{942}\right)$	$e\left(\frac{269}{314}\right)$
$\chi_{30148}(11,\cdot)$	30148.bn	7536	yes	$1$	$1$	$e\left(\frac{1235}{1884}\right)$	$e\left(\frac{255}{2512}\right)$	$e\left(\frac{6511}{7536}\right)$	$e\left(\frac{293}{942}\right)$	$e\left(\frac{6889}{7536}\right)$	$e\left(\frac{329}{3768}\right)$	$e\left(\frac{5705}{7536}\right)$	$e\left(\frac{2455}{2512}\right)$	$e\left(\frac{5669}{7536}\right)$	$e\left(\frac{1305}{2512}\right)$
$\chi_{30148}(13,\cdot)$	30148.bk	3768	no	$1$	$1$	$e\left(\frac{595}{942}\right)$	$e\left(\frac{311}{1256}\right)$	$e\left(\frac{3503}{3768}\right)$	$e\left(\frac{124}{471}\right)$	$e\left(\frac{329}{3768}\right)$	$e\left(\frac{517}{1884}\right)$	$e\left(\frac{3313}{3768}\right)$	$e\left(\frac{359}{1256}\right)$	$e\left(\frac{565}{3768}\right)$	$e\left(\frac{705}{1256}\right)$
$\chi_{30148}(15,\cdot)$	30148.bn	7536	yes	$1$	$1$	$e\left(\frac{1579}{1884}\right)$	$e\left(\frac{1999}{2512}\right)$	$e\left(\frac{3983}{7536}\right)$	$e\left(\frac{637}{942}\right)$	$e\left(\frac{5705}{7536}\right)$	$e\left(\frac{3313}{3768}\right)$	$e\left(\frac{4777}{7536}\right)$	$e\left(\frac{1415}{2512}\right)$	$e\left(\frac{2101}{7536}\right)$	$e\left(\frac{921}{2512}\right)$
$\chi_{30148}(17,\cdot)$	30148.bj	2512	no	$-1$	$1$	$e\left(\frac{251}{628}\right)$	$e\left(\frac{411}{2512}\right)$	$e\left(\frac{65}{2512}\right)$	$e\left(\frac{251}{314}\right)$	$e\left(\frac{2455}{2512}\right)$	$e\left(\frac{359}{1256}\right)$	$e\left(\frac{1415}{2512}\right)$	$e\left(\frac{115}{2512}\right)$	$e\left(\frac{1307}{2512}\right)$	$e\left(\frac{1069}{2512}\right)$
$\chi_{30148}(19,\cdot)$	30148.bn	7536	yes	$1$	$1$	$e\left(\frac{151}{1884}\right)$	$e\left(\frac{499}{2512}\right)$	$e\left(\frac{851}{7536}\right)$	$e\left(\frac{151}{942}\right)$	$e\left(\frac{5669}{7536}\right)$	$e\left(\frac{565}{3768}\right)$	$e\left(\frac{2101}{7536}\right)$	$e\left(\frac{1307}{2512}\right)$	$e\left(\frac{4513}{7536}\right)$	$e\left(\frac{485}{2512}\right)$
$\chi_{30148}(21,\cdot)$	30148.bj	2512	no	$-1$	$1$	$e\left(\frac{269}{628}\right)$	$e\left(\frac{2357}{2512}\right)$	$e\left(\frac{495}{2512}\right)$	$e\left(\frac{269}{314}\right)$	$e\left(\frac{1305}{2512}\right)$	$e\left(\frac{705}{1256}\right)$	$e\left(\frac{921}{2512}\right)$	$e\left(\frac{1069}{2512}\right)$	$e\left(\frac{485}{2512}\right)$	$e\left(\frac{1571}{2512}\right)$
$\chi_{30148}(23,\cdot)$	30148.bl	3768	yes	$-1$	$1$	$e\left(\frac{305}{471}\right)$	$e\left(\frac{869}{1256}\right)$	$e\left(\frac{41}{3768}\right)$	$e\left(\frac{139}{471}\right)$	$e\left(\frac{3191}{3768}\right)$	$e\left(\frac{439}{1884}\right)$	$e\left(\frac{1279}{3768}\right)$	$e\left(\frac{781}{1256}\right)$	$e\left(\frac{979}{3768}\right)$	$e\left(\frac{827}{1256}\right)$
$\chi_{30148}(25,\cdot)$	30148.bf	1256	no	$1$	$1$	$e\left(\frac{67}{314}\right)$	$e\left(\frac{475}{1256}\right)$	$e\left(\frac{833}{1256}\right)$	$e\left(\frac{67}{157}\right)$	$e\left(\frac{255}{1256}\right)$	$e\left(\frac{311}{628}\right)$	$e\left(\frac{743}{1256}\right)$	$e\left(\frac{411}{1256}\right)$	$e\left(\frac{499}{1256}\right)$	$e\left(\frac{1101}{1256}\right)$
$\chi_{30148}(27,\cdot)$	30148.ba	628	yes	$-1$	$1$	$e\left(\frac{61}{314}\right)$	$e\left(\frac{201}{628}\right)$	$e\left(\frac{57}{628}\right)$	$e\left(\frac{61}{157}\right)$	$e\left(\frac{607}{628}\right)$	$e\left(\frac{281}{314}\right)$	$e\left(\frac{323}{628}\right)$	$e\left(\frac{125}{628}\right)$	$e\left(\frac{151}{628}\right)$	$e\left(\frac{179}{628}\right)$
$\chi_{30148}(29,\cdot)$	30148.bm	7536	no	$-1$	$1$	$e\left(\frac{113}{1884}\right)$	$e\left(\frac{2351}{2512}\right)$	$e\left(\frac{2839}{7536}\right)$	$e\left(\frac{113}{942}\right)$	$e\left(\frac{2689}{7536}\right)$	$e\left(\frac{1265}{3768}\right)$	$e\left(\frac{7505}{7536}\right)$	$e\left(\frac{1159}{2512}\right)$	$e\left(\frac{701}{7536}\right)$	$e\left(\frac{1097}{2512}\right)$
$\chi_{30148}(31,\cdot)$	30148.bc	942	yes	$-1$	$1$	$e\left(\frac{731}{942}\right)$	$e\left(\frac{63}{314}\right)$	$e\left(\frac{35}{471}\right)$	$e\left(\frac{260}{471}\right)$	$e\left(\frac{392}{471}\right)$	$e\left(\frac{290}{471}\right)$	$e\left(\frac{460}{471}\right)$	$e\left(\frac{311}{314}\right)$	$e\left(\frac{112}{471}\right)$	$e\left(\frac{267}{314}\right)$
$\chi_{30148}(33,\cdot)$	30148.bj	2512	no	$-1$	$1$	$e\left(\frac{243}{628}\right)$	$e\left(\frac{523}{2512}\right)$	$e\left(\frac{1409}{2512}\right)$	$e\left(\frac{243}{314}\right)$	$e\left(\frac{1431}{2512}\right)$	$e\left(\frac{903}{1256}\right)$	$e\left(\frac{1495}{2512}\right)$	$e\left(\frac{947}{2512}\right)$	$e\left(\frac{2091}{2512}\right)$	$e\left(\frac{2381}{2512}\right)$
$\chi_{30148}(35,\cdot)$	30148.bg	1884	yes	$-1$	$1$	$e\left(\frac{757}{942}\right)$	$e\left(\frac{327}{628}\right)$	$e\left(\frac{625}{1884}\right)$	$e\left(\frac{286}{471}\right)$	$e\left(\frac{1819}{1884}\right)$	$e\left(\frac{167}{942}\right)$	$e\left(\frac{611}{1884}\right)$	$e\left(\frac{119}{628}\right)$	$e\left(\frac{587}{1884}\right)$	$e\left(\frac{85}{628}\right)$
$\chi_{30148}(37,\cdot)$	30148.bh	1884	no	$1$	$1$	$e\left(\frac{43}{471}\right)$	$e\left(\frac{375}{628}\right)$	$e\left(\frac{155}{1884}\right)$	$e\left(\frac{86}{471}\right)$	$e\left(\frac{1265}{1884}\right)$	$e\left(\frac{373}{942}\right)$	$e\left(\frac{1297}{1884}\right)$	$e\left(\frac{27}{628}\right)$	$e\left(\frac{25}{1884}\right)$	$e\left(\frac{109}{628}\right)$
$\chi_{30148}(39,\cdot)$	30148.be	1256	yes	$-1$	$1$	$e\left(\frac{57}{157}\right)$	$e\left(\frac{445}{1256}\right)$	$e\left(\frac{787}{1256}\right)$	$e\left(\frac{114}{157}\right)$	$e\left(\frac{933}{1256}\right)$	$e\left(\frac{569}{628}\right)$	$e\left(\frac{901}{1256}\right)$	$e\left(\frac{861}{1256}\right)$	$e\left(\frac{289}{1256}\right)$	$e\left(\frac{1243}{1256}\right)$
$\chi_{30148}(41,\cdot)$	30148.bj	2512	no	$-1$	$1$	$e\left(\frac{565}{628}\right)$	$e\left(\frac{725}{2512}\right)$	$e\left(\frac{1007}{2512}\right)$	$e\left(\frac{251}{314}\right)$	$e\left(\frac{1513}{2512}\right)$	$e\left(\frac{673}{1256}\right)$	$e\left(\frac{473}{2512}\right)$	$e\left(\frac{429}{2512}\right)$	$e\left(\frac{1621}{2512}\right)$	$e\left(\frac{755}{2512}\right)$
$\chi_{30148}(43,\cdot)$	30148.bn	7536	yes	$1$	$1$	$e\left(\frac{1421}{1884}\right)$	$e\left(\frac{1585}{2512}\right)$	$e\left(\frac{4465}{7536}\right)$	$e\left(\frac{479}{942}\right)$	$e\left(\frac{1495}{7536}\right)$	$e\left(\frac{3695}{3768}\right)$	$e\left(\frac{2903}{7536}\right)$	$e\left(\frac{89}{2512}\right)$	$e\left(\frac{5339}{7536}\right)$	$e\left(\frac{871}{2512}\right)$
$\chi_{30148}(45,\cdot)$	30148.bm	7536	no	$-1$	$1$	$e\left(\frac{1073}{1884}\right)$	$e\left(\frac{2267}{2512}\right)$	$e\left(\frac{1699}{7536}\right)$	$e\left(\frac{131}{942}\right)$	$e\left(\frac{3109}{7536}\right)$	$e\left(\frac{1925}{3768}\right)$	$e\left(\frac{3557}{7536}\right)$	$e\left(\frac{2419}{2512}\right)$	$e\left(\frac{2705}{7536}\right)$	$e\left(\frac{1997}{2512}\right)$
$\chi_{30148}(47,\cdot)$	30148.be	1256	yes	$-1$	$1$	$e\left(\frac{33}{157}\right)$	$e\left(\frac{1117}{1256}\right)$	$e\left(\frac{59}{1256}\right)$	$e\left(\frac{66}{157}\right)$	$e\left(\frac{1069}{1256}\right)$	$e\left(\frac{65}{628}\right)$	$e\left(\frac{125}{1256}\right)$	$e\left(\frac{829}{1256}\right)$	$e\left(\frac{1225}{1256}\right)$	$e\left(\frac{323}{1256}\right)$
$\chi_{30148}(49,\cdot)$	30148.bk	3768	no	$1$	$1$	$e\left(\frac{371}{942}\right)$	$e\left(\frac{833}{1256}\right)$	$e\left(\frac{1}{3768}\right)$	$e\left(\frac{371}{471}\right)$	$e\left(\frac{2743}{3768}\right)$	$e\left(\frac{1619}{1884}\right)$	$e\left(\frac{215}{3768}\right)$	$e\left(\frac{65}{1256}\right)$	$e\left(\frac{851}{3768}\right)$	$e\left(\frac{495}{1256}\right)$
$\chi_{30148}(51,\cdot)$	30148.bn	7536	yes	$1$	$1$	$e\left(\frac{247}{1884}\right)$	$e\left(\frac{679}{2512}\right)$	$e\left(\frac{5447}{7536}\right)$	$e\left(\frac{247}{942}\right)$	$e\left(\frac{4769}{7536}\right)$	$e\left(\frac{3457}{3768}\right)$	$e\left(\frac{3025}{7536}\right)$	$e\left(\frac{1119}{2512}\right)$	$e\left(\frac{4525}{7536}\right)$	$e\left(\frac{2145}{2512}\right)$
$\chi_{30148}(53,\cdot)$	30148.bk	3768	no	$1$	$1$	$e\left(\frac{337}{942}\right)$	$e\left(\frac{259}{1256}\right)$	$e\left(\frac{3515}{3768}\right)$	$e\left(\frac{337}{471}\right)$	$e\left(\frac{3101}{3768}\right)$	$e\left(\frac{1105}{1884}\right)$	$e\left(\frac{2125}{3768}\right)$	$e\left(\frac{1139}{1256}\right)$	$e\left(\frac{3241}{3768}\right)$	$e\left(\frac{365}{1256}\right)$
$\chi_{30148}(55,\cdot)$	30148.bl	3768	yes	$-1$	$1$	$e\left(\frac{359}{471}\right)$	$e\left(\frac{993}{1256}\right)$	$e\left(\frac{2621}{3768}\right)$	$e\left(\frac{247}{471}\right)$	$e\left(\frac{59}{3768}\right)$	$e\left(\frac{631}{1884}\right)$	$e\left(\frac{2083}{3768}\right)$	$e\left(\frac{177}{1256}\right)$	$e\left(\frac{3583}{3768}\right)$	$e\left(\frac{575}{1256}\right)$
$\chi_{30148}(57,\cdot)$	30148.bm	7536	no	$-1$	$1$	$e\left(\frac{1529}{1884}\right)$	$e\left(\frac{767}{2512}\right)$	$e\left(\frac{6103}{7536}\right)$	$e\left(\frac{587}{942}\right)$	$e\left(\frac{3073}{7536}\right)$	$e\left(\frac{2945}{3768}\right)$	$e\left(\frac{881}{7536}\right)$	$e\left(\frac{2311}{2512}\right)$	$e\left(\frac{5117}{7536}\right)$	$e\left(\frac{1561}{2512}\right)$
$\chi_{30148}(59,\cdot)$	30148.bn	7536	yes	$1$	$1$	$e\left(\frac{1549}{1884}\right)$	$e\left(\frac{1197}{2512}\right)$	$e\left(\frac{2429}{7536}\right)$	$e\left(\frac{607}{942}\right)$	$e\left(\frac{923}{7536}\right)$	$e\left(\frac{643}{3768}\right)$	$e\left(\frac{2251}{7536}\right)$	$e\left(\frac{885}{2512}\right)$	$e\left(\frac{5983}{7536}\right)$	$e\left(\frac{363}{2512}\right)$
$\chi_{30148}(61,\cdot)$	30148.y	471	no	$1$	$1$	$e\left(\frac{464}{471}\right)$	$e\left(\frac{139}{157}\right)$	$e\left(\frac{451}{471}\right)$	$e\left(\frac{457}{471}\right)$	$e\left(\frac{247}{471}\right)$	$e\left(\frac{238}{471}\right)$	$e\left(\frac{410}{471}\right)$	$e\left(\frac{113}{157}\right)$	$e\left(\frac{407}{471}\right)$	$e\left(\frac{148}{157}\right)$
$\chi_{30148}(63,\cdot)$	30148.bn	7536	yes	$1$	$1$	$e\left(\frac{301}{1884}\right)$	$e\left(\frac{113}{2512}\right)$	$e\left(\frac{6737}{7536}\right)$	$e\left(\frac{301}{942}\right)$	$e\left(\frac{1319}{7536}\right)$	$e\left(\frac{727}{3768}\right)$	$e\left(\frac{1543}{7536}\right)$	$e\left(\frac{2073}{2512}\right)$	$e\left(\frac{2059}{7536}\right)$	$e\left(\frac{135}{2512}\right)$

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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	$30148$
Structure	\(C_{2}\times C_{7536}\)
Order	$15072$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{30148}(1,\cdot)\)	30148.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{30148}(3,\cdot)\)	30148.bg	1884	yes	\(-1\)	\(1\)	\(e\left(\frac{689}{942}\right)\)	\(e\left(\frac{67}{628}\right)\)	\(e\left(\frac{1313}{1884}\right)\)	\(e\left(\frac{218}{471}\right)\)	\(e\left(\frac{1235}{1884}\right)\)	\(e\left(\frac{595}{942}\right)\)	\(e\left(\frac{1579}{1884}\right)\)	\(e\left(\frac{251}{628}\right)\)	\(e\left(\frac{151}{1884}\right)\)	\(e\left(\frac{269}{628}\right)\)
\(\chi_{30148}(5,\cdot)\)	30148.bj	2512	no	\(-1\)	\(1\)	\(e\left(\frac{67}{628}\right)\)	\(e\left(\frac{1731}{2512}\right)\)	\(e\left(\frac{2089}{2512}\right)\)	\(e\left(\frac{67}{314}\right)\)	\(e\left(\frac{255}{2512}\right)\)	\(e\left(\frac{311}{1256}\right)\)	\(e\left(\frac{1999}{2512}\right)\)	\(e\left(\frac{411}{2512}\right)\)	\(e\left(\frac{499}{2512}\right)\)	\(e\left(\frac{2357}{2512}\right)\)
\(\chi_{30148}(7,\cdot)\)	30148.bn	7536	yes	\(1\)	\(1\)	\(e\left(\frac{1313}{1884}\right)\)	\(e\left(\frac{2089}{2512}\right)\)	\(e\left(\frac{3769}{7536}\right)\)	\(e\left(\frac{371}{942}\right)\)	\(e\left(\frac{6511}{7536}\right)\)	\(e\left(\frac{3503}{3768}\right)\)	\(e\left(\frac{3983}{7536}\right)\)	\(e\left(\frac{65}{2512}\right)\)	\(e\left(\frac{851}{7536}\right)\)	\(e\left(\frac{495}{2512}\right)\)
\(\chi_{30148}(9,\cdot)\)	30148.bd	942	no	\(1\)	\(1\)	\(e\left(\frac{218}{471}\right)\)	\(e\left(\frac{67}{314}\right)\)	\(e\left(\frac{371}{942}\right)\)	\(e\left(\frac{436}{471}\right)\)	\(e\left(\frac{293}{942}\right)\)	\(e\left(\frac{124}{471}\right)\)	\(e\left(\frac{637}{942}\right)\)	\(e\left(\frac{251}{314}\right)\)	\(e\left(\frac{151}{942}\right)\)	\(e\left(\frac{269}{314}\right)\)
\(\chi_{30148}(11,\cdot)\)	30148.bn	7536	yes	\(1\)	\(1\)	\(e\left(\frac{1235}{1884}\right)\)	\(e\left(\frac{255}{2512}\right)\)	\(e\left(\frac{6511}{7536}\right)\)	\(e\left(\frac{293}{942}\right)\)	\(e\left(\frac{6889}{7536}\right)\)	\(e\left(\frac{329}{3768}\right)\)	\(e\left(\frac{5705}{7536}\right)\)	\(e\left(\frac{2455}{2512}\right)\)	\(e\left(\frac{5669}{7536}\right)\)	\(e\left(\frac{1305}{2512}\right)\)
\(\chi_{30148}(13,\cdot)\)	30148.bk	3768	no	\(1\)	\(1\)	\(e\left(\frac{595}{942}\right)\)	\(e\left(\frac{311}{1256}\right)\)	\(e\left(\frac{3503}{3768}\right)\)	\(e\left(\frac{124}{471}\right)\)	\(e\left(\frac{329}{3768}\right)\)	\(e\left(\frac{517}{1884}\right)\)	\(e\left(\frac{3313}{3768}\right)\)	\(e\left(\frac{359}{1256}\right)\)	\(e\left(\frac{565}{3768}\right)\)	\(e\left(\frac{705}{1256}\right)\)
\(\chi_{30148}(15,\cdot)\)	30148.bn	7536	yes	\(1\)	\(1\)	\(e\left(\frac{1579}{1884}\right)\)	\(e\left(\frac{1999}{2512}\right)\)	\(e\left(\frac{3983}{7536}\right)\)	\(e\left(\frac{637}{942}\right)\)	\(e\left(\frac{5705}{7536}\right)\)	\(e\left(\frac{3313}{3768}\right)\)	\(e\left(\frac{4777}{7536}\right)\)	\(e\left(\frac{1415}{2512}\right)\)	\(e\left(\frac{2101}{7536}\right)\)	\(e\left(\frac{921}{2512}\right)\)
\(\chi_{30148}(17,\cdot)\)	30148.bj	2512	no	\(-1\)	\(1\)	\(e\left(\frac{251}{628}\right)\)	\(e\left(\frac{411}{2512}\right)\)	\(e\left(\frac{65}{2512}\right)\)	\(e\left(\frac{251}{314}\right)\)	\(e\left(\frac{2455}{2512}\right)\)	\(e\left(\frac{359}{1256}\right)\)	\(e\left(\frac{1415}{2512}\right)\)	\(e\left(\frac{115}{2512}\right)\)	\(e\left(\frac{1307}{2512}\right)\)	\(e\left(\frac{1069}{2512}\right)\)
\(\chi_{30148}(19,\cdot)\)	30148.bn	7536	yes	\(1\)	\(1\)	\(e\left(\frac{151}{1884}\right)\)	\(e\left(\frac{499}{2512}\right)\)	\(e\left(\frac{851}{7536}\right)\)	\(e\left(\frac{151}{942}\right)\)	\(e\left(\frac{5669}{7536}\right)\)	\(e\left(\frac{565}{3768}\right)\)	\(e\left(\frac{2101}{7536}\right)\)	\(e\left(\frac{1307}{2512}\right)\)	\(e\left(\frac{4513}{7536}\right)\)	\(e\left(\frac{485}{2512}\right)\)
\(\chi_{30148}(21,\cdot)\)	30148.bj	2512	no	\(-1\)	\(1\)	\(e\left(\frac{269}{628}\right)\)	\(e\left(\frac{2357}{2512}\right)\)	\(e\left(\frac{495}{2512}\right)\)	\(e\left(\frac{269}{314}\right)\)	\(e\left(\frac{1305}{2512}\right)\)	\(e\left(\frac{705}{1256}\right)\)	\(e\left(\frac{921}{2512}\right)\)	\(e\left(\frac{1069}{2512}\right)\)	\(e\left(\frac{485}{2512}\right)\)	\(e\left(\frac{1571}{2512}\right)\)
\(\chi_{30148}(23,\cdot)\)	30148.bl	3768	yes	\(-1\)	\(1\)	\(e\left(\frac{305}{471}\right)\)	\(e\left(\frac{869}{1256}\right)\)	\(e\left(\frac{41}{3768}\right)\)	\(e\left(\frac{139}{471}\right)\)	\(e\left(\frac{3191}{3768}\right)\)	\(e\left(\frac{439}{1884}\right)\)	\(e\left(\frac{1279}{3768}\right)\)	\(e\left(\frac{781}{1256}\right)\)	\(e\left(\frac{979}{3768}\right)\)	\(e\left(\frac{827}{1256}\right)\)
\(\chi_{30148}(25,\cdot)\)	30148.bf	1256	no	\(1\)	\(1\)	\(e\left(\frac{67}{314}\right)\)	\(e\left(\frac{475}{1256}\right)\)	\(e\left(\frac{833}{1256}\right)\)	\(e\left(\frac{67}{157}\right)\)	\(e\left(\frac{255}{1256}\right)\)	\(e\left(\frac{311}{628}\right)\)	\(e\left(\frac{743}{1256}\right)\)	\(e\left(\frac{411}{1256}\right)\)	\(e\left(\frac{499}{1256}\right)\)	\(e\left(\frac{1101}{1256}\right)\)
\(\chi_{30148}(27,\cdot)\)	30148.ba	628	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{314}\right)\)	\(e\left(\frac{201}{628}\right)\)	\(e\left(\frac{57}{628}\right)\)	\(e\left(\frac{61}{157}\right)\)	\(e\left(\frac{607}{628}\right)\)	\(e\left(\frac{281}{314}\right)\)	\(e\left(\frac{323}{628}\right)\)	\(e\left(\frac{125}{628}\right)\)	\(e\left(\frac{151}{628}\right)\)	\(e\left(\frac{179}{628}\right)\)
\(\chi_{30148}(29,\cdot)\)	30148.bm	7536	no	\(-1\)	\(1\)	\(e\left(\frac{113}{1884}\right)\)	\(e\left(\frac{2351}{2512}\right)\)	\(e\left(\frac{2839}{7536}\right)\)	\(e\left(\frac{113}{942}\right)\)	\(e\left(\frac{2689}{7536}\right)\)	\(e\left(\frac{1265}{3768}\right)\)	\(e\left(\frac{7505}{7536}\right)\)	\(e\left(\frac{1159}{2512}\right)\)	\(e\left(\frac{701}{7536}\right)\)	\(e\left(\frac{1097}{2512}\right)\)
\(\chi_{30148}(31,\cdot)\)	30148.bc	942	yes	\(-1\)	\(1\)	\(e\left(\frac{731}{942}\right)\)	\(e\left(\frac{63}{314}\right)\)	\(e\left(\frac{35}{471}\right)\)	\(e\left(\frac{260}{471}\right)\)	\(e\left(\frac{392}{471}\right)\)	\(e\left(\frac{290}{471}\right)\)	\(e\left(\frac{460}{471}\right)\)	\(e\left(\frac{311}{314}\right)\)	\(e\left(\frac{112}{471}\right)\)	\(e\left(\frac{267}{314}\right)\)
\(\chi_{30148}(33,\cdot)\)	30148.bj	2512	no	\(-1\)	\(1\)	\(e\left(\frac{243}{628}\right)\)	\(e\left(\frac{523}{2512}\right)\)	\(e\left(\frac{1409}{2512}\right)\)	\(e\left(\frac{243}{314}\right)\)	\(e\left(\frac{1431}{2512}\right)\)	\(e\left(\frac{903}{1256}\right)\)	\(e\left(\frac{1495}{2512}\right)\)	\(e\left(\frac{947}{2512}\right)\)	\(e\left(\frac{2091}{2512}\right)\)	\(e\left(\frac{2381}{2512}\right)\)
\(\chi_{30148}(35,\cdot)\)	30148.bg	1884	yes	\(-1\)	\(1\)	\(e\left(\frac{757}{942}\right)\)	\(e\left(\frac{327}{628}\right)\)	\(e\left(\frac{625}{1884}\right)\)	\(e\left(\frac{286}{471}\right)\)	\(e\left(\frac{1819}{1884}\right)\)	\(e\left(\frac{167}{942}\right)\)	\(e\left(\frac{611}{1884}\right)\)	\(e\left(\frac{119}{628}\right)\)	\(e\left(\frac{587}{1884}\right)\)	\(e\left(\frac{85}{628}\right)\)
\(\chi_{30148}(37,\cdot)\)	30148.bh	1884	no	\(1\)	\(1\)	\(e\left(\frac{43}{471}\right)\)	\(e\left(\frac{375}{628}\right)\)	\(e\left(\frac{155}{1884}\right)\)	\(e\left(\frac{86}{471}\right)\)	\(e\left(\frac{1265}{1884}\right)\)	\(e\left(\frac{373}{942}\right)\)	\(e\left(\frac{1297}{1884}\right)\)	\(e\left(\frac{27}{628}\right)\)	\(e\left(\frac{25}{1884}\right)\)	\(e\left(\frac{109}{628}\right)\)
\(\chi_{30148}(39,\cdot)\)	30148.be	1256	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{157}\right)\)	\(e\left(\frac{445}{1256}\right)\)	\(e\left(\frac{787}{1256}\right)\)	\(e\left(\frac{114}{157}\right)\)	\(e\left(\frac{933}{1256}\right)\)	\(e\left(\frac{569}{628}\right)\)	\(e\left(\frac{901}{1256}\right)\)	\(e\left(\frac{861}{1256}\right)\)	\(e\left(\frac{289}{1256}\right)\)	\(e\left(\frac{1243}{1256}\right)\)
\(\chi_{30148}(41,\cdot)\)	30148.bj	2512	no	\(-1\)	\(1\)	\(e\left(\frac{565}{628}\right)\)	\(e\left(\frac{725}{2512}\right)\)	\(e\left(\frac{1007}{2512}\right)\)	\(e\left(\frac{251}{314}\right)\)	\(e\left(\frac{1513}{2512}\right)\)	\(e\left(\frac{673}{1256}\right)\)	\(e\left(\frac{473}{2512}\right)\)	\(e\left(\frac{429}{2512}\right)\)	\(e\left(\frac{1621}{2512}\right)\)	\(e\left(\frac{755}{2512}\right)\)
\(\chi_{30148}(43,\cdot)\)	30148.bn	7536	yes	\(1\)	\(1\)	\(e\left(\frac{1421}{1884}\right)\)	\(e\left(\frac{1585}{2512}\right)\)	\(e\left(\frac{4465}{7536}\right)\)	\(e\left(\frac{479}{942}\right)\)	\(e\left(\frac{1495}{7536}\right)\)	\(e\left(\frac{3695}{3768}\right)\)	\(e\left(\frac{2903}{7536}\right)\)	\(e\left(\frac{89}{2512}\right)\)	\(e\left(\frac{5339}{7536}\right)\)	\(e\left(\frac{871}{2512}\right)\)
\(\chi_{30148}(45,\cdot)\)	30148.bm	7536	no	\(-1\)	\(1\)	\(e\left(\frac{1073}{1884}\right)\)	\(e\left(\frac{2267}{2512}\right)\)	\(e\left(\frac{1699}{7536}\right)\)	\(e\left(\frac{131}{942}\right)\)	\(e\left(\frac{3109}{7536}\right)\)	\(e\left(\frac{1925}{3768}\right)\)	\(e\left(\frac{3557}{7536}\right)\)	\(e\left(\frac{2419}{2512}\right)\)	\(e\left(\frac{2705}{7536}\right)\)	\(e\left(\frac{1997}{2512}\right)\)
\(\chi_{30148}(47,\cdot)\)	30148.be	1256	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{157}\right)\)	\(e\left(\frac{1117}{1256}\right)\)	\(e\left(\frac{59}{1256}\right)\)	\(e\left(\frac{66}{157}\right)\)	\(e\left(\frac{1069}{1256}\right)\)	\(e\left(\frac{65}{628}\right)\)	\(e\left(\frac{125}{1256}\right)\)	\(e\left(\frac{829}{1256}\right)\)	\(e\left(\frac{1225}{1256}\right)\)	\(e\left(\frac{323}{1256}\right)\)
\(\chi_{30148}(49,\cdot)\)	30148.bk	3768	no	\(1\)	\(1\)	\(e\left(\frac{371}{942}\right)\)	\(e\left(\frac{833}{1256}\right)\)	\(e\left(\frac{1}{3768}\right)\)	\(e\left(\frac{371}{471}\right)\)	\(e\left(\frac{2743}{3768}\right)\)	\(e\left(\frac{1619}{1884}\right)\)	\(e\left(\frac{215}{3768}\right)\)	\(e\left(\frac{65}{1256}\right)\)	\(e\left(\frac{851}{3768}\right)\)	\(e\left(\frac{495}{1256}\right)\)
\(\chi_{30148}(51,\cdot)\)	30148.bn	7536	yes	\(1\)	\(1\)	\(e\left(\frac{247}{1884}\right)\)	\(e\left(\frac{679}{2512}\right)\)	\(e\left(\frac{5447}{7536}\right)\)	\(e\left(\frac{247}{942}\right)\)	\(e\left(\frac{4769}{7536}\right)\)	\(e\left(\frac{3457}{3768}\right)\)	\(e\left(\frac{3025}{7536}\right)\)	\(e\left(\frac{1119}{2512}\right)\)	\(e\left(\frac{4525}{7536}\right)\)	\(e\left(\frac{2145}{2512}\right)\)
\(\chi_{30148}(53,\cdot)\)	30148.bk	3768	no	\(1\)	\(1\)	\(e\left(\frac{337}{942}\right)\)	\(e\left(\frac{259}{1256}\right)\)	\(e\left(\frac{3515}{3768}\right)\)	\(e\left(\frac{337}{471}\right)\)	\(e\left(\frac{3101}{3768}\right)\)	\(e\left(\frac{1105}{1884}\right)\)	\(e\left(\frac{2125}{3768}\right)\)	\(e\left(\frac{1139}{1256}\right)\)	\(e\left(\frac{3241}{3768}\right)\)	\(e\left(\frac{365}{1256}\right)\)
\(\chi_{30148}(55,\cdot)\)	30148.bl	3768	yes	\(-1\)	\(1\)	\(e\left(\frac{359}{471}\right)\)	\(e\left(\frac{993}{1256}\right)\)	\(e\left(\frac{2621}{3768}\right)\)	\(e\left(\frac{247}{471}\right)\)	\(e\left(\frac{59}{3768}\right)\)	\(e\left(\frac{631}{1884}\right)\)	\(e\left(\frac{2083}{3768}\right)\)	\(e\left(\frac{177}{1256}\right)\)	\(e\left(\frac{3583}{3768}\right)\)	\(e\left(\frac{575}{1256}\right)\)
\(\chi_{30148}(57,\cdot)\)	30148.bm	7536	no	\(-1\)	\(1\)	\(e\left(\frac{1529}{1884}\right)\)	\(e\left(\frac{767}{2512}\right)\)	\(e\left(\frac{6103}{7536}\right)\)	\(e\left(\frac{587}{942}\right)\)	\(e\left(\frac{3073}{7536}\right)\)	\(e\left(\frac{2945}{3768}\right)\)	\(e\left(\frac{881}{7536}\right)\)	\(e\left(\frac{2311}{2512}\right)\)	\(e\left(\frac{5117}{7536}\right)\)	\(e\left(\frac{1561}{2512}\right)\)
\(\chi_{30148}(59,\cdot)\)	30148.bn	7536	yes	\(1\)	\(1\)	\(e\left(\frac{1549}{1884}\right)\)	\(e\left(\frac{1197}{2512}\right)\)	\(e\left(\frac{2429}{7536}\right)\)	\(e\left(\frac{607}{942}\right)\)	\(e\left(\frac{923}{7536}\right)\)	\(e\left(\frac{643}{3768}\right)\)	\(e\left(\frac{2251}{7536}\right)\)	\(e\left(\frac{885}{2512}\right)\)	\(e\left(\frac{5983}{7536}\right)\)	\(e\left(\frac{363}{2512}\right)\)
\(\chi_{30148}(61,\cdot)\)	30148.y	471	no	\(1\)	\(1\)	\(e\left(\frac{464}{471}\right)\)	\(e\left(\frac{139}{157}\right)\)	\(e\left(\frac{451}{471}\right)\)	\(e\left(\frac{457}{471}\right)\)	\(e\left(\frac{247}{471}\right)\)	\(e\left(\frac{238}{471}\right)\)	\(e\left(\frac{410}{471}\right)\)	\(e\left(\frac{113}{157}\right)\)	\(e\left(\frac{407}{471}\right)\)	\(e\left(\frac{148}{157}\right)\)
\(\chi_{30148}(63,\cdot)\)	30148.bn	7536	yes	\(1\)	\(1\)	\(e\left(\frac{301}{1884}\right)\)	\(e\left(\frac{113}{2512}\right)\)	\(e\left(\frac{6737}{7536}\right)\)	\(e\left(\frac{301}{942}\right)\)	\(e\left(\frac{1319}{7536}\right)\)	\(e\left(\frac{727}{3768}\right)\)	\(e\left(\frac{1543}{7536}\right)\)	\(e\left(\frac{2073}{2512}\right)\)	\(e\left(\frac{2059}{7536}\right)\)	\(e\left(\frac{135}{2512}\right)\)

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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.