LMFDB - Embedded newform 700.2.bj.a.323.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(127,700)] 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("700.127"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$90$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			323.1
Character	$\chi$	$=$	700.323
Dual form			700.2.bj.a.687.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41339 + 0.0483313i) q^{2} +(-0.993217 - 1.94930i) q^{3} +(1.99533 - 0.136622i) q^{4} +(-0.0255244 + 2.23592i) q^{5} +(1.49801 + 2.70711i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.81357 + 0.289536i) q^{8} +(-1.04993 + 1.44510i) q^{9} +(-0.0719891 - 3.16146i) q^{10} +(-0.720247 - 0.991334i) q^{11} +(-2.24811 - 3.75379i) q^{12} +(-0.598148 - 3.77656i) q^{13} +(-1.03359 - 0.965240i) q^{14} +(4.38383 - 2.17100i) q^{15} +(3.96267 - 0.545210i) q^{16} +(0.871876 + 0.444243i) q^{17} +(1.41411 - 2.09323i) q^{18} +(2.07265 + 6.37897i) q^{19} +(0.254546 + 4.46489i) q^{20} +(0.676051 - 2.08067i) q^{21} +(1.06590 + 1.36633i) q^{22} +(-0.887367 + 5.60261i) q^{23} +(3.35888 + 5.19691i) q^{24} +(-4.99870 - 0.114141i) q^{25} +(1.02794 + 5.30883i) q^{26} +(-2.62270 - 0.415395i) q^{27} +(1.50752 + 1.31430i) q^{28} +(8.54637 + 2.77688i) q^{29} +(-6.09112 + 3.28034i) q^{30} +(6.40884 - 2.08236i) q^{31} +(-5.57444 + 0.962114i) q^{32} +(-1.21704 + 2.38859i) q^{33} +(-1.25377 - 0.585748i) q^{34} +(-1.59908 + 1.56299i) q^{35} +(-1.89752 + 3.02689i) q^{36} +(7.20941 - 1.14186i) q^{37} +(-3.23776 - 8.91578i) q^{38} +(-6.76755 + 4.91691i) q^{39} +(-0.575566 - 6.29831i) q^{40} +(-2.05887 - 1.49585i) q^{41} +(-0.854961 + 2.97347i) q^{42} +(6.58605 - 6.58605i) q^{43} +(-1.57257 - 1.87964i) q^{44} +(-3.20433 - 2.38444i) q^{45} +(0.983412 - 7.96155i) q^{46} +(1.31064 - 0.667805i) q^{47} +(-4.99857 - 7.18291i) q^{48} +1.00000i q^{49} +(7.07061 - 0.0802678i) q^{50} -2.14078i q^{51} +(-1.70946 - 7.45376i) q^{52} +(2.94493 - 1.50052i) q^{53} +(3.72697 + 0.460356i) q^{54} +(2.23493 - 1.58511i) q^{55} +(-2.19423 - 1.78476i) q^{56} +(10.3759 - 10.3759i) q^{57} +(-12.2135 - 3.51176i) q^{58} +(5.67531 + 4.12336i) q^{59} +(8.45057 - 4.93079i) q^{60} +(2.07670 - 1.50881i) q^{61} +(-8.95754 + 3.25293i) q^{62} +(-1.76425 + 0.279430i) q^{63} +(7.83234 - 1.62926i) q^{64} +(8.45936 - 1.24102i) q^{65} +(1.60471 - 3.43482i) q^{66} +(5.09044 - 9.99055i) q^{67} +(1.80037 + 0.767293i) q^{68} +(11.8025 - 3.83487i) q^{69} +(2.18458 - 2.28639i) q^{70} +(-3.11308 - 1.01150i) q^{71} +(2.53563 - 4.36988i) q^{72} +(-3.90944 - 0.619194i) q^{73} +(-10.1345 + 1.96233i) q^{74} +(4.74230 + 9.85732i) q^{75} +(5.00713 + 12.4450i) q^{76} +(0.191688 - 1.21027i) q^{77} +(9.32753 - 7.27659i) q^{78} +(-2.41406 + 7.42971i) q^{79} +(1.11790 + 8.87414i) q^{80} +(3.45112 + 10.6215i) q^{81} +(2.98227 + 2.01471i) q^{82} +(-0.861689 - 0.439052i) q^{83} +(1.06468 - 4.24399i) q^{84} +(-1.01555 + 1.93811i) q^{85} +(-8.99033 + 9.62695i) q^{86} +(-3.07543 - 19.4175i) q^{87} +(2.31349 + 2.58065i) q^{88} +(-4.36461 - 6.00737i) q^{89} +(4.64421 + 3.21527i) q^{90} +(2.24748 - 3.09339i) q^{91} +(-1.00515 + 11.3003i) q^{92} +(-10.4245 - 10.4245i) q^{93} +(-1.82017 + 1.00721i) q^{94} +(-14.3158 + 4.47147i) q^{95} +(7.41207 + 9.91065i) q^{96} +(5.07067 + 9.95176i) q^{97} +(-0.0483313 - 1.41339i) q^{98} +2.18878 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) $ 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

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

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

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

$2$	−1.41339	+	0.0483313i	−0.999416	+	0.0341754i
$2$	−1.41339	+	0.0483313i	−0.999416	+	0.0341754i
$3$	−0.993217	−	1.94930i	−0.573434	−	1.12543i	−0.977547	−	0.210719i	$-0.932420\pi$
$3$	−0.993217	−	1.94930i	−0.573434	−	1.12543i	0.404113	−	0.914709i	$-0.367580\pi$
$4$	1.99533	−	0.136622i	0.997664	−	0.0683108i
$5$	−0.0255244	+	2.23592i	−0.0114149	+	0.999935i
$5$	−0.0255244	+	2.23592i	−0.0114149	+	0.999935i
$6$	1.49801	+	2.70711i	0.611561	+	1.10517i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−2.81357	+	0.289536i	−0.994747	+	0.102366i
$9$	−1.04993	+	1.44510i	−0.349976	+	0.481700i
$10$	−0.0719891	−	3.16146i	−0.0227650	−	0.999741i
$11$	−0.720247	−	0.991334i	−0.217163	−	0.298899i	0.686512	−	0.727118i	$-0.259141\pi$
$11$	−0.720247	−	0.991334i	−0.217163	−	0.298899i	−0.903675	+	0.428220i	$0.859141\pi$
$12$	−2.24811	−	3.75379i	−0.648974	−	1.08363i
$13$	−0.598148	−	3.77656i	−0.165897	−	1.04743i	−0.920356	−	0.391082i	$-0.872101\pi$
$13$	−0.598148	−	3.77656i	−0.165897	−	1.04743i	0.754459	−	0.656347i	$-0.227899\pi$
$14$	−1.03359	−	0.965240i	−0.276239	−	0.257971i
$15$	4.38383	−	2.17100i	1.13190	−	0.560550i
$16$	3.96267	−	0.545210i	0.990667	−	0.136303i
$17$	0.871876	+	0.444243i	0.211461	+	0.107745i	0.556513	−	0.830839i	$-0.312139\pi$
$17$	0.871876	+	0.444243i	0.211461	+	0.107745i	−0.345052	+	0.938583i	$0.612139\pi$
$18$	1.41411	−	2.09323i	0.333309	−	0.493379i
$19$	2.07265	+	6.37897i	0.475499	+	1.46344i	0.845284	+	0.534318i	$0.179432\pi$
$19$	2.07265	+	6.37897i	0.475499	+	1.46344i	−0.369784	+	0.929118i	$0.620568\pi$
$20$	0.254546	+	4.46489i	0.0569182	+	0.998379i
$21$	0.676051	−	2.08067i	0.147527	−	0.454040i
$22$	1.06590	+	1.36633i	0.227251	+	0.291302i
$23$	−0.887367	+	5.60261i	−0.185029	+	1.16823i	0.703940	+	0.710259i	$0.251422\pi$
$23$	−0.887367	+	5.60261i	−0.185029	+	1.16823i	−0.888969	+	0.457967i	$0.848578\pi$
$24$	3.35888	+	5.19691i	0.685628	+	1.06082i
$25$	−4.99870	−	0.114141i	−0.999739	−	0.0228282i
$26$	1.02794	+	5.30883i	0.201596	+	1.04115i
$27$	−2.62270	−	0.415395i	−0.504739	−	0.0799429i
$28$	1.50752	+	1.31430i	0.284894	+	0.248380i
$29$	8.54637	+	2.77688i	1.58702	+	0.515655i	0.963853	−	0.266433i	$-0.0858452\pi$
$29$	8.54637	+	2.77688i	1.58702	+	0.515655i	0.623168	+	0.782088i	$0.285845\pi$
$30$	−6.09112	+	3.28034i	−1.11208	+	0.598906i
$31$	6.40884	−	2.08236i	1.15106	−	0.374003i	0.329519	−	0.944149i	$-0.393113\pi$
$31$	6.40884	−	2.08236i	1.15106	−	0.374003i	0.821543	+	0.570146i	$0.193113\pi$
$32$	−5.57444	+	0.962114i	−0.985430	+	0.170079i
$33$	−1.21704	+	2.38859i	−0.211860	+	0.415799i
$34$	−1.25377	−	0.585748i	−0.215020	−	0.100455i
$35$	−1.59908	+	1.56299i	−0.270295	+	0.264193i
$36$	−1.89752	+	3.02689i	−0.316253	+	0.504482i
$37$	7.20941	−	1.14186i	1.18522	−	0.187720i	0.467462	−	0.884013i	$-0.345168\pi$
$37$	7.20941	−	1.14186i	1.18522	−	0.187720i	0.717758	+	0.696293i	$0.245168\pi$
$38$	−3.23776	−	8.91578i	−0.525235	−	1.44633i
$39$	−6.76755	+	4.91691i	−1.08368	+	0.787336i
$40$	−0.575566	−	6.29831i	−0.0910049	−	0.995850i
$41$	−2.05887	−	1.49585i	−0.321541	−	0.233613i	0.415292	−	0.909688i	$-0.363679\pi$
$41$	−2.05887	−	1.49585i	−0.321541	−	0.233613i	−0.736833	+	0.676075i	$0.763679\pi$
$42$	−0.854961	+	2.97347i	−0.131923	+	0.458816i
$43$	6.58605	−	6.58605i	1.00436	−	1.00436i	0.00437278	−	0.999990i	$-0.498608\pi$
$43$	6.58605	−	6.58605i	1.00436	−	1.00436i	0.999990	−	0.00437278i	$-0.00139190\pi$
$44$	−1.57257	−	1.87964i	−0.237073	−	0.283366i
$45$	−3.20433	−	2.38444i	−0.477674	−	0.355452i
$46$	0.983412	−	7.96155i	0.144996	−	1.17387i
$47$	1.31064	−	0.667805i	0.191177	−	0.0974094i	−0.355782	−	0.934569i	$-0.615785\pi$
$47$	1.31064	−	0.667805i	0.191177	−	0.0974094i	0.546959	+	0.837160i	$0.315785\pi$
$48$	−4.99857	−	7.18291i	−0.721481	−	1.03676i
$49$			1.00000i			0.142857i
$50$	7.07061	−	0.0802678i	0.999936	−	0.0113516i
$51$		−	2.14078i		−	0.299768i
$52$	−1.70946	−	7.45376i	−0.237060	−	1.03365i
$53$	2.94493	−	1.50052i	0.404517	−	0.206112i	−0.239880	−	0.970802i	$-0.577108\pi$
$53$	2.94493	−	1.50052i	0.404517	−	0.206112i	0.644398	+	0.764691i	$0.277108\pi$
$54$	3.72697	+	0.460356i	0.507177	+	0.0626465i
$55$	2.23493	−	1.58511i	0.301358	−	0.213736i
$56$	−2.19423	−	1.78476i	−0.293216	−	0.238499i
$57$	10.3759	−	10.3759i	1.37432	−	1.37432i
$58$	−12.2135	−	3.51176i	−1.60372	−	0.461116i
$59$	5.67531	+	4.12336i	0.738863	+	0.536815i	0.892355	−	0.451335i	$-0.149052\pi$
$59$	5.67531	+	4.12336i	0.738863	+	0.536815i	−0.153492	+	0.988150i	$0.549052\pi$
$60$	8.45057	−	4.93079i	1.09096	−	0.636562i
$61$	2.07670	−	1.50881i	0.265895	−	0.193184i	−0.446847	−	0.894610i	$-0.647453\pi$
$61$	2.07670	−	1.50881i	0.265895	−	0.193184i	0.712742	+	0.701427i	$0.247453\pi$
$62$	−8.95754	+	3.25293i	−1.13761	+	0.413122i
$63$	−1.76425	+	0.279430i	−0.222275	+	0.0352049i
$64$	7.83234	−	1.62926i	0.979042	−	0.203657i
$65$	8.45936	−	1.24102i	1.04925	−	0.153929i
$66$	1.60471	−	3.43482i	0.197526	−	0.422797i
$67$	5.09044	−	9.99055i	0.621896	−	1.22054i	−0.338254	−	0.941055i	$-0.609836\pi$
$67$	5.09044	−	9.99055i	0.621896	−	1.22054i	0.960150	−	0.279485i	$-0.0901638\pi$
$68$	1.80037	+	0.767293i	0.218327	+	0.0930480i
$69$	11.8025	−	3.83487i	1.42086	−	0.461664i
$70$	2.18458	−	2.28639i	0.261108	−	0.273276i
$71$	−3.11308	−	1.01150i	−0.369454	−	0.120043i	0.118405	−	0.992965i	$-0.462222\pi$
$71$	−3.11308	−	1.01150i	−0.369454	−	0.120043i	−0.487859	+	0.872922i	$0.662222\pi$
$72$	2.53563	−	4.36988i	0.298827	−	0.514996i
$73$	−3.90944	−	0.619194i	−0.457565	−	0.0724711i	−0.0766025	−	0.997062i	$-0.524407\pi$
$73$	−3.90944	−	0.619194i	−0.457565	−	0.0724711i	−0.380962	+	0.924591i	$0.624407\pi$
$74$	−10.1345	+	1.96233i	−1.17811	+	0.228116i
$75$	4.74230	+	9.85732i	0.547593	+	1.13822i
$76$	5.00713	+	12.4450i	0.574357	+	1.42754i
$77$	0.191688	−	1.21027i	0.0218449	−	0.137923i
$78$	9.32753	−	7.27659i	1.05613	−	0.823911i
$79$	−2.41406	+	7.42971i	−0.271603	+	0.835907i	0.718496	+	0.695532i	$0.244831\pi$
$79$	−2.41406	+	7.42971i	−0.271603	+	0.835907i	−0.990098	+	0.140376i	$0.955169\pi$
$80$	1.11790	+	8.87414i	0.124985	+	0.992159i
$81$	3.45112	+	10.6215i	0.383458	+	1.18016i
$82$	2.98227	+	2.01471i	0.329337	+	0.222488i
$83$	−0.861689	−	0.439052i	−0.0945826	−	0.0481923i	0.406059	−	0.913847i	$-0.366903\pi$
$83$	−0.861689	−	0.439052i	−0.0945826	−	0.0481923i	−0.500642	+	0.865654i	$0.666903\pi$
$84$	1.06468	−	4.24399i	0.116166	−	0.463057i
$85$	−1.01555	+	1.93811i	−0.110151	+	0.210217i
$86$	−8.99033	+	9.62695i	−0.969452	+	1.03810i
$87$	−3.07543	−	19.4175i	−0.329720	−	2.08177i
$88$	2.31349	+	2.58065i	0.246619	+	0.275098i
$89$	−4.36461	−	6.00737i	−0.462648	−	0.636780i	0.512407	−	0.858743i	$-0.328754\pi$
$89$	−4.36461	−	6.00737i	−0.462648	−	0.636780i	−0.975055	+	0.221962i	$0.928754\pi$
$90$	4.64421	+	3.21527i	0.489543	+	0.338919i
$91$	2.24748	−	3.09339i	0.235600	−	0.324275i
$92$	−1.00515	+	11.3003i	−0.104794	+	1.17814i
$93$	−10.4245	−	10.4245i	−1.08097	−	1.08097i
$94$	−1.82017	+	1.00721i	−0.187736	+	0.103886i
$95$	−14.3158	+	4.47147i	−1.46877	+	0.458763i
$96$	7.41207	+	9.91065i	0.756491	+	1.01150i
$97$	5.07067	+	9.95176i	0.514849	+	1.01045i	0.991346	+	0.131272i	$0.0419062\pi$
$97$	5.07067	+	9.95176i	0.514849	+	1.01045i	−0.476497	+	0.879176i	$0.658094\pi$
$98$	−0.0483313	−	1.41339i	−0.00488220	−	0.142774i
$99$	2.18878			0.219981
$100$	−9.98964	+	0.455181i	−0.998964	+	0.0455181i
$101$	1.14986			0.114415			0.0572076	−	0.998362i	$-0.481780\pi$
$101$	1.14986			0.114415			0.0572076	+	0.998362i	$0.481780\pi$
$102$	0.103466	+	3.02574i	0.0102447	+	0.299593i
$103$	−3.59773	−	7.06094i	−0.354495	−	0.695736i	0.643046	−	0.765828i	$-0.277671\pi$
$103$	−3.59773	−	7.06094i	−0.354495	−	0.695736i	−0.997541	+	0.0700924i	$0.977671\pi$
$104$	2.77638	+	10.4524i	0.272247	+	1.02494i
$105$	4.63497	+	1.56471i	0.452326	+	0.152700i
$106$	−4.08981	+	2.26314i	−0.397237	+	0.219816i
$107$	8.23561	+	8.23561i	0.796167	+	0.796167i	0.982489	−	0.186322i	$-0.0596567\pi$
$107$	8.23561	+	8.23561i	0.796167	+	0.796167i	−0.186322	+	0.982489i	$0.559657\pi$
$108$	−5.28990	−	0.470532i	−0.509021	−	0.0452770i
$109$	9.42837	−	12.9770i	0.903075	−	1.24298i	−0.0664024	−	0.997793i	$-0.521152\pi$
$109$	9.42837	−	12.9770i	0.903075	−	1.24298i	0.969477	−	0.245183i	$-0.0788479\pi$
$110$	−3.08221	+	2.34839i	−0.293877	+	0.223911i
$111$	−9.38633	−	12.9192i	−0.890911	−	1.22623i
$112$	3.18755	+	2.41651i	0.301195	+	0.228339i
$113$	3.14744	+	19.8722i	0.296086	+	1.86941i	0.467183	+	0.884161i	$0.345269\pi$
$113$	3.14744	+	19.8722i	0.296086	+	1.86941i	−0.171097	+	0.985254i	$0.554731\pi$
$114$	−14.1637	+	15.1667i	−1.32655	+	1.42049i
$115$	−12.5044	−	2.12709i	−1.16604	−	0.198352i
$116$	17.4322	+	4.37318i	1.61854	+	0.406039i
$117$	6.08552	+	3.10073i	0.562607	+	0.286663i
$118$	−8.22071	−	5.55361i	−0.756777	−	0.511251i
$119$	0.302382	+	0.930636i	0.0277193	+	0.0853113i
$120$	−11.7056	+	7.37754i	−1.06857	+	0.673474i
$121$	2.93520	−	9.03361i	0.266836	−	0.821237i
$122$	−2.86226	+	2.23291i	−0.259137	+	0.202158i
$123$	−0.870964	+	5.49905i	−0.0785322	+	0.495833i
$124$	12.5033	−	5.03058i	1.12283	−	0.451759i
$125$	0.382799	−	11.1738i	0.0342386	−	0.999414i
$126$	2.48007	−	0.480211i	0.220942	−	0.0427806i
$127$	16.8833	+	2.67406i	1.49815	+	0.237284i	0.851037	−	0.525106i	$-0.175974\pi$
$127$	16.8833	+	2.67406i	1.49815	+	0.237284i	0.647117	+	0.762391i	$0.275974\pi$
$128$	−10.9914	+	2.68132i	−0.971510	+	0.236998i
$129$	−19.3796	−	6.29680i	−1.70627	−	0.554402i
$130$	−11.8964	+	2.16289i	−1.04338	+	0.189698i
$131$	11.4801	−	3.73012i	1.00302	−	0.325902i	0.238951	−	0.971032i	$-0.423196\pi$
$131$	11.4801	−	3.73012i	1.00302	−	0.325902i	0.764074	+	0.645129i	$0.223196\pi$
$132$	−2.10207	+	4.93229i	−0.182962	+	0.429300i
$133$	−3.04503	+	5.97620i	−0.264037	+	0.518202i
$134$	−6.71191	+	14.3665i	−0.579821	+	1.24108i
$135$	0.995734	−	5.85356i	0.0856992	−	0.503794i
$136$	−2.58171	−	0.997468i	−0.221380	−	0.0855322i
$137$	5.11378	−	0.809943i	0.436899	−	0.0691981i	0.0658894	−	0.997827i	$-0.479012\pi$
$137$	5.11378	−	0.809943i	0.436899	−	0.0691981i	0.371010	+	0.928629i	$0.379012\pi$
$138$	−16.4962	+	5.99059i	−1.40425	+	0.509953i
$139$	−7.90096	+	5.74038i	−0.670151	+	0.486893i	−0.870076	−	0.492918i	$-0.835930\pi$
$139$	−7.90096	+	5.74038i	−0.670151	+	0.486893i	0.199925	+	0.979811i	$0.435930\pi$
$140$	−2.97716	+	3.33714i	−0.251616	+	0.282040i
$141$	−2.60350	−	1.89156i	−0.219255	−	0.159298i
$142$	4.44887	+	1.27918i	0.373341	+	0.107347i
$143$	−3.31302	+	3.31302i	−0.277049	+	0.277049i
$144$	−3.37263	+	6.29889i	−0.281053	+	0.524907i
$145$	−6.42704	+	19.0381i	−0.533737	+	1.58103i
$146$	5.55547	+	0.686213i	0.459774	+	0.0567914i
$147$	1.94930	−	0.993217i	0.160775	−	0.0819192i
$148$	14.2291	−	3.26334i	1.16963	−	0.268245i
$149$		−	16.9355i		−	1.38741i	−0.720257	−	0.693707i	$-0.755976\pi$
$149$		−	16.9355i		−	1.38741i	0.720257	−	0.693707i	$-0.244024\pi$
$150$	−7.17912	−	13.7030i	−0.586173	−	1.11885i
$151$			14.7489i			1.20025i	0.799907	+	0.600124i	$0.204882\pi$
$151$			14.7489i			1.20025i	−0.799907	+	0.600124i	$0.795118\pi$
$152$	−7.67849	−	17.3476i	−0.622808	−	1.40707i
$153$	−1.55738	+	0.793526i	−0.125907	+	0.0641527i
$154$	−0.212435	+	1.71985i	−0.0171185	+	0.138589i
$155$	4.49241	+	14.3828i	0.360839	+	1.15526i
$156$	−12.8317	+	10.7355i	−1.02736	+	0.859524i
$157$	−10.4688	+	10.4688i	−0.835502	+	0.835502i	−0.988263	−	0.152761i	$-0.951183\pi$
$157$	−10.4688	+	10.4688i	−0.835502	+	0.835502i	0.152761	+	0.988263i	$0.451183\pi$
$158$	3.05291	−	10.6177i	0.242877	−	0.844701i
$159$	−5.84991	−	4.25021i	−0.463928	−	0.337063i
$160$	−2.00893	−	12.4886i	−0.158820	−	0.987308i
$161$	−4.58911	+	3.33418i	−0.361673	+	0.262770i
$162$	−5.39112	−	14.8454i	−0.423566	−	1.16637i
$163$	−8.63319	+	1.36736i	−0.676204	+	0.107100i	−0.485085	−	0.874467i	$-0.661211\pi$
$163$	−8.63319	+	1.36736i	−0.676204	+	0.107100i	−0.191118	+	0.981567i	$0.561211\pi$
$164$	−4.31248	−	2.70343i	−0.336748	−	0.211103i
$165$	−5.30963	−	2.78219i	−0.413354	−	0.216593i
$166$	1.23912	+	0.578905i	0.0961744	+	0.0449317i
$167$	−5.44088	+	10.6783i	−0.421028	+	0.826313i	0.578913	+	0.815390i	$0.303477\pi$
$167$	−5.44088	+	10.6783i	−0.421028	+	0.826313i	−0.999940	+	0.0109239i	$0.996523\pi$
$168$	−1.29969	+	6.04986i	−0.100273	+	0.466757i
$169$	−1.54089	+	0.500667i	−0.118530	+	0.0385128i
$170$	1.34169	−	2.78838i	0.102903	−	0.213859i
$171$	−11.3944	−	3.70226i	−0.871351	−	0.283119i
$172$	12.2415	−	14.0411i	0.933408	−	1.07063i
$173$	−8.30813	−	1.31588i	−0.631656	−	0.100044i	−0.167607	−	0.985854i	$-0.553604\pi$
$173$	−8.30813	−	1.31588i	−0.631656	−	0.100044i	−0.464049	+	0.885809i	$0.653604\pi$
$174$	5.28524	+	27.2958i	0.400673	+	2.06929i
$175$	−3.45390	−	3.61532i	−0.261090	−	0.273293i
$176$	−3.39458	−	3.53564i	−0.255876	−	0.266509i
$177$	2.40083	−	15.1583i	0.180458	−	1.13937i
$178$	6.45923	+	8.27980i	0.484140	+	0.620597i
$179$	−4.48300	+	13.7973i	−0.335075	+	1.03126i	0.631610	+	0.775286i	$0.282394\pi$
$179$	−4.48300	+	13.7973i	−0.335075	+	1.03126i	−0.966685	+	0.255969i	$0.917606\pi$
$180$	−6.71947	−	4.31996i	−0.500839	−	0.321991i
$181$	3.10761	+	9.56423i	0.230987	+	0.710903i	0.997629	+	0.0688286i	$0.0219262\pi$
$181$	3.10761	+	9.56423i	0.230987	+	0.710903i	−0.766642	+	0.642075i	$0.778074\pi$
$182$	−3.02705	+	4.48078i	−0.224380	+	0.332137i
$183$	−5.00374	−	2.54953i	−0.369887	−	0.188467i
$184$	0.874509	−	16.0203i	0.0644696	−	1.18103i
$185$	2.36909	+	16.1488i	0.174179	+	1.18729i
$186$	15.2377	+	14.2300i	1.11728	+	1.04340i
$187$	−0.187572	−	1.18428i	−0.0137166	−	0.0866035i
$188$	2.52392	−	1.51155i	0.184076	−	0.110241i
$189$	−1.56080	−	2.14826i	−0.113532	−	0.156263i
$190$	20.0176	−	7.01182i	1.45223	−	0.508691i
$191$	10.7422	−	14.7854i	0.777280	−	1.06983i	−0.218296	−	0.975883i	$-0.570050\pi$
$191$	10.7422	−	14.7854i	0.777280	−	1.06983i	0.995577	−	0.0939520i	$-0.0299500\pi$
$192$	−10.9551	−	13.6494i	−0.790618	−	0.985057i
$193$	1.63504	+	1.63504i	0.117693	+	0.117693i	0.763500	−	0.645807i	$-0.223479\pi$
$193$	1.63504	+	1.63504i	0.117693	+	0.117693i	−0.645807	+	0.763500i	$0.723479\pi$
$194$	−7.64781	−	13.8206i	−0.549081	−	0.992263i
$195$	−10.8211	−	15.2572i	−0.774915	−	1.09259i
$196$	0.136622	+	1.99533i	0.00975869	+	0.142523i
$197$	−6.57068	−	12.8957i	−0.468141	−	0.918779i	−0.997519	−	0.0703929i	$-0.977575\pi$
$197$	−6.57068	−	12.8957i	−0.468141	−	0.918779i	0.529378	−	0.848386i	$-0.322425\pi$
$198$	−3.09360	+	0.105787i	−0.219853	+	0.00751794i
$199$	−24.3332			−1.72494			−0.862468	−	0.506112i	$-0.831082\pi$
$199$	−24.3332			−1.72494			−0.862468	+	0.506112i	$0.831082\pi$
$200$	14.0972	−	1.12616i	0.996824	−	0.0796315i
$201$	−24.5305			−1.73025
$202$	−1.62519	+	0.0555741i	−0.114348	+	0.00391018i
$203$	4.07964	+	8.00675i	0.286335	+	0.561964i
$204$	−0.292476	−	4.27155i	−0.0204774	−	0.299068i
$205$	3.39716	−	4.56528i	0.237268	−	0.318853i
$206$	5.42625	+	9.80597i	0.378065	+	0.683214i
$207$	−7.16467	−	7.16467i	−0.497979	−	0.497979i
$208$	−4.42928	−	14.6391i	−0.307116	−	1.01504i
$209$	4.83087	−	6.64912i	0.334158	−	0.459929i
$210$	−6.62663	−	1.98752i	−0.457281	−	0.137152i
$211$	3.04667	+	4.19338i	0.209741	+	0.288684i	0.900907	−	0.434012i	$-0.142903\pi$
$211$	3.04667	+	4.19338i	0.209741	+	0.288684i	−0.691166	+	0.722696i	$0.742903\pi$
$212$	5.67110	−	3.39637i	0.389493	−	0.233263i
$213$	1.12025	+	7.07295i	0.0767580	+	0.484631i
$214$	−12.0382	−	11.2421i	−0.822911	−	0.768493i
$215$	14.5578	+	14.8940i	0.992833	+	1.01576i
$216$	7.49943	+	0.409376i	0.510271	+	0.0278545i
$217$	6.00419	+	3.05929i	0.407591	+	0.207678i
$218$	−12.6987	+	18.7973i	−0.860068	+	1.27311i
$219$	2.67592	+	8.23565i	0.180822	+	0.556514i
$220$	4.24286	−	3.46816i	0.286053	−	0.233823i
$221$	1.15620	−	3.55841i	0.0777744	−	0.239365i
$222$	13.8909	+	17.8062i	0.932298	+	1.19507i
$223$	−0.411232	+	2.59642i	−0.0275381	+	0.173869i	−0.997624	−	0.0688929i	$-0.978053\pi$
$223$	−0.411232	+	2.59642i	−0.0275381	+	0.173869i	0.970086	+	0.242762i	$0.0780533\pi$
$224$	−4.62204	−	3.26140i	−0.308823	−	0.217912i
$225$	5.41321	−	7.10378i	0.360881	−	0.473585i
$226$	−5.40900	−	27.9349i	−0.359801	−	1.85820i
$227$	−0.529288	−	0.0838309i	−0.0351301	−	0.00556405i	0.138845	−	0.990314i	$-0.455661\pi$
$227$	−0.529288	−	0.0838309i	−0.0351301	−	0.00556405i	−0.173975	+	0.984750i	$0.555661\pi$
$228$	19.2858	−	22.1209i	1.27723	−	1.46499i
$229$	−10.6115	−	3.44788i	−0.701227	−	0.227843i	−0.0633622	−	0.997991i	$-0.520182\pi$
$229$	−10.6115	−	3.44788i	−0.701227	−	0.227843i	−0.637865	+	0.770148i	$0.720182\pi$
$230$	17.7763	+	2.40205i	1.17214	+	0.158386i
$231$	−2.54957	+	0.828404i	−0.167749	+	0.0545050i
$232$	−24.8498	−	5.33847i	−1.63147	−	0.350488i
$233$	−10.4715	+	20.5515i	−0.686011	+	1.34637i	0.240700	+	0.970599i	$0.422623\pi$
$233$	−10.4715	+	20.5515i	−0.686011	+	1.34637i	−0.926712	+	0.375773i	$0.877377\pi$
$234$	−8.75107	−	4.08841i	−0.572075	−	0.267268i
$235$	1.45971	+	2.94754i	0.0952208	+	0.192276i
$236$	11.8875	+	7.45208i	0.773807	+	0.485089i
$237$	16.8804	−	2.67359i	1.09650	−	0.173668i
$238$	−0.472362	−	1.30074i	−0.0306187	−	0.0843141i
$239$	4.98845	−	3.62432i	0.322676	−	0.234438i	−0.414641	−	0.909985i	$-0.636093\pi$
$239$	4.98845	−	3.62432i	0.322676	−	0.234438i	0.737316	+	0.675548i	$0.236093\pi$
$240$	16.1880	−	10.9931i	1.04493	−	0.709600i
$241$	−19.4855	−	14.1570i	−1.25517	−	0.911935i	−0.256661	−	0.966502i	$-0.582622\pi$
$241$	−19.4855	−	14.1570i	−1.25517	−	0.911935i	−0.998510	+	0.0545666i	$0.982622\pi$
$242$	−3.71197	+	12.9099i	−0.238614	+	0.829877i
$243$	11.6437	−	11.6437i	0.746946	−	0.746946i
$244$	3.93757	−	3.29430i	0.252077	−	0.210896i
$245$	−2.23592	−	0.0255244i	−0.142848	−	0.00163069i
$246$	0.965233	−	7.81438i	0.0615410	−	0.498227i
$247$	22.8508	−	11.6431i	1.45396	−	0.740831i
$248$	−17.4288	+	7.71445i	−1.10673	+	0.489868i
$249$			2.11576i			0.134081i
$250$	−0.00100066	+	15.8114i	−6.32875e−5	+	1.00000i
$251$			8.78795i			0.554691i	0.960770	+	0.277345i	$0.0894546\pi$
$251$			8.78795i			0.554691i	−0.960770	+	0.277345i	$0.910545\pi$
$252$	−3.48208	+	0.798589i	−0.219351	+	0.0503064i
$253$	6.19319	−	3.15559i	0.389362	−	0.198390i
$254$	−23.9919	−	2.96349i	−1.50539	−	0.185946i
$255$	4.78661	+	0.0546420i	0.299749	+	0.00342181i
$256$	15.4055	−	4.32097i	0.962843	−	0.270061i
$257$	−5.32742	+	5.32742i	−0.332315	+	0.332315i	−0.853465	−	0.521150i	$-0.825503\pi$
$257$	−5.32742	+	5.32742i	−0.332315	+	0.332315i	0.521150	+	0.853465i	$0.325503\pi$
$258$	27.6951	+	7.96318i	1.72422	+	0.495766i
$259$	5.90524	+	4.29041i	0.366934	+	0.266593i
$260$	16.7097	−	3.63197i	1.03629	−	0.225245i
$261$	−12.9859	+	9.43484i	−0.803810	+	0.584002i
$262$	−16.0456	+	5.82696i	−0.991301	+	0.359991i
$263$	−20.6864	+	3.27641i	−1.27558	+	0.202032i	−0.757236	−	0.653141i	$-0.773451\pi$
$263$	−20.6864	+	3.27641i	−1.27558	+	0.202032i	−0.518343	+	0.855173i	$0.673451\pi$
$264$	2.73266	−	7.07283i	0.168183	−	0.435302i
$265$	3.27987	+	6.62294i	0.201481	+	0.406844i
$266$	4.01496	−	8.59385i	0.246173	−	0.526923i
$267$	−7.37516	+	14.4746i	−0.451352	+	0.885829i
$268$	8.79217	−	20.6299i	0.537067	−	1.26017i
$269$	−27.6149	+	8.97262i	−1.68371	+	0.547071i	−0.985625	−	0.168945i	$-0.945964\pi$
$269$	−27.6149	+	8.97262i	−1.68371	+	0.547071i	−0.698084	+	0.716015i	$0.745964\pi$
$270$	−1.12445	+	8.32147i	−0.0684318	+	0.506428i
$271$	−0.437920	−	0.142289i	−0.0266017	−	0.00864343i	0.295686	−	0.955285i	$-0.404452\pi$
$271$	−0.437920	−	0.142289i	−0.0266017	−	0.00864343i	−0.322288	+	0.946642i	$0.604452\pi$
$272$	3.69716	+	1.28503i	0.224173	+	0.0779165i
$273$	−8.26216	−	1.30860i	−0.500049	−	0.0792000i
$274$	−7.18860	+	1.39192i	−0.434279	+	0.0840889i
$275$	3.48714	+	5.03759i	0.210283	+	0.303778i
$276$	23.0260	−	9.26430i	1.38600	−	0.557645i
$277$	−0.412081	+	2.60178i	−0.0247595	+	0.156326i	−0.996970	−	0.0777810i	$-0.975216\pi$
$277$	−0.412081	+	2.60178i	−0.0247595	+	0.156326i	0.972211	+	0.234107i	$0.0752165\pi$
$278$	10.8897	−	8.49525i	0.653120	−	0.509511i
$279$	−3.71960	+	11.4478i	−0.222687	+	0.685359i
$280$	4.04659	−	4.86056i	0.241830	−	0.290474i
$281$	5.20189	+	16.0098i	0.310319	+	0.955063i	0.977639	+	0.210292i	$0.0674415\pi$
$281$	5.20189	+	16.0098i	0.310319	+	0.955063i	−0.667320	+	0.744771i	$0.732559\pi$
$282$	3.77118	+	2.54767i	0.224571	+	0.151712i
$283$	20.3304	+	10.3588i	1.20852	+	0.615769i	0.937896	−	0.346917i	$-0.112772\pi$
$283$	20.3304	+	10.3588i	1.20852	+	0.615769i	0.270619	+	0.962686i	$0.412772\pi$
$284$	−6.34980	−	1.59296i	−0.376791	−	0.0945248i
$285$	22.9349	+	23.4646i	1.35855	+	1.38992i
$286$	4.52246	−	4.84270i	0.267419	−	0.286355i
$287$	−0.398110	−	2.51357i	−0.0234997	−	0.148371i
$288$	4.46240	−	9.06577i	0.262949	−	0.534206i
$289$	−9.42953	−	12.9786i	−0.554678	−	0.763449i
$290$	8.16376	−	27.2189i	0.479392	−	1.59835i
$291$	14.3627	−	19.7685i	0.841954	−	1.15885i
$292$	−7.88520	−	0.701381i	−0.461447	−	0.0410452i
$293$	−9.00852	−	9.00852i	−0.526284	−	0.526284i	0.393179	−	0.919462i	$-0.371375\pi$
$293$	−9.00852	−	9.00852i	−0.526284	−	0.526284i	−0.919462	+	0.393179i	$0.871375\pi$
$294$	−2.70711	+	1.49801i	−0.157882	+	0.0873659i
$295$	−9.36437	+	12.5843i	−0.545214	+	0.732687i
$296$	−19.9536	+	5.30008i	−1.15978	+	0.308061i
$297$	1.47720	+	2.89916i	0.0857157	+	0.168226i
$298$	0.818517	+	23.9365i	0.0474154	+	1.38660i
$299$	21.6894			1.25433
$300$	10.8092	+	19.0207i	0.624067	+	1.09816i
$301$	9.31408			0.536855
$302$	−0.712833	−	20.8459i	−0.0410189	−	1.19955i
$303$	−1.14206	−	2.24142i	−0.0656095	−	0.128766i
$304$	11.6911	+	24.1477i	0.670531	+	1.38497i
$305$	3.32058	+	4.68186i	0.190136	+	0.268082i
$306$	2.16283	−	1.19683i	0.123641	−	0.0684182i
$307$	−11.3287	−	11.3287i	−0.646563	−	0.646563i	0.305598	−	0.952161i	$-0.401144\pi$
$307$	−11.3287	−	11.3287i	−0.646563	−	0.646563i	−0.952161	+	0.305598i	$0.901144\pi$
$308$	0.217131	−	2.44108i	0.0123722	−	0.139093i
$309$	−10.1906	+	14.0261i	−0.579721	+	0.797917i
$310$	−7.04466	−	20.1114i	−0.400110	−	1.14225i
$311$	−4.97918	−	6.85325i	−0.282343	−	0.388612i	0.644165	−	0.764887i	$-0.277205\pi$
$311$	−4.97918	−	6.85325i	−0.282343	−	0.388612i	−0.926508	+	0.376274i	$0.877205\pi$
$312$	17.6173	−	15.7935i	0.997386	−	0.894132i
$313$	3.06517	+	19.3527i	0.173254	+	1.09388i	0.909053	+	0.416681i	$0.136807\pi$
$313$	3.06517	+	19.3527i	0.173254	+	1.09388i	−0.735799	+	0.677200i	$0.763193\pi$
$314$	14.2905	−	15.3025i	0.806460	−	0.863567i
$315$	−0.579752	−	3.95186i	−0.0326653	−	0.222662i
$316$	−3.80178	+	15.1545i	−0.213867	+	0.852508i
$317$	19.6793	+	10.0271i	1.10530	+	0.563178i	0.908761	−	0.417318i	$-0.137030\pi$
$317$	19.6793	+	10.0271i	1.10530	+	0.563178i	0.196539	+	0.980496i	$0.437030\pi$
$318$	8.47361	+	5.72446i	0.475176	+	0.321012i
$319$	−3.40267	−	10.4724i	−0.190513	−	0.586339i
$320$	3.44298	+	17.5541i	0.192469	+	0.981303i
$321$	7.87392	−	24.2334i	0.439479	−	1.35258i
$322$	6.32505	−	4.93429i	0.352481	−	0.274977i
$323$	−1.02672	+	6.48243i	−0.0571280	+	0.360692i
$324$	8.33724	+	20.7218i	0.463180	+	1.15121i
$325$	2.55890	+	18.9462i	0.141942	+	1.05094i
$326$	12.1360	−	2.34987i	0.672148	−	0.130147i
$327$	−34.6605	−	5.48969i	−1.91673	−	0.303581i
$328$	6.22586	+	3.61257i	0.343766	+	0.199471i
$329$	1.39897	+	0.454554i	0.0771279	+	0.0250604i
$330$	7.63903	+	3.67568i	0.420515	+	0.202340i
$331$	22.8536	−	7.42560i	1.25615	−	0.408148i	0.396029	−	0.918238i	$-0.370388\pi$
$331$	22.8536	−	7.42560i	1.25615	−	0.408148i	0.860121	+	0.510090i	$0.170388\pi$
$332$	−1.77934	−	0.758328i	−0.0976537	−	0.0416187i
$333$	−5.91926	+	11.6172i	−0.324373	+	0.636618i
$334$	7.17397	−	15.3556i	0.392542	−	0.840220i
$335$	22.2082	+	11.6368i	1.21336	+	0.635788i
$336$	1.54456	−	8.61361i	0.0842629	−	0.469911i
$337$	13.0991	−	2.07470i	0.713554	−	0.113016i	0.210905	−	0.977507i	$-0.432359\pi$
$337$	13.0991	−	2.07470i	0.713554	−	0.113016i	0.502649	+	0.864491i	$0.332359\pi$
$338$	2.15368	−	0.782110i	0.117145	−	0.0425412i
$339$	35.6107	−	25.8727i	1.93411	−	1.40521i
$340$	−1.76156	+	4.00591i	−0.0955341	+	0.217251i
$341$	−6.68026	−	4.85349i	−0.361756	−	0.262831i
$342$	16.2836	+	4.68202i	0.880517	+	0.253175i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−16.6234	+	20.4372i	−0.896274	+	1.10190i
$345$	8.27322	+	26.4874i	0.445415	+	1.42603i
$346$	11.8062	+	1.45830i	0.634706	+	0.0783989i
$347$	22.2452	−	11.3345i	1.19418	−	0.608467i	0.260121	−	0.965576i	$-0.416238\pi$
$347$	22.2452	−	11.3345i	1.19418	−	0.608467i	0.934063	+	0.357109i	$0.116238\pi$
$348$	−8.78933	−	38.3241i	−0.471158	−	2.05439i
$349$			2.39003i			0.127935i	0.997952	+	0.0639677i	$0.0203755\pi$
$349$			2.39003i			0.127935i	−0.997952	+	0.0639677i	$0.979625\pi$
$350$	5.05644	+	4.94292i	0.270278	+	0.264210i
$351$			10.1533i			0.541941i
$352$	4.96874	+	4.83317i	0.264835	+	0.257609i
$353$	26.9975	−	13.7559i	1.43693	−	0.732152i	0.449959	−	0.893049i	$-0.351439\pi$
$353$	26.9975	−	13.7559i	1.43693	−	0.732152i	0.986971	+	0.160897i	$0.0514386\pi$
$354$	−2.66069	+	21.5405i	−0.141414	+	1.14487i
$355$	2.34109	−	6.93478i	0.124252	−	0.368060i
$356$	−9.52957	−	11.3904i	−0.505066	−	0.603689i
$357$	1.51376	−	1.51376i	0.0801165	−	0.0801165i
$358$	5.66938	−	19.7175i	0.299636	−	1.04210i
$359$	−16.0536	−	11.6636i	−0.847276	−	0.615582i	0.0771179	−	0.997022i	$-0.475428\pi$
$359$	−16.0536	−	11.6636i	−0.847276	−	0.615582i	−0.924394	+	0.381440i	$0.875428\pi$
$360$	9.70600	+	5.78102i	0.511551	+	0.304686i
$361$	−21.0240	+	15.2748i	−1.10653	+	0.803939i
$362$	−4.85450	−	13.3678i	−0.255147	−	0.702594i
$363$	−20.5245	+	3.25076i	−1.07726	+	0.170621i
$364$	4.06183	−	6.47938i	0.212898	−	0.339612i
$365$	1.48425	−	8.72539i	0.0776895	−	0.456708i
$366$	7.19545	+	3.36164i	0.376112	+	0.175716i
$367$	−9.60586	+	18.8526i	−0.501422	+	0.984096i	0.492109	+	0.870534i	$0.336226\pi$
$367$	−9.60586	+	18.8526i	−0.501422	+	0.984096i	−0.993531	+	0.113562i	$0.963774\pi$
$368$	−0.461740	+	22.6851i	−0.0240698	+	1.18254i
$369$	4.32332	−	1.40473i	0.225063	−	0.0731274i
$370$	−4.12894	−	22.7101i	−0.214653	−	1.18064i
$371$	3.14341	+	1.02135i	0.163198	+	0.0530261i
$372$	−22.2245	−	19.3761i	−1.15229	−	1.00460i
$373$	8.21646	+	1.30136i	0.425432	+	0.0673818i	0.365480	−	0.930819i	$-0.380905\pi$
$373$	8.21646	+	1.30136i	0.425432	+	0.0673818i	0.0599527	+	0.998201i	$0.480905\pi$
$374$	0.322350	+	1.66479i	0.0166683	+	0.0860841i
$375$	−22.1612	+	10.3518i	−1.14440	+	0.534565i
$376$	−3.49423	+	2.25839i	−0.180201	+	0.116468i
$377$	5.37507	−	33.9369i	0.276830	−	1.74784i
$378$	2.30985	+	2.96089i	0.118806	+	0.152292i
$379$	4.62563	−	14.2362i	0.237603	−	0.731266i	−0.759163	−	0.650901i	$-0.774391\pi$
$379$	4.62563	−	14.2362i	0.237603	−	0.731266i	0.996765	−	0.0803653i	$-0.0256087\pi$
$380$	−27.9538	+	10.8779i	−1.43400	+	0.558024i
$381$	−11.5563	−	35.5666i	−0.592046	−	1.82213i
$382$	−14.4683	+	21.4167i	−0.740264	+	1.09577i
$383$	−16.6063	−	8.46131i	−0.848540	−	0.432353i	−0.0250519	−	0.999686i	$-0.507975\pi$
$383$	−16.6063	−	8.46131i	−0.848540	−	0.432353i	−0.823488	+	0.567333i	$0.807975\pi$
$384$	16.1435	+	18.7623i	0.823821	+	0.957462i
$385$	2.70118	+	0.459491i	0.137665	+	0.0234178i
$386$	−2.38997	−	2.23193i	−0.121646	−	0.113602i
$387$	2.60263	+	16.4324i	0.132299	+	0.835305i
$388$	11.4773	+	19.1643i	0.582671	+	0.972918i
$389$	−4.13772	−	5.69508i	−0.209790	−	0.288752i	0.691135	−	0.722726i	$-0.257111\pi$
$389$	−4.13772	−	5.69508i	−0.209790	−	0.288752i	−0.900925	+	0.433974i	$0.857111\pi$
$390$	16.0318	+	21.0414i	0.811802	+	1.06547i
$391$	−3.26260	+	4.49058i	−0.164997	+	0.227098i
$392$	−0.289536	−	2.81357i	−0.0146238	−	0.142107i
$393$	−18.6734	−	18.6734i	−0.941948	−	0.941948i
$394$	9.91018	+	17.9090i	0.499267	+	0.902243i
$395$	−16.5506	−	5.58728i	−0.832752	−	0.281127i
$396$	4.36734	−	0.299035i	0.219467	−	0.0150271i
$397$	−3.67184	−	7.20639i	−0.184284	−	0.361678i	0.780320	−	0.625381i	$-0.215056\pi$
$397$	−3.67184	−	7.20639i	−0.184284	−	0.361678i	−0.964604	+	0.263702i	$0.915056\pi$
$398$	34.3923	−	1.17606i	1.72393	−	0.0589503i
$399$	14.6738			0.734607
$400$	−19.8704	+	2.27304i	−0.993521	+	0.113652i
$401$	−34.0933			−1.70254			−0.851268	−	0.524731i	$-0.824166\pi$
$401$	−34.0933			−1.70254			−0.851268	+	0.524731i	$0.824166\pi$
$402$	34.6711	−	1.18559i	1.72924	−	0.0591318i
$403$	−11.6976	−	22.9578i	−0.582699	−	1.14361i
$404$	2.29434	−	0.157095i	0.114148	−	0.00781579i
$405$	−23.8368	+	7.44533i	−1.18446	+	0.369962i
$406$	−6.15309	−	11.1195i	−0.305373	−	0.551850i
$407$	−6.32452	−	6.32452i	−0.313495	−	0.313495i
$408$	0.619832	+	6.02322i	0.0306862	+	0.298194i
$409$	2.23030	−	3.06975i	0.110281	−	0.151789i	−0.750309	−	0.661088i	$-0.770095\pi$
$409$	2.23030	−	3.06975i	0.110281	−	0.151789i	0.860590	+	0.509299i	$0.170095\pi$
$410$	−4.58086	+	6.61670i	−0.226233	+	0.326776i
$411$	−6.65791	−	9.16383i	−0.328410	−	0.452018i
$412$	−8.14333	−	13.5974i	−0.401193	−	0.669895i
$413$	1.09740	+	6.92871i	0.0539995	+	0.340939i
$414$	10.4727	+	9.78018i	0.514707	+	0.480670i
$415$	1.00368	−	1.91546i	0.0492688	−	0.0940264i
$416$	6.96782	+	20.4767i	0.341626	+	1.00395i
$417$	19.0371	+	9.69988i	0.932250	+	0.475005i
$418$	−6.50653	+	9.63127i	−0.318245	+	0.471081i
$419$	−6.26712	−	19.2882i	−0.306169	−	0.942290i	−0.979239	−	0.202711i	$-0.935025\pi$
$419$	−6.26712	−	19.2882i	−0.306169	−	0.942290i	0.673070	−	0.739579i	$-0.264975\pi$
$420$	9.46205	+	2.48887i	0.461701	+	0.121444i
$421$	−9.93241	+	30.5688i	−0.484076	+	1.48983i	0.349239	+	0.937034i	$0.386440\pi$
$421$	−9.93241	+	30.5688i	−0.484076	+	1.48983i	−0.833315	+	0.552799i	$0.813560\pi$
$422$	−4.50880	−	5.77962i	−0.219485	−	0.281348i
$423$	−0.411033	+	2.59516i	−0.0199851	+	0.126181i
$424$	−7.85131	+	5.07447i	−0.381293	+	0.246438i
$425$	−4.30754	−	2.32015i	−0.208946	−	0.112544i
$426$	−1.92519	−	9.94268i	−0.0932755	−	0.481724i
$427$	2.53534	+	0.401559i	0.122694	+	0.0194328i
$428$	17.5579	+	15.3076i	0.848694	+	0.739920i
$429$	9.74861	+	3.16752i	0.470667	+	0.152929i
$430$	−21.2956	−	20.3474i	−1.02697	−	0.981239i
$431$	10.8658	−	3.53050i	0.523385	−	0.170058i	−0.0353959	−	0.999373i	$-0.511269\pi$
$431$	10.8658	−	3.53050i	0.523385	−	0.170058i	0.558781	+	0.829315i	$0.311269\pi$
$432$	−10.6194	−	0.216150i	−0.510925	−	0.0103995i
$433$	−16.2555	+	31.9032i	−0.781190	+	1.53317i	0.0635404	+	0.997979i	$0.479761\pi$
$433$	−16.2555	+	31.9032i	−0.781190	+	1.53317i	−0.844730	+	0.535192i	$0.820239\pi$
$434$	−8.63410	−	4.03377i	−0.414450	−	0.193627i
$435$	43.4945	−	6.38079i	2.08540	−	0.305936i
$436$	17.0398	−	27.1816i	0.816056	−	1.30176i
$437$	−37.5781	+	5.95179i	−1.79760	+	0.284713i
$438$	−4.18016	−	11.5108i	−0.199736	−	0.550009i
$439$	33.2540	−	24.1604i	1.58712	−	1.15311i	0.679222	−	0.733933i	$-0.262317\pi$
$439$	33.2540	−	24.1604i	1.58712	−	1.15311i	0.907903	−	0.419181i	$-0.137683\pi$
$440$	−5.82918	+	5.10691i	−0.277895	+	0.243463i
$441$	−1.44510	−	1.04993i	−0.0688143	−	0.0499965i
$442$	−1.46217	+	5.08530i	−0.0695485	+	0.241883i
$443$	11.2416	−	11.2416i	0.534107	−	0.534107i	−0.387685	−	0.921792i	$-0.626725\pi$
$443$	11.2416	−	11.2416i	0.534107	−	0.534107i	0.921792	+	0.387685i	$0.126725\pi$
$444$	−20.4939	−	24.4956i	−0.972595	−	1.16251i
$445$	13.5434	−	9.60560i	0.642020	−	0.455349i
$446$	0.455742	−	3.68962i	0.0215800	−	0.174708i
$447$	−33.0124	+	16.8207i	−1.56143	+	0.795591i
$448$	6.69036	+	4.38624i	0.316090	+	0.207230i
$449$		−	25.2964i		−	1.19381i	−0.802311	−	0.596906i	$-0.796396\pi$
$449$		−	25.2964i		−	1.19381i	0.802311	−	0.596906i	$-0.203604\pi$
$450$	−7.30763	+	10.3020i	−0.344485	+	0.485642i
$451$			3.11841i			0.146840i
$452$	8.99514	+	39.2215i	0.423096	+	1.84482i
$453$	28.7500	−	14.6488i	1.35079	−	0.688263i
$454$	0.752140	+	0.0929044i	0.0352997	+	0.00436022i
$455$	6.85921	+	5.10414i	0.321565	+	0.239286i
$456$	−26.1892	+	32.1976i	−1.22642	+	1.50779i
$457$	−27.7072	+	27.7072i	−1.29609	+	1.29609i	−0.365135	+	0.930954i	$0.618977\pi$
$457$	−27.7072	+	27.7072i	−1.29609	+	1.29609i	−0.930954	+	0.365135i	$0.881023\pi$
$458$	15.1648	+	4.36033i	0.708604	+	0.203745i
$459$	−2.10213	−	1.52729i	−0.0981192	−	0.0712878i
$460$	−25.2409	−	2.53587i	−1.17686	−	0.118236i
$461$	0.280095	−	0.203501i	0.0130453	−	0.00947798i	−0.581243	−	0.813730i	$-0.697434\pi$
$461$	0.280095	−	0.203501i	0.0130453	−	0.00947798i	0.594289	+	0.804252i	$0.297434\pi$
$462$	3.56349	−	1.29408i	0.165788	−	0.0602060i
$463$	−4.43977	+	0.703191i	−0.206334	+	0.0326801i	−0.258746	−	0.965945i	$-0.583309\pi$
$463$	−4.43977	+	0.703191i	−0.206334	+	0.0326801i	0.0524119	+	0.998626i	$0.483309\pi$
$464$	35.3804	+	6.34431i	1.64250	+	0.294527i
$465$	23.5745	−	23.0423i	1.09324	−	1.06856i
$466$	13.8070	−	29.5533i	0.639598	−	1.36903i
$467$	2.08831	−	4.09854i	0.0966356	−	0.189658i	−0.837628	−	0.546241i	$-0.816058\pi$
$467$	2.08831	−	4.09854i	0.0966356	−	0.189658i	0.934264	+	0.356583i	$0.116058\pi$
$468$	12.5662	+	5.35556i	0.580875	+	0.247561i
$469$	10.6639	−	3.46490i	0.492412	−	0.159994i
$470$	−2.20559	−	4.09547i	−0.101736	−	0.188910i
$471$	30.8046	+	10.0090i	1.41940	+	0.461192i
$472$	−17.1617	−	9.95814i	−0.789933	−	0.458361i
$473$	−11.2726	−	1.78540i	−0.518313	−	0.0820927i
$474$	−23.7293	+	4.59467i	−1.08992	+	0.211040i
$475$	−9.63246	−	32.1231i	−0.441968	−	1.47391i
$476$	0.730497	+	1.81561i	0.0334823	+	0.0832185i
$477$	−0.923564	+	5.83116i	−0.0422871	+	0.266990i
$478$	−6.87544	+	5.36366i	−0.314475	+	0.245328i
$479$	1.72769	−	5.31730i	0.0789403	−	0.242953i	−0.903796	−	0.427963i	$-0.859231\pi$
$479$	1.72769	−	5.31730i	0.0789403	−	0.242953i	0.982737	+	0.185009i	$0.0592315\pi$
$480$	−22.3486	+	16.3199i	−1.02007	+	0.744896i
$481$	−8.62460	−	26.5438i	−0.393248	−	1.21029i
$482$	28.2248	+	19.0676i	1.28560	+	0.868506i
$483$	11.0573	+	5.63398i	0.503125	+	0.256355i
$484$	4.62250	−	18.4260i	0.210113	−	0.837547i
$485$	−22.3808	+	11.0836i	−1.01626	+	0.503281i
$486$	−15.8944	+	17.0199i	−0.720983	+	0.772037i
$487$	−0.0334481	−	0.211183i	−0.00151568	−	0.00956961i	0.986919	−	0.161217i	$-0.0515420\pi$
$487$	−0.0334481	−	0.211183i	−0.00151568	−	0.00956961i	−0.988435	+	0.151648i	$0.951542\pi$
$488$	−5.40609	+	4.84643i	−0.244722	+	0.219388i
$489$	11.2400	+	15.4706i	0.508292	+	0.699603i
$490$	3.16146	−	0.0719891i	0.142820	−	0.00325214i
$491$	−18.4488	+	25.3926i	−0.832582	+	1.14595i	0.154855	+	0.987937i	$0.450509\pi$
$491$	−18.4488	+	25.3926i	−0.832582	+	1.14595i	−0.987437	+	0.158014i	$0.949491\pi$
$492$	−0.986569	+	11.0914i	−0.0444780	+	0.500039i
$493$	6.21776	+	6.21776i	0.280034	+	0.280034i
$494$	−31.7343	+	17.5606i	−1.42779	+	0.790088i
$495$	−0.0558674	+	4.89395i	−0.00251105	+	0.219967i
$496$	24.2608	−	11.7459i	1.08934	−	0.527405i
$497$	−1.48604	−	2.91652i	−0.0666579	−	0.130824i
$498$	−0.102258	−	2.99039i	−0.00458227	−	0.134003i
$499$	−10.3971			−0.465437			−0.232719	−	0.972544i	$-0.574762\pi$
$499$	−10.3971			−0.465437			−0.232719	+	0.972544i	$0.574762\pi$
$500$	−0.762770	−	22.3477i	−0.0341121	−	0.999418i
$501$	26.2192			1.17139
$502$	−0.424733	−	12.4208i	−0.0189568	−	0.554367i
$503$	−14.2158	−	27.9000i	−0.633850	−	1.24400i	−0.954897	−	0.296938i	$-0.904035\pi$
$503$	−14.2158	−	27.9000i	−0.633850	−	1.24400i	0.321046	−	0.947064i	$-0.395965\pi$
$504$	4.88294	−	1.29701i	0.217503	−	0.0577734i
$505$	−0.0293494	+	2.57099i	−0.00130603	+	0.114408i
$506$	−8.60086	+	4.75939i	−0.382355	+	0.211581i
$507$	2.50639	+	2.50639i	0.111313	+	0.111313i
$508$	34.0531	+	3.02899i	1.51086	+	0.134390i
$509$	23.9314	−	32.9387i	1.06074	−	1.45998i	0.181628	−	0.983367i	$-0.441863\pi$
$509$	23.9314	−	32.9387i	1.06074	−	1.45998i	0.879112	−	0.476615i	$-0.158137\pi$
$510$	−6.76797	+	0.154113i	−0.299691	+	0.00682422i
$511$	−2.32655	−	3.20222i	−0.102921	−	0.141658i
$512$	−21.5651	+	6.85178i	−0.953051	+	0.302809i
$513$	−2.78616	−	17.5911i	−0.123012	−	0.776666i
$514$	7.27223	−	7.78719i	0.320764	−	0.343478i
$515$	15.8796	−	7.86402i	0.699737	−	0.346530i
$516$	−39.5288	−	9.91651i	−1.74016	−	0.436550i
$517$	−1.60600	−	0.818300i	−0.0706320	−	0.0359888i
$518$	−8.55375	−	5.77860i	−0.375830	−	0.253897i
$519$	5.68674	+	17.5020i	0.249620	+	0.768252i
$520$	−23.4417	+	5.94098i	−1.02799	+	0.260529i
$521$	2.74160	−	8.43778i	0.120112	−	0.369666i	−0.872867	−	0.487958i	$-0.837742\pi$
$521$	2.74160	−	8.43778i	0.120112	−	0.369666i	0.992979	+	0.118292i	$0.0377419\pi$
$522$	17.8982	−	13.9627i	0.783382	−	0.611132i
$523$	4.01732	−	25.3644i	0.175665	−	1.10911i	−0.729479	−	0.684003i	$-0.760238\pi$
$523$	4.01732	−	25.3644i	0.175665	−	1.10911i	0.905145	−	0.425104i	$-0.139762\pi$
$524$	22.3970	−	9.01126i	0.978419	−	0.393659i
$525$	−3.61687	+	10.3235i	−0.157853	+	0.450554i
$526$	29.0796	−	5.63063i	1.26793	−	0.245507i
$527$	6.51279	+	1.03152i	0.283702	+	0.0449339i
$528$	−3.52047	+	10.1287i	−0.153209	+	0.440796i
$529$	−8.72757	−	2.83576i	−0.379460	−	0.123294i
$530$	−4.95583	−	9.20225i	−0.215267	−	0.399720i
$531$	−11.9173	+	3.87218i	−0.517168	+	0.168038i
$532$	−5.25935	+	12.3405i	−0.228022	+	0.535028i
$533$	−4.41767	+	8.67017i	−0.191351	+	0.375547i
$534$	9.72438	−	20.8146i	0.420815	−	0.900736i
$535$	−18.6244	+	18.2040i	−0.805203	+	0.787027i
$536$	−11.4297	+	29.5830i	−0.493687	+	1.27779i
$537$	31.3476	−	4.96496i	1.35275	−	0.214254i
$538$	38.5969	−	14.0165i	1.66403	−	0.604292i
$539$	0.991334	−	0.720247i	0.0426998	−	0.0310232i
$540$	1.18709	−	11.8158i	0.0510844	−	0.508471i
$541$	4.73292	+	3.43867i	0.203484	+	0.147840i	0.684861	−	0.728674i	$-0.259863\pi$
$541$	4.73292	+	3.43867i	0.203484	+	0.147840i	−0.481376	+	0.876514i	$0.659863\pi$
$542$	0.625828	+	0.179944i	0.0268816	+	0.00772926i
$543$	15.5570	−	15.5570i	0.667615	−	0.667615i
$544$	−5.28763	−	1.63756i	−0.226705	−	0.0702098i
$545$	28.7750	+	21.4123i	1.23259	+	0.917204i
$546$	11.7409	+	1.45024i	0.502464	+	0.0620643i
$547$	−3.74033	+	1.90579i	−0.159925	+	0.0814858i	−0.532121	−	0.846668i	$-0.678605\pi$
$547$	−3.74033	+	1.90579i	−0.159925	+	0.0814858i	0.372196	+	0.928154i	$0.378605\pi$
$548$	10.0930	−	2.31475i	0.431152	−	0.0988814i
$549$			4.58519i			0.195691i
$550$	−5.17216	−	6.95153i	−0.220541	−	0.296414i
$551$			60.2726i			2.56770i
$552$	−32.0969	+	14.2069i	−1.36613	+	0.604687i
$553$	−6.96059	+	3.54660i	−0.295994	+	0.150817i
$554$	0.456683	−	3.69724i	0.0194026	−	0.157080i
$555$	29.1259	−	20.6574i	1.23632	−	0.876856i
$556$	−14.9807	+	12.5334i	−0.635325	+	0.531534i
$557$	25.2231	−	25.2231i	1.06874	−	1.06874i	0.0712816	−	0.997456i	$-0.477291\pi$
$557$	25.2231	−	25.2231i	1.06874	−	1.06874i	0.997456	−	0.0712816i	$-0.0227089\pi$
$558$	4.70395	−	16.3599i	0.199134	−	0.692569i
$559$	−28.8121	−	20.9332i	−1.21862	−	0.885379i
$560$	−5.48449	+	7.06544i	−0.231762	+	0.298569i
$561$	−2.12222	+	1.54189i	−0.0896004	+	0.0650985i
$562$	−8.12606	−	22.3766i	−0.342777	−	0.943900i
$563$	−1.41976	+	0.224869i	−0.0598359	+	0.00947708i	−0.186281	−	0.982497i	$-0.559643\pi$
$563$	−1.41976	+	0.224869i	−0.0598359	+	0.00947708i	0.126445	+	0.991974i	$0.459643\pi$
$564$	−5.45327	−	3.41858i	−0.229624	−	0.143948i
$565$	−44.5129	+	6.53021i	−1.87267	+	0.274728i
$566$	−29.2353	−	13.6585i	−1.22885	−	0.574108i
$567$	−5.07020	+	9.95082i	−0.212928	+	0.417895i
$568$	9.05172	+	1.94458i	0.379802	+	0.0815926i
$569$	6.20952	−	2.01759i	0.260316	−	0.0845820i	−0.175951	−	0.984399i	$-0.556300\pi$
$569$	6.20952	−	2.01759i	0.260316	−	0.0845820i	0.436268	+	0.899817i	$0.356300\pi$
$570$	−33.5500	−	32.0561i	−1.40525	−	1.34268i
$571$	−19.8028	−	6.43431i	−0.828720	−	0.269267i	−0.136214	−	0.990679i	$-0.543493\pi$
$571$	−19.8028	−	6.43431i	−0.828720	−	0.269267i	−0.692506	+	0.721412i	$0.743493\pi$
$572$	−6.15793	+	7.06319i	−0.257476	+	0.295327i
$573$	−39.4905	−	6.25469i	−1.64974	−	0.261293i
$574$	0.684167	+	3.53340i	0.0285566	+	0.147481i
$575$	5.07517	−	27.9045i	0.211649	−	1.16370i
$576$	−5.86894	+	13.0291i	−0.244539	+	0.542880i
$577$	−4.44832	+	28.0856i	−0.185186	+	1.16922i	0.703498	+	0.710697i	$0.251620\pi$
$577$	−4.44832	+	28.0856i	−0.185186	+	1.16922i	−0.888684	+	0.458520i	$0.848380\pi$
$578$	13.9549	+	17.8881i	0.580446	+	0.744047i
$579$	1.56323	−	4.81114i	0.0649658	−	0.199944i
$580$	−10.2230	+	38.8654i	−0.424488	+	1.61380i
$581$	−0.298849	−	0.919763i	−0.0123983	−	0.0381582i
$582$	−19.3446	+	28.6347i	−0.801858	+	1.18695i
$583$	−3.60859	−	1.83867i	−0.149453	−	0.0761499i
$584$	11.1787	+	0.610221i	0.462580	+	0.0252511i
$585$	−7.08832	+	13.5276i	−0.293066	+	0.559298i
$586$	13.1679	+	12.2971i	0.543962	+	0.507990i
$587$	4.18787	+	26.4412i	0.172852	+	1.09134i	0.909694	+	0.415279i	$0.136316\pi$
$587$	4.18787	+	26.4412i	0.172852	+	1.09134i	−0.736842	+	0.676065i	$0.763684\pi$
$588$	3.75379	−	2.24811i	0.154804	−	0.0927105i
$589$	26.5666	+	36.5658i	1.09466	+	1.50667i
$590$	12.6273	−	18.2391i	0.519856	−	0.750892i
$591$	−18.6114	+	25.6164i	−0.765571	+	1.05372i
$592$	27.9460	−	8.45545i	1.14857	−	0.347517i
$593$	−11.1929	−	11.1929i	−0.459638	−	0.459638i	0.438899	−	0.898537i	$-0.355369\pi$
$593$	−11.1929	−	11.1929i	−0.459638	−	0.459638i	−0.898537	+	0.438899i	$0.855369\pi$
$594$	−2.22797	−	4.02624i	−0.0914148	−	0.165199i
$595$	−2.08855	+	0.652349i	−0.0856221	+	0.0267437i
$596$	−2.31376	−	33.7920i	−0.0947754	−	1.38417i
$597$	24.1682	+	47.4327i	0.989137	+	1.94129i
$598$	−30.6555	+	1.04828i	−1.25360	+	0.0428672i
$599$	−28.1480			−1.15010			−0.575049	−	0.818119i	$-0.695017\pi$
$599$	−28.1480			−1.15010			−0.575049	+	0.818119i	$0.695017\pi$
$600$	−16.1968	−	26.3612i	−0.661233	−	1.07619i
$601$	−2.55046			−0.104035			−0.0520177	−	0.998646i	$-0.516565\pi$
$601$	−2.55046			−0.104035			−0.0520177	+	0.998646i	$0.516565\pi$
$602$	−13.1644	+	0.450161i	−0.536541	+	0.0183472i
$603$	9.09276	+	17.8456i	0.370286	+	0.726727i
$604$	2.01502	+	29.4289i	0.0819899	+	1.19744i
$605$	20.1235	+	6.79345i	0.818138	+	0.276193i
$606$	1.72250	+	3.11279i	0.0699718	+	0.126449i
$607$	−2.86036	−	2.86036i	−0.116098	−	0.116098i	0.646671	−	0.762769i	$-0.276161\pi$
$607$	−2.86036	−	2.86036i	−0.116098	−	0.116098i	−0.762769	+	0.646671i	$0.776161\pi$
$608$	−17.6912	−	33.5650i	−0.717471	−	1.36124i
$609$	11.5556	−	15.9049i	0.468256	−	0.644498i
$610$	−4.91955	−	6.45679i	−0.199187	−	0.261428i
$611$	−3.30597	−	4.55027i	−0.133745	−	0.184084i
$612$	−2.99908	+	1.79612i	−0.121230	+	0.0726037i
$613$	−2.86698	−	18.1014i	−0.115796	−	0.731109i	−0.975448	−	0.220229i	$-0.929320\pi$
$613$	−2.86698	−	18.1014i	−0.115796	−	0.731109i	0.859652	−	0.510880i	$-0.170680\pi$
$614$	16.5594	+	15.4643i	0.668282	+	0.624089i
$615$	−12.2732	−	2.08777i	−0.494904	−	0.0841869i
$616$	−0.188910	+	3.46068i	−0.00761142	+	0.139435i
$617$	−40.5881	−	20.6806i	−1.63401	−	0.832571i	−0.998152	−	0.0607683i	$-0.980645\pi$
$617$	−40.5881	−	20.6806i	−1.63401	−	0.832571i	−0.635862	−	0.771803i	$-0.719355\pi$
$618$	13.7253	−	20.3168i	0.552113	−	0.817263i
$619$	3.93226	+	12.1023i	0.158051	+	0.486431i	0.998457	−	0.0555260i	$-0.0176836\pi$
$619$	3.93226	+	12.1023i	0.158051	+	0.486431i	−0.840406	+	0.541957i	$0.817684\pi$
$620$	10.9288	+	28.0847i	0.438913	+	1.12791i
$621$	4.65460	−	14.3254i	0.186783	−	0.574858i
$622$	7.36873	+	9.44565i	0.295459	+	0.378736i
$623$	1.16161	−	7.33410i	0.0465388	−	0.293835i
$624$	−24.1368	+	23.1738i	−0.966246	+	0.927696i
$625$	24.9739	+	1.14111i	0.998958	+	0.0456446i
$626$	−5.26761	−	27.2047i	−0.210536	−	1.08732i
$627$	−17.7592	−	2.81278i	−0.709235	−	0.112332i
$628$	−19.4584	+	22.3190i	−0.776476	+	0.890624i
$629$	6.79297	+	2.20717i	0.270854	+	0.0880057i
$630$	1.01041	+	5.55749i	0.0402558	+	0.221416i
$631$	8.60901	−	2.79724i	0.342719	−	0.111356i	−0.132600	−	0.991170i	$-0.542333\pi$
$631$	8.60901	−	2.79724i	0.342719	−	0.111356i	0.475319	+	0.879813i	$0.342333\pi$
$632$	4.64095	−	21.6029i	0.184607	−	0.859319i
$633$	5.14814	−	10.1038i	0.204620	−	0.401590i
$634$	−28.2991	−	13.2211i	−1.12390	−	0.525075i
$635$	−6.40992	+	37.6816i	−0.254370	+	1.49535i
$636$	−12.2532	−	7.68134i	−0.485869	−	0.304585i
$637$	3.77656	−	0.598148i	0.149633	−	0.0236995i
$638$	5.31544	+	14.6370i	0.210440	+	0.579486i
$639$	4.73022	−	3.43671i	0.187125	−	0.135954i
$640$	−5.71468	−	24.6443i	−0.225893	−	0.974152i
$641$	11.1533	+	8.10334i	0.440528	+	0.320063i	0.785845	−	0.618424i	$-0.212228\pi$
$641$	11.1533	+	8.10334i	0.440528	+	0.320063i	−0.345316	+	0.938486i	$0.612228\pi$
$642$	−9.95766	+	34.6318i	−0.392998	+	1.36681i
$643$	−14.8581	+	14.8581i	−0.585947	+	0.585947i	−0.936531	−	0.350584i	$-0.885983\pi$
$643$	−14.8581	+	14.8581i	−0.585947	+	0.585947i	0.350584	+	0.936531i	$0.385983\pi$
$644$	−8.70126	+	7.27976i	−0.342878	+	0.286863i
$645$	14.5738	−	43.1704i	0.573843	−	1.69983i
$646$	1.13784	−	9.21180i	0.0447678	−	0.362434i
$647$	−8.09621	+	4.12523i	−0.318295	+	0.162179i	−0.605837	−	0.795589i	$-0.707162\pi$
$647$	−8.09621	+	4.12523i	−0.318295	+	0.162179i	0.287542	+	0.957768i	$0.407162\pi$
$648$	−12.7853	−	28.8850i	−0.502253	−	1.13471i
$649$		−	8.59597i		−	0.337421i
$650$	−4.53241	−	26.6546i	−0.177776	−	1.04548i
$651$		−	14.7425i		−	0.577804i
$652$	−17.0392	+	3.90782i	−0.667308	+	0.153042i
$653$	−1.48207	+	0.755155i	−0.0579981	+	0.0295515i	−0.482749	−	0.875759i	$-0.660362\pi$
$653$	−1.48207	+	0.755155i	−0.0579981	+	0.0295515i	0.424751	+	0.905310i	$0.360362\pi$
$654$	49.2541	+	6.08387i	1.92599	+	0.237898i
$655$	8.04724	+	25.7639i	0.314432	+	1.00668i
$656$	−8.97416	−	4.80506i	−0.350382	−	0.187606i
$657$	4.99942	−	4.99942i	0.195046	−	0.195046i
$658$	−1.99926	−	0.574847i	−0.0779393	−	0.0224099i
$659$	−28.4638	−	20.6801i	−1.10879	−	0.805584i	−0.126318	−	0.991990i	$-0.540316\pi$
$659$	−28.4638	−	20.6801i	−1.10879	−	0.805584i	−0.982473	+	0.186406i	$0.940316\pi$
$660$	−10.9746	−	4.82596i	−0.427184	−	0.187850i
$661$	30.3417	−	22.0446i	1.18016	−	0.857434i	0.187967	−	0.982175i	$-0.439810\pi$
$661$	30.3417	−	22.0446i	1.18016	−	0.857434i	0.992189	+	0.124741i	$0.0398101\pi$
$662$	−31.9422	+	11.5998i	−1.24147	+	0.450839i
$663$	−8.08477	+	1.28050i	−0.313986	+	0.0497306i
$664$	2.55154	+	0.985814i	0.0990190	+	0.0382570i
$665$	−13.2846	−	6.96098i	−0.515154	−	0.269935i
$666$	7.80473	−	16.7057i	0.302427	−	0.647332i
$667$	−23.1416	+	45.4179i	−0.896046	+	1.75859i
$668$	−9.39745	+	22.0501i	−0.363598	+	0.853144i
$669$	5.46963	−	1.77719i	0.211468	−	0.0687102i
$670$	−31.9512	−	15.3740i	−1.23438	−	0.593949i
$671$	−2.99148	−	0.971989i	−0.115485	−	0.0375232i
$672$	−1.76676	+	12.2490i	−0.0681543	+	0.472516i
$673$	36.5646	+	5.79126i	1.40946	+	0.223237i	0.814335	−	0.580395i	$-0.197102\pi$
$673$	36.5646	+	5.79126i	1.40946	+	0.223237i	0.595126	+	0.803632i	$0.297102\pi$
$674$	−18.4138	+	3.56544i	−0.709275	+	0.137336i
$675$	13.0627	+	2.37579i	0.502783	+	0.0914443i
$676$	−3.00619	+	1.20951i	−0.115623	+	0.0465198i
$677$	0.595042	−	3.75695i	0.0228693	−	0.144391i	−0.973612	−	0.228212i	$-0.926712\pi$
$677$	0.595042	−	3.75695i	0.0228693	−	0.144391i	0.996481	+	0.0838204i	$0.0267122\pi$
$678$	−49.0812	+	38.2892i	−1.88495	+	1.47049i
$679$	−3.45145	+	10.6225i	−0.132454	+	0.407653i
$680$	2.29616	−	5.74704i	0.0880536	−	0.220389i
$681$	0.362286	+	1.11500i	0.0138828	+	0.0427270i
$682$	9.67637	+	6.53700i	0.370528	+	0.250315i
$683$	33.4428	+	17.0399i	1.27965	+	0.652015i	0.955779	−	0.294085i	$-0.0950150\pi$
$683$	33.4428	+	17.0399i	1.27965	+	0.652015i	0.323873	+	0.946101i	$0.395015\pi$
$684$	−23.2414	−	5.83051i	−0.888655	−	0.222935i
$685$	1.68044	+	11.4547i	0.0642064	+	0.437661i
$686$	0.965240	−	1.03359i	0.0368531	−	0.0394627i
$687$	3.81856	+	24.1095i	0.145687	+	0.919833i
$688$	22.5076	−	29.6891i	0.858093	−	1.13189i
$689$	−7.42830	−	10.2242i	−0.282996	−	0.389510i
$690$	−12.9734	−	37.0371i	−0.493890	−	1.40998i
$691$	−6.32986	+	8.71231i	−0.240799	+	0.331432i	−0.912262	−	0.409606i	$-0.865666\pi$
$691$	−6.32986	+	8.71231i	−0.240799	+	0.331432i	0.671463	+	0.741038i	$0.265666\pi$
$692$	−16.7572	−	1.49054i	−0.637014	−	0.0566618i
$693$	1.54770	+	1.54770i	0.0587924	+	0.0587924i
$694$	−30.8932	+	17.0952i	−1.17269	+	0.648923i
$695$	−12.6334	−	17.8125i	−0.479212	−	0.675665i
$696$	14.2750	+	53.7420i	0.541092	+	2.03708i
$697$	−1.13055	−	2.21883i	−0.0428227	−	0.0840443i
$698$	−0.115513	−	3.37804i	−0.00437224	−	0.127861i
$699$	50.4615			1.90863
$700$	−7.38560	−	6.74188i	−0.279149	−	0.254819i
$701$	6.51359			0.246015			0.123007	−	0.992406i	$-0.460746\pi$
$701$	6.51359			0.246015			0.123007	+	0.992406i	$0.460746\pi$
$702$	−0.490720	−	14.3505i	−0.0185210	−	0.541625i
$703$	22.2265	+	43.6219i	0.838288	+	1.64523i
$704$	−7.25635	−	6.59100i	−0.273484	−	0.248408i
$705$	4.29583	−	5.77295i	0.161790	−	0.217422i
$706$	−37.4930	+	20.7472i	−1.41107	+	0.780832i
$707$	0.813072	+	0.813072i	0.0305787	+	0.0305787i
$708$	2.71950	−	30.5737i	0.102205	−	1.14903i
$709$	−21.9500	+	30.2115i	−0.824349	+	1.13462i	0.164600	+	0.986360i	$0.447367\pi$
$709$	−21.9500	+	30.2115i	−0.824349	+	1.13462i	−0.988949	+	0.148258i	$0.952633\pi$
$710$	−2.97371	+	9.91468i	−0.111601	+	0.372091i
$711$	−8.20209	−	11.2892i	−0.307602	−	0.423378i
$712$	14.0195	+	15.6384i	0.525403	+	0.586076i
$713$	5.97966	+	37.7541i	0.223940	+	1.41390i
$714$	−2.06636	+	2.21269i	−0.0773317	+	0.0828077i
$715$	−7.32309	−	7.49222i	−0.273868	−	0.280193i
$716$	−7.06005	+	28.1425i	−0.263847	+	1.05174i
$717$	−12.0195	−	6.12423i	−0.448876	−	0.228714i
$718$	23.2536	+	15.7093i	0.867818	+	0.586266i
$719$	13.2745	+	40.8546i	0.495054	+	1.52362i	0.816873	+	0.576818i	$0.195706\pi$
$719$	13.2745	+	40.8546i	0.495054	+	1.52362i	−0.321819	+	0.946801i	$0.604294\pi$
$720$	−13.9977	−	7.70172i	−0.521665	−	0.287026i
$721$	2.44886	−	7.53682i	0.0912004	−	0.280686i
$722$	28.9768	−	22.6054i	1.07841	−	0.841286i
$723$	−8.24297	+	52.0440i	−0.306559	+	1.93554i
$724$	7.50737	+	18.6592i	0.279009	+	0.693464i
$725$	−42.4038	−	14.8563i	−1.57484	−	0.551749i
$726$	28.8519	−	5.58656i	1.07080	−	0.207337i
$727$	11.2964	+	1.78918i	0.418962	+	0.0663570i	0.362356	−	0.932040i	$-0.381972\pi$
$727$	11.2964	+	1.78918i	0.418962	+	0.0663570i	0.0566053	+	0.998397i	$0.481972\pi$
$728$	−5.42778	+	9.35418i	−0.201167	+	0.346689i
$729$	−2.39749	−	0.778992i	−0.0887959	−	0.0288515i
$730$	−1.67612	+	12.4041i	−0.0620359	+	0.459096i
$731$	8.66802	−	2.81641i	0.320598	−	0.104169i
$732$	−10.3324	−	4.40354i	−0.381898	−	0.162759i
$733$	8.56496	−	16.8097i	0.316354	−	0.620880i	−0.676999	−	0.735984i	$-0.736720\pi$
$733$	8.56496	−	16.8097i	0.316354	−	0.620880i	0.993353	+	0.115104i	$0.0367200\pi$
$734$	12.6656	−	27.1102i	0.467497	−	1.00066i
$735$	2.17100	+	4.38383i	0.0800786	+	0.161700i
$736$	−0.443783	−	32.0852i	−0.0163581	−	1.18267i
$737$	−13.5703	+	2.14933i	−0.499870	+	0.0791717i
$738$	−6.04263	+	2.19438i	−0.222432	+	0.0807763i
$739$	−11.2438	+	8.16911i	−0.413610	+	0.300506i	−0.775062	−	0.631885i	$-0.782281\pi$
$739$	−11.2438	+	8.16911i	−0.413610	+	0.300506i	0.361451	+	0.932391i	$0.382281\pi$
$740$	6.93339	+	31.8985i	0.254877	+	1.17261i
$741$	−45.3916	−	32.9789i	−1.66750	−	1.21151i
$742$	−4.49221	−	1.29164i	−0.164914	−	0.0474178i
$743$	−1.21619	+	1.21619i	−0.0446177	+	0.0446177i	−0.729064	−	0.684446i	$-0.760044\pi$
$743$	−1.21619	+	1.21619i	−0.0446177	+	0.0446177i	0.684446	+	0.729064i	$0.260044\pi$
$744$	32.3484	+	26.3118i	1.18595	+	0.964638i
$745$	37.8666	+	0.432270i	1.38732	+	0.0158371i
$746$	−11.6759	−	1.44221i	−0.427486	−	0.0528032i
$747$	1.53919	−	0.784254i	0.0563159	−	0.0286944i
$748$	−0.536067	−	2.33741i	−0.0196006	−	0.0854642i
$749$			11.6469i			0.425569i
$750$	30.8221	−	15.7022i	1.12546	−	0.573363i
$751$			20.3953i			0.744235i	0.928186	+	0.372117i	$0.121368\pi$
$751$			20.3953i			0.744235i	−0.928186	+	0.372117i	$0.878632\pi$
$752$	4.82955	−	3.36087i	0.176115	−	0.122558i
$753$	17.1303	−	8.72834i	0.624264	−	0.318079i
$754$	−5.95685	+	48.2258i	−0.216936	+	1.75628i
$755$	−32.9774	−	0.376457i	−1.20017	−	0.0137007i
$756$	−3.40781	−	4.07324i	−0.123941	−	0.148142i
$757$	−19.3845	+	19.3845i	−0.704543	+	0.704543i	−0.965382	−	0.260839i	$-0.916001\pi$
$757$	−19.3845	+	19.3845i	−0.704543	+	0.704543i	0.260839	+	0.965382i	$0.416001\pi$
$758$	−5.84976	+	20.3449i	−0.212473	+	0.738959i
$759$	−12.3024	−	8.93819i	−0.446547	−	0.324436i
$760$	38.9838	−	16.7257i	1.41409	−	0.606706i
$761$	11.5203	−	8.36997i	0.417609	−	0.303411i	−0.359066	−	0.933312i	$-0.616905\pi$
$761$	11.5203	−	8.36997i	0.417609	−	0.303411i	0.776675	+	0.629901i	$0.216905\pi$
$762$	18.0525	+	49.7108i	0.653972	+	1.80083i
$763$	15.8430	−	2.50929i	0.573556	−	0.0908423i
$764$	19.4143	−	30.9694i	0.702383	−	1.12043i
$765$	−1.73451	−	3.50244i	−0.0627114	−	0.126631i
$766$	23.8800	+	11.1565i	0.862820	+	0.403101i
$767$	12.1774	−	23.8995i	0.439701	−	0.862963i
$768$	−23.7239	−	25.7382i	−0.856061	−	0.928748i
$769$	30.8005	−	10.0077i	1.11069	−	0.360886i	0.304485	−	0.952517i	$-0.401516\pi$
$769$	30.8005	−	10.0077i	1.11069	−	0.360886i	0.806209	+	0.591631i	$0.201516\pi$
$770$	−3.84002	−	0.518887i	−0.138385	−	0.0186994i
$771$	15.6760	+	5.09344i	0.564558	+	0.183436i
$772$	3.48583	+	3.03907i	0.125458	+	0.109378i
$773$	24.0600	+	3.81073i	0.865377	+	0.137062i	0.573313	−	0.819336i	$-0.305658\pi$
$773$	24.0600	+	3.81073i	0.865377	+	0.137062i	0.292064	+	0.956399i	$0.405658\pi$
$774$	−4.47273	−	23.0995i	−0.160769	−	0.830296i
$775$	−32.2736	+	9.67757i	−1.15930	+	0.347629i
$776$	−17.1481	−	26.5318i	−0.615580	−	0.952437i
$777$	2.49810	−	15.7724i	0.0896188	−	0.565831i
$778$	6.12345	+	7.84937i	0.219536	+	0.281413i
$779$	5.27469	−	16.2338i	0.188985	−	0.581637i
$780$	−23.6761	−	28.9648i	−0.847741	−	1.03710i
$781$	1.23945	+	3.81463i	0.0443509	+	0.136498i
$782$	4.39428	−	6.50461i	0.157139	−	0.232604i
$783$	−21.2611	−	10.8331i	−0.759809	−	0.387142i
$784$	0.545210	+	3.96267i	0.0194718	+	0.141524i
$785$	−23.1402	−	23.6747i	−0.825910	−	0.844985i
$786$	27.2953	+	25.4902i	0.973589	+	0.909207i
$787$	−7.06148	−	44.5844i	−0.251714	−	1.58926i	−0.712449	−	0.701724i	$-0.752414\pi$
$787$	−7.06148	−	44.5844i	−0.251714	−	1.58926i	0.460734	−	0.887538i	$-0.347586\pi$
$788$	−14.8725	−	24.8334i	−0.529810	−	0.884654i
$789$	26.9328	+	37.0698i	0.958833	+	1.31972i
$790$	23.6625	+	7.09708i	0.841874	+	0.252503i
$791$	−11.8262	+	16.2773i	−0.420490	+	0.578755i
$792$	−6.15830	+	0.633732i	−0.218826	+	0.0225187i
$793$	−6.94030	−	6.94030i	−0.246457	−	0.246457i
$794$	5.53803	+	10.0080i	0.196537	+	0.355169i
$795$	9.65245	−	12.9715i	0.342337	−	0.460050i
$796$	−48.5527	+	3.32444i	−1.72091	+	0.117832i
$797$	−22.1004	−	43.3745i	−0.782837	−	1.53640i	−0.842814	−	0.538204i	$-0.819103\pi$
$797$	−22.1004	−	43.3745i	−0.782837	−	1.53640i	0.0599775	−	0.998200i	$-0.480897\pi$
$798$	−20.7397	+	0.709202i	−0.734178	+	0.0251055i
$799$	1.43938			0.0509218
$800$	27.9747	−	4.17304i	0.989056	−	0.147539i
$801$	13.2638			0.468653
$802$	48.1870	−	1.64777i	1.70154	−	0.0581848i
$803$	2.20193	+	4.32153i	0.0777044	+	0.152503i
$804$	−48.9463	+	3.35139i	−1.72620	+	0.118195i
$805$	−7.33784	−	10.3460i	−0.258625	−	0.364648i
$806$	17.6428	+	31.8829i	0.621442	+	1.12303i
$807$	44.9179	+	44.9179i	1.58119	+	1.58119i
$808$	−3.23520	+	0.332925i	−0.113814	+	0.0117123i
$809$	9.19243	−	12.6523i	0.323188	−	0.444831i	−0.616249	−	0.787551i	$-0.711348\pi$
$809$	9.19243	−	12.6523i	0.323188	−	0.444831i	0.939437	+	0.342721i	$0.111348\pi$
$810$	33.3309	−	11.6752i	1.17113	−	0.410225i
$811$	−10.0269	−	13.8008i	−0.352092	−	0.484613i	0.595832	−	0.803109i	$-0.296822\pi$
$811$	−10.0269	−	13.8008i	−0.352092	−	0.484613i	−0.947924	+	0.318496i	$0.896822\pi$
$812$	9.23412	+	15.4187i	0.324054	+	0.541091i
$813$	0.157586	+	0.994960i	0.00552679	+	0.0348948i
$814$	9.24467	+	8.63332i	0.324025	+	0.302598i
$815$	−2.83696	−	19.3380i	−0.0993744	−	0.677382i
$816$	−1.16717	−	8.48318i	−0.0408592	−	0.296971i
$817$	55.6628	+	28.3616i	1.94739	+	0.992247i
$818$	−3.00392	+	4.44653i	−0.105029	+	0.155469i
$819$	2.11057	+	6.49566i	0.0737492	+	0.226977i
$820$	6.15474	−	9.57336i	0.214933	−	0.334316i
$821$	8.91513	−	27.4379i	0.311140	−	0.957591i	−0.666174	−	0.745796i	$-0.732069\pi$
$821$	8.91513	−	27.4379i	0.311140	−	0.957591i	0.977314	−	0.211795i	$-0.0679308\pi$
$822$	9.85311	+	12.6303i	0.343667	+	0.440531i
$823$	1.99484	−	12.5949i	0.0695358	−	0.439032i	−0.928218	−	0.372038i	$-0.878659\pi$
$823$	1.99484	−	12.5949i	0.0695358	−	0.439032i	0.997753	−	0.0669941i	$-0.0213409\pi$
$824$	12.1669	+	18.8248i	0.423853	+	0.655792i
$825$	6.35627	−	11.8009i	0.221297	−	0.410855i
$826$	−1.88592	−	9.73991i	−0.0656197	−	0.338895i
$827$	−0.598427	−	0.0947815i	−0.0208093	−	0.00329588i	0.146021	−	0.989281i	$-0.453353\pi$
$827$	−0.598427	−	0.0947815i	−0.0208093	−	0.00329588i	−0.166830	+	0.985986i	$0.553353\pi$
$828$	−15.2747	−	13.3170i	−0.530833	−	0.462799i
$829$	−27.0491	−	8.78880i	−0.939456	−	0.305248i	−0.201032	−	0.979585i	$-0.564430\pi$
$829$	−27.0491	−	8.78880i	−0.939456	−	0.305248i	−0.738424	+	0.674337i	$0.764430\pi$
$830$	−1.32601	+	2.75580i	−0.0460266	+	0.0956552i
$831$	5.48092	−	1.78086i	0.190131	−	0.0617774i
$832$	−10.8379	−	28.6048i	−0.375736	−	0.991692i
$833$	−0.444243	+	0.871876i	−0.0153921	+	0.0302087i
$834$	−27.3756	−	12.7896i	−0.947939	−	0.442868i
$835$	−23.7370	−	12.4379i	−0.821454	−	0.430433i
$836$	8.73076	−	13.9272i	0.301959	−	0.481682i
$837$	−17.6735	+	2.79921i	−0.610885	+	0.0967547i
$838$	9.79009	+	26.9588i	0.338193	+	0.931276i
$839$	19.9690	−	14.5083i	0.689406	−	0.500883i	−0.187059	−	0.982349i	$-0.559895\pi$
$839$	19.9690	−	14.5083i	0.689406	−	0.500883i	0.876465	+	0.481466i	$0.159895\pi$
$840$	−13.4938	−	3.06042i	−0.465582	−	0.105594i
$841$	41.8679	+	30.4188i	1.44372	+	1.04892i
$842$	12.5609	−	43.6856i	0.432878	−	1.50551i
$843$	26.0412	−	26.0412i	0.896907	−	0.896907i
$844$	6.65201	+	7.95093i	0.228972	+	0.273682i
$845$	−1.08012	−	3.45810i	−0.0371573	−	0.118962i
$846$	0.455521	−	3.68783i	0.0156611	−	0.126790i
$847$	8.46323	−	4.31223i	0.290800	−	0.148170i
$848$	10.8517	−	7.55166i	0.372649	−	0.259325i
$849$		−	49.9185i		−	1.71320i
$850$	6.20035	+	3.07109i	0.212670	+	0.105337i
$851$			41.4048i			1.41934i
$852$	3.20158	+	13.9598i	0.109684	+	0.478255i
$853$	−19.2804	+	9.82384i	−0.660148	+	0.336362i	−0.751764	−	0.659432i	$-0.770797\pi$
$853$	−19.2804	+	9.82384i	−0.660148	+	0.336362i	0.0916163	+	0.995794i	$0.470797\pi$
$854$	−3.60283	−	0.445022i	−0.123286	−	0.0152283i
$855$	8.56880	−	25.3825i	0.293047	−	0.868062i
$856$	−25.5560	−	20.7870i	−0.873485	−	0.710484i
$857$	38.6930	−	38.6930i	1.32173	−	1.32173i	0.409349	−	0.912378i	$-0.365756\pi$
$857$	38.6930	−	38.6930i	1.32173	−	1.32173i	0.912378	−	0.409349i	$-0.134244\pi$
$858$	−13.9317	−	4.00576i	−0.475619	−	0.136755i
$859$	3.17523	+	2.30694i	0.108337	+	0.0787117i	0.640635	−	0.767846i	$-0.278671\pi$
$859$	3.17523	+	2.30694i	0.108337	+	0.0787117i	−0.532298	+	0.846557i	$0.678671\pi$
$860$	31.0824	+	27.7295i	1.05990	+	0.945568i
$861$	−4.50428	+	3.27255i	−0.153505	+	0.111528i
$862$	−15.1869	+	5.51512i	−0.517268	+	0.187846i
$863$	2.08751	−	0.330629i	0.0710596	−	0.0112547i	−0.120803	−	0.992676i	$-0.538547\pi$
$863$	2.08751	−	0.330629i	0.0710596	−	0.0112547i	0.191863	+	0.981422i	$0.438547\pi$
$864$	15.0197	−	0.207744i	0.510982	−	0.00706761i
$865$	3.15426	−	18.5428i	0.107248	−	0.630473i
$866$	21.4334	−	45.8773i	0.728337	−	1.55897i
$867$	−15.9337	+	31.2716i	−0.541136	+	1.06204i
$868$	12.3983	+	5.28398i	0.420825	+	0.179350i
$869$	9.10404	−	2.95808i	0.308833	−	0.100346i
$870$	−61.1661	+	11.1207i	−2.07373	+	0.377026i
$871$	−40.7748	−	13.2485i	−1.38160	−	0.448909i
$872$	−22.7701	+	39.2417i	−0.771091	+	1.32889i
$873$	−19.7051	−	3.12099i	−0.666918	−	0.105629i
$874$	52.8248	−	10.2284i	1.78682	−	0.345980i
$875$	8.17174	−	7.63038i	0.276255	−	0.257954i
$876$	6.46451	+	16.0672i	0.218416	+	0.542861i
$877$	1.63026	−	10.2931i	0.0550501	−	0.347572i	−0.944754	−	0.327780i	$-0.893700\pi$
$877$	1.63026	−	10.2931i	0.0550501	−	0.347572i	0.999804	−	0.0197923i	$-0.00630050\pi$
$878$	−45.8330	+	35.7552i	−1.54679	+	1.20668i
$879$	−8.61288	+	26.5077i	−0.290505	+	0.894083i
$880$	7.99207	−	7.49978i	0.269413	−	0.252818i
$881$	4.76593	+	14.6680i	0.160568	+	0.494179i	0.998682	−	0.0513164i	$-0.0163417\pi$
$881$	4.76593	+	14.6680i	0.160568	+	0.494179i	−0.838114	+	0.545495i	$0.816342\pi$
$882$	2.09323	+	1.41411i	0.0704828	+	0.0476156i
$883$	25.5955	+	13.0415i	0.861356	+	0.438883i	0.828111	−	0.560564i	$-0.189416\pi$
$883$	25.5955	+	13.0415i	0.861356	+	0.438883i	0.0332452	+	0.999447i	$0.489416\pi$
$884$	1.82084	−	7.25817i	0.0612415	−	0.244119i
$885$	33.8314	+	5.75498i	1.13723	+	0.193452i
$886$	−15.3455	+	16.4321i	−0.515541	+	0.552048i
$887$	−5.40148	−	34.1036i	−0.181364	−	1.14509i	−0.895494	−	0.445074i	$-0.853177\pi$
$887$	−5.40148	−	34.1036i	−0.181364	−	1.14509i	0.714130	−	0.700013i	$-0.246823\pi$
$888$	30.1497	+	33.6313i	1.01176	+	1.12859i
$889$	10.0475	+	13.8292i	0.336982	+	0.463815i
$890$	−18.6779	+	14.2310i	−0.626083	+	0.477024i
$891$	8.04376	−	11.0713i	0.269476	−	0.370902i
$892$	−0.465816	+	5.23688i	−0.0155967	+	0.175344i
$893$	6.97642	+	6.97642i	0.233457	+	0.233457i
$894$	45.8464	−	25.3697i	1.53333	−	0.848488i
$895$	−30.7352	−	10.3758i	−1.02736	−	0.346825i
$896$	−9.66806	−	5.87610i	−0.322987	−	0.196307i
$897$	−21.5423	−	42.2791i	−0.719276	−	1.41166i
$898$	1.22261	+	35.7537i	0.0407990	+	1.19311i
$899$	60.5548			2.01962
$900$	9.83061	−	14.9139i	0.327687	−	0.497131i
$901$	3.23421			0.107747
$902$	−0.150717	−	4.40752i	−0.00501831	−	0.146754i
$903$	−9.25090	−	18.1559i	−0.307851	−	0.604191i
$904$	−14.6092	−	55.0004i	−0.485896	−	1.82929i
$905$	−21.4642	+	6.70424i	−0.713494	+	0.222857i
$906$	−39.9269	+	22.0940i	−1.32648	+	0.734025i
$907$	26.7285	+	26.7285i	0.887506	+	0.887506i	0.994283	−	0.106777i	$-0.0340530\pi$
$907$	26.7285	+	26.7285i	0.887506	+	0.887506i	−0.106777	+	0.994283i	$0.534053\pi$
$908$	−1.06756	−	0.0949581i	−0.0354281	−	0.00315129i
$909$	−1.20727	+	1.66166i	−0.0400425	+	0.0551138i
$910$	−9.94141	−	6.88261i	−0.329554	−	0.228156i
$911$	−16.3202	−	22.4629i	−0.540713	−	0.744228i	0.448002	−	0.894032i	$-0.352136\pi$
$911$	−16.3202	−	22.4629i	−0.540713	−	0.744228i	−0.988716	+	0.149804i	$0.952136\pi$
$912$	35.4593	−	46.7734i	1.17417	−	1.54882i
$913$	0.185381	+	1.17045i	0.00613520	+	0.0387362i
$914$	37.8219	−	40.5002i	1.25104	−	1.33963i
$915$	5.82828	−	11.1229i	0.192677	−	0.367712i
$916$	−21.6445	−	5.42990i	−0.715153	−	0.179409i
$917$	10.7553	+	5.48009i	0.355171	+	0.180969i
$918$	3.04495	+	2.05705i	0.100498	+	0.0678929i
$919$	0.494149	+	1.52083i	0.0163005	+	0.0501677i	0.958876	−	0.283826i	$-0.0916037\pi$
$919$	0.494149	+	1.52083i	0.0163005	+	0.0501677i	−0.942575	+	0.333993i	$0.891604\pi$
$920$	35.7977	+	2.36424i	1.18022	+	0.0779467i
$921$	−10.8312	+	33.3349i	−0.356899	+	1.09842i
$922$	−0.386047	+	0.301163i	−0.0127138	+	0.00991828i
$923$	−1.95791	+	12.3617i	−0.0644453	+	0.406892i
$924$	−4.97404	+	2.00126i	−0.163634	+	0.0658367i
$925$	−36.1680	+	4.88491i	−1.18920	+	0.160615i
$926$	6.24113	−	1.20846i	0.205096	−	0.0397125i
$927$	13.9811	+	2.21439i	0.459201	+	0.0727302i
$928$	−50.3129	−	7.25698i	−1.65160	−	0.238222i
$929$	−32.5499	−	10.5761i	−1.06793	−	0.346990i	−0.278247	−	0.960510i	$-0.589753\pi$
$929$	−32.5499	−	10.5761i	−1.06793	−	0.346990i	−0.789680	+	0.613519i	$0.789753\pi$
$930$	−32.2062	+	33.7071i	−1.05608	+	1.10530i
$931$	−6.37897	+	2.07265i	−0.209062	+	0.0679284i
$932$	−18.0863	+	42.4376i	−0.592437	+	1.39009i
$933$	−8.41362	+	16.5127i	−0.275450	+	0.540600i
$934$	−2.75351	+	5.89376i	−0.0900975	+	0.192850i
$935$	2.65276	−	0.389169i	0.0867544	−	0.0127272i
$936$	−18.0198	−	6.96214i	−0.588996	−	0.227565i
$937$	2.54590	−	0.403231i	0.0831710	−	0.0131730i	−0.114710	−	0.993399i	$-0.536594\pi$
$937$	2.54590	−	0.403231i	0.0831710	−	0.0131730i	0.197881	+	0.980226i	$0.436594\pi$
$938$	−14.9047	+	5.41265i	−0.486656	+	0.176729i
$939$	34.6798	−	25.1964i	1.13173	−	0.822253i
$940$	3.31529	+	5.68188i	0.108133	+	0.185323i
$941$	30.9256	+	22.4688i	1.00815	+	0.732461i	0.963819	−	0.266556i	$-0.0858859\pi$
$941$	30.9256	+	22.4688i	1.00815	+	0.732461i	0.0443263	+	0.999017i	$0.485886\pi$
$942$	−44.0226	−	12.6578i	−1.43433	−	0.412414i
$943$	10.2077	−	10.2077i	0.332407	−	0.332407i
$944$	24.7375	+	13.2453i	0.805137	+	0.431097i
$945$	4.84318	−	3.43500i	0.157549	−	0.111741i
$946$	16.0188	+	1.97864i	0.520816	+	0.0643312i
$947$	−22.2615	+	11.3428i	−0.723400	+	0.368591i	−0.776601	−	0.629993i	$-0.783058\pi$
$947$	−22.2615	+	11.3428i	−0.723400	+	0.368591i	0.0532004	+	0.998584i	$0.483058\pi$
$948$	33.3167	−	7.64092i	1.08207	−	0.248166i
$949$			15.1346i			0.491290i
$950$	15.1669	+	44.9368i	0.492081	+	1.45794i
$951$		−	48.3199i		−	1.56688i
$952$	−1.12023	−	2.53086i	−0.0363067	−	0.0820256i
$953$	−16.2318	+	8.27052i	−0.525800	+	0.267908i	−0.696678	−	0.717384i	$-0.745339\pi$
$953$	−16.2318	+	8.27052i	−0.525800	+	0.267908i	0.170878	+	0.985292i	$0.445339\pi$
$954$	1.02353	−	8.28632i	0.0331379	−	0.268280i
$955$	32.7848	+	24.3962i	1.06089	+	0.789442i
$956$	9.45843	−	7.91323i	0.305907	−	0.255932i
$957$	−17.0341	+	17.0341i	−0.550636	+	0.550636i
$958$	−2.18491	+	7.59890i	−0.0705912	+	0.245509i
$959$	4.18870	+	3.04327i	0.135260	+	0.0982723i
$960$	30.7985	−	24.1464i	0.994018	−	0.779322i
$961$	11.6575	−	8.46969i	0.376049	−	0.273216i
$962$	13.4728	+	37.0998i	0.434380	+	1.19615i
$963$	−20.5481	+	3.25450i	−0.662153	+	0.104875i
$964$	−40.8141	−	25.5858i	−1.31453	−	0.824063i
$965$	−3.69756	+	3.61410i	−0.119029	+	0.116342i
$966$	−15.9005	−	7.42858i	−0.511592	−	0.239011i
$967$	15.6311	−	30.6778i	0.502662	−	0.986530i	−0.490681	−	0.871339i	$-0.663252\pi$
$967$	15.6311	−	30.6778i	0.502662	−	0.986530i	0.993343	−	0.115191i	$-0.0367480\pi$
$968$	−5.64283	+	26.2665i	−0.181367	+	0.844238i
$969$	13.6559	−	4.43708i	0.438692	−	0.142540i
$970$	31.0970	−	16.7471i	0.998466	−	0.537718i
$971$	−9.26125	−	3.00916i	−0.297208	−	0.0965686i	0.156618	−	0.987659i	$-0.449941\pi$
$971$	−9.26125	−	3.00916i	−0.297208	−	0.0965686i	−0.453825	+	0.891091i	$0.649941\pi$
$972$	21.6423	−	24.8239i	0.694177	−	0.796226i
$973$	−9.64589	−	1.52776i	−0.309233	−	0.0489777i
$974$	0.0574818	+	0.296867i	0.00184184	+	0.00951222i
$975$	34.3902	−	23.8057i	1.10137	−	0.762393i
$976$	7.40667	−	7.11117i	0.237082	−	0.227623i
$977$	8.35252	−	52.7357i	0.267221	−	1.68716i	−0.380099	−	0.924946i	$-0.624110\pi$
$977$	8.35252	−	52.7357i	0.267221	−	1.68716i	0.647319	−	0.762219i	$-0.275890\pi$
$978$	−16.6342	−	21.3227i	−0.531904	−	0.681824i
$979$	−2.81172	+	8.65358i	−0.0898629	+	0.276570i
$980$	−4.46489	+	0.254546i	−0.142626	+	0.00813117i
$981$	8.85403	+	27.2499i	0.282687	+	0.870023i
$982$	24.8480	−	36.7812i	0.792932	−	1.17374i
$983$	−35.7345	−	18.2076i	−1.13975	−	0.580734i	−0.220887	−	0.975300i	$-0.570895\pi$
$983$	−35.7345	−	18.2076i	−1.13975	−	0.580734i	−0.918868	+	0.394566i	$0.870895\pi$
$984$	0.858343	−	15.7241i	0.0273630	−	0.501267i
$985$	29.0014	−	14.3624i	0.924063	−	0.457623i
$986$	−9.08862	−	8.48760i	−0.289441	−	0.270300i
$987$	−0.503423	−	3.17849i	−0.0160241	−	0.101172i
$988$	44.0042	−	26.3537i	1.39996	−	0.838421i
$989$	31.0549	+	42.7433i	0.987487	+	1.35916i
$990$	−0.157569	−	6.91975i	−0.00500786	−	0.219924i
$991$	16.6826	−	22.9616i	0.529939	−	0.729398i	−0.457182	−	0.889373i	$-0.651141\pi$
$991$	16.6826	−	22.9616i	0.529939	−	0.729398i	0.987121	+	0.159975i	$0.0511413\pi$
$992$	−33.7222	+	17.7740i	−1.07068	+	0.564326i
$993$	−37.1733	−	37.1733i	−1.17966	−	1.17966i
$994$	2.24131	+	4.05034i	0.0710900	+	0.128469i
$995$	0.621091	−	54.4072i	0.0196899	−	1.72482i
$996$	0.289059	+	4.22164i	0.00915918	+	0.133768i
$997$	23.3931	+	45.9116i	0.740867	+	1.45403i	0.885544	+	0.464555i	$0.153786\pi$
$997$	23.3931	+	45.9116i	0.740867	+	1.45403i	−0.144677	+	0.989479i	$0.546214\pi$
$998$	14.6951	−	0.502504i	0.465166	−	0.0159065i
$999$	−19.3825			−0.613234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.bj.a.323.1	✓	720
4.3	odd	2	inner	700.2.bj.a.323.80	yes	720
25.12	odd	20	inner	700.2.bj.a.687.80	yes	720
100.87	even	20	inner	700.2.bj.a.687.1	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.bj.a.323.1	✓	720	1.1	even	1	trivial
700.2.bj.a.323.80	yes	720	4.3	odd	2	inner
700.2.bj.a.687.1	yes	720	100.87	even	20	inner
700.2.bj.a.687.80	yes	720	25.12	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41339 + 0.0483313i) q^{2} +(-0.993217 - 1.94930i) q^{3} +(1.99533 - 0.136622i) q^{4} +(-0.0255244 + 2.23592i) q^{5} +(1.49801 + 2.70711i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.81357 + 0.289536i) q^{8} +(-1.04993 + 1.44510i) q^{9} +(-0.0719891 - 3.16146i) q^{10} +(-0.720247 - 0.991334i) q^{11} +(-2.24811 - 3.75379i) q^{12} +(-0.598148 - 3.77656i) q^{13} +(-1.03359 - 0.965240i) q^{14} +(4.38383 - 2.17100i) q^{15} +(3.96267 - 0.545210i) q^{16} +(0.871876 + 0.444243i) q^{17} +(1.41411 - 2.09323i) q^{18} +(2.07265 + 6.37897i) q^{19} +(0.254546 + 4.46489i) q^{20} +(0.676051 - 2.08067i) q^{21} +(1.06590 + 1.36633i) q^{22} +(-0.887367 + 5.60261i) q^{23} +(3.35888 + 5.19691i) q^{24} +(-4.99870 - 0.114141i) q^{25} +(1.02794 + 5.30883i) q^{26} +(-2.62270 - 0.415395i) q^{27} +(1.50752 + 1.31430i) q^{28} +(8.54637 + 2.77688i) q^{29} +(-6.09112 + 3.28034i) q^{30} +(6.40884 - 2.08236i) q^{31} +(-5.57444 + 0.962114i) q^{32} +(-1.21704 + 2.38859i) q^{33} +(-1.25377 - 0.585748i) q^{34} +(-1.59908 + 1.56299i) q^{35} +(-1.89752 + 3.02689i) q^{36} +(7.20941 - 1.14186i) q^{37} +(-3.23776 - 8.91578i) q^{38} +(-6.76755 + 4.91691i) q^{39} +(-0.575566 - 6.29831i) q^{40} +(-2.05887 - 1.49585i) q^{41} +(-0.854961 + 2.97347i) q^{42} +(6.58605 - 6.58605i) q^{43} +(-1.57257 - 1.87964i) q^{44} +(-3.20433 - 2.38444i) q^{45} +(0.983412 - 7.96155i) q^{46} +(1.31064 - 0.667805i) q^{47} +(-4.99857 - 7.18291i) q^{48} +1.00000i q^{49} +(7.07061 - 0.0802678i) q^{50} -2.14078i q^{51} +(-1.70946 - 7.45376i) q^{52} +(2.94493 - 1.50052i) q^{53} +(3.72697 + 0.460356i) q^{54} +(2.23493 - 1.58511i) q^{55} +(-2.19423 - 1.78476i) q^{56} +(10.3759 - 10.3759i) q^{57} +(-12.2135 - 3.51176i) q^{58} +(5.67531 + 4.12336i) q^{59} +(8.45057 - 4.93079i) q^{60} +(2.07670 - 1.50881i) q^{61} +(-8.95754 + 3.25293i) q^{62} +(-1.76425 + 0.279430i) q^{63} +(7.83234 - 1.62926i) q^{64} +(8.45936 - 1.24102i) q^{65} +(1.60471 - 3.43482i) q^{66} +(5.09044 - 9.99055i) q^{67} +(1.80037 + 0.767293i) q^{68} +(11.8025 - 3.83487i) q^{69} +(2.18458 - 2.28639i) q^{70} +(-3.11308 - 1.01150i) q^{71} +(2.53563 - 4.36988i) q^{72} +(-3.90944 - 0.619194i) q^{73} +(-10.1345 + 1.96233i) q^{74} +(4.74230 + 9.85732i) q^{75} +(5.00713 + 12.4450i) q^{76} +(0.191688 - 1.21027i) q^{77} +(9.32753 - 7.27659i) q^{78} +(-2.41406 + 7.42971i) q^{79} +(1.11790 + 8.87414i) q^{80} +(3.45112 + 10.6215i) q^{81} +(2.98227 + 2.01471i) q^{82} +(-0.861689 - 0.439052i) q^{83} +(1.06468 - 4.24399i) q^{84} +(-1.01555 + 1.93811i) q^{85} +(-8.99033 + 9.62695i) q^{86} +(-3.07543 - 19.4175i) q^{87} +(2.31349 + 2.58065i) q^{88} +(-4.36461 - 6.00737i) q^{89} +(4.64421 + 3.21527i) q^{90} +(2.24748 - 3.09339i) q^{91} +(-1.00515 + 11.3003i) q^{92} +(-10.4245 - 10.4245i) q^{93} +(-1.82017 + 1.00721i) q^{94} +(-14.3158 + 4.47147i) q^{95} +(7.41207 + 9.91065i) q^{96} +(5.07067 + 9.95176i) q^{97} +(-0.0483313 - 1.41339i) q^{98} +2.18878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) \) 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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