LMFDB - Embedded newform 627.2.j.a.58.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(58,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("627.58");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			58.3
Character	$\chi$	$=$	627.58
Dual form			627.2.j.a.400.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.271454 - 0.197223i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.583244 + 1.79504i) q^{4} +(-2.01616 - 1.46483i) q^{5} +(0.271454 + 0.197223i) q^{6} +(-0.281064 + 0.865027i) q^{7} +(0.403072 + 1.24053i) q^{8} +(-0.809017 + 0.587785i) q^{9} -0.836193 q^{10} +(-1.01652 + 3.15701i) q^{11} -1.88742 q^{12} +(2.01119 - 1.46121i) q^{13} +(0.0943071 + 0.290248i) q^{14} +(0.770105 - 2.37014i) q^{15} +(-2.69983 - 1.96154i) q^{16} +(-6.32308 - 4.59398i) q^{17} +(-0.103686 + 0.319114i) q^{18} +(0.309017 + 0.951057i) q^{19} +(3.80534 - 2.76474i) q^{20} -0.909543 q^{21} +(0.346695 + 1.05746i) q^{22} -7.23909 q^{23} +(-1.05526 + 0.766688i) q^{24} +(0.374105 + 1.15138i) q^{25} +(0.257761 - 0.793306i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.38883 - 1.00904i) q^{28} +(-2.19995 + 6.77075i) q^{29} +(-0.258398 - 0.795267i) q^{30} +(4.66974 - 3.39276i) q^{31} -3.72848 q^{32} +(-3.31661 + 0.00879787i) q^{33} -2.62247 q^{34} +(1.83379 - 1.33232i) q^{35} +(-0.583244 - 1.79504i) q^{36} +(-3.12139 + 9.60665i) q^{37} +(0.271454 + 0.197223i) q^{38} +(2.01119 + 1.46121i) q^{39} +(1.00450 - 3.09153i) q^{40} +(1.33433 + 4.10663i) q^{41} +(-0.246899 + 0.179383i) q^{42} -1.26242 q^{43} +(-5.07407 - 3.66600i) q^{44} +2.49211 q^{45} +(-1.96508 + 1.42772i) q^{46} +(-3.52150 - 10.8381i) q^{47} +(1.03124 - 3.17384i) q^{48} +(4.99384 + 3.62824i) q^{49} +(0.328630 + 0.238764i) q^{50} +(2.41520 - 7.43322i) q^{51} +(1.44992 + 4.46241i) q^{52} +(-3.84930 + 2.79668i) q^{53} -0.335536 q^{54} +(6.67394 - 4.87600i) q^{55} -1.18638 q^{56} +(-0.809017 + 0.587785i) q^{57} +(0.738163 + 2.27183i) q^{58} +(0.796776 - 2.45222i) q^{59} +(3.80534 + 2.76474i) q^{60} +(-7.30073 - 5.30429i) q^{61} +(0.598489 - 1.84196i) q^{62} +(-0.281064 - 0.865027i) q^{63} +(4.38754 - 3.18774i) q^{64} -6.19531 q^{65} +(-0.898574 + 0.656501i) q^{66} +2.84348 q^{67} +(11.9343 - 8.67076i) q^{68} +(-2.23700 - 6.88479i) q^{69} +(0.235024 - 0.723330i) q^{70} +(10.9767 + 7.97503i) q^{71} +(-1.05526 - 0.766688i) q^{72} +(-2.83023 + 8.71055i) q^{73} +(1.04734 + 3.22338i) q^{74} +(-0.979419 + 0.711589i) q^{75} -1.88742 q^{76} +(-2.44519 - 1.76664i) q^{77} +0.834131 q^{78} +(-6.73616 + 4.89411i) q^{79} +(2.56997 + 7.90956i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.17213 + 0.851604i) q^{82} +(10.8732 + 7.89986i) q^{83} +(0.530485 - 1.63266i) q^{84} +(6.01895 + 18.5244i) q^{85} +(-0.342688 + 0.248977i) q^{86} -7.11919 q^{87} +(-4.32608 + 0.0114757i) q^{88} +8.67792 q^{89} +(0.676495 - 0.491502i) q^{90} +(0.698716 + 2.15043i) q^{91} +(4.22215 - 12.9945i) q^{92} +(4.66974 + 3.39276i) q^{93} +(-3.09344 - 2.24752i) q^{94} +(0.770105 - 2.37014i) q^{95} +(-1.15216 - 3.54599i) q^{96} +(-10.4341 + 7.58082i) q^{97} +2.07117 q^{98} +(-1.03326 - 3.15157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 6 q^{3} - 5 q^{4} + 8 q^{5} + 3 q^{6} + q^{7} + 5 q^{8} - 6 q^{9} + 2 q^{10} - 10 q^{11} + 10 q^{12} + 6 q^{13} + 12 q^{14} - 2 q^{15} + 11 q^{16} - 8 q^{17} - 2 q^{18} - 6 q^{19} + 9 q^{20}+ \cdots - 22 q^{98}+O(q^{100}) $ 24 * q + 3 * q^2 - 6 * q^3 - 5 * q^4 + 8 * q^5 + 3 * q^6 + q^7 + 5 * q^8 - 6 * q^9 + 2 * q^10 - 10 * q^11 + 10 * q^12 + 6 * q^13 + 12 * q^14 - 2 * q^15 + 11 * q^16 - 8 * q^17 - 2 * q^18 - 6 * q^19 + 9 * q^20 - 4 * q^21 + 4 * q^22 - 32 * q^23 - 5 * q^24 + 28 * q^25 - 23 * q^26 - 6 * q^27 + 4 * q^28 + 7 * q^29 - 3 * q^30 + 20 * q^31 + 8 * q^32 + 10 * q^33 - 66 * q^34 - 22 * q^35 - 5 * q^36 + q^37 + 3 * q^38 + 6 * q^39 - 2 * q^40 - 2 * q^41 - 8 * q^42 + 28 * q^43 - 40 * q^44 - 12 * q^45 - 35 * q^46 + 25 * q^47 + 6 * q^48 + 25 * q^49 - 18 * q^50 + 2 * q^51 + q^52 + 2 * q^53 - 2 * q^54 - 31 * q^55 - 32 * q^56 - 6 * q^57 + 14 * q^58 + 37 * q^59 + 9 * q^60 - 21 * q^61 - 61 * q^62 + q^63 + 5 * q^64 - 28 * q^65 + 14 * q^66 - 76 * q^67 + 16 * q^68 + 28 * q^69 - 31 * q^70 + 42 * q^71 - 5 * q^72 - 44 * q^73 + 56 * q^74 - 12 * q^75 + 10 * q^76 + 28 * q^77 - 8 * q^78 - 43 * q^79 + 21 * q^80 - 6 * q^81 + 28 * q^82 + 26 * q^83 - q^84 + 4 * q^85 - 52 * q^86 + 2 * q^87 + 39 * q^88 - 6 * q^89 + 2 * q^90 + 53 * q^91 + 11 * q^92 + 20 * q^93 - 6 * q^94 - 2 * q^95 - 17 * q^96 + 11 * q^97 - 22 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.271454	−	0.197223i	0.191947	−	0.139458i	−0.487661	−	0.873033i	$-0.662150\pi$
$2$	0.271454	−	0.197223i	0.191947	−	0.139458i	0.679608	+	0.733575i	$0.262150\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.583244	+	1.79504i	−0.291622	+	0.897519i
$5$	−2.01616	−	1.46483i	−0.901655	−	0.655091i	0.0372355	−	0.999307i	$-0.488145\pi$
$5$	−2.01616	−	1.46483i	−0.901655	−	0.655091i	−0.938891	+	0.344216i	$0.888145\pi$
$6$	0.271454	+	0.197223i	0.110821	+	0.0805160i
$7$	−0.281064	+	0.865027i	−0.106232	+	0.326949i	−0.990018	−	0.140943i	$-0.954987\pi$
$7$	−0.281064	+	0.865027i	−0.106232	+	0.326949i	0.883785	+	0.467892i	$0.154987\pi$
$8$	0.403072	+	1.24053i	0.142507	+	0.438593i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.836193			−0.264428
$11$	−1.01652	+	3.15701i	−0.306493	+	0.951873i
$11$	−1.01652	+	3.15701i	−0.306493	+	0.951873i
$12$	−1.88742			−0.544850
$13$	2.01119	−	1.46121i	0.557804	−	0.405268i	−0.272851	−	0.962056i	$-0.587967\pi$
$13$	2.01119	−	1.46121i	0.557804	−	0.405268i	0.830654	+	0.556788i	$0.187967\pi$
$14$	0.0943071	+	0.290248i	0.0252046	+	0.0775719i
$15$	0.770105	−	2.37014i	0.198840	−	0.611968i
$16$	−2.69983	−	1.96154i	−0.674957	−	0.490385i
$17$	−6.32308	−	4.59398i	−1.53357	−	1.11420i	−0.954211	−	0.299133i	$-0.903303\pi$
$17$	−6.32308	−	4.59398i	−1.53357	−	1.11420i	−0.579360	−	0.815072i	$-0.696697\pi$
$18$	−0.103686	+	0.319114i	−0.0244391	+	0.0752158i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	3.80534	−	2.76474i	0.850899	−	0.618214i
$21$	−0.909543			−0.198479
$22$	0.346695	+	1.05746i	0.0739156	+	0.225452i
$23$	−7.23909			−1.50946			−0.754728	−	0.656038i	$-0.772231\pi$
$23$	−7.23909			−1.50946			−0.754728	+	0.656038i	$0.772231\pi$
$24$	−1.05526	+	0.766688i	−0.215403	+	0.156500i
$25$	0.374105	+	1.15138i	0.0748209	+	0.230275i
$26$	0.257761	−	0.793306i	0.0505510	−	0.155580i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−1.38883	−	1.00904i	−0.262464	−	0.190691i
$29$	−2.19995	+	6.77075i	−0.408521	+	1.25730i	0.509399	+	0.860531i	$0.329868\pi$
$29$	−2.19995	+	6.77075i	−0.408521	+	1.25730i	−0.917919	+	0.396767i	$0.870132\pi$
$30$	−0.258398	−	0.795267i	−0.0471768	−	0.145195i
$31$	4.66974	−	3.39276i	0.838710	−	0.609358i	−0.0833004	−	0.996524i	$-0.526546\pi$
$31$	4.66974	−	3.39276i	0.838710	−	0.609358i	0.922010	+	0.387166i	$0.126546\pi$
$32$	−3.72848			−0.659107
$33$	−3.31661	+	0.00879787i	−0.577348	+	0.00153151i
$34$	−2.62247			−0.449749
$35$	1.83379	−	1.33232i	0.309966	−	0.225204i
$36$	−0.583244	−	1.79504i	−0.0972073	−	0.299173i
$37$	−3.12139	+	9.60665i	−0.513153	+	1.57932i	0.273464	+	0.961882i	$0.411831\pi$
$37$	−3.12139	+	9.60665i	−0.513153	+	1.57932i	−0.786617	+	0.617441i	$0.788169\pi$
$38$	0.271454	+	0.197223i	0.0440357	+	0.0319938i
$39$	2.01119	+	1.46121i	0.322048	+	0.233982i
$40$	1.00450	−	3.09153i	0.158825	−	0.488814i
$41$	1.33433	+	4.10663i	0.208387	+	0.641349i	0.999557	+	0.0297530i	$0.00947206\pi$
$41$	1.33433	+	4.10663i	0.208387	+	0.641349i	−0.791170	+	0.611596i	$0.790528\pi$
$42$	−0.246899	+	0.179383i	−0.0380974	+	0.0276794i
$43$	−1.26242			−0.192517			−0.0962583	−	0.995356i	$-0.530687\pi$
$43$	−1.26242			−0.192517			−0.0962583	+	0.995356i	$0.530687\pi$
$44$	−5.07407	−	3.66600i	−0.764944	−	0.552670i
$45$	2.49211			0.371502
$46$	−1.96508	+	1.42772i	−0.289736	+	0.210505i
$47$	−3.52150	−	10.8381i	−0.513664	−	1.58089i	−0.785700	−	0.618607i	$-0.787697\pi$
$47$	−3.52150	−	10.8381i	−0.513664	−	1.58089i	0.272037	−	0.962287i	$-0.412303\pi$
$48$	1.03124	−	3.17384i	0.148847	−	0.458104i
$49$	4.99384	+	3.62824i	0.713406	+	0.518320i
$50$	0.328630	+	0.238764i	0.0464753	+	0.0337663i
$51$	2.41520	−	7.43322i	0.338196	−	1.04086i
$52$	1.44992	+	4.46241i	0.201068	+	0.618824i
$53$	−3.84930	+	2.79668i	−0.528743	+	0.384154i	−0.819887	−	0.572525i	$-0.805964\pi$
$53$	−3.84930	+	2.79668i	−0.528743	+	0.384154i	0.291145	+	0.956679i	$0.405964\pi$
$54$	−0.335536			−0.0456607
$55$	6.67394	−	4.87600i	0.899914	−	0.657480i
$56$	−1.18638			−0.158536
$57$	−0.809017	+	0.587785i	−0.107157	+	0.0778541i
$58$	0.738163	+	2.27183i	0.0969255	+	0.298306i
$59$	0.796776	−	2.45222i	0.103731	−	0.319252i	−0.885699	−	0.464259i	$-0.846321\pi$
$59$	0.796776	−	2.45222i	0.103731	−	0.319252i	0.989431	+	0.145007i	$0.0463205\pi$
$60$	3.80534	+	2.76474i	0.491267	+	0.356926i
$61$	−7.30073	−	5.30429i	−0.934763	−	0.679145i	0.0123914	−	0.999923i	$-0.496056\pi$
$61$	−7.30073	−	5.30429i	−0.934763	−	0.679145i	−0.947154	+	0.320778i	$0.896056\pi$
$62$	0.598489	−	1.84196i	0.0760082	−	0.233929i
$63$	−0.281064	−	0.865027i	−0.0354108	−	0.108983i
$64$	4.38754	−	3.18774i	0.548443	−	0.398467i
$65$	−6.19531			−0.768434
$66$	−0.898574	+	0.656501i	−0.110607	+	0.0808097i
$67$	2.84348			0.347386			0.173693	−	0.984800i	$-0.444430\pi$
$67$	2.84348			0.347386			0.173693	+	0.984800i	$0.444430\pi$
$68$	11.9343	−	8.67076i	1.44724	−	1.05148i
$69$	−2.23700	−	6.88479i	−0.269303	−	0.828831i
$70$	0.235024	−	0.723330i	0.0280907	−	0.0864544i
$71$	10.9767	+	7.97503i	1.30269	+	0.946462i	0.999978	−	0.00661910i	$-0.00210694\pi$
$71$	10.9767	+	7.97503i	1.30269	+	0.946462i	0.302715	+	0.953081i	$0.402107\pi$
$72$	−1.05526	−	0.766688i	−0.124363	−	0.0903550i
$73$	−2.83023	+	8.71055i	−0.331253	+	1.01949i	0.637285	+	0.770628i	$0.280057\pi$
$73$	−2.83023	+	8.71055i	−0.331253	+	1.01949i	−0.968538	+	0.248864i	$0.919943\pi$
$74$	1.04734	+	3.22338i	0.121751	+	0.374710i
$75$	−0.979419	+	0.711589i	−0.113094	+	0.0821673i
$76$	−1.88742			−0.216501
$77$	−2.44519	−	1.76664i	−0.278655	−	0.201327i
$78$	0.834131			0.0944467
$79$	−6.73616	+	4.89411i	−0.757877	+	0.550630i	−0.898259	−	0.439467i	$-0.855167\pi$
$79$	−6.73616	+	4.89411i	−0.757877	+	0.550630i	0.140381	+	0.990098i	$0.455167\pi$
$80$	2.56997	+	7.90956i	0.287332	+	0.884316i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	1.17213	+	0.851604i	0.129440	+	0.0940439i
$83$	10.8732	+	7.89986i	1.19349	+	0.867123i	0.993629	−	0.112701i	$-0.0359503\pi$
$83$	10.8732	+	7.89986i	1.19349	+	0.867123i	0.199863	+	0.979824i	$0.435950\pi$
$84$	0.530485	−	1.63266i	0.0578807	−	0.178138i
$85$	6.01895	+	18.5244i	0.652847	+	2.00926i
$86$	−0.342688	+	0.248977i	−0.0369530	+	0.0268479i
$87$	−7.11919			−0.763258
$88$	−4.32608	+	0.0114757i	−0.461162	+	0.00122331i
$89$	8.67792			0.919858			0.459929	−	0.887956i	$-0.347875\pi$
$89$	8.67792			0.919858			0.459929	+	0.887956i	$0.347875\pi$
$90$	0.676495	−	0.491502i	0.0713088	−	0.0518089i
$91$	0.698716	+	2.15043i	0.0732454	+	0.225426i
$92$	4.22215	−	12.9945i	0.440190	−	1.35477i
$93$	4.66974	+	3.39276i	0.484229	+	0.351813i
$94$	−3.09344	−	2.24752i	−0.319064	−	0.231814i
$95$	0.770105	−	2.37014i	0.0790111	−	0.243171i
$96$	−1.15216	−	3.54599i	−0.117592	−	0.361911i
$97$	−10.4341	+	7.58082i	−1.05942	+	0.769716i	−0.973982	−	0.226627i	$-0.927230\pi$
$97$	−10.4341	+	7.58082i	−1.05942	+	0.769716i	−0.0854414	+	0.996343i	$0.527230\pi$
$98$	2.07117			0.209220
$99$	−1.03326	−	3.15157i	−0.103846	−	0.316744i
$100$	−2.28496			−0.228496
$101$	5.99526	−	4.35581i	0.596550	−	0.433419i	−0.248102	−	0.968734i	$-0.579807\pi$
$101$	5.99526	−	4.35581i	0.596550	−	0.433419i	0.844653	+	0.535315i	$0.179807\pi$
$102$	−0.810386	−	2.49411i	−0.0802402	−	0.246954i
$103$	−1.25217	+	3.85378i	−0.123380	+	0.379724i	−0.993602	−	0.112935i	$-0.963975\pi$
$103$	−1.25217	+	3.85378i	−0.123380	+	0.379724i	0.870223	+	0.492659i	$0.163975\pi$
$104$	2.62333	+	1.90596i	0.257239	+	0.186895i
$105$	1.83379	+	1.33232i	0.178959	+	0.130021i
$106$	−0.493340	+	1.51834i	−0.0479174	+	0.147475i
$107$	3.68781	+	11.3499i	0.356514	+	1.09724i	0.955126	+	0.296198i	$0.0957189\pi$
$107$	3.68781	+	11.3499i	0.356514	+	1.09724i	−0.598612	+	0.801039i	$0.704281\pi$
$108$	1.52695	−	1.10940i	0.146931	−	0.106752i
$109$	15.3614			1.47135			0.735676	−	0.677334i	$-0.236865\pi$
$109$	15.3614			1.47135			0.735676	+	0.677334i	$0.236865\pi$
$110$	0.850009	−	2.63987i	0.0810452	−	0.251701i
$111$	−10.1010			−0.958747
$112$	2.45561	−	1.78410i	0.232033	−	0.168582i
$113$	0.0328895	+	0.101224i	0.00309399	+	0.00952231i	0.952592	−	0.304252i	$-0.0984065\pi$
$113$	0.0328895	+	0.101224i	0.00309399	+	0.00952231i	−0.949498	+	0.313774i	$0.898406\pi$
$114$	−0.103686	+	0.319114i	−0.00971111	+	0.0298877i
$115$	14.5952	+	10.6040i	1.36101	+	0.988830i
$116$	−10.8707	−	7.89800i	−1.00932	−	0.733311i
$117$	−0.768206	+	2.36429i	−0.0710207	+	0.218579i
$118$	−0.267347	−	0.822809i	−0.0246113	−	0.0757457i
$119$	5.75111	−	4.17843i	0.527203	−	0.383036i
$120$	3.25063			0.296741
$121$	−8.93336	−	6.41833i	−0.812124	−	0.583485i
$122$	−3.02794			−0.274137
$123$	−3.49331	+	2.53804i	−0.314981	+	0.228847i
$124$	3.36655	+	10.3612i	0.302325	+	0.930460i
$125$	−2.91822	+	8.98134i	−0.261013	+	0.803316i
$126$	−0.246899	−	0.179383i	−0.0219955	−	0.0159807i
$127$	−3.19548	−	2.32165i	−0.283553	−	0.206013i	0.436913	−	0.899504i	$-0.356072\pi$
$127$	−3.19548	−	2.32165i	−0.283553	−	0.206013i	−0.720466	+	0.693491i	$0.756072\pi$
$128$	2.86665	−	8.82263i	0.253378	−	0.779818i
$129$	−0.390108	−	1.20063i	−0.0343471	−	0.105709i
$130$	−1.68174	+	1.22186i	−0.147499	+	0.107164i
$131$	−12.0449			−1.05237			−0.526185	−	0.850370i	$-0.676378\pi$
$131$	−12.0449			−1.05237			−0.526185	+	0.850370i	$0.676378\pi$
$132$	1.91860	−	5.95858i	0.166993	−	0.518628i
$133$	−0.909543			−0.0788674
$134$	0.771874	−	0.560799i	0.0666797	−	0.0484457i
$135$	0.770105	+	2.37014i	0.0662801	+	0.203989i
$136$	3.15031	−	9.69565i	0.270137	−	0.831395i
$137$	3.74838	+	2.72336i	0.320246	+	0.232672i	0.736280	−	0.676677i	$-0.236580\pi$
$137$	3.74838	+	2.72336i	0.320246	+	0.232672i	−0.416035	+	0.909349i	$0.636580\pi$
$138$	−1.96508	−	1.42772i	−0.167279	−	0.121535i
$139$	0.340778	−	1.04881i	0.0289044	−	0.0889587i	−0.935564	−	0.353158i	$-0.885108\pi$
$139$	0.340778	−	1.04881i	0.0289044	−	0.0889587i	0.964468	+	0.264199i	$0.0851077\pi$
$140$	1.32203	+	4.06879i	0.111732	+	0.343875i
$141$	9.21941	−	6.69829i	0.776414	−	0.564098i
$142$	4.55253			0.382040
$143$	2.56864	+	7.83469i	0.214801	+	0.655170i
$144$	3.33717			0.278097
$145$	14.3534	−	10.4284i	1.19199	−	0.866030i
$146$	0.949643	+	2.92270i	0.0785930	+	0.241885i
$147$	−1.90748	+	5.87062i	−0.157326	+	0.484200i
$148$	−15.4238	−	11.2060i	−1.26783	−	0.921130i
$149$	−12.9895	−	9.43744i	−1.06414	−	0.773145i	−0.0892925	−	0.996005i	$-0.528461\pi$
$149$	−12.9895	−	9.43744i	−1.06414	−	0.773145i	−0.974850	+	0.222860i	$0.928461\pi$
$150$	−0.125526	+	0.386328i	−0.0102491	+	0.0315435i
$151$	−1.59843	−	4.91947i	−0.130079	−	0.400341i	0.864714	−	0.502265i	$-0.167500\pi$
$151$	−1.59843	−	4.91947i	−0.130079	−	0.400341i	−0.994792	+	0.101925i	$0.967500\pi$
$152$	−1.05526	+	0.766688i	−0.0855925	+	0.0621866i
$153$	7.81575			0.631866
$154$	−1.01218	+	0.00268497i	−0.0815636	+	0.000216361i
$155$	−14.3848			−1.15541
$156$	−3.79595	+	2.75792i	−0.303919	+	0.220810i
$157$	4.67828	+	14.3983i	0.373367	+	1.14911i	0.944574	+	0.328300i	$0.106476\pi$
$157$	4.67828	+	14.3983i	0.373367	+	1.14911i	−0.571206	+	0.820806i	$0.693524\pi$
$158$	−0.863329	+	2.65705i	−0.0686827	+	0.211384i
$159$	−3.84930	−	2.79668i	−0.305270	−	0.221791i
$160$	7.51721	+	5.46157i	0.594288	+	0.431775i
$161$	2.03465	−	6.26201i	0.160353	−	0.493515i
$162$	−0.103686	−	0.319114i	−0.00814636	−	0.0250719i
$163$	3.11617	−	2.26403i	0.244077	−	0.177332i	−0.459021	−	0.888426i	$-0.651800\pi$
$163$	3.11617	−	2.26403i	0.244077	−	0.177332i	0.703098	+	0.711093i	$0.251800\pi$
$164$	−8.14981			−0.636393
$165$	6.69972	+	4.84053i	0.521572	+	0.376835i
$166$	4.50962			0.350014
$167$	3.36122	−	2.44207i	0.260099	−	0.188973i	−0.450092	−	0.892982i	$-0.648609\pi$
$167$	3.36122	−	2.44207i	0.260099	−	0.188973i	0.710191	+	0.704009i	$0.248609\pi$
$168$	−0.366611	−	1.12831i	−0.0282847	−	0.0870512i
$169$	−2.10749	+	6.48618i	−0.162114	+	0.498937i
$170$	5.28732	+	3.84146i	0.405519	+	0.294626i
$171$	−0.809017	−	0.587785i	−0.0618671	−	0.0449491i
$172$	0.736296	−	2.26609i	0.0561420	−	0.172787i
$173$	−7.35968	−	22.6508i	−0.559546	−	1.72211i	−0.683625	−	0.729833i	$-0.739598\pi$
$173$	−7.35968	−	22.6508i	−0.559546	−	1.72211i	0.124080	−	0.992272i	$-0.460402\pi$
$174$	−1.93253	+	1.40407i	−0.146505	+	0.106442i
$175$	−1.10112			−0.0832367
$176$	8.93702	−	6.52942i	0.673653	−	0.492173i
$177$	2.57842			0.193806
$178$	2.35566	−	1.71149i	0.176564	−	0.128281i
$179$	1.06971	+	3.29223i	0.0799538	+	0.246073i	0.983041	−	0.183384i	$-0.0587051\pi$
$179$	1.06971	+	3.29223i	0.0799538	+	0.246073i	−0.903088	+	0.429457i	$0.858705\pi$
$180$	−1.45351	+	4.47344i	−0.108338	+	0.333431i
$181$	15.3514	+	11.1534i	1.14106	+	0.829028i	0.987266	−	0.159076i	$-0.0508513\pi$
$181$	15.3514	+	11.1534i	1.14106	+	0.829028i	0.153792	+	0.988103i	$0.450851\pi$
$182$	0.613783	+	0.445940i	0.0454966	+	0.0330552i
$183$	2.78863	−	8.58253i	0.206142	−	0.634439i
$184$	−2.91787	−	8.98029i	−0.215108	−	0.662036i
$185$	20.3653	−	14.7963i	1.49729	−	1.08784i
$186$	1.93675			0.142009
$187$	20.9308	−	15.2921i	1.53061	−	1.11827i
$188$	21.5086			1.56868
$189$	0.735836	−	0.534616i	0.0535242	−	0.0388876i
$190$	−0.258398	−	0.795267i	−0.0187462	−	0.0576947i
$191$	2.05731	−	6.33173i	0.148861	−	0.458148i	−0.848626	−	0.528993i	$-0.822570\pi$
$191$	2.05731	−	6.33173i	0.148861	−	0.458148i	0.997487	+	0.0708452i	$0.0225696\pi$
$192$	4.38754	+	3.18774i	0.316644	+	0.230055i
$193$	5.29086	+	3.84404i	0.380845	+	0.276700i	0.761693	−	0.647938i	$-0.224368\pi$
$193$	5.29086	+	3.84404i	0.380845	+	0.276700i	−0.380849	+	0.924637i	$0.624368\pi$
$194$	−1.33727	+	4.11569i	−0.0960104	+	0.295490i
$195$	−1.91446	−	5.89209i	−0.137097	−	0.421941i
$196$	−9.42546	+	6.84800i	−0.673247	+	0.489143i
$197$	−19.7664			−1.40829			−0.704147	−	0.710054i	$-0.748671\pi$
$197$	−19.7664			−1.40829			−0.704147	+	0.710054i	$0.748671\pi$
$198$	−0.902044	−	0.651724i	−0.0641055	−	0.0463160i
$199$	−3.62149			−0.256721			−0.128360	−	0.991728i	$-0.540971\pi$
$199$	−3.62149			−0.256721			−0.128360	+	0.991728i	$0.540971\pi$
$200$	−1.27752	+	0.928174i	−0.0903344	+	0.0656318i
$201$	0.878682	+	2.70431i	0.0619775	+	0.190747i
$202$	0.768372	−	2.36481i	0.0540625	−	0.166387i
$203$	−5.23856	−	3.80603i	−0.367675	−	0.267131i
$204$	11.9343	+	8.67076i	0.835566	+	0.607074i
$205$	3.32529	−	10.2342i	0.232249	−	0.714787i
$206$	0.420147	+	1.29308i	0.0292730	+	0.0900932i
$207$	5.85655	−	4.25503i	0.407058	−	0.295745i
$208$	−8.29609			−0.575230
$209$	−3.31661	+	0.00879787i	−0.229415	+	0.000608562i
$210$	0.760554			0.0524832
$211$	7.41500	−	5.38731i	0.510470	−	0.370878i	−0.302532	−	0.953139i	$-0.597832\pi$
$211$	7.41500	−	5.38731i	0.510470	−	0.370878i	0.813002	+	0.582261i	$0.197832\pi$
$212$	−2.77507	−	8.54080i	−0.190593	−	0.586584i
$213$	−4.19272	+	12.9039i	−0.287281	+	0.884159i
$214$	3.23954	+	2.35366i	0.221450	+	0.160893i
$215$	2.54523	+	1.84922i	0.173584	+	0.126116i
$216$	0.403072	−	1.24053i	0.0274256	−	0.0844072i
$217$	1.62233	+	4.99303i	0.110131	+	0.338949i
$218$	4.16991	−	3.02961i	0.282422	−	0.205191i
$219$	−9.15881			−0.618895
$220$	4.86008	+	14.8239i	0.327667	+	0.999426i
$221$	−19.4297			−1.30698
$222$	−2.74197	+	1.99216i	−0.184029	+	0.133705i
$223$	−8.09236	−	24.9057i	−0.541904	−	1.66781i	−0.728239	−	0.685324i	$-0.759661\pi$
$223$	−8.09236	−	24.9057i	−0.541904	−	1.66781i	0.186334	−	0.982486i	$-0.440339\pi$
$224$	1.04794	−	3.22523i	0.0700185	−	0.215495i
$225$	−0.979419	−	0.711589i	−0.0652946	−	0.0474393i
$226$	0.0288916	+	0.0209910i	0.00192184	+	0.00139630i
$227$	−5.10864	+	15.7228i	−0.339072	+	1.04356i	0.625609	+	0.780137i	$0.284851\pi$
$227$	−5.10864	+	15.7228i	−0.339072	+	1.04356i	−0.964681	+	0.263421i	$0.915149\pi$
$228$	−0.583244	−	1.79504i	−0.0386262	−	0.118879i
$229$	−22.3355	+	16.2277i	−1.47597	+	1.07236i	−0.497144	+	0.867668i	$0.665618\pi$
$229$	−22.3355	+	16.2277i	−1.47597	+	1.07236i	−0.978827	+	0.204688i	$0.934382\pi$
$230$	6.05328			0.399142
$231$	0.924571	−	2.87143i	0.0608323	−	0.188926i
$232$	−9.28604			−0.609659
$233$	−6.81202	+	4.94922i	−0.446270	+	0.324234i	−0.788121	−	0.615520i	$-0.788946\pi$
$233$	−6.81202	+	4.94922i	−0.446270	+	0.324234i	0.341851	+	0.939754i	$0.388946\pi$
$234$	0.257761	+	0.793306i	0.0168503	+	0.0518600i
$235$	−8.77598	+	27.0097i	−0.572482	+	1.76192i
$236$	3.93712	+	2.86049i	0.256285	+	0.186202i
$237$	−6.73616	−	4.89411i	−0.437561	−	0.317906i
$238$	0.737081	−	2.26850i	0.0477779	−	0.147045i
$239$	3.57299	+	10.9965i	0.231117	+	0.711306i	0.997613	+	0.0690562i	$0.0219988\pi$
$239$	3.57299	+	10.9965i	0.231117	+	0.711306i	−0.766495	+	0.642250i	$0.778001\pi$
$240$	−6.72827	+	4.88838i	−0.434308	+	0.315543i
$241$	−10.9212			−0.703494			−0.351747	−	0.936095i	$-0.614412\pi$
$241$	−10.9212			−0.703494			−0.351747	+	0.936095i	$0.614412\pi$
$242$	−3.69084	+	0.0195813i	−0.237256	+	0.00125873i
$243$	1.00000			0.0641500
$244$	13.7795	−	10.0114i	0.882143	−	0.640915i
$245$	−4.75365	−	14.6302i	−0.303700	−	0.934692i
$246$	−0.447714	+	1.37792i	−0.0285452	+	0.0878532i
$247$	2.01119	+	1.46121i	0.127969	+	0.0929748i
$248$	6.09105	+	4.42541i	0.386782	+	0.281014i
$249$	−4.15320	+	12.7822i	−0.263199	+	0.810042i
$250$	0.979166	+	3.01356i	0.0619279	+	0.190594i
$251$	4.02364	−	2.92335i	0.253970	−	0.184520i	−0.453514	−	0.891249i	$-0.649830\pi$
$251$	4.02364	−	2.92335i	0.253970	−	0.184520i	0.707484	+	0.706729i	$0.249830\pi$
$252$	1.71669			0.108141
$253$	7.35870	−	22.8539i	0.462638	−	1.43681i
$254$	−1.32531			−0.0831573
$255$	−15.7578	+	11.4487i	−0.986793	+	0.716947i
$256$	2.38992	+	7.35542i	0.149370	+	0.459714i
$257$	−6.72861	+	20.7085i	−0.419719	+	1.29176i	0.488242	+	0.872708i	$0.337638\pi$
$257$	−6.72861	+	20.7085i	−0.419719	+	1.29176i	−0.907961	+	0.419054i	$0.862362\pi$
$258$	−0.342688	−	0.248977i	−0.0213348	−	0.0155007i
$259$	−7.43270	−	5.40017i	−0.461845	−	0.335550i
$260$	3.61337	−	11.1208i	0.224092	−	0.689684i
$261$	−2.19995	−	6.77075i	−0.136174	−	0.419099i
$262$	−3.26964	+	2.37554i	−0.201999	+	0.146761i
$263$	−15.9746			−0.985035			−0.492518	−	0.870303i	$-0.663923\pi$
$263$	−15.9746			−0.985035			−0.492518	+	0.870303i	$0.663923\pi$
$264$	−1.34775	−	4.11080i	−0.0829481	−	0.253002i
$265$	11.8575			0.728399
$266$	−0.246899	+	0.179383i	−0.0151384	+	0.0109987i
$267$	2.68162	+	8.25319i	0.164113	+	0.505087i
$268$	−1.65844	+	5.10415i	−0.101305	+	0.311786i
$269$	22.9479	+	16.6726i	1.39916	+	1.01655i	0.994790	+	0.101949i	$0.0325078\pi$
$269$	22.9479	+	16.6726i	1.39916	+	1.01655i	0.404366	+	0.914597i	$0.367492\pi$
$270$	0.676495	+	0.491502i	0.0411702	+	0.0299119i
$271$	6.86783	−	21.1370i	0.417191	−	1.28398i	−0.493085	−	0.869981i	$-0.664131\pi$
$271$	6.86783	−	21.1370i	0.417191	−	1.28398i	0.910276	−	0.414001i	$-0.135869\pi$
$272$	8.05993	+	24.8059i	0.488705	+	1.50408i
$273$	−1.82926	+	1.32904i	−0.110712	+	0.0804370i
$274$	1.55462			0.0939182
$275$	−4.01519	+	0.0106510i	−0.242125	+	0.000642277i
$276$	13.6632			0.822427
$277$	−0.661635	+	0.480706i	−0.0397538	+	0.0288828i	−0.607485	−	0.794331i	$-0.707821\pi$
$277$	−0.661635	+	0.480706i	−0.0397538	+	0.0288828i	0.567731	+	0.823214i	$0.307821\pi$
$278$	−0.114343	−	0.351913i	−0.00685786	−	0.0211063i
$279$	−1.78368	+	5.48961i	−0.106786	+	0.328654i
$280$	2.39193	+	1.73784i	0.142945	+	0.103856i
$281$	−2.17276	−	1.57860i	−0.129616	−	0.0941714i	0.521088	−	0.853503i	$-0.325526\pi$
$281$	−2.17276	−	1.57860i	−0.129616	−	0.0941714i	−0.650704	+	0.759331i	$0.725526\pi$
$282$	1.18159	−	3.63656i	0.0703627	−	0.216554i
$283$	−5.98851	−	18.4307i	−0.355980	−	1.09559i	−0.955439	−	0.295188i	$-0.904618\pi$
$283$	−5.98851	−	18.4307i	−0.355980	−	1.09559i	0.599459	−	0.800405i	$-0.295382\pi$
$284$	−20.7176	+	15.0522i	−1.22936	+	0.893184i
$285$	2.49211			0.147620
$286$	2.24245	+	1.62016i	0.132599	+	0.0958024i
$287$	−3.92738			−0.231826
$288$	3.01640	−	2.19154i	0.177743	−	0.129138i
$289$	13.6233	+	41.9283i	0.801372	+	2.46637i
$290$	1.83958	−	5.66166i	0.108024	−	0.332464i
$291$	−10.4341	−	7.58082i	−0.611658	−	0.444396i
$292$	−13.9851	−	10.1607i	−0.818414	−	0.594612i
$293$	4.45105	−	13.6989i	0.260033	−	0.800300i	−0.732763	−	0.680484i	$-0.761770\pi$
$293$	4.45105	−	13.6989i	0.260033	−	0.800300i	0.992796	−	0.119816i	$-0.0382304\pi$
$294$	0.640028	+	1.96980i	0.0373272	+	0.114881i
$295$	−5.19851	+	3.77694i	−0.302669	+	0.219902i
$296$	−13.1755			−0.765808
$297$	2.67803	−	1.95657i	0.155395	−	0.113532i
$298$	−5.38734			−0.312080
$299$	−14.5592	+	10.5779i	−0.841979	+	0.611734i
$300$	−0.706091	−	2.17312i	−0.0407662	−	0.125465i
$301$	0.354820	−	1.09202i	0.0204515	−	0.0629432i
$302$	−1.40413	−	1.02016i	−0.0807988	−	0.0587038i
$303$	5.99526	+	4.35581i	0.344419	+	0.250235i
$304$	1.03124	−	3.17384i	0.0591458	−	0.182032i
$305$	6.94959	+	21.3886i	0.397932	+	1.22471i
$306$	2.12162	−	1.54145i	0.121285	−	0.0881186i
$307$	0.0689145			0.00393316			0.00196658	−	0.999998i	$-0.499374\pi$
$307$	0.0689145			0.00393316			0.00196658	+	0.999998i	$0.499374\pi$
$308$	4.59733	−	3.35882i	0.261957	−	0.191387i
$309$	−4.05210			−0.230516
$310$	−3.90480	+	2.83701i	−0.221778	+	0.161131i
$311$	−2.54209	−	7.82376i	−0.144149	−	0.443645i	0.852752	−	0.522317i	$-0.174932\pi$
$311$	−2.54209	−	7.82376i	−0.144149	−	0.443645i	−0.996901	+	0.0786719i	$0.974932\pi$
$312$	−1.00202	+	3.08391i	−0.0567284	+	0.174592i
$313$	−24.5962	−	17.8702i	−1.39026	−	1.01008i	−0.995837	−	0.0911551i	$-0.970944\pi$
$313$	−24.5962	−	17.8702i	−1.39026	−	1.01008i	−0.394424	−	0.918929i	$-0.629056\pi$
$314$	4.10961	+	2.98580i	0.231919	+	0.168499i
$315$	−0.700444	+	2.15574i	−0.0394655	+	0.121462i
$316$	−4.85629	−	14.9461i	−0.273188	−	0.840785i
$317$	23.4277	−	17.0212i	1.31583	−	0.956006i	0.315856	−	0.948807i	$-0.397708\pi$
$317$	23.4277	−	17.0212i	1.31583	−	0.956006i	0.999974	−	0.00719913i	$-0.00229157\pi$
$318$	−1.59648			−0.0895262
$319$	−19.1390	−	13.8279i	−1.07158	−	0.774213i
$320$	−13.5155			−0.755538
$321$	−9.65481	+	7.01463i	−0.538879	+	0.391518i
$322$	−0.682698	−	2.10113i	−0.0380453	−	0.117091i
$323$	2.41520	−	7.43322i	0.134385	−	0.413596i
$324$	1.52695	+	1.10940i	0.0848306	+	0.0616331i
$325$	2.43480	+	1.76899i	0.135059	+	0.0981258i
$326$	0.399378	−	1.22916i	0.0221195	−	0.0680769i
$327$	4.74692	+	14.6095i	0.262505	+	0.807909i
$328$	−4.55656	+	3.31054i	−0.251594	+	0.182794i
$329$	10.3650			0.571440
$330$	2.77333	−	0.00735672i	0.152667	−	0.000404974i
$331$	−2.46229			−0.135340			−0.0676698	−	0.997708i	$-0.521556\pi$
$331$	−2.46229			−0.135340			−0.0676698	+	0.997708i	$0.521556\pi$
$332$	−20.5223	+	14.9103i	−1.12631	+	0.818310i
$333$	−3.12139	−	9.60665i	−0.171051	−	0.526441i
$334$	0.430785	−	1.32582i	0.0235715	−	0.0725456i
$335$	−5.73291	−	4.16520i	−0.313222	−	0.227569i
$336$	2.45561	+	1.78410i	0.133964	+	0.0973308i
$337$	1.09642	−	3.37445i	0.0597260	−	0.183818i	−0.916742	−	0.399480i	$-0.869191\pi$
$337$	1.09642	−	3.37445i	0.0597260	−	0.183818i	0.976468	+	0.215662i	$0.0691909\pi$
$338$	0.707137	+	2.17635i	0.0384632	+	0.118378i
$339$	−0.0861059	+	0.0625596i	−0.00467663	+	0.00339777i
$340$	−36.7626			−1.99373
$341$	5.96408	+	18.1912i	0.322973	+	0.985109i
$342$	−0.335536			−0.0181437
$343$	−9.69297	+	7.04235i	−0.523371	+	0.380251i
$344$	−0.508844	−	1.56606i	−0.0274350	−	0.0844363i
$345$	−5.57486	+	17.1577i	−0.300141	+	0.923738i
$346$	−6.46507	−	4.69715i	−0.347564	−	0.252520i
$347$	−22.4427	−	16.3056i	−1.20479	−	0.875330i	−0.210041	−	0.977692i	$-0.567360\pi$
$347$	−22.4427	−	16.3056i	−1.20479	−	0.875330i	−0.994747	+	0.102362i	$0.967360\pi$
$348$	4.15222	−	12.7792i	0.222583	−	0.685039i
$349$	−9.62177	−	29.6128i	−0.515041	−	1.58513i	−0.783207	−	0.621761i	$-0.786417\pi$
$349$	−9.62177	−	29.6128i	−0.515041	−	1.58513i	0.268165	−	0.963373i	$-0.413583\pi$
$350$	−0.298903	+	0.217166i	−0.0159770	+	0.0116080i
$351$	−2.48597			−0.132691
$352$	3.79008	−	11.7708i	0.202012	−	0.627387i
$353$	0.921389			0.0490406			0.0245203	−	0.999699i	$-0.492194\pi$
$353$	0.921389			0.0490406			0.0245203	+	0.999699i	$0.492194\pi$
$354$	0.699923	−	0.508524i	0.0372005	−	0.0270277i
$355$	−10.4487	−	32.1579i	−0.554561	−	1.70676i
$356$	−5.06134	+	15.5772i	−0.268250	+	0.825590i
$357$	5.75111	+	4.17843i	0.304381	+	0.221146i
$358$	0.939680	+	0.682718i	0.0496636	+	0.0360827i
$359$	3.53828	−	10.8897i	0.186743	−	0.574737i	−0.813231	−	0.581942i	$-0.802293\pi$
$359$	3.53828	−	10.8897i	0.186743	−	0.574737i	0.999974	+	0.00720437i	$0.00229324\pi$
$360$	1.00450	+	3.09153i	0.0529418	+	0.162938i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	6.36691			0.334637
$363$	3.34364	−	10.4795i	0.175495	−	0.550032i
$364$	−4.26762			−0.223684
$365$	18.4656	−	13.4161i	0.966536	−	0.702230i
$366$	−0.935686	−	2.87975i	−0.0489091	−	0.150527i
$367$	−6.29823	+	19.3839i	−0.328765	+	1.01183i	0.640948	+	0.767584i	$0.278541\pi$
$367$	−6.29823	+	19.3839i	−0.328765	+	1.01183i	−0.969712	+	0.244249i	$0.921459\pi$
$368$	19.5443	+	14.1998i	1.01882	+	0.740214i
$369$	−3.49331	−	2.53804i	−0.181855	−	0.132125i
$370$	2.61009	−	8.03302i	0.135692	−	0.417617i
$371$	−1.33730	−	4.11580i	−0.0694294	−	0.213682i
$372$	−8.81373	+	6.40355i	−0.456971	+	0.332009i
$373$	38.3906			1.98779			0.993894	−	0.110341i	$-0.0351944\pi$
$373$	38.3906			1.98779			0.993894	+	0.110341i	$0.0351944\pi$
$374$	2.66580	−	8.27914i	0.137845	−	0.428104i
$375$	−9.44354			−0.487662
$376$	12.0255	−	8.73703i	0.620168	−	0.450578i
$377$	5.46901	+	16.8319i	0.281668	+	0.866885i
$378$	0.0943071	−	0.290248i	0.00485064	−	0.0149287i
$379$	9.00630	+	6.54346i	0.462623	+	0.336115i	0.794559	−	0.607187i	$-0.207702\pi$
$379$	9.00630	+	6.54346i	0.462623	+	0.336115i	−0.331937	+	0.943302i	$0.607702\pi$
$380$	3.80534	+	2.76474i	0.195210	+	0.141828i
$381$	1.22056	−	3.75651i	0.0625314	−	0.192452i
$382$	−0.690300	−	2.12452i	−0.0353188	−	0.108700i
$383$	−18.0630	+	13.1236i	−0.922977	+	0.670582i	−0.944263	−	0.329191i	$-0.893224\pi$
$383$	−18.0630	+	13.1236i	−0.922977	+	0.670582i	0.0212860	+	0.999773i	$0.493224\pi$
$384$	9.27666			0.473398
$385$	2.34207	+	7.14361i	0.119363	+	0.364072i
$386$	2.19436			0.111690
$387$	1.02132	−	0.742029i	0.0519164	−	0.0377195i
$388$	−7.52225	−	23.1511i	−0.381884	−	1.17532i
$389$	2.06915	−	6.36819i	0.104910	−	0.322880i	−0.884799	−	0.465972i	$-0.845705\pi$
$389$	2.06915	−	6.36819i	0.104910	−	0.322880i	0.989709	+	0.143092i	$0.0457046\pi$
$390$	−1.68174	−	1.22186i	−0.0851584	−	0.0618712i
$391$	45.7733	+	33.2563i	2.31486	+	1.68184i
$392$	−2.48805	+	7.65744i	−0.125666	+	0.386759i
$393$	−3.72208	−	11.4554i	−0.187754	−	0.577848i
$394$	−5.36566	+	3.89838i	−0.270318	+	0.196398i
$395$	20.7502			1.04406
$396$	6.25983	−	0.0166052i	0.314568	−	0.000834445i
$397$	−12.2071			−0.612658			−0.306329	−	0.951926i	$-0.599101\pi$
$397$	−12.2071			−0.612658			−0.306329	+	0.951926i	$0.599101\pi$
$398$	−0.983070	+	0.714242i	−0.0492769	+	0.0358017i
$399$	−0.281064	−	0.865027i	−0.0140708	−	0.0433055i
$400$	1.24845	−	3.84234i	0.0624225	−	0.192117i
$401$	12.8248	+	9.31778i	0.640441	+	0.465308i	0.860002	−	0.510291i	$-0.170462\pi$
$401$	12.8248	+	9.31778i	0.640441	+	0.465308i	−0.219560	+	0.975599i	$0.570462\pi$
$402$	0.771874	+	0.560799i	0.0384976	+	0.0279701i
$403$	4.43417	−	13.6470i	0.220882	−	0.679804i
$404$	4.32215	+	13.3022i	0.215035	+	0.661810i
$405$	−2.01616	+	1.46483i	−0.100184	+	0.0727879i
$406$	−2.17267			−0.107828
$407$	−27.1553	−	19.6196i	−1.34604	−	0.972508i
$408$	10.1946			0.504709
$409$	−16.6896	+	12.1257i	−0.825248	+	0.599578i	−0.918211	−	0.396092i	$-0.870366\pi$
$409$	−16.6896	+	12.1257i	−0.825248	+	0.599578i	0.0929631	+	0.995670i	$0.470366\pi$
$410$	−1.11576	−	3.43394i	−0.0551032	−	0.169590i
$411$	−1.43175	+	4.40648i	−0.0706232	+	0.217356i
$412$	−6.18736	−	4.49538i	−0.304829	−	0.221471i
$413$	1.89729	+	1.37846i	0.0933597	+	0.0678298i
$414$	0.750595	−	2.31009i	0.0368897	−	0.113535i
$415$	−10.3503	−	31.8548i	−0.508074	−	1.56369i
$416$	−7.49867	+	5.44810i	−0.367652	+	0.267115i
$417$	1.10278			0.0540035
$418$	−0.898574	+	0.656501i	−0.0439507	+	0.0321105i
$419$	11.2902			0.551561			0.275781	−	0.961221i	$-0.411064\pi$
$419$	11.2902			0.551561			0.275781	+	0.961221i	$0.411064\pi$
$420$	−3.46112	+	2.51465i	−0.168885	+	0.122702i
$421$	−7.47758	−	23.0136i	−0.364435	−	1.12161i	−0.950334	−	0.311231i	$-0.899259\pi$
$421$	−7.47758	−	23.0136i	−0.364435	−	1.12161i	0.585900	−	0.810384i	$-0.300741\pi$
$422$	0.950331	−	2.92482i	0.0462614	−	0.142378i
$423$	9.21941	+	6.69829i	0.448263	+	0.325682i
$424$	−5.02091	−	3.64790i	−0.243837	−	0.177158i
$425$	2.92391	−	8.99887i	0.141830	−	0.436509i
$426$	1.40681	+	4.32971i	0.0681601	+	0.209775i
$427$	6.64033	−	4.82448i	0.321348	−	0.233473i
$428$	−22.5244			−1.08876
$429$	−6.65748	+	4.86398i	−0.321426	+	0.234835i
$430$	1.05562			0.0509067
$431$	7.73133	−	5.61714i	0.372405	−	0.270568i	−0.385802	−	0.922581i	$-0.626075\pi$
$431$	7.73133	−	5.61714i	0.372405	−	0.270568i	0.758208	+	0.652013i	$0.226075\pi$
$432$	1.03124	+	3.17384i	0.0496157	+	0.152701i
$433$	−5.30049	+	16.3132i	−0.254725	+	0.783963i	0.739159	+	0.673532i	$0.235223\pi$
$433$	−5.30049	+	16.3132i	−0.254725	+	0.783963i	−0.993884	+	0.110432i	$0.964777\pi$
$434$	1.42513	+	1.03542i	0.0684084	+	0.0497016i
$435$	14.3534	+	10.4284i	0.688195	+	0.500003i
$436$	−8.95942	+	27.5742i	−0.429078	+	1.32057i
$437$	−2.23700	−	6.88479i	−0.107010	−	0.329344i
$438$	−2.48620	+	1.80633i	−0.118795	+	0.0863097i
$439$	5.10608			0.243700			0.121850	−	0.992549i	$-0.461117\pi$
$439$	5.10608			0.243700			0.121850	+	0.992549i	$0.461117\pi$
$440$	8.73889	+	6.31383i	0.416610	+	0.301000i
$441$	−6.17273			−0.293940
$442$	−5.27427	+	3.83198i	−0.250872	+	0.182269i
$443$	6.45197	+	19.8571i	0.306542	+	0.943440i	0.979097	+	0.203393i	$0.0651968\pi$
$443$	6.45197	+	19.8571i	0.306542	+	0.943440i	−0.672555	+	0.740047i	$0.734803\pi$
$444$	5.89136	−	18.1317i	0.279592	−	0.860494i
$445$	−17.4961	−	12.7117i	−0.829394	−	0.602590i
$446$	−7.10869	−	5.16476i	−0.336606	−	0.244559i
$447$	4.96155	−	15.2701i	0.234673	−	0.722251i
$448$	1.52430	+	4.69130i	0.0720162	+	0.221643i
$449$	−23.0551	+	16.7505i	−1.08804	+	0.790505i	−0.979067	−	0.203540i	$-0.934755\pi$
$449$	−23.0551	+	16.7505i	−1.08804	+	0.790505i	−0.108970	+	0.994045i	$0.534755\pi$
$450$	−0.406209			−0.0191489
$451$	−14.3210	+	0.0379890i	−0.674351	+	0.00178883i
$452$	−0.200883			−0.00944873
$453$	4.18475	−	3.04040i	0.196617	−	0.142850i
$454$	1.71413	+	5.27556i	0.0804482	+	0.247594i
$455$	1.74128	−	5.35911i	0.0816325	−	0.251239i
$456$	−1.05526	−	0.766688i	−0.0494169	−	0.0359035i
$457$	23.1030	+	16.7853i	1.08071	+	0.785185i	0.977807	−	0.209506i	$-0.0671856\pi$
$457$	23.1030	+	16.7853i	1.08071	+	0.785185i	0.102907	+	0.994691i	$0.467186\pi$
$458$	−2.86259	+	8.81015i	−0.133760	+	0.411671i
$459$	2.41520	+	7.43322i	0.112732	+	0.346953i
$460$	−27.5472	+	20.0142i	−1.28439	+	0.933167i
$461$	0.799377			0.0372307			0.0186154	−	0.999827i	$-0.494074\pi$
$461$	0.799377			0.0372307			0.0186154	+	0.999827i	$0.494074\pi$
$462$	−0.315334	−	0.961809i	−0.0146707	−	0.0447474i
$463$	−23.3696			−1.08608			−0.543038	−	0.839708i	$-0.682726\pi$
$463$	−23.3696			−1.08608			−0.543038	+	0.839708i	$0.682726\pi$
$464$	19.2206	−	13.9646i	0.892293	−	0.648289i
$465$	−4.44513	−	13.6807i	−0.206138	−	0.634428i
$466$	−0.873051	+	2.68697i	−0.0404433	+	0.124472i
$467$	2.18138	+	1.58487i	0.100942	+	0.0733389i	0.637111	−	0.770772i	$-0.280129\pi$
$467$	2.18138	+	1.58487i	0.100942	+	0.0733389i	−0.536169	+	0.844111i	$0.680129\pi$
$468$	−3.79595	−	2.75792i	−0.175468	−	0.127485i
$469$	−0.799199	+	2.45968i	−0.0369036	+	0.113578i
$470$	2.94466	+	9.06272i	0.135827	+	0.418032i
$471$	−12.2479	+	8.89861i	−0.564353	+	0.410026i
$472$	3.36321			0.154804
$473$	1.28327	−	3.98545i	0.0590050	−	0.183251i
$474$	−2.79379			−0.128323
$475$	−0.979419	+	0.711589i	−0.0449388	+	0.0326500i
$476$	4.14614	+	12.7605i	0.190038	+	0.584877i
$477$	1.47030	−	4.52513i	0.0673206	−	0.207191i
$478$	3.13867	+	2.28038i	0.143559	+	0.104302i
$479$	15.6140	+	11.3442i	0.713423	+	0.518332i	0.884276	−	0.466965i	$-0.154652\pi$
$479$	15.6140	+	11.3442i	0.713423	+	0.518332i	−0.170853	+	0.985296i	$0.554652\pi$
$480$	−2.87132	+	8.83701i	−0.131057	+	0.403352i
$481$	7.75967	+	23.8818i	0.353810	+	1.08892i
$482$	−2.96460	+	2.15390i	−0.135034	+	0.0981077i
$483$	6.58427			0.299594
$484$	16.7315	−	12.2923i	0.760522	−	0.558740i
$485$	32.1414			1.45947
$486$	0.271454	−	0.197223i	0.0123134	−	0.00894622i
$487$	−4.48727	−	13.8104i	−0.203338	−	0.625809i	−0.999778	−	0.0210915i	$-0.993286\pi$
$487$	−4.48727	−	13.8104i	−0.203338	−	0.625809i	0.796440	−	0.604718i	$-0.206714\pi$
$488$	3.63740	−	11.1948i	0.164657	−	0.506763i
$489$	3.11617	+	2.26403i	0.140918	+	0.102383i
$490$	−4.17582	−	3.03391i	−0.188644	−	0.137058i
$491$	5.57486	−	17.1577i	0.251590	−	0.774314i	−0.742892	−	0.669411i	$-0.766547\pi$
$491$	5.57486	−	17.1577i	0.251590	−	0.774314i	0.994482	−	0.104904i	$-0.0334534\pi$
$492$	−2.51843	−	7.75093i	−0.113540	−	0.349439i
$493$	45.0152	−	32.7055i	2.02738	−	1.47298i
$494$	0.834131			0.0375293
$495$	−2.53329	+	7.86761i	−0.113863	+	0.353623i
$496$	−19.2625			−0.864912
$497$	−9.98377	+	7.25363i	−0.447833	+	0.325370i
$498$	1.39355	+	4.28890i	0.0624464	+	0.192190i
$499$	−6.76893	+	20.8326i	−0.303019	+	0.932597i	0.677390	+	0.735624i	$0.263111\pi$
$499$	−6.76893	+	20.8326i	−0.303019	+	0.932597i	−0.980409	+	0.196973i	$0.936889\pi$
$500$	−14.4198	−	10.4766i	−0.644874	−	0.468529i
$501$	3.36122	+	2.44207i	0.150168	+	0.109104i
$502$	0.515683	−	1.58711i	0.0230161	−	0.0708362i
$503$	5.90754	+	18.1815i	0.263404	+	0.810674i	0.992057	+	0.125791i	$0.0401468\pi$
$503$	5.90754	+	18.1815i	0.263404	+	0.810674i	−0.728653	+	0.684883i	$0.759853\pi$
$504$	0.959800	−	0.697336i	0.0427529	−	0.0310618i
$505$	−18.4679			−0.821812
$506$	−2.50976	−	7.65508i	−0.111572	−	0.340310i
$507$	−6.81997			−0.302886
$508$	6.03120	−	4.38192i	0.267591	−	0.194416i
$509$	6.88543	+	21.1912i	0.305191	+	0.939282i	0.979606	+	0.200929i	$0.0643962\pi$
$509$	6.88543	+	21.1912i	0.305191	+	0.939282i	−0.674414	+	0.738353i	$0.735604\pi$
$510$	−2.01957	+	6.21561i	−0.0894283	+	0.275232i
$511$	−6.73938	−	4.89645i	−0.298133	−	0.216606i
$512$	17.1094	+	12.4307i	0.756134	+	0.549364i
$513$	0.309017	−	0.951057i	0.0136434	−	0.0419902i
$514$	2.25769	+	6.94846i	0.0995824	+	0.306483i
$515$	8.16969	−	5.93563i	0.360000	−	0.261555i
$516$	2.38270			0.104893
$517$	37.7955	−	0.100259i	1.66224	−	0.00440938i
$518$	−3.08268			−0.135445
$519$	19.2679	−	13.9989i	0.845766	−	0.614485i
$520$	−2.49715	−	7.68545i	−0.109507	−	0.337029i
$521$	9.71578	−	29.9021i	0.425656	−	1.31004i	−0.476708	−	0.879061i	$-0.658170\pi$
$521$	9.71578	−	29.9021i	0.425656	−	1.31004i	0.902365	−	0.430974i	$-0.141830\pi$
$522$	−1.93253	−	1.40407i	−0.0845848	−	0.0614544i
$523$	−26.2367	−	19.0621i	−1.14725	−	0.833528i	−0.159140	−	0.987256i	$-0.550872\pi$
$523$	−26.2367	−	19.0621i	−1.14725	−	0.833528i	−0.988113	+	0.153728i	$0.950872\pi$
$524$	7.02512	−	21.6211i	0.306894	−	0.944522i
$525$	−0.340264	−	1.04723i	−0.0148503	−	0.0457047i
$526$	−4.33637	+	3.15056i	−0.189075	+	0.137371i
$527$	−45.1134			−1.96517
$528$	8.97154	+	6.48191i	0.390436	+	0.282089i
$529$	29.4045			1.27846
$530$	3.21876	−	2.33857i	0.139814	−	0.101581i
$531$	0.796776	+	2.45222i	0.0345771	+	0.106417i
$532$	0.530485	−	1.63266i	0.0229994	−	0.0707850i
$533$	8.68426	+	6.30948i	0.376157	+	0.273294i
$534$	2.35566	+	1.71149i	0.101939	+	0.0740632i
$535$	9.19044	−	28.2853i	0.397337	−	1.22288i
$536$	1.14612	+	3.52741i	0.0495051	+	0.152361i
$537$	−2.80054	+	2.03471i	−0.120852	+	0.0878041i
$538$	9.51751			0.410329
$539$	−16.5307	+	12.0774i	−0.712029	+	0.520211i
$540$	−4.70365			−0.202413
$541$	21.9417	−	15.9415i	0.943346	−	0.685381i	−0.00587804	−	0.999983i	$-0.501871\pi$
$541$	21.9417	−	15.9415i	0.943346	−	0.685381i	0.949224	+	0.314602i	$0.101871\pi$
$542$	−2.30440	−	7.09223i	−0.0989826	−	0.304637i
$543$	−5.86370	+	18.0466i	−0.251636	+	0.774455i
$544$	23.5754	+	17.1286i	1.01079	+	0.734381i
$545$	−30.9710	−	22.5017i	−1.32665	−	0.963869i
$546$	−0.234444	+	0.721546i	−0.0100333	+	0.0308793i
$547$	−8.32831	−	25.6319i	−0.356093	−	1.09594i	−0.955373	−	0.295402i	$-0.904547\pi$
$547$	−8.32831	−	25.6319i	−0.356093	−	1.09594i	0.599280	−	0.800539i	$-0.295453\pi$
$548$	−7.07475	+	5.14011i	−0.302218	+	0.219575i
$549$	9.02420			0.385144
$550$	−1.08784	+	0.794778i	−0.0463856	+	0.0338895i
$551$	−7.11919			−0.303288
$552$	7.63909	−	5.55013i	0.325141	−	0.236229i
$553$	−2.34024	−	7.20252i	−0.0995171	−	0.306282i
$554$	−0.0847973	+	0.260979i	−0.00360269	+	0.0110879i
$555$	20.3653	+	14.7963i	0.864459	+	0.628066i
$556$	1.68389	+	1.22342i	0.0714130	+	0.0518846i
$557$	−3.12482	+	9.61721i	−0.132403	+	0.407494i	−0.995177	−	0.0980954i	$-0.968725\pi$
$557$	−3.12482	+	9.61721i	−0.132403	+	0.407494i	0.862774	+	0.505590i	$0.168725\pi$
$558$	0.598489	+	1.84196i	0.0253361	+	0.0779764i
$559$	−2.53896	+	1.84466i	−0.107386	+	0.0780208i
$560$	−7.56431			−0.319650
$561$	21.0116	+	15.1808i	0.887111	+	0.640935i
$562$	−0.901141			−0.0380123
$563$	−3.59582	+	2.61252i	−0.151546	+	0.110104i	−0.660974	−	0.750408i	$-0.729857\pi$
$563$	−3.59582	+	2.61252i	−0.151546	+	0.110104i	0.509429	+	0.860513i	$0.329857\pi$
$564$	6.64654	+	20.4559i	0.279870	+	0.861350i
$565$	0.0819644	−	0.252260i	0.00344827	−	0.0106127i
$566$	−5.26057	−	3.82203i	−0.221118	−	0.160652i
$567$	0.735836	+	0.534616i	0.0309022	+	0.0224518i
$568$	−5.46885	+	16.8314i	−0.229468	+	0.706229i
$569$	−2.10035	−	6.46422i	−0.0880513	−	0.270994i	0.897329	−	0.441362i	$-0.145504\pi$
$569$	−2.10035	−	6.46422i	−0.0880513	−	0.270994i	−0.985381	+	0.170368i	$0.945504\pi$
$570$	0.676495	−	0.491502i	0.0283352	−	0.0205868i
$571$	−16.1697			−0.676681			−0.338341	−	0.941024i	$-0.609866\pi$
$571$	−16.1697			−0.676681			−0.338341	+	0.941024i	$0.609866\pi$
$572$	−15.5617	+	0.0412801i	−0.650668	+	0.00172601i
$573$	6.65758			0.278124
$574$	−1.06610	+	0.774570i	−0.0444983	+	0.0323299i
$575$	−2.70818	−	8.33492i	−0.112939	−	0.347590i
$576$	−1.67589	+	5.15787i	−0.0698288	+	0.214911i
$577$	0.750345	+	0.545157i	0.0312373	+	0.0226952i	0.603294	−	0.797519i	$-0.293854\pi$
$577$	0.750345	+	0.545157i	0.0312373	+	0.0226952i	−0.572057	+	0.820214i	$0.693854\pi$
$578$	11.9673	+	8.69477i	0.497775	+	0.361655i
$579$	−2.02093	+	6.21978i	−0.0839869	+	0.258485i
$580$	10.3478	+	31.8473i	0.429669	+	1.32239i
$581$	−9.88967	+	7.18526i	−0.410293	+	0.298095i
$582$	−4.32750			−0.179380
$583$	−4.91624	−	14.9952i	−0.203610	−	0.621036i
$584$	−11.9465			−0.494348
$585$	5.01211	−	3.64151i	0.207225	−	0.150558i
$586$	−1.49349	−	4.59648i	−0.0616954	−	0.189879i
$587$	−2.11236	+	6.50118i	−0.0871865	+	0.268333i	−0.985139	−	0.171760i	$-0.945055\pi$
$587$	−2.11236	+	6.50118i	−0.0871865	+	0.268333i	0.897952	+	0.440093i	$0.145055\pi$
$588$	−9.42546	−	6.84800i	−0.388699	−	0.282407i
$589$	4.66974	+	3.39276i	0.192413	+	0.139796i
$590$	−0.666259	+	2.05053i	−0.0274294	+	0.0844191i
$591$	−6.10814	−	18.7989i	−0.251255	−	0.773284i
$592$	27.2710	−	19.8136i	1.12083	−	0.814332i
$593$	30.4399			1.25002			0.625009	−	0.780617i	$-0.285095\pi$
$593$	30.4399			1.25002			0.625009	+	0.780617i	$0.285095\pi$
$594$	0.341080	−	1.05929i	0.0139947	−	0.0434631i
$595$	−17.7158			−0.726279
$596$	24.5166	−	17.8124i	1.00424	−	0.729623i
$597$	−1.11910	−	3.44425i	−0.0458019	−	0.140964i
$598$	−1.86595	+	5.74281i	−0.0763045	+	0.234841i
$599$	20.1262	+	14.6226i	0.822336	+	0.597462i	0.917381	−	0.398011i	$-0.130299\pi$
$599$	20.1262	+	14.6226i	0.822336	+	0.597462i	−0.0950446	+	0.995473i	$0.530299\pi$
$600$	−1.27752	−	0.928174i	−0.0521546	−	0.0378925i
$601$	−3.86863	+	11.9064i	−0.157805	+	0.485672i	−0.998434	−	0.0559379i	$-0.982185\pi$
$601$	−3.86863	+	11.9064i	−0.157805	+	0.485672i	0.840630	+	0.541610i	$0.182185\pi$
$602$	−0.119055	−	0.366413i	−0.00485231	−	0.0149339i
$603$	−2.30042	+	1.67135i	−0.0936804	+	0.0680628i
$604$	9.76291			0.397247
$605$	8.60936	+	26.0262i	0.350020	+	1.05812i
$606$	2.48650			0.101007
$607$	22.3187	−	16.2155i	0.905887	−	0.658166i	−0.0340841	−	0.999419i	$-0.510851\pi$
$607$	22.3187	−	16.2155i	0.905887	−	0.658166i	0.939971	+	0.341253i	$0.110851\pi$
$608$	−1.15216	−	3.54599i	−0.0467263	−	0.143809i
$609$	2.00095	−	6.15829i	0.0810826	−	0.249547i
$610$	6.10482	+	4.43541i	0.247177	+	0.179585i
$611$	−22.9191	−	16.6517i	−0.927209	−	0.673657i
$612$	−4.55849	+	14.0296i	−0.184266	+	0.567112i
$613$	9.06521	+	27.8998i	0.366140	+	1.12686i	0.949264	+	0.314481i	$0.101830\pi$
$613$	9.06521	+	27.8998i	0.366140	+	1.12686i	−0.583124	+	0.812383i	$0.698170\pi$
$614$	0.0187071	−	0.0135915i	0.000754959	−	0.000548510i
$615$	10.7609			0.433920
$616$	1.20598	−	3.74540i	0.0485903	−	0.150907i
$617$	12.7952			0.515114			0.257557	−	0.966263i	$-0.417082\pi$
$617$	12.7952			0.515114			0.257557	+	0.966263i	$0.417082\pi$
$618$	−1.09996	+	0.799168i	−0.0442469	+	0.0321472i
$619$	7.35983	+	22.6512i	0.295817	+	0.910430i	0.982946	+	0.183895i	$0.0588706\pi$
$619$	7.35983	+	22.6512i	0.295817	+	0.910430i	−0.687129	+	0.726535i	$0.741129\pi$
$620$	8.38982	−	25.8212i	0.336943	−	1.03700i
$621$	5.85655	+	4.25503i	0.235015	+	0.170749i
$622$	−2.23309	−	1.62243i	−0.0895387	−	0.0650536i
$623$	−2.43905	+	7.50663i	−0.0977186	+	0.300747i
$624$	−2.56363	−	7.89005i	−0.102627	−	0.315855i
$625$	23.9368	−	17.3911i	0.957472	−	0.695644i
$626$	−10.2012			−0.407721
$627$	−1.03326	−	3.15157i	−0.0412643	−	0.125861i
$628$	−28.5740			−1.14023
$629$	63.8696	−	46.4040i	2.54665	−	1.85025i
$630$	0.235024	+	0.723330i	0.00936358	+	0.0288181i
$631$	−1.55033	+	4.77141i	−0.0617175	+	0.189947i	−0.977161	−	0.212499i	$-0.931840\pi$
$631$	−1.55033	+	4.77141i	−0.0617175	+	0.189947i	0.915444	+	0.402446i	$0.131840\pi$
$632$	−8.78643	−	6.38371i	−0.349505	−	0.253931i
$633$	7.41500	+	5.38731i	0.294720	+	0.214126i
$634$	3.00257	−	9.24096i	0.119247	−	0.367005i
$635$	3.04179	+	9.36165i	0.120710	+	0.371506i
$636$	7.26524	−	5.27850i	0.288085	−	0.209306i
$637$	15.3452			0.607999
$638$	−7.92254	+	0.0210159i	−0.313656	+	0.000832026i
$639$	−13.5679			−0.536739
$640$	−18.7033	+	13.5887i	−0.739311	+	0.537141i
$641$	5.21881	+	16.0618i	0.206131	+	0.634404i	0.999665	+	0.0258793i	$0.00823856\pi$
$641$	5.21881	+	16.0618i	0.206131	+	0.634404i	−0.793535	+	0.608525i	$0.791761\pi$
$642$	−1.23739	+	3.80830i	−0.0488360	+	0.150302i
$643$	2.40085	+	1.74432i	0.0946804	+	0.0687893i	0.634118	−	0.773236i	$-0.281363\pi$
$643$	2.40085	+	1.74432i	0.0946804	+	0.0687893i	−0.539438	+	0.842025i	$0.681363\pi$
$644$	10.0539	+	7.30455i	0.396177	+	0.287840i
$645$	−0.972193	+	2.99210i	−0.0382801	+	0.117814i
$646$	−0.810386	−	2.49411i	−0.0318842	−	0.0981296i
$647$	−0.209243	+	0.152024i	−0.00822619	+	0.00597668i	−0.591891	−	0.806018i	$-0.701618\pi$
$647$	−0.209243	+	0.152024i	−0.00822619	+	0.00597668i	0.583665	+	0.811995i	$0.301618\pi$
$648$	1.30437			0.0512404
$649$	6.93174	+	5.00816i	0.272095	+	0.196588i
$650$	1.00982			0.0396085
$651$	−4.24733	+	3.08586i	−0.166466	+	0.120945i
$652$	2.24653	+	6.91412i	0.0879810	+	0.270778i
$653$	6.56923	−	20.2180i	0.257074	−	0.791192i	−0.736340	−	0.676612i	$-0.763448\pi$
$653$	6.56923	−	20.2180i	0.257074	−	0.791192i	0.993414	−	0.114581i	$-0.0365524\pi$
$654$	4.16991	+	3.02961i	0.163056	+	0.118467i
$655$	24.2845	+	17.6437i	0.948874	+	0.689397i
$656$	4.45287	−	13.7045i	0.173856	−	0.535072i
$657$	−2.83023	−	8.71055i	−0.110418	−	0.339831i
$658$	2.81362	−	2.04421i	0.109686	−	0.0796917i
$659$	−37.2792			−1.45219			−0.726095	−	0.687594i	$-0.758667\pi$
$659$	−37.2792			−1.45219			−0.726095	+	0.687594i	$0.758667\pi$
$660$	−12.5965	+	9.20305i	−0.490318	+	0.358228i
$661$	−18.5045			−0.719740			−0.359870	−	0.933002i	$-0.617179\pi$
$661$	−18.5045			−0.719740			−0.359870	+	0.933002i	$0.617179\pi$
$662$	−0.668398	+	0.485620i	−0.0259780	+	0.0188741i
$663$	−6.00411	−	18.4787i	−0.233180	−	0.717655i
$664$	−5.41730	+	16.6727i	−0.210232	+	0.647028i
$665$	1.83379	+	1.33232i	0.0711112	+	0.0516653i
$666$	−2.74197	−	1.99216i	−0.106249	−	0.0771945i
$667$	15.9257	−	49.0141i	0.616644	−	1.89783i
$668$	2.42320	+	7.45784i	0.0937564	+	0.288552i
$669$	21.1861	−	15.3926i	0.819101	−	0.595111i
$670$	−2.37770			−0.0918584
$671$	24.1670	−	17.6565i	0.932958	−	0.681622i
$672$	3.39121			0.130819
$673$	−18.4531	+	13.4070i	−0.711315	+	0.516801i	−0.883598	−	0.468247i	$-0.844886\pi$
$673$	−18.4531	+	13.4070i	−0.711315	+	0.516801i	0.172283	+	0.985048i	$0.444886\pi$
$674$	−0.367890	−	1.13225i	−0.0141706	−	0.0436125i
$675$	0.374105	−	1.15138i	0.0143993	−	0.0443165i
$676$	−10.4138	−	7.56604i	−0.400529	−	0.291002i
$677$	19.5315	+	14.1905i	0.750658	+	0.545385i	0.896031	−	0.443992i	$-0.146438\pi$
$677$	19.5315	+	14.1905i	0.750658	+	0.545385i	−0.145373	+	0.989377i	$0.546438\pi$
$678$	−0.0110356	+	0.0339641i	−0.000423820	+	0.00130438i
$679$	−3.62496	−	11.1565i	−0.139113	−	0.428146i
$680$	−20.5540	+	14.9333i	−0.788210	+	0.572668i
$681$	−16.5319			−0.633504
$682$	5.20670	+	3.76183i	0.199375	+	0.144048i
$683$	−0.588022			−0.0225000			−0.0112500	−	0.999937i	$-0.503581\pi$
$683$	−0.588022			−0.0225000			−0.0112500	+	0.999937i	$0.503581\pi$
$684$	1.52695	−	1.10940i	0.0583844	−	0.0424188i
$685$	−3.56809	−	10.9815i	−0.136330	−	0.419580i
$686$	−1.24228	+	3.82335i	−0.0474306	+	0.145976i
$687$	−22.3355	−	16.2277i	−0.852152	−	0.619125i
$688$	3.40830	+	2.47628i	0.129940	+	0.0944072i
$689$	−3.65513	+	11.2493i	−0.139249	+	0.428565i
$690$	1.87057	+	5.75701i	0.0712113	+	0.219166i
$691$	32.0314	−	23.2722i	1.21853	−	0.885316i	0.222555	−	0.974920i	$-0.428560\pi$
$691$	32.0314	−	23.2722i	1.21853	−	0.885316i	0.995977	+	0.0896044i	$0.0285603\pi$
$692$	44.9515			1.70880
$693$	3.01660	−	0.00800204i	0.114591	−	0.000303972i
$694$	−9.30801			−0.353327
$695$	−2.22339	+	1.61539i	−0.0843379	+	0.0612750i
$696$	−2.86955	−	8.83155i	−0.108770	−	0.334759i
$697$	10.4288	−	32.0964i	0.395018	−	1.21574i
$698$	−8.45219	−	6.14087i	−0.319920	−	0.232435i
$699$	−6.81202	−	4.94922i	−0.257654	−	0.187197i
$700$	0.642220	−	1.97655i	0.0242736	−	0.0747066i
$701$	8.42736	+	25.9367i	0.318297	+	0.979617i	0.974376	+	0.224925i	$0.0722137\pi$
$701$	8.42736	+	25.9367i	0.318297	+	0.979617i	−0.656079	+	0.754692i	$0.727786\pi$
$702$	−0.674826	+	0.490290i	−0.0254697	+	0.0185048i
$703$	−10.1010			−0.380968
$704$	5.60366	+	17.0919i	0.211196	+	0.644175i
$705$	−28.3997			−1.06959
$706$	0.250115	−	0.181719i	0.00941320	−	0.00683909i
$707$	2.08284	+	6.41032i	0.0783332	+	0.241085i
$708$	−1.50385	+	4.62836i	−0.0565180	+	0.173945i
$709$	25.8021	+	18.7463i	0.969018	+	0.704032i	0.955227	−	0.295872i	$-0.0956103\pi$
$709$	25.8021	+	18.7463i	0.969018	+	0.704032i	0.0137901	+	0.999905i	$0.495610\pi$
$710$	−9.17863	−	6.66867i	−0.344468	−	0.250271i
$711$	2.57298	−	7.91883i	0.0964945	−	0.296979i
$712$	3.49782	+	10.7652i	0.131086	+	0.403443i
$713$	−33.8047	+	24.5605i	−1.26599	+	0.919799i
$714$	2.38524			0.0892655
$715$	6.29767	−	19.5586i	0.235520	−	0.731451i
$716$	−6.53358			−0.244171
$717$	−9.35420	+	6.79623i	−0.349339	+	0.253810i
$718$	−1.18722	−	3.65389i	−0.0443067	−	0.136362i
$719$	1.49569	−	4.60326i	0.0557798	−	0.171673i	−0.919285	−	0.393592i	$-0.871232\pi$
$719$	1.49569	−	4.60326i	0.0557798	−	0.171673i	0.975065	+	0.221920i	$0.0712322\pi$
$720$	−6.72827	−	4.88838i	−0.250748	−	0.182179i
$721$	−2.98168	−	2.16632i	−0.111044	−	0.0806779i
$722$	−0.103686	+	0.319114i	−0.00385880	+	0.0118762i
$723$	−3.37482	−	10.3866i	−0.125511	−	0.386283i
$724$	−28.9744	+	21.0512i	−1.07683	+	0.782360i
$725$	−8.61869			−0.320090
$726$	−1.15916	−	3.50415i	−0.0430203	−	0.130051i
$727$	39.8974			1.47971			0.739856	−	0.672765i	$-0.234894\pi$
$727$	39.8974			1.47971			0.739856	+	0.672765i	$0.234894\pi$
$728$	−2.38603	+	1.73355i	−0.0884322	+	0.0642497i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	2.36662	−	7.28370i	0.0875925	−	0.269582i
$731$	7.98235	+	5.79952i	0.295238	+	0.214503i
$732$	13.7795	+	10.0114i	0.509306	+	0.370032i
$733$	8.20512	−	25.2527i	0.303063	−	0.932732i	−0.677330	−	0.735679i	$-0.736863\pi$
$733$	8.20512	−	25.2527i	0.303063	−	0.932732i	0.980393	−	0.197052i	$-0.0631369\pi$
$734$	2.11328	+	6.50401i	0.0780026	+	0.240067i
$735$	12.4452	−	9.04199i	0.459049	−	0.333519i
$736$	26.9908			0.994893
$737$	−2.89046	+	8.97687i	−0.106471	+	0.330667i
$738$	−1.44883			−0.0533323
$739$	−4.94872	+	3.59545i	−0.182042	+	0.132261i	−0.675074	−	0.737750i	$-0.735888\pi$
$739$	−4.94872	+	3.59545i	−0.182042	+	0.132261i	0.493033	+	0.870011i	$0.335888\pi$
$740$	14.6819	+	45.1863i	0.539719	+	1.66108i
$741$	−0.768206	+	2.36429i	−0.0282207	+	0.0868545i
$742$	−1.17475	−	0.853504i	−0.0431263	−	0.0313331i
$743$	−12.7683	−	9.27670i	−0.468423	−	0.340329i	0.328403	−	0.944538i	$-0.393489\pi$
$743$	−12.7683	−	9.27670i	−0.468423	−	0.340329i	−0.796826	+	0.604208i	$0.793489\pi$
$744$	−2.32658	+	7.16046i	−0.0852964	+	0.262515i
$745$	12.3648	+	38.0548i	0.453010	+	1.39422i
$746$	10.4213	−	7.57150i	0.381550	−	0.277212i
$747$	−13.4401			−0.491746
$748$	15.2422	+	46.4906i	0.557309	+	1.69986i
$749$	−10.8545			−0.396614
$750$	−2.56349	+	1.86248i	−0.0936054	+	0.0680083i
$751$	−4.02308	−	12.3818i	−0.146804	−	0.451818i	0.850434	−	0.526081i	$-0.176339\pi$
$751$	−4.02308	−	12.3818i	−0.146804	−	0.451818i	−0.997239	+	0.0742638i	$0.976339\pi$
$752$	−11.7518	+	36.1685i	−0.428546	+	1.31893i
$753$	4.02364	+	2.92335i	0.146630	+	0.106533i
$754$	4.80422	+	3.49047i	0.174959	+	0.127115i
$755$	−3.98347	+	12.2599i	−0.144973	+	0.446182i
$756$	0.530485	+	1.63266i	0.0192936	+	0.0593794i
$757$	10.3390	−	7.51176i	0.375779	−	0.273019i	−0.383824	−	0.923406i	$-0.625393\pi$
$757$	10.3390	−	7.51176i	0.375779	−	0.273019i	0.759603	+	0.650387i	$0.225393\pi$
$758$	3.73532			0.135673
$759$	24.0093	−	0.0636886i	0.871481	−	0.00231175i
$760$	3.25063			0.117913
$761$	−16.1178	+	11.7102i	−0.584269	+	0.424496i	−0.840261	−	0.542183i	$-0.817598\pi$
$761$	−16.1178	+	11.7102i	−0.584269	+	0.424496i	0.255992	+	0.966679i	$0.417598\pi$
$762$	−0.409543	−	1.26044i	−0.0148362	−	0.0456611i
$763$	−4.31753	+	13.2880i	−0.156305	+	0.481057i
$764$	10.1658	+	7.38589i	0.367786	+	0.267212i
$765$	−15.7578	−	11.4487i	−0.569725	−	0.413930i
$766$	−2.31502	+	7.12489i	−0.0836450	+	0.257433i
$767$	−1.98076	−	6.09614i	−0.0715210	−	0.220119i
$768$	−6.25690	+	4.54590i	−0.225776	+	0.164036i
$769$	−32.2343			−1.16240			−0.581199	−	0.813762i	$-0.697416\pi$
$769$	−32.2343			−1.16240			−0.581199	+	0.813762i	$0.697416\pi$
$770$	2.04465	+	1.47725i	0.0736840	+	0.0532365i
$771$	−21.7742			−0.784180
$772$	−9.98605	+	7.25529i	−0.359406	+	0.261124i
$773$	−12.9520	−	39.8622i	−0.465852	−	1.43374i	−0.857908	−	0.513803i	$-0.828236\pi$
$773$	−12.9520	−	39.8622i	−0.465852	−	1.43374i	0.392057	−	0.919941i	$-0.371764\pi$
$774$	0.130895	−	0.402854i	0.00470493	−	0.0144803i
$775$	5.65331	+	4.10737i	0.203073	+	0.147541i
$776$	−13.6099	−	9.88818i	−0.488567	−	0.354965i
$777$	2.83904	−	8.73766i	0.101850	−	0.313462i
$778$	−0.694274	−	2.13676i	−0.0248909	−	0.0766064i
$779$	−3.49331	+	2.53804i	−0.125161	+	0.0909347i
$780$	11.6931			0.418681
$781$	−36.3353	+	26.5467i	−1.30018	+	0.949914i
$782$	18.9843			0.678876
$783$	5.75955	−	4.18456i	0.205829	−	0.149544i
$784$	−6.36558	−	19.5912i	−0.227342	−	0.699687i
$785$	11.6588	−	35.8821i	0.416120	−	1.28069i
$786$	−3.26964	−	2.37554i	−0.116624	−	0.0847325i
$787$	−5.63792	−	4.09619i	−0.200970	−	0.146013i	0.482749	−	0.875759i	$-0.339639\pi$
$787$	−5.63792	−	4.09619i	−0.200970	−	0.146013i	−0.683719	+	0.729746i	$0.739639\pi$
$788$	11.5286	−	35.4814i	0.410689	−	1.26397i
$789$	−4.93642	−	15.1927i	−0.175741	−	0.540876i
$790$	5.63273	−	4.09242i	0.200404	−	0.145602i
$791$	−0.0968051			−0.00344199
$792$	3.49313	−	2.55209i	0.124123	−	0.0906846i
$793$	−22.4339			−0.796650
$794$	−3.31368	+	2.40753i	−0.117598	+	0.0854400i
$795$	3.66416	+	11.2771i	0.129954	+	0.399959i
$796$	2.11221	−	6.50072i	0.0748654	−	0.230412i
$797$	−0.209047	−	0.151882i	−0.00740484	−	0.00537993i	0.584077	−	0.811698i	$-0.301457\pi$
$797$	−0.209047	−	0.151882i	−0.00740484	−	0.00537993i	−0.591482	+	0.806319i	$0.701457\pi$
$798$	−0.246899	−	0.179383i	−0.00874014	−	0.00635008i
$799$	−27.5232	+	84.7076i	−0.973700	+	2.99674i
$800$	−1.39484	−	4.29288i	−0.0493150	−	0.151776i
$801$	−7.02058	+	5.10075i	−0.248060	+	0.180226i
$802$	5.31904			0.187822
$803$	−24.6223	−	17.7895i	−0.868900	−	0.627778i
$804$	−5.36682			−0.189273
$805$	−13.2749	+	9.64481i	−0.467880	+	0.339935i
$806$	−1.48782	−	4.57905i	−0.0524063	−	0.161290i
$807$	−8.76530	+	26.9768i	−0.308553	+	0.949629i
$808$	7.82002	+	5.68158i	0.275107	+	0.199877i
$809$	−7.58656	−	5.51196i	−0.266729	−	0.193790i	0.446379	−	0.894844i	$-0.352713\pi$
$809$	−7.58656	−	5.51196i	−0.266729	−	0.193790i	−0.713108	+	0.701054i	$0.752713\pi$
$810$	−0.258398	+	0.795267i	−0.00907918	+	0.0279428i
$811$	9.69501	+	29.8382i	0.340438	+	1.04776i	0.963981	+	0.265971i	$0.0856925\pi$
$811$	9.69501	+	29.8382i	0.340438	+	1.04776i	−0.623543	+	0.781789i	$0.714308\pi$
$812$	9.88733	−	7.18357i	0.346977	−	0.252094i
$813$	22.2248			0.779457
$814$	−11.2409	+	0.0298183i	−0.393992	+	0.00104513i
$815$	−9.59911			−0.336242
$816$	−21.1012	+	15.3309i	−0.738689	+	0.536689i
$817$	−0.390108	−	1.20063i	−0.0136481	−	0.0420047i
$818$	−2.13899	+	6.58315i	−0.0747882	+	0.230174i
$819$	−1.82926	−	1.32904i	−0.0639196	−	0.0464403i
$820$	16.4313	+	11.9381i	0.573807	+	0.416895i
$821$	−14.5043	+	44.6397i	−0.506204	+	1.55794i	0.292532	+	0.956256i	$0.405502\pi$
$821$	−14.5043	+	44.6397i	−0.506204	+	1.55794i	−0.798737	+	0.601681i	$0.794498\pi$
$822$	0.480405	+	1.47853i	0.0167560	+	0.0515698i
$823$	10.8974	−	7.91742i	0.379859	−	0.275984i	−0.381428	−	0.924398i	$-0.624568\pi$
$823$	10.8974	−	7.91742i	0.379859	−	0.275984i	0.761287	+	0.648415i	$0.224568\pi$
$824$	−5.28543			−0.184127
$825$	−1.25089	−	3.81538i	−0.0435504	−	0.132834i
$826$	0.786893			0.0273795
$827$	13.9279	−	10.1192i	0.484319	−	0.351878i	−0.318676	−	0.947864i	$-0.603238\pi$
$827$	13.9279	−	10.1192i	0.484319	−	0.351878i	0.802995	+	0.595985i	$0.203238\pi$
$828$	4.22215	+	12.9945i	0.146730	+	0.451588i
$829$	7.44421	−	22.9109i	0.258548	−	0.795729i	−0.734562	−	0.678542i	$-0.762612\pi$
$829$	7.44421	−	22.9109i	0.258548	−	0.795729i	0.993110	−	0.117187i	$-0.0373878\pi$
$830$	−9.09212	−	6.60581i	−0.315592	−	0.229291i
$831$	−0.661635	−	0.480706i	−0.0229519	−	0.0166755i
$832$	4.16621	−	12.8223i	0.144437	−	0.444533i
$833$	−14.9084	−	45.8833i	−0.516545	−	1.58976i
$834$	0.299355	−	0.217494i	0.0103658	−	0.00753120i
$835$	−10.3540			−0.358314
$836$	1.91860	−	5.95858i	0.0663562	−	0.206082i
$837$	−5.77211			−0.199513
$838$	3.06477	−	2.22668i	0.105871	−	0.0769195i
$839$	8.13283	+	25.0303i	0.280776	+	0.864141i	0.987633	+	0.156784i	$0.0501126\pi$
$839$	8.13283	+	25.0303i	0.280776	+	0.864141i	−0.706857	+	0.707357i	$0.749887\pi$
$840$	−0.913636	+	2.81188i	−0.0315234	+	0.0970192i
$841$	−17.5418	−	12.7449i	−0.604891	−	0.439479i
$842$	−6.56863	−	4.77239i	−0.226370	−	0.164467i
$843$	0.829920	−	2.55423i	0.0285840	−	0.0879724i
$844$	5.34568	+	16.4523i	0.184006	+	0.566312i
$845$	13.7502	−	9.99008i	0.473020	−	0.343669i
$846$	3.82371			0.131462
$847$	8.06288	−	5.92363i	0.277044	−	0.203538i
$848$	15.8783			0.545262
$849$	15.6781	−	11.3908i	0.538072	−	0.390932i
$850$	−0.981077	−	3.01944i	−0.0336506	−	0.103566i
$851$	22.5960	−	69.5434i	0.774582	−	2.38392i
$852$	−20.7176	−	15.0522i	−0.709772	−	0.515680i
$853$	−29.4040	−	21.3633i	−1.00677	−	0.731464i	−0.0432443	−	0.999065i	$-0.513769\pi$
$853$	−29.4040	−	21.3633i	−1.00677	−	0.731464i	−0.963530	+	0.267600i	$0.913769\pi$
$854$	0.851047	−	2.61925i	0.0291222	−	0.0896290i
$855$	0.770105	+	2.37014i	0.0263370	+	0.0810571i
$856$	−12.5934	+	9.14965i	−0.430434	+	0.312729i
$857$	−21.7298			−0.742274			−0.371137	−	0.928578i	$-0.621032\pi$
$857$	−21.7298			−0.742274			−0.371137	+	0.928578i	$0.621032\pi$
$858$	−0.847913	+	2.63336i	−0.0289473	+	0.0899013i
$859$	20.4025			0.696123			0.348061	−	0.937472i	$-0.386840\pi$
$859$	20.4025			0.696123			0.348061	+	0.937472i	$0.386840\pi$
$860$	−4.80391	+	3.49025i	−0.163812	+	0.119016i
$861$	−1.21363	−	3.73516i	−0.0413603	−	0.127294i
$862$	0.990873	−	3.04959i	0.0337493	−	0.103870i
$863$	−2.17317	−	1.57890i	−0.0739754	−	0.0537463i	0.550183	−	0.835044i	$-0.314558\pi$
$863$	−2.17317	−	1.57890i	−0.0739754	−	0.0537463i	−0.624158	+	0.781298i	$0.714558\pi$
$864$	3.01640	+	2.19154i	0.102620	+	0.0745578i
$865$	−18.3411	+	56.4483i	−0.623618	+	1.91930i
$866$	1.77850	+	5.47367i	0.0604360	+	0.186003i
$867$	−35.6663	+	25.9131i	−1.21129	+	0.880055i
$868$	−9.90890			−0.336330
$869$	−8.60326	−	26.2411i	−0.291846	−	0.890167i
$870$	5.95302			0.201826
$871$	5.71877	−	4.15493i	0.193773	−	0.140784i
$872$	6.19173	+	19.0562i	0.209678	+	0.645324i
$873$	3.98547	−	12.2660i	0.134888	−	0.415142i
$874$	−1.96508	−	1.42772i	−0.0664699	−	0.0482932i
$875$	−6.94890	−	5.04867i	−0.234916	−	0.170676i
$876$	5.34182	−	16.4404i	0.180483	−	0.555470i
$877$	−10.4871	−	32.2760i	−0.354125	−	1.08988i	−0.956515	−	0.291683i	$-0.905785\pi$
$877$	−10.4871	−	32.2760i	−0.354125	−	1.08988i	0.602390	−	0.798202i	$-0.294215\pi$
$878$	1.38607	−	1.00704i	0.0467775	−	0.0339859i
$879$	14.4039			0.485832
$880$	−27.5830	+	0.0731684i	−0.929821	+	0.00246651i
$881$	1.74919			0.0589318			0.0294659	−	0.999566i	$-0.490619\pi$
$881$	1.74919			0.0589318			0.0294659	+	0.999566i	$0.490619\pi$
$882$	−1.67561	+	1.21740i	−0.0564209	+	0.0409922i
$883$	−4.99716	−	15.3797i	−0.168168	−	0.517567i	0.831088	−	0.556141i	$-0.187719\pi$
$883$	−4.99716	−	15.3797i	−0.168168	−	0.517567i	−0.999256	+	0.0385738i	$0.987719\pi$
$884$	11.3322	−	34.8771i	0.381145	−	1.17304i
$885$	−5.19851	−	3.77694i	−0.174746	−	0.126960i
$886$	5.66769	+	4.11782i	0.190410	+	0.138341i
$887$	−10.7122	+	32.9688i	−0.359681	+	1.10698i	0.593564	+	0.804787i	$0.297720\pi$
$887$	−10.7122	+	32.9688i	−0.359681	+	1.10698i	−0.953245	+	0.302198i	$0.902280\pi$
$888$	−4.07144	−	12.5306i	−0.136629	−	0.420499i
$889$	2.90643	−	2.11164i	0.0974784	−	0.0708222i
$890$	−7.25642			−0.243236
$891$	2.68837	+	1.94234i	0.0900637	+	0.0650708i
$892$	49.4265			1.65492
$893$	9.21941	−	6.69829i	0.308516	−	0.224150i
$894$	−1.66478	−	5.12367i	−0.0556786	−	0.171361i
$895$	2.66584	−	8.20460i	0.0891091	−	0.274250i
$896$	6.82610	+	4.95945i	0.228044	+	0.165684i
$897$	−14.5592	−	10.5779i	−0.486117	−	0.353185i
$898$	−2.95482	+	9.09399i	−0.0986035	+	0.303470i
$899$	12.6984	+	39.0816i	0.423514	+	1.30344i
$900$	1.84857	−	1.34306i	0.0616190	−	0.0447688i
$901$	37.1874			1.23889
$902$	−3.88002	+	2.83475i	−0.129190	+	0.0943869i
$903$	1.14822			0.0382104
$904$	−0.112314	+	0.0816007i	−0.00373550	+	0.00271400i
$905$	−14.6130	−	44.9742i	−0.485753	−	1.49499i
$906$	0.536331	−	1.65066i	0.0178184	−	0.0548395i
$907$	27.6465	+	20.0863i	0.917986	+	0.666956i	0.943022	−	0.332731i	$-0.107970\pi$
$907$	27.6465	+	20.0863i	0.917986	+	0.666956i	−0.0250361	+	0.999687i	$0.507970\pi$
$908$	−25.2434	−	18.3404i	−0.837732	−	0.608648i
$909$	−2.28998	+	7.04785i	−0.0759540	+	0.233762i
$910$	−0.584262	−	1.79817i	−0.0193681	−	0.0596089i
$911$	20.7519	−	15.0771i	0.687541	−	0.499528i	−0.188310	−	0.982110i	$-0.560301\pi$
$911$	20.7519	−	15.0771i	0.687541	−	0.499528i	0.875851	+	0.482582i	$0.160301\pi$
$912$	3.33717			0.110505
$913$	−35.9928	+	26.2965i	−1.19119	+	0.870286i
$914$	9.58187			0.316940
$915$	−18.1943	+	13.2189i	−0.601483	+	0.437003i
$916$	−16.1023	−	49.5578i	−0.532035	−	1.63744i
$917$	3.38540	−	10.4192i	0.111796	−	0.344071i
$918$	2.12162	+	1.54145i	0.0700239	+	0.0508753i
$919$	−13.8058	−	10.0305i	−0.455410	−	0.330875i	0.336318	−	0.941749i	$-0.390818\pi$
$919$	−13.8058	−	10.0305i	−0.455410	−	0.330875i	−0.791728	+	0.610874i	$0.790818\pi$
$920$	−7.27167	+	22.3799i	−0.239740	+	0.737844i
$921$	0.0212958	+	0.0655416i	0.000701719	+	0.00215967i
$922$	0.216994	−	0.157656i	0.00714633	−	0.00519211i
$923$	33.7294			1.11022
$924$	4.61508	+	3.33438i	0.151825	+	0.109693i
$925$	−12.2286			−0.402074
$926$	−6.34377	+	4.60902i	−0.208469	+	0.151462i
$927$	−1.25217	−	3.85378i	−0.0411266	−	0.126575i
$928$	8.20246	−	25.2446i	0.269259	−	0.828694i
$929$	−5.74928	−	4.17710i	−0.188628	−	0.137046i	0.489464	−	0.872024i	$-0.337193\pi$
$929$	−5.74928	−	4.17710i	−0.188628	−	0.137046i	−0.678091	+	0.734978i	$0.737193\pi$
$930$	−3.90480	−	2.83701i	−0.128044	−	0.0930291i
$931$	−1.90748	+	5.87062i	−0.0625151	+	0.192402i
$932$	−4.91098	−	15.1144i	−0.160864	−	0.495090i
$933$	6.65529	−	4.83535i	0.217884	−	0.158302i
$934$	0.904718			0.0296033
$935$	−64.6001	+	0.171363i	−2.11265	+	0.00560416i
$936$	−3.24261			−0.105988
$937$	−48.5665	+	35.2857i	−1.58660	+	1.15273i	−0.678001	+	0.735061i	$0.737154\pi$
$937$	−48.5665	+	35.2857i	−1.58660	+	1.15273i	−0.908598	+	0.417671i	$0.862846\pi$
$938$	0.268160	+	0.825312i	0.00875574	+	0.0269474i
$939$	9.39492	−	28.9146i	0.306592	−	0.943592i
$940$	−43.3649	−	31.5064i	−1.41441	−	1.02763i
$941$	−13.6447	−	9.91349i	−0.444806	−	0.323171i	0.342736	−	0.939432i	$-0.388646\pi$
$941$	−13.6447	−	9.91349i	−0.444806	−	0.323171i	−0.787542	+	0.616261i	$0.788646\pi$
$942$	−1.56973	+	4.83113i	−0.0511446	+	0.157407i
$943$	−9.65931	−	29.7283i	−0.314551	−	0.968087i
$944$	−6.96129	+	5.05767i	−0.226571	+	0.164613i
$945$	−2.26668			−0.0737352
$946$	−0.437673	−	1.33496i	−0.0142300	−	0.0434033i
$947$	20.1240			0.653942			0.326971	−	0.945034i	$-0.393972\pi$
$947$	20.1240			0.653942			0.326971	+	0.945034i	$0.393972\pi$
$948$	12.7139	−	9.23721i	0.412929	−	0.300011i
$949$	7.03585	+	21.6541i	0.228393	+	0.702923i
$950$	−0.125526	+	0.386328i	−0.00407259	+	0.0125341i
$951$	23.4277	+	17.0212i	0.759695	+	0.551951i
$952$	7.50156	+	5.45020i	0.243127	+	0.176642i
$953$	−10.8384	+	33.3570i	−0.351089	+	1.08054i	0.607154	+	0.794584i	$0.292311\pi$
$953$	−10.8384	+	33.3570i	−0.351089	+	1.08054i	−0.958243	+	0.285956i	$0.907689\pi$
$954$	−0.493340	−	1.51834i	−0.0159725	−	0.0491582i
$955$	−13.4228	+	9.75221i	−0.434350	+	0.315574i
$956$	−21.8231			−0.705810
$957$	7.23682	−	22.4753i	0.233933	−	0.726524i
$958$	6.47584			0.209225
$959$	−3.40931	+	2.47701i	−0.110092	+	0.0799868i
$960$	−4.17651	−	12.8540i	−0.134796	−	0.414861i
$961$	0.716079	−	2.20386i	0.0230993	−	0.0710924i
$962$	6.81644	+	4.95243i	0.219771	+	0.159673i
$963$	−9.65481	−	7.01463i	−0.311122	−	0.226043i
$964$	6.36970	−	19.6039i	0.205154	−	0.631399i
$965$	−5.03638	−	15.5004i	−0.162127	−	0.498975i
$966$	1.78733	−	1.29857i	0.0575063	−	0.0417808i
$967$	−32.6003			−1.04836			−0.524178	−	0.851609i	$-0.675627\pi$
$967$	−32.6003			−1.04836			−0.524178	+	0.851609i	$0.675627\pi$
$968$	4.36133	−	13.6691i	0.140179	−	0.439342i
$969$	7.81575			0.251078
$970$	8.72493	−	6.33903i	0.280141	−	0.203534i
$971$	14.1133	+	43.4364i	0.452918	+	1.39394i	0.873562	+	0.486713i	$0.161804\pi$
$971$	14.1133	+	43.4364i	0.452918	+	1.39394i	−0.420643	+	0.907226i	$0.638196\pi$
$972$	−0.583244	+	1.79504i	−0.0187075	+	0.0575759i
$973$	0.811466	+	0.589565i	0.0260144	+	0.0189006i
$974$	−3.94182	−	2.86390i	−0.126304	−	0.0917653i
$975$	−0.930012	+	2.86228i	−0.0297842	+	0.0916664i
$976$	9.30614	+	28.6413i	0.297882	+	0.916787i
$977$	−1.62488	+	1.18054i	−0.0519845	+	0.0377690i	−0.613474	−	0.789715i	$-0.710228\pi$
$977$	−1.62488	+	1.18054i	−0.0519845	+	0.0377690i	0.561490	+	0.827484i	$0.310228\pi$
$978$	1.29241			0.0413269
$979$	−8.82130	+	27.3962i	−0.281930	+	0.875587i
$980$	29.0344			0.927470
$981$	−12.4276	+	9.02918i	−0.396783	+	0.288280i
$982$	−1.87057	−	5.75701i	−0.0596922	−	0.183714i
$983$	6.05736	−	18.6426i	0.193200	−	0.594608i	−0.806793	−	0.590834i	$-0.798799\pi$
$983$	6.05736	−	18.6426i	0.193200	−	0.594608i	0.999993	−	0.00377358i	$-0.00120117\pi$
$984$	−4.55656	−	3.31054i	−0.145258	−	0.105536i
$985$	39.8522	+	28.9543i	1.26980	+	0.922561i
$986$	5.76930	−	17.7561i	0.183732	−	0.565468i
$987$	3.20296	+	9.85768i	0.101951	+	0.313774i
$988$	−3.79595	+	2.75792i	−0.120765	+	0.0877411i
$989$	9.13874			0.290595
$990$	0.864003	+	2.63532i	0.0274598	+	0.0837560i
$991$	45.3764			1.44143			0.720714	−	0.693232i	$-0.243814\pi$
$991$	45.3764			1.44143			0.720714	+	0.693232i	$0.243814\pi$
$992$	−17.4110	+	12.6498i	−0.552800	+	0.401633i
$993$	−0.760888	−	2.34177i	−0.0241461	−	0.0743139i
$994$	−1.27955	+	3.93806i	−0.0405850	+	0.124908i
$995$	7.30152	+	5.30486i	0.231474	+	0.168176i
$996$	−20.5223	−	14.9103i	−0.650274	−	0.472452i
$997$	1.01618	−	3.12749i	0.0321829	−	0.0990486i	−0.933675	−	0.358122i	$-0.883417\pi$
$997$	1.01618	−	3.12749i	0.0321829	−	0.0990486i	0.965858	+	0.259073i	$0.0834172\pi$
$998$	2.27122	+	6.99010i	0.0718942	+	0.221268i
$999$	8.17190	−	5.93724i	0.258548	−	0.187846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.j.a.58.3	✓	24
11.2	odd	10		6897.2.a.bg.1.7		12
11.4	even	5	inner	627.2.j.a.400.3	yes	24
11.9	even	5		6897.2.a.bf.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.j.a.58.3	✓	24	1.1	even	1	trivial
627.2.j.a.400.3	yes	24	11.4	even	5	inner
6897.2.a.bf.1.6		12	11.9	even	5
6897.2.a.bg.1.7		12	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.271454 - 0.197223i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.583244 + 1.79504i) q^{4} +(-2.01616 - 1.46483i) q^{5} +(0.271454 + 0.197223i) q^{6} +(-0.281064 + 0.865027i) q^{7} +(0.403072 + 1.24053i) q^{8} +(-0.809017 + 0.587785i) q^{9} -0.836193 q^{10} +(-1.01652 + 3.15701i) q^{11} -1.88742 q^{12} +(2.01119 - 1.46121i) q^{13} +(0.0943071 + 0.290248i) q^{14} +(0.770105 - 2.37014i) q^{15} +(-2.69983 - 1.96154i) q^{16} +(-6.32308 - 4.59398i) q^{17} +(-0.103686 + 0.319114i) q^{18} +(0.309017 + 0.951057i) q^{19} +(3.80534 - 2.76474i) q^{20} -0.909543 q^{21} +(0.346695 + 1.05746i) q^{22} -7.23909 q^{23} +(-1.05526 + 0.766688i) q^{24} +(0.374105 + 1.15138i) q^{25} +(0.257761 - 0.793306i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.38883 - 1.00904i) q^{28} +(-2.19995 + 6.77075i) q^{29} +(-0.258398 - 0.795267i) q^{30} +(4.66974 - 3.39276i) q^{31} -3.72848 q^{32} +(-3.31661 + 0.00879787i) q^{33} -2.62247 q^{34} +(1.83379 - 1.33232i) q^{35} +(-0.583244 - 1.79504i) q^{36} +(-3.12139 + 9.60665i) q^{37} +(0.271454 + 0.197223i) q^{38} +(2.01119 + 1.46121i) q^{39} +(1.00450 - 3.09153i) q^{40} +(1.33433 + 4.10663i) q^{41} +(-0.246899 + 0.179383i) q^{42} -1.26242 q^{43} +(-5.07407 - 3.66600i) q^{44} +2.49211 q^{45} +(-1.96508 + 1.42772i) q^{46} +(-3.52150 - 10.8381i) q^{47} +(1.03124 - 3.17384i) q^{48} +(4.99384 + 3.62824i) q^{49} +(0.328630 + 0.238764i) q^{50} +(2.41520 - 7.43322i) q^{51} +(1.44992 + 4.46241i) q^{52} +(-3.84930 + 2.79668i) q^{53} -0.335536 q^{54} +(6.67394 - 4.87600i) q^{55} -1.18638 q^{56} +(-0.809017 + 0.587785i) q^{57} +(0.738163 + 2.27183i) q^{58} +(0.796776 - 2.45222i) q^{59} +(3.80534 + 2.76474i) q^{60} +(-7.30073 - 5.30429i) q^{61} +(0.598489 - 1.84196i) q^{62} +(-0.281064 - 0.865027i) q^{63} +(4.38754 - 3.18774i) q^{64} -6.19531 q^{65} +(-0.898574 + 0.656501i) q^{66} +2.84348 q^{67} +(11.9343 - 8.67076i) q^{68} +(-2.23700 - 6.88479i) q^{69} +(0.235024 - 0.723330i) q^{70} +(10.9767 + 7.97503i) q^{71} +(-1.05526 - 0.766688i) q^{72} +(-2.83023 + 8.71055i) q^{73} +(1.04734 + 3.22338i) q^{74} +(-0.979419 + 0.711589i) q^{75} -1.88742 q^{76} +(-2.44519 - 1.76664i) q^{77} +0.834131 q^{78} +(-6.73616 + 4.89411i) q^{79} +(2.56997 + 7.90956i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.17213 + 0.851604i) q^{82} +(10.8732 + 7.89986i) q^{83} +(0.530485 - 1.63266i) q^{84} +(6.01895 + 18.5244i) q^{85} +(-0.342688 + 0.248977i) q^{86} -7.11919 q^{87} +(-4.32608 + 0.0114757i) q^{88} +8.67792 q^{89} +(0.676495 - 0.491502i) q^{90} +(0.698716 + 2.15043i) q^{91} +(4.22215 - 12.9945i) q^{92} +(4.66974 + 3.39276i) q^{93} +(-3.09344 - 2.24752i) q^{94} +(0.770105 - 2.37014i) q^{95} +(-1.15216 - 3.54599i) q^{96} +(-10.4341 + 7.58082i) q^{97} +2.07117 q^{98} +(-1.03326 - 3.15157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 6 q^{3} - 5 q^{4} + 8 q^{5} + 3 q^{6} + q^{7} + 5 q^{8} - 6 q^{9} + 2 q^{10} - 10 q^{11} + 10 q^{12} + 6 q^{13} + 12 q^{14} - 2 q^{15} + 11 q^{16} - 8 q^{17} - 2 q^{18} - 6 q^{19} + 9 q^{20}+ \cdots - 22 q^{98}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 5 * q^4 + 8 * q^5 + 3 * q^6 + q^7 + 5 * q^8 - 6 * q^9 + 2 * q^10 - 10 * q^11 + 10 * q^12 + 6 * q^13 + 12 * q^14 - 2 * q^15 + 11 * q^16 - 8 * q^17 - 2 * q^18 - 6 * q^19 + 9 * q^20 - 4 * q^21 + 4 * q^22 - 32 * q^23 - 5 * q^24 + 28 * q^25 - 23 * q^26 - 6 * q^27 + 4 * q^28 + 7 * q^29 - 3 * q^30 + 20 * q^31 + 8 * q^32 + 10 * q^33 - 66 * q^34 - 22 * q^35 - 5 * q^36 + q^37 + 3 * q^38 + 6 * q^39 - 2 * q^40 - 2 * q^41 - 8 * q^42 + 28 * q^43 - 40 * q^44 - 12 * q^45 - 35 * q^46 + 25 * q^47 + 6 * q^48 + 25 * q^49 - 18 * q^50 + 2 * q^51 + q^52 + 2 * q^53 - 2 * q^54 - 31 * q^55 - 32 * q^56 - 6 * q^57 + 14 * q^58 + 37 * q^59 + 9 * q^60 - 21 * q^61 - 61 * q^62 + q^63 + 5 * q^64 - 28 * q^65 + 14 * q^66 - 76 * q^67 + 16 * q^68 + 28 * q^69 - 31 * q^70 + 42 * q^71 - 5 * q^72 - 44 * q^73 + 56 * q^74 - 12 * q^75 + 10 * q^76 + 28 * q^77 - 8 * q^78 - 43 * q^79 + 21 * q^80 - 6 * q^81 + 28 * q^82 + 26 * q^83 - q^84 + 4 * q^85 - 52 * q^86 + 2 * q^87 + 39 * q^88 - 6 * q^89 + 2 * q^90 + 53 * q^91 + 11 * q^92 + 20 * q^93 - 6 * q^94 - 2 * q^95 - 17 * q^96 + 11 * q^97 - 22 * q^98

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