LMFDB - Embedded newform 66.3.g.a.53.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [66,3,Mod(5,66)] 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("66.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(66, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	66.g (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.79836974478$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			53.7
Character	$\chi$	$=$	66.53
Dual form			66.3.g.a.5.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34500 + 0.437016i) q^{2} +(1.95466 - 2.27581i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-1.55423 + 0.504998i) q^{5} +(3.62358 - 2.20673i) q^{6} +(0.373199 + 0.271145i) q^{7} +(1.66251 + 2.28825i) q^{8} +(-1.35858 - 8.89687i) q^{9} -2.31112 q^{10} +(-7.63276 + 7.92092i) q^{11} +(5.83808 - 1.38449i) q^{12} +(-1.47781 + 4.54823i) q^{13} +(0.383457 + 0.527784i) q^{14} +(-1.88871 + 4.52422i) q^{15} +(1.23607 + 3.80423i) q^{16} +(7.34866 - 2.38773i) q^{17} +(2.06079 - 12.5600i) q^{18} +(-19.8950 + 14.4546i) q^{19} +(-3.10845 - 1.01000i) q^{20} +(1.34655 - 0.319331i) q^{21} +(-13.7276 + 7.31798i) q^{22} -22.4669i q^{23} +(8.45725 + 0.689206i) q^{24} +(-18.0648 + 13.1249i) q^{25} +(-3.97530 + 5.47153i) q^{26} +(-22.9031 - 14.2985i) q^{27} +(0.285099 + 0.877444i) q^{28} +(21.3868 - 29.4364i) q^{29} +(-4.51746 + 5.25966i) q^{30} +(5.71622 - 17.5927i) q^{31} +5.65685i q^{32} +(3.10701 + 32.8534i) q^{33} +10.9274 q^{34} +(-0.716964 - 0.232956i) q^{35} +(8.26067 - 15.9925i) q^{36} +(19.2530 + 13.9881i) q^{37} +(-33.0756 + 10.7469i) q^{38} +(7.46227 + 12.2535i) q^{39} +(-3.73947 - 2.71689i) q^{40} +(38.6755 + 53.2323i) q^{41} +(1.95066 + 0.158965i) q^{42} +64.1379 q^{43} +(-21.6617 + 3.84348i) q^{44} +(6.60444 + 13.1417i) q^{45} +(9.81842 - 30.2180i) q^{46} +(-40.1636 - 55.2805i) q^{47} +(11.0738 + 4.62293i) q^{48} +(-15.0761 - 46.3994i) q^{49} +(-30.0329 + 9.75829i) q^{50} +(8.93017 - 21.3913i) q^{51} +(-7.73792 + 5.62193i) q^{52} +(93.7067 + 30.4471i) q^{53} +(-24.5559 - 29.2405i) q^{54} +(7.86297 - 16.1654i) q^{55} +1.30475i q^{56} +(-5.99226 + 73.5310i) q^{57} +(41.6294 - 30.2455i) q^{58} +(15.0359 - 20.6951i) q^{59} +(-8.37453 + 5.10002i) q^{60} +(-3.97349 - 12.2291i) q^{61} +(15.3766 - 21.1641i) q^{62} +(1.90532 - 3.68868i) q^{63} +(-2.47214 + 7.60845i) q^{64} -7.81527i q^{65} +(-10.1785 + 45.5456i) q^{66} -45.1058 q^{67} +(14.6973 + 4.77545i) q^{68} +(-51.1304 - 43.9153i) q^{69} +(-0.862509 - 0.626649i) q^{70} +(-107.664 + 34.9821i) q^{71} +(18.0996 - 17.8999i) q^{72} +(9.15291 + 6.64998i) q^{73} +(19.7822 + 27.2279i) q^{74} +(-5.44102 + 66.7667i) q^{75} -49.1832 q^{76} +(-4.99626 + 0.886499i) q^{77} +(4.68177 + 19.7420i) q^{78} +(15.8300 - 48.7197i) q^{79} +(-3.84226 - 5.28841i) q^{80} +(-77.3085 + 24.1742i) q^{81} +(28.7551 + 88.4991i) q^{82} +(-97.0734 + 31.5411i) q^{83} +(2.55417 + 1.06628i) q^{84} +(-10.2157 + 7.42213i) q^{85} +(86.2653 + 28.0293i) q^{86} +(-25.1876 - 106.211i) q^{87} +(-30.8145 - 4.29702i) q^{88} +8.59365i q^{89} +(3.13984 + 20.5617i) q^{90} +(-1.78475 + 1.29670i) q^{91} +(26.4115 - 36.3523i) q^{92} +(-28.8643 - 47.3969i) q^{93} +(-29.8615 - 91.9042i) q^{94} +(23.6218 - 32.5126i) q^{95} +(12.8739 + 11.0572i) q^{96} +(-23.3643 + 71.9079i) q^{97} -68.9955i q^{98} +(80.8411 + 57.1464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 12 q^{6} - 8 q^{7} + 26 q^{9} + 16 q^{10} - 24 q^{12} + 8 q^{13} - 82 q^{15} - 32 q^{16} - 8 q^{18} - 4 q^{19} - 100 q^{21} - 24 q^{24} - 88 q^{25} - 106 q^{27} - 24 q^{28} - 36 q^{30}+ \cdots + 470 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 12 * q^6 - 8 * q^7 + 26 * q^9 + 16 * q^10 - 24 * q^12 + 8 * q^13 - 82 * q^15 - 32 * q^16 - 8 * q^18 - 4 * q^19 - 100 * q^21 - 24 * q^24 - 88 * q^25 - 106 * q^27 - 24 * q^28 - 36 * q^30 - 148 * q^31 + 78 * q^33 - 32 * q^34 + 8 * q^36 + 96 * q^37 + 362 * q^39 + 48 * q^40 + 152 * q^42 + 560 * q^43 - 20 * q^45 + 176 * q^46 + 8 * q^48 + 208 * q^49 - 82 * q^51 + 24 * q^52 - 176 * q^54 - 108 * q^55 - 142 * q^57 - 144 * q^58 - 36 * q^60 - 384 * q^61 + 506 * q^63 + 64 * q^64 + 400 * q^66 - 680 * q^67 + 136 * q^69 - 400 * q^70 + 16 * q^72 - 92 * q^73 + 90 * q^75 + 128 * q^76 + 152 * q^78 + 320 * q^79 - 198 * q^81 - 328 * q^82 - 240 * q^84 - 1024 * q^85 - 1332 * q^87 - 736 * q^90 - 264 * q^91 - 226 * q^93 - 64 * q^94 - 32 * q^96 - 248 * q^97 + 470 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	1.34500	+	0.437016i	0.672499	+	0.218508i
$2$	1.34500	+	0.437016i	0.672499	+	0.218508i
$3$	1.95466	−	2.27581i	0.651555	−	0.758602i
$3$	1.95466	−	2.27581i	0.651555	−	0.758602i
$4$	1.61803	+	1.17557i	0.404508	+	0.293893i
$5$	−1.55423	+	0.504998i	−0.310845	+	0.101000i	−0.460285	−	0.887771i	$-0.652253\pi$
$5$	−1.55423	+	0.504998i	−0.310845	+	0.101000i	0.149440	+	0.988771i	$0.452253\pi$
$6$	3.62358	−	2.20673i	0.603930	−	0.367789i
$7$	0.373199	+	0.271145i	0.0533142	+	0.0387350i	0.614123	−	0.789210i	$-0.289510\pi$
$7$	0.373199	+	0.271145i	0.0533142	+	0.0387350i	−0.560809	+	0.827945i	$0.689510\pi$
$8$	1.66251	+	2.28825i	0.207813	+	0.286031i
$9$	−1.35858	−	8.89687i	−0.150953	−	0.988541i
$10$	−2.31112			−0.231112
$11$	−7.63276	+	7.92092i	−0.693887	+	0.720084i
$11$	−7.63276	+	7.92092i	−0.693887	+	0.720084i
$12$	5.83808	−	1.38449i	0.486507	−	0.115374i
$13$	−1.47781	+	4.54823i	−0.113678	+	0.349864i	−0.991669	−	0.128813i	$-0.958883\pi$
$13$	−1.47781	+	4.54823i	−0.113678	+	0.349864i	0.877991	+	0.478677i	$0.158883\pi$
$14$	0.383457	+	0.527784i	0.0273898	+	0.0376988i
$15$	−1.88871	+	4.52422i	−0.125914	+	0.301614i
$16$	1.23607	+	3.80423i	0.0772542	+	0.237764i
$17$	7.34866	−	2.38773i	0.432274	−	0.140454i	−0.0847941	−	0.996398i	$-0.527023\pi$
$17$	7.34866	−	2.38773i	0.432274	−	0.140454i	0.517068	+	0.855944i	$0.327023\pi$
$18$	2.06079	−	12.5600i	0.114488	−	0.697777i
$19$	−19.8950	+	14.4546i	−1.04711	+	0.760767i	−0.971660	−	0.236383i	$-0.924038\pi$
$19$	−19.8950	+	14.4546i	−1.04711	+	0.760767i	−0.0754456	+	0.997150i	$0.524038\pi$
$20$	−3.10845	−	1.01000i	−0.155423	−	0.0504998i
$21$	1.34655	−	0.319331i	0.0641216	−	0.0152063i
$22$	−13.7276	+	7.31798i	−0.623982	+	0.332636i
$23$		−	22.4669i		−	0.976824i	−0.872613	−	0.488412i	$-0.837576\pi$
$23$		−	22.4669i		−	0.976824i	0.872613	−	0.488412i	$-0.162424\pi$
$24$	8.45725	+	0.689206i	0.352385	+	0.0287169i
$25$	−18.0648	+	13.1249i	−0.722593	+	0.524995i
$26$	−3.97530	+	5.47153i	−0.152896	+	0.210444i
$27$	−22.9031	−	14.2985i	−0.848263	−	0.529575i
$28$	0.285099	+	0.877444i	0.0101821	+	0.0313373i
$29$	21.3868	−	29.4364i	0.737477	−	1.01505i	−0.261283	−	0.965262i	$-0.584146\pi$
$29$	21.3868	−	29.4364i	0.737477	−	1.01505i	0.998760	−	0.0497875i	$-0.0158544\pi$
$30$	−4.51746	+	5.25966i	−0.150582	+	0.175322i
$31$	5.71622	−	17.5927i	0.184394	−	0.567507i	−0.815543	−	0.578696i	$-0.803562\pi$
$31$	5.71622	−	17.5927i	0.184394	−	0.567507i	0.999937	+	0.0111891i	$0.00356167\pi$
$32$			5.65685i			0.176777i
$33$	3.10701	+	32.8534i	0.0941519	+	0.995558i
$34$	10.9274			0.321394
$35$	−0.716964	−	0.232956i	−0.0204847	−	0.00665588i
$36$	8.26067	−	15.9925i	0.229463	−	0.444237i
$37$	19.2530	+	13.9881i	0.520352	+	0.378058i	0.816736	−	0.577011i	$-0.195781\pi$
$37$	19.2530	+	13.9881i	0.520352	+	0.378058i	−0.296385	+	0.955069i	$0.595781\pi$
$38$	−33.0756	+	10.7469i	−0.870411	+	0.282814i
$39$	7.46227	+	12.2535i	0.191340	+	0.314192i
$40$	−3.73947	−	2.71689i	−0.0934868	−	0.0679221i
$41$	38.6755	+	53.2323i	0.943305	+	1.29835i	0.954438	+	0.298410i	$0.0964564\pi$
$41$	38.6755	+	53.2323i	0.943305	+	1.29835i	−0.0111323	+	0.999938i	$0.503544\pi$
$42$	1.95066	+	0.158965i	0.0464444	+	0.00378489i
$43$	64.1379			1.49158			0.745790	−	0.666181i	$-0.232072\pi$
$43$	64.1379			1.49158			0.745790	+	0.666181i	$0.232072\pi$
$44$	−21.6617	+	3.84348i	−0.492311	+	0.0873519i
$45$	6.60444	+	13.1417i	0.146765	+	0.292037i
$46$	9.81842	−	30.2180i	0.213444	−	0.656913i
$47$	−40.1636	−	55.2805i	−0.854545	−	1.17618i	−0.982843	−	0.184445i	$-0.940951\pi$
$47$	−40.1636	−	55.2805i	−0.854545	−	1.17618i	0.128298	−	0.991736i	$-0.459049\pi$
$48$	11.0738	+	4.62293i	0.230704	+	0.0963111i
$49$	−15.0761	−	46.3994i	−0.307675	−	0.946926i
$50$	−30.0329	+	9.75829i	−0.600658	+	0.195166i
$51$	8.93017	−	21.3913i	0.175101	−	0.419438i
$52$	−7.73792	+	5.62193i	−0.148806	+	0.108114i
$53$	93.7067	+	30.4471i	1.76805	+	0.574474i	0.997983	−	0.0634880i	$-0.0202224\pi$
$53$	93.7067	+	30.4471i	1.76805	+	0.574474i	0.770068	+	0.637962i	$0.220222\pi$
$54$	−24.5559	−	29.2405i	−0.454739	−	0.541491i
$55$	7.86297	−	16.1654i	0.142963	−	0.293917i
$56$			1.30475i			0.0232992i
$57$	−5.99226	+	73.5310i	−0.105127	+	1.29002i
$58$	41.6294	−	30.2455i	0.717749	−	0.521475i
$59$	15.0359	−	20.6951i	0.254846	−	0.350765i	−0.662355	−	0.749190i	$-0.730443\pi$
$59$	15.0359	−	20.6951i	0.254846	−	0.350765i	0.917201	+	0.398425i	$0.130443\pi$
$60$	−8.37453	+	5.10002i	−0.139576	+	0.0850004i
$61$	−3.97349	−	12.2291i	−0.0651391	−	0.200478i	0.913190	−	0.407535i	$-0.133611\pi$
$61$	−3.97349	−	12.2291i	−0.0651391	−	0.200478i	−0.978329	+	0.207057i	$0.933611\pi$
$62$	15.3766	−	21.1641i	0.248010	−	0.341356i
$63$	1.90532	−	3.68868i	0.0302432	−	0.0585505i
$64$	−2.47214	+	7.60845i	−0.0386271	+	0.118882i
$65$		−	7.81527i		−	0.120235i
$66$	−10.1785	+	45.5456i	−0.154220	+	0.690084i
$67$	−45.1058			−0.673220			−0.336610	−	0.941644i	$-0.609280\pi$
$67$	−45.1058			−0.673220			−0.336610	+	0.941644i	$0.609280\pi$
$68$	14.6973	+	4.77545i	0.216137	+	0.0702272i
$69$	−51.1304	−	43.9153i	−0.741020	−	0.636454i
$70$	−0.862509	−	0.626649i	−0.0123216	−	0.00895213i
$71$	−107.664	+	34.9821i	−1.51639	+	0.492706i	−0.944748	−	0.327796i	$-0.893694\pi$
$71$	−107.664	+	34.9821i	−1.51639	+	0.492706i	−0.571644	+	0.820502i	$0.693694\pi$
$72$	18.0996	−	17.8999i	0.251383	−	0.248609i
$73$	9.15291	+	6.64998i	0.125382	+	0.0910956i	0.648709	−	0.761037i	$-0.275309\pi$
$73$	9.15291	+	6.64998i	0.125382	+	0.0910956i	−0.523327	+	0.852132i	$0.675309\pi$
$74$	19.7822	+	27.2279i	0.267327	+	0.367944i
$75$	−5.44102	+	66.7667i	−0.0725470	+	0.890223i
$76$	−49.1832			−0.647147
$77$	−4.99626	+	0.886499i	−0.0648865	+	0.0115130i
$78$	4.68177	+	19.7420i	0.0600227	+	0.253103i
$79$	15.8300	−	48.7197i	0.200379	−	0.616705i	−0.799492	−	0.600677i	$-0.794898\pi$
$79$	15.8300	−	48.7197i	0.200379	−	0.616705i	0.999872	−	0.0160279i	$-0.00510206\pi$
$80$	−3.84226	−	5.28841i	−0.0480282	−	0.0661051i
$81$	−77.3085	+	24.1742i	−0.954426	+	0.298447i
$82$	28.7551	+	88.4991i	0.350672	+	1.07926i
$83$	−97.0734	+	31.5411i	−1.16956	+	0.380013i	−0.828478	−	0.560021i	$-0.810793\pi$
$83$	−97.0734	+	31.5411i	−1.16956	+	0.380013i	−0.341081	+	0.940034i	$0.610793\pi$
$84$	2.55417	+	1.06628i	0.0304067	+	0.0126938i
$85$	−10.2157	+	7.42213i	−0.120184	+	0.0873191i
$86$	86.2653	+	28.0293i	1.00309	+	0.325922i
$87$	−25.1876	−	106.211i	−0.289512	−	1.22081i
$88$	−30.8145	−	4.29702i	−0.350165	−	0.0488298i
$89$			8.59365i			0.0965579i	0.998834	+	0.0482789i	$0.0153736\pi$
$89$			8.59365i			0.0965579i	−0.998834	+	0.0482789i	$0.984626\pi$
$90$	3.13984	+	20.5617i	0.0348871	+	0.228464i
$91$	−1.78475	+	1.29670i	−0.0196126	+	0.0142494i
$92$	26.4115	−	36.3523i	0.287081	−	0.395134i
$93$	−28.8643	−	47.3969i	−0.310369	−	0.509644i
$94$	−29.8615	−	91.9042i	−0.317676	−	0.977705i
$95$	23.6218	−	32.5126i	0.248650	−	0.342238i
$96$	12.8739	+	11.0572i	0.134103	+	0.115180i
$97$	−23.3643	+	71.9079i	−0.240869	+	0.741318i	0.755420	+	0.655241i	$0.227433\pi$
$97$	−23.3643	+	71.9079i	−0.240869	+	0.741318i	−0.996288	+	0.0860770i	$0.972567\pi$
$98$		−	68.9955i		−	0.704036i
$99$	80.8411	+	57.1464i	0.816577	+	0.577236i
$100$	−44.6587			−0.446587
$101$	−45.5964	−	14.8152i	−0.451449	−	0.146685i	0.0744627	−	0.997224i	$-0.476276\pi$
$101$	−45.5964	−	14.8152i	−0.451449	−	0.146685i	−0.525912	+	0.850539i	$0.676276\pi$
$102$	21.3594	−	24.8687i	0.209406	−	0.243810i
$103$	−61.3405	−	44.5665i	−0.595539	−	0.432684i	0.248754	−	0.968567i	$-0.419979\pi$
$103$	−61.3405	−	44.5665i	−0.595539	−	0.432684i	−0.844293	+	0.535883i	$0.819979\pi$
$104$	−12.8643	+	4.17988i	−0.123696	+	0.0401911i
$105$	−1.93158	+	1.17632i	−0.0183960	+	0.0112030i
$106$	112.729	+	81.9026i	1.06348	+	0.772666i
$107$	43.3978	+	59.7319i	0.405587	+	0.558242i	0.962135	−	0.272573i	$-0.0878746\pi$
$107$	43.3978	+	59.7319i	0.405587	+	0.558242i	−0.556548	+	0.830815i	$0.687875\pi$
$108$	−20.2491	−	50.0597i	−0.187492	−	0.463516i
$109$	137.096			1.25776			0.628880	−	0.777502i	$-0.283514\pi$
$109$	137.096			1.25776			0.628880	+	0.777502i	$0.283514\pi$
$110$	17.6402	−	18.3062i	0.160366	−	0.166420i
$111$	69.4674	−	16.4740i	0.625833	−	0.148415i
$112$	−0.570198	+	1.75489i	−0.00509105	+	0.0156687i
$113$	−29.6047	−	40.7474i	−0.261989	−	0.360597i	0.657676	−	0.753301i	$-0.271540\pi$
$113$	−29.6047	−	40.7474i	−0.261989	−	0.360597i	−0.919665	+	0.392704i	$0.871540\pi$
$114$	−40.1938	+	96.2802i	−0.352577	+	0.844563i
$115$	11.3458	+	34.9187i	0.0986589	+	0.303641i
$116$	69.2092	−	22.4874i	0.596631	−	0.193857i
$117$	42.4728	+	6.96875i	0.363015	+	0.0595619i
$118$	29.2673	−	21.2640i	0.248028	−	0.180203i
$119$	3.38994	+	1.10146i	0.0284869	+	0.00925595i
$120$	−13.4925	+	3.19971i	−0.112438	+	0.0266643i
$121$	−4.48209	−	120.917i	−0.0370421	−	0.999314i
$122$		−	18.1846i		−	0.149054i
$123$	196.744	+	16.0333i	1.59954	+	0.130352i
$124$	29.9305	−	21.7458i	0.241375	−	0.175369i
$125$	45.4629	−	62.5743i	0.363703	−	0.500594i
$126$	4.17466	−	4.12861i	0.0331323	−	0.0327667i
$127$	71.2349	+	219.239i	0.560905	+	1.72629i	0.679815	+	0.733383i	$0.262060\pi$
$127$	71.2349	+	219.239i	0.560905	+	1.72629i	−0.118910	+	0.992905i	$0.537940\pi$
$128$	−6.65003	+	9.15298i	−0.0519534	+	0.0715077i
$129$	125.368	−	145.965i	0.971846	−	1.13152i
$130$	3.41540	−	10.5115i	0.0262723	−	0.0808578i
$131$			166.511i			1.27107i	0.772071	+	0.635537i	$0.219221\pi$
$131$			166.511i			1.27107i	−0.772071	+	0.635537i	$0.780779\pi$
$132$	−33.5942	+	56.8104i	−0.254502	+	0.430382i
$133$	−11.3441			−0.0852939
$134$	−60.6671	−	19.7119i	−0.452740	−	0.147104i
$135$	42.8173	+	10.6571i	0.317165	+	0.0789414i
$136$	17.6809	+	12.8459i	0.130007	+	0.0944554i
$137$	−26.7012	+	8.67575i	−0.194899	+	0.0633266i	−0.404840	−	0.914387i	$-0.632673\pi$
$137$	−26.7012	+	8.67575i	−0.194899	+	0.0633266i	0.209941	+	0.977714i	$0.432673\pi$
$138$	−49.5785	−	81.4108i	−0.359265	−	0.589933i
$139$	−134.117	−	97.4417i	−0.964870	−	0.701019i	−0.0105936	−	0.999944i	$-0.503372\pi$
$139$	−134.117	−	97.4417i	−0.964870	−	0.701019i	−0.954277	+	0.298925i	$0.903372\pi$
$140$	−0.886216	−	1.21977i	−0.00633011	−	0.00871266i
$141$	−204.314	−	16.6502i	−1.44904	−	0.118086i
$142$	−160.095			−1.12743
$143$	−24.7464	−	46.4212i	−0.173052	−	0.324624i
$144$	32.1664	−	16.1655i	0.223378	−	0.112260i
$145$	−18.3746	+	56.5512i	−0.126721	+	0.390008i
$146$	9.40449	+	12.9442i	0.0644143	+	0.0886587i
$147$	−135.065	−	56.3850i	−0.918807	−	0.383571i
$148$	14.7080	+	45.2666i	0.0993784	+	0.305855i
$149$	67.4845	−	21.9271i	0.452916	−	0.147161i	−0.0736708	−	0.997283i	$-0.523471\pi$
$149$	67.4845	−	21.9271i	0.452916	−	0.147161i	0.526587	+	0.850121i	$0.323471\pi$
$150$	−36.4963	+	87.4233i	−0.243309	+	0.582822i
$151$	−51.2445	+	37.2313i	−0.339368	+	0.246565i	−0.744395	−	0.667740i	$-0.767262\pi$
$151$	−51.2445	+	37.2313i	−0.339368	+	0.246565i	0.405027	+	0.914305i	$0.367262\pi$
$152$	−66.1512	−	21.4938i	−0.435205	−	0.141407i
$153$	−31.2270	−	62.1362i	−0.204098	−	0.406119i
$154$	−7.10737	−	0.991107i	−0.0461518	−	0.00643576i
$155$			30.2297i			0.195031i
$156$	−2.33062	+	28.5990i	−0.0149398	+	0.183327i
$157$	−182.834	+	132.837i	−1.16455	+	0.846093i	−0.990346	−	0.138617i	$-0.955734\pi$
$157$	−182.834	+	132.837i	−1.16455	+	0.846093i	−0.174201	+	0.984710i	$0.555734\pi$
$158$	42.5825	−	58.6098i	0.269510	−	0.370948i
$159$	252.457	−	153.744i	1.58778	−	0.966945i
$160$	−2.85670	−	8.79203i	−0.0178544	−	0.0549502i
$161$	6.09181	−	8.38465i	0.0378373	−	0.0520786i
$162$	−114.544	−	1.27081i	−0.707063	−	0.00784451i
$163$	−19.0464	+	58.6189i	−0.116849	+	0.359625i	−0.992328	−	0.123631i	$-0.960546\pi$
$163$	−19.0464	+	58.6189i	−0.116849	+	0.359625i	0.875479	+	0.483256i	$0.160546\pi$
$164$			131.597i			0.802423i
$165$	−21.4199	−	49.4926i	−0.129818	−	0.299955i
$166$	−144.347			−0.869562
$167$	−162.492	−	52.7968i	−0.973006	−	0.316149i	−0.220977	−	0.975279i	$-0.570925\pi$
$167$	−162.492	−	52.7968i	−0.973006	−	0.316149i	−0.752029	+	0.659130i	$0.770925\pi$
$168$	2.96936	+	2.55035i	0.0176748	+	0.0151807i
$169$	118.221	+	85.8929i	0.699535	+	0.508242i
$170$	−16.9837	+	5.51832i	−0.0999038	+	0.0324607i
$171$	155.629	+	157.366i	0.910113	+	0.920266i
$172$	103.777	+	75.3987i	0.603357	+	0.438364i
$173$	−13.4384	−	18.4964i	−0.0776788	−	0.106916i	0.768409	−	0.639958i	$-0.221048\pi$
$173$	−13.4384	−	18.4964i	−0.0776788	−	0.106916i	−0.846088	+	0.533043i	$0.821048\pi$
$174$	12.5385	−	153.860i	0.0720606	−	0.884255i
$175$	−10.3005			−0.0588602
$176$	−39.5676	−	19.2459i	−0.224816	−	0.109352i
$177$	−17.7080	−	74.6708i	−0.100045	−	0.421869i
$178$	−3.75556	+	11.5584i	−0.0210987	+	0.0649350i
$179$	176.104	+	242.386i	0.983819	+	1.35411i	0.934746	+	0.355316i	$0.115627\pi$
$179$	176.104	+	242.386i	0.983819	+	1.35411i	0.0490727	+	0.998795i	$0.484373\pi$
$180$	−4.76273	+	29.0276i	−0.0264596	+	0.161265i
$181$	−24.2046	−	74.4941i	−0.133727	−	0.411570i	0.861663	−	0.507481i	$-0.169423\pi$
$181$	−24.2046	−	74.4941i	−0.133727	−	0.411570i	−0.995390	+	0.0959116i	$0.969423\pi$
$182$	−2.96716	+	0.964089i	−0.0163031	+	0.00529719i
$183$	−35.5979	−	14.8610i	−0.194524	−	0.0812074i
$184$	51.4099	−	37.3515i	0.279402	−	0.202997i
$185$	−36.9875	−	12.0180i	−0.199932	−	0.0649620i
$186$	−18.1092	−	76.3628i	−0.0973615	−	0.410553i
$187$	−37.1776	+	76.4331i	−0.198811	+	0.408733i
$188$		−	136.661i		−	0.726920i
$189$	−4.67045	−	11.5463i	−0.0247114	−	0.0610914i
$190$	45.9798	−	33.4062i	0.241999	−	0.175822i
$191$	153.717	−	211.573i	0.804799	−	1.10771i	−0.187306	−	0.982302i	$-0.559975\pi$
$191$	153.717	−	211.573i	0.804799	−	1.10771i	0.992105	−	0.125410i	$-0.0400245\pi$
$192$	12.4832	+	20.4981i	0.0650165	+	0.106761i
$193$	−44.5869	−	137.224i	−0.231020	−	0.711007i	−0.997624	−	0.0688869i	$-0.978055\pi$
$193$	−44.5869	−	137.224i	−0.231020	−	0.711007i	0.766604	−	0.642120i	$-0.221945\pi$
$194$	−62.8498	+	86.5053i	−0.323968	+	0.445904i
$195$	−17.7860	−	15.2762i	−0.0912104	−	0.0783396i
$196$	30.1521	−	92.7988i	0.153837	−	0.473463i
$197$			298.625i			1.51586i	0.652334	+	0.757932i	$0.273790\pi$
$197$			298.625i			1.51586i	−0.652334	+	0.757932i	$0.726210\pi$
$198$	83.7572	+	112.191i	0.423016	+	0.566619i
$199$	241.473			1.21343			0.606717	−	0.794918i	$-0.292486\pi$
$199$	241.473			1.21343			0.606717	+	0.794918i	$0.292486\pi$
$200$	−60.0658	−	19.5166i	−0.300329	−	0.0975829i
$201$	−88.1666	+	102.652i	−0.438640	+	0.510706i
$202$	−54.8525	−	39.8527i	−0.271547	−	0.197291i
$203$	15.9631	−	5.18673i	0.0786360	−	0.0255504i
$204$	39.5963	−	24.1139i	0.194100	−	0.118205i
$205$	−86.9927	−	63.2039i	−0.424355	−	0.308312i
$206$	−63.0265	−	86.7486i	−0.305954	−	0.421109i
$207$	−199.885	+	30.5232i	−0.965630	+	0.147455i
$208$	−19.1292			−0.0919672
$209$	37.3602	−	267.915i	0.178757	−	1.28189i
$210$	−3.11205	+	0.738014i	−0.0148193	+	0.00351435i
$211$	64.9129	−	199.781i	0.307644	−	0.946831i	−0.671033	−	0.741427i	$-0.734149\pi$
$211$	64.9129	−	199.781i	0.307644	−	0.946831i	0.978677	−	0.205404i	$-0.0658508\pi$
$212$	115.828	+	159.423i	0.546358	+	0.751997i
$213$	−130.834	+	313.400i	−0.614245	+	1.47136i
$214$	32.2661	+	99.3048i	0.150776	+	0.464041i
$215$	−99.6848	+	32.3896i	−0.463650	+	0.150649i
$216$	−5.35807	−	76.1793i	−0.0248059	−	0.352682i
$217$	6.90347	−	5.01567i	0.0318132	−	0.0231137i
$218$	184.394	+	59.9131i	0.845842	+	0.274831i
$219$	33.0249	−	7.83177i	0.150799	−	0.0357615i
$220$	31.7261	−	16.9127i	0.144210	−	0.0768761i
$221$			36.9520i			0.167204i
$222$	100.633	+	8.20088i	0.453301	+	0.0369409i
$223$	146.335	−	106.318i	0.656210	−	0.476764i	−0.209171	−	0.977879i	$-0.567077\pi$
$223$	146.335	−	106.318i	0.656210	−	0.476764i	0.865381	+	0.501115i	$0.167077\pi$
$224$	−1.53383	+	2.11113i	−0.00684745	+	0.00942471i
$225$	141.313	+	142.889i	0.628057	+	0.635063i
$226$	−22.0110	−	67.7429i	−0.0973939	−	0.299747i
$227$	−109.360	+	150.521i	−0.481761	+	0.663087i	−0.978842	−	0.204617i	$-0.934405\pi$
$227$	−109.360	+	150.521i	−0.481761	+	0.663087i	0.497081	+	0.867704i	$0.334405\pi$
$228$	−96.1365	+	111.931i	−0.421651	+	0.490927i
$229$	126.660	−	389.821i	0.553102	−	1.70227i	−0.147801	−	0.989017i	$-0.547220\pi$
$229$	126.660	−	389.821i	0.553102	−	1.70227i	0.700903	−	0.713256i	$-0.252780\pi$
$230$			51.9238i			0.225756i
$231$	−7.74851	+	13.1033i	−0.0335433	+	0.0567243i
$232$	102.914			0.443593
$233$	−244.627	−	79.4843i	−1.04990	−	0.341134i	−0.267273	−	0.963621i	$-0.586122\pi$
$233$	−244.627	−	79.4843i	−1.04990	−	0.341134i	−0.782630	+	0.622487i	$0.786122\pi$
$234$	54.0803	+	27.9342i	0.231112	+	0.119377i
$235$	90.3399	+	65.6358i	0.384425	+	0.279301i
$236$	48.6572	−	15.8097i	0.206175	−	0.0669902i
$237$	−79.9342	−	131.256i	−0.337275	−	0.553825i
$238$	4.07810	+	2.96291i	0.0171349	+	0.0124492i
$239$	−168.983	−	232.586i	−0.707043	−	0.973161i	−0.999856	−	0.0169915i	$-0.994591\pi$
$239$	−168.983	−	232.586i	−0.707043	−	0.973161i	0.292813	−	0.956170i	$-0.405409\pi$
$240$	−19.5457	−	1.59284i	−0.0814405	−	0.00663683i
$241$	224.506			0.931559			0.465780	−	0.884901i	$-0.345774\pi$
$241$	224.506			0.931559			0.465780	+	0.884901i	$0.345774\pi$
$242$	46.8142	−	164.592i	0.193447	−	0.680131i
$243$	−96.0963	+	223.192i	−0.395458	+	0.918484i
$244$	7.94697	−	24.4583i	0.0325695	−	0.100239i
$245$	46.8632	+	64.5017i	0.191278	+	0.263272i
$246$	257.613	+	107.545i	1.04721	+	0.437175i
$247$	−36.3417	−	111.848i	−0.147132	−	0.452827i
$248$	49.7597	−	16.1679i	0.200644	−	0.0651932i
$249$	−117.965	+	282.572i	−0.473753	+	1.13483i
$250$	88.4934	−	64.2942i	0.353974	−	0.257177i
$251$	101.440	+	32.9598i	0.404143	+	0.131314i	0.504033	−	0.863684i	$-0.331849\pi$
$251$	101.440	+	32.9598i	0.404143	+	0.131314i	−0.0998897	+	0.994999i	$0.531849\pi$
$252$	7.41918	−	3.72857i	0.0294412	−	0.0147959i
$253$	177.959	+	171.485i	0.703395	+	0.677805i
$254$			326.006i			1.28349i
$255$	−3.07690	+	37.7567i	−0.0120663	+	0.148065i
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	147.024	−	202.361i	0.572078	−	0.787397i	−0.420721	−	0.907190i	$-0.638223\pi$
$257$	147.024	−	202.361i	0.572078	−	0.787397i	0.992799	+	0.119793i	$0.0382230\pi$
$258$	232.409	−	141.535i	0.900810	−	0.548586i
$259$	3.39240	+	10.4407i	0.0130981	+	0.0403117i
$260$	9.18740	−	12.6454i	0.0353362	−	0.0486360i
$261$	−290.948	−	150.284i	−1.11474	−	0.575801i
$262$	−72.7678	+	223.956i	−0.277740	+	0.854795i
$263$		−	32.3578i		−	0.123033i	−0.998106	−	0.0615166i	$-0.980406\pi$
$263$		−	32.3578i		−	0.123033i	0.998106	−	0.0615166i	$-0.0195937\pi$
$264$	−70.0112	+	61.7287i	−0.265194	+	0.233821i
$265$	−161.017			−0.607611
$266$	−15.2578	−	4.95755i	−0.0573600	−	0.0186374i
$267$	19.5575	+	16.7977i	0.0732490	+	0.0629127i
$268$	−72.9827	−	53.0250i	−0.272323	−	0.197855i
$269$	328.564	−	106.757i	1.22143	−	0.396866i	0.373825	−	0.927499i	$-0.378046\pi$
$269$	328.564	−	106.757i	1.22143	−	0.396866i	0.847601	+	0.530634i	$0.178046\pi$
$270$	52.9318	+	33.0456i	0.196044	+	0.122391i
$271$	−319.440	−	232.086i	−1.17874	−	0.856408i	−0.186715	−	0.982414i	$-0.559784\pi$
$271$	−319.440	−	232.086i	−1.17874	−	0.856408i	−0.992029	+	0.126006i	$0.959784\pi$
$272$	18.1669	+	25.0046i	0.0667901	+	0.0919286i
$273$	−0.537556	+	6.59635i	−0.00196907	+	0.0241624i
$274$	−39.7045			−0.144907
$275$	33.9233	−	243.269i	0.123358	−	0.884615i
$276$	−31.1052	−	131.164i	−0.112700	−	0.475231i
$277$	−111.559	+	343.342i	−0.402738	+	1.23950i	0.520030	+	0.854148i	$0.325921\pi$
$277$	−111.559	+	343.342i	−0.402738	+	1.23950i	−0.922769	+	0.385354i	$0.874079\pi$
$278$	−137.803	−	189.670i	−0.495696	−	0.682266i
$279$	−164.286	−	26.9553i	−0.588839	−	0.0966142i
$280$	−0.658898	−	2.02788i	−0.00235321	−	0.00724243i
$281$	−22.4482	+	7.29387i	−0.0798869	+	0.0259568i	−0.348688	−	0.937239i	$-0.613373\pi$
$281$	−22.4482	+	7.29387i	−0.0798869	+	0.0259568i	0.268801	+	0.963196i	$0.413373\pi$
$282$	−267.525	−	111.683i	−0.948672	−	0.396039i
$283$	−172.511	+	125.337i	−0.609581	+	0.442887i	−0.849267	−	0.527964i	$-0.822956\pi$
$283$	−172.511	+	125.337i	−0.609581	+	0.442887i	0.239686	+	0.970851i	$0.422956\pi$
$284$	−215.328	−	69.9642i	−0.758196	−	0.246353i
$285$	−27.8197	−	117.310i	−0.0976130	−	0.411613i
$286$	−12.9971	−	73.2509i	−0.0454444	−	0.256122i
$287$			30.3529i			0.105759i
$288$	50.3283	−	7.68529i	0.174751	−	0.0266850i
$289$	−185.504	+	134.777i	−0.641883	+	0.466356i
$290$	−49.4275	+	68.0312i	−0.170440	+	0.234590i
$291$	117.979	+	193.728i	0.405426	+	0.665733i
$292$	6.99220	+	21.5198i	0.0239459	+	0.0736979i
$293$	−96.8220	+	133.264i	−0.330450	+	0.454826i	−0.941622	−	0.336672i	$-0.890699\pi$
$293$	−96.8220	+	133.264i	−0.330450	+	0.454826i	0.611171	+	0.791498i	$0.290699\pi$
$294$	−157.020	−	134.863i	−0.534083	−	0.458718i
$295$	−12.9182	+	39.7580i	−0.0437904	+	0.134773i
$296$			67.3110i			0.227402i
$297$	288.071	−	72.2767i	0.969937	−	0.243356i
$298$	100.349			0.336741
$299$	102.185	+	33.2019i	0.341756	+	0.111043i
$300$	−87.2928	+	101.635i	−0.290976	+	0.338782i
$301$	23.9362	+	17.3907i	0.0795224	+	0.0577764i
$302$	−85.1944	+	27.6813i	−0.282101	+	0.0916600i
$303$	−122.842	+	74.8098i	−0.405419	+	0.246897i
$304$	−79.5800	−	57.8183i	−0.261776	−	0.190192i
$305$	12.3514	+	17.0002i	0.0404963	+	0.0557384i
$306$	−14.8458	−	97.2197i	−0.0485156	−	0.317711i
$307$	−140.552			−0.457823			−0.228912	−	0.973447i	$-0.573517\pi$
$307$	−140.552			−0.457823			−0.228912	+	0.973447i	$0.573517\pi$
$308$	−9.12626	−	4.43907i	−0.0296307	−	0.0144126i
$309$	−221.325	+	52.4865i	−0.716261	+	0.169859i
$310$	−13.2109	+	40.6589i	−0.0426157	+	0.131158i
$311$	−6.42187	−	8.83895i	−0.0206491	−	0.0284210i	0.798568	−	0.601905i	$-0.205591\pi$
$311$	−6.42187	−	8.83895i	−0.0206491	−	0.0284210i	−0.819217	+	0.573484i	$0.805591\pi$
$312$	−15.6329	+	37.4470i	−0.0501054	+	0.120022i
$313$	−77.7859	−	239.400i	−0.248517	−	0.764858i	−0.995038	−	0.0994956i	$-0.968277\pi$
$313$	−77.7859	−	239.400i	−0.248517	−	0.764858i	0.746521	−	0.665362i	$-0.231723\pi$
$314$	−303.963	+	98.7635i	−0.968034	+	0.314533i
$315$	−1.09852	+	6.69522i	−0.00348737	+	0.0212547i
$316$	82.8868	−	60.2208i	0.262300	−	0.190572i
$317$	296.083	+	96.2033i	0.934017	+	0.303480i	0.736204	−	0.676759i	$-0.236616\pi$
$317$	296.083	+	96.2033i	0.934017	+	0.303480i	0.197813	+	0.980240i	$0.436616\pi$
$318$	406.742	−	96.4578i	1.27906	−	0.303327i
$319$	69.9234	+	394.085i	0.219196	+	1.23537i
$320$		−	13.0737i		−	0.0408552i
$321$	220.766	+	17.9909i	0.687746	+	0.0560465i
$322$	11.8577	−	8.61511i	0.0368251	−	0.0267550i
$323$	−111.688	+	153.726i	−0.345784	+	0.475931i
$324$	−153.506	−	51.7669i	−0.473785	−	0.159774i
$325$	−32.9986	−	101.559i	−0.101534	−	0.312490i
$326$	−51.2348	+	70.5187i	−0.157162	+	0.216315i
$327$	267.976	−	312.004i	0.819500	−	0.954140i
$328$	−57.5102	+	176.998i	−0.175336	+	0.539629i
$329$		−	31.5208i		−	0.0958080i
$330$	−7.18068	−	75.9282i	−0.0217596	−	0.230085i
$331$	144.935			0.437869			0.218934	−	0.975740i	$-0.429742\pi$
$331$	144.935			0.437869			0.218934	+	0.975740i	$0.429742\pi$
$332$	−194.147	−	63.0821i	−0.584779	−	0.190006i
$333$	98.2938	−	190.296i	0.295177	−	0.571458i
$334$	−195.478	−	142.023i	−0.585264	−	0.425219i
$335$	70.1045	−	22.7783i	0.209267	−	0.0679950i
$336$	2.87924	+	4.72788i	0.00856917	+	0.0140711i
$337$	396.762	+	288.264i	1.17734	+	0.855384i	0.991869	−	0.127266i	$-0.0406203\pi$
$337$	396.762	+	288.264i	1.17734	+	0.855384i	0.185467	+	0.982651i	$0.440620\pi$
$338$	121.471	+	167.190i	0.359381	+	0.494646i
$339$	−150.601	−	12.2729i	−0.444249	−	0.0362032i
$340$	−25.2546			−0.0742781
$341$	95.7201	+	179.559i	0.280704	+	0.526565i
$342$	140.550	+	279.669i	0.410964	+	0.817745i
$343$	13.9395	−	42.9014i	0.0406400	−	0.125077i
$344$	106.630	+	146.763i	0.309970	+	0.426638i
$345$	101.645	+	42.4335i	0.294624	+	0.122996i
$346$	−9.99142	−	30.7504i	−0.0288769	−	0.0888741i
$347$	−0.782030	+	0.254097i	−0.00225369	+	0.000732268i	−0.310144	−	0.950690i	$-0.600377\pi$
$347$	−0.782030	+	0.254097i	−0.00225369	+	0.000732268i	0.307890	+	0.951422i	$0.400377\pi$
$348$	84.1037	−	201.462i	0.241677	−	0.578914i
$349$	−106.821	+	77.6098i	−0.306077	+	0.222378i	−0.730211	−	0.683222i	$-0.760578\pi$
$349$	−106.821	+	77.6098i	−0.306077	+	0.222378i	0.424135	+	0.905599i	$0.360578\pi$
$350$	−13.8542	−	4.50150i	−0.0395834	−	0.0128614i
$351$	98.8795	−	83.0382i	0.281708	−	0.236576i
$352$	−44.8075	−	43.1774i	−0.127294	−	0.122663i
$353$		−	173.251i		−	0.490795i	−0.969422	−	0.245398i	$-0.921081\pi$
$353$		−	173.251i		−	0.490795i	0.969422	−	0.245398i	$-0.0789185\pi$
$354$	8.81516	−	108.171i	0.0249016	−	0.305567i
$355$	149.668	−	108.740i	0.421600	−	0.306310i
$356$	−10.1024	+	13.9048i	−0.0283776	+	0.0390585i
$357$	9.13289	−	5.56186i	0.0255823	−	0.0155794i
$358$	130.932	+	402.968i	0.365733	+	1.12561i
$359$	99.2057	−	136.545i	0.276339	−	0.380348i	−0.648178	−	0.761489i	$-0.724469\pi$
$359$	99.2057	−	136.545i	0.276339	−	0.380348i	0.924517	+	0.381141i	$0.124469\pi$
$360$	−19.0914	+	36.9607i	−0.0530317	+	0.102669i
$361$	75.3216	−	231.816i	0.208647	−	0.642150i
$362$		−	110.772i		−	0.306000i
$363$	−283.944	−	226.152i	−0.782216	−	0.623007i
$364$	−4.41214			−0.0121213
$365$	−17.5839	−	5.71336i	−0.0481751	−	0.0156530i
$366$	−41.3847	−	35.5448i	−0.113073	−	0.0971170i
$367$	16.8883	+	12.2701i	0.0460171	+	0.0334334i	0.610556	−	0.791973i	$-0.290946\pi$
$367$	16.8883	+	12.2701i	0.0460171	+	0.0334334i	−0.564539	+	0.825406i	$0.690946\pi$
$368$	85.4693	−	27.7707i	0.232254	−	0.0754638i
$369$	421.057	−	416.411i	1.14108	−	1.12849i
$370$	−44.4960	−	32.3283i	−0.120260	−	0.0873737i
$371$	26.7157	+	36.7710i	0.0720099	+	0.0991131i
$372$	9.01490	−	110.622i	0.0242336	−	0.297370i
$373$	−239.122			−0.641077			−0.320538	−	0.947236i	$-0.603864\pi$
$373$	−239.122			−0.641077			−0.320538	+	0.947236i	$0.603864\pi$
$374$	−83.4062	+	86.5552i	−0.223011	+	0.231431i
$375$	−53.5423	−	225.776i	−0.142779	−	0.602070i
$376$	59.7230	−	183.808i	0.158838	−	0.488852i
$377$	102.278	+	140.774i	0.271295	+	0.373405i
$378$	−1.23584	−	17.5708i	−0.00326941	−	0.0464835i
$379$	104.871	+	322.759i	0.276704	+	0.851607i	0.988764	+	0.149488i	$0.0477626\pi$
$379$	104.871	+	322.759i	0.276704	+	0.851607i	−0.712060	+	0.702119i	$0.752237\pi$
$380$	76.4417	−	24.8374i	0.201162	−	0.0653616i
$381$	638.185	+	266.421i	1.67503	+	0.699267i
$382$	299.209	−	217.388i	0.783270	−	0.569079i
$383$	−56.2644	−	18.2814i	−0.146904	−	0.0477321i	0.234642	−	0.972082i	$-0.424608\pi$
$383$	−56.2644	−	18.2814i	−0.146904	−	0.0477321i	−0.381546	+	0.924350i	$0.624608\pi$
$384$	7.83183	+	33.0252i	0.0203954	+	0.0860031i
$385$	7.31763	−	3.90092i	0.0190068	−	0.0101323i
$386$		−	204.051i		−	0.528631i
$387$	−87.1365	−	570.627i	−0.225159	−	1.47449i
$388$	−122.337	+	88.8830i	−0.315302	+	0.229080i
$389$	−25.3576	+	34.9018i	−0.0651867	+	0.0897219i	−0.840366	−	0.542020i	$-0.817660\pi$
$389$	−25.3576	+	34.9018i	−0.0651867	+	0.0897219i	0.775179	+	0.631742i	$0.217660\pi$
$390$	−17.2462	−	28.3193i	−0.0442210	−	0.0726135i
$391$	−53.6449	−	165.102i	−0.137199	−	0.422256i
$392$	81.1091	−	111.637i	0.206911	−	0.284789i
$393$	378.946	+	325.472i	0.964239	+	0.828174i
$394$	−130.504	+	401.650i	−0.331228	+	1.01942i
$395$			83.7154i			0.211938i
$396$	63.6241	+	187.499i	0.160667	+	0.473483i
$397$	−88.1293			−0.221988			−0.110994	−	0.993821i	$-0.535403\pi$
$397$	−88.1293			−0.221988			−0.110994	+	0.993821i	$0.535403\pi$
$398$	324.781	+	105.528i	0.816033	+	0.265145i
$399$	−22.1739	+	25.8169i	−0.0555736	+	0.0647041i
$400$	−72.2593	−	52.4995i	−0.180648	−	0.131249i
$401$	−456.939	+	148.468i	−1.13950	+	0.370246i	−0.817178	−	0.576385i	$-0.804463\pi$
$401$	−456.939	+	148.468i	−1.13950	+	0.370246i	−0.322320	+	0.946631i	$0.604463\pi$
$402$	−163.444	+	99.5363i	−0.406578	+	0.247603i
$403$	71.5683	+	51.9974i	0.177589	+	0.129026i
$404$	−56.3602	−	77.5732i	−0.139505	−	0.192013i
$405$	107.947	−	76.6129i	0.266536	−	0.189168i
$406$	23.7370			0.0584655
$407$	−257.753	+	45.7337i	−0.633299	+	0.112368i
$408$	63.7951	−	15.1288i	0.156361	−	0.0370805i
$409$	−212.996	+	655.536i	−0.520774	+	1.60278i	0.251751	+	0.967792i	$0.418994\pi$
$409$	−212.996	+	655.536i	−0.520774	+	1.60278i	−0.772525	+	0.634985i	$0.781006\pi$
$410$	−89.3838	−	123.026i	−0.218009	−	0.300064i
$411$	−32.4476	+	77.7249i	−0.0789478	+	0.189112i
$412$	−46.8600	−	144.220i	−0.113738	−	0.350049i
$413$	11.2228	−	3.64650i	0.0271738	−	0.00882930i
$414$	−282.184	−	46.2996i	−0.681605	−	0.111835i
$415$	134.946	−	98.0438i	0.325170	−	0.236250i
$416$	−25.7287	−	8.35976i	−0.0618478	−	0.0200956i
$417$	−483.912	+	114.758i	−1.16046	+	0.275200i
$418$	167.332	−	344.018i	0.400317	−	0.823009i
$419$		−	339.406i		−	0.810038i	−0.914308	−	0.405019i	$-0.867265\pi$
$419$		−	339.406i		−	0.810038i	0.914308	−	0.405019i	$-0.132735\pi$
$420$	−4.50822	−	0.367388i	−0.0107339	−	0.000874734i
$421$	157.022	−	114.083i	0.372975	−	0.270982i	−0.385469	−	0.922721i	$-0.625960\pi$
$421$	157.022	−	114.083i	0.372975	−	0.270982i	0.758443	+	0.651739i	$0.225960\pi$
$422$	174.615	−	240.337i	0.413780	−	0.569520i
$423$	−437.258	+	432.433i	−1.03371	+	1.02230i
$424$	86.1175	+	265.042i	0.203107	+	0.625100i
$425$	−101.414	+	139.584i	−0.238621	+	0.328433i
$426$	−312.932	+	364.346i	−0.734583	+	0.855272i
$427$	1.83297	−	5.64130i	0.00429267	−	0.0132115i
$428$			147.665i			0.345013i
$429$	−154.017	−	34.4197i	−0.359013	−	0.0802324i
$430$	−148.231			−0.344722
$431$	161.518	+	52.4804i	0.374752	+	0.121764i	0.490336	−	0.871533i	$-0.336874\pi$
$431$	161.518	+	52.4804i	0.374752	+	0.121764i	−0.115584	+	0.993298i	$0.536874\pi$
$432$	26.0850	−	104.803i	0.0603820	−	0.242598i
$433$	−76.0377	−	55.2446i	−0.175607	−	0.127586i	0.496510	−	0.868031i	$-0.334615\pi$
$433$	−76.0377	−	55.2446i	−0.175607	−	0.127586i	−0.672117	+	0.740445i	$0.734615\pi$
$434$	11.4771	−	3.72913i	0.0264449	−	0.00859246i
$435$	92.7833	+	152.356i	0.213295	+	0.350243i
$436$	221.826	+	161.166i	0.508775	+	0.369647i
$437$	324.750	+	446.980i	0.743135	+	1.02284i
$438$	47.8410	+	3.89871i	0.109226	+	0.00890117i
$439$	−616.308			−1.40389			−0.701946	−	0.712230i	$-0.747685\pi$
$439$	−616.308			−1.40389			−0.701946	+	0.712230i	$0.747685\pi$
$440$	50.0627	−	8.88275i	0.113779	−	0.0201881i
$441$	−392.327	+	197.167i	−0.889631	+	0.447091i
$442$	−16.1486	+	49.7004i	−0.0365354	+	0.112444i
$443$	−380.364	−	523.527i	−0.858610	−	1.18178i	−0.981899	−	0.189405i	$-0.939344\pi$
$443$	−380.364	−	523.527i	−0.858610	−	1.18178i	0.123289	−	0.992371i	$-0.460656\pi$
$444$	131.767	+	55.0084i	0.296773	+	0.123893i
$445$	−4.33978	−	13.3565i	−0.00975231	−	0.0300145i
$446$	243.283	−	79.0474i	0.545477	−	0.177236i
$447$	82.0078	−	196.442i	0.183463	−	0.439467i
$448$	−2.98560	+	2.16916i	−0.00666428	+	0.00484188i
$449$	−284.053	−	92.2943i	−0.632634	−	0.205555i	−0.0248924	−	0.999690i	$-0.507924\pi$
$449$	−284.053	−	92.2943i	−0.632634	−	0.205555i	−0.607742	+	0.794135i	$0.707924\pi$
$450$	127.620	+	253.942i	0.283601	+	0.564315i
$451$	−716.850	−	99.9631i	−1.58947	−	0.221648i
$452$		−	100.733i		−	0.222861i
$453$	−15.4345	+	189.397i	−0.0340718	+	0.418095i
$454$	−212.868	+	154.658i	−0.468873	+	0.340656i
$455$	2.11907	−	2.91665i	0.00465730	−	0.00641023i
$456$	−178.219	+	108.534i	−0.390831	+	0.238013i
$457$	−91.5567	−	281.782i	−0.200343	−	0.616592i	−0.999873	−	0.0159653i	$-0.994918\pi$
$457$	−91.5567	−	281.782i	−0.200343	−	0.616592i	0.799530	−	0.600627i	$-0.205082\pi$
$458$	340.716	−	468.955i	0.743921	−	1.02392i
$459$	−202.448	−	50.3887i	−0.441064	−	0.109779i
$460$	−22.6915	+	69.8374i	−0.0493294	+	0.151820i
$461$		−	365.986i		−	0.793896i	−0.917841	−	0.396948i	$-0.870069\pi$
$461$		−	365.986i		−	0.793896i	0.917841	−	0.396948i	$-0.129931\pi$
$462$	−16.1481	+	14.2377i	−0.0349526	+	0.0308176i
$463$	479.394			1.03541			0.517704	−	0.855560i	$-0.326787\pi$
$463$	479.394			1.03541			0.517704	+	0.855560i	$0.326787\pi$
$464$	138.418	+	44.9749i	0.298316	+	0.0969286i
$465$	68.7970	+	59.0890i	0.147951	+	0.127073i
$466$	−294.287	−	213.812i	−0.631518	−	0.458824i
$467$	−628.642	+	204.258i	−1.34613	+	0.437383i	−0.891388	−	0.453241i	$-0.850268\pi$
$467$	−628.642	+	204.258i	−1.34613	+	0.437383i	−0.454740	+	0.890624i	$0.650268\pi$
$468$	60.5301	+	61.2054i	0.129338	+	0.130781i
$469$	−16.8334	−	12.2302i	−0.0358922	−	0.0260772i
$470$	92.8230	+	127.760i	0.197496	+	0.271830i
$471$	−55.0685	+	675.745i	−0.116918	+	1.43470i
$472$	72.3529			0.153290
$473$	−489.549	+	508.032i	−1.03499	+	1.07406i
$474$	−50.1500	−	211.472i	−0.105802	−	0.446144i
$475$	169.686	−	522.239i	0.357233	−	1.09945i
$476$	4.19019	+	5.76731i	0.00880293	+	0.0121162i
$477$	143.576	−	875.061i	0.300998	−	1.83451i
$478$	−125.638	−	386.675i	−0.262842	−	0.808944i
$479$	167.532	−	54.4345i	0.349754	−	0.113642i	−0.128871	−	0.991661i	$-0.541135\pi$
$479$	167.532	−	54.4345i	0.349754	−	0.113642i	0.478625	+	0.878019i	$0.341135\pi$
$480$	−25.5928	−	10.6842i	−0.0533184	−	0.0222587i
$481$	−92.0736	+	66.8954i	−0.191421	+	0.139076i
$482$	301.960	+	98.1126i	0.626472	+	0.203553i
$483$	−7.17440	−	30.2529i	−0.0148538	−	0.0626355i
$484$	134.894	−	200.917i	0.278707	−	0.415117i
$485$		−	123.560i		−	0.254763i
$486$	−226.788	+	258.196i	−0.466641	+	0.531268i
$487$	571.858	−	415.479i	1.17425	−	0.853139i	0.182734	−	0.983162i	$-0.441505\pi$
$487$	571.858	−	415.479i	1.17425	−	0.853139i	0.991511	+	0.130023i	$0.0415051\pi$
$488$	21.3773	−	29.4233i	0.0438059	−	0.0602937i
$489$	96.1759	+	157.926i	0.196679	+	0.322958i
$490$	34.8426	+	107.235i	0.0711074	+	0.218846i
$491$	360.550	−	496.255i	0.734318	−	1.01070i	−0.264608	−	0.964356i	$-0.585242\pi$
$491$	360.550	−	496.255i	0.734318	−	1.01070i	0.998925	−	0.0463457i	$-0.0147576\pi$
$492$	299.490	+	257.229i	0.608720	+	0.522823i
$493$	86.8785	−	267.384i	0.176224	−	0.542362i
$494$		−	166.317i		−	0.336675i
$495$	−154.504	−	47.9937i	−0.312130	−	0.0969571i
$496$	73.9923			0.149178
$497$	−49.6653	−	16.1372i	−0.0999302	−	0.0324693i
$498$	−282.151	+	328.506i	−0.566567	+	0.659652i
$499$	389.281	+	282.829i	0.780122	+	0.566792i	0.905016	−	0.425378i	$-0.139859\pi$
$499$	389.281	+	282.829i	0.780122	+	0.566792i	−0.124893	+	0.992170i	$0.539859\pi$
$500$	147.121	−	47.8025i	0.294242	−	0.0956050i
$501$	−437.772	+	266.600i	−0.873797	+	0.532136i
$502$	122.032	+	88.6618i	0.243093	+	0.176617i
$503$	431.343	+	593.693i	0.857542	+	1.18030i	0.982150	+	0.188099i	$0.0602325\pi$
$503$	431.343	+	593.693i	0.857542	+	1.18030i	−0.124608	+	0.992206i	$0.539767\pi$
$504$	11.6082	−	1.77261i	0.0230322	−	0.00351709i
$505$	78.3487			0.155146
$506$	164.413	+	308.417i	0.324926	+	0.609520i
$507$	426.558	−	101.157i	0.841338	−	0.199521i
$508$	−142.470	+	438.477i	−0.280453	+	0.863144i
$509$	−144.149	−	198.404i	−0.283201	−	0.389793i	0.643590	−	0.765370i	$-0.277444\pi$
$509$	−144.149	−	198.404i	−0.283201	−	0.389793i	−0.926791	+	0.375578i	$0.877444\pi$
$510$	−20.6387	+	49.4379i	−0.0404680	+	0.0969372i
$511$	1.61275	+	4.96354i	0.00315607	+	0.00971338i
$512$	−21.5200	+	6.99226i	−0.0420312	+	0.0136568i
$513$	662.336	−	46.5854i	1.29110	−	0.0908097i
$514$	286.182	−	207.923i	0.556774	−	0.404520i
$515$	117.843	+	38.2895i	0.228821	+	0.0743485i
$516$	374.443	−	88.7981i	0.725664	−	0.172089i
$517$	744.432	+	103.809i	1.43991	+	0.200792i
$518$			15.5253i			0.0299716i
$519$	−68.3618	−	5.57101i	−0.131718	−	0.0107341i
$520$	17.8833	−	12.9929i	0.0343909	−	0.0249864i
$521$	−425.264	+	585.326i	−0.816246	+	1.12347i	0.174083	+	0.984731i	$0.444304\pi$
$521$	−425.264	+	585.326i	−0.816246	+	1.12347i	−0.990329	+	0.138736i	$0.955696\pi$
$522$	−325.647	−	329.280i	−0.623846	−	0.630805i
$523$	−74.3821	−	228.924i	−0.142222	−	0.437714i	0.854421	−	0.519581i	$-0.173912\pi$
$523$	−74.3821	−	228.924i	−0.142222	−	0.437714i	−0.996643	+	0.0818667i	$0.973912\pi$
$524$	−195.745	+	269.420i	−0.373559	+	0.514160i
$525$	−20.1341	+	23.4420i	−0.0383506	+	0.0446514i
$526$	14.1409	−	43.5211i	0.0268838	−	0.0827397i
$527$		−	142.932i		−	0.271218i
$528$	−121.141	+	52.4288i	−0.229434	+	0.0992970i
$529$	24.2362			0.0458152
$530$	−216.567	−	70.3670i	−0.408618	−	0.132768i
$531$	−204.549	−	105.656i	−0.385215	−	0.198976i
$532$	−18.3551	−	13.3358i	−0.0345021	−	0.0250673i
$533$	−299.268	+	97.2380i	−0.561478	+	0.182435i
$534$	18.9639	+	31.1398i	0.0355129	+	0.0583142i
$535$	−97.6145	−	70.9211i	−0.182457	−	0.132563i
$536$	−74.9887	−	103.213i	−0.139904	−	0.192562i
$537$	895.846	+	73.0052i	1.66824	+	0.135950i
$538$	488.572			0.908126
$539$	482.598	+	234.739i	0.895358	+	0.435508i
$540$	56.7517	+	67.5783i	0.105096	+	0.125145i
$541$	186.349	−	573.524i	0.344453	−	1.06012i	−0.617422	−	0.786632i	$-0.711823\pi$
$541$	186.349	−	573.524i	0.344453	−	1.06012i	0.961876	−	0.273487i	$-0.0881769\pi$
$542$	−328.220	−	451.756i	−0.605572	−	0.833498i
$543$	−216.846	−	90.5260i	−0.399348	−	0.166714i
$544$	13.5070	+	41.5703i	0.0248291	+	0.0764160i
$545$	−213.078	+	69.2332i	−0.390969	+	0.127033i
$546$	−3.60572	+	8.63715i	−0.00660389	+	0.0158190i
$547$	−41.6750	+	30.2786i	−0.0761882	+	0.0553540i	−0.625227	−	0.780443i	$-0.714994\pi$
$547$	−41.6750	+	30.2786i	−0.0761882	+	0.0553540i	0.549039	+	0.835797i	$0.314994\pi$
$548$	−53.4024	−	17.3515i	−0.0974496	−	0.0316633i
$549$	−103.403	+	51.9658i	−0.188347	+	0.0946554i
$550$	151.939	−	312.371i	0.276253	−	0.567948i
$551$			894.775i			1.62391i
$552$	15.4844	−	190.008i	0.0280514	−	0.344218i
$553$	19.1178	−	13.8899i	0.0345711	−	0.0251174i
$554$	−300.092	+	413.041i	−0.541682	+	0.745561i
$555$	−99.6487	+	60.6853i	−0.179547	+	0.109343i
$556$	−102.456	−	315.328i	−0.184274	−	0.567137i
$557$	194.652	−	267.916i	0.349466	−	0.480998i	−0.597710	−	0.801712i	$-0.703923\pi$
$557$	194.652	−	267.916i	0.349466	−	0.480998i	0.947176	+	0.320714i	$0.103923\pi$
$558$	−209.184	−	108.051i	−0.374882	−	0.193639i
$559$	−94.7837	+	291.714i	−0.169559	+	0.521850i
$560$		−	3.01544i		−	0.00538472i
$561$	101.277	+	234.010i	0.180530	+	0.417130i
$562$	−33.3803			−0.0593956
$563$	832.953	+	270.643i	1.47949	+	0.480715i	0.933960	−	0.357376i	$-0.116329\pi$
$563$	832.953	+	270.643i	1.47949	+	0.480715i	0.545529	+	0.838092i	$0.316329\pi$
$564$	−311.014	−	267.126i	−0.551443	−	0.473628i
$565$	66.5898	+	48.3803i	0.117858	+	0.0856289i
$566$	−286.802	+	93.1875i	−0.506717	+	0.164642i
$567$	−35.4062	−	11.9400i	−0.0624448	−	0.0210583i
$568$	−259.040	−	188.203i	−0.456056	−	0.331344i
$569$	−460.533	−	633.869i	−0.809373	−	1.11401i	−0.991420	−	0.130716i	$-0.958272\pi$
$569$	−460.533	−	633.869i	−0.809373	−	1.11401i	0.182047	−	0.983290i	$-0.441728\pi$
$570$	13.8488	−	169.939i	0.0242962	−	0.298139i
$571$	619.455			1.08486			0.542430	−	0.840101i	$-0.317504\pi$
$571$	619.455			1.08486			0.542430	+	0.840101i	$0.317504\pi$
$572$	14.5308	−	104.202i	0.0254035	−	0.182172i
$573$	−181.034	−	763.383i	−0.315941	−	1.33226i
$574$	−13.2647	+	40.8246i	−0.0231093	+	0.0711230i
$575$	294.876	+	405.862i	0.512827	+	0.705846i
$576$	71.0500	+	11.6576i	0.123351	+	0.0202388i
$577$	−120.190	−	369.907i	−0.208302	−	0.641087i	−0.999562	−	0.0296068i	$-0.990574\pi$
$577$	−120.190	−	369.907i	−0.208302	−	0.641087i	0.791260	−	0.611480i	$-0.209426\pi$
$578$	−308.402	+	100.206i	−0.533568	+	0.173367i
$579$	−399.448	−	166.756i	−0.689893	−	0.288007i
$580$	−96.2106	+	69.9011i	−0.165880	+	0.120519i
$581$	−44.7799	−	14.5499i	−0.0770739	−	0.0250428i
$582$	74.0191	+	312.123i	0.127181	+	0.536293i
$583$	−956.410	+	509.848i	−1.64050	+	0.874525i
$584$			31.9998i			0.0547941i
$585$	−69.5314	+	10.6177i	−0.118857	+	0.0181499i
$586$	−188.464	+	136.927i	−0.321611	+	0.233664i
$587$	−50.4661	+	69.4606i	−0.0859729	+	0.118332i	−0.849837	−	0.527045i	$-0.823300\pi$
$587$	−50.4661	+	69.4606i	−0.0859729	+	0.118332i	0.763864	+	0.645377i	$0.223300\pi$
$588$	−152.255	−	250.011i	−0.258936	−	0.425188i
$589$	140.571	+	432.633i	0.238660	+	0.734521i
$590$	−34.7498	+	47.8290i	−0.0588979	+	0.0810660i
$591$	679.613	+	583.712i	1.14994	+	0.987668i
$592$	−29.4160	+	90.5331i	−0.0496892	+	0.152928i
$593$		−	1110.08i		−	1.87198i	−0.352026	−	0.935990i	$-0.614507\pi$
$593$		−	1110.08i		−	1.87198i	0.352026	−	0.935990i	$-0.385493\pi$
$594$	419.041	+	28.6799i	0.705456	+	0.0482826i
$595$	−5.82496			−0.00978985
$596$	134.969	+	43.8541i	0.226458	+	0.0735807i
$597$	471.999	−	549.546i	0.790618	−	0.920513i
$598$	122.929	+	89.3129i	0.205566	+	0.149353i
$599$	780.529	−	253.609i	1.30305	−	0.423388i	0.426410	−	0.904530i	$-0.359778\pi$
$599$	780.529	−	253.609i	1.30305	−	0.423388i	0.876643	+	0.481142i	$0.159778\pi$
$600$	−161.824	+	98.5498i	−0.269707	+	0.164250i
$601$	−240.573	−	174.787i	−0.400288	−	0.290826i	0.369370	−	0.929282i	$-0.379573\pi$
$601$	−240.573	−	174.787i	−0.400288	−	0.290826i	−0.769658	+	0.638456i	$0.779573\pi$
$602$	24.5942	+	33.8510i	0.0408541	+	0.0562308i
$603$	61.2798	+	401.300i	0.101625	+	0.665506i
$604$	−126.683			−0.209741
$605$	68.0290	+	185.669i	0.112445	+	0.306890i
$606$	−197.915	+	46.9351i	−0.326593	+	0.0774506i
$607$	−136.690	+	420.690i	−0.225190	+	0.693063i	0.773082	+	0.634306i	$0.218714\pi$
$607$	−136.690	+	420.690i	−0.225190	+	0.693063i	−0.998272	+	0.0587577i	$0.981286\pi$
$608$	−81.7674	−	112.543i	−0.134486	−	0.185104i
$609$	19.3985	−	46.4672i	0.0318531	−	0.0763009i
$610$	9.18320	+	28.2630i	0.0150544	+	0.0463328i
$611$	310.783	−	100.979i	0.508646	−	0.165269i
$612$	22.5191	−	137.248i	0.0367959	−	0.224261i
$613$	−800.318	+	581.465i	−1.30558	+	0.948556i	−0.999993	−	0.00360913i	$-0.998851\pi$
$613$	−800.318	+	581.465i	−1.30558	+	0.948556i	−0.305582	+	0.952166i	$0.598851\pi$
$614$	−189.042	−	61.4234i	−0.307885	−	0.100038i
$615$	−313.881	+	74.4361i	−0.510376	+	0.121034i
$616$	−10.3348	−	9.95886i	−0.0167774	−	0.0161670i
$617$			257.998i			0.418149i	0.977900	+	0.209075i	$0.0670452\pi$
$617$			257.998i			0.418149i	−0.977900	+	0.209075i	$0.932955\pi$
$618$	−320.618	−	26.1282i	−0.518800	−	0.0422786i
$619$	−84.8895	+	61.6758i	−0.137140	+	0.0996378i	−0.654240	−	0.756287i	$-0.727011\pi$
$619$	−84.8895	+	61.6758i	−0.137140	+	0.0996378i	0.517100	+	0.855925i	$0.327011\pi$
$620$	−35.5372	+	48.9127i	−0.0573180	+	0.0788915i
$621$	−321.244	+	514.563i	−0.517301	+	0.828604i
$622$	−4.77464	−	14.6948i	−0.00767626	−	0.0236251i
$623$	−2.33013	+	3.20715i	−0.00374017	+	0.00514791i
$624$	−37.3911	+	43.5343i	−0.0599217	+	0.0697665i
$625$	133.444	−	410.699i	0.213511	−	0.657118i
$626$		−	355.987i		−	0.568669i
$627$	−536.696	−	608.708i	−0.855974	−	0.970826i
$628$	−451.990			−0.719730
$629$	174.884	+	56.8232i	0.278035	+	0.0903389i
$630$	−4.40343	+	8.52498i	−0.00698957	+	0.0135317i
$631$	252.088	+	183.153i	0.399506	+	0.290258i	0.769340	−	0.638840i	$-0.220585\pi$
$631$	252.088	+	183.153i	0.399506	+	0.290258i	−0.369834	+	0.929098i	$0.620585\pi$
$632$	137.800	−	44.7739i	0.218038	−	0.0708448i
$633$	−327.781	−	538.234i	−0.517821	−	0.850291i
$634$	356.189	+	258.786i	0.561812	+	0.408180i
$635$	−221.430	−	304.773i	−0.348709	−	0.479957i
$636$	589.221	+	48.0174i	0.926448	+	0.0754990i
$637$	233.315			0.366271
$638$	−78.1745	+	560.600i	−0.122531	+	0.878684i
$639$	457.501	+	910.345i	0.715964	+	1.42464i
$640$	5.71340	−	17.5841i	0.00892719	−	0.0274751i
$641$	−579.689	−	797.874i	−0.904351	−	1.24473i	−0.969059	−	0.246828i	$-0.920612\pi$
$641$	−579.689	−	797.874i	−0.904351	−	1.24473i	0.0647080	−	0.997904i	$-0.479388\pi$
$642$	289.068	+	120.676i	0.450261	+	0.187969i
$643$	246.310	+	758.065i	0.383064	+	1.17895i	0.937875	+	0.346974i	$0.112791\pi$
$643$	246.310	+	758.065i	0.383064	+	1.17895i	−0.554811	+	0.831977i	$0.687209\pi$
$644$	19.7135	−	6.40530i	0.0306110	−	0.00994612i
$645$	−121.138	+	290.174i	−0.187811	+	0.449882i
$646$	−217.401	+	157.951i	−0.336534	+	0.244506i
$647$	113.996	+	37.0395i	0.176191	+	0.0572480i	0.395784	−	0.918344i	$-0.370473\pi$
$647$	113.996	+	37.0395i	0.176191	+	0.0572480i	−0.219593	+	0.975592i	$0.570473\pi$
$648$	−183.843	−	136.711i	−0.283708	−	0.210974i
$649$	49.1593	+	277.059i	0.0757462	+	0.426902i
$650$		−	151.018i		−	0.232335i
$651$	2.07929	−	25.5149i	0.00319399	−	0.0391934i
$652$	−99.7285	+	72.4570i	−0.152958	+	0.111130i
$653$	−66.1431	+	91.0382i	−0.101291	+	0.139415i	−0.856654	−	0.515892i	$-0.827461\pi$
$653$	−66.1431	+	91.0382i	−0.101291	+	0.139415i	0.755363	+	0.655307i	$0.227461\pi$
$654$	496.778	−	302.534i	0.759599	−	0.462590i
$655$	−84.0876	−	258.795i	−0.128378	−	0.395107i
$656$	−154.702	+	212.929i	−0.235826	+	0.324587i
$657$	46.7290	−	90.4668i	0.0711249	−	0.137697i
$658$	13.7751	−	42.3954i	0.0209348	−	0.0644307i
$659$		−	567.382i		−	0.860974i	−0.902597	−	0.430487i	$-0.858342\pi$
$659$		−	567.382i		−	0.860974i	0.902597	−	0.430487i	$-0.141658\pi$
$660$	23.5238	−	105.261i	0.0356422	−	0.159487i
$661$	−1269.59			−1.92072			−0.960358	−	0.278769i	$-0.910074\pi$
$661$	−1269.59			−1.92072			−0.960358	+	0.278769i	$0.910074\pi$
$662$	194.937	+	63.3387i	0.294466	+	0.0956778i
$663$	84.0957	+	72.2288i	0.126841	+	0.108942i
$664$	−233.559	−	169.690i	−0.351745	−	0.255558i
$665$	17.6313	−	5.72875i	0.0265132	−	0.00861466i
$666$	215.367	−	212.991i	0.323374	−	0.319806i
$667$	−661.347	−	480.497i	−0.991525	−	0.720385i
$668$	−200.851	−	276.448i	−0.300675	−	0.413844i
$669$	44.0752	−	540.846i	0.0658822	−	0.808440i
$670$	104.245			0.155589
$671$	127.195	+	61.8683i	0.189560	+	0.0922031i
$672$	1.80641	+	7.61725i	0.00268811	+	0.0113352i
$673$	−11.4795	+	35.3303i	−0.0170572	+	0.0524967i	−0.959223	−	0.282651i	$-0.908786\pi$
$673$	−11.4795	+	35.3303i	−0.0170572	+	0.0524967i	0.942166	+	0.335148i	$0.108786\pi$
$674$	407.668	+	561.106i	0.604848	+	0.832502i
$675$	601.407	−	42.2999i	0.890973	−	0.0626665i
$676$	90.3131	+	277.955i	0.133599	+	0.411176i
$677$	42.8172	−	13.9122i	0.0632455	−	0.0205497i	−0.277223	−	0.960806i	$-0.589414\pi$
$677$	42.8172	−	13.9122i	0.0632455	−	0.0205497i	0.340469	+	0.940256i	$0.389414\pi$
$678$	−197.194	−	82.3219i	−0.290846	−	0.121419i
$679$	−28.2170	+	20.5009i	−0.0415567	+	0.0301927i
$680$	−33.9673	−	11.0366i	−0.0499519	−	0.0162304i
$681$	128.794	+	543.099i	0.189125	+	0.797502i
$682$	50.2732	+	283.337i	0.0737144	+	0.415450i
$683$		−	326.171i		−	0.477556i	−0.971074	−	0.238778i	$-0.923253\pi$
$683$		−	326.171i		−	0.477556i	0.971074	−	0.238778i	$-0.0767469\pi$
$684$	66.8193	+	437.576i	0.0976890	+	0.639731i
$685$	37.1184	−	26.9681i	0.0541875	−	0.0393695i
$686$	37.4972	−	51.6105i	0.0546607	−	0.0752339i
$687$	−639.577	−	1050.22i	−0.930971	−	1.52871i
$688$	79.2789	+	243.995i	0.115231	+	0.354644i
$689$	−276.961	+	381.205i	−0.401976	+	0.553272i
$690$	118.169	+	101.494i	0.171259	+	0.147092i
$691$	−38.8345	+	119.520i	−0.0562005	+	0.172967i	−0.975216	−	0.221253i	$-0.928985\pi$
$691$	−38.8345	+	119.520i	−0.0562005	+	0.172967i	0.919016	+	0.394220i	$0.128985\pi$
$692$		−	45.7256i		−	0.0660775i
$693$	14.6749	+	43.2467i	0.0211759	+	0.0624050i
$694$	−1.16287			−0.00167561
$695$	257.656	+	83.7175i	0.370728	+	0.120457i
$696$	201.161	−	234.211i	0.289025	−	0.336510i
$697$	411.318	+	298.840i	0.590126	+	0.428751i
$698$	−177.590	+	57.7026i	−0.254427	+	0.0826684i
$699$	−659.055	+	401.359i	−0.942854	+	0.574191i
$700$	−16.6666	−	12.1090i	−0.0238094	−	0.0172986i
$701$	−440.354	−	606.095i	−0.628180	−	0.864615i	0.369737	−	0.929137i	$-0.379448\pi$
$701$	−440.354	−	606.095i	−0.628180	−	0.864615i	−0.997916	+	0.0645216i	$0.979448\pi$
$702$	169.282	−	68.4742i	0.241142	−	0.0975416i
$703$	−585.231			−0.832477
$704$	−41.3968	−	77.6551i	−0.0588022	−	0.110305i
$705$	325.958	−	77.3001i	0.462352	−	0.109646i
$706$	75.7134	−	233.022i	0.107243	−	0.330059i
$707$	−12.9995	−	17.8922i	−0.0183868	−	0.0253073i
$708$	59.1287	−	141.637i	0.0835151	−	0.200052i
$709$	−37.1106	−	114.215i	−0.0523422	−	0.161093i	0.921468	−	0.388453i	$-0.126990\pi$
$709$	−37.1106	−	114.215i	−0.0523422	−	0.161093i	−0.973811	+	0.227360i	$0.926990\pi$
$710$	248.824	−	80.8479i	0.350457	−	0.113870i
$711$	−454.959	−	74.6476i	−0.639886	−	0.104990i
$712$	−19.6644	+	14.2870i	−0.0276185	+	0.0200660i
$713$	−395.255	−	128.426i	−0.554355	−	0.180121i
$714$	14.7143	−	3.48946i	0.0206083	−	0.00488721i
$715$	61.9042	+	59.6520i	0.0865793	+	0.0834294i
$716$			599.211i			0.836886i
$717$	−859.625	−	70.0534i	−1.19892	−	0.0977035i
$718$	193.104	−	140.298i	0.268947	−	0.195401i
$719$	−650.159	+	894.867i	−0.904254	+	1.24460i	0.0648368	+	0.997896i	$0.479347\pi$
$719$	−650.159	+	894.867i	−0.904254	+	1.24460i	−0.969091	+	0.246703i	$0.920653\pi$
$720$	−41.8303	+	41.3688i	−0.0580976	+	0.0574566i
$721$	−10.8082	−	33.2644i	−0.0149906	−	0.0461364i
$722$	202.615	−	278.875i	0.280630	−	0.386254i
$723$	438.833	−	510.931i	0.606962	−	0.706682i
$724$	48.4092	−	148.988i	0.0668636	−	0.205785i
$725$			812.464i			1.12064i
$726$	−283.073	−	428.262i	−0.389907	−	0.589892i
$727$	1220.54			1.67888			0.839438	−	0.543456i	$-0.182884\pi$
$727$	1220.54			1.67888			0.839438	+	0.543456i	$0.182884\pi$
$728$	−5.93432	−	1.92818i	−0.00815154	−	0.00264860i
$729$	320.105	+	654.961i	0.439101	+	0.898438i
$730$	−21.1535	−	15.3689i	−0.0289774	−	0.0210533i
$731$	471.328	−	153.144i	0.644772	−	0.209499i
$732$	−40.1286	−	65.8934i	−0.0548205	−	0.0900183i
$733$	934.648	+	679.062i	1.27510	+	0.926414i	0.999393	−	0.0348274i	$-0.0110882\pi$
$733$	934.648	+	679.062i	1.27510	+	0.926414i	0.275707	+	0.961242i	$0.411088\pi$
$734$	17.3525	+	23.8836i	0.0236410	+	0.0325390i
$735$	238.395	+	19.4275i	0.324347	+	0.0264320i
$736$	127.092			0.172680
$737$	344.281	−	357.279i	0.467139	−	0.484775i
$738$	748.299	−	376.063i	1.01395	−	0.509571i
$739$	225.723	−	694.703i	0.305443	−	0.940058i	−0.674068	−	0.738669i	$-0.735455\pi$
$739$	225.723	−	694.703i	0.305443	−	0.940058i	0.979511	−	0.201389i	$-0.0645455\pi$
$740$	−45.7191	−	62.9269i	−0.0617825	−	0.0850364i
$741$	−325.581	−	135.919i	−0.439380	−	0.183427i
$742$	19.8630	+	61.1320i	0.0267695	+	0.0823882i
$743$	730.662	−	237.407i	0.983395	−	0.319524i	0.227184	−	0.973852i	$-0.427048\pi$
$743$	730.662	−	237.407i	0.983395	−	0.319524i	0.756211	+	0.654328i	$0.227048\pi$
$744$	60.4685	−	144.846i	0.0812749	−	0.194686i
$745$	−93.8130	+	68.1591i	−0.125924	+	0.0914888i
$746$	−321.618	−	104.500i	−0.431123	−	0.140080i
$747$	412.499	+	820.798i	0.552207	+	1.09879i
$748$	−150.007	+	79.9666i	−0.200544	+	0.106907i
$749$			34.0590i			0.0454727i
$750$	26.6537	−	327.067i	0.0355383	−	0.436090i
$751$	−379.605	+	275.799i	−0.505466	+	0.367243i	−0.811101	−	0.584906i	$-0.801131\pi$
$751$	−379.605	+	275.799i	−0.505466	+	0.367243i	0.305635	+	0.952149i	$0.401131\pi$
$752$	160.655	−	221.122i	0.213636	−	0.294045i
$753$	273.291	−	166.432i	0.362937	−	0.221026i
$754$	76.0434	+	234.037i	0.100853	+	0.310394i
$755$	60.8437	−	83.7442i	0.0805877	−	0.110920i
$756$	6.01650	−	24.1727i	0.00795834	−	0.0319745i
$757$	48.9820	−	150.751i	0.0647054	−	0.199143i	−0.913477	−	0.406890i	$-0.866613\pi$
$757$	48.9820	−	150.751i	0.0647054	−	0.199143i	0.978183	+	0.207747i	$0.0666132\pi$
$758$			479.940i			0.633167i
$759$	738.116	−	69.8051i	0.972485	−	0.0919698i
$760$	113.668			0.149563
$761$	48.8309	+	15.8661i	0.0641667	+	0.0208490i	0.340924	−	0.940091i	$-0.389260\pi$
$761$	48.8309	+	15.8661i	0.0641667	+	0.0208490i	−0.276758	+	0.960940i	$0.589260\pi$
$762$	741.926	+	637.232i	0.973657	+	0.836263i
$763$	51.1641	+	37.1729i	0.0670565	+	0.0487194i
$764$	497.438	−	161.627i	0.651096	−	0.211554i
$765$	79.9125	+	80.8040i	0.104461	+	0.105626i
$766$	−67.6861	−	49.1769i	−0.0883631	−	0.0641996i
$767$	71.9061	+	98.9703i	0.0937498	+	0.129036i
$768$	−3.89874	+	47.8414i	−0.00507648	+	0.0622935i
$769$	841.280			1.09399			0.546996	−	0.837135i	$-0.315771\pi$
$769$	841.280			1.09399			0.546996	+	0.837135i	$0.315771\pi$
$770$	11.5470	−	2.04881i	0.0149961	−	0.00266079i
$771$	−173.152	−	730.146i	−0.224581	−	0.947012i
$772$	89.1737	−	274.449i	0.115510	−	0.355503i
$773$	727.969	+	1001.96i	0.941745	+	1.29620i	0.955098	+	0.296291i	$0.0957497\pi$
$773$	727.969	+	1001.96i	0.941745	+	1.29620i	−0.0133524	+	0.999911i	$0.504250\pi$
$774$	132.175	−	805.571i	0.170768	−	1.04079i
$775$	127.640	+	392.834i	0.164696	+	0.506883i
$776$	−203.386	+	66.0842i	−0.262096	+	0.0851600i
$777$	30.3921	+	12.6877i	0.0391146	+	0.0163291i
$778$	−49.3586	+	35.8611i	−0.0634429	+	0.0460940i
$779$	−1538.90	−	500.019i	−1.97548	−	0.641873i
$780$	−10.8201	−	45.6262i	−0.0138720	−	0.0584951i
$781$	544.681	−	1119.81i	0.697415	−	1.43381i
$782$		−	245.505i		−	0.313946i
$783$	−910.722	+	368.386i	−1.16312	+	0.470480i
$784$	157.879	−	114.706i	0.201376	−	0.146308i
$785$	217.083	−	298.789i	0.276539	−	0.380623i
$786$	367.444	+	603.365i	0.467487	+	0.767640i
$787$	−133.708	−	411.511i	−0.169896	−	0.522886i	0.829468	−	0.558555i	$-0.188644\pi$
$787$	−133.708	−	411.511i	−0.169896	−	0.522886i	−0.999364	+	0.0356687i	$0.988644\pi$
$788$	−351.055	+	483.186i	−0.445501	+	0.613180i
$789$	−73.6399	−	63.2485i	−0.0933333	−	0.0801629i
$790$	−36.5850	+	112.597i	−0.0463101	+	0.142528i
$791$		−	23.2341i		−	0.0293731i
$792$	3.63400	+	279.991i	0.00458838	+	0.353524i
$793$	61.4930			0.0775448
$794$	−118.534	−	38.5139i	−0.149287	−	0.0485062i
$795$	−314.734	+	366.443i	−0.395892	+	0.460935i
$796$	390.712	+	283.869i	0.490844	+	0.356619i
$797$	969.083	−	314.874i	1.21591	−	0.395074i	0.370322	−	0.928904i	$-0.379247\pi$
$797$	969.083	−	314.874i	1.21591	−	0.395074i	0.845592	+	0.533829i	$0.179247\pi$
$798$	−41.1062	+	25.0334i	−0.0515116	+	0.0313701i
$799$	−427.144	−	310.338i	−0.534598	−	0.388408i
$800$	−74.2455	−	102.190i	−0.0928068	−	0.127738i
$801$	76.4566	−	11.6752i	0.0954514	−	0.0145757i
$802$	−679.465			−0.847213
$803$	−122.536	+	21.7419i	−0.152598	+	0.0270758i
$804$	−263.331	+	62.4483i	−0.327526	+	0.0776720i
$805$	−5.23380	+	16.1080i	−0.00650162	+	0.0200099i
$806$	73.5355	+	101.213i	0.0912351	+	0.125574i
$807$	399.274	−	956.421i	0.494763	−	1.18516i
$808$	−41.9036	−	128.966i	−0.0518609	−	0.159611i
$809$	273.488	−	88.8617i	0.338057	−	0.109841i	−0.135069	−	0.990836i	$-0.543126\pi$
$809$	273.488	−	88.8617i	0.338057	−	0.109841i	0.473126	+	0.880995i	$0.343126\pi$
$810$	178.669	−	55.8695i	0.220579	−	0.0689747i
$811$	167.430	−	121.645i	0.206449	−	0.149994i	−0.479756	−	0.877402i	$-0.659275\pi$
$811$	167.430	−	121.645i	0.206449	−	0.149994i	0.686206	+	0.727408i	$0.259275\pi$
$812$	31.9262	+	10.3735i	0.0393180	+	0.0127752i
$813$	−1152.58	+	273.331i	−1.41769	+	0.336201i
$814$	−366.663	−	51.1303i	−0.450446	−	0.0628137i
$815$		−	100.725i		−	0.123590i
$816$	92.4158	+	7.53124i	0.113255	+	0.00922946i
$817$	−1276.02	+	927.086i	−1.56184	+	1.13474i
$818$	−572.959	+	788.611i	−0.700439	+	0.964072i
$819$	13.9613	+	14.1170i	0.0170467	+	0.0172369i
$820$	−66.4565	−	204.532i	−0.0810445	−	0.249429i
$821$	−468.687	+	645.092i	−0.570873	+	0.785740i	−0.992658	−	0.120956i	$-0.961404\pi$
$821$	−468.687	+	645.092i	−0.570873	+	0.785740i	0.421784	+	0.906696i	$0.361404\pi$
$822$	−77.6089	+	90.3597i	−0.0944147	+	0.109927i
$823$	133.512	−	410.907i	0.162226	−	0.499280i	−0.836595	−	0.547821i	$-0.815457\pi$
$823$	133.512	−	410.907i	0.162226	−	0.499280i	0.998821	+	0.0485415i	$0.0154573\pi$
$824$		−	214.454i		−	0.260260i
$825$	−487.324	−	552.712i	−0.590696	−	0.669954i
$826$	16.6882			0.0202036
$827$	−1253.82	−	407.390i	−1.51610	−	0.492612i	−0.571437	−	0.820646i	$-0.693614\pi$
$827$	−1253.82	−	407.390i	−1.51610	−	0.492612i	−0.944666	+	0.328034i	$0.893614\pi$
$828$	−359.304	−	185.592i	−0.433942	−	0.224145i
$829$	−1048.35	−	761.669i	−1.26459	−	0.918781i	−0.265620	−	0.964078i	$-0.585576\pi$
$829$	−1048.35	−	761.669i	−1.26459	−	0.918781i	−0.998974	+	0.0452973i	$0.985576\pi$
$830$	224.348	−	72.8952i	0.270299	−	0.0878255i
$831$	563.320	+	925.004i	0.677882	+	1.11312i
$832$	−30.9517	−	22.4877i	−0.0372015	−	0.0270285i
$833$	−221.578	−	304.976i	−0.266000	−	0.366118i
$834$	−701.011	−	57.1275i	−0.840541	−	0.0684982i
$835$	279.211			0.334385
$836$	375.403	−	389.576i	0.449047	−	0.466000i
$837$	−382.469	+	321.195i	−0.456952	+	0.383745i
$838$	148.326	−	456.500i	0.177000	−	0.544750i
$839$	236.251	+	325.172i	0.281587	+	0.387571i	0.926259	−	0.376888i	$-0.123006\pi$
$839$	236.251	+	325.172i	0.281587	+	0.387571i	−0.644672	+	0.764459i	$0.723006\pi$
$840$	−5.90298	−	2.46430i	−0.00702736	−	0.00293369i
$841$	−149.224	−	459.266i	−0.177437	−	0.546095i
$842$	261.051	−	84.8206i	0.310037	−	0.100737i
$843$	−27.2793	+	65.3448i	−0.0323598	+	0.0775146i
$844$	339.888	−	246.943i	0.402711	−	0.292587i
$845$	−227.118	−	73.7952i	−0.268779	−	0.0873316i
$846$	−777.091	+	390.533i	−0.918547	+	0.461623i
$847$	31.1133	−	46.3414i	0.0367336	−	0.0547124i
$848$			394.116i			0.464760i
$849$	−51.9594	+	637.594i	−0.0612008	+	0.750994i
$850$	−197.402	+	143.421i	−0.232237	+	0.168730i
$851$	314.271	−	432.557i	0.369296	−	0.508292i
$852$	−580.118	+	353.287i	−0.680890	+	0.414657i
$853$	303.712	+	934.729i	0.356052	+	1.09581i	0.955397	+	0.295324i	$0.0954275\pi$
$853$	303.712	+	934.729i	0.356052	+	1.09581i	−0.599346	+	0.800490i	$0.704572\pi$
$854$	4.93067	−	6.78649i	0.00577362	−	0.00794671i
$855$	−321.352	−	165.989i	−0.375851	−	0.194139i
$856$	−64.5322	+	198.610i	−0.0753881	+	0.232021i
$857$			1185.84i			1.38372i	0.722033	+	0.691858i	$0.243208\pi$
$857$			1185.84i			1.38372i	−0.722033	+	0.691858i	$0.756792\pi$
$858$	−192.110	−	113.602i	−0.223904	−	0.132403i
$859$	−896.376			−1.04351			−0.521756	−	0.853095i	$-0.674723\pi$
$859$	−896.376			−1.04351			−0.521756	+	0.853095i	$0.674723\pi$
$860$	−199.370	−	64.7791i	−0.231825	−	0.0753246i
$861$	69.0774	+	59.3298i	0.0802292	+	0.0689080i
$862$	194.307	+	141.172i	0.225414	+	0.163773i
$863$	446.888	−	145.203i	0.517830	−	0.168253i	−0.0384301	−	0.999261i	$-0.512236\pi$
$863$	446.888	−	145.203i	0.517830	−	0.168253i	0.556260	+	0.831008i	$0.312236\pi$
$864$	80.8846	−	129.560i	0.0936165	−	0.149953i
$865$	30.2270	+	21.9612i	0.0349445	+	0.0253887i
$866$	−78.1276	−	107.533i	−0.0902167	−	0.124173i
$867$	−55.8728	+	685.615i	−0.0644438	+	0.790790i
$868$	17.0663			0.0196617
$869$	265.078	+	497.253i	0.305038	+	0.572213i
$870$	58.2115	+	245.466i	0.0669098	+	0.282144i
$871$	66.6578	−	205.152i	0.0765302	−	0.235536i
$872$	227.923	+	313.709i	0.261380	+	0.359758i
$873$	671.497	+	110.176i	0.769184	+	0.126204i
$874$	241.450	+	743.108i	0.276259	+	0.850238i
$875$	33.9334	−	11.0256i	0.0387811	−	0.0126007i
$876$	62.6423	+	26.1511i	0.0715094	+	0.0298528i
$877$	43.1803	−	31.3723i	0.0492364	−	0.0357723i	−0.562895	−	0.826529i	$-0.690312\pi$
$877$	43.1803	−	31.3723i	0.0492364	−	0.0357723i	0.612131	+	0.790756i	$0.290312\pi$
$878$	−828.933	−	269.337i	−0.944115	−	0.306762i
$879$	114.029	+	480.834i	0.129725	+	0.547024i
$880$	71.2161	+	9.93093i	0.0809274	+	0.0112852i
$881$		−	1123.85i		−	1.27566i	−0.770178	−	0.637829i	$-0.779833\pi$
$881$		−	1123.85i		−	1.27566i	0.770178	−	0.637829i	$-0.220167\pi$
$882$	−613.844	+	93.7360i	−0.695968	+	0.106277i
$883$	457.899	−	332.683i	0.518572	−	0.376765i	−0.297494	−	0.954724i	$-0.596151\pi$
$883$	457.899	−	332.683i	0.518572	−	0.376765i	0.816066	+	0.577959i	$0.196151\pi$
$884$	−43.4397	+	59.7897i	−0.0491400	+	0.0676354i
$885$	65.2308	+	107.113i	0.0737072	+	0.121031i
$886$	−282.799	−	870.367i	−0.319187	−	0.982355i
$887$	−553.224	+	761.447i	−0.623702	+	0.858452i	−0.997616	−	0.0690113i	$-0.978016\pi$
$887$	−553.224	+	761.447i	−0.623702	+	0.858452i	0.373914	+	0.927463i	$0.378016\pi$
$888$	153.187	+	131.570i	0.172508	+	0.148165i
$889$	−32.8607	+	101.135i	−0.0369636	+	0.113762i
$890$		−	19.8610i		−	0.0223157i
$891$	398.595	−	796.871i	0.447357	−	0.894356i
$892$	361.760			0.405560
$893$	1598.11	+	519.258i	1.78960	+	0.581476i
$894$	196.148	−	228.375i	0.219405	−	0.255453i
$895$	−396.109	−	287.790i	−0.442580	−	0.321553i
$896$	−4.96358	+	1.61276i	−0.00553970	+	0.00179996i
$897$	275.298	−	167.654i	0.306910	−	0.186906i
$898$	−341.716	−	248.271i	−0.380530	−	0.276471i
$899$	−395.615	−	544.518i	−0.440062	−	0.605693i
$900$	60.6725	+	397.323i	0.0674138	+	0.441470i
$901$	761.318			0.844970
$902$	−920.475	−	447.725i	−1.02048	−	0.496369i
$903$	86.3652	−	20.4813i	0.0956425	−	0.0226814i
$904$	44.0220	−	135.486i	0.0486969	−	0.149874i
$905$	75.2388	+	103.557i	0.0831368	+	0.114428i
$906$	−103.529	+	247.994i	−0.114270	+	0.273724i
$907$	60.2325	+	185.377i	0.0664085	+	0.204384i	0.978754	−	0.205036i	$-0.0657311\pi$
$907$	60.2325	+	185.377i	0.0664085	+	0.204384i	−0.912346	+	0.409420i	$0.865731\pi$
$908$	−353.895	+	114.988i	−0.389753	+	0.126638i
$909$	−69.8622	+	425.792i	−0.0768561	+	0.468419i
$910$	4.12477	−	2.99682i	0.00453272	−	0.00329321i
$911$	−724.808	−	235.504i	−0.795618	−	0.258512i	−0.117123	−	0.993117i	$-0.537367\pi$
$911$	−724.808	−	235.504i	−0.795618	−	0.258512i	−0.678494	+	0.734606i	$0.737367\pi$
$912$	−287.135	+	68.0934i	−0.314841	+	0.0746638i
$913$	491.103	−	1009.66i	0.537900	−	1.10587i
$914$		−	419.008i		−	0.458434i
$915$	62.8320	+	5.12037i	0.0686688	+	0.00559603i
$916$	663.202	−	481.845i	0.724020	−	0.526031i
$917$	−45.1486	+	62.1417i	−0.0492351	+	0.0677663i
$918$	−250.272	−	156.246i	−0.272627	−	0.170202i
$919$	178.084	+	548.085i	0.193780	+	0.596393i	0.999989	+	0.00476175i	$0.00151572\pi$
$919$	178.084	+	548.085i	0.193780	+	0.596393i	−0.806209	+	0.591631i	$0.798484\pi$
$920$	−61.0401	+	84.0145i	−0.0663480	+	0.0913201i
$921$	−274.731	+	319.868i	−0.298297	+	0.347305i
$922$	159.942	−	492.250i	0.173473	−	0.533894i
$923$		−	541.377i		−	0.586541i
$924$	−27.9412	+	12.0927i	−0.0302394	+	0.0130873i
$925$	−531.395			−0.574481
$926$	644.783	+	209.503i	0.696310	+	0.226245i
$927$	−313.166	+	606.285i	−0.337827	+	0.654030i
$928$	166.518	+	120.982i	0.179437	+	0.130369i
$929$	1371.38	−	445.590i	1.47619	−	0.479645i	0.543221	−	0.839590i	$-0.317205\pi$
$929$	1371.38	−	445.590i	1.47619	−	0.479645i	0.932973	+	0.359945i	$0.117205\pi$
$930$	66.7089	+	109.540i	0.0717300	+	0.117785i
$931$	970.622	+	705.198i	1.04256	+	0.757463i
$932$	−302.376	−	416.185i	−0.324438	−	0.446550i
$933$	−32.6683	−	2.66224i	−0.0350143	−	0.00285342i
$934$	−934.785			−1.00084
$935$	19.1837	−	137.569i	0.0205173	−	0.147133i
$936$	54.6651	+	108.774i	0.0584029	+	0.116211i
$937$	−179.492	+	552.419i	−0.191560	+	0.589561i	0.808440	+	0.588579i	$0.200312\pi$
$937$	−179.492	+	552.419i	−0.191560	+	0.589561i	−1.00000		0.000981694i	$0.999688\pi$
$938$	−17.2961	−	23.8061i	−0.0184394	−	0.0253796i
$939$	−696.874	−	290.922i	−0.742145	−	0.309821i
$940$	69.0135	+	212.402i	0.0734186	+	0.225959i
$941$	−157.464	+	51.1630i	−0.167336	+	0.0543709i	−0.391487	−	0.920184i	$-0.628039\pi$
$941$	−157.464	+	51.1630i	−0.167336	+	0.0543709i	0.224151	+	0.974555i	$0.428039\pi$
$942$	−369.378	+	884.809i	−0.392121	+	0.939288i
$943$	1195.97	−	868.921i	1.26826	−	0.921443i
$944$	97.3144	+	31.6194i	0.103087	+	0.0334951i
$945$	13.0898	+	15.5869i	0.0138516	+	0.0164941i
$946$	−880.460	+	469.360i	−0.930719	+	0.496153i
$947$			647.752i			0.684005i	0.939699	+	0.342002i	$0.111105\pi$
$947$			647.752i			0.684005i	−0.939699	+	0.342002i	$0.888895\pi$
$948$	24.9650	−	306.346i	0.0263344	−	0.323149i
$949$	−43.7719	+	31.8022i	−0.0461243	+	0.0335112i
$950$	456.453	−	628.254i	0.480477	−	0.661320i
$951$	797.683	−	485.783i	0.838784	−	0.510813i
$952$	3.11539	+	9.58819i	0.00327247	+	0.0100716i
$953$	365.281	−	502.767i	0.383296	−	0.527562i	−0.573158	−	0.819445i	$-0.694282\pi$
$953$	365.281	−	502.767i	0.383296	−	0.527562i	0.956454	+	0.291883i	$0.0942818\pi$
$954$	575.525	−	1114.21i	0.603276	−	1.16793i
$955$	−132.066	+	406.459i	−0.138289	+	0.425611i
$956$		−	574.983i		−	0.601447i
$957$	1033.54	+	611.171i	1.07998	+	0.638632i
$958$	249.119			0.260041
$959$	−12.3173	−	4.00212i	−0.0128439	−	0.00417322i
$960$	−29.7531	−	25.5546i	−0.0309928	−	0.0266194i
$961$	500.637	+	363.734i	0.520954	+	0.378495i
$962$	−153.073	+	49.7365i	−0.159120	+	0.0517011i
$963$	472.468	−	467.255i	0.490621	−	0.485208i
$964$	363.258	+	263.922i	0.376824	+	0.273778i
$965$	138.596	+	190.761i	0.143623	+	0.197680i
$966$	3.57147	−	43.8254i	0.00369717	−	0.0453680i
$967$	−995.335			−1.02930			−0.514651	−	0.857400i	$-0.672079\pi$
$967$	−995.335			−1.02930			−0.514651	+	0.857400i	$0.672079\pi$
$968$	269.236	−	211.282i	0.278137	−	0.218266i
$969$	131.537	+	554.662i	0.135745	+	0.572407i
$970$	53.9977	−	166.188i	0.0556677	−	0.171328i
$971$	176.156	+	242.459i	0.181418	+	0.249700i	0.890034	−	0.455894i	$-0.150680\pi$
$971$	176.156	+	242.459i	0.181418	+	0.249700i	−0.708617	+	0.705594i	$0.750680\pi$
$972$	−417.865	+	248.164i	−0.429902	+	0.255312i
$973$	−23.6315	−	72.7304i	−0.0242873	−	0.0747486i
$974$	950.718	−	308.907i	0.976096	−	0.317153i
$975$	−295.630	−	123.416i	−0.303210	−	0.126580i
$976$	41.6109	−	30.2321i	0.0426341	−	0.0309755i
$977$	812.827	+	264.104i	0.831963	+	0.270321i	0.693872	−	0.720099i	$-0.255903\pi$
$977$	812.827	+	264.104i	0.831963	+	0.270321i	0.138091	+	0.990420i	$0.455903\pi$
$978$	60.3400	+	254.441i	0.0616973	+	0.260164i
$979$	−68.0697	−	65.5932i	−0.0695298	−	0.0670002i
$980$			159.457i			0.162711i
$981$	−186.256	−	1219.72i	−0.189863	−	1.24335i
$982$	701.810	−	509.895i	0.714674	−	0.519241i
$983$	−173.454	+	238.739i	−0.176454	+	0.242868i	−0.888078	−	0.459692i	$-0.847960\pi$
$983$	−173.454	+	238.739i	−0.176454	+	0.242868i	0.711624	+	0.702560i	$0.247960\pi$
$984$	290.400	+	476.854i	0.295122	+	0.484608i
$985$	−150.805	−	464.131i	−0.153102	−	0.471199i
$986$	233.703	−	321.664i	0.237021	−	0.326231i
$987$	−71.7353	−	61.6126i	−0.0726801	−	0.0624241i
$988$	72.6834	−	223.696i	0.0735662	−	0.226413i
$989$		−	1440.98i		−	1.45701i
$990$	−186.834	−	132.072i	−0.188721	−	0.133406i
$991$	18.9414			0.0191134			0.00955672	−	0.999954i	$-0.496958\pi$
$991$	18.9414			0.0191134			0.00955672	+	0.999954i	$0.496958\pi$
$992$	99.5195	+	32.3358i	0.100322	+	0.0325966i
$993$	283.298	−	329.843i	0.285295	−	0.332168i
$994$	−59.7475	−	43.4091i	−0.0601081	−	0.0436711i
$995$	−375.304	+	121.944i	−0.377190	+	0.122556i
$996$	−523.054	+	318.536i	−0.525155	+	0.319815i
$997$	−409.812	−	297.746i	−0.411045	−	0.298642i	0.362980	−	0.931797i	$-0.381759\pi$
$997$	−409.812	−	297.746i	−0.411045	−	0.298642i	−0.774025	+	0.633155i	$0.781759\pi$
$998$	399.981	+	550.527i	0.400783	+	0.551630i
$999$	−240.944	−	595.661i	−0.241185	−	0.596258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.3.g.a.53.7	yes	32
3.2	odd	2	inner	66.3.g.a.53.4	yes	32
11.4	even	5		726.3.c.h.485.9		16
11.5	even	5	inner	66.3.g.a.5.4	✓	32
11.7	odd	10		726.3.c.i.485.1		16
33.5	odd	10	inner	66.3.g.a.5.7	yes	32
33.26	odd	10		726.3.c.h.485.1		16
33.29	even	10		726.3.c.i.485.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.g.a.5.4	✓	32	11.5	even	5	inner
66.3.g.a.5.7	yes	32	33.5	odd	10	inner
66.3.g.a.53.4	yes	32	3.2	odd	2	inner
66.3.g.a.53.7	yes	32	1.1	even	1	trivial
726.3.c.h.485.1		16	33.26	odd	10
726.3.c.h.485.9		16	11.4	even	5
726.3.c.i.485.1		16	11.7	odd	10
726.3.c.i.485.9		16	33.29	even	10

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	66.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34500 + 0.437016i) q^{2} +(1.95466 - 2.27581i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-1.55423 + 0.504998i) q^{5} +(3.62358 - 2.20673i) q^{6} +(0.373199 + 0.271145i) q^{7} +(1.66251 + 2.28825i) q^{8} +(-1.35858 - 8.89687i) q^{9} -2.31112 q^{10} +(-7.63276 + 7.92092i) q^{11} +(5.83808 - 1.38449i) q^{12} +(-1.47781 + 4.54823i) q^{13} +(0.383457 + 0.527784i) q^{14} +(-1.88871 + 4.52422i) q^{15} +(1.23607 + 3.80423i) q^{16} +(7.34866 - 2.38773i) q^{17} +(2.06079 - 12.5600i) q^{18} +(-19.8950 + 14.4546i) q^{19} +(-3.10845 - 1.01000i) q^{20} +(1.34655 - 0.319331i) q^{21} +(-13.7276 + 7.31798i) q^{22} -22.4669i q^{23} +(8.45725 + 0.689206i) q^{24} +(-18.0648 + 13.1249i) q^{25} +(-3.97530 + 5.47153i) q^{26} +(-22.9031 - 14.2985i) q^{27} +(0.285099 + 0.877444i) q^{28} +(21.3868 - 29.4364i) q^{29} +(-4.51746 + 5.25966i) q^{30} +(5.71622 - 17.5927i) q^{31} +5.65685i q^{32} +(3.10701 + 32.8534i) q^{33} +10.9274 q^{34} +(-0.716964 - 0.232956i) q^{35} +(8.26067 - 15.9925i) q^{36} +(19.2530 + 13.9881i) q^{37} +(-33.0756 + 10.7469i) q^{38} +(7.46227 + 12.2535i) q^{39} +(-3.73947 - 2.71689i) q^{40} +(38.6755 + 53.2323i) q^{41} +(1.95066 + 0.158965i) q^{42} +64.1379 q^{43} +(-21.6617 + 3.84348i) q^{44} +(6.60444 + 13.1417i) q^{45} +(9.81842 - 30.2180i) q^{46} +(-40.1636 - 55.2805i) q^{47} +(11.0738 + 4.62293i) q^{48} +(-15.0761 - 46.3994i) q^{49} +(-30.0329 + 9.75829i) q^{50} +(8.93017 - 21.3913i) q^{51} +(-7.73792 + 5.62193i) q^{52} +(93.7067 + 30.4471i) q^{53} +(-24.5559 - 29.2405i) q^{54} +(7.86297 - 16.1654i) q^{55} +1.30475i q^{56} +(-5.99226 + 73.5310i) q^{57} +(41.6294 - 30.2455i) q^{58} +(15.0359 - 20.6951i) q^{59} +(-8.37453 + 5.10002i) q^{60} +(-3.97349 - 12.2291i) q^{61} +(15.3766 - 21.1641i) q^{62} +(1.90532 - 3.68868i) q^{63} +(-2.47214 + 7.60845i) q^{64} -7.81527i q^{65} +(-10.1785 + 45.5456i) q^{66} -45.1058 q^{67} +(14.6973 + 4.77545i) q^{68} +(-51.1304 - 43.9153i) q^{69} +(-0.862509 - 0.626649i) q^{70} +(-107.664 + 34.9821i) q^{71} +(18.0996 - 17.8999i) q^{72} +(9.15291 + 6.64998i) q^{73} +(19.7822 + 27.2279i) q^{74} +(-5.44102 + 66.7667i) q^{75} -49.1832 q^{76} +(-4.99626 + 0.886499i) q^{77} +(4.68177 + 19.7420i) q^{78} +(15.8300 - 48.7197i) q^{79} +(-3.84226 - 5.28841i) q^{80} +(-77.3085 + 24.1742i) q^{81} +(28.7551 + 88.4991i) q^{82} +(-97.0734 + 31.5411i) q^{83} +(2.55417 + 1.06628i) q^{84} +(-10.2157 + 7.42213i) q^{85} +(86.2653 + 28.0293i) q^{86} +(-25.1876 - 106.211i) q^{87} +(-30.8145 - 4.29702i) q^{88} +8.59365i q^{89} +(3.13984 + 20.5617i) q^{90} +(-1.78475 + 1.29670i) q^{91} +(26.4115 - 36.3523i) q^{92} +(-28.8643 - 47.3969i) q^{93} +(-29.8615 - 91.9042i) q^{94} +(23.6218 - 32.5126i) q^{95} +(12.8739 + 11.0572i) q^{96} +(-23.3643 + 71.9079i) q^{97} -68.9955i q^{98} +(80.8411 + 57.1464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 12 q^{6} - 8 q^{7} + 26 q^{9} + 16 q^{10} - 24 q^{12} + 8 q^{13} - 82 q^{15} - 32 q^{16} - 8 q^{18} - 4 q^{19} - 100 q^{21} - 24 q^{24} - 88 q^{25} - 106 q^{27} - 24 q^{28} - 36 q^{30}+ \cdots + 470 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 12 * q^6 - 8 * q^7 + 26 * q^9 + 16 * q^10 - 24 * q^12 + 8 * q^13 - 82 * q^15 - 32 * q^16 - 8 * q^18 - 4 * q^19 - 100 * q^21 - 24 * q^24 - 88 * q^25 - 106 * q^27 - 24 * q^28 - 36 * q^30 - 148 * q^31 + 78 * q^33 - 32 * q^34 + 8 * q^36 + 96 * q^37 + 362 * q^39 + 48 * q^40 + 152 * q^42 + 560 * q^43 - 20 * q^45 + 176 * q^46 + 8 * q^48 + 208 * q^49 - 82 * q^51 + 24 * q^52 - 176 * q^54 - 108 * q^55 - 142 * q^57 - 144 * q^58 - 36 * q^60 - 384 * q^61 + 506 * q^63 + 64 * q^64 + 400 * q^66 - 680 * q^67 + 136 * q^69 - 400 * q^70 + 16 * q^72 - 92 * q^73 + 90 * q^75 + 128 * q^76 + 152 * q^78 + 320 * q^79 - 198 * q^81 - 328 * q^82 - 240 * q^84 - 1024 * q^85 - 1332 * q^87 - 736 * q^90 - 264 * q^91 - 226 * q^93 - 64 * q^94 - 32 * q^96 - 248 * q^97 + 470 * q^99

Introduction

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