LMFDB - Embedded newform 640.2.bm.a.101.32

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			101.32
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.000707051 + 1.41421i) q^{2} +(-2.41638 + 1.29158i) q^{3} +(-2.00000 - 0.00199984i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-1.82486 - 3.41819i) q^{6} +(2.17792 - 1.45524i) q^{7} +(0.00424230 - 2.82842i) q^{8} +(2.50399 - 3.74748i) q^{9} +(-1.09365 + 0.896621i) q^{10} +(4.03282 - 1.22334i) q^{11} +(4.83533 - 2.57833i) q^{12} +(3.04226 + 2.49672i) q^{13} +(2.05648 + 3.08107i) q^{14} +(-2.53134 - 1.04851i) q^{15} +(3.99999 + 0.00799936i) q^{16} +(3.62737 - 1.50251i) q^{17} +(5.29796 + 3.54382i) q^{18} +(-0.0641155 - 0.650975i) q^{19} +(-1.26724 - 1.54729i) q^{20} +(-3.38311 + 6.32935i) q^{21} +(1.72722 + 5.70414i) q^{22} +(-3.39079 + 0.674470i) q^{23} +(3.64289 + 6.84002i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-3.53305 + 4.30065i) q^{26} +(-0.404730 + 4.10930i) q^{27} +(-4.35874 + 2.90612i) q^{28} +(1.32265 - 4.36020i) q^{29} +(1.48461 - 3.57911i) q^{30} +(-7.40867 - 7.40867i) q^{31} +(-0.0141410 + 5.65684i) q^{32} +(-8.16478 + 8.16478i) q^{33} +(2.12230 + 5.13094i) q^{34} +(2.50657 + 0.760359i) q^{35} +(-5.01546 + 7.48995i) q^{36} +(10.4359 + 1.02785i) q^{37} +(0.920663 - 0.0902127i) q^{38} +(-10.5760 - 2.10369i) q^{39} +(2.18909 - 1.79105i) q^{40} +(-0.852401 - 4.28531i) q^{41} +(-8.94866 - 4.78891i) q^{42} +(2.70791 + 1.44741i) q^{43} +(-8.06809 + 2.43862i) q^{44} +(4.48535 - 0.441769i) q^{45} +(-0.951446 - 4.79577i) q^{46} +(0.521679 + 1.25945i) q^{47} +(-9.67582 + 5.14698i) q^{48} +(-0.0531821 + 0.128393i) q^{49} +(-1.38690 - 0.276593i) q^{50} +(-6.82449 + 8.31567i) q^{51} +(-6.07953 - 4.99953i) q^{52} +(3.96919 + 13.0847i) q^{53} +(-5.81114 - 0.575281i) q^{54} +(3.50405 + 2.34133i) q^{55} +(-4.10679 - 6.16624i) q^{56} +(0.995714 + 1.49019i) q^{57} +(6.16532 + 1.87360i) q^{58} +(-2.82633 + 2.31951i) q^{59} +(5.06058 + 2.10209i) q^{60} +(-0.949007 - 1.77547i) q^{61} +(10.4827 - 10.4722i) q^{62} -11.8056i q^{63} +(-7.99996 - 0.0239981i) q^{64} +3.93561i q^{65} +(-11.5410 - 11.5525i) q^{66} +(1.42355 + 2.66328i) q^{67} +(-7.25775 + 2.99776i) q^{68} +(7.32229 - 6.00925i) q^{69} +(-1.07708 + 3.54428i) q^{70} +(5.87229 + 8.78850i) q^{71} +(-10.5888 - 7.09823i) q^{72} +(10.9573 + 7.32143i) q^{73} +(-1.46098 + 14.7579i) q^{74} +(-0.795351 - 2.62192i) q^{75} +(0.126929 + 1.30208i) q^{76} +(7.00290 - 8.53305i) q^{77} +(2.98255 - 14.9552i) q^{78} +(3.75048 - 9.05447i) q^{79} +(2.53138 + 3.09711i) q^{80} +(0.844821 + 2.03958i) q^{81} +(6.06094 - 1.20245i) q^{82} +(-14.9411 + 1.47157i) q^{83} +(6.77887 - 12.6519i) q^{84} +(3.46264 + 1.85082i) q^{85} +(-2.04886 + 3.82853i) q^{86} +(2.43552 + 12.2442i) q^{87} +(-3.44303 - 11.4117i) q^{88} +(3.59376 + 0.714842i) q^{89} +(0.621584 + 6.34356i) q^{90} +(10.2591 + 1.01043i) q^{91} +(6.78292 - 1.34216i) q^{92} +(27.4710 + 8.33325i) q^{93} +(-1.78149 + 0.736875i) q^{94} +(0.462536 - 0.462536i) q^{95} +(-7.27209 - 13.6873i) q^{96} +(-6.55229 - 6.55229i) q^{97} +(-0.181538 - 0.0753017i) q^{98} +(5.51368 - 18.1762i) 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 $

$2$	−0.000707051		1.41421i	−0.000499960		1.00000i
$2$	−0.000707051		1.41421i	−0.000499960		1.00000i
$3$	−2.41638	+	1.29158i	−1.39510	+	0.745694i	−0.985992	−	0.166794i	$-0.946659\pi$
$3$	−2.41638	+	1.29158i	−1.39510	+	0.745694i	−0.409104	+	0.912488i	$0.634159\pi$
$4$	−2.00000	−	0.00199984i	−1.00000	−	0.000999921i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	−1.82486	−	3.41819i	−0.744997	−	1.39547i
$7$	2.17792	−	1.45524i	0.823175	−	0.550028i	−0.0711400	−	0.997466i	$-0.522664\pi$
$7$	2.17792	−	1.45524i	0.823175	−	0.550028i	0.894315	+	0.447439i	$0.147664\pi$
$8$	0.00424230	−	2.82842i	0.00149988	−	0.999999i
$9$	2.50399	−	3.74748i	0.834662	−	1.24916i
$10$	−1.09365	+	0.896621i	−0.345843	+	0.283536i
$11$	4.03282	−	1.22334i	1.21594	−	0.368852i	0.383801	−	0.923416i	$-0.374615\pi$
$11$	4.03282	−	1.22334i	1.21594	−	0.368852i	0.832141	+	0.554564i	$0.187115\pi$
$12$	4.83533	−	2.57833i	1.39584	−	0.744299i
$13$	3.04226	+	2.49672i	0.843772	+	0.692466i	0.953466	−	0.301499i	$-0.0974871\pi$
$13$	3.04226	+	2.49672i	0.843772	+	0.692466i	−0.109694	+	0.993965i	$0.534987\pi$
$14$	2.05648	+	3.08107i	0.549616	+	0.823450i
$15$	−2.53134	−	1.04851i	−0.653589	−	0.270725i
$16$	3.99999	+	0.00799936i	0.999998	+	0.00199984i
$17$	3.62737	−	1.50251i	0.879767	−	0.364412i	0.103361	−	0.994644i	$-0.467040\pi$
$17$	3.62737	−	1.50251i	0.879767	−	0.364412i	0.776407	+	0.630232i	$0.217040\pi$
$18$	5.29796	+	3.54382i	1.24874	+	0.835286i
$19$	−0.0641155	−	0.650975i	−0.0147091	−	0.149344i	0.985025	−	0.172413i	$-0.0551563\pi$
$19$	−0.0641155	−	0.650975i	−0.0147091	−	0.149344i	−0.999734	+	0.0230689i	$0.992656\pi$
$20$	−1.26724	−	1.54729i	−0.283363	−	0.345984i
$21$	−3.38311	+	6.32935i	−0.738255	+	1.38118i
$22$	1.72722	+	5.70414i	0.368244	+	1.21613i
$23$	−3.39079	+	0.674470i	−0.707028	+	0.140637i	−0.535491	−	0.844541i	$-0.679873\pi$
$23$	−3.39079	+	0.674470i	−0.707028	+	0.140637i	−0.171537	+	0.985178i	$0.554873\pi$
$24$	3.64289	+	6.84002i	0.743601	+	1.39621i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	−3.53305	+	4.30065i	−0.692888	+	0.843426i
$27$	−0.404730	+	4.10930i	−0.0778904	+	0.790834i
$28$	−4.35874	+	2.90612i	−0.823724	+	0.549204i
$29$	1.32265	−	4.36020i	0.245611	−	0.809669i	−0.744284	−	0.667863i	$-0.767209\pi$
$29$	1.32265	−	4.36020i	0.245611	−	0.809669i	0.989894	−	0.141806i	$-0.0452909\pi$
$30$	1.48461	−	3.57911i	0.271052	−	0.653453i
$31$	−7.40867	−	7.40867i	−1.33064	−	1.33064i	−0.904800	−	0.425837i	$-0.859980\pi$
$31$	−7.40867	−	7.40867i	−1.33064	−	1.33064i	−0.425837	−	0.904800i	$-0.640020\pi$
$32$	−0.0141410	+	5.65684i	−0.00249980	+	0.999997i
$33$	−8.16478	+	8.16478i	−1.42131	+	1.42131i
$34$	2.12230	+	5.13094i	0.363972	+	0.879950i
$35$	2.50657	+	0.760359i	0.423687	+	0.128524i
$36$	−5.01546	+	7.48995i	−0.835910	+	1.24832i
$37$	10.4359	+	1.02785i	1.71566	+	0.168977i	0.907517	−	0.420015i	$-0.137975\pi$
$37$	10.4359	+	1.02785i	1.71566	+	0.168977i	0.808138	+	0.588993i	$0.200475\pi$
$38$	0.920663	−	0.0902127i	0.149351	−	0.0146344i
$39$	−10.5760	−	2.10369i	−1.69351	−	0.336860i
$40$	2.18909	−	1.79105i	0.346126	−	0.283190i
$41$	−0.852401	−	4.28531i	−0.133123	−	0.669253i	−0.988497	−	0.151242i	$-0.951673\pi$
$41$	−0.852401	−	4.28531i	−0.133123	−	0.669253i	0.855374	−	0.518011i	$-0.173327\pi$
$42$	−8.94866	−	4.78891i	−1.38081	−	0.738945i
$43$	2.70791	+	1.44741i	0.412952	+	0.220727i	0.664771	−	0.747047i	$-0.268529\pi$
$43$	2.70791	+	1.44741i	0.412952	+	0.220727i	−0.251820	+	0.967774i	$0.581029\pi$
$44$	−8.06809	+	2.43862i	−1.21631	+	0.367636i
$45$	4.48535	−	0.441769i	0.668637	−	0.0658550i
$46$	−0.951446	−	4.79577i	−0.140283	−	0.707098i
$47$	0.521679	+	1.25945i	0.0760947	+	0.183709i	0.957349	−	0.288933i	$-0.0933004\pi$
$47$	0.521679	+	1.25945i	0.0760947	+	0.183709i	−0.881255	+	0.472642i	$0.843300\pi$
$48$	−9.67582	+	5.14698i	−1.39658	+	0.742903i
$49$	−0.0531821	+	0.128393i	−0.00759745	+	0.0183419i
$50$	−1.38690	−	0.276593i	−0.196138	−	0.0391161i
$51$	−6.82449	+	8.31567i	−0.955620	+	1.16443i
$52$	−6.07953	−	4.99953i	−0.843080	−	0.693310i
$53$	3.96919	+	13.0847i	0.545211	+	1.79732i	0.601462	+	0.798902i	$0.294585\pi$
$53$	3.96919	+	13.0847i	0.545211	+	1.79732i	−0.0562513	+	0.998417i	$0.517915\pi$
$54$	−5.81114	−	0.575281i	−0.790795	−	0.0782858i
$55$	3.50405	+	2.34133i	0.472487	+	0.315705i
$56$	−4.10679	−	6.16624i	−0.548792	−	0.823999i
$57$	0.995714	+	1.49019i	0.131886	+	0.197381i
$58$	6.16532	+	1.87360i	0.809547	+	0.246015i
$59$	−2.82633	+	2.31951i	−0.367957	+	0.301975i	−0.800142	−	0.599810i	$-0.795243\pi$
$59$	−2.82633	+	2.31951i	−0.367957	+	0.301975i	0.432185	+	0.901785i	$0.357743\pi$
$60$	5.06058	+	2.10209i	0.653318	+	0.271379i
$61$	−0.949007	−	1.77547i	−0.121508	−	0.227325i	0.813812	−	0.581128i	$-0.197388\pi$
$61$	−0.949007	−	1.77547i	−0.121508	−	0.227325i	−0.935320	+	0.353803i	$0.884888\pi$
$62$	10.4827	−	10.4722i	1.33130	−	1.32997i
$63$		−	11.8056i		−	1.48736i
$64$	−7.99996	−	0.0239981i	−0.999996	−	0.00299976i
$65$			3.93561i			0.488152i
$66$	−11.5410	−	11.5525i	−1.42059	−	1.42202i
$67$	1.42355	+	2.66328i	0.173915	+	0.325371i	0.953744	−	0.300621i	$-0.0971940\pi$
$67$	1.42355	+	2.66328i	0.173915	+	0.325371i	−0.779829	+	0.625993i	$0.784694\pi$
$68$	−7.25775	+	2.99776i	−0.880131	+	0.363532i
$69$	7.32229	−	6.00925i	0.881500	−	0.723428i
$70$	−1.07708	+	3.54428i	−0.128736	+	0.423623i
$71$	5.87229	+	8.78850i	0.696912	+	1.04300i	0.996050	+	0.0887931i	$0.0283010\pi$
$71$	5.87229	+	8.78850i	0.696912	+	1.04300i	−0.299138	+	0.954210i	$0.596699\pi$
$72$	−10.5888	−	7.09823i	−1.24791	−	0.836534i
$73$	10.9573	+	7.32143i	1.28245	+	0.856908i	0.994901	−	0.100857i	$-0.0321584\pi$
$73$	10.9573	+	7.32143i	1.28245	+	0.856908i	0.287552	+	0.957765i	$0.407158\pi$
$74$	−1.46098	+	14.7579i	−0.169835	+	1.71557i
$75$	−0.795351	−	2.62192i	−0.0918392	−	0.302753i
$76$	0.126929	+	1.30208i	0.0145598	+	0.149359i
$77$	7.00290	−	8.53305i	0.798054	−	0.972432i
$78$	2.98255	−	14.9552i	0.337707	−	1.69334i
$79$	3.75048	−	9.05447i	0.421962	−	1.01871i	−0.559806	−	0.828624i	$-0.689124\pi$
$79$	3.75048	−	9.05447i	0.421962	−	1.01871i	0.981768	−	0.190083i	$-0.0608758\pi$
$80$	2.53138	+	3.09711i	0.283017	+	0.346267i
$81$	0.844821	+	2.03958i	0.0938690	+	0.226620i
$82$	6.06094	−	1.20245i	0.669319	−	0.132788i
$83$	−14.9411	+	1.47157i	−1.64000	+	0.161526i	−0.875541	−	0.483144i	$-0.839495\pi$
$83$	−14.9411	+	1.47157i	−1.64000	+	0.161526i	−0.764461	+	0.644670i	$0.776995\pi$
$84$	6.77887	−	12.6519i	0.739636	−	1.38044i
$85$	3.46264	+	1.85082i	0.375576	+	0.200749i
$86$	−2.04886	+	3.82853i	−0.220934	+	0.412841i
$87$	2.43552	+	12.2442i	0.261116	+	1.31272i
$88$	−3.44303	−	11.4117i	−0.367028	−	1.21649i
$89$	3.59376	+	0.714842i	0.380937	+	0.0757731i	0.381845	−	0.924226i	$-0.375289\pi$
$89$	3.59376	+	0.714842i	0.380937	+	0.0757731i	−0.000907505		1.00000i	$0.500289\pi$
$90$	0.621584	+	6.34356i	0.0655207	+	0.668670i
$91$	10.2591	+	1.01043i	1.07545	+	0.105922i
$92$	6.78292	−	1.34216i	0.707168	−	0.139930i
$93$	27.4710	+	8.33325i	2.84861	+	0.864117i
$94$	−1.78149	+	0.736875i	−0.183747	+	0.0760029i
$95$	0.462536	−	0.462536i	0.0474552	−	0.0474552i
$96$	−7.27209	−	13.6873i	−0.742204	−	1.39696i
$97$	−6.55229	−	6.55229i	−0.665285	−	0.665285i	0.291336	−	0.956621i	$-0.405900\pi$
$97$	−6.55229	−	6.55229i	−0.665285	−	0.665285i	−0.956621	+	0.291336i	$0.905900\pi$
$98$	−0.181538	−	0.0753017i	−0.0183381	−	0.00760662i
$99$	5.51368	−	18.1762i	0.554146	−	1.82677i
$100$	0.392142	−	1.96118i	0.0392142	−	0.196118i
$101$	−0.601967	+	6.11187i	−0.0598979	+	0.608154i	0.917643	+	0.397407i	$0.130090\pi$
$101$	−0.601967	+	6.11187i	−0.0598979	+	0.608154i	−0.977541	+	0.210747i	$0.932410\pi$
$102$	−11.7553	−	9.65717i	−1.16395	−	0.956202i
$103$	1.97689	−	9.93847i	0.194788	−	0.979267i	−0.752429	−	0.658674i	$-0.771118\pi$
$103$	1.97689	−	9.93847i	0.194788	−	0.979267i	0.947217	−	0.320593i	$-0.103882\pi$
$104$	7.07470	−	8.59422i	0.693731	−	0.842733i
$105$	−7.03888	+	1.40012i	−0.686924	+	0.136638i
$106$	−18.5073	+	5.60403i	−1.79759	+	0.544312i
$107$	−1.96799	+	3.68185i	−0.190253	+	0.355938i	−0.958904	−	0.283730i	$-0.908428\pi$
$107$	−1.96799	+	3.68185i	−0.190253	+	0.355938i	0.768651	+	0.639668i	$0.220928\pi$
$108$	0.817678	−	8.21778i	0.0786811	−	0.790756i
$109$	−0.910503	−	9.24449i	−0.0872103	−	0.885461i	−0.934886	−	0.354947i	$-0.884499\pi$
$109$	−0.910503	−	9.24449i	−0.0872103	−	0.885461i	0.847676	−	0.530514i	$-0.178001\pi$
$110$	−3.31362	+	4.95383i	−0.315942	+	0.472329i
$111$	−26.5447	+	10.9952i	−2.51951	+	1.04361i
$112$	8.72328	−	5.80351i	0.824273	−	0.548380i
$113$	−16.3620	−	6.77735i	−1.53921	−	0.637560i	−0.557881	−	0.829921i	$-0.688386\pi$
$113$	−16.3620	−	6.77735i	−1.53921	−	0.637560i	−0.981324	+	0.192361i	$0.938386\pi$
$114$	−2.10815	+	1.40710i	−0.197447	+	0.131787i
$115$	−2.67246	−	2.19324i	−0.249209	−	0.204520i
$116$	−2.65402	+	8.71776i	−0.246420	+	0.809423i
$117$	16.9742	−	5.14907i	1.56927	−	0.476031i
$118$	−3.27829	−	3.99868i	−0.301791	−	0.368108i
$119$	5.71361	−	8.55102i	0.523766	−	0.783871i
$120$	−2.97638	+	7.15525i	−0.271705	+	0.653182i
$121$	5.62094	−	3.75579i	0.510995	−	0.341436i
$122$	2.51156	−	1.34084i	0.227386	−	0.121394i
$123$	7.59454	+	9.25397i	0.684776	+	0.834403i
$124$	14.8025	+	14.8322i	1.32931	+	1.33197i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	16.6956	+	0.00834715i	1.48736	+	0.000743623i
$127$	5.98132			0.530756			0.265378	−	0.964144i	$-0.414503\pi$
$127$	5.98132			0.530756			0.265378	+	0.964144i	$0.414503\pi$
$128$	0.0395948	−	11.3136i	0.00349972	−	0.999994i
$129$	−8.41276			−0.740702
$130$	−5.56579	−	0.00278267i	−0.488152	−	0.000244057i
$131$	16.9473	−	9.05854i	1.48069	−	0.791448i	0.484189	−	0.874964i	$-0.339115\pi$
$131$	16.9473	−	9.05854i	1.48069	−	0.791448i	0.996506	+	0.0835157i	$0.0266149\pi$
$132$	16.3459	−	16.3132i	1.42273	−	1.41988i
$133$	−1.08696	−	1.32447i	−0.0942515	−	0.114846i
$134$	−3.76745	+	2.01132i	−0.325458	+	0.173752i
$135$	−3.43329	+	2.29405i	−0.295490	+	0.197440i
$136$	−4.23434	−	10.2661i	−0.363092	−	0.880313i
$137$	4.34744	−	6.50641i	0.371427	−	0.555880i	−0.597926	−	0.801551i	$-0.704008\pi$
$137$	4.34744	−	6.50641i	0.371427	−	0.555880i	0.969353	+	0.245671i	$0.0790084\pi$
$138$	8.49318	+	10.3595i	0.722987	+	0.881861i
$139$	7.61832	−	2.31099i	0.646177	−	0.196016i	0.0498495	−	0.998757i	$-0.484126\pi$
$139$	7.61832	−	2.31099i	0.646177	−	0.196016i	0.596328	+	0.802741i	$0.296626\pi$
$140$	−5.01161	−	1.52573i	−0.423559	−	0.128948i
$141$	−2.88725	−	2.36950i	−0.243150	−	0.199548i
$142$	−12.4330	+	8.29845i	−1.04335	+	0.696391i
$143$	15.3233	+	6.34711i	1.28140	+	0.530772i
$144$	10.0459	−	14.9699i	0.837158	−	1.24749i
$145$	4.20957	−	1.74366i	0.349585	−	0.144803i
$146$	−10.3618	+	15.4908i	−0.857549	+	1.28202i
$147$	−0.0373218	−	0.378935i	−0.00307825	−	0.0312540i
$148$	−20.8698	−	2.07657i	−1.71549	−	0.170693i
$149$	−9.72828	+	18.2003i	−0.796971	+	1.49103i	0.0726762	+	0.997356i	$0.476846\pi$
$149$	−9.72828	+	18.2003i	−0.796971	+	1.49103i	−0.869648	+	0.493673i	$0.835654\pi$
$150$	3.70852	−	1.12294i	0.302799	−	0.0916879i
$151$	−9.86861	+	1.96299i	−0.803096	+	0.159746i	−0.579538	−	0.814945i	$-0.696767\pi$
$151$	−9.86861	+	1.96299i	−0.803096	+	0.159746i	−0.223558	+	0.974691i	$0.571767\pi$
$152$	−1.84151	+	0.178584i	−0.149366	+	0.0144851i
$153$	3.45228	−	17.3558i	0.279100	−	1.40313i
$154$	12.0626	+	9.90962i	0.972033	+	0.798540i
$155$	1.02697	−	10.4270i	0.0824881	−	0.837516i
$156$	21.1477	+	4.22853i	1.69317	+	0.338554i
$157$	−1.94011	+	6.39569i	−0.154838	+	0.510432i	−0.999698	−	0.0245545i	$-0.992183\pi$
$157$	−1.94011	+	6.39569i	−0.154838	+	0.510432i	0.844861	+	0.534986i	$0.179683\pi$
$158$	12.8023	+	5.31039i	1.01850	+	0.422472i
$159$	−26.4910	−	26.4910i	−2.10087	−	2.10087i
$160$	−4.38176	+	3.57773i	−0.346409	+	0.282844i
$161$	−6.40334	+	6.40334i	−0.504654	+	0.504654i
$162$	−2.88500	+	1.19331i	−0.226667	+	0.0937557i
$163$	13.9874	+	4.24302i	1.09557	+	0.332339i	0.785806	−	0.618473i	$-0.212248\pi$
$163$	13.9874	+	4.24302i	1.09557	+	0.332339i	0.309769	+	0.950812i	$0.399748\pi$
$164$	1.69623	+	8.57231i	0.132453	+	0.669385i
$165$	−11.4911	−	1.13178i	−0.894584	−	0.0881088i
$166$	−2.07055	−	21.1310i	−0.160706	−	1.64008i
$167$	−0.545292	−	0.108465i	−0.0421960	−	0.00839331i	0.173947	−	0.984755i	$-0.444348\pi$
$167$	−0.545292	−	0.108465i	−0.0421960	−	0.00839331i	−0.216143	+	0.976362i	$0.569348\pi$
$168$	17.8877	+	9.59572i	1.38007	+	0.740326i
$169$	0.485579	+	2.44117i	0.0373523	+	0.187782i
$170$	−2.61990	+	4.89560i	−0.200937	+	0.375475i
$171$	−2.60006	−	1.38976i	−0.198832	−	0.106278i
$172$	−5.41292	−	2.90023i	−0.412731	−	0.221140i
$173$	−11.2934	+	1.11230i	−0.858620	+	0.0845667i	−0.517738	−	0.855539i	$-0.673226\pi$
$173$	−11.2934	+	1.11230i	−0.858620	+	0.0845667i	−0.340882	+	0.940106i	$0.610726\pi$
$174$	−17.3176	+	3.43569i	−1.31285	+	0.260459i
$175$	1.00238	+	2.41997i	0.0757731	+	0.182933i
$176$	16.1411	−	4.86111i	1.21668	−	0.366420i
$177$	3.83365	−	9.25525i	0.288155	−	0.695668i
$178$	−1.01348	+	5.08183i	−0.0759636	+	0.380899i
$179$	−6.91010	+	8.41998i	−0.516485	+	0.629339i	−0.964308	−	0.264783i	$-0.914700\pi$
$179$	−6.91010	+	8.41998i	−0.516485	+	0.629339i	0.447823	+	0.894122i	$0.352200\pi$
$180$	−8.97158	+	0.874567i	−0.668702	+	0.0651864i
$181$	−6.71957	−	22.1515i	−0.499462	−	1.64650i	−0.737573	−	0.675267i	$-0.764028\pi$
$181$	−6.71957	−	22.1515i	−0.499462	−	1.64650i	0.238111	−	0.971238i	$-0.423472\pi$
$182$	−1.43622	+	14.5079i	−0.106460	+	1.07539i
$183$	4.58632	+	3.06448i	0.339030	+	0.226533i
$184$	1.89330	+	9.59345i	0.139576	+	0.707238i
$185$	5.82594	+	8.71914i	0.428332	+	0.641044i
$186$	−11.8044	+	38.8440i	−0.865541	+	2.84818i
$187$	12.7905	−	10.4969i	0.935333	−	0.767608i
$188$	−1.04084	−	2.51993i	−0.0759110	−	0.183785i
$189$	5.09853	+	9.53868i	0.370863	+	0.693837i
$190$	0.653798	+	0.654452i	0.0474315	+	0.0474789i
$191$			20.4911i			1.48269i	0.671126	+	0.741343i	$0.265811\pi$
$191$			20.4911i			1.48269i	−0.671126	+	0.741343i	$0.734189\pi$
$192$	19.3619	−	10.2746i	1.39733	−	0.741506i
$193$		−	3.05381i		−	0.219818i	−0.993942	−	0.109909i	$-0.964944\pi$
$193$		−	3.05381i		−	0.219818i	0.993942	−	0.109909i	$-0.0350560\pi$
$194$	9.27097	−	9.26171i	0.665617	−	0.664952i
$195$	−5.08315	−	9.50991i	−0.364012	−	0.681019i
$196$	0.106621	−	0.256680i	0.00761578	−	0.0183343i
$197$	−1.48213	+	1.21635i	−0.105597	+	0.0866613i	−0.685710	−	0.727875i	$-0.740508\pi$
$197$	−1.48213	+	1.21635i	−0.105597	+	0.0866613i	0.580113	+	0.814536i	$0.303008\pi$
$198$	25.7011	+	7.81037i	1.82650	+	0.555059i
$199$	11.9270	+	17.8501i	0.845485	+	1.26536i	0.962242	+	0.272197i	$0.0877502\pi$
$199$	11.9270	+	17.8501i	0.845485	+	1.26536i	−0.116757	+	0.993161i	$0.537250\pi$
$200$	2.77325	+	0.555959i	0.196098	+	0.0393122i
$201$	−6.87968	−	4.59685i	−0.485255	−	0.324237i
$202$	−8.64306	−	0.855631i	−0.608124	−	0.0602020i
$203$	−3.46450	−	11.4209i	−0.243160	−	0.801592i
$204$	13.6656	−	16.6177i	0.956784	−	1.16347i
$205$	2.77183	−	3.37748i	0.193593	−	0.235894i
$206$	14.0537	+	2.80276i	0.979169	+	0.195278i
$207$	−5.96292	+	14.3958i	−0.414452	+	1.00057i
$208$	12.1491	+	10.0112i	0.842386	+	0.694152i
$209$	−1.05493	−	2.54683i	−0.0729712	−	0.176168i
$210$	−1.97509	−	9.95546i	−0.136294	−	0.686992i
$211$	−6.49205	+	0.639412i	−0.446931	+	0.0440189i	−0.318980	−	0.947762i	$-0.603340\pi$
$211$	−6.49205	+	0.639412i	−0.446931	+	0.0440189i	−0.127952	+	0.991780i	$0.540840\pi$
$212$	−7.91221	−	26.1773i	−0.543413	−	1.79786i
$213$	−25.5407	−	13.6518i	−1.75002	−	0.935406i
$214$	−5.20553	−	2.78576i	−0.355843	−	0.190431i
$215$	0.599018	+	3.01146i	0.0408527	+	0.205380i
$216$	11.6211	+	1.16218i	0.790717	+	0.0790765i
$217$	−26.9168	−	5.35409i	−1.82723	−	0.363459i
$218$	13.0743	−	1.28111i	0.885505	−	0.0867676i
$219$	−35.9331	−	3.53911i	−2.42814	−	0.239151i
$220$	−7.00342	−	4.68967i	−0.472171	−	0.316178i
$221$	14.7868	+	4.48552i	0.994666	+	0.301729i
$222$	−15.5307	−	37.5476i	−1.04235	−	2.52003i
$223$	1.35894	−	1.35894i	0.0910012	−	0.0910012i	−0.660141	−	0.751142i	$-0.729503\pi$
$223$	1.35894	−	1.35894i	0.0910012	−	0.0910012i	0.751142	+	0.660141i	$0.229503\pi$
$224$	8.20124	+	12.3407i	0.547968	+	0.824547i
$225$	3.18697	+	3.18697i	0.212465	+	0.212465i
$226$	9.59619	−	23.1345i	0.638329	−	1.53889i
$227$	−6.65198	+	21.9287i	−0.441508	+	1.45546i	0.400653	+	0.916230i	$0.368783\pi$
$227$	−6.65198	+	21.9287i	−0.441508	+	1.45546i	−0.842161	+	0.539226i	$0.818717\pi$
$228$	−1.98845	−	2.98237i	−0.131688	−	0.197512i
$229$	0.211392	−	2.14630i	0.0139692	−	0.141832i	−0.985670	−	0.168684i	$-0.946048\pi$
$229$	0.211392	−	2.14630i	0.0139692	−	0.141832i	0.999639	+	0.0268522i	$0.00854835\pi$
$230$	3.10359	−	3.77788i	0.204645	−	0.249106i
$231$	−5.90051	+	29.6639i	−0.388225	+	1.95174i
$232$	−12.3269	−	3.75952i	−0.809300	−	0.246825i
$233$	15.8408	−	3.15093i	1.03777	−	0.206425i	0.353331	−	0.935498i	$-0.385049\pi$
$233$	15.8408	−	3.15093i	1.03777	−	0.206425i	0.684435	+	0.729074i	$0.260049\pi$
$234$	7.26988	+	24.0088i	0.475247	+	1.56950i
$235$	−0.642615	+	1.20225i	−0.0419195	+	0.0784260i
$236$	5.65731	−	4.63337i	0.368259	−	0.301607i
$237$	2.63199	+	26.7230i	0.170966	+	1.73585i
$238$	12.0889	+	8.08631i	0.783609	+	0.524158i
$239$	17.1956	−	7.12267i	1.11229	−	0.460727i	0.250567	−	0.968099i	$-0.419383\pi$
$239$	17.1956	−	7.12267i	1.11229	−	0.460727i	0.861727	+	0.507372i	$0.169383\pi$
$240$	−10.1169	−	4.21430i	−0.653046	−	0.272032i
$241$	−6.39766	−	2.65000i	−0.412109	−	0.170701i	0.166989	−	0.985959i	$-0.446595\pi$
$241$	−6.39766	−	2.65000i	−0.412109	−	0.170701i	−0.579099	+	0.815257i	$0.696595\pi$
$242$	5.30752	+	7.95186i	0.341180	+	0.511165i
$243$	−14.2514	−	11.6958i	−0.914226	−	0.750286i
$244$	1.89446	+	3.55283i	0.121281	+	0.227447i
$245$	−0.132988	+	0.0403413i	−0.00849626	+	0.00257731i
$246$	−13.0925	+	10.7338i	−0.834745	+	0.684359i
$247$	1.43025	−	2.14052i	0.0910045	−	0.136198i
$248$	−20.9863	+	20.9234i	−1.33263	+	1.32864i
$249$	34.2027	−	22.8535i	2.16751	−	1.44828i
$250$	−0.666032	−	1.24756i	−0.0421236	−	0.0789025i
$251$	−3.59858	−	4.38488i	−0.227140	−	0.276771i	0.646953	−	0.762530i	$-0.276043\pi$
$251$	−3.59858	−	4.38488i	−0.227140	−	0.276771i	−0.874093	+	0.485759i	$0.838543\pi$
$252$	−0.0236093	+	23.6112i	−0.00148725	+	1.48736i
$253$	−12.8493	+	6.86812i	−0.807831	+	0.431795i
$254$	−0.00422910	+	8.45886i	−0.000265357	+	0.530756i
$255$	−10.7575			−0.673661
$256$	15.9999	+	0.0639948i	0.999992	+	0.00399967i
$257$	−17.6384			−1.10025			−0.550125	−	0.835082i	$-0.685420\pi$
$257$	−17.6384			−1.10025			−0.550125	+	0.835082i	$0.685420\pi$
$258$	0.00594825	−	11.8974i	0.000370322	−	0.740702i
$259$	24.2243	−	12.9482i	1.50523	−	0.804560i
$260$	0.00787059	−	7.87121i	0.000488113	−	0.488152i
$261$	−13.0279	−	15.8745i	−0.806405	−	0.982607i
$262$	12.7987	+	23.9735i	0.790708	+	1.48109i
$263$	−2.58736	+	1.72882i	−0.159544	+	0.106604i	−0.632779	−	0.774332i	$-0.718086\pi$
$263$	−2.58736	+	1.72882i	−0.159544	+	0.106604i	0.473236	+	0.880936i	$0.343086\pi$
$264$	23.0588	+	23.1281i	1.41917	+	1.42344i
$265$	−7.59656	+	11.3691i	−0.466653	+	0.698396i
$266$	1.87385	−	1.53626i	0.114893	−	0.0941940i
$267$	−9.60714	+	2.91429i	−0.587948	+	0.178352i
$268$	−2.84178	−	5.32940i	−0.173589	−	0.325545i
$269$	−7.92307	−	6.50230i	−0.483078	−	0.396452i	0.361090	−	0.932531i	$-0.382405\pi$
$269$	−7.92307	−	6.50230i	−0.483078	−	0.396452i	−0.844168	+	0.536079i	$0.819905\pi$
$270$	−3.24185	−	4.85702i	−0.197293	−	0.295589i
$271$	2.70882	+	1.12203i	0.164549	+	0.0681584i	0.463437	−	0.886130i	$-0.346616\pi$
$271$	2.70882	+	1.12203i	0.164549	+	0.0681584i	−0.298889	+	0.954288i	$0.596616\pi$
$272$	14.5215	−	5.98100i	0.880494	−	0.362651i
$273$	−26.0949	+	10.8089i	−1.57934	+	0.654183i
$274$	9.19838	+	6.15281i	0.555694	+	0.371705i
$275$	0.413073	+	4.19400i	0.0249092	+	0.252908i
$276$	−14.6566	+	12.0038i	−0.882223	+	0.722546i
$277$	−1.79306	+	3.35458i	−0.107735	+	0.201557i	−0.930012	−	0.367530i	$-0.880203\pi$
$277$	−1.79306	+	3.35458i	−0.107735	+	0.201557i	0.822277	+	0.569088i	$0.192703\pi$
$278$	3.26285	+	10.7756i	0.195693	+	0.646275i
$279$	−46.3150	+	9.21263i	−2.77281	+	0.551546i
$280$	2.16125	−	7.08641i	0.129159	−	0.423494i
$281$	5.87659	−	29.5436i	0.350568	−	1.76242i	−0.255304	−	0.966861i	$-0.582175\pi$
$281$	5.87659	−	29.5436i	0.350568	−	1.76242i	0.605871	−	0.795563i	$-0.292825\pi$
$282$	3.35302	−	4.08151i	0.199670	−	0.243050i
$283$	0.721862	−	7.32919i	0.0429102	−	0.435675i	−0.949596	−	0.313478i	$-0.898506\pi$
$283$	0.721862	−	7.32919i	0.0429102	−	0.435675i	0.992506	−	0.122197i	$-0.0389941\pi$
$284$	−11.7270	−	17.5887i	−0.695869	−	1.04370i
$285$	−0.520259	+	1.71506i	−0.0308175	+	0.101592i
$286$	−8.98700	+	21.6659i	−0.531412	+	1.28113i
$287$	−8.09259	−	8.09259i	−0.477691	−	0.477691i
$288$	21.1635	+	14.2176i	1.24707	+	0.837782i
$289$	−1.12050	+	1.12050i	−0.0659118	+	0.0659118i
$290$	2.46293	+	5.95446i	0.144628	+	0.349658i
$291$	24.2956	+	7.37000i	1.42423	+	0.432037i
$292$	−21.8999	−	14.6648i	−1.28160	−	0.858190i
$293$	−5.29848	−	0.521854i	−0.309540	−	0.0304871i	−0.0579456	−	0.998320i	$-0.518455\pi$
$293$	−5.29848	−	0.521854i	−0.309540	−	0.0304871i	−0.251595	+	0.967833i	$0.580955\pi$
$294$	0.535921	−	0.0525131i	0.0312556	−	0.00306263i
$295$	−3.58602	−	0.713303i	−0.208786	−	0.0415301i
$296$	2.95146	−	29.5129i	0.171550	−	1.71540i
$297$	3.39488	+	17.0672i	0.196991	+	0.990339i
$298$	−25.7323	−	13.7707i	−1.49063	−	0.797717i
$299$	−11.9996	−	6.41394i	−0.693957	−	0.370928i
$300$	1.58546	+	5.24543i	0.0915365	+	0.302845i
$301$	8.00391	−	0.788316i	0.461338	−	0.0454378i
$302$	−2.76911	−	13.9577i	−0.159344	−	0.803176i
$303$	−6.43939	−	15.5461i	−0.369933	−	0.893098i
$304$	−0.251254	−	2.60441i	−0.0144104	−	0.149373i
$305$	0.770411	−	1.85994i	0.0441136	−	0.106500i
$306$	24.5423	+	4.89453i	1.40299	+	0.279801i
$307$	−6.47958	+	7.89539i	−0.369809	+	0.450614i	−0.924352	−	0.381542i	$-0.875393\pi$
$307$	−6.47958	+	7.89539i	−0.369809	+	0.450614i	0.554543	+	0.832155i	$0.312893\pi$
$308$	−14.0229	+	17.0521i	−0.799026	+	0.971633i
$309$	8.05944	+	26.5684i	0.458485	+	1.51142i
$310$	14.7453	+	1.45973i	0.837475	+	0.0829069i
$311$	−8.27967	−	5.53230i	−0.469497	−	0.313708i	0.298220	−	0.954497i	$-0.403607\pi$
$311$	−8.27967	−	5.53230i	−0.469497	−	0.313708i	−0.767717	+	0.640789i	$0.778607\pi$
$312$	−5.99500	+	29.9044i	−0.339400	+	1.69300i
$313$	−18.5718	−	27.7947i	−1.04974	−	1.57105i	−0.797438	−	0.603401i	$-0.793812\pi$
$313$	−18.5718	−	27.7947i	−1.04974	−	1.57105i	−0.252304	−	0.967648i	$-0.581188\pi$
$314$	−9.04350	−	2.74826i	−0.510355	−	0.155093i
$315$	9.12584	−	7.48938i	0.514183	−	0.421979i
$316$	−7.51907	+	18.1014i	−0.422981	+	1.01828i
$317$	13.2762	+	24.8380i	0.745664	+	1.39504i	0.912509	+	0.409057i	$0.134142\pi$
$317$	13.2762	+	24.8380i	0.745664	+	1.39504i	−0.166845	+	0.985983i	$0.553358\pi$
$318$	37.4826	−	37.4452i	2.10192	−	2.09982i
$319$		−	19.2020i		−	1.07511i
$320$	−5.05657	−	6.19928i	−0.282671	−	0.346550i
$321$		−	11.4386i		−	0.638438i
$322$	−9.05115	−	9.06021i	−0.504401	−	0.504906i
$323$	−1.21067	−	2.26500i	−0.0673633	−	0.126028i
$324$	−1.68556	−	4.08084i	−0.0936423	−	0.226714i
$325$	−3.04226	+	2.49672i	−0.168754	+	0.138493i
$326$	−6.01043	+	19.7781i	−0.332887	+	1.09541i
$327$	14.1401	+	21.1622i	0.781950	+	1.17027i
$328$	−12.1243	+	2.39277i	−0.669451	+	0.132119i
$329$	2.96896	+	1.98380i	0.163684	+	0.109370i
$330$	1.60870	−	16.2501i	0.0885561	−	0.894540i
$331$	−8.62016	−	28.4169i	−0.473807	−	1.56193i	−0.789920	−	0.613210i	$-0.789878\pi$
$331$	−8.62016	−	28.4169i	−0.473807	−	1.56193i	0.316113	−	0.948722i	$-0.397622\pi$
$332$	29.8852	−	2.91326i	1.64016	−	0.159886i
$333$	29.9832	−	36.5347i	1.64307	−	2.00209i
$334$	0.153779	−	0.771083i	0.00841440	−	0.0421918i
$335$	−1.15565	+	2.78999i	−0.0631399	+	0.152433i
$336$	−13.5830	+	25.2903i	−0.741016	+	1.37970i
$337$	−1.06193	−	2.56372i	−0.0578469	−	0.139655i	0.892314	−	0.451416i	$-0.149081\pi$
$337$	−1.06193	−	2.56372i	−0.0578469	−	0.139655i	−0.950160	+	0.311761i	$0.899081\pi$
$338$	−3.45268	+	0.684987i	−0.187801	+	0.0372584i
$339$	48.2902	−	4.75617i	2.62276	−	0.258320i
$340$	−6.92157	−	3.70856i	−0.375375	−	0.201125i
$341$	−38.9412	−	20.8145i	−2.10879	−	1.12717i
$342$	1.96726	−	3.67606i	0.106377	−	0.198778i
$343$	3.64809	+	18.3402i	0.196979	+	0.990278i
$344$	4.10537	−	7.65297i	0.221346	−	0.412620i
$345$	9.29042	+	1.84798i	0.500179	+	0.0994919i
$346$	−1.56505	−	15.9720i	−0.0841374	−	0.858662i
$347$	11.6430	+	1.14673i	0.625027	+	0.0615598i	0.405572	−	0.914063i	$-0.367072\pi$
$347$	11.6430	+	1.14673i	0.625027	+	0.0615598i	0.219455	+	0.975623i	$0.429572\pi$
$348$	−4.84656	−	24.4933i	−0.259803	−	1.31298i
$349$	10.1411	+	3.07626i	0.542839	+	0.164668i	0.549783	−	0.835307i	$-0.314710\pi$
$349$	10.1411	+	3.07626i	0.542839	+	0.164668i	−0.00694401	+	0.999976i	$0.502210\pi$
$350$	−3.42306	+	1.41587i	−0.182970	+	0.0756817i
$351$	−11.4911	+	11.4911i	−0.613348	+	0.613348i
$352$	6.86323	+	22.8303i	0.365811	+	1.21686i
$353$	11.5126	+	11.5126i	0.612752	+	0.612752i	0.943662	−	0.330910i	$-0.107356\pi$
$353$	11.5126	+	11.5126i	0.612752	+	0.612752i	−0.330910	+	0.943662i	$0.607356\pi$
$354$	13.0862	+	5.42815i	0.695523	+	0.288503i
$355$	−3.06826	+	10.1147i	−0.162846	+	0.536833i
$356$	−7.18608	−	1.43687i	−0.380861	−	0.0761540i
$357$	−2.76190	+	28.0421i	−0.146175	+	1.48414i
$358$	−11.9028	−	9.77831i	−0.629081	−	0.516800i
$359$	−4.71823	+	23.7201i	−0.249019	+	1.25190i	0.630558	+	0.776142i	$0.282826\pi$
$359$	−4.71823	+	23.7201i	−0.249019	+	1.25190i	−0.879576	+	0.475758i	$0.842174\pi$
$360$	−1.23048	−	12.6884i	−0.0648520	−	0.668735i
$361$	18.2153	−	3.62324i	0.958698	−	0.190697i
$362$	31.3316	−	9.48725i	1.64675	−	0.498639i
$363$	−8.73140	+	16.3353i	−0.458280	+	0.857381i
$364$	−20.5162	−	2.04139i	−1.07534	−	0.106998i
$365$	1.29169	+	13.1148i	0.0676102	+	0.686458i
$366$	−4.33707	+	6.48386i	−0.226702	+	0.338917i
$367$	−9.92920	+	4.11281i	−0.518300	+	0.214687i	−0.626470	−	0.779445i	$-0.715501\pi$
$367$	−9.92920	+	4.11281i	−0.518300	+	0.214687i	0.108170	+	0.994132i	$0.465501\pi$
$368$	−13.5685	+	2.67075i	−0.707308	+	0.139222i
$369$	−18.1935	−	7.53599i	−0.947116	−	0.392308i
$370$	−12.3348	+	8.23296i	−0.641258	+	0.428011i
$371$	27.6859	+	22.7212i	1.43738	+	1.17963i
$372$	−54.9254	−	16.7214i	−2.84775	−	0.866965i
$373$	−20.0705	+	6.08833i	−1.03921	+	0.315242i	−0.763370	−	0.645961i	$-0.776457\pi$
$373$	−20.0705	+	6.08833i	−1.03921	+	0.315242i	−0.275842	+	0.961203i	$0.588957\pi$
$374$	14.8358	+	18.0959i	0.767140	+	0.935716i
$375$	1.52221	−	2.27814i	0.0786064	−	0.117643i
$376$	3.56446	−	1.47019i	0.183823	−	0.0758191i
$377$	14.9101	−	9.96260i	0.767908	−	0.513100i
$378$	−13.4933	+	7.20366i	−0.694022	+	0.370516i
$379$	−5.51341	−	6.71811i	−0.283205	−	0.345086i	0.611905	−	0.790931i	$-0.290403\pi$
$379$	−5.51341	−	6.71811i	−0.283205	−	0.345086i	−0.895110	+	0.445845i	$0.852903\pi$
$380$	−0.925997	+	0.924147i	−0.0475026	+	0.0474077i
$381$	−14.4531	+	7.72535i	−0.740456	+	0.395782i
$382$	−28.9788	−	0.0144883i	−1.48269	−	0.000741284i
$383$	−10.4414			−0.533528			−0.266764	−	0.963762i	$-0.585954\pi$
$383$	−10.4414			−0.533528			−0.266764	+	0.963762i	$0.585954\pi$
$384$	14.5168	+	27.3892i	0.740807	+	1.39770i
$385$	11.0387			0.562586
$386$	4.31874	+	0.00215920i	0.219818	+	0.000109900i
$387$	12.2047	−	6.52354i	0.620399	−	0.331610i
$388$	13.0915	+	13.1177i	0.664619	+	0.665949i
$389$	23.2785	+	28.3649i	1.18027	+	1.43816i	0.873805	+	0.486277i	$0.161645\pi$
$389$	23.2785	+	28.3649i	1.18027	+	1.43816i	0.306462	+	0.951883i	$0.400855\pi$
$390$	13.4526	−	7.18194i	0.681200	−	0.363671i
$391$	−11.2863	+	7.54124i	−0.570771	+	0.381377i
$392$	0.362924	+	0.150966i	0.0183304	+	0.00762495i
$393$	−29.2513	+	43.7777i	−1.47553	+	2.20829i
$394$	−1.71913	−	2.09690i	−0.0866085	−	0.105640i
$395$	9.37848	−	2.84493i	0.471882	−	0.143144i
$396$	−11.0637	+	36.3413i	−0.555972	+	1.82622i
$397$	−3.43456	−	2.81867i	−0.172376	−	0.141465i	0.544250	−	0.838923i	$-0.316814\pi$
$397$	−3.43456	−	2.81867i	−0.172376	−	0.141465i	−0.716626	+	0.697458i	$0.754314\pi$
$398$	−25.2522	+	16.8547i	−1.26578	+	0.844852i
$399$	4.33716	+	1.79651i	0.217130	+	0.0899380i
$400$	−0.788205	+	3.92157i	−0.0394103	+	0.196079i
$401$	26.7575	−	11.0833i	1.33621	−	0.553474i	0.403786	−	0.914853i	$-0.367694\pi$
$401$	26.7575	−	11.0833i	1.33621	−	0.553474i	0.932419	+	0.361379i	$0.117694\pi$
$402$	6.50579	−	9.72608i	0.324480	−	0.485093i
$403$	−4.04175	−	41.0365i	−0.201334	−	2.04418i
$404$	1.21616	−	12.2225i	0.0605060	−	0.608094i
$405$	−1.04067	+	1.94695i	−0.0517111	+	0.0967447i
$406$	16.1541	−	4.89147i	0.801713	−	0.242759i
$407$	43.3437	−	8.62159i	2.14847	−	0.427356i
$408$	23.4913	+	19.3378i	1.16299	+	0.957366i
$409$	−4.02361	+	20.2280i	−0.198955	+	1.00021i	0.744225	+	0.667929i	$0.232819\pi$
$409$	−4.02361	+	20.2280i	−0.198955	+	1.00021i	−0.943180	+	0.332283i	$0.892181\pi$
$410$	4.77452	+	3.92235i	0.235797	+	0.193711i
$411$	−2.10151	+	21.3370i	−0.103660	+	1.05248i
$412$	−3.97364	+	19.8730i	−0.195767	+	0.979072i
$413$	−2.78008	+	9.16469i	−0.136799	+	0.450965i
$414$	−20.3545	−	8.44302i	−1.00037	−	0.414952i
$415$	−10.6161	−	10.6161i	−0.521123	−	0.521123i
$416$	−14.1666	+	17.1743i	−0.694573	+	0.842039i
$417$	−15.4239	+	15.4239i	−0.755311	+	0.755311i
$418$	3.60251	−	1.49010i	0.176205	−	0.0728832i
$419$	−18.6056	−	5.64395i	−0.908944	−	0.275725i	−0.199013	−	0.979997i	$-0.563774\pi$
$419$	−18.6056	−	5.64395i	−0.908944	−	0.275725i	−0.709930	+	0.704272i	$0.751274\pi$
$420$	14.0805	−	2.78616i	0.687060	−	0.135951i
$421$	24.0957	+	2.37322i	1.17435	+	0.115664i	0.666314	−	0.745671i	$-0.267871\pi$
$421$	24.0957	+	2.37322i	1.17435	+	0.115664i	0.508038	+	0.861335i	$0.330371\pi$
$422$	−0.899674	−	9.18160i	−0.0437955	−	0.446953i
$423$	6.02602	+	1.19865i	0.292995	+	0.0582804i
$424$	37.0258	−	11.1710i	1.79813	−	0.542514i
$425$	0.765972	+	3.85080i	0.0371551	+	0.186791i
$426$	19.3246	−	36.1104i	0.936280	−	1.74955i
$427$	−4.65058	−	2.48579i	−0.225057	−	0.120296i
$428$	3.94334	−	7.35977i	0.190609	−	0.355748i
$429$	−45.2246	+	4.45423i	−2.18346	+	0.215052i
$430$	−4.25928	+	0.845009i	−0.205401	+	0.0407500i
$431$	6.66435	+	16.0892i	0.321010	+	0.774988i	0.999196	+	0.0400969i	$0.0127666\pi$
$431$	6.66435	+	16.0892i	0.321010	+	0.774988i	−0.678185	+	0.734891i	$0.737233\pi$
$432$	−1.65179	+	16.4339i	−0.0794718	+	0.790677i
$433$	2.75830	−	6.65912i	0.132555	−	0.320017i	−0.843640	−	0.536909i	$-0.819592\pi$
$433$	2.75830	−	6.65912i	0.132555	−	0.320017i	0.976196	+	0.216892i	$0.0695920\pi$
$434$	7.59086	−	38.0624i	0.364373	−	1.82705i
$435$	−7.91982	+	9.65033i	−0.379726	+	0.462698i
$436$	1.80252	+	18.4908i	0.0863249	+	0.885548i
$437$	0.656465	+	2.16407i	0.0314030	+	0.103522i
$438$	5.03046	−	50.8146i	0.240365	−	2.42802i
$439$	−2.40157	−	1.60468i	−0.114621	−	0.0765872i	0.496939	−	0.867786i	$-0.334457\pi$
$439$	−2.40157	−	1.60468i	−0.114621	−	0.0765872i	−0.611559	+	0.791199i	$0.709457\pi$
$440$	6.63715	−	9.90102i	0.316414	−	0.472013i
$441$	0.347983	+	0.520793i	0.0165706	+	0.0247997i
$442$	−6.35394	+	20.9085i	−0.302226	+	0.994515i
$443$	−8.67936	+	7.12297i	−0.412369	+	0.338422i	−0.817595	−	0.575794i	$-0.804693\pi$
$443$	−8.67936	+	7.12297i	−0.412369	+	0.338422i	0.405226	+	0.914217i	$0.367193\pi$
$444$	53.1113	−	21.9372i	2.52055	−	1.04109i
$445$	1.72727	+	3.23150i	0.0818806	+	0.153188i
$446$	1.92087	+	1.92279i	0.0909557	+	0.0910467i
$447$		−	56.5437i		−	2.67442i
$448$	−17.4582	+	11.5896i	−0.824821	+	0.547556i
$449$		−	11.5967i		−	0.547284i	−0.961832	−	0.273642i	$-0.911772\pi$
$449$		−	11.5967i		−	0.547284i	0.961832	−	0.273642i	$-0.0882284\pi$
$450$	−4.50931	+	4.50480i	−0.212571	+	0.212358i
$451$	−8.67999	−	16.2391i	−0.408725	−	0.764670i
$452$	32.7104	+	13.5874i	1.53857	+	0.639099i
$453$	21.3109	−	17.4894i	1.00127	−	0.821725i
$454$	−31.0071	−	9.42283i	−1.45524	−	0.442235i
$455$	5.72724	+	8.57142i	0.268497	+	0.401834i
$456$	4.21912	−	2.80998i	0.197578	−	0.131589i
$457$	−17.0254	−	11.3760i	−0.796415	−	0.532148i	0.0895042	−	0.995986i	$-0.471472\pi$
$457$	−17.0254	−	11.3760i	−0.796415	−	0.532148i	−0.885920	+	0.463839i	$0.846472\pi$
$458$	3.03518	+	0.300471i	0.141825	+	0.0140401i
$459$	4.70614	+	15.5141i	0.219664	+	0.724135i
$460$	5.34054	+	4.39181i	0.249004	+	0.204769i
$461$	−19.6770	+	23.9764i	−0.916447	+	1.11669i	0.0763729	+	0.997079i	$0.475666\pi$
$461$	−19.6770	+	23.9764i	−0.916447	+	1.11669i	−0.992820	+	0.119615i	$0.961834\pi$
$462$	−41.9469	−	8.36556i	−1.95155	−	0.389201i
$463$	2.51436	−	6.07021i	0.116852	−	0.282107i	−0.854622	−	0.519250i	$-0.826211\pi$
$463$	2.51436	−	6.07021i	0.116852	−	0.282107i	0.971475	+	0.237144i	$0.0762112\pi$
$464$	5.32548	−	17.4302i	0.247229	−	0.809177i
$465$	10.9858	+	26.5220i	0.509452	+	1.22993i
$466$	4.44489	+	22.4045i	0.205906	+	1.03787i
$467$	18.3603	−	1.80833i	0.849613	−	0.0836795i	0.336168	−	0.941802i	$-0.390869\pi$
$467$	18.3603	−	1.80833i	0.849613	−	0.0836795i	0.513445	+	0.858123i	$0.328369\pi$
$468$	−33.9587	+	10.2642i	−1.56974	+	0.474462i
$469$	6.97608	+	3.72879i	0.322125	+	0.172180i
$470$	−1.69978	−	0.909644i	−0.0784050	−	0.0419588i
$471$	−3.57251	−	17.9602i	−0.164613	−	0.827563i
$472$	6.54858	+	8.00391i	0.301423	+	0.368410i
$473$	12.6912	+	2.52443i	0.583541	+	0.116074i
$474$	−37.7940	+	3.70330i	−1.73593	+	0.170098i
$475$	0.650975	+	0.0641155i	0.0298688	+	0.00294182i
$476$	−11.4443	+	17.0906i	−0.524549	+	0.783347i
$477$	58.9733	+	17.8894i	2.70020	+	0.819098i
$478$	10.0608	+	24.3233i	0.460171	+	1.11252i
$479$	−14.6850	+	14.6850i	−0.670977	+	0.670977i	−0.957941	−	0.286964i	$-0.907354\pi$
$479$	−14.6850	+	14.6850i	−0.670977	+	0.670977i	0.286964	+	0.957941i	$0.407354\pi$
$480$	5.96707	−	14.3045i	0.272358	−	0.652910i
$481$	29.1826	+	29.1826i	1.33061	+	1.33061i
$482$	3.75218	−	9.04578i	0.170907	−	0.412024i
$483$	7.20245	−	23.7433i	0.327723	−	1.08036i
$484$	−11.2494	+	7.50034i	−0.511336	+	0.340925i
$485$	0.908260	−	9.22172i	0.0412420	−	0.418737i
$486$	16.5504	−	20.1462i	0.750743	−	0.913851i
$487$	−0.764376	+	3.84278i	−0.0346372	+	0.174133i	−0.994232	−	0.107254i	$-0.965794\pi$
$487$	−0.764376	+	3.84278i	−0.0346372	+	0.174133i	0.959595	+	0.281387i	$0.0907943\pi$
$488$	−5.02580	+	2.67666i	−0.227507	+	0.121167i
$489$	−39.2789	+	7.81307i	−1.77625	+	0.353319i
$490$	−0.0569572	−	0.188101i	−0.00257306	−	0.00849755i
$491$	4.61003	−	8.62475i	0.208048	−	0.389230i	−0.756157	−	0.654391i	$-0.772925\pi$
$491$	4.61003	−	8.62475i	0.208048	−	0.389230i	0.964204	+	0.265161i	$0.0854251\pi$
$492$	−15.1706	−	18.5231i	−0.683942	−	0.835087i
$493$	−1.75348	−	17.8034i	−0.0789728	−	0.801824i
$494$	3.02614	+	2.02419i	0.136152	+	0.0910726i
$495$	17.5482	−	7.26870i	0.788733	−	0.326704i
$496$	−29.5754	−	29.6939i	−1.32797	−	1.33330i
$497$	25.5787	+	10.5950i	1.14736	+	0.475253i
$498$	32.2956	+	48.3861i	1.44720	+	2.16823i
$499$	−29.7459	−	24.4118i	−1.33161	−	1.09282i	−0.988123	−	0.153667i	$-0.950892\pi$
$499$	−29.7459	−	24.4118i	−1.33161	−	1.09282i	−0.343487	−	0.939157i	$-0.611608\pi$
$500$	1.76478	−	0.941029i	0.0789236	−	0.0420841i
$501$	1.45772	−	0.442196i	0.0651263	−	0.0197558i
$502$	6.20370	−	5.08606i	0.276885	−	0.227002i
$503$	2.14948	−	3.21692i	0.0958404	−	0.143435i	−0.780451	−	0.625217i	$-0.785010\pi$
$503$	2.14948	−	3.21692i	0.0958404	−	0.143435i	0.876291	+	0.481782i	$0.160010\pi$
$504$	−33.3912	−	0.0500829i	−1.48736	−	0.00223087i
$505$	−5.10642	+	3.41200i	−0.227233	+	0.151832i
$506$	−9.70390	−	18.1766i	−0.431391	−	0.808047i
$507$	−4.32631	−	5.27163i	−0.192138	−	0.234121i
$508$	−11.9626	−	0.0119617i	−0.530756	−	0.000530714i
$509$	31.9970	−	17.1027i	1.41824	−	0.758066i	0.428855	−	0.903374i	$-0.358917\pi$
$509$	31.9970	−	17.1027i	1.41824	−	0.758066i	0.989386	+	0.145308i	$0.0464173\pi$
$510$	0.00760611	−	15.2134i	0.000336804	−	0.673661i
$511$	34.5184			1.52701
$512$	−0.101815	+	22.6272i	−0.00449963	+	0.999990i
$513$	2.70100			0.119252
$514$	0.0124712	−	24.9444i	0.000550082	−	1.10025i
$515$	8.93667	−	4.77675i	0.393797	−	0.210489i
$516$	16.8255	+	0.0168242i	0.740702	+	0.000740644i
$517$	3.64458	+	4.44093i	0.160288	+	0.195312i
$518$	18.2943	+	34.2675i	0.803807	+	1.50563i
$519$	25.8524	−	17.2740i	1.13480	−	0.758247i
$520$	11.1316	+	0.0166960i	0.488151	+	0.000732170i
$521$	−2.27225	+	3.40067i	−0.0995492	+	0.148986i	−0.877901	−	0.478843i	$-0.841056\pi$
$521$	−2.27225	+	3.40067i	−0.0995492	+	0.148986i	0.778351	+	0.627829i	$0.216056\pi$
$522$	22.4591	−	18.4130i	0.983010	−	0.805913i
$523$	−2.83969	+	0.861409i	−0.124171	+	0.0376668i	−0.351758	−	0.936091i	$-0.614416\pi$
$523$	−2.83969	+	0.861409i	−0.124171	+	0.0376668i	0.227588	+	0.973758i	$0.426916\pi$
$524$	−33.9128	+	18.0832i	−1.48149	+	0.789967i
$525$	−5.54772	−	4.55290i	−0.242122	−	0.198705i
$526$	−2.44309	−	3.66030i	−0.106524	−	0.159597i
$527$	−38.0056	−	15.7424i	−1.65555	−	0.685751i
$528$	−32.7244	+	32.5937i	−1.42414	+	1.41846i
$529$	−10.2067	+	4.22775i	−0.443770	+	0.183815i
$530$	−16.0729	−	10.7512i	−0.698162	−	0.467002i
$531$	1.61523	+	16.3997i	0.0700948	+	0.711684i
$532$	2.17127	+	2.65110i	0.0941366	+	0.114940i
$533$	8.10599	−	15.1652i	0.351110	−	0.656880i
$534$	−4.11464	−	13.5886i	−0.178058	−	0.588037i
$535$	−4.09459	+	0.814465i	−0.177025	+	0.0352124i
$536$	7.53892	−	4.01511i	0.325632	−	0.173426i
$537$	5.82232	−	29.2708i	0.251252	−	1.26313i
$538$	9.20124	−	11.2003i	0.396693	−	0.482880i
$539$	−0.0574054	+	0.582847i	−0.00247262	+	0.0251050i
$540$	6.87116	−	4.58123i	0.295688	−	0.197145i
$541$	4.95191	−	16.3243i	0.212899	−	0.701834i	−0.783827	−	0.620980i	$-0.786735\pi$
$541$	4.95191	−	16.3243i	0.212899	−	0.701834i	0.996726	−	0.0808548i	$-0.0257650\pi$
$542$	−1.58870	+	3.83005i	−0.0682406	+	0.164515i
$543$	44.8474	+	44.8474i	1.92459	+	1.92459i
$544$	8.44815	+	20.5407i	0.362211	+	0.880676i
$545$	6.56847	−	6.56847i	0.281362	−	0.281362i
$546$	−15.2676	−	36.9115i	−0.653394	−	1.57966i
$547$	18.3161	+	5.55614i	0.783142	+	0.237563i	0.656441	−	0.754377i	$-0.272061\pi$
$547$	18.3161	+	5.55614i	0.783142	+	0.237563i	0.126701	+	0.991941i	$0.459561\pi$
$548$	−8.70789	+	13.0041i	−0.371983	+	0.555508i
$549$	−9.02982	−	0.889360i	−0.385384	−	0.0379570i
$550$	−5.93150	+	0.581208i	−0.252920	+	0.0247828i
$551$	−2.92319	−	0.581458i	−0.124532	−	0.0247709i
$552$	−16.9656	−	20.7360i	−0.722105	−	0.882584i
$553$	−5.00816	−	25.1777i	−0.212968	−	1.07066i
$554$	−4.74283	−	2.53814i	−0.201504	−	0.107835i
$555$	−25.3391	−	13.5440i	−1.07559	−	0.574913i
$556$	−15.2413	+	4.60675i	−0.646373	+	0.195370i
$557$	−43.0556	+	4.24061i	−1.82433	+	0.179680i	−0.951356	−	0.308094i	$-0.900309\pi$
$557$	−43.0556	+	4.24061i	−1.82433	+	0.179680i	−0.872970	+	0.487774i	$0.837809\pi$
$558$	−12.9959	−	65.5059i	−0.550160	−	2.77308i
$559$	4.62440	+	11.1643i	0.195591	+	0.472199i
$560$	10.0202	+	3.06148i	0.423429	+	0.129371i
$561$	−17.3491	+	41.8843i	−0.732478	+	1.76836i
$562$	41.7768	+	8.33164i	1.76225	+	0.351449i
$563$	−27.4452	+	33.4420i	−1.15668	+	1.40941i	−0.260637	+	0.965437i	$0.583933\pi$
$563$	−27.4452	+	33.4420i	−1.15668	+	1.40941i	−0.896039	+	0.443976i	$0.853567\pi$
$564$	5.76975	+	4.74478i	0.242950	+	0.199791i
$565$	−5.14096	−	16.9475i	−0.216282	−	0.712986i
$566$	10.3645	+	1.02605i	0.435653	+	0.0431280i
$567$	4.80802	+	3.21261i	0.201918	+	0.134917i
$568$	24.8825	−	16.5720i	1.04405	−	0.695347i
$569$	−17.3575	−	25.9773i	−0.727662	−	1.08902i	−0.992201	−	0.124649i	$-0.960220\pi$
$569$	−17.3575	−	25.9773i	−0.727662	−	1.08902i	0.264539	−	0.964375i	$-0.414780\pi$
$570$	−2.42510	−	0.736970i	−0.101576	−	0.0308683i
$571$	5.09994	−	4.18542i	0.213426	−	0.175154i	−0.521606	−	0.853186i	$-0.674667\pi$
$571$	5.09994	−	4.18542i	0.213426	−	0.175154i	0.735032	+	0.678032i	$0.237167\pi$
$572$	−30.6338	−	12.7249i	−1.28086	−	0.532053i
$573$	−26.4659	−	49.5143i	−1.10563	−	2.06849i
$574$	11.4504	−	11.4389i	0.477929	−	0.477452i
$575$		−	3.45722i		−	0.144176i
$576$	−20.1217	+	29.9196i	−0.838405	+	1.24665i
$577$		−	41.1680i		−	1.71384i	−0.515446	−	0.856922i	$-0.672374\pi$
$577$		−	41.1680i		−	1.71384i	0.515446	−	0.856922i	$-0.327626\pi$
$578$	−1.58384	−	1.58542i	−0.0658789	−	0.0659448i
$579$	3.94424	+	7.37915i	0.163917	+	0.306667i
$580$	−8.42261	+	3.47890i	−0.349730	+	0.144453i
$581$	−30.3990	+	24.9478i	−1.26116	+	1.03501i
$582$	−10.4399	+	34.3540i	−0.432749	+	1.42402i
$583$	32.0141	+	47.9125i	1.32589	+	1.98433i
$584$	20.7546	−	30.9608i	0.858831	−	1.28117i
$585$	14.7486	+	9.85470i	0.609780	+	0.407442i
$586$	0.741760	−	7.49281i	0.0306418	−	0.309525i
$587$	1.00852	+	3.32463i	0.0416259	+	0.137222i	0.975290	−	0.220927i	$-0.0709081\pi$
$587$	1.00852	+	3.32463i	0.0416259	+	0.137222i	−0.933665	+	0.358149i	$0.883408\pi$
$588$	0.0738858	+	0.757944i	0.00304700	+	0.0312571i
$589$	−4.34785	+	5.29787i	−0.179150	+	0.218295i
$590$	1.01130	−	5.07089i	0.0416345	−	0.208765i
$591$	2.01036	−	4.85344i	0.0826952	−	0.199644i
$592$	41.7354	+	4.19487i	1.71531	+	0.172408i
$593$	−14.4867	−	34.9740i	−0.594897	−	1.43621i	−0.878722	−	0.477333i	$-0.841603\pi$
$593$	−14.4867	−	34.9740i	−0.594897	−	1.43621i	0.283825	−	0.958876i	$-0.408397\pi$
$594$	−24.1391	+	4.78901i	−0.990438	+	0.196496i
$595$	10.2347	−	1.00803i	0.419582	−	0.0413252i
$596$	19.4929	−	36.3812i	0.798462	−	1.49023i
$597$	−51.8750	−	27.7278i	−2.12310	−	1.13482i
$598$	9.07916	−	16.9655i	0.371275	−	0.693771i
$599$	−4.77332	−	23.9971i	−0.195033	−	0.980495i	−0.946985	−	0.321278i	$-0.895888\pi$
$599$	−4.77332	−	23.9971i	−0.195033	−	0.980495i	0.751953	−	0.659217i	$-0.229112\pi$
$600$	−7.41928	+	2.23847i	−0.302891	+	0.0913850i
$601$	6.99313	+	1.39102i	0.285256	+	0.0567409i	0.335644	−	0.941989i	$-0.391046\pi$
$601$	6.99313	+	1.39102i	0.285256	+	0.0567409i	−0.0503886	+	0.998730i	$0.516046\pi$
$602$	1.10919	+	11.3198i	0.0452071	+	0.461360i
$603$	13.5451	+	1.33408i	0.551601	+	0.0543279i
$604$	19.7411	−	3.90624i	0.803256	−	0.158943i
$605$	6.46915	+	1.96240i	0.263008	+	0.0797827i
$606$	21.9900	−	9.09568i	0.893283	−	0.369487i
$607$	−12.0360	+	12.0360i	−0.488528	+	0.488528i	−0.907841	−	0.419314i	$-0.862271\pi$
$607$	−12.0360	+	12.0360i	−0.488528	+	0.488528i	0.419314	+	0.907841i	$0.362271\pi$
$608$	3.68337	−	0.353485i	0.149380	−	0.0143357i
$609$	23.1226	+	23.1226i	0.936974	+	0.936974i
$610$	2.62980	+	1.09084i	0.106478	+	0.0441668i
$611$	−1.55740	+	5.13405i	−0.0630056	+	0.207702i
$612$	−6.93926	+	34.7046i	−0.280503	+	1.40285i
$613$	0.616021	−	6.25457i	0.0248809	−	0.252620i	−0.974696	−	0.223534i	$-0.928241\pi$
$613$	0.616021	−	6.25457i	0.0248809	−	0.252620i	0.999577	−	0.0290854i	$-0.00925947\pi$
$614$	−11.1612	−	9.16909i	−0.450429	−	0.370034i
$615$	−2.33549	+	11.7413i	−0.0941762	+	0.473456i
$616$	−24.1054	−	19.8434i	−0.971234	−	0.799512i
$617$	4.29286	−	0.853903i	0.172824	−	0.0343768i	−0.107920	−	0.994160i	$-0.534419\pi$
$617$	4.29286	−	0.853903i	0.172824	−	0.0343768i	0.280744	+	0.959783i	$0.409419\pi$
$618$	−37.5791	+	11.3790i	−1.51165	+	0.457730i
$619$	−21.0534	+	39.3882i	−0.846209	+	1.58315i	−0.0342634	+	0.999413i	$0.510909\pi$
$619$	−21.0534	+	39.3882i	−0.846209	+	1.58315i	−0.811946	+	0.583733i	$0.801591\pi$
$620$	−2.07479	+	20.8519i	−0.0833255	+	0.837433i
$621$	−1.39924	−	14.2067i	−0.0561496	−	0.570096i
$622$	7.82971	−	11.7053i	0.313943	−	0.469340i
$623$	8.86716	−	3.67290i	0.355255	−	0.147152i
$624$	−42.2870	−	8.49935i	−1.69283	−	0.340246i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	39.3208	−	26.2449i	1.57157	−	1.04896i
$627$	5.83856	+	4.79158i	0.233169	+	0.191357i
$628$	3.89301	−	12.7875i	0.155348	−	0.510277i
$629$	39.3993	−	11.9517i	1.57095	−	0.476544i
$630$	10.5851	+	12.9112i	0.421722	+	0.514394i
$631$	23.8537	−	35.6996i	0.949601	−	1.42118i	0.0430538	−	0.999073i	$-0.486291\pi$
$631$	23.8537	−	35.6996i	0.949601	−	1.42118i	0.906547	−	0.422105i	$-0.138709\pi$
$632$	−25.5940	−	10.6464i	−1.01807	−	0.423490i
$633$	14.8614	−	9.93007i	0.590687	−	0.394685i
$634$	−35.1356	+	18.7578i	−1.39541	+	0.744967i
$635$	3.79451	+	4.62362i	0.150581	+	0.183483i
$636$	52.9289	+	53.0349i	2.09877	+	2.10297i
$637$	−0.482356	+	0.257825i	−0.0191116	+	0.0102154i
$638$	27.1557	+	0.0135768i	1.07511	+	0.000537510i
$639$	47.6388			1.88456
$640$	8.77068	−	7.14669i	0.346692	−	0.282498i
$641$	−20.7046			−0.817783			−0.408891	−	0.912583i	$-0.634084\pi$
$641$	−20.7046			−0.817783			−0.408891	+	0.912583i	$0.634084\pi$
$642$	16.1766	+	0.00808764i	0.638438	+	0.000319194i
$643$	27.9248	−	14.9261i	1.10125	−	0.588628i	0.182392	−	0.983226i	$-0.441616\pi$
$643$	27.9248	−	14.9261i	1.10125	−	0.588628i	0.918854	+	0.394598i	$0.129116\pi$
$644$	12.8195	−	12.7939i	0.505158	−	0.504149i
$645$	−5.33700	−	6.50315i	−0.210144	−	0.256061i
$646$	3.20404	−	1.71054i	0.126061	−	0.0673002i
$647$	25.3130	−	16.9136i	0.995157	−	0.664943i	0.0524704	−	0.998622i	$-0.483290\pi$
$647$	25.3130	−	16.9136i	0.995157	−	0.664943i	0.942686	+	0.333680i	$0.108290\pi$
$648$	5.77238	−	2.38086i	0.226760	−	0.0935290i
$649$	−8.56055	+	12.8118i	−0.336031	+	0.502906i
$650$	−3.52875	−	4.30418i	−0.138409	−	0.168824i
$651$	71.9564	−	21.8277i	2.82019	−	0.855497i
$652$	−27.9662	−	8.51401i	−1.09524	−	0.333434i
$653$	11.9537	+	9.81015i	0.467784	+	0.383901i	0.838549	−	0.544826i	$-0.183404\pi$
$653$	11.9537	+	9.81015i	0.467784	+	0.383901i	−0.370765	+	0.928727i	$0.620904\pi$
$654$	−29.9378	+	19.9822i	−1.17066	+	0.781365i
$655$	17.7536	+	7.35379i	0.693691	+	0.287336i
$656$	−3.37532	−	17.1480i	−0.131784	−	0.669517i
$657$	54.8738	−	22.7295i	2.14083	−	0.886761i
$658$	−2.80761	+	4.19735i	−0.109452	+	0.163630i
$659$	−2.53535	−	25.7419i	−0.0987633	−	1.00276i	−0.909039	−	0.416711i	$-0.863183\pi$
$659$	−2.53535	−	25.7419i	−0.0987633	−	1.00276i	0.810275	−	0.586049i	$-0.199317\pi$
$660$	22.9800	+	2.28654i	0.894495	+	0.0890033i
$661$	−3.96963	+	7.42666i	−0.154401	+	0.288864i	−0.947215	−	0.320600i	$-0.896115\pi$
$661$	−3.96963	+	7.42666i	−0.154401	+	0.288864i	0.792814	+	0.609464i	$0.208615\pi$
$662$	40.1936	−	12.1707i	1.56217	−	0.473026i
$663$	−41.5238	+	8.25960i	−1.61265	+	0.320776i
$664$	4.09885	+	42.2661i	0.159066	+	1.64024i
$665$	0.334265	−	1.68046i	0.0129622	−	0.0651656i
$666$	51.6466	+	42.4285i	2.00127	+	1.64407i
$667$	−1.54401	+	15.6766i	−0.0597844	+	0.607001i
$668$	1.09037	+	0.218021i	0.0421876	+	0.00843549i
$669$	−1.52853	+	5.03888i	−0.0590963	+	0.194814i
$670$	−3.94482	−	1.63631i	−0.152402	−	0.0632161i
$671$	−5.99919	−	5.99919i	−0.231596	−	0.231596i
$672$	−35.7563	−	19.2272i	−1.37933	−	0.741705i
$673$	−24.6317	+	24.6317i	−0.949483	+	0.949483i	−0.998784	−	0.0493006i	$-0.984301\pi$
$673$	−24.6317	+	24.6317i	−0.949483	+	0.949483i	0.0493006	+	0.998784i	$0.484301\pi$
$674$	3.62640	−	1.49998i	0.139684	−	0.0577770i
$675$	−3.95138	−	1.19864i	−0.152089	−	0.0461356i
$676$	−0.966276	−	4.88331i	−0.0371645	−	0.187820i
$677$	−44.0630	−	4.33983i	−1.69348	−	0.166793i	−0.795238	−	0.606297i	$-0.792654\pi$
$677$	−44.0630	−	4.33983i	−1.69348	−	0.166793i	−0.898241	+	0.439504i	$0.855154\pi$
$678$	6.69209	+	68.2960i	0.257008	+	2.62289i
$679$	−23.8055	−	4.73520i	−0.913570	−	0.181720i
$680$	5.24959	−	9.78595i	0.201312	−	0.375274i
$681$	−12.2489	−	61.5795i	−0.469379	−	2.35973i
$682$	29.4637	−	55.0565i	1.12822	−	2.10822i
$683$	−37.7004	−	20.1513i	−1.44256	−	0.771066i	−0.450027	−	0.893015i	$-0.648586\pi$
$683$	−37.7004	−	20.1513i	−1.44256	−	0.771066i	−0.992536	+	0.121948i	$0.961086\pi$
$684$	5.19734	+	2.78472i	0.198725	+	0.106476i
$685$	7.78751	−	0.767003i	0.297546	−	0.0293057i
$686$	−25.9395	+	5.14622i	−0.990376	+	0.196483i
$687$	2.26132	+	5.45930i	0.0862746	+	0.208285i
$688$	10.8200	+	5.81127i	0.412510	+	0.221553i
$689$	−20.5935	+	49.7170i	−0.784548	+	1.89407i
$690$	−2.62001	+	13.1373i	−0.0997419	+	0.500130i
$691$	20.1417	−	24.5427i	0.766225	−	0.933648i	−0.233021	−	0.972472i	$-0.574861\pi$
$691$	20.1417	−	24.5427i	0.766225	−	0.933648i	0.999246	+	0.0388235i	$0.0123610\pi$
$692$	22.5890	−	2.20202i	0.858704	−	0.0837081i
$693$	−14.4423	−	47.6098i	−0.548617	−	1.80855i
$694$	−1.62996	+	16.4648i	−0.0618723	+	0.624996i
$695$	6.61943	+	4.42296i	0.251089	+	0.167773i
$696$	34.6421	−	6.83675i	1.31311	−	0.259146i
$697$	−9.53068	−	14.2637i	−0.361000	−	0.540275i
$698$	−4.35766	+	14.3395i	−0.164940	+	0.542757i
$699$	−34.2077	+	28.0735i	−1.29385	+	1.06184i
$700$	−1.99993	−	4.84194i	−0.0755902	−	0.183008i
$701$	−11.6098	−	21.7203i	−0.438495	−	0.820366i	0.561480	−	0.827490i	$-0.310232\pi$
$701$	−11.6098	−	21.7203i	−0.438495	−	0.820366i	−0.999975	+	0.00712432i	$0.997732\pi$
$702$	−16.2427	−	16.2589i	−0.613041	−	0.613654i
$703$		−	6.85943i		−	0.258708i
$704$	−32.2918	+	9.68993i	−1.21704	+	0.365203i
$705$		−	3.73507i		−	0.140671i
$706$	−16.2894	+	16.2731i	−0.613058	+	0.612446i
$707$	7.58318	+	14.1871i	0.285195	+	0.533562i
$708$	−7.68581	+	18.5028i	−0.288850	+	0.695379i
$709$	−17.8241	+	14.6279i	−0.669399	+	0.549362i	−0.906543	−	0.422113i	$-0.861289\pi$
$709$	−17.8241	+	14.6279i	−0.669399	+	0.549362i	0.237144	+	0.971474i	$0.423789\pi$
$710$	−14.3022	−	4.34633i	−0.536751	−	0.163115i
$711$	−24.5403	−	36.7271i	−0.920332	−	1.37737i
$712$	2.03712	−	10.1616i	0.0763444	−	0.380823i
$713$	30.1182	+	20.1243i	1.12793	+	0.753661i
$714$	−39.6555	−	3.92575i	−1.48407	−	0.146917i
$715$	4.81460	+	15.8716i	0.180056	+	0.593565i
$716$	13.8370	−	16.8261i	0.517114	−	0.628822i
$717$	−32.3517	+	39.4206i	−1.20819	+	1.47219i
$718$	−33.5420	−	6.68935i	−1.25178	−	0.249644i
$719$	−14.4556	+	34.8988i	−0.539101	+	1.30151i	0.386250	+	0.922394i	$0.373770\pi$
$719$	−14.4556	+	34.8988i	−0.539101	+	1.30151i	−0.925351	+	0.379111i	$0.876230\pi$
$720$	17.9449	−	1.73119i	0.668767	−	0.0645177i
$721$	−10.1573	−	24.5220i	−0.378279	−	0.913247i
$722$	5.11116	+	25.7628i	0.190218	+	0.958793i
$723$	18.8818	−	1.85970i	0.702223	−	0.0691629i
$724$	13.3948	+	44.3163i	0.497815	+	1.64700i
$725$	4.01839	+	2.14787i	0.149239	+	0.0797700i
$726$	−23.0954	−	12.3596i	−0.857152	−	0.458708i
$727$	0.0865164	+	0.434947i	0.00320872	+	0.0161313i	0.982356	−	0.187018i	$-0.0598823\pi$
$727$	0.0865164	+	0.434947i	0.00320872	+	0.0161313i	−0.979148	+	0.203149i	$0.934882\pi$
$728$	2.90146	−	29.0128i	0.107535	−	1.07529i
$729$	43.0472	+	8.56261i	1.59434	+	0.317134i
$730$	−18.5480	+	1.81745i	−0.686492	+	0.0672670i
$731$	11.9973	+	1.18163i	0.443737	+	0.0437043i
$732$	−9.16650	−	6.13813i	−0.338804	−	0.226872i
$733$	−23.0429	−	6.98997i	−0.851107	−	0.258181i	−0.165552	−	0.986201i	$-0.552941\pi$
$733$	−23.0429	−	6.98997i	−0.851107	−	0.258181i	−0.685555	+	0.728021i	$0.740441\pi$
$734$	−5.80937	−	14.0449i	−0.214428	−	0.518407i
$735$	0.269244	−	0.269244i	0.00993121	−	0.00993121i
$736$	−3.76741	−	19.1907i	−0.138869	−	0.707377i
$737$	8.99904	+	8.99904i	0.331484	+	0.331484i
$738$	10.6704	−	25.7242i	0.392782	−	0.946919i
$739$	1.79947	−	5.93207i	0.0661947	−	0.218215i	−0.917603	−	0.397499i	$-0.869878\pi$
$739$	1.79947	−	5.93207i	0.0661947	−	0.218215i	0.983797	+	0.179284i	$0.0573782\pi$
$740$	−11.6344	−	17.4499i	−0.427691	−	0.641472i
$741$	−0.691368	+	7.01958i	−0.0253980	+	0.257871i
$742$	−32.1522	+	39.1376i	−1.18034	+	1.43679i
$743$	5.39242	−	27.1095i	0.197829	−	0.994551i	−0.746459	−	0.665431i	$-0.768248\pi$
$743$	5.39242	−	27.1095i	0.197829	−	0.994551i	0.944288	−	0.329120i	$-0.106752\pi$
$744$	23.6865	−	77.6644i	0.868389	−	2.84731i
$745$	−20.2406	+	4.02610i	−0.741558	+	0.147505i
$746$	−8.59600	−	28.3883i	−0.314722	−	1.03937i
$747$	−31.8977	+	59.6763i	−1.16707	+	2.18344i
$748$	−25.6019	+	20.9682i	−0.936100	+	0.766672i
$749$	1.07185	+	10.8827i	0.0391645	+	0.397644i
$750$	3.22071	+	2.15434i	0.117604	+	0.0786652i
$751$	17.0199	−	7.04986i	0.621064	−	0.257253i	−0.0498872	−	0.998755i	$-0.515886\pi$
$751$	17.0199	−	7.04986i	0.621064	−	0.257253i	0.670951	+	0.741502i	$0.265886\pi$
$752$	2.07664	+	5.04194i	0.0757272	+	0.183861i
$753$	14.3589	+	5.94767i	0.523269	+	0.216745i
$754$	14.0787	+	21.0931i	0.512716	+	0.768165i
$755$	−7.77799	−	6.38323i	−0.283070	−	0.232310i
$756$	−10.1780	−	19.0875i	−0.370169	−	0.694207i
$757$	20.9571	−	6.35726i	0.761698	−	0.231058i	0.114544	−	0.993418i	$-0.463459\pi$
$757$	20.9571	−	6.35726i	0.761698	−	0.231058i	0.647153	+	0.762360i	$0.275959\pi$
$758$	9.50474	−	7.79239i	0.345228	−	0.283032i
$759$	22.1781	−	33.1919i	0.805015	−	1.20479i
$760$	−1.30629	−	1.31021i	−0.0473840	−	0.0475263i
$761$	−10.0406	+	6.70892i	−0.363972	+	0.243198i	−0.724085	−	0.689710i	$-0.757738\pi$
$761$	−10.0406	+	6.70892i	−0.363972	+	0.243198i	0.360114	+	0.932908i	$0.382738\pi$
$762$	−10.9151	−	20.4453i	−0.395412	−	0.740654i
$763$	−15.4359	−	18.8087i	−0.558818	−	0.680921i
$764$	0.0409790	−	40.9822i	0.00148257	−	1.48269i
$765$	15.6063	−	8.34174i	0.564247	−	0.301596i
$766$	0.00738257	−	14.7663i	0.000266743	−	0.533528i
$767$	−14.3896			−0.519580
$768$	−38.7444	+	20.5105i	−1.39807	+	0.740108i
$769$	−19.7665			−0.712798			−0.356399	−	0.934334i	$-0.615996\pi$
$769$	−19.7665			−0.712798			−0.356399	+	0.934334i	$0.615996\pi$
$770$	−0.00780494	+	15.6111i	−0.000281271	+	0.562586i
$771$	42.6209	−	22.7814i	1.53496	−	0.820451i
$772$	−0.00610714	+	6.10762i	−0.000219801	+	0.219818i
$773$	−14.8199	−	18.0581i	−0.533036	−	0.649506i	0.434967	−	0.900447i	$-0.356760\pi$
$773$	−14.8199	−	18.0581i	−0.533036	−	0.649506i	−0.968003	+	0.250941i	$0.919260\pi$
$774$	9.21705	+	17.2646i	0.331300	+	0.620565i
$775$	8.71168	−	5.82096i	0.312933	−	0.209095i
$776$	−18.5605	+	18.5049i	−0.666282	+	0.664286i
$777$	−41.8115	+	62.5753i	−1.49998	+	2.24488i
$778$	−40.1305	+	32.9007i	−1.43875	+	1.17955i
$779$	−2.73498	+	0.829646i	−0.0979907	+	0.0297252i
$780$	10.1473	+	19.0300i	0.363331	+	0.681382i
$781$	34.4333	+	28.2587i	1.23212	+	1.01117i
$782$	−10.6569	−	15.9665i	−0.381091	−	0.570961i
$783$	17.3820	+	7.19988i	0.621184	+	0.257303i
$784$	−0.213755	+	0.513146i	−0.00763411	+	0.0183266i
$785$	−6.17473	+	2.55766i	−0.220386	+	0.0912867i
$786$	−61.8903	−	41.3985i	−2.20755	−	1.47664i
$787$	3.12129	+	31.6910i	0.111262	+	1.12966i	0.874996	+	0.484131i	$0.160864\pi$
$787$	3.12129	+	31.6910i	0.111262	+	1.12966i	−0.763734	+	0.645532i	$0.776636\pi$
$788$	2.96668	−	2.42973i	0.105684	−	0.0865557i
$789$	4.01913	−	7.51927i	0.143085	−	0.267693i
$790$	4.01671	+	13.2652i	0.142908	+	0.471954i
$791$	−45.4977	+	9.05005i	−1.61771	+	0.321783i
$792$	−51.3865	−	15.6721i	−1.82594	−	0.556885i
$793$	1.54572	−	7.77085i	0.0548900	−	0.275951i
$794$	3.98863	−	4.85521i	0.141551	−	0.172305i
$795$	3.67210	−	37.2835i	0.130236	−	1.32231i
$796$	−23.8184	−	35.7240i	−0.844219	−	1.26620i
$797$	4.49371	−	14.8138i	0.159175	−	0.524731i	−0.840684	−	0.541527i	$-0.817847\pi$
$797$	4.49371	−	14.8138i	0.159175	−	0.524731i	0.999859	+	0.0167959i	$0.00534655\pi$
$798$	−2.54372	+	6.13240i	−0.0900466	+	0.217085i
$799$	3.78465	+	3.78465i	0.133891	+	0.133891i
$800$	−5.54538	−	1.11746i	−0.196059	−	0.0395083i
$801$	11.6776	−	11.6776i	0.412607	−	0.412607i
$802$	15.6553	+	37.8486i	0.552806	+	1.33648i
$803$	53.1454	+	16.1215i	1.87546	+	0.568915i
$804$	13.7502	+	9.20746i	0.484930	+	0.324722i
$805$	−9.01208	−	0.887612i	−0.317634	−	0.0312842i
$806$	58.0373	−	5.68688i	2.04428	−	0.200312i
$807$	27.5434	+	5.47872i	0.969572	+	0.192860i
$808$	17.2844	+	1.72855i	0.608063	+	0.0608100i
$809$	−9.07499	−	45.6231i	−0.319060	−	1.60402i	−0.724082	−	0.689714i	$-0.757736\pi$
$809$	−9.07499	−	45.6231i	−0.319060	−	1.60402i	0.405022	−	0.914307i	$-0.367264\pi$
$810$	−2.75267	−	1.47310i	−0.0967189	−	0.0517595i
$811$	−7.49643	−	4.00693i	−0.263235	−	0.140702i	0.334500	−	0.942396i	$-0.391433\pi$
$811$	−7.49643	−	4.00693i	−0.263235	−	0.140702i	−0.597735	+	0.801694i	$0.703933\pi$
$812$	6.90616	+	22.8488i	0.242359	+	0.801835i
$813$	−7.99471	+	0.787410i	−0.280387	+	0.0276157i
$814$	12.1621	+	61.3033i	0.426282	+	2.14868i
$815$	5.59359	+	13.5041i	0.195935	+	0.473029i
$816$	−27.3644	+	33.2080i	−0.957947	+	1.16251i
$817$	0.768607	−	1.85558i	0.0268901	−	0.0649186i
$818$	−28.6039	−	5.70454i	−1.00011	−	0.199455i
$819$	29.4753	−	35.9157i	1.02995	−	1.25500i
$820$	−5.55041	+	6.74942i	−0.193829	+	0.235700i
$821$	−3.17304	−	10.4601i	−0.110740	−	0.365061i	0.884001	−	0.467485i	$-0.154840\pi$
$821$	−3.17304	−	10.4601i	−0.110740	−	0.365061i	−0.994741	+	0.102425i	$0.967340\pi$
$822$	−30.1736	−	2.98707i	−1.05242	−	0.104186i
$823$	33.9112	+	22.6587i	1.18207	+	0.789834i	0.981802	−	0.189907i	$-0.0608186\pi$
$823$	33.9112	+	22.6587i	1.18207	+	0.789834i	0.200268	+	0.979741i	$0.435819\pi$
$824$	−28.1018	−	5.63363i	−0.978974	−	0.196257i
$825$	−6.41502	−	9.60076i	−0.223342	−	0.334256i
$826$	−12.9589	−	3.93810i	−0.450896	−	0.137024i
$827$	−26.6357	+	21.8593i	−0.926213	+	0.760123i	−0.971051	−	0.238871i	$-0.923223\pi$
$827$	−26.6357	+	21.8593i	−0.926213	+	0.760123i	0.0448383	+	0.998994i	$0.485723\pi$
$828$	11.9546	−	28.7796i	0.415452	−	1.00016i
$829$	18.2857	+	34.2101i	0.635088	+	1.18817i	0.969350	+	0.245686i	$0.0790131\pi$
$829$	18.2857	+	34.2101i	0.635088	+	1.18817i	−0.334262	+	0.942480i	$0.608487\pi$
$830$	15.0209	−	15.0059i	0.521384	−	0.520863i
$831$		−	10.4218i		−	0.361529i
$832$	−24.2781	−	20.0467i	−0.841691	−	0.694994i
$833$			0.545636i			0.0189052i
$834$	−21.8018	−	21.8236i	−0.754934	−	0.755689i
$835$	−0.262085	−	0.490327i	−0.00906982	−	0.0169684i
$836$	2.10477	+	5.09577i	0.0727951	+	0.176241i
$837$	33.4429	−	27.4459i	1.15596	−	0.948669i
$838$	7.99491	−	26.3083i	0.276179	−	0.908806i
$839$	−26.3146	−	39.3826i	−0.908480	−	1.35964i	−0.932977	−	0.359937i	$-0.882798\pi$
$839$	−26.3146	−	39.3826i	−0.908480	−	1.35964i	0.0244963	−	0.999700i	$-0.492202\pi$
$840$	3.93027	+	19.9149i	0.135607	+	0.687128i
$841$	6.85066	+	4.57746i	0.236230	+	0.157844i
$842$	−3.37327	+	34.0748i	−0.116251	+	1.17429i
$843$	23.9579	+	78.9785i	0.825153	+	2.72017i
$844$	12.9854	−	1.26584i	0.446975	−	0.0435720i
$845$	−1.57900	+	1.92402i	−0.0543194	+	0.0661883i
$846$	−1.69941	+	8.52123i	−0.0584268	+	0.292966i
$847$	6.77637	−	16.3596i	0.232839	−	0.562122i
$848$	15.7721	+	52.3703i	0.541615	+	1.79840i
$849$	7.72194	+	18.6424i	0.265016	+	0.639806i
$850$	−5.44639	+	1.08052i	−0.186810	+	0.0370617i
$851$	−36.0793	+	3.55350i	−1.23678	+	0.121812i
$852$	51.0541	+	27.3547i	1.74908	+	0.937155i
$853$	23.3327	+	12.4716i	0.798897	+	0.427019i	0.819720	−	0.572764i	$-0.194129\pi$
$853$	23.3327	+	12.4716i	0.798897	+	0.427019i	−0.0208236	+	0.999783i	$0.506629\pi$
$854$	3.51872	−	6.57516i	0.120408	−	0.224997i
$855$	−0.575161	−	2.89153i	−0.0196701	−	0.0988882i
$856$	10.4055	+	5.58193i	0.355652	+	0.190787i
$857$	−31.2736	−	6.22070i	−1.06829	−	0.212495i	−0.370522	−	0.928824i	$-0.620821\pi$
$857$	−31.2736	−	6.22070i	−1.06829	−	0.212495i	−0.697763	+	0.716329i	$0.745821\pi$
$858$	−6.26726	−	63.9604i	−0.213961	−	2.18357i
$859$	−39.6534	−	3.90552i	−1.35296	−	0.133255i	−0.604589	−	0.796538i	$-0.706663\pi$
$859$	−39.6534	−	3.90552i	−1.35296	−	0.133255i	−0.748369	+	0.663283i	$0.769163\pi$
$860$	−1.19201	−	6.02412i	−0.0406473	−	0.205421i
$861$	30.0070	+	9.10252i	1.02264	+	0.310213i
$862$	−22.7582	+	9.41344i	−0.775148	+	0.320623i
$863$	−22.4733	+	22.4733i	−0.765001	+	0.765001i	−0.977222	−	0.212221i	$-0.931930\pi$
$863$	−22.4733	+	22.4733i	−0.765001	+	0.765001i	0.212221	+	0.977222i	$0.431930\pi$
$864$	−23.2399	−	2.34760i	−0.790637	−	0.0798671i
$865$	−8.02427	−	8.02427i	−0.272833	−	0.272833i
$866$	9.41546	+	3.90553i	0.319950	+	0.132715i
$867$	1.26034	−	4.15477i	0.0428032	−	0.141103i
$868$	53.8229	+	10.7620i	1.82687	+	0.365286i
$869$	4.04831	−	41.1032i	0.137330	−	1.39433i
$870$	−13.6420	−	11.2071i	−0.462508	−	0.379958i
$871$	−2.31864	+	11.6566i	−0.0785643	+	0.394969i
$872$	−26.1512	+	2.53607i	−0.885591	+	0.0858821i
$873$	−40.9614	+	8.14773i	−1.38633	+	0.275759i
$874$	−3.06093	+	0.926851i	−0.103537	+	0.0313512i
$875$	−1.23476	+	2.31007i	−0.0417424	+	0.0780945i
$876$	71.8592	+	7.15007i	2.42790	+	0.241578i
$877$	5.12607	+	52.0459i	0.173095	+	1.75747i	0.553689	+	0.832723i	$0.313219\pi$
$877$	5.12607	+	52.0459i	0.173095	+	1.75747i	−0.380594	+	0.924742i	$0.624281\pi$
$878$	2.27106	−	3.39520i	0.0766445	−	0.114583i
$879$	13.4771	−	5.58241i	0.454572	−	0.188290i
$880$	13.9975	+	9.39335i	0.471854	+	0.316650i
$881$	14.2241	+	5.89184i	0.479224	+	0.198501i	0.609201	−	0.793016i	$-0.291490\pi$
$881$	14.2241	+	5.89184i	0.479224	+	0.198501i	−0.129977	+	0.991517i	$0.541490\pi$
$882$	−0.736759	+	0.491754i	−0.0248080	+	0.0165582i
$883$	−27.4786	−	22.5511i	−0.924727	−	0.758904i	0.0460370	−	0.998940i	$-0.485341\pi$
$883$	−27.4786	−	22.5511i	−0.924727	−	0.758904i	−0.970764	+	0.240036i	$0.922841\pi$
$884$	−29.5646	−	9.00061i	−0.994364	−	0.302723i
$885$	9.58645	−	2.90802i	0.322245	−	0.0977520i
$886$	−10.0673	−	12.2795i	−0.338216	−	0.412538i
$887$	−27.3412	+	40.9190i	−0.918027	+	1.37392i	0.00941473	+	0.999956i	$0.497003\pi$
$887$	−27.3412	+	40.9190i	−0.918027	+	1.37392i	−0.927441	+	0.373968i	$0.877997\pi$
$888$	30.9864	+	75.1262i	1.03983	+	2.52107i
$889$	13.0268	−	8.70424i	0.436905	−	0.291931i
$890$	−4.57125	+	2.44045i	−0.153229	+	0.0818040i
$891$	5.90212	+	7.19175i	0.197728	+	0.240933i
$892$	−2.72059	+	2.71516i	−0.0910922	+	0.0909102i
$893$	0.786420	−	0.420350i	0.0263165	−	0.0140665i
$894$	79.9648	+	0.0399793i	2.67442	+	0.00133711i
$895$	−10.8925			−0.364095
$896$	−16.3778	−	24.6978i	−0.547143	−	0.825095i
$897$	37.2798			1.24473
$898$	16.4003	+	0.00819948i	0.547284	+	0.000273620i
$899$	−42.1024	+	22.5042i	−1.40419	+	0.750557i
$900$	−6.36756	−	6.38031i	−0.212252	−	0.212677i
$901$	34.0576	+	41.4993i	1.13462	+	1.38254i
$902$	22.9717	−	12.2639i	0.764874	−	0.408342i
$903$	−18.3223	+	12.2426i	−0.609727	+	0.407407i
$904$	−19.2386	+	46.2499i	−0.639868	+	1.53825i
$905$	12.8605	−	19.2470i	0.427496	−	0.639793i
$906$	24.7187	+	30.1506i	0.821224	+	1.00169i
$907$	54.7546	−	16.6096i	1.81810	−	0.551514i	0.818365	−	0.574698i	$-0.194881\pi$
$907$	54.7546	−	16.6096i	1.81810	−	0.551514i	0.999731	+	0.0231847i	$0.00738057\pi$
$908$	13.3478	−	43.8440i	0.442963	−	1.45501i
$909$	21.3968	+	17.5599i	0.709687	+	0.582425i
$910$	−12.1259	+	8.09348i	−0.401968	+	0.268296i
$911$	20.9185	+	8.66471i	0.693060	+	0.287075i	0.701274	−	0.712892i	$-0.252615\pi$
$911$	20.9185	+	8.66471i	0.693060	+	0.287075i	−0.00821472	+	0.999966i	$0.502615\pi$
$912$	3.97093	+	5.96872i	0.131491	+	0.197644i
$913$	−58.4547	+	24.2127i	−1.93457	+	0.801324i
$914$	16.1002	−	24.0695i	0.532546	−	0.796149i
$915$	0.540654	+	5.48935i	0.0178735	+	0.181472i
$916$	−0.427076	+	4.29218i	−0.0141110	+	0.141817i
$917$	23.7275	−	44.3911i	0.783552	−	1.46592i
$918$	−21.9435	+	6.64452i	−0.724244	+	0.219302i
$919$	58.3980	−	11.6161i	1.92637	−	0.383180i	0.926396	−	0.376551i	$-0.122890\pi$
$919$	58.3980	−	11.6161i	1.92637	−	0.383180i	0.999978	−	0.00662819i	$-0.00210984\pi$
$920$	−6.21474	+	7.54956i	−0.204894	+	0.248902i
$921$	5.45957	−	27.4471i	0.179899	−	0.904414i
$922$	−33.8939	−	27.8444i	−1.11624	−	0.917006i
$923$	−4.07739	+	41.3984i	−0.134209	+	1.36265i
$924$	11.8603	−	59.3159i	0.390177	−	1.95135i
$925$	−3.04405	+	10.0349i	−0.100088	+	0.329945i
$926$	8.58280	+	3.56014i	0.282048	+	0.116993i
$927$	−32.2941	−	32.2941i	−1.06068	−	1.06068i
$928$	24.6463	+	7.54369i	0.809053	+	0.247634i
$929$	−8.56044	+	8.56044i	−0.280859	+	0.280859i	−0.833452	−	0.552593i	$-0.813639\pi$
$929$	−8.56044	+	8.56044i	−0.280859	+	0.280859i	0.552593	+	0.833452i	$0.313639\pi$
$930$	−37.5155	+	15.5174i	−1.23018	+	0.508837i
$931$	0.0869905	+	0.0263883i	0.00285100	+	0.000864841i
$932$	−31.6879	+	6.27019i	−1.03797	+	0.205387i
$933$	27.1522	+	2.67426i	0.888924	+	0.0875513i
$934$	2.54438	+	25.9666i	0.0832547	+	0.849654i
$935$	16.2284	+	3.22803i	0.530725	+	0.105568i
$936$	−14.4917	−	48.0321i	−0.473677	−	1.56998i
$937$	1.27512	+	6.41045i	0.0416563	+	0.209420i	0.996008	−	0.0892652i	$-0.0284519\pi$
$937$	1.27512	+	6.41045i	0.0416563	+	0.209420i	−0.954352	+	0.298685i	$0.903452\pi$
$938$	−5.27824	+	9.86302i	−0.172341	+	0.322039i
$939$	80.7756	+	43.1755i	2.63601	+	1.40898i
$940$	1.28763	−	2.40321i	0.0419979	−	0.0783840i
$941$	−30.3945	+	2.99359i	−0.990831	+	0.0975884i	−0.580424	−	0.814314i	$-0.697113\pi$
$941$	−30.3945	+	2.99359i	−0.990831	+	0.0975884i	−0.410407	+	0.911902i	$0.634613\pi$
$942$	25.4021	−	5.03959i	0.827645	−	0.164199i
$943$	5.78062	+	13.9556i	0.188243	+	0.454458i
$944$	−11.3239	+	9.25542i	−0.368561	+	0.301238i
$945$	−4.13902	+	9.99249i	−0.134642	+	0.325056i
$946$	−3.57906	+	17.9463i	−0.116365	+	0.583483i
$947$	−28.0355	+	34.1613i	−0.911030	+	1.11009i	0.0825078	+	0.996590i	$0.473707\pi$
$947$	−28.0355	+	34.1613i	−0.911030	+	1.11009i	−0.993538	+	0.113503i	$0.963793\pi$
$948$	−5.21054	−	53.4513i	−0.169230	−	1.73602i
$949$	15.0554	+	49.6310i	0.488719	+	1.61109i
$950$	−0.0911332	+	0.920573i	−0.00295675	+	0.0298673i
$951$	−64.1605	−	42.8707i	−2.08055	−	1.39018i
$952$	−24.1617	−	16.1968i	−0.783084	−	0.524941i
$953$	33.5893	+	50.2699i	1.08806	+	1.62840i	0.712607	+	0.701563i	$0.247514\pi$
$953$	33.5893	+	50.2699i	1.08806	+	1.62840i	0.375457	+	0.926840i	$0.377486\pi$
$954$	−25.3411	+	83.3882i	−0.820448	+	2.69979i
$955$	−15.8399	+	12.9994i	−0.512566	+	0.420652i
$956$	−34.4055	+	14.2109i	−1.11275	+	0.459615i
$957$	24.8009	+	46.3993i	0.801700	+	1.49987i
$958$	−20.7574	−	20.7782i	−0.670641	−	0.671312i
$959$		−	20.4970i		−	0.661882i
$960$	20.2255	+	8.44883i	0.652774	+	0.272685i
$961$			78.7768i			2.54119i
$962$	−41.2910	+	41.2498i	−1.33128	+	1.32995i
$963$	8.86985	+	16.5943i	0.285827	+	0.534744i
$964$	12.7900	+	5.31278i	0.411938	+	0.171113i
$965$	2.36063	−	1.93732i	0.0759913	−	0.0623644i
$966$	33.5730	+	10.2026i	1.08019	+	0.328263i
$967$	−8.42620	−	12.6107i	−0.270968	−	0.405533i	0.670883	−	0.741564i	$-0.265915\pi$
$967$	−8.42620	−	12.6107i	−0.270968	−	0.405533i	−0.941851	+	0.336031i	$0.890915\pi$
$968$	−10.5991	−	15.9143i	−0.340669	−	0.511506i
$969$	5.85085	+	3.90941i	0.187956	+	0.125588i
$970$	13.0408	+	1.29099i	0.418716	+	0.0414513i
$971$	4.11646	+	13.5701i	0.132103	+	0.435487i	0.997890	−	0.0649268i	$-0.0206814\pi$
$971$	4.11646	+	13.5701i	0.132103	+	0.435487i	−0.865787	+	0.500413i	$0.833181\pi$
$972$	28.4794	+	23.4201i	0.913476	+	0.751200i
$973$	13.2290	−	16.1196i	0.424103	−	0.516771i
$974$	−5.43397	−	1.08371i	−0.174116	−	0.0347242i
$975$	4.12654	−	9.96235i	0.132155	−	0.319051i
$976$	−3.78182	−	7.10945i	−0.121053	−	0.227568i
$977$	−23.3558	−	56.3860i	−0.747219	−	1.80395i	−0.573604	−	0.819133i	$-0.694455\pi$
$977$	−23.3558	−	56.3860i	−0.747219	−	1.80395i	−0.173615	−	0.984814i	$-0.555545\pi$
$978$	−11.0216	−	55.5543i	−0.352431	−	1.77643i
$979$	15.3675	−	1.51357i	0.491147	−	0.0483738i
$980$	0.266056	−	0.0804167i	0.00849883	−	0.00256882i
$981$	−36.9234	−	19.7360i	−1.17887	−	0.630121i
$982$	12.1940	+	6.52566i	0.389126	+	0.208242i
$983$	5.38299	+	27.0621i	0.171691	+	0.863148i	0.966574	+	0.256386i	$0.0825319\pi$
$983$	5.38299	+	27.0621i	0.171691	+	0.863148i	−0.794884	+	0.606762i	$0.792468\pi$
$984$	26.2064	−	21.4413i	0.835429	−	0.683524i
$985$	−1.88050	−	0.374055i	−0.0599178	−	0.0119184i
$986$	25.1790	−	2.46721i	0.801864	−	0.0785719i
$987$	−9.73637	−	0.958949i	−0.309912	−	0.0305237i
$988$	−2.86478	+	4.27817i	−0.0911406	+	0.136107i
$989$	−10.1582	−	3.08145i	−0.323011	−	0.0979843i
$990$	10.2671	+	24.8220i	0.326310	+	0.788896i
$991$	3.44044	−	3.44044i	0.109289	−	0.109289i	−0.650348	−	0.759637i	$-0.725377\pi$
$991$	3.44044	−	3.44044i	0.109289	−	0.109289i	0.759637	+	0.650348i	$0.225377\pi$
$992$	42.0144	−	41.8049i	1.33396	−	1.32731i
$993$	57.5322	+	57.5322i	1.82573	+	1.82573i
$994$	−15.0017	+	36.1662i	−0.475826	+	1.14712i
$995$	−6.23186	+	20.5437i	−0.197563	+	0.651278i
$996$	−68.4511	+	45.6386i	−2.16896	+	1.44612i
$997$	2.87974	−	29.2385i	0.0912022	−	0.925991i	−0.835323	−	0.549759i	$-0.814720\pi$
$997$	2.87974	−	29.2385i	0.0912022	−	0.925991i	0.926525	−	0.376232i	$-0.122780\pi$
$998$	34.5446	−	42.0498i	1.09349	−	1.33106i
$999$	−8.44747	+	42.4683i	−0.267266	+	1.34364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.32	✓	1024
128.109	even	32	inner	640.2.bm.a.621.32	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.32	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.32	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+(-0.000707051 + 1.41421i) q^{2} +(-2.41638 + 1.29158i) q^{3} +(-2.00000 - 0.00199984i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-1.82486 - 3.41819i) q^{6} +(2.17792 - 1.45524i) q^{7} +(0.00424230 - 2.82842i) q^{8} +(2.50399 - 3.74748i) q^{9} +(-1.09365 + 0.896621i) q^{10} +(4.03282 - 1.22334i) q^{11} +(4.83533 - 2.57833i) q^{12} +(3.04226 + 2.49672i) q^{13} +(2.05648 + 3.08107i) q^{14} +(-2.53134 - 1.04851i) q^{15} +(3.99999 + 0.00799936i) q^{16} +(3.62737 - 1.50251i) q^{17} +(5.29796 + 3.54382i) q^{18} +(-0.0641155 - 0.650975i) q^{19} +(-1.26724 - 1.54729i) q^{20} +(-3.38311 + 6.32935i) q^{21} +(1.72722 + 5.70414i) q^{22} +(-3.39079 + 0.674470i) q^{23} +(3.64289 + 6.84002i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-3.53305 + 4.30065i) q^{26} +(-0.404730 + 4.10930i) q^{27} +(-4.35874 + 2.90612i) q^{28} +(1.32265 - 4.36020i) q^{29} +(1.48461 - 3.57911i) q^{30} +(-7.40867 - 7.40867i) q^{31} +(-0.0141410 + 5.65684i) q^{32} +(-8.16478 + 8.16478i) q^{33} +(2.12230 + 5.13094i) q^{34} +(2.50657 + 0.760359i) q^{35} +(-5.01546 + 7.48995i) q^{36} +(10.4359 + 1.02785i) q^{37} +(0.920663 - 0.0902127i) q^{38} +(-10.5760 - 2.10369i) q^{39} +(2.18909 - 1.79105i) q^{40} +(-0.852401 - 4.28531i) q^{41} +(-8.94866 - 4.78891i) q^{42} +(2.70791 + 1.44741i) q^{43} +(-8.06809 + 2.43862i) q^{44} +(4.48535 - 0.441769i) q^{45} +(-0.951446 - 4.79577i) q^{46} +(0.521679 + 1.25945i) q^{47} +(-9.67582 + 5.14698i) q^{48} +(-0.0531821 + 0.128393i) q^{49} +(-1.38690 - 0.276593i) q^{50} +(-6.82449 + 8.31567i) q^{51} +(-6.07953 - 4.99953i) q^{52} +(3.96919 + 13.0847i) q^{53} +(-5.81114 - 0.575281i) q^{54} +(3.50405 + 2.34133i) q^{55} +(-4.10679 - 6.16624i) q^{56} +(0.995714 + 1.49019i) q^{57} +(6.16532 + 1.87360i) q^{58} +(-2.82633 + 2.31951i) q^{59} +(5.06058 + 2.10209i) q^{60} +(-0.949007 - 1.77547i) q^{61} +(10.4827 - 10.4722i) q^{62} -11.8056i q^{63} +(-7.99996 - 0.0239981i) q^{64} +3.93561i q^{65} +(-11.5410 - 11.5525i) q^{66} +(1.42355 + 2.66328i) q^{67} +(-7.25775 + 2.99776i) q^{68} +(7.32229 - 6.00925i) q^{69} +(-1.07708 + 3.54428i) q^{70} +(5.87229 + 8.78850i) q^{71} +(-10.5888 - 7.09823i) q^{72} +(10.9573 + 7.32143i) q^{73} +(-1.46098 + 14.7579i) q^{74} +(-0.795351 - 2.62192i) q^{75} +(0.126929 + 1.30208i) q^{76} +(7.00290 - 8.53305i) q^{77} +(2.98255 - 14.9552i) q^{78} +(3.75048 - 9.05447i) q^{79} +(2.53138 + 3.09711i) q^{80} +(0.844821 + 2.03958i) q^{81} +(6.06094 - 1.20245i) q^{82} +(-14.9411 + 1.47157i) q^{83} +(6.77887 - 12.6519i) q^{84} +(3.46264 + 1.85082i) q^{85} +(-2.04886 + 3.82853i) q^{86} +(2.43552 + 12.2442i) q^{87} +(-3.44303 - 11.4117i) q^{88} +(3.59376 + 0.714842i) q^{89} +(0.621584 + 6.34356i) q^{90} +(10.2591 + 1.01043i) q^{91} +(6.78292 - 1.34216i) q^{92} +(27.4710 + 8.33325i) q^{93} +(-1.78149 + 0.736875i) q^{94} +(0.462536 - 0.462536i) q^{95} +(-7.27209 - 13.6873i) q^{96} +(-6.55229 - 6.55229i) q^{97} +(-0.181538 - 0.0753017i) q^{98} +(5.51368 - 18.1762i) 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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