LMFDB - Embedded newform 242.2.g.a.15.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [242,2,Mod(5,242)] 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("242.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(242, base_ring=CyclotomicField(110)) chi = DirichletCharacter(H, H._module([74])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	242.g (of order $55$, degree $40$, minimal)

Newform invariants

comment:select newform

sage:traces = [200] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.93237972891$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$5$ over $\Q(\zeta_{55})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{55}]$

Embedding invariants

Embedding label			15.1
Character	$\chi$	$=$	242.15
Dual form			242.2.g.a.113.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0855750 - 0.996332i) q^{2} +(-0.871571 + 2.68242i) q^{3} +(-0.985354 + 0.170522i) q^{4} +(1.17984 - 0.0674655i) q^{5} +(2.74716 + 0.638826i) q^{6} +(0.234620 + 0.343121i) q^{7} +(0.254218 + 0.967147i) q^{8} +(-4.00869 - 2.91248i) q^{9} +(-0.168183 - 1.16974i) q^{10} +(-0.173957 + 3.31206i) q^{11} +(0.401394 - 2.79175i) q^{12} +(-4.26172 + 4.38520i) q^{13} +(0.321785 - 0.263122i) q^{14} +(-0.847340 + 3.22362i) q^{15} +(0.941844 - 0.336049i) q^{16} +(-0.754691 - 0.426193i) q^{17} +(-2.55875 + 4.24322i) q^{18} +(3.13190 + 2.87443i) q^{19} +(-1.15105 + 0.267666i) q^{20} +(-1.12488 + 0.330295i) q^{21} +(3.31480 - 0.110110i) q^{22} +(3.88627 + 1.14111i) q^{23} +(-2.81586 - 0.161017i) q^{24} +(-3.57995 + 0.410761i) q^{25} +(4.73381 + 3.87082i) q^{26} +(4.46094 - 3.24107i) q^{27} +(-0.289694 - 0.298088i) q^{28} +(-2.06862 - 0.237352i) q^{29} +(3.28430 + 0.568371i) q^{30} +(4.19330 - 7.94718i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(-8.73272 - 3.35332i) q^{33} +(-0.360047 + 0.788394i) q^{34} +(0.299962 + 0.388998i) q^{35} +(4.44662 + 2.18625i) q^{36} +(7.03853 - 3.46061i) q^{37} +(2.59587 - 3.36639i) q^{38} +(-8.04857 - 15.2537i) q^{39} +(0.365185 + 1.12392i) q^{40} +(3.51700 - 1.48630i) q^{41} +(0.425346 + 1.09249i) q^{42} +(-1.35611 + 0.871516i) q^{43} +(-0.393370 - 3.29321i) q^{44} +(-4.92609 - 3.16580i) q^{45} +(0.804358 - 3.96966i) q^{46} +(4.41909 + 7.32824i) q^{47} +(0.0805413 + 2.81931i) q^{48} +(2.47697 - 6.36204i) q^{49} +(0.715608 + 3.53166i) q^{50} +(1.80100 - 1.65294i) q^{51} +(3.45153 - 5.04769i) q^{52} +(0.0254036 + 0.00906398i) q^{53} +(-3.61092 - 4.16723i) q^{54} +(0.0182087 + 3.91943i) q^{55} +(-0.272204 + 0.314140i) q^{56} +(-10.4401 + 5.89579i) q^{57} +(-0.0594591 + 2.08134i) q^{58} +(11.6516 + 4.92403i) q^{59} +(0.285232 - 3.32089i) q^{60} +(0.0849315 - 0.988840i) q^{61} +(-8.27687 - 3.49784i) q^{62} +(0.0588150 - 2.05879i) q^{63} +(-0.870746 + 0.491733i) q^{64} +(-4.73228 + 5.46134i) q^{65} +(-2.59372 + 8.98764i) q^{66} +(-3.90442 - 4.50594i) q^{67} +(0.816313 + 0.291260i) q^{68} +(-6.44810 + 9.43004i) q^{69} +(0.361902 - 0.332151i) q^{70} +(1.91549 + 9.45331i) q^{71} +(1.79772 - 4.61739i) q^{72} +(-0.192621 - 6.74261i) q^{73} +(-4.05024 - 6.71657i) q^{74} +(2.01834 - 9.96092i) q^{75} +(-3.57618 - 2.29827i) q^{76} +(-1.17725 + 0.717388i) q^{77} +(-14.5090 + 9.32438i) q^{78} +(-2.87077 - 7.37351i) q^{79} +(1.08855 - 0.460025i) q^{80} +(0.212322 + 0.653461i) q^{81} +(-1.78181 - 3.37691i) q^{82} +(-4.56586 + 5.92111i) q^{83} +(1.05209 - 0.517275i) q^{84} +(-0.919165 - 0.451923i) q^{85} +(0.984368 + 1.27655i) q^{86} +(2.43962 - 5.34203i) q^{87} +(-3.24747 + 0.673744i) q^{88} +(-4.40062 - 9.63601i) q^{89} +(-2.73264 + 5.17893i) q^{90} +(-2.50454 - 0.433428i) q^{91} +(-4.02393 - 0.461703i) q^{92} +(17.6629 + 18.1747i) q^{93} +(6.92320 - 5.03000i) q^{94} +(3.88905 + 3.18006i) q^{95} +(2.80208 - 0.321509i) q^{96} +(12.9562 + 0.740865i) q^{97} +(-6.55067 - 1.92345i) q^{98} +(10.3437 - 12.7704i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 5 q^{2} + 10 q^{3} + 5 q^{4} - q^{5} + q^{6} - 5 q^{8} - 40 q^{9} - 4 q^{10} - 11 q^{11} + 4 q^{12} - 32 q^{13} - 11 q^{14} - 24 q^{15} + 5 q^{16} + 2 q^{17} - 4 q^{18} + q^{19} - q^{20} - 8 q^{21}+ \cdots + 22 q^{99}+O(q^{100}) $ 200 * q - 5 * q^2 + 10 * q^3 + 5 * q^4 - q^5 + q^6 - 5 * q^8 - 40 * q^9 - 4 * q^10 - 11 * q^11 + 4 * q^12 - 32 * q^13 - 11 * q^14 - 24 * q^15 + 5 * q^16 + 2 * q^17 - 4 * q^18 + q^19 - q^20 - 8 * q^21 - 22 * q^22 + 41 * q^23 + q^24 + 2 * q^25 - q^26 - 59 * q^27 + 3 * q^29 + 13 * q^30 + 18 * q^31 + 20 * q^32 + 8 * q^34 + 4 * q^35 + 4 * q^36 + 17 * q^37 - 34 * q^38 - 172 * q^39 - 10 * q^40 + 6 * q^41 + 42 * q^42 - 20 * q^43 + 11 * q^44 + 64 * q^45 - 9 * q^46 + 7 * q^47 - q^48 - 43 * q^49 - 2 * q^50 - 135 * q^51 + q^52 - 80 * q^53 - 16 * q^54 - 22 * q^55 + 11 * q^56 + 41 * q^57 - 157 * q^58 + 30 * q^59 + 31 * q^60 + 40 * q^61 + 4 * q^62 - 45 * q^63 + 5 * q^64 - 7 * q^65 + 55 * q^66 - 19 * q^67 + 2 * q^68 - 8 * q^69 - 70 * q^70 + 5 * q^71 - 4 * q^72 + 34 * q^73 + 5 * q^74 - 11 * q^75 - 15 * q^76 - 198 * q^77 + 16 * q^78 - 47 * q^79 - q^80 - 18 * q^81 - 28 * q^82 + 9 * q^83 - 174 * q^84 - 100 * q^85 - 5 * q^86 + 37 * q^87 - 11 * q^88 - 67 * q^89 - 28 * q^90 - 166 * q^91 - 46 * q^92 - 47 * q^93 - 18 * q^94 + 129 * q^95 + q^96 - 3 * q^97 - 40 * q^98 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{26}{55}\right)$

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 $

$2$	−0.0855750	−	0.996332i	−0.0605107	−	0.704513i
$2$	−0.0855750	−	0.996332i	−0.0605107	−	0.704513i
$3$	−0.871571	+	2.68242i	−0.503202	+	1.54870i	0.300571	+	0.953759i	$0.402823\pi$
$3$	−0.871571	+	2.68242i	−0.503202	+	1.54870i	−0.803773	+	0.594936i	$0.797177\pi$
$4$	−0.985354	+	0.170522i	−0.492677	+	0.0852611i
$5$	1.17984	−	0.0674655i	0.527639	−	0.0301715i	0.208760	−	0.977967i	$-0.433057\pi$
$5$	1.17984	−	0.0674655i	0.527639	−	0.0301715i	0.318879	+	0.947795i	$0.396694\pi$
$6$	2.74716	+	0.638826i	1.12153	+	0.260799i
$7$	0.234620	+	0.343121i	0.0886781	+	0.129688i	0.867260	−	0.497855i	$-0.165879\pi$
$7$	0.234620	+	0.343121i	0.0886781	+	0.129688i	−0.778582	+	0.627543i	$0.784061\pi$
$8$	0.254218	+	0.967147i	0.0898798	+	0.341938i
$9$	−4.00869	−	2.91248i	−1.33623	−	0.970827i
$10$	−0.168183	−	1.16974i	−0.0531840	−	0.369903i
$11$	−0.173957	+	3.31206i	−0.0524501	+	0.998624i
$11$	−0.173957	+	3.31206i	−0.0524501	+	0.998624i
$12$	0.401394	−	2.79175i	0.115872	−	0.805910i
$13$	−4.26172	+	4.38520i	−1.18199	+	1.21624i	−0.210902	+	0.977507i	$0.567640\pi$
$13$	−4.26172	+	4.38520i	−1.18199	+	1.21624i	−0.971086	+	0.238729i	$0.923269\pi$
$14$	0.321785	−	0.263122i	0.0860006	−	0.0703224i
$15$	−0.847340	+	3.22362i	−0.218782	+	0.832334i
$16$	0.941844	−	0.336049i	0.235461	−	0.0840123i
$17$	−0.754691	−	0.426193i	−0.183039	−	0.103367i	0.397490	−	0.917607i	$-0.369881\pi$
$17$	−0.754691	−	0.426193i	−0.183039	−	0.103367i	−0.580529	+	0.814240i	$0.697154\pi$
$18$	−2.55875	+	4.24322i	−0.603104	+	1.00014i
$19$	3.13190	+	2.87443i	0.718506	+	0.659439i	0.949590	−	0.313495i	$-0.101500\pi$
$19$	3.13190	+	2.87443i	0.718506	+	0.659439i	−0.231084	+	0.972934i	$0.574227\pi$
$20$	−1.15105	+	0.267666i	−0.257383	+	0.0598519i
$21$	−1.12488	+	0.330295i	−0.245470	+	0.0720764i
$22$	3.31480	−	0.110110i	0.706717	−	0.0234756i
$23$	3.88627	+	1.14111i	0.810343	+	0.237938i	0.660553	−	0.750780i	$-0.270322\pi$
$23$	3.88627	+	1.14111i	0.810343	+	0.237938i	0.149790	+	0.988718i	$0.452140\pi$
$24$	−2.81586	−	0.161017i	−0.574786	−	0.0328674i
$25$	−3.57995	+	0.410761i	−0.715989	+	0.0821521i
$26$	4.73381	+	3.87082i	0.928377	+	0.759130i
$27$	4.46094	−	3.24107i	0.858509	−	0.623743i
$28$	−0.289694	−	0.298088i	−0.0547470	−	0.0563333i
$29$	−2.06862	−	0.237352i	−0.384132	−	0.0440751i	−0.0802252	−	0.996777i	$-0.525564\pi$
$29$	−2.06862	−	0.237352i	−0.384132	−	0.0440751i	−0.303907	+	0.952702i	$0.598291\pi$
$30$	3.28430	+	0.568371i	0.599629	+	0.103770i
$31$	4.19330	−	7.94718i	0.753139	−	1.42736i	−0.145815	−	0.989312i	$-0.546580\pi$
$31$	4.19330	−	7.94718i	0.753139	−	1.42736i	0.898953	−	0.438044i	$-0.144329\pi$
$32$	−0.415415	−	0.909632i	−0.0734357	−	0.160802i
$33$	−8.73272	−	3.35332i	−1.52017	−	0.583738i
$34$	−0.360047	+	0.788394i	−0.0617476	+	0.135208i
$35$	0.299962	+	0.388998i	0.0507029	+	0.0657527i
$36$	4.44662	+	2.18625i	0.741103	+	0.364376i
$37$	7.03853	−	3.46061i	1.15713	−	0.568921i	0.241283	−	0.970455i	$-0.422432\pi$
$37$	7.03853	−	3.46061i	1.15713	−	0.568921i	0.915844	+	0.401534i	$0.131523\pi$
$38$	2.59587	−	3.36639i	0.421106	−	0.546100i
$39$	−8.04857	−	15.2537i	−1.28880	−	2.44255i
$40$	0.365185	+	1.12392i	0.0577408	+	0.177708i
$41$	3.51700	−	1.48630i	0.549263	−	0.232121i	−0.0969342	−	0.995291i	$-0.530904\pi$
$41$	3.51700	−	1.48630i	0.549263	−	0.232121i	0.646198	+	0.763170i	$0.276358\pi$
$42$	0.425346	+	1.09249i	0.0656323	+	0.168575i
$43$	−1.35611	+	0.871516i	−0.206804	+	0.132905i	−0.639943	−	0.768422i	$-0.721042\pi$
$43$	−1.35611	+	0.871516i	−0.206804	+	0.132905i	0.433139	+	0.901327i	$0.357406\pi$
$44$	−0.393370	−	3.29321i	−0.0593028	−	0.496471i
$45$	−4.92609	−	3.16580i	−0.734338	−	0.471930i
$46$	0.804358	−	3.96966i	0.118596	−	0.585295i
$47$	4.41909	+	7.32824i	0.644591	+	1.06893i	0.991383	+	0.130992i	$0.0418162\pi$
$47$	4.41909	+	7.32824i	0.644591	+	1.06893i	−0.346793	+	0.937942i	$0.612729\pi$
$48$	0.0805413	+	2.81931i	0.0116251	+	0.406933i
$49$	2.47697	−	6.36204i	0.353853	−	0.908863i
$50$	0.715608	+	3.53166i	0.101202	+	0.499453i
$51$	1.80100	−	1.65294i	0.252190	−	0.231458i
$52$	3.45153	−	5.04769i	0.478640	−	0.699989i
$53$	0.0254036	+	0.00906398i	0.00348945	+	0.00124503i	0.337794	−	0.941220i	$-0.390319\pi$
$53$	0.0254036	+	0.00906398i	0.00348945	+	0.00124503i	−0.334304	+	0.942465i	$0.608501\pi$
$54$	−3.61092	−	4.16723i	−0.491384	−	0.567088i
$55$	0.0182087	+	3.91943i	0.00245526	+	0.528495i
$56$	−0.272204	+	0.314140i	−0.0363748	+	0.0419787i
$57$	−10.4401	+	5.89579i	−1.38282	+	0.780917i
$58$	−0.0594591	+	2.08134i	−0.00780736	+	0.273293i
$59$	11.6516	+	4.92403i	1.51692	+	0.641054i	0.979351	−	0.202169i	$-0.0647989\pi$
$59$	11.6516	+	4.92403i	1.51692	+	0.641054i	0.537565	+	0.843223i	$0.319344\pi$
$60$	0.285232	−	3.32089i	0.0368233	−	0.428726i
$61$	0.0849315	−	0.988840i	0.0108744	−	0.126608i	−0.988881	−	0.148706i	$-0.952489\pi$
$61$	0.0849315	−	0.988840i	0.0108744	−	0.126608i	0.999756	+	0.0220981i	$0.00703463\pi$
$62$	−8.27687	−	3.49784i	−1.05116	−	0.444226i
$63$	0.0588150	−	2.05879i	0.00740999	−	0.259383i
$64$	−0.870746	+	0.491733i	−0.108843	+	0.0614666i
$65$	−4.73228	+	5.46134i	−0.586967	+	0.677396i
$66$	−2.59372	+	8.98764i	−0.319265	+	1.10630i
$67$	−3.90442	−	4.50594i	−0.477001	−	0.550488i	0.465345	−	0.885129i	$-0.345930\pi$
$67$	−3.90442	−	4.50594i	−0.477001	−	0.550488i	−0.942346	+	0.334641i	$0.891385\pi$
$68$	0.816313	+	0.291260i	0.0989925	+	0.0353204i
$69$	−6.44810	+	9.43004i	−0.776260	+	1.13524i
$70$	0.361902	−	0.332151i	0.0432556	−	0.0396996i
$71$	1.91549	+	9.45331i	0.227327	+	1.12190i	0.917340	+	0.398105i	$0.130332\pi$
$71$	1.91549	+	9.45331i	0.227327	+	1.12190i	−0.690013	+	0.723797i	$0.742395\pi$
$72$	1.79772	−	4.61739i	0.211863	−	0.544165i
$73$	−0.192621	−	6.74261i	−0.0225446	−	0.789163i	−0.929689	−	0.368344i	$-0.879925\pi$
$73$	−0.192621	−	6.74261i	−0.0225446	−	0.789163i	0.907145	−	0.420819i	$-0.138257\pi$
$74$	−4.05024	−	6.71657i	−0.470831	−	0.780785i
$75$	2.01834	−	9.96092i	0.233058	−	1.15019i
$76$	−3.57618	−	2.29827i	−0.410216	−	0.263630i
$77$	−1.17725	+	0.717388i	−0.134160	+	0.0817539i
$78$	−14.5090	+	9.32438i	−1.64282	+	1.05578i
$79$	−2.87077	−	7.37351i	−0.322987	−	0.829585i	−0.995950	−	0.0899090i	$-0.971342\pi$
$79$	−2.87077	−	7.37351i	−0.322987	−	0.829585i	0.672963	−	0.739676i	$-0.265021\pi$
$80$	1.08855	−	0.460025i	0.121704	−	0.0514324i
$81$	0.212322	+	0.653461i	0.0235914	+	0.0726068i
$82$	−1.78181	−	3.37691i	−0.196768	−	0.372917i
$83$	−4.56586	+	5.92111i	−0.501168	+	0.649926i	−0.972739	−	0.231902i	$-0.925505\pi$
$83$	−4.56586	+	5.92111i	−0.501168	+	0.649926i	0.471571	+	0.881828i	$0.343687\pi$
$84$	1.05209	−	0.517275i	0.114792	−	0.0564394i
$85$	−0.919165	−	0.451923i	−0.0996974	−	0.0490179i
$86$	0.984368	+	1.27655i	0.106147	+	0.137654i
$87$	2.43962	−	5.34203i	0.261555	−	0.572725i
$88$	−3.24747	+	0.673744i	−0.346182	+	0.0718214i
$89$	−4.40062	−	9.63601i	−0.466464	−	1.02141i	−0.985966	−	0.166945i	$-0.946610\pi$
$89$	−4.40062	−	9.63601i	−0.466464	−	1.02141i	0.519502	−	0.854469i	$-0.326118\pi$
$90$	−2.73264	+	5.17893i	−0.288046	+	0.545907i
$91$	−2.50454	−	0.433428i	−0.262547	−	0.0454356i
$92$	−4.02393	−	0.461703i	−0.419524	−	0.0481359i
$93$	17.6629	+	18.1747i	1.83156	+	1.88463i
$94$	6.92320	−	5.03000i	0.714073	−	0.518805i
$95$	3.88905	+	3.18006i	0.399008	+	0.326267i
$96$	2.80208	−	0.321509i	0.285986	−	0.0328138i
$97$	12.9562	+	0.740865i	1.31551	+	0.0752234i	0.700701	−	0.713455i	$-0.252871\pi$
$97$	12.9562	+	0.740865i	1.31551	+	0.0752234i	0.614806	+	0.788678i	$0.289234\pi$
$98$	−6.55067	−	1.92345i	−0.661718	−	0.194298i
$99$	10.3437	−	12.7704i	1.03958	−	1.28347i
$100$	3.45747	−	1.01520i	0.345747	−	0.101520i
$101$	13.8903	−	3.23004i	1.38213	−	0.321401i	0.531453	−	0.847087i	$-0.321646\pi$
$101$	13.8903	−	3.23004i	1.38213	−	0.321401i	0.850678	+	0.525686i	$0.176191\pi$
$102$	−1.80100	−	1.65294i	−0.178325	−	0.163665i
$103$	0.887830	−	1.47230i	0.0874805	−	0.145070i	−0.809531	−	0.587077i	$-0.800279\pi$
$103$	0.887830	−	1.47230i	0.0874805	−	0.145070i	0.897012	+	0.442007i	$0.145733\pi$
$104$	−5.32454	−	3.00691i	−0.522114	−	0.294852i
$105$	−1.30489	+	0.465585i	−0.127345	+	0.0454365i
$106$	0.00685682	−	0.0260860i	0.000665993	−	0.00253370i
$107$	−13.3716	+	10.9339i	−1.29268	+	1.05702i	−0.297944	+	0.954583i	$0.596301\pi$
$107$	−13.3716	+	10.9339i	−1.29268	+	1.05702i	−0.994739	+	0.102439i	$0.967335\pi$
$108$	−3.84294	+	3.95429i	−0.369787	+	0.380501i
$109$	−1.43518	+	9.98192i	−0.137466	+	0.956094i	0.797995	+	0.602664i	$0.205894\pi$
$109$	−1.43518	+	9.98192i	−0.137466	+	0.956094i	−0.935461	+	0.353430i	$0.885015\pi$
$110$	3.90349	−	0.353547i	0.372183	−	0.0337094i
$111$	3.14824	+	21.8965i	0.298817	+	2.07832i
$112$	0.336281	+	0.244323i	0.0317756	+	0.0230863i
$113$	1.55245	+	5.90612i	0.146042	+	0.555601i	0.999412	+	0.0342951i	$0.0109186\pi$
$113$	1.55245	+	5.90612i	0.146042	+	0.555601i	−0.853370	+	0.521306i	$0.825445\pi$
$114$	6.76758	+	9.89726i	0.633842	+	0.926964i
$115$	4.66215	+	1.08414i	0.434748	+	0.101096i
$116$	2.07879	−	0.118870i	0.193011	−	0.0110368i
$117$	29.8557	−	5.16674i	2.76016	−	0.477665i
$118$	3.90888	−	12.0303i	0.359841	−	1.10748i
$119$	−0.0308297	−	0.358944i	−0.00282616	−	0.0329043i
$120$	−3.33312			−0.304271
$121$	−10.9395	−	1.15231i	−0.994498	−	0.104756i
$122$	−0.992480			−0.0898549
$123$	0.921556	+	10.7295i	0.0830940	+	0.967445i
$124$	−2.77671	+	8.54584i	−0.249356	+	0.767439i
$125$	−10.0183	+	1.73374i	−0.896066	+	0.155070i
$126$	−2.05627	+	0.117582i	−0.183187	+	0.0104750i
$127$	15.0743	+	3.50538i	1.33763	+	0.311053i	0.833473	−	0.552560i	$-0.186349\pi$
$127$	15.0743	+	3.50538i	1.33763	+	0.311053i	0.504157	+	0.863612i	$0.331803\pi$
$128$	0.564443	+	0.825472i	0.0498902	+	0.0729621i
$129$	−1.15583	−	4.39723i	−0.101765	−	0.387155i
$130$	5.84627	+	4.24757i	0.512752	+	0.372536i
$131$	−2.76457	−	19.2280i	−0.241542	−	1.67996i	−0.644393	−	0.764694i	$-0.722890\pi$
$131$	−2.76457	−	19.2280i	−0.241542	−	1.67996i	0.402852	−	0.915265i	$-0.368019\pi$
$132$	9.17663	+	1.81509i	0.798723	+	0.157983i
$133$	−0.251471	+	1.74902i	−0.0218053	+	0.151659i
$134$	−4.15529	+	4.27569i	−0.358962	+	0.369363i
$135$	5.04453	−	4.12489i	0.434164	−	0.355014i
$136$	0.220335	−	0.838243i	0.0188936	−	0.0718787i
$137$	−2.63764	+	0.941107i	−0.225349	+	0.0804042i	−0.446310	−	0.894878i	$-0.647262\pi$
$137$	−2.63764	+	0.941107i	−0.225349	+	0.0804042i	0.220962	+	0.975282i	$0.429080\pi$
$138$	9.94725	+	5.61747i	0.846766	+	0.478191i
$139$	2.89381	−	4.79884i	0.245450	−	0.407033i	−0.709089	−	0.705119i	$-0.750894\pi$
$139$	2.89381	−	4.79884i	0.245450	−	0.407033i	0.954539	+	0.298086i	$0.0963483\pi$
$140$	−0.361902	−	0.332151i	−0.0305863	−	0.0280718i
$141$	−23.5090	+	5.46678i	−1.97981	+	0.460386i
$142$	9.25472	−	2.71743i	0.776639	−	0.228042i
$143$	−13.7827	−	14.8779i	−1.15257	−	1.24415i
$144$	−4.75430	−	1.39599i	−0.396191	−	0.116332i
$145$	−2.45664	−	0.140476i	−0.204013	−	0.0116659i
$146$	−6.70139	+	0.768913i	−0.554611	+	0.0636357i
$147$	14.9068	+	12.1892i	1.22949	+	1.00535i
$148$	−6.34533	+	4.61015i	−0.521583	+	0.378952i
$149$	13.8032	+	14.2032i	1.13081	+	1.16357i	0.984692	+	0.174304i	$0.0557674\pi$
$149$	13.8032	+	14.2032i	1.13081	+	1.16357i	0.146114	+	0.989268i	$0.453323\pi$
$150$	−10.0971	−	1.15853i	−0.824425	−	0.0945940i
$151$	−15.4553	−	2.67465i	−1.25774	−	0.217660i	−0.497590	−	0.867412i	$-0.665782\pi$
$151$	−15.4553	−	2.67465i	−1.25774	−	0.217660i	−0.760146	+	0.649753i	$0.774872\pi$
$152$	−1.98381	+	3.75974i	−0.160908	+	0.304955i
$153$	1.78404	+	3.90650i	0.144231	+	0.315822i
$154$	0.815500	+	1.11154i	0.0657148	+	0.0895707i
$155$	4.41125	−	9.65928i	0.354320	−	0.775852i
$156$	10.5318	+	13.6579i	0.843218	+	1.09350i
$157$	0.418111	+	0.205571i	0.0333689	+	0.0164064i	0.457829	−	0.889040i	$-0.348627\pi$
$157$	0.418111	+	0.205571i	0.0333689	+	0.0164064i	−0.424460	+	0.905446i	$0.639536\pi$
$158$	−7.10080	+	3.49123i	−0.564909	+	0.277747i
$159$	−0.0464544	+	0.0602431i	−0.00368407	+	0.00477759i
$160$	−0.551491	−	1.04519i	−0.0435992	−	0.0826296i
$161$	0.520258	+	1.60119i	0.0410021	+	0.126191i
$162$	0.632894	−	0.267463i	0.0497249	−	0.0210139i
$163$	−3.29630	−	8.46649i	−0.258186	−	0.663147i	0.741785	−	0.670637i	$-0.233979\pi$
$163$	−3.29630	−	8.46649i	−0.258186	−	0.663147i	−0.999972	+	0.00749066i	$0.997616\pi$
$164$	−3.21204	+	2.06426i	−0.250819	+	0.161191i
$165$	−10.5294	−	3.36721i	−0.819714	−	0.262137i
$166$	6.29012	+	4.04241i	0.488208	+	0.313752i
$167$	−3.29736	+	16.2731i	−0.255157	+	1.25925i	0.623510	+	0.781816i	$0.285706\pi$
$167$	−3.29736	+	16.2731i	−0.255157	+	1.25925i	−0.878667	+	0.477435i	$0.841567\pi$
$168$	−0.605410	−	1.00396i	−0.0467084	−	0.0774572i
$169$	−0.696546	−	24.3823i	−0.0535805	−	1.87556i
$170$	−0.371608	+	0.954467i	−0.0285010	+	0.0732042i
$171$	−4.18307	−	20.6443i	−0.319888	−	1.57871i
$172$	1.18763	−	1.09000i	0.0905560	−	0.0831115i
$173$	−5.77627	+	8.44753i	−0.439162	+	0.642254i	−0.980029	−	0.198854i	$-0.936278\pi$
$173$	−5.77627	+	8.44753i	−0.439162	+	0.642254i	0.540867	+	0.841108i	$0.318096\pi$
$174$	−5.53120	−	1.97353i	−0.419319	−	0.149613i
$175$	−0.980868	−	1.13198i	−0.0741467	−	0.0855698i
$176$	0.949175	+	3.17790i	0.0715468	+	0.239543i
$177$	−23.3635	+	26.9630i	−1.75611	+	2.02666i
$178$	−9.22407	+	5.20907i	−0.691374	+	0.390437i
$179$	−0.0130388	+	0.456416i	−0.000974563	+	0.0341142i	−0.999934	−	0.0114948i	$-0.996341\pi$
$179$	−0.0130388	+	0.456416i	−0.000974563	+	0.0341142i	0.998959	+	0.0456090i	$0.0145228\pi$
$180$	5.39378	+	2.27943i	0.402029	+	0.169899i
$181$	1.89522	−	22.0657i	0.140871	−	1.64013i	−0.495402	−	0.868664i	$-0.664979\pi$
$181$	1.89522	−	22.0657i	0.140871	−	1.64013i	0.636273	−	0.771464i	$-0.280475\pi$
$182$	−0.217512	+	2.53244i	−0.0161231	+	0.187717i
$183$	2.57846	+	1.08967i	0.190605	+	0.0805504i
$184$	−0.115662	+	4.04868i	−0.00852669	+	0.298473i
$185$	8.07084	−	4.55781i	0.593380	−	0.335097i
$186$	16.5965	−	19.1534i	1.21692	−	1.40440i
$187$	1.54286	−	2.42544i	0.112825	−	0.177366i
$188$	−5.60400	−	6.46736i	−0.408714	−	0.471681i
$189$	2.15871	+	0.770225i	0.157023	+	0.0560256i
$190$	2.83559	−	4.14692i	0.205715	−	0.300849i
$191$	−7.88091	+	7.23303i	−0.570243	+	0.523364i	−0.908607	−	0.417651i	$-0.862853\pi$
$191$	−7.88091	+	7.23303i	−0.570243	+	0.523364i	0.338365	+	0.941015i	$0.390126\pi$
$192$	−0.560117	−	2.76429i	−0.0404230	−	0.199495i
$193$	−6.18110	+	15.8760i	−0.444925	+	1.14278i	0.513665	+	0.857991i	$0.328288\pi$
$193$	−6.18110	+	15.8760i	−0.444925	+	1.14278i	−0.958590	+	0.284790i	$0.908076\pi$
$194$	−0.370584	−	12.9721i	−0.0266064	−	0.931344i
$195$	−10.5251	−	17.4539i	−0.753718	−	1.24990i
$196$	−1.35582	+	6.69124i	−0.0968444	+	0.477946i
$197$	−0.166658	−	0.107105i	−0.0118739	−	0.00763088i	0.534690	−	0.845048i	$-0.320428\pi$
$197$	−0.166658	−	0.107105i	−0.0118739	−	0.00763088i	−0.546564	+	0.837417i	$0.684065\pi$
$198$	−13.6087	−	9.21288i	−0.967126	−	0.654731i
$199$	−13.5055	+	8.67948i	−0.957381	+	0.615272i	−0.923272	−	0.384146i	$-0.874496\pi$
$199$	−13.5055	+	8.67948i	−0.957381	+	0.615272i	−0.0341092	+	0.999418i	$0.510859\pi$
$200$	−1.30735	−	3.35791i	−0.0924439	−	0.237440i
$201$	15.4898	−	6.54604i	1.09257	−	0.461722i
$202$	−4.40685	−	13.5629i	−0.310065	−	0.954282i
$203$	−0.403899	−	0.765473i	−0.0283481	−	0.0537257i
$204$	−1.49276	+	1.93584i	−0.104514	+	0.135536i
$205$	4.04921	−	1.99086i	0.282809	−	0.139048i
$206$	−1.54288	−	0.758581i	−0.107497	−	0.0528529i
$207$	−12.2554	−	15.8930i	−0.851807	−	1.10464i
$208$	−2.54023	+	5.56233i	−0.176133	+	0.385678i
$209$	−10.0651	+	9.87300i	−0.696217	+	0.682930i
$210$	0.575544	+	1.26027i	0.0397163	+	0.0869666i
$211$	2.44899	−	4.64134i	0.168595	−	0.319523i	−0.785586	−	0.618752i	$-0.787638\pi$
$211$	2.44899	−	4.64134i	0.168595	−	0.319523i	0.954181	+	0.299229i	$0.0967294\pi$
$212$	−0.0265771	−	0.00459935i	−0.00182532	−	0.000315885i
$213$	−27.0272	−	3.10109i	−1.85188	−	0.212483i
$214$	12.0381	+	12.3869i	0.822907	+	0.846751i
$215$	−1.54119	+	1.11974i	−0.105108	+	0.0763654i
$216$	4.26864	+	3.49045i	0.290444	+	0.237495i
$217$	3.71068	−	0.425761i	0.251897	−	0.0289025i
$218$	10.0681	+	0.575716i	0.681899	+	0.0389924i
$219$	18.2544	+	5.35997i	1.23352	+	0.362193i
$220$	−0.686291	−	3.85892i	−0.0462697	−	0.260168i
$221$	5.08522	−	1.49316i	0.342069	−	0.100441i
$222$	21.5467	−	5.01048i	1.44612	−	0.336281i
$223$	16.8487	+	15.4636i	1.12827	+	1.03552i	0.999036	+	0.0439078i	$0.0139808\pi$
$223$	16.8487	+	15.4636i	1.12827	+	1.03552i	0.129239	+	0.991613i	$0.458746\pi$
$224$	0.214649	−	0.355956i	0.0143419	−	0.0237833i
$225$	15.5472	+	8.77992i	1.03648	+	0.585328i
$226$	5.75160	−	2.05217i	0.382591	−	0.136508i
$227$	5.36165	−	20.3978i	0.355865	−	1.35385i	−0.512824	−	0.858494i	$-0.671401\pi$
$227$	5.36165	−	20.3978i	0.355865	−	1.35385i	0.868689	−	0.495358i	$-0.164963\pi$
$228$	9.28182	−	7.58971i	0.614704	−	0.502641i
$229$	−7.98135	+	8.21262i	−0.527423	+	0.542705i	−0.927523	−	0.373766i	$-0.878066\pi$
$229$	−7.98135	+	8.21262i	−0.527423	+	0.542705i	0.400100	+	0.916471i	$0.368975\pi$
$230$	0.681196	−	4.73782i	0.0449167	−	0.312403i
$231$	−0.898277	−	3.78314i	−0.0591023	−	0.248912i
$232$	−0.296326	−	2.06099i	−0.0194548	−	0.135311i
$233$	9.57748	+	6.95845i	0.627442	+	0.455863i	0.855513	−	0.517781i	$-0.173242\pi$
$233$	9.57748	+	6.95845i	0.627442	+	0.455863i	−0.228071	+	0.973644i	$0.573242\pi$
$234$	−7.70269	−	29.3041i	−0.503540	−	1.91567i
$235$	5.70821	+	8.34799i	0.372363	+	0.544563i
$236$	−12.3207	−	2.86504i	−0.802006	−	0.186499i
$237$	22.2809	−	1.27407i	1.44730	−	0.0827597i
$238$	−0.354989	+	0.0614333i	−0.0230105	+	0.00398213i
$239$	1.70927	−	5.26059i	0.110564	−	0.340280i	−0.880432	−	0.474172i	$-0.842748\pi$
$239$	1.70927	−	5.26059i	0.110564	−	0.340280i	0.990996	+	0.133892i	$0.0427476\pi$
$240$	0.285232	+	3.32089i	0.0184116	+	0.214363i
$241$	−2.48185			−0.159870			−0.0799351	−	0.996800i	$-0.525471\pi$
$241$	−2.48185			−0.159870			−0.0799351	+	0.996800i	$0.525471\pi$
$242$	−0.211940	+	10.9980i	−0.0136240	+	0.706976i
$243$	14.6042			0.936859
$244$	0.0849315	+	0.988840i	0.00543718	+	0.0633040i
$245$	2.49320	−	7.67328i	0.159285	−	0.490228i
$246$	10.6113	−	1.83635i	0.676550	−	0.117082i
$247$	−25.9522	+	1.48400i	−1.65130	+	0.0944248i
$248$	8.75211	+	2.03522i	0.555759	+	0.129236i
$249$	−11.9034	−	17.4082i	−0.754350	−	1.10320i
$250$	2.58470	+	9.83320i	0.163471	+	0.621906i
$251$	10.2523	+	7.44873i	0.647119	+	0.470160i	0.862289	−	0.506417i	$-0.169030\pi$
$251$	10.2523	+	7.44873i	0.647119	+	0.470160i	−0.215169	+	0.976577i	$0.569030\pi$
$252$	0.293116	+	2.03867i	0.0184646	+	0.128424i
$253$	−4.45547	+	12.6730i	−0.280113	+	0.796748i
$254$	2.20254	−	15.3190i	0.138200	−	0.961200i
$255$	2.01336	−	2.07170i	0.126082	−	0.129735i
$256$	0.774142	−	0.633012i	0.0483839	−	0.0395633i
$257$	5.99569	−	22.8100i	0.374001	−	1.42285i	−0.468171	−	0.883638i	$-0.655087\pi$
$257$	5.99569	−	22.8100i	0.374001	−	1.42285i	0.842172	−	0.539209i	$-0.181277\pi$
$258$	−4.28219	+	1.52788i	−0.266598	+	0.0951218i
$259$	2.83879	+	1.60314i	0.176394	+	0.0996142i
$260$	3.73169	−	6.18831i	0.231430	−	0.383783i
$261$	7.60115	+	6.97627i	0.470499	+	0.431820i
$262$	−18.9209	+	4.39987i	−1.16894	+	0.271825i
$263$	−0.284027	+	0.0833979i	−0.0175139	+	0.00514254i	−0.290478	−	0.956882i	$-0.593814\pi$
$263$	−0.284027	+	0.0833979i	−0.0175139	+	0.00514254i	0.272964	+	0.962024i	$0.411996\pi$
$264$	1.02314	−	9.29830i	0.0629697	−	0.572271i
$265$	0.0305836	+	0.00898015i	0.00187873	+	0.000551646i
$266$	1.76412	+	0.100876i	0.108165	+	0.00618512i
$267$	29.6833	−	3.40584i	1.81659	−	0.208434i
$268$	4.61560	+	3.77415i	0.281942	+	0.230543i
$269$	3.51758	−	2.55567i	0.214471	−	0.155822i	−0.475363	−	0.879790i	$-0.657683\pi$
$269$	3.51758	−	2.55567i	0.214471	−	0.155822i	0.689834	+	0.723967i	$0.257683\pi$
$270$	−4.54144	−	4.67303i	−0.276383	−	0.284392i
$271$	−25.7731	−	2.95719i	−1.56560	−	0.179636i	−0.712611	−	0.701559i	$-0.752488\pi$
$271$	−25.7731	−	2.95719i	−1.56560	−	0.179636i	−0.852993	+	0.521923i	$0.825215\pi$
$272$	−0.854023	−	0.147795i	−0.0517828	−	0.00896136i
$273$	3.34552	−	6.34047i	0.202480	−	0.383743i
$274$	1.16337	+	2.54743i	0.0702818	+	0.153896i
$275$	−0.737706	−	11.9284i	−0.0444853	−	0.719313i
$276$	4.74563	−	10.3915i	0.285653	−	0.625493i
$277$	−13.1159	−	17.0090i	−0.788060	−	1.02197i	−0.999010	−	0.0444778i	$-0.985838\pi$
$277$	−13.1159	−	17.0090i	−0.788060	−	1.02197i	0.210950	−	0.977497i	$-0.432344\pi$
$278$	−5.02888	−	2.47253i	−0.301612	−	0.148293i
$279$	−39.9556	+	19.6449i	−2.39208	+	1.17611i
$280$	−0.299962	+	0.388998i	−0.0179262	+	0.0232471i
$281$	−9.23069	−	17.4941i	−0.550657	−	1.04361i	−0.989430	−	0.145012i	$-0.953678\pi$
$281$	−9.23069	−	17.4941i	−0.550657	−	1.04361i	0.438773	−	0.898598i	$-0.355413\pi$
$282$	7.45850	+	22.9549i	0.444147	+	1.36695i
$283$	29.9963	−	12.6765i	1.78309	−	0.753541i	0.793694	−	0.608318i	$-0.208155\pi$
$283$	29.9963	−	12.6765i	1.78309	−	0.753541i	0.989399	−	0.145223i	$-0.0463901\pi$
$284$	−3.49943	−	8.98823i	−0.207653	−	0.533353i
$285$	−11.9198	+	7.66042i	−0.706071	+	0.453764i
$286$	−13.6439	+	15.0053i	−0.806779	+	0.887283i
$287$	1.33514	+	0.858042i	0.0788108	+	0.0506486i
$288$	−0.984018	+	4.85632i	−0.0579838	+	0.286161i
$289$	−8.39084	−	13.9146i	−0.493579	−	0.818509i
$290$	0.0702666	+	2.45965i	0.00412620	+	0.144436i
$291$	−13.2796	+	34.1084i	−0.778464	+	1.99947i
$292$	1.33956	+	6.61101i	0.0783921	+	0.386880i
$293$	16.0359	−	14.7176i	0.936827	−	0.859812i	−0.0534995	−	0.998568i	$-0.517038\pi$
$293$	16.0359	−	14.7176i	0.936827	−	0.859812i	0.990327	+	0.138756i	$0.0443103\pi$
$294$	10.8689	−	15.8952i	0.633886	−	0.927028i
$295$	14.0792	+	5.02346i	0.819725	+	0.292477i
$296$	5.13624	+	5.92754i	0.298538	+	0.344531i
$297$	9.95859	+	15.3387i	0.577856	+	0.890043i
$298$	12.9699	−	14.9680i	0.751325	−	0.867076i
$299$	−21.5662	+	12.1790i	−1.24720	+	0.704329i
$300$	−0.290225	+	10.1592i	−0.0167562	+	0.586542i
$301$	−0.617205	−	0.260833i	−0.0355751	−	0.0150342i
$302$	−1.34225	+	15.6275i	−0.0772376	+	0.899262i
$303$	−3.44202	+	40.0747i	−0.197739	+	2.30223i
$304$	3.91571	+	1.65479i	0.224581	+	0.0949089i
$305$	0.0334927	−	1.17240i	0.00191779	−	0.0671314i
$306$	3.73950	−	2.11179i	0.213773	−	0.120723i
$307$	−12.7471	+	14.7110i	−0.727518	+	0.839601i	−0.992190	−	0.124738i	$-0.960191\pi$
$307$	−12.7471	+	14.7110i	−0.727518	+	0.839601i	0.264672	+	0.964339i	$0.414736\pi$
$308$	1.03768	−	0.907628i	0.0591272	−	0.0517169i
$309$	3.17552	+	3.66475i	0.180649	+	0.208480i
$310$	−10.0013	−	3.56847i	−0.568038	−	0.202676i
$311$	−2.98005	+	4.35818i	−0.168983	+	0.247130i	−0.900663	−	0.434519i	$-0.856918\pi$
$311$	−2.98005	+	4.35818i	−0.168983	+	0.247130i	0.731680	+	0.681648i	$0.238737\pi$
$312$	12.7065	−	11.6619i	0.719364	−	0.660226i
$313$	2.36595	+	11.6764i	0.133732	+	0.659991i	0.989723	+	0.143001i	$0.0456751\pi$
$313$	2.36595	+	11.6764i	0.133732	+	0.659991i	−0.855991	+	0.516991i	$0.827052\pi$
$314$	0.169037	−	0.434169i	0.00953932	−	0.0245016i
$315$	−0.0695054	−	2.43301i	−0.00391619	−	0.137084i
$316$	4.08607	+	6.77599i	0.229860	+	0.381179i
$317$	−0.570525	+	2.81565i	−0.0320439	+	0.158143i	−0.992910	−	0.118872i	$-0.962072\pi$
$317$	−0.570525	+	2.81565i	−0.0320439	+	0.158143i	0.960866	+	0.277014i	$0.0893450\pi$
$318$	0.0639975	+	0.0411287i	0.00358880	+	0.00230638i
$319$	1.14597	−	6.81009i	0.0641622	−	0.381292i
$320$	−0.994163	+	0.638910i	−0.0555754	+	0.0357161i
$321$	−17.6750	−	45.3980i	−0.986525	−	2.53387i
$322$	1.55079	−	0.655371i	0.0864224	−	0.0365224i
$323$	−1.13855	−	3.50410i	−0.0633507	−	0.194973i
$324$	−0.320642	−	0.607685i	−0.0178135	−	0.0337603i
$325$	13.4555	−	17.4493i	0.746374	−	0.967915i
$326$	−8.15335	+	4.00873i	−0.451572	+	0.222023i
$327$	−25.5248	−	12.5497i	−1.41153	−	0.694001i
$328$	2.33155	+	3.02361i	0.128739	+	0.166951i
$329$	−1.47767	+	3.23564i	−0.0814664	+	0.178387i
$330$	−2.45381	+	10.7789i	−0.135078	+	0.593361i
$331$	13.2501	+	29.0138i	0.728293	+	1.59474i	0.801904	+	0.597453i	$0.203821\pi$
$331$	13.2501	+	29.0138i	0.728293	+	1.59474i	−0.0736105	+	0.997287i	$0.523452\pi$
$332$	3.48931	−	6.61297i	0.191501	−	0.362934i
$333$	−38.2942	−	6.62708i	−2.09851	−	0.363162i
$334$	16.4956	+	1.89269i	0.902598	+	0.103563i
$335$	−4.91057	−	5.05286i	−0.268293	−	0.276067i
$336$	−0.948469	+	0.689103i	−0.0517432	+	0.0375937i
$337$	12.2392	+	10.0080i	0.666714	+	0.545169i	0.904673	−	0.426106i	$-0.140115\pi$
$337$	12.2392	+	10.0080i	0.666714	+	0.545169i	−0.237959	+	0.971275i	$0.576478\pi$
$338$	−24.2333	+	2.78051i	−1.31812	+	0.151240i
$339$	−17.1958	−	0.983289i	−0.933945	−	0.0534049i
$340$	0.982766	+	0.288566i	0.0532980	+	0.0156497i
$341$	25.5921	+	15.2709i	1.38589	+	0.826967i
$342$	−20.2106	+	5.93436i	−1.09286	+	0.320894i
$343$	5.59815	−	1.30179i	0.302272	−	0.0702903i
$344$	−1.18763	−	1.09000i	−0.0640328	−	0.0587687i
$345$	−6.97150	+	11.5609i	−0.375333	+	0.622420i
$346$	8.91085	+	5.03219i	0.479050	+	0.270532i
$347$	−21.5347	+	7.68355i	−1.15604	+	0.412475i	−0.843342	−	0.537378i	$-0.819415\pi$
$347$	−21.5347	+	7.68355i	−1.15604	+	0.412475i	−0.312699	+	0.949852i	$0.601233\pi$
$348$	−1.49296	+	5.67980i	−0.0800309	+	0.304469i
$349$	−4.89258	+	4.00064i	−0.261894	+	0.214149i	−0.754838	−	0.655912i	$-0.772284\pi$
$349$	−4.89258	+	4.00064i	−0.261894	+	0.214149i	0.492944	+	0.870061i	$0.335921\pi$
$350$	−1.04389	+	1.07414i	−0.0557984	+	0.0574152i
$351$	−4.79855	+	33.3747i	−0.256128	+	1.78141i
$352$	3.08502	−	1.21764i	0.164432	−	0.0649005i
$353$	2.42130	+	16.8405i	0.128873	+	0.896331i	0.946986	+	0.321274i	$0.104111\pi$
$353$	2.42130	+	16.8405i	0.128873	+	0.896331i	−0.818113	+	0.575057i	$0.804980\pi$
$354$	28.8634	+	20.9705i	1.53407	+	1.11457i
$355$	2.89774	+	11.0241i	0.153796	+	0.585100i
$356$	5.97932	+	8.74447i	0.316903	+	0.463456i
$357$	0.989709	+	0.230147i	0.0523809	+	0.0121807i
$358$	0.455858	−	0.0260669i	0.0240928	−	0.00137768i
$359$	9.97975	−	1.72706i	0.526711	−	0.0911510i	0.0990367	−	0.995084i	$-0.468424\pi$
$359$	9.97975	−	1.72706i	0.526711	−	0.0911510i	0.427674	+	0.903933i	$0.359333\pi$
$360$	1.80950	−	5.56906i	0.0953688	−	0.293515i
$361$	−0.0794889	−	0.925473i	−0.00418363	−	0.0487091i
$362$	−22.1469			−1.16402
$363$	12.6255	−	28.3399i	0.662668	−	1.48746i
$364$	2.54177			0.133225
$365$	−0.682155	−	7.94218i	−0.0357056	−	0.415713i
$366$	0.865017	−	2.66225i	0.0452152	−	0.139158i
$367$	−23.7462	+	4.10945i	−1.23954	+	0.214512i	−0.752339	−	0.658776i	$-0.771074\pi$
$367$	−23.7462	+	4.10945i	−1.23954	+	0.214512i	−0.487205	+	0.873288i	$0.661984\pi$
$368$	4.04373	−	0.231229i	0.210794	−	0.0120536i
$369$	−18.4274	−	4.28510i	−0.959291	−	0.223073i
$370$	−5.23176	−	7.65120i	−0.271986	−	0.397767i
$371$	0.00285015	+	0.0108431i	0.000147972	+	0.000562946i
$372$	−20.5034	−	14.8966i	−1.06305	−	0.772353i
$373$	−4.07061	−	28.3117i	−0.210768	−	1.46592i	−0.770601	−	0.637318i	$-0.780044\pi$
$373$	−4.07061	−	28.3117i	−0.210768	−	1.46592i	0.559833	−	0.828606i	$-0.310865\pi$
$374$	−2.54857	−	1.32965i	−0.131784	−	0.0687543i
$375$	4.08106	−	28.3844i	0.210745	−	1.46576i
$376$	−5.96407	+	6.13688i	−0.307574	+	0.316486i
$377$	9.85669	−	8.05978i	0.507645	−	0.415100i
$378$	0.582668	−	2.21670i	0.0299692	−	0.114015i
$379$	8.37715	−	2.98896i	0.430305	−	0.153533i	−0.112011	−	0.993707i	$-0.535729\pi$
$379$	8.37715	−	2.98896i	0.430305	−	0.153533i	0.542316	+	0.840174i	$0.317547\pi$
$380$	−4.37436	−	2.47032i	−0.224400	−	0.126725i
$381$	−22.5413	+	37.3805i	−1.15482	+	1.91506i
$382$	7.88091	+	7.23303i	0.403222	+	0.370074i
$383$	33.3897	−	7.76444i	1.70613	−	0.396744i	0.743754	−	0.668453i	$-0.233043\pi$
$383$	33.3897	−	7.76444i	1.70613	−	0.396744i	0.962380	+	0.271709i	$0.0875887\pi$
$384$	−2.70621	+	0.794616i	−0.138101	+	0.0405501i
$385$	−1.34057	+	0.925824i	−0.0683216	+	0.0471844i
$386$	16.3467	+	4.79983i	0.832027	+	0.244305i
$387$	7.97447	+	0.455997i	0.405365	+	0.0231796i
$388$	−12.8928	+	1.47931i	−0.654534	+	0.0751008i
$389$	3.90341	+	3.19180i	0.197911	+	0.161831i	0.726775	−	0.686876i	$-0.241018\pi$
$389$	3.90341	+	3.19180i	0.197911	+	0.161831i	−0.528864	+	0.848706i	$0.677382\pi$
$390$	−16.4892	+	11.9801i	−0.834963	+	0.606636i
$391$	−2.44660	−	2.51749i	−0.123730	−	0.127315i
$392$	6.78272	+	0.778245i	0.342579	+	0.0393073i
$393$	53.9871	+	9.34284i	2.72329	+	0.471284i
$394$	−0.0924499	+	0.175212i	−0.00465756	+	0.00882706i
$395$	−3.88450	−	8.50586i	−0.195450	−	0.427976i
$396$	−8.01453	+	14.3471i	−0.402745	+	0.720971i
$397$	12.4792	−	27.3256i	0.626311	−	1.37143i	−0.284528	−	0.958668i	$-0.591837\pi$
$397$	12.4792	−	27.3256i	0.626311	−	1.37143i	0.910839	−	0.412762i	$-0.135436\pi$
$398$	9.80337	+	12.7132i	0.491399	+	0.637257i
$399$	−4.47243	−	2.19895i	−0.223901	−	0.110085i
$400$	−3.23372	+	1.58991i	−0.161686	+	0.0794956i
$401$	22.9855	−	29.8081i	1.14784	−	1.48854i	0.303422	−	0.952856i	$-0.401871\pi$
$401$	22.9855	−	29.8081i	1.14784	−	1.48854i	0.844416	−	0.535687i	$-0.179947\pi$
$402$	−7.84757	−	14.8728i	−0.391401	−	0.741788i
$403$	16.9794	+	52.2571i	0.845802	+	2.60311i
$404$	−13.1360	+	5.55133i	−0.653541	+	0.276189i
$405$	0.294592	+	0.756653i	0.0146384	+	0.0375984i
$406$	−0.728102	+	0.467923i	−0.0361351	+	0.0232226i
$407$	10.2374	+	23.9140i	0.507447	+	1.18537i
$408$	2.05648	+	1.32162i	0.101811	+	0.0654299i
$409$	0.788259	−	3.89021i	0.0389769	−	0.192359i	−0.955863	−	0.293811i	$-0.905076\pi$
$409$	0.788259	−	3.89021i	0.0389769	−	0.192359i	0.994840	+	0.101453i	$0.0323490\pi$
$410$	−2.33007	−	3.86399i	−0.115074	−	0.190829i
$411$	−0.225556	−	7.89549i	−0.0111259	−	0.389456i
$412$	−0.623767	+	1.60213i	−0.0307308	+	0.0789314i
$413$	1.04417	+	5.15320i	0.0513805	+	0.253573i
$414$	−14.7860	+	13.5705i	−0.726692	+	0.666952i
$415$	−4.98750	+	7.29398i	−0.244827	+	0.358048i
$416$	5.75930	+	2.05492i	0.282373	+	0.100751i
$417$	10.3503	+	11.9449i	0.506859	+	0.584946i
$418$	10.6981	+	9.18329i	0.523261	+	0.449170i
$419$	3.66210	−	4.22629i	0.178905	−	0.206468i	−0.659213	−	0.751956i	$-0.729110\pi$
$419$	3.66210	−	4.22629i	0.178905	−	0.206468i	0.838118	+	0.545489i	$0.183656\pi$
$420$	1.20639	−	0.681280i	0.0588658	−	0.0332431i
$421$	−0.660438	+	23.1184i	−0.0321878	+	1.12672i	0.809624	+	0.586949i	$0.199671\pi$
$421$	−0.660438	+	23.1184i	−0.0321878	+	1.12672i	−0.841812	+	0.539771i	$0.818511\pi$
$422$	−4.83389	−	2.04282i	−0.235310	−	0.0994429i
$423$	3.62861	−	42.2472i	0.176429	−	2.05413i
$424$	−0.00230814	+	0.0268732i	−0.000112093	+	0.00130508i
$425$	2.87682	+	1.21575i	0.139546	+	0.0589726i
$426$	−0.776855	+	27.1935i	−0.0376387	+	1.31753i
$427$	0.359218	−	0.202860i	0.0173838	−	0.00981708i
$428$	11.3113	−	13.0539i	0.546753	−	0.630986i
$429$	51.9214	−	24.0038i	2.50679	−	1.15892i
$430$	1.24752	+	1.43971i	0.0601606	+	0.0694290i
$431$	20.7126	+	7.39024i	0.997691	+	0.355975i	0.783889	−	0.620902i	$-0.213233\pi$
$431$	20.7126	+	7.39024i	0.997691	+	0.355975i	0.213802	+	0.976877i	$0.431415\pi$
$432$	3.11236	−	4.55168i	0.149743	−	0.218993i
$433$	9.24461	−	8.48463i	0.444268	−	0.407745i	−0.422574	−	0.906328i	$-0.638873\pi$
$433$	9.24461	−	8.48463i	0.444268	−	0.407745i	0.866842	+	0.498583i	$0.166146\pi$
$434$	−0.741740	−	3.66063i	−0.0356047	−	0.175716i
$435$	2.51795	−	6.46731i	0.120727	−	0.310084i
$436$	−0.287975	−	10.0805i	−0.0137915	−	0.482766i
$437$	8.89135	+	14.7446i	0.425331	+	0.705332i
$438$	3.77819	−	18.6461i	0.180529	−	0.890946i
$439$	−10.2608	−	6.59419i	−0.489719	−	0.314723i	0.272373	−	0.962192i	$-0.412191\pi$
$439$	−10.2608	−	6.59419i	−0.489719	−	0.314723i	−0.762092	+	0.647468i	$0.775828\pi$
$440$	−3.78603	+	1.01400i	−0.180492	+	0.0483406i
$441$	−28.4587	+	18.2893i	−1.35518	+	0.870919i
$442$	−1.92285	−	4.93879i	−0.0914605	−	0.234914i
$443$	−5.86924	+	2.48036i	−0.278856	+	0.117846i	−0.524213	−	0.851587i	$-0.675640\pi$
$443$	−5.86924	+	2.48036i	−0.278856	+	0.117846i	0.245357	+	0.969433i	$0.421095\pi$
$444$	−6.83596	−	21.0389i	−0.324420	−	0.998463i
$445$	−5.84211	−	11.0720i	−0.276942	−	0.524864i
$446$	13.9651	−	18.1102i	0.661265	−	0.857544i
$447$	−50.1294	+	24.6470i	−2.37104	+	1.16576i
$448$	−0.373019	−	0.183401i	−0.0176235	−	0.00866488i
$449$	12.9629	+	16.8106i	0.611758	+	0.793342i	0.991270	−	0.131845i	$-0.0420901\pi$
$449$	12.9629	+	16.8106i	0.611758	+	0.793342i	−0.379513	+	0.925187i	$0.623908\pi$
$450$	7.41726	−	16.2415i	0.349653	−	0.765633i
$451$	4.31090	+	11.9071i	0.202992	+	0.560682i
$452$	−2.53683	−	5.55489i	−0.119323	−	0.261280i
$453$	20.6449	−	39.1265i	0.969983	−	1.83832i
$454$	−20.7818	−	3.59644i	−0.975340	−	0.168789i
$455$	−2.98419	−	0.342404i	−0.139901	−	0.0160521i
$456$	−8.35616	−	8.59829i	−0.391313	−	0.402652i
$457$	−20.0634	+	14.5769i	−0.938526	+	0.681879i	−0.948065	−	0.318076i	$-0.896963\pi$
$457$	−20.0634	+	14.5769i	−0.938526	+	0.681879i	0.00953972	+	0.999954i	$0.496963\pi$
$458$	8.86550	+	7.24928i	0.414257	+	0.338737i
$459$	−4.74795	+	0.544777i	−0.221616	+	0.0254280i
$460$	−4.77873	−	0.273258i	−0.222810	−	0.0127407i
$461$	−26.5686	−	7.80125i	−1.23742	−	0.363340i	−0.403377	−	0.915034i	$-0.632164\pi$
$461$	−26.5686	−	7.80125i	−1.23742	−	0.363340i	−0.834047	+	0.551694i	$0.813982\pi$
$462$	−3.69239	+	1.21872i	−0.171786	+	0.0567002i
$463$	5.79371	−	1.70119i	0.269256	−	0.0790608i	−0.144317	−	0.989531i	$-0.546099\pi$
$463$	5.79371	−	1.70119i	0.269256	−	0.0790608i	0.413574	+	0.910471i	$0.364280\pi$
$464$	−2.02808	+	0.471609i	−0.0941511	+	0.0218939i
$465$	22.0655	+	20.2516i	1.02326	+	0.939143i
$466$	6.11333	−	10.1378i	0.283195	−	0.469625i
$467$	−32.6953	−	18.4639i	−1.51296	−	0.854407i	−0.512966	−	0.858409i	$-0.671453\pi$
$467$	−32.6953	−	18.4639i	−1.51296	−	0.854407i	−0.999992	+	0.00400240i	$0.998726\pi$
$468$	−28.5374	+	10.1821i	−1.31914	+	0.470669i
$469$	0.630027	−	2.39687i	0.0290920	−	0.110677i
$470$	7.82889	−	6.40165i	0.361120	−	0.295286i
$471$	−0.915841	+	0.942378i	−0.0421997	+	0.0434225i
$472$	−1.80020	+	12.5206i	−0.0828607	+	0.576309i
$473$	−2.65061	−	4.64311i	−0.121875	−	0.213490i
$474$	−3.17609	−	22.0902i	−0.145883	−	1.01464i
$475$	−12.3927	−	9.00384i	−0.568617	−	0.413125i
$476$	0.0915861	+	0.348430i	0.00419784	+	0.0159702i
$477$	−0.0754363	−	0.110322i	−0.00345399	−	0.00505130i
$478$	−5.38757	−	1.25283i	−0.246422	−	0.0573029i
$479$	5.15579	−	0.294819i	0.235574	−	0.0134706i	0.0610970	−	0.998132i	$-0.480540\pi$
$479$	5.15579	−	0.294819i	0.235574	−	0.0134706i	0.174477	+	0.984661i	$0.444176\pi$
$480$	3.28430	−	0.568371i	0.149907	−	0.0259425i
$481$	−14.8207	+	45.6135i	−0.675767	+	2.07980i
$482$	0.212385	+	2.47275i	0.00967385	+	0.112631i
$483$	−4.74850			−0.216064
$484$	10.9758	−	0.729987i	0.498898	−	0.0331812i
$485$	15.3362			0.696383
$486$	−1.24975	−	14.5506i	−0.0566899	−	0.660029i
$487$	−3.95429	+	12.1701i	−0.179186	+	0.551478i	−0.999800	−	0.0200051i	$-0.993632\pi$
$487$	−3.95429	+	12.1701i	−0.179186	+	0.551478i	0.820614	+	0.571483i	$0.193632\pi$
$488$	0.977944	−	0.169240i	0.0442695	−	0.00766113i
$489$	25.5836	−	1.46293i	1.15693	−	0.0661558i
$490$	−7.85849	−	1.82741i	−0.355010	−	0.0825541i
$491$	−4.17928	−	6.11200i	−0.188608	−	0.275831i	0.719565	−	0.694425i	$-0.244341\pi$
$491$	−4.17928	−	6.11200i	−0.188608	−	0.275831i	−0.908173	+	0.418594i	$0.862523\pi$
$492$	−2.73767	−	10.4152i	−0.123424	−	0.469553i
$493$	1.46001	+	1.06076i	0.0657554	+	0.0477741i
$494$	3.69942	+	25.7300i	0.166445	+	1.15765i
$495$	11.3423	−	15.7648i	0.509797	−	0.708574i
$496$	1.27879	−	8.89416i	0.0574193	−	0.399360i
$497$	−2.79422	+	2.87518i	−0.125338	+	0.128970i
$498$	−16.3257	+	13.3495i	−0.731573	+	0.598204i
$499$	11.0084	−	41.8802i	0.492802	−	1.87481i	0.00840836	−	0.999965i	$-0.497324\pi$
$499$	11.0084	−	41.8802i	0.492802	−	1.87481i	0.484394	−	0.874850i	$-0.339040\pi$
$500$	9.57595	−	3.41669i	0.428249	−	0.152799i
$501$	−40.7774	−	23.0281i	−1.82180	−	1.02882i
$502$	6.54407	−	10.8521i	0.292076	−	0.484354i
$503$	−20.4651	−	18.7827i	−0.912492	−	0.837478i	0.0746687	−	0.997208i	$-0.476210\pi$
$503$	−20.4651	−	18.7827i	−0.912492	−	0.837478i	−0.987161	+	0.159731i	$0.948937\pi$
$504$	2.00611	−	0.466500i	0.0893591	−	0.0207796i
$505$	16.1703	−	4.74803i	0.719569	−	0.211285i
$506$	13.0078	+	3.35463i	0.578269	+	0.149132i
$507$	66.0107	+	19.3825i	2.93164	+	0.860806i
$508$	−15.4513	−	0.883537i	−0.685540	−	0.0392006i
$509$	17.6418	−	2.02420i	0.781957	−	0.0897212i	0.286185	−	0.958174i	$-0.407613\pi$
$509$	17.6418	−	2.02420i	0.781957	−	0.0897212i	0.495771	+	0.868453i	$0.334885\pi$
$510$	−2.23640	−	1.82869i	−0.0990293	−	0.0809759i
$511$	2.26834	−	1.64805i	0.100345	−	0.0729052i
$512$	−0.696938	−	0.717132i	−0.0308006	−	0.0316930i
$513$	23.2874	+	2.67198i	1.02817	+	0.117971i
$514$	−23.2394	−	4.02173i	−1.02504	−	0.177391i
$515$	0.948165	−	1.79697i	0.0417811	−	0.0791841i
$516$	1.88873	+	4.13573i	0.0831465	+	0.182066i
$517$	−25.0403	+	13.3615i	−1.10127	+	0.587638i
$518$	1.35433	−	2.96557i	0.0595058	−	0.130299i
$519$	−17.6254	−	22.8570i	−0.773669	−	1.00331i
$520$	−6.48495	−	3.18844i	−0.284384	−	0.139822i
$521$	−5.60258	+	2.75460i	−0.245454	+	0.120681i	−0.559802	−	0.828626i	$-0.689123\pi$
$521$	−5.60258	+	2.75460i	−0.245454	+	0.120681i	0.314349	+	0.949308i	$0.398214\pi$
$522$	6.30021	−	8.17026i	0.275753	−	0.357603i
$523$	11.3876	+	21.5819i	0.497944	+	0.943709i	0.997019	+	0.0771501i	$0.0245821\pi$
$523$	11.3876	+	21.5819i	0.497944	+	0.943709i	−0.499076	+	0.866558i	$0.666327\pi$
$524$	6.00288	+	18.4750i	0.262237	+	0.807083i
$525$	3.89135	−	1.64450i	0.169832	−	0.0717718i
$526$	0.107398	+	0.275849i	0.00468276	+	0.0120276i
$527$	−6.55168	+	4.21051i	−0.285396	+	0.183413i
$528$	−9.35174	−	0.223682i	−0.406982	−	0.00973452i
$529$	−5.54788	−	3.56541i	−0.241212	−	0.155018i
$530$	0.00633002	−	0.0312399i	0.000274958	−	0.00135697i
$531$	−32.3667	−	53.6741i	−1.40459	−	2.32926i
$532$	−0.0504587	−	1.76628i	−0.00218766	−	0.0765781i
$533$	−8.47075	+	21.7570i	−0.366909	+	0.942398i
$534$	−5.93349	−	29.2829i	−0.256767	−	1.26720i
$535$	−15.0387	+	13.8024i	−0.650178	+	0.596728i
$536$	3.36533	−	4.92164i	0.145360	−	0.212582i
$537$	−1.21294	−	0.432775i	−0.0523420	−	0.0186756i
$538$	−2.84732	−	3.28598i	−0.122757	−	0.141669i
$539$	20.6406	+	9.31059i	0.889053	+	0.401036i
$540$	−4.26726	+	4.92468i	−0.183634	+	0.211924i
$541$	−8.19648	+	4.62877i	−0.352394	+	0.199006i	−0.657758	−	0.753230i	$-0.728495\pi$
$541$	−8.19648	+	4.62877i	−0.352394	+	0.199006i	0.305363	+	0.952236i	$0.401222\pi$
$542$	−0.740807	+	25.9316i	−0.0318204	+	1.11386i
$543$	57.5375	+	24.3156i	2.46917	+	1.04348i
$544$	−0.0741693	+	0.863538i	−0.00317998	+	0.0370239i
$545$	−1.01985	+	11.8739i	−0.0436854	+	0.508620i
$546$	−6.60350	−	2.79066i	−0.282604	−	0.119429i
$547$	0.119967	−	4.19941i	0.00512944	−	0.179554i	−0.992988	−	0.118218i	$-0.962282\pi$
$547$	0.119967	−	4.19941i	0.00512944	−	0.179554i	0.998117	−	0.0613362i	$-0.0195362\pi$
$548$	2.43853	−	1.37710i	0.104169	−	0.0588268i
$549$	−3.22044	+	3.71659i	−0.137445	+	0.158620i
$550$	−11.8216	+	1.75578i	−0.504073	+	0.0748666i
$551$	−5.79644	−	6.68945i	−0.246937	−	0.284980i
$552$	−10.7595	−	3.83897i	−0.457953	−	0.163397i
$553$	1.85647	−	2.71500i	0.0789450	−	0.115453i
$554$	−15.8243	+	14.5234i	−0.672308	+	0.617039i
$555$	5.19166	+	25.6218i	0.220374	+	1.08759i
$556$	−2.03312	+	5.22202i	−0.0862233	+	0.221463i
$557$	−0.398376	−	13.9450i	−0.0168797	−	0.590868i	−0.963376	−	0.268154i	$-0.913587\pi$
$557$	−0.398376	−	13.9450i	−0.0168797	−	0.590868i	0.946496	−	0.322714i	$-0.104595\pi$
$558$	22.9920	+	38.1280i	0.973329	+	1.61409i
$559$	1.95756	−	9.66095i	0.0827961	−	0.408615i
$560$	0.413240	+	0.265574i	0.0174626	+	0.0112225i
$561$	5.16134	+	6.25255i	0.217912	+	0.263983i
$562$	−16.6400	+	10.6939i	−0.701916	+	0.451094i
$563$	−3.38249	−	8.68786i	−0.142555	−	0.366149i	0.842426	−	0.538812i	$-0.181127\pi$
$563$	−3.38249	−	8.68786i	−0.142555	−	0.366149i	−0.984981	+	0.172662i	$0.944763\pi$
$564$	22.2324	−	9.39551i	0.936155	−	0.395622i
$565$	2.23009	+	6.86352i	0.0938207	+	0.288750i
$566$	−15.1970	−	28.8014i	−0.638776	−	1.21061i
$567$	−0.174401	+	0.226167i	−0.00732416	+	0.00949814i
$568$	−8.65579	+	4.25577i	−0.363189	+	0.178568i
$569$	16.9837	+	8.35035i	0.711996	+	0.350065i	0.761016	−	0.648733i	$-0.224701\pi$
$569$	16.9837	+	8.35035i	0.711996	+	0.350065i	−0.0490204	+	0.998798i	$0.515610\pi$
$570$	8.65236	+	11.2206i	0.362407	+	0.469978i
$571$	−2.65375	+	5.81089i	−0.111056	+	0.243178i	−0.956997	−	0.290098i	$-0.906312\pi$
$571$	−2.65375	+	5.81089i	−0.111056	+	0.243178i	0.845941	+	0.533276i	$0.179039\pi$
$572$	16.1178	+	12.3097i	0.673921	+	0.514696i
$573$	−12.5333	−	27.4440i	−0.523584	−	1.14649i
$574$	0.740640	−	1.40367i	0.0309137	−	0.0585880i
$575$	−14.3814	−	2.48879i	−0.599744	−	0.103790i
$576$	4.92271	+	0.564829i	0.205113	+	0.0235345i
$577$	−32.9631	−	33.9182i	−1.37227	−	1.41204i	−0.811903	−	0.583793i	$-0.801568\pi$
$577$	−32.9631	−	33.9182i	−1.37227	−	1.41204i	−0.560370	−	0.828243i	$-0.689341\pi$
$578$	−13.1456	+	9.55081i	−0.546783	+	0.397261i
$579$	−37.1989	−	30.4174i	−1.54593	−	1.26410i
$580$	2.44462	−	0.280493i	0.101507	−	0.0116469i
$581$	−3.10290	−	0.177430i	−0.128730	−	0.00736105i
$582$	35.1197	+	10.3121i	1.45576	+	0.427449i
$583$	−0.0344396	+	0.0825614i	−0.00142634	+	0.00341934i
$584$	6.47213	−	1.90039i	0.267819	−	0.0786386i
$585$	34.8763	−	8.11013i	1.44196	−	0.335313i
$586$	−16.0359	−	14.7176i	−0.662437	−	0.607979i
$587$	−3.97038	+	6.58414i	−0.163875	+	0.271756i	−0.927438	−	0.373977i	$-0.877994\pi$
$587$	−3.97038	+	6.58414i	−0.163875	+	0.271756i	0.763563	+	0.645734i	$0.223448\pi$
$588$	−16.7670	−	9.46877i	−0.691460	−	0.390486i
$589$	35.9766	−	12.8364i	1.48239	−	0.528916i
$590$	3.80020	−	14.4575i	0.156452	−	0.595205i
$591$	0.432553	−	0.353697i	0.0177929	−	0.0145492i
$592$	5.46626	−	5.62465i	0.224662	−	0.231172i
$593$	3.09359	−	21.5164i	0.127039	−	0.883573i	−0.822241	−	0.569139i	$-0.807276\pi$
$593$	3.09359	−	21.5164i	0.127039	−	0.883573i	0.949280	−	0.314433i	$-0.101814\pi$
$594$	14.4302	−	11.2347i	0.592080	−	0.460964i
$595$	−0.0605904	−	0.421415i	−0.00248396	−	0.0172763i
$596$	−16.0230	−	11.6414i	−0.656329	−	0.476851i
$597$	−11.5110	−	43.7923i	−0.471113	−	1.79230i
$598$	13.9798	+	20.4449i	0.571678	+	0.836052i
$599$	5.43202	+	1.26316i	0.221946	+	0.0516114i	0.335995	−	0.941864i	$-0.390927\pi$
$599$	5.43202	+	1.26316i	0.221946	+	0.0516114i	−0.114049	+	0.993475i	$0.536382\pi$
$600$	10.1468	−	0.580214i	0.414240	−	0.0236871i
$601$	8.82316	−	1.52691i	0.359904	−	0.0622838i	0.0122976	−	0.999924i	$-0.496085\pi$
$601$	8.82316	−	1.52691i	0.359904	−	0.0622838i	0.347606	+	0.937641i	$0.386995\pi$
$602$	−0.207059	+	0.637262i	−0.00843909	+	0.0259729i
$603$	2.52813	+	29.4344i	0.102953	+	1.19866i
$604$	15.6850			0.638215
$605$	−12.9845	−	0.621504i	−0.527897	−	0.0252677i
$606$	40.2222			1.63392
$607$	1.99660	+	23.2459i	0.0810393	+	0.943524i	0.918083	+	0.396388i	$0.129736\pi$
$607$	1.99660	+	23.2459i	0.0810393	+	0.943524i	−0.837044	+	0.547136i	$0.815718\pi$
$608$	1.31364	−	4.04295i	0.0532750	−	0.163963i
$609$	2.40535	−	0.416262i	0.0974696	−	0.0168678i
$610$	−1.17096	+	0.0669582i	−0.0474110	+	0.00271106i
$611$	−50.9688	−	11.8523i	−2.06198	−	0.479492i
$612$	−2.42405	−	3.54507i	−0.0979866	−	0.143301i
$613$	−2.93619	−	11.1704i	−0.118592	−	0.451169i	0.881175	−	0.472791i	$-0.156753\pi$
$613$	−2.93619	−	11.1704i	−0.118592	−	0.451169i	−0.999766	+	0.0216219i	$0.993117\pi$
$614$	15.7479	+	11.4415i	0.635532	+	0.461741i
$615$	1.81116	+	12.5969i	0.0730329	+	0.507955i
$616$	−0.993098	−	0.956202i	−0.0400131	−	0.0385265i
$617$	5.20982	−	36.2351i	0.209740	−	1.45877i	−0.564267	−	0.825592i	$-0.690841\pi$
$617$	5.20982	−	36.2351i	0.209740	−	1.45877i	0.774006	−	0.633178i	$-0.218250\pi$
$618$	3.37956	−	3.47748i	0.135946	−	0.139885i
$619$	21.1669	−	17.3080i	0.850768	−	0.695669i	−0.103498	−	0.994630i	$-0.533004\pi$
$619$	21.1669	−	17.3080i	0.850768	−	0.695669i	0.954265	+	0.298960i	$0.0966399\pi$
$620$	−2.69952	+	10.2700i	−0.108415	+	0.412454i
$621$	21.0348	−	7.50522i	0.844099	−	0.301174i
$622$	4.59721	+	2.59616i	0.184331	+	0.104097i
$623$	2.27384	−	3.77075i	0.0910996	−	0.151072i
$624$	−12.7065	−	11.6619i	−0.508667	−	0.466851i
$625$	5.84593	−	1.35941i	0.233837	−	0.0543765i
$626$	11.4311	−	3.35648i	0.456880	−	0.134152i
$627$	−17.7111	−	35.6038i	−0.707313	−	1.42188i
$628$	−0.447041	−	0.131263i	−0.0178389	−	0.00523797i
$629$	−6.78680	−	0.388083i	−0.270608	−	0.0154739i
$630$	−2.41813	+	0.277455i	−0.0963408	+	0.0110541i
$631$	−22.4245	−	18.3364i	−0.892704	−	0.729961i	0.0708462	−	0.997487i	$-0.477430\pi$
$631$	−22.4245	−	18.3364i	−0.892704	−	0.729961i	−0.963550	+	0.267527i	$0.913794\pi$
$632$	6.40147	−	4.65094i	0.254637	−	0.185004i
$633$	10.3156	+	10.6145i	0.410007	+	0.421887i
$634$	2.85415	+	0.327483i	0.113353	+	0.0130060i
$635$	18.0217	+	3.11878i	0.715171	+	0.123765i
$636$	0.0355012	−	0.0672823i	0.00140772	−	0.00266792i
$637$	17.3427	+	37.9752i	0.687143	+	1.50463i
$638$	−6.88317	−	0.558996i	−0.272507	−	0.0221309i
$639$	19.8540	−	43.4742i	0.785412	−	1.71981i
$640$	0.721642	+	0.935841i	0.0285254	+	0.0369924i
$641$	13.9470	+	6.85727i	0.550873	+	0.270846i	0.695361	−	0.718661i	$-0.255244\pi$
$641$	13.9470	+	6.85727i	0.550873	+	0.270846i	−0.144488	+	0.989507i	$0.546154\pi$
$642$	−43.7189	+	21.4951i	−1.72545	+	0.848346i
$643$	−8.34315	+	10.8196i	−0.329022	+	0.426683i	−0.927134	−	0.374729i	$-0.877736\pi$
$643$	−8.34315	+	10.8196i	−0.329022	+	0.426683i	0.598113	+	0.801412i	$0.295918\pi$
$644$	−0.785676	−	1.48902i	−0.0309600	−	0.0586757i
$645$	−1.66035	−	5.11003i	−0.0653763	−	0.201207i
$646$	−3.39381	+	1.43424i	−0.133528	+	0.0564293i
$647$	7.02677	+	18.0481i	0.276251	+	0.709544i	0.999814	+	0.0192861i	$0.00613934\pi$
$647$	7.02677	+	18.0481i	0.276251	+	0.709544i	−0.723563	+	0.690258i	$0.757497\pi$
$648$	−0.578017	+	0.371469i	−0.0227066	+	0.0145927i
$649$	−18.3356	+	37.7344i	−0.719734	+	1.48120i
$650$	−18.5368	−	11.9129i	−0.727072	−	0.467261i
$651$	−2.09205	+	10.3247i	−0.0819939	+	0.404656i
$652$	4.69175	+	7.78039i	0.183743	+	0.304704i
$653$	0.596346	+	20.8748i	0.0233368	+	0.816895i	0.924003	+	0.382384i	$0.124897\pi$
$653$	0.596346	+	20.8748i	0.0233368	+	0.816895i	−0.900667	+	0.434511i	$0.856921\pi$
$654$	−10.3194	+	26.5051i	−0.403520	+	1.03643i
$655$	−4.55897	−	22.4994i	−0.178134	−	0.879124i
$656$	2.81300	−	2.58175i	0.109829	−	0.100800i
$657$	−18.8656	+	27.5900i	−0.736016	+	1.07639i
$658$	3.35022	+	1.19536i	0.130605	+	0.0465998i
$659$	−15.2165	−	17.5608i	−0.592750	−	0.684070i	0.377546	−	0.925991i	$-0.376768\pi$
$659$	−15.2165	−	17.5608i	−0.592750	−	0.684070i	−0.970296	+	0.241921i	$0.922223\pi$
$660$	10.9494	+	1.52240i	0.426204	+	0.0592593i
$661$	−16.6150	+	19.1747i	−0.646248	+	0.745810i	−0.980467	−	0.196686i	$-0.936982\pi$
$661$	−16.6150	+	19.1747i	−0.646248	+	0.745810i	0.334219	+	0.942495i	$0.391528\pi$
$662$	27.7734	−	15.6844i	1.07945	−	0.609591i
$663$	−0.426861	+	14.9421i	−0.0165779	+	0.580303i
$664$	−6.88731	−	2.91060i	−0.267279	−	0.112953i
$665$	−0.178696	+	2.08052i	−0.00692954	+	0.0806792i
$666$	−3.32574	+	38.7209i	−0.128870	+	1.50040i
$667$	−7.76835	−	3.28293i	−0.300792	−	0.127116i
$668$	0.474139	−	16.5970i	0.0183450	−	0.642159i
$669$	−56.1648	+	31.7177i	−2.17146	+	1.22628i
$670$	−4.61410	+	5.32496i	−0.178258	+	0.205721i
$671$	3.26032	+	0.453314i	0.125863	+	0.0175000i
$672$	0.767741	+	0.886020i	0.0296162	+	0.0341790i
$673$	−38.8703	−	13.8689i	−1.49834	−	0.534606i	−0.545507	−	0.838106i	$-0.683663\pi$
$673$	−38.8703	−	13.8689i	−1.49834	−	0.534606i	−0.952831	+	0.303500i	$0.901845\pi$
$674$	8.92389	−	13.0508i	0.343736	−	0.502697i
$675$	−14.6386	+	13.4352i	−0.563441	+	0.517122i
$676$	4.84407	+	23.9064i	0.186310	+	0.919478i
$677$	−16.6319	+	42.7186i	−0.639214	+	1.64181i	0.121399	+	0.992604i	$0.461262\pi$
$677$	−16.6319	+	42.7186i	−0.639214	+	1.64181i	−0.760613	+	0.649205i	$0.775102\pi$
$678$	0.491845	+	17.2168i	0.0188892	+	0.661208i
$679$	2.78559	+	4.61938i	0.106901	+	0.177276i
$680$	0.203407	−	1.00385i	0.00780031	−	0.0384961i
$681$	50.0425	+	32.1603i	1.91763	+	1.23239i
$682$	13.0249	−	26.8050i	0.498748	−	1.02642i
$683$	−21.4632	+	13.7936i	−0.821268	+	0.527797i	−0.882492	−	0.470327i	$-0.844136\pi$
$683$	−21.4632	+	13.7936i	−0.821268	+	0.527797i	0.0612240	+	0.998124i	$0.480500\pi$
$684$	7.64211	+	19.6286i	0.292204	+	0.750519i
$685$	−3.04849	+	1.28830i	−0.116477	+	0.0492235i
$686$	−1.77608	−	5.46621i	−0.0678110	−	0.208701i
$687$	−15.0734	−	28.5672i	−0.575085	−	1.08991i
$688$	−0.984368	+	1.27655i	−0.0375287	+	0.0486680i
$689$	−0.148010	+	0.0727717i	−0.00563874	+	0.00277238i
$690$	12.1151	+	5.95660i	0.461214	+	0.226764i
$691$	3.77013	+	4.88920i	0.143423	+	0.185994i	0.858134	−	0.513426i	$-0.171624\pi$
$691$	3.77013	+	4.88920i	0.143423	+	0.185994i	−0.714711	+	0.699419i	$0.753442\pi$
$692$	4.25118	−	9.30879i	0.161606	−	0.353867i
$693$	6.80861	+	0.552940i	0.258638	+	0.0210045i
$694$	9.49819	+	20.7981i	0.360546	+	0.789487i
$695$	3.09046	−	5.85708i	0.117228	−	0.222172i
$696$	5.78672	+	1.00143i	0.219345	+	0.0379592i
$697$	−3.28770	−	0.377228i	−0.124530	−	0.0142885i
$698$	4.40465	+	4.53228i	0.166718	+	0.171549i
$699$	−27.0129	+	19.6260i	−1.02172	+	0.742325i
$700$	1.15953	+	0.948143i	0.0438261	+	0.0358365i
$701$	−10.8210	+	1.24159i	−0.408702	+	0.0468942i	−0.315905	−	0.948791i	$-0.602308\pi$
$701$	−10.8210	+	1.24159i	−0.408702	+	0.0468942i	−0.0927972	+	0.995685i	$0.529581\pi$
$702$	33.6629	+	1.92491i	1.27052	+	0.0726511i
$703$	31.9912	+	9.39347i	1.20657	+	0.354282i
$704$	−1.47718	−	2.96950i	−0.0556732	−	0.111917i
$705$	−27.3679	+	8.03595i	−1.03074	+	0.302651i
$706$	16.5716	−	3.85355i	0.623679	−	0.145030i
$707$	4.36723	+	4.00821i	0.164247	+	0.150744i
$708$	18.4236	−	30.5521i	0.692400	−	1.14822i
$709$	15.9370	+	9.00004i	0.598527	+	0.338004i	0.761042	−	0.648702i	$-0.224688\pi$
$709$	15.9370	+	9.00004i	0.598527	+	0.338004i	−0.162515	+	0.986706i	$0.551961\pi$
$710$	10.7357	−	3.83050i	0.402904	−	0.143756i
$711$	−9.96720	+	37.9192i	−0.373799	+	1.42208i
$712$	8.20071	−	6.70569i	0.307335	−	0.251306i
$713$	25.3649	−	26.0999i	0.949923	−	0.977448i
$714$	0.144608	−	1.00577i	0.00541183	−	0.0376401i
$715$	−17.2651	−	16.6236i	−0.645677	−	0.621689i
$716$	−0.0649813	−	0.451955i	−0.00242847	−	0.0168903i
$717$	12.6214	+	9.16996i	0.471354	+	0.342458i
$718$	−2.57475	−	9.79535i	−0.0960887	−	0.365559i
$719$	7.18073	+	10.5015i	0.267796	+	0.391639i	0.935807	−	0.352512i	$-0.114672\pi$
$719$	7.18073	+	10.5015i	0.267796	+	0.391639i	−0.668011	+	0.744151i	$0.732854\pi$
$720$	−5.70347	−	1.32629i	−0.212556	−	0.0494278i
$721$	0.713481	−	0.0407983i	0.0265714	−	0.00151941i
$722$	−0.915275	+	0.158395i	−0.0340630	+	0.00589484i
$723$	2.16311	−	6.65737i	0.0804469	−	0.247590i
$724$	1.89522	+	22.0657i	0.0704353	+	0.820064i
$725$	7.50303			0.278655
$726$	−29.3164	−	10.1540i	−1.08803	−	0.376851i
$727$	−20.9634			−0.777489			−0.388744	−	0.921346i	$-0.627091\pi$
$727$	−20.9634			−0.777489			−0.388744	+	0.921346i	$0.627091\pi$
$728$	−0.217512	−	2.53244i	−0.00806153	−	0.0938587i
$729$	−13.3655	+	41.1349i	−0.495020	+	1.52352i
$730$	−7.85467	+	1.35930i	−0.290715	+	0.0503101i
$731$	1.39487	−	0.0797618i	0.0515913	−	0.00295010i
$732$	−2.72651	−	0.634022i	−0.100775	−	0.0234341i
$733$	−13.6620	−	19.9800i	−0.504618	−	0.737980i	0.486102	−	0.873902i	$-0.338418\pi$
$733$	−13.6620	−	19.9800i	−0.504618	−	0.737980i	−0.990720	+	0.135922i	$0.956600\pi$
$734$	6.12646	+	23.3075i	0.226132	+	0.860295i
$735$	18.4100	+	13.3756i	0.679061	+	0.493367i
$736$	−0.576423	−	4.00911i	−0.0212472	−	0.147778i
$737$	15.6031	−	12.1478i	0.574749	−	0.447471i
$738$	−2.69246	+	18.7265i	−0.0991108	+	0.689331i
$739$	2.46914	−	2.54069i	0.0908288	−	0.0934607i	−0.670193	−	0.742187i	$-0.733789\pi$
$739$	2.46914	−	2.54069i	0.0908288	−	0.0934607i	0.761022	+	0.648726i	$0.224698\pi$
$740$	−7.17543	+	5.86732i	−0.263774	+	0.215687i
$741$	18.6385	−	70.9081i	0.684702	−	2.60488i
$742$	0.0105594	−	0.00376759i	0.000387648	−	0.000138313i
$743$	11.5079	+	6.49881i	0.422184	+	0.238418i	0.688156	−	0.725562i	$-0.258420\pi$
$743$	11.5079	+	6.49881i	0.422184	+	0.238418i	−0.265972	+	0.963981i	$0.585693\pi$
$744$	−13.0874	+	21.7030i	−0.479807	+	0.795670i
$745$	17.2438	+	15.8262i	0.631764	+	0.579828i
$746$	−27.8595	+	6.47845i	−1.02001	+	0.237193i
$747$	35.5482	−	10.4379i	1.30064	−	0.381903i
$748$	−1.10667	+	2.65301i	−0.0404640	+	0.0970036i
$749$	−6.88891	−	2.02277i	−0.251715	−	0.0739103i
$750$	−28.6295	−	1.63710i	−1.04540	−	0.0597783i
$751$	9.80655	−	1.12520i	0.357846	−	0.0410590i	0.0667956	−	0.997767i	$-0.478722\pi$
$751$	9.80655	−	1.12520i	0.357846	−	0.0410590i	0.291051	+	0.956708i	$0.405995\pi$
$752$	6.62475	+	5.41703i	0.241580	+	0.197539i
$753$	−28.9162	+	21.0089i	−1.05377	+	0.765606i
$754$	−8.87370	−	9.13082i	−0.323161	−	0.332525i
$755$	−18.4152	−	2.11295i	−0.670197	−	0.0768980i
$756$	−2.25843	−	0.390837i	−0.0821383	−	0.0142146i
$757$	−19.8035	+	37.5319i	−0.719772	+	1.36412i	0.203156	+	0.979146i	$0.434880\pi$
$757$	−19.8035	+	37.5319i	−0.719772	+	1.36412i	−0.922928	+	0.384973i	$0.874211\pi$
$758$	−3.69487	−	8.09064i	−0.134204	−	0.293865i
$759$	−30.1112	−	22.9969i	−1.09297	−	0.834735i
$760$	−2.08692	+	4.56971i	−0.0757005	+	0.165761i
$761$	25.9031	+	33.5918i	0.938988	+	1.21770i	0.975863	+	0.218381i	$0.0700777\pi$
$761$	25.9031	+	33.5918i	0.938988	+	1.21770i	−0.0368755	+	0.999320i	$0.511740\pi$
$762$	39.1723	+	19.2597i	1.41906	+	0.697706i
$763$	−3.76173	+	1.84952i	−0.136184	+	0.0669570i
$764$	6.53209	−	8.47097i	0.236323	−	0.306469i
$765$	2.36843	+	4.48867i	0.0856307	+	0.162288i
$766$	−10.5933	−	32.6028i	−0.382751	−	1.17799i
$767$	−71.2489	+	30.1100i	−2.57265	+	1.08721i
$768$	1.02329	+	2.62829i	0.0369246	+	0.0948402i
$769$	33.6661	−	21.6359i	1.21403	−	0.780209i	0.232701	−	0.972548i	$-0.425244\pi$
$769$	33.6661	−	21.6359i	1.21403	−	0.780209i	0.981329	+	0.192339i	$0.0616074\pi$
$770$	1.03715	+	1.25642i	0.0373762	+	0.0452783i
$771$	55.9602	+	35.9635i	2.01536	+	1.29519i
$772$	3.38335	−	16.6975i	0.121770	−	0.600957i
$773$	−10.5623	−	17.5157i	−0.379901	−	0.629995i	0.606360	−	0.795190i	$-0.292629\pi$
$773$	−10.5623	−	17.5157i	−0.379901	−	0.629995i	−0.986261	+	0.165195i	$0.947175\pi$
$774$	−0.228091	−	7.98424i	−0.00819858	−	0.286988i
$775$	−11.7474	+	30.1729i	−0.421979	+	1.08384i
$776$	2.57719	+	12.7189i	0.0925157	+	0.456583i
$777$	−6.77450	+	6.21758i	−0.243034	+	0.223054i
$778$	2.84606	−	4.16223i	0.102036	−	0.149223i
$779$	15.2871	+	5.45444i	0.547719	+	0.195426i
$780$	13.3472	+	15.4035i	0.477907	+	0.551534i
$781$	−31.6432	+	4.69974i	−1.13228	+	0.168170i
$782$	−2.29889	+	2.65306i	−0.0822080	+	0.0948731i
$783$	−9.99725	+	5.64571i	−0.357273	+	0.201761i
$784$	0.194958	−	6.82444i	0.00696280	−	0.243730i
$785$	0.507171	+	0.214332i	0.0181017	+	0.00764985i
$786$	4.68862	−	54.5886i	0.167237	−	1.94711i
$787$	4.12323	−	48.0058i	0.146977	−	1.71122i	−0.437007	−	0.899458i	$-0.643961\pi$
$787$	4.12323	−	48.0058i	0.146977	−	1.71122i	0.583984	−	0.811765i	$-0.301493\pi$
$788$	0.182481	+	0.0771170i	0.00650061	+	0.00274718i
$789$	0.0238417	−	0.834567i	0.000848786	−	0.0297114i
$790$	−8.14225	+	4.59814i	−0.289688	+	0.163594i
$791$	−1.66228	+	1.91837i	−0.0591039	+	0.0682095i
$792$	14.9804	+	6.75737i	0.532304	+	0.240113i
$793$	3.97431	+	4.58660i	0.141132	+	0.162875i
$794$	−28.2932	−	10.0950i	−1.00409	−	0.358258i
$795$	−0.0507443	+	0.0742111i	−0.00179971	+	0.00263200i
$796$	11.8277	−	10.8553i	0.419221	−	0.384758i
$797$	−2.62454	−	12.9526i	−0.0929659	−	0.458805i	−0.999340	−	0.0363286i	$-0.988434\pi$
$797$	−2.62454	−	12.9526i	−0.0929659	−	0.458805i	0.906374	−	0.422476i	$-0.138839\pi$
$798$	−1.80815	+	4.64420i	−0.0640078	+	0.164403i
$799$	−0.211799	−	7.41394i	−0.00749292	−	0.262286i
$800$	1.86080	+	3.08580i	0.0657894	+	0.109099i
$801$	−10.4240	+	51.4444i	−0.368314	+	1.81770i
$802$	−31.6657	−	20.3503i	−1.11815	−	0.718594i
$803$	22.3654	+	0.534954i	0.789259	+	0.0188781i
$804$	−14.1467	+	9.09152i	−0.498915	+	0.320633i
$805$	0.721844	+	1.85404i	0.0254417	+	0.0653464i
$806$	50.6124	−	21.3890i	1.78275	−	0.753395i
$807$	3.78957	+	11.6631i	0.133399	+	0.410560i
$808$	6.65508	+	12.6128i	0.234125	+	0.443716i
$809$	−9.31498	+	12.0799i	−0.327497	+	0.424706i	−0.926648	−	0.375930i	$-0.877323\pi$
$809$	−9.31498	+	12.0799i	−0.327497	+	0.424706i	0.599151	+	0.800636i	$0.295505\pi$
$810$	0.728667	−	0.358262i	0.0256028	−	0.0125880i
$811$	21.8390	+	10.7375i	0.766871	+	0.377045i	0.782353	−	0.622835i	$-0.214019\pi$
$811$	21.8390	+	10.7375i	0.766871	+	0.377045i	−0.0154819	+	0.999880i	$0.504928\pi$
$812$	0.528513	+	0.685388i	0.0185472	+	0.0240524i
$813$	30.3955	−	66.5569i	1.06602	−	2.33425i
$814$	22.9502	−	12.2462i	0.804406	−	0.429230i
$815$	−4.46030	−	9.76669i	−0.156237	−	0.342112i
$816$	1.14079	−	2.16203i	0.0399356	−	0.0756864i
$817$	−6.75229	−	1.16853i	−0.236233	−	0.0408817i
$818$	−3.94340	−	0.452463i	−0.137878	−	0.0158200i
$819$	8.77757	+	9.03191i	0.306713	+	0.315600i
$820$	−3.65042	+	2.65219i	−0.127478	+	0.0926184i
$821$	9.82148	+	8.03099i	0.342772	+	0.280283i	0.788691	−	0.614790i	$-0.210759\pi$
$821$	9.82148	+	8.03099i	0.342772	+	0.280283i	−0.445919	+	0.895074i	$0.647123\pi$
$822$	−7.84723	+	0.900385i	−0.273703	+	0.0314045i
$823$	−17.8207	−	1.01902i	−0.621189	−	0.0355209i	−0.256339	−	0.966587i	$-0.582516\pi$
$823$	−17.8207	−	1.01902i	−0.621189	−	0.0355209i	−0.364850	+	0.931066i	$0.618880\pi$
$824$	1.64963	+	0.484376i	0.0574677	+	0.0168740i
$825$	32.6401	+	8.41765i	1.13638	+	0.293065i
$826$	5.04495	−	1.48133i	0.175536	−	0.0515420i
$827$	−8.30536	+	1.93133i	−0.288806	+	0.0671589i	−0.368397	−	0.929669i	$-0.620093\pi$
$827$	−8.30536	+	1.93133i	−0.288806	+	0.0671589i	0.0795909	+	0.996828i	$0.474639\pi$
$828$	14.7860	+	13.5705i	0.513849	+	0.471606i
$829$	−3.65623	+	6.06318i	−0.126986	+	0.210583i	−0.913344	−	0.407188i	$-0.866509\pi$
$829$	−3.65623	+	6.06318i	−0.126986	+	0.210583i	0.786358	+	0.617771i	$0.211964\pi$
$830$	7.69403	+	4.34502i	0.267064	+	0.150818i
$831$	57.0569	−	20.3578i	1.97928	−	0.706206i
$832$	1.55452	−	5.91403i	0.0538935	−	0.205032i
$833$	−4.58081	+	3.74571i	−0.158715	+	0.129781i
$834$	11.0154	−	11.3346i	0.381432	−	0.392484i
$835$	−2.79247	+	19.4221i	−0.0966374	+	0.672128i
$836$	8.23412	−	11.4447i	0.284783	−	0.395824i
$837$	−7.05128	−	49.0427i	−0.243728	−	1.69516i
$838$	−4.52417	−	3.28700i	−0.156285	−	0.113548i
$839$	−10.1367	−	38.5640i	−0.349957	−	1.33138i	−0.876571	−	0.481272i	$-0.840175\pi$
$839$	−10.1367	−	38.5640i	−0.349957	−	1.33138i	0.526614	−	0.850105i	$-0.323461\pi$
$840$	−0.782018	−	1.14366i	−0.0269822	−	0.0394602i
$841$	−24.0235	−	5.58643i	−0.828397	−	0.192635i
$842$	23.0901	−	1.32034i	0.795736	−	0.0455018i
$843$	54.9717	−	9.51323i	1.89333	−	0.327653i
$844$	−1.62167	+	4.99097i	−0.0558200	+	0.171796i
$845$	−2.46678	−	28.7201i	−0.0848596	−	0.988003i
$846$	−42.4027			−1.45783
$847$	−2.17124	−	4.02392i	−0.0746047	−	0.138264i
$848$	0.0269722			0.000926228
$849$	7.85989	+	91.5110i	0.269751	+	3.14065i
$850$	0.965109	−	2.97030i	0.0331030	−	0.101880i
$851$	31.3026	−	5.41712i	1.07304	−	0.185697i
$852$	27.1602	−	1.55308i	0.930493	−	0.0532075i
$853$	12.3080	+	2.86211i	0.421419	+	0.0979968i	0.431843	−	0.901949i	$-0.357864\pi$
$853$	12.3080	+	2.86211i	0.421419	+	0.0979968i	−0.0104239	+	0.999946i	$0.503318\pi$
$854$	−0.232856	−	0.340541i	−0.00796817	−	0.0116531i
$855$	−6.32812	−	24.0747i	−0.216417	−	0.823336i
$856$	−13.9740	−	10.1527i	−0.477622	−	0.347013i
$857$	−6.01270	−	41.8193i	−0.205390	−	1.42852i	−0.787954	−	0.615734i	$-0.788860\pi$
$857$	−6.01270	−	41.8193i	−0.205390	−	1.42852i	0.582564	−	0.812785i	$-0.302049\pi$
$858$	−28.3590	−	49.6768i	−0.968159	−	1.69594i
$859$	1.83039	−	12.7306i	0.0624521	−	0.434364i	−0.934475	−	0.356029i	$-0.884130\pi$
$859$	1.83039	−	12.7306i	0.0624521	−	0.434364i	0.996927	−	0.0783351i	$-0.0249604\pi$
$860$	1.32767	−	1.36614i	0.0452733	−	0.0465851i
$861$	−3.46530	+	2.83356i	−0.118097	+	0.0965675i
$862$	5.59065	−	21.2690i	0.190418	−	0.724426i
$863$	−24.8139	+	8.85357i	−0.844673	+	0.301379i	−0.722706	−	0.691155i	$-0.757102\pi$
$863$	−24.8139	+	8.85357i	−0.844673	+	0.301379i	−0.121967	+	0.992534i	$0.538920\pi$
$864$	−4.80132	−	2.71143i	−0.163344	−	0.0922447i
$865$	−6.24514	+	10.3564i	−0.212341	+	0.352128i
$866$	−9.24461	−	8.48463i	−0.314145	−	0.288319i
$867$	44.6381	−	10.3802i	1.51599	−	0.352528i
$868$	−3.58373	+	1.05228i	−0.121640	+	0.0357167i
$869$	24.9209	−	8.22549i	0.845384	−	0.279031i
$870$	−6.65906	−	1.95528i	−0.225763	−	0.0662901i
$871$	36.3990	+	2.08137i	1.23333	+	0.0705245i
$872$	−10.0188	+	1.14955i	−0.339280	+	0.0389288i
$873$	−49.7798	−	40.7047i	−1.68479	−	1.37765i
$874$	13.9297	−	10.1205i	0.471179	−	0.342331i
$875$	−2.94538	−	3.03073i	−0.0995721	−	0.102457i
$876$	−18.9010	−	2.16869i	−0.638607	−	0.0732733i
$877$	−21.3887	−	3.70145i	−0.722243	−	0.124989i	−0.202464	−	0.979290i	$-0.564895\pi$
$877$	−21.3887	−	3.70145i	−0.722243	−	0.124989i	−0.519779	+	0.854301i	$0.673986\pi$
$878$	−5.69193	+	10.7874i	−0.192093	+	0.364058i
$879$	25.5024	+	55.8424i	0.860174	+	1.88352i
$880$	1.33427	+	3.68537i	0.0449782	+	0.124234i
$881$	−4.65178	+	10.1860i	−0.156723	+	0.343175i	−0.971663	−	0.236370i	$-0.924042\pi$
$881$	−4.65178	+	10.1860i	−0.156723	+	0.343175i	0.814941	+	0.579545i	$0.196770\pi$
$882$	20.6576	+	26.7892i	0.695577	+	0.902040i
$883$	−5.57334	−	2.74023i	−0.187558	−	0.0922159i	0.345026	−	0.938593i	$-0.387870\pi$
$883$	−5.57334	−	2.74023i	−0.187558	−	0.0922159i	−0.532584	+	0.846377i	$0.678779\pi$
$884$	−4.75613	+	2.33843i	−0.159966	+	0.0786499i
$885$	−25.7461	+	33.3881i	−0.865445	+	1.12233i
$886$	2.97352	+	5.63545i	0.0998975	+	0.189327i
$887$	7.23097	+	22.2546i	0.242792	+	0.747238i	0.995992	+	0.0894454i	$0.0285095\pi$
$887$	7.23097	+	22.2546i	0.242792	+	0.747238i	−0.753200	+	0.657792i	$0.771491\pi$
$888$	−20.3768	+	8.61129i	−0.683799	+	0.288976i
$889$	2.33397	+	5.99475i	0.0782788	+	0.201058i
$890$	−10.5315	+	6.76816i	−0.353016	+	0.226869i
$891$	−2.20124	+	0.589550i	−0.0737442	+	0.0197507i
$892$	−19.2389	−	12.3641i	−0.644165	−	0.413979i
$893$	−7.22437	+	35.6537i	−0.241754	+	1.19310i
$894$	28.8464	+	47.8364i	0.964768	+	1.59989i
$895$	0.0154087	+	0.539376i	0.000515057	+	0.0180294i
$896$	−0.150807	+	0.387345i	−0.00503811	+	0.0129403i
$897$	−13.8727	−	68.4644i	−0.463196	−	2.28596i
$898$	15.6396	−	14.3539i	0.521902	−	0.478997i
$899$	−10.5606	+	15.4444i	−0.352216	+	0.515099i
$900$	−16.8167	−	6.00018i	−0.560556	−	0.200006i
$901$	−0.0153088	−	0.0176673i	−0.000510011	−	0.000588584i
$902$	11.4945	−	5.31403i	0.382725	−	0.176938i
$903$	1.23760	−	1.42827i	0.0411848	−	0.0475298i
$904$	−5.31743	+	3.00289i	−0.176855	+	0.0998746i
$905$	0.747381	−	26.1617i	0.0248438	−	0.869646i
$906$	−40.7496	−	17.2209i	−1.35382	−	0.572128i
$907$	−1.22485	+	14.2607i	−0.0406706	+	0.473519i	0.947457	+	0.319883i	$0.103644\pi$
$907$	−1.22485	+	14.2607i	−0.0406706	+	0.473519i	−0.988128	+	0.153636i	$0.950902\pi$
$908$	−1.80484	+	21.0134i	−0.0598957	+	0.697353i
$909$	−65.0891	−	27.5069i	−2.15887	−	0.912346i
$910$	−0.0857758	+	3.00255i	−0.00284344	+	0.0995334i
$911$	3.59625	−	2.03090i	0.119149	−	0.0672866i	−0.431006	−	0.902349i	$-0.641841\pi$
$911$	3.59625	−	2.03090i	0.119149	−	0.0672866i	0.550155	+	0.835062i	$0.314569\pi$
$912$	−7.85167	+	9.06131i	−0.259995	+	0.300050i
$913$	−18.8168	−	16.1524i	−0.622746	−	0.534567i
$914$	16.2404	+	18.7424i	0.537183	+	0.619942i
$915$	3.11567	+	1.11167i	0.103001	+	0.0367507i
$916$	6.46402	−	9.45333i	0.213577	−	0.312347i
$917$	5.94891	−	5.45986i	0.196450	−	0.180301i
$918$	0.949085	+	4.68392i	0.0313245	+	0.154592i
$919$	12.2644	−	31.5010i	0.404567	−	1.03912i	−0.571298	−	0.820743i	$-0.693560\pi$
$919$	12.2644	−	31.5010i	0.404567	−	1.03912i	0.975864	−	0.218378i	$-0.0700766\pi$
$920$	0.136685	+	4.78459i	0.00450636	+	0.157743i
$921$	−28.3510	−	47.0149i	−0.934197	−	1.54919i
$922$	−5.49902	+	27.1387i	−0.181101	+	0.893767i
$923$	−49.6180	−	31.8875i	−1.63320	−	1.04959i
$924$	1.53023	+	3.57455i	0.0503408	+	0.117594i
$925$	−23.7761	+	15.2800i	−0.781752	+	0.502402i
$926$	−2.19074	−	5.62687i	−0.0719922	−	0.184911i
$927$	−7.84708	+	3.31621i	−0.257732	+	0.108918i
$928$	0.643431	+	1.98028i	0.0211217	+	0.0650058i
$929$	−0.104490	−	0.198031i	−0.00342821	−	0.00649718i	0.882713	−	0.469913i	$-0.155715\pi$
$929$	−0.104490	−	0.198031i	−0.00342821	−	0.00649718i	−0.886141	+	0.463416i	$0.846624\pi$
$930$	18.2890	−	23.7176i	0.599720	−	0.777731i
$931$	26.0448	−	12.8054i	0.853585	−	0.419680i
$932$	−10.6238	−	5.22336i	−0.347993	−	0.171097i
$933$	−9.09314	−	11.7922i	−0.297696	−	0.386059i
$934$	−15.5983	+	34.1554i	−0.510390	+	1.11760i
$935$	1.65669	−	2.96571i	0.0541796	−	0.0969892i
$936$	12.5869	+	27.5614i	0.411414	+	0.900872i
$937$	9.25469	−	17.5396i	0.302338	−	0.572994i	−0.685576	−	0.728001i	$-0.740449\pi$
$937$	9.25469	−	17.5396i	0.302338	−	0.572994i	0.987913	+	0.155008i	$0.0495403\pi$
$938$	−2.44200	−	0.422604i	−0.0797340	−	0.0137985i
$939$	−33.3832	−	3.83036i	−1.08942	−	0.124999i
$940$	−7.04812	−	7.25235i	−0.229884	−	0.236546i
$941$	−39.9845	+	29.0505i	−1.30346	+	0.947018i	−0.999983	−	0.00582119i	$-0.998147\pi$
$941$	−39.9845	+	29.0505i	−1.30346	+	0.947018i	−0.303475	+	0.952839i	$0.598147\pi$
$942$	1.01729	+	0.831838i	0.0331452	+	0.0271027i
$943$	15.3640	−	1.76286i	0.500322	−	0.0574066i
$944$	12.6288	+	0.722138i	0.411031	+	0.0235036i
$945$	2.59888	+	0.763101i	0.0845417	+	0.0248237i
$946$	−4.39925	+	3.03822i	−0.143032	+	0.0987810i
$947$	−40.0321	+	11.7545i	−1.30087	+	0.381970i	−0.857553	−	0.514396i	$-0.828016\pi$
$947$	−40.0321	+	11.7545i	−1.30087	+	0.381970i	−0.443316	+	0.896365i	$0.646198\pi$
$948$	−21.7373	+	5.05480i	−0.705996	+	0.164172i
$949$	30.3886	+	27.8904i	0.986456	+	0.905362i
$950$	−7.91030	+	13.1178i	−0.256644	+	0.425597i
$951$	−7.05550	−	3.98443i	−0.228790	−	0.129204i
$952$	0.339314	−	0.121067i	0.0109972	−	0.00392380i
$953$	5.15498	−	19.6116i	0.166986	−	0.635281i	−0.830004	−	0.557757i	$-0.811662\pi$
$953$	5.15498	−	19.6116i	0.166986	−	0.635281i	0.996990	−	0.0775241i	$-0.0247015\pi$
$954$	−0.103462	+	0.0846004i	−0.00334970	+	0.00273904i
$955$	−8.81020	+	9.06549i	−0.285091	+	0.293352i
$956$	−0.787188	+	5.47502i	−0.0254595	+	0.177075i
$957$	17.2687	+	9.00946i	0.558218	+	0.291234i
$958$	−0.734945	−	5.11165i	−0.0237450	−	0.165150i
$959$	−0.941757	−	0.684226i	−0.0304109	−	0.0220948i
$960$	−0.847340	−	3.22362i	−0.0273478	−	0.104042i
$961$	−28.0762	−	41.0602i	−0.905685	−	1.32452i
$962$	46.7145	+	10.8630i	1.50614	+	0.350237i
$963$	85.4475	−	4.88606i	2.75351	−	0.157451i
$964$	2.44550	−	0.423211i	0.0787644	−	0.0136307i
$965$	−6.22160	+	19.1481i	−0.200280	+	0.616400i
$966$	0.406353	+	4.73108i	0.0130742	+	0.152220i
$967$	36.3381			1.16856			0.584278	−	0.811554i	$-0.301378\pi$
$967$	36.3381			1.16856			0.584278	+	0.811554i	$0.301378\pi$
$968$	−1.66656	−	10.8730i	−0.0535653	−	0.349472i
$969$	10.3918			0.333832
$970$	−1.31240	−	15.2800i	−0.0421386	−	0.490611i
$971$	7.19835	−	22.1542i	0.231006	−	0.710963i	−0.766620	−	0.642101i	$-0.778063\pi$
$971$	7.19835	−	22.1542i	0.231006	−	0.710963i	0.997626	−	0.0688625i	$-0.0219370\pi$
$972$	−14.3903	+	2.49034i	−0.461569	+	0.0798776i
$973$	2.32553	−	0.132979i	0.0745531	−	0.00426310i
$974$	12.4638	+	2.89833i	0.399366	+	0.0928686i
$975$	35.0791	+	51.3015i	1.12343	+	1.64296i
$976$	−0.252307	−	0.959874i	−0.00807614	−	0.0307248i
$977$	−41.7398	−	30.3257i	−1.33537	−	0.970206i	−0.999601	−	0.0282627i	$-0.991003\pi$
$977$	−41.7398	−	30.3257i	−1.33537	−	0.970206i	−0.335773	−	0.941943i	$-0.608997\pi$
$978$	−3.64688	−	25.3646i	−0.116614	−	0.811070i
$979$	32.6805	−	12.8989i	1.04447	−	0.412249i
$980$	−1.14822	+	7.98604i	−0.0366785	+	0.255105i
$981$	34.8253	−	35.8344i	1.11189	−	1.14411i
$982$	−5.73194	+	4.68698i	−0.182914	+	0.149568i
$983$	2.41746	−	9.19698i	0.0771051	−	0.293338i	−0.917408	−	0.397947i	$-0.869723\pi$
$983$	2.41746	−	9.19698i	0.0771051	−	0.293338i	0.994513	+	0.104609i	$0.0333591\pi$
$984$	−10.1427	+	3.61891i	−0.323338	+	0.115367i
$985$	−0.203855	−	0.115122i	−0.00649536	−	0.00366810i
$986$	0.931926	−	1.54543i	0.0296786	−	0.0492164i
$987$	−7.39145	−	6.78381i	−0.235272	−	0.215931i
$988$	25.3191	−	5.88770i	0.805507	−	0.187313i
$989$	−6.26469	+	1.83948i	−0.199205	+	0.0584920i
$990$	−16.6776	−	9.95158i	−0.530048	−	0.316282i
$991$	34.7279	+	10.1970i	1.10317	+	0.323919i	0.782110	−	0.623141i	$-0.214144\pi$
$991$	34.7279	+	10.1970i	1.10317	+	0.323919i	0.321057	+	0.947060i	$0.395962\pi$
$992$	−8.97097	−	0.512979i	−0.284829	−	0.0162871i
$993$	−89.3755	+	10.2549i	−2.83625	+	0.325429i
$994$	3.10375	+	2.53793i	0.0984450	+	0.0804981i
$995$	−15.3487	+	11.1515i	−0.486588	+	0.353527i
$996$	14.6976	+	15.1235i	0.465711	+	0.479205i
$997$	18.6103	+	2.13533i	0.589395	+	0.0676267i	0.403558	−	0.914954i	$-0.367773\pi$
$997$	18.6103	+	2.13533i	0.589395	+	0.0676267i	0.185836	+	0.982581i	$0.440501\pi$
$998$	−42.6686	−	7.38409i	−1.35065	−	0.233739i
$999$	20.1824	−	38.2499i	0.638543	−	1.21017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.2.g.a.15.1	✓	200
121.113	even	55	inner	242.2.g.a.113.1	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
242.2.g.a.15.1	✓	200	1.1	even	1	trivial
242.2.g.a.113.1	yes	200	121.113	even	55	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	242.g (of order \(55\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0855750 - 0.996332i) q^{2} +(-0.871571 + 2.68242i) q^{3} +(-0.985354 + 0.170522i) q^{4} +(1.17984 - 0.0674655i) q^{5} +(2.74716 + 0.638826i) q^{6} +(0.234620 + 0.343121i) q^{7} +(0.254218 + 0.967147i) q^{8} +(-4.00869 - 2.91248i) q^{9} +(-0.168183 - 1.16974i) q^{10} +(-0.173957 + 3.31206i) q^{11} +(0.401394 - 2.79175i) q^{12} +(-4.26172 + 4.38520i) q^{13} +(0.321785 - 0.263122i) q^{14} +(-0.847340 + 3.22362i) q^{15} +(0.941844 - 0.336049i) q^{16} +(-0.754691 - 0.426193i) q^{17} +(-2.55875 + 4.24322i) q^{18} +(3.13190 + 2.87443i) q^{19} +(-1.15105 + 0.267666i) q^{20} +(-1.12488 + 0.330295i) q^{21} +(3.31480 - 0.110110i) q^{22} +(3.88627 + 1.14111i) q^{23} +(-2.81586 - 0.161017i) q^{24} +(-3.57995 + 0.410761i) q^{25} +(4.73381 + 3.87082i) q^{26} +(4.46094 - 3.24107i) q^{27} +(-0.289694 - 0.298088i) q^{28} +(-2.06862 - 0.237352i) q^{29} +(3.28430 + 0.568371i) q^{30} +(4.19330 - 7.94718i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(-8.73272 - 3.35332i) q^{33} +(-0.360047 + 0.788394i) q^{34} +(0.299962 + 0.388998i) q^{35} +(4.44662 + 2.18625i) q^{36} +(7.03853 - 3.46061i) q^{37} +(2.59587 - 3.36639i) q^{38} +(-8.04857 - 15.2537i) q^{39} +(0.365185 + 1.12392i) q^{40} +(3.51700 - 1.48630i) q^{41} +(0.425346 + 1.09249i) q^{42} +(-1.35611 + 0.871516i) q^{43} +(-0.393370 - 3.29321i) q^{44} +(-4.92609 - 3.16580i) q^{45} +(0.804358 - 3.96966i) q^{46} +(4.41909 + 7.32824i) q^{47} +(0.0805413 + 2.81931i) q^{48} +(2.47697 - 6.36204i) q^{49} +(0.715608 + 3.53166i) q^{50} +(1.80100 - 1.65294i) q^{51} +(3.45153 - 5.04769i) q^{52} +(0.0254036 + 0.00906398i) q^{53} +(-3.61092 - 4.16723i) q^{54} +(0.0182087 + 3.91943i) q^{55} +(-0.272204 + 0.314140i) q^{56} +(-10.4401 + 5.89579i) q^{57} +(-0.0594591 + 2.08134i) q^{58} +(11.6516 + 4.92403i) q^{59} +(0.285232 - 3.32089i) q^{60} +(0.0849315 - 0.988840i) q^{61} +(-8.27687 - 3.49784i) q^{62} +(0.0588150 - 2.05879i) q^{63} +(-0.870746 + 0.491733i) q^{64} +(-4.73228 + 5.46134i) q^{65} +(-2.59372 + 8.98764i) q^{66} +(-3.90442 - 4.50594i) q^{67} +(0.816313 + 0.291260i) q^{68} +(-6.44810 + 9.43004i) q^{69} +(0.361902 - 0.332151i) q^{70} +(1.91549 + 9.45331i) q^{71} +(1.79772 - 4.61739i) q^{72} +(-0.192621 - 6.74261i) q^{73} +(-4.05024 - 6.71657i) q^{74} +(2.01834 - 9.96092i) q^{75} +(-3.57618 - 2.29827i) q^{76} +(-1.17725 + 0.717388i) q^{77} +(-14.5090 + 9.32438i) q^{78} +(-2.87077 - 7.37351i) q^{79} +(1.08855 - 0.460025i) q^{80} +(0.212322 + 0.653461i) q^{81} +(-1.78181 - 3.37691i) q^{82} +(-4.56586 + 5.92111i) q^{83} +(1.05209 - 0.517275i) q^{84} +(-0.919165 - 0.451923i) q^{85} +(0.984368 + 1.27655i) q^{86} +(2.43962 - 5.34203i) q^{87} +(-3.24747 + 0.673744i) q^{88} +(-4.40062 - 9.63601i) q^{89} +(-2.73264 + 5.17893i) q^{90} +(-2.50454 - 0.433428i) q^{91} +(-4.02393 - 0.461703i) q^{92} +(17.6629 + 18.1747i) q^{93} +(6.92320 - 5.03000i) q^{94} +(3.88905 + 3.18006i) q^{95} +(2.80208 - 0.321509i) q^{96} +(12.9562 + 0.740865i) q^{97} +(-6.55067 - 1.92345i) q^{98} +(10.3437 - 12.7704i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 5 q^{2} + 10 q^{3} + 5 q^{4} - q^{5} + q^{6} - 5 q^{8} - 40 q^{9} - 4 q^{10} - 11 q^{11} + 4 q^{12} - 32 q^{13} - 11 q^{14} - 24 q^{15} + 5 q^{16} + 2 q^{17} - 4 q^{18} + q^{19} - q^{20} - 8 q^{21}+ \cdots + 22 q^{99}+O(q^{100}) \) 200 * q - 5 * q^2 + 10 * q^3 + 5 * q^4 - q^5 + q^6 - 5 * q^8 - 40 * q^9 - 4 * q^10 - 11 * q^11 + 4 * q^12 - 32 * q^13 - 11 * q^14 - 24 * q^15 + 5 * q^16 + 2 * q^17 - 4 * q^18 + q^19 - q^20 - 8 * q^21 - 22 * q^22 + 41 * q^23 + q^24 + 2 * q^25 - q^26 - 59 * q^27 + 3 * q^29 + 13 * q^30 + 18 * q^31 + 20 * q^32 + 8 * q^34 + 4 * q^35 + 4 * q^36 + 17 * q^37 - 34 * q^38 - 172 * q^39 - 10 * q^40 + 6 * q^41 + 42 * q^42 - 20 * q^43 + 11 * q^44 + 64 * q^45 - 9 * q^46 + 7 * q^47 - q^48 - 43 * q^49 - 2 * q^50 - 135 * q^51 + q^52 - 80 * q^53 - 16 * q^54 - 22 * q^55 + 11 * q^56 + 41 * q^57 - 157 * q^58 + 30 * q^59 + 31 * q^60 + 40 * q^61 + 4 * q^62 - 45 * q^63 + 5 * q^64 - 7 * q^65 + 55 * q^66 - 19 * q^67 + 2 * q^68 - 8 * q^69 - 70 * q^70 + 5 * q^71 - 4 * q^72 + 34 * q^73 + 5 * q^74 - 11 * q^75 - 15 * q^76 - 198 * q^77 + 16 * q^78 - 47 * q^79 - q^80 - 18 * q^81 - 28 * q^82 + 9 * q^83 - 174 * q^84 - 100 * q^85 - 5 * q^86 + 37 * q^87 - 11 * q^88 - 67 * q^89 - 28 * q^90 - 166 * q^91 - 46 * q^92 - 47 * q^93 - 18 * q^94 + 129 * q^95 + q^96 - 3 * q^97 - 40 * q^98 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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