LMFDB - Embedded newform 345.2.t.a.4.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [345,2,Mod(4,345)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(345, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 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("345.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.t (of order $22$, degree $10$, 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:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	345.4
Dual form			345.2.t.a.259.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.50929 + 1.14595i) q^{2} +(-0.281733 - 0.959493i) q^{3} +(3.67359 - 4.23955i) q^{4} +(2.18488 + 0.475730i) q^{5} +(1.80648 + 2.08479i) q^{6} +(4.53926 - 0.652647i) q^{7} +(-2.80541 + 9.55436i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(-6.02764 + 1.31002i) q^{10} +(0.742396 - 1.62562i) q^{11} +(-5.10279 - 2.33037i) q^{12} +(-0.440188 - 0.0632895i) q^{13} +(-10.6424 + 6.83946i) q^{14} +(-0.159091 - 2.23040i) q^{15} +(-2.31256 - 16.0842i) q^{16} +(3.15694 - 2.73551i) q^{17} +(1.49140 - 2.32066i) q^{18} +(-1.97660 + 2.28112i) q^{19} +(10.0432 - 7.51526i) q^{20} +(-1.90507 - 4.17151i) q^{21} +4.92990i q^{22} +(-4.33473 + 2.05185i) q^{23} +9.95771 q^{24} +(4.54736 + 2.07882i) q^{25} +(1.17708 - 0.345623i) q^{26} +(0.755750 + 0.654861i) q^{27} +(13.9085 - 21.6420i) q^{28} +(0.305888 + 0.353014i) q^{29} +(2.95514 + 5.41441i) q^{30} +(-5.11673 - 1.50241i) q^{31} +(13.4676 + 20.9559i) q^{32} +(-1.76893 - 0.254334i) q^{33} +(-4.78692 + 10.4819i) q^{34} +(10.2282 + 0.733509i) q^{35} +(-0.798348 + 5.55263i) q^{36} +(0.829390 + 1.29056i) q^{37} +(2.34580 - 7.98907i) q^{38} +(0.0632895 + 0.440188i) q^{39} +(-10.6748 + 19.5405i) q^{40} +(1.29270 + 0.830767i) q^{41} +(9.56072 + 8.28441i) q^{42} +(1.10275 + 3.75563i) q^{43} +(-4.16464 - 9.11930i) q^{44} +(-2.09523 + 0.781023i) q^{45} +(8.52576 - 10.1161i) q^{46} -5.06600i q^{47} +(-14.7812 + 6.75034i) q^{48} +(13.4625 - 3.95294i) q^{49} +(-13.7929 - 0.00529699i) q^{50} +(-3.51411 - 2.25838i) q^{51} +(-1.88539 + 1.63370i) q^{52} +(3.35460 - 0.482319i) q^{53} +(-2.64683 - 0.777180i) q^{54} +(2.39540 - 3.19860i) q^{55} +(-6.49887 + 45.2006i) q^{56} +(2.74559 + 1.25387i) q^{57} +(-1.17210 - 0.535279i) q^{58} +(1.04770 - 7.28690i) q^{59} +(-10.0403 - 7.51911i) q^{60} +(12.2396 + 3.59387i) q^{61} +(14.5610 - 2.09356i) q^{62} +(-3.46582 + 3.00315i) q^{63} +(-30.4684 - 19.5809i) q^{64} +(-0.931647 - 0.347690i) q^{65} +(4.73021 - 1.38891i) q^{66} +(-3.10451 + 1.41778i) q^{67} -23.4332i q^{68} +(3.18997 + 3.58107i) q^{69} +(-26.5061 + 9.88045i) q^{70} +(-0.588693 - 1.28906i) q^{71} +(-2.80541 - 9.55436i) q^{72} +(-11.7420 - 10.1745i) q^{73} +(-3.56010 - 2.28794i) q^{74} +(0.713475 - 4.94883i) q^{75} +(2.40969 + 16.7598i) q^{76} +(2.30897 - 7.86364i) q^{77} +(-0.663246 - 1.03203i) q^{78} +(0.519230 - 3.61133i) q^{79} +(2.59909 - 36.2422i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-4.19577 - 0.603261i) q^{82} +(2.53083 + 3.93805i) q^{83} +(-24.6838 - 7.24782i) q^{84} +(8.19889 - 4.47489i) q^{85} +(-7.07089 - 8.16024i) q^{86} +(0.252535 - 0.392953i) q^{87} +(13.4490 + 11.6537i) q^{88} +(-7.76556 + 2.28017i) q^{89} +(4.36253 - 4.36085i) q^{90} -2.03943 q^{91} +(-7.22511 + 25.9150i) q^{92} +5.33275i q^{93} +(5.80540 + 12.7121i) q^{94} +(-5.40382 + 4.04363i) q^{95} +(16.3128 - 18.8260i) q^{96} +(-8.76606 + 13.6403i) q^{97} +(-29.2513 + 25.3464i) q^{98} +(0.254334 + 1.76893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) $ 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$	$-1$

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 $

$2$	−2.50929	+	1.14595i	−1.77433	+	0.810311i	−0.795414	+	0.606066i	$0.792747\pi$
$2$	−2.50929	+	1.14595i	−1.77433	+	0.810311i	−0.978920	+	0.204245i	$0.934526\pi$
$3$	−0.281733	−	0.959493i	−0.162658	−	0.553964i
$3$	−0.281733	−	0.959493i	−0.162658	−	0.553964i
$4$	3.67359	−	4.23955i	1.83680	−	2.11978i
$5$	2.18488	+	0.475730i	0.977106	+	0.212753i
$5$	2.18488	+	0.475730i	0.977106	+	0.212753i
$6$	1.80648	+	2.08479i	0.737493	+	0.851112i
$7$	4.53926	−	0.652647i	1.71568	−	0.246677i	0.786838	−	0.617159i	$-0.211716\pi$
$7$	4.53926	−	0.652647i	1.71568	−	0.246677i	0.928840	+	0.370482i	$0.120807\pi$
$8$	−2.80541	+	9.55436i	−0.991863	+	3.37797i
$9$	−0.841254	+	0.540641i	−0.280418	+	0.180214i
$10$	−6.02764	+	1.31002i	−1.90611	+	0.414265i
$11$	0.742396	−	1.62562i	0.223841	−	0.490143i	−0.764076	−	0.645126i	$-0.776805\pi$
$11$	0.742396	−	1.62562i	0.223841	−	0.490143i	0.987917	+	0.154983i	$0.0495322\pi$
$12$	−5.10279	−	2.33037i	−1.47305	−	0.672719i
$13$	−0.440188	−	0.0632895i	−0.122086	−	0.0175533i	0.0810009	−	0.996714i	$-0.474188\pi$
$13$	−0.440188	−	0.0632895i	−0.122086	−	0.0175533i	−0.203087	+	0.979161i	$0.565097\pi$
$14$	−10.6424	+	6.83946i	−2.84430	+	1.82792i
$15$	−0.159091	−	2.23040i	−0.0410771	−	0.575887i
$16$	−2.31256	−	16.0842i	−0.578141	−	4.02106i
$17$	3.15694	−	2.73551i	0.765671	−	0.663458i	−0.181787	−	0.983338i	$-0.558188\pi$
$17$	3.15694	−	2.73551i	0.765671	−	0.663458i	0.947458	+	0.319880i	$0.103643\pi$
$18$	1.49140	−	2.32066i	0.351526	−	0.546985i
$19$	−1.97660	+	2.28112i	−0.453463	+	0.523324i	−0.935738	−	0.352696i	$-0.885265\pi$
$19$	−1.97660	+	2.28112i	−0.453463	+	0.523324i	0.482275	+	0.876020i	$0.339811\pi$
$20$	10.0432	−	7.51526i	2.24573	−	1.68046i
$21$	−1.90507	−	4.17151i	−0.415720	−	0.910299i
$22$			4.92990i			1.05106i
$23$	−4.33473	+	2.05185i	−0.903854	+	0.427841i
$23$	−4.33473	+	2.05185i	−0.903854	+	0.427841i
$24$	9.95771			2.03261
$25$	4.54736	+	2.07882i	0.909472	+	0.415764i
$26$	1.17708	−	0.345623i	0.230845	−	0.0677823i
$27$	0.755750	+	0.654861i	0.145444	+	0.126028i
$28$	13.9085	−	21.6420i	2.62845	−	4.08995i
$29$	0.305888	+	0.353014i	0.0568020	+	0.0655530i	0.783439	−	0.621468i	$-0.213463\pi$
$29$	0.305888	+	0.353014i	0.0568020	+	0.0655530i	−0.726638	+	0.687021i	$0.758918\pi$
$30$	2.95514	+	5.41441i	0.539532	+	0.988531i
$31$	−5.11673	−	1.50241i	−0.918993	−	0.269841i	−0.212171	−	0.977233i	$-0.568053\pi$
$31$	−5.11673	−	1.50241i	−0.918993	−	0.269841i	−0.706822	+	0.707392i	$0.749872\pi$
$32$	13.4676	+	20.9559i	2.38075	+	3.70452i
$33$	−1.76893	−	0.254334i	−0.307931	−	0.0442738i
$34$	−4.78692	+	10.4819i	−0.820949	+	1.79763i
$35$	10.2282	+	0.733509i	1.72888	+	0.123986i
$36$	−0.798348	+	5.55263i	−0.133058	+	0.925439i
$37$	0.829390	+	1.29056i	0.136351	+	0.212166i	0.902714	−	0.430242i	$-0.141572\pi$
$37$	0.829390	+	1.29056i	0.136351	+	0.212166i	−0.766363	+	0.642408i	$0.777935\pi$
$38$	2.34580	−	7.98907i	0.380539	−	1.29600i
$39$	0.0632895	+	0.440188i	0.0101344	+	0.0704865i
$40$	−10.6748	+	19.5405i	−1.68783	+	3.08962i
$41$	1.29270	+	0.830767i	0.201886	+	0.129744i	0.637678	−	0.770303i	$-0.279895\pi$
$41$	1.29270	+	0.830767i	0.201886	+	0.129744i	−0.435792	+	0.900047i	$0.643532\pi$
$42$	9.56072	+	8.28441i	1.47525	+	1.27831i
$43$	1.10275	+	3.75563i	0.168168	+	0.572728i	0.999847	+	0.0174714i	$0.00556160\pi$
$43$	1.10275	+	3.75563i	0.168168	+	0.572728i	−0.831679	+	0.555256i	$0.812620\pi$
$44$	−4.16464	−	9.11930i	−0.627844	−	1.37479i
$45$	−2.09523	+	0.781023i	−0.312339	+	0.116428i
$46$	8.52576	−	10.1161i	1.25706	−	1.49154i
$47$		−	5.06600i		−	0.738952i	−0.929240	−	0.369476i	$-0.879537\pi$
$47$		−	5.06600i		−	0.738952i	0.929240	−	0.369476i	$-0.120463\pi$
$48$	−14.7812	+	6.75034i	−2.13348	+	0.974328i
$49$	13.4625	−	3.95294i	1.92321	−	0.564705i
$50$	−13.7929	−	0.00529699i	−1.95061	−	0.000749107i
$51$	−3.51411	−	2.25838i	−0.492074	−	0.316237i
$52$	−1.88539	+	1.63370i	−0.261457	+	0.226553i
$53$	3.35460	−	0.482319i	0.460790	−	0.0662516i	0.0919892	−	0.995760i	$-0.470677\pi$
$53$	3.35460	−	0.482319i	0.460790	−	0.0662516i	0.368801	+	0.929508i	$0.379768\pi$
$54$	−2.64683	−	0.777180i	−0.360188	−	0.105761i
$55$	2.39540	−	3.19860i	0.322996	−	0.431299i
$56$	−6.49887	+	45.2006i	−0.868448	+	6.04019i
$57$	2.74559	+	1.25387i	0.363662	+	0.166079i
$58$	−1.17210	−	0.535279i	−0.153904	−	0.0702856i
$59$	1.04770	−	7.28690i	0.136399	−	0.948674i	−0.800565	−	0.599246i	$-0.795467\pi$
$59$	1.04770	−	7.28690i	0.136399	−	0.948674i	0.936963	−	0.349428i	$-0.113624\pi$
$60$	−10.0403	−	7.51911i	−1.29620	−	0.970713i
$61$	12.2396	+	3.59387i	1.56712	+	0.460148i	0.946162	−	0.323695i	$-0.104925\pi$
$61$	12.2396	+	3.59387i	1.56712	+	0.460148i	0.620959	+	0.783843i	$0.286743\pi$
$62$	14.5610	−	2.09356i	1.84925	−	0.265883i
$63$	−3.46582	+	3.00315i	−0.436652	+	0.378361i
$64$	−30.4684	−	19.5809i	−3.80855	−	2.44761i
$65$	−0.931647	−	0.347690i	−0.115557	−	0.0431257i
$66$	4.73021	−	1.38891i	0.582248	−	0.170963i
$67$	−3.10451	+	1.41778i	−0.379276	+	0.173210i	−0.595925	−	0.803040i	$-0.703215\pi$
$67$	−3.10451	+	1.41778i	−0.379276	+	0.173210i	0.216649	+	0.976250i	$0.430487\pi$
$68$		−	23.4332i		−	2.84169i
$69$	3.18997	+	3.58107i	0.384027	+	0.431110i
$70$	−26.5061	+	9.88045i	−3.16808	+	1.18094i
$71$	−0.588693	−	1.28906i	−0.0698651	−	0.152983i	0.871478	−	0.490435i	$-0.163162\pi$
$71$	−0.588693	−	1.28906i	−0.0698651	−	0.152983i	−0.941343	+	0.337452i	$0.890435\pi$
$72$	−2.80541	−	9.55436i	−0.330621	−	1.12599i
$73$	−11.7420	−	10.1745i	−1.37430	−	1.19084i	−0.959766	−	0.280800i	$-0.909400\pi$
$73$	−11.7420	−	10.1745i	−1.37430	−	1.19084i	−0.414531	−	0.910035i	$-0.636054\pi$
$74$	−3.56010	−	2.28794i	−0.413853	−	0.265967i
$75$	0.713475	−	4.94883i	0.0823850	−	0.571442i
$76$	2.40969	+	16.7598i	0.276411	+	1.92248i
$77$	2.30897	−	7.86364i	0.263132	−	0.896145i
$78$	−0.663246	−	1.03203i	−0.0750978	−	0.116855i
$79$	0.519230	−	3.61133i	0.0584180	−	0.406306i	−0.939540	−	0.342438i	$-0.888747\pi$
$79$	0.519230	−	3.61133i	0.0584180	−	0.406306i	0.997958	−	0.0638678i	$-0.0203436\pi$
$80$	2.59909	−	36.2422i	0.290587	−	4.05200i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−4.19577	−	0.603261i	−0.463346	−	0.0666191i
$83$	2.53083	+	3.93805i	0.277795	+	0.432258i	0.951914	−	0.306365i	$-0.0991129\pi$
$83$	2.53083	+	3.93805i	0.277795	+	0.432258i	−0.674119	+	0.738623i	$0.735477\pi$
$84$	−24.6838	−	7.24782i	−2.69322	−	0.790802i
$85$	8.19889	−	4.47489i	0.889295	−	0.485370i
$86$	−7.07089	−	8.16024i	−0.762474	−	0.879942i
$87$	0.252535	−	0.392953i	0.0270746	−	0.0421290i
$88$	13.4490	+	11.6537i	1.43367	+	1.24228i
$89$	−7.76556	+	2.28017i	−0.823147	+	0.241698i	−0.666071	−	0.745889i	$-0.732025\pi$
$89$	−7.76556	+	2.28017i	−0.823147	+	0.241698i	−0.157077	+	0.987586i	$0.550207\pi$
$90$	4.36253	−	4.36085i	0.459851	−	0.459674i
$91$	−2.03943			−0.213791
$92$	−7.22511	+	25.9150i	−0.753270	+	2.70182i
$93$			5.33275i			0.552980i
$94$	5.80540	+	12.7121i	0.598781	+	1.31115i
$95$	−5.40382	+	4.04363i	−0.554420	+	0.414868i
$96$	16.3128	−	18.8260i	1.66492	−	1.92142i
$97$	−8.76606	+	13.6403i	−0.890058	+	1.38496i	0.0326534	+	0.999467i	$0.489604\pi$
$97$	−8.76606	+	13.6403i	−0.890058	+	1.38496i	−0.922712	+	0.385491i	$0.874032\pi$
$98$	−29.2513	+	25.3464i	−2.95483	+	2.56037i
$99$	0.254334	+	1.76893i	0.0255615	+	0.177784i
$100$	25.5184	−	11.6420i	2.55184	−	1.16420i
$101$	−12.4501	+	8.00122i	−1.23883	+	0.796151i	−0.985243	−	0.171161i	$-0.945248\pi$
$101$	−12.4501	+	8.00122i	−1.23883	+	0.796151i	−0.253592	+	0.967311i	$0.581612\pi$
$102$	11.4059	+	1.63992i	1.12935	+	0.162377i
$103$	−2.39515	−	1.09383i	−0.236001	−	0.107778i	0.293904	−	0.955835i	$-0.405045\pi$
$103$	−2.39515	−	1.09383i	−0.236001	−	0.107778i	−0.529906	+	0.848057i	$0.677773\pi$
$104$	1.83960	−	4.02816i	0.180387	−	0.394993i
$105$	−2.17782	−	10.0205i	−0.212533	−	0.977904i
$106$	−7.86495	+	5.05450i	−0.763911	+	0.490936i
$107$	4.80058	−	16.3493i	0.464090	−	1.58054i	−0.312102	−	0.950048i	$-0.601033\pi$
$107$	4.80058	−	16.3493i	0.464090	−	1.58054i	0.776192	−	0.630496i	$-0.217149\pi$
$108$	5.55263	−	0.798348i	0.534302	−	0.0768211i
$109$	7.33678	+	8.46710i	0.702736	+	0.811001i	0.989120	−	0.147114i	$-0.0469985\pi$
$109$	7.33678	+	8.46710i	0.702736	+	0.811001i	−0.286383	+	0.958115i	$0.592453\pi$
$110$	−2.34530	+	10.7712i	−0.223616	+	1.02700i
$111$	1.00461	−	1.15939i	0.0953537	−	0.110044i
$112$	−20.9946	−	71.5012i	−1.98381	−	6.75623i
$113$	−10.3407	+	4.72242i	−0.972767	+	0.444248i	−0.837426	−	0.546551i	$-0.815940\pi$
$113$	−10.3407	+	4.72242i	−0.972767	+	0.444248i	−0.135341	+	0.990799i	$0.543213\pi$
$114$	−8.32634			−0.779833
$115$	−10.4470	+	2.42088i	−0.974186	+	0.225748i
$116$	2.62033			0.243291
$117$	0.404526	−	0.184741i	0.0373985	−	0.0170793i
$118$	5.72147	+	19.4855i	0.526704	+	1.79379i
$119$	12.5449	−	14.4775i	1.14999	−	1.32715i
$120$	21.7564	+	4.73718i	1.98608	+	0.432444i
$121$	5.11198	+	5.89953i	0.464725	+	0.536321i
$122$	−34.8311	+	5.00796i	−3.15346	+	0.453399i
$123$	0.432920	−	1.47439i	0.0390351	−	0.132941i
$124$	−25.1663	+	16.1734i	−2.26000	+	1.45242i
$125$	8.94646	+	6.70528i	0.800196	+	0.599739i
$126$	5.25527	−	11.5074i	0.468176	−	1.02516i
$127$	3.48224	+	1.59028i	0.308999	+	0.141115i	0.563878	−	0.825858i	$-0.309309\pi$
$127$	3.48224	+	1.59028i	0.308999	+	0.141115i	−0.254880	+	0.966973i	$0.582036\pi$
$128$	49.5791	+	7.12840i	4.38221	+	0.630067i
$129$	3.29282	−	2.11616i	0.289916	−	0.186318i
$130$	2.73621	−	0.195169i	0.239981	−	0.0171175i
$131$	−1.74743	−	12.1537i	−0.152674	−	1.06187i	−0.911714	−	0.410826i	$-0.865240\pi$
$131$	−1.74743	−	12.1537i	−0.152674	−	1.06187i	0.759040	−	0.651044i	$-0.225669\pi$
$132$	−7.57659	+	6.56515i	−0.659457	+	0.571423i
$133$	−7.48353	+	11.6446i	−0.648904	+	1.00971i
$134$	6.16539	−	7.11524i	0.532609	−	0.614663i
$135$	1.33968	+	1.79032i	0.115301	+	0.154086i
$136$	17.2795	+	37.8368i	1.48170	+	3.24448i
$137$			11.4034i			0.974259i	0.873330	+	0.487129i	$0.161956\pi$
$137$			11.4034i			0.974259i	−0.873330	+	0.487129i	$0.838044\pi$
$138$	−12.1083	−	5.33038i	−1.03073	−	0.453752i
$139$	3.33298			0.282699			0.141350	−	0.989960i	$-0.454856\pi$
$139$	3.33298			0.282699			0.141350	+	0.989960i	$0.454856\pi$
$140$	40.6840	−	40.6684i	3.43842	−	3.43710i
$141$	−4.86079	+	1.42726i	−0.409353	+	0.120197i
$142$	2.95440	+	2.56000i	0.247928	+	0.214831i
$143$	−0.429679	+	0.668593i	−0.0359315	+	0.0559105i
$144$	10.6412	+	12.2806i	0.886770	+	1.02339i
$145$	0.500388	+	0.916811i	0.0415550	+	0.0761370i
$146$	41.1236	+	12.0750i	3.40341	+	0.999331i
$147$	−7.58563	−	11.8035i	−0.625652	−	0.973534i
$148$	8.51823	+	1.22474i	0.700194	+	0.100673i
$149$	1.13788	−	2.49161i	0.0932189	−	0.204121i	−0.857279	−	0.514852i	$-0.827847\pi$
$149$	1.13788	−	2.49161i	0.0932189	−	0.204121i	0.950498	+	0.310731i	$0.100574\pi$
$150$	3.88082	+	13.2357i	0.316867	+	1.08069i
$151$	1.24896	−	8.68671i	0.101639	−	0.706914i	−0.873742	−	0.486389i	$-0.838314\pi$
$151$	1.24896	−	8.68671i	0.101639	−	0.706914i	0.975381	−	0.220525i	$-0.0707771\pi$
$152$	−16.2494	−	25.2846i	−1.31800	−	2.05085i
$153$	−1.17686	+	4.00803i	−0.0951438	+	0.324030i
$154$	3.21748	+	22.3781i	0.259272	+	1.80328i
$155$	−10.4647	−	5.71676i	−0.840544	−	0.459181i
$156$	2.09870	+	1.34875i	0.168030	+	0.107987i
$157$	15.6025	+	13.5196i	1.24522	+	1.07899i	0.993809	+	0.111103i	$0.0354385\pi$
$157$	15.6025	+	13.5196i	1.24522	+	1.07899i	0.251406	+	0.967882i	$0.419107\pi$
$158$	2.83551	+	9.65687i	0.225581	+	0.768259i
$159$	−1.40788	−	3.08283i	−0.111652	−	0.244485i
$160$	19.4556	+	52.1931i	1.53810	+	4.12622i
$161$	−18.3373	+	12.1429i	−1.44518	+	0.956997i
$162$			2.75857i			0.216734i
$163$	−14.5296	+	6.63545i	−1.13805	+	0.519729i	−0.893122	−	0.449814i	$-0.851490\pi$
$163$	−14.5296	+	6.63545i	−1.13805	+	0.519729i	−0.244924	+	0.969542i	$0.578763\pi$
$164$	8.27093	−	2.42856i	0.645851	−	0.189639i
$165$	−3.74390	−	1.39722i	−0.291462	−	0.108773i
$166$	−10.8634	−	6.98149i	−0.843164	−	0.541869i
$167$	−5.86441	+	5.08154i	−0.453802	+	0.393221i	−0.851550	−	0.524273i	$-0.824337\pi$
$167$	−5.86441	+	5.08154i	−0.453802	+	0.393221i	0.397749	+	0.917494i	$0.369792\pi$
$168$	45.2006	−	6.49887i	3.48730	−	0.501399i
$169$	−12.2836	−	3.60680i	−0.944896	−	0.277447i
$170$	−15.4454	+	20.6243i	−1.18461	+	1.58181i
$171$	0.429556	−	2.98763i	0.0328490	−	0.228470i
$172$	19.9732	+	9.12147i	1.52294	+	0.695505i
$173$	7.85248	+	3.58611i	0.597013	+	0.272647i	0.690916	−	0.722935i	$-0.257207\pi$
$173$	7.85248	+	3.58611i	0.597013	+	0.272647i	−0.0939035	+	0.995581i	$0.529935\pi$
$174$	−0.183378	+	1.27543i	−0.0139019	+	0.0966897i
$175$	21.9984	+	6.46849i	1.66292	+	0.488972i
$176$	−27.8637	−	8.18152i	−2.10031	−	0.616705i
$177$	−7.28690	+	1.04770i	−0.547717	+	0.0787498i
$178$	16.8730	−	14.6206i	1.26469	−	1.09586i
$179$	−1.54213	−	0.991066i	−0.115264	−	0.0740757i	0.481739	−	0.876315i	$-0.340005\pi$
$179$	−1.54213	−	0.991066i	−0.115264	−	0.0740757i	−0.597003	+	0.802239i	$0.703642\pi$
$180$	−4.38585	+	11.7520i	−0.326902	+	0.875943i
$181$	−6.28456	+	1.84531i	−0.467128	+	0.137161i	−0.506822	−	0.862051i	$-0.669180\pi$
$181$	−6.28456	+	1.84531i	−0.467128	+	0.137161i	0.0396940	+	0.999212i	$0.487362\pi$
$182$	5.11752	−	2.33709i	0.379336	−	0.173237i
$183$		−	12.7563i		−	0.942975i
$184$	−7.44340	−	47.1719i	−0.548735	−	3.47756i
$185$	1.19816	+	3.21427i	0.0880904	+	0.236318i
$186$	−6.11108	−	13.3814i	−0.448086	−	0.981172i
$187$	−2.10320	−	7.16283i	−0.153801	−	0.523798i
$188$	−21.4776	−	18.6104i	−1.56641	−	1.35731i
$189$	3.85794	+	2.47934i	0.280623	+	0.180346i
$190$	8.92592	−	16.3391i	0.647555	−	1.18537i
$191$	0.779407	+	5.42089i	0.0563959	+	0.392242i	0.998395	+	0.0566277i	$0.0180348\pi$
$191$	0.779407	+	5.42089i	0.0563959	+	0.392242i	−0.941999	+	0.335614i	$0.891056\pi$
$192$	−10.2038	+	34.7508i	−0.736392	+	2.50792i
$193$	−12.0117	−	18.6906i	−0.864621	−	1.34538i	−0.937482	−	0.348034i	$-0.886849\pi$
$193$	−12.0117	−	18.6906i	−0.864621	−	1.34538i	0.0728610	−	0.997342i	$-0.476787\pi$
$194$	6.36547	−	44.2728i	0.457014	−	3.17860i
$195$	−0.0711310	+	0.991864i	−0.00509379	+	0.0710289i
$196$	32.6969	−	71.5963i	2.33550	−	5.11402i
$197$	6.64061	+	0.954776i	0.473124	+	0.0680249i	0.374753	−	0.927125i	$-0.377728\pi$
$197$	6.64061	+	0.954776i	0.473124	+	0.0680249i	0.0983712	+	0.995150i	$0.468637\pi$
$198$	−2.66531	−	4.14730i	−0.189415	−	0.294736i
$199$	−6.19957	−	1.82036i	−0.439476	−	0.129042i	0.0545072	−	0.998513i	$-0.482641\pi$
$199$	−6.19957	−	1.82036i	−0.439476	−	0.129042i	−0.493983	+	0.869472i	$0.664459\pi$
$200$	−32.6190	+	37.6152i	−2.30651	+	2.65979i
$201$	2.23499	+	2.57932i	0.157644	+	0.181931i
$202$	22.0719	−	34.3446i	1.55298	−	2.41648i
$203$	1.61890	+	1.40278i	0.113624	+	0.0984561i
$204$	−22.4840	+	6.60189i	−1.57419	+	0.462225i
$205$	2.42917	+	2.43010i	0.169660	+	0.169725i
$206$	7.26360			0.506079
$207$	2.53729	−	4.06966i	0.176354	−	0.282861i
$208$			7.22644i			0.501064i
$209$	2.24081	+	4.90669i	0.155000	+	0.339403i
$210$	16.9478	+	22.6487i	1.16951	+	1.56291i
$211$	−7.67670	+	8.85938i	−0.528485	+	0.609905i	−0.955735	−	0.294229i	$-0.904937\pi$
$211$	−7.67670	+	8.85938i	−0.528485	+	0.609905i	0.427249	+	0.904134i	$0.359483\pi$
$212$	10.2786	−	15.9939i	0.705939	−	1.09846i
$213$	−1.07099	+	0.928017i	−0.0733829	+	0.0635867i
$214$	6.68947	+	46.5263i	0.457283	+	3.18047i
$215$	0.622710	+	8.73019i	0.0424685	+	0.595394i
$216$	−8.37696	+	5.38355i	−0.569980	+	0.366304i
$217$	−24.2067	−	3.48040i	−1.64326	−	0.236265i
$218$	−28.1130	−	12.8388i	−1.90405	−	0.869552i
$219$	−6.45426	+	14.1329i	−0.436138	+	0.955010i
$220$	−4.76091	−	21.9058i	−0.320980	−	1.47689i
$221$	−1.56278	+	1.00434i	−0.105124	+	0.0675590i
$222$	−1.19226	+	4.06047i	−0.0800194	+	0.272521i
$223$	−3.06985	+	0.441377i	−0.205572	+	0.0295568i	−0.244332	−	0.969692i	$-0.578569\pi$
$223$	−3.06985	+	0.441377i	−0.205572	+	0.0295568i	0.0387593	+	0.999249i	$0.487659\pi$
$224$	74.8096	+	86.3349i	4.99843	+	5.76849i
$225$	−4.94938	+	0.709673i	−0.329959	+	0.0473116i
$226$	20.5360	−	23.6998i	1.36604	−	1.57649i
$227$	2.23086	+	7.59762i	0.148068	+	0.504272i	0.999806	−	0.0196954i	$-0.00626965\pi$
$227$	2.23086	+	7.59762i	0.148068	+	0.504272i	−0.851739	+	0.523967i	$0.824451\pi$
$228$	15.4020	−	7.03386i	1.02002	−	0.465829i
$229$	−15.7605			−1.04148			−0.520742	−	0.853714i	$-0.674345\pi$
$229$	−15.7605			−1.04148			−0.520742	+	0.853714i	$0.674345\pi$
$230$	23.4403	−	18.0464i	1.54560	−	1.18995i
$231$	−8.19562			−0.539232
$232$	−4.23096	+	1.93221i	−0.277776	+	0.126856i
$233$	−4.22030	−	14.3730i	−0.276481	−	0.941608i	−0.974285	−	0.225319i	$-0.927658\pi$
$233$	−4.22030	−	14.3730i	−0.276481	−	0.941608i	0.697804	−	0.716289i	$-0.254161\pi$
$234$	−0.803369	+	0.927137i	−0.0525178	+	0.0606088i
$235$	2.41005	−	11.0686i	0.157214	−	0.722035i
$236$	−27.0444	−	31.2109i	−1.76044	−	2.03166i
$237$	−3.61133	+	0.519230i	−0.234581	+	0.0337276i
$238$	−14.8881	+	50.7041i	−0.965051	+	3.28666i
$239$	−18.7576	+	12.0548i	−1.21333	+	0.779760i	−0.981213	−	0.192928i	$-0.938202\pi$
$239$	−18.7576	+	12.0548i	−1.21333	+	0.779760i	−0.232117	+	0.972688i	$0.574565\pi$
$240$	−35.5064	+	7.71680i	−2.29193	+	0.498117i
$241$	−1.05466	+	2.30938i	−0.0679366	+	0.148760i	−0.940554	−	0.339644i	$-0.889694\pi$
$241$	−1.05466	+	2.30938i	−0.0679366	+	0.148760i	0.872618	+	0.488404i	$0.162421\pi$
$242$	−19.5880	−	8.94554i	−1.25916	−	0.575041i
$243$	−0.989821	−	0.142315i	−0.0634971	−	0.00912950i
$244$	60.1997	−	38.6880i	3.85389	−	2.47675i
$245$	31.2943	−	2.23218i	1.99932	−	0.142608i
$246$	0.603261	+	4.19577i	0.0384625	+	0.267513i
$247$	1.01445	−	0.879022i	0.0645476	−	0.0559308i
$248$	28.7091	−	44.6722i	1.82303	−	2.83669i
$249$	3.06552	−	3.53780i	0.194269	−	0.224199i
$250$	−30.1332	−	6.57326i	−1.90579	−	0.415729i
$251$	7.48842	+	16.3974i	0.472665	+	1.03499i	0.984416	+	0.175858i	$0.0562700\pi$
$251$	7.48842	+	16.3974i	0.472665	+	1.03499i	−0.511750	+	0.859134i	$0.671003\pi$
$252$			25.7259i			1.62058i
$253$	0.117443	+	8.56992i	0.00738357	+	0.538786i
$254$	−10.5603			−0.662614
$255$	−6.60352	−	6.60606i	−0.413529	−	0.413687i
$256$	−63.0754	+	18.5206i	−3.94221	+	1.15754i
$257$	15.9307	+	13.8041i	0.993732	+	0.861074i	0.990304	−	0.138920i	$-0.0443631\pi$
$257$	15.9307	+	13.8041i	0.993732	+	0.861074i	0.00342874	+	0.999994i	$0.498909\pi$
$258$	−5.83760	+	9.08348i	−0.363433	+	0.565513i
$259$	4.60709	+	5.31687i	0.286271	+	0.330374i
$260$	−4.89654	+	2.67249i	−0.303671	+	0.165741i
$261$	−0.448183	−	0.131598i	−0.0277418	−	0.00814573i
$262$	18.3123	+	28.4945i	1.13134	+	1.76040i
$263$	13.9773	+	2.00964i	0.861879	+	0.123919i	0.559058	−	0.829128i	$-0.311163\pi$
$263$	13.9773	+	2.00964i	0.861879	+	0.123919i	0.302820	+	0.953048i	$0.402072\pi$
$264$	7.39257	−	16.1875i	0.454981	−	0.996270i
$265$	7.55885	+	0.542078i	0.464336	+	0.0332996i
$266$	5.43416	−	37.7954i	0.333190	−	2.31739i
$267$	4.37562	+	6.80860i	0.267784	+	0.416679i
$268$	−5.39394	+	18.3701i	−0.329487	+	1.12213i
$269$	−1.53007	−	10.6419i	−0.0932901	−	0.648847i	−0.981790	−	0.189970i	$-0.939161\pi$
$269$	−1.53007	−	10.6419i	−0.0932901	−	0.648847i	0.888500	−	0.458877i	$-0.151748\pi$
$270$	−5.41327	−	2.95722i	−0.329441	−	0.179971i
$271$	−24.7661	−	15.9162i	−1.50443	−	0.966842i	−0.994285	−	0.106756i	$-0.965954\pi$
$271$	−24.7661	−	15.9162i	−1.50443	−	0.966842i	−0.510150	−	0.860086i	$-0.670410\pi$
$272$	−51.2992	−	44.4510i	−3.11047	−	2.69524i
$273$	0.574574	+	1.95682i	0.0347748	+	0.118432i
$274$	−13.0678	−	28.6144i	−0.789453	−	1.72866i
$275$	6.75532	−	5.84898i	0.407361	−	0.352707i
$276$	26.9008	−	0.368651i	1.61924	−	0.0221902i
$277$		−	26.6391i		−	1.60059i	−0.599607	−	0.800295i	$-0.704676\pi$
$277$		−	26.6391i		−	1.60059i	0.599607	−	0.800295i	$-0.295324\pi$
$278$	−8.36340	+	3.81944i	−0.501603	+	0.229075i
$279$	5.11673	−	1.50241i	0.306331	−	0.0899469i
$280$	−35.7025	+	95.6660i	−2.13363	+	5.71714i
$281$	21.2460	+	13.6540i	1.26743	+	0.814527i	0.989283	−	0.146012i	$-0.0466438\pi$
$281$	21.2460	+	13.6540i	1.26743	+	0.814527i	0.278146	+	0.960539i	$0.410280\pi$
$282$	10.5616	−	9.15164i	0.628932	−	0.544972i
$283$	−12.7973	+	1.83998i	−0.760721	+	0.109375i	−0.511749	−	0.859135i	$-0.671002\pi$
$283$	−12.7973	+	1.83998i	−0.760721	+	0.109375i	−0.248973	+	0.968511i	$0.580093\pi$
$284$	−7.62765	−	2.23968i	−0.452618	−	0.132901i
$285$	5.40226	+	4.04570i	0.320003	+	0.239647i
$286$	0.312011	−	2.17008i	0.0184496	−	0.128320i
$287$	6.41009	+	2.92739i	0.378376	+	0.172798i
$288$	−22.6593	−	10.3481i	−1.33521	−	0.609770i
$289$	0.0639422	−	0.444728i	0.00376131	−	0.0261605i
$290$	−2.30624	−	1.72712i	−0.135427	−	0.101420i
$291$	15.5574	+	4.56807i	0.911991	+	0.267785i
$292$	−86.2707	+	12.4038i	−5.04861	+	0.725880i
$293$	3.14493	−	2.72509i	0.183729	−	0.159202i	−0.558141	−	0.829746i	$-0.688485\pi$
$293$	3.14493	−	2.72509i	0.183729	−	0.159202i	0.741869	+	0.670545i	$0.233940\pi$
$294$	32.5607	+	20.9255i	1.89898	+	1.22040i
$295$	5.75569	−	15.4226i	0.335109	−	0.897936i
$296$	−14.6572	+	4.30375i	−0.851934	+	0.250150i
$297$	1.62562	−	0.742396i	0.0943281	−	0.0430782i
$298$			7.55613i			0.437715i
$299$	2.03796	−	0.628857i	0.117858	−	0.0363677i
$300$	−18.3598	−	21.2048i	−1.06000	−	1.22426i
$301$	7.45677	+	16.3280i	0.429801	+	0.941133i
$302$	6.82056	+	23.2287i	0.392479	+	1.33666i
$303$	11.1847	+	9.69161i	0.642545	+	0.556769i
$304$	41.2610	+	26.5168i	2.36648	+	1.52085i
$305$	25.0323	+	13.6749i	1.43335	+	0.783023i
$306$	−1.63992	−	11.4059i	−0.0937482	−	0.652033i
$307$	5.92884	−	20.1918i	0.338377	−	1.15241i	−0.598026	−	0.801477i	$-0.704048\pi$
$307$	5.92884	−	20.1918i	0.338377	−	1.15241i	0.936402	−	0.350928i	$-0.114134\pi$
$308$	−24.8561	−	38.6768i	−1.41631	−	2.20382i
$309$	−0.374729	+	2.60630i	−0.0213176	+	0.148267i
$310$	32.8100	+	2.35295i	1.86349	+	0.133639i
$311$	−7.25066	+	15.8767i	−0.411147	+	0.900287i	0.584870	+	0.811127i	$0.301146\pi$
$311$	−7.25066	+	15.8767i	−0.411147	+	0.900287i	−0.996017	+	0.0891600i	$0.971582\pi$
$312$	−4.38326	−	0.630218i	−0.248153	−	0.0356791i
$313$	−1.37262	−	2.13583i	−0.0775849	−	0.120725i	0.800293	−	0.599610i	$-0.204677\pi$
$313$	−1.37262	−	2.13583i	−0.0775849	−	0.120725i	−0.877878	+	0.478885i	$0.841041\pi$
$314$	−54.6440	−	16.0449i	−3.08374	−	0.905468i
$315$	−9.00107	+	4.91271i	−0.507153	+	0.276800i
$316$	−13.4030	−	15.4678i	−0.753976	−	0.870134i
$317$	−8.34827	+	12.9902i	−0.468886	+	0.729600i	−0.992485	−	0.122364i	$-0.960952\pi$
$317$	−8.34827	+	12.9902i	−0.468886	+	0.729600i	0.523600	+	0.851964i	$0.324589\pi$
$318$	7.06557	+	6.12235i	0.396217	+	0.343324i
$319$	0.800956	−	0.235182i	0.0448450	−	0.0131677i
$320$	−57.2545	−	57.2765i	−3.20062	−	3.20185i
$321$	−17.0395			−0.951052
$322$	32.0984	−	51.4838i	1.78877	−	2.86908i
$323$			12.6084i			0.701548i
$324$	−2.33037	−	5.10279i	−0.129465	−	0.283488i
$325$	−1.87013	−	1.20287i	−0.103736	−	0.0667233i
$326$	28.8551	−	33.3005i	1.59813	−	1.84434i
$327$	6.05711	−	9.42505i	0.334959	−	0.521206i
$328$	−11.5640	+	10.0203i	−0.638515	+	0.553276i
$329$	−3.30631	−	22.9959i	−0.182283	−	1.26780i
$330$	10.9957	−	0.784303i	0.605291	−	0.0431745i
$331$	−6.10895	+	3.92599i	−0.335778	+	0.215792i	−0.697654	−	0.716435i	$-0.745773\pi$
$331$	−6.10895	+	3.92599i	−0.335778	+	0.215792i	0.361876	+	0.932226i	$0.382136\pi$
$332$	25.9928	+	3.73721i	1.42654	+	0.205106i
$333$	−1.39546	−	0.637283i	−0.0764705	−	0.0349229i
$334$	8.89228	−	19.4714i	0.486564	−	1.06543i
$335$	−7.45744	+	1.62077i	−0.407444	+	0.0885520i
$336$	−62.6900	+	40.2884i	−3.42002	+	2.19791i
$337$	−2.27578	+	7.75059i	−0.123970	+	0.422201i	−0.997967	−	0.0637285i	$-0.979701\pi$
$337$	−2.27578	+	7.75059i	−0.123970	+	0.422201i	0.873998	+	0.485930i	$0.161519\pi$
$338$	34.9564	−	5.02598i	1.90138	−	0.273377i
$339$	7.44443	+	8.59133i	0.404326	+	0.466617i
$340$	11.1479	−	51.1986i	0.604578	−	2.77663i
$341$	−6.24099	+	7.20249i	−0.337969	+	0.390037i
$342$	2.34580	+	7.98907i	0.126846	+	0.431999i
$343$	29.3291	−	13.3942i	1.58362	−	0.723217i
$344$	−38.9763			−2.10146
$345$	5.26607	+	9.34176i	0.283516	+	0.502944i
$346$	−23.8136			−1.28023
$347$	4.68575	−	2.13991i	0.251544	−	0.114876i	−0.285653	−	0.958333i	$-0.592210\pi$
$347$	4.68575	−	2.13991i	0.251544	−	0.114876i	0.537197	+	0.843457i	$0.319483\pi$
$348$	−0.738232	−	2.51419i	−0.0395734	−	0.134775i
$349$	2.91973	−	3.36955i	0.156290	−	0.180368i	−0.672205	−	0.740365i	$-0.734653\pi$
$349$	2.91973	−	3.36955i	0.156290	−	0.180368i	0.828494	+	0.559998i	$0.189198\pi$
$350$	−62.6129	+	8.97783i	−3.34680	+	0.479885i
$351$	−0.291226	−	0.336093i	−0.0155445	−	0.0179393i
$352$	44.0647	−	6.33555i	2.34866	−	0.337686i
$353$	−1.55878	+	5.30871i	−0.0829654	+	0.282554i	−0.990518	−	0.137385i	$-0.956130\pi$
$353$	−1.55878	+	5.30871i	−0.0829654	+	0.282554i	0.907552	+	0.419939i	$0.137949\pi$
$354$	17.0843	−	10.9794i	0.908021	−	0.583550i
$355$	−0.672978	−	3.09649i	−0.0357180	−	0.164345i
$356$	−18.8606	+	41.2989i	−0.999609	+	2.18884i
$357$	−17.4254	−	7.95791i	−0.922250	−	0.421177i
$358$	5.00536	+	0.719662i	0.264541	+	0.0380353i
$359$	−13.7407	+	8.83063i	−0.725208	+	0.466063i	−0.850445	−	0.526064i	$-0.823667\pi$
$359$	−13.7407	+	8.83063i	−0.725208	+	0.466063i	0.125237	+	0.992127i	$0.460031\pi$
$360$	−1.58418	−	22.2097i	−0.0834937	−	1.17055i
$361$	1.40743	+	9.78890i	0.0740754	+	0.515205i
$362$	13.6551	−	11.8322i	0.717698	−	0.621889i
$363$	4.22035	−	6.56700i	0.221511	−	0.344678i
$364$	−7.49204	+	8.64628i	−0.392690	+	0.453188i
$365$	−20.8145	−	27.8160i	−1.08948	−	1.45596i
$366$	14.6182	+	32.0093i	0.764103	+	1.67315i
$367$		−	5.40123i		−	0.281942i	−0.990014	−	0.140971i	$-0.954978\pi$
$367$		−	5.40123i		−	0.281942i	0.990014	−	0.140971i	$-0.0450224\pi$
$368$	43.0268	+	64.9758i	2.24293	+	3.38710i
$369$	−1.53663			−0.0799940
$370$	−6.68993	−	6.69250i	−0.347793	−	0.347926i
$371$	14.9126	−	4.37874i	0.774225	−	0.227333i
$372$	22.6085	+	19.5903i	1.17219	+	1.01571i
$373$	0.840913	−	1.30849i	0.0435408	−	0.0677509i	−0.818801	−	0.574078i	$-0.805361\pi$
$373$	0.840913	−	1.30849i	0.0435408	−	0.0677509i	0.862342	+	0.506327i	$0.168997\pi$
$374$	13.4858	+	15.5634i	0.697333	+	0.804766i
$375$	3.91316	−	10.4732i	0.202075	−	0.540832i
$376$	48.4024	+	14.2122i	2.49616	+	0.732940i
$377$	−0.112306	−	0.174752i	−0.00578406	−	0.00900017i
$378$	−12.5219	−	1.80037i	−0.644056	−	0.0926013i
$379$	3.51918	−	7.70593i	0.180768	−	0.395827i	−0.797456	−	0.603377i	$-0.793822\pi$
$379$	3.51918	−	7.70593i	0.180768	−	0.395827i	0.978224	+	0.207550i	$0.0665489\pi$
$380$	−2.70825	+	37.7644i	−0.138930	+	1.93727i
$381$	0.544807	−	3.78922i	0.0279113	−	0.194127i
$382$	−8.16784	−	12.7094i	−0.417903	−	0.650270i
$383$	−3.31349	+	11.2847i	−0.169311	+	0.576621i	0.830497	+	0.557024i	$0.188057\pi$
$383$	−3.31349	+	11.2847i	−0.169311	+	0.576621i	−0.999808	+	0.0195976i	$0.993761\pi$
$384$	−7.12840	−	49.5791i	−0.363770	−	2.53007i
$385$	8.78578	−	16.0826i	0.447765	−	0.819646i
$386$	51.5593	+	33.1352i	2.62430	+	1.68654i
$387$	−2.95814	−	2.56324i	−0.150371	−	0.130297i
$388$	25.6256	+	87.2729i	1.30094	+	4.43061i
$389$	7.65072	+	16.7527i	0.387907	+	0.849398i	0.998355	+	0.0573411i	$0.0182623\pi$
$389$	7.65072	+	16.7527i	0.387907	+	0.849398i	−0.610448	+	0.792057i	$0.709010\pi$
$390$	−0.958142	−	2.57039i	−0.0485174	−	0.130157i
$391$	−8.07166	+	18.3353i	−0.408201	+	0.927255i
$392$			139.715i			7.05666i
$393$	−11.1690	+	5.10073i	−0.563403	+	0.257298i
$394$	−17.7573	+	5.21402i	−0.894601	+	0.262679i
$395$	2.85247	−	7.64329i	0.143523	−	0.384575i
$396$	8.43379	+	5.42007i	0.423814	+	0.272369i
$397$	−2.62792	+	2.27711i	−0.131892	+	0.114285i	−0.718309	−	0.695725i	$-0.755083\pi$
$397$	−2.62792	+	2.27711i	−0.131892	+	0.114285i	0.586417	+	0.810009i	$0.300538\pi$
$398$	17.6425	−	2.53661i	0.884340	−	0.127149i
$399$	13.2813	+	3.89973i	0.664895	+	0.195231i
$400$	22.9202	−	77.9482i	1.14601	−	3.89741i
$401$	−2.67002	+	18.5704i	−0.133334	+	0.927360i	0.807831	+	0.589414i	$0.200641\pi$
$401$	−2.67002	+	18.5704i	−0.133334	+	0.927360i	−0.941165	+	0.337946i	$0.890268\pi$
$402$	−8.56402	−	3.91105i	−0.427134	−	0.195066i
$403$	2.15724	+	0.985177i	0.107460	+	0.0490752i
$404$	−11.8152	+	82.1762i	−0.587826	+	4.08842i
$405$	1.34037	−	1.78981i	0.0666035	−	0.0889362i
$406$	−5.66980	−	1.66480i	−0.281388	−	0.0826229i
$407$	2.71369	−	0.390170i	0.134513	−	0.0193400i
$408$	31.4359	−	27.2394i	1.55631	−	1.34855i
$409$	9.29832	+	5.97567i	0.459772	+	0.295478i	0.749949	−	0.661495i	$-0.230078\pi$
$409$	9.29832	+	5.97567i	0.459772	+	0.295478i	−0.290177	+	0.956973i	$0.593714\pi$
$410$	−8.88025	−	3.31411i	−0.438564	−	0.163672i
$411$	10.9415	−	3.21271i	0.539704	−	0.158471i
$412$	−13.4362	+	6.13609i	−0.661952	+	0.302303i
$413$		−	33.7609i		−	1.66127i
$414$	−1.70316	+	13.1196i	−0.0837058	+	0.644792i
$415$	3.65611	+	9.80815i	0.179471	+	0.481463i
$416$	−4.60197	−	10.0769i	−0.225630	−	0.494061i
$417$	−0.939008	−	3.19797i	−0.0459834	−	0.156605i
$418$	−11.2457	−	9.74444i	−0.550044	−	0.476616i
$419$	−24.7064	−	15.8779i	−1.20699	−	0.775685i	−0.226837	−	0.973933i	$-0.572839\pi$
$419$	−24.7064	−	15.8779i	−1.20699	−	0.775685i	−0.980152	+	0.198248i	$0.936475\pi$
$420$	−50.4830	−	27.5784i	−2.46332	−	1.34569i
$421$	−2.21624	−	15.4143i	−0.108013	−	0.751248i	−0.969787	−	0.243955i	$-0.921555\pi$
$421$	−2.21624	−	15.4143i	−0.108013	−	0.751248i	0.861773	−	0.507293i	$-0.169354\pi$
$422$	9.11060	−	31.0279i	0.443497	−	1.51041i
$423$	2.73889	+	4.26179i	0.133169	+	0.207215i
$424$	−4.80280	+	33.4042i	−0.233244	+	1.62225i
$425$	20.0424	−	5.87662i	0.972199	−	0.285058i
$426$	1.62395	−	3.55596i	0.0786808	−	0.172287i
$427$	57.9043	+	8.32538i	2.80218	+	0.402893i
$428$	−51.6783	−	80.4129i	−2.49796	−	3.88691i
$429$	0.762565	+	0.223909i	0.0368170	+	0.0108104i
$430$	−11.5669	−	21.1929i	−0.557808	−	1.02201i
$431$	−15.2986	−	17.6555i	−0.736906	−	0.850435i	0.256325	−	0.966591i	$-0.417488\pi$
$431$	−15.2986	−	17.6555i	−0.736906	−	0.850435i	−0.993231	+	0.116156i	$0.962943\pi$
$432$	8.78521	−	13.6701i	0.422679	−	0.657701i
$433$	−15.9103	−	13.7863i	−0.764600	−	0.662530i	0.182595	−	0.983188i	$-0.441550\pi$
$433$	−15.9103	−	13.7863i	−0.764600	−	0.662530i	−0.947195	+	0.320659i	$0.896096\pi$
$434$	64.7300	−	19.0064i	3.10714	−	0.912338i
$435$	0.738698	−	0.738414i	0.0354179	−	0.0354043i
$436$	62.8491			3.00992
$437$	3.88752	−	13.9437i	0.185965	−	0.667018i
$438$		−	42.8597i		−	2.04791i
$439$	16.0808	+	35.2120i	0.767494	+	1.68058i	0.732092	+	0.681205i	$0.238544\pi$
$439$	16.0808	+	35.2120i	0.767494	+	1.68058i	0.0354021	+	0.999373i	$0.488729\pi$
$440$	23.8405	+	31.8599i	1.13655	+	1.51886i
$441$	−9.18823	+	10.6038i	−0.437535	+	0.504942i
$442$	2.77054	−	4.31104i	0.131781	−	0.205055i
$443$	−4.01705	+	3.48079i	−0.190856	+	0.165378i	−0.745047	−	0.667012i	$-0.767573\pi$
$443$	−4.01705	+	3.48079i	−0.190856	+	0.165378i	0.554191	+	0.832389i	$0.313028\pi$
$444$	−1.22474	−	8.51823i	−0.0581234	−	0.404257i
$445$	−18.0515	+	1.28759i	−0.855724	+	0.0610374i
$446$	7.19733	−	4.62544i	0.340804	−	0.219021i
$447$	−2.71126	−	0.389821i	−0.128238	−	0.0184379i
$448$	−151.083	−	68.9975i	−7.13802	−	3.25982i
$449$	12.3759	−	27.0994i	0.584055	−	1.27890i	−0.354914	−	0.934899i	$-0.615490\pi$
$449$	12.3759	−	27.0994i	0.584055	−	1.27890i	0.938969	−	0.344002i	$-0.111783\pi$
$450$	11.6062	−	7.45253i	0.547120	−	0.351316i
$451$	2.31021	−	1.48468i	0.108783	−	0.0699109i
$452$	−17.9664	+	61.1880i	−0.845069	+	2.87804i
$453$	−8.68671	+	1.24896i	−0.408137	+	0.0586813i
$454$	−14.3044	−	16.5081i	−0.671338	−	0.774766i
$455$	−4.45590	−	0.970219i	−0.208896	−	0.0454846i
$456$	−19.6824	+	22.7147i	−0.921713	+	1.06371i
$457$	8.97934	+	30.5808i	0.420036	+	1.43051i	0.849577	+	0.527464i	$0.176857\pi$
$457$	8.97934	+	30.5808i	0.420036	+	1.43051i	−0.429541	+	0.903047i	$0.641325\pi$
$458$	39.5477	−	18.0608i	1.84794	−	0.843927i
$459$	4.17724			0.194977
$460$	−28.1145	+	53.1838i	−1.31085	+	2.47971i
$461$	17.4707			0.813692			0.406846	−	0.913497i	$-0.366629\pi$
$461$	17.4707			0.813692			0.406846	+	0.913497i	$0.366629\pi$
$462$	20.5652	−	9.39179i	0.956778	−	0.436946i
$463$	−8.01765	−	27.3056i	−0.372612	−	1.26900i	−0.906054	−	0.423163i	$-0.860920\pi$
$463$	−8.01765	−	27.3056i	−0.372612	−	1.26900i	0.533442	−	0.845837i	$-0.320898\pi$
$464$	4.97057	−	5.73634i	0.230753	−	0.266303i
$465$	−2.53695	+	11.6514i	−0.117648	+	0.540320i
$466$	27.0607	+	31.2298i	1.25357	+	1.44669i
$467$	−21.7134	+	3.12192i	−1.00478	+	0.144465i	−0.625010	−	0.780617i	$-0.714905\pi$
$467$	−21.7134	+	3.12192i	−1.00478	+	0.144465i	−0.379768	+	0.925082i	$0.623996\pi$
$468$	0.702846	−	2.39367i	0.0324891	−	0.110648i
$469$	−13.1669	+	8.46182i	−0.607989	+	0.390731i
$470$	6.63657	+	30.5361i	0.306122	+	1.40852i
$471$	8.57627	−	18.7794i	0.395174	−	0.865310i
$472$	66.6824	+	30.4529i	3.06931	+	1.40171i
$473$	6.92390	+	0.995507i	0.318361	+	0.0457735i
$474$	8.46684	−	5.44131i	0.388895	−	0.249928i
$475$	−13.7303	+	6.26407i	−0.629991	+	0.287415i
$476$	−15.2936	−	106.369i	−0.700980	−	4.87543i
$477$	−2.56131	+	2.21939i	−0.117274	+	0.101619i
$478$	33.2541	−	51.7443i	1.52101	−	2.36673i
$479$	−4.89402	+	5.64799i	−0.223613	+	0.258063i	−0.856460	−	0.516214i	$-0.827341\pi$
$479$	−4.89402	+	5.64799i	−0.223613	+	0.258063i	0.632846	+	0.774277i	$0.281886\pi$
$480$	44.5976	−	33.3720i	2.03559	−	1.52322i
$481$	−0.283409	−	0.620579i	−0.0129223	−	0.0282960i
$482$		−	7.00349i		−	0.319000i
$483$	16.8173	+	14.1735i	0.765213	+	0.644916i
$484$	43.7907			1.99049
$485$	−25.6418	+	25.6320i	−1.16434	+	1.16389i
$486$	2.64683	−	0.777180i	0.120063	−	0.0352536i
$487$	4.47519	+	3.87777i	0.202790	+	0.175719i	0.750335	−	0.661058i	$-0.229892\pi$
$487$	4.47519	+	3.87777i	0.202790	+	0.175719i	−0.547545	+	0.836776i	$0.684438\pi$
$488$	−68.6743	+	106.859i	−3.10874	+	4.83729i
$489$	10.4601	+	12.0716i	0.473024	+	0.545898i
$490$	−75.9685	+	41.4630i	−3.43191	+	1.87311i
$491$	9.16168	+	2.69011i	0.413461	+	0.121403i	0.481846	−	0.876256i	$-0.339967\pi$
$491$	9.16168	+	2.69011i	0.413461	+	0.121403i	−0.0683852	+	0.997659i	$0.521785\pi$
$492$	−4.66038	−	7.25170i	−0.210106	−	0.326932i
$493$	1.93134	+	0.277685i	0.0869833	+	0.0125063i
$494$	−1.53822	+	3.36823i	−0.0692077	+	0.151544i
$495$	−0.285845	+	3.98588i	−0.0128478	+	0.179152i
$496$	−12.3323	+	85.7731i	−0.553737	+	3.85133i
$497$	−3.51353	−	5.46716i	−0.157603	−	0.245236i
$498$	−3.63812	+	12.3903i	−0.163028	+	0.555222i
$499$	−1.56314	−	10.8719i	−0.0699758	−	0.486692i	−0.994430	−	0.105399i	$-0.966388\pi$
$499$	−1.56314	−	10.8719i	−0.0699758	−	0.486692i	0.924454	−	0.381293i	$-0.124521\pi$
$500$	61.2931	−	13.2965i	2.74111	−	0.594638i
$501$	6.52790	+	4.19522i	0.291645	+	0.187429i
$502$	−37.5812	−	32.5643i	−1.67733	−	1.45342i
$503$	−2.97553	−	10.1337i	−0.132673	−	0.451841i	0.866180	−	0.499732i	$-0.166568\pi$
$503$	−2.97553	−	10.1337i	−0.132673	−	0.451841i	−0.998853	+	0.0478909i	$0.984750\pi$
$504$	−18.9701	−	41.5387i	−0.844996	−	1.85028i
$505$	−31.0084	+	11.5588i	−1.37986	+	0.514358i
$506$	−10.1154	−	21.3698i	−0.449685	−	0.950004i
$507$			12.8022i			0.568567i
$508$	19.5344	−	8.92107i	0.866700	−	0.395808i
$509$	39.0056	−	11.4531i	1.72889	−	0.507649i	0.742192	−	0.670187i	$-0.233786\pi$
$509$	39.0056	−	11.4531i	1.72889	−	0.507649i	0.986702	+	0.162538i	$0.0519681\pi$
$510$	24.1404	+	9.00917i	1.06895	+	0.398933i
$511$	−59.9403	−	38.5213i	−2.65160	−	1.70408i
$512$	61.3412	−	53.1525i	2.71093	−	2.34903i
$513$	−2.98763	+	0.429556i	−0.131907	+	0.0189654i
$514$	−55.7936	−	16.3825i	−2.46095	−	0.722600i
$515$	−4.71274	−	3.52933i	−0.207668	−	0.155521i
$516$	3.12488	−	21.7340i	0.137565	−	0.956786i
$517$	−8.23540	−	3.76098i	−0.362193	−	0.165408i
$518$	−17.6534	−	8.06204i	−0.775646	−	0.354226i
$519$	1.22855	−	8.54472i	0.0539272	−	0.375072i
$520$	5.93561	−	7.92587i	0.260294	−	0.347573i
$521$	−34.4172	−	10.1058i	−1.50784	−	0.442743i	−0.579659	−	0.814859i	$-0.696814\pi$
$521$	−34.4172	−	10.1058i	−1.50784	−	0.442743i	−0.928186	+	0.372116i	$0.878632\pi$
$522$	1.27543	−	0.183378i	0.0558238	−	0.00802626i
$523$	8.06221	−	6.98595i	0.352536	−	0.305474i	−0.460532	−	0.887643i	$-0.652341\pi$
$523$	8.06221	−	6.98595i	0.352536	−	0.305474i	0.813068	+	0.582169i	$0.197796\pi$
$524$	−57.9454	−	37.2392i	−2.53136	−	1.62680i
$525$	0.00880587	−	22.9297i	0.000384320	−	1.00073i
$526$	−37.3761	+	10.9746i	−1.62967	+	0.478516i
$527$	−20.2631	+	9.25385i	−0.882674	+	0.403104i
$528$			29.0400i			1.26381i
$529$	14.5798	−	17.7885i	0.633905	−	0.773411i
$530$	−19.5885	+	7.30185i	−0.850871	+	0.317172i
$531$	3.05822	+	6.69656i	0.132715	+	0.290606i
$532$	21.8764	+	74.5043i	0.948464	+	3.23017i
$533$	−0.516452	−	0.447508i	−0.0223700	−	0.0193837i
$534$	−18.7820	−	12.0705i	−0.812778	−	0.522340i
$535$	18.2665	−	33.4374i	0.789731	−	1.44562i
$536$	−4.83656	−	33.6390i	−0.208908	−	1.45299i
$537$	−0.516453	+	1.75888i	−0.0222866	+	0.0759011i
$538$	16.0345	+	24.9502i	0.691296	+	1.07568i
$539$	3.56851	−	24.8195i	0.153706	−	1.06905i
$540$	12.5116	+	0.897263i	0.538414	+	0.0386120i
$541$	−5.08985	+	11.1452i	−0.218830	+	0.479170i	−0.986928	−	0.161162i	$-0.948476\pi$
$541$	−5.08985	+	11.1452i	−0.218830	+	0.479170i	0.768098	+	0.640332i	$0.221203\pi$
$542$	80.3846	+	11.5576i	3.45281	+	0.496440i
$543$	3.54113	+	5.51011i	0.151965	+	0.236461i
$544$	99.8415	+	29.3161i	4.28067	+	1.25692i
$545$	12.0019	+	21.9899i	0.514105	+	0.941943i
$546$	−3.68420	−	4.25179i	−0.157669	−	0.181960i
$547$	−22.4826	+	34.9836i	−0.961287	+	1.49579i	−0.0954694	+	0.995432i	$0.530435\pi$
$547$	−22.4826	+	34.9836i	−0.961287	+	1.49579i	−0.865818	+	0.500360i	$0.833201\pi$
$548$	48.3453	+	41.8915i	2.06521	+	1.78952i
$549$	−12.2396	+	3.59387i	−0.522374	+	0.153383i
$550$	−10.2484	+	22.4180i	−0.436993	+	0.955909i
$551$	−1.40988			−0.0600630
$552$	−43.1640	+	20.4317i	−1.83718	+	0.869633i
$553$		−	16.7316i		−	0.711501i
$554$	30.5272	+	66.8452i	1.29698	+	2.83998i
$555$	2.74651	−	2.05519i	0.116583	−	0.0872379i
$556$	12.2440	−	14.1303i	0.519261	−	0.599260i
$557$	16.8172	−	26.1681i	0.712567	−	1.10878i	−0.276458	−	0.961026i	$-0.589161\pi$
$557$	16.8172	−	26.1681i	0.712567	−	1.10878i	0.989025	−	0.147750i	$-0.0472031\pi$
$558$	−11.1177	+	9.63351i	−0.470648	+	0.407819i
$559$	−0.247726	−	1.72297i	−0.0104777	−	0.0728740i
$560$	−11.8554	−	166.209i	−0.500983	−	7.02361i
$561$	−6.28014	+	4.03600i	−0.265148	+	0.170400i
$562$	−68.9591	−	9.91481i	−2.90886	−	0.418231i
$563$	22.6080	+	10.3247i	0.952815	+	0.435136i	0.830291	−	0.557329i	$-0.188174\pi$
$563$	22.6080	+	10.3247i	0.952815	+	0.435136i	0.122524	+	0.992466i	$0.460901\pi$
$564$	−11.8056	+	25.8508i	−0.497107	+	1.08851i
$565$	−24.8396	+	5.39854i	−1.04501	+	0.227118i
$566$	30.0036	−	19.2821i	1.26115	−	0.810489i
$567$	1.29201	−	4.40017i	0.0542592	−	0.184790i
$568$	13.9677	−	2.00825i	0.586070	−	0.0842641i
$569$	−12.1642	−	14.0382i	−0.509948	−	0.588511i	0.441137	−	0.897440i	$-0.354575\pi$
$569$	−12.1642	−	14.0382i	−0.509948	−	0.588511i	−0.951085	+	0.308928i	$0.900030\pi$
$570$	−18.1920	−	3.96109i	−0.761980	−	0.165912i
$571$	−1.78931	+	2.06497i	−0.0748802	+	0.0864164i	−0.791954	−	0.610581i	$-0.790936\pi$
$571$	−1.78931	+	2.06497i	−0.0748802	+	0.0864164i	0.717073	+	0.696998i	$0.245481\pi$
$572$	1.25607	+	4.27778i	0.0525189	+	0.178863i
$573$	4.98172	−	2.27508i	0.208115	−	0.0950427i
$574$	−19.4394			−0.811386
$575$	−23.9770	+	0.319374i	−0.999911	+	0.0133188i
$576$	36.2179			1.50908
$577$	−9.71170	+	4.43519i	−0.404304	+	0.184639i	−0.607179	−	0.794565i	$-0.707699\pi$
$577$	−9.71170	+	4.43519i	−0.404304	+	0.184639i	0.202875	+	0.979205i	$0.434971\pi$
$578$	0.349188	+	1.18922i	0.0145243	+	0.0494652i
$579$	−14.5494	+	16.7909i	−0.604652	+	0.697805i
$580$	5.72509	+	1.24657i	0.237721	+	0.0517609i
$581$	14.0583	+	16.2241i	0.583235	+	0.673089i
$582$	−44.2728	+	6.36547i	−1.83517	+	0.263857i
$583$	1.70638	−	5.81139i	0.0706709	−	0.240683i
$584$	130.152	−	83.6436i	5.38573	−	3.46120i
$585$	0.971727	−	0.211191i	0.0401760	−	0.00873167i
$586$	−4.76869	+	10.4420i	−0.196993	+	0.431354i
$587$	−7.07641	−	3.23169i	−0.292075	−	0.133386i	0.263989	−	0.964526i	$-0.414962\pi$
$587$	−7.07641	−	3.23169i	−0.292075	−	0.133386i	−0.556064	+	0.831140i	$0.687689\pi$
$588$	−77.9079	−	11.2015i	−3.21287	−	0.461941i
$589$	13.5409	−	8.70221i	0.557943	−	0.358568i
$590$	3.23085	+	45.2954i	0.133012	+	1.86478i
$591$	−0.954776	−	6.64061i	−0.0392742	−	0.273158i
$592$	18.8396	−	16.3246i	0.774303	−	0.670937i
$593$	−18.5011	+	28.7883i	−0.759751	+	1.18220i	0.218716	+	0.975789i	$0.429813\pi$
$593$	−18.5011	+	28.7883i	−0.759751	+	1.18220i	−0.978466	+	0.206407i	$0.933823\pi$
$594$	−3.22840	+	3.72577i	−0.132463	+	0.152870i
$595$	34.2964	−	25.6637i	1.40601	−	1.05211i
$596$	−6.38321	−	13.9773i	−0.261467	−	0.572532i
$597$			6.46129i			0.264443i
$598$	−4.39318	+	3.91339i	−0.179650	+	0.160030i
$599$	−41.9332			−1.71335			−0.856673	−	0.515860i	$-0.827472\pi$
$599$	−41.9332			−1.71335			−0.856673	+	0.515860i	$0.827472\pi$
$600$	45.2813	+	20.7003i	1.84860	+	0.845087i
$601$	16.9433	−	4.97501i	0.691133	−	0.202935i	0.0827401	−	0.996571i	$-0.473633\pi$
$601$	16.9433	−	4.97501i	0.691133	−	0.202935i	0.608392	+	0.793636i	$0.291815\pi$
$602$	−37.4224	−	32.4267i	−1.52522	−	1.32161i
$603$	1.84517	−	2.87114i	0.0751410	−	0.116922i
$604$	−32.2396	−	37.2065i	−1.31181	−	1.51391i
$605$	8.36245	+	15.3217i	0.339982	+	0.622914i
$606$	−39.1718	−	11.5019i	−1.59125	−	0.467232i
$607$	−2.56878	−	3.99710i	−0.104264	−	0.162237i	0.785202	−	0.619240i	$-0.212559\pi$
$607$	−2.56878	−	3.99710i	−0.104264	−	0.162237i	−0.889465	+	0.457003i	$0.848923\pi$
$608$	−74.4229	−	10.7004i	−3.01825	−	0.433959i
$609$	0.889864	−	1.94853i	0.0360591	−	0.0789584i
$610$	−78.4841	−	5.62844i	−3.17773	−	0.227889i
$611$	−0.320625	+	2.22999i	−0.0129711	+	0.0902159i
$612$	12.6689	+	19.7132i	0.512111	+	0.796861i
$613$	−10.3363	+	35.2023i	−0.417481	+	1.42181i	0.435652	+	0.900115i	$0.356518\pi$
$613$	−10.3363	+	35.2023i	−0.417481	+	1.42181i	−0.853133	+	0.521694i	$0.825300\pi$
$614$	8.26166	+	57.4611i	0.333414	+	2.31894i
$615$	1.64729	−	3.01541i	0.0664250	−	0.121593i
$616$	68.6544	+	44.1215i	2.76616	+	1.77771i
$617$	15.6840	+	13.5903i	0.631414	+	0.547123i	0.910692	−	0.413087i	$-0.135549\pi$
$617$	15.6840	+	13.5903i	0.631414	+	0.547123i	−0.279278	+	0.960210i	$0.590095\pi$
$618$	−2.04639	−	6.96938i	−0.0823180	−	0.280349i
$619$	8.08525	+	17.7042i	0.324974	+	0.711593i	0.999648	−	0.0265221i	$-0.00844325\pi$
$619$	8.08525	+	17.7042i	0.324974	+	0.711593i	−0.674674	+	0.738115i	$0.735716\pi$
$620$	−62.6795	+	23.3645i	−2.51727	+	0.938342i
$621$	−4.61965	−	1.28796i	−0.185380	−	0.0516841i
$622$		−	48.1482i		−	1.93057i
$623$	−33.7617	+	15.4185i	−1.35263	+	0.617728i
$624$	6.93372	−	2.03592i	0.277571	−	0.0815022i
$625$	16.3570	+	18.9063i	0.654280	+	0.756252i
$626$	5.89186	+	3.78647i	0.235486	+	0.151338i
$627$	4.07663	−	3.53242i	0.162805	−	0.141071i
$628$	114.634	−	16.4819i	4.57441	−	0.657701i
$629$	6.14867	+	1.80541i	0.245163	+	0.0719865i
$630$	16.9565	−	22.6422i	0.675565	−	0.902088i
$631$	4.25238	−	29.5760i	0.169285	−	1.17740i	−0.711083	−	0.703109i	$-0.751795\pi$
$631$	4.25238	−	29.5760i	0.169285	−	1.17740i	0.880367	−	0.474293i	$-0.157296\pi$
$632$	33.0472	+	15.0922i	1.31455	+	0.600334i
$633$	10.6633	+	4.86976i	0.423828	+	0.193556i
$634$	6.06209	−	42.1628i	0.240756	−	1.67450i
$635$	6.85171	+	5.13118i	0.271902	+	0.203625i
$636$	−18.2418	−	5.35628i	−0.723335	−	0.212390i
$637$	−6.17619	+	0.888002i	−0.244710	+	0.0351839i
$638$	−1.74032	+	1.50800i	−0.0689000	+	0.0597022i
$639$	1.19216	+	0.766154i	0.0471610	+	0.0303086i
$640$	104.933	+	39.1609i	4.14784	+	1.54797i
$641$	18.2731	−	5.36546i	0.721744	−	0.211923i	0.0998251	−	0.995005i	$-0.468172\pi$
$641$	18.2731	−	5.36546i	0.721744	−	0.211923i	0.621919	+	0.783082i	$0.286353\pi$
$642$	42.7570	−	19.5265i	1.68748	−	0.770648i
$643$		−	14.5087i		−	0.572167i	−0.958205	−	0.286084i	$-0.907646\pi$
$643$		−	14.5087i		−	0.572167i	0.958205	−	0.286084i	$-0.0923535\pi$
$644$	−15.8833	+	122.350i	−0.625891	+	4.82128i
$645$	8.20111	−	3.05706i	0.322919	−	0.120372i
$646$	−14.4486	−	31.6380i	−0.568472	−	1.24478i
$647$	−10.6160	−	36.1547i	−0.417357	−	1.42139i	−0.853303	−	0.521416i	$-0.825404\pi$
$647$	−10.6160	−	36.1547i	−0.417357	−	1.42139i	0.435945	−	0.899973i	$-0.356414\pi$
$648$	7.52554	+	6.52092i	0.295631	+	0.256166i
$649$	−11.0679	−	7.11293i	−0.434455	−	0.279207i
$650$	6.07112	+	0.875275i	0.238129	+	0.0343311i
$651$	3.48040	+	24.2067i	0.136408	+	0.948736i
$652$	−25.2445	+	85.9750i	−0.988652	+	3.36704i
$653$	18.3356	+	28.5307i	0.717527	+	1.11649i	0.988103	+	0.153796i	$0.0491497\pi$
$653$	18.3356	+	28.5307i	0.717527	+	1.11649i	−0.270575	+	0.962699i	$0.587214\pi$
$654$	−4.39837	+	30.5913i	−0.171990	+	1.19622i
$655$	1.96394	−	27.3855i	0.0767374	−	1.07004i
$656$	10.3728	−	22.7133i	0.404990	−	0.886804i
$657$	15.3788	+	2.21113i	0.599982	+	0.0862644i
$658$	34.6487	+	53.9144i	1.35075	+	2.10180i
$659$	23.8292	+	6.99690i	0.928256	+	0.272560i	0.710706	−	0.703489i	$-0.248375\pi$
$659$	23.8292	+	6.99690i	0.928256	+	0.272560i	0.217549	+	0.976049i	$0.430194\pi$
$660$	−19.6771	+	10.7396i	−0.765932	+	0.418039i
$661$	−17.3684	−	20.0442i	−0.675551	−	0.779628i	0.309683	−	0.950840i	$-0.399777\pi$
$661$	−17.3684	−	20.0442i	−0.675551	−	0.779628i	−0.985234	+	0.171212i	$0.945232\pi$
$662$	10.8301	−	16.8520i	0.420925	−	0.654972i
$663$	1.40394	+	1.21652i	0.0545245	+	0.0472457i
$664$	−44.7256	+	13.1326i	−1.73569	+	0.509645i
$665$	−21.8903	+	21.8819i	−0.848868	+	0.848542i
$666$	4.23189			0.163983
$667$	−2.05027	−	0.902583i	−0.0793869	−	0.0349481i
$668$			43.5300i			1.68423i
$669$	1.28837	+	2.82115i	0.0498114	+	0.109072i
$670$	16.8555	−	12.6129i	0.651187	−	0.487277i
$671$	14.9289	−	17.2289i	0.576324	−	0.665114i
$672$	61.7614	−	96.1026i	2.38250	−	3.70724i
$673$	8.35400	−	7.23879i	0.322023	−	0.279035i	−0.478815	−	0.877916i	$-0.658933\pi$
$673$	8.35400	−	7.23879i	0.322023	−	0.279035i	0.800838	+	0.598881i	$0.204388\pi$
$674$	−3.17123	−	22.0564i	−0.122151	−	0.849580i
$675$	2.07533	+	4.54896i	0.0798794	+	0.175089i
$676$	−60.4164	+	38.8272i	−2.32371	+	1.49336i
$677$	−9.45378	−	1.35925i	−0.363338	−	0.0522401i	−0.0417718	−	0.999127i	$-0.513300\pi$
$677$	−9.45378	−	1.35925i	−0.363338	−	0.0522401i	−0.321566	+	0.946887i	$0.604209\pi$
$678$	−28.5255	−	13.0271i	−1.09551	−	0.500305i
$679$	−30.8891	+	67.6378i	−1.18542	+	2.59570i
$680$	19.7534	+	90.8891i	0.757509	+	3.48544i
$681$	6.66136	−	4.28099i	0.255264	−	0.164048i
$682$	7.40673	−	25.2250i	0.283618	−	0.965915i
$683$	11.0663	−	1.59110i	0.423441	−	0.0608816i	0.0726992	−	0.997354i	$-0.476839\pi$
$683$	11.0663	−	1.59110i	0.423441	−	0.0608816i	0.350741	+	0.936472i	$0.385930\pi$
$684$	−11.0882	−	12.7965i	−0.423968	−	0.489285i
$685$	−5.42494	+	24.9150i	−0.207276	+	0.951954i
$686$	−58.2461	+	67.2196i	−2.22385	+	2.56646i
$687$	4.44025	+	15.1221i	0.169406	+	0.576945i
$688$	57.8562	−	26.4220i	2.20575	−	1.00733i
$689$	−1.50718			−0.0574190
$690$	−23.9193	−	17.4065i	−0.910592	−	0.662654i
$691$	47.0270			1.78899			0.894496	−	0.447075i	$-0.147534\pi$
$691$	47.0270			1.78899			0.894496	+	0.447075i	$0.147534\pi$
$692$	44.0503	−	20.1171i	1.67454	−	0.764737i
$693$	2.30897	+	7.86364i	0.0877106	+	0.298715i
$694$	−9.30566	+	10.7393i	−0.353238	+	0.407659i
$695$	7.28214	+	1.58560i	0.276227	+	0.0601451i
$696$	3.04595	+	3.51521i	0.115456	+	0.133244i
$697$	6.35355	−	0.913503i	0.240658	−	0.0346014i
$698$	−3.46510	+	11.8010i	−0.131156	+	0.446676i
$699$	−12.6018	+	8.09869i	−0.476644	+	0.306321i
$700$	108.237	−	69.5007i	4.09096	−	2.62688i
$701$	17.2993	−	37.8802i	0.653385	−	1.43071i	−0.235174	−	0.971953i	$-0.575566\pi$
$701$	17.2993	−	37.8802i	0.653385	−	1.43071i	0.888560	−	0.458761i	$-0.151707\pi$
$702$	1.11592	+	0.509622i	0.0421175	+	0.0192344i
$703$	−4.58328	−	0.658977i	−0.172862	−	0.0248538i
$704$	−54.4507	+	34.9933i	−2.05219	+	1.31886i
$705$	−11.2992	+	0.805955i	−0.425553	+	0.0303540i
$706$	−2.17211	−	15.1074i	−0.0817485	−	0.568573i
$707$	−51.2924	+	44.4451i	−1.92905	+	1.67153i
$708$	−22.3273	+	34.7420i	−0.839113	+	1.30569i
$709$	−12.8633	+	14.8451i	−0.483092	+	0.557518i	−0.944007	−	0.329926i	$-0.892976\pi$
$709$	−12.8633	+	14.8451i	−0.483092	+	0.557518i	0.460914	+	0.887445i	$0.347522\pi$
$710$	5.23713	+	6.99879i	0.196546	+	0.262660i
$711$	1.51563	+	3.31876i	0.0568404	+	0.124463i
$712$		−	80.5917i		−	3.02030i
$713$	25.2624	−	3.98624i	0.946084	−	0.149286i
$714$	52.8447			1.97766
$715$	−1.25686	+	1.25638i	−0.0470040	+	0.0469860i
$716$	−9.86683	+	2.89716i	−0.368741	+	0.108272i
$717$	16.8511	+	14.6016i	0.629317	+	0.545306i
$718$	24.3599	−	37.9048i	0.909105	−	1.41460i
$719$	−23.6536	−	27.2978i	−0.882132	−	1.01803i	−0.999688	−	0.0249683i	$-0.992052\pi$
$719$	−23.6536	−	27.2978i	−0.882132	−	1.01803i	0.117556	−	0.993066i	$-0.462494\pi$
$720$	17.4075	+	31.8940i	0.648740	+	1.18862i
$721$	−11.5861	−	3.40199i	−0.431489	−	0.126697i
$722$	−14.7493	−	22.9503i	−0.548911	−	0.854122i
$723$	2.51297	+	0.361310i	0.0934583	+	0.0134373i
$724$	−15.2636	+	33.4227i	−0.567268	+	1.24214i
$725$	0.657131	+	2.24117i	0.0244052	+	0.0832349i
$726$	−3.06461	+	21.3148i	−0.113738	+	0.791067i
$727$	−5.35561	−	8.33349i	−0.198629	−	0.309072i	0.727623	−	0.685977i	$-0.240625\pi$
$727$	−5.35561	−	8.33349i	−0.198629	−	0.309072i	−0.926252	+	0.376905i	$0.876988\pi$
$728$	5.72145	−	19.4855i	0.212051	−	0.722179i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	84.1054	+	45.9460i	3.11288	+	1.70054i
$731$	13.7549	+	8.83972i	0.508742	+	0.326949i
$732$	−54.0811	−	46.8616i	−1.99890	−	1.73205i
$733$	2.22839	+	7.58919i	0.0823073	+	0.280313i	0.990355	−	0.138554i	$-0.0442455\pi$
$733$	2.22839	+	7.58919i	0.0823073	+	0.280313i	−0.908048	+	0.418867i	$0.862427\pi$
$734$	6.18955	+	13.5532i	0.228461	+	0.500259i
$735$	−10.9584	−	29.3978i	−0.404206	−	1.08436i
$736$	−101.377	−	63.2050i	−3.73680	−	2.32977i
$737$			6.09931i			0.224671i
$738$	3.85586	−	1.76091i	0.141936	−	0.0648200i
$739$	37.8587	−	11.1163i	1.39266	−	0.408920i	0.502500	−	0.864577i	$-0.332414\pi$
$739$	37.8587	−	11.1163i	1.39266	−	0.408920i	0.890155	+	0.455657i	$0.150596\pi$
$740$	18.0286	+	6.72827i	0.662745	+	0.247336i
$741$	−1.12922	−	0.725704i	−0.0414829	−	0.0266594i
$742$	−32.4022	+	28.0767i	−1.18952	+	1.03073i
$743$	25.3168	−	3.64001i	0.928784	−	0.133539i	0.338713	−	0.940890i	$-0.390009\pi$
$743$	25.3168	−	3.64001i	0.928784	−	0.133539i	0.590072	+	0.807351i	$0.299099\pi$
$744$	−50.9510	−	14.9606i	−1.86795	−	0.548481i
$745$	3.67147	−	4.90254i	0.134512	−	0.179615i
$746$	−0.610629	+	4.24702i	−0.0223567	+	0.155494i
$747$	−4.25815	−	1.94463i	−0.155797	−	0.0711503i
$748$	−38.0935	−	17.3967i	−1.39283	−	0.636086i
$749$	11.1208	−	77.3467i	0.406344	−	2.82619i
$750$	2.18251	+	30.7645i	0.0796939	+	1.12336i
$751$	11.0497	+	3.24450i	0.403211	+	0.118393i	0.477049	−	0.878877i	$-0.341707\pi$
$751$	11.0497	+	3.24450i	0.403211	+	0.118393i	−0.0738378	+	0.997270i	$0.523525\pi$
$752$	−81.4828	+	11.7155i	−2.97137	+	0.427219i
$753$	13.6234	−	11.8048i	0.496465	−	0.430189i
$754$	0.482066	+	0.309805i	0.0175558	+	0.0112824i
$755$	6.86135	−	18.3852i	0.249710	−	0.669106i
$756$	24.6838	−	7.24782i	0.897741	−	0.263601i
$757$	−28.4678	+	13.0008i	−1.03468	+	0.472522i	−0.859027	−	0.511930i	$-0.828931\pi$
$757$	−28.4678	+	13.0008i	−1.03468	+	0.472522i	−0.175652	+	0.984452i	$0.556203\pi$
$758$			23.3692i			0.848808i
$759$	8.18969	−	2.52711i	0.297267	−	0.0917283i
$760$	−23.4743	−	62.9740i	−0.851503	−	2.28431i
$761$	−9.95070	−	21.7890i	−0.360713	−	0.789850i	−0.999786	−	0.0207043i	$-0.993409\pi$
$761$	−9.95070	−	21.7890i	−0.360713	−	0.789850i	0.639073	−	0.769146i	$-0.279318\pi$
$762$	2.97519	+	10.1326i	0.107780	+	0.367064i
$763$	38.8296	+	33.6460i	1.40573	+	1.21807i
$764$	25.8454	+	16.6098i	0.935053	+	0.600922i
$765$	−4.47804	+	8.19717i	−0.161904	+	0.296369i
$766$	−4.61725	−	32.1136i	−0.166828	−	1.16031i
$767$	−0.922368	+	3.14130i	−0.0333048	+	0.113426i
$768$	35.5408	+	55.3026i	1.28247	+	1.99556i
$769$	2.51457	−	17.4892i	0.0906776	−	0.630677i	−0.892909	−	0.450238i	$-0.851339\pi$
$769$	2.51457	−	17.4892i	0.0906776	−	0.630677i	0.983586	−	0.180439i	$-0.0577518\pi$
$770$	−3.61613	+	50.4240i	−0.130316	+	1.81716i
$771$	8.75670	−	19.1745i	0.315365	−	0.690552i
$772$	−123.366	−	17.7373i	−4.44003	−	0.638380i
$773$	−6.71867	−	10.4545i	−0.241654	−	0.376021i	0.699149	−	0.714976i	$-0.253563\pi$
$773$	−6.71867	−	10.4545i	−0.241654	−	0.376021i	−0.940802	+	0.338956i	$0.889926\pi$
$774$	10.3602	+	3.04202i	0.372389	+	0.109343i
$775$	−20.1444	−	17.4688i	−0.723608	−	0.627497i
$776$	−105.731	−	122.021i	−3.79554	−	4.38028i
$777$	3.80353	−	5.91841i	0.136451	−	0.212322i
$778$	−38.3957	−	33.2701i	−1.37655	−	1.19279i
$779$	−4.45022	+	1.30670i	−0.159446	+	0.0468175i
$780$	3.94375	+	3.94527i	0.141209	+	0.141263i
$781$	−2.53256			−0.0906223
$782$	−0.757263	−	55.2582i	−0.0270797	−	1.97603i
$783$			0.467104i			0.0166929i
$784$	−94.7127	−	207.392i	−3.38260	−	7.40686i
$785$	27.6578	+	36.9613i	0.987150	+	1.31921i
$786$	22.1811	−	25.5984i	0.791175	−	0.913064i
$787$	2.72569	−	4.24126i	0.0971605	−	0.151185i	−0.789270	−	0.614046i	$-0.789541\pi$
$787$	2.72569	−	4.24126i	0.0971605	−	0.151185i	0.886431	+	0.462861i	$0.153177\pi$
$788$	28.4427	−	24.6458i	1.01323	−	0.877969i
$789$	−2.00964	−	13.9773i	−0.0715449	−	0.497606i
$790$	1.60118	+	22.4480i	0.0569674	+	0.798664i
$791$	−43.8568	+	28.1851i	−1.55937	+	1.00215i
$792$	−17.6145	−	2.53258i	−0.625904	−	0.0899914i
$793$	−5.16027	−	2.35662i	−0.183247	−	0.0836859i
$794$	3.98475	−	8.72539i	0.141414	−	0.309653i
$795$	−1.60945	−	7.40538i	−0.0570814	−	0.262642i
$796$	−30.4922	+	19.5961i	−1.08077	+	0.694567i
$797$	13.3686	−	45.5292i	0.473539	−	1.61273i	−0.283236	−	0.959050i	$-0.591408\pi$
$797$	13.3686	−	45.5292i	0.473539	−	1.61273i	0.756775	−	0.653676i	$-0.226774\pi$
$798$	−37.7954	+	5.43416i	−1.33794	+	0.192367i
$799$	−13.8581	−	15.9931i	−0.490264	−	0.565795i
$800$	17.6782	+	123.291i	0.625020	+	4.35899i
$801$	5.30005	−	6.11658i	0.187268	−	0.216119i
$802$	−14.5809	−	49.6581i	−0.514871	−	1.75349i
$803$	−25.2571	+	11.5345i	−0.891304	+	0.407045i
$804$	19.1456			0.675214
$805$	−45.8416	+	17.8072i	−1.61570	+	0.627620i
$806$	−6.54210			−0.230436
$807$	−9.77974	+	4.46626i	−0.344263	+	0.157220i
$808$	−41.5187	−	141.400i	−1.46062	−	4.97442i
$809$	−29.8465	+	34.4447i	−1.04935	+	1.21101i	−0.0724348	+	0.997373i	$0.523077\pi$
$809$	−29.8465	+	34.4447i	−1.04935	+	1.21101i	−0.976913	+	0.213639i	$0.931469\pi$
$810$	−1.31234	+	6.02714i	−0.0461108	+	0.211772i
$811$	5.25069	+	6.05962i	0.184377	+	0.212782i	0.840412	−	0.541948i	$-0.182313\pi$
$811$	5.25069	+	6.05962i	0.184377	+	0.212782i	−0.656035	+	0.754730i	$0.727768\pi$
$812$	11.8943	−	1.71015i	0.417410	−	0.0600144i
$813$	−8.29408	+	28.2470i	−0.290886	+	0.990667i
$814$	−6.36232	+	4.08881i	−0.222999	+	0.143313i
$815$	−34.9021	+	7.58546i	−1.22257	+	0.265707i
$816$	−28.1978	+	61.7445i	−0.987119	+	2.16149i
$817$	−10.7467	−	4.90786i	−0.375980	−	0.171704i
$818$	−30.1800	−	4.33923i	−1.05522	−	0.151718i
$819$	1.71568	−	1.10260i	0.0599507	−	0.0385280i
$820$	19.2263	−	1.37138i	0.671411	−	0.0478907i
$821$	4.36476	+	30.3576i	0.152331	+	1.05949i	0.912298	+	0.409526i	$0.134306\pi$
$821$	4.36476	+	30.3576i	0.152331	+	1.05949i	−0.759967	+	0.649961i	$0.774785\pi$
$822$	−23.7737	+	20.6001i	−0.829204	+	0.718509i
$823$	19.4007	−	30.1881i	0.676265	−	1.05229i	−0.318281	−	0.947996i	$-0.603106\pi$
$823$	19.4007	−	30.1881i	0.676265	−	1.05229i	0.994547	−	0.104293i	$-0.0332580\pi$
$824$	17.1702	−	19.8155i	0.598153	−	0.690306i
$825$	−7.51525	−	4.83384i	−0.261647	−	0.168293i
$826$	38.6884	+	84.7158i	1.34614	+	2.94764i
$827$			40.6780i			1.41451i	0.706956	+	0.707257i	$0.250068\pi$
$827$			40.6780i			1.41451i	−0.706956	+	0.707257i	$0.749932\pi$
$828$	−7.93255	−	25.7073i	−0.275675	−	0.893389i
$829$	−29.5523			−1.02639			−0.513196	−	0.858271i	$-0.671539\pi$
$829$	−29.5523			−1.02639			−0.513196	+	0.858271i	$0.671539\pi$
$830$	−20.4139	−	20.4217i	−0.708577	−	0.708849i
$831$	−25.5600	+	7.50511i	−0.886668	+	0.260349i
$832$	12.1726	+	10.5476i	0.422008	+	0.365672i
$833$	31.6870	−	49.3059i	1.09789	−	1.70835i
$834$	6.02096	+	6.94856i	0.208489	+	0.240609i
$835$	−15.2304	+	8.31266i	−0.527071	+	0.287671i
$836$	29.0340	+	8.52516i	1.00416	+	0.294849i
$837$	−2.88310	−	4.48619i	−0.0996546	−	0.155066i
$838$	80.1909	+	11.5297i	2.77015	+	0.398287i
$839$	8.08730	−	17.7087i	0.279205	−	0.611373i	−0.717128	−	0.696942i	$-0.754544\pi$
$839$	8.08730	−	17.7087i	0.279205	−	0.611373i	0.996332	+	0.0855690i	$0.0272708\pi$
$840$	101.849	+	7.30407i	3.51414	+	0.252015i
$841$	4.09608	−	28.4889i	0.141244	−	0.982374i
$842$	23.2253	+	36.1393i	0.800396	+	1.24544i
$843$	7.11519	−	24.2321i	0.245060	−	0.834599i
$844$	9.35875	+	65.0915i	0.322141	+	2.24054i
$845$	−25.1224	−	13.7241i	−0.864236	−	0.472124i
$846$	−11.7565	−	7.55543i	−0.404196	−	0.259761i
$847$	27.0549	+	23.4432i	0.929617	+	0.805518i
$848$	−15.5155	−	52.8408i	−0.532803	−	1.81456i
$849$	5.37086	+	11.7605i	0.184328	+	0.403621i
$850$	−43.5578	+	37.7138i	−1.49402	+	1.29357i
$851$	−6.24322	−	3.89243i	−0.214015	−	0.133431i
$852$			7.94967i			0.272351i
$853$	32.9059	−	15.0276i	1.12668	−	0.514537i	0.237176	−	0.971467i	$-0.423778\pi$
$853$	32.9059	−	15.0276i	1.12668	−	0.514537i	0.889503	+	0.456930i	$0.151051\pi$
$854$	−154.839	+	45.4648i	−5.29848	+	1.55577i
$855$	2.35983	−	6.32324i	0.0807045	−	0.216250i
$856$	142.739	+	91.7330i	4.87873	+	3.13537i
$857$	−0.833773	+	0.722468i	−0.0284811	+	0.0246791i	−0.668985	−	0.743276i	$-0.733271\pi$
$857$	−0.833773	+	0.722468i	−0.0284811	+	0.0246791i	0.640504	+	0.767955i	$0.278726\pi$
$858$	−2.17008	+	0.312011i	−0.0740854	+	0.0106519i
$859$	38.0453	+	11.1711i	1.29809	+	0.381153i	0.856539	−	0.516083i	$-0.172610\pi$
$859$	38.0453	+	11.1711i	1.29809	+	0.381153i	0.441551	+	0.897236i	$0.354428\pi$
$860$	39.2997	+	29.4311i	1.34011	+	1.00359i
$861$	1.00288	−	6.97518i	0.0341780	−	0.237713i
$862$	58.6208	+	26.7712i	1.99663	+	0.911832i
$863$	9.72221	+	4.43999i	0.330948	+	0.151139i	0.573958	−	0.818885i	$-0.305407\pi$
$863$	9.72221	+	4.43999i	0.330948	+	0.151139i	−0.243010	+	0.970024i	$0.578135\pi$
$864$	−3.54512	+	24.6568i	−0.120607	+	0.838842i
$865$	15.4507	+	11.5709i	0.525339	+	0.393421i
$866$	55.7220	+	16.3615i	1.89351	+	0.555985i
$867$	−0.444728	+	0.0639422i	−0.0151038	+	0.00217159i
$868$	−103.681	+	89.8401i	−3.51916	+	3.04937i
$869$	−5.48517	−	3.52511i	−0.186072	−	0.119581i
$870$	−1.00742	+	2.69941i	−0.0341546	+	0.0915185i
$871$	1.45630	−	0.427607i	0.0493448	−	0.0144889i
$872$	−101.480	+	46.3445i	−3.43656	+	1.56942i
$873$		−	16.2142i		−	0.548767i
$874$	6.22395	+	39.4437i	0.210528	+	1.33420i
$875$	44.9865	+	24.5981i	1.52082	+	0.831569i
$876$	36.2067	+	79.2815i	1.22331	+	2.67867i
$877$	12.7961	+	43.5795i	0.432093	+	1.47158i	0.831874	+	0.554964i	$0.187268\pi$
$877$	12.7961	+	43.5795i	0.432093	+	1.47158i	−0.399781	+	0.916611i	$0.630914\pi$
$878$	−80.7027	−	69.9293i	−2.72358	−	2.36000i
$879$	−3.50074	−	2.24979i	−0.118077	−	0.0758834i
$880$	−56.9865	−	31.1312i	−1.92102	−	1.04943i
$881$	3.41871	+	23.7776i	0.115179	+	0.801088i	0.962747	+	0.270402i	$0.0871567\pi$
$881$	3.41871	+	23.7776i	0.115179	+	0.801088i	−0.847568	+	0.530686i	$0.821934\pi$
$882$	10.9045	−	37.1372i	0.367173	−	1.25047i
$883$	−8.25310	−	12.8421i	−0.277739	−	0.432170i	0.674159	−	0.738587i	$-0.264506\pi$
$883$	−8.25310	−	12.8421i	−0.277739	−	0.432170i	−0.951898	+	0.306416i	$0.900870\pi$
$884$	−1.48307	+	10.3150i	−0.0498811	+	0.346931i
$885$	−16.4194	−	1.17751i	−0.551932	−	0.0395815i
$886$	6.09111	−	13.3377i	0.204635	−	0.448088i
$887$	−13.7691	−	1.97970i	−0.462322	−	0.0664719i	−0.0927817	−	0.995686i	$-0.529576\pi$
$887$	−13.7691	−	1.97970i	−0.462322	−	0.0664719i	−0.369541	+	0.929215i	$0.620485\pi$
$888$	8.25883	+	12.8510i	0.277148	+	0.431251i
$889$	16.8447	+	4.94604i	0.564952	+	0.165885i
$890$	43.8209	−	23.9171i	1.46888	−	0.801704i
$891$	−1.17031	−	1.35061i	−0.0392070	−	0.0452473i
$892$	−9.40613	+	14.6362i	−0.314940	+	0.490057i
$893$	11.5561	+	10.0135i	0.386712	+	0.335087i
$894$	7.25006	−	2.12881i	0.242478	−	0.0711980i
$895$	−2.89788	−	2.89899i	−0.0968654	−	0.0969026i
$896$	229.705			7.67389
$897$	−1.17754	−	1.77824i	−0.0393170	−	0.0593736i
$898$			82.1824i			2.74246i
$899$	−1.03478	−	2.26585i	−0.0345117	−	0.0755702i
$900$	−15.1733	+	23.5902i	−0.505777	+	0.786340i
$901$	9.27091	−	10.6992i	0.308859	−	0.356442i
$902$	−4.09560	+	6.37288i	−0.136369	+	0.212194i
$903$	13.5658	−	11.7549i	0.451443	−	0.391177i
$904$	−16.1099	−	112.047i	−0.535807	−	3.72662i
$905$	−14.6089	+	1.04203i	−0.485615	+	0.0346381i
$906$	20.3662	−	13.0886i	0.676622	−	0.434838i
$907$	9.54604	+	1.37251i	0.316971	+	0.0455736i	0.298964	−	0.954264i	$-0.403359\pi$
$907$	9.54604	+	1.37251i	0.316971	+	0.0455736i	0.0180069	+	0.999838i	$0.494268\pi$
$908$	40.4058	+	18.4527i	1.34091	+	0.612374i
$909$	6.14794	−	13.4621i	0.203914	−	0.446510i
$910$	12.2930	−	2.67170i	0.407508	−	0.0885660i
$911$	24.8457	−	15.9674i	0.823175	−	0.529022i	−0.0599276	−	0.998203i	$-0.519087\pi$
$911$	24.8457	−	15.9674i	0.823175	−	0.529022i	0.883102	+	0.469180i	$0.155451\pi$
$912$	13.8182	−	47.0603i	0.457565	−	1.55832i
$913$	8.28067	−	1.19058i	0.274050	−	0.0394024i
$914$	−57.5760	−	66.4462i	−1.90444	−	2.19784i
$915$	6.06857	−	27.8710i	0.200621	−	0.921386i
$916$	−57.8977	+	66.8176i	−1.91300	+	2.20771i
$917$	−15.8641	−	54.0281i	−0.523878	−	1.78417i
$918$	−10.4819	+	4.78692i	−0.345954	+	0.157992i
$919$	32.1774			1.06144			0.530718	−	0.847549i	$-0.321922\pi$
$919$	32.1774			1.06144			0.530718	+	0.847549i	$0.321922\pi$
$920$	6.17816	−	106.606i	0.203688	−	3.51469i
$921$	−21.0442			−0.693430
$922$	−43.8390	+	20.0206i	−1.44376	+	0.659343i
$923$	0.177552	+	0.604686i	0.00584419	+	0.0199035i
$924$	−30.1074	+	34.7457i	−0.990459	+	1.14305i
$925$	1.08870	+	7.59278i	0.0357963	+	0.249649i
$926$	51.4096	+	59.3298i	1.68942	+	1.94970i
$927$	2.60630	−	0.374729i	0.0856021	−	0.0123077i
$928$	−3.27817	+	11.1644i	−0.107611	+	0.366490i
$929$	7.29630	−	4.68904i	0.239384	−	0.153843i	−0.415449	−	0.909617i	$-0.636375\pi$
$929$	7.29630	−	4.68904i	0.239384	−	0.153843i	0.654833	+	0.755774i	$0.272739\pi$
$930$	−6.98602	−	32.1439i	−0.229080	−	1.05404i
$931$	−17.5928	+	38.5228i	−0.576580	+	1.26253i
$932$	−76.4388	−	34.9084i	−2.50384	−	1.14346i
$933$	17.2764	+	2.48397i	0.565603	+	0.0813214i
$934$	50.9077	−	32.7164i	1.66575	−	1.07051i
$935$	−1.18765	−	16.6504i	−0.0388403	−	0.544528i
$936$	0.630218	+	4.38326i	0.0205993	+	0.143271i
$937$	35.7882	−	31.0107i	1.16915	−	1.01307i	0.169529	−	0.985525i	$-0.445775\pi$
$937$	35.7882	−	31.0107i	1.16915	−	1.01307i	0.999620	−	0.0275491i	$-0.00877025\pi$
$938$	23.3426	−	36.3217i	0.762162	−	1.18595i
$939$	−1.66261	+	1.91875i	−0.0542571	+	0.0626161i
$940$	−38.0723	−	50.8790i	−1.24178	−	1.65949i
$941$	1.03727	+	2.27130i	0.0338139	+	0.0740422i	0.925785	−	0.378050i	$-0.123405\pi$
$941$	1.03727	+	2.27130i	0.0338139	+	0.0740422i	−0.891971	+	0.452092i	$0.850678\pi$
$942$			56.9509i			1.85556i
$943$	−7.30812	−	0.948728i	−0.237985	−	0.0308948i
$944$	−119.627			−3.89353
$945$	7.24961	+	7.25239i	0.235830	+	0.235920i
$946$	−18.5149	+	5.43646i	−0.601970	+	0.176754i
$947$	−41.6752	−	36.1118i	−1.35426	−	1.17348i	−0.967960	−	0.251103i	$-0.919207\pi$
$947$	−41.6752	−	36.1118i	−1.35426	−	1.17348i	−0.386302	−	0.922372i	$-0.626248\pi$
$948$	−11.0652	+	17.2178i	−0.359382	+	0.559210i
$949$	4.52475	+	5.22184i	0.146880	+	0.169508i
$950$	27.2751	−	31.4527i	0.884920	−	1.02046i
$951$	14.8160	+	4.35036i	0.480440	+	0.141070i
$952$	103.130	+	160.474i	3.34247	+	5.20098i
$953$	40.0105	+	5.75265i	1.29607	+	0.186347i	0.755609	−	0.655023i	$-0.227341\pi$
$953$	40.0105	+	5.75265i	1.29607	+	0.186347i	0.540460	+	0.841370i	$0.318250\pi$
$954$	3.88375	−	8.50423i	0.125741	−	0.275334i
$955$	−0.875975	+	12.2148i	−0.0283459	+	0.395260i
$956$	−17.8010	+	123.808i	−0.575724	+	4.00425i
$957$	−0.451311	−	0.702254i	−0.0145888	−	0.0227006i
$958$	5.80815	−	19.7808i	0.187653	−	0.639087i
$959$	7.44240	+	51.7630i	0.240328	+	1.67151i
$960$	−38.8259	+	71.0719i	−1.25310	+	2.29384i
$961$	−2.15512	−	1.38501i	−0.0695200	−	0.0446778i
$962$	1.42231	+	1.23244i	0.0458571	+	0.0397354i
$963$	4.80058	+	16.3493i	0.154697	+	0.526848i
$964$	5.91636	+	12.9550i	0.190553	+	0.417253i
$965$	−17.3524	−	46.5509i	−0.558593	−	1.49853i
$966$	−58.4415	−	16.2935i	−1.88033	−	0.524236i
$967$		−	19.1974i		−	0.617348i	−0.951168	−	0.308674i	$-0.900115\pi$
$967$		−	19.1974i		−	0.617348i	0.951168	−	0.308674i	$-0.0998851\pi$
$968$	−70.7075	+	32.2910i	−2.27262	+	1.03787i
$969$	12.0976	−	3.55219i	0.388632	−	0.114113i
$970$	34.9697	−	93.7023i	1.12281	−	3.00860i
$971$	−23.3812	−	15.0262i	−0.750337	−	0.482212i	0.108733	−	0.994071i	$-0.465321\pi$
$971$	−23.3812	−	15.0262i	−0.750337	−	0.482212i	−0.859070	+	0.511859i	$0.828957\pi$
$972$	−4.23955	+	3.67359i	−0.135984	+	0.117831i
$973$	15.1292	−	2.17526i	0.485021	−	0.0697355i
$974$	−15.6733	−	4.60209i	−0.502204	−	0.147460i
$975$	−0.627272	+	2.13326i	−0.0200888	+	0.0683190i
$976$	29.4998	−	205.176i	0.944266	−	6.56751i
$977$	−33.9821	−	15.5191i	−1.08719	−	0.496501i	−0.210514	−	0.977591i	$-0.567514\pi$
$977$	−33.9821	−	15.5191i	−1.08719	−	0.496501i	−0.876671	+	0.481090i	$0.840241\pi$
$978$	−40.0810	−	18.3044i	−1.28165	−	0.585310i
$979$	−2.05842	+	14.3166i	−0.0657875	+	0.457562i
$980$	105.499	−	140.874i	3.37005	−	4.50006i
$981$	−10.7498	−	3.15641i	−0.343213	−	0.100777i
$982$	−26.0720	+	3.74859i	−0.831992	+	0.119622i
$983$	19.9170	−	17.2582i	0.635254	−	0.550451i	−0.276590	−	0.960988i	$-0.589204\pi$
$983$	19.9170	−	17.2582i	0.635254	−	0.550451i	0.911844	+	0.410537i	$0.134659\pi$
$984$	12.8723	+	8.27254i	0.410355	+	0.263719i
$985$	14.0547	+	5.24520i	0.447820	+	0.167126i
$986$	−5.16451	+	1.51644i	−0.164471	+	0.0482932i
$987$	−21.1329	+	9.65107i	−0.672668	+	0.307197i
$988$		−	7.52996i		−	0.239560i
$989$	−12.4861	−	14.0170i	−0.397035	−	0.445713i
$990$	−3.85037	−	10.3293i	−0.122373	−	0.328287i
$991$	11.4687	+	25.1131i	0.364317	+	0.797743i	0.999674	+	0.0255243i	$0.00812553\pi$
$991$	11.4687	+	25.1131i	0.364317	+	0.797743i	−0.635357	+	0.772218i	$0.719147\pi$
$992$	−37.4256	−	127.460i	−1.18826	−	4.04685i
$993$	5.48805	+	4.75542i	0.174158	+	0.150909i
$994$	15.0816	+	9.69234i	0.478358	+	0.307422i
$995$	−12.6793	−	6.92657i	−0.401960	−	0.219587i
$996$	−3.73721	−	25.9928i	−0.118418	−	0.823615i
$997$	10.7786	−	36.7084i	0.341361	−	1.16257i	−0.592691	−	0.805430i	$-0.701935\pi$
$997$	10.7786	−	36.7084i	0.341361	−	1.16257i	0.934052	−	0.357137i	$-0.116247\pi$
$998$	16.3810	+	25.4894i	0.518533	+	0.806853i
$999$	−0.218323	+	1.51847i	−0.00690745	+	0.0480424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.t.a.4.1	✓	240
5.4	even	2	inner	345.2.t.a.4.24	yes	240
23.6	even	11	inner	345.2.t.a.259.24	yes	240
115.29	even	22	inner	345.2.t.a.259.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.t.a.4.1	✓	240	1.1	even	1	trivial
345.2.t.a.4.24	yes	240	5.4	even	2	inner
345.2.t.a.259.1	yes	240	115.29	even	22	inner
345.2.t.a.259.24	yes	240	23.6	even	11	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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.50929 + 1.14595i) q^{2} +(-0.281733 - 0.959493i) q^{3} +(3.67359 - 4.23955i) q^{4} +(2.18488 + 0.475730i) q^{5} +(1.80648 + 2.08479i) q^{6} +(4.53926 - 0.652647i) q^{7} +(-2.80541 + 9.55436i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(-6.02764 + 1.31002i) q^{10} +(0.742396 - 1.62562i) q^{11} +(-5.10279 - 2.33037i) q^{12} +(-0.440188 - 0.0632895i) q^{13} +(-10.6424 + 6.83946i) q^{14} +(-0.159091 - 2.23040i) q^{15} +(-2.31256 - 16.0842i) q^{16} +(3.15694 - 2.73551i) q^{17} +(1.49140 - 2.32066i) q^{18} +(-1.97660 + 2.28112i) q^{19} +(10.0432 - 7.51526i) q^{20} +(-1.90507 - 4.17151i) q^{21} +4.92990i q^{22} +(-4.33473 + 2.05185i) q^{23} +9.95771 q^{24} +(4.54736 + 2.07882i) q^{25} +(1.17708 - 0.345623i) q^{26} +(0.755750 + 0.654861i) q^{27} +(13.9085 - 21.6420i) q^{28} +(0.305888 + 0.353014i) q^{29} +(2.95514 + 5.41441i) q^{30} +(-5.11673 - 1.50241i) q^{31} +(13.4676 + 20.9559i) q^{32} +(-1.76893 - 0.254334i) q^{33} +(-4.78692 + 10.4819i) q^{34} +(10.2282 + 0.733509i) q^{35} +(-0.798348 + 5.55263i) q^{36} +(0.829390 + 1.29056i) q^{37} +(2.34580 - 7.98907i) q^{38} +(0.0632895 + 0.440188i) q^{39} +(-10.6748 + 19.5405i) q^{40} +(1.29270 + 0.830767i) q^{41} +(9.56072 + 8.28441i) q^{42} +(1.10275 + 3.75563i) q^{43} +(-4.16464 - 9.11930i) q^{44} +(-2.09523 + 0.781023i) q^{45} +(8.52576 - 10.1161i) q^{46} -5.06600i q^{47} +(-14.7812 + 6.75034i) q^{48} +(13.4625 - 3.95294i) q^{49} +(-13.7929 - 0.00529699i) q^{50} +(-3.51411 - 2.25838i) q^{51} +(-1.88539 + 1.63370i) q^{52} +(3.35460 - 0.482319i) q^{53} +(-2.64683 - 0.777180i) q^{54} +(2.39540 - 3.19860i) q^{55} +(-6.49887 + 45.2006i) q^{56} +(2.74559 + 1.25387i) q^{57} +(-1.17210 - 0.535279i) q^{58} +(1.04770 - 7.28690i) q^{59} +(-10.0403 - 7.51911i) q^{60} +(12.2396 + 3.59387i) q^{61} +(14.5610 - 2.09356i) q^{62} +(-3.46582 + 3.00315i) q^{63} +(-30.4684 - 19.5809i) q^{64} +(-0.931647 - 0.347690i) q^{65} +(4.73021 - 1.38891i) q^{66} +(-3.10451 + 1.41778i) q^{67} -23.4332i q^{68} +(3.18997 + 3.58107i) q^{69} +(-26.5061 + 9.88045i) q^{70} +(-0.588693 - 1.28906i) q^{71} +(-2.80541 - 9.55436i) q^{72} +(-11.7420 - 10.1745i) q^{73} +(-3.56010 - 2.28794i) q^{74} +(0.713475 - 4.94883i) q^{75} +(2.40969 + 16.7598i) q^{76} +(2.30897 - 7.86364i) q^{77} +(-0.663246 - 1.03203i) q^{78} +(0.519230 - 3.61133i) q^{79} +(2.59909 - 36.2422i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-4.19577 - 0.603261i) q^{82} +(2.53083 + 3.93805i) q^{83} +(-24.6838 - 7.24782i) q^{84} +(8.19889 - 4.47489i) q^{85} +(-7.07089 - 8.16024i) q^{86} +(0.252535 - 0.392953i) q^{87} +(13.4490 + 11.6537i) q^{88} +(-7.76556 + 2.28017i) q^{89} +(4.36253 - 4.36085i) q^{90} -2.03943 q^{91} +(-7.22511 + 25.9150i) q^{92} +5.33275i q^{93} +(5.80540 + 12.7121i) q^{94} +(-5.40382 + 4.04363i) q^{95} +(16.3128 - 18.8260i) q^{96} +(-8.76606 + 13.6403i) q^{97} +(-29.2513 + 25.3464i) q^{98} +(0.254334 + 1.76893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) \) 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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