LMFDB - Embedded newform 620.2.k.d.187.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [620,2,Mod(63,620)] 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("620.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(620, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 620 = 2^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	620.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.95072492532$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.9
Character	$\chi$	$=$	620.187
Dual form			620.2.k.d.63.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19714 - 0.752899i) q^{2} +(-2.32623 - 2.32623i) q^{3} +(0.866287 + 1.80265i) q^{4} +(2.15511 - 0.596241i) q^{5} +(1.03341 + 4.53624i) q^{6} +(-0.483723 + 0.483723i) q^{7} +(0.320145 - 2.81025i) q^{8} +7.82269i q^{9} +(-3.02888 - 0.908795i) q^{10} -0.611810i q^{11} +(2.17819 - 6.20856i) q^{12} +(3.25195 - 3.25195i) q^{13} +(0.943279 - 0.214890i) q^{14} +(-6.40027 - 3.62629i) q^{15} +(-2.49909 + 3.12323i) q^{16} +(3.15741 + 3.15741i) q^{17} +(5.88969 - 9.36485i) q^{18} +5.82338 q^{19} +(2.94176 + 3.36839i) q^{20} +2.25050 q^{21} +(-0.460631 + 0.732422i) q^{22} +(5.77417 + 5.77417i) q^{23} +(-7.28202 + 5.79256i) q^{24} +(4.28899 - 2.56993i) q^{25} +(-6.34143 + 1.44465i) q^{26} +(11.2187 - 11.2187i) q^{27} +(-1.29103 - 0.452940i) q^{28} -1.88211i q^{29} +(4.93180 + 9.15993i) q^{30} -1.00000i q^{31} +(5.34323 - 1.85737i) q^{32} +(-1.42321 + 1.42321i) q^{33} +(-1.40265 - 6.15707i) q^{34} +(-0.754061 + 1.33089i) q^{35} +(-14.1016 + 6.77670i) q^{36} +(-5.83854 - 5.83854i) q^{37} +(-6.97140 - 4.38441i) q^{38} -15.1296 q^{39} +(-0.985638 - 6.24728i) q^{40} -1.16432 q^{41} +(-2.69417 - 1.69440i) q^{42} +(-7.31547 - 7.31547i) q^{43} +(1.10288 - 0.530003i) q^{44} +(4.66421 + 16.8587i) q^{45} +(-2.56512 - 11.2599i) q^{46} +(-1.53702 + 1.53702i) q^{47} +(13.0788 - 1.45188i) q^{48} +6.53202i q^{49} +(-7.06942 - 0.152613i) q^{50} -14.6897i q^{51} +(8.67926 + 3.04501i) q^{52} +(-6.12008 + 6.12008i) q^{53} +(-21.8769 + 4.98380i) q^{54} +(-0.364786 - 1.31852i) q^{55} +(1.20452 + 1.51425i) q^{56} +(-13.5465 - 13.5465i) q^{57} +(-1.41704 + 2.25315i) q^{58} +4.45477 q^{59} +(0.992448 - 14.6789i) q^{60} +8.28126 q^{61} +(-0.752899 + 1.19714i) q^{62} +(-3.78402 - 3.78402i) q^{63} +(-7.79501 - 1.79938i) q^{64} +(5.06937 - 8.94726i) q^{65} +(2.77531 - 0.632249i) q^{66} +(-0.0933865 + 0.0933865i) q^{67} +(-2.95648 + 8.42693i) q^{68} -26.8641i q^{69} +(1.90474 - 1.02553i) q^{70} +4.88336i q^{71} +(21.9837 + 2.50440i) q^{72} +(3.57550 - 3.57550i) q^{73} +(2.59372 + 11.3854i) q^{74} +(-15.9554 - 3.99894i) q^{75} +(5.04472 + 10.4975i) q^{76} +(0.295947 + 0.295947i) q^{77} +(18.1122 + 11.3910i) q^{78} +5.60298 q^{79} +(-3.52362 + 8.22095i) q^{80} -28.7264 q^{81} +(1.39385 + 0.876612i) q^{82} +(1.46421 + 1.46421i) q^{83} +(1.94958 + 4.05687i) q^{84} +(8.68714 + 4.92199i) q^{85} +(3.24983 + 14.2654i) q^{86} +(-4.37822 + 4.37822i) q^{87} +(-1.71934 - 0.195868i) q^{88} -16.9786i q^{89} +(7.10922 - 23.6940i) q^{90} +3.14609i q^{91} +(-5.40672 + 15.4109i) q^{92} +(-2.32623 + 2.32623i) q^{93} +(2.99725 - 0.682808i) q^{94} +(12.5500 - 3.47214i) q^{95} +(-16.7503 - 8.10891i) q^{96} +(-4.67352 - 4.67352i) q^{97} +(4.91795 - 7.81975i) q^{98} +4.78600 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 2 q^{2} + 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 10 q^{10} - 12 q^{12} - 6 q^{13} + 22 q^{14} - 2 q^{15} + 8 q^{16} - 2 q^{17} - 24 q^{18} + 8 q^{19} + 8 q^{20} - 16 q^{21} - 16 q^{22} + 10 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) $ 88 * q + 2 * q^2 + 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^8 - 10 * q^10 - 12 * q^12 - 6 * q^13 + 22 * q^14 - 2 * q^15 + 8 * q^16 - 2 * q^17 - 24 * q^18 + 8 * q^19 + 8 * q^20 - 16 * q^21 - 16 * q^22 + 10 * q^23 - 44 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 + 46 * q^28 + 16 * q^30 - 8 * q^32 - 8 * q^33 + 40 * q^34 - 12 * q^35 - 20 * q^36 + 10 * q^37 - 64 * q^38 + 8 * q^39 + 8 * q^41 + 28 * q^42 + 10 * q^43 - 16 * q^44 + 6 * q^45 - 24 * q^46 - 64 * q^47 + 88 * q^48 - 14 * q^50 + 20 * q^52 + 18 * q^53 + 36 * q^54 + 40 * q^55 - 24 * q^56 - 24 * q^57 - 52 * q^58 - 32 * q^60 + 20 * q^61 + 2 * q^62 - 4 * q^63 - 150 * q^64 - 18 * q^65 + 8 * q^66 + 116 * q^67 + 68 * q^68 - 6 * q^70 - 26 * q^72 + 38 * q^73 + 36 * q^74 - 70 * q^75 - 8 * q^76 + 40 * q^77 - 152 * q^78 + 32 * q^79 + 68 * q^80 - 60 * q^81 + 14 * q^82 - 14 * q^83 - 120 * q^84 + 6 * q^85 + 4 * q^86 - 44 * q^87 + 52 * q^88 - 68 * q^90 - 92 * q^92 + 2 * q^93 + 112 * q^94 + 104 * q^95 - 20 * q^96 + 16 * q^97 - 62 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/620\mathbb{Z}\right)^\times$.

$n$	$311$	$497$	$561$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.19714	−	0.752899i	−0.846506	−	0.532380i
$2$	−1.19714	−	0.752899i	−0.846506	−	0.532380i
$3$	−2.32623	−	2.32623i	−1.34305	−	1.34305i	−0.893008	−	0.450042i	$-0.851409\pi$
$3$	−2.32623	−	2.32623i	−1.34305	−	1.34305i	−0.450042	−	0.893008i	$-0.648591\pi$
$4$	0.866287	+	1.80265i	0.433144	+	0.901325i
$5$	2.15511	−	0.596241i	0.963794	−	0.266647i
$5$	2.15511	−	0.596241i	0.963794	−	0.266647i
$6$	1.03341	+	4.53624i	0.421887	+	1.85191i
$7$	−0.483723	+	0.483723i	−0.182830	+	0.182830i	−0.792588	−	0.609758i	$-0.791267\pi$
$7$	−0.483723	+	0.483723i	−0.182830	+	0.182830i	0.609758	+	0.792588i	$0.291267\pi$
$8$	0.320145	−	2.81025i	0.113188	−	0.993574i
$9$			7.82269i			2.60756i
$10$	−3.02888	−	0.908795i	−0.957815	−	0.287386i
$11$		−	0.611810i		−	0.184468i	−0.995737	−	0.0922338i	$-0.970599\pi$
$11$		−	0.611810i		−	0.184468i	0.995737	−	0.0922338i	$-0.0294007\pi$
$12$	2.17819	−	6.20856i	0.628790	−	1.79226i
$13$	3.25195	−	3.25195i	0.901929	−	0.901929i	−0.0936737	−	0.995603i	$-0.529861\pi$
$13$	3.25195	−	3.25195i	0.901929	−	0.901929i	0.995603	+	0.0936737i	$0.0298611\pi$
$14$	0.943279	−	0.214890i	0.252102	−	0.0574317i
$15$	−6.40027	−	3.62629i	−1.65254	−	0.936303i
$16$	−2.49909	+	3.12323i	−0.624773	+	0.780806i
$17$	3.15741	+	3.15741i	0.765784	+	0.765784i	0.977361	−	0.211577i	$-0.0678599\pi$
$17$	3.15741	+	3.15741i	0.765784	+	0.765784i	−0.211577	+	0.977361i	$0.567860\pi$
$18$	5.88969	−	9.36485i	1.38821	−	2.20732i
$19$	5.82338			1.33597			0.667987	−	0.744173i	$-0.267156\pi$
$19$	5.82338			1.33597			0.667987	+	0.744173i	$0.267156\pi$
$20$	2.94176	+	3.36839i	0.657797	+	0.753195i
$21$	2.25050			0.491100
$22$	−0.460631	+	0.732422i	−0.0982068	+	0.156153i
$23$	5.77417	+	5.77417i	1.20400	+	1.20400i	0.972940	+	0.231058i	$0.0742187\pi$
$23$	5.77417	+	5.77417i	1.20400	+	1.20400i	0.231058	+	0.972940i	$0.425781\pi$
$24$	−7.28202	+	5.79256i	−1.48644	+	1.18240i
$25$	4.28899	−	2.56993i	0.857799	−	0.513986i
$26$	−6.34143	+	1.44465i	−1.24366	+	0.283319i
$27$	11.2187	−	11.2187i	2.15904	−	2.15904i
$28$	−1.29103	−	0.452940i	−0.243981	−	0.0855977i
$29$		−	1.88211i		−	0.349499i	−0.984613	−	0.174749i	$-0.944088\pi$
$29$		−	1.88211i		−	0.349499i	0.984613	−	0.174749i	$-0.0559115\pi$
$30$	4.93180	+	9.15993i	0.900418	+	1.67237i
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$	5.34323	−	1.85737i	0.944559	−	0.328341i
$33$	−1.42321	+	1.42321i	−0.247749	+	0.247749i
$34$	−1.40265	−	6.15707i	−0.240553	−	1.05593i
$35$	−0.754061	+	1.33089i	−0.127460	+	0.224962i
$36$	−14.1016	+	6.77670i	−2.35026	+	1.12945i
$37$	−5.83854	−	5.83854i	−0.959851	−	0.959851i	0.0393740	−	0.999225i	$-0.487464\pi$
$37$	−5.83854	−	5.83854i	−0.959851	−	0.959851i	−0.999225	+	0.0393740i	$0.987464\pi$
$38$	−6.97140	−	4.38441i	−1.13091	−	0.711246i
$39$	−15.1296			−2.42267
$40$	−0.985638	−	6.24728i	−0.155843	−	0.987782i
$41$	−1.16432			−0.181836			−0.0909179	−	0.995858i	$-0.528980\pi$
$41$	−1.16432			−0.181836			−0.0909179	+	0.995858i	$0.528980\pi$
$42$	−2.69417	−	1.69440i	−0.415719	−	0.261452i
$43$	−7.31547	−	7.31547i	−1.11560	−	1.11560i	−0.992380	−	0.123218i	$-0.960678\pi$
$43$	−7.31547	−	7.31547i	−1.11560	−	1.11560i	−0.123218	−	0.992380i	$-0.539322\pi$
$44$	1.10288	−	0.530003i	0.166265	−	0.0799010i
$45$	4.66421	+	16.8587i	0.695299	+	2.51315i
$46$	−2.56512	−	11.2599i	−0.378207	−	1.66018i
$47$	−1.53702	+	1.53702i	−0.224197	+	0.224197i	−0.810263	−	0.586066i	$-0.800676\pi$
$47$	−1.53702	+	1.53702i	−0.224197	+	0.224197i	0.586066	+	0.810263i	$0.300676\pi$
$48$	13.0788	−	1.45188i	1.88776	−	0.209560i
$49$			6.53202i			0.933146i
$50$	−7.06942	−	0.152613i	−0.999767	−	0.0215828i
$51$		−	14.6897i		−	2.05697i
$52$	8.67926	+	3.04501i	1.20360	+	0.422266i
$53$	−6.12008	+	6.12008i	−0.840658	+	0.840658i	−0.988944	−	0.148287i	$-0.952624\pi$
$53$	−6.12008	+	6.12008i	−0.840658	+	0.840658i	0.148287	+	0.988944i	$0.452624\pi$
$54$	−21.8769	+	4.98380i	−2.97706	+	0.678209i
$55$	−0.364786	−	1.31852i	−0.0491877	−	0.177789i
$56$	1.20452	+	1.51425i	0.160961	+	0.202350i
$57$	−13.5465	−	13.5465i	−1.79428	−	1.79428i
$58$	−1.41704	+	2.25315i	−0.186066	+	0.295853i
$59$	4.45477			0.579961			0.289981	−	0.957032i	$-0.406351\pi$
$59$	4.45477			0.579961			0.289981	+	0.957032i	$0.406351\pi$
$60$	0.992448	−	14.6789i	0.128125	−	1.89503i
$61$	8.28126			1.06031			0.530154	−	0.847902i	$-0.322134\pi$
$61$	8.28126			1.06031			0.530154	+	0.847902i	$0.322134\pi$
$62$	−0.752899	+	1.19714i	−0.0956182	+	0.152037i
$63$	−3.78402	−	3.78402i	−0.476741	−	0.476741i
$64$	−7.79501	−	1.79938i	−0.974377	−	0.224922i
$65$	5.06937	−	8.94726i	0.628777	−	1.10977i
$66$	2.77531	−	0.632249i	0.341618	−	0.0778244i
$67$	−0.0933865	+	0.0933865i	−0.0114090	+	0.0114090i	−0.712788	−	0.701379i	$-0.752568\pi$
$67$	−0.0933865	+	0.0933865i	−0.0114090	+	0.0114090i	0.701379	+	0.712788i	$0.252568\pi$
$68$	−2.95648	+	8.42693i	−0.358526	+	1.02192i
$69$		−	26.8641i		−	3.23406i
$70$	1.90474	−	1.02553i	0.227660	−	0.122575i
$71$			4.88336i			0.579548i	0.957095	+	0.289774i	$0.0935802\pi$
$71$			4.88336i			0.579548i	−0.957095	+	0.289774i	$0.906420\pi$
$72$	21.9837	+	2.50440i	2.59081	+	0.295146i
$73$	3.57550	−	3.57550i	0.418481	−	0.418481i	−0.466199	−	0.884680i	$-0.654377\pi$
$73$	3.57550	−	3.57550i	0.418481	−	0.418481i	0.884680	+	0.466199i	$0.154377\pi$
$74$	2.59372	+	11.3854i	0.301514	+	1.32352i
$75$	−15.9554	−	3.99894i	−1.84237	−	0.461758i
$76$	5.04472	+	10.4975i	0.578669	+	1.20415i
$77$	0.295947	+	0.295947i	0.0337263	+	0.0337263i
$78$	18.1122	+	11.3910i	2.05080	+	1.28978i
$79$	5.60298			0.630384			0.315192	−	0.949028i	$-0.397931\pi$
$79$	5.60298			0.630384			0.315192	+	0.949028i	$0.397931\pi$
$80$	−3.52362	+	8.22095i	−0.393953	+	0.919131i
$81$	−28.7264			−3.19182
$82$	1.39385	+	0.876612i	0.153925	+	0.0968056i
$83$	1.46421	+	1.46421i	0.160718	+	0.160718i	0.782885	−	0.622167i	$-0.213747\pi$
$83$	1.46421	+	1.46421i	0.160718	+	0.160718i	−0.622167	+	0.782885i	$0.713747\pi$
$84$	1.94958	+	4.05687i	0.212717	+	0.442641i
$85$	8.68714	+	4.92199i	0.942253	+	0.533864i
$86$	3.24983	+	14.2654i	0.350438	+	1.53828i
$87$	−4.37822	+	4.37822i	−0.469394	+	0.469394i
$88$	−1.71934	−	0.195868i	−0.183282	−	0.0208796i
$89$		−	16.9786i		−	1.79973i	−0.436172	−	0.899863i	$-0.643666\pi$
$89$		−	16.9786i		−	1.79973i	0.436172	−	0.899863i	$-0.356334\pi$
$90$	7.10922	−	23.6940i	0.749378	−	2.49756i
$91$			3.14609i			0.329800i
$92$	−5.40672	+	15.4109i	−0.563689	+	1.60670i
$93$	−2.32623	+	2.32623i	−0.241219	+	0.241219i
$94$	2.99725	−	0.682808i	0.309143	−	0.0704263i
$95$	12.5500	−	3.47214i	1.28760	−	0.356234i
$96$	−16.7503	−	8.10891i	−1.70957	−	0.827612i
$97$	−4.67352	−	4.67352i	−0.474524	−	0.474524i	0.428851	−	0.903375i	$-0.358918\pi$
$97$	−4.67352	−	4.67352i	−0.474524	−	0.474524i	−0.903375	+	0.428851i	$0.858918\pi$
$98$	4.91795	−	7.81975i	0.496788	−	0.789914i
$99$	4.78600			0.481011
$100$	8.34818	+	5.50526i	0.834818	+	0.550526i
$101$	−5.61619			−0.558832			−0.279416	−	0.960170i	$-0.590141\pi$
$101$	−5.61619			−0.558832			−0.279416	+	0.960170i	$0.590141\pi$
$102$	−11.0599	+	17.5856i	−1.09509	+	1.74124i
$103$	−6.83814	−	6.83814i	−0.673782	−	0.673782i	0.284804	−	0.958586i	$-0.408072\pi$
$103$	−6.83814	−	6.83814i	−0.673782	−	0.673782i	−0.958586	+	0.284804i	$0.908072\pi$
$104$	−8.09770	−	10.1799i	−0.794045	−	0.998221i
$105$	4.85008	−	1.34184i	0.473319	−	0.130950i
$106$	11.9344	−	2.71879i	1.15917	−	0.264072i
$107$	−2.83502	+	2.83502i	−0.274072	+	0.274072i	−0.830737	−	0.556665i	$-0.812081\pi$
$107$	−2.83502	+	2.83502i	−0.274072	+	0.274072i	0.556665	+	0.830737i	$0.312081\pi$
$108$	29.9419	+	10.5047i	2.88117	+	1.01082i
$109$		−	6.77612i		−	0.649034i	−0.945880	−	0.324517i	$-0.894798\pi$
$109$		−	6.77612i		−	0.649034i	0.945880	−	0.324517i	$-0.105202\pi$
$110$	−0.556010	+	1.85310i	−0.0530135	+	0.176686i
$111$			27.1636i			2.57825i
$112$	−0.301908	−	2.71965i	−0.0285276	−	0.256982i
$113$	−5.66216	+	5.66216i	−0.532651	+	0.532651i	−0.921361	−	0.388709i	$-0.872921\pi$
$113$	−5.66216	+	5.66216i	−0.532651	+	0.532651i	0.388709	+	0.921361i	$0.372921\pi$
$114$	6.01792	+	26.4162i	0.563630	+	2.47411i
$115$	15.8868	+	9.00117i	1.48145	+	0.839364i
$116$	3.39278	−	1.63045i	0.315012	−	0.151383i
$117$	25.4390	+	25.4390i	2.35184	+	2.35184i
$118$	−5.33298	−	3.35399i	−0.490941	−	0.308760i
$119$	−3.05463			−0.280017
$120$	−12.2398	+	16.8254i	−1.11733	+	1.53594i
$121$	10.6257			0.965972
$122$	−9.91383	−	6.23495i	−0.897556	−	0.564486i
$123$	2.70847	+	2.70847i	0.244214	+	0.244214i
$124$	1.80265	−	0.866287i	0.161883	−	0.0777949i
$125$	7.71095	−	8.09575i	0.689689	−	0.724106i
$126$	1.68102	+	7.37898i	0.149757	+	0.657372i
$127$	10.9103	−	10.9103i	0.968129	−	0.968129i	−0.0313784	−	0.999508i	$-0.509990\pi$
$127$	10.9103	−	10.9103i	0.968129	−	0.968129i	0.999508	+	0.0313784i	$0.00998970\pi$
$128$	7.97697	+	8.02296i	0.705071	+	0.709136i
$129$			34.0349i			2.99661i
$130$	−12.8051	+	6.89440i	−1.12308	+	0.604679i
$131$			12.9615i			1.13245i	0.824251	+	0.566224i	$0.191596\pi$
$131$			12.9615i			1.13245i	−0.824251	+	0.566224i	$0.808404\pi$
$132$	−3.79846	−	1.33264i	−0.330613	−	0.115991i
$133$	−2.81690	+	2.81690i	−0.244257	+	0.244257i
$134$	0.182107	−	0.0414861i	0.0157317	−	0.00358386i
$135$	17.4884	−	30.8665i	1.50517	−	2.65657i
$136$	9.88394	−	7.86228i	0.847541	−	0.674185i
$137$	−4.73775	−	4.73775i	−0.404774	−	0.404774i	0.475138	−	0.879911i	$-0.342398\pi$
$137$	−4.73775	−	4.73775i	−0.404774	−	0.404774i	−0.879911	+	0.475138i	$0.842398\pi$
$138$	−20.2259	+	32.1601i	−1.72175	+	2.73765i
$139$	8.88843			0.753906			0.376953	−	0.926232i	$-0.376972\pi$
$139$	8.88843			0.753906			0.376953	+	0.926232i	$0.376972\pi$
$140$	−3.05237	−	0.206373i	−0.257972	−	0.0174417i
$141$	7.15093			0.602217
$142$	3.67667	−	5.84606i	0.308540	−	0.490591i
$143$	−1.98958	−	1.98958i	−0.166377	−	0.166377i
$144$	−24.4320	−	19.5496i	−2.03600	−	1.62913i
$145$	−1.12219	−	4.05615i	−0.0931928	−	0.336845i
$146$	−6.97237	+	1.58839i	−0.577037	+	0.131456i
$147$	15.1950	−	15.1950i	1.25326	−	1.25326i
$148$	5.46699	−	15.5827i	0.449384	−	1.28089i
$149$		−	12.2725i		−	1.00540i	−0.864461	−	0.502700i	$-0.832340\pi$
$149$		−	12.2725i		−	1.00540i	0.864461	−	0.502700i	$-0.167660\pi$
$150$	16.0901	+	16.8001i	1.31375	+	1.37172i
$151$		−	2.57347i		−	0.209426i	−0.994502	−	0.104713i	$-0.966608\pi$
$151$		−	2.57347i		−	0.209426i	0.994502	−	0.104713i	$-0.0333924\pi$
$152$	1.86433	−	16.3652i	0.151217	−	1.32739i
$153$	−24.6994	+	24.6994i	−1.99683	+	1.99683i
$154$	−0.131472	−	0.577107i	−0.0105943	−	0.0465046i
$155$	−0.596241	−	2.15511i	−0.0478912	−	0.173103i
$156$	−13.1066	−	27.2733i	−1.04936	−	2.18361i
$157$	8.57036	+	8.57036i	0.683989	+	0.683989i	0.960897	−	0.276907i	$-0.0893095\pi$
$157$	8.57036	+	8.57036i	0.683989	+	0.683989i	−0.276907	+	0.960897i	$0.589310\pi$
$158$	−6.70755	−	4.21847i	−0.533624	−	0.335604i
$159$	28.4734			2.25809
$160$	10.4078	−	7.18870i	0.822810	−	0.568317i
$161$	−5.58620			−0.440254
$162$	34.3895	+	21.6280i	2.70189	+	1.69926i
$163$	−2.09145	−	2.09145i	−0.163815	−	0.163815i	0.620439	−	0.784254i	$-0.286954\pi$
$163$	−2.09145	−	2.09145i	−0.163815	−	0.163815i	−0.784254	+	0.620439i	$0.786954\pi$
$164$	−1.00863	−	2.09886i	−0.0787610	−	0.163893i
$165$	−2.21860	+	3.91575i	−0.172718	+	0.304841i
$166$	−0.650464	−	2.85527i	−0.0504858	−	0.221612i
$167$	3.19551	−	3.19551i	0.247276	−	0.247276i	−0.572576	−	0.819852i	$-0.694056\pi$
$167$	3.19551	−	3.19551i	0.247276	−	0.247276i	0.819852	+	0.572576i	$0.194056\pi$
$168$	0.720488	−	6.32448i	0.0555869	−	0.487944i
$169$		−	8.15038i		−	0.626953i
$170$	−6.69396	−	12.4328i	−0.513404	−	0.953555i
$171$			45.5545i			3.48364i
$172$	6.84993	−	19.5245i	0.522302	−	1.48873i
$173$	−8.10812	+	8.10812i	−0.616449	+	0.616449i	−0.944619	−	0.328170i	$-0.893568\pi$
$173$	−8.10812	+	8.10812i	−0.616449	+	0.616449i	0.328170	+	0.944619i	$0.393568\pi$
$174$	8.53769	−	1.94498i	0.647240	−	0.147449i
$175$	−0.831552	+	3.31782i	−0.0628594	+	0.250804i
$176$	1.91082	+	1.52897i	0.144033	+	0.115250i
$177$	−10.3628	−	10.3628i	−0.778917	−	0.778917i
$178$	−12.7832	+	20.3257i	−0.958138	+	1.52348i
$179$	−4.03738			−0.301768			−0.150884	−	0.988551i	$-0.548212\pi$
$179$	−4.03738			−0.301768			−0.150884	+	0.988551i	$0.548212\pi$
$180$	−26.3499	+	23.0125i	−1.96400	+	1.71525i
$181$	7.41836			0.551402			0.275701	−	0.961243i	$-0.411090\pi$
$181$	7.41836			0.551402			0.275701	+	0.961243i	$0.411090\pi$
$182$	2.36869	−	3.76631i	0.175579	−	0.279177i
$183$	−19.2641	−	19.2641i	−1.42404	−	1.42404i
$184$	18.0754	−	14.3783i	1.33254	−	1.05998i
$185$	−16.0639	−	9.10152i	−1.18104	−	0.669157i
$186$	4.53624	−	1.03341i	0.332613	−	0.0757731i
$187$	1.93173	−	1.93173i	0.141262	−	0.141262i
$188$	−4.10221	−	1.43921i	−0.299185	−	0.104965i
$189$			10.8535i			0.789474i
$190$	−17.6383	−	5.29226i	−1.27962	−	0.383941i
$191$			4.29702i			0.310922i	0.987842	+	0.155461i	$0.0496862\pi$
$191$			4.29702i			0.310922i	−0.987842	+	0.155461i	$0.950314\pi$
$192$	13.9472	+	22.3188i	1.00655	+	1.61072i
$193$	−1.10335	+	1.10335i	−0.0794207	+	0.0794207i	−0.745701	−	0.666280i	$-0.767885\pi$
$193$	−1.10335	+	1.10335i	−0.0794207	+	0.0794207i	0.666280	+	0.745701i	$0.267885\pi$
$194$	2.07617	+	9.11354i	0.149060	+	0.654314i
$195$	−32.6059	+	9.02087i	−2.33496	+	0.645998i
$196$	−11.7750	+	5.65861i	−0.841068	+	0.404186i
$197$	4.77507	+	4.77507i	0.340210	+	0.340210i	0.856446	−	0.516237i	$-0.172667\pi$
$197$	4.77507	+	4.77507i	0.340210	+	0.340210i	−0.516237	+	0.856446i	$0.672667\pi$
$198$	−5.72951	−	3.60337i	−0.407178	−	0.256080i
$199$	−9.77288			−0.692781			−0.346390	−	0.938090i	$-0.612593\pi$
$199$	−9.77288			−0.692781			−0.346390	+	0.938090i	$0.612593\pi$
$200$	−5.84904	−	12.8759i	−0.413590	−	0.910463i
$201$	0.434477			0.0306456
$202$	6.72337	+	4.22842i	0.473055	+	0.297511i
$203$	0.910420	+	0.910420i	0.0638989	+	0.0638989i
$204$	26.4804	−	12.7255i	1.85400	−	0.890965i
$205$	−2.50923	+	0.694213i	−0.175252	+	0.0484860i
$206$	3.03779	+	13.3346i	0.211653	+	0.929069i
$207$	−45.1695	+	45.1695i	−3.13950	+	3.13950i
$208$	2.02965	+	18.2835i	0.140731	+	1.26773i
$209$		−	3.56280i		−	0.246444i
$210$	−6.81649	−	2.04525i	−0.470383	−	0.141135i
$211$			10.6928i			0.736125i	0.929801	+	0.368062i	$0.119979\pi$
$211$			10.6928i			0.736125i	−0.929801	+	0.368062i	$0.880021\pi$
$212$	−16.3341	−	5.73061i	−1.12183	−	0.393580i
$213$	11.3598	−	11.3598i	0.778362	−	0.778362i
$214$	5.52840	−	1.25943i	0.377914	−	0.0860931i
$215$	−20.1274	−	11.4038i	−1.37268	−	0.777736i
$216$	−27.9357	−	35.1189i	−1.90078	−	2.38954i
$217$	0.483723	+	0.483723i	0.0328373	+	0.0328373i
$218$	−5.10173	+	8.11196i	−0.345533	+	0.549411i
$219$	−16.6349			−1.12408
$220$	2.06082	−	1.79980i	0.138940	−	0.121342i
$221$	20.5355			1.38137
$222$	20.4514	−	32.5186i	1.37261	−	2.18251i
$223$	18.1948	+	18.1948i	1.21841	+	1.21841i	0.968187	+	0.250227i	$0.0805053\pi$
$223$	18.1948	+	18.1948i	1.21841	+	1.21841i	0.250227	+	0.968187i	$0.419495\pi$
$224$	−1.68619	+	3.48310i	−0.112663	+	0.232725i
$225$	20.1038	+	33.5515i	1.34025	+	2.23676i
$226$	11.0414	−	2.51537i	0.734465	−	0.167320i
$227$	6.13354	−	6.13354i	0.407098	−	0.407098i	−0.473628	−	0.880725i	$-0.657056\pi$
$227$	6.13354	−	6.13354i	0.407098	−	0.407098i	0.880725	+	0.473628i	$0.157056\pi$
$228$	12.6844	−	36.1548i	0.840048	−	2.39441i
$229$		−	15.9643i		−	1.05495i	−0.849571	−	0.527474i	$-0.823139\pi$
$229$		−	15.9643i		−	1.05495i	0.849571	−	0.527474i	$-0.176861\pi$
$230$	−12.2417	−	22.7368i	−0.807195	−	1.49922i
$231$		−	1.37688i		−	0.0905920i
$232$	−5.28920	−	0.602548i	−0.347253	−	0.0395592i
$233$	12.9449	−	12.9449i	0.848051	−	0.848051i	−0.141839	−	0.989890i	$-0.545301\pi$
$233$	12.9449	−	12.9449i	0.848051	−	0.848051i	0.989890	+	0.141839i	$0.0453014\pi$
$234$	−11.3011	−	49.6070i	−0.738773	−	3.24291i
$235$	−2.39601	+	4.22888i	−0.156299	+	0.275862i
$236$	3.85911	+	8.03039i	0.251207	+	0.522734i
$237$	−13.0338	−	13.0338i	−0.846637	−	0.846637i
$238$	3.65681	+	2.29982i	0.237036	+	0.149075i
$239$	2.96454			0.191760			0.0958800	−	0.995393i	$-0.469433\pi$
$239$	2.96454			0.191760			0.0958800	+	0.995393i	$0.469433\pi$
$240$	27.3206	−	10.9271i	1.76354	−	0.705339i
$241$	−23.9141			−1.54044			−0.770221	−	0.637777i	$-0.779854\pi$
$241$	−23.9141			−1.54044			−0.770221	+	0.637777i	$0.779854\pi$
$242$	−12.7204	−	8.00007i	−0.817701	−	0.514264i
$243$	33.1681	+	33.1681i	2.12774	+	2.12774i
$244$	7.17395	+	14.9282i	0.459265	+	0.955681i
$245$	3.89466	+	14.0772i	0.248821	+	0.899361i
$246$	−1.20321	−	5.28162i	−0.0767141	−	0.336744i
$247$	18.9374	−	18.9374i	1.20495	−	1.20495i
$248$	−2.81025	−	0.320145i	−0.178451	−	0.0203293i
$249$		−	6.81219i		−	0.431705i
$250$	−15.3264	+	3.88618i	−0.969325	+	0.245784i
$251$			9.91181i			0.625628i	0.949814	+	0.312814i	$0.101272\pi$
$251$			9.91181i			0.625628i	−0.949814	+	0.312814i	$0.898728\pi$
$252$	3.54321	−	10.0993i	0.223201	−	0.636196i
$253$	3.53270	−	3.53270i	0.222099	−	0.222099i
$254$	−21.2754	+	4.84679i	−1.33494	+	0.304115i
$255$	−8.75861	−	31.6580i	−0.548486	−	1.98250i
$256$	−3.50908	−	15.6105i	−0.219317	−	0.975654i
$257$	10.0498	+	10.0498i	0.626887	+	0.626887i	0.947284	−	0.320396i	$-0.103816\pi$
$257$	10.0498	+	10.0498i	0.626887	+	0.626887i	−0.320396	+	0.947284i	$0.603816\pi$
$258$	25.6248	−	40.7445i	1.59533	−	2.53664i
$259$	5.64848			0.350979
$260$	20.5203	+	1.38739i	1.27262	+	0.0860425i
$261$	14.7231			0.911340
$262$	9.75866	−	15.5167i	0.602892	−	0.958624i
$263$	6.07934	+	6.07934i	0.374868	+	0.374868i	0.869247	−	0.494378i	$-0.164604\pi$
$263$	6.07934	+	6.07934i	0.374868	+	0.374868i	−0.494378	+	0.869247i	$0.664604\pi$
$264$	3.54394	+	4.45521i	0.218115	+	0.274199i
$265$	−9.54040	+	16.8385i	−0.586062	+	1.03438i
$266$	5.49307	−	1.25139i	0.336802	−	0.0767273i
$267$	−39.4961	+	39.4961i	−2.41712	+	2.41712i
$268$	−0.249243	−	0.0874436i	−0.0152249	−	0.00534147i
$269$			5.71293i			0.348324i	0.984717	+	0.174162i	$0.0557216\pi$
$269$			5.71293i			0.348324i	−0.984717	+	0.174162i	$0.944278\pi$
$270$	−44.1755	+	23.7845i	−2.68843	+	1.44748i
$271$		−	28.9050i		−	1.75585i	−0.478796	−	0.877926i	$-0.658927\pi$
$271$		−	28.9050i		−	1.75585i	0.478796	−	0.877926i	$-0.341073\pi$
$272$	−17.7520	+	1.97064i	−1.07637	+	0.119488i
$273$	7.31853	−	7.31853i	0.442937	−	0.442937i
$274$	2.10471	+	9.23880i	0.127150	+	0.558136i
$275$	−1.57231	−	2.62405i	−0.0948137	−	0.158236i
$276$	48.4266	−	23.2720i	2.91494	−	1.40081i
$277$	13.3417	+	13.3417i	0.801626	+	0.801626i	0.983350	−	0.181724i	$-0.0581677\pi$
$277$	13.3417	+	13.3417i	0.801626	+	0.801626i	−0.181724	+	0.983350i	$0.558168\pi$
$278$	−10.6407	−	6.69208i	−0.638186	−	0.401364i
$279$	7.82269			0.468332
$280$	3.49873	+	2.54518i	0.209089	+	0.152104i
$281$	−1.56039			−0.0930850			−0.0465425	−	0.998916i	$-0.514820\pi$
$281$	−1.56039			−0.0930850			−0.0465425	+	0.998916i	$0.514820\pi$
$282$	−8.56066	−	5.38392i	−0.509780	−	0.320608i
$283$	−16.9925	−	16.9925i	−1.01010	−	1.01010i	−0.999948	−	0.0101511i	$-0.996769\pi$
$283$	−16.9925	−	16.9925i	−1.01010	−	1.01010i	−0.0101511	−	0.999948i	$-0.503231\pi$
$284$	−8.80299	+	4.23039i	−0.522361	+	0.251028i
$285$	−37.2712	−	21.1172i	−2.20776	−	1.25088i
$286$	0.883852	+	3.87975i	0.0522633	+	0.229414i
$287$	0.563207	−	0.563207i	0.0332451	−	0.0332451i
$288$	14.5297	+	41.7985i	0.856168	+	2.46300i
$289$			2.93847i			0.172851i
$290$	−1.71045	+	5.70067i	−0.100441	+	0.334755i
$291$			21.7433i			1.27462i
$292$	9.54279	+	3.34797i	0.558450	+	0.195925i
$293$	−21.7795	+	21.7795i	−1.27237	+	1.27237i	−0.327530	+	0.944841i	$0.606216\pi$
$293$	−21.7795	+	21.7795i	−1.27237	+	1.27237i	−0.944841	+	0.327530i	$0.893784\pi$
$294$	−29.6308	+	6.75024i	−1.72810	+	0.393682i
$295$	9.60051	−	2.65611i	0.558963	−	0.154645i
$296$	−18.2769	+	14.5386i	−1.06233	+	0.845038i
$297$	−6.86370	−	6.86370i	−0.398272	−	0.398272i
$298$	−9.23993	+	14.6919i	−0.535255	+	0.851077i
$299$	37.5547			2.17184
$300$	−6.61330	−	32.2263i	−0.381819	−	1.86059i
$301$	7.07732			0.407930
$302$	−1.93756	+	3.08080i	−0.111494	+	0.177280i
$303$	13.0646	+	13.0646i	0.750539	+	0.750539i
$304$	−14.5532	+	18.1877i	−0.834681	+	1.04314i
$305$	17.8470	−	4.93763i	1.02192	−	0.282728i
$306$	48.1648	−	10.9725i	2.75340	−	0.627256i
$307$	−17.8116	+	17.8116i	−1.01656	+	1.01656i	−0.0166989	+	0.999861i	$0.505316\pi$
$307$	−17.8116	+	17.8116i	−1.01656	+	1.01656i	−0.999861	+	0.0166989i	$0.994684\pi$
$308$	−0.277113	+	0.789863i	−0.0157900	+	0.0450066i
$309$			31.8142i			1.80985i
$310$	−0.908795	+	3.02888i	−0.0516161	+	0.172029i
$311$			6.17773i			0.350307i	0.984541	+	0.175153i	$0.0560421\pi$
$311$			6.17773i			0.350307i	−0.984541	+	0.175153i	$0.943958\pi$
$312$	−4.84366	+	42.5179i	−0.274218	+	2.40710i
$313$	−3.23247	+	3.23247i	−0.182710	+	0.182710i	−0.792536	−	0.609826i	$-0.791239\pi$
$313$	−3.23247	+	3.23247i	−0.182710	+	0.182710i	0.609826	+	0.792536i	$0.291239\pi$
$314$	−3.80731	−	16.7125i	−0.214859	−	0.943143i
$315$	−10.4112	−	5.89878i	−0.586602	−	0.332359i
$316$	4.85379	+	10.1002i	0.273047	+	0.568181i
$317$	−18.1714	−	18.1714i	−1.02061	−	1.02061i	−0.999783	−	0.0208254i	$-0.993371\pi$
$317$	−18.1714	−	18.1714i	−1.02061	−	1.02061i	−0.0208254	−	0.999783i	$-0.506629\pi$
$318$	−34.0867	−	21.4376i	−1.91149	−	1.20216i
$319$	−1.15149			−0.0644712
$320$	−17.8720	+	0.769851i	−0.999074	+	0.0430360i
$321$	13.1898			0.736184
$322$	6.68747	+	4.20584i	0.372678	+	0.234383i
$323$	18.3868	+	18.3868i	1.02307	+	1.02307i
$324$	−24.8853	−	51.7836i	−1.38252	−	2.87687i
$325$	5.59032	−	22.3049i	0.310095	−	1.23725i
$326$	0.929109	+	4.07841i	0.0514586	+	0.225882i
$327$	−15.7628	+	15.7628i	−0.871685	+	0.871685i
$328$	−0.372751	+	3.27202i	−0.0205817	+	0.180667i
$329$		−	1.48699i		−	0.0819802i
$330$	5.60413	−	3.01732i	0.308497	−	0.166098i
$331$		−	30.0986i		−	1.65437i	−0.561929	−	0.827185i	$-0.689941\pi$
$331$		−	30.0986i		−	1.65437i	0.561929	−	0.827185i	$-0.310059\pi$
$332$	−1.37103	+	3.90789i	−0.0752453	+	0.214474i
$333$	45.6731	−	45.6731i	2.50287	−	2.50287i
$334$	−6.23137	+	1.41958i	−0.340965	+	0.0776758i
$335$	−0.145577	+	0.256939i	−0.00795374	+	0.0140381i
$336$	−5.62421	+	7.02883i	−0.306826	+	0.383454i
$337$	11.6917	+	11.6917i	0.636888	+	0.636888i	0.949787	−	0.312898i	$-0.101300\pi$
$337$	11.6917	+	11.6917i	0.636888	+	0.636888i	−0.312898	+	0.949787i	$0.601300\pi$
$338$	−6.13641	+	9.75715i	−0.333777	+	0.530719i
$339$	26.3430			1.43075
$340$	−1.34706	+	19.9237i	−0.0730545	+	1.08052i
$341$	−0.611810			−0.0331314
$342$	34.2979	−	54.5351i	1.85462	−	2.94892i
$343$	−6.54576	−	6.54576i	−0.353438	−	0.353438i
$344$	−22.9003	+	18.2163i	−1.23470	+	0.982156i
$345$	−16.0175	−	57.8951i	−0.862352	−	3.11697i
$346$	15.8111	−	3.60196i	0.850012	−	0.193643i
$347$	−16.0495	+	16.0495i	−0.861582	+	0.861582i	−0.991522	−	0.129940i	$-0.958522\pi$
$347$	−16.0495	+	16.0495i	−0.861582	+	0.861582i	0.129940	+	0.991522i	$0.458522\pi$
$348$	−11.6852	−	4.09960i	−0.626392	−	0.219761i
$349$			3.30057i			0.176675i	0.996091	+	0.0883376i	$0.0281554\pi$
$349$			3.30057i			0.176675i	−0.996091	+	0.0883376i	$0.971845\pi$
$350$	3.49347	−	3.34582i	0.186734	−	0.178842i
$351$		−	72.9652i		−	3.89459i
$352$	−1.13636	−	3.26904i	−0.0605682	−	0.174241i
$353$	−5.98766	+	5.98766i	−0.318691	+	0.318691i	−0.848264	−	0.529573i	$-0.822352\pi$
$353$	−5.98766	+	5.98766i	−0.318691	+	0.318691i	0.529573	+	0.848264i	$0.322352\pi$
$354$	4.60359	+	20.2079i	0.244678	+	1.07404i
$355$	2.91166	+	10.5242i	0.154535	+	0.558565i
$356$	30.6064	−	14.7083i	1.62214	−	0.779540i
$357$	7.10576	+	7.10576i	0.376077	+	0.376077i
$358$	4.83330	+	3.03974i	0.255448	+	0.160655i
$359$	−29.2698			−1.54480			−0.772402	−	0.635134i	$-0.780945\pi$
$359$	−29.2698			−1.54480			−0.772402	+	0.635134i	$0.780945\pi$
$360$	48.8705	−	7.71034i	2.57570	−	0.406370i
$361$	14.9118			0.784829
$362$	−8.88081	−	5.58527i	−0.466765	−	0.293555i
$363$	−24.7178	−	24.7178i	−1.29735	−	1.29735i
$364$	−5.67130	+	2.72542i	−0.297257	+	0.142851i
$365$	5.57374	−	9.83746i	0.291743	−	0.514916i
$366$	8.55792	+	37.5658i	0.447329	+	1.96359i
$367$	−6.84449	+	6.84449i	−0.357279	+	0.357279i	−0.862809	−	0.505530i	$-0.831297\pi$
$367$	−6.84449	+	6.84449i	−0.357279	+	0.357279i	0.505530	+	0.862809i	$0.331297\pi$
$368$	−32.4642	+	3.60385i	−1.69231	+	0.187864i
$369$		−	9.10808i		−	0.474148i
$370$	12.3782	+	22.9903i	0.643511	+	1.19521i
$371$		−	5.92085i		−	0.307395i
$372$	−6.20856	−	2.17819i	−0.321899	−	0.112934i
$373$	−15.5005	+	15.5005i	−0.802586	+	0.802586i	−0.983499	−	0.180913i	$-0.942095\pi$
$373$	−15.5005	+	15.5005i	−0.802586	+	0.802586i	0.180913	+	0.983499i	$0.442095\pi$
$374$	−3.76696	+	0.858156i	−0.194785	+	0.0443742i
$375$	−36.7700	+	0.895127i	−1.89880	+	0.0462242i
$376$	3.82734	+	4.81148i	0.197380	+	0.248133i
$377$	−6.12053	−	6.12053i	−0.315223	−	0.315223i
$378$	8.17156	−	12.9931i	0.420300	−	0.668294i
$379$	−24.6318			−1.26525			−0.632625	−	0.774458i	$-0.718023\pi$
$379$	−24.6318			−1.26525			−0.632625	+	0.774458i	$0.718023\pi$
$380$	17.1310	+	19.6154i	0.878800	+	1.00625i
$381$	−50.7595			−2.60049
$382$	3.23522	−	5.14414i	0.165528	−	0.263197i
$383$	1.55916	+	1.55916i	0.0796696	+	0.0796696i	0.745819	−	0.666149i	$-0.232059\pi$
$383$	1.55916	+	1.55916i	0.0796696	+	0.0796696i	−0.666149	+	0.745819i	$0.732059\pi$
$384$	0.106979	−	37.2195i	0.00545927	−	1.89935i
$385$	0.814253	+	0.461342i	0.0414982	+	0.0235122i
$386$	2.15157	−	0.490153i	0.109512	−	0.0249481i
$387$	57.2266	−	57.2266i	2.90899	−	2.90899i
$388$	4.37611	−	12.4733i	0.222163	−	0.633237i
$389$		−	2.26974i		−	0.115080i	−0.998343	−	0.0575401i	$-0.981674\pi$
$389$		−	2.26974i		−	0.115080i	0.998343	−	0.0575401i	$-0.0183257\pi$
$390$	45.8256	+	13.7497i	2.32047	+	0.696242i
$391$			36.4629i			1.84401i
$392$	18.3566	+	2.09120i	0.927149	+	0.105621i
$393$	30.1513	−	30.1513i	1.52093	−	1.52093i
$394$	−2.12128	−	9.31157i	−0.106869	−	0.469110i
$395$	12.0750	−	3.34072i	0.607561	−	0.168090i
$396$	4.14605	+	8.62748i	0.208347	+	0.433547i
$397$	−2.42350	−	2.42350i	−0.121632	−	0.121632i	0.643671	−	0.765303i	$-0.277411\pi$
$397$	−2.42350	−	2.42350i	−0.121632	−	0.121632i	−0.765303	+	0.643671i	$0.777411\pi$
$398$	11.6995	+	7.35799i	0.586443	+	0.368822i
$399$	13.1055			0.656097
$400$	−2.69212	+	19.8180i	−0.134606	+	0.990899i
$401$	32.2602			1.61100			0.805498	−	0.592598i	$-0.201898\pi$
$401$	32.2602			1.61100			0.805498	+	0.592598i	$0.201898\pi$
$402$	−0.520129	−	0.327117i	−0.0259417	−	0.0163151i
$403$	−3.25195	−	3.25195i	−0.161991	−	0.161991i
$404$	−4.86524	−	10.1240i	−0.242055	−	0.503689i
$405$	−61.9085	+	17.1278i	−3.07626	+	0.851089i
$406$	−0.404446	−	1.77535i	−0.0200723	−	0.0881093i
$407$	−3.57208	+	3.57208i	−0.177061	+	0.177061i
$408$	−41.2818	−	4.70285i	−2.04375	−	0.232826i
$409$			3.76269i			0.186053i	0.995664	+	0.0930265i	$0.0296541\pi$
$409$			3.76269i			0.186053i	−0.995664	+	0.0930265i	$0.970346\pi$
$410$	3.52657	+	1.05813i	0.174165	+	0.0522571i
$411$			22.0422i			1.08726i
$412$	6.40298	−	18.2506i	0.315452	−	0.899141i
$413$	−2.15488	+	2.15488i	−0.106034	+	0.106034i
$414$	88.0823	−	20.0662i	4.32901	−	0.986198i
$415$	4.02856	+	2.28252i	0.197754	+	0.112044i
$416$	11.3359	−	23.4160i	0.555786	−	1.14807i
$417$	−20.6765	−	20.6765i	−1.01253	−	1.01253i
$418$	−2.68243	+	4.26517i	−0.131202	+	0.208616i
$419$	23.7514			1.16033			0.580166	−	0.814499i	$-0.302988\pi$
$419$	23.7514			1.16033			0.580166	+	0.814499i	$0.302988\pi$
$420$	6.62043	+	7.58058i	0.323044	+	0.369894i
$421$	−5.18656			−0.252777			−0.126389	−	0.991981i	$-0.540339\pi$
$421$	−5.18656			−0.252777			−0.126389	+	0.991981i	$0.540339\pi$
$422$	8.05061	−	12.8008i	0.391898	−	0.623134i
$423$	−12.0236	−	12.0236i	−0.584609	−	0.584609i
$424$	15.2396	+	19.1583i	0.740103	+	0.930408i
$425$	21.6564	+	5.42779i	1.05049	+	0.263287i
$426$	−22.1521	+	5.04650i	−1.07327	+	0.244504i
$427$	−4.00584	+	4.00584i	−0.193856	+	0.193856i
$428$	−7.56650	−	2.65461i	−0.365740	−	0.128315i
$429$			9.25642i			0.446904i
$430$	15.5094	+	28.8059i	0.747929	+	1.38914i
$431$		−	14.9928i		−	0.722176i	−0.932532	−	0.361088i	$-0.882405\pi$
$431$		−	14.9928i		−	0.722176i	0.932532	−	0.361088i	$-0.117595\pi$
$432$	7.00195	+	63.0750i	0.336881	+	3.03470i
$433$	2.12930	−	2.12930i	0.102328	−	0.102328i	−0.654090	−	0.756417i	$-0.726948\pi$
$433$	2.12930	−	2.12930i	0.102328	−	0.102328i	0.756417	+	0.654090i	$0.226948\pi$
$434$	−0.214890	−	0.943279i	−0.0103150	−	0.0452788i
$435$	−6.82506	+	12.0460i	−0.327237	+	0.577562i
$436$	12.2150	−	5.87006i	0.584991	−	0.281125i
$437$	33.6252	+	33.6252i	1.60851	+	1.60851i
$438$	19.9143	+	12.5244i	0.951541	+	0.598438i
$439$	−15.8994			−0.758839			−0.379419	−	0.925225i	$-0.623876\pi$
$439$	−15.8994			−0.758839			−0.379419	+	0.925225i	$0.623876\pi$
$440$	−3.82215	+	0.603023i	−0.182214	+	0.0287480i
$441$	−51.0980			−2.43324
$442$	−24.5839	−	15.4611i	−1.16933	−	0.735412i
$443$	7.03278	+	7.03278i	0.334138	+	0.334138i	0.854155	−	0.520018i	$-0.174075\pi$
$443$	7.03278	+	7.03278i	0.334138	+	0.334138i	−0.520018	+	0.854155i	$0.674075\pi$
$444$	−48.9664	+	23.5315i	−2.32384	+	1.11675i
$445$	−10.1233	−	36.5907i	−0.479892	−	1.73457i
$446$	−8.08288	−	35.4806i	−0.382736	−	1.68005i
$447$	−28.5486	+	28.5486i	−1.35030	+	1.35030i
$448$	4.64103	−	2.90023i	0.219268	−	0.137023i
$449$			35.6653i			1.68315i	0.540141	+	0.841575i	$0.318371\pi$
$449$			35.6653i			1.68315i	−0.540141	+	0.841575i	$0.681629\pi$
$450$	1.19384	−	55.3019i	0.0562784	−	2.60696i
$451$			0.712340i			0.0335428i
$452$	−15.1120	−	5.30184i	−0.710807	−	0.249377i
$453$	−5.98647	+	5.98647i	−0.281269	+	0.281269i
$454$	−11.9606	+	2.72477i	−0.561341	+	0.127880i
$455$	1.87583	+	6.78017i	0.0879402	+	0.317859i
$456$	−42.4060	+	33.7323i	−1.98584	+	1.57966i
$457$	22.4233	+	22.4233i	1.04892	+	1.04892i	0.998740	+	0.0501755i	$0.0159781\pi$
$457$	22.4233	+	22.4233i	1.04892	+	1.04892i	0.0501755	+	0.998740i	$0.484022\pi$
$458$	−12.0195	+	19.1115i	−0.561633	+	0.893020i
$459$	70.8439			3.30671
$460$	−2.46346	+	36.4359i	−0.114859	+	1.69883i
$461$	−0.384645			−0.0179147			−0.00895736	−	0.999960i	$-0.502851\pi$
$461$	−0.384645			−0.0179147			−0.00895736	+	0.999960i	$0.502851\pi$
$462$	−1.03665	+	1.64832i	−0.0482294	+	0.0766867i
$463$	−21.8350	−	21.8350i	−1.01476	−	1.01476i	−0.999889	−	0.0148674i	$-0.995267\pi$
$463$	−21.8350	−	21.8350i	−1.01476	−	1.01476i	−0.0148674	−	0.999889i	$-0.504733\pi$
$464$	5.87825	+	4.70356i	0.272891	+	0.218357i
$465$	−3.62629	+	6.40027i	−0.168165	+	0.296806i
$466$	−25.2431	+	5.75068i	−1.16937	+	0.266395i
$467$	16.9566	−	16.9566i	0.784656	−	0.784656i	−0.195956	−	0.980613i	$-0.562781\pi$
$467$	16.9566	−	16.9566i	0.784656	−	0.784656i	0.980613	+	0.195956i	$0.0627811\pi$
$468$	−23.8201	+	67.8951i	−1.10109	+	3.13845i
$469$		−	0.0903464i		−	0.00417181i
$470$	6.05228	−	3.25861i	0.279171	−	0.150308i
$471$		−	39.8733i		−	1.83726i
$472$	1.42617	−	12.5190i	0.0656449	−	0.576234i
$473$	−4.47567	+	4.47567i	−0.205792	+	0.205792i
$474$	5.79016	+	25.4164i	0.265951	+	1.16742i
$475$	24.9764	−	14.9657i	1.14600	−	0.686672i
$476$	−2.64618	−	5.50642i	−0.121288	−	0.252386i
$477$	−47.8755	−	47.8755i	−2.19207	−	2.19207i
$478$	−3.54897	−	2.23200i	−0.162326	−	0.102089i
$479$	5.48247			0.250501			0.125250	−	0.992125i	$-0.460027\pi$
$479$	5.48247			0.250501			0.125250	+	0.992125i	$0.460027\pi$
$480$	−40.9335	−	7.48840i	−1.86835	−	0.341797i
$481$	−37.9733			−1.73143
$482$	28.6285	+	18.0049i	1.30399	+	0.820100i
$483$	12.9948	+	12.9948i	0.591283	+	0.591283i
$484$	9.20490	+	19.1544i	0.418405	+	0.870654i
$485$	−12.8585	−	7.28540i	−0.583874	−	0.330813i
$486$	−14.7346	−	64.6791i	−0.668377	−	2.93390i
$487$	−14.7941	+	14.7941i	−0.670385	+	0.670385i	−0.957805	−	0.287420i	$-0.907202\pi$
$487$	−14.7941	+	14.7941i	−0.670385	+	0.670385i	0.287420	+	0.957805i	$0.407202\pi$
$488$	2.65121	−	23.2724i	0.120015	−	1.05349i
$489$			9.73040i			0.440024i
$490$	5.93627	−	19.7847i	0.268173	−	0.893781i
$491$		−	3.83185i		−	0.172929i	−0.996255	−	0.0864645i	$-0.972443\pi$
$491$		−	3.83185i		−	0.172929i	0.996255	−	0.0864645i	$-0.0275569\pi$
$492$	−2.53611	+	7.22873i	−0.114337	+	0.325896i
$493$	5.94259	−	5.94259i	0.267641	−	0.267641i
$494$	−36.9286	+	8.41275i	−1.66149	+	0.378508i
$495$	10.3143	−	2.85361i	0.463595	−	0.128260i
$496$	3.12323	+	2.49909i	0.140237	+	0.112213i
$497$	−2.36220	−	2.36220i	−0.105959	−	0.105959i
$498$	−5.12889	+	8.15515i	−0.229831	+	0.365441i
$499$	−3.54089			−0.158512			−0.0792561	−	0.996854i	$-0.525254\pi$
$499$	−3.54089			−0.158512			−0.0792561	+	0.996854i	$0.525254\pi$
$500$	21.2737	+	6.88690i	0.951389	+	0.307992i
$501$	−14.8670			−0.664208
$502$	7.46259	−	11.8658i	0.333072	−	0.529598i
$503$	25.8928	+	25.8928i	1.15450	+	1.15450i	0.985639	+	0.168865i	$0.0540103\pi$
$503$	25.8928	+	25.8928i	1.15450	+	1.15450i	0.168865	+	0.985639i	$0.445990\pi$
$504$	−11.8455	+	9.42260i	−0.527639	+	0.419716i
$505$	−12.1035	+	3.34860i	−0.538599	+	0.149011i
$506$	−6.88889	+	1.56937i	−0.306249	+	0.0697670i
$507$	−18.9597	+	18.9597i	−0.842028	+	0.842028i
$508$	29.1188	+	10.2160i	1.29194	+	0.453260i
$509$			20.2711i			0.898503i	0.893405	+	0.449251i	$0.148309\pi$
$509$			20.2711i			0.898503i	−0.893405	+	0.449251i	$0.851691\pi$
$510$	−13.3499	+	44.4933i	−0.591146	+	1.97020i
$511$			3.45911i			0.153022i
$512$	−7.55224	+	21.3299i	−0.333765	+	0.942656i
$513$	65.3306	−	65.3306i	2.88442	−	2.88442i
$514$	−4.46452	−	19.5974i	−0.196922	−	0.864406i
$515$	−18.8141	−	10.6598i	−0.829050	−	0.469725i
$516$	−61.3530	+	29.4840i	−2.70092	+	1.29796i
$517$	0.940364	+	0.940364i	0.0413572	+	0.0413572i
$518$	−6.76202	−	4.25273i	−0.297106	−	0.186854i
$519$	37.7227			1.65584
$520$	−23.5211	−	17.1106i	−1.03147	−	0.750350i
$521$	−20.4136			−0.894335			−0.447168	−	0.894450i	$-0.647567\pi$
$521$	−20.4136			−0.894335			−0.447168	+	0.894450i	$0.647567\pi$
$522$	−17.6257	−	11.0850i	−0.771454	−	0.485179i
$523$	−16.1058	−	16.1058i	−0.704258	−	0.704258i	0.261063	−	0.965322i	$-0.415927\pi$
$523$	−16.1058	−	16.1058i	−0.704258	−	0.704258i	−0.965322	+	0.261063i	$0.915927\pi$
$524$	−23.3650	+	11.2283i	−1.02070	+	0.490513i
$525$	9.65239	−	5.78363i	0.421265	−	0.252418i
$526$	−2.70069	−	11.8550i	−0.117756	−	0.516900i
$527$	3.15741	−	3.15741i	0.137539	−	0.137539i
$528$	−0.888273	−	8.00174i	−0.0386571	−	0.348231i
$529$			43.6821i			1.89922i
$530$	24.0989	−	12.9751i	1.04679	−	0.563601i
$531$			34.8483i			1.51229i
$532$	−7.51814	−	2.63764i	−0.325953	−	0.114356i
$533$	−3.78630	+	3.78630i	−0.164003	+	0.164003i
$534$	77.0189	−	17.5458i	3.33293	−	0.759281i
$535$	−4.41943	+	7.80014i	−0.191068	+	0.337229i
$536$	0.232542	+	0.292337i	0.0100443	+	0.0126270i
$537$	9.39186	+	9.39186i	0.405289	+	0.405289i
$538$	4.30126	−	6.83918i	0.185440	−	0.294858i
$539$	3.99636			0.172135
$540$	70.7915	+	4.78627i	3.04638	+	0.205968i
$541$	25.3352			1.08924			0.544622	−	0.838682i	$-0.316673\pi$
$541$	25.3352			1.08924			0.544622	+	0.838682i	$0.316673\pi$
$542$	−21.7625	+	34.6033i	−0.934780	+	1.48634i
$543$	−17.2568	−	17.2568i	−0.740560	−	0.740560i
$544$	22.7353	+	11.0063i	0.974767	+	0.471891i
$545$	−4.04020	−	14.6033i	−0.173063	−	0.625535i
$546$	−14.2714	+	3.25119i	−0.610760	+	0.139138i
$547$	25.8545	−	25.8545i	1.10546	−	1.10546i	0.111721	−	0.993740i	$-0.464364\pi$
$547$	25.8545	−	25.8545i	1.10546	−	1.10546i	0.993740	−	0.111721i	$-0.0356363\pi$
$548$	4.43625	−	12.6448i	0.189507	−	0.540158i
$549$			64.7817i			2.76482i
$550$	−0.0933702	+	4.32514i	−0.00398132	+	0.184425i
$551$		−	10.9602i		−	0.466922i
$552$	−75.4948	−	8.60042i	−3.21327	−	0.366058i
$553$	−2.71029	+	2.71029i	−0.115253	+	0.115253i
$554$	−5.92694	−	26.0168i	−0.251811	−	1.10535i
$555$	16.1960	+	58.5405i	0.687484	+	2.48491i
$556$	7.69993	+	16.0227i	0.326550	+	0.679515i
$557$	−0.127023	−	0.127023i	−0.00538215	−	0.00538215i	0.704411	−	0.709793i	$-0.251211\pi$
$557$	−0.127023	−	0.127023i	−0.00538215	−	0.00538215i	−0.709793	+	0.704411i	$0.751211\pi$
$558$	−9.36485	−	5.88969i	−0.396446	−	0.249330i
$559$	−47.5791			−2.01238
$560$	−2.27221	−	5.68113i	−0.0960183	−	0.240071i
$561$	−8.98732			−0.379445
$562$	1.86800	+	1.17481i	0.0787970	+	0.0495566i
$563$	−17.4490	−	17.4490i	−0.735388	−	0.735388i	0.236294	−	0.971682i	$-0.424067\pi$
$563$	−17.4490	−	17.4490i	−0.735388	−	0.735388i	−0.971682	+	0.236294i	$0.924067\pi$
$564$	6.19476	+	12.8906i	0.260846	+	0.542793i
$565$	−8.82657	+	15.5786i	−0.371337	+	0.655396i
$566$	7.54877	+	33.1360i	0.317299	+	1.39281i
$567$	13.8956	−	13.8956i	0.583561	−	0.583561i
$568$	13.7235	+	1.56339i	0.575824	+	0.0655982i
$569$			43.3422i			1.81700i	0.417884	+	0.908501i	$0.362772\pi$
$569$			43.3422i			1.81700i	−0.417884	+	0.908501i	$0.637228\pi$
$570$	28.7197	+	53.3417i	1.20294	+	2.23424i
$571$			31.1653i			1.30423i	0.758121	+	0.652114i	$0.226118\pi$
$571$			31.1653i			1.30423i	−0.758121	+	0.652114i	$0.773882\pi$
$572$	1.86296	−	5.31005i	0.0778945	−	0.222025i
$573$	9.99586	−	9.99586i	0.417583	−	0.417583i
$574$	−1.09828	+	0.250200i	−0.0458411	+	0.0104431i
$575$	39.6046	+	9.92617i	1.65163	+	0.413950i
$576$	14.0760	−	60.9780i	0.586499	−	2.54075i
$577$	−6.05746	−	6.05746i	−0.252175	−	0.252175i	0.569687	−	0.821862i	$-0.307065\pi$
$577$	−6.05746	−	6.05746i	−0.252175	−	0.252175i	−0.821862	+	0.569687i	$0.807065\pi$
$578$	2.21237	−	3.51776i	0.0920225	−	0.146320i
$579$	5.13328			0.213332
$580$	6.33968	−	5.53671i	0.263241	−	0.229899i
$581$	−1.41655			−0.0587683
$582$	16.3705	−	26.0298i	0.678581	−	1.07897i
$583$	3.74433	+	3.74433i	0.155074	+	0.155074i
$584$	−8.90338	−	11.1927i	−0.368424	−	0.463159i
$585$	69.9916	+	39.6561i	2.89380	+	1.63958i
$586$	42.4708	−	9.67534i	1.75445	−	0.399685i
$587$	19.1182	−	19.1182i	0.789091	−	0.789091i	−0.192254	−	0.981345i	$-0.561580\pi$
$587$	19.1182	−	19.1182i	0.789091	−	0.789091i	0.981345	+	0.192254i	$0.0615797\pi$
$588$	40.5545	+	14.2280i	1.67244	+	0.586753i
$589$		−	5.82338i		−	0.239948i
$590$	−13.4929	−	4.04847i	−0.555496	−	0.166673i
$591$		−	22.2158i		−	0.913836i
$592$	32.8261	−	3.64403i	1.34915	−	0.149769i
$593$	−24.5379	+	24.5379i	−1.00765	+	1.00765i	−0.00767892	+	0.999971i	$0.502444\pi$
$593$	−24.5379	+	24.5379i	−1.00765	+	1.00765i	−0.999971	+	0.00767892i	$0.997556\pi$
$594$	3.04914	+	13.3845i	0.125108	+	0.549172i
$595$	−6.58305	+	1.82129i	−0.269879	+	0.0746657i
$596$	22.1230	−	10.6315i	0.906192	−	0.435483i
$597$	22.7340	+	22.7340i	0.930439	+	0.930439i
$598$	−44.9582	−	28.2749i	−1.83848	−	1.15624i
$599$	23.1146			0.944437			0.472218	−	0.881482i	$-0.343453\pi$
$599$	23.1146			0.944437			0.472218	+	0.881482i	$0.343453\pi$
$600$	−16.3461	+	43.5585i	−0.667326	+	1.77827i
$601$	28.3137			1.15494			0.577469	−	0.816412i	$-0.304040\pi$
$601$	28.3137			1.15494			0.577469	+	0.816412i	$0.304040\pi$
$602$	−8.47254	−	5.32851i	−0.345315	−	0.217174i
$603$	−0.730533	−	0.730533i	−0.0297496	−	0.0297496i
$604$	4.63906	−	2.22936i	0.188761	−	0.0907114i
$605$	22.8995	−	6.33547i	0.930998	−	0.257573i
$606$	−5.80381	−	25.4764i	−0.235764	−	1.03491i
$607$	−10.1476	+	10.1476i	−0.411878	+	0.411878i	−0.882392	−	0.470514i	$-0.844068\pi$
$607$	−10.1476	+	10.1476i	−0.411878	+	0.411878i	0.470514	+	0.882392i	$0.344068\pi$
$608$	31.1157	−	10.8162i	1.26191	−	0.438655i
$609$		−	4.23569i		−	0.171639i
$610$	−25.0829	−	7.52597i	−1.01558	−	0.304718i
$611$			9.99663i			0.404421i
$612$	−65.9212	−	23.1276i	−2.66471	−	0.934878i
$613$	−0.0298204	+	0.0298204i	−0.00120444	+	0.00120444i	−0.707709	−	0.706504i	$-0.750271\pi$
$613$	−0.0298204	+	0.0298204i	−0.00120444	+	0.00120444i	0.706504	+	0.707709i	$0.250271\pi$
$614$	34.7332	−	7.91263i	1.40172	−	0.319328i
$615$	7.45194	+	4.22215i	0.300491	+	0.170253i
$616$	0.926430	−	0.736938i	0.0373269	−	0.0296921i
$617$	−10.5401	−	10.5401i	−0.424329	−	0.424329i	0.462362	−	0.886691i	$-0.347002\pi$
$617$	−10.5401	−	10.5401i	−0.424329	−	0.424329i	−0.886691	+	0.462362i	$0.847002\pi$
$618$	23.9529	−	38.0860i	0.963525	−	1.53204i
$619$	−47.0803			−1.89232			−0.946159	−	0.323701i	$-0.895073\pi$
$619$	−47.0803			−1.89232			−0.946159	+	0.323701i	$0.895073\pi$
$620$	3.36839	−	2.94176i	0.135278	−	0.118144i
$621$	129.557			5.19895
$622$	4.65120	−	7.39560i	0.186496	−	0.296537i
$623$	8.21294	+	8.21294i	0.329044	+	0.329044i
$624$	37.8102	−	47.2531i	1.51362	−	1.89164i
$625$	11.7909	−	22.0448i	0.471637	−	0.881793i
$626$	6.30344	−	1.43600i	0.251936	−	0.0573939i
$627$	−8.28789	+	8.28789i	−0.330987	+	0.330987i
$628$	−8.02496	+	22.8738i	−0.320231	+	0.912762i
$629$		−	36.8693i		−	1.47008i
$630$	8.02242	+	14.9002i	0.319621	+	0.593639i
$631$		−	27.3050i		−	1.08700i	−0.839410	−	0.543498i	$-0.817099\pi$
$631$		−	27.3050i		−	1.08700i	0.839410	−	0.543498i	$-0.182901\pi$
$632$	1.79377	−	15.7458i	0.0713522	−	0.626333i
$633$	24.8740	−	24.8740i	0.988652	−	0.988652i
$634$	8.07249	+	35.4350i	0.320600	+	1.40730i
$635$	17.0077	−	30.0180i	0.674929	−	1.19123i
$636$	24.6662	+	51.3276i	0.978077	+	2.03527i
$637$	21.2418	+	21.2418i	0.841632	+	0.841632i
$638$	1.37850	+	0.866957i	0.0545752	+	0.0343232i
$639$	−38.2010			−1.51121
$640$	21.9749	+	12.5342i	0.868633	+	0.495456i
$641$	−8.08131			−0.319193			−0.159596	−	0.987182i	$-0.551019\pi$
$641$	−8.08131			−0.319193			−0.159596	+	0.987182i	$0.551019\pi$
$642$	−15.7901	−	9.93060i	−0.623184	−	0.391929i
$643$	−0.269257	−	0.269257i	−0.0106185	−	0.0106185i	0.701778	−	0.712396i	$-0.252390\pi$
$643$	−0.269257	−	0.269257i	−0.0106185	−	0.0106185i	−0.712396	+	0.701778i	$0.752390\pi$
$644$	−4.83926	−	10.0700i	−0.190693	−	0.396812i
$645$	20.2930	+	73.3489i	0.799036	+	2.88811i
$646$	−8.16817	−	35.8550i	−0.321372	−	1.41069i
$647$	−10.5537	+	10.5537i	−0.414907	+	0.414907i	−0.883444	−	0.468537i	$-0.844781\pi$
$647$	−10.5537	+	10.5537i	−0.414907	+	0.414907i	0.468537	+	0.883444i	$0.344781\pi$
$648$	−9.19662	+	80.7283i	−0.361277	+	3.17131i
$649$		−	2.72547i		−	0.106984i
$650$	−23.4857	+	22.4931i	−0.921185	+	0.882253i
$651$		−	2.25050i		−	0.0882042i
$652$	1.95836	−	5.58196i	0.0766952	−	0.218606i
$653$	22.2631	−	22.2631i	0.871221	−	0.871221i	−0.121385	−	0.992606i	$-0.538733\pi$
$653$	22.2631	−	22.2631i	0.871221	−	0.871221i	0.992606	+	0.121385i	$0.0387334\pi$
$654$	30.7381	−	7.00249i	1.20195	−	0.273819i
$655$	7.72815	+	27.9334i	0.301964	+	1.09145i
$656$	2.90973	−	3.63642i	0.113606	−	0.141978i
$657$	27.9700	+	27.9700i	1.09122	+	1.09122i
$658$	−1.11955	+	1.78013i	−0.0436446	+	0.0693967i
$659$	9.75764			0.380104			0.190052	−	0.981774i	$-0.439134\pi$
$659$	9.75764			0.380104			0.190052	+	0.981774i	$0.439134\pi$
$660$	−8.98067	−	0.607190i	−0.349572	−	0.0236348i
$661$	−28.0256			−1.09007			−0.545034	−	0.838414i	$-0.683483\pi$
$661$	−28.0256			−1.09007			−0.545034	+	0.838414i	$0.683483\pi$
$662$	−22.6612	+	36.0323i	−0.880753	+	1.40043i
$663$	−47.7703	−	47.7703i	−1.85524	−	1.85524i
$664$	4.58357	−	3.64605i	0.177877	−	0.141494i
$665$	−4.39118	+	7.75029i	−0.170283	+	0.300543i
$666$	−89.0643	+	20.2899i	−3.45117	+	0.786217i
$667$	10.8676	−	10.8676i	0.420796	−	0.420796i
$668$	8.52862	+	2.99216i	0.329982	+	0.115770i
$669$		−	84.6506i		−	3.27278i
$670$	0.367725	−	0.197987i	0.0142065	−	0.00764890i
$671$		−	5.06656i		−	0.195592i
$672$	12.0250	−	4.18003i	0.463873	−	0.161248i
$673$	−31.0977	+	31.0977i	−1.19873	+	1.19873i	−0.224183	+	0.974547i	$0.571971\pi$
$673$	−31.0977	+	31.0977i	−1.19873	+	1.19873i	−0.974547	+	0.224183i	$0.928029\pi$
$674$	−5.19394	−	22.7993i	−0.200063	−	0.878196i
$675$	19.2856	−	76.9480i	0.742304	−	2.96173i
$676$	14.6923	−	7.06057i	0.565088	−	0.271561i
$677$	−5.38942	−	5.38942i	−0.207132	−	0.207132i	0.595915	−	0.803047i	$-0.296789\pi$
$677$	−5.38942	−	5.38942i	−0.207132	−	0.207132i	−0.803047	+	0.595915i	$0.796789\pi$
$678$	−31.5362	−	19.8336i	−1.21114	−	0.761705i
$679$	4.52138			0.173515
$680$	16.6132	−	22.8373i	0.637086	−	0.875770i
$681$	−28.5361			−1.09350
$682$	0.732422	+	0.460631i	0.0280459	+	0.0176385i
$683$	29.3998	+	29.3998i	1.12495	+	1.12495i	0.990986	+	0.133968i	$0.0427720\pi$
$683$	29.3998	+	29.3998i	1.12495	+	1.12495i	0.133968	+	0.990986i	$0.457228\pi$
$684$	−82.1188	+	39.4633i	−3.13989	+	1.50892i
$685$	−13.0352	−	7.38553i	−0.498050	−	0.282187i
$686$	2.90789	+	12.7645i	0.111024	+	0.487350i
$687$	−37.1366	+	37.1366i	−1.41685	+	1.41685i
$688$	41.1299	−	4.56582i	1.56806	−	0.174070i
$689$			39.8044i			1.51643i
$690$	−24.4140	+	81.3680i	−0.929424	+	3.09763i
$691$			45.9853i			1.74936i	0.484697	+	0.874682i	$0.338930\pi$
$691$			45.9853i			1.74936i	−0.484697	+	0.874682i	$0.661070\pi$
$692$	−21.6401	−	7.59213i	−0.822631	−	0.288610i
$693$	−2.31510	+	2.31510i	−0.0879433	+	0.0879433i
$694$	31.2971	−	7.12985i	1.18802	−	0.270645i
$695$	19.1555	−	5.29964i	0.726611	−	0.201027i
$696$	10.9022	+	13.7055i	0.413247	+	0.519507i
$697$	−3.67622	−	3.67622i	−0.139247	−	0.139247i
$698$	2.48499	−	3.95124i	0.0940583	−	0.149557i
$699$	−60.2258			−2.27795
$700$	−6.70123	+	1.37519i	−0.253283	+	0.0519773i
$701$	−42.5404			−1.60673			−0.803364	−	0.595488i	$-0.796959\pi$
$701$	−42.5404			−1.60673			−0.803364	+	0.595488i	$0.796959\pi$
$702$	−54.9354	+	87.3495i	−2.07340	+	3.29680i
$703$	−34.0001	−	34.0001i	−1.28234	−	1.28234i
$704$	−1.10088	+	4.76907i	−0.0414909	+	0.179741i
$705$	15.4110	−	4.26367i	0.580413	−	0.160579i
$706$	11.6762	−	2.65997i	0.439439	−	0.100109i
$707$	2.71668	−	2.71668i	0.102171	−	0.102171i
$708$	9.70335	−	27.6577i	0.364674	−	1.03944i
$709$		−	24.0334i		−	0.902593i	−0.892374	−	0.451296i	$-0.850962\pi$
$709$		−	24.0334i		−	0.902593i	0.892374	−	0.451296i	$-0.149038\pi$
$710$	4.43797	−	14.7911i	0.166554	−	0.555100i
$711$			43.8303i			1.64377i
$712$	−47.7141	−	5.43562i	−1.78816	−	0.203708i
$713$	5.77417	−	5.77417i	0.216244	−	0.216244i
$714$	−3.15667	−	13.8565i	−0.118135	−	0.518567i
$715$	−5.47402	−	3.10149i	−0.204717	−	0.115989i
$716$	−3.49753	−	7.27798i	−0.130709	−	0.271991i
$717$	−6.89620	−	6.89620i	−0.257543	−	0.257543i
$718$	35.0401	+	22.0372i	1.30768	+	0.822422i
$719$	−42.9756			−1.60272			−0.801360	−	0.598183i	$-0.795890\pi$
$719$	−42.9756			−1.60272			−0.801360	+	0.598183i	$0.795890\pi$
$720$	−64.3100	−	27.5642i	−2.39669	−	1.02726i
$721$	6.61554			0.246376
$722$	−17.8515	−	11.2270i	−0.664362	−	0.417827i
$723$	55.6297	+	55.6297i	2.06889	+	2.06889i
$724$	6.42643	+	13.3727i	0.238836	+	0.496993i
$725$	−4.83688	−	8.07235i	−0.179637	−	0.299800i
$726$	10.9807	+	48.2006i	0.407531	+	1.78889i
$727$	32.3424	−	32.3424i	1.19951	−	1.19951i	0.225202	−	0.974312i	$-0.427696\pi$
$727$	32.3424	−	32.3424i	1.19951	−	1.19951i	0.974312	−	0.225202i	$-0.0723042\pi$
$728$	8.84130	+	1.00721i	0.327680	+	0.0373295i
$729$		−	68.1341i		−	2.52349i
$730$	−14.0792	+	7.58036i	−0.521093	+	0.280562i
$731$		−	46.1958i		−	1.70861i
$732$	18.0382	−	51.4147i	0.666711	−	1.90034i
$733$	−25.7092	+	25.7092i	−0.949590	+	0.949590i	−0.998789	−	0.0491985i	$-0.984333\pi$
$733$	−25.7092	+	25.7092i	−0.949590	+	0.949590i	0.0491985	+	0.998789i	$0.484333\pi$
$734$	13.3470	−	3.04060i	0.492647	−	0.112231i
$735$	23.6870	−	41.8067i	0.873708	−	1.54206i
$736$	41.5776	+	20.1280i	1.53257	+	0.741926i
$737$	0.0571348	+	0.0571348i	0.00210459	+	0.00210459i
$738$	−6.85746	+	10.9037i	−0.252427	+	0.401369i
$739$	−6.20498			−0.228254			−0.114127	−	0.993466i	$-0.536407\pi$
$739$	−6.20498			−0.228254			−0.114127	+	0.993466i	$0.536407\pi$
$740$	2.49092	−	36.8421i	0.0915680	−	1.35434i
$741$	−88.1053			−3.23663
$742$	−4.45780	+	7.08809i	−0.163651	+	0.260212i
$743$	−30.8065	−	30.8065i	−1.13018	−	1.13018i	−0.990147	−	0.140034i	$-0.955279\pi$
$743$	−30.8065	−	30.8065i	−1.13018	−	1.13018i	−0.140034	−	0.990147i	$-0.544721\pi$
$744$	5.79256	+	7.28202i	0.212365	+	0.266972i
$745$	−7.31735	−	26.4485i	−0.268087	−	0.968999i
$746$	30.2266	−	6.88596i	1.10667	−	0.252113i
$747$	−11.4541	+	11.4541i	−0.419083	+	0.419083i
$748$	5.15568	+	1.80880i	0.188510	+	0.0661364i
$749$		−	2.74273i		−	0.100217i
$750$	44.6928	+	26.6125i	1.63195	+	0.971751i
$751$			2.69103i			0.0981972i	0.998794	+	0.0490986i	$0.0156349\pi$
$751$			2.69103i			0.0981972i	−0.998794	+	0.0490986i	$0.984365\pi$
$752$	−0.959306	−	8.64162i	−0.0349823	−	0.315127i
$753$	23.0572	−	23.0572i	0.840249	−	0.840249i
$754$	2.71899	+	11.9353i	0.0990198	+	0.434657i
$755$	−1.53441	−	5.54610i	−0.0558428	−	0.201843i
$756$	−19.5650	+	9.40223i	−0.711573	+	0.341956i
$757$	−7.83670	−	7.83670i	−0.284830	−	0.284830i	0.550202	−	0.835032i	$-0.314551\pi$
$757$	−7.83670	−	7.83670i	−0.284830	−	0.284830i	−0.835032	+	0.550202i	$0.814551\pi$
$758$	29.4877	+	18.5452i	1.07104	+	0.673593i
$759$	−16.4357			−0.596579
$760$	−5.73974	−	36.3803i	−0.208202	−	1.31965i
$761$	−15.4454			−0.559894			−0.279947	−	0.960015i	$-0.590317\pi$
$761$	−15.4454			−0.559894			−0.279947	+	0.960015i	$0.590317\pi$
$762$	60.7663	+	38.2168i	2.20133	+	1.38445i
$763$	3.27777	+	3.27777i	0.118663	+	0.118663i
$764$	−7.74603	+	3.72246i	−0.280241	+	0.134674i
$765$	−38.5032	+	67.9568i	−1.39208	+	2.45698i
$766$	−0.692645	−	3.04043i	−0.0250263	−	0.109855i
$767$	14.4867	−	14.4867i	0.523084	−	0.523084i
$768$	−28.1506	+	44.4764i	−1.01580	+	1.60490i
$769$		−	4.01035i		−	0.144617i	−0.997382	−	0.0723084i	$-0.976963\pi$
$769$		−	4.01035i		−	0.144617i	0.997382	−	0.0723084i	$-0.0230366\pi$
$770$	−0.627431	−	1.16534i	−0.0226110	−	0.0419960i
$771$		−	46.7561i		−	1.68388i
$772$	−2.94477	−	1.03313i	−0.105984	−	0.0371833i
$773$	−5.08140	+	5.08140i	−0.182765	+	0.182765i	−0.792560	−	0.609794i	$-0.791252\pi$
$773$	−5.08140	+	5.08140i	−0.182765	+	0.182765i	0.609794	+	0.792560i	$0.291252\pi$
$774$	−111.594	+	25.4224i	−4.01117	+	0.913790i
$775$	−2.56993	−	4.28899i	−0.0923146	−	0.154065i
$776$	−14.6300	+	11.6375i	−0.525185	+	0.417764i
$777$	−13.1397	−	13.1397i	−0.471383	−	0.471383i
$778$	−1.70888	+	2.71719i	−0.0612664	+	0.0974161i
$779$	−6.78026			−0.242928
$780$	−44.5075	−	50.9623i	−1.59363	−	1.82474i
$781$	2.98769			0.106908
$782$	27.4528	−	43.6511i	0.981711	−	1.56096i
$783$	−21.1148	−	21.1148i	−0.754580	−	0.754580i
$784$	−20.4010	−	16.3241i	−0.728607	−	0.583005i
$785$	23.5801	+	13.3601i	0.841609	+	0.476841i
$786$	−58.7963	+	13.3945i	−2.09719	+	0.477765i
$787$	−3.04645	+	3.04645i	−0.108594	+	0.108594i	−0.759316	−	0.650722i	$-0.774466\pi$
$787$	−3.04645	+	3.04645i	−0.108594	+	0.108594i	0.650722	+	0.759316i	$0.274466\pi$
$788$	−4.47119	+	12.7444i	−0.159280	+	0.453999i
$789$		−	28.2839i		−	1.00693i
$790$	−16.9707	−	5.09196i	−0.603791	−	0.181164i
$791$		−	5.47784i		−	0.194770i
$792$	1.53221	−	13.4499i	0.0544449	−	0.477920i
$793$	26.9303	−	26.9303i	0.956322	−	0.956322i
$794$	1.07662	+	4.72591i	0.0382077	+	0.167716i
$795$	61.3634	−	16.9770i	2.17633	−	0.602113i
$796$	−8.46612	−	17.6171i	−0.300074	−	0.624421i
$797$	−11.0518	−	11.0518i	−0.391476	−	0.391476i	0.483737	−	0.875213i	$-0.339279\pi$
$797$	−11.0518	−	11.0518i	−0.391476	−	0.391476i	−0.875213	+	0.483737i	$0.839279\pi$
$798$	−15.6892	−	9.86714i	−0.555390	−	0.349293i
$799$	−9.70601			−0.343374
$800$	18.1438	−	21.6980i	0.641479	−	0.767140i
$801$	132.818			4.69290
$802$	−38.6200	−	24.2887i	−1.36372	−	0.857662i
$803$	−2.18753	−	2.18753i	−0.0771962	−	0.0771962i
$804$	0.376382	+	0.783209i	0.0132740	+	0.0276217i
$805$	−12.0389	+	3.33072i	−0.424315	+	0.117393i
$806$	1.44465	+	6.34143i	0.0508857	+	0.223367i
$807$	13.2896	−	13.2896i	0.467816	−	0.467816i
$808$	−1.79800	+	15.7829i	−0.0632534	+	0.555241i
$809$		−	2.12723i		−	0.0747896i	−0.999301	−	0.0373948i	$-0.988094\pi$
$809$		−	2.12723i		−	0.0747896i	0.999301	−	0.0373948i	$-0.0119059\pi$
$810$	87.0086	+	26.1064i	3.05717	+	0.917285i
$811$		−	0.160251i		−	0.00562717i	−0.999996	−	0.00281359i	$-0.999104\pi$
$811$		−	0.160251i		−	0.00562717i	0.999996	−	0.00281359i	$-0.000895594\pi$
$812$	−0.852483	+	2.42985i	−0.0299163	+	0.0852711i
$813$	−67.2396	+	67.2396i	−2.35820	+	2.35820i
$814$	6.96569	−	1.58686i	0.244147	−	0.0556196i
$815$	−5.75432	−	3.26030i	−0.201565	−	0.114203i
$816$	45.8793	+	36.7110i	1.60610	+	1.28514i
$817$	−42.6007	−	42.6007i	−1.49041	−	1.49041i
$818$	2.83292	−	4.50447i	0.0990508	−	0.157495i
$819$	−24.6109			−0.859974
$820$	−3.42514	−	3.92187i	−0.119611	−	0.136958i
$821$	−12.7604			−0.445342			−0.222671	−	0.974894i	$-0.571477\pi$
$821$	−12.7604			−0.445342			−0.222671	+	0.974894i	$0.571477\pi$
$822$	16.5955	−	26.3876i	0.578836	−	0.920373i
$823$	30.4438	+	30.4438i	1.06120	+	1.06120i	0.998001	+	0.0632023i	$0.0201313\pi$
$823$	30.4438	+	30.4438i	1.06120	+	1.06120i	0.0632023	+	0.998001i	$0.479869\pi$
$824$	−21.4061	+	17.0277i	−0.745717	+	0.593188i
$825$	−2.44659	+	9.76169i	−0.0851793	+	0.339858i
$826$	4.20209	−	0.957284i	0.146209	−	0.0333082i
$827$	−32.1973	+	32.1973i	−1.11961	+	1.11961i	−0.127810	+	0.991799i	$0.540795\pi$
$827$	−32.1973	+	32.1973i	−1.11961	+	1.11961i	−0.991799	+	0.127810i	$0.959205\pi$
$828$	−120.555	−	42.2951i	−4.18956	−	1.46985i
$829$		−	1.34701i		−	0.0467836i	−0.999726	−	0.0233918i	$-0.992553\pi$
$829$		−	1.34701i		−	0.0467836i	0.999726	−	0.0233918i	$-0.00744652\pi$
$830$	−3.10425	−	5.76559i	−0.107750	−	0.200127i
$831$		−	62.0718i		−	2.15325i
$832$	−31.2005	+	19.4975i	−1.08168	+	0.675955i
$833$	−20.6243	+	20.6243i	−0.714589	+	0.714589i
$834$	9.18536	+	40.3200i	0.318063	+	1.39617i
$835$	4.98138	−	8.79197i	0.172388	−	0.304259i
$836$	6.42248	−	3.08641i	0.222126	−	0.106746i
$837$	−11.2187	−	11.2187i	−0.387774	−	0.387774i
$838$	−28.4337	−	17.8824i	−0.982227	−	0.617737i
$839$	39.0608			1.34853			0.674265	−	0.738490i	$-0.264461\pi$
$839$	39.0608			1.34853			0.674265	+	0.738490i	$0.264461\pi$
$840$	−2.21818	−	14.0595i	−0.0765345	−	0.485100i
$841$	25.4577			0.877851
$842$	6.20904	+	3.90495i	0.213978	+	0.134574i
$843$	3.62982	+	3.62982i	0.125018	+	0.125018i
$844$	−19.2754	+	9.26306i	−0.663487	+	0.318848i
$845$	−4.85959	−	17.5650i	−0.167175	−	0.604253i
$846$	5.34139	+	23.4465i	0.183641	+	0.806109i
$847$	−5.13989	+	5.13989i	−0.176609	+	0.176609i
$848$	−3.81975	−	34.4090i	−0.131171	−	1.18161i
$849$			79.0569i			2.71323i
$850$	−21.8392	−	22.8029i	−0.749078	−	0.782134i
$851$		−	67.4255i		−	2.31132i
$852$	30.3186	+	10.6369i	1.03870	+	0.364414i
$853$	10.4050	−	10.4050i	0.356260	−	0.356260i	−0.506172	−	0.862432i	$-0.668940\pi$
$853$	10.4050	−	10.4050i	0.356260	−	0.356260i	0.862432	+	0.506172i	$0.168940\pi$
$854$	7.81154	−	1.77956i	0.267305	−	0.0608953i
$855$	27.1614	+	98.1749i	0.928902	+	3.35751i
$856$	7.05950	+	8.87474i	0.241289	+	0.303332i
$857$	31.2295	+	31.2295i	1.06678	+	1.06678i	0.997605	+	0.0691744i	$0.0220365\pi$
$857$	31.2295	+	31.2295i	1.06678	+	1.06678i	0.0691744	+	0.997605i	$0.477963\pi$
$858$	6.96915	−	11.0812i	0.237923	−	0.378307i
$859$	21.2826			0.726151			0.363076	−	0.931760i	$-0.381727\pi$
$859$	21.2826			0.726151			0.363076	+	0.931760i	$0.381727\pi$
$860$	3.12103	−	46.1617i	0.106426	−	1.57410i
$861$	−2.62030			−0.0892995
$862$	−11.2880	+	17.9484i	−0.384472	+	0.611326i
$863$	−10.1839	−	10.1839i	−0.346664	−	0.346664i	0.512202	−	0.858865i	$-0.328830\pi$
$863$	−10.1839	−	10.1839i	−0.346664	−	0.346664i	−0.858865	+	0.512202i	$0.828830\pi$
$864$	39.1067	−	80.7813i	1.33044	−	2.74824i
$865$	−12.6395	+	22.3083i	−0.429755	+	0.758504i
$866$	−4.15221	+	0.945922i	−0.141098	+	0.0321437i
$867$	6.83556	−	6.83556i	0.232148	−	0.232148i
$868$	−0.452940	+	1.29103i	−0.0153738	+	0.0438203i
$869$		−	3.42796i		−	0.116285i
$870$	17.2400	−	9.28217i	0.584490	−	0.314695i
$871$			0.607377i			0.0205802i
$872$	−19.0426	−	2.16934i	−0.644863	−	0.0734632i
$873$	36.5595	−	36.5595i	1.23735	−	1.23735i
$874$	−14.9377	−	65.5704i	−0.505275	−	2.21795i
$875$	0.186136	+	7.64607i	0.00629253	+	0.258484i
$876$	−14.4106	−	29.9869i	−0.486889	−	1.01316i
$877$	9.79862	+	9.79862i	0.330876	+	0.330876i	0.852919	−	0.522043i	$-0.174830\pi$
$877$	9.79862	+	9.79862i	0.330876	+	0.330876i	−0.522043	+	0.852919i	$0.674830\pi$
$878$	19.0339	+	11.9707i	0.642361	+	0.403990i
$879$	101.328			3.41771
$880$	5.02966	+	2.15579i	0.169550	+	0.0726716i
$881$	−37.1204			−1.25062			−0.625309	−	0.780377i	$-0.715027\pi$
$881$	−37.1204			−1.25062			−0.625309	+	0.780377i	$0.715027\pi$
$882$	61.1714	+	38.4716i	2.05975	+	1.29541i
$883$	−13.7690	−	13.7690i	−0.463364	−	0.463364i	0.436392	−	0.899757i	$-0.356256\pi$
$883$	−13.7690	−	13.7690i	−0.463364	−	0.463364i	−0.899757	+	0.436392i	$0.856256\pi$
$884$	17.7896	+	37.0183i	0.598330	+	1.24506i
$885$	−28.5117	−	16.1543i	−0.958411	−	0.543020i
$886$	−3.12425	−	13.7142i	−0.104961	−	0.460737i
$887$	11.8585	−	11.8585i	0.398168	−	0.398168i	−0.479419	−	0.877586i	$-0.659152\pi$
$887$	11.8585	−	11.8585i	0.398168	−	0.398168i	0.877586	+	0.479419i	$0.159152\pi$
$888$	76.3365	+	8.69629i	2.56168	+	0.291829i
$889$			10.5551i			0.354007i
$890$	−15.4301	+	51.4260i	−0.517217	+	1.72380i
$891$			17.5751i			0.588787i
$892$	−17.0369	+	48.5608i	−0.570439	+	1.62594i
$893$	−8.95065	+	8.95065i	−0.299522	+	0.299522i
$894$	55.6708	−	12.6825i	1.86191	−	0.424165i
$895$	−8.70099	+	2.40725i	−0.290842	+	0.0804655i
$896$	−7.73954	−	0.0222456i	−0.258560	−	0.000743174i
$897$	−87.3608	−	87.3608i	−2.91689	−	2.91689i
$898$	26.8523	−	42.6963i	0.896074	−	1.42480i
$899$	−1.88211			−0.0627718
$900$	−43.0659	+	65.3052i	−1.43553	+	2.17684i
$901$	−38.6472			−1.28753
$902$	0.536320	−	0.852771i	0.0178575	−	0.0283942i
$903$	−16.4635	−	16.4635i	−0.547870	−	0.547870i
$904$	14.0994	+	17.7248i	0.468938	+	0.589518i
$905$	15.9874	−	4.42313i	0.531438	−	0.147030i
$906$	11.6739	−	2.65944i	0.387838	−	0.0883539i
$907$	−35.9185	+	35.9185i	−1.19265	+	1.19265i	−0.216334	+	0.976319i	$0.569410\pi$
$907$	−35.9185	+	35.9185i	−1.19265	+	1.19265i	−0.976319	+	0.216334i	$0.930590\pi$
$908$	16.3700	+	5.74322i	0.543259	+	0.190595i
$909$		−	43.9337i		−	1.45719i
$910$	2.85915	−	9.52912i	0.0947800	−	0.315887i
$911$			37.5263i			1.24330i	0.783294	+	0.621651i	$0.213538\pi$
$911$			37.5263i			1.24330i	−0.783294	+	0.621651i	$0.786462\pi$
$912$	76.1628	−	8.45483i	2.52200	−	0.279967i
$913$	0.895820	−	0.895820i	0.0296473	−	0.0296473i
$914$	−9.96134	−	43.7262i	−0.329492	−	1.44633i
$915$	−53.0023	−	30.0302i	−1.75220	−	0.992769i
$916$	28.7780	−	13.8296i	0.950852	−	0.456944i
$917$	−6.26976	−	6.26976i	−0.207046	−	0.207046i
$918$	−84.8101	−	53.3383i	−2.79915	−	1.76043i
$919$	16.1593			0.533045			0.266522	−	0.963829i	$-0.414125\pi$
$919$	16.1593			0.533045			0.266522	+	0.963829i	$0.414125\pi$
$920$	30.3816	−	41.7641i	1.00165	−	1.37692i
$921$	82.8676			2.73058
$922$	0.460474	+	0.289599i	0.0151649	+	0.00953744i
$923$	15.8805	+	15.8805i	0.522711	+	0.522711i
$924$	2.48203	−	1.19277i	0.0816529	−	0.0392394i
$925$	−40.0461	−	10.0368i	−1.31671	−	0.330009i
$926$	9.69999	+	42.5790i	0.318761	+	1.39923i
$927$	53.4927	−	53.4927i	1.75693	−	1.75693i
$928$	−3.49578	−	10.0565i	−0.114755	−	0.330122i
$929$			22.1903i			0.728042i	0.931391	+	0.364021i	$0.118596\pi$
$929$			22.1903i			0.728042i	−0.931391	+	0.364021i	$0.881404\pi$
$930$	9.15993	−	4.93180i	0.300366	−	0.161720i
$931$			38.0385i			1.24666i
$932$	34.5492	+	12.1212i	1.13170	+	0.397042i
$933$	14.3708	−	14.3708i	0.470479	−	0.470479i
$934$	−33.0659	+	7.53280i	−1.08195	+	0.246481i
$935$	3.01132	−	5.31488i	0.0984807	−	0.173815i
$936$	79.6341	−	63.3458i	2.60292	−	2.07052i
$937$	23.9342	+	23.9342i	0.781898	+	0.781898i	0.980151	−	0.198253i	$-0.0635268\pi$
$937$	23.9342	+	23.9342i	0.781898	+	0.781898i	−0.198253	+	0.980151i	$0.563527\pi$
$938$	−0.0680217	+	0.108157i	−0.00222099	+	0.00353146i
$939$	15.0389			0.490777
$940$	−9.69883	−	0.655745i	−0.316341	−	0.0213880i
$941$	37.7635			1.23106			0.615528	−	0.788115i	$-0.288943\pi$
$941$	37.7635			1.23106			0.615528	+	0.788115i	$0.288943\pi$
$942$	−30.0205	+	47.7339i	−0.978121	+	1.55525i
$943$	−6.72296	−	6.72296i	−0.218930	−	0.218930i
$944$	−11.1329	+	13.9132i	−0.362344	+	0.452838i
$945$	6.47128	+	23.3904i	0.210511	+	0.760890i
$946$	8.72774	−	1.98828i	0.283763	−	0.0646445i
$947$	21.6518	−	21.6518i	0.703590	−	0.703590i	−0.261590	−	0.965179i	$-0.584247\pi$
$947$	21.6518	−	21.6518i	0.703590	−	0.703590i	0.965179	+	0.261590i	$0.0842467\pi$
$948$	12.2044	−	34.7864i	0.396379	−	1.12981i
$949$		−	23.2547i		−	0.754880i
$950$	−41.1679	−	0.888724i	−1.33566	−	0.0288340i
$951$			84.5418i			2.74145i
$952$	−0.977924	+	8.58426i	−0.0316947	+	0.278218i
$953$	3.23123	−	3.23123i	0.104670	−	0.104670i	−0.652833	−	0.757502i	$-0.726419\pi$
$953$	3.23123	−	3.23123i	0.104670	−	0.104670i	0.757502	+	0.652833i	$0.226419\pi$
$954$	21.2683	+	93.3590i	0.688585	+	3.02261i
$955$	2.56206	+	9.26055i	0.0829063	+	0.299664i
$956$	2.56814	+	5.34402i	0.0830596	+	0.172838i
$957$	2.67864	+	2.67864i	0.0865880	+	0.0865880i
$958$	−6.56329	−	4.12775i	−0.212050	−	0.133361i
$959$	4.58352			0.148010
$960$	43.3652	+	39.7835i	1.39960	+	1.28401i
$961$	−1.00000			−0.0322581
$962$	45.4594	+	28.5901i	1.46567	+	0.921781i
$963$	−22.1775	−	22.1775i	−0.714660	−	0.714660i
$964$	−20.7165	−	43.1087i	−0.667233	−	1.38844i
$965$	−1.71997	+	3.03570i	−0.0553679	+	0.0977225i
$966$	−5.77282	−	25.3403i	−0.185737	−	0.815312i
$967$	0.111476	−	0.111476i	0.00358482	−	0.00358482i	−0.705312	−	0.708897i	$-0.749193\pi$
$967$	0.111476	−	0.111476i	0.00358482	−	0.00358482i	0.708897	+	0.705312i	$0.249193\pi$
$968$	3.40176	−	29.8608i	0.109337	−	0.959764i
$969$		−	85.5438i		−	2.74806i
$970$	9.90824	+	18.4028i	0.318134	+	0.590877i
$971$			14.8876i			0.477766i	0.971048	+	0.238883i	$0.0767813\pi$
$971$			14.8876i			0.477766i	−0.971048	+	0.238883i	$0.923219\pi$
$972$	−31.0574	+	88.5236i	−0.996166	+	2.83940i
$973$	−4.29954	+	4.29954i	−0.137837	+	0.137837i
$974$	28.8491	−	6.57215i	0.924383	−	0.210585i
$975$	−64.8906	+	38.8819i	−2.07816	+	1.24522i
$976$	−20.6956	+	25.8643i	−0.662451	+	0.827895i
$977$	7.60231	+	7.60231i	0.243220	+	0.243220i	0.818181	−	0.574961i	$-0.194983\pi$
$977$	7.60231	+	7.60231i	0.243220	+	0.243220i	−0.574961	+	0.818181i	$0.694983\pi$
$978$	7.32600	−	11.6486i	0.234260	−	0.372483i
$979$	−10.3877			−0.331991
$980$	−22.0024	+	19.2156i	−0.702841	+	0.613821i
$981$	53.0074			1.69240
$982$	−2.88500	+	4.58726i	−0.0920639	+	0.146385i
$983$	3.81760	+	3.81760i	0.121762	+	0.121762i	0.765362	−	0.643600i	$-0.222560\pi$
$983$	3.81760	+	3.81760i	0.121762	+	0.121762i	−0.643600	+	0.765362i	$0.722560\pi$
$984$	8.47858	−	6.74437i	0.270287	−	0.215003i
$985$	13.1379	+	7.44370i	0.418608	+	0.237176i
$986$	−11.5883	+	2.63994i	−0.369046	+	0.0840729i
$987$	−3.45907	+	3.45907i	−0.110103	+	0.110103i
$988$	50.5426	+	17.7322i	1.60797	+	0.564137i
$989$		−	84.4815i		−	2.68636i
$990$	−14.4962	−	4.34949i	−0.460719	−	0.138236i
$991$		−	48.7811i		−	1.54958i	−0.632218	−	0.774791i	$-0.717855\pi$
$991$		−	48.7811i		−	1.54958i	0.632218	−	0.774791i	$-0.282145\pi$
$992$	−1.85737	−	5.34323i	−0.0589717	−	0.169648i
$993$	−70.0163	+	70.0163i	−2.22190	+	2.22190i
$994$	1.04938	+	4.60637i	0.0332845	+	0.146105i
$995$	−21.0616	+	5.82699i	−0.667698	+	0.184728i
$996$	12.2800	−	5.90132i	0.389107	−	0.186990i
$997$	10.0739	+	10.0739i	0.319044	+	0.319044i	0.848400	−	0.529356i	$-0.177566\pi$
$997$	10.0739	+	10.0739i	0.319044	+	0.319044i	−0.529356	+	0.848400i	$0.677566\pi$
$998$	4.23895	+	2.66593i	0.134181	+	0.0843887i
$999$	−131.001			−4.14470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	620.2.k.d.187.9	yes	88
4.3	odd	2		620.2.k.c.187.14	yes	88
5.3	odd	4		620.2.k.c.63.14	✓	88
20.3	even	4	inner	620.2.k.d.63.9	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
620.2.k.c.63.14	✓	88	5.3	odd	4
620.2.k.c.187.14	yes	88	4.3	odd	2
620.2.k.d.63.9	yes	88	20.3	even	4	inner
620.2.k.d.187.9	yes	88	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 620 = 2^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	620.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19714 - 0.752899i) q^{2} +(-2.32623 - 2.32623i) q^{3} +(0.866287 + 1.80265i) q^{4} +(2.15511 - 0.596241i) q^{5} +(1.03341 + 4.53624i) q^{6} +(-0.483723 + 0.483723i) q^{7} +(0.320145 - 2.81025i) q^{8} +7.82269i q^{9} +(-3.02888 - 0.908795i) q^{10} -0.611810i q^{11} +(2.17819 - 6.20856i) q^{12} +(3.25195 - 3.25195i) q^{13} +(0.943279 - 0.214890i) q^{14} +(-6.40027 - 3.62629i) q^{15} +(-2.49909 + 3.12323i) q^{16} +(3.15741 + 3.15741i) q^{17} +(5.88969 - 9.36485i) q^{18} +5.82338 q^{19} +(2.94176 + 3.36839i) q^{20} +2.25050 q^{21} +(-0.460631 + 0.732422i) q^{22} +(5.77417 + 5.77417i) q^{23} +(-7.28202 + 5.79256i) q^{24} +(4.28899 - 2.56993i) q^{25} +(-6.34143 + 1.44465i) q^{26} +(11.2187 - 11.2187i) q^{27} +(-1.29103 - 0.452940i) q^{28} -1.88211i q^{29} +(4.93180 + 9.15993i) q^{30} -1.00000i q^{31} +(5.34323 - 1.85737i) q^{32} +(-1.42321 + 1.42321i) q^{33} +(-1.40265 - 6.15707i) q^{34} +(-0.754061 + 1.33089i) q^{35} +(-14.1016 + 6.77670i) q^{36} +(-5.83854 - 5.83854i) q^{37} +(-6.97140 - 4.38441i) q^{38} -15.1296 q^{39} +(-0.985638 - 6.24728i) q^{40} -1.16432 q^{41} +(-2.69417 - 1.69440i) q^{42} +(-7.31547 - 7.31547i) q^{43} +(1.10288 - 0.530003i) q^{44} +(4.66421 + 16.8587i) q^{45} +(-2.56512 - 11.2599i) q^{46} +(-1.53702 + 1.53702i) q^{47} +(13.0788 - 1.45188i) q^{48} +6.53202i q^{49} +(-7.06942 - 0.152613i) q^{50} -14.6897i q^{51} +(8.67926 + 3.04501i) q^{52} +(-6.12008 + 6.12008i) q^{53} +(-21.8769 + 4.98380i) q^{54} +(-0.364786 - 1.31852i) q^{55} +(1.20452 + 1.51425i) q^{56} +(-13.5465 - 13.5465i) q^{57} +(-1.41704 + 2.25315i) q^{58} +4.45477 q^{59} +(0.992448 - 14.6789i) q^{60} +8.28126 q^{61} +(-0.752899 + 1.19714i) q^{62} +(-3.78402 - 3.78402i) q^{63} +(-7.79501 - 1.79938i) q^{64} +(5.06937 - 8.94726i) q^{65} +(2.77531 - 0.632249i) q^{66} +(-0.0933865 + 0.0933865i) q^{67} +(-2.95648 + 8.42693i) q^{68} -26.8641i q^{69} +(1.90474 - 1.02553i) q^{70} +4.88336i q^{71} +(21.9837 + 2.50440i) q^{72} +(3.57550 - 3.57550i) q^{73} +(2.59372 + 11.3854i) q^{74} +(-15.9554 - 3.99894i) q^{75} +(5.04472 + 10.4975i) q^{76} +(0.295947 + 0.295947i) q^{77} +(18.1122 + 11.3910i) q^{78} +5.60298 q^{79} +(-3.52362 + 8.22095i) q^{80} -28.7264 q^{81} +(1.39385 + 0.876612i) q^{82} +(1.46421 + 1.46421i) q^{83} +(1.94958 + 4.05687i) q^{84} +(8.68714 + 4.92199i) q^{85} +(3.24983 + 14.2654i) q^{86} +(-4.37822 + 4.37822i) q^{87} +(-1.71934 - 0.195868i) q^{88} -16.9786i q^{89} +(7.10922 - 23.6940i) q^{90} +3.14609i q^{91} +(-5.40672 + 15.4109i) q^{92} +(-2.32623 + 2.32623i) q^{93} +(2.99725 - 0.682808i) q^{94} +(12.5500 - 3.47214i) q^{95} +(-16.7503 - 8.10891i) q^{96} +(-4.67352 - 4.67352i) q^{97} +(4.91795 - 7.81975i) q^{98} +4.78600 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 2 q^{2} + 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 10 q^{10} - 12 q^{12} - 6 q^{13} + 22 q^{14} - 2 q^{15} + 8 q^{16} - 2 q^{17} - 24 q^{18} + 8 q^{19} + 8 q^{20} - 16 q^{21} - 16 q^{22} + 10 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) \) 88 * q + 2 * q^2 + 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^8 - 10 * q^10 - 12 * q^12 - 6 * q^13 + 22 * q^14 - 2 * q^15 + 8 * q^16 - 2 * q^17 - 24 * q^18 + 8 * q^19 + 8 * q^20 - 16 * q^21 - 16 * q^22 + 10 * q^23 - 44 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 + 46 * q^28 + 16 * q^30 - 8 * q^32 - 8 * q^33 + 40 * q^34 - 12 * q^35 - 20 * q^36 + 10 * q^37 - 64 * q^38 + 8 * q^39 + 8 * q^41 + 28 * q^42 + 10 * q^43 - 16 * q^44 + 6 * q^45 - 24 * q^46 - 64 * q^47 + 88 * q^48 - 14 * q^50 + 20 * q^52 + 18 * q^53 + 36 * q^54 + 40 * q^55 - 24 * q^56 - 24 * q^57 - 52 * q^58 - 32 * q^60 + 20 * q^61 + 2 * q^62 - 4 * q^63 - 150 * q^64 - 18 * q^65 + 8 * q^66 + 116 * q^67 + 68 * q^68 - 6 * q^70 - 26 * q^72 + 38 * q^73 + 36 * q^74 - 70 * q^75 - 8 * q^76 + 40 * q^77 - 152 * q^78 + 32 * q^79 + 68 * q^80 - 60 * q^81 + 14 * q^82 - 14 * q^83 - 120 * q^84 + 6 * q^85 + 4 * q^86 - 44 * q^87 + 52 * q^88 - 68 * q^90 - 92 * q^92 + 2 * q^93 + 112 * q^94 + 104 * q^95 - 20 * q^96 + 16 * q^97 - 62 * q^98 - 8 * q^99

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