LMFDB - Embedded newform 384.2.v.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06073 - 0.935332i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(0.250309 + 1.98427i) q^{4} +(-0.385901 - 3.91812i) q^{5} +(-0.587142 + 1.28657i) q^{6} +(-2.38112 + 3.56360i) q^{7} +(1.59044 - 2.33891i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-1.06073 - 0.935332i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(0.250309 + 1.98427i) q^{4} +(-0.385901 - 3.91812i) q^{5} +(-0.587142 + 1.28657i) q^{6} +(-2.38112 + 3.56360i) q^{7} +(1.59044 - 2.33891i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-3.25540 + 4.51703i) q^{10} +(-5.30688 + 2.83658i) q^{11} +(1.82617 - 0.815535i) q^{12} +(2.04975 + 0.201883i) q^{13} +(5.85888 - 1.55289i) q^{14} +(-3.63739 + 1.50666i) q^{15} +(-3.87469 + 0.993364i) q^{16} +(-1.75009 - 0.724912i) q^{17} +(1.40161 + 0.188388i) q^{18} +(3.42826 - 2.81350i) q^{19} +(7.67803 - 1.74648i) q^{20} +(4.10136 + 1.24413i) q^{21} +(8.28232 + 1.95483i) q^{22} +(-0.247363 + 1.24358i) q^{23} +(-2.69988 - 0.843011i) q^{24} +(-10.2988 + 2.04856i) q^{25} +(-1.98541 - 2.13134i) q^{26} +(0.773010 + 0.634393i) q^{27} +(-7.66718 - 3.83280i) q^{28} +(-2.41573 + 4.51951i) q^{29} +(5.26752 + 1.80400i) q^{30} +(-4.26568 + 4.26568i) q^{31} +(5.03914 + 2.57043i) q^{32} +(4.25495 + 4.25495i) q^{33} +(1.17835 + 2.40586i) q^{34} +(14.8815 + 7.95433i) q^{35} +(-1.31053 - 1.51080i) q^{36} +(-1.72240 + 2.09874i) q^{37} +(-6.26802 - 0.222187i) q^{38} +(-0.401822 - 2.02009i) q^{39} +(-9.77788 - 5.32896i) q^{40} +(2.36639 + 0.470705i) q^{41} +(-3.18677 - 5.15582i) q^{42} +(2.56696 - 8.46214i) q^{43} +(-6.95692 - 9.82027i) q^{44} +(2.49766 + 3.04340i) q^{45} +(1.42554 - 1.08774i) q^{46} +(-2.96974 + 7.16958i) q^{47} +(2.07535 + 3.41949i) q^{48} +(-4.35073 - 10.5036i) q^{49} +(12.8404 + 7.45984i) q^{50} +(-0.185673 + 1.88517i) q^{51} +(0.112481 + 4.11780i) q^{52} +(-1.42695 - 2.66964i) q^{53} +(-0.226590 - 1.39594i) q^{54} +(13.1620 + 19.6983i) q^{55} +(4.54789 + 11.2369i) q^{56} +(-3.68752 - 2.46392i) q^{57} +(6.78969 - 2.53449i) q^{58} +(-5.09931 + 0.502238i) q^{59} +(-3.90009 - 6.84044i) q^{60} +(-9.81634 + 2.97775i) q^{61} +(8.51456 - 0.534921i) q^{62} -4.28591i q^{63} +(-2.94098 - 7.43980i) q^{64} -8.10908i q^{65} +(-0.533576 - 8.49315i) q^{66} +(4.02627 - 1.22136i) q^{67} +(1.00036 - 3.65412i) q^{68} +(1.26183 - 0.124280i) q^{69} +(-8.34536 - 22.3566i) q^{70} +(-11.6047 - 7.75400i) q^{71} +(-0.0229781 + 2.82833i) q^{72} +(1.68904 + 2.52783i) q^{73} +(3.79002 - 0.615197i) q^{74} +(4.94995 + 9.26070i) q^{75} +(6.44088 + 6.09836i) q^{76} +(2.52786 - 25.6658i) q^{77} +(-1.46323 + 2.51862i) q^{78} +(-4.52669 - 10.9284i) q^{79} +(5.38737 + 14.7982i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-2.06985 - 2.71266i) q^{82} +(0.813545 + 0.991307i) q^{83} +(-1.44209 + 8.44964i) q^{84} +(-2.16493 + 7.13682i) q^{85} +(-10.6378 + 6.57511i) q^{86} +(5.02615 + 0.999764i) q^{87} +(-1.80578 + 16.9237i) q^{88} +(-0.287119 - 1.44344i) q^{89} +(0.197245 - 5.56438i) q^{90} +(-5.60014 + 6.82379i) q^{91} +(-2.52951 - 0.179557i) q^{92} +(5.32026 + 2.84374i) q^{93} +(9.85604 - 4.82732i) q^{94} +(-12.3466 - 12.3466i) q^{95} +(0.996961 - 5.56831i) q^{96} +(3.16976 - 3.16976i) q^{97} +(-5.20938 + 15.2109i) q^{98} +(2.83658 - 5.30688i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.06073	−	0.935332i	−0.750052	−	0.661379i
$2$	−1.06073	−	0.935332i	−0.750052	−	0.661379i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$4$	0.250309	+	1.98427i	0.125155	+	0.992137i
$5$	−0.385901	−	3.91812i	−0.172580	−	1.75224i	−0.558317	−	0.829628i	$-0.688553\pi$
$5$	−0.385901	−	3.91812i	−0.172580	−	1.75224i	0.385736	−	0.922609i	$-0.373947\pi$
$6$	−0.587142	+	1.28657i	−0.239700	+	0.525240i
$7$	−2.38112	+	3.56360i	−0.899980	+	1.34691i	0.0376543	+	0.999291i	$0.488011\pi$
$7$	−2.38112	+	3.56360i	−0.899980	+	1.34691i	−0.937634	+	0.347624i	$0.886989\pi$
$8$	1.59044	−	2.33891i	0.562307	−	0.826929i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	−3.25540	+	4.51703i	−1.02945	+	1.42841i
$11$	−5.30688	+	2.83658i	−1.60008	+	0.855262i	−0.601682	+	0.798736i	$0.705503\pi$
$11$	−5.30688	+	2.83658i	−1.60008	+	0.855262i	−0.998401	+	0.0565264i	$0.981997\pi$
$12$	1.82617	−	0.815535i	0.527170	−	0.235425i
$13$	2.04975	+	0.201883i	0.568499	+	0.0559922i	0.378183	−	0.925731i	$-0.376549\pi$
$13$	2.04975	+	0.201883i	0.568499	+	0.0559922i	0.190315	+	0.981723i	$0.439049\pi$
$14$	5.85888	−	1.55289i	1.56585	−	0.415027i
$15$	−3.63739	+	1.50666i	−0.939169	+	0.389017i
$16$	−3.87469	+	0.993364i	−0.968673	+	0.248341i
$17$	−1.75009	−	0.724912i	−0.424460	−	0.175817i	0.160220	−	0.987081i	$-0.448780\pi$
$17$	−1.75009	−	0.724912i	−0.424460	−	0.175817i	−0.584680	+	0.811264i	$0.698780\pi$
$18$	1.40161	+	0.188388i	0.330363	+	0.0444035i
$19$	3.42826	−	2.81350i	0.786496	−	0.645461i	−0.152921	−	0.988238i	$-0.548868\pi$
$19$	3.42826	−	2.81350i	0.786496	−	0.645461i	0.939416	+	0.342778i	$0.111368\pi$
$20$	7.67803	−	1.74648i	1.71686	−	0.390524i
$21$	4.10136	+	1.24413i	0.894990	+	0.271492i
$22$	8.28232	+	1.95483i	1.76580	+	0.416771i
$23$	−0.247363	+	1.24358i	−0.0515787	+	0.259304i	−0.997967	−	0.0637264i	$-0.979701\pi$
$23$	−0.247363	+	1.24358i	−0.0515787	+	0.259304i	0.946389	+	0.323030i	$0.104701\pi$
$24$	−2.69988	−	0.843011i	−0.551110	−	0.172079i
$25$	−10.2988	+	2.04856i	−2.05977	+	0.409713i
$26$	−1.98541	−	2.13134i	−0.389371	−	0.417990i
$27$	0.773010	+	0.634393i	0.148766	+	0.122089i
$28$	−7.66718	−	3.83280i	−1.44896	−	0.724331i
$29$	−2.41573	+	4.51951i	−0.448590	+	0.839252i	0.551398	+	0.834242i	$0.314095\pi$
$29$	−2.41573	+	4.51951i	−0.448590	+	0.839252i	−0.999987	+	0.00500979i	$0.998405\pi$
$30$	5.26752	+	1.80400i	0.961713	+	0.329365i
$31$	−4.26568	+	4.26568i	−0.766138	+	0.766138i	−0.977424	−	0.211286i	$-0.932235\pi$
$31$	−4.26568	+	4.26568i	−0.766138	+	0.766138i	0.211286	+	0.977424i	$0.432235\pi$
$32$	5.03914	+	2.57043i	0.890802	+	0.454392i
$33$	4.25495	+	4.25495i	0.740691	+	0.740691i
$34$	1.17835	+	2.40586i	0.202085	+	0.412601i
$35$	14.8815	+	7.95433i	2.51543	+	1.34453i
$36$	−1.31053	−	1.51080i	−0.218421	−	0.251800i
$37$	−1.72240	+	2.09874i	−0.283160	+	0.345031i	−0.895094	−	0.445877i	$-0.852892\pi$
$37$	−1.72240	+	2.09874i	−0.283160	+	0.345031i	0.611934	+	0.790909i	$0.290392\pi$
$38$	−6.26802	−	0.222187i	−1.01681	−	0.0360435i
$39$	−0.401822	−	2.02009i	−0.0643429	−	0.323474i
$40$	−9.77788	−	5.32896i	−1.54602	−	0.842583i
$41$	2.36639	+	0.470705i	0.369569	+	0.0735118i	0.376381	−	0.926465i	$-0.377168\pi$
$41$	2.36639	+	0.470705i	0.369569	+	0.0735118i	−0.00681215	+	0.999977i	$0.502168\pi$
$42$	−3.18677	−	5.15582i	−0.491729	−	0.795561i
$43$	2.56696	−	8.46214i	0.391458	−	1.29046i	−0.510960	−	0.859604i	$-0.670710\pi$
$43$	2.56696	−	8.46214i	0.391458	−	1.29046i	0.902419	−	0.430860i	$-0.141790\pi$
$44$	−6.95692	−	9.82027i	−1.04880	−	1.48046i
$45$	2.49766	+	3.04340i	0.372329	+	0.453684i
$46$	1.42554	−	1.08774i	0.210185	−	0.160378i
$47$	−2.96974	+	7.16958i	−0.433181	+	1.04579i	0.545075	+	0.838388i	$0.316501\pi$
$47$	−2.96974	+	7.16958i	−0.433181	+	1.04579i	−0.978255	+	0.207404i	$0.933499\pi$
$48$	2.07535	+	3.41949i	0.299551	+	0.493561i
$49$	−4.35073	−	10.5036i	−0.621533	−	1.50051i
$50$	12.8404	+	7.45984i	1.81591	+	1.05498i
$51$	−0.185673	+	1.88517i	−0.0259994	+	0.263976i
$52$	0.112481	+	4.11780i	0.0155982	+	0.571036i
$53$	−1.42695	−	2.66964i	−0.196007	−	0.366704i	0.764648	−	0.644448i	$-0.222913\pi$
$53$	−1.42695	−	2.66964i	−0.196007	−	0.366704i	−0.960655	+	0.277745i	$0.910413\pi$
$54$	−0.226590	−	1.39594i	−0.0308349	−	0.189964i
$55$	13.1620	+	19.6983i	1.77476	+	2.65612i
$56$	4.54789	+	11.2369i	0.607738	+	1.50160i
$57$	−3.68752	−	2.46392i	−0.488424	−	0.326354i
$58$	6.78969	−	2.53449i	0.891530	−	0.332794i
$59$	−5.09931	+	0.502238i	−0.663874	+	0.0653858i	−0.424341	−	0.905502i	$-0.639494\pi$
$59$	−5.09931	+	0.502238i	−0.663874	+	0.0653858i	−0.239533	+	0.970888i	$0.576994\pi$
$60$	−3.90009	−	6.84044i	−0.503499	−	0.883098i
$61$	−9.81634	+	2.97775i	−1.25685	+	0.381262i	−0.847344	−	0.531044i	$-0.821800\pi$
$61$	−9.81634	+	2.97775i	−1.25685	+	0.381262i	−0.409509	+	0.912306i	$0.634300\pi$
$62$	8.51456	−	0.534921i	1.08135	−	0.0679351i
$63$		−	4.28591i		−	0.539974i
$64$	−2.94098	−	7.43980i	−0.367622	−	0.929975i
$65$		−	8.10908i		−	1.00581i
$66$	−0.533576	−	8.49315i	−0.0656787	−	1.04543i
$67$	4.02627	−	1.22136i	0.491887	−	0.149212i	−0.0345899	−	0.999402i	$-0.511013\pi$
$67$	4.02627	−	1.22136i	0.491887	−	0.149212i	0.526477	+	0.850189i	$0.323513\pi$
$68$	1.00036	−	3.65412i	0.121312	−	0.443127i
$69$	1.26183	−	0.124280i	0.151907	−	0.0149615i
$70$	−8.34536	−	22.3566i	−0.997462	−	2.67212i
$71$	−11.6047	−	7.75400i	−1.37722	−	0.920231i	−0.377240	−	0.926116i	$-0.623127\pi$
$71$	−11.6047	−	7.75400i	−1.37722	−	0.920231i	−0.999983	+	0.00588476i	$0.998127\pi$
$72$	−0.0229781	+	2.82833i	−0.00270799	+	0.333322i
$73$	1.68904	+	2.52783i	0.197687	+	0.295860i	0.917048	−	0.398777i	$-0.130565\pi$
$73$	1.68904	+	2.52783i	0.197687	+	0.295860i	−0.719361	+	0.694637i	$0.755565\pi$
$74$	3.79002	−	0.615197i	0.440581	−	0.0715152i
$75$	4.94995	+	9.26070i	0.571570	+	1.06933i
$76$	6.44088	+	6.09836i	0.738819	+	0.699530i
$77$	2.52786	−	25.6658i	0.288077	−	2.92489i
$78$	−1.46323	+	2.51862i	−0.165678	+	0.285177i
$79$	−4.52669	−	10.9284i	−0.509292	−	1.22954i	−0.944292	−	0.329109i	$-0.893252\pi$
$79$	−4.52669	−	10.9284i	−0.509292	−	1.22954i	0.435000	−	0.900431i	$-0.356748\pi$
$80$	5.38737	+	14.7982i	0.602326	+	1.65449i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−2.06985	−	2.71266i	−0.228576	−	0.299563i
$83$	0.813545	+	0.991307i	0.0892981	+	0.108810i	0.815743	−	0.578415i	$-0.196329\pi$
$83$	0.813545	+	0.991307i	0.0892981	+	0.108810i	−0.726444	+	0.687225i	$0.758829\pi$
$84$	−1.44209	+	8.44964i	−0.157345	+	0.921931i
$85$	−2.16493	+	7.13682i	−0.234820	+	0.774097i
$86$	−10.6378	+	6.57511i	−1.14710	+	0.709013i
$87$	5.02615	+	0.999764i	0.538860	+	0.107186i
$88$	−1.80578	+	16.9237i	−0.192497	+	1.80407i
$89$	−0.287119	−	1.44344i	−0.0304345	−	0.153005i	0.962580	−	0.270998i	$-0.0873538\pi$
$89$	−0.287119	−	1.44344i	−0.0304345	−	0.153005i	−0.993014	+	0.117994i	$0.962354\pi$
$90$	0.197245	−	5.56438i	0.0207914	−	0.586537i
$91$	−5.60014	+	6.82379i	−0.587054	+	0.715327i
$92$	−2.52951	−	0.179557i	−0.263720	−	0.0187201i
$93$	5.32026	+	2.84374i	0.551685	+	0.294882i
$94$	9.85604	−	4.82732i	1.01657	−	0.497900i
$95$	−12.3466	−	12.3466i	−1.26673	−	1.26673i
$96$	0.996961	−	5.56831i	0.101752	−	0.568313i
$97$	3.16976	−	3.16976i	0.321840	−	0.321840i	−0.527632	−	0.849473i	$-0.676920\pi$
$97$	3.16976	−	3.16976i	0.321840	−	0.321840i	0.849473	+	0.527632i	$0.176920\pi$
$98$	−5.20938	+	15.2109i	−0.526227	+	1.53653i
$99$	2.83658	−	5.30688i	0.285087	−	0.533361i
$100$	−6.64280	−	19.9229i	−0.664280	−	1.99229i
$101$	−9.42536	−	7.73519i	−0.937858	−	0.769680i	0.0354052	−	0.999373i	$-0.488728\pi$
$101$	−9.42536	−	7.73519i	−0.937858	−	0.769680i	−0.973263	+	0.229693i	$0.926228\pi$
$102$	1.96020	−	1.82599i	0.194089	−	0.180800i
$103$	−1.52313	+	0.302970i	−0.150079	+	0.0298525i	−0.269558	−	0.962984i	$-0.586878\pi$
$103$	−1.52313	+	0.302970i	−0.150079	+	0.0298525i	0.119479	+	0.992837i	$0.461878\pi$
$104$	3.73220	−	4.47310i	0.365972	−	0.438623i
$105$	3.29195	−	16.5497i	0.321261	−	1.61509i
$106$	−0.983384	+	4.16645i	−0.0955147	+	0.404682i
$107$	−6.88749	−	2.08930i	−0.665839	−	0.201980i	−0.0607683	−	0.998152i	$-0.519355\pi$
$107$	−6.88749	−	2.08930i	−0.665839	−	0.201980i	−0.605071	+	0.796172i	$0.706855\pi$
$108$	−1.06532	+	1.69266i	−0.102510	+	0.162876i
$109$	−2.46480	+	2.02281i	−0.236085	+	0.193750i	−0.744996	−	0.667069i	$-0.767548\pi$
$109$	−2.46480	+	2.02281i	−0.236085	+	0.193750i	0.508911	+	0.860819i	$0.330048\pi$
$110$	4.46310	−	33.2055i	0.425540	−	3.16602i
$111$	2.50836	+	1.03900i	0.238083	+	0.0986171i
$112$	5.68616	−	16.1732i	0.537291	−	1.52822i
$113$	−7.49356	+	3.10393i	−0.704935	+	0.291994i	−0.706207	−	0.708006i	$-0.749595\pi$
$113$	−7.49356	+	3.10393i	−0.704935	+	0.291994i	0.00127204	+	0.999999i	$0.499595\pi$
$114$	1.60689	+	6.06262i	0.150499	+	0.567816i
$115$	4.96794	+	0.489299i	0.463263	+	0.0456274i
$116$	−9.57263	−	3.66219i	−0.888796	−	0.340026i
$117$	−1.81647	+	0.970921i	−0.167932	+	0.0897617i
$118$	5.87877	+	4.23681i	0.541184	+	0.390030i
$119$	6.75048	−	4.51053i	0.618816	−	0.413480i
$120$	−2.26113	+	10.9038i	−0.206412	+	0.995373i
$121$	14.0054	−	20.9606i	1.27322	−	1.90551i
$122$	13.1977	+	6.02293i	1.19486	+	0.545291i
$123$	−0.236491	−	2.40114i	−0.0213237	−	0.216503i
$124$	−9.53201	−	7.39653i	−0.856000	−	0.664228i
$125$	6.28648	+	20.7238i	0.562280	+	1.85359i
$126$	−4.00874	+	4.54620i	−0.357127	+	0.405008i
$127$	−5.90648			−0.524115			−0.262058	−	0.965052i	$-0.584401\pi$
$127$	−5.90648			−0.524115			−0.262058	+	0.965052i	$0.584401\pi$
$128$	−3.83909	+	10.6424i	−0.339331	+	0.940667i
$129$	−8.84292			−0.778575
$130$	−7.58468	+	8.60157i	−0.665220	+	0.754408i
$131$	−1.79015	−	5.90134i	−0.156406	−	0.515603i	0.843357	−	0.537354i	$-0.180576\pi$
$131$	−1.79015	−	5.90134i	−0.156406	−	0.515603i	−0.999763	+	0.0217508i	$0.993076\pi$
$132$	−7.37793	+	9.50803i	−0.642166	+	0.827568i
$133$	1.86309	+	18.9162i	0.161550	+	1.64024i
$134$	−5.41317	−	2.47037i	−0.467627	−	0.213407i
$135$	2.18732	−	3.27356i	0.188255	−	0.281743i
$136$	−4.47893	+	2.94037i	−0.384065	+	0.252135i
$137$	15.6989	−	10.4897i	1.34125	−	0.896196i	0.342195	−	0.939629i	$-0.388830\pi$
$137$	15.6989	−	10.4897i	1.34125	−	0.896196i	0.999056	+	0.0434332i	$0.0138296\pi$
$138$	−1.45471	−	1.04841i	−0.123833	−	0.0892462i
$139$	−10.4000	+	5.55892i	−0.882118	+	0.471502i	−0.849270	−	0.527959i	$-0.822958\pi$
$139$	−10.4000	+	5.55892i	−0.882118	+	0.471502i	−0.0328476	+	0.999460i	$0.510458\pi$
$140$	−12.0586	+	31.5200i	−1.01914	+	2.66393i
$141$	7.72293	+	0.760642i	0.650388	+	0.0640577i
$142$	5.05691	+	19.0792i	0.424366	+	1.60109i
$143$	−11.4504	+	4.74292i	−0.957533	+	0.396623i
$144$	2.66980	−	2.97861i	0.222484	−	0.248218i
$145$	18.6402	+	7.72103i	1.54799	+	0.641197i
$146$	0.572737	−	4.26117i	0.0474000	−	0.352657i
$147$	−8.78836	+	7.21242i	−0.724851	+	0.594870i
$148$	−4.59562	−	2.89237i	−0.377757	−	0.237751i
$149$	16.0374	+	4.86489i	1.31383	+	0.398547i	0.867998	−	0.496568i	$-0.165407\pi$
$149$	16.0374	+	4.86489i	1.31383	+	0.398547i	0.445835	+	0.895115i	$0.352907\pi$
$150$	3.41125	−	14.4530i	0.278528	−	1.18008i
$151$	0.296647	−	1.49134i	0.0241408	−	0.121364i	−0.966836	−	0.255398i	$-0.917793\pi$
$151$	0.296647	−	1.49134i	0.0241408	−	0.121364i	0.990977	+	0.134035i	$0.0427933\pi$
$152$	−1.12806	−	12.4931i	−0.0914979	−	1.01332i
$153$	1.85789	−	0.369557i	0.150201	−	0.0298769i
$154$	−26.6875	+	24.8602i	−2.15054	+	2.00329i
$155$	18.3596	+	15.0673i	1.47468	+	1.21023i
$156$	3.90784	−	1.30297i	0.312878	−	0.104321i
$157$	−1.63350	+	3.05606i	−0.130367	+	0.243900i	−0.938633	−	0.344918i	$-0.887907\pi$
$157$	−1.63350	+	3.05606i	−0.130367	+	0.243900i	0.808265	+	0.588818i	$0.200407\pi$
$158$	−5.42006	+	15.8261i	−0.431197	+	1.25905i
$159$	−2.14047	+	2.14047i	−0.169750	+	0.169750i
$160$	8.12663	−	20.7359i	0.642467	−	1.63932i
$161$	−3.84261	−	3.84261i	−0.302840	−	0.302840i
$162$	−1.27006	+	0.622054i	−0.0997852	+	0.0488731i
$163$	19.8076	+	10.5874i	1.55145	+	0.829268i	0.999988	−	0.00493066i	$-0.00156948\pi$
$163$	19.8076	+	10.5874i	1.55145	+	0.829268i	0.551464	+	0.834199i	$0.314069\pi$
$164$	−0.341678	+	4.81340i	−0.0266806	+	0.375863i
$165$	15.0294	−	18.3134i	1.17004	−	1.42569i
$166$	0.0642472	−	1.81245i	0.00498655	−	0.140673i
$167$	0.199796	+	1.00444i	0.0154606	+	0.0777259i	0.987745	−	0.156074i	$-0.0498839\pi$
$167$	0.199796	+	1.00444i	0.0154606	+	0.0777259i	−0.972285	+	0.233800i	$0.924884\pi$
$168$	9.43289	−	7.61397i	0.727763	−	0.587431i
$169$	−8.58949	−	1.70855i	−0.660730	−	0.131427i
$170$	8.97171	−	5.54533i	0.688099	−	0.425308i
$171$	−1.28740	+	4.24397i	−0.0984496	+	0.324545i
$172$	17.4337	+	2.97541i	1.32931	+	0.226873i
$173$	3.73861	+	4.55551i	0.284241	+	0.346349i	0.895484	−	0.445094i	$-0.146830\pi$
$173$	3.73861	+	4.55551i	0.284241	+	0.346349i	−0.611242	+	0.791444i	$0.709330\pi$
$174$	−4.39629	−	5.76160i	−0.333282	−	0.436786i
$175$	17.2225	−	41.5788i	1.30190	−	3.14306i
$176$	17.7447	−	16.2625i	1.33756	−	1.22584i
$177$	1.96086	+	4.73394i	0.147388	+	0.355825i
$178$	−1.04554	+	1.79966i	−0.0783667	+	0.134890i
$179$	−0.341828	+	3.47064i	−0.0255494	+	0.259407i	0.973922	+	0.226885i	$0.0728541\pi$
$179$	−0.341828	+	3.47064i	−0.0255494	+	0.259407i	−0.999471	+	0.0325226i	$0.989646\pi$
$180$	−5.41376	+	5.71783i	−0.403518	+	0.426182i
$181$	−1.40056	−	2.62026i	−0.104103	−	0.194762i	0.824477	−	0.565895i	$-0.191469\pi$
$181$	−1.40056	−	2.62026i	−0.104103	−	0.194762i	−0.928580	+	0.371133i	$0.878969\pi$
$182$	12.3228	−	2.00023i	0.913424	−	0.148267i
$183$	5.69907	+	8.52925i	0.421287	+	0.630501i
$184$	2.51519	+	2.55640i	0.185423	+	0.188460i
$185$	8.88781	+	5.93864i	0.653445	+	0.436618i
$186$	−2.98354	−	7.99265i	−0.218763	−	0.586050i
$187$	11.3438	−	1.11727i	0.829541	−	0.0817026i
$188$	−14.9698	−	4.09816i	−1.09178	−	0.298889i
$189$	−4.10136	+	1.24413i	−0.298330	+	0.0904974i
$190$	1.54828	+	24.6446i	0.112324	+	1.78791i
$191$			22.6909i			1.64186i	0.571032	+	0.820928i	$0.306543\pi$
$191$			22.6909i			1.64186i	−0.571032	+	0.820928i	$0.693457\pi$
$192$	−6.26573	+	4.97400i	−0.452190	+	0.358968i
$193$			17.6389i			1.26968i	0.772645	+	0.634838i	$0.218933\pi$
$193$			17.6389i			1.26968i	−0.772645	+	0.634838i	$0.781067\pi$
$194$	−6.32705	+	0.397492i	−0.454256	+	0.0285383i
$195$	−7.75991	+	2.35394i	−0.555698	+	0.168569i
$196$	19.7530	−	11.2622i	1.41093	−	0.804442i
$197$	−9.78937	+	0.964169i	−0.697464	+	0.0686942i	−0.440534	−	0.897736i	$-0.645211\pi$
$197$	−9.78937	+	0.964169i	−0.697464	+	0.0686942i	−0.256930	+	0.966430i	$0.582711\pi$
$198$	−7.97255	+	2.97603i	−0.566584	+	0.211497i
$199$	−0.0856110	−	0.0572035i	−0.00606880	−	0.00405505i	0.552532	−	0.833492i	$-0.313662\pi$
$199$	−0.0856110	−	0.0572035i	−0.00606880	−	0.00405505i	−0.558601	+	0.829437i	$0.688662\pi$
$200$	−11.5883	+	27.3461i	−0.819417	+	1.93366i
$201$	−2.33753	−	3.49836i	−0.164877	−	0.246755i
$202$	2.76282	+	17.0208i	0.194391	+	1.19758i
$203$	−10.3536	−	19.3702i	−0.726680	−	1.35952i
$204$	−3.78716	+	0.103449i	−0.265154	+	0.00724287i
$205$	0.931085	−	9.45347i	0.0650298	−	0.660259i
$206$	1.89902	+	1.10326i	0.132311	+	0.0768681i
$207$	−0.485219	−	1.17142i	−0.0337251	−	0.0814196i
$208$	−8.14270	+	1.25392i	−0.564594	+	0.0869434i
$209$	−10.2126	+	24.6554i	−0.706421	+	1.70545i
$210$	−18.9714	+	14.4758i	−1.30915	+	0.998924i
$211$	−15.7623	−	19.2064i	−1.08512	−	1.32222i	−0.943155	−	0.332354i	$-0.892157\pi$
$211$	−15.7623	−	19.2064i	−1.08512	−	1.32222i	−0.141967	−	0.989871i	$-0.545343\pi$
$212$	4.94012	−	3.49970i	0.339289	−	0.240361i
$213$	−4.05146	+	13.3559i	−0.277601	+	0.915128i
$214$	5.35160	+	8.65828i	0.365828	+	0.591868i
$215$	−34.1463	−	6.79212i	−2.32876	−	0.463219i
$216$	2.71322	−	0.799033i	0.184611	−	0.0543673i
$217$	−5.04407	−	25.3583i	−0.342414	−	1.72143i
$218$	4.50649	+	0.159745i	0.305218	+	0.0108193i
$219$	1.92868	−	2.35010i	0.130328	−	0.158805i
$220$	−35.7923	+	31.0477i	−2.41312	+	2.09324i
$221$	−3.44091	−	1.83920i	−0.231461	−	0.123718i
$222$	−1.68889	−	3.44824i	−0.113351	−	0.231431i
$223$	19.7603	+	19.7603i	1.32325	+	1.32325i	0.911131	+	0.412116i	$0.135210\pi$
$223$	19.7603	+	19.7603i	1.32325	+	1.32325i	0.412116	+	0.911131i	$0.364790\pi$
$224$	−21.1588	+	11.8370i	−1.41373	+	0.790891i
$225$	7.42504	−	7.42504i	0.495003	−	0.495003i
$226$	10.8519	+	3.71652i	0.721856	+	0.247219i
$227$	6.31927	−	11.8225i	0.419425	−	0.784689i	−0.580130	−	0.814524i	$-0.696998\pi$
$227$	6.31927	−	11.8225i	0.419425	−	0.784689i	0.999555	+	0.0298353i	$0.00949827\pi$
$228$	3.96608	−	7.93379i	0.262660	−	0.525428i
$229$	−6.98571	−	5.73302i	−0.461629	−	0.378849i	0.374639	−	0.927171i	$-0.377767\pi$
$229$	−6.98571	−	5.73302i	−0.461629	−	0.378849i	−0.836267	+	0.548322i	$0.815267\pi$
$230$	−4.81200	−	5.16569i	−0.317294	−	0.340615i
$231$	−25.2945	+	5.03138i	−1.66425	+	0.331041i
$232$	6.72864	+	12.8382i	0.441757	+	0.842869i
$233$	0.862489	−	4.33602i	0.0565035	−	0.284062i	−0.942195	−	0.335065i	$-0.891242\pi$
$233$	0.862489	−	4.33602i	0.0565035	−	0.284062i	0.998699	+	0.0510027i	$0.0162417\pi$
$234$	2.83492	+	0.669110i	0.185324	+	0.0437411i
$235$	29.2373	+	8.86904i	1.90723	+	0.578553i
$236$	−2.27298	−	9.99272i	−0.147959	−	0.650470i
$237$	−9.14379	+	7.50411i	−0.593953	+	0.487445i
$238$	−11.3793	−	1.52947i	−0.737611	−	0.0991411i
$239$	8.03761	+	3.32929i	0.519910	+	0.215354i	0.627177	−	0.778877i	$-0.284210\pi$
$239$	8.03761	+	3.32929i	0.519910	+	0.215354i	−0.107268	+	0.994230i	$0.534210\pi$
$240$	12.5971	−	9.45107i	0.813139	−	0.610064i
$241$	−3.50390	+	1.45136i	−0.225706	+	0.0934905i	−0.492671	−	0.870216i	$-0.663979\pi$
$241$	−3.50390	+	1.45136i	−0.225706	+	0.0934905i	0.266965	+	0.963706i	$0.413979\pi$
$242$	−34.4612	+	9.13389i	−2.21525	+	0.587149i
$243$	−0.995185	−	0.0980171i	−0.0638411	−	0.00628780i
$244$	−8.36580	−	18.7330i	−0.535565	−	1.19925i
$245$	−39.4754	+	21.1000i	−2.52199	+	1.34803i
$246$	−1.99501	+	2.76816i	−0.127197	+	0.176492i
$247$	7.59507	−	5.07486i	0.483263	−	0.322906i
$248$	3.19270	+	16.7613i	0.202737	+	1.06435i
$249$	0.712462	−	1.06628i	0.0451505	−	0.0675724i
$250$	12.7153	−	27.8623i	0.804187	−	1.76217i
$251$	−1.45410	−	14.7637i	−0.0917818	−	0.931877i	−0.925262	−	0.379328i	$-0.876155\pi$
$251$	−1.45410	−	14.7637i	−0.0917818	−	0.931877i	0.833481	−	0.552549i	$-0.186345\pi$
$252$	8.50442	−	1.07280i	0.535728	−	0.0675802i
$253$	−2.21479	−	7.30117i	−0.139242	−	0.459021i
$254$	6.26520	+	5.52452i	0.393113	+	0.346639i
$255$	7.45796			0.467035
$256$	14.0265	−	7.69796i	0.876653	−	0.481122i
$257$	−7.32702			−0.457047			−0.228524	−	0.973538i	$-0.573390\pi$
$257$	−7.32702			−0.457047			−0.228524	+	0.973538i	$0.573390\pi$
$258$	9.37997	+	8.27106i	0.583972	+	0.514934i
$259$	−3.37786	−	11.1353i	−0.209890	−	0.691914i
$260$	16.0906	−	2.02978i	0.997899	−	0.125881i
$261$	−0.502301	−	5.09994i	−0.0310916	−	0.315679i
$262$	−3.62084	+	7.93414i	−0.223696	+	0.490173i
$263$	−1.30294	+	1.94999i	−0.0803427	+	0.120241i	−0.869465	−	0.493995i	$-0.835536\pi$
$263$	−1.30294	+	1.94999i	−0.0803427	+	0.120241i	0.789122	+	0.614237i	$0.210536\pi$
$264$	16.7192	−	3.18467i	1.02899	−	0.196003i
$265$	−9.90932	+	6.62119i	−0.608725	+	0.406737i
$266$	15.7167	−	21.8077i	0.963653	−	1.33711i
$267$	−1.29794	+	0.693765i	−0.0794328	+	0.0424577i
$268$	3.43132	+	7.68351i	0.209601	+	0.469345i
$269$	24.8939	+	2.45184i	1.51781	+	0.149491i	0.822312	−	0.569037i	$-0.192684\pi$
$269$	24.8939	+	2.45184i	1.51781	+	0.149491i	0.695498	+	0.718528i	$0.255184\pi$
$270$	−5.38203	+	1.42650i	−0.327540	+	0.0868141i
$271$	−2.90105	+	1.20165i	−0.176226	+	0.0729953i	−0.469052	−	0.883171i	$-0.655404\pi$
$271$	−2.90105	+	1.20165i	−0.176226	+	0.0729953i	0.292826	+	0.956166i	$0.405404\pi$
$272$	7.50117	+	1.07033i	0.454825	+	0.0648983i
$273$	8.15559	+	3.37816i	0.493599	+	0.204455i
$274$	−26.4637	−	3.55695i	−1.59873	−	0.214883i
$275$	48.8437	−	40.0850i	2.94538	−	2.41721i
$276$	0.562454	+	2.47272i	0.0338557	+	0.148840i
$277$	−7.72290	−	2.34272i	−0.464024	−	0.140760i	0.0496116	−	0.998769i	$-0.484202\pi$
$277$	−7.72290	−	2.34272i	−0.464024	−	0.140760i	−0.513636	+	0.858008i	$0.671702\pi$
$278$	16.2311	+	3.83093i	0.973475	+	0.229764i
$279$	1.17690	−	5.91666i	0.0704590	−	0.354221i
$280$	42.2726	−	22.1555i	2.52627	−	1.32405i
$281$	−4.98157	+	0.990895i	−0.297175	+	0.0591118i	−0.341426	−	0.939909i	$-0.610910\pi$
$281$	−4.98157	+	0.990895i	−0.297175	+	0.0591118i	0.0442508	+	0.999020i	$0.485910\pi$
$282$	−7.48052	−	8.03034i	−0.445458	−	0.478200i
$283$	4.01292	+	3.29332i	0.238543	+	0.195768i	0.746068	−	0.665870i	$-0.231939\pi$
$283$	4.01292	+	3.29332i	0.238543	+	0.195768i	−0.507525	+	0.861637i	$0.669439\pi$
$284$	12.4813	−	24.9678i	0.740629	−	1.48157i
$285$	−8.23093	+	15.3990i	−0.487558	+	0.912157i
$286$	16.5821	+	5.67898i	0.980518	+	0.335805i
$287$	−7.31208	+	7.31208i	−0.431619	+	0.431619i
$288$	−5.61794	+	0.662363i	−0.331040	+	0.0390301i
$289$	−9.48349	−	9.48349i	−0.557852	−	0.557852i
$290$	−12.5506	−	25.6248i	−0.736995	−	1.50474i
$291$	−3.95340	−	2.11314i	−0.231753	−	0.123874i
$292$	−4.59313	+	3.98426i	−0.268792	+	0.233161i
$293$	2.28119	−	2.77963i	0.133268	−	0.162388i	−0.702100	−	0.712078i	$-0.747754\pi$
$293$	2.28119	−	2.77963i	0.133268	−	0.162388i	0.835369	+	0.549690i	$0.185254\pi$
$294$	16.0681	+	0.569579i	0.937111	+	0.0332185i
$295$	3.93566	+	19.7859i	0.229143	+	1.15198i
$296$	2.16940	+	7.36646i	0.126094	+	0.428167i
$297$	−5.90178	−	1.17394i	−0.342456	−	0.0681187i
$298$	−12.4611	−	20.1606i	−0.721852	−	1.16787i
$299$	−0.758089	+	2.49908i	−0.0438414	+	0.144526i
$300$	−17.1367	+	12.1401i	−0.989391	+	0.700908i
$301$	24.0435	+	29.2970i	1.38584	+	1.68865i
$302$	−1.70956	+	1.30445i	−0.0983744	+	0.0750629i
$303$	−4.66608	+	11.2649i	−0.268059	+	0.647152i
$304$	−10.4886	+	14.3069i	−0.601563	+	0.820559i
$305$	15.4553	+	37.3125i	0.884970	+	2.13651i
$306$	−2.31638	−	1.34574i	−0.132419	−	0.0769309i
$307$	1.97109	−	20.0128i	0.112496	−	1.14219i	−0.758763	−	0.651367i	$-0.774196\pi$
$307$	1.97109	−	20.0128i	0.112496	−	1.14219i	0.871259	−	0.490824i	$-0.163304\pi$
$308$	51.5608	−	1.40842i	2.93795	−	0.0802521i
$309$	0.732067	+	1.36960i	0.0416458	+	0.0779138i
$310$	−5.38167	−	33.1547i	−0.305658	−	1.88306i
$311$	11.9550	+	17.8919i	0.677906	+	1.01456i	0.997747	+	0.0670872i	$0.0213706\pi$
$311$	11.9550	+	17.8919i	0.677906	+	1.01456i	−0.319841	+	0.947471i	$0.603629\pi$
$312$	−5.36389	−	2.27302i	−0.303670	−	0.128684i
$313$	16.9413	+	11.3198i	0.957580	+	0.639834i	0.933005	−	0.359864i	$-0.117177\pi$
$313$	16.9413	+	11.3198i	0.957580	+	0.639834i	0.0245748	+	0.999698i	$0.492177\pi$
$314$	4.59114	−	1.71380i	0.259093	−	0.0967155i
$315$	−16.7927	+	1.65394i	−0.946162	+	0.0931888i
$316$	20.5519	−	11.7177i	1.15613	−	0.659170i
$317$	7.66314	−	2.32459i	0.430405	−	0.130562i	−0.0676466	−	0.997709i	$-0.521549\pi$
$317$	7.66314	−	2.32459i	0.430405	−	0.130562i	0.498051	+	0.867147i	$0.334049\pi$
$318$	4.27251	−	0.268417i	0.239590	−	0.0150521i
$319$		−	30.8369i		−	1.72654i
$320$	−28.0151	+	14.3941i	−1.56609	+	0.804657i
$321$			7.19741i			0.401720i
$322$	0.481868	+	7.67010i	0.0268535	+	0.427438i
$323$	−8.03931	+	2.43870i	−0.447319	+	0.135693i
$324$	1.92902	+	0.528093i	0.107168	+	0.0293385i
$325$	−21.5236	+	2.11989i	−1.19391	+	0.117590i
$326$	−11.1079	−	29.7571i	−0.615208	−	1.64809i
$327$	2.65120	+	1.77148i	0.146612	+	0.0979628i
$328$	4.86455	−	4.78615i	0.268600	−	0.264271i
$329$	−18.4782	−	27.6546i	−1.01874	−	1.52465i
$330$	−33.0713	+	5.36813i	−1.82051	+	0.295506i
$331$	−1.68119	−	3.14528i	−0.0924065	−	0.172880i	0.831472	−	0.555567i	$-0.187499\pi$
$331$	−1.68119	−	3.14528i	−0.0924065	−	0.172880i	−0.923878	+	0.382687i	$0.874999\pi$
$332$	−1.76339	+	1.86243i	−0.0967785	+	0.102214i
$333$	0.266119	−	2.70195i	0.0145832	−	0.148066i
$334$	0.727555	−	1.25232i	0.0398100	−	0.0685238i
$335$	−6.33916	−	15.3041i	−0.346346	−	0.836152i
$336$	−17.1274	−	0.746489i	−0.934375	−	0.0407243i
$337$	−3.83443	+	9.25712i	−0.208874	+	0.504268i	−0.993247	−	0.116023i	$-0.962985\pi$
$337$	−3.83443	+	9.25712i	−0.208874	+	0.504268i	0.784372	+	0.620291i	$0.212985\pi$
$338$	7.51309	+	9.84634i	0.408658	+	0.535570i
$339$	5.14554	+	6.26986i	0.279468	+	0.340532i
$340$	−14.7033	−	2.50941i	−0.797399	−	0.136092i
$341$	10.5375	−	34.7374i	0.570635	−	1.88113i
$342$	5.33511	−	3.29758i	0.288490	−	0.178313i
$343$	18.3653	+	3.65309i	0.991635	+	0.197248i
$344$	−15.7096	−	19.4625i	−0.847003	−	1.04934i
$345$	−0.973887	−	4.89606i	−0.0524323	−	0.263595i
$346$	0.295245	−	8.32902i	0.0158725	−	0.447771i
$347$	9.69494	−	11.8133i	0.520452	−	0.634172i	−0.444757	−	0.895651i	$-0.646710\pi$
$347$	9.69494	−	11.8133i	0.520452	−	0.634172i	0.965209	+	0.261479i	$0.0842101\pi$
$348$	−0.725714	+	10.2235i	−0.0389023	+	0.548038i
$349$	13.8204	+	7.38714i	0.739787	+	0.395424i	0.797824	−	0.602890i	$-0.205984\pi$
$349$	13.8204	+	7.38714i	0.739787	+	0.395424i	−0.0580372	+	0.998314i	$0.518484\pi$
$350$	−57.1584	+	27.9953i	−3.05525	+	1.49641i
$351$	1.45641	+	1.45641i	0.0777372	+	0.0777372i
$352$	−34.0333	+	0.653002i	−1.81398	+	0.0348051i
$353$	21.6434	−	21.6434i	1.15196	−	1.15196i	0.165804	−	0.986159i	$-0.446978\pi$
$353$	21.6434	−	21.6434i	1.15196	−	1.15196i	0.986159	−	0.165804i	$-0.0530218\pi$
$354$	2.34785	−	6.85551i	0.124787	−	0.364366i
$355$	−25.9029	+	48.4608i	−1.37478	+	2.57203i
$356$	2.79232	−	0.931030i	0.147993	−	0.0493445i
$357$	−6.27587	−	5.15047i	−0.332154	−	0.272592i
$358$	3.60878	−	3.36170i	0.190730	−	0.177671i
$359$	−3.61895	+	0.719853i	−0.191001	+	0.0379924i	−0.289664	−	0.957129i	$-0.593543\pi$
$359$	−3.61895	+	0.719853i	−0.191001	+	0.0379924i	0.0986629	+	0.995121i	$0.468543\pi$
$360$	11.0906	−	1.00143i	0.584527	−	0.0527798i
$361$	0.130459	−	0.655860i	0.00686624	−	0.0345189i
$362$	−0.965194	+	4.08938i	−0.0507295	+	0.214933i
$363$	−24.1236	−	7.31782i	−1.26616	−	0.384086i
$364$	−14.9420	−	9.40416i	−0.783176	−	0.492912i
$365$	9.25254	−	7.59336i	0.484300	−	0.397455i
$366$	1.93249	−	14.3778i	0.101013	−	0.751538i
$367$	2.16481	+	0.896692i	0.113002	+	0.0468070i	0.438468	−	0.898747i	$-0.355521\pi$
$367$	2.16481	+	0.896692i	0.113002	+	0.0468070i	−0.325466	+	0.945554i	$0.605521\pi$
$368$	−0.276870	−	5.06420i	−0.0144329	−	0.263989i
$369$	−2.22910	+	0.923321i	−0.116042	+	0.0480662i
$370$	−3.87299	−	14.6124i	−0.201347	−	0.759661i
$371$	12.9113	+	1.27165i	0.670321	+	0.0660208i
$372$	−4.31104	+	11.2687i	−0.223517	+	0.584253i
$373$	5.02978	−	2.68847i	0.260432	−	0.139204i	−0.336014	−	0.941857i	$-0.609079\pi$
$373$	5.02978	−	2.68847i	0.260432	−	0.139204i	0.596446	+	0.802653i	$0.296579\pi$
$374$	−13.0778	−	9.42509i	−0.676235	−	0.487360i
$375$	18.0065	−	12.0316i	0.929853	−	0.621308i
$376$	12.0458	+	18.3488i	0.621214	+	0.946265i
$377$	−5.86406	+	8.77618i	−0.302014	+	0.451996i
$378$	5.51412	+	2.51644i	0.283616	+	0.129432i
$379$	1.09708	+	11.1388i	0.0563530	+	0.572162i	0.981356	+	0.192201i	$0.0615625\pi$
$379$	1.09708	+	11.1388i	0.0563530	+	0.572162i	−0.925003	+	0.379961i	$0.875938\pi$
$380$	21.4086	−	27.5895i	1.09824	−	1.41531i
$381$	1.71456	+	5.65215i	0.0878396	+	0.289568i
$382$	21.2235	−	24.0690i	1.08589	−	1.23148i
$383$	−36.9339			−1.88723			−0.943616	−	0.331042i	$-0.892600\pi$
$383$	−36.9339			−1.88723			−0.943616	+	0.331042i	$0.892600\pi$
$384$	11.2986	+	0.584444i	0.576579	+	0.0298248i
$385$	−101.537			−5.17482
$386$	16.4982	−	18.7102i	0.839738	−	0.952323i
$387$	2.56696	+	8.46214i	0.130486	+	0.430155i
$388$	7.08310	+	5.49625i	0.359590	+	0.279030i
$389$	1.66545	+	16.9096i	0.0844417	+	0.857351i	0.940347	+	0.340218i	$0.110501\pi$
$389$	1.66545	+	16.9096i	0.0844417	+	0.857351i	−0.855905	+	0.517133i	$0.826999\pi$
$390$	10.4329	+	4.76118i	0.528291	+	0.241092i
$391$	1.33439	−	1.99706i	0.0674831	−	0.100996i
$392$	−31.4865	−	6.52941i	−1.59031	−	0.329785i
$393$	−5.12758	+	3.42614i	−0.258652	+	0.172826i
$394$	11.2857	+	8.13359i	0.568567	+	0.409764i
$395$	−41.0719	+	21.9534i	−2.06655	+	1.10459i
$396$	11.2403	+	4.30020i	0.564847	+	0.216093i
$397$	37.8228	+	3.72522i	1.89827	+	0.186964i	0.978607	−	0.205738i	$-0.0659596\pi$
$397$	37.8228	+	3.72522i	1.89827	+	0.186964i	0.919666	+	0.392702i	$0.128460\pi$
$398$	0.0373062	+	0.140752i	0.00186999	+	0.00705528i
$399$	17.5609	−	7.27395i	0.879143	−	0.364153i
$400$	37.8698	−	18.1680i	1.89349	−	0.908402i
$401$	4.60807	+	1.90872i	0.230116	+	0.0953171i	0.494762	−	0.869028i	$-0.335255\pi$
$401$	4.60807	+	1.90872i	0.230116	+	0.0953171i	−0.264646	+	0.964346i	$0.585255\pi$
$402$	−0.792633	+	5.89719i	−0.0395329	+	0.294125i
$403$	−9.60474	+	7.88241i	−0.478446	+	0.392651i
$404$	12.9895	−	20.6387i	0.646251	−	1.02681i
$405$	−3.76755	−	1.14287i	−0.187211	−	0.0567899i
$406$	−7.13517	+	30.2307i	−0.354113	+	1.50032i
$407$	3.18727	−	16.0235i	0.157987	−	0.794255i
$408$	4.11393	+	3.43252i	0.203670	+	0.169935i
$409$	−3.46210	+	0.688654i	−0.171190	+	0.0340517i	−0.279941	−	0.960017i	$-0.590315\pi$
$409$	−3.46210	+	0.688654i	−0.171190	+	0.0340517i	0.108751	+	0.994069i	$0.465315\pi$
$410$	−9.82976	+	9.15673i	−0.485457	+	0.452219i
$411$	−14.5952	−	11.9780i	−0.719927	−	0.590829i
$412$	−0.982430	−	2.94648i	−0.0484009	−	0.145163i
$413$	10.3523	−	19.3678i	0.509404	−	0.953027i
$414$	−0.580981	+	1.69641i	−0.0285537	+	0.0833739i
$415$	3.57011	−	3.57011i	0.175250	−	0.175250i
$416$	9.81005	+	6.28605i	0.480977	+	0.308199i
$417$	8.33852	+	8.33852i	0.408339	+	0.408339i
$418$	33.8938	−	16.6006i	1.65780	−	0.811964i
$419$	−27.5810	−	14.7423i	−1.34742	−	0.720210i	−0.369507	−	0.929228i	$-0.620473\pi$
$419$	−27.5810	−	14.7423i	−1.34742	−	0.720210i	−0.977912	+	0.209017i	$0.932973\pi$
$420$	33.6632	+	2.38957i	1.64260	+	0.116599i
$421$	−14.5330	+	17.7085i	−0.708296	+	0.863061i	−0.995495	−	0.0948097i	$-0.969776\pi$
$421$	−14.5330	+	17.7085i	−0.708296	+	0.863061i	0.287199	+	0.957871i	$0.407276\pi$
$422$	−1.24478	+	35.1159i	−0.0605949	+	1.70941i
$423$	−1.51396	−	7.61119i	−0.0736112	−	0.370069i
$424$	−8.51353	−	0.908403i	−0.413454	−	0.0441159i
$425$	19.5089	+	3.88057i	0.946322	+	0.188235i
$426$	16.7897	−	10.3775i	0.813462	−	0.502794i
$427$	12.7624	−	42.0719i	0.617615	−	2.03600i
$428$	2.42174	−	14.1896i	0.117059	−	0.685882i
$429$	7.86258	+	9.58058i	0.379609	+	0.462555i
$430$	29.8672	+	39.1427i	1.44033	+	1.88763i
$431$	−8.93866	+	21.5798i	−0.430560	+	1.03946i	0.548547	+	0.836119i	$0.315181\pi$
$431$	−8.93866	+	21.5798i	−0.430560	+	1.03946i	−0.979107	+	0.203344i	$0.934819\pi$
$432$	−3.62536	−	1.69020i	−0.174425	−	0.0813196i
$433$	−8.34537	−	20.1475i	−0.401053	−	0.968227i	−0.987411	−	0.158175i	$-0.949439\pi$
$433$	−8.34537	−	20.1475i	−0.401053	−	0.968227i	0.586358	−	0.810052i	$-0.300561\pi$
$434$	−18.3680	+	31.6162i	−0.881691	+	1.51763i
$435$	1.97760	−	20.0789i	0.0948185	−	0.962709i
$436$	−4.63077	−	4.38451i	−0.221774	−	0.209980i
$437$	2.65078	+	4.95925i	0.126804	+	0.237233i
$438$	−4.24394	+	0.688877i	−0.202783	+	0.0329158i
$439$	−19.4738	−	29.1446i	−0.929432	−	1.39099i	−0.920376	−	0.391035i	$-0.872117\pi$
$439$	−19.4738	−	29.1446i	−0.929432	−	1.39099i	−0.00905616	−	0.999959i	$-0.502883\pi$
$440$	67.0060	+	0.544374i	3.19439	+	0.0259520i
$441$	9.45298	+	6.31628i	0.450142	+	0.300775i
$442$	1.92962	+	5.16929i	0.0917826	+	0.245878i
$443$	−17.1558	+	1.68969i	−0.815094	+	0.0802798i	−0.496968	−	0.867769i	$-0.665554\pi$
$443$	−17.1558	+	1.68969i	−0.815094	+	0.0802798i	−0.318126	+	0.948048i	$0.603054\pi$
$444$	−1.43379	+	5.23734i	−0.0680446	+	0.248553i
$445$	−5.54479	+	1.68199i	−0.262848	+	0.0797341i
$446$	−2.47797	−	39.4428i	−0.117335	−	1.86767i
$447$		−	16.7590i		−	0.792674i
$448$	33.5153	+	7.23460i	1.58345	+	0.341803i
$449$			20.9244i			0.987485i	0.869608	+	0.493743i	$0.164371\pi$
$449$			20.9244i			0.987485i	−0.869608	+	0.493743i	$0.835629\pi$
$450$	−14.8209	+	0.931110i	−0.698662	+	0.0438929i
$451$	−13.8934	+	4.21450i	−0.654213	+	0.198453i
$452$	−8.03476	−	14.0923i	−0.377923	−	0.662848i
$453$	−1.51324	+	0.149041i	−0.0710982	+	0.00700256i
$454$	−17.7610	+	6.62993i	−0.833567	+	0.311158i
$455$	28.8975	+	19.3087i	1.35474	+	0.905206i
$456$	−11.6277	+	4.70604i	−0.544516	+	0.220380i
$457$	6.11647	+	9.15394i	0.286116	+	0.428203i	0.946490	−	0.322734i	$-0.104602\pi$
$457$	6.11647	+	9.15394i	0.286116	+	0.428203i	−0.660373	+	0.750937i	$0.729602\pi$
$458$	2.04769	+	12.6152i	0.0956825	+	0.589468i
$459$	−0.892961	−	1.67061i	−0.0416798	−	0.0779775i
$460$	0.272617	+	9.98023i	0.0127108	+	0.465331i
$461$	−1.70166	+	17.2772i	−0.0792542	+	0.804681i	0.870601	+	0.491990i	$0.163730\pi$
$461$	−1.70166	+	17.2772i	−0.0792542	+	0.804681i	−0.949855	+	0.312691i	$0.898770\pi$
$462$	31.5367	+	18.3218i	1.46722	+	0.852406i
$463$	−12.7872	−	30.8709i	−0.594270	−	1.43469i	−0.879343	−	0.476188i	$-0.842018\pi$
$463$	−12.7872	−	30.8709i	−0.594270	−	1.43469i	0.285074	−	0.958506i	$-0.407982\pi$
$464$	4.87068	−	19.9114i	0.226116	−	0.924364i
$465$	9.08901	−	21.9428i	0.421493	−	1.01757i
$466$	−4.97049	+	3.79265i	−0.230254	+	0.175691i
$467$	12.0927	+	14.7350i	0.559583	+	0.681853i	0.973559	−	0.228434i	$-0.0733606\pi$
$467$	12.0927	+	14.7350i	0.559583	+	0.681853i	−0.413977	+	0.910287i	$0.635861\pi$
$468$	−2.38125	−	3.36134i	−0.110073	−	0.155378i
$469$	−5.23462	+	17.2562i	−0.241712	+	0.796819i
$470$	−22.7175	−	36.7543i	−1.04788	−	1.69535i
$471$	3.39865	+	0.676033i	0.156601	+	0.0311500i
$472$	−6.93548	+	12.7256i	−0.319231	+	0.585743i
$473$	10.3810	+	52.1889i	0.477320	+	2.39965i
$474$	16.7180	+	0.592614i	0.767881	+	0.0272197i
$475$	−29.5434	+	35.9987i	−1.35554	+	1.65173i
$476$	10.6398	+	12.2658i	0.487676	+	0.562201i
$477$	2.66964	+	1.42695i	0.122235	+	0.0653357i
$478$	−5.41177	−	11.0493i	−0.247529	−	0.505384i
$479$	9.77776	+	9.77776i	0.446757	+	0.446757i	0.894275	−	0.447518i	$-0.147692\pi$
$479$	9.77776	+	9.77776i	0.446757	+	0.446757i	−0.447518	+	0.894275i	$0.647692\pi$
$480$	−22.2020	−	1.75739i	−1.01338	−	0.0802137i
$481$	−3.95418	+	3.95418i	−0.180295	+	0.180295i
$482$	5.07421	+	1.73780i	0.231124	+	0.0791546i
$483$	−2.56170	+	4.79260i	−0.116561	+	0.218071i
$484$	45.0973	+	22.5440i	2.04988	+	1.02473i
$485$	−13.6427	−	11.1963i	−0.619484	−	0.508397i
$486$	0.963947	+	1.03480i	0.0437255	+	0.0469394i
$487$	−15.8131	+	3.14542i	−0.716560	+	0.142533i	−0.539888	−	0.841737i	$-0.681533\pi$
$487$	−15.8131	+	3.14542i	−0.716560	+	0.142533i	−0.176672	+	0.984270i	$0.556533\pi$
$488$	−8.64764	+	27.6955i	−0.391460	+	1.25371i
$489$	4.38165	−	22.0281i	0.198145	−	0.996143i
$490$	61.6084	+	14.5411i	2.78318	+	0.656899i
$491$	22.9572	+	6.96400i	1.03605	+	0.314281i	0.762097	−	0.647463i	$-0.224170\pi$
$491$	22.9572	+	6.96400i	1.03605	+	0.314281i	0.273949	+	0.961744i	$0.411670\pi$
$492$	4.70532	−	1.07029i	0.212132	−	0.0482524i
$493$	7.50400	−	6.15837i	0.337963	−	0.277359i
$494$	−12.8030	−	1.72083i	−0.576035	−	0.0774240i
$495$	−21.8876	−	9.06615i	−0.983775	−	0.407493i
$496$	12.2908	−	20.7655i	0.551873	−	0.932400i
$497$	55.2644	−	22.8912i	2.47894	−	1.02681i
$498$	−1.75305	+	0.464645i	−0.0785562	+	0.0208212i
$499$	17.1076	+	1.68495i	0.765840	+	0.0754286i	0.473391	−	0.880852i	$-0.343030\pi$
$499$	17.1076	+	1.68495i	0.765840	+	0.0754286i	0.292449	+	0.956281i	$0.405530\pi$
$500$	−39.5481	+	17.6615i	−1.76864	+	0.789844i
$501$	0.903192	−	0.482766i	0.0403516	−	0.0215684i
$502$	−12.2665	+	17.0204i	−0.547483	+	0.759658i
$503$	17.5591	−	11.7326i	0.782923	−	0.523133i	−0.0986826	−	0.995119i	$-0.531463\pi$
$503$	17.5591	−	11.7326i	0.782923	−	0.523133i	0.881606	+	0.471986i	$0.156463\pi$
$504$	−10.0243	−	6.81649i	−0.446520	−	0.303631i
$505$	−26.6702	+	39.9147i	−1.18681	+	1.77618i
$506$	−4.47972	+	9.81615i	−0.199148	+	0.436381i
$507$	0.858411	+	8.71559i	0.0381234	+	0.387073i
$508$	−1.47845	−	11.7201i	−0.0655954	−	0.519994i
$509$	6.31909	+	20.8313i	0.280089	+	0.923329i	0.978257	+	0.207396i	$0.0664988\pi$
$509$	6.31909	+	20.8313i	0.280089	+	0.923329i	−0.698168	+	0.715934i	$0.746001\pi$
$510$	−7.91090	−	6.97566i	−0.350301	−	0.308888i
$511$	−13.0300			−0.576413
$512$	−22.0785	−	4.95391i	−0.975740	−	0.218934i
$513$	4.43494			0.195807
$514$	7.77202	+	6.85320i	0.342809	+	0.302282i
$515$	1.77485	+	5.85091i	0.0782094	+	0.257822i
$516$	−2.21346	−	17.5468i	−0.0974423	−	0.772454i
$517$	−4.57709	−	46.4720i	−0.201300	−	2.04384i
$518$	−6.83219	+	14.9710i	−0.300189	+	0.657788i
$519$	3.27409	−	4.90002i	0.143717	−	0.215087i
$520$	−18.9664	−	12.8970i	−0.831731	−	0.565572i
$521$	−19.5149	+	13.0395i	−0.854965	+	0.571270i	−0.904002	−	0.427527i	$-0.859385\pi$
$521$	−19.5149	+	13.0395i	−0.854965	+	0.571270i	0.0490371	+	0.998797i	$0.484385\pi$
$522$	−4.23733	+	5.87950i	−0.185463	+	0.257339i
$523$	22.1843	−	11.8577i	0.970050	−	0.518503i	0.0913203	−	0.995822i	$-0.470891\pi$
$523$	22.1843	−	11.8577i	0.970050	−	0.518503i	0.878730	+	0.477319i	$0.158391\pi$
$524$	11.2618	−	5.02932i	0.491974	−	0.219707i
$525$	−44.7879	−	4.41122i	−1.95470	−	0.192521i
$526$	3.20596	−	0.849735i	0.139786	−	0.0370502i
$527$	10.5576	−	4.37309i	0.459895	−	0.190495i
$528$	−20.7133	−	12.2599i	−0.901431	−	0.533543i
$529$	19.7639	+	8.18649i	0.859302	+	0.355934i
$530$	16.7042	+	2.24518i	0.725582	+	0.0975244i
$531$	3.96089	−	3.25062i	0.171888	−	0.141065i
$532$	−37.0686	+	8.43178i	−1.60713	+	0.365564i
$533$	4.75549	+	1.44256i	0.205983	+	0.0624843i
$534$	2.02567	+	0.478108i	0.0876594	+	0.0206898i
$535$	−5.52823	+	27.7923i	−0.239006	+	1.20157i
$536$	3.54692	−	11.3596i	0.153204	−	0.490659i
$537$	3.42042	−	0.680364i	0.147602	−	0.0293599i
$538$	−24.1125	−	25.8848i	−1.03957	−	1.11597i
$539$	52.8831	+	43.4000i	2.27784	+	1.86937i
$540$	7.04315	+	3.52085i	0.303089	+	0.151513i
$541$	18.7049	−	34.9945i	0.804187	−	1.50453i	−0.0582141	−	0.998304i	$-0.518541\pi$
$541$	18.7049	−	34.9945i	0.804187	−	1.50453i	0.862402	−	0.506225i	$-0.168959\pi$
$542$	4.20118	+	1.43881i	0.180456	+	0.0618021i
$543$	−2.10087	+	2.10087i	−0.0901571	+	0.0901571i
$544$	−6.95563	−	8.15142i	−0.298220	−	0.349489i
$545$	8.87678	+	8.87678i	0.380239	+	0.380239i
$546$	−5.49121	−	11.2115i	−0.235002	−	0.479808i
$547$	−32.3715	−	17.3029i	−1.38410	−	0.739819i	−0.399851	−	0.916580i	$-0.630938\pi$
$547$	−32.3715	−	17.3029i	−1.38410	−	0.739819i	−0.984254	+	0.176761i	$0.943438\pi$
$548$	24.7440	+	28.5254i	1.05701	+	1.21854i
$549$	6.50764	−	7.92958i	0.277739	−	0.338426i
$550$	−89.3028	−	3.16559i	−3.80789	−	0.134981i
$551$	4.43389	+	22.2907i	0.188890	+	0.949615i
$552$	1.71620	−	3.14897i	0.0730462	−	0.134029i
$553$	49.7230	+	9.89052i	2.11444	+	0.420588i
$554$	6.00072	+	9.70847i	0.254946	+	0.412473i
$555$	3.10293	−	10.2290i	0.131712	−	0.434197i
$556$	−13.6336	−	19.2450i	−0.578196	−	0.816171i
$557$	−20.8474	−	25.4026i	−0.883332	−	1.07634i	−0.996568	−	0.0827753i	$-0.973622\pi$
$557$	−20.8474	−	25.4026i	−0.883332	−	1.07634i	0.113236	−	0.993568i	$-0.463878\pi$
$558$	−6.78242	+	5.17521i	−0.287123	+	0.219084i
$559$	6.97000	−	16.8271i	0.294799	−	0.711709i
$560$	−65.5628	−	16.0378i	−2.77053	−	0.677721i
$561$	−4.36209	−	10.5310i	−0.184168	−	0.444620i
$562$	6.21093	+	3.60834i	0.261992	+	0.152209i
$563$	−3.19645	+	32.4541i	−0.134714	+	1.36778i	0.655615	+	0.755095i	$0.272409\pi$
$563$	−3.19645	+	32.4541i	−0.134714	+	1.36778i	−0.790329	+	0.612682i	$0.790091\pi$
$564$	0.423798	+	15.5148i	0.0178451	+	0.653292i
$565$	15.0534	+	28.1629i	0.633300	+	1.18482i
$566$	−1.17629	−	7.24675i	−0.0494433	−	0.304604i
$567$	2.38112	+	3.56360i	0.0999977	+	0.149657i
$568$	−36.5925	+	14.8100i	−1.53539	+	0.621413i
$569$	−35.3817	−	23.6413i	−1.48328	−	0.991096i	−0.992818	−	0.119633i	$-0.961828\pi$
$569$	−35.3817	−	23.6413i	−1.48328	−	0.991096i	−0.490461	−	0.871463i	$-0.663172\pi$
$570$	23.1340	−	8.63556i	0.968975	−	0.361704i
$571$	−12.9645	+	1.27689i	−0.542546	+	0.0534361i	−0.365579	−	0.930780i	$-0.619129\pi$
$571$	−12.9645	+	1.27689i	−0.542546	+	0.0534361i	−0.176968	+	0.984217i	$0.556629\pi$
$572$	−12.2774	−	21.5336i	−0.513344	−	0.900365i
$573$	21.7138	−	6.58682i	0.907108	−	0.275168i
$574$	14.5954	−	0.916945i	0.609200	−	0.0382725i
$575$		−	13.3141i		−	0.555237i
$576$	6.57867	+	4.55205i	0.274111	+	0.189669i
$577$			6.09418i			0.253704i	0.991922	+	0.126852i	$0.0404874\pi$
$577$			6.09418i			0.253704i	−0.991922	+	0.126852i	$0.959513\pi$
$578$	1.18924	+	18.9297i	0.0494659	+	0.787370i
$579$	16.8794	−	5.12030i	0.701483	−	0.212793i
$580$	−10.6548	+	38.9200i	−0.442418	+	1.61606i
$581$	−5.46977	+	0.538726i	−0.226924	+	0.0223501i
$582$	2.21702	+	5.93922i	0.0918985	+	0.246189i
$583$	15.1453	+	10.1198i	0.627255	+	0.419119i
$584$	8.59869	+	0.0698579i	0.355816	+	0.00289074i
$585$	4.50516	+	6.74245i	0.186266	+	0.278766i
$586$	−5.01961	+	0.814783i	−0.207358	+	0.0336584i
$587$	−14.9149	−	27.9038i	−0.615604	−	1.15171i	−0.975764	−	0.218824i	$-0.929778\pi$
$587$	−14.9149	−	27.9038i	−0.615604	−	1.15171i	0.360160	−	0.932891i	$-0.382722\pi$
$588$	−16.5112	−	15.6332i	−0.680911	−	0.644701i
$589$	−2.62236	+	26.6253i	−0.108053	+	1.09708i
$590$	14.3317	−	24.6687i	0.590026	−	1.01559i
$591$	3.76436	+	9.08796i	0.154845	+	0.373829i
$592$	4.58893	−	9.84295i	0.188604	−	0.404543i
$593$	−17.0913	+	41.2620i	−0.701854	+	1.69443i	0.0175605	+	0.999846i	$0.494410\pi$
$593$	−17.0913	+	41.2620i	−0.701854	+	1.69443i	−0.719415	+	0.694581i	$0.755590\pi$
$594$	5.16219	+	6.76536i	0.211807	+	0.277586i
$595$	−20.2778	−	24.7086i	−0.831310	−	1.01295i
$596$	−5.63897	+	33.0403i	−0.230981	+	1.35338i
$597$	−0.0298887	+	0.0985299i	−0.00122326	+	0.00403256i
$598$	3.14160	−	1.94180i	0.128470	−	0.0794060i
$599$	4.06107	+	0.807797i	0.165931	+	0.0330057i	0.277356	−	0.960767i	$-0.410542\pi$
$599$	4.06107	+	0.807797i	0.165931	+	0.0330057i	−0.111426	+	0.993773i	$0.535542\pi$
$600$	29.5325	+	3.15115i	1.20566	+	0.128645i
$601$	7.62237	+	38.3203i	0.310923	+	1.56312i	0.748004	+	0.663694i	$0.231012\pi$
$601$	7.62237	+	38.3203i	0.310923	+	1.56312i	−0.437081	+	0.899422i	$0.643988\pi$
$602$	1.89876	−	53.5649i	0.0773876	−	2.18314i
$603$	−2.66917	+	3.25240i	−0.108697	+	0.132448i
$604$	3.03349	+	0.215332i	0.123431	+	0.00876172i
$605$	−87.5310	−	46.7863i	−3.55864	−	1.90213i
$606$	15.4859	−	7.58473i	0.629071	−	0.308109i
$607$	3.50527	+	3.50527i	0.142275	+	0.142275i	0.774657	−	0.632382i	$-0.217923\pi$
$607$	3.50527	+	3.50527i	0.142275	+	0.142275i	−0.632382	+	0.774657i	$0.717923\pi$
$608$	24.5073	−	5.36552i	0.993904	−	0.217600i
$609$	−15.5306	+	15.5306i	−0.629333	+	0.629333i
$610$	18.5056	−	54.0345i	0.749268	−	2.18779i
$611$	−7.53464	+	14.0963i	−0.304819	+	0.570276i
$612$	1.19835	+	3.59406i	0.0484404	+	0.145281i
$613$	−21.1610	−	17.3664i	−0.854684	−	0.701421i	0.101295	−	0.994856i	$-0.467701\pi$
$613$	−21.1610	−	17.3664i	−0.854684	−	0.701421i	−0.955979	+	0.293435i	$0.905201\pi$
$614$	−20.8094	+	19.3846i	−0.839799	+	0.782299i
$615$	−9.31668	+	1.85320i	−0.375685	+	0.0747284i
$616$	−56.0096	−	46.7325i	−2.25669	−	1.88291i
$617$	−1.60916	+	8.08981i	−0.0647825	+	0.325684i	−0.999564	−	0.0295408i	$-0.990596\pi$
$617$	−1.60916	+	8.08981i	−0.0647825	+	0.325684i	0.934781	+	0.355224i	$0.115596\pi$
$618$	0.504503	−	2.13751i	0.0202941	−	0.0859831i
$619$	−30.6432	−	9.29551i	−1.23165	−	0.373618i	−0.393639	−	0.919265i	$-0.628784\pi$
$619$	−30.6432	−	9.29551i	−1.23165	−	0.373618i	−0.838015	+	0.545647i	$0.816284\pi$
$620$	−25.3021	+	40.2019i	−1.01616	+	1.61455i
$621$	−0.980131	+	0.804372i	−0.0393313	+	0.0322784i
$622$	4.05382	−	30.1605i	0.162543	−	1.20932i
$623$	5.82752	+	2.41384i	0.233475	+	0.0967084i
$624$	3.56362	+	7.42808i	0.142659	+	0.297361i
$625$	30.2658	−	12.5365i	1.21063	−	0.501461i
$626$	−7.38242	−	27.8531i	−0.295061	−	1.11323i
$627$	26.5583	+	2.61577i	1.06064	+	0.104464i
$628$	−6.47295	−	2.47635i	−0.258299	−	0.0988172i
$629$	4.53576	−	2.42441i	0.180852	−	0.0966677i
$630$	19.3596	+	13.9524i	0.771303	+	0.555875i
$631$	12.0183	−	8.03036i	0.478440	−	0.319684i	−0.292860	−	0.956155i	$-0.594607\pi$
$631$	12.0183	−	8.03036i	0.478440	−	0.319684i	0.771300	+	0.636472i	$0.219607\pi$
$632$	−32.7599	−	6.79348i	−1.30312	−	0.270230i
$633$	−13.8038	+	20.6589i	−0.548654	+	0.821118i
$634$	−10.3028	−	4.70181i	−0.409177	−	0.186733i
$635$	2.27932	+	23.1423i	0.0904519	+	0.918374i
$636$	−4.78305	−	3.71149i	−0.189660	−	0.147170i
$637$	−6.79742	−	22.4081i	−0.269323	−	0.887840i
$638$	−28.8427	+	32.7097i	−1.14189	+	1.29499i
$639$	13.9568			0.552124
$640$	43.1799	+	10.9351i	1.70683	+	0.432247i
$641$	35.8818			1.41724			0.708622	−	0.705588i	$-0.249317\pi$
$641$	35.8818			1.41724			0.708622	+	0.705588i	$0.249317\pi$
$642$	6.73196	−	7.63453i	0.265689	−	0.301311i
$643$	8.57341	+	28.2627i	0.338102	+	1.11457i	0.946975	+	0.321306i	$0.104122\pi$
$643$	8.57341	+	28.2627i	0.338102	+	1.11457i	−0.608873	+	0.793268i	$0.708378\pi$
$644$	6.66295	−	8.58663i	0.262557	−	0.338361i
$645$	3.41249	+	34.6476i	0.134367	+	1.36425i
$646$	10.8085	+	4.93261i	0.425257	+	0.194071i
$647$	−21.2867	+	31.8578i	−0.836866	+	1.25246i	0.128539	+	0.991704i	$0.458971\pi$
$647$	−21.2867	+	31.8578i	−0.836866	+	1.25246i	−0.965405	+	0.260754i	$0.916029\pi$
$648$	−1.55223	−	2.36444i	−0.0609775	−	0.0928840i
$649$	25.6368	−	17.1299i	1.00633	−	0.672409i
$650$	24.8136	+	17.8831i	0.973269	+	0.701432i
$651$	−22.8021	+	12.1880i	−0.893686	+	0.477685i
$652$	−16.0503	+	41.9539i	−0.628577	+	1.64304i
$653$	−32.6894	−	3.21962i	−1.27923	−	0.125994i	−0.564526	−	0.825416i	$-0.690941\pi$
$653$	−32.6894	−	3.21962i	−1.27923	−	0.125994i	−0.714709	+	0.699422i	$0.753441\pi$
$654$	−1.15530	−	4.35882i	−0.0451758	−	0.170443i
$655$	−22.4314	+	9.29137i	−0.876466	+	0.363044i
$656$	−9.63663	+	0.526855i	−0.376247	+	0.0205702i
$657$	−2.80877	−	1.16343i	−0.109581	−	0.0453898i
$658$	−6.26578	+	46.6174i	−0.244265	+	1.81734i
$659$	12.2693	−	10.0691i	0.477943	−	0.392238i	−0.364346	−	0.931264i	$-0.618707\pi$
$659$	12.2693	−	10.0691i	0.477943	−	0.392238i	0.842289	+	0.539026i	$0.181207\pi$
$660$	40.1008	+	25.2385i	1.56092	+	0.982406i
$661$	−6.43890	−	1.95322i	−0.250444	−	0.0759714i	0.162566	−	0.986698i	$-0.448023\pi$
$661$	−6.43890	−	1.95322i	−0.250444	−	0.0759714i	−0.413011	+	0.910726i	$0.635523\pi$
$662$	−1.15859	+	4.90877i	−0.0450299	+	0.190785i
$663$	−0.761165	+	3.82664i	−0.0295612	+	0.148614i
$664$	3.61247	−	0.326188i	0.140191	−	0.0126585i
$665$	73.3971	−	14.5996i	2.84622	−	0.566148i
$666$	−2.80950	+	2.61714i	−0.108866	+	0.101412i
$667$	−5.02280	−	4.12210i	−0.194483	−	0.159608i
$668$	−1.94307	+	0.647870i	−0.0751798	+	0.0250668i
$669$	13.1733	−	24.6455i	0.509310	−	0.952852i
$670$	−7.59025	+	22.1628i	−0.293237	+	0.856223i
$671$	43.6474	−	43.6474i	1.68499	−	1.68499i
$672$	17.4694	+	16.8116i	0.673895	+	0.648521i
$673$	−21.7467	−	21.7467i	−0.838274	−	0.838274i	0.150358	−	0.988632i	$-0.451957\pi$
$673$	−21.7467	−	21.7467i	−0.838274	−	0.838274i	−0.988632	+	0.150358i	$0.951957\pi$
$674$	12.7258	−	6.23288i	0.490179	−	0.240081i
$675$	−9.26070	−	4.94995i	−0.356444	−	0.190523i
$676$	1.24021	−	17.4716i	0.0477006	−	0.671983i
$677$	30.7812	−	37.5070i	1.18302	−	1.44151i	0.312125	−	0.950041i	$-0.398959\pi$
$677$	30.7812	−	37.5070i	1.18302	−	1.44151i	0.870893	−	0.491472i	$-0.163541\pi$
$678$	0.406354	−	11.4634i	0.0156059	−	0.440251i
$679$	3.74818	+	18.8434i	0.143842	+	0.723141i
$680$	13.2492	+	16.4143i	0.508082	+	0.629459i
$681$	−13.1478	−	2.61527i	−0.503826	−	0.100217i
$682$	−43.6684	+	26.9910i	−1.67215	+	1.03354i
$683$	6.69108	−	22.0575i	0.256027	−	0.844008i	−0.730850	−	0.682538i	$-0.760876\pi$
$683$	6.69108	−	22.0575i	0.256027	−	0.844008i	0.986878	−	0.161471i	$-0.0516237\pi$
$684$	−8.74346	−	1.49224i	−0.334314	−	0.0570572i
$685$	−47.1582	−	57.4624i	−1.80182	−	2.19553i
$686$	−16.0639	−	21.0526i	−0.613321	−	0.803793i
$687$	−3.45832	+	8.34912i	−0.131943	+	0.318539i
$688$	−1.54020	+	35.3381i	−0.0587195	+	1.34725i
$689$	−2.38594	−	5.76018i	−0.0908972	−	0.219445i
$690$	−3.54641	+	6.10432i	−0.135009	+	0.232387i
$691$	0.726340	−	7.37466i	0.0276313	−	0.280545i	−0.971434	−	0.237311i	$-0.923734\pi$
$691$	0.726340	−	7.37466i	0.0276313	−	0.280545i	0.999065	−	0.0432340i	$-0.0137661\pi$
$692$	−8.10358	+	8.55872i	−0.308052	+	0.325354i
$693$	12.1573	+	22.7448i	0.461819	+	0.864003i
$694$	−21.3331	+	3.46279i	−0.809794	+	0.131446i
$695$	25.7939	+	38.6033i	0.978419	+	1.46431i
$696$	10.3322	−	10.1656i	0.391640	−	0.385328i
$697$	−3.80019	−	2.53921i	−0.143943	−	0.0961793i
$698$	−7.75029	−	20.7624i	−0.293353	−	0.785869i
$699$	−4.39968	+	0.433331i	−0.166411	+	0.0163901i
$700$	86.8147	+	23.7666i	3.28129	+	0.898294i
$701$	−3.50887	+	1.06440i	−0.132528	+	0.0402020i	−0.355852	−	0.934542i	$-0.615809\pi$
$701$	−3.50887	+	1.06440i	−0.132528	+	0.0402020i	0.223324	+	0.974744i	$0.428309\pi$
$702$	−0.182635	−	2.90708i	−0.00689312	−	0.109721i
$703$			12.0410i			0.454134i
$704$	36.7110	+	31.1398i	1.38360	+	1.17362i
$705$		−	30.5529i		−	1.15069i
$706$	−43.2016	+	2.71411i	−1.62592	+	0.102147i
$707$	50.0081	−	15.1698i	1.88075	−	0.570518i
$708$	−8.90262	+	5.07584i	−0.334581	+	0.190762i
$709$	40.6235	−	4.00107i	1.52565	−	0.150263i	0.699875	−	0.714266i	$-0.253239\pi$
$709$	40.6235	−	4.00107i	1.52565	−	0.150263i	0.825773	+	0.564002i	$0.190739\pi$
$710$	72.8030	−	27.1762i	2.73225	−	1.01991i
$711$	9.83529	+	6.57173i	0.368852	+	0.246459i
$712$	−3.83273	−	1.62417i	−0.143638	−	0.0608684i
$713$	−4.24952	−	6.35986i	−0.159146	−	0.238179i
$714$	1.83962	+	11.3333i	0.0688461	+	0.424138i
$715$	23.0021	+	43.0339i	0.860229	+	1.60938i
$716$	−6.97226	+	0.190452i	−0.260565	+	0.00711752i
$717$	0.852734	−	8.65795i	0.0318459	−	0.323337i
$718$	4.51204	+	2.62134i	0.168388	+	0.0978277i
$719$	−3.88796	−	9.38637i	−0.144996	−	0.350052i	0.834651	−	0.550780i	$-0.185670\pi$
$719$	−3.88796	−	9.38637i	−0.144996	−	0.350052i	−0.979647	+	0.200727i	$0.935670\pi$
$720$	−12.7009	−	9.31116i	−0.473333	−	0.347007i
$721$	2.54710	−	6.14925i	0.0948591	−	0.229010i
$722$	−0.751828	+	0.573670i	−0.0279801	+	0.0213498i
$723$	2.40600	+	2.93171i	0.0894800	+	0.109032i
$724$	4.84874	−	3.43497i	0.180202	−	0.127660i
$725$	15.6207	−	51.4944i	0.580137	−	1.91246i
$726$	18.7441	+	30.3259i	0.695660	+	1.12550i
$727$	1.01493	+	0.201882i	0.0376417	+	0.00748740i	0.213875	−	0.976861i	$-0.431391\pi$
$727$	1.01493	+	0.201882i	0.0376417	+	0.00748740i	−0.176234	+	0.984348i	$0.556391\pi$
$728$	7.05351	+	23.9511i	0.261420	+	0.887685i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	−16.9168	−	0.599663i	−0.626118	−	0.0221945i
$731$	−10.6267	+	12.9487i	−0.393044	+	0.478925i
$732$	−15.4979	+	13.4435i	−0.572817	+	0.496885i
$733$	3.04136	+	1.62564i	0.112335	+	0.0600445i	0.526607	−	0.850109i	$-0.323464\pi$
$733$	3.04136	+	1.62564i	0.112335	+	0.0600445i	−0.414272	+	0.910153i	$0.635964\pi$
$734$	−1.45758	−	2.97596i	−0.0538002	−	0.109845i
$735$	31.6506	+	31.6506i	1.16745	+	1.16745i
$736$	−4.44302	+	5.63073i	−0.163772	+	0.207551i
$737$	−17.9024	+	17.9024i	−0.659445	+	0.659445i
$738$	3.22809	+	1.10555i	0.118828	+	0.0406957i
$739$	−0.0209360	+	0.0391685i	−0.000770144	+	0.00144084i	−0.882306	−	0.470676i	$-0.844010\pi$
$739$	−0.0209360	+	0.0391685i	−0.000770144	+	0.00144084i	0.881536	+	0.472117i	$0.156510\pi$
$740$	−9.55920	+	19.1224i	−0.351403	+	0.702952i
$741$	−7.06107	−	5.79487i	−0.259395	−	0.212880i
$742$	−12.5060	−	13.4252i	−0.459110	−	0.492855i
$743$	−27.4347	+	5.45710i	−1.00648	+	0.200202i	−0.670693	−	0.741735i	$-0.734003\pi$
$743$	−27.4347	+	5.45710i	−1.00648	+	0.200202i	−0.335789	+	0.941937i	$0.609003\pi$
$744$	15.1128	−	7.92079i	0.554062	−	0.290390i
$745$	12.8724	−	64.7138i	0.471607	−	2.37093i
$746$	−7.84987	−	1.85276i	−0.287404	−	0.0678344i
$747$	−1.22718	−	0.372261i	−0.0449001	−	0.0136203i
$748$	5.05642	+	22.2295i	0.184881	+	0.812793i
$749$	23.8454	−	19.5694i	0.871291	−	0.715050i
$750$	−30.3536	−	4.07979i	−1.10836	−	0.148973i
$751$	−31.5379	−	13.0634i	−1.15083	−	0.476691i	−0.276020	−	0.961152i	$-0.589016\pi$
$751$	−31.5379	−	13.0634i	−1.15083	−	0.476691i	−0.874813	+	0.484461i	$0.839016\pi$
$752$	4.38481	−	30.7299i	0.159898	−	1.12061i
$753$	−13.7059	+	5.67716i	−0.499470	+	0.206887i
$754$	14.4288	−	3.82435i	0.525467	−	0.139274i
$755$	−5.95774	−	0.586787i	−0.216825	−	0.0213553i
$756$	−3.49531	−	7.82680i	−0.127123	−	0.284658i
$757$	−24.5996	+	13.1488i	−0.894089	+	0.477900i	−0.853391	−	0.521271i	$-0.825458\pi$
$757$	−24.5996	+	13.1488i	−0.894089	+	0.477900i	−0.0406977	+	0.999172i	$0.512958\pi$
$758$	9.25476	−	12.8414i	0.336148	−	0.466421i
$759$	−6.34387	+	4.23884i	−0.230268	+	0.153860i
$760$	−48.5141	+	9.24098i	−1.75979	+	0.335206i
$761$	−27.1461	+	40.6271i	−0.984047	+	1.47273i	−0.105878	+	0.994379i	$0.533765\pi$
$761$	−27.1461	+	40.6271i	−0.984047	+	1.47273i	−0.878169	+	0.478351i	$0.841235\pi$
$762$	3.46794	−	7.59910i	0.125630	−	0.275286i
$763$	−1.33949	−	13.6001i	−0.0484930	−	0.492357i
$764$	−45.0250	+	5.67974i	−1.62895	+	0.205486i
$765$	−2.16493	−	7.13682i	−0.0782732	−	0.258032i
$766$	39.1770	+	34.5454i	1.41552	+	1.24818i
$767$	−10.5537			−0.381072
$768$	−11.4382	−	11.1879i	−0.412739	−	0.403708i
$769$	27.4616			0.990290			0.495145	−	0.868810i	$-0.335115\pi$
$769$	27.4616			0.990290			0.495145	+	0.868810i	$0.335115\pi$
$770$	107.704	+	94.9711i	3.88138	+	3.42252i
$771$	2.12692	+	7.01152i	0.0765993	+	0.252514i
$772$	−35.0004	+	4.41518i	−1.25969	+	0.158906i
$773$	−4.55657	−	46.2636i	−0.163888	−	1.66399i	−0.628003	−	0.778211i	$-0.716128\pi$
$773$	−4.55657	−	46.2636i	−0.163888	−	1.66399i	0.464115	−	0.885775i	$-0.346372\pi$
$774$	5.19205	−	11.3770i	0.186624	−	0.408939i
$775$	35.1929	−	52.6700i	1.26417	−	1.89196i
$776$	−2.37245	−	12.4551i	−0.0851661	−	0.447112i
$777$	−9.67528	+	6.46481i	−0.347099	+	0.231924i
$778$	14.0495	−	19.4943i	0.503699	−	0.698906i
$779$	9.43694	−	5.04415i	0.338113	−	0.180725i
$780$	−6.61324	−	14.8086i	−0.236792	−	0.530232i
$781$	83.5795	+	8.23186i	2.99071	+	0.294559i
$782$	−3.28335	+	0.870247i	−0.117412	+	0.0311200i
$783$	−4.73453	+	1.96111i	−0.169198	+	0.0700843i
$784$	27.2916	+	36.3763i	0.974701	+	1.29915i
$785$	12.6044	+	5.22091i	0.449870	+	0.186342i
$786$	8.64357	+	1.16177i	0.308306	+	0.0414389i
$787$	−5.26387	+	4.31995i	−0.187637	+	0.153990i	−0.723522	−	0.690301i	$-0.757478\pi$
$787$	−5.26387	+	4.31995i	−0.187637	+	0.153990i	0.535885	+	0.844291i	$0.319978\pi$
$788$	−4.36355	−	19.1835i	−0.155445	−	0.683383i
$789$	2.24424	+	0.680784i	0.0798972	+	0.0242366i
$790$	64.1000	+	15.1292i	2.28058	+	0.538272i
$791$	6.78190	−	34.0949i	0.241137	−	1.21228i
$792$	−7.90086	−	15.0748i	−0.280745	−	0.535659i
$793$	−20.7222	+	4.12190i	−0.735867	+	0.146373i
$794$	−36.6356	−	39.3283i	−1.30015	−	1.39571i
$795$	9.21261	+	7.56059i	0.326738	+	0.268147i
$796$	0.0920781	−	0.184194i	0.00326362	−	0.00652859i
$797$	−11.5872	+	21.6781i	−0.410440	+	0.767878i	−0.999182	−	0.0404424i	$-0.987123\pi$
$797$	−11.5872	+	21.6781i	−0.410440	+	0.767878i	0.588742	+	0.808321i	$0.299623\pi$
$798$	−25.4310	−	8.70952i	−0.900246	−	0.308314i
$799$	10.3946	−	10.3946i	0.367736	−	0.367736i
$800$	−57.1629	−	16.1494i	−2.02101	−	0.570967i
$801$	1.04066	+	1.04066i	0.0367701	+	0.0367701i
$802$	−3.10264	−	6.33472i	−0.109558	−	0.223687i
$803$	−16.1339	−	8.62377i	−0.569354	−	0.304326i
$804$	6.35660	−	5.51397i	0.224180	−	0.194463i
$805$	−13.5729	+	16.5387i	−0.478383	+	0.582912i
$806$	17.5607	+	0.622489i	0.618550	+	0.0219262i
$807$	−4.88007	−	24.5337i	−0.171786	−	0.863629i
$808$	−33.0824	+	9.74265i	−1.16383	+	0.342745i
$809$	−38.7616	−	7.71015i	−1.36278	−	0.271075i	−0.541071	−	0.840977i	$-0.681981\pi$
$809$	−38.7616	−	7.71015i	−1.36278	−	0.271075i	−0.821713	+	0.569902i	$0.806981\pi$
$810$	2.92740	+	4.73619i	0.102858	+	0.166413i
$811$	−4.74260	+	15.6343i	−0.166535	+	0.548993i	−0.999994	−	0.00358903i	$-0.998858\pi$
$811$	−4.74260	+	15.6343i	−0.166535	+	0.548993i	0.833458	+	0.552582i	$0.186358\pi$
$812$	35.8442	−	25.3929i	1.25789	−	0.891116i
$813$	1.99204	+	2.42731i	0.0698639	+	0.0851294i
$814$	−18.3681	+	14.0155i	−0.643802	+	0.491243i
$815$	33.8389	−	81.6943i	1.18532	−	2.86163i
$816$	−1.15323	−	7.48887i	−0.0403712	−	0.262163i
$817$	−15.0080	−	36.2325i	−0.525064	−	1.26762i
$818$	4.31648	+	2.50773i	0.150922	+	0.0876807i
$819$	0.865251	−	8.78504i	0.0302343	−	0.306974i
$820$	18.9913	−	0.518761i	0.663206	−	0.0181159i
$821$	−16.5234	−	30.9132i	−0.576672	−	1.07888i	−0.986040	−	0.166508i	$-0.946751\pi$
$821$	−16.5234	−	30.9132i	−0.576672	−	1.07888i	0.409368	−	0.912369i	$-0.365749\pi$
$822$	4.27823	+	26.3568i	0.149220	+	0.919297i
$823$	2.09105	+	3.12947i	0.0728894	+	0.109087i	0.866123	−	0.499830i	$-0.166604\pi$
$823$	2.09105	+	3.12947i	0.0728894	+	0.109087i	−0.793234	+	0.608917i	$0.791604\pi$
$824$	−1.71384	+	4.04433i	−0.0597044	+	0.140891i
$825$	−52.5375	−	35.1044i	−1.82912	−	1.22218i
$826$	−29.0963	+	10.8612i	−1.01239	+	0.377910i
$827$	35.9934	−	3.54505i	1.25161	−	0.123273i	0.549595	−	0.835431i	$-0.314782\pi$
$827$	35.9934	−	3.54505i	1.25161	−	0.123273i	0.702020	+	0.712158i	$0.252282\pi$
$828$	2.20297	−	1.25603i	0.0765585	−	0.0436499i
$829$	−36.5596	+	11.0902i	−1.26977	+	0.385179i	−0.852080	−	0.523412i	$-0.824659\pi$
$829$	−36.5596	+	11.0902i	−1.26977	+	0.385179i	−0.417686	+	0.908591i	$0.637159\pi$
$830$	−7.12618	+	0.447697i	−0.247353	+	0.0155398i
$831$			8.07041i			0.279959i
$832$	−4.52630	−	15.8435i	−0.156921	−	0.549274i
$833$			21.5362i			0.746183i
$834$	−1.04566	−	16.6442i	−0.0362083	−	0.576343i
$835$	3.85842	−	1.17044i	0.133526	−	0.0405047i
$836$	−51.4794	−	14.0931i	−1.78045	−	0.487421i
$837$	−6.00353	+	0.591296i	−0.207512	+	0.0204382i
$838$	15.4671	+	41.4351i	0.534301	+	1.43135i
$839$	−25.1679	−	16.8167i	−0.868892	−	0.580575i	0.0392535	−	0.999229i	$-0.487502\pi$
$839$	−25.1679	−	16.8167i	−0.868892	−	0.580575i	−0.908146	+	0.418654i	$0.862502\pi$
$840$	−33.4726	−	34.0210i	−1.15492	−	1.17383i
$841$	1.52130	+	2.27678i	0.0524586	+	0.0785098i
$842$	31.9790	−	5.19083i	1.10207	−	0.178888i
$843$	2.39430	+	4.47942i	0.0824641	+	0.154279i
$844$	34.1654	−	36.0843i	1.17602	−	1.24207i
$845$	−3.37963	+	34.3140i	−0.116263	+	1.18044i
$846$	−5.51308	+	9.48949i	−0.189544	+	0.326256i
$847$	41.3466	+	99.8196i	1.42069	+	3.42984i
$848$	8.18093	+	8.92655i	0.280934	+	0.306539i
$849$	1.98662	−	4.79613i	0.0681807	−	0.164603i
$850$	−17.0642	−	22.3636i	−0.585296	−	0.767064i
$851$	−2.18389	−	2.66108i	−0.0748629	−	0.0912207i
$852$	−27.5158	−	4.69611i	−0.942676	−	0.160886i
$853$	0.229421	−	0.756299i	0.00785521	−	0.0258952i	−0.952925	−	0.303206i	$-0.901943\pi$
$853$	0.229421	−	0.756299i	0.00785521	−	0.0258952i	0.960780	+	0.277311i	$0.0894431\pi$
$854$	−52.8887	+	32.6900i	−1.80981	+	1.11863i
$855$	17.1252	+	3.40642i	0.585670	+	0.116497i
$856$	−15.8408	+	12.7863i	−0.541429	+	0.437027i
$857$	−0.811104	−	4.07770i	−0.0277068	−	0.139291i	0.964456	−	0.264244i	$-0.0851223\pi$
$857$	−0.811104	−	4.07770i	−0.0277068	−	0.139291i	−0.992163	+	0.124952i	$0.960122\pi$
$858$	0.620923	−	17.5166i	0.0211980	−	0.598005i
$859$	−1.02995	+	1.25500i	−0.0351414	+	0.0428199i	−0.790285	−	0.612740i	$-0.790067\pi$
$859$	−1.02995	+	1.25500i	−0.0351414	+	0.0428199i	0.755143	+	0.655560i	$0.227567\pi$
$860$	4.93030	−	69.4558i	0.168122	−	2.36842i
$861$	9.11981	+	4.87464i	0.310802	+	0.166127i
$862$	29.6658	−	14.5298i	1.01042	−	0.494888i
$863$	30.5042	+	30.5042i	1.03837	+	1.03837i	0.999234	+	0.0391401i	$0.0124619\pi$
$863$	30.5042	+	30.5042i	1.03837	+	1.03837i	0.0391401	+	0.999234i	$0.487538\pi$
$864$	2.26464	+	5.18376i	0.0770448	+	0.176355i
$865$	16.4063	−	16.4063i	0.557831	−	0.557831i
$866$	−9.99239	+	29.1768i	−0.339555	+	0.991469i
$867$	−6.32222	+	11.8280i	−0.214714	+	0.401701i
$868$	49.0552	−	16.3562i	1.66504	−	0.555167i
$869$	55.0218	+	45.1553i	1.86649	+	1.53179i
$870$	−20.8781	+	19.4486i	−0.707835	+	0.659370i
$871$	8.49943	−	1.69064i	0.287992	−	0.0572852i
$872$	0.811038	+	8.98210i	0.0274652	+	0.304172i
$873$	−0.874535	+	4.39658i	−0.0295985	+	0.148802i
$874$	1.82678	−	7.73980i	0.0617918	−	0.261803i
$875$	−88.8201	−	26.9433i	−3.00267	−	0.910849i
$876$	5.14601	+	3.23878i	0.173868	+	0.109428i
$877$	−12.5816	+	10.3254i	−0.424850	+	0.348665i	−0.822395	−	0.568918i	$-0.807362\pi$
$877$	−12.5816	+	10.3254i	−0.424850	+	0.348665i	0.397545	+	0.917583i	$0.369862\pi$
$878$	−6.60336	+	49.1290i	−0.222852	+	1.65802i
$879$	−3.32214	−	1.37607i	−0.112053	−	0.0464138i
$880$	−70.5663	−	63.2503i	−2.37879	−	2.13217i
$881$	−17.7954	+	7.37109i	−0.599542	+	0.248338i	−0.661750	−	0.749725i	$-0.730186\pi$
$881$	−17.7954	+	7.37109i	−0.599542	+	0.248338i	0.0622077	+	0.998063i	$0.480186\pi$
$882$	−4.11927	−	15.5416i	−0.138703	−	0.523311i
$883$	−56.0892	−	5.52430i	−1.88755	−	0.185908i	−0.912680	−	0.408675i	$-0.865991\pi$
$883$	−56.0892	−	5.52430i	−1.88755	−	0.185908i	−0.974872	+	0.222767i	$0.928491\pi$
$884$	2.78819	−	7.28808i	0.0937771	−	0.245125i
$885$	17.7915	−	9.50973i	0.598053	−	0.319666i
$886$	19.7781	+	14.2540i	0.664458	+	0.478873i
$887$	−19.7434	+	13.1921i	−0.662919	+	0.442948i	−0.840976	−	0.541072i	$-0.818019\pi$
$887$	−19.7434	+	13.1921i	−0.662919	+	0.442948i	0.178058	+	0.984020i	$0.443019\pi$
$888$	6.41952	−	4.21435i	0.215425	−	0.141424i
$889$	14.0640	−	21.0483i	0.471693	−	0.705938i
$890$	7.45476	+	3.40207i	0.249884	+	0.114038i
$891$	0.589809	+	5.98843i	0.0197593	+	0.200620i
$892$	−34.2637	+	44.1560i	−1.14723	+	1.47845i
$893$	9.99058	+	32.9345i	0.334322	+	1.10211i
$894$	−15.6752	+	17.7768i	−0.524258	+	0.594547i
$895$	13.7303			0.458953
$896$	−28.7841	−	39.0219i	−0.961608	−	1.30363i
$897$	2.61154			0.0871967
$898$	19.5713	−	22.1952i	0.653102	−	0.740665i
$899$	−8.97405	−	29.5835i	−0.299301	−	0.986665i
$900$	16.5919	+	12.8748i	0.553062	+	0.429159i
$901$	0.562045	+	5.70654i	0.0187244	+	0.190112i
$902$	18.6791	+	8.52443i	0.621946	+	0.283833i
$903$	21.0561	−	31.5126i	0.700702	−	1.04867i
$904$	−4.65827	+	22.4634i	−0.154932	+	0.747121i
$905$	−9.72602	+	6.49872i	−0.323304	+	0.216025i
$906$	1.74455	+	1.25729i	0.0579587	+	0.0417706i
$907$	−45.2176	+	24.1693i	−1.50142	+	0.802528i	−0.998103	−	0.0615705i	$-0.980389\pi$
$907$	−45.2176	+	24.1693i	−1.50142	+	0.802528i	−0.503322	+	0.864099i	$0.667889\pi$
$908$	25.0409	+	9.57988i	0.831012	+	0.317920i
$909$	12.1343	+	1.19513i	0.402471	+	0.0396399i
$910$	−12.5925	−	47.5102i	−0.417438	−	1.57495i
$911$	42.3587	−	17.5455i	1.40341	−	0.581310i	0.452772	−	0.891626i	$-0.350435\pi$
$911$	42.3587	−	17.5455i	1.40341	−	0.581310i	0.950633	+	0.310317i	$0.100435\pi$
$912$	16.7356	+	5.88388i	0.554170	+	0.194835i
$913$	−7.12931	−	2.95306i	−0.235946	−	0.0977319i
$914$	2.07403	−	15.4308i	0.0686028	−	0.510406i
$915$	31.2194	−	25.6211i	1.03208	−	0.847007i
$916$	9.62731	−	15.2966i	0.318095	−	0.505414i
$917$	25.2926	+	7.67243i	0.835236	+	0.253366i
$918$	−0.615383	+	2.60729i	−0.0203107	+	0.0860533i
$919$	−5.46849	+	27.4919i	−0.180389	+	0.906876i	0.779480	+	0.626427i	$0.215483\pi$
$919$	−5.46849	+	27.4919i	−0.180389	+	0.906876i	−0.959869	+	0.280449i	$0.909517\pi$
$920$	9.04566	−	10.8414i	0.298226	−	0.357429i
$921$	−19.7232	+	3.92319i	−0.649902	+	0.129274i
$922$	17.9650	−	16.7349i	0.591644	−	0.551135i
$923$	−22.2213	−	18.2366i	−0.731424	−	0.600264i
$924$	−16.3151	−	48.9318i	−0.536727	−	1.60974i
$925$	13.4392	−	25.1430i	0.441879	−	0.826698i
$926$	−15.3108	+	44.7060i	−0.503144	+	1.46913i
$927$	1.09812	−	1.09812i	0.0360669	−	0.0360669i
$928$	−23.7903	+	16.5650i	−0.780954	+	0.543772i
$929$	−19.1702	−	19.1702i	−0.628954	−	0.628954i	0.318851	−	0.947805i	$-0.396703\pi$
$929$	−19.1702	−	19.1702i	−0.628954	−	0.628954i	−0.947805	+	0.318851i	$0.896703\pi$
$930$	−30.1648	+	14.7742i	−0.989144	+	0.484466i
$931$	−44.4672	−	23.7682i	−1.45735	−	0.778972i
$932$	8.81975	+	0.626068i	0.288900	+	0.0205075i
$933$	13.6512	−	16.6340i	0.446919	−	0.544572i
$934$	0.954982	−	26.9405i	0.0312480	−	0.881521i
$935$	−8.75517	−	44.0152i	−0.286325	−	1.43945i
$936$	−0.618092	+	5.79274i	−0.0202030	+	0.189342i
$937$	31.7186	+	6.30923i	1.03620	+	0.206114i	0.683750	−	0.729716i	$-0.260348\pi$
$937$	31.7186	+	6.30923i	1.03620	+	0.206114i	0.352453	+	0.935830i	$0.385348\pi$
$938$	21.6928	−	13.4081i	0.708296	−	0.437791i
$939$	5.91459	−	19.4978i	0.193015	−	0.636287i
$940$	−10.2802	+	60.2349i	−0.335305	+	1.96464i
$941$	5.68363	+	6.92553i	0.185281	+	0.225766i	0.857364	−	0.514710i	$-0.172100\pi$
$941$	5.68363	+	6.92553i	0.185281	+	0.225766i	−0.672083	+	0.740476i	$0.734600\pi$
$942$	−2.97274	−	3.89596i	−0.0968572	−	0.126937i
$943$	−1.17072	+	2.82636i	−0.0381238	+	0.0920389i
$944$	19.2593	−	7.01149i	0.626838	−	0.228205i
$945$	6.45738	+	15.5895i	0.210059	+	0.507127i
$946$	37.8025	−	65.0682i	1.22906	−	2.11555i
$947$	−2.29066	+	23.2575i	−0.0744364	+	0.755766i	0.883432	+	0.468559i	$0.155227\pi$
$947$	−2.29066	+	23.2575i	−0.0744364	+	0.755766i	−0.957869	+	0.287207i	$0.907273\pi$
$948$	−17.1790	−	16.2654i	−0.557948	−	0.528277i
$949$	2.95179	+	5.52241i	0.0958192	+	0.179265i
$950$	65.0084	−	10.5522i	2.10915	−	0.342358i
$951$	−4.44898	−	6.65838i	−0.144268	−	0.215913i
$952$	0.186553	−	22.9625i	0.00604622	−	0.744219i
$953$	1.70283	+	1.13780i	0.0551601	+	0.0368568i	0.582845	−	0.812584i	$-0.301940\pi$
$953$	1.70283	+	1.13780i	0.0551601	+	0.0368568i	−0.527684	+	0.849440i	$0.676940\pi$
$954$	−1.49710	−	4.01062i	−0.0484705	−	0.129849i
$955$	88.9057	−	8.75645i	2.87692	−	0.283352i
$956$	−4.59433	+	16.7822i	−0.148591	+	0.542774i
$957$	−29.5091	+	8.95148i	−0.953893	+	0.289360i
$958$	−1.22614	−	19.5170i	−0.0396149	−	0.630567i
$959$			80.9221i			2.61311i
$960$	21.9067	+	22.6304i	0.707035	+	0.730393i
$961$		−	5.39197i		−	0.173935i
$962$	7.89280	−	0.495860i	0.254474	−	0.0159872i
$963$	6.88749	−	2.08930i	0.221946	−	0.0673267i
$964$	−3.75696	−	6.58941i	−0.121004	−	0.212231i
$965$	69.1114	−	6.80688i	2.22477	−	0.219121i
$966$	7.19995	−	2.68763i	0.231655	−	0.0864731i
$967$	−0.108636	−	0.0725883i	−0.00349350	−	0.00233428i	0.553822	−	0.832635i	$-0.313169\pi$
$967$	−0.108636	−	0.0725883i	−0.00349350	−	0.00233428i	−0.557316	+	0.830301i	$0.688169\pi$
$968$	−26.7501	−	66.0941i	−0.859781	−	2.12435i
$969$	4.66737	+	6.98522i	0.149938	+	0.224398i
$970$	3.99904	+	24.6367i	0.128401	+	0.791038i
$971$	14.9026	+	27.8808i	0.478247	+	0.894738i	0.999154	+	0.0411243i	$0.0130940\pi$
$971$	14.9026	+	27.8808i	0.478247	+	0.894738i	−0.520907	+	0.853614i	$0.674406\pi$
$972$	−0.0546110	−	1.99925i	−0.00175165	−	0.0641261i
$973$	4.95392	−	50.2980i	0.158815	−	1.61248i
$974$	19.7155	+	11.4540i	0.631725	+	0.367011i
$975$	8.27658	+	19.9814i	0.265063	+	0.639918i
$976$	35.0773	−	21.2891i	1.12280	−	0.681447i
$977$	5.38390	−	12.9979i	0.172246	−	0.415839i	−0.814056	−	0.580786i	$-0.802745\pi$
$977$	5.38390	−	12.9979i	0.172246	−	0.415839i	0.986302	+	0.164947i	$0.0527453\pi$
$978$	−25.2513	+	19.2676i	−0.807448	+	0.616110i
$979$	5.61815	+	6.84574i	0.179557	+	0.218791i
$980$	−51.7493	−	73.0485i	−1.65307	−	2.33345i
$981$	0.925594	−	3.05127i	0.0295519	−	0.0974197i
$982$	−17.8378	−	28.8596i	−0.569228	−	0.920946i
$983$	−24.3535	−	4.84421i	−0.776756	−	0.154506i	−0.209235	−	0.977865i	$-0.567097\pi$
$983$	−24.3535	−	4.84421i	−0.776756	−	0.154506i	−0.567521	+	0.823359i	$0.692097\pi$
$984$	−5.99216	−	3.26574i	−0.191023	−	0.104108i
$985$	7.55546	+	37.9839i	0.240737	+	1.21027i
$986$	−13.7199	−	0.486339i	−0.436929	−	0.0154882i
$987$	−21.0999	+	25.7103i	−0.671616	+	0.818367i
$988$	11.9710	+	13.8004i	0.380849	+	0.439050i
$989$	9.88835	+	5.28543i	0.314431	+	0.168067i
$990$	14.7371	+	30.0889i	0.468375	+	0.956290i
$991$	27.8118	+	27.8118i	0.883470	+	0.883470i	0.993885	−	0.110416i	$-0.0352182\pi$
$991$	27.8118	+	27.8118i	0.883470	+	0.883470i	−0.110416	+	0.993885i	$0.535218\pi$
$992$	−32.4599	+	10.5307i	−1.03060	+	0.334351i
$993$	−2.52182	+	2.52182i	−0.0800277	+	0.0800277i
$994$	−80.0316	−	27.4090i	−2.53845	−	0.869361i
$995$	−0.191093	+	0.357509i	−0.00605805	+	0.0113338i
$996$	2.29412	+	1.14682i	0.0726919	+	0.0363385i
$997$	−35.2257	−	28.9090i	−1.11561	−	0.915558i	−0.118609	−	0.992941i	$-0.537843\pi$
$997$	−35.2257	−	28.9090i	−1.11561	−	0.915558i	−0.997001	+	0.0773835i	$0.975343\pi$
$998$	−16.5706	−	17.7885i	−0.524532	−	0.563086i
$999$	−2.66286	+	0.529676i	−0.0842491	+	0.0167582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.8	✓	512
128.69	even	32	inner	384.2.v.a.325.8	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.8	✓	512	1.1	even	1	trivial
384.2.v.a.325.8	yes	512	128.69	even	32	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06073 - 0.935332i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(0.250309 + 1.98427i) q^{4} +(-0.385901 - 3.91812i) q^{5} +(-0.587142 + 1.28657i) q^{6} +(-2.38112 + 3.56360i) q^{7} +(1.59044 - 2.33891i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-1.06073 - 0.935332i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(0.250309 + 1.98427i) q^{4} +(-0.385901 - 3.91812i) q^{5} +(-0.587142 + 1.28657i) q^{6} +(-2.38112 + 3.56360i) q^{7} +(1.59044 - 2.33891i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-3.25540 + 4.51703i) q^{10} +(-5.30688 + 2.83658i) q^{11} +(1.82617 - 0.815535i) q^{12} +(2.04975 + 0.201883i) q^{13} +(5.85888 - 1.55289i) q^{14} +(-3.63739 + 1.50666i) q^{15} +(-3.87469 + 0.993364i) q^{16} +(-1.75009 - 0.724912i) q^{17} +(1.40161 + 0.188388i) q^{18} +(3.42826 - 2.81350i) q^{19} +(7.67803 - 1.74648i) q^{20} +(4.10136 + 1.24413i) q^{21} +(8.28232 + 1.95483i) q^{22} +(-0.247363 + 1.24358i) q^{23} +(-2.69988 - 0.843011i) q^{24} +(-10.2988 + 2.04856i) q^{25} +(-1.98541 - 2.13134i) q^{26} +(0.773010 + 0.634393i) q^{27} +(-7.66718 - 3.83280i) q^{28} +(-2.41573 + 4.51951i) q^{29} +(5.26752 + 1.80400i) q^{30} +(-4.26568 + 4.26568i) q^{31} +(5.03914 + 2.57043i) q^{32} +(4.25495 + 4.25495i) q^{33} +(1.17835 + 2.40586i) q^{34} +(14.8815 + 7.95433i) q^{35} +(-1.31053 - 1.51080i) q^{36} +(-1.72240 + 2.09874i) q^{37} +(-6.26802 - 0.222187i) q^{38} +(-0.401822 - 2.02009i) q^{39} +(-9.77788 - 5.32896i) q^{40} +(2.36639 + 0.470705i) q^{41} +(-3.18677 - 5.15582i) q^{42} +(2.56696 - 8.46214i) q^{43} +(-6.95692 - 9.82027i) q^{44} +(2.49766 + 3.04340i) q^{45} +(1.42554 - 1.08774i) q^{46} +(-2.96974 + 7.16958i) q^{47} +(2.07535 + 3.41949i) q^{48} +(-4.35073 - 10.5036i) q^{49} +(12.8404 + 7.45984i) q^{50} +(-0.185673 + 1.88517i) q^{51} +(0.112481 + 4.11780i) q^{52} +(-1.42695 - 2.66964i) q^{53} +(-0.226590 - 1.39594i) q^{54} +(13.1620 + 19.6983i) q^{55} +(4.54789 + 11.2369i) q^{56} +(-3.68752 - 2.46392i) q^{57} +(6.78969 - 2.53449i) q^{58} +(-5.09931 + 0.502238i) q^{59} +(-3.90009 - 6.84044i) q^{60} +(-9.81634 + 2.97775i) q^{61} +(8.51456 - 0.534921i) q^{62} -4.28591i q^{63} +(-2.94098 - 7.43980i) q^{64} -8.10908i q^{65} +(-0.533576 - 8.49315i) q^{66} +(4.02627 - 1.22136i) q^{67} +(1.00036 - 3.65412i) q^{68} +(1.26183 - 0.124280i) q^{69} +(-8.34536 - 22.3566i) q^{70} +(-11.6047 - 7.75400i) q^{71} +(-0.0229781 + 2.82833i) q^{72} +(1.68904 + 2.52783i) q^{73} +(3.79002 - 0.615197i) q^{74} +(4.94995 + 9.26070i) q^{75} +(6.44088 + 6.09836i) q^{76} +(2.52786 - 25.6658i) q^{77} +(-1.46323 + 2.51862i) q^{78} +(-4.52669 - 10.9284i) q^{79} +(5.38737 + 14.7982i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-2.06985 - 2.71266i) q^{82} +(0.813545 + 0.991307i) q^{83} +(-1.44209 + 8.44964i) q^{84} +(-2.16493 + 7.13682i) q^{85} +(-10.6378 + 6.57511i) q^{86} +(5.02615 + 0.999764i) q^{87} +(-1.80578 + 16.9237i) q^{88} +(-0.287119 - 1.44344i) q^{89} +(0.197245 - 5.56438i) q^{90} +(-5.60014 + 6.82379i) q^{91} +(-2.52951 - 0.179557i) q^{92} +(5.32026 + 2.84374i) q^{93} +(9.85604 - 4.82732i) q^{94} +(-12.3466 - 12.3466i) q^{95} +(0.996961 - 5.56831i) q^{96} +(3.16976 - 3.16976i) q^{97} +(-5.20938 + 15.2109i) q^{98} +(2.83658 - 5.30688i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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