LMFDB - Embedded newform 97.3.l.a.5.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,3,Mod(5,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(96)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.5"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	97.l (of order $96$, degree $32$, 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:	$2.64305856429$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$15$ over $\Q(\zeta_{96})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{96}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	97.5
Dual form			97.3.l.a.39.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.65450 - 3.35499i) q^{2} +(-2.33421 + 2.66165i) q^{3} +(-6.08354 + 7.92822i) q^{4} +(6.93452 + 0.227013i) q^{5} +(12.7918 + 3.42754i) q^{6} +(-3.26636 - 5.25273i) q^{7} +(21.9887 + 4.37383i) q^{8} +(-0.461140 - 3.50270i) q^{9} +(-10.7115 - 23.6408i) q^{10} +(11.5280 - 3.91321i) q^{11} +(-6.90194 - 34.6984i) q^{12} +(10.2719 + 10.9672i) q^{13} +(-12.2187 + 19.6492i) q^{14} +(-16.7908 + 17.9274i) q^{15} +(-11.3603 - 42.3972i) q^{16} +(-4.51360 + 1.05242i) q^{17} +(-10.9886 + 7.34233i) q^{18} +(28.8161 - 15.4025i) q^{19} +(-43.9862 + 53.5973i) q^{20} +(21.6053 + 3.56705i) q^{21} +(-32.2017 - 32.2017i) q^{22} +(-2.28559 + 1.63783i) q^{23} +(-62.9679 + 48.3169i) q^{24} +(23.0895 + 1.51337i) q^{25} +(19.8000 - 52.6075i) q^{26} +(-16.0926 - 10.7528i) q^{27} +(61.5158 + 6.05877i) q^{28} +(48.7154 + 22.0727i) q^{29} +(87.9265 + 26.6722i) q^{30} +(2.07916 + 31.7219i) q^{31} +(-56.0230 + 49.1309i) q^{32} +(-16.4930 + 39.8177i) q^{33} +(10.9986 + 13.4018i) q^{34} +(-21.4582 - 37.1666i) q^{35} +(30.5756 + 17.6528i) q^{36} +(29.1864 - 4.81869i) q^{37} +(-99.3515 - 71.1943i) q^{38} +(-53.1678 + 1.74053i) q^{39} +(151.488 + 35.3221i) q^{40} +(-40.7607 + 15.3412i) q^{41} +(-23.7785 - 78.3872i) q^{42} +(-63.7542 - 8.39340i) q^{43} +(-39.1059 + 115.202i) q^{44} +(-2.40262 - 24.3942i) q^{45} +(9.27640 + 4.95834i) q^{46} +(-20.8304 + 8.62823i) q^{47} +(139.364 + 68.7267i) q^{48} +(4.75008 - 9.63221i) q^{49} +(-33.1242 - 79.9689i) q^{50} +(7.73449 - 14.4702i) q^{51} +(-149.440 + 14.7186i) q^{52} +(-3.68594 - 1.25121i) q^{53} +(-9.45015 + 71.7810i) q^{54} +(80.8291 - 24.5192i) q^{55} +(-48.8485 - 129.787i) q^{56} +(-26.2666 + 112.651i) q^{57} +(-6.54597 - 199.959i) q^{58} +(-29.5455 + 41.2308i) q^{59} +(-39.9846 - 242.183i) q^{60} +(-6.08858 + 10.5457i) q^{61} +(102.987 - 59.4594i) q^{62} +(-16.8925 + 13.8633i) q^{63} +(95.3167 + 39.4815i) q^{64} +(68.7412 + 78.3843i) q^{65} +(160.875 - 10.5443i) q^{66} +(30.5501 - 100.710i) q^{67} +(19.1148 - 42.1872i) q^{68} +(0.975704 - 9.90649i) q^{69} +(-89.1911 + 133.484i) q^{70} +(-17.1956 - 6.47197i) q^{71} +(5.18035 - 79.0369i) q^{72} +(-0.809638 - 1.05514i) q^{73} +(-64.4554 - 89.9474i) q^{74} +(-57.9238 + 57.9238i) q^{75} +(-53.1892 + 322.162i) q^{76} +(-58.2094 - 47.7712i) q^{77} +(93.8054 + 175.498i) q^{78} +(-54.4687 - 81.5181i) q^{79} +(-69.1535 - 296.583i) q^{80} +(96.8966 - 25.9634i) q^{81} +(118.908 + 111.370i) q^{82} +(94.9480 + 59.0424i) q^{83} +(-159.717 + 149.591i) q^{84} +(-31.5385 + 6.27340i) q^{85} +(77.3214 + 227.781i) q^{86} +(-172.462 + 78.1414i) q^{87} +(270.601 - 35.6252i) q^{88} +(10.0331 - 50.4398i) q^{89} +(-77.8673 + 48.4210i) q^{90} +(24.0561 - 89.7785i) q^{91} +(0.919390 - 28.0845i) q^{92} +(-89.2860 - 68.5115i) q^{93} +(63.4114 + 55.6103i) q^{94} +(203.322 - 100.268i) q^{95} -263.796i q^{96} +(-50.8030 - 82.6321i) q^{97} -40.1749 q^{98} +(-19.0228 - 38.5745i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} + 64 q^{9} - 32 q^{10} - 32 q^{11} - 224 q^{12} - 32 q^{13} - 32 q^{14} + 224 q^{15} - 32 q^{16} + 48 q^{17} - 32 q^{18}+ \cdots - 512 q^{99}+O(q^{100}) $ 480 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 + 64 * q^9 - 32 * q^10 - 32 * q^11 - 224 * q^12 - 32 * q^13 - 32 * q^14 + 224 * q^15 - 32 * q^16 + 48 * q^17 - 32 * q^18 - 32 * q^19 - 416 * q^20 - 32 * q^21 - 32 * q^22 - 144 * q^23 - 32 * q^24 + 288 * q^25 + 48 * q^26 - 32 * q^27 - 272 * q^28 + 256 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 + 144 * q^33 - 432 * q^34 - 16 * q^35 - 48 * q^36 - 272 * q^37 - 32 * q^38 - 384 * q^39 + 544 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 + 496 * q^44 - 240 * q^45 - 32 * q^46 - 800 * q^47 - 912 * q^48 - 32 * q^49 - 32 * q^50 + 160 * q^51 + 352 * q^52 - 32 * q^53 + 1376 * q^54 - 352 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 544 * q^59 + 1408 * q^60 - 16 * q^61 - 48 * q^62 - 288 * q^63 - 32 * q^64 + 544 * q^65 - 1696 * q^66 - 32 * q^67 + 1696 * q^68 - 32 * q^69 - 1728 * q^70 + 16 * q^71 - 96 * q^72 - 176 * q^73 - 752 * q^74 - 32 * q^75 + 2368 * q^76 - 32 * q^77 - 32 * q^78 + 1776 * q^79 + 1760 * q^80 - 160 * q^81 + 80 * q^82 + 384 * q^83 + 2272 * q^84 + 944 * q^85 + 1888 * q^86 + 1760 * q^87 + 2272 * q^88 + 640 * q^89 + 2240 * q^90 + 928 * q^91 - 624 * q^92 + 784 * q^93 + 224 * q^94 - 448 * q^95 - 192 * q^97 - 768 * q^98 - 512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{96}\right)$

Coefficient data

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

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

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

$2$	−1.65450	−	3.35499i	−0.827248	−	1.67749i	−0.731247	−	0.682112i	$-0.761061\pi$
$2$	−1.65450	−	3.35499i	−0.827248	−	1.67749i	−0.0960010	−	0.995381i	$-0.530605\pi$
$3$	−2.33421	+	2.66165i	−0.778069	+	0.887218i	−0.996055	−	0.0887339i	$-0.971718\pi$
$3$	−2.33421	+	2.66165i	−0.778069	+	0.887218i	0.217986	+	0.975952i	$0.430051\pi$
$4$	−6.08354	+	7.92822i	−1.52088	+	1.98205i
$5$	6.93452	+	0.227013i	1.38690	+	0.0454025i	0.717014	−	0.697059i	$-0.245508\pi$
$5$	6.93452	+	0.227013i	1.38690	+	0.0454025i	0.669889	+	0.742461i	$0.266342\pi$
$6$	12.7918	+	3.42754i	2.13196	+	0.571257i
$7$	−3.26636	−	5.25273i	−0.466622	−	0.750390i	0.528511	−	0.848926i	$-0.322750\pi$
$7$	−3.26636	−	5.25273i	−0.466622	−	0.750390i	−0.995133	+	0.0985367i	$0.968584\pi$
$8$	21.9887	+	4.37383i	2.74859	+	0.546729i
$9$	−0.461140	−	3.50270i	−0.0512378	−	0.389189i
$10$	−10.7115	−	23.6408i	−1.07115	−	2.36408i
$11$	11.5280	−	3.91321i	1.04800	−	0.355747i	0.256258	−	0.966608i	$-0.417510\pi$
$11$	11.5280	−	3.91321i	1.04800	−	0.355747i	0.791737	+	0.610862i	$0.209177\pi$
$12$	−6.90194	−	34.6984i	−0.575161	−	2.89153i
$13$	10.2719	+	10.9672i	0.790149	+	0.843633i	0.990702	−	0.136050i	$-0.0434406\pi$
$13$	10.2719	+	10.9672i	0.790149	+	0.843633i	−0.200553	+	0.979683i	$0.564274\pi$
$14$	−12.2187	+	19.6492i	−0.872761	+	1.40351i
$15$	−16.7908	+	17.9274i	−1.11939	+	1.19516i
$16$	−11.3603	−	42.3972i	−0.710019	−	2.64983i
$17$	−4.51360	+	1.05242i	−0.265506	+	0.0619072i	−0.357709	−	0.933833i	$-0.616442\pi$
$17$	−4.51360	+	1.05242i	−0.265506	+	0.0619072i	0.0922038	+	0.995740i	$0.470609\pi$
$18$	−10.9886	+	7.34233i	−0.610476	+	0.407907i
$19$	28.8161	−	15.4025i	1.51664	−	0.810660i	0.517648	−	0.855594i	$-0.326808\pi$
$19$	28.8161	−	15.4025i	1.51664	−	0.810660i	0.998990	+	0.0449338i	$0.0143077\pi$
$20$	−43.9862	+	53.5973i	−2.19931	+	2.67987i
$21$	21.6053	+	3.56705i	1.02882	+	0.169859i
$22$	−32.2017	−	32.2017i	−1.46372	−	1.46372i
$23$	−2.28559	+	1.63783i	−0.0993735	+	0.0712100i	−0.631075	−	0.775722i	$-0.717386\pi$
$23$	−2.28559	+	1.63783i	−0.0993735	+	0.0712100i	0.531702	+	0.846932i	$0.321553\pi$
$24$	−62.9679	+	48.3169i	−2.62366	+	2.01321i
$25$	23.0895	+	1.51337i	0.923581	+	0.0605347i
$26$	19.8000	−	52.6075i	0.761540	−	2.02336i
$27$	−16.0926	−	10.7528i	−0.596024	−	0.398250i
$28$	61.5158	+	6.05877i	2.19699	+	0.216385i
$29$	48.7154	+	22.0727i	1.67984	+	0.761127i	0.999604	+	0.0281358i	$0.00895707\pi$
$29$	48.7154	+	22.0727i	1.67984	+	0.761127i	0.680238	+	0.732991i	$0.261876\pi$
$30$	87.9265	+	26.6722i	2.93088	+	0.889074i
$31$	2.07916	+	31.7219i	0.0670698	+	1.02329i	0.890240	+	0.455492i	$0.150537\pi$
$31$	2.07916	+	31.7219i	0.0670698	+	1.02329i	−0.823170	+	0.567795i	$0.807797\pi$
$32$	−56.0230	+	49.1309i	−1.75072	+	1.53534i
$33$	−16.4930	+	39.8177i	−0.499788	+	1.20660i
$34$	10.9986	+	13.4018i	0.323488	+	0.394171i
$35$	−21.4582	−	37.1666i	−0.613090	−	1.06190i
$36$	30.5756	+	17.6528i	0.849321	+	0.490356i
$37$	29.1864	−	4.81869i	0.788821	−	0.130235i	0.245096	−	0.969499i	$-0.421180\pi$
$37$	29.1864	−	4.81869i	0.788821	−	0.130235i	0.543724	+	0.839264i	$0.317014\pi$
$38$	−99.3515	−	71.1943i	−2.61451	−	1.87353i
$39$	−53.1678	+	1.74053i	−1.36328	+	0.0446291i
$40$	151.488	+	35.3221i	3.78721	+	0.883053i
$41$	−40.7607	+	15.3412i	−0.994163	+	0.374177i	−0.795541	−	0.605900i	$-0.792813\pi$
$41$	−40.7607	+	15.3412i	−0.994163	+	0.374177i	−0.198622	+	0.980076i	$0.563647\pi$
$42$	−23.7785	−	78.3872i	−0.566154	−	1.86636i
$43$	−63.7542	−	8.39340i	−1.48266	−	0.195195i	−0.654657	−	0.755926i	$-0.727187\pi$
$43$	−63.7542	−	8.39340i	−1.48266	−	0.195195i	−0.827998	+	0.560730i	$0.810520\pi$
$44$	−39.1059	+	115.202i	−0.888770	+	2.61823i
$45$	−2.40262	−	24.3942i	−0.0533916	−	0.542094i
$46$	9.27640	+	4.95834i	0.201661	+	0.107790i
$47$	−20.8304	+	8.62823i	−0.443200	+	0.183579i	−0.593112	−	0.805120i	$-0.702101\pi$
$47$	−20.8304	+	8.62823i	−0.443200	+	0.183579i	0.149912	+	0.988699i	$0.452101\pi$
$48$	139.364	+	68.7267i	2.90342	+	1.43181i
$49$	4.75008	−	9.63221i	0.0969404	−	0.196576i
$50$	−33.1242	−	79.9689i	−0.662484	−	1.59938i
$51$	7.73449	−	14.4702i	0.151657	−	0.283730i
$52$	−149.440	+	14.7186i	−2.87385	+	0.283050i
$53$	−3.68594	−	1.25121i	−0.0695461	−	0.0236077i	0.286450	−	0.958095i	$-0.407525\pi$
$53$	−3.68594	−	1.25121i	−0.0695461	−	0.0236077i	−0.355996	+	0.934488i	$0.615858\pi$
$54$	−9.45015	+	71.7810i	−0.175003	+	1.32928i
$55$	80.8291	−	24.5192i	1.46962	−	0.445804i
$56$	−48.8485	−	129.787i	−0.872294	−	2.31763i
$57$	−26.2666	+	112.651i	−0.460817	+	1.97634i
$58$	−6.54597	−	199.959i	−0.112862	−	3.44757i
$59$	−29.5455	+	41.2308i	−0.500772	+	0.698826i	−0.984300	−	0.176502i	$-0.943522\pi$
$59$	−29.5455	+	41.2308i	−0.500772	+	0.698826i	0.483528	+	0.875329i	$0.339355\pi$
$60$	−39.9846	−	242.183i	−0.666410	−	4.03639i
$61$	−6.08858	+	10.5457i	−0.0998128	+	0.172881i	−0.911607	−	0.411063i	$-0.865158\pi$
$61$	−6.08858	+	10.5457i	−0.0998128	+	0.172881i	0.811794	+	0.583944i	$0.198491\pi$
$62$	102.987	−	59.4594i	1.66108	−	0.959022i
$63$	−16.8925	+	13.8633i	−0.268135	+	0.220053i
$64$	95.3167	+	39.4815i	1.48932	+	0.616898i
$65$	68.7412	+	78.3843i	1.05756	+	1.20591i
$66$	160.875	−	10.5443i	2.43751	−	0.159763i
$67$	30.5501	−	100.710i	0.455971	−	1.50314i	−0.364366	−	0.931256i	$-0.618714\pi$
$67$	30.5501	−	100.710i	0.455971	−	1.50314i	0.820337	−	0.571880i	$-0.193786\pi$
$68$	19.1148	−	42.1872i	0.281100	−	0.620400i
$69$	0.975704	−	9.90649i	0.0141406	−	0.143572i
$70$	−89.1911	+	133.484i	−1.27416	+	1.90691i
$71$	−17.1956	−	6.47197i	−0.242192	−	0.0911545i	0.228193	−	0.973616i	$-0.426718\pi$
$71$	−17.1956	−	6.47197i	−0.242192	−	0.0911545i	−0.470385	+	0.882461i	$0.655885\pi$
$72$	5.18035	−	79.0369i	0.0719494	−	1.09774i
$73$	−0.809638	−	1.05514i	−0.0110909	−	0.0144540i	0.787775	−	0.615963i	$-0.211233\pi$
$73$	−0.809638	−	1.05514i	−0.0110909	−	0.0144540i	−0.798866	+	0.601509i	$0.794566\pi$
$74$	−64.4554	−	89.9474i	−0.871019	−	1.21551i
$75$	−57.9238	+	57.9238i	−0.772317	+	0.772317i
$76$	−53.1892	+	322.162i	−0.699858	+	4.23898i
$77$	−58.2094	−	47.7712i	−0.755967	−	0.620406i
$78$	93.8054	+	175.498i	1.20263	+	2.24997i
$79$	−54.4687	−	81.5181i	−0.689477	−	1.03187i	−0.996774	−	0.0802612i	$-0.974425\pi$
$79$	−54.4687	−	81.5181i	−0.689477	−	1.03187i	0.307297	−	0.951614i	$-0.400575\pi$
$80$	−69.1535	−	296.583i	−0.864419	−	3.70729i
$81$	96.8966	−	25.9634i	1.19625	−	0.320535i
$82$	118.908	+	111.370i	1.45010	+	1.35817i
$83$	94.9480	+	59.0424i	1.14395	+	0.711355i	0.962295	−	0.272007i	$-0.0876875\pi$
$83$	94.9480	+	59.0424i	1.14395	+	0.711355i	0.181656	+	0.983362i	$0.441854\pi$
$84$	−159.717	+	149.591i	−1.90139	+	1.78085i
$85$	−31.5385	+	6.27340i	−0.371041	+	0.0738047i
$86$	77.3214	+	227.781i	0.899086	+	2.64862i
$87$	−172.462	+	78.1414i	−1.98232	+	0.898177i
$88$	270.601	−	35.6252i	3.07501	−	0.404832i
$89$	10.0331	−	50.4398i	0.112732	−	0.566740i	−0.882592	−	0.470140i	$-0.844203\pi$
$89$	10.0331	−	50.4398i	0.112732	−	0.566740i	0.995323	−	0.0965995i	$-0.0307966\pi$
$90$	−77.8673	+	48.4210i	−0.865192	+	0.538011i
$91$	24.0561	−	89.7785i	0.264353	−	0.986577i
$92$	0.919390	−	28.0845i	0.00999337	−	0.305266i
$93$	−89.2860	−	68.5115i	−0.960064	−	0.736683i
$94$	63.4114	+	55.6103i	0.674590	+	0.591599i
$95$	203.322	−	100.268i	2.14024	−	1.05545i
$96$		−	263.796i		−	2.74787i
$97$	−50.8030	−	82.6321i	−0.523742	−	0.851877i
$97$	−50.8030	−	82.6321i	−0.523742	−	0.851877i
$98$	−40.1749			−0.409948
$99$	−19.0228	−	38.5745i	−0.192150	−	0.389641i
$100$	−152.464	+	173.852i	−1.52464	+	1.73852i
$101$	−36.6043	+	47.7037i	−0.362419	+	0.472314i	−0.938599	−	0.345009i	$-0.887876\pi$
$101$	−36.6043	+	47.7037i	−0.362419	+	0.472314i	0.576180	+	0.817323i	$0.304543\pi$
$102$	−61.3440	−	2.00820i	−0.601412	−	0.0196882i
$103$	−61.6879	−	16.5292i	−0.598911	−	0.160478i	−0.0533886	−	0.998574i	$-0.517002\pi$
$103$	−61.6879	−	16.5292i	−0.598911	−	0.160478i	−0.545523	+	0.838096i	$0.683669\pi$
$104$	177.898	+	286.083i	1.71056	+	2.75080i
$105$	149.013	+	29.6404i	1.41917	+	0.282290i
$106$	1.90059	+	14.4364i	0.0179301	+	0.136193i
$107$	−22.7757	−	50.2672i	−0.212857	−	0.469786i	0.773627	−	0.633641i	$-0.218440\pi$
$107$	−22.7757	−	50.2672i	−0.212857	−	0.469786i	−0.986484	+	0.163855i	$0.947607\pi$
$108$	183.150	−	62.1712i	1.69584	−	0.575659i
$109$	−1.61864	−	8.13746i	−0.0148499	−	0.0746556i	0.972650	−	0.232277i	$-0.0746175\pi$
$109$	−1.61864	−	8.13746i	−0.0148499	−	0.0746556i	−0.987500	+	0.157621i	$0.949618\pi$
$110$	−215.993	−	230.614i	−1.96358	−	2.09649i
$111$	−55.3014	+	88.9318i	−0.498211	+	0.801188i
$112$	−185.594	+	198.157i	−1.65709	+	1.76926i
$113$	14.8046	+	55.2516i	0.131014	+	0.488953i	0.999983	−	0.00591557i	$-0.00188300\pi$
$113$	14.8046	+	55.2516i	0.131014	+	0.488953i	−0.868968	+	0.494868i	$0.835216\pi$
$114$	421.402	−	98.2571i	3.69651	−	0.861904i
$115$	−16.2213	+	10.8387i	−0.141055	+	0.0942496i
$116$	−471.359	+	251.947i	−4.06344	+	2.17195i
$117$	33.6782	−	41.0370i	0.287848	−	0.350743i
$118$	187.212	+	30.9088i	1.58654	+	0.261939i
$119$	20.2711	+	20.2711i	0.170345	+	0.170345i
$120$	−447.620	+	320.760i	−3.73017	+	2.67300i
$121$	21.5847	−	16.5625i	0.178386	−	0.136880i
$122$	45.4544	+	2.97924i	0.372577	+	0.0244200i
$123$	54.3109	−	144.301i	0.441552	−	1.17317i
$124$	−264.147	−	176.497i	−2.13022	−	1.42337i
$125$	−12.8495	−	1.26556i	−0.102796	−	0.0101245i
$126$	74.4598	+	33.7373i	0.590951	+	0.267757i
$127$	22.9311	+	6.95606i	0.180560	+	0.0547721i	0.379270	−	0.925286i	$-0.376175\pi$
$127$	22.9311	+	6.95606i	0.180560	+	0.0547721i	−0.198710	+	0.980058i	$0.563675\pi$
$128$	−5.74738	−	87.6881i	−0.0449014	−	0.685063i
$129$	171.156	−	150.100i	1.32679	−	1.16356i
$130$	149.246	−	360.312i	1.14805	−	2.77163i
$131$	95.1916	+	115.991i	0.726653	+	0.885430i	0.997005	−	0.0773317i	$-0.0246401\pi$
$131$	95.1916	+	115.991i	0.726653	+	0.885430i	−0.270352	+	0.962762i	$0.587140\pi$
$132$	−215.347	−	372.992i	−1.63142	−	2.82570i
$133$	−175.029	−	101.053i	−1.31601	−	0.759797i
$134$	−388.426	+	64.1294i	−2.89870	+	0.478578i
$135$	−109.154	−	78.2184i	−0.808546	−	0.579396i
$136$	−103.851	+	3.39974i	−0.763613	+	0.0249981i
$137$	−120.415	−	28.0769i	−0.878944	−	0.204941i	−0.236831	−	0.971551i	$-0.576109\pi$
$137$	−120.415	−	28.0769i	−0.878944	−	0.204941i	−0.642113	+	0.766610i	$0.721942\pi$
$138$	−34.8504	+	13.1168i	−0.252539	+	0.0950491i
$139$	24.8848	+	82.0342i	0.179027	+	0.590174i	0.999820	+	0.0189484i	$0.00603182\pi$
$139$	24.8848	+	82.0342i	0.179027	+	0.590174i	−0.820793	+	0.571225i	$0.806468\pi$
$140$	425.207	+	55.9795i	3.03719	+	0.399854i
$141$	25.6571	−	75.5834i	0.181965	−	0.536053i
$142$	6.73670	+	68.3989i	0.0474416	+	0.481682i
$143$	161.331	+	86.2335i	1.12819	+	0.603031i
$144$	−143.266	+	59.3428i	−0.994904	+	0.412103i
$145$	332.807	+	164.122i	2.29522	+	1.13188i
$146$	−2.20044	+	4.46205i	−0.0150715	+	0.0305620i
$147$	14.5499	+	35.1267i	0.0989792	+	0.238957i
$148$	−139.353	+	260.711i	−0.941572	+	1.76156i
$149$	−20.0755	+	1.97727i	−0.134735	+	0.0132703i	−0.165160	−	0.986267i	$-0.552814\pi$
$149$	−20.0755	+	1.97727i	−0.134735	+	0.0132703i	0.0304247	+	0.999537i	$0.490314\pi$
$150$	290.168	+	98.4989i	1.93446	+	0.656659i
$151$	−9.24814	+	70.2466i	−0.0612459	+	0.465209i	0.933150	+	0.359488i	$0.117049\pi$
$151$	−9.24814	+	70.2466i	−0.0612459	+	0.465209i	−0.994396	+	0.105721i	$0.966285\pi$
$152$	700.998	−	212.645i	4.61183	−	1.39898i
$153$	5.76772	+	15.3245i	0.0376975	+	0.100160i
$154$	−63.9646	+	274.329i	−0.415355	+	1.78136i
$155$	7.21673	+	220.448i	0.0465595	+	1.42225i
$156$	309.649	−	432.115i	1.98493	−	2.76996i
$157$	2.23434	+	13.5332i	0.0142315	+	0.0861987i	0.992817	−	0.119641i	$-0.0381742\pi$
$157$	2.23434	+	13.5332i	0.0142315	+	0.0861987i	−0.978586	+	0.205839i	$0.934008\pi$
$158$	−183.374	+	317.613i	−1.16059	+	2.01021i
$159$	11.9340	−	6.89012i	0.0750569	−	0.0433341i
$160$	−399.646	+	327.981i	−2.49779	+	2.04988i
$161$	16.0686	+	6.65584i	0.0998052	+	0.0413406i
$162$	−247.422	−	282.131i	−1.52730	−	1.74155i
$163$	−233.503	+	15.3046i	−1.43253	+	0.0938933i	−0.761804	−	0.647808i	$-0.775686\pi$
$163$	−233.503	+	15.3046i	−1.43253	+	0.0938933i	−0.670731	+	0.741701i	$0.734019\pi$
$164$	126.340	−	416.489i	0.770368	−	2.53956i
$165$	−123.410	+	272.372i	−0.747941	+	1.65074i
$166$	40.9955	−	416.235i	0.246961	−	2.50744i
$167$	−13.6105	+	20.3696i	−0.0815001	+	0.121974i	−0.869980	−	0.493087i	$-0.835868\pi$
$167$	−13.6105	+	20.3696i	−0.0815001	+	0.121974i	0.788480	+	0.615061i	$0.210868\pi$
$168$	459.471	+	172.933i	2.73495	+	1.02936i
$169$	−3.71443	+	56.6712i	−0.0219789	+	0.335333i
$170$	73.2276	+	95.4320i	0.430750	+	0.561365i
$171$	−67.2388	−	93.8316i	−0.393209	−	0.548723i
$172$	454.396	−	454.396i	2.64184	−	2.64184i
$173$	7.62172	−	46.1641i	0.0440562	−	0.266844i	−0.955552	−	0.294821i	$-0.904740\pi$
$173$	7.62172	−	46.1641i	0.0440562	−	0.266844i	0.999609	+	0.0279770i	$0.00890650\pi$
$174$	547.501	+	449.322i	3.14656	+	2.58231i
$175$	−67.4693	−	126.226i	−0.385539	−	0.721292i
$176$	−296.870	−	444.298i	−1.68676	−	2.52442i
$177$	−40.7766	−	174.881i	−0.230376	−	0.988029i
$178$	−185.825	+	49.7916i	−1.04396	+	0.279728i
$179$	139.190	+	130.365i	0.777595	+	0.728298i	0.967325	−	0.253539i	$-0.0815945\pi$
$179$	139.190	+	130.365i	0.777595	+	0.728298i	−0.189730	+	0.981836i	$0.560761\pi$
$180$	208.019	+	129.355i	1.15566	+	0.718637i
$181$	201.240	−	188.481i	1.11182	−	1.04133i	0.112960	−	0.993599i	$-0.463967\pi$
$181$	201.240	−	188.481i	1.11182	−	1.04133i	0.998860	−	0.0477341i	$-0.0152000\pi$
$182$	−341.007	+	67.8304i	−1.87366	+	0.372695i
$183$	−13.8571	−	40.8216i	−0.0757218	−	0.223069i
$184$	−57.4208	+	26.0170i	−0.312070	+	0.141397i
$185$	203.487	−	26.7896i	1.09993	−	0.144809i
$186$	−82.1320	+	412.905i	−0.441570	+	2.21992i
$187$	−47.9142	+	29.7949i	−0.256225	+	0.159331i
$188$	58.3159	−	217.638i	0.310191	−	1.15765i
$189$	−3.91702	+	119.653i	−0.0207250	+	0.633083i
$190$	−672.793	−	516.252i	−3.54101	−	2.71712i
$191$	−200.677	−	175.989i	−1.05066	−	0.921407i	−0.0536445	−	0.998560i	$-0.517084\pi$
$191$	−200.677	−	175.989i	−1.05066	−	0.921407i	−0.997019	+	0.0771527i	$0.975417\pi$
$192$	−327.575	+	161.542i	−1.70612	+	0.841365i
$193$		−	21.1896i		−	0.109791i	−0.998492	−	0.0548954i	$-0.982517\pi$
$193$		−	21.1896i		−	0.109791i	0.998492	−	0.0548954i	$-0.0174825\pi$
$194$	−193.176	+	307.158i	−0.995754	+	1.58329i
$195$	−369.088			−1.89276
$196$	47.4690	+	96.2576i	0.242189	+	0.491110i
$197$	−23.2676	+	26.5316i	−0.118110	+	0.134678i	−0.807873	−	0.589357i	$-0.799381\pi$
$197$	−23.2676	+	26.5316i	−0.118110	+	0.134678i	0.689763	+	0.724035i	$0.257715\pi$
$198$	−97.9437	+	127.643i	−0.494665	+	0.644660i
$199$	−161.847	−	5.29833i	−0.813302	−	0.0266248i	−0.376763	−	0.926310i	$-0.622963\pi$
$199$	−161.847	−	5.29833i	−0.813302	−	0.0266248i	−0.436539	+	0.899685i	$0.643796\pi$
$200$	501.090	+	134.267i	2.50545	+	0.671333i
$201$	196.745	+	316.392i	0.978832	+	1.57409i
$202$	220.607	+	43.8815i	1.09211	+	0.217235i
$203$	−43.1802	−	327.986i	−0.212710	−	1.61569i
$204$	67.6699	+	149.351i	0.331715	+	0.732111i
$205$	−286.138	+	97.1309i	−1.39580	+	0.473809i
$206$	46.6071	+	234.310i	0.226248	+	1.13743i
$207$	6.79081	+	7.25048i	0.0328059	+	0.0350265i
$208$	348.288	−	560.092i	1.67446	−	2.69275i
$209$	271.917	−	290.323i	1.30104	−	1.38911i
$210$	−147.097	−	548.975i	−0.700464	−	2.61417i
$211$	−87.6805	+	20.4442i	−0.415547	+	0.0968920i	−0.429622	−	0.903009i	$-0.641353\pi$
$211$	−87.6805	+	20.4442i	−0.415547	+	0.0968920i	0.0140745	+	0.999901i	$0.495520\pi$
$212$	32.3434	−	21.6112i	0.152563	−	0.101940i
$213$	57.3643	−	30.6618i	0.269316	−	0.143952i
$214$	−130.963	+	159.579i	−0.611978	+	0.745697i
$215$	−440.199	−	72.6772i	−2.04744	−	0.338033i
$216$	−306.826	−	306.826i	−1.42049	−	1.42049i
$217$	159.835	−	114.536i	0.736568	−	0.527817i
$218$	−24.6230	+	18.8939i	−0.112950	+	0.0866693i
$219$	4.69828	+	0.307942i	0.0214533	+	0.00140613i
$220$	−297.333	+	789.995i	−1.35151	+	3.59088i
$221$	−57.9055	−	38.6912i	−0.262016	−	0.175073i
$222$	389.861	+	38.3980i	1.75613	+	0.172964i
$223$	307.394	+	139.278i	1.37845	+	0.624566i	0.959050	−	0.283236i	$-0.0914081\pi$
$223$	307.394	+	139.278i	1.37845	+	0.624566i	0.419397	+	0.907803i	$0.362241\pi$
$224$	441.062	+	133.795i	1.96903	+	0.597298i
$225$	−5.34662	−	81.5736i	−0.0237627	−	0.362549i
$226$	160.874	−	141.083i	0.711833	−	0.624261i
$227$	−18.7370	+	45.2351i	−0.0825419	+	0.199274i	−0.959762	−	0.280815i	$-0.909395\pi$
$227$	−18.7370	+	45.2351i	−0.0825419	+	0.199274i	0.877220	+	0.480088i	$0.159395\pi$
$228$	−733.330	−	893.565i	−3.21636	−	3.91915i
$229$	−107.228	−	185.725i	−0.468246	−	0.811025i	0.531096	−	0.847312i	$-0.321780\pi$
$229$	−107.228	−	185.725i	−0.468246	−	0.811025i	−0.999341	+	0.0362867i	$0.988447\pi$
$230$	63.2018	+	36.4896i	0.274790	+	0.158650i
$231$	263.023	−	43.4253i	1.13863	−	0.187988i
$232$	974.648	+	698.423i	4.20107	+	3.01044i
$233$	−9.76329	+	0.319617i	−0.0419025	+	0.00137175i	−0.0536632	−	0.998559i	$-0.517090\pi$
$233$	−9.76329	+	0.319617i	−0.0419025	+	0.00137175i	0.0117606	+	0.999931i	$0.496256\pi$
$234$	−193.399	−	45.0943i	−0.826491	−	0.192711i
$235$	−146.407	+	55.1039i	−0.623010	+	0.234485i
$236$	−147.145	−	485.072i	−0.623496	−	2.05539i
$237$	344.114	+	45.3035i	1.45196	+	0.191154i
$238$	34.4708	−	101.548i	0.144835	−	0.426671i
$239$	−22.6153	−	229.617i	−0.0946247	−	0.960741i	−0.918884	−	0.394528i	$-0.870908\pi$
$239$	−22.6153	−	229.617i	−0.0946247	−	0.960741i	0.824259	−	0.566213i	$-0.191592\pi$
$240$	950.820	+	508.224i	3.96175	+	2.11760i
$241$	−373.639	+	154.766i	−1.55037	+	0.642185i	−0.983383	−	0.181542i	$-0.941891\pi$
$241$	−373.639	+	154.766i	−1.55037	+	0.642185i	−0.566987	+	0.823726i	$0.691891\pi$
$242$	−91.2788	−	45.0137i	−0.377185	−	0.186007i
$243$	−80.0290	+	162.283i	−0.329338	+	0.667831i
$244$	−46.5688	−	112.427i	−0.190856	−	0.460766i
$245$	35.1262	−	65.7164i	0.143372	−	0.268230i
$246$	−573.984	+	56.5324i	−2.33327	+	0.229807i
$247$	464.920	+	157.819i	1.88227	+	0.638944i
$248$	−93.0281	+	706.618i	−0.375113	+	2.84927i
$249$	−378.779	+	114.901i	−1.52120	+	0.461451i
$250$	17.0135	+	45.2037i	0.0680539	+	0.180815i
$251$	−92.4577	+	396.530i	−0.368358	+	1.57980i	0.385466	+	0.922722i	$0.374041\pi$
$251$	−92.4577	+	396.530i	−0.368358	+	1.57980i	−0.753823	+	0.657077i	$0.771793\pi$
$252$	−7.14527	−	218.265i	−0.0283542	−	0.866133i
$253$	−19.9390	+	27.8248i	−0.0788103	+	0.109980i
$254$	−14.6019	−	88.4422i	−0.0574877	−	0.348198i
$255$	56.9198	−	98.5881i	0.223215	−	0.386620i
$256$	72.7082	−	41.9781i	0.284016	−	0.163977i
$257$	−129.305	+	106.118i	−0.503133	+	0.412911i	−0.851426	−	0.524475i	$-0.824262\pi$
$257$	−129.305	+	106.118i	−0.503133	+	0.412911i	0.348293	+	0.937386i	$0.386762\pi$
$258$	−786.759	−	325.886i	−3.04946	−	1.26313i
$259$	−120.644	−	137.568i	−0.465808	−	0.531152i
$260$	−1039.64	+	68.1414i	−3.99861	+	0.262082i
$261$	54.8494	−	180.814i	0.210151	−	0.692775i
$262$	231.655	−	511.274i	0.884180	−	1.95143i
$263$	−25.2870	+	256.743i	−0.0961481	+	0.976208i	0.819190	+	0.573522i	$0.194423\pi$
$263$	−25.2870	+	256.743i	−0.0961481	+	0.976208i	−0.915338	+	0.402686i	$0.868077\pi$
$264$	−536.816	+	803.402i	−2.03339	+	3.04319i
$265$	−25.2762	−	9.51329i	−0.0953819	−	0.0358992i
$266$	−49.4468	+	754.412i	−0.185890	+	2.83614i
$267$	110.834	+	144.442i	0.415109	+	0.540980i
$268$	612.599	+	854.881i	2.28582	+	3.18986i
$269$	107.987	−	107.987i	0.401438	−	0.401438i	−0.477302	−	0.878739i	$-0.658385\pi$
$269$	107.987	−	107.987i	0.401438	−	0.401438i	0.878739	+	0.477302i	$0.158385\pi$
$270$	−81.8274	+	495.621i	−0.303065	+	1.83563i
$271$	−188.409	−	154.623i	−0.695237	−	0.570566i	0.219010	−	0.975723i	$-0.429717\pi$
$271$	−188.409	−	154.623i	−0.695237	−	0.570566i	−0.914247	+	0.405156i	$0.867217\pi$
$272$	95.8956	+	179.408i	0.352557	+	0.659589i
$273$	182.808	+	273.591i	0.669625	+	1.00216i
$274$	105.029	+	450.445i	0.383318	+	1.64396i
$275$	272.097	−	72.9082i	0.989443	−	0.265121i
$276$	72.6051	+	68.0021i	0.263062	+	0.246384i
$277$	53.8343	+	33.4763i	0.194348	+	0.120853i	0.621773	−	0.783197i	$-0.286413\pi$
$277$	53.8343	+	33.4763i	0.194348	+	0.120853i	−0.427425	+	0.904051i	$0.640579\pi$
$278$	234.052	−	219.213i	0.841913	−	0.788537i
$279$	110.154	−	21.9109i	0.394816	−	0.0785338i
$280$	−309.277	−	911.101i	−1.10456	−	3.25393i
$281$	240.611	−	109.020i	0.856268	−	0.387970i	0.0638580	−	0.997959i	$-0.479660\pi$
$281$	240.611	−	109.020i	0.856268	−	0.387970i	0.792410	+	0.609989i	$0.208826\pi$
$282$	−296.031	+	38.9732i	−1.04976	+	0.138203i
$283$	42.7013	−	214.674i	0.150888	−	0.758565i	−0.829036	−	0.559195i	$-0.811110\pi$
$283$	42.7013	−	214.674i	0.150888	−	0.758565i	0.979924	−	0.199370i	$-0.0638896\pi$
$284$	155.921	−	96.9581i	0.549018	−	0.341402i
$285$	−207.719	+	775.219i	−0.728840	+	2.72007i
$286$	22.3898	−	683.938i	0.0782861	−	2.39139i
$287$	213.722	+	163.995i	0.744677	+	0.571411i
$288$	197.925	+	173.576i	0.687241	+	0.602694i
$289$	−239.931	+	118.321i	−0.830212	+	0.409415i
$290$		−	1388.10i		−	4.78656i
$291$	338.523	+	57.6605i	1.16331	+	0.198146i
$292$	13.2908			0.0455166
$293$	−157.401	−	319.178i	−0.537206	−	1.08935i	−0.981142	−	0.193287i	$-0.938085\pi$
$293$	−157.401	−	319.178i	−0.537206	−	1.08935i	0.443937	−	0.896058i	$-0.353582\pi$
$294$	93.7767	−	106.932i	0.318968	−	0.363714i
$295$	−214.244	+	279.208i	−0.726251	+	0.946468i
$296$	662.847	+	21.6994i	2.23935	+	0.0733087i
$297$	−227.593	−	60.9834i	−0.766307	−	0.205331i
$298$	39.8486	+	64.0818i	0.133720	+	0.215040i
$299$	−41.4399	−	8.24291i	−0.138595	−	0.0275683i
$300$	−106.851	−	811.614i	−0.356170	−	2.70538i
$301$	164.156	+	362.299i	0.545368	+	1.20365i
$302$	250.977	−	85.1953i	0.831051	−	0.282104i
$303$	−41.5286	−	208.778i	−0.137058	−	0.689038i
$304$	−980.385	−	1046.75i	−3.22495	−	3.44324i
$305$	−44.6154	+	71.7474i	−0.146280	+	0.235237i
$306$	41.8707	−	44.7049i	0.136833	−	0.146095i
$307$	56.5763	+	211.145i	0.184288	+	0.687770i	0.994782	+	0.102024i	$0.0325318\pi$
$307$	56.5763	+	211.145i	0.184288	+	0.687770i	−0.810494	+	0.585746i	$0.800801\pi$
$308$	732.860	−	170.879i	2.37942	−	0.554802i
$309$	187.987	−	125.609i	0.608373	−	0.406502i
$310$	727.661	−	388.943i	2.34729	−	1.25465i
$311$	160.523	−	195.597i	0.516150	−	0.628930i	−0.448081	−	0.893993i	$-0.647893\pi$
$311$	160.523	−	195.597i	0.516150	−	0.628930i	0.964231	+	0.265062i	$0.0853926\pi$
$312$	−1176.70	−	194.275i	−3.77149	−	0.622675i
$313$	−347.367	−	347.367i	−1.10980	−	1.10980i	−0.993176	−	0.116621i	$-0.962794\pi$
$313$	−347.367	−	347.367i	−1.10980	−	1.10980i	−0.116621	−	0.993176i	$-0.537206\pi$
$314$	41.7070	−	29.8868i	0.132825	−	0.0951809i
$315$	−120.288	+	92.3006i	−0.381868	+	0.293018i
$316$	977.655	+	64.0789i	3.09385	+	0.202781i
$317$	−125.596	+	333.700i	−0.396201	+	1.05268i	0.575777	+	0.817607i	$0.304700\pi$
$317$	−125.596	+	333.700i	−0.396201	+	1.05268i	−0.971978	+	0.235073i	$0.924467\pi$
$318$	−42.8611	−	28.6389i	−0.134783	−	0.0900594i
$319$	647.964	+	63.8189i	2.03124	+	0.200059i
$320$	652.013	+	295.423i	2.03754	+	0.923197i
$321$	186.957	+	56.7128i	0.582421	+	0.176675i
$322$	−4.25522	−	64.9221i	−0.0132150	−	0.201621i
$323$	−113.854	+	99.8476i	−0.352490	+	0.309126i
$324$	−383.631	+	926.167i	−1.18405	+	2.85854i
$325$	220.577	+	268.773i	0.678697	+	0.826995i
$326$	437.677	+	758.079i	1.34257	+	2.32539i
$327$	25.4373	+	14.6863i	0.0777900	+	0.0449121i
$328$	−963.375	+	159.054i	−2.93712	+	0.484921i
$329$	113.361	+	81.2335i	0.344563	+	0.246910i
$330$	1117.99	−	36.5991i	3.38784	−	0.110906i
$331$	−159.226	−	37.1263i	−0.481046	−	0.112164i	−0.0204810	−	0.999790i	$-0.506520\pi$
$331$	−159.226	−	37.1263i	−0.481046	−	0.112164i	−0.460565	+	0.887626i	$0.652353\pi$
$332$	−1045.72	+	393.581i	−3.14976	+	1.18549i
$333$	−30.3374	−	100.009i	−0.0911034	−	0.300328i
$334$	90.8583	+	11.9617i	0.272031	+	0.0358135i
$335$	234.712	−	691.441i	0.700634	−	2.06400i
$336$	−94.2097	−	956.527i	−0.280386	−	2.84681i
$337$	−44.6463	−	23.8639i	−0.132481	−	0.0708128i	0.403824	−	0.914837i	$-0.367681\pi$
$337$	−44.6463	−	23.8639i	−0.132481	−	0.0708128i	−0.536306	+	0.844024i	$0.680181\pi$
$338$	196.277	−	81.3005i	0.580700	−	0.240534i
$339$	−181.618	−	89.5640i	−0.535746	−	0.264201i
$340$	142.129	−	288.209i	0.418026	−	0.847673i
$341$	148.103	+	357.553i	0.434320	+	1.04854i
$342$	−203.558	+	380.829i	−0.595198	+	1.11354i
$343$	−367.740	+	36.2192i	−1.07213	+	0.105595i
$344$	−1365.16	−	463.410i	−3.96849	−	1.34712i
$345$	9.01493	−	68.4752i	0.0261302	−	0.198479i
$346$	−167.490	+	50.8076i	−0.484075	+	0.146843i
$347$	−72.6143	−	192.932i	−0.209263	−	0.555999i	0.789033	−	0.614351i	$-0.210582\pi$
$347$	−72.6143	−	192.932i	−0.209263	−	0.555999i	−0.998296	+	0.0583520i	$0.981415\pi$
$348$	429.655	−	1842.69i	1.23464	−	5.29509i
$349$	−0.0824225	−	2.51775i	−0.000236168	−	0.00721418i	0.999340	−	0.0363260i	$-0.0115655\pi$
$349$	−0.0824225	−	2.51775i	−0.000236168	−	0.00721418i	−0.999576	+	0.0291118i	$0.990732\pi$
$350$	−311.859	+	435.199i	−0.891027	+	1.24343i
$351$	−47.3745	−	286.943i	−0.134970	−	0.817503i
$352$	−453.571	+	785.609i	−1.28856	+	2.23184i
$353$	113.117	−	65.3084i	0.320446	−	0.185010i	−0.331145	−	0.943580i	$-0.607435\pi$
$353$	113.117	−	65.3084i	0.320446	−	0.185010i	0.651591	+	0.758570i	$0.274102\pi$
$354$	−519.259	+	426.145i	−1.46683	+	1.20380i
$355$	−117.774	−	48.7836i	−0.331758	−	0.137419i
$356$	338.861	+	386.397i	0.951857	+	1.08538i
$357$	−101.272	+	6.63769i	−0.283674	+	0.0185930i
$358$	207.085	−	682.668i	0.578450	−	1.90689i
$359$	32.4895	−	71.7058i	0.0904999	−	0.199738i	−0.860122	−	0.510088i	$-0.829613\pi$
$359$	32.4895	−	71.7058i	0.0904999	−	0.199738i	0.950622	+	0.310350i	$0.100446\pi$
$360$	53.8656	−	546.907i	0.149627	−	1.51919i
$361$	392.570	−	587.522i	1.08745	−	1.62749i
$362$	−965.303	−	363.314i	−2.66658	−	1.00363i
$363$	−6.29947	+	96.1113i	−0.0173539	+	0.264769i
$364$	565.438	+	736.893i	1.55340	+	2.02443i
$365$	−5.37492	−	7.50069i	−0.0147258	−	0.0205498i
$366$	−114.030	+	114.030i	−0.311556	+	0.311556i
$367$	39.2796	−	237.913i	0.107029	−	0.648264i	−0.878367	−	0.477986i	$-0.841367\pi$
$367$	39.2796	−	237.913i	0.107029	−	0.648264i	0.985396	−	0.170278i	$-0.0544666\pi$
$368$	95.4045	+	78.2964i	0.259251	+	0.212762i
$369$	72.5322	+	135.698i	0.196564	+	0.367746i
$370$	−426.548	−	638.374i	−1.15283	−	1.72533i
$371$	5.46734	+	23.4481i	0.0147368	+	0.0632026i
$372$	1086.35	−	291.086i	2.92029	−	0.782490i
$373$	−293.203	−	274.615i	−0.786068	−	0.736233i	0.182977	−	0.983117i	$-0.441427\pi$
$373$	−293.203	−	274.615i	−0.786068	−	0.736233i	−0.969045	+	0.246884i	$0.920593\pi$
$374$	179.235	+	111.456i	0.479239	+	0.298010i
$375$	33.3618	−	31.2468i	0.0889649	−	0.0833247i
$376$	−495.772	+	98.6152i	−1.31854	+	0.262275i
$377$	258.326	+	761.002i	0.685214	+	2.01857i
$378$	407.914	−	184.823i	1.07914	−	0.488950i
$379$	41.3991	−	5.45029i	0.109232	−	0.0143807i	−0.0757118	−	0.997130i	$-0.524123\pi$
$379$	41.3991	−	5.45029i	0.109232	−	0.0143807i	0.184944	+	0.982749i	$0.440790\pi$
$380$	−441.976	+	2221.97i	−1.16310	+	5.84728i
$381$	−72.0405	+	44.7977i	−0.189083	+	0.117579i
$382$	−258.421	+	964.441i	−0.676495	+	2.52471i
$383$	−16.3137	+	498.332i	−0.0425946	+	1.30113i	0.737449	+	0.675403i	$0.236030\pi$
$383$	−16.3137	+	498.332i	−0.0425946	+	1.30113i	−0.780043	+	0.625726i	$0.784803\pi$
$384$	246.811	+	189.385i	0.642737	+	0.493189i
$385$	−392.810	−	344.485i	−1.02028	−	0.894766i
$386$	−71.0909	+	35.0581i	−0.184173	+	0.0908242i
$387$			227.183i			0.587035i
$388$	964.187	+	99.9181i	2.48502	+	0.257521i
$389$	−600.079			−1.54262			−0.771310	−	0.636460i	$-0.780398\pi$
$389$	−600.079			−1.54262			−0.771310	+	0.636460i	$0.780398\pi$
$390$	610.655	+	1238.29i	1.56578	+	3.17509i
$391$	8.59254	−	9.79791i	0.0219758	−	0.0250586i
$392$	146.578	−	191.024i	0.373923	−	0.487306i
$393$	−530.926	−	17.3807i	−1.35096	−	0.0442257i
$394$	127.510	+	34.1661i	0.323628	+	0.0867159i
$395$	−359.208	−	577.654i	−0.909388	−	1.46241i
$396$	421.553	+	83.8521i	1.06453	+	0.211748i
$397$	12.1929	+	92.6144i	0.0307126	+	0.233286i	0.999916	−	0.0129769i	$-0.00413078\pi$
$397$	12.1929	+	92.6144i	0.0307126	+	0.233286i	−0.969203	+	0.246263i	$0.920797\pi$
$398$	250.000	+	551.761i	0.628140	+	1.38633i
$399$	677.522	−	229.988i	1.69805	−	0.576411i
$400$	−198.141	−	996.124i	−0.495353	−	2.49031i
$401$	233.049	+	248.824i	0.581169	+	0.620508i	0.951224	−	0.308502i	$-0.0998278\pi$
$401$	233.049	+	248.824i	0.581169	+	0.620508i	−0.370055	+	0.929010i	$0.620661\pi$
$402$	735.977	−	1183.55i	1.83079	−	2.94415i
$403$	−326.545	+	348.648i	−0.810284	+	0.865132i
$404$	−155.521	−	580.414i	−0.384954	−	1.43667i
$405$	677.825	−	158.047i	1.67364	−	0.390239i
$406$	−1028.95	+	687.521i	−2.53435	+	1.69340i
$407$	317.602	−	169.762i	0.780350	−	0.417106i
$408$	233.362	−	284.352i	0.571965	−	0.696941i
$409$	614.756	+	101.497i	1.50307	+	0.248158i	0.857078	−	0.515187i	$-0.172277\pi$
$409$	614.756	+	101.497i	1.50307	+	0.248158i	0.645992	+	0.763344i	$0.276444\pi$
$410$	799.288	+	799.288i	1.94948	+	1.94948i
$411$	355.805	−	254.967i	0.865706	−	0.620356i
$412$	506.328	−	388.519i	1.22895	−	0.943007i
$413$	313.080	+	20.5204i	0.758063	+	0.0496861i
$414$	13.0899	−	34.7790i	0.0316181	−	0.0840072i
$415$	645.015	+	430.985i	1.55425	+	1.03852i
$416$	−1114.29	−	109.748i	−2.67859	−	0.263818i
$417$	−276.433	−	125.250i	−0.662909	−	0.300360i
$418$	−1423.92	−	431.941i	−3.40650	−	1.03335i
$419$	35.1045	+	535.591i	0.0837815	+	1.27826i	0.808204	+	0.588903i	$0.200440\pi$
$419$	35.1045	+	535.591i	0.0837815	+	1.27826i	−0.724422	+	0.689356i	$0.757893\pi$
$420$	−1141.52	+	1001.09i	−2.71790	+	2.38354i
$421$	284.355	−	686.493i	0.675427	−	1.63063i	−0.0968192	−	0.995302i	$-0.530867\pi$
$421$	284.355	−	686.493i	0.675427	−	1.63063i	0.772246	−	0.635323i	$-0.219133\pi$
$422$	213.657	+	260.342i	0.506297	+	0.616924i
$423$	39.8279	+	68.9839i	0.0941557	+	0.163083i
$424$	−75.5766	−	43.6342i	−0.178247	−	0.102911i
$425$	−105.809	+	17.4692i	−0.248963	+	0.0411040i
$426$	−197.779	−	141.726i	−0.464270	−	0.332691i
$427$	75.2814	−	2.46446i	0.176303	−	0.00577156i
$428$	537.086	+	125.231i	1.25487	+	0.292596i
$429$	−606.105	+	228.122i	−1.41283	+	0.531752i
$430$	484.477	+	1597.11i	1.12669	+	3.71420i
$431$	489.007	+	64.3790i	1.13459	+	0.149371i	0.674341	−	0.738420i	$-0.264428\pi$
$431$	489.007	+	64.3790i	1.13459	+	0.149371i	0.460246	+	0.887792i	$0.347761\pi$
$432$	−273.070	+	804.438i	−0.632106	+	1.86212i
$433$	−57.7777	−	586.626i	−0.133436	−	1.35480i	−0.795776	−	0.605592i	$-0.792936\pi$
$433$	−57.7777	−	586.626i	−0.133436	−	1.35480i	0.662340	−	0.749204i	$-0.269564\pi$
$434$	−648.715	−	346.745i	−1.49473	−	0.798952i
$435$	−1213.68	+	502.722i	−2.79006	+	1.15568i
$436$	74.3626	+	36.6716i	0.170556	+	0.0841091i
$437$	−40.6351	+	82.3998i	−0.0929865	+	0.188558i
$438$	−6.74015	−	16.2722i	−0.0153885	−	0.0371511i
$439$	−43.2891	+	80.9883i	−0.0986085	+	0.184484i	−0.926388	−	0.376569i	$-0.877104\pi$
$439$	−43.2891	+	80.9883i	−0.0986085	+	0.184484i	0.827780	+	0.561053i	$0.189604\pi$
$440$	1884.57	−	185.614i	4.28312	−	0.421850i
$441$	−35.9292	−	12.1963i	−0.0814722	−	0.0276561i
$442$	−34.0041	+	258.287i	−0.0769324	+	0.584359i
$443$	117.898	−	35.7640i	0.266136	−	0.0807314i	−0.154397	−	0.988009i	$-0.549343\pi$
$443$	117.898	−	35.7640i	0.266136	−	0.0807314i	0.420532	+	0.907278i	$0.361843\pi$
$444$	−368.643	−	979.461i	−0.830277	−	2.20599i
$445$	81.0252	−	347.498i	0.182079	−	0.780895i
$446$	−41.3050	−	1261.74i	−0.0926121	−	2.82901i
$447$	41.5977	−	58.0495i	0.0930597	−	0.129865i
$448$	−103.953	−	629.633i	−0.232038	−	1.40543i
$449$	351.255	−	608.392i	0.782305	−	1.35499i	−0.148290	−	0.988944i	$-0.547377\pi$
$449$	351.255	−	608.392i	0.782305	−	1.35499i	0.930596	−	0.366049i	$-0.119290\pi$
$450$	−264.832	+	152.901i	−0.588517	+	0.339780i
$451$	−409.854	+	336.358i	−0.908767	+	0.745806i
$452$	−528.112	−	218.751i	−1.16839	−	0.483962i
$453$	−165.385	−	188.585i	−0.365088	−	0.416303i
$454$	182.764	−	11.9790i	0.402563	−	0.0263854i
$455$	187.198	−	617.110i	0.411425	−	1.35629i
$456$	−1070.29	+	2362.17i	−2.34712	+	5.18020i
$457$	−72.2079	+	733.139i	−0.158004	+	1.60424i	0.510060	+	0.860139i	$0.329623\pi$
$457$	−72.2079	+	733.139i	−0.158004	+	1.60424i	−0.668064	+	0.744104i	$0.732877\pi$
$458$	−445.695	+	667.030i	−0.973134	+	1.45640i
$459$	83.9521	+	31.5973i	0.182902	+	0.0688395i
$460$	12.7510	−	194.543i	0.0277197	−	0.422920i
$461$	−288.340	−	375.772i	−0.625466	−	0.815124i	0.367930	−	0.929853i	$-0.380066\pi$
$461$	−288.340	−	375.772i	−0.625466	−	0.815124i	−0.993397	+	0.114730i	$0.963400\pi$
$462$	−580.863	−	810.593i	−1.25728	−	1.75453i
$463$	142.934	−	142.934i	0.308712	−	0.308712i	−0.535698	−	0.844410i	$-0.679951\pi$
$463$	142.934	−	142.934i	0.308712	−	0.308712i	0.844410	+	0.535698i	$0.179951\pi$
$464$	382.398	−	2316.15i	0.824134	−	4.99170i
$465$	−603.602	−	495.363i	−1.29807	−	1.06530i
$466$	17.2256	+	32.2269i	0.0369649	+	0.0691564i
$467$	127.349	+	190.591i	0.272696	+	0.408118i	0.942389	−	0.334520i	$-0.108574\pi$
$467$	127.349	+	190.591i	0.272696	+	0.408118i	−0.669693	+	0.742638i	$0.733574\pi$
$468$	120.468	+	516.658i	0.257410	+	1.10397i
$469$	−628.790	+	168.484i	−1.34070	+	0.359241i
$470$	427.103	+	400.026i	0.908731	+	0.851119i
$471$	−41.2361	−	25.6423i	−0.0875501	−	0.0544421i
$472$	−830.005	+	777.384i	−1.75848	+	1.64700i
$473$	−767.801	+	152.725i	−1.62326	+	0.322886i
$474$	−417.343	−	1229.45i	−0.880471	−	2.59378i
$475$	688.660	−	312.028i	1.44981	−	0.656901i
$476$	−284.034	+	37.3937i	−0.596709	+	0.0785583i
$477$	−2.68288	+	13.4878i	−0.00562449	+	0.0282762i
$478$	−732.946	+	455.775i	−1.53336	+	0.953504i
$479$	8.38783	−	31.3038i	0.0175111	−	0.0653524i	−0.956617	−	0.291347i	$-0.905897\pi$
$479$	8.38783	−	31.3038i	0.0175111	−	0.0653524i	0.974129	+	0.225995i	$0.0725632\pi$
$480$	59.8849	−	1829.30i	0.124760	−	3.81103i
$481$	352.648	+	270.596i	0.733156	+	0.562570i
$482$	1137.42	+	997.495i	2.35980	+	2.06949i
$483$	−55.2231	+	27.2330i	−0.114333	+	0.0563830i
$484$			271.887i			0.561749i
$485$	−333.536	−	584.546i	−0.687702	−	1.20525i
$486$	676.865			1.39273
$487$	−50.1495	−	101.693i	−0.102976	−	0.208815i	0.839287	−	0.543689i	$-0.182973\pi$
$487$	−50.1495	−	101.693i	−0.102976	−	0.208815i	−0.942263	+	0.334874i	$0.891306\pi$
$488$	−180.005	+	205.257i	−0.368864	+	0.420608i
$489$	504.309	−	657.229i	1.03131	−	1.34403i
$490$	−278.594	−	9.12022i	−0.568559	−	0.0186127i
$491$	−800.562	−	214.510i	−1.63047	−	0.436884i	−0.676418	−	0.736518i	$-0.736469\pi$
$491$	−800.562	−	214.510i	−1.63047	−	0.436884i	−0.954054	+	0.299635i	$0.903135\pi$
$492$	813.644	+	1308.45i	1.65375	+	2.65944i
$493$	−243.112	−	48.3579i	−0.493127	−	0.0980890i
$494$	−239.728	−	1820.91i	−0.485279	−	3.68606i
$495$	−123.157	−	271.814i	−0.248802	−	0.549119i
$496$	1321.30	−	448.521i	2.66391	−	0.904277i
$497$	22.1715	+	111.464i	0.0446106	+	0.224273i
$498$	1012.18	+	1080.69i	2.03249	+	2.17007i
$499$	−299.007	+	480.843i	−0.599213	+	0.963613i	0.399684	+	0.916653i	$0.369120\pi$
$499$	−299.007	+	480.843i	−0.599213	+	0.963613i	−0.998897	+	0.0469596i	$0.985047\pi$
$500$	88.2039	−	94.1743i	0.176408	−	0.188349i
$501$	−22.4470	−	83.7734i	−0.0448044	−	0.167212i
$502$	1483.32	−	345.862i	2.95483	−	0.688969i
$503$	398.748	−	266.435i	0.792740	−	0.529692i	−0.0920101	−	0.995758i	$-0.529329\pi$
$503$	398.748	−	266.435i	0.792740	−	0.529692i	0.884750	+	0.466066i	$0.154329\pi$
$504$	−432.080	+	230.952i	−0.857302	+	0.458238i
$505$	−264.663	+	322.492i	−0.524084	+	0.638599i
$506$	126.341	+	20.8590i	0.249686	+	0.0412233i
$507$	−142.169	−	142.169i	−0.280412	−	0.280412i
$508$	−194.651	+	139.485i	−0.383171	+	0.274577i
$509$	246.735	−	189.326i	0.484744	−	0.371957i	−0.337285	−	0.941403i	$-0.609509\pi$
$509$	246.735	−	189.326i	0.484744	−	0.371957i	0.822029	+	0.569445i	$0.192842\pi$
$510$	−424.935	−	27.8517i	−0.833207	−	0.0546112i
$511$	−2.89780	+	7.69927i	−0.00567084	+	0.0150671i
$512$	−553.397	−	369.768i	−1.08085	−	0.722203i
$513$	−629.347	−	61.9853i	−1.22680	−	0.120829i
$514$	569.960	+	258.245i	1.10887	+	0.502423i
$515$	−424.023	−	128.626i	−0.823346	−	0.249759i
$516$	148.790	+	2270.10i	0.288353	+	4.39941i
$517$	−206.368	+	180.980i	−0.399164	+	0.350057i
$518$	−261.935	+	632.367i	−0.505666	+	1.22079i
$519$	105.082	+	128.043i	0.202470	+	0.246711i
$520$	1168.69	+	2024.23i	2.24748	+	3.89276i
$521$	−654.351	−	377.790i	−1.25595	−	0.725124i	−0.283666	−	0.958923i	$-0.591551\pi$
$521$	−654.351	−	377.790i	−1.25595	−	0.725124i	−0.972285	+	0.233799i	$0.924884\pi$
$522$	−697.378	+	115.138i	−1.33597	+	0.220570i
$523$	525.514	+	376.578i	1.00481	+	0.720034i	0.960298	−	0.278975i	$-0.0899945\pi$
$523$	525.514	+	376.578i	1.00481	+	0.720034i	0.0445084	+	0.999009i	$0.485828\pi$
$524$	−1498.71	+	49.0625i	−2.86013	+	0.0936308i
$525$	493.458	+	115.058i	0.939919	+	0.219158i
$526$	903.206	−	339.943i	1.71712	−	0.646279i
$527$	−42.7694	−	140.992i	−0.0811563	−	0.267537i
$528$	1875.52	+	246.917i	3.55213	+	0.467647i
$529$	−167.500	+	493.439i	−0.316635	+	0.932777i
$530$	9.90243	+	100.541i	0.0186838	+	0.189700i
$531$	158.044	+	84.4761i	0.297634	+	0.159089i
$532$	1865.97	−	772.908i	3.50745	−	1.45284i
$533$	−586.942	−	289.448i	−1.10120	−	0.543054i
$534$	301.226	−	610.825i	0.564093	−	1.14387i
$535$	−146.528	−	353.749i	−0.273883	−	0.661213i
$536$	1112.25	−	2080.87i	2.07509	−	3.88221i
$537$	−671.885	+	66.1749i	−1.25118	+	0.123231i
$538$	−540.958	−	183.630i	−1.00550	−	0.341320i
$539$	17.0658	−	129.628i	0.0316620	−	0.240497i
$540$	1284.17	−	389.550i	2.37810	−	0.721388i
$541$	−10.4897	−	27.8704i	−0.0193894	−	0.0515164i	0.925857	−	0.377875i	$-0.123345\pi$
$541$	−10.4897	−	27.8704i	−0.0193894	−	0.0515164i	−0.945246	+	0.326358i	$0.894178\pi$
$542$	−207.037	+	887.935i	−0.381988	+	1.63826i
$543$	31.9373	+	975.585i	0.0588165	+	1.79666i
$544$	201.159	−	280.717i	0.369777	−	0.516024i
$545$	−9.37718	−	56.7968i	−0.0172058	−	0.104214i
$546$	615.439	−	1065.97i	1.12718	−	1.95233i
$547$	−22.9158	+	13.2304i	−0.0418935	+	0.0241872i	−0.520800	−	0.853678i	$-0.674366\pi$
$547$	−22.9158	+	13.2304i	−0.0418935	+	0.0241872i	0.478907	+	0.877866i	$0.341033\pi$
$548$	955.151	−	783.872i	1.74298	−	1.43042i
$549$	39.7463	+	16.4634i	0.0723976	+	0.0299881i
$550$	−694.789	−	792.255i	−1.26325	−	1.44046i
$551$	1743.76	−	114.292i	3.16473	−	0.207427i
$552$	64.7838	−	213.563i	0.117362	−	0.386890i
$553$	−250.278	+	552.376i	−0.452583	+	0.998872i
$554$	23.2440	−	236.000i	0.0419566	−	0.425993i
$555$	−403.677	+	604.145i	−0.727346	+	1.08855i
$556$	−801.772	−	301.766i	−1.44204	−	0.542744i
$557$	−43.6267	+	665.616i	−0.0783245	+	1.19500i	0.760035	+	0.649883i	$0.225182\pi$
$557$	−43.6267	+	665.616i	−0.0783245	+	1.19500i	−0.838359	+	0.545118i	$0.816485\pi$
$558$	−255.760	−	333.313i	−0.458351	−	0.597335i
$559$	−562.827	−	785.424i	−1.00685	−	1.40505i
$560$	−1331.99	+	1331.99i	−2.37855	+	2.37855i
$561$	32.5378	−	197.079i	0.0579996	−	0.351299i
$562$	−763.850	−	626.875i	−1.35916	−	1.11544i
$563$	147.503	+	275.959i	0.261995	+	0.490158i	0.978182	−	0.207751i	$-0.0666142\pi$
$563$	147.503	+	275.959i	0.261995	+	0.490158i	−0.716187	+	0.697908i	$0.754114\pi$
$564$	443.156	+	663.229i	0.785737	+	1.17594i
$565$	90.1202	+	386.504i	0.159505	+	0.684078i
$566$	−790.877	+	211.915i	−1.39731	+	0.374408i
$567$	−452.877	−	424.166i	−0.798726	−	0.748088i
$568$	−349.802	−	217.521i	−0.615849	−	0.382959i
$569$	587.434	−	550.192i	1.03240	−	0.966946i	0.0329262	−	0.999458i	$-0.489517\pi$
$569$	587.434	−	550.192i	1.03240	−	0.966946i	0.999471	+	0.0325120i	$0.0103507\pi$
$570$	2944.52	−	585.702i	5.16583	−	1.02755i
$571$	−214.188	−	630.979i	−0.375111	−	1.10504i	−0.956579	−	0.291473i	$-0.905855\pi$
$571$	−214.188	−	630.979i	−0.375111	−	1.10504i	0.581468	−	0.813569i	$-0.302479\pi$
$572$	−1665.14	+	754.467i	−2.91109	+	1.31900i
$573$	936.843	−	123.338i	1.63498	−	0.215249i
$574$	196.598	−	988.364i	0.342505	−	1.72189i
$575$	−55.2518	+	34.3578i	−0.0960901	+	0.0597527i
$576$	94.3376	−	352.073i	0.163781	−	0.611237i
$577$	−33.6268	+	1027.19i	−0.0582788	+	1.78023i	0.425419	+	0.904997i	$0.360127\pi$
$577$	−33.6268	+	1027.19i	−0.0582788	+	1.78023i	−0.483698	+	0.875235i	$0.660707\pi$
$578$	793.931	+	609.205i	1.37358	+	1.05399i
$579$	56.3994	+	49.4609i	0.0974083	+	0.0854248i
$580$	−3325.84	+	1640.12i	−5.73421	+	2.82780i
$581$		−	691.589i		−	1.19034i
$582$	−366.634	−	1231.14i	−0.629956	−	2.11536i
$583$	−47.3876			−0.0812824
$584$	−13.1879	−	26.7424i	−0.0225820	−	0.0457918i
$585$	242.858	−	276.926i	0.415141	−	0.473378i
$586$	−810.419	+	1056.16i	−1.38297	+	1.80232i
$587$	742.785	+	24.3163i	1.26539	+	0.0414246i	0.658024	−	0.752997i	$-0.271392\pi$
$587$	742.785	+	24.3163i	1.26539	+	0.0414246i	0.607367	+	0.794421i	$0.292226\pi$
$588$	−367.007	−	98.3392i	−0.624161	−	0.167244i
$589$	548.511	+	882.078i	0.931259	+	1.49759i
$590$	1291.21	+	256.837i	2.18848	+	0.435317i
$591$	−16.3066	−	123.861i	−0.0275915	−	0.209578i
$592$	−535.865	−	1182.68i	−0.905177	−	1.99777i
$593$	−499.299	+	169.489i	−0.841988	+	0.285816i	−0.708919	−	0.705290i	$-0.750817\pi$
$593$	−499.299	+	169.489i	−0.841988	+	0.285816i	−0.133069	+	0.991107i	$0.542483\pi$
$594$	171.953	+	864.469i	0.289484	+	1.45533i
$595$	135.968	+	145.172i	0.228518	+	0.243987i
$596$	106.454	−	171.192i	0.178614	−	0.287235i
$597$	391.887	−	418.414i	0.656427	−	0.700860i
$598$	40.9073	+	152.668i	0.0684069	+	0.255298i
$599$	−1003.22	+	233.918i	−1.67482	+	0.390514i	−0.953335	−	0.301914i	$-0.902374\pi$
$599$	−1003.22	+	233.918i	−1.67482	+	0.390514i	−0.721487	+	0.692428i	$0.756541\pi$
$600$	−1527.02	+	1020.32i	−2.54503	+	1.70054i
$601$	−182.888	+	97.7555i	−0.304306	+	0.162655i	−0.616481	−	0.787370i	$-0.711442\pi$
$601$	−182.888	+	97.7555i	−0.304306	+	0.162655i	0.312175	+	0.950024i	$0.398942\pi$
$602$	943.914	−	1150.16i	1.56796	−	1.91057i
$603$	−366.846	−	60.5665i	−0.608367	−	0.100442i
$604$	−500.669	−	500.669i	−0.828922	−	0.828922i
$605$	153.439	−	109.953i	0.253619	−	0.181741i
$606$	−631.740	+	484.751i	−1.04248	+	0.799919i
$607$	679.273	+	44.5219i	1.11907	+	0.0733474i	0.613686	−	0.789550i	$-0.289686\pi$
$607$	679.273	+	44.5219i	1.11907	+	0.0733474i	0.505379	+	0.862897i	$0.331353\pi$
$608$	−857.626	+	2278.66i	−1.41057	+	3.74779i
$609$	973.777	+	650.657i	1.59898	+	1.06840i
$610$	314.528	+	30.9783i	0.515619	+	0.0507840i
$611$	−308.596	−	139.823i	−0.505068	−	0.228843i
$612$	−156.584	−	47.4992i	−0.255856	−	0.0776131i
$613$	52.4604	+	800.391i	0.0855797	+	1.30569i	0.797451	+	0.603384i	$0.206181\pi$
$613$	52.4604	+	800.391i	0.0855797	+	1.30569i	−0.711871	+	0.702310i	$0.752152\pi$
$614$	614.785	−	539.152i	1.00128	−	0.878098i
$615$	409.378	−	988.325i	0.665655	−	1.60703i
$616$	−1071.01	−	1305.03i	−1.73865	−	2.11855i
$617$	235.994	+	408.753i	0.382486	+	0.662484i	0.991417	−	0.130739i	$-0.0417349\pi$
$617$	235.994	+	408.753i	0.382486	+	0.662484i	−0.608931	+	0.793223i	$0.708402\pi$
$618$	−732.442	−	422.875i	−1.18518	−	0.684264i
$619$	615.504	−	101.620i	0.994353	−	0.164168i	0.356474	−	0.934305i	$-0.383979\pi$
$619$	615.504	−	101.620i	0.994353	−	0.164168i	0.637879	+	0.770137i	$0.279812\pi$
$620$	−1791.66	−	1283.89i	−2.88978	−	2.07079i
$621$	54.3924	−	1.78062i	0.0875884	−	0.00286735i
$622$	−921.811	−	214.936i	−1.48201	−	0.345556i
$623$	−297.718	+	112.053i	−0.477879	+	0.179861i
$624$	677.796	+	2234.39i	1.08621	+	3.58076i
$625$	−662.345	−	87.1994i	−1.05975	−	0.139519i
$626$	−590.694	+	1740.13i	−0.943600	+	2.77976i
$627$	138.028	+	1401.43i	0.220141	+	2.23513i
$628$	−120.887	−	64.6153i	−0.192495	−	0.102891i
$629$	−126.664	+	52.4660i	−0.201374	+	0.0834118i
$630$	508.684	+	250.855i	0.807435	+	0.398183i
$631$	−343.492	+	696.534i	−0.544362	+	1.10386i	0.434753	+	0.900550i	$0.356836\pi$
$631$	−343.492	+	696.534i	−0.544362	+	1.10386i	−0.979115	+	0.203307i	$0.934831\pi$
$632$	−841.150	−	2030.72i	−1.33093	−	3.21316i
$633$	150.249	−	281.096i	0.237360	−	0.444070i
$634$	1327.36	−	130.733i	2.09362	−	0.206204i
$635$	157.437	+	53.4426i	0.247932	+	0.0841615i
$636$	−17.9748	+	136.532i	−0.0282622	+	0.214673i
$637$	154.431	−	46.8462i	0.242435	−	0.0735419i
$638$	−857.943	−	2279.50i	−1.34474	−	3.57288i
$639$	−14.7398	+	63.2156i	−0.0230670	+	0.0989290i
$640$	−19.9490	−	609.379i	−0.0311703	−	0.952155i
$641$	375.430	−	523.912i	0.585694	−	0.817335i	−0.409799	−	0.912176i	$-0.634401\pi$
$641$	375.430	−	523.912i	0.585694	−	0.817335i	0.995492	+	0.0948413i	$0.0302344\pi$
$642$	−119.049	−	721.070i	−0.185435	−	1.12316i
$643$	27.2663	−	47.2267i	0.0424049	−	0.0734474i	−0.844044	−	0.536274i	$-0.819831\pi$
$643$	27.2663	−	47.2267i	0.0424049	−	0.0734474i	0.886449	+	0.462827i	$0.153165\pi$
$644$	−150.523	+	86.9045i	−0.233731	+	0.134945i
$645$	1220.96	−	1002.01i	1.89296	−	1.55351i
$646$	523.359	+	216.782i	0.810153	+	0.335576i
$647$	46.5507	+	53.0809i	0.0719485	+	0.0820415i	0.786694	−	0.617343i	$-0.211791\pi$
$647$	46.5507	+	53.0809i	0.0719485	+	0.0820415i	−0.714746	+	0.699384i	$0.753458\pi$
$648$	2244.19	−	147.092i	3.46326	−	0.226994i
$649$	−179.255	+	590.924i	−0.276202	+	0.910515i
$650$	536.788	−	1184.72i	0.825827	−	1.82264i
$651$	−68.2327	+	692.778i	−0.104812	+	1.06417i
$652$	1299.19	−	1944.37i	1.99262	−	2.98216i
$653$	25.8221	+	9.71874i	0.0395438	+	0.0148832i	0.371943	−	0.928255i	$-0.378692\pi$
$653$	25.8221	+	9.71874i	0.0395438	+	0.0148832i	−0.332400	+	0.943139i	$0.607858\pi$
$654$	7.18620	−	109.640i	0.0109881	−	0.167646i
$655$	633.776	+	825.953i	0.967597	+	1.26100i
$656$	1113.48	+	1553.86i	1.69738	+	2.36869i
$657$	−3.32249	+	3.32249i	−0.00505706	+	0.00505706i
$658$	84.9816	−	514.726i	0.129151	−	0.782259i
$659$	758.404	+	622.406i	1.15084	+	0.944471i	0.999034	−	0.0439392i	$-0.0139908\pi$
$659$	758.404	+	622.406i	1.15084	+	0.944471i	0.151807	+	0.988410i	$0.451491\pi$
$660$	−1408.66	−	2635.41i	−2.13433	−	3.99304i
$661$	−629.128	−	941.556i	−0.951782	−	1.42444i	−0.904940	−	0.425539i	$-0.860084\pi$
$661$	−629.128	−	941.556i	−0.951782	−	1.42444i	−0.0468416	−	0.998902i	$-0.514916\pi$
$662$	138.881	+	595.627i	0.209790	+	0.899739i
$663$	238.146	−	63.8111i	0.359195	−	0.0962460i
$664$	1829.54	+	1713.55i	2.75534	+	2.58065i
$665$	−1190.80	−	740.488i	−1.79068	−	1.11352i
$666$	−285.336	+	267.246i	−0.428433	+	0.401271i
$667$	−147.495	+	29.3385i	−0.221132	+	0.0439858i
$668$	−78.6944	−	231.826i	−0.117806	−	0.347045i
$669$	−1088.23	+	493.071i	−1.62665	+	0.737027i
$670$	−2708.11	+	356.529i	−4.04195	+	0.532133i
$671$	−28.9212	+	145.397i	−0.0431016	+	0.216687i
$672$	−1385.65	+	861.651i	−2.06197	+	1.28222i
$673$	186.532	−	696.147i	0.277165	−	1.03439i	−0.677212	−	0.735788i	$-0.736812\pi$
$673$	186.532	−	696.147i	0.277165	−	1.03439i	0.954377	−	0.298605i	$-0.0965214\pi$
$674$	−6.19607	+	189.270i	−0.00919299	+	0.280817i
$675$	−355.298	−	272.630i	−0.526368	−	0.403896i
$676$	−426.705	−	374.210i	−0.631220	−	0.553565i
$677$	864.832	−	426.488i	1.27745	−	0.629967i	0.328233	−	0.944597i	$-0.393547\pi$
$677$	864.832	−	426.488i	1.27745	−	0.629967i	0.949215	+	0.314629i	$0.101880\pi$
$678$			757.509i			1.11727i
$679$	−268.103	+	536.760i	−0.394850	+	0.790515i
$680$	−720.930			−1.06019
$681$	−76.6642	−	155.460i	−0.112576	−	0.228281i
$682$	954.548	−	1088.45i	1.39963	−	1.59597i
$683$	−707.448	+	921.964i	−1.03579	+	1.34987i	−0.100920	+	0.994895i	$0.532179\pi$
$683$	−707.448	+	921.964i	−1.03579	+	1.34987i	−0.934874	+	0.354979i	$0.884488\pi$
$684$	1152.97	+	37.7442i	1.68562	+	0.0551816i
$685$	−828.648	−	222.036i	−1.20971	−	0.324140i
$686$	729.940	+	1173.84i	1.06405	+	1.71114i
$687$	744.628	+	148.116i	1.08388	+	0.215598i
$688$	368.410	+	2798.35i	0.535480	+	4.06737i
$689$	−24.1395	−	53.2769i	−0.0350355	−	0.0773250i
$690$	−244.649	+	83.0470i	−0.354563	+	0.120358i
$691$	−117.659	−	591.510i	−0.170273	−	0.856021i	−0.967603	−	0.252477i	$-0.918755\pi$
$691$	−117.659	−	591.510i	−0.170273	−	0.856021i	0.797330	−	0.603544i	$-0.206245\pi$
$692$	319.632	+	341.268i	0.461896	+	0.493161i
$693$	−140.486	+	225.920i	−0.202721	+	0.326002i
$694$	−527.143	+	562.825i	−0.759572	+	0.810987i
$695$	153.941	+	574.516i	0.221498	+	0.826642i
$696$	−4133.99	+	963.911i	−5.93964	+	1.38493i
$697$	167.832	−	112.142i	0.240792	−	0.160892i
$698$	−8.31064	+	4.44213i	−0.0119064	+	0.00636408i
$699$	21.9388	−	26.7325i	0.0313860	−	0.0382440i
$700$	1411.20	+	232.990i	2.01600	+	0.332843i
$701$	−29.7089	−	29.7089i	−0.0423807	−	0.0423807i	0.685599	−	0.727980i	$-0.259540\pi$
$701$	−29.7089	−	29.7089i	−0.0423807	−	0.0423807i	−0.727980	+	0.685599i	$0.759540\pi$
$702$	−884.310	+	633.688i	−1.25970	+	0.902689i
$703$	766.818	−	588.400i	1.09078	−	0.836984i
$704$	1253.31	+	82.1460i	1.78026	+	0.116685i
$705$	195.078	−	518.310i	0.276706	−	0.735191i
$706$	−406.261	−	271.455i	−0.575441	−	0.384497i
$707$	370.137	+	36.4553i	0.523532	+	0.0515634i
$708$	1634.56	+	740.610i	2.30870	+	1.04606i
$709$	653.807	+	198.330i	0.922154	+	0.279732i	0.715444	−	0.698670i	$-0.246224\pi$
$709$	653.807	+	198.330i	0.922154	+	0.279732i	0.206710	+	0.978402i	$0.433724\pi$
$710$	31.1884	+	475.843i	0.0439273	+	0.670201i
$711$	−260.416	+	228.379i	−0.366267	+	0.321208i
$712$	441.230	−	1065.22i	0.619705	−	1.49610i
$713$	−56.7073	−	69.0980i	−0.0795333	−	0.0969116i
$714$	189.823	+	328.783i	0.265858	+	0.460480i
$715$	1099.18	+	634.612i	1.53731	+	0.887569i
$716$	−1880.33	+	310.444i	−2.62616	+	0.433580i
$717$	663.950	+	475.780i	0.926011	+	0.663570i
$718$	−294.326	+	9.63523i	−0.409925	+	0.0134195i
$719$	438.918	+	102.341i	0.610456	+	0.142338i	0.520863	−	0.853640i	$-0.325610\pi$
$719$	438.918	+	102.341i	0.610456	+	0.142338i	0.0895929	+	0.995978i	$0.471443\pi$
$720$	−1006.95	+	378.991i	−1.39855	+	0.526376i
$721$	114.671	+	378.020i	0.159044	+	0.524299i
$722$	−2620.64	−	345.013i	−3.62969	−	0.477858i
$723$	460.217	−	1355.76i	0.636538	−	1.87518i
$724$	270.074	+	2742.10i	0.373030	+	3.78744i
$725$	1091.41	+	583.372i	1.50540	+	0.804651i
$726$	332.875	−	137.881i	0.458505	−	0.189919i
$727$	607.949	+	299.807i	0.836243	+	0.412390i	0.809405	−	0.587250i	$-0.199790\pi$
$727$	607.949	+	299.807i	0.836243	+	0.412390i	0.0268379	+	0.999640i	$0.491456\pi$
$728$	921.639	−	1868.90i	1.26599	−	2.56717i
$729$	100.363	+	242.297i	0.137672	+	0.332369i
$730$	−16.2719	+	30.4426i	−0.0222903	+	0.0417022i
$731$	296.594	−	29.2120i	0.405738	−	0.0399617i
$732$	407.943	+	138.478i	0.557299	+	0.189178i
$733$	113.800	−	864.393i	0.155252	−	1.17925i	−0.719433	−	0.694562i	$-0.755598\pi$
$733$	113.800	−	864.393i	0.155252	−	1.17925i	0.874685	−	0.484692i	$-0.161068\pi$
$734$	−863.183	+	261.844i	−1.17600	+	0.356735i
$735$	92.9226	+	246.889i	0.126425	+	0.335904i
$736$	47.5776	−	204.049i	0.0646435	−	0.277241i
$737$	−41.9202	−	1280.53i	−0.0568795	−	1.73749i
$738$	335.261	−	467.857i	0.454284	−	0.633952i
$739$	−211.769	−	1282.66i	−0.286561	−	1.73568i	−0.612666	−	0.790342i	$-0.709903\pi$
$739$	−211.769	−	1282.66i	−0.286561	−	1.73568i	0.326105	−	0.945334i	$-0.394264\pi$
$740$	−1025.53	+	1776.27i	−1.38585	+	2.40036i
$741$	−1505.28	+	869.075i	−2.03142	+	1.17284i
$742$	69.6225	−	57.1377i	0.0938309	−	0.0770050i
$743$	228.775	+	94.7617i	0.307907	+	0.127539i	0.531286	−	0.847192i	$-0.321709\pi$
$743$	228.775	+	94.7617i	0.307907	+	0.127539i	−0.223379	+	0.974732i	$0.571709\pi$
$744$	−1663.63	−	1897.00i	−2.23606	−	2.54973i
$745$	−139.663	+	9.15400i	−0.187467	+	0.0122872i
$746$	−436.226	+	1438.04i	−0.584753	+	1.92767i
$747$	163.024	−	359.801i	0.218238	−	0.481662i
$748$	55.2667	−	561.132i	0.0738860	−	0.750177i
$749$	−189.646	+	283.825i	−0.253199	+	0.378939i
$750$	−160.030	−	60.2309i	−0.213373	−	0.0803078i
$751$	73.6059	−	1123.01i	0.0980106	−	1.49535i	−0.611830	−	0.790990i	$-0.709566\pi$
$751$	73.6059	−	1123.01i	0.0980106	−	1.49535i	0.709840	−	0.704363i	$-0.248767\pi$
$752$	602.453	+	785.132i	0.801134	+	1.04406i
$753$	−839.609	−	1171.67i	−1.11502	−	1.55601i
$754$	2125.75	−	2125.75i	2.81930	−	2.81930i
$755$	−80.0782	+	485.027i	−0.106064	+	0.642419i
$756$	−924.803	−	758.966i	−1.22328	−	1.00392i
$757$	−120.794	−	225.989i	−0.159569	−	0.298533i	0.789413	−	0.613862i	$-0.210385\pi$
$757$	−120.794	−	225.989i	−0.159569	−	0.298533i	−0.948982	+	0.315329i	$0.897885\pi$
$758$	−86.7803	−	129.876i	−0.114486	−	0.171340i
$759$	−27.5183	−	118.020i	−0.0362560	−	0.155494i
$760$	4909.35	−	1315.46i	6.45968	−	1.73086i
$761$	101.416	+	94.9869i	0.133267	+	0.124818i	0.747371	−	0.664407i	$-0.231316\pi$
$761$	101.416	+	94.9869i	0.133267	+	0.124818i	−0.614104	+	0.789225i	$0.710482\pi$
$762$	269.486	+	167.577i	0.353657	+	0.219918i
$763$	−37.4568	+	35.0821i	−0.0490915	+	0.0459792i
$764$	2616.10	−	520.375i	3.42422	−	0.681119i
$765$	36.5175	+	107.577i	0.0477353	+	0.140624i
$766$	1698.89	−	769.757i	2.21787	−	1.00490i
$767$	−755.677	+	99.4868i	−0.985237	+	0.129709i
$768$	−57.9849	+	291.510i	−0.0755011	+	0.379570i
$769$	−821.995	+	511.150i	−1.06891	+	0.664694i	−0.944824	−	0.327577i	$-0.893768\pi$
$769$	−821.995	+	511.150i	−1.06891	+	0.664694i	−0.124090	+	0.992271i	$0.539601\pi$
$770$	−505.840	+	1887.82i	−0.656935	+	2.45171i
$771$	19.3757	−	591.867i	0.0251307	−	0.767662i
$772$	167.996	+	128.908i	0.217611	+	0.166979i
$773$	653.511	+	573.113i	0.845421	+	0.741415i	0.967975	−	0.251047i	$-0.0807750\pi$
$773$	653.511	+	573.113i	0.845421	+	0.741415i	−0.122554	+	0.992462i	$0.539108\pi$
$774$	762.195	−	375.873i	0.984748	−	0.485624i
$775$			735.590i			0.949149i
$776$	−755.674	−	2039.18i	−0.973806	−	2.62781i
$777$	647.769			0.833679
$778$	992.828	+	2013.26i	1.27613	+	2.58773i
$779$	−938.271	+	1069.89i	−1.20446	+	1.37342i
$780$	2245.36	−	2926.21i	2.87867	−	3.75155i
$781$	−223.556	−	7.31848i	−0.286244	−	0.00937065i
$782$	−47.0882	−	12.6172i	−0.0602151	−	0.0161346i
$783$	−546.618	−	879.033i	−0.698107	−	1.12265i
$784$	−462.341	−	91.9654i	−0.589721	−	0.117303i
$785$	12.4219	+	94.3534i	0.0158240	+	0.120195i
$786$	820.103	+	1810.01i	1.04339	+	2.30281i
$787$	−858.816	+	291.529i	−1.09125	+	0.370430i	−0.808340	−	0.588716i	$-0.799634\pi$
$787$	−858.816	+	291.529i	−1.09125	+	0.370430i	−0.282912	+	0.959146i	$0.591301\pi$
$788$	−68.7992	−	345.877i	−0.0873086	−	0.438930i
$789$	−624.335	−	666.596i	−0.791300	−	0.844862i
$790$	−1343.71	+	2160.87i	−1.70090	+	2.73527i
$791$	241.865	−	258.236i	0.305771	−	0.326468i
$792$	−249.569	−	931.406i	−0.315113	−	1.17602i
$793$	−178.199	+	41.5502i	−0.224715	+	0.0523962i
$794$	290.547	−	194.137i	0.365928	−	0.244505i
$795$	84.3210	−	45.0705i	0.106064	−	0.0566925i
$796$	1026.61	−	1250.93i	1.28971	−	1.57152i
$797$	43.2275	+	7.13688i	0.0542377	+	0.00895469i	0.189953	−	0.981793i	$-0.439167\pi$
$797$	43.2275	+	7.13688i	0.0542377	+	0.00895469i	−0.135715	+	0.990748i	$0.543333\pi$
$798$	−1892.57	−	1892.57i	−2.37164	−	2.37164i
$799$	84.9395	−	60.8667i	0.106307	−	0.0761787i
$800$	−1367.90	+	1049.63i	−1.70987	+	1.31203i
$801$	−181.302	−	11.8832i	−0.226345	−	0.0148354i
$802$	449.222	−	1193.55i	0.560127	−	1.48822i
$803$	−13.4625	−	8.99532i	−0.0167652	−	0.0112021i
$804$	−3705.33	−	364.943i	−4.60862	−	0.453910i
$805$	109.917	+	49.8028i	0.136543	+	0.0618669i
$806$	1709.98	+	518.716i	2.12156	+	0.643568i
$807$	35.3598	+	539.487i	0.0438164	+	0.668509i
$808$	−1013.53	+	888.842i	−1.25437	+	1.10005i
$809$	55.8915	−	134.934i	0.0690872	−	0.166791i	−0.885564	−	0.464517i	$-0.846228\pi$
$809$	55.8915	−	134.934i	0.0690872	−	0.166791i	0.954651	+	0.297726i	$0.0962280\pi$
$810$	−1651.70	−	2012.61i	−2.03914	−	2.48470i
$811$	74.1121	+	128.366i	0.0913836	+	0.158281i	0.908094	−	0.418767i	$-0.137538\pi$
$811$	74.1121	+	128.366i	0.0913836	+	0.158281i	−0.816710	+	0.577048i	$0.804204\pi$
$812$	2863.03	+	1652.97i	3.52590	+	2.03568i
$813$	851.340	−	140.557i	1.04716	−	0.172887i
$814$	−1095.02	−	784.681i	−1.34524	−	0.963982i
$815$	−1622.71	+	53.1219i	−1.99105	+	0.0651802i
$816$	−701.363	−	163.535i	−0.859513	−	0.200410i
$817$	−1966.43	+	740.111i	−2.40689	+	0.905889i
$818$	−676.591	−	2230.42i	−0.827129	−	2.72668i
$819$	−325.561	−	42.8609i	−0.397510	−	0.0523332i
$820$	970.658	−	2859.47i	1.18373	−	3.48715i
$821$	116.810	+	1185.99i	0.142278	+	1.44457i	0.755753	+	0.654857i	$0.227271\pi$
$821$	116.810	+	1185.99i	0.142278	+	1.44457i	−0.613475	+	0.789714i	$0.710229\pi$
$822$	−1444.09	−	771.881i	−1.75680	−	0.939028i
$823$	−833.208	+	345.126i	−1.01240	+	0.419351i	−0.826331	−	0.563185i	$-0.809576\pi$
$823$	−833.208	+	345.126i	−1.01240	+	0.419351i	−0.186072	+	0.982536i	$0.559576\pi$
$824$	−1284.14	−	633.268i	−1.55842	−	0.768530i
$825$	−441.075	+	894.411i	−0.534636	+	1.08413i
$826$	−449.144	−	1084.33i	−0.543758	−	1.31275i
$827$	249.382	−	466.561i	0.301550	−	0.564160i	−0.684818	−	0.728714i	$-0.740118\pi$
$827$	249.382	−	466.561i	0.301550	−	0.564160i	0.986368	+	0.164554i	$0.0526184\pi$
$828$	−98.7955	+	9.73051i	−0.119318	+	0.0117518i
$829$	597.460	+	202.810i	0.720700	+	0.244645i	0.657605	−	0.753363i	$-0.271570\pi$
$829$	597.460	+	202.810i	0.720700	+	0.244645i	0.0630950	+	0.998008i	$0.479903\pi$
$830$	378.775	−	2877.08i	0.456355	−	3.46636i
$831$	−214.763	+	65.1476i	−0.258439	+	0.0783967i
$832$	546.084	+	1450.91i	0.656352	+	1.74388i
$833$	−11.3028	+	48.4750i	−0.0135688	+	0.0581933i
$834$	37.1447	+	1134.65i	0.0445381	+	1.36050i
$835$	−99.0066	+	138.163i	−0.118571	+	0.165465i
$836$	647.527	+	3922.01i	0.774554	+	4.69140i
$837$	307.639	−	532.846i	0.367550	−	0.636614i
$838$	1738.82	−	1003.91i	2.07496	−	1.19798i
$839$	−299.352	+	245.672i	−0.356796	+	0.292815i	−0.795666	−	0.605736i	$-0.792879\pi$
$839$	−299.352	+	245.672i	−0.356796	+	0.292815i	0.438870	+	0.898551i	$0.355379\pi$
$840$	3146.95	+	1303.51i	3.74637	+	1.55180i
$841$	1331.48	+	1518.26i	1.58321	+	1.80531i
$842$	−2773.64	+	181.794i	−3.29411	+	0.215907i
$843$	−271.464	+	894.898i	−0.322022	+	1.06156i
$844$	371.321	−	819.523i	0.439954	−	0.970999i
$845$	−38.6228	+	392.144i	−0.0457075	+	0.464076i
$846$	165.545	−	247.756i	0.195680	−	0.292855i
$847$	−157.502	−	59.2794i	−0.185952	−	0.0699875i
$848$	−11.1744	+	170.488i	−0.0131773	+	0.201047i
$849$	471.714	+	614.750i	0.555611	+	0.724087i
$850$	233.670	+	326.087i	0.274906	+	0.383631i
$851$	−58.8159	+	58.8159i	−0.0691138	+	0.0691138i
$852$	−105.884	+	641.329i	−0.124277	+	0.752733i
$853$	340.961	+	279.820i	0.399720	+	0.328042i	0.812683	−	0.582706i	$-0.198006\pi$
$853$	340.961	+	279.820i	0.399720	+	0.328042i	−0.412963	+	0.910748i	$0.635506\pi$
$854$	−132.821	−	248.491i	−0.155528	−	0.290973i
$855$	−444.968	−	665.941i	−0.520430	−	0.778878i
$856$	−280.950	−	1204.93i	−0.328212	−	1.40763i
$857$	604.490	−	161.973i	0.705356	−	0.189000i	0.111727	−	0.993739i	$-0.464362\pi$
$857$	604.490	−	161.973i	0.705356	−	0.189000i	0.593628	+	0.804739i	$0.297695\pi$
$858$	1768.14	+	1656.05i	2.06077	+	1.93013i
$859$	−842.046	−	523.618i	−0.980263	−	0.609567i	−0.0588979	−	0.998264i	$-0.518759\pi$
$859$	−842.046	−	523.618i	−0.980263	−	0.609567i	−0.921366	+	0.388697i	$0.872925\pi$
$860$	3254.17	−	3047.86i	3.78392	−	3.54402i
$861$	−935.370	+	186.057i	−1.08638	+	0.216094i
$862$	−593.069	−	1747.13i	−0.688016	−	2.02683i
$863$	−143.716	+	65.1168i	−0.166531	+	0.0754541i	−0.494244	−	0.869323i	$-0.664555\pi$
$863$	−143.716	+	65.1168i	−0.166531	+	0.0754541i	0.327714	+	0.944777i	$0.393722\pi$
$864$	1429.85	−	188.244i	1.65492	−	0.217874i
$865$	63.3328	−	318.395i	0.0732171	−	0.368087i
$866$	−1872.53	+	1164.41i	−2.16228	+	1.34459i
$867$	245.120	−	914.800i	0.282722	−	1.05513i
$868$	−64.2945	+	1963.99i	−0.0740720	+	2.26267i
$869$	−946.910	−	726.589i	−1.08965	−	0.836121i
$870$	3694.65	+	3240.12i	4.24673	+	3.72428i
$871$	1418.32	−	699.438i	1.62838	−	0.803028i
$872$		−	186.012i		−	0.213316i
$873$	−266.008	+	216.053i	−0.304706	+	0.247483i
$874$	343.681			0.393228
$875$	35.3233	+	71.6286i	0.0403695	+	0.0818612i
$876$	−31.0236	+	35.3756i	−0.0354151	+	0.0403831i
$877$	−473.023	+	616.455i	−0.539364	+	0.702913i	−0.980940	−	0.194311i	$-0.937753\pi$
$877$	−473.023	+	616.455i	−0.539364	+	0.702913i	0.441576	+	0.897224i	$0.354420\pi$
$878$	343.336	+	11.2397i	0.391044	+	0.0128014i
$879$	1216.95	+	326.081i	1.38447	+	0.370968i
$880$	−1957.79	−	3148.38i	−2.22476	−	3.57771i
$881$	−702.394	−	139.715i	−0.797269	−	0.158587i	−0.220385	−	0.975413i	$-0.570732\pi$
$881$	−702.394	−	139.715i	−0.797269	−	0.158587i	−0.576884	+	0.816826i	$0.695732\pi$
$882$	18.5263	+	140.721i	0.0210048	+	0.159548i
$883$	−262.226	−	578.745i	−0.296972	−	0.655431i	0.701382	−	0.712785i	$-0.252567\pi$
$883$	−262.226	−	578.745i	−0.296972	−	0.655431i	−0.998354	+	0.0573549i	$0.981733\pi$
$884$	659.023	−	223.708i	0.745501	−	0.253063i
$885$	−243.066	−	1221.97i	−0.274650	−	1.38076i
$886$	−315.050	−	336.375i	−0.355587	−	0.379656i
$887$	268.479	−	431.749i	0.302682	−	0.486752i	−0.662239	−	0.749292i	$-0.730394\pi$
$887$	268.479	−	431.749i	0.302682	−	0.486752i	0.964921	+	0.262541i	$0.0845604\pi$
$888$	−1604.98	+	1713.62i	−1.80741	+	1.92975i
$889$	−38.3627	−	143.172i	−0.0431527	−	0.161048i
$890$	−1299.91	+	303.096i	−1.46057	+	0.340557i
$891$	1015.42	−	678.482i	1.13964	−	0.761483i
$892$	−2974.27	+	1589.78i	−3.33438	+	1.78226i
$893$	−467.355	+	569.473i	−0.523353	+	0.637708i
$894$	−263.579	−	43.5170i	−0.294831	−	0.0486767i
$895$	935.618	+	935.618i	1.04538	+	1.04538i
$896$	−441.829	+	316.610i	−0.493112	+	0.353359i
$897$	118.669	−	91.0580i	0.132296	−	0.101514i
$898$	−2622.30	−	171.874i	−2.92015	−	0.191397i
$899$	−598.900	+	1591.24i	−0.666185	+	1.77001i
$900$	679.260	+	453.867i	0.754733	+	0.504296i
$901$	17.9537	+	1.76828i	0.0199264	+	0.00196258i
$902$	1806.58	+	818.551i	2.00286	+	0.907484i
$903$	−1347.49	−	408.756i	−1.49224	−	0.452665i
$904$	83.8737	+	1279.67i	0.0927807	+	1.41556i
$905$	1438.29	−	1261.34i	1.58927	−	1.39375i
$906$	−359.073	+	866.878i	−0.396328	+	0.956820i
$907$	−176.979	−	215.649i	−0.195126	−	0.237761i	0.666252	−	0.745727i	$-0.267898\pi$
$907$	−176.979	−	215.649i	−0.195126	−	0.237761i	−0.861377	+	0.507966i	$0.830398\pi$
$908$	−244.647	−	423.740i	−0.269435	−	0.466675i
$909$	183.972	+	106.216i	0.202389	+	0.116849i
$910$	−2380.11	+	392.958i	−2.61551	+	0.431822i
$911$	−694.832	−	497.910i	−0.762713	−	0.546553i	0.133036	−	0.991111i	$-0.457527\pi$
$911$	−694.832	−	497.910i	−0.762713	−	0.546553i	−0.895750	+	0.444558i	$0.853361\pi$
$912$	5074.50	−	166.122i	5.56414	−	0.182151i
$913$	1325.60	+	309.087i	1.45192	+	0.338540i
$914$	2579.14	−	970.719i	2.82182	−	1.06206i
$915$	−86.8251	−	286.224i	−0.0948909	−	0.312813i
$916$	2124.79	+	279.734i	2.31964	+	0.305387i
$917$	298.341	−	878.884i	0.325345	−	0.958434i
$918$	−32.8898	−	333.936i	−0.0358277	−	0.363765i
$919$	−209.411	−	111.932i	−0.227868	−	0.121798i	0.353513	−	0.935430i	$-0.384987\pi$
$919$	−209.411	−	111.932i	−0.227868	−	0.121798i	−0.581380	+	0.813632i	$0.697487\pi$
$920$	−404.092	+	167.380i	−0.439230	+	0.181935i
$921$	−694.057	−	342.271i	−0.753591	−	0.371630i
$922$	−783.653	+	1589.09i	−0.849949	+	1.72353i
$923$	−105.653	−	255.068i	−0.114466	−	0.276346i
$924$	−1255.83	+	2349.49i	−1.35912	+	2.54273i
$925$	681.191	−	67.0915i	0.736423	−	0.0725314i
$926$	−716.024	−	243.058i	−0.773245	−	0.262481i
$927$	−29.4502	+	223.697i	−0.0317694	+	0.241312i
$928$	−3813.64	+	1156.85i	−4.10952	+	1.24661i
$929$	424.119	+	1126.86i	0.456533	+	1.21298i	0.941071	+	0.338209i	$0.109821\pi$
$929$	424.119	+	1126.86i	0.456533	+	1.21298i	−0.484538	+	0.874770i	$0.661012\pi$
$930$	−663.280	+	2844.65i	−0.713205	+	3.05877i
$931$	−11.4816	−	350.726i	−0.0123325	−	0.376720i
$932$	56.8613	−	79.3499i	0.0610100	−	0.0851393i
$933$	145.919	+	883.820i	0.156398	+	0.947289i
$934$	428.733	−	742.587i	0.459028	−	0.795061i
$935$	−339.025	+	195.736i	−0.362594	+	0.209344i
$936$	920.029	−	755.048i	0.982937	−	0.806675i
$937$	714.287	+	295.868i	0.762313	+	0.315760i	0.729754	−	0.683709i	$-0.239634\pi$
$937$	714.287	+	295.868i	0.762313	+	0.315760i	0.0325587	+	0.999470i	$0.489634\pi$
$938$	1605.59	+	1830.83i	1.71172	+	1.95184i
$939$	1735.40	−	113.744i	1.84813	−	0.121133i
$940$	453.799	−	1495.98i	0.482765	−	1.59146i
$941$	349.682	−	771.765i	0.371607	−	0.820154i	−0.627529	−	0.778593i	$-0.715934\pi$
$941$	349.682	−	771.765i	0.371607	−	0.820154i	0.999136	−	0.0415610i	$-0.0132331\pi$
$942$	−17.8044	+	180.772i	−0.0189007	+	0.191902i
$943$	68.0359	−	101.823i	0.0721483	−	0.107978i
$944$	2083.72	+	784.255i	2.20733	+	0.830779i
$945$	−54.3253	+	828.844i	−0.0574871	+	0.877083i
$946$	1782.71	+	2323.28i	1.88448	+	2.45590i
$947$	−609.990	−	851.240i	−0.644129	−	0.898881i	0.355226	−	0.934780i	$-0.384404\pi$
$947$	−609.990	−	851.240i	−0.644129	−	0.898881i	−0.999355	+	0.0358993i	$0.988570\pi$
$948$	−2452.61	+	2452.61i	−2.58714	+	2.58714i
$949$	3.25543	−	19.7178i	0.00343037	−	0.0207775i
$950$	−2186.23	−	1794.20i	−2.30130	−	1.88863i
$951$	−595.027	−	1113.22i	−0.625685	−	1.17057i
$952$	357.073	+	534.398i	0.375077	+	0.561342i
$953$	−10.5120	−	45.0836i	−0.0110305	−	0.0473071i	0.968074	−	0.250663i	$-0.0806485\pi$
$953$	−10.5120	−	45.0836i	−0.0110305	−	0.0473071i	−0.979105	+	0.203356i	$0.934815\pi$
$954$	49.6901	−	13.3144i	0.0520860	−	0.0139564i
$955$	−1351.64	−	1265.95i	−1.41533	−	1.32561i
$956$	1958.04	+	1217.58i	2.04815	+	1.27362i
$957$	−1682.35	+	1575.69i	−1.75794	+	1.64649i
$958$	−118.901	+	23.6510i	−0.124114	+	0.0246879i
$959$	245.839	+	724.218i	0.256349	+	0.755180i
$960$	−2308.25	+	1045.85i	−2.40442	+	1.08943i
$961$	−49.1787	+	6.47449i	−0.0511745	+	0.00673725i
$962$	324.392	−	1630.83i	0.337206	−	1.69525i
$963$	−165.568	+	102.957i	−0.171930	+	0.106913i
$964$	1046.03	−	3903.82i	1.08509	−	4.04961i
$965$	4.81031	−	146.940i	0.00498477	−	0.152269i
$966$	182.733	+	140.216i	0.189164	+	0.145151i
$967$	−1019.40	−	893.988i	−1.05419	−	0.924496i	−0.0569186	−	0.998379i	$-0.518128\pi$
$967$	−1019.40	−	893.988i	−1.05419	−	0.924496i	−0.997267	+	0.0738829i	$0.976461\pi$
$968$	547.061	−	269.781i	0.565146	−	0.278699i
$969$		−	536.106i		−	0.553257i
$970$	−1409.31	+	2086.14i	−1.45290	+	2.15066i
$971$	841.784			0.866925			0.433463	−	0.901172i	$-0.357292\pi$
$971$	841.784			0.866925			0.433463	+	0.901172i	$0.357292\pi$
$972$	−799.754	−	1621.74i	−0.822792	−	1.66846i
$973$	349.621	−	398.666i	0.359322	−	0.409728i
$974$	−258.207	+	336.502i	−0.265099	+	0.345484i
$975$	−1230.25	−	40.2743i	−1.26180	−	0.0413070i
$976$	516.278	+	138.336i	0.528973	+	0.141738i
$977$	−510.673	−	821.228i	−0.522695	−	0.840561i	0.476561	−	0.879141i	$-0.341883\pi$
$977$	−510.673	−	821.228i	−0.522695	−	0.840561i	−0.999256	+	0.0385801i	$0.987717\pi$
$978$	−3039.37	−	604.569i	−3.10774	−	0.618168i
$979$	−81.7206	−	620.729i	−0.0834735	−	0.634044i
$980$	307.323	+	678.276i	0.313595	+	0.692118i
$981$	−27.7567	+	9.42212i	−0.0282943	+	0.00960461i
$982$	604.849	+	3040.78i	0.615936	+	3.09652i
$983$	612.577	+	654.042i	0.623171	+	0.665353i	0.961222	−	0.275775i	$-0.0889344\pi$
$983$	612.577	+	654.042i	0.623171	+	0.665353i	−0.338051	+	0.941128i	$0.609768\pi$
$984$	1825.37	−	2935.44i	1.85505	−	2.98317i
$985$	−167.373	+	178.702i	−0.169922	+	0.181423i
$986$	239.987	+	895.644i	0.243395	+	0.908361i
$987$	−480.824	+	112.112i	−0.487157	+	0.113589i
$988$	−4079.59	+	2725.89i	−4.12913	+	2.75900i
$989$	159.463	−	85.2347i	0.161237	−	0.0861827i
$990$	−708.168	+	862.906i	−0.715322	+	0.871622i
$991$	100.337	+	16.5657i	0.101248	+	0.0167161i	0.213305	−	0.976986i	$-0.431577\pi$
$991$	100.337	+	16.5657i	0.101248	+	0.0167161i	−0.112057	+	0.993702i	$0.535744\pi$
$992$	−1675.01	−	1675.01i	−1.68852	−	1.68852i
$993$	470.484	−	337.144i	0.473801	−	0.339521i
$994$	337.276	−	258.801i	0.339312	−	0.260363i
$995$	−1121.13	−	73.4827i	−1.12676	−	0.0738519i
$996$	1393.35	−	3702.05i	1.39895	−	3.71691i
$997$	544.959	+	364.130i	0.546599	+	0.365226i	0.798000	−	0.602657i	$-0.205891\pi$
$997$	544.959	+	364.130i	0.546599	+	0.365226i	−0.251401	+	0.967883i	$0.580891\pi$
$998$	2107.93	+	207.613i	2.11215	+	0.208029i
$999$	−521.500	−	236.289i	−0.522022	−	0.236525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.3.l.a.5.1	✓	480
97.39	odd	96	inner	97.3.l.a.39.1	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.3.l.a.5.1	✓	480	1.1	even	1	trivial
97.3.l.a.39.1	yes	480	97.39	odd	96	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:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	97.l (of order \(96\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65450 - 3.35499i) q^{2} +(-2.33421 + 2.66165i) q^{3} +(-6.08354 + 7.92822i) q^{4} +(6.93452 + 0.227013i) q^{5} +(12.7918 + 3.42754i) q^{6} +(-3.26636 - 5.25273i) q^{7} +(21.9887 + 4.37383i) q^{8} +(-0.461140 - 3.50270i) q^{9} +(-10.7115 - 23.6408i) q^{10} +(11.5280 - 3.91321i) q^{11} +(-6.90194 - 34.6984i) q^{12} +(10.2719 + 10.9672i) q^{13} +(-12.2187 + 19.6492i) q^{14} +(-16.7908 + 17.9274i) q^{15} +(-11.3603 - 42.3972i) q^{16} +(-4.51360 + 1.05242i) q^{17} +(-10.9886 + 7.34233i) q^{18} +(28.8161 - 15.4025i) q^{19} +(-43.9862 + 53.5973i) q^{20} +(21.6053 + 3.56705i) q^{21} +(-32.2017 - 32.2017i) q^{22} +(-2.28559 + 1.63783i) q^{23} +(-62.9679 + 48.3169i) q^{24} +(23.0895 + 1.51337i) q^{25} +(19.8000 - 52.6075i) q^{26} +(-16.0926 - 10.7528i) q^{27} +(61.5158 + 6.05877i) q^{28} +(48.7154 + 22.0727i) q^{29} +(87.9265 + 26.6722i) q^{30} +(2.07916 + 31.7219i) q^{31} +(-56.0230 + 49.1309i) q^{32} +(-16.4930 + 39.8177i) q^{33} +(10.9986 + 13.4018i) q^{34} +(-21.4582 - 37.1666i) q^{35} +(30.5756 + 17.6528i) q^{36} +(29.1864 - 4.81869i) q^{37} +(-99.3515 - 71.1943i) q^{38} +(-53.1678 + 1.74053i) q^{39} +(151.488 + 35.3221i) q^{40} +(-40.7607 + 15.3412i) q^{41} +(-23.7785 - 78.3872i) q^{42} +(-63.7542 - 8.39340i) q^{43} +(-39.1059 + 115.202i) q^{44} +(-2.40262 - 24.3942i) q^{45} +(9.27640 + 4.95834i) q^{46} +(-20.8304 + 8.62823i) q^{47} +(139.364 + 68.7267i) q^{48} +(4.75008 - 9.63221i) q^{49} +(-33.1242 - 79.9689i) q^{50} +(7.73449 - 14.4702i) q^{51} +(-149.440 + 14.7186i) q^{52} +(-3.68594 - 1.25121i) q^{53} +(-9.45015 + 71.7810i) q^{54} +(80.8291 - 24.5192i) q^{55} +(-48.8485 - 129.787i) q^{56} +(-26.2666 + 112.651i) q^{57} +(-6.54597 - 199.959i) q^{58} +(-29.5455 + 41.2308i) q^{59} +(-39.9846 - 242.183i) q^{60} +(-6.08858 + 10.5457i) q^{61} +(102.987 - 59.4594i) q^{62} +(-16.8925 + 13.8633i) q^{63} +(95.3167 + 39.4815i) q^{64} +(68.7412 + 78.3843i) q^{65} +(160.875 - 10.5443i) q^{66} +(30.5501 - 100.710i) q^{67} +(19.1148 - 42.1872i) q^{68} +(0.975704 - 9.90649i) q^{69} +(-89.1911 + 133.484i) q^{70} +(-17.1956 - 6.47197i) q^{71} +(5.18035 - 79.0369i) q^{72} +(-0.809638 - 1.05514i) q^{73} +(-64.4554 - 89.9474i) q^{74} +(-57.9238 + 57.9238i) q^{75} +(-53.1892 + 322.162i) q^{76} +(-58.2094 - 47.7712i) q^{77} +(93.8054 + 175.498i) q^{78} +(-54.4687 - 81.5181i) q^{79} +(-69.1535 - 296.583i) q^{80} +(96.8966 - 25.9634i) q^{81} +(118.908 + 111.370i) q^{82} +(94.9480 + 59.0424i) q^{83} +(-159.717 + 149.591i) q^{84} +(-31.5385 + 6.27340i) q^{85} +(77.3214 + 227.781i) q^{86} +(-172.462 + 78.1414i) q^{87} +(270.601 - 35.6252i) q^{88} +(10.0331 - 50.4398i) q^{89} +(-77.8673 + 48.4210i) q^{90} +(24.0561 - 89.7785i) q^{91} +(0.919390 - 28.0845i) q^{92} +(-89.2860 - 68.5115i) q^{93} +(63.4114 + 55.6103i) q^{94} +(203.322 - 100.268i) q^{95} -263.796i q^{96} +(-50.8030 - 82.6321i) q^{97} -40.1749 q^{98} +(-19.0228 - 38.5745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} + 64 q^{9} - 32 q^{10} - 32 q^{11} - 224 q^{12} - 32 q^{13} - 32 q^{14} + 224 q^{15} - 32 q^{16} + 48 q^{17} - 32 q^{18}+ \cdots - 512 q^{99}+O(q^{100}) \) 480 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 + 64 * q^9 - 32 * q^10 - 32 * q^11 - 224 * q^12 - 32 * q^13 - 32 * q^14 + 224 * q^15 - 32 * q^16 + 48 * q^17 - 32 * q^18 - 32 * q^19 - 416 * q^20 - 32 * q^21 - 32 * q^22 - 144 * q^23 - 32 * q^24 + 288 * q^25 + 48 * q^26 - 32 * q^27 - 272 * q^28 + 256 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 + 144 * q^33 - 432 * q^34 - 16 * q^35 - 48 * q^36 - 272 * q^37 - 32 * q^38 - 384 * q^39 + 544 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 + 496 * q^44 - 240 * q^45 - 32 * q^46 - 800 * q^47 - 912 * q^48 - 32 * q^49 - 32 * q^50 + 160 * q^51 + 352 * q^52 - 32 * q^53 + 1376 * q^54 - 352 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 544 * q^59 + 1408 * q^60 - 16 * q^61 - 48 * q^62 - 288 * q^63 - 32 * q^64 + 544 * q^65 - 1696 * q^66 - 32 * q^67 + 1696 * q^68 - 32 * q^69 - 1728 * q^70 + 16 * q^71 - 96 * q^72 - 176 * q^73 - 752 * q^74 - 32 * q^75 + 2368 * q^76 - 32 * q^77 - 32 * q^78 + 1776 * q^79 + 1760 * q^80 - 160 * q^81 + 80 * q^82 + 384 * q^83 + 2272 * q^84 + 944 * q^85 + 1888 * q^86 + 1760 * q^87 + 2272 * q^88 + 640 * q^89 + 2240 * q^90 + 928 * q^91 - 624 * q^92 + 784 * q^93 + 224 * q^94 - 448 * q^95 - 192 * q^97 - 768 * q^98 - 512 * q^99

Introduction

L-functions

Modular forms

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