LMFDB - Embedded newform 847.2.r.c.766.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [847,2,Mod(40,847)] 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("847.40"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(847, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([25, 21])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.r (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,5,-9] 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			766.1
Character	$\chi$	$=$	847.766
Dual form			847.2.r.c.481.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.05902 - 0.216412i) q^{2} +(-2.33449 + 2.10199i) q^{3} +(2.23645 + 0.475371i) q^{4} +(0.483200 - 1.08528i) q^{5} +(5.26167 - 3.82283i) q^{6} +(-2.02173 + 1.70664i) q^{7} +(-0.563952 - 0.183239i) q^{8} +(0.717924 - 6.83059i) q^{9} +(-1.22979 + 2.13006i) q^{10} +(-6.22020 + 3.59123i) q^{12} +(-0.000347326 - 0.000252347i) q^{13} +(4.53213 - 3.07648i) q^{14} +(1.15323 + 3.54927i) q^{15} +(-3.05594 - 1.36059i) q^{16} +(0.192581 + 1.83228i) q^{17} +(-2.95645 + 13.9090i) q^{18} +(1.89260 - 0.402285i) q^{19} +(1.59656 - 2.19748i) q^{20} +(1.13239 - 8.23379i) q^{21} +(2.83507 + 4.91048i) q^{23} +(1.70171 - 0.757650i) q^{24} +(2.40129 + 2.66691i) q^{25} +(0.000660541 + 0.000594754i) q^{26} +(7.14248 + 9.83078i) q^{27} +(-5.33278 + 2.85573i) q^{28} +(4.88867 - 1.58843i) q^{29} +(-1.60642 - 7.55760i) q^{30} +(0.176317 + 0.396015i) q^{31} +(7.02487 + 4.05581i) q^{32} -3.81439i q^{34} +(0.875286 + 3.01880i) q^{35} +(4.85267 - 14.9350i) q^{36} +(0.251703 - 0.279544i) q^{37} +(-3.98397 + 0.418732i) q^{38} +(0.00134126 - 0.000140972i) q^{39} +(-0.471368 + 0.523507i) q^{40} +(-0.760621 + 2.34095i) q^{41} +(-4.11351 + 16.7085i) q^{42} +5.03264i q^{43} +(-7.06624 - 4.07969i) q^{45} +(-4.77478 - 10.7243i) q^{46} +(-0.385768 - 1.81490i) q^{47} +(9.99404 - 3.24726i) q^{48} +(1.17479 - 6.90072i) q^{49} +(-4.36717 - 6.01089i) q^{50} +(-4.30102 - 3.87266i) q^{51} +(-0.000656817 - 0.000729469i) q^{52} +(1.20901 - 0.538288i) q^{53} +(-12.5790 - 21.7875i) q^{54} +(1.45288 - 0.592000i) q^{56} +(-3.57267 + 4.91735i) q^{57} +(-10.4096 + 2.21264i) q^{58} +(-2.53655 + 11.9335i) q^{59} +(0.891911 + 8.48597i) q^{60} +(-6.95359 - 3.09594i) q^{61} +(-0.277339 - 0.853562i) q^{62} +(10.2059 + 15.0349i) q^{63} +(-8.17409 - 5.93882i) q^{64} +(-0.000441696 + 0.000255013i) q^{65} +(6.72641 - 11.6505i) q^{67} +(-0.440319 + 4.18935i) q^{68} +(-16.9402 - 5.50421i) q^{69} +(-1.14893 - 6.40520i) q^{70} +(-6.82813 + 4.96093i) q^{71} +(-1.65651 + 3.72057i) q^{72} +(-13.3457 - 2.83671i) q^{73} +(-0.578758 + 0.521116i) q^{74} +(-11.2116 - 1.17839i) q^{75} +4.42393 q^{76} -0.00279219 q^{78} +(-1.63180 - 0.171509i) q^{79} +(-2.95326 + 2.65913i) q^{80} +(-17.1839 - 3.65255i) q^{81} +(2.07275 - 4.65546i) q^{82} +(-7.86628 + 5.71519i) q^{83} +(6.44664 - 17.8761i) q^{84} +(2.08161 + 0.676354i) q^{85} +(1.08912 - 10.3623i) q^{86} +(-8.07373 + 13.9841i) q^{87} +(-6.24880 + 3.60774i) q^{89} +(13.6667 + 9.92940i) q^{90} +(0.00113286 - 8.25811e-5i) q^{91} +(4.00617 + 12.3297i) q^{92} +(-1.24403 - 0.553878i) q^{93} +(0.401540 + 3.82040i) q^{94} +(0.477911 - 2.24839i) q^{95} +(-24.9248 + 5.29793i) q^{96} +(-2.39869 + 3.30152i) q^{97} +(-3.91231 + 13.9545i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} + 5 q^{7} - 11 q^{9} - 12 q^{12} - 8 q^{14} - 27 q^{16} - 15 q^{17} - 20 q^{18} + 15 q^{19} + 10 q^{23} - 75 q^{24} + q^{25} + 27 q^{26} + 40 q^{28} + 40 q^{29}+ \cdots - 75 q^{96}+O(q^{100}) $ 48 * q + 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 + 5 * q^7 - 11 * q^9 - 12 * q^12 - 8 * q^14 - 27 * q^16 - 15 * q^17 - 20 * q^18 + 15 * q^19 + 10 * q^23 - 75 * q^24 + q^25 + 27 * q^26 + 40 * q^28 + 40 * q^29 - 25 * q^30 + 9 * q^31 - 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 + 45 * q^39 - 75 * q^40 + 64 * q^42 - 84 * q^45 + 20 * q^46 + 3 * q^47 + 59 * q^49 - 30 * q^50 - 55 * q^51 + 15 * q^52 - 3 * q^53 - 8 * q^56 - 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 + 30 * q^61 + 40 * q^63 + 12 * q^64 + 44 * q^67 + 75 * q^68 - 27 * q^70 + 20 * q^71 + 60 * q^72 + 60 * q^73 - 45 * q^74 - 57 * q^75 + 92 * q^78 + 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 + 125 * q^84 - 10 * q^85 - 62 * q^86 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 - 105 * q^94 - 30 * q^95 - 75 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−2.05902	−	0.216412i	−1.45595	−	0.153026i	−0.656757	−	0.754102i	$-0.728072\pi$
$2$	−2.05902	−	0.216412i	−1.45595	−	0.153026i	−0.799192	+	0.601076i	$0.794739\pi$
$3$	−2.33449	+	2.10199i	−1.34782	+	1.21358i	−0.391883	+	0.920015i	$0.628176\pi$
$3$	−2.33449	+	2.10199i	−1.34782	+	1.21358i	−0.955938	+	0.293568i	$0.905157\pi$
$4$	2.23645	+	0.475371i	1.11822	+	0.237686i
$5$	0.483200	−	1.08528i	0.216094	−	0.485354i	−0.772676	−	0.634800i	$-0.781082\pi$
$5$	0.483200	−	1.08528i	0.216094	−	0.485354i	0.988770	+	0.149446i	$0.0477491\pi$
$6$	5.26167	−	3.82283i	2.14807	−	1.56066i
$7$	−2.02173	+	1.70664i	−0.764142	+	0.645048i
$7$	−2.02173	+	1.70664i	−0.764142	+	0.645048i
$8$	−0.563952	−	0.183239i	−0.199387	−	0.0647848i
$9$	0.717924	−	6.83059i	0.239308	−	2.27686i
$10$	−1.22979	+	2.13006i	−0.388893	+	0.673583i
$11$		0			0
$11$		0			0
$12$	−6.22020	+	3.59123i	−1.79562	+	1.03670i
$13$	−0.000347326	0	0.000252347i	−9.63308e−5	0	6.99885e-5i	0.587737	−	0.809052i	$-0.300019\pi$
$13$	−0.000347326	0	0.000252347i	−9.63308e−5	0	6.99885e-5i	−0.587833	+	0.808982i	$0.700019\pi$
$14$	4.53213	−	3.07648i	1.21126	−	0.822223i
$15$	1.15323	+	3.54927i	0.297762	+	0.916418i
$16$	−3.05594	−	1.36059i	−0.763986	−	0.340149i
$17$	0.192581	+	1.83228i	0.0467077	+	0.444394i	0.992736	+	0.120311i	$0.0383892\pi$
$17$	0.192581	+	1.83228i	0.0467077	+	0.444394i	−0.946029	+	0.324083i	$0.894944\pi$
$18$	−2.95645	+	13.9090i	−0.696841	+	3.27838i
$19$	1.89260	−	0.402285i	0.434192	−	0.0922904i	0.0143700	−	0.999897i	$-0.495426\pi$
$19$	1.89260	−	0.402285i	0.434192	−	0.0922904i	0.419822	+	0.907606i	$0.362092\pi$
$20$	1.59656	−	2.19748i	0.357003	−	0.491372i
$21$	1.13239	−	8.23379i	0.247108	−	1.79676i
$22$		0			0
$23$	2.83507	+	4.91048i	0.591152	+	1.02391i	0.994078	+	0.108673i	$0.0346600\pi$
$23$	2.83507	+	4.91048i	0.591152	+	1.02391i	−0.402926	+	0.915233i	$0.632007\pi$
$24$	1.70171	−	0.757650i	0.347360	−	0.154655i
$25$	2.40129	+	2.66691i	0.480259	+	0.533381i
$26$	0.000660541	0	0.000594754i	0.000129543	0	0.000116641i
$27$	7.14248	+	9.83078i	1.37457	+	1.89194i
$28$	−5.33278	+	2.85573i	−1.00780	+	0.539682i
$29$	4.88867	−	1.58843i	0.907804	−	0.294963i	0.182350	−	0.983234i	$-0.441630\pi$
$29$	4.88867	−	1.58843i	0.907804	−	0.294963i	0.725454	+	0.688270i	$0.241630\pi$
$30$	−1.60642	−	7.55760i	−0.293291	−	1.37982i
$31$	0.176317	+	0.396015i	0.0316675	+	0.0711264i	0.928687	−	0.370865i	$-0.120939\pi$
$31$	0.176317	+	0.396015i	0.0316675	+	0.0711264i	−0.897019	+	0.441992i	$0.854272\pi$
$32$	7.02487	+	4.05581i	1.24183	+	0.716973i
$33$		0			0
$34$		−	3.81439i		−	0.654163i
$35$	0.875286	+	3.01880i	0.147950	+	0.510270i
$36$	4.85267	−	14.9350i	0.808778	−	2.48916i
$37$	0.251703	−	0.279544i	0.0413796	−	0.0459568i	−0.722100	−	0.691789i	$-0.756823\pi$
$37$	0.251703	−	0.279544i	0.0413796	−	0.0459568i	0.763479	+	0.645832i	$0.223489\pi$
$38$	−3.98397	+	0.418732i	−0.646285	+	0.0679273i
$39$	0.00134126		0.000140972i	0.000214774		2.25736e-5i
$40$	−0.471368	+	0.523507i	−0.0745298	+	0.0827737i
$41$	−0.760621	+	2.34095i	−0.118789	+	0.365595i	−0.992718	−	0.120458i	$-0.961564\pi$
$41$	−0.760621	+	2.34095i	−0.118789	+	0.365595i	0.873929	+	0.486053i	$0.161564\pi$
$42$	−4.11351	+	16.7085i	−0.634728	+	2.57818i
$43$			5.03264i			0.767471i	0.923443	+	0.383735i	$0.125363\pi$
$43$			5.03264i			0.767471i	−0.923443	+	0.383735i	$0.874637\pi$
$44$		0			0
$45$	−7.06624	−	4.07969i	−1.05337	−	0.608165i
$46$	−4.77478	−	10.7243i	−0.704003	−	1.58122i
$47$	−0.385768	−	1.81490i	−0.0562700	−	0.264730i	0.941015	−	0.338364i	$-0.109874\pi$
$47$	−0.385768	−	1.81490i	−0.0562700	−	0.264730i	−0.997285	+	0.0736344i	$0.976540\pi$
$48$	9.99404	−	3.24726i	1.44252	−	0.468702i
$49$	1.17479	−	6.90072i	0.167827	−	0.985816i
$50$	−4.36717	−	6.01089i	−0.617611	−	0.850068i
$51$	−4.30102	−	3.87266i	−0.602263	−	0.542280i
$52$	−0.000656817	0	0.000729469i	−9.10842e−5	0	0.000101159i
$53$	1.20901	−	0.538288i	0.166071	−	0.0739395i	−0.322018	−	0.946734i	$-0.604361\pi$
$53$	1.20901	−	0.538288i	0.166071	−	0.0739395i	0.488088	+	0.872794i	$0.337694\pi$
$54$	−12.5790	−	21.7875i	−1.71179	−	2.96491i
$55$		0			0
$56$	1.45288	−	0.592000i	0.194149	−	0.0791094i
$57$	−3.57267	+	4.91735i	−0.473211	+	0.651320i
$58$	−10.4096	+	2.21264i	−1.36685	+	0.290534i
$59$	−2.53655	+	11.9335i	−0.330230	+	1.55361i	0.429314	+	0.903155i	$0.358755\pi$
$59$	−2.53655	+	11.9335i	−0.330230	+	1.55361i	−0.759544	+	0.650456i	$0.774578\pi$
$60$	0.891911	+	8.48597i	0.115145	+	1.09553i
$61$	−6.95359	−	3.09594i	−0.890316	−	0.396394i	−0.0899784	−	0.995944i	$-0.528680\pi$
$61$	−6.95359	−	3.09594i	−0.890316	−	0.396394i	−0.800338	+	0.599549i	$0.795346\pi$
$62$	−0.277339	−	0.853562i	−0.0352221	−	0.108402i
$63$	10.2059	+	15.0349i	1.28582	+	1.89421i
$64$	−8.17409	−	5.93882i	−1.02176	−	0.742353i
$65$	−0.000441696	0	0.000255013i	−5.47856e−5	0	3.16305e-5i
$66$		0			0
$67$	6.72641	−	11.6505i	0.821762	−	1.42333i	−0.0826073	−	0.996582i	$-0.526325\pi$
$67$	6.72641	−	11.6505i	0.821762	−	1.42333i	0.904369	−	0.426751i	$-0.140342\pi$
$68$	−0.440319	+	4.18935i	−0.0533965	+	0.508034i
$69$	−16.9402	−	5.50421i	−2.03936	−	0.662629i
$70$	−1.14893	−	6.40520i	−0.137323	−	0.765568i
$71$	−6.82813	+	4.96093i	−0.810350	+	0.588754i	−0.913932	−	0.405867i	$-0.866970\pi$
$71$	−6.82813	+	4.96093i	−0.810350	+	0.588754i	0.103582	+	0.994621i	$0.466970\pi$
$72$	−1.65651	+	3.72057i	−0.195221	+	0.438474i
$73$	−13.3457	−	2.83671i	−1.56199	−	0.332012i	−0.655820	−	0.754918i	$-0.727677\pi$
$73$	−13.3457	−	2.83671i	−1.56199	−	0.332012i	−0.906174	+	0.422906i	$0.861010\pi$
$74$	−0.578758	+	0.521116i	−0.0672793	+	0.0605785i
$75$	−11.2116	−	1.17839i	−1.29461	−	0.136068i
$76$	4.42393			0.507460
$77$		0			0
$78$	−0.00279219			−0.000316154
$79$	−1.63180	−	0.171509i	−0.183592	−	0.0192963i	0.0122861	−	0.999925i	$-0.496089\pi$
$79$	−1.63180	−	0.171509i	−0.183592	−	0.0192963i	−0.195878	+	0.980628i	$0.562756\pi$
$80$	−2.95326	+	2.65913i	−0.330185	+	0.297300i
$81$	−17.1839	−	3.65255i	−1.90932	−	0.405839i
$82$	2.07275	−	4.65546i	0.228896	−	0.514110i
$83$	−7.86628	+	5.71519i	−0.863436	+	0.627323i	−0.928818	−	0.370537i	$-0.879174\pi$
$83$	−7.86628	+	5.71519i	−0.863436	+	0.627323i	0.0653813	+	0.997860i	$0.479174\pi$
$84$	6.44664	−	17.8761i	0.703386	−	1.95044i
$85$	2.08161	+	0.676354i	0.225782	+	0.0733609i
$86$	1.08912	−	10.3623i	0.117443	−	1.11740i
$87$	−8.07373	+	13.9841i	−0.865595	+	1.49925i
$88$		0			0
$89$	−6.24880	+	3.60774i	−0.662371	+	0.382420i	−0.793180	−	0.608988i	$-0.791576\pi$
$89$	−6.24880	+	3.60774i	−0.662371	+	0.382420i	0.130809	+	0.991408i	$0.458243\pi$
$90$	13.6667	+	9.92940i	1.44059	+	1.04665i
$91$	0.00113286		8.25811e-5i	0.000118756		8.65685e-6i
$92$	4.00617	+	12.3297i	0.417672	+	1.28546i
$93$	−1.24403	−	0.553878i	−0.129000	−	0.0574345i
$94$	0.401540	+	3.82040i	0.0414157	+	0.394044i
$95$	0.477911	−	2.24839i	0.0490326	−	0.230680i
$96$	−24.9248	+	5.29793i	−2.54388	+	0.540718i
$97$	−2.39869	+	3.30152i	−0.243551	+	0.335219i	−0.913239	−	0.407423i	$-0.866427\pi$
$97$	−2.39869	+	3.30152i	−0.243551	+	0.335219i	0.669689	+	0.742642i	$0.266427\pi$
$98$	−3.91231	+	13.9545i	−0.395203	+	1.40962i
$99$		0			0
$100$	4.10259	+	7.10590i	0.410259	+	0.710590i
$101$	13.3672	−	5.95145i	1.33008	−	0.592192i	0.386184	−	0.922422i	$-0.373793\pi$
$101$	13.3672	−	5.95145i	1.33008	−	0.592192i	0.943900	+	0.330230i	$0.107126\pi$
$102$	8.01781	+	8.90468i	0.793881	+	0.881695i
$103$	−9.06224	−	8.15968i	−0.892929	−	0.803997i	0.0884495	−	0.996081i	$-0.471809\pi$
$103$	−9.06224	−	8.15968i	−0.892929	−	0.803997i	−0.981379	+	0.192084i	$0.938475\pi$
$104$	0.000149635	0	0.000205955i	1.46729e−5	0	2.01956e-5i
$105$	−8.38883	−	5.20753i	−0.818666	−	0.508203i
$106$	−2.60588	+	0.846701i	−0.253105	+	0.0822389i
$107$	0.403800	+	1.89973i	0.0390369	+	0.183654i	0.993346	−	0.115167i	$-0.0367402\pi$
$107$	0.403800	+	1.89973i	0.0390369	+	0.183654i	−0.954309	+	0.298820i	$0.903407\pi$
$108$	11.3005	+	25.3814i	1.08739	+	2.44232i
$109$	−10.1746	−	5.87432i	−0.974552	−	0.562658i	−0.0739308	−	0.997263i	$-0.523554\pi$
$109$	−10.1746	−	5.87432i	−0.974552	−	0.562658i	−0.900621	+	0.434606i	$0.856888\pi$
$110$		0			0
$111$			1.18167i			0.112159i
$112$	8.50034	−	2.46463i	0.803206	−	0.232886i
$113$	−1.58699	+	4.88424i	−0.149291	+	0.459471i	−0.997538	−	0.0701305i	$-0.977658\pi$
$113$	−1.58699	+	4.88424i	−0.149291	+	0.459471i	0.848247	+	0.529601i	$0.177658\pi$
$114$	8.42038	−	9.35178i	0.788641	−	0.875874i
$115$	6.69917	−	0.704111i	0.624701	−	0.0656587i
$116$	11.6884	−	1.22850i	1.08524	−	0.114063i
$117$	−0.00197303	+	0.00219128i	−0.000182407	+	0.000202584i
$118$	7.80536	−	24.0224i	0.718542	−	2.21144i
$119$	−3.51639	−	3.37572i	−0.322347	−	0.309452i
$120$		−	2.21293i		−	0.202012i
$121$		0			0
$122$	13.6476	+	7.87945i	1.23560	+	0.713372i
$123$	−3.14498	−	7.06375i	−0.283574	−	0.636917i
$124$	0.206070	+	0.969483i	0.0185056	+	0.0870622i
$125$	9.70389	−	3.15299i	0.867943	−	0.282012i
$126$	−17.7604	−	33.1658i	−1.58223	−	2.95464i
$127$	0.721232	+	0.992691i	0.0639990	+	0.0880870i	0.839817	−	0.542870i	$-0.182662\pi$
$127$	0.721232	+	0.992691i	0.0639990	+	0.0880870i	−0.775818	+	0.630957i	$0.782662\pi$
$128$	3.48918	+	3.14167i	0.308403	+	0.277687i
$129$	−10.5786	−	11.7487i	−0.931390	−	1.03441i
$130$	0.000964650	0	0.000429490i	8.46054e−5	0	3.76688e-5i
$131$	6.38697	+	11.0626i	0.558032	+	0.966541i	0.997661	+	0.0683607i	$0.0217769\pi$
$131$	6.38697	+	11.0626i	0.558032	+	0.966541i	−0.439628	+	0.898180i	$0.644890\pi$
$132$		0			0
$133$	−3.13977	+	4.04329i	−0.272253	+	0.350598i
$134$	−16.3711	+	22.5329i	−1.41425	+	1.94655i
$135$	14.1204	−	3.00139i	1.21529	−	0.258319i
$136$	0.227140	−	1.06861i	0.0194771	−	0.0916324i
$137$	−0.118584	−	1.12826i	−0.0101313	−	0.0963933i	0.988288	−	0.152602i	$-0.0487654\pi$
$137$	−0.118584	−	1.12826i	−0.0101313	−	0.0963933i	−0.998419	+	0.0562090i	$0.982099\pi$
$138$	33.6891	+	14.9994i	2.86781	+	1.27683i
$139$	1.53841	+	4.73474i	0.130486	+	0.401595i	0.994861	−	0.101253i	$-0.0322853\pi$
$139$	1.53841	+	4.73474i	0.130486	+	0.401595i	−0.864374	+	0.502849i	$0.832285\pi$
$140$	0.522479	+	7.16747i	0.0441575	+	0.605762i
$141$	4.71546	+	3.42598i	0.397114	+	0.288520i
$142$	15.1329	−	8.73697i	1.26992	−	0.733191i
$143$		0			0
$144$	−11.4876	+	19.8971i	−0.957301	+	1.65809i
$145$	0.638312	−	6.07313i	0.0530089	−	0.504346i
$146$	26.8652	+	8.72902i	2.22338	+	0.722419i
$147$	11.7627	+	18.5791i	0.970170	+	1.53238i
$148$	0.695807	−	0.505533i	0.0571950	−	0.0415546i
$149$	−3.92884	+	8.82432i	−0.321863	+	0.722916i	−0.999927	−	0.0120868i	$-0.996153\pi$
$149$	−3.92884	+	8.82432i	−0.321863	+	0.722916i	0.678064	+	0.735003i	$0.262819\pi$
$150$	22.8299	+	4.85265i	1.86406	+	0.396218i
$151$	6.41153	−	5.77297i	0.521763	−	0.469798i	−0.365663	−	0.930747i	$-0.619158\pi$
$151$	6.41153	−	5.77297i	0.521763	−	0.469798i	0.887426	+	0.460950i	$0.152491\pi$
$152$	−1.14105	−	0.119929i	−0.0925513	−	0.00972754i
$153$	12.6539			1.02300
$154$		0			0
$155$	0.514986			0.0413646
$156$	0.00306667		0.000322320i	0.000245530		2.58063e-5i
$157$	−4.67879	+	4.21280i	−0.373408	+	0.336218i	−0.834373	−	0.551200i	$-0.814170\pi$
$157$	−4.67879	+	4.21280i	−0.373408	+	0.336218i	0.460965	+	0.887418i	$0.347503\pi$
$158$	3.32280	+	0.706284i	0.264348	+	0.0561889i
$159$	−1.69096	+	3.79796i	−0.134102	+	0.301198i
$160$	7.79613	−	5.66422i	0.616338	−	0.447796i
$161$	−14.1121	−	5.08924i	−1.11219	−	0.401088i
$162$	34.5916	+	11.2395i	2.71777	+	0.883057i
$163$	−1.15633	+	11.0017i	−0.0905707	+	0.861722i	0.851059	+	0.525071i	$0.175961\pi$
$163$	−1.15633	+	11.0017i	−0.0905707	+	0.861722i	−0.941629	+	0.336652i	$0.890706\pi$
$164$	−2.81391	+	4.87383i	−0.219729	+	0.380582i
$165$		0			0
$166$	17.4337	−	10.0653i	1.35312	−	0.781222i
$167$	5.65523	+	4.10876i	0.437614	+	0.317946i	0.784686	−	0.619893i	$-0.212824\pi$
$167$	5.65523	+	4.10876i	0.437614	+	0.317946i	−0.347072	+	0.937839i	$0.612824\pi$
$168$	−2.14736	+	4.43596i	−0.165673	+	0.342242i
$169$	−4.01722	−	12.3637i	−0.309017	−	0.951057i
$170$	−4.13970	−	1.84311i	−0.317501	−	0.141360i
$171$	−1.38910	−	13.2164i	−0.106227	−	1.01068i
$172$	−2.39237	+	11.2552i	−0.182417	+	0.858204i
$173$	−20.3844	+	4.33284i	−1.54980	+	0.329419i	−0.901776	−	0.432203i	$-0.857736\pi$
$173$	−20.3844	+	4.33284i	−1.54980	+	0.329419i	−0.648020	+	0.761623i	$0.724403\pi$
$174$	19.6503	−	27.0464i	1.48969	−	2.05038i
$175$	−9.40620	−	1.29363i	−0.711042	−	0.0977894i
$176$		0			0
$177$	−19.1625	−	33.1905i	−1.44035	−	2.49475i
$178$	13.6472	−	6.07611i	1.02290	−	0.455424i
$179$	−9.58592	−	10.6462i	−0.716485	−	0.795737i	0.269424	−	0.963022i	$-0.413167\pi$
$179$	−9.58592	−	10.6462i	−0.716485	−	0.795737i	−0.985909	+	0.167285i	$0.946500\pi$
$180$	−13.8639	−	12.4831i	−1.03335	−	0.930436i
$181$	7.72615	+	10.6341i	0.574280	+	0.790429i	0.993054	−	0.117662i	$-0.0375399\pi$
$181$	7.72615	+	10.6341i	0.574280	+	0.790429i	−0.418774	+	0.908091i	$0.637540\pi$
$182$	−0.00235046		7.51289e-5i	−0.000174228		5.56893e-6i
$183$	22.7407	−	7.38892i	1.68104	−	0.546204i
$184$	−0.699049	−	3.28877i	−0.0515346	−	0.242451i
$185$	−0.181762	−	0.408245i	−0.0133634	−	0.0300147i
$186$	2.44162	+	1.40967i	0.179028	+	0.103362i
$187$		0			0
$188$		−	4.24230i		−	0.309402i
$189$	−31.2177	−	7.68558i	−2.27076	−	0.559044i
$190$	−1.47061	+	4.52607i	−0.106689	+	0.328356i
$191$	0.188138	−	0.208948i	0.0136132	−	0.0151190i	−0.736300	−	0.676655i	$-0.763429\pi$
$191$	0.188138	−	0.208948i	0.0136132	−	0.0151190i	0.749913	+	0.661537i	$0.230095\pi$
$192$	31.5657	−	3.31769i	2.27806	−	0.239434i
$193$	11.8423	−	1.24468i	0.852430	−	0.0895940i	0.331772	−	0.943359i	$-0.392353\pi$
$193$	11.8423	−	1.24468i	0.852430	−	0.0895940i	0.520658	+	0.853765i	$0.325687\pi$
$194$	5.65346	−	6.27880i	0.405894	−	0.450791i
$195$	0.000495102	−	0.00152377i	3.54550e−5	−	0.000109119i
$196$	5.90775	−	14.8746i	0.421982	−	1.06247i
$197$			8.08377i			0.575944i	0.957639	+	0.287972i	$0.0929811\pi$
$197$			8.08377i			0.575944i	−0.957639	+	0.287972i	$0.907019\pi$
$198$		0			0
$199$	1.36908	+	0.790438i	0.0970514	+	0.0560327i	0.547740	−	0.836648i	$-0.315488\pi$
$199$	1.36908	+	0.790438i	0.0970514	+	0.0560327i	−0.450689	+	0.892681i	$0.648822\pi$
$200$	−0.865532	−	1.94402i	−0.0612024	−	0.137463i
$201$	8.78641	+	41.3368i	0.619746	+	2.91568i
$202$	−28.8113	+	9.36136i	−2.02716	+	0.658663i
$203$	−7.17272	+	11.5546i	−0.503426	+	0.810971i
$204$	−7.77805	−	10.7056i	−0.544573	−	0.749540i
$205$	2.17306	+	1.95664i	0.151773	+	0.136657i
$206$	16.8935	+	18.7621i	1.17703	+	1.30722i
$207$	35.5768	−	15.8398i	2.47276	−	1.10094i
$208$	0.000718067		0.00124373i	4.97890e−5		8.62370e-5i
$209$		0			0
$210$	16.1458	+	12.5379i	1.11417	+	0.865195i
$211$	−1.71163	+	2.35586i	−0.117834	+	0.162184i	−0.863859	−	0.503733i	$-0.831960\pi$
$211$	−1.71163	+	2.35586i	−0.117834	+	0.162184i	0.746026	+	0.665917i	$0.231960\pi$
$212$	2.95978	−	0.629121i	0.203279	−	0.0432082i
$213$	5.51242	−	25.9339i	0.377705	−	1.77696i
$214$	−0.420310	−	3.99898i	−0.0287318	−	0.273365i
$215$	5.46185	+	2.43177i	0.372495	+	0.165845i
$216$	−2.22663	−	6.85287i	−0.151503	−	0.466279i
$217$	−1.03232	−	0.499727i	−0.0700784	−	0.0339236i
$218$	19.6785	+	14.2973i	1.33280	+	0.968333i
$219$	37.1181	−	21.4302i	2.50821	−	1.44812i
$220$		0			0
$221$	0.000395483	0	0.000684997i	2.66031e−5	0	4.60779e-5i
$222$	0.255728	−	2.43309i	0.0171633	−	0.163298i
$223$	−21.1608	−	6.87555i	−1.41703	−	0.460421i	−0.502372	−	0.864652i	$-0.667539\pi$
$223$	−21.1608	−	6.87555i	−1.41703	−	0.460421i	−0.914657	+	0.404231i	$0.867539\pi$
$224$	−21.1242	+	3.78914i	−1.41142	+	0.253173i
$225$	19.9405	−	14.4876i	1.32937	−	0.965841i
$226$	4.32465	−	9.71332i	0.287671	−	0.646121i
$227$	2.36270	+	0.502208i	0.156818	+	0.0333327i	0.285652	−	0.958334i	$-0.407790\pi$
$227$	2.36270	+	0.502208i	0.156818	+	0.0333327i	−0.128834	+	0.991666i	$0.541123\pi$
$228$	−10.3277	+	9.29906i	−0.683965	+	0.615845i
$229$	−16.2514	−	1.70809i	−1.07392	−	0.112874i	−0.448977	−	0.893543i	$-0.648211\pi$
$229$	−16.2514	−	1.70809i	−1.07392	−	0.112874i	−0.624944	+	0.780670i	$0.714878\pi$
$230$	−13.9461			−0.919580
$231$		0			0
$232$	−3.04804			−0.200114
$233$	−15.9931	−	1.68095i	−1.04774	−	0.110122i	−0.435021	−	0.900420i	$-0.643259\pi$
$233$	−15.9931	−	1.68095i	−1.04774	−	0.110122i	−0.612723	+	0.790298i	$0.709926\pi$
$234$	0.00453674	−	0.00408490i	0.000296576	−	0.000267038i
$235$	−2.15608	−	0.458289i	−0.140647	−	0.0298955i
$236$	−11.3457	+	25.4829i	−0.738542	+	1.65879i
$237$	4.16995	−	3.02964i	0.270867	−	0.196796i
$238$	6.50978	+	7.71167i	0.421966	+	0.499874i
$239$	9.20478	+	2.99081i	0.595408	+	0.193460i	0.591191	−	0.806531i	$-0.298658\pi$
$239$	9.20478	+	2.99081i	0.595408	+	0.193460i	0.00421649	+	0.999991i	$0.498658\pi$
$240$	1.30492	−	12.4155i	0.0842320	−	0.801414i
$241$	5.21513	−	9.03287i	0.335936	−	0.581858i	−0.647728	−	0.761872i	$-0.724281\pi$
$241$	5.21513	−	9.03287i	0.335936	−	0.581858i	0.983664	+	0.180013i	$0.0576140\pi$
$242$		0			0
$243$	16.2227	−	9.36620i	1.04069	−	0.600842i
$244$	−14.0796	−	10.2294i	−0.901355	−	0.654873i
$245$	−6.92158	−	4.60940i	−0.442204	−	0.294484i
$246$	4.94691	+	15.2250i	0.315404	+	0.970713i
$247$	−0.000758864	0	0.000337868i	−4.82854e−5	0	2.14980e-5i
$248$	−0.0268690	−	0.255642i	−0.00170619	−	0.0162333i
$249$	6.35053	−	29.8769i	0.402449	−	1.89337i
$250$	−20.6629	+	4.39203i	−1.30684	+	0.277776i
$251$	−13.9846	+	19.2482i	−0.882701	+	1.21493i	0.0929641	+	0.995669i	$0.470366\pi$
$251$	−13.9846	+	19.2482i	−0.882701	+	1.21493i	−0.975665	+	0.219265i	$0.929634\pi$
$252$	15.6778	+	38.4762i	0.987608	+	2.42378i
$253$		0			0
$254$	−1.27020	−	2.20006i	−0.0796996	−	0.138044i
$255$	−6.28118	+	2.79656i	−0.393343	+	0.175128i
$256$	7.01703	+	7.79320i	0.438564	+	0.487075i
$257$	5.38538	+	4.84902i	0.335931	+	0.302473i	0.819781	−	0.572678i	$-0.194095\pi$
$257$	5.38538	+	4.84902i	0.335931	+	0.302473i	−0.483850	+	0.875151i	$0.660762\pi$
$258$	19.2389	+	26.4801i	1.19776	+	1.64858i
$259$	−0.0317949	+	0.994727i	−0.00197564	+	0.0618093i
$260$	−0.00110906		0.000360354i	−6.87807e−5		2.23482e-5i
$261$	−7.34020	−	34.5329i	−0.454347	−	2.13753i
$262$	−10.7569	−	24.1603i	−0.664561	−	1.49263i
$263$	−13.2235	−	7.63460i	−0.815397	−	0.470770i	0.0334298	−	0.999441i	$-0.489357\pi$
$263$	−13.2235	−	7.63460i	−0.815397	−	0.470770i	−0.848826	+	0.528672i	$0.822690\pi$
$264$		0			0
$265$		−	1.57222i		−	0.0965810i
$266$	7.33988	−	7.64574i	0.450037	−	0.468791i
$267$	7.00434	−	21.5572i	0.428659	−	1.31928i
$268$	20.5816	−	22.8581i	1.25722	−	1.39628i
$269$	−12.2435	+	1.28684i	−0.746498	+	0.0784601i	−0.470137	−	0.882594i	$-0.655795\pi$
$269$	−12.2435	+	1.28684i	−0.746498	+	0.0784601i	−0.276362	+	0.961054i	$0.589129\pi$
$270$	−29.7239	+	3.12410i	−1.80894	+	0.190127i
$271$	−19.0319	+	21.1371i	−1.15611	+	1.28399i	−0.203740	+	0.979025i	$0.565310\pi$
$271$	−19.0319	+	21.1371i	−1.15611	+	1.28399i	−0.952365	+	0.304960i	$0.901357\pi$
$272$	1.90448	−	5.86139i	0.115476	−	0.355399i
$273$	−0.00247108	+	0.00257405i	−0.000149557	+	0.000155789i
$274$			2.34877i			0.141894i
$275$		0			0
$276$	−35.2693	−	20.3628i	−2.12296	−	1.22569i
$277$	1.27270	+	2.85852i	0.0764690	+	0.171752i	0.947735	−	0.319060i	$-0.103367\pi$
$277$	1.27270	+	2.85852i	0.0764690	+	0.171752i	−0.871266	+	0.490812i	$0.836700\pi$
$278$	−2.14297	−	10.0819i	−0.128527	−	0.604670i
$279$	2.83160	−	0.920043i	0.169524	−	0.0550815i
$280$	0.0595429	−	1.86284i	0.00355837	−	0.111326i
$281$	−0.637471	−	0.877404i	−0.0380283	−	0.0523415i	0.789579	−	0.613648i	$-0.210299\pi$
$281$	−0.637471	−	0.877404i	−0.0380283	−	0.0523415i	−0.827608	+	0.561307i	$0.810299\pi$
$282$	−8.96782	−	8.07466i	−0.534026	−	0.480839i
$283$	6.75841	+	7.50598i	0.401746	+	0.446184i	0.909741	−	0.415176i	$-0.136280\pi$
$283$	6.75841	+	7.50598i	0.401746	+	0.446184i	−0.507995	+	0.861360i	$0.669613\pi$
$284$	−17.6290	+	7.84895i	−1.04609	+	0.465750i
$285$	3.61042	+	6.25343i	0.213863	+	0.370421i
$286$		0			0
$287$	−2.45738	−	6.03087i	−0.145054	−	0.355991i
$288$	32.7469	−	45.0723i	1.92963	−	2.65591i
$289$	13.3083	−	2.82877i	0.782843	−	0.166398i
$290$	−2.62860	+	12.3666i	−0.154357	+	0.726190i
$291$	−1.34002	−	12.7494i	−0.0785532	−	0.747383i
$292$	−28.4984	−	12.6883i	−1.66774	−	0.742527i
$293$	7.22252	+	22.2286i	0.421944	+	1.29861i	0.905890	+	0.423513i	$0.139203\pi$
$293$	7.22252	+	22.2286i	0.421944	+	1.29861i	−0.483946	+	0.875098i	$0.660797\pi$
$294$	−20.1989	−	40.8003i	−1.17802	−	2.37952i
$295$	11.7256	+	8.51914i	0.682691	+	0.496004i
$296$	−0.193172	+	0.111528i	−0.0112279	+	0.00648241i
$297$		0			0
$298$	9.99926	−	17.3192i	0.579241	−	1.00328i
$299$	0.000254453	−	0.00242096i	1.47154e−5	−	0.000140007i
$300$	−24.5140	−	7.96508i	−1.41532	−	0.459864i
$301$	−8.58889	−	10.1746i	−0.495055	−	0.586457i
$302$	−14.4508	+	10.4991i	−0.831552	+	0.604158i
$303$	−18.6957	+	41.9913i	−1.07404	+	2.41234i
$304$	−6.33103	−	1.34570i	−0.363109	−	0.0771813i
$305$	−6.71995	+	6.05067i	−0.384783	+	0.346460i
$306$	−26.0546	−	2.73845i	−1.48944	−	0.156547i
$307$	−31.5257			−1.79927			−0.899633	−	0.436646i	$-0.856166\pi$
$307$	−31.5257			−1.79927			−0.899633	+	0.436646i	$0.856166\pi$
$308$		0			0
$309$	38.3073			2.17923
$310$	−1.06037	−	0.111449i	−0.0602248	−	0.00632988i
$311$	13.0575	−	11.7570i	0.740421	−	0.666678i	−0.209980	−	0.977706i	$-0.567340\pi$
$311$	13.0575	−	11.7570i	0.740421	−	0.666678i	0.950401	+	0.311027i	$0.100673\pi$
$312$	−0.000782238	0	0.000166270i	−4.42855e−5	0	9.41317e-6i
$313$	−8.43226	+	18.9392i	−0.476620	+	1.07051i	0.502008	+	0.864863i	$0.332595\pi$
$313$	−8.43226	+	18.9392i	−0.476620	+	1.07051i	−0.978627	+	0.205642i	$0.934072\pi$
$314$	10.5454	−	7.66170i	0.595113	−	0.432375i
$315$	21.2486	−	3.81145i	1.19722	−	0.214751i
$316$	−3.56791	−	1.15928i	−0.200711	−	0.0652148i
$317$	−3.28492	+	31.2539i	−0.184499	+	1.75539i	0.375428	+	0.926852i	$0.377496\pi$
$317$	−3.28492	+	31.2539i	−0.184499	+	1.75539i	−0.559927	+	0.828542i	$0.689171\pi$
$318$	4.30365	−	7.45415i	0.241337	−	0.418008i
$319$		0			0
$320$	−10.3950	+	6.00157i	−0.581100	+	0.335498i
$321$	−4.93588	−	3.58613i	−0.275494	−	0.200158i
$322$	27.9558	+	13.5329i	1.55792	+	0.754159i
$323$	1.10158	+	3.39031i	0.0612935	+	0.188642i
$324$	−36.6945	−	16.3375i	−2.03858	−	0.907636i
$325$	−0.000161045	−	0.00153224i	−8.93319e−6	−	8.49936e-5i
$326$	4.76182	−	22.4026i	0.263733	−	1.24076i
$327$	36.1003	−	7.67336i	1.99635	−	0.424338i
$328$	0.857907	−	1.18081i	0.0473700	−	0.0651992i
$329$	3.87728	+	3.01086i	0.213762	+	0.165994i
$330$		0			0
$331$	11.9178	+	20.6422i	0.655062	+	1.13460i	0.981878	+	0.189513i	$0.0606908\pi$
$331$	11.9178	+	20.6422i	0.655062	+	1.13460i	−0.326816	+	0.945088i	$0.605976\pi$
$332$	−20.3094	+	9.04231i	−1.11462	+	0.496261i
$333$	−1.72875	−	1.91997i	−0.0947348	−	0.105214i
$334$	−10.7551	−	9.68389i	−0.588490	−	0.529879i
$335$	−9.39389	−	12.9296i	−0.513243	−	0.706418i
$336$	−14.6634	+	23.6213i	−0.799952	+	1.28865i
$337$	13.5619	−	4.40653i	0.738765	−	0.240039i	0.0846249	−	0.996413i	$-0.473031\pi$
$337$	13.5619	−	4.40653i	0.738765	−	0.240039i	0.654140	+	0.756374i	$0.273031\pi$
$338$	5.59589	+	26.3266i	0.304376	+	1.43198i
$339$	−6.56181	−	14.7381i	−0.356388	−	0.800461i
$340$	4.33388	+	2.50217i	0.235038	+	0.135699i
$341$		0			0
$342$			27.5135i			1.48776i
$343$	9.40190	+	15.9563i	0.507655	+	0.861560i
$344$	0.922177	−	2.83817i	0.0497204	−	0.153024i
$345$	−14.1591	+	15.7253i	−0.762302	+	0.846623i
$346$	42.9096	−	4.50998i	2.30683	−	0.242458i
$347$	16.0640	−	1.68839i	0.862360	−	0.0906377i	0.336987	−	0.941509i	$-0.390592\pi$
$347$	16.0640	−	1.68839i	0.862360	−	0.0906377i	0.525374	+	0.850872i	$0.323926\pi$
$348$	−24.7041	+	27.4367i	−1.32428	+	1.47076i
$349$	−4.01326	+	12.3515i	−0.214825	+	0.661163i	0.784341	+	0.620330i	$0.213001\pi$
$349$	−4.01326	+	12.3515i	−0.214825	+	0.661163i	−0.999166	+	0.0408333i	$0.986999\pi$
$350$	19.0876	+	4.69923i	1.02028	+	0.251185i
$351$		−	0.00521687i		−	0.000278456i
$352$		0			0
$353$	26.5104	+	15.3058i	1.41100	+	0.814644i	0.995483	−	0.0949399i	$-0.0302659\pi$
$353$	26.5104	+	15.3058i	1.41100	+	0.814644i	0.415521	+	0.909584i	$0.363599\pi$
$354$	32.2733	+	72.4870i	1.71531	+	3.85264i
$355$	2.08467	+	9.80758i	0.110643	+	0.520532i
$356$	−15.6901	+	5.09803i	−0.831575	+	0.270195i
$357$	15.3047	+	0.489191i	0.810011	+	0.0258908i
$358$	17.4336	+	23.9954i	0.921397	+	1.26819i
$359$	−13.9345	−	12.5467i	−0.735436	−	0.662190i	0.213756	−	0.976887i	$-0.431430\pi$
$359$	−13.9345	−	12.5467i	−0.735436	−	0.662190i	−0.949192	+	0.314697i	$0.898097\pi$
$360$	3.23746	+	3.59556i	0.170629	+	0.189503i
$361$	−13.9373	+	6.20527i	−0.733540	+	0.326593i
$362$	−13.6070	−	23.5680i	−0.715166	−	1.23870i
$363$		0			0
$364$	0.00257285		0.000353843i	0.000134854		1.85464e-5i
$365$	−9.52727	+	13.1132i	−0.498680	+	0.686374i
$366$	−48.4228	+	10.2926i	−2.53110	+	0.538002i
$367$	−4.60215	+	21.6514i	−0.240230	+	1.13019i	0.678282	+	0.734801i	$0.262725\pi$
$367$	−4.60215	+	21.6514i	−0.240230	+	1.13019i	−0.918512	+	0.395392i	$0.870609\pi$
$368$	−1.98264	−	18.8635i	−0.103352	−	0.983329i
$369$	15.4440	+	6.87612i	0.803983	+	0.357956i
$370$	0.285903	+	0.879920i	0.0148634	+	0.0457449i
$371$	−1.52564	+	3.15162i	−0.0792072	+	0.163624i
$372$	−2.51891	−	1.83010i	−0.130599	−	0.0948861i
$373$	−17.2376	+	9.95215i	−0.892531	+	0.515303i	−0.874769	−	0.484540i	$-0.838987\pi$
$373$	−17.2376	+	9.95215i	−0.892531	+	0.515303i	−0.0177612	+	0.999842i	$0.505654\pi$
$374$		0			0
$375$	−16.0261	+	27.7581i	−0.827587	+	1.43342i
$376$	−0.115005	+	1.09420i	−0.00593094	+	0.0564291i
$377$	−0.00209880		0.000681941i	−0.000108094		3.51217e-5i
$378$	62.6148	+	22.5807i	3.22056	+	1.16142i
$379$	−11.5817	+	8.41461i	−0.594913	+	0.432229i	−0.844070	−	0.536234i	$-0.819847\pi$
$379$	−11.5817	+	8.41461i	−0.594913	+	0.432229i	0.249157	+	0.968463i	$0.419847\pi$
$380$	2.13764	−	4.80123i	0.109659	−	0.246298i
$381$	−3.77034	−	0.801410i	−0.193160	−	0.0410575i
$382$	−0.432599	+	0.389514i	−0.0221337	+	0.0199293i
$383$	15.9956	+	1.68121i	0.817339	+	0.0859058i	0.503965	−	0.863724i	$-0.331874\pi$
$383$	15.9956	+	1.68121i	0.817339	+	0.0859058i	0.313374	+	0.949630i	$0.398541\pi$
$384$	−14.7492			−0.752668
$385$		0			0
$386$	−24.6530			−1.25481
$387$	34.3759	+	3.61306i	1.74743	+	0.183662i
$388$	−6.93400	+	6.24340i	−0.352021	+	0.316961i
$389$	33.2245	+	7.06209i	1.68455	+	0.358062i	0.947988	−	0.318307i	$-0.103114\pi$
$389$	33.2245	+	7.06209i	1.68455	+	0.358062i	0.736563	+	0.676369i	$0.236447\pi$
$390$	−0.00134919	+	0.00303033i	−6.83188e−5	+	0.000153446i
$391$	−8.45141	+	6.14031i	−0.427406	+	0.310529i
$392$	−1.92700	+	3.67640i	−0.0973284	+	0.185686i
$393$	−38.1637	−	12.4001i	−1.92511	−	0.625505i
$394$	1.74942	−	16.6447i	0.0881347	−	0.838546i
$395$	−0.974623	+	1.68810i	−0.0490386	+	0.0849374i
$396$		0			0
$397$	−19.3209	+	11.1549i	−0.969687	+	0.559849i	−0.899141	−	0.437659i	$-0.855808\pi$
$397$	−19.3209	+	11.1549i	−0.969687	+	0.559849i	−0.0705464	+	0.997508i	$0.522474\pi$
$398$	−2.64790	−	1.92381i	−0.132727	−	0.0964321i
$399$	−1.16916	−	16.0388i	−0.0585314	−	0.802945i
$400$	−3.70964	−	11.4171i	−0.185482	−	0.570855i
$401$	−6.47528	−	2.88298i	−0.323360	−	0.143969i	0.238636	−	0.971109i	$-0.423300\pi$
$401$	−6.47528	−	2.88298i	−0.323360	−	0.143969i	−0.561996	+	0.827140i	$0.689966\pi$
$402$	−9.14564	−	87.0150i	−0.456143	−	4.33991i
$403$	3.86937e−5	0	0.000182039i	1.92747e−6	0	9.06803e-6i
$404$	32.7241	−	6.95573i	1.62809	−	0.346061i
$405$	−12.2673	+	16.8845i	−0.609567	+	0.838997i
$406$	17.2693	−	22.2388i	0.857063	−	1.10370i
$407$		0			0
$408$	1.71595	+	2.97211i	0.0849520	+	0.147141i
$409$	14.9226	−	6.64399i	0.737877	−	0.328524i	−0.00315356	−	0.999995i	$-0.501004\pi$
$409$	14.9226	−	6.64399i	0.737877	−	0.328524i	0.741031	+	0.671471i	$0.234337\pi$
$410$	−4.05095	−	4.49904i	−0.200062	−	0.222192i
$411$	2.64841	+	2.38464i	0.130637	+	0.117626i
$412$	−16.3883	−	22.5566i	−0.807396	−	1.11128i
$413$	−15.2379	−	28.4553i	−0.749810	−	1.40019i
$414$	−76.6815	+	24.9153i	−3.76869	+	1.22452i
$415$	2.40162	+	11.2987i	0.117891	+	0.554633i
$416$	−0.00141645	−	0.00318139i	−6.94471e−5	−	0.000155981i
$417$	−13.5438	−	7.81950i	−0.663241	−	0.382923i
$418$		0			0
$419$		−	33.3519i		−	1.62935i	−0.579921	−	0.814673i	$-0.696917\pi$
$419$		−	33.3519i		−	1.62935i	0.579921	−	0.814673i	$-0.303083\pi$
$420$	−16.2857	−	15.6342i	−0.794659	−	0.762870i
$421$	1.80630	−	5.55923i	0.0880338	−	0.270940i	−0.897342	−	0.441336i	$-0.854505\pi$
$421$	1.80630	−	5.55923i	0.0880338	−	0.270940i	0.985376	+	0.170396i	$0.0545047\pi$
$422$	4.03412	−	4.48035i	0.196378	−	0.218100i
$423$	−12.6738	+	1.33207i	−0.616220	+	0.0647673i
$424$	−0.780461	+	0.0820297i	−0.0379025	+	0.00398372i
$425$	−4.42409	+	4.91345i	−0.214600	+	0.238337i
$426$	−16.9626	+	52.2056i	−0.821841	+	2.52937i
$427$	19.3419	−	5.60809i	0.936021	−	0.271395i
$428$			4.44060i			0.214645i
$429$		0			0
$430$	−10.7198	−	6.18908i	−0.516955	−	0.298464i
$431$	−7.99498	−	17.9570i	−0.385105	−	0.864960i	−0.997243	−	0.0742086i	$-0.976357\pi$
$431$	−7.99498	−	17.9570i	−0.385105	−	0.864960i	0.612138	−	0.790751i	$-0.290310\pi$
$432$	−8.45133	−	39.7604i	−0.406615	−	1.91297i
$433$	−0.490372	+	0.159332i	−0.0235658	+	0.00765699i	−0.320776	−	0.947155i	$-0.603944\pi$
$433$	−0.490372	+	0.159332i	−0.0235658	+	0.00765699i	0.297210	+	0.954812i	$0.403944\pi$
$434$	2.01742	+	1.25235i	0.0968394	+	0.0601150i
$435$	11.2755	+	15.5194i	0.540620	+	0.744099i
$436$	−19.9625	−	17.9743i	−0.956031	−	0.860814i
$437$	7.34106	+	8.15307i	0.351170	+	0.390014i
$438$	−81.0649	+	36.0924i	−3.87343	+	1.72456i
$439$	−11.7590	−	20.3672i	−0.561227	−	0.972073i	−0.997390	−	0.0722055i	$-0.976996\pi$
$439$	−11.7590	−	20.3672i	−0.561227	−	0.972073i	0.436163	−	0.899868i	$-0.356337\pi$
$440$		0			0
$441$	−46.2926	−	12.9787i	−2.20441	−	0.618033i
$442$	−0.000962550		0.00132484i	−4.57839e−5		6.30161e-5i
$443$	17.4650	−	3.71230i	0.829787	−	0.176377i	0.226611	−	0.973985i	$-0.427235\pi$
$443$	17.4650	−	3.71230i	0.829787	−	0.176377i	0.603175	+	0.797609i	$0.293902\pi$
$444$	−0.561732	+	2.64274i	−0.0266586	+	0.125419i
$445$	0.896012	+	8.52498i	0.0424750	+	0.404123i
$446$	42.0825	+	18.7364i	1.99267	+	0.887192i
$447$	−9.37676	−	28.8587i	−0.443505	−	1.36497i
$448$	26.6612	−	1.94349i	1.25962	−	0.0918214i
$449$	−5.77400	−	4.19506i	−0.272492	−	0.197977i	0.443144	−	0.896450i	$-0.353863\pi$
$449$	−5.77400	−	4.19506i	−0.272492	−	0.197977i	−0.715636	+	0.698473i	$0.753863\pi$
$450$	−44.1932	+	25.5150i	−2.08329	+	1.20279i
$451$		0			0
$452$	−5.87104	+	10.1689i	−0.276150	+	0.478307i
$453$	−2.83297	+	26.9539i	−0.133105	+	1.26641i
$454$	−4.75618	−	1.54538i	−0.223218	−	0.0725280i
$455$	0.000457775	−	0.00126938i	2.14608e−5	−	5.95096e-5i
$456$	2.91586	−	2.11850i	0.136548	−	0.0992078i
$457$	9.88287	−	22.1973i	0.462301	−	1.03835i	−0.520531	−	0.853843i	$-0.674266\pi$
$457$	9.88287	−	22.1973i	0.462301	−	1.03835i	0.982832	−	0.184503i	$-0.0590674\pi$
$458$	33.0923	+	7.03398i	1.54630	+	0.328676i
$459$	−16.6373	+	14.9803i	−0.776562	+	0.699220i
$460$	15.3170	+	1.60989i	0.714161	+	0.0750614i
$461$	20.4135			0.950750			0.475375	−	0.879783i	$-0.342312\pi$
$461$	20.4135			0.950750			0.475375	+	0.879783i	$0.342312\pi$
$462$		0			0
$463$	−35.5035			−1.64999			−0.824994	−	0.565142i	$-0.808822\pi$
$463$	−35.5035			−1.64999			−0.824994	+	0.565142i	$0.808822\pi$
$464$	−17.1007	−	1.79736i	−0.793881	−	0.0834403i
$465$	−1.20223	+	1.08249i	−0.0557521	+	0.0501995i
$466$	32.5664	+	6.92221i	1.50861	+	0.320665i
$467$	9.08858	−	20.4133i	0.420569	−	0.944614i	−0.571694	−	0.820467i	$-0.693714\pi$
$467$	9.08858	−	20.4133i	0.420569	−	0.944614i	0.992264	−	0.124148i	$-0.0396196\pi$
$468$	−0.00545425	+	0.00396275i	−0.000252123	+	0.000183178i
$469$	6.28415	+	35.0337i	0.290175	+	1.61770i
$470$	4.34024	+	1.41023i	0.200200	+	0.0650491i
$471$	2.06735	−	19.6695i	0.0952584	−	0.906323i
$472$	3.61718	−	6.26513i	0.166494	−	0.288376i
$473$		0			0
$474$	−9.24167	+	5.33568i	−0.424484	+	0.245076i
$475$	5.61754	+	4.08138i	0.257750	+	0.187267i
$476$	−6.25950	−	9.22121i	−0.286904	−	0.422653i
$477$	−2.80884	−	8.64473i	−0.128608	−	0.395815i
$478$	−18.3056	−	8.15018i	−0.837279	−	0.372781i
$479$	4.03070	+	38.3496i	0.184167	+	1.75224i	0.562712	+	0.826653i	$0.309758\pi$
$479$	4.03070	+	38.3496i	0.184167	+	1.75224i	−0.378545	+	0.925583i	$0.623575\pi$
$480$	−6.29390	+	29.6105i	−0.287276	+	1.35153i
$481$	−0.000157965	0	3.35765e-5i	−7.20258e−6	0	1.53096e-6i
$482$	−12.6929	+	17.4703i	−0.578146	+	0.795749i
$483$	43.6422	−	17.7827i	1.98579	−	0.809143i
$484$		0			0
$485$	2.42404	+	4.19856i	0.110070	+	0.190647i
$486$	−35.4299	+	15.7744i	−1.60713	+	0.715542i
$487$	−26.5052	−	29.4370i	−1.20107	−	1.33392i	−0.928297	−	0.371840i	$-0.878727\pi$
$487$	−26.5052	−	29.4370i	−1.20107	−	1.33392i	−0.272770	−	0.962079i	$-0.587940\pi$
$488$	3.35419	+	3.02013i	0.151837	+	0.136715i
$489$	−20.4261	−	28.1141i	−0.923699	−	1.27136i
$490$	13.2542	+	10.9888i	0.598762	+	0.496423i
$491$	−5.67873	+	1.84513i	−0.256277	+	0.0832696i	−0.434338	−	0.900750i	$-0.643018\pi$
$491$	−5.67873	+	1.84513i	−0.256277	+	0.0832696i	0.178061	+	0.984020i	$0.443018\pi$
$492$	−3.67569	−	17.2927i	−0.165713	−	0.779617i
$493$	3.85192	+	8.65154i	0.173482	+	0.389646i
$494$	0.00148940		0.000859906i	6.70113e−5		3.86890e-5i
$495$		0			0
$496$		−	1.45010i		−	0.0651113i
$497$	5.33814	−	21.6828i	0.239448	−	0.972606i
$498$	−19.5416	+	60.1429i	−0.875681	+	2.69507i
$499$	7.58023	−	8.41870i	0.339338	−	0.376873i	−0.549188	−	0.835699i	$-0.685063\pi$
$499$	7.58023	−	8.41870i	0.339338	−	0.376873i	0.888526	+	0.458826i	$0.151730\pi$
$500$	23.2011	−	2.43853i	1.03758	−	0.109054i
$501$	−21.8387	+	2.29534i	−0.975680	+	0.102548i
$502$	32.9602	−	36.6060i	1.47109	−	1.63381i
$503$	8.56066	−	26.3470i	0.381701	−	1.17475i	−0.557145	−	0.830416i	$-0.688103\pi$
$503$	8.56066	−	26.3470i	0.381701	−	1.17475i	0.938845	−	0.344339i	$-0.111897\pi$
$504$	−3.00066	−	10.3491i	−0.133660	−	0.460983i
$505$		−	17.3829i		−	0.773530i
$506$		0			0
$507$	35.3666	+	20.4189i	1.57069	+	0.906836i
$508$	1.14110	+	2.56295i	0.0506281	+	0.113713i
$509$	−2.78467	−	13.1008i	−0.123428	−	0.580684i	−0.995777	−	0.0918009i	$-0.970738\pi$
$509$	−2.78467	−	13.1008i	−0.123428	−	0.580684i	0.872349	−	0.488883i	$-0.162596\pi$
$510$	13.5383	−	4.39887i	0.599487	−	0.194785i
$511$	31.8226	−	17.0411i	1.40775	−	0.753856i
$512$	−18.2812	−	25.1619i	−0.807921	−	1.11201i
$513$	17.4726	+	15.7324i	0.771436	+	0.694604i
$514$	−10.0392	−	11.1497i	−0.442812	−	0.491792i
$515$	−13.2344	+	5.89235i	−0.583179	+	0.259648i
$516$	−18.0734	−	31.3040i	−0.795637	−	1.37808i
$517$		0			0
$518$	0.280737	−	2.04129i	0.0123349	−	0.0896889i
$519$	38.4797	−	52.9627i	1.68907	−	2.32481i
$520$	0.000295824	0	6.28793e-5i	1.29727e−5	0	2.75744e-6i
$521$	3.48457	−	16.3936i	0.152662	−	0.718217i	−0.833512	−	0.552501i	$-0.813673\pi$
$521$	3.48457	−	16.3936i	0.152662	−	0.718217i	0.986174	−	0.165715i	$-0.0529933\pi$
$522$	7.64030	+	72.6926i	0.334407	+	3.18167i
$523$	−39.1905	−	17.4487i	−1.71368	−	0.762980i	−0.997908	−	0.0646477i	$-0.979408\pi$
$523$	−39.1905	−	17.4487i	−1.71368	−	0.762980i	−0.715774	−	0.698333i	$-0.753926\pi$
$524$	9.02530	+	27.7770i	0.394272	+	1.21344i
$525$	24.6779	−	16.7518i	1.07703	−	0.731106i
$526$	25.5753	+	18.5815i	1.11514	+	0.810194i
$527$	−0.691657	+	0.399328i	−0.0301291	+	0.0173950i
$528$		0			0
$529$	−4.57519	+	7.92447i	−0.198921	+	0.344542i
$530$	−0.340248	+	3.23725i	−0.0147794	+	0.140617i
$531$	79.6919	+	25.8935i	3.45834	+	1.12368i
$532$	−8.94400	+	7.55004i	−0.387772	+	0.327336i
$533$	0.000854915	0	0.000621132i	3.70305e−5	0	2.69042e-5i
$534$	−19.0873	+	42.8709i	−0.825990	+	1.85520i
$535$	2.25687	+	0.479712i	0.0975728	+	0.0207397i
$536$	−5.92820	+	5.33777i	−0.256059	+	0.230557i
$537$	44.7565	+	4.70410i	1.93139	+	0.202997i
$538$	25.4881			1.09887
$539$		0			0
$540$	33.0064			1.42037
$541$	37.5817	+	3.94999i	1.61576	+	0.169823i	0.868842	−	0.495090i	$-0.164865\pi$
$541$	37.5817	+	3.94999i	1.61576	+	0.169823i	0.746920	+	0.664913i	$0.231532\pi$
$542$	43.7614	−	39.4030i	1.87971	−	1.69250i
$543$	−40.3895	−	8.58505i	−1.73328	−	0.368420i
$544$	−6.07855	+	13.6526i	−0.260616	+	0.585352i
$545$	−11.2917	+	8.20389i	−0.483682	+	0.351416i
$546$	0.00564506	−	0.00476526i	0.000241586	−	0.000203934i
$547$	−33.2931	−	10.8176i	−1.42351	−	0.462527i	−0.506795	−	0.862067i	$-0.669170\pi$
$547$	−33.2931	−	10.8176i	−1.42351	−	0.462527i	−0.916716	+	0.399540i	$0.869170\pi$
$548$	0.271133	−	2.57965i	0.0115822	−	0.110197i
$549$	−26.1393	+	45.2745i	−1.11560	+	1.93227i
$550$		0			0
$551$	8.61331	−	4.97290i	0.366939	−	0.211852i
$552$	8.54488	+	6.20822i	0.363694	+	0.264239i
$553$	3.59177	−	2.43815i	0.152738	−	0.103681i
$554$	−2.00189	−	6.16120i	−0.0850523	−	0.261764i
$555$	1.28245	+	0.570983i	0.0544369	+	0.0242369i
$556$	1.18981	+	11.3203i	0.0504593	+	0.480088i
$557$	−3.55324	+	16.7167i	−0.150555	+	0.708308i	0.836505	+	0.547959i	$0.184595\pi$
$557$	−3.55324	+	16.7167i	−0.150555	+	0.708308i	−0.987060	+	0.160348i	$0.948738\pi$
$558$	−6.02944	+	1.28160i	−0.255247	+	0.0542544i
$559$	0.00126997	−	0.00174797i	5.37141e−5	−	7.39311e-5i
$560$	1.43254	−	10.4162i	0.0605357	−	0.440164i
$561$		0			0
$562$	1.12269	+	1.94455i	0.0473577	+	0.0820259i
$563$	−11.3614	+	5.05843i	−0.478827	+	0.213188i	−0.631934	−	0.775022i	$-0.717739\pi$
$563$	−11.3614	+	5.05843i	−0.478827	+	0.213188i	0.153107	+	0.988210i	$0.451072\pi$
$564$	8.91727	+	9.90363i	0.375485	+	0.417018i
$565$	4.53396	+	4.08240i	0.190745	+	0.171748i
$566$	−12.2913	−	16.9176i	−0.516644	−	0.711099i
$567$	40.9748	−	21.9422i	1.72078	−	0.921484i
$568$	4.75977	−	1.54654i	0.199716	−	0.0648915i
$569$	−5.30820	−	24.9731i	−0.222531	−	1.04693i	−0.937558	−	0.347830i	$-0.886919\pi$
$569$	−5.30820	−	24.9731i	−0.222531	−	1.04693i	0.715026	−	0.699098i	$-0.246415\pi$
$570$	−6.08062	−	13.6573i	−0.254689	−	0.572041i
$571$	18.4338	+	10.6428i	0.771431	+	0.445386i	0.833385	−	0.552693i	$-0.186400\pi$
$571$	18.4338	+	10.6428i	0.771431	+	0.445386i	−0.0619540	+	0.998079i	$0.519733\pi$
$572$		0			0
$573$			0.883252i			0.0368984i
$574$	3.75465	+	12.9495i	0.156716	+	0.540502i
$575$	−6.28796	+	19.3523i	−0.262226	+	0.807049i
$576$	−46.4341	+	51.5703i	−1.93475	+	2.14876i
$577$	17.0780	−	1.79497i	0.710965	−	0.0747255i	0.257860	−	0.966182i	$-0.416983\pi$
$577$	17.0780	−	1.79497i	0.710965	−	0.0747255i	0.453106	+	0.891457i	$0.350316\pi$
$578$	−28.0143	+	2.94443i	−1.16524	+	0.122472i
$579$	−25.0296	+	27.7982i	−1.04019	+	1.15525i
$580$	4.31454	−	13.2788i	0.179152	−	0.551372i
$581$	6.14976	−	24.9794i	0.255135	−	1.03632i
$582$			26.5413i			1.10017i
$583$		0			0
$584$	7.00652	+	4.04522i	0.289932	+	0.167392i
$585$	0.00142479	+	0.00320013i	5.89077e−5	+	0.000132309i
$586$	−10.0608	−	47.3323i	−0.415608	−	1.95528i
$587$	−8.45024	+	2.74565i	−0.348779	+	0.113325i	−0.478167	−	0.878269i	$-0.658699\pi$
$587$	−8.45024	+	2.74565i	−0.348779	+	0.113325i	0.129388	+	0.991594i	$0.458699\pi$
$588$	17.4747	+	47.1428i	0.720643	+	1.94413i
$589$	0.493009	+	0.678569i	0.0203141	+	0.0279599i
$590$	−22.2996	−	20.0787i	−0.918061	−	0.826626i
$591$	−16.9920	−	18.8715i	−0.698957	−	0.776270i
$592$	−1.14954	+	0.511806i	−0.0472456	+	0.0210351i
$593$	4.15338	+	7.19387i	0.170559	+	0.295417i	0.938615	−	0.344965i	$-0.112109\pi$
$593$	4.15338	+	7.19387i	0.170559	+	0.295417i	−0.768056	+	0.640382i	$0.778776\pi$
$594$		0			0
$595$	−5.36274	+	2.18514i	−0.219851	+	0.0895818i
$596$	−12.9815	+	17.8675i	−0.531742	+	0.731879i
$597$	−4.85760	+	1.03251i	−0.198808	+	0.0422580i
$598$	−0.00104785	+	0.00492974i	−4.28497e−5	+	0.000201592i
$599$	1.69187	+	16.0970i	0.0691278	+	0.657707i	0.973142	+	0.230205i	$0.0739397\pi$
$599$	1.69187	+	16.0970i	0.0691278	+	0.657707i	−0.904014	+	0.427502i	$0.859394\pi$
$600$	6.10688	+	2.71896i	0.249312	+	0.111001i
$601$	−2.71097	−	8.34352i	−0.110583	−	0.340339i	0.880417	−	0.474200i	$-0.157263\pi$
$601$	−2.71097	−	8.34352i	−0.110583	−	0.340339i	−0.991000	+	0.133861i	$0.957263\pi$
$602$	15.4828	+	22.8086i	0.631032	+	0.929608i
$603$	−74.7507	−	54.3096i	−3.04408	−	2.21166i
$604$	17.0834	−	9.86308i	0.695112	−	0.401323i
$605$		0			0
$606$	47.5824	−	82.4151i	1.93290	−	3.34788i
$607$	1.80489	−	17.1724i	0.0732583	−	0.697006i	−0.894832	−	0.446404i	$-0.852705\pi$
$607$	1.80489	−	17.1724i	0.0732583	−	0.697006i	0.968090	−	0.250603i	$-0.0806288\pi$
$608$	14.9269	+	4.85003i	0.605364	+	0.196695i
$609$	−7.54288	−	42.0510i	−0.305653	−	1.70399i
$610$	15.1460	−	11.0042i	0.613242	−	0.445547i
$611$	−0.000323996	0	0.000727707i	−1.31075e−5	0	2.94399e-5i
$612$	28.2997	+	6.01528i	1.14395	+	0.243153i
$613$	10.2995	−	9.27376i	0.415995	−	0.374563i	−0.434390	−	0.900725i	$-0.643036\pi$
$613$	10.2995	−	9.27376i	0.415995	−	0.374563i	0.850385	+	0.526162i	$0.176369\pi$
$614$	64.9121	+	6.82254i	2.61964	+	0.275335i
$615$	−9.18583			−0.370409
$616$		0			0
$617$	1.77082			0.0712903			0.0356452	−	0.999365i	$-0.488651\pi$
$617$	1.77082			0.0712903			0.0356452	+	0.999365i	$0.488651\pi$
$618$	−78.8756	−	8.29016i	−3.17284	−	0.333479i
$619$	−8.23672	+	7.41638i	−0.331062	+	0.298089i	−0.817851	−	0.575430i	$-0.804835\pi$
$619$	−8.23672	+	7.41638i	−0.331062	+	0.298089i	0.486789	+	0.873520i	$0.338168\pi$
$620$	1.15174	+	0.244809i	0.0462549	+	0.00983179i
$621$	−28.0244	+	62.9439i	−1.12458	+	2.52585i
$622$	−29.4300	+	21.3821i	−1.18004	+	0.857346i
$623$	6.47628	−	17.9583i	0.259467	−	0.719484i
$624$	−0.00429062	−	0.00139411i	−0.000171762	−	5.58090e-5i
$625$	−0.608561	+	5.79008i	−0.0243425	+	0.231603i
$626$	21.4609	−	37.1713i	0.857749	−	1.48567i
$627$		0			0
$628$	−12.4665	+	7.19754i	−0.497468	+	0.287213i
$629$	0.560677	+	0.407356i	0.0223557	+	0.0162423i
$630$	−44.5762	+	3.24942i	−1.77596	+	0.129460i
$631$	13.8840	+	42.7304i	0.552712	+	1.70107i	0.701911	+	0.712265i	$0.252330\pi$
$631$	13.8840	+	42.7304i	0.552712	+	1.70107i	−0.149199	+	0.988807i	$0.547670\pi$
$632$	0.888831	+	0.395733i	0.0353558	+	0.0157414i
$633$	−0.956193	−	9.09757i	−0.0380053	−	0.361596i
$634$	13.5274	−	63.6416i	0.537243	−	2.52753i
$635$	1.42585	−	0.303074i	0.0565832	−	0.0120271i
$636$	−5.58719	+	7.69010i	−0.221546	+	0.304932i
$637$	−0.00214941	+	0.00210034i	−8.51627e−5	+	8.32186e-5i
$638$		0			0
$639$	28.9840	+	50.2018i	1.14659	+	1.98595i
$640$	5.09557	−	2.26870i	0.201420	−	0.0896781i
$641$	−11.9836	−	13.3091i	−0.473323	−	0.525678i	0.458450	−	0.888720i	$-0.348405\pi$
$641$	−11.9836	−	13.3091i	−0.473323	−	0.525678i	−0.931773	+	0.363042i	$0.881738\pi$
$642$	9.38702	+	8.45211i	0.370476	+	0.333578i
$643$	28.9300	+	39.8187i	1.14089	+	1.57030i	0.765508	+	0.643427i	$0.222488\pi$
$643$	28.9300	+	39.8187i	1.14089	+	1.57030i	0.375380	+	0.926871i	$0.377512\pi$
$644$	−29.1418	−	18.0903i	−1.14835	−	0.712858i
$645$	−17.8622	+	5.80378i	−0.703324	+	0.228524i
$646$	−1.53447	−	7.21912i	−0.0603730	−	0.284033i
$647$	−17.1857	−	38.5997i	−0.675639	−	1.51751i	−0.846598	−	0.532232i	$-0.821353\pi$
$647$	−17.1857	−	38.5997i	−0.675639	−	1.51751i	0.170959	−	0.985278i	$-0.445313\pi$
$648$	9.02159	+	5.20862i	0.354402	+	0.204614i
$649$		0			0
$650$			0.00318978i			0.000125113i
$651$	3.46036	−	1.00332i	0.135622	−	0.0393230i
$652$	−7.81598	+	24.0551i	−0.306097	+	0.942071i
$653$	7.59158	−	8.43131i	0.297082	−	0.329943i	−0.576062	−	0.817406i	$-0.695411\pi$
$653$	7.59158	−	8.43131i	0.297082	−	0.329943i	0.873143	+	0.487464i	$0.162078\pi$
$654$	−75.9920	+	7.98709i	−2.97152	+	0.312320i
$655$	15.0922	−	1.58626i	0.589701	−	0.0619801i
$656$	5.50950	−	6.11892i	0.215110	−	0.238904i
$657$	−28.9576	+	89.1224i	−1.12974	+	3.47699i
$658$	−7.33183	−	7.03853i	−0.285825	−	0.274391i
$659$			13.2959i			0.517935i	0.965886	+	0.258968i	$0.0833823\pi$
$659$			13.2959i			0.517935i	−0.965886	+	0.258968i	$0.916618\pi$
$660$		0			0
$661$	−8.51808	−	4.91791i	−0.331315	−	0.191285i	0.325110	−	0.945676i	$-0.394599\pi$
$661$	−8.51808	−	4.91791i	−0.331315	−	0.191285i	−0.656425	+	0.754392i	$0.727932\pi$
$662$	−20.0718	−	45.0820i	−0.780113	−	1.75216i
$663$	0.000516602		0.00243042i	2.00632e−5		9.43898e-5i
$664$	5.48345	−	1.78168i	0.212799	−	0.0691426i
$665$	2.87098	+	5.36127i	0.111332	+	0.207901i
$666$	3.14403	+	4.32738i	0.121829	+	0.167683i
$667$	21.6596	+	19.5024i	0.838665	+	0.755137i
$668$	10.6944	+	11.8774i	0.413780	+	0.459549i
$669$	63.8520	−	28.4287i	2.46866	−	1.09912i
$670$	16.5441	+	28.6553i	0.639155	+	1.10705i
$671$		0			0
$672$	41.3496	−	53.2485i	1.59510	−	2.05411i
$673$	−22.9971	+	31.6528i	−0.886473	+	1.22013i	0.0881121	+	0.996111i	$0.471917\pi$
$673$	−22.9971	+	31.6528i	−0.886473	+	1.22013i	−0.974586	+	0.224016i	$0.928083\pi$
$674$	−28.8779	+	6.13819i	−1.11234	+	0.236434i
$675$	−9.06658	+	42.6549i	−0.348973	+	1.64179i
$676$	−3.10693	−	29.5605i	−0.119497	−	1.13694i
$677$	15.7525	+	7.01349i	0.605420	+	0.269550i	0.686468	−	0.727160i	$-0.259160\pi$
$677$	15.7525	+	7.01349i	0.605420	+	0.269550i	−0.0810485	+	0.996710i	$0.525827\pi$
$678$	10.3214	+	31.7661i	0.396392	+	1.21997i
$679$	−0.784978	−	10.7685i	−0.0301247	−	0.413256i
$680$	−1.04999	−	0.762863i	−0.0402653	−	0.0292545i
$681$	−6.57135	+	3.79397i	−0.251815	+	0.145385i
$682$		0			0
$683$	−3.17953	+	5.50711i	−0.121661	+	0.210724i	−0.920423	−	0.390924i	$-0.872156\pi$
$683$	−3.17953	+	5.50711i	−0.121661	+	0.210724i	0.798762	+	0.601648i	$0.205489\pi$
$684$	3.17605	−	30.2181i	0.121439	−	1.15542i
$685$	−1.28178	−	0.416475i	−0.0489742	−	0.0159127i
$686$	−15.9056	−	34.8891i	−0.607278	−	1.33207i
$687$	41.5291	−	30.1727i	1.58443	−	1.15116i
$688$	6.84739	−	15.3795i	0.261054	−	0.586337i
$689$	−0.000555757	0	0.000118130i	−2.11726e−5	0	4.50039e-6i
$690$	32.5571	−	29.3146i	1.23943	−	1.11599i
$691$	−19.7488	−	2.07568i	−0.751278	−	0.0789625i	−0.278854	−	0.960334i	$-0.589954\pi$
$691$	−19.7488	−	2.07568i	−0.751278	−	0.0789625i	−0.472425	+	0.881371i	$0.656621\pi$
$692$	−47.6483			−1.81132
$693$		0			0
$694$	−33.4415			−1.26942
$695$	5.88190	+	0.618212i	0.223113	+	0.0234501i
$696$	7.11563	−	6.40694i	0.269717	−	0.242855i
$697$	−4.43577	−	0.942851i	−0.168017	−	0.0357130i
$698$	10.9364	−	24.5636i	0.413950	−	0.929746i
$699$	40.8692	−	29.6932i	1.54581	−	1.12310i
$700$	−20.4215	−	7.36458i	−0.771861	−	0.278355i
$701$	40.7737	+	13.2482i	1.54000	+	0.500376i	0.951376	−	0.308031i	$-0.0996700\pi$
$701$	40.7737	+	13.2482i	1.54000	+	0.500376i	0.588624	+	0.808407i	$0.299670\pi$
$702$	−0.00112899	+	0.0107417i	−4.26111e−5	+	0.000405418i
$703$	0.363916	−	0.630321i	0.0137254	−	0.0237730i
$704$		0			0
$705$	5.99668	−	3.46218i	0.225848	−	0.130393i
$706$	−51.2731	−	37.2521i	−1.92969	−	1.40200i
$707$	−16.8679	+	34.8451i	−0.634382	+	1.31049i
$708$	−27.0782	−	83.3381i	−1.01766	−	3.13204i
$709$	−32.4451	−	14.4455i	−1.21850	−	0.542512i	−0.306175	−	0.951975i	$-0.599049\pi$
$709$	−32.4451	−	14.4455i	−1.21850	−	0.542512i	−0.912326	+	0.409464i	$0.865716\pi$
$710$	−2.16990	−	20.6452i	−0.0814348	−	0.774800i
$711$	−2.34302	+	11.0231i	−0.0878702	+	0.413397i
$712$	4.18510	−	0.889570i	0.156843	−	0.0333381i
$713$	−1.44475	+	1.98853i	−0.0541064	+	0.0744711i
$714$	−31.4069	−	4.31938i	−1.17537	−	0.161649i
$715$		0			0
$716$	−16.3775	−	28.3666i	−0.612055	−	1.06011i
$717$	−27.7752	+	12.3663i	−1.03728	+	0.461828i
$718$	25.9763	+	28.8496i	0.969426	+	1.07666i
$719$	7.72319	+	6.95399i	0.288026	+	0.259340i	0.800459	−	0.599387i	$-0.204589\pi$
$719$	7.72319	+	6.95399i	0.288026	+	0.259340i	−0.512433	+	0.858727i	$0.671256\pi$
$720$	16.0432	+	22.0816i	0.597896	+	0.822933i
$721$	32.2470	+	1.03073i	1.20094	+	0.0383862i
$722$	30.0400	−	9.76060i	1.11797	−	0.363252i
$723$	6.81230	+	32.0493i	0.253352	+	1.19193i
$724$	12.2240	+	27.4555i	0.454300	+	1.02037i
$725$	15.9753	+	9.22336i	0.593309	+	0.342547i
$726$		0			0
$727$		−	6.55794i		−	0.243220i	−0.992578	−	0.121610i	$-0.961194\pi$
$727$		−	6.55794i		−	0.243220i	0.992578	−	0.121610i	$-0.0388058\pi$
$728$	−0.000654013	0	0.000161013i	−2.42393e−5	0	5.96754e-6i
$729$	−1.89800	+	5.84145i	−0.0702964	+	0.216350i
$730$	22.4547	−	24.9385i	0.831086	−	0.923015i
$731$	−9.22123	+	0.969191i	−0.341060	+	0.0358468i
$732$	54.3709	−	5.71462i	2.00961	−	0.211218i
$733$	33.1339	−	36.7989i	1.22383	−	1.35920i	0.311233	−	0.950334i	$-0.399258\pi$
$733$	33.1339	−	36.7989i	1.22383	−	1.35920i	0.912595	−	0.408865i	$-0.134075\pi$
$734$	14.1615	−	43.5848i	0.522712	−	1.60874i
$735$	25.8473	−	3.78846i	0.953392	−	0.139739i
$736$			45.9940i			1.69536i
$737$		0			0
$738$	−30.3115	−	17.5004i	−1.11578	−	0.644197i
$739$	0.750614	+	1.68591i	0.0276118	+	0.0620171i	0.926825	−	0.375494i	$-0.122527\pi$
$739$	0.750614	+	1.68591i	0.0276118	+	0.0620171i	−0.899213	+	0.437511i	$0.855860\pi$
$740$	−0.212434	−	0.999422i	−0.00780922	−	0.0367395i
$741$	0.00248176		0.000806372i	9.11697e−5		2.96228e-5i
$742$	3.82337	−	6.15909i	0.140360	−	0.226107i
$743$	−26.0131	−	35.8039i	−0.954327	−	1.31352i	−0.949578	−	0.313529i	$-0.898489\pi$
$743$	−26.0131	−	35.8039i	−0.954327	−	1.31352i	−0.00474837	−	0.999989i	$-0.501511\pi$
$744$	0.600082	+	0.540316i	0.0220001	+	0.0198089i
$745$	7.67848	+	8.52782i	0.281318	+	0.312435i
$746$	37.6464	−	16.7613i	1.37833	−	0.613674i
$747$	33.3907	+	57.8344i	1.22170	+	2.11605i
$748$		0			0
$749$	−4.05852	−	3.15160i	−0.148295	−	0.115157i
$750$	39.0054	−	53.6863i	1.42428	−	1.96035i
$751$	0.893325	−	0.189882i	0.0325979	−	0.00692890i	−0.191584	−	0.981476i	$-0.561362\pi$
$751$	0.893325	−	0.189882i	0.0325979	−	0.00692890i	0.224182	+	0.974547i	$0.428029\pi$
$752$	−1.29045	+	6.07110i	−0.0470579	+	0.221390i
$753$	−7.81243	−	74.3303i	−0.284701	−	2.70875i
$754$	0.00417389	+	0.00185834i	0.000152004	+	6.76766e-5i
$755$	−3.16726	−	9.74784i	−0.115269	−	0.354760i
$756$	−66.1633	−	32.0284i	−2.40634	−	1.16486i
$757$	13.3894	+	9.72799i	0.486647	+	0.353570i	0.803893	−	0.594773i	$-0.202758\pi$
$757$	13.3894	+	9.72799i	0.486647	+	0.353570i	−0.317246	+	0.948343i	$0.602758\pi$
$758$	25.6680	−	14.8195i	0.932305	−	0.538267i
$759$		0			0
$760$	−0.681512	+	1.18041i	−0.0247210	+	0.0428181i
$761$	−3.40080	+	32.3564i	−0.123279	+	1.17292i	0.741566	+	0.670880i	$0.234083\pi$
$761$	−3.40080	+	32.3564i	−0.123279	+	1.17292i	−0.864845	+	0.502039i	$0.832583\pi$
$762$	7.58977	+	2.46607i	0.274949	+	0.0893362i
$763$	30.5957	−	5.48808i	1.10764	−	0.198682i
$764$	0.520088	−	0.377866i	0.0188161	−	0.0136707i
$765$	6.11434	−	13.7330i	0.221064	−	0.496519i
$766$	−32.5716	−	6.92330i	−1.17686	−	0.250149i
$767$	0.00389239	−	0.00350473i	0.000140546	−	0.000126548i
$768$	−32.7624	−	3.44347i	−1.18221	−	0.124255i
$769$	3.13977			0.113223			0.0566116	−	0.998396i	$-0.481970\pi$
$769$	3.13977			0.113223			0.0566116	+	0.998396i	$0.481970\pi$
$770$		0			0
$771$	−22.7647			−0.819851
$772$	27.0764	+	2.84585i	0.974503	+	0.102424i
$773$	−5.77719	+	5.20180i	−0.207791	+	0.187096i	−0.766455	−	0.642298i	$-0.777981\pi$
$773$	−5.77719	+	5.20180i	−0.207791	+	0.187096i	0.558664	+	0.829394i	$0.311314\pi$
$774$	−69.9990	−	14.8787i	−2.51606	−	0.534805i
$775$	−0.632746	+	1.42117i	−0.0227289	+	0.0510499i
$776$	1.95772	−	1.42236i	0.0702779	−	0.0510599i
$777$	−2.01668	−	2.38902i	−0.0723480	−	0.0857055i
$778$	−66.8818	−	21.7312i	−2.39783	−	0.779101i
$779$	−0.497823	+	4.73647i	−0.0178364	+	0.169702i
$780$	0.00183162	−	0.00317247i	6.55827e−5	−	0.000113593i
$781$		0			0
$782$	18.7305	−	10.8141i	0.669801	−	0.386710i
$783$	50.5328	+	36.7142i	1.80589	+	1.31206i
$784$	−12.9792	+	19.4898i	−0.463542	+	0.696064i
$785$	2.31130	+	7.11344i	0.0824937	+	0.253889i
$786$	75.8965	+	33.7913i	2.70714	+	1.20530i
$787$	5.42476	+	51.6132i	0.193372	+	1.83981i	0.474639	+	0.880181i	$0.342579\pi$
$787$	5.42476	+	51.6132i	0.193372	+	1.83981i	−0.281267	+	0.959630i	$0.590755\pi$
$788$	−3.84279	+	18.0789i	−0.136894	+	0.644035i
$789$	46.9181	−	9.97274i	1.67033	−	0.355039i
$790$	2.37210	−	3.26491i	0.0843954	−	0.116160i
$791$	−5.12716	−	12.5830i	−0.182301	−	0.447401i
$792$		0			0
$793$	0.00163391	+	0.00283002i	5.80219e−5	+	0.000100497i
$794$	42.1962	−	18.7870i	1.49749	−	0.666724i
$795$	3.30480	+	3.67035i	0.117209	+	0.130174i
$796$	2.68612	+	2.41859i	0.0952070	+	0.0857248i
$797$	−15.0416	−	20.7030i	−0.532800	−	0.733337i	0.454754	−	0.890617i	$-0.349727\pi$
$797$	−15.0416	−	20.7030i	−0.532800	−	0.733337i	−0.987554	+	0.157281i	$0.949727\pi$
$798$	−1.06366	+	33.2773i	−0.0376531	+	1.17800i
$799$	3.25111	−	1.05635i	0.115016	−	0.0373710i
$800$	6.05231	+	28.4739i	0.213981	+	1.00670i
$801$	20.1569	+	45.2731i	0.712208	+	1.59965i
$802$	12.7088	+	7.33745i	0.448764	+	0.259094i
$803$		0			0
$804$			96.6244i			3.40768i
$805$	−12.3423	+	12.8566i	−0.435007	+	0.453134i
$806$	−0.000119067	0	0.000366450i	−4.19395e−6	0	1.29076e-5i
$807$	25.8774	−	28.7398i	0.910928	−	1.01169i
$808$	−8.62898	+	0.906943i	−0.303567	+	0.0319061i
$809$	−13.0491	+	1.37152i	−0.458782	+	0.0482200i	−0.331101	−	0.943595i	$-0.607420\pi$
$809$	−13.0491	+	1.37152i	−0.458782	+	0.0482200i	−0.127681	+	0.991815i	$0.540753\pi$
$810$	28.9127	−	32.1108i	1.01589	−	1.12826i
$811$	−12.0585	+	37.1123i	−0.423431	+	1.30319i	0.481057	+	0.876689i	$0.340253\pi$
$811$	−12.0585	+	37.1123i	−0.423431	+	1.30319i	−0.904488	+	0.426498i	$0.859747\pi$
$812$	−21.5341	+	22.4315i	−0.755699	+	0.787190i
$813$		−	89.3492i		−	3.13361i
$814$		0			0
$815$	11.3813	+	6.57098i	0.398669	+	0.230171i
$816$	7.87457	+	17.6866i	0.275665	+	0.619154i
$817$	2.02455	+	9.52478i	0.0708302	+	0.333230i
$818$	−32.1639	+	10.4507i	−1.12458	+	0.365400i
$819$	0.000249232	−	0.00779742i	8.70889e−6	−	0.000272464i
$820$	3.92982	+	5.40893i	0.137235	+	0.188888i
$821$	18.0393	+	16.2426i	0.629575	+	0.566872i	0.920923	−	0.389745i	$-0.127437\pi$
$821$	18.0393	+	16.2426i	0.629575	+	0.566872i	−0.291347	+	0.956617i	$0.594104\pi$
$822$	−4.93708	−	5.48318i	−0.172200	−	0.191248i
$823$	9.25766	−	4.12178i	0.322702	−	0.143676i	−0.238992	−	0.971022i	$-0.576817\pi$
$823$	9.25766	−	4.12178i	0.322702	−	0.143676i	0.561693	+	0.827346i	$0.310150\pi$
$824$	3.61550	+	6.26222i	0.125952	+	0.218155i
$825$		0			0
$826$	25.2172	+	61.8878i	0.877419	+	2.15335i
$827$	−3.75863	+	5.17332i	−0.130701	+	0.179894i	−0.869352	−	0.494194i	$-0.835463\pi$
$827$	−3.75863	+	5.17332i	−0.130701	+	0.179894i	0.738651	+	0.674088i	$0.235463\pi$
$828$	87.0955	−	18.5127i	3.02678	−	0.643362i
$829$	−7.58832	+	35.7002i	−0.263553	+	1.23992i	0.624809	+	0.780778i	$0.285177\pi$
$829$	−7.58832	+	35.7002i	−0.263553	+	1.23992i	−0.888362	+	0.459143i	$0.848157\pi$
$830$	−2.49981	−	23.7841i	−0.0867696	−	0.825558i
$831$	−8.97969	−	3.99802i	−0.311502	−	0.138690i
$832$	0.00134043	+	0.00412541i	4.64710e−5	+	0.000143023i
$833$	12.8703	+	0.823601i	0.445930	+	0.0285361i
$834$	26.1947	+	19.0316i	0.907048	+	0.659009i
$835$	7.19178	−	4.15218i	0.248882	−	0.143692i
$836$		0			0
$837$	−2.63380	+	4.56187i	−0.0910373	+	0.157681i
$838$	−7.21775	+	68.6723i	−0.249333	+	2.37224i
$839$	41.7978	+	13.5809i	1.44302	+	0.468866i	0.922838	−	0.385188i	$-0.125863\pi$
$839$	41.7978	+	13.5809i	1.44302	+	0.468866i	0.520184	+	0.854054i	$0.325863\pi$
$840$	3.77667	+	4.47396i	0.130308	+	0.154366i
$841$	−2.08545	+	1.51517i	−0.0719121	+	0.0522472i
$842$	−4.92230	+	11.0557i	−0.169634	+	0.381004i
$843$	3.33247	+	0.708337i	0.114776	+	0.0243964i
$844$	−4.94788	+	4.45509i	−0.170313	+	0.153351i
$845$	−15.3593	−	1.61433i	−0.528376	−	0.0555345i
$846$	26.3839			0.907096
$847$		0			0
$848$	−4.42707			−0.152026
$849$	−31.5550	−	3.31656i	−1.08296	−	0.113824i
$850$	10.1726	−	9.15947i	0.348918	−	0.314167i
$851$	2.08629	+	0.443454i	0.0715170	+	0.0152014i
$852$	24.6565	−	55.3794i	0.844717	−	1.89727i
$853$	28.6425	−	20.8100i	0.980699	−	0.712520i	0.0228344	−	0.999739i	$-0.492731\pi$
$853$	28.6425	−	20.8100i	0.980699	−	0.712520i	0.957865	+	0.287220i	$0.0927310\pi$
$854$	−41.0391	+	7.36137i	−1.40433	+	0.251901i
$855$	−15.0148	−	4.87859i	−0.513494	−	0.166844i
$856$	0.120381	−	1.14535i	0.00411454	−	0.0391472i
$857$	3.84956	−	6.66764i	0.131499	−	0.227762i	−0.792756	−	0.609539i	$-0.791354\pi$
$857$	3.84956	−	6.66764i	0.131499	−	0.227762i	0.924254	+	0.381777i	$0.124688\pi$
$858$		0			0
$859$	32.8820	−	18.9844i	1.12192	−	0.647740i	0.180029	−	0.983661i	$-0.442381\pi$
$859$	32.8820	−	18.9844i	1.12192	−	0.647740i	0.941890	+	0.335921i	$0.109047\pi$
$860$	11.0591	+	8.03494i	0.377114	+	0.273989i
$861$	18.4136	+	8.91366i	0.627532	+	0.303777i
$862$	12.5757	+	38.7041i	0.428331	+	1.31827i
$863$	10.9037	+	4.85464i	0.371167	+	0.165254i	0.583839	−	0.811870i	$-0.301550\pi$
$863$	10.9037	+	4.85464i	0.371167	+	0.165254i	−0.212672	+	0.977124i	$0.568217\pi$
$864$	10.3032	+	98.0286i	0.350523	+	3.33500i
$865$	−5.14737	+	24.2165i	−0.175016	+	0.823385i
$866$	1.04417	−	0.221945i	0.0354823	−	0.00754200i
$867$	−25.1222	+	34.5777i	−0.853194	+	1.17432i
$868$	−2.07117	−	1.60835i	−0.0703002	−	0.0545909i
$869$		0			0
$870$	−19.8580	−	34.3950i	−0.673248	−	1.16610i
$871$	−0.00527622	+	0.00234912i	−0.000178778	+	7.95970e-5i
$872$	4.66159	+	5.17722i	0.157861	+	0.175323i
$873$	20.8293	+	18.7548i	0.704964	+	0.634752i
$874$	−13.3510	−	18.3760i	−0.451604	−	0.621579i
$875$	−14.2377	+	22.9355i	−0.481321	+	0.775361i
$876$	93.2000	−	30.2825i	3.14894	−	1.02315i
$877$	4.83109	+	22.7285i	0.163134	+	0.767487i	0.981297	+	0.192500i	$0.0616596\pi$
$877$	4.83109	+	22.7285i	0.163134	+	0.767487i	−0.818162	+	0.574987i	$0.805007\pi$
$878$	19.8044	+	44.4813i	0.668365	+	1.50117i
$879$	−63.5853	−	36.7110i	−2.14468	−	1.23823i
$880$		0			0
$881$			36.6233i			1.23387i	0.787014	+	0.616935i	$0.211626\pi$
$881$			36.6233i			1.23387i	−0.787014	+	0.616935i	$0.788374\pi$
$882$	92.5088	+	36.7417i	3.11493	+	1.23716i
$883$	4.94860	−	15.2302i	0.166534	−	0.512537i	−0.832613	−	0.553856i	$-0.813156\pi$
$883$	4.94860	−	15.2302i	0.166534	−	0.512537i	0.999146	+	0.0413185i	$0.0131558\pi$
$884$	0.00121010	−	0.00134396i	4.07002e−5	−	4.52022e-5i
$885$	−45.2805	+	4.75917i	−1.52209	+	0.159978i
$886$	−36.7642	+	3.86407i	−1.23512	+	0.129816i
$887$	−11.8349	+	13.1440i	−0.397377	+	0.441332i	−0.908316	−	0.418285i	$-0.862631\pi$
$887$	−11.8349	+	13.1440i	−0.397377	+	0.441332i	0.510939	+	0.859617i	$0.329298\pi$
$888$	0.216528	−	0.666405i	0.00726621	−	0.0223631i
$889$	−3.15230	−	0.776073i	−0.105725	−	0.0260286i
$890$		−	17.7470i		−	0.594882i
$891$		0			0
$892$	−44.0565	−	25.4360i	−1.47512	−	0.851661i
$893$	−1.46021	−	3.27968i	−0.0488640	−	0.109750i
$894$	13.0616	+	61.4500i	0.436845	+	2.05519i
$895$	−16.1861	+	5.25919i	−0.541042	+	0.175795i
$896$	−12.4159	−	0.396854i	−0.414785	−	0.0132580i
$897$	0.00449480	+	0.00618656i	0.000150077	+	0.000206563i
$898$	10.9809	+	9.88728i	0.366439	+	0.329943i
$899$	1.49100	+	1.65592i	0.0497276	+	0.0552281i
$900$	51.4829	−	22.9216i	1.71610	−	0.764055i
$901$	1.21913	+	2.11159i	0.0406151	+	0.0703474i
$902$		0			0
$903$	41.4377	+	5.69892i	1.37896	+	0.189648i
$904$	1.78997	−	2.46368i	0.0595334	−	0.0819407i
$905$	15.2743	−	3.24666i	0.507736	−	0.107923i
$906$	11.6663	−	54.8857i	0.387587	−	1.82346i
$907$	2.87638	+	27.3669i	0.0955087	+	0.908704i	0.932423	+	0.361370i	$0.117691\pi$
$907$	2.87638	+	27.3669i	0.0955087	+	0.908704i	−0.836914	+	0.547335i	$0.815643\pi$
$908$	5.04532	+	2.24632i	0.167435	+	0.0745468i
$909$	−31.0553	−	95.5785i	−1.03004	−	3.17014i
$910$	−0.00121728	+	0.00251462i	−4.03524e−5	+	8.33588e-5i
$911$	−19.5497	−	14.2037i	−0.647709	−	0.470588i	0.214781	−	0.976662i	$-0.431096\pi$
$911$	−19.5497	−	14.2037i	−0.647709	−	0.470588i	−0.862490	+	0.506074i	$0.831096\pi$
$912$	17.6084	−	10.1662i	0.583072	−	0.336637i
$913$		0			0
$914$	−25.1528	+	43.5660i	−0.831981	+	1.44103i
$915$	2.96925	−	28.2505i	0.0981603	−	0.933933i
$916$	−35.5333	−	11.5455i	−1.17405	−	0.381473i
$917$	−31.7925	−	11.4653i	−1.04988	−	0.378617i
$918$	37.4985	−	27.2442i	1.23763	−	0.899194i
$919$	15.6235	−	35.0910i	0.515373	−	1.15755i	−0.449128	−	0.893467i	$-0.648265\pi$
$919$	15.6235	−	35.0910i	0.515373	−	1.15755i	0.964501	−	0.264079i	$-0.0850680\pi$
$920$	−3.90703	−	0.830465i	−0.128811	−	0.0273796i
$921$	73.5966	−	66.2666i	2.42509	−	2.18356i
$922$	−42.0318	−	4.41772i	−1.38424	−	0.145490i
$923$	0.00362346			0.000119268
$924$		0			0
$925$	1.34993			0.0443854
$926$	73.1025	+	7.68339i	2.40230	+	0.252492i
$927$	−62.2415	+	56.0425i	−2.04428	+	1.84068i
$928$	40.7847	+	8.66905i	1.33882	+	0.284576i
$929$	−1.33338	+	2.99482i	−0.0437468	+	0.0982568i	−0.934097	−	0.357020i	$-0.883793\pi$
$929$	−1.33338	+	2.99482i	−0.0437468	+	0.0982568i	0.890350	+	0.455276i	$0.150460\pi$
$930$	2.70969	−	1.96870i	0.0888541	−	0.0645563i
$931$	−0.552647	−	13.5329i	−0.0181123	−	0.443523i
$932$	−34.9687	−	11.3620i	−1.14544	−	0.372175i
$933$	−5.76952	+	54.8933i	−0.188886	+	1.79713i
$934$	−23.1313	+	40.0645i	−0.756878	+	1.31095i
$935$		0			0
$936$	0.00151422		0.000874237i	4.94939e−5		2.85753e-5i
$937$	−34.0171	−	24.7148i	−1.11129	−	0.807398i	−0.128423	−	0.991720i	$-0.540991\pi$
$937$	−34.0171	−	24.7148i	−1.11129	−	0.807398i	−0.982866	+	0.184321i	$0.940991\pi$
$938$	−5.35749	−	73.4951i	−0.174928	−	2.39970i
$939$	−20.1248	−	61.9379i	−0.656749	−	2.02127i
$940$	−4.60410	−	2.04988i	−0.150169	−	0.0668597i
$941$	−3.34342	−	31.8105i	−0.108992	−	1.03699i	−0.903163	−	0.429298i	$-0.858761\pi$
$941$	−3.34342	−	31.8105i	−0.108992	−	1.03699i	0.794171	−	0.607695i	$-0.207905\pi$
$942$	−8.51344	+	40.0526i	−0.277383	+	1.30498i
$943$	−13.6516	+	2.90174i	−0.444557	+	0.0944935i
$944$	23.9882	−	33.0169i	0.780750	−	1.07461i
$945$	−23.4254	+	30.1665i	−0.762030	+	0.981315i
$946$		0			0
$947$	−14.5194	−	25.1484i	−0.471818	−	0.817212i	0.527662	−	0.849454i	$-0.323069\pi$
$947$	−14.5194	−	25.1484i	−0.471818	−	0.817212i	−0.999480	+	0.0322419i	$0.989735\pi$
$948$	10.7661	−	4.79336i	0.349666	−	0.155681i
$949$	0.00391946	+	0.00435300i	0.000127231	+	0.000141304i
$950$	−10.6834	−	9.61937i	−0.346615	−	0.312093i
$951$	−58.0267	−	79.8669i	−1.88164	−	2.58986i
$952$	1.36451	+	2.54808i	0.0442240	+	0.0825839i
$953$	−9.63423	+	3.13035i	−0.312083	+	0.101402i	−0.460871	−	0.887467i	$-0.652463\pi$
$953$	−9.63423	+	3.13035i	−0.312083	+	0.101402i	0.148788	+	0.988869i	$0.452463\pi$
$954$	3.91265	+	18.4076i	0.126677	+	0.595967i
$955$	−0.135860	−	0.305147i	−0.00439633	−	0.00987432i
$956$	19.1643	+	11.0645i	0.619816	+	0.357851i
$957$		0			0
$958$		−	79.8349i		−	2.57935i
$959$	2.16527	+	2.07865i	0.0699201	+	0.0671230i
$960$	11.6519	−	35.8609i	0.376064	−	1.15740i
$961$	20.6173	−	22.8978i	0.665074	−	0.738640i
$962$	0.000332520	0	3.49492e-5i	1.07209e−5	0	1.12681e-6i
$963$	13.2662	−	1.39433i	0.427497	−	0.0449318i
$964$	15.9573	−	17.7224i	0.513951	−	0.570801i
$965$	4.37138	−	13.4537i	0.140720	−	0.433091i
$966$	−93.7087	+	27.1704i	−3.01503	+	0.874193i
$967$		−	6.35801i		−	0.204460i	−0.994761	−	0.102230i	$-0.967402\pi$
$967$		−	6.35801i		−	0.204460i	0.994761	−	0.102230i	$-0.0325978\pi$
$968$		0			0
$969$	−9.69802	−	5.59915i	−0.311545	−	0.179871i
$970$	−4.08253	−	9.16952i	−0.131082	−	0.294416i
$971$	10.5440	+	49.6058i	0.338374	+	1.59193i	0.737707	+	0.675121i	$0.235908\pi$
$971$	10.5440	+	49.6058i	0.338374	+	1.59193i	−0.399333	+	0.916806i	$0.630758\pi$
$972$	40.7337	−	13.2352i	1.30653	−	0.424519i
$973$	−11.1907	−	6.94686i	−0.358758	−	0.222706i
$974$	48.2044	+	66.3476i	1.54457	+	2.12591i
$975$	0.00359672	+	0.00323850i	0.000115187	+	0.000103715i
$976$	17.0375	+	18.9220i	0.545356	+	0.605680i
$977$	−4.37011	+	1.94570i	−0.139812	+	0.0622484i	−0.475450	−	0.879743i	$-0.657715\pi$
$977$	−4.37011	+	1.94570i	−0.139812	+	0.0622484i	0.335638	+	0.941991i	$0.391048\pi$
$978$	35.9735	+	62.3080i	1.15031	+	1.99239i
$979$		0			0
$980$	−13.2886	−	13.5990i	−0.424488	−	0.434404i
$981$	−47.4297	+	65.2814i	−1.51431	+	2.08427i
$982$	12.0919	−	2.57022i	0.385869	−	0.0820191i
$983$	4.55430	−	21.4263i	0.145260	−	0.683393i	−0.843894	−	0.536510i	$-0.819743\pi$
$983$	4.55430	−	21.4263i	0.145260	−	0.683393i	0.989154	−	0.146883i	$-0.0469242\pi$
$984$	0.479265	+	4.55990i	0.0152784	+	0.145364i
$985$	8.77319	+	3.90607i	0.279537	+	0.124458i
$986$	−6.05888	−	18.6473i	−0.192954	−	0.593852i
$987$	−15.3803	+	1.12116i	−0.489560	+	0.0356869i
$988$	−0.00153655	−	0.00111637i	−4.88841e−5	−	3.55163e-5i
$989$	−24.7127	+	14.2679i	−0.785817	+	0.453692i
$990$		0			0
$991$	−15.6744	+	27.1488i	−0.497912	+	0.862410i	−0.999997	−	0.00240886i	$-0.999233\pi$
$991$	−15.6744	+	27.1488i	−0.497912	+	0.862410i	0.502085	+	0.864818i	$0.332567\pi$
$992$	−0.367557	+	3.49707i	−0.0116699	+	0.111032i
$993$	−71.2118	−	23.1381i	−2.25984	−	0.734266i
$994$	−15.6838	+	43.4901i	−0.497459	+	1.37942i
$995$	1.51939	−	1.10390i	0.0481679	−	0.0349960i
$996$	28.4053	−	63.7992i	0.900055	−	2.02156i
$997$	26.8552	+	5.70825i	0.850513	+	0.180782i	0.612491	−	0.790478i	$-0.290168\pi$
$997$	26.8552	+	5.70825i	0.850513	+	0.180782i	0.238022	+	0.971260i	$0.423501\pi$
$998$	−17.4298	+	15.6938i	−0.551730	+	0.496780i
$999$	4.54592	+	0.477795i	0.143826	+	0.0151168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.r.c.766.1		48
7.5	odd	6	inner	847.2.r.c.40.6		48
11.2	odd	10		847.2.r.a.94.1		48
11.3	even	5		77.2.n.a.52.1	yes	48
11.4	even	5		847.2.r.a.717.1		48
11.5	even	5		847.2.i.b.241.21		48
11.6	odd	10		847.2.i.b.241.4		48
11.7	odd	10		847.2.r.d.717.6		48
11.8	odd	10	inner	847.2.r.c.360.6		48
11.9	even	5		847.2.r.d.94.6		48
11.10	odd	2		77.2.n.a.73.6	yes	48
33.14	odd	10		693.2.cg.a.514.6		48
33.32	even	2		693.2.cg.a.73.1		48
77.3	odd	30		539.2.m.a.195.2		48
77.5	odd	30		847.2.i.b.362.4		48
77.10	even	6		539.2.m.a.293.1		48
77.19	even	30	inner	847.2.r.c.481.1		48
77.25	even	15		539.2.m.a.195.1		48
77.26	odd	30		847.2.r.a.838.1		48
77.32	odd	6		539.2.m.a.293.2		48
77.40	even	30		847.2.r.d.838.6		48
77.47	odd	30		77.2.n.a.19.6	✓	48
77.54	even	6		77.2.n.a.40.1	yes	48
77.58	even	15		539.2.s.d.19.6		48
77.61	even	30		847.2.i.b.362.21		48
77.65	odd	6		539.2.s.d.117.1		48
77.68	even	30		847.2.r.a.215.1		48
77.69	odd	10		539.2.s.d.129.1		48
77.75	odd	30		847.2.r.d.215.6		48
77.76	even	2		539.2.s.d.227.6		48
231.47	even	30		693.2.cg.a.19.1		48
231.131	odd	6		693.2.cg.a.271.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.19.6	✓	48	77.47	odd	30
77.2.n.a.40.1	yes	48	77.54	even	6
77.2.n.a.52.1	yes	48	11.3	even	5
77.2.n.a.73.6	yes	48	11.10	odd	2
539.2.m.a.195.1		48	77.25	even	15
539.2.m.a.195.2		48	77.3	odd	30
539.2.m.a.293.1		48	77.10	even	6
539.2.m.a.293.2		48	77.32	odd	6
539.2.s.d.19.6		48	77.58	even	15
539.2.s.d.117.1		48	77.65	odd	6
539.2.s.d.129.1		48	77.69	odd	10
539.2.s.d.227.6		48	77.76	even	2
693.2.cg.a.19.1		48	231.47	even	30
693.2.cg.a.73.1		48	33.32	even	2
693.2.cg.a.271.6		48	231.131	odd	6
693.2.cg.a.514.6		48	33.14	odd	10
847.2.i.b.241.4		48	11.6	odd	10
847.2.i.b.241.21		48	11.5	even	5
847.2.i.b.362.4		48	77.5	odd	30
847.2.i.b.362.21		48	77.61	even	30
847.2.r.a.94.1		48	11.2	odd	10
847.2.r.a.215.1		48	77.68	even	30
847.2.r.a.717.1		48	11.4	even	5
847.2.r.a.838.1		48	77.26	odd	30
847.2.r.c.40.6		48	7.5	odd	6	inner
847.2.r.c.360.6		48	11.8	odd	10	inner
847.2.r.c.481.1		48	77.19	even	30	inner
847.2.r.c.766.1		48	1.1	even	1	trivial
847.2.r.d.94.6		48	11.9	even	5
847.2.r.d.215.6		48	77.75	odd	30
847.2.r.d.717.6		48	11.7	odd	10
847.2.r.d.838.6		48	77.40	even	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.r (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.05902 - 0.216412i) q^{2} +(-2.33449 + 2.10199i) q^{3} +(2.23645 + 0.475371i) q^{4} +(0.483200 - 1.08528i) q^{5} +(5.26167 - 3.82283i) q^{6} +(-2.02173 + 1.70664i) q^{7} +(-0.563952 - 0.183239i) q^{8} +(0.717924 - 6.83059i) q^{9} +(-1.22979 + 2.13006i) q^{10} +(-6.22020 + 3.59123i) q^{12} +(-0.000347326 - 0.000252347i) q^{13} +(4.53213 - 3.07648i) q^{14} +(1.15323 + 3.54927i) q^{15} +(-3.05594 - 1.36059i) q^{16} +(0.192581 + 1.83228i) q^{17} +(-2.95645 + 13.9090i) q^{18} +(1.89260 - 0.402285i) q^{19} +(1.59656 - 2.19748i) q^{20} +(1.13239 - 8.23379i) q^{21} +(2.83507 + 4.91048i) q^{23} +(1.70171 - 0.757650i) q^{24} +(2.40129 + 2.66691i) q^{25} +(0.000660541 + 0.000594754i) q^{26} +(7.14248 + 9.83078i) q^{27} +(-5.33278 + 2.85573i) q^{28} +(4.88867 - 1.58843i) q^{29} +(-1.60642 - 7.55760i) q^{30} +(0.176317 + 0.396015i) q^{31} +(7.02487 + 4.05581i) q^{32} -3.81439i q^{34} +(0.875286 + 3.01880i) q^{35} +(4.85267 - 14.9350i) q^{36} +(0.251703 - 0.279544i) q^{37} +(-3.98397 + 0.418732i) q^{38} +(0.00134126 - 0.000140972i) q^{39} +(-0.471368 + 0.523507i) q^{40} +(-0.760621 + 2.34095i) q^{41} +(-4.11351 + 16.7085i) q^{42} +5.03264i q^{43} +(-7.06624 - 4.07969i) q^{45} +(-4.77478 - 10.7243i) q^{46} +(-0.385768 - 1.81490i) q^{47} +(9.99404 - 3.24726i) q^{48} +(1.17479 - 6.90072i) q^{49} +(-4.36717 - 6.01089i) q^{50} +(-4.30102 - 3.87266i) q^{51} +(-0.000656817 - 0.000729469i) q^{52} +(1.20901 - 0.538288i) q^{53} +(-12.5790 - 21.7875i) q^{54} +(1.45288 - 0.592000i) q^{56} +(-3.57267 + 4.91735i) q^{57} +(-10.4096 + 2.21264i) q^{58} +(-2.53655 + 11.9335i) q^{59} +(0.891911 + 8.48597i) q^{60} +(-6.95359 - 3.09594i) q^{61} +(-0.277339 - 0.853562i) q^{62} +(10.2059 + 15.0349i) q^{63} +(-8.17409 - 5.93882i) q^{64} +(-0.000441696 + 0.000255013i) q^{65} +(6.72641 - 11.6505i) q^{67} +(-0.440319 + 4.18935i) q^{68} +(-16.9402 - 5.50421i) q^{69} +(-1.14893 - 6.40520i) q^{70} +(-6.82813 + 4.96093i) q^{71} +(-1.65651 + 3.72057i) q^{72} +(-13.3457 - 2.83671i) q^{73} +(-0.578758 + 0.521116i) q^{74} +(-11.2116 - 1.17839i) q^{75} +4.42393 q^{76} -0.00279219 q^{78} +(-1.63180 - 0.171509i) q^{79} +(-2.95326 + 2.65913i) q^{80} +(-17.1839 - 3.65255i) q^{81} +(2.07275 - 4.65546i) q^{82} +(-7.86628 + 5.71519i) q^{83} +(6.44664 - 17.8761i) q^{84} +(2.08161 + 0.676354i) q^{85} +(1.08912 - 10.3623i) q^{86} +(-8.07373 + 13.9841i) q^{87} +(-6.24880 + 3.60774i) q^{89} +(13.6667 + 9.92940i) q^{90} +(0.00113286 - 8.25811e-5i) q^{91} +(4.00617 + 12.3297i) q^{92} +(-1.24403 - 0.553878i) q^{93} +(0.401540 + 3.82040i) q^{94} +(0.477911 - 2.24839i) q^{95} +(-24.9248 + 5.29793i) q^{96} +(-2.39869 + 3.30152i) q^{97} +(-3.91231 + 13.9545i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} + 5 q^{7} - 11 q^{9} - 12 q^{12} - 8 q^{14} - 27 q^{16} - 15 q^{17} - 20 q^{18} + 15 q^{19} + 10 q^{23} - 75 q^{24} + q^{25} + 27 q^{26} + 40 q^{28} + 40 q^{29}+ \cdots - 75 q^{96}+O(q^{100}) \) 48 * q + 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 + 5 * q^7 - 11 * q^9 - 12 * q^12 - 8 * q^14 - 27 * q^16 - 15 * q^17 - 20 * q^18 + 15 * q^19 + 10 * q^23 - 75 * q^24 + q^25 + 27 * q^26 + 40 * q^28 + 40 * q^29 - 25 * q^30 + 9 * q^31 - 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 + 45 * q^39 - 75 * q^40 + 64 * q^42 - 84 * q^45 + 20 * q^46 + 3 * q^47 + 59 * q^49 - 30 * q^50 - 55 * q^51 + 15 * q^52 - 3 * q^53 - 8 * q^56 - 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 + 30 * q^61 + 40 * q^63 + 12 * q^64 + 44 * q^67 + 75 * q^68 - 27 * q^70 + 20 * q^71 + 60 * q^72 + 60 * q^73 - 45 * q^74 - 57 * q^75 + 92 * q^78 + 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 + 125 * q^84 - 10 * q^85 - 62 * q^86 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 - 105 * q^94 - 30 * q^95 - 75 * q^96

Introduction

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