LMFDB - Embedded newform 640.2.bm.a.101.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] 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("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39147 + 0.252599i) q^{2} +(-1.88532 + 1.00772i) q^{3} +(1.87239 - 0.702968i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(2.36881 - 1.87845i) q^{6} +(-0.780006 + 0.521184i) q^{7} +(-2.42781 + 1.45112i) q^{8} +(0.872201 - 1.30534i) q^{9} +(1.07800 + 0.915375i) q^{10} +(4.10414 - 1.24498i) q^{11} +(-2.82165 + 3.21216i) q^{12} +(-3.53663 - 2.90244i) q^{13} +(0.953707 - 0.922241i) q^{14} +(1.97501 + 0.818077i) q^{15} +(3.01167 - 2.63246i) q^{16} +(-1.91756 + 0.794278i) q^{17} +(-0.883916 + 2.03666i) q^{18} +(0.281813 + 2.86130i) q^{19} +(-1.73123 - 1.00142i) q^{20} +(0.945350 - 1.76863i) q^{21} +(-5.39632 + 2.76905i) q^{22} +(9.21664 - 1.83330i) q^{23} +(3.11485 - 5.18238i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(5.65428 + 3.14531i) q^{26} +(0.299652 - 3.04241i) q^{27} +(-1.09410 + 1.52418i) q^{28} +(-0.848106 + 2.79583i) q^{29} +(-2.95482 - 0.639445i) q^{30} +(-2.47410 - 2.47410i) q^{31} +(-3.52570 + 4.42373i) q^{32} +(-6.48301 + 6.48301i) q^{33} +(2.46759 - 1.58959i) q^{34} +(0.897711 + 0.272318i) q^{35} +(0.715486 - 3.05723i) q^{36} +(0.881591 + 0.0868291i) q^{37} +(-1.11489 - 3.91023i) q^{38} +(9.59252 + 1.90807i) q^{39} +(2.66192 + 0.956137i) q^{40} +(1.97707 + 9.93941i) q^{41} +(-0.868675 + 2.69979i) q^{42} +(0.764650 + 0.408714i) q^{43} +(6.80936 - 5.21616i) q^{44} +(-1.56236 + 0.153879i) q^{45} +(-12.3616 + 4.87910i) q^{46} +(2.73475 + 6.60228i) q^{47} +(-3.02517 + 7.99794i) q^{48} +(-2.34201 + 5.65410i) q^{49} +(0.0237177 - 1.41401i) q^{50} +(2.81479 - 3.42983i) q^{51} +(-8.66227 - 2.94835i) q^{52} +(3.44815 + 11.3670i) q^{53} +(0.351553 + 4.30912i) q^{54} +(-3.56602 - 2.38274i) q^{55} +(1.13740 - 2.39722i) q^{56} +(-3.41470 - 5.11046i) q^{57} +(0.473892 - 4.10455i) q^{58} +(-4.78435 + 3.92642i) q^{59} +(4.27307 + 0.143387i) q^{60} +(-6.43562 - 12.0402i) q^{61} +(4.06759 + 2.81769i) q^{62} +1.47275i q^{63} +(3.78849 - 7.04609i) q^{64} +4.57514i q^{65} +(7.38333 - 10.6585i) q^{66} +(4.75202 + 8.89040i) q^{67} +(-3.03206 + 2.83518i) q^{68} +(-15.5288 + 12.7442i) q^{69} +(-1.31793 - 0.152162i) q^{70} +(6.36920 + 9.53218i) q^{71} +(-0.223325 + 4.43479i) q^{72} +(4.72067 + 3.15425i) q^{73} +(-1.24864 + 0.101868i) q^{74} +(-0.620552 - 2.04569i) q^{75} +(2.53906 + 5.15935i) q^{76} +(-2.55239 + 3.11010i) q^{77} +(-13.8297 - 0.231969i) q^{78} +(-5.04893 + 12.1892i) q^{79} +(-3.94550 - 0.658041i) q^{80} +(4.30332 + 10.3891i) q^{81} +(-5.26172 - 13.3310i) q^{82} +(4.23332 - 0.416945i) q^{83} +(0.526775 - 3.97610i) q^{84} +(1.83047 + 0.978407i) q^{85} +(-1.16723 - 0.375564i) q^{86} +(-1.21847 - 6.12568i) q^{87} +(-8.15744 + 8.97817i) q^{88} +(2.50244 + 0.497766i) q^{89} +(2.13511 - 0.608769i) q^{90} +(4.27130 + 0.420686i) q^{91} +(15.9684 - 9.91165i) q^{92} +(7.15767 + 2.17125i) q^{93} +(-5.47306 - 8.49609i) q^{94} +(2.03303 - 2.03303i) q^{95} +(2.18917 - 11.8931i) q^{96} +(2.08093 + 2.08093i) q^{97} +(1.83062 - 8.45911i) q^{98} +(1.95452 - 6.44317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	−1.39147	+	0.252599i	−0.983919	+	0.178614i
$2$	−1.39147	+	0.252599i	−0.983919	+	0.178614i
$3$	−1.88532	+	1.00772i	−1.08849	+	0.581809i	−0.915174	−	0.403058i	$-0.867947\pi$
$3$	−1.88532	+	1.00772i	−1.08849	+	0.581809i	−0.173313	+	0.984867i	$0.555447\pi$
$4$	1.87239	−	0.702968i	0.936194	−	0.351484i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$6$	2.36881	−	1.87845i	0.967065	−	0.766872i
$7$	−0.780006	+	0.521184i	−0.294815	+	0.196989i	−0.694177	−	0.719804i	$-0.744232\pi$
$7$	−0.780006	+	0.521184i	−0.294815	+	0.196989i	0.399362	+	0.916793i	$0.369232\pi$
$8$	−2.42781	+	1.45112i	−0.858359	+	0.513049i
$9$	0.872201	−	1.30534i	0.290734	−	0.435114i
$10$	1.07800	+	0.915375i	0.340894	+	0.289467i
$11$	4.10414	−	1.24498i	1.23744	−	0.375375i	0.397276	−	0.917699i	$-0.369956\pi$
$11$	4.10414	−	1.24498i	1.23744	−	0.375375i	0.840169	+	0.542324i	$0.182456\pi$
$12$	−2.82165	+	3.21216i	−0.814539	+	0.927272i
$13$	−3.53663	−	2.90244i	−0.980885	−	0.804992i	−8.36858e−5	−	1.00000i	$-0.500027\pi$
$13$	−3.53663	−	2.90244i	−0.980885	−	0.804992i	−0.980802	+	0.195008i	$0.937527\pi$
$14$	0.953707	−	0.922241i	0.254889	−	0.246479i
$15$	1.97501	+	0.818077i	0.509946	+	0.211226i
$16$	3.01167	−	2.63246i	0.752918	−	0.658114i
$17$	−1.91756	+	0.794278i	−0.465076	+	0.192641i	−0.602901	−	0.797816i	$-0.705989\pi$
$17$	−1.91756	+	0.794278i	−0.465076	+	0.192641i	0.137825	+	0.990457i	$0.455989\pi$
$18$	−0.883916	+	2.03666i	−0.208341	+	0.480046i
$19$	0.281813	+	2.86130i	0.0646523	+	0.656426i	0.971831	+	0.235680i	$0.0757317\pi$
$19$	0.281813	+	2.86130i	0.0646523	+	0.656426i	−0.907178	+	0.420746i	$0.861768\pi$
$20$	−1.73123	−	1.00142i	−0.387115	−	0.223924i
$21$	0.945350	−	1.76863i	0.206292	−	0.385946i
$22$	−5.39632	+	2.76905i	−1.15050	+	0.590364i
$23$	9.21664	−	1.83330i	1.92180	−	0.382270i	0.921816	−	0.387628i	$-0.126705\pi$
$23$	9.21664	−	1.83330i	1.92180	−	0.382270i	0.999986	+	0.00535760i	$0.00170539\pi$
$24$	3.11485	−	5.18238i	0.635817	−	1.05785i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	5.65428	+	3.14531i	1.10889	+	0.616847i
$27$	0.299652	−	3.04241i	0.0576680	−	0.585513i
$28$	−1.09410	+	1.52418i	−0.206765	+	0.288042i
$29$	−0.848106	+	2.79583i	−0.157489	+	0.519173i	−0.999804	−	0.0198139i	$-0.993693\pi$
$29$	−0.848106	+	2.79583i	−0.157489	+	0.519173i	0.842314	+	0.538987i	$0.181193\pi$
$30$	−2.95482	−	0.639445i	−0.539474	−	0.116746i
$31$	−2.47410	−	2.47410i	−0.444361	−	0.444361i	0.449113	−	0.893475i	$-0.351740\pi$
$31$	−2.47410	−	2.47410i	−0.444361	−	0.444361i	−0.893475	+	0.449113i	$0.851740\pi$
$32$	−3.52570	+	4.42373i	−0.623262	+	0.782013i
$33$	−6.48301	+	6.48301i	−1.12855	+	1.12855i
$34$	2.46759	−	1.58959i	0.423189	−	0.272612i
$35$	0.897711	+	0.272318i	0.151741	+	0.0460301i
$36$	0.715486	−	3.05723i	0.119248	−	0.509539i
$37$	0.881591	+	0.0868291i	0.144933	+	0.0142746i	0.170223	−	0.985406i	$-0.445551\pi$
$37$	0.881591	+	0.0868291i	0.144933	+	0.0142746i	−0.0252906	+	0.999680i	$0.508051\pi$
$38$	−1.11489	−	3.91023i	−0.180860	−	0.634323i
$39$	9.59252	+	1.90807i	1.53603	+	0.305536i
$40$	2.66192	+	0.956137i	0.420886	+	0.151179i
$41$	1.97707	+	9.93941i	0.308767	+	1.55227i	0.754009	+	0.656864i	$0.228118\pi$
$41$	1.97707	+	9.93941i	0.308767	+	1.55227i	−0.445242	+	0.895410i	$0.646882\pi$
$42$	−0.868675	+	2.69979i	−0.134040	+	0.416586i
$43$	0.764650	+	0.408714i	0.116608	+	0.0623283i	0.528669	−	0.848828i	$-0.322691\pi$
$43$	0.764650	+	0.408714i	0.116608	+	0.0623283i	−0.412061	+	0.911156i	$0.635191\pi$
$44$	6.80936	−	5.21616i	1.02655	−	0.786366i
$45$	−1.56236	+	0.153879i	−0.232903	+	0.0229389i
$46$	−12.3616	+	4.87910i	−1.82262	+	0.719384i
$47$	2.73475	+	6.60228i	0.398905	+	0.963041i	0.987926	+	0.154924i	$0.0495132\pi$
$47$	2.73475	+	6.60228i	0.398905	+	0.963041i	−0.589022	+	0.808117i	$0.700487\pi$
$48$	−3.02517	+	7.99794i	−0.436645	+	1.15440i
$49$	−2.34201	+	5.65410i	−0.334572	+	0.807729i
$50$	0.0237177	−	1.41401i	0.00335418	−	0.199972i
$51$	2.81479	−	3.42983i	0.394149	−	0.480272i
$52$	−8.66227	−	2.94835i	−1.20124	−	0.408863i
$53$	3.44815	+	11.3670i	0.473639	+	1.56138i	0.790226	+	0.612816i	$0.209963\pi$
$53$	3.44815	+	11.3670i	0.473639	+	1.56138i	−0.316587	+	0.948564i	$0.602537\pi$
$54$	0.351553	+	4.30912i	0.0478403	+	0.586398i
$55$	−3.56602	−	2.38274i	−0.480842	−	0.321288i
$56$	1.13740	−	2.39722i	0.151992	−	0.320342i
$57$	−3.41470	−	5.11046i	−0.452288	−	0.676897i
$58$	0.473892	−	4.10455i	0.0622251	−	0.538954i
$59$	−4.78435	+	3.92642i	−0.622870	+	0.511176i	−0.892063	−	0.451910i	$-0.850743\pi$
$59$	−4.78435	+	3.92642i	−0.622870	+	0.511176i	0.269194	+	0.963086i	$0.413243\pi$
$60$	4.27307	+	0.143387i	0.551651	+	0.0185112i
$61$	−6.43562	−	12.0402i	−0.823997	−	1.54159i	−0.840555	−	0.541726i	$-0.817771\pi$
$61$	−6.43562	−	12.0402i	−0.823997	−	1.54159i	0.0165584	−	0.999863i	$-0.494729\pi$
$62$	4.06759	+	2.81769i	0.516585	+	0.357847i
$63$			1.47275i			0.185549i
$64$	3.78849	−	7.04609i	0.473561	−	0.880761i
$65$			4.57514i			0.567476i
$66$	7.38333	−	10.6585i	0.908825	−	1.31197i
$67$	4.75202	+	8.89040i	0.580551	+	1.08613i	0.985159	+	0.171645i	$0.0549080\pi$
$67$	4.75202	+	8.89040i	0.580551	+	1.08613i	−0.404608	+	0.914490i	$0.632592\pi$
$68$	−3.03206	+	2.83518i	−0.367691	+	0.343816i
$69$	−15.5288	+	12.7442i	−1.86945	+	1.53422i
$70$	−1.31793	−	0.152162i	−0.157522	−	0.0181868i
$71$	6.36920	+	9.53218i	0.755885	+	1.13126i	0.987371	+	0.158424i	$0.0506412\pi$
$71$	6.36920	+	9.53218i	0.755885	+	1.13126i	−0.231486	+	0.972838i	$0.574359\pi$
$72$	−0.223325	+	4.43479i	−0.0263191	+	0.522645i
$73$	4.72067	+	3.15425i	0.552512	+	0.369177i	0.800265	−	0.599646i	$-0.204692\pi$
$73$	4.72067	+	3.15425i	0.552512	+	0.369177i	−0.247753	+	0.968823i	$0.579692\pi$
$74$	−1.24864	+	0.101868i	−0.145152	+	0.0118420i
$75$	−0.620552	−	2.04569i	−0.0716552	−	0.236216i
$76$	2.53906	+	5.15935i	0.291250	+	0.591818i
$77$	−2.55239	+	3.11010i	−0.290872	+	0.354429i
$78$	−13.8297	−	0.231969i	−1.56591	−	0.0262654i
$79$	−5.04893	+	12.1892i	−0.568049	+	1.37139i	0.335148	+	0.942165i	$0.391214\pi$
$79$	−5.04893	+	12.1892i	−0.568049	+	1.37139i	−0.903197	+	0.429226i	$0.858786\pi$
$80$	−3.94550	−	0.658041i	−0.441120	−	0.0735713i
$81$	4.30332	+	10.3891i	0.478146	+	1.15435i
$82$	−5.26172	−	13.3310i	−0.581060	−	1.47216i
$83$	4.23332	−	0.416945i	0.464667	−	0.0457657i	0.137025	−	0.990568i	$-0.456246\pi$
$83$	4.23332	−	0.416945i	0.464667	−	0.0457657i	0.327642	+	0.944802i	$0.393746\pi$
$84$	0.526775	−	3.97610i	0.0574759	−	0.433828i
$85$	1.83047	+	0.978407i	0.198542	+	0.106123i
$86$	−1.16723	−	0.375564i	−0.125866	−	0.0404981i
$87$	−1.21847	−	6.12568i	−0.130634	−	0.656742i
$88$	−8.15744	+	8.97817i	−0.869586	+	0.957077i
$89$	2.50244	+	0.497766i	0.265258	+	0.0527631i	0.325927	−	0.945395i	$-0.394323\pi$
$89$	2.50244	+	0.497766i	0.265258	+	0.0527631i	−0.0606693	+	0.998158i	$0.519323\pi$
$90$	2.13511	−	0.608769i	0.225061	−	0.0641699i
$91$	4.27130	+	0.420686i	0.447754	+	0.0440999i
$92$	15.9684	−	9.91165i	1.66482	−	1.03336i
$93$	7.15767	+	2.17125i	0.742215	+	0.225149i
$94$	−5.47306	−	8.49609i	−0.564503	−	0.876305i
$95$	2.03303	−	2.03303i	0.208585	−	0.208585i
$96$	2.18917	−	11.8931i	0.223431	−	1.21383i
$97$	2.08093	+	2.08093i	0.211287	+	0.211287i	0.804814	−	0.593527i	$-0.202265\pi$
$97$	2.08093	+	2.08093i	0.211287	+	0.211287i	−0.593527	+	0.804814i	$0.702265\pi$
$98$	1.83062	−	8.45911i	0.184920	−	0.854500i
$99$	1.95452	−	6.44317i	0.196436	−	0.647563i
$100$	0.324176	+	1.97355i	0.0324176	+	0.197355i
$101$	1.50977	−	15.3289i	0.150227	−	1.52528i	−0.564238	−	0.825613i	$-0.690830\pi$
$101$	1.50977	−	15.3289i	0.150227	−	1.52528i	0.714465	−	0.699671i	$-0.246670\pi$
$102$	−3.05033	+	5.48353i	−0.302028	+	0.542950i
$103$	−0.712535	+	3.58216i	−0.0702082	+	0.352960i	−0.999881	−	0.0154258i	$-0.995090\pi$
$103$	−0.712535	+	3.58216i	−0.0702082	+	0.352960i	0.929673	+	0.368386i	$0.120090\pi$
$104$	12.7981	+	1.91447i	1.25495	+	0.187730i
$105$	−1.96689	+	0.391239i	−0.191949	+	0.0381810i
$106$	−7.66929	−	14.9459i	−0.744907	−	1.45167i
$107$	2.45983	−	4.60201i	0.237800	−	0.444893i	−0.734506	−	0.678602i	$-0.762586\pi$
$107$	2.45983	−	4.60201i	0.237800	−	0.444893i	0.972307	+	0.233709i	$0.0750862\pi$
$108$	−1.57765	−	5.90722i	−0.151810	−	0.568423i
$109$	−1.55434	−	15.7815i	−0.148879	−	1.51159i	−0.721868	−	0.692030i	$-0.756716\pi$
$109$	−1.55434	−	15.7815i	−0.148879	−	1.51159i	0.572989	−	0.819563i	$-0.305784\pi$
$110$	5.56389	+	2.41474i	0.530496	+	0.230237i
$111$	−1.74958	+	0.724699i	−0.166063	+	0.0687853i
$112$	−0.977130	+	3.62297i	−0.0923301	+	0.342338i
$113$	5.29524	+	2.19336i	0.498134	+	0.206334i	0.617582	−	0.786507i	$-0.288112\pi$
$113$	5.29524	+	2.19336i	0.498134	+	0.206334i	−0.119448	+	0.992840i	$0.538112\pi$
$114$	6.04235	+	6.24851i	0.565918	+	0.585226i
$115$	−7.26414	−	5.96152i	−0.677384	−	0.555915i
$116$	0.377396	+	5.83107i	0.0350403	+	0.541401i
$117$	−6.87333	+	2.08500i	−0.635439	+	0.192758i
$118$	5.66548	−	6.67202i	0.521550	−	0.614209i
$119$	1.08174	−	1.61894i	0.0991631	−	0.148408i
$120$	−5.98208	+	0.879852i	−0.546086	+	0.0803192i
$121$	6.14783	−	4.10785i	0.558894	−	0.373441i
$122$	11.9963	+	15.1280i	1.08610	+	1.36962i
$123$	−13.7436	−	16.7466i	−1.23922	−	1.50999i
$124$	−6.37169	−	2.89326i	−0.572194	−	0.259823i
$125$	0.881921	−	0.471397i	0.0788814	−	0.0421630i
$126$	−0.372015	−	2.04929i	−0.0331417	−	0.182565i
$127$	8.48961			0.753331			0.376665	−	0.926349i	$-0.377071\pi$
$127$	8.48961			0.753331			0.376665	+	0.926349i	$0.377071\pi$
$128$	−3.49174	+	10.7614i	−0.308629	+	0.951182i
$129$	−1.85348			−0.163190
$130$	−1.15567	−	6.36618i	−0.101359	−	0.558351i
$131$	18.5283	−	9.90360i	1.61883	−	0.865282i	0.622233	−	0.782832i	$-0.286226\pi$
$131$	18.5283	−	9.90360i	1.61883	−	0.865282i	0.996595	−	0.0824498i	$-0.0262744\pi$
$132$	−7.58136	+	16.6961i	−0.659873	+	1.45321i
$133$	−1.71108	−	2.08495i	−0.148369	−	0.180788i
$134$	−8.85800	−	11.1704i	−0.765215	−	0.964974i
$135$	−2.54191	+	1.69845i	−0.218773	+	0.146180i
$136$	3.50286	−	4.71097i	0.300368	−	0.403962i
$137$	−2.03174	+	3.04071i	−0.173583	+	0.259785i	−0.908052	−	0.418856i	$-0.862431\pi$
$137$	−2.03174	+	3.04071i	−0.173583	+	0.259785i	0.734469	+	0.678642i	$0.237431\pi$
$138$	18.3887	−	21.6557i	1.56535	−	1.84346i
$139$	−4.75605	+	1.44273i	−0.403403	+	0.122371i	−0.485465	−	0.874256i	$-0.661350\pi$
$139$	−4.75605	+	1.44273i	−0.403403	+	0.122371i	0.0820618	+	0.996627i	$0.473850\pi$
$140$	1.87229	−	0.121178i	0.158238	−	0.0102414i
$141$	−11.8091	−	9.69151i	−0.994509	−	0.816172i
$142$	−11.2704	−	11.6549i	−0.945789	−	0.978059i
$143$	−18.1283	−	7.50899i	−1.51597	−	0.627933i
$144$	−0.809470	−	6.22729i	−0.0674558	−	0.518941i
$145$	2.69924	−	1.11806i	0.224160	−	0.0928499i
$146$	−7.36543	−	3.19661i	−0.609568	−	0.264554i
$147$	−1.28234	−	13.0199i	−0.105766	−	1.07386i
$148$	1.71172	−	0.457152i	0.140702	−	0.0375777i
$149$	1.34304	−	2.51265i	0.110026	−	0.205844i	−0.820882	−	0.571098i	$-0.806518\pi$
$149$	1.34304	−	2.51265i	0.110026	−	0.205844i	0.930908	+	0.365254i	$0.119018\pi$
$150$	1.38022	+	2.68977i	0.112694	+	0.219618i
$151$	16.7647	−	3.33470i	1.36429	−	0.271374i	0.541970	−	0.840398i	$-0.317679\pi$
$151$	16.7647	−	3.33470i	1.36429	−	0.271374i	0.822321	+	0.569024i	$0.192679\pi$
$152$	−4.83628	−	6.53773i	−0.392274	−	0.530280i
$153$	−0.635692	+	3.19584i	−0.0513926	+	0.258368i
$154$	2.76598	−	4.97235i	0.222889	−	0.400683i
$155$	−0.342953	+	3.48206i	−0.0275466	+	0.279686i
$156$	19.3022	−	3.17058i	1.54542	−	0.253850i
$157$	−2.74826	+	9.05980i	−0.219335	+	0.723051i	0.776354	+	0.630297i	$0.217067\pi$
$157$	−2.74826	+	9.05980i	−0.219335	+	0.723051i	−0.995689	+	0.0927537i	$0.970433\pi$
$158$	3.94647	−	18.2363i	0.313964	−	1.45080i
$159$	−17.9556	−	17.9556i	−1.42397	−	1.42397i
$160$	5.65627	−	0.0809822i	0.447168	−	0.00640220i
$161$	−6.23355	+	6.23355i	−0.491272	+	0.491272i
$162$	−8.61223	−	13.3692i	−0.676640	−	1.05038i
$163$	−0.00568121	−	0.00172338i	−0.000444986	−	0.000134985i	0.290062	−	0.957008i	$-0.406324\pi$
$163$	−0.00568121	−	0.00172338i	−0.000444986	−	0.000134985i	−0.290507	+	0.956873i	$0.593824\pi$
$164$	10.6889	+	17.2206i	0.834665	+	1.34470i
$165$	9.12421	+	0.898656i	0.710319	+	0.0699603i
$166$	−5.78522	+	1.64950i	−0.449020	+	0.128026i
$167$	4.79723	+	0.954228i	0.371221	+	0.0738404i	0.377175	−	0.926142i	$-0.376895\pi$
$167$	4.79723	+	0.954228i	0.371221	+	0.0738404i	−0.00595458	+	0.999982i	$0.501895\pi$
$168$	0.271366	+	5.66570i	0.0209363	+	0.437118i
$169$	1.54744	+	7.77951i	0.119034	+	0.598424i
$170$	−2.79419	−	0.899052i	−0.214305	−	0.0689541i
$171$	3.98076	+	2.12776i	0.304417	+	0.162714i
$172$	1.71903	+	0.227747i	0.131075	+	0.0173655i
$173$	−11.6435	+	1.14679i	−0.885241	+	0.0871886i	−0.530410	−	0.847742i	$-0.677962\pi$
$173$	−11.6435	+	1.14679i	−0.885241	+	0.0871886i	−0.354832	+	0.934930i	$0.615462\pi$
$174$	3.24281	+	8.21592i	0.245837	+	0.622848i
$175$	−0.358997	−	0.866697i	−0.0271377	−	0.0655161i
$176$	9.08298	−	14.5534i	0.684655	−	1.09701i
$177$	5.06328	−	12.2238i	0.380579	−	0.918800i
$178$	−3.60781	−	0.0605148i	−0.270417	−	0.00453578i
$179$	−15.3859	+	18.7477i	−1.14999	+	1.40127i	−0.248417	+	0.968653i	$0.579910\pi$
$179$	−15.3859	+	18.7477i	−1.14999	+	1.40127i	−0.901577	+	0.432619i	$0.857590\pi$
$180$	−2.81717	+	1.38641i	−0.209980	+	0.103337i
$181$	−2.34391	−	7.72684i	−0.174222	−	0.574332i	−0.999947	−	0.0102598i	$-0.996734\pi$
$181$	−2.34391	−	7.72684i	−0.174222	−	0.574332i	0.825726	−	0.564072i	$-0.190766\pi$
$182$	−6.04966	+	0.493551i	−0.448430	+	0.0365845i
$183$	24.2663	+	16.2143i	1.79382	+	1.19859i
$184$	−19.7159	+	17.8254i	−1.45347	+	1.31410i
$185$	−0.492156	−	0.736563i	−0.0361840	−	0.0541532i
$186$	−10.5081	−	1.21322i	−0.770495	−	0.0889578i
$187$	−6.88107	+	5.64715i	−0.503193	+	0.412960i
$188$	9.76171	+	10.4396i	0.711946	+	0.761385i
$189$	1.35193	+	2.52927i	0.0983381	+	0.183978i
$190$	−2.31536	+	3.34245i	−0.167974	+	0.242487i
$191$		−	3.77187i		−	0.272923i	−0.990645	−	0.136461i	$-0.956427\pi$
$191$		−	3.77187i		−	0.272923i	0.990645	−	0.136461i	$-0.0435730\pi$
$192$	−0.0419928	+	17.1018i	−0.00303057	+	1.23422i
$193$			2.64588i			0.190455i	0.995456	+	0.0952273i	$0.0303578\pi$
$193$			2.64588i			0.190455i	−0.995456	+	0.0952273i	$0.969642\pi$
$194$	−3.42120	−	2.36992i	−0.245628	−	0.170150i
$195$	−4.61047	−	8.62559i	−0.330163	−	0.617691i
$196$	−0.410491	+	12.2330i	−0.0293208	+	0.873788i
$197$	11.3001	−	9.27373i	0.805097	−	0.660726i	−0.139038	−	0.990287i	$-0.544401\pi$
$197$	11.3001	−	9.27373i	0.805097	−	0.660726i	0.944134	+	0.329561i	$0.106901\pi$
$198$	−1.09212	+	9.45920i	−0.0776133	+	0.672236i
$199$	3.61365	+	5.40821i	0.256165	+	0.383378i	0.937154	−	0.348915i	$-0.113450\pi$
$199$	3.61365	+	5.40821i	0.256165	+	0.383378i	−0.680989	+	0.732293i	$0.738450\pi$
$200$	−0.949598	−	2.66426i	−0.0671467	−	0.188391i
$201$	−17.9181	−	11.9725i	−1.26385	−	0.844475i
$202$	1.77127	+	21.7111i	0.124626	+	1.52759i
$203$	−0.795613	−	2.62278i	−0.0558411	−	0.184083i
$204$	2.85932	−	8.40068i	0.200192	−	0.588165i
$205$	6.42902	−	7.83379i	0.449023	−	0.547136i
$206$	0.0866249	−	5.16446i	0.00603544	−	0.359825i
$207$	5.64567	−	13.6299i	0.392402	−	0.947341i
$208$	−18.2917	+	0.568836i	−1.26830	+	0.0394416i
$209$	4.71885	+	11.3923i	0.326410	+	0.788022i
$210$	2.63805	−	1.04123i	0.182042	−	0.0718518i
$211$	−6.38650	+	0.629015i	−0.439665	+	0.0433032i	−0.315428	−	0.948949i	$-0.602148\pi$
$211$	−6.38650	+	0.629015i	−0.439665	+	0.0433032i	−0.124236	+	0.992253i	$0.539648\pi$
$212$	14.4469	+	18.8595i	0.992218	+	1.29528i
$213$	−21.6138	−	11.5528i	−1.48095	−	0.791584i
$214$	−2.26032	+	7.02492i	−0.154512	+	0.480213i
$215$	−0.169149	−	0.850368i	−0.0115358	−	0.0579946i
$216$	3.68742	+	7.82122i	0.250897	+	0.532167i
$217$	3.21927	+	0.640353i	0.218539	+	0.0434700i
$218$	6.14921	+	21.5669i	0.416477	+	1.46069i
$219$	−12.0786	−	1.18963i	−0.816193	−	0.0803880i
$220$	−8.35196	−	1.95461i	−0.563089	−	0.131780i
$221$	9.08704	+	2.75652i	0.611261	+	0.185424i
$222$	2.25143	−	1.45034i	0.151106	−	0.0973403i
$223$	18.5083	−	18.5083i	1.23941	−	1.23941i	0.279166	−	0.960243i	$-0.409942\pi$
$223$	18.5083	−	18.5083i	1.23941	−	1.23941i	0.960243	−	0.279166i	$-0.0900580\pi$
$224$	0.444493	−	5.28808i	0.0296989	−	0.353325i
$225$	1.11010	+	1.11010i	0.0740068	+	0.0740068i
$226$	−7.92221	−	1.71443i	−0.526978	−	0.114042i
$227$	0.989667	−	3.26250i	0.0656865	−	0.216539i	−0.917952	−	0.396690i	$-0.870159\pi$
$227$	0.989667	−	3.26250i	0.0656865	−	0.216539i	0.983639	+	0.180151i	$0.0576586\pi$
$228$	−9.98613	−	7.16833i	−0.661347	−	0.474735i
$229$	−2.33543	+	23.7120i	−0.154330	+	1.56694i	0.536488	+	0.843908i	$0.319751\pi$
$229$	−2.33543	+	23.7120i	−0.154330	+	1.56694i	−0.690818	+	0.723029i	$0.742749\pi$
$230$	11.6137	+	6.46038i	0.765785	+	0.425985i
$231$	1.67795	−	8.43563i	0.110401	−	0.555023i
$232$	−1.99806	−	8.01844i	−0.131179	−	0.526436i
$233$	−13.5907	+	2.70335i	−0.890353	+	0.177102i	−0.619013	−	0.785381i	$-0.712467\pi$
$233$	−13.5907	+	2.70335i	−0.890353	+	0.177102i	−0.271341	+	0.962483i	$0.587467\pi$
$234$	9.03737	−	4.63741i	0.590792	−	0.303157i
$235$	3.36872	−	6.30243i	0.219751	−	0.411125i
$236$	−6.19802	+	10.7150i	−0.403457	+	0.697488i
$237$	−2.76450	−	28.0684i	−0.179573	−	1.82324i
$238$	−1.09627	+	2.52596i	−0.0710607	+	0.163734i
$239$	−3.02615	+	1.25347i	−0.195746	+	0.0810805i	−0.478403	−	0.878141i	$-0.658784\pi$
$239$	−3.02615	+	1.25347i	−0.195746	+	0.0810805i	0.282657	+	0.959221i	$0.408784\pi$
$240$	8.10164	−	2.73535i	0.522959	−	0.176566i
$241$	−3.30473	−	1.36886i	−0.212877	−	0.0881763i	0.273697	−	0.961816i	$-0.411753\pi$
$241$	−3.30473	−	1.36886i	−0.212877	−	0.0881763i	−0.486574	+	0.873640i	$0.661753\pi$
$242$	−7.51690	+	7.26889i	−0.483205	+	0.467262i
$243$	−11.4929	−	9.43196i	−0.737269	−	0.605061i
$244$	−20.5138	−	18.0199i	−1.31326	−	1.15360i
$245$	5.85643	−	1.77653i	0.374154	−	0.113498i
$246$	23.3539	+	19.8308i	1.48899	+	1.26437i
$247$	7.30807	−	10.9373i	0.465001	−	0.695923i
$248$	9.59686	+	2.41641i	0.609401	+	0.153442i
$249$	−7.56098	+	5.05208i	−0.479157	+	0.320163i
$250$	−1.10809	+	0.878707i	−0.0700820	+	0.0555743i
$251$	15.8571	+	19.3220i	1.00089	+	1.21959i	0.975519	+	0.219914i	$0.0705777\pi$
$251$	15.8571	+	19.3220i	1.00089	+	1.21959i	0.0253742	+	0.999678i	$0.491922\pi$
$252$	1.03530	+	2.75756i	0.0652176	+	0.173710i
$253$	35.5440	−	18.9986i	2.23463	−	1.19443i
$254$	−11.8130	+	2.14446i	−0.741217	+	0.134556i
$255$	−4.43698			−0.277854
$256$	2.14034	−	15.8562i	0.133771	−	0.991012i
$257$	−3.76653			−0.234949			−0.117475	−	0.993076i	$-0.537480\pi$
$257$	−3.76653			−0.234949			−0.117475	+	0.993076i	$0.537480\pi$
$258$	2.57906	−	0.468186i	0.160565	−	0.0291480i
$259$	−0.732900	+	0.391743i	−0.0455402	+	0.0243418i
$260$	3.21618	+	8.56644i	0.199459	+	0.531268i
$261$	2.90979	+	3.54559i	0.180112	+	0.219467i
$262$	−23.2800	+	18.4608i	−1.43824	+	1.14051i
$263$	−1.46078	+	0.976060i	−0.0900753	+	0.0601864i	−0.599792	−	0.800156i	$-0.704750\pi$
$263$	−1.46078	+	0.976060i	−0.0900753	+	0.0601864i	0.509717	+	0.860342i	$0.329750\pi$
$264$	6.33185	−	25.1471i	0.389698	−	1.54770i
$265$	6.59934	−	9.87661i	0.405394	−	0.606715i
$266$	2.90757	+	2.46894i	0.178275	+	0.151380i
$267$	−5.21950	+	1.58332i	−0.319428	+	0.0968975i
$268$	15.1473	+	13.3058i	0.925267	+	0.812778i
$269$	19.7844	+	16.2367i	1.20628	+	0.989967i	0.999934	+	0.0114876i	$0.00365671\pi$
$269$	19.7844	+	16.2367i	1.20628	+	0.989967i	0.206344	+	0.978479i	$0.433843\pi$
$270$	3.10798	−	3.00543i	0.189145	−	0.182905i
$271$	−7.35211	−	3.04534i	−0.446609	−	0.184991i	0.148033	−	0.988982i	$-0.452706\pi$
$271$	−7.35211	−	3.04534i	−0.446609	−	0.184991i	−0.594641	+	0.803991i	$0.702706\pi$
$272$	−3.68415	+	7.43999i	−0.223385	+	0.451116i
$273$	−8.47668	+	3.51116i	−0.513032	+	0.212505i
$274$	2.05903	−	4.74428i	0.124390	−	0.286612i
$275$	0.420377	+	4.26816i	0.0253497	+	0.257380i
$276$	−20.1172	+	34.7783i	−1.21091	+	2.09341i
$277$	−1.86353	+	3.48642i	−0.111969	+	0.209479i	−0.931664	−	0.363321i	$-0.881643\pi$
$277$	−1.86353	+	3.48642i	−0.111969	+	0.209479i	0.819695	+	0.572800i	$0.194143\pi$
$278$	6.25347	−	3.20889i	0.375058	−	0.192457i
$279$	−5.38746	+	1.07163i	−0.322539	+	0.0641569i
$280$	−2.57463	+	0.641554i	−0.153864	+	0.0383402i
$281$	4.00076	−	20.1132i	0.238666	−	1.19985i	−0.656572	−	0.754263i	$-0.727994\pi$
$281$	4.00076	−	20.1132i	0.238666	−	1.19985i	0.895238	−	0.445589i	$-0.147006\pi$
$282$	18.8801	+	10.5025i	1.12430	+	0.625414i
$283$	−1.75861	+	17.8555i	−0.104539	+	1.06140i	0.789605	+	0.613616i	$0.210286\pi$
$283$	−1.75861	+	17.8555i	−0.104539	+	1.06140i	−0.894143	+	0.447781i	$0.852214\pi$
$284$	18.6264	+	13.3706i	1.10528	+	0.793399i
$285$	−1.78418	+	5.88164i	−0.105685	+	0.348398i
$286$	27.1218	+	5.86936i	1.60375	+	0.347063i
$287$	−6.72238	−	6.72238i	−0.396810	−	0.396810i
$288$	2.69936	+	8.46063i	0.159061	+	0.498547i
$289$	−8.97467	+	8.97467i	−0.527922	+	0.527922i
$290$	−3.47349	+	2.23757i	−0.203971	+	0.131395i
$291$	−6.02022	−	1.82621i	−0.352912	−	0.107055i
$292$	11.0563	+	2.58750i	0.647018	+	0.151422i
$293$	21.7662	+	2.14378i	1.27159	+	0.125241i	0.711203	−	0.702987i	$-0.248151\pi$
$293$	21.7662	+	2.14378i	1.27159	+	0.125241i	0.560391	+	0.828228i	$0.310651\pi$
$294$	5.07315	+	17.7929i	0.295872	+	1.03770i
$295$	6.07032	+	1.20746i	0.353428	+	0.0703012i
$296$	−2.26633	+	1.06849i	−0.131728	+	0.0621049i
$297$	−2.55792	−	12.8596i	−0.148426	−	0.746187i
$298$	−1.23411	+	3.83553i	−0.0714899	+	0.222186i
$299$	−37.9169	−	20.2670i	−2.19279	−	1.17207i
$300$	−2.59997	−	3.39409i	−0.150109	−	0.195958i
$301$	−0.809447	+	0.0797235i	−0.0466557	+	0.00459519i
$302$	−22.4852	+	8.87488i	−1.29388	+	0.510692i
$303$	12.6009	+	30.4213i	0.723903	+	1.74766i
$304$	8.38097	+	7.87543i	0.480681	+	0.451687i
$305$	−5.22448	+	12.6130i	−0.299153	+	0.722219i
$306$	0.0772827	−	4.60749i	0.00441796	−	0.263393i
$307$	−1.00067	+	1.21932i	−0.0571111	+	0.0695900i	−0.800782	−	0.598955i	$-0.795583\pi$
$307$	−1.00067	+	1.21932i	−0.0571111	+	0.0695900i	0.743671	+	0.668545i	$0.233083\pi$
$308$	−2.59277	+	7.61757i	−0.147737	+	0.434051i
$309$	−2.26647	−	7.47154i	−0.128935	−	0.425041i
$310$	−0.402354	−	4.93181i	−0.0228522	−	0.280108i
$311$	−3.90976	−	2.61242i	−0.221702	−	0.148137i	0.439760	−	0.898115i	$-0.355064\pi$
$311$	−3.90976	−	2.61242i	−0.221702	−	0.148137i	−0.661462	+	0.749979i	$0.730064\pi$
$312$	−26.0576	+	9.28750i	−1.47522	+	0.525801i
$313$	−10.4244	−	15.6012i	−0.589220	−	0.881829i	0.410327	−	0.911938i	$-0.365415\pi$
$313$	−10.4244	−	15.6012i	−0.589220	−	0.881829i	−0.999547	+	0.0301090i	$0.990415\pi$
$314$	1.53563	−	13.3007i	0.0866608	−	0.750600i
$315$	1.13845	−	0.934303i	0.0641445	−	0.0526420i
$316$	−0.884943	+	26.3721i	−0.0497819	+	1.48355i
$317$	−0.964704	−	1.80483i	−0.0541832	−	0.101370i	0.853372	−	0.521302i	$-0.174554\pi$
$317$	−0.964704	−	1.80483i	−0.0541832	−	0.101370i	−0.907555	+	0.419933i	$0.862054\pi$
$318$	29.5203	+	20.4492i	1.65542	+	1.14673i
$319$			12.5304i			0.701565i
$320$	−7.85009	+	1.54145i	−0.438833	+	0.0861698i
$321$			11.1551i			0.622615i
$322$	7.09922	−	10.2484i	0.395624	−	0.571121i
$323$	−2.81306	−	5.26286i	−0.156523	−	0.292833i
$324$	15.3607	+	16.4274i	0.853372	+	0.912632i
$325$	3.53663	−	2.90244i	0.196177	−	0.160998i
$326$	0.00834056		0.000962963i	0.000461941		5.33336e-5i
$327$	18.8338	+	28.1868i	1.04151	+	1.55873i
$328$	−19.2232	−	21.2620i	−1.06143	−	1.17400i
$329$	−5.57412	−	3.72451i	−0.307311	−	0.205339i
$330$	−12.9231	+	1.05431i	−0.711392	+	0.0580378i
$331$	9.45022	+	31.1532i	0.519431	+	1.71234i	0.687164	+	0.726503i	$0.258856\pi$
$331$	9.45022	+	31.1532i	0.519431	+	1.71234i	−0.167732	+	0.985833i	$0.553644\pi$
$332$	7.63331	−	3.75657i	0.418933	−	0.206169i
$333$	0.882266	−	1.07504i	0.0483479	−	0.0589121i
$334$	−6.91625	−	0.116008i	−0.378440	−	0.00634768i
$335$	3.85772	−	9.31337i	0.210770	−	0.508844i
$336$	−1.80875	−	7.81511i	−0.0986751	−	0.426349i
$337$	3.25626	+	7.86130i	0.177380	+	0.428232i	0.987415	−	0.158148i	$-0.0505524\pi$
$337$	3.25626	+	7.86130i	0.177380	+	0.428232i	−0.810036	+	0.586380i	$0.800552\pi$
$338$	−4.11831	−	10.4341i	−0.224007	−	0.567540i
$339$	−12.1935	+	1.20095i	−0.662259	+	0.0652269i
$340$	4.11514	+	0.545196i	0.223175	+	0.0295674i
$341$	−13.2343	−	7.07386i	−0.716675	−	0.383071i
$342$	−6.07659	−	1.95519i	−0.328584	−	0.105724i
$343$	−2.40115	−	12.0714i	−0.129650	−	0.651795i
$344$	−2.44952	+	0.117323i	−0.132069	+	0.00632561i
$345$	19.7027	+	3.91912i	1.06076	+	0.210998i
$346$	15.9120	−	4.53686i	0.855433	−	0.243903i
$347$	−11.0445	−	1.08779i	−0.592898	−	0.0583954i	−0.202882	−	0.979203i	$-0.565031\pi$
$347$	−11.0445	−	1.08779i	−0.592898	−	0.0583954i	−0.390017	+	0.920808i	$0.627531\pi$
$348$	−6.58761	−	10.6131i	−0.353133	−	0.568922i
$349$	16.9809	+	5.15109i	0.908966	+	0.275732i	0.709940	−	0.704262i	$-0.248722\pi$
$349$	16.9809	+	5.15109i	0.908966	+	0.275732i	0.199026	+	0.979994i	$0.436222\pi$
$350$	0.718461	+	1.11530i	0.0384034	+	0.0596154i
$351$	−9.89018	+	9.89018i	−0.527899	+	0.527899i
$352$	−8.96253	+	22.5450i	−0.477704	+	1.20165i
$353$	−8.25121	−	8.25121i	−0.439168	−	0.439168i	0.452564	−	0.891732i	$-0.350509\pi$
$353$	−8.25121	−	8.25121i	−0.439168	−	0.439168i	−0.891732	+	0.452564i	$0.850509\pi$
$354$	−3.95768	+	18.2881i	−0.210349	+	0.972001i
$355$	3.32790	−	10.9706i	0.176627	−	0.582260i
$356$	5.03545	−	0.827123i	0.266878	−	0.0438375i
$357$	−0.407982	+	4.14231i	−0.0215927	+	0.219234i
$358$	16.6734	−	29.9734i	0.881214	−	1.58414i
$359$	3.95633	−	19.8898i	0.208807	−	1.04974i	−0.724119	−	0.689675i	$-0.757753\pi$
$359$	3.95633	−	19.8898i	0.208807	−	1.04974i	0.932926	−	0.360069i	$-0.117247\pi$
$360$	3.56981	−	2.64077i	0.188146	−	0.139181i
$361$	10.5273	−	2.09402i	0.554070	−	0.110211i
$362$	5.21328	+	10.1596i	0.274004	+	0.533977i
$363$	−7.45104	+	13.9399i	−0.391078	+	0.731655i
$364$	8.29326	−	2.21490i	0.434685	−	0.116092i
$365$	−0.556492	−	5.65016i	−0.0291281	−	0.295743i
$366$	−37.8616	−	16.4320i	−1.97906	−	0.858916i
$367$	23.4060	−	9.69509i	1.22178	−	0.506080i	0.323808	−	0.946123i	$-0.395037\pi$
$367$	23.4060	−	9.69509i	1.22178	−	0.506080i	0.897977	+	0.440043i	$0.145037\pi$
$368$	22.9314	−	29.7837i	1.19538	−	1.55258i
$369$	14.6987	+	6.08841i	0.765185	+	0.316950i
$370$	0.870875	+	0.900589i	0.0452747	+	0.0468194i
$371$	−8.61388	−	7.06922i	−0.447210	−	0.367016i
$372$	14.9282	−	0.966179i	0.773994	−	0.0500940i
$373$	−13.2867	+	4.03047i	−0.687957	+	0.208690i	−0.614861	−	0.788635i	$-0.710788\pi$
$373$	−13.2867	+	4.03047i	−0.687957	+	0.208690i	−0.0730962	+	0.997325i	$0.523288\pi$
$374$	8.14835	−	9.59599i	0.421341	−	0.496197i
$375$	−1.18766	+	1.77746i	−0.0613307	+	0.0917878i
$376$	−16.2202	−	12.0606i	−0.836491	−	0.621977i
$377$	11.1142	−	7.42625i	0.572409	−	0.382471i
$378$	−2.52006	−	3.17792i	−0.129618	−	0.163455i
$379$	−3.44108	−	4.19297i	−0.176757	−	0.215379i	0.677094	−	0.735896i	$-0.263239\pi$
$379$	−3.44108	−	4.19297i	−0.176757	−	0.215379i	−0.853851	+	0.520518i	$0.825739\pi$
$380$	2.37747	−	5.23578i	0.121962	−	0.268590i
$381$	−16.0056	+	8.55517i	−0.819991	+	0.438294i
$382$	0.952769	+	5.24845i	0.0487479	+	0.268534i
$383$	−22.4047			−1.14482			−0.572412	−	0.819966i	$-0.693992\pi$
$383$	−22.4047			−1.14482			−0.572412	+	0.819966i	$0.693992\pi$
$384$	−4.26147	−	23.8073i	−0.217467	−	1.21491i
$385$	4.02336			0.205049
$386$	−0.668346	−	3.68167i	−0.0340179	−	0.187392i
$387$	1.20044	−	0.641648i	0.0610218	−	0.0326168i
$388$	5.35915	+	2.43349i	0.272069	+	0.123542i
$389$	−0.421134	−	0.513154i	−0.0213524	−	0.0260179i	0.762225	−	0.647312i	$-0.224107\pi$
$389$	−0.421134	−	0.513154i	−0.0213524	−	0.0260179i	−0.783577	+	0.621294i	$0.786607\pi$
$390$	8.59415	+	10.8377i	0.435182	+	0.548786i
$391$	−16.2173	+	10.8360i	−0.820143	+	0.548002i
$392$	−2.51886	−	17.1256i	−0.127222	−	0.864974i
$393$	−24.9517	+	37.3428i	−1.25865	+	1.88370i
$394$	−13.3812	+	15.7585i	−0.674135	+	0.793902i
$395$	12.6254	−	3.82987i	0.635252	−	0.192702i
$396$	−0.869733	−	13.4381i	−0.0437057	−	0.675289i
$397$	−14.4731	−	11.8777i	−0.726383	−	0.596127i	0.196820	−	0.980440i	$-0.436938\pi$
$397$	−14.4731	−	11.8777i	−0.726383	−	0.596127i	−0.923203	+	0.384313i	$0.874438\pi$
$398$	−6.39440	−	6.61257i	−0.320522	−	0.331458i
$399$	5.32697	+	2.20650i	0.266682	+	0.110463i
$400$	1.99433	+	3.46737i	0.0997163	+	0.173369i
$401$	−13.1591	+	5.45067i	−0.657134	+	0.272194i	−0.686232	−	0.727383i	$-0.740736\pi$
$401$	−13.1591	+	5.45067i	−0.657134	+	0.272194i	0.0290982	+	0.999577i	$0.490736\pi$
$402$	27.9568	+	12.1333i	1.39436	+	0.605154i
$403$	1.56906	+	15.9309i	0.0781603	+	0.793575i
$404$	−7.94886	−	29.7630i	−0.395471	−	1.48076i
$405$	5.30091	−	9.91730i	0.263404	−	0.492795i
$406$	1.76958	+	3.44856i	0.0878230	+	0.171149i
$407$	3.72627	−	0.741202i	0.184705	−	0.0367400i
$408$	−1.85666	+	12.4116i	−0.0919183	+	0.614464i
$409$	4.50030	−	22.6245i	0.222525	−	1.11871i	−0.694381	−	0.719608i	$-0.744322\pi$
$409$	4.50030	−	22.6245i	0.222525	−	1.11871i	0.916906	−	0.399103i	$-0.130678\pi$
$410$	−6.96700	+	12.5245i	−0.344076	+	0.618539i
$411$	0.766275	−	7.78012i	0.0377976	−	0.383765i
$412$	1.18400	+	7.20808i	0.0583314	+	0.355116i
$413$	1.68544	−	5.55615i	0.0829351	−	0.273400i
$414$	−4.41291	+	20.3917i	−0.216883	+	1.00220i
$415$	−3.00789	−	3.00789i	−0.147652	−	0.147652i
$416$	25.3087	−	5.41198i	1.24086	−	0.265344i
$417$	7.51278	−	7.51278i	0.367902	−	0.367902i
$418$	−9.44383	−	14.6601i	−0.461913	−	0.717049i
$419$	29.4007	+	8.91862i	1.43632	+	0.435703i	0.910009	−	0.414589i	$-0.136075\pi$
$419$	29.4007	+	8.91862i	1.43632	+	0.435703i	0.526311	+	0.850292i	$0.323575\pi$
$420$	−3.40775	+	2.11521i	−0.166281	+	0.103212i
$421$	−17.0064	−	1.67499i	−0.828843	−	0.0816339i	−0.325307	−	0.945608i	$-0.605468\pi$
$421$	−17.0064	−	1.67499i	−0.828843	−	0.0816339i	−0.503535	+	0.863975i	$0.667968\pi$
$422$	8.72774	−	2.48848i	0.424860	−	0.121137i
$423$	11.0035	+	2.18873i	0.535007	+	0.106420i
$424$	−24.8664	−	22.5932i	−1.20762	−	1.09722i
$425$	−0.404920	−	2.03567i	−0.0196415	−	0.0987444i
$426$	32.9931	+	10.6158i	1.59852	+	0.514336i
$427$	11.2950	+	6.03729i	0.546602	+	0.292165i
$428$	1.37068	−	10.3459i	0.0662544	−	0.500089i
$429$	41.7446	−	4.11148i	2.01545	−	0.198504i
$430$	0.450167	+	1.14054i	0.0217090	+	0.0550015i
$431$	−3.39135	−	8.18743i	−0.163355	−	0.394375i	0.820913	−	0.571053i	$-0.193465\pi$
$431$	−3.39135	−	8.18743i	−0.163355	−	0.394375i	−0.984269	+	0.176678i	$0.943465\pi$
$432$	−7.10657	−	9.95157i	−0.341915	−	0.478795i
$433$	−12.5585	+	30.3189i	−0.603523	+	1.45703i	0.266409	+	0.963860i	$0.414163\pi$
$433$	−12.5585	+	30.3189i	−0.603523	+	1.45703i	−0.869932	+	0.493172i	$0.835837\pi$
$434$	−4.64128	−	0.0778495i	−0.222789	−	0.00373690i
$435$	−3.96222	+	4.82798i	−0.189974	+	0.231484i
$436$	−14.0042	−	28.4564i	−0.670680	−	1.36282i
$437$	7.84299	+	25.8549i	0.375181	+	1.23681i
$438$	17.1075	−	1.39568i	0.817427	−	0.0666884i
$439$	4.80765	+	3.21237i	0.229457	+	0.153318i	0.664984	−	0.746857i	$-0.268438\pi$
$439$	4.80765	+	3.21237i	0.229457	+	0.153318i	−0.435528	+	0.900175i	$0.643438\pi$
$440$	12.1153	+	0.610095i	0.577572	+	0.0290851i
$441$	5.33783	+	7.98863i	0.254183	+	0.380411i
$442$	−13.3407	−	1.54025i	−0.634550	−	0.0732623i
$443$	19.4330	−	15.9482i	0.923288	−	0.757723i	−0.0471968	−	0.998886i	$-0.515029\pi$
$443$	19.4330	−	15.9482i	0.923288	−	0.757723i	0.970485	+	0.241163i	$0.0775288\pi$
$444$	−2.76645	+	2.58681i	−0.131290	+	0.122765i
$445$	−1.20275	−	2.25019i	−0.0570159	−	0.106669i
$446$	−21.0786	+	30.4290i	−0.998102	+	1.44085i
$447$			6.09054i			0.288073i
$448$	0.717262	+	7.47049i	0.0338875	+	0.352947i
$449$			3.89835i			0.183974i	0.995760	+	0.0919872i	$0.0293219\pi$
$449$			3.89835i			0.183974i	−0.995760	+	0.0919872i	$0.970678\pi$
$450$	−1.82508	−	1.26426i	−0.0860353	−	0.0595980i
$451$	20.4885	+	38.3313i	0.964766	+	1.80495i
$452$	11.4566	+	0.384437i	0.538873	+	0.0180824i
$453$	−28.2463	+	23.1811i	−1.32713	+	1.08914i
$454$	−0.552992	+	4.78966i	−0.0259532	+	0.224790i
$455$	−2.38449	−	3.56864i	−0.111787	−	0.167300i
$456$	15.7061	+	7.45205i	0.735507	+	0.348974i
$457$	−34.9257	−	23.3366i	−1.63376	−	1.09164i	−0.920503	−	0.390736i	$-0.872220\pi$
$457$	−34.9257	−	23.3366i	−1.63376	−	1.09164i	−0.713254	−	0.700905i	$-0.752780\pi$
$458$	−2.73994	−	33.5846i	−0.128029	−	1.56930i
$459$	1.84192	+	6.07201i	0.0859737	+	0.283417i
$460$	−17.7920	−	6.05583i	−0.829558	−	0.282354i
$461$	−21.9308	+	26.7228i	−1.02142	+	1.24460i	−0.0521398	+	0.998640i	$0.516604\pi$
$461$	−21.9308	+	26.7228i	−1.02142	+	1.24460i	−0.969279	+	0.245963i	$0.920896\pi$
$462$	−0.203993	+	12.1618i	−0.00949061	+	0.565817i
$463$	−6.16671	+	14.8877i	−0.286591	+	0.691892i	−0.999960	−	0.00889600i	$-0.997168\pi$
$463$	−6.16671	+	14.8877i	−0.286591	+	0.691892i	0.713369	+	0.700788i	$0.247168\pi$
$464$	4.80569	+	10.6527i	0.223098	+	0.494540i
$465$	−2.86237	−	6.91038i	−0.132739	−	0.320461i
$466$	18.2281	−	7.19461i	0.844403	−	0.333284i
$467$	−27.2359	+	2.68250i	−1.26033	+	0.124131i	−0.706027	−	0.708185i	$-0.749514\pi$
$467$	−27.2359	+	2.68250i	−1.26033	+	0.124131i	−0.554300	+	0.832317i	$0.687014\pi$
$468$	−11.4038	+	8.73566i	−0.527143	+	0.403806i
$469$	−8.34013	−	4.45789i	−0.385111	−	0.205846i
$470$	−3.09549	+	9.62059i	−0.142784	+	0.443765i
$471$	−3.94842	−	19.8501i	−0.181934	−	0.914643i
$472$	5.91777	−	16.4753i	0.272387	−	0.758335i
$473$	3.64707	+	0.725447i	0.167692	+	0.0333561i
$474$	10.9368	+	38.3581i	0.502342	+	1.76185i
$475$	−2.86130	−	0.281813i	−0.131285	−	0.0129305i
$476$	0.887377	−	3.79172i	0.0406729	−	0.173793i
$477$	17.8453	+	5.41331i	0.817080	+	0.247859i
$478$	3.89418	−	2.50857i	0.178116	−	0.114740i
$479$	1.02961	−	1.02961i	0.0470442	−	0.0470442i	−0.683193	−	0.730238i	$-0.739409\pi$
$479$	1.02961	−	1.02961i	0.0470442	−	0.0470442i	0.730238	+	0.683193i	$0.239409\pi$
$480$	−10.5823	+	5.85263i	−0.483012	+	0.267135i
$481$	−2.86585	−	2.86585i	−0.130671	−	0.130671i
$482$	4.94422	+	1.06997i	0.225203	+	0.0487356i
$483$	5.47052	−	18.0339i	0.248917	−	0.820570i
$484$	8.62344	−	12.0132i	0.391975	−	0.546056i
$485$	0.288453	−	2.92871i	0.0130980	−	0.132986i
$486$	18.3745	+	10.2212i	0.833485	+	0.463644i
$487$	0.743832	−	3.73949i	0.0337062	−	0.169453i	−0.960266	−	0.279087i	$-0.909968\pi$
$487$	0.743832	−	3.73949i	0.0337062	−	0.169453i	0.993972	+	0.109635i	$0.0349681\pi$
$488$	33.0962	+	19.8924i	1.49820	+	0.900486i
$489$	0.0124476	−	0.00247597i	0.000562898	−	0.000111967i
$490$	−7.70031	+	3.95132i	−0.347865	+	0.178502i
$491$	−11.1158	+	20.7961i	−0.501647	+	0.938516i	0.495891	+	0.868385i	$0.334842\pi$
$491$	−11.1158	+	20.7961i	−0.501647	+	0.938516i	−0.997538	+	0.0701308i	$0.977658\pi$
$492$	−37.5056	−	21.6948i	−1.69088	−	0.978078i
$493$	−0.594376	−	6.03480i	−0.0267693	−	0.271794i
$494$	−7.40622	+	17.0649i	−0.333222	+	0.767788i
$495$	−6.22057	+	2.57665i	−0.279594	+	0.115812i
$496$	−13.9641	−	0.938218i	−0.627008	−	0.0421272i
$497$	−9.93603	−	4.11564i	−0.445692	−	0.184612i
$498$	9.24474	−	8.93972i	0.414267	−	0.400599i
$499$	−22.6197	−	18.5635i	−1.01260	−	0.831016i	−0.0269149	−	0.999638i	$-0.508568\pi$
$499$	−22.6197	−	18.5635i	−1.01260	−	0.831016i	−0.985681	+	0.168622i	$0.946068\pi$
$500$	1.31992	−	1.50260i	0.0590287	−	0.0671983i
$501$	−10.0059	+	3.03525i	−0.447030	+	0.135605i
$502$	−26.9455	−	22.8805i	−1.20263	−	1.02121i
$503$	15.2868	−	22.8782i	0.681603	−	1.02009i	−0.315853	−	0.948808i	$-0.602291\pi$
$503$	15.2868	−	22.8782i	0.681603	−	1.02009i	0.997456	−	0.0712827i	$-0.0227092\pi$
$504$	−2.13714	−	3.57555i	−0.0951959	−	0.159268i
$505$	−12.8072	+	8.55749i	−0.569913	+	0.380803i
$506$	−44.6594	+	35.4144i	−1.98535	+	1.57436i
$507$	−10.7570	−	13.1074i	−0.477735	−	0.582122i
$508$	15.8958	−	5.96792i	0.705264	−	0.264784i
$509$	29.3693	−	15.6982i	1.30177	−	0.695810i	0.332802	−	0.942997i	$-0.392006\pi$
$509$	29.3693	−	15.6982i	1.30177	−	0.695810i	0.968968	+	0.247187i	$0.0795060\pi$
$510$	6.17393	−	1.12078i	0.273386	−	0.0496288i
$511$	−5.32609			−0.235612
$512$	1.02703	+	22.6041i	0.0453886	+	0.998969i
$513$	8.78969			0.388074
$514$	5.24102	−	0.951420i	0.231171	−	0.0419653i
$515$	3.22107	−	1.72170i	0.141937	−	0.0758671i
$516$	−3.47043	+	1.30293i	−0.152777	+	0.0573585i
$517$	19.4435	+	23.6920i	0.855124	+	1.04197i
$518$	0.920856	−	0.730230i	0.0404601	−	0.0320844i
$519$	20.7961	−	13.8955i	0.912847	−	0.609945i
$520$	−6.63909	−	11.1076i	−0.291143	−	0.487099i
$521$	−15.3458	+	22.9666i	−0.672311	+	1.00619i	0.325841	+	0.945425i	$0.394353\pi$
$521$	−15.3458	+	22.9666i	−0.672311	+	1.00619i	−0.998152	+	0.0607605i	$0.980647\pi$
$522$	−4.94451	−	4.19858i	−0.216415	−	0.183767i
$523$	−18.3187	+	5.55692i	−0.801021	+	0.242987i	−0.664148	−	0.747602i	$-0.731205\pi$
$523$	−18.3187	+	5.55692i	−0.801021	+	0.242987i	−0.136873	+	0.990589i	$0.543705\pi$
$524$	27.7303	−	31.5682i	1.21140	−	1.37906i
$525$	1.55021	+	1.27223i	0.0676568	+	0.0555245i
$526$	1.78608	−	1.72715i	0.0778767	−	0.0753073i
$527$	6.70935	+	2.77911i	0.292264	+	0.121060i
$528$	−2.45846	+	36.5909i	−0.106991	+	1.59242i
$529$	60.3362	−	24.9921i	2.62331	−	1.08661i
$530$	−6.68798	+	15.4100i	−0.290507	+	0.669368i
$531$	0.952396	+	9.66984i	0.0413305	+	0.419635i
$532$	−4.66945	−	2.70101i	−0.202446	−	0.117104i
$533$	21.8563	−	40.8903i	0.946703	−	1.77116i
$534$	6.86284	−	3.52158i	0.296984	−	0.152394i
$535$	−5.11790	+	1.01801i	−0.221266	+	0.0440126i
$536$	−24.4380	−	14.6884i	−1.05556	−	0.634442i
$537$	10.1147	−	50.8501i	0.436482	−	2.19434i
$538$	−31.6308	−	17.5953i	−1.36370	−	0.758589i
$539$	−2.57269	+	26.1210i	−0.110814	+	1.12511i
$540$	−3.56549	+	4.96705i	−0.153434	+	0.213748i
$541$	4.30438	−	14.1896i	0.185060	−	0.610061i	−0.814493	−	0.580173i	$-0.802985\pi$
$541$	4.30438	−	14.1896i	0.185060	−	0.610061i	0.999553	−	0.0298877i	$-0.00951498\pi$
$542$	10.9995	+	2.38038i	0.472469	+	0.102246i
$543$	12.2055	+	12.2055i	0.523789	+	0.523789i
$544$	3.24706	−	11.2832i	0.139217	−	0.483761i
$545$	−11.2132	+	11.2132i	−0.480321	+	0.480321i
$546$	10.9082	−	7.02687i	0.466826	−	0.300722i
$547$	−21.3351	−	6.47195i	−0.912225	−	0.276720i	−0.200923	−	0.979607i	$-0.564394\pi$
$547$	−21.3351	−	6.47195i	−0.912225	−	0.276720i	−0.711302	+	0.702887i	$0.751894\pi$
$548$	−1.66668	+	7.12163i	−0.0711970	+	0.304221i
$549$	−21.3297	−	2.10079i	−0.910330	−	0.0896597i
$550$	−1.66308	−	5.83284i	−0.0709138	−	0.248713i
$551$	−8.23870	−	1.63878i	−0.350981	−	0.0698144i
$552$	19.2076	−	53.4746i	0.817530	−	2.27603i
$553$	−2.41461	−	12.1391i	−0.102680	−	0.516206i
$554$	1.71239	−	5.32199i	0.0727523	−	0.226110i
$555$	1.67012	+	0.892698i	0.0708926	+	0.0378929i
$556$	−7.89097	+	6.04470i	−0.334652	+	0.256352i
$557$	−11.4838	+	1.13105i	−0.486584	+	0.0479243i	−0.338335	−	0.941026i	$-0.609864\pi$
$557$	−11.4838	+	1.13105i	−0.486584	+	0.0479243i	−0.148249	+	0.988950i	$0.547364\pi$
$558$	7.22580	−	2.85201i	0.305893	−	0.120735i
$559$	−1.51802	−	3.66482i	−0.0642053	−	0.155005i
$560$	3.42048	−	1.54305i	0.144541	−	0.0652059i
$561$	7.28223	−	17.5809i	0.307456	−	0.742265i
$562$	−0.486384	+	28.9975i	−0.0205169	+	1.22319i
$563$	14.6234	−	17.8187i	0.616303	−	0.750967i	−0.367539	−	0.930008i	$-0.619800\pi$
$563$	14.6234	−	17.8187i	0.616303	−	0.750967i	0.983842	+	0.179041i	$0.0572996\pi$
$564$	−28.9241	−	9.84482i	−1.21792	−	0.414542i
$565$	−1.66377	−	5.48472i	−0.0699955	−	0.230744i
$566$	−2.06321	−	25.2896i	−0.0867232	−	1.06300i
$567$	−8.77126	−	5.86077i	−0.368358	−	0.246129i
$568$	−29.2956	−	13.8998i	−1.22921	−	0.583223i
$569$	1.68594	+	2.52319i	0.0706784	+	0.105778i	0.865125	−	0.501556i	$-0.167239\pi$
$569$	1.68594	+	2.52319i	0.0706784	+	0.105778i	−0.794447	+	0.607334i	$0.792239\pi$
$570$	0.996936	−	8.63481i	0.0417570	−	0.361673i
$571$	−10.8728	+	8.92311i	−0.455014	+	0.373420i	−0.833802	−	0.552063i	$-0.813841\pi$
$571$	−10.8728	+	8.92311i	−0.455014	+	0.373420i	0.378788	+	0.925483i	$0.376341\pi$
$572$	−39.2218	−	1.31613i	−1.63995	−	0.0550300i
$573$	3.80100	+	7.11116i	0.158789	+	0.297073i
$574$	11.0521	+	7.65594i	0.461304	+	0.319553i
$575$			9.39720i			0.391890i
$576$	−5.89323	−	11.0909i	−0.245551	−	0.462120i
$577$			36.5204i			1.52036i	0.649711	+	0.760181i	$0.274890\pi$
$577$			36.5204i			1.52036i	−0.649711	+	0.760181i	$0.725110\pi$
$578$	10.2210	−	14.7550i	0.425138	−	0.613726i
$579$	−2.66631	−	4.98832i	−0.110808	−	0.207308i
$580$	4.26806	−	3.99092i	0.177222	−	0.165714i
$581$	−3.08471	+	2.53156i	−0.127975	+	0.105027i
$582$	8.83827	+	1.02043i	0.366358	+	0.0422980i
$583$	28.3033	+	42.3590i	1.17220	+	1.75433i
$584$	−16.0381	−	0.807639i	−0.663660	−	0.0334203i
$585$	5.97212	+	3.99044i	0.246917	+	0.164985i
$586$	−30.8286	+	2.51510i	−1.27352	+	0.103898i
$587$	13.8342	+	45.6052i	0.570998	+	1.88233i	0.458546	+	0.888670i	$0.348370\pi$
$587$	13.8342	+	45.6052i	0.570998	+	1.88233i	0.112451	+	0.993657i	$0.464130\pi$
$588$	−11.5536	−	23.4768i	−0.476462	−	0.968166i
$589$	6.38190	−	7.77637i	0.262962	−	0.320420i
$590$	−8.75168	−	0.146794i	−0.360301	−	0.00604343i
$591$	−11.9589	+	28.8712i	−0.491922	+	1.18760i
$592$	2.88364	−	2.05925i	0.118517	−	0.0846346i
$593$	1.42883	+	3.44951i	0.0586751	+	0.141654i	0.950498	−	0.310730i	$-0.100574\pi$
$593$	1.42883	+	3.44951i	0.0586751	+	0.141654i	−0.891823	+	0.452384i	$0.850574\pi$
$594$	6.80758	+	17.2476i	0.279319	+	0.707677i
$595$	−1.93771	+	0.190848i	−0.0794383	+	0.00782399i
$596$	0.748378	−	5.64876i	0.0306547	−	0.231382i
$597$	−12.2628	−	6.55463i	−0.501885	−	0.268263i
$598$	57.8797	+	18.6232i	2.36688	+	0.761560i
$599$	−5.64562	−	28.3824i	−0.230674	−	1.15968i	−0.906367	−	0.422492i	$-0.861155\pi$
$599$	−5.64562	−	28.3824i	−0.230674	−	1.15968i	0.675693	−	0.737183i	$-0.263845\pi$
$600$	4.47512	+	4.06603i	0.182696	+	0.165995i
$601$	25.1869	+	5.00998i	1.02739	+	0.204361i	0.679888	−	0.733316i	$-0.262029\pi$
$601$	25.1869	+	5.00998i	1.02739	+	0.204361i	0.347506	+	0.937678i	$0.387029\pi$
$602$	1.10618	−	0.315398i	0.0450847	−	0.0128547i
$603$	15.7497	+	1.55121i	0.641378	+	0.0631702i
$604$	29.0458	−	18.0289i	1.18186	−	0.733585i
$605$	−7.07556	−	2.14635i	−0.287662	−	0.0872614i
$606$	−25.2182	−	39.1474i	−1.02442	−	1.59025i
$607$	34.0549	−	34.0549i	1.38224	−	1.38224i	0.541624	−	0.840621i	$-0.317810\pi$
$607$	34.0549	−	34.0549i	1.38224	−	1.38224i	0.840621	−	0.541624i	$-0.182190\pi$
$608$	−13.6512	−	8.84141i	−0.553629	−	0.358567i
$609$	4.14302	+	4.14302i	0.167884	+	0.167884i
$610$	4.08369	−	18.8704i	0.165344	−	0.764039i
$611$	9.49089	−	31.2873i	0.383960	−	1.26575i
$612$	1.05631	+	6.43072i	0.0426988	+	0.259946i
$613$	0.759075	−	7.70702i	0.0306588	−	0.311284i	−0.967609	−	0.252453i	$-0.918763\pi$
$613$	0.759075	−	7.70702i	0.0306588	−	0.311284i	0.998268	−	0.0588308i	$-0.0187372\pi$
$614$	1.08440	−	1.94941i	0.0437629	−	0.0786718i
$615$	−4.22646	+	21.2478i	−0.170427	+	0.856795i
$616$	1.68358	−	11.2546i	0.0678334	−	0.453459i
$617$	27.4098	−	5.45214i	1.10348	−	0.219495i	0.390444	−	0.920627i	$-0.372322\pi$
$617$	27.4098	−	5.45214i	1.10348	−	0.219495i	0.713031	+	0.701132i	$0.247322\pi$
$618$	5.04102	+	9.82393i	0.202780	+	0.395176i
$619$	7.61572	−	14.2480i	0.306102	−	0.572676i	−0.681093	−	0.732197i	$-0.738495\pi$
$619$	7.61572	−	14.2480i	0.306102	−	0.572676i	0.987195	+	0.159521i	$0.0509950\pi$
$620$	1.80563	+	6.76085i	0.0725160	+	0.271522i
$621$	−2.81589	−	28.5902i	−0.112998	−	1.14728i
$622$	6.10021	+	2.64751i	0.244596	+	0.106155i
$623$	−2.21135	+	0.915970i	−0.0885957	+	0.0366976i
$624$	33.9124	−	19.5054i	1.35758	−	0.780841i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	18.4460	+	19.0754i	0.737252	+	0.762406i
$627$	−20.3768	−	16.7228i	−0.813771	−	0.667845i
$628$	1.22294	+	18.8954i	0.0488006	+	0.754008i
$629$	−1.75947	+	0.533729i	−0.0701546	+	0.0212812i
$630$	−1.34812	+	1.58763i	−0.0537104	+	0.0632526i
$631$	−3.69320	+	5.52727i	−0.147024	+	0.220037i	−0.897671	−	0.440667i	$-0.854742\pi$
$631$	−3.69320	+	5.52727i	−0.147024	+	0.220037i	0.750647	+	0.660704i	$0.229742\pi$
$632$	−5.43019	−	36.9196i	−0.216001	−	1.46858i
$633$	11.4067	−	7.62171i	0.453375	−	0.302936i
$634$	1.79826	+	2.26769i	0.0714179	+	0.0900616i
$635$	−5.38575	−	6.56255i	−0.213727	−	0.260427i
$636$	−46.2422	−	20.9977i	−1.83362	−	0.832612i
$637$	24.6935	−	13.1990i	0.978392	−	0.522962i
$638$	−3.16515	−	17.4356i	−0.125309	−	0.690283i
$639$	17.9980			0.711989
$640$	10.5338	−	4.12781i	0.416385	−	0.163166i
$641$	43.5923			1.72179			0.860896	−	0.508781i	$-0.169904\pi$
$641$	43.5923			1.72179			0.860896	+	0.508781i	$0.169904\pi$
$642$	−2.81775	−	15.5220i	−0.111208	−	0.612603i
$643$	−10.2087	+	5.45664i	−0.402590	+	0.215189i	−0.660249	−	0.751047i	$-0.729549\pi$
$643$	−10.2087	+	5.45664i	−0.402590	+	0.215189i	0.257658	+	0.966236i	$0.417049\pi$
$644$	−7.28963	+	16.0536i	−0.287252	+	0.632601i
$645$	1.17583	+	1.43276i	0.0462984	+	0.0564147i
$646$	5.24368	+	6.61255i	0.206310	+	0.260167i
$647$	−5.97729	+	3.99389i	−0.234991	+	0.157016i	−0.667491	−	0.744618i	$-0.732632\pi$
$647$	−5.97729	+	3.99389i	−0.234991	+	0.157016i	0.432500	+	0.901634i	$0.357632\pi$
$648$	−25.5235	−	18.9781i	−1.00266	−	0.745532i
$649$	−14.7474	+	22.0710i	−0.578884	+	0.866361i
$650$	−4.18797	+	4.93201i	−0.164266	+	0.193449i
$651$	−6.71465	+	2.03687i	−0.263168	+	0.0798311i
$652$	−0.0118489		0.000766879i	−0.000464039		3.00333e-5i
$653$	−26.1762	−	21.4822i	−1.02435	−	0.840665i	−0.0370186	−	0.999315i	$-0.511786\pi$
$653$	−26.1762	−	21.4822i	−1.02435	−	0.840665i	−0.987335	+	0.158649i	$0.949286\pi$
$654$	−33.3266	−	34.4637i	−1.30317	−	1.34764i
$655$	−19.4098	−	8.03982i	−0.758405	−	0.314142i
$656$	32.1193	+	24.7297i	1.25405	+	0.965532i
$657$	8.23474	−	3.41094i	0.321268	−	0.133074i
$658$	8.69704	+	3.77453i	0.339046	+	0.147147i
$659$	1.76509	+	17.9212i	0.0687580	+	0.698112i	0.966341	+	0.257266i	$0.0828216\pi$
$659$	1.76509	+	17.9212i	0.0687580	+	0.698112i	−0.897583	+	0.440846i	$0.854678\pi$
$660$	17.7158	−	4.73139i	0.689586	−	0.184169i
$661$	10.6536	−	19.9315i	0.414377	−	0.775245i	−0.584982	−	0.811047i	$-0.698898\pi$
$661$	10.6536	−	19.9315i	0.414377	−	0.775245i	0.999359	+	0.0358011i	$0.0113983\pi$
$662$	−21.0190	−	40.9617i	−0.816926	−	1.59202i
$663$	−19.9098	+	3.96030i	−0.773231	+	0.153805i
$664$	−9.67264	+	7.15533i	−0.375371	+	0.277681i
$665$	−0.526195	+	2.64536i	−0.0204050	+	0.102583i
$666$	−0.956094	+	1.71875i	−0.0370479	+	0.0666003i
$667$	−2.69108	+	27.3230i	−0.104199	+	1.05795i
$668$	9.65307	−	1.58561i	0.373488	−	0.0613492i
$669$	−16.2428	+	53.5453i	−0.627982	+	2.07018i
$670$	−3.01537	+	13.9337i	−0.116494	+	0.538307i
$671$	−41.4025	−	41.4025i	−1.59832	−	1.59832i
$672$	4.49091	+	10.4176i	0.173240	+	0.401869i
$673$	9.50868	−	9.50868i	0.366533	−	0.366533i	−0.499678	−	0.866211i	$-0.666548\pi$
$673$	9.50868	−	9.50868i	0.366533	−	0.366533i	0.866211	+	0.499678i	$0.166548\pi$
$674$	−6.51674	−	10.1162i	−0.251015	−	0.389663i
$675$	2.92550	+	0.887439i	0.112602	+	0.0341576i
$676$	8.36615	+	13.4785i	0.321775	+	0.518402i
$677$	−10.7482	−	1.05860i	−0.413085	−	0.0406854i	−0.110660	−	0.993858i	$-0.535296\pi$
$677$	−10.7482	−	1.05860i	−0.413085	−	0.0406854i	−0.302426	+	0.953173i	$0.597796\pi$
$678$	16.6635	−	4.75115i	0.639959	−	0.182467i
$679$	−2.70769	−	0.538593i	−0.103912	−	0.0206693i
$680$	−5.86382	+	0.280855i	−0.224867	+	0.0107703i
$681$	1.42185	+	7.14814i	0.0544856	+	0.273917i
$682$	20.2019	+	6.50012i	0.773572	+	0.248902i
$683$	−42.2018	−	22.5574i	−1.61481	−	0.863133i	−0.997049	−	0.0767664i	$-0.975540\pi$
$683$	−42.2018	−	22.5574i	−1.61481	−	0.863133i	−0.617760	−	0.786367i	$-0.711960\pi$
$684$	8.94928	+	1.18565i	0.342184	+	0.0453344i
$685$	3.63942	−	0.358452i	0.139055	−	0.0136957i
$686$	6.39036	+	16.1905i	0.243985	+	0.618156i
$687$	−19.4921	−	47.0582i	−0.743671	−	1.79538i
$688$	3.37880	−	0.781995i	0.128815	−	0.0298133i
$689$	20.7972	−	50.2090i	0.792312	−	1.91281i
$690$	−28.4058	−	0.476458i	−1.08139	−	0.0181384i
$691$	25.8568	−	31.5066i	0.983638	−	1.19857i	0.00355212	−	0.999994i	$-0.498869\pi$
$691$	25.8568	−	31.5066i	0.983638	−	1.19857i	0.980086	−	0.198573i	$-0.0636307\pi$
$692$	−20.9950	+	10.3323i	−0.798112	+	0.392774i
$693$	1.83354	+	6.04438i	0.0696505	+	0.229607i
$694$	15.6428	−	1.27620i	0.593794	−	0.0484437i
$695$	4.13245	+	2.76122i	0.156753	+	0.104739i
$696$	11.8473	+	13.1038i	0.449072	+	0.496698i
$697$	−11.6858	−	17.4890i	−0.442631	−	0.662445i
$698$	−24.9296	−	2.87826i	−0.943599	−	0.108944i
$699$	22.8984	−	18.7923i	0.866099	−	0.710789i
$700$	−1.28144	−	1.37043i	−0.0484340	−	0.0517973i
$701$	19.3694	+	36.2376i	0.731573	+	1.36868i	0.922083	+	0.386992i	$0.126486\pi$
$701$	19.3694	+	36.2376i	0.731573	+	1.36868i	−0.190510	+	0.981685i	$0.561014\pi$
$702$	11.2637	−	16.2601i	0.425119	−	0.613700i
$703$			2.54696i			0.0960605i
$704$	6.77626	−	33.6347i	0.255390	−	1.26766i
$705$			15.2768i			0.575358i
$706$	13.5656	+	9.39709i	0.510547	+	0.353664i
$707$	6.81155	+	12.7435i	0.256175	+	0.479269i
$708$	0.887458	−	26.4471i	0.0333527	−	0.993942i
$709$	27.4741	−	22.5474i	1.03181	−	0.846785i	0.0434711	−	0.999055i	$-0.486158\pi$
$709$	27.4741	−	22.5474i	1.03181	−	0.846785i	0.988339	+	0.152270i	$0.0486583\pi$
$710$	−1.85952	+	16.1059i	−0.0697864	+	0.604444i
$711$	11.5074	+	17.2220i	0.431560	+	0.645876i
$712$	−6.79776	+	2.42287i	−0.254757	+	0.0908008i
$713$	−27.3387	−	18.2671i	−1.02384	−	0.684109i
$714$	−0.478647	−	5.86697i	−0.0179129	−	0.219566i
$715$	5.69595	+	18.7770i	0.213016	+	0.702221i
$716$	−15.6293	+	45.9188i	−0.584093	+	1.71607i
$717$	4.44210	−	5.41271i	0.165893	−	0.202142i
$718$	−0.480982	+	28.6755i	−0.0179501	+	1.07016i
$719$	−11.3917	+	27.5020i	−0.424839	+	1.02565i	0.556061	+	0.831141i	$0.312312\pi$
$719$	−11.3917	+	27.5020i	−0.424839	+	1.02565i	−0.980900	+	0.194511i	$0.937688\pi$
$720$	−4.30024	+	4.57628i	−0.160260	+	0.170548i
$721$	−1.31118	−	3.16547i	−0.0488309	−	0.117888i
$722$	−14.1195	+	5.57295i	−0.525475	+	0.207404i
$723$	7.60990	−	0.749510i	0.283015	−	0.0278746i
$724$	−9.82043	−	12.8199i	−0.364973	−	0.476450i
$725$	−2.57665	−	1.37725i	−0.0956944	−	0.0511497i
$726$	6.84671	−	21.2791i	0.254105	−	0.789742i
$727$	−0.622243	−	3.12823i	−0.0230777	−	0.116020i	0.967529	−	0.252759i	$-0.0813378\pi$
$727$	−0.622243	−	3.12823i	−0.0230777	−	0.116020i	−0.990607	+	0.136739i	$0.956338\pi$
$728$	−10.9804	+	5.17683i	−0.406959	+	0.191866i
$729$	−1.91461	−	0.380840i	−0.0709115	−	0.0141052i
$730$	2.20157	+	7.72147i	0.0814836	+	0.285784i
$731$	−1.79089	−	0.176388i	−0.0662386	−	0.00652393i
$732$	56.8341	+	13.3009i	2.10065	+	0.491616i
$733$	28.0550	+	8.51038i	1.03623	+	0.314338i	0.762173	−	0.647374i	$-0.224133\pi$
$733$	28.0550	+	8.51038i	1.03623	+	0.314338i	0.274062	+	0.961712i	$0.411633\pi$
$734$	−30.1199	+	19.4028i	−1.11174	+	0.716170i
$735$	−9.25098	+	9.25098i	−0.341228	+	0.341228i
$736$	−24.3851	+	47.2356i	−0.898846	+	1.74113i
$737$	30.5713	+	30.5713i	1.12611	+	1.12611i
$738$	−21.9908	−	4.75897i	−0.809492	−	0.175180i
$739$	2.69115	−	8.87152i	0.0989954	−	0.326344i	−0.893428	−	0.449206i	$-0.851707\pi$
$739$	2.69115	−	8.87152i	0.0989954	−	0.326344i	0.992424	+	0.122861i	$0.0392071\pi$
$740$	−1.43929	−	1.03316i	−0.0529092	−	0.0379798i
$741$	−2.75626	+	27.9848i	−0.101254	+	1.02805i
$742$	13.7716	+	7.66077i	0.505573	+	0.281236i
$743$	−8.16660	+	41.0563i	−0.299604	+	1.50621i	0.478508	+	0.878083i	$0.341178\pi$
$743$	−8.16660	+	41.0563i	−0.299604	+	1.50621i	−0.778112	+	0.628126i	$0.783822\pi$
$744$	−20.5282	+	5.11527i	−0.752600	+	0.187535i
$745$	−2.79432	+	0.555824i	−0.102376	+	0.0203638i
$746$	17.4699	−	8.96447i	0.639620	−	0.328213i
$747$	3.14805	−	5.88959i	0.115181	−	0.215489i
$748$	−8.91427	+	15.4108i	−0.325938	+	0.563475i
$749$	0.479812	+	4.87162i	0.0175320	+	0.178005i
$750$	1.20361	−	2.77329i	0.0439498	−	0.101266i
$751$	−46.3523	+	19.1998i	−1.69142	+	0.700610i	−0.999766	−	0.0216185i	$-0.993118\pi$
$751$	−46.3523	+	19.1998i	−1.69142	+	0.700610i	−0.691655	+	0.722228i	$0.743118\pi$
$752$	25.6164	+	12.6848i	0.934134	+	0.462566i
$753$	−49.3669	−	20.4484i	−1.79903	−	0.745182i
$754$	−13.5892	+	13.1408i	−0.494889	+	0.478561i
$755$	−13.2132	−	10.8438i	−0.480876	−	0.394645i
$756$	4.30933	+	3.78542i	0.156729	+	0.137675i
$757$	−9.86511	+	2.99255i	−0.358553	+	0.108766i	−0.464422	−	0.885614i	$-0.653738\pi$
$757$	−9.86511	+	2.99255i	−0.358553	+	0.108766i	0.105868	+	0.994380i	$0.466238\pi$
$758$	5.84731	+	4.96519i	0.212384	+	0.180344i
$759$	−47.8662	+	71.6369i	−1.73743	+	2.60025i
$760$	−1.98563	+	7.88598i	−0.0720263	+	0.286055i
$761$	2.32424	−	1.55301i	0.0842537	−	0.0562965i	−0.512730	−	0.858550i	$-0.671366\pi$
$761$	2.32424	−	1.55301i	0.0842537	−	0.0562965i	0.596984	+	0.802253i	$0.296366\pi$
$762$	20.1103	−	15.9473i	0.728519	−	0.577708i
$763$	9.43745	+	11.4996i	0.341659	+	0.416312i
$764$	−2.65150	−	7.06240i	−0.0959280	−	0.255509i
$765$	2.87369	−	1.53602i	0.103899	−	0.0555350i
$766$	31.1754	−	5.65938i	1.12641	−	0.204482i
$767$	28.3167			1.02246
$768$	11.9434	+	32.0508i	0.430971	+	1.15653i
$769$	21.7429			0.784068			0.392034	−	0.919951i	$-0.371772\pi$
$769$	21.7429			0.784068			0.392034	+	0.919951i	$0.371772\pi$
$770$	−5.59839	+	1.01630i	−0.201752	+	0.0366248i
$771$	7.10109	−	3.79561i	0.255740	−	0.136696i
$772$	1.85997	+	4.95411i	0.0669417	+	0.178302i
$773$	−24.5304	−	29.8904i	−0.882297	−	1.07508i	−0.996662	−	0.0816433i	$-0.973983\pi$
$773$	−24.5304	−	29.8904i	−0.882297	−	1.07508i	0.114364	−	0.993439i	$-0.463517\pi$
$774$	−1.50830	+	1.19606i	−0.0542147	+	0.0429917i
$775$	2.90923	−	1.94389i	0.104503	−	0.0698265i
$776$	−8.07179	−	2.03241i	−0.289761	−	0.0729594i
$777$	0.986980	−	1.47712i	0.0354077	−	0.0529914i
$778$	0.715619	+	0.607661i	0.0256562	+	0.0217857i
$779$	−27.8824	+	8.45804i	−0.998991	+	0.303041i
$780$	−14.6961	−	12.9094i	−0.526205	−	0.462232i
$781$	38.0075	+	31.1919i	1.36001	+	1.11613i
$782$	19.8287	−	19.1745i	0.709074	−	0.685679i
$783$	8.25193	+	3.41806i	0.294900	+	0.122152i
$784$	7.83083	+	23.1935i	0.279672	+	0.828341i
$785$	8.74680	−	3.62304i	0.312187	−	0.129312i
$786$	25.2868	−	58.2643i	0.901951	−	2.07822i
$787$	3.76497	+	38.2263i	0.134207	+	1.36262i	0.792505	+	0.609865i	$0.208776\pi$
$787$	3.76497	+	38.2263i	0.134207	+	1.36262i	−0.658299	+	0.752757i	$0.728724\pi$
$788$	14.6390	−	25.3076i	0.521492	−	0.901546i
$789$	1.77043	−	3.31224i	0.0630289	−	0.117919i
$790$	−16.6004	+	8.51831i	−0.590617	+	0.303068i
$791$	−5.27346	+	1.04896i	−0.187503	+	0.0372966i
$792$	4.60465	+	18.4790i	0.163619	+	0.656623i
$793$	−12.1855	+	61.2607i	−0.432720	+	2.17543i
$794$	23.1392	+	12.8717i	0.821179	+	0.456798i
$795$	−2.48896	+	25.2708i	−0.0882743	+	0.896264i
$796$	10.5680	+	7.58599i	0.374571	+	0.268878i
$797$	−4.02096	+	13.2553i	−0.142430	+	0.469528i	−0.998911	−	0.0466498i	$-0.985146\pi$
$797$	−4.02096	+	13.2553i	−0.142430	+	0.469528i	0.856482	+	0.516177i	$0.172646\pi$
$798$	−7.96969	−	1.72470i	−0.282124	−	0.0610538i
$799$	−10.4881	−	10.4881i	−0.371042	−	0.371042i
$800$	−3.65090	−	4.32098i	−0.129079	−	0.152770i
$801$	2.83239	−	2.83239i	0.100077	−	0.100077i
$802$	16.9337	−	10.9084i	0.597949	−	0.385190i
$803$	23.3012	+	7.06836i	0.822283	+	0.249437i
$804$	−41.9659	−	9.82130i	−1.48002	−	0.346371i
$805$	8.77312	+	0.864077i	0.309212	+	0.0304547i
$806$	−6.20742	−	21.7711i	−0.218647	−	0.766853i
$807$	−53.6620	−	10.6740i	−1.88899	−	0.375744i
$808$	18.5787	+	39.4065i	0.653597	+	1.38632i
$809$	9.52976	+	47.9093i	0.335049	+	1.68440i	0.670154	+	0.742222i	$0.266228\pi$
$809$	9.52976	+	47.9093i	0.335049	+	1.68440i	−0.335105	+	0.942181i	$0.608772\pi$
$810$	−4.87097	+	15.1386i	−0.171148	+	0.531918i
$811$	17.2252	+	9.20704i	0.604857	+	0.323303i	0.745242	−	0.666794i	$-0.232334\pi$
$811$	17.2252	+	9.20704i	0.604857	+	0.323303i	−0.140385	+	0.990097i	$0.544834\pi$
$812$	−3.33343	−	4.35158i	−0.116980	−	0.152710i
$813$	16.9299	−	1.66745i	0.593758	−	0.0584801i
$814$	−4.99778	+	1.97261i	−0.175172	+	0.0691401i
$815$	0.00227193	+	0.00548493i	7.95823e−5	+	0.000192129i
$816$	−0.551658	−	17.7393i	−0.0193119	−	0.621001i
$817$	−0.953963	+	2.30307i	−0.0333749	+	0.0805742i
$818$	−0.547113	+	32.6182i	−0.0191294	+	1.14047i
$819$	4.27457	−	5.20858i	0.149366	−	0.182002i
$820$	6.53073	−	19.1873i	0.228063	−	0.670049i
$821$	6.25195	+	20.6099i	0.218195	+	0.719291i	0.995884	+	0.0906419i	$0.0288919\pi$
$821$	6.25195	+	20.6099i	0.218195	+	0.719291i	−0.777689	+	0.628649i	$0.783608\pi$
$822$	0.898998	+	11.0194i	0.0313562	+	0.384345i
$823$	10.3399	+	6.90893i	0.360428	+	0.240830i	0.722578	−	0.691290i	$-0.242957\pi$
$823$	10.3399	+	6.90893i	0.360428	+	0.240830i	−0.362150	+	0.932120i	$0.617957\pi$
$824$	−3.46825	−	9.73076i	−0.120822	−	0.338987i
$825$	−5.09367	−	7.62321i	−0.177339	−	0.265406i
$826$	−0.941767	+	8.15697i	−0.0327683	+	0.283817i
$827$	0.794790	−	0.652268i	0.0276376	−	0.0226816i	−0.620473	−	0.784228i	$-0.713059\pi$
$827$	0.794790	−	0.652268i	0.0276376	−	0.0226816i	0.648111	+	0.761546i	$0.275559\pi$
$828$	0.989537	−	29.4891i	0.0343888	−	1.02482i
$829$	−2.63579	−	4.93122i	−0.0915448	−	0.171268i	0.831981	−	0.554803i	$-0.187207\pi$
$829$	−2.63579	−	4.93122i	−0.0915448	−	0.171268i	−0.923526	+	0.383535i	$0.874707\pi$
$830$	4.94519	+	3.42561i	0.171650	+	0.118905i
$831$		−	8.45093i		−	0.293160i
$832$	−33.8493	+	13.9236i	−1.17351	+	0.482713i
$833$		−	12.7023i		−	0.440108i
$834$	−8.55610	+	12.3515i	−0.296274	+	0.427699i
$835$	−2.30570	−	4.31366i	−0.0797921	−	0.149281i
$836$	16.8439	+	18.0136i	0.582560	+	0.623014i
$837$	−8.26860	+	6.78587i	−0.285805	+	0.234554i
$838$	−43.1631	−	4.98342i	−1.49105	−	0.172149i
$839$	−23.5309	−	35.2165i	−0.812378	−	1.21581i	−0.973457	−	0.228868i	$-0.926498\pi$
$839$	−23.5309	−	35.2165i	−0.812378	−	1.21581i	0.161080	−	0.986941i	$-0.448502\pi$
$840$	4.20749	−	3.80405i	0.145172	−	0.131252i
$841$	17.0152	+	11.3692i	0.586732	+	0.392042i
$842$	24.0871	−	1.96510i	0.830095	−	0.0677219i
$843$	12.7258	+	41.9514i	0.438300	+	1.44488i
$844$	−11.5158	+	5.66726i	−0.396391	+	0.195075i
$845$	5.03196	−	6.13146i	0.173105	−	0.210929i
$846$	−15.8639	−	0.266090i	−0.545412	−	0.00914835i
$847$	−2.65440	+	6.40830i	−0.0912064	+	0.220192i
$848$	40.3079	+	25.1566i	1.38418	+	0.863882i
$849$	−14.6778	−	35.4354i	−0.503741	−	1.21614i
$850$	1.07764	+	2.73029i	0.0369628	+	0.0936483i
$851$	8.28449	−	0.815951i	0.283989	−	0.0279704i
$852$	−48.5906	−	6.43753i	−1.66469	−	0.220546i
$853$	20.3011	+	10.8511i	0.695095	+	0.371536i	0.780797	−	0.624785i	$-0.214813\pi$
$853$	20.3011	+	10.8511i	0.695095	+	0.371536i	−0.0857017	+	0.996321i	$0.527313\pi$
$854$	−17.2417	−	5.54762i	−0.589997	−	0.189836i
$855$	−0.880587	−	4.42701i	−0.0301154	−	0.151401i
$856$	0.706101	+	14.7423i	0.0241340	+	0.503881i
$857$	−4.09217	−	0.813982i	−0.139786	−	0.0278051i	0.124701	−	0.992194i	$-0.460203\pi$
$857$	−4.09217	−	0.813982i	−0.139786	−	0.0278051i	−0.264487	+	0.964389i	$0.585203\pi$
$858$	−57.0478	+	16.2656i	−1.94758	+	0.555299i
$859$	−30.3140	−	2.98567i	−1.03430	−	0.101870i	−0.433407	−	0.901198i	$-0.642689\pi$
$859$	−30.3140	−	2.98567i	−1.03430	−	0.101870i	−0.600894	+	0.799329i	$0.705189\pi$
$860$	−0.914493	−	1.47331i	−0.0311840	−	0.0502395i
$861$	19.4481	+	5.89952i	0.662790	+	0.201055i
$862$	6.78710	+	10.5359i	0.231169	+	0.358855i
$863$	−5.51487	+	5.51487i	−0.187728	+	0.187728i	−0.794713	−	0.606985i	$-0.792379\pi$
$863$	−5.51487	+	5.51487i	−0.187728	+	0.187728i	0.606985	+	0.794713i	$0.292379\pi$
$864$	12.4023	+	12.0522i	0.421936	+	0.410025i
$865$	8.27306	+	8.27306i	0.281292	+	0.281292i
$866$	9.81628	−	45.3601i	0.333571	−	1.54140i
$867$	7.87611	−	25.9641i	0.267487	−	0.881785i
$868$	6.47788	−	1.06406i	0.219873	−	0.0361164i
$869$	−5.54625	+	56.3120i	−0.188143	+	1.91025i
$870$	4.29378	−	7.71885i	0.145573	−	0.261694i
$871$	8.99770	−	45.2345i	0.304875	−	1.53271i
$872$	26.6745	+	36.0589i	0.903313	+	1.22111i
$873$	4.53132	−	0.901336i	0.153362	−	0.0305056i
$874$	−17.4442	−	33.9952i	−0.590059	−	1.14990i
$875$	−0.442220	+	0.827335i	−0.0149498	+	0.0279690i
$876$	−23.4520	+	6.26338i	−0.792370	+	0.211620i
$877$	0.968197	+	9.83027i	0.0326937	+	0.331945i	0.997594	+	0.0693279i	$0.0220855\pi$
$877$	0.968197	+	9.83027i	0.0326937	+	0.331945i	−0.964900	+	0.262617i	$0.915415\pi$
$878$	−7.50115	−	3.25552i	−0.253152	−	0.109868i
$879$	−43.1965	+	17.8926i	−1.45698	+	0.603501i
$880$	−17.0121	+	2.21137i	−0.573479	+	0.0745451i
$881$	−42.7064	−	17.6896i	−1.43882	−	0.595977i	−0.479305	−	0.877648i	$-0.659111\pi$
$881$	−42.7064	−	17.6896i	−1.43882	−	0.595977i	−0.959511	+	0.281671i	$0.909111\pi$
$882$	−9.44536	−	9.76763i	−0.318042	−	0.328893i
$883$	−4.15791	−	3.41231i	−0.139925	−	0.114833i	0.561827	−	0.827255i	$-0.310099\pi$
$883$	−4.15791	−	3.41231i	−0.139925	−	0.114833i	−0.701752	+	0.712421i	$0.747599\pi$
$884$	18.9522	−	1.22662i	0.637432	−	0.0412556i
$885$	−12.6613	+	3.84075i	−0.425604	+	0.129105i
$886$	−23.0119	+	27.1002i	−0.773101	+	0.910450i
$887$	−26.8599	+	40.1986i	−0.901866	+	1.34974i	0.0347551	+	0.999396i	$0.488935\pi$
$887$	−26.8599	+	40.1986i	−0.901866	+	1.34974i	−0.936622	+	0.350343i	$0.886065\pi$
$888$	3.19601	−	4.29828i	0.107251	−	0.144241i
$889$	−6.62195	+	4.42464i	−0.222093	+	0.148398i
$890$	2.24199	+	2.82727i	0.0751517	+	0.0947701i
$891$	30.5957	+	37.2809i	1.02499	+	1.24896i
$892$	21.6440	−	47.6655i	0.724695	−	1.59596i
$893$	−18.1204	+	9.68554i	−0.606375	+	0.324114i
$894$	−1.53846	−	8.47482i	−0.0514539	−	0.283440i
$895$	24.2529			0.810685
$896$	−2.88509	−	10.2138i	−0.0963840	−	0.341219i
$897$	91.9089			3.06875
$898$	−0.984718	−	5.42444i	−0.0328605	−	0.181016i
$899$	9.01546	−	4.81886i	0.300682	−	0.160718i
$900$	2.85891	+	1.29817i	0.0952969	+	0.0432725i
$901$	−15.6406	−	19.0581i	−0.521064	−	0.634918i
$902$	−38.1916	−	48.1616i	−1.27164	−	1.60360i
$903$	1.44572	−	0.966001i	0.0481107	−	0.0321465i
$904$	−16.0386	+	2.35899i	−0.533437	+	0.0784587i
$905$	−4.48597	+	6.71372i	−0.149119	+	0.223172i
$906$	33.4484	−	39.3908i	1.11125	−	1.30867i
$907$	26.9813	−	8.18468i	0.895899	−	0.271768i	0.191433	−	0.981506i	$-0.438687\pi$
$907$	26.9813	−	8.18468i	0.895899	−	0.271768i	0.704466	+	0.709738i	$0.251187\pi$
$908$	−0.440389	−	6.80436i	−0.0146148	−	0.225811i
$909$	−18.6926	−	15.3407i	−0.619996	−	0.508817i
$910$	4.21938	+	4.36334i	0.139871	+	0.144643i
$911$	48.5347	+	20.1037i	1.60803	+	0.666066i	0.992522	−	0.122068i	$-0.0389526\pi$
$911$	48.5347	+	20.1037i	1.60803	+	0.666066i	0.615504	+	0.788134i	$0.288953\pi$
$912$	−23.7370	−	6.40198i	−0.786011	−	0.211991i
$913$	16.8550	−	6.98159i	0.557821	−	0.231057i
$914$	54.4930	+	23.6501i	1.80247	+	0.782275i
$915$	−2.86062	−	29.0444i	−0.0945692	−	0.960177i
$916$	12.2960	+	46.0399i	0.406270	+	1.52120i
$917$	−9.29062	+	17.3815i	−0.306803	+	0.573989i
$918$	−4.09677	−	7.98376i	−0.135213	−	0.263503i
$919$	−12.4161	+	2.46971i	−0.409568	+	0.0814682i	−0.395574	−	0.918434i	$-0.629454\pi$
$919$	−12.4161	+	2.46971i	−0.409568	+	0.0814682i	−0.0139937	+	0.999902i	$0.504454\pi$
$920$	26.2868	+	3.93227i	0.866650	+	0.129643i
$921$	0.657841	−	3.30719i	0.0216766	−	0.108976i
$922$	23.7660	−	42.7237i	0.782690	−	1.40703i
$923$	5.14106	−	52.1980i	0.169220	−	1.71812i
$924$	−2.78820	−	16.9743i	−0.0917250	−	0.558414i
$925$	−0.257151	+	0.847712i	−0.00845506	+	0.0278726i
$926$	4.82017	−	22.2736i	0.158401	−	0.731955i
$927$	4.05446	+	4.05446i	0.133166	+	0.133166i
$928$	−9.37784	−	13.6091i	−0.307843	−	0.446739i
$929$	−22.6893	+	22.6893i	−0.744412	+	0.744412i	−0.973424	−	0.229012i	$-0.926451\pi$
$929$	−22.6893	+	22.6893i	−0.744412	+	0.744412i	0.229012	+	0.973424i	$0.426451\pi$
$930$	5.72846	+	8.89257i	0.187844	+	0.291599i
$931$	−16.8381	−	5.10777i	−0.551845	−	0.167401i
$932$	−23.5466	+	14.6155i	−0.771295	+	0.478747i
$933$	10.0037	+	0.985281i	0.327507	+	0.0322566i
$934$	37.2204	−	10.6124i	1.21789	−	0.347248i
$935$	8.73061	+	1.73663i	0.285521	+	0.0567937i
$936$	13.6615	−	15.0360i	0.446541	−	0.491468i
$937$	−5.01253	−	25.1997i	−0.163752	−	0.823238i	−0.972106	−	0.234541i	$-0.924641\pi$
$937$	−5.01253	−	25.1997i	−0.163752	−	0.823238i	0.808354	−	0.588697i	$-0.200359\pi$
$938$	12.7311	+	4.09633i	0.415686	+	0.133750i
$939$	35.3748	+	18.9082i	1.15441	+	0.617047i
$940$	1.87714	−	14.1687i	0.0612257	−	0.462132i
$941$	−13.5054	+	1.33017i	−0.440265	+	0.0433623i	−0.315722	−	0.948852i	$-0.602247\pi$
$941$	−13.5054	+	1.33017i	−0.440265	+	0.0433623i	−0.124543	+	0.992214i	$0.539747\pi$
$942$	10.5082	+	26.6234i	0.342376	+	0.867439i
$943$	36.4439	+	87.9833i	1.18678	+	2.86513i
$944$	−4.07278	+	24.4197i	−0.132558	+	0.794793i
$945$	1.09750	−	2.64961i	0.0357018	−	0.0861917i
$946$	−5.25804	−	0.0881946i	−0.170954	−	0.00286745i
$947$	34.8484	−	42.4629i	1.13242	−	1.37986i	0.217583	−	0.976042i	$-0.430183\pi$
$947$	34.8484	−	42.4629i	1.13242	−	1.37986i	0.914839	−	0.403818i	$-0.132317\pi$
$948$	−24.9074	−	50.6116i	−0.808955	−	1.64379i
$949$	−7.54025	−	24.8569i	−0.244767	−	0.806888i
$950$	4.05260	−	0.330625i	0.131484	−	0.0107269i
$951$	3.63754	+	2.43053i	0.117955	+	0.0788153i
$952$	−0.276978	+	5.50022i	−0.00897690	+	0.178263i
$953$	−22.1609	−	33.1662i	−0.717863	−	1.07436i	−0.993581	−	0.113119i	$-0.963916\pi$
$953$	−22.1609	−	33.1662i	−0.717863	−	1.07436i	0.275719	−	0.961238i	$-0.411084\pi$
$954$	−26.1986	−	3.02477i	−0.848212	−	0.0979307i
$955$	−2.91569	+	2.39285i	−0.0943496	+	0.0774307i
$956$	−4.78498	+	4.47428i	−0.154757	+	0.144708i
$957$	−12.6271	−	23.6237i	−0.408177	−	0.763645i
$958$	−1.17260	+	1.69275i	−0.0378849	+	0.0546904i
$959$		−	3.43068i		−	0.110782i
$960$	13.2465	−	10.8168i	0.427530	−	0.349112i
$961$		−	18.7577i		−	0.605086i
$962$	4.71165	+	3.26384i	0.151910	+	0.105230i
$963$	−3.86173	−	7.22479i	−0.124443	−	0.232816i
$964$	−7.15001	−	0.239926i	−0.230286	−	0.00772748i
$965$	2.04529	−	1.67853i	0.0658403	−	0.0540338i
$966$	−3.05674	+	26.4755i	−0.0983490	+	0.851835i
$967$	−1.07857	−	1.61419i	−0.0346844	−	0.0519088i	0.813722	−	0.581254i	$-0.197438\pi$
$967$	−1.07857	−	1.61419i	−0.0346844	−	0.0519088i	−0.848407	+	0.529345i	$0.822438\pi$
$968$	−8.96476	+	18.8943i	−0.288138	+	0.607287i
$969$	10.6070	+	7.08738i	0.340746	+	0.227679i
$970$	0.338415	+	4.14809i	0.0108658	+	0.133187i
$971$	−4.28892	−	14.1387i	−0.137638	−	0.453731i	0.860841	−	0.508875i	$-0.169938\pi$
$971$	−4.28892	−	14.1387i	−0.137638	−	0.453731i	−0.998478	+	0.0551435i	$0.982438\pi$
$972$	−28.1495	−	9.58117i	−0.902895	−	0.307316i
$973$	2.95782	−	3.60411i	0.0948233	−	0.115543i
$974$	−0.0904296	+	5.39129i	−0.00289755	+	0.172748i
$975$	−3.74282	+	9.03596i	−0.119866	+	0.289382i
$976$	−51.0773	−	19.3196i	−1.63494	−	0.618407i
$977$	5.22357	+	12.6108i	0.167117	+	0.403456i	0.985146	−	0.171722i	$-0.0549330\pi$
$977$	5.22357	+	12.6108i	0.167117	+	0.403456i	−0.818029	+	0.575177i	$0.804933\pi$
$978$	−0.0166950	+	0.00658948i	−0.000533847	+	0.000210708i
$979$	10.8901	−	1.07258i	0.348048	−	0.0342798i
$980$	9.71667	−	7.44324i	0.310388	−	0.237766i
$981$	−21.9559	−	11.7357i	−0.700999	−	0.374692i
$982$	10.2142	−	31.7450i	0.325948	−	1.01302i
$983$	1.23474	+	6.20744i	0.0393820	+	0.197987i	0.995468	−	0.0951008i	$-0.0303173\pi$
$983$	1.23474	+	6.20744i	0.0393820	+	0.197987i	−0.956086	+	0.293087i	$0.905317\pi$
$984$	57.6681	+	20.7139i	1.83839	+	0.660334i
$985$	−14.3374	−	2.85188i	−0.456827	−	0.0908685i
$986$	2.35144	+	8.24711i	0.0748851	+	0.262642i
$987$	14.2623	+	1.40471i	0.453973	+	0.0447124i
$988$	5.99497	−	25.6162i	0.190725	−	0.814960i
$989$	7.79680	+	2.36513i	0.247924	+	0.0752068i
$990$	8.00489	−	5.15664i	0.254412	−	0.163889i
$991$	−4.90692	+	4.90692i	−0.155874	+	0.155874i	−0.780735	−	0.624862i	$-0.785155\pi$
$991$	−4.90692	+	4.90692i	−0.155874	+	0.155874i	0.624862	+	0.780735i	$0.285155\pi$
$992$	19.6677	−	2.22182i	0.624450	−	0.0705428i
$993$	−49.2104	−	49.2104i	−1.56165	−	1.56165i
$994$	14.8653	+	3.21697i	0.471499	+	0.102036i
$995$	1.88813	−	6.22432i	0.0598577	−	0.197324i
$996$	−10.6056	+	14.7746i	−0.336052	+	0.468151i
$997$	−0.323960	+	3.28922i	−0.0102599	+	0.104171i	−0.998951	−	0.0457975i	$-0.985417\pi$
$997$	−0.323960	+	3.28922i	−0.0102599	+	0.104171i	0.988691	+	0.149968i	$0.0479171\pi$
$998$	36.1638	+	20.1169i	1.14474	+	0.636788i
$999$	0.528340	−	2.65615i	0.0167159	−	0.0840367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.4	✓	1024
128.109	even	32	inner	640.2.bm.a.621.4	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.4	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.4	yes	1024	128.109	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39147 + 0.252599i) q^{2} +(-1.88532 + 1.00772i) q^{3} +(1.87239 - 0.702968i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(2.36881 - 1.87845i) q^{6} +(-0.780006 + 0.521184i) q^{7} +(-2.42781 + 1.45112i) q^{8} +(0.872201 - 1.30534i) q^{9} +(1.07800 + 0.915375i) q^{10} +(4.10414 - 1.24498i) q^{11} +(-2.82165 + 3.21216i) q^{12} +(-3.53663 - 2.90244i) q^{13} +(0.953707 - 0.922241i) q^{14} +(1.97501 + 0.818077i) q^{15} +(3.01167 - 2.63246i) q^{16} +(-1.91756 + 0.794278i) q^{17} +(-0.883916 + 2.03666i) q^{18} +(0.281813 + 2.86130i) q^{19} +(-1.73123 - 1.00142i) q^{20} +(0.945350 - 1.76863i) q^{21} +(-5.39632 + 2.76905i) q^{22} +(9.21664 - 1.83330i) q^{23} +(3.11485 - 5.18238i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(5.65428 + 3.14531i) q^{26} +(0.299652 - 3.04241i) q^{27} +(-1.09410 + 1.52418i) q^{28} +(-0.848106 + 2.79583i) q^{29} +(-2.95482 - 0.639445i) q^{30} +(-2.47410 - 2.47410i) q^{31} +(-3.52570 + 4.42373i) q^{32} +(-6.48301 + 6.48301i) q^{33} +(2.46759 - 1.58959i) q^{34} +(0.897711 + 0.272318i) q^{35} +(0.715486 - 3.05723i) q^{36} +(0.881591 + 0.0868291i) q^{37} +(-1.11489 - 3.91023i) q^{38} +(9.59252 + 1.90807i) q^{39} +(2.66192 + 0.956137i) q^{40} +(1.97707 + 9.93941i) q^{41} +(-0.868675 + 2.69979i) q^{42} +(0.764650 + 0.408714i) q^{43} +(6.80936 - 5.21616i) q^{44} +(-1.56236 + 0.153879i) q^{45} +(-12.3616 + 4.87910i) q^{46} +(2.73475 + 6.60228i) q^{47} +(-3.02517 + 7.99794i) q^{48} +(-2.34201 + 5.65410i) q^{49} +(0.0237177 - 1.41401i) q^{50} +(2.81479 - 3.42983i) q^{51} +(-8.66227 - 2.94835i) q^{52} +(3.44815 + 11.3670i) q^{53} +(0.351553 + 4.30912i) q^{54} +(-3.56602 - 2.38274i) q^{55} +(1.13740 - 2.39722i) q^{56} +(-3.41470 - 5.11046i) q^{57} +(0.473892 - 4.10455i) q^{58} +(-4.78435 + 3.92642i) q^{59} +(4.27307 + 0.143387i) q^{60} +(-6.43562 - 12.0402i) q^{61} +(4.06759 + 2.81769i) q^{62} +1.47275i q^{63} +(3.78849 - 7.04609i) q^{64} +4.57514i q^{65} +(7.38333 - 10.6585i) q^{66} +(4.75202 + 8.89040i) q^{67} +(-3.03206 + 2.83518i) q^{68} +(-15.5288 + 12.7442i) q^{69} +(-1.31793 - 0.152162i) q^{70} +(6.36920 + 9.53218i) q^{71} +(-0.223325 + 4.43479i) q^{72} +(4.72067 + 3.15425i) q^{73} +(-1.24864 + 0.101868i) q^{74} +(-0.620552 - 2.04569i) q^{75} +(2.53906 + 5.15935i) q^{76} +(-2.55239 + 3.11010i) q^{77} +(-13.8297 - 0.231969i) q^{78} +(-5.04893 + 12.1892i) q^{79} +(-3.94550 - 0.658041i) q^{80} +(4.30332 + 10.3891i) q^{81} +(-5.26172 - 13.3310i) q^{82} +(4.23332 - 0.416945i) q^{83} +(0.526775 - 3.97610i) q^{84} +(1.83047 + 0.978407i) q^{85} +(-1.16723 - 0.375564i) q^{86} +(-1.21847 - 6.12568i) q^{87} +(-8.15744 + 8.97817i) q^{88} +(2.50244 + 0.497766i) q^{89} +(2.13511 - 0.608769i) q^{90} +(4.27130 + 0.420686i) q^{91} +(15.9684 - 9.91165i) q^{92} +(7.15767 + 2.17125i) q^{93} +(-5.47306 - 8.49609i) q^{94} +(2.03303 - 2.03303i) q^{95} +(2.18917 - 11.8931i) q^{96} +(2.08093 + 2.08093i) q^{97} +(1.83062 - 8.45911i) q^{98} +(1.95452 - 6.44317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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