LMFDB - Embedded newform 1400.2.bh.a.249.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1400,2,Mod(249,1400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1400.249"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1400, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.bh (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,0,0,-4,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1400.249
Dual form			1400.2.bh.a.849.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(1.73205 - 2.00000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +6.00000i q^{13} +(4.33013 + 2.50000i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-2.50000 + 0.866025i) q^{21} +(6.06218 - 3.50000i) q^{23} +5.00000i q^{27} -2.00000 q^{29} +(2.50000 - 4.33013i) q^{31} +(2.59808 - 1.50000i) q^{33} +(2.59808 - 1.50000i) q^{37} +(3.00000 - 5.19615i) q^{39} -2.00000 q^{41} +4.00000i q^{43} +(4.33013 - 2.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-2.50000 - 4.33013i) q^{51} +(-0.866025 - 0.500000i) q^{53} -1.00000i q^{57} +(7.50000 - 12.9904i) q^{59} +(2.50000 + 4.33013i) q^{61} +(-5.19615 - 1.00000i) q^{63} +(7.79423 + 4.50000i) q^{67} -7.00000 q^{69} +(6.06218 + 3.50000i) q^{73} +(2.59808 + 7.50000i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -12.0000i q^{83} +(1.73205 + 1.00000i) q^{87} +(3.50000 + 6.06218i) q^{89} +(12.0000 + 10.3923i) q^{91} +(-4.33013 + 2.50000i) q^{93} -2.00000i q^{97} +6.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{9} - 6 q^{11} + 2 q^{19} - 10 q^{21} - 8 q^{29} + 10 q^{31} + 12 q^{39} - 8 q^{41} - 4 q^{49} - 10 q^{51} + 30 q^{59} + 10 q^{61} - 28 q^{69} + 2 q^{79} - 2 q^{81} + 14 q^{89} + 48 q^{91} + 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^9 - 6 * q^11 + 2 * q^19 - 10 * q^21 - 8 * q^29 + 10 * q^31 + 12 * q^39 - 8 * q^41 - 4 * q^49 - 10 * q^51 + 30 * q^59 + 10 * q^61 - 28 * q^69 + 2 * q^79 - 2 * q^81 + 14 * q^89 + 48 * q^91 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i	0.228714	−	0.973494i	$-0.426548\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i	−0.728714	+	0.684819i	$0.759881\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$8$		0			0
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		0			0
$13$			6.00000i			1.66410i	0.554700	+	0.832050i	$0.312833\pi$
$13$			6.00000i			1.66410i	−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.33013	+	2.50000i	1.05021	+	0.606339i	0.922708	−	0.385499i	$-0.125971\pi$
$17$	4.33013	+	2.50000i	1.05021	+	0.606339i	0.127502	+	0.991838i	$0.459304\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	−2.50000	+	0.866025i	−0.545545	+	0.188982i
$22$		0			0
$23$	6.06218	−	3.50000i	1.26405	−	0.729800i	0.290196	−	0.956967i	$-0.406280\pi$
$23$	6.06218	−	3.50000i	1.26405	−	0.729800i	0.973856	+	0.227167i	$0.0729463\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			5.00000i			0.962250i
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	−0.549309	−	0.835619i	$-0.685109\pi$
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	0.998322	+	0.0579057i	$0.0184423\pi$
$32$		0			0
$33$	2.59808	−	1.50000i	0.452267	−	0.261116i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	−0.270998	−	0.962580i	$-0.587354\pi$
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	0.698119	+	0.715981i	$0.254020\pi$
$38$		0			0
$39$	3.00000	−	5.19615i	0.480384	−	0.832050i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.33013	−	2.50000i	0.631614	−	0.364662i	−0.149763	−	0.988722i	$-0.547851\pi$
$47$	4.33013	−	2.50000i	0.631614	−	0.364662i	0.781377	+	0.624059i	$0.214518\pi$
$48$		0			0
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$		0			0
$51$	−2.50000	−	4.33013i	−0.350070	−	0.606339i
$52$		0			0
$53$	−0.866025	−	0.500000i	−0.118958	−	0.0686803i	0.439340	−	0.898321i	$-0.355212\pi$
$53$	−0.866025	−	0.500000i	−0.118958	−	0.0686803i	−0.558298	+	0.829640i	$0.688546\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	1.00000i		−	0.132453i
$58$		0			0
$59$	7.50000	−	12.9904i	0.976417	−	1.69120i	0.301239	−	0.953549i	$-0.402600\pi$
$59$	7.50000	−	12.9904i	0.976417	−	1.69120i	0.675178	−	0.737655i	$-0.264067\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$		0			0
$63$	−5.19615	−	1.00000i	−0.654654	−	0.125988i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	7.79423	+	4.50000i	0.952217	+	0.549762i	0.893769	−	0.448528i	$-0.148052\pi$
$67$	7.79423	+	4.50000i	0.952217	+	0.549762i	0.0584478	+	0.998290i	$0.481385\pi$
$68$		0			0
$69$	−7.00000			−0.842701
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	6.06218	+	3.50000i	0.709524	+	0.409644i	0.810885	−	0.585206i	$-0.198986\pi$
$73$	6.06218	+	3.50000i	0.709524	+	0.409644i	−0.101361	+	0.994850i	$0.532320\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.59808	+	7.50000i	0.296078	+	0.854704i
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.73205	+	1.00000i	0.185695	+	0.107211i
$88$		0			0
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	0.989720	−	0.143022i	$-0.0456819\pi$
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	−0.618720	+	0.785611i	$0.712349\pi$
$90$		0			0
$91$	12.0000	+	10.3923i	1.25794	+	1.08941i
$92$		0			0
$93$	−4.33013	+	2.50000i	−0.449013	+	0.259238i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$		0			0
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$		0			0
$103$	12.9904	−	7.50000i	1.27998	−	0.738997i	0.303136	−	0.952947i	$-0.401966\pi$
$103$	12.9904	−	7.50000i	1.27998	−	0.738997i	0.976845	+	0.213950i	$0.0686331\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.79423	−	4.50000i	0.753497	−	0.435031i	−0.0734594	−	0.997298i	$-0.523404\pi$
$107$	7.79423	−	4.50000i	0.753497	−	0.435031i	0.826956	+	0.562267i	$0.190071\pi$
$108$		0			0
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	−0.960558	−	0.278078i	$-0.910303\pi$
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	0.721102	+	0.692829i	$0.243636\pi$
$110$		0			0
$111$	−3.00000			−0.284747
$112$		0			0
$113$			18.0000i			1.69330i	0.532152	+	0.846649i	$0.321383\pi$
$113$			18.0000i			1.69330i	−0.532152	+	0.846649i	$0.678617\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	10.3923	−	6.00000i	0.960769	−	0.554700i
$118$		0			0
$119$	12.5000	−	4.33013i	1.14587	−	0.396942i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	1.73205	+	1.00000i	0.156174	+	0.0901670i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$		0			0
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$		0			0
$131$	−2.50000	−	4.33013i	−0.218426	−	0.378325i	0.735901	−	0.677089i	$-0.236759\pi$
$131$	−2.50000	−	4.33013i	−0.218426	−	0.378325i	−0.954327	+	0.298764i	$0.903426\pi$
$132$		0			0
$133$	2.59808	+	0.500000i	0.225282	+	0.0433555i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.52628	−	5.50000i	−0.813885	−	0.469897i	0.0344182	−	0.999408i	$-0.489042\pi$
$137$	−9.52628	−	5.50000i	−0.813885	−	0.469897i	−0.848303	+	0.529511i	$0.822376\pi$
$138$		0			0
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$		0			0
$141$	−5.00000			−0.421076
$142$		0			0
$143$	−15.5885	−	9.00000i	−1.30357	−	0.752618i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−2.59808	+	6.50000i	−0.214286	+	0.536111i
$148$		0			0
$149$	−8.50000	−	14.7224i	−0.696347	−	1.20611i	−0.969724	−	0.244202i	$-0.921474\pi$
$149$	−8.50000	−	14.7224i	−0.696347	−	1.20611i	0.273377	−	0.961907i	$-0.411859\pi$
$150$		0			0
$151$	2.50000	−	4.33013i	0.203447	−	0.352381i	−0.746190	−	0.665733i	$-0.768119\pi$
$151$	2.50000	−	4.33013i	0.203447	−	0.352381i	0.949637	+	0.313353i	$0.101452\pi$
$152$		0			0
$153$		−	10.0000i		−	0.808452i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7.79423	+	4.50000i	0.622047	+	0.359139i	0.777666	−	0.628678i	$-0.216404\pi$
$157$	7.79423	+	4.50000i	0.622047	+	0.359139i	−0.155618	+	0.987817i	$0.549737\pi$
$158$		0			0
$159$	0.500000	+	0.866025i	0.0396526	+	0.0686803i
$160$		0			0
$161$	3.50000	−	18.1865i	0.275839	−	1.43330i
$162$		0			0
$163$	−11.2583	+	6.50000i	−0.881820	+	0.509119i	−0.871258	−	0.490825i	$-0.836695\pi$
$163$	−11.2583	+	6.50000i	−0.881820	+	0.509119i	−0.0105623	+	0.999944i	$0.503362\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	12.0000i		−	0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$		−	12.0000i		−	0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$		0			0
$169$	−23.0000			−1.76923
$170$		0			0
$171$	1.00000	−	1.73205i	0.0764719	−	0.132453i
$172$		0			0
$173$	11.2583	−	6.50000i	0.855955	−	0.494186i	−0.00670064	−	0.999978i	$-0.502133\pi$
$173$	11.2583	−	6.50000i	0.855955	−	0.494186i	0.862656	+	0.505792i	$0.168800\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−12.9904	+	7.50000i	−0.976417	+	0.563735i
$178$		0			0
$179$	−6.50000	+	11.2583i	−0.485833	+	0.841487i	−0.999867	−	0.0162823i	$-0.994817\pi$
$179$	−6.50000	+	11.2583i	−0.485833	+	0.841487i	0.514035	+	0.857769i	$0.328150\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$		−	5.00000i		−	0.369611i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−12.9904	+	7.50000i	−0.949951	+	0.548454i
$188$		0			0
$189$	10.0000	+	8.66025i	0.727393	+	0.629941i
$190$		0			0
$191$	5.50000	+	9.52628i	0.397966	+	0.689297i	0.993475	−	0.114051i	$-0.0363829\pi$
$191$	5.50000	+	9.52628i	0.397966	+	0.689297i	−0.595509	+	0.803349i	$0.703050\pi$
$192$		0			0
$193$	2.59808	+	1.50000i	0.187014	+	0.107972i	0.590584	−	0.806976i	$-0.298898\pi$
$193$	2.59808	+	1.50000i	0.187014	+	0.107972i	−0.403570	+	0.914949i	$0.632231\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	6.00000i		−	0.427482i	−0.976890	−	0.213741i	$-0.931435\pi$
$197$		−	6.00000i		−	0.427482i	0.976890	−	0.213741i	$-0.0685649\pi$
$198$		0			0
$199$	−6.50000	+	11.2583i	−0.460773	+	0.798082i	−0.999000	−	0.0447181i	$-0.985761\pi$
$199$	−6.50000	+	11.2583i	−0.460773	+	0.798082i	0.538227	+	0.842800i	$0.319094\pi$
$200$		0			0
$201$	−4.50000	−	7.79423i	−0.317406	−	0.549762i
$202$		0			0
$203$	−3.46410	+	4.00000i	−0.243132	+	0.280745i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−12.1244	−	7.00000i	−0.842701	−	0.486534i
$208$		0			0
$209$	−3.00000			−0.207514
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−4.33013	−	12.5000i	−0.293948	−	0.848555i
$218$		0			0
$219$	−3.50000	−	6.06218i	−0.236508	−	0.409644i
$220$		0			0
$221$	−15.0000	+	25.9808i	−1.00901	+	1.74766i
$222$		0			0
$223$			24.0000i			1.60716i	0.595198	+	0.803579i	$0.297074\pi$
$223$			24.0000i			1.60716i	−0.595198	+	0.803579i	$0.702926\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.52628	−	5.50000i	−0.632281	−	0.365048i	0.149354	−	0.988784i	$-0.452281\pi$
$227$	−9.52628	−	5.50000i	−0.632281	−	0.365048i	−0.781635	+	0.623736i	$0.785614\pi$
$228$		0			0
$229$	11.5000	+	19.9186i	0.759941	+	1.31626i	0.942880	+	0.333133i	$0.108106\pi$
$229$	11.5000	+	19.9186i	0.759941	+	1.31626i	−0.182939	+	0.983124i	$0.558561\pi$
$230$		0			0
$231$	1.50000	−	7.79423i	0.0986928	−	0.512823i
$232$		0			0
$233$	−9.52628	+	5.50000i	−0.624087	+	0.360317i	−0.778459	−	0.627696i	$-0.783998\pi$
$233$	−9.52628	+	5.50000i	−0.624087	+	0.360317i	0.154371	+	0.988013i	$0.450665\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	1.00000i		−	0.0649570i
$238$		0			0
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$		0			0
$241$	8.50000	−	14.7224i	0.547533	−	0.948355i	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	8.50000	−	14.7224i	0.547533	−	0.948355i	0.998443	−	0.0557856i	$-0.0177663\pi$
$242$		0			0
$243$	13.8564	−	8.00000i	0.888889	−	0.513200i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.19615	+	3.00000i	−0.330623	+	0.190885i
$248$		0			0
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$	16.0000			1.00991			0.504956	−	0.863145i	$-0.331509\pi$
$251$	16.0000			1.00991			0.504956	+	0.863145i	$0.331509\pi$
$252$		0			0
$253$			21.0000i			1.32026i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−18.1865	+	10.5000i	−1.13444	+	0.654972i	−0.945049	−	0.326929i	$-0.893986\pi$
$257$	−18.1865	+	10.5000i	−1.13444	+	0.654972i	−0.189396	+	0.981901i	$0.560653\pi$
$258$		0			0
$259$	1.50000	−	7.79423i	0.0932055	−	0.484310i
$260$		0			0
$261$	2.00000	+	3.46410i	0.123797	+	0.214423i
$262$		0			0
$263$	−7.79423	−	4.50000i	−0.480613	−	0.277482i	0.240059	−	0.970758i	$-0.422833\pi$
$263$	−7.79423	−	4.50000i	−0.480613	−	0.277482i	−0.720672	+	0.693276i	$0.756167\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	7.00000i		−	0.428393i
$268$		0			0
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	−0.969976	−	0.243201i	$-0.921803\pi$
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	0.695606	+	0.718423i	$0.255136\pi$
$270$		0			0
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	0.952531	−	0.304443i	$-0.0984703\pi$
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	−0.739921	+	0.672694i	$0.765137\pi$
$272$		0			0
$273$	−5.19615	−	15.0000i	−0.314485	−	0.907841i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	14.7224	+	8.50000i	0.884585	+	0.510716i	0.872167	−	0.489207i	$-0.162714\pi$
$277$	14.7224	+	8.50000i	0.884585	+	0.510716i	0.0124177	+	0.999923i	$0.496047\pi$
$278$		0			0
$279$	−10.0000			−0.598684
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	−11.2583	−	6.50000i	−0.669238	−	0.386385i	0.126550	−	0.991960i	$-0.459610\pi$
$283$	−11.2583	−	6.50000i	−0.669238	−	0.386385i	−0.795788	+	0.605575i	$0.792943\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.46410	+	4.00000i	−0.204479	+	0.236113i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−1.00000	+	1.73205i	−0.0586210	+	0.101535i
$292$		0			0
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−12.9904	−	7.50000i	−0.753778	−	0.435194i
$298$		0			0
$299$	21.0000	+	36.3731i	1.21446	+	2.10351i
$300$		0			0
$301$	8.00000	+	6.92820i	0.461112	+	0.399335i
$302$		0			0
$303$	2.59808	−	1.50000i	0.149256	−	0.0861727i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			4.00000i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$			4.00000i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$		0			0
$309$	−15.0000			−0.853320
$310$		0			0
$311$	−7.50000	+	12.9904i	−0.425286	+	0.736617i	−0.996447	−	0.0842210i	$-0.973160\pi$
$311$	−7.50000	+	12.9904i	−0.425286	+	0.736617i	0.571161	+	0.820838i	$0.306493\pi$
$312$		0			0
$313$	0.866025	−	0.500000i	0.0489506	−	0.0282617i	−0.475325	−	0.879810i	$-0.657669\pi$
$313$	0.866025	−	0.500000i	0.0489506	−	0.0282617i	0.524276	+	0.851549i	$0.324336\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.59808	−	1.50000i	0.145922	−	0.0842484i	−0.425261	−	0.905071i	$-0.639818\pi$
$317$	2.59808	−	1.50000i	0.145922	−	0.0842484i	0.571184	+	0.820822i	$0.306484\pi$
$318$		0			0
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$		0			0
$321$	−9.00000			−0.502331
$322$		0			0
$323$			5.00000i			0.278207i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	4.33013	−	2.50000i	0.239457	−	0.138250i
$328$		0			0
$329$	2.50000	−	12.9904i	0.137829	−	0.716183i
$330$		0			0
$331$	−14.5000	−	25.1147i	−0.796992	−	1.38043i	−0.921567	−	0.388221i	$-0.873090\pi$
$331$	−14.5000	−	25.1147i	−0.796992	−	1.38043i	0.124574	−	0.992210i	$-0.460243\pi$
$332$		0			0
$333$	−5.19615	−	3.00000i	−0.284747	−	0.164399i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	10.0000i		−	0.544735i	−0.962193	−	0.272367i	$-0.912193\pi$
$337$		−	10.0000i		−	0.544735i	0.962193	−	0.272367i	$-0.0878066\pi$
$338$		0			0
$339$	9.00000	−	15.5885i	0.488813	−	0.846649i
$340$		0			0
$341$	7.50000	+	12.9904i	0.406148	+	0.703469i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.9904	−	7.50000i	−0.697360	−	0.402621i	0.109003	−	0.994041i	$-0.465234\pi$
$347$	−12.9904	−	7.50000i	−0.697360	−	0.402621i	−0.806363	+	0.591420i	$0.798567\pi$
$348$		0			0
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	−30.0000			−1.60128
$352$		0			0
$353$	2.59808	+	1.50000i	0.138282	+	0.0798369i	0.567545	−	0.823343i	$-0.307893\pi$
$353$	2.59808	+	1.50000i	0.138282	+	0.0798369i	−0.429263	+	0.903179i	$0.641227\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−12.9904	−	2.50000i	−0.687524	−	0.132314i
$358$		0			0
$359$	10.5000	+	18.1865i	0.554169	+	0.959849i	0.997968	+	0.0637221i	$0.0202971\pi$
$359$	10.5000	+	18.1865i	0.554169	+	0.959849i	−0.443799	+	0.896126i	$0.646370\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$		−	2.00000i		−	0.104973i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−19.9186	−	11.5000i	−1.03974	−	0.600295i	−0.119982	−	0.992776i	$-0.538284\pi$
$367$	−19.9186	−	11.5000i	−1.03974	−	0.600295i	−0.919760	+	0.392481i	$0.871617\pi$
$368$		0			0
$369$	2.00000	+	3.46410i	0.104116	+	0.180334i
$370$		0			0
$371$	−2.50000	+	0.866025i	−0.129794	+	0.0449618i
$372$		0			0
$373$	−9.52628	+	5.50000i	−0.493252	+	0.284779i	−0.725923	−	0.687776i	$-0.758587\pi$
$373$	−9.52628	+	5.50000i	−0.493252	+	0.284779i	0.232671	+	0.972556i	$0.425254\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	12.0000i		−	0.618031i
$378$		0			0
$379$	−24.0000			−1.23280			−0.616399	−	0.787434i	$-0.711409\pi$
$379$	−24.0000			−1.23280			−0.616399	+	0.787434i	$0.711409\pi$
$380$		0			0
$381$	4.00000	−	6.92820i	0.204926	−	0.354943i
$382$		0			0
$383$	2.59808	−	1.50000i	0.132755	−	0.0766464i	−0.432151	−	0.901801i	$-0.642245\pi$
$383$	2.59808	−	1.50000i	0.132755	−	0.0766464i	0.564907	+	0.825155i	$0.308912\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.92820	−	4.00000i	0.352180	−	0.203331i
$388$		0			0
$389$	−14.5000	+	25.1147i	−0.735179	+	1.27337i	0.219465	+	0.975620i	$0.429569\pi$
$389$	−14.5000	+	25.1147i	−0.735179	+	1.27337i	−0.954645	+	0.297747i	$0.903765\pi$
$390$		0			0
$391$	35.0000			1.77003
$392$		0			0
$393$			5.00000i			0.252217i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−14.7224	+	8.50000i	−0.738898	+	0.426603i	−0.821668	−	0.569966i	$-0.806956\pi$
$397$	−14.7224	+	8.50000i	−0.738898	+	0.426603i	0.0827707	+	0.996569i	$0.473623\pi$
$398$		0			0
$399$	−2.00000	−	1.73205i	−0.100125	−	0.0867110i
$400$		0			0
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	−0.976714	−	0.214544i	$-0.931173\pi$
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	0.302556	−	0.953131i	$-0.402160\pi$
$402$		0			0
$403$	25.9808	+	15.0000i	1.29419	+	0.747203i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			9.00000i			0.446113i
$408$		0			0
$409$	13.5000	−	23.3827i	0.667532	−	1.15620i	−0.311060	−	0.950390i	$-0.600684\pi$
$409$	13.5000	−	23.3827i	0.667532	−	1.15620i	0.978592	−	0.205809i	$-0.0659826\pi$
$410$		0			0
$411$	5.50000	+	9.52628i	0.271295	+	0.469897i
$412$		0			0
$413$	−12.9904	−	37.5000i	−0.639215	−	1.84525i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−10.3923	−	6.00000i	−0.508913	−	0.293821i
$418$		0			0
$419$	−20.0000			−0.977064			−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000			−0.977064			−0.488532	+	0.872546i	$0.662467\pi$
$420$		0			0
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$		0			0
$423$	−8.66025	−	5.00000i	−0.421076	−	0.243108i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	12.9904	+	2.50000i	0.628649	+	0.120983i
$428$		0			0
$429$	9.00000	+	15.5885i	0.434524	+	0.752618i
$430$		0			0
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	−0.899888	−	0.436121i	$-0.856352\pi$
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	0.827636	+	0.561266i	$0.189685\pi$
$432$		0			0
$433$			2.00000i			0.0961139i	0.998845	+	0.0480569i	$0.0153029\pi$
$433$			2.00000i			0.0961139i	−0.998845	+	0.0480569i	$0.984697\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.06218	+	3.50000i	0.289993	+	0.167428i
$438$		0			0
$439$	10.5000	+	18.1865i	0.501138	+	0.867996i	0.999999	+	0.00131415i	$0.000418308\pi$
$439$	10.5000	+	18.1865i	0.501138	+	0.867996i	−0.498861	+	0.866682i	$0.666248\pi$
$440$		0			0
$441$	−11.0000	+	8.66025i	−0.523810	+	0.412393i
$442$		0			0
$443$	26.8468	−	15.5000i	1.27553	−	0.736427i	0.299506	−	0.954094i	$-0.403178\pi$
$443$	26.8468	−	15.5000i	1.27553	−	0.736427i	0.976023	+	0.217667i	$0.0698447\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			17.0000i			0.804072i
$448$		0			0
$449$	26.0000			1.22702			0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000			1.22702			0.613508	+	0.789689i	$0.289758\pi$
$450$		0			0
$451$	3.00000	−	5.19615i	0.141264	−	0.244677i
$452$		0			0
$453$	−4.33013	+	2.50000i	−0.203447	+	0.117460i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14.7224	+	8.50000i	−0.688686	+	0.397613i	−0.803120	−	0.595818i	$-0.796828\pi$
$457$	−14.7224	+	8.50000i	−0.688686	+	0.397613i	0.114433	+	0.993431i	$0.463495\pi$
$458$		0			0
$459$	−12.5000	+	21.6506i	−0.583450	+	1.01057i
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.59808	+	1.50000i	−0.120225	+	0.0694117i	−0.558906	−	0.829231i	$-0.688779\pi$
$467$	−2.59808	+	1.50000i	−0.120225	+	0.0694117i	0.438682	+	0.898642i	$0.355446\pi$
$468$		0			0
$469$	22.5000	−	7.79423i	1.03895	−	0.359904i
$470$		0			0
$471$	−4.50000	−	7.79423i	−0.207349	−	0.359139i
$472$		0			0
$473$	−10.3923	−	6.00000i	−0.477839	−	0.275880i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			2.00000i			0.0915737i
$478$		0			0
$479$	15.5000	−	26.8468i	0.708213	−	1.22666i	−0.257306	−	0.966330i	$-0.582835\pi$
$479$	15.5000	−	26.8468i	0.708213	−	1.22666i	0.965519	−	0.260331i	$-0.0838317\pi$
$480$		0			0
$481$	9.00000	+	15.5885i	0.410365	+	0.710772i
$482$		0			0
$483$	−12.1244	+	14.0000i	−0.551677	+	0.637022i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−6.06218	−	3.50000i	−0.274703	−	0.158600i	0.356320	−	0.934364i	$-0.384031\pi$
$487$	−6.06218	−	3.50000i	−0.274703	−	0.158600i	−0.631023	+	0.775764i	$0.717365\pi$
$488$		0			0
$489$	13.0000			0.587880
$490$		0			0
$491$	−24.0000			−1.08310			−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000			−1.08310			−0.541552	+	0.840667i	$0.682163\pi$
$492$		0			0
$493$	−8.66025	−	5.00000i	−0.390038	−	0.225189i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−17.5000	−	30.3109i	−0.783408	−	1.35690i	−0.929946	−	0.367697i	$-0.880146\pi$
$499$	−17.5000	−	30.3109i	−0.783408	−	1.35690i	0.146538	−	0.989205i	$-0.453187\pi$
$500$		0			0
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$		0			0
$503$			32.0000i			1.42681i	0.700752	+	0.713405i	$0.252848\pi$
$503$			32.0000i			1.42681i	−0.700752	+	0.713405i	$0.747152\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	19.9186	+	11.5000i	0.884615	+	0.510733i
$508$		0			0
$509$	−4.50000	−	7.79423i	−0.199459	−	0.345473i	0.748894	−	0.662690i	$-0.230585\pi$
$509$	−4.50000	−	7.79423i	−0.199459	−	0.345473i	−0.948353	+	0.317217i	$0.897252\pi$
$510$		0			0
$511$	17.5000	−	6.06218i	0.774154	−	0.268175i
$512$		0			0
$513$	−4.33013	+	2.50000i	−0.191180	+	0.110378i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			15.0000i			0.659699i
$518$		0			0
$519$	−13.0000			−0.570637
$520$		0			0
$521$	16.5000	−	28.5788i	0.722878	−	1.25206i	−0.236963	−	0.971519i	$-0.576152\pi$
$521$	16.5000	−	28.5788i	0.722878	−	1.25206i	0.959841	−	0.280543i	$-0.0905145\pi$
$522$		0			0
$523$	6.06218	−	3.50000i	0.265081	−	0.153044i	−0.361569	−	0.932345i	$-0.617759\pi$
$523$	6.06218	−	3.50000i	0.265081	−	0.153044i	0.626650	+	0.779301i	$0.284426\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	21.6506	−	12.5000i	0.943116	−	0.544509i
$528$		0			0
$529$	13.0000	−	22.5167i	0.565217	−	0.978985i
$530$		0			0
$531$	−30.0000			−1.30189
$532$		0			0
$533$		−	12.0000i		−	0.519778i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	11.2583	−	6.50000i	0.485833	−	0.280496i
$538$		0			0
$539$	19.5000	+	7.79423i	0.839924	+	0.335721i
$540$		0			0
$541$	20.5000	+	35.5070i	0.881364	+	1.52657i	0.849825	+	0.527064i	$0.176707\pi$
$541$	20.5000	+	35.5070i	0.881364	+	1.52657i	0.0315385	+	0.999503i	$0.489959\pi$
$542$		0			0
$543$	8.66025	+	5.00000i	0.371647	+	0.214571i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$		0			0
$549$	5.00000	−	8.66025i	0.213395	−	0.369611i
$550$		0			0
$551$	−1.00000	−	1.73205i	−0.0426014	−	0.0737878i
$552$		0			0
$553$	2.59808	+	0.500000i	0.110481	+	0.0212622i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.33013	+	2.50000i	0.183473	+	0.105928i	0.588924	−	0.808189i	$-0.299552\pi$
$557$	4.33013	+	2.50000i	0.183473	+	0.105928i	−0.405450	+	0.914117i	$0.632885\pi$
$558$		0			0
$559$	−24.0000			−1.01509
$560$		0			0
$561$	15.0000			0.633300
$562$		0			0
$563$	−35.5070	−	20.5000i	−1.49644	−	0.863972i	−0.496452	−	0.868064i	$-0.665364\pi$
$563$	−35.5070	−	20.5000i	−1.49644	−	0.863972i	−0.999992	+	0.00409232i	$0.998697\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.866025	+	2.50000i	0.0363696	+	0.104990i
$568$		0			0
$569$	−16.5000	−	28.5788i	−0.691716	−	1.19809i	−0.971275	−	0.237959i	$-0.923522\pi$
$569$	−16.5000	−	28.5788i	−0.691716	−	1.19809i	0.279559	−	0.960128i	$-0.409812\pi$
$570$		0			0
$571$	6.50000	−	11.2583i	0.272017	−	0.471146i	−0.697362	−	0.716720i	$-0.745643\pi$
$571$	6.50000	−	11.2583i	0.272017	−	0.471146i	0.969378	+	0.245573i	$0.0789761\pi$
$572$		0			0
$573$		−	11.0000i		−	0.459532i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	28.5788	+	16.5000i	1.18975	+	0.686904i	0.958250	−	0.285930i	$-0.0923026\pi$
$577$	28.5788	+	16.5000i	1.18975	+	0.686904i	0.231502	+	0.972834i	$0.425636\pi$
$578$		0			0
$579$	−1.50000	−	2.59808i	−0.0623379	−	0.107972i
$580$		0			0
$581$	−24.0000	−	20.7846i	−0.995688	−	0.862291i
$582$		0			0
$583$	2.59808	−	1.50000i	0.107601	−	0.0621237i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	20.0000i		−	0.825488i	−0.910847	−	0.412744i	$-0.864570\pi$
$587$		−	20.0000i		−	0.825488i	0.910847	−	0.412744i	$-0.135430\pi$
$588$		0			0
$589$	5.00000			0.206021
$590$		0			0
$591$	−3.00000	+	5.19615i	−0.123404	+	0.213741i
$592$		0			0
$593$	38.9711	−	22.5000i	1.60035	−	0.923964i	0.608937	−	0.793219i	$-0.291596\pi$
$593$	38.9711	−	22.5000i	1.60035	−	0.923964i	0.991416	−	0.130746i	$-0.0417372\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	11.2583	−	6.50000i	0.460773	−	0.266027i
$598$		0			0
$599$	−8.50000	+	14.7224i	−0.347301	+	0.601542i	−0.985769	−	0.168106i	$-0.946235\pi$
$599$	−8.50000	+	14.7224i	−0.347301	+	0.601542i	0.638468	+	0.769648i	$0.279568\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$		0			0
$603$		−	18.0000i		−	0.733017i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	11.2583	−	6.50000i	0.456962	−	0.263827i	−0.253804	−	0.967256i	$-0.581682\pi$
$607$	11.2583	−	6.50000i	0.456962	−	0.263827i	0.710766	+	0.703429i	$0.248349\pi$
$608$		0			0
$609$	5.00000	−	1.73205i	0.202610	−	0.0701862i
$610$		0			0
$611$	15.0000	+	25.9808i	0.606835	+	1.05107i
$612$		0			0
$613$	37.2391	+	21.5000i	1.50407	+	0.868377i	0.999989	+	0.00472215i	$0.00150311\pi$
$613$	37.2391	+	21.5000i	1.50407	+	0.868377i	0.504084	+	0.863655i	$0.331830\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			30.0000i			1.20775i	0.797077	+	0.603877i	$0.206378\pi$
$617$			30.0000i			1.20775i	−0.797077	+	0.603877i	$0.793622\pi$
$618$		0			0
$619$	−4.50000	+	7.79423i	−0.180870	+	0.313276i	−0.942177	−	0.335115i	$-0.891225\pi$
$619$	−4.50000	+	7.79423i	−0.180870	+	0.313276i	0.761307	+	0.648392i	$0.224558\pi$
$620$		0			0
$621$	17.5000	+	30.3109i	0.702251	+	1.21633i
$622$		0			0
$623$	18.1865	+	3.50000i	0.728628	+	0.140225i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	2.59808	+	1.50000i	0.103757	+	0.0599042i
$628$		0			0
$629$	15.0000			0.598089
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$	3.46410	+	2.00000i	0.137686	+	0.0794929i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	41.5692	−	6.00000i	1.64703	−	0.237729i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.50000	−	14.7224i	0.335730	−	0.581501i	−0.647895	−	0.761730i	$-0.724350\pi$
$641$	8.50000	−	14.7224i	0.335730	−	0.581501i	0.983625	+	0.180229i	$0.0576838\pi$
$642$		0			0
$643$			44.0000i			1.73519i	0.497271	+	0.867595i	$0.334335\pi$
$643$			44.0000i			1.73519i	−0.497271	+	0.867595i	$0.665665\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.9904	−	7.50000i	−0.510705	−	0.294855i	0.222419	−	0.974951i	$-0.428605\pi$
$647$	−12.9904	−	7.50000i	−0.510705	−	0.294855i	−0.733123	+	0.680096i	$0.761938\pi$
$648$		0			0
$649$	22.5000	+	38.9711i	0.883202	+	1.52975i
$650$		0			0
$651$	−2.50000	+	12.9904i	−0.0979827	+	0.509133i
$652$		0			0
$653$	−30.3109	+	17.5000i	−1.18616	+	0.684828i	−0.957431	−	0.288663i	$-0.906789\pi$
$653$	−30.3109	+	17.5000i	−1.18616	+	0.684828i	−0.228726	+	0.973491i	$0.573456\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	14.0000i		−	0.546192i
$658$		0			0
$659$	−44.0000			−1.71400			−0.856998	−	0.515319i	$-0.827673\pi$
$659$	−44.0000			−1.71400			−0.856998	+	0.515319i	$0.827673\pi$
$660$		0			0
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	−0.998209	−	0.0598209i	$-0.980947\pi$
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	0.550911	+	0.834564i	$0.314280\pi$
$662$		0			0
$663$	25.9808	−	15.0000i	1.00901	−	0.582552i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−12.1244	+	7.00000i	−0.469457	+	0.271041i
$668$		0			0
$669$	12.0000	−	20.7846i	0.463947	−	0.803579i
$670$		0			0
$671$	−15.0000			−0.579069
$672$		0			0
$673$			26.0000i			1.00223i	0.865382	+	0.501113i	$0.167076\pi$
$673$			26.0000i			1.00223i	−0.865382	+	0.501113i	$0.832924\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	33.7750	−	19.5000i	1.29808	−	0.749446i	0.318006	−	0.948089i	$-0.396987\pi$
$677$	33.7750	−	19.5000i	1.29808	−	0.749446i	0.980072	+	0.198643i	$0.0636533\pi$
$678$		0			0
$679$	−4.00000	−	3.46410i	−0.153506	−	0.132940i
$680$		0			0
$681$	5.50000	+	9.52628i	0.210760	+	0.365048i
$682$		0			0
$683$	23.3827	+	13.5000i	0.894714	+	0.516563i	0.875481	−	0.483252i	$-0.160544\pi$
$683$	23.3827	+	13.5000i	0.894714	+	0.516563i	0.0192323	+	0.999815i	$0.493878\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	23.0000i		−	0.877505i
$688$		0			0
$689$	3.00000	−	5.19615i	0.114291	−	0.197958i
$690$		0			0
$691$	−2.50000	−	4.33013i	−0.0951045	−	0.164726i	0.814548	−	0.580097i	$-0.196985\pi$
$691$	−2.50000	−	4.33013i	−0.0951045	−	0.164726i	−0.909652	+	0.415371i	$0.863652\pi$
$692$		0			0
$693$	10.3923	−	12.0000i	0.394771	−	0.455842i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−8.66025	−	5.00000i	−0.328031	−	0.189389i
$698$		0			0
$699$	11.0000			0.416058
$700$		0			0
$701$	−50.0000			−1.88847			−0.944237	−	0.329267i	$-0.893198\pi$
$701$	−50.0000			−1.88847			−0.944237	+	0.329267i	$0.893198\pi$
$702$		0			0
$703$	2.59808	+	1.50000i	0.0979883	+	0.0565736i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.59808	+	7.50000i	0.0977107	+	0.282067i
$708$		0			0
$709$	−14.5000	−	25.1147i	−0.544559	−	0.943204i	−0.998635	−	0.0522406i	$-0.983364\pi$
$709$	−14.5000	−	25.1147i	−0.544559	−	0.943204i	0.454076	−	0.890963i	$-0.349970\pi$
$710$		0			0
$711$	1.00000	−	1.73205i	0.0375029	−	0.0649570i
$712$		0			0
$713$		−	35.0000i		−	1.31076i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	17.3205	+	10.0000i	0.646846	+	0.373457i
$718$		0			0
$719$	−19.5000	−	33.7750i	−0.727227	−	1.25959i	−0.958051	−	0.286599i	$-0.907475\pi$
$719$	−19.5000	−	33.7750i	−0.727227	−	1.25959i	0.230823	−	0.972996i	$-0.425858\pi$
$720$		0			0
$721$	7.50000	−	38.9711i	0.279315	−	1.45136i
$722$		0			0
$723$	−14.7224	+	8.50000i	−0.547533	+	0.316118i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			32.0000i			1.18681i	0.804902	+	0.593407i	$0.202218\pi$
$727$			32.0000i			1.18681i	−0.804902	+	0.593407i	$0.797782\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−10.0000	+	17.3205i	−0.369863	+	0.640622i
$732$		0			0
$733$	−16.4545	+	9.50000i	−0.607760	+	0.350891i	−0.772088	−	0.635515i	$-0.780788\pi$
$733$	−16.4545	+	9.50000i	−0.607760	+	0.350891i	0.164328	+	0.986406i	$0.447454\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−23.3827	+	13.5000i	−0.861312	+	0.497279i
$738$		0			0
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	−0.908337	−	0.418238i	$-0.862648\pi$
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	0.816373	+	0.577524i	$0.195981\pi$
$740$		0			0
$741$	6.00000			0.220416
$742$		0			0
$743$			16.0000i			0.586983i	0.955962	+	0.293492i	$0.0948173\pi$
$743$			16.0000i			0.586983i	−0.955962	+	0.293492i	$0.905183\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−20.7846	+	12.0000i	−0.760469	+	0.439057i
$748$		0			0
$749$	4.50000	−	23.3827i	0.164426	−	0.854385i
$750$		0			0
$751$	−26.5000	−	45.8993i	−0.966999	−	1.67489i	−0.704146	−	0.710055i	$-0.748670\pi$
$751$	−26.5000	−	45.8993i	−0.966999	−	1.67489i	−0.262852	−	0.964836i	$-0.584663\pi$
$752$		0			0
$753$	−13.8564	−	8.00000i	−0.504956	−	0.291536i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			10.0000i			0.363456i	0.983349	+	0.181728i	$0.0581691\pi$
$757$			10.0000i			0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$		0			0
$759$	10.5000	−	18.1865i	0.381126	−	0.660129i
$760$		0			0
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	0.837557	−	0.546350i	$-0.183983\pi$
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	−0.891932	+	0.452170i	$0.850650\pi$
$762$		0			0
$763$	4.33013	+	12.5000i	0.156761	+	0.452530i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	77.9423	+	45.0000i	2.81433	+	1.62486i
$768$		0			0
$769$	−22.0000			−0.793340			−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000			−0.793340			−0.396670	+	0.917961i	$0.629834\pi$
$770$		0			0
$771$	21.0000			0.756297
$772$		0			0
$773$	16.4545	+	9.50000i	0.591827	+	0.341691i	0.765819	−	0.643056i	$-0.222334\pi$
$773$	16.4545	+	9.50000i	0.591827	+	0.341691i	−0.173993	+	0.984747i	$0.555667\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−5.19615	+	6.00000i	−0.186411	+	0.215249i
$778$		0			0
$779$	−1.00000	−	1.73205i	−0.0358287	−	0.0620572i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	10.0000i		−	0.357371i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	14.7224	+	8.50000i	0.524798	+	0.302992i	0.738896	−	0.673820i	$-0.235348\pi$
$787$	14.7224	+	8.50000i	0.524798	+	0.302992i	−0.214097	+	0.976812i	$0.568681\pi$
$788$		0			0
$789$	4.50000	+	7.79423i	0.160204	+	0.277482i
$790$		0			0
$791$	36.0000	+	31.1769i	1.28001	+	1.10852i
$792$		0			0
$793$	−25.9808	+	15.0000i	−0.922604	+	0.532666i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			18.0000i			0.637593i	0.947823	+	0.318796i	$0.103279\pi$
$797$			18.0000i			0.637593i	−0.947823	+	0.318796i	$0.896721\pi$
$798$		0			0
$799$	25.0000			0.884436
$800$		0			0
$801$	7.00000	−	12.1244i	0.247333	−	0.428393i
$802$		0			0
$803$	−18.1865	+	10.5000i	−0.641789	+	0.370537i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	7.79423	−	4.50000i	0.274370	−	0.158408i
$808$		0			0
$809$	19.5000	−	33.7750i	0.685583	−	1.18747i	−0.287670	−	0.957730i	$-0.592880\pi$
$809$	19.5000	−	33.7750i	0.685583	−	1.18747i	0.973253	−	0.229736i	$-0.0737862\pi$
$810$		0			0
$811$	12.0000			0.421377			0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000			0.421377			0.210688	+	0.977553i	$0.432429\pi$
$812$		0			0
$813$		−	7.00000i		−	0.245501i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−3.46410	+	2.00000i	−0.121194	+	0.0699711i
$818$		0			0
$819$	6.00000	−	31.1769i	0.209657	−	1.08941i
$820$		0			0
$821$	4.50000	+	7.79423i	0.157051	+	0.272020i	0.933804	−	0.357785i	$-0.116468\pi$
$821$	4.50000	+	7.79423i	0.157051	+	0.272020i	−0.776753	+	0.629805i	$0.783135\pi$
$822$		0			0
$823$	40.7032	+	23.5000i	1.41882	+	0.819159i	0.996196	−	0.0871445i	$-0.0277742\pi$
$823$	40.7032	+	23.5000i	1.41882	+	0.819159i	0.422628	+	0.906303i	$0.361108\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	36.0000i		−	1.25184i	−0.779886	−	0.625921i	$-0.784723\pi$
$827$		−	36.0000i		−	1.25184i	0.779886	−	0.625921i	$-0.215277\pi$
$828$		0			0
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	−0.754567	−	0.656223i	$-0.772153\pi$
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	0.945589	+	0.325362i	$0.105486\pi$
$830$		0			0
$831$	−8.50000	−	14.7224i	−0.294862	−	0.510716i
$832$		0			0
$833$	12.9904	−	32.5000i	0.450090	−	1.12606i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	21.6506	+	12.5000i	0.748355	+	0.432063i
$838$		0			0
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	−5.19615	−	3.00000i	−0.178965	−	0.103325i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.19615	+	1.00000i	0.178542	+	0.0343604i
$848$		0			0
$849$	6.50000	+	11.2583i	0.223079	+	0.386385i
$850$		0			0
$851$	10.5000	−	18.1865i	0.359935	−	0.623426i
$852$		0			0
$853$		−	34.0000i		−	1.16414i	−0.813139	−	0.582069i	$-0.802243\pi$
$853$		−	34.0000i		−	1.16414i	0.813139	−	0.582069i	$-0.197757\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−33.7750	−	19.5000i	−1.15373	−	0.666107i	−0.203938	−	0.978984i	$-0.565374\pi$
$857$	−33.7750	−	19.5000i	−1.15373	−	0.666107i	−0.949794	+	0.312877i	$0.898707\pi$
$858$		0			0
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	0.874429	−	0.485153i	$-0.161236\pi$
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	−0.857369	+	0.514701i	$0.827903\pi$
$860$		0			0
$861$	5.00000	−	1.73205i	0.170400	−	0.0590281i
$862$		0			0
$863$	−14.7224	+	8.50000i	−0.501157	+	0.289343i	−0.729191	−	0.684310i	$-0.760104\pi$
$863$	−14.7224	+	8.50000i	−0.501157	+	0.289343i	0.228034	+	0.973653i	$0.426770\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	8.00000i		−	0.271694i
$868$		0			0
$869$	−3.00000			−0.101768
$870$		0			0
$871$	−27.0000	+	46.7654i	−0.914860	+	1.58458i
$872$		0			0
$873$	−3.46410	+	2.00000i	−0.117242	+	0.0676897i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	19.9186	−	11.5000i	0.672603	−	0.388327i	−0.124459	−	0.992225i	$-0.539720\pi$
$877$	19.9186	−	11.5000i	0.672603	−	0.388327i	0.797062	+	0.603897i	$0.206386\pi$
$878$		0			0
$879$	−3.00000	+	5.19615i	−0.101187	+	0.175262i
$880$		0			0
$881$	−14.0000			−0.471672			−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000			−0.471672			−0.235836	+	0.971793i	$0.575783\pi$
$882$		0			0
$883$			20.0000i			0.673054i	0.941674	+	0.336527i	$0.109252\pi$
$883$			20.0000i			0.673054i	−0.941674	+	0.336527i	$0.890748\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.59808	+	1.50000i	−0.0872349	+	0.0503651i	−0.542983	−	0.839744i	$-0.682705\pi$
$887$	−2.59808	+	1.50000i	−0.0872349	+	0.0503651i	0.455748	+	0.890109i	$0.349372\pi$
$888$		0			0
$889$	16.0000	+	13.8564i	0.536623	+	0.464729i
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$		0			0
$893$	4.33013	+	2.50000i	0.144902	+	0.0836593i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	42.0000i		−	1.40234i
$898$		0			0
$899$	−5.00000	+	8.66025i	−0.166759	+	0.288836i
$900$		0			0
$901$	−2.50000	−	4.33013i	−0.0832871	−	0.144257i
$902$		0			0
$903$	−3.46410	−	10.0000i	−0.115278	−	0.332779i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.866025	+	0.500000i	0.0287559	+	0.0166022i	0.514309	−	0.857605i	$-0.328048\pi$
$907$	0.866025	+	0.500000i	0.0287559	+	0.0166022i	−0.485553	+	0.874207i	$0.661382\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$		0			0
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$		0			0
$913$	31.1769	+	18.0000i	1.03181	+	0.595713i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−12.9904	−	2.50000i	−0.428980	−	0.0825573i
$918$		0			0
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	0.760939	−	0.648824i	$-0.224739\pi$
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	−0.942367	+	0.334581i	$0.891405\pi$
$920$		0			0
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−25.9808	−	15.0000i	−0.853320	−	0.492665i
$928$		0			0
$929$	3.50000	+	6.06218i	0.114831	+	0.198894i	0.917712	−	0.397246i	$-0.130034\pi$
$929$	3.50000	+	6.06218i	0.114831	+	0.198894i	−0.802881	+	0.596139i	$0.796701\pi$
$930$		0			0
$931$	5.50000	−	4.33013i	0.180255	−	0.141914i
$932$		0			0
$933$	12.9904	−	7.50000i	0.425286	−	0.245539i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	6.00000i		−	0.196011i	−0.995186	−	0.0980057i	$-0.968754\pi$
$937$		−	6.00000i		−	0.196011i	0.995186	−	0.0980057i	$-0.0312463\pi$
$938$		0			0
$939$	−1.00000			−0.0326338
$940$		0			0
$941$	16.5000	−	28.5788i	0.537885	−	0.931644i	−0.461133	−	0.887331i	$-0.652557\pi$
$941$	16.5000	−	28.5788i	0.537885	−	0.931644i	0.999018	−	0.0443125i	$-0.0141097\pi$
$942$		0			0
$943$	−12.1244	+	7.00000i	−0.394823	+	0.227951i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	32.0429	−	18.5000i	1.04126	−	0.601169i	0.121067	−	0.992644i	$-0.461368\pi$
$947$	32.0429	−	18.5000i	1.04126	−	0.601169i	0.920189	+	0.391475i	$0.128035\pi$
$948$		0			0
$949$	−21.0000	+	36.3731i	−0.681689	+	1.18072i
$950$		0			0
$951$	−3.00000			−0.0972817
$952$		0			0
$953$		−	22.0000i		−	0.712650i	−0.934362	−	0.356325i	$-0.884030\pi$
$953$		−	22.0000i		−	0.712650i	0.934362	−	0.356325i	$-0.115970\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−5.19615	+	3.00000i	−0.167968	+	0.0969762i
$958$		0			0
$959$	−27.5000	+	9.52628i	−0.888021	+	0.307620i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$		0			0
$963$	−15.5885	−	9.00000i	−0.502331	−	0.290021i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			48.0000i			1.54358i	0.635880	+	0.771788i	$0.280637\pi$
$967$			48.0000i			1.54358i	−0.635880	+	0.771788i	$0.719363\pi$
$968$		0			0
$969$	2.50000	−	4.33013i	0.0803116	−	0.139104i
$970$		0			0
$971$	17.5000	+	30.3109i	0.561602	+	0.972723i	0.997357	+	0.0726575i	$0.0231480\pi$
$971$	17.5000	+	30.3109i	0.561602	+	0.972723i	−0.435755	+	0.900065i	$0.643519\pi$
$972$		0			0
$973$	20.7846	−	24.0000i	0.666324	−	0.769405i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.59808	−	1.50000i	−0.0831198	−	0.0479893i	0.457864	−	0.889022i	$-0.348615\pi$
$977$	−2.59808	−	1.50000i	−0.0831198	−	0.0479893i	−0.540984	+	0.841033i	$0.681948\pi$
$978$		0			0
$979$	−21.0000			−0.671163
$980$		0			0
$981$	10.0000			0.319275
$982$		0			0
$983$	−18.1865	−	10.5000i	−0.580060	−	0.334898i	0.181097	−	0.983465i	$-0.442035\pi$
$983$	−18.1865	−	10.5000i	−0.580060	−	0.334898i	−0.761157	+	0.648567i	$0.775369\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−8.66025	+	10.0000i	−0.275659	+	0.318304i
$988$		0			0
$989$	14.0000	+	24.2487i	0.445174	+	0.771064i
$990$		0			0
$991$	−7.50000	+	12.9904i	−0.238245	+	0.412653i	−0.960211	−	0.279276i	$-0.909906\pi$
$991$	−7.50000	+	12.9904i	−0.238245	+	0.412653i	0.721966	+	0.691929i	$0.243239\pi$
$992$		0			0
$993$			29.0000i			0.920287i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	35.5070	+	20.5000i	1.12452	+	0.649242i	0.942551	−	0.334063i	$-0.108420\pi$
$997$	35.5070	+	20.5000i	1.12452	+	0.649242i	0.181968	+	0.983304i	$0.441753\pi$
$998$		0			0
$999$	7.50000	+	12.9904i	0.237289	+	0.410997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.a.249.1		4
5.2	odd	4		1400.2.q.d.1201.1		2
5.3	odd	4		56.2.i.b.25.1	yes	2
5.4	even	2	inner	1400.2.bh.a.249.2		4
7.2	even	3	inner	1400.2.bh.a.849.2		4
15.8	even	4		504.2.s.c.361.1		2
20.3	even	4		112.2.i.a.81.1		2
35.2	odd	12		1400.2.q.d.401.1		2
35.3	even	12		392.2.a.e.1.1		1
35.9	even	6	inner	1400.2.bh.a.849.1		4
35.13	even	4		392.2.i.b.361.1		2
35.17	even	12		9800.2.a.s.1.1		1
35.18	odd	12		392.2.a.c.1.1		1
35.23	odd	12		56.2.i.b.9.1	✓	2
35.32	odd	12		9800.2.a.be.1.1		1
35.33	even	12		392.2.i.b.177.1		2
40.3	even	4		448.2.i.d.193.1		2
40.13	odd	4		448.2.i.b.193.1		2
60.23	odd	4		1008.2.s.g.865.1		2
105.23	even	12		504.2.s.c.289.1		2
105.38	odd	12		3528.2.a.j.1.1		1
105.53	even	12		3528.2.a.p.1.1		1
105.68	odd	12		3528.2.s.q.3313.1		2
105.83	odd	4		3528.2.s.q.361.1		2
140.3	odd	12		784.2.a.c.1.1		1
140.23	even	12		112.2.i.a.65.1		2
140.83	odd	4		784.2.i.h.753.1		2
140.103	odd	12		784.2.i.h.177.1		2
140.123	even	12		784.2.a.h.1.1		1
280.3	odd	12		3136.2.a.t.1.1		1
280.53	odd	12		3136.2.a.u.1.1		1
280.93	odd	12		448.2.i.b.65.1		2
280.123	even	12		3136.2.a.j.1.1		1
280.163	even	12		448.2.i.d.65.1		2
280.213	even	12		3136.2.a.i.1.1		1
420.23	odd	12		1008.2.s.g.289.1		2
420.143	even	12		7056.2.a.u.1.1		1
420.263	odd	12		7056.2.a.bj.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.i.b.9.1	✓	2	35.23	odd	12
56.2.i.b.25.1	yes	2	5.3	odd	4
112.2.i.a.65.1		2	140.23	even	12
112.2.i.a.81.1		2	20.3	even	4
392.2.a.c.1.1		1	35.18	odd	12
392.2.a.e.1.1		1	35.3	even	12
392.2.i.b.177.1		2	35.33	even	12
392.2.i.b.361.1		2	35.13	even	4
448.2.i.b.65.1		2	280.93	odd	12
448.2.i.b.193.1		2	40.13	odd	4
448.2.i.d.65.1		2	280.163	even	12
448.2.i.d.193.1		2	40.3	even	4
504.2.s.c.289.1		2	105.23	even	12
504.2.s.c.361.1		2	15.8	even	4
784.2.a.c.1.1		1	140.3	odd	12
784.2.a.h.1.1		1	140.123	even	12
784.2.i.h.177.1		2	140.103	odd	12
784.2.i.h.753.1		2	140.83	odd	4
1008.2.s.g.289.1		2	420.23	odd	12
1008.2.s.g.865.1		2	60.23	odd	4
1400.2.q.d.401.1		2	35.2	odd	12
1400.2.q.d.1201.1		2	5.2	odd	4
1400.2.bh.a.249.1		4	1.1	even	1	trivial
1400.2.bh.a.249.2		4	5.4	even	2	inner
1400.2.bh.a.849.1		4	35.9	even	6	inner
1400.2.bh.a.849.2		4	7.2	even	3	inner
3136.2.a.i.1.1		1	280.213	even	12
3136.2.a.j.1.1		1	280.123	even	12
3136.2.a.t.1.1		1	280.3	odd	12
3136.2.a.u.1.1		1	280.53	odd	12
3528.2.a.j.1.1		1	105.38	odd	12
3528.2.a.p.1.1		1	105.53	even	12
3528.2.s.q.361.1		2	105.83	odd	4
3528.2.s.q.3313.1		2	105.68	odd	12
7056.2.a.u.1.1		1	420.143	even	12
7056.2.a.bj.1.1		1	420.263	odd	12
9800.2.a.s.1.1		1	35.17	even	12
9800.2.a.be.1.1		1	35.32	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(1.73205 - 2.00000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +6.00000i q^{13} +(4.33013 + 2.50000i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-2.50000 + 0.866025i) q^{21} +(6.06218 - 3.50000i) q^{23} +5.00000i q^{27} -2.00000 q^{29} +(2.50000 - 4.33013i) q^{31} +(2.59808 - 1.50000i) q^{33} +(2.59808 - 1.50000i) q^{37} +(3.00000 - 5.19615i) q^{39} -2.00000 q^{41} +4.00000i q^{43} +(4.33013 - 2.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-2.50000 - 4.33013i) q^{51} +(-0.866025 - 0.500000i) q^{53} -1.00000i q^{57} +(7.50000 - 12.9904i) q^{59} +(2.50000 + 4.33013i) q^{61} +(-5.19615 - 1.00000i) q^{63} +(7.79423 + 4.50000i) q^{67} -7.00000 q^{69} +(6.06218 + 3.50000i) q^{73} +(2.59808 + 7.50000i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -12.0000i q^{83} +(1.73205 + 1.00000i) q^{87} +(3.50000 + 6.06218i) q^{89} +(12.0000 + 10.3923i) q^{91} +(-4.33013 + 2.50000i) q^{93} -2.00000i q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{9} - 6 q^{11} + 2 q^{19} - 10 q^{21} - 8 q^{29} + 10 q^{31} + 12 q^{39} - 8 q^{41} - 4 q^{49} - 10 q^{51} + 30 q^{59} + 10 q^{61} - 28 q^{69} + 2 q^{79} - 2 q^{81} + 14 q^{89} + 48 q^{91} + 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^9 - 6 * q^11 + 2 * q^19 - 10 * q^21 - 8 * q^29 + 10 * q^31 + 12 * q^39 - 8 * q^41 - 4 * q^49 - 10 * q^51 + 30 * q^59 + 10 * q^61 - 28 * q^69 + 2 * q^79 - 2 * q^81 + 14 * q^89 + 48 * q^91 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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