LMFDB - Embedded newform 728.2.cz.a.309.49

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(309,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.309"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			309.49
Character	$\chi$	$=$	728.309
Dual form			728.2.cz.a.589.49

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.293640 - 1.38339i) q^{2} +(-2.98372 + 1.72265i) q^{3} +(-1.82755 - 0.812438i) q^{4} +1.10429 q^{5} +(1.50696 + 4.63349i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-1.66056 + 2.28966i) q^{8} +(4.43504 - 7.68171i) q^{9} +(0.324264 - 1.52767i) q^{10} +(-0.632386 - 1.09532i) q^{11} +(6.85244 - 0.724147i) q^{12} +(2.90558 - 2.13486i) q^{13} +(-0.945996 + 1.05123i) q^{14} +(-3.29490 + 1.90231i) q^{15} +(2.67989 + 2.96954i) q^{16} +(-1.97509 + 3.42096i) q^{17} +(-9.32452 - 8.39105i) q^{18} +(-1.08237 + 1.87472i) q^{19} +(-2.01815 - 0.897169i) q^{20} +3.44530 q^{21} +(-1.70096 + 0.553207i) q^{22} +(-1.81870 - 3.15008i) q^{23} +(1.01037 - 9.69225i) q^{24} -3.78054 q^{25} +(-2.10016 - 4.64643i) q^{26} +20.2242i q^{27} +(1.17649 + 1.61737i) q^{28} +(-2.32909 + 1.34470i) q^{29} +(1.66413 + 5.11673i) q^{30} +7.35070i q^{31} +(4.89497 - 2.83537i) q^{32} +(3.77372 + 2.17876i) q^{33} +(4.15256 + 3.73686i) q^{34} +(-0.956346 - 0.552146i) q^{35} +(-14.3462 + 10.4355i) q^{36} +(3.35653 + 5.81368i) q^{37} +(2.27564 + 2.04783i) q^{38} +(-4.99180 + 11.3751i) q^{39} +(-1.83375 + 2.52845i) q^{40} +(-4.17385 + 2.40977i) q^{41} +(1.01168 - 4.76620i) q^{42} +(-7.53494 - 4.35030i) q^{43} +(0.265835 + 2.51553i) q^{44} +(4.89758 - 8.48286i) q^{45} +(-4.89185 + 1.59099i) q^{46} +6.57532i q^{47} +(-13.1115 - 4.24376i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-1.11012 + 5.22997i) q^{50} -13.6096i q^{51} +(-7.04453 + 1.54097i) q^{52} +12.0976i q^{53} +(27.9780 + 5.93861i) q^{54} +(-0.698339 - 1.20956i) q^{55} +(2.58292 - 1.15262i) q^{56} -7.45817i q^{57} +(1.17634 + 3.61690i) q^{58} +(3.99638 - 6.92193i) q^{59} +(7.56710 - 0.799671i) q^{60} +(-8.38431 - 4.84068i) q^{61} +(10.1689 + 2.15846i) q^{62} +(-7.68171 + 4.43504i) q^{63} +(-2.48507 - 7.60424i) q^{64} +(3.20861 - 2.35751i) q^{65} +(4.12219 - 4.58076i) q^{66} +(6.00436 + 10.3999i) q^{67} +(6.38890 - 4.64734i) q^{68} +(10.8530 + 6.26597i) q^{69} +(-1.04466 + 1.16087i) q^{70} +(-0.561897 - 0.324412i) q^{71} +(10.2238 + 22.9107i) q^{72} +1.33955i q^{73} +(9.02821 - 2.93627i) q^{74} +(11.2800 - 6.51254i) q^{75} +(3.50118 - 2.54679i) q^{76} +1.26477i q^{77} +(14.2704 + 10.2458i) q^{78} -4.65512 q^{79} +(2.95938 + 3.27925i) q^{80} +(-21.5340 - 37.2980i) q^{81} +(2.10806 + 6.48168i) q^{82} +1.16159 q^{83} +(-6.29646 - 2.79909i) q^{84} +(-2.18108 + 3.77774i) q^{85} +(-8.23073 + 9.14636i) q^{86} +(4.63289 - 8.02440i) q^{87} +(3.55803 + 0.370906i) q^{88} +(-3.20425 + 1.84998i) q^{89} +(-10.2970 - 9.26618i) q^{90} +(-3.58373 + 0.396054i) q^{91} +(0.764525 + 7.23452i) q^{92} +(-12.6627 - 21.9324i) q^{93} +(9.09625 + 1.93077i) q^{94} +(-1.19525 + 2.07024i) q^{95} +(-9.72085 + 16.8922i) q^{96} +(5.43009 + 3.13506i) q^{97} +(1.34487 - 0.437397i) q^{98} -11.2186 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 18 q^{6} + 84 q^{9} - 8 q^{10} - 4 q^{12} + 8 q^{16} + 4 q^{17} - 18 q^{22} + 24 q^{23} + 48 q^{24} + 160 q^{25} - 30 q^{26} - 8 q^{30} + 22 q^{36} - 20 q^{38} - 48 q^{39} + 4 q^{40} + 12 q^{41}+ \cdots - 104 q^{95}+O(q^{100}) $ 168 * q - 18 * q^6 + 84 * q^9 - 8 * q^10 - 4 * q^12 + 8 * q^16 + 4 * q^17 - 18 * q^22 + 24 * q^23 + 48 * q^24 + 160 * q^25 - 30 * q^26 - 8 * q^30 + 22 * q^36 - 20 * q^38 - 48 * q^39 + 4 * q^40 + 12 * q^41 - 54 * q^48 + 84 * q^49 - 30 * q^50 - 58 * q^52 + 24 * q^54 - 32 * q^55 - 12 * q^58 + 28 * q^62 - 36 * q^64 + 12 * q^65 - 60 * q^66 - 64 * q^68 - 132 * q^72 + 62 * q^74 - 78 * q^76 + 30 * q^78 - 80 * q^79 + 48 * q^80 - 84 * q^81 - 18 * q^82 - 42 * q^84 - 24 * q^87 + 42 * q^88 + 40 * q^90 - 24 * q^92 + 12 * q^94 - 104 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.293640	−	1.38339i	0.207634	−	0.978206i
$2$	0.293640	−	1.38339i	0.207634	−	0.978206i
$3$	−2.98372	+	1.72265i	−1.72265	+	0.994572i	−0.809298	+	0.587398i	$0.800152\pi$
$3$	−2.98372	+	1.72265i	−1.72265	+	0.994572i	−0.913351	+	0.407173i	$0.866515\pi$
$4$	−1.82755	−	0.812438i	−0.913776	−	0.406219i
$5$	1.10429			0.493855			0.246927	−	0.969034i	$-0.420579\pi$
$5$	1.10429			0.493855			0.246927	+	0.969034i	$0.420579\pi$
$6$	1.50696	+	4.63349i	0.615215	+	1.89161i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	−1.66056	+	2.28966i	−0.587097	+	0.809516i
$9$	4.43504	−	7.68171i	1.47835	−	2.56057i
$10$	0.324264	−	1.52767i	0.102541	−	0.483092i
$11$	−0.632386	−	1.09532i	−0.190671	−	0.330253i	0.754802	−	0.655953i	$-0.227733\pi$
$11$	−0.632386	−	1.09532i	−0.190671	−	0.330253i	−0.945473	+	0.325701i	$0.894400\pi$
$12$	6.85244	−	0.724147i	1.97813	−	0.209043i
$13$	2.90558	−	2.13486i	0.805862	−	0.592103i
$13$	2.90558	−	2.13486i	0.805862	−	0.592103i
$14$	−0.945996	+	1.05123i	−0.252828	+	0.280954i
$15$	−3.29490	+	1.90231i	−0.850738	+	0.491174i
$16$	2.67989	+	2.96954i	0.669973	+	0.742386i
$17$	−1.97509	+	3.42096i	−0.479030	+	0.829704i	−0.999711	−	0.0240472i	$-0.992345\pi$
$17$	−1.97509	+	3.42096i	−0.479030	+	0.829704i	0.520681	+	0.853751i	$0.325678\pi$
$18$	−9.32452	−	8.39105i	−2.19781	−	1.97779i
$19$	−1.08237	+	1.87472i	−0.248312	+	0.430090i	−0.963058	−	0.269295i	$-0.913209\pi$
$19$	−1.08237	+	1.87472i	−0.248312	+	0.430090i	0.714745	+	0.699385i	$0.246543\pi$
$20$	−2.01815	−	0.897169i	−0.451273	−	0.200613i
$21$	3.44530			0.751826
$22$	−1.70096	+	0.553207i	−0.362645	+	0.117944i
$23$	−1.81870	−	3.15008i	−0.379226	−	0.656838i	0.611724	−	0.791071i	$-0.290476\pi$
$23$	−1.81870	−	3.15008i	−0.379226	−	0.656838i	−0.990950	+	0.134233i	$0.957143\pi$
$24$	1.01037	−	9.69225i	0.206240	−	1.97842i
$25$	−3.78054			−0.756108
$26$	−2.10016	−	4.64643i	−0.411875	−	0.911240i
$27$			20.2242i			3.89214i
$28$	1.17649	+	1.61737i	0.222335	+	0.305654i
$29$	−2.32909	+	1.34470i	−0.432501	+	0.249704i	−0.700411	−	0.713739i	$-0.747000\pi$
$29$	−2.32909	+	1.34470i	−0.432501	+	0.249704i	0.267911	+	0.963444i	$0.413667\pi$
$30$	1.66413	+	5.11673i	0.303827	+	0.934182i
$31$			7.35070i			1.32023i	0.751167	+	0.660113i	$0.229491\pi$
$31$			7.35070i			1.32023i	−0.751167	+	0.660113i	$0.770509\pi$
$32$	4.89497	−	2.83537i	0.865316	−	0.501227i
$33$	3.77372	+	2.17876i	0.656920	+	0.379273i
$34$	4.15256	+	3.73686i	0.712159	+	0.640865i
$35$	−0.956346	−	0.552146i	−0.161652	−	0.0933298i
$36$	−14.3462	+	10.4355i	−2.39103	+	1.73926i
$37$	3.35653	+	5.81368i	0.551810	+	0.955763i	0.998144	+	0.0608964i	$0.0193959\pi$
$37$	3.35653	+	5.81368i	0.551810	+	0.955763i	−0.446334	+	0.894866i	$0.647271\pi$
$38$	2.27564	+	2.04783i	0.369158	+	0.332202i
$39$	−4.99180	+	11.3751i	−0.799328	+	1.82147i
$40$	−1.83375	+	2.52845i	−0.289941	+	0.399784i
$41$	−4.17385	+	2.40977i	−0.651846	+	0.376343i	−0.789163	−	0.614184i	$-0.789485\pi$
$41$	−4.17385	+	2.40977i	−0.651846	+	0.376343i	0.137317	+	0.990527i	$0.456152\pi$
$42$	1.01168	−	4.76620i	0.156105	−	0.735441i
$43$	−7.53494	−	4.35030i	−1.14907	−	0.663414i	−0.200408	−	0.979713i	$-0.564227\pi$
$43$	−7.53494	−	4.35030i	−1.14907	−	0.663414i	−0.948660	+	0.316298i	$0.897560\pi$
$44$	0.265835	+	2.51553i	0.0400761	+	0.379231i
$45$	4.89758	−	8.48286i	0.730088	−	1.26455i
$46$	−4.89185	+	1.59099i	−0.721263	+	0.234579i
$47$			6.57532i			0.959109i	0.877512	+	0.479554i	$0.159202\pi$
$47$			6.57532i			0.959109i	−0.877512	+	0.479554i	$0.840798\pi$
$48$	−13.1115	−	4.24376i	−1.89248	−	0.612534i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−1.11012	+	5.22997i	−0.156994	+	0.739629i
$51$		−	13.6096i		−	1.90572i
$52$	−7.04453	+	1.54097i	−0.976901	+	0.213694i
$53$			12.0976i			1.66173i	0.556472	+	0.830866i	$0.312155\pi$
$53$			12.0976i			1.66173i	−0.556472	+	0.830866i	$0.687845\pi$
$54$	27.9780	+	5.93861i	3.80732	+	0.808143i
$55$	−0.698339	−	1.20956i	−0.0941640	−	0.163097i
$56$	2.58292	−	1.15262i	0.345157	−	0.154025i
$57$		−	7.45817i		−	0.987858i
$58$	1.17634	+	3.61690i	0.154460	+	0.474922i
$59$	3.99638	−	6.92193i	0.520284	−	0.901159i	−0.479437	−	0.877576i	$-0.659159\pi$
$59$	3.99638	−	6.92193i	0.520284	−	0.901159i	0.999722	−	0.0235830i	$-0.00750740\pi$
$60$	7.56710	−	0.799671i	0.976908	−	0.103237i
$61$	−8.38431	−	4.84068i	−1.07350	−	0.619786i	−0.144365	−	0.989524i	$-0.546114\pi$
$61$	−8.38431	−	4.84068i	−1.07350	−	0.619786i	−0.929136	+	0.369738i	$0.879447\pi$
$62$	10.1689	+	2.15846i	1.29145	+	0.274124i
$63$	−7.68171	+	4.43504i	−0.967805	+	0.558762i
$64$	−2.48507	−	7.60424i	−0.310634	−	0.950530i
$65$	3.20861	−	2.35751i	0.397979	−	0.292413i
$66$	4.12219	−	4.58076i	0.507406	−	0.563853i
$67$	6.00436	+	10.3999i	0.733550	+	1.27055i	0.955357	+	0.295455i	$0.0954711\pi$
$67$	6.00436	+	10.3999i	0.733550	+	1.27055i	−0.221807	+	0.975091i	$0.571196\pi$
$68$	6.38890	−	4.64734i	0.774767	−	0.563573i
$69$	10.8530	+	6.26597i	1.30655	+	0.754334i
$70$	−1.04466	+	1.16087i	−0.124860	+	0.138750i
$71$	−0.561897	−	0.324412i	−0.0666850	−	0.0385006i	0.466287	−	0.884634i	$-0.345591\pi$
$71$	−0.561897	−	0.324412i	−0.0666850	−	0.0385006i	−0.532972	+	0.846133i	$0.678925\pi$
$72$	10.2238	+	22.9107i	1.20489	+	2.70005i
$73$			1.33955i			0.156783i	0.996923	+	0.0783915i	$0.0249784\pi$
$73$			1.33955i			0.156783i	−0.996923	+	0.0783915i	$0.975022\pi$
$74$	9.02821	−	2.93627i	1.04951	−	0.341335i
$75$	11.2800	−	6.51254i	1.30251	−	0.752003i
$76$	3.50118	−	2.54679i	0.401612	−	0.292136i
$77$			1.26477i			0.144134i
$78$	14.2704	+	10.2458i	1.61581	+	1.16011i
$79$	−4.65512			−0.523742			−0.261871	−	0.965103i	$-0.584340\pi$
$79$	−4.65512			−0.523742			−0.261871	+	0.965103i	$0.584340\pi$
$80$	2.95938	+	3.27925i	0.330869	+	0.366631i
$81$	−21.5340	−	37.2980i	−2.39267	−	4.14422i
$82$	2.10806	+	6.48168i	0.232796	+	0.715782i
$83$	1.16159			0.127501			0.0637505	−	0.997966i	$-0.479694\pi$
$83$	1.16159			0.127501			0.0637505	+	0.997966i	$0.479694\pi$
$84$	−6.29646	−	2.79909i	−0.687000	−	0.305406i
$85$	−2.18108	+	3.77774i	−0.236571	+	0.409753i
$86$	−8.23073	+	9.14636i	−0.887542	+	0.986277i
$87$	4.63289	−	8.02440i	0.496698	−	0.860306i
$88$	3.55803	+	0.370906i	0.379288	+	0.0395387i
$89$	−3.20425	+	1.84998i	−0.339650	+	0.196097i	−0.660117	−	0.751163i	$-0.729493\pi$
$89$	−3.20425	+	1.84998i	−0.339650	+	0.196097i	0.320467	+	0.947260i	$0.396160\pi$
$90$	−10.2970	−	9.26618i	−1.08540	−	0.976741i
$91$	−3.58373	+	0.396054i	−0.375677	+	0.0415177i
$92$	0.764525	+	7.23452i	0.0797072	+	0.754251i
$93$	−12.6627	−	21.9324i	−1.31306	−	2.27428i
$94$	9.09625	+	1.93077i	0.938206	+	0.199144i
$95$	−1.19525	+	2.07024i	−0.122630	+	0.212402i
$96$	−9.72085	+	16.8922i	−0.992130	+	1.72406i
$97$	5.43009	+	3.13506i	0.551342	+	0.318317i	0.749663	−	0.661820i	$-0.230216\pi$
$97$	5.43009	+	3.13506i	0.551342	+	0.318317i	−0.198321	+	0.980137i	$0.563549\pi$
$98$	1.34487	−	0.437397i	0.135853	−	0.0441838i
$99$	−11.2186			−1.12751
$100$	6.90913	+	3.07145i	0.690913	+	0.307145i
$101$	4.35178	−	2.51250i	0.433018	−	0.250003i	−0.267613	−	0.963526i	$-0.586235\pi$
$101$	4.35178	−	2.51250i	0.433018	−	0.250003i	0.700632	+	0.713523i	$0.252902\pi$
$102$	−18.8274	−	3.99630i	−1.86419	−	0.395693i
$103$	8.11441			0.799537			0.399769	−	0.916616i	$-0.369091\pi$
$103$	8.11441			0.799537			0.399769	+	0.916616i	$0.369091\pi$
$104$	0.0632087	+	10.1978i	0.00619812	+	0.999981i
$105$	3.80462			0.371293
$106$	16.7357	+	3.55233i	1.62552	+	0.345033i
$107$	−13.2688	+	7.66077i	−1.28275	+	0.740595i	−0.977350	−	0.211630i	$-0.932123\pi$
$107$	−13.2688	+	7.66077i	−1.28275	+	0.740595i	−0.305398	+	0.952225i	$0.598790\pi$
$108$	16.4309	−	36.9607i	1.58106	−	3.55654i
$109$	−6.99621			−0.670115			−0.335058	−	0.942198i	$-0.608756\pi$
$109$	−6.99621			−0.670115			−0.335058	+	0.942198i	$0.608756\pi$
$110$	−1.87835	+	0.610903i	−0.179094	+	0.0582473i
$111$	−20.0299	−	11.5642i	−1.90115	−	1.09763i
$112$	−0.836081	−	3.91165i	−0.0790023	−	0.369616i
$113$	−9.99894	+	17.3187i	−0.940621	+	1.62920i	−0.176332	+	0.984331i	$0.556423\pi$
$113$	−9.99894	+	17.3187i	−0.940621	+	1.62920i	−0.764290	+	0.644873i	$0.776910\pi$
$114$	−10.3176	−	2.19001i	−0.966329	−	0.205113i
$115$	−2.00838	−	3.47862i	−0.187282	−	0.324383i
$116$	5.34901	−	0.565269i	0.496643	−	0.0524839i
$117$	−3.51303	−	31.7880i	−0.324780	−	2.93880i
$118$	−8.40226	−	7.56112i	−0.773491	−	0.696057i
$119$	3.42096	−	1.97509i	0.313599	−	0.181056i
$120$	1.11574	−	10.7031i	0.101853	−	0.977053i
$121$	4.70018	−	8.14095i	0.427289	−	0.740086i
$122$	−9.15853	+	10.1774i	−0.829175	+	0.921417i
$123$	8.30239	−	14.3802i	0.748601	−	1.29661i
$124$	5.97199	−	13.4338i	0.536300	−	1.20639i
$125$	−9.69628			−0.867262
$126$	3.87975	+	11.9291i	0.345635	+	1.06273i
$127$	−6.63803	−	11.4974i	−0.589030	−	1.02023i	−0.994360	−	0.106059i	$-0.966177\pi$
$127$	−6.63803	−	11.4974i	−0.589030	−	1.02023i	0.405330	−	0.914171i	$-0.367157\pi$
$128$	−11.2494	+	1.20492i	−0.994313	+	0.106501i
$129$	29.9761			2.63925
$130$	−2.31919	−	5.13102i	−0.203406	−	0.450020i
$131$			1.38878i			0.121338i	0.998158	+	0.0606692i	$0.0193235\pi$
$131$			1.38878i			0.121338i	−0.998158	+	0.0606692i	$0.980677\pi$
$132$	−5.12656	−	7.04770i	−0.446210	−	0.613423i
$133$	1.87472	−	1.08237i	0.162559	−	0.0938533i
$134$	16.1502	−	5.25258i	1.39517	−	0.453754i
$135$			22.3334i			1.92215i
$136$	−4.55306	−	10.2030i	−0.390422	−	0.874900i
$137$	5.74298	+	3.31571i	0.490656	+	0.283280i	0.724846	−	0.688910i	$-0.241911\pi$
$137$	5.74298	+	3.31571i	0.490656	+	0.283280i	−0.234191	+	0.972191i	$0.575244\pi$
$138$	11.8552	−	13.1740i	1.00918	−	1.12145i
$139$	6.96487	+	4.02117i	0.590753	+	0.341071i	0.765395	−	0.643561i	$-0.222544\pi$
$139$	6.96487	+	4.02117i	0.590753	+	0.341071i	−0.174642	+	0.984632i	$0.555877\pi$
$140$	1.29919	+	1.78605i	0.109801	+	0.150949i
$141$	−11.3270	−	19.6189i	−0.953902	−	1.65221i
$142$	−0.613784	+	0.682065i	−0.0515076	+	0.0572376i
$143$	−4.17581	−	1.83249i	−0.349199	−	0.153241i
$144$	34.6966	−	7.41611i	2.89138	−	0.618009i
$145$	−2.57199	+	1.48494i	−0.213593	+	0.123318i
$146$	1.85313	+	0.393346i	0.153366	+	0.0325535i
$147$	−2.98372	−	1.72265i	−0.246093	−	0.142082i
$148$	−1.41098	−	13.3518i	−0.115982	−	1.09751i
$149$	−0.146820	+	0.254300i	−0.0120280	+	0.0208331i	−0.871977	−	0.489547i	$-0.837162\pi$
$149$	−0.146820	+	0.254300i	−0.0120280	+	0.0208331i	0.859949	+	0.510380i	$0.170495\pi$
$150$	−5.69713	−	17.5171i	−0.465169	−	1.43026i
$151$			5.20111i			0.423261i	0.977350	+	0.211630i	$0.0678773\pi$
$151$			5.20111i			0.423261i	−0.977350	+	0.211630i	$0.932123\pi$
$152$	−2.49512	−	5.59134i	−0.202381	−	0.453518i
$153$	17.5192	+	30.3442i	1.41634	+	2.45318i
$154$	1.74968	+	0.371387i	0.140993	+	0.0299272i
$155$			8.11733i			0.651999i
$156$	18.3643	−	16.7331i	1.47032	−	1.33972i
$157$			18.9389i			1.51149i	0.654865	+	0.755746i	$0.272725\pi$
$157$			18.9389i			1.51149i	−0.654865	+	0.755746i	$0.727275\pi$
$158$	−1.36693	+	6.43986i	−0.108747	+	0.512328i
$159$	−20.8399	−	36.0958i	−1.65271	−	2.86258i
$160$	5.40548	−	3.13107i	0.427340	−	0.247533i
$161$			3.63740i			0.286668i
$162$	−57.9210	+	18.8378i	−4.55070	+	1.48004i
$163$	−0.304087	+	0.526695i	−0.0238180	+	0.0412539i	−0.877689	−	0.479231i	$-0.840916\pi$
$163$	−0.304087	+	0.526695i	−0.0238180	+	0.0412539i	0.853871	+	0.520485i	$0.174249\pi$
$164$	9.58572	−	1.01299i	0.748519	−	0.0791014i
$165$	4.16729	+	2.40598i	0.324423	+	0.187306i
$166$	0.341088	−	1.60693i	0.0264736	−	0.124722i
$167$	−2.93500	+	1.69452i	−0.227117	+	0.131126i	−0.609241	−	0.792985i	$-0.708526\pi$
$167$	−2.93500	+	1.69452i	−0.227117	+	0.131126i	0.382124	+	0.924111i	$0.375193\pi$
$168$	−5.72113	+	7.88855i	−0.441395	+	0.608615i
$169$	3.88475	−	12.4060i	0.298827	−	0.954307i
$170$	4.58565	+	4.12658i	0.351703	+	0.316494i
$171$	9.60069	+	16.6289i	0.734183	+	1.27164i
$172$	10.2361	+	14.0721i	0.780499	+	1.07298i
$173$	−7.33583	−	4.23534i	−0.557733	−	0.322007i	0.194502	−	0.980902i	$-0.437691\pi$
$173$	−7.33583	−	4.23534i	−0.557733	−	0.322007i	−0.752235	+	0.658895i	$0.771024\pi$
$174$	−9.74050	−	8.76539i	−0.738425	−	0.664502i
$175$	3.27404	+	1.89027i	0.247494	+	0.142891i
$176$	1.55789	−	4.81324i	0.117430	−	0.362812i
$177$			27.5374i			2.06984i
$178$	1.61835	+	4.97597i	0.121300	+	0.372964i
$179$	9.86267	−	5.69421i	0.737170	−	0.425606i	−0.0838692	−	0.996477i	$-0.526728\pi$
$179$	9.86267	−	5.69421i	0.737170	−	0.425606i	0.821040	+	0.570871i	$0.193394\pi$
$180$	−15.8424	+	11.5239i	−1.18082	+	0.858939i
$181$			17.4262i			1.29528i	0.761946	+	0.647641i	$0.224244\pi$
$181$			17.4262i			1.29528i	−0.761946	+	0.647641i	$0.775756\pi$
$182$	−0.504427	+	5.07401i	−0.0373906	+	0.376110i
$183$	33.3552			2.46569
$184$	10.2327	+	1.06670i	0.754363	+	0.0786384i
$185$	3.70659	+	6.42000i	0.272514	+	0.472008i
$186$	−34.0594	+	11.0772i	−2.49736	+	0.812223i
$187$	4.99608			0.365349
$188$	5.34203	−	12.0167i	0.389608	−	0.876410i
$189$	10.1121	−	17.5146i	0.735545	−	1.27400i
$190$	2.51298	+	2.26141i	0.182311	+	0.164060i
$191$	−3.37648	+	5.84823i	−0.244313	+	0.423163i	−0.961938	−	0.273267i	$-0.911896\pi$
$191$	−3.37648	+	5.84823i	−0.244313	+	0.423163i	0.717625	+	0.696430i	$0.245229\pi$
$192$	20.5142	+	18.4080i	1.48048	+	1.32848i
$193$	23.9017	−	13.7996i	1.72048	−	0.993320i	0.802546	−	0.596590i	$-0.203478\pi$
$193$	23.9017	−	13.7996i	1.72048	−	0.993320i	0.917935	−	0.396731i	$-0.129855\pi$
$194$	5.93151	−	6.59137i	0.425858	−	0.473233i
$195$	−5.51241	+	12.5614i	−0.394752	+	0.899543i
$196$	−0.210184	−	1.98892i	−0.0150132	−	0.142066i
$197$	−9.81939	−	17.0077i	−0.699602	−	1.21175i	−0.968604	−	0.248607i	$-0.920027\pi$
$197$	−9.81939	−	17.0077i	−0.699602	−	1.21175i	0.269002	−	0.963140i	$-0.413306\pi$
$198$	−3.29423	+	15.5198i	−0.234111	+	1.10294i
$199$	1.84857	−	3.20182i	0.131042	−	0.226971i	−0.793037	−	0.609174i	$-0.791501\pi$
$199$	1.84857	−	3.20182i	0.131042	−	0.226971i	0.924078	+	0.382203i	$0.124835\pi$
$200$	6.27782	−	8.65614i	0.443909	−	0.612081i
$201$	−35.8306	−	20.6868i	−2.52730	−	1.45914i
$202$	−2.19792	−	6.75799i	−0.154645	−	0.475491i
$203$	2.68940			0.188759
$204$	−11.0569	+	24.8722i	−0.774139	+	1.74140i
$205$	−4.60915	+	2.66110i	−0.321917	+	0.185859i
$206$	2.38271	−	11.2254i	0.166011	−	0.782112i
$207$	−32.2640			−2.24251
$208$	14.1262	+	2.90705i	0.979475	+	0.201567i
$209$	2.73790			0.189384
$210$	1.11719	−	5.26328i	0.0770931	−	0.363201i
$211$	13.5954	−	7.84932i	0.935948	−	0.540370i	0.0472599	−	0.998883i	$-0.484951\pi$
$211$	13.5954	−	7.84932i	0.935948	−	0.540370i	0.888688	+	0.458513i	$0.151618\pi$
$212$	9.82854	−	22.1090i	0.675027	−	1.51845i
$213$	2.23539			0.153166
$214$	6.70160	+	20.6055i	0.458112	+	1.40857i
$215$	−8.32078	−	4.80400i	−0.567472	−	0.327630i
$216$	−46.3064	−	33.5835i	−3.15075	−	2.28507i
$217$	3.67535	−	6.36590i	0.249499	−	0.432145i
$218$	−2.05436	+	9.67850i	−0.139139	+	0.655511i
$219$	−2.30758	−	3.99685i	−0.155932	−	0.270082i
$220$	0.293560	+	2.77789i	0.0197918	+	0.187285i
$221$	1.56449	+	14.1564i	0.105239	+	0.952262i
$222$	−21.8794	+	24.3134i	−1.46845	+	1.63181i
$223$	−4.63105	+	2.67374i	−0.310118	+	0.179047i	−0.646979	−	0.762508i	$-0.723968\pi$
$223$	−4.63105	+	2.67374i	−0.310118	+	0.179047i	0.336861	+	0.941554i	$0.390635\pi$
$224$	−5.65685	+	0.00801551i	−0.377964	+	0.000535559i
$225$	−16.7668	+	29.0410i	−1.11779	+	1.93607i
$226$	21.0224	+	18.9179i	1.39839	+	1.25840i
$227$	−8.50643	+	14.7336i	−0.564591	+	0.977901i	0.432496	+	0.901636i	$0.357633\pi$
$227$	−8.50643	+	14.7336i	−0.564591	+	0.977901i	−0.997088	+	0.0762650i	$0.975700\pi$
$228$	−6.05929	+	13.6302i	−0.401287	+	0.902681i
$229$	−16.7910			−1.10958			−0.554790	−	0.831990i	$-0.687201\pi$
$229$	−16.7910			−1.10958			−0.554790	+	0.831990i	$0.687201\pi$
$230$	−5.40203	+	1.75692i	−0.356199	+	0.115848i
$231$	−2.17876	−	3.77372i	−0.143352	−	0.248292i
$232$	0.788692	−	7.56577i	0.0517802	−	0.496717i
$233$	3.45393			0.226275			0.113137	−	0.993579i	$-0.463910\pi$
$233$	3.45393			0.226275			0.113137	+	0.993579i	$0.463910\pi$
$234$	−45.0068	−	4.47431i	−2.94219	−	0.292495i
$235$			7.26107i			0.473660i
$236$	−12.9272	+	9.40338i	−0.841491	+	0.612108i
$237$	13.8896	−	8.01914i	0.902224	−	0.520899i
$238$	−1.72780	−	5.31249i	−0.111997	−	0.344358i
$239$		−	5.91119i		−	0.382363i	−0.981555	−	0.191182i	$-0.938768\pi$
$239$		−	5.91119i		−	0.382363i	0.981555	−	0.191182i	$-0.0612319\pi$
$240$	−14.4789	−	4.68636i	−0.934612	−	0.302503i
$241$	−25.1316	−	14.5097i	−1.61887	−	0.934653i	−0.987214	−	0.159402i	$-0.949043\pi$
$241$	−25.1316	−	14.5097i	−1.61887	−	0.934653i	−0.631653	−	0.775251i	$-0.717623\pi$
$242$	−9.88197	−	8.89269i	−0.635237	−	0.571644i
$243$	75.9588	+	43.8548i	4.87276	+	2.81329i
$244$	11.3900	+	15.6583i	0.729171	+	1.00242i
$245$	0.552146	+	0.956346i	0.0352753	+	0.0610987i
$246$	−17.4555	−	15.7080i	−1.11292	−	1.00151i
$247$	0.857353	+	7.75784i	0.0545521	+	0.493620i
$248$	−16.8306	−	12.2063i	−1.06874	−	0.775101i
$249$	−3.46585	+	2.00101i	−0.219639	+	0.126809i
$250$	−2.84721	+	13.4138i	−0.180073	+	0.848361i
$251$	6.08959	+	3.51583i	0.384372	+	0.221917i	0.679719	−	0.733473i	$-0.262102\pi$
$251$	6.08959	+	3.51583i	0.384372	+	0.221917i	−0.295347	+	0.955390i	$0.595435\pi$
$252$	17.6419	−	1.86435i	1.11134	−	0.117443i
$253$	−2.30024	+	3.98414i	−0.144615	+	0.250480i
$254$	−17.8546	+	5.80691i	−1.12030	+	0.364358i
$255$		−	15.0289i		−	0.941148i
$256$	−1.63638	+	15.9161i	−0.102273	+	0.994756i
$257$	3.89472	+	6.74585i	0.242946	+	0.420795i	0.961552	−	0.274623i	$-0.0885529\pi$
$257$	3.89472	+	6.74585i	0.242946	+	0.420795i	−0.718606	+	0.695417i	$0.755220\pi$
$258$	8.80218	−	41.4688i	0.548000	−	2.58173i
$259$		−	6.71306i		−	0.417129i
$260$	−7.77922	+	1.70168i	−0.482447	+	0.105534i
$261$			23.8552i			1.47660i
$262$	1.92123	+	0.407801i	0.118694	+	0.0251941i
$263$	−8.40398	−	14.5561i	−0.518212	−	0.897569i	−0.999776	−	0.0211582i	$-0.993265\pi$
$263$	−8.40398	−	14.5561i	−0.518212	−	0.897569i	0.481565	−	0.876411i	$-0.340069\pi$
$264$	−11.2551	+	5.02256i	−0.692703	+	0.309117i
$265$			13.3593i			0.820655i
$266$	−0.946850	−	2.91130i	−0.0580551	−	0.178503i
$267$	6.37372	−	11.0396i	0.390065	−	0.675613i
$268$	−2.52404	−	23.8845i	−0.154181	−	1.45898i
$269$	−2.18354	−	1.26066i	−0.133133	−	0.0768641i	0.431955	−	0.901895i	$-0.357824\pi$
$269$	−2.18354	−	1.26066i	−0.133133	−	0.0768641i	−0.565087	+	0.825031i	$0.691157\pi$
$270$	30.8959	+	6.55797i	1.88026	+	0.399105i
$271$	15.4415	−	8.91518i	0.938007	−	0.541559i	0.0486721	−	0.998815i	$-0.484501\pi$
$271$	15.4415	−	8.91518i	0.938007	−	0.541559i	0.889335	+	0.457256i	$0.151168\pi$
$272$	−15.4517	+	3.30267i	−0.936898	+	0.200254i
$273$	10.0106	−	7.35523i	0.605868	−	0.445159i
$274$	6.27329	−	6.97117i	0.378984	−	0.421144i
$275$	2.39076	+	4.14091i	0.144168	+	0.249706i
$276$	−14.7437	−	20.2688i	−0.887465	−	1.22004i
$277$	10.2186	+	5.89973i	0.613978	+	0.354480i	0.774521	−	0.632549i	$-0.217991\pi$
$277$	10.2186	+	5.89973i	0.613978	+	0.354480i	−0.160543	+	0.987029i	$0.551325\pi$
$278$	7.60802	−	8.45438i	0.456299	−	0.507060i
$279$	56.4660	+	32.6006i	3.38053	+	1.95175i
$280$	2.85230	−	1.27283i	0.170457	−	0.0760662i
$281$			4.24747i			0.253383i	0.991942	+	0.126691i	$0.0404357\pi$
$281$			4.24747i			0.253383i	−0.991942	+	0.126691i	$0.959564\pi$
$282$	−30.4667	+	9.90876i	−1.81426	+	0.590058i
$283$	0.825038	−	0.476336i	0.0490434	−	0.0283152i	−0.475278	−	0.879836i	$-0.657652\pi$
$283$	0.825038	−	0.476336i	0.0490434	−	0.0283152i	0.524321	+	0.851521i	$0.324319\pi$
$284$	0.763332	+	1.04939i	0.0452954	+	0.0622696i
$285$		−	8.23600i		−	0.487858i
$286$	−3.76124	+	5.23869i	−0.222407	+	0.309770i
$287$	4.81955			0.284489
$288$	−0.0710982	−	50.1767i	−0.00418950	−	2.95669i
$289$	0.698032	+	1.20903i	0.0410607	+	0.0711192i
$290$	1.29902	+	3.99412i	0.0762810	+	0.234543i
$291$	−21.6024			−1.26636
$292$	1.08830	−	2.44810i	0.0636882	−	0.143264i
$293$	−10.3823	+	17.9827i	−0.606540	+	1.05056i	0.385266	+	0.922806i	$0.374110\pi$
$293$	−10.3823	+	17.9827i	−0.606540	+	1.05056i	−0.991806	+	0.127753i	$0.959224\pi$
$294$	−3.25924	+	3.62181i	−0.190083	+	0.211228i
$295$	4.41317	−	7.64384i	0.256945	−	0.445042i
$296$	−18.8851	−	1.96867i	−1.09767	−	0.114427i
$297$	22.1520	−	12.7895i	1.28539	−	0.742120i
$298$	0.308684	+	0.277782i	0.0178816	+	0.0160915i
$299$	−12.0094	−	5.27014i	−0.694520	−	0.304780i
$300$	−25.9059	+	2.73767i	−1.49568	+	0.158059i
$301$	4.35030	+	7.53494i	0.250747	+	0.434307i
$302$	7.19518	+	1.52725i	0.414036	+	0.0878835i
$303$	−8.65631	+	14.9932i	−0.497292	+	0.861336i
$304$	−8.46769	+	1.80990i	−0.485655	+	0.103805i
$305$	−9.25873	−	5.34553i	−0.530154	−	0.306084i
$306$	47.1222	−	15.3257i	2.69380	−	0.876112i
$307$	12.9029			0.736406			0.368203	−	0.929745i	$-0.379973\pi$
$307$	12.9029			0.736406			0.368203	+	0.929745i	$0.379973\pi$
$308$	1.02755	−	2.31143i	0.0585500	−	0.131706i
$309$	−24.2111	+	13.9783i	−1.37732	+	0.795197i
$310$	11.2295	+	2.38357i	0.637790	+	0.135378i
$311$	−15.4118			−0.873921			−0.436961	−	0.899481i	$-0.643945\pi$
$311$	−15.4118			−0.873921			−0.436961	+	0.899481i	$0.643945\pi$
$312$	−17.7559	−	30.3186i	−1.00523	−	1.71645i
$313$	9.85936			0.557284			0.278642	−	0.960395i	$-0.410116\pi$
$313$	9.85936			0.557284			0.278642	+	0.960395i	$0.410116\pi$
$314$	26.2000	+	5.56122i	1.47855	+	0.313838i
$315$	−8.48286	+	4.89758i	−0.477955	+	0.275947i
$316$	8.50748	+	3.78200i	0.478583	+	0.212754i
$317$	6.09198			0.342160			0.171080	−	0.985257i	$-0.445274\pi$
$317$	6.09198			0.342160			0.171080	+	0.985257i	$0.445274\pi$
$318$	−56.0541	+	18.2306i	−3.14336	+	1.02232i
$319$	2.94576	+	1.70074i	0.164931	+	0.0952230i
$320$	−2.74424	−	8.39730i	−0.153408	−	0.469424i
$321$	26.3936	−	45.7151i	1.47315	−	2.55157i
$322$	5.03196	+	1.06809i	0.280420	+	0.0595221i
$323$	−4.27555	−	7.40548i	−0.237898	−	0.412052i
$324$	9.05222	+	85.6590i	0.502901	+	4.75884i
$325$	−10.9846	+	8.07092i	−0.609318	+	0.447694i
$326$	0.639334	+	0.575331i	0.0354094	+	0.0318646i
$327$	20.8747	−	12.0520i	1.15437	−	0.666478i
$328$	1.41338	−	13.5583i	0.0780407	−	0.748630i
$329$	3.28766	−	5.69439i	0.181254	−	0.313942i
$330$	4.55210	−	5.05850i	0.250585	−	0.278461i
$331$	13.6426	−	23.6296i	0.749864	−	1.29880i	−0.198023	−	0.980197i	$-0.563452\pi$
$331$	13.6426	−	23.6296i	0.749864	−	1.29880i	0.947887	−	0.318605i	$-0.103215\pi$
$332$	−2.12286	−	0.943718i	−0.116507	−	0.0517933i
$333$	59.5453			3.26306
$334$	1.48236	+	4.55783i	0.0811110	+	0.249394i
$335$	6.63057	+	11.4845i	0.362267	+	0.627465i
$336$	9.23302	+	10.2310i	0.503703	+	0.558145i
$337$	29.8797			1.62765			0.813825	−	0.581111i	$-0.197382\pi$
$337$	29.8797			1.62765			0.813825	+	0.581111i	$0.197382\pi$
$338$	−16.0216	−	9.01703i	−0.871463	−	0.490462i
$339$		−	68.8987i		−	3.74206i
$340$	7.05521	−	5.13202i	0.382623	−	0.278323i
$341$	8.05140	−	4.64848i	0.436008	−	0.251729i
$342$	25.8234	−	8.39863i	1.39637	−	0.454146i
$343$		−	1.00000i		−	0.0539949i
$344$	22.4729	−	10.0285i	1.21166	−	0.540700i
$345$	11.9849	+	6.91946i	0.645243	+	0.372531i
$346$	−8.01324	+	8.90467i	−0.430794	+	0.478718i
$347$	−25.1665	−	14.5299i	−1.35101	−	0.780004i	−0.362617	−	0.931938i	$-0.618117\pi$
$347$	−25.1665	−	14.5299i	−1.35101	−	0.780004i	−0.988391	+	0.151934i	$0.951450\pi$
$348$	−14.9862	+	10.9011i	−0.803343	+	0.584359i
$349$	−9.12705	−	15.8085i	−0.488560	−	0.846210i	0.511354	−	0.859370i	$-0.329144\pi$
$349$	−9.12705	−	15.8085i	−0.488560	−	0.846210i	−0.999913	+	0.0131602i	$0.995811\pi$
$350$	3.57637	−	3.97423i	0.191165	−	0.212431i
$351$	43.1757	+	58.7628i	2.30455	+	3.13653i
$352$	−6.20115	−	3.56853i	−0.330522	−	0.190203i
$353$	−22.9048	+	13.2241i	−1.21910	+	0.703846i	−0.964725	−	0.263260i	$-0.915202\pi$
$353$	−22.9048	+	13.2241i	−1.21910	+	0.703846i	−0.254373	+	0.967106i	$0.581869\pi$
$354$	38.0951	+	8.08608i	2.02473	+	0.429770i
$355$	−0.620499	−	0.358245i	−0.0329327	−	0.0190137i
$356$	7.35893	−	0.777672i	0.390022	−	0.0412165i
$357$	−6.80478	+	11.7862i	−0.360147	+	0.623793i
$358$	−4.98127	−	15.3160i	−0.263268	−	0.809475i
$359$			6.00101i			0.316721i	0.987381	+	0.158361i	$0.0506209\pi$
$359$			6.00101i			0.316721i	−0.987381	+	0.158361i	$0.949379\pi$
$360$	11.2901	+	25.3001i	0.595041	+	1.33343i
$361$	7.15696	+	12.3962i	0.376682	+	0.652432i
$362$	24.1073	+	5.11703i	1.26705	+	0.268945i
$363$			32.3870i			1.69988i
$364$	6.87123	+	2.18775i	0.360150	+	0.114669i
$365$			1.47926i			0.0774280i
$366$	9.79440	−	46.1433i	0.511962	−	2.41195i
$367$	3.22529	+	5.58636i	0.168359	+	0.291606i	0.937843	−	0.347060i	$-0.112820\pi$
$367$	3.22529	+	5.58636i	0.168359	+	0.291606i	−0.769484	+	0.638666i	$0.779487\pi$
$368$	4.48039	−	13.8426i	0.233556	−	0.721595i
$369$			42.7497i			2.22546i
$370$	9.96979	−	3.24250i	0.518305	−	0.168570i
$371$	6.04880	−	10.4768i	0.314038	−	0.543930i
$372$	5.32299	+	50.3702i	0.275984	+	2.61158i
$373$	−18.4098	−	10.6289i	−0.953225	−	0.550345i	−0.0591439	−	0.998249i	$-0.518837\pi$
$373$	−18.4098	−	10.6289i	−0.953225	−	0.550345i	−0.894081	+	0.447905i	$0.852170\pi$
$374$	1.46705	−	6.91154i	0.0758591	−	0.357387i
$375$	28.9309	−	16.7033i	1.49399	−	0.862554i
$376$	−15.0552	−	10.9187i	−0.776414	−	0.563090i
$377$	−3.89660	+	8.87940i	−0.200685	+	0.457313i
$378$	−21.2603	−	19.1320i	−1.09351	−	0.984042i
$379$	6.31800	+	10.9431i	0.324534	+	0.562109i	0.981418	−	0.191882i	$-0.0614592\pi$
$379$	6.31800	+	10.9431i	0.324534	+	0.562109i	−0.656884	+	0.753992i	$0.728126\pi$
$380$	3.86632	−	2.81240i	0.198338	−	0.144273i
$381$	39.6120	+	22.8700i	2.02938	+	1.17167i
$382$	7.09893	+	6.38827i	0.363213	+	0.326852i
$383$	−8.84255	−	5.10525i	−0.451833	−	0.260866i	0.256771	−	0.966472i	$-0.417341\pi$
$383$	−8.84255	−	5.10525i	−0.451833	−	0.260866i	−0.708604	+	0.705606i	$0.750675\pi$
$384$	31.4892	−	22.9738i	1.60693	−	1.17238i
$385$			1.39668i			0.0711813i
$386$	−12.0719	−	37.1176i	−0.614441	−	1.88923i
$387$	−66.8355	+	38.5875i	−3.39744	+	1.96151i
$388$	−7.37672	−	10.1411i	−0.374496	−	0.514836i
$389$		−	31.6941i		−	1.60695i	−0.595337	−	0.803476i	$-0.702981\pi$
$389$		−	31.6941i		−	1.60695i	0.595337	−	0.803476i	$-0.297019\pi$
$390$	15.7587	+	11.3144i	0.797975	+	0.572925i
$391$	14.3684			0.726642
$392$	−2.81318	−	0.293260i	−0.142087	−	0.0148118i
$393$	−2.39238	−	4.14373i	−0.120680	−	0.209024i
$394$	−26.4117	+	8.58995i	−1.33060	+	0.432755i
$395$	−5.14062			−0.258653
$396$	20.5026	+	9.11442i	1.03029	+	0.458017i
$397$	−9.95374	+	17.2404i	−0.499564	+	0.865270i	−1.00000		0.000503431i	$-0.999840\pi$
$397$	−9.95374	+	17.2404i	−0.499564	+	0.865270i	0.500436	+	0.865774i	$0.333173\pi$
$398$	−3.88656	−	3.49748i	−0.194815	−	0.175313i
$399$	−3.72908	+	6.45896i	−0.186688	+	0.323352i
$400$	−10.1314	−	11.2265i	−0.506571	−	0.561324i
$401$	−0.260772	+	0.150557i	−0.0130223	+	0.00751844i	−0.506497	−	0.862242i	$-0.669060\pi$
$401$	−0.260772	+	0.150557i	−0.0130223	+	0.00751844i	0.493475	+	0.869760i	$0.335727\pi$
$402$	−39.1393	+	43.4934i	−1.95209	+	2.16925i
$403$	15.6927	+	21.3580i	0.781710	+	1.06392i
$404$	−9.99435	+	1.05618i	−0.497238	+	0.0525467i
$405$	−23.7798	−	41.1879i	−1.18163	−	2.04664i
$406$	0.789714	−	3.72050i	0.0391928	−	0.184645i
$407$	4.24524	−	7.35297i	0.210429	−	0.364473i
$408$	31.1612	+	22.5995i	1.54271	+	1.11884i
$409$	−4.79913	−	2.77078i	−0.237302	−	0.137006i	0.376634	−	0.926362i	$-0.377081\pi$
$409$	−4.79913	−	2.77078i	−0.237302	−	0.137006i	−0.613936	+	0.789356i	$0.710415\pi$
$410$	2.32791	+	7.15767i	0.114967	+	0.353492i
$411$	−22.8472			−1.12697
$412$	−14.8295	−	6.59246i	−0.730598	−	0.324787i
$413$	−6.92193	+	3.99638i	−0.340606	+	0.196649i
$414$	−9.47400	+	44.6339i	−0.465622	+	2.19363i
$415$	1.28273			0.0629669
$416$	8.16959	−	18.6884i	0.400547	−	0.916276i
$417$	−27.7083			−1.35688
$418$	0.803955	−	3.78759i	0.0393227	−	0.185257i
$419$	−13.5303	+	7.81172i	−0.660998	+	0.381627i	−0.792657	−	0.609668i	$-0.791303\pi$
$419$	−13.5303	+	7.81172i	−0.660998	+	0.381627i	0.131659	+	0.991295i	$0.457970\pi$
$420$	−6.95313	−	3.09101i	−0.339278	−	0.150826i
$421$	−30.1317			−1.46853			−0.734264	−	0.678864i	$-0.762473\pi$
$421$	−30.1317			−1.46853			−0.734264	+	0.678864i	$0.762473\pi$
$422$	−6.86654	−	21.1127i	−0.334258	−	1.02775i
$423$	50.5097	+	29.1618i	2.45586	+	1.41789i
$424$	−27.6994	−	20.0888i	−1.34520	−	0.975599i
$425$	7.46691	−	12.9331i	0.362198	−	0.627346i
$426$	0.656399	−	3.09242i	0.0318026	−	0.149828i
$427$	4.84068	+	8.38431i	0.234257	+	0.405745i
$428$	30.4734	−	3.22035i	1.47299	−	0.155661i
$429$	15.6162	−	1.72581i	0.753955	−	0.0833229i
$430$	−9.08913	+	10.1003i	−0.438317	+	0.487078i
$431$	−22.7231	+	13.1192i	−1.09453	+	0.631929i	−0.934780	−	0.355228i	$-0.884403\pi$
$431$	−22.7231	+	13.1192i	−1.09453	+	0.631929i	−0.159754	+	0.987157i	$0.551070\pi$
$432$	−60.0565	+	54.1985i	−2.88947	+	2.60763i
$433$	−1.39910	+	2.42331i	−0.0672363	+	0.116457i	−0.897684	−	0.440640i	$-0.854751\pi$
$433$	−1.39910	+	2.42331i	−0.0672363	+	0.116457i	0.830448	+	0.557097i	$0.188085\pi$
$434$	−7.72731	−	6.95373i	−0.370923	−	0.333790i
$435$	5.11607	−	8.86129i	0.245297	−	0.424866i
$436$	12.7859	+	5.68398i	0.612335	+	0.272213i
$437$	7.87403			0.376666
$438$	−6.20681	+	2.01866i	−0.296573	+	0.0964553i
$439$	−8.43792	−	14.6149i	−0.402720	−	0.697531i	0.591333	−	0.806427i	$-0.298602\pi$
$439$	−8.43792	−	14.6149i	−0.402720	−	0.697531i	−0.994053	+	0.108896i	$0.965268\pi$
$440$	3.92911	+	0.409589i	0.187313	+	0.0195264i
$441$	8.87008			0.422385
$442$	20.0433	+	1.99258i	0.953360	+	0.0947773i
$443$			1.24499i			0.0591514i	0.999563	+	0.0295757i	$0.00941562\pi$
$443$			1.24499i			0.0591514i	−0.999563	+	0.0295757i	$0.990584\pi$
$444$	27.2104	+	37.4072i	1.29135	+	1.77527i
$445$	−3.53843	+	2.04292i	−0.167738	+	0.0968435i
$446$	2.33897	+	7.19167i	0.110753	+	0.340536i
$447$		−	1.01168i		−	0.0478507i
$448$	−1.64999	+	7.82800i	−0.0779545	+	0.369838i
$449$	−17.3926	−	10.0416i	−0.820809	−	0.473894i	0.0298862	−	0.999553i	$-0.490485\pi$
$449$	−17.3926	−	10.0416i	−0.820809	−	0.473894i	−0.850695	+	0.525659i	$0.823819\pi$
$450$	35.2517	+	31.7227i	1.66178	+	1.49542i
$451$	5.27896	+	3.04781i	0.248577	+	0.143516i
$452$	32.3439	−	23.5273i	1.52133	−	1.10663i
$453$	−8.95969	−	15.5186i	−0.420963	−	0.729129i
$454$	17.8845	+	16.0941i	0.839360	+	0.755333i
$455$	−3.95749	+	0.437360i	−0.185530	+	0.0205037i
$456$	17.0766	+	12.3847i	0.799687	+	0.579969i
$457$	24.0678	−	13.8956i	1.12585	−	0.650007i	0.182959	−	0.983121i	$-0.441432\pi$
$457$	24.0678	−	13.8956i	1.12585	−	0.650007i	0.942887	+	0.333113i	$0.108099\pi$
$458$	−4.93050	+	23.2285i	−0.230387	+	1.08540i
$459$	−69.1860	−	39.9445i	−3.22933	−	1.86445i
$460$	0.844259	+	7.98903i	0.0393638	+	0.372491i
$461$	−8.46825	+	14.6674i	−0.394406	+	0.683131i	−0.993025	−	0.117903i	$-0.962383\pi$
$461$	−8.46825	+	14.6674i	−0.394406	+	0.683131i	0.598619	+	0.801034i	$0.295716\pi$
$462$	−5.86030	+	1.90596i	−0.272646	+	0.0886735i
$463$		−	24.6494i		−	1.14555i	−0.819711	−	0.572777i	$-0.805866\pi$
$463$		−	24.6494i		−	1.14555i	0.819711	−	0.572777i	$-0.194134\pi$
$464$	−10.2348	−	3.31268i	−0.475141	−	0.153787i
$465$	−13.9833	−	24.2198i	−0.648460	−	1.12317i
$466$	1.01421	−	4.77814i	0.0469824	−	0.221343i
$467$		−	15.9645i		−	0.738750i	−0.929280	−	0.369375i	$-0.879572\pi$
$467$		−	15.9645i		−	0.738750i	0.929280	−	0.369375i	$-0.120428\pi$
$468$	−19.4055	+	60.9483i	−0.897020	+	2.81734i
$469$		−	12.0087i		−	0.554511i
$470$	10.0449	+	2.13214i	0.463338	+	0.0983482i
$471$	−32.6251	−	56.5084i	−1.50329	−	2.60377i
$472$	9.21263	+	20.6446i	0.424046	+	0.950247i
$473$			11.0043i			0.505977i
$474$	−7.01510	−	21.5695i	−0.322214	−	0.990718i
$475$	4.09194	−	7.08744i	0.187751	−	0.325194i
$476$	−7.85662	+	0.830266i	−0.360107	+	0.0380552i
$477$	92.9302	+	53.6533i	4.25498	+	2.45662i
$478$	−8.17750	−	1.73576i	−0.374030	−	0.0793918i
$479$	−30.2351	+	17.4562i	−1.38147	+	0.797595i	−0.992334	−	0.123583i	$-0.960561\pi$
$479$	−30.2351	+	17.4562i	−1.38147	+	0.797595i	−0.389141	+	0.921178i	$0.627228\pi$
$480$	−10.7347	+	18.6540i	−0.489968	+	0.851433i
$481$	22.1640	+	9.72637i	1.01059	+	0.443484i
$482$	−27.4523	+	30.5062i	−1.25042	+	1.38952i
$483$	−6.26597	−	10.8530i	−0.285111	−	0.493828i
$484$	−15.2038	+	11.0594i	−0.691083	+	0.502700i
$485$	5.99641	+	3.46203i	0.272283	+	0.157203i
$486$	82.9730	−	92.2033i	3.76373	−	4.18243i
$487$	−17.6240	−	10.1752i	−0.798619	−	0.461083i	0.0443690	−	0.999015i	$-0.485872\pi$
$487$	−17.6240	−	10.1752i	−0.798619	−	0.461083i	−0.842988	+	0.537932i	$0.819206\pi$
$488$	25.0062	−	11.1590i	1.13198	−	0.505142i
$489$		−	2.09534i		−	0.0947547i
$490$	1.48513	−	0.483015i	0.0670915	−	0.0218204i
$491$	−0.207172	+	0.119611i	−0.00934956	+	0.00539797i	−0.504667	−	0.863314i	$-0.668385\pi$
$491$	−0.207172	+	0.119611i	−0.00934956	+	0.00539797i	0.495318	+	0.868712i	$0.335052\pi$
$492$	−26.8560	+	19.5353i	−1.21076	+	0.880720i
$493$		−	10.6236i		−	0.478464i
$494$	10.9839	+	1.09195i	0.494189	+	0.0491293i
$495$	−12.3886			−0.556828
$496$	−21.8282	+	19.6991i	−0.980117	+	0.884515i
$497$	0.324412	+	0.561897i	0.0145519	+	0.0252045i
$498$	1.75047	+	5.38221i	0.0784405	+	0.241182i
$499$	−23.8499			−1.06767			−0.533834	−	0.845589i	$-0.679249\pi$
$499$	−23.8499			−1.06767			−0.533834	+	0.845589i	$0.679249\pi$
$500$	17.7205	+	7.87763i	0.792483	+	0.352298i
$501$	5.83813	−	10.1119i	0.260829	−	0.451768i
$502$	6.65192	−	7.39191i	0.296890	−	0.329917i
$503$	−3.40289	+	5.89398i	−0.151727	+	0.262799i	−0.931863	−	0.362811i	$-0.881817\pi$
$503$	−3.40289	+	5.89398i	−0.151727	+	0.262799i	0.780135	+	0.625611i	$0.215150\pi$
$504$	2.60123	−	24.9531i	0.115868	−	1.11150i
$505$	4.80564	−	2.77454i	0.213848	−	0.123465i
$506$	4.83618	+	4.35204i	0.214995	+	0.193472i
$507$	9.78018	+	43.7080i	0.434353	+	1.94114i
$508$	2.79042	+	26.4051i	0.123805	+	1.17154i
$509$	−8.77597	−	15.2004i	−0.388988	−	0.673747i	0.603326	−	0.797495i	$-0.293842\pi$
$509$	−8.77597	−	15.2004i	−0.388988	−	0.673747i	−0.992314	+	0.123748i	$0.960509\pi$
$510$	−20.7909	−	4.41309i	−0.920637	−	0.195415i
$511$	0.669777	−	1.16009i	0.0296292	−	0.0513193i
$512$	21.5377	+	6.93735i	0.951842	+	0.306590i
$513$	−37.9146	−	21.8900i	−1.67397	−	0.966467i
$514$	10.4758	−	3.40708i	0.462068	−	0.150280i
$515$	8.96069			0.394855
$516$	−54.7830	−	24.3538i	−2.41169	−	1.07211i
$517$	7.20210	−	4.15814i	0.316748	−	0.182875i
$518$	−9.28680	−	1.97122i	−0.408038	−	0.0866104i
$519$	29.1840			1.28104
$520$	0.0698009	+	11.2614i	0.00306097	+	0.493845i
$521$	−2.15389			−0.0943636			−0.0471818	−	0.998886i	$-0.515024\pi$
$521$	−2.15389			−0.0943636			−0.0471818	+	0.998886i	$0.515024\pi$
$522$	33.0011	+	7.00482i	1.44442	+	0.306593i
$523$	−8.11481	+	4.68509i	−0.354836	+	0.204865i	−0.666813	−	0.745225i	$-0.732342\pi$
$523$	−8.11481	+	4.68509i	−0.354836	+	0.204865i	0.311977	+	0.950090i	$0.399009\pi$
$524$	1.12830	−	2.53807i	0.0492900	−	0.110876i
$525$	−13.0251			−0.568461
$526$	−22.6046	+	7.35175i	−0.985606	+	0.320552i
$527$	−25.1464	−	14.5183i	−1.09540	−	0.632427i
$528$	3.64324	+	17.0450i	0.158551	+	0.741790i
$529$	4.88465	−	8.46045i	0.212376	−	0.367846i
$530$	18.4811	+	3.92281i	0.802770	+	0.170396i
$531$	−35.4482	−	61.3981i	−1.53832	−	2.66445i
$532$	−4.30550	+	0.454994i	−0.186667	+	0.0197265i
$533$	−6.98291	+	15.9124i	−0.302464	+	0.689241i
$534$	−13.4005	−	12.0590i	−0.579898	−	0.521845i
$535$	−14.6527	+	8.45974i	−0.633491	+	0.365746i
$536$	−33.7827	−	3.52167i	−1.45919	−	0.152113i
$537$	−19.6183	+	33.9798i	−0.846591	+	1.46634i
$538$	−2.38517	+	2.65051i	−0.102832	+	0.114271i
$539$	0.632386	−	1.09532i	0.0272388	−	0.0471789i
$540$	18.1445	−	40.8154i	0.780814	−	1.75642i
$541$	39.3061			1.68990			0.844951	−	0.534844i	$-0.179630\pi$
$541$	39.3061			1.68990			0.844951	+	0.534844i	$0.179630\pi$
$542$	−7.79895	−	23.9796i	−0.334994	−	1.03001i
$543$	−30.0193	−	51.9949i	−1.28825	−	2.23131i
$544$	0.0316627	+	22.3456i	0.00135753	+	0.958059i
$545$	−7.72586			−0.330940
$546$	−7.23567	−	16.0083i	−0.309658	−	0.685094i
$547$		−	21.7249i		−	0.928891i	−0.885602	−	0.464445i	$-0.846254\pi$
$547$		−	21.7249i		−	0.928891i	0.885602	−	0.464445i	$-0.153746\pi$
$548$	−7.80178	−	10.7254i	−0.333276	−	0.458168i
$549$	−74.3695	+	42.9372i	−3.17401	+	1.83252i
$550$	6.43053	−	2.09142i	0.274199	−	0.0891785i
$551$		−	5.82184i		−	0.248019i
$552$	−32.3690	+	14.4446i	−1.37771	+	0.614802i
$553$	4.03145	+	2.32756i	0.171435	+	0.0989780i
$554$	11.1622	−	12.4040i	0.474238	−	0.526995i
$555$	−22.1188	−	12.7703i	−0.938892	−	0.542069i
$556$	−9.46172	−	13.0074i	−0.401266	−	0.551638i
$557$	5.40611	+	9.36365i	0.229064	+	0.396751i	0.957531	−	0.288330i	$-0.0931001\pi$
$557$	5.40611	+	9.36365i	0.229064	+	0.396751i	−0.728467	+	0.685081i	$0.759767\pi$
$558$	61.6801	−	68.5418i	2.61113	−	2.90161i
$559$	−31.1806	+	3.44591i	−1.31880	+	0.145746i
$560$	−0.923279	−	4.31960i	−0.0390156	−	0.182536i
$561$	−14.9069	+	8.60648i	−0.629368	+	0.363366i
$562$	5.87591	+	1.24722i	0.247860	+	0.0526109i
$563$	−3.09561	−	1.78725i	−0.130465	−	0.0753237i	0.433347	−	0.901227i	$-0.357332\pi$
$563$	−3.09561	−	1.78725i	−0.130465	−	0.0753237i	−0.563812	+	0.825903i	$0.690666\pi$
$564$	4.76150	+	45.0570i	0.200495	+	1.89724i
$565$	−11.0418	+	19.1249i	−0.464530	+	0.804590i
$566$	−0.416696	−	1.28122i	−0.0175150	−	0.0538538i
$567$			43.0680i			1.80869i
$568$	1.67586	−	0.747848i	0.0703174	−	0.0313790i
$569$	−1.81135	−	3.13735i	−0.0759357	−	0.131524i	0.825557	−	0.564319i	$-0.190861\pi$
$569$	−1.81135	−	3.13735i	−0.0759357	−	0.131524i	−0.901493	+	0.432794i	$0.857528\pi$
$570$	−11.3936	−	2.41841i	−0.477226	−	0.101296i
$571$		−	16.8388i		−	0.704680i	−0.935872	−	0.352340i	$-0.885386\pi$
$571$		−	16.8388i		−	0.704680i	0.935872	−	0.352340i	$-0.114614\pi$
$572$	6.14272	+	6.74156i	0.256840	+	0.281879i
$573$		−	23.2659i		−	0.971949i
$574$	1.41521	−	6.66733i	0.0590697	−	0.278289i
$575$	6.87567	+	11.9090i	0.286735	+	0.496640i
$576$	−69.4349	−	14.6355i	−2.89312	−	0.609812i
$577$		−	46.1091i		−	1.91955i	−0.280775	−	0.959774i	$-0.590591\pi$
$577$		−	46.1091i		−	1.91955i	0.280775	−	0.959774i	$-0.409409\pi$
$578$	1.87753	−	0.610634i	0.0780949	−	0.0253990i
$579$	−47.5439	+	82.3484i	−1.97586	+	3.42228i
$580$	5.90688	−	0.624223i	0.245270	−	0.0259194i
$581$	−1.00597	−	0.580794i	−0.0417345	−	0.0240954i
$582$	−6.34333	+	29.8847i	−0.262940	+	1.23876i
$583$	13.2508	−	7.65035i	0.548792	−	0.316845i
$584$	−3.06712	−	2.22441i	−0.126918	−	0.0920468i
$585$	−3.87941	−	35.1032i	−0.160394	−	1.45134i
$586$	21.8284	+	19.6432i	0.901724	+	0.811453i
$587$	−7.97486	−	13.8129i	−0.329158	−	0.570118i	0.653187	−	0.757197i	$-0.273431\pi$
$587$	−7.97486	−	13.8129i	−0.329158	−	0.570118i	−0.982345	+	0.187078i	$0.940098\pi$
$588$	4.05335	+	5.57231i	0.167157	+	0.229798i
$589$	−13.7805	−	7.95617i	−0.567815	−	0.327828i
$590$	−9.27855	−	8.34969i	−0.381992	−	0.343751i
$591$	58.5965	+	33.8307i	2.41034	+	1.39161i
$592$	−8.26884	+	25.5474i	−0.339847	+	1.04999i
$593$			28.4223i			1.16716i	0.812055	+	0.583581i	$0.198349\pi$
$593$			28.4223i			1.16716i	−0.812055	+	0.583581i	$0.801651\pi$
$594$	−11.1882	−	34.4004i	−0.459055	−	1.41147i
$595$	3.77774	−	2.18108i	0.154872	−	0.0894155i
$596$	0.474924	−	0.345464i	0.0194536	−	0.0141508i
$597$			12.7377i			0.521321i
$598$	−10.8171	+	15.0661i	−0.442344	+	0.616101i
$599$	27.5687			1.12643			0.563214	−	0.826311i	$-0.309565\pi$
$599$	27.5687			1.12643			0.563214	+	0.826311i	$0.309565\pi$
$600$	−3.81973	+	36.6419i	−0.155940	+	1.49590i
$601$	3.07039	+	5.31807i	0.125244	+	0.216929i	0.921828	−	0.387599i	$-0.126695\pi$
$601$	3.07039	+	5.31807i	0.125244	+	0.216929i	−0.796584	+	0.604527i	$0.793362\pi$
$602$	11.7012	−	3.80562i	0.476905	−	0.155105i
$603$	106.518			4.33776
$604$	4.22558	−	9.50530i	0.171936	−	0.386765i
$605$	5.19037	−	8.98999i	0.211019	−	0.365495i
$606$	18.1996	+	16.3777i	0.739309	+	0.665297i
$607$	−23.4410	+	40.6010i	−0.951442	+	1.64795i	−0.209133	+	0.977887i	$0.567064\pi$
$607$	−23.4410	+	40.6010i	−0.951442	+	1.64795i	−0.742309	+	0.670058i	$0.766269\pi$
$608$	0.0173515	+	12.2456i	0.000703695	+	0.496624i
$609$	−8.02440	+	4.63289i	−0.325165	+	0.187734i
$610$	−10.1137	+	11.2388i	−0.409492	+	0.455046i
$611$	14.0374	+	19.1051i	0.567891	+	0.772909i
$612$	−7.36452	−	69.6888i	−0.297693	−	2.81700i
$613$	18.4898	+	32.0253i	0.746796	+	1.29349i	0.949351	+	0.314218i	$0.101742\pi$
$613$	18.4898	+	32.0253i	0.746796	+	1.29349i	−0.202554	+	0.979271i	$0.564924\pi$
$614$	3.78879	−	17.8497i	0.152903	−	0.720357i
$615$	9.16826	−	15.8799i	0.369700	−	0.640339i
$616$	−2.89589	−	2.10023i	−0.116679	−	0.0846207i
$617$	13.3398	+	7.70175i	0.537041	+	0.310061i	0.743879	−	0.668314i	$-0.232984\pi$
$617$	13.3398	+	7.70175i	0.537041	+	0.310061i	−0.206838	+	0.978375i	$0.566317\pi$
$618$	12.2281	+	37.5980i	0.491887	+	1.51242i
$619$	−4.42797			−0.177975			−0.0889875	−	0.996033i	$-0.528363\pi$
$619$	−4.42797			−0.177975			−0.0889875	+	0.996033i	$0.528363\pi$
$620$	6.59482	−	14.8348i	0.264854	−	0.595781i
$621$	63.7078	−	36.7817i	2.55651	−	1.47600i
$622$	−4.52550	+	21.3205i	−0.181456	+	0.854875i
$623$	3.69995			0.148235
$624$	−47.1563	+	15.6607i	−1.88776	+	0.626928i
$625$	8.19515			0.327806
$626$	2.89510	−	13.6394i	0.115711	−	0.545139i
$627$	−8.16911	+	4.71644i	−0.326243	+	0.188356i
$628$	15.3867	−	34.6119i	0.613996	−	1.38116i
$629$	−26.5178			−1.05733
$630$	4.28438	+	13.1732i	0.170694	+	0.524835i
$631$	22.1892	+	12.8110i	0.883339	+	0.509996i	0.871758	−	0.489937i	$-0.162980\pi$
$631$	22.1892	+	12.8110i	0.883339	+	0.509996i	0.0115813	+	0.999933i	$0.496313\pi$
$632$	7.73012	−	10.6586i	0.307488	−	0.423978i
$633$	−27.0432	+	46.8403i	−1.07487	+	1.86173i
$634$	1.78885	−	8.42760i	0.0710442	−	0.334703i
$635$	−7.33033	−	12.6965i	−0.290895	−	0.503845i
$636$	8.76044	+	82.8980i	0.347374	+	3.28712i
$637$	3.30163	+	1.44887i	0.130815	+	0.0574065i
$638$	3.21778	−	3.57574i	0.127393	−	0.141565i
$639$	−4.98407	+	2.87756i	−0.197167	+	0.113834i
$640$	−12.4226	+	1.33059i	−0.491046	+	0.0525961i
$641$	−15.6599	+	27.1237i	−0.618527	+	1.07132i	0.371228	+	0.928542i	$0.378937\pi$
$641$	−15.6599	+	27.1237i	−0.618527	+	1.07132i	−0.989755	+	0.142778i	$0.954396\pi$
$642$	−55.4918	−	49.9365i	−2.19009	−	1.97084i
$643$	15.2048	−	26.3356i	0.599621	−	1.03857i	−0.393256	−	0.919429i	$-0.628651\pi$
$643$	15.2048	−	26.3356i	0.599621	−	1.03857i	0.992877	−	0.119145i	$-0.0380152\pi$
$644$	2.95516	−	6.64754i	0.116450	−	0.261950i
$645$	33.1024			1.30341
$646$	−11.5002	+	3.74023i	−0.452468	+	0.147157i
$647$	21.7095	+	37.6020i	0.853490	+	1.47829i	0.878039	+	0.478589i	$0.158852\pi$
$647$	21.7095	+	37.6020i	0.853490	+	1.47829i	−0.0245488	+	0.999699i	$0.507815\pi$
$648$	121.158	+	12.6301i	4.75954	+	0.496157i
$649$	−10.1090			−0.396813
$650$	7.93972	+	17.5660i	0.311422	+	0.688996i
$651$			25.3254i			0.992579i
$652$	0.983642	−	0.715510i	0.0385224	−	0.0280215i
$653$	−8.99373	+	5.19253i	−0.351952	+	0.203200i	−0.665545	−	0.746358i	$-0.731801\pi$
$653$	−8.99373	+	5.19253i	−0.351952	+	0.203200i	0.313593	+	0.949558i	$0.398467\pi$
$654$	−10.5430	−	32.4168i	−0.412265	−	1.26760i
$655$			1.53362i			0.0599236i
$656$	−18.3414	−	5.93650i	−0.716111	−	0.231781i
$657$	10.2901	+	5.94097i	0.401454	+	0.231779i
$658$	−6.91219	−	6.22022i	−0.269465	−	0.242489i
$659$	−10.2079	−	5.89351i	−0.397642	−	0.229579i	0.287824	−	0.957683i	$-0.407068\pi$
$659$	−10.2079	−	5.89351i	−0.397642	−	0.229579i	−0.685466	+	0.728105i	$0.740401\pi$
$660$	−5.66122	−	7.78272i	−0.220363	−	0.302942i
$661$	8.20076	+	14.2041i	0.318973	+	0.552477i	0.980274	−	0.197643i	$-0.0633288\pi$
$661$	8.20076	+	14.2041i	0.318973	+	0.552477i	−0.661301	+	0.750120i	$0.729995\pi$
$662$	−28.6831	−	25.8116i	−1.11480	−	1.00320i
$663$	−29.0545	−	39.5436i	−1.12838	−	1.53575i
$664$	−1.92889	+	2.65964i	−0.0748554	+	0.103214i
$665$	2.07024	−	1.19525i	0.0802804	−	0.0463499i
$666$	17.4849	−	82.3746i	0.677525	−	3.19195i
$667$	8.47183	+	4.89122i	0.328031	+	0.189389i
$668$	6.74056	−	0.712324i	0.260800	−	0.0275606i
$669$	9.21182	−	15.9553i	0.356149	−	0.616869i
$670$	17.8346	−	5.80039i	0.689009	−	0.224089i
$671$			12.2447i			0.472702i
$672$	16.8646	−	9.76868i	0.650567	−	0.376835i
$673$	−12.6399	−	21.8930i	−0.487233	−	0.843913i	0.512659	−	0.858592i	$-0.328661\pi$
$673$	−12.6399	−	21.8930i	−0.487233	−	0.843913i	−0.999892	+	0.0146794i	$0.995327\pi$
$674$	8.77385	−	41.3353i	0.337956	−	1.59218i
$675$		−	76.4582i		−	2.94288i
$676$	−17.1787	+	19.5165i	−0.660718	+	0.750634i
$677$		−	3.57525i		−	0.137408i	−0.997637	−	0.0687041i	$-0.978114\pi$
$677$		−	3.57525i		−	0.137408i	0.997637	−	0.0687041i	$-0.0218864\pi$
$678$	−95.3139	−	20.2314i	−3.66051	−	0.776981i
$679$	−3.13506	−	5.43009i	−0.120313	−	0.208388i
$680$	−5.02792	−	11.2671i	−0.192812	−	0.432073i
$681$		−	58.6143i		−	2.24611i
$682$	−4.06646	−	12.5032i	−0.155713	−	0.478773i
$683$	19.9823	−	34.6104i	0.764601	−	1.32433i	−0.175856	−	0.984416i	$-0.556269\pi$
$683$	19.9823	−	34.6104i	0.764601	−	1.32433i	0.940457	−	0.339913i	$-0.110398\pi$
$684$	−4.03583	−	38.1901i	−0.154314	−	1.46024i
$685$	6.34193	+	3.66151i	0.242313	+	0.139899i
$686$	−1.38339	−	0.293640i	−0.0528182	−	0.0112112i
$687$	50.0996	−	28.9250i	1.91142	−	1.10356i
$688$	−7.27441	−	34.0337i	−0.277334	−	1.29752i
$689$	25.8267	+	35.1505i	0.983918	+	1.33913i
$690$	13.0916	−	14.5479i	0.498387	−	0.553831i
$691$	12.6471	+	21.9054i	0.481117	+	0.833319i	0.999765	−	0.0216687i	$-0.00689789\pi$
$691$	12.6471	+	21.9054i	0.481117	+	0.833319i	−0.518648	+	0.854988i	$0.673565\pi$
$692$	9.96566	+	13.7002i	0.378838	+	0.520804i
$693$	9.71561	+	5.60931i	0.369065	+	0.213080i
$694$	−27.4904	+	30.5486i	−1.04352	+	1.15961i
$695$	7.69126	+	4.44055i	0.291746	+	0.168440i
$696$	10.6799	+	23.9327i	0.404822	+	0.907169i
$697$		−	19.0381i		−	0.721119i
$698$	−24.5494	+	7.98429i	−0.929210	+	0.302210i
$699$	−10.3055	+	5.94991i	−0.389792	+	0.225046i
$700$	−4.44775	−	6.11452i	−0.168109	−	0.231107i
$701$			35.0284i			1.32300i	0.749943	+	0.661502i	$0.230081\pi$
$701$			35.0284i			1.32300i	−0.749943	+	0.661502i	$0.769919\pi$
$702$	93.9702	−	42.4739i	3.54668	−	1.60307i
$703$	−14.5320			−0.548085
$704$	−6.75758	+	7.53077i	−0.254686	+	0.283826i
$705$	−12.5083	−	21.6650i	−0.471089	−	0.815950i
$706$	11.5683	+	35.5694i	0.435380	+	1.33867i
$707$	−5.02500			−0.188985
$708$	22.3725	−	50.3261i	0.840808	−	1.89137i
$709$	5.56014	−	9.63044i	0.208815	−	0.361679i	−0.742526	−	0.669817i	$-0.766373\pi$
$709$	5.56014	−	9.63044i	0.208815	−	0.361679i	0.951342	+	0.308138i	$0.0997059\pi$
$710$	−0.677797	+	0.753199i	−0.0254373	+	0.0282671i
$711$	−20.6456	+	35.7593i	−0.774272	+	1.34108i
$712$	1.08505	−	10.4086i	0.0406638	−	0.390080i
$713$	23.1553	−	13.3687i	0.867174	−	0.500663i
$714$	14.3068	+	12.8746i	0.535419	+	0.481819i
$715$	−4.61131	−	2.02361i	−0.172453	−	0.0756787i
$716$	−22.6507	+	2.39367i	−0.846498	+	0.0894556i
$717$	10.1829	+	17.6373i	0.380287	+	0.658677i
$718$	8.30176	+	1.76213i	0.309819	+	0.0657623i
$719$	22.7537	−	39.4106i	0.848571	−	1.46977i	−0.0339119	−	0.999425i	$-0.510797\pi$
$719$	22.7537	−	39.4106i	0.848571	−	1.46977i	0.882483	−	0.470344i	$-0.155870\pi$
$720$	38.3152	−	8.18955i	1.42792	−	0.305207i
$721$	−7.02729	−	4.05721i	−0.261710	−	0.151098i
$722$	19.2504	−	6.26086i	0.716425	−	0.233005i
$723$	99.9806			3.71832
$724$	14.1577	−	31.8473i	0.526168	−	1.18360i
$725$	8.80520	−	5.08369i	0.327017	−	0.188803i
$726$	44.8040	+	9.51011i	1.66283	+	0.352953i
$727$	1.65786			0.0614865			0.0307432	−	0.999527i	$-0.490213\pi$
$727$	1.65786			0.0614865			0.0307432	+	0.999527i	$0.490213\pi$
$728$	5.04418	−	8.86320i	0.186950	−	0.328492i
$729$	−172.982			−6.40673
$730$	2.04640	+	0.434369i	0.0757406	+	0.0160767i
$731$	29.7644	−	17.1845i	1.10088	−	0.635591i
$732$	−60.9583	−	27.0990i	−2.25309	−	1.00161i
$733$	−7.61233			−0.281168			−0.140584	−	0.990069i	$-0.544898\pi$
$733$	−7.61233			−0.281168			−0.140584	+	0.990069i	$0.544898\pi$
$734$	8.67521	−	2.82146i	0.320208	−	0.104142i
$735$	−3.29490	−	1.90231i	−0.121534	−	0.0701677i
$736$	−17.8341	−	10.2629i	−0.657375	−	0.378295i
$737$	7.59414	−	13.1534i	0.279734	−	0.484513i
$738$	59.1397	+	12.5530i	2.17696	+	0.462083i
$739$	7.45828	+	12.9181i	0.274357	+	0.475201i	0.969973	−	0.243214i	$-0.0782016\pi$
$739$	7.45828	+	12.9181i	0.274357	+	0.475201i	−0.695616	+	0.718414i	$0.744868\pi$
$740$	−1.55813	−	14.7443i	−0.0572781	−	0.542010i
$741$	−15.9221	−	21.6703i	−0.584914	−	0.796077i
$742$	−12.7174	−	11.4443i	−0.466870	−	0.420133i
$743$	−33.0679	+	19.0918i	−1.21314	+	0.700409i	−0.963443	−	0.267914i	$-0.913666\pi$
$743$	−33.0679	+	19.0918i	−1.21314	+	0.700409i	−0.249701	+	0.968323i	$0.580332\pi$
$744$	71.2449	+	7.42690i	2.61196	+	0.272283i
$745$	−0.162132	+	0.280821i	−0.00594007	+	0.0102885i
$746$	−20.1098	+	22.3470i	−0.736273	+	0.818181i
$747$	5.15169	−	8.92299i	0.188490	−	0.326475i
$748$	−9.13059	−	4.05900i	−0.333847	−	0.148412i
$749$	15.3215			0.559837
$750$	−14.6119	−	44.9276i	−0.533553	−	1.64052i
$751$	13.2212	+	22.8998i	0.482449	+	0.835626i	0.999797	−	0.0201491i	$-0.00641408\pi$
$751$	13.2212	+	22.8998i	0.482449	+	0.835626i	−0.517348	+	0.855775i	$0.673081\pi$
$752$	−19.5257	+	17.6211i	−0.712029	+	0.642576i
$753$	−24.2261			−0.882850
$754$	11.1395	+	7.99787i	0.405677	+	0.291265i
$755$			5.74355i			0.209029i
$756$	−32.7099	+	23.7935i	−1.18965	+	0.865360i
$757$	−6.58378	+	3.80115i	−0.239292	+	0.138155i	−0.614851	−	0.788643i	$-0.710784\pi$
$757$	−6.58378	+	3.80115i	−0.239292	+	0.138155i	0.375560	+	0.926798i	$0.377451\pi$
$758$	16.9938	−	5.52695i	0.617243	−	0.200748i
$759$		−	15.8500i		−	0.575320i
$760$	−2.75535	−	6.17448i	−0.0999469	−	0.223972i
$761$	−37.4145	−	21.6013i	−1.35628	−	0.783046i	−0.367156	−	0.930159i	$-0.619669\pi$
$761$	−37.4145	−	21.6013i	−1.35628	−	0.783046i	−0.989120	+	0.147113i	$0.953002\pi$
$762$	43.2698	−	48.0834i	1.56750	−	1.74188i
$763$	6.05889	+	3.49810i	0.219347	+	0.126640i
$764$	10.9220	−	7.94477i	0.395144	−	0.287432i
$765$	19.3463	+	33.5088i	0.699468	+	1.21151i
$766$	−9.65908	+	10.7336i	−0.348997	+	0.387821i
$767$	−3.16557	−	28.6439i	−0.114302	−	1.03427i
$768$	−22.5354	−	50.3080i	−0.813175	−	1.81533i
$769$	6.75904	−	3.90233i	0.243737	−	0.140722i	−0.373156	−	0.927769i	$-0.621724\pi$
$769$	6.75904	−	3.90233i	0.243737	−	0.140722i	0.616893	+	0.787047i	$0.288391\pi$
$770$	1.93215	+	0.410120i	0.0696300	+	0.0147797i
$771$	−23.2415	−	13.4185i	−0.837021	−	0.483254i
$772$	−54.8929	+	5.80094i	−1.97564	+	0.208780i
$773$	23.2920	−	40.3429i	0.837754	−	1.45103i	−0.0540138	−	0.998540i	$-0.517201\pi$
$773$	23.2920	−	40.3429i	0.837754	−	1.45103i	0.891768	−	0.452493i	$-0.149465\pi$
$774$	33.7561	+	103.791i	1.21334	+	3.73067i
$775$		−	27.7896i		−	0.998232i
$776$	−16.1952	+	7.22708i	−0.581374	+	0.259437i
$777$	11.5642	+	20.0299i	0.414865	+	0.718567i
$778$	−43.8453	−	9.30663i	−1.57193	−	0.333659i
$779$		−	10.4331i		−	0.373803i
$780$	20.2796	−	18.4782i	0.726126	−	0.661625i
$781$			0.820613i			0.0293638i
$782$	4.21913	−	19.8772i	0.150876	−	0.710806i
$783$	−27.1954	−	47.1038i	−0.971885	−	1.68335i
$784$	−1.23175	+	3.80562i	−0.0439912	+	0.135915i
$785$			20.9141i			0.746457i
$786$	−6.43491	+	2.09284i	−0.229526	+	0.0746493i
$787$	0.937909	−	1.62451i	0.0334328	−	0.0579074i	−0.848825	−	0.528674i	$-0.822689\pi$
$787$	0.937909	−	1.62451i	0.0334328	−	0.0579074i	0.882258	+	0.470767i	$0.156023\pi$
$788$	4.12776	+	39.0601i	0.147045	+	1.39146i
$789$	50.1502	+	28.9542i	1.78539	+	1.03080i
$790$	−1.50949	+	7.11149i	−0.0537052	+	0.253016i
$791$	17.3187	−	9.99894i	0.615781	−	0.355521i
$792$	18.6292	−	25.6868i	0.661960	−	0.912740i
$793$	−34.6954	+	3.83435i	−1.23207	+	0.136162i
$794$	20.9274	+	18.8324i	0.742686	+	0.668337i
$795$	−23.0134	−	39.8603i	−0.816200	−	1.41370i
$796$	−5.97963	+	4.34964i	−0.211942	+	0.154169i
$797$	24.2725	+	14.0137i	0.859775	+	0.496391i	0.863937	−	0.503600i	$-0.167991\pi$
$797$	24.2725	+	14.0137i	0.859775	+	0.496391i	−0.00416199	+	0.999991i	$0.501325\pi$
$798$	7.84027	+	7.05539i	0.277543	+	0.249758i
$799$	−22.4939	−	12.9868i	−0.795776	−	0.459442i
$800$	−18.5056	+	10.7192i	−0.654272	+	0.378981i
$801$			32.8189i			1.15960i
$802$	0.131706	+	0.404959i	0.00465070	+	0.0142996i
$803$	1.46725	−	0.847115i	0.0517780	−	0.0298940i
$804$	48.6756	+	66.9164i	1.71665	+	2.35996i
$805$			4.01676i			0.141572i
$806$	34.1545	−	15.4376i	1.20304	−	0.543767i
$807$	8.68673			0.305787
$808$	−1.47363	+	14.1363i	−0.0518421	+	0.497312i
$809$	19.5564	+	33.8726i	0.687565	+	1.19090i	0.972623	+	0.232387i	$0.0746537\pi$
$809$	19.5564	+	33.8726i	0.687565	+	1.19090i	−0.285058	+	0.958510i	$0.592013\pi$
$810$	−63.9618	+	20.8025i	−2.24739	+	0.730924i
$811$	47.3022			1.66100			0.830502	−	0.557016i	$-0.188054\pi$
$811$	47.3022			1.66100			0.830502	+	0.557016i	$0.188054\pi$
$812$	−4.91502	−	2.18497i	−0.172483	−	0.0766774i
$813$	−30.7155	+	53.2007i	−1.07724	+	1.86583i
$814$	−8.92548	−	8.03196i	−0.312838	−	0.281520i
$815$	−0.335801	+	0.581625i	−0.0117626	+	0.0203734i
$816$	40.4142	−	36.4721i	1.41478	−	1.27678i
$817$	16.3112	−	9.41726i	0.570655	−	0.329468i
$818$	−5.24229	+	5.82547i	−0.183292	+	0.203683i
$819$	−12.8516	+	29.2857i	−0.449072	+	1.02333i
$820$	10.5854	−	1.11864i	0.369659	−	0.0390646i
$821$	−15.2523	−	26.4177i	−0.532308	−	0.921985i	−0.999288	−	0.0377170i	$-0.987991\pi$
$821$	−15.2523	−	26.4177i	−0.532308	−	0.921985i	0.466980	−	0.884268i	$-0.345342\pi$
$822$	−6.70884	+	31.6067i	−0.233998	+	1.10241i
$823$	−4.02994	+	6.98006i	−0.140475	+	0.243310i	−0.927676	−	0.373387i	$-0.878196\pi$
$823$	−4.02994	+	6.98006i	−0.140475	+	0.243310i	0.787201	+	0.616697i	$0.211530\pi$
$824$	−13.4745	+	18.5792i	−0.469406	+	0.647238i
$825$	−14.2667	−	8.23687i	−0.496702	−	0.286771i
$826$	3.49601	+	10.7492i	0.121642	+	0.374014i
$827$	−11.7262			−0.407759			−0.203880	−	0.978996i	$-0.565355\pi$
$827$	−11.7262			−0.407759			−0.203880	+	0.978996i	$0.565355\pi$
$828$	58.9642	+	26.2125i	2.04915	+	0.910948i
$829$	31.8276	−	18.3757i	1.10542	−	0.638214i	0.167780	−	0.985825i	$-0.446340\pi$
$829$	31.8276	−	18.3757i	1.10542	−	0.638214i	0.937639	+	0.347611i	$0.113007\pi$
$830$	0.376661	−	1.77453i	0.0130741	−	0.0615947i
$831$	−40.6526			−1.41022
$832$	−23.4545	−	16.7894i	−0.813140	−	0.582068i
$833$	−3.95018			−0.136866
$834$	−8.13624	+	38.3314i	−0.281735	+	1.32731i
$835$	−3.24110	+	1.87125i	−0.112163	+	0.0647572i
$836$	−5.00365	−	2.22437i	−0.173055	−	0.0769315i
$837$	−148.662			−5.13850
$838$	6.83365	+	21.0115i	0.236064	+	0.725832i
$839$	−17.8201	−	10.2884i	−0.615217	−	0.355196i	0.159788	−	0.987151i	$-0.448919\pi$
$839$	−17.8201	−	10.2884i	−0.615217	−	0.355196i	−0.775004	+	0.631956i	$0.782252\pi$
$840$	−6.31780	+	8.71127i	−0.217985	+	0.300567i
$841$	−10.8836	+	18.8509i	−0.375295	+	0.650031i
$842$	−8.84785	+	41.6839i	−0.304917	+	1.43652i
$843$	−7.31689	−	12.6732i	−0.252007	−	0.436489i
$844$	−31.2234	+	3.29961i	−1.07475	+	0.113577i
$845$	4.28990	−	13.6998i	0.147577	−	0.471289i
$846$	55.1738	−	61.3117i	1.89692	−	2.10794i
$847$	−8.14095	+	4.70018i	−0.279726	+	0.161500i
$848$	−35.9243	+	32.4202i	−1.23365	+	1.11332i
$849$	−1.64112	+	2.84250i	−0.0563231	+	0.0975544i
$850$	−15.6989	−	14.1273i	−0.538469	−	0.484563i
$851$	12.2091	−	21.1467i	0.418521	−	0.724899i
$852$	−4.08529	−	1.81611i	−0.139960	−	0.0622191i
$853$	−29.1651			−0.998595			−0.499298	−	0.866431i	$-0.666409\pi$
$853$	−29.1651			−0.998595			−0.499298	+	0.866431i	$0.666409\pi$
$854$	13.0202	−	4.23460i	0.445542	−	0.144905i
$855$	10.6020	+	18.3632i	0.362580	+	0.628007i
$856$	4.49319	−	43.1023i	0.153574	−	1.47321i
$857$	−9.90801			−0.338451			−0.169226	−	0.985577i	$-0.554127\pi$
$857$	−9.90801			−0.338451			−0.169226	+	0.985577i	$0.554127\pi$
$858$	2.19805	−	22.1101i	0.0750401	−	0.754825i
$859$		−	18.1763i		−	0.620168i	−0.950709	−	0.310084i	$-0.899643\pi$
$859$		−	18.1763i		−	0.620168i	0.950709	−	0.310084i	$-0.100357\pi$
$860$	11.3037	+	15.5397i	0.385453	+	0.529899i
$861$	−14.3802	+	8.30239i	−0.490074	+	0.282945i
$862$	11.4766	+	35.2873i	0.390894	+	1.20189i
$863$		−	1.24206i		−	0.0422804i	−0.999777	−	0.0211402i	$-0.993270\pi$
$863$		−	1.24206i		−	0.0422804i	0.999777	−	0.0211402i	$-0.00672963\pi$
$864$	57.3429	+	98.9966i	1.95084	+	3.36793i
$865$	−8.10091	−	4.67706i	−0.275439	−	0.159025i
$866$	2.94155	+	2.64708i	0.0999581	+	0.0899514i
$867$	−4.16546	−	2.40493i	−0.141466	−	0.0816756i
$868$	−11.8888	+	8.64801i	−0.403532	+	0.293533i
$869$	2.94383	+	5.09887i	0.0998627	+	0.172967i
$870$	−10.7564	−	9.67955i	−0.364675	−	0.328168i
$871$	39.6484	+	17.3991i	1.34343	+	0.589547i
$872$	11.6176	−	16.0189i	0.393423	−	0.542469i
$873$	48.1653	−	27.8082i	1.63015	−	0.941166i
$874$	2.31212	−	10.8929i	0.0782088	−	0.368457i
$875$	8.39723	+	4.84814i	0.283878	+	0.163897i
$876$	0.970034	+	9.17921i	0.0327744	+	0.310137i
$877$	4.55150	−	7.88344i	0.153693	−	0.266205i	−0.778889	−	0.627162i	$-0.784217\pi$
$877$	4.55150	−	7.88344i	0.153693	−	0.266205i	0.932582	+	0.360957i	$0.117550\pi$
$878$	−22.6959	+	7.38144i	−0.765948	+	0.249112i
$879$		−	71.5402i		−	2.41299i
$880$	1.72036	−	5.31523i	0.0579935	−	0.179176i
$881$	15.1949	+	26.3183i	0.511929	+	0.886687i	0.999904	+	0.0138294i	$0.00440219\pi$
$881$	15.1949	+	26.3183i	0.511929	+	0.886687i	−0.487976	+	0.872857i	$0.662264\pi$
$882$	2.60460	−	12.2708i	0.0877016	−	0.413179i
$883$			18.5296i			0.623569i	0.950153	+	0.311785i	$0.100927\pi$
$883$			18.5296i			0.623569i	−0.950153	+	0.311785i	$0.899073\pi$
$884$	8.64201	−	27.1426i	0.290662	−	0.912904i
$885$			30.4094i			1.02220i
$886$	1.72232	+	0.365579i	0.0578623	+	0.0122819i
$887$	24.8601	+	43.0590i	0.834721	+	1.44578i	0.894258	+	0.447553i	$0.147704\pi$
$887$	24.8601	+	43.0590i	0.834721	+	1.44578i	−0.0595369	+	0.998226i	$0.518962\pi$
$888$	59.7390	−	26.6584i	2.00471	−	0.894597i
$889$			13.2761i			0.445265i
$890$	1.78713	+	5.49492i	0.0599047	+	0.184190i
$891$	−27.2356	+	47.1734i	−0.912427	+	1.58037i
$892$	10.6357	−	1.12395i	0.356110	−	0.0376328i
$893$	−12.3269	−	7.11692i	−0.412503	−	0.238159i
$894$	−1.39955	−	0.297069i	−0.0468079	−	0.00993546i
$895$	10.8913	−	6.28808i	0.364055	−	0.210187i
$896$	10.3447	+	4.58119i	0.345592	+	0.153047i
$897$	44.9111	−	4.96333i	1.49954	−	0.165721i
$898$	−18.9987	+	21.1122i	−0.633995	+	0.704524i
$899$	−9.88449	−	17.1204i	−0.329666	−	0.570998i
$900$	54.2362	−	39.4519i	1.80787	−	1.31506i
$901$	−41.3854	−	23.8939i	−1.37875	−	0.796020i
$902$	5.76643	−	6.40792i	0.192001	−	0.213361i
$903$	−25.9601	−	14.9881i	−0.863898	−	0.498772i
$904$	−23.0500	−	51.6529i	−0.766631	−	1.71795i
$905$			19.2437i			0.639681i
$906$	−24.0993	+	7.83789i	−0.800645	+	0.260396i
$907$	28.4746	−	16.4398i	0.945483	−	0.545875i	0.0538084	−	0.998551i	$-0.482864\pi$
$907$	28.4746	−	16.4398i	0.945483	−	0.545875i	0.891675	+	0.452676i	$0.149531\pi$
$908$	27.5160	−	20.0154i	0.913152	−	0.664234i
$909$		−	44.5722i		−	1.47836i
$910$	−0.557035	+	5.60319i	−0.0184655	+	0.185744i
$911$	−24.3931			−0.808180			−0.404090	−	0.914719i	$-0.632412\pi$
$911$	−24.3931			−0.808180			−0.404090	+	0.914719i	$0.632412\pi$
$912$	22.1473	−	19.9871i	0.733372	−	0.661838i
$913$	−0.734572	−	1.27232i	−0.0243108	−	0.0421075i
$914$	−12.1558	−	37.3756i	−0.402077	−	1.23627i
$915$	36.8339			1.21769
$916$	30.6864	+	13.6416i	1.01391	+	0.450732i
$917$	0.694391	−	1.20272i	0.0229308	−	0.0397173i
$918$	−75.5747	+	83.9821i	−2.49434	+	2.77182i
$919$	4.43574	−	7.68293i	0.146322	−	0.253437i	−0.783544	−	0.621337i	$-0.786590\pi$
$919$	4.43574	−	7.68293i	0.146322	−	0.253437i	0.929865	+	0.367900i	$0.119923\pi$
$920$	11.2999	+	1.17795i	0.372546	+	0.0388360i
$921$	−38.4985	+	22.2271i	−1.26857	+	0.732408i
$922$	17.8042	+	16.0219i	0.586351	+	0.527652i
$923$	−2.32521	+	0.256969i	−0.0765352	+	0.00845824i
$924$	0.915881	+	8.66677i	0.0301303	+	0.285116i
$925$	−12.6895	−	21.9788i	−0.417228	−	0.722659i
$926$	−34.0998	−	7.23803i	−1.12059	−	0.237856i
$927$	35.9877	−	62.3326i	1.18199	−	2.04727i
$928$	−7.58809	+	13.1861i	−0.249091	+	0.432854i
$929$	9.22172	+	5.32417i	0.302555	+	0.174680i	0.643590	−	0.765370i	$-0.277444\pi$
$929$	9.22172	+	5.32417i	0.302555	+	0.174680i	−0.341035	+	0.940051i	$0.610778\pi$
$930$	−37.6115	+	12.2325i	−1.23333	+	0.401120i
$931$	−2.16474			−0.0709464
$932$	−6.31224	−	2.80610i	−0.206764	−	0.0919170i
$933$	45.9843	−	26.5491i	1.50546	−	0.869177i
$934$	−22.0852	−	4.68782i	−0.722650	−	0.153390i
$935$	5.51713			0.180429
$936$	78.6172	+	44.7423i	2.56968	+	1.46245i
$937$	−30.5472			−0.997932			−0.498966	−	0.866622i	$-0.666287\pi$
$937$	−30.5472			−0.997932			−0.498966	+	0.866622i	$0.666287\pi$
$938$	−16.6128	−	3.52624i	−0.542427	−	0.115136i
$939$	−29.4175	+	16.9842i	−0.960004	+	0.554259i
$940$	5.89917	−	13.2700i	0.192410	−	0.432819i
$941$	36.7037			1.19651			0.598253	−	0.801307i	$-0.295862\pi$
$941$	36.7037			1.19651			0.598253	+	0.801307i	$0.295862\pi$
$942$	−87.7533	+	28.5403i	−2.85916	+	0.929893i
$943$	15.1820	+	8.76532i	0.494393	+	0.285438i
$944$	31.2648	−	6.68260i	1.01758	−	0.217500i
$945$	11.1667	−	19.3413i	0.363253	−	0.629172i
$946$	15.2232	+	3.23129i	0.494950	+	0.105058i
$947$	1.61970	+	2.80540i	0.0526332	+	0.0911633i	0.891142	−	0.453725i	$-0.149905\pi$
$947$	1.61970	+	2.80540i	0.0526332	+	0.0911633i	−0.838508	+	0.544889i	$0.816572\pi$
$948$	−31.8989	+	3.37099i	−1.03603	+	0.109485i
$949$	2.85976	+	3.89218i	0.0928317	+	0.126345i
$950$	−8.60316	−	7.74191i	−0.279123	−	0.251181i
$951$	−18.1767	+	10.4943i	−0.589421	+	0.340302i
$952$	−1.15843	+	11.1126i	−0.0375449	+	0.360161i
$953$	3.80104	−	6.58359i	0.123128	−	0.213263i	−0.797872	−	0.602827i	$-0.794041\pi$
$953$	3.80104	−	6.58359i	0.123128	−	0.213263i	0.921000	+	0.389564i	$0.127374\pi$
$954$	101.512	−	112.804i	3.28656	−	3.65217i
$955$	−3.72862	+	6.45816i	−0.120655	+	0.208981i
$956$	−4.80247	+	10.8030i	−0.155323	+	0.349394i
$957$	−11.7191			−0.378824
$958$	15.2706	+	46.9528i	0.493371	+	1.51698i
$959$	−3.31571	−	5.74298i	−0.107070	−	0.185450i
$960$	22.6536	+	20.3278i	0.731143	+	0.656077i
$961$	−23.0328			−0.742995
$962$	19.9636	−	27.8055i	0.643653	−	0.896486i
$963$			135.903i			4.37942i
$964$	34.1410	+	46.9351i	1.09961	+	1.51168i
$965$	26.3945	−	15.2389i	0.849668	−	0.490556i
$966$	−16.8539	+	5.48143i	−0.542264	+	0.176362i
$967$		−	28.9220i		−	0.930069i	−0.885293	−	0.465035i	$-0.846042\pi$
$967$		−	28.9220i		−	0.930069i	0.885293	−	0.465035i	$-0.153958\pi$
$968$	10.8350	+	24.2803i	0.348252	+	0.780400i
$969$	25.5141	+	14.7306i	0.819630	+	0.473214i
$970$	6.55012	−	7.27880i	0.210312	−	0.233708i
$971$	−4.75294	−	2.74411i	−0.152529	−	0.0880627i	0.421793	−	0.906692i	$-0.361401\pi$
$971$	−4.75294	−	2.74411i	−0.152529	−	0.0880627i	−0.574322	+	0.818629i	$0.694734\pi$
$972$	−103.189	−	141.859i	−3.30980	−	4.55012i
$973$	−4.02117	−	6.96487i	−0.128913	−	0.223284i
$974$	−19.2514	+	21.3931i	−0.616855	+	0.685478i
$975$	18.8717	−	43.0040i	0.604378	−	1.37723i
$976$	−8.09441	−	37.8701i	−0.259096	−	1.21219i
$977$	−24.7660	+	14.2987i	−0.792335	+	0.457455i	−0.840784	−	0.541371i	$-0.817906\pi$
$977$	−24.7660	+	14.2987i	−0.792335	+	0.457455i	0.0484489	+	0.998826i	$0.484572\pi$
$978$	−2.89868	−	0.615276i	−0.0926897	−	0.0196743i
$979$	4.05265	+	2.33980i	0.129523	+	0.0747802i
$980$	−0.232105	−	2.19636i	−0.00741432	−	0.0701600i
$981$	−31.0284	+	53.7428i	−0.990662	+	1.71588i
$982$	0.104635	+	0.321723i	0.00333904	+	0.0102666i
$983$		−	51.2819i		−	1.63564i	−0.575476	−	0.817819i	$-0.695183\pi$
$983$		−	51.2819i		−	1.63564i	0.575476	−	0.817819i	$-0.304817\pi$
$984$	19.1390	+	42.8888i	0.610129	+	1.36724i
$985$	−10.8435	−	18.7815i	−0.345502	−	0.598427i
$986$	−14.6966	−	3.11951i	−0.468036	−	0.0993455i
$987$			22.6539i			0.721082i
$988$	4.73590	−	14.8744i	0.150669	−	0.473218i
$989$			31.6476i			1.00633i
$990$	−3.63779	+	17.1383i	−0.115617	+	0.544692i
$991$	31.3486	+	54.2973i	0.995820	+	1.72481i	0.577014	+	0.816734i	$0.304218\pi$
$991$	31.3486	+	54.2973i	0.995820	+	1.72481i	0.418806	+	0.908076i	$0.362449\pi$
$992$	20.8419	+	35.9814i	0.661732	+	1.14241i
$993$			94.0055i			2.98317i
$994$	0.872585	−	0.283793i	0.0276767	−	0.00900138i
$995$	2.04136	−	3.53574i	0.0647155	−	0.112091i
$996$	7.95972	−	0.841161i	0.252213	−	0.0266532i
$997$	−38.7393	−	22.3662i	−1.22689	−	0.708344i	−0.260510	−	0.965471i	$-0.583891\pi$
$997$	−38.7393	−	22.3662i	−1.22689	−	0.708344i	−0.966377	+	0.257127i	$0.917224\pi$
$998$	−7.00327	+	32.9938i	−0.221685	+	1.04440i
$999$	−117.577	+	67.8830i	−3.71996	+	2.14772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.cz.a.309.49	✓	168
8.5	even	2	inner	728.2.cz.a.309.77	yes	168
13.4	even	6	inner	728.2.cz.a.589.77	yes	168
104.69	even	6	inner	728.2.cz.a.589.49	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.cz.a.309.49	✓	168	1.1	even	1	trivial
728.2.cz.a.309.77	yes	168	8.5	even	2	inner
728.2.cz.a.589.49	yes	168	104.69	even	6	inner
728.2.cz.a.589.77	yes	168	13.4	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.293640 - 1.38339i) q^{2} +(-2.98372 + 1.72265i) q^{3} +(-1.82755 - 0.812438i) q^{4} +1.10429 q^{5} +(1.50696 + 4.63349i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-1.66056 + 2.28966i) q^{8} +(4.43504 - 7.68171i) q^{9} +(0.324264 - 1.52767i) q^{10} +(-0.632386 - 1.09532i) q^{11} +(6.85244 - 0.724147i) q^{12} +(2.90558 - 2.13486i) q^{13} +(-0.945996 + 1.05123i) q^{14} +(-3.29490 + 1.90231i) q^{15} +(2.67989 + 2.96954i) q^{16} +(-1.97509 + 3.42096i) q^{17} +(-9.32452 - 8.39105i) q^{18} +(-1.08237 + 1.87472i) q^{19} +(-2.01815 - 0.897169i) q^{20} +3.44530 q^{21} +(-1.70096 + 0.553207i) q^{22} +(-1.81870 - 3.15008i) q^{23} +(1.01037 - 9.69225i) q^{24} -3.78054 q^{25} +(-2.10016 - 4.64643i) q^{26} +20.2242i q^{27} +(1.17649 + 1.61737i) q^{28} +(-2.32909 + 1.34470i) q^{29} +(1.66413 + 5.11673i) q^{30} +7.35070i q^{31} +(4.89497 - 2.83537i) q^{32} +(3.77372 + 2.17876i) q^{33} +(4.15256 + 3.73686i) q^{34} +(-0.956346 - 0.552146i) q^{35} +(-14.3462 + 10.4355i) q^{36} +(3.35653 + 5.81368i) q^{37} +(2.27564 + 2.04783i) q^{38} +(-4.99180 + 11.3751i) q^{39} +(-1.83375 + 2.52845i) q^{40} +(-4.17385 + 2.40977i) q^{41} +(1.01168 - 4.76620i) q^{42} +(-7.53494 - 4.35030i) q^{43} +(0.265835 + 2.51553i) q^{44} +(4.89758 - 8.48286i) q^{45} +(-4.89185 + 1.59099i) q^{46} +6.57532i q^{47} +(-13.1115 - 4.24376i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-1.11012 + 5.22997i) q^{50} -13.6096i q^{51} +(-7.04453 + 1.54097i) q^{52} +12.0976i q^{53} +(27.9780 + 5.93861i) q^{54} +(-0.698339 - 1.20956i) q^{55} +(2.58292 - 1.15262i) q^{56} -7.45817i q^{57} +(1.17634 + 3.61690i) q^{58} +(3.99638 - 6.92193i) q^{59} +(7.56710 - 0.799671i) q^{60} +(-8.38431 - 4.84068i) q^{61} +(10.1689 + 2.15846i) q^{62} +(-7.68171 + 4.43504i) q^{63} +(-2.48507 - 7.60424i) q^{64} +(3.20861 - 2.35751i) q^{65} +(4.12219 - 4.58076i) q^{66} +(6.00436 + 10.3999i) q^{67} +(6.38890 - 4.64734i) q^{68} +(10.8530 + 6.26597i) q^{69} +(-1.04466 + 1.16087i) q^{70} +(-0.561897 - 0.324412i) q^{71} +(10.2238 + 22.9107i) q^{72} +1.33955i q^{73} +(9.02821 - 2.93627i) q^{74} +(11.2800 - 6.51254i) q^{75} +(3.50118 - 2.54679i) q^{76} +1.26477i q^{77} +(14.2704 + 10.2458i) q^{78} -4.65512 q^{79} +(2.95938 + 3.27925i) q^{80} +(-21.5340 - 37.2980i) q^{81} +(2.10806 + 6.48168i) q^{82} +1.16159 q^{83} +(-6.29646 - 2.79909i) q^{84} +(-2.18108 + 3.77774i) q^{85} +(-8.23073 + 9.14636i) q^{86} +(4.63289 - 8.02440i) q^{87} +(3.55803 + 0.370906i) q^{88} +(-3.20425 + 1.84998i) q^{89} +(-10.2970 - 9.26618i) q^{90} +(-3.58373 + 0.396054i) q^{91} +(0.764525 + 7.23452i) q^{92} +(-12.6627 - 21.9324i) q^{93} +(9.09625 + 1.93077i) q^{94} +(-1.19525 + 2.07024i) q^{95} +(-9.72085 + 16.8922i) q^{96} +(5.43009 + 3.13506i) q^{97} +(1.34487 - 0.437397i) q^{98} -11.2186 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 18 q^{6} + 84 q^{9} - 8 q^{10} - 4 q^{12} + 8 q^{16} + 4 q^{17} - 18 q^{22} + 24 q^{23} + 48 q^{24} + 160 q^{25} - 30 q^{26} - 8 q^{30} + 22 q^{36} - 20 q^{38} - 48 q^{39} + 4 q^{40} + 12 q^{41}+ \cdots - 104 q^{95}+O(q^{100}) \) 168 * q - 18 * q^6 + 84 * q^9 - 8 * q^10 - 4 * q^12 + 8 * q^16 + 4 * q^17 - 18 * q^22 + 24 * q^23 + 48 * q^24 + 160 * q^25 - 30 * q^26 - 8 * q^30 + 22 * q^36 - 20 * q^38 - 48 * q^39 + 4 * q^40 + 12 * q^41 - 54 * q^48 + 84 * q^49 - 30 * q^50 - 58 * q^52 + 24 * q^54 - 32 * q^55 - 12 * q^58 + 28 * q^62 - 36 * q^64 + 12 * q^65 - 60 * q^66 - 64 * q^68 - 132 * q^72 + 62 * q^74 - 78 * q^76 + 30 * q^78 - 80 * q^79 + 48 * q^80 - 84 * q^81 - 18 * q^82 - 42 * q^84 - 24 * q^87 + 42 * q^88 + 40 * q^90 - 24 * q^92 + 12 * q^94 - 104 * q^95

Introduction

L-functions

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