LMFDB - Embedded newform 97.3.l.a.7.1

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			7.1
Character	$\chi$	$=$	97.7
Dual form			97.3.l.a.14.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.72531 + 0.244169i) q^{2} +(1.40357 - 4.13477i) q^{3} +(9.85250 - 1.29711i) q^{4} +(1.47402 + 2.37041i) q^{5} +(-4.21913 + 15.7460i) q^{6} +(8.21761 + 0.269017i) q^{7} +(-21.7406 + 4.32448i) q^{8} +(-7.98615 - 6.12799i) q^{9} +(-6.06995 - 8.47060i) q^{10} +(1.39475 - 1.22317i) q^{11} +(8.46539 - 42.5584i) q^{12} +(13.3425 + 3.11104i) q^{13} +(-30.6788 + 1.00432i) q^{14} +(11.8700 - 2.76769i) q^{15} +(41.5389 - 11.1303i) q^{16} +(17.5509 - 18.7390i) q^{17} +(31.2471 + 20.8787i) q^{18} +(-26.6344 - 14.2364i) q^{19} +(17.5974 + 21.4425i) q^{20} +(12.6463 - 33.6004i) q^{21} +(-4.89722 + 4.89722i) q^{22} +(-37.3182 + 16.9087i) q^{23} +(-12.6337 + 95.9621i) q^{24} +(7.61109 - 15.4338i) q^{25} +(-50.4647 - 8.33175i) q^{26} +(-3.87142 + 2.58680i) q^{27} +(81.3130 - 8.00863i) q^{28} +(1.94546 + 1.39410i) q^{29} +(-43.5436 + 13.2088i) q^{30} +(-12.0395 + 5.93721i) q^{31} +(-68.0667 + 23.1055i) q^{32} +(-3.09988 - 7.48378i) q^{33} +(-60.8072 + 74.0937i) q^{34} +(11.4752 + 19.8757i) q^{35} +(-86.6323 - 50.0172i) q^{36} +(25.5149 + 67.7915i) q^{37} +(102.697 + 46.5316i) q^{38} +(31.5906 - 50.8018i) q^{39} +(-42.2968 - 45.1598i) q^{40} +(-0.976473 - 5.91441i) q^{41} +(-38.9071 + 128.259i) q^{42} +(-29.5979 - 38.5727i) q^{43} +(12.1552 - 13.8604i) q^{44} +(2.75414 - 27.9632i) q^{45} +(134.893 - 72.1019i) q^{46} +(48.3093 + 20.0104i) q^{47} +(12.2813 - 187.376i) q^{48} +(18.5617 + 1.21660i) q^{49} +(-24.5852 + 59.3539i) q^{50} +(-52.8474 - 98.8705i) q^{51} +(135.493 + 13.3449i) q^{52} +(9.47531 + 8.30963i) q^{53} +(13.7906 - 10.5819i) q^{54} +(4.95529 + 1.50317i) q^{55} +(-179.819 + 29.6883i) q^{56} +(-96.2473 + 90.1455i) q^{57} +(-7.58782 - 4.71841i) q^{58} +(-7.52802 + 16.6147i) q^{59} +(113.359 - 42.6653i) q^{60} +(1.08065 - 1.87174i) q^{61} +(43.4010 - 25.0576i) q^{62} +(-63.9786 - 52.5059i) q^{63} +(89.0047 - 36.8670i) q^{64} +(12.2927 + 36.2131i) q^{65} +(13.3753 + 27.1225i) q^{66} +(16.0241 + 52.8244i) q^{67} +(148.614 - 207.391i) q^{68} +(17.5349 + 178.035i) q^{69} +(-47.6017 - 71.2410i) q^{70} +(-10.1668 + 61.5796i) q^{71} +(200.124 + 98.6903i) q^{72} +(39.9926 + 5.26513i) q^{73} +(-111.604 - 246.314i) q^{74} +(-53.1324 - 53.1324i) q^{75} +(-280.882 - 105.716i) q^{76} +(11.7906 - 9.67628i) q^{77} +(-105.280 + 196.966i) q^{78} +(-44.4114 + 66.4664i) q^{79} +(87.6124 + 82.0580i) q^{80} +(-18.1862 - 67.8718i) q^{81} +(5.08178 + 21.7946i) q^{82} +(-2.02386 - 61.8225i) q^{83} +(81.0142 - 347.451i) q^{84} +(70.2894 + 13.9814i) q^{85} +(119.679 + 136.468i) q^{86} +(8.49484 - 6.08732i) q^{87} +(-25.0332 + 32.6239i) q^{88} +(-6.64039 - 33.3835i) q^{89} +(-3.43224 + 104.844i) q^{90} +(108.807 + 29.1547i) q^{91} +(-345.746 + 214.998i) q^{92} +(7.65081 + 58.1137i) q^{93} +(-184.853 - 62.7491i) q^{94} +(-5.51346 - 84.1192i) q^{95} +313.870i q^{96} +(-75.8455 - 60.4686i) q^{97} -69.4449 q^{98} +(-18.6343 + 1.22135i) 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 $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{31}{96}\right)$

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 $

$2$	−3.72531	+	0.244169i	−1.86265	+	0.122085i	−0.954808	−	0.297222i	$-0.903940\pi$
$2$	−3.72531	+	0.244169i	−1.86265	+	0.122085i	−0.907844	+	0.419307i	$0.862273\pi$
$3$	1.40357	−	4.13477i	0.467855	−	1.37826i	−0.415517	−	0.909585i	$-0.636399\pi$
$3$	1.40357	−	4.13477i	0.467855	−	1.37826i	0.883372	−	0.468672i	$-0.155267\pi$
$4$	9.85250	−	1.29711i	2.46313	−	0.324277i
$5$	1.47402	+	2.37041i	0.294803	+	0.474082i	0.962850	−	0.270037i	$-0.0870360\pi$
$5$	1.47402	+	2.37041i	0.294803	+	0.474082i	−0.668047	+	0.744119i	$0.732869\pi$
$6$	−4.21913	+	15.7460i	−0.703188	+	2.62433i
$7$	8.21761	+	0.269017i	1.17394	+	0.0384310i	0.613454	−	0.789730i	$-0.289779\pi$
$7$	8.21761	+	0.269017i	1.17394	+	0.0384310i	0.560490	+	0.828161i	$0.310613\pi$
$8$	−21.7406	+	4.32448i	−2.71758	+	0.540560i
$9$	−7.98615	−	6.12799i	−0.887350	−	0.680888i
$10$	−6.06995	−	8.47060i	−0.606995	−	0.847060i
$11$	1.39475	−	1.22317i	0.126796	−	0.111197i	−0.593600	−	0.804760i	$-0.702294\pi$
$11$	1.39475	−	1.22317i	0.126796	−	0.111197i	0.720395	+	0.693564i	$0.243960\pi$
$12$	8.46539	−	42.5584i	0.705450	−	3.54653i
$13$	13.3425	+	3.11104i	1.02635	+	0.239311i	0.706167	−	0.708045i	$-0.250423\pi$
$13$	13.3425	+	3.11104i	1.02635	+	0.239311i	0.320182	+	0.947356i	$0.396256\pi$
$14$	−30.6788	+	1.00432i	−2.19134	+	0.0717371i
$15$	11.8700	−	2.76769i	0.791333	−	0.184513i
$16$	41.5389	−	11.1303i	2.59618	−	0.695644i
$17$	17.5509	−	18.7390i	1.03241	−	1.10229i	0.0377276	−	0.999288i	$-0.487988\pi$
$17$	17.5509	−	18.7390i	1.03241	−	1.10229i	0.994681	−	0.103003i	$-0.0328453\pi$
$18$	31.2471	+	20.8787i	1.73595	+	1.15993i
$19$	−26.6344	−	14.2364i	−1.40181	−	0.749284i	−0.414796	−	0.909914i	$-0.636147\pi$
$19$	−26.6344	−	14.2364i	−1.40181	−	0.749284i	−0.987015	+	0.160631i	$0.948647\pi$
$20$	17.5974	+	21.4425i	0.879872	+	1.07213i
$21$	12.6463	−	33.6004i	0.602204	−	1.60002i
$22$	−4.89722	+	4.89722i	−0.222601	+	0.222601i
$23$	−37.3182	+	16.9087i	−1.62253	+	0.735160i	−0.998915	−	0.0465704i	$-0.985171\pi$
$23$	−37.3182	+	16.9087i	−1.62253	+	0.735160i	−0.623617	+	0.781730i	$0.714337\pi$
$24$	−12.6337	+	95.9621i	−0.526402	+	3.99842i
$25$	7.61109	−	15.4338i	0.304444	−	0.617351i
$26$	−50.4647	−	8.33175i	−1.94095	−	0.320452i
$27$	−3.87142	+	2.58680i	−0.143386	+	0.0958074i
$28$	81.3130	−	8.00863i	2.90403	−	0.286022i
$29$	1.94546	+	1.39410i	0.0670847	+	0.0480723i	0.615524	−	0.788118i	$-0.288944\pi$
$29$	1.94546	+	1.39410i	0.0670847	+	0.0480723i	−0.548439	+	0.836190i	$0.684778\pi$
$30$	−43.5436	+	13.2088i	−1.45145	+	0.440293i
$31$	−12.0395	+	5.93721i	−0.388370	+	0.191523i	−0.625982	−	0.779837i	$-0.715302\pi$
$31$	−12.0395	+	5.93721i	−0.388370	+	0.191523i	0.237612	+	0.971360i	$0.423635\pi$
$32$	−68.0667	+	23.1055i	−2.12708	+	0.722048i
$33$	−3.09988	−	7.48378i	−0.0939358	−	0.226781i
$34$	−60.8072	+	74.0937i	−1.78845	+	2.17923i
$35$	11.4752	+	19.8757i	0.327863	+	0.567876i
$36$	−86.6323	−	50.0172i	−2.40645	−	1.38937i
$37$	25.5149	+	67.7915i	0.689593	+	1.83220i	0.536309	+	0.844022i	$0.319818\pi$
$37$	25.5149	+	67.7915i	0.689593	+	1.83220i	0.153283	+	0.988182i	$0.451015\pi$
$38$	102.697	+	46.5316i	2.70256	+	1.22452i
$39$	31.5906	−	50.8018i	0.810015	−	1.30261i
$40$	−42.2968	−	45.1598i	−1.05742	−	1.12900i
$41$	−0.976473	−	5.91441i	−0.0238164	−	0.144254i	0.972095	−	0.234587i	$-0.0753736\pi$
$41$	−0.976473	−	5.91441i	−0.0238164	−	0.144254i	−0.995912	+	0.0903327i	$0.971207\pi$
$42$	−38.9071	+	128.259i	−0.926359	+	3.05380i
$43$	−29.5979	−	38.5727i	−0.688323	−	0.897039i	0.310239	−	0.950659i	$-0.399591\pi$
$43$	−29.5979	−	38.5727i	−0.688323	−	0.897039i	−0.998561	+	0.0536192i	$0.982924\pi$
$44$	12.1552	−	13.8604i	0.276255	−	0.315009i
$45$	2.75414	−	27.9632i	0.0612031	−	0.621405i
$46$	134.893	−	72.1019i	2.93246	−	1.56743i
$47$	48.3093	+	20.0104i	1.02786	+	0.425752i	0.831939	−	0.554868i	$-0.187231\pi$
$47$	48.3093	+	20.0104i	1.02786	+	0.425752i	0.195919	+	0.980620i	$0.437231\pi$
$48$	12.2813	−	187.376i	0.255860	−	3.90366i
$49$	18.5617	+	1.21660i	0.378810	+	0.0248285i
$50$	−24.5852	+	59.3539i	−0.491704	+	1.18708i
$51$	−52.8474	−	98.8705i	−1.03622	−	1.93864i
$52$	135.493	+	13.3449i	2.60563	+	0.256632i
$53$	9.47531	+	8.30963i	0.178779	+	0.156785i	0.744059	−	0.668114i	$-0.232898\pi$
$53$	9.47531	+	8.30963i	0.178779	+	0.156785i	−0.565279	+	0.824900i	$0.691232\pi$
$54$	13.7906	−	10.5819i	0.255381	−	0.195961i
$55$	4.95529	+	1.50317i	0.0900963	+	0.0273304i
$56$	−179.819	+	29.6883i	−3.21106	+	0.530148i
$57$	−96.2473	+	90.1455i	−1.68855	+	1.58150i
$58$	−7.58782	−	4.71841i	−0.130824	−	0.0813519i
$59$	−7.52802	+	16.6147i	−0.127594	+	0.281605i	−0.963712	−	0.266944i	$-0.913986\pi$
$59$	−7.52802	+	16.6147i	−0.127594	+	0.281605i	0.836118	+	0.548549i	$0.184820\pi$
$60$	113.359	−	42.6653i	1.88932	−	0.711089i
$61$	1.08065	−	1.87174i	0.0177155	−	0.0306842i	−0.857032	−	0.515264i	$-0.827694\pi$
$61$	1.08065	−	1.87174i	0.0177155	−	0.0306842i	0.874747	+	0.484579i	$0.161027\pi$
$62$	43.4010	−	25.0576i	0.700016	−	0.404155i
$63$	−63.9786	−	52.5059i	−1.01553	−	0.833426i
$64$	89.0047	−	36.8670i	1.39070	−	0.576046i
$65$	12.2927	+	36.2131i	0.189118	+	0.557124i
$66$	13.3753	+	27.1225i	0.202656	+	0.410946i
$67$	16.0241	+	52.8244i	0.239166	+	0.788423i	0.991553	+	0.129702i	$0.0414022\pi$
$67$	16.0241	+	52.8244i	0.239166	+	0.788423i	−0.752387	+	0.658721i	$0.771098\pi$
$68$	148.614	−	207.391i	2.18550	−	3.04987i
$69$	17.5349	+	178.035i	0.254129	+	2.58021i
$70$	−47.6017	−	71.2410i	−0.680024	−	1.01773i
$71$	−10.1668	+	61.5796i	−0.143195	+	0.867318i	0.814633	+	0.579976i	$0.196938\pi$
$71$	−10.1668	+	61.5796i	−0.143195	+	0.867318i	−0.957828	+	0.287342i	$0.907228\pi$
$72$	200.124	+	98.6903i	2.77950	+	1.37070i
$73$	39.9926	+	5.26513i	0.547844	+	0.0721251i	0.399368	−	0.916791i	$-0.369230\pi$
$73$	39.9926	+	5.26513i	0.547844	+	0.0721251i	0.148477	+	0.988916i	$0.452563\pi$
$74$	−111.604	−	246.314i	−1.50816	−	3.32857i
$75$	−53.1324	−	53.1324i	−0.708432	−	0.708432i
$76$	−280.882	−	105.716i	−3.69581	−	1.39101i
$77$	11.7906	−	9.67628i	0.153125	−	0.125666i
$78$	−105.280	+	196.966i	−1.34975	+	2.52520i
$79$	−44.4114	+	66.4664i	−0.562170	+	0.841347i	−0.998285	−	0.0585440i	$-0.981354\pi$
$79$	−44.4114	+	66.4664i	−0.562170	+	0.841347i	0.436115	+	0.899891i	$0.356354\pi$
$80$	87.6124	+	82.0580i	1.09516	+	1.02572i
$81$	−18.1862	−	67.8718i	−0.224521	−	0.837923i
$82$	5.08178	+	21.7946i	0.0619729	+	0.265787i
$83$	−2.02386	−	61.8225i	−0.0243838	−	0.744849i	−0.939677	−	0.342062i	$-0.888875\pi$
$83$	−2.02386	−	61.8225i	−0.0243838	−	0.744849i	0.915294	−	0.402787i	$-0.131959\pi$
$84$	81.0142	−	347.451i	0.964455	−	4.13632i
$85$	70.2894	+	13.9814i	0.826935	+	0.164488i
$86$	119.679	+	136.468i	1.39162	+	1.58684i
$87$	8.49484	−	6.08732i	0.0976419	−	0.0699692i
$88$	−25.0332	+	32.6239i	−0.284468	+	0.370727i
$89$	−6.64039	−	33.3835i	−0.0746111	−	0.375096i	0.925381	−	0.379038i	$-0.123745\pi$
$89$	−6.64039	−	33.3835i	−0.0746111	−	0.375096i	−0.999992	+	0.00394249i	$0.998745\pi$
$90$	−3.43224	+	104.844i	−0.0381360	+	1.16493i
$91$	108.807	+	29.1547i	1.19568	+	0.320382i
$92$	−345.746	+	214.998i	−3.75811	+	2.33694i
$93$	7.65081	+	58.1137i	0.0822668	+	0.624878i
$94$	−184.853	−	62.7491i	−1.96652	−	0.667543i
$95$	−5.51346	−	84.1192i	−0.0580365	−	0.885465i
$96$			313.870i			3.26948i
$97$	−75.8455	−	60.4686i	−0.781913	−	0.623388i
$97$	−75.8455	−	60.4686i	−0.781913	−	0.623388i
$98$	−69.4449			−0.708622
$99$	−18.6343	+	1.22135i	−0.188225	+	0.0123369i
$100$	54.9690	−	161.934i	0.549690	−	1.61934i
$101$	−22.4738	+	2.95873i	−0.222513	+	0.0292944i	−0.240958	−	0.970536i	$-0.577462\pi$
$101$	−22.4738	+	2.95873i	−0.222513	+	0.0292944i	0.0184454	+	0.999830i	$0.494128\pi$
$102$	221.014	+	355.419i	2.16680	+	3.48450i
$103$	−18.2008	+	67.9262i	−0.176706	+	0.659478i	0.819548	+	0.573010i	$0.194224\pi$
$103$	−18.2008	+	67.9262i	−0.176706	+	0.659478i	−0.996255	+	0.0864673i	$0.972442\pi$
$104$	−303.529	−	9.93650i	−2.91854	−	0.0955433i
$105$	98.2875	−	19.5506i	0.936072	−	0.186196i
$106$	−37.3274	−	28.6423i	−0.352145	−	0.270211i
$107$	46.8374	+	65.3616i	0.437733	+	0.610856i	0.972148	−	0.234366i	$-0.0753015\pi$
$107$	46.8374	+	65.3616i	0.437733	+	0.610856i	−0.534415	+	0.845222i	$0.679468\pi$
$108$	−34.7878	+	30.5081i	−0.322109	+	0.282482i
$109$	−18.1125	+	91.0577i	−0.166170	+	0.835392i	0.804310	+	0.594210i	$0.202535\pi$
$109$	−18.1125	+	91.0577i	−0.166170	+	0.835392i	−0.970480	+	0.241182i	$0.922465\pi$
$110$	−18.8270	−	4.38984i	−0.171155	−	0.0399077i
$111$	316.114	−	10.3485i	2.84788	−	0.0932298i
$112$	344.345	−	80.2899i	3.07451	−	0.716874i
$113$	−48.5298	+	13.0035i	−0.429467	+	0.115075i	−0.467076	−	0.884217i	$-0.654693\pi$
$113$	−48.5298	+	13.0035i	−0.429467	+	0.115075i	0.0376090	+	0.999293i	$0.488026\pi$
$114$	336.540	−	359.320i	2.95211	−	3.15193i
$115$	−95.0882	−	63.5359i	−0.826854	−	0.552486i
$116$	20.9759	+	11.2119i	0.180827	+	0.0966540i
$117$	−87.4911	−	106.608i	−0.747788	−	0.911182i
$118$	23.9874	−	63.7330i	0.203283	−	0.540110i
$119$	149.268	−	149.268i	1.25435	−	1.25435i
$120$	−246.092	+	111.503i	−2.05077	+	0.929190i
$121$	−15.3445	+	116.553i	−0.126814	+	0.963246i
$122$	−3.56872	+	7.23665i	−0.0292518	+	0.0593168i
$123$	−25.8253	−	4.26377i	−0.209962	−	0.0346648i
$124$	−110.918	+	74.1128i	−0.894498	+	0.597684i
$125$	117.251	−	11.5482i	0.938006	−	0.0923855i
$126$	251.160	+	179.979i	1.99333	+	1.42840i
$127$	−32.2584	+	9.78549i	−0.254003	+	0.0770511i	−0.414719	−	0.909950i	$-0.636120\pi$
$127$	−32.2584	+	9.78549i	−0.254003	+	0.0770511i	0.160715	+	0.987001i	$0.448620\pi$
$128$	−64.6940	+	31.9036i	−0.505422	+	0.249247i
$129$	−201.032	+	68.2411i	−1.55839	+	0.529001i
$130$	−54.6361	−	131.903i	−0.420278	−	1.01464i
$131$	33.6703	−	41.0274i	0.257025	−	0.313186i	−0.628471	−	0.777833i	$-0.716319\pi$
$131$	33.6703	−	41.0274i	0.257025	−	0.313186i	0.885496	+	0.464647i	$0.153819\pi$
$132$	−40.2488	−	69.7130i	−0.304915	−	0.528129i
$133$	−215.041	−	124.154i	−1.61685	−	0.933490i
$134$	−72.5927	−	192.874i	−0.541737	−	1.43936i
$135$	−11.8383	−	5.36387i	−0.0876912	−	0.0397324i
$136$	−300.532	+	483.295i	−2.20979	+	3.55364i
$137$	119.979	+	128.100i	0.875757	+	0.935036i	0.998350	−	0.0574210i	$-0.0182877\pi$
$137$	119.979	+	128.100i	0.875757	+	0.935036i	−0.122593	+	0.992457i	$0.539121\pi$
$138$	−108.793	−	658.952i	−0.788359	−	4.77502i
$139$	−15.5640	+	51.3075i	−0.111971	+	0.369118i	−0.994960	−	0.100275i	$-0.968028\pi$
$139$	−15.5640	+	51.3075i	−0.111971	+	0.369118i	0.882989	+	0.469394i	$0.155528\pi$
$140$	138.840	+	180.940i	0.991717	+	1.29243i
$141$	150.544	−	171.662i	1.06768	−	1.21746i
$142$	22.8387	−	231.885i	0.160836	−	1.63299i
$143$	22.4149	−	11.9810i	0.156747	−	0.0837832i
$144$	−399.942	−	165.662i	−2.77738	−	1.15043i
$145$	−0.436943	+	6.66646i	−0.00301340	+	0.0459756i
$146$	−150.270	−	9.84924i	−1.02925	−	0.0674606i
$147$	31.0829	−	75.0407i	0.211448	−	0.510481i
$148$	339.319	+	634.821i	2.29269	+	4.28933i
$149$	69.7951	+	6.87422i	0.468424	+	0.0461357i	0.329476	−	0.944164i	$-0.393128\pi$
$149$	69.7951	+	6.87422i	0.468424	+	0.0461357i	0.138948	+	0.990300i	$0.455628\pi$
$150$	210.908	+	184.961i	1.40605	+	1.23307i
$151$	−117.066	+	89.8281i	−0.775273	+	0.594888i	−0.918784	−	0.394761i	$-0.870827\pi$
$151$	−117.066	+	89.8281i	−0.775273	+	0.594888i	0.143511	+	0.989649i	$0.454161\pi$
$152$	640.613	+	194.328i	4.21456	+	1.27847i
$153$	−254.997	+	42.1001i	−1.66665	+	0.275164i
$154$	−41.5609	+	38.9260i	−0.269876	+	0.252766i
$155$	−31.8200	−	19.7870i	−0.205290	−	0.127658i
$156$	245.351	−	541.501i	1.57276	−	3.47116i
$157$	−92.7921	+	34.9245i	−0.591033	+	0.222449i	−0.629746	−	0.776801i	$-0.716841\pi$
$157$	−92.7921	+	34.9245i	−0.591033	+	0.222449i	0.0387129	+	0.999250i	$0.487674\pi$
$158$	149.217	−	258.452i	0.944412	−	1.63577i
$159$	47.6576	−	27.5151i	0.299733	−	0.173051i
$160$	−155.101	−	127.288i	−0.969382	−	0.795551i
$161$	−311.215	+	128.910i	−1.93302	+	0.800681i
$162$	84.3213	+	248.403i	0.520502	+	1.53335i
$163$	1.93558	+	3.92497i	0.0118747	+	0.0240795i	0.902729	−	0.430209i	$-0.141560\pi$
$163$	1.93558	+	3.92497i	0.0118747	+	0.0240795i	−0.890855	+	0.454289i	$0.849893\pi$
$164$	−17.2923	−	57.0051i	−0.105441	−	0.347592i
$165$	13.1704	−	18.3792i	0.0798203	−	0.111389i
$166$	22.6347	+	229.814i	0.136353	+	1.38442i
$167$	−154.686	−	231.504i	−0.926262	−	1.38625i	−0.922391	−	0.386257i	$-0.873768\pi$
$167$	−154.686	−	231.504i	−0.926262	−	1.38625i	−0.00387091	−	0.999993i	$-0.501232\pi$
$168$	−129.634	+	785.181i	−0.771630	+	4.67369i
$169$	16.7734	+	8.27171i	0.0992507	+	0.0489450i
$170$	−265.263	−	34.9226i	−1.56037	−	0.205427i
$171$	125.466	+	276.909i	0.733719	+	1.61935i
$172$	−341.646	−	341.646i	−1.98631	−	1.98631i
$173$	52.0049	+	19.5733i	0.300607	+	0.113140i	0.497981	−	0.867188i	$-0.334075\pi$
$173$	52.0049	+	19.5733i	0.300607	+	0.113140i	−0.197375	+	0.980328i	$0.563242\pi$
$174$	−30.1595	+	24.7513i	−0.173331	+	0.142249i
$175$	66.6969	−	124.781i	0.381125	−	0.713035i
$176$	44.3223	−	66.3329i	0.251831	−	0.376892i
$177$	58.1319	+	54.4465i	0.328429	+	0.307607i
$178$	32.8887	+	122.742i	0.184768	+	0.689564i
$179$	43.5341	+	186.708i	0.243208	+	1.04306i	0.944065	+	0.329759i	$0.106967\pi$
$179$	43.5341	+	186.708i	0.243208	+	1.04306i	−0.700858	+	0.713301i	$0.747199\pi$
$180$	−9.13614	−	279.080i	−0.0507563	−	1.55045i
$181$	−23.7127	+	101.698i	−0.131009	+	0.561869i	0.866972	+	0.498357i	$0.166063\pi$
$181$	−23.7127	+	101.698i	−0.131009	+	0.561869i	−0.997981	+	0.0635113i	$0.979770\pi$
$182$	−412.458	−	82.0429i	−2.26625	−	0.450785i
$183$	−6.22244	−	7.09534i	−0.0340024	−	0.0387723i
$184$	738.200	−	528.987i	4.01196	−	2.87493i
$185$	−123.084	+	160.407i	−0.665321	+	0.867064i
$186$	−42.6912	−	214.623i	−0.229523	−	1.15389i
$187$	1.55839	−	47.6039i	0.00833364	−	0.254566i
$188$	501.923	+	134.490i	2.66980	+	0.715372i
$189$	−32.5097	+	20.2158i	−0.172009	+	0.106962i
$190$	41.0787	+	312.023i	0.216204	+	1.64223i
$191$	−325.010	−	110.326i	−1.70162	−	0.577623i	−0.709704	−	0.704500i	$-0.751171\pi$
$191$	−325.010	−	110.326i	−1.70162	−	0.577623i	−0.991919	+	0.126877i	$0.959505\pi$
$192$	−27.5125	−	419.759i	−0.143294	−	2.18625i
$193$		−	140.655i		−	0.728781i	−0.931246	−	0.364391i	$-0.881277\pi$
$193$		−	140.655i		−	0.728781i	0.931246	−	0.364391i	$-0.118723\pi$
$194$	297.312	+	206.745i	1.53254	+	1.06570i
$195$	166.986			0.856340
$196$	184.457	−	12.0899i	0.941107	−	0.0616834i
$197$	24.7707	−	72.9721i	0.125739	−	0.370417i	−0.865772	−	0.500439i	$-0.833172\pi$
$197$	24.7707	−	72.9721i	0.125739	−	0.370417i	0.991511	+	0.130023i	$0.0415051\pi$
$198$	69.1201	−	9.09983i	0.349091	−	0.0459587i
$199$	−108.536	−	174.540i	−0.545406	−	0.877084i	0.454501	−	0.890746i	$-0.349818\pi$
$199$	−108.536	−	174.540i	−0.545406	−	0.877084i	−0.999907	+	0.0136625i	$0.995651\pi$
$200$	−98.7268	+	368.453i	−0.493634	+	1.84227i
$201$	240.907	+	7.88649i	1.19854	+	0.0392363i
$202$	82.9993	−	16.5096i	0.410887	−	0.0817306i
$203$	15.6120	+	11.9795i	0.0769063	+	0.0590123i
$204$	−648.925	−	905.573i	−3.18100	−	4.43908i
$205$	12.5802	−	11.0326i	0.0613671	−	0.0538175i
$206$	51.2179	−	257.490i	0.248631	−	1.24995i
$207$	401.645	+	93.6506i	1.94032	+	0.452418i
$208$	588.861	−	19.2773i	2.83106	−	0.0926794i
$209$	−54.5619	+	12.7220i	−0.261062	+	0.0608710i
$210$	−361.377	+	96.8308i	−1.72084	+	0.461099i
$211$	135.581	−	144.758i	0.642562	−	0.686057i	−0.322950	−	0.946416i	$-0.604674\pi$
$211$	135.581	−	144.758i	0.642562	−	0.686057i	0.965512	+	0.260360i	$0.0838411\pi$
$212$	104.134	+	69.5801i	0.491198	+	0.328208i
$213$	240.348	+	128.469i	1.12839	+	0.603139i
$214$	−190.443	−	232.056i	−0.889921	−	1.08437i
$215$	47.8054	−	127.016i	0.222351	−	0.590772i
$216$	72.9804	−	72.9804i	0.337872	−	0.337872i
$217$	−100.533	+	45.5508i	−0.463285	+	0.209912i
$218$	45.2411	−	343.640i	0.207528	−	1.57633i
$219$	77.9024	−	157.970i	0.355719	−	0.721326i
$220$	50.7718	+	8.38246i	0.230781	+	0.0381021i
$221$	292.472	−	195.424i	1.32340	−	0.884269i
$222$	−1175.10	+	115.737i	−5.29322	+	0.521337i
$223$	−109.016	−	78.1199i	−0.488862	−	0.350313i	0.311087	−	0.950381i	$-0.399307\pi$
$223$	−109.016	−	78.1199i	−0.488862	−	0.350313i	−0.799949	+	0.600068i	$0.795140\pi$
$224$	−565.561	+	171.561i	−2.52483	+	0.765898i
$225$	−155.361	+	76.6157i	−0.690495	+	0.340514i
$226$	177.613	−	60.2915i	0.785899	−	0.266777i
$227$	72.4390	+	174.883i	0.319114	+	0.770410i	0.999301	+	0.0373717i	$0.0118985\pi$
$227$	72.4390	+	174.883i	0.319114	+	0.770410i	−0.680187	+	0.733039i	$0.738101\pi$
$228$	−831.349	+	1013.00i	−3.64627	+	4.44299i
$229$	198.851	+	344.421i	0.868347	+	1.50402i	0.863685	+	0.504032i	$0.168151\pi$
$229$	198.851	+	344.421i	0.868347	+	1.50402i	0.00466199	+	0.999989i	$0.498516\pi$
$230$	369.746	+	213.473i	1.60759	+	0.928144i
$231$	−23.4604	−	62.3327i	−0.101560	−	0.269838i
$232$	−48.3242	−	21.8954i	−0.208294	−	0.0943767i
$233$	−140.130	+	225.348i	−0.601418	+	0.967159i	0.397356	+	0.917665i	$0.369928\pi$
$233$	−140.130	+	225.348i	−0.601418	+	0.967159i	−0.998774	+	0.0494948i	$0.984239\pi$
$234$	351.962	+	375.786i	1.50411	+	1.60592i
$235$	23.7759	+	144.009i	0.101174	+	0.612802i
$236$	−52.6188	+	173.461i	−0.222961	+	0.735005i
$237$	212.489	+	276.921i	0.896578	+	1.16844i
$238$	−519.622	+	592.515i	−2.18329	+	2.48956i
$239$	−18.6952	+	189.816i	−0.0782227	+	0.794209i	0.873413	+	0.486980i	$0.161902\pi$
$239$	−18.6952	+	189.816i	−0.0782227	+	0.794209i	−0.951636	+	0.307229i	$0.900598\pi$
$240$	462.261	−	247.084i	1.92609	−	1.02951i
$241$	−166.663	−	69.0342i	−0.691549	−	0.286449i	0.00909648	−	0.999959i	$-0.497104\pi$
$241$	−166.663	−	69.0342i	−0.691549	−	0.286449i	−0.700645	+	0.713510i	$0.747104\pi$
$242$	28.7042	−	437.941i	0.118612	−	1.80968i
$243$	−347.975	−	22.8075i	−1.43200	−	0.0938580i
$244$	8.21924	−	19.8430i	0.0336854	−	0.0813238i
$245$	24.4764	+	45.7921i	0.0999036	+	0.186906i
$246$	97.2481	+	9.57810i	0.395317	+	0.0389354i
$247$	−311.081	−	272.810i	−1.25944	−	1.10450i
$248$	236.070	−	181.143i	0.951895	−	0.730415i
$249$	−258.462	−	78.4037i	−1.03800	−	0.314874i
$250$	−433.975	+	71.6496i	−1.73590	+	0.286598i
$251$	249.772	−	233.937i	0.995108	−	0.932020i	−0.00257937	−	0.999997i	$-0.500821\pi$
$251$	249.772	−	233.937i	0.995108	−	0.932020i	0.997687	+	0.0679768i	$0.0216544\pi$
$252$	−698.455	−	434.327i	−2.77165	−	1.72352i
$253$	−31.3676	+	69.2298i	−0.123983	+	0.273636i
$254$	117.783	−	44.3305i	0.463713	−	0.174529i
$255$	156.466	−	271.007i	0.613592	−	1.06277i
$256$	−100.510	+	58.0292i	−0.392615	+	0.226677i
$257$	202.314	+	166.035i	0.787214	+	0.646049i	0.939601	−	0.342271i	$-0.111196\pi$
$257$	202.314	+	166.035i	0.787214	+	0.646049i	−0.152388	+	0.988321i	$0.548696\pi$
$258$	732.242	−	303.305i	2.83815	−	1.17560i
$259$	191.435	+	563.948i	0.739130	+	2.17741i
$260$	168.086	+	340.844i	0.646484	+	1.31094i
$261$	−6.99372	−	23.0552i	−0.0267959	−	0.0883341i
$262$	−115.414	+	161.061i	−0.440513	+	0.614735i
$263$	−13.6015	−	138.099i	−0.0517169	−	0.525091i	−0.985787	−	0.168001i	$-0.946269\pi$
$263$	−13.6015	−	138.099i	−0.0517169	−	0.525091i	0.934070	−	0.357090i	$-0.116231\pi$
$264$	99.7567	+	149.296i	0.377866	+	0.565517i
$265$	−5.73047	+	34.7089i	−0.0216244	+	0.130977i
$266$	831.409	+	410.006i	3.12560	+	1.54138i
$267$	−147.353	−	19.3994i	−0.551885	−	0.0726571i
$268$	226.396	+	499.667i	0.844762	+	1.86443i
$269$	−200.069	−	200.069i	−0.743751	−	0.743751i	0.229547	−	0.973298i	$-0.426276\pi$
$269$	−200.069	−	200.069i	−0.743751	−	0.743751i	−0.973298	+	0.229547i	$0.926276\pi$
$270$	45.4110	+	17.0915i	0.168189	+	0.0633019i
$271$	278.463	−	228.528i	1.02754	−	0.843279i	0.0397699	−	0.999209i	$-0.487338\pi$
$271$	278.463	−	228.528i	1.02754	−	0.843279i	0.987768	+	0.155930i	$0.0498375\pi$
$272$	520.476	−	973.743i	1.91352	−	3.57994i
$273$	273.266	−	408.971i	1.00097	−	1.49806i
$274$	−478.235	−	447.916i	−1.74538	−	1.63473i
$275$	−8.26246	−	30.8359i	−0.0300453	−	0.112131i
$276$	403.693	+	1731.34i	1.46265	+	6.27298i
$277$	3.91465	+	119.580i	0.0141323	+	0.431697i	0.982945	+	0.183902i	$0.0588728\pi$
$277$	3.91465	+	119.580i	0.0141323	+	0.431697i	−0.968812	+	0.247796i	$0.920294\pi$
$278$	45.4528	−	194.936i	0.163499	−	0.701209i
$279$	132.532	+	26.3623i	0.475026	+	0.0944885i
$280$	−335.430	−	382.485i	−1.19796	−	1.36602i
$281$	−312.829	+	224.170i	−1.11327	+	0.797759i	−0.981106	−	0.193469i	$-0.938026\pi$
$281$	−312.829	+	224.170i	−1.11327	+	0.797759i	−0.132165	+	0.991228i	$0.542193\pi$
$282$	−518.906	+	676.251i	−1.84009	+	2.39805i
$283$	−41.7678	−	209.981i	−0.147589	−	0.741981i	−0.981707	−	0.190396i	$-0.939023\pi$
$283$	−41.7678	−	209.981i	−0.147589	−	0.741981i	0.834118	−	0.551586i	$-0.185977\pi$
$284$	−20.2934	+	619.901i	−0.0714558	+	2.18275i
$285$	−355.552	−	95.2699i	−1.24755	−	0.334280i
$286$	−80.5768	+	50.1059i	−0.281737	+	0.175195i
$287$	−6.43320	−	48.8650i	−0.0224153	−	0.170261i
$288$	685.182	+	232.588i	2.37910	+	0.807597i
$289$	−24.2112	−	369.392i	−0.0837758	−	1.27817i
$290$		−	24.9413i		−	0.0860044i
$291$	−356.478	+	228.732i	−1.22501	+	0.786022i
$292$	400.857			1.37280
$293$	177.812	−	11.6544i	0.606868	−	0.0397763i	0.241128	−	0.970493i	$-0.422483\pi$
$293$	177.812	−	11.6544i	0.606868	−	0.0397763i	0.365740	+	0.930717i	$0.380816\pi$
$294$	−97.4705	+	287.139i	−0.331532	+	0.976663i
$295$	−50.4801	+	6.64584i	−0.171119	+	0.0225283i
$296$	−847.873	−	1363.49i	−2.86444	−	4.60639i
$297$	−2.23559	+	8.34333i	−0.00752723	+	0.0280920i
$298$	−261.687	−	8.56673i	−0.878143	−	0.0287474i
$299$	−550.524	+	109.506i	−1.84122	+	0.366241i
$300$	−592.406	−	454.569i	−1.97469	−	1.51523i
$301$	−232.847	−	324.938i	−0.773578	−	1.07953i
$302$	414.174	−	363.221i	1.37144	−	1.20272i
$303$	−19.3098	+	97.0767i	−0.0637286	+	0.320385i
$304$	−1264.82	−	294.914i	−4.16059	−	0.970113i
$305$	6.02968	−	0.197391i	0.0197694	−	0.000647185i
$306$	939.661	−	219.098i	3.07079	−	0.716007i
$307$	323.505	−	86.6828i	1.05376	−	0.282355i	0.309956	−	0.950751i	$-0.399686\pi$
$307$	323.505	−	86.6828i	1.05376	−	0.282355i	0.743805	+	0.668396i	$0.233019\pi$
$308$	103.616	−	110.629i	0.336414	−	0.359186i
$309$	255.313	+	170.595i	0.826256	+	0.552087i
$310$	123.371	+	65.9430i	0.397970	+	0.212719i
$311$	−87.3900	−	106.485i	−0.280997	−	0.342396i	0.613316	−	0.789838i	$-0.289835\pi$
$311$	−87.3900	−	106.485i	−0.280997	−	0.342396i	−0.894313	+	0.447442i	$0.852335\pi$
$312$	−467.108	+	1241.07i	−1.49714	+	3.97780i
$313$	374.185	−	374.185i	1.19548	−	1.19548i	0.219972	−	0.975506i	$-0.429403\pi$
$313$	374.185	−	374.185i	1.19548	−	1.19548i	0.975506	−	0.219972i	$-0.0705966\pi$
$314$	337.152	−	152.761i	1.07373	−	0.486501i
$315$	30.1550	−	229.050i	0.0957302	−	0.727143i
$316$	−351.350	+	712.467i	−1.11187	+	2.25464i
$317$	−378.864	−	62.5508i	−1.19516	−	0.197321i	−0.467959	−	0.883750i	$-0.655011\pi$
$317$	−378.864	−	62.5508i	−1.19516	−	0.197321i	−0.727197	+	0.686429i	$0.759177\pi$
$318$	−170.821	+	114.139i	−0.537172	+	0.358927i
$319$	4.41864	−	0.435198i	0.0138515	−	0.00136426i
$320$	218.584	+	156.635i	0.683076	+	0.489486i
$321$	335.994	−	101.923i	1.04671	−	0.317517i
$322$	1127.90	−	556.217i	3.50279	−	1.72738i
$323$	−734.234	+	249.239i	−2.27317	+	0.771637i
$324$	−267.216	−	645.117i	−0.824742	−	1.99110i
$325$	149.566	−	182.247i	0.460204	−	0.560761i
$326$	−8.16898	−	14.1491i	−0.0250582	−	0.0434021i
$327$	351.081	+	202.697i	1.07364	+	0.619867i
$328$	46.8058	+	124.360i	0.142701	+	0.379147i
$329$	391.604	+	177.433i	1.19029	+	0.539311i
$330$	−44.5759	+	71.6840i	−0.135079	+	0.217224i
$331$	85.6009	+	91.3951i	0.258613	+	0.276118i	0.845994	−	0.533192i	$-0.179008\pi$
$331$	85.6009	+	91.3951i	0.258613	+	0.276118i	−0.587381	+	0.809310i	$0.699841\pi$
$332$	−100.130	−	606.481i	−0.301598	−	1.82675i
$333$	211.660	−	697.749i	0.635615	−	2.09534i
$334$	632.778	+	824.652i	1.89454	+	2.46902i
$335$	−101.596	+	115.848i	−0.303271	+	0.345814i
$336$	151.330	−	1536.48i	0.450387	−	4.57285i
$337$	341.801	−	182.696i	1.01425	−	0.542125i	0.121455	−	0.992597i	$-0.461244\pi$
$337$	341.801	−	182.696i	1.01425	−	0.542125i	0.892791	+	0.450471i	$0.148744\pi$
$338$	−64.5056	−	26.7191i	−0.190845	−	0.0790506i
$339$	−14.3482	+	218.911i	−0.0423250	+	0.645754i
$340$	710.662	+	46.5793i	2.09018	+	0.136998i
$341$	−9.52989	+	23.0072i	−0.0279469	+	0.0674698i
$342$	−535.012	−	1000.94i	−1.56436	−	2.92672i
$343$	−248.733	−	24.4981i	−0.725170	−	0.0714230i
$344$	810.282	+	710.599i	2.35547	+	2.06569i
$345$	−396.169	+	303.991i	−1.14832	+	0.881134i
$346$	−198.513	−	60.2184i	−0.573738	−	0.174042i
$347$	293.849	−	48.5146i	0.846826	−	0.139812i	0.276280	−	0.961077i	$-0.410898\pi$
$347$	293.849	−	48.5146i	0.846826	−	0.139812i	0.570546	+	0.821266i	$0.306732\pi$
$348$	75.7996	−	70.9940i	0.217815	−	0.204006i
$349$	297.013	+	184.695i	0.851041	+	0.529211i	0.882510	−	0.470293i	$-0.155852\pi$
$349$	297.013	+	184.695i	0.851041	+	0.529211i	−0.0314691	+	0.999505i	$0.510019\pi$
$350$	−217.999	+	481.133i	−0.622853	+	1.37467i
$351$	−59.7022	+	22.4703i	−0.170092	+	0.0640180i
$352$	−66.6743	+	115.483i	−0.189416	+	0.328078i
$353$	−110.035	+	63.5286i	−0.311713	+	0.179968i	−0.647693	−	0.761901i	$-0.724266\pi$
$353$	−110.035	+	63.5286i	−0.311713	+	0.179968i	0.335980	+	0.941869i	$0.390933\pi$
$354$	−229.853	−	188.636i	−0.649303	−	0.532869i
$355$	−160.955	+	66.6698i	−0.453395	+	0.187802i
$356$	−108.726	−	320.298i	−0.305411	−	0.899713i
$357$	−407.681	−	826.696i	−1.14196	−	2.31568i
$358$	−207.766	−	684.914i	−0.580353	−	1.91317i
$359$	104.778	−	146.218i	0.291861	−	0.407292i	−0.640993	−	0.767547i	$-0.721477\pi$
$359$	104.778	−	146.218i	0.291861	−	0.407292i	0.932854	+	0.360255i	$0.117310\pi$
$360$	61.0497	+	619.848i	0.169583	+	1.72180i
$361$	306.156	+	458.195i	0.848078	+	1.26924i
$362$	63.5054	−	384.647i	0.175429	−	1.06256i
$363$	460.382	+	227.035i	1.26827	+	0.625442i
$364$	1109.84	+	146.113i	3.04900	+	0.401409i
$365$	46.4693	+	102.560i	0.127313	+	0.280986i
$366$	24.9130	+	24.9130i	0.0680682	+	0.0680682i
$367$	267.159	+	100.552i	0.727954	+	0.273983i	0.688498	−	0.725239i	$-0.258271\pi$
$367$	267.159	+	100.552i	0.727954	+	0.273983i	0.0394569	+	0.999221i	$0.487437\pi$
$368$	−1361.96	+	1117.73i	−3.70098	+	3.03731i
$369$	−28.4452	+	53.2172i	−0.0770872	+	0.144220i
$370$	419.361	−	627.618i	1.13341	−	1.69626i
$371$	75.6290	+	70.8343i	0.203852	+	0.190928i
$372$	150.759	+	562.641i	0.405267	+	1.51248i
$373$	−122.700	−	526.231i	−0.328954	−	1.41081i	−0.835925	−	0.548843i	$-0.815068\pi$
$373$	−122.700	−	526.231i	−0.328954	−	1.41081i	0.506972	−	0.861963i	$-0.330765\pi$
$374$	5.81794	+	177.720i	0.0155560	+	0.475186i
$375$	116.820	−	501.014i	0.311520	−	1.33604i
$376$	−1136.81	−	226.125i	−3.02342	−	0.601397i
$377$	21.6203	+	24.6532i	0.0573482	+	0.0653931i
$378$	116.172	−	83.2480i	0.307335	−	0.220233i
$379$	91.4563	−	119.188i	0.241309	−	0.314481i	−0.656960	−	0.753925i	$-0.728158\pi$
$379$	91.4563	−	119.188i	0.241309	−	0.314481i	0.898270	+	0.439445i	$0.144825\pi$
$380$	−163.433	−	821.633i	−0.430087	−	2.16219i
$381$	−4.81607	+	147.116i	−0.0126406	+	0.386131i
$382$	1237.70	+	331.641i	3.24005	+	0.868169i
$383$	30.1301	−	18.7361i	0.0786688	−	0.0489194i	−0.488167	−	0.872750i	$-0.662334\pi$
$383$	30.1301	−	18.7361i	0.0786688	−	0.0489194i	0.566835	+	0.823831i	$0.308168\pi$
$384$	41.1116	+	312.274i	0.107062	+	0.813213i
$385$	40.3163	+	13.6855i	0.104718	+	0.0355469i
$386$	34.3436	+	523.982i	0.0889731	+	1.35747i
$387$			489.423i			1.26466i
$388$	−825.703	−	497.387i	−2.12810	−	1.28193i
$389$	204.919			0.526784			0.263392	−	0.964689i	$-0.415159\pi$
$389$	204.919			0.526784			0.263392	+	0.964689i	$0.415159\pi$
$390$	−622.075	+	40.7729i	−1.59506	+	0.104546i
$391$	−338.120	+	996.068i	−0.864756	+	2.54749i
$392$	−408.803	+	53.8200i	−1.04287	+	0.137296i
$393$	−122.380	−	196.803i	−0.311400	−	0.500772i
$394$	−74.4608	+	277.891i	−0.188987	+	0.705308i
$395$	−223.016	−	7.30079i	−0.564598	−	0.0184830i
$396$	−182.010	+	36.2040i	−0.459621	+	0.0914243i
$397$	−145.492	−	111.640i	−0.366479	−	0.281209i	0.409062	−	0.912507i	$-0.365856\pi$
$397$	−145.492	−	111.640i	−0.366479	−	0.281209i	−0.775541	+	0.631297i	$0.782523\pi$
$398$	446.946	+	623.713i	1.12298	+	1.56712i
$399$	−815.174	+	714.888i	−2.04304	+	1.79170i
$400$	144.374	−	725.815i	0.360934	−	1.81454i
$401$	−191.630	−	44.6819i	−0.477880	−	0.111426i	−0.0188046	−	0.999823i	$-0.505986\pi$
$401$	−191.630	−	44.6819i	−0.477880	−	0.111426i	−0.459076	+	0.888397i	$0.651819\pi$
$402$	−899.380	+	29.4426i	−2.23726	+	0.0732404i
$403$	−179.108	+	41.7621i	−0.444437	+	0.103628i
$404$	−217.585	+	58.3018i	−0.538577	+	0.144311i
$405$	134.077	−	143.153i	0.331055	−	0.353464i
$406$	−61.0844	−	40.8153i	−0.150454	−	0.100530i
$407$	118.507	+	63.3435i	0.291173	+	0.155635i
$408$	1576.50	+	1920.97i	3.86396	+	4.70825i
$409$	−13.3909	+	35.5788i	−0.0327406	+	0.0869897i	−0.951265	−	0.308375i	$-0.900215\pi$
$409$	−13.3909	+	35.5788i	−0.0327406	+	0.0869897i	0.918524	+	0.395364i	$0.129382\pi$
$410$	−44.1714	+	44.1714i	−0.107735	+	0.107735i
$411$	698.062	−	316.288i	1.69845	−	0.769556i
$412$	−91.2156	+	692.851i	−0.221397	+	1.68168i
$413$	−66.3320	+	134.508i	−0.160610	+	0.325685i
$414$	−1519.12	−	250.807i	−3.66937	−	0.605815i
$415$	143.562	−	95.9248i	0.345931	−	0.231144i
$416$	−980.065	+	96.5280i	−2.35593	+	0.232038i
$417$	190.300	+	136.367i	0.456354	+	0.327019i
$418$	200.153	−	60.7158i	0.478836	−	0.145253i
$419$	−302.717	+	149.284i	−0.722476	+	0.356286i	−0.766064	−	0.642764i	$-0.777788\pi$
$419$	−302.717	+	149.284i	−0.722476	+	0.356286i	0.0435887	+	0.999050i	$0.486121\pi$
$420$	943.019	−	320.112i	2.24528	−	0.762171i
$421$	179.494	+	433.338i	0.426353	+	1.02931i	0.980435	+	0.196844i	$0.0630693\pi$
$421$	179.494	+	433.338i	0.426353	+	1.02931i	−0.554082	+	0.832462i	$0.686931\pi$
$422$	−469.734	+	572.372i	−1.11311	+	1.35633i
$423$	−263.182	−	455.845i	−0.622180	−	1.07765i
$424$	−241.934	−	139.681i	−0.570599	−	0.329435i
$425$	−155.631	−	413.501i	−0.366190	−	0.972944i
$426$	−926.737	−	419.899i	−2.17544	−	0.985678i
$427$	9.38387	−	15.0905i	0.0219763	−	0.0353407i
$428$	546.247	+	583.222i	1.27628	+	1.36267i
$429$	−18.0779	−	109.496i	−0.0421397	−	0.255237i
$430$	−147.076	+	484.846i	−0.342038	+	1.12755i
$431$	−275.856	−	359.503i	−0.640038	−	0.834113i	0.354869	−	0.934916i	$-0.384525\pi$
$431$	−275.856	−	359.503i	−0.640038	−	0.834113i	−0.994906	+	0.100803i	$0.967859\pi$
$432$	−132.022	+	150.543i	−0.305608	+	0.348479i
$433$	7.57430	−	76.9031i	0.0174926	−	0.177605i	−0.982468	−	0.186429i	$-0.940309\pi$
$433$	7.57430	−	76.9031i	0.0174926	−	0.177605i	0.999961	+	0.00882344i	$0.00280862\pi$
$434$	363.394	−	194.238i	0.837312	−	0.447553i
$435$	26.9510	+	11.1635i	0.0619563	+	0.0256631i
$436$	−60.3419	+	920.640i	−0.138399	+	2.11156i
$437$	1234.67	+	80.9244i	2.82533	+	0.185182i
$438$	−251.639	+	607.510i	−0.574518	+	1.38701i
$439$	−392.312	−	733.964i	−0.893649	−	1.67190i	−0.727846	−	0.685741i	$-0.759478\pi$
$439$	−392.312	−	733.964i	−0.893649	−	1.67190i	−0.165803	−	0.986159i	$-0.553022\pi$
$440$	−114.232	−	11.2508i	−0.259617	−	0.0255701i
$441$	−140.781	−	123.462i	−0.319231	−	0.279958i
$442$	−1041.83	+	799.425i	−2.35708	+	1.80865i
$443$	−251.115	−	76.1751i	−0.566852	−	0.171953i	−0.00616578	−	0.999981i	$-0.501963\pi$
$443$	−251.115	−	76.1751i	−0.566852	−	0.171953i	−0.560686	+	0.828028i	$0.689463\pi$
$444$	3101.09	−	511.993i	6.98445	−	1.15314i
$445$	69.3446	−	64.9483i	0.155831	−	0.145951i
$446$	425.193	+	264.402i	0.953348	+	0.592830i
$447$	126.385	−	278.938i	0.282741	−	0.624023i
$448$	741.324	−	279.015i	1.65474	−	0.622801i
$449$	−40.2463	+	69.7087i	−0.0896355	+	0.155253i	−0.907357	−	0.420361i	$-0.861904\pi$
$449$	−40.2463	+	69.7087i	−0.0896355	+	0.155253i	0.817722	+	0.575614i	$0.195237\pi$
$450$	560.061	−	323.351i	1.24458	−	0.718559i
$451$	−8.59624	−	7.05475i	−0.0190604	−	0.0156425i
$452$	−461.273	+	191.065i	−1.02051	+	0.422711i
$453$	207.108	+	610.122i	0.457193	+	1.34685i
$454$	−312.558	−	633.806i	−0.688455	−	1.39605i
$455$	91.2745	+	300.892i	0.200603	+	0.661301i
$456$	1702.64	−	2376.04i	3.73387	−	5.21061i
$457$	−65.9610	−	669.713i	−0.144335	−	1.46546i	−0.745593	−	0.666401i	$-0.767834\pi$
$457$	−65.9610	−	669.713i	−0.144335	−	1.46546i	0.601258	−	0.799055i	$-0.294666\pi$
$458$	−824.879	−	1234.52i	−1.80105	−	2.69546i
$459$	−19.4731	+	117.947i	−0.0424251	+	0.256965i
$460$	−1019.27	−	502.648i	−2.21580	−	1.09271i
$461$	−415.421	−	54.6912i	−0.901131	−	0.118636i	−0.334296	−	0.942468i	$-0.608499\pi$
$461$	−415.421	−	54.6912i	−0.901131	−	0.118636i	−0.566834	+	0.823832i	$0.691832\pi$
$462$	102.617	+	226.480i	0.222114	+	0.490216i
$463$	−46.9178	−	46.9178i	−0.101334	−	0.101334i	0.654622	−	0.755956i	$-0.272828\pi$
$463$	−46.9178	−	46.9178i	−0.101334	−	0.101334i	−0.755956	+	0.654622i	$0.772828\pi$
$464$	96.3288	+	36.2556i	0.207605	+	0.0781371i
$465$	−126.476	+	103.796i	−0.271991	+	0.223218i
$466$	467.006	−	873.706i	1.00216	−	1.87491i
$467$	−385.086	+	576.321i	−0.824595	+	1.23409i	0.145013	+	0.989430i	$0.453677\pi$
$467$	−385.086	+	576.321i	−0.824595	+	1.23409i	−0.969608	+	0.244663i	$0.921323\pi$
$468$	−1000.29	−	936.873i	−2.13737	−	2.00187i
$469$	117.469	+	438.401i	0.250467	+	0.934756i
$470$	−123.735	−	530.670i	−0.263266	−	1.12909i
$471$	14.1649	+	432.693i	0.0300741	+	0.918669i
$472$	91.8140	−	393.769i	0.194521	−	0.834255i
$473$	−88.4625	−	17.5963i	−0.187024	−	0.0372014i
$474$	−859.202	−	979.732i	−1.81266	−	2.06695i
$475$	−422.438	+	302.715i	−0.889343	+	0.637294i
$476$	1277.05	−	1664.28i	2.68287	−	3.49638i
$477$	−24.7500	−	124.427i	−0.0518868	−	0.260852i
$478$	23.2982	−	711.687i	0.0487411	−	1.48889i
$479$	−7.51430	−	2.01345i	−0.0156875	−	0.00420345i	0.250967	−	0.967996i	$-0.419252\pi$
$479$	−7.51430	−	2.01345i	−0.0156875	−	0.00420345i	−0.266654	+	0.963792i	$0.585918\pi$
$480$	−744.002	+	462.650i	−1.55000	+	0.963855i
$481$	129.532	+	983.890i	0.269296	+	2.04551i
$482$	637.728	+	216.479i	1.32309	+	0.449127i
$483$	96.2006	+	1467.74i	0.199173	+	3.03879i
$484$			1168.24i			2.41372i
$485$	31.5379	−	268.917i	0.0650266	−	0.554468i
$486$	1301.88			2.67877
$487$	39.2664	−	2.57365i	0.0806291	−	0.00528471i	−0.0250352	−	0.999687i	$-0.507970\pi$
$487$	39.2664	−	2.57365i	0.0806291	−	0.00528471i	0.105664	+	0.994402i	$0.466303\pi$
$488$	−15.3997	+	45.3659i	−0.0315567	+	0.0929630i
$489$	18.9455	−	2.49423i	0.0387434	−	0.00510067i
$490$	−102.363	−	164.613i	−0.208904	−	0.335945i
$491$	42.8609	−	159.959i	0.0872931	−	0.325782i	−0.908445	−	0.418003i	$-0.862730\pi$
$491$	42.8609	−	159.959i	0.0872931	−	0.325782i	0.995739	+	0.0922211i	$0.0293966\pi$
$492$	−259.974	−	8.51067i	−0.528403	−	0.0172981i
$493$	60.2685	−	11.9882i	0.122249	−	0.0243167i
$494$	1225.48	+	940.346i	2.48073	+	1.90353i
$495$	−30.3623	−	42.3706i	−0.0613380	−	0.0855971i
$496$	−434.023	+	380.628i	−0.875046	+	0.767395i
$497$	−100.113	+	503.302i	−0.201435	+	1.01268i
$498$	981.995	+	228.969i	1.97188	+	0.459778i
$499$	540.336	−	17.6888i	1.08284	−	0.0354484i	0.513916	−	0.857840i	$-0.328194\pi$
$499$	540.336	−	17.6888i	1.08284	−	0.0354484i	0.568921	+	0.822392i	$0.307361\pi$
$500$	1140.23	−	265.865i	2.28047	−	0.531730i
$501$	−1174.33	+	314.660i	−2.34396	+	0.628063i
$502$	−873.357	+	932.473i	−1.73975	+	1.85752i
$503$	319.258	+	213.321i	0.634708	+	0.424098i	0.830865	−	0.556474i	$-0.187846\pi$
$503$	319.258	+	213.321i	0.634708	+	0.424098i	−0.196157	+	0.980573i	$0.562846\pi$
$504$	1617.99	+	864.836i	3.21030	+	1.71594i
$505$	−40.1401	−	48.9109i	−0.0794854	−	0.0968533i
$506$	99.9501	−	265.561i	0.197530	−	0.524824i
$507$	57.7441	−	57.7441i	0.113894	−	0.113894i
$508$	−305.134	+	138.254i	−0.600657	+	0.272154i
$509$	−6.90356	+	52.4378i	−0.0135630	+	0.103021i	−0.996887	−	0.0788393i	$-0.974879\pi$
$509$	−6.90356	+	52.4378i	−0.0135630	+	0.103021i	0.983324	+	0.181860i	$0.0582119\pi$
$510$	−516.712	+	1047.79i	−1.01316	+	2.05449i
$511$	327.228	+	54.0255i	0.640367	+	0.105725i
$512$	600.165	−	401.018i	1.17220	−	0.783237i
$513$	139.940	−	13.7828i	0.272787	−	0.0268671i
$514$	−794.222	−	569.131i	−1.54518	−	1.10726i
$515$	−187.841	+	56.9810i	−0.364740	+	0.110643i
$516$	−1892.15	+	933.105i	−3.66696	+	1.80834i
$517$	91.8555	−	31.1807i	0.177670	−	0.0603109i
$518$	−850.852	−	2054.14i	−1.64257	−	3.96552i
$519$	153.923	−	187.556i	0.296577	−	0.361380i
$520$	−423.853	−	734.135i	−0.815101	−	1.41180i
$521$	151.017	+	87.1895i	0.289859	+	0.167350i	0.637878	−	0.770137i	$-0.279812\pi$
$521$	151.017	+	87.1895i	0.289859	+	0.167350i	−0.348019	+	0.937487i	$0.613146\pi$
$522$	31.6831	+	84.1800i	0.0606956	+	0.161264i
$523$	632.718	+	286.681i	1.20979	+	0.548147i	0.913456	−	0.406938i	$-0.133404\pi$
$523$	632.718	+	286.681i	1.20979	+	0.548147i	0.296331	+	0.955085i	$0.404237\pi$
$524$	278.520	−	447.896i	0.531526	−	0.854763i
$525$	−422.328	−	450.915i	−0.804434	−	0.858886i
$526$	84.3894	+	511.139i	0.160436	+	0.971748i
$527$	−100.047	+	329.811i	−0.189842	+	0.625827i
$528$	−212.062	−	276.365i	−0.401633	−	0.523419i
$529$	757.954	−	864.280i	1.43280	−	1.63380i
$530$	12.8729	−	130.701i	0.0242885	−	0.246605i
$531$	161.935	−	86.5559i	0.304962	−	0.163005i
$532$	−2279.74	−	944.298i	−4.28522	−	1.77500i
$533$	5.37136	−	81.9511i	0.0100776	−	0.153754i
$534$	553.673	+	36.2897i	1.03684	+	0.0679581i
$535$	−85.8947	+	207.368i	−0.160551	+	0.387604i
$536$	−576.811	−	1079.14i	−1.07614	−	2.01332i
$537$	833.097	+	82.0529i	1.55139	+	0.152799i
$538$	794.169	+	696.467i	1.47615	+	1.29455i
$539$	27.3770	−	21.0071i	0.0507923	−	0.0389743i
$540$	−123.595	−	37.4920i	−0.228879	−	0.0694296i
$541$	−778.348	+	128.506i	−1.43872	+	0.237534i	−0.830848	−	0.556500i	$-0.812144\pi$
$541$	−778.348	+	128.506i	−1.43872	+	0.237534i	−0.607874	+	0.794034i	$0.707977\pi$
$542$	−981.559	+	919.331i	−1.81099	+	1.69618i
$543$	387.216	+	240.787i	0.713106	+	0.443438i
$544$	−761.662	+	1681.02i	−1.40011	+	3.09012i
$545$	−242.542	+	91.2865i	−0.445032	+	0.167498i
$546$	−918.140	+	1590.27i	−1.68158	+	2.91257i
$547$	92.7774	−	53.5651i	0.169611	−	0.0979252i	−0.412791	−	0.910826i	$-0.635446\pi$
$547$	92.7774	−	53.5651i	0.169611	−	0.0979252i	0.582403	+	0.812901i	$0.302113\pi$
$548$	1348.25	+	1106.48i	2.46031	+	2.01912i
$549$	−20.1002	+	8.32578i	−0.0366124	+	0.0151654i
$550$	38.3094	+	112.856i	0.0696534	+	0.205192i
$551$	−31.9692	−	64.8272i	−0.0580204	−	0.117654i
$552$	−1151.13	−	3794.76i	−2.08537	−	6.87456i
$553$	−382.837	+	534.248i	−0.692290	+	0.966090i
$554$	−43.7811	−	444.517i	−0.0790272	−	0.802377i
$555$	490.488	+	734.067i	0.883762	+	1.32264i
$556$	−86.7926	+	525.695i	−0.156102	+	0.945495i
$557$	−674.316	−	332.536i	−1.21062	−	0.597012i	−0.278946	−	0.960307i	$-0.589985\pi$
$557$	−674.316	−	332.536i	−1.21062	−	0.597012i	−0.931674	+	0.363295i	$0.881652\pi$
$558$	−500.160	−	65.8473i	−0.896344	−	0.118006i
$559$	−274.909	−	606.738i	−0.491788	−	1.08540i
$560$	697.890	+	697.890i	1.24623	+	1.24623i
$561$	−194.644	−	73.2588i	−0.346959	−	0.130586i
$562$	1110.65	−	911.486i	1.97624	−	1.62186i
$563$	−242.715	+	454.088i	−0.431111	+	0.806551i	−0.999873	−	0.0159509i	$-0.994922\pi$
$563$	−242.715	+	454.088i	−0.431111	+	0.806551i	0.568762	+	0.822502i	$0.307422\pi$
$564$	1260.57	−	1886.57i	2.23505	−	3.34498i
$565$	−102.357	−	95.8681i	−0.181163	−	0.169678i
$566$	206.869	+	772.044i	0.365492	+	1.36404i
$567$	−131.188	−	562.636i	−0.231373	−	0.992303i
$568$	−45.2664	−	1382.74i	−0.0796943	−	2.43441i
$569$	169.687	−	727.748i	0.298220	−	1.27899i	−0.585383	−	0.810757i	$-0.699056\pi$
$569$	169.687	−	727.748i	0.298220	−	1.27899i	0.883602	−	0.468238i	$-0.155111\pi$
$570$	1347.80	+	268.095i	2.36457	+	0.470341i
$571$	−583.969	−	665.889i	−1.02271	−	1.16618i	−0.985982	−	0.166854i	$-0.946639\pi$
$571$	−583.969	−	665.889i	−1.02271	−	1.16618i	−0.0367305	−	0.999325i	$-0.511694\pi$
$572$	205.302	−	147.117i	0.358919	−	0.257198i
$573$	−912.346	+	1188.99i	−1.59223	+	2.07503i
$574$	35.8970	+	180.466i	0.0625383	+	0.314401i
$575$	−23.0680	+	704.654i	−0.0401182	+	1.22549i
$576$	−936.726	−	250.995i	−1.62626	−	0.435755i
$577$	−63.3512	+	39.3943i	−0.109794	+	0.0682743i	−0.581860	−	0.813289i	$-0.697675\pi$
$577$	−63.3512	+	39.3943i	−0.109794	+	0.0682743i	0.472066	+	0.881563i	$0.343508\pi$
$578$	180.388	+	1370.18i	0.312090	+	2.37056i
$579$	−581.575	−	197.418i	−1.00445	−	0.340964i
$580$	4.34213	+	66.2480i	0.00748642	+	0.114221i
$581$		−	508.578i		−	0.875349i
$582$	1272.14	−	939.139i	2.18581	−	1.61364i
$583$	23.3798			0.0401025
$584$	−892.233	+	58.4801i	−1.52780	+	0.100137i
$585$	123.742	−	364.532i	0.211525	−	0.623132i
$586$	−659.560	+	86.8327i	−1.12553	+	0.148179i
$587$	−245.168	−	394.262i	−0.417663	−	0.671656i	0.571145	−	0.820849i	$-0.306499\pi$
$587$	−245.168	−	394.262i	−0.417663	−	0.671656i	−0.988808	+	0.149193i	$0.952333\pi$
$588$	208.908	−	779.656i	0.355286	−	1.32595i
$589$	405.188	+	13.2645i	0.687926	+	0.0225204i
$590$	186.431	−	37.0835i	0.315985	−	0.0628533i
$591$	−266.955	−	204.842i	−0.451701	−	0.346603i
$592$	1814.40	+	2532.00i	3.06487	+	4.27702i
$593$	433.296	−	379.991i	0.730685	−	0.640794i	−0.210924	−	0.977503i	$-0.567647\pi$
$593$	433.296	−	379.991i	0.730685	−	0.640794i	0.941609	+	0.336709i	$0.109314\pi$
$594$	6.29106	−	31.6273i	0.0105910	−	0.0532446i
$595$	573.850	+	133.803i	0.964454	+	0.224879i
$596$	696.573	−	22.8034i	1.16875	−	0.0382608i
$597$	−874.019	+	203.793i	−1.46402	+	0.341361i
$598$	2024.13	−	542.364i	3.38484	−	0.906964i
$599$	−519.025	+	554.157i	−0.866486	+	0.925138i	−0.997806	−	0.0662023i	$-0.978912\pi$
$599$	−519.025	+	554.157i	−0.866486	+	0.925138i	0.131320	+	0.991340i	$0.458078\pi$
$600$	1384.90	+	925.361i	2.30817	+	1.54227i
$601$	−105.593	−	56.4408i	−0.175696	−	0.0939114i	0.381204	−	0.924491i	$-0.375509\pi$
$601$	−105.593	−	56.4408i	−0.175696	−	0.0939114i	−0.556900	+	0.830579i	$0.688009\pi$
$602$	946.766	+	1153.64i	1.57270	+	1.91634i
$603$	195.736	−	520.059i	0.324604	−	0.862453i
$604$	−1036.88	+	1036.88i	−1.71669	+	1.71669i
$605$	−298.896	+	135.428i	−0.494043	+	0.223848i
$606$	48.2316	−	366.355i	0.0795901	−	0.604547i
$607$	416.676	−	844.936i	0.686452	−	1.39199i	−0.222436	−	0.974947i	$-0.571401\pi$
$607$	416.676	−	844.936i	0.686452	−	1.39199i	0.908888	−	0.417040i	$-0.136932\pi$
$608$	2141.86	+	353.622i	3.52279	+	0.581615i
$609$	71.4449	−	47.7380i	0.117315	−	0.0783874i
$610$	−22.4142	+	2.20761i	−0.0367446	+	0.00361903i
$611$	582.316	+	417.281i	0.953053	+	0.682948i
$612$	−2457.75	+	745.550i	−4.01593	+	1.21822i
$613$	301.520	−	148.693i	0.491877	−	0.242567i	−0.179396	−	0.983777i	$-0.557414\pi$
$613$	301.520	−	148.693i	0.491877	−	0.242567i	0.671273	+	0.741210i	$0.265748\pi$
$614$	−1183.99	+	401.910i	−1.92832	+	0.654577i
$615$	−27.9600	−	67.5014i	−0.0454634	−	0.109758i
$616$	−214.490	+	261.356i	−0.348198	+	0.424280i
$617$	−495.116	−	857.566i	−0.802457	−	1.38990i	−0.917995	−	0.396593i	$-0.870192\pi$
$617$	−495.116	−	857.566i	−0.802457	−	1.38990i	0.115538	−	0.993303i	$-0.463141\pi$
$618$	−992.774	−	573.178i	−1.60643	−	0.927473i
$619$	−170.830	−	453.883i	−0.275977	−	0.733252i	−0.999095	−	0.0425284i	$-0.986459\pi$
$619$	−170.830	−	453.883i	−0.275977	−	0.733252i	0.723119	−	0.690724i	$-0.242708\pi$
$620$	−339.172	−	153.677i	−0.547052	−	0.247866i
$621$	100.735	−	161.995i	0.162214	−	0.260862i
$622$	351.555	+	375.351i	0.565201	+	0.603459i
$623$	−45.5874	−	276.119i	−0.0731741	−	0.443209i
$624$	746.798	−	2461.86i	1.19679	−	3.94529i
$625$	−61.6921	−	80.3987i	−0.0987073	−	0.128638i
$626$	−1302.59	+	1485.32i	−2.08081	+	2.37271i
$627$	−23.9784	+	243.457i	−0.0382431	+	0.388289i
$628$	−868.934	+	464.455i	−1.38365	+	0.739578i
$629$	1718.15	+	711.683i	2.73156	+	1.13145i
$630$	−56.4096	+	860.644i	−0.0895391	+	1.36610i
$631$	787.887	+	51.6408i	1.24863	+	0.0818396i	0.675337	−	0.737509i	$-0.263998\pi$
$631$	787.887	+	51.6408i	1.24863	+	0.0818396i	0.573295	+	0.819349i	$0.305665\pi$
$632$	678.099	−	1637.08i	1.07294	−	2.59031i
$633$	−408.245	−	763.772i	−0.644936	−	1.20659i
$634$	1426.66	+	140.514i	2.25025	+	0.221630i
$635$	−70.7451	−	62.0418i	−0.111410	−	0.0977036i
$636$	433.857	−	332.910i	0.682165	−	0.523443i
$637$	243.875	+	73.9787i	0.382849	+	0.116136i
$638$	−16.3545	+	2.70014i	−0.0256341	+	0.00423220i
$639$	458.553	−	429.482i	0.717611	−	0.672116i
$640$	−170.985	−	106.325i	−0.267164	−	0.166133i
$641$	409.986	−	904.858i	0.639603	−	1.41163i	−0.255954	−	0.966689i	$-0.582390\pi$
$641$	409.986	−	904.858i	0.639603	−	1.41163i	0.895558	−	0.444946i	$-0.146777\pi$
$642$	−1226.80	+	461.733i	−1.91090	+	0.719211i
$643$	−456.470	+	790.629i	−0.709906	+	1.22959i	0.254986	+	0.966945i	$0.417929\pi$
$643$	−456.470	+	790.629i	−0.709906	+	1.22959i	−0.964892	+	0.262648i	$0.915404\pi$
$644$	−2899.04	+	1673.76i	−4.50162	+	2.59901i
$645$	−458.084	−	375.940i	−0.710207	−	0.582852i
$646$	2674.39	−	1107.77i	4.13992	−	1.71481i
$647$	35.0422	+	103.231i	0.0541611	+	0.159554i	0.970644	−	0.240520i	$-0.0773179\pi$
$647$	35.0422	+	103.231i	0.0541611	+	0.159554i	−0.916483	+	0.400073i	$0.868985\pi$
$648$	688.888	+	1396.93i	1.06310	+	2.15575i
$649$	9.82280	+	32.3814i	0.0151353	+	0.0498943i
$650$	−512.681	+	715.446i	−0.788741	+	1.10069i
$651$	47.2379	+	479.614i	0.0725620	+	0.736734i
$652$	24.1614	+	36.1601i	0.0370574	+	0.0554603i
$653$	77.0710	−	466.812i	0.118026	−	0.714874i	−0.860609	−	0.509267i	$-0.829917\pi$
$653$	77.0710	−	466.812i	0.118026	−	0.714874i	0.978635	−	0.205607i	$-0.0659167\pi$
$654$	−1357.37	−	669.383i	−2.07550	−	1.02352i
$655$	146.882	+	19.3374i	0.224248	+	0.0295228i
$656$	−106.391	−	234.809i	−0.162181	−	0.357941i
$657$	−287.123	−	287.123i	−0.437021	−	0.437021i
$658$	−1502.17	−	565.376i	−2.28293	−	0.859234i
$659$	−541.362	+	444.284i	−0.821490	+	0.674180i	−0.948170	−	0.317764i	$-0.897068\pi$
$659$	−541.362	+	444.284i	−0.821490	+	0.674180i	0.126680	+	0.991944i	$0.459568\pi$
$660$	105.921	−	198.165i	0.160487	−	0.300249i
$661$	−548.252	+	820.516i	−0.829427	+	1.24133i	0.138567	+	0.990353i	$0.455750\pi$
$661$	−548.252	+	820.516i	−0.829427	+	1.24133i	−0.967994	+	0.250973i	$0.919250\pi$
$662$	−341.205	−	319.574i	−0.515416	−	0.482740i
$663$	−397.528	−	1483.59i	−0.599590	−	2.23770i
$664$	311.350	+	1335.31i	0.468900	+	2.01100i
$665$	−22.6780	−	692.742i	−0.0341023	−	1.04172i
$666$	−618.129	+	2651.01i	−0.928121	+	3.98049i
$667$	−96.1733	−	19.1301i	−0.144188	−	0.0286808i
$668$	−1824.33	−	2080.25i	−2.73103	−	3.11414i
$669$	−476.019	+	341.110i	−0.711538	+	0.509881i
$670$	350.189	−	456.375i	0.522670	−	0.681156i
$671$	−0.782207	−	3.93242i	−0.00116573	−	0.00586054i
$672$	−84.4364	+	2579.26i	−0.125649	+	3.83819i
$673$	237.420	+	63.6164i	0.352778	+	0.0945266i	0.430856	−	0.902421i	$-0.358212\pi$
$673$	237.420	+	63.6164i	0.352778	+	0.0945266i	−0.0780779	+	0.996947i	$0.524878\pi$
$674$	−1228.70	+	764.057i	−1.82300	+	1.13362i
$675$	10.4583	+	79.4389i	0.0154938	+	0.117687i
$676$	175.989	+	59.7402i	0.260339	+	0.0883731i
$677$	6.22365	+	94.9546i	0.00919299	+	0.140258i	0.999988	+	0.00488754i	$0.00155576\pi$
$677$	6.22365	+	94.9546i	0.00919299	+	0.140258i	−0.990795	+	0.135370i	$0.956778\pi$
$678$		−	819.013i		−	1.20798i
$679$	−607.002	−	517.311i	−0.893965	−	0.761872i
$680$	−1588.60			−2.33617
$681$	824.774	−	54.0586i	1.21112	−	0.0793812i
$682$	29.8841	−	88.0357i	0.0438183	−	0.129085i
$683$	1246.92	−	164.160i	1.82565	−	0.240351i	0.861885	−	0.507104i	$-0.169284\pi$
$683$	1246.92	−	164.160i	1.82565	−	0.240351i	0.963765	+	0.266753i	$0.0859508\pi$
$684$	1595.34	+	2565.51i	2.33236	+	3.75074i
$685$	−126.799	+	473.220i	−0.185108	+	0.690833i
$686$	932.589	+	30.5298i	1.35946	+	0.0445041i
$687$	1703.20	−	338.788i	2.47919	−	0.493141i
$688$	−1658.79	−	1272.83i	−2.41103	−	1.85005i
$689$	100.573	+	140.350i	0.145970	+	0.203701i
$690$	1401.63	−	1229.19i	2.03134	−	1.78144i
$691$	216.522	−	1088.53i	0.313346	−	1.57530i	−0.427750	−	0.903897i	$-0.640694\pi$
$691$	216.522	−	1088.53i	0.313346	−	1.57530i	0.741096	−	0.671399i	$-0.234306\pi$
$692$	537.767	+	125.390i	0.777121	+	0.181199i
$693$	−153.458	+	5.02368i	−0.221440	+	0.00724918i
$694$	−1082.83	+	252.481i	−1.56027	+	0.363805i
$695$	−144.561	+	38.7351i	−0.208002	+	0.0557340i
$696$	−158.359	+	169.078i	−0.227527	+	0.242928i
$697$	−127.968	−	85.5054i	−0.183598	−	0.122676i
$698$	−1151.56	−	615.523i	−1.64980	−	0.881838i
$699$	735.081	+	895.698i	1.05162	+	1.28140i
$700$	495.277	−	1315.92i	0.707539	−	1.87989i
$701$	495.699	−	495.699i	0.707131	−	0.707131i	−0.258800	−	0.965931i	$-0.583327\pi$
$701$	495.699	−	495.699i	0.707131	−	0.707131i	0.965931	+	0.258800i	$0.0833270\pi$
$702$	216.922	−	98.2863i	0.309006	−	0.140009i
$703$	285.532	−	2168.83i	0.406162	−	3.08510i
$704$	79.0452	−	160.288i	0.112280	−	0.227682i
$705$	628.813	+	103.817i	0.891934	+	0.147259i
$706$	394.402	−	263.531i	0.558642	−	0.373273i
$707$	−185.477	+	18.2679i	−0.262343	+	0.0258386i
$708$	643.368	+	461.031i	0.908712	+	0.651174i
$709$	−298.764	+	90.6291i	−0.421388	+	0.127827i	−0.493855	−	0.869544i	$-0.664413\pi$
$709$	−298.764	+	90.6291i	−0.421388	+	0.127827i	0.0724672	+	0.997371i	$0.476913\pi$
$710$	583.328	−	287.666i	0.821589	−	0.405163i
$711$	761.982	−	258.658i	1.07171	−	0.363795i
$712$	288.732	+	697.062i	0.405523	+	0.979019i
$713$	348.901	−	425.138i	0.489343	−	0.596266i
$714$	1720.59	+	2980.15i	2.40979	+	4.17388i
$715$	61.4398	+	35.4723i	0.0859298	+	0.0496116i
$716$	671.100	+	1783.07i	0.937291	+	2.49032i
$717$	758.605	+	343.720i	1.05803	+	0.479386i
$718$	−354.629	+	570.289i	−0.493912	+	0.794275i
$719$	512.007	+	546.664i	0.712110	+	0.760312i	0.979098	−	0.203388i	$-0.0651952\pi$
$719$	512.007	+	546.664i	0.712110	+	0.760312i	−0.266988	+	0.963700i	$0.586029\pi$
$720$	−196.836	−	1192.22i	−0.273383	−	1.65586i
$721$	−167.840	+	553.295i	−0.232788	+	0.767399i
$722$	−1252.40	−	1632.16i	−1.73463	−	2.26061i
$723$	−519.363	+	592.220i	−0.718345	+	0.819115i
$724$	−101.716	+	1032.74i	−0.140492	+	1.42644i
$725$	36.3232	−	19.4152i	0.0501010	−	0.0267795i
$726$	−1770.50	−	733.365i	−2.43870	−	1.01014i
$727$	−41.1429	+	627.720i	−0.0565928	+	0.863439i	0.871337	+	0.490685i	$0.163253\pi$
$727$	−41.1429	+	627.720i	−0.0565928	+	0.863439i	−0.927930	+	0.372754i	$0.878413\pi$
$728$	−2491.61	−	163.309i	−3.42254	−	0.224325i
$729$	−340.703	+	822.529i	−0.467356	+	1.12830i
$730$	−198.154	−	370.721i	−0.271444	−	0.507837i
$731$	−1242.28	−	122.354i	−1.69943	−	0.167379i
$732$	−70.5100	−	61.8356i	−0.0963252	−	0.0844749i
$733$	817.649	−	627.404i	1.11548	−	0.855940i	0.124807	−	0.992181i	$-0.460169\pi$
$733$	817.649	−	627.404i	1.11548	−	0.855940i	0.990676	+	0.136241i	$0.0435021\pi$
$734$	−1019.80	−	309.353i	−1.38938	−	0.421462i
$735$	223.694	−	36.9320i	0.304346	−	0.0502477i
$736$	2149.45	−	2013.18i	2.92044	−	2.73529i
$737$	86.9626	+	54.0768i	0.117995	+	0.0733742i
$738$	92.9730	−	205.196i	0.125980	−	0.278043i
$739$	612.049	−	230.359i	0.828212	−	0.311717i	0.0982133	−	0.995165i	$-0.468687\pi$
$739$	612.049	−	230.359i	0.828212	−	0.311717i	0.729999	+	0.683448i	$0.239521\pi$
$740$	−1004.63	+	1740.06i	−1.35760	+	2.35143i
$741$	−1564.63	+	903.340i	−2.11151	+	1.21908i
$742$	−299.037	−	245.413i	−0.403014	−	0.330745i
$743$	−664.321	+	275.171i	−0.894106	+	0.370351i	−0.781951	−	0.623340i	$-0.785775\pi$
$743$	−664.321	+	275.171i	−0.894106	+	0.370351i	−0.112155	+	0.993691i	$0.535775\pi$
$744$	−417.645	−	1230.34i	−0.561350	−	1.65368i
$745$	86.5844	+	175.576i	0.116221	+	0.235672i
$746$	585.583	+	1930.41i	0.784964	+	2.58768i
$747$	−362.685	+	506.126i	−0.485522	+	0.677545i
$748$	−46.3933	−	471.039i	−0.0620231	−	0.629731i
$749$	367.308	+	549.716i	0.490398	+	0.733933i
$750$	−312.858	+	1894.95i	−0.417144	+	2.52660i
$751$	123.894	+	61.0976i	0.164972	+	0.0813550i	0.522900	−	0.852394i	$-0.324850\pi$
$751$	123.894	+	61.0976i	0.164972	+	0.0813550i	−0.357928	+	0.933749i	$0.616517\pi$
$752$	2229.44	+	293.511i	2.96467	+	0.390307i
$753$	−616.705	−	1361.10i	−0.818997	−	1.80756i
$754$	−86.5616	−	86.5616i	−0.114803	−	0.114803i
$755$	−385.487	−	145.087i	−0.510579	−	0.192168i
$756$	−294.080	+	241.345i	−0.388994	+	0.319239i
$757$	60.0456	−	112.337i	0.0793205	−	0.148398i	−0.839134	−	0.543924i	$-0.816938\pi$
$757$	60.0456	−	112.337i	0.0793205	−	0.148398i	0.918455	+	0.395526i	$0.129438\pi$
$758$	−311.601	+	466.343i	−0.411083	+	0.615228i
$759$	242.223	+	226.866i	0.319134	+	0.298902i
$760$	483.638	+	1804.96i	0.636365	+	2.37495i
$761$	201.086	+	862.411i	0.264239	+	1.13326i	0.924184	+	0.381947i	$0.124746\pi$
$761$	201.086	+	862.411i	0.264239	+	1.13326i	−0.659945	+	0.751314i	$0.729421\pi$
$762$	−17.9798	−	549.227i	−0.0235956	−	0.720771i
$763$	−173.338	+	743.404i	−0.227179	+	0.974317i
$764$	−3345.27	−	665.415i	−4.37862	−	0.870962i
$765$	−475.664	−	542.391i	−0.621783	−	0.709008i
$766$	−107.669	+	77.1547i	−0.140560	+	0.100724i
$767$	−152.132	+	198.262i	−0.198347	+	0.258491i
$768$	98.8658	+	497.032i	0.128731	+	0.647177i
$769$	43.0329	−	1314.52i	0.0559596	−	1.70939i	−0.490120	−	0.871655i	$-0.663047\pi$
$769$	43.0329	−	1314.52i	0.0559596	−	1.70939i	0.546079	−	0.837734i	$-0.316120\pi$
$770$	−153.532	−	41.1388i	−0.199392	−	0.0534270i
$771$	970.476	−	603.481i	1.25872	−	0.782725i
$772$	−182.444	−	1385.80i	−0.236327	−	1.79508i
$773$	−462.630	−	157.042i	−0.598486	−	0.203159i	0.00572415	−	0.999984i	$-0.498178\pi$
$773$	−462.630	−	157.042i	−0.598486	−	0.203159i	−0.604210	+	0.796825i	$0.706511\pi$
$774$	−119.502	−	1823.25i	−0.154396	−	2.35562i
$775$			231.003i			0.298068i
$776$	1910.42	+	986.632i	2.46189	+	1.27143i
$777$	2600.49			3.34683
$778$	−763.386	+	50.0350i	−0.981216	+	0.0643123i
$779$	−58.1920	+	171.428i	−0.0747009	+	0.220062i
$780$	1645.23	−	216.599i	2.10927	−	0.277691i
$781$	61.1418	+	98.3240i	0.0782866	+	0.125895i
$782$	1016.39	−	3793.22i	1.29973	−	4.85066i
$783$	−11.1379	−	0.364618i	−0.0142247	−	0.000465668i
$784$	784.572	−	156.061i	1.00073	−	0.199058i
$785$	−219.563	−	168.476i	−0.279698	−	0.214620i
$786$	503.957	+	703.271i	0.641167	+	0.894747i
$787$	−763.528	+	669.596i	−0.970175	+	0.850821i	−0.988836	−	0.149005i	$-0.952393\pi$
$787$	−763.528	+	669.596i	−0.970175	+	0.850821i	0.0186615	+	0.999826i	$0.494060\pi$
$788$	149.401	−	751.088i	0.189595	−	0.953157i
$789$	−590.098	−	137.591i	−0.747906	−	0.174387i
$790$	832.585	−	27.2560i	1.05391	−	0.0345013i
$791$	−402.297	+	93.8025i	−0.508593	+	0.118587i
$792$	399.838	−	107.136i	0.504846	−	0.135273i
$793$	20.2416	−	21.6118i	0.0255254	−	0.0272532i
$794$	569.262	+	380.369i	0.716955	+	0.479054i
$795$	135.470	+	72.4104i	0.170403	+	0.0910823i
$796$	−1295.75	−	1578.87i	−1.62782	−	1.98351i
$797$	106.529	−	283.042i	0.133663	−	0.355134i	−0.852075	−	0.523419i	$-0.824656\pi$
$797$	106.529	−	283.042i	0.133663	−	0.355134i	0.985738	+	0.168285i	$0.0538229\pi$
$798$	2862.22	−	2862.22i	3.58674	−	3.58674i
$799$	1222.85	−	554.065i	1.53047	−	0.693448i
$800$	−161.456	+	1226.38i	−0.201821	+	1.53298i
$801$	−151.543	+	307.298i	−0.189192	+	0.383643i
$802$	724.790	+	119.663i	0.903729	+	0.149206i
$803$	62.2200	−	41.5741i	0.0774844	−	0.0517734i
$804$	2383.77	−	234.781i	2.96489	−	0.292016i
$805$	−764.306	−	547.694i	−0.949448	−	0.680365i
$806$	657.035	−	199.309i	0.815180	−	0.247282i
$807$	−1108.05	+	546.430i	−1.37305	+	0.677112i
$808$	475.799	−	161.512i	0.588860	−	0.199891i
$809$	−99.0038	−	239.016i	−0.122378	−	0.295447i	0.850804	−	0.525483i	$-0.176115\pi$
$809$	−99.0038	−	239.016i	−0.122378	−	0.295447i	−0.973182	+	0.230036i	$0.926115\pi$
$810$	−464.525	+	566.026i	−0.573488	+	0.698797i
$811$	442.056	+	765.664i	0.545075	+	0.944098i	0.998602	+	0.0528557i	$0.0168323\pi$
$811$	442.056	+	765.664i	0.545075	+	0.944098i	−0.453527	+	0.891243i	$0.649834\pi$
$812$	169.356	+	97.7776i	0.208566	+	0.120416i
$813$	−554.072	−	1472.13i	−0.681516	−	1.81074i
$814$	−456.942	−	207.038i	−0.561354	−	0.254346i
$815$	−6.45071	+	10.3736i	−0.00791498	+	0.0127283i
$816$	−3295.68	−	3518.76i	−4.03882	−	4.31221i
$817$	239.186	+	1448.73i	0.292761	+	1.77323i
$818$	41.1980	−	135.812i	0.0503643	−	0.166029i
$819$	−690.289	−	899.602i	−0.842843	−	1.09841i
$820$	109.636	−	125.016i	0.133703	−	0.152459i
$821$	−137.009	+	1391.08i	−0.166881	+	1.69437i	0.438736	+	0.898616i	$0.355426\pi$
$821$	−137.009	+	1391.08i	−0.166881	+	1.69437i	−0.605617	+	0.795756i	$0.707074\pi$
$822$	−2523.27	+	1348.71i	−3.06967	+	1.64077i
$823$	−1006.78	−	417.022i	−1.22330	−	0.506709i	−0.324846	−	0.945767i	$-0.605312\pi$
$823$	−1006.78	−	417.022i	−1.22330	−	0.506709i	−0.898459	+	0.439058i	$0.855312\pi$
$824$	101.951	−	1555.47i	0.123726	−	1.88770i
$825$	−139.096	−	9.11685i	−0.168602	−	0.0110507i
$826$	214.264	−	517.280i	0.259400	−	0.626247i
$827$	723.709	+	1353.96i	0.875101	+	1.63720i	0.765697	+	0.643202i	$0.222394\pi$
$827$	723.709	+	1353.96i	0.875101	+	1.63720i	0.109405	+	0.993997i	$0.465106\pi$
$828$	4078.69	+	401.716i	4.92595	+	0.485164i
$829$	183.192	+	160.655i	0.220979	+	0.193794i	0.762677	−	0.646780i	$-0.223885\pi$
$829$	183.192	+	160.655i	0.220979	+	0.193794i	−0.541697	+	0.840574i	$0.682218\pi$
$830$	−511.389	+	392.402i	−0.616131	+	0.472774i
$831$	499.931	+	151.652i	0.601602	+	0.182494i
$832$	1302.24	−	215.001i	1.56520	−	0.258415i
$833$	348.573	−	326.474i	0.418455	−	0.391925i
$834$	−742.221	−	461.543i	−0.889953	−	0.553408i
$835$	320.750	−	707.909i	0.384131	−	0.847796i
$836$	−521.069	+	196.117i	−0.623288	+	0.234589i
$837$	31.2514	−	54.1291i	0.0373374	−	0.0646704i
$838$	1091.26	−	630.041i	1.30222	−	0.751839i
$839$	−928.593	−	762.076i	−1.10679	−	0.908315i	−0.110453	−	0.993881i	$-0.535230\pi$
$839$	−928.593	−	762.076i	−1.10679	−	0.908315i	−0.996332	+	0.0855661i	$0.972730\pi$
$840$	−2052.28	+	850.084i	−2.44320	+	1.01200i
$841$	−268.489	−	790.944i	−0.319250	−	0.940480i
$842$	−774.479	−	1570.49i	−0.919809	−	1.86519i
$843$	487.816	+	1608.11i	0.578667	+	1.90761i
$844$	1148.04	−	1602.09i	1.36024	−	1.89821i
$845$	5.11687	+	51.9524i	0.00605546	+	0.0614822i
$846$	1091.74	+	1633.90i	1.29047	+	1.93132i
$847$	−157.450	+	953.658i	−0.185891	+	1.12592i
$848$	486.083	+	239.709i	0.573211	+	0.282676i
$849$	−926.846	−	122.022i	−1.09169	−	0.143724i
$850$	680.736	+	1502.42i	0.800866	+	1.76755i
$851$	−2098.44	−	2098.44i	−2.46585	−	2.46585i
$852$	2534.66	+	953.980i	2.97496	+	1.11969i
$853$	−709.930	+	582.624i	−0.832274	+	0.683030i	−0.950761	−	0.309926i	$-0.899696\pi$
$853$	−709.930	+	582.624i	−0.832274	+	0.683030i	0.118487	+	0.992956i	$0.462196\pi$
$854$	−31.2731	+	58.5079i	−0.0366196	+	0.0685105i
$855$	−471.450	+	705.575i	−0.551404	+	0.825234i
$856$	−1300.93	−	1218.45i	−1.51978	−	1.42343i
$857$	343.301	+	1281.22i	0.400584	+	1.49500i	0.812057	+	0.583579i	$0.198348\pi$
$857$	343.301	+	1281.22i	0.400584	+	1.49500i	−0.411472	+	0.911422i	$0.634985\pi$
$858$	94.0815	+	403.494i	0.109652	+	0.470272i
$859$	4.85219	+	148.219i	0.00564865	+	0.172549i	0.998558	+	0.0536773i	$0.0170942\pi$
$859$	4.85219	+	148.219i	0.00564865	+	0.172549i	−0.992910	+	0.118871i	$0.962072\pi$
$860$	306.250	−	1313.43i	0.356104	−	1.52725i
$861$	−211.075	−	41.9854i	−0.245151	−	0.0487636i
$862$	1115.43	+	1271.90i	1.29400	+	1.47552i
$863$	−29.7793	+	21.3395i	−0.0345067	+	0.0247271i	−0.599600	−	0.800300i	$-0.704674\pi$
$863$	−29.7793	+	21.3395i	−0.0345067	+	0.0247271i	0.565093	+	0.825027i	$0.308840\pi$
$864$	203.745	−	265.526i	0.235816	−	0.307322i
$865$	30.2594	+	152.124i	0.0349820	+	0.175866i
$866$	−9.43918	+	288.337i	−0.0108997	+	0.332953i
$867$	−1561.33	−	418.358i	−1.80084	−	0.482535i
$868$	−931.416	+	579.192i	−1.07306	+	0.667272i
$869$	19.3564	+	147.027i	0.0222744	+	0.169191i
$870$	−103.126	−	35.0067i	−0.118536	−	0.0402376i
$871$	49.4632	+	754.663i	0.0567890	+	0.866433i
$872$		−	2057.98i		−	2.36007i
$873$	235.163	+	947.692i	0.269373	+	1.08556i
$874$	−4619.27			−5.28521
$875$	966.627	−	63.3561i	1.10472	−	0.0724070i
$876$	562.629	−	1657.45i	0.642271	−	1.89207i
$877$	705.345	−	92.8604i	0.804270	−	0.105884i	0.282828	−	0.959171i	$-0.408728\pi$
$877$	705.345	−	92.8604i	0.804270	−	0.105884i	0.521442	+	0.853287i	$0.325394\pi$
$878$	1640.69	+	2638.45i	1.86867	+	3.00507i
$879$	201.383	−	751.571i	0.229105	−	0.855030i
$880$	222.568	+	7.28613i	0.252918	+	0.00827969i
$881$	1096.37	−	218.081i	1.24446	−	0.247538i	0.471426	−	0.881906i	$-0.343739\pi$
$881$	1096.37	−	218.081i	1.24446	−	0.247538i	0.773031	+	0.634368i	$0.218739\pi$
$882$	554.598	+	425.558i	0.628796	+	0.482492i
$883$	430.596	+	600.896i	0.487651	+	0.680516i	0.982029	−	0.188731i	$-0.0604374\pi$
$883$	430.596	+	600.896i	0.487651	+	0.680516i	−0.494378	+	0.869247i	$0.664604\pi$
$884$	2628.10	−	2304.78i	2.97296	−	2.60722i
$885$	−43.3732	+	218.052i	−0.0490092	+	0.246386i
$886$	954.082	+	222.461i	1.07684	+	0.251084i
$887$	−287.971	+	9.42720i	−0.324657	+	0.0106282i	−0.194613	−	0.980880i	$-0.562345\pi$
$887$	−287.971	+	9.42720i	−0.324657	+	0.0106282i	−0.130044	+	0.991508i	$0.541512\pi$
$888$	−6827.77	+	1592.01i	−7.68893	+	1.79281i
$889$	−267.720	+	71.7353i	−0.301147	+	0.0806921i
$890$	−242.471	+	258.884i	−0.272440	+	0.290881i
$891$	−108.384	−	72.4196i	−0.121643	−	0.0812790i
$892$	−1175.41	−	628.271i	−1.31773	−	0.704339i
$893$	−1001.81	−	1220.71i	−1.12185	−	1.36698i
$894$	−402.716	+	1069.99i	−0.450465	+	1.19686i
$895$	−378.404	+	378.404i	−0.422798	+	0.422798i
$896$	−540.213	+	244.767i	−0.602916	+	0.273178i
$897$	−319.914	+	2429.99i	−0.356649	+	2.70902i
$898$	132.909	−	269.513i	0.148006	−	0.300126i
$899$	−31.6993	−	5.23358i	−0.0352606	−	0.00582155i
$900$	−1431.32	+	956.377i	−1.59035	+	1.06264i
$901$	322.014	−	31.7157i	0.357397	−	0.0352005i
$902$	33.7462	+	24.1822i	0.0374126	+	0.0268095i
$903$	−1670.36	+	506.698i	−1.84979	+	0.561127i
$904$	998.833	−	492.570i	1.10490	−	0.544878i
$905$	−276.020	+	93.6960i	−0.304994	+	0.103532i
$906$	−920.515	−	2222.32i	−1.01602	−	2.45289i
$907$	39.7621	−	48.4502i	0.0438391	−	0.0534181i	−0.750629	−	0.660724i	$-0.770250\pi$
$907$	39.7621	−	48.4502i	0.0438391	−	0.0534181i	0.794468	+	0.607305i	$0.207750\pi$
$908$	940.547	+	1629.08i	1.03584	+	1.79414i
$909$	197.610	+	114.090i	0.217393	+	0.125512i
$910$	−413.494	−	1098.63i	−0.454389	−	1.20728i
$911$	−805.110	−	364.791i	−0.883765	−	0.400429i	−0.0809931	−	0.996715i	$-0.525809\pi$
$911$	−805.110	−	364.791i	−0.883765	−	0.400429i	−0.802772	+	0.596286i	$0.796643\pi$
$912$	−2994.66	+	4815.80i	−3.28362	+	5.28049i
$913$	−78.4419	−	83.7516i	−0.0859167	−	0.0917323i
$914$	409.248	+	2478.78i	0.447755	+	2.71201i
$915$	7.64688	−	25.2084i	0.00835725	−	0.0275502i
$916$	2405.94	+	3135.48i	2.62657	+	3.42301i
$917$	287.726	−	328.089i	0.313769	−	0.357785i
$918$	43.7443	−	444.144i	0.0476518	−	0.483817i
$919$	1025.41	−	548.094i	1.11579	−	0.596403i	0.192805	−	0.981237i	$-0.438241\pi$
$919$	1025.41	−	548.094i	1.11579	−	0.596403i	0.922986	+	0.384834i	$0.125741\pi$
$920$	2342.04	+	970.103i	2.54569	+	1.05446i
$921$	95.6465	−	1459.28i	0.103851	−	1.58445i
$922$	1560.92	+	102.308i	1.69298	+	0.110964i
$923$	−327.228	+	789.999i	−0.354527	+	0.855904i
$924$	−311.995	−	583.702i	−0.337657	−	0.631712i
$925$	1240.48	+	122.176i	1.34105	+	0.132082i
$926$	186.239	+	163.327i	0.201122	+	0.176379i
$927$	561.605	−	430.935i	0.605831	−	0.464870i
$928$	−164.632	−	49.9406i	−0.177405	−	0.0538153i
$929$	549.223	−	90.6770i	0.591198	−	0.0976071i	0.140186	−	0.990125i	$-0.455230\pi$
$929$	549.223	−	90.6770i	0.591198	−	0.0976071i	0.451012	+	0.892518i	$0.351063\pi$
$930$	445.818	−	417.554i	0.479374	−	0.448983i
$931$	−477.059	−	296.654i	−0.512416	−	0.318641i
$932$	−1088.34	+	2402.01i	−1.16774	+	2.57726i
$933$	−562.949	+	211.879i	−0.603375	+	0.227094i
$934$	1293.84	−	2241.00i	1.38527	−	2.39936i
$935$	115.138	−	66.4749i	0.123142	−	0.0710962i
$936$	2363.14	+	1939.38i	2.52472	+	2.07198i
$937$	−1652.83	+	684.625i	−1.76396	+	0.730656i	−0.768042	+	0.640399i	$0.778769\pi$
$937$	−1652.83	+	684.625i	−1.76396	+	0.730656i	−0.995919	+	0.0902569i	$0.971231\pi$
$938$	−544.652	−	1604.49i	−0.580653	−	1.71055i
$939$	−1021.98	−	2072.36i	−1.08837	−	2.20699i
$940$	421.047	+	1388.00i	0.447922	+	1.47660i
$941$	526.852	−	735.221i	0.559885	−	0.781319i	−0.432872	−	0.901455i	$-0.642500\pi$
$941$	526.852	−	735.221i	0.559885	−	0.781319i	0.992757	+	0.120136i	$0.0383331\pi$
$942$	−158.419	−	1608.46i	−0.168173	−	1.70749i
$943$	136.445	+	204.204i	0.144693	+	0.216548i
$944$	−127.779	+	773.945i	−0.135359	+	0.819858i
$945$	−95.8397	−	47.2629i	−0.101418	−	0.0500137i
$946$	333.846	+	43.9517i	0.352903	+	0.0464606i
$947$	429.732	+	948.439i	0.453783	+	1.00152i	0.987754	+	0.156017i	$0.0498656\pi$
$947$	429.732	+	948.439i	0.453783	+	1.00152i	−0.533972	+	0.845502i	$0.679301\pi$
$948$	2452.75	+	2452.75i	2.58728	+	2.58728i
$949$	517.223	+	194.669i	0.545019	+	0.205131i
$950$	1499.80	−	1230.85i	1.57873	−	1.29563i
$951$	−790.394	+	1478.72i	−0.831119	+	1.55491i
$952$	−2599.67	+	3890.68i	−2.73075	+	4.08685i
$953$	848.651	+	794.848i	0.890505	+	0.834049i	0.986906	−	0.161294i	$-0.0515667\pi$
$953$	848.651	+	794.848i	0.890505	+	0.834049i	−0.0964018	+	0.995343i	$0.530733\pi$
$954$	122.582	+	457.484i	0.128493	+	0.479543i
$955$	−217.552	−	933.030i	−0.227803	−	0.976995i
$956$	62.0166	+	1894.41i	0.0648709	+	1.98160i
$957$	4.40241	−	18.8809i	0.00460022	−	0.0197293i
$958$	28.4847	+	5.66596i	0.0297335	+	0.00591436i
$959$	951.477	+	1084.95i	0.992155	+	1.13134i
$960$	954.449	−	683.948i	0.994218	−	0.712446i
$961$	−475.321	+	619.451i	−0.494611	+	0.644590i
$962$	−722.780	−	3633.66i	−0.751331	−	3.77720i
$963$	26.4841	−	809.007i	0.0275017	−	0.840090i
$964$	−1731.60	−	463.979i	−1.79626	−	0.481307i
$965$	333.410	−	207.328i	0.345502	−	0.214847i
$966$	−716.753	−	5444.28i	−0.741981	−	5.63590i
$967$	828.247	+	281.152i	0.856512	+	0.290747i	0.714944	−	0.699182i	$-0.246452\pi$
$967$	828.247	+	281.152i	0.856512	+	0.290747i	0.141568	+	0.989929i	$0.454786\pi$
$968$	−170.432	−	2600.29i	−0.176066	−	2.68625i
$969$			3385.71i			3.49403i
$970$	−51.8271	+	1009.50i	−0.0534300	+	1.04072i
$971$	1318.16			1.35753			0.678763	−	0.734358i	$-0.262516\pi$
$971$	1318.16			1.35753			0.678763	+	0.734358i	$0.262516\pi$
$972$	−3458.01	+	226.650i	−3.55762	+	0.233179i
$973$	−141.701	+	417.438i	−0.145633	+	0.429021i
$974$	−145.651	+	19.1753i	−0.149539	+	0.0196872i
$975$	−543.624	−	874.219i	−0.557563	−	0.896635i
$976$	24.0559	−	89.7778i	0.0246474	−	0.0919854i
$977$	646.710	+	21.1711i	0.661934	+	0.0216695i	0.361840	−	0.932240i	$-0.382149\pi$
$977$	646.710	+	21.1711i	0.661934	+	0.0216695i	0.300094	+	0.953910i	$0.402982\pi$
$978$	−69.9689	+	13.9177i	−0.0715429	+	0.0142308i
$979$	−50.0953	−	38.4394i	−0.0511698	−	0.0392640i
$980$	300.551	+	419.418i	0.306685	+	0.427978i
$981$	702.650	−	616.208i	0.716259	−	0.628142i
$982$	−120.613	+	606.362i	−0.122824	+	0.617477i
$983$	−285.645	−	66.6031i	−0.290585	−	0.0677549i	0.0792425	−	0.996855i	$-0.474750\pi$
$983$	−285.645	−	66.6031i	−0.290585	−	0.0677549i	−0.369827	+	0.929100i	$0.620583\pi$
$984$	579.896	−	18.9838i	0.589325	−	0.0192925i
$985$	209.486	−	48.8453i	0.212676	−	0.0495892i
$986$	−221.591	+	59.3753i	−0.224738	+	0.0602183i
$987$	1283.29	−	1370.15i	1.30019	−	1.38820i
$988$	−3418.79	−	2284.36i	−3.46031	−	2.31211i
$989$	1756.75	+	939.004i	1.77629	+	0.949448i
$990$	123.455	+	150.430i	0.124702	+	0.151949i
$991$	642.854	−	1708.02i	0.648693	−	1.72353i	−0.0407246	−	0.999170i	$-0.512967\pi$
$991$	642.854	−	1708.02i	0.648693	−	1.72353i	0.689417	−	0.724365i	$-0.257867\pi$
$992$	682.304	−	682.304i	0.687807	−	0.687807i
$993$	498.044	−	225.661i	0.501555	−	0.227252i
$994$	250.061	−	1899.40i	0.251570	−	1.91086i
$995$	253.747	−	514.549i	0.255023	−	0.517135i
$996$	−2648.20	−	437.220i	−2.65884	−	0.438975i
$997$	−1363.07	+	910.777i	−1.36718	+	0.913518i	−0.999863	−	0.0165798i	$-0.994722\pi$
$997$	−1363.07	+	910.777i	−1.36718	+	0.913518i	−0.367313	+	0.930097i	$0.619722\pi$
$998$	−2008.60	+	197.830i	−2.01262	+	0.198226i
$999$	−274.142	−	196.447i	−0.274416	−	0.196644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.3.l.a.7.1	✓	480
97.14	odd	96	inner	97.3.l.a.14.1	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.3.l.a.7.1	✓	480	1.1	even	1	trivial
97.3.l.a.14.1	yes	480	97.14	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+(-3.72531 + 0.244169i) q^{2} +(1.40357 - 4.13477i) q^{3} +(9.85250 - 1.29711i) q^{4} +(1.47402 + 2.37041i) q^{5} +(-4.21913 + 15.7460i) q^{6} +(8.21761 + 0.269017i) q^{7} +(-21.7406 + 4.32448i) q^{8} +(-7.98615 - 6.12799i) q^{9} +(-6.06995 - 8.47060i) q^{10} +(1.39475 - 1.22317i) q^{11} +(8.46539 - 42.5584i) q^{12} +(13.3425 + 3.11104i) q^{13} +(-30.6788 + 1.00432i) q^{14} +(11.8700 - 2.76769i) q^{15} +(41.5389 - 11.1303i) q^{16} +(17.5509 - 18.7390i) q^{17} +(31.2471 + 20.8787i) q^{18} +(-26.6344 - 14.2364i) q^{19} +(17.5974 + 21.4425i) q^{20} +(12.6463 - 33.6004i) q^{21} +(-4.89722 + 4.89722i) q^{22} +(-37.3182 + 16.9087i) q^{23} +(-12.6337 + 95.9621i) q^{24} +(7.61109 - 15.4338i) q^{25} +(-50.4647 - 8.33175i) q^{26} +(-3.87142 + 2.58680i) q^{27} +(81.3130 - 8.00863i) q^{28} +(1.94546 + 1.39410i) q^{29} +(-43.5436 + 13.2088i) q^{30} +(-12.0395 + 5.93721i) q^{31} +(-68.0667 + 23.1055i) q^{32} +(-3.09988 - 7.48378i) q^{33} +(-60.8072 + 74.0937i) q^{34} +(11.4752 + 19.8757i) q^{35} +(-86.6323 - 50.0172i) q^{36} +(25.5149 + 67.7915i) q^{37} +(102.697 + 46.5316i) q^{38} +(31.5906 - 50.8018i) q^{39} +(-42.2968 - 45.1598i) q^{40} +(-0.976473 - 5.91441i) q^{41} +(-38.9071 + 128.259i) q^{42} +(-29.5979 - 38.5727i) q^{43} +(12.1552 - 13.8604i) q^{44} +(2.75414 - 27.9632i) q^{45} +(134.893 - 72.1019i) q^{46} +(48.3093 + 20.0104i) q^{47} +(12.2813 - 187.376i) q^{48} +(18.5617 + 1.21660i) q^{49} +(-24.5852 + 59.3539i) q^{50} +(-52.8474 - 98.8705i) q^{51} +(135.493 + 13.3449i) q^{52} +(9.47531 + 8.30963i) q^{53} +(13.7906 - 10.5819i) q^{54} +(4.95529 + 1.50317i) q^{55} +(-179.819 + 29.6883i) q^{56} +(-96.2473 + 90.1455i) q^{57} +(-7.58782 - 4.71841i) q^{58} +(-7.52802 + 16.6147i) q^{59} +(113.359 - 42.6653i) q^{60} +(1.08065 - 1.87174i) q^{61} +(43.4010 - 25.0576i) q^{62} +(-63.9786 - 52.5059i) q^{63} +(89.0047 - 36.8670i) q^{64} +(12.2927 + 36.2131i) q^{65} +(13.3753 + 27.1225i) q^{66} +(16.0241 + 52.8244i) q^{67} +(148.614 - 207.391i) q^{68} +(17.5349 + 178.035i) q^{69} +(-47.6017 - 71.2410i) q^{70} +(-10.1668 + 61.5796i) q^{71} +(200.124 + 98.6903i) q^{72} +(39.9926 + 5.26513i) q^{73} +(-111.604 - 246.314i) q^{74} +(-53.1324 - 53.1324i) q^{75} +(-280.882 - 105.716i) q^{76} +(11.7906 - 9.67628i) q^{77} +(-105.280 + 196.966i) q^{78} +(-44.4114 + 66.4664i) q^{79} +(87.6124 + 82.0580i) q^{80} +(-18.1862 - 67.8718i) q^{81} +(5.08178 + 21.7946i) q^{82} +(-2.02386 - 61.8225i) q^{83} +(81.0142 - 347.451i) q^{84} +(70.2894 + 13.9814i) q^{85} +(119.679 + 136.468i) q^{86} +(8.49484 - 6.08732i) q^{87} +(-25.0332 + 32.6239i) q^{88} +(-6.64039 - 33.3835i) q^{89} +(-3.43224 + 104.844i) q^{90} +(108.807 + 29.1547i) q^{91} +(-345.746 + 214.998i) q^{92} +(7.65081 + 58.1137i) q^{93} +(-184.853 - 62.7491i) q^{94} +(-5.51346 - 84.1192i) q^{95} +313.870i q^{96} +(-75.8455 - 60.4686i) q^{97} -69.4449 q^{98} +(-18.6343 + 1.22135i) 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

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