LMFDB - Embedded newform 230.3.k.a.223.11

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			223.11
Character	$\chi$	$=$	230.223
Dual form			230.3.k.a.197.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.100889 + 1.41061i) q^{2} +(4.61186 + 1.00325i) q^{3} +(-1.97964 + 0.284630i) q^{4} +(1.70867 + 4.69898i) q^{5} +(-0.949908 + 6.60675i) q^{6} +(-4.20636 + 7.70337i) q^{7} +(-0.601225 - 2.76379i) q^{8} +(12.0761 + 5.51495i) q^{9} +(-6.45605 + 2.88435i) q^{10} +(-8.13630 - 9.38979i) q^{11} +(-9.41539 - 0.673402i) q^{12} +(-0.616250 - 1.12858i) q^{13} +(-11.2908 - 5.15635i) q^{14} +(3.16592 + 23.3853i) q^{15} +(3.83797 - 1.12693i) q^{16} +(-8.81103 - 11.7702i) q^{17} +(-6.56111 + 17.5910i) q^{18} +(26.9883 - 3.88033i) q^{19} +(-4.72004 - 8.81597i) q^{20} +(-27.1275 + 31.3068i) q^{21} +(12.4245 - 12.4245i) q^{22} +(22.9773 - 1.02190i) q^{23} -13.3494i q^{24} +(-19.1609 + 16.0581i) q^{25} +(1.52981 - 0.983150i) q^{26} +(16.1552 + 12.0937i) q^{27} +(6.13448 - 16.4472i) q^{28} +(47.5368 + 6.83476i) q^{29} +(-32.6681 + 6.82519i) q^{30} +(17.4061 + 11.1862i) q^{31} +(1.97687 + 5.30019i) q^{32} +(-28.1032 - 51.4671i) q^{33} +(15.7142 - 13.6164i) q^{34} +(-43.3853 - 6.60305i) q^{35} +(-25.4760 - 7.48043i) q^{36} +(-18.2339 - 48.8870i) q^{37} +(8.19644 + 37.6784i) q^{38} +(-1.70981 - 5.82310i) q^{39} +(11.9597 - 7.54756i) q^{40} +(20.6473 + 45.2113i) q^{41} +(-46.8986 - 35.1078i) q^{42} +(-11.5166 - 2.50528i) 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} +(18.8308 - 1.34680i) q^{48} +(-15.1570 - 23.5848i) q^{49} +(-24.5848 - 25.4084i) q^{50} +(-28.8268 - 63.1220i) q^{51} +(1.54118 + 2.05878i) q^{52} +(10.0802 + 5.50423i) q^{53} +(-15.4296 + 24.0088i) q^{54} +(30.2202 - 54.2764i) q^{55} +(23.8194 + 6.99402i) q^{56} +(128.359 + 9.18042i) q^{57} +(-4.84525 + 67.7454i) q^{58} +(9.51039 - 32.3894i) q^{59} +(-12.9235 - 45.3934i) q^{60} +(-6.34157 - 4.07548i) q^{61} +(-14.0233 + 25.6818i) q^{62} +(-93.2799 + 69.8284i) q^{63} +(-7.27706 + 3.32332i) q^{64} +(4.25020 - 4.82412i) q^{65} +(69.7648 - 44.8351i) q^{66} +(-6.38852 - 89.3232i) 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} +(7.98172 - 36.6914i) q^{72} +(-16.3838 + 21.8862i) q^{73} +(67.1209 - 30.6531i) q^{74} +(-104.477 + 54.8344i) q^{75} +(-52.3227 + 15.3633i) q^{76} +(106.557 - 23.1801i) q^{77} +(8.04162 - 2.99937i) q^{78} +(-23.0320 + 78.4397i) q^{79} +(11.8533 + 16.1090i) q^{80} +(-15.8712 - 18.3164i) q^{81} +(-61.6924 + 33.6866i) q^{82} +(39.5955 - 14.7683i) q^{83} +(44.7919 - 69.6976i) q^{84} +(40.2526 - 61.5143i) q^{85} +(2.37208 - 16.4982i) q^{86} +(212.376 + 79.2121i) q^{87} +(-21.0597 + 28.1324i) q^{88} +(-51.8960 - 80.7517i) q^{89} +(-93.8706 - 0.773212i) q^{90} +11.2860 q^{91} +(-45.1960 + 8.56302i) q^{92} +(69.0518 + 69.0518i) q^{93} +(-81.2402 - 70.3950i) q^{94} +(64.3477 + 120.187i) q^{95} +(3.79963 + 26.4270i) q^{96} +(-94.9012 - 35.3963i) q^{97} +(31.7398 - 23.7601i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.100889	+	1.41061i	0.0504444	+	0.705305i
$2$	0.100889	+	1.41061i	0.0504444	+	0.705305i
$3$	4.61186	+	1.00325i	1.53729	+	0.334416i	0.899889	−	0.436119i	$-0.143647\pi$
$3$	4.61186	+	1.00325i	1.53729	+	0.334416i	0.637398	+	0.770535i	$0.280011\pi$
$4$	−1.97964	+	0.284630i	−0.494911	+	0.0711574i
$5$	1.70867	+	4.69898i	0.341735	+	0.939796i
$5$	1.70867	+	4.69898i	0.341735	+	0.939796i
$6$	−0.949908	+	6.60675i	−0.158318	+	1.10113i
$7$	−4.20636	+	7.70337i	−0.600908	+	1.10048i	0.383327	+	0.923613i	$0.374778\pi$
$7$	−4.20636	+	7.70337i	−0.600908	+	1.10048i	−0.984235	+	0.176868i	$0.943403\pi$
$8$	−0.601225	−	2.76379i	−0.0751532	−	0.345474i
$9$	12.0761	+	5.51495i	1.34178	+	0.612772i
$10$	−6.45605	+	2.88435i	−0.645605	+	0.288435i
$11$	−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	$0.963754\pi$
$12$	−9.41539	−	0.673402i	−0.784616	−	0.0561168i
$13$	−0.616250	−	1.12858i	−0.0474039	−	0.0868137i	0.852903	−	0.522069i	$-0.174840\pi$
$13$	−0.616250	−	1.12858i	−0.0474039	−	0.0868137i	−0.900307	+	0.435256i	$0.856658\pi$
$14$	−11.2908	−	5.15635i	−0.806487	−	0.368310i
$15$	3.16592	+	23.3853i	0.211061	+	1.55902i
$16$	3.83797	−	1.12693i	0.239873	−	0.0704331i
$17$	−8.81103	−	11.7702i	−0.518296	−	0.692362i	0.462673	−	0.886529i	$-0.346891\pi$
$17$	−8.81103	−	11.7702i	−0.518296	−	0.692362i	−0.980969	+	0.194167i	$0.937800\pi$
$18$	−6.56111	+	17.5910i	−0.364506	+	0.977278i
$19$	26.9883	−	3.88033i	1.42043	−	0.204228i	0.611090	−	0.791561i	$-0.290731\pi$
$19$	26.9883	−	3.88033i	1.42043	−	0.204228i	0.809345	+	0.587334i	$0.199822\pi$
$20$	−4.72004	−	8.81597i	−0.236002	−	0.440798i
$21$	−27.1275	+	31.3068i	−1.29179	+	1.49080i
$22$	12.4245	−	12.4245i	0.564749	−	0.564749i
$23$	22.9773	−	1.02190i	0.999012	−	0.0444305i
$23$	22.9773	−	1.02190i	0.999012	−	0.0444305i
$24$		−	13.3494i		−	0.556224i
$25$	−19.1609	+	16.0581i	−0.766434	+	0.642323i
$26$	1.52981	−	0.983150i	0.0588389	−	0.0378135i
$27$	16.1552	+	12.0937i	0.598342	+	0.447913i
$28$	6.13448	−	16.4472i	0.219088	−	0.587399i
$29$	47.5368	+	6.83476i	1.63920	+	0.235681i	0.899394	−	0.437140i	$-0.144008\pi$
$29$	47.5368	+	6.83476i	1.63920	+	0.235681i	0.739805	+	0.672821i	$0.234918\pi$
$30$	−32.6681	+	6.82519i	−1.08894	+	0.227506i
$31$	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	$0.573514\pi$
$32$	1.97687	+	5.30019i	0.0617771	+	0.165631i
$33$	−28.1032	−	51.4671i	−0.851612	−	1.55961i
$34$	15.7142	−	13.6164i	0.462182	−	0.400483i
$35$	−43.3853	−	6.60305i	−1.23958	−	0.188658i
$36$	−25.4760	−	7.48043i	−0.707667	−	0.207790i
$37$	−18.2339	−	48.8870i	−0.492808	−	1.32127i	−0.910811	−	0.412824i	$-0.864543\pi$
$37$	−18.2339	−	48.8870i	−0.492808	−	1.32127i	0.418003	−	0.908446i	$-0.362730\pi$
$38$	8.19644	+	37.6784i	0.215696	+	0.991538i
$39$	−1.70981	−	5.82310i	−0.0438414	−	0.149310i
$40$	11.9597	−	7.54756i	0.298992	−	0.188689i
$41$	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	$0.656357\pi$
$42$	−46.8986	−	35.1078i	−1.11663	−	0.835901i
$43$	−11.5166	−	2.50528i	−0.267828	−	0.0582624i	0.0766457	−	0.997058i	$-0.475579\pi$
$43$	−11.5166	−	2.50528i	−0.267828	−	0.0582624i	−0.344474	+	0.938796i	$0.611943\pi$
$44$	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	−0.155786	+	0.987791i	$0.549791\pi$
$47$	−53.7481	+	53.7481i	−1.14358	+	1.14358i	−0.987791	+	0.155786i	$0.950209\pi$
$48$	18.8308	−	1.34680i	0.392308	−	0.0280584i
$49$	−15.1570	−	23.5848i	−0.309327	−	0.481322i
$50$	−24.5848	−	25.4084i	−0.491696	−	0.508169i
$51$	−28.8268	−	63.1220i	−0.565232	−	1.23769i
$52$	1.54118	+	2.05878i	0.0296381	+	0.0395919i
$53$	10.0802	+	5.50423i	0.190193	+	0.103853i	0.571524	−	0.820585i	$-0.306352\pi$
$53$	10.0802	+	5.50423i	0.190193	+	0.103853i	−0.381331	+	0.924439i	$0.624534\pi$
$54$	−15.4296	+	24.0088i	−0.285732	+	0.444608i
$55$	30.2202	−	54.2764i	0.549458	−	0.986844i
$56$	23.8194	+	6.99402i	0.425347	+	0.124893i
$57$	128.359	+	9.18042i	2.25191	+	0.161060i
$58$	−4.84525	+	67.7454i	−0.0835388	+	1.16802i
$59$	9.51039	−	32.3894i	0.161193	−	0.548973i	−0.838797	−	0.544445i	$-0.816740\pi$
$59$	9.51039	−	32.3894i	0.161193	−	0.548973i	0.999990	−	0.00452840i	$-0.00144144\pi$
$60$	−12.9235	−	45.3934i	−0.215392	−	0.756556i
$61$	−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	$0.701499\pi$
$62$	−14.0233	+	25.6818i	−0.226182	+	0.414222i
$63$	−93.2799	+	69.8284i	−1.48063	+	1.10839i
$64$	−7.27706	+	3.32332i	−0.113704	+	0.0519269i
$65$	4.25020	−	4.82412i	0.0653876	−	0.0742172i
$66$	69.7648	−	44.8351i	1.05704	−	0.679320i
$67$	−6.38852	−	89.3232i	−0.0953511	−	1.33318i	−0.789677	−	0.613522i	$-0.789752\pi$
$67$	−6.38852	−	89.3232i	−0.0953511	−	1.33318i	0.694326	−	0.719660i	$-0.255702\pi$
$68$	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	$0.0186856\pi$
$72$	7.98172	−	36.6914i	0.110857	−	0.509603i
$73$	−16.3838	+	21.8862i	−0.224436	+	0.299811i	−0.898599	−	0.438772i	$-0.855414\pi$
$73$	−16.3838	+	21.8862i	−0.224436	+	0.299811i	0.674163	+	0.738583i	$0.264505\pi$
$74$	67.1209	−	30.6531i	0.907039	−	0.414231i
$75$	−104.477	+	54.8344i	−1.39303	+	0.731126i
$76$	−52.3227	+	15.3633i	−0.688456	+	0.202149i
$77$	106.557	−	23.1801i	1.38386	−	0.301040i
$78$	8.04162	−	2.99937i	0.103098	−	0.0384534i
$79$	−23.0320	+	78.4397i	−0.291544	+	0.992907i	0.675301	+	0.737542i	$0.264014\pi$
$79$	−23.0320	+	78.4397i	−0.291544	+	0.992907i	−0.966845	+	0.255365i	$0.917804\pi$
$80$	11.8533	+	16.1090i	0.148166	+	0.201363i
$81$	−15.8712	−	18.3164i	−0.195941	−	0.226128i
$82$	−61.6924	+	33.6866i	−0.752346	+	0.410812i
$83$	39.5955	−	14.7683i	0.477054	−	0.177932i	−0.0994233	−	0.995045i	$-0.531700\pi$
$83$	39.5955	−	14.7683i	0.477054	−	0.177932i	0.576477	+	0.817113i	$0.304427\pi$
$84$	44.7919	−	69.6976i	0.533237	−	0.829734i
$85$	40.2526	−	61.5143i	0.473560	−	0.723697i
$86$	2.37208	−	16.4982i	0.0275824	−	0.191839i
$87$	212.376	+	79.2121i	2.44110	+	0.910484i
$88$	−21.0597	+	28.1324i	−0.239314	+	0.319686i
$89$	−51.8960	−	80.7517i	−0.583101	−	0.907323i	0.416898	−	0.908953i	$-0.363117\pi$
$89$	−51.8960	−	80.7517i	−0.583101	−	0.907323i	−0.999999	+	0.00163076i	$0.999481\pi$
$90$	−93.8706	−	0.773212i	−1.04301	−	0.00859125i
$91$	11.2860			0.124022
$92$	−45.1960	+	8.56302i	−0.491260	+	0.0930763i
$93$	69.0518	+	69.0518i	0.742493	+	0.742493i
$94$	−81.2402	−	70.3950i	−0.864257	−	0.748883i
$95$	64.3477	+	120.187i	0.677345	+	1.26513i
$96$	3.79963	+	26.4270i	0.0395795	+	0.275281i
$97$	−94.9012	−	35.3963i	−0.978363	−	0.364910i	−0.191129	−	0.981565i	$-0.561215\pi$
$97$	−94.9012	−	35.3963i	−0.978363	−	0.364910i	−0.787234	+	0.616654i	$0.788488\pi$
$98$	31.7398	−	23.7601i	0.323875	−	0.242450i
$99$	−46.4702	−	158.263i	−0.469396	−	1.59862i
$100$	33.3611	−	37.2430i	0.333611	−	0.372430i
$101$	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	$-0.219690\pi$
$102$	86.1322	−	47.0317i	0.844433	−	0.461096i
$103$	−0.331832	+	4.63962i	−0.00322167	+	0.0450448i	−0.998809	−	0.0487986i	$-0.984461\pi$
$103$	−0.331832	+	4.63962i	−0.00322167	+	0.0450448i	0.995587	+	0.0938434i	$0.0299153\pi$
$104$	−2.74865	+	2.38171i	−0.0264293	+	0.0229011i
$105$	−193.462	−	73.9785i	−1.84250	−	0.704558i
$106$	−6.74734	+	14.7746i	−0.0636541	+	0.139383i
$107$	13.5960	−	2.95763i	0.127066	−	0.0276414i	−0.148583	−	0.988900i	$-0.547471\pi$
$107$	13.5960	−	2.95763i	0.127066	−	0.0276414i	0.275648	+	0.961259i	$0.411107\pi$
$108$	−35.4238	−	19.3429i	−0.327998	−	0.179101i
$109$	−115.806	−	16.6505i	−1.06244	−	0.152756i	−0.411140	−	0.911572i	$-0.634869\pi$
$109$	−115.806	−	16.6505i	−1.06244	−	0.152756i	−0.651305	+	0.758816i	$0.725778\pi$
$110$	79.6118	+	37.1530i	0.723744	+	0.337755i
$111$	−35.0464	−	243.753i	−0.315733	−	2.19597i
$112$	−7.46272	+	34.3056i	−0.0666314	+	0.306300i
$113$	64.0184	−	4.57869i	0.566535	−	0.0405194i	0.214865	−	0.976644i	$-0.431069\pi$
$113$	64.0184	−	4.57869i	0.566535	−	0.0405194i	0.351669	+	0.936124i	$0.385614\pi$
$114$			181.991i			1.59641i
$115$	44.0626	+	106.224i	0.383153	+	0.923685i
$116$	−96.0512			−0.828028
$117$	−1.21782	−	17.0274i	−0.0104087	−	0.145533i
$118$	46.6483	+	10.1477i	0.395325	+	0.0859977i
$119$	127.732	−	18.3651i	1.07338	−	0.154329i
$120$	62.7285	−	22.8098i	0.522738	−	0.190081i
$121$	−4.74871	+	33.0280i	−0.0392456	+	0.272959i
$122$	5.10912	−	9.35665i	0.0418780	−	0.0766938i
$123$	49.8643	+	229.222i	0.405401	+	1.86360i
$124$	−37.6417	−	17.1904i	−0.303562	−	0.138632i
$125$	−108.196	−	62.5985i	−0.865570	−	0.500788i
$126$	−107.912	−	124.537i	−0.856441	−	0.988386i
$127$	67.5724	+	4.83287i	0.532066	+	0.0380541i	0.334788	−	0.942293i	$-0.391335\pi$
$127$	67.5724	+	4.83287i	0.532066	+	0.0380541i	0.197278	+	0.980348i	$0.436790\pi$
$128$	−5.42208	−	9.92980i	−0.0423600	−	0.0775766i
$129$	−50.5995	−	23.1080i	−0.392245	−	0.179132i
$130$	7.23375	+	5.50867i	0.0556442	+	0.0423744i
$131$	−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	$0.469619\pi$
$132$	70.2834	+	93.8876i	0.532450	+	0.711270i
$133$	−83.6307	+	224.222i	−0.628802	+	1.68588i
$134$	125.356	−	18.0234i	0.935491	−	0.134503i
$135$	−29.2238	+	96.5773i	−0.216473	+	0.715387i
$136$	−27.2328	+	31.4283i	−0.200241	+	0.231091i
$137$	−185.977	+	185.977i	−1.35749	+	1.35749i	−0.480499	+	0.876995i	$0.659545\pi$
$137$	−185.977	+	185.977i	−1.35749	+	1.35749i	−0.876995	+	0.480499i	$0.840455\pi$
$138$	−15.0749	+	152.776i	−0.109238	+	1.10707i
$139$		−	90.0698i		−	0.647984i	−0.946060	−	0.323992i	$-0.894975\pi$
$139$		−	90.0698i		−	0.647984i	0.946060	−	0.323992i	$-0.105025\pi$
$140$	87.7668	+	0.722935i	0.626906	+	0.00516382i
$141$	−301.801	+	193.956i	−2.14044	+	1.37557i
$142$	97.9682	+	73.3381i	0.689917	+	0.516465i
$143$	−5.58312	+	14.9689i	−0.0390428	+	0.104678i
$144$	52.5625	+	7.55735i	0.365018	+	0.0524816i
$145$	49.1085	+	235.053i	0.338679	+	1.62105i
$146$	−32.5259	−	20.9031i	−0.222780	−	0.143172i
$147$	−46.2407	−	123.976i	−0.314562	−	0.843374i
$148$	50.0113	+	91.5888i	0.337914	+	0.618843i
$149$	−165.675	+	143.558i	−1.11191	+	0.963475i	−0.999544	−	0.0301919i	$-0.990388\pi$
$149$	−165.675	+	143.558i	−1.11191	+	0.963475i	−0.112365	+	0.993667i	$0.535843\pi$
$150$	−87.8906	−	141.845i	−0.585937	−	0.945632i
$151$	−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	$0.645090\pi$
$152$	−26.9504	−	72.2569i	−0.177305	−	0.475374i
$153$	−41.4907	−	190.729i	−0.271181	−	1.24660i
$154$	43.4485	+	147.972i	0.282133	+	0.960858i
$155$	−22.8225	+	100.904i	−0.147242	+	0.650996i
$156$	5.04225	+	11.0410i	0.0323221	+	0.0707755i
$157$	−145.957	−	109.262i	−0.929663	−	0.695937i	0.0230742	−	0.999734i	$-0.492655\pi$
$157$	−145.957	−	109.262i	−0.929663	−	0.695937i	−0.952737	+	0.303797i	$0.901746\pi$
$158$	−112.971	−	24.5754i	−0.715009	−	0.155541i
$159$	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
$163$	−218.326	+	15.6150i	−1.33942	+	0.0957975i	−0.722580	−	0.691288i	$-0.757044\pi$
$163$	−218.326	+	15.6150i	−1.33942	+	0.0957975i	−0.616844	+	0.787085i	$0.711589\pi$
$164$	−53.7427	−	83.6253i	−0.327700	−	0.509910i
$165$	193.824	−	219.997i	1.17469	−	1.33332i
$166$	24.8271	+	54.3638i	0.149561	+	0.327493i
$167$	99.0752	+	132.349i	0.593264	+	0.792508i	0.992225	−	0.124460i	$-0.0397198\pi$
$167$	99.0752	+	132.349i	0.593264	+	0.792508i	−0.398960	+	0.916968i	$0.630629\pi$
$168$	102.835	+	56.1523i	0.612114	+	0.334240i
$169$	90.4744	−	140.781i	0.535351	−	0.833023i
$170$	90.8337	+	50.5746i	0.534316	+	0.297498i
$171$	347.311	+	101.980i	2.03106	+	0.596373i
$172$	23.5118	+	1.68160i	0.136697	+	0.00977674i
$173$	20.8692	−	291.790i	0.120631	−	1.68665i	−0.472336	−	0.881419i	$-0.656589\pi$
$173$	20.8692	−	291.790i	0.120631	−	1.68665i	0.592967	−	0.805227i	$-0.297956\pi$
$174$	−90.3111	+	307.571i	−0.519029	+	1.76765i
$175$	−43.1037	−	215.149i	−0.246307	−	1.22942i
$176$	−41.8085	−	26.8687i	−0.237549	−	0.152663i
$177$	76.3552	−	139.834i	0.431386	−	0.790024i
$178$	108.673	−	81.3519i	0.610525	−	0.457033i
$179$	−42.6728	+	19.4880i	−0.238395	+	0.108872i	−0.531031	−	0.847353i	$-0.678195\pi$
$179$	−42.6728	+	19.4880i	−0.238395	+	0.108872i	0.292635	+	0.956224i	$0.405468\pi$
$180$	−8.37980	−	132.493i	−0.0465544	−	0.736071i
$181$	−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	$0.570523\pi$
$182$	1.13863	+	15.9202i	0.00625623	+	0.0874735i
$183$	−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
$187$	−38.8302	+	178.499i	−0.207648	+	0.954542i
$188$	91.1037	−	121.700i	0.484594	−	0.647342i
$189$	−161.117	+	73.5794i	−0.852468	+	0.389309i
$190$	−163.045	+	102.895i	−0.858133	+	0.541553i
$191$	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	$0.0326890\pi$
$192$	−36.8949	+	8.02599i	−0.192161	+	0.0418020i
$193$	−187.141	+	69.8000i	−0.969642	+	0.361658i	−0.783863	−	0.620934i	$-0.786754\pi$
$193$	−187.141	+	69.8000i	−0.969642	+	0.361658i	−0.185779	+	0.982592i	$0.559481\pi$
$194$	40.3559	−	137.440i	0.208020	−	0.708452i
$195$	24.4411	−	17.9842i	0.125339	−	0.0922265i
$196$	36.7184	+	42.3753i	0.187339	+	0.216201i
$197$	24.0113	−	13.1112i	0.121885	−	0.0665542i	−0.417150	−	0.908838i	$-0.636971\pi$
$197$	24.0113	−	13.1112i	0.121885	−	0.0665542i	0.539035	+	0.842284i	$0.318789\pi$
$198$	218.559	−	81.5183i	1.10383	−	0.411709i
$199$	84.2613	−	131.113i	0.423424	−	0.658860i	−0.562358	−	0.826894i	$-0.690106\pi$
$199$	84.2613	−	131.113i	0.423424	−	0.658860i	0.985781	+	0.168034i	$0.0537419\pi$
$200$	55.9011	+	43.3021i	0.279505	+	0.216510i
$201$	60.1504	−	418.356i	0.299256	−	2.08137i
$202$	240.754	+	89.7966i	1.19185	+	0.444538i
$203$	−252.607	+	337.444i	−1.24437	+	1.66228i
$204$	75.0332	+	116.754i	0.367810	+	0.572324i
$205$	−177.167	+	174.273i	−0.864231	+	0.850110i
$206$	−6.57817			−0.0319329
$207$	283.111	+	114.378i	1.36768	+	0.552551i
$208$	−3.63698	−	3.63698i	−0.0174855	−	0.0174855i
$209$	−256.020	−	221.843i	−1.22498	−	1.06145i
$210$	84.8367	−	280.364i	0.403984	−	1.33506i
$211$	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	$0.787602\pi$
$212$	−21.5219	−	8.02727i	−0.101519	−	0.0378645i
$213$	326.954	−	244.755i	1.53499	−	1.14908i
$214$	5.54376	+	18.8803i	0.0259054	+	0.0882257i
$215$	−7.90585	−	58.3970i	−0.0367714	−	0.271614i
$216$	23.7114	−	51.9207i	0.109775	−	0.240373i
$217$	−159.388	+	87.0322i	−0.734505	+	0.401070i
$218$	11.8037	−	165.038i	0.0541455	−	0.757053i
$219$	−97.5171	+	84.4991i	−0.445284	+	0.385841i
$220$	−44.3765	+	116.050i	−0.201711	+	0.527498i
$221$	−7.85374	+	17.1973i	−0.0355373	+	0.0778158i
$222$	340.305	−	74.0288i	1.53290	−	0.333463i
$223$	−26.4590	−	14.4477i	−0.118650	−	0.0647878i	0.418828	−	0.908066i	$-0.362441\pi$
$223$	−26.4590	−	14.4477i	−0.118650	−	0.0647878i	−0.537478	+	0.843278i	$0.680623\pi$
$224$	−49.1447	−	7.06594i	−0.219396	−	0.0315444i
$225$	−319.947	+	88.2469i	−1.42199	+	0.392208i
$226$	12.9175	+	89.8431i	0.0571570	+	0.397536i
$227$	−20.9974	+	96.5236i	−0.0924997	+	0.425214i	0.907487	+	0.420080i	$0.137998\pi$
$227$	−20.9974	+	96.5236i	−0.0924997	+	0.425214i	−0.999987	+	0.00513426i	$0.998366\pi$
$228$	−256.718	+	18.3608i	−1.12596	+	0.0805300i
$229$			9.75527i			0.0425994i	0.999773	+	0.0212997i	$0.00678042\pi$
$229$			9.75527i			0.0425994i	−0.999773	+	0.0212997i	$0.993220\pi$
$230$	−145.395	+	72.8720i	−0.632152	+	0.316835i
$231$	514.682			2.22806
$232$	−9.69050	−	135.491i	−0.0417694	−	0.584012i
$233$	162.573	+	35.3656i	0.697738	+	0.151784i	0.547425	−	0.836855i	$-0.315608\pi$
$233$	162.573	+	35.3656i	0.697738	+	0.151784i	0.150313	+	0.988638i	$0.451972\pi$
$234$	23.8961	−	3.43574i	0.102120	−	0.0146827i
$235$	−344.399	−	160.723i	−1.46553	−	0.683929i
$236$	−9.60819	+	66.8264i	−0.0407127	+	0.283163i
$237$	−184.915	+	338.646i	−0.780231	+	1.42889i
$238$	38.7928	+	178.328i	0.162995	+	0.749275i
$239$	81.3378	+	37.1457i	0.340326	+	0.155421i	0.578244	−	0.815864i	$-0.303738\pi$
$239$	81.3378	+	37.1457i	0.340326	+	0.155421i	−0.237919	+	0.971285i	$0.576465\pi$
$240$	38.5043	+	86.1842i	0.160435	+	0.359101i
$241$	−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	$0.823250\pi$
$242$	−47.0688	−	3.36642i	−0.194499	−	0.0139108i
$243$	−141.863	−	259.803i	−0.583798	−	1.06915i
$244$	13.7140	+	6.26299i	0.0562051	+	0.0256680i
$245$	84.9261	−	111.521i	0.346637	−	0.455189i
$246$	−318.313	+	93.4650i	−1.29395	+	0.379939i
$247$	−21.0108	−	28.0671i	−0.0850638	−	0.113632i
$248$	20.4513	−	54.8322i	0.0824651	−	0.221097i
$249$	197.425	−	28.3854i	0.792872	−	0.113998i
$250$	77.3864	−	158.938i	0.309545	−	0.635753i
$251$	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
$253$	−196.546	−	207.437i	−0.776860	−	0.819911i
$254$			95.8059i			0.377188i
$255$	247.353	−	243.312i	0.970013	−	0.954164i
$256$	13.4601	−	8.65025i	0.0525783	−	0.0337901i
$257$	−191.445	−	143.314i	−0.744924	−	0.557643i	0.158002	−	0.987439i	$-0.449495\pi$
$257$	−191.445	−	143.314i	−0.744924	−	0.557643i	−0.902926	+	0.429796i	$0.858586\pi$
$258$	27.4915	−	73.7076i	0.106556	−	0.285688i
$259$	453.293	+	65.1736i	1.75016	+	0.251636i
$260$	−7.04078	+	10.7598i	−0.0270799	+	0.0413837i
$261$	536.363	+	344.700i	2.05503	+	1.32069i
$262$	−24.4742	−	65.6179i	−0.0934130	−	0.250450i
$263$	136.532	+	250.040i	0.519134	+	0.950722i	0.997369	+	0.0724907i	$0.0230948\pi$
$263$	136.532	+	250.040i	0.519134	+	0.950722i	−0.478235	+	0.878232i	$0.658723\pi$
$264$	−125.348	+	108.615i	−0.474803	+	0.411419i
$265$	−8.64041	+	56.7718i	−0.0326053	+	0.214233i
$266$	−324.728	−	95.3487i	−1.22078	−	0.358454i
$267$	−158.323	−	424.480i	−0.592970	−	1.58981i
$268$	38.0710	+	175.010i	0.142056	+	0.653022i
$269$	15.7774	+	53.7329i	0.0586520	+	0.199750i	0.983607	−	0.180327i	$-0.0577156\pi$
$269$	15.7774	+	53.7329i	0.0586520	+	0.199750i	−0.924955	+	0.380077i	$0.875897\pi$
$270$	−139.181	−	31.4799i	−0.515486	−	0.116592i
$271$	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	$0.802865\pi$
$272$	−47.0806	−	35.2441i	−0.173091	−	0.129574i
$273$	52.0495	+	11.3227i	0.190658	+	0.0414750i
$274$	−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	−0.997793	−	0.0663958i	$-0.978850\pi$
$277$	−257.997	+	257.997i	−0.931398	+	0.931398i	0.0663958	+	0.997793i	$0.478850\pi$
$278$	127.053	−	9.08704i	0.457026	−	0.0326872i
$279$	148.505	+	231.079i	0.532277	+	0.828240i
$280$	7.83491	+	123.878i	0.0279818	+	0.442420i
$281$	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	$0.519721\pi$
$282$	−304.045	−	406.156i	−1.07817	−	1.44027i
$283$	209.494	+	114.392i	0.740260	+	0.404213i	0.804679	−	0.593710i	$-0.202337\pi$
$283$	209.494	+	114.392i	0.740260	+	0.404213i	−0.0644186	+	0.997923i	$0.520519\pi$
$284$	−93.5675	+	145.594i	−0.329463	+	0.512655i
$285$	176.185	+	618.843i	0.618193	+	2.17138i
$286$	−21.6786	−	6.36540i	−0.0757992	−	0.0222567i
$287$	−435.129	−	31.1210i	−1.51613	−	0.108436i
$288$	−5.35750	+	74.9077i	−0.0186024	+	0.260096i
$289$	20.5183	−	69.8790i	0.0709976	−	0.241796i
$290$	−326.613	+	92.9871i	−1.12625	+	0.320645i
$291$	−402.160	−	258.452i	−1.38199	−	0.888152i
$292$	26.2046	−	47.9902i	0.0897419	−	0.164350i
$293$	223.728	−	167.481i	0.763577	−	0.571606i	−0.144947	−	0.989439i	$-0.546301\pi$
$293$	223.728	−	167.481i	0.763577	−	0.571606i	0.908524	+	0.417833i	$0.137210\pi$
$294$	170.217	−	77.7353i	0.578968	−	0.264406i
$295$	168.447	−	10.6538i	0.571008	−	0.0361147i
$296$	−124.151	+	79.7867i	−0.419428	+	0.269550i
$297$	−17.8869	−	250.092i	−0.0602253	−	0.842060i
$298$	−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
$302$	15.3785	−	70.6936i	0.0509220	−	0.234085i
$303$	513.910	−	686.503i	1.69607	−	2.26569i
$304$	99.2073	−	45.3065i	0.326340	−	0.149034i
$305$	8.31492	−	36.7626i	0.0272620	−	0.120533i
$306$	264.859	−	77.7696i	0.865552	−	0.254149i
$307$	512.605	−	111.510i	1.66972	−	0.363226i	0.724405	−	0.689374i	$-0.242114\pi$
$307$	512.605	−	111.510i	1.66972	−	0.363226i	0.945319	+	0.326148i	$0.105751\pi$
$308$	−204.347	+	76.2177i	−0.663466	+	0.247460i
$309$	−6.18505	+	21.0644i	−0.0200164	+	0.0681695i
$310$	−144.639	−	22.0135i	−0.466579	−	0.0710112i
$311$	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	$0.657489\pi$
$312$	−15.0658	+	8.22656i	−0.0482879	+	0.0263672i
$313$	−172.228	+	64.2378i	−0.550250	+	0.205233i	−0.609184	−	0.793029i	$-0.708503\pi$
$313$	−172.228	+	64.2378i	−0.550250	+	0.205233i	0.0589334	+	0.998262i	$0.481230\pi$
$314$	139.401	−	216.912i	0.443951	−	0.690802i
$315$	−487.508	−	319.006i	−1.54764	−	1.01272i
$316$	23.2688	−	161.838i	0.0736355	−	0.512146i
$317$	310.053	+	115.644i	0.978084	+	0.364806i	0.787126	−	0.616792i	$-0.211568\pi$
$317$	310.053	+	115.644i	0.978084	+	0.364806i	0.190958	+	0.981598i	$0.438841\pi$
$318$	−45.9404	+	61.3691i	−0.144467	+	0.192985i
$319$	−322.597	−	501.970i	−1.01127	−	1.57357i
$320$	−28.0503	−	28.5163i	−0.0876573	−	0.0891134i
$321$	65.6702			0.204580
$322$	−264.702	−	106.941i	−0.822055	−	0.332114i
$323$	−283.466	−	283.466i	−0.877605	−	0.877605i
$324$	36.6328	+	31.7425i	0.113064	+	0.0979706i
$325$	29.9307	+	11.7287i	0.0920943	+	0.0360884i
$326$	−44.0533	−	306.398i	−0.135133	−	0.939870i
$327$	−517.379	−	192.972i	−1.58220	−	0.590129i
$328$	112.541	−	84.2469i	0.343112	−	0.256850i
$329$	−187.958	−	640.125i	−0.571300	−	1.94567i
$330$	329.885	+	251.215i	0.999651	+	0.761257i
$331$	−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	$0.981336\pi$
$332$	−74.1814	+	40.5061i	−0.223438	+	0.122006i
$333$	49.4156	−	690.921i	0.148395	−	2.07484i
$334$	−176.697	+	153.109i	−0.529033	+	0.458410i
$335$	408.812	−	182.644i	1.22034	−	0.545206i
$336$	−68.8340	+	150.726i	−0.204863	+	0.448588i
$337$	−435.979	+	94.8415i	−1.29371	+	0.281429i	−0.806176	−	0.591676i	$-0.798466\pi$
$337$	−435.979	+	94.8415i	−1.29371	+	0.281429i	−0.487532	+	0.873105i	$0.662103\pi$
$338$	207.715	+	113.421i	0.614541	+	0.335565i
$339$	299.838	+	43.1101i	0.884477	+	0.127169i
$340$	−62.1770	+	133.233i	−0.182873	+	0.391863i
$341$	−36.5849	−	254.454i	−0.107287	−	0.746199i
$342$	−108.814	+	500.210i	−0.318170	+	1.46260i
$343$	−183.538	+	13.1269i	−0.535096	+	0.0382708i
$344$			33.3357i			0.0969061i
$345$	96.6417	+	534.095i	0.280121	+	1.54810i
$346$	413.707			1.19568
$347$	33.9537	+	474.735i	0.0978494	+	1.36811i	0.774857	+	0.632137i	$0.217822\pi$
$347$	33.9537	+	474.735i	0.0978494	+	1.36811i	−0.677008	+	0.735976i	$0.736724\pi$
$348$	−442.975	−	96.3633i	−1.27292	−	0.276906i
$349$	−470.760	+	67.6850i	−1.34888	+	0.193940i	−0.778606	−	0.627513i	$-0.784073\pi$
$349$	−470.760	+	67.6850i	−1.34888	+	0.193940i	−0.570276	+	0.821453i	$0.693164\pi$
$350$	299.143	−	82.5087i	0.854694	−	0.235739i
$351$	3.69297	−	25.6852i	0.0105213	−	0.0731771i
$352$	33.6833	−	61.6863i	0.0956911	−	0.175245i
$353$	62.5033	+	287.323i	0.177063	+	0.813947i	0.976895	+	0.213722i	$0.0685586\pi$
$353$	62.5033	+	287.323i	0.177063	+	0.813947i	−0.799831	+	0.600225i	$0.795078\pi$
$354$	204.955	+	93.5998i	0.578969	+	0.264406i
$355$	404.131	+	154.536i	1.13840	+	0.435314i
$356$	125.720	+	145.088i	0.353146	+	0.407552i
$357$	607.508	+	43.4498i	1.70170	+	0.121708i
$358$	−31.7952	−	58.2285i	−0.0888134	−	0.162650i
$359$	631.346	+	288.326i	1.75862	+	0.803136i	0.985672	+	0.168671i	$0.0539474\pi$
$359$	631.346	+	288.326i	1.75862	+	0.803136i	0.772951	+	0.634466i	$0.218780\pi$
$360$	186.050	−	25.1877i	0.516807	−	0.0699658i
$361$	366.932	−	107.741i	1.01643	−	0.298451i
$362$	−218.528	−	291.920i	−0.603669	−	0.806408i
$363$	−55.0357	+	147.556i	−0.151614	+	0.406492i
$364$	−22.3423	+	3.21234i	−0.0613799	+	0.00882510i
$365$	−130.837	−	39.5908i	−0.358459	−	0.108468i
$366$	32.9496	−	38.0258i	0.0900262	−	0.103896i
$367$	−143.745	+	143.745i	−0.391676	+	0.391676i	−0.875284	−	0.483609i	$-0.839326\pi$
$367$	−143.745	+	143.745i	−0.391676	+	0.391676i	0.483609	+	0.875284i	$0.339326\pi$
$368$	87.0346	−	29.8158i	0.236507	−	0.0810213i
$369$			659.842i			1.78819i
$370$	258.726	+	263.024i	0.699259	+	0.710875i
$371$	−84.8021	+	54.4990i	−0.228577	+	0.146898i
$372$	−156.352	−	117.044i	−0.420302	−	0.314634i
$373$	−7.75678	+	20.7967i	−0.0207957	+	0.0557553i	−0.946933	−	0.321432i	$-0.895836\pi$
$373$	−7.75678	+	20.7967i	−0.0207957	+	0.0557553i	0.926137	+	0.377187i	$0.123109\pi$
$374$	−255.711	−	36.7656i	−0.683718	−	0.0983038i
$375$	−436.184	−	397.243i	−1.16316	−	1.05932i
$376$	180.863	+	116.234i	0.481019	+	0.309132i
$377$	−21.5810	−	57.8609i	−0.0572440	−	0.153477i
$378$	−120.047	−	219.849i	−0.317584	−	0.581612i
$379$	77.0720	−	66.7833i	0.203356	−	0.176209i	−0.547229	−	0.836983i	$-0.684317\pi$
$379$	77.0720	−	66.7833i	0.203356	−	0.176209i	0.750585	+	0.660774i	$0.229772\pi$
$380$	−161.594	−	219.612i	−0.425248	−	0.577927i
$381$	306.786	+	90.0804i	0.805212	+	0.236432i
$382$	174.737	+	468.487i	0.457425	+	1.22641i
$383$	99.4176	+	457.015i	0.259576	+	1.19325i	0.903644	+	0.428284i	$0.140882\pi$
$383$	99.4176	+	457.015i	0.259576	+	1.19325i	−0.644068	+	0.764968i	$0.722755\pi$
$384$	−15.0438	−	51.2346i	−0.0391766	−	0.133423i
$385$	290.995	+	461.103i	0.755830	+	1.19767i
$386$	−117.341	−	256.941i	−0.303992	−	0.665650i
$387$	−125.259	−	93.7674i	−0.323666	−	0.242293i
$388$	197.945	+	43.0604i	0.510168	+	0.110980i
$389$	−236.679	−	205.084i	−0.608430	−	0.527208i	0.295248	−	0.955421i	$-0.404598\pi$
$389$	−236.679	−	205.084i	−0.608430	−	0.527208i	−0.903678	+	0.428213i	$0.859143\pi$
$390$	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
$393$	−233.131	+	16.6738i	−0.593208	+	0.0424270i
$394$	20.9172	+	32.5478i	0.0530894	+	0.0826087i
$395$	−407.941	+	25.8011i	−1.03276	+	0.0653192i
$396$	137.041	+	300.077i	0.346062	+	0.757771i
$397$	50.6593	+	67.6729i	0.127605	+	0.170461i	0.859794	−	0.510641i	$-0.170592\pi$
$397$	50.6593	+	67.6729i	0.127605	+	0.170461i	−0.732189	+	0.681102i	$0.761501\pi$
$398$	193.451	+	105.632i	0.486057	+	0.265407i
$399$	−610.644	+	950.180i	−1.53044	+	2.38140i
$400$	−55.4425	+	83.2233i	−0.138606	+	0.208058i
$401$	−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	$0.713335\pi$
$402$	596.205	+	42.6414i	1.48310	+	0.106073i
$403$	1.89801	−	26.5376i	0.00470970	−	0.0658502i
$404$	−102.379	+	348.670i	−0.253413	+	0.863044i
$405$	58.9496	−	105.875i	0.145555	−	0.261421i
$406$	−501.487	−	322.286i	−1.23519	−	0.793808i
$407$	−310.682	+	568.972i	−0.763347	+	1.39796i
$408$	−157.124	+	117.622i	−0.385109	+	0.288289i
$409$	−168.344	+	76.8800i	−0.411598	+	0.187971i	−0.610443	−	0.792060i	$-0.709008\pi$
$409$	−168.344	+	76.8800i	−0.411598	+	0.187971i	0.198844	+	0.980031i	$0.436281\pi$
$410$	−263.705	−	232.332i	−0.643183	−	0.566663i
$411$	−1044.28	+	671.118i	−2.54083	+	1.63289i
$412$	−0.663664	−	9.27924i	−0.00161084	−	0.0225224i
$413$	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
$417$	90.3624	−	415.389i	0.216696	−	0.996137i
$418$	287.104	−	383.526i	0.686852	−	0.917526i
$419$	283.975	−	129.687i	0.677744	−	0.309515i	−0.0466403	−	0.998912i	$-0.514851\pi$
$419$	283.975	−	129.687i	0.677744	−	0.309515i	0.724384	+	0.689397i	$0.242124\pi$
$420$	404.043	+	91.3860i	0.962007	+	0.217586i
$421$	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	$0.294531\pi$
$422$	−292.018	+	63.5247i	−0.691986	+	0.150532i
$423$	−945.483	+	352.647i	−2.23518	+	0.833681i
$424$	9.15202	−	31.1689i	0.0215850	−	0.0735116i
$425$	357.833	+	84.0383i	0.841960	+	0.197737i
$426$	378.239	+	436.511i	0.887886	+	1.02467i
$427$	58.0698	−	31.7085i	0.135995	−	0.0742588i
$428$	−26.0734	+	9.72489i	−0.0609193	+	0.0227217i
$429$	−40.7661	+	63.4333i	−0.0950259	+	0.147863i
$430$	81.5778	−	17.0437i	0.189716	−	0.0396365i
$431$	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	$-0.0242759\pi$
$432$	75.6320	+	28.2093i	0.175074	+	0.0652993i
$433$	334.488	−	446.824i	0.772491	−	1.03193i	−0.225840	−	0.974164i	$-0.572513\pi$
$433$	334.488	−	446.824i	0.772491	−	1.03193i	0.998330	−	0.0577622i	$-0.0183965\pi$
$434$	−138.849	−	216.053i	−0.319929	−	0.497819i
$435$	−9.33498	+	1133.30i	−0.0214597	+	2.60528i
$436$	233.995			0.536685
$437$	616.152	−	116.739i	1.40996	−	0.267137i
$438$	−129.034	−	129.034i	−0.294597	−	0.294597i
$439$	317.502	+	275.117i	0.723238	+	0.626689i	0.936647	−	0.350273i	$-0.113911\pi$
$439$	317.502	+	275.117i	0.723238	+	0.626689i	−0.213409	+	0.976963i	$0.568457\pi$
$440$	−168.178	−	50.8898i	−0.382222	−	0.115659i
$441$	−52.9681	−	368.401i	−0.120109	−	0.835377i
$442$	−25.0510	−	9.34356i	−0.0566766	−	0.0211393i
$443$	530.071	−	396.806i	1.19655	−	0.895724i	0.200086	−	0.979778i	$-0.435878\pi$
$443$	530.071	−	396.806i	1.19655	−	0.895724i	0.996461	+	0.0840539i	$0.0267868\pi$
$444$	138.759	+	472.569i	0.312520	+	1.06434i
$445$	290.777	−	381.837i	0.653433	−	0.858060i
$446$	17.7106	−	38.7809i	0.0397099	−	0.0869526i
$447$	−908.092	+	495.856i	−2.03153	+	1.10930i
$448$	5.00914	−	70.0369i	0.0111811	−	0.156332i
$449$	−348.948	+	302.365i	−0.777168	+	0.673419i	−0.950250	−	0.311488i	$-0.899173\pi$
$449$	−348.948	+	302.365i	−0.777168	+	0.673419i	0.173083	+	0.984907i	$0.444627\pi$
$450$	−156.761	−	442.417i	−0.348358	−	0.983150i
$451$	256.532	−	561.726i	0.568807	−	1.24551i
$452$	−125.430	+	27.2857i	−0.277501	+	0.0603666i
$453$	−211.913	−	115.713i	−0.467799	−	0.255437i
$454$	−138.276	−	19.8810i	−0.304572	−	0.0437908i
$455$	19.2841	+	53.0328i	0.0423827	+	0.116556i
$456$	−51.8000	−	360.277i	−0.113596	−	0.790080i
$457$	29.6038	−	136.087i	0.0647786	−	0.297782i	−0.933347	−	0.358974i	$-0.883127\pi$
$457$	29.6038	−	136.087i	0.0647786	−	0.297782i	0.998126	+	0.0611920i	$0.0194902\pi$
$458$	−13.7609	+	0.984197i	−0.0300456	+	0.00214890i
$459$		−	296.707i		−	0.646421i
$460$	−117.463	−	197.744i	−0.255354	−	0.429877i
$461$	194.548			0.422013			0.211007	−	0.977485i	$-0.432326\pi$
$461$	194.548			0.422013			0.211007	+	0.977485i	$0.432326\pi$
$462$	51.9257	+	726.016i	0.112393	+	1.57146i
$463$	155.235	+	33.7692i	0.335280	+	0.0729357i	0.377054	−	0.926191i	$-0.376937\pi$
$463$	155.235	+	33.7692i	0.335280	+	0.0729357i	−0.0417738	+	0.999127i	$0.513301\pi$
$464$	190.147	−	27.3390i	0.409800	−	0.0589203i
$465$	−206.486	+	442.461i	−0.444056	+	0.951528i
$466$	−33.4853	+	232.895i	−0.0718568	+	0.499775i
$467$	283.295	−	518.817i	0.606628	−	1.11096i	−0.376218	−	0.926531i	$-0.622776\pi$
$467$	283.295	−	518.817i	0.606628	−	1.11096i	0.982846	−	0.184426i	$-0.0590425\pi$
$468$	7.25734	+	33.3615i	0.0155071	+	0.0712852i
$469$	714.962	+	326.512i	1.52444	+	0.696188i
$470$	191.972	−	502.028i	0.408451	−	1.06815i
$471$	−563.516	−	650.332i	−1.19643	−	1.38075i
$472$	−95.2354	−	6.81137i	−0.201770	−	0.0144309i
$473$	70.1785	+	128.522i	0.148369	+	0.271717i
$474$	−496.353	−	226.677i	−1.04716	−	0.478221i
$475$	−454.808	+	507.729i	−0.957490	+	1.06890i
$476$	−247.637	+	72.7127i	−0.520246	+	0.152758i
$477$	91.3740	+	122.061i	0.191560	+	0.255894i
$478$	−44.1921	+	118.484i	−0.0924520	+	0.247874i
$479$	−22.7186	+	3.26645i	−0.0474293	+	0.00681930i	−0.165989	−	0.986128i	$-0.553082\pi$
$479$	−22.7186	+	3.26645i	−0.0474293	+	0.00681930i	0.118559	+	0.992947i	$0.462172\pi$
$480$	−117.688	+	63.0096i	−0.245183	+	0.131270i
$481$	−43.9361	+	50.7050i	−0.0913433	+	0.105416i
$482$	76.1826	−	76.1826i	0.158055	−	0.158055i
$483$	−591.324	+	747.068i	−1.22427	+	1.54672i
$484$		−	66.7353i		−	0.137883i
$485$	4.17138	−	506.420i	0.00860078	−	1.04416i
$486$	352.168	−	226.324i	0.724625	−	0.465688i
$487$	−570.663	−	427.193i	−1.17179	−	0.877193i	−0.177525	−	0.984116i	$-0.556809\pi$
$487$	−570.663	−	427.193i	−1.17179	−	0.877193i	−0.994267	+	0.106923i	$0.965900\pi$
$488$	−7.45105	+	19.9770i	−0.0152685	+	0.0409365i
$489$	−1022.56	−	147.021i	−2.09111	−	0.300657i
$490$	165.881	+	108.546i	0.338533	+	0.221523i
$491$	−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	$-0.660706\pi$
$492$	−163.957	−	439.586i	−0.333246	−	0.893466i
$493$	−338.402	−	619.737i	−0.686413	−	1.25707i
$494$	37.4720	−	32.4697i	0.0758542	−	0.0657281i
$495$	664.272	−	488.783i	1.34196	−	0.987440i
$496$	79.4101	+	23.3169i	0.160101	+	0.0470099i
$497$	265.420	+	711.619i	0.534045	+	1.43183i
$498$	59.9588	+	275.626i	0.120399	+	0.553466i
$499$	119.237	+	406.085i	0.238952	+	0.813797i	0.988418	+	0.151754i	$0.0484922\pi$
$499$	119.237	+	406.085i	0.238952	+	0.813797i	−0.749466	+	0.662043i	$0.769690\pi$
$500$	232.007	+	93.1269i	0.464015	+	0.186254i
$501$	324.142	+	709.772i	0.646990	+	1.41671i
$502$	102.345	+	76.6142i	0.203874	+	0.152618i
$503$	−733.541	−	159.572i	−1.45833	−	0.317241i	−0.587661	−	0.809107i	$-0.699951\pi$
$503$	−733.541	−	159.572i	−1.45833	−	0.317241i	−0.870671	+	0.491866i	$0.836315\pi$
$504$	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
$508$	−135.145	+	9.66574i	−0.266033	+	0.0190271i
$509$	−120.844	−	188.038i	−0.237415	−	0.369426i	0.702017	−	0.712160i	$-0.252283\pi$
$509$	−120.844	−	188.038i	−0.237415	−	0.369426i	−0.939432	+	0.342735i	$0.888647\pi$
$510$	368.173	+	324.372i	0.721908	+	0.636023i
$511$	−99.6813	−	218.272i	−0.195071	−	0.427146i
$512$	13.5601	+	18.1142i	0.0264846	+	0.0353793i
$513$	482.929	+	263.699i	0.941382	+	0.514033i
$514$	182.846	−	284.514i	0.355731	−	0.553528i
$515$	−22.3685	+	6.36833i	−0.0434339	+	0.0123657i
$516$	106.746	+	31.3435i	0.206873	+	0.0607433i
$517$	941.994	+	67.3728i	1.82204	+	0.130315i
$518$	−46.2024	+	645.994i	−0.0891939	+	1.24709i
$519$	388.983	−	1324.76i	0.749486	−	2.55252i
$520$	−15.8882	−	8.84626i	−0.0305542	−	0.0170120i
$521$	−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	$0.998079\pi$
$522$	−432.124	+	791.376i	−0.827824	+	1.51605i
$523$	139.067	−	104.104i	0.265903	−	0.199052i	−0.458004	−	0.888950i	$-0.651435\pi$
$523$	139.067	−	104.104i	0.265903	−	0.199052i	0.723907	+	0.689898i	$0.242345\pi$
$524$	90.0921	−	41.1437i	0.171931	−	0.0785185i
$525$	17.0597	−	1035.48i	0.0324946	−	1.97235i
$526$	−338.934	+	217.820i	−0.644362	+	0.414106i
$527$	−21.7021	−	303.434i	−0.0411804	−	0.575777i
$528$	−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
$532$	101.738	−	467.684i	0.191238	−	0.879106i
$533$	38.3005	−	51.1635i	0.0718584	−	0.0959916i
$534$	582.803	−	266.157i	1.09139	−	0.498422i
$535$	37.1291	+	58.8338i	0.0694001	+	0.109970i
$536$	−243.030	+	71.3599i	−0.453413	+	0.133134i
$537$	−216.352	+	47.0645i	−0.402890	+	0.0876435i
$538$	−74.2044	+	27.6768i	−0.137926	+	0.0514439i
$539$	−98.1342	+	334.214i	−0.182067	+	0.620064i
$540$	30.3640	−	199.506i	0.0562296	−	0.369456i
$541$	−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	$0.869054\pi$
$542$	−127.660	+	69.7077i	−0.235535	+	0.128612i
$543$	−1140.24	+	425.288i	−2.09989	+	0.783220i
$544$	44.9658	−	69.9682i	0.0826577	−	0.128618i
$545$	−119.635	−	572.623i	−0.219514	−	1.05068i
$546$	−10.7207	+	74.5639i	−0.0196349	+	0.136564i
$547$	−662.978	−	247.278i	−1.21203	−	0.452062i	−0.339489	−	0.940610i	$-0.610254\pi$
$547$	−662.978	−	247.278i	−1.21203	−	0.452062i	−0.872537	+	0.488548i	$0.837527\pi$
$548$	315.233	−	421.102i	0.575243	−	0.768434i
$549$	−54.1051	−	84.1891i	−0.0985520	−	0.153350i
$550$	−38.5507	+	437.577i	−0.0700921	+	0.795594i
$551$	1309.46			2.37651
$552$	−13.6418	−	306.733i	−0.0247133	−	0.555675i
$553$	−507.369	−	507.369i	−0.917484	−	0.917484i
$554$	−389.962	−	337.904i	−0.703903	−	0.609936i
$555$	1085.51	−	581.177i	1.95587	−	1.04717i
$556$	25.6365	+	178.306i	0.0461089	+	0.320694i
$557$	83.1590	+	31.0167i	0.149298	+	0.0556853i	0.423002	−	0.906129i	$-0.360976\pi$
$557$	83.1590	+	31.0167i	0.149298	+	0.0556853i	−0.273704	+	0.961814i	$0.588249\pi$
$558$	−310.980	+	232.797i	−0.557311	+	0.417198i
$559$	4.26970	+	14.5413i	0.00763811	+	0.0260130i
$560$	−173.953	+	23.5499i	−0.310630	+	0.0420533i
$561$	−358.158	+	784.258i	−0.638429	+	1.39796i
$562$	−615.371	+	336.018i	−1.09497	+	0.597897i
$563$	−5.90353	+	82.5422i	−0.0104858	+	0.146611i	0.989512	+	0.144452i	$0.0461419\pi$
$563$	−5.90353	+	82.5422i	−0.0104858	+	0.146611i	−0.999998	+	0.00215939i	$0.999313\pi$
$564$	542.253	−	469.865i	0.961442	−	0.833094i
$565$	130.902	+	292.998i	0.231685	+	0.518580i
$566$	−140.227	+	307.055i	−0.247751	+	0.542500i
$567$	207.858	−	45.2167i	0.366593	−	0.0797473i
$568$	−214.816	−	117.299i	−0.378198	−	0.206512i
$569$	−426.422	−	61.3102i	−0.749423	−	0.107751i	−0.242989	−	0.970029i	$-0.578128\pi$
$569$	−426.422	−	61.3102i	−0.749423	−	0.107751i	−0.506435	+	0.862278i	$0.669037\pi$
$570$	−855.171	+	310.963i	−1.50030	+	0.545549i
$571$	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	$0.841859\pi$
$572$	6.79198	−	31.2222i	0.0118741	−	0.0545843i
$573$	1664.46	−	119.045i	2.90482	−	0.207757i
$574$		−	616.937i		−	1.07480i
$575$	−423.855	+	388.551i	−0.737139	+	0.675741i
$576$	−106.206			−0.184386
$577$	−47.8106	−	668.479i	−0.0828606	−	1.15854i	−0.853437	−	0.521196i	$-0.825486\pi$
$577$	−47.8106	−	668.479i	−0.0828606	−	1.15854i	0.770577	−	0.637348i	$-0.219968\pi$
$578$	100.642	+	21.8933i	0.174121	+	0.0378778i
$579$	−933.095	+	134.159i	−1.61156	+	0.231708i
$580$	−164.120	−	451.343i	−0.282966	−	0.778177i
$581$	−52.7866	+	367.139i	−0.0908548	+	0.631909i
$582$	324.002	−	593.366i	0.556705	−	1.01953i
$583$	−30.3323	−	139.435i	−0.0520280	−	0.239169i
$584$	70.3392	+	32.1228i	0.120444	+	0.0550049i
$585$	77.9304	−	34.8167i	0.133214	−	0.0595158i
$586$	258.822	+	298.696i	0.441675	+	0.509720i
$587$	143.884	+	10.2908i	0.245117	+	0.0175311i	0.193357	−	0.981128i	$-0.438062\pi$
$587$	143.884	+	10.2908i	0.245117	+	0.0175311i	0.0517600	+	0.998660i	$0.483517\pi$
$588$	126.827	+	232.267i	0.215693	+	0.395011i
$589$	513.166	+	234.355i	0.871249	+	0.397886i
$590$	32.0229	+	236.539i	0.0542760	+	0.400913i
$591$	123.891	−	36.3776i	0.209629	−	0.0615526i
$592$	−125.073	−	167.078i	−0.211273	−	0.282227i
$593$	−213.466	+	572.325i	−0.359977	+	0.965134i	0.623133	+	0.782116i	$0.285860\pi$
$593$	−213.466	+	572.325i	−0.359977	+	0.965134i	−0.983109	+	0.183018i	$0.941413\pi$
$594$	350.978	−	50.4630i	0.590871	−	0.0849545i
$595$	304.550	+	568.831i	0.511849	+	0.956019i
$596$	287.116	−	331.349i	0.481738	−	0.555955i
$597$	520.140	−	520.140i	0.871257	−	0.871257i
$598$	34.1462	−	24.1534i	0.0571007	−	0.0403903i
$599$			266.922i			0.445612i	0.974863	+	0.222806i	$0.0715217\pi$
$599$			266.922i			0.445612i	−0.974863	+	0.222806i	$0.928478\pi$
$600$	214.365	+	255.786i	0.357275	+	0.426310i
$601$	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	$0.217712\pi$
$602$	117.114	+	87.6703i	0.194541	+	0.145632i
$603$	415.465	−	1113.90i	0.688997	−	1.84727i
$604$	101.273	+	14.5608i	0.167670	+	0.0241073i
$605$	−163.312	+	34.1200i	−0.269937	+	0.0563968i
$606$	1020.24	+	655.666i	1.68356	+	1.08196i
$607$	50.1097	+	134.349i	0.0825531	+	0.221333i	0.971668	−	0.236351i	$-0.0759516\pi$
$607$	50.1097	+	134.349i	0.0825531	+	0.221333i	−0.889115	+	0.457685i	$0.848679\pi$
$608$	73.9187	+	135.372i	0.121577	+	0.222651i
$609$	−1503.53	+	1302.82i	−2.46885	+	2.13927i
$610$	52.6965	+	8.02018i	0.0863878	+	0.0131478i
$611$	93.7812	+	27.5366i	0.153488	+	0.0450682i
$612$	136.424	+	365.767i	0.222915	+	0.597658i
$613$	8.12262	+	37.3391i	0.0132506	+	0.0609121i	0.983297	−	0.182006i	$-0.0582590\pi$
$613$	8.12262	+	37.3391i	0.0132506	+	0.0609121i	−0.970047	+	0.242918i	$0.921895\pi$
$614$	209.014	+	711.836i	0.340414	+	1.15934i
$615$	−991.910	+	625.978i	−1.61286	+	1.01785i
$616$	−128.130	−	280.565i	−0.208003	−	0.455463i
$617$	−189.142	−	141.590i	−0.306552	−	0.229482i	0.434915	−	0.900472i	$-0.356778\pi$
$617$	−189.142	−	141.590i	−0.306552	−	0.229482i	−0.741467	+	0.670990i	$0.765869\pi$
$618$	−30.3376	−	6.59954i	−0.0490900	−	0.0106789i
$619$	−102.785	−	89.0639i	−0.166050	−	0.143884i	0.567872	−	0.823117i	$-0.307767\pi$
$619$	−102.785	−	89.0639i	−0.166050	−	0.143884i	−0.733922	+	0.679233i	$0.762312\pi$
$620$	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
$623$	840.353	−	60.1032i	1.34888	−	0.0964739i
$624$	−13.1244	−	20.4220i	−0.0210328	−	0.0327276i
$625$	109.277	−	615.373i	0.174844	−	0.984596i
$626$	−107.990	−	236.466i	−0.172509	−	0.377741i
$627$	−958.165	−	1279.96i	−1.52817	−	2.04140i
$628$	320.042	+	174.756i	0.509621	+	0.278274i
$629$	−414.748	+	645.361i	−0.659377	+	1.02601i
$630$	400.810	−	719.867i	0.636206	−	1.14265i
$631$	−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	$0.861609\pi$
$632$	230.638	+	16.4956i	0.364934	+	0.0261006i
$633$	−71.1508	+	994.818i	−0.112402	+	1.57159i
$634$	−131.847	+	449.030i	−0.207961	+	0.708250i
$635$	92.7496	+	325.779i	0.146062	+	0.513038i
$636$	−91.2028	−	58.6125i	−0.143401	−	0.0921580i
$637$	−17.2768	+	31.6400i	−0.0271221	+	0.0496703i
$638$	675.538	−	505.701i	1.05884	−	0.792635i
$639$	1044.99	−	477.230i	1.63535	−	0.746839i
$640$	37.3954	−	42.4451i	0.0584303	−	0.0663204i
$641$	−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	$0.325890\pi$
$642$	6.62539	+	92.6351i	0.0103199	+	0.144291i
$643$	84.5004	+	84.5004i	0.131416	+	0.131416i	0.769755	−	0.638339i	$-0.220378\pi$
$643$	84.5004	+	84.5004i	0.131416	+	0.131416i	−0.638339	+	0.769755i	$0.720378\pi$
$644$	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
$647$	−177.000	+	813.657i	−0.273571	+	1.25758i	0.611169	+	0.791500i	$0.290699\pi$
$647$	−177.000	+	813.657i	−0.273571	+	1.25758i	−0.884740	+	0.466085i	$0.845664\pi$
$648$	−41.0804	+	54.8770i	−0.0633957	+	0.0846868i
$649$	−381.509	+	174.230i	−0.587842	+	0.268458i
$650$	−13.5250	+	43.4038i	−0.0208077	+	0.0667751i
$651$	−822.388	+	241.475i	−1.26327	+	0.370929i
$652$	427.763	−	93.0542i	0.656079	−	0.142721i
$653$	−254.796	+	95.0340i	−0.390193	+	0.145534i	−0.536901	−	0.843645i	$-0.680405\pi$
$653$	−254.796	+	95.0340i	−0.390193	+	0.145534i	0.146708	+	0.989180i	$0.453132\pi$
$654$	220.011	−	749.288i	0.336408	−	1.14570i
$655$	−146.747	−	199.434i	−0.224041	−	0.304480i
$656$	130.194	+	150.251i	0.198466	+	0.229042i
$657$	−318.553	+	173.943i	−0.484860	+	0.264754i
$658$	884.004	−	329.716i	1.34347	−	0.501089i
$659$	536.688	−	835.104i	0.814398	−	1.26723i	−0.146191	−	0.989256i	$-0.546701\pi$
$659$	536.688	−	835.104i	0.814398	−	1.26723i	0.960589	−	0.277972i	$-0.0896623\pi$
$660$	−321.085	+	490.684i	−0.486492	+	0.743460i
$661$	−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	$0.889381\pi$
$662$	−410.526	−	153.118i	−0.620130	−	0.231296i
$663$	−53.4735	+	71.4323i	−0.0806539	+	0.107741i
$664$	−64.6224	−	100.554i	−0.0973228	−	0.151437i
$665$	−1196.51	−	9.85569i	−1.79927	−	0.0148206i
$666$	979.605			1.47088
$667$	1099.25	+	108.466i	1.64805	+	0.162618i
$668$	−233.804	−	233.804i	−0.350006	−	0.350006i
$669$	−107.530	−	93.1756i	−0.160733	−	0.139276i
$670$	298.884	+	558.248i	0.446096	+	0.833206i
$671$	13.3290	+	92.7053i	0.0198644	+	0.138160i
$672$	−219.560	−	81.8915i	−0.326726	−	0.121862i
$673$	−168.932	+	126.461i	−0.251013	+	0.187906i	−0.717374	−	0.696689i	$-0.754656\pi$
$673$	−168.932	+	126.461i	−0.251013	+	0.187906i	0.466360	+	0.884595i	$0.345565\pi$
$674$	−177.770	−	605.429i	−0.263754	−	0.898262i
$675$	−503.749	+	27.6969i	−0.746295	+	0.0410324i
$676$	−139.037	+	304.448i	−0.205675	+	0.450366i
$677$	746.641	−	407.697i	1.10287	−	0.602211i	0.178587	−	0.983924i	$-0.442848\pi$
$677$	746.641	−	407.697i	1.10287	−	0.602211i	0.924281	+	0.381713i	$0.124666\pi$
$678$	−30.5613	+	427.303i	−0.0450757	+	0.630241i
$679$	671.859	−	582.169i	0.989483	−	0.857392i
$680$	−194.213	−	74.2657i	−0.285608	−	0.109214i
$681$	−193.674	+	424.088i	−0.284397	+	0.622743i
$682$	355.244	−	77.2787i	0.520886	−	0.113312i
$683$	139.979	+	76.4342i	0.204947	+	0.111910i	0.578445	−	0.815722i	$-0.303660\pi$
$683$	139.979	+	76.4342i	0.204947	+	0.111910i	−0.373498	+	0.927631i	$0.621842\pi$
$684$	−716.579	−	103.029i	−1.04763	−	0.150627i
$685$	−1191.68	−	556.128i	−1.73967	−	0.811865i
$686$	−37.0339	−	257.576i	−0.0539852	−	0.375475i
$687$	−9.78696	+	44.9899i	−0.0142459	+	0.0654875i
$688$	−47.0237	+	3.36320i	−0.0683484	+	0.00488837i
$689$		−	14.7683i		−	0.0214344i
$690$	−743.650	+	190.208i	−1.07775	+	0.275664i
$691$	230.763			0.333955			0.166978	−	0.985961i	$-0.446599\pi$
$691$	230.763			0.333955			0.166978	+	0.985961i	$0.446599\pi$
$692$	41.7384	+	583.579i	0.0603156	+	0.843323i
$693$	1414.63	+	307.733i	2.04131	+	0.444060i
$694$	−666.241	+	95.7909i	−0.960001	+	0.138027i
$695$	423.236	−	153.900i	0.608973	−	0.221439i
$696$	91.2398	−	634.587i	0.131092	−	0.911762i
$697$	350.220	−	641.380i	0.502467	−	0.920200i
$698$	−142.972	−	657.230i	−0.204830	−	0.941590i
$699$	714.284	+	326.202i	1.02186	+	0.466670i
$700$	146.568	+	413.650i	0.209383	+	0.590928i
$701$	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	$0.429558\pi$
$702$	36.6043	+	2.61799i	0.0521429	+	0.00372933i
$703$	−681.798	−	1248.62i	−0.969841	−	1.77613i
$704$	90.4136	+	41.2905i	0.128428	+	0.0586513i
$705$	−1427.08	−	1086.75i	−2.02422	−	1.54149i
$706$	−398.995	+	117.156i	−0.565149	+	0.165943i
$707$	955.686	+	1276.65i	1.35175	+	1.80572i
$708$	−111.355	+	298.555i	−0.157281	+	0.421687i
$709$	1403.05	−	201.729i	1.97892	−	0.284526i	0.985610	−	0.169033i	$-0.0540644\pi$
$709$	1403.05	−	201.729i	1.97892	−	0.284526i	0.993308	−	0.115493i	$-0.0368447\pi$
$710$	−177.219	+	585.662i	−0.249604	+	0.824876i
$711$	−710.726	+	820.222i	−0.999615	+	1.15362i
$712$	−191.979	+	191.979i	−0.269634	+	0.269634i
$713$	411.376	+	239.241i	0.576964	+	0.335542i
$714$			861.340i			1.20636i
$715$	−79.8784	−	0.657958i	−0.111718	−	0.000920221i
$716$	78.9300	−	50.7252i	0.110237	−	0.0708453i
$717$	337.852	+	252.913i	0.471202	+	0.352738i
$718$	−343.020	+	919.672i	−0.477743	+	1.28088i
$719$	−1143.77	−	164.450i	−1.59078	−	0.228720i	−0.710685	−	0.703510i	$-0.751615\pi$
$719$	−1143.77	−	164.450i	−1.59078	−	0.228720i	−0.880099	+	0.474790i	$0.842524\pi$
$720$	54.3004	+	259.903i	0.0754172	+	0.360977i
$721$	−34.3449	−	22.0721i	−0.0476351	−	0.0306132i
$722$	189.000	+	506.728i	0.261773	+	0.701840i
$723$	−172.319	−	315.579i	−0.238339	−	0.436485i
$724$	389.738	−	337.710i	0.538312	−	0.466450i
$725$	−1020.60	+	632.389i	−1.40772	+	0.872260i
$726$	−213.697	−	62.7472i	−0.294349	−	0.0864286i
$727$	51.1022	+	137.010i	0.0702919	+	0.188460i	0.967345	−	0.253462i	$-0.0815694\pi$
$727$	51.1022	+	137.010i	0.0702919	+	0.188460i	−0.897053	+	0.441922i	$0.854297\pi$
$728$	−6.78544	−	31.1922i	−0.00932066	−	0.0428464i
$729$	−332.153	−	1131.21i	−0.455628	−	1.55173i
$730$	42.6472	−	188.555i	0.0584208	−	0.258294i
$731$	71.9856	+	157.626i	0.0984755	+	0.215631i
$732$	56.9639	+	42.6426i	0.0778195	+	0.0582550i
$733$	−149.214	−	32.4595i	−0.203566	−	0.0442831i	0.109626	−	0.993973i	$-0.465035\pi$
$733$	−149.214	−	32.4595i	−0.203566	−	0.0442831i	−0.313192	+	0.949690i	$0.601398\pi$
$734$	−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
$738$	−930.780	+	66.5707i	−1.26122	+	0.0902042i
$739$	−684.684	−	1065.39i	−0.926501	−	1.44166i	−0.896966	−	0.442100i	$-0.854234\pi$
$739$	−684.684	−	1065.39i	−0.926501	−	1.44166i	−0.0295347	−	0.999564i	$-0.509403\pi$
$740$	−344.921	+	391.498i	−0.466110	+	0.529051i
$741$	−68.7404	−	150.521i	−0.0927671	−	0.203132i
$742$	−85.4325	−	114.124i	−0.115138	−	0.153807i
$743$	954.187	+	521.026i	1.28424	+	0.701246i	0.968834	−	0.247712i	$-0.0796787\pi$
$743$	954.187	+	521.026i	1.28424	+	0.701246i	0.315402	+	0.948958i	$0.397861\pi$
$744$	149.329	−	232.360i	0.200711	−	0.312312i
$745$	−957.659	−	533.208i	−1.28545	−	0.715715i
$746$	−30.1187	−	8.84364i	−0.0403735	−	0.0118547i
$747$	559.604	+	40.0236i	0.749135	+	0.0535792i
$748$	26.0636	−	364.417i	0.0348444	−	0.487189i
$749$	−34.4060	+	117.176i	−0.0459359	+	0.156443i
$750$	516.350	−	655.363i	0.688466	−	0.873817i
$751$	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	$0.378082\pi$
$752$	−145.713	+	266.854i	−0.193768	+	0.354859i
$753$	341.559	−	255.688i	0.453598	−	0.339559i
$754$	79.4419	−	36.2799i	0.105361	−	0.0481166i
$755$	−16.1454	−	255.275i	−0.0213847	−	0.338113i
$756$	298.010	−	191.520i	0.394193	−	0.253333i
$757$	8.90280	+	124.477i	0.0117606	+	0.164435i	0.999938	+	0.0111211i	$0.00354004\pi$
$757$	8.90280	+	124.477i	0.0117606	+	0.164435i	−0.988178	+	0.153314i	$0.951005\pi$
$758$	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	$0.279915\pi$
$762$	−96.1171	+	441.843i	−0.126138	+	0.579847i
$763$	615.388	−	822.062i	0.806537	−	1.07741i
$764$	−643.223	+	293.750i	−0.841915	+	0.384490i
$765$	825.340	−	520.859i	1.07888	−	0.680861i
$766$	−634.640	+	186.347i	−0.828512	+	0.243273i
$767$	−42.4148	+	9.22677i	−0.0552996	+	0.0120297i
$768$	70.7542	−	26.3900i	0.0921279	−	0.0343619i
$769$	−241.165	+	821.331i	−0.313608	+	1.06805i	0.640343	+	0.768089i	$0.278792\pi$
$769$	−241.165	+	821.331i	−0.313608	+	1.06805i	−0.953951	+	0.299962i	$0.903026\pi$
$770$	−621.079	+	457.000i	−0.806596	+	0.593507i
$771$	−739.139	−	853.012i	−0.958676	−	1.10637i
$772$	350.605	−	191.445i	0.454152	−	0.247986i
$773$	−209.390	+	78.0986i	−0.270880	+	0.101033i	−0.481234	−	0.876592i	$-0.659811\pi$
$773$	−209.390	+	78.0986i	−0.270880	+	0.101033i	0.210354	+	0.977625i	$0.432538\pi$
$774$	119.632	−	186.151i	0.154563	−	0.240505i
$775$	−513.144	+	65.1705i	−0.662122	+	0.0840910i
$776$	−40.7709	+	283.568i	−0.0525399	+	0.365423i
$777$	2025.14	+	755.337i	2.60635	+	0.972119i
$778$	265.415	−	354.553i	0.341151	−	0.455724i
$779$	732.669	+	1140.05i	0.940525	+	1.46348i
$780$	−43.2658	+	42.5589i	−0.0554690	+	0.0545627i
$781$	−1075.14			−1.37662
$782$	347.154	−	328.926i	0.443932	−	0.420622i
$783$	685.310	+	685.310i	0.875237	+	0.875237i
$784$	−84.7506	−	73.4368i	−0.108100	−	0.0936694i
$785$	264.027	−	872.543i	0.336341	−	1.11152i
$786$	−47.0405	−	327.174i	−0.0598480	−	0.416252i
$787$	−782.706	−	291.934i	−0.994543	−	0.370946i	−0.201088	−	0.979573i	$-0.564448\pi$
$787$	−782.706	−	291.934i	−0.994543	−	0.370946i	−0.793456	+	0.608628i	$0.791720\pi$
$788$	−43.8020	+	32.7898i	−0.0555863	+	0.0416114i
$789$	378.815	+	1290.13i	0.480120	+	1.63514i
$790$	−77.5520	−	572.842i	−0.0981670	−	0.725117i
$791$	−234.013	+	512.417i	−0.295845	+	0.647809i
$792$	−409.466	+	223.586i	−0.517003	+	0.282305i
$793$	−0.691502	+	9.66846i	−0.000872008	+	0.0121923i
$794$	−90.3492	+	78.2880i	−0.113790	+	0.0985995i
$795$	−96.8046	+	253.155i	−0.121767	+	0.318434i
$796$	−129.489	+	283.540i	−0.162674	+	0.356207i
$797$	−1426.37	+	310.289i	−1.78968	+	0.389321i	−0.980229	−	0.197868i	$-0.936598\pi$
$797$	−1426.37	+	310.289i	−1.78968	+	0.389321i	−0.809450	+	0.587189i	$0.800235\pi$
$798$	−1401.94	−	765.518i	−1.75682	−	0.959295i
$799$	1106.20	+	159.048i	1.38448	+	0.199058i
$800$	−122.989	−	69.8115i	−0.153737	−	0.0872644i
$801$	−181.357	−	1261.37i	−0.226413	−	1.57474i
$802$	90.4572	−	415.825i	0.112789	−	0.518485i
$803$	338.811	−	24.2322i	0.421931	−	0.0301771i
$804$			845.315i			1.05139i
$805$	−1003.62	−	107.385i	−1.24674	−	0.133397i
$806$	37.6257			0.0466820
$807$	18.8557	+	263.637i	0.0233652	+	0.326688i
$808$	−502.166	−	109.240i	−0.621493	−	0.135197i
$809$	1390.54	−	199.930i	1.71884	−	0.247132i	0.788817	−	0.614629i	$-0.210694\pi$
$809$	1390.54	−	199.930i	1.71884	−	0.247132i	0.930025	+	0.367496i	$0.119785\pi$
$810$	155.296	+	72.4733i	0.191724	+	0.0894732i
$811$	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	$-0.139194\pi$
$812$	404.026	−	739.918i	0.497569	−	0.911229i
$813$	103.184	+	474.330i	0.126918	+	0.583431i
$814$	−833.942	−	380.848i	−1.02450	−	0.467873i
$815$	−446.423	−	999.229i	−0.547758	−	1.22605i
$816$	−181.771	−	209.775i	−0.222758	−	0.257077i
$817$	−320.534	−	22.9251i	−0.392331	−	0.0280601i
$818$	−125.432	−	229.711i	−0.153339	−	0.280820i
$819$	136.291	+	62.2418i	0.166411	+	0.0759973i
$820$	301.125	−	395.425i	0.367226	−	0.482225i
$821$	−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	$0.645746\pi$
$822$	−1052.04	−	1405.36i	−1.27986	−	1.70969i
$823$	−387.728	+	1039.54i	−0.471115	+	1.26311i	0.456551	+	0.889697i	$0.349085\pi$
$823$	−387.728	+	1039.54i	−0.471115	+	1.26311i	−0.927666	+	0.373411i	$0.878188\pi$
$824$	13.0224	−	1.87234i	0.0158039	−	0.00227226i
$825$	1364.94	+	534.872i	1.65448	+	0.648330i
$826$	−274.391	+	316.664i	−0.332193	+	0.383371i
$827$	−225.106	+	225.106i	−0.272196	+	0.272196i	−0.829984	−	0.557787i	$-0.811650\pi$
$827$	−225.106	+	225.106i	−0.272196	+	0.272196i	0.557787	+	0.829984i	$0.311650\pi$
$828$	−593.013	−	145.846i	−0.716200	−	0.176142i
$829$		−	403.014i		−	0.486145i	−0.970008	−	0.243072i	$-0.921845\pi$
$829$		−	403.014i		−	0.486145i	0.970008	−	0.243072i	$-0.0781553\pi$
$830$	−213.033	+	209.552i	−0.256666	+	0.252473i
$831$	−1448.68	+	931.011i	−1.74330	+	1.12035i
$832$	8.23511	+	6.16473i	0.00989797	+	0.00740953i
$833$	−144.048	+	386.207i	−0.172926	+	0.463634i
$834$	595.069	+	85.5580i	0.713512	+	0.102588i
$835$	−452.618	+	691.694i	−0.542057	+	0.828376i
$836$	569.971	+	366.298i	0.681784	+	0.438156i
$837$	145.917	+	391.219i	0.174333	+	0.467406i
$838$	211.588	+	387.494i	0.252491	+	0.462403i
$839$	−751.508	+	651.185i	−0.895718	+	0.776144i	−0.975346	−	0.220680i	$-0.929172\pi$
$839$	−751.508	+	651.185i	−0.895718	+	0.776144i	0.0796279	+	0.996825i	$0.474627\pi$
$840$	−88.1466	+	579.167i	−0.104936	+	0.689484i
$841$	1406.10	+	412.867i	1.67194	+	0.490924i
$842$	146.554	+	392.926i	0.174054	+	0.466658i
$843$	497.388	+	2286.45i	0.590021	+	2.71228i
$844$	−119.070	−	405.515i	−0.141078	−	0.480468i
$845$	816.118	+	184.589i	0.965820	+	0.218448i
$846$	−592.836	−	1298.13i	−0.700752	−	1.53443i
$847$	−234.452	−	175.509i	−0.276803	−	0.207212i
$848$	44.8905	+	9.76534i	0.0529370	+	0.0115157i
$849$	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
$853$	−673.418	+	48.1638i	−0.789470	+	0.0564640i	−0.460250	−	0.887789i	$-0.652240\pi$
$853$	−673.418	+	48.1638i	−0.789470	+	0.0564640i	−0.329220	+	0.944253i	$0.606786\pi$
$854$	50.5869	+	78.7148i	0.0592353	+	0.0921719i
$855$	114.241	+	1806.26i	0.133615	+	2.11259i
$856$	−16.3486	−	35.7983i	−0.0190988	−	0.0418205i
$857$	−107.949	−	144.202i	−0.125961	−	0.168264i	0.733128	−	0.680091i	$-0.238060\pi$
$857$	−107.949	−	144.202i	−0.125961	−	0.168264i	−0.859089	+	0.511827i	$0.828969\pi$
$858$	−93.5925	−	51.1054i	−0.109082	−	0.0595634i
$859$	32.5577	−	50.6607i	0.0379018	−	0.0589764i	−0.821786	−	0.569797i	$-0.807022\pi$
$859$	32.5577	−	50.6607i	0.0379018	−	0.0589764i	0.859687	+	0.510820i	$0.170658\pi$
$860$	32.2723	+	113.355i	0.0375259	+	0.131808i
$861$	−1975.53	−	580.068i	−2.29446	−	0.673714i
$862$	264.246	+	18.8992i	0.306549	+	0.0219248i
$863$	−100.683	+	1407.73i	−0.116666	+	1.63121i	0.515864	+	0.856671i	$0.327471\pi$
$863$	−100.683	+	1407.73i	−0.116666	+	1.63121i	−0.632530	+	0.774536i	$0.717984\pi$
$864$	−32.1619	+	109.533i	−0.0372244	+	0.126775i
$865$	1406.77	−	400.510i	1.62633	−	0.463017i
$866$	664.041	+	426.753i	0.766791	+	0.492787i
$867$	164.734	−	301.687i	0.190004	−	0.347967i
$868$	290.759	−	217.659i	0.334975	−	0.250759i
$869$	923.927	−	421.944i	1.06321	−	0.485551i
$870$	−1599.58	+	101.169i	−1.83860	+	0.116286i
$871$	−96.8713	+	62.2554i	−0.111218	+	0.0714758i
$872$	23.6075	+	330.075i	0.0270728	+	0.378527i
$873$	−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
$877$	−272.066	+	1250.67i	−0.310223	+	1.42607i	0.513015	+	0.858379i	$0.328528\pi$
$877$	−272.066	+	1250.67i	−0.310223	+	1.42607i	−0.823239	+	0.567695i	$0.807835\pi$
$878$	−356.050	+	475.627i	−0.405524	+	0.541717i
$879$	1199.83	−	547.943i	1.36499	−	0.623370i
$880$	54.8184	−	242.367i	0.0622937	−	0.275418i
$881$	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	$0.190371\pi$
$882$	514.327	−	111.885i	0.583137	−	0.126854i
$883$	595.001	−	221.924i	0.673840	−	0.251329i	0.0108318	−	0.999941i	$-0.496552\pi$
$883$	595.001	−	221.924i	0.673840	−	0.251329i	0.663008	+	0.748612i	$0.269279\pi$
$884$	10.6527	−	36.2799i	0.0120506	−	0.0410406i
$885$	787.545	+	119.861i	0.889881	+	0.135436i
$886$	613.217	+	707.690i	0.692118	+	0.798747i
$887$	−558.135	+	304.765i	−0.629239	+	0.343590i	−0.762018	−	0.647555i	$-0.775791\pi$
$887$	−558.135	+	304.765i	−0.629239	+	0.343590i	0.132780	+	0.991146i	$0.457610\pi$
$888$	−652.611	+	243.411i	−0.734922	+	0.274112i
$889$	−321.463	+	500.206i	−0.361601	+	0.562661i
$890$	567.959	+	371.651i	0.638156	+	0.417585i
$891$	−42.8539	+	298.055i	−0.0480964	+	0.334518i
$892$	56.4915	+	21.0702i	0.0633313	+	0.0236214i
$893$	−1242.01	+	1659.13i	−1.39083	+	1.85793i
$894$	−791.075	−	1230.94i	−0.884872	−	1.37689i
$895$	−164.488	−	167.220i	−0.183785	−	0.186838i
$896$	99.3001			0.110826
$897$	−45.2375	−	132.052i	−0.0504320	−	0.147215i
$898$	−461.725	−	461.725i	−0.514170	−	0.514170i
$899$	750.974	+	650.723i	0.835344	+	0.723829i
$900$	608.263	−	265.764i	0.675848	−	0.295293i
$901$	−24.0317	−	167.144i	−0.0266722	−	0.185509i
$902$	818.258	+	305.194i	0.907160	+	0.338353i
$903$	390.849	−	292.586i	0.432834	−	0.324016i
$904$	−51.1440	−	174.181i	−0.0565753	−	0.192678i
$905$	−1025.69	−	781.089i	−1.13336	−	0.863082i
$906$	141.847	−	310.601i	0.156564	−	0.342826i
$907$	458.862	−	250.558i	0.505912	−	0.276249i	−0.205957	−	0.978561i	$-0.566031\pi$
$907$	458.862	−	250.558i	0.505912	−	0.276249i	0.711869	+	0.702312i	$0.247849\pi$
$908$	14.0939	−	197.059i	0.0155219	−	0.217025i
$909$	1822.97	−	1579.61i	2.00547	−	1.73775i
$910$	−72.8630	+	32.5528i	−0.0800693	+	0.0357723i
$911$	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	$-0.186891\pi$
$912$	502.984	−	109.417i	0.551517	−	0.119975i
$913$	−460.832	−	251.633i	−0.504745	−	0.275612i
$914$	194.952	+	28.0298i	0.213295	+	0.0306672i
$915$	75.2292	−	161.202i	0.0822178	−	0.176177i
$916$	−2.77664	−	19.3119i	−0.00303126	−	0.0210829i
$917$	92.3907	−	424.713i	0.100753	−	0.463155i
$918$	418.538	−	29.9344i	0.455924	−	0.0326083i
$919$			1550.41i			1.68706i	0.537082	+	0.843530i	$0.319526\pi$
$919$			1550.41i			1.68706i	−0.537082	+	0.843530i	$0.680474\pi$
$920$	267.088	−	185.644i	0.290314	−	0.201787i
$921$	2475.94			2.68831
$922$	19.6277	+	274.432i	0.0212882	+	0.297648i
$923$	−108.728	−	23.6524i	−0.117799	−	0.0256255i
$924$	−1018.89	+	146.494i	−1.10269	+	0.158543i
$925$	1134.41	+	643.915i	1.22639	+	0.696125i
$926$	−31.9738	+	222.382i	−0.0345289	+	0.240154i
$927$	−29.5945	+	54.1983i	−0.0319250	+	0.0584663i
$928$	57.7484	+	265.465i	0.0622289	+	0.286062i
$929$	−451.710	−	206.289i	−0.486233	−	0.222055i	0.157187	−	0.987569i	$-0.449758\pi$
$929$	−451.710	−	206.289i	−0.486233	−	0.222055i	−0.643419	+	0.765514i	$0.722485\pi$
$930$	−644.972	−	246.632i	−0.693518	−	0.265196i
$931$	−500.578	−	577.698i	−0.537678	−	0.620514i
$932$	−331.903	−	23.7381i	−0.356119	−	0.0254701i
$933$	498.293	+	912.555i	0.534076	+	0.978087i
$934$	760.430	+	347.277i	0.814165	+	0.371816i
$935$	−905.113	+	122.535i	−0.968036	+	0.131054i
$936$	−46.3278	+	13.6031i	−0.0494955	+	0.0145332i
$937$	85.6061	+	114.356i	0.0913619	+	0.122045i	0.843893	−	0.536511i	$-0.180258\pi$
$937$	85.6061	+	114.356i	0.0913619	+	0.122045i	−0.752531	+	0.658557i	$0.771167\pi$
$938$	−388.450	+	1041.47i	−0.414126	+	1.11031i
$939$	−858.739	+	123.468i	−0.914525	+	0.131489i
$940$	727.534	+	220.149i	0.773973	+	0.234201i
$941$	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
$943$	520.620	+	1017.73i	0.552089	+	1.07925i
$944$		−	135.027i		−	0.143037i
$945$	−621.044	−	631.360i	−0.657190	−	0.668106i
$946$	−174.215	+	111.961i	−0.184159	+	0.118352i
$947$	411.646	+	308.154i	0.434684	+	0.325401i	0.794111	−	0.607773i	$-0.207937\pi$
$947$	411.646	+	308.154i	0.434684	+	0.325401i	−0.359427	+	0.933173i	$0.617028\pi$
$948$	269.676	−	723.030i	0.284469	−	0.762690i
$949$	34.7968	+	5.00303i	0.0366668	+	0.00527189i
$950$	−762.093	−	590.332i	−0.802204	−	0.621402i
$951$	1313.90	+	844.392i	1.38160	+	0.887899i
$952$	−127.553	−	341.983i	−0.133984	−	0.359226i
$953$	344.723	+	631.313i	0.361724	+	0.662448i	0.993642	−	0.112587i	$-0.0359138\pi$
$953$	344.723	+	631.313i	0.361724	+	0.662448i	−0.631918	+	0.775035i	$0.717732\pi$
$954$	−162.962	+	141.208i	−0.170820	+	0.148016i
$955$	1047.72	+	1423.88i	1.09709	+	1.49098i
$956$	−171.593	−	50.3841i	−0.179490	−	0.0527031i
$957$	−984.170	−	2638.66i	−1.02839	−	2.75722i
$958$	−6.89974	−	31.7176i	−0.00720223	−	0.0331081i
$959$	−650.363	−	2214.93i	−0.678167	−	2.30963i
$960$	−100.755	−	159.655i	−0.104953	−	0.166307i
$961$	−221.373	−	484.740i	−0.230357	−	0.504412i
$962$	−75.9576	−	56.8612i	−0.0789580	−	0.0591072i
$963$	180.498	+	39.2648i	0.187433	+	0.0407735i
$964$	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	−0.454463	−	0.890766i	$-0.650169\pi$
$967$	421.905	−	421.905i	0.436303	−	0.436303i	0.890766	+	0.454463i	$0.150169\pi$
$968$	94.1375	−	6.73285i	0.0972495	−	0.00695542i
$969$	−1022.92	−	1591.69i	−1.05565	−	1.64262i
$970$	714.782	−	45.2079i	0.736888	−	0.0466061i
$971$	−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	$0.951751\pi$
$972$	354.785	+	473.938i	0.365006	+	0.487590i
$973$	693.841	+	378.866i	0.713094	+	0.389379i
$974$	545.029	−	848.082i	0.559578	−	0.870721i
$975$	126.269	+	84.1192i	0.129507	+	0.0862761i
$976$	−28.9315	−	8.49506i	−0.0296430	−	0.00870396i
$977$	−563.264	−	40.2854i	−0.576524	−	0.0412338i	−0.219967	−	0.975507i	$-0.570595\pi$
$977$	−563.264	−	40.2854i	−0.576524	−	0.0412338i	−0.356557	+	0.934274i	$0.616049\pi$
$978$	104.225	−	1457.26i	0.106570	−	1.49004i
$979$	−336.001	+	1144.31i	−0.343208	+	1.16886i
$980$	−136.381	+	244.945i	−0.139164	+	0.249944i
$981$	−1306.66	−	839.739i	−1.33197	−	0.856003i
$982$	585.760	−	1072.74i	0.596496	−	1.09240i
$983$	−313.190	+	234.451i	−0.318606	+	0.238506i	−0.746596	−	0.665278i	$-0.768313\pi$
$983$	−313.190	+	234.451i	−0.318606	+	0.238506i	0.427989	+	0.903784i	$0.359222\pi$
$984$	603.542	−	275.629i	0.613356	−	0.280110i
$985$	102.637	+	90.4260i	0.104200	+	0.0918031i
$986$	840.066	−	539.878i	0.851994	−	0.547543i
$987$	−224.630	−	3140.73i	−0.227588	−	3.18210i
$988$	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	$0.0766960\pi$
$992$	−24.8795	+	114.369i	−0.0250801	+	0.115291i
$993$	−876.301	+	1170.60i	−0.882479	+	1.17885i
$994$	−977.039	+	446.199i	−0.982937	+	0.448892i
$995$	760.073	+	171.913i	0.763893	+	0.172776i
$996$	−382.752	+	112.386i	−0.384289	+	0.112837i
$997$	1197.90	−	260.587i	1.20150	−	0.261371i	0.433105	−	0.901343i	$-0.357418\pi$
$997$	1197.90	−	260.587i	1.20150	−	0.261371i	0.768398	+	0.639973i	$0.221054\pi$
$998$	−560.798	+	209.167i	−0.561922	+	0.209586i
$999$	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.223.11	yes	240
5.2	odd	4	inner	230.3.k.a.177.11	yes	240
23.13	even	11	inner	230.3.k.a.13.11	✓	240
115.82	odd	44	inner	230.3.k.a.197.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.k.a.13.11	✓	240	23.13	even	11	inner
230.3.k.a.177.11	yes	240	5.2	odd	4	inner
230.3.k.a.197.11	yes	240	115.82	odd	44	inner
230.3.k.a.223.11	yes	240	1.1	even	1	trivial

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+(0.100889 + 1.41061i) q^{2} +(4.61186 + 1.00325i) q^{3} +(-1.97964 + 0.284630i) q^{4} +(1.70867 + 4.69898i) q^{5} +(-0.949908 + 6.60675i) q^{6} +(-4.20636 + 7.70337i) q^{7} +(-0.601225 - 2.76379i) q^{8} +(12.0761 + 5.51495i) q^{9} +(-6.45605 + 2.88435i) q^{10} +(-8.13630 - 9.38979i) q^{11} +(-9.41539 - 0.673402i) q^{12} +(-0.616250 - 1.12858i) q^{13} +(-11.2908 - 5.15635i) q^{14} +(3.16592 + 23.3853i) q^{15} +(3.83797 - 1.12693i) q^{16} +(-8.81103 - 11.7702i) q^{17} +(-6.56111 + 17.5910i) q^{18} +(26.9883 - 3.88033i) q^{19} +(-4.72004 - 8.81597i) q^{20} +(-27.1275 + 31.3068i) q^{21} +(12.4245 - 12.4245i) q^{22} +(22.9773 - 1.02190i) q^{23} -13.3494i q^{24} +(-19.1609 + 16.0581i) q^{25} +(1.52981 - 0.983150i) q^{26} +(16.1552 + 12.0937i) q^{27} +(6.13448 - 16.4472i) q^{28} +(47.5368 + 6.83476i) q^{29} +(-32.6681 + 6.82519i) q^{30} +(17.4061 + 11.1862i) q^{31} +(1.97687 + 5.30019i) q^{32} +(-28.1032 - 51.4671i) q^{33} +(15.7142 - 13.6164i) q^{34} +(-43.3853 - 6.60305i) q^{35} +(-25.4760 - 7.48043i) q^{36} +(-18.2339 - 48.8870i) q^{37} +(8.19644 + 37.6784i) q^{38} +(-1.70981 - 5.82310i) q^{39} +(11.9597 - 7.54756i) q^{40} +(20.6473 + 45.2113i) q^{41} +(-46.8986 - 35.1078i) q^{42} +(-11.5166 - 2.50528i) 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} +(18.8308 - 1.34680i) q^{48} +(-15.1570 - 23.5848i) q^{49} +(-24.5848 - 25.4084i) q^{50} +(-28.8268 - 63.1220i) q^{51} +(1.54118 + 2.05878i) q^{52} +(10.0802 + 5.50423i) q^{53} +(-15.4296 + 24.0088i) q^{54} +(30.2202 - 54.2764i) q^{55} +(23.8194 + 6.99402i) q^{56} +(128.359 + 9.18042i) q^{57} +(-4.84525 + 67.7454i) q^{58} +(9.51039 - 32.3894i) q^{59} +(-12.9235 - 45.3934i) q^{60} +(-6.34157 - 4.07548i) q^{61} +(-14.0233 + 25.6818i) q^{62} +(-93.2799 + 69.8284i) q^{63} +(-7.27706 + 3.32332i) q^{64} +(4.25020 - 4.82412i) q^{65} +(69.7648 - 44.8351i) q^{66} +(-6.38852 - 89.3232i) 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} +(7.98172 - 36.6914i) q^{72} +(-16.3838 + 21.8862i) q^{73} +(67.1209 - 30.6531i) q^{74} +(-104.477 + 54.8344i) q^{75} +(-52.3227 + 15.3633i) q^{76} +(106.557 - 23.1801i) q^{77} +(8.04162 - 2.99937i) q^{78} +(-23.0320 + 78.4397i) q^{79} +(11.8533 + 16.1090i) q^{80} +(-15.8712 - 18.3164i) q^{81} +(-61.6924 + 33.6866i) q^{82} +(39.5955 - 14.7683i) q^{83} +(44.7919 - 69.6976i) q^{84} +(40.2526 - 61.5143i) q^{85} +(2.37208 - 16.4982i) q^{86} +(212.376 + 79.2121i) q^{87} +(-21.0597 + 28.1324i) q^{88} +(-51.8960 - 80.7517i) q^{89} +(-93.8706 - 0.773212i) q^{90} +11.2860 q^{91} +(-45.1960 + 8.56302i) q^{92} +(69.0518 + 69.0518i) q^{93} +(-81.2402 - 70.3950i) q^{94} +(64.3477 + 120.187i) q^{95} +(3.79963 + 26.4270i) q^{96} +(-94.9012 - 35.3963i) q^{97} +(31.7398 - 23.7601i) 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

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