LMFDB - Embedded newform 672.2.bd.a.431.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,2,Mod(431,672)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("672.431"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bd (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.18
Character	$\chi$	$=$	672.431
Dual form			672.2.bd.a.527.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.402456 + 1.68465i) q^{3} +(1.09212 + 1.89161i) q^{5} +(-0.451847 + 2.60688i) q^{7} +(-2.67606 + 1.35599i) q^{9} +(-1.45052 - 0.837460i) q^{11} +1.56085i q^{13} +(-2.74716 + 2.60112i) q^{15} +(0.278795 + 0.160963i) q^{17} +(-2.87437 - 4.97856i) q^{19} +(-4.57352 + 0.287952i) q^{21} +(3.26717 + 5.65891i) q^{23} +(0.114544 - 0.198397i) q^{25} +(-3.36136 - 3.96248i) q^{27} +7.04205 q^{29} +(-7.76983 - 4.48591i) q^{31} +(0.827052 - 2.78066i) q^{33} +(-5.42467 + 1.99231i) q^{35} +(-0.946173 + 0.546273i) q^{37} +(-2.62949 + 0.628175i) q^{39} +3.44933i q^{41} +11.6570 q^{43} +(-5.48758 - 3.58115i) q^{45} +(2.25371 + 3.90354i) q^{47} +(-6.59167 - 2.35583i) q^{49} +(-0.158962 + 0.534452i) q^{51} +(-4.42876 + 7.67084i) q^{53} -3.65843i q^{55} +(7.23030 - 6.84595i) q^{57} +(5.37016 + 3.10046i) q^{59} +(-3.80578 + 2.19727i) q^{61} +(-2.32574 - 7.58887i) q^{63} +(-2.95253 + 1.70464i) q^{65} +(-0.716072 + 1.24027i) q^{67} +(-8.21836 + 7.78149i) q^{69} +6.37080 q^{71} +(-4.49012 + 7.77711i) q^{73} +(0.380327 + 0.113121i) q^{75} +(2.83858 - 3.40294i) q^{77} +(-3.58799 + 2.07153i) q^{79} +(5.32258 - 7.25742i) q^{81} +9.06459i q^{83} +0.703162i q^{85} +(2.83411 + 11.8634i) q^{87} +(-4.57586 + 2.64187i) q^{89} +(-4.06896 - 0.705268i) q^{91} +(4.43016 - 14.8948i) q^{93} +(6.27833 - 10.8744i) q^{95} +4.23153 q^{97} +(5.01728 + 0.274197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.402456	+	1.68465i	0.232358	+	0.972630i
$3$	0.402456	+	1.68465i	0.232358	+	0.972630i
$4$		0			0
$5$	1.09212	+	1.89161i	0.488411	+	0.845953i	0.999911	−	0.0133302i	$-0.00424327\pi$
$5$	1.09212	+	1.89161i	0.488411	+	0.845953i	−0.511500	+	0.859283i	$0.670910\pi$
$6$		0			0
$7$	−0.451847	+	2.60688i	−0.170782	+	0.985309i
$7$	−0.451847	+	2.60688i	−0.170782	+	0.985309i
$8$		0			0
$9$	−2.67606	+	1.35599i	−0.892020	+	0.451997i
$10$		0			0
$11$	−1.45052	−	0.837460i	−0.437349	−	0.252504i	0.265123	−	0.964215i	$-0.414587\pi$
$11$	−1.45052	−	0.837460i	−0.437349	−	0.252504i	−0.702473	+	0.711711i	$0.747921\pi$
$12$		0			0
$13$			1.56085i			0.432903i	0.976293	+	0.216452i	$0.0694483\pi$
$13$			1.56085i			0.432903i	−0.976293	+	0.216452i	$0.930552\pi$
$14$		0			0
$15$	−2.74716	+	2.60112i	−0.709313	+	0.671608i
$16$		0			0
$17$	0.278795	+	0.160963i	0.0676178	+	0.0390392i	0.533428	−	0.845846i	$-0.320904\pi$
$17$	0.278795	+	0.160963i	0.0676178	+	0.0390392i	−0.465810	+	0.884885i	$0.654237\pi$
$18$		0			0
$19$	−2.87437	−	4.97856i	−0.659427	−	1.14216i	−0.980764	−	0.195196i	$-0.937466\pi$
$19$	−2.87437	−	4.97856i	−0.659427	−	1.14216i	0.321337	−	0.946965i	$-0.395868\pi$
$20$		0			0
$21$	−4.57352	+	0.287952i	−0.998024	+	0.0628364i
$22$		0			0
$23$	3.26717	+	5.65891i	0.681252	+	1.17996i	0.974599	+	0.223958i	$0.0718977\pi$
$23$	3.26717	+	5.65891i	0.681252	+	1.17996i	−0.293346	+	0.956006i	$0.594769\pi$
$24$		0			0
$25$	0.114544	−	0.198397i	0.0229089	−	0.0396793i
$26$		0			0
$27$	−3.36136	−	3.96248i	−0.646894	−	0.762580i
$28$		0			0
$29$	7.04205			1.30768			0.653838	−	0.756635i	$-0.273158\pi$
$29$	7.04205			1.30768			0.653838	+	0.756635i	$0.273158\pi$
$30$		0			0
$31$	−7.76983	−	4.48591i	−1.39550	−	0.805694i	−0.401585	−	0.915822i	$-0.631541\pi$
$31$	−7.76983	−	4.48591i	−1.39550	−	0.805694i	−0.993917	+	0.110128i	$0.964874\pi$
$32$		0			0
$33$	0.827052	−	2.78066i	0.143971	−	0.484051i
$34$		0			0
$35$	−5.42467	+	1.99231i	−0.916937	+	0.336762i
$36$		0			0
$37$	−0.946173	+	0.546273i	−0.155550	+	0.0898068i	−0.575755	−	0.817623i	$-0.695292\pi$
$37$	−0.946173	+	0.546273i	−0.155550	+	0.0898068i	0.420205	+	0.907429i	$0.361958\pi$
$38$		0			0
$39$	−2.62949	+	0.628175i	−0.421055	+	0.100588i
$40$		0			0
$41$			3.44933i			0.538694i	0.963043	+	0.269347i	$0.0868079\pi$
$41$			3.44933i			0.538694i	−0.963043	+	0.269347i	$0.913192\pi$
$42$		0			0
$43$	11.6570			1.77768			0.888841	−	0.458215i	$-0.151511\pi$
$43$	11.6570			1.77768			0.888841	+	0.458215i	$0.151511\pi$
$44$		0			0
$45$	−5.48758	−	3.58115i	−0.818041	−	0.533846i
$46$		0			0
$47$	2.25371	+	3.90354i	0.328737	+	0.569390i	0.982262	−	0.187516i	$-0.0600436\pi$
$47$	2.25371	+	3.90354i	0.328737	+	0.569390i	−0.653524	+	0.756906i	$0.726710\pi$
$48$		0			0
$49$	−6.59167	−	2.35583i	−0.941667	−	0.336546i
$50$		0			0
$51$	−0.158962	+	0.534452i	−0.0222591	+	0.0748382i
$52$		0			0
$53$	−4.42876	+	7.67084i	−0.608337	+	1.05367i	0.383177	+	0.923675i	$0.374830\pi$
$53$	−4.42876	+	7.67084i	−0.608337	+	1.05367i	−0.991515	+	0.129996i	$0.958504\pi$
$54$		0			0
$55$		−	3.65843i		−	0.493303i
$56$		0			0
$57$	7.23030	−	6.84595i	0.957677	−	0.906769i
$58$		0			0
$59$	5.37016	+	3.10046i	0.699135	+	0.403646i	0.807025	−	0.590517i	$-0.201076\pi$
$59$	5.37016	+	3.10046i	0.699135	+	0.403646i	−0.107890	+	0.994163i	$0.534409\pi$
$60$		0			0
$61$	−3.80578	+	2.19727i	−0.487280	+	0.281331i	−0.723445	−	0.690382i	$-0.757443\pi$
$61$	−3.80578	+	2.19727i	−0.487280	+	0.281331i	0.236165	+	0.971713i	$0.424109\pi$
$62$		0			0
$63$	−2.32574	−	7.58887i	−0.293015	−	0.956108i
$64$		0			0
$65$	−2.95253	+	1.70464i	−0.366216	+	0.211435i
$66$		0			0
$67$	−0.716072	+	1.24027i	−0.0874821	+	0.151523i	−0.906446	−	0.422321i	$-0.861215\pi$
$67$	−0.716072	+	1.24027i	−0.0874821	+	0.151523i	0.818964	+	0.573845i	$0.194549\pi$
$68$		0			0
$69$	−8.21836	+	7.78149i	−0.989374	+	0.936781i
$70$		0			0
$71$	6.37080			0.756074			0.378037	−	0.925790i	$-0.376599\pi$
$71$	6.37080			0.756074			0.378037	+	0.925790i	$0.376599\pi$
$72$		0			0
$73$	−4.49012	+	7.77711i	−0.525528	+	0.910242i	0.474030	+	0.880509i	$0.342799\pi$
$73$	−4.49012	+	7.77711i	−0.525528	+	0.910242i	−0.999558	+	0.0297328i	$0.990534\pi$
$74$		0			0
$75$	0.380327	+	0.113121i	0.0439164	+	0.0130621i
$76$		0			0
$77$	2.83858	−	3.40294i	0.323486	−	0.387801i
$78$		0			0
$79$	−3.58799	+	2.07153i	−0.403681	+	0.233065i	−0.688071	−	0.725643i	$-0.741542\pi$
$79$	−3.58799	+	2.07153i	−0.403681	+	0.233065i	0.284390	+	0.958709i	$0.408209\pi$
$80$		0			0
$81$	5.32258	−	7.25742i	0.591398	−	0.806380i
$82$		0			0
$83$			9.06459i			0.994968i	0.867473	+	0.497484i	$0.165743\pi$
$83$			9.06459i			0.994968i	−0.867473	+	0.497484i	$0.834257\pi$
$84$		0			0
$85$			0.703162i			0.0762687i
$86$		0			0
$87$	2.83411	+	11.8634i	0.303849	+	1.27189i
$88$		0			0
$89$	−4.57586	+	2.64187i	−0.485040	+	0.280038i	−0.722515	−	0.691356i	$-0.757014\pi$
$89$	−4.57586	+	2.64187i	−0.485040	+	0.280038i	0.237474	+	0.971394i	$0.423680\pi$
$90$		0			0
$91$	−4.06896	−	0.705268i	−0.426543	−	0.0739322i
$92$		0			0
$93$	4.43016	−	14.8948i	0.459386	−	1.54452i
$94$		0			0
$95$	6.27833	−	10.8744i	0.644143	−	1.11569i
$96$		0			0
$97$	4.23153			0.429647			0.214823	−	0.976653i	$-0.431082\pi$
$97$	4.23153			0.429647			0.214823	+	0.976653i	$0.431082\pi$
$98$		0			0
$99$	5.01728	+	0.274197i	0.504255	+	0.0275578i
$100$		0			0
$101$	2.47136	−	4.28052i	0.245909	−	0.425927i	−0.716478	−	0.697610i	$-0.754247\pi$
$101$	2.47136	−	4.28052i	0.245909	−	0.425927i	0.962387	+	0.271683i	$0.0875802\pi$
$102$		0			0
$103$	15.8817	−	9.16928i	1.56487	−	0.903476i	0.568114	−	0.822950i	$-0.307673\pi$
$103$	15.8817	−	9.16928i	1.56487	−	0.903476i	0.996752	−	0.0805264i	$-0.0256601\pi$
$104$		0			0
$105$	−5.53953	−	8.33683i	−0.540603	−	0.813591i
$106$		0			0
$107$	−3.83045	+	2.21151i	−0.370303	+	0.213795i	−0.673591	−	0.739104i	$-0.735249\pi$
$107$	−3.83045	+	2.21151i	−0.370303	+	0.213795i	0.303288	+	0.952899i	$0.401916\pi$
$108$		0			0
$109$	7.04986	+	4.07024i	0.675255	+	0.389858i	0.798065	−	0.602572i	$-0.205857\pi$
$109$	7.04986	+	4.07024i	0.675255	+	0.389858i	−0.122810	+	0.992430i	$0.539191\pi$
$110$		0			0
$111$	−1.30107	−	1.37411i	−0.123492	−	0.130425i
$112$		0			0
$113$		−	13.4000i		−	1.26056i	−0.776367	−	0.630281i	$-0.782940\pi$
$113$		−	13.4000i		−	1.26056i	0.776367	−	0.630281i	$-0.217060\pi$
$114$		0			0
$115$	−7.13629	+	12.3604i	−0.665463	+	1.15262i
$116$		0			0
$117$	−2.11650	−	4.17694i	−0.195671	−	0.386158i
$118$		0			0
$119$	−0.545583	+	0.654056i	−0.0500136	+	0.0599572i
$120$		0			0
$121$	−4.09732	−	7.09677i	−0.372484	−	0.645161i
$122$		0			0
$123$	−5.81089	+	1.38820i	−0.523951	+	0.125170i
$124$		0			0
$125$	11.4216			1.02158
$126$		0			0
$127$			12.5356i			1.11236i	0.831063	+	0.556178i	$0.187733\pi$
$127$			12.5356i			1.11236i	−0.831063	+	0.556178i	$0.812267\pi$
$128$		0			0
$129$	4.69144	+	19.6380i	0.413059	+	1.72903i
$130$		0			0
$131$	14.8145	−	8.55318i	1.29435	−	0.747295i	0.314930	−	0.949115i	$-0.398019\pi$
$131$	14.8145	−	8.55318i	1.29435	−	0.747295i	0.979423	+	0.201820i	$0.0646855\pi$
$132$		0			0
$133$	14.2773	−	5.24361i	1.23800	−	0.454678i
$134$		0			0
$135$	3.82446	−	10.6859i	0.329157	−	0.919694i
$136$		0			0
$137$	17.9399	+	10.3576i	1.53271	+	0.884909i	0.999236	+	0.0390917i	$0.0124464\pi$
$137$	17.9399	+	10.3576i	1.53271	+	0.884909i	0.533472	+	0.845818i	$0.320887\pi$
$138$		0			0
$139$	−1.27255			−0.107936			−0.0539682	−	0.998543i	$-0.517187\pi$
$139$	−1.27255			−0.107936			−0.0539682	+	0.998543i	$0.517187\pi$
$140$		0			0
$141$	−5.66906	+	5.36770i	−0.477421	+	0.452042i
$142$		0			0
$143$	1.30715	−	2.26406i	0.109310	−	0.189330i
$144$		0			0
$145$	7.69077	+	13.3208i	0.638684	+	1.10623i
$146$		0			0
$147$	1.31587	−	12.0527i	0.108532	−	0.994093i
$148$		0			0
$149$	2.47136	+	4.28052i	0.202461	+	0.350674i	0.949321	−	0.314308i	$-0.101773\pi$
$149$	2.47136	+	4.28052i	0.202461	+	0.350674i	−0.746859	+	0.664982i	$0.768439\pi$
$150$		0			0
$151$	5.48605	+	3.16737i	0.446448	+	0.257757i	0.706329	−	0.707884i	$-0.250350\pi$
$151$	5.48605	+	3.16737i	0.446448	+	0.257757i	−0.259881	+	0.965641i	$0.583683\pi$
$152$		0			0
$153$	−0.964337	−	0.0527015i	−0.0779620	−	0.00426066i
$154$		0			0
$155$		−	19.5966i		−	1.57404i
$156$		0			0
$157$	−2.09256	−	1.20814i	−0.167004	−	0.0964199i	0.414168	−	0.910200i	$-0.364072\pi$
$157$	−2.09256	−	1.20814i	−0.167004	−	0.0964199i	−0.581172	+	0.813780i	$0.697406\pi$
$158$		0			0
$159$	−14.7050	−	4.37372i	−1.16618	−	0.346858i
$160$		0			0
$161$	−16.2284	+	5.96017i	−1.27897	+	0.469727i
$162$		0			0
$163$	−4.46077	−	7.72628i	−0.349395	−	0.605169i	0.636747	−	0.771072i	$-0.280279\pi$
$163$	−4.46077	−	7.72628i	−0.349395	−	0.605169i	−0.986142	+	0.165903i	$0.946946\pi$
$164$		0			0
$165$	6.16316	−	1.47236i	0.479801	−	0.114623i
$166$		0			0
$167$	−7.01131			−0.542551			−0.271276	−	0.962502i	$-0.587445\pi$
$167$	−7.01131			−0.542551			−0.271276	+	0.962502i	$0.587445\pi$
$168$		0			0
$169$	10.5637			0.812595
$170$		0			0
$171$	14.4429	+	9.42530i	1.10447	+	0.720771i
$172$		0			0
$173$	−7.11660	−	12.3263i	−0.541065	−	0.937152i	−0.998843	−	0.0480854i	$-0.984688\pi$
$173$	−7.11660	−	12.3263i	−0.541065	−	0.937152i	0.457778	−	0.889066i	$-0.348645\pi$
$174$		0			0
$175$	0.465440	+	0.388249i	0.0351840	+	0.0293488i
$176$		0			0
$177$	−3.06193	+	10.2946i	−0.230149	+	0.773790i
$178$		0			0
$179$	1.07613	+	0.621304i	0.0804338	+	0.0464384i	0.539677	−	0.841872i	$-0.318546\pi$
$179$	1.07613	+	0.621304i	0.0804338	+	0.0464384i	−0.459244	+	0.888310i	$0.651880\pi$
$180$		0			0
$181$		−	20.9487i		−	1.55710i	−0.627580	−	0.778552i	$-0.715954\pi$
$181$		−	20.9487i		−	1.55710i	0.627580	−	0.778552i	$-0.284046\pi$
$182$		0			0
$183$	−5.23327	−	5.52709i	−0.386855	−	0.408574i
$184$		0			0
$185$	−2.06667	−	1.19319i	−0.151945	−	0.0877253i
$186$		0			0
$187$	−0.269600	−	0.466960i	−0.0197151	−	0.0341475i
$188$		0			0
$189$	11.8485	−	6.97223i	0.861855	−	0.507155i
$190$		0			0
$191$	−12.2119	−	21.1516i	−0.883621	−	1.53048i	−0.847287	−	0.531136i	$-0.821765\pi$
$191$	−12.2119	−	21.1516i	−0.883621	−	1.53048i	−0.0363339	−	0.999340i	$-0.511568\pi$
$192$		0			0
$193$	0.00662606	−	0.0114767i	0.000476954	−	0.000826109i	−0.865787	−	0.500413i	$-0.833182\pi$
$193$	0.00662606	−	0.0114767i	0.000476954	−	0.000826109i	0.866264	+	0.499587i	$0.166515\pi$
$194$		0			0
$195$	−4.05998	−	4.28792i	−0.290741	−	0.307064i
$196$		0			0
$197$	6.48422			0.461981			0.230991	−	0.972956i	$-0.425803\pi$
$197$	6.48422			0.461981			0.230991	+	0.972956i	$0.425803\pi$
$198$		0			0
$199$	4.47013	+	2.58083i	0.316879	+	0.182950i	0.650001	−	0.759934i	$-0.274769\pi$
$199$	4.47013	+	2.58083i	0.316879	+	0.182950i	−0.333121	+	0.942884i	$0.608102\pi$
$200$		0			0
$201$	−2.37761	−	0.707172i	−0.167703	−	0.0498801i
$202$		0			0
$203$	−3.18193	+	18.3578i	−0.223328	+	1.28846i
$204$		0			0
$205$	−6.52478	+	3.76708i	−0.455710	+	0.263104i
$206$		0			0
$207$	−16.4166	−	10.7133i	−1.14103	−	0.744627i
$208$		0			0
$209$			9.62870i			0.666031i
$210$		0			0
$211$	16.8357			1.15902			0.579509	−	0.814966i	$-0.303244\pi$
$211$	16.8357			1.15902			0.579509	+	0.814966i	$0.303244\pi$
$212$		0			0
$213$	2.56396	+	10.7325i	0.175680	+	0.735381i
$214$		0			0
$215$	12.7309	+	22.0506i	0.868240	+	1.50384i
$216$		0			0
$217$	15.2050	−	18.2281i	1.03218	−	1.23740i
$218$		0			0
$219$	−14.9087	−	4.43431i	−1.00744	−	0.299643i
$220$		0			0
$221$	−0.251239	+	0.435159i	−0.0169002	+	0.0292720i
$222$		0			0
$223$		−	1.80170i		−	0.120651i	−0.998179	−	0.0603254i	$-0.980786\pi$
$223$		−	1.80170i		−	0.120651i	0.998179	−	0.0603254i	$-0.0192138\pi$
$224$		0			0
$225$	−0.0375035	+	0.686242i	−0.00250023	+	0.0457495i
$226$		0			0
$227$	−10.0476	−	5.80096i	−0.666879	−	0.385023i	0.128014	−	0.991772i	$-0.459140\pi$
$227$	−10.0476	−	5.80096i	−0.666879	−	0.385023i	−0.794893	+	0.606749i	$0.792473\pi$
$228$		0			0
$229$	−8.50697	+	4.91150i	−0.562156	+	0.324561i	−0.754010	−	0.656862i	$-0.771883\pi$
$229$	−8.50697	+	4.91150i	−0.562156	+	0.324561i	0.191854	+	0.981423i	$0.438550\pi$
$230$		0			0
$231$	6.87515	+	3.41246i	0.452352	+	0.224523i
$232$		0			0
$233$	6.94161	−	4.00774i	0.454760	−	0.262556i	−0.255079	−	0.966920i	$-0.582101\pi$
$233$	6.94161	−	4.00774i	0.454760	−	0.262556i	0.709838	+	0.704365i	$0.248768\pi$
$234$		0			0
$235$	−4.92265	+	8.52627i	−0.321118	+	0.556193i
$236$		0			0
$237$	−4.93380	−	5.21080i	−0.320485	−	0.338478i
$238$		0			0
$239$	6.02441			0.389686			0.194843	−	0.980834i	$-0.437580\pi$
$239$	6.02441			0.389686			0.194843	+	0.980834i	$0.437580\pi$
$240$		0			0
$241$	5.11917	−	8.86666i	0.329755	−	0.571152i	−0.652708	−	0.757609i	$-0.726367\pi$
$241$	5.11917	−	8.86666i	0.329755	−	0.571152i	0.982463	+	0.186457i	$0.0597006\pi$
$242$		0			0
$243$	14.3683	+	6.04587i	0.921726	+	0.387843i
$244$		0			0
$245$	−2.74260	−	15.0417i	−0.175218	−	0.960979i
$246$		0			0
$247$	7.77081	−	4.48648i	0.494445	−	0.285468i
$248$		0			0
$249$	−15.2706	+	3.64810i	−0.967736	+	0.231189i
$250$		0			0
$251$			9.97684i			0.629733i	0.949136	+	0.314866i	$0.101960\pi$
$251$			9.97684i			0.629733i	−0.949136	+	0.314866i	$0.898040\pi$
$252$		0			0
$253$		−	10.9445i		−	0.688075i
$254$		0			0
$255$	−1.18458	+	0.282992i	−0.0741812	+	0.0177216i
$256$		0			0
$257$	17.1555	−	9.90475i	1.07013	−	0.617841i	0.141915	−	0.989879i	$-0.454674\pi$
$257$	17.1555	−	9.90475i	1.07013	−	0.617841i	0.928218	+	0.372038i	$0.121341\pi$
$258$		0			0
$259$	−0.996544	−	2.71339i	−0.0619222	−	0.168602i
$260$		0			0
$261$	−18.8449	+	9.54895i	−1.16647	+	0.591065i
$262$		0			0
$263$	−3.41780	+	5.91981i	−0.210751	+	0.365031i	−0.951950	−	0.306254i	$-0.900924\pi$
$263$	−3.41780	+	5.91981i	−0.210751	+	0.365031i	0.741199	+	0.671285i	$0.234258\pi$
$264$		0			0
$265$	−19.3470			−1.18847
$266$		0			0
$267$	−6.29220	−	6.64546i	−0.385077	−	0.406696i
$268$		0			0
$269$	−12.0822	+	20.9270i	−0.736665	+	1.27594i	0.217324	+	0.976099i	$0.430267\pi$
$269$	−12.0822	+	20.9270i	−0.736665	+	1.27594i	−0.953989	+	0.299842i	$0.903066\pi$
$270$		0			0
$271$	−15.2835	+	8.82392i	−0.928405	+	0.536015i	−0.886307	−	0.463099i	$-0.846738\pi$
$271$	−15.2835	+	8.82392i	−0.928405	+	0.536015i	−0.0420983	+	0.999113i	$0.513404\pi$
$272$		0			0
$273$	−0.449452	−	7.13860i	−0.0272021	−	0.432048i
$274$		0			0
$275$	−0.332299	+	0.191853i	−0.0200384	+	0.0115692i
$276$		0			0
$277$	−12.9250	−	7.46224i	−0.776587	−	0.448363i	0.0586324	−	0.998280i	$-0.481326\pi$
$277$	−12.9250	−	7.46224i	−0.776587	−	0.448363i	−0.835219	+	0.549917i	$0.814659\pi$
$278$		0			0
$279$	26.8754	+	1.46875i	1.60899	+	0.0879320i
$280$		0			0
$281$		−	13.8890i		−	0.828547i	−0.910152	−	0.414273i	$-0.864036\pi$
$281$		−	13.8890i		−	0.828547i	0.910152	−	0.414273i	$-0.135964\pi$
$282$		0			0
$283$	−2.88865	+	5.00329i	−0.171712	+	0.297415i	−0.939019	−	0.343866i	$-0.888263\pi$
$283$	−2.88865	+	5.00329i	−0.171712	+	0.297415i	0.767306	+	0.641281i	$0.221597\pi$
$284$		0			0
$285$	20.8462	+	6.20030i	1.23482	+	0.367274i
$286$		0			0
$287$	−8.99199	−	1.55857i	−0.530780	−	0.0919994i
$288$		0			0
$289$	−8.44818	−	14.6327i	−0.496952	−	0.860746i
$290$		0			0
$291$	1.70300	+	7.12863i	0.0998319	+	0.417888i
$292$		0			0
$293$	−15.6381			−0.913587			−0.456794	−	0.889573i	$-0.651002\pi$
$293$	−15.6381			−0.913587			−0.456794	+	0.889573i	$0.651002\pi$
$294$		0			0
$295$			13.5443i			0.788581i
$296$		0			0
$297$	1.55731	+	8.56268i	0.0903641	+	0.496857i
$298$		0			0
$299$	−8.83273	+	5.09958i	−0.510810	+	0.294916i
$300$		0			0
$301$	−5.26720	+	30.3885i	−0.303597	+	1.75157i
$302$		0			0
$303$	8.20576	+	2.44064i	0.471409	+	0.140211i
$304$		0			0
$305$	−8.31274	−	4.79936i	−0.475986	−	0.274811i
$306$		0			0
$307$	−7.19887			−0.410861			−0.205430	−	0.978672i	$-0.565859\pi$
$307$	−7.19887			−0.410861			−0.205430	+	0.978672i	$0.565859\pi$
$308$		0			0
$309$	21.8387	+	23.0647i	1.24236	+	1.31211i
$310$		0			0
$311$	−4.35089	+	7.53597i	−0.246717	+	0.427326i	−0.962613	−	0.270881i	$-0.912685\pi$
$311$	−4.35089	+	7.53597i	−0.246717	+	0.427326i	0.715896	+	0.698207i	$0.246018\pi$
$312$		0			0
$313$	9.57541	+	16.5851i	0.541234	+	0.937445i	0.998834	+	0.0482863i	$0.0153760\pi$
$313$	9.57541	+	16.5851i	0.541234	+	0.937445i	−0.457600	+	0.889158i	$0.651291\pi$
$314$		0			0
$315$	11.8152	−	12.6873i	0.665710	−	0.714851i
$316$		0			0
$317$	1.83178	+	3.17274i	0.102883	+	0.178199i	0.912871	−	0.408247i	$-0.133860\pi$
$317$	1.83178	+	3.17274i	0.102883	+	0.178199i	−0.809988	+	0.586446i	$0.800527\pi$
$318$		0			0
$319$	−10.2147	−	5.89744i	−0.571911	−	0.330193i
$320$		0			0
$321$	−5.26720	−	5.56291i	−0.293986	−	0.310491i
$322$		0			0
$323$		−	1.85067i		−	0.102974i
$324$		0			0
$325$	0.309668	+	0.178787i	0.0171773	+	0.00991732i
$326$		0			0
$327$	−4.01965	+	13.5146i	−0.222287	+	0.747360i
$328$		0			0
$329$	−11.1944	+	4.11135i	−0.617167	+	0.226666i
$330$		0			0
$331$	−5.41365	−	9.37672i	−0.297561	−	0.515391i	0.678016	−	0.735047i	$-0.262840\pi$
$331$	−5.41365	−	9.37672i	−0.297561	−	0.515391i	−0.975577	+	0.219656i	$0.929507\pi$
$332$		0			0
$333$	1.79127	−	2.74486i	0.0981612	−	0.150417i
$334$		0			0
$335$	−3.12815			−0.170909
$336$		0			0
$337$	−20.0426			−1.09179			−0.545894	−	0.837854i	$-0.683810\pi$
$337$	−20.0426			−1.09179			−0.545894	+	0.837854i	$0.683810\pi$
$338$		0			0
$339$	22.5742	−	5.39289i	1.22606	−	0.292901i
$340$		0			0
$341$	7.51355	+	13.0139i	0.406882	+	0.704740i
$342$		0			0
$343$	9.11979	−	16.1192i	0.492422	−	0.870357i
$344$		0			0
$345$	−23.6950	−	7.04760i	−1.27569	−	0.379430i
$346$		0			0
$347$	5.06136	+	2.92218i	0.271708	+	0.156871i	0.629664	−	0.776868i	$-0.283193\pi$
$347$	5.06136	+	2.92218i	0.271708	+	0.156871i	−0.357955	+	0.933739i	$0.616526\pi$
$348$		0			0
$349$			18.6166i			0.996526i	0.867026	+	0.498263i	$0.166029\pi$
$349$			18.6166i			0.996526i	−0.867026	+	0.498263i	$0.833971\pi$
$350$		0			0
$351$	6.18486	−	5.24659i	0.330123	−	0.280042i
$352$		0			0
$353$	5.78219	+	3.33835i	0.307755	+	0.177682i	0.645921	−	0.763404i	$-0.276473\pi$
$353$	5.78219	+	3.33835i	0.307755	+	0.177682i	−0.338167	+	0.941086i	$0.609807\pi$
$354$		0			0
$355$	6.95768	+	12.0511i	0.369275	+	0.639603i
$356$		0			0
$357$	−1.32143	−	0.655886i	−0.0699373	−	0.0347132i
$358$		0			0
$359$	12.1282	+	21.0067i	0.640102	+	1.10869i	0.985410	+	0.170200i	$0.0544414\pi$
$359$	12.1282	+	21.0067i	0.640102	+	1.10869i	−0.345307	+	0.938490i	$0.612225\pi$
$360$		0			0
$361$	−7.02406	+	12.1660i	−0.369687	+	0.640317i
$362$		0			0
$363$	10.3065	−	9.75866i	0.540953	−	0.512197i
$364$		0			0
$365$	−19.6150			−1.02670
$366$		0			0
$367$	−6.54864	−	3.78086i	−0.341836	−	0.197359i	0.319248	−	0.947671i	$-0.396570\pi$
$367$	−6.54864	−	3.78086i	−0.341836	−	0.197359i	−0.661084	+	0.750312i	$0.729903\pi$
$368$		0			0
$369$	−4.67725	−	9.23060i	−0.243488	−	0.480526i
$370$		0			0
$371$	−17.9958	−	15.0113i	−0.934298	−	0.779348i
$372$		0			0
$373$	16.9620	−	9.79302i	0.878260	−	0.507063i	0.00817543	−	0.999967i	$-0.497398\pi$
$373$	16.9620	−	9.79302i	0.878260	−	0.507063i	0.870084	+	0.492903i	$0.164064\pi$
$374$		0			0
$375$	4.59669	+	19.2413i	0.237372	+	0.993618i
$376$		0			0
$377$			10.9916i			0.566097i
$378$		0			0
$379$	−4.99759			−0.256709			−0.128354	−	0.991728i	$-0.540969\pi$
$379$	−4.99759			−0.256709			−0.128354	+	0.991728i	$0.540969\pi$
$380$		0			0
$381$	−21.1181	+	5.04503i	−1.08191	+	0.258465i
$382$		0			0
$383$	−15.1532	−	26.2461i	−0.774292	−	1.34111i	−0.935192	−	0.354142i	$-0.884773\pi$
$383$	−15.1532	−	26.2461i	−0.774292	−	1.34111i	0.160900	−	0.986971i	$-0.448560\pi$
$384$		0			0
$385$	9.53710	+	1.65305i	0.486056	+	0.0842474i
$386$		0			0
$387$	−31.1949	+	15.8068i	−1.58573	+	0.803507i
$388$		0			0
$389$	2.13059	−	3.69030i	0.108025	−	0.187106i	−0.806945	−	0.590627i	$-0.798881\pi$
$389$	2.13059	−	3.69030i	0.108025	−	0.187106i	0.914970	+	0.403521i	$0.132214\pi$
$390$		0			0
$391$			2.10357i			0.106382i
$392$		0			0
$393$	20.3713	+	21.5150i	1.02760	+	1.08529i
$394$		0			0
$395$	−7.83704	−	4.52472i	−0.394324	−	0.227663i
$396$		0			0
$397$	−17.1398	+	9.89568i	−0.860223	+	0.496650i	−0.864087	−	0.503343i	$-0.832103\pi$
$397$	−17.1398	+	9.89568i	−0.860223	+	0.496650i	0.00386406	+	0.999993i	$0.498770\pi$
$398$		0			0
$399$	14.5796	+	21.9419i	0.729893	+	1.09847i
$400$		0			0
$401$	1.98773	−	1.14762i	0.0992627	−	0.0573094i	−0.449547	−	0.893257i	$-0.648415\pi$
$401$	1.98773	−	1.14762i	0.0992627	−	0.0573094i	0.548810	+	0.835947i	$0.315081\pi$
$402$		0			0
$403$	7.00186	−	12.1276i	0.348787	−	0.604118i
$404$		0			0
$405$	19.5411	+	2.14226i	0.971005	+	0.106450i
$406$		0			0
$407$	1.82993			0.0907062
$408$		0			0
$409$	−0.750621	+	1.30011i	−0.0371158	+	0.0642865i	−0.883987	−	0.467512i	$-0.845150\pi$
$409$	−0.750621	+	1.30011i	−0.0371158	+	0.0642865i	0.846871	+	0.531799i	$0.178484\pi$
$410$		0			0
$411$	−10.2289	+	34.3908i	−0.504553	+	1.69637i
$412$		0			0
$413$	−10.5090	+	12.5984i	−0.517116	+	0.619928i
$414$		0			0
$415$	−17.1467	+	9.89963i	−0.841696	+	0.485954i
$416$		0			0
$417$	−0.512145	−	2.14380i	−0.0250799	−	0.104982i
$418$		0			0
$419$			8.44514i			0.412572i	0.978492	+	0.206286i	$0.0661378\pi$
$419$			8.44514i			0.412572i	−0.978492	+	0.206286i	$0.933862\pi$
$420$		0			0
$421$		−	13.9326i		−	0.679032i	−0.940600	−	0.339516i	$-0.889737\pi$
$421$		−	13.9326i		−	0.679032i	0.940600	−	0.339516i	$-0.110263\pi$
$422$		0			0
$423$	−11.3242	−	7.39009i	−0.550602	−	0.359319i
$424$		0			0
$425$	0.0638689	−	0.0368747i	0.00309809	−	0.00178869i
$426$		0			0
$427$	−4.00839	−	10.9140i	−0.193979	−	0.528168i
$428$		0			0
$429$	4.34020	+	1.29091i	0.209547	+	0.0623256i
$430$		0			0
$431$	−16.9743	+	29.4004i	−0.817624	+	1.41617i	0.0898039	+	0.995959i	$0.471376\pi$
$431$	−16.9743	+	29.4004i	−0.817624	+	1.41617i	−0.907428	+	0.420207i	$0.861957\pi$
$432$		0			0
$433$	4.44336			0.213534			0.106767	−	0.994284i	$-0.465950\pi$
$433$	4.44336			0.213534			0.106767	+	0.994284i	$0.465950\pi$
$434$		0			0
$435$	−19.3456	+	18.3173i	−0.927552	+	0.878245i
$436$		0			0
$437$	18.7822	−	32.5316i	0.898472	−	1.55620i
$438$		0			0
$439$	−7.55680	+	4.36292i	−0.360667	+	0.208231i	−0.669373	−	0.742926i	$-0.733437\pi$
$439$	−7.55680	+	4.36292i	−0.360667	+	0.208231i	0.308707	+	0.951157i	$0.400104\pi$
$440$		0			0
$441$	20.8342	−	2.63391i	0.992103	−	0.125424i
$442$		0			0
$443$	32.0121	−	18.4822i	1.52094	−	0.878115i	0.521244	−	0.853407i	$-0.325468\pi$
$443$	32.0121	−	18.4822i	1.52094	−	0.878115i	0.999695	−	0.0247072i	$-0.00786534\pi$
$444$		0			0
$445$	−9.99478	−	5.77049i	−0.473798	−	0.273548i
$446$		0			0
$447$	−6.21654	+	5.88608i	−0.294032	+	0.278402i
$448$		0			0
$449$		−	23.4269i		−	1.10559i	−0.833319	−	0.552793i	$-0.813562\pi$
$449$		−	23.4269i		−	1.10559i	0.833319	−	0.552793i	$-0.186438\pi$
$450$		0			0
$451$	2.88868	−	5.00333i	0.136022	−	0.235598i
$452$		0			0
$453$	−3.12801	+	10.5168i	−0.146967	+	0.494121i
$454$		0			0
$455$	−3.10971	−	8.46712i	−0.145785	−	0.396945i
$456$		0			0
$457$	0.661376	+	1.14554i	0.0309378	+	0.0535859i	0.881080	−	0.472968i	$-0.156817\pi$
$457$	0.661376	+	1.14554i	0.0309378	+	0.0535859i	−0.850142	+	0.526554i	$0.823484\pi$
$458$		0			0
$459$	−0.299319	−	1.64577i	−0.0139710	−	0.0768182i
$460$		0			0
$461$	−23.5461			−1.09665			−0.548325	−	0.836266i	$-0.684734\pi$
$461$	−23.5461			−1.09665			−0.548325	+	0.836266i	$0.684734\pi$
$462$		0			0
$463$		−	14.4502i		−	0.671557i	−0.941941	−	0.335778i	$-0.891001\pi$
$463$		−	14.4502i		−	0.671557i	0.941941	−	0.335778i	$-0.108999\pi$
$464$		0			0
$465$	33.0134	−	7.88678i	1.53096	−	0.365741i
$466$		0			0
$467$	13.0084	−	7.51039i	0.601956	−	0.347540i	−0.167855	−	0.985812i	$-0.553684\pi$
$467$	13.0084	−	7.51039i	0.601956	−	0.347540i	0.769811	+	0.638272i	$0.220351\pi$
$468$		0			0
$469$	−2.90969	−	2.42713i	−0.134357	−	0.112074i
$470$		0			0
$471$	1.19312	−	4.01144i	0.0549762	−	0.184837i
$472$		0			0
$473$	−16.9088	−	9.76231i	−0.777468	−	0.448872i
$474$		0			0
$475$	−1.31697			−0.0604269
$476$		0			0
$477$	1.45004	−	26.5330i	0.0663928	−	1.21486i
$478$		0			0
$479$	10.9550	−	18.9745i	0.500545	−	0.866969i	−0.499455	−	0.866340i	$-0.666466\pi$
$479$	10.9550	−	18.9745i	0.500545	−	0.866969i	1.00000		0.000629369i	$-0.000200335\pi$
$480$		0			0
$481$	−0.852653	−	1.47684i	−0.0388776	−	0.0673380i
$482$		0			0
$483$	−16.5720	−	24.9403i	−0.754051	−	1.13482i
$484$		0			0
$485$	4.62134	+	8.00440i	0.209844	+	0.363461i
$486$		0			0
$487$	9.51388	+	5.49284i	0.431115	+	0.248904i	0.699821	−	0.714318i	$-0.253263\pi$
$487$	9.51388	+	5.49284i	0.431115	+	0.248904i	−0.268707	+	0.963222i	$0.586596\pi$
$488$		0			0
$489$	11.2208	−	10.6243i	0.507421	−	0.480448i
$490$		0			0
$491$		−	32.3525i		−	1.46005i	−0.683422	−	0.730024i	$-0.739509\pi$
$491$		−	32.3525i		−	1.46005i	0.683422	−	0.730024i	$-0.260491\pi$
$492$		0			0
$493$	1.96329	+	1.13351i	0.0884222	+	0.0510506i
$494$		0			0
$495$	4.96080	+	9.79018i	0.222971	+	0.440036i
$496$		0			0
$497$	−2.87863	+	16.6079i	−0.129124	+	0.744967i
$498$		0			0
$499$	7.10372	+	12.3040i	0.318006	+	0.550803i	0.980072	−	0.198643i	$-0.0636534\pi$
$499$	7.10372	+	12.3040i	0.318006	+	0.550803i	−0.662066	+	0.749446i	$0.730320\pi$
$500$		0			0
$501$	−2.82174	−	11.8116i	−0.126066	−	0.527702i
$502$		0			0
$503$	−33.4106			−1.48970			−0.744852	−	0.667229i	$-0.767480\pi$
$503$	−33.4106			−1.48970			−0.744852	+	0.667229i	$0.767480\pi$
$504$		0			0
$505$	10.7961			0.480419
$506$		0			0
$507$	4.25144	+	17.7961i	0.188813	+	0.790354i
$508$		0			0
$509$	8.44815	+	14.6326i	0.374458	+	0.648580i	0.990246	−	0.139332i	$-0.0444956\pi$
$509$	8.44815	+	14.6326i	0.374458	+	0.648580i	−0.615788	+	0.787912i	$0.711162\pi$
$510$		0			0
$511$	−18.2452	−	15.2193i	−0.807118	−	0.673261i
$512$		0			0
$513$	−10.0657	+	28.1244i	−0.444410	+	1.24172i
$514$		0			0
$515$	34.6894	+	20.0279i	1.52860	+	0.882536i
$516$		0			0
$517$		−	7.54957i		−	0.332030i
$518$		0			0
$519$	17.9013	−	16.9497i	0.785781	−	0.744011i
$520$		0			0
$521$	−31.0684	−	17.9374i	−1.36113	−	0.785850i	−0.371358	−	0.928490i	$-0.621108\pi$
$521$	−31.0684	−	17.9374i	−1.36113	−	0.785850i	−0.989775	+	0.142639i	$0.954441\pi$
$522$		0			0
$523$	1.10840	+	1.91980i	0.0484669	+	0.0839471i	0.889241	−	0.457439i	$-0.151233\pi$
$523$	1.10840	+	1.91980i	0.0484669	+	0.0839471i	−0.840774	+	0.541386i	$0.817900\pi$
$524$		0			0
$525$	−0.466742	+	0.940354i	−0.0203703	+	0.0410404i
$526$		0			0
$527$	−1.44413	−	2.50130i	−0.0629072	−	0.108959i
$528$		0			0
$529$	−9.84883	+	17.0587i	−0.428210	+	0.741681i
$530$		0			0
$531$	−18.5751	−	1.01514i	−0.806089	−	0.0440532i
$532$		0			0
$533$	−5.38390			−0.233202
$534$		0			0
$535$	−8.36662	−	4.83047i	−0.361721	−	0.208840i
$536$		0			0
$537$	−0.613582	+	2.06295i	−0.0264780	+	0.0890227i
$538$		0			0
$539$	7.58846	+	8.93744i	0.326858	+	0.384963i
$540$		0			0
$541$	32.2404	−	18.6140i	1.38612	−	0.800279i	0.393248	−	0.919432i	$-0.371351\pi$
$541$	32.2404	−	18.6140i	1.38612	−	0.800279i	0.992876	+	0.119153i	$0.0380180\pi$
$542$		0			0
$543$	35.2911	−	8.43092i	1.51449	−	0.361806i
$544$		0			0
$545$			17.7808i			0.761645i
$546$		0			0
$547$	−12.2271			−0.522792			−0.261396	−	0.965232i	$-0.584183\pi$
$547$	−12.2271			−0.522792			−0.261396	+	0.965232i	$0.584183\pi$
$548$		0			0
$549$	7.20502	−	11.0406i	0.307503	−	0.471202i
$550$		0			0
$551$	−20.2415	−	35.0593i	−0.862317	−	1.49358i
$552$		0			0
$553$	−3.77901	−	10.2895i	−0.160700	−	0.437554i
$554$		0			0
$555$	1.17836	−	3.96181i	0.0500187	−	0.168170i
$556$		0			0
$557$	0.649106	−	1.12428i	0.0275035	−	0.0476375i	−0.851946	−	0.523630i	$-0.824578\pi$
$557$	0.649106	−	1.12428i	0.0275035	−	0.0476375i	0.879450	+	0.475992i	$0.157911\pi$
$558$		0			0
$559$			18.1949i			0.769564i
$560$		0			0
$561$	0.678160	−	0.642111i	0.0286320	−	0.0271099i
$562$		0			0
$563$	−24.2080	−	13.9765i	−1.02024	−	0.589038i	−0.106070	−	0.994359i	$-0.533827\pi$
$563$	−24.2080	−	13.9765i	−1.02024	−	0.589038i	−0.914175	+	0.405320i	$0.867160\pi$
$564$		0			0
$565$	25.3475	−	14.6344i	1.06638	−	0.615672i
$566$		0			0
$567$	16.5142	+	17.1546i	0.693533	+	0.720425i
$568$		0			0
$569$	26.1457	−	15.0952i	1.09608	−	0.632825i	0.160895	−	0.986972i	$-0.448562\pi$
$569$	26.1457	−	15.0952i	1.09608	−	0.632825i	0.935190	+	0.354147i	$0.115229\pi$
$570$		0			0
$571$	16.0016	−	27.7156i	0.669646	−	1.15986i	−0.308357	−	0.951271i	$-0.599779\pi$
$571$	16.0016	−	27.7156i	0.669646	−	1.15986i	0.978003	−	0.208591i	$-0.0668877\pi$
$572$		0			0
$573$	30.7182	−	29.0853i	1.28327	−	1.21505i
$574$		0			0
$575$	1.49694			0.0624269
$576$		0			0
$577$	7.72204	−	13.3750i	0.321473	−	0.556807i	−0.659319	−	0.751863i	$-0.729155\pi$
$577$	7.72204	−	13.3750i	0.321473	−	0.556807i	0.980792	+	0.195056i	$0.0624888\pi$
$578$		0			0
$579$	0.0220008	+	0.00654370i	0.000914322	+	0.000271947i
$580$		0			0
$581$	−23.6303	−	4.09581i	−0.980351	−	0.169923i
$582$		0			0
$583$	12.8480	−	7.41782i	0.532112	−	0.307215i
$584$		0			0
$585$	5.58965	−	8.56532i	0.231104	−	0.354132i
$586$		0			0
$587$		−	1.97510i		−	0.0815212i	−0.999169	−	0.0407606i	$-0.987022\pi$
$587$		−	1.97510i		−	0.0815212i	0.999169	−	0.0407606i	$-0.0129781\pi$
$588$		0			0
$589$			51.5768i			2.12518i
$590$		0			0
$591$	2.60961	+	10.9236i	0.107345	+	0.449337i
$592$		0			0
$593$	14.0265	−	8.09823i	0.576001	−	0.332554i	−0.183542	−	0.983012i	$-0.558756\pi$
$593$	14.0265	−	8.09823i	0.576001	−	0.332554i	0.759543	+	0.650458i	$0.225423\pi$
$594$		0			0
$595$	−1.83306	−	0.317722i	−0.0751482	−	0.0130253i
$596$		0			0
$597$	−2.54876	+	8.56926i	−0.104314	+	0.350717i
$598$		0			0
$599$	7.00327	−	12.1300i	0.286146	−	0.495619i	−0.686741	−	0.726903i	$-0.740959\pi$
$599$	7.00327	−	12.1300i	0.286146	−	0.495619i	0.972886	+	0.231283i	$0.0742925\pi$
$600$		0			0
$601$	−15.5923			−0.636024			−0.318012	−	0.948087i	$-0.603015\pi$
$601$	−15.5923			−0.636024			−0.318012	+	0.948087i	$0.603015\pi$
$602$		0			0
$603$	0.234452	−	4.29003i	0.00954764	−	0.174704i
$604$		0			0
$605$	8.94954	−	15.5011i	0.363850	−	0.630207i
$606$		0			0
$607$	28.3416	−	16.3630i	1.15035	−	0.664155i	0.201378	−	0.979514i	$-0.435458\pi$
$607$	28.3416	−	16.3630i	1.15035	−	0.664155i	0.948973	+	0.315359i	$0.102125\pi$
$608$		0			0
$609$	−32.2070	+	2.02778i	−1.30509	+	0.0821696i
$610$		0			0
$611$	−6.09286	+	3.51771i	−0.246491	+	0.142311i
$612$		0			0
$613$	0.287887	+	0.166212i	0.0116277	+	0.00671323i	0.505803	−	0.862649i	$-0.331196\pi$
$613$	0.287887	+	0.166212i	0.0116277	+	0.00671323i	−0.494175	+	0.869363i	$0.664530\pi$
$614$		0			0
$615$	−8.97213	−	9.47585i	−0.361791	−	0.382103i
$616$		0			0
$617$			39.1386i			1.57566i	0.615893	+	0.787830i	$0.288795\pi$
$617$			39.1386i			1.57566i	−0.615893	+	0.787830i	$0.711205\pi$
$618$		0			0
$619$	−1.61116	+	2.79062i	−0.0647581	+	0.112164i	−0.896587	−	0.442868i	$-0.853961\pi$
$619$	−1.61116	+	2.79062i	−0.0647581	+	0.112164i	0.831829	+	0.555033i	$0.187294\pi$
$620$		0			0
$621$	11.4412	−	31.9677i	0.459119	−	1.28282i
$622$		0			0
$623$	−4.81946	−	13.1225i	−0.193088	−	0.525740i
$624$		0			0
$625$	11.9010	+	20.6132i	0.476042	+	0.824528i
$626$		0			0
$627$	−16.2209	+	3.87513i	−0.647802	+	0.154758i
$628$		0			0
$629$	−0.351718			−0.0140239
$630$		0			0
$631$		−	10.2850i		−	0.409441i	−0.978820	−	0.204721i	$-0.934371\pi$
$631$		−	10.2850i		−	0.409441i	0.978820	−	0.204721i	$-0.0656286\pi$
$632$		0			0
$633$	6.77563	+	28.3622i	0.269307	+	1.12730i
$634$		0			0
$635$	−23.7125	+	13.6904i	−0.941002	+	0.543287i
$636$		0			0
$637$	3.67710	−	10.2886i	0.145692	−	0.407650i
$638$		0			0
$639$	−17.0486	+	8.63874i	−0.674433	+	0.341743i
$640$		0			0
$641$	26.2428	+	15.1513i	1.03653	+	0.598439i	0.918848	−	0.394612i	$-0.129121\pi$
$641$	26.2428	+	15.1513i	1.03653	+	0.598439i	0.117680	+	0.993052i	$0.462454\pi$
$642$		0			0
$643$	37.4668			1.47755			0.738773	−	0.673955i	$-0.235406\pi$
$643$	37.4668			1.47755			0.738773	+	0.673955i	$0.235406\pi$
$644$		0			0
$645$	−32.0238	+	30.3214i	−1.26093	+	1.19390i
$646$		0			0
$647$	−0.130900	+	0.226726i	−0.00514622	+	0.00891351i	−0.868587	−	0.495537i	$-0.834971\pi$
$647$	−0.130900	+	0.226726i	−0.00514622	+	0.00891351i	0.863441	+	0.504450i	$0.168305\pi$
$648$		0			0
$649$	−5.19303	−	8.99459i	−0.203844	−	0.353069i
$650$		0			0
$651$	36.8272	+	18.2791i	1.44337	+	0.716413i
$652$		0			0
$653$	−22.1548	−	38.3732i	−0.866984	−	1.50166i	−0.865064	−	0.501662i	$-0.832722\pi$
$653$	−22.1548	−	38.3732i	−0.866984	−	1.50166i	−0.00192051	−	0.999998i	$-0.500611\pi$
$654$		0			0
$655$	32.3586	+	18.6822i	1.26435	+	0.729975i
$656$		0			0
$657$	1.47013	−	26.9006i	0.0573552	−	1.04949i
$658$		0			0
$659$			23.4513i			0.913534i	0.889586	+	0.456767i	$0.150993\pi$
$659$			23.4513i			0.913534i	−0.889586	+	0.456767i	$0.849007\pi$
$660$		0			0
$661$	29.3695	+	16.9565i	1.14234	+	0.659531i	0.947009	−	0.321206i	$-0.104088\pi$
$661$	29.3695	+	16.9565i	1.14234	+	0.659531i	0.195332	+	0.980737i	$0.437422\pi$
$662$		0			0
$663$	−0.834201	−	0.248117i	−0.0323977	−	0.00963605i
$664$		0			0
$665$	25.5114	+	21.2804i	0.989289	+	0.825219i
$666$		0			0
$667$	23.0076	+	39.8503i	0.890857	+	1.54301i
$668$		0			0
$669$	3.03523	−	0.725105i	0.117349	−	0.0280342i
$670$		0			0
$671$	7.36050			0.284149
$672$		0			0
$673$	−13.3855			−0.515973			−0.257986	−	0.966149i	$-0.583059\pi$
$673$	−13.3855			−0.515973			−0.257986	+	0.966149i	$0.583059\pi$
$674$		0			0
$675$	−1.17117	+	0.213002i	−0.0450783	+	0.00819845i
$676$		0			0
$677$	−13.0777	−	22.6513i	−0.502618	−	0.870559i	−0.999995	−	0.00302522i	$-0.999037\pi$
$677$	−13.0777	−	22.6513i	−0.502618	−	0.870559i	0.497378	−	0.867534i	$-0.334296\pi$
$678$		0			0
$679$	−1.91201	+	11.0311i	−0.0733761	+	0.423335i
$680$		0			0
$681$	5.72886	−	19.2612i	0.219530	−	0.738090i
$682$		0			0
$683$	−19.0543	−	11.0010i	−0.729092	−	0.420942i	0.0889978	−	0.996032i	$-0.471634\pi$
$683$	−19.0543	−	11.0010i	−0.729092	−	0.420942i	−0.818090	+	0.575090i	$0.804967\pi$
$684$		0			0
$685$			45.2470i			1.72880i
$686$		0			0
$687$	−11.6978	−	12.3546i	−0.446299	−	0.471356i
$688$		0			0
$689$	−11.9731	−	6.91265i	−0.456137	−	0.263351i
$690$		0			0
$691$	−17.0852	−	29.5924i	−0.649952	−	1.12575i	−0.983134	−	0.182887i	$-0.941456\pi$
$691$	−17.0852	−	29.5924i	−0.649952	−	1.12575i	0.333182	−	0.942862i	$-0.391878\pi$
$692$		0			0
$693$	−2.98184	+	12.9556i	−0.113271	+	0.492141i
$694$		0			0
$695$	−1.38978	−	2.40717i	−0.0527173	−	0.0913091i
$696$		0			0
$697$	−0.555213	+	0.961656i	−0.0210302	+	0.0364253i
$698$		0			0
$699$	9.54531	+	10.0812i	0.361037	+	0.381306i
$700$		0			0
$701$	25.6168			0.967533			0.483767	−	0.875197i	$-0.339268\pi$
$701$	25.6168			0.967533			0.483767	+	0.875197i	$0.339268\pi$
$702$		0			0
$703$	5.43931	+	3.14039i	0.205147	+	0.118442i
$704$		0			0
$705$	−16.3449	−	4.86146i	−0.615584	−	0.183093i
$706$		0			0
$707$	10.0421	+	8.37668i	0.377673	+	0.315037i
$708$		0			0
$709$	0.228674	−	0.132025i	0.00858802	−	0.00495830i	−0.495700	−	0.868494i	$-0.665088\pi$
$709$	0.228674	−	0.132025i	0.00858802	−	0.00495830i	0.504288	+	0.863536i	$0.331755\pi$
$710$		0			0
$711$	6.79271	−	10.4088i	0.254746	−	0.390361i
$712$		0			0
$713$		−	58.6250i		−	2.19552i
$714$		0			0
$715$	5.71028			0.213552
$716$		0			0
$717$	2.42456	+	10.1490i	0.0905467	+	0.379021i
$718$		0			0
$719$	19.9630	+	34.5770i	0.744496	+	1.28950i	0.950430	+	0.310939i	$0.100643\pi$
$719$	19.9630	+	34.5770i	0.744496	+	1.28950i	−0.205934	+	0.978566i	$0.566023\pi$
$720$		0			0
$721$	16.7271	+	45.5447i	0.622952	+	1.69617i
$722$		0			0
$723$	16.9974	+	5.05555i	0.632141	+	0.188018i
$724$		0			0
$725$	0.806627	−	1.39712i	0.0299574	−	0.0518877i
$726$		0			0
$727$		−	4.46181i		−	0.165479i	−0.996571	−	0.0827397i	$-0.973633\pi$
$727$		−	4.46181i		−	0.165479i	0.996571	−	0.0827397i	$-0.0263670\pi$
$728$		0			0
$729$	−4.40255	+	26.6386i	−0.163057	+	0.986617i
$730$		0			0
$731$	3.24993	+	1.87635i	0.120203	+	0.0693992i
$732$		0			0
$733$	3.91514	−	2.26041i	0.144609	−	0.0834900i	−0.425950	−	0.904747i	$-0.640060\pi$
$733$	3.91514	−	2.26041i	0.144609	−	0.0834900i	0.570559	+	0.821257i	$0.306727\pi$
$734$		0			0
$735$	24.2362	−	10.6739i	0.893964	−	0.393714i
$736$		0			0
$737$	2.07736	−	1.19936i	0.0765205	−	0.0441791i
$738$		0			0
$739$	0.571921	−	0.990596i	0.0210384	−	0.0364397i	−0.855315	−	0.518109i	$-0.826636\pi$
$739$	0.571921	−	0.990596i	0.0210384	−	0.0364397i	0.876353	+	0.481670i	$0.159969\pi$
$740$		0			0
$741$	10.6855	+	11.2854i	0.392543	+	0.414581i
$742$		0			0
$743$	−13.5335			−0.496495			−0.248248	−	0.968697i	$-0.579855\pi$
$743$	−13.5335			−0.496495			−0.248248	+	0.968697i	$0.579855\pi$
$744$		0			0
$745$	−5.39804	+	9.34968i	−0.197769	+	0.342546i
$746$		0			0
$747$	−12.2915	−	24.2574i	−0.449722	−	0.887531i
$748$		0			0
$749$	−4.03437	−	10.9848i	−0.147413	−	0.401375i
$750$		0			0
$751$	13.7335	−	7.92906i	0.501144	−	0.289336i	−0.228042	−	0.973651i	$-0.573232\pi$
$751$	13.7335	−	7.92906i	0.501144	−	0.289336i	0.729186	+	0.684316i	$0.239899\pi$
$752$		0			0
$753$	−16.8074	+	4.01524i	−0.612497	+	0.146323i
$754$		0			0
$755$			13.8366i			0.503566i
$756$		0			0
$757$		−	41.0141i		−	1.49068i	−0.666683	−	0.745341i	$-0.732287\pi$
$757$		−	41.0141i		−	1.49068i	0.666683	−	0.745341i	$-0.267713\pi$
$758$		0			0
$759$	18.4376	−	4.40468i	0.669243	−	0.159880i
$760$		0			0
$761$	8.79472	−	5.07763i	0.318808	−	0.184064i	−0.332053	−	0.943261i	$-0.607741\pi$
$761$	8.79472	−	5.07763i	0.318808	−	0.184064i	0.650861	+	0.759197i	$0.274408\pi$
$762$		0			0
$763$	−13.7961	+	16.5390i	−0.499452	+	0.598753i
$764$		0			0
$765$	−0.953481	−	1.88170i	−0.0344732	−	0.0680331i
$766$		0			0
$767$	−4.83937	+	8.38203i	−0.174740	+	0.302658i
$768$		0			0
$769$	15.2996			0.551719			0.275859	−	0.961198i	$-0.411038\pi$
$769$	15.2996			0.551719			0.275859	+	0.961198i	$0.411038\pi$
$770$		0			0
$771$	23.5903	+	24.9148i	0.849585	+	0.897283i
$772$		0			0
$773$	−18.3453	+	31.7750i	−0.659835	+	1.14287i	0.320823	+	0.947139i	$0.396040\pi$
$773$	−18.3453	+	31.7750i	−0.659835	+	1.14287i	−0.980658	+	0.195728i	$0.937293\pi$
$774$		0			0
$775$	−1.77998	+	1.02767i	−0.0639388	+	0.0369151i
$776$		0			0
$777$	4.17004	−	2.77084i	0.149599	−	0.0994035i
$778$		0			0
$779$	17.1727	−	9.91466i	0.615276	−	0.355230i
$780$		0			0
$781$	−9.24099	−	5.33529i	−0.330669	−	0.190912i
$782$		0			0
$783$	−23.6709	−	27.9040i	−0.845927	−	0.997208i
$784$		0			0
$785$		−	5.27773i		−	0.188370i
$786$		0			0
$787$	−14.6430	+	25.3624i	−0.521965	+	0.904071i	0.477708	+	0.878519i	$0.341468\pi$
$787$	−14.6430	+	25.3624i	−0.521965	+	0.904071i	−0.999673	+	0.0255520i	$0.991866\pi$
$788$		0			0
$789$	−11.3483	−	3.37533i	−0.404010	−	0.120165i
$790$		0			0
$791$	34.9321	+	6.05473i	1.24204	+	0.215281i
$792$		0			0
$793$	−3.42962	−	5.94027i	−0.121789	−	0.210945i
$794$		0			0
$795$	−7.78630	−	32.5928i	−0.276152	−	1.15595i
$796$		0			0
$797$	18.4577			0.653805			0.326903	−	0.945058i	$-0.393995\pi$
$797$	18.4577			0.653805			0.326903	+	0.945058i	$0.393995\pi$
$798$		0			0
$799$			1.45105i			0.0513345i
$800$		0			0
$801$	8.66291	−	13.2746i	0.306089	−	0.469036i
$802$		0			0
$803$	13.0260	−	7.52059i	0.459679	−	0.265396i
$804$		0			0
$805$	−28.9976	−	24.1885i	−1.02203	−	0.852533i
$806$		0			0
$807$	−40.1171	−	11.9320i	−1.41219	−	0.420028i
$808$		0			0
$809$	−12.9060	−	7.45126i	−0.453750	−	0.261972i	0.255663	−	0.966766i	$-0.417706\pi$
$809$	−12.9060	−	7.45126i	−0.453750	−	0.261972i	−0.709412	+	0.704794i	$0.751040\pi$
$810$		0			0
$811$	−29.7496			−1.04465			−0.522325	−	0.852747i	$-0.674935\pi$
$811$	−29.7496			−1.04465			−0.522325	+	0.852747i	$0.674935\pi$
$812$		0			0
$813$	−21.0161	−	22.1960i	−0.737067	−	0.778448i
$814$		0			0
$815$	9.74341	−	16.8761i	0.341297	−	0.591143i
$816$		0			0
$817$	−33.5067	−	58.0353i	−1.17225	−	2.03040i
$818$		0			0
$819$	11.8451	−	3.63014i	0.413902	−	0.126847i
$820$		0			0
$821$	7.25813	+	12.5715i	0.253311	+	0.438747i	0.964435	−	0.264319i	$-0.0851472\pi$
$821$	7.25813	+	12.5715i	0.253311	+	0.438747i	−0.711125	+	0.703066i	$0.751814\pi$
$822$		0			0
$823$	−42.5817	−	24.5846i	−1.48431	−	0.856965i	−0.484465	−	0.874810i	$-0.660986\pi$
$823$	−42.5817	−	24.5846i	−1.48431	−	0.856965i	−0.999841	+	0.0178459i	$0.994319\pi$
$824$		0			0
$825$	−0.456939	−	0.482593i	−0.0159086	−	0.0168017i
$826$		0			0
$827$		−	0.00653186i		−	0.000227135i	−1.00000		0.000113567i	$-0.999964\pi$
$827$		−	0.00653186i		−	0.000227135i	1.00000		0.000113567i	$-3.61496e-5\pi$
$828$		0			0
$829$	−7.61159	−	4.39455i	−0.264361	−	0.152629i	0.361961	−	0.932193i	$-0.382107\pi$
$829$	−7.61159	−	4.39455i	−0.264361	−	0.152629i	−0.626322	+	0.779564i	$0.715441\pi$
$830$		0			0
$831$	7.36950	−	24.7772i	0.255645	−	0.859513i
$832$		0			0
$833$	−1.45853	−	1.71781i	−0.0505350	−	0.0595184i
$834$		0			0
$835$	−7.65719	−	13.2626i	−0.264988	−	0.458973i
$836$		0			0
$837$	8.34182	+	45.8666i	0.288336	+	1.58538i
$838$		0			0
$839$	35.4452			1.22371			0.611853	−	0.790972i	$-0.290425\pi$
$839$	35.4452			1.22371			0.611853	+	0.790972i	$0.290425\pi$
$840$		0			0
$841$	20.5905			0.710017
$842$		0			0
$843$	23.3980	−	5.58970i	0.805870	−	0.192519i
$844$		0			0
$845$	11.5369	+	19.9825i	0.396881	+	0.687417i
$846$		0			0
$847$	20.3518	−	7.47458i	0.699296	−	0.256829i
$848$		0			0
$849$	−9.59132	−	2.85275i	−0.329173	−	0.0979061i
$850$		0			0
$851$	−6.18262	−	3.56954i	−0.211937	−	0.122362i
$852$		0			0
$853$		−	23.8784i		−	0.817581i	−0.912628	−	0.408791i	$-0.865951\pi$
$853$		−	23.8784i		−	0.817581i	0.912628	−	0.408791i	$-0.134049\pi$
$854$		0			0
$855$	−2.05562	+	37.6138i	−0.0703006	+	1.28637i
$856$		0			0
$857$	−46.6784	−	26.9498i	−1.59451	−	0.920588i	−0.992520	−	0.122081i	$-0.961043\pi$
$857$	−46.6784	−	26.9498i	−1.59451	−	0.920588i	−0.601985	−	0.798507i	$-0.705623\pi$
$858$		0			0
$859$	−9.18799	−	15.9141i	−0.313490	−	0.542981i	0.665625	−	0.746286i	$-0.268165\pi$
$859$	−9.18799	−	15.9141i	−0.313490	−	0.542981i	−0.979115	+	0.203305i	$0.934832\pi$
$860$		0			0
$861$	−0.993242	−	15.7756i	−0.0338496	−	0.537630i
$862$		0			0
$863$	24.6737	+	42.7360i	0.839901	+	1.45475i	0.889977	+	0.456006i	$0.150721\pi$
$863$	24.6737	+	42.7360i	0.839901	+	1.45475i	−0.0500753	+	0.998745i	$0.515946\pi$
$864$		0			0
$865$	15.5444	−	26.9236i	0.528524	−	0.915431i
$866$		0			0
$867$	21.2509	−	20.1212i	0.721717	−	0.683352i
$868$		0			0
$869$	6.93929			0.235399
$870$		0			0
$871$	−1.93589	−	1.11768i	−0.0655950	−	0.0378713i
$872$		0			0
$873$	−11.3238	+	5.73792i	−0.383253	+	0.194199i
$874$		0			0
$875$	−5.16082	+	29.7747i	−0.174467	+	1.00657i
$876$		0			0
$877$	−51.2316	+	29.5786i	−1.72997	+	0.998797i	−0.840467	+	0.541863i	$0.817719\pi$
$877$	−51.2316	+	29.5786i	−1.72997	+	0.998797i	−0.889500	+	0.456935i	$0.848947\pi$
$878$		0			0
$879$	−6.29364	−	26.3446i	−0.212279	−	0.888583i
$880$		0			0
$881$			51.0955i			1.72145i	0.509068	+	0.860726i	$0.329990\pi$
$881$			51.0955i			1.72145i	−0.509068	+	0.860726i	$0.670010\pi$
$882$		0			0
$883$	−10.4148			−0.350486			−0.175243	−	0.984525i	$-0.556071\pi$
$883$	−10.4148			−0.350486			−0.175243	+	0.984525i	$0.556071\pi$
$884$		0			0
$885$	−22.8174	+	5.45099i	−0.766997	+	0.183233i
$886$		0			0
$887$	−12.2631	−	21.2404i	−0.411756	−	0.713183i	0.583326	−	0.812238i	$-0.301751\pi$
$887$	−12.2631	−	21.2404i	−0.411756	−	0.713183i	−0.995082	+	0.0990557i	$0.968418\pi$
$888$		0			0
$889$	−32.6789	−	5.66419i	−1.09601	−	0.189971i
$890$		0			0
$891$	−13.7983	+	6.06961i	−0.462262	+	0.203340i
$892$		0			0
$893$	12.9560	−	22.4405i	0.433556	−	0.750942i
$894$		0			0
$895$			2.71416i			0.0907242i
$896$		0			0
$897$	−12.1458	−	12.8277i	−0.405535	−	0.428303i
$898$		0			0
$899$	−54.7155	−	31.5900i	−1.82487	−	1.05359i
$900$		0			0
$901$	−2.46944	+	1.42573i	−0.0822688	+	0.0474979i
$902$		0			0
$903$	−53.3137	+	3.35667i	−1.77417	+	0.111703i
$904$		0			0
$905$	39.6267	−	22.8785i	1.31724	−	0.760507i
$906$		0			0
$907$	−14.6718	+	25.4124i	−0.487170	+	0.843803i	−0.999891	−	0.0147518i	$-0.995304\pi$
$907$	−14.6718	+	25.4124i	−0.487170	+	0.843803i	0.512721	+	0.858555i	$0.328638\pi$
$908$		0			0
$909$	−0.809158	+	14.8060i	−0.0268381	+	0.491086i
$910$		0			0
$911$	−21.9953			−0.728738			−0.364369	−	0.931255i	$-0.618715\pi$
$911$	−21.9953			−0.728738			−0.364369	+	0.931255i	$0.618715\pi$
$912$		0			0
$913$	7.59124	−	13.1484i	0.251233	−	0.435149i
$914$		0			0
$915$	4.73971	−	15.9356i	0.156690	−	0.526813i
$916$		0			0
$917$	15.6032	+	42.4845i	0.515264	+	1.40296i
$918$		0			0
$919$	−32.9464	+	19.0216i	−1.08680	+	0.627464i	−0.932723	−	0.360594i	$-0.882574\pi$
$919$	−32.9464	+	19.0216i	−1.08680	+	0.627464i	−0.154077	+	0.988059i	$0.549241\pi$
$920$		0			0
$921$	−2.89722	−	12.1275i	−0.0954668	−	0.399616i
$922$		0			0
$923$			9.94388i			0.327307i
$924$		0			0
$925$			0.250290i			0.00822948i
$926$		0			0
$927$	−30.0668	+	46.0729i	−0.987523	+	1.51323i
$928$		0			0
$929$	−26.6079	+	15.3621i	−0.872978	+	0.504014i	−0.868337	−	0.495975i	$-0.834811\pi$
$929$	−26.6079	+	15.3621i	−0.872978	+	0.504014i	−0.00464125	+	0.999989i	$0.501477\pi$
$930$		0			0
$931$	7.21830	+	39.5886i	0.236570	+	1.29746i
$932$		0			0
$933$	−14.4465	−	4.29682i	−0.472957	−	0.140672i
$934$		0			0
$935$	0.588871	−	1.01995i	0.0192581	−	0.0333561i
$936$		0			0
$937$	37.2804			1.21790			0.608949	−	0.793210i	$-0.291592\pi$
$937$	37.2804			1.21790			0.608949	+	0.793210i	$0.291592\pi$
$938$		0			0
$939$	−24.0863	+	22.8059i	−0.786027	+	0.744243i
$940$		0			0
$941$	16.0848	−	27.8596i	0.524348	−	0.908198i	−0.475250	−	0.879851i	$-0.657642\pi$
$941$	16.0848	−	27.8596i	0.524348	−	0.908198i	0.999598	−	0.0283471i	$-0.00902436\pi$
$942$		0			0
$943$	−19.5194	+	11.2695i	−0.635640	+	0.366987i
$944$		0			0
$945$	26.1288	+	14.7983i	0.849969	+	0.481389i
$946$		0			0
$947$	33.3248	−	19.2401i	1.08291	−	0.625219i	0.151231	−	0.988498i	$-0.451676\pi$
$947$	33.3248	−	19.2401i	1.08291	−	0.625219i	0.931680	+	0.363279i	$0.118343\pi$
$948$		0			0
$949$	−12.1389	−	7.00842i	−0.394046	−	0.227503i
$950$		0			0
$951$	−4.60773	+	4.36279i	−0.149416	+	0.141473i
$952$		0			0
$953$			37.1213i			1.20248i	0.799070	+	0.601238i	$0.205326\pi$
$953$			37.1213i			1.20248i	−0.799070	+	0.601238i	$0.794674\pi$
$954$		0			0
$955$	26.6737	−	46.2002i	0.863140	−	1.49500i
$956$		0			0
$957$	5.82414	−	19.5815i	0.188268	−	0.632981i
$958$		0			0
$959$	−35.1071	+	42.0871i	−1.13367	+	1.35906i
$960$		0			0
$961$	24.7469	+	42.8628i	0.798286	+	1.38267i
$962$		0			0
$963$	7.25172	−	11.1122i	0.233683	−	0.358085i
$964$		0			0
$965$	0.0289458			0.000931799
$966$		0			0
$967$			28.7342i			0.924030i	0.886872	+	0.462015i	$0.152873\pi$
$967$			28.7342i			0.924030i	−0.886872	+	0.462015i	$0.847127\pi$
$968$		0			0
$969$	3.11772	−	0.744812i	0.100156	−	0.0239268i
$970$		0			0
$971$	−17.2557	+	9.96261i	−0.553763	+	0.319715i	−0.750638	−	0.660713i	$-0.770254\pi$
$971$	−17.2557	+	9.96261i	−0.553763	+	0.319715i	0.196875	+	0.980429i	$0.436921\pi$
$972$		0			0
$973$	0.574998	−	3.31739i	0.0184336	−	0.106351i
$974$		0			0
$975$	−0.176565	+	0.593635i	−0.00565460	+	0.0190115i
$976$		0			0
$977$	11.6105	+	6.70332i	0.371453	+	0.214458i	0.674093	−	0.738647i	$-0.264535\pi$
$977$	11.6105	+	6.70332i	0.371453	+	0.214458i	−0.302640	+	0.953105i	$0.597868\pi$
$978$		0			0
$979$	8.84986			0.282843
$980$		0			0
$981$	−24.3851	−	1.33266i	−0.778555	−	0.0425484i
$982$		0			0
$983$	10.2774	−	17.8010i	0.327799	−	0.567765i	−0.654276	−	0.756256i	$-0.727026\pi$
$983$	10.2774	−	17.8010i	0.327799	−	0.567765i	0.982075	+	0.188491i	$0.0603597\pi$
$984$		0			0
$985$	7.08155	+	12.2656i	0.225637	+	0.390814i
$986$		0			0
$987$	−11.4314	−	17.2040i	−0.363866	−	0.547608i
$988$		0			0
$989$	38.0856	+	65.9661i	1.21105	+	2.09760i
$990$		0			0
$991$	−4.87181	−	2.81274i	−0.154758	−	0.0893497i	0.420621	−	0.907236i	$-0.361812\pi$
$991$	−4.87181	−	2.81274i	−0.154758	−	0.0893497i	−0.575379	+	0.817887i	$0.695146\pi$
$992$		0			0
$993$	13.6177	−	12.8938i	0.432144	−	0.409172i
$994$		0			0
$995$			11.2743i			0.357420i
$996$		0			0
$997$	2.03245	+	1.17343i	0.0643683	+	0.0371631i	0.531839	−	0.846846i	$-0.321501\pi$
$997$	2.03245	+	1.17343i	0.0643683	+	0.0371631i	−0.467470	+	0.884009i	$0.654835\pi$
$998$		0			0
$999$	5.34502	+	1.91297i	0.169109	+	0.0605238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bd.a.431.18		56
3.2	odd	2	inner	672.2.bd.a.431.3		56
4.3	odd	2		168.2.v.a.11.20	yes	56
7.2	even	3	inner	672.2.bd.a.527.4		56
8.3	odd	2	inner	672.2.bd.a.431.17		56
8.5	even	2		168.2.v.a.11.27	yes	56
12.11	even	2		168.2.v.a.11.9	yes	56
21.2	odd	6	inner	672.2.bd.a.527.17		56
24.5	odd	2		168.2.v.a.11.2	✓	56
24.11	even	2	inner	672.2.bd.a.431.4		56
28.23	odd	6		168.2.v.a.107.2	yes	56
56.37	even	6		168.2.v.a.107.9	yes	56
56.51	odd	6	inner	672.2.bd.a.527.3		56
84.23	even	6		168.2.v.a.107.27	yes	56
168.107	even	6	inner	672.2.bd.a.527.18		56
168.149	odd	6		168.2.v.a.107.20	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.2	✓	56	24.5	odd	2
168.2.v.a.11.9	yes	56	12.11	even	2
168.2.v.a.11.20	yes	56	4.3	odd	2
168.2.v.a.11.27	yes	56	8.5	even	2
168.2.v.a.107.2	yes	56	28.23	odd	6
168.2.v.a.107.9	yes	56	56.37	even	6
168.2.v.a.107.20	yes	56	168.149	odd	6
168.2.v.a.107.27	yes	56	84.23	even	6
672.2.bd.a.431.3		56	3.2	odd	2	inner
672.2.bd.a.431.4		56	24.11	even	2	inner
672.2.bd.a.431.17		56	8.3	odd	2	inner
672.2.bd.a.431.18		56	1.1	even	1	trivial
672.2.bd.a.527.3		56	56.51	odd	6	inner
672.2.bd.a.527.4		56	7.2	even	3	inner
672.2.bd.a.527.17		56	21.2	odd	6	inner
672.2.bd.a.527.18		56	168.107	even	6	inner

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bd (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.402456 + 1.68465i) q^{3} +(1.09212 + 1.89161i) q^{5} +(-0.451847 + 2.60688i) q^{7} +(-2.67606 + 1.35599i) q^{9} +(-1.45052 - 0.837460i) q^{11} +1.56085i q^{13} +(-2.74716 + 2.60112i) q^{15} +(0.278795 + 0.160963i) q^{17} +(-2.87437 - 4.97856i) q^{19} +(-4.57352 + 0.287952i) q^{21} +(3.26717 + 5.65891i) q^{23} +(0.114544 - 0.198397i) q^{25} +(-3.36136 - 3.96248i) q^{27} +7.04205 q^{29} +(-7.76983 - 4.48591i) q^{31} +(0.827052 - 2.78066i) q^{33} +(-5.42467 + 1.99231i) q^{35} +(-0.946173 + 0.546273i) q^{37} +(-2.62949 + 0.628175i) q^{39} +3.44933i q^{41} +11.6570 q^{43} +(-5.48758 - 3.58115i) q^{45} +(2.25371 + 3.90354i) q^{47} +(-6.59167 - 2.35583i) q^{49} +(-0.158962 + 0.534452i) q^{51} +(-4.42876 + 7.67084i) q^{53} -3.65843i q^{55} +(7.23030 - 6.84595i) q^{57} +(5.37016 + 3.10046i) q^{59} +(-3.80578 + 2.19727i) q^{61} +(-2.32574 - 7.58887i) q^{63} +(-2.95253 + 1.70464i) q^{65} +(-0.716072 + 1.24027i) q^{67} +(-8.21836 + 7.78149i) q^{69} +6.37080 q^{71} +(-4.49012 + 7.77711i) q^{73} +(0.380327 + 0.113121i) q^{75} +(2.83858 - 3.40294i) q^{77} +(-3.58799 + 2.07153i) q^{79} +(5.32258 - 7.25742i) q^{81} +9.06459i q^{83} +0.703162i q^{85} +(2.83411 + 11.8634i) q^{87} +(-4.57586 + 2.64187i) q^{89} +(-4.06896 - 0.705268i) q^{91} +(4.43016 - 14.8948i) q^{93} +(6.27833 - 10.8744i) q^{95} +4.23153 q^{97} +(5.01728 + 0.274197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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