LMFDB - Embedded newform 153.3.q.a.104.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(2,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([4, 21])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.2"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.q (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$34$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			104.26
Character	$\chi$	$=$	153.104
Dual form			153.3.q.a.128.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.02458 + 0.542484i) q^{2} +(-2.93844 + 0.604630i) q^{3} +(0.340523 + 0.196601i) q^{4} +(0.673658 - 5.11694i) q^{5} +(-6.27710 - 0.369936i) q^{6} +(12.8501 - 1.69175i) q^{7} +(-5.34561 - 5.34561i) q^{8} +(8.26885 - 3.55333i) q^{9} +(4.13973 - 9.99420i) q^{10} +(-3.69787 + 0.486833i) q^{11} +(-1.11948 - 0.371810i) q^{12} +(3.61010 + 2.08429i) q^{13} +(26.9338 + 3.54590i) q^{14} +(1.11435 + 15.4431i) q^{15} +(-8.70910 - 15.0846i) q^{16} +(13.5097 - 10.3193i) q^{17} +(18.6685 - 2.70829i) q^{18} +(-9.40500 - 9.40500i) q^{19} +(1.23539 - 1.61000i) q^{20} +(-36.7364 + 12.7407i) q^{21} +(-7.75071 - 1.02040i) q^{22} +(7.71580 + 10.0554i) q^{23} +(18.9399 + 12.4756i) q^{24} +(-1.58116 - 0.423670i) q^{25} +(6.17823 + 6.17823i) q^{26} +(-22.1490 + 15.4408i) q^{27} +(4.70837 + 1.95027i) q^{28} +(-30.3514 - 23.2895i) q^{29} +(-6.12156 + 31.8704i) q^{30} +(-6.22376 + 47.2741i) q^{31} +(-1.62258 - 6.05553i) q^{32} +(10.5716 - 3.66637i) q^{33} +(32.9495 - 13.5635i) q^{34} -66.8930i q^{35} +(3.51432 + 0.415672i) q^{36} +(-7.56153 + 3.13209i) q^{37} +(-13.9391 - 24.1432i) q^{38} +(-11.8683 - 3.94179i) q^{39} +(-30.9543 + 23.7521i) q^{40} +(-51.4740 + 39.4974i) q^{41} +(-81.2873 + 5.86556i) q^{42} +(31.7128 + 8.49743i) q^{43} +(-1.35492 - 0.561227i) q^{44} +(-12.6118 - 44.7050i) q^{45} +(10.1663 + 24.5437i) q^{46} +(13.2524 + 22.9539i) q^{47} +(34.7118 + 39.0594i) q^{48} +(114.933 - 30.7963i) q^{49} +(-2.97134 - 1.71550i) q^{50} +(-33.4580 + 38.4911i) q^{51} +(0.819549 + 1.41950i) q^{52} +(12.2800 - 12.2800i) q^{53} +(-53.2189 + 19.2457i) q^{54} +19.2497i q^{55} +(-77.7352 - 59.6483i) q^{56} +(33.3225 + 21.9495i) q^{57} +(-48.8146 - 63.6165i) q^{58} +(88.3899 - 23.6840i) q^{59} +(-2.65668 + 5.47783i) q^{60} +(31.5024 - 4.14737i) q^{61} +(-38.2459 + 92.3339i) q^{62} +(100.244 - 59.6496i) q^{63} +56.5327i q^{64} +(13.0972 - 17.0686i) q^{65} +(23.3920 - 1.68793i) q^{66} +(-4.90058 + 8.48806i) q^{67} +(6.62915 - 0.857949i) q^{68} +(-28.7522 - 24.8821i) q^{69} +(36.2884 - 135.430i) q^{70} +(-9.60716 - 23.1937i) q^{71} +(-63.1968 - 25.2073i) q^{72} +(38.8387 + 93.7649i) q^{73} +(-17.0080 + 2.23915i) q^{74} +(4.90230 + 0.288913i) q^{75} +(-1.35359 - 5.05165i) q^{76} +(-46.6944 + 12.5117i) q^{77} +(-21.8899 - 14.4188i) q^{78} +(14.5504 + 110.521i) q^{79} +(-83.0540 + 34.4021i) q^{80} +(55.7476 - 58.7640i) q^{81} +(-125.640 + 52.0417i) q^{82} +(0.266089 + 0.0712983i) q^{83} +(-15.0144 - 2.88393i) q^{84} +(-43.7025 - 76.0800i) q^{85} +(59.5954 + 34.4074i) q^{86} +(103.267 + 50.0833i) q^{87} +(22.3698 + 17.1649i) q^{88} -122.477 q^{89} +(-1.28192 - 97.3504i) q^{90} +(49.9164 + 20.6760i) q^{91} +(0.650501 + 4.94104i) q^{92} +(-10.2952 - 142.675i) q^{93} +(14.3784 + 53.6611i) q^{94} +(-54.4606 + 41.7891i) q^{95} +(8.42919 + 16.8128i) q^{96} +(-41.0583 + 53.5082i) q^{97} +249.398 q^{98} +(-28.8472 + 17.1653i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 12 q^{2} - 8 q^{3} - 12 q^{5} - 8 q^{6} - 4 q^{7} + 16 q^{9} - 16 q^{10} - 84 q^{11} - 140 q^{12} - 12 q^{14} + 44 q^{15} + 440 q^{16} - 48 q^{18} - 16 q^{19} - 12 q^{20} - 4 q^{22} - 120 q^{23}+ \cdots - 832 q^{99}+O(q^{100}) $ 272 * q - 12 * q^2 - 8 * q^3 - 12 * q^5 - 8 * q^6 - 4 * q^7 + 16 * q^9 - 16 * q^10 - 84 * q^11 - 140 * q^12 - 12 * q^14 + 44 * q^15 + 440 * q^16 - 48 * q^18 - 16 * q^19 - 12 * q^20 - 4 * q^22 - 120 * q^23 + 112 * q^24 - 4 * q^25 + 40 * q^27 - 144 * q^28 - 12 * q^29 - 4 * q^31 - 204 * q^32 + 112 * q^33 - 28 * q^34 - 200 * q^36 - 16 * q^37 - 148 * q^39 + 60 * q^40 - 12 * q^41 - 624 * q^42 + 116 * q^43 + 44 * q^45 - 352 * q^46 - 168 * q^48 - 4 * q^49 - 24 * q^50 - 256 * q^51 - 264 * q^52 - 20 * q^54 + 708 * q^56 + 76 * q^57 - 4 * q^58 + 492 * q^59 - 656 * q^60 - 4 * q^61 + 708 * q^63 + 348 * q^65 - 508 * q^66 - 8 * q^67 - 204 * q^68 + 176 * q^69 + 12 * q^70 - 16 * q^73 + 492 * q^74 - 868 * q^75 + 92 * q^76 + 528 * q^77 + 864 * q^78 - 4 * q^79 + 176 * q^82 + 1428 * q^83 - 440 * q^84 + 188 * q^85 - 1824 * q^86 - 796 * q^87 + 156 * q^88 - 1000 * q^90 - 744 * q^91 - 12 * q^92 + 44 * q^93 + 28 * q^94 - 12 * q^95 - 1452 * q^96 - 364 * q^97 - 832 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.02458	+	0.542484i	1.01229	+	0.271242i	0.726585	−	0.687076i	$-0.241106\pi$
$2$	2.02458	+	0.542484i	1.01229	+	0.271242i	0.285703	+	0.958318i	$0.407773\pi$
$3$	−2.93844	+	0.604630i	−0.979480	+	0.201543i
$3$	−2.93844	+	0.604630i	−0.979480	+	0.201543i
$4$	0.340523	+	0.196601i	0.0851308	+	0.0491503i
$5$	0.673658	−	5.11694i	0.134732	−	1.02339i	−0.781829	−	0.623493i	$-0.785713\pi$
$5$	0.673658	−	5.11694i	0.134732	−	1.02339i	0.916561	−	0.399896i	$-0.130954\pi$
$6$	−6.27710	−	0.369936i	−1.04618	−	0.0616560i
$7$	12.8501	−	1.69175i	1.83573	−	0.241679i	0.868521	−	0.495653i	$-0.165071\pi$
$7$	12.8501	−	1.69175i	1.83573	−	0.241679i	0.967211	+	0.253974i	$0.0817378\pi$
$8$	−5.34561	−	5.34561i	−0.668201	−	0.668201i
$9$	8.26885	−	3.55333i	0.918761	−	0.394815i
$10$	4.13973	−	9.99420i	0.413973	−	0.999420i
$11$	−3.69787	+	0.486833i	−0.336170	+	0.0442576i	−0.296722	−	0.954964i	$-0.595893\pi$
$11$	−3.69787	+	0.486833i	−0.336170	+	0.0442576i	−0.0394481	+	0.999222i	$0.512560\pi$
$12$	−1.11948	−	0.371810i	−0.0932898	−	0.0309842i
$13$	3.61010	+	2.08429i	0.277700	+	0.160330i	0.632382	−	0.774657i	$-0.282077\pi$
$13$	3.61010	+	2.08429i	0.277700	+	0.160330i	−0.354682	+	0.934987i	$0.615411\pi$
$14$	26.9338	+	3.54590i	1.92384	+	0.253279i
$15$	1.11435	+	15.4431i	0.0742901	+	1.02954i
$16$	−8.70910	−	15.0846i	−0.544319	−	0.942788i
$17$	13.5097	−	10.3193i	0.794687	−	0.607019i
$17$	13.5097	−	10.3193i	0.794687	−	0.607019i
$18$	18.6685	−	2.70829i	1.03714	−	0.150460i
$19$	−9.40500	−	9.40500i	−0.495000	−	0.495000i	0.414878	−	0.909877i	$-0.363824\pi$
$19$	−9.40500	−	9.40500i	−0.495000	−	0.495000i	−0.909877	+	0.414878i	$0.863824\pi$
$20$	1.23539	−	1.61000i	0.0617697	−	0.0804998i
$21$	−36.7364	+	12.7407i	−1.74935	+	0.606699i
$22$	−7.75071	−	1.02040i	−0.352305	−	0.0463819i
$23$	7.71580	+	10.0554i	0.335470	+	0.437193i	0.930378	−	0.366601i	$-0.119478\pi$
$23$	7.71580	+	10.0554i	0.335470	+	0.437193i	−0.594909	+	0.803793i	$0.702812\pi$
$24$	18.9399	+	12.4756i	0.789161	+	0.519818i
$25$	−1.58116	−	0.423670i	−0.0632463	−	0.0169468i
$26$	6.17823	+	6.17823i	0.237624	+	0.237624i
$27$	−22.1490	+	15.4408i	−0.820335	+	0.571883i
$28$	4.70837	+	1.95027i	0.168156	+	0.0696525i
$29$	−30.3514	−	23.2895i	−1.04660	−	0.803085i	−0.0657477	−	0.997836i	$-0.520943\pi$
$29$	−30.3514	−	23.2895i	−1.04660	−	0.803085i	−0.980853	+	0.194752i	$0.937610\pi$
$30$	−6.12156	+	31.8704i	−0.204052	+	1.06235i
$31$	−6.22376	+	47.2741i	−0.200766	+	1.52497i	0.533319	+	0.845914i	$0.320945\pi$
$31$	−6.22376	+	47.2741i	−0.200766	+	1.52497i	−0.734085	+	0.679058i	$0.762389\pi$
$32$	−1.62258	−	6.05553i	−0.0507055	−	0.189235i
$33$	10.5716	−	3.66637i	0.320351	−	0.111102i
$34$	32.9495	−	13.5635i	0.969102	−	0.398926i
$35$		−	66.8930i		−	1.91123i
$36$	3.51432	+	0.415672i	0.0976201	+	0.0115464i
$37$	−7.56153	+	3.13209i	−0.204366	+	0.0846511i	−0.482518	−	0.875886i	$-0.660278\pi$
$37$	−7.56153	+	3.13209i	−0.204366	+	0.0846511i	0.278153	+	0.960537i	$0.410278\pi$
$38$	−13.9391	−	24.1432i	−0.366818	−	0.635347i
$39$	−11.8683	−	3.94179i	−0.304315	−	0.101072i
$40$	−30.9543	+	23.7521i	−0.773858	+	0.593802i
$41$	−51.4740	+	39.4974i	−1.25546	+	0.963351i	−0.999994	−	0.00346616i	$-0.998897\pi$
$41$	−51.4740	+	39.4974i	−1.25546	+	0.963351i	−0.255469	+	0.966817i	$0.582230\pi$
$42$	−81.2873	+	5.86556i	−1.93541	+	0.139656i
$43$	31.7128	+	8.49743i	0.737508	+	0.197615i	0.607970	−	0.793960i	$-0.291984\pi$
$43$	31.7128	+	8.49743i	0.737508	+	0.197615i	0.129538	+	0.991575i	$0.458651\pi$
$44$	−1.35492	−	0.561227i	−0.0307937	−	0.0127552i
$45$	−12.6118	−	44.7050i	−0.280263	−	0.993444i
$46$	10.1663	+	24.5437i	0.221007	+	0.533559i
$47$	13.2524	+	22.9539i	0.281966	+	0.488380i	0.971869	−	0.235522i	$-0.0756801\pi$
$47$	13.2524	+	22.9539i	0.281966	+	0.488380i	−0.689903	+	0.723902i	$0.742347\pi$
$48$	34.7118	+	39.0594i	0.723162	+	0.813738i
$49$	114.933	−	30.7963i	2.34558	−	0.628495i
$50$	−2.97134	−	1.71550i	−0.0594268	−	0.0343101i
$51$	−33.4580	+	38.4911i	−0.656040	+	0.754727i
$52$	0.819549	+	1.41950i	0.0157606	+	0.0272981i
$53$	12.2800	−	12.2800i	0.231698	−	0.231698i	−0.581703	−	0.813401i	$-0.697613\pi$
$53$	12.2800	−	12.2800i	0.231698	−	0.231698i	0.813401	+	0.581703i	$0.197613\pi$
$54$	−53.2189	+	19.2457i	−0.985535	+	0.356402i
$55$			19.2497i			0.349995i
$56$	−77.7352	−	59.6483i	−1.38813	−	1.06515i
$57$	33.3225	+	21.9495i	0.584606	+	0.385078i
$58$	−48.8146	−	63.6165i	−0.841631	−	1.09684i
$59$	88.3899	−	23.6840i	1.49813	−	0.401424i	0.585659	−	0.810558i	$-0.300836\pi$
$59$	88.3899	−	23.6840i	1.49813	−	0.401424i	0.912474	+	0.409134i	$0.134169\pi$
$60$	−2.65668	+	5.47783i	−0.0442780	+	0.0912972i
$61$	31.5024	−	4.14737i	0.516433	−	0.0679897i	0.132195	−	0.991224i	$-0.457798\pi$
$61$	31.5024	−	4.14737i	0.516433	−	0.0679897i	0.384238	+	0.923234i	$0.374464\pi$
$62$	−38.2459	+	92.3339i	−0.616870	+	1.48926i
$63$	100.244	−	59.6496i	1.59118	−	0.946819i
$64$			56.5327i			0.883323i
$65$	13.0972	−	17.0686i	0.201495	−	0.262594i
$66$	23.3920	−	1.68793i	0.354424	−	0.0255746i
$67$	−4.90058	+	8.48806i	−0.0731430	+	0.126687i	−0.900277	−	0.435317i	$-0.856636\pi$
$67$	−4.90058	+	8.48806i	−0.0731430	+	0.126687i	0.827134	+	0.562004i	$0.189970\pi$
$68$	6.62915	−	0.857949i	0.0974875	−	0.0126169i
$69$	−28.7522	−	24.8821i	−0.416699	−	0.360610i
$70$	36.2884	−	135.430i	0.518406	−	1.93472i
$71$	−9.60716	−	23.1937i	−0.135312	−	0.326672i	0.841670	−	0.539992i	$-0.181573\pi$
$71$	−9.60716	−	23.1937i	−0.135312	−	0.326672i	−0.976983	+	0.213319i	$0.931573\pi$
$72$	−63.1968	−	25.2073i	−0.877733	−	0.350101i
$73$	38.8387	+	93.7649i	0.532037	+	1.28445i	0.930172	+	0.367124i	$0.119658\pi$
$73$	38.8387	+	93.7649i	0.532037	+	1.28445i	−0.398135	+	0.917327i	$0.630342\pi$
$74$	−17.0080	+	2.23915i	−0.229838	+	0.0302588i
$75$	4.90230	+	0.288913i	0.0653640	+	0.00385218i
$76$	−1.35359	−	5.05165i	−0.0178103	−	0.0664691i
$77$	−46.6944	+	12.5117i	−0.606421	+	0.162490i
$78$	−21.8899	−	14.4188i	−0.280640	−	0.184857i
$79$	14.5504	+	110.521i	0.184182	+	1.39900i	0.794700	+	0.607002i	$0.207628\pi$
$79$	14.5504	+	110.521i	0.184182	+	1.39900i	−0.610518	+	0.792003i	$0.709039\pi$
$80$	−83.0540	+	34.4021i	−1.03818	+	0.430026i
$81$	55.7476	−	58.7640i	0.688242	−	0.725481i
$82$	−125.640	+	52.0417i	−1.53219	+	0.634655i
$83$	0.266089	+	0.0712983i	0.00320589	+	0.000859015i	0.260422	−	0.965495i	$-0.416138\pi$
$83$	0.266089	+	0.0712983i	0.00320589	+	0.000859015i	−0.257216	+	0.966354i	$0.582805\pi$
$84$	−15.0144	−	2.88393i	−0.178743	−	0.0343325i
$85$	−43.7025	−	76.0800i	−0.514147	−	0.895059i
$86$	59.5954	+	34.4074i	0.692969	+	0.400086i
$87$	103.267	+	50.0833i	1.18698	+	0.575670i
$88$	22.3698	+	17.1649i	0.254202	+	0.195056i
$89$	−122.477			−1.37614			−0.688071	−	0.725643i	$-0.741542\pi$
$89$	−122.477			−1.37614			−0.688071	+	0.725643i	$0.741542\pi$
$90$	−1.28192	−	97.3504i	−0.0142436	−	1.08167i
$91$	49.9164	+	20.6760i	0.548531	+	0.227209i
$92$	0.650501	+	4.94104i	0.00707066	+	0.0537070i
$93$	−10.2952	−	142.675i	−0.110701	−	1.53414i
$94$	14.3784	+	53.6611i	0.152962	+	0.570862i
$95$	−54.4606	+	41.7891i	−0.573269	+	0.439885i
$96$	8.42919	+	16.8128i	0.0878041	+	0.175133i
$97$	−41.0583	+	53.5082i	−0.423281	+	0.551631i	−0.955506	−	0.294972i	$-0.904690\pi$
$97$	−41.0583	+	53.5082i	−0.423281	+	0.551631i	0.532224	+	0.846603i	$0.321356\pi$
$98$	249.398			2.54488
$99$	−28.8472	+	17.1653i	−0.291386	+	0.173387i
$100$	−0.455127	−	0.455127i	−0.00455127	−	0.00455127i
$101$	−64.1346	+	37.0281i	−0.634996	+	0.366615i	−0.782684	−	0.622419i	$-0.786150\pi$
$101$	−64.1346	+	37.0281i	−0.634996	+	0.366615i	0.147688	+	0.989034i	$0.452817\pi$
$102$	−88.6191	+	59.7777i	−0.868815	+	0.586056i
$103$	−38.5891	+	66.8383i	−0.374652	+	0.648916i	−0.990275	−	0.139125i	$-0.955571\pi$
$103$	−38.5891	+	66.8383i	−0.374652	+	0.648916i	0.615623	+	0.788041i	$0.288904\pi$
$104$	−8.15638	−	30.4400i	−0.0784267	−	0.292693i
$105$	40.4455	+	196.561i	0.385195	+	1.87201i
$106$	31.5235	−	18.2001i	0.297392	−	0.171699i
$107$	64.1461	−	26.5702i	0.599496	−	0.248319i	−0.0622339	−	0.998062i	$-0.519822\pi$
$107$	64.1461	−	26.5702i	0.599496	−	0.248319i	0.661730	+	0.749742i	$0.269822\pi$
$108$	−10.5780	+	0.903438i	−0.0979440	+	0.00836517i
$109$	33.3391	−	80.4878i	0.305864	−	0.738420i	−0.693967	−	0.720007i	$-0.744139\pi$
$109$	33.3391	−	80.4878i	0.305864	−	0.738420i	0.999830	−	0.0184130i	$-0.00586137\pi$
$110$	−10.4427	+	38.9726i	−0.0949333	+	0.354296i
$111$	20.3253	−	13.7754i	0.183111	−	0.124103i
$112$	−137.432	−	179.105i	−1.22708	−	1.59916i
$113$	−68.3810	−	89.1158i	−0.605141	−	0.788635i	0.385850	−	0.922562i	$-0.373908\pi$
$113$	−68.3810	−	89.1158i	−0.605141	−	0.788635i	−0.990991	+	0.133926i	$0.957242\pi$
$114$	55.5568	+	62.5153i	0.487341	+	0.548380i
$115$	56.6509	−	32.7074i	0.492616	−	0.284412i
$116$	−5.75662	−	13.8977i	−0.0496261	−	0.119808i
$117$	37.2576	+	4.40680i	0.318441	+	0.0376650i
$118$	191.800			1.62543
$119$	156.143	−	155.460i	1.31213	−	1.30638i
$120$	76.5961	−	88.5099i	0.638301	−	0.737583i
$121$	−103.440	+	27.7166i	−0.854875	+	0.229063i
$122$	66.0289	+	8.69287i	0.541221	+	0.0712531i
$123$	127.372	−	147.183i	1.03554	−	1.19661i
$124$	−11.4135	+	14.8743i	−0.0920442	+	0.119954i
$125$	46.1436	−	111.401i	0.369149	−	0.891204i
$126$	235.311	−	66.3843i	1.86755	−	0.526860i
$127$	163.914	−	163.914i	1.29066	−	1.29066i	0.356281	−	0.934379i	$-0.384044\pi$
$127$	163.914	−	163.914i	1.29066	−	1.29066i	0.934379	−	0.356281i	$-0.115956\pi$
$128$	−37.1584	+	138.677i	−0.290300	+	1.08341i
$129$	−98.3240	−	5.79465i	−0.762202	−	0.0449198i
$130$	35.7757	−	27.4517i	0.275198	−	0.211167i
$131$	−2.66343	+	20.2308i	−0.0203315	+	0.154433i	−0.998599	−	0.0529131i	$-0.983149\pi$
$131$	−2.66343	+	20.2308i	−0.0203315	+	0.154433i	0.978268	+	0.207346i	$0.0664827\pi$
$132$	4.32069	+	0.829905i	0.0327325	+	0.00628716i
$133$	−136.766	−	104.944i	−1.02832	−	0.789056i
$134$	−14.5262	+	14.5262i	−0.108405	+	0.108405i
$135$	64.0891	+	123.737i	0.474734	+	0.916573i
$136$	−127.381	−	17.0544i	−0.936622	−	0.125400i
$137$	53.7644	−	31.0409i	0.392441	−	0.226576i	−0.290776	−	0.956791i	$-0.593914\pi$
$137$	53.7644	−	31.0409i	0.392441	−	0.226576i	0.683217	+	0.730215i	$0.260580\pi$
$138$	−44.7130	−	65.9733i	−0.324007	−	0.478067i
$139$	−24.6109	+	186.938i	−0.177057	+	1.34488i	0.640023	+	0.768356i	$0.278925\pi$
$139$	−24.6109	+	186.938i	−0.177057	+	1.34488i	−0.817080	+	0.576525i	$0.804408\pi$
$140$	13.1512	−	22.7786i	0.0939375	−	0.162704i
$141$	−52.8200	−	59.4357i	−0.374610	−	0.421530i
$142$	−6.86821	−	52.1692i	−0.0483677	−	0.367389i
$143$	−14.3644	−	5.94992i	−0.100450	−	0.0416078i
$144$	−125.615	−	93.7859i	−0.872325	−	0.651291i
$145$	−139.617	+	139.617i	−0.962878	+	0.962878i
$146$	27.7660	+	210.904i	0.190178	+	1.44455i
$147$	−319.104	+	159.985i	−2.17078	+	1.08833i
$148$	−3.19065	−	0.420057i	−0.0215584	−	0.00283822i
$149$	38.1498	−	66.0775i	0.256039	−	0.443473i	−0.709138	−	0.705070i	$-0.750916\pi$
$149$	38.1498	−	66.0775i	0.256039	−	0.443473i	0.965177	+	0.261597i	$0.0842490\pi$
$150$	9.76835	+	3.24434i	0.0651223	+	0.0216290i
$151$	31.1666	−	116.315i	0.206401	−	0.770300i	−0.782617	−	0.622504i	$-0.786115\pi$
$151$	31.1666	−	116.315i	0.206401	−	0.770300i	0.989018	−	0.147796i	$-0.0472178\pi$
$152$			100.551i			0.661519i
$153$	75.0415	−	133.333i	0.490467	−	0.871460i
$154$	−101.324			−0.657947
$155$	237.706	+	63.6932i	1.53359	+	0.410924i
$156$	−3.26647	−	3.67559i	−0.0209389	−	0.0235615i
$157$	−252.055	−	145.524i	−1.60545	−	0.926905i	−0.990371	−	0.138435i	$-0.955793\pi$
$157$	−252.055	−	145.524i	−1.60545	−	0.926905i	−0.615074	−	0.788469i	$-0.710874\pi$
$158$	−30.4976	+	231.652i	−0.193023	+	1.46615i
$159$	−28.6592	+	43.5089i	−0.180246	+	0.273641i
$160$	−32.0789	+	4.22327i	−0.200493	+	0.0263954i
$161$	116.160	+	116.160i	0.721493	+	0.721493i
$162$	144.744	−	88.7300i	0.893481	−	0.547716i
$163$	−48.4445	+	116.955i	−0.297206	+	0.717518i	0.702776	+	0.711411i	$0.251944\pi$
$163$	−48.4445	+	116.955i	−0.297206	+	0.717518i	−0.999981	+	0.00610623i	$0.998056\pi$
$164$	−25.2933	+	3.32993i	−0.154228	+	0.0203044i
$165$	−11.6390	−	56.5642i	−0.0705391	−	0.342813i
$166$	0.500039	+	0.288698i	0.00301228	+	0.00173914i
$167$	−38.0477	−	5.00907i	−0.227830	−	0.0299944i	0.0157466	−	0.999876i	$-0.494987\pi$
$167$	−38.0477	−	5.00907i	−0.227830	−	0.0299944i	−0.243577	+	0.969882i	$0.578321\pi$
$168$	264.485	+	128.272i	1.57432	+	0.763523i
$169$	−75.8114	−	131.309i	−0.448588	−	0.776978i
$170$	−47.2069	−	177.738i	−0.277688	−	1.04552i
$171$	−111.188	−	44.3494i	−0.650220	−	0.259353i
$172$	9.12835	+	9.12835i	0.0530718	+	0.0530718i
$173$	−169.093	+	220.366i	−0.977414	+	1.27379i	−0.0156593	+	0.999877i	$0.504985\pi$
$173$	−169.093	+	220.366i	−0.977414	+	1.27379i	−0.961754	+	0.273913i	$0.911682\pi$
$174$	181.903	+	157.418i	1.04542	+	0.904703i
$175$	−21.0348	−	2.76929i	−0.120199	−	0.0158245i
$176$	39.5488	+	51.5410i	0.224709	+	0.292846i
$177$	−245.408	+	123.037i	−1.38649	+	0.695125i
$178$	−247.963	−	66.4416i	−1.39305	−	0.373267i
$179$	179.893	+	179.893i	1.00499	+	1.00499i	0.999987	+	0.00500183i	$0.00159214\pi$
$179$	179.893	+	179.893i	1.00499	+	1.00499i	0.00500183	+	0.999987i	$0.498408\pi$
$180$	4.49442	−	17.7026i	0.0249690	−	0.0983477i
$181$	254.065	+	105.237i	1.40367	+	0.581421i	0.950703	−	0.310104i	$-0.100364\pi$
$181$	254.065	+	105.237i	1.40367	+	0.581421i	0.452972	+	0.891525i	$0.350364\pi$
$182$	89.8431	+	68.9390i	0.493643	+	0.378786i
$183$	−90.0603	+	31.2341i	−0.492133	+	0.170678i
$184$	12.5067	−	94.9981i	0.0679714	−	0.516294i
$185$	10.9328	+	40.8019i	0.0590964	+	0.220551i
$186$	56.5556	−	294.442i	0.304062	−	1.58302i
$187$	−44.9332	+	44.7364i	−0.240285	+	0.239232i
$188$			10.4218i			0.0554349i
$189$	−258.496	+	235.887i	−1.36770	+	1.24808i
$190$	−132.930	+	55.0612i	−0.699629	+	0.289796i
$191$	39.6650	+	68.7017i	0.207670	+	0.359695i	0.950980	−	0.309252i	$-0.100079\pi$
$191$	39.6650	+	68.7017i	0.207670	+	0.359695i	−0.743310	+	0.668947i	$0.766745\pi$
$192$	−34.1813	−	166.118i	−0.178028	−	0.865197i
$193$	50.6006	−	38.8272i	0.262179	−	0.201177i	−0.469304	−	0.883037i	$-0.655495\pi$
$193$	50.6006	−	38.8272i	0.262179	−	0.201177i	0.731483	+	0.681859i	$0.238828\pi$
$194$	−112.153	+	86.0581i	−0.578109	+	0.443598i
$195$	−28.1651	+	58.0739i	−0.144436	+	0.297815i
$196$	45.1920	+	12.1092i	0.230572	+	0.0617815i
$197$	−268.509	−	111.220i	−1.36299	−	0.564569i	−0.423111	−	0.906078i	$-0.639062\pi$
$197$	−268.509	−	111.220i	−1.36299	−	0.564569i	−0.939878	+	0.341509i	$0.889062\pi$
$198$	−67.7153	+	19.1033i	−0.341996	+	0.0964815i
$199$	−113.809	−	274.758i	−0.571902	−	1.38069i	−0.899934	−	0.436027i	$-0.856385\pi$
$199$	−113.809	−	274.758i	−0.571902	−	1.38069i	0.328032	−	0.944667i	$-0.393615\pi$
$200$	6.18748	+	10.7170i	0.0309374	+	0.0535851i
$201$	9.26793	−	27.9047i	0.0461091	−	0.138829i
$202$	−149.933	+	40.1743i	−0.742241	+	0.198883i
$203$	−429.419	−	247.925i	−2.11537	−	1.22131i
$204$	−18.9606	+	6.52921i	−0.0929442	+	0.0320059i
$205$	167.430	+	289.997i	0.816732	+	1.41462i
$206$	−114.385	+	114.385i	−0.555269	+	0.555269i
$207$	99.5311	+	55.7300i	0.480827	+	0.269227i
$208$		−	72.6093i		−	0.349083i
$209$	39.3571	+	30.1997i	0.188311	+	0.144496i
$210$	−24.7462	+	419.894i	−0.117839	+	1.99950i
$211$	−56.1848	−	73.2215i	−0.266279	−	0.347021i	0.641008	−	0.767535i	$-0.278517\pi$
$211$	−56.1848	−	73.2215i	−0.266279	−	0.347021i	−0.907286	+	0.420513i	$0.861850\pi$
$212$	6.59589	−	1.76736i	0.0311127	−	0.00833662i
$213$	42.2537	+	62.3446i	0.198374	+	0.292698i
$214$	144.283	−	18.9952i	0.674218	−	0.0887625i
$215$	64.8445	−	156.548i	0.301602	−	0.728132i
$216$	200.941	+	35.8594i	0.930282	+	0.166016i
$217$			618.007i			2.84796i
$218$	111.161	−	144.868i	0.509913	−	0.664531i
$219$	−170.818	−	252.039i	−0.779992	−	1.15086i
$220$	−3.78452	+	6.55498i	−0.0172024	+	0.0297954i
$221$	70.2798	−	9.09566i	0.318008	−	0.0411568i
$222$	48.6232	−	16.8631i	0.219023	−	0.0759601i
$223$	17.0165	−	63.5063i	0.0763070	−	0.284781i	−0.917220	−	0.398382i	$-0.869572\pi$
$223$	17.0165	−	63.5063i	0.0763070	−	0.284781i	0.993526	+	0.113601i	$0.0362385\pi$
$224$	−31.0947	−	75.0693i	−0.138816	−	0.335131i
$225$	−14.5798	+	2.11512i	−0.0647990	+	0.00940053i
$226$	−90.0987	−	217.517i	−0.398667	−	0.962466i
$227$	−257.886	+	33.9513i	−1.13606	+	0.149565i	−0.675010	−	0.737809i	$-0.735861\pi$
$227$	−257.886	+	33.9513i	−1.13606	+	0.149565i	−0.461050	+	0.887374i	$0.652527\pi$
$228$	7.03181	+	14.0256i	0.0308413	+	0.0615156i
$229$	16.1744	+	60.3635i	0.0706304	+	0.263596i	0.992207	−	0.124600i	$-0.0397649\pi$
$229$	16.1744	+	60.3635i	0.0706304	+	0.263596i	−0.921577	+	0.388196i	$0.873098\pi$
$230$	132.437	−	35.4865i	0.575815	−	0.154289i
$231$	129.644	−	64.9978i	0.561228	−	0.281376i
$232$	37.7505	+	286.743i	0.162717	+	1.23596i
$233$	84.5331	−	35.0148i	0.362803	−	0.150278i	−0.193833	−	0.981035i	$-0.562092\pi$
$233$	84.5331	−	35.0148i	0.362803	−	0.150278i	0.556636	+	0.830757i	$0.312092\pi$
$234$	73.0402	+	29.1335i	0.312138	+	0.124502i
$235$	126.381	−	52.3488i	0.537792	−	0.222761i
$236$	34.7551	+	9.31260i	0.147267	+	0.0394602i
$237$	−109.580	−	315.963i	−0.462363	−	1.33318i
$238$	400.459	−	230.035i	1.68260	−	0.966532i
$239$	76.2737	+	44.0366i	0.319137	+	0.184254i	0.651008	−	0.759071i	$-0.274347\pi$
$239$	76.2737	+	44.0366i	0.319137	+	0.184254i	−0.331871	+	0.943325i	$0.607680\pi$
$240$	223.249	−	151.305i	0.930203	−	0.630439i
$241$	321.330	+	246.565i	1.33332	+	1.02309i	0.996677	+	0.0814579i	$0.0259576\pi$
$241$	321.330	+	246.565i	1.33332	+	1.02309i	0.336641	+	0.941633i	$0.390709\pi$
$242$	−224.458			−0.927511
$243$	−128.281	+	206.381i	−0.527904	+	0.849304i
$244$	11.5427	+	4.78113i	0.0473061	+	0.0195948i
$245$	−80.1571	−	608.853i	−0.327172	−	2.48512i
$246$	337.719	−	228.887i	1.37284	−	0.930435i
$247$	−14.3502	−	53.5558i	−0.0580981	−	0.216825i
$248$	285.979	−	219.439i	1.15314	−	0.884836i
$249$	−0.824994	−	0.0486204i	−0.00331323	−	0.000195263i
$250$	153.854	−	200.507i	0.615417	−	0.802027i
$251$	313.006			1.24704			0.623518	−	0.781809i	$-0.285703\pi$
$251$	313.006			1.24704			0.623518	+	0.781809i	$0.285703\pi$
$252$	45.8627	−	0.603925i	0.181995	−	0.00239653i
$253$	−33.4273	−	33.4273i	−0.132124	−	0.132124i
$254$	420.777	−	242.936i	1.65660	−	0.956439i
$255$	174.417	+	197.133i	0.683989	+	0.773069i
$256$	−37.3946	+	64.7694i	−0.146073	+	0.253005i
$257$	−3.99304	−	14.9022i	−0.0155371	−	0.0579854i	0.957722	−	0.287695i	$-0.0928890\pi$
$257$	−3.99304	−	14.9022i	−0.0155371	−	0.0579854i	−0.973259	+	0.229710i	$0.926222\pi$
$258$	−195.921	−	65.0709i	−0.759384	−	0.252213i
$259$	−91.8679	+	53.0400i	−0.354702	+	0.204787i
$260$	7.81560	−	3.23733i	0.0300600	−	0.0124513i
$261$	−333.726	−	84.7282i	−1.27864	−	0.324629i
$262$	−16.3672	+	39.5139i	−0.0624702	+	0.150816i
$263$	0.871831	−	3.25372i	0.00331495	−	0.0123715i	−0.964249	−	0.265000i	$-0.914628\pi$
$263$	0.871831	−	3.25372i	0.00331495	−	0.0123715i	0.967563	+	0.252628i	$0.0812949\pi$
$264$	−76.1106	−	36.9127i	−0.288298	−	0.139821i
$265$	−54.5636	−	71.1086i	−0.205900	−	0.268334i
$266$	−219.963	−	286.662i	−0.826929	−	1.07768i
$267$	359.890	−	74.0530i	1.34790	−	0.277352i
$268$	−3.33752	+	1.92692i	−0.0124534	+	0.00719000i
$269$	131.292	+	316.967i	0.488075	+	1.17832i	0.955688	+	0.294383i	$0.0951141\pi$
$269$	131.292	+	316.967i	0.488075	+	1.17832i	−0.467613	+	0.883933i	$0.654886\pi$
$270$	62.6278	+	285.283i	0.231955	+	1.05660i
$271$	70.4160			0.259838			0.129919	−	0.991525i	$-0.458528\pi$
$271$	70.4160			0.259838			0.129919	+	0.991525i	$0.458528\pi$
$272$	−273.320	−	113.916i	−1.00485	−	0.418810i
$273$	−159.177	−	30.5743i	−0.583068	−	0.111994i
$274$	125.689	−	33.6784i	0.458720	−	0.122914i
$275$	6.05316	+	0.796914i	0.0220115	+	0.00289787i
$276$	−4.89896	−	14.1256i	−0.0177498	−	0.0511799i
$277$	176.625	−	230.182i	0.637636	−	0.830983i	−0.357034	−	0.934091i	$-0.616212\pi$
$277$	176.625	−	230.182i	0.637636	−	0.830983i	0.994670	+	0.103108i	$0.0328788\pi$
$278$	−151.238	+	365.120i	−0.544021	+	1.31338i
$279$	116.518	+	413.018i	0.417626	+	1.48035i
$280$	−357.584	+	357.584i	−1.27709	+	1.27709i
$281$	33.5321	−	125.144i	0.119331	−	0.445351i	−0.880243	−	0.474523i	$-0.842620\pi$
$281$	33.5321	−	125.144i	0.119331	−	0.445351i	0.999574	+	0.0291722i	$0.00928712\pi$
$282$	−74.6952	−	148.986i	−0.264877	−	0.528320i
$283$	−242.262	+	185.894i	−0.856049	+	0.656869i	−0.940588	−	0.339551i	$-0.889725\pi$
$283$	−242.262	+	185.894i	−0.856049	+	0.656869i	0.0845390	+	0.996420i	$0.473058\pi$
$284$	1.28845	−	9.78678i	0.00453681	−	0.0344605i
$285$	134.762	−	155.723i	0.472850	−	0.546397i
$286$	−25.8541	−	19.8385i	−0.0903988	−	0.0693654i
$287$	−594.627	+	594.627i	−2.07187	+	2.07187i
$288$	−34.9342	−	44.3067i	−0.121299	−	0.153843i
$289$	76.0232	−	278.822i	0.263056	−	0.964781i
$290$	−358.406	+	206.926i	−1.23588	+	0.713538i
$291$	88.2946	−	182.056i	0.303418	−	0.625621i
$292$	−5.20881	+	39.5649i	−0.0178384	+	0.135496i
$293$	11.4188	−	19.7779i	0.0389720	−	0.0675014i	−0.845882	−	0.533371i	$-0.820925\pi$
$293$	11.4188	−	19.7779i	0.0389720	−	0.0675014i	0.884853	+	0.465869i	$0.154258\pi$
$294$	−732.840	+	150.793i	−2.49265	+	0.512902i
$295$	−61.6451	−	468.241i	−0.208966	−	1.58726i
$296$	57.1639	+	23.6781i	0.193121	+	0.0799935i
$297$	74.3871	−	67.8811i	0.250462	−	0.228556i
$298$	113.083	−	113.083i	0.379474	−	0.379474i
$299$	6.89637	+	52.3831i	0.0230648	+	0.175194i
$300$	1.61255	+	1.06218i	0.00537515	+	0.00354060i
$301$	421.889	+	55.5428i	1.40163	+	0.184528i
$302$	126.198	−	218.582i	0.417875	−	0.723781i
$303$	166.067	−	147.583i	0.548077	−	0.487071i
$304$	−59.9616	+	223.780i	−0.197242	+	0.736117i
$305$		−	163.990i		−	0.537672i
$306$	224.258	−	229.235i	0.732871	−	0.749133i
$307$	271.736			0.885135			0.442568	−	0.896735i	$-0.354068\pi$
$307$	271.736			0.885135			0.442568	+	0.896735i	$0.354068\pi$
$308$	−18.3604	−	4.91964i	−0.0596115	−	0.0159729i
$309$	72.9794	−	219.732i	0.236179	−	0.711108i
$310$	446.703	+	257.904i	1.44098	+	0.831948i
$311$	−9.73314	+	73.9306i	−0.0312963	+	0.237719i	−0.999942	−	0.0107254i	$-0.996586\pi$
$311$	−9.73314	+	73.9306i	−0.0312963	+	0.237719i	0.968646	+	0.248444i	$0.0799193\pi$
$312$	42.3720	+	84.5146i	0.135808	+	0.270880i
$313$	197.259	−	25.9696i	0.630219	−	0.0829699i	0.191351	−	0.981522i	$-0.438713\pi$
$313$	197.259	−	25.9696i	0.630219	−	0.0829699i	0.438868	+	0.898552i	$0.355380\pi$
$314$	−431.360	−	431.360i	−1.37376	−	1.37376i
$315$	−237.693	−	553.128i	−0.754582	−	1.75596i
$316$	−16.7739	+	40.4957i	−0.0530819	+	0.128151i
$317$	375.775	−	49.4717i	1.18541	−	0.156062i	0.488071	−	0.872804i	$-0.337701\pi$
$317$	375.775	−	49.4717i	1.18541	−	0.156062i	0.697339	+	0.716741i	$0.254367\pi$
$318$	−81.6256	+	72.5400i	−0.256684	+	0.228113i
$319$	123.573	+	71.3452i	0.387378	+	0.223653i
$320$	289.275	+	38.0837i	0.903983	+	0.119012i
$321$	−172.424	+	116.859i	−0.537147	+	0.364048i
$322$	172.160	+	298.191i	0.534660	+	0.926058i
$323$	−224.112	−	30.0053i	−0.693844	−	0.0928958i
$324$	30.5364	−	9.05044i	0.0942482	−	0.0279335i
$325$	−4.82509	−	4.82509i	−0.0148464	−	0.0148464i
$326$	−161.526	+	210.505i	−0.495479	+	0.645720i
$327$	−49.2997	+	256.666i	−0.150764	+	0.784912i
$328$	486.298	+	64.0223i	1.48261	+	0.195190i
$329$	209.127	+	272.540i	0.635645	+	0.828389i
$330$	7.12117	−	120.832i	0.0215793	−	0.366159i
$331$	−586.967	−	157.277i	−1.77331	−	0.475158i	−0.783976	−	0.620791i	$-0.786811\pi$
$331$	−586.967	−	157.277i	−1.77331	−	0.475158i	−0.989339	+	0.145633i	$0.953478\pi$
$332$	0.0765921	+	0.0765921i	0.000230699	+	0.000230699i
$333$	−51.3958	+	52.7674i	−0.154342	+	0.158461i
$334$	−74.3131	−	30.7815i	−0.222494	−	0.0921602i
$335$	40.1316	+	30.7941i	0.119796	+	0.0919225i
$336$	512.129	+	443.195i	1.52419	+	1.31903i
$337$	−13.7605	+	104.521i	−0.0408322	+	0.310152i	0.958826	+	0.283995i	$0.0916601\pi$
$337$	−13.7605	+	104.521i	−0.0408322	+	0.310152i	−0.999658	+	0.0261562i	$0.991673\pi$
$338$	−82.2530	−	306.972i	−0.243352	−	0.908202i
$339$	254.815	+	220.516i	0.751668	+	0.650490i
$340$	0.0757079	−	34.4990i	0.000222670	−	0.101468i
$341$		−	177.843i		−	0.521535i
$342$	−201.049	−	150.106i	−0.587863	−	0.438907i
$343$	838.061	−	347.136i	2.44333	−	1.01206i
$344$	−124.101	−	214.948i	−0.360757	−	0.624850i
$345$	−146.689	+	130.362i	−0.425186	+	0.377859i
$346$	−461.886	+	354.417i	−1.33493	+	1.02433i
$347$	−250.892	+	192.516i	−0.723031	+	0.554801i	−0.903401	−	0.428798i	$-0.858937\pi$
$347$	−250.892	+	192.516i	−0.723031	+	0.554801i	0.180370	+	0.983599i	$0.442271\pi$
$348$	25.3185	+	37.3570i	0.0727542	+	0.107348i
$349$	−373.565	−	100.096i	−1.07039	−	0.286809i	−0.319734	−	0.947507i	$-0.603594\pi$
$349$	−373.565	−	100.096i	−1.07039	−	0.286809i	−0.750652	+	0.660698i	$0.770260\pi$
$350$	−41.0843	−	17.0177i	−0.117384	−	0.0486219i
$351$	−112.144	+	9.57792i	−0.319497	+	0.0272875i
$352$	8.94810	+	21.6026i	0.0254207	+	0.0613711i
$353$	−149.460	−	258.872i	−0.423398	−	0.733347i	0.572871	−	0.819645i	$-0.305830\pi$
$353$	−149.460	−	258.872i	−0.423398	−	0.733347i	−0.996269	+	0.0862982i	$0.972496\pi$
$354$	−563.593	+	115.968i	−1.59207	+	0.327594i
$355$	−125.153	+	33.5346i	−0.352544	+	0.0944638i
$356$	−41.7061	−	24.0791i	−0.117152	−	0.0676378i
$357$	−364.822	+	551.217i	−1.02191	+	1.54403i
$358$	266.618	+	461.797i	0.744744	+	1.28993i
$359$	−0.672237	+	0.672237i	−0.00187253	+	0.00187253i	−0.708042	−	0.706170i	$-0.750421\pi$
$359$	−0.672237	+	0.672237i	−0.00187253	+	0.00187253i	0.706170	+	0.708042i	$0.250421\pi$
$360$	−171.557	+	306.393i	−0.476548	+	0.851093i
$361$		−	184.092i		−	0.509950i
$362$	457.285	+	350.887i	1.26322	+	0.969301i
$363$	287.193	−	143.986i	0.791166	−	0.396657i
$364$	12.9327	+	16.8543i	0.0355295	+	0.0463030i
$365$	505.954	−	135.570i	1.38617	−	0.371424i
$366$	−199.278	+	14.3796i	−0.544475	+	0.0392885i
$367$	−35.8165	+	4.71533i	−0.0975926	+	0.0128483i	−0.179164	−	0.983819i	$-0.557339\pi$
$367$	−35.8165	+	4.71533i	−0.0975926	+	0.0128483i	0.0815717	+	0.996667i	$0.474006\pi$
$368$	84.4845	−	203.964i	0.229577	−	0.554249i
$369$	−285.283	+	509.502i	−0.773125	+	1.38076i
$370$			88.5375i			0.239290i
$371$	137.025	−	178.574i	0.369339	−	0.481332i
$372$	24.5444	−	50.6083i	0.0659795	−	0.136044i
$373$	−155.685	+	269.655i	−0.417387	+	0.722935i	−0.995676	−	0.0928970i	$-0.970387\pi$
$373$	−155.685	+	269.655i	−0.417387	+	0.722935i	0.578289	+	0.815832i	$0.303721\pi$
$374$	−115.240	+	66.1968i	−0.308127	+	0.176997i
$375$	−68.2341	+	355.243i	−0.181958	+	0.947316i
$376$	51.8601	−	193.545i	0.137926	−	0.514746i
$377$	−61.0296	−	147.339i	−0.161882	−	0.390818i
$378$	−651.310	+	337.342i	−1.72304	+	0.892440i
$379$	−90.5856	−	218.693i	−0.239012	−	0.577026i	0.758169	−	0.652058i	$-0.226094\pi$
$379$	−90.5856	−	218.693i	−0.239012	−	0.577026i	−0.997181	+	0.0750318i	$0.976094\pi$
$380$	−26.7609	+	3.52314i	−0.0704234	+	0.00927141i
$381$	−382.544	+	580.758i	−1.00405	+	1.52430i
$382$	43.0352	+	160.610i	0.112658	+	0.420444i
$383$	−320.011	+	85.7468i	−0.835539	+	0.223882i	−0.651129	−	0.758967i	$-0.725704\pi$
$383$	−320.011	+	85.7468i	−0.835539	+	0.223882i	−0.184410	+	0.982849i	$0.559038\pi$
$384$	25.3394	−	429.961i	0.0659881	−	1.11969i
$385$	32.5657	+	247.361i	0.0845864	+	0.642497i
$386$	123.508	−	51.1587i	0.319969	−	0.132535i
$387$	292.423	−	42.4224i	0.755614	−	0.109619i
$388$	−24.5011	+	10.1487i	−0.0631471	+	0.0261564i
$389$	11.5320	+	3.08998i	0.0296451	+	0.00794339i	0.273611	−	0.961840i	$-0.411782\pi$
$389$	11.5320	+	3.08998i	0.0296451	+	0.00794339i	−0.243966	+	0.969784i	$0.578449\pi$
$390$	−88.5266	+	102.296i	−0.226991	+	0.262298i
$391$	208.003	+	56.2238i	0.531978	+	0.143795i
$392$	−779.014	−	449.764i	−1.98728	−	1.14736i
$393$	−4.40579	−	61.0573i	−0.0112107	−	0.155362i
$394$	−483.282	−	370.835i	−1.22660	−	0.941206i
$395$	575.334			1.45654
$396$	−13.1979	+	0.173791i	−0.0333279	+	0.000438866i
$397$	−616.760	−	255.470i	−1.55355	−	0.643502i	−0.569597	−	0.821924i	$-0.692901\pi$
$397$	−616.760	−	255.470i	−1.55355	−	0.643502i	−0.983954	+	0.178422i	$0.942901\pi$
$398$	−81.3623	−	618.008i	−0.204428	−	1.55278i
$399$	465.332	+	225.680i	1.16625	+	0.565614i
$400$	7.37957	+	27.5409i	0.0184489	+	0.0688523i
$401$	−113.546	+	87.1272i	−0.283158	+	0.217275i	−0.740568	−	0.671981i	$-0.765444\pi$
$401$	−113.546	+	87.1272i	−0.283158	+	0.217275i	0.457411	+	0.889256i	$0.348777\pi$
$402$	33.9015	−	51.4675i	0.0843320	−	0.128029i
$403$	−121.002	+	157.692i	−0.300252	+	0.391296i
$404$	−29.1191			−0.0720770
$405$	−263.137	−	324.844i	−0.649721	−	0.802085i
$406$	−734.897	−	734.897i	−1.81009	−	1.81009i
$407$	26.4367	−	15.2632i	0.0649551	−	0.0375018i
$408$	384.612	−	26.9047i	0.942676	−	0.0659428i
$409$	289.741	−	501.847i	0.708414	−	1.22701i	−0.257031	−	0.966403i	$-0.582744\pi$
$409$	289.741	−	501.847i	0.708414	−	1.22701i	0.965445	−	0.260606i	$-0.0839224\pi$
$410$	181.656	+	677.950i	0.443064	+	1.65354i
$411$	−139.215	+	123.719i	−0.338723	+	0.301020i
$412$	−26.2810	+	15.1733i	−0.0637888	+	0.0368285i
$413$	1095.75	−	453.876i	2.65316	−	1.09897i
$414$	171.276	+	166.824i	0.413710	+	0.402956i
$415$	0.544082	−	1.31353i	0.00131104	−	0.00316513i
$416$	6.76384	−	25.2430i	0.0162592	−	0.0606803i
$417$	−40.7109	−	564.188i	−0.0976280	−	1.35297i
$418$	63.2986	+	82.4923i	0.151432	+	0.197350i
$419$	111.522	+	145.339i	0.266163	+	0.346870i	0.907245	−	0.420602i	$-0.138181\pi$
$419$	111.522	+	145.339i	0.266163	+	0.346870i	−0.641082	+	0.767472i	$0.721514\pi$
$420$	−24.8715	+	74.8852i	−0.0592179	+	0.178298i
$421$	−138.101	+	79.7325i	−0.328030	+	0.189388i	−0.654966	−	0.755658i	$-0.727317\pi$
$421$	−138.101	+	79.7325i	−0.328030	+	0.189388i	0.326936	+	0.945046i	$0.393984\pi$
$422$	−74.0291	−	178.722i	−0.175424	−	0.423512i
$423$	191.145	+	142.712i	0.451879	+	0.337380i
$424$	−131.288			−0.309642
$425$	−25.7329	+	10.5928i	−0.0605481	+	0.0249243i
$426$	51.7249	+	149.143i	0.121420	+	0.350102i
$427$	397.793	−	106.588i	0.931601	−	0.249622i
$428$	27.0670	+	3.56343i	0.0632406	+	0.00832578i
$429$	45.8063	+	8.79835i	0.106775	+	0.0205090i
$430$	216.208	−	281.767i	0.502809	−	0.655273i
$431$	−155.819	+	376.179i	−0.361528	+	0.872806i	0.633549	+	0.773702i	$0.281597\pi$
$431$	−155.819	+	376.179i	−0.361528	+	0.872806i	−0.995077	+	0.0991034i	$0.968403\pi$
$432$	425.817	+	199.634i	0.985688	+	0.462115i
$433$	−297.401	+	297.401i	−0.686839	+	0.686839i	−0.961532	−	0.274693i	$-0.911424\pi$
$433$	−297.401	+	297.401i	−0.686839	+	0.686839i	0.274693	+	0.961532i	$0.411424\pi$
$434$	−335.259	+	1251.20i	−0.772486	+	2.88296i
$435$	325.840	−	494.674i	0.749058	−	1.13718i
$436$	27.1767	−	20.8534i	0.0623320	−	0.0478290i
$437$	22.0042	−	167.138i	0.0503528	−	0.382468i
$438$	−209.107	−	602.939i	−0.477414	−	1.37657i
$439$	−370.979	−	284.663i	−0.845056	−	0.648434i	0.0927136	−	0.995693i	$-0.470446\pi$
$439$	−370.979	−	284.663i	−0.845056	−	0.648434i	−0.937769	+	0.347259i	$0.887113\pi$
$440$	102.902	−	102.902i	0.233867	−	0.233867i
$441$	840.936	−	663.046i	1.90688	−	1.50351i
$442$	147.221	+	19.7108i	0.333080	+	0.0445946i
$443$	−456.046	+	263.298i	−1.02945	+	0.594352i	−0.916827	−	0.399286i	$-0.869258\pi$
$443$	−456.046	+	263.298i	−1.02945	+	0.594352i	−0.112622	+	0.993638i	$0.535925\pi$
$444$	9.62951	−	0.694850i	0.0216881	−	0.00156498i
$445$	−82.5074	+	626.706i	−0.185410	+	1.40833i
$446$	68.9022	−	119.342i	0.154489	−	0.267583i
$447$	−72.1486	+	217.231i	−0.161406	+	0.485976i
$448$	95.6392	+	726.452i	0.213480	+	1.62154i
$449$	−93.0206	−	38.5304i	−0.207173	−	0.0858138i	0.276684	−	0.960961i	$-0.410764\pi$
$449$	−93.0206	−	38.5304i	−0.207173	−	0.0858138i	−0.483857	+	0.875147i	$0.660764\pi$
$450$	−30.6653	−	3.62707i	−0.0681452	−	0.00806017i
$451$	171.115	−	171.115i	0.379413	−	0.379413i
$452$	−5.76503	−	43.7898i	−0.0127545	−	0.0968800i
$453$	−21.2534	+	360.629i	−0.0469171	+	0.796092i
$454$	−540.528	−	71.1618i	−1.19059	−	0.156744i
$455$	139.425	−	241.491i	0.306428	−	0.530749i
$456$	−60.7961	−	295.463i	−0.133325	−	0.647944i
$457$	63.8765	−	238.390i	0.139774	−	0.521642i	−0.860159	−	0.510026i	$-0.829636\pi$
$457$	63.8765	−	238.390i	0.139774	−	0.521642i	0.999933	−	0.0116159i	$-0.00369754\pi$
$458$			130.985i			0.285993i
$459$	−139.888	+	437.164i	−0.304766	+	0.952427i
$460$	25.7213			0.0559158
$461$	−110.519	−	29.6134i	−0.239737	−	0.0642373i	0.136950	−	0.990578i	$-0.456270\pi$
$461$	−110.519	−	29.6134i	−0.239737	−	0.0642373i	−0.376687	+	0.926341i	$0.622937\pi$
$462$	297.734	−	61.2634i	0.644446	−	0.132605i
$463$	−56.5451	−	32.6463i	−0.122128	−	0.0705104i	0.437692	−	0.899125i	$-0.355796\pi$
$463$	−56.5451	−	32.6463i	−0.122128	−	0.0705104i	−0.559819	+	0.828615i	$0.689129\pi$
$464$	−86.9787	+	660.669i	−0.187454	+	1.42386i
$465$	−736.997	−	43.4344i	−1.58494	−	0.0934072i
$466$	190.139	−	25.0322i	0.408023	−	0.0537172i
$467$	365.847	+	365.847i	0.783399	+	0.783399i	0.980403	−	0.197004i	$-0.0631212\pi$
$467$	365.847	+	365.847i	0.783399	+	0.783399i	−0.197004	+	0.980403i	$0.563121\pi$
$468$	11.8207	+	8.82550i	0.0252579	+	0.0188579i
$469$	−48.6134	+	117.363i	−0.103653	+	0.250241i
$470$	284.267	−	37.4244i	0.604823	−	0.0796265i
$471$	828.636	+	275.213i	1.75931	+	0.584317i
$472$	−599.103	−	345.892i	−1.26929	−	0.732823i
$473$	−121.407	−	15.9835i	−0.256674	−	0.0337917i
$474$	−50.4485	−	699.136i	−0.106432	−	1.47497i
$475$	10.8862	+	18.8554i	0.0229182	+	0.0396956i
$476$	83.7340	−	22.2396i	0.175912	−	0.0467219i
$477$	57.9065	−	145.176i	0.121397	−	0.304353i
$478$	130.533	+	130.533i	0.273081	+	0.273081i
$479$	174.313	−	227.169i	0.363909	−	0.474256i	−0.575132	−	0.818061i	$-0.695049\pi$
$479$	174.313	−	227.169i	0.363909	−	0.474256i	0.939041	+	0.343805i	$0.111716\pi$
$480$	91.7083	−	31.8057i	0.191059	−	0.0662618i
$481$	−33.8261	−	4.45329i	−0.0703245	−	0.00925840i
$482$	516.799	+	673.506i	1.07220	+	1.39732i
$483$	−411.564	−	271.096i	−0.852099	−	0.561275i
$484$	−40.6728	−	10.8982i	−0.0840347	−	0.0225170i
$485$	246.139	+	246.139i	0.507504	+	0.507504i
$486$	−371.672	+	348.244i	−0.764758	+	0.716552i
$487$	−505.862	−	209.535i	−1.03873	−	0.430256i	−0.202874	−	0.979205i	$-0.565028\pi$
$487$	−505.862	−	209.535i	−1.03873	−	0.430256i	−0.835856	+	0.548949i	$0.815028\pi$
$488$	−190.570	−	146.229i	−0.390512	−	0.299650i
$489$	71.6365	−	372.957i	0.146496	−	0.762694i
$490$	168.009	−	1276.15i	0.342875	−	2.60440i
$491$	9.41303	+	35.1299i	0.0191711	+	0.0715477i	0.974849	−	0.222868i	$-0.0715418\pi$
$491$	9.41303	+	35.1299i	0.0191711	+	0.0715477i	−0.955678	+	0.294415i	$0.904875\pi$
$492$	72.3095	−	25.0779i	0.146971	−	0.0509713i
$493$	−650.369	−	1.42723i	−1.31921	−	0.00289500i
$494$		−	116.213i		−	0.235248i
$495$	68.4007	+	159.173i	0.138183	+	0.321562i
$496$	767.315	−	317.832i	1.54701	−	0.640791i
$497$	−162.691	−	281.789i	−0.327346	−	0.566981i
$498$	−1.64389	−	0.545982i	−0.00330098	−	0.00109635i
$499$	480.550	−	368.739i	0.963026	−	0.738956i	−0.00230119	−	0.999997i	$-0.500732\pi$
$499$	480.550	−	368.739i	0.963026	−	0.738956i	0.965328	+	0.261041i	$0.0840658\pi$
$500$	37.6144	−	28.8626i	0.0752289	−	0.0577252i
$501$	114.829	−	8.28590i	0.229200	−	0.0165387i
$502$	633.705	+	169.801i	1.26236	+	0.338249i
$503$	−724.239	−	299.990i	−1.43984	−	0.596401i	−0.480079	−	0.877225i	$-0.659392\pi$
$503$	−724.239	−	299.990i	−1.43984	−	0.596401i	−0.959759	+	0.280824i	$0.909392\pi$
$504$	−854.731	−	217.004i	−1.69589	−	0.430563i
$505$	146.266	+	353.118i	0.289636	+	0.699243i
$506$	−49.5424	−	85.8100i	−0.0979099	−	0.169585i
$507$	302.161	+	340.006i	0.595978	+	0.670624i
$508$	88.0421	−	23.5908i	0.173311	−	0.0464386i
$509$	489.685	+	282.720i	0.962052	+	0.555441i	0.896804	−	0.442428i	$-0.145883\pi$
$509$	489.685	+	282.720i	0.962052	+	0.555441i	0.0652481	+	0.997869i	$0.479216\pi$
$510$	246.180	+	493.729i	0.482706	+	0.968096i
$511$	657.709	+	1139.19i	1.28710	+	2.22933i
$512$	295.230	−	295.230i	0.576620	−	0.576620i
$513$	353.533	+	63.0906i	0.689148	+	0.122984i
$514$		−	32.3369i		−	0.0629123i
$515$	316.012	+	242.485i	0.613616	+	0.470844i
$516$	−32.3424	−	21.3038i	−0.0626790	−	0.0412865i
$517$	−60.1803	−	78.4285i	−0.116403	−	0.151699i
$518$	−214.767	+	57.5466i	−0.414608	+	0.111094i
$519$	363.629	−	749.770i	0.700633	−	1.44464i
$520$	−161.255	+	21.2296i	−0.310105	+	0.0408261i
$521$	277.820	−	670.717i	0.533244	−	1.28736i	−0.396120	−	0.918199i	$-0.629644\pi$
$521$	277.820	−	670.717i	0.533244	−	1.28736i	0.929364	−	0.369165i	$-0.120356\pi$
$522$	−629.691	−	352.580i	−1.20630	−	0.675441i
$523$			186.077i			0.355788i	0.984050	+	0.177894i	$0.0569284\pi$
$523$			186.077i			0.355788i	−0.984050	+	0.177894i	$0.943072\pi$
$524$	−4.88435	+	6.36541i	−0.00932128	+	0.0121477i
$525$	63.4839	−	4.58089i	0.120922	−	0.00872551i
$526$	3.53018	−	6.11445i	0.00671136	−	0.0116244i
$527$	403.756	+	702.884i	0.766140	+	1.33375i
$528$	−147.375	−	127.538i	−0.279119	−	0.241548i
$529$	95.3372	−	355.803i	0.180222	−	0.672596i
$530$	−71.8929	−	173.565i	−0.135647	−	0.327481i
$531$	646.725	−	509.918i	1.21794	−	0.960298i
$532$	−25.9399	−	62.6244i	−0.0487592	−	0.117715i
$533$	−268.151	+	35.3027i	−0.503097	+	0.0662339i
$534$	768.798	+	45.3085i	1.43970	+	0.0848475i
$535$	−92.7456	−	346.131i	−0.173356	−	0.646974i
$536$	71.5704	−	19.1772i	0.133527	−	0.0357784i
$537$	−637.374	−	419.836i	−1.18692	−	0.781818i
$538$	93.8614	+	712.948i	0.174464	+	1.32518i
$539$	−410.015	+	169.834i	−0.760696	+	0.315091i
$540$	−2.50309	+	54.7354i	−0.00463535	+	0.101362i
$541$	−0.0682046	+	0.0282513i	−0.000126071	+	5.22205e-5i	−0.382746	−	0.923853i	$-0.625022\pi$
$541$	−0.0682046	+	0.0282513i	−0.000126071	+	5.22205e-5i	0.382620	+	0.923906i	$0.375022\pi$
$542$	142.563	+	38.1996i	0.263031	+	0.0704789i
$543$	−810.184	−	155.618i	−1.49205	−	0.286589i
$544$	−84.4095	−	65.0645i	−0.155164	−	0.119604i
$545$	−389.392	−	224.816i	−0.714481	−	0.412506i
$546$	−305.681	−	148.251i	−0.559855	−	0.271523i
$547$	−535.544	−	410.938i	−0.979057	−	0.751257i	−0.0104736	−	0.999945i	$-0.503334\pi$
$547$	−535.544	−	410.938i	−0.979057	−	0.751257i	−0.968584	+	0.248688i	$0.920001\pi$
$548$	24.4107			0.0445451
$549$	245.752	−	146.233i	0.447635	−	0.266362i
$550$	11.8228	+	4.89716i	0.0214960	+	0.00890392i
$551$	66.4176	+	504.492i	0.120540	+	0.915594i
$552$	20.6884	+	286.708i	0.0374790	+	0.519399i
$553$	373.949	+	1395.60i	0.676219	+	2.52368i
$554$	482.461	−	370.206i	0.870869	−	0.668241i
$555$	−56.7955	−	113.284i	−0.102334	−	0.204115i
$556$	−45.1329	+	58.8184i	−0.0811743	+	0.105788i
$557$	−43.5586			−0.0782022			−0.0391011	−	0.999235i	$-0.512449\pi$
$557$	−43.5586			−0.0782022			−0.0391011	+	0.999235i	$0.512449\pi$
$558$	11.8433	+	899.395i	0.0212246	+	1.61182i
$559$	96.7754	+	96.7754i	0.173122	+	0.173122i
$560$	−1009.05	+	582.578i	−1.80188	+	1.04032i
$561$	104.985	−	158.623i	0.187138	−	0.282751i
$562$	135.777	−	235.172i	0.241596	−	0.418456i
$563$	−84.6977	−	316.096i	−0.150440	−	0.561449i	−0.999453	−	0.0330772i	$-0.989469\pi$
$563$	−84.6977	−	316.096i	−0.150440	−	0.561449i	0.849013	−	0.528372i	$-0.177197\pi$
$564$	−6.30130	−	30.6237i	−0.0111725	−	0.0542973i
$565$	−502.066	+	289.868i	−0.888612	+	0.513041i
$566$	−591.322	+	244.934i	−1.04474	+	0.432745i
$567$	616.950	−	849.435i	1.08810	−	1.49812i
$568$	−72.6285	+	175.341i	−0.127867	+	0.308699i
$569$	−144.227	+	538.264i	−0.253475	+	0.945982i	0.715457	+	0.698657i	$0.246218\pi$
$569$	−144.227	+	538.264i	−0.253475	+	0.945982i	−0.968932	+	0.247326i	$0.920448\pi$
$570$	357.314	−	242.167i	0.626866	−	0.424855i
$571$	17.9842	+	23.4375i	0.0314960	+	0.0410463i	0.808836	−	0.588035i	$-0.200098\pi$
$571$	17.9842	+	23.4375i	0.0314960	+	0.0410463i	−0.777340	+	0.629081i	$0.783431\pi$
$572$	−3.72164	−	4.85014i	−0.00650637	−	0.00847926i
$573$	−158.092	−	177.893i	−0.275903	−	0.310459i
$574$	−1526.45	+	881.294i	−2.65931	+	1.53535i
$575$	−7.93972	−	19.1682i	−0.0138082	−	0.0333359i
$576$	200.880	+	467.460i	0.348749	+	0.811563i
$577$	435.187			0.754224			0.377112	−	0.926168i	$-0.376917\pi$
$577$	435.187			0.754224			0.377112	+	0.926168i	$0.376917\pi$
$578$	305.171	−	523.255i	0.527978	−	0.905285i
$579$	−125.211	+	144.686i	−0.216253	+	0.249890i
$580$	−74.9919	+	20.0940i	−0.129296	+	0.0346448i
$581$	3.53989	+	0.466036i	0.00609276	+	0.000802127i
$582$	277.522	−	320.687i	0.476841	−	0.551009i
$583$	−39.4315	+	51.3881i	−0.0676355	+	0.0881443i
$584$	293.614	−	708.847i	0.502764	−	1.21378i
$585$	47.6482	−	187.676i	0.0814500	−	0.320814i
$586$	33.8474	−	33.8474i	0.0577601	−	0.0577601i
$587$	17.1550	−	64.0233i	0.0292249	−	0.109069i	−0.949773	−	0.312941i	$-0.898686\pi$
$587$	17.1550	−	64.0233i	0.0292249	−	0.109069i	0.978998	+	0.203872i	$0.0653526\pi$
$588$	−140.116	−	8.25761i	−0.238292	−	0.0140436i
$589$	503.147	−	386.079i	0.854240	−	0.655482i
$590$	129.208	−	981.431i	0.218996	−	1.66344i
$591$	856.244	+	164.465i	1.44881	+	0.278282i
$592$	113.100	+	86.7850i	0.191048	+	0.146596i
$593$	−497.377	+	497.377i	−0.838748	+	0.838748i	−0.988694	−	0.149946i	$-0.952090\pi$
$593$	−497.377	+	497.377i	−0.838748	+	0.838748i	0.149946	+	0.988694i	$0.452090\pi$
$594$	187.427	−	97.0767i	0.315533	−	0.163429i
$595$	−690.291	−	903.704i	−1.16015	−	1.51883i
$596$	25.9818	−	15.0006i	0.0435937	−	0.0251688i
$597$	500.546	+	738.548i	0.838436	+	1.23710i
$598$	−14.4548	+	109.795i	−0.0241719	+	0.183603i
$599$	−563.111	+	975.337i	−0.940086	+	1.62828i	−0.174782	+	0.984607i	$0.555922\pi$
$599$	−563.111	+	975.337i	−0.940086	+	1.62828i	−0.765304	+	0.643669i	$0.777411\pi$
$600$	−24.6614	−	27.7502i	−0.0411023	−	0.0462503i
$601$	−148.180	−	1125.54i	−0.246556	−	1.87278i	−0.449070	−	0.893496i	$-0.648245\pi$
$601$	−148.180	−	1125.54i	−0.246556	−	1.87278i	0.202515	−	0.979279i	$-0.435089\pi$
$602$	824.016	+	341.319i	1.36880	+	0.566975i
$603$	−10.3612	+	87.5998i	−0.0171828	+	0.145273i
$604$	33.4807	−	33.4807i	0.0554315	−	0.0554315i
$605$	72.1413	+	547.967i	0.119242	+	0.905731i
$606$	416.277	−	208.704i	0.686926	−	0.344395i
$607$	−586.917	−	77.2690i	−0.966914	−	0.127297i	−0.369501	−	0.929230i	$-0.620471\pi$
$607$	−586.917	−	77.2690i	−0.966914	−	0.127297i	−0.597413	+	0.801934i	$0.703805\pi$
$608$	−41.6919	+	72.2126i	−0.0685723	+	0.118771i
$609$	1411.73	+	468.874i	2.31810	+	0.769908i
$610$	88.9619	−	332.010i	0.145839	−	0.544279i
$611$			110.488i			0.180831i
$612$	51.7669	−	30.6498i	0.0845864	−	0.0500814i
$613$	163.780			0.267178			0.133589	−	0.991037i	$-0.457350\pi$
$613$	163.780			0.267178			0.133589	+	0.991037i	$0.457350\pi$
$614$	550.152	+	147.413i	0.896012	+	0.240086i
$615$	−667.324	−	750.906i	−1.08508	−	1.22099i
$616$	316.493	+	182.727i	0.513788	+	0.296635i
$617$	−102.978	+	782.199i	−0.166902	+	1.26775i	0.678893	+	0.734237i	$0.262460\pi$
$617$	−102.978	+	782.199i	−0.166902	+	1.26775i	−0.845795	+	0.533509i	$0.820873\pi$
$618$	266.954	−	405.275i	0.431964	−	0.655785i
$619$	−496.902	+	65.4184i	−0.802750	+	0.105684i	−0.520727	−	0.853723i	$-0.674339\pi$
$619$	−496.902	+	65.4184i	−0.802750	+	0.105684i	−0.282023	+	0.959408i	$0.591006\pi$
$620$	68.4224	+	68.4224i	0.110359	+	0.110359i
$621$	−326.162	−	103.580i	−0.525221	−	0.166795i
$622$	−59.8116	+	144.398i	−0.0961602	+	0.232151i
$623$	−1573.84	+	207.200i	−2.52623	+	0.332584i
$624$	43.9017	+	213.358i	0.0703553	+	0.341920i
$625$	−574.386	−	331.622i	−0.919018	−	0.530595i
$626$	413.453	+	54.4322i	0.660469	+	0.0869523i
$627$	−133.908	−	64.9436i	−0.213569	−	0.103578i
$628$	−57.2204	−	99.1086i	−0.0911153	−	0.157816i
$629$	−69.8329	+	120.343i	−0.111022	+	0.191325i
$630$	−181.165	−	1248.80i	−0.287564	−	1.98221i
$631$	−121.202	−	121.202i	−0.192080	−	0.192080i	0.604514	−	0.796594i	$-0.293367\pi$
$631$	−121.202	−	121.202i	−0.192080	−	0.192080i	−0.796594	+	0.604514i	$0.793367\pi$
$632$	513.023	−	668.585i	0.811746	−	1.05789i
$633$	209.368	+	181.186i	0.330755	+	0.286234i
$634$	787.623	+	103.693i	1.24231	+	0.163553i
$635$	−728.316	−	949.160i	−1.14695	−	1.49474i
$636$	−18.3130	+	9.18136i	−0.0287941	+	0.0144361i
$637$	479.109	+	128.377i	0.752134	+	0.201534i
$638$	211.480	+	211.480i	0.331474	+	0.331474i
$639$	−161.855	−	157.648i	−0.253295	−	0.246710i
$640$	684.570	+	283.558i	1.06964	+	0.443060i
$641$	−194.266	−	149.065i	−0.303066	−	0.232551i	0.446021	−	0.895023i	$-0.352841\pi$
$641$	−194.266	−	149.065i	−0.303066	−	0.232551i	−0.749087	+	0.662472i	$0.769507\pi$
$642$	−412.481	+	143.054i	−0.642493	+	0.222825i
$643$	−93.3126	+	708.779i	−0.145121	+	1.10230i	0.751573	+	0.659650i	$0.229295\pi$
$643$	−93.3126	+	708.779i	−0.145121	+	1.10230i	−0.896694	+	0.442651i	$0.854038\pi$
$644$	16.7180	+	62.3925i	0.0259597	+	0.0968828i
$645$	−95.8877	+	499.215i	−0.148663	+	0.773977i
$646$	−437.454	−	182.325i	−0.677173	−	0.282237i
$647$			73.8451i			0.114135i	0.998370	+	0.0570673i	$0.0181750\pi$
$647$			73.8451i			0.114135i	−0.998370	+	0.0570673i	$0.981825\pi$
$648$	−612.134	+	16.1241i	−0.944652	+	0.0248829i
$649$	−315.324	+	130.611i	−0.485861	+	0.201250i
$650$	−7.15123	−	12.3863i	−0.0110019	−	0.0190558i
$651$	−373.666	−	1815.98i	−0.573987	−	2.78952i
$652$	−39.4900	+	30.3018i	−0.0605675	+	0.0464751i
$653$	790.144	−	606.299i	1.21002	−	0.928483i	0.211221	−	0.977438i	$-0.432256\pi$
$653$	790.144	−	606.299i	1.21002	−	0.928483i	0.998801	+	0.0489557i	$0.0155893\pi$
$654$	−239.048	+	492.896i	−0.365517	+	0.753664i
$655$	101.725	+	27.2573i	0.155306	+	0.0416141i
$656$	1044.09	+	432.478i	1.59161	+	0.659266i
$657$	654.329	+	637.321i	0.995935	+	0.970047i
$658$	275.546	+	665.227i	0.418763	+	1.01098i
$659$	−98.8066	−	171.138i	−0.149934	−	0.259693i	0.781269	−	0.624195i	$-0.214573\pi$
$659$	−98.8066	−	171.138i	−0.149934	−	0.259693i	−0.931203	+	0.364501i	$0.881239\pi$
$660$	7.15724	−	21.5496i	0.0108443	−	0.0326510i
$661$	−345.973	+	92.7031i	−0.523408	+	0.140247i	−0.510843	−	0.859674i	$-0.670667\pi$
$661$	−345.973	+	92.7031i	−0.523408	+	0.140247i	−0.0125655	+	0.999921i	$0.504000\pi$
$662$	−1103.04	−	636.840i	−1.66622	−	0.961995i
$663$	−201.013	+	69.2203i	−0.303188	+	0.104405i
$664$	−1.04127	−	1.80354i	−0.00156818	−	0.00271617i
$665$	−629.129	+	629.129i	−0.946058	+	0.946058i
$666$	−132.680	+	78.9503i	−0.199220	+	0.118544i
$667$		−	484.893i		−	0.726976i
$668$	−11.9713	−	9.18592i	−0.0179211	−	0.0137514i
$669$	−11.6040	+	196.898i	−0.0173453	+	0.294317i
$670$	64.5442	+	84.1157i	0.0963347	+	0.125546i
$671$	−114.473	+	30.6728i	−0.170600	+	0.0457121i
$672$	136.759	+	201.786i	0.203511	+	0.300277i
$673$	414.182	−	54.5281i	0.615427	−	0.0810225i	0.183633	−	0.982995i	$-0.441214\pi$
$673$	414.182	−	54.5281i	0.615427	−	0.0810225i	0.431794	+	0.901972i	$0.357881\pi$
$674$	−84.5601	+	204.146i	−0.125460	+	0.302888i
$675$	41.5629	−	15.0305i	0.0615747	−	0.0222674i
$676$		−	59.6185i		−	0.0881930i
$677$	8.35128	−	10.8836i	0.0123357	−	0.0160762i	−0.787145	−	0.616768i	$-0.788442\pi$
$677$	8.35128	−	10.8836i	0.0123357	−	0.0160762i	0.799480	+	0.600692i	$0.205108\pi$
$678$	396.267	+	584.685i	0.584464	+	0.862368i
$679$	−437.082	+	757.048i	−0.643714	+	1.11494i
$680$	−173.078	+	640.311i	−0.254526	+	0.941633i
$681$	737.253	−	255.689i	1.08260	−	0.375461i
$682$	96.4771	−	360.058i	0.141462	−	0.527944i
$683$	−299.577	−	723.242i	−0.438619	−	1.05892i	−0.976426	−	0.215852i	$-0.930747\pi$
$683$	−299.577	−	723.242i	−0.438619	−	1.05892i	0.537807	−	0.843068i	$-0.319253\pi$
$684$	−29.1428	−	36.9616i	−0.0426064	−	0.0540374i
$685$	−122.616	−	296.020i	−0.179001	−	0.432147i
$686$	1885.04	−	248.170i	2.74786	−	0.361763i
$687$	−84.0249	−	167.595i	−0.122307	−	0.243952i
$688$	−148.010	−	552.380i	−0.215131	−	0.802879i
$689$	69.9272	−	18.7369i	0.101491	−	0.0271944i
$690$	−367.703	+	184.350i	−0.532903	+	0.267175i
$691$	67.3242	+	511.378i	0.0974301	+	0.740055i	0.968521	+	0.248933i	$0.0800798\pi$
$691$	67.3242	+	511.378i	0.0974301	+	0.740055i	−0.871091	+	0.491122i	$0.836587\pi$
$692$	−100.904	+	41.7959i	−0.145815	+	0.0603986i
$693$	−341.651	+	269.379i	−0.493002	+	0.388714i
$694$	−612.387	+	253.659i	−0.882401	+	0.365503i
$695$	939.974	+	251.865i	1.35248	+	0.362396i
$696$	−284.301	−	819.752i	−0.408478	−	1.17781i
$697$	−287.811	+	1064.77i	−0.412929	+	1.52765i
$698$	−702.010	−	405.306i	−1.00575	−	0.580667i
$699$	−227.224	+	154.000i	−0.325071	+	0.220315i
$700$	−6.61840	−	5.07847i	−0.00945485	−	0.00725496i
$701$	−456.032			−0.650545			−0.325272	−	0.945620i	$-0.605456\pi$
$701$	−456.032			−0.650545			−0.325272	+	0.945620i	$0.605456\pi$
$702$	−232.239	−	41.4448i	−0.330825	−	0.0590382i
$703$	100.573	+	41.6589i	0.143063	+	0.0592587i
$704$	−27.5220	−	209.050i	−0.0390937	−	0.296946i
$705$	−339.712	+	230.238i	−0.481861	+	0.326578i
$706$	−162.159	−	605.185i	−0.229687	−	0.857203i
$707$	−761.495	+	584.316i	−1.07708	+	0.826472i
$708$	−107.756	−	6.35054i	−0.152198	−	0.00896970i
$709$	208.598	−	271.850i	0.294214	−	0.383427i	−0.622734	−	0.782434i	$-0.713978\pi$
$709$	208.598	−	271.850i	0.294214	−	0.383427i	0.916948	+	0.399006i	$0.130645\pi$
$710$	−271.574			−0.382498
$711$	513.035	+	862.182i	0.721568	+	1.21263i
$712$	654.713	+	654.713i	0.919540	+	0.919540i
$713$	−523.383	+	302.175i	−0.734058	+	0.423808i
$714$	−1037.64	+	918.072i	−1.45327	+	1.28582i
$715$	−40.1221	+	69.4935i	−0.0561148	+	0.0971937i
$716$	25.8906	+	96.6250i	0.0361600	+	0.134951i
$717$	−250.751	−	83.2816i	−0.349723	−	0.116153i
$718$	−1.72567	+	0.996318i	−0.00240345	+	0.00138763i
$719$	−176.063	+	72.9276i	−0.244872	+	0.101429i	−0.501744	−	0.865016i	$-0.667308\pi$
$719$	−176.063	+	72.9276i	−0.244872	+	0.101429i	0.256872	+	0.966445i	$0.417308\pi$
$720$	−564.519	+	579.585i	−0.784054	+	0.804979i
$721$	−382.801	+	924.164i	−0.530931	+	1.28178i
$722$	99.8670	−	372.709i	0.138320	−	0.516217i
$723$	−1093.29	−	530.230i	−1.51215	−	0.733375i
$724$	65.8253	+	85.7852i	0.0909189	+	0.118488i
$725$	38.1233	+	49.6833i	0.0525839	+	0.0685286i
$726$	659.555	−	135.714i	0.908478	−	0.186934i
$727$	148.091	−	85.5005i	0.203702	−	0.117607i	−0.394679	−	0.918819i	$-0.629144\pi$
$727$	148.091	−	85.5005i	0.203702	−	0.117607i	0.598381	+	0.801212i	$0.295811\pi$
$728$	−156.307	−	377.359i	−0.214708	−	0.518351i
$729$	252.161	−	684.000i	0.345899	−	0.938272i
$730$	1097.89			1.50395
$731$	516.118	−	212.457i	0.706044	−	0.290639i
$732$	−36.8083	−	7.07002i	−0.0502845	−	0.00965850i
$733$	687.999	−	184.349i	0.938607	−	0.251499i	0.243086	−	0.970005i	$-0.421840\pi$
$733$	687.999	−	184.349i	0.938607	−	0.251499i	0.695521	+	0.718506i	$0.255174\pi$
$734$	−75.0712	−	9.88332i	−0.102277	−	0.0134650i
$735$	603.667	+	1740.61i	0.821316	+	2.36818i
$736$	48.3715	−	63.0390i	0.0657222	−	0.0856508i
$737$	13.9894	−	33.7735i	0.0189816	−	0.0458256i
$738$	−853.975	+	876.765i	−1.15715	+	1.18803i
$739$	459.846	−	459.846i	0.622254	−	0.622254i	−0.323853	−	0.946107i	$-0.604978\pi$
$739$	459.846	−	459.846i	0.622254	−	0.622254i	0.946107	+	0.323853i	$0.104978\pi$
$740$	−4.29882	+	16.0434i	−0.00580921	+	0.0216803i
$741$	74.5487	+	148.694i	0.100605	+	0.200666i
$742$	374.291	−	287.204i	0.504436	−	0.387067i
$743$	−23.9779	+	182.130i	−0.0322717	+	0.245128i	−0.999976	−	0.00696107i	$-0.997784\pi$
$743$	−23.9779	+	182.130i	−0.0322717	+	0.245128i	0.967704	+	0.252089i	$0.0811175\pi$
$744$	−707.652	+	817.721i	−0.951145	+	1.09909i
$745$	−312.415	−	239.724i	−0.419349	−	0.321778i
$746$	−461.480	+	461.480i	−0.618606	+	0.618606i
$747$	2.45359	−	0.355948i	0.00328460	−	0.000476503i
$748$	−24.0960	+	6.39987i	−0.0322139	+	0.00855598i
$749$	779.335	−	449.949i	1.04050	−	0.600733i
$750$	−330.859	+	682.202i	−0.441145	+	0.909603i
$751$	11.1610	−	84.7762i	0.0148615	−	0.112884i	−0.982406	−	0.186757i	$-0.940202\pi$
$751$	11.1610	−	84.7762i	0.0148615	−	0.112884i	0.997268	+	0.0738723i	$0.0235357\pi$
$752$	230.833	−	399.815i	0.306959	−	0.531669i
$753$	−919.749	+	189.253i	−1.22145	+	0.251332i
$754$	−43.6304	−	331.406i	−0.0578653	−	0.439530i
$755$	−574.183	−	237.834i	−0.760507	−	0.315012i
$756$	−134.400	+	29.5045i	−0.177777	+	0.0390272i
$757$	30.4793	−	30.4793i	0.0402633	−	0.0402633i	−0.686689	−	0.726952i	$-0.740936\pi$
$757$	30.4793	−	30.4793i	0.0402633	−	0.0402633i	0.726952	+	0.686689i	$0.240936\pi$
$758$	−64.7601	−	491.902i	−0.0854355	−	0.648947i
$759$	118.435	+	78.0130i	0.156041	+	0.102784i
$760$	514.513	+	67.7370i	0.676991	+	0.0891276i
$761$	554.164	−	959.841i	0.728205	−	1.26129i	−0.229436	−	0.973324i	$-0.573688\pi$
$761$	554.164	−	959.841i	0.728205	−	1.26129i	0.957641	−	0.287965i	$-0.0929786\pi$
$762$	−1089.54	+	968.266i	−1.42984	+	1.27069i
$763$	292.247	−	1090.68i	0.383023	−	1.42946i
$764$			31.1927i			0.0408281i
$765$	−631.707	−	473.804i	−0.825761	−	0.619352i
$766$	−694.404			−0.906533
$767$	368.461	+	98.7288i	0.480392	+	0.128721i
$768$	70.7203	−	212.931i	0.0920838	−	0.277254i
$769$	−353.787	−	204.259i	−0.460061	−	0.265617i	0.252009	−	0.967725i	$-0.418909\pi$
$769$	−353.787	−	204.259i	−0.460061	−	0.265617i	−0.712070	+	0.702108i	$0.752242\pi$
$770$	−68.2577	+	518.469i	−0.0886464	+	0.673336i
$771$	20.7436	+	41.3750i	0.0269049	+	0.0536641i
$772$	24.8642	−	3.27343i	0.0322075	−	0.00424019i
$773$	971.389	+	971.389i	1.25665	+	1.25665i	0.952683	+	0.303965i	$0.0983106\pi$
$773$	971.389	+	971.389i	1.25665	+	1.25665i	0.303965	+	0.952683i	$0.401689\pi$
$774$	615.046	+	72.7472i	0.794633	+	0.0939887i
$775$	29.8694	−	72.1110i	0.0385411	−	0.0930465i
$776$	505.516	−	66.5524i	0.651438	−	0.0857634i
$777$	237.879	−	211.401i	0.306150	−	0.272073i
$778$	21.6711	+	12.5118i	0.0278548	+	0.0160820i
$779$	855.586	+	112.640i	1.09831	+	0.144596i
$780$	−21.0083	+	14.2382i	−0.0269337	+	0.0182541i
$781$	46.8175	+	81.0902i	0.0599455	+	0.103829i
$782$	390.618	+	226.668i	0.499512	+	0.289857i
$783$	1031.86	+	47.1878i	1.31783	+	0.0602654i
$784$	−1465.52	−	1465.52i	−1.86928	−	1.86928i
$785$	−914.437	+	1191.72i	−1.16489	+	1.51811i
$786$	24.2027	−	126.005i	0.0307923	−	0.160312i
$787$	−1162.43	−	153.037i	−1.47704	−	0.194456i	−0.651436	−	0.758704i	$-0.725833\pi$
$787$	−1162.43	−	153.037i	−1.47704	−	0.194456i	−0.825606	+	0.564247i	$0.809166\pi$
$788$	−69.5675	−	90.6622i	−0.0882837	−	0.115054i
$789$	−0.594528	+	10.0880i	−0.000753521	+	0.0127858i
$790$	1164.81	+	312.109i	1.47444	+	0.395075i
$791$	−1029.47	−	1029.47i	−1.30147	−	1.30147i
$792$	245.965	+	62.4469i	0.310562	+	0.0788471i
$793$	122.371	+	50.6878i	0.154314	+	0.0639191i
$794$	−1110.09	−	851.801i	−1.39810	−	1.07280i
$795$	203.326	+	175.958i	0.255756	+	0.221330i
$796$	15.2633	−	115.936i	0.0191750	−	0.145649i
$797$	−252.713	−	943.136i	−0.317080	−	1.18336i	−0.922038	−	0.387100i	$-0.873477\pi$
$797$	−252.713	−	943.136i	−0.317080	−	1.18336i	0.604958	−	0.796258i	$-0.293190\pi$
$798$	819.673	+	709.341i	1.02716	+	0.888899i
$799$	415.904	+	173.343i	0.520531	+	0.216950i
$800$			10.2622i			0.0128277i
$801$	−1012.74	+	435.200i	−1.26435	+	0.543321i
$802$	−277.148	+	114.799i	−0.345572	+	0.143140i
$803$	−189.268	−	327.822i	−0.235701	−	0.408247i
$804$	8.64203	−	7.68010i	0.0107488	−	0.00955237i
$805$	672.638	−	516.133i	0.835575	−	0.641159i
$806$	−330.523	+	253.619i	−0.410078	+	0.314664i
$807$	−577.441	−	852.005i	−0.715541	−	1.05577i
$808$	540.777	+	144.901i	0.669278	+	0.179333i
$809$	883.039	+	365.767i	1.09152	+	0.452122i	0.854536	−	0.519392i	$-0.173841\pi$
$809$	883.039	+	365.767i	1.09152	+	0.452122i	0.236983	+	0.971514i	$0.423841\pi$
$810$	−356.518	−	800.420i	−0.440146	−	0.988173i
$811$	−71.8431	−	173.444i	−0.0885858	−	0.213865i	0.873377	−	0.487044i	$-0.161925\pi$
$811$	−71.8431	−	173.444i	−0.0885858	−	0.213865i	−0.961963	+	0.273179i	$0.911925\pi$
$812$	−97.4848	−	168.849i	−0.120055	−	0.207942i
$813$	−206.913	+	42.5756i	−0.254506	+	0.0523685i
$814$	61.8033	−	16.5601i	0.0759254	−	0.0203441i
$815$	565.819	+	326.676i	0.694256	+	0.400829i
$816$	872.012	+	169.478i	1.06864	+	0.207694i
$817$	−218.341	−	378.177i	−0.267247	−	0.462885i
$818$	858.848	−	858.848i	1.04994	−	1.04994i
$819$	486.220	−	6.40259i	0.593675	−	0.00781757i
$820$			131.668i			0.160570i
$821$	157.906	+	121.165i	0.192333	+	0.147583i	0.700439	−	0.713712i	$-0.252987\pi$
$821$	157.906	+	121.165i	0.192333	+	0.147583i	−0.508106	+	0.861295i	$0.669654\pi$
$822$	−348.968	+	174.957i	−0.424535	+	0.212843i
$823$	−409.349	−	533.475i	−0.497387	−	0.648207i	0.475438	−	0.879749i	$-0.342290\pi$
$823$	−409.349	−	533.475i	−0.497387	−	0.648207i	−0.972825	+	0.231542i	$0.925623\pi$
$824$	563.574	−	151.009i	0.683949	−	0.183264i
$825$	−18.2687	+	1.31824i	−0.0221439	+	0.00159787i
$826$	2464.66	−	324.478i	2.98385	−	0.392831i
$827$	−258.085	+	623.073i	−0.312074	+	0.753413i	0.687554	+	0.726133i	$0.258685\pi$
$827$	−258.085	+	623.073i	−0.312074	+	0.753413i	−0.999628	+	0.0272799i	$0.991315\pi$
$828$	22.9361	+	38.5453i	0.0277006	+	0.0465523i
$829$		−	157.363i		−	0.189823i	−0.995486	−	0.0949115i	$-0.969743\pi$
$829$		−	157.363i		−	0.189823i	0.995486	−	0.0949115i	$-0.0302568\pi$
$830$	1.81411	−	2.36419i	0.00218567	−	0.00284842i
$831$	−379.827	+	783.169i	−0.457072	+	0.942442i
$832$	−117.831	+	204.089i	−0.141623	+	0.245299i
$833$	1234.92	−	1602.08i	1.48249	−	1.92327i
$834$	223.640	−	1164.33i	0.268154	−	1.39608i
$835$	−51.2623	+	191.313i	−0.0613919	+	0.229118i
$836$	7.46469	+	18.0214i	0.00892906	+	0.0215567i
$837$	−592.102	−	1143.18i	−0.707410	−	1.36580i
$838$	146.942	+	354.749i	0.175348	+	0.423328i
$839$	1578.83	−	207.857i	1.88180	−	0.247743i	0.899754	−	0.436397i	$-0.143746\pi$
$839$	1578.83	−	207.857i	1.88180	−	0.247743i	0.982044	+	0.188654i	$0.0604125\pi$
$840$	834.533	−	1266.95i	0.993492	−	1.50827i
$841$	161.142	+	601.392i	0.191608	+	0.715091i
$842$	−322.849	+	86.5072i	−0.383431	+	0.102740i
$843$	−22.8666	+	388.002i	−0.0271252	+	0.460263i
$844$	−4.73681	−	35.9796i	−0.00561233	−	0.0426299i
$845$	−722.973	+	299.465i	−0.855590	+	0.354397i
$846$	309.569	+	392.624i	0.365921	+	0.464094i
$847$	−1282.32	+	531.156i	−1.51396	+	0.627103i
$848$	−292.187	−	78.2912i	−0.344560	−	0.0923246i
$849$	599.474	−	692.717i	0.706095	−	0.815921i
$850$	−57.8447	+	7.48630i	−0.0680526	+	0.00880741i
$851$	−89.8378	−	51.8679i	−0.105567	−	0.0609493i
$852$	2.13133	+	29.5369i	0.00250157	+	0.0346677i
$853$	950.764	+	729.547i	1.11461	+	0.855272i	0.990570	−	0.137005i	$-0.0437476\pi$
$853$	950.764	+	729.547i	1.11461	+	0.855272i	0.124042	+	0.992277i	$0.460414\pi$
$854$	863.186			1.01076
$855$	−301.836	+	539.064i	−0.353024	+	0.630484i
$856$	−484.934	−	200.866i	−0.566512	−	0.234657i
$857$	−46.4357	−	352.714i	−0.0541840	−	0.411568i	−0.996945	−	0.0781005i	$-0.975115\pi$
$857$	−46.4357	−	352.714i	−0.0541840	−	0.411568i	0.942762	−	0.333468i	$-0.108219\pi$
$858$	87.9655	+	42.6621i	0.102524	+	0.0497228i
$859$	113.960	+	425.304i	0.132666	+	0.495115i	0.999997	−	0.00261704i	$-0.000833030\pi$
$859$	113.960	+	425.304i	0.132666	+	0.495115i	−0.867331	+	0.497732i	$0.834166\pi$
$860$	52.8587	−	40.5599i	0.0614636	−	0.0471626i
$861$	1387.75	−	2106.81i	1.61179	−	2.44693i
$862$	−519.538	+	677.075i	−0.602712	+	0.785470i
$863$	−708.843			−0.821371			−0.410685	−	0.911777i	$-0.634711\pi$
$863$	−708.843			−0.821371			−0.410685	+	0.911777i	$0.634711\pi$
$864$	129.441	+	109.070i	0.149816	+	0.126239i
$865$	1013.69	+	1013.69i	1.17189	+	1.17189i
$866$	−763.447	+	440.776i	−0.881578	+	0.508980i
$867$	−54.8057	+	865.266i	−0.0632130	+	0.998000i
$868$	−121.501	+	210.446i	−0.139978	+	0.242449i
$869$	−107.611	−	401.610i	−0.123833	−	0.462151i
$870$	928.041	−	824.742i	1.06671	−	0.947980i
$871$	−35.3832	+	20.4285i	−0.0406236	+	0.0234541i
$872$	−608.474	+	252.038i	−0.697792	+	0.289035i
$873$	−149.372	+	588.345i	−0.171102	+	0.673935i
$874$	135.219	−	326.448i	0.154713	−	0.373510i
$875$	404.489	−	1509.57i	0.462273	−	1.72523i
$876$	−8.61631	−	119.408i	−0.00983597	−	0.136311i
$877$	−49.3171	−	64.2713i	−0.0562338	−	0.0732853i	0.764390	−	0.644754i	$-0.223040\pi$
$877$	−49.3171	−	64.2713i	−0.0562338	−	0.0732853i	−0.820624	+	0.571469i	$0.806374\pi$
$878$	−596.652	−	777.572i	−0.679558	−	0.885617i
$879$	−21.5951	+	65.0204i	−0.0245678	+	0.0739708i
$880$	290.375	−	167.648i	0.329971	−	0.190509i
$881$	−326.398	−	787.994i	−0.370486	−	0.894432i	−0.993668	−	0.112355i	$-0.964161\pi$
$881$	−326.398	−	787.994i	−0.370486	−	0.894432i	0.623182	−	0.782077i	$-0.285839\pi$
$882$	2062.23	−	886.194i	2.33813	−	1.00475i
$883$	32.8666			0.0372215			0.0186108	−	0.999827i	$-0.494076\pi$
$883$	32.8666			0.0372215			0.0186108	+	0.999827i	$0.494076\pi$
$884$	25.7201	+	10.7198i	0.0290952	+	0.0121265i
$885$	464.253	+	1338.62i	0.524579	+	1.51257i
$886$	−1066.13	+	285.670i	−1.20331	+	0.322426i
$887$	64.5527	+	8.49853i	0.0727765	+	0.00958121i	0.166826	−	0.985986i	$-0.446648\pi$
$887$	64.5527	+	8.49853i	0.0727765	+	0.00958121i	−0.0940500	+	0.995567i	$0.529981\pi$
$888$	−182.289	−	35.0136i	−0.205281	−	0.0394297i
$889$	1829.01	−	2383.61i	2.05738	−	2.68123i
$890$	−507.021	+	1224.06i	−0.569686	+	1.37534i
$891$	−177.539	+	244.441i	−0.199258	+	0.274345i
$892$	18.2799	−	18.2799i	0.0204932	−	0.0204932i
$893$	91.2420	−	340.520i	0.102175	−	0.381321i
$894$	−263.915	+	400.662i	−0.295207	+	0.448168i
$895$	1041.69	−	799.316i	1.16390	−	0.893091i
$896$	−242.883	+	1844.88i	−0.271075	+	2.05902i
$897$	−51.9369	−	149.755i	−0.0579007	−	0.166951i
$898$	−167.425	−	128.470i	−0.186442	−	0.143062i
$899$	1289.89	−	1289.89i	1.43480	−	1.43480i
$900$	−5.38059	−	2.14616i	−0.00597843	−	0.00238462i
$901$	39.1777	−	292.620i	0.0434824	−	0.324773i
$902$	439.263	−	253.609i	0.486988	−	0.281163i
$903$	−1273.28	+	91.8777i	−1.41005	+	0.101747i
$904$	−110.840	+	841.917i	−0.122611	+	0.931324i
$905$	709.646	−	1229.14i	0.784139	−	1.35817i
$906$	−238.665	+	718.593i	−0.263427	+	0.793149i
$907$	−6.89523	−	52.3745i	−0.00760224	−	0.0577448i	0.987223	−	0.159343i	$-0.0509376\pi$
$907$	−6.89523	−	52.3745i	−0.00760224	−	0.0577448i	−0.994825	+	0.101598i	$0.967604\pi$
$908$	−94.4909	−	39.1394i	−0.104065	−	0.0431051i
$909$	−398.746	+	534.072i	−0.438664	+	0.587538i
$910$	413.281	−	413.281i	0.454155	−	0.454155i
$911$	232.453	+	1765.66i	0.255162	+	1.93815i	0.336998	+	0.941505i	$0.390588\pi$
$911$	232.453	+	1765.66i	0.255162	+	1.93815i	−0.0818354	+	0.996646i	$0.526078\pi$
$912$	40.8896	−	693.817i	0.0448351	−	0.760765i
$913$	−1.01867	−	0.134111i	−0.00111574	−	0.000146890i
$914$	258.646	−	447.988i	0.282982	−	0.490140i
$915$	99.1532	+	481.874i	0.108364	+	0.526639i
$916$	−6.35979	+	23.7351i	−0.00694301	+	0.0259117i
$917$			264.474i			0.288412i
$918$	−520.368	+	809.186i	−0.566849	+	0.881466i
$919$	619.101			0.673668			0.336834	−	0.941564i	$-0.390644\pi$
$919$	619.101			0.673668			0.336834	+	0.941564i	$0.390644\pi$
$920$	−477.675	−	127.993i	−0.519212	−	0.139122i
$921$	−798.481	+	164.300i	−0.866972	+	0.178393i
$922$	−207.689	−	119.909i	−0.225259	−	0.130053i
$923$	13.6597	−	103.756i	0.0147993	−	0.112412i
$924$	56.9253	+	3.35485i	0.0616075	+	0.00363079i
$925$	13.2829	−	1.74873i	0.0143599	−	0.00189052i
$926$	−96.7698	−	96.7698i	−0.104503	−	0.104503i
$927$	−81.5886	+	689.796i	−0.0880136	+	0.744117i
$928$	−91.7826	+	221.583i	−0.0989037	+	0.238775i
$929$	1.80800	−	0.238028i	0.00194618	−	0.000256220i	−0.129553	−	0.991572i	$-0.541354\pi$
$929$	1.80800	−	0.238028i	0.00194618	−	0.000256220i	0.131499	+	0.991316i	$0.458021\pi$
$930$	−1468.54	−	487.745i	−1.57908	−	0.524457i
$931$	−1370.59	−	791.308i	−1.47217	−	0.849955i
$932$	35.6694	+	4.69597i	0.0382719	+	0.00503859i
$933$	−16.1004	−	223.125i	−0.0172566	−	0.239148i
$934$	542.220	+	939.152i	0.580535	+	1.00552i
$935$	198.644	+	260.058i	0.212454	+	0.278137i
$936$	−175.607	−	222.722i	−0.187615	−	0.237950i
$937$	645.982	+	645.982i	0.689415	+	0.689415i	0.962103	−	0.272688i	$-0.0879126\pi$
$937$	645.982	+	645.982i	0.689415	+	0.689415i	−0.272688	+	0.962103i	$0.587913\pi$
$938$	−162.089	+	211.239i	−0.172803	+	0.225201i
$939$	−563.930	+	195.578i	−0.600565	+	0.208284i
$940$	53.3276	+	7.02071i	0.0567314	+	0.00746884i
$941$	297.437	+	387.627i	0.316086	+	0.411931i	0.924194	−	0.381923i	$-0.124738\pi$
$941$	297.437	+	387.627i	0.316086	+	0.411931i	−0.608108	+	0.793854i	$0.708071\pi$
$942$	1528.34	+	1006.71i	1.62244	+	1.06870i
$943$	−794.326	−	212.839i	−0.842340	−	0.225704i
$944$	−1127.06	−	1127.06i	−1.19392	−	1.19392i
$945$	1032.88	+	1481.62i	1.09300	+	1.56785i
$946$	−237.126	−	98.2209i	−0.250662	−	0.103828i
$947$	−843.580	−	647.301i	−0.890792	−	0.683529i	0.0583776	−	0.998295i	$-0.481407\pi$
$947$	−843.580	−	647.301i	−0.890792	−	0.683529i	−0.949169	+	0.314766i	$0.898074\pi$
$948$	24.8041	−	129.136i	0.0261647	−	0.136220i
$949$	−55.2219	+	419.452i	−0.0581896	+	0.441994i
$950$	11.8111	+	44.0798i	0.0124328	+	0.0463998i
$951$	−1074.28	+	372.574i	−1.12963	+	0.391771i
$952$	−1665.71	−	3.65539i	−1.74969	−	0.00383970i
$953$			316.632i			0.332248i	0.986105	+	0.166124i	$0.0531252\pi$
$953$			316.632i			0.332248i	−0.986105	+	0.166124i	$0.946875\pi$
$954$	195.992	−	262.508i	0.205442	−	0.275165i
$955$	378.263	−	156.682i	0.396087	−	0.164065i
$956$	17.3153	+	29.9910i	0.0181122	+	0.0313713i
$957$	−406.251	−	134.927i	−0.424504	−	0.140990i
$958$	476.145	−	365.359i	0.497019	−	0.381376i
$959$	638.366	−	489.835i	0.665658	−	0.510777i
$960$	−873.042	+	62.9973i	−0.909419	+	0.0656222i
$961$	−1267.85	−	339.720i	−1.31931	−	0.353507i
$962$	−66.0677	−	27.3661i	−0.0686774	−	0.0284471i
$963$	436.001	−	447.637i	0.452753	−	0.464836i
$964$	60.9453	+	147.135i	0.0632212	+	0.152630i
$965$	−164.589	−	285.077i	−0.170559	−	0.295416i
$966$	−686.178	−	772.122i	−0.710329	−	0.799298i
$967$	500.112	−	134.005i	0.517179	−	0.138578i	0.00921779	−	0.999958i	$-0.497066\pi$
$967$	500.112	−	134.005i	0.517179	−	0.138578i	0.507962	+	0.861380i	$0.330399\pi$
$968$	701.111	+	404.787i	0.724289	+	0.418168i
$969$	676.681	−	47.3357i	0.698329	−	0.0488501i
$970$	364.801	+	631.855i	0.376084	+	0.651397i
$971$	−866.130	+	866.130i	−0.891998	+	0.891998i	−0.994711	−	0.102713i	$-0.967248\pi$
$971$	−866.130	+	866.130i	−0.891998	+	0.891998i	0.102713	+	0.994711i	$0.467248\pi$
$972$	−84.2572	+	45.0574i	−0.0866844	+	0.0463553i
$973$			2443.82i			2.51163i
$974$	−910.487	−	698.641i	−0.934791	−	0.717291i
$975$	17.0956	+	11.2608i	0.0175340	+	0.0115496i
$976$	−336.919	−	439.081i	−0.345204	−	0.449879i
$977$	−1570.48	+	420.809i	−1.60745	+	0.430715i	−0.947282	−	0.320402i	$-0.896182\pi$
$977$	−1570.48	+	420.809i	−1.60745	+	0.430715i	−0.660169	+	0.751117i	$0.729515\pi$
$978$	347.357	−	716.219i	0.355171	−	0.732330i
$979$	452.902	−	59.6257i	0.462617	−	0.0609047i
$980$	92.4059	−	223.088i	0.0942918	−	0.227640i
$981$	−10.3239	−	784.006i	−0.0105238	−	0.799191i
$982$			76.2296i			0.0776269i
$983$	−353.758	+	461.027i	−0.359876	+	0.469000i	−0.937843	−	0.347061i	$-0.887180\pi$
$983$	−353.758	+	461.027i	−0.359876	+	0.469000i	0.577967	+	0.816060i	$0.303846\pi$
$984$	−1467.67	+	105.904i	−1.49153	+	0.107626i
$985$	−749.990	+	1299.02i	−0.761411	+	1.31880i
$986$	−1315.95	−	355.704i	−1.33463	−	0.360755i
$987$	−779.294	−	674.398i	−0.789558	−	0.683280i
$988$	5.64254	−	21.0582i	0.00571107	−	0.0213140i
$989$	159.245	+	384.451i	0.161016	+	0.388727i
$990$	52.1338	+	359.364i	0.0526604	+	0.362994i
$991$	460.450	+	1111.63i	0.464632	+	1.12172i	0.966475	+	0.256762i	$0.0826557\pi$
$991$	460.450	+	1111.63i	0.464632	+	1.12172i	−0.501843	+	0.864959i	$0.667344\pi$
$992$	296.369	−	39.0177i	0.298759	−	0.0393323i
$993$	1819.86	+	107.252i	1.83269	+	0.108008i
$994$	−176.515	−	658.762i	−0.177580	−	0.662738i
$995$	−1482.59	+	397.259i	−1.49004	+	0.399255i
$996$	−0.271371	−	0.178751i	−0.000272461	−	0.000179469i
$997$	−43.3567	−	329.327i	−0.0434872	−	0.330318i	−0.999335	−	0.0364565i	$-0.988393\pi$
$997$	−43.3567	−	329.327i	−0.0434872	−	0.330318i	0.955848	−	0.293861i	$-0.0949404\pi$
$998$	1172.95	−	485.850i	1.17530	−	0.486824i
$999$	119.119	−	186.129i	0.119238	−	0.186316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.q.a.104.26	yes	272
9.2	odd	6	inner	153.3.q.a.2.26	✓	272
17.9	even	8	inner	153.3.q.a.77.26	yes	272
153.128	odd	24	inner	153.3.q.a.128.26	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.q.a.2.26	✓	272	9.2	odd	6	inner
153.3.q.a.77.26	yes	272	17.9	even	8	inner
153.3.q.a.104.26	yes	272	1.1	even	1	trivial
153.3.q.a.128.26	yes	272	153.128	odd	24	inner

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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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.q (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.02458 + 0.542484i) q^{2} +(-2.93844 + 0.604630i) q^{3} +(0.340523 + 0.196601i) q^{4} +(0.673658 - 5.11694i) q^{5} +(-6.27710 - 0.369936i) q^{6} +(12.8501 - 1.69175i) q^{7} +(-5.34561 - 5.34561i) q^{8} +(8.26885 - 3.55333i) q^{9} +(4.13973 - 9.99420i) q^{10} +(-3.69787 + 0.486833i) q^{11} +(-1.11948 - 0.371810i) q^{12} +(3.61010 + 2.08429i) q^{13} +(26.9338 + 3.54590i) q^{14} +(1.11435 + 15.4431i) q^{15} +(-8.70910 - 15.0846i) q^{16} +(13.5097 - 10.3193i) q^{17} +(18.6685 - 2.70829i) q^{18} +(-9.40500 - 9.40500i) q^{19} +(1.23539 - 1.61000i) q^{20} +(-36.7364 + 12.7407i) q^{21} +(-7.75071 - 1.02040i) q^{22} +(7.71580 + 10.0554i) q^{23} +(18.9399 + 12.4756i) q^{24} +(-1.58116 - 0.423670i) q^{25} +(6.17823 + 6.17823i) q^{26} +(-22.1490 + 15.4408i) q^{27} +(4.70837 + 1.95027i) q^{28} +(-30.3514 - 23.2895i) q^{29} +(-6.12156 + 31.8704i) q^{30} +(-6.22376 + 47.2741i) q^{31} +(-1.62258 - 6.05553i) q^{32} +(10.5716 - 3.66637i) q^{33} +(32.9495 - 13.5635i) q^{34} -66.8930i q^{35} +(3.51432 + 0.415672i) q^{36} +(-7.56153 + 3.13209i) q^{37} +(-13.9391 - 24.1432i) q^{38} +(-11.8683 - 3.94179i) q^{39} +(-30.9543 + 23.7521i) q^{40} +(-51.4740 + 39.4974i) q^{41} +(-81.2873 + 5.86556i) q^{42} +(31.7128 + 8.49743i) q^{43} +(-1.35492 - 0.561227i) q^{44} +(-12.6118 - 44.7050i) q^{45} +(10.1663 + 24.5437i) q^{46} +(13.2524 + 22.9539i) q^{47} +(34.7118 + 39.0594i) q^{48} +(114.933 - 30.7963i) q^{49} +(-2.97134 - 1.71550i) q^{50} +(-33.4580 + 38.4911i) q^{51} +(0.819549 + 1.41950i) q^{52} +(12.2800 - 12.2800i) q^{53} +(-53.2189 + 19.2457i) q^{54} +19.2497i q^{55} +(-77.7352 - 59.6483i) q^{56} +(33.3225 + 21.9495i) q^{57} +(-48.8146 - 63.6165i) q^{58} +(88.3899 - 23.6840i) q^{59} +(-2.65668 + 5.47783i) q^{60} +(31.5024 - 4.14737i) q^{61} +(-38.2459 + 92.3339i) q^{62} +(100.244 - 59.6496i) q^{63} +56.5327i q^{64} +(13.0972 - 17.0686i) q^{65} +(23.3920 - 1.68793i) q^{66} +(-4.90058 + 8.48806i) q^{67} +(6.62915 - 0.857949i) q^{68} +(-28.7522 - 24.8821i) q^{69} +(36.2884 - 135.430i) q^{70} +(-9.60716 - 23.1937i) q^{71} +(-63.1968 - 25.2073i) q^{72} +(38.8387 + 93.7649i) q^{73} +(-17.0080 + 2.23915i) q^{74} +(4.90230 + 0.288913i) q^{75} +(-1.35359 - 5.05165i) q^{76} +(-46.6944 + 12.5117i) q^{77} +(-21.8899 - 14.4188i) q^{78} +(14.5504 + 110.521i) q^{79} +(-83.0540 + 34.4021i) q^{80} +(55.7476 - 58.7640i) q^{81} +(-125.640 + 52.0417i) q^{82} +(0.266089 + 0.0712983i) q^{83} +(-15.0144 - 2.88393i) q^{84} +(-43.7025 - 76.0800i) q^{85} +(59.5954 + 34.4074i) q^{86} +(103.267 + 50.0833i) q^{87} +(22.3698 + 17.1649i) q^{88} -122.477 q^{89} +(-1.28192 - 97.3504i) q^{90} +(49.9164 + 20.6760i) q^{91} +(0.650501 + 4.94104i) q^{92} +(-10.2952 - 142.675i) q^{93} +(14.3784 + 53.6611i) q^{94} +(-54.4606 + 41.7891i) q^{95} +(8.42919 + 16.8128i) q^{96} +(-41.0583 + 53.5082i) q^{97} +249.398 q^{98} +(-28.8472 + 17.1653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 12 q^{2} - 8 q^{3} - 12 q^{5} - 8 q^{6} - 4 q^{7} + 16 q^{9} - 16 q^{10} - 84 q^{11} - 140 q^{12} - 12 q^{14} + 44 q^{15} + 440 q^{16} - 48 q^{18} - 16 q^{19} - 12 q^{20} - 4 q^{22} - 120 q^{23}+ \cdots - 832 q^{99}+O(q^{100}) \) 272 * q - 12 * q^2 - 8 * q^3 - 12 * q^5 - 8 * q^6 - 4 * q^7 + 16 * q^9 - 16 * q^10 - 84 * q^11 - 140 * q^12 - 12 * q^14 + 44 * q^15 + 440 * q^16 - 48 * q^18 - 16 * q^19 - 12 * q^20 - 4 * q^22 - 120 * q^23 + 112 * q^24 - 4 * q^25 + 40 * q^27 - 144 * q^28 - 12 * q^29 - 4 * q^31 - 204 * q^32 + 112 * q^33 - 28 * q^34 - 200 * q^36 - 16 * q^37 - 148 * q^39 + 60 * q^40 - 12 * q^41 - 624 * q^42 + 116 * q^43 + 44 * q^45 - 352 * q^46 - 168 * q^48 - 4 * q^49 - 24 * q^50 - 256 * q^51 - 264 * q^52 - 20 * q^54 + 708 * q^56 + 76 * q^57 - 4 * q^58 + 492 * q^59 - 656 * q^60 - 4 * q^61 + 708 * q^63 + 348 * q^65 - 508 * q^66 - 8 * q^67 - 204 * q^68 + 176 * q^69 + 12 * q^70 - 16 * q^73 + 492 * q^74 - 868 * q^75 + 92 * q^76 + 528 * q^77 + 864 * q^78 - 4 * q^79 + 176 * q^82 + 1428 * q^83 - 440 * q^84 + 188 * q^85 - 1824 * q^86 - 796 * q^87 + 156 * q^88 - 1000 * q^90 - 744 * q^91 - 12 * q^92 + 44 * q^93 + 28 * q^94 - 12 * q^95 - 1452 * q^96 - 364 * q^97 - 832 * q^99

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