LMFDB - Embedded newform 230.3.k.a.177.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,3,Mod(3,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.3"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([33, 32])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.k (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			177.11
Character	$\chi$	$=$	230.177
Dual form			230.3.k.a.13.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41061 + 0.100889i) q^{2} +(1.00325 - 4.61186i) q^{3} +(1.97964 - 0.284630i) q^{4} +(2.43231 + 4.36851i) q^{5} +(-0.949908 + 6.60675i) q^{6} +(-7.70337 - 4.20636i) q^{7} +(-2.76379 + 0.601225i) q^{8} +(-12.0761 - 5.51495i) q^{9} +(-3.87177 - 5.91687i) q^{10} +(-8.13630 - 9.38979i) q^{11} +(0.673402 - 9.41539i) q^{12} +(-1.12858 + 0.616250i) q^{13} +(11.2908 + 5.15635i) q^{14} +(22.5872 - 6.83477i) q^{15} +(3.83797 - 1.12693i) q^{16} +(11.7702 - 8.81103i) q^{17} +(17.5910 + 6.56111i) q^{18} +(-26.9883 + 3.88033i) q^{19} +(6.05851 + 7.95578i) q^{20} +(-27.1275 + 31.3068i) q^{21} +(12.4245 + 12.4245i) q^{22} +(-1.02190 - 22.9773i) q^{23} +13.3494i q^{24} +(-13.1677 + 21.2511i) q^{25} +(1.52981 - 0.983150i) q^{26} +(-12.0937 + 16.1552i) q^{27} +(-16.4472 - 6.13448i) q^{28} +(-47.5368 - 6.83476i) q^{29} +(-31.1721 + 11.9200i) q^{30} +(17.4061 + 11.1862i) q^{31} +(-5.30019 + 1.97687i) q^{32} +(-51.4671 + 28.1032i) q^{33} +(-15.7142 + 13.6164i) q^{34} +(-0.361467 - 43.8834i) q^{35} +(-25.4760 - 7.48043i) q^{36} +(48.8870 - 18.2339i) q^{37} +(37.6784 - 8.19644i) q^{38} +(1.70981 + 5.82310i) q^{39} +(-9.34885 - 10.6113i) q^{40} +(20.6473 + 45.2113i) q^{41} +(35.1078 - 46.8986i) q^{42} +(-2.50528 + 11.5166i) q^{43} +(-18.7796 - 16.2726i) q^{44} +(-5.28060 - 66.1684i) q^{45} +(3.75966 + 32.3089i) q^{46} +(-53.7481 - 53.7481i) q^{47} +(-1.34680 - 18.8308i) q^{48} +(15.1570 + 23.5848i) q^{49} +(16.4305 - 31.3055i) q^{50} +(-28.8268 - 63.1220i) q^{51} +(-2.05878 + 1.54118i) q^{52} +(5.50423 - 10.0802i) q^{53} +(15.4296 - 24.0088i) q^{54} +(21.2294 - 58.3824i) q^{55} +(23.8194 + 6.99402i) q^{56} +(-9.18042 + 128.359i) q^{57} +(67.7454 + 4.84525i) q^{58} +(-9.51039 + 32.3894i) q^{59} +(42.7691 - 19.9594i) q^{60} +(-6.34157 - 4.07548i) q^{61} +(-25.6818 - 14.0233i) q^{62} +(69.8284 + 93.2799i) q^{63} +(7.27706 - 3.32332i) q^{64} +(-5.43715 - 3.43129i) q^{65} +(69.7648 - 44.8351i) q^{66} +(89.3232 - 6.38852i) q^{67} +(20.7928 - 20.7928i) q^{68} +(-106.993 - 18.3391i) q^{69} +(4.93723 + 61.8659i) q^{70} +(56.6677 - 65.3980i) q^{71} +(36.6914 + 7.98172i) q^{72} +(21.8862 + 16.3838i) q^{73} +(-67.1209 + 30.6531i) q^{74} +(84.7967 + 82.0479i) q^{75} +(-52.3227 + 15.3633i) q^{76} +(23.1801 + 106.557i) q^{77} +(-2.99937 - 8.04162i) q^{78} +(23.0320 - 78.4397i) q^{79} +(14.2581 + 14.0252i) q^{80} +(-15.8712 - 18.3164i) q^{81} +(-33.6866 - 61.6924i) q^{82} +(-14.7683 - 39.5955i) q^{83} +(-44.7919 + 69.6976i) q^{84} +(67.1197 + 29.9869i) q^{85} +(2.37208 - 16.4982i) q^{86} +(-79.2121 + 212.376i) q^{87} +(28.1324 + 21.0597i) q^{88} +(51.8960 + 80.7517i) q^{89} +(14.1245 + 92.8051i) q^{90} +11.2860 q^{91} +(-8.56302 - 45.1960i) q^{92} +(69.0518 - 69.0518i) q^{93} +(81.2402 + 70.3950i) q^{94} +(-82.5950 - 108.460i) q^{95} +(3.79963 + 26.4270i) q^{96} +(35.3963 - 94.9012i) q^{97} +(-23.7601 - 31.7398i) q^{98} +(46.4702 + 158.263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{2} - 4 q^{5} - 74 q^{7} + 48 q^{8} - 16 q^{10} + 8 q^{11} + 44 q^{12} + 24 q^{13} + 24 q^{15} + 96 q^{16} + 12 q^{17} + 88 q^{18} - 24 q^{20} + 24 q^{21} + 8 q^{22} - 44 q^{23} - 128 q^{25}+ \cdots - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^2 - 4 * q^5 - 74 * q^7 + 48 * q^8 - 16 * q^10 + 8 * q^11 + 44 * q^12 + 24 * q^13 + 24 * q^15 + 96 * q^16 + 12 * q^17 + 88 * q^18 - 24 * q^20 + 24 * q^21 + 8 * q^22 - 44 * q^23 - 128 * q^25 + 48 * q^26 - 60 * q^27 - 116 * q^28 + 120 * q^30 - 12 * q^31 + 96 * q^32 - 334 * q^33 - 224 * q^35 - 176 * q^36 + 188 * q^37 + 76 * q^38 - 16 * q^40 - 116 * q^41 + 24 * q^42 + 120 * q^43 + 204 * q^45 + 396 * q^46 - 144 * q^47 - 88 * q^48 + 170 * q^50 - 176 * q^51 + 48 * q^52 + 192 * q^53 - 312 * q^55 + 296 * q^56 + 88 * q^57 - 28 * q^58 - 72 * q^60 - 552 * q^61 - 12 * q^62 - 122 * q^63 - 392 * q^65 - 8 * q^66 - 72 * q^67 - 24 * q^68 + 100 * q^70 + 424 * q^71 - 176 * q^72 + 452 * q^73 + 604 * q^75 - 112 * q^76 + 356 * q^77 + 32 * q^78 + 16 * q^80 - 704 * q^81 + 148 * q^82 - 360 * q^83 + 428 * q^85 - 376 * q^86 - 462 * q^87 - 104 * q^88 - 510 * q^90 + 432 * q^91 - 192 * q^93 - 166 * q^95 - 1042 * q^97 - 88 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−1.41061	+	0.100889i	−0.705305	+	0.0504444i
$2$	−1.41061	+	0.100889i	−0.705305	+	0.0504444i
$3$	1.00325	−	4.61186i	0.334416	−	1.53729i	−0.436119	−	0.899889i	$-0.643647\pi$
$3$	1.00325	−	4.61186i	0.334416	−	1.53729i	0.770535	−	0.637398i	$-0.219989\pi$
$4$	1.97964	−	0.284630i	0.494911	−	0.0711574i
$5$	2.43231	+	4.36851i	0.486462	+	0.873702i
$5$	2.43231	+	4.36851i	0.486462	+	0.873702i
$6$	−0.949908	+	6.60675i	−0.158318	+	1.10113i
$7$	−7.70337	−	4.20636i	−1.10048	−	0.600908i	−0.176868	−	0.984235i	$-0.556597\pi$
$7$	−7.70337	−	4.20636i	−1.10048	−	0.600908i	−0.923613	+	0.383327i	$0.874778\pi$
$8$	−2.76379	+	0.601225i	−0.345474	+	0.0751532i
$9$	−12.0761	−	5.51495i	−1.34178	−	0.612772i
$10$	−3.87177	−	5.91687i	−0.387177	−	0.591687i
$11$	−8.13630	−	9.38979i	−0.739664	−	0.853618i	0.253860	−	0.967241i	$-0.418300\pi$
$11$	−8.13630	−	9.38979i	−0.739664	−	0.853618i	−0.993524	+	0.113623i	$0.963754\pi$
$12$	0.673402	−	9.41539i	0.0561168	−	0.784616i
$13$	−1.12858	+	0.616250i	−0.0868137	+	0.0474039i	−0.522069	−	0.852903i	$-0.674840\pi$
$13$	−1.12858	+	0.616250i	−0.0868137	+	0.0474039i	0.435256	+	0.900307i	$0.356658\pi$
$14$	11.2908	+	5.15635i	0.806487	+	0.368310i
$15$	22.5872	−	6.83477i	1.50581	−	0.455651i
$16$	3.83797	−	1.12693i	0.239873	−	0.0704331i
$17$	11.7702	−	8.81103i	0.692362	−	0.518296i	−0.194167	−	0.980969i	$-0.562200\pi$
$17$	11.7702	−	8.81103i	0.692362	−	0.518296i	0.886529	+	0.462673i	$0.153109\pi$
$18$	17.5910	+	6.56111i	0.977278	+	0.364506i
$19$	−26.9883	+	3.88033i	−1.42043	+	0.204228i	−0.809345	−	0.587334i	$-0.800178\pi$
$19$	−26.9883	+	3.88033i	−1.42043	+	0.204228i	−0.611090	+	0.791561i	$0.709269\pi$
$20$	6.05851	+	7.95578i	0.302926	+	0.397789i
$21$	−27.1275	+	31.3068i	−1.29179	+	1.49080i
$22$	12.4245	+	12.4245i	0.564749	+	0.564749i
$23$	−1.02190	−	22.9773i	−0.0444305	−	0.999012i
$23$	−1.02190	−	22.9773i	−0.0444305	−	0.999012i
$24$			13.3494i			0.556224i
$25$	−13.1677	+	21.2511i	−0.526710	+	0.850045i
$26$	1.52981	−	0.983150i	0.0588389	−	0.0378135i
$27$	−12.0937	+	16.1552i	−0.447913	+	0.598342i
$28$	−16.4472	−	6.13448i	−0.587399	−	0.219088i
$29$	−47.5368	−	6.83476i	−1.63920	−	0.235681i	−0.739805	−	0.672821i	$-0.765082\pi$
$29$	−47.5368	−	6.83476i	−1.63920	−	0.235681i	−0.899394	+	0.437140i	$0.855992\pi$
$30$	−31.1721	+	11.9200i	−1.03907	+	0.397333i
$31$	17.4061	+	11.1862i	0.561486	+	0.360845i	0.790390	−	0.612604i	$-0.209878\pi$
$31$	17.4061	+	11.1862i	0.561486	+	0.360845i	−0.228904	+	0.973449i	$0.573514\pi$
$32$	−5.30019	+	1.97687i	−0.165631	+	0.0617771i
$33$	−51.4671	+	28.1032i	−1.55961	+	0.851612i
$34$	−15.7142	+	13.6164i	−0.462182	+	0.400483i
$35$	−0.361467	−	43.8834i	−0.0103276	−	1.25381i
$36$	−25.4760	−	7.48043i	−0.707667	−	0.207790i
$37$	48.8870	−	18.2339i	1.32127	−	0.492808i	0.412824	−	0.910811i	$-0.364543\pi$
$37$	48.8870	−	18.2339i	1.32127	−	0.492808i	0.908446	+	0.418003i	$0.137270\pi$
$38$	37.6784	−	8.19644i	0.991538	−	0.215696i
$39$	1.70981	+	5.82310i	0.0438414	+	0.149310i
$40$	−9.34885	−	10.6113i	−0.233721	−	0.265282i
$41$	20.6473	+	45.2113i	0.503592	+	1.10271i	0.975285	+	0.220950i	$0.0709159\pi$
$41$	20.6473	+	45.2113i	0.503592	+	1.10271i	−0.471693	+	0.881763i	$0.656357\pi$
$42$	35.1078	−	46.8986i	0.835901	−	1.11663i
$43$	−2.50528	+	11.5166i	−0.0582624	+	0.267828i	−0.997058	−	0.0766457i	$-0.975579\pi$
$43$	−2.50528	+	11.5166i	−0.0582624	+	0.267828i	0.938796	+	0.344474i	$0.111943\pi$
$44$	−18.7796	−	16.2726i	−0.426809	−	0.369832i
$45$	−5.28060	−	66.1684i	−0.117347	−	1.47041i
$46$	3.75966	+	32.3089i	0.0817317	+	0.702367i
$47$	−53.7481	−	53.7481i	−1.14358	−	1.14358i	−0.987791	−	0.155786i	$-0.950209\pi$
$47$	−53.7481	−	53.7481i	−1.14358	−	1.14358i	−0.155786	−	0.987791i	$-0.549791\pi$
$48$	−1.34680	−	18.8308i	−0.0280584	−	0.392308i
$49$	15.1570	+	23.5848i	0.309327	+	0.481322i
$50$	16.4305	−	31.3055i	0.328611	−	0.626111i
$51$	−28.8268	−	63.1220i	−0.565232	−	1.23769i
$52$	−2.05878	+	1.54118i	−0.0395919	+	0.0296381i
$53$	5.50423	−	10.0802i	0.103853	−	0.190193i	−0.820585	−	0.571524i	$-0.806352\pi$
$53$	5.50423	−	10.0802i	0.103853	−	0.190193i	0.924439	+	0.381331i	$0.124534\pi$
$54$	15.4296	−	24.0088i	0.285732	−	0.444608i
$55$	21.2294	−	58.3824i	0.385989	−	1.06150i
$56$	23.8194	+	6.99402i	0.425347	+	0.124893i
$57$	−9.18042	+	128.359i	−0.161060	+	2.25191i
$58$	67.7454	+	4.84525i	1.16802	+	0.0835388i
$59$	−9.51039	+	32.3894i	−0.161193	+	0.548973i	0.838797	+	0.544445i	$0.183260\pi$
$59$	−9.51039	+	32.3894i	−0.161193	+	0.548973i	−0.999990	+	0.00452840i	$0.998559\pi$
$60$	42.7691	−	19.9594i	0.712819	−	0.332656i
$61$	−6.34157	−	4.07548i	−0.103960	−	0.0668111i	0.487628	−	0.873052i	$-0.337862\pi$
$61$	−6.34157	−	4.07548i	−0.103960	−	0.0668111i	−0.591588	+	0.806241i	$0.701499\pi$
$62$	−25.6818	−	14.0233i	−0.414222	−	0.226182i
$63$	69.8284	+	93.2799i	1.10839	+	1.48063i
$64$	7.27706	−	3.32332i	0.113704	−	0.0519269i
$65$	−5.43715	−	3.43129i	−0.0836484	−	0.0527891i
$66$	69.7648	−	44.8351i	1.05704	−	0.679320i
$67$	89.3232	−	6.38852i	1.33318	−	0.0953511i	0.613522	−	0.789677i	$-0.289752\pi$
$67$	89.3232	−	6.38852i	1.33318	−	0.0953511i	0.719660	+	0.694326i	$0.244298\pi$
$68$	20.7928	−	20.7928i	0.305777	−	0.305777i
$69$	−106.993	−	18.3391i	−1.55063	−	0.265784i
$70$	4.93723	+	61.8659i	0.0705319	+	0.883798i
$71$	56.6677	−	65.3980i	0.798136	−	0.921098i	−0.200141	−	0.979767i	$-0.564140\pi$
$71$	56.6677	−	65.3980i	0.798136	−	0.921098i	0.998278	+	0.0586688i	$0.0186856\pi$
$72$	36.6914	+	7.98172i	0.509603	+	0.110857i
$73$	21.8862	+	16.3838i	0.299811	+	0.224436i	0.738583	−	0.674163i	$-0.235495\pi$
$73$	21.8862	+	16.3838i	0.299811	+	0.224436i	−0.438772	+	0.898599i	$0.644586\pi$
$74$	−67.1209	+	30.6531i	−0.907039	+	0.414231i
$75$	84.7967	+	82.0479i	1.13062	+	1.09397i
$76$	−52.3227	+	15.3633i	−0.688456	+	0.202149i
$77$	23.1801	+	106.557i	0.301040	+	1.38386i
$78$	−2.99937	−	8.04162i	−0.0384534	−	0.103098i
$79$	23.0320	−	78.4397i	0.291544	−	0.992907i	−0.675301	−	0.737542i	$-0.735986\pi$
$79$	23.0320	−	78.4397i	0.291544	−	0.992907i	0.966845	−	0.255365i	$-0.0821956\pi$
$80$	14.2581	+	14.0252i	0.178227	+	0.175315i
$81$	−15.8712	−	18.3164i	−0.195941	−	0.226128i
$82$	−33.6866	−	61.6924i	−0.410812	−	0.752346i
$83$	−14.7683	−	39.5955i	−0.177932	−	0.477054i	0.817113	−	0.576477i	$-0.195573\pi$
$83$	−14.7683	−	39.5955i	−0.177932	−	0.477054i	−0.995045	+	0.0994233i	$0.968300\pi$
$84$	−44.7919	+	69.6976i	−0.533237	+	0.829734i
$85$	67.1197	+	29.9869i	0.789644	+	0.352787i
$86$	2.37208	−	16.4982i	0.0275824	−	0.191839i
$87$	−79.2121	+	212.376i	−0.910484	+	2.44110i
$88$	28.1324	+	21.0597i	0.319686	+	0.239314i
$89$	51.8960	+	80.7517i	0.583101	+	0.907323i	0.999999	−	0.00163076i	$-0.000519087\pi$
$89$	51.8960	+	80.7517i	0.583101	+	0.907323i	−0.416898	+	0.908953i	$0.636883\pi$
$90$	14.1245	+	92.8051i	0.156939	+	1.03117i
$91$	11.2860			0.124022
$92$	−8.56302	−	45.1960i	−0.0930763	−	0.491260i
$93$	69.0518	−	69.0518i	0.742493	−	0.742493i
$94$	81.2402	+	70.3950i	0.864257	+	0.748883i
$95$	−82.5950	−	108.460i	−0.869421	−	1.14169i
$96$	3.79963	+	26.4270i	0.0395795	+	0.275281i
$97$	35.3963	−	94.9012i	0.364910	−	0.978363i	−0.616654	−	0.787234i	$-0.711512\pi$
$97$	35.3963	−	94.9012i	0.364910	−	0.978363i	0.981565	−	0.191129i	$-0.0612149\pi$
$98$	−23.7601	−	31.7398i	−0.242450	−	0.323875i
$99$	46.4702	+	158.263i	0.469396	+	1.59862i
$100$	−20.0187	+	45.8176i	−0.200187	+	0.458176i
$101$	75.4787	−	165.275i	0.747314	−	1.63639i	−0.0238192	−	0.999716i	$-0.507583\pi$
$101$	75.4787	−	165.275i	0.747314	−	1.63639i	0.771133	−	0.636674i	$-0.219690\pi$
$102$	47.0317	+	86.1322i	0.461096	+	0.844433i
$103$	4.63962	+	0.331832i	0.0450448	+	0.00322167i	0.0938434	−	0.995587i	$-0.470085\pi$
$103$	4.63962	+	0.331832i	0.0450448	+	0.00322167i	−0.0487986	+	0.998809i	$0.515539\pi$
$104$	2.74865	−	2.38171i	0.0264293	−	0.0229011i
$105$	−202.747	−	42.3589i	−1.93092	−	0.403418i
$106$	−6.74734	+	14.7746i	−0.0636541	+	0.139383i
$107$	2.95763	+	13.5960i	0.0276414	+	0.127066i	0.988900	−	0.148583i	$-0.0474711\pi$
$107$	2.95763	+	13.5960i	0.0276414	+	0.127066i	−0.961259	+	0.275648i	$0.911107\pi$
$108$	−19.3429	+	35.4238i	−0.179101	+	0.327998i
$109$	115.806	+	16.6505i	1.06244	+	0.152756i	0.651305	−	0.758816i	$-0.274222\pi$
$109$	115.806	+	16.6505i	1.06244	+	0.152756i	0.411140	+	0.911572i	$0.365131\pi$
$110$	−24.0563	+	84.4966i	−0.218693	+	0.768151i
$111$	−35.0464	−	243.753i	−0.315733	−	2.19597i
$112$	−34.3056	−	7.46272i	−0.306300	−	0.0666314i
$113$	−4.57869	−	64.0184i	−0.0405194	−	0.566535i	−0.976644	−	0.214865i	$-0.931069\pi$
$113$	−4.57869	−	64.0184i	−0.0405194	−	0.566535i	0.936124	−	0.351669i	$-0.114386\pi$
$114$		−	181.991i		−	1.59641i
$115$	97.8909	−	60.3521i	0.851225	−	0.524801i
$116$	−96.0512			−0.828028
$117$	17.0274	−	1.21782i	0.145533	−	0.0104087i
$118$	10.1477	−	46.6483i	0.0859977	−	0.395325i
$119$	−127.732	+	18.3651i	−1.07338	+	0.154329i
$120$	−58.3169	+	32.4698i	−0.485974	+	0.270582i
$121$	−4.74871	+	33.0280i	−0.0392456	+	0.272959i
$122$	9.35665	+	5.10912i	0.0766938	+	0.0418780i
$123$	229.222	−	49.8643i	1.86360	−	0.405401i
$124$	37.6417	+	17.1904i	0.303562	+	0.138632i
$125$	−124.864	−	5.83405i	−0.998910	−	0.0466724i
$126$	−107.912	−	124.537i	−0.856441	−	0.988386i
$127$	−4.83287	+	67.5724i	−0.0380541	+	0.532066i	0.942293	+	0.334788i	$0.108665\pi$
$127$	−4.83287	+	67.5724i	−0.0380541	+	0.532066i	−0.980348	+	0.197278i	$0.936790\pi$
$128$	−9.92980	+	5.42208i	−0.0775766	+	0.0423600i
$129$	50.5995	+	23.1080i	0.392245	+	0.179132i
$130$	8.01587	+	4.29167i	0.0616606	+	0.0330128i
$131$	−47.5152	+	13.9517i	−0.362712	+	0.106502i	−0.458010	−	0.888947i	$-0.651438\pi$
$131$	−47.5152	+	13.9517i	−0.362712	+	0.106502i	0.0952985	+	0.995449i	$0.469619\pi$
$132$	−93.8876	+	70.2834i	−0.711270	+	0.532450i
$133$	224.222	+	83.6307i	1.68588	+	0.628802i
$134$	−125.356	+	18.0234i	−0.935491	+	0.134503i
$135$	−99.9898	−	13.5367i	−0.740665	−	0.100272i
$136$	−27.2328	+	31.4283i	−0.200241	+	0.231091i
$137$	−185.977	−	185.977i	−1.35749	−	1.35749i	−0.876995	−	0.480499i	$-0.840455\pi$
$137$	−185.977	−	185.977i	−1.35749	−	1.35749i	−0.480499	−	0.876995i	$-0.659545\pi$
$138$	152.776	+	15.0749i	1.10707	+	0.109238i
$139$			90.0698i			0.647984i	0.946060	+	0.323992i	$0.105025\pi$
$139$			90.0698i			0.647984i	−0.946060	+	0.323992i	$0.894975\pi$
$140$	−13.2061	−	86.7706i	−0.0943292	−	0.619790i
$141$	−301.801	+	193.956i	−2.14044	+	1.37557i
$142$	−73.3381	+	97.9682i	−0.516465	+	0.689917i
$143$	14.9689	+	5.58312i	0.104678	+	0.0390428i
$144$	−52.5625	−	7.55735i	−0.365018	−	0.0524816i
$145$	−85.7665	−	224.289i	−0.591493	−	1.54682i
$146$	−32.5259	−	20.9031i	−0.222780	−	0.143172i
$147$	123.976	−	46.2407i	0.843374	−	0.314562i
$148$	91.5888	−	50.0113i	0.618843	−	0.337914i
$149$	165.675	−	143.558i	1.11191	−	0.963475i	0.112365	−	0.993667i	$-0.464157\pi$
$149$	165.675	−	143.558i	1.11191	−	0.963475i	0.999544	+	0.0301919i	$0.00961183\pi$
$150$	−127.893	−	107.183i	−0.852619	−	0.714551i
$151$	−49.0848	−	14.4126i	−0.325065	−	0.0954477i	0.115129	−	0.993351i	$-0.463272\pi$
$151$	−49.0848	−	14.4126i	−0.325065	−	0.0954477i	−0.440194	+	0.897903i	$0.645090\pi$
$152$	72.2569	−	26.9504i	0.475374	−	0.177305i
$153$	−190.729	+	41.4907i	−1.24660	+	0.271181i
$154$	−43.4485	−	147.972i	−0.282133	−	0.960858i
$155$	−6.53007	+	103.247i	−0.0421295	+	0.666109i
$156$	5.04225	+	11.0410i	0.0323221	+	0.0707755i
$157$	109.262	−	145.957i	0.695937	−	0.929663i	−0.303797	−	0.952737i	$-0.598254\pi$
$157$	109.262	−	145.957i	0.695937	−	0.929663i	0.999734	+	0.0230742i	$0.00734540\pi$
$158$	−24.5754	+	112.971i	−0.155541	+	0.715009i
$159$	−40.9665	−	35.4977i	−0.257651	−	0.223256i
$160$	−21.5277	−	18.3456i	−0.134548	−	0.114660i
$161$	−88.7786	+	181.301i	−0.551420	+	1.12609i
$162$	24.2361	+	24.2361i	0.149605	+	0.149605i
$163$	15.6150	+	218.326i	0.0957975	+	1.33942i	0.787085	+	0.616844i	$0.211589\pi$
$163$	15.6150	+	218.326i	0.0957975	+	1.33942i	−0.691288	+	0.722580i	$0.742956\pi$
$164$	53.7427	+	83.6253i	0.327700	+	0.509910i
$165$	−247.953	−	156.479i	−1.50275	−	0.948358i
$166$	24.8271	+	54.3638i	0.149561	+	0.327493i
$167$	−132.349	+	99.0752i	−0.792508	+	0.593264i	−0.916968	−	0.398960i	$-0.869371\pi$
$167$	−132.349	+	99.0752i	−0.792508	+	0.593264i	0.124460	+	0.992225i	$0.460280\pi$
$168$	56.1523	−	102.835i	0.334240	−	0.612114i
$169$	−90.4744	+	140.781i	−0.535351	+	0.833023i
$170$	−97.7051	−	35.5282i	−0.574736	−	0.208989i
$171$	347.311	+	101.980i	2.03106	+	0.596373i
$172$	−1.68160	+	23.5118i	−0.00977674	+	0.136697i
$173$	−291.790	−	20.8692i	−1.68665	−	0.120631i	−0.805227	−	0.592967i	$-0.797956\pi$
$173$	−291.790	−	20.8692i	−1.68665	−	0.120631i	−0.881419	+	0.472336i	$0.843411\pi$
$174$	90.3111	−	307.571i	0.519029	−	1.76765i
$175$	190.826	−	108.317i	1.09043	−	0.618955i
$176$	−41.8085	−	26.8687i	−0.237549	−	0.152663i
$177$	139.834	+	76.3552i	0.790024	+	0.431386i
$178$	−81.3519	−	108.673i	−0.457033	−	0.610525i
$179$	42.6728	−	19.4880i	0.238395	−	0.108872i	−0.292635	−	0.956224i	$-0.594532\pi$
$179$	42.6728	−	19.4880i	0.238395	−	0.108872i	0.531031	+	0.847353i	$0.321805\pi$
$180$	−29.2872	−	129.487i	−0.162707	−	0.719371i
$181$	−216.916	+	139.403i	−1.19843	+	0.770185i	−0.978684	−	0.205372i	$-0.934159\pi$
$181$	−216.916	+	139.403i	−1.19843	+	0.770185i	−0.219747	+	0.975557i	$0.570523\pi$
$182$	−15.9202	+	1.13863i	−0.0874735	+	0.00625623i
$183$	−25.1577	+	25.1577i	−0.137474	+	0.137474i
$184$	16.6388	+	62.8900i	0.0904285	+	0.341793i
$185$	198.563	+	169.213i	1.07331	+	0.914663i
$186$	−90.4387	+	104.372i	−0.486229	+	0.561139i
$187$	−178.499	−	38.8302i	−0.954542	−	0.207648i
$188$	−121.700	−	91.1037i	−0.647342	−	0.484594i
$189$	161.117	−	73.5794i	0.852468	−	0.389309i
$190$	127.452	+	144.662i	0.670799	+	0.761380i
$191$	339.241	−	99.6100i	1.77613	−	0.521519i	0.781397	−	0.624034i	$-0.214507\pi$
$191$	339.241	−	99.6100i	1.77613	−	0.521519i	0.994731	+	0.102515i	$0.0326890\pi$
$192$	−8.02599	−	36.8949i	−0.0418020	−	0.192161i
$193$	69.8000	+	187.141i	0.361658	+	0.969642i	0.982592	+	0.185779i	$0.0594809\pi$
$193$	69.8000	+	187.141i	0.361658	+	0.969642i	−0.620934	+	0.783863i	$0.713246\pi$
$194$	−40.3559	+	137.440i	−0.208020	+	0.708452i
$195$	−21.2794	+	21.6329i	−0.109125	+	0.110938i
$196$	36.7184	+	42.3753i	0.187339	+	0.216201i
$197$	13.1112	+	24.0113i	0.0665542	+	0.121885i	0.908838	−	0.417150i	$-0.136971\pi$
$197$	13.1112	+	24.0113i	0.0665542	+	0.121885i	−0.842284	+	0.539035i	$0.818789\pi$
$198$	−81.5183	−	218.559i	−0.411709	−	1.10383i
$199$	−84.2613	+	131.113i	−0.423424	+	0.658860i	−0.985781	−	0.168034i	$-0.946258\pi$
$199$	−84.2613	+	131.113i	−0.423424	+	0.658860i	0.562358	+	0.826894i	$0.309894\pi$
$200$	23.6161	−	66.6504i	0.118081	−	0.333252i
$201$	60.1504	−	418.356i	0.299256	−	2.08137i
$202$	−89.7966	+	240.754i	−0.444538	+	1.19185i
$203$	337.444	+	252.607i	1.66228	+	1.24437i
$204$	−75.0332	−	116.754i	−0.367810	−	0.572324i
$205$	−147.285	+	200.166i	−0.718464	+	0.976418i
$206$	−6.57817			−0.0319329
$207$	−114.378	+	283.111i	−0.552551	+	1.36768i
$208$	−3.63698	+	3.63698i	−0.0174855	+	0.0174855i
$209$	256.020	+	221.843i	1.22498	+	1.06145i
$210$	290.270	+	39.2970i	1.38224	+	0.187129i
$211$	30.0736	+	209.166i	0.142529	+	0.991310i	0.928045	+	0.372469i	$0.121489\pi$
$211$	30.0736	+	209.166i	0.142529	+	0.991310i	−0.785516	+	0.618842i	$0.787602\pi$
$212$	8.02727	−	21.5219i	0.0378645	−	0.101519i
$213$	−244.755	−	326.954i	−1.14908	−	1.53499i
$214$	−5.54376	−	18.8803i	−0.0259054	−	0.0882257i
$215$	−56.4040	+	17.0676i	−0.262344	+	0.0793842i
$216$	23.7114	−	51.9207i	0.109775	−	0.240373i
$217$	−87.0322	−	159.388i	−0.401070	−	0.734505i
$218$	−165.038	−	11.8037i	−0.757053	−	0.0541455i
$219$	97.5171	−	84.4991i	0.445284	−	0.385841i
$220$	25.4092	−	121.619i	0.115497	−	0.552813i
$221$	−7.85374	+	17.1973i	−0.0355373	+	0.0778158i
$222$	74.0288	+	340.305i	0.333463	+	1.53290i
$223$	−14.4477	+	26.4590i	−0.0647878	+	0.118650i	−0.908066	−	0.418828i	$-0.862441\pi$
$223$	−14.4477	+	26.4590i	−0.0647878	+	0.118650i	0.843278	+	0.537478i	$0.180623\pi$
$224$	49.1447	+	7.06594i	0.219396	+	0.0315444i
$225$	276.213	−	184.010i	1.22761	−	0.817824i
$226$	12.9175	+	89.8431i	0.0571570	+	0.397536i
$227$	−96.5236	−	20.9974i	−0.425214	−	0.0924997i	−0.00513426	−	0.999987i	$-0.501634\pi$
$227$	−96.5236	−	20.9974i	−0.425214	−	0.0924997i	−0.420080	+	0.907487i	$0.637998\pi$
$228$	18.3608	+	256.718i	0.0805300	+	1.12596i
$229$		−	9.75527i		−	0.0425994i	−0.999773	−	0.0212997i	$-0.993220\pi$
$229$		−	9.75527i		−	0.0425994i	0.999773	−	0.0212997i	$-0.00678042\pi$
$230$	−131.997	+	95.0093i	−0.573900	+	0.413084i
$231$	514.682			2.22806
$232$	135.491	−	9.69050i	0.584012	−	0.0417694i
$233$	35.3656	−	162.573i	0.151784	−	0.697738i	−0.836855	−	0.547425i	$-0.815608\pi$
$233$	35.3656	−	162.573i	0.151784	−	0.697738i	0.988638	−	0.150313i	$-0.0480282\pi$
$234$	−23.8961	+	3.43574i	−0.102120	+	0.0146827i
$235$	104.067	−	365.531i	0.442838	−	1.55545i
$236$	−9.60819	+	66.8264i	−0.0407127	+	0.283163i
$237$	−338.646	−	184.915i	−1.42889	−	0.780231i
$238$	178.328	−	38.7928i	0.749275	−	0.162995i
$239$	−81.3378	−	37.1457i	−0.340326	−	0.155421i	0.237919	−	0.971285i	$-0.423535\pi$
$239$	−81.3378	−	37.1457i	−0.340326	−	0.155421i	−0.578244	+	0.815864i	$0.696262\pi$
$240$	78.9866	−	51.6858i	0.329111	−	0.215358i
$241$	−49.8890	−	57.5750i	−0.207008	−	0.238900i	0.642746	−	0.766079i	$-0.277795\pi$
$241$	−49.8890	−	57.5750i	−0.207008	−	0.238900i	−0.849754	+	0.527179i	$0.823250\pi$
$242$	3.36642	−	47.0688i	0.0139108	−	0.194499i
$243$	−259.803	+	141.863i	−1.06915	+	0.583798i
$244$	−13.7140	−	6.26299i	−0.0562051	−	0.0256680i
$245$	−66.1638	+	123.579i	−0.270056	+	0.504404i
$246$	−318.313	+	93.4650i	−1.29395	+	0.379939i
$247$	28.0671	−	21.0108i	0.113632	−	0.0850638i
$248$	−54.8322	−	20.4513i	−0.221097	−	0.0824651i
$249$	−197.425	+	28.3854i	−0.792872	+	0.113998i
$250$	176.723	−	4.36779i	0.706891	−	0.0174711i
$251$	59.1991	−	68.3194i	0.235853	−	0.272189i	−0.625468	−	0.780250i	$-0.715092\pi$
$251$	59.1991	−	68.3194i	0.235853	−	0.272189i	0.861321	+	0.508061i	$0.169637\pi$
$252$	164.786	+	164.786i	0.653911	+	0.653911i
$253$	−207.437	+	196.546i	−0.819911	+	0.776860i
$254$		−	95.8059i		−	0.377188i
$255$	205.633	−	279.463i	0.806404	−	1.09593i
$256$	13.4601	−	8.65025i	0.0525783	−	0.0337901i
$257$	143.314	−	191.445i	0.557643	−	0.744924i	−0.429796	−	0.902926i	$-0.641414\pi$
$257$	143.314	−	191.445i	0.557643	−	0.744924i	0.987439	+	0.158002i	$0.0505054\pi$
$258$	−73.7076	−	27.4915i	−0.285688	−	0.106556i
$259$	−453.293	−	65.1736i	−1.75016	−	0.251636i
$260$	−11.7403	−	5.24516i	−0.0451548	−	0.0201737i
$261$	536.363	+	344.700i	2.05503	+	1.32069i
$262$	65.6179	−	24.4742i	0.250450	−	0.0934130i
$263$	250.040	−	136.532i	0.950722	−	0.519134i	0.0724907	−	0.997369i	$-0.476905\pi$
$263$	250.040	−	136.532i	0.950722	−	0.519134i	0.878232	+	0.478235i	$0.158723\pi$
$264$	125.348	−	108.615i	0.474803	−	0.411419i
$265$	57.4236	−	0.472998i	0.216693	−	0.00178490i
$266$	−324.728	−	95.3487i	−1.22078	−	0.358454i
$267$	424.480	−	158.323i	1.58981	−	0.592970i
$268$	175.010	−	38.0710i	0.653022	−	0.142056i
$269$	−15.7774	−	53.7329i	−0.0586520	−	0.199750i	0.924955	−	0.380077i	$-0.124103\pi$
$269$	−15.7774	−	53.7329i	−0.0586520	−	0.199750i	−0.983607	+	0.180327i	$0.942284\pi$
$270$	142.412	+	9.00717i	0.527453	+	0.0333599i
$271$	42.7254	+	93.5557i	0.157658	+	0.345224i	0.971934	−	0.235255i	$-0.0755926\pi$
$271$	42.7254	+	93.5557i	0.157658	+	0.345224i	−0.814275	+	0.580479i	$0.802865\pi$
$272$	35.2441	−	47.0806i	0.129574	−	0.173091i
$273$	11.3227	−	52.0495i	0.0414750	−	0.190658i
$274$	281.104	+	243.578i	1.02593	+	0.888970i
$275$	306.680	−	49.2633i	1.11520	−	0.179139i
$276$	−217.028	−	5.85135i	−0.786334	−	0.0212005i
$277$	−257.997	−	257.997i	−0.931398	−	0.931398i	0.0663958	−	0.997793i	$-0.478850\pi$
$277$	−257.997	−	257.997i	−0.931398	−	0.931398i	−0.997793	+	0.0663958i	$0.978850\pi$
$278$	−9.08704	−	127.053i	−0.0326872	−	0.457026i
$279$	−148.505	−	231.079i	−0.532277	−	0.828240i
$280$	27.3828	+	121.067i	0.0977958	+	0.432382i
$281$	205.953	+	450.975i	0.732930	+	1.60489i	0.794846	+	0.606811i	$0.207551\pi$
$281$	205.953	+	450.975i	0.732930	+	1.60489i	−0.0619166	+	0.998081i	$0.519721\pi$
$282$	406.156	−	304.045i	1.44027	−	1.07817i
$283$	114.392	−	209.494i	0.404213	−	0.740260i	−0.593710	−	0.804679i	$-0.702337\pi$
$283$	114.392	−	209.494i	0.404213	−	0.740260i	0.997923	+	0.0644186i	$0.0205193\pi$
$284$	93.5675	−	145.594i	0.329463	−	0.512655i
$285$	−583.067	+	272.104i	−2.04585	+	0.954751i
$286$	−21.6786	−	6.36540i	−0.0757992	−	0.0222567i
$287$	31.1210	−	435.129i	0.108436	−	1.51613i
$288$	74.9077	+	5.35750i	0.260096	+	0.0186024i
$289$	−20.5183	+	69.8790i	−0.0709976	+	0.241796i
$290$	143.611	+	307.732i	0.495211	+	1.06114i
$291$	−402.160	−	258.452i	−1.38199	−	0.888152i
$292$	47.9902	+	26.2046i	0.164350	+	0.0897419i
$293$	−167.481	−	223.728i	−0.571606	−	0.763577i	0.417833	−	0.908524i	$-0.362790\pi$
$293$	−167.481	−	223.728i	−0.571606	−	0.763577i	−0.989439	+	0.144947i	$0.953699\pi$
$294$	−170.217	+	77.7353i	−0.578968	+	0.264406i
$295$	−164.626	+	37.2349i	−0.558053	+	0.126220i
$296$	−124.151	+	79.7867i	−0.419428	+	0.269550i
$297$	250.092	−	17.8869i	0.842060	−	0.0602253i
$298$	−219.219	+	219.219i	−0.735634	+	0.735634i
$299$	15.3131	+	25.3019i	0.0512142	+	0.0846218i
$300$	191.221	+	138.290i	0.637402	+	0.460967i
$301$	67.7421	−	78.1785i	0.225057	−	0.259729i
$302$	70.6936	+	15.3785i	0.234085	+	0.0509220i
$303$	−686.503	−	513.910i	−2.26569	−	1.69607i
$304$	−99.2073	+	45.3065i	−0.326340	+	0.149034i
$305$	2.37911	−	37.6160i	0.00780035	−	0.123331i
$306$	264.859	−	77.7696i	0.865552	−	0.254149i
$307$	111.510	+	512.605i	0.363226	+	1.66972i	0.689374	+	0.724405i	$0.257886\pi$
$307$	111.510	+	512.605i	0.363226	+	1.66972i	−0.326148	+	0.945319i	$0.605751\pi$
$308$	76.2177	+	204.347i	0.247460	+	0.663466i
$309$	6.18505	−	21.0644i	0.0200164	−	0.0681695i
$310$	−1.20507	−	146.300i	−0.00388733	−	0.471935i
$311$	144.263	+	166.489i	0.463869	+	0.535334i	0.938696	−	0.344745i	$-0.112035\pi$
$311$	144.263	+	166.489i	0.463869	+	0.535334i	−0.474827	+	0.880079i	$0.657489\pi$
$312$	−8.22656	−	15.0658i	−0.0263672	−	0.0482879i
$313$	64.2378	+	172.228i	0.205233	+	0.550250i	0.998262	−	0.0589334i	$-0.0187700\pi$
$313$	64.2378	+	172.228i	0.205233	+	0.550250i	−0.793029	+	0.609184i	$0.791497\pi$
$314$	−139.401	+	216.912i	−0.443951	+	0.690802i
$315$	−237.650	+	531.932i	−0.754443	+	1.68867i
$316$	23.2688	−	161.838i	0.0736355	−	0.512146i
$317$	−115.644	+	310.053i	−0.364806	+	0.978084i	0.616792	+	0.787126i	$0.288432\pi$
$317$	−115.644	+	310.053i	−0.364806	+	0.978084i	−0.981598	+	0.190958i	$0.938841\pi$
$318$	61.3691	+	45.9404i	0.192985	+	0.144467i
$319$	322.597	+	501.970i	1.01127	+	1.57357i
$320$	32.2180	+	23.7065i	0.100681	+	0.0740829i
$321$	65.6702			0.204580
$322$	106.941	−	264.702i	0.332114	−	0.822055i
$323$	−283.466	+	283.466i	−0.877605	+	0.877605i
$324$	−36.6328	−	31.7425i	−0.113064	−	0.0979706i
$325$	1.76481	−	32.0982i	0.00543017	−	0.0987636i
$326$	−44.0533	−	306.398i	−0.135133	−	0.939870i
$327$	192.972	−	517.379i	0.590129	−	1.58220i
$328$	−84.2469	−	112.541i	−0.256850	−	0.343112i
$329$	187.958	+	640.125i	0.571300	+	1.94567i
$330$	365.552	+	195.715i	1.10773	+	0.593077i
$331$	−128.704	+	281.822i	−0.388833	+	0.851426i	0.609448	+	0.792826i	$0.291391\pi$
$331$	−128.704	+	281.822i	−0.388833	+	0.851426i	−0.998282	+	0.0586002i	$0.981336\pi$
$332$	−40.5061	−	74.1814i	−0.122006	−	0.223438i
$333$	−690.921	−	49.4156i	−2.07484	−	0.148395i
$334$	176.697	−	153.109i	0.529033	−	0.458410i
$335$	245.170	+	374.671i	0.731851	+	1.11842i
$336$	−68.8340	+	150.726i	−0.204863	+	0.448588i
$337$	−94.8415	−	435.979i	−0.281429	−	1.29371i	−0.873105	−	0.487532i	$-0.837897\pi$
$337$	−94.8415	−	435.979i	−0.281429	−	1.29371i	0.591676	−	0.806176i	$-0.298466\pi$
$338$	113.421	−	207.715i	0.335565	−	0.614541i
$339$	−299.838	−	43.1101i	−0.884477	−	0.127169i
$340$	141.408	+	40.2591i	0.415907	+	0.118409i
$341$	−36.5849	−	254.454i	−0.107287	−	0.746199i
$342$	−500.210	−	108.814i	−1.46260	−	0.318170i
$343$	13.1269	+	183.538i	0.0382708	+	0.535096i
$344$		−	33.3357i		−	0.0969061i
$345$	−180.126	−	512.007i	−0.522105	−	1.48408i
$346$	413.707			1.19568
$347$	−474.735	+	33.9537i	−1.36811	+	0.0978494i	−0.735976	−	0.677008i	$-0.763276\pi$
$347$	−474.735	+	33.9537i	−1.36811	+	0.0978494i	−0.632137	+	0.774857i	$0.717822\pi$
$348$	−96.3633	+	442.975i	−0.276906	+	1.27292i
$349$	470.760	−	67.6850i	1.34888	−	0.193940i	0.570276	−	0.821453i	$-0.306836\pi$
$349$	470.760	−	67.6850i	1.34888	−	0.193940i	0.778606	+	0.627513i	$0.215927\pi$
$350$	−258.253	+	172.045i	−0.737865	+	0.491558i
$351$	3.69297	−	25.6852i	0.0105213	−	0.0731771i
$352$	61.6863	+	33.6833i	0.175245	+	0.0956911i
$353$	287.323	−	62.5033i	0.813947	−	0.177063i	0.213722	−	0.976895i	$-0.431441\pi$
$353$	287.323	−	62.5033i	0.813947	−	0.177063i	0.600225	+	0.799831i	$0.295078\pi$
$354$	−204.955	−	93.5998i	−0.578969	−	0.264406i
$355$	423.525	+	88.4851i	1.19303	+	0.249254i
$356$	125.720	+	145.088i	0.353146	+	0.407552i
$357$	−43.4498	+	607.508i	−0.121708	+	1.70170i
$358$	−58.2285	+	31.7952i	−0.162650	+	0.0888134i
$359$	−631.346	−	288.326i	−1.75862	−	0.803136i	−0.985672	−	0.168671i	$-0.946053\pi$
$359$	−631.346	−	288.326i	−1.75862	−	0.803136i	−0.772951	−	0.634466i	$-0.781220\pi$
$360$	54.3766	+	179.701i	0.151046	+	0.499169i
$361$	366.932	−	107.741i	1.01643	−	0.298451i
$362$	291.920	−	218.528i	0.806408	−	0.603669i
$363$	147.556	+	55.0357i	0.406492	+	0.151614i
$364$	22.3423	−	3.21234i	0.0613799	−	0.00882510i
$365$	−18.3388	+	135.461i	−0.0502432	+	0.371125i
$366$	32.9496	−	38.0258i	0.0900262	−	0.103896i
$367$	−143.745	−	143.745i	−0.391676	−	0.391676i	0.483609	−	0.875284i	$-0.339326\pi$
$367$	−143.745	−	143.745i	−0.391676	−	0.391676i	−0.875284	+	0.483609i	$0.839326\pi$
$368$	−29.8158	−	87.0346i	−0.0810213	−	0.236507i
$369$		−	659.842i		−	1.78819i
$370$	−297.167	−	218.660i	−0.803154	−	0.590974i
$371$	−84.8021	+	54.4990i	−0.228577	+	0.146898i
$372$	117.044	−	156.352i	0.314634	−	0.420302i
$373$	20.7967	+	7.75678i	0.0557553	+	0.0207957i	0.377187	−	0.926137i	$-0.376891\pi$
$373$	20.7967	+	7.75678i	0.0557553	+	0.0207957i	−0.321432	+	0.946933i	$0.604164\pi$
$374$	255.711	+	36.7656i	0.683718	+	0.0983038i
$375$	−152.175	+	570.001i	−0.405801	+	1.52000i
$376$	180.863	+	116.234i	0.481019	+	0.309132i
$377$	57.8609	−	21.5810i	0.153477	−	0.0572440i
$378$	−219.849	+	120.047i	−0.581612	+	0.317584i
$379$	−77.0720	+	66.7833i	−0.203356	+	0.176209i	−0.750585	−	0.660774i	$-0.770228\pi$
$379$	−77.0720	+	66.7833i	−0.203356	+	0.176209i	0.547229	+	0.836983i	$0.315683\pi$
$380$	−194.380	−	191.204i	−0.511525	−	0.503167i
$381$	306.786	+	90.0804i	0.805212	+	0.236432i
$382$	−468.487	+	174.737i	−1.22641	+	0.457425i
$383$	457.015	−	99.4176i	1.19325	−	0.259576i	0.428284	−	0.903644i	$-0.359118\pi$
$383$	457.015	−	99.4176i	1.19325	−	0.259576i	0.764968	+	0.644068i	$0.222755\pi$
$384$	15.0438	+	51.2346i	0.0391766	+	0.133423i
$385$	−409.115	+	360.443i	−1.06264	+	0.936215i
$386$	−117.341	−	256.941i	−0.303992	−	0.665650i
$387$	93.7674	−	125.259i	0.242293	−	0.323666i
$388$	43.0604	−	197.945i	0.110980	−	0.510168i
$389$	236.679	+	205.084i	0.608430	+	0.527208i	0.903678	−	0.428213i	$-0.140857\pi$
$389$	236.679	+	205.084i	0.608430	+	0.527208i	−0.295248	+	0.955421i	$0.595402\pi$
$390$	27.8345	−	32.6625i	0.0713705	−	0.0837499i
$391$	−214.482	−	261.442i	−0.548546	−	0.668650i
$392$	−56.0706	−	56.0706i	−0.143037	−	0.143037i
$393$	16.6738	+	233.131i	0.0424270	+	0.593208i
$394$	−20.9172	−	32.5478i	−0.0530894	−	0.0826087i
$395$	398.685	−	90.1742i	1.00933	−	0.228289i
$396$	137.041	+	300.077i	0.346062	+	0.757771i
$397$	−67.6729	+	50.6593i	−0.170461	+	0.127605i	−0.681102	−	0.732189i	$-0.738499\pi$
$397$	−67.6729	+	50.6593i	−0.170461	+	0.127605i	0.510641	+	0.859794i	$0.329408\pi$
$398$	105.632	−	193.451i	0.265407	−	0.486057i
$399$	610.644	−	950.180i	1.53044	−	2.38140i
$400$	−26.5889	+	96.4004i	−0.0664722	+	0.241001i
$401$	−288.720	−	84.7760i	−0.720001	−	0.211411i	−0.0988501	−	0.995102i	$-0.531516\pi$
$401$	−288.720	−	84.7760i	−0.720001	−	0.211411i	−0.621151	+	0.783691i	$0.713335\pi$
$402$	−42.6414	+	596.205i	−0.106073	+	1.48310i
$403$	−26.5376	−	1.89801i	−0.0658502	−	0.00470970i
$404$	102.379	−	348.670i	0.253413	−	0.863044i
$405$	41.4115	−	113.885i	0.102251	−	0.281197i
$406$	−501.487	−	322.286i	−1.23519	−	0.793808i
$407$	−568.972	−	310.682i	−1.39796	−	0.763347i
$408$	117.622	+	157.124i	0.288289	+	0.385109i
$409$	168.344	−	76.8800i	0.411598	−	0.187971i	−0.198844	−	0.980031i	$-0.563719\pi$
$409$	168.344	−	76.8800i	0.411598	−	0.187971i	0.610443	+	0.792060i	$0.290992\pi$
$410$	187.567	−	297.215i	0.457482	−	0.724915i
$411$	−1044.28	+	671.118i	−2.54083	+	1.63289i
$412$	9.27924	−	0.663664i	0.0225224	−	0.00161084i
$413$	209.503	−	209.503i	0.507272	−	0.507272i
$414$	132.780	−	410.898i	0.320725	−	0.992508i
$415$	137.052	−	160.824i	0.330246	−	0.387528i
$416$	4.76343	−	5.49729i	0.0114506	−	0.0132146i
$417$	415.389	+	90.3624i	0.996137	+	0.216696i
$418$	−383.526	−	287.104i	−0.917526	−	0.686852i
$419$	−283.975	+	129.687i	−0.677744	+	0.309515i	−0.724384	−	0.689397i	$-0.757876\pi$
$419$	−283.975	+	129.687i	−0.677744	+	0.309515i	0.0466403	+	0.998912i	$0.485149\pi$
$420$	−413.423	−	26.1478i	−0.984340	−	0.0622567i
$421$	284.525	−	83.5442i	0.675832	−	0.198442i	0.0742337	−	0.997241i	$-0.476349\pi$
$421$	284.525	−	83.5442i	0.675832	−	0.198442i	0.601598	+	0.798799i	$0.294531\pi$
$422$	−63.5247	−	292.018i	−0.150532	−	0.691986i
$423$	352.647	+	945.483i	0.833681	+	2.23518i
$424$	−9.15202	+	31.1689i	−0.0215850	+	0.0735116i
$425$	32.2580	+	366.151i	0.0759012	+	0.861531i
$426$	378.239	+	436.511i	0.887886	+	1.02467i
$427$	31.7085	+	58.0698i	0.0742588	+	0.135995i
$428$	9.72489	+	26.0734i	0.0227217	+	0.0609193i
$429$	40.7661	−	63.4333i	0.0950259	−	0.147863i
$430$	77.8422	−	29.7663i	0.181028	−	0.0692239i
$431$	26.6594	−	185.420i	0.0618548	−	0.430210i	−0.935238	−	0.354019i	$-0.884815\pi$
$431$	26.6594	−	185.420i	0.0618548	−	0.430210i	0.997093	−	0.0761912i	$-0.0242759\pi$
$432$	−28.2093	+	75.6320i	−0.0652993	+	0.175074i
$433$	−446.824	−	334.488i	−1.03193	−	0.772491i	−0.0577622	−	0.998330i	$-0.518397\pi$
$433$	−446.824	−	334.488i	−1.03193	−	0.772491i	−0.974164	+	0.225840i	$0.927487\pi$
$434$	138.849	+	216.053i	0.319929	+	0.497819i
$435$	−1120.43	+	170.525i	−2.57571	+	0.392012i
$436$	233.995			0.536685
$437$	116.739	+	616.152i	0.267137	+	1.40996i
$438$	−129.034	+	129.034i	−0.294597	+	0.294597i
$439$	−317.502	−	275.117i	−0.723238	−	0.626689i	0.213409	−	0.976963i	$-0.431543\pi$
$439$	−317.502	−	275.117i	−0.723238	−	0.626689i	−0.936647	+	0.350273i	$0.886089\pi$
$440$	−23.5726	+	174.120i	−0.0535740	+	0.395728i
$441$	−52.9681	−	368.401i	−0.120109	−	0.835377i
$442$	9.34356	−	25.0510i	0.0211393	−	0.0566766i
$443$	−396.806	−	530.071i	−0.895724	−	1.19655i	−0.979778	−	0.200086i	$-0.935878\pi$
$443$	−396.806	−	530.071i	−0.895724	−	1.19655i	0.0840539	−	0.996461i	$-0.473213\pi$
$444$	−138.759	−	472.569i	−0.312520	−	1.06434i
$445$	−226.537	+	423.121i	−0.509073	+	0.950834i
$446$	17.7106	−	38.7809i	0.0397099	−	0.0869526i
$447$	−495.856	−	908.092i	−1.10930	−	2.03153i
$448$	−70.0369	−	5.00914i	−0.156332	−	0.0111811i
$449$	348.948	−	302.365i	0.777168	−	0.673419i	−0.173083	−	0.984907i	$-0.555373\pi$
$449$	348.948	−	302.365i	0.777168	−	0.673419i	0.950250	+	0.311488i	$0.100827\pi$
$450$	−371.065	+	287.434i	−0.824588	+	0.638742i
$451$	256.532	−	561.726i	0.568807	−	1.24551i
$452$	−27.2857	−	125.430i	−0.0603666	−	0.277501i
$453$	−115.713	+	211.913i	−0.255437	+	0.467799i
$454$	138.276	+	19.8810i	0.304572	+	0.0437908i
$455$	27.4511	+	49.3031i	0.0603321	+	0.108358i
$456$	−51.8000	−	360.277i	−0.113596	−	0.790080i
$457$	136.087	+	29.6038i	0.297782	+	0.0647786i	0.358974	−	0.933347i	$-0.383127\pi$
$457$	136.087	+	29.6038i	0.297782	+	0.0647786i	−0.0611920	+	0.998126i	$0.519490\pi$
$458$	0.984197	+	13.7609i	0.00214890	+	0.0300456i
$459$			296.707i			0.646421i
$460$	176.611	−	147.338i	0.383937	−	0.320300i
$461$	194.548			0.422013			0.211007	−	0.977485i	$-0.432326\pi$
$461$	194.548			0.422013			0.211007	+	0.977485i	$0.432326\pi$
$462$	−726.016	+	51.9257i	−1.57146	+	0.112393i
$463$	33.7692	−	155.235i	0.0729357	−	0.335280i	−0.926191	−	0.377054i	$-0.876937\pi$
$463$	33.7692	−	155.235i	0.0729357	−	0.335280i	0.999127	+	0.0417738i	$0.0133009\pi$
$464$	−190.147	+	27.3390i	−0.409800	+	0.0589203i
$465$	469.609	+	133.698i	1.00991	+	0.287523i
$466$	−33.4853	+	232.895i	−0.0718568	+	0.499775i
$467$	518.817	+	283.295i	1.11096	+	0.606628i	0.926531	−	0.376218i	$-0.122776\pi$
$467$	518.817	+	283.295i	1.11096	+	0.606628i	0.184426	+	0.982846i	$0.440957\pi$
$468$	33.3615	−	7.25734i	0.0712852	−	0.0155071i
$469$	−714.962	−	326.512i	−1.52444	−	0.696188i
$470$	−109.920	+	526.121i	−0.233872	+	1.11941i
$471$	−563.516	−	650.332i	−1.19643	−	1.38075i
$472$	6.81137	−	95.2354i	0.0144309	−	0.201770i
$473$	128.522	−	70.1785i	0.271717	−	0.148369i
$474$	496.353	+	226.677i	1.04716	+	0.478221i
$475$	272.913	−	624.626i	0.574554	−	1.31500i
$476$	−247.637	+	72.7127i	−0.520246	+	0.152758i
$477$	−122.061	+	91.3740i	−0.255894	+	0.191560i
$478$	118.484	+	44.1921i	0.247874	+	0.0924520i
$479$	22.7186	−	3.26645i	0.0474293	−	0.00681930i	−0.118559	−	0.992947i	$-0.537828\pi$
$479$	22.7186	−	3.26645i	0.0474293	−	0.00681930i	0.165989	+	0.986128i	$0.446918\pi$
$480$	−106.205	+	80.8774i	−0.221260	+	0.168495i
$481$	−43.9361	+	50.7050i	−0.0913433	+	0.105416i
$482$	76.1826	+	76.1826i	0.158055	+	0.158055i
$483$	747.068	+	591.324i	1.54672	+	1.22427i
$484$			66.7353i			0.137883i
$485$	500.672	−	76.2000i	1.03231	−	0.157113i
$486$	352.168	−	226.324i	0.724625	−	0.465688i
$487$	427.193	−	570.663i	0.877193	−	1.17179i	−0.106923	−	0.994267i	$-0.534100\pi$
$487$	427.193	−	570.663i	0.877193	−	1.17179i	0.984116	−	0.177525i	$-0.0568091\pi$
$488$	19.9770	+	7.45105i	0.0409365	+	0.0152685i
$489$	1022.56	+	147.021i	2.09111	+	0.300657i
$490$	80.8636	−	180.997i	0.165028	−	0.369382i
$491$	−727.060	−	467.253i	−1.48077	−	0.951635i	−0.997077	−	0.0763992i	$-0.975658\pi$
$491$	−727.060	−	467.253i	−1.48077	−	0.951635i	−0.483696	−	0.875236i	$-0.660706\pi$
$492$	439.586	−	163.957i	0.893466	−	0.333246i
$493$	−619.737	+	338.402i	−1.25707	+	0.686413i
$494$	−37.4720	+	32.4697i	−0.0758542	+	0.0657281i
$495$	−578.343	+	587.950i	−1.16837	+	1.18778i
$496$	79.4101	+	23.3169i	0.160101	+	0.0470099i
$497$	−711.619	+	265.420i	−1.43183	+	0.534045i
$498$	275.626	−	59.9588i	0.553466	−	0.120399i
$499$	−119.237	−	406.085i	−0.238952	−	0.813797i	−0.988418	−	0.151754i	$-0.951508\pi$
$499$	−119.237	−	406.085i	−0.238952	−	0.813797i	0.749466	−	0.662043i	$-0.230310\pi$
$500$	−248.846	+	23.9906i	−0.497692	+	0.0479812i
$501$	324.142	+	709.772i	0.646990	+	1.41671i
$502$	−76.6142	+	102.345i	−0.152618	+	0.203874i
$503$	−159.572	+	733.541i	−0.317241	+	1.45833i	0.491866	+	0.870671i	$0.336315\pi$
$503$	−159.572	+	733.541i	−0.317241	+	1.45833i	−0.809107	+	0.587661i	$0.800049\pi$
$504$	−249.073	−	215.823i	−0.494193	−	0.428221i
$505$	905.595	−	72.2714i	1.79326	−	0.143112i
$506$	272.784	−	298.177i	0.539099	−	0.589283i
$507$	558.493	+	558.493i	1.10156	+	1.10156i
$508$	9.66574	+	135.145i	0.0190271	+	0.266033i
$509$	120.844	+	188.038i	0.237415	+	0.369426i	0.939432	−	0.342735i	$-0.111353\pi$
$509$	120.844	+	188.038i	0.237415	+	0.369426i	−0.702017	+	0.712160i	$0.747717\pi$
$510$	−261.874	+	414.959i	−0.513478	+	0.813645i
$511$	−99.6813	−	218.272i	−0.195071	−	0.427146i
$512$	−18.1142	+	13.5601i	−0.0353793	+	0.0264846i
$513$	263.699	−	482.929i	0.514033	−	0.941382i
$514$	−182.846	+	284.514i	−0.355731	+	0.553528i
$515$	9.83538	+	21.0753i	0.0190978	+	0.0409230i
$516$	106.746	+	31.3435i	0.206873	+	0.0607433i
$517$	−67.3728	+	941.994i	−0.130315	+	1.82204i
$518$	645.994	+	46.2024i	1.24709	+	0.0891939i
$519$	−388.983	+	1324.76i	−0.749486	+	2.55252i
$520$	17.0901	+	6.21441i	0.0328656	+	0.0119508i
$521$	−734.557	−	472.071i	−1.40990	−	0.906087i	−0.409917	−	0.912123i	$-0.634442\pi$
$521$	−734.557	−	472.071i	−1.40990	−	0.906087i	−0.999982	+	0.00603576i	$0.998079\pi$
$522$	−791.376	−	432.124i	−1.51605	−	0.827824i
$523$	−104.104	−	139.067i	−0.199052	−	0.265903i	0.689898	−	0.723907i	$-0.257655\pi$
$523$	−104.104	−	139.067i	−0.199052	−	0.265903i	−0.888950	+	0.458004i	$0.848565\pi$
$524$	−90.0921	+	41.1437i	−0.171931	+	0.0785185i
$525$	−308.097	−	988.731i	−0.586852	−	1.88330i
$526$	−338.934	+	217.820i	−0.644362	+	0.414106i
$527$	303.434	−	21.7021i	0.575777	−	0.0411804i
$528$	−165.859	+	165.859i	−0.314127	+	0.314127i
$529$	−526.911	+	46.9610i	−0.996052	+	0.0887732i
$530$	−80.9546	+	6.46062i	−0.152745	+	0.0121898i
$531$	293.474	−	338.687i	0.552682	−	0.637829i
$532$	467.684	+	101.738i	0.879106	+	0.191238i
$533$	−51.1635	−	38.3005i	−0.0959916	−	0.0718584i
$534$	−582.803	+	266.157i	−1.09139	+	0.498422i
$535$	−52.2005	+	45.9902i	−0.0975710	+	0.0859630i
$536$	−243.030	+	71.3599i	−0.453413	+	0.133134i
$537$	−47.0645	−	216.352i	−0.0876435	−	0.402890i
$538$	27.6768	+	74.2044i	0.0514439	+	0.137926i
$539$	98.1342	−	334.214i	0.182067	−	0.620064i
$540$	−201.797	+	1.66220i	−0.373698	+	0.00307815i
$541$	−211.167	−	243.700i	−0.390327	−	0.450461i	0.526244	−	0.850334i	$-0.323600\pi$
$541$	−211.167	−	243.700i	−0.390327	−	0.450461i	−0.916571	+	0.399872i	$0.869054\pi$
$542$	−69.7077	−	127.660i	−0.128612	−	0.235535i
$543$	425.288	+	1140.24i	0.783220	+	2.09989i
$544$	−44.9658	+	69.9682i	−0.0826577	+	0.128618i
$545$	208.940	+	546.401i	0.383375	+	1.00257i
$546$	−10.7207	+	74.5639i	−0.0196349	+	0.136564i
$547$	247.278	−	662.978i	0.452062	−	1.21203i	−0.488548	−	0.872537i	$-0.662473\pi$
$547$	247.278	−	662.978i	0.452062	−	1.21203i	0.940610	−	0.339489i	$-0.110254\pi$
$548$	−421.102	−	315.233i	−0.768434	−	0.575243i
$549$	54.1051	+	84.1891i	0.0985520	+	0.153350i
$550$	−427.637	+	100.432i	−0.777521	+	0.182604i
$551$	1309.46			2.37651
$552$	306.733	−	13.6418i	0.555675	−	0.0247133i
$553$	−507.369	+	507.369i	−0.917484	+	0.917484i
$554$	389.962	+	337.904i	0.703903	+	0.609936i
$555$	979.593	−	745.983i	1.76503	−	1.34411i
$556$	25.6365	+	178.306i	0.0461089	+	0.320694i
$557$	−31.0167	+	83.1590i	−0.0556853	+	0.149298i	−0.961814	−	0.273704i	$-0.911751\pi$
$557$	−31.0167	+	83.1590i	−0.0556853	+	0.149298i	0.906129	+	0.423002i	$0.139024\pi$
$558$	232.797	+	310.980i	0.417198	+	0.557311i
$559$	−4.26970	−	14.5413i	−0.00763811	−	0.0260130i
$560$	−50.8408	−	168.016i	−0.0907872	−	0.300028i
$561$	−358.158	+	784.258i	−0.638429	+	1.39796i
$562$	−336.018	−	615.371i	−0.597897	−	1.09497i
$563$	82.5422	+	5.90353i	0.146611	+	0.0104858i	0.144452	−	0.989512i	$-0.453858\pi$
$563$	82.5422	+	5.90353i	0.146611	+	0.0104858i	0.00215939	+	0.999998i	$0.499313\pi$
$564$	−542.253	+	469.865i	−0.961442	+	0.833094i
$565$	268.528	−	175.715i	0.475271	−	0.310999i
$566$	−140.227	+	307.055i	−0.247751	+	0.542500i
$567$	45.2167	+	207.858i	0.0797473	+	0.366593i
$568$	−117.299	+	214.816i	−0.206512	+	0.378198i
$569$	426.422	+	61.3102i	0.749423	+	0.107751i	0.506435	−	0.862278i	$-0.330963\pi$
$569$	426.422	+	61.3102i	0.749423	+	0.107751i	0.242989	+	0.970029i	$0.421872\pi$
$570$	795.028	−	442.658i	1.39479	−	0.776593i
$571$	56.3415	+	391.864i	0.0986717	+	0.686276i	0.977777	+	0.209649i	$0.0672320\pi$
$571$	56.3415	+	391.864i	0.0986717	+	0.686276i	−0.879105	+	0.476628i	$0.841859\pi$
$572$	31.2222	+	6.79198i	0.0545843	+	0.0118741i
$573$	−119.045	−	1664.46i	−0.207757	−	2.90482i
$574$			616.937i			1.07480i
$575$	501.749	+	280.842i	0.872608	+	0.488422i
$576$	−106.206			−0.184386
$577$	668.479	−	47.8106i	1.15854	−	0.0828606i	0.521196	−	0.853437i	$-0.325486\pi$
$577$	668.479	−	47.8106i	1.15854	−	0.0828606i	0.637348	+	0.770577i	$0.280032\pi$
$578$	21.8933	−	100.642i	0.0378778	−	0.174121i
$579$	933.095	−	134.159i	1.61156	−	0.231708i
$580$	−233.626	−	419.601i	−0.402804	−	0.723449i
$581$	−52.7866	+	367.139i	−0.0908548	+	0.631909i
$582$	593.366	+	324.002i	1.01953	+	0.556705i
$583$	−139.435	+	30.3323i	−0.239169	+	0.0520280i
$584$	−70.3392	−	32.1228i	−0.120444	−	0.0550049i
$585$	46.7359	+	71.4220i	0.0798904	+	0.122089i
$586$	258.822	+	298.696i	0.441675	+	0.509720i
$587$	−10.2908	+	143.884i	−0.0175311	+	0.245117i	0.981128	+	0.193357i	$0.0619376\pi$
$587$	−10.2908	+	143.884i	−0.0175311	+	0.245117i	−0.998660	+	0.0517600i	$0.983517\pi$
$588$	232.267	−	126.827i	0.395011	−	0.215693i
$589$	−513.166	−	234.355i	−0.871249	−	0.397886i
$590$	228.466	−	69.1328i	0.387231	−	0.117174i
$591$	123.891	−	36.3776i	0.209629	−	0.0615526i
$592$	167.078	−	125.073i	0.282227	−	0.211273i
$593$	572.325	+	213.466i	0.965134	+	0.359977i	0.782116	−	0.623133i	$-0.214140\pi$
$593$	572.325	+	213.466i	0.965134	+	0.359977i	0.183018	+	0.983109i	$0.441413\pi$
$594$	−350.978	+	50.4630i	−0.590871	+	0.0849545i
$595$	−390.912	−	513.330i	−0.656996	−	0.862739i
$596$	287.116	−	331.349i	0.481738	−	0.555955i
$597$	520.140	+	520.140i	0.871257	+	0.871257i
$598$	−24.1534	−	34.1462i	−0.0403903	−	0.0571007i
$599$		−	266.922i		−	0.445612i	−0.974863	−	0.222806i	$-0.928478\pi$
$599$		−	266.922i		−	0.445612i	0.974863	−	0.222806i	$-0.0715217\pi$
$600$	−283.690	−	175.781i	−0.472816	−	0.292969i
$601$	313.894	−	201.728i	0.522287	−	0.335653i	−0.252789	−	0.967521i	$-0.581348\pi$
$601$	313.894	−	201.728i	0.522287	−	0.335653i	0.775076	+	0.631868i	$0.217712\pi$
$602$	−87.6703	+	117.114i	−0.145632	+	0.194541i
$603$	−1113.90	−	415.465i	−1.84727	−	0.688997i
$604$	−101.273	−	14.5608i	−0.167670	−	0.0241073i
$605$	−155.834	+	59.5896i	−0.257576	+	0.0984952i
$606$	1020.24	+	655.666i	1.68356	+	1.08196i
$607$	−134.349	+	50.1097i	−0.221333	+	0.0825531i	−0.457685	−	0.889115i	$-0.651321\pi$
$607$	−134.349	+	50.1097i	−0.221333	+	0.0825531i	0.236351	+	0.971668i	$0.424048\pi$
$608$	135.372	−	73.9187i	0.222651	−	0.121577i
$609$	1503.53	−	1302.82i	2.46885	−	2.13927i
$610$	0.439045	+	53.3016i	0.000719746	+	0.0873796i
$611$	93.7812	+	27.5366i	0.153488	+	0.0450682i
$612$	−365.767	+	136.424i	−0.597658	+	0.222915i
$613$	37.3391	−	8.12262i	0.0609121	−	0.0132506i	−0.182006	−	0.983297i	$-0.558259\pi$
$613$	37.3391	−	8.12262i	0.0609121	−	0.0132506i	0.242918	+	0.970047i	$0.421895\pi$
$614$	−209.014	−	711.836i	−0.340414	−	1.15934i
$615$	775.372	+	880.074i	1.26077	+	1.43102i
$616$	−128.130	−	280.565i	−0.208003	−	0.455463i
$617$	141.590	−	189.142i	0.229482	−	0.306552i	−0.670990	−	0.741467i	$-0.734131\pi$
$617$	141.590	−	189.142i	0.229482	−	0.306552i	0.900472	+	0.434915i	$0.143222\pi$
$618$	−6.59954	+	30.3376i	−0.0106789	+	0.0490900i
$619$	102.785	+	89.0639i	0.166050	+	0.143884i	0.733922	−	0.679233i	$-0.237688\pi$
$619$	102.785	+	89.0639i	0.166050	+	0.143884i	−0.567872	+	0.823117i	$0.692233\pi$
$620$	16.4599	+	206.251i	0.0265483	+	0.332662i
$621$	383.562	+	261.370i	0.617652	+	0.420886i
$622$	−220.296	−	220.296i	−0.354174	−	0.354174i
$623$	−60.1032	−	840.353i	−0.0964739	−	1.34888i
$624$	13.1244	+	20.4220i	0.0210328	+	0.0327276i
$625$	−278.221	−	559.659i	−0.445154	−	0.895454i
$626$	−107.990	−	236.466i	−0.172509	−	0.377741i
$627$	1279.96	−	958.165i	2.04140	−	1.52817i
$628$	174.756	−	320.042i	0.278274	−	0.509621i
$629$	414.748	−	645.361i	0.659377	−	1.02601i
$630$	281.565	−	774.324i	0.446928	−	1.22909i
$631$	−910.052	−	267.215i	−1.44224	−	0.423479i	−0.535271	−	0.844680i	$-0.679791\pi$
$631$	−910.052	−	267.215i	−1.44224	−	0.423479i	−0.906967	+	0.421201i	$0.861609\pi$
$632$	−16.4956	+	230.638i	−0.0261006	+	0.364934i
$633$	994.818	+	71.1508i	1.57159	+	0.112402i
$634$	131.847	−	449.030i	0.207961	−	0.708250i
$635$	−306.946	+	143.245i	−0.483379	+	0.225582i
$636$	−91.2028	−	58.6125i	−0.143401	−	0.0921580i
$637$	−31.6400	−	17.2768i	−0.0496703	−	0.0271221i
$638$	−505.701	−	675.538i	−0.792635	−	1.05884i
$639$	−1044.99	+	477.230i	−1.63535	+	0.746839i
$640$	−47.8388	−	30.1903i	−0.0747481	−	0.0471723i
$641$	−26.1156	+	16.7835i	−0.0407420	+	0.0261833i	−0.560853	−	0.827915i	$-0.689527\pi$
$641$	−26.1156	+	16.7835i	−0.0407420	+	0.0261833i	0.520111	+	0.854099i	$0.325890\pi$
$642$	−92.6351	+	6.62539i	−0.144291	+	0.0103199i
$643$	84.5004	−	84.5004i	0.131416	−	0.131416i	−0.638339	−	0.769755i	$-0.720378\pi$
$643$	84.5004	−	84.5004i	0.131416	−	0.131416i	0.769755	+	0.638339i	$0.220378\pi$
$644$	−124.146	+	384.180i	−0.192774	+	0.596553i
$645$	22.1261	+	277.250i	0.0343040	+	0.429846i
$646$	371.262	−	428.459i	0.574709	−	0.663250i
$647$	−813.657	−	177.000i	−1.25758	−	0.273571i	−0.466085	−	0.884740i	$-0.654336\pi$
$647$	−813.657	−	177.000i	−1.25758	−	0.273571i	−0.791500	+	0.611169i	$0.790699\pi$
$648$	54.8770	+	41.0804i	0.0846868	+	0.0633957i
$649$	381.509	−	174.230i	0.587842	−	0.268458i
$650$	0.748894	+	45.4561i	0.00115214	+	0.0699324i
$651$	−822.388	+	241.475i	−1.26327	+	0.370929i
$652$	93.0542	+	427.763i	0.142721	+	0.656079i
$653$	95.0340	+	254.796i	0.145534	+	0.390193i	0.989180	−	0.146708i	$-0.0468677\pi$
$653$	95.0340	+	254.796i	0.145534	+	0.390193i	−0.843645	+	0.536901i	$0.819595\pi$
$654$	−220.011	+	749.288i	−0.336408	+	1.14570i
$655$	−176.520	−	173.636i	−0.269496	−	0.265093i
$656$	130.194	+	150.251i	0.198466	+	0.229042i
$657$	−173.943	−	318.553i	−0.264754	−	0.484860i
$658$	−329.716	−	884.004i	−0.501089	−	1.34347i
$659$	−536.688	+	835.104i	−0.814398	+	1.26723i	0.146191	+	0.989256i	$0.453299\pi$
$659$	−536.688	+	835.104i	−0.814398	+	1.26723i	−0.960589	+	0.277972i	$0.910338\pi$
$660$	−535.397	−	239.198i	−0.811208	−	0.362421i
$661$	−88.5966	+	616.203i	−0.134034	+	0.932228i	0.806186	+	0.591662i	$0.201528\pi$
$661$	−88.5966	+	616.203i	−0.134034	+	0.932228i	−0.940220	+	0.340566i	$0.889381\pi$
$662$	153.118	−	410.526i	0.231296	−	0.620130i
$663$	71.4323	+	53.4735i	0.107741	+	0.0806539i
$664$	64.6224	+	100.554i	0.0973228	+	0.151437i
$665$	180.037	+	1182.93i	0.270733	+	1.77885i
$666$	979.605			1.47088
$667$	−108.466	+	1099.25i	−0.162618	+	1.64805i
$668$	−233.804	+	233.804i	−0.350006	+	0.350006i
$669$	107.530	+	93.1756i	0.160733	+	0.139276i
$670$	−383.640	−	503.779i	−0.572596	−	0.751909i
$671$	13.3290	+	92.7053i	0.0198644	+	0.138160i
$672$	81.8915	−	219.560i	0.121862	−	0.326726i
$673$	126.461	+	168.932i	0.187906	+	0.251013i	0.884595	−	0.466360i	$-0.154435\pi$
$673$	126.461	+	168.932i	0.187906	+	0.251013i	−0.696689	+	0.717374i	$0.745344\pi$
$674$	177.770	+	605.429i	0.263754	+	0.898262i
$675$	−184.071	−	469.732i	−0.272698	−	0.695899i
$676$	−139.037	+	304.448i	−0.205675	+	0.450366i
$677$	407.697	+	746.641i	0.602211	+	1.10287i	0.983924	+	0.178587i	$0.0571525\pi$
$677$	407.697	+	746.641i	0.602211	+	1.10287i	−0.381713	+	0.924281i	$0.624666\pi$
$678$	427.303	+	30.5613i	0.630241	+	0.0450757i
$679$	−671.859	+	582.169i	−0.989483	+	0.857392i
$680$	−203.534	−	42.5233i	−0.299314	−	0.0625343i
$681$	−193.674	+	424.088i	−0.284397	+	0.622743i
$682$	77.2787	+	355.244i	0.113312	+	0.520886i
$683$	76.4342	−	139.979i	0.111910	−	0.204947i	−0.815722	−	0.578445i	$-0.803660\pi$
$683$	76.4342	−	139.979i	0.111910	−	0.204947i	0.927631	+	0.373498i	$0.121842\pi$
$684$	716.579	+	103.029i	1.04763	+	0.150627i
$685$	360.088	−	1264.79i	0.525676	−	1.84641i
$686$	−37.0339	−	257.576i	−0.0539852	−	0.375475i
$687$	−44.9899	−	9.78696i	−0.0654875	−	0.0142459i
$688$	3.36320	+	47.0237i	0.00488837	+	0.0683484i
$689$			14.7683i			0.0214344i
$690$	305.744	+	704.070i	0.443107	+	1.02039i
$691$	230.763			0.333955			0.166978	−	0.985961i	$-0.446599\pi$
$691$	230.763			0.333955			0.166978	+	0.985961i	$0.446599\pi$
$692$	−583.579	+	41.7384i	−0.843323	+	0.0603156i
$693$	307.733	−	1414.63i	0.444060	−	2.04131i
$694$	666.241	−	95.7909i	0.960001	−	0.138027i
$695$	−393.471	+	219.078i	−0.566145	+	0.315220i
$696$	91.2398	−	634.587i	0.131092	−	0.911762i
$697$	641.380	+	350.220i	0.920200	+	0.502467i
$698$	−657.230	+	142.972i	−0.941590	+	0.204830i
$699$	−714.284	−	326.202i	−1.02186	−	0.466670i
$700$	346.937	−	268.744i	0.495624	−	0.383920i
$701$	808.914	+	933.537i	1.15394	+	1.33172i	0.934444	+	0.356109i	$0.115897\pi$
$701$	808.914	+	933.537i	1.15394	+	1.33172i	0.219499	+	0.975613i	$0.429558\pi$
$702$	−2.61799	+	36.6043i	−0.00372933	+	0.0521429i
$703$	−1248.62	+	681.798i	−1.77613	+	0.969841i
$704$	−90.4136	−	41.2905i	−0.128428	−	0.0586513i
$705$	−1581.37	−	846.661i	−2.24308	−	1.20094i
$706$	−398.995	+	117.156i	−0.565149	+	0.165943i
$707$	−1276.65	+	955.686i	−1.80572	+	1.35175i
$708$	298.555	+	111.355i	0.421687	+	0.157281i
$709$	−1403.05	+	201.729i	−1.97892	+	0.284526i	−0.985610	+	0.169033i	$0.945936\pi$
$709$	−1403.05	+	201.729i	−1.97892	+	0.284526i	−0.993308	+	0.115493i	$0.963155\pi$
$710$	−606.356	−	82.0890i	−0.854022	−	0.115618i
$711$	−710.726	+	820.222i	−0.999615	+	1.15362i
$712$	−191.979	−	191.979i	−0.269634	−	0.269634i
$713$	239.241	−	411.376i	0.335542	−	0.576964i
$714$		−	861.340i		−	1.20636i
$715$	12.0191	+	78.9717i	0.0168100	+	0.110450i
$716$	78.9300	−	50.7252i	0.110237	−	0.0708453i
$717$	−252.913	+	337.852i	−0.352738	+	0.471202i
$718$	919.672	+	343.020i	1.28088	+	0.477743i
$719$	1143.77	+	164.450i	1.59078	+	0.228720i	0.880099	−	0.474790i	$-0.157476\pi$
$719$	1143.77	+	164.450i	1.59078	+	0.228720i	0.710685	+	0.703510i	$0.248385\pi$
$720$	−94.8340	−	248.002i	−0.131714	−	0.344447i
$721$	−34.3449	−	22.0721i	−0.0476351	−	0.0306132i
$722$	−506.728	+	189.000i	−0.701840	+	0.261773i
$723$	−315.579	+	172.319i	−0.436485	+	0.238339i
$724$	−389.738	+	337.710i	−0.538312	+	0.466450i
$725$	771.198	−	920.212i	1.06372	−	1.26926i
$726$	−213.697	−	62.7472i	−0.294349	−	0.0864286i
$727$	−137.010	+	51.1022i	−0.188460	+	0.0702919i	−0.441922	−	0.897053i	$-0.645703\pi$
$727$	−137.010	+	51.1022i	−0.188460	+	0.0702919i	0.253462	+	0.967345i	$0.418431\pi$
$728$	−31.1922	+	6.78544i	−0.0428464	+	0.00932066i
$729$	332.153	+	1131.21i	0.455628	+	1.55173i
$730$	12.2024	−	192.932i	0.0167156	−	0.264291i
$731$	71.9856	+	157.626i	0.0984755	+	0.215631i
$732$	−42.6426	+	56.9639i	−0.0582550	+	0.0778195i
$733$	−32.4595	+	149.214i	−0.0442831	+	0.203566i	−0.993973	−	0.109626i	$-0.965035\pi$
$733$	−32.4595	+	149.214i	−0.0442831	+	0.203566i	0.949690	+	0.313192i	$0.101398\pi$
$734$	217.271	+	188.266i	0.296009	+	0.256493i
$735$	503.551	+	429.119i	0.685103	+	0.583835i
$736$	50.8393	+	119.764i	0.0690752	+	0.162723i
$737$	−786.748	−	786.748i	−1.06750	−	1.06750i
$738$	66.5707	+	930.780i	0.0902042	+	1.26122i
$739$	684.684	+	1065.39i	0.926501	+	1.44166i	0.896966	+	0.442100i	$0.145766\pi$
$739$	684.684	+	1065.39i	0.926501	+	1.44166i	0.0295347	+	0.999564i	$0.490597\pi$
$740$	441.247	+	278.464i	0.596280	+	0.376302i
$741$	−68.7404	−	150.521i	−0.0927671	−	0.203132i
$742$	114.124	−	85.4325i	0.153807	−	0.115138i
$743$	521.026	−	954.187i	0.701246	−	1.28424i	−0.247712	−	0.968834i	$-0.579679\pi$
$743$	521.026	−	954.187i	0.701246	−	1.28424i	0.948958	−	0.315402i	$-0.102139\pi$
$744$	−149.329	+	232.360i	−0.200711	+	0.312312i
$745$	1030.11	+	374.574i	1.38269	+	0.502783i
$746$	−30.1187	−	8.84364i	−0.0403735	−	0.0118547i
$747$	−40.0236	+	559.604i	−0.0535792	+	0.749135i
$748$	−364.417	−	26.0636i	−0.487189	−	0.0348444i
$749$	34.4060	−	117.176i	0.0459359	−	0.156443i
$750$	157.153	−	819.402i	0.209538	−	1.09254i
$751$	1030.89	+	662.514i	1.37269	+	0.882175i	0.998970	−	0.0453659i	$-0.0144454\pi$
$751$	1030.89	+	662.514i	1.37269	+	0.882175i	0.373721	+	0.927541i	$0.378082\pi$
$752$	−266.854	−	145.713i	−0.354859	−	0.193768i
$753$	−255.688	−	341.559i	−0.339559	−	0.453598i
$754$	−79.4419	+	36.2799i	−0.105361	+	0.0481166i
$755$	−56.4279	−	249.483i	−0.0747389	−	0.330441i
$756$	298.010	−	191.520i	0.394193	−	0.253333i
$757$	−124.477	+	8.90280i	−0.164435	+	0.0117606i	−0.153314	−	0.988178i	$-0.548995\pi$
$757$	−124.477	+	8.90280i	−0.164435	+	0.0117606i	−0.0111211	+	0.999938i	$0.503540\pi$
$758$	101.981	−	101.981i	0.134539	−	0.134539i
$759$	698.329	+	1153.86i	0.920065	+	1.52023i
$760$	293.484	+	250.103i	0.386164	+	0.329083i
$761$	−164.083	+	189.361i	−0.215614	+	0.248832i	−0.853245	−	0.521510i	$-0.825369\pi$
$761$	−164.083	+	189.361i	−0.215614	+	0.248832i	0.637631	+	0.770342i	$0.279915\pi$
$762$	−441.843	−	96.1171i	−0.579847	−	0.126138i
$763$	−822.062	−	615.388i	−1.07741	−	0.806537i
$764$	643.223	−	293.750i	0.841915	−	0.384490i
$765$	−645.166	−	732.285i	−0.843354	−	0.957236i
$766$	−634.640	+	186.347i	−0.828512	+	0.243273i
$767$	−9.22677	−	42.4148i	−0.0120297	−	0.0552996i
$768$	−26.3900	−	70.7542i	−0.0343619	−	0.0921279i
$769$	241.165	−	821.331i	0.313608	−	1.06805i	−0.640343	−	0.768089i	$-0.721208\pi$
$769$	241.165	−	821.331i	0.313608	−	1.06805i	0.953951	−	0.299962i	$-0.0969740\pi$
$770$	540.737	−	549.719i	0.702256	−	0.713921i
$771$	−739.139	−	853.012i	−0.958676	−	1.10637i
$772$	191.445	+	350.605i	0.247986	+	0.454152i
$773$	78.0986	+	209.390i	0.101033	+	0.270880i	0.977625	−	0.210354i	$-0.0674615\pi$
$773$	78.0986	+	209.390i	0.101033	+	0.270880i	−0.876592	+	0.481234i	$0.840189\pi$
$774$	−119.632	+	186.151i	−0.154563	+	0.240505i
$775$	−466.918	+	222.602i	−0.602475	+	0.287228i
$776$	−40.7709	+	283.568i	−0.0525399	+	0.365423i
$777$	−755.337	+	2025.14i	−0.972119	+	2.60635i
$778$	−354.553	−	265.415i	−0.455724	−	0.341151i
$779$	−732.669	−	1140.05i	−0.940525	−	1.46348i
$780$	−35.9683	+	48.8822i	−0.0461132	+	0.0626695i
$781$	−1075.14			−1.37662
$782$	328.926	+	347.154i	0.420622	+	0.443932i
$783$	685.310	−	685.310i	0.875237	−	0.875237i
$784$	84.7506	+	73.4368i	0.108100	+	0.0936694i
$785$	903.374	+	122.300i	1.15079	+	0.155796i
$786$	−47.0405	−	327.174i	−0.0598480	−	0.416252i
$787$	291.934	−	782.706i	0.370946	−	0.994543i	−0.608628	−	0.793456i	$-0.708280\pi$
$787$	291.934	−	782.706i	0.370946	−	0.994543i	0.979573	−	0.201088i	$-0.0644476\pi$
$788$	32.7898	+	43.8020i	0.0416114	+	0.0555863i
$789$	−378.815	−	1290.13i	−0.480120	−	1.63514i
$790$	−553.292	+	167.424i	−0.700370	+	0.211929i
$791$	−234.013	+	512.417i	−0.295845	+	0.647809i
$792$	−223.586	−	409.466i	−0.282305	−	0.517003i
$793$	9.66846	+	0.691502i	0.0121923	+	0.000872008i
$794$	90.3492	−	78.2880i	0.113790	−	0.0985995i
$795$	55.4287	−	265.304i	0.0697217	−	0.333716i
$796$	−129.489	+	283.540i	−0.162674	+	0.356207i
$797$	−310.289	−	1426.37i	−0.389321	−	1.78968i	−0.587189	−	0.809450i	$-0.699765\pi$
$797$	−310.289	−	1426.37i	−0.389321	−	1.78968i	0.197868	−	0.980229i	$-0.436598\pi$
$798$	−765.518	+	1401.94i	−0.959295	+	1.75682i
$799$	−1106.20	−	159.048i	−1.38448	−	0.199058i
$800$	27.7808	−	138.666i	0.0347260	−	0.173332i
$801$	−181.357	−	1261.37i	−0.226413	−	1.57474i
$802$	415.825	+	90.4572i	0.518485	+	0.112789i
$803$	−24.2322	−	338.811i	−0.0301771	−	0.421931i
$804$		−	845.315i		−	1.05139i
$805$	−1007.95	+	53.1500i	−1.25211	+	0.0660249i
$806$	37.6257			0.0466820
$807$	−263.637	+	18.8557i	−0.326688	+	0.0233652i
$808$	−109.240	+	502.166i	−0.135197	+	0.621493i
$809$	−1390.54	+	199.930i	−1.71884	+	0.247132i	−0.930025	−	0.367496i	$-0.880215\pi$
$809$	−1390.54	+	199.930i	−1.71884	+	0.247132i	−0.788817	+	0.614629i	$0.789306\pi$
$810$	−46.9258	+	164.825i	−0.0579331	+	0.203488i
$811$	126.521	−	879.970i	0.156006	−	1.08504i	−0.749896	−	0.661556i	$-0.769897\pi$
$811$	126.521	−	879.970i	0.156006	−	1.08504i	0.905902	−	0.423488i	$-0.139194\pi$
$812$	739.918	+	404.026i	0.911229	+	0.497569i
$813$	474.330	−	103.184i	0.583431	−	0.126918i
$814$	833.942	+	380.848i	1.02450	+	0.467873i
$815$	−915.779	+	599.251i	−1.12366	+	0.735277i
$816$	−181.771	−	209.775i	−0.222758	−	0.257077i
$817$	22.9251	−	320.534i	0.0280601	−	0.392331i
$818$	−229.711	+	125.432i	−0.280820	+	0.153339i
$819$	−136.291	−	62.2418i	−0.166411	−	0.0759973i
$820$	−234.599	+	438.178i	−0.286096	+	0.534364i
$821$	−1066.37	+	313.114i	−1.29887	+	0.381381i	−0.856822	−	0.515612i	$-0.827564\pi$
$821$	−1066.37	+	313.114i	−1.29887	+	0.381381i	−0.442043	+	0.896994i	$0.645746\pi$
$822$	1405.36	−	1052.04i	1.70969	−	1.27986i
$823$	1039.54	+	387.728i	1.26311	+	0.471115i	0.889697	−	0.456551i	$-0.150915\pi$
$823$	1039.54	+	387.728i	1.26311	+	0.471115i	0.373411	+	0.927666i	$0.378188\pi$
$824$	−13.0224	+	1.87234i	−0.0158039	+	0.00227226i
$825$	80.4814	−	1463.79i	0.0975532	−	1.77429i
$826$	−274.391	+	316.664i	−0.332193	+	0.383371i
$827$	−225.106	−	225.106i	−0.272196	−	0.272196i	0.557787	−	0.829984i	$-0.311650\pi$
$827$	−225.106	−	225.106i	−0.272196	−	0.272196i	−0.829984	+	0.557787i	$0.811650\pi$
$828$	−145.846	+	593.013i	−0.176142	+	0.716200i
$829$			403.014i			0.486145i	0.970008	+	0.243072i	$0.0781553\pi$
$829$			403.014i			0.486145i	−0.970008	+	0.243072i	$0.921845\pi$
$830$	−177.101	+	240.687i	−0.213375	+	0.289984i
$831$	−1448.68	+	931.011i	−1.74330	+	1.12035i
$832$	−6.16473	+	8.23511i	−0.00740953	+	0.00989797i
$833$	386.207	+	144.048i	0.463634	+	0.172926i
$834$	−595.069	−	85.5580i	−0.713512	−	0.102588i
$835$	−754.724	−	337.186i	−0.903861	−	0.403815i
$836$	569.971	+	366.298i	0.681784	+	0.438156i
$837$	−391.219	+	145.917i	−0.467406	+	0.174333i
$838$	387.494	−	211.588i	0.462403	−	0.252491i
$839$	751.508	−	651.185i	0.895718	−	0.776144i	−0.0796279	−	0.996825i	$-0.525373\pi$
$839$	751.508	−	651.185i	0.895718	−	0.776144i	0.975346	+	0.220680i	$0.0708278\pi$
$840$	585.816	−	4.82537i	0.697400	−	0.00574449i
$841$	1406.10	+	412.867i	1.67194	+	0.490924i
$842$	−392.926	+	146.554i	−0.466658	+	0.174054i
$843$	2286.45	−	497.388i	2.71228	−	0.590021i
$844$	119.070	+	405.515i	0.141078	+	0.480468i
$845$	−835.064	−	52.8154i	−0.988242	−	0.0625035i
$846$	−592.836	−	1298.13i	−0.700752	−	1.53443i
$847$	175.509	−	234.452i	0.207212	−	0.276803i
$848$	9.76534	−	44.8905i	0.0115157	−	0.0529370i
$849$	−851.392	−	737.735i	−1.00282	−	0.868946i
$850$	−82.4440	−	513.241i	−0.0969929	−	0.603813i
$851$	−468.923	−	1104.66i	−0.551026	−	1.29807i
$852$	−577.587	−	577.587i	−0.677919	−	0.677919i
$853$	48.1638	+	673.418i	0.0564640	+	0.789470i	0.944253	+	0.329220i	$0.106786\pi$
$853$	48.1638	+	673.418i	0.0564640	+	0.789470i	−0.887789	+	0.460250i	$0.847760\pi$
$854$	−50.5869	−	78.7148i	−0.0592353	−	0.0921719i
$855$	399.269	+	1765.28i	0.466981	+	2.06465i
$856$	−16.3486	−	35.7983i	−0.0190988	−	0.0418205i
$857$	144.202	−	107.949i	0.168264	−	0.125961i	−0.511827	−	0.859089i	$-0.671031\pi$
$857$	144.202	−	107.949i	0.168264	−	0.125961i	0.680091	+	0.733128i	$0.261940\pi$
$858$	−51.1054	+	93.5925i	−0.0595634	+	0.109082i
$859$	−32.5577	+	50.6607i	−0.0379018	+	0.0589764i	−0.859687	−	0.510820i	$-0.829342\pi$
$859$	−32.5577	+	50.6607i	−0.0379018	+	0.0589764i	0.821786	+	0.569797i	$0.192978\pi$
$860$	−106.802	+	49.8420i	−0.124188	+	0.0579558i
$861$	−1975.53	−	580.068i	−2.29446	−	0.673714i
$862$	−18.8992	+	264.246i	−0.0219248	+	0.306549i
$863$	1407.73	+	100.683i	1.63121	+	0.116666i	0.856671	−	0.515864i	$-0.172529\pi$
$863$	1407.73	+	100.683i	1.63121	+	0.116666i	0.774536	+	0.632530i	$0.217984\pi$
$864$	32.1619	−	109.533i	0.0372244	−	0.126775i
$865$	−618.556	−	1325.45i	−0.715093	−	1.53231i
$866$	664.041	+	426.753i	0.766791	+	0.492787i
$867$	301.687	+	164.734i	0.347967	+	0.190004i
$868$	−217.659	−	290.759i	−0.250759	−	0.334975i
$869$	−923.927	+	421.944i	−1.06321	+	0.485551i
$870$	1563.29	−	353.584i	1.79689	−	0.406418i
$871$	−96.8713	+	62.2554i	−0.111218	+	0.0714758i
$872$	−330.075	+	23.6075i	−0.378527	+	0.0270728i
$873$	−950.823	+	950.823i	−1.08914	+	1.08914i
$874$	−226.836	−	857.372i	−0.259537	−	0.980975i
$875$	937.331	+	570.163i	1.07124	+	0.651615i
$876$	168.998	−	195.034i	0.192920	−	0.222642i
$877$	−1250.67	−	272.066i	−1.42607	−	0.310223i	−0.567695	−	0.823239i	$-0.692165\pi$
$877$	−1250.67	−	272.066i	−1.42607	−	0.310223i	−0.858379	+	0.513015i	$0.828528\pi$
$878$	475.627	+	356.050i	0.541717	+	0.405524i
$879$	−1199.83	+	547.943i	−1.36499	+	0.623370i
$880$	15.6849	−	247.994i	0.0178238	−	0.281811i
$881$	1072.40	−	314.885i	1.21725	−	0.357417i	0.390827	−	0.920464i	$-0.372189\pi$
$881$	1072.40	−	314.885i	1.21725	−	0.357417i	0.826425	+	0.563047i	$0.190371\pi$
$882$	111.885	+	514.327i	0.126854	+	0.583137i
$883$	−221.924	−	595.001i	−0.251329	−	0.673840i	−0.999941	−	0.0108318i	$-0.996552\pi$
$883$	−221.924	−	595.001i	−0.251329	−	0.673840i	0.748612	−	0.663008i	$-0.230721\pi$
$884$	−10.6527	+	36.2799i	−0.0120506	+	0.0410406i
$885$	6.56148	+	796.586i	0.00741410	+	0.900098i
$886$	613.217	+	707.690i	0.692118	+	0.798747i
$887$	−304.765	−	558.135i	−0.343590	−	0.629239i	0.647555	−	0.762018i	$-0.275791\pi$
$887$	−304.765	−	558.135i	−0.343590	−	0.629239i	−0.991146	+	0.132780i	$0.957610\pi$
$888$	243.411	+	652.611i	0.274112	+	0.734922i
$889$	321.463	−	500.206i	0.361601	−	0.562661i
$890$	276.868	−	619.714i	0.311088	−	0.696308i
$891$	−42.8539	+	298.055i	−0.0480964	+	0.334518i
$892$	−21.0702	+	56.4915i	−0.0236214	+	0.0633313i
$893$	1659.13	+	1242.01i	1.85793	+	1.39083i
$894$	791.075	+	1230.94i	0.884872	+	1.37689i
$895$	188.927	+	139.016i	0.211092	+	0.155325i
$896$	99.3001			0.110826
$897$	132.052	−	45.2375i	0.147215	−	0.0504320i
$898$	−461.725	+	461.725i	−0.514170	+	0.514170i
$899$	−750.974	−	650.723i	−0.835344	−	0.723829i
$900$	494.429	−	442.893i	0.549365	−	0.492104i
$901$	−24.0317	−	167.144i	−0.0266722	−	0.185509i
$902$	−305.194	+	818.258i	−0.338353	+	0.907160i
$903$	−292.586	−	390.849i	−0.324016	−	0.432834i
$904$	51.1440	+	174.181i	0.0565753	+	0.192678i
$905$	−1136.59	−	608.527i	−1.25590	−	0.672406i
$906$	141.847	−	310.601i	0.156564	−	0.342826i
$907$	250.558	+	458.862i	0.276249	+	0.505912i	0.978561	−	0.205957i	$-0.0660307\pi$
$907$	250.558	+	458.862i	0.276249	+	0.505912i	−0.702312	+	0.711869i	$0.747849\pi$
$908$	−197.059	−	14.0939i	−0.217025	−	0.0155219i
$909$	−1822.97	+	1579.61i	−2.00547	+	1.73775i
$910$	−43.6969	−	66.7779i	−0.0480186	−	0.0733823i
$911$	643.174	−	1408.35i	0.706009	−	1.54594i	−0.126522	−	0.991964i	$-0.540381\pi$
$911$	643.174	−	1408.35i	0.706009	−	1.54594i	0.832530	−	0.553980i	$-0.186891\pi$
$912$	109.417	+	502.984i	0.119975	+	0.551517i
$913$	−251.633	+	460.832i	−0.275612	+	0.504745i
$914$	−194.952	−	28.0298i	−0.213295	−	0.0306672i
$915$	−171.093	−	48.7103i	−0.186987	−	0.0532353i
$916$	−2.77664	−	19.3119i	−0.00303126	−	0.0210829i
$917$	424.713	+	92.3907i	0.463155	+	0.100753i
$918$	−29.9344	−	418.538i	−0.0326083	−	0.455924i
$919$		−	1550.41i		−	1.68706i	−0.537082	−	0.843530i	$-0.680474\pi$
$919$		−	1550.41i		−	1.68706i	0.537082	−	0.843530i	$-0.319526\pi$
$920$	−234.265	+	225.655i	−0.254635	+	0.245277i
$921$	2475.94			2.68831
$922$	−274.432	+	19.6277i	−0.297648	+	0.0212882i
$923$	−23.6524	+	108.728i	−0.0256255	+	0.117799i
$924$	1018.89	−	146.494i	1.10269	−	0.158543i
$925$	−256.240	+	1279.00i	−0.277016	+	1.38271i
$926$	−31.9738	+	222.382i	−0.0345289	+	0.240154i
$927$	−54.1983	−	29.5945i	−0.0584663	−	0.0319250i
$928$	265.465	−	57.7484i	0.286062	−	0.0622289i
$929$	451.710	+	206.289i	0.486233	+	0.222055i	0.643419	−	0.765514i	$-0.277515\pi$
$929$	451.710	+	206.289i	0.486233	+	0.222055i	−0.157187	+	0.987569i	$0.550242\pi$
$930$	−675.924	−	141.218i	−0.726800	−	0.151847i
$931$	−500.578	−	577.698i	−0.537678	−	0.620514i
$932$	23.7381	−	331.903i	0.0254701	−	0.356119i
$933$	912.555	−	498.293i	0.978087	−	0.534076i
$934$	−760.430	−	347.277i	−0.814165	−	0.371816i
$935$	−264.536	−	874.223i	−0.282926	−	0.934998i
$936$	−46.3278	+	13.6031i	−0.0494955	+	0.0145332i
$937$	−114.356	+	85.6061i	−0.122045	+	0.0913619i	−0.658557	−	0.752531i	$-0.728833\pi$
$937$	−114.356	+	85.6061i	−0.122045	+	0.0913619i	0.536511	+	0.843893i	$0.319742\pi$
$938$	1041.47	+	388.450i	1.11031	+	0.414126i
$939$	858.739	−	123.468i	0.914525	−	0.131489i
$940$	101.975	−	753.242i	0.108484	−	0.801321i
$941$	284.145	−	327.920i	0.301960	−	0.348481i	−0.584409	−	0.811459i	$-0.698674\pi$
$941$	284.145	−	327.920i	0.301960	−	0.348481i	0.886370	+	0.462978i	$0.153219\pi$
$942$	860.513	+	860.513i	0.913496	+	0.913496i
$943$	1017.73	−	520.620i	1.07925	−	0.552089i
$944$			135.027i			0.143037i
$945$	713.318	+	524.871i	0.754834	+	0.555419i
$946$	−174.215	+	111.961i	−0.184159	+	0.118352i
$947$	−308.154	+	411.646i	−0.325401	+	0.434684i	−0.933173	−	0.359427i	$-0.882972\pi$
$947$	−308.154	+	411.646i	−0.325401	+	0.434684i	0.607773	+	0.794111i	$0.292063\pi$
$948$	−723.030	−	269.676i	−0.762690	−	0.284469i
$949$	−34.7968	−	5.00303i	−0.0366668	−	0.00527189i
$950$	−321.956	+	908.638i	−0.338901	+	0.956461i
$951$	1313.90	+	844.392i	1.38160	+	0.887899i
$952$	341.983	−	127.553i	0.359226	−	0.133984i
$953$	631.313	−	344.723i	0.662448	−	0.361724i	−0.112587	−	0.993642i	$-0.535914\pi$
$953$	631.313	−	344.723i	0.662448	−	0.361724i	0.775035	+	0.631918i	$0.217732\pi$
$954$	162.962	−	141.208i	0.170820	−	0.148016i
$955$	1260.29	+	1239.69i	1.31967	+	1.29811i
$956$	−171.593	−	50.3841i	−0.179490	−	0.0527031i
$957$	2638.66	−	984.170i	2.75722	−	1.02839i
$958$	−31.7176	+	6.89974i	−0.0331081	+	0.00720223i
$959$	650.363	+	2214.93i	0.678167	+	2.30963i
$960$	141.654	−	124.801i	0.147556	−	0.130001i
$961$	−221.373	−	484.740i	−0.230357	−	0.504412i
$962$	56.8612	−	75.9576i	0.0591072	−	0.0789580i
$963$	39.2648	−	180.498i	0.0407735	−	0.187433i
$964$	−115.150	−	99.7780i	−0.119450	−	0.103504i
$965$	−647.752	+	760.107i	−0.671246	+	0.787675i
$966$	−1113.48	−	758.757i	−1.15267	−	0.785463i
$967$	421.905	+	421.905i	0.436303	+	0.436303i	0.890766	−	0.454463i	$-0.150169\pi$
$967$	421.905	+	421.905i	0.436303	+	0.436303i	−0.454463	+	0.890766i	$0.650169\pi$
$968$	−6.73285	−	94.1375i	−0.00695542	−	0.0972495i
$969$	1022.92	+	1591.69i	1.05565	+	1.64262i
$970$	−698.565	+	158.001i	−0.720170	+	0.162887i
$971$	−220.479	−	482.781i	−0.227064	−	0.497200i	0.761470	−	0.648200i	$-0.224478\pi$
$971$	−220.479	−	482.781i	−0.227064	−	0.497200i	−0.988534	+	0.151000i	$0.951751\pi$
$972$	−473.938	+	354.785i	−0.487590	+	0.365006i
$973$	378.866	−	693.841i	0.389379	−	0.713094i
$974$	−545.029	+	848.082i	−0.559578	+	0.870721i
$975$	−146.262	−	40.3415i	−0.150012	−	0.0413759i
$976$	−28.9315	−	8.49506i	−0.0296430	−	0.00870396i
$977$	40.2854	−	563.264i	0.0412338	−	0.576524i	−0.934274	−	0.356557i	$-0.883951\pi$
$977$	40.2854	−	563.264i	0.0412338	−	0.576524i	0.975507	−	0.219967i	$-0.0705949\pi$
$978$	−1457.26	−	104.225i	−1.49004	−	0.106570i
$979$	336.001	−	1144.31i	0.343208	−	1.16886i
$980$	−95.8064	+	263.475i	−0.0977616	+	0.268852i
$981$	−1306.66	−	839.739i	−1.33197	−	0.856003i
$982$	1072.74	+	585.760i	1.09240	+	0.596496i
$983$	234.451	+	313.190i	0.238506	+	0.318606i	0.903784	−	0.427989i	$-0.140778\pi$
$983$	234.451	+	313.190i	0.238506	+	0.318606i	−0.665278	+	0.746596i	$0.731687\pi$
$984$	−603.542	+	275.629i	−0.613356	+	0.280110i
$985$	−73.0032	+	115.679i	−0.0741149	+	0.117441i
$986$	840.066	−	539.878i	0.851994	−	0.547543i
$987$	3140.73	−	224.630i	3.18210	−	0.227588i
$988$	49.5825	−	49.5825i	0.0501848	−	0.0501848i
$989$	267.180	+	45.7958i	0.270152	+	0.0463052i
$990$	756.499	−	887.717i	0.764141	−	0.896684i
$991$	591.344	−	682.447i	0.596714	−	0.688645i	−0.374398	−	0.927268i	$-0.622151\pi$
$991$	591.344	−	682.447i	0.596714	−	0.688645i	0.971112	+	0.238623i	$0.0766960\pi$
$992$	−114.369	−	24.8795i	−0.115291	−	0.0250801i
$993$	1170.60	+	876.301i	1.17885	+	0.882479i
$994$	977.039	−	446.199i	0.982937	−	0.448892i
$995$	−777.718	−	49.1885i	−0.781626	−	0.0494356i
$996$	−382.752	+	112.386i	−0.384289	+	0.112837i
$997$	260.587	+	1197.90i	0.261371	+	1.20150i	0.901343	+	0.433105i	$0.142582\pi$
$997$	260.587	+	1197.90i	0.261371	+	1.20150i	−0.639973	+	0.768398i	$0.721054\pi$
$998$	209.167	+	560.798i	0.209586	+	0.561922i
$999$	−296.649	+	1010.29i	−0.296946	+	1.01131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.k.a.177.11	yes	240
5.3	odd	4	inner	230.3.k.a.223.11	yes	240
23.13	even	11	inner	230.3.k.a.197.11	yes	240
115.13	odd	44	inner	230.3.k.a.13.11	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.k.a.13.11	✓	240	115.13	odd	44	inner
230.3.k.a.177.11	yes	240	1.1	even	1	trivial
230.3.k.a.197.11	yes	240	23.13	even	11	inner
230.3.k.a.223.11	yes	240	5.3	odd	4	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.k (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41061 + 0.100889i) q^{2} +(1.00325 - 4.61186i) q^{3} +(1.97964 - 0.284630i) q^{4} +(2.43231 + 4.36851i) q^{5} +(-0.949908 + 6.60675i) q^{6} +(-7.70337 - 4.20636i) q^{7} +(-2.76379 + 0.601225i) q^{8} +(-12.0761 - 5.51495i) q^{9} +(-3.87177 - 5.91687i) q^{10} +(-8.13630 - 9.38979i) q^{11} +(0.673402 - 9.41539i) q^{12} +(-1.12858 + 0.616250i) q^{13} +(11.2908 + 5.15635i) q^{14} +(22.5872 - 6.83477i) q^{15} +(3.83797 - 1.12693i) q^{16} +(11.7702 - 8.81103i) q^{17} +(17.5910 + 6.56111i) q^{18} +(-26.9883 + 3.88033i) q^{19} +(6.05851 + 7.95578i) q^{20} +(-27.1275 + 31.3068i) q^{21} +(12.4245 + 12.4245i) q^{22} +(-1.02190 - 22.9773i) q^{23} +13.3494i q^{24} +(-13.1677 + 21.2511i) q^{25} +(1.52981 - 0.983150i) q^{26} +(-12.0937 + 16.1552i) q^{27} +(-16.4472 - 6.13448i) q^{28} +(-47.5368 - 6.83476i) q^{29} +(-31.1721 + 11.9200i) q^{30} +(17.4061 + 11.1862i) q^{31} +(-5.30019 + 1.97687i) q^{32} +(-51.4671 + 28.1032i) q^{33} +(-15.7142 + 13.6164i) q^{34} +(-0.361467 - 43.8834i) q^{35} +(-25.4760 - 7.48043i) q^{36} +(48.8870 - 18.2339i) q^{37} +(37.6784 - 8.19644i) q^{38} +(1.70981 + 5.82310i) q^{39} +(-9.34885 - 10.6113i) q^{40} +(20.6473 + 45.2113i) q^{41} +(35.1078 - 46.8986i) q^{42} +(-2.50528 + 11.5166i) q^{43} +(-18.7796 - 16.2726i) q^{44} +(-5.28060 - 66.1684i) q^{45} +(3.75966 + 32.3089i) q^{46} +(-53.7481 - 53.7481i) q^{47} +(-1.34680 - 18.8308i) q^{48} +(15.1570 + 23.5848i) q^{49} +(16.4305 - 31.3055i) q^{50} +(-28.8268 - 63.1220i) q^{51} +(-2.05878 + 1.54118i) q^{52} +(5.50423 - 10.0802i) q^{53} +(15.4296 - 24.0088i) q^{54} +(21.2294 - 58.3824i) q^{55} +(23.8194 + 6.99402i) q^{56} +(-9.18042 + 128.359i) q^{57} +(67.7454 + 4.84525i) q^{58} +(-9.51039 + 32.3894i) q^{59} +(42.7691 - 19.9594i) q^{60} +(-6.34157 - 4.07548i) q^{61} +(-25.6818 - 14.0233i) q^{62} +(69.8284 + 93.2799i) q^{63} +(7.27706 - 3.32332i) q^{64} +(-5.43715 - 3.43129i) q^{65} +(69.7648 - 44.8351i) q^{66} +(89.3232 - 6.38852i) q^{67} +(20.7928 - 20.7928i) q^{68} +(-106.993 - 18.3391i) q^{69} +(4.93723 + 61.8659i) q^{70} +(56.6677 - 65.3980i) q^{71} +(36.6914 + 7.98172i) q^{72} +(21.8862 + 16.3838i) q^{73} +(-67.1209 + 30.6531i) q^{74} +(84.7967 + 82.0479i) q^{75} +(-52.3227 + 15.3633i) q^{76} +(23.1801 + 106.557i) q^{77} +(-2.99937 - 8.04162i) q^{78} +(23.0320 - 78.4397i) q^{79} +(14.2581 + 14.0252i) q^{80} +(-15.8712 - 18.3164i) q^{81} +(-33.6866 - 61.6924i) q^{82} +(-14.7683 - 39.5955i) q^{83} +(-44.7919 + 69.6976i) q^{84} +(67.1197 + 29.9869i) q^{85} +(2.37208 - 16.4982i) q^{86} +(-79.2121 + 212.376i) q^{87} +(28.1324 + 21.0597i) q^{88} +(51.8960 + 80.7517i) q^{89} +(14.1245 + 92.8051i) q^{90} +11.2860 q^{91} +(-8.56302 - 45.1960i) q^{92} +(69.0518 - 69.0518i) q^{93} +(81.2402 + 70.3950i) q^{94} +(-82.5950 - 108.460i) q^{95} +(3.79963 + 26.4270i) q^{96} +(35.3963 - 94.9012i) q^{97} +(-23.7601 - 31.7398i) q^{98} +(46.4702 + 158.263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{2} - 4 q^{5} - 74 q^{7} + 48 q^{8} - 16 q^{10} + 8 q^{11} + 44 q^{12} + 24 q^{13} + 24 q^{15} + 96 q^{16} + 12 q^{17} + 88 q^{18} - 24 q^{20} + 24 q^{21} + 8 q^{22} - 44 q^{23} - 128 q^{25}+ \cdots - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^2 - 4 * q^5 - 74 * q^7 + 48 * q^8 - 16 * q^10 + 8 * q^11 + 44 * q^12 + 24 * q^13 + 24 * q^15 + 96 * q^16 + 12 * q^17 + 88 * q^18 - 24 * q^20 + 24 * q^21 + 8 * q^22 - 44 * q^23 - 128 * q^25 + 48 * q^26 - 60 * q^27 - 116 * q^28 + 120 * q^30 - 12 * q^31 + 96 * q^32 - 334 * q^33 - 224 * q^35 - 176 * q^36 + 188 * q^37 + 76 * q^38 - 16 * q^40 - 116 * q^41 + 24 * q^42 + 120 * q^43 + 204 * q^45 + 396 * q^46 - 144 * q^47 - 88 * q^48 + 170 * q^50 - 176 * q^51 + 48 * q^52 + 192 * q^53 - 312 * q^55 + 296 * q^56 + 88 * q^57 - 28 * q^58 - 72 * q^60 - 552 * q^61 - 12 * q^62 - 122 * q^63 - 392 * q^65 - 8 * q^66 - 72 * q^67 - 24 * q^68 + 100 * q^70 + 424 * q^71 - 176 * q^72 + 452 * q^73 + 604 * q^75 - 112 * q^76 + 356 * q^77 + 32 * q^78 + 16 * q^80 - 704 * q^81 + 148 * q^82 - 360 * q^83 + 428 * q^85 - 376 * q^86 - 462 * q^87 - 104 * q^88 - 510 * q^90 + 432 * q^91 - 192 * q^93 - 166 * q^95 - 1042 * q^97 - 88 * q^98

Introduction

L-functions

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