LMFDB - Embedded newform 620.2.k.d.63.9

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			63.9
Character	$\chi$	$=$	620.63
Dual form			620.2.k.d.187.9

$q$-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 $\left(\mathbb{Z}/620\mathbb{Z}\right)^\times$.

$n$	$311$	$497$	$561$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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	−0.450042	+	0.893008i	$0.648591\pi$
$3$	−2.32623	+	2.32623i	−1.34305	+	1.34305i	−0.893008	+	0.450042i	$0.851409\pi$
$4$	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	0.609758	−	0.792588i	$-0.291267\pi$
$7$	−0.483723	−	0.483723i	−0.182830	−	0.182830i	−0.792588	+	0.609758i	$0.791267\pi$
$8$	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	$0.0294007\pi$
$11$			0.611810i			0.184468i	−0.995737	+	0.0922338i	$0.970599\pi$
$12$	2.17819	+	6.20856i	0.628790	+	1.79226i
$13$	3.25195	+	3.25195i	0.901929	+	0.901929i	0.995603	−	0.0936737i	$-0.0298611\pi$
$13$	3.25195	+	3.25195i	0.901929	+	0.901929i	−0.0936737	+	0.995603i	$0.529861\pi$
$14$	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	−0.211577	−	0.977361i	$-0.567860\pi$
$17$	3.15741	−	3.15741i	0.765784	−	0.765784i	0.977361	+	0.211577i	$0.0678599\pi$
$18$	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	0.231058	−	0.972940i	$-0.425781\pi$
$23$	5.77417	−	5.77417i	1.20400	−	1.20400i	0.972940	−	0.231058i	$-0.0742187\pi$
$24$	−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	$0.0559115\pi$
$29$			1.88211i			0.349499i	−0.984613	+	0.174749i	$0.944088\pi$
$30$	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	−0.999225	−	0.0393740i	$-0.987464\pi$
$37$	−5.83854	+	5.83854i	−0.959851	+	0.959851i	0.0393740	+	0.999225i	$0.487464\pi$
$38$	−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	−0.123218	+	0.992380i	$0.539322\pi$
$43$	−7.31547	+	7.31547i	−1.11560	+	1.11560i	−0.992380	+	0.123218i	$0.960678\pi$
$44$	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	0.586066	−	0.810263i	$-0.300676\pi$
$47$	−1.53702	−	1.53702i	−0.224197	−	0.224197i	−0.810263	+	0.586066i	$0.800676\pi$
$48$	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	0.148287	−	0.988944i	$-0.452624\pi$
$53$	−6.12008	−	6.12008i	−0.840658	−	0.840658i	−0.988944	+	0.148287i	$0.952624\pi$
$54$	−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	0.701379	−	0.712788i	$-0.252568\pi$
$67$	−0.0933865	−	0.0933865i	−0.0114090	−	0.0114090i	−0.712788	+	0.701379i	$0.752568\pi$
$68$	−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	$-0.906420\pi$
$71$		−	4.88336i		−	0.579548i	0.957095	−	0.289774i	$-0.0935802\pi$
$72$	21.9837	−	2.50440i	2.59081	−	0.295146i
$73$	3.57550	+	3.57550i	0.418481	+	0.418481i	0.884680	−	0.466199i	$-0.154377\pi$
$73$	3.57550	+	3.57550i	0.418481	+	0.418481i	−0.466199	+	0.884680i	$0.654377\pi$
$74$	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	−0.622167	−	0.782885i	$-0.713747\pi$
$83$	1.46421	−	1.46421i	0.160718	−	0.160718i	0.782885	+	0.622167i	$0.213747\pi$
$84$	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	$0.356334\pi$
$89$			16.9786i			1.79973i	−0.436172	+	0.899863i	$0.643666\pi$
$90$	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	−0.903375	−	0.428851i	$-0.858918\pi$
$97$	−4.67352	+	4.67352i	−0.474524	+	0.474524i	0.428851	+	0.903375i	$0.358918\pi$
$98$	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	−0.958586	−	0.284804i	$-0.908072\pi$
$103$	−6.83814	+	6.83814i	−0.673782	+	0.673782i	0.284804	+	0.958586i	$0.408072\pi$
$104$	−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	0.556665	−	0.830737i	$-0.312081\pi$
$107$	−2.83502	−	2.83502i	−0.274072	−	0.274072i	−0.830737	+	0.556665i	$0.812081\pi$
$108$	29.9419	−	10.5047i	2.88117	−	1.01082i
$109$			6.77612i			0.649034i	0.945880	+	0.324517i	$0.105202\pi$
$109$			6.77612i			0.649034i	−0.945880	+	0.324517i	$0.894798\pi$
$110$	−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	0.388709	−	0.921361i	$-0.372921\pi$
$113$	−5.66216	−	5.66216i	−0.532651	−	0.532651i	−0.921361	+	0.388709i	$0.872921\pi$
$114$	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	0.999508	−	0.0313784i	$-0.00998970\pi$
$127$	10.9103	+	10.9103i	0.968129	+	0.968129i	−0.0313784	+	0.999508i	$0.509990\pi$
$128$	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	$-0.808404\pi$
$131$		−	12.9615i		−	1.13245i	0.824251	−	0.566224i	$-0.191596\pi$
$132$	−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	−0.879911	−	0.475138i	$-0.842398\pi$
$137$	−4.73775	+	4.73775i	−0.404774	+	0.404774i	0.475138	+	0.879911i	$0.342398\pi$
$138$	−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	$0.167660\pi$
$149$			12.2725i			1.00540i	−0.864461	+	0.502700i	$0.832340\pi$
$150$	16.0901	−	16.8001i	1.31375	−	1.37172i
$151$			2.57347i			0.209426i	0.994502	+	0.104713i	$0.0333924\pi$
$151$			2.57347i			0.209426i	−0.994502	+	0.104713i	$0.966608\pi$
$152$	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	−0.276907	−	0.960897i	$-0.589310\pi$
$157$	8.57036	−	8.57036i	0.683989	−	0.683989i	0.960897	+	0.276907i	$0.0893095\pi$
$158$	−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	−0.784254	−	0.620439i	$-0.786954\pi$
$163$	−2.09145	+	2.09145i	−0.163815	+	0.163815i	0.620439	+	0.784254i	$0.286954\pi$
$164$	−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	0.819852	−	0.572576i	$-0.194056\pi$
$167$	3.19551	+	3.19551i	0.247276	+	0.247276i	−0.572576	+	0.819852i	$0.694056\pi$
$168$	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	0.328170	−	0.944619i	$-0.393568\pi$
$173$	−8.10812	−	8.10812i	−0.616449	−	0.616449i	−0.944619	+	0.328170i	$0.893568\pi$
$174$	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	$-0.950314\pi$
$191$		−	4.29702i		−	0.310922i	0.987842	−	0.155461i	$-0.0496862\pi$
$192$	13.9472	−	22.3188i	1.00655	−	1.61072i
$193$	−1.10335	−	1.10335i	−0.0794207	−	0.0794207i	0.666280	−	0.745701i	$-0.267885\pi$
$193$	−1.10335	−	1.10335i	−0.0794207	−	0.0794207i	−0.745701	+	0.666280i	$0.767885\pi$
$194$	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	−0.516237	−	0.856446i	$-0.672667\pi$
$197$	4.77507	−	4.77507i	0.340210	−	0.340210i	0.856446	+	0.516237i	$0.172667\pi$
$198$	−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	$-0.880021\pi$
$211$		−	10.6928i		−	0.736125i	0.929801	−	0.368062i	$-0.119979\pi$
$212$	−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	0.250227	−	0.968187i	$-0.419495\pi$
$223$	18.1948	−	18.1948i	1.21841	−	1.21841i	0.968187	−	0.250227i	$-0.0805053\pi$
$224$	−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	0.880725	−	0.473628i	$-0.157056\pi$
$227$	6.13354	+	6.13354i	0.407098	+	0.407098i	−0.473628	+	0.880725i	$0.657056\pi$
$228$	12.6844	+	36.1548i	0.840048	+	2.39441i
$229$			15.9643i			1.05495i	0.849571	+	0.527474i	$0.176861\pi$
$229$			15.9643i			1.05495i	−0.849571	+	0.527474i	$0.823139\pi$
$230$	−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	0.989890	−	0.141839i	$-0.0453014\pi$
$233$	12.9449	+	12.9449i	0.848051	+	0.848051i	−0.141839	+	0.989890i	$0.545301\pi$
$234$	−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	$-0.898728\pi$
$251$		−	9.91181i		−	0.625628i	0.949814	−	0.312814i	$-0.101272\pi$
$252$	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	−0.320396	−	0.947284i	$-0.603816\pi$
$257$	10.0498	−	10.0498i	0.626887	−	0.626887i	0.947284	+	0.320396i	$0.103816\pi$
$258$	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	−0.494378	−	0.869247i	$-0.664604\pi$
$263$	6.07934	−	6.07934i	0.374868	−	0.374868i	0.869247	+	0.494378i	$0.164604\pi$
$264$	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	$-0.944278\pi$
$269$		−	5.71293i		−	0.348324i	0.984717	−	0.174162i	$-0.0557216\pi$
$270$	−44.1755	−	23.7845i	−2.68843	−	1.44748i
$271$			28.9050i			1.75585i	0.478796	+	0.877926i	$0.341073\pi$
$271$			28.9050i			1.75585i	−0.478796	+	0.877926i	$0.658927\pi$
$272$	−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	−0.181724	−	0.983350i	$-0.558168\pi$
$277$	13.3417	−	13.3417i	0.801626	−	0.801626i	0.983350	+	0.181724i	$0.0581677\pi$
$278$	−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	−0.0101511	+	0.999948i	$0.503231\pi$
$283$	−16.9925	+	16.9925i	−1.01010	+	1.01010i	−0.999948	+	0.0101511i	$0.996769\pi$
$284$	−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	−0.944841	−	0.327530i	$-0.893784\pi$
$293$	−21.7795	−	21.7795i	−1.27237	−	1.27237i	−0.327530	−	0.944841i	$-0.606216\pi$
$294$	−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	−0.999861	−	0.0166989i	$-0.994684\pi$
$307$	−17.8116	−	17.8116i	−1.01656	−	1.01656i	−0.0166989	−	0.999861i	$-0.505316\pi$
$308$	−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	$-0.943958\pi$
$311$		−	6.17773i		−	0.350307i	0.984541	−	0.175153i	$-0.0560421\pi$
$312$	−4.84366	−	42.5179i	−0.274218	−	2.40710i
$313$	−3.23247	−	3.23247i	−0.182710	−	0.182710i	0.609826	−	0.792536i	$-0.291239\pi$
$313$	−3.23247	−	3.23247i	−0.182710	−	0.182710i	−0.792536	+	0.609826i	$0.791239\pi$
$314$	−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	−0.0208254	+	0.999783i	$0.506629\pi$
$317$	−18.1714	+	18.1714i	−1.02061	+	1.02061i	−0.999783	+	0.0208254i	$0.993371\pi$
$318$	−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	$0.310059\pi$
$331$			30.0986i			1.65437i	−0.561929	+	0.827185i	$0.689941\pi$
$332$	−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	−0.312898	−	0.949787i	$-0.601300\pi$
$337$	11.6917	−	11.6917i	0.636888	−	0.636888i	0.949787	+	0.312898i	$0.101300\pi$
$338$	−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	0.129940	−	0.991522i	$-0.458522\pi$
$347$	−16.0495	−	16.0495i	−0.861582	−	0.861582i	−0.991522	+	0.129940i	$0.958522\pi$
$348$	−11.6852	+	4.09960i	−0.626392	+	0.219761i
$349$		−	3.30057i		−	0.176675i	−0.996091	−	0.0883376i	$-0.971845\pi$
$349$		−	3.30057i		−	0.176675i	0.996091	−	0.0883376i	$-0.0281554\pi$
$350$	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	0.529573	−	0.848264i	$-0.322352\pi$
$353$	−5.98766	−	5.98766i	−0.318691	−	0.318691i	−0.848264	+	0.529573i	$0.822352\pi$
$354$	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	0.505530	−	0.862809i	$-0.331297\pi$
$367$	−6.84449	−	6.84449i	−0.357279	−	0.357279i	−0.862809	+	0.505530i	$0.831297\pi$
$368$	−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	0.180913	−	0.983499i	$-0.442095\pi$
$373$	−15.5005	−	15.5005i	−0.802586	−	0.802586i	−0.983499	+	0.180913i	$0.942095\pi$
$374$	−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	−0.666149	−	0.745819i	$-0.732059\pi$
$383$	1.55916	−	1.55916i	0.0796696	−	0.0796696i	0.745819	+	0.666149i	$0.232059\pi$
$384$	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	$0.0183257\pi$
$389$			2.26974i			0.115080i	−0.998343	+	0.0575401i	$0.981674\pi$
$390$	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	−0.765303	−	0.643671i	$-0.777411\pi$
$397$	−2.42350	+	2.42350i	−0.121632	+	0.121632i	0.643671	+	0.765303i	$0.277411\pi$
$398$	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	$-0.970346\pi$
$409$		−	3.76269i		−	0.186053i	0.995664	−	0.0930265i	$-0.0296541\pi$
$410$	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	$0.117595\pi$
$431$			14.9928i			0.722176i	−0.932532	+	0.361088i	$0.882405\pi$
$432$	7.00195	−	63.0750i	0.336881	−	3.03470i
$433$	2.12930	+	2.12930i	0.102328	+	0.102328i	0.756417	−	0.654090i	$-0.226948\pi$
$433$	2.12930	+	2.12930i	0.102328	+	0.102328i	−0.654090	+	0.756417i	$0.726948\pi$
$434$	−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	−0.520018	−	0.854155i	$-0.674075\pi$
$443$	7.03278	−	7.03278i	0.334138	−	0.334138i	0.854155	+	0.520018i	$0.174075\pi$
$444$	−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	$-0.681629\pi$
$449$		−	35.6653i		−	1.68315i	0.540141	−	0.841575i	$-0.318371\pi$
$450$	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	0.0501755	−	0.998740i	$-0.484022\pi$
$457$	22.4233	−	22.4233i	1.04892	−	1.04892i	0.998740	−	0.0501755i	$-0.0159781\pi$
$458$	−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	−0.0148674	+	0.999889i	$0.504733\pi$
$463$	−21.8350	+	21.8350i	−1.01476	+	1.01476i	−0.999889	+	0.0148674i	$0.995267\pi$
$464$	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	0.980613	−	0.195956i	$-0.0627811\pi$
$467$	16.9566	+	16.9566i	0.784656	+	0.784656i	−0.195956	+	0.980613i	$0.562781\pi$
$468$	−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	0.287420	−	0.957805i	$-0.407202\pi$
$487$	−14.7941	−	14.7941i	−0.670385	−	0.670385i	−0.957805	+	0.287420i	$0.907202\pi$
$488$	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	$0.0275569\pi$
$491$			3.83185i			0.172929i	−0.996255	+	0.0864645i	$0.972443\pi$
$492$	−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	0.168865	−	0.985639i	$-0.445990\pi$
$503$	25.8928	−	25.8928i	1.15450	−	1.15450i	0.985639	−	0.168865i	$-0.0540103\pi$
$504$	−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	$-0.851691\pi$
$509$		−	20.2711i		−	0.898503i	0.893405	−	0.449251i	$-0.148309\pi$
$510$	−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	−0.965322	−	0.261063i	$-0.915927\pi$
$523$	−16.1058	+	16.1058i	−0.704258	+	0.704258i	0.261063	+	0.965322i	$0.415927\pi$
$524$	−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	0.993740	+	0.111721i	$0.0356363\pi$
$547$	25.8545	+	25.8545i	1.10546	+	1.10546i	0.111721	+	0.993740i	$0.464364\pi$
$548$	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	−0.709793	−	0.704411i	$-0.751211\pi$
$557$	−0.127023	+	0.127023i	−0.00538215	+	0.00538215i	0.704411	+	0.709793i	$0.251211\pi$
$558$	−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	−0.971682	−	0.236294i	$-0.924067\pi$
$563$	−17.4490	+	17.4490i	−0.735388	+	0.735388i	0.236294	+	0.971682i	$0.424067\pi$
$564$	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	$-0.637228\pi$
$569$		−	43.3422i		−	1.81700i	0.417884	−	0.908501i	$-0.362772\pi$
$570$	28.7197	−	53.3417i	1.20294	−	2.23424i
$571$		−	31.1653i		−	1.30423i	−0.758121	−	0.652114i	$-0.773882\pi$
$571$		−	31.1653i		−	1.30423i	0.758121	−	0.652114i	$-0.226118\pi$
$572$	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	−0.821862	−	0.569687i	$-0.807065\pi$
$577$	−6.05746	+	6.05746i	−0.252175	+	0.252175i	0.569687	+	0.821862i	$0.307065\pi$
$578$	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	0.981345	−	0.192254i	$-0.0615797\pi$
$587$	19.1182	+	19.1182i	0.789091	+	0.789091i	−0.192254	+	0.981345i	$0.561580\pi$
$588$	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	−0.999971	−	0.00767892i	$-0.997556\pi$
$593$	−24.5379	−	24.5379i	−1.00765	−	1.00765i	−0.00767892	−	0.999971i	$-0.502444\pi$
$594$	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	0.470514	−	0.882392i	$-0.344068\pi$
$607$	−10.1476	−	10.1476i	−0.411878	−	0.411878i	−0.882392	+	0.470514i	$0.844068\pi$
$608$	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	0.706504	−	0.707709i	$-0.250271\pi$
$613$	−0.0298204	−	0.0298204i	−0.00120444	−	0.00120444i	−0.707709	+	0.706504i	$0.750271\pi$
$614$	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	−0.886691	−	0.462362i	$-0.847002\pi$
$617$	−10.5401	+	10.5401i	−0.424329	+	0.424329i	0.462362	+	0.886691i	$0.347002\pi$
$618$	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	$0.182901\pi$
$631$			27.3050i			1.08700i	−0.839410	+	0.543498i	$0.817099\pi$
$632$	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	−0.712396	−	0.701778i	$-0.752390\pi$
$643$	−0.269257	+	0.269257i	−0.0106185	+	0.0106185i	0.701778	+	0.712396i	$0.252390\pi$
$644$	−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	0.468537	−	0.883444i	$-0.344781\pi$
$647$	−10.5537	−	10.5537i	−0.414907	−	0.414907i	−0.883444	+	0.468537i	$0.844781\pi$
$648$	−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	0.992606	−	0.121385i	$-0.0387334\pi$
$653$	22.2631	+	22.2631i	0.871221	+	0.871221i	−0.121385	+	0.992606i	$0.538733\pi$
$654$	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	−0.974547	−	0.224183i	$-0.928029\pi$
$673$	−31.0977	−	31.0977i	−1.19873	−	1.19873i	−0.224183	−	0.974547i	$-0.571971\pi$
$674$	−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	−0.803047	−	0.595915i	$-0.796789\pi$
$677$	−5.38942	+	5.38942i	−0.207132	+	0.207132i	0.595915	+	0.803047i	$0.296789\pi$
$678$	−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	0.133968	−	0.990986i	$-0.457228\pi$
$683$	29.3998	−	29.3998i	1.12495	−	1.12495i	0.990986	−	0.133968i	$-0.0427720\pi$
$684$	−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	$-0.661070\pi$
$691$		−	45.9853i		−	1.74936i	0.484697	−	0.874682i	$-0.338930\pi$
$692$	−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	$0.149038\pi$
$709$			24.0334i			0.902593i	−0.892374	+	0.451296i	$0.850962\pi$
$710$	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	0.974312	+	0.225202i	$0.0723042\pi$
$727$	32.3424	+	32.3424i	1.19951	+	1.19951i	0.225202	+	0.974312i	$0.427696\pi$
$728$	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	0.0491985	−	0.998789i	$-0.484333\pi$
$733$	−25.7092	−	25.7092i	−0.949590	−	0.949590i	−0.998789	+	0.0491985i	$0.984333\pi$
$734$	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	−0.140034	+	0.990147i	$0.544721\pi$
$743$	−30.8065	+	30.8065i	−1.13018	+	1.13018i	−0.990147	+	0.140034i	$0.955279\pi$
$744$	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	$-0.984365\pi$
$751$		−	2.69103i		−	0.0981972i	0.998794	−	0.0490986i	$-0.0156349\pi$
$752$	−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	−0.835032	−	0.550202i	$-0.814551\pi$
$757$	−7.83670	+	7.83670i	−0.284830	+	0.284830i	0.550202	+	0.835032i	$0.314551\pi$
$758$	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	$0.0230366\pi$
$769$			4.01035i			0.144617i	−0.997382	+	0.0723084i	$0.976963\pi$
$770$	−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	0.609794	−	0.792560i	$-0.291252\pi$
$773$	−5.08140	−	5.08140i	−0.182765	−	0.182765i	−0.792560	+	0.609794i	$0.791252\pi$
$774$	−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	0.650722	−	0.759316i	$-0.274466\pi$
$787$	−3.04645	−	3.04645i	−0.108594	−	0.108594i	−0.759316	+	0.650722i	$0.774466\pi$
$788$	−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	−0.875213	−	0.483737i	$-0.839279\pi$
$797$	−11.0518	+	11.0518i	−0.391476	+	0.391476i	0.483737	+	0.875213i	$0.339279\pi$
$798$	−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	$0.0119059\pi$
$809$			2.12723i			0.0747896i	−0.999301	+	0.0373948i	$0.988094\pi$
$810$	87.0086	−	26.1064i	3.05717	−	0.917285i
$811$			0.160251i			0.00562717i	0.999996	+	0.00281359i	$0.000895594\pi$
$811$			0.160251i			0.00562717i	−0.999996	+	0.00281359i	$0.999104\pi$
$812$	−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	0.0632023	−	0.998001i	$-0.479869\pi$
$823$	30.4438	−	30.4438i	1.06120	−	1.06120i	0.998001	−	0.0632023i	$-0.0201313\pi$
$824$	−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	−0.991799	−	0.127810i	$-0.959205\pi$
$827$	−32.1973	−	32.1973i	−1.11961	−	1.11961i	−0.127810	−	0.991799i	$-0.540795\pi$
$828$	−120.555	+	42.2951i	−4.18956	+	1.46985i
$829$			1.34701i			0.0467836i	0.999726	+	0.0233918i	$0.00744652\pi$
$829$			1.34701i			0.0467836i	−0.999726	+	0.0233918i	$0.992553\pi$
$830$	−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	0.862432	−	0.506172i	$-0.168940\pi$
$853$	10.4050	+	10.4050i	0.356260	+	0.356260i	−0.506172	+	0.862432i	$0.668940\pi$
$854$	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	0.0691744	−	0.997605i	$-0.477963\pi$
$857$	31.2295	−	31.2295i	1.06678	−	1.06678i	0.997605	−	0.0691744i	$-0.0220365\pi$
$858$	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	−0.858865	−	0.512202i	$-0.828830\pi$
$863$	−10.1839	+	10.1839i	−0.346664	+	0.346664i	0.512202	+	0.858865i	$0.328830\pi$
$864$	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	−0.522043	−	0.852919i	$-0.674830\pi$
$877$	9.79862	−	9.79862i	0.330876	−	0.330876i	0.852919	+	0.522043i	$0.174830\pi$
$878$	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	−0.899757	−	0.436392i	$-0.856256\pi$
$883$	−13.7690	+	13.7690i	−0.463364	+	0.463364i	0.436392	+	0.899757i	$0.356256\pi$
$884$	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	0.877586	−	0.479419i	$-0.159152\pi$
$887$	11.8585	+	11.8585i	0.398168	+	0.398168i	−0.479419	+	0.877586i	$0.659152\pi$
$888$	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	−0.976319	−	0.216334i	$-0.930590\pi$
$907$	−35.9185	−	35.9185i	−1.19265	−	1.19265i	−0.216334	−	0.976319i	$-0.569410\pi$
$908$	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	$-0.786462\pi$
$911$		−	37.5263i		−	1.24330i	0.783294	−	0.621651i	$-0.213538\pi$
$912$	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	$-0.881404\pi$
$929$		−	22.1903i		−	0.728042i	0.931391	−	0.364021i	$-0.118596\pi$
$930$	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	−0.198253	−	0.980151i	$-0.563527\pi$
$937$	23.9342	−	23.9342i	0.781898	−	0.781898i	0.980151	+	0.198253i	$0.0635268\pi$
$938$	−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	0.965179	−	0.261590i	$-0.0842467\pi$
$947$	21.6518	+	21.6518i	0.703590	+	0.703590i	−0.261590	+	0.965179i	$0.584247\pi$
$948$	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	0.757502	−	0.652833i	$-0.226419\pi$
$953$	3.23123	+	3.23123i	0.104670	+	0.104670i	−0.652833	+	0.757502i	$0.726419\pi$
$954$	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	0.708897	−	0.705312i	$-0.249193\pi$
$967$	0.111476	+	0.111476i	0.00358482	+	0.00358482i	−0.705312	+	0.708897i	$0.749193\pi$
$968$	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	$-0.923219\pi$
$971$		−	14.8876i		−	0.477766i	0.971048	−	0.238883i	$-0.0767813\pi$
$972$	−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	−0.574961	−	0.818181i	$-0.694983\pi$
$977$	7.60231	−	7.60231i	0.243220	−	0.243220i	0.818181	+	0.574961i	$0.194983\pi$
$978$	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	−0.643600	−	0.765362i	$-0.722560\pi$
$983$	3.81760	−	3.81760i	0.121762	−	0.121762i	0.765362	+	0.643600i	$0.222560\pi$
$984$	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	$0.282145\pi$
$991$			48.7811i			1.54958i	−0.632218	+	0.774791i	$0.717855\pi$
$992$	−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	−0.529356	−	0.848400i	$-0.677566\pi$
$997$	10.0739	−	10.0739i	0.319044	−	0.319044i	0.848400	+	0.529356i	$0.177566\pi$
$998$	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.63.9	yes	88
4.3	odd	2		620.2.k.c.63.14	✓	88
5.2	odd	4		620.2.k.c.187.14	yes	88
20.7	even	4	inner	620.2.k.d.187.9	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
620.2.k.c.63.14	✓	88	4.3	odd	2
620.2.k.c.187.14	yes	88	5.2	odd	4
620.2.k.d.63.9	yes	88	1.1	even	1	trivial
620.2.k.d.187.9	yes	88	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 620 = 2^{2} \cdot 5 \cdot 31 \)
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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