LMFDB - Embedded newform 820.2.j.c.483.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(483,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.483"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			483.19
Character	$\chi$	$=$	820.483
Dual form			820.2.j.c.747.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23475 + 0.689491i) q^{2} +2.13292i q^{3} +(1.04921 - 1.70269i) q^{4} +(1.66560 - 1.49190i) q^{5} +(-1.47063 - 2.63362i) q^{6} +3.79559 q^{7} +(-0.121513 + 2.82582i) q^{8} -1.54935 q^{9} +(-1.02794 + 2.99054i) q^{10} +(-1.18738 - 1.18738i) q^{11} +(3.63171 + 2.23787i) q^{12} -5.25705 q^{13} +(-4.68660 + 2.61703i) q^{14} +(3.18211 + 3.55260i) q^{15} +(-1.79834 - 3.57295i) q^{16} +6.80287 q^{17} +(1.91306 - 1.06826i) q^{18} +(0.539583 + 0.539583i) q^{19} +(-0.792697 - 4.40132i) q^{20} +8.09570i q^{21} +(2.28480 + 0.647426i) q^{22} +(2.86694 - 2.86694i) q^{23} +(-6.02724 - 0.259177i) q^{24} +(0.548453 - 4.96983i) q^{25} +(6.49114 - 3.62469i) q^{26} +3.09412i q^{27} +(3.98236 - 6.46273i) q^{28} +(0.631885 + 0.631885i) q^{29} +(-6.37859 - 2.19252i) q^{30} +6.03484i q^{31} +(4.68401 + 3.17176i) q^{32} +(2.53258 - 2.53258i) q^{33} +(-8.39983 + 4.69052i) q^{34} +(6.32194 - 5.66266i) q^{35} +(-1.62559 + 2.63807i) q^{36} +(6.56359 - 6.56359i) q^{37} +(-1.03829 - 0.294211i) q^{38} -11.2129i q^{39} +(4.01345 + 4.88797i) q^{40} +(-1.60372 - 6.19904i) q^{41} +(-5.58191 - 9.99615i) q^{42} +(6.88851 + 6.88851i) q^{43} +(-3.26754 + 0.775937i) q^{44} +(-2.58060 + 2.31148i) q^{45} +(-1.56322 + 5.51668i) q^{46} -6.94756i q^{47} +(7.62083 - 3.83571i) q^{48} +7.40653 q^{49} +(2.74945 + 6.51464i) q^{50} +14.5100i q^{51} +(-5.51573 + 8.95115i) q^{52} -1.29473 q^{53} +(-2.13336 - 3.82046i) q^{54} +(-3.74915 - 0.206245i) q^{55} +(-0.461213 + 10.7256i) q^{56} +(-1.15089 + 1.15089i) q^{57} +(-1.21590 - 0.344540i) q^{58} -3.32033 q^{59} +(9.38767 - 1.69076i) q^{60} +9.00272i q^{61} +(-4.16096 - 7.45150i) q^{62} -5.88071 q^{63} +(-7.97047 - 0.686746i) q^{64} +(-8.75615 + 7.84301i) q^{65} +(-1.38091 + 4.87329i) q^{66} +13.9012i q^{67} +(7.13761 - 11.5832i) q^{68} +(6.11496 + 6.11496i) q^{69} +(-3.90166 + 11.3509i) q^{70} +(-4.57139 - 4.57139i) q^{71} +(0.188266 - 4.37818i) q^{72} +(-2.83212 + 2.83212i) q^{73} +(-3.57885 + 12.6299i) q^{74} +(10.6003 + 1.16981i) q^{75} +(1.48488 - 0.352611i) q^{76} +(-4.50680 - 4.50680i) q^{77} +(7.73117 + 13.8451i) q^{78} +(3.21799 - 3.21799i) q^{79} +(-8.32581 - 3.26817i) q^{80} -11.2476 q^{81} +(6.25436 + 6.54851i) q^{82} +(-3.90777 + 3.90777i) q^{83} +(13.7845 + 8.49405i) q^{84} +(11.3309 - 10.1492i) q^{85} +(-13.2551 - 3.75601i) q^{86} +(-1.34776 + 1.34776i) q^{87} +(3.49959 - 3.21103i) q^{88} +(1.76118 + 1.76118i) q^{89} +(1.59265 - 4.63340i) q^{90} -19.9536 q^{91} +(-1.87351 - 7.88953i) q^{92} -12.8718 q^{93} +(4.79027 + 8.57848i) q^{94} +(1.70373 + 0.0937245i) q^{95} +(-6.76511 + 9.99062i) q^{96} -13.6640 q^{97} +(-9.14520 + 5.10673i) q^{98} +(1.83966 + 1.83966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.23475	+	0.689491i	−0.873099	+	0.487543i
$2$	−1.23475	+	0.689491i	−0.873099	+	0.487543i
$3$			2.13292i			1.23144i	0.787964	+	0.615721i	$0.211135\pi$
$3$			2.13292i			1.23144i	−0.787964	+	0.615721i	$0.788865\pi$
$4$	1.04921	−	1.70269i	0.524603	−	0.851347i
$5$	1.66560	−	1.49190i	0.744879	−	0.667199i
$5$	1.66560	−	1.49190i	0.744879	−	0.667199i
$6$	−1.47063	−	2.63362i	−0.600382	−	1.07517i
$7$	3.79559			1.43460			0.717300	−	0.696765i	$-0.245378\pi$
$7$	3.79559			1.43460			0.717300	+	0.696765i	$0.245378\pi$
$8$	−0.121513	+	2.82582i	−0.0429613	+	0.999077i
$9$	−1.54935			−0.516451
$10$	−1.02794	+	2.99054i	−0.325065	+	0.945692i
$11$	−1.18738	−	1.18738i	−0.358008	−	0.358008i	0.505071	−	0.863078i	$-0.331466\pi$
$11$	−1.18738	−	1.18738i	−0.358008	−	0.358008i	−0.863078	+	0.505071i	$0.831466\pi$
$12$	3.63171	+	2.23787i	1.04839	+	0.646018i
$13$	−5.25705			−1.45804			−0.729022	−	0.684490i	$-0.760025\pi$
$13$	−5.25705			−1.45804			−0.729022	+	0.684490i	$0.760025\pi$
$14$	−4.68660	+	2.61703i	−1.25255	+	0.699430i
$15$	3.18211	+	3.55260i	0.821617	+	0.917276i
$16$	−1.79834	−	3.57295i	−0.449584	−	0.893238i
$17$	6.80287			1.64994			0.824969	−	0.565177i	$-0.191192\pi$
$17$	6.80287			1.64994			0.824969	+	0.565177i	$0.191192\pi$
$18$	1.91306	−	1.06826i	0.450912	−	0.251792i
$19$	0.539583	+	0.539583i	0.123789	+	0.123789i	0.766287	−	0.642498i	$-0.222102\pi$
$19$	0.539583	+	0.539583i	0.123789	+	0.123789i	−0.642498	+	0.766287i	$0.722102\pi$
$20$	−0.792697	−	4.40132i	−0.177252	−	0.984165i
$21$			8.09570i			1.76663i
$22$	2.28480	+	0.647426i	0.487120	+	0.138032i
$23$	2.86694	−	2.86694i	0.597799	−	0.597799i	−0.341928	−	0.939726i	$-0.611080\pi$
$23$	2.86694	−	2.86694i	0.597799	−	0.597799i	0.939726	+	0.341928i	$0.111080\pi$
$24$	−6.02724	−	0.259177i	−1.23031	−	0.0529043i
$25$	0.548453	−	4.96983i	0.109691	−	0.993966i
$26$	6.49114	−	3.62469i	1.27302	−	0.710860i
$27$			3.09412i			0.595463i
$28$	3.98236	−	6.46273i	0.752595	−	1.22134i
$29$	0.631885	+	0.631885i	0.117338	+	0.117338i	0.763338	−	0.646000i	$-0.223559\pi$
$29$	0.631885	+	0.631885i	0.117338	+	0.117338i	−0.646000	+	0.763338i	$0.723559\pi$
$30$	−6.37859	−	2.19252i	−1.16457	−	0.400298i
$31$			6.03484i			1.08389i	0.840414	+	0.541944i	$0.182312\pi$
$31$			6.03484i			1.08389i	−0.840414	+	0.541944i	$0.817688\pi$
$32$	4.68401	+	3.17176i	0.828024	+	0.560693i
$33$	2.53258	−	2.53258i	0.440866	−	0.440866i
$34$	−8.39983	+	4.69052i	−1.44056	+	0.804417i
$35$	6.32194	−	5.66266i	1.06860	−	0.957164i
$36$	−1.62559	+	2.63807i	−0.270931	+	0.439679i
$37$	6.56359	−	6.56359i	1.07905	−	1.07905i	0.0824524	−	0.996595i	$-0.473725\pi$
$37$	6.56359	−	6.56359i	1.07905	−	1.07905i	0.996595	−	0.0824524i	$-0.0262752\pi$
$38$	−1.03829	−	0.294211i	−0.168432	−	0.0477274i
$39$		−	11.2129i		−	1.79550i
$40$	4.01345	+	4.88797i	0.634582	+	0.772855i
$41$	−1.60372	−	6.19904i	−0.250458	−	0.968127i
$41$	−1.60372	−	6.19904i	−0.250458	−	0.968127i
$42$	−5.58191	−	9.99615i	−0.861307	−	1.54244i
$43$	6.88851	+	6.88851i	1.05049	+	1.05049i	0.998656	+	0.0518314i	$0.0165058\pi$
$43$	6.88851	+	6.88851i	1.05049	+	1.05049i	0.0518314	+	0.998656i	$0.483494\pi$
$44$	−3.26754	+	0.775937i	−0.492600	+	0.116977i
$45$	−2.58060	+	2.31148i	−0.384693	+	0.344575i
$46$	−1.56322	+	5.51668i	−0.230484	+	0.813390i
$47$		−	6.94756i		−	1.01341i	−0.862121	−	0.506703i	$-0.830864\pi$
$47$		−	6.94756i		−	1.01341i	0.862121	−	0.506703i	$-0.169136\pi$
$48$	7.62083	−	3.83571i	1.09997	−	0.553637i
$49$	7.40653			1.05808
$50$	2.74945	+	6.51464i	0.388831	+	0.921309i
$51$			14.5100i			2.03180i
$52$	−5.51573	+	8.95115i	−0.764894	+	1.24130i
$53$	−1.29473			−0.177844			−0.0889221	−	0.996039i	$-0.528342\pi$
$53$	−1.29473			−0.177844			−0.0889221	+	0.996039i	$0.528342\pi$
$54$	−2.13336	−	3.82046i	−0.290314	−	0.519898i
$55$	−3.74915	−	0.206245i	−0.505535	−	0.0278101i
$56$	−0.461213	+	10.7256i	−0.0616322	+	1.43327i
$57$	−1.15089	+	1.15089i	−0.152439	+	0.152439i
$58$	−1.21590	−	0.344540i	−0.159655	−	0.0452403i
$59$	−3.32033			−0.432270			−0.216135	−	0.976363i	$-0.569345\pi$
$59$	−3.32033			−0.432270			−0.216135	+	0.976363i	$0.569345\pi$
$60$	9.38767	−	1.69076i	1.21194	−	0.218276i
$61$			9.00272i			1.15268i	0.817210	+	0.576340i	$0.195520\pi$
$61$			9.00272i			1.15268i	−0.817210	+	0.576340i	$0.804480\pi$
$62$	−4.16096	−	7.45150i	−0.528443	−	0.946342i
$63$	−5.88071			−0.740900
$64$	−7.97047	−	0.686746i	−0.996309	−	0.0858432i
$65$	−8.75615	+	7.84301i	−1.08607	+	0.972806i
$66$	−1.38091	+	4.87329i	−0.169978	+	0.599860i
$67$			13.9012i			1.69831i	0.528146	+	0.849154i	$0.322887\pi$
$67$			13.9012i			1.69831i	−0.528146	+	0.849154i	$0.677113\pi$
$68$	7.13761	−	11.5832i	0.865562	−	1.40467i
$69$	6.11496	+	6.11496i	0.736154	+	0.736154i
$70$	−3.90166	+	11.3509i	−0.466337	+	1.35669i
$71$	−4.57139	−	4.57139i	−0.542524	−	0.542524i	0.381744	−	0.924268i	$-0.375324\pi$
$71$	−4.57139	−	4.57139i	−0.542524	−	0.542524i	−0.924268	+	0.381744i	$0.875324\pi$
$72$	0.188266	−	4.37818i	0.0221874	−	0.515974i
$73$	−2.83212	+	2.83212i	−0.331475	+	0.331475i	−0.853146	−	0.521672i	$-0.825309\pi$
$73$	−2.83212	+	2.83212i	−0.331475	+	0.331475i	0.521672	+	0.853146i	$0.325309\pi$
$74$	−3.57885	+	12.6299i	−0.416032	+	1.46820i
$75$	10.6003	+	1.16981i	1.22401	+	0.135078i
$76$	1.48488	−	0.352611i	0.170327	−	0.0404473i
$77$	−4.50680	−	4.50680i	−0.513597	−	0.513597i
$78$	7.73117	+	13.8451i	0.875383	+	1.56765i
$79$	3.21799	−	3.21799i	0.362052	−	0.362052i	−0.502516	−	0.864568i	$-0.667592\pi$
$79$	3.21799	−	3.21799i	0.362052	−	0.362052i	0.864568	+	0.502516i	$0.167592\pi$
$80$	−8.32581	−	3.26817i	−0.930853	−	0.365393i
$81$	−11.2476			−1.24973
$82$	6.25436	+	6.54851i	0.690679	+	0.723162i
$83$	−3.90777	+	3.90777i	−0.428933	+	0.428933i	−0.888265	−	0.459332i	$-0.848089\pi$
$83$	−3.90777	+	3.90777i	−0.428933	+	0.428933i	0.459332	+	0.888265i	$0.348089\pi$
$84$	13.7845	+	8.49405i	1.50401	+	0.926777i
$85$	11.3309	−	10.1492i	1.22901	−	1.10084i
$86$	−13.2551	−	3.75601i	−1.42934	−	0.405021i
$87$	−1.34776	+	1.34776i	−0.144495	+	0.144495i
$88$	3.49959	−	3.21103i	0.373057	−	0.342297i
$89$	1.76118	+	1.76118i	0.186684	+	0.186684i	0.794261	−	0.607577i	$-0.207858\pi$
$89$	1.76118	+	1.76118i	0.186684	+	0.186684i	−0.607577	+	0.794261i	$0.707858\pi$
$90$	1.59265	−	4.63340i	0.167880	−	0.488403i
$91$	−19.9536			−2.09171
$92$	−1.87351	−	7.88953i	−0.195327	−	0.822541i
$93$	−12.8718			−1.33475
$94$	4.79027	+	8.57848i	0.494079	+	0.884803i
$95$	1.70373	+	0.0937245i	0.174799	+	0.00961593i
$96$	−6.76511	+	9.99062i	−0.690462	+	1.01966i
$97$	−13.6640			−1.38737			−0.693686	−	0.720278i	$-0.744014\pi$
$97$	−13.6640			−1.38737			−0.693686	+	0.720278i	$0.744014\pi$
$98$	−9.14520	+	5.10673i	−0.923804	+	0.515858i
$99$	1.83966	+	1.83966i	0.184893	+	0.184893i
$100$	−7.88666	−	6.14822i	−0.788666	−	0.614822i
$101$	11.8444	+	11.8444i	1.17856	+	1.17856i	0.980111	+	0.198452i	$0.0635914\pi$
$101$	11.8444	+	11.8444i	1.17856	+	1.17856i	0.198452	+	0.980111i	$0.436409\pi$
$102$	−10.0045	−	17.9162i	−0.990593	−	1.77397i
$103$	6.27427	+	6.27427i	0.618222	+	0.618222i	0.945075	−	0.326853i	$-0.105988\pi$
$103$	6.27427	+	6.27427i	0.618222	+	0.618222i	−0.326853	+	0.945075i	$0.605988\pi$
$104$	0.638799	−	14.8555i	0.0626394	−	1.45670i
$105$	12.0780	+	13.4842i	1.17869	+	1.31592i
$106$	1.59866	−	0.892701i	0.155276	−	0.0867068i
$107$	−11.2921	−	11.2921i	−1.09165	−	1.09165i	−0.995353	−	0.0962926i	$-0.969302\pi$
$107$	−11.2921	−	11.2921i	−1.09165	−	1.09165i	−0.0962926	−	0.995353i	$-0.530698\pi$
$108$	5.26834	+	3.24637i	0.506946	+	0.312382i
$109$	−6.65133	+	6.65133i	−0.637082	+	0.637082i	−0.949835	−	0.312753i	$-0.898749\pi$
$109$	−6.65133	+	6.65133i	−0.637082	+	0.637082i	0.312753	+	0.949835i	$0.398749\pi$
$110$	4.77145	−	2.33034i	0.454940	−	0.222189i
$111$	13.9996	+	13.9996i	1.32878	+	1.32878i
$112$	−6.82575	−	13.5615i	−0.644973	−	1.28144i
$113$	−7.82171	−	7.82171i	−0.735805	−	0.735805i	0.235958	−	0.971763i	$-0.424177\pi$
$113$	−7.82171	−	7.82171i	−0.735805	−	0.735805i	−0.971763	+	0.235958i	$0.924177\pi$
$114$	0.627530	−	2.21458i	0.0587736	−	0.207415i
$115$	0.497982	−	9.05238i	0.0464371	−	0.844138i
$116$	1.73888	−	0.412930i	0.161451	−	0.0383396i
$117$	8.14503			0.753008
$118$	4.09977	−	2.28934i	0.377414	−	0.210750i
$119$	25.8209			2.36700
$120$	−10.4256	+	8.56037i	−0.951727	+	0.781452i
$121$		−	8.18027i		−	0.743661i
$122$	−6.20729	−	11.1161i	−0.561982	−	1.00640i
$123$	13.2221	−	3.42060i	1.19219	−	0.308425i
$124$	10.2755	+	6.33178i	0.922766	+	0.568611i
$125$	−6.50100	−	9.09599i	−0.581467	−	0.813570i
$126$	7.26120	−	4.05469i	0.646879	−	0.361221i
$127$	11.7119	+	11.7119i	1.03926	+	1.03926i	0.999197	+	0.0400669i	$0.0127571\pi$
$127$	11.7119	+	11.7119i	1.03926	+	1.03926i	0.0400669	+	0.999197i	$0.487243\pi$
$128$	10.3150	−	4.64761i	0.911728	−	0.410794i
$129$	−14.6926	+	14.6926i	−1.29361	+	1.29361i
$130$	5.40396	−	15.7214i	0.473959	−	1.37886i
$131$	0.293595			0.0256515			0.0128258	−	0.999918i	$-0.495917\pi$
$131$	0.293595			0.0256515			0.0128258	+	0.999918i	$0.495917\pi$
$132$	−1.65501	−	6.96941i	−0.144050	−	0.606609i
$133$	2.04804	+	2.04804i	0.177587	+	0.177587i
$134$	−9.58478	−	17.1645i	−0.827999	−	1.48279i
$135$	4.61612	+	5.15356i	0.397293	+	0.443548i
$136$	−0.826636	+	19.2237i	−0.0708835	+	1.64842i
$137$	11.3525			0.969909			0.484955	−	0.874539i	$-0.338836\pi$
$137$	11.3525			0.969909			0.484955	+	0.874539i	$0.338836\pi$
$138$	−11.7666	−	3.33423i	−1.00164	−	0.283828i
$139$	−19.7558			−1.67567			−0.837833	−	0.545927i	$-0.816178\pi$
$139$	−19.7558			−1.67567			−0.837833	+	0.545927i	$0.816178\pi$
$140$	−3.00875	−	16.7056i	−0.254286	−	1.41188i
$141$	14.8186			1.24795
$142$	8.79644	+	2.49258i	0.738181	+	0.209173i
$143$	6.24210	+	6.24210i	0.521991	+	0.521991i
$144$	2.78625	+	5.53576i	0.232188	+	0.461313i
$145$	1.99518	+	0.109757i	0.165691	+	0.00911485i
$146$	1.54424	−	5.44968i	0.127802	−	0.451019i
$147$			15.7975i			1.30296i
$148$	−4.28923	−	18.0623i	−0.352573	−	1.48472i
$149$	11.4030	−	11.4030i	0.934171	−	0.934171i	−0.0637922	−	0.997963i	$-0.520319\pi$
$149$	11.4030	−	11.4030i	0.934171	−	0.934171i	0.997963	+	0.0637922i	$0.0203195\pi$
$150$	−13.8952	+	5.86436i	−1.13454	+	0.478823i
$151$	−6.73143	−	6.73143i	−0.547796	−	0.547796i	0.378007	−	0.925803i	$-0.376610\pi$
$151$	−6.73143	−	6.73143i	−0.547796	−	0.547796i	−0.925803	+	0.378007i	$0.876610\pi$
$152$	−1.59033	+	1.45919i	−0.128993	+	0.118356i
$153$	−10.5400			−0.852112
$154$	8.67216	+	2.45737i	0.698822	+	0.198020i
$155$	9.00339	+	10.0516i	0.723170	+	0.807366i
$156$	−19.0921	−	11.7646i	−1.52859	−	0.941923i
$157$		−	2.78990i		−	0.222658i	−0.993784	−	0.111329i	$-0.964489\pi$
$157$		−	2.78990i		−	0.222658i	0.993784	−	0.111329i	$-0.0355108\pi$
$158$	−1.75463	+	6.19218i	−0.139591	+	0.492623i
$159$		−	2.76155i		−	0.219005i
$160$	12.5336	−	1.70520i	0.990872	−	0.134808i
$161$	10.8817	−	10.8817i	0.857601	−	0.857601i
$162$	13.8879	−	7.75509i	1.09114	−	0.609297i
$163$	−1.35473	+	1.35473i	−0.106111	+	0.106111i	−0.758169	−	0.652058i	$-0.773906\pi$
$163$	−1.35473	+	1.35473i	−0.106111	+	0.106111i	0.652058	+	0.758169i	$0.273906\pi$
$164$	−12.2377	−	3.77343i	−0.955604	−	0.294655i
$165$	0.439905	−	7.99663i	0.0342465	−	0.622537i
$166$	2.13074	−	7.51948i	0.165377	−	0.583624i
$167$	−6.83522			−0.528925			−0.264462	−	0.964396i	$-0.585195\pi$
$167$	−6.83522			−0.528925			−0.264462	+	0.964396i	$0.585195\pi$
$168$	−22.8770	−	0.983731i	−1.76500	−	0.0758965i
$169$	14.6366			1.12589
$170$	−6.99298	+	20.3443i	−0.536337	+	1.56033i
$171$	−0.836003	−	0.836003i	−0.0639308	−	0.0639308i
$172$	18.9565	−	4.50156i	1.44542	−	0.343241i
$173$	12.0418	−	12.0418i	0.915518	−	0.915518i	−0.0811817	−	0.996699i	$-0.525869\pi$
$173$	12.0418	−	12.0418i	0.915518	−	0.915518i	0.996699	+	0.0811817i	$0.0258694\pi$
$174$	0.734877	−	2.59341i	0.0557109	−	0.196606i
$175$	2.08170	−	18.8634i	0.157362	−	1.42594i
$176$	−2.10714	+	6.37774i	−0.158832	+	0.480740i
$177$		−	7.08200i		−	0.532316i
$178$	−3.38892	−	0.960295i	−0.254011	−	0.0719771i
$179$	2.36638	+	2.36638i	0.176872	+	0.176872i	0.789991	−	0.613119i	$-0.210085\pi$
$179$	2.36638	+	2.36638i	0.176872	+	0.176872i	−0.613119	+	0.789991i	$0.710085\pi$
$180$	1.22817	+	6.81920i	0.0915421	+	0.508273i
$181$	−5.80793	−	5.80793i	−0.431700	−	0.431700i	0.457506	−	0.889206i	$-0.348743\pi$
$181$	−5.80793	−	5.80793i	−0.431700	−	0.431700i	−0.889206	+	0.457506i	$0.848743\pi$
$182$	24.6377	−	13.7578i	1.82627	−	1.01980i
$183$	−19.2021			−1.41946
$184$	7.75308	+	8.44982i	0.571564	+	0.622929i
$185$	1.14008	−	20.7246i	0.0838206	−	1.52370i
$186$	15.8935	−	8.87501i	1.16537	−	0.650747i
$187$	−8.07757	−	8.07757i	−0.590691	−	0.590691i
$188$	−11.8296	−	7.28941i	−0.862760	−	0.531635i
$189$			11.7440i			0.854251i
$190$	−2.16830	+	1.05898i	−0.157305	+	0.0768267i
$191$	−9.98578	+	9.98578i	−0.722545	+	0.722545i	−0.969123	−	0.246578i	$-0.920694\pi$
$191$	−9.98578	+	9.98578i	−0.722545	+	0.722545i	0.246578	+	0.969123i	$0.420694\pi$
$192$	1.46477	−	17.0004i	0.105711	−	1.22690i
$193$	4.94076			0.355644			0.177822	−	0.984063i	$-0.443095\pi$
$193$	4.94076			0.355644			0.177822	+	0.984063i	$0.443095\pi$
$194$	16.8716	−	9.42122i	1.21131	−	0.676404i
$195$	−16.7285	−	18.6762i	−1.19795	−	1.33743i
$196$	7.77097	−	12.6111i	0.555069	−	0.900789i
$197$	−2.69442	−	2.69442i	−0.191969	−	0.191969i	0.604577	−	0.796547i	$-0.293342\pi$
$197$	−2.69442	−	2.69442i	−0.191969	−	0.191969i	−0.796547	+	0.604577i	$0.793342\pi$
$198$	−3.53995	−	1.00309i	−0.251574	−	0.0712866i
$199$	−3.98148	−	3.98148i	−0.282240	−	0.282240i	0.551762	−	0.834002i	$-0.313956\pi$
$199$	−3.98148	−	3.98148i	−0.282240	−	0.282240i	−0.834002	+	0.551762i	$0.813956\pi$
$200$	13.9772	+	2.15372i	0.988336	+	0.152291i
$201$	−29.6503			−2.09137
$202$	−22.7915	−	6.45825i	−1.60360	−	0.454401i
$203$	2.39838	+	2.39838i	0.168333	+	0.168333i
$204$	24.7061	+	15.2240i	1.72977	+	1.06589i
$205$	−11.9195	−	7.93254i	−0.832495	−	0.554033i
$206$	−12.0732	−	3.42109i	−0.841179	−	0.238359i
$207$	−4.44190	+	4.44190i	−0.308733	+	0.308733i
$208$	9.45394	+	18.7832i	0.655513	+	1.30238i
$209$		−	1.28138i		−	0.0886346i
$210$	−24.2105	−	8.32193i	−1.67068	−	0.574268i
$211$	−4.26868	+	4.26868i	−0.293868	+	0.293868i	−0.838606	−	0.544738i	$-0.816629\pi$
$211$	−4.26868	+	4.26868i	−0.293868	+	0.293868i	0.544738	+	0.838606i	$0.316629\pi$
$212$	−1.35843	+	2.20452i	−0.0932976	+	0.151407i
$213$	9.75041	−	9.75041i	0.668087	−	0.668087i
$214$	21.7286	+	6.15709i	1.48534	+	0.420890i
$215$	21.7505	+	1.19652i	1.48337	+	0.0816020i
$216$	−8.74341	−	0.375975i	−0.594913	−	0.0255819i
$217$			22.9058i			1.55495i
$218$	3.62669	−	12.7987i	0.245630	−	0.866841i
$219$	−6.04069	−	6.04069i	−0.408192	−	0.408192i
$220$	−4.28480	+	6.16726i	−0.288881	+	0.415796i
$221$	−35.7631			−2.40568
$222$	−26.9386	−	7.63340i	−1.80800	−	0.512320i
$223$	−10.7438	+	10.7438i	−0.719458	+	0.719458i	−0.968494	−	0.249036i	$-0.919886\pi$
$223$	−10.7438	+	10.7438i	−0.719458	+	0.719458i	0.249036	+	0.968494i	$0.419886\pi$
$224$	17.7786	+	12.0387i	1.18788	+	0.804370i
$225$	−0.849746	+	7.70001i	−0.0566497	+	0.513334i
$226$	15.0508	+	4.26485i	1.00117	+	0.283693i
$227$		−	4.00580i		−	0.265875i	−0.991124	−	0.132937i	$-0.957559\pi$
$227$		−	4.00580i		−	0.265875i	0.991124	−	0.132937i	$-0.0424409\pi$
$228$	0.752092	+	3.16713i	0.0498085	+	0.209748i
$229$	−15.2903	+	15.2903i	−1.01041	+	1.01041i	−0.0104690	+	0.999945i	$0.503332\pi$
$229$	−15.2903	+	15.2903i	−1.01041	+	1.01041i	−0.999945	+	0.0104690i	$0.996668\pi$
$230$	5.62665	+	11.5208i	0.371010	+	0.759656i
$231$	9.61265	−	9.61265i	0.632466	−	0.632466i
$232$	−1.86237	+	1.70881i	−0.122271	+	0.112189i
$233$	−12.7190			−0.833248			−0.416624	−	0.909079i	$-0.636787\pi$
$233$	−12.7190			−0.833248			−0.416624	+	0.909079i	$0.636787\pi$
$234$	−10.0571	+	5.61592i	−0.657450	+	0.367124i
$235$	−10.3651	−	11.5719i	−0.676143	−	0.754865i
$236$	−3.48371	+	5.65350i	−0.226770	+	0.368012i
$237$	6.86372	+	6.86372i	0.445846	+	0.445846i
$238$	−31.8823	+	17.8033i	−2.06663	+	1.15402i
$239$	3.34373	−	3.34373i	0.216288	−	0.216288i	−0.590644	−	0.806932i	$-0.701126\pi$
$239$	3.34373	−	3.34373i	0.216288	−	0.216288i	0.806932	+	0.590644i	$0.201126\pi$
$240$	6.97075	−	17.7583i	0.449960	−	1.14629i
$241$		−	12.6414i		−	0.814302i	−0.913361	−	0.407151i	$-0.866522\pi$
$241$		−	12.6414i		−	0.814302i	0.913361	−	0.407151i	$-0.133478\pi$
$242$	5.64022	+	10.1006i	0.362567	+	0.649290i
$243$		−	14.7078i		−	0.943507i
$244$	15.3289	+	9.44570i	0.981331	+	0.604699i
$245$	12.3363	−	11.0498i	0.788138	−	0.705947i
$246$	−13.9674	+	13.3401i	−0.890532	+	0.850531i
$247$	−2.83661	−	2.83661i	−0.180489	−	0.180489i
$248$	−17.0533	−	0.733310i	−1.08289	−	0.0465652i
$249$	−8.33496	−	8.33496i	−0.528206	−	0.528206i
$250$	14.2987	+	6.74888i	0.904329	+	0.426837i
$251$	−21.7813			−1.37482			−0.687411	−	0.726268i	$-0.741253\pi$
$251$	−21.7813			−1.37482			−0.687411	+	0.726268i	$0.741253\pi$
$252$	−6.17007	+	10.0131i	−0.388678	+	0.630763i
$253$	−6.80828			−0.428033
$254$	−22.5365	−	6.38601i	−1.41407	−	0.400694i
$255$	21.6475	+	24.1679i	1.35562	+	1.51345i
$256$	−9.53198	+	12.8507i	−0.595749	+	0.803171i
$257$			14.8162i			0.924207i	0.886826	+	0.462104i	$0.152905\pi$
$257$			14.8162i			0.924207i	−0.886826	+	0.462104i	$0.847095\pi$
$258$	8.01127	−	28.2721i	0.498760	−	1.76015i
$259$	24.9127	−	24.9127i	1.54800	−	1.54800i
$260$	4.16725	+	23.1380i	0.258442	+	1.43496i
$261$	−0.979013	−	0.979013i	−0.0605994	−	0.0605994i
$262$	−0.362516	+	0.202431i	−0.0223963	+	0.0125062i
$263$	1.52403			0.0939759			0.0469880	−	0.998895i	$-0.485038\pi$
$263$	1.52403			0.0939759			0.0469880	+	0.998895i	$0.485038\pi$
$264$	6.84887	+	7.46435i	0.421519	+	0.459399i
$265$	−2.15650	+	1.93160i	−0.132473	+	0.118658i
$266$	−3.94091	−	1.11671i	−0.241633	−	0.0684697i
$267$	−3.75645	+	3.75645i	−0.229891	+	0.229891i
$268$	23.6696	+	14.5853i	1.44585	+	0.890937i
$269$		−	32.6160i		−	1.98863i	−0.106471	−	0.994316i	$-0.533955\pi$
$269$		−	32.6160i		−	1.98863i	0.106471	−	0.994316i	$-0.466045\pi$
$270$	−9.25308	−	3.18058i	−0.563125	−	0.193564i
$271$		−	22.5274i		−	1.36844i	−0.729274	−	0.684221i	$-0.760142\pi$
$271$		−	22.5274i		−	1.36844i	0.729274	−	0.684221i	$-0.239858\pi$
$272$	−12.2338	−	24.3063i	−0.741786	−	1.47379i
$273$		−	42.5595i		−	2.57582i
$274$	−14.0175	+	7.82744i	−0.846826	+	0.472873i
$275$	−6.55228	+	5.24984i	−0.395117	+	0.316577i
$276$	16.8278	−	3.99606i	1.01291	−	0.240534i
$277$	11.4879	−	11.4879i	0.690243	−	0.690243i	−0.272042	−	0.962285i	$-0.587699\pi$
$277$	11.4879	−	11.4879i	0.690243	−	0.690243i	0.962285	+	0.272042i	$0.0876990\pi$
$278$	24.3934	−	13.6214i	1.46302	−	0.816960i
$279$		−	9.35009i		−	0.559775i
$280$	15.2334	+	18.5527i	0.910371	+	1.10874i
$281$	7.43982	+	7.43982i	0.443822	+	0.443822i	0.893294	−	0.449472i	$-0.148388\pi$
$281$	7.43982	+	7.43982i	0.443822	+	0.443822i	−0.449472	+	0.893294i	$0.648388\pi$
$282$	−18.2972	+	10.2173i	−1.08958	+	0.608430i
$283$	−2.86216	+	2.86216i	−0.170138	+	0.170138i	−0.787040	−	0.616902i	$-0.788387\pi$
$283$	−2.86216	+	2.86216i	−0.170138	+	0.170138i	0.616902	+	0.787040i	$0.288387\pi$
$284$	−12.5800	+	2.98735i	−0.746486	+	0.177267i
$285$	−0.199907	+	3.63393i	−0.0118415	+	0.215255i
$286$	−12.0113	−	3.40355i	−0.710243	−	0.201256i
$287$	−6.08705	−	23.5290i	−0.359307	−	1.38887i
$288$	−7.25718	−	4.91417i	−0.427633	−	0.289570i
$289$	29.2791			1.72230
$290$	−2.53922	+	1.24013i	−0.149108	+	0.0728232i
$291$		−	29.1443i		−	1.70847i
$292$	1.85076	+	7.79372i	0.108308	+	0.456093i
$293$			17.6019i			1.02831i	0.857697	+	0.514156i	$0.171895\pi$
$293$			17.6019i			1.02831i	−0.857697	+	0.514156i	$0.828105\pi$
$294$	−10.8923	−	19.5060i	−0.635249	−	1.13761i
$295$	−5.53034	+	4.95361i	−0.321989	+	0.288410i
$296$	17.7499	+	19.3451i	1.03169	+	1.12441i
$297$	3.67388	−	3.67388i	0.213180	−	0.213180i
$298$	−6.21758	+	21.9421i	−0.360175	+	1.27107i
$299$	−15.0717	+	15.0717i	−0.871617	+	0.871617i
$300$	13.1137	−	16.8216i	0.757118	−	0.971197i
$301$	26.1460	+	26.1460i	1.50703	+	1.50703i
$302$	12.9529	+	3.67037i	0.745355	+	0.211206i
$303$	−25.2632	+	25.2632i	−1.45133	+	1.45133i
$304$	0.957552	−	2.89825i	0.0549194	−	0.166226i
$305$	13.4312	+	14.9949i	0.769067	+	0.858608i
$306$	13.0143	−	7.26726i	0.743978	−	0.415442i
$307$	−3.91273	+	3.91273i	−0.223312	+	0.223312i	−0.809891	−	0.586580i	$-0.800474\pi$
$307$	−3.91273	+	3.91273i	−0.223312	+	0.223312i	0.586580	+	0.809891i	$0.300474\pi$
$308$	−12.4023	+	2.94514i	−0.706684	+	0.167815i
$309$	−13.3825	+	13.3825i	−0.761305	+	0.761305i
$310$	−18.0474	−	6.20348i	−1.02502	−	0.352334i
$311$	−3.91988	+	3.91988i	−0.222276	+	0.222276i	−0.809456	−	0.587180i	$-0.800238\pi$
$311$	−3.91988	+	3.91988i	−0.222276	+	0.222276i	0.587180	+	0.809456i	$0.300238\pi$
$312$	31.6855	+	1.36251i	1.79384	+	0.0771368i
$313$			19.0627i			1.07749i	0.842470	+	0.538743i	$0.181101\pi$
$313$			19.0627i			1.07749i	−0.842470	+	0.538743i	$0.818899\pi$
$314$	1.92361	+	3.44483i	0.108556	+	0.194403i
$315$	−9.79492	+	8.77345i	−0.551881	+	0.494328i
$316$	−2.10292	−	8.85558i	−0.118298	−	0.498165i
$317$		−	4.78035i		−	0.268491i	−0.990948	−	0.134246i	$-0.957139\pi$
$317$		−	4.78035i		−	0.268491i	0.990948	−	0.134246i	$-0.0428612\pi$
$318$	1.90406	+	3.40982i	0.106774	+	0.191213i
$319$		−	1.50057i		−	0.0840159i
$320$	−14.3002	+	10.7473i	−0.799404	+	0.600793i
$321$	24.0851	−	24.0851i	1.34430	−	1.34430i
$322$	−5.93335	+	20.9391i	−0.330653	+	1.16689i
$323$	3.67071	+	3.67071i	0.204244	+	0.204244i
$324$	−11.8010	+	19.1512i	−0.655611	+	1.06395i
$325$	−2.88324	+	26.1267i	−0.159934	+	1.44925i
$326$	0.738679	−	2.60683i	0.0409117	−	0.144379i
$327$	−14.1868	−	14.1868i	−0.784530	−	0.784530i
$328$	17.7122	−	3.77854i	0.977994	−	0.208635i
$329$		−	26.3701i		−	1.45383i
$330$	4.97043	+	10.1771i	0.273613	+	0.560233i
$331$	0.127120	+	0.127120i	0.00698714	+	0.00698714i	0.710592	−	0.703605i	$-0.248427\pi$
$331$	0.127120	+	0.127120i	0.00698714	+	0.00698714i	−0.703605	+	0.710592i	$0.748427\pi$
$332$	2.55368	+	10.7538i	0.140151	+	0.590190i
$333$	−10.1693	+	10.1693i	−0.557275	+	0.557275i
$334$	8.43977	−	4.71282i	0.461804	−	0.257874i
$335$	20.7393	+	23.1539i	1.13311	+	1.26503i
$336$	28.9256	−	14.5588i	1.57802	−	0.794247i
$337$	−1.53712	−	1.53712i	−0.0837321	−	0.0837321i	0.664000	−	0.747732i	$-0.268857\pi$
$337$	−1.53712	−	1.53712i	−0.0837321	−	0.0837321i	−0.747732	+	0.664000i	$0.768857\pi$
$338$	−18.0725	+	10.0918i	−0.983015	+	0.548921i
$339$	16.6831	−	16.6831i	0.906101	−	0.906101i
$340$	−5.39261	−	29.9416i	−0.292456	−	1.62381i
$341$	7.16562	−	7.16562i	0.388040	−	0.388040i
$342$	1.60867	+	0.455837i	0.0869869	+	0.0246489i
$343$	1.54301			0.0833149
$344$	−20.3027	+	18.6286i	−1.09465	+	1.00439i
$345$	19.3080	+	1.06216i	1.03951	+	0.0571846i
$346$	−6.56586	+	23.1712i	−0.352983	+	1.24569i
$347$		−	4.28660i		−	0.230117i	−0.993359	−	0.115058i	$-0.963294\pi$
$347$		−	4.28660i		−	0.230117i	0.993359	−	0.115058i	$-0.0367055\pi$
$348$	0.880747	+	3.70890i	0.0472130	+	0.198818i
$349$	−26.6440			−1.42622			−0.713110	−	0.701053i	$-0.752714\pi$
$349$	−26.6440			−1.42622			−0.713110	+	0.701053i	$0.752714\pi$
$350$	10.4358	+	24.7269i	0.557817	+	1.32171i
$351$		−	16.2659i		−	0.868212i
$352$	−1.79561	−	9.32776i	−0.0957062	−	0.497171i
$353$	23.7186	+	23.7186i	1.26241	+	1.26241i	0.949920	+	0.312494i	$0.101164\pi$
$353$	23.7186	+	23.7186i	1.26241	+	1.26241i	0.312494	+	0.949920i	$0.398836\pi$
$354$	4.88297	+	8.74448i	0.259527	+	0.464764i
$355$	−14.4342	−	0.794042i	−0.766087	−	0.0421434i
$356$	4.84658	−	1.15091i	0.256868	−	0.0609981i
$357$			55.0740i			2.91483i
$358$	−4.55348	−	1.29029i	−0.240659	−	0.0681938i
$359$	−24.6134			−1.29905			−0.649523	−	0.760342i	$-0.725031\pi$
$359$	−24.6134			−1.29905			−0.649523	+	0.760342i	$0.725031\pi$
$360$	−6.21825	−	7.57318i	−0.327730	−	0.399142i
$361$		−	18.4177i		−	0.969353i
$362$	11.1758	+	3.16682i	0.587389	+	0.166444i
$363$	17.4479			0.915776
$364$	−20.9355	+	33.9749i	−1.09732	+	1.78077i
$365$	−0.491934	+	8.94244i	−0.0257490	+	0.468069i
$366$	23.7097	−	13.2397i	1.23933	−	0.692048i
$367$	13.9218	−	13.9218i	0.726714	−	0.726714i	−0.243250	−	0.969964i	$-0.578213\pi$
$367$	13.9218	−	13.9218i	0.726714	−	0.726714i	0.969964	+	0.243250i	$0.0782134\pi$
$368$	−15.3992	−	5.08772i	−0.802737	−	0.265216i
$369$	2.48472	+	9.60450i	0.129349	+	0.499990i
$370$	12.8817	+	26.3757i	0.669686	+	1.37121i
$371$	−4.91425			−0.255135
$372$	−13.5052	+	21.9168i	−0.700212	+	1.13633i
$373$	14.5185	+	14.5185i	0.751741	+	0.751741i	0.974804	−	0.223063i	$-0.0716056\pi$
$373$	14.5185	+	14.5185i	0.751741	+	0.751741i	−0.223063	+	0.974804i	$0.571606\pi$
$374$	15.5432	+	4.40436i	0.803718	+	0.227744i
$375$	19.4010	−	13.8661i	1.00186	−	0.716043i
$376$	19.6325	+	0.844217i	1.01247	+	0.0435372i
$377$	−3.32185	−	3.32185i	−0.171084	−	0.171084i
$378$	−8.09739	−	14.5009i	−0.416485	−	0.745846i
$379$	−15.5630			−0.799419			−0.399709	−	0.916642i	$-0.630889\pi$
$379$	−15.5630			−0.799419			−0.399709	+	0.916642i	$0.630889\pi$
$380$	1.94715	−	2.80260i	0.0998868	−	0.143770i
$381$	−24.9806	+	24.9806i	−1.27979	+	1.27979i
$382$	5.44482	−	19.2150i	0.278581	−	0.983126i
$383$	0.130134			0.00664953			0.00332476	−	0.999994i	$-0.498942\pi$
$383$	0.130134			0.00664953			0.00332476	+	0.999994i	$0.498942\pi$
$384$	9.91298	+	22.0011i	0.505869	+	1.12274i
$385$	−14.2302	−	0.782823i	−0.725240	−	0.0398963i
$386$	−6.10060	+	3.40661i	−0.310512	+	0.173392i
$387$	−10.6727	−	10.6727i	−0.542525	−	0.542525i
$388$	−14.3364	+	23.2657i	−0.727819	+	1.18113i
$389$	10.7898			0.547064			0.273532	−	0.961863i	$-0.411808\pi$
$389$	10.7898			0.547064			0.273532	+	0.961863i	$0.411808\pi$
$390$	33.5326	+	11.5262i	1.69799	+	0.583653i
$391$	19.5034	−	19.5034i	0.986331	−	0.986331i
$392$	−0.899988	+	20.9295i	−0.0454563	+	1.05710i
$393$			0.626215i			0.0315884i
$394$	5.18470	+	1.46915i	0.261202	+	0.0740148i
$395$	0.558959	−	10.1608i	0.0281243	−	0.511246i
$396$	5.06257	−	1.20220i	0.254404	−	0.0604128i
$397$			2.29560i			0.115213i	0.998339	+	0.0576065i	$0.0183469\pi$
$397$			2.29560i			0.115213i	−0.998339	+	0.0576065i	$0.981653\pi$
$398$	7.66132	+	2.17093i	0.384027	+	0.108819i
$399$	−4.36830	+	4.36830i	−0.218689	+	0.218689i
$400$	−18.7433	+	6.97783i	−0.937163	+	0.348891i
$401$		−	7.05550i		−	0.352335i	−0.984360	−	0.176167i	$-0.943630\pi$
$401$		−	7.05550i		−	0.352335i	0.984360	−	0.176167i	$-0.0563700\pi$
$402$	36.6106	−	20.4436i	1.82597	−	1.01963i
$403$		−	31.7255i		−	1.58036i
$404$	32.5946	−	7.74019i	1.62164	−	0.385089i
$405$	−18.7340	+	16.7803i	−0.930898	+	0.833818i
$406$	−4.61505	−	1.30773i	−0.229041	−	0.0649018i
$407$	−15.5869			−0.772614
$408$	−41.0026	−	1.76315i	−2.02993	−	0.0872889i
$409$		−	20.3305i		−	1.00528i	−0.864497	−	0.502639i	$-0.832363\pi$
$409$		−	20.3305i		−	1.00528i	0.864497	−	0.502639i	$-0.167637\pi$
$410$	20.1870	+	1.57630i	0.996965	+	0.0778477i
$411$			24.2140i			1.19439i
$412$	17.2662	−	4.10016i	0.850642	−	0.202001i
$413$	−12.6026			−0.620134
$414$	2.42198	−	8.54728i	0.119034	−	0.420076i
$415$	−0.678772	+	12.3388i	−0.0333196	+	0.605687i
$416$	−24.6241	−	16.6741i	−1.20729	−	0.817516i
$417$		−	42.1376i		−	2.06349i
$418$	0.883496	+	1.58218i	0.0432132	+	0.0773868i
$419$		−	40.2294i		−	1.96534i	−0.185374	−	0.982668i	$-0.559350\pi$
$419$		−	40.2294i		−	1.96534i	0.185374	−	0.982668i	$-0.440650\pi$
$420$	35.6318	−	6.41743i	1.73865	−	0.313139i
$421$	−1.28823	+	1.28823i	−0.0627843	+	0.0627843i	−0.737802	−	0.675017i	$-0.764136\pi$
$421$	−1.28823	+	1.28823i	−0.0627843	+	0.0627843i	0.675017	+	0.737802i	$0.264136\pi$
$422$	2.32753	−	8.21395i	0.113302	−	0.399849i
$423$			10.7642i			0.523374i
$424$	0.157326	−	3.65866i	0.00764041	−	0.177680i
$425$	3.73105	−	33.8091i	0.180983	−	1.63998i
$426$	−5.31649	+	18.7621i	−0.257585	+	0.909028i
$427$			34.1707i			1.65363i
$428$	−31.0746	+	7.37924i	−1.50205	+	0.356689i
$429$	−13.3139	+	13.3139i	−0.642802	+	0.642802i
$430$	−27.6814	+	13.5193i	−1.33491	+	0.651961i
$431$	23.7048			1.14182			0.570909	−	0.821013i	$-0.306591\pi$
$431$	23.7048			1.14182			0.570909	+	0.821013i	$0.306591\pi$
$432$	11.0551	−	5.56426i	0.531890	−	0.267711i
$433$	−0.0608646	−	0.0608646i	−0.00292496	−	0.00292496i	0.705643	−	0.708568i	$-0.250658\pi$
$433$	−0.0608646	−	0.0608646i	−0.00292496	−	0.00292496i	−0.708568	+	0.705643i	$0.750658\pi$
$434$	−15.7933	−	28.2829i	−0.758104	−	1.35762i
$435$	−0.234104	+	4.25556i	−0.0112244	+	0.204039i
$436$	4.34657	+	18.3038i	0.208163	+	0.876593i
$437$	3.09390			0.148001
$438$	11.6237	+	3.29373i	0.555404	+	0.157381i
$439$	16.1547	−	16.1547i	0.771022	−	0.771022i	−0.207263	−	0.978285i	$-0.566456\pi$
$439$	16.1547	−	16.1547i	0.771022	−	0.771022i	0.978285	+	0.207263i	$0.0664557\pi$
$440$	1.03838	−	10.5693i	0.0495028	−	0.503873i
$441$	−11.4753			−0.546444
$442$	44.1584	−	24.6583i	2.10040	−	1.17288i
$443$	11.2601	+	11.2601i	0.534984	+	0.534984i	0.922051	−	0.387067i	$-0.126512\pi$
$443$	11.2601	+	11.2601i	0.534984	+	0.534984i	−0.387067	+	0.922051i	$0.626512\pi$
$444$	38.5255	−	9.14859i	1.82834	−	0.434173i
$445$	5.56092	+	0.305913i	0.263613	+	0.0145017i
$446$	5.85814	−	20.6736i	0.277391	−	0.978925i
$447$	24.3217	+	24.3217i	1.15038	+	1.15038i
$448$	−30.2527	−	2.60661i	−1.42930	−	0.123151i
$449$	−36.0289			−1.70031			−0.850155	−	0.526533i	$-0.823492\pi$
$449$	−36.0289			−1.70031			−0.850155	+	0.526533i	$0.823492\pi$
$450$	−4.25987	−	10.0935i	−0.200812	−	0.475811i
$451$	−5.45638	+	9.26481i	−0.256931	+	0.436263i
$452$	−21.5246	+	5.11140i	−1.01243	+	0.240420i
$453$	14.3576	−	14.3576i	0.674580	−	0.674580i
$454$	2.76196	+	4.94616i	0.129625	+	0.232135i
$455$	−33.2348	+	29.7689i	−1.55807	+	1.39559i
$456$	−3.11235	−	3.39204i	−0.145749	−	0.158847i
$457$	19.8177			0.927032			0.463516	−	0.886088i	$-0.346588\pi$
$457$	19.8177			0.927032			0.463516	+	0.886088i	$0.346588\pi$
$458$	8.33717	−	29.4223i	0.389571	−	1.37481i
$459$			21.0489i			0.982478i
$460$	−14.8909	−	10.3457i	−0.694294	−	0.482371i
$461$	5.78625			0.269492			0.134746	−	0.990880i	$-0.456978\pi$
$461$	5.78625			0.269492			0.134746	+	0.990880i	$0.456978\pi$
$462$	−5.24137	+	18.4970i	−0.243850	+	0.860559i
$463$		−	13.6863i		−	0.636056i	−0.948081	−	0.318028i	$-0.896979\pi$
$463$		−	13.6863i		−	0.636056i	0.948081	−	0.318028i	$-0.103021\pi$
$464$	1.12135	−	3.39404i	0.0520576	−	0.157564i
$465$	−21.4393	+	19.2035i	−0.994225	+	0.890542i
$466$	15.7047	−	8.76962i	0.727508	−	0.406245i
$467$	−29.2702	−	29.2702i	−1.35446	−	1.35446i	−0.880599	−	0.473862i	$-0.842860\pi$
$467$	−29.2702	−	29.2702i	−1.35446	−	1.35446i	−0.473862	−	0.880599i	$-0.657140\pi$
$468$	8.54581	−	13.8685i	0.395030	−	0.641071i
$469$			52.7635i			2.43639i
$470$	20.7769	+	7.14170i	0.958369	+	0.329422i
$471$	5.95064			0.274191
$472$	0.403462	−	9.38264i	0.0185709	−	0.431871i
$473$		−	16.3585i		−	0.752165i
$474$	−13.2074	−	3.74249i	−0.606637	−	0.171898i
$475$	2.97757	−	2.38570i	0.136620	−	0.109463i
$476$	27.0915	−	43.9652i	1.24174	−	2.01514i
$477$	2.00599			0.0918478
$478$	−1.82319	+	6.43413i	−0.0833909	+	0.294290i
$479$	−19.0585	+	19.0585i	−0.870806	+	0.870806i	−0.992560	−	0.121754i	$-0.961148\pi$
$479$	−19.0585	+	19.0585i	−0.870806	+	0.870806i	0.121754	+	0.992560i	$0.461148\pi$
$480$	3.63705	+	26.7333i	0.166008	+	1.22020i
$481$	−34.5051	+	34.5051i	−1.57330	+	1.57330i
$482$	8.71610	+	15.6089i	0.397008	+	0.710966i
$483$	23.2099	+	23.2099i	1.05609	+	1.05609i
$484$	−13.9285	−	8.58279i	−0.633114	−	0.390127i
$485$	−22.7588	+	20.3854i	−1.03342	+	0.925653i
$486$	10.1409	+	18.1604i	0.460001	+	0.823774i
$487$	−1.43115	+	1.43115i	−0.0648517	+	0.0648517i	−0.738789	−	0.673937i	$-0.764602\pi$
$487$	−1.43115	+	1.43115i	−0.0648517	+	0.0648517i	0.673937	+	0.738789i	$0.264602\pi$
$488$	−25.4400	−	1.09395i	−1.15162	−	0.0495206i
$489$	−2.88954	−	2.88954i	−0.130670	−	0.130670i
$490$	−7.61350	+	22.1495i	−0.343943	+	1.00061i
$491$		−	8.72193i		−	0.393615i	−0.980442	−	0.196808i	$-0.936943\pi$
$491$		−	8.72193i		−	0.393615i	0.980442	−	0.196808i	$-0.0630575\pi$
$492$	8.04843	−	26.1020i	0.362851	−	1.17677i
$493$	4.29863	+	4.29863i	0.193601	+	0.193601i
$494$	5.45832	+	1.54669i	0.245582	+	0.0695887i
$495$	5.80875	+	0.319546i	0.261084	+	0.0143625i
$496$	21.5622	−	10.8527i	0.968171	−	0.487299i
$497$	−17.3511	−	17.3511i	−0.778305	−	0.778305i
$498$	16.0384	+	4.54470i	0.718700	+	0.203653i
$499$	9.64801	−	9.64801i	0.431904	−	0.431904i	−0.457371	−	0.889276i	$-0.651209\pi$
$499$	9.64801	−	9.64801i	0.431904	−	0.431904i	0.889276	+	0.457371i	$0.151209\pi$
$500$	−22.3086	+	1.52565i	−0.997670	+	0.0682292i
$501$		−	14.5790i		−	0.651341i
$502$	26.8944	−	15.0180i	1.20036	−	0.670286i
$503$		−	15.3459i		−	0.684238i	−0.939657	−	0.342119i	$-0.888855\pi$
$503$		−	15.3459i		−	0.684238i	0.939657	−	0.342119i	$-0.111145\pi$
$504$	0.714582	−	16.6178i	0.0318300	−	0.740216i
$505$	37.3988	+	2.05735i	1.66422	+	0.0915510i
$506$	8.40651	−	4.69424i	0.373715	−	0.208685i
$507$			31.2187i			1.38647i
$508$	32.2300	−	7.65360i	1.42997	−	0.339574i
$509$	0.483014	−	0.483014i	0.0214092	−	0.0214092i	−0.696321	−	0.717730i	$-0.745181\pi$
$509$	0.483014	−	0.483014i	0.0214092	−	0.0214092i	0.717730	+	0.696321i	$0.245181\pi$
$510$	−43.3927	−	14.9155i	−1.92146	−	0.660468i
$511$	−10.7496	+	10.7496i	−0.475534	+	0.475534i
$512$	2.90913	−	22.4396i	0.128567	−	0.991701i
$513$	−1.66953	+	1.66953i	−0.0737116	+	0.0737116i
$514$	−10.2156	−	18.2942i	−0.450591	−	0.806924i
$515$	19.8110	+	1.08983i	0.872978	+	0.0480236i
$516$	9.60147	+	40.4327i	0.422681	+	1.77995i
$517$	−8.24937	+	8.24937i	−0.362807	+	0.362807i
$518$	−13.5838	+	47.9380i	−0.596840	+	2.10628i
$519$	25.6841	+	25.6841i	1.12741	+	1.12741i
$520$	−21.0989	−	25.6963i	−0.925249	−	1.12686i
$521$	−4.92026	+	4.92026i	−0.215561	+	0.215561i	−0.806625	−	0.591064i	$-0.798708\pi$
$521$	−4.92026	+	4.92026i	−0.215561	+	0.215561i	0.591064	+	0.806625i	$0.298708\pi$
$522$	1.88385	+	0.533814i	0.0824540	+	0.0233644i
$523$	22.2043	−	22.2043i	0.970927	−	0.970927i	−0.0286619	−	0.999589i	$-0.509125\pi$
$523$	22.2043	−	22.2043i	0.970927	−	0.970927i	0.999589	+	0.0286619i	$0.00912462\pi$
$524$	0.308041	−	0.499902i	0.0134568	−	0.0218383i
$525$	40.2342	+	4.44011i	1.75597	+	0.193782i
$526$	−1.88180	+	1.05081i	−0.0820502	+	0.0458173i
$527$			41.0542i			1.78835i
$528$	−13.6032	−	4.49436i	−0.592004	−	0.195592i
$529$			6.56130i			0.285274i
$530$	1.33091	−	3.87193i	0.0578109	−	0.168186i
$531$	5.14436			0.223246
$532$	5.63599	−	1.33837i	0.244351	−	0.0580256i
$533$	8.43082	+	32.5887i	0.365179	+	1.41157i
$534$	2.04823	−	7.22831i	0.0886357	−	0.312799i
$535$	−35.6548	−	1.96141i	−1.54149	−	0.0847992i
$536$	−39.2824	−	1.68918i	−1.69674	−	0.0729614i
$537$	−5.04730	+	5.04730i	−0.217807	+	0.217807i
$538$	22.4884	+	40.2725i	0.969544	+	1.73627i
$539$	−8.79434	−	8.79434i	−0.378799	−	0.378799i
$540$	13.6182	−	2.45270i	0.586034	−	0.105547i
$541$			16.2492i			0.698607i	0.937010	+	0.349303i	$0.113582\pi$
$541$			16.2492i			0.698607i	−0.937010	+	0.349303i	$0.886418\pi$
$542$	15.5324	+	27.8157i	0.667175	+	1.19479i
$543$	12.3879	−	12.3879i	0.531614	−	0.531614i
$544$	31.8647	+	21.5771i	1.36619	+	0.925110i
$545$	−1.15532	+	21.0016i	−0.0494886	+	0.899610i
$546$	29.3444	+	52.5503i	1.25582	+	2.24894i
$547$		−	23.9813i		−	1.02537i	−0.858578	−	0.512684i	$-0.828651\pi$
$547$		−	23.9813i		−	1.02537i	0.858578	−	0.512684i	$-0.171349\pi$
$548$	11.9111	−	19.3298i	0.508817	−	0.825729i
$549$		−	13.9484i		−	0.595302i
$550$	4.47070	−	11.0000i	0.190631	−	0.469040i
$551$			0.681909i			0.0290503i
$552$	−18.0228	+	16.5367i	−0.767101	+	0.703849i
$553$	12.2142	−	12.2142i	0.519400	−	0.519400i
$554$	−6.26388	+	22.1055i	−0.266127	+	0.939174i
$555$	44.2038	+	2.43171i	1.87635	+	0.103220i
$556$	−20.7279	+	33.6381i	−0.879059	+	1.42657i
$557$	0.333252			0.0141203			0.00706017	−	0.999975i	$-0.497753\pi$
$557$	0.333252			0.0141203			0.00706017	+	0.999975i	$0.497753\pi$
$558$	6.44680	+	11.5450i	0.272915	+	0.488739i
$559$	−36.2132	−	36.2132i	−1.53166	−	1.53166i
$560$	−31.6014	−	12.4046i	−1.33540	−	0.524192i
$561$	17.2288	−	17.2288i	0.727401	−	0.727401i
$562$	−14.3160	−	4.05662i	−0.603883	−	0.171118i
$563$			2.33241i			0.0982992i	0.998791	+	0.0491496i	$0.0156511\pi$
$563$			2.33241i			0.0982992i	−0.998791	+	0.0491496i	$0.984349\pi$
$564$	15.5477	−	25.2315i	0.654678	−	1.06244i
$565$	−24.6971	−	1.35862i	−1.03901	−	0.0571574i
$566$	1.56061	−	5.50748i	0.0655975	−	0.231497i
$567$	−42.6912			−1.79286
$568$	13.4734	−	12.3624i	0.565331	−	0.518716i
$569$	−14.2563			−0.597655			−0.298827	−	0.954307i	$-0.596595\pi$
$569$	−14.2563			−0.597655			−0.298827	+	0.954307i	$0.596595\pi$
$570$	−2.25873	−	4.62482i	−0.0946076	−	0.193712i
$571$	5.51345	+	5.51345i	0.230731	+	0.230731i	0.812998	−	0.582267i	$-0.197834\pi$
$571$	5.51345	+	5.51345i	0.230731	+	0.230731i	−0.582267	+	0.812998i	$0.697834\pi$
$572$	17.1776	−	4.07914i	0.718233	−	0.170558i
$573$	−21.2989	−	21.2989i	−0.889773	−	0.889773i
$574$	23.7390	+	24.8555i	0.990848	+	1.03745i
$575$	−12.6758	−	15.8206i	−0.528618	−	0.659764i
$576$	12.3491	+	1.06401i	0.514544	+	0.0443338i
$577$		−	24.6132i		−	1.02466i	−0.858788	−	0.512331i	$-0.828782\pi$
$577$		−	24.6132i		−	1.02466i	0.858788	−	0.512331i	$-0.171218\pi$
$578$	−36.1523	+	20.1876i	−1.50374	+	0.839695i
$579$			10.5383i			0.437955i
$580$	2.28024	−	3.28202i	0.0946817	−	0.136279i
$581$	−14.8323	+	14.8323i	−0.615347	+	0.615347i
$582$	20.0947	+	35.9859i	0.832953	+	1.49166i
$583$	1.53733	+	1.53733i	0.0636696	+	0.0636696i
$584$	−7.65892	−	8.34720i	−0.316928	−	0.345409i
$585$	13.5664	−	12.1516i	0.560900	−	0.502406i
$586$	−12.1363	−	21.7339i	−0.501347	−	0.897818i
$587$	−19.7772			−0.816291			−0.408146	−	0.912917i	$-0.633824\pi$
$587$	−19.7772			−0.816291			−0.408146	+	0.912917i	$0.633824\pi$
$588$	26.8984	+	16.5749i	1.10927	+	0.683536i
$589$	−3.25629	+	3.25629i	−0.134173	+	0.134173i
$590$	3.41311	−	9.92957i	0.140516	−	0.408794i
$591$	5.74698	−	5.74698i	0.236399	−	0.236399i
$592$	−35.2549	−	11.6479i	−1.44897	−	0.478724i
$593$			4.91495i			0.201833i	0.994895	+	0.100916i	$0.0321775\pi$
$593$			4.91495i			0.201833i	−0.994895	+	0.100916i	$0.967823\pi$
$594$	−2.00321	+	7.06943i	−0.0821928	+	0.290062i
$595$	43.0074	−	38.5223i	1.76313	−	1.57926i
$596$	−7.45174	−	31.3799i	−0.305235	−	1.28537i
$597$	8.49219	−	8.49219i	0.347562	−	0.347562i
$598$	8.21793	−	29.0015i	0.336056	−	1.18596i
$599$	−1.03660			−0.0423544			−0.0211772	−	0.999776i	$-0.506741\pi$
$599$	−1.03660			−0.0423544			−0.0211772	+	0.999776i	$0.506741\pi$
$600$	−4.59372	+	29.8122i	−0.187538	+	1.21708i
$601$	−6.81030	−	6.81030i	−0.277798	−	0.277798i	0.554431	−	0.832229i	$-0.312936\pi$
$601$	−6.81030	−	6.81030i	−0.277798	−	0.277798i	−0.832229	+	0.554431i	$0.812936\pi$
$602$	−50.3111	−	14.2563i	−2.05053	−	0.581043i
$603$		−	21.5379i		−	0.877092i
$604$	−18.5242	+	4.39892i	−0.753740	+	0.178989i
$605$	−12.2042	−	13.6251i	−0.496170	−	0.553938i
$606$	13.7749	−	48.6124i	0.559569	−	1.97474i
$607$	−28.1561	+	28.1561i	−1.14282	+	1.14282i	−0.154890	+	0.987932i	$0.549502\pi$
$607$	−28.1561	+	28.1561i	−1.14282	+	1.14282i	−0.987932	+	0.154890i	$0.950498\pi$
$608$	0.815983	+	4.23884i	0.0330925	+	0.171908i
$609$	−5.11555	+	5.11555i	−0.207293	+	0.207293i
$610$	−26.9230	−	9.25430i	−1.09008	−	0.374696i
$611$			36.5237i			1.47759i
$612$	−11.0587	+	17.9465i	−0.447020	+	0.725443i
$613$	−17.5994	+	17.5994i	−0.710831	+	0.710831i	−0.966709	−	0.255878i	$-0.917636\pi$
$613$	−17.5994	+	17.5994i	−0.710831	+	0.710831i	0.255878	+	0.966709i	$0.417636\pi$
$614$	2.13345	−	7.52903i	0.0860989	−	0.303847i
$615$	16.9195	−	25.4234i	0.682259	−	1.02517i
$616$	13.2830	−	12.1877i	0.535188	−	0.491058i
$617$	−26.7297	−	26.7297i	−1.07610	−	1.07610i	−0.996855	−	0.0792413i	$-0.974750\pi$
$617$	−26.7297	−	26.7297i	−1.07610	−	1.07610i	−0.0792413	−	0.996855i	$-0.525250\pi$
$618$	7.29692	−	25.7512i	0.293525	−	1.03586i
$619$	−24.1522			−0.970759			−0.485380	−	0.874303i	$-0.661319\pi$
$619$	−24.1522			−0.970759			−0.485380	+	0.874303i	$0.661319\pi$
$620$	26.5613	−	4.78380i	1.06673	−	0.192122i
$621$	8.87065	+	8.87065i	0.355967	+	0.355967i
$622$	2.13735	−	7.54279i	0.0856998	−	0.302438i
$623$	6.68471	+	6.68471i	0.267817	+	0.267817i
$624$	−40.0631	+	20.1645i	−1.60381	+	0.807227i
$625$	−24.3984	−	5.45143i	−0.975936	−	0.218057i
$626$	−13.1435	−	23.5376i	−0.525321	−	0.940752i
$627$	2.73307			0.109148
$628$	−4.75035	−	2.92718i	−0.189560	−	0.116807i
$629$	44.6513	−	44.6513i	1.78036	−	1.78036i
$630$	6.04504	−	17.5865i	0.240840	−	0.700663i
$631$			25.9194i			1.03183i	0.856638	+	0.515917i	$0.172549\pi$
$631$			25.9194i			1.03183i	−0.856638	+	0.515917i	$0.827451\pi$
$632$	8.70242	+	9.48447i	0.346164	+	0.377272i
$633$	−9.10475	−	9.10475i	−0.361881	−	0.361881i
$634$	3.29601	+	5.90253i	0.130901	+	0.234420i
$635$	36.9804	+	2.03434i	1.46752	+	0.0807302i
$636$	−4.70207	−	2.89743i	−0.186449	−	0.114891i
$637$	−38.9365			−1.54272
$638$	1.03463	+	1.85283i	0.0409614	+	0.0733541i
$639$	7.08269	+	7.08269i	0.280187	+	0.280187i
$640$	10.2469	−	23.1301i	0.405046	−	0.914296i
$641$	12.9169	+	12.9169i	0.510187	+	0.510187i	0.914584	−	0.404397i	$-0.132518\pi$
$641$	12.9169	+	12.9169i	0.510187	+	0.510187i	−0.404397	+	0.914584i	$0.632518\pi$
$642$	−13.1326	+	46.3455i	−0.518301	+	1.82911i
$643$			23.5362i			0.928176i	0.885789	+	0.464088i	$0.153618\pi$
$643$			23.5362i			0.928176i	−0.885789	+	0.464088i	$0.846382\pi$
$644$	−7.11110	−	29.9455i	−0.280216	−	1.18002i
$645$	−2.55208	+	46.3921i	−0.100488	+	1.82669i
$646$	−7.06333	−	2.00148i	−0.277903	−	0.0787473i
$647$	−5.54813	+	5.54813i	−0.218119	+	0.218119i	−0.807706	−	0.589586i	$-0.799291\pi$
$647$	−5.54813	+	5.54813i	−0.218119	+	0.218119i	0.589586	+	0.807706i	$0.299291\pi$
$648$	1.36672	−	31.7835i	0.0536900	−	1.24858i
$649$	3.94248	+	3.94248i	0.154756	+	0.154756i
$650$	−14.4540	−	34.2478i	−0.566933	−	1.34331i
$651$	−48.8562			−1.91483
$652$	0.885304	+	3.72809i	0.0346712	+	0.146003i
$653$	19.8841			0.778126			0.389063	−	0.921211i	$-0.372799\pi$
$653$	19.8841			0.778126			0.389063	+	0.921211i	$0.372799\pi$
$654$	27.2987	+	7.73544i	1.06746	+	0.302480i
$655$	0.489012	−	0.438015i	0.0191073	−	0.0171147i
$656$	−19.2649	+	16.8780i	−0.752166	+	0.658973i
$657$	4.38795	−	4.38795i	0.171190	−	0.171190i
$658$	18.1819	+	32.5604i	0.708806	+	1.26934i
$659$	11.2904	−	11.2904i	0.439813	−	0.439813i	−0.452136	−	0.891949i	$-0.649338\pi$
$659$	11.2904	−	11.2904i	0.439813	−	0.439813i	0.891949	+	0.452136i	$0.149338\pi$
$660$	−13.1543	−	9.13913i	−0.512029	−	0.355740i
$661$		−	7.08423i		−	0.275545i	−0.990464	−	0.137772i	$-0.956006\pi$
$661$		−	7.08423i		−	0.275545i	0.990464	−	0.137772i	$-0.0439942\pi$
$662$	−0.244609	−	0.0693131i	−0.00950700	−	0.00269393i
$663$		−	76.2798i		−	2.96246i
$664$	−10.5678	−	11.5175i	−0.410110	−	0.446965i
$665$	6.46668	+	0.355740i	0.250767	+	0.0137950i
$666$	5.54489	−	19.5682i	0.214860	−	0.758252i
$667$	3.62315			0.140289
$668$	−7.17155	+	11.6383i	−0.277475	+	0.450299i
$669$	−22.9157	−	22.9157i	−0.885971	−	0.885971i
$670$	−41.5722	−	14.2897i	−1.60608	−	0.552060i
$671$	10.6896	−	10.6896i	0.412668	−	0.412668i
$672$	−25.6776	+	37.9203i	−0.990536	+	1.46281i
$673$			20.1396i			0.776325i	0.921591	+	0.388163i	$0.126890\pi$
$673$			20.1396i			0.776325i	−0.921591	+	0.388163i	$0.873110\pi$
$674$	2.95778	+	0.838124i	0.113929	+	0.0322833i
$675$	15.3772	+	1.69698i	0.591870	+	0.0653167i
$676$	15.3568	−	24.9217i	0.590646	−	0.958525i
$677$	17.7389	+	17.7389i	0.681761	+	0.681761i	0.960397	−	0.278636i	$-0.0898822\pi$
$677$	17.7389	+	17.7389i	0.681761	+	0.681761i	−0.278636	+	0.960397i	$0.589882\pi$
$678$	−9.09658	+	32.1023i	−0.349352	+	1.23288i
$679$	−51.8631			−1.99032
$680$	27.3030	+	33.2522i	1.04702	+	1.27516i
$681$	8.54406			0.327409
$682$	−3.90711	+	13.7884i	−0.149611	+	0.527984i
$683$	−26.4254			−1.01114			−0.505570	−	0.862786i	$-0.668718\pi$
$683$	−26.4254			−1.01114			−0.505570	+	0.862786i	$0.668718\pi$
$684$	−2.30060	+	0.546319i	−0.0879656	+	0.0208890i
$685$	18.9087	−	16.9368i	0.722465	−	0.647123i
$686$	−1.90523	+	1.06389i	−0.0727421	+	0.0406196i
$687$	−32.6131	−	32.6131i	−1.24427	−	1.24427i
$688$	12.2245	−	37.0001i	0.466053	−	1.41062i
$689$	6.80644			0.259305
$690$	−24.5729	+	12.0012i	−0.935473	+	0.456877i
$691$	−26.1406	+	26.1406i	−0.994434	+	0.994434i	−0.999985	−	0.00555091i	$-0.998233\pi$
$691$	−26.1406	+	26.1406i	−0.994434	+	0.994434i	0.00555091	+	0.999985i	$0.498233\pi$
$692$	−7.86915	−	33.1377i	−0.299140	−	1.25971i
$693$	6.98262	+	6.98262i	0.265248	+	0.265248i
$694$	2.95557	+	5.29287i	0.112192	+	0.200915i
$695$	−32.9053	+	29.4737i	−1.24817	+	1.11800i
$696$	−3.64475	−	3.97229i	−0.138154	−	0.150569i
$697$	−10.9099	−	42.1713i	−0.413241	−	1.59735i
$698$	32.8986	−	18.3708i	1.24523	−	0.695344i
$699$		−	27.1286i		−	1.02610i
$700$	−29.9346	−	23.3361i	−1.13142	−	0.882023i
$701$	10.0862			0.380949			0.190475	−	0.981692i	$-0.438997\pi$
$701$	10.0862			0.380949			0.190475	+	0.981692i	$0.438997\pi$
$702$	11.2152	+	20.0843i	0.423291	+	0.758034i
$703$	7.08320			0.267148
$704$	8.64852	+	10.2794i	0.325953	+	0.387419i
$705$	24.6819	−	22.1079i	0.929572	−	0.832631i
$706$	−45.6403	−	12.9327i	−1.71769	−	0.486730i
$707$	44.9566	+	44.9566i	1.69077	+	1.69077i
$708$	−12.0585	−	7.43047i	−0.453185	−	0.279254i
$709$	−18.2745	−	18.2745i	−0.686313	−	0.686313i	0.275102	−	0.961415i	$-0.411288\pi$
$709$	−18.2745	−	18.2745i	−0.686313	−	0.686313i	−0.961415	+	0.275102i	$0.911288\pi$
$710$	18.3701	−	8.97179i	0.689416	−	0.336705i
$711$	−4.98580	+	4.98580i	−0.186982	+	0.186982i
$712$	−5.19077	+	4.76276i	−0.194532	+	0.178492i
$713$	17.3015	+	17.3015i	0.647947	+	0.647947i
$714$	−37.9730	−	68.0025i	−1.42110	−	2.54493i
$715$	19.7095	+	1.08424i	0.737092	+	0.0405483i
$716$	6.51204	−	1.54640i	0.243366	−	0.0577918i
$717$	7.13191	+	7.13191i	0.266346	+	0.266346i
$718$	30.3913	−	16.9707i	1.13419	−	0.633341i
$719$	27.5925	+	27.5925i	1.02903	+	1.02903i	0.999566	+	0.0294593i	$0.00937853\pi$
$719$	27.5925	+	27.5925i	1.02903	+	1.02903i	0.0294593	+	0.999566i	$0.490621\pi$
$720$	12.8996	+	5.06355i	0.480740	+	0.188707i
$721$	23.8146	+	23.8146i	0.886901	+	0.886901i
$722$	12.6988	+	22.7412i	0.472602	+	0.846341i
$723$	26.9630			1.00277
$724$	−15.9828	+	3.79542i	−0.593997	+	0.141056i
$725$	3.48692	−	2.79380i	0.129501	−	0.103759i
$726$	−21.5437	+	12.0301i	−0.799563	+	0.446481i
$727$	44.9610			1.66751			0.833756	−	0.552134i	$-0.186186\pi$
$727$	44.9610			1.66751			0.833756	+	0.552134i	$0.186186\pi$
$728$	2.42462	−	56.3853i	0.0898625	−	2.08978i
$729$	−2.37209			−0.0878551
$730$	−5.55831	−	11.3808i	−0.205722	−	0.421224i
$731$	46.8616	+	46.8616i	1.73324	+	1.73324i
$732$	−20.1469	+	32.6953i	−0.744652	+	1.20845i
$733$	9.18384	−	9.18384i	0.339213	−	0.339213i	−0.516858	−	0.856071i	$-0.672899\pi$
$733$	9.18384	−	9.18384i	0.339213	−	0.339213i	0.856071	+	0.516858i	$0.172899\pi$
$734$	−7.59099	+	26.7889i	−0.280188	+	0.988798i
$735$	23.5684	+	26.3124i	0.869333	+	0.970547i
$736$	22.5220	−	4.33553i	0.830173	−	0.159810i
$737$	16.5060	−	16.5060i	0.608007	−	0.608007i
$738$	−9.69021	−	10.1459i	−0.356702	−	0.373477i
$739$	2.64278			0.0972161			0.0486081	−	0.998818i	$-0.484521\pi$
$739$	2.64278			0.0972161			0.0486081	+	0.998818i	$0.484521\pi$
$740$	−34.0914	−	23.6855i	−1.25322	−	0.870697i
$741$	6.05027	−	6.05027i	0.222262	−	0.222262i
$742$	6.06786	−	3.38833i	0.222758	−	0.124390i
$743$	−8.78535	−	8.78535i	−0.322303	−	0.322303i	0.527347	−	0.849650i	$-0.323187\pi$
$743$	−8.78535	−	8.78535i	−0.322303	−	0.322303i	−0.849650	+	0.527347i	$0.823187\pi$
$744$	1.56409	−	36.3734i	0.0573424	−	1.33351i
$745$	1.98068	−	36.0050i	0.0725666	−	1.31912i
$746$	−27.9371	−	7.91634i	−1.02285	−	0.289838i
$747$	6.05451	−	6.05451i	0.221523	−	0.221523i
$748$	−22.2287	+	5.27860i	−0.812761	+	0.193005i
$749$	−42.8601	−	42.8601i	−1.56607	−	1.56607i
$750$	−14.3948	+	30.4980i	−0.525625	+	1.11363i
$751$	−10.2291	−	10.2291i	−0.373265	−	0.373265i	0.495400	−	0.868665i	$-0.335022\pi$
$751$	−10.2291	−	10.2291i	−0.373265	−	0.373265i	−0.868665	+	0.495400i	$0.835022\pi$
$752$	−24.8233	+	12.4940i	−0.905212	+	0.455611i
$753$		−	46.4578i		−	1.69302i
$754$	6.39204	+	1.81127i	0.232784	+	0.0659624i
$755$	−21.2545	−	1.16924i	−0.773532	−	0.0425529i
$756$	19.9965	+	12.3219i	0.727264	+	0.448142i
$757$	27.8696			1.01294			0.506468	−	0.862259i	$-0.330951\pi$
$757$	27.8696			1.01294			0.506468	+	0.862259i	$0.330951\pi$
$758$	19.2164	−	10.7306i	0.697972	−	0.389751i
$759$		−	14.5215i		−	0.527098i
$760$	−0.471874	+	4.80305i	−0.0171167	+	0.174225i
$761$	−43.6459			−1.58216			−0.791081	−	0.611712i	$-0.790481\pi$
$761$	−43.6459			−1.58216			−0.791081	+	0.611712i	$0.790481\pi$
$762$	13.6208	−	48.0686i	0.493431	−	1.74134i
$763$	−25.2457	+	25.2457i	−0.913957	+	0.913957i
$764$	6.52559	+	27.4799i	0.236088	+	0.994186i
$765$	−17.5555	+	15.7247i	−0.634721	+	0.568528i
$766$	−0.160682	+	0.0897260i	−0.00580569	+	0.00324193i
$767$	17.4551			0.630269
$768$	−27.4096	−	20.3310i	−0.989059	−	0.733630i
$769$			11.1493i			0.402053i	0.979586	+	0.201027i	$0.0644278\pi$
$769$			11.1493i			0.402053i	−0.979586	+	0.201027i	$0.935572\pi$
$770$	18.1105	−	8.84502i	0.652657	−	0.318752i
$771$	−31.6017			−1.13811
$772$	5.18388	−	8.41261i	0.186572	−	0.302776i
$773$			2.22633i			0.0800755i	0.999198	+	0.0400378i	$0.0127478\pi$
$773$			2.22633i			0.0800755i	−0.999198	+	0.0400378i	$0.987252\pi$
$774$	20.5369	+	5.81938i	0.738182	+	0.209173i
$775$	29.9921	+	3.30982i	1.07735	+	0.118892i
$776$	1.66035	−	38.6120i	0.0596032	−	1.38609i
$777$	53.1368	+	53.1368i	1.90627	+	1.90627i
$778$	−13.3227	+	7.43946i	−0.477641	+	0.266718i
$779$	2.47956	−	4.21023i	0.0888394	−	0.150847i
$780$	−49.3515	+	8.88841i	−1.76707	+	0.318256i
$781$			10.8559i			0.388455i
$782$	−10.6344	+	37.5293i	−0.380285	+	1.34204i
$783$	−1.95513	+	1.95513i	−0.0698705	+	0.0698705i
$784$	−13.3194	−	26.4632i	−0.475694	−	0.945113i
$785$	−4.16226	−	4.64686i	−0.148557	−	0.165854i
$786$	−0.431769	−	0.773217i	−0.0154007	−	0.0275797i
$787$	20.8719	−	20.8719i	0.744004	−	0.744004i	−0.229342	−	0.973346i	$-0.573657\pi$
$787$	20.8719	−	20.8719i	0.744004	−	0.744004i	0.973346	+	0.229342i	$0.0736575\pi$
$788$	−7.41477	+	1.76077i	−0.264140	+	0.0627249i
$789$			3.25064i			0.115726i
$790$	6.31561	+	12.9314i	0.224699	+	0.460080i
$791$	−29.6880	−	29.6880i	−1.05559	−	1.05559i
$792$	−5.42210	+	4.97501i	−0.192666	+	0.176779i
$793$		−	47.3278i		−	1.68066i
$794$	−1.58280	−	2.83449i	−0.0561713	−	0.100592i
$795$	−4.11996	−	4.59964i	−0.146120	−	0.163132i
$796$	−10.9566	+	2.60185i	−0.388348	+	0.0922203i
$797$	−24.8010	+	24.8010i	−0.878498	+	0.878498i	−0.993379	−	0.114881i	$-0.963351\pi$
$797$	−24.8010	+	24.8010i	−0.878498	+	0.878498i	0.114881	+	0.993379i	$0.463351\pi$
$798$	2.38185	−	8.40565i	0.0843165	−	0.297557i
$799$		−	47.2633i		−	1.67206i
$800$	18.3321	−	21.5392i	0.648136	−	0.761524i
$801$	−2.72868	−	2.72868i	−0.0964133	−	0.0964133i
$802$	4.86470	+	8.71177i	0.171779	+	0.307623i
$803$	6.72559			0.237341
$804$	−31.1092	+	50.4853i	−1.09714	+	1.78048i
$805$	1.89014	−	34.3591i	0.0666186	−	1.21100i
$806$	21.8744	+	39.1729i	0.770493	+	1.37981i
$807$	69.5673			2.44889
$808$	−34.9094	+	32.0309i	−1.22811	+	1.12684i
$809$	24.2246	+	24.2246i	0.851691	+	0.851691i	0.990341	−	0.138650i	$-0.0442764\pi$
$809$	24.2246	+	24.2246i	0.851691	+	0.851691i	−0.138650	+	0.990341i	$0.544276\pi$
$810$	11.5619	−	33.6363i	0.406243	−	1.18186i
$811$	−0.574172			−0.0201619			−0.0100810	−	0.999949i	$-0.503209\pi$
$811$	−0.574172			−0.0201619			−0.0100810	+	0.999949i	$0.503209\pi$
$812$	6.60010	−	1.56731i	0.231618	−	0.0550019i
$813$	48.0492			1.68516
$814$	19.2459	−	10.7470i	0.674568	−	0.376683i
$815$	−0.235315	+	4.27758i	−0.00824272	+	0.149837i
$816$	51.8435	−	26.0938i	1.81489	−	0.913467i
$817$			7.43384i			0.260077i
$818$	14.0177	+	25.1030i	0.490116	+	0.877706i
$819$	30.9152			1.08026
$820$	−26.0127	+	11.9724i	−0.908403	+	0.418095i
$821$	21.9550			0.766234			0.383117	−	0.923700i	$-0.374851\pi$
$821$	21.9550			0.766234			0.383117	+	0.923700i	$0.374851\pi$
$822$	−16.6953	−	29.8982i	−0.582316	−	1.04282i
$823$			19.3515i			0.674550i	0.941406	+	0.337275i	$0.109505\pi$
$823$			19.3515i			0.674550i	−0.941406	+	0.337275i	$0.890495\pi$
$824$	−18.4923	+	16.9675i	−0.644211	+	0.591092i
$825$	−11.1975	−	13.9755i	−0.389847	−	0.486564i
$826$	15.5611	−	8.68938i	0.541438	−	0.302342i
$827$	9.30624			0.323610			0.161805	−	0.986823i	$-0.448268\pi$
$827$	9.30624			0.323610			0.161805	+	0.986823i	$0.448268\pi$
$828$	2.90273	+	12.2237i	0.100877	+	0.424802i
$829$	10.3721			0.360238			0.180119	−	0.983645i	$-0.442352\pi$
$829$	10.3721			0.360238			0.180119	+	0.983645i	$0.442352\pi$
$830$	−7.66937	−	15.7033i	−0.266208	−	0.545069i
$831$	24.5029	+	24.5029i	0.849995	+	0.849995i
$832$	41.9012	+	3.61026i	1.45266	+	0.125163i
$833$	50.3857			1.74576
$834$	29.0535	+	52.0293i	1.00604	+	1.80163i
$835$	−11.3847	+	10.1975i	−0.393985	+	0.352898i
$836$	−2.18179	−	1.34443i	−0.0754588	−	0.0464980i
$837$	−18.6725			−0.645416
$838$	27.7378	+	49.6732i	0.958187	+	1.71593i
$839$	24.7870	+	24.7870i	0.855743	+	0.855743i	0.990833	−	0.135090i	$-0.0431325\pi$
$839$	24.7870	+	24.7870i	0.855743	+	0.855743i	−0.135090	+	0.990833i	$0.543133\pi$
$840$	−39.5715	+	32.4917i	−1.36535	+	1.12107i
$841$		−	28.2014i		−	0.972464i
$842$	0.702415	−	2.47885i	0.0242068	−	0.0854270i
$843$	−15.8685	+	15.8685i	−0.546542	+	0.546542i
$844$	2.78953	+	11.7470i	0.0960197	+	0.404347i
$845$	24.3787	−	21.8364i	0.838654	−	0.751194i
$846$	−7.42182	−	13.2911i	−0.255167	−	0.456957i
$847$		−	31.0490i		−	1.06686i
$848$	2.32835	+	4.62599i	0.0799559	+	0.158857i
$849$	−6.10476	−	6.10476i	−0.209515	−	0.209515i
$850$	18.7042	+	44.3183i	0.641547	+	1.52010i
$851$		−	37.6348i		−	1.29011i
$852$	−6.37179	−	26.8322i	−0.218294	−	0.919255i
$853$	−23.2385	+	23.2385i	−0.795672	+	0.795672i	−0.982410	−	0.186738i	$-0.940209\pi$
$853$	−23.2385	+	23.2385i	−0.795672	+	0.795672i	0.186738	+	0.982410i	$0.440209\pi$
$854$	−23.5603	−	42.1922i	−0.806219	−	1.44379i
$855$	−2.63968	−	0.145212i	−0.0902753	−	0.00496615i
$856$	33.2814	−	30.5372i	1.13754	−	1.04374i
$857$	22.2672	−	22.2672i	0.760632	−	0.760632i	−0.215805	−	0.976437i	$-0.569237\pi$
$857$	22.2672	−	22.2672i	0.760632	−	0.760632i	0.976437	+	0.215805i	$0.0692374\pi$
$858$	7.25951	−	25.6191i	0.247836	−	0.874623i
$859$		−	46.8265i		−	1.59770i	−0.601530	−	0.798851i	$-0.705442\pi$
$859$		−	46.8265i		−	1.59770i	0.601530	−	0.798851i	$-0.294558\pi$
$860$	24.8580	−	35.7790i	0.847652	−	1.22005i
$861$	50.1856	−	12.9832i	1.71032	−	0.442466i
$862$	−29.2694	+	16.3442i	−0.996921	+	0.556686i
$863$	30.2514	+	30.2514i	1.02977	+	1.02977i	0.999543	+	0.0302260i	$0.00962271\pi$
$863$	30.2514	+	30.2514i	1.02977	+	1.02977i	0.0302260	+	0.999543i	$0.490377\pi$
$864$	−9.81380	+	14.4929i	−0.333872	+	0.493058i
$865$	2.09163	−	38.0219i	0.0711176	−	1.29278i
$866$	0.117118	+	0.0331869i	0.00397983	+	0.00112774i
$867$			62.4499i			2.12091i
$868$	39.0016	+	24.0329i	1.32380	+	0.815729i
$869$	−7.64193			−0.259235
$870$	−2.64511	−	5.41596i	−0.0896776	−	0.183618i
$871$		−	73.0796i		−	2.47621i
$872$	−17.9872	−	19.6037i	−0.609124	−	0.663864i
$873$	21.1704			0.716509
$874$	−3.82019	+	2.13322i	−0.129220	+	0.0721571i
$875$	−24.6751	−	34.5247i	−0.834172	−	1.16715i
$876$	−16.6234	+	3.94753i	−0.561652	+	0.133375i
$877$	−9.68882	+	9.68882i	−0.327168	+	0.327168i	−0.851509	−	0.524341i	$-0.824312\pi$
$877$	−9.68882	+	9.68882i	−0.327168	+	0.327168i	0.524341	+	0.851509i	$0.324312\pi$
$878$	−8.80847	+	31.0855i	−0.297272	+	1.04909i
$879$	−37.5434			−1.26631
$880$	6.00532	+	13.7664i	0.202439	+	0.464066i
$881$			44.0125i			1.48282i	0.671054	+	0.741409i	$0.265842\pi$
$881$			44.0125i			1.48282i	−0.671054	+	0.741409i	$0.734158\pi$
$882$	14.1691	−	7.91212i	0.477099	−	0.266415i
$883$	−52.2259			−1.75754			−0.878770	−	0.477245i	$-0.841635\pi$
$883$	−52.2259			−1.75754			−0.878770	+	0.477245i	$0.841635\pi$
$884$	−37.5228	+	60.8936i	−1.26203	+	2.04807i
$885$	−10.5657	−	11.7958i	−0.355161	−	0.396511i
$886$	−21.6671	−	6.13966i	−0.727922	−	0.206266i
$887$			49.4435i			1.66015i	0.557652	+	0.830075i	$0.311702\pi$
$887$			49.4435i			1.66015i	−0.557652	+	0.830075i	$0.688298\pi$
$888$	−41.2615	+	37.8592i	−1.38464	+	1.27047i
$889$	44.4536	+	44.4536i	1.49093	+	1.49093i
$890$	−7.07726	+	3.45648i	−0.237230	+	0.115861i
$891$	13.3551	+	13.3551i	0.447413	+	0.447413i
$892$	7.02095	+	29.5659i	0.235079	+	0.989938i
$893$	3.74878	−	3.74878i	0.125448	−	0.125448i
$894$	−46.8008	−	13.2616i	−1.56525	−	0.443534i
$895$	7.47185	+	0.411036i	0.249757	+	0.0137394i
$896$	39.1516	−	17.6404i	1.30796	−	0.589325i
$897$	−32.1467	−	32.1467i	−1.07335	−	1.07335i
$898$	44.4866	−	24.8416i	1.48454	−	0.828975i
$899$	−3.81332	+	3.81332i	−0.127181	+	0.127181i
$900$	12.2192	+	9.52576i	0.407307	+	0.317525i
$901$	−8.80785			−0.293432
$902$	0.349258	−	15.2018i	0.0116290	−	0.506166i
$903$	−55.7673	+	55.7673i	−1.85582	+	1.85582i
$904$	23.0532	−	21.1523i	0.766736	−	0.703514i
$905$	−18.3386	−	1.00883i	−0.609594	−	0.0335345i
$906$	−7.82860	+	27.6275i	−0.260088	+	0.917862i
$907$	−23.0761	+	23.0761i	−0.766229	+	0.766229i	−0.977440	−	0.211212i	$-0.932259\pi$
$907$	−23.0761	+	23.0761i	−0.766229	+	0.766229i	0.211212	+	0.977440i	$0.432259\pi$
$908$	−6.82066	−	4.20291i	−0.226352	−	0.139479i
$909$	−18.3512	−	18.3512i	−0.608670	−	0.608670i
$910$	20.5112	−	59.6721i	0.679941	−	1.97811i
$911$	−33.1983			−1.09991			−0.549954	−	0.835195i	$-0.685355\pi$
$911$	−33.1983			−1.09991			−0.549954	+	0.835195i	$0.685355\pi$
$912$	6.18175	+	2.04238i	0.204698	+	0.0676301i
$913$	9.27998			0.307123
$914$	−24.4699	+	13.6641i	−0.809391	+	0.451969i
$915$	−31.9830	+	28.6477i	−1.05733	+	0.947062i
$916$	9.99207	+	42.0775i	0.330147	+	1.39028i
$917$	1.11437			0.0367996
$918$	−14.5130	−	25.9901i	−0.479001	−	0.857800i
$919$	32.9114	+	32.9114i	1.08565	+	1.08565i	0.995971	+	0.0896774i	$0.0285836\pi$
$919$	32.9114	+	32.9114i	1.08565	+	1.08565i	0.0896774	+	0.995971i	$0.471416\pi$
$920$	25.5198	+	2.50719i	0.841364	+	0.0826595i
$921$	−8.34555	−	8.34555i	−0.274995	−	0.274995i
$922$	−7.14456	+	3.98956i	−0.235293	+	0.131389i
$923$	24.0320	+	24.0320i	0.791024	+	0.791024i
$924$	−6.28176	−	26.4530i	−0.206655	−	0.870241i
$925$	−29.0201	−	36.2197i	−0.954175	−	1.19090i
$926$	9.43657	+	16.8991i	0.310105	+	0.555340i
$927$	−9.72105	−	9.72105i	−0.319281	−	0.319281i
$928$	0.955567	+	4.96394i	0.0313680	+	0.162949i
$929$	−9.80422	+	9.80422i	−0.321666	+	0.321666i	−0.849406	−	0.527740i	$-0.823040\pi$
$929$	−9.80422	+	9.80422i	−0.321666	+	0.321666i	0.527740	+	0.849406i	$0.323040\pi$
$930$	13.2315	−	38.4937i	0.433879	−	1.26226i
$931$	3.99643	+	3.99643i	0.130978	+	0.130978i
$932$	−13.3448	+	21.6565i	−0.437124	+	0.709383i
$933$	−8.36080	−	8.36080i	−0.273720	−	0.273720i
$934$	56.3228	+	15.9598i	1.84294	+	0.522220i
$935$	−25.5050	−	1.40306i	−0.834101	−	0.0458849i
$936$	−0.989725	+	23.0163i	−0.0323502	+	0.752313i
$937$	−32.1288			−1.04960			−0.524801	−	0.851225i	$-0.675860\pi$
$937$	−32.1288			−1.04960			−0.524801	+	0.851225i	$0.675860\pi$
$938$	−36.3799	−	65.1496i	−1.18785	−	2.12721i
$939$	−40.6592			−1.32686
$940$	−30.5784	+	5.50730i	−0.997358	+	0.179628i
$941$		−	46.4869i		−	1.51543i	−0.652587	−	0.757714i	$-0.726316\pi$
$941$		−	46.4869i		−	1.51543i	0.652587	−	0.757714i	$-0.273684\pi$
$942$	−7.34754	+	4.10291i	−0.239396	+	0.133680i
$943$	−22.3700	−	13.1745i	−0.728469	−	0.429022i
$944$	5.97106	+	11.8634i	0.194342	+	0.386120i
$945$	17.5209	+	19.5608i	0.569956	+	0.636314i
$946$	11.2790	+	20.1986i	0.366713	+	0.656714i
$947$	1.70879	+	1.70879i	0.0555281	+	0.0555281i	0.734326	−	0.678797i	$-0.237499\pi$
$947$	1.70879	+	1.70879i	0.0555281	+	0.0555281i	−0.678797	+	0.734326i	$0.737499\pi$
$948$	18.8883	−	4.48536i	0.613462	−	0.145678i
$949$	14.8886	−	14.8886i	0.483305	−	0.483305i
$950$	−2.03163	+	4.99874i	−0.0659148	+	0.162181i
$951$	10.1961			0.330632
$952$	−3.13757	+	72.9652i	−0.101689	+	2.36482i
$953$	36.9507	+	36.9507i	1.19695	+	1.19695i	0.975075	+	0.221878i	$0.0712185\pi$
$953$	36.9507	+	36.9507i	1.19695	+	1.19695i	0.221878	+	0.975075i	$0.428781\pi$
$954$	−2.47689	+	1.38311i	−0.0801922	+	0.0447798i
$955$	−1.73451	+	31.5301i	−0.0561275	+	1.02029i
$956$	−2.18509	−	9.20161i	−0.0706709	−	0.297601i
$957$	3.20060			0.103461
$958$	10.3918	−	36.6732i	0.335744	−	1.18486i
$959$	43.0895			1.39143
$960$	−22.9232	−	30.5012i	−0.739843	−	0.984420i
$961$	−5.41926			−0.174815
$962$	18.8142	−	66.3961i	0.606594	−	2.14070i
$963$	17.4954	+	17.4954i	0.563781	+	0.563781i
$964$	−21.5244	−	13.2634i	−0.693254	−	0.427185i
$965$	8.22934	−	7.37114i	0.264912	−	0.237285i
$966$	−44.6614	−	12.6554i	−1.43696	−	0.407180i
$967$			27.9108i			0.897550i	0.893645	+	0.448775i	$0.148140\pi$
$967$			27.9108i			0.897550i	−0.893645	+	0.448775i	$0.851860\pi$
$968$	23.1159	+	0.994008i	0.742975	+	0.0319486i
$969$	−7.82934	+	7.82934i	−0.251515	+	0.251515i
$970$	14.0459	−	40.8628i	0.450985	−	1.31203i
$971$	17.5385	+	17.5385i	0.562838	+	0.562838i	0.930113	−	0.367274i	$-0.119709\pi$
$971$	17.5385	+	17.5385i	0.562838	+	0.562838i	−0.367274	+	0.930113i	$0.619709\pi$
$972$	−25.0429	−	15.4315i	−0.803252	−	0.494966i
$973$	−74.9850			−2.40391
$974$	0.780346	−	2.75388i	0.0250039	−	0.0882399i
$975$	−55.7261	−	6.14973i	−1.78466	−	0.196949i
$976$	32.1663	−	16.1899i	1.02962	−	0.518226i
$977$			31.3371i			1.00256i	0.865284	+	0.501282i	$0.167138\pi$
$977$			31.3371i			1.00256i	−0.865284	+	0.501282i	$0.832862\pi$
$978$	5.56017	+	1.57554i	0.177795	+	0.0503803i
$979$		−	4.18236i		−	0.133669i
$980$	−5.87113	−	32.5985i	−0.187546	−	1.04132i
$981$	10.3053	−	10.3053i	0.329021	−	0.329021i
$982$	6.01369	+	10.7694i	0.191905	+	0.343665i
$983$	−2.62116	+	2.62116i	−0.0836021	+	0.0836021i	−0.747671	−	0.664069i	$-0.768828\pi$
$983$	−2.62116	+	2.62116i	−0.0836021	+	0.0836021i	0.664069	+	0.747671i	$0.268828\pi$
$984$	8.05933	+	37.7788i	0.256922	+	1.20434i
$985$	−8.50764	−	0.468016i	−0.271076	−	0.0149122i
$986$	−8.27160	−	2.34386i	−0.263421	−	0.0746438i
$987$	56.2453			1.79031
$988$	−7.80608	+	1.85370i	−0.248344	+	0.0589739i
$989$	39.4979			1.25596
$990$	−7.39266	+	3.61052i	−0.234954	+	0.114750i
$991$	0.239446	+	0.239446i	0.00760624	+	0.00760624i	0.710900	−	0.703293i	$-0.248288\pi$
$991$	0.239446	+	0.239446i	0.00760624	+	0.00760624i	−0.703293	+	0.710900i	$0.748288\pi$
$992$	−19.1411	+	28.2672i	−0.607729	+	0.897485i
$993$	−0.271137	+	0.271137i	−0.00860427	+	0.00860427i
$994$	33.3877	+	9.46084i	1.05899	+	0.300079i
$995$	−12.5715	−	0.691576i	−0.398545	−	0.0219244i
$996$	−22.9370	+	5.44680i	−0.726786	+	0.172588i
$997$			47.2742i			1.49719i	0.663029	+	0.748594i	$0.269271\pi$
$997$			47.2742i			1.49719i	−0.663029	+	0.748594i	$0.730729\pi$
$998$	−5.26065	+	18.5651i	−0.166523	+	0.587667i
$999$	20.3085	+	20.3085i	0.642533	+	0.642533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.j.c.483.19	✓	240
4.3	odd	2	inner	820.2.j.c.483.81	yes	240
5.2	odd	4		820.2.s.c.647.40	yes	240
20.7	even	4		820.2.s.c.647.102	yes	240
41.9	even	4		820.2.s.c.583.102	yes	240
164.91	odd	4		820.2.s.c.583.40	yes	240
205.132	odd	4	inner	820.2.j.c.747.81	yes	240
820.747	even	4	inner	820.2.j.c.747.19	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.19	✓	240	1.1	even	1	trivial
820.2.j.c.483.81	yes	240	4.3	odd	2	inner
820.2.j.c.747.19	yes	240	820.747	even	4	inner
820.2.j.c.747.81	yes	240	205.132	odd	4	inner
820.2.s.c.583.40	yes	240	164.91	odd	4
820.2.s.c.583.102	yes	240	41.9	even	4
820.2.s.c.647.40	yes	240	5.2	odd	4
820.2.s.c.647.102	yes	240	20.7	even	4

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23475 + 0.689491i) q^{2} +2.13292i q^{3} +(1.04921 - 1.70269i) q^{4} +(1.66560 - 1.49190i) q^{5} +(-1.47063 - 2.63362i) q^{6} +3.79559 q^{7} +(-0.121513 + 2.82582i) q^{8} -1.54935 q^{9} +(-1.02794 + 2.99054i) q^{10} +(-1.18738 - 1.18738i) q^{11} +(3.63171 + 2.23787i) q^{12} -5.25705 q^{13} +(-4.68660 + 2.61703i) q^{14} +(3.18211 + 3.55260i) q^{15} +(-1.79834 - 3.57295i) q^{16} +6.80287 q^{17} +(1.91306 - 1.06826i) q^{18} +(0.539583 + 0.539583i) q^{19} +(-0.792697 - 4.40132i) q^{20} +8.09570i q^{21} +(2.28480 + 0.647426i) q^{22} +(2.86694 - 2.86694i) q^{23} +(-6.02724 - 0.259177i) q^{24} +(0.548453 - 4.96983i) q^{25} +(6.49114 - 3.62469i) q^{26} +3.09412i q^{27} +(3.98236 - 6.46273i) q^{28} +(0.631885 + 0.631885i) q^{29} +(-6.37859 - 2.19252i) q^{30} +6.03484i q^{31} +(4.68401 + 3.17176i) q^{32} +(2.53258 - 2.53258i) q^{33} +(-8.39983 + 4.69052i) q^{34} +(6.32194 - 5.66266i) q^{35} +(-1.62559 + 2.63807i) q^{36} +(6.56359 - 6.56359i) q^{37} +(-1.03829 - 0.294211i) q^{38} -11.2129i q^{39} +(4.01345 + 4.88797i) q^{40} +(-1.60372 - 6.19904i) q^{41} +(-5.58191 - 9.99615i) q^{42} +(6.88851 + 6.88851i) q^{43} +(-3.26754 + 0.775937i) q^{44} +(-2.58060 + 2.31148i) q^{45} +(-1.56322 + 5.51668i) q^{46} -6.94756i q^{47} +(7.62083 - 3.83571i) q^{48} +7.40653 q^{49} +(2.74945 + 6.51464i) q^{50} +14.5100i q^{51} +(-5.51573 + 8.95115i) q^{52} -1.29473 q^{53} +(-2.13336 - 3.82046i) q^{54} +(-3.74915 - 0.206245i) q^{55} +(-0.461213 + 10.7256i) q^{56} +(-1.15089 + 1.15089i) q^{57} +(-1.21590 - 0.344540i) q^{58} -3.32033 q^{59} +(9.38767 - 1.69076i) q^{60} +9.00272i q^{61} +(-4.16096 - 7.45150i) q^{62} -5.88071 q^{63} +(-7.97047 - 0.686746i) q^{64} +(-8.75615 + 7.84301i) q^{65} +(-1.38091 + 4.87329i) q^{66} +13.9012i q^{67} +(7.13761 - 11.5832i) q^{68} +(6.11496 + 6.11496i) q^{69} +(-3.90166 + 11.3509i) q^{70} +(-4.57139 - 4.57139i) q^{71} +(0.188266 - 4.37818i) q^{72} +(-2.83212 + 2.83212i) q^{73} +(-3.57885 + 12.6299i) q^{74} +(10.6003 + 1.16981i) q^{75} +(1.48488 - 0.352611i) q^{76} +(-4.50680 - 4.50680i) q^{77} +(7.73117 + 13.8451i) q^{78} +(3.21799 - 3.21799i) q^{79} +(-8.32581 - 3.26817i) q^{80} -11.2476 q^{81} +(6.25436 + 6.54851i) q^{82} +(-3.90777 + 3.90777i) q^{83} +(13.7845 + 8.49405i) q^{84} +(11.3309 - 10.1492i) q^{85} +(-13.2551 - 3.75601i) q^{86} +(-1.34776 + 1.34776i) q^{87} +(3.49959 - 3.21103i) q^{88} +(1.76118 + 1.76118i) q^{89} +(1.59265 - 4.63340i) q^{90} -19.9536 q^{91} +(-1.87351 - 7.88953i) q^{92} -12.8718 q^{93} +(4.79027 + 8.57848i) q^{94} +(1.70373 + 0.0937245i) q^{95} +(-6.76511 + 9.99062i) q^{96} -13.6640 q^{97} +(-9.14520 + 5.10673i) q^{98} +(1.83966 + 1.83966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Introduction

L-functions

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