LMFDB - Embedded newform 110.4.k.a.7.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,4,Mod(7,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	110.k (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:	$6.49021010063$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.15
Character	$\chi$	$=$	110.7
Dual form			110.4.k.a.63.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.97538 - 0.312869i) q^{2} +(0.114151 + 0.224033i) q^{3} +(3.80423 - 1.23607i) q^{4} +(1.74009 - 11.0441i) q^{5} +(0.295583 + 0.406836i) q^{6} +(-27.7439 - 14.1362i) q^{7} +(7.12805 - 3.63192i) q^{8} +(15.8330 - 21.7923i) q^{9} +(-0.0180186 - 22.3607i) q^{10} +(34.4581 - 11.9849i) q^{11} +(0.711175 + 0.711175i) q^{12} +(4.15742 + 26.2489i) q^{13} +(-59.2275 - 19.2442i) q^{14} +(2.67288 - 0.870852i) q^{15} +(12.9443 - 9.40456i) q^{16} +(-15.2990 + 96.5943i) q^{17} +(24.4581 - 48.0017i) q^{18} +(27.3619 - 84.2113i) q^{19} +(-7.03155 - 44.1651i) q^{20} -7.82922i q^{21} +(64.3181 - 34.4556i) q^{22} +(78.8253 - 78.8253i) q^{23} +(1.62734 + 1.18233i) q^{24} +(-118.944 - 38.4355i) q^{25} +(16.4250 + 50.5508i) q^{26} +(13.3948 + 2.12153i) q^{27} +(-123.018 - 19.4841i) q^{28} +(77.1760 + 237.523i) q^{29} +(5.00748 - 2.55652i) q^{30} +(-92.6147 - 67.2885i) q^{31} +(22.6274 - 22.6274i) q^{32} +(6.61843 + 6.35168i) q^{33} +195.597i q^{34} +(-204.399 + 281.808i) q^{35} +(33.2957 - 102.474i) q^{36} +(-36.7376 + 72.1017i) q^{37} +(27.7030 - 174.910i) q^{38} +(-5.40606 + 3.92773i) q^{39} +(-27.7079 - 85.0428i) q^{40} +(-26.6955 - 8.67388i) q^{41} +(-2.44952 - 15.4657i) q^{42} +(359.233 + 359.233i) q^{43} +(116.272 - 88.1858i) q^{44} +(-213.125 - 212.782i) q^{45} +(131.048 - 180.372i) q^{46} +(-53.6379 + 27.3299i) q^{47} +(3.58453 + 1.82641i) q^{48} +(368.282 + 506.897i) q^{49} +(-246.985 - 38.7106i) q^{50} +(-23.3867 + 7.59881i) q^{51} +(48.2613 + 94.7181i) q^{52} +(-74.6761 + 11.8275i) q^{53} +27.1235 q^{54} +(-72.4020 - 401.414i) q^{55} -249.102 q^{56} +(21.9895 - 3.48280i) q^{57} +(226.765 + 445.052i) q^{58} +(27.1949 - 8.83616i) q^{59} +(9.09179 - 6.61677i) q^{60} +(-10.0528 - 13.8364i) q^{61} +(-204.001 - 103.944i) q^{62} +(-747.332 + 380.785i) q^{63} +(37.6183 - 51.7771i) q^{64} +(297.130 - 0.239432i) q^{65} +(15.0611 + 10.4763i) q^{66} +(304.284 + 304.284i) q^{67} +(61.1962 + 386.377i) q^{68} +(26.6574 + 8.66152i) q^{69} +(-315.596 + 620.628i) q^{70} +(593.777 - 431.405i) q^{71} +(33.7107 - 212.841i) q^{72} +(127.554 - 250.339i) q^{73} +(-50.0123 + 153.922i) q^{74} +(-4.96672 - 31.0349i) q^{75} -354.180i q^{76} +(-1125.43 - 154.600i) q^{77} +(-9.45014 + 9.45014i) q^{78} +(-700.041 - 508.610i) q^{79} +(-81.3407 - 159.323i) q^{80} +(-223.692 - 688.454i) q^{81} +(-55.4474 - 8.78200i) q^{82} +(746.359 + 118.212i) q^{83} +(-9.67745 - 29.7841i) q^{84} +(1040.18 + 337.047i) q^{85} +(822.013 + 597.228i) q^{86} +(-44.4034 + 44.4034i) q^{87} +(202.091 - 210.578i) q^{88} +965.838i q^{89} +(-487.576 - 353.645i) q^{90} +(255.718 - 787.019i) q^{91} +(202.436 - 397.303i) q^{92} +(4.50283 - 28.4298i) q^{93} +(-97.4045 + 70.7685i) q^{94} +(-882.426 - 448.723i) q^{95} +(7.65222 + 2.48636i) q^{96} +(199.941 + 1262.38i) q^{97} +(886.088 + 886.088i) q^{98} +(284.398 - 940.679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) $ 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	1.97538	−	0.312869i	0.698401	−	0.110616i
$2$	1.97538	−	0.312869i	0.698401	−	0.110616i
$3$	0.114151	+	0.224033i	0.0219683	+	0.0431152i	0.901730	−	0.432300i	$-0.142298\pi$
$3$	0.114151	+	0.224033i	0.0219683	+	0.0431152i	−0.879762	+	0.475415i	$0.842298\pi$
$4$	3.80423	−	1.23607i	0.475528	−	0.154508i
$5$	1.74009	−	11.0441i	0.155639	−	0.987814i
$5$	1.74009	−	11.0441i	0.155639	−	0.987814i
$6$	0.295583	+	0.406836i	0.0201119	+	0.0276817i
$7$	−27.7439	−	14.1362i	−1.49803	−	0.763285i	−0.503137	−	0.864207i	$-0.667821\pi$
$7$	−27.7439	−	14.1362i	−1.49803	−	0.763285i	−0.994894	+	0.100922i	$0.967821\pi$
$8$	7.12805	−	3.63192i	0.315018	−	0.160510i
$9$	15.8330	−	21.7923i	0.586409	−	0.807123i
$10$	−0.0180186	−	22.3607i	−0.000569798	−	0.707107i
$11$	34.4581	−	11.9849i	0.944501	−	0.328507i
$11$	34.4581	−	11.9849i	0.944501	−	0.328507i
$12$	0.711175	+	0.711175i	0.0171082	+	0.0171082i
$13$	4.15742	+	26.2489i	0.0886971	+	0.560011i	0.991515	+	0.129989i	$0.0414943\pi$
$13$	4.15742	+	26.2489i	0.0886971	+	0.560011i	−0.902818	+	0.430022i	$0.858506\pi$
$14$	−59.2275	−	19.2442i	−1.13066	−	0.367373i
$15$	2.67288	−	0.870852i	0.0460089	−	0.0149902i
$16$	12.9443	−	9.40456i	0.202254	−	0.146946i
$17$	−15.2990	+	96.5943i	−0.218268	+	1.37809i	0.598498	+	0.801124i	$0.295764\pi$
$17$	−15.2990	+	96.5943i	−0.218268	+	1.37809i	−0.816767	+	0.576968i	$0.804236\pi$
$18$	24.4581	−	48.0017i	0.320268	−	0.628562i
$19$	27.3619	−	84.2113i	0.330382	−	1.01681i	−0.638571	−	0.769563i	$-0.720474\pi$
$19$	27.3619	−	84.2113i	0.330382	−	1.01681i	0.968952	−	0.247247i	$-0.0795260\pi$
$20$	−7.03155	−	44.1651i	−0.0786152	−	0.493781i
$21$		−	7.82922i		−	0.0813560i
$22$	64.3181	−	34.4556i	0.623303	−	0.333907i
$23$	78.8253	−	78.8253i	0.714618	−	0.714618i	−0.252880	−	0.967498i	$-0.581378\pi$
$23$	78.8253	−	78.8253i	0.714618	−	0.714618i	0.967498	+	0.252880i	$0.0813778\pi$
$24$	1.62734	+	1.18233i	0.0138408	+	0.0100560i
$25$	−118.944	−	38.4355i	−0.951553	−	0.307484i
$26$	16.4250	+	50.5508i	0.123892	+	0.381301i
$27$	13.3948	+	2.12153i	0.0954752	+	0.0151218i
$28$	−123.018	−	19.4841i	−0.830290	−	0.131505i
$29$	77.1760	+	237.523i	0.494180	+	1.52093i	0.818231	+	0.574890i	$0.194955\pi$
$29$	77.1760	+	237.523i	0.494180	+	1.52093i	−0.324050	+	0.946040i	$0.605045\pi$
$30$	5.00748	−	2.55652i	0.0304745	−	0.0155585i
$31$	−92.6147	−	67.2885i	−0.536583	−	0.389851i	0.286231	−	0.958161i	$-0.407597\pi$
$31$	−92.6147	−	67.2885i	−0.536583	−	0.389851i	−0.822815	+	0.568310i	$0.807597\pi$
$32$	22.6274	−	22.6274i	0.125000	−	0.125000i
$33$	6.61843	+	6.35168i	0.0349127	+	0.0335056i
$34$			195.597i			0.986605i
$35$	−204.399	+	281.808i	−0.987135	+	1.36098i
$36$	33.2957	−	102.474i	0.154147	−	0.474415i
$37$	−36.7376	+	72.1017i	−0.163233	+	0.320363i	−0.958106	−	0.286412i	$-0.907537\pi$
$37$	−36.7376	+	72.1017i	−0.163233	+	0.320363i	0.794873	+	0.606776i	$0.207537\pi$
$38$	27.7030	−	174.910i	0.118264	−	0.746687i
$39$	−5.40606	+	3.92773i	−0.0221965	+	0.0161267i
$40$	−27.7079	−	85.0428i	−0.109525	−	0.336161i
$41$	−26.6955	−	8.67388i	−0.101686	−	0.0330398i	0.257732	−	0.966216i	$-0.417025\pi$
$41$	−26.6955	−	8.67388i	−0.101686	−	0.0330398i	−0.359418	+	0.933177i	$0.617025\pi$
$42$	−2.44952	−	15.4657i	−0.00899926	−	0.0568191i
$43$	359.233	+	359.233i	1.27401	+	1.27401i	0.943964	+	0.330047i	$0.107065\pi$
$43$	359.233	+	359.233i	1.27401	+	1.27401i	0.330047	+	0.943964i	$0.392935\pi$
$44$	116.272	−	88.1858i	0.398380	−	0.302148i
$45$	−213.125	−	212.782i	−0.706019	−	0.704882i
$46$	131.048	−	180.372i	0.420042	−	0.578138i
$47$	−53.6379	+	27.3299i	−0.166466	+	0.0848186i	−0.535238	−	0.844701i	$-0.679778\pi$
$47$	−53.6379	+	27.3299i	−0.166466	+	0.0848186i	0.368772	+	0.929520i	$0.379778\pi$
$48$	3.58453	+	1.82641i	0.0107788	+	0.00549207i
$49$	368.282	+	506.897i	1.07371	+	1.47783i
$50$	−246.985	−	38.7106i	−0.698578	−	0.109490i
$51$	−23.3867	+	7.59881i	−0.0642117	+	0.0208636i
$52$	48.2613	+	94.7181i	0.128704	+	0.252597i
$53$	−74.6761	+	11.8275i	−0.193539	+	0.0306535i	−0.252451	−	0.967610i	$-0.581237\pi$
$53$	−74.6761	+	11.8275i	−0.193539	+	0.0306535i	0.0589125	+	0.998263i	$0.481237\pi$
$54$	27.1235			0.0683527
$55$	−72.4020	−	401.414i	−0.177503	−	0.984120i
$56$	−249.102			−0.594422
$57$	21.9895	−	3.48280i	0.0510979	−	0.00809311i
$58$	226.765	+	445.052i	0.513375	+	1.00756i
$59$	27.1949	−	8.83616i	0.0600081	−	0.0194978i	−0.278859	−	0.960332i	$-0.589956\pi$
$59$	27.1949	−	8.83616i	0.0600081	−	0.0194978i	0.338867	+	0.940834i	$0.389956\pi$
$60$	9.09179	−	6.61677i	0.0195624	−	0.0142370i
$61$	−10.0528	−	13.8364i	−0.0211004	−	0.0290422i	0.798336	−	0.602212i	$-0.205714\pi$
$61$	−10.0528	−	13.8364i	−0.0211004	−	0.0290422i	−0.819437	+	0.573169i	$0.805714\pi$
$62$	−204.001	−	103.944i	−0.417874	−	0.212917i
$63$	−747.332	+	380.785i	−1.49452	+	0.761498i
$64$	37.6183	−	51.7771i	0.0734732	−	0.101127i
$65$	297.130	−	0.239432i	0.566992	−	0.000456891i
$66$	15.0611	+	10.4763i	0.0280894	+	0.0195385i
$67$	304.284	+	304.284i	0.554840	+	0.554840i	0.927834	−	0.372994i	$-0.121669\pi$
$67$	304.284	+	304.284i	0.554840	+	0.554840i	−0.372994	+	0.927834i	$0.621669\pi$
$68$	61.1962	+	386.377i	0.109134	+	0.689046i
$69$	26.6574	+	8.66152i	0.0465098	+	0.0151120i
$70$	−315.596	+	620.628i	−0.538870	+	1.05970i
$71$	593.777	−	431.405i	0.992513	−	0.721103i	0.0320429	−	0.999486i	$-0.489799\pi$
$71$	593.777	−	431.405i	0.992513	−	0.721103i	0.960470	+	0.278384i	$0.0897987\pi$
$72$	33.7107	−	212.841i	0.0551784	−	0.348383i
$73$	127.554	−	250.339i	0.204508	−	0.401369i	−0.765858	−	0.643010i	$-0.777685\pi$
$73$	127.554	−	250.339i	0.204508	−	0.401369i	0.970366	+	0.241640i	$0.0776855\pi$
$74$	−50.0123	+	153.922i	−0.0785650	+	0.241798i
$75$	−4.96672	−	31.0349i	−0.00764677	−	0.0477813i
$76$		−	354.180i		−	0.534569i
$77$	−1125.43	−	154.600i	−1.66564	−	0.228810i
$78$	−9.45014	+	9.45014i	−0.0137182	+	0.0137182i
$79$	−700.041	−	508.610i	−0.996972	−	0.724342i	−0.0355349	−	0.999368i	$-0.511313\pi$
$79$	−700.041	−	508.610i	−0.996972	−	0.724342i	−0.961437	+	0.275026i	$0.911313\pi$
$80$	−81.3407	−	159.323i	−0.113677	−	0.222660i
$81$	−223.692	−	688.454i	−0.306848	−	0.944381i
$82$	−55.4474	−	8.78200i	−0.0746724	−	0.0118270i
$83$	746.359	+	118.212i	0.987031	+	0.156330i	0.629022	−	0.777388i	$-0.283456\pi$
$83$	746.359	+	118.212i	0.987031	+	0.156330i	0.358009	+	0.933718i	$0.383456\pi$
$84$	−9.67745	−	29.7841i	−0.0125702	−	0.0386871i
$85$	1040.18	+	337.047i	1.32733	+	0.430093i
$86$	822.013	+	597.228i	1.03070	+	0.748845i
$87$	−44.4034	+	44.4034i	−0.0547189	+	0.0547189i
$88$	202.091	−	210.578i	0.244807	−	0.255088i
$89$			965.838i			1.15032i	0.818040	+	0.575161i	$0.195060\pi$
$89$			965.838i			1.15032i	−0.818040	+	0.575161i	$0.804940\pi$
$90$	−487.576	−	353.645i	−0.571056	−	0.414194i
$91$	255.718	−	787.019i	0.294577	−	0.906616i
$92$	202.436	−	397.303i	0.229406	−	0.450235i
$93$	4.50283	−	28.4298i	0.00502067	−	0.0316992i
$94$	−97.4045	+	70.7685i	−0.106878	+	0.0776512i
$95$	−882.426	−	448.723i	−0.953000	−	0.484611i
$96$	7.65222	+	2.48636i	0.00813544	+	0.00264336i
$97$	199.941	+	1262.38i	0.209288	+	1.32139i	0.838817	+	0.544414i	$0.183248\pi$
$97$	199.941	+	1262.38i	0.209288	+	1.32139i	−0.629529	+	0.776977i	$0.716752\pi$
$98$	886.088	+	886.088i	0.913351	+	0.913351i
$99$	284.398	−	940.679i	0.288718	−	0.954968i
$100$	−499.999	+	0.805815i	−0.499999	+	0.000805815i
$101$	730.484	−	1005.42i	0.719662	−	0.990529i	−0.279873	−	0.960037i	$-0.590292\pi$
$101$	730.484	−	1005.42i	0.719662	−	0.990529i	0.999535	−	0.0304925i	$-0.00970757\pi$
$102$	−43.8202	+	22.3275i	−0.0425377	+	0.0216740i
$103$	−1345.16	−	685.395i	−1.28682	−	0.655670i	−0.329355	−	0.944206i	$-0.606831\pi$
$103$	−1345.16	−	685.395i	−1.28682	−	0.655670i	−0.957469	+	0.288537i	$0.906831\pi$
$104$	124.969	+	172.004i	0.117829	+	0.162177i
$105$	−86.4667	−	13.6236i	−0.0803646	−	0.0126621i
$106$	−143.813	+	46.7276i	−0.131777	+	0.0428169i
$107$	−916.618	−	1798.96i	−0.828157	−	1.62535i	−0.779390	−	0.626539i	$-0.784471\pi$
$107$	−916.618	−	1798.96i	−0.828157	−	1.62535i	−0.0487666	−	0.998810i	$-0.515529\pi$
$108$	53.5792	−	8.48611i	0.0477376	−	0.00756090i
$109$	1426.47			1.25350			0.626750	−	0.779221i	$-0.284385\pi$
$109$	1426.47			1.25350			0.626750	+	0.779221i	$0.284385\pi$
$110$	−268.611	−	770.291i	−0.232828	−	0.667676i
$111$	−20.3468			−0.0173985
$112$	−492.070	+	77.9362i	−0.415145	+	0.0657525i
$113$	−385.304	−	756.202i	−0.320764	−	0.629536i	0.673173	−	0.739485i	$-0.264931\pi$
$113$	−385.304	−	756.202i	−0.320764	−	0.629536i	−0.993937	+	0.109950i	$0.964931\pi$
$114$	42.3479	−	13.7597i	0.0347916	−	0.0113045i
$115$	−733.391	−	1007.72i	−0.594687	−	0.817131i
$116$	587.190	+	808.198i	0.469993	+	0.646890i
$117$	637.850	+	325.001i	0.504011	+	0.256806i
$118$	50.9556	−	25.9632i	0.0397529	−	0.0202551i
$119$	1789.94	−	2463.64i	1.37885	−	1.89782i
$120$	15.8895	−	15.9152i	0.0120876	−	0.0121071i
$121$	1043.72	−	825.954i	0.784166	−	0.620551i
$122$	−24.1870	−	24.1870i	−0.0179491	−	0.0179491i
$123$	−1.10407	−	6.97080i	−0.000809352	−	0.00511005i
$124$	−435.500	−	141.503i	−0.315396	−	0.102478i
$125$	−631.459	+	1246.75i	−0.451835	+	0.892101i
$126$	−1357.13	+	986.010i	−0.959543	+	0.697149i
$127$	−238.086	+	1503.21i	−0.166352	+	1.05030i	0.753331	+	0.657642i	$0.228446\pi$
$127$	−238.086	+	1503.21i	−0.166352	+	1.05030i	−0.919683	+	0.392663i	$0.871554\pi$
$128$	58.1108	−	114.049i	0.0401275	−	0.0787546i
$129$	−39.4734	+	121.487i	−0.0269414	+	0.0829171i
$130$	586.869	−	93.4358i	0.395937	−	0.0630374i
$131$			80.2189i			0.0535020i	0.999642	+	0.0267510i	$0.00851612\pi$
$131$			80.2189i			0.0535020i	−0.999642	+	0.0267510i	$0.991484\pi$
$132$	33.0291	+	15.9824i	0.0217789	+	0.0105386i
$133$	−1949.56	+	1949.56i	−1.27104	+	1.27104i
$134$	696.278	+	505.875i	0.448875	+	0.326127i
$135$	46.7386	−	144.242i	0.0297971	−	0.0919582i
$136$	241.771	+	744.094i	0.152439	+	0.469159i
$137$	−64.7412	−	10.2540i	−0.0403738	−	0.00639458i	0.136215	−	0.990679i	$-0.456506\pi$
$137$	−64.7412	−	10.2540i	−0.0403738	−	0.00639458i	−0.176589	+	0.984285i	$0.556506\pi$
$138$	55.3684	+	8.76949i	0.0341541	+	0.00540948i
$139$	534.609	+	1645.36i	0.326223	+	1.00401i	0.970886	+	0.239543i	$0.0769976\pi$
$139$	534.609	+	1645.36i	0.326223	+	1.00401i	−0.644663	+	0.764467i	$0.723002\pi$
$140$	−429.246	+	1324.71i	−0.259128	+	0.799705i
$141$	−12.2456	−	8.89695i	−0.00731394	−	0.00531389i
$142$	1037.96	−	1037.96i	0.613407	−	0.613407i
$143$	457.848	+	854.663i	0.267742	+	0.499794i
$144$		−	430.988i		−	0.249415i
$145$	2757.52	−	439.027i	1.57931	−	0.251443i
$146$	173.644	−	534.421i	0.0984307	−	0.302939i
$147$	−71.5221	+	140.370i	−0.0401295	+	0.0787586i
$148$	−50.6357	+	319.701i	−0.0281232	+	0.177563i
$149$	−2359.01	+	1713.92i	−1.29703	+	0.942347i	−0.999922	−	0.0124974i	$-0.996022\pi$
$149$	−2359.01	+	1713.92i	−1.29703	+	0.942347i	−0.297107	+	0.954844i	$0.596022\pi$
$150$	−19.5210	−	59.7516i	−0.0106259	−	0.0325247i
$151$	186.509	+	60.6004i	0.100516	+	0.0326596i	0.358843	−	0.933398i	$-0.383171\pi$
$151$	186.509	+	60.6004i	0.100516	+	0.0326596i	−0.258327	+	0.966057i	$0.583171\pi$
$152$	−110.812	−	699.639i	−0.0591318	−	0.373344i
$153$	1862.78	+	1862.78i	0.984295	+	0.984295i
$154$	−2271.51	+	46.7168i	−1.18859	+	0.0244451i
$155$	−904.299	+	905.757i	−0.468613	+	0.469369i
$156$	−15.7109	+	21.6242i	−0.00806334	+	0.0110982i
$157$	−1364.71	+	695.354i	−0.693730	+	0.353473i	−0.765042	−	0.643981i	$-0.777282\pi$
$157$	−1364.71	+	695.354i	−0.693730	+	0.353473i	0.0713112	+	0.997454i	$0.477282\pi$
$158$	−1541.97	−	785.674i	−0.776410	−	0.395601i
$159$	−11.1741	−	15.3798i	−0.00557334	−	0.00767105i
$160$	−210.526	−	289.273i	−0.104022	−	0.142932i
$161$	−3301.22	+	1072.63i	−1.61598	+	0.525063i
$162$	−657.272	−	1289.97i	−0.318766	−	0.625614i
$163$	792.149	−	125.464i	0.380650	−	0.0602890i	0.0368223	−	0.999322i	$-0.488276\pi$
$163$	792.149	−	125.464i	0.380650	−	0.0602890i	0.343828	+	0.939033i	$0.388276\pi$
$164$	−112.277			−0.0534596
$165$	81.6652	−	62.0421i	0.0385311	−	0.0292725i
$166$	1511.33			0.706636
$167$	−1084.43	+	171.756i	−0.502487	+	0.0795861i	−0.402532	−	0.915406i	$-0.631870\pi$
$167$	−1084.43	+	171.756i	−0.502487	+	0.0795861i	−0.0999549	+	0.994992i	$0.531870\pi$
$168$	−28.4351	−	55.8071i	−0.0130584	−	0.0256286i
$169$	1417.75	−	460.654i	0.645311	−	0.209674i
$170$	2160.19	+	340.356i	0.974582	+	0.153554i
$171$	−1401.94	−	1929.60i	−0.626952	−	0.862925i
$172$	1810.64	+	922.567i	0.802674	+	0.408983i
$173$	−3277.01	+	1669.72i	−1.44015	+	0.733795i	−0.987460	−	0.157870i	$-0.949537\pi$
$173$	−3277.01	+	1669.72i	−1.44015	+	0.733795i	−0.452695	+	0.891666i	$0.649537\pi$
$174$	−73.8210	+	101.606i	−0.0321630	+	0.0442685i
$175$	2756.65	+	2747.77i	1.19076	+	1.18693i
$176$	333.323	−	479.199i	0.142756	−	0.205233i
$177$	5.08391	+	5.08391i	0.00215893	+	0.00215893i
$178$	302.181	+	1907.89i	0.127244	+	0.803386i
$179$	−1396.57	−	453.773i	−0.583153	−	0.189478i	0.00255942	−	0.999997i	$-0.499185\pi$
$179$	−1396.57	−	453.773i	−0.583153	−	0.189478i	−0.585713	+	0.810519i	$0.699185\pi$
$180$	−1073.79	−	546.034i	−0.444642	−	0.226106i
$181$	1126.43	−	818.399i	0.462579	−	0.336083i	−0.331963	−	0.943292i	$-0.607711\pi$
$181$	1126.43	−	818.399i	0.462579	−	0.336083i	0.794542	+	0.607209i	$0.207711\pi$
$182$	258.906	−	1634.67i	0.105447	−	0.665766i
$183$	1.95229	−	3.83159i	0.000788620	−	0.00154775i
$184$	275.583	−	848.158i	0.110415	−	0.339821i
$185$	732.371	+	531.198i	0.291054	+	0.211105i
$186$		−	57.5683i		−	0.0226942i
$187$	630.496	+	3511.82i	0.246559	+	1.37331i
$188$	−170.269	+	170.269i	−0.0660541	+	0.0660541i
$189$	−341.634	−	248.212i	−0.131483	−	0.0955277i
$190$	−1883.51	−	610.313i	−0.719182	−	0.233036i
$191$	796.486	+	2451.33i	0.301736	+	0.928649i	0.980875	+	0.194639i	$0.0623536\pi$
$191$	796.486	+	2451.33i	0.301736	+	0.928649i	−0.679138	+	0.734010i	$0.737646\pi$
$192$	15.8939	+	2.51735i	0.00597420	+	0.000946220i
$193$	1566.67	+	248.136i	0.584308	+	0.0925453i	0.441588	−	0.897218i	$-0.354415\pi$
$193$	1566.67	+	248.136i	0.584308	+	0.0925453i	0.142720	+	0.989763i	$0.454415\pi$
$194$	789.917	+	2431.11i	0.292334	+	0.899710i
$195$	33.9712	+	66.5397i	0.0124755	+	0.0244359i
$196$	2027.59	+	1473.13i	0.738916	+	0.536854i
$197$	1147.33	−	1147.33i	0.414942	−	0.414942i	−0.468514	−	0.883456i	$-0.655210\pi$
$197$	1147.33	−	1147.33i	0.414942	−	0.414942i	0.883456	+	0.468514i	$0.155210\pi$
$198$	267.485	−	1947.18i	0.0960066	−	0.698888i
$199$			708.654i			0.252438i	0.992002	+	0.126219i	$0.0402842\pi$
$199$			708.654i			0.252438i	−0.992002	+	0.126219i	$0.959716\pi$
$200$	−987.435	+	158.026i	−0.349111	+	0.0558706i
$201$	−33.4356	+	102.904i	−0.0117331	+	0.0361109i
$202$	1128.41	−	2214.64i	0.393044	−	0.771393i
$203$	1216.52	−	7680.81i	0.420606	−	2.65560i
$204$	−79.5757	+	57.8152i	−0.0273109	+	0.0198425i
$205$	−142.248	+	279.734i	−0.0484635	+	0.0953047i
$206$	−2871.64	−	933.053i	−0.971247	−	0.315577i
$207$	−469.741	−	2965.83i	−0.157726	−	0.995842i
$208$	300.675	+	300.675i	0.100231	+	0.100231i
$209$	−66.4232	−	3229.69i	−0.0219837	−	1.06891i
$210$	−175.067	+	0.141071i	−0.0575274	+	4.63565e-5i
$211$	−2039.29	+	2806.84i	−0.665358	+	0.915786i	−0.999644	−	0.0266852i	$-0.991505\pi$
$211$	−2039.29	+	2806.84i	−0.665358	+	0.915786i	0.334286	+	0.942472i	$0.391505\pi$
$212$	−269.465	+	137.299i	−0.0872968	+	0.0444800i
$213$	164.429	+	83.7807i	0.0528943	+	0.0269510i
$214$	−2373.50	−	3266.85i	−0.758175	−	1.04354i
$215$	4592.50	−	3342.31i	1.45677	−	1.06020i
$216$	103.184	−	33.5265i	0.0325036	−	0.0105611i
$217$	1618.29	+	3176.07i	0.506251	+	0.993574i
$218$	2817.82	−	446.299i	0.875446	−	0.138657i
$219$	70.6446			0.0217978
$220$	−771.608	−	1437.57i	−0.236463	−	0.440551i
$221$	−2599.10			−0.791107
$222$	−40.1926	+	6.36588i	−0.0121511	+	0.00192455i
$223$	−1337.83	−	2625.64i	−0.401739	−	0.788458i	0.598178	−	0.801364i	$-0.295892\pi$
$223$	−1337.83	−	2625.64i	−0.401739	−	0.788458i	−0.999917	+	0.0129061i	$0.995892\pi$
$224$	−947.640	+	307.907i	−0.282665	+	0.0918433i
$225$	−2720.85	+	1983.52i	−0.806177	+	0.587709i
$226$	−997.713	−	1373.23i	−0.293659	−	0.404187i
$227$	−442.446	−	225.438i	−0.129366	−	0.0659155i	0.388109	−	0.921613i	$-0.373128\pi$
$227$	−442.446	−	225.438i	−0.129366	−	0.0659155i	−0.517476	+	0.855698i	$0.673128\pi$
$228$	79.3481	−	40.4299i	0.0230480	−	0.0117436i
$229$	72.4946	−	99.7803i	0.0209196	−	0.0287933i	−0.798429	−	0.602089i	$-0.794335\pi$
$229$	72.4946	−	99.7803i	0.0209196	−	0.0287933i	0.819349	+	0.573296i	$0.194335\pi$
$230$	−1764.01	−	1761.17i	−0.505718	−	0.504904i
$231$	−93.8324	−	269.780i	−0.0267260	−	0.0768408i
$232$	1412.78	+	1412.78i	0.399800	+	0.399800i
$233$	−761.717	−	4809.29i	−0.214171	−	1.35222i	−0.827088	−	0.562073i	$-0.810004\pi$
$233$	−761.717	−	4809.29i	−0.214171	−	1.35222i	0.612917	−	0.790147i	$-0.289996\pi$
$234$	1361.68	+	442.435i	0.380408	+	0.123602i
$235$	208.499	+	639.939i	0.0578765	+	0.177638i
$236$	92.5335	−	67.2295i	0.0255230	−	0.0185435i
$237$	34.0353	−	214.890i	0.00932840	−	0.0588972i
$238$	2765.00	−	5426.62i	0.753061	−	1.47797i
$239$	−1143.10	+	3518.11i	−0.309378	+	0.952167i	0.668630	+	0.743596i	$0.266881\pi$
$239$	−1143.10	+	3518.11i	−0.309378	+	0.952167i	−0.978007	+	0.208571i	$0.933119\pi$
$240$	26.4085	−	36.4098i	0.00710274	−	0.00979267i
$241$			6903.48i			1.84520i	0.385761	+	0.922599i	$0.373939\pi$
$241$			6903.48i			1.84520i	−0.385761	+	0.922599i	$0.626061\pi$
$242$	1803.33	−	1958.12i	0.479019	−	0.520135i
$243$	387.622	−	387.622i	0.102329	−	0.102329i
$244$	−55.3457	−	40.2110i	−0.0145211	−	0.0105502i
$245$	6239.06	−	3185.30i	1.62693	−	0.830617i
$246$	−4.36189	−	13.4245i	−0.00113050	−	0.00347933i
$247$	2324.21	+	368.119i	0.598729	+	0.0948294i
$248$	−904.549	−	143.266i	−0.231608	−	0.0366832i
$249$	58.7140	+	180.703i	0.0149432	+	0.0459903i
$250$	−857.300	+	2660.36i	−0.216882	+	0.673025i
$251$	−4164.04	−	3025.35i	−1.04714	−	0.760791i	−0.0754726	−	0.997148i	$-0.524047\pi$
$251$	−4164.04	−	3025.35i	−1.04714	−	0.760791i	−0.971666	+	0.236357i	$0.924047\pi$
$252$	−2372.34	+	2372.34i	−0.593030	+	0.593030i
$253$	1771.46	−	3660.88i	0.440200	−	0.909715i
$254$			3043.90i			0.751935i
$255$	43.2269	+	271.508i	0.0106156	+	0.0666764i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	−572.584	+	1123.76i	−0.138976	+	0.272756i	−0.949996	−	0.312263i	$-0.898913\pi$
$257$	−572.584	+	1123.76i	−0.138976	+	0.272756i	0.811020	+	0.585019i	$0.198913\pi$
$258$	−39.9655	+	252.332i	−0.00964396	+	0.0608896i
$259$	2038.49	−	1481.05i	0.489057	−	0.355321i
$260$	1130.05	−	368.184i	0.269550	−	0.0878223i
$261$	6398.11	+	2078.87i	1.51737	+	0.493023i
$262$	25.0980	+	158.463i	0.00591817	+	0.0373658i
$263$	−1929.34	−	1929.34i	−0.452350	−	0.452350i	0.443784	−	0.896134i	$-0.353636\pi$
$263$	−1929.34	−	1929.34i	−0.452350	−	0.452350i	−0.896134	+	0.443784i	$0.853636\pi$
$264$	70.2453	+	21.2375i	0.0163761	+	0.00495105i
$265$	0.681165	+	845.311i	0.000157900	+	0.195951i
$266$	−3241.16	+	4461.07i	−0.747098	+	1.02829i
$267$	−216.380	+	110.251i	−0.0495963	+	0.0252706i
$268$	1533.68	+	781.451i	0.349569	+	0.178115i
$269$	−4272.65	−	5880.80i	−0.968432	−	1.33293i	−0.942835	−	0.333260i	$-0.891851\pi$
$269$	−4272.65	−	5880.80i	−0.968432	−	1.33293i	−0.0255966	−	0.999672i	$-0.508149\pi$
$270$	47.1974	−	299.555i	0.0106383	−	0.0675198i
$271$	−3905.27	+	1268.90i	−0.875382	+	0.284429i	−0.712039	−	0.702140i	$-0.752228\pi$
$271$	−3905.27	+	1268.90i	−0.875382	+	0.284429i	−0.163344	+	0.986569i	$0.552228\pi$
$272$	710.393	+	1394.22i	0.158360	+	0.310799i
$273$	205.509	−	32.5494i	0.0455603	−	0.00721604i
$274$	−131.096			−0.0289045
$275$	−4559.24	+	101.118i	−0.999754	+	0.0221733i
$276$	112.117			0.0244517
$277$	4483.24	−	710.075i	0.972461	−	0.154023i	0.350065	−	0.936725i	$-0.386159\pi$
$277$	4483.24	−	710.075i	0.972461	−	0.154023i	0.622396	+	0.782703i	$0.286159\pi$
$278$	1570.84	+	3082.94i	0.338894	+	0.665116i
$279$	−2932.74	+	952.906i	−0.629315	+	0.204477i
$280$	−433.460	+	2751.11i	−0.0925150	+	0.587179i
$281$	3649.26	+	5022.77i	0.774720	+	1.06631i	0.995845	+	0.0910654i	$0.0290272\pi$
$281$	3649.26	+	5022.77i	0.774720	+	1.06631i	−0.221125	+	0.975246i	$0.570973\pi$
$282$	−26.9733	−	13.7436i	−0.00569587	−	0.00290219i
$283$	−4163.05	+	2121.18i	−0.874444	+	0.445552i	−0.832796	−	0.553581i	$-0.813261\pi$
$283$	−4163.05	+	2121.18i	−0.874444	+	0.445552i	−0.0416489	+	0.999132i	$0.513261\pi$
$284$	1725.62	−	2375.11i	0.360551	−	0.496256i
$285$	−0.200579	−	248.915i	−4.16888e−5	−	0.0517348i
$286$	1171.82	+	1545.04i	0.242277	+	0.319440i
$287$	618.021	+	618.021i	0.127110	+	0.127110i
$288$	−134.843	−	851.365i	−0.0275892	−	0.174191i
$289$	−4423.86	−	1437.40i	−0.900440	−	0.292571i
$290$	5309.79	−	1729.99i	1.07518	−	0.350305i
$291$	−259.991	+	188.894i	−0.0523743	+	0.0380522i
$292$	175.809	−	1110.01i	0.0352343	−	0.222461i
$293$	−2163.41	+	4245.93i	−0.431358	+	0.846588i	0.568359	+	0.822781i	$0.307579\pi$
$293$	−2163.41	+	4245.93i	−0.431358	+	0.846588i	−0.999717	+	0.0238067i	$0.992421\pi$
$294$	−97.3656	+	299.661i	−0.0193146	+	0.0594441i
$295$	−50.2658	−	315.719i	−0.00992064	−	0.0623114i
$296$			647.373i			0.127121i
$297$	486.986	−	87.4314i	0.0951441	−	0.0170818i
$298$	−4123.69	+	4123.69i	−0.801608	+	0.801608i
$299$	2396.79	+	1741.37i	0.463578	+	0.336809i
$300$	−57.2558	−	111.924i	−0.0110189	−	0.0215399i
$301$	−4888.33	−	15044.7i	−0.936075	−	2.88094i
$302$	387.385	+	61.3558i	0.0738130	+	0.0116908i
$303$	308.634	+	48.8828i	0.0585166	+	0.00926812i
$304$	−437.791	−	1347.38i	−0.0825954	−	0.254203i
$305$	−170.304	+	86.9469i	−0.0319723	+	0.0163232i
$306$	4262.51	+	3096.89i	0.796311	+	0.578554i
$307$	−56.3287	+	56.3287i	−0.0104718	+	0.0104718i	−0.712323	−	0.701851i	$-0.752357\pi$
$307$	−56.3287	+	56.3287i	−0.0104718	+	0.0104718i	0.701851	+	0.712323i	$0.252357\pi$
$308$	−4472.47	+	802.967i	−0.827411	+	0.148550i
$309$		−	379.599i		−	0.0698856i
$310$	−1502.95	+	2072.14i	−0.275360	+	0.379644i
$311$	−567.553	+	1746.75i	−0.103482	+	0.318486i	−0.989371	−	0.145412i	$-0.953549\pi$
$311$	−567.553	+	1746.75i	−0.103482	+	0.318486i	0.885889	+	0.463897i	$0.153549\pi$
$312$	−24.2695	+	47.6315i	−0.00440381	+	0.00864296i
$313$	−854.427	+	5394.64i	−0.154297	+	0.974195i	0.782074	+	0.623185i	$0.214162\pi$
$313$	−854.427	+	5394.64i	−0.154297	+	0.974195i	−0.936372	+	0.351010i	$0.885838\pi$
$314$	−2478.26	+	1800.56i	−0.445402	+	0.323604i
$315$	2905.00	+	8916.21i	0.519613	+	1.59483i
$316$	−3291.79	−	1069.57i	−0.586005	−	0.190405i
$317$	−308.888	−	1950.24i	−0.0547283	−	0.345541i	−0.999824	−	0.0187478i	$-0.994032\pi$
$317$	−308.888	−	1950.24i	−0.0547283	−	0.345541i	0.945096	−	0.326793i	$-0.105968\pi$
$318$	−26.8849	−	26.8849i	−0.00474097	−	0.00474097i
$319$	5506.03	+	7259.66i	0.966391	+	1.27418i
$320$	−506.372	−	505.557i	−0.0884595	−	0.0883171i
$321$	298.395	−	410.705i	0.0518841	−	0.0714123i
$322$	−6185.55	+	3151.70i	−1.07052	+	0.545457i
$323$	7715.72	+	3931.36i	1.32915	+	0.677234i
$324$	−1701.95	−	2342.53i	−0.291830	−	0.401669i
$325$	514.389	−	3281.95i	0.0877944	−	0.560154i
$326$	1525.54	−	495.678i	0.259177	−	0.0842118i
$327$	162.833	+	319.578i	0.0275372	+	0.0540449i
$328$	−221.790	+	35.1280i	−0.0373362	+	0.00591348i
$329$	1874.47			0.314112
$330$	141.909	−	148.107i	0.0236722	−	0.0247061i
$331$	2747.88			0.456306			0.228153	−	0.973625i	$-0.426731\pi$
$331$	2747.88			0.456306			0.228153	+	0.973625i	$0.426731\pi$
$332$	2985.44	−	472.847i	0.493515	−	0.0781652i
$333$	989.594	+	1942.19i	0.162851	+	0.319613i
$334$	−2088.41	+	678.566i	−0.342134	+	0.111166i
$335$	3890.03	−	2831.06i	0.634433	−	0.461724i
$336$	−73.6304	−	101.344i	−0.0119550	−	0.0164546i
$337$	−3894.43	−	1984.31i	−0.629505	−	0.320749i	0.109968	−	0.993935i	$-0.464925\pi$
$337$	−3894.43	−	1984.31i	−0.629505	−	0.320749i	−0.739473	+	0.673186i	$0.764925\pi$
$338$	2656.46	−	1353.54i	0.427493	−	0.217818i
$339$	125.432	−	172.642i	0.0200959	−	0.0276596i
$340$	4373.68	−	3.52438i	0.697635	−	0.000562165i
$341$	−3997.77	−	1208.66i	−0.634872	−	0.191943i
$342$	−3373.07	−	3373.07i	−0.533317	−	0.533317i
$343$	−1381.22	−	8720.68i	−0.217431	−	1.37281i
$344$	3865.34	+	1255.92i	0.605829	+	0.196846i
$345$	142.045	−	279.335i	0.0221665	−	0.0435910i
$346$	−5950.93	+	4323.61i	−0.924636	+	0.671788i
$347$	−67.9311	+	428.900i	−0.0105093	+	0.0663532i	−0.992386	−	0.123170i	$-0.960694\pi$
$347$	−67.9311	+	428.900i	−0.0105093	+	0.0663532i	0.981876	+	0.189523i	$0.0606941\pi$
$348$	−114.035	+	223.806i	−0.0175659	+	0.0344749i
$349$	2784.18	−	8568.82i	0.427030	−	1.31426i	−0.474006	−	0.880521i	$-0.657193\pi$
$349$	2784.18	−	8568.82i	0.427030	−	1.31426i	0.901037	−	0.433743i	$-0.142807\pi$
$350$	6305.11	+	4565.42i	0.962920	+	0.697234i
$351$			360.420i			0.0548085i
$352$	508.511	−	1050.89i	0.0769993	−	0.159126i
$353$	−21.8661	+	21.8661i	−0.00329693	+	0.00329693i	−0.708753	−	0.705456i	$-0.750742\pi$
$353$	−21.8661	+	21.8661i	−0.00329693	+	0.00329693i	0.705456	+	0.708753i	$0.250742\pi$
$354$	11.6332	+	8.45204i	0.00174661	+	0.00126898i
$355$	−3731.25	−	7308.42i	−0.557842	−	1.09265i
$356$	1193.84	+	3674.27i	0.177734	+	0.547010i
$357$	756.258	+	119.780i	0.112116	+	0.0177574i
$358$	−2900.72	−	459.429i	−0.428234	−	0.0678256i
$359$	1074.51	+	3307.01i	0.157968	+	0.486176i	0.998450	−	0.0556645i	$-0.0177277\pi$
$359$	1074.51	+	3307.01i	0.157968	+	0.486176i	−0.840481	+	0.541840i	$0.817728\pi$
$360$	−2291.98	−	742.668i	−0.335550	−	0.108728i
$361$	−793.822	−	576.746i	−0.115734	−	0.0840860i
$362$	1969.07	−	1969.07i	0.285890	−	0.285890i
$363$	304.183	+	139.546i	0.0439820	+	0.0201770i
$364$		−	3310.08i		−	0.476636i
$365$	−2542.81	−	1844.33i	−0.364649	−	0.264484i
$366$	2.65772	−	8.17964i	0.000379567	−	0.00116819i
$367$	192.562	−	377.923i	0.0273886	−	0.0537533i	−0.876907	−	0.480661i	$-0.840397\pi$
$367$	192.562	−	377.923i	0.0273886	−	0.0537533i	0.904295	+	0.426907i	$0.140397\pi$
$368$	279.018	−	1761.65i	0.0395240	−	0.249545i
$369$	−611.694	+	444.422i	−0.0862968	+	0.0626983i
$370$	1612.90	+	820.179i	0.226624	+	0.115241i
$371$	2239.00	+	727.497i	0.313324	+	0.101805i
$372$	−18.0113	−	113.719i	−0.00251033	−	0.0158496i
$373$	−2704.20	−	2704.20i	−0.375384	−	0.375384i	0.494050	−	0.869434i	$-0.335516\pi$
$373$	−2704.20	−	2704.20i	−0.375384	−	0.375384i	−0.869434	+	0.494050i	$0.835516\pi$
$374$	2344.21	+	6739.90i	0.324107	+	0.931850i
$375$	−351.395	+	0.849480i	−0.0483892	+	0.000116979i
$376$	−283.074	+	389.618i	−0.0388256	+	0.0534389i
$377$	−5913.88	+	3013.27i	−0.807906	+	0.411649i
$378$	−752.514	−	383.425i	−0.102395	−	0.0521726i
$379$	1103.57	+	1518.94i	0.149569	+	0.205864i	0.877227	−	0.480076i	$-0.159391\pi$
$379$	1103.57	+	1518.94i	0.149569	+	0.205864i	−0.727658	+	0.685940i	$0.759391\pi$
$380$	−3911.60	−	616.306i	−0.528055	−	0.0831995i
$381$	−363.948	+	118.254i	−0.0489386	+	0.0159011i
$382$	2340.30	+	4593.11i	0.313456	+	0.615193i
$383$	−4223.08	+	668.871i	−0.563419	+	0.0892368i	−0.431646	−	0.902043i	$-0.642067\pi$
$383$	−4223.08	+	668.871i	−0.563419	+	0.0892368i	−0.131773	+	0.991280i	$0.542067\pi$
$384$	32.1841			0.00427705
$385$	−3665.76	+	12160.3i	−0.485259	+	1.60973i
$386$	3172.40			0.418318
$387$	13516.3	−	2140.77i	1.77538	−	0.281192i
$388$	2321.00	+	4555.22i	0.303688	+	0.596022i
$389$	−7373.41	+	2395.77i	−0.961046	+	0.312263i	−0.747196	−	0.664604i	$-0.768600\pi$
$389$	−7373.41	+	2395.77i	−0.961046	+	0.312263i	−0.213850	+	0.976866i	$0.568600\pi$
$390$	87.9242	+	120.812i	0.0114159	+	0.0156861i
$391$	6408.12	+	8820.03i	0.828831	+	1.14079i
$392$	4466.14	+	2275.61i	0.575445	+	0.293204i
$393$	−17.9717	+	9.15704i	−0.00230675	+	0.00117535i
$394$	1907.44	−	2625.37i	0.243897	−	0.335695i
$395$	−6835.27	+	6846.29i	−0.870683	+	0.872087i
$396$	−80.8279	−	3930.09i	−0.0102570	−	0.498724i
$397$	−9113.74	−	9113.74i	−1.15216	−	1.15216i	−0.986120	−	0.166036i	$-0.946903\pi$
$397$	−9113.74	−	9113.74i	−1.15216	−	1.15216i	−0.166036	−	0.986120i	$-0.553097\pi$
$398$	221.716	+	1399.86i	0.0279236	+	0.176303i
$399$	−659.309	−	214.222i	−0.0827236	−	0.0268785i
$400$	−1901.11	+	621.099i	−0.237639	+	0.0776373i
$401$	1678.92	−	1219.81i	0.209081	−	0.151906i	−0.478317	−	0.878187i	$-0.658753\pi$
$401$	1678.92	−	1219.81i	0.209081	−	0.151906i	0.687398	+	0.726281i	$0.258753\pi$
$402$	−33.8523	+	213.735i	−0.00420000	+	0.0265178i
$403$	1381.21	−	2710.78i	0.170727	−	0.335071i
$404$	1536.15	−	4727.79i	0.189174	−	0.582219i
$405$	−7992.59	+	1272.51i	−0.980630	+	0.156127i
$406$		−	15553.1i		−	1.90120i
$407$	−401.779	+	2924.79i	−0.0489324	+	0.356207i
$408$	−139.104	+	139.104i	−0.0168790	+	0.0168790i
$409$	−3.61368	−	2.62549i	−0.000436883	−	0.000317414i	0.587567	−	0.809176i	$-0.300086\pi$
$409$	−3.61368	−	2.62549i	−0.000436883	−	0.000317414i	−0.588004	+	0.808858i	$0.700086\pi$
$410$	−193.473	+	597.085i	−0.0233047	+	0.0719217i
$411$	−5.09301	−	15.6747i	−0.000611240	−	0.00188120i
$412$	−5964.50	−	944.684i	−0.713228	−	0.112964i
$413$	−879.404	−	139.284i	−0.104776	−	0.0165949i
$414$	−1855.83	−	5711.66i	−0.220312	−	0.678050i
$415$	2604.27	−	8037.16i	0.308045	−	0.950672i
$416$	688.018	+	499.874i	0.0810885	+	0.0589143i
$417$	−307.589	+	307.589i	−0.0361215	+	0.0361215i
$418$	−1141.68	−	6359.08i	−0.133592	−	0.744097i
$419$		−	1909.07i		−	0.222588i	−0.993788	−	0.111294i	$-0.964501\pi$
$419$		−	1909.07i		−	0.222588i	0.993788	−	0.111294i	$-0.0354995\pi$
$420$	−345.778	+	55.0516i	−0.0401720	+	0.00639581i
$421$	2665.38	−	8203.19i	0.308557	−	0.949641i	−0.669769	−	0.742570i	$-0.733607\pi$
$421$	2665.38	−	8203.19i	0.308557	−	0.949641i	0.978326	−	0.207071i	$-0.0663932\pi$
$422$	−3150.19	+	6182.60i	−0.363386	+	0.713185i
$423$	−253.670	+	1601.61i	−0.0291581	+	0.184097i
$424$	−489.338	+	355.525i	−0.0560480	+	0.0407213i
$425$	5532.38	−	10901.3i	0.631435	−	1.24421i
$426$	351.022	+	114.054i	0.0399226	+	0.0129717i
$427$	83.3078	+	525.985i	0.00944156	+	0.0596117i
$428$	−5710.66	−	5710.66i	−0.644942	−	0.644942i
$429$	−139.209	+	200.133i	−0.0156669	+	0.0225234i
$430$	8026.22	−	8039.16i	0.900136	−	0.901588i
$431$	2267.18	−	3120.51i	0.253379	−	0.348746i	−0.663312	−	0.748343i	$-0.730850\pi$
$431$	2267.18	−	3120.51i	0.253379	−	0.348746i	0.916691	+	0.399597i	$0.130850\pi$
$432$	193.338	−	98.5106i	0.0215324	−	0.0109713i
$433$	14310.3	+	7291.47i	1.58825	+	0.809251i	1.00000		0.000568597i	$0.000180990\pi$
$433$	14310.3	+	7291.47i	1.58825	+	0.809251i	0.588245	+	0.808683i	$0.299819\pi$
$434$	4190.42	+	5767.62i	0.463472	+	0.637914i
$435$	413.130	+	567.662i	0.0455357	+	0.0625685i
$436$	5426.63	−	1763.22i	0.596074	−	0.193676i
$437$	−4481.17	−	8794.79i	−0.490534	−	0.962727i
$438$	139.550	−	22.1025i	0.0152236	−	0.00241118i
$439$	−2285.91			−0.248520			−0.124260	−	0.992250i	$-0.539656\pi$
$439$	−2285.91			−0.248520			−0.124260	+	0.992250i	$0.539656\pi$
$440$	−1973.99	−	2598.34i	−0.213878	−	0.281525i
$441$	16877.5			1.82242
$442$	−5134.21	+	813.179i	−0.552510	+	0.0875090i
$443$	6549.28	+	12853.7i	0.702405	+	1.37855i	0.915821	+	0.401586i	$0.131541\pi$
$443$	6549.28	+	12853.7i	0.702405	+	1.37855i	−0.213416	+	0.976961i	$0.568459\pi$
$444$	−77.4038	+	25.1500i	−0.00827347	+	0.00268821i
$445$	10666.8	+	1680.65i	1.13630	+	0.179034i
$446$	−3464.20	−	4768.07i	−0.367791	−	0.506221i
$447$	−653.257	−	332.851i	−0.0691230	−	0.0352199i
$448$	−1775.61	+	904.719i	−0.187254	+	0.0954106i
$449$	1727.91	−	2378.27i	0.181615	−	0.249972i	−0.708496	−	0.705714i	$-0.750626\pi$
$449$	1727.91	−	2378.27i	0.181615	−	0.249972i	0.890112	+	0.455742i	$0.150626\pi$
$450$	−4754.11	+	4769.46i	−0.498025	+	0.499633i
$451$	−1023.83	+	21.0565i	−0.106897	+	0.00219848i
$452$	−2400.50	−	2400.50i	−0.249801	−	0.249801i
$453$	7.71360	+	48.7018i	0.000800037	+	0.00505123i
$454$	−944.530	−	306.896i	−0.0976409	−	0.0317255i
$455$	−8246.94	−	4193.66i	−0.849720	−	0.432092i
$456$	144.093	−	104.690i	0.0147978	−	0.0107512i
$457$	900.297	−	5684.25i	0.0921534	−	0.581834i	−0.897796	−	0.440412i	$-0.854833\pi$
$457$	900.297	−	5684.25i	0.0921534	−	0.581834i	0.989949	−	0.141422i	$-0.0451675\pi$
$458$	111.986	−	219.785i	0.0114253	−	0.0224233i
$459$	−409.855	+	1261.40i	−0.0416784	+	0.128273i
$460$	−4035.59	−	2927.06i	−0.409044	−	0.296685i
$461$			7120.96i			0.719428i	0.933063	+	0.359714i	$0.117126\pi$
$461$			7120.96i			0.719428i	−0.933063	+	0.359714i	$0.882874\pi$
$462$	−269.760	−	503.560i	−0.0271653	−	0.0507094i
$463$	−10644.6	+	10644.6i	−1.06846	+	1.06846i	−0.0709861	+	0.997477i	$0.522615\pi$
$463$	−10644.6	+	10644.6i	−1.06846	+	1.06846i	−0.997477	+	0.0709861i	$0.977385\pi$
$464$	3232.79	+	2348.76i	0.323445	+	0.234997i
$465$	−306.146	−	99.2001i	−0.0305316	−	0.00989311i
$466$	−3009.36	−	9261.85i	−0.299154	−	0.920701i
$467$	−3179.53	−	503.588i	−0.315056	−	0.0498999i	−0.00309584	−	0.999995i	$-0.500985\pi$
$467$	−3179.53	−	503.588i	−0.315056	−	0.0498999i	−0.311960	+	0.950095i	$0.600985\pi$
$468$	2828.25	+	447.950i	0.279350	+	0.0442447i
$469$	−4140.61	−	12743.5i	−0.407666	−	1.25467i
$470$	612.081	+	1198.89i	0.0600707	+	0.117661i
$471$	−311.565	−	226.365i	−0.0304801	−	0.0221451i
$472$	161.754	−	161.754i	0.0157741	−	0.0157741i
$473$	16683.9	+	8073.13i	1.62183	+	0.784784i
$474$		−	435.138i		−	0.0421657i
$475$	−6491.24	+	8964.78i	−0.627029	+	0.865962i
$476$	3764.10	−	11584.7i	0.362452	−	1.11551i
$477$	−924.600	+	1814.63i	−0.0887516	+	0.174185i
$478$	−1157.35	+	7307.24i	−0.110745	+	0.699216i
$479$	−14861.7	+	10797.7i	−1.41764	+	1.02998i	−0.425486	+	0.904965i	$0.639897\pi$
$479$	−14861.7	+	10797.7i	−1.41764	+	1.02998i	−0.992155	+	0.125011i	$0.960103\pi$
$480$	40.7752	−	80.1854i	0.00387734	−	0.00762489i
$481$	−2045.33	−	664.567i	−0.193885	−	0.0629972i
$482$	2159.89	+	13637.0i	0.204108	+	1.28869i
$483$	−617.140	−	617.140i	−0.0581384	−	0.0581384i
$484$	2949.63	−	4432.23i	0.277013	−	0.416250i
$485$	14289.7	−	11.5149i	1.33786	−	0.00107807i
$486$	644.424	−	886.973i	0.0601475	−	0.0827859i
$487$	13323.3	−	6788.58i	1.23971	−	0.631663i	0.293729	−	0.955889i	$-0.405104\pi$
$487$	13323.3	−	6788.58i	1.23971	−	0.631663i	0.945980	+	0.324226i	$0.105104\pi$
$488$	−121.909	−	62.1159i	−0.0113086	−	0.00576200i
$489$	118.532	+	163.146i	0.0109616	+	0.0150873i
$490$	11327.9	−	8244.17i	1.04437	−	0.760068i
$491$	−4180.96	+	1358.48i	−0.384285	+	0.124862i	−0.494787	−	0.869014i	$-0.664754\pi$
$491$	−4180.96	+	1358.48i	−0.384285	+	0.124862i	0.110502	+	0.993876i	$0.464754\pi$
$492$	−12.8165	−	25.1538i	−0.00117442	−	0.00230492i
$493$	−24124.1	+	3820.89i	−2.20385	+	0.349055i
$494$	4706.37			0.428643
$495$	−9894.08	−	4777.79i	−0.898395	−	0.433830i
$496$	−1831.65			−0.165813
$497$	−22572.2	+	3575.08i	−2.03722	+	0.322664i
$498$	172.519	+	338.587i	0.0155236	+	0.0304668i
$499$	16150.7	−	5247.68i	1.44891	−	0.470778i	0.524245	−	0.851567i	$-0.324348\pi$
$499$	16150.7	−	5247.68i	1.44891	−	0.470778i	0.924662	+	0.380789i	$0.124348\pi$
$500$	−861.145	+	5523.44i	−0.0770232	+	0.494032i
$501$	−162.267	−	223.341i	−0.0144702	−	0.0199165i
$502$	−9172.09	−	4673.41i	−0.815479	−	0.415507i
$503$	12463.4	−	6350.40i	1.10480	−	0.562923i	0.196188	−	0.980566i	$-0.437144\pi$
$503$	12463.4	−	6350.40i	1.10480	−	0.562923i	0.908611	+	0.417643i	$0.137144\pi$
$504$	−3944.04	+	5428.51i	−0.348574	+	0.479772i
$505$	−9832.90	−	9817.06i	−0.866452	−	0.865057i
$506$	2353.92	−	7785.86i	0.206807	−	0.684039i
$507$	265.039	+	265.039i	0.0232165	+	0.0232165i
$508$	952.343	+	6012.86i	0.0831760	+	0.525152i
$509$	18565.3	+	6032.24i	1.61669	+	0.525293i	0.971157	−	0.238441i	$-0.0766365\pi$
$509$	18565.3	+	6032.24i	1.61669	+	0.525293i	0.645530	+	0.763735i	$0.276636\pi$
$510$	170.336	+	522.806i	0.0147894	+	0.0453926i
$511$	−7077.70	+	5142.25i	−0.612718	+	0.445166i
$512$	80.0944	−	505.696i	0.00691349	−	0.0436501i
$513$	545.164	−	1069.94i	0.0469193	−	0.0920842i
$514$	−779.480	+	2398.99i	−0.0668898	+	0.205866i
$515$	−9910.28	+	13663.5i	−0.847959	+	1.16910i
$516$			510.955i			0.0435921i
$517$	−1520.72	+	1584.58i	−0.129364	+	0.134797i
$518$	3563.42	−	3563.42i	0.302254	−	0.302254i
$519$	−748.146	−	543.560i	−0.0632755	−	0.0459723i
$520$	2117.09	−	1080.86i	0.178539	−	0.0911517i
$521$	3857.34	+	11871.7i	0.324363	+	0.998287i	0.971727	+	0.236106i	$0.0758713\pi$
$521$	3857.34	+	11871.7i	0.324363	+	0.998287i	−0.647364	+	0.762181i	$0.724129\pi$
$522$	13289.1	+	2104.79i	1.11427	+	0.176483i
$523$	−4220.28	−	668.427i	−0.352849	−	0.0558858i	−0.0225060	−	0.999747i	$-0.507164\pi$
$523$	−4220.28	−	668.427i	−0.352849	−	0.0558858i	−0.330343	+	0.943861i	$0.607164\pi$
$524$	99.1560	+	305.171i	0.00826651	+	0.0254417i
$525$	−300.920	+	931.240i	−0.0250157	+	0.0774146i
$526$	−4414.80	−	3207.54i	−0.365959	−	0.265885i
$527$	7916.60	−	7916.60i	0.654369	−	0.654369i
$528$	145.406	+	19.9744i	0.0119848	+	0.00164636i
$529$		−	259.849i		−	0.0213569i
$530$	265.817	+	1669.59i	0.0217856	+	0.136835i
$531$	238.018	−	732.543i	0.0194521	−	0.0598675i
$532$	−5006.77	+	9826.35i	−0.408028	+	0.800801i
$533$	116.696	−	736.789i	0.00948341	−	0.0598759i
$534$	−392.937	+	285.486i	−0.0318428	+	0.0231352i
$535$	−21462.9	+	6992.85i	−1.73444	+	0.565098i
$536$	3274.09	+	1063.82i	0.263842	+	0.0857274i
$537$	−57.7590	−	364.676i	−0.00464150	−	0.0293053i
$538$	−10280.0	−	10280.0i	−0.823797	−	0.823797i
$539$	18765.4	+	13052.9i	1.49960	+	1.04309i
$540$	−0.488728	−	606.501i	−3.89472e−5	−	0.0483327i
$541$	−2954.77	+	4066.89i	−0.234816	+	0.323196i	−0.910121	−	0.414342i	$-0.864012\pi$
$541$	−2954.77	+	4066.89i	−0.234816	+	0.323196i	0.675306	+	0.737538i	$0.264012\pi$
$542$	−7317.39	+	3728.40i	−0.579905	+	0.295477i
$543$	311.931	+	158.937i	0.0246524	+	0.0125610i
$544$	1839.50	+	2531.86i	0.144978	+	0.199545i
$545$	2482.20	−	15754.1i	0.195093	−	1.23822i
$546$	395.773	−	128.595i	0.0310211	−	0.0100794i
$547$	1559.51	+	3060.71i	0.121901	+	0.239244i	0.943891	−	0.330258i	$-0.107136\pi$
$547$	1559.51	+	3060.71i	0.121901	+	0.239244i	−0.821990	+	0.569502i	$0.807136\pi$
$548$	−258.965	+	41.0160i	−0.0201869	+	0.00319729i
$549$	−460.693			−0.0358140
$550$	−8974.58	+	1626.19i	−0.695777	+	0.126075i
$551$	22113.8			1.70977
$552$	221.474	−	35.0780i	0.0170771	−	0.00270474i
$553$	12232.1	+	24006.8i	0.940615	+	1.84606i
$554$	8633.93	−	2805.33i	0.662131	−	0.215139i
$555$	−35.4053	+	224.712i	−0.00270787	+	0.0171865i
$556$	4067.55	+	5598.50i	0.310256	+	0.427031i
$557$	6180.90	+	3149.33i	0.470185	+	0.239571i	0.672995	−	0.739647i	$-0.265007\pi$
$557$	6180.90	+	3149.33i	0.470185	+	0.239571i	−0.202810	+	0.979218i	$0.565007\pi$
$558$	−5495.14	+	2799.91i	−0.416896	+	0.212419i
$559$	−7936.00	+	10923.0i	−0.600460	+	0.826462i
$560$	4.48846	+	5570.09i	0.000338700	+	0.420320i
$561$	−714.792	+	542.128i	−0.0537942	+	0.0407998i
$562$	8780.13	+	8780.13i	0.659016	+	0.659016i
$563$	−1868.22	−	11795.5i	−0.139851	−	0.882986i	−0.953448	−	0.301557i	$-0.902494\pi$
$563$	−1868.22	−	11795.5i	−0.139851	−	0.882986i	0.813597	−	0.581429i	$-0.197506\pi$
$564$	−57.5823	−	18.7096i	−0.00429903	−	0.00139684i
$565$	−9022.04	+	2939.48i	−0.671787	+	0.218876i
$566$	−7559.95	+	5492.62i	−0.561428	+	0.407901i
$567$	−3526.05	+	22262.6i	−0.261164	+	1.64892i
$568$	2665.65	−	5231.63i	0.196916	−	0.386469i
$569$	−4385.52	+	13497.2i	−0.323112	+	0.994435i	0.649174	+	0.760640i	$0.275115\pi$
$569$	−4385.52	+	13497.2i	−0.323112	+	0.994435i	−0.972286	+	0.233796i	$0.924885\pi$
$570$	−78.2739	−	491.637i	−0.00575181	−	0.0361271i
$571$		−	21949.4i		−	1.60867i	−0.594174	−	0.804336i	$-0.702521\pi$
$571$		−	21949.4i		−	1.60867i	0.594174	−	0.804336i	$-0.297479\pi$
$572$	2798.18	+	2685.40i	0.204541	+	0.196298i
$573$	−458.260	+	458.260i	−0.0334103	+	0.0334103i
$574$	1414.18	+	1027.46i	0.102834	+	0.0747135i
$575$	−12405.5	+	6346.12i	−0.899730	+	0.460263i
$576$	−532.731	−	1639.58i	−0.0385367	−	0.118604i
$577$	15081.9	+	2388.74i	1.08816	+	0.172347i	0.674639	−	0.738148i	$-0.264299\pi$
$577$	15081.9	+	2388.74i	1.08816	+	0.172347i	0.413520	+	0.910495i	$0.364299\pi$
$578$	−9188.51	−	1455.32i	−0.661231	−	0.104729i
$579$	123.246	+	379.311i	0.00884614	+	0.0272256i
$580$	9947.58	−	5078.64i	0.712156	−	0.363585i
$581$	−19035.9	−	13830.4i	−1.35928	−	0.987574i
$582$	−454.481	+	454.481i	−0.0323691	+	0.0323691i
$583$	−2431.45	+	1302.54i	−0.172728	+	0.0925311i
$584$		−	2247.70i		−	0.159264i
$585$	4699.26	−	6478.94i	0.332120	−	0.457900i
$586$	−2945.13	+	9064.19i	−0.207615	+	0.638973i
$587$	−194.811	+	382.338i	−0.0136980	+	0.0268838i	−0.897754	−	0.440497i	$-0.854802\pi$
$587$	−194.811	+	382.338i	−0.0136980	+	0.0268838i	0.884056	+	0.467381i	$0.154802\pi$
$588$	−98.5793	+	622.405i	−0.00691385	+	0.0436523i
$589$	−8200.57	+	5958.06i	−0.573682	+	0.416804i
$590$	−198.073	−	607.937i	−0.0138212	−	0.0424210i
$591$	388.007	+	126.071i	0.0270059	+	0.00877475i
$592$	202.543	+	1278.81i	0.0140616	+	0.0887814i
$593$	1780.68	+	1780.68i	0.123312	+	0.123312i	0.766069	−	0.642758i	$-0.222210\pi$
$593$	1780.68	+	1780.68i	0.123312	+	0.123312i	−0.642758	+	0.766069i	$0.722210\pi$
$594$	934.626	−	325.073i	0.0645592	−	0.0224544i
$595$	−24094.0	−	24055.2i	−1.66010	−	1.65742i
$596$	−6855.67	+	9436.03i	−0.471173	+	0.648515i
$597$	−158.762	+	80.8933i	−0.0108839	+	0.00554563i
$598$	5279.38	+	2689.98i	0.361020	+	0.183949i
$599$	12991.6	+	17881.4i	0.886180	+	1.21972i	0.974671	+	0.223645i	$0.0717956\pi$
$599$	12991.6	+	17881.4i	0.886180	+	1.21972i	−0.0884907	+	0.996077i	$0.528204\pi$
$600$	−148.119	−	203.179i	−0.0100782	−	0.0138246i
$601$	−6668.37	+	2166.68i	−0.452593	+	0.147056i	−0.526438	−	0.850213i	$-0.676473\pi$
$601$	−6668.37	+	2166.68i	−0.452593	+	0.147056i	0.0738453	+	0.997270i	$0.476473\pi$
$602$	−14363.3	−	28189.6i	−0.972434	−	1.90851i
$603$	11448.8	−	1813.31i	0.773187	−	0.122461i
$604$	784.429			0.0528443
$605$	−7305.74	−	12964.2i	−0.490943	−	0.871192i
$606$	624.961			0.0418933
$607$	21898.4	−	3468.36i	1.46429	−	0.231922i	0.627148	−	0.778900i	$-0.284222\pi$
$607$	21898.4	−	3468.36i	1.46429	−	0.231922i	0.837147	+	0.546978i	$0.184222\pi$
$608$	−1286.35	−	2524.61i	−0.0858036	−	0.168399i
$609$	1859.62	−	604.228i	0.123737	−	0.0402045i
$610$	−309.211	+	225.036i	−0.0205239	+	0.0149368i
$611$	−940.377	−	1294.32i	−0.0622644	−	0.0856996i
$612$	9388.98	+	4783.92i	0.620142	+	0.315978i
$613$	10082.6	−	5137.34i	0.664326	−	0.338491i	−0.0891008	−	0.996023i	$-0.528399\pi$
$613$	10082.6	−	5137.34i	0.664326	−	0.338491i	0.753427	+	0.657531i	$0.228399\pi$
$614$	−93.6468	+	128.894i	−0.00615518	+	0.00847188i
$615$	−78.9073	+	0.0635848i	−0.00517374	+	4.16908e-6i
$616$	−8583.58	+	2985.46i	−0.561433	+	0.195272i
$617$	−12139.8	−	12139.8i	−0.792108	−	0.792108i	0.189728	−	0.981837i	$-0.439239\pi$
$617$	−12139.8	−	12139.8i	−0.792108	−	0.792108i	−0.981837	+	0.189728i	$0.939239\pi$
$618$	−118.765	−	749.852i	−0.00773046	−	0.0488082i
$619$	−20296.8	−	6594.83i	−1.31793	−	0.428220i	−0.436144	−	0.899877i	$-0.643656\pi$
$619$	−20296.8	−	6594.83i	−1.31793	−	0.428220i	−0.881782	+	0.471656i	$0.843656\pi$
$620$	−2320.58	+	4563.48i	−0.150317	+	0.295603i
$621$	1223.08	−	888.619i	0.0790346	−	0.0574220i
$622$	−574.628	+	3628.06i	−0.0370426	+	0.233878i
$623$	13653.3	−	26796.1i	0.878023	−	1.72322i
$624$	−33.0389	+	101.683i	−0.00211957	+	0.00652338i
$625$	12670.4	+	9143.35i	0.810907	+	0.585175i
$626$			10923.8i			0.697446i
$627$	715.976	−	383.552i	0.0456034	−	0.0244300i
$628$	−4332.16	+	4332.16i	−0.275274	+	0.275274i
$629$	−6402.56	−	4651.73i	−0.405862	−	0.294876i
$630$	8528.07	+	16704.0i	0.539312	+	1.05635i
$631$	1262.83	+	3886.58i	0.0796708	+	0.245202i	0.982957	−	0.183838i	$-0.0588521\pi$
$631$	1262.83	+	3886.58i	0.0796708	+	0.245202i	−0.903286	+	0.429039i	$0.858852\pi$
$632$	−6837.16	−	1082.90i	−0.430328	−	0.0681573i
$633$	−861.612	−	136.466i	−0.0541011	−	0.00856877i
$634$	−1220.34	−	3755.82i	−0.0764446	−	0.235272i
$635$	16187.4	+	5245.17i	1.01162	+	0.327793i
$636$	−61.5192	−	44.6963i	−0.00383553	−	0.00278667i
$637$	−11774.4	+	11774.4i	−0.732368	+	0.732368i
$638$	13147.8	+	12617.9i	0.815873	+	0.782990i
$639$		−	19770.2i		−	1.22394i
$640$	−1158.45	−	840.237i	−0.0715495	−	0.0518957i
$641$	8977.80	−	27630.8i	0.553201	−	1.70258i	−0.147447	−	0.989070i	$-0.547106\pi$
$641$	8977.80	−	27630.8i	0.553201	−	1.70258i	0.700648	−	0.713507i	$-0.252894\pi$
$642$	460.946	−	904.657i	0.0283366	−	0.0556136i
$643$	2088.13	−	13184.0i	0.128068	−	0.808592i	−0.837117	−	0.547024i	$-0.815761\pi$
$643$	2088.13	−	13184.0i	0.128068	−	0.808592i	0.965185	−	0.261568i	$-0.0842395\pi$
$644$	−11232.7	+	8161.05i	−0.687316	+	0.499364i
$645$	1273.02	+	647.346i	0.0777136	+	0.0395182i
$646$	16471.5	+	5351.90i	1.00319	+	0.325956i
$647$	−4113.99	−	25974.7i	−0.249981	−	1.57832i	−0.718923	−	0.695090i	$-0.755365\pi$
$647$	−4113.99	−	25974.7i	−0.249981	−	1.57832i	0.468942	−	0.883229i	$-0.344635\pi$
$648$	−4094.90	−	4094.90i	−0.248245	−	0.248245i
$649$	831.185	−	630.406i	0.0502725	−	0.0381288i
$650$	−10.7077	−	6644.03i	−0.000646141	−	0.400923i
$651$	−526.816	+	725.100i	−0.0317167	+	0.0436543i
$652$	2858.43	−	1456.44i	0.171695	−	0.0874828i
$653$	−10718.8	−	5461.48i	−0.642355	−	0.327296i	0.102293	−	0.994754i	$-0.467382\pi$
$653$	−10718.8	−	5461.48i	−0.642355	−	0.327296i	−0.744647	+	0.667458i	$0.767382\pi$
$654$	421.642	+	580.341i	0.0252103	+	0.0346990i
$655$	885.945	+	139.588i	0.0528500	+	0.00832697i
$656$	−427.127	+	138.782i	−0.0254215	+	0.00825996i
$657$	−3435.90	−	6743.33i	−0.204029	−	0.400429i
$658$	3702.78	−	586.463i	0.219376	−	0.0347458i
$659$	−16150.4			−0.954675			−0.477337	−	0.878720i	$-0.658398\pi$
$659$	−16150.4			−0.954675			−0.477337	+	0.878720i	$0.658398\pi$
$660$	233.985	−	336.966i	0.0137998	−	0.0198733i
$661$	9796.20			0.576442			0.288221	−	0.957564i	$-0.406936\pi$
$661$	9796.20			0.576442			0.288221	+	0.957564i	$0.406936\pi$
$662$	5428.10	−	859.727i	0.318685	−	0.0504747i
$663$	−296.689	−	582.285i	−0.0173793	−	0.0341087i
$664$	5749.42	−	1868.10i	0.336025	−	0.109181i
$665$	18138.7	+	24923.5i	1.05773	+	1.45337i
$666$	2562.47	+	3526.94i	0.149090	+	0.205204i
$667$	24806.3	+	12639.4i	1.44003	+	0.733734i
$668$	−3913.10	+	1993.82i	−0.226650	+	0.115484i
$669$	435.517	−	599.437i	0.0251690	−	0.0346421i
$670$	6798.52	−	6809.49i	0.392015	−	0.392647i
$671$	−512.227	−	356.296i	−0.0294699	−	0.0204987i
$672$	−177.155	−	177.155i	−0.0101695	−	0.0101695i
$673$	−880.314	−	5558.08i	−0.0504214	−	0.318348i	−0.999989	−	0.00478445i	$-0.998477\pi$
$673$	−880.314	−	5558.08i	−0.0504214	−	0.318348i	0.949567	−	0.313564i	$-0.101523\pi$
$674$	−8313.80	−	2701.32i	−0.475127	−	0.154378i
$675$	−1511.69	−	767.179i	−0.0862001	−	0.0437463i
$676$	4824.04	−	3504.87i	0.274467	−	0.199412i
$677$	4062.69	−	25650.8i	0.230638	−	1.45619i	−0.552069	−	0.833798i	$-0.686162\pi$
$677$	4062.69	−	25650.8i	0.230638	−	1.45619i	0.782707	−	0.622391i	$-0.213838\pi$
$678$	193.760	−	380.276i	0.0109754	−	0.0215405i
$679$	12298.1	−	37849.7i	0.695078	−	2.13923i
$680$	8638.55	−	1375.35i	0.487167	−	0.0775621i
$681$		−	124.856i		−	0.00702571i
$682$	−8275.26	−	1136.78i	−0.464628	−	0.0638262i
$683$	14510.7	−	14510.7i	0.812935	−	0.812935i	−0.172138	−	0.985073i	$-0.555067\pi$
$683$	14510.7	−	14510.7i	0.812935	−	0.812935i	0.985073	+	0.172138i	$0.0550673\pi$
$684$	−7718.40	−	5607.75i	−0.431463	−	0.313476i
$685$	−225.902	+	697.165i	−0.0126004	+	0.0388866i
$686$	−5456.86	−	16794.5i	−0.303708	−	0.934717i
$687$	30.6294	+	4.85122i	0.00170100	+	0.000269411i
$688$	8028.44	+	1271.58i	0.444886	+	0.0704630i
$689$	−620.920	−	1911.00i	−0.0343326	−	0.105665i
$690$	193.197	−	596.234i	0.0106593	−	0.0328960i
$691$	3646.61	+	2649.42i	0.200758	+	0.145859i	0.683622	−	0.729836i	$-0.260404\pi$
$691$	3646.61	+	2649.42i	0.200758	+	0.145859i	−0.482864	+	0.875695i	$0.660404\pi$
$692$	−10402.6	+	10402.6i	−0.571457	+	0.571457i
$693$	−21188.0	+	22077.8i	−1.16142	+	1.21020i
$694$			868.493i			0.0475037i
$695$	19101.8	−	3041.20i	1.04255	−	0.165985i
$696$	−155.240	+	477.780i	−0.00845454	+	0.0260204i
$697$	1246.26	−	2445.93i	0.0677268	−	0.132921i
$698$	2818.88	−	17797.7i	0.152860	−	0.965120i
$699$	990.491	−	719.633i	0.0535963	−	0.0389400i
$700$	13883.3	+	7045.75i	0.749630	+	0.380435i
$701$	388.808	+	126.331i	0.0209488	+	0.00680667i	0.319473	−	0.947596i	$-0.396494\pi$
$701$	388.808	+	126.331i	0.0209488	+	0.00680667i	−0.298524	+	0.954402i	$0.596494\pi$
$702$	112.764	+	711.964i	0.00606269	+	0.0382783i
$703$	5066.57	+	5066.57i	0.271820	+	0.271820i
$704$	675.712	−	2234.99i	0.0361745	−	0.119651i
$705$	−119.567	+	119.760i	−0.00638747	+	0.00639777i
$706$	−36.3526	+	50.0351i	−0.00193789	+	0.00266727i
$707$	−34479.4	+	17568.1i	−1.83413	+	0.934537i
$708$	25.6244	+	13.0563i	0.00136020	+	0.000693058i
$709$	−20308.4	−	27952.1i	−1.07574	−	1.48063i	−0.864128	−	0.503271i	$-0.832130\pi$
$709$	−20308.4	−	27952.1i	−1.07574	−	1.48063i	−0.211609	−	0.977354i	$-0.567870\pi$
$710$	−9657.19	−	13269.5i	−0.510462	−	0.701401i
$711$	−22167.6	+	7202.67i	−1.16927	+	0.379918i
$712$	3507.85	+	6884.54i	0.184638	+	0.362372i
$713$	−12604.4	+	1996.34i	−0.662046	+	0.104858i
$714$	1531.37			0.0802662
$715$	10235.7	−	3569.32i	0.535374	−	0.186692i
$716$	−5873.76			−0.306582
$717$	−918.660	+	145.501i	−0.0478494	+	0.00757859i
$718$	3157.22	+	6196.40i	0.164104	+	0.322072i
$719$	11365.7	−	3692.94i	0.589526	−	0.191549i	0.000962624	−	1.00000i	$-0.499694\pi$
$719$	11365.7	−	3692.94i	0.589526	−	0.191549i	0.588564	+	0.808451i	$0.299694\pi$
$720$	−4759.88	−	749.959i	−0.246375	−	0.0388185i
$721$	27631.2	+	38031.1i	1.42724	+	1.96443i
$722$	−1748.54	−	890.928i	−0.0901303	−	0.0459237i
$723$	−1546.61	+	788.037i	−0.0795560	+	0.0405358i
$724$	3273.60	−	4505.72i	0.168042	−	0.231290i
$725$	−50.3125	−	31218.3i	−0.00257732	−	1.59920i
$726$	644.535	+	180.486i	0.0329490	+	0.00922655i
$727$	−12870.7	−	12870.7i	−0.656598	−	0.656598i	0.297975	−	0.954574i	$-0.403689\pi$
$727$	−12870.7	−	12870.7i	−0.656598	−	0.656598i	−0.954574	+	0.297975i	$0.903689\pi$
$728$	−1035.62	−	6538.66i	−0.0527235	−	0.332883i
$729$	−18457.2	−	5997.10i	−0.937721	−	0.304684i
$730$	−5600.05	−	2847.68i	−0.283927	−	0.144380i
$731$	−40195.8	+	29203.9i	−2.03378	+	1.47763i
$732$	2.69085	−	16.9894i	0.000135870	−	0.000857849i
$733$	3923.87	−	7701.04i	0.197724	−	0.388055i	−0.770762	−	0.637123i	$-0.780124\pi$
$733$	3923.87	−	7701.04i	0.197724	−	0.388055i	0.968486	+	0.249068i	$0.0801243\pi$
$734$	262.141	−	806.788i	0.0131823	−	0.0405710i
$735$	1425.80	+	1034.15i	0.0715532	+	0.0518984i
$736$		−	3567.22i		−	0.178654i
$737$	14131.9	+	6838.25i	0.706316	+	0.341778i
$738$	−1069.28	+	1069.28i	−0.0533344	+	0.0533344i
$739$	6216.91	+	4516.85i	0.309463	+	0.224838i	0.731666	−	0.681663i	$-0.238743\pi$
$739$	6216.91	+	4516.85i	0.309463	+	0.224838i	−0.422203	+	0.906501i	$0.638743\pi$
$740$	3442.70	+	1115.54i	0.171022	+	0.0554161i
$741$	182.839	+	562.722i	0.00906447	+	0.0278976i
$742$	4650.49	+	736.565i	0.230087	+	0.0364422i
$743$	−19783.9	−	3133.46i	−0.976851	−	0.154718i	−0.352457	−	0.935828i	$-0.614654\pi$
$743$	−19783.9	−	3133.46i	−0.976851	−	0.154718i	−0.624394	+	0.781110i	$0.714654\pi$
$744$	−71.1583	−	219.003i	−0.00350644	−	0.0107917i
$745$	14823.8	+	29035.5i	0.728996	+	1.42789i
$746$	−6187.87	−	4495.75i	−0.303692	−	0.220645i
$747$	14393.2	−	14393.2i	0.704982	−	0.704982i
$748$	6739.39	+	12580.4i	0.329434	+	0.614954i
$749$			62867.8i			3.06694i
$750$	−693.871	+	111.619i	−0.0337821	+	0.00543431i
$751$	802.517	−	2469.89i	0.0389937	−	0.120010i	−0.929665	−	0.368406i	$-0.879903\pi$
$751$	802.517	−	2469.89i	0.0389937	−	0.120010i	0.968659	+	0.248396i	$0.0799035\pi$
$752$	−437.278	+	858.207i	−0.0212047	+	0.0416165i
$753$	202.452	−	1278.23i	0.00979780	−	0.0618609i
$754$	−10739.4	+	7802.62i	−0.518707	+	0.376863i
$755$	993.820	−	1954.37i	0.0479057	−	0.0942078i
$756$	−1606.46	−	521.970i	−0.0772836	−	0.0251110i
$757$	5762.46	+	36382.7i	0.276671	+	1.74683i	0.599499	+	0.800376i	$0.295367\pi$
$757$	5762.46	+	36382.7i	0.276671	+	1.74683i	−0.322828	+	0.946458i	$0.604633\pi$
$758$	2655.20	+	2655.20i	0.127231	+	0.127231i
$759$	1022.37	−	21.0265i	0.0488930	−	0.00100555i
$760$	−7919.70	+	6.38182i	−0.377997	+	0.000304596i
$761$	−2435.56	+	3352.26i	−0.116017	+	0.159684i	−0.863076	−	0.505074i	$-0.831465\pi$
$761$	−2435.56	+	3352.26i	−0.116017	+	0.159684i	0.747059	+	0.664758i	$0.231465\pi$
$762$	−681.936	+	347.464i	−0.0324198	+	0.0165187i
$763$	−39576.0	−	20165.0i	−1.87778	−	0.956778i
$764$	6060.02	+	8340.90i	0.286968	+	0.394978i
$765$	23814.2	−	17331.3i	1.12549	−	0.819106i
$766$	−8132.91	+	2642.54i	−0.383622	+	0.124646i
$767$	345.001	+	677.102i	0.0162415	+	0.0318758i
$768$	63.5757	−	10.0694i	0.00298710	−	0.000473110i
$769$	−17583.2			−0.824535			−0.412268	−	0.911063i	$-0.635263\pi$
$769$	−17583.2			−0.824535			−0.412268	+	0.911063i	$0.635263\pi$
$770$	−3436.69	+	25168.0i	−0.160844	+	1.17791i
$771$	−317.120			−0.0148130
$772$	6266.69	−	992.546i	0.292154	−	0.0462727i
$773$	12308.1	+	24156.0i	0.572692	+	1.12397i	0.977768	+	0.209689i	$0.0672451\pi$
$773$	12308.1	+	24156.0i	0.572692	+	1.12397i	−0.405076	+	0.914283i	$0.632755\pi$
$774$	26029.9	−	8457.64i	1.20882	−	0.392769i
$775$	8429.71	+	11563.3i	0.390715	+	0.535954i
$776$	6010.04	+	8272.11i	0.278026	+	0.382670i
$777$	564.500	+	287.627i	0.0260635	+	0.0132800i
$778$	−13815.7	+	7039.46i	−0.636654	+	0.324392i
$779$	−1460.88	+	2010.73i	−0.0671905	+	0.0924798i
$780$	211.482	+	211.141i	0.00970803	+	0.00969240i
$781$	15290.1	−	21981.7i	0.700542	−	1.00713i
$782$	15418.0	+	15418.0i	0.705045	+	0.705045i
$783$	529.845	+	3345.31i	0.0241828	+	0.152684i
$784$	9534.29	+	3097.88i	0.434324	+	0.141120i
$785$	5304.84	+	16282.0i	0.241195	+	0.740291i
$786$	−32.6359	+	23.7114i	−0.00148102	+	0.00107603i
$787$	1665.25	−	10514.0i	0.0754253	−	0.476217i	−0.920845	−	0.389929i	$-0.872500\pi$
$787$	1665.25	−	10514.0i	0.0754253	−	0.476217i	0.996270	−	0.0862877i	$-0.0275004\pi$
$788$	2946.52	−	5782.86i	0.133205	−	0.261429i
$789$	212.001	−	652.471i	0.00956581	−	0.0294405i
$790$	−11360.2	+	15662.6i	−0.511619	+	0.705378i
$791$			26426.8i			1.18790i
$792$	−1389.27	−	7738.13i	−0.0623302	−	0.347175i
$793$	321.398	−	321.398i	0.0143924	−	0.0143924i
$794$	−20854.5	−	15151.7i	−0.932113	−	0.677220i
$795$	−189.300	+	96.6453i	−0.00844500	+	0.00431152i
$796$	875.944	+	2695.88i	0.0390038	+	0.120041i
$797$	5351.76	+	847.635i	0.237853	+	0.0376722i	0.274223	−	0.961666i	$-0.411579\pi$
$797$	5351.76	+	847.635i	0.237853	+	0.0376722i	−0.0363697	+	0.999338i	$0.511579\pi$
$798$	−1369.41	−	216.893i	−0.0607475	−	0.00962145i
$799$	−1819.30	−	5599.24i	−0.0805536	−	0.247919i
$800$	−3561.09	+	1821.70i	−0.157380	+	0.0805087i
$801$	21047.8	+	15292.2i	0.928450	+	0.674559i
$802$	2934.87	−	2934.87i	0.129219	−	0.129219i
$803$	1394.99	−	10154.9i	0.0613052	−	0.446276i
$804$			432.799i			0.0189846i
$805$	6101.81	+	38325.4i	0.267156	+	1.67800i
$806$	1880.30	−	5786.96i	0.0821720	−	0.252899i
$807$	829.768	−	1628.51i	0.0361948	−	0.0710364i
$808$	1555.30	−	9819.78i	0.0677169	−	0.427548i
$809$	14702.1	−	10681.7i	0.638937	−	0.464215i	−0.220548	−	0.975376i	$-0.570785\pi$
$809$	14702.1	−	10681.7i	0.638937	−	0.464215i	0.859485	+	0.511161i	$0.170785\pi$
$810$	−15390.3	+	5014.31i	−0.667603	+	0.217512i
$811$	−13765.4	−	4472.65i	−0.596016	−	0.193657i	−0.00455325	−	0.999990i	$-0.501449\pi$
$811$	−13765.4	−	4472.65i	−0.596016	−	0.193657i	−0.591463	+	0.806332i	$0.701449\pi$
$812$	−4866.08	−	30723.2i	−0.210303	−	1.32780i
$813$	−730.065	−	730.065i	−0.0314939	−	0.0314939i
$814$	121.409	+	5903.26i	0.00522774	+	0.254188i
$815$	−7.22567	−	8966.89i	−0.000310557	−	0.385395i
$816$	−231.261	+	318.303i	−0.00992125	+	0.0136554i
$817$	40080.8	−	20422.2i	1.71634	−	0.874518i
$818$	−7.95981	−	4.05573i	−0.000340230	−	0.000173356i
$819$	−13102.2	−	18033.6i	−0.559007	−	0.769408i
$820$	−195.372	+	1240.00i	−0.00832037	+	0.0528081i
$821$	−32506.1	+	10561.9i	−1.38182	+	0.448979i	−0.903266	−	0.429081i	$-0.858838\pi$
$821$	−32506.1	+	10561.9i	−1.38182	+	0.448979i	−0.478550	+	0.878060i	$0.658838\pi$
$822$	−14.9647	−	29.3699i	−0.000634982	−	0.00124622i
$823$	17143.0	−	2715.18i	0.726083	−	0.115000i	0.217558	−	0.976047i	$-0.430191\pi$
$823$	17143.0	−	2715.18i	0.726083	−	0.115000i	0.508525	+	0.861047i	$0.330191\pi$
$824$	−12077.7			−0.510615
$825$	−543.094	−	1009.88i	−0.0229189	−	0.0426175i
$826$	−1780.73			−0.0750116
$827$	−10434.8	+	1652.71i	−0.438760	+	0.0694927i	−0.371907	−	0.928270i	$-0.621296\pi$
$827$	−10434.8	+	1652.71i	−0.438760	+	0.0694927i	−0.0668530	+	0.997763i	$0.521296\pi$
$828$	−5452.97	−	10702.1i	−0.228869	−	0.449181i
$829$	14741.8	−	4789.89i	0.617614	−	0.200675i	0.0165335	−	0.999863i	$-0.494737\pi$
$829$	14741.8	−	4789.89i	0.617614	−	0.200675i	0.601081	+	0.799188i	$0.294737\pi$
$830$	2629.84	−	16691.2i	0.109980	−	0.698025i
$831$	670.845	+	923.339i	0.0280040	+	0.0385442i
$832$	1515.49	+	772.180i	0.0631492	+	0.0321761i
$833$	−54597.7	+	27818.9i	−2.27095	+	1.15711i
$834$	−511.368	+	703.838i	−0.0212317	+	0.0292229i
$835$	9.89169	+	12275.4i	0.000409959	+	0.508750i
$836$	−4244.81	−	12204.4i	−0.175610	−	0.504901i
$837$	−1097.80	−	1097.80i	−0.0453352	−	0.0453352i
$838$	−597.289	−	3771.14i	−0.0246217	−	0.155456i
$839$	43740.2	+	14212.0i	1.79985	+	0.584808i	0.999884	−	0.0152306i	$-0.00484824\pi$
$839$	43740.2	+	14212.0i	1.79985	+	0.584808i	0.799971	+	0.600039i	$0.204848\pi$
$840$	−665.819	+	216.931i	−0.0273487	+	0.00891051i
$841$	−30730.1	+	22326.7i	−1.26000	+	0.915442i
$842$	2698.60	−	17038.3i	0.110451	−	0.697362i
$843$	−708.702	+	1390.91i	−0.0289549	+	0.0568273i
$844$	−4288.47	+	13198.6i	−0.174900	+	0.538286i
$845$	−2620.50	−	16459.3i	−0.106684	−	0.670081i
$846$			3243.15i			0.131799i
$847$	−40632.9	+	8160.86i	−1.64836	+	0.331063i
$848$	−855.395	+	855.395i	−0.0346396	+	0.0346396i
$849$	−950.430	−	690.528i	−0.0384201	−	0.0279138i
$850$	7517.86	−	23265.1i	0.303365	−	0.938807i
$851$	2787.58	+	8579.29i	0.112288	+	0.345587i
$852$	729.084	+	115.475i	0.0293169	+	0.00464334i
$853$	−4926.36	−	780.258i	−0.197744	−	0.0313195i	0.0567769	−	0.998387i	$-0.481918\pi$
$853$	−4926.36	−	780.258i	−0.197744	−	0.0313195i	−0.254520	+	0.967067i	$0.581918\pi$
$854$	329.129	+	1012.95i	0.0131880	+	0.0405885i
$855$	−23750.2	+	12125.4i	−0.949988	+	0.485008i
$856$	−13067.4	−	9494.02i	−0.521769	−	0.379088i
$857$	−19293.5	+	19293.5i	−0.769024	+	0.769024i	−0.977935	−	0.208911i	$-0.933008\pi$
$857$	−19293.5	+	19293.5i	−0.769024	+	0.769024i	0.208911	+	0.977935i	$0.433008\pi$
$858$	−212.375	+	438.893i	−0.00845032	+	0.0174634i
$859$			33398.5i			1.32659i	0.748357	+	0.663296i	$0.230843\pi$
$859$			33398.5i			1.32659i	−0.748357	+	0.663296i	$0.769157\pi$
$860$	13339.6	−	18391.5i	0.528926	−	0.729239i
$861$	−67.9097	+	209.005i	−0.00268799	+	0.00827277i
$862$	3502.23	−	6873.51i	0.138383	−	0.271593i
$863$	4378.25	−	27643.2i	0.172697	−	1.09036i	−0.737244	−	0.675626i	$-0.763873\pi$
$863$	4378.25	−	27643.2i	0.172697	−	1.09036i	0.909941	−	0.414738i	$-0.136127\pi$
$864$	351.095	−	255.085i	0.0138246	−	0.0100442i
$865$	12738.3	+	39097.1i	0.500710	+	1.53681i
$866$	30549.5	+	9926.15i	1.19875	+	0.389497i
$867$	−182.961	−	1155.17i	−0.00716689	−	0.0452499i
$868$	10082.2	+	10082.2i	0.394253	+	0.394253i
$869$	−30217.7	−	9135.82i	−1.17959	−	0.356630i
$870$	993.690	+	992.090i	0.0387233	+	0.0386609i
$871$	−6722.11	+	9252.18i	−0.261504	+	0.359929i
$872$	10168.0	−	5180.85i	0.394875	−	0.201199i
$873$	30675.8	+	15630.1i	1.18925	+	0.605954i
$874$	−11603.6	−	15971.0i	−0.449082	−	0.618109i
$875$	35143.5	−	25663.3i	1.35779	−	0.991517i
$876$	268.748	−	87.3215i	0.0103655	−	0.00336795i
$877$	14133.3	+	27738.1i	0.544180	+	1.06801i	0.985343	+	0.170587i	$0.0545663\pi$
$877$	14133.3	+	27738.1i	0.544180	+	1.06801i	−0.441162	+	0.897427i	$0.645434\pi$
$878$	−4515.53	+	715.190i	−0.173567	+	0.0274903i
$879$	−1198.18			−0.0459770
$880$	−4712.31	−	4515.10i	−0.180514	−	0.172959i
$881$	9872.59			0.377544			0.188772	−	0.982021i	$-0.439549\pi$
$881$	9872.59			0.377544			0.188772	+	0.982021i	$0.439549\pi$
$882$	33339.4	−	5280.44i	1.27278	−	0.201589i
$883$	−5868.69	−	11517.9i	−0.223666	−	0.438969i	0.751717	−	0.659485i	$-0.229226\pi$
$883$	−5868.69	−	11517.9i	−0.223666	−	0.438969i	−0.975383	+	0.220516i	$0.929226\pi$
$884$	−9887.58	+	3212.67i	−0.376194	+	0.122233i
$885$	64.9936	−	47.3007i	0.00246863	−	0.00179661i
$886$	16958.8	+	23341.8i	0.643050	+	0.885082i
$887$	23445.4	+	11946.0i	0.887507	+	0.452208i	0.837434	−	0.546538i	$-0.184055\pi$
$887$	23445.4	+	11946.0i	0.887507	+	0.452208i	0.0500731	+	0.998746i	$0.484055\pi$
$888$	−145.033	+	73.8980i	−0.00548084	+	0.00279263i
$889$	27855.2	−	38339.4i	1.05088	−	1.44642i
$890$	21596.8	−	17.4030i	0.813400	−	0.000655451i
$891$	−15959.1	−	21041.9i	−0.600054	−	0.791167i
$892$	−8334.89	−	8334.89i	−0.312862	−	0.312862i
$893$	833.850	+	5264.72i	0.0312472	+	0.197287i
$894$	−1394.57	−	453.122i	−0.0521714	−	0.0169515i
$895$	−7441.67	+	14634.2i	−0.277930	+	0.546557i
$896$	−3224.44	+	2342.69i	−0.120224	+	0.0873482i
$897$	−116.530	+	735.739i	−0.00433758	+	0.0273864i
$898$	2669.19	−	5238.59i	0.0991895	−	0.194670i
$899$	8834.96	−	27191.2i	0.327767	−	1.00876i
$900$	−7898.95	+	10908.9i	−0.292554	+	0.404033i
$901$		−	7394.23i		−	0.273405i
$902$	−2015.86	+	361.920i	−0.0744135	+	0.0133599i
$903$	2812.51	−	2812.51i	0.103648	−	0.103648i
$904$	−5492.94	−	3990.85i	−0.202093	−	0.146829i
$905$	−7078.39	−	13864.5i	−0.259993	−	0.509250i
$906$	30.4745	+	93.7910i	0.00111749	+	0.00343929i
$907$	3947.10	+	625.159i	0.144500	+	0.0228865i	0.228265	−	0.973599i	$-0.426695\pi$
$907$	3947.10	+	625.159i	0.144500	+	0.0228865i	−0.0837655	+	0.996485i	$0.526695\pi$
$908$	−1961.82	−	310.722i	−0.0717019	−	0.0113565i
$909$	−10344.7	−	31837.9i	−0.377463	−	1.16171i
$910$	−17602.9	−	5703.85i	−0.641242	−	0.207781i
$911$	−13314.8	−	9673.76i	−0.484235	−	0.351818i	0.318728	−	0.947846i	$-0.396744\pi$
$911$	−13314.8	−	9673.76i	−0.484235	−	0.351818i	−0.802963	+	0.596029i	$0.796744\pi$
$912$	251.884	−	251.884i	0.00914552	−	0.00914552i
$913$	27134.9	−	4871.68i	0.983608	−	0.176593i
$914$		−	11510.2i		−	0.416547i
$915$	−38.9192	−	28.2286i	−0.00140615	−	0.00101990i
$916$	152.451	−	469.195i	0.00549903	−	0.0169243i
$917$	1133.99	−	2225.59i	0.0408373	−	0.0801476i
$918$	−414.964	+	2619.98i	−0.0149192	+	0.0941963i
$919$	−32627.7	+	23705.4i	−1.17115	+	0.850892i	−0.991146	−	0.132774i	$-0.957612\pi$
$919$	−32627.7	+	23705.4i	−1.17115	+	0.850892i	−0.180005	+	0.983666i	$0.557612\pi$
$920$	−8887.60	−	4519.44i	−0.318495	−	0.161958i
$921$	−19.0494	−	6.18954i	−0.000681542	−	0.000221446i
$922$	2227.93	+	14066.6i	0.0795801	+	0.502449i
$923$	13792.5	+	13792.5i	0.491859	+	0.491859i
$924$	−690.426	−	910.322i	−0.0245816	−	0.0324106i
$925$	7140.99	−	7164.05i	0.253832	−	0.254651i
$926$	−17696.8	+	24357.6i	−0.628027	+	0.864405i
$927$	−36234.4	+	18462.3i	−1.28381	+	0.654134i
$928$	7120.83	+	3628.25i	0.251889	+	0.128344i
$929$	−20344.3	−	28001.5i	−0.718486	−	0.988911i	−0.999573	−	0.0292288i	$-0.990695\pi$
$929$	−20344.3	−	28001.5i	−0.718486	−	0.988911i	0.281087	−	0.959682i	$-0.409305\pi$
$930$	−635.790	−	100.174i	−0.0224176	−	0.00353209i
$931$	52763.3	−	17143.8i	1.85741	−	0.603509i
$932$	−8842.36	−	17354.1i	−0.310774	−	0.609928i
$933$	−456.116	+	72.2418i	−0.0160049	+	0.00253493i
$934$	−6438.32			−0.225555
$935$	39882.0	−	852.380i	1.39495	−	0.0298137i
$936$	5727.00			0.199993
$937$	−50336.4	+	7972.50i	−1.75498	+	0.277962i	−0.949296	−	0.314382i	$-0.898203\pi$
$937$	−50336.4	+	7972.50i	−1.75498	+	0.277962i	−0.805685	+	0.592344i	$0.798203\pi$
$938$	−12166.3	−	23877.7i	−0.423501	−	0.831167i
$939$	−1306.11	+	424.381i	−0.0453923	+	0.0147488i
$940$	1584.19	+	2176.75i	0.0549686	+	0.0755297i
$941$	−22699.7	−	31243.5i	−0.786386	−	1.08237i	−0.994549	−	0.104273i	$-0.966748\pi$
$941$	−22699.7	−	31243.5i	−0.786386	−	1.08237i	0.208163	−	0.978094i	$-0.433252\pi$
$942$	−686.281	−	349.677i	−0.0237370	−	0.0120946i
$943$	−2788.00	+	1420.56i	−0.0962775	+	0.0490559i
$944$	268.918	−	370.134i	0.00927175	−	0.0127615i
$945$	−3335.75	+	3341.13i	−0.114827	+	0.115013i
$946$	35482.7	+	10727.6i	1.21950	+	0.368694i
$947$	−1525.93	−	1525.93i	−0.0523611	−	0.0523611i	0.680441	−	0.732803i	$-0.261788\pi$
$947$	−1525.93	−	1525.93i	−0.0523611	−	0.0523611i	−0.732803	+	0.680441i	$0.761788\pi$
$948$	−136.141	−	859.562i	−0.00466420	−	0.0294486i
$949$	7101.43	+	2307.39i	0.242911	+	0.0789264i
$950$	−10017.8	+	19739.7i	−0.342128	+	0.674148i
$951$	401.659	−	291.822i	0.0136958	−	0.00995056i
$952$	3811.02	−	24061.8i	0.129744	−	0.819169i
$953$	−484.305	+	950.502i	−0.0164619	+	0.0323083i	−0.899091	−	0.437762i	$-0.855771\pi$
$953$	−484.305	+	950.502i	−0.0164619	+	0.0323083i	0.882629	+	0.470070i	$0.155771\pi$
$954$	−1258.69	+	3873.86i	−0.0427166	+	0.131468i
$955$	28458.7	−	4530.92i	0.964295	−	0.153526i
$956$			14796.7i			0.500584i
$957$	−997.888	+	2062.23i	−0.0337065	+	0.0696577i
$958$	−25979.3	+	25979.3i	−0.876150	+	0.876150i
$959$	1651.22	+	1199.68i	0.0556004	+	0.0403960i
$960$	55.4588	−	171.154i	0.00186450	−	0.00575413i
$961$	−5156.19	−	15869.1i	−0.173079	−	0.532682i
$962$	−4248.21	−	672.851i	−0.142378	−	0.0225505i
$963$	−53716.4	−	8507.84i	−1.79749	−	0.284695i
$964$	8533.18	+	26262.4i	0.285099	+	0.877443i
$965$	5466.59	−	16870.7i	0.182358	−	0.562784i
$966$	−1412.17	−	1026.00i	−0.0470350	−	0.0341729i
$967$	15514.6	−	15514.6i	0.515941	−	0.515941i	−0.400400	−	0.916341i	$-0.631129\pi$
$967$	15514.6	−	15514.6i	0.515941	−	0.515941i	0.916341	+	0.400400i	$0.131129\pi$
$968$	4439.92	−	9678.17i	0.147422	−	0.321351i
$969$			2177.34i			0.0721841i
$970$	28224.0	−	4493.56i	0.934245	−	0.148742i
$971$	843.555	−	2596.20i	0.0278795	−	0.0858042i	−0.936149	−	0.351605i	$-0.885636\pi$
$971$	843.555	−	2596.20i	0.0278795	−	0.0858042i	0.964028	+	0.265800i	$0.0856362\pi$
$972$	995.474	−	1953.73i	0.0328496	−	0.0644710i
$973$	8427.01	−	53206.0i	0.277654	−	1.75304i
$974$	24194.7	−	17578.5i	0.795942	−	0.578286i
$975$	793.984	−	259.396i	0.0260798	−	0.00852034i
$976$	−260.251	−	84.5607i	−0.00853528	−	0.00277328i
$977$	3033.53	+	19153.0i	0.0993359	+	0.627182i	0.986252	+	0.165251i	$0.0528434\pi$
$977$	3033.53	+	19153.0i	0.0993359	+	0.627182i	−0.886916	+	0.461932i	$0.847157\pi$
$978$	285.190	+	285.190i	0.00932449	+	0.00932449i
$979$	11575.5	+	33281.0i	0.377889	+	1.08648i
$980$	19797.6	−	19829.5i	0.645316	−	0.646357i
$981$	22585.4	−	31086.2i	0.735063	−	1.01173i
$982$	−7833.94	+	3991.59i	−0.254574	+	0.129712i
$983$	24271.1	+	12366.7i	0.787514	+	0.401259i	0.801010	−	0.598650i	$-0.204296\pi$
$983$	24271.1	+	12366.7i	0.787514	+	0.401259i	−0.0134962	+	0.999909i	$0.504296\pi$
$984$	−33.1872	−	45.6783i	−0.00107517	−	0.00147985i
$985$	−10674.7	−	14667.6i	−0.345305	−	0.474467i
$986$	−46458.8	+	15095.4i	−1.50056	+	0.487561i
$987$	213.972	+	419.943i	0.00690050	+	0.0135430i
$988$	9296.85	−	1472.48i	0.299365	−	0.0474147i
$989$	56633.3			1.82086
$990$	−21039.4	−	6342.39i	−0.675429	−	0.203610i
$991$	15685.4			0.502789			0.251395	−	0.967885i	$-0.419111\pi$
$991$	15685.4			0.502789			0.251395	+	0.967885i	$0.419111\pi$
$992$	−3618.20	+	573.066i	−0.115804	+	0.0183416i
$993$	313.672	+	615.617i	0.0100243	+	0.0196737i
$994$	−43470.0	+	14124.3i	−1.38711	+	0.450698i
$995$	7826.44	+	1233.12i	0.249362	+	0.0392891i
$996$	446.723	+	614.861i	0.0142118	+	0.0195609i
$997$	18156.4	+	9251.12i	0.576748	+	0.293868i	0.717929	−	0.696116i	$-0.245090\pi$
$997$	18156.4	+	9251.12i	0.576748	+	0.293868i	−0.141182	+	0.989984i	$0.545090\pi$
$998$	30261.9	−	15419.2i	0.959843	−	0.489064i
$999$	−645.059	+	887.848i	−0.0204292	+	0.0281184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.k.a.7.15	✓	144
5.3	odd	4	inner	110.4.k.a.73.4	yes	144
11.8	odd	10	inner	110.4.k.a.107.4	yes	144
55.8	even	20	inner	110.4.k.a.63.15	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.k.a.7.15	✓	144	1.1	even	1	trivial
110.4.k.a.63.15	yes	144	55.8	even	20	inner
110.4.k.a.73.4	yes	144	5.3	odd	4	inner
110.4.k.a.107.4	yes	144	11.8	odd	10	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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.97538 - 0.312869i) q^{2} +(0.114151 + 0.224033i) q^{3} +(3.80423 - 1.23607i) q^{4} +(1.74009 - 11.0441i) q^{5} +(0.295583 + 0.406836i) q^{6} +(-27.7439 - 14.1362i) q^{7} +(7.12805 - 3.63192i) q^{8} +(15.8330 - 21.7923i) q^{9} +(-0.0180186 - 22.3607i) q^{10} +(34.4581 - 11.9849i) q^{11} +(0.711175 + 0.711175i) q^{12} +(4.15742 + 26.2489i) q^{13} +(-59.2275 - 19.2442i) q^{14} +(2.67288 - 0.870852i) q^{15} +(12.9443 - 9.40456i) q^{16} +(-15.2990 + 96.5943i) q^{17} +(24.4581 - 48.0017i) q^{18} +(27.3619 - 84.2113i) q^{19} +(-7.03155 - 44.1651i) q^{20} -7.82922i q^{21} +(64.3181 - 34.4556i) q^{22} +(78.8253 - 78.8253i) q^{23} +(1.62734 + 1.18233i) q^{24} +(-118.944 - 38.4355i) q^{25} +(16.4250 + 50.5508i) q^{26} +(13.3948 + 2.12153i) q^{27} +(-123.018 - 19.4841i) q^{28} +(77.1760 + 237.523i) q^{29} +(5.00748 - 2.55652i) q^{30} +(-92.6147 - 67.2885i) q^{31} +(22.6274 - 22.6274i) q^{32} +(6.61843 + 6.35168i) q^{33} +195.597i q^{34} +(-204.399 + 281.808i) q^{35} +(33.2957 - 102.474i) q^{36} +(-36.7376 + 72.1017i) q^{37} +(27.7030 - 174.910i) q^{38} +(-5.40606 + 3.92773i) q^{39} +(-27.7079 - 85.0428i) q^{40} +(-26.6955 - 8.67388i) q^{41} +(-2.44952 - 15.4657i) q^{42} +(359.233 + 359.233i) q^{43} +(116.272 - 88.1858i) q^{44} +(-213.125 - 212.782i) q^{45} +(131.048 - 180.372i) q^{46} +(-53.6379 + 27.3299i) q^{47} +(3.58453 + 1.82641i) q^{48} +(368.282 + 506.897i) q^{49} +(-246.985 - 38.7106i) q^{50} +(-23.3867 + 7.59881i) q^{51} +(48.2613 + 94.7181i) q^{52} +(-74.6761 + 11.8275i) q^{53} +27.1235 q^{54} +(-72.4020 - 401.414i) q^{55} -249.102 q^{56} +(21.9895 - 3.48280i) q^{57} +(226.765 + 445.052i) q^{58} +(27.1949 - 8.83616i) q^{59} +(9.09179 - 6.61677i) q^{60} +(-10.0528 - 13.8364i) q^{61} +(-204.001 - 103.944i) q^{62} +(-747.332 + 380.785i) q^{63} +(37.6183 - 51.7771i) q^{64} +(297.130 - 0.239432i) q^{65} +(15.0611 + 10.4763i) q^{66} +(304.284 + 304.284i) q^{67} +(61.1962 + 386.377i) q^{68} +(26.6574 + 8.66152i) q^{69} +(-315.596 + 620.628i) q^{70} +(593.777 - 431.405i) q^{71} +(33.7107 - 212.841i) q^{72} +(127.554 - 250.339i) q^{73} +(-50.0123 + 153.922i) q^{74} +(-4.96672 - 31.0349i) q^{75} -354.180i q^{76} +(-1125.43 - 154.600i) q^{77} +(-9.45014 + 9.45014i) q^{78} +(-700.041 - 508.610i) q^{79} +(-81.3407 - 159.323i) q^{80} +(-223.692 - 688.454i) q^{81} +(-55.4474 - 8.78200i) q^{82} +(746.359 + 118.212i) q^{83} +(-9.67745 - 29.7841i) q^{84} +(1040.18 + 337.047i) q^{85} +(822.013 + 597.228i) q^{86} +(-44.4034 + 44.4034i) q^{87} +(202.091 - 210.578i) q^{88} +965.838i q^{89} +(-487.576 - 353.645i) q^{90} +(255.718 - 787.019i) q^{91} +(202.436 - 397.303i) q^{92} +(4.50283 - 28.4298i) q^{93} +(-97.4045 + 70.7685i) q^{94} +(-882.426 - 448.723i) q^{95} +(7.65222 + 2.48636i) q^{96} +(199.941 + 1262.38i) q^{97} +(886.088 + 886.088i) q^{98} +(284.398 - 940.679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) \) 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

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