LMFDB - Embedded newform 87.2.k.a.2.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,2,Mod(2,87)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("87.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.k (of order $28$, degree $12$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			2.8
Character	$\chi$	$=$	87.2
Dual form			87.2.k.a.44.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.261972 - 2.32506i) q^{2} +(1.21083 + 1.23850i) q^{3} +(-3.38744 - 0.773161i) q^{4} +(-0.273793 - 0.343325i) q^{5} +(3.19680 - 2.49081i) q^{6} +(-0.670558 - 2.93790i) q^{7} +(-1.13950 + 3.25651i) q^{8} +(-0.0677777 + 2.99923i) q^{9} +(-0.869979 + 0.546644i) q^{10} +(1.80846 + 5.16827i) q^{11} +(-3.14405 - 5.13152i) q^{12} +(-1.42901 + 2.96736i) q^{13} +(-7.00648 + 0.789441i) q^{14} +(0.0936925 - 0.754802i) q^{15} +(1.01216 + 0.487430i) q^{16} +(0.0231533 + 0.0231533i) q^{17} +(6.95566 + 0.943302i) q^{18} +(1.59781 + 2.54289i) q^{19} +(0.662010 + 1.37468i) q^{20} +(2.82667 - 4.38779i) q^{21} +(12.4903 - 2.85084i) q^{22} +(-5.72233 - 4.56340i) q^{23} +(-5.41295 + 2.53181i) q^{24} +(1.06969 - 4.68664i) q^{25} +(6.52494 + 4.09989i) q^{26} +(-3.79663 + 3.54762i) q^{27} +10.4704i q^{28} +(4.89452 - 2.24581i) q^{29} +(-1.73042 - 0.415578i) q^{30} +(-3.75513 - 0.423102i) q^{31} +(-2.27269 + 3.61696i) q^{32} +(-4.21119 + 8.49768i) q^{33} +(0.0598983 - 0.0477673i) q^{34} +(-0.825063 + 1.03460i) q^{35} +(2.54848 - 10.1073i) q^{36} +(-4.50934 - 1.57789i) q^{37} +(6.33097 - 3.04884i) q^{38} +(-5.40537 + 1.82314i) q^{39} +(1.43003 - 0.500389i) q^{40} +(5.19822 - 5.19822i) q^{41} +(-9.46139 - 7.72167i) q^{42} +(-0.517730 - 4.59498i) q^{43} +(-2.13013 - 18.9054i) q^{44} +(1.04827 - 0.797899i) q^{45} +(-12.1093 + 12.1093i) q^{46} +(0.857949 - 0.300209i) q^{47} +(0.621870 + 1.84376i) q^{48} +(-1.87485 + 0.902882i) q^{49} +(-10.6165 - 3.71488i) q^{50} +(-0.000640695 + 0.0567100i) q^{51} +(7.13491 - 8.94690i) q^{52} +(1.75058 - 1.39604i) q^{53} +(7.25384 + 9.75678i) q^{54} +(1.27926 - 2.03592i) q^{55} +(10.3314 + 1.16407i) q^{56} +(-1.21471 + 5.05790i) q^{57} +(-3.93944 - 11.9684i) q^{58} +11.8163i q^{59} +(-0.900961 + 2.48440i) q^{60} +(0.807366 + 0.507302i) q^{61} +(-1.96748 + 8.62008i) q^{62} +(8.85691 - 1.81203i) q^{63} +(9.57093 + 7.63256i) q^{64} +(1.41002 - 0.321828i) q^{65} +(18.6545 + 12.0174i) q^{66} +(0.522314 + 1.08460i) q^{67} +(-0.0605290 - 0.0963314i) q^{68} +(-1.27698 - 12.6126i) q^{69} +(2.18936 + 2.18936i) q^{70} +(-3.35796 - 1.61711i) q^{71} +(-9.68982 - 3.63836i) q^{72} +(0.707680 - 0.0797363i) q^{73} +(-4.85001 + 10.0711i) q^{74} +(7.09964 - 4.34991i) q^{75} +(-3.44641 - 9.84926i) q^{76} +(13.9712 - 8.77870i) q^{77} +(2.82287 + 13.0454i) q^{78} +(-4.21488 + 12.0454i) q^{79} +(-0.109775 - 0.480955i) q^{80} +(-8.99081 - 0.406563i) q^{81} +(-10.7244 - 13.4480i) q^{82} +(-8.94353 - 2.04130i) q^{83} +(-12.9676 + 12.6779i) q^{84} +(0.00160990 - 0.0142883i) q^{85} -10.8193 q^{86} +(8.70788 + 3.34257i) q^{87} -18.8913 q^{88} +(1.34559 - 11.9424i) q^{89} +(-1.58055 - 2.64632i) q^{90} +(9.67605 + 2.20850i) q^{91} +(15.8558 + 19.8825i) q^{92} +(-4.02282 - 5.16304i) q^{93} +(-0.473248 - 2.07343i) q^{94} +(0.435572 - 1.24479i) q^{95} +(-7.23146 + 1.56480i) q^{96} +(12.3474 - 7.75841i) q^{97} +(1.60810 + 4.59568i) q^{98} +(-15.6234 + 5.07369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) $ 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.261972	−	2.32506i	0.185242	−	1.64407i	−0.465701	−	0.884942i	$-0.654198\pi$
$2$	0.261972	−	2.32506i	0.185242	−	1.64407i	0.650943	−	0.759127i	$-0.274374\pi$
$3$	1.21083	+	1.23850i	0.699073	+	0.715050i
$3$	1.21083	+	1.23850i	0.699073	+	0.715050i
$4$	−3.38744	−	0.773161i	−1.69372	−	0.386580i
$5$	−0.273793	−	0.343325i	−0.122444	−	0.153540i	0.716831	−	0.697247i	$-0.245592\pi$
$5$	−0.273793	−	0.343325i	−0.122444	−	0.153540i	−0.839275	+	0.543707i	$0.817020\pi$
$6$	3.19680	−	2.49081i	1.30509	−	1.01687i
$7$	−0.670558	−	2.93790i	−0.253447	−	1.11042i	−0.928112	−	0.372300i	$-0.878569\pi$
$7$	−0.670558	−	2.93790i	−0.253447	−	1.11042i	0.674666	−	0.738124i	$-0.264288\pi$
$8$	−1.13950	+	3.25651i	−0.402875	+	1.15135i
$9$	−0.0677777	+	2.99923i	−0.0225926	+	0.999745i
$10$	−0.869979	+	0.546644i	−0.275111	+	0.172864i
$11$	1.80846	+	5.16827i	0.545270	+	1.55829i	0.805407	+	0.592722i	$0.201947\pi$
$11$	1.80846	+	5.16827i	0.545270	+	1.55829i	−0.260137	+	0.965572i	$0.583768\pi$
$12$	−3.14405	−	5.13152i	−0.907610	−	1.48134i
$13$	−1.42901	+	2.96736i	−0.396335	+	0.822998i	0.603340	+	0.797484i	$0.293836\pi$
$13$	−1.42901	+	2.96736i	−0.396335	+	0.822998i	−0.999674	+	0.0255133i	$0.991878\pi$
$14$	−7.00648	+	0.789441i	−1.87256	+	0.210987i
$15$	0.0936925	−	0.754802i	0.0241913	−	0.194889i
$16$	1.01216	+	0.487430i	0.253040	+	0.121858i
$17$	0.0231533	+	0.0231533i	0.00561549	+	0.00561549i	0.709909	−	0.704293i	$-0.248736\pi$
$17$	0.0231533	+	0.0231533i	0.00561549	+	0.00561549i	−0.704293	+	0.709909i	$0.748736\pi$
$18$	6.95566	+	0.943302i	1.63946	+	0.222339i
$19$	1.59781	+	2.54289i	0.366562	+	0.583380i	0.978176	−	0.207776i	$-0.0666225\pi$
$19$	1.59781	+	2.54289i	0.366562	+	0.583380i	−0.611614	+	0.791156i	$0.709480\pi$
$20$	0.662010	+	1.37468i	0.148030	+	0.307387i
$21$	2.82667	−	4.38779i	0.616830	−	0.957495i
$22$	12.4903	−	2.85084i	2.66295	−	0.607801i
$23$	−5.72233	−	4.56340i	−1.19319	−	0.951535i	−0.193624	−	0.981076i	$-0.562024\pi$
$23$	−5.72233	−	4.56340i	−1.19319	−	0.951535i	−0.999564	+	0.0295408i	$0.990596\pi$
$24$	−5.41295	+	2.53181i	−1.10491	+	0.516803i
$25$	1.06969	−	4.68664i	0.213939	−	0.937328i
$26$	6.52494	+	4.09989i	1.27965	+	0.804055i
$27$	−3.79663	+	3.54762i	−0.730661	+	0.682740i
$28$			10.4704i			1.97872i
$29$	4.89452	−	2.24581i	0.908889	−	0.417037i
$29$	4.89452	−	2.24581i	0.908889	−	0.417037i
$30$	−1.73042	−	0.415578i	−0.315930	−	0.0758738i
$31$	−3.75513	−	0.423102i	−0.674441	−	0.0759913i	−0.231900	−	0.972740i	$-0.574494\pi$
$31$	−3.75513	−	0.423102i	−0.674441	−	0.0759913i	−0.442541	+	0.896748i	$0.645923\pi$
$32$	−2.27269	+	3.61696i	−0.401759	+	0.639395i
$33$	−4.21119	+	8.49768i	−0.733073	+	1.47926i
$34$	0.0598983	−	0.0477673i	0.0102725	−	0.00819202i
$35$	−0.825063	+	1.03460i	−0.139461	+	0.174879i
$36$	2.54848	−	10.1073i	0.424747	−	1.68455i
$37$	−4.50934	−	1.57789i	−0.741331	−	0.259403i	−0.0669194	−	0.997758i	$-0.521317\pi$
$37$	−4.50934	−	1.57789i	−0.741331	−	0.259403i	−0.674412	+	0.738355i	$0.735603\pi$
$38$	6.33097	−	3.04884i	1.02702	−	0.494587i
$39$	−5.40537	+	1.82314i	−0.865551	+	0.291937i
$40$	1.43003	−	0.500389i	0.226108	−	0.0791185i
$41$	5.19822	−	5.19822i	0.811826	−	0.811826i	−0.173081	−	0.984908i	$-0.555372\pi$
$41$	5.19822	−	5.19822i	0.811826	−	0.811826i	0.984908	+	0.173081i	$0.0553723\pi$
$42$	−9.46139	−	7.72167i	−1.45992	−	1.19148i
$43$	−0.517730	−	4.59498i	−0.0789530	−	0.700728i	−0.969374	−	0.245590i	$-0.921018\pi$
$43$	−0.517730	−	4.59498i	−0.0789530	−	0.700728i	0.890421	−	0.455138i	$-0.150410\pi$
$44$	−2.13013	−	18.9054i	−0.321129	−	2.85010i
$45$	1.04827	−	0.797899i	0.156267	−	0.118944i
$46$	−12.1093	+	12.1093i	−1.78542	+	1.78542i
$47$	0.857949	−	0.300209i	0.125145	−	0.0437900i	−0.266980	−	0.963702i	$-0.586026\pi$
$47$	0.857949	−	0.300209i	0.125145	−	0.0437900i	0.392125	+	0.919912i	$0.371740\pi$
$48$	0.621870	+	1.84376i	0.0897592	+	0.266123i
$49$	−1.87485	+	0.902882i	−0.267836	+	0.128983i
$50$	−10.6165	−	3.71488i	−1.50140	−	0.525363i
$51$	−0.000640695		0.0567100i	−8.97152e−5		0.00794099i
$52$	7.13491	−	8.94690i	0.989435	−	1.24071i
$53$	1.75058	−	1.39604i	0.240460	−	0.191761i	−0.495843	−	0.868412i	$-0.665141\pi$
$53$	1.75058	−	1.39604i	0.240460	−	0.191761i	0.736304	+	0.676651i	$0.236570\pi$
$54$	7.25384	+	9.75678i	0.987123	+	1.32773i
$55$	1.27926	−	2.03592i	0.172495	−	0.274524i
$56$	10.3314	+	1.16407i	1.38060	+	0.155556i
$57$	−1.21471	+	5.05790i	−0.160892	+	0.669936i
$58$	−3.93944	−	11.9684i	−0.517274	−	1.57153i
$59$			11.8163i			1.53836i	0.639034	+	0.769179i	$0.279334\pi$
$59$			11.8163i			1.53836i	−0.639034	+	0.769179i	$0.720666\pi$
$60$	−0.900961	+	2.48440i	−0.116314	+	0.320735i
$61$	0.807366	+	0.507302i	0.103373	+	0.0649533i	0.582726	−	0.812669i	$-0.301986\pi$
$61$	0.807366	+	0.507302i	0.103373	+	0.0649533i	−0.479354	+	0.877622i	$0.659129\pi$
$62$	−1.96748	+	8.62008i	−0.249870	+	1.09475i
$63$	8.85691	−	1.81203i	1.11587	−	0.228295i
$64$	9.57093	+	7.63256i	1.19637	+	0.954070i
$65$	1.41002	−	0.321828i	0.174892	−	0.0399178i
$66$	18.6545	+	12.0174i	2.29620	+	1.47924i
$67$	0.522314	+	1.08460i	0.0638108	+	0.132504i	0.930435	−	0.366457i	$-0.119429\pi$
$67$	0.522314	+	1.08460i	0.0638108	+	0.132504i	−0.866624	+	0.498961i	$0.833715\pi$
$68$	−0.0605290	−	0.0963314i	−0.00734022	−	0.0116819i
$69$	−1.27698	−	12.6126i	−0.153731	−	1.51838i
$70$	2.18936	+	2.18936i	0.261678	+	0.261678i
$71$	−3.35796	−	1.61711i	−0.398517	−	0.191916i	0.223881	−	0.974616i	$-0.428127\pi$
$71$	−3.35796	−	1.61711i	−0.398517	−	0.191916i	−0.622398	+	0.782701i	$0.713842\pi$
$72$	−9.68982	−	3.63836i	−1.14196	−	0.428785i
$73$	0.707680	−	0.0797363i	0.0828276	−	0.00933243i	−0.0704534	−	0.997515i	$-0.522445\pi$
$73$	0.707680	−	0.0797363i	0.0828276	−	0.00933243i	0.153281	+	0.988183i	$0.451016\pi$
$74$	−4.85001	+	10.0711i	−0.563802	+	1.17075i
$75$	7.09964	−	4.34991i	0.819795	−	0.502284i
$76$	−3.44641	−	9.84926i	−0.395330	−	1.12979i
$77$	13.9712	−	8.77870i	1.59217	−	1.00043i
$78$	2.82287	+	13.0454i	0.319627	+	1.47710i
$79$	−4.21488	+	12.0454i	−0.474211	+	1.35522i	0.419982	+	0.907533i	$0.362037\pi$
$79$	−4.21488	+	12.0454i	−0.474211	+	1.35522i	−0.894192	+	0.447683i	$0.852249\pi$
$80$	−0.109775	−	0.480955i	−0.0122732	−	0.0537724i
$81$	−8.99081	−	0.406563i	−0.998979	−	0.0451736i
$82$	−10.7244	−	13.4480i	−1.18431	−	1.48508i
$83$	−8.94353	−	2.04130i	−0.981680	−	0.224062i	−0.298578	−	0.954385i	$-0.596512\pi$
$83$	−8.94353	−	2.04130i	−0.981680	−	0.224062i	−0.683102	+	0.730323i	$0.739369\pi$
$84$	−12.9676	+	12.6779i	−1.41489	+	1.38327i
$85$	0.00160990	−	0.0142883i	0.000174618	−	0.00154978i
$86$	−10.8193			−1.16667
$87$	8.70788	+	3.34257i	0.933583	+	0.358361i
$88$	−18.8913			−2.01382
$89$	1.34559	−	11.9424i	0.142632	−	1.26589i	−0.694741	−	0.719260i	$-0.744481\pi$
$89$	1.34559	−	11.9424i	0.142632	−	1.26589i	0.837373	−	0.546633i	$-0.184091\pi$
$90$	−1.58055	−	2.64632i	−0.166604	−	0.278947i
$91$	9.67605	+	2.20850i	1.01433	+	0.231513i
$92$	15.8558	+	19.8825i	1.65308	+	2.07290i
$93$	−4.02282	−	5.16304i	−0.417147	−	0.535383i
$94$	−0.473248	−	2.07343i	−0.0488118	−	0.213858i
$95$	0.435572	−	1.24479i	0.0446887	−	0.127713i
$96$	−7.23146	+	1.56480i	−0.738058	+	0.159707i
$97$	12.3474	−	7.75841i	1.25369	−	0.787748i	0.269185	−	0.963088i	$-0.413246\pi$
$97$	12.3474	−	7.75841i	1.25369	−	0.787748i	0.984508	+	0.175341i	$0.0561027\pi$
$98$	1.60810	+	4.59568i	0.162443	+	0.464234i
$99$	−15.6234	+	5.07369i	−1.57021	+	0.509925i
$100$	−7.24705	+	15.0487i	−0.724705	+	1.50487i
$101$	3.62673	−	0.408634i	0.360873	−	0.0406606i	0.0703332	−	0.997524i	$-0.477594\pi$
$101$	3.62673	−	0.408634i	0.360873	−	0.0406606i	0.290540	+	0.956863i	$0.406165\pi$
$102$	0.131687	+	0.0163461i	0.0130389	+	0.00161850i
$103$	13.6392	+	6.56831i	1.34391	+	0.647195i	0.960990	−	0.276585i	$-0.0892026\pi$
$103$	13.6392	+	6.56831i	1.34391	+	0.647195i	0.382925	+	0.923780i	$0.374917\pi$
$104$	−8.03489	−	8.03489i	−0.787886	−	0.787886i
$105$	−2.28036	+	0.230878i	−0.222540	+	0.0225314i
$106$	−2.78728	−	4.43593i	−0.270725	−	0.430856i
$107$	1.24440	+	2.58402i	0.120300	+	0.249806i	0.952419	−	0.304791i	$-0.0985866\pi$
$107$	1.24440	+	2.58402i	0.120300	+	0.249806i	−0.832119	+	0.554597i	$0.812872\pi$
$108$	15.6037	−	9.08195i	1.50147	−	0.873911i
$109$	−4.67087	+	1.06610i	−0.447388	+	0.102114i	−0.440279	−	0.897861i	$-0.645120\pi$
$109$	−4.67087	+	1.06610i	−0.447388	+	0.102114i	−0.00710991	+	0.999975i	$0.502263\pi$
$110$	−4.39853	−	3.50771i	−0.419383	−	0.334447i
$111$	−3.50583	−	7.49539i	−0.332759	−	0.711431i
$112$	0.753312	−	3.30048i	0.0711813	−	0.311866i
$113$	3.61299	+	2.27019i	0.339881	+	0.213561i	0.691147	−	0.722714i	$-0.257106\pi$
$113$	3.61299	+	2.27019i	0.339881	+	0.213561i	−0.351266	+	0.936276i	$0.614249\pi$
$114$	11.4417	+	4.14930i	1.07162	+	0.388618i
$115$			3.21404i			0.299711i
$116$	−18.3163	+	3.82331i	−1.70062	+	0.354985i
$117$	−8.80295	−	4.48704i	−0.813833	−	0.414827i
$118$	27.4738	+	3.09555i	2.52916	+	0.284968i
$119$	0.0524965	−	0.0835476i	0.00481234	−	0.00765880i
$120$	2.35126	+	1.16521i	0.214640	+	0.106369i
$121$	−14.8404	+	11.8348i	−1.34913	+	1.07589i
$122$	1.39102	−	1.74428i	0.125937	−	0.157920i
$123$	12.7322	+	0.143845i	1.14802	+	0.0129700i
$124$	12.3932	+	4.33655i	1.11294	+	0.389434i
$125$	−3.88013	+	1.86857i	−0.347049	+	0.167130i
$126$	−1.89284	−	21.0676i	−0.168627	−	1.87685i
$127$	1.20424	−	0.421381i	0.106859	−	0.0373915i	−0.276320	−	0.961066i	$-0.589115\pi$
$127$	1.20424	−	0.421381i	0.106859	−	0.0373915i	0.383179	+	0.923674i	$0.374829\pi$
$128$	14.2124	−	14.2124i	1.25621	−	1.25621i
$129$	5.06401	−	6.20495i	0.445861	−	0.546315i
$130$	−0.378885	−	3.36270i	−0.0332304	−	0.294928i
$131$	0.674951	+	5.99035i	0.0589707	+	0.523380i	0.988121	+	0.153678i	$0.0491117\pi$
$131$	0.674951	+	5.99035i	0.0589707	+	0.523380i	−0.929150	+	0.369702i	$0.879460\pi$
$132$	20.8352	−	25.5295i	1.81347	−	2.22205i
$133$	6.39936	−	6.39936i	0.554895	−	0.554895i
$134$	2.65859	−	0.930279i	0.229667	−	0.0803639i
$135$	2.25748	+	0.332165i	0.194293	+	0.0285882i
$136$	−0.101782	+	0.0490157i	−0.00872774	+	0.00420306i
$137$	−9.27340	−	3.24490i	−0.792280	−	0.277231i	−0.0963568	−	0.995347i	$-0.530719\pi$
$137$	−9.27340	−	3.24490i	−0.792280	−	0.277231i	−0.695923	+	0.718116i	$0.745005\pi$
$138$	−29.6597	−	0.335087i	−2.52480	−	0.0285245i
$139$	−1.61843	+	2.02944i	−0.137273	+	0.172135i	−0.845716	−	0.533633i	$-0.820826\pi$
$139$	−1.61843	+	2.02944i	−0.137273	+	0.172135i	0.708443	+	0.705768i	$0.249398\pi$
$140$	3.59476	−	2.86672i	0.303813	−	0.242282i
$141$	1.41064	+	0.699069i	0.118797	+	0.0588723i
$142$	−4.63958	+	7.38385i	−0.389345	+	0.619639i
$143$	−17.9204	−	2.01915i	−1.49858	−	0.168850i
$144$	−1.53052	+	3.00267i	−0.127543	+	0.250222i
$145$	−2.11113	−	1.06552i	−0.175320	−	0.0884869i
$146$		−	1.66629i		−	0.137903i
$147$	−3.38835	−	1.22877i	−0.279467	−	0.101348i
$148$	14.0552	+	8.83144i	1.15533	+	0.725940i
$149$	−0.115010	+	0.503893i	−0.00942202	+	0.0412806i	−0.979420	−	0.201831i	$-0.935311\pi$
$149$	−0.115010	+	0.503893i	−0.00942202	+	0.0412806i	0.969998	+	0.243111i	$0.0781680\pi$
$150$	−8.25391	−	17.6467i	−0.673929	−	1.44084i
$151$	−5.13795	−	4.09738i	−0.418121	−	0.333440i	0.391726	−	0.920082i	$-0.371878\pi$
$151$	−5.13795	−	4.09738i	−0.418121	−	0.333440i	−0.809847	+	0.586642i	$0.800450\pi$
$152$	−10.1017	+	2.30564i	−0.819354	+	0.187012i
$153$	−0.0710113	+	0.0678728i	−0.00574092	+	0.00548719i
$154$	−16.7510	−	34.7838i	−1.34983	−	2.80296i
$155$	0.882866	+	1.40507i	0.0709135	+	0.112858i
$156$	19.7199	−	1.99657i	1.57886	−	0.159854i
$157$	7.40489	+	7.40489i	0.590975	+	0.590975i	0.937895	−	0.346920i	$-0.112772\pi$
$157$	7.40489	+	7.40489i	0.590975	+	0.590975i	−0.346920	+	0.937895i	$0.612772\pi$
$158$	26.9022	+	12.9554i	2.14022	+	1.03068i
$159$	3.84865	+	0.477728i	0.305218	+	0.0378863i
$160$	1.86404	−	0.210027i	0.147365	−	0.0166041i
$161$	−9.56969	+	19.8717i	−0.754197	+	1.56611i
$162$	−3.30062	+	20.7977i	−0.259321	+	1.63402i
$163$	−4.12150	−	11.7786i	−0.322821	−	0.922568i	−0.984898	−	0.173133i	$-0.944611\pi$
$163$	−4.12150	−	11.7786i	−0.322821	−	0.922568i	0.662078	−	0.749435i	$-0.269675\pi$
$164$	−21.6277	+	13.5896i	−1.68884	+	1.06117i
$165$	4.07046	−	0.880798i	0.316885	−	0.0685700i
$166$	−7.08911	+	20.2595i	−0.550222	+	1.57244i
$167$	3.51365	+	15.3943i	0.271894	+	1.19125i	0.907774	+	0.419459i	$0.137780\pi$
$167$	3.51365	+	15.3943i	0.271894	+	1.19125i	−0.635880	+	0.771788i	$0.719363\pi$
$168$	11.0679	+	14.2050i	0.853908	+	1.09594i
$169$	1.34220	+	1.68306i	0.103246	+	0.129466i
$170$	−0.0327994	−	0.00748626i	−0.00251560	−	0.000574170i
$171$	−7.73503	+	4.61984i	−0.591513	+	0.353288i
$172$	−1.79888	+	15.9655i	−0.137163	+	1.21736i
$173$	14.6332			1.11254			0.556271	−	0.831001i	$-0.312232\pi$
$173$	14.6332			1.11254			0.556271	+	0.831001i	$0.312232\pi$
$174$	10.0529	−	19.3707i	0.762110	−	1.46849i
$175$	−14.4862			−1.09505
$176$	−0.688726	+	6.11261i	−0.0519147	+	0.460756i
$177$	−14.6346	+	14.3076i	−1.10000	+	1.07542i
$178$	−27.4144	−	6.25715i	−2.05479	−	0.468993i
$179$	−11.7860	−	14.7792i	−0.880929	−	1.10465i	−0.993816	−	0.111042i	$-0.964581\pi$
$179$	−11.7860	−	14.7792i	−0.880929	−	1.10465i	0.112887	−	0.993608i	$-0.463990\pi$
$180$	−4.16785	+	1.89235i	−0.310653	+	0.141048i
$181$	0.988209	+	4.32963i	0.0734530	+	0.321819i	0.998284	−	0.0585599i	$-0.0186509\pi$
$181$	0.988209	+	4.32963i	0.0734530	+	0.321819i	−0.924831	+	0.380378i	$0.875794\pi$
$182$	7.66975	−	21.9189i	0.568519	−	1.62474i
$183$	0.349289	+	1.61418i	0.0258202	+	0.119324i
$184$	21.3814	−	13.4348i	1.57626	−	0.990428i
$185$	0.692897	+	1.98018i	0.0509428	+	0.145586i
$186$	−13.0583	+	8.00073i	−0.957479	+	0.586642i
$187$	−0.0777907	+	0.161534i	−0.00568862	+	0.0118125i
$188$	−3.13836	+	0.353608i	−0.228888	+	0.0257895i
$189$	12.9684	+	8.77524i	0.943315	+	0.638305i
$190$	−2.78012	−	1.33883i	−0.201691	−	0.0971292i
$191$	11.5911	+	11.5911i	0.838703	+	0.838703i	0.988688	−	0.149986i	$-0.0479227\pi$
$191$	11.5911	+	11.5911i	0.838703	+	0.838703i	−0.149986	+	0.988688i	$0.547923\pi$
$192$	2.13583	+	21.0954i	0.154140	+	1.52243i
$193$	−3.91803	−	6.23550i	−0.282026	−	0.448841i	0.675429	−	0.737425i	$-0.263958\pi$
$193$	−3.91803	−	6.23550i	−0.282026	−	0.448841i	−0.957455	+	0.288584i	$0.906816\pi$
$194$	−14.8041	−	30.7411i	−1.06287	−	2.20708i
$195$	2.10588	+	1.35663i	0.150805	+	0.0971506i
$196$	7.04902	−	1.60889i	0.503502	−	0.114921i
$197$	9.96095	+	7.94359i	0.709688	+	0.565958i	0.910418	−	0.413689i	$-0.135760\pi$
$197$	9.96095	+	7.94359i	0.709688	+	0.565958i	−0.200730	+	0.979647i	$0.564331\pi$
$198$	7.70376	+	37.6547i	0.547483	+	2.67600i
$199$	4.46447	−	19.5601i	0.316478	−	1.38658i	−0.527205	−	0.849738i	$-0.676760\pi$
$199$	4.46447	−	19.5601i	0.316478	−	1.38658i	0.843683	−	0.536842i	$-0.180383\pi$
$200$	14.0432	+	8.82392i	0.993003	+	0.623945i
$201$	−0.710841	+	1.96015i	−0.0501388	+	0.138258i
$202$		−	8.53942i		−	0.600832i
$203$	−9.88005	−	12.8737i	−0.693443	−	0.903555i
$204$	0.0460163	−	0.191606i	0.00322178	−	0.0134151i
$205$	−3.20792	−	0.361445i	−0.224051	−	0.0252444i
$206$	18.8448	−	29.9914i	1.31298	−	2.08960i
$207$	14.0746	−	16.8533i	0.978249	−	1.17139i
$208$	−2.89276	+	2.30690i	−0.200577	+	0.159955i
$209$	−10.2528	+	12.8566i	−0.709202	+	0.889311i
$210$	−0.0605837	+	5.36247i	−0.00418068	+	0.370046i
$211$	0.297195	+	0.103993i	0.0204598	+	0.00715918i	0.340490	−	0.940248i	$-0.389407\pi$
$211$	0.297195	+	0.103993i	0.0204598	+	0.00715918i	−0.320030	+	0.947407i	$0.603693\pi$
$212$	−7.00934	+	3.37552i	−0.481403	+	0.231832i
$213$	−2.06313	−	6.11689i	−0.141363	−	0.419123i
$214$	6.33400	−	2.21636i	0.432983	−	0.151507i
$215$	−1.43582	+	1.43582i	−0.0979222	+	0.0979222i
$216$	−7.22661	−	16.4063i	−0.491709	−	1.11631i
$217$	1.27500	+	11.3159i	0.0865526	+	0.768175i
$218$	1.25511	+	11.1394i	0.0850065	+	0.754453i
$219$	0.955634	+	0.779916i	0.0645758	+	0.0527018i
$220$	−5.90750	+	5.90750i	−0.398283	+	0.398283i
$221$	−0.101790	+	0.0356179i	−0.00684715	+	0.00239592i
$222$	−18.3457	+	6.18771i	−1.23128	+	0.415292i
$223$	1.42628	−	0.686858i	0.0955105	−	0.0459954i	−0.385519	−	0.922700i	$-0.625977\pi$
$223$	1.42628	−	0.686858i	0.0955105	−	0.0459954i	0.481029	+	0.876705i	$0.340263\pi$
$224$	12.1503	+	4.25156i	0.811824	+	0.284069i
$225$	13.9838	+	3.52592i	0.932255	+	0.235061i
$226$	6.22484	−	7.80570i	0.414070	−	0.519227i
$227$	1.96001	−	1.56306i	0.130091	−	0.103744i	−0.556283	−	0.830993i	$-0.687773\pi$
$227$	1.96001	−	1.56306i	0.130091	−	0.103744i	0.686374	+	0.727249i	$0.259202\pi$
$228$	8.02532	−	16.1942i	0.531490	−	1.07249i
$229$	−0.668603	+	1.06408i	−0.0441826	+	0.0703161i	−0.868085	−	0.496415i	$-0.834649\pi$
$229$	−0.668603	+	1.06408i	−0.0441826	+	0.0703161i	0.823903	+	0.566731i	$0.191792\pi$
$230$	7.47286	+	0.841989i	0.492746	+	0.0555191i
$231$	27.7892	+	6.67388i	1.82840	+	0.439109i
$232$	1.73621	+	18.4982i	0.113988	+	1.21447i
$233$			3.96686i			0.259878i	0.991522	+	0.129939i	$0.0414781\pi$
$233$			3.96686i			0.259878i	−0.991522	+	0.129939i	$0.958522\pi$
$234$	−12.7388	+	19.2920i	−0.832761	+	1.26115i
$235$	−0.337970	−	0.212360i	−0.0220467	−	0.0138529i
$236$	9.13593	−	40.0271i	0.594699	−	2.60555i
$237$	−20.0218	+	9.36483i	−1.30056	+	0.608311i
$238$	−0.180501	−	0.143945i	−0.0117001	−	0.00933055i
$239$	−25.8931	+	5.90994i	−1.67489	+	0.382282i	−0.951376	−	0.308031i	$-0.900330\pi$
$239$	−25.8931	+	5.90994i	−1.67489	+	0.382282i	−0.723511	+	0.690313i	$0.757473\pi$
$240$	0.462745	−	0.718311i	0.0298701	−	0.0463668i
$241$	11.6517	+	24.1950i	0.750551	+	1.55854i	0.827477	+	0.561499i	$0.189775\pi$
$241$	11.6517	+	24.1950i	0.750551	+	1.55854i	−0.0769261	+	0.997037i	$0.524511\pi$
$242$	23.6290	+	37.6053i	1.51893	+	2.41736i
$243$	−10.3828	−	11.6274i	−0.666058	−	0.745900i
$244$	−2.34268	−	2.34268i	−0.149975	−	0.149975i
$245$	0.823303	+	0.396482i	0.0525989	+	0.0253303i
$246$	3.66992	−	29.5655i	0.233986	−	1.88503i
$247$	−9.82896	+	1.10746i	−0.625402	+	0.0704658i
$248$	5.65682	−	11.7465i	0.359209	−	0.745904i
$249$	−8.30094	−	13.5483i	−0.526051	−	0.858586i
$250$	3.32806	+	9.51105i	0.210485	+	0.601532i
$251$	7.40810	−	4.65482i	0.467595	−	0.293809i	−0.277551	−	0.960711i	$-0.589523\pi$
$251$	7.40810	−	4.65482i	0.467595	−	0.293809i	0.745146	+	0.666901i	$0.232380\pi$
$252$	−31.4032	−	0.709661i	−1.97822	−	0.0447045i
$253$	13.2363	−	37.8273i	0.832161	−	2.37818i
$254$	−0.664262	−	2.91032i	−0.0416795	−	0.182610i
$255$	0.0196454	−	0.0153068i	0.00123024	−	0.000958550i
$256$	−14.0564	−	17.6261i	−0.878523	−	1.10163i
$257$	−27.1130	−	6.18837i	−1.69126	−	0.386020i	−0.734895	−	0.678181i	$-0.762769\pi$
$257$	−27.1130	−	6.18837i	−1.69126	−	0.386020i	−0.956369	+	0.292161i	$0.905626\pi$
$258$	−13.1003	−	13.3997i	−0.815588	−	0.834227i
$259$	−1.61191	+	14.3061i	−0.100159	+	0.888937i
$260$	−5.02518			−0.311649
$261$	6.40399	+	14.8320i	0.396397	+	0.918079i
$262$	14.1048			0.871396
$263$	1.28932	−	11.4430i	0.0795026	−	0.705605i	−0.889224	−	0.457473i	$-0.848755\pi$
$263$	1.28932	−	11.4430i	0.0795026	−	0.705605i	0.968726	−	0.248132i	$-0.0798168\pi$
$264$	−22.8742	−	23.3969i	−1.40781	−	1.43998i
$265$	−0.958591	−	0.218792i	−0.0588858	−	0.0134403i
$266$	−13.2025	−	16.5554i	−0.809495	−	1.01508i
$267$	16.4200	−	12.7937i	1.00489	−	0.782963i
$268$	−0.930739	−	4.07783i	−0.0568539	−	0.249093i
$269$	7.03436	−	20.1030i	0.428893	−	1.22570i	−0.503417	−	0.864043i	$-0.667924\pi$
$269$	7.03436	−	20.1030i	0.428893	−	1.22570i	0.932310	−	0.361661i	$-0.117790\pi$
$270$	1.36370	−	5.16176i	0.0829921	−	0.314135i
$271$	−0.314343	+	0.197515i	−0.0190950	+	0.0119982i	−0.541546	−	0.840671i	$-0.682161\pi$
$271$	−0.314343	+	0.197515i	−0.0190950	+	0.0119982i	0.522451	+	0.852669i	$0.325018\pi$
$272$	0.0121492	+	0.0347204i	0.000736653	+	0.00210523i
$273$	8.98083	+	14.6579i	0.543545	+	0.887138i
$274$	−9.97398	+	20.7112i	−0.602550	+	1.25121i
$275$	26.1563	−	2.94711i	1.57729	−	0.177718i
$276$	−5.42589	+	43.7118i	−0.326600	+	2.63114i
$277$	−13.9315	−	6.70906i	−0.837063	−	0.403108i	−0.0343035	−	0.999411i	$-0.510921\pi$
$277$	−13.9315	−	6.70906i	−0.837063	−	0.403108i	−0.802759	+	0.596303i	$0.796636\pi$
$278$	4.29461	+	4.29461i	0.257573	+	0.257573i
$279$	1.52350	−	11.2338i	0.0912093	−	0.672552i
$280$	−2.42901	−	3.86575i	−0.145161	−	0.231023i
$281$	9.59432	+	19.9228i	0.572349	+	1.18850i	0.963386	+	0.268120i	$0.0864023\pi$
$281$	9.59432	+	19.9228i	0.572349	+	1.18850i	−0.391037	+	0.920375i	$0.627883\pi$
$282$	1.99493	−	3.09669i	0.118796	−	0.184405i
$283$	8.57168	−	1.95643i	0.509534	−	0.116298i	0.0399779	−	0.999201i	$-0.487271\pi$
$283$	8.57168	−	1.95643i	0.509534	−	0.116298i	0.469556	+	0.882903i	$0.344414\pi$
$284$	10.1246	+	8.07411i	0.600785	+	0.479110i
$285$	2.06908	−	0.967777i	0.122562	−	0.0573261i
$286$	−9.38929	+	41.1372i	−0.555201	+	2.43249i
$287$	−18.7576	−	11.7862i	−1.10723	−	0.695716i
$288$	−10.6941	−	7.06148i	−0.630155	−	0.416102i
$289$		−	16.9989i		−	0.999937i
$290$	−3.03047	+	4.62937i	−0.177955	+	0.271846i
$291$	24.5595	+	5.89822i	1.43970	+	0.345760i
$292$	−2.45887	−	0.277048i	−0.143894	−	0.0162130i
$293$	−3.01703	+	4.80158i	−0.176257	+	0.280511i	−0.923156	−	0.384427i	$-0.874399\pi$
$293$	−3.01703	+	4.80158i	−0.176257	+	0.280511i	0.746899	+	0.664938i	$0.231542\pi$
$294$	−3.74463	+	7.55623i	−0.218391	+	0.440688i
$295$	4.05685	−	3.23523i	0.236199	−	0.188362i
$296$	10.2768	−	12.8867i	0.597328	−	0.749026i
$297$	−25.2011	−	13.2063i	−1.46232	−	0.766306i
$298$	1.14145	+	0.399412i	0.0661227	+	0.0231373i
$299$	21.7185	−	10.4591i	1.25601	−	0.604864i
$300$	−27.4128	+	9.24589i	−1.58268	+	0.533811i
$301$	−13.1524	+	4.60224i	−0.758094	+	0.265269i
$302$	−10.8727	+	10.8727i	−0.625652	+	0.625652i
$303$	4.89745	+	3.99692i	0.281351	+	0.229617i
$304$	0.377751	+	3.35263i	0.0216655	+	0.192287i
$305$	−0.0468815	−	0.416085i	−0.00268443	−	0.0238249i
$306$	0.139206	+	0.182887i	0.00795785	+	0.0104549i
$307$	−7.10347	+	7.10347i	−0.405416	+	0.405416i	−0.880137	−	0.474720i	$-0.842549\pi$
$307$	−7.10347	+	7.10347i	−0.405416	+	0.405416i	0.474720	+	0.880137i	$0.342549\pi$
$308$	−54.1140	+	18.9353i	−3.08343	+	1.07894i
$309$	8.37994	+	24.8453i	0.476718	+	1.41340i
$310$	3.49817	−	1.68463i	0.198683	−	0.0956806i
$311$	15.5436	+	5.43893i	0.881395	+	0.308414i	0.732767	−	0.680480i	$-0.238228\pi$
$311$	15.5436	+	5.43893i	0.881395	+	0.308414i	0.148628	+	0.988893i	$0.452514\pi$
$312$	0.222341	−	19.6801i	0.0125876	−	1.11417i
$313$	9.28300	−	11.6405i	0.524706	−	0.657961i	−0.446894	−	0.894587i	$-0.647470\pi$
$313$	9.28300	−	11.6405i	0.524706	−	0.657961i	0.971601	+	0.236626i	$0.0760415\pi$
$314$	19.1567	−	15.2770i	1.08108	−	0.862130i
$315$	−3.04707	−	2.54468i	−0.171683	−	0.143376i
$316$	23.5907	−	37.5444i	1.32708	−	2.11204i
$317$	−3.82827	−	0.431343i	−0.215017	−	0.0242266i	0.00379864	−	0.999993i	$-0.498791\pi$
$317$	−3.82827	−	0.431343i	−0.215017	−	0.0242266i	−0.218816	+	0.975766i	$0.570219\pi$
$318$	2.11899	−	8.82321i	0.118827	−	0.494781i
$319$	20.4585	+	21.2348i	1.14546	+	1.18892i
$320$		−	5.37568i		−	0.300510i
$321$	−1.69356	+	4.67000i	−0.0945252	+	0.260654i
$322$	43.6959	+	27.4560i	2.43508	+	1.53006i
$323$	−0.0218819	+	0.0958707i	−0.00121754	+	0.00533439i
$324$	30.1415	+	8.32855i	1.67453	+	0.462697i
$325$	12.3783	+	9.87140i	0.686627	+	0.547567i
$326$	−28.4656	+	6.49709i	−1.57657	+	0.359841i
$327$	−6.97600	−	4.49403i	−0.385774	−	0.248520i
$328$	11.0047	+	22.8515i	0.607633	+	1.26176i
$329$	−1.45729	−	2.31926i	−0.0803430	−	0.127865i
$330$	−0.981566	−	9.69483i	−0.0540334	−	0.533683i
$331$	−17.5043	−	17.5043i	−0.962125	−	0.962125i	0.0371839	−	0.999308i	$-0.488161\pi$
$331$	−17.5043	−	17.5043i	−0.962125	−	0.962125i	−0.999308	+	0.0371839i	$0.988161\pi$
$332$	28.7174	+	13.8296i	1.57607	+	0.758996i
$333$	5.03809	−	13.4176i	0.276085	−	0.735282i
$334$	36.7132	−	4.13659i	2.00886	−	0.226344i
$335$	0.229363	−	0.476278i	0.0125315	−	0.0260218i
$336$	4.99978	−	3.06334i	0.272761	−	0.167119i
$337$	6.67582	+	19.0784i	0.363655	+	1.03927i	0.969798	+	0.243910i	$0.0784303\pi$
$337$	6.67582	+	19.0784i	0.363655	+	1.03927i	−0.606143	+	0.795356i	$0.707284\pi$
$338$	4.26485	−	2.67978i	0.231977	−	0.145761i
$339$	1.56308	+	7.22351i	0.0848948	+	0.392327i
$340$	−0.0165006	+	0.0471560i	−0.000894870	+	0.00255739i
$341$	−4.60429	−	20.1727i	−0.249336	−	1.09241i
$342$	8.71507	+	19.1947i	0.471257	+	1.03793i
$343$	−9.24225	−	11.5894i	−0.499034	−	0.625769i
$344$	15.5536	+	3.55000i	0.838592	+	0.191403i
$345$	−3.98060	+	3.89166i	−0.214308	+	0.209520i
$346$	3.83349	−	34.0231i	0.206089	−	1.82909i
$347$	−5.63729			−0.302625			−0.151313	−	0.988486i	$-0.548350\pi$
$347$	−5.63729			−0.302625			−0.151313	+	0.988486i	$0.548350\pi$
$348$	−26.9131	−	18.0554i	−1.44269	−	0.967869i
$349$	−25.6287			−1.37187			−0.685936	−	0.727662i	$-0.740607\pi$
$349$	−25.6287			−1.37187			−0.685936	+	0.727662i	$0.740607\pi$
$350$	−3.79497	+	33.6813i	−0.202850	+	1.80034i
$351$	−5.10167	−	16.3355i	−0.272307	−	0.871926i
$352$	−22.8035	−	5.20476i	−1.21543	−	0.277414i
$353$	3.72864	+	4.67556i	0.198455	+	0.248855i	0.871094	−	0.491116i	$-0.163411\pi$
$353$	3.72864	+	4.67556i	0.198455	+	0.248855i	−0.672639	+	0.739971i	$0.734839\pi$
$354$	29.4322	+	37.7745i	1.56431	+	2.00769i
$355$	0.364191	+	1.59563i	0.0193293	+	0.0846871i
$356$	−13.7915	+	39.4138i	−0.730948	+	2.08893i
$357$	0.167038	−	0.0361450i	0.00884060	−	0.00191300i
$358$	−37.4502	+	23.5315i	−1.97931	+	1.24368i
$359$	−1.17168	−	3.34846i	−0.0618388	−	0.176725i	0.908819	−	0.417191i	$-0.136985\pi$
$359$	−1.17168	−	3.34846i	−0.0618388	−	0.176725i	−0.970658	+	0.240466i	$0.922700\pi$
$360$	1.40386	+	4.32291i	0.0739900	+	0.227838i
$361$	4.33046	−	8.99230i	0.227919	−	0.473279i
$362$	10.3255	−	1.16341i	0.542698	−	0.0611474i
$363$	−32.6267	−	4.04990i	−1.71246	−	0.212565i
$364$	−31.0695	−	14.9623i	−1.62848	−	0.784237i
$365$	−0.221133	−	0.221133i	−0.0115746	−	0.0115746i
$366$	3.84458	−	0.389250i	0.200959	−	0.0203464i
$367$	−7.25529	−	11.5467i	−0.378723	−	0.602734i	0.601916	−	0.798560i	$-0.294404\pi$
$367$	−7.25529	−	11.5467i	−0.378723	−	0.602734i	−0.980639	+	0.195825i	$0.937261\pi$
$368$	−3.56756	−	7.40812i	−0.185972	−	0.386175i
$369$	15.2384	+	15.9430i	0.793278	+	0.829960i
$370$	4.78558	−	1.09228i	0.248790	−	0.0567847i
$371$	−5.27529	−	4.20691i	−0.273880	−	0.218412i
$372$	9.63518	+	20.5998i	0.499561	+	1.06805i
$373$	−2.53676	+	11.1143i	−0.131349	+	0.575475i	0.865825	+	0.500346i	$0.166794\pi$
$373$	−2.53676	+	11.1143i	−0.131349	+	0.575475i	−0.997174	+	0.0751290i	$0.976063\pi$
$374$	0.355198	+	0.223186i	0.0183669	+	0.0115407i
$375$	−7.01240	−	2.54302i	−0.362119	−	0.131321i
$376$			3.13601i			0.161728i
$377$	−0.330152	+	17.7331i	−0.0170037	+	0.913300i
$378$	23.8004	−	27.8536i	1.22416	−	1.43263i
$379$	−33.0724	−	3.72636i	−1.69882	−	0.191410i	−0.791299	−	0.611429i	$-0.790595\pi$
$379$	−33.0724	−	3.72636i	−1.69882	−	0.191410i	−0.907516	+	0.420018i	$0.862024\pi$
$380$	−2.43790	+	3.87989i	−0.125062	+	0.199034i
$381$	1.98001	+	0.981231i	0.101439	+	0.0502700i
$382$	29.9866	−	23.9135i	1.53425	−	1.22352i
$383$	−23.8038	+	29.8490i	−1.21632	+	1.52521i	−0.435850	+	0.900019i	$0.643552\pi$
$383$	−23.8038	+	29.8490i	−1.21632	+	1.52521i	−0.780468	+	0.625196i	$0.785019\pi$
$384$	34.8109	+	0.393284i	1.77644	+	0.0200697i
$385$	−6.83917	−	2.39313i	−0.348556	−	0.121965i
$386$	−15.5244	+	7.47613i	−0.790169	+	0.380525i
$387$	13.8165	−	1.24136i	0.702333	−	0.0631016i
$388$	−47.8247	+	16.7346i	−2.42793	+	0.849570i
$389$	−8.49080	+	8.49080i	−0.430501	+	0.430501i	−0.888799	−	0.458298i	$-0.848459\pi$
$389$	−8.49080	+	8.49080i	−0.430501	+	0.430501i	0.458298	+	0.888799i	$0.348459\pi$
$390$	3.70594	−	4.54091i	0.187658	−	0.229938i
$391$	−0.0268328	−	0.238148i	−0.00135699	−	0.0120437i
$392$	−0.803845	−	7.13433i	−0.0406003	−	0.360338i
$393$	−6.60182	+	8.08923i	−0.333018	+	0.408048i
$394$	21.0789	−	21.0789i	1.06194	−	1.06194i
$395$	5.28950	−	1.85088i	0.266144	−	0.0931277i
$396$	56.8462	−	5.10740i	2.85663	−	0.256656i
$397$	17.5137	−	8.43416i	0.878988	−	0.423298i	0.0607332	−	0.998154i	$-0.480656\pi$
$397$	17.5137	−	8.43416i	0.878988	−	0.423298i	0.818255	+	0.574856i	$0.194942\pi$
$398$	−44.3089	−	15.5044i	−2.22101	−	0.777164i
$399$	15.6742	+	0.177083i	0.784690	+	0.00886521i
$400$	3.36711	−	4.22222i	0.168356	−	0.211111i
$401$	−1.61261	+	1.28602i	−0.0805301	+	0.0642206i	−0.662927	−	0.748684i	$-0.730686\pi$
$401$	−1.61261	+	1.28602i	−0.0805301	+	0.0642206i	0.582397	+	0.812904i	$0.302115\pi$
$402$	4.37125	+	2.16625i	0.218018	+	0.108043i
$403$	6.62160	−	10.5382i	0.329845	−	0.524946i
$404$	−12.6013	−	1.41982i	−0.626936	−	0.0706387i
$405$	2.32204	+	3.19809i	0.115383	+	0.158914i
$406$	−32.5204	+	19.5992i	−1.61396	+	0.972692i
$407$		−	26.1591i		−	1.29666i
$408$	−0.183947	−	0.0667077i	−0.00910673	−	0.00330252i
$409$	−18.3656	−	11.5399i	−0.908122	−	0.570611i	−0.00499680	−	0.999988i	$-0.501591\pi$
$409$	−18.3656	−	11.5399i	−0.908122	−	0.570611i	−0.903126	+	0.429376i	$0.858733\pi$
$410$	−1.68077	+	7.36392i	−0.0830072	+	0.363678i
$411$	−7.20970	−	15.4142i	−0.355628	−	0.760325i
$412$	−41.1237	−	32.7951i	−2.02602	−	1.61570i
$413$	34.7153	−	7.92354i	1.70823	−	0.389892i
$414$	−35.4979	−	37.1393i	−1.74462	−	1.82530i
$415$	1.74784	+	3.62943i	0.0857982	+	0.178162i
$416$	−7.48515	−	11.9125i	−0.366990	−	0.584061i
$417$	−4.47312	+	0.452886i	−0.219049	+	0.0221779i
$418$	27.2065	+	27.2065i	1.33071	+	1.33071i
$419$	17.8585	+	8.60022i	0.872447	+	0.420148i	0.815860	−	0.578250i	$-0.196264\pi$
$419$	17.8585	+	8.60022i	0.872447	+	0.420148i	0.0565867	+	0.998398i	$0.481978\pi$
$420$	7.90309	+	0.981000i	0.385631	+	0.0478679i
$421$	−3.14053	+	0.353853i	−0.153060	+	0.0172458i	−0.188162	−	0.982138i	$-0.560253\pi$
$421$	−3.14053	+	0.353853i	−0.153060	+	0.0172458i	0.0351018	+	0.999384i	$0.488824\pi$
$422$	0.319647	−	0.663755i	0.0155602	−	0.0323111i
$423$	0.842248	+	2.59354i	0.0409515	+	0.126102i
$424$	2.55143	+	7.29158i	0.123909	+	0.354110i
$425$	0.133278	−	0.0837440i	0.00646493	−	0.00406218i
$426$	−14.7627	+	3.19446i	−0.715253	+	0.154772i
$427$	0.949019	−	2.71214i	0.0459262	−	0.131250i
$428$	−2.21746	−	9.71532i	−0.107185	−	0.469608i
$429$	−19.1979	−	24.6393i	−0.926883	−	1.18960i
$430$	2.96223	+	3.71452i	0.142851	+	0.179130i
$431$	0.799505	+	0.182482i	0.0385108	+	0.00878984i	0.241733	−	0.970343i	$-0.422284\pi$
$431$	0.799505	+	0.182482i	0.0385108	+	0.00878984i	−0.203222	+	0.979133i	$0.565141\pi$
$432$	−5.57201	+	1.74017i	−0.268083	+	0.0837239i
$433$	−3.06207	+	27.1766i	−0.147153	+	1.30602i	0.675449	+	0.737406i	$0.263950\pi$
$433$	−3.06207	+	27.1766i	−0.147153	+	1.30602i	−0.822603	+	0.568617i	$0.807479\pi$
$434$	26.6443			1.27897
$435$	−1.23656	−	3.90481i	−0.0592887	−	0.187221i
$436$	16.6466			0.797226
$437$	2.46108	−	21.8427i	0.117729	−	1.04488i
$438$	2.06370	−	2.01759i	0.0986076	−	0.0964044i
$439$	27.9818	+	6.38665i	1.33550	+	0.304818i	0.829881	−	0.557941i	$-0.188408\pi$
$439$	27.9818	+	6.38665i	1.33550	+	0.304818i	0.505615	+	0.862759i	$0.331266\pi$
$440$	5.17230	+	6.48586i	0.246580	+	0.309201i
$441$	−2.58088	−	5.68432i	−0.122899	−	0.270682i
$442$	0.0561478	+	0.246000i	0.00267068	+	0.0117010i
$443$	0.618545	−	1.76770i	0.0293880	−	0.0839860i	−0.928255	−	0.371945i	$-0.878691\pi$
$443$	0.618545	−	1.76770i	0.0293880	−	0.0839860i	0.957643	+	0.287959i	$0.0929767\pi$
$444$	6.08066	+	28.1007i	0.288575	+	1.33360i
$445$	−4.46854	+	2.80777i	−0.211829	+	0.133101i
$446$	−1.22335	−	3.49612i	−0.0579271	−	0.165546i
$447$	−0.763331	+	0.467689i	−0.0361043	+	0.0221209i
$448$	16.0059	−	33.2366i	0.756207	−	1.57028i
$449$	−8.55720	+	0.964165i	−0.403839	+	0.0455017i	−0.311548	−	0.950230i	$-0.600848\pi$
$449$	−8.55720	+	0.964165i	−0.403839	+	0.0455017i	−0.0922909	+	0.995732i	$0.529419\pi$
$450$	11.8613	−	31.5896i	0.559149	−	1.48915i
$451$	36.2666	+	17.4651i	1.70773	+	0.822399i
$452$	−10.4835	−	10.4835i	−0.493105	−	0.493105i
$453$	−1.14657	−	11.3246i	−0.0538708	−	0.532076i
$454$	−3.12074	−	4.96663i	−0.146464	−	0.233095i
$455$	−1.89100	−	3.92670i	−0.0886514	−	0.184087i
$456$	−15.0870	−	9.71921i	−0.706512	−	0.455144i
$457$	5.30701	−	1.21129i	0.248251	−	0.0566617i	−0.0965844	−	0.995325i	$-0.530792\pi$
$457$	5.30701	−	1.21129i	0.248251	−	0.0566617i	0.344836	+	0.938663i	$0.387935\pi$
$458$	2.29889	+	1.83330i	0.107420	+	0.0856647i
$459$	−0.170043	−	0.00576527i	−0.00793694	−	0.000269100i
$460$	2.48497	−	10.8874i	0.115862	−	0.507627i
$461$	−16.4372	−	10.3282i	−0.765559	−	0.481033i	0.0917835	−	0.995779i	$-0.470743\pi$
$461$	−16.4372	−	10.3282i	−0.765559	−	0.481033i	−0.857343	+	0.514746i	$0.827886\pi$
$462$	22.7972	−	62.8634i	1.06062	−	2.92467i
$463$			35.4582i			1.64788i	0.566674	+	0.823942i	$0.308230\pi$
$463$			35.4582i			1.64788i	−0.566674	+	0.823942i	$0.691770\pi$
$464$	6.04871	+	0.112614i	0.280804	+	0.00522797i
$465$	−0.671185	+	2.79474i	−0.0311255	+	0.129603i
$466$	9.22320	+	1.03921i	0.427257	+	0.0481402i
$467$	−12.4655	+	19.8387i	−0.576832	+	0.918024i	0.423096	+	0.906085i	$0.360943\pi$
$467$	−12.4655	+	19.8387i	−0.576832	+	0.918024i	−0.999929	+	0.0119388i	$0.996200\pi$
$468$	26.3503	+	22.0057i	1.21804	+	1.01721i
$469$	2.83620	−	2.26179i	0.130963	−	0.104440i
$470$	−0.582290	+	0.730168i	−0.0268590	+	0.0336802i
$471$	−0.204908	+	18.1371i	−0.00944164	+	0.835711i
$472$	−38.4801	−	13.4648i	−1.77119	−	0.619766i
$473$	22.8118	−	10.9856i	1.04889	−	0.505118i
$474$	16.5287	+	49.0053i	0.759188	+	2.25089i
$475$	13.6268	−	4.76822i	0.625240	−	0.218781i
$476$	−0.242424	+	0.242424i	−0.0111115	+	0.0111115i
$477$	4.06840	+	5.34501i	0.186279	+	0.244731i
$478$	6.95772	+	61.7514i	0.318238	+	2.82444i
$479$	3.45845	+	30.6946i	0.158020	+	1.40247i	0.783093	+	0.621904i	$0.213641\pi$
$479$	3.45845	+	30.6946i	0.158020	+	1.40247i	−0.625073	+	0.780566i	$0.714931\pi$
$480$	2.51716	+	2.05431i	0.114892	+	0.0937661i
$481$	11.1260	−	11.1260i	0.507303	−	0.507303i
$482$	59.3073	−	20.7525i	2.70137	−	0.945252i
$483$	−36.1984	+	12.2091i	−1.64708	+	0.555535i
$484$	59.4211	−	28.6157i	2.70096	−	1.30071i
$485$	−6.04430	−	2.11499i	−0.274457	−	0.0960368i
$486$	−29.7545	+	21.0947i	−1.34969	+	0.956874i
$487$	−4.18824	+	5.25189i	−0.189787	+	0.237986i	−0.867617	−	0.497233i	$-0.834349\pi$
$487$	−4.18824	+	5.25189i	−0.189787	+	0.237986i	0.677830	+	0.735219i	$0.262921\pi$
$488$	−2.57203	+	2.05113i	−0.116430	+	0.0928502i
$489$	9.59734	−	19.3663i	0.434007	−	0.875776i
$490$	1.13753	−	1.81037i	0.0513883	−	0.0817840i
$491$	43.1411	+	4.86084i	1.94693	+	0.219366i	0.995952	−	0.0898873i	$-0.0286507\pi$
$491$	43.1411	+	4.86084i	1.94693	+	0.219366i	0.950980	+	0.309254i	$0.100079\pi$
$492$	−43.0183	−	10.3313i	−1.93941	−	0.465771i
$493$	0.165322	+	0.0613261i	0.00744573	+	0.00276199i
$494$			23.1431i			1.04126i
$495$	6.01951	+	3.97478i	0.270557	+	0.178653i
$496$	−3.59456	−	2.25861i	−0.161400	−	0.101415i
$497$	−2.49921	+	10.9497i	−0.112105	+	0.491163i
$498$	−33.6752	+	15.7510i	−1.50902	+	0.705817i
$499$	−29.6382	−	23.6356i	−1.32679	−	1.05808i	−0.993329	−	0.115311i	$-0.963213\pi$
$499$	−29.6382	−	23.6356i	−1.32679	−	1.05808i	−0.333457	−	0.942765i	$-0.608215\pi$
$500$	14.5884	−	3.32970i	0.652413	−	0.148909i
$501$	−14.8114	+	22.9916i	−0.661727	+	1.02719i
$502$	−8.88204	−	18.4437i	−0.396425	−	0.823184i
$503$	−16.9370	−	26.9552i	−0.755186	−	1.20187i	−0.974098	−	0.226127i	$-0.927394\pi$
$503$	−16.9370	−	26.9552i	−0.755186	−	1.20187i	0.218912	−	0.975745i	$-0.429749\pi$
$504$	−4.19157	+	30.9075i	−0.186707	+	1.37673i
$505$	−1.13327	−	1.13327i	−0.0504297	−	0.0504297i
$506$	−84.4833	−	40.6850i	−3.75574	−	1.80867i
$507$	−0.459303	+	3.70022i	−0.0203984	+	0.164333i
$508$	−4.40508	+	0.496333i	−0.195444	+	0.0220212i
$509$	−0.955091	+	1.98327i	−0.0423337	+	0.0879068i	−0.921063	−	0.389414i	$-0.872678\pi$
$509$	−0.955091	+	1.98327i	−0.0423337	+	0.0879068i	0.878729	+	0.477321i	$0.158392\pi$
$510$	−0.0304428	−	0.0496868i	−0.00134803	−	0.00220017i
$511$	−0.708798	−	2.02563i	−0.0313554	−	0.0896085i
$512$	−10.6270	+	6.67738i	−0.469651	+	0.295101i
$513$	−15.0875	−	3.98601i	−0.666130	−	0.175987i
$514$	−21.4912	+	61.4184i	−0.947937	+	2.70905i
$515$	−1.47926	−	6.48105i	−0.0651839	−	0.285589i
$516$	−21.9514	+	17.1036i	−0.966359	+	0.752944i
$517$	3.10313	+	3.89120i	0.136475	+	0.171135i
$518$	32.8403	+	7.49558i	1.44292	+	0.329337i
$519$	17.7183	+	18.1233i	0.777748	+	0.795523i
$520$	−0.558686	+	4.95848i	−0.0245000	+	0.217444i
$521$	−21.5793			−0.945408			−0.472704	−	0.881221i	$-0.656722\pi$
$521$	−21.5793			−0.945408			−0.472704	+	0.881221i	$0.656722\pi$
$522$	36.1631	−	11.0041i	1.58281	−	0.481637i
$523$	24.5657			1.07418			0.537091	−	0.843525i	$-0.319523\pi$
$523$	24.5657			1.07418			0.537091	+	0.843525i	$0.319523\pi$
$524$	2.34515	−	20.8138i	0.102448	−	0.909255i
$525$	−17.5403	−	17.9412i	−0.765523	−	0.783018i
$526$	−26.2679	−	5.99548i	−1.14534	−	0.261416i
$527$	−0.0771473	−	0.0967397i	−0.00336059	−	0.00421405i
$528$	−8.40442	+	6.54835i	−0.365755	+	0.284980i
$529$	6.80239	+	29.8032i	0.295756	+	1.29579i
$530$	−0.759830	+	2.17147i	−0.0330049	+	0.0943226i
$531$	−35.4400	−	0.800885i	−1.53796	−	0.0347555i
$532$	−26.6252	+	16.7297i	−1.15435	+	0.725325i
$533$	7.99671	+	22.8533i	0.346376	+	0.989886i
$534$	−25.4447	−	41.5291i	−1.10110	−	1.79714i
$535$	0.546451	−	1.13472i	0.0236251	−	0.0490581i
$536$	−4.12718	+	0.465021i	−0.178267	+	0.0200859i
$537$	4.03321	−	32.4921i	0.174046	−	1.40214i
$538$	−44.8981	−	21.6218i	−1.93569	−	0.932181i
$539$	−8.05693	−	8.05693i	−0.347037	−	0.347037i
$540$	−7.39025	−	2.87058i	−0.318026	−	0.123530i
$541$	5.56872	+	8.86256i	0.239418	+	0.381031i	0.944721	−	0.327874i	$-0.106332\pi$
$541$	5.56872	+	8.86256i	0.239418	+	0.381031i	−0.705304	+	0.708905i	$0.749189\pi$
$542$	0.376886	+	0.782612i	0.0161886	+	0.0336161i
$543$	−4.16570	+	6.46634i	−0.178767	+	0.277497i
$544$	−0.136365	+	0.0311243i	−0.00584659	+	0.00133444i
$545$	1.64487	+	1.31174i	0.0704584	+	0.0561887i
$546$	36.4334	−	17.0410i	1.55920	−	0.729290i
$547$	−4.66187	+	20.4250i	−0.199327	+	0.873310i	0.772011	+	0.635609i	$0.219251\pi$
$547$	−4.66187	+	20.4250i	−0.199327	+	0.873310i	−0.971338	+	0.237701i	$0.923606\pi$
$548$	28.9042	+	18.1617i	1.23473	+	0.775831i
$549$	−1.57624	+	2.38710i	−0.0672722	+	0.101879i
$550$		−	61.5872i		−	2.62609i
$551$	13.5314	+	8.85787i	0.576456	+	0.377358i
$552$	42.5283	+	10.2136i	1.81013	+	0.434721i
$553$	38.2146	+	4.30575i	1.62505	+	0.183099i
$554$	−19.2486	+	30.6340i	−0.817797	+	1.30152i
$555$	−1.61348	+	3.25582i	−0.0684886	+	0.138202i
$556$	7.05141	−	5.62331i	0.299047	−	0.238482i
$557$	9.21226	−	11.5518i	0.390336	−	0.489466i	−0.547373	−	0.836889i	$-0.684372\pi$
$557$	9.21226	−	11.5518i	0.390336	−	0.489466i	0.937708	+	0.347423i	$0.112943\pi$
$558$	−25.7203	−	6.48517i	−1.08883	−	0.274539i
$559$	14.3748	+	5.02996i	0.607989	+	0.212745i
$560$	−1.33939	+	0.645015i	−0.0565995	+	0.0272569i
$561$	−0.294252	+	0.0992464i	−0.0124233	+	0.00419019i
$562$	48.8352	−	17.0882i	2.05999	−	0.720822i
$563$	5.48563	−	5.48563i	0.231192	−	0.231192i	−0.581998	−	0.813190i	$-0.697729\pi$
$563$	5.48563	−	5.48563i	0.231192	−	0.231192i	0.813190	+	0.581998i	$0.197729\pi$
$564$	−4.23797	−	3.45871i	−0.178451	−	0.145638i
$565$	−0.209796	−	1.86199i	−0.00882618	−	0.0783345i
$566$	−2.30329	−	20.4422i	−0.0968144	−	0.859251i
$567$	4.83441	+	26.6868i	0.203026	+	1.12074i
$568$	9.09256	−	9.09256i	0.381515	−	0.381515i
$569$	8.49016	−	2.97084i	0.355926	−	0.124544i	−0.146392	−	0.989227i	$-0.546766\pi$
$569$	8.49016	−	2.97084i	0.355926	−	0.124544i	0.502318	+	0.864683i	$0.332481\pi$
$570$	−1.70810	−	5.06428i	−0.0715445	−	0.212119i
$571$	12.6597	−	6.09658i	0.529791	−	0.255134i	−0.149811	−	0.988715i	$-0.547867\pi$
$571$	12.6597	−	6.09658i	0.529791	−	0.255134i	0.679602	+	0.733581i	$0.262152\pi$
$572$	59.1432	+	20.6951i	2.47290	+	0.865306i
$573$	−0.320748	+	28.3905i	−0.0133994	+	1.18603i
$574$	−32.3176	+	40.5250i	−1.34891	+	1.69148i
$575$	−27.5082	+	21.9370i	−1.14717	+	0.914837i
$576$	−23.5405	+	28.1881i	−0.980856	+	1.17451i
$577$	−13.8214	+	21.9966i	−0.575393	+	0.915732i	0.424554	+	0.905403i	$0.360431\pi$
$577$	−13.8214	+	21.9966i	−0.575393	+	0.915732i	−0.999947	+	0.0103298i	$0.996712\pi$
$578$	−39.5236	−	4.45324i	−1.64396	−	0.185230i
$579$	2.97862	−	12.4026i	0.123787	−	0.515435i
$580$	6.32750	+	5.24164i	0.262735	+	0.217647i
$581$			27.6440i			1.14687i
$582$	20.1476	−	55.5572i	0.835146	−	2.30292i
$583$	10.3810	+	6.52279i	0.429936	+	0.270146i
$584$	−0.546741	+	2.39543i	−0.0226243	+	0.0991235i
$585$	0.869669	+	4.25079i	0.0359564	+	0.175749i
$586$	10.3736	+	8.27268i	0.428530	+	0.341741i
$587$	29.2515	−	6.67645i	1.20734	−	0.275567i	0.428936	−	0.903335i	$-0.358888\pi$
$587$	29.2515	−	6.67645i	1.20734	−	0.275567i	0.778401	+	0.627768i	$0.216031\pi$
$588$	10.5278	+	6.78214i	0.434159	+	0.279691i
$589$	−4.92407	−	10.2249i	−0.202893	−	0.421311i
$590$	−6.45933	−	10.2800i	−0.265927	−	0.423220i
$591$	2.22286	+	21.9550i	0.0914364	+	0.903109i
$592$	−3.79506	−	3.79506i	−0.155976	−	0.155976i
$593$	−24.2579	−	11.6820i	−0.996151	−	0.479721i	−0.136521	−	0.990637i	$-0.543592\pi$
$593$	−24.2579	−	11.6820i	−0.996151	−	0.479721i	−0.859631	+	0.510916i	$0.829306\pi$
$594$	−37.3074	+	55.1346i	−1.53074	+	2.26220i
$595$	−0.0430571	+	0.00485138i	−0.00176517	+	0.000198887i
$596$	0.779181	−	1.61799i	0.0319165	−	0.0662753i
$597$	29.6310	−	18.1547i	1.21271	−	0.743024i
$598$	−18.6284	−	53.2369i	−0.761771	−	2.17702i
$599$	33.5637	−	21.0895i	1.37138	−	0.861693i	0.373551	−	0.927610i	$-0.378140\pi$
$599$	33.5637	−	21.0895i	1.37138	−	0.861693i	0.997825	+	0.0659169i	$0.0209972\pi$
$600$	6.07548	+	28.0768i	0.248030	+	1.14623i
$601$	5.61878	−	16.0576i	0.229195	−	0.655002i	−0.770648	−	0.637261i	$-0.780067\pi$
$601$	5.61878	−	16.0576i	0.229195	−	0.655002i	0.999843	−	0.0177401i	$-0.00564714\pi$
$602$	7.25493	+	31.7859i	0.295689	+	1.29550i
$603$	−3.28836	+	1.49303i	−0.133912	+	0.0608009i
$604$	14.2366	+	17.8521i	0.579278	+	0.726392i
$605$	8.12638	+	1.85479i	0.330384	+	0.0754081i
$606$	10.5761	−	10.3398i	0.429625	−	0.420026i
$607$	3.41182	−	30.2808i	0.138482	−	1.22906i	−0.711668	−	0.702516i	$-0.752060\pi$
$607$	3.41182	−	30.2808i	0.138482	−	1.22906i	0.850149	−	0.526542i	$-0.176512\pi$
$608$	−12.8289			−0.520280
$609$	3.98102	−	27.8243i	0.161319	−	1.12750i
$610$	−0.979705			−0.0396671
$611$	−0.335184	+	2.97484i	−0.0135601	+	0.120349i
$612$	0.293023	−	0.175012i	0.0118448	−	0.00707443i
$613$	26.7287	+	6.10065i	1.07956	+	0.246403i	0.725083	−	0.688662i	$-0.241801\pi$
$613$	26.7287	+	6.10065i	1.07956	+	0.246403i	0.354478	+	0.935064i	$0.384659\pi$
$614$	14.6551	+	18.3769i	0.591432	+	0.741632i
$615$	−3.43659	−	4.41066i	−0.138577	−	0.177855i
$616$	12.6677	+	55.5008i	0.510396	+	2.23619i
$617$	−2.90792	+	8.31035i	−0.117068	+	0.334562i	−0.987476	−	0.157770i	$-0.949570\pi$
$617$	−2.90792	+	8.31035i	−0.117068	+	0.334562i	0.870408	+	0.492332i	$0.163855\pi$
$618$	59.9623	−	12.9751i	2.41204	−	0.521936i
$619$	19.7277	−	12.3958i	0.792925	−	0.498228i	−0.0736445	−	0.997285i	$-0.523463\pi$
$619$	19.7277	−	12.3958i	0.792925	−	0.498228i	0.866569	+	0.499057i	$0.166320\pi$
$620$	−1.90431	−	5.44220i	−0.0764788	−	0.218564i
$621$	37.9148	−	2.97511i	1.52147	−	0.119387i
$622$	16.7178	−	34.7150i	0.670325	−	1.39194i
$623$	−35.9880	+	4.05487i	−1.44183	+	0.162455i
$624$	−6.35975	−	0.789427i	−0.254594	−	0.0316024i
$625$	−19.9517	−	9.60821i	−0.798066	−	0.384328i
$626$	−24.6331	−	24.6331i	−0.984535	−	0.984535i
$627$	−28.3374	+	2.86906i	−1.13169	+	0.114579i
$628$	−19.3585	−	30.8088i	−0.772486	−	1.22940i
$629$	−0.0678727	−	0.140939i	−0.00270626	−	0.00561961i
$630$	−6.71479	+	6.41801i	−0.267524	+	0.255700i
$631$	−38.4622	+	8.77874i	−1.53115	+	0.349476i	−0.903353	−	0.428897i	$-0.858902\pi$
$631$	−38.4622	+	8.77874i	−1.53115	+	0.349476i	−0.627801	+	0.778374i	$0.716045\pi$
$632$	−34.4232	−	27.4516i	−1.36928	−	1.09197i
$633$	0.231057	+	0.493995i	0.00918371	+	0.0196345i
$634$	−2.00580	+	8.78798i	−0.0796605	+	0.349015i
$635$	−0.474382	−	0.298074i	−0.0188253	−	0.0118287i
$636$	−12.6677	−	4.59390i	−0.502308	−	0.182160i
$637$		−	6.85359i		−	0.271549i
$638$	54.7317	−	42.0045i	2.16685	−	1.66297i
$639$	5.07769	−	9.96172i	0.200870	−	0.394079i
$640$	−8.77072	−	0.988223i	−0.346693	−	0.0390630i
$641$	16.3275	−	25.9851i	0.644898	−	1.02635i	−0.351045	−	0.936359i	$-0.614173\pi$
$641$	16.3275	−	25.9851i	0.644898	−	1.02635i	0.995943	−	0.0899905i	$-0.0286837\pi$
$642$	10.4144	+	5.16104i	0.411023	+	0.203690i
$643$	−30.1761	+	24.0647i	−1.19003	+	0.949018i	−0.999467	−	0.0326565i	$-0.989603\pi$
$643$	−30.1761	+	24.0647i	−1.19003	+	0.949018i	−0.190564	+	0.981675i	$0.561032\pi$
$644$	47.7807	−	59.9151i	1.88282	−	2.36099i
$645$	−3.51680	−	0.0397319i	−0.138474	−	0.00156444i
$646$	0.217173	+	0.0759921i	0.00854456	+	0.00298987i
$647$	−13.7236	+	6.60892i	−0.539529	+	0.259824i	−0.683743	−	0.729723i	$-0.739649\pi$
$647$	−13.7236	+	6.60892i	−0.539529	+	0.259824i	0.144214	+	0.989547i	$0.453935\pi$
$648$	11.5690	−	28.8154i	0.454475	−	1.13198i
$649$	−61.0701	+	21.3694i	−2.39721	+	0.838821i
$650$	26.1944	−	26.1944i	1.02743	−	1.02743i
$651$	−12.4710	+	15.2808i	−0.488777	+	0.598900i
$652$	4.85460	+	43.0857i	0.190121	+	1.68737i
$653$	−3.35625	−	29.7875i	−0.131340	−	1.16568i	−0.870508	−	0.492154i	$-0.836210\pi$
$653$	−3.35625	−	29.7875i	−0.131340	−	1.16568i	0.739168	−	0.673521i	$-0.235219\pi$
$654$	−12.2764	+	15.0423i	−0.480046	+	0.588202i
$655$	1.87184	−	1.87184i	0.0731389	−	0.0731389i
$656$	7.79520	−	2.72766i	0.304352	−	0.106497i
$657$	0.191183	+	2.12790i	0.00745876	+	0.0830173i
$658$	−5.77421	+	2.78071i	−0.225102	+	0.108403i
$659$	−13.2115	−	4.62291i	−0.514648	−	0.180083i	0.0604446	−	0.998172i	$-0.480748\pi$
$659$	−13.2115	−	4.62291i	−0.514648	−	0.180083i	−0.575092	+	0.818089i	$0.695034\pi$
$660$	−14.4694	−	0.163472i	−0.563222	−	0.00636313i
$661$	21.4778	−	26.9323i	0.835390	−	1.04755i	−0.162755	−	0.986667i	$-0.552038\pi$
$661$	21.4778	−	26.9323i	0.835390	−	1.04755i	0.998145	−	0.0608797i	$-0.0193906\pi$
$662$	−45.2843	+	36.1130i	−1.76002	+	1.40357i
$663$	−0.167364	−	0.0829401i	−0.00649986	−	0.00322113i
$664$	16.8387	−	26.7987i	0.653469	−	1.03999i
$665$	−3.94916	−	0.444963i	−0.153142	−	0.0172549i
$666$	−29.8770	−	15.2289i	−1.15771	−	0.590108i
$667$	−38.2566	−	9.48437i	−1.48130	−	0.367236i
$668$		−	54.8639i		−	2.12275i
$669$	2.57765	+	0.934777i	0.0996579	+	0.0361406i
$670$	−1.04729	−	0.658055i	−0.0404603	−	0.0254229i
$671$	−1.16179	+	5.09012i	−0.0448503	+	0.196502i
$672$	9.44634	+	20.1961i	0.364401	+	0.779080i
$673$	−26.5470	−	21.1705i	−1.02331	−	0.816063i	−0.0402210	−	0.999191i	$-0.512806\pi$
$673$	−26.5470	−	21.1705i	−1.02331	−	0.816063i	−0.983089	+	0.183128i	$0.941378\pi$
$674$	46.1074	−	10.5237i	1.77599	−	0.405358i
$675$	12.5652	+	21.5883i	0.483635	+	0.830934i
$676$	−3.24534	−	6.73901i	−0.124821	−	0.259193i
$677$	6.54574	+	10.4175i	0.251573	+	0.400377i	0.948506	−	0.316760i	$-0.102595\pi$
$677$	6.54574	+	10.4175i	0.251573	+	0.400377i	−0.696932	+	0.717137i	$0.745452\pi$
$678$	17.2046	−	1.74190i	0.660739	−	0.0668974i
$679$	−31.0732	−	31.0732i	−1.19248	−	1.19248i
$680$	0.0446955	+	0.0215242i	0.00171399	+	0.000825416i
$681$	4.30909	+	0.534882i	0.165125	+	0.0204967i
$682$	−48.1090	+	5.42059i	−1.84219	+	0.207565i
$683$	18.6365	−	38.6990i	0.713105	−	1.48078i	−0.156837	−	0.987624i	$-0.550130\pi$
$683$	18.6365	−	38.6990i	0.713105	−	1.48078i	0.869942	−	0.493153i	$-0.164156\pi$
$684$	29.7738	−	9.66902i	1.13843	−	0.369704i
$685$	1.42493	+	4.07222i	0.0544439	+	0.155592i
$686$	−29.3673	+	18.4527i	−1.12125	+	0.704528i
$687$	−2.12743	+	0.460349i	−0.0811664	+	0.0175634i
$688$	1.71571	−	4.90321i	0.0654107	−	0.186933i
$689$	1.64097	+	7.18954i	0.0625158	+	0.273900i
$690$	8.00556	+	10.2747i	0.304767	+	0.391150i
$691$	0.803687	+	1.00779i	0.0305737	+	0.0383382i	0.796883	−	0.604133i	$-0.206481\pi$
$691$	0.803687	+	1.00779i	0.0305737	+	0.0383382i	−0.766310	+	0.642471i	$0.777909\pi$
$692$	−49.5691	−	11.3138i	−1.88433	−	0.430087i
$693$	25.3824	+	42.4980i	0.964199	+	1.61436i
$694$	−1.47681	+	13.1071i	−0.0560590	+	0.497537i
$695$	1.13987			0.0432378
$696$	−20.8078	+	24.5485i	−0.788718	+	0.930507i
$697$	0.240712			0.00911760
$698$	−6.71399	+	59.5883i	−0.254128	+	2.25545i
$699$	−4.91296	+	4.80319i	−0.185825	+	0.181673i
$700$	49.0711	+	11.2002i	1.85471	+	0.423326i
$701$	13.9080	+	17.4401i	0.525297	+	0.658702i	0.971724	−	0.236118i	$-0.0758752\pi$
$701$	13.9080	+	17.4401i	0.525297	+	0.658702i	−0.446427	+	0.894820i	$0.647304\pi$
$702$	−39.3177	+	7.58227i	−1.48395	+	0.286174i
$703$	−3.19266	−	13.9879i	−0.120413	−	0.527565i
$704$	−22.1386	+	63.2684i	−0.834378	+	2.38452i
$705$	−0.146215	−	0.675709i	−0.00550678	−	0.0254487i
$706$	11.8478	−	7.44445i	0.445897	−	0.280176i
$707$	−3.63246	−	10.3810i	−0.136613	−	0.390416i
$708$	60.6358	−	37.1512i	2.27883	−	1.39623i
$709$	−20.2076	+	41.9615i	−0.758913	+	1.57590i	0.0574424	+	0.998349i	$0.481705\pi$
$709$	−20.2076	+	41.9615i	−0.758913	+	1.57590i	−0.816355	+	0.577550i	$0.804009\pi$
$710$	3.80534	−	0.428759i	0.142812	−	0.0160910i
$711$	−35.8414	−	13.4578i	−1.34416	−	0.504707i
$712$	37.3573	+	17.9903i	1.40003	+	0.674217i
$713$	19.5573	+	19.5573i	0.732427	+	0.732427i
$714$	−0.0402802	−	0.397844i	−0.00150745	−	0.0148889i
$715$	4.21326	+	6.70536i	0.157567	+	0.250766i
$716$	28.4977	+	59.1761i	1.06501	+	2.21152i
$717$	−38.6717	−	24.9128i	−1.44422	−	0.930385i
$718$	−8.09234	+	1.84702i	−0.302003	+	0.0689303i
$719$	21.3823	+	17.0518i	0.797426	+	0.635926i	0.935033	−	0.354561i	$-0.115370\pi$
$719$	21.3823	+	17.0518i	0.797426	+	0.635926i	−0.137607	+	0.990487i	$0.543941\pi$
$720$	1.44994	−	0.296642i	0.0540359	−	0.0110552i
$721$	10.1512	−	44.4752i	0.378050	−	1.65634i
$722$	−19.7732	−	12.4243i	−0.735883	−	0.462386i
$723$	−15.8573	+	43.7267i	−0.589740	+	1.62621i
$724$		−	15.4304i		−	0.573466i
$725$	−5.28968	−	25.3412i	−0.196454	−	0.941148i
$726$	−17.9636	+	74.7981i	−0.666690	+	2.77602i
$727$	0.528397	+	0.0595361i	0.0195972	+	0.00220807i	0.121758	−	0.992560i	$-0.461147\pi$
$727$	0.528397	+	0.0595361i	0.0195972	+	0.00220807i	−0.102160	+	0.994768i	$0.532576\pi$
$728$	−18.2179	+	28.9936i	−0.675200	+	1.07457i
$729$	1.82875	−	26.9380i	0.0677316	−	0.997704i
$730$	−0.572079	+	0.456218i	−0.0211736	+	0.0168854i
$731$	0.0944016	−	0.118376i	0.00349157	−	0.00437829i
$732$	0.0648264	−	5.73800i	0.00239605	−	0.212083i
$733$	−14.8831	−	5.20781i	−0.549719	−	0.192355i	0.0411060	−	0.999155i	$-0.486912\pi$
$733$	−14.8831	−	5.20781i	−0.549719	−	0.192355i	−0.590825	+	0.806800i	$0.701198\pi$
$734$	−28.7476	+	13.8441i	−1.06109	+	0.510995i
$735$	0.505837	+	1.49974i	0.0186581	+	0.0553186i
$736$	29.5107	−	10.3263i	1.08778	−	0.380631i
$737$	−4.66090	+	4.66090i	−0.171687	+	0.171687i
$738$	41.0606	−	31.2536i	1.51146	−	1.15046i
$739$	2.59893	+	23.0661i	0.0956031	+	0.848501i	0.946398	+	0.323003i	$0.104692\pi$
$739$	2.59893	+	23.0661i	0.0956031	+	0.848501i	−0.850795	+	0.525498i	$0.823879\pi$
$740$	−0.816143	−	7.24347i	−0.0300020	−	0.266275i
$741$	−13.2728	−	10.8322i	−0.487588	−	0.397933i
$742$	−11.1633	+	11.1633i	−0.409818	+	0.409818i
$743$	−3.51766	+	1.23088i	−0.129051	+	0.0451567i	−0.394032	−	0.919097i	$-0.628920\pi$
$743$	−3.51766	+	1.23088i	−0.129051	+	0.0451567i	0.264981	+	0.964254i	$0.414634\pi$
$744$	21.3975	−	7.21705i	0.784472	−	0.264590i
$745$	0.204488	−	0.0984763i	0.00749187	−	0.00360789i
$746$	25.1768	+	8.80976i	0.921790	+	0.322548i
$747$	6.72851	−	26.6854i	0.246183	−	0.976367i
$748$	0.388403	−	0.487042i	0.0142014	−	0.0178080i
$749$	6.75715	−	5.38865i	0.246901	−	0.196897i
$750$	−7.74975	+	15.6381i	−0.282981	+	0.571022i
$751$	25.3354	−	40.3211i	0.924503	−	1.47134i	0.0430467	−	0.999073i	$-0.486294\pi$
$751$	25.3354	−	40.3211i	0.924503	−	1.47134i	0.881456	−	0.472265i	$-0.156564\pi$
$752$	1.01471	+	0.114331i	0.0370027	+	0.00416921i
$753$	14.7350	+	3.53875i	0.536972	+	0.128959i
$754$	41.1441	+	5.41319i	1.49838	+	0.197137i
$755$			2.88582i			0.105026i
$756$	−37.1451	−	39.7523i	−1.35095	−	1.44578i
$757$	−13.6198	−	8.55790i	−0.495021	−	0.311042i	0.261283	−	0.965262i	$-0.415854\pi$
$757$	−13.6198	−	8.55790i	−0.495021	−	0.311042i	−0.756304	+	0.654220i	$0.772997\pi$
$758$	−17.3281	+	75.9193i	−0.629384	+	2.75751i
$759$	62.8761	−	29.4092i	2.28226	−	1.06749i
$760$	3.55735	+	2.83689i	0.129039	+	0.102905i
$761$	17.5787	−	4.01223i	0.637228	−	0.145443i	0.108311	−	0.994117i	$-0.465456\pi$
$761$	17.5787	−	4.01223i	0.637228	−	0.145443i	0.528916	+	0.848674i	$0.322598\pi$
$762$	2.80013	−	4.34660i	0.101438	−	0.157461i
$763$	6.26418	+	13.0077i	0.226778	+	0.470910i
$764$	−30.3024	−	48.2259i	−1.09630	−	1.74475i
$765$	0.0427448	+	0.00579690i	0.00154544	+	0.000209587i
$766$	63.1650	+	63.1650i	2.28224	+	2.28224i
$767$	−35.0633	−	16.8856i	−1.26606	−	0.609704i
$768$	4.81012	−	38.7511i	0.173570	−	1.39831i
$769$	40.1591	−	4.52484i	1.44817	−	0.163170i	0.647407	−	0.762145i	$-0.275854\pi$
$769$	40.1591	−	4.52484i	1.44817	−	0.163170i	0.800768	+	0.598975i	$0.204425\pi$
$770$	−7.35584	+	15.2746i	−0.265086	+	0.550457i
$771$	−25.1650	−	41.0726i	−0.906294	−	1.47919i
$772$	8.45102	+	24.1516i	0.304159	+	0.869237i
$773$	0.0187725	−	0.0117955i	0.000675200	−	0.000424256i	−0.531694	−	0.846936i	$-0.678445\pi$
$773$	0.0187725	−	0.0117955i	0.000675200	−	0.000424256i	0.532370	+	0.846512i	$0.321302\pi$
$774$	0.733304	−	32.4495i	0.0263581	−	1.16637i
$775$	−5.99977	+	17.1464i	−0.215518	+	0.615915i
$776$	11.1954	+	49.0504i	0.401892	+	1.76081i
$777$	−19.6699	+	15.3259i	−0.705653	+	0.549813i
$778$	17.5173	+	21.9660i	0.628026	+	0.787519i
$779$	21.5243	+	4.91278i	0.771188	+	0.176019i
$780$	−6.08465	−	6.22370i	−0.217865	−	0.222844i
$781$	2.28493	−	20.2794i	0.0817614	−	0.725652i
$782$	−0.560739			−0.0200520
$783$	−10.6154	+	25.8904i	−0.379362	+	0.925248i
$784$	−2.33774			−0.0834908
$785$	0.514881	−	4.56969i	0.0183769	−	0.163099i
$786$	17.0785	+	17.4688i	0.609170	+	0.623092i
$787$	16.6425	+	3.79854i	0.593241	+	0.135403i	0.508592	−	0.861008i	$-0.330166\pi$
$787$	16.6425	+	3.79854i	0.593241	+	0.135403i	0.0846485	+	0.996411i	$0.473023\pi$
$788$	−27.6004	−	34.6099i	−0.983225	−	1.23293i
$789$	15.7333	−	12.2587i	0.560121	−	0.436422i
$790$	−2.91771	−	12.7833i	−0.103807	−	0.454809i
$791$	4.24689	−	12.1369i	0.151002	−	0.431539i
$792$	1.28041	−	56.6594i	0.0454974	−	2.01331i
$793$	−2.65908	+	1.67081i	−0.0944266	+	0.0593322i
$794$	−15.0219	−	42.9300i	−0.533106	−	1.52353i
$795$	−0.889717	−	1.45214i	−0.0315550	−	0.0515020i
$796$	−30.2462	+	62.8069i	−1.07205	+	2.22613i
$797$	−42.3347	+	4.76997i	−1.49957	+	0.168961i	−0.823264	−	0.567659i	$-0.807849\pi$
$797$	−42.3347	+	4.76997i	−1.49957	+	0.168961i	−0.676307	+	0.736620i	$0.736421\pi$
$798$	4.51792	−	36.3971i	0.159933	−	1.28844i
$799$	0.0268151	+	0.0129135i	0.000948651	+	0.000456846i
$800$	14.5203	+	14.5203i	0.513371	+	0.513371i
$801$	35.7269	+	4.84516i	1.26235	+	0.171195i
$802$	2.56761	+	4.08633i	0.0906655	+	0.144293i
$803$	1.69191	+	3.51328i	0.0597061	+	0.123981i
$804$	3.92344	−	6.09029i	0.138369	−	0.214788i
$805$	9.44255	−	2.15520i	0.332806	−	0.0759609i
$806$	−22.7673	−	18.1564i	−0.801946	−	0.639530i
$807$	33.4151	−	15.6293i	1.17627	−	0.550178i
$808$	−2.80195	+	12.2761i	−0.0985721	+	0.431873i
$809$	−9.81805	−	6.16909i	−0.345184	−	0.216894i	0.348270	−	0.937394i	$-0.386769\pi$
$809$	−9.81805	−	6.16909i	−0.345184	−	0.216894i	−0.693454	+	0.720501i	$0.743912\pi$
$810$	8.04406	−	4.56107i	0.282640	−	0.160260i
$811$			9.33485i			0.327791i	0.986478	+	0.163895i	$0.0524059\pi$
$811$			9.33485i			0.327791i	−0.986478	+	0.163895i	$0.947594\pi$
$812$	23.5146	+	51.2477i	0.825202	+	1.79844i
$813$	−0.625239	−	0.150158i	−0.0219281	−	0.00526626i
$814$	−60.8215	−	6.85294i	−2.13179	−	0.240195i
$815$	−2.91544	+	4.63990i	−0.102123	+	0.162528i
$816$	−0.0282907	+	0.0570873i	−0.000990372	+	0.00199846i
$817$	10.8573	−	8.65842i	0.379849	−	0.302920i
$818$	−31.6423	+	39.6782i	−1.10635	+	1.38731i
$819$	−7.27962	+	28.8711i	−0.254370	+	1.00884i
$820$	10.5872	+	3.70461i	0.369720	+	0.129371i
$821$	−14.9365	+	7.19302i	−0.521286	+	0.251038i	−0.675974	−	0.736925i	$-0.736277\pi$
$821$	−14.9365	+	7.19302i	−0.521286	+	0.251038i	0.154688	+	0.987963i	$0.450563\pi$
$822$	−37.7277	+	12.7249i	−1.31590	+	0.443833i
$823$	−1.57323	+	0.550496i	−0.0548393	+	0.0191891i	−0.357559	−	0.933890i	$-0.616391\pi$
$823$	−1.57323	+	0.550496i	−0.0548393	+	0.0191891i	0.302720	+	0.953080i	$0.402105\pi$
$824$	−36.9318	+	36.9318i	−1.28658	+	1.28658i
$825$	35.3209	+	28.8262i	1.22972	+	1.00360i
$826$	−9.32831	−	82.7910i	−0.324573	−	2.88067i
$827$	4.27712	+	37.9605i	0.148730	+	1.32002i	0.817234	+	0.576307i	$0.195507\pi$
$827$	4.27712	+	37.9605i	0.148730	+	1.32002i	−0.668504	+	0.743709i	$0.733065\pi$
$828$	−60.7070	+	46.2076i	−2.10971	+	1.60583i
$829$	−21.5163	+	21.5163i	−0.747292	+	0.747292i	−0.973970	−	0.226678i	$-0.927214\pi$
$829$	−21.5163	+	21.5163i	−0.747292	+	0.747292i	0.226678	+	0.973970i	$0.427214\pi$
$830$	8.89655	−	3.11304i	0.308804	−	0.108055i
$831$	−8.55950	−	25.3777i	−0.296926	−	0.880344i
$832$	−36.3255	+	17.4934i	−1.25936	+	0.606475i
$833$	−0.0643136	−	0.0225043i	−0.00222833	−	0.000779728i
$834$	−0.118840	+	10.5189i	−0.00411509	+	0.364241i
$835$	4.32324	−	5.42117i	0.149612	−	0.187607i
$836$	44.6710	−	35.6239i	1.54498	−	1.23208i
$837$	15.7578	−	11.7154i	0.544671	−	0.404944i
$838$	24.6745	−	39.2692i	0.852366	−	1.35653i
$839$	10.3292	+	1.16382i	0.356603	+	0.0401795i	0.288449	−	0.957495i	$-0.406861\pi$
$839$	10.3292	+	1.16382i	0.356603	+	0.0401795i	0.0681540	+	0.997675i	$0.478289\pi$
$840$	1.84662	−	7.68912i	0.0637145	−	0.265300i
$841$	18.9126	−	21.9844i	0.652160	−	0.758082i
$842$			7.39464i			0.254836i
$843$	−13.0574	+	36.0057i	−0.449719	+	1.24010i
$844$	−0.926327	−	0.582050i	−0.0318855	−	0.0200350i
$845$	0.210354	−	0.921621i	0.00723639	−	0.0317047i
$846$	6.25079	−	1.27885i	0.214906	−	0.0439677i
$847$	44.7209	+	35.6637i	1.53663	+	1.22542i
$848$	2.45234	−	0.559730i	0.0842136	−	0.0192212i
$849$	12.8019	+	8.24714i	0.439360	+	0.283041i
$850$	−0.159795	−	0.331818i	−0.00548093	−	0.0113813i
$851$	18.6034	+	29.6071i	0.637716	+	1.01492i
$852$	2.25939	+	22.3157i	0.0774053	+	0.764525i
$853$	4.02890	+	4.02890i	0.137947	+	0.137947i	0.772708	−	0.634761i	$-0.218902\pi$
$853$	4.02890	+	4.02890i	0.137947	+	0.137947i	−0.634761	+	0.772708i	$0.718902\pi$
$854$	−6.05728	−	2.91703i	−0.207276	−	0.0998188i
$855$	3.70390	+	1.39075i	0.126671	+	0.0475627i
$856$	−9.83288	+	1.10790i	−0.336081	+	0.0378672i
$857$	23.5051	−	48.8088i	0.802918	−	1.66728i	0.0597098	−	0.998216i	$-0.480982\pi$
$857$	23.5051	−	48.8088i	0.802918	−	1.66728i	0.743208	−	0.669060i	$-0.233303\pi$
$858$	−62.3174	+	38.1815i	−2.12748	+	1.30349i
$859$	9.78133	+	27.9534i	0.333735	+	0.953759i	0.981423	+	0.191854i	$0.0614500\pi$
$859$	9.78133	+	27.9534i	0.333735	+	0.953759i	−0.647689	+	0.761905i	$0.724264\pi$
$860$	5.97388	−	3.75363i	0.203707	−	0.127998i
$861$	−8.11506	−	37.5024i	−0.276561	−	1.27808i
$862$	0.633730	−	1.81110i	0.0215849	−	0.0616862i
$863$	−8.13915	−	35.6599i	−0.277060	−	1.21388i	−0.901491	−	0.432798i	$-0.857526\pi$
$863$	−8.13915	−	35.6599i	−0.277060	−	1.21388i	0.624431	−	0.781080i	$-0.285331\pi$
$864$	−4.20307	−	21.7949i	−0.142991	−	0.741478i
$865$	−4.00646	−	5.02395i	−0.136224	−	0.170819i
$866$	62.3851	+	14.2390i	2.11993	+	0.483861i
$867$	21.0532	−	20.5828i	0.715005	−	0.699029i
$868$	4.43005	−	39.3178i	0.150366	−	1.33453i
$869$	−69.8765			−2.37040
$870$	−9.40287	+	1.85214i	−0.318787	+	0.0627935i
$871$	−3.96477			−0.134341
$872$	1.85072	−	16.4256i	0.0626733	−	0.556241i
$873$	22.4324	+	37.5587i	0.759222	+	1.27117i
$874$	−50.1410	−	11.4443i	−1.69604	−	0.387111i
$875$	8.09153	+	10.1465i	0.273544	+	0.343013i
$876$	−2.63415	−	3.38078i	−0.0889997	−	0.114226i
$877$	2.01156	+	8.81320i	0.0679254	+	0.297601i	0.997468	−	0.0711135i	$-0.0226552\pi$
$877$	2.01156	+	8.81320i	0.0679254	+	0.297601i	−0.929543	+	0.368714i	$0.879798\pi$
$878$	22.1798	−	63.3862i	0.748532	−	2.13918i
$879$	−9.59989	+	2.07730i	−0.323796	+	0.0700655i
$880$	2.28718	−	1.43713i	0.0771009	−	0.0484457i
$881$	8.33265	+	23.8133i	0.280734	+	0.802292i	0.994766	+	0.102179i	$0.0325814\pi$
$881$	8.33265	+	23.8133i	0.280734	+	0.802292i	−0.714032	+	0.700113i	$0.753133\pi$
$882$	−13.8925	+	4.51158i	−0.467786	+	0.151913i
$883$	5.95756	−	12.3710i	0.200488	−	0.416317i	−0.776349	−	0.630303i	$-0.782930\pi$
$883$	5.95756	−	12.3710i	0.200488	−	0.416317i	0.976837	+	0.213986i	$0.0686448\pi$
$884$	0.372346	−	0.0419533i	0.0125234	−	0.00141104i
$885$	8.91900	+	1.10710i	0.299809	+	0.0372149i
$886$	−3.94797	−	1.90124i	−0.132635	−	0.0638736i
$887$	5.34488	+	5.34488i	0.179464	+	0.179464i	0.791122	−	0.611658i	$-0.209497\pi$
$887$	5.34488	+	5.34488i	0.179464	+	0.179464i	−0.611658	+	0.791122i	$0.709497\pi$
$888$	28.4037	−	2.87577i	0.953167	−	0.0965047i
$889$	−2.04549	−	3.25538i	−0.0686035	−	0.109182i
$890$	5.35762	+	11.1252i	0.179588	+	0.372918i
$891$	−14.1583	−	47.2022i	−0.474320	−	1.58133i
$892$	−5.36247	+	1.22395i	−0.179549	+	0.0409809i
$893$	2.13424	+	1.70200i	0.0714195	+	0.0569552i
$894$	0.887435	+	1.89732i	0.0296803	+	0.0634557i
$895$	−1.84715	+	8.09288i	−0.0617433	+	0.270515i
$896$	−51.2849	−	32.2244i	−1.71331	−	1.07654i
$897$	39.2510	+	14.2342i	1.31055	+	0.475267i
$898$			20.1486i			0.672368i
$899$	−19.3298	+	6.36245i	−0.644684	+	0.212200i
$900$	−44.6433	−	22.7556i	−1.48811	−	0.758519i
$901$	0.0728544	+	0.00820872i	0.00242713	+	0.000273472i
$902$	50.1083	−	79.7469i	1.66842	−	2.65528i
$903$	−21.6253	−	10.7168i	−0.719644	−	0.356633i
$904$	−11.5099	+	9.17885i	−0.382814	+	0.305284i
$905$	1.21590	−	1.52470i	0.0404180	−	0.0506826i
$906$	−26.6308	−	0.300868i	−0.884749	−	0.00999566i
$907$	−40.9412	−	14.3259i	−1.35943	−	0.475685i	−0.450553	−	0.892749i	$-0.648773\pi$
$907$	−40.9412	−	14.3259i	−1.35943	−	0.475685i	−0.908877	+	0.417064i	$0.863059\pi$
$908$	−7.84791	+	3.77935i	−0.260442	+	0.125422i
$909$	0.979778	+	10.9051i	0.0324972	+	0.361699i
$910$	−9.62522	+	3.36801i	−0.319073	+	0.111648i
$911$	−5.81843	+	5.81843i	−0.192773	+	0.192773i	−0.796893	−	0.604120i	$-0.793525\pi$
$911$	−5.81843	+	5.81843i	−0.192773	+	0.192773i	0.604120	+	0.796893i	$0.293525\pi$
$912$	−3.69485	+	4.52732i	−0.122349	+	0.149914i
$913$	−5.62398	−	49.9142i	−0.186127	−	1.65192i
$914$	−1.42604	−	12.6565i	−0.0471692	−	0.418638i
$915$	0.458556	−	0.561871i	0.0151594	−	0.0185749i
$916$	3.08755	−	3.08755i	0.102016	−	0.102016i
$917$	17.1465	−	5.99982i	0.566227	−	0.198131i
$918$	−0.0579512	+	0.393851i	−0.00191267	+	0.0129990i
$919$	−23.9640	+	11.5404i	−0.790498	+	0.380684i	−0.785153	−	0.619302i	$-0.787416\pi$
$919$	−23.9640	+	11.5404i	−0.790498	+	0.380684i	−0.00534500	+	0.999986i	$0.501701\pi$
$920$	−10.4666	−	3.66241i	−0.345073	−	0.120746i
$921$	−17.3988	−	0.196567i	−0.573309	−	0.00647709i
$922$	−28.3198	+	35.5120i	−0.932664	+	1.16952i
$923$	9.59710	−	7.65343i	0.315892	−	0.251916i
$924$	−88.9743	−	44.0929i	−2.92704	−	1.45055i
$925$	−12.2186	+	19.4458i	−0.401745	+	0.639374i
$926$	82.4427	+	9.28906i	2.70923	+	0.305257i
$927$	−20.6243	+	40.4621i	−0.677392	+	1.32895i
$928$	−3.00069	+	22.8073i	−0.0985024	+	0.748688i
$929$		−	39.5497i		−	1.29758i	−0.760966	−	0.648792i	$-0.775275\pi$
$929$		−	39.5497i		−	1.29758i	0.760966	−	0.648792i	$-0.224725\pi$
$930$	6.32211	+	2.29269i	0.207310	+	0.0751803i
$931$	−5.29159	−	3.32492i	−0.173425	−	0.108970i
$932$	3.06702	−	13.4375i	0.100464	−	0.440160i
$933$	12.0845	+	25.8364i	0.395629	+	0.845845i
$934$	42.8606	+	34.1802i	1.40244	+	1.11841i
$935$	0.0767572	−	0.0175193i	0.00251023	−	0.000572943i
$936$	24.6431	−	23.5539i	0.805485	−	0.769885i
$937$	12.6996	+	26.3709i	0.414876	+	0.861500i	0.998766	+	0.0496666i	$0.0158159\pi$
$937$	12.6996	+	26.3709i	0.414876	+	0.861500i	−0.583889	+	0.811833i	$0.698470\pi$
$938$	−4.51581	−	7.18686i	−0.147446	−	0.234659i
$939$	25.6570	−	2.59767i	0.837283	−	0.0847719i
$940$	0.980662	+	0.980662i	0.0319857	+	0.0319857i
$941$	−14.0633	−	6.77251i	−0.458449	−	0.220777i	0.190382	−	0.981710i	$-0.439027\pi$
$941$	−14.0633	−	6.77251i	−0.458449	−	0.220777i	−0.648831	+	0.760933i	$0.724742\pi$
$942$	42.1161	+	5.22782i	1.37222	+	0.170332i
$943$	−53.4675	+	6.02434i	−1.74114	+	0.196180i
$944$	−5.75964	+	11.9600i	−0.187460	+	0.389266i
$945$	−0.537900	−	6.85499i	−0.0174979	−	0.222993i
$946$	−19.5662	−	55.9169i	−0.636151	−	1.81801i
$947$	−27.2243	+	17.1062i	−0.884672	+	0.555876i	−0.895997	−	0.444060i	$-0.853538\pi$
$947$	−27.2243	+	17.1062i	−0.884672	+	0.555876i	0.0113255	+	0.999936i	$0.496395\pi$
$948$	75.0631	−	16.2427i	2.43794	−	0.527540i
$949$	−0.774671	+	2.21388i	−0.0251469	+	0.0718657i
$950$	−7.51659	−	32.9323i	−0.243870	−	1.06847i
$951$	−4.10117	−	5.26361i	−0.132990	−	0.170684i
$952$	0.212254	+	0.266158i	0.00687920	+	0.00862624i
$953$	32.7679	+	7.47905i	1.06146	+	0.242270i	0.717387	−	0.696675i	$-0.245338\pi$
$953$	32.7679	+	7.47905i	1.06146	+	0.242270i	0.344068	+	0.938945i	$0.388195\pi$
$954$	13.4933	−	8.05905i	0.436862	−	0.260921i
$955$	0.805958	−	7.15307i	0.0260802	−	0.231468i
$956$	92.2807			2.98457
$957$	−1.52750	+	51.0496i	−0.0493771	+	1.65020i
$958$	72.2728			2.33503
$959$	−3.31487	+	29.4203i	−0.107043	+	0.950030i
$960$	6.65780	−	6.50904i	0.214879	−	0.210078i
$961$	−16.3008	−	3.72054i	−0.525831	−	0.120018i
$962$	−22.9540	−	28.7834i	−0.740068	−	0.928016i
$963$	−7.83441	+	3.55710i	−0.252460	+	0.114626i
$964$	−20.7628	−	90.9676i	−0.668724	−	2.92987i
$965$	−1.06808	+	3.05239i	−0.0343826	+	0.0982599i
$966$	18.9041	+	87.3620i	0.608229	+	2.81083i
$967$	40.3899	−	25.3787i	1.29885	−	0.816123i	0.308041	−	0.951373i	$-0.400327\pi$
$967$	40.3899	−	25.3787i	1.29885	−	0.816123i	0.990812	+	0.135250i	$0.0431837\pi$
$968$	−21.6296	−	61.8138i	−0.695201	−	1.98677i
$969$	−0.145231	+	0.0889824i	−0.00466550	+	0.00285853i
$970$	−6.50093	+	13.4993i	−0.208732	+	0.433437i
$971$	4.40564	−	0.496396i	0.141384	−	0.0159301i	−0.0409890	−	0.999160i	$-0.513051\pi$
$971$	4.40564	−	0.496396i	0.141384	−	0.0159301i	0.182373	+	0.983229i	$0.441622\pi$
$972$	26.1813	+	47.4148i	0.839766	+	1.52083i
$973$	7.04756	+	3.39393i	0.225935	+	0.108804i
$974$	11.1138	+	11.1138i	0.356108	+	0.356108i
$975$	2.76233	+	27.2832i	0.0884652	+	0.873762i
$976$	0.569909	+	0.907005i	0.0182423	+	0.0290325i
$977$	−13.8023	−	28.6609i	−0.441576	−	0.916942i	−0.996384	−	0.0849639i	$-0.972922\pi$
$977$	−13.8023	−	28.6609i	−0.441576	−	0.916942i	0.554808	−	0.831979i	$-0.312792\pi$
$978$	−42.5137	−	27.3879i	−1.35944	−	0.875768i
$979$	64.1551	−	14.6430i	2.05041	−	0.467992i
$980$	−2.48234	−	1.97960i	−0.0792956	−	0.0632361i
$981$	−2.88089	−	14.0813i	−0.0919798	−	0.449581i
$982$	22.6035	−	99.0325i	0.721307	−	3.16025i
$983$	11.2352	+	7.05955i	0.358347	+	0.225165i	0.699158	−	0.714968i	$-0.253559\pi$
$983$	11.2352	+	7.05955i	0.358347	+	0.225165i	−0.340810	+	0.940132i	$0.610701\pi$
$984$	−14.9768	+	41.2986i	−0.477443	+	1.31655i
$985$		−	5.59474i		−	0.178263i
$986$	0.185897	−	0.368318i	0.00592016	−	0.0117296i
$987$	1.10788	−	4.61310i	0.0352643	−	0.146836i
$988$	34.1512	+	3.84792i	1.08650	+	0.122419i
$989$	−18.0061	+	28.6566i	−0.572561	+	0.911226i
$990$	10.8186	−	12.9545i	0.343836	−	0.411720i
$991$	7.18627	−	5.73086i	0.228279	−	0.182047i	−0.502670	−	0.864478i	$-0.667649\pi$
$991$	7.18627	−	5.73086i	0.228279	−	0.182047i	0.730949	+	0.682432i	$0.239077\pi$
$992$	10.0646	−	12.6206i	0.319551	−	0.400704i
$993$	0.484378	−	42.8739i	0.0153713	−	1.36056i
$994$	24.8041	+	8.67934i	0.786739	+	0.275292i
$995$	−7.93782	+	3.82265i	−0.251646	+	0.121186i
$996$	17.6439	+	52.3118i	0.559070	+	1.65756i
$997$	−19.9945	+	6.99639i	−0.633233	+	0.221578i	−0.627760	−	0.778407i	$-0.716028\pi$
$997$	−19.9945	+	6.99639i	−0.633233	+	0.221578i	−0.00547353	+	0.999985i	$0.501742\pi$
$998$	−62.7188	+	62.7188i	−1.98533	+	1.98533i
$999$	22.7180	−	10.0068i	0.718767	−	0.316601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.k.a.2.8	yes	96
3.2	odd	2	inner	87.2.k.a.2.1	✓	96
29.15	odd	28	inner	87.2.k.a.44.1	yes	96
87.44	even	28	inner	87.2.k.a.44.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.k.a.2.1	✓	96	3.2	odd	2	inner
87.2.k.a.2.8	yes	96	1.1	even	1	trivial
87.2.k.a.44.1	yes	96	29.15	odd	28	inner
87.2.k.a.44.8	yes	96	87.44	even	28	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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.k (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.261972 - 2.32506i) q^{2} +(1.21083 + 1.23850i) q^{3} +(-3.38744 - 0.773161i) q^{4} +(-0.273793 - 0.343325i) q^{5} +(3.19680 - 2.49081i) q^{6} +(-0.670558 - 2.93790i) q^{7} +(-1.13950 + 3.25651i) q^{8} +(-0.0677777 + 2.99923i) q^{9} +(-0.869979 + 0.546644i) q^{10} +(1.80846 + 5.16827i) q^{11} +(-3.14405 - 5.13152i) q^{12} +(-1.42901 + 2.96736i) q^{13} +(-7.00648 + 0.789441i) q^{14} +(0.0936925 - 0.754802i) q^{15} +(1.01216 + 0.487430i) q^{16} +(0.0231533 + 0.0231533i) q^{17} +(6.95566 + 0.943302i) q^{18} +(1.59781 + 2.54289i) q^{19} +(0.662010 + 1.37468i) q^{20} +(2.82667 - 4.38779i) q^{21} +(12.4903 - 2.85084i) q^{22} +(-5.72233 - 4.56340i) q^{23} +(-5.41295 + 2.53181i) q^{24} +(1.06969 - 4.68664i) q^{25} +(6.52494 + 4.09989i) q^{26} +(-3.79663 + 3.54762i) q^{27} +10.4704i q^{28} +(4.89452 - 2.24581i) q^{29} +(-1.73042 - 0.415578i) q^{30} +(-3.75513 - 0.423102i) q^{31} +(-2.27269 + 3.61696i) q^{32} +(-4.21119 + 8.49768i) q^{33} +(0.0598983 - 0.0477673i) q^{34} +(-0.825063 + 1.03460i) q^{35} +(2.54848 - 10.1073i) q^{36} +(-4.50934 - 1.57789i) q^{37} +(6.33097 - 3.04884i) q^{38} +(-5.40537 + 1.82314i) q^{39} +(1.43003 - 0.500389i) q^{40} +(5.19822 - 5.19822i) q^{41} +(-9.46139 - 7.72167i) q^{42} +(-0.517730 - 4.59498i) q^{43} +(-2.13013 - 18.9054i) q^{44} +(1.04827 - 0.797899i) q^{45} +(-12.1093 + 12.1093i) q^{46} +(0.857949 - 0.300209i) q^{47} +(0.621870 + 1.84376i) q^{48} +(-1.87485 + 0.902882i) q^{49} +(-10.6165 - 3.71488i) q^{50} +(-0.000640695 + 0.0567100i) q^{51} +(7.13491 - 8.94690i) q^{52} +(1.75058 - 1.39604i) q^{53} +(7.25384 + 9.75678i) q^{54} +(1.27926 - 2.03592i) q^{55} +(10.3314 + 1.16407i) q^{56} +(-1.21471 + 5.05790i) q^{57} +(-3.93944 - 11.9684i) q^{58} +11.8163i q^{59} +(-0.900961 + 2.48440i) q^{60} +(0.807366 + 0.507302i) q^{61} +(-1.96748 + 8.62008i) q^{62} +(8.85691 - 1.81203i) q^{63} +(9.57093 + 7.63256i) q^{64} +(1.41002 - 0.321828i) q^{65} +(18.6545 + 12.0174i) q^{66} +(0.522314 + 1.08460i) q^{67} +(-0.0605290 - 0.0963314i) q^{68} +(-1.27698 - 12.6126i) q^{69} +(2.18936 + 2.18936i) q^{70} +(-3.35796 - 1.61711i) q^{71} +(-9.68982 - 3.63836i) q^{72} +(0.707680 - 0.0797363i) q^{73} +(-4.85001 + 10.0711i) q^{74} +(7.09964 - 4.34991i) q^{75} +(-3.44641 - 9.84926i) q^{76} +(13.9712 - 8.77870i) q^{77} +(2.82287 + 13.0454i) q^{78} +(-4.21488 + 12.0454i) q^{79} +(-0.109775 - 0.480955i) q^{80} +(-8.99081 - 0.406563i) q^{81} +(-10.7244 - 13.4480i) q^{82} +(-8.94353 - 2.04130i) q^{83} +(-12.9676 + 12.6779i) q^{84} +(0.00160990 - 0.0142883i) q^{85} -10.8193 q^{86} +(8.70788 + 3.34257i) q^{87} -18.8913 q^{88} +(1.34559 - 11.9424i) q^{89} +(-1.58055 - 2.64632i) q^{90} +(9.67605 + 2.20850i) q^{91} +(15.8558 + 19.8825i) q^{92} +(-4.02282 - 5.16304i) q^{93} +(-0.473248 - 2.07343i) q^{94} +(0.435572 - 1.24479i) q^{95} +(-7.23146 + 1.56480i) q^{96} +(12.3474 - 7.75841i) q^{97} +(1.60810 + 4.59568i) q^{98} +(-15.6234 + 5.07369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) \) 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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