LMFDB - Embedded newform 220.2.r.d.151.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(51,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			151.10
Character	$\chi$	$=$	220.151
Dual form			220.2.r.d.51.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.893756 + 1.09599i) q^{2} +(2.27074 - 0.737810i) q^{3} +(-0.402399 + 1.95910i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.83813 + 1.82930i) q^{6} +(0.461886 - 1.42154i) q^{7} +(-2.50681 + 1.30993i) q^{8} +(2.18487 - 1.58740i) q^{9} +(-0.0788559 - 1.41201i) q^{10} +(1.72348 + 2.83366i) q^{11} +(0.531698 + 4.74551i) q^{12} +(-1.61471 - 2.22245i) q^{13} +(1.97081 - 0.764287i) q^{14} +(-2.27074 - 0.737810i) q^{15} +(-3.67615 - 1.57668i) q^{16} +(-3.56124 + 4.90162i) q^{17} +(3.69251 + 0.975849i) q^{18} +(-1.25160 - 3.85204i) q^{19} +(1.47708 - 1.34842i) q^{20} -3.56874i q^{21} +(-1.56530 + 4.42152i) q^{22} -7.20345i q^{23} +(-4.72584 + 4.82407i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.992638 - 3.75604i) q^{26} +(-0.420118 + 0.578243i) q^{27} +(2.59908 + 1.47691i) q^{28} +(1.78189 + 0.578971i) q^{29} +(-1.22086 - 3.14814i) q^{30} +(-0.545968 - 0.751461i) q^{31} +(-1.55755 - 5.43820i) q^{32} +(6.00428 + 5.16291i) q^{33} +(-8.55502 + 0.477767i) q^{34} +(-1.20923 + 0.878560i) q^{35} +(2.23068 + 4.91914i) q^{36} +(-2.08272 + 6.40994i) q^{37} +(3.10318 - 4.81453i) q^{38} +(-5.30634 - 3.85528i) q^{39} +(2.79801 + 0.413706i) q^{40} +(-3.96497 + 1.28830i) q^{41} +(3.91131 - 3.18958i) q^{42} -5.04924 q^{43} +(-6.24495 + 2.23621i) q^{44} -2.70064 q^{45} +(7.89493 - 6.43813i) q^{46} +(8.50853 - 2.76459i) q^{47} +(-9.51089 - 0.867940i) q^{48} +(3.85568 + 2.80132i) q^{49} +(-0.766165 + 1.18869i) q^{50} +(-4.47019 + 13.7578i) q^{51} +(5.00377 - 2.26906i) q^{52} +(6.02442 - 4.37700i) q^{53} +(-1.00923 + 0.0563621i) q^{54} +(0.271257 - 3.30551i) q^{55} +(0.704262 + 4.16857i) q^{56} +(-5.68414 - 7.82355i) q^{57} +(0.958027 + 2.47039i) q^{58} +(11.1961 + 3.63782i) q^{59} +(2.35919 - 4.15172i) q^{60} +(1.84322 - 2.53697i) q^{61} +(0.335633 - 1.27000i) q^{62} +(-1.24739 - 3.83907i) q^{63} +(4.56816 - 6.56749i) q^{64} +2.74711i q^{65} +(-0.292147 + 11.1950i) q^{66} -11.6402i q^{67} +(-8.16973 - 8.94923i) q^{68} +(-5.31478 - 16.3572i) q^{69} +(-2.04366 - 0.540093i) q^{70} +(-7.69755 + 10.5948i) q^{71} +(-3.39765 + 6.84132i) q^{72} +(-7.42303 - 2.41189i) q^{73} +(-8.88669 + 3.44628i) q^{74} +(1.40340 + 1.93161i) q^{75} +(8.05017 - 0.901959i) q^{76} +(4.82421 - 1.14117i) q^{77} +(-0.517215 - 9.26139i) q^{78} +(-3.96666 + 2.88195i) q^{79} +(2.04732 + 3.43635i) q^{80} +(-3.03098 + 9.32840i) q^{81} +(-4.95569 - 3.19416i) q^{82} +(2.82727 + 2.05413i) q^{83} +(6.99152 + 1.43606i) q^{84} +(5.76220 - 1.87225i) q^{85} +(-4.51279 - 5.53393i) q^{86} +4.47338 q^{87} +(-8.03233 - 4.84579i) q^{88} +4.08661 q^{89} +(-2.41372 - 2.95988i) q^{90} +(-3.90512 + 1.26885i) q^{91} +(14.1123 + 2.89866i) q^{92} +(-1.79419 - 1.30355i) q^{93} +(10.6345 + 6.85442i) q^{94} +(-1.25160 + 3.85204i) q^{95} +(-7.54916 - 11.1996i) q^{96} +(12.0540 - 8.75773i) q^{97} +(0.375818 + 6.72949i) q^{98} +(8.26371 + 3.45531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{5} + 20 q^{6} + 16 q^{9} + 14 q^{12} - 10 q^{13} - 21 q^{14} - 4 q^{16} - 25 q^{18} + 5 q^{20} + 15 q^{22} - 30 q^{24} - 12 q^{25} - 4 q^{26} - 60 q^{28} + 20 q^{29} - 10 q^{33} - 18 q^{34}+ \cdots + 38 q^{97}+O(q^{100}) $ 48 * q - 12 * q^5 + 20 * q^6 + 16 * q^9 + 14 * q^12 - 10 * q^13 - 21 * q^14 - 4 * q^16 - 25 * q^18 + 5 * q^20 + 15 * q^22 - 30 * q^24 - 12 * q^25 - 4 * q^26 - 60 * q^28 + 20 * q^29 - 10 * q^33 - 18 * q^34 + 66 * q^36 - 44 * q^37 + 11 * q^38 - 10 * q^41 + 19 * q^42 - 35 * q^44 - 44 * q^45 + 5 * q^46 + 41 * q^48 - 2 * q^49 + 50 * q^52 - 36 * q^53 - 28 * q^56 + 30 * q^57 - 38 * q^58 - 21 * q^60 + 36 * q^64 + 43 * q^66 - 65 * q^68 + 24 * q^69 - 21 * q^70 - 60 * q^72 - 20 * q^73 - 70 * q^74 + 16 * q^77 - 56 * q^78 + q^80 + 50 * q^81 + 35 * q^82 + 60 * q^84 + 10 * q^85 + 38 * q^86 - 101 * q^88 + 64 * q^89 + 70 * q^92 - 28 * q^93 + 130 * q^94 + 105 * q^96 + 38 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

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 $

$2$	0.893756	+	1.09599i	0.631981	+	0.774984i
$2$	0.893756	+	1.09599i	0.631981	+	0.774984i
$3$	2.27074	−	0.737810i	1.31101	−	0.425975i	0.431615	−	0.902058i	$-0.357944\pi$
$3$	2.27074	−	0.737810i	1.31101	−	0.425975i	0.879400	+	0.476084i	$0.157944\pi$
$4$	−0.402399	+	1.95910i	−0.201200	+	0.979550i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	2.83813	+	1.82930i	1.15866	+	0.746807i
$7$	0.461886	−	1.42154i	0.174577	−	0.537292i	−0.825037	−	0.565078i	$-0.808846\pi$
$7$	0.461886	−	1.42154i	0.174577	−	0.537292i	0.999614	+	0.0277867i	$0.00884592\pi$
$8$	−2.50681	+	1.30993i	−0.886290	+	0.463131i
$9$	2.18487	−	1.58740i	0.728288	−	0.529133i
$10$	−0.0788559	−	1.41201i	−0.0249364	−	0.446518i
$11$	1.72348	+	2.83366i	0.519649	+	0.854380i
$11$	1.72348	+	2.83366i	0.519649	+	0.854380i
$12$	0.531698	+	4.74551i	0.153488	+	1.36991i
$13$	−1.61471	−	2.22245i	−0.447839	−	0.616398i	0.524092	−	0.851662i	$-0.324405\pi$
$13$	−1.61471	−	2.22245i	−0.447839	−	0.616398i	−0.971932	+	0.235263i	$0.924405\pi$
$14$	1.97081	−	0.764287i	0.526721	−	0.204264i
$15$	−2.27074	−	0.737810i	−0.586304	−	0.190502i
$16$	−3.67615	−	1.57668i	−0.919037	−	0.394170i
$17$	−3.56124	+	4.90162i	−0.863727	+	1.18882i	0.116941	+	0.993139i	$0.462691\pi$
$17$	−3.56124	+	4.90162i	−0.863727	+	1.18882i	−0.980668	+	0.195679i	$0.937309\pi$
$18$	3.69251	+	0.975849i	0.870334	+	0.230010i
$19$	−1.25160	−	3.85204i	−0.287137	−	0.883718i	−0.985750	−	0.168218i	$-0.946199\pi$
$19$	−1.25160	−	3.85204i	−0.287137	−	0.883718i	0.698612	−	0.715500i	$-0.253801\pi$
$20$	1.47708	−	1.34842i	0.330285	−	0.301516i
$21$		−	3.56874i		−	0.778763i
$22$	−1.56530	+	4.42152i	−0.333722	+	0.942671i
$23$		−	7.20345i		−	1.50202i	−0.660289	−	0.751012i	$-0.729566\pi$
$23$		−	7.20345i		−	1.50202i	0.660289	−	0.751012i	$-0.270434\pi$
$24$	−4.72584	+	4.82407i	−0.964657	+	0.984708i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.992638	−	3.75604i	0.194672	−	0.736620i
$27$	−0.420118	+	0.578243i	−0.0808518	+	0.111283i
$28$	2.59908	+	1.47691i	0.491179	+	0.279109i
$29$	1.78189	+	0.578971i	0.330888	+	0.107512i	0.469750	−	0.882800i	$-0.344344\pi$
$29$	1.78189	+	0.578971i	0.330888	+	0.107512i	−0.138861	+	0.990312i	$0.544344\pi$
$30$	−1.22086	−	3.14814i	−0.222897	−	0.574769i
$31$	−0.545968	−	0.751461i	−0.0980588	−	0.134966i	0.757168	−	0.653220i	$-0.226582\pi$
$31$	−0.545968	−	0.751461i	−0.0980588	−	0.134966i	−0.855227	+	0.518254i	$0.826582\pi$
$32$	−1.55755	−	5.43820i	−0.275339	−	0.961347i
$33$	6.00428	+	5.16291i	1.04521	+	0.898748i
$34$	−8.55502	+	0.477767i	−1.46717	+	0.0819364i
$35$	−1.20923	+	0.878560i	−0.204398	+	0.148504i
$36$	2.23068	+	4.91914i	0.371781	+	0.819856i
$37$	−2.08272	+	6.40994i	−0.342396	+	1.05379i	0.620566	+	0.784154i	$0.286903\pi$
$37$	−2.08272	+	6.40994i	−0.342396	+	1.05379i	−0.962963	+	0.269634i	$0.913097\pi$
$38$	3.10318	−	4.81453i	0.503402	−	0.781020i
$39$	−5.30634	−	3.85528i	−0.849694	−	0.617339i
$40$	2.79801	+	0.413706i	0.442404	+	0.0654127i
$41$	−3.96497	+	1.28830i	−0.619225	+	0.201198i	−0.601796	−	0.798650i	$-0.705548\pi$
$41$	−3.96497	+	1.28830i	−0.619225	+	0.201198i	−0.0174288	+	0.999848i	$0.505548\pi$
$42$	3.91131	−	3.18958i	0.603528	−	0.492163i
$43$	−5.04924			−0.770002			−0.385001	−	0.922916i	$-0.625799\pi$
$43$	−5.04924			−0.770002			−0.385001	+	0.922916i	$0.625799\pi$
$44$	−6.24495	+	2.23621i	−0.941461	+	0.337121i
$45$	−2.70064			−0.402588
$46$	7.89493	−	6.43813i	1.16404	−	0.949251i
$47$	8.50853	−	2.76459i	1.24110	−	0.403257i	0.386374	−	0.922342i	$-0.373727\pi$
$47$	8.50853	−	2.76459i	1.24110	−	0.403257i	0.854722	+	0.519085i	$0.173727\pi$
$48$	−9.51089	−	0.867940i	−1.37278	−	0.125276i
$49$	3.85568	+	2.80132i	0.550812	+	0.400188i
$50$	−0.766165	+	1.18869i	−0.108352	+	0.168107i
$51$	−4.47019	+	13.7578i	−0.625952	+	1.92648i
$52$	5.00377	−	2.26906i	0.693898	−	0.314662i
$53$	6.02442	−	4.37700i	0.827518	−	0.601227i	−0.0913378	−	0.995820i	$-0.529114\pi$
$53$	6.02442	−	4.37700i	0.827518	−	0.601227i	0.918856	+	0.394593i	$0.129114\pi$
$54$	−1.00923	+	0.0563621i	−0.137339	+	0.00766991i
$55$	0.271257	−	3.30551i	0.0365763	−	0.445715i
$56$	0.704262	+	4.16857i	0.0941109	+	0.557048i
$57$	−5.68414	−	7.82355i	−0.752883	−	1.03625i
$58$	0.958027	+	2.47039i	0.125795	+	0.324379i
$59$	11.1961	+	3.63782i	1.45760	+	0.473604i	0.927337	−	0.374227i	$-0.122092\pi$
$59$	11.1961	+	3.63782i	1.45760	+	0.473604i	0.530267	+	0.847831i	$0.322092\pi$
$60$	2.35919	−	4.15172i	0.304570	−	0.535985i
$61$	1.84322	−	2.53697i	0.236000	−	0.324826i	−0.674547	−	0.738232i	$-0.735661\pi$
$61$	1.84322	−	2.53697i	0.236000	−	0.324826i	0.910547	+	0.413406i	$0.135661\pi$
$62$	0.335633	−	1.27000i	0.0426254	−	0.161290i
$63$	−1.24739	−	3.83907i	−0.157156	−	0.483677i
$64$	4.56816	−	6.56749i	0.571019	−	0.820937i
$65$			2.74711i			0.340736i
$66$	−0.292147	+	11.1950i	−0.0359608	+	1.37801i
$67$		−	11.6402i		−	1.42207i	−0.703155	−	0.711036i	$-0.748226\pi$
$67$		−	11.6402i		−	1.42207i	0.703155	−	0.711036i	$-0.251774\pi$
$68$	−8.16973	−	8.94923i	−0.990725	−	1.08525i
$69$	−5.31478	−	16.3572i	−0.639824	−	1.96918i
$70$	−2.04366	−	0.540093i	−0.244264	−	0.0645535i
$71$	−7.69755	+	10.5948i	−0.913532	+	1.25737i	0.0524146	+	0.998625i	$0.483308\pi$
$71$	−7.69755	+	10.5948i	−0.913532	+	1.25737i	−0.965946	+	0.258743i	$0.916692\pi$
$72$	−3.39765	+	6.84132i	−0.400417	+	0.806258i
$73$	−7.42303	−	2.41189i	−0.868800	−	0.282290i	−0.159501	−	0.987198i	$-0.550988\pi$
$73$	−7.42303	−	2.41189i	−0.868800	−	0.282290i	−0.709299	+	0.704908i	$0.750988\pi$
$74$	−8.88669	+	3.44628i	−1.03306	+	0.400622i
$75$	1.40340	+	1.93161i	0.162050	+	0.223043i
$76$	8.05017	−	0.901959i	0.923418	−	0.103462i
$77$	4.82421	−	1.14117i	0.549770	−	0.130048i
$78$	−0.517215	−	9.26139i	−0.0585631	−	1.04865i
$79$	−3.96666	+	2.88195i	−0.446284	+	0.324244i	−0.788127	−	0.615513i	$-0.788949\pi$
$79$	−3.96666	+	2.88195i	−0.446284	+	0.324244i	0.341843	+	0.939757i	$0.388949\pi$
$80$	2.04732	+	3.43635i	0.228897	+	0.384195i
$81$	−3.03098	+	9.32840i	−0.336776	+	1.03649i
$82$	−4.95569	−	3.19416i	−0.547264	−	0.352736i
$83$	2.82727	+	2.05413i	0.310333	+	0.225470i	0.732039	−	0.681262i	$-0.238569\pi$
$83$	2.82727	+	2.05413i	0.310333	+	0.225470i	−0.421706	+	0.906732i	$0.638569\pi$
$84$	6.99152	+	1.43606i	0.762837	+	0.156687i
$85$	5.76220	−	1.87225i	0.624998	−	0.203074i
$86$	−4.51279	−	5.53393i	−0.486627	−	0.596739i
$87$	4.47338			0.479597
$88$	−8.03233	−	4.84579i	−0.856249	−	0.516563i
$89$	4.08661			0.433180			0.216590	−	0.976263i	$-0.430507\pi$
$89$	4.08661			0.433180			0.216590	+	0.976263i	$0.430507\pi$
$90$	−2.41372	−	2.95988i	−0.254428	−	0.311999i
$91$	−3.90512	+	1.26885i	−0.409368	+	0.133012i
$92$	14.1123	+	2.89866i	1.47131	+	0.302207i
$93$	−1.79419	−	1.30355i	−0.186049	−	0.135172i
$94$	10.6345	+	6.85442i	1.09687	+	0.706979i
$95$	−1.25160	+	3.85204i	−0.128412	+	0.395211i
$96$	−7.54916	−	11.1996i	−0.770483	−	1.14305i
$97$	12.0540	−	8.75773i	1.22390	−	0.889212i	0.227478	−	0.973783i	$-0.426952\pi$
$97$	12.0540	−	8.75773i	1.22390	−	0.889212i	0.996417	+	0.0845708i	$0.0269519\pi$
$98$	0.375818	+	6.72949i	0.0379633	+	0.679781i
$99$	8.26371	+	3.45531i	0.830534	+	0.347272i
$100$	−1.98756	+	0.222691i	−0.198756	+	0.0222691i
$101$	3.03294	+	4.17448i	0.301789	+	0.415376i	0.932798	−	0.360398i	$-0.117359\pi$
$101$	3.03294	+	4.17448i	0.301789	+	0.415376i	−0.631010	+	0.775775i	$0.717359\pi$
$102$	−19.0738	+	7.39686i	−1.88858	+	0.732398i
$103$	−1.08769	−	0.353411i	−0.107173	−	0.0348226i	0.254940	−	0.966957i	$-0.417944\pi$
$103$	−1.08769	−	0.353411i	−0.107173	−	0.0348226i	−0.362113	+	0.932134i	$0.617944\pi$
$104$	6.95902	+	3.45611i	0.682389	+	0.338899i
$105$	−2.09765	+	2.88717i	−0.204710	+	0.281759i
$106$	10.1815	+	2.69075i	0.988917	+	0.261349i
$107$	5.74489	+	17.6809i	0.555379	+	1.70928i	0.694940	+	0.719068i	$0.255431\pi$
$107$	5.74489	+	17.6809i	0.555379	+	1.70928i	−0.139561	+	0.990214i	$0.544569\pi$
$108$	−0.963781	−	1.05574i	−0.0927399	−	0.101588i
$109$			14.8856i			1.42578i	0.701277	+	0.712889i	$0.252614\pi$
$109$			14.8856i			1.42578i	−0.701277	+	0.712889i	$0.747386\pi$
$110$	3.86526	−	2.65703i	0.368538	−	0.253338i
$111$			16.0920i			1.52738i
$112$	−3.93928	+	4.49755i	−0.372227	+	0.424978i
$113$	−0.147163	−	0.452920i	−0.0138439	−	0.0426071i	0.943896	−	0.330243i	$-0.107131\pi$
$113$	−0.147163	−	0.452920i	−0.0138439	−	0.0426071i	−0.957740	+	0.287636i	$0.907131\pi$
$114$	3.49431	−	13.2221i	0.327272	−	1.23836i
$115$	−4.23408	+	5.82772i	−0.394830	+	0.543437i
$116$	−1.85129	+	3.25792i	−0.171888	+	0.302490i
$117$	−7.05584	−	2.29258i	−0.652312	−	0.211949i
$118$	6.01953	+	15.5221i	0.554143	+	1.42893i
$119$	5.32296	+	7.32643i	0.487955	+	0.671613i
$120$	6.65880	−	1.12498i	0.607862	−	0.102696i
$121$	−5.05923	+	9.76751i	−0.459930	+	0.887955i
$122$	4.42789	−	0.247281i	0.400882	−	0.0223878i
$123$	−8.05292	+	5.85079i	−0.726108	+	0.527548i
$124$	1.69188	−	0.767219i	0.151936	−	0.0688983i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	3.09273	−	4.79832i	0.275522	−	0.427469i
$127$	−12.8617	−	9.34455i	−1.14129	−	0.829194i	−0.153990	−	0.988072i	$-0.549212\pi$
$127$	−12.8617	−	9.34455i	−1.14129	−	0.829194i	−0.987298	+	0.158878i	$0.949212\pi$
$128$	11.2807	−	0.863075i	0.997086	−	0.0762857i
$129$	−11.4655	+	3.72538i	−1.00948	+	0.328001i
$130$	−3.01081	+	2.45524i	−0.264065	+	0.215339i
$131$	8.63344			0.754308			0.377154	−	0.926151i	$-0.376903\pi$
$131$	8.63344			0.754308			0.377154	+	0.926151i	$0.376903\pi$
$132$	−12.5308	+	9.68544i	−1.09066	+	0.843010i
$133$	−6.05392			−0.524942
$134$	12.7575	−	10.4035i	1.10208	−	0.898723i
$135$	0.679766	−	0.220869i	0.0585049	−	0.0190094i
$136$	2.50654	−	16.9524i	0.214934	−	1.45366i
$137$	0.634506	+	0.460995i	0.0542095	+	0.0393855i	0.614560	−	0.788870i	$-0.289334\pi$
$137$	0.634506	+	0.460995i	0.0542095	+	0.0393855i	−0.560351	+	0.828256i	$0.689334\pi$
$138$	13.1773	−	20.4443i	1.12172	−	1.74034i
$139$	2.44161	−	7.51449i	0.207094	−	0.637371i	−0.792527	−	0.609837i	$-0.791235\pi$
$139$	2.44161	−	7.51449i	0.207094	−	0.637371i	0.999621	−	0.0275335i	$-0.00876528\pi$
$140$	−1.23459	−	2.72254i	−0.104342	−	0.230097i
$141$	17.2810	−	12.5553i	1.45532	−	1.05735i
$142$	−18.4915	+	1.03269i	−1.55177	+	0.0866610i
$143$	3.51476	−	8.40589i	0.293919	−	0.702936i
$144$	−10.5347	+	2.39068i	−0.877893	+	0.199223i
$145$	−1.10127	−	1.51576i	−0.0914553	−	0.125877i
$146$	−3.99097	−	10.2912i	−0.330295	−	0.851708i
$147$	10.8221	+	3.51631i	0.892592	+	0.290021i
$148$	−11.7196	−	6.65961i	−0.963348	−	0.547416i
$149$	−12.3098	+	16.9429i	−1.00845	+	1.38802i	−0.0884639	+	0.996079i	$0.528196\pi$
$149$	−12.3098	+	16.9429i	−1.00845	+	1.38802i	−0.919991	+	0.391940i	$0.871804\pi$
$150$	−0.862735	+	3.26450i	−0.0704420	+	0.266545i
$151$	−3.56352	−	10.9674i	−0.289996	−	0.892514i	−0.984857	−	0.173371i	$-0.944534\pi$
$151$	−3.56352	−	10.9674i	−0.289996	−	0.892514i	0.694861	−	0.719144i	$-0.255466\pi$
$152$	8.18343	+	8.01680i	0.663764	+	0.650248i
$153$			16.3625i			1.32283i
$154$	5.56238	+	4.26737i	0.448229	+	0.343875i
$155$			0.928856i			0.0746075i
$156$	9.68814	−	8.84429i	0.775672	−	0.708110i
$157$	0.617240	+	1.89967i	0.0492611	+	0.151610i	0.972661	−	0.232229i	$-0.0746018\pi$
$157$	0.617240	+	1.89967i	0.0492611	+	0.151610i	−0.923400	+	0.383839i	$0.874602\pi$
$158$	−6.70382	−	1.77167i	−0.533327	−	0.140947i
$159$	10.4505	−	14.3839i	0.828781	−	1.14072i
$160$	−1.93641	+	5.31510i	−0.153086	+	0.420196i
$161$	−10.2400	−	3.32718i	−0.807025	−	0.262218i
$162$	−12.9328	+	5.01538i	−1.01610	+	0.394046i
$163$	9.26652	+	12.7543i	0.725810	+	0.998992i	0.999311	+	0.0371201i	$0.0118184\pi$
$163$	9.26652	+	12.7543i	0.725810	+	0.998992i	−0.273501	+	0.961872i	$0.588182\pi$
$164$	−0.928404	−	8.28619i	−0.0724962	−	0.647043i
$165$	−1.82288	−	7.70611i	−0.141911	−	0.599920i
$166$	0.275577	+	4.93456i	0.0213890	+	0.382996i
$167$	14.7402	−	10.7094i	1.14063	−	0.828719i	0.153426	−	0.988160i	$-0.450969\pi$
$167$	14.7402	−	10.7094i	1.14063	−	0.828719i	0.987207	+	0.159441i	$0.0509692\pi$
$168$	4.67481	+	8.94614i	0.360669	+	0.690209i
$169$	1.68520	−	5.18650i	0.129631	−	0.398962i
$170$	7.20198	+	4.64199i	0.552367	+	0.356025i
$171$	−8.84930	−	6.42939i	−0.676723	−	0.491668i
$172$	2.03181	−	9.89198i	0.154924	−	0.754256i
$173$	−1.81105	+	0.588447i	−0.137692	+	0.0447388i	−0.377052	−	0.926192i	$-0.623062\pi$
$173$	−1.81105	+	0.588447i	−0.137692	+	0.0447388i	0.239360	+	0.970931i	$0.423062\pi$
$174$	3.99811	+	4.90279i	0.303096	+	0.371680i
$175$	1.49470			0.112988
$176$	−1.86800	−	13.1343i	−0.140806	−	0.990037i
$177$	28.1074			2.11268
$178$	3.65243	+	4.47889i	0.273761	+	0.335707i
$179$	−8.14680	+	2.64706i	−0.608921	+	0.197850i	−0.597215	−	0.802081i	$-0.703726\pi$
$179$	−8.14680	+	2.64706i	−0.608921	+	0.197850i	−0.0117057	+	0.999931i	$0.503726\pi$
$180$	1.08674	−	5.29083i	0.0810005	−	0.394355i
$181$	−9.25624	−	6.72505i	−0.688011	−	0.499869i	0.187995	−	0.982170i	$-0.439801\pi$
$181$	−9.25624	−	6.72505i	−0.688011	−	0.499869i	−0.876006	+	0.482301i	$0.839801\pi$
$182$	−4.88088	−	3.14594i	−0.361795	−	0.233193i
$183$	2.31367	−	7.12075i	0.171032	−	0.526381i
$184$	9.43604	+	18.0577i	0.695634	+	1.33123i
$185$	5.45262	−	3.96156i	0.400885	−	0.291260i
$186$	−0.174882	−	3.13148i	−0.0128230	−	0.229611i
$187$	−20.0272	−	1.64348i	−1.46454	−	0.120183i
$188$	1.99228	+	17.7815i	0.145302	+	1.29685i
$189$	0.627949	+	0.864298i	0.0456766	+	0.0628684i
$190$	−5.34043	+	2.07104i	−0.387436	+	0.150249i
$191$	−23.3042	−	7.57198i	−1.68623	−	0.547890i	−0.700127	−	0.714019i	$-0.746873\pi$
$191$	−23.3042	−	7.57198i	−1.68623	−	0.547890i	−0.986104	+	0.166129i	$0.946873\pi$
$192$	5.52755	−	18.2835i	0.398917	−	1.31950i
$193$	10.6573	−	14.6685i	0.767127	−	1.05586i	−0.229460	−	0.973318i	$-0.573696\pi$
$193$	10.6573	−	14.6685i	0.767127	−	1.05586i	0.996588	−	0.0825420i	$-0.0263038\pi$
$194$	20.3717	+	5.38379i	1.46260	+	0.386534i
$195$	2.02684	+	6.23797i	0.145145	+	0.446711i
$196$	−7.03958	+	6.42642i	−0.502827	+	0.459030i
$197$			6.00094i			0.427549i	0.976883	+	0.213775i	$0.0685759\pi$
$197$			6.00094i			0.427549i	−0.976883	+	0.213775i	$0.931424\pi$
$198$	3.59875	+	12.1452i	0.255752	+	0.863120i
$199$		−	7.65184i		−	0.542425i	−0.962520	−	0.271212i	$-0.912575\pi$
$199$		−	7.65184i		−	0.542425i	0.962520	−	0.271212i	$-0.0874246\pi$
$200$	−2.02047	−	1.97932i	−0.142868	−	0.139959i
$201$	−8.58823	−	26.4318i	−0.605767	−	1.86436i
$202$	−1.86449	+	7.05505i	−0.131185	+	0.496391i
$203$	1.64606	−	2.26561i	0.115531	−	0.159014i
$204$	−25.1542	−	14.2937i	−1.76115	−	1.00076i
$205$	3.96497	+	1.28830i	0.276926	+	0.0899787i
$206$	−0.584792	−	1.50796i	−0.0407444	−	0.105065i
$207$	−11.4347	−	15.7386i	−0.794770	−	1.09391i
$208$	2.43181	+	10.7160i	0.168615	+	0.743018i
$209$	8.75824	−	10.1855i	0.605820	−	0.704547i
$210$	−5.03911	+	0.281416i	−0.347731	+	0.0194195i
$211$	4.73012	−	3.43663i	0.325635	−	0.236588i	−0.412941	−	0.910758i	$-0.635499\pi$
$211$	4.73012	−	3.43663i	0.325635	−	0.236588i	0.738576	+	0.674170i	$0.235499\pi$
$212$	6.15076	+	13.5638i	0.422436	+	0.931562i
$213$	−9.66225	+	29.7374i	−0.662047	+	2.03757i
$214$	−14.2437	+	22.0988i	−0.973676	+	1.51064i
$215$	4.08492	+	2.96787i	0.278589	+	0.202407i
$216$	0.295696	−	1.99987i	0.0201195	−	0.136074i
$217$	−1.32041	+	0.429026i	−0.0896350	+	0.0291242i
$218$	−16.3145	+	13.3041i	−1.10496	+	0.901065i
$219$	−18.6353			−1.25926
$220$	6.36668	+	1.86156i	0.429241	+	0.125506i
$221$	16.6440			1.11960
$222$	−17.6367	+	14.3823i	−1.18370	+	0.965278i
$223$	−9.42981	+	3.06393i	−0.631467	+	0.205176i	−0.607225	−	0.794530i	$-0.707717\pi$
$223$	−9.42981	+	3.06393i	−0.631467	+	0.205176i	−0.0242422	+	0.999706i	$0.507717\pi$
$224$	−8.45003	−	0.297708i	−0.564592	−	0.0198914i
$225$	2.18487	+	1.58740i	0.145658	+	0.105827i
$226$	0.364869	−	0.566089i	0.0242707	−	0.0376557i
$227$	7.92324	−	24.3852i	0.525884	−	1.61850i	−0.236677	−	0.971588i	$-0.576058\pi$
$227$	7.92324	−	24.3852i	0.525884	−	1.61850i	0.762561	−	0.646916i	$-0.223942\pi$
$228$	17.6144	−	7.98761i	1.16654	−	0.528993i
$229$	−8.52027	+	6.19034i	−0.563036	+	0.409069i	−0.832569	−	0.553922i	$-0.813131\pi$
$229$	−8.52027	+	6.19034i	−0.563036	+	0.409069i	0.269533	+	0.962991i	$0.413131\pi$
$230$	−10.1714	+	0.568035i	−0.670680	+	0.0374551i
$231$	10.1126	−	6.15065i	0.665359	−	0.404683i
$232$	−5.22526	+	0.882786i	−0.343055	+	0.0579577i
$233$	−15.8055	−	21.7544i	−1.03545	−	1.42518i	−0.900775	−	0.434286i	$-0.857001\pi$
$233$	−15.8055	−	21.7544i	−1.03545	−	1.42518i	−0.134676	−	0.990890i	$-0.542999\pi$
$234$	−3.79355	−	9.78215i	−0.247992	−	0.639479i
$235$	−8.50853	−	2.76459i	−0.555035	−	0.180342i
$236$	−11.6321	+	20.4704i	−0.757188	+	1.33251i
$237$	−6.88094	+	9.47081i	−0.446965	+	0.615195i
$238$	−3.27228	+	12.3820i	−0.212110	+	0.802604i
$239$	−5.24581	−	16.1450i	−0.339324	−	1.04433i	−0.964553	−	0.263889i	$-0.914995\pi$
$239$	−5.24581	−	16.1450i	−0.339324	−	1.04433i	0.625229	−	0.780441i	$-0.285005\pi$
$240$	7.18431	+	6.29254i	0.463745	+	0.406181i
$241$			13.2102i			0.850943i	0.904972	+	0.425471i	$0.139892\pi$
$241$			13.2102i			0.850943i	−0.904972	+	0.425471i	$0.860108\pi$
$242$	−15.2268	+	3.18489i	−0.978818	+	0.204733i
$243$			21.2744i			1.36476i
$244$	4.22847	+	4.63192i	0.270700	+	0.296528i
$245$	−1.47274	−	4.53263i	−0.0940899	−	0.289579i
$246$	−13.6098	−	3.59676i	−0.867728	−	0.229321i
$247$	−6.54001	+	9.00155i	−0.416131	+	0.572755i
$248$	2.35300	+	1.16859i	0.149416	+	0.0742052i
$249$	7.93556	+	2.57842i	0.502896	+	0.163401i
$250$	1.31854	−	0.511333i	0.0833916	−	0.0323395i
$251$	−0.369382	−	0.508410i	−0.0233152	−	0.0320906i	0.797200	−	0.603715i	$-0.206313\pi$
$251$	−0.369382	−	0.508410i	−0.0233152	−	0.0320906i	−0.820515	+	0.571624i	$0.806313\pi$
$252$	8.02307	−	0.898923i	0.505406	−	0.0566268i
$253$	20.4121	−	12.4150i	1.28330	−	0.780525i
$254$	−1.25364	−	22.4480i	−0.0786605	−	1.40852i
$255$	11.7031	−	8.50281i	0.732878	−	0.532467i
$256$	11.0282	+	11.5922i	0.689260	+	0.724514i
$257$	5.88838	−	18.1226i	0.367307	−	1.13045i	−0.581217	−	0.813749i	$-0.697423\pi$
$257$	5.88838	−	18.1226i	0.367307	−	1.13045i	0.948524	−	0.316706i	$-0.102577\pi$
$258$	−14.3304	−	9.23656i	−0.892171	−	0.575043i
$259$	8.15001	+	5.92133i	0.506417	+	0.367934i
$260$	−5.38186	−	1.10543i	−0.333768	−	0.0685560i
$261$	4.81224	−	1.56359i	0.297870	−	0.0967839i
$262$	7.71620	+	9.46219i	0.476708	+	0.584576i
$263$	0.265027			0.0163422			0.00817112	−	0.999967i	$-0.497399\pi$
$263$	0.265027			0.0163422			0.00817112	+	0.999967i	$0.497399\pi$
$264$	−21.8146	−	5.07722i	−1.34260	−	0.312481i
$265$	−7.44660			−0.457441
$266$	−5.41073	−	6.63506i	−0.331753	−	0.406821i
$267$	9.27964	−	3.01514i	0.567905	−	0.184524i
$268$	22.8043	+	4.68399i	1.39299	+	0.286120i
$269$	6.21737	+	4.51719i	0.379080	+	0.275418i	0.760966	−	0.648792i	$-0.224725\pi$
$269$	6.21737	+	4.51719i	0.379080	+	0.275418i	−0.381886	+	0.924209i	$0.624725\pi$
$270$	0.849616	+	0.547615i	0.0517060	+	0.0333268i
$271$	1.23235	−	3.79279i	0.0748601	−	0.230396i	−0.906624	−	0.421940i	$-0.861349\pi$
$271$	1.23235	−	3.79279i	0.0748601	−	0.230396i	0.981484	+	0.191544i	$0.0613494\pi$
$272$	20.8199	−	12.4042i	1.26239	−	0.752113i
$273$	−7.93136	+	5.76247i	−0.480028	+	0.348761i
$274$	0.0618460	+	1.10743i	0.00373625	+	0.0669023i
$275$	−2.16238	+	2.51478i	−0.130397	+	0.151647i
$276$	34.1841	−	3.83006i	2.05764	−	0.230542i
$277$	−4.66561	−	6.42166i	−0.280329	−	0.385840i	0.645514	−	0.763749i	$-0.276643\pi$
$277$	−4.66561	−	6.42166i	−0.280329	−	0.385840i	−0.925843	+	0.377909i	$0.876643\pi$
$278$	10.4180	−	4.04014i	0.624832	−	0.242312i
$279$	−2.38573	−	0.775172i	−0.142830	−	0.0464083i
$280$	1.88046	−	3.78639i	0.112379	−	0.226280i
$281$	−8.74108	+	12.0311i	−0.521449	+	0.717713i	−0.985797	−	0.167940i	$-0.946289\pi$
$281$	−8.74108	+	12.0311i	−0.521449	+	0.717713i	0.464348	+	0.885653i	$0.346289\pi$
$282$	29.2055	+	7.71837i	1.73916	+	0.459622i
$283$	0.779777	+	2.39991i	0.0463529	+	0.142660i	0.971554	−	0.236817i	$-0.0761041\pi$
$283$	0.779777	+	2.39991i	0.0463529	+	0.142660i	−0.925201	+	0.379476i	$0.876104\pi$
$284$	−17.6587	−	19.3436i	−1.04785	−	1.14783i
$285$			9.67044i			0.572827i
$286$	12.3541	−	3.66067i	0.730515	−	0.216460i
$287$			6.23142i			0.367829i
$288$	−12.0356	−	9.40928i	−0.709206	−	0.554447i
$289$	−6.09020	−	18.7437i	−0.358247	−	1.10257i
$290$	0.677002	−	2.56171i	0.0397549	−	0.150429i
$291$	20.9100	−	28.7801i	1.22576	−	1.68712i
$292$	7.71215	−	13.5719i	0.451320	−	0.794236i
$293$	1.06396	+	0.345702i	0.0621573	+	0.0201961i	0.339931	−	0.940451i	$-0.389596\pi$
$293$	1.06396	+	0.345702i	0.0621573	+	0.0201961i	−0.277773	+	0.960647i	$0.589596\pi$
$294$	5.81847	+	15.0037i	0.339340	+	0.875032i
$295$	−6.91955	−	9.52394i	−0.402872	−	0.554505i
$296$	−3.17562	−	18.7967i	−0.184579	−	1.09254i
$297$	−2.36261	−	0.193881i	−0.137092	−	0.0112501i
$298$	−29.5713	+	1.65145i	−1.71302	+	0.0956658i
$299$	−16.0093	+	11.6315i	−0.925845	+	0.672665i
$300$	−4.34894	+	1.97212i	−0.251086	+	0.113860i
$301$	−2.33218	+	7.17770i	−0.134424	+	0.413716i
$302$	8.83527	−	13.7078i	0.508412	−	0.788794i
$303$	9.96700	+	7.24145i	0.572589	+	0.416010i
$304$	−1.47235	+	16.1340i	−0.0844452	+	0.925351i
$305$	−2.98239	+	0.969036i	−0.170771	+	0.0554868i
$306$	−17.9332	+	14.6241i	−1.02517	+	0.836002i
$307$	1.22257			0.0697755			0.0348878	−	0.999391i	$-0.488893\pi$
$307$	1.22257			0.0697755			0.0348878	+	0.999391i	$0.488893\pi$
$308$	0.294406	+	9.91032i	0.0167753	+	0.564693i
$309$	−2.73061			−0.155339
$310$	−1.01802	+	0.830171i	−0.0578196	+	0.0471506i
$311$	−1.88498	+	0.612469i	−0.106888	+	0.0347299i	−0.361973	−	0.932189i	$-0.617897\pi$
$311$	−1.88498	+	0.612469i	−0.106888	+	0.0347299i	0.255085	+	0.966919i	$0.417897\pi$
$312$	18.3521	+	2.71350i	1.03898	+	0.153622i
$313$	−9.56044	−	6.94607i	−0.540388	−	0.392615i	0.283841	−	0.958871i	$-0.408391\pi$
$313$	−9.56044	−	6.94607i	−0.540388	−	0.392615i	−0.824229	+	0.566256i	$0.808391\pi$
$314$	−1.53036	+	2.37433i	−0.0863633	+	0.133991i
$315$	−1.24739	+	3.83907i	−0.0702825	+	0.216307i
$316$	−4.04985	−	8.93078i	−0.227822	−	0.502396i
$317$	−28.4325	+	20.6574i	−1.59693	+	1.16023i	−0.703830	+	0.710369i	$0.748528\pi$
$317$	−28.4325	+	20.6574i	−1.59693	+	1.16023i	−0.893096	+	0.449866i	$0.851472\pi$
$318$	25.1049	−	1.40202i	1.40781	−	0.0786213i
$319$	1.43044	+	6.04711i	0.0800895	+	0.338573i
$320$	−7.55599	+	2.62812i	−0.422393	+	0.146916i
$321$	26.0903	+	35.9103i	1.45622	+	2.00432i
$322$	−5.50550	−	14.1966i	−0.306810	−	0.791148i
$323$	23.3385	+	7.58313i	1.29859	+	0.421937i
$324$	−17.0556	−	9.69173i	−0.947534	−	0.538430i
$325$	1.61471	−	2.22245i	0.0895679	−	0.123280i
$326$	−5.69658	+	21.5553i	−0.315504	+	1.19384i
$327$	10.9827	+	33.8013i	0.607345	+	1.86922i
$328$	8.25184	−	8.42336i	0.455632	−	0.465102i
$329$		−	13.3721i		−	0.737230i
$330$	6.81663	−	8.88525i	0.375243	−	0.489117i
$331$		−	4.79024i		−	0.263295i	−0.991297	−	0.131648i	$-0.957973\pi$
$331$		−	4.79024i		−	0.263295i	0.991297	−	0.131648i	$-0.0420267\pi$
$332$	−5.16194	+	4.71232i	−0.283298	+	0.258622i
$333$	5.62467	+	17.3110i	0.308230	+	0.948635i
$334$	24.9116	+	6.58359i	1.36310	+	0.360238i
$335$	−6.84192	+	9.41709i	−0.373814	+	0.514511i
$336$	−5.62676	+	13.1192i	−0.306965	+	0.715712i
$337$	−22.4373	−	7.29031i	−1.22224	−	0.397129i	−0.374340	−	0.927291i	$-0.622131\pi$
$337$	−22.4373	−	7.29031i	−1.22224	−	0.397129i	−0.847896	+	0.530163i	$0.822131\pi$
$338$	7.19053	−	2.78851i	0.391113	−	0.151675i
$339$	−0.668337	−	0.919887i	−0.0362991	−	0.0499614i
$340$	1.34923	+	12.0421i	0.0731721	+	0.653076i
$341$	1.18842	−	2.84221i	0.0643564	−	0.153915i
$342$	−0.862552	−	15.4451i	−0.0466415	−	0.835174i
$343$	14.2277	−	10.3370i	0.768224	−	0.558148i
$344$	12.6575	−	6.61417i	0.682445	−	0.356612i
$345$	−5.31478	+	16.3572i	−0.286138	+	0.880642i
$346$	−2.26358	−	1.45897i	−0.121691	−	0.0784349i
$347$	17.1962	+	12.4938i	0.923142	+	0.670702i	0.944304	−	0.329074i	$-0.106737\pi$
$347$	17.1962	+	12.4938i	0.923142	+	0.670702i	−0.0211619	+	0.999776i	$0.506737\pi$
$348$	−1.80008	+	8.76381i	−0.0964947	+	0.469789i
$349$	25.7042	−	8.35180i	1.37591	−	0.447062i	0.474591	−	0.880207i	$-0.342596\pi$
$349$	25.7042	−	8.35180i	1.37591	−	0.447062i	0.901324	+	0.433145i	$0.142596\pi$
$350$	1.33589	+	1.63818i	0.0714065	+	0.0875642i
$351$	1.96349			0.104803
$352$	12.7256	−	13.7862i	0.678276	−	0.734807i
$353$	16.7869			0.893478			0.446739	−	0.894664i	$-0.352585\pi$
$353$	16.7869			0.893478			0.446739	+	0.894664i	$0.352585\pi$
$354$	25.1212	+	30.8055i	1.33518	+	1.63730i
$355$	12.4549	−	4.04684i	0.661038	−	0.214784i
$356$	−1.64445	+	8.00608i	−0.0871556	+	0.424321i
$357$	17.4926	+	12.7091i	0.925807	+	0.672638i
$358$	−10.1824	−	6.56301i	−0.538157	−	0.346866i
$359$	−5.71621	+	17.5927i	−0.301690	+	0.928507i	0.679201	+	0.733952i	$0.262326\pi$
$359$	−5.71621	+	17.5927i	−0.301690	+	0.928507i	−0.980892	+	0.194555i	$0.937674\pi$
$360$	6.76999	−	3.53766i	0.356810	−	0.186451i
$361$	2.09964	−	1.52548i	0.110507	−	0.0802883i
$362$	−0.902217	−	16.1553i	−0.0474195	−	0.849105i
$363$	−4.28166	+	25.9123i	−0.224729	+	1.36004i
$364$	−0.914389	−	8.16111i	−0.0479270	−	0.427758i
$365$	4.58768	+	6.31441i	0.240130	+	0.330511i
$366$	9.87215	−	3.82845i	0.516025	−	0.200116i
$367$	−30.0190	−	9.75378i	−1.56698	−	0.509143i	−0.608320	−	0.793692i	$-0.708156\pi$
$367$	−30.0190	−	9.75378i	−1.56698	−	0.509143i	−0.958662	+	0.284549i	$0.908156\pi$
$368$	−11.3575	+	26.4810i	−0.592053	+	1.38042i
$369$	−6.61789	+	9.10875i	−0.344514	+	0.474183i
$370$	9.21516	+	2.43536i	0.479073	+	0.126608i
$371$	−3.43948	−	10.5856i	−0.178569	−	0.549579i
$372$	3.27577	−	2.99045i	0.169841	−	0.155047i
$373$			7.22859i			0.374282i	0.982333	+	0.187141i	$0.0599221\pi$
$373$			7.22859i			0.374282i	−0.982333	+	0.187141i	$0.940078\pi$
$374$	−16.0982	−	23.4186i	−0.832420	−	1.21095i
$375$		−	2.38760i		−	0.123295i
$376$	−17.7078	+	18.0759i	−0.913211	+	0.932193i
$377$	−1.59049	−	4.89503i	−0.0819146	−	0.252107i
$378$	−0.386030	+	1.46070i	−0.0198553	+	0.0751302i
$379$	7.87593	−	10.8403i	0.404559	−	0.556828i	−0.557322	−	0.830297i	$-0.688171\pi$
$379$	7.87593	−	10.8403i	0.404559	−	0.556828i	0.961881	+	0.273469i	$0.0881709\pi$
$380$	−7.04288	−	4.00207i	−0.361292	−	0.205302i
$381$	−36.1000	−	11.7296i	−1.84946	−	0.600926i
$382$	−12.5294	−	32.3087i	−0.641061	−	1.65306i
$383$	−7.69525	−	10.5916i	−0.393209	−	0.541206i	0.565814	−	0.824533i	$-0.308562\pi$
$383$	−7.69525	−	10.5916i	−0.393209	−	0.541206i	−0.959023	+	0.283327i	$0.908562\pi$
$384$	24.9789	−	10.2829i	1.27470	−	0.524745i
$385$	−4.57363	−	1.91237i	−0.233094	−	0.0974637i
$386$	25.6015	−	1.42975i	1.30308	−	0.0727726i
$387$	−11.0319	+	8.01516i	−0.560784	+	0.407433i
$388$	12.3068	+	27.1391i	0.624781	+	1.37778i
$389$	1.92062	−	5.91108i	0.0973796	−	0.299703i	−0.890487	−	0.455009i	$-0.849636\pi$
$389$	1.92062	−	5.91108i	0.0973796	−	0.299703i	0.987867	+	0.155305i	$0.0496361\pi$
$390$	−5.02527	+	7.79663i	−0.254464	+	0.394798i
$391$	35.3086	+	25.6532i	1.78563	+	1.29734i
$392$	−13.3350	−	1.97168i	−0.673518	−	0.0995847i
$393$	19.6043	−	6.36984i	0.988908	−	0.321316i
$394$	−6.57699	+	5.36338i	−0.331344	+	0.270203i
$395$	4.90306			0.246700
$396$	−10.0946	+	14.7990i	−0.507273	+	0.743679i
$397$	3.04173			0.152660			0.0763300	−	0.997083i	$-0.475680\pi$
$397$	3.04173			0.152660			0.0763300	+	0.997083i	$0.475680\pi$
$398$	8.38636	−	6.83888i	0.420370	−	0.342802i
$399$	−13.7469	+	4.46664i	−0.688206	+	0.223612i
$400$	0.363520	−	3.98345i	0.0181760	−	0.199172i
$401$	−6.98629	−	5.07584i	−0.348879	−	0.253475i	0.399520	−	0.916725i	$-0.369177\pi$
$401$	−6.98629	−	5.07584i	−0.348879	−	0.253475i	−0.748398	+	0.663249i	$0.769177\pi$
$402$	21.2933	−	33.0363i	1.06201	−	1.64770i
$403$	−0.788508	+	2.42678i	−0.0392784	+	0.120886i
$404$	−9.39868	+	4.26202i	−0.467602	+	0.212044i
$405$	7.93521	−	5.76527i	0.394304	−	0.286478i
$406$	3.95426	−	0.220831i	0.196247	−	0.0109597i
$407$	−21.7531	+	5.14570i	−1.07826	+	0.255063i
$408$	−6.81593	−	40.3439i	−0.337439	−	1.99732i
$409$	3.46580	+	4.77026i	0.171373	+	0.235874i	0.886061	−	0.463569i	$-0.153431\pi$
$409$	3.46580	+	4.77026i	0.171373	+	0.235874i	−0.714688	+	0.699443i	$0.753431\pi$
$410$	2.13176	+	5.49701i	0.105280	+	0.271478i
$411$	1.78093	+	0.578658i	0.0878466	+	0.0285431i
$412$	1.13005	−	1.98868i	0.0556737	−	0.0979751i
$413$	10.3426	−	14.2354i	0.508927	−	0.700478i
$414$	7.02948	−	26.5988i	0.345480	−	1.30726i
$415$	−1.07992	−	3.32365i	−0.0530112	−	0.163152i
$416$	−9.57116	+	12.2427i	−0.469265	+	0.600248i
$417$		−	18.8649i		−	0.923820i
$418$	18.9910	+	0.495591i	0.928880	+	0.0242401i
$419$			19.9341i			0.973847i	0.873445	+	0.486923i	$0.161881\pi$
$419$			19.9341i			0.973847i	−0.873445	+	0.486923i	$0.838119\pi$
$420$	−4.81216	−	5.27131i	−0.234810	−	0.257213i
$421$	−2.49760	−	7.68681i	−0.121725	−	0.374632i	0.871565	−	0.490280i	$-0.163106\pi$
$421$	−2.49760	−	7.68681i	−0.121725	−	0.374632i	−0.993290	+	0.115648i	$0.963106\pi$
$422$	7.99410	+	2.11266i	0.389147	+	0.102843i
$423$	14.2015	−	19.5467i	0.690500	−	0.950392i
$424$	−9.36849	+	18.8639i	−0.454974	+	0.916111i
$425$	−5.76220	−	1.87225i	−0.279508	−	0.0908176i
$426$	−41.2276	+	15.9882i	−1.99748	+	0.774630i
$427$	−2.75505	−	3.79200i	−0.133326	−	0.183508i
$428$	−36.9505	+	4.14002i	−1.78607	+	0.200115i
$429$	1.77918	−	21.6808i	0.0858994	−	1.04676i
$430$	0.398162	+	7.12960i	0.0192011	+	0.343820i
$431$	−6.83208	+	4.96380i	−0.329090	+	0.239098i	−0.740044	−	0.672558i	$-0.765196\pi$
$431$	−6.83208	+	4.96380i	−0.329090	+	0.239098i	0.410954	+	0.911656i	$0.365196\pi$
$432$	2.45612	−	1.46332i	0.118170	−	0.0704038i
$433$	−2.78006	+	8.55615i	−0.133601	+	0.411182i	−0.995370	−	0.0961193i	$-0.969357\pi$
$433$	−2.78006	+	8.55615i	−0.133601	+	0.411182i	0.861769	+	0.507302i	$0.169357\pi$
$434$	−1.65033	−	1.06371i	−0.0792184	−	0.0510598i
$435$	−3.61904	−	2.62939i	−0.173520	−	0.126070i
$436$	−29.1623	−	5.98994i	−1.39662	−	0.286866i
$437$	−27.7480	+	9.01586i	−1.32737	+	0.431287i
$438$	−16.6554	−	20.4242i	−0.795827	−	0.975904i
$439$	8.37075			0.399514			0.199757	−	0.979845i	$-0.435985\pi$
$439$	8.37075			0.399514			0.199757	+	0.979845i	$0.435985\pi$
$440$	3.65001	+	8.64161i	0.174007	+	0.411973i
$441$	12.8709			0.612902
$442$	14.8757	+	18.2417i	0.707563	+	0.867669i
$443$	−36.9238	+	11.9973i	−1.75430	+	0.570008i	−0.996585	−	0.0825746i	$-0.973686\pi$
$443$	−36.9238	+	11.9973i	−1.75430	+	0.570008i	−0.757718	+	0.652582i	$0.773686\pi$
$444$	−31.5258	−	6.47540i	−1.49615	−	0.307309i
$445$	−3.30614	−	2.40205i	−0.156726	−	0.113868i
$446$	−11.7860	−	7.59660i	−0.558083	−	0.359709i
$447$	−15.4517	+	47.5553i	−0.730838	+	2.24929i
$448$	−7.22599	−	9.52725i	−0.341396	−	0.450120i
$449$	17.1085	−	12.4300i	0.807399	−	0.586610i	−0.105676	−	0.994401i	$-0.533701\pi$
$449$	17.1085	−	12.4300i	0.807399	−	0.586610i	0.913075	+	0.407791i	$0.133701\pi$
$450$	0.212961	+	3.81334i	0.0100391	+	0.179763i
$451$	−10.4842	−	9.01502i	−0.493679	−	0.424501i
$452$	0.946533	−	0.106052i	0.0445212	−	0.00498825i
$453$	−16.1837	−	22.2750i	−0.760377	−	1.04657i
$454$	33.8075	−	13.1106i	1.58666	−	0.615313i
$455$	3.90512	+	1.26885i	0.183075	+	0.0594846i
$456$	24.4974	+	12.1663i	1.14719	+	0.569738i
$457$	−12.9435	+	17.8152i	−0.605473	+	0.833362i	−0.996196	−	0.0871464i	$-0.972225\pi$
$457$	−12.9435	+	17.8152i	−0.605473	+	0.833362i	0.390723	+	0.920509i	$0.372225\pi$
$458$	−14.3996	−	3.80550i	−0.672850	−	0.177819i
$459$	−1.33819	−	4.11852i	−0.0624613	−	0.192236i
$460$	−9.71329	−	10.6401i	−0.452885	−	0.496096i
$461$		−	19.1537i		−	0.892077i	−0.895014	−	0.446039i	$-0.852834\pi$
$461$		−	19.1537i		−	0.892077i	0.895014	−	0.446039i	$-0.147166\pi$
$462$	15.7793	+	5.58613i	0.734117	+	0.259890i
$463$			3.11378i			0.144710i	0.997379	+	0.0723549i	$0.0230514\pi$
$463$			3.11378i			0.144710i	−0.997379	+	0.0723549i	$0.976949\pi$
$464$	−5.63764	−	4.93785i	−0.261721	−	0.229234i
$465$	0.685319	+	2.10920i	0.0317809	+	0.0978116i
$466$	9.71638	−	36.7658i	0.450103	−	1.70314i
$467$	−15.9177	+	21.9088i	−0.736584	+	1.01382i	0.262224	+	0.965007i	$0.415544\pi$
$467$	−15.9177	+	21.9088i	−0.736584	+	1.01382i	−0.998808	+	0.0488135i	$0.984456\pi$
$468$	7.33066	−	12.9006i	0.338860	−	0.596329i
$469$	−16.5470	−	5.37644i	−0.764068	−	0.248261i
$470$	−4.57458	−	11.7962i	−0.211010	−	0.544116i
$471$	2.80319	+	3.85826i	0.129164	+	0.177779i
$472$	−32.8317	+	5.54677i	−1.51120	+	0.255311i
$473$	−8.70227	−	14.3078i	−0.400131	−	0.657875i
$474$	−16.5298	+	0.923131i	−0.759240	+	0.0424008i
$475$	3.27674	−	2.38069i	0.150347	−	0.109234i
$476$	−16.4952	+	7.48007i	−0.756055	+	0.342849i
$477$	6.21452	−	19.1263i	0.284543	−	0.875734i
$478$	13.0063	−	20.1790i	0.594893	−	0.922967i
$479$	10.1335	+	7.36243i	0.463012	+	0.336398i	0.794712	−	0.606987i	$-0.207622\pi$
$479$	10.1335	+	7.36243i	0.463012	+	0.336398i	−0.331699	+	0.943385i	$0.607622\pi$
$480$	−0.475553	+	13.4979i	−0.0217059	+	0.616094i
$481$	17.6088	−	5.72144i	0.802891	−	0.260875i
$482$	−14.4783	+	11.8067i	−0.659467	+	0.537780i
$483$	−25.7072			−1.16972
$484$	−17.0997	−	13.8420i	−0.777259	−	0.629181i
$485$	−14.8995			−0.676553
$486$	−23.3166	+	19.0142i	−1.05766	+	0.862501i
$487$	13.1913	−	4.28612i	0.597756	−	0.194223i	0.00551675	−	0.999985i	$-0.498244\pi$
$487$	13.1913	−	4.28612i	0.597756	−	0.194223i	0.592239	+	0.805762i	$0.298244\pi$
$488$	−1.29733	+	8.77418i	−0.0587273	+	0.397188i
$489$	30.4521	+	22.1248i	1.37709	+	1.00052i
$490$	3.65145	−	5.66517i	0.164956	−	0.255926i
$491$	10.6184	−	32.6801i	0.479202	−	1.47483i	−0.361003	−	0.932565i	$-0.617566\pi$
$491$	10.6184	−	32.6801i	0.479202	−	1.47483i	0.840205	−	0.542268i	$-0.182434\pi$
$492$	−8.22180	−	18.1308i	−0.370667	−	0.817401i
$493$	−9.18362	+	6.67229i	−0.413609	+	0.300505i
$494$	−15.7108	+	0.877392i	−0.706862	+	0.0394757i
$495$	−4.65450	−	7.65269i	−0.209204	−	0.343963i
$496$	0.822247	+	3.62330i	0.0369200	+	0.162691i
$497$	11.5055	+	15.8360i	0.516092	+	0.710340i
$498$	4.26653	+	11.0018i	0.191188	+	0.493002i
$499$	24.2220	+	7.87022i	1.08433	+	0.352319i	0.796052	−	0.605228i	$-0.206918\pi$
$499$	24.2220	+	7.87022i	1.08433	+	0.352319i	0.288275	+	0.957548i	$0.406918\pi$
$500$	1.73887	+	0.988100i	0.0777645	+	0.0441892i
$501$	25.5698	−	35.1938i	1.14237	−	1.57234i
$502$	0.227077	−	0.859235i	0.0101349	−	0.0383495i
$503$	−13.5574	−	41.7255i	−0.604496	−	1.86045i	−0.500221	−	0.865898i	$-0.666748\pi$
$503$	−13.5574	−	41.7255i	−0.604496	−	1.86045i	−0.104275	−	0.994549i	$-0.533252\pi$
$504$	8.15589	+	7.98981i	0.363292	+	0.355894i
$505$		−	5.15994i		−	0.229614i
$506$	31.8502	+	11.2755i	1.41592	+	0.501259i
$507$		−	13.0206i		−	0.578264i
$508$	23.4824	−	21.4371i	1.04186	−	0.951116i
$509$	13.0716	+	40.2301i	0.579387	+	1.78317i	0.620729	+	0.784025i	$0.286837\pi$
$509$	13.0716	+	40.2301i	0.579387	+	1.78317i	−0.0413423	+	0.999145i	$0.513163\pi$
$510$	19.7788	+	5.22709i	0.875818	+	0.231459i
$511$	−6.85719	+	9.43811i	−0.303344	+	0.417518i
$512$	−2.84851	+	22.4474i	−0.125888	+	0.992045i
$513$	2.75324	+	0.894580i	0.121558	+	0.0394967i
$514$	25.1250	−	9.74354i	1.10822	−	0.429769i
$515$	0.672228	+	0.925242i	0.0296219	+	0.0407711i
$516$	−2.68467	−	23.9612i	−0.118186	−	1.05483i
$517$	22.4982	+	19.3455i	0.989469	+	0.850816i
$518$	0.794391	+	14.2246i	0.0349036	+	0.624992i
$519$	−3.67828	+	2.67243i	−0.161459	+	0.117307i
$520$	−3.59852	−	6.88646i	−0.157806	−	0.301991i
$521$	−7.67816	+	23.6309i	−0.336386	+	1.03529i	0.629649	+	0.776880i	$0.283199\pi$
$521$	−7.67816	+	23.6309i	−0.336386	+	1.03529i	−0.966035	+	0.258410i	$0.916801\pi$
$522$	6.01466	+	3.87671i	0.263254	+	0.169679i
$523$	−9.24816	−	6.71918i	−0.404394	−	0.293809i	0.366934	−	0.930247i	$-0.380407\pi$
$523$	−9.24816	−	6.71918i	−0.404394	−	0.293809i	−0.771328	+	0.636437i	$0.780407\pi$
$524$	−3.47409	+	16.9138i	−0.151766	+	0.738882i
$525$	3.39407	−	1.10280i	0.148129	−	0.0481302i
$526$	0.236869	+	0.290467i	0.0103280	+	0.0126650i
$527$	5.62770			0.245146
$528$	−13.9324	−	28.4465i	−0.606329	−	1.23797i
$529$	−28.8897			−1.25608
$530$	−6.65544	−	8.16142i	−0.289094	−	0.354509i
$531$	30.2366	−	9.82446i	1.31216	−	0.426345i
$532$	2.43609	−	11.8602i	0.105618	−	0.514207i
$533$	9.26546	+	6.73175i	0.401332	+	0.291585i
$534$	11.5983	+	7.47562i	0.501908	+	0.323502i
$535$	5.74489	−	17.6809i	0.248373	−	0.764414i
$536$	15.2478	+	29.1796i	0.658606	+	1.26037i
$537$	−16.5463	+	12.0216i	−0.714025	+	0.518769i
$538$	0.606015	+	10.8515i	0.0261272	+	0.467840i
$539$	−1.29278	+	15.7537i	−0.0556840	+	0.678560i
$540$	0.159168	+	1.42061i	0.00684950	+	0.0611332i
$541$	20.8667	+	28.7205i	0.897128	+	1.23479i	0.971375	+	0.237550i	$0.0763445\pi$
$541$	20.8667	+	28.7205i	0.897128	+	1.23479i	−0.0742475	+	0.997240i	$0.523655\pi$
$542$	5.25829	−	2.03918i	0.225863	−	0.0875904i
$543$	−25.9804	−	8.44153i	−1.11492	−	0.362261i
$544$	32.2028	+	11.7322i	1.38068	+	0.503013i
$545$	8.74952	−	12.0427i	0.374788	−	0.515852i
$546$	−13.4043	−	3.54247i	−0.573652	−	0.151604i
$547$	3.64594	+	11.2210i	0.155889	+	0.479777i	0.998250	−	0.0591368i	$-0.0188348\pi$
$547$	3.64594	+	11.2210i	0.155889	+	0.479777i	−0.842361	+	0.538914i	$0.818835\pi$
$548$	−1.15846	+	1.05756i	−0.0494870	+	0.0451766i
$549$		−	8.46885i		−	0.361442i
$550$	−4.68882	−	0.122360i	−0.199932	−	0.00521745i
$551$		−	7.58854i		−	0.323283i
$552$	34.7499	+	34.0423i	1.47906	+	1.44894i
$553$	2.26466	+	6.96990i	0.0963031	+	0.296390i
$554$	2.86817	−	10.8529i	0.121857	−	0.461094i
$555$	9.45863	−	13.0187i	0.401497	−	0.552613i
$556$	13.7391	+	7.80718i	0.582670	+	0.331098i
$557$	14.6398	+	4.75676i	0.620308	+	0.201550i	0.602277	−	0.798287i	$-0.294260\pi$
$557$	14.6398	+	4.75676i	0.620308	+	0.201550i	0.0180310	+	0.999837i	$0.494260\pi$
$558$	−1.28268	−	3.30756i	−0.0543003	−	0.140020i
$559$	8.15305	+	11.2217i	0.344837	+	0.474628i
$560$	5.83054	−	1.32314i	0.246385	−	0.0559130i
$561$	−46.6893	+	11.0444i	−1.97122	+	0.466294i
$562$	−20.9983	+	1.17268i	−0.885762	+	0.0494666i
$563$	2.29097	−	1.66449i	0.0965530	−	0.0701499i	−0.538461	−	0.842650i	$-0.680994\pi$
$563$	2.29097	−	1.66449i	0.0965530	−	0.0701499i	0.635014	+	0.772500i	$0.280994\pi$
$564$	17.6433	+	38.9074i	0.742919	+	1.63830i
$565$	−0.147163	+	0.452920i	−0.00619117	+	0.0190545i
$566$	−1.93335	+	2.99956i	−0.0812648	+	0.126081i
$567$	11.8607	+	8.61732i	0.498104	+	0.361893i
$568$	5.41784	−	36.6423i	0.227328	−	1.53748i
$569$	−36.9789	+	12.0152i	−1.55023	+	0.503702i	−0.954178	−	0.299240i	$-0.903267\pi$
$569$	−36.9789	+	12.0152i	−1.55023	+	0.503702i	−0.596057	+	0.802942i	$0.703267\pi$
$570$	−10.5987	+	8.64301i	−0.443932	+	0.362016i
$571$	−5.36220			−0.224401			−0.112201	−	0.993686i	$-0.535790\pi$
$571$	−5.36220			−0.224401			−0.112201	+	0.993686i	$0.535790\pi$
$572$	15.0536	+	10.2683i	0.629424	+	0.429339i
$573$	−58.5045			−2.44406
$574$	−6.82959	+	5.56937i	−0.285061	+	0.232461i
$575$	6.85089	−	2.22599i	0.285702	−	0.0928302i
$576$	−0.444418	−	21.6006i	−0.0185174	−	0.900024i
$577$	6.07915	+	4.41676i	0.253078	+	0.183872i	0.707090	−	0.707124i	$-0.250008\pi$
$577$	6.07915	+	4.41676i	0.253078	+	0.183872i	−0.454012	+	0.890996i	$0.650008\pi$
$578$	15.0998	−	23.4271i	0.628069	−	0.974440i
$579$	13.3774	−	41.1714i	0.555946	−	1.71102i
$580$	3.41268	−	1.54755i	0.141704	−	0.0642586i
$581$	4.22591	−	3.07030i	0.175320	−	0.127378i
$582$	50.2312	−	2.80523i	2.08215	−	0.116281i
$583$	22.7859	+	9.52748i	0.943695	+	0.394588i
$584$	21.7675	−	3.67753i	0.900746	−	0.152177i
$585$	4.36075	+	6.00205i	0.180295	+	0.248154i
$586$	0.572036	+	1.47507i	0.0236306	+	0.0609345i
$587$	−25.3326	−	8.23106i	−1.04559	−	0.339732i	−0.264653	−	0.964344i	$-0.585257\pi$
$587$	−25.3326	−	8.23106i	−1.04559	−	0.339732i	−0.780936	+	0.624611i	$0.785257\pi$
$588$	−11.2436	+	19.7866i	−0.463679	+	0.815987i
$589$	−2.21132	+	3.04362i	−0.0911158	+	0.125410i
$590$	4.25378	−	16.0959i	0.175125	−	0.662656i
$591$	4.42755	+	13.6266i	0.182125	+	0.560524i
$592$	17.7628	−	20.2801i	0.730047	−	0.833508i
$593$			36.4358i			1.49624i	0.663565	+	0.748119i	$0.269043\pi$
$593$			36.4358i			1.49624i	−0.663565	+	0.748119i	$0.730957\pi$
$594$	−1.89910	−	2.76268i	−0.0779212	−	0.113354i
$595$		−	9.05597i		−	0.371259i
$596$	−28.2395	−	30.9339i	−1.15673	−	1.26710i
$597$	−5.64560	−	17.3754i	−0.231059	−	0.711127i
$598$	−27.0565	−	7.15042i	−1.10642	−	0.292403i
$599$	−9.03169	+	12.4310i	−0.369025	+	0.507919i	−0.952635	−	0.304115i	$-0.901639\pi$
$599$	−9.03169	+	12.4310i	−0.369025	+	0.507919i	0.583611	+	0.812034i	$0.301639\pi$
$600$	−6.04832	−	3.00382i	−0.246922	−	0.122630i
$601$	4.82865	+	1.56892i	0.196965	+	0.0639977i	0.405838	−	0.913945i	$-0.366980\pi$
$601$	4.82865	+	1.56892i	0.196965	+	0.0639977i	−0.208873	+	0.977943i	$0.566980\pi$
$602$	−9.95111	+	3.85907i	−0.405577	+	0.157284i
$603$	−18.4776	−	25.4322i	−0.752465	−	1.03568i
$604$	22.9202	−	2.56803i	0.932610	−	0.104492i
$605$	9.83420	−	4.92834i	0.399817	−	0.200365i
$606$	0.971495	+	17.3958i	0.0394643	+	0.706658i
$607$	2.29835	−	1.66985i	0.0932871	−	0.0677770i	−0.540164	−	0.841560i	$-0.681638\pi$
$607$	2.29835	−	1.66985i	0.0932871	−	0.0677770i	0.633451	+	0.773783i	$0.281638\pi$
$608$	−18.9987	+	12.8062i	−0.770500	+	0.519361i
$609$	2.06619	−	6.35909i	0.0837264	−	0.257683i
$610$	−3.72758	−	2.40259i	−0.150925	−	0.0972781i
$611$	−19.8830	−	14.4458i	−0.804379	−	0.584415i
$612$	−32.0557	−	6.58425i	−1.29578	−	0.266152i
$613$	39.6012	−	12.8672i	1.59948	−	0.519702i	0.632501	−	0.774560i	$-0.282029\pi$
$613$	39.6012	−	12.8672i	1.59948	−	0.519702i	0.966979	+	0.254857i	$0.0820286\pi$
$614$	1.09268	+	1.33992i	0.0440968	+	0.0540749i
$615$	9.95396			0.401382
$616$	−10.5985	+	9.18008i	−0.427026	+	0.369876i
$617$	31.3109			1.26053			0.630265	−	0.776380i	$-0.282946\pi$
$617$	31.3109			1.26053			0.630265	+	0.776380i	$0.282946\pi$
$618$	−2.44050	−	2.99273i	−0.0981713	−	0.120385i
$619$	−13.9947	+	4.54716i	−0.562495	+	0.182766i	−0.576444	−	0.817137i	$-0.695560\pi$
$619$	−13.9947	+	4.54716i	−0.562495	+	0.182766i	0.0139484	+	0.999903i	$0.495560\pi$
$620$	−1.81972	−	0.373771i	−0.0730818	−	0.0150110i
$621$	4.16535	+	3.02630i	0.167150	+	0.121441i
$622$	−2.35598	−	1.51853i	−0.0944661	−	0.0608876i
$623$	1.88755	−	5.80928i	0.0756231	−	0.232744i
$624$	13.4283	+	22.5390i	0.537564	+	0.902281i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−0.931868	−	16.6863i	−0.0372449	−	0.666917i
$627$	12.3728	−	29.5906i	0.494120	−	1.18174i
$628$	−3.97002	+	0.444810i	−0.158421	+	0.0177499i
$629$	−24.0021	−	33.0360i	−0.957025	−	1.31723i
$630$	−5.32246	+	2.06406i	−0.212052	+	0.0822343i
$631$	28.6235	+	9.30035i	1.13948	+	0.370241i	0.817173	−	0.576392i	$-0.195540\pi$
$631$	28.6235	+	9.30035i	1.13948	+	0.370241i	0.322312	+	0.946634i	$0.395540\pi$
$632$	6.16849	−	12.4205i	0.245370	−	0.494063i
$633$	8.20531	−	11.2936i	0.326132	−	0.448882i
$634$	−48.0520	−	12.6991i	−1.90839	−	0.504345i
$635$	4.91272	+	15.1198i	0.194955	+	0.600011i
$636$	23.9743	+	26.2617i	0.950642	+	1.04135i
$637$		−	13.0924i		−	0.518739i
$638$	−5.34911	+	6.97240i	−0.211773	+	0.276040i
$639$			35.3672i			1.39911i
$640$	−9.63361	−	5.93241i	−0.380802	−	0.234499i
$641$	−0.473686	−	1.45786i	−0.0187095	−	0.0575818i	0.941266	−	0.337666i	$-0.109638\pi$
$641$	−0.473686	−	1.45786i	−0.0187095	−	0.0575818i	−0.959975	+	0.280084i	$0.909638\pi$
$642$	−16.0390	+	60.6898i	−0.633008	+	2.39524i
$643$	−11.1519	+	15.3492i	−0.439786	+	0.605314i	−0.970165	−	0.242447i	$-0.922050\pi$
$643$	−11.1519	+	15.3492i	−0.439786	+	0.605314i	0.530378	+	0.847761i	$0.322050\pi$
$644$	10.6388	−	18.7223i	0.419229	−	0.737763i
$645$	11.4655	+	3.72538i	0.451455	+	0.146687i
$646$	12.5479	+	32.3563i	0.493689	+	1.27304i
$647$	14.4967	+	19.9530i	0.569925	+	0.784435i	0.992546	−	0.121872i	$-0.0388898\pi$
$647$	14.4967	+	19.9530i	0.569925	+	0.784435i	−0.422621	+	0.906307i	$0.638890\pi$
$648$	−4.62149	−	27.3549i	−0.181549	−	1.07460i
$649$	8.98786	+	37.9955i	0.352804	+	1.49146i
$650$	3.87895	−	0.216625i	0.152145	−	0.00849675i
$651$	−2.68177	+	1.94842i	−0.105107	+	0.0763645i
$652$	−28.7157	+	13.0217i	−1.12460	+	0.509971i
$653$	5.82347	−	17.9228i	0.227890	−	0.701373i	−0.770095	−	0.637929i	$-0.779791\pi$
$653$	5.82347	−	17.9228i	0.227890	−	0.701373i	0.997985	−	0.0634444i	$-0.0202085\pi$
$654$	−27.2301	+	42.2471i	−1.06478	+	1.65199i
$655$	−6.98460	−	5.07461i	−0.272911	−	0.198281i
$656$	16.6071	+	1.51552i	0.648397	+	0.0591711i
$657$	−20.0469	+	6.51365i	−0.782106	+	0.254122i
$658$	14.6558	−	11.9514i	0.571341	−	0.465916i
$659$	−0.236391			−0.00920847			−0.00460424	−	0.999989i	$-0.501466\pi$
$659$	−0.236391			−0.00920847			−0.00460424	+	0.999989i	$0.501466\pi$
$660$	15.8306	−	0.470279i	0.616204	−	0.0183056i
$661$	−10.1986			−0.396680			−0.198340	−	0.980133i	$-0.563555\pi$
$661$	−10.1986			−0.396680			−0.198340	+	0.980133i	$0.563555\pi$
$662$	5.25006	−	4.28130i	0.204049	−	0.166398i
$663$	37.7942	−	12.2801i	1.46781	−	0.476919i
$664$	−9.77819	−	1.44578i	−0.379467	−	0.0561071i
$665$	4.89773	+	3.55841i	0.189926	+	0.137989i
$666$	−13.9456	+	21.6364i	−0.540381	+	0.838393i
$667$	4.17059	−	12.8357i	0.161486	−	0.497002i
$668$	15.0494	+	33.1871i	0.582277	+	1.28405i
$669$	−19.1521	+	13.9148i	−0.740463	+	0.537978i
$670$	−16.4361	+	0.917896i	−0.634981	+	0.0354614i
$671$	10.3656	+	0.850627i	0.400161	+	0.0328381i
$672$	−19.4075	+	5.55850i	−0.748661	+	0.214424i
$673$	16.4759	+	22.6771i	0.635099	+	0.874138i	0.998342	−	0.0575559i	$-0.0183307\pi$
$673$	16.4759	+	22.6771i	0.635099	+	0.874138i	−0.363244	+	0.931694i	$0.618331\pi$
$674$	−12.0633	−	31.1068i	−0.464662	−	1.19819i
$675$	−0.679766	−	0.220869i	−0.0261642	−	0.00850126i
$676$	9.48276	+	5.38852i	0.364722	+	0.207251i
$677$	18.8164	−	25.8985i	0.723173	−	0.995362i	−0.276240	−	0.961089i	$-0.589088\pi$
$677$	18.8164	−	25.8985i	0.723173	−	0.995362i	0.999412	−	0.0342733i	$-0.0109117\pi$
$678$	0.410859	−	1.55465i	0.0157789	−	0.0597059i
$679$	−6.88189	−	21.1803i	−0.264103	−	0.812825i
$680$	−11.9922	+	12.2415i	−0.459880	+	0.469439i
$681$		−	61.2185i		−	2.34590i
$682$	4.17720	−	1.23775i	0.159953	−	0.0473959i
$683$		−	33.8277i		−	1.29438i	−0.762328	−	0.647191i	$-0.775944\pi$
$683$		−	33.8277i		−	1.29438i	0.762328	−	0.647191i	$-0.224056\pi$
$684$	16.1568	−	14.7495i	0.617770	−	0.563961i
$685$	−0.242360	−	0.745906i	−0.00926008	−	0.0284996i
$686$	24.0454	+	6.35467i	0.918058	+	0.242622i
$687$	−14.7801	+	20.3430i	−0.563895	+	0.776135i
$688$	18.5618	+	7.96104i	0.707661	+	0.303512i
$689$	−19.4554	−	6.32143i	−0.741191	−	0.240827i
$690$	−22.6775	+	8.79440i	−0.863317	+	0.334797i
$691$	12.6642	+	17.4308i	0.481769	+	0.663099i	0.978844	−	0.204609i	$-0.0655924\pi$
$691$	12.6642	+	17.4308i	0.481769	+	0.663099i	−0.497074	+	0.867708i	$0.665592\pi$
$692$	−0.424061	−	3.78483i	−0.0161204	−	0.143878i
$693$	8.72876	−	10.1512i	0.331578	−	0.385614i
$694$	1.67614	+	30.0134i	0.0636253	+	1.13929i
$695$	−6.39221	+	4.64421i	−0.242470	+	0.176165i
$696$	−11.2139	+	5.85983i	−0.425062	+	0.222116i
$697$	7.80546	−	24.0227i	0.295653	−	0.909926i
$698$	32.1268	+	20.7071i	1.21602	+	0.783777i
$699$	−51.9408	−	37.7372i	−1.96458	−	1.42735i
$700$	−0.601464	+	2.92826i	−0.0227332	+	0.110678i
$701$	−25.6608	+	8.33769i	−0.969194	+	0.314910i	−0.750491	−	0.660881i	$-0.770183\pi$
$701$	−25.6608	+	8.33769i	−0.969194	+	0.314910i	−0.218703	+	0.975791i	$0.570183\pi$
$702$	1.75488	+	2.15197i	0.0662337	+	0.0812208i
$703$	27.2981			1.02957
$704$	26.4832	+	1.62564i	0.998121	+	0.0612688i
$705$	−21.3604			−0.804480
$706$	15.0034	+	18.3983i	0.564661	+	0.692431i
$707$	7.33506	−	2.38331i	0.275863	−	0.0896335i
$708$	−11.3104	+	55.0653i	−0.425071	+	2.06948i
$709$	11.0842	+	8.05315i	0.416276	+	0.302442i	0.776138	−	0.630563i	$-0.217176\pi$
$709$	11.0842	+	8.05315i	0.416276	+	0.302442i	−0.359862	+	0.933006i	$0.617176\pi$
$710$	15.5670	+	10.0336i	0.584218	+	0.376554i
$711$	−4.09182	+	12.5933i	−0.153455	+	0.472287i
$712$	−10.2443	+	5.35318i	−0.383923	+	0.200619i
$713$	−5.41311	+	3.93286i	−0.202723	+	0.147287i
$714$	1.70503	+	30.5306i	0.0638090	+	1.14258i
$715$	−7.78436	+	4.73458i	−0.291118	+	0.177063i
$716$	−1.90758	−	17.0256i	−0.0712898	−	0.636276i
$717$	−23.8238	−	32.7907i	−0.889716	−	1.22459i
$718$	−24.3904	+	9.45866i	−0.910240	+	0.352994i
$719$	−8.92521	−	2.89998i	−0.332854	−	0.108151i	0.137822	−	0.990457i	$-0.455990\pi$
$719$	−8.92521	−	2.89998i	−0.332854	−	0.108151i	−0.470676	+	0.882306i	$0.655990\pi$
$720$	9.92796	+	4.25805i	0.369993	+	0.158688i
$721$	−1.00478	+	1.38296i	−0.0374198	+	0.0515040i
$722$	3.54848	+	0.937785i	0.132061	+	0.0349007i
$723$	9.74660	+	29.9970i	0.362480	+	1.11560i
$724$	16.8998	−	15.4278i	0.628075	−	0.573368i
$725$			1.87359i			0.0695833i
$726$	−32.2264	+	18.4666i	−1.19603	+	0.685359i
$727$			31.6702i			1.17458i	0.809376	+	0.587291i	$0.199805\pi$
$727$			31.6702i			1.17458i	−0.809376	+	0.587291i	$0.800195\pi$
$728$	8.12727	−	8.29621i	0.301217	−	0.307478i
$729$	6.60355	+	20.3236i	0.244576	+	0.752727i
$730$	−2.82027	+	10.6716i	−0.104383	+	0.394974i
$731$	17.9815	−	24.7495i	0.665072	−	0.915393i
$732$	13.0192	+	7.39810i	0.481205	+	0.273442i
$733$	−21.5149	−	6.99061i	−0.794670	−	0.258204i	−0.116579	−	0.993181i	$-0.537193\pi$
$733$	−21.5149	−	6.99061i	−0.794670	−	0.258204i	−0.678091	+	0.734978i	$0.737193\pi$
$734$	−16.1396	−	41.6181i	−0.595725	−	1.53615i
$735$	−6.68843	−	9.20583i	−0.246706	−	0.339562i
$736$	−39.1738	+	11.2198i	−1.44397	+	0.413566i
$737$	32.9843	−	20.0616i	1.21499	−	0.738979i
$738$	−15.8979	+	0.887841i	−0.585210	+	0.0326819i
$739$	11.5306	−	8.37744i	0.424158	−	0.308169i	−0.355151	−	0.934809i	$-0.615570\pi$
$739$	11.5306	−	8.37744i	0.424158	−	0.308169i	0.779309	+	0.626640i	$0.215570\pi$
$740$	5.56697	+	12.2764i	0.204646	+	0.451288i
$741$	−8.20925	+	25.2655i	−0.301574	+	0.928151i
$742$	8.52772	−	13.2306i	0.313062	−	0.485712i
$743$	−34.0655	−	24.7500i	−1.24974	−	0.907991i	−0.251535	−	0.967848i	$-0.580935\pi$
$743$	−34.0655	−	24.7500i	−1.24974	−	0.907991i	−0.998207	+	0.0598573i	$0.980935\pi$
$744$	6.20525	+	0.917493i	0.227496	+	0.0336369i
$745$	19.9176	−	6.47162i	0.729725	−	0.237102i
$746$	−7.92248	+	6.46060i	−0.290063	+	0.236539i
$747$	9.43793			0.345316
$748$	11.2787	−	38.5740i	0.412389	−	1.41041i
$749$	27.7877			1.01534
$750$	2.61679	−	2.13393i	0.0955518	−	0.0779203i
$751$	−28.8547	+	9.37547i	−1.05292	+	0.342116i	−0.783815	−	0.620994i	$-0.786729\pi$
$751$	−28.8547	+	9.37547i	−1.05292	+	0.342116i	−0.269109	+	0.963110i	$0.586729\pi$
$752$	−35.6375	−	3.25219i	−1.29957	−	0.118595i
$753$	−1.21388	−	0.881936i	−0.0442363	−	0.0321396i
$754$	3.94341	−	6.11814i	0.143610	−	0.222809i
$755$	−3.56352	+	10.9674i	−0.129690	+	0.399145i
$756$	−1.94593	+	0.882423i	−0.0707729	+	0.0320934i
$757$	−8.07084	+	5.86381i	−0.293340	+	0.213124i	−0.724715	−	0.689049i	$-0.758029\pi$
$757$	−8.07084	+	5.86381i	−0.293340	+	0.213124i	0.431375	+	0.902173i	$0.358029\pi$
$758$	18.9200	−	1.05662i	0.687207	−	0.0383780i
$759$	37.1908	−	43.2516i	1.34994	−	1.56993i
$760$	−1.90838	−	11.2958i	−0.0692243	−	0.409743i
$761$	25.3957	+	34.9541i	0.920593	+	1.26709i	0.963418	+	0.268004i	$0.0863641\pi$
$761$	25.3957	+	34.9541i	0.920593	+	1.26709i	−0.0428252	+	0.999083i	$0.513636\pi$
$762$	−19.4091	−	50.0488i	−0.703117	−	1.81308i
$763$	21.1604	+	6.87544i	0.766059	+	0.248908i
$764$	24.2119	−	42.6083i	0.875954	−	1.54151i
$765$	9.61762	−	13.2375i	0.347726	−	0.478604i
$766$	4.73064	−	17.9003i	0.170925	−	0.646763i
$767$	−9.99348	−	30.7568i	−0.360844	−	1.11056i
$768$	33.5950	+	18.1863i	1.21225	+	0.656242i
$769$		−	52.1713i		−	1.88135i	−0.339315	−	0.940673i	$-0.610195\pi$
$769$		−	52.1713i		−	1.88135i	0.339315	−	0.940673i	$-0.389805\pi$
$770$	−1.99176	−	6.72186i	−0.0717781	−	0.242239i
$771$		−	45.4962i		−	1.63851i
$772$	24.4485	+	26.7812i	0.879922	+	0.963878i
$773$	14.6157	+	44.9824i	0.525689	+	1.61790i	0.762949	+	0.646459i	$0.223751\pi$
$773$	14.6157	+	44.9824i	0.525689	+	1.61790i	−0.237260	+	0.971446i	$0.576249\pi$
$774$	−18.6444	−	4.92730i	−0.670159	−	0.177108i
$775$	0.545968	−	0.751461i	0.0196118	−	0.0269933i
$776$	−18.7450	+	37.7438i	−0.672905	+	1.35492i
$777$	22.8754	+	7.43267i	0.820651	+	0.266646i
$778$	8.19507	−	3.17807i	0.293807	−	0.113939i
$779$	9.92515	+	13.6608i	0.355605	+	0.489449i
$780$	−13.0364	+	1.46063i	−0.466779	+	0.0522989i
$781$	−43.2885	−	3.55235i	−1.54899	−	0.127113i
$782$	3.44157	+	61.6257i	0.123070	+	2.20373i
$783$	−1.08339	+	0.787129i	−0.0387172	+	0.0281297i
$784$	−9.75728	−	16.3772i	−0.348474	−	0.584901i
$785$	0.617240	−	1.89967i	0.0220302	−	0.0678021i
$786$	24.5028	+	15.7931i	0.873986	+	0.563322i
$787$	−17.1819	−	12.4834i	−0.612469	−	0.444985i	0.237814	−	0.971311i	$-0.423569\pi$
$787$	−17.1819	−	12.4834i	−0.612469	−	0.444985i	−0.850283	+	0.526326i	$0.823569\pi$
$788$	−11.7565	−	2.41477i	−0.418806	−	0.0860228i
$789$	0.601807	−	0.195539i	0.0214249	−	0.00696138i
$790$	4.38214	+	5.37372i	0.155910	+	0.191188i
$791$	−0.711816			−0.0253093
$792$	−25.2418	+	2.16311i	−0.896927	+	0.0768626i
$793$	−8.61456			−0.305912
$794$	2.71856	+	3.33371i	0.0964782	+	0.118309i
$795$	−16.9093	+	5.49417i	−0.599712	+	0.194858i
$796$	14.9907	+	3.07910i	0.531332	+	0.109136i
$797$	0.851561	+	0.618696i	0.0301639	+	0.0219153i	0.602765	−	0.797919i	$-0.294066\pi$
$797$	0.851561	+	0.618696i	0.0301639	+	0.0219153i	−0.572601	+	0.819834i	$0.694066\pi$
$798$	−17.1818	−	11.0744i	−0.608229	−	0.392030i
$799$	−16.7499	+	51.5509i	−0.592569	+	1.82374i
$800$	4.69073	−	3.16182i	0.165842	−	0.111787i
$801$	8.92869	−	6.48707i	0.315480	−	0.229209i
$802$	−0.680962	−	12.1935i	−0.0240456	−	0.430567i
$803$	−5.95898	−	25.1912i	−0.210288	−	0.888977i
$804$	55.2385	−	6.18905i	1.94811	−	0.218271i
$805$	6.32867	+	8.71066i	0.223056	+	0.307011i
$806$	−3.36447	+	1.30475i	−0.118508	+	0.0459579i
$807$	17.4509	+	5.67014i	0.614300	+	0.199598i
$808$	−13.0713	−	6.49167i	−0.459846	−	0.228376i
$809$	−10.8589	+	14.9460i	−0.381779	+	0.525474i	−0.956055	−	0.293188i	$-0.905284\pi$
$809$	−10.8589	+	14.9460i	−0.381779	+	0.525474i	0.574276	+	0.818662i	$0.305284\pi$
$810$	13.4108	+	3.54419i	0.471209	+	0.124530i
$811$	5.92848	+	18.2460i	0.208177	+	0.640703i	0.999568	+	0.0293925i	$0.00935728\pi$
$811$	5.92848	+	18.2460i	0.208177	+	0.640703i	−0.791391	+	0.611310i	$0.790643\pi$
$812$	3.77618	+	4.13647i	0.132518	+	0.145162i
$813$		−	9.52170i		−	0.333941i
$814$	−25.0816	−	19.2422i	−0.879110	−	0.674440i
$815$		−	15.7652i		−	0.552229i
$816$	38.1248	−	43.5278i	1.33464	−	1.52378i
$817$	6.31965	+	19.4499i	0.221096	+	0.680465i
$818$	−2.13059	+	8.06194i	−0.0744944	+	0.281879i
$819$	−6.51799	+	8.97125i	−0.227757	+	0.313481i
$820$	−4.11941	+	7.24937i	−0.143856	+	0.253159i
$821$	51.7550	+	16.8162i	1.80626	+	0.586890i	0.999989	−	0.00465170i	$-0.00148069\pi$
$821$	51.7550	+	16.8162i	1.80626	+	0.586890i	0.806274	+	0.591542i	$0.201481\pi$
$822$	0.957509	+	2.46906i	0.0333970	+	0.0861184i
$823$	24.0266	+	33.0697i	0.837513	+	1.15274i	0.986478	+	0.163896i	$0.0524061\pi$
$823$	24.0266	+	33.0697i	0.837513	+	1.15274i	−0.148964	+	0.988843i	$0.547594\pi$
$824$	3.18957	−	0.538864i	0.111114	−	0.0187722i
$825$	−3.05480	+	7.30584i	−0.106354	+	0.254357i
$826$	24.8457	−	1.38754i	0.864492	−	0.0482787i
$827$	11.2156	−	8.14861i	0.390005	−	0.283355i	−0.375453	−	0.926842i	$-0.622513\pi$
$827$	11.2156	−	8.14861i	0.390005	−	0.283355i	0.765457	+	0.643487i	$0.222513\pi$
$828$	35.4348	−	16.0686i	1.23144	−	0.558423i
$829$	5.11970	−	15.7568i	0.177814	−	0.547257i	−0.821936	−	0.569579i	$-0.807106\pi$
$829$	5.11970	−	15.7568i	0.177814	−	0.547257i	0.999751	+	0.0223228i	$0.00710615\pi$
$830$	2.67751	−	4.15412i	0.0929379	−	0.144192i
$831$	−15.3324	−	11.1396i	−0.531874	−	0.386429i
$832$	−21.9722	+	0.452064i	−0.761749	+	0.0156725i
$833$	−27.4620	+	8.92294i	−0.951501	+	0.309162i
$834$	20.6758	−	16.8607i	0.715945	−	0.583837i
$835$	−18.2199			−0.630527
$836$	16.4302	+	21.2569i	0.568249	+	0.735186i
$837$	0.663898			0.0229477
$838$	−21.8477	+	17.8163i	−0.754715	+	0.615453i
$839$	−20.3183	+	6.60182i	−0.701466	+	0.227920i	−0.637969	−	0.770062i	$-0.720225\pi$
$839$	−20.3183	+	6.60182i	−0.701466	+	0.227920i	−0.0634967	+	0.997982i	$0.520225\pi$
$840$	1.47641	−	9.98536i	0.0509410	−	0.344528i
$841$	−20.6216	−	14.9825i	−0.711089	−	0.516636i
$842$	6.19245	−	9.60748i	0.213406	−	0.331096i
$843$	−10.9721	+	33.7687i	−0.377900	+	1.16306i
$844$	4.82931	+	10.6497i	0.166232	+	0.366577i
$845$	−4.41190	+	3.20544i	−0.151774	+	0.110270i
$846$	34.1157	−	1.90524i	1.17292	−	0.0655034i
$847$	11.5481	+	11.7034i	0.396798	+	0.402133i
$848$	−29.0478	+	6.59192i	−0.997506	+	0.226367i
$849$	3.54135	+	4.87425i	0.121539	+	0.167284i
$850$	−3.09803	−	7.98867i	−0.106262	−	0.274009i
$851$	46.1737	+	15.0028i	1.58281	+	0.514288i
$852$	−54.3704	−	30.8956i	−1.86270	−	1.05847i
$853$	−13.2374	+	18.2198i	−0.453241	+	0.623833i	−0.973090	−	0.230425i	$-0.925988\pi$
$853$	−13.2374	+	18.2198i	−0.453241	+	0.623833i	0.519849	+	0.854258i	$0.325988\pi$
$854$	1.69366	−	6.40863i	0.0579558	−	0.219299i
$855$	3.38013	+	10.4030i	0.115598	+	0.355774i
$856$	−37.5622	−	36.7973i	−1.28385	−	1.25771i
$857$		−	19.0733i		−	0.651531i	−0.945451	−	0.325766i	$-0.894378\pi$
$857$		−	19.0733i		−	0.651531i	0.945451	−	0.325766i	$-0.105622\pi$
$858$	25.3522	−	17.4274i	0.865509	−	0.594963i
$859$		−	53.0065i		−	1.80856i	−0.426943	−	0.904279i	$-0.640409\pi$
$859$		−	53.0065i		−	1.80856i	0.426943	−	0.904279i	$-0.359591\pi$
$860$	−7.45813	+	6.80851i	−0.254320	+	0.232168i
$861$	4.59760	+	14.1500i	0.156686	+	0.482229i
$862$	−11.5465	−	3.05148i	−0.393275	−	0.103934i
$863$	5.29025	−	7.28140i	0.180082	−	0.247862i	−0.709427	−	0.704779i	$-0.751046\pi$
$863$	5.29025	−	7.28140i	0.180082	−	0.247862i	0.889509	+	0.456917i	$0.151046\pi$
$864$	3.79896	+	1.38404i	0.129243	+	0.0470861i
$865$	1.81105	+	0.588447i	0.0615777	+	0.0200078i
$866$	−11.8622	+	4.60019i	−0.403093	+	0.156321i
$867$	−27.6586	−	38.0687i	−0.939334	−	1.29288i
$868$	−0.309175	−	2.75945i	−0.0104941	−	0.0936618i
$869$	−15.0029	−	6.27318i	−0.508939	−	0.212803i
$870$	−0.352752	−	6.31648i	−0.0119594	−	0.214149i
$871$	−25.8697	+	18.7955i	−0.876563	+	0.636860i
$872$	−19.4991	−	37.3152i	−0.660322	−	1.26365i
$873$	12.4343	−	38.2689i	0.420838	−	1.29521i
$874$	−34.6812	−	22.3536i	−1.17311	−	0.756121i
$875$	−1.20923	−	0.878560i	−0.0408796	−	0.0297008i
$876$	7.49883	−	36.5085i	0.253362	−	1.23351i
$877$	8.82479	−	2.86735i	0.297992	−	0.0968234i	−0.156205	−	0.987725i	$-0.549926\pi$
$877$	8.82479	−	2.86735i	0.297992	−	0.0968234i	0.454197	+	0.890901i	$0.349926\pi$
$878$	7.48141	+	9.17428i	0.252485	+	0.309617i
$879$	2.67105			0.0900922
$880$	−6.20892	+	11.7239i	−0.209303	+	0.395212i
$881$	−6.09163			−0.205232			−0.102616	−	0.994721i	$-0.532721\pi$
$881$	−6.09163			−0.205232			−0.102616	+	0.994721i	$0.532721\pi$
$882$	11.5035	+	14.1065i	0.387343	+	0.474989i
$883$	−8.81205	+	2.86321i	−0.296549	+	0.0963546i	−0.453513	−	0.891250i	$-0.649829\pi$
$883$	−8.81205	+	2.86321i	−0.296549	+	0.0963546i	0.156964	+	0.987604i	$0.449829\pi$
$884$	−6.69753	+	32.6072i	−0.225262	+	1.09670i
$885$	−22.7394	−	16.5211i	−0.764376	−	0.555352i
$886$	−46.1498	−	29.7456i	−1.55043	−	0.999322i
$887$	−5.25130	+	16.1618i	−0.176321	+	0.542662i	−0.999691	−	0.0248434i	$-0.992091\pi$
$887$	−5.25130	+	16.1618i	−0.176321	+	0.542662i	0.823370	+	0.567505i	$0.192091\pi$
$888$	−21.0794	−	40.3395i	−0.707379	−	1.35370i
$889$	−19.2243	+	13.9673i	−0.644761	+	0.468447i
$890$	−0.322253	−	5.77035i	−0.0108019	−	0.193422i
$891$	−31.6573	+	7.48855i	−1.06056	+	0.250876i
$892$	−2.20800	−	19.7069i	−0.0739294	−	0.659835i
$893$	−21.2986	−	29.3150i	−0.712730	−	0.980989i
$894$	−65.9303	+	25.5680i	−2.20504	+	0.855121i
$895$	8.14680	+	2.64706i	0.272318	+	0.0884814i
$896$	3.98353	−	16.4347i	0.133080	−	0.549044i
$897$	−27.7713	+	38.2240i	−0.927258	+	1.27626i
$898$	28.9140	+	7.64134i	0.964874	+	0.254995i
$899$	−0.537781	−	1.65512i	−0.0179360	−	0.0552013i
$900$	−3.98906	+	3.64160i	−0.132969	+	0.121387i
$901$			45.1170i			1.50306i
$902$	0.510121	−	19.5478i	0.0169852	−	0.650870i
$903$			18.0194i			0.599649i
$904$	0.962202	+	0.942609i	0.0320024	+	0.0313507i
$905$	3.53557	+	10.8814i	0.117526	+	0.361709i
$906$	9.94890	−	37.6456i	0.330530	−	1.25069i
$907$	−5.01090	+	6.89691i	−0.166384	+	0.229008i	−0.884065	−	0.467364i	$-0.845204\pi$
$907$	−5.01090	+	6.89691i	−0.166384	+	0.229008i	0.717681	+	0.696372i	$0.245204\pi$
$908$	44.5848	+	25.3350i	1.47960	+	0.840772i
$909$	13.2531	+	4.30620i	0.439578	+	0.142828i
$910$	2.09958	+	5.41403i	0.0696002	+	0.179473i
$911$	−9.42310	−	12.9698i	−0.312201	−	0.429708i	0.623865	−	0.781532i	$-0.285562\pi$
$911$	−9.42310	−	12.9698i	−0.312201	−	0.429708i	−0.936066	+	0.351824i	$0.885562\pi$
$912$	8.56051	+	37.7226i	0.283467	+	1.24912i
$913$	−0.947962	+	11.5518i	−0.0313730	+	0.382308i
$914$	−31.0937	+	1.73647i	−1.02849	+	0.0574374i
$915$	−6.05727	+	4.40087i	−0.200247	+	0.145488i
$916$	−8.69895	−	19.1831i	−0.287421	−	0.633826i
$917$	3.98767	−	12.2728i	0.131684	−	0.405283i
$918$	3.31785	−	5.14760i	0.109505	−	0.169896i
$919$	25.5360	+	18.5530i	0.842353	+	0.612006i	0.923027	−	0.384735i	$-0.125707\pi$
$919$	25.5360	+	18.5530i	0.842353	+	0.612006i	−0.0806737	+	0.996741i	$0.525707\pi$
$920$	2.98011	−	20.1553i	0.0982515	−	0.664501i
$921$	2.77613	−	0.902021i	0.0914767	−	0.0297226i
$922$	20.9923	−	17.1188i	0.691345	−	0.563776i
$923$	35.9757			1.18415
$924$	7.98045	+	22.2866i	0.262537	+	0.733175i
$925$	−6.73981			−0.221604
$926$	−3.41268	+	2.78296i	−0.112148	+	0.0914539i
$927$	−2.93746	+	0.954437i	−0.0964787	+	0.0313478i
$928$	0.373174	−	10.5920i	0.0122500	−	0.347701i
$929$	−41.7693	−	30.3472i	−1.37041	−	0.995658i	−0.997705	−	0.0677067i	$-0.978432\pi$
$929$	−41.7693	−	30.3472i	−1.37041	−	0.995658i	−0.372701	−	0.927952i	$-0.621568\pi$
$930$	−1.69915	+	2.63621i	−0.0557175	+	0.0864448i
$931$	5.96499	−	18.3584i	0.195495	−	0.601671i
$932$	48.9791	−	22.2106i	1.60436	−	0.727531i
$933$	−3.82843	+	2.78152i	−0.125337	+	0.0910628i
$934$	−38.2385	+	2.13548i	−1.25120	+	0.0698751i
$935$	15.2364	+	13.1013i	0.498282	+	0.428459i
$936$	20.6907	−	3.49561i	0.676298	−	0.114258i
$937$	−14.0351	−	19.3176i	−0.458506	−	0.631080i	0.515692	−	0.856774i	$-0.327535\pi$
$937$	−14.0351	−	19.3176i	−0.458506	−	0.631080i	−0.974198	+	0.225694i	$0.927535\pi$
$938$	−8.89642	−	22.9406i	−0.290479	−	0.749036i
$939$	−26.8342	−	8.71896i	−0.875701	−	0.284532i
$940$	8.83993	−	15.5566i	0.288327	−	0.507400i
$941$	5.74899	−	7.91280i	0.187412	−	0.257950i	−0.704964	−	0.709243i	$-0.749037\pi$
$941$	5.74899	−	7.91280i	0.187412	−	0.257950i	0.892376	+	0.451293i	$0.149037\pi$
$942$	−1.72325	+	6.52062i	−0.0561466	+	0.212453i
$943$	9.28020	+	28.5615i	0.302205	+	0.930091i
$944$	−35.4227	−	31.0258i	−1.15291	−	1.00980i
$945$		−	1.06833i		−	0.0347528i
$946$	7.90356	−	22.3253i	0.256967	−	0.725859i
$947$		−	11.7018i		−	0.380257i	−0.981759	−	0.190129i	$-0.939109\pi$
$947$		−	11.7018i		−	0.380257i	0.981759	−	0.190129i	$-0.0608905\pi$
$948$	−15.7854	−	17.2915i	−0.512685	−	0.561602i
$949$	6.62571	+	20.3918i	0.215080	+	0.661947i
$950$	5.53782	+	1.46352i	0.179671	+	0.0474830i
$951$	−49.3216	+	67.8854i	−1.59936	+	2.20133i
$952$	−22.9408	−	11.3932i	−0.743515	−	0.369257i
$953$	37.4762	+	12.1768i	1.21397	+	0.394444i	0.844884	−	0.534950i	$-0.179669\pi$
$953$	37.4762	+	12.1768i	1.21397	+	0.394444i	0.369090	+	0.929394i	$0.379669\pi$
$954$	26.5166	−	10.2832i	0.858505	−	0.332931i
$955$	14.4028	+	19.8237i	0.466063	+	0.641480i
$956$	33.7405	−	3.78036i	1.09125	−	0.122266i
$957$	7.70979	+	12.6760i	0.249222	+	0.409758i
$958$	0.987726	+	17.6865i	0.0319120	+	0.571424i
$959$	0.948393	−	0.689048i	0.0306252	−	0.0222505i
$960$	−15.2187	+	11.5427i	−0.491180	+	0.372538i
$961$	9.31291	−	28.6622i	0.300417	−	0.924587i
$962$	22.0086	+	14.1855i	0.709586	+	0.457360i
$963$	40.6185	+	29.5111i	1.30891	+	0.950981i
$964$	−25.8801	−	5.31577i	−0.833541	−	0.171209i
$965$	−17.2438	+	5.60286i	−0.555098	+	0.180362i
$966$	−22.9760	−	28.1749i	−0.739241	−	0.906514i
$967$	17.8298			0.573368			0.286684	−	0.958025i	$-0.407447\pi$
$967$	17.8298			0.573368			0.286684	+	0.958025i	$0.407447\pi$
$968$	−0.112257	−	31.1125i	−0.00360808	−	0.999993i
$969$	58.5906			1.88220
$970$	−13.3166	−	16.3298i	−0.427569	−	0.524318i
$971$	1.05503	−	0.342801i	0.0338577	−	0.0110010i	−0.292039	−	0.956406i	$-0.594334\pi$
$971$	1.05503	−	0.342801i	0.0338577	−	0.0110010i	0.325897	+	0.945405i	$0.394334\pi$
$972$	−41.6788	−	8.56082i	−1.33685	−	0.274588i
$973$	−9.55441	−	6.94168i	−0.306300	−	0.222540i
$974$	16.4874	+	10.6268i	0.528290	+	0.340506i
$975$	2.02684	−	6.23797i	0.0649108	−	0.199775i
$976$	−10.7759	+	6.42012i	−0.344929	+	0.205503i
$977$	−46.7622	+	33.9747i	−1.49606	+	1.08695i	−0.524136	+	0.851635i	$0.675612\pi$
$977$	−46.7622	+	33.9747i	−1.49606	+	1.08695i	−0.971920	+	0.235313i	$0.924388\pi$
$978$	2.96821	+	53.1495i	0.0949128	+	1.69953i
$979$	7.04319	+	11.5801i	0.225101	+	0.370100i
$980$	9.47250	−	1.06132i	0.302588	−	0.0339026i
$981$	23.6293	+	32.5230i	0.754426	+	1.03838i
$982$	45.3074	−	17.5704i	1.44582	−	0.560693i
$983$	−29.3068	−	9.52235i	−0.934741	−	0.303716i	−0.198241	−	0.980153i	$-0.563523\pi$
$983$	−29.3068	−	9.52235i	−0.934741	−	0.303716i	−0.736500	+	0.676437i	$0.763523\pi$
$984$	12.5230	−	25.2156i	0.399218	−	0.803844i
$985$	3.52727	−	4.85486i	0.112388	−	0.154689i
$986$	−15.5207	−	4.10178i	−0.494280	−	0.130627i
$987$	−9.86609	−	30.3647i	−0.314041	−	0.966519i
$988$	−15.0032	−	16.4347i	−0.477317	−	0.522859i
$989$			36.3720i			1.15656i
$990$	4.22730	−	11.9409i	0.134353	−	0.379508i
$991$			33.1521i			1.05311i	0.850141	+	0.526556i	$0.176517\pi$
$991$			33.1521i			1.05311i	−0.850141	+	0.526556i	$0.823483\pi$
$992$	−3.23622	+	4.13952i	−0.102750	+	0.131430i
$993$	−3.53428	−	10.8774i	−0.112157	−	0.345184i
$994$	−7.07298	+	26.7634i	−0.224341	+	0.848885i
$995$	−4.49764	+	6.19047i	−0.142585	+	0.196251i
$996$	−8.24465	+	14.5090i	−0.261242	+	0.459736i
$997$	11.1958	+	3.63774i	0.354575	+	0.115208i	0.480888	−	0.876782i	$-0.340314\pi$
$997$	11.1958	+	3.63774i	0.354575	+	0.115208i	−0.126313	+	0.991990i	$0.540314\pi$
$998$	13.0229	+	33.5812i	0.412233	+	1.06300i
$999$	−2.83152	−	3.89725i	−0.0895853	−	0.123304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.r.d.151.10	yes	48
4.3	odd	2	inner	220.2.r.d.151.9	yes	48
11.7	odd	10	inner	220.2.r.d.51.9	✓	48
44.7	even	10	inner	220.2.r.d.51.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.r.d.51.9	✓	48	11.7	odd	10	inner
220.2.r.d.51.10	yes	48	44.7	even	10	inner
220.2.r.d.151.9	yes	48	4.3	odd	2	inner
220.2.r.d.151.10	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.893756 + 1.09599i) q^{2} +(2.27074 - 0.737810i) q^{3} +(-0.402399 + 1.95910i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.83813 + 1.82930i) q^{6} +(0.461886 - 1.42154i) q^{7} +(-2.50681 + 1.30993i) q^{8} +(2.18487 - 1.58740i) q^{9} +(-0.0788559 - 1.41201i) q^{10} +(1.72348 + 2.83366i) q^{11} +(0.531698 + 4.74551i) q^{12} +(-1.61471 - 2.22245i) q^{13} +(1.97081 - 0.764287i) q^{14} +(-2.27074 - 0.737810i) q^{15} +(-3.67615 - 1.57668i) q^{16} +(-3.56124 + 4.90162i) q^{17} +(3.69251 + 0.975849i) q^{18} +(-1.25160 - 3.85204i) q^{19} +(1.47708 - 1.34842i) q^{20} -3.56874i q^{21} +(-1.56530 + 4.42152i) q^{22} -7.20345i q^{23} +(-4.72584 + 4.82407i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.992638 - 3.75604i) q^{26} +(-0.420118 + 0.578243i) q^{27} +(2.59908 + 1.47691i) q^{28} +(1.78189 + 0.578971i) q^{29} +(-1.22086 - 3.14814i) q^{30} +(-0.545968 - 0.751461i) q^{31} +(-1.55755 - 5.43820i) q^{32} +(6.00428 + 5.16291i) q^{33} +(-8.55502 + 0.477767i) q^{34} +(-1.20923 + 0.878560i) q^{35} +(2.23068 + 4.91914i) q^{36} +(-2.08272 + 6.40994i) q^{37} +(3.10318 - 4.81453i) q^{38} +(-5.30634 - 3.85528i) q^{39} +(2.79801 + 0.413706i) q^{40} +(-3.96497 + 1.28830i) q^{41} +(3.91131 - 3.18958i) q^{42} -5.04924 q^{43} +(-6.24495 + 2.23621i) q^{44} -2.70064 q^{45} +(7.89493 - 6.43813i) q^{46} +(8.50853 - 2.76459i) q^{47} +(-9.51089 - 0.867940i) q^{48} +(3.85568 + 2.80132i) q^{49} +(-0.766165 + 1.18869i) q^{50} +(-4.47019 + 13.7578i) q^{51} +(5.00377 - 2.26906i) q^{52} +(6.02442 - 4.37700i) q^{53} +(-1.00923 + 0.0563621i) q^{54} +(0.271257 - 3.30551i) q^{55} +(0.704262 + 4.16857i) q^{56} +(-5.68414 - 7.82355i) q^{57} +(0.958027 + 2.47039i) q^{58} +(11.1961 + 3.63782i) q^{59} +(2.35919 - 4.15172i) q^{60} +(1.84322 - 2.53697i) q^{61} +(0.335633 - 1.27000i) q^{62} +(-1.24739 - 3.83907i) q^{63} +(4.56816 - 6.56749i) q^{64} +2.74711i q^{65} +(-0.292147 + 11.1950i) q^{66} -11.6402i q^{67} +(-8.16973 - 8.94923i) q^{68} +(-5.31478 - 16.3572i) q^{69} +(-2.04366 - 0.540093i) q^{70} +(-7.69755 + 10.5948i) q^{71} +(-3.39765 + 6.84132i) q^{72} +(-7.42303 - 2.41189i) q^{73} +(-8.88669 + 3.44628i) q^{74} +(1.40340 + 1.93161i) q^{75} +(8.05017 - 0.901959i) q^{76} +(4.82421 - 1.14117i) q^{77} +(-0.517215 - 9.26139i) q^{78} +(-3.96666 + 2.88195i) q^{79} +(2.04732 + 3.43635i) q^{80} +(-3.03098 + 9.32840i) q^{81} +(-4.95569 - 3.19416i) q^{82} +(2.82727 + 2.05413i) q^{83} +(6.99152 + 1.43606i) q^{84} +(5.76220 - 1.87225i) q^{85} +(-4.51279 - 5.53393i) q^{86} +4.47338 q^{87} +(-8.03233 - 4.84579i) q^{88} +4.08661 q^{89} +(-2.41372 - 2.95988i) q^{90} +(-3.90512 + 1.26885i) q^{91} +(14.1123 + 2.89866i) q^{92} +(-1.79419 - 1.30355i) q^{93} +(10.6345 + 6.85442i) q^{94} +(-1.25160 + 3.85204i) q^{95} +(-7.54916 - 11.1996i) q^{96} +(12.0540 - 8.75773i) q^{97} +(0.375818 + 6.72949i) q^{98} +(8.26371 + 3.45531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{5} + 20 q^{6} + 16 q^{9} + 14 q^{12} - 10 q^{13} - 21 q^{14} - 4 q^{16} - 25 q^{18} + 5 q^{20} + 15 q^{22} - 30 q^{24} - 12 q^{25} - 4 q^{26} - 60 q^{28} + 20 q^{29} - 10 q^{33} - 18 q^{34}+ \cdots + 38 q^{97}+O(q^{100}) \) 48 * q - 12 * q^5 + 20 * q^6 + 16 * q^9 + 14 * q^12 - 10 * q^13 - 21 * q^14 - 4 * q^16 - 25 * q^18 + 5 * q^20 + 15 * q^22 - 30 * q^24 - 12 * q^25 - 4 * q^26 - 60 * q^28 + 20 * q^29 - 10 * q^33 - 18 * q^34 + 66 * q^36 - 44 * q^37 + 11 * q^38 - 10 * q^41 + 19 * q^42 - 35 * q^44 - 44 * q^45 + 5 * q^46 + 41 * q^48 - 2 * q^49 + 50 * q^52 - 36 * q^53 - 28 * q^56 + 30 * q^57 - 38 * q^58 - 21 * q^60 + 36 * q^64 + 43 * q^66 - 65 * q^68 + 24 * q^69 - 21 * q^70 - 60 * q^72 - 20 * q^73 - 70 * q^74 + 16 * q^77 - 56 * q^78 + q^80 + 50 * q^81 + 35 * q^82 + 60 * q^84 + 10 * q^85 + 38 * q^86 - 101 * q^88 + 64 * q^89 + 70 * q^92 - 28 * q^93 + 130 * q^94 + 105 * q^96 + 38 * q^97

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