LMFDB - Embedded newform 363.3.h.q.269.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,3,Mod(245,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.245"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-4,18,0,10,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.1
Character	$\chi$	$=$	363.269
Dual form			363.3.h.q.251.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.32956 + 1.08184i) q^{2} +(2.68613 - 1.33594i) q^{3} +(6.67952 - 4.85296i) q^{4} +(-7.51264 - 2.44100i) q^{5} +(-7.49835 + 7.35404i) q^{6} +(-1.46803 + 1.06658i) q^{7} +(-8.75863 + 12.0552i) q^{8} +(5.43055 - 7.17698i) q^{9} +27.6545 q^{10} +(11.4588 - 21.9591i) q^{12} +(0.0219178 + 0.0674561i) q^{13} +(3.73401 - 5.13943i) q^{14} +(-23.4409 + 3.47955i) q^{15} +(5.91516 - 18.2050i) q^{16} +(-3.48121 - 1.13111i) q^{17} +(-10.3170 + 29.7712i) q^{18} +(-21.2992 - 15.4748i) q^{19} +(-62.0269 + 20.1538i) q^{20} +(-2.51842 + 4.82617i) q^{21} +6.84236i q^{23} +(-7.42179 + 44.0828i) q^{24} +(30.2558 + 21.9821i) q^{25} +(-0.145953 - 0.200887i) q^{26} +(4.99916 - 26.5332i) q^{27} +(-4.62964 + 14.2486i) q^{28} +(17.7569 + 24.4403i) q^{29} +(74.2836 - 36.9447i) q^{30} +(13.0523 + 40.1709i) q^{31} +7.40958i q^{32} +12.8146 q^{34} +(13.6323 - 4.42940i) q^{35} +(1.44390 - 74.2931i) q^{36} +(-2.99344 + 2.17486i) q^{37} +(87.6582 + 28.4819i) q^{38} +(0.148991 + 0.151915i) q^{39} +(95.2272 - 69.1866i) q^{40} +(-41.7768 + 57.5009i) q^{41} +(3.16409 - 18.7936i) q^{42} -13.8601 q^{43} +(-58.3168 + 40.6621i) q^{45} +(-7.40233 - 22.7820i) q^{46} +(-16.0807 + 22.1332i) q^{47} +(-8.43183 - 56.8032i) q^{48} +(-14.1243 + 43.4702i) q^{49} +(-124.520 - 40.4589i) q^{50} +(-10.8621 + 1.61236i) q^{51} +(0.473762 + 0.344208i) q^{52} +(-20.6619 + 6.71345i) q^{53} +(12.0596 + 93.7520i) q^{54} -27.0392i q^{56} +(-77.8857 - 13.1128i) q^{57} +(-85.5633 - 62.1654i) q^{58} +(46.9059 + 64.5605i) q^{59} +(-139.688 + 137.000i) q^{60} +(24.4640 - 75.2925i) q^{61} +(-86.9169 - 119.631i) q^{62} +(-0.317340 + 16.3282i) q^{63} +(15.6447 + 48.1493i) q^{64} -0.560274i q^{65} -101.689 q^{67} +(-28.7421 + 9.33887i) q^{68} +(9.14095 + 18.3794i) q^{69} +(-40.5976 + 29.4959i) q^{70} +(-44.1378 - 14.3412i) q^{71} +(38.9559 + 128.327i) q^{72} +(-93.4412 + 67.8890i) q^{73} +(7.61398 - 10.4797i) q^{74} +(110.638 + 18.6270i) q^{75} -217.367 q^{76} +(-0.660422 - 0.344625i) q^{78} +(19.4337 + 59.8107i) q^{79} +(-88.8769 + 122.329i) q^{80} +(-22.0182 - 77.9500i) q^{81} +(76.8918 - 236.649i) q^{82} +(80.3644 + 26.1120i) q^{83} +(6.59936 + 44.4583i) q^{84} +(23.3920 + 16.9953i) q^{85} +(46.1481 - 14.9944i) q^{86} +(80.3481 + 41.9277i) q^{87} -45.3523i q^{89} +(150.179 - 198.476i) q^{90} +(-0.104124 - 0.0756502i) q^{91} +(33.2057 + 45.7037i) q^{92} +(88.7259 + 90.4670i) q^{93} +(29.5971 - 91.0905i) q^{94} +(122.239 + 168.248i) q^{95} +(9.89872 + 19.9031i) q^{96} +(-29.7481 - 91.5551i) q^{97} -160.017i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−3.32956	+	1.08184i	−1.66478	+	0.540920i	−0.981866	−	0.189579i	$-0.939288\pi$
$2$	−3.32956	+	1.08184i	−1.66478	+	0.540920i	−0.682914	+	0.730498i	$0.739288\pi$
$3$	2.68613	−	1.33594i	0.895376	−	0.445312i
$3$	2.68613	−	1.33594i	0.895376	−	0.445312i
$4$	6.67952	−	4.85296i	1.66988	−	1.21324i
$5$	−7.51264	−	2.44100i	−1.50253	−	0.488201i	−0.561773	−	0.827291i	$-0.689881\pi$
$5$	−7.51264	−	2.44100i	−1.50253	−	0.488201i	−0.940754	+	0.339090i	$0.889881\pi$
$6$	−7.49835	+	7.35404i	−1.24973	+	1.22567i
$7$	−1.46803	+	1.06658i	−0.209718	+	0.152369i	−0.687686	−	0.726008i	$-0.741374\pi$
$7$	−1.46803	+	1.06658i	−0.209718	+	0.152369i	0.477968	+	0.878377i	$0.341374\pi$
$8$	−8.75863	+	12.0552i	−1.09483	+	1.50690i
$9$	5.43055	−	7.17698i	0.603395	−	0.797443i
$10$	27.6545			2.76545
$11$		0			0
$11$		0			0
$12$	11.4588	−	21.9591i	0.954901	−	1.82992i
$13$	0.0219178	+	0.0674561i	0.00168599	+	0.00518893i	0.951896	−	0.306421i	$-0.0991317\pi$
$13$	0.0219178	+	0.0674561i	0.00168599	+	0.00518893i	−0.950210	+	0.311610i	$0.899132\pi$
$14$	3.73401	−	5.13943i	0.266715	−	0.367102i
$15$	−23.4409	+	3.47955i	−1.56273	+	0.231970i
$16$	5.91516	−	18.2050i	0.369697	−	1.13781i
$17$	−3.48121	−	1.13111i	−0.204777	−	0.0665361i	0.204832	−	0.978797i	$-0.434335\pi$
$17$	−3.48121	−	1.13111i	−0.204777	−	0.0665361i	−0.409610	+	0.912261i	$0.634335\pi$
$18$	−10.3170	+	29.7712i	−0.573167	+	1.65395i
$19$	−21.2992	−	15.4748i	−1.12101	−	0.814462i	−0.136649	−	0.990620i	$-0.543633\pi$
$19$	−21.2992	−	15.4748i	−1.12101	−	0.814462i	−0.984362	+	0.176157i	$0.943633\pi$
$20$	−62.0269	+	20.1538i	−3.10135	+	1.00769i
$21$	−2.51842	+	4.82617i	−0.119925	+	0.229818i
$22$		0			0
$23$			6.84236i			0.297494i	0.988875	+	0.148747i	$0.0475240\pi$
$23$			6.84236i			0.297494i	−0.988875	+	0.148747i	$0.952476\pi$
$24$	−7.42179	+	44.0828i	−0.309241	+	1.83678i
$25$	30.2558	+	21.9821i	1.21023	+	0.879284i
$26$	−0.145953	−	0.200887i	−0.00561359	−	0.00772644i
$27$	4.99916	−	26.5332i	0.185154	−	0.982709i
$28$	−4.62964	+	14.2486i	−0.165344	+	0.508877i
$29$	17.7569	+	24.4403i	0.612308	+	0.842770i	0.996765	−	0.0803733i	$-0.0256112\pi$
$29$	17.7569	+	24.4403i	0.612308	+	0.842770i	−0.384457	+	0.923143i	$0.625611\pi$
$30$	74.2836	−	36.9447i	2.47612	−	1.23149i
$31$	13.0523	+	40.1709i	0.421042	+	1.29583i	0.906733	+	0.421704i	$0.138568\pi$
$31$	13.0523	+	40.1709i	0.421042	+	1.29583i	−0.485691	+	0.874131i	$0.661432\pi$
$32$			7.40958i			0.231549i
$33$		0			0
$34$	12.8146			0.376899
$35$	13.6323	−	4.42940i	0.389494	−	0.126554i
$36$	1.44390	−	74.2931i	0.0401082	−	2.06370i
$37$	−2.99344	+	2.17486i	−0.0809037	+	0.0587800i	−0.627502	−	0.778615i	$-0.715923\pi$
$37$	−2.99344	+	2.17486i	−0.0809037	+	0.0587800i	0.546598	+	0.837395i	$0.315923\pi$
$38$	87.6582	+	28.4819i	2.30680	+	0.749523i
$39$	0.148991	+	0.151915i	0.00382028	+	0.00389525i
$40$	95.2272	−	69.1866i	2.38068	−	1.72967i
$41$	−41.7768	+	57.5009i	−1.01895	+	1.40246i	−0.106008	+	0.994365i	$0.533807\pi$
$41$	−41.7768	+	57.5009i	−1.01895	+	1.40246i	−0.912939	+	0.408096i	$0.866193\pi$
$42$	3.16409	−	18.7936i	0.0753354	−	0.447466i
$43$	−13.8601			−0.322329			−0.161164	−	0.986928i	$-0.551525\pi$
$43$	−13.8601			−0.322329			−0.161164	+	0.986928i	$0.551525\pi$
$44$		0			0
$45$	−58.3168	+	40.6621i	−1.29593	+	0.903602i
$46$	−7.40233	−	22.7820i	−0.160920	−	0.495262i
$47$	−16.0807	+	22.1332i	−0.342143	+	0.470919i	−0.945066	−	0.326880i	$-0.894003\pi$
$47$	−16.0807	+	22.1332i	−0.342143	+	0.470919i	0.602923	+	0.797799i	$0.294003\pi$
$48$	−8.43183	−	56.8032i	−0.175663	−	1.18340i
$49$	−14.1243	+	43.4702i	−0.288252	+	0.887147i
$50$	−124.520	−	40.4589i	−2.49039	−	0.809177i
$51$	−10.8621	+	1.61236i	−0.212982	+	0.0316149i
$52$	0.473762	+	0.344208i	0.00911081	+	0.00661939i
$53$	−20.6619	+	6.71345i	−0.389846	+	0.126669i	−0.497380	−	0.867533i	$-0.665705\pi$
$53$	−20.6619	+	6.71345i	−0.389846	+	0.126669i	0.107534	+	0.994201i	$0.465705\pi$
$54$	12.0596	+	93.7520i	0.223326	+	1.73615i
$55$		0			0
$56$		−	27.0392i		−	0.482843i
$57$	−77.8857	−	13.1128i	−1.36642	−	0.230050i
$58$	−85.5633	−	62.1654i	−1.47523	−	1.07182i
$59$	46.9059	+	64.5605i	0.795016	+	1.09425i	0.993465	+	0.114134i	$0.0364093\pi$
$59$	46.9059	+	64.5605i	0.795016	+	1.09425i	−0.198450	+	0.980111i	$0.563591\pi$
$60$	−139.688	+	137.000i	−2.32813	+	2.28333i
$61$	24.4640	−	75.2925i	0.401050	−	1.23430i	−0.523100	−	0.852272i	$-0.675224\pi$
$61$	24.4640	−	75.2925i	0.401050	−	1.23430i	0.924149	−	0.382032i	$-0.124776\pi$
$62$	−86.9169	−	119.631i	−1.40189	−	1.92953i
$63$	−0.317340	+	16.3282i	−0.00503714	+	0.259177i
$64$	15.6447	+	48.1493i	0.244448	+	0.752333i
$65$		−	0.560274i		−	0.00861961i
$66$		0			0
$67$	−101.689			−1.51775			−0.758874	−	0.651238i	$-0.774250\pi$
$67$	−101.689			−1.51775			−0.758874	+	0.651238i	$0.774250\pi$
$68$	−28.7421	+	9.33887i	−0.422678	+	0.137336i
$69$	9.14095	+	18.3794i	0.132478	+	0.266369i
$70$	−40.5976	+	29.4959i	−0.579966	+	0.421370i
$71$	−44.1378	−	14.3412i	−0.621659	−	0.201989i	−0.0187823	−	0.999824i	$-0.505979\pi$
$71$	−44.1378	−	14.3412i	−0.621659	−	0.201989i	−0.602877	+	0.797834i	$0.705979\pi$
$72$	38.9559	+	128.327i	0.541054	+	1.78232i
$73$	−93.4412	+	67.8890i	−1.28002	+	0.929987i	−0.999554	−	0.0298780i	$-0.990488\pi$
$73$	−93.4412	+	67.8890i	−1.28002	+	0.929987i	−0.280463	+	0.959865i	$0.590488\pi$
$74$	7.61398	−	10.4797i	0.102892	−	0.141618i
$75$	110.638	+	18.6270i	1.47517	+	0.248359i
$76$	−217.367			−2.86009
$77$		0			0
$78$	−0.660422	−	0.344625i	−0.00846695	−	0.00441827i
$79$	19.4337	+	59.8107i	0.245996	+	0.757098i	0.995471	+	0.0950654i	$0.0303060\pi$
$79$	19.4337	+	59.8107i	0.245996	+	0.757098i	−0.749475	+	0.662033i	$0.769694\pi$
$80$	−88.8769	+	122.329i	−1.11096	+	1.52911i
$81$	−22.0182	−	77.9500i	−0.271830	−	0.962345i
$82$	76.8918	−	236.649i	0.937705	−	2.88596i
$83$	80.3644	+	26.1120i	0.968246	+	0.314602i	0.750108	−	0.661316i	$-0.230002\pi$
$83$	80.3644	+	26.1120i	0.968246	+	0.314602i	0.218138	+	0.975918i	$0.430002\pi$
$84$	6.59936	+	44.4583i	0.0785639	+	0.529266i
$85$	23.3920	+	16.9953i	0.275200	+	0.199945i
$86$	46.1481	−	14.9944i	0.536606	−	0.174354i
$87$	80.3481	+	41.9277i	0.923541	+	0.481927i
$88$		0			0
$89$		−	45.3523i		−	0.509577i	−0.966997	−	0.254788i	$-0.917994\pi$
$89$		−	45.3523i		−	0.509577i	0.966997	−	0.254788i	$-0.0820058\pi$
$90$	150.179	−	198.476i	1.66866	−	2.20529i
$91$	−0.104124	−	0.0756502i	−0.00114422	−	0.000831321i
$92$	33.2057	+	45.7037i	0.360931	+	0.496779i
$93$	88.7259	+	90.4670i	0.954042	+	0.972764i
$94$	29.5971	−	91.0905i	0.314863	−	0.969048i
$95$	122.239	+	168.248i	1.28673	+	1.77103i
$96$	9.89872	+	19.9031i	0.103112	+	0.207324i
$97$	−29.7481	−	91.5551i	−0.306681	−	0.943867i	−0.979045	−	0.203646i	$-0.934721\pi$
$97$	−29.7481	−	91.5551i	−0.306681	−	0.943867i	0.672363	−	0.740221i	$-0.265279\pi$
$98$		−	160.017i		−	1.63283i
$99$		0			0
$100$	308.772			3.08772
$101$	−52.9697	+	17.2109i	−0.524452	+	0.170405i	−0.559265	−	0.828989i	$-0.688917\pi$
$101$	−52.9697	+	17.2109i	−0.524452	+	0.170405i	0.0348128	+	0.999394i	$0.488917\pi$
$102$	34.4216	−	17.1195i	0.337467	−	0.167838i
$103$	−105.559	+	76.6932i	−1.02485	+	0.744594i	−0.967271	−	0.253747i	$-0.918337\pi$
$103$	−105.559	+	76.6932i	−1.02485	+	0.744594i	−0.0575756	+	0.998341i	$0.518337\pi$
$104$	−1.00517	−	0.326599i	−0.00966507	−	0.00314037i
$105$	30.7007	−	30.1098i	0.292387	−	0.286760i
$106$	61.5320	−	44.7056i	0.580491	−	0.421751i
$107$	34.1736	−	47.0359i	0.319379	−	0.439588i	−0.618898	−	0.785471i	$-0.712421\pi$
$107$	34.1736	−	47.0359i	0.319379	−	0.439588i	0.938278	+	0.345883i	$0.112421\pi$
$108$	−95.3723	−	201.490i	−0.883077	−	1.86564i
$109$	49.0112			0.449644			0.224822	−	0.974400i	$-0.427820\pi$
$109$	49.0112			0.449644			0.224822	+	0.974400i	$0.427820\pi$
$110$		0			0
$111$	−5.13528	+	9.84099i	−0.0462638	+	0.0886575i
$112$	10.7335	+	33.0344i	0.0958352	+	0.294950i
$113$	30.6859	−	42.2355i	0.271557	−	0.373766i	−0.651358	−	0.758771i	$-0.725800\pi$
$113$	30.6859	−	42.2355i	0.271557	−	0.373766i	0.922915	+	0.385005i	$0.125800\pi$
$114$	273.511	−	40.5998i	2.39922	−	0.356139i
$115$	16.7022	−	51.4041i	0.145237	−	0.446993i
$116$	237.216	+	77.0761i	2.04496	+	0.664449i
$117$	0.603157	+	0.209020i	0.00515519	+	0.00178650i
$118$	−226.020	−	164.213i	−1.91542	−	1.39164i
$119$	6.31694	−	2.05250i	0.0530836	−	0.0172479i
$120$	163.363	−	313.061i	1.36136	−	2.60884i
$121$		0			0
$122$			277.157i			2.27178i
$123$	−35.4004	+	210.266i	−0.287808	+	1.70948i
$124$	282.131	+	204.980i	2.27525	+	1.65306i
$125$	−57.5656	−	79.2323i	−0.460525	−	0.633858i
$126$	−16.6078	−	54.7089i	−0.131808	−	0.434198i
$127$	−18.0690	+	55.6105i	−0.142275	+	0.437878i	−0.996651	−	0.0817783i	$-0.973940\pi$
$127$	−18.0690	+	55.6105i	−0.142275	+	0.437878i	0.854375	+	0.519656i	$0.173940\pi$
$128$	−121.601	−	167.369i	−0.950005	−	1.30757i
$129$	−37.2301	+	18.5162i	−0.288605	+	0.143537i
$130$	0.606127	+	1.86547i	0.00466252	+	0.0143497i
$131$		−	147.683i		−	1.12735i	−0.825997	−	0.563675i	$-0.809387\pi$
$131$		−	147.683i		−	1.12735i	0.825997	−	0.563675i	$-0.190613\pi$
$132$		0			0
$133$	47.7730			0.359196
$134$	338.580	−	110.011i	2.52672	−	0.820980i
$135$	−102.324	+	187.131i	−0.757959	+	1.38616i
$136$	44.1264	−	32.0597i	0.324459	−	0.235733i
$137$	−157.356	−	51.1281i	−1.14858	−	0.373198i	−0.327974	−	0.944687i	$-0.606366\pi$
$137$	−157.356	−	51.1281i	−1.14858	−	0.373198i	−0.820610	+	0.571489i	$0.806366\pi$
$138$	−50.3189	−	51.3064i	−0.364630	−	0.371786i
$139$	42.1468	−	30.6214i	0.303214	−	0.220298i	−0.425765	−	0.904834i	$-0.639995\pi$
$139$	42.1468	−	30.6214i	0.303214	−	0.220298i	0.728979	+	0.684536i	$0.239995\pi$
$140$	69.5615	−	95.7433i	0.496868	−	0.683880i
$141$	−13.6263	+	80.9353i	−0.0966403	+	0.574009i
$142$	162.474			1.14419
$143$		0			0
$144$	−98.5343	−	141.316i	−0.684266	−	0.981362i
$145$	−73.7425	−	226.956i	−0.508569	−	1.56521i
$146$	237.673	−	327.129i	1.62790	−	2.24061i
$147$	20.1337	+	135.636i	0.136964	+	0.922692i
$148$	−9.44023	+	29.0541i	−0.0637854	+	0.196311i
$149$	−29.0495	−	9.43876i	−0.194963	−	0.0633474i	0.209908	−	0.977721i	$-0.432684\pi$
$149$	−29.0495	−	9.43876i	−0.194963	−	0.0633474i	−0.404871	+	0.914374i	$0.632684\pi$
$150$	−388.526	+	57.6725i	−2.59017	+	0.384483i
$151$	133.712	+	97.1472i	0.885508	+	0.643359i	0.934703	−	0.355430i	$-0.115666\pi$
$151$	133.712	+	97.1472i	0.885508	+	0.643359i	−0.0491952	+	0.998789i	$0.515666\pi$
$152$	373.104	−	121.229i	2.45463	−	0.797557i
$153$	−27.0229	+	18.8420i	−0.176620	+	0.123150i
$154$		0			0
$155$		−	333.650i		−	2.15258i
$156$	1.73242	+	0.291671i	0.0111053	+	0.00186969i
$157$	170.804	+	124.096i	1.08792	+	0.790421i	0.979047	−	0.203634i	$-0.0652754\pi$
$157$	170.804	+	124.096i	1.08792	+	0.790421i	0.108874	+	0.994056i	$0.465275\pi$
$158$	−129.411	−	178.119i	−0.819059	−	1.12734i
$159$	−46.5316	+	45.6361i	−0.292652	+	0.287019i
$160$	18.0868	−	55.6655i	0.113043	−	0.347909i
$161$	−7.29795	−	10.0448i	−0.0453289	−	0.0623899i
$162$	157.640	+	235.719i	0.973088	+	1.45506i
$163$	−27.0122	−	83.1350i	−0.165719	−	0.510031i	0.833370	−	0.552716i	$-0.186409\pi$
$163$	−27.0122	−	83.1350i	−0.165719	−	0.510031i	−0.999089	+	0.0426855i	$0.986409\pi$
$164$			586.820i			3.57817i
$165$		0			0
$166$	−295.827			−1.78209
$167$	39.3415	−	12.7828i	0.235578	−	0.0765439i	−0.188849	−	0.982006i	$-0.560476\pi$
$167$	39.3415	−	12.7828i	0.235578	−	0.0765439i	0.424427	+	0.905462i	$0.360476\pi$
$168$	−36.1226	−	72.6307i	−0.215016	−	0.432326i
$169$	136.720	−	99.3328i	0.808993	−	0.587768i
$170$	−96.2713	−	31.2804i	−0.566302	−	0.184003i
$171$	−226.729	+	68.8275i	−1.32590	+	0.402500i
$172$	−92.5791	+	67.2626i	−0.538250	+	0.391062i
$173$	−121.574	+	167.332i	−0.702740	+	0.967238i	0.297183	+	0.954820i	$0.403953\pi$
$173$	−121.574	+	167.332i	−0.702740	+	0.967238i	−0.999923	+	0.0124175i	$0.996047\pi$
$174$	−312.883	−	52.6770i	−1.79818	−	0.302741i
$175$	−67.8621			−0.387784
$176$		0			0
$177$	212.244	+	110.754i	1.19912	+	0.625730i
$178$	49.0639	+	151.003i	0.275640	+	0.848333i
$179$	−81.2859	+	111.880i	−0.454111	+	0.625030i	−0.973275	−	0.229645i	$-0.926244\pi$
$179$	−81.2859	+	111.880i	−0.454111	+	0.625030i	0.519164	+	0.854675i	$0.326244\pi$
$180$	−192.197	+	554.612i	−1.06776	+	3.08118i
$181$	−19.1377	+	58.8999i	−0.105733	+	0.325414i	−0.989902	−	0.141754i	$-0.954726\pi$
$181$	−19.1377	+	58.8999i	−0.105733	+	0.325414i	0.884168	+	0.467168i	$0.154726\pi$
$182$	0.428527	+	0.139237i	0.00235454	+	0.000765038i
$183$	−34.8725	−	234.928i	−0.190560	−	1.28376i
$184$	−82.4861	−	59.9297i	−0.448294	−	0.325705i
$185$	27.7974	−	9.03194i	0.150256	−	0.0488213i
$186$	−393.289	−	205.228i	−2.11446	−	1.10338i
$187$		0			0
$188$			225.878i			1.20148i
$189$	20.9610	+	44.2834i	0.110905	+	0.234304i
$190$	−589.020	−	427.948i	−3.10011	−	2.25236i
$191$	−14.2774	−	19.6512i	−0.0747508	−	0.102886i	0.770004	−	0.638039i	$-0.220254\pi$
$191$	−14.2774	−	19.6512i	−0.0747508	−	0.102886i	−0.844755	+	0.535153i	$0.820254\pi$
$192$	106.348	+	108.435i	0.553895	+	0.564765i
$193$	62.3636	−	191.935i	0.323127	−	0.994484i	−0.649151	−	0.760659i	$-0.724876\pi$
$193$	62.3636	−	191.935i	0.323127	−	0.994484i	0.972279	−	0.233825i	$-0.0751241\pi$
$194$	198.096	+	272.656i	1.02111	+	1.40544i
$195$	−0.748490	−	1.50497i	−0.00383841	−	0.00771778i
$196$	116.615	+	358.905i	0.594976	+	1.83115i
$197$		−	64.9088i		−	0.329486i	−0.986337	−	0.164743i	$-0.947320\pi$
$197$		−	64.9088i		−	0.329486i	0.986337	−	0.164743i	$-0.0526795\pi$
$198$		0			0
$199$	136.263			0.684741			0.342370	−	0.939565i	$-0.388770\pi$
$199$	136.263			0.684741			0.342370	+	0.939565i	$0.388770\pi$
$200$	−529.998	+	172.207i	−2.64999	+	0.861034i
$201$	−273.150	+	135.850i	−1.35895	+	0.675871i
$202$	157.746	−	114.609i	0.780922	−	0.567373i
$203$	−52.1353	−	16.9398i	−0.256824	−	0.0834473i
$204$	−64.7287	+	63.4829i	−0.317298	+	0.311191i
$205$	454.214	−	330.006i	2.21568	−	1.60978i
$206$	268.496	−	369.553i	1.30338	−	1.79395i
$207$	49.1075	+	37.1578i	0.237234	+	0.179506i
$208$	1.35768			0.00652733
$209$		0			0
$210$	−69.6458	+	133.466i	−0.331647	+	0.635550i
$211$	−0.383783	−	1.18116i	−0.00181888	−	0.00559793i	0.950143	−	0.311815i	$-0.100937\pi$
$211$	−0.383783	−	1.18116i	−0.00181888	−	0.00559793i	−0.951962	+	0.306217i	$0.900937\pi$
$212$	−105.431	+	145.114i	−0.497318	+	0.684499i
$213$	−137.719	+	20.4429i	−0.646567	+	0.0959759i
$214$	−62.8977	+	193.579i	−0.293915	+	0.904576i
$215$	104.126	+	33.8326i	0.484307	+	0.157361i
$216$	276.077	+	292.660i	1.27813	+	1.35491i
$217$	−62.0068	−	45.0506i	−0.285746	−	0.207606i
$218$	−163.186	+	53.0222i	−0.748558	+	0.243221i
$219$	−160.300	+	307.190i	−0.731962	+	1.40269i
$220$		0			0
$221$		−	0.259620i		−	0.00117475i
$222$	6.45185	−	38.3217i	0.0290624	−	0.172620i
$223$	−100.528	−	73.0378i	−0.450798	−	0.327524i	0.339113	−	0.940746i	$-0.389873\pi$
$223$	−100.528	−	73.0378i	−0.450798	−	0.327524i	−0.789911	+	0.613222i	$0.789873\pi$
$224$	−7.90294	−	10.8775i	−0.0352810	−	0.0485601i
$225$	322.071	−	97.7703i	1.43143	−	0.434535i
$226$	−56.4785	+	173.823i	−0.249905	+	0.769128i
$227$	28.0418	+	38.5962i	0.123532	+	0.170027i	0.866304	−	0.499517i	$-0.166489\pi$
$227$	28.0418	+	38.5962i	0.123532	+	0.170027i	−0.742772	+	0.669545i	$0.766489\pi$
$228$	−583.875	+	290.388i	−2.56086	+	1.27363i
$229$	−22.6223	−	69.6244i	−0.0987874	−	0.304037i	0.889435	−	0.457062i	$-0.151098\pi$
$229$	−22.6223	−	69.6244i	−0.0987874	−	0.304037i	−0.988222	+	0.153026i	$0.951098\pi$
$230$			189.222i			0.822706i
$231$		0			0
$232$	−450.160			−1.94034
$233$	−176.322	+	57.2904i	−0.756745	+	0.245881i	−0.661881	−	0.749609i	$-0.730242\pi$
$233$	−176.322	+	57.2904i	−0.756745	+	0.245881i	−0.0948641	+	0.995490i	$0.530242\pi$
$234$	−2.23437	−	0.0434253i	−0.00954860	−	0.000185578i
$235$	174.836	−	127.026i	0.743981	−	0.540534i
$236$	626.618	+	203.601i	2.65516	+	0.862715i
$237$	132.105	+	134.697i	0.557404	+	0.568342i
$238$	−18.8122	+	13.6678i	−0.0790427	+	0.0574279i
$239$	206.294	−	283.939i	0.863154	−	1.18803i	−0.117655	−	0.993055i	$-0.537538\pi$
$239$	206.294	−	283.939i	0.863154	−	1.18803i	0.980808	−	0.194975i	$-0.0624624\pi$
$240$	−75.3115	+	447.324i	−0.313798	+	1.86385i
$241$	−175.508			−0.728248			−0.364124	−	0.931351i	$-0.618631\pi$
$241$	−175.508			−0.728248			−0.364124	+	0.931351i	$0.618631\pi$
$242$		0			0
$243$	−163.280	−	179.969i	−0.671934	−	0.740611i
$244$	−201.983	−	621.641i	−0.827801	−	2.54771i
$245$	212.222	−	292.098i	0.866212	−	1.19224i
$246$	−109.606	−	738.390i	−0.445554	−	3.00159i
$247$	0.577036	−	1.77593i	0.00233618	−	0.00719002i
$248$	−598.589	−	194.493i	−2.41367	−	0.784247i
$249$	250.753	−	37.2216i	1.00704	−	0.149484i
$250$	277.385	+	201.532i	1.10954	+	0.806128i
$251$	−132.205	+	42.9562i	−0.526715	+	0.171140i	−0.560291	−	0.828296i	$-0.689311\pi$
$251$	−132.205	+	42.9562i	−0.526715	+	0.171140i	0.0335755	+	0.999436i	$0.489311\pi$
$252$	77.1202	+	110.604i	0.306032	+	0.438906i
$253$		0			0
$254$		−	204.706i		−	0.805930i
$255$	85.5385	+	14.4013i	0.335445	+	0.0564756i
$256$	422.110	+	306.681i	1.64887	+	1.19797i
$257$	−251.203	−	345.752i	−0.977445	−	1.34534i	−0.938194	−	0.346109i	$-0.887503\pi$
$257$	−251.203	−	345.752i	−0.977445	−	1.34534i	−0.0392507	−	0.999229i	$-0.512497\pi$
$258$	103.928	−	101.928i	0.402822	−	0.395069i
$259$	2.07478	−	6.38551i	0.00801072	−	0.0246545i
$260$	−2.71899	−	3.74237i	−0.0104576	−	0.0143937i
$261$	271.838	+	5.28320i	1.04152	+	0.0202422i
$262$	159.769	+	491.719i	0.609806	+	1.87679i
$263$		−	201.638i		−	0.766686i	−0.923606	−	0.383343i	$-0.874773\pi$
$263$		−	201.638i		−	0.766686i	0.923606	−	0.383343i	$-0.125227\pi$
$264$		0			0
$265$	171.613			0.647595
$266$	−159.063	+	51.6827i	−0.597981	+	0.194296i
$267$	−60.5878	−	121.822i	−0.226921	−	0.456263i
$268$	−679.235	+	493.493i	−2.53446	+	1.84139i
$269$	−326.260	−	106.008i	−1.21286	−	0.394083i	−0.368385	−	0.929673i	$-0.620089\pi$
$269$	−326.260	−	106.008i	−1.21286	−	0.394083i	−0.844478	+	0.535590i	$0.820089\pi$
$270$	138.250	−	733.762i	0.512035	−	2.71764i
$271$	−329.745	+	239.574i	−1.21677	+	0.884035i	−0.995828	−	0.0912517i	$-0.970913\pi$
$271$	−329.745	+	239.574i	−1.21677	+	0.884035i	−0.220942	+	0.975287i	$0.570913\pi$
$272$	−41.1838	+	56.6847i	−0.151411	+	0.208400i
$273$	−0.380753	−	0.0641036i	−0.00139470	−	0.000234812i
$274$	579.239			2.11401
$275$		0			0
$276$	150.252	+	78.4053i	0.544391	+	0.284077i
$277$	153.580	+	472.671i	0.554441	+	1.70639i	0.697416	+	0.716667i	$0.254333\pi$
$277$	153.580	+	472.671i	0.554441	+	1.70639i	−0.142975	+	0.989726i	$0.545667\pi$
$278$	−107.203	+	147.552i	−0.385622	+	0.530763i
$279$	359.187	+	124.474i	1.28741	+	0.446143i
$280$	−66.0028	+	203.136i	−0.235724	+	0.725485i
$281$	368.065	+	119.591i	1.30984	+	0.425593i	0.878994	−	0.476833i	$-0.158215\pi$
$281$	368.065	+	119.591i	1.30984	+	0.425593i	0.430845	+	0.902426i	$0.358215\pi$
$282$	−42.1895	−	284.220i	−0.149608	−	1.00787i
$283$	−179.404	−	130.344i	−0.633935	−	0.460581i	0.223826	−	0.974629i	$-0.428145\pi$
$283$	−179.404	−	130.344i	−0.633935	−	0.460581i	−0.857761	+	0.514048i	$0.828145\pi$
$284$	−364.417	+	118.406i	−1.28316	+	0.416923i
$285$	553.118	+	288.631i	1.94077	+	1.01274i
$286$		0			0
$287$		−	128.971i		−	0.449378i
$288$	53.1784	+	40.2381i	0.184647	+	0.139716i
$289$	−222.967	−	161.995i	−0.771510	−	0.560535i
$290$	491.060	+	675.886i	1.69331	+	2.33064i
$291$	−202.219	−	206.187i	−0.694910	−	0.708547i
$292$	−294.680	+	906.933i	−1.00918	+	3.10593i
$293$	−260.247	−	358.200i	−0.888216	−	1.22252i	−0.974077	−	0.226217i	$-0.927364\pi$
$293$	−260.247	−	358.200i	−0.888216	−	1.22252i	0.0858612	−	0.996307i	$-0.472636\pi$
$294$	−213.772	−	429.826i	−0.727117	−	1.46199i
$295$	−194.795	−	599.517i	−0.660321	−	2.03226i
$296$		−	55.1353i		−	0.186268i
$297$		0			0
$298$	106.933			0.358837
$299$	−0.461559	+	0.149969i	−0.00154367	+	0.000501570i
$300$	829.402	−	412.500i	2.76467	−	1.37500i
$301$	20.3471	−	14.7830i	0.0675982	−	0.0491130i
$302$	−550.299	−	178.803i	−1.82218	−	0.592062i
$303$	−119.291	+	116.995i	−0.393698	+	0.386121i
$304$	−407.706	+	296.216i	−1.34114	+	0.974395i
$305$	−367.579	+	505.929i	−1.20518	+	1.65878i
$306$	69.5903	−	91.9701i	0.227419	−	0.300556i
$307$	−324.906			−1.05832			−0.529162	−	0.848521i	$-0.677494\pi$
$307$	−324.906			−1.05832			−0.529162	+	0.848521i	$0.677494\pi$
$308$		0			0
$309$	−181.088	+	347.028i	−0.586046	+	1.12307i
$310$	360.956	+	1110.91i	1.16437	+	3.58357i
$311$	68.7732	−	94.6582i	0.221136	−	0.304367i	−0.684007	−	0.729476i	$-0.739764\pi$
$311$	68.7732	−	94.6582i	0.221136	−	0.304367i	0.905142	+	0.425109i	$0.139764\pi$
$312$	−3.13632	+	0.465554i	−0.0100523	+	0.00149216i
$313$	−45.1399	+	138.926i	−0.144217	+	0.443854i	−0.996909	−	0.0785593i	$-0.974968\pi$
$313$	−45.1399	+	138.926i	−0.144217	+	0.443854i	0.852693	+	0.522413i	$0.174968\pi$
$314$	−702.953	−	228.403i	−2.23870	−	0.727399i
$315$	42.2411	−	121.893i	0.134099	−	0.386962i
$316$	420.067	+	305.196i	1.32933	+	0.965811i
$317$	−64.2560	+	20.8781i	−0.202700	+	0.0658614i	−0.408608	−	0.912710i	$-0.633986\pi$
$317$	−64.2560	+	20.8781i	−0.202700	+	0.0658614i	0.205907	+	0.978572i	$0.433986\pi$
$318$	105.559	−	202.288i	0.331946	−	0.636125i
$319$		0			0
$320$		−	399.917i		−	1.24974i
$321$	28.9576	−	171.998i	0.0902107	−	0.535820i
$322$	35.1658	+	25.5495i	0.109211	+	0.0793461i
$323$	56.6433	+	77.9628i	0.175366	+	0.241371i
$324$	−525.359	−	413.815i	−1.62148	−	1.27721i
$325$	−0.819687	+	2.52274i	−0.00252211	+	0.00776226i
$326$	179.878	+	247.580i	0.551772	+	0.759448i
$327$	131.650	−	65.4758i	0.402600	−	0.200232i
$328$	−327.278	−	1007.26i	−0.997799	−	3.07091i
$329$		−	49.6436i		−	0.150892i
$330$		0			0
$331$	303.465			0.916814			0.458407	−	0.888742i	$-0.348420\pi$
$331$	303.465			0.916814			0.458407	+	0.888742i	$0.348420\pi$
$332$	663.516	−	215.589i	1.99854	−	0.649366i
$333$	−0.647084	+	33.2945i	−0.00194320	+	0.0999836i
$334$	−117.161	+	85.1224i	−0.350781	+	0.254857i
$335$	763.953	+	248.223i	2.28046	+	0.740966i
$336$	72.9635	+	74.3954i	0.217153	+	0.221415i
$337$	−449.359	+	326.478i	−1.33341	+	0.968779i	−0.333751	+	0.942661i	$0.608314\pi$
$337$	−449.359	+	326.478i	−1.33341	+	0.968779i	−0.999659	+	0.0261175i	$0.991686\pi$
$338$	−347.755	+	478.643i	−1.02886	+	1.41610i
$339$	26.0023	−	154.444i	0.0767029	−	0.455588i
$340$	238.725			0.702132
$341$		0			0
$342$	680.447	−	474.449i	1.98961	−	1.38728i
$343$	−53.1059	−	163.443i	−0.154828	−	0.476510i
$344$	121.396	−	167.087i	0.352894	−	0.485718i
$345$	−23.8084	−	160.391i	−0.0690097	−	0.464902i
$346$	223.761	−	688.666i	0.646708	−	1.99036i
$347$	−368.981	−	119.889i	−1.06335	−	0.345502i	−0.275454	−	0.961314i	$-0.588828\pi$
$347$	−368.981	−	119.889i	−1.06335	−	0.345502i	−0.787893	+	0.615812i	$0.788828\pi$
$348$	740.160	−	109.869i	2.12690	−	0.315715i
$349$	365.704	+	265.700i	1.04786	+	0.761317i	0.971805	−	0.235787i	$-0.0757667\pi$
$349$	365.704	+	265.700i	1.04786	+	0.761317i	0.0760578	+	0.997103i	$0.475767\pi$
$350$	225.951	−	73.4159i	0.645574	−	0.209760i
$351$	1.89939	−	0.244325i	0.00541138	−	0.000696082i
$352$		0			0
$353$			304.454i			0.862476i	0.902238	+	0.431238i	$0.141923\pi$
$353$			304.454i			0.862476i	−0.902238	+	0.431238i	$0.858077\pi$
$354$	−826.497	−	139.149i	−2.33474	−	0.393077i
$355$	296.584	+	215.481i	0.835448	+	0.606989i
$356$	−220.093	−	302.932i	−0.618239	−	0.850932i
$357$	14.2261	−	13.9523i	0.0398490	−	0.0390821i
$358$	149.610	−	460.451i	0.417904	−	1.28618i
$359$	178.166	+	245.224i	0.496284	+	0.683076i	0.981532	−	0.191301i	$-0.0612705\pi$
$359$	178.166	+	245.224i	0.496284	+	0.683076i	−0.485248	+	0.874377i	$0.661270\pi$
$360$	20.5850	−	1059.17i	0.0571806	−	2.94213i
$361$	102.632	+	315.870i	0.284300	+	0.874986i
$362$		−	216.815i		−	0.598936i
$363$		0			0
$364$	−1.06262			−0.00291929
$365$	867.707	−	281.935i	2.37728	−	0.772425i
$366$	370.264	+	744.479i	1.01165	+	2.03410i
$367$	339.757	−	246.848i	0.925770	−	0.672611i	−0.0191838	−	0.999816i	$-0.506107\pi$
$367$	339.757	−	246.848i	0.925770	−	0.672611i	0.944953	+	0.327205i	$0.106107\pi$
$368$	124.565	+	40.4736i	0.338492	+	0.109983i
$369$	185.812	+	612.093i	0.503555	+	1.65879i
$370$	−82.7822	+	60.1448i	−0.223736	+	0.162553i
$371$	23.1717	−	31.8932i	0.0624575	−	0.0859654i
$372$	1031.68	+	173.694i	2.77333	+	0.466919i
$373$	198.795			0.532963			0.266482	−	0.963840i	$-0.414139\pi$
$373$	198.795			0.532963			0.266482	+	0.963840i	$0.414139\pi$
$374$		0			0
$375$	−260.478	−	135.924i	−0.694608	−	0.362464i
$376$	−125.975	−	387.713i	−0.335041	−	1.03115i
$377$	−1.25945	+	1.73349i	−0.00334073	+	0.00459812i
$378$	−117.698	−	124.768i	−0.311371	−	0.330074i
$379$	22.3758	−	68.8656i	0.0590390	−	0.181703i	−0.917188	−	0.398455i	$-0.869546\pi$
$379$	22.3758	−	68.8656i	0.0590390	−	0.181703i	0.976227	+	0.216752i	$0.0695463\pi$
$380$	1633.00	+	530.594i	4.29737	+	1.39630i
$381$	25.7566	+	173.516i	0.0676026	+	0.455422i
$382$	68.7969	+	49.9839i	0.180097	+	0.130848i
$383$	−499.215	+	162.205i	−1.30343	+	0.423511i	−0.876775	−	0.480901i	$-0.840309\pi$
$383$	−499.215	+	162.205i	−1.30343	+	0.423511i	−0.426659	+	0.904413i	$0.640309\pi$
$384$	−550.229	−	287.123i	−1.43289	−	0.747717i
$385$		0			0
$386$			706.528i			1.83038i
$387$	−75.2682	+	99.4739i	−0.194491	+	0.257039i
$388$	−643.016	−	467.179i	−1.65726	−	1.20407i
$389$	219.197	+	301.699i	0.563489	+	0.775576i	0.991765	−	0.128072i	$-0.0408788\pi$
$389$	219.197	+	301.699i	0.563489	+	0.775576i	−0.428276	+	0.903648i	$0.640879\pi$
$390$	4.12028	+	4.20113i	0.0105648	+	0.0107721i
$391$	7.73949	−	23.8197i	0.0197941	−	0.0609199i
$392$	−400.333	−	551.011i	−1.02126	−	1.40564i
$393$	−197.295	−	396.695i	−0.502022	−	1.00940i
$394$	70.2209	+	216.118i	0.178226	+	0.548522i
$395$		−	496.774i		−	1.25766i
$396$		0			0
$397$	−184.584			−0.464947			−0.232474	−	0.972603i	$-0.574682\pi$
$397$	−184.584			−0.464947			−0.232474	+	0.972603i	$0.574682\pi$
$398$	−453.697	+	147.415i	−1.13994	+	0.370390i
$399$	128.324	−	63.8217i	0.321615	−	0.159954i
$400$	579.152	−	420.778i	1.44788	−	1.05195i
$401$	−86.3473	−	28.0559i	−0.215330	−	0.0699649i	0.199366	−	0.979925i	$-0.436112\pi$
$401$	−86.3473	−	28.0559i	−0.215330	−	0.0699649i	−0.414695	+	0.909960i	$0.636112\pi$
$402$	762.501	−	747.825i	1.89677	−	1.86026i
$403$	−2.42369	+	1.76092i	−0.00601412	+	0.00436952i
$404$	−270.288	+	372.020i	−0.669031	+	0.920842i
$405$	−24.8613	+	639.356i	−0.0613860	+	1.57866i
$406$	191.914			0.472694
$407$		0			0
$408$	75.6995	−	145.067i	0.185538	−	0.355555i
$409$	−169.936	−	523.008i	−0.415490	−	1.27875i	−0.911812	−	0.410609i	$-0.865316\pi$
$409$	−169.936	−	523.008i	−0.415490	−	1.27875i	0.496321	−	0.868139i	$-0.334684\pi$
$410$	−1155.32	+	1590.16i	−2.81785	+	3.87844i
$411$	−490.982	+	72.8811i	−1.19460	+	0.177326i
$412$	−332.896	+	1024.55i	−0.808000	+	2.48677i
$413$	−137.718	−	44.7474i	−0.333459	−	0.108347i
$414$	−203.705	−	70.5926i	−0.492041	−	0.170514i
$415$	−540.009	−	392.339i	−1.30123	−	0.945396i
$416$	−0.499821	+	0.162402i	−0.00120149	+	0.000390389i
$417$	72.3034	−	138.558i	0.173389	−	0.332275i
$418$		0			0
$419$			298.402i			0.712176i	0.934452	+	0.356088i	$0.115890\pi$
$419$			298.402i			0.712176i	−0.934452	+	0.356088i	$0.884110\pi$
$420$	58.9443	−	350.108i	0.140344	−	0.833591i
$421$	99.1856	+	72.0626i	0.235595	+	0.171170i	0.699319	−	0.714810i	$-0.253487\pi$
$421$	99.1856	+	72.0626i	0.235595	+	0.171170i	−0.463723	+	0.885980i	$0.653487\pi$
$422$	2.55566	+	3.51756i	0.00605606	+	0.00833545i
$423$	71.5224	+	235.606i	0.169084	+	0.556989i
$424$	100.037	−	307.884i	0.235937	−	0.726141i
$425$	−80.4625	−	110.747i	−0.189323	−	0.260581i
$426$	436.427	−	217.055i	1.02448	−	0.509519i
$427$	44.3920	+	136.624i	0.103962	+	0.319964i
$428$		−	480.021i		−	1.12154i
$429$		0			0
$430$	−383.296			−0.891385
$431$	−562.102	+	182.638i	−1.30418	+	0.423754i	−0.877034	−	0.480428i	$-0.840481\pi$
$431$	−562.102	+	182.638i	−1.30418	+	0.423754i	−0.427147	+	0.904182i	$0.640481\pi$
$432$	−453.465	−	247.957i	−1.04969	−	0.573976i
$433$	−519.659	+	377.554i	−1.20014	+	0.871950i	−0.994298	−	0.106636i	$-0.965992\pi$
$433$	−519.659	+	377.554i	−1.20014	+	0.871950i	−0.205838	+	0.978586i	$0.565992\pi$
$434$	255.193	+	82.9172i	0.588002	+	0.191053i
$435$	−501.280	−	511.117i	−1.15237	−	1.17498i
$436$	327.371	−	237.849i	0.750851	−	0.545526i
$437$	105.884	−	145.737i	0.242297	−	0.333494i
$438$	201.397	−	1196.23i	0.459810	−	2.73111i
$439$	−476.217			−1.08478			−0.542388	−	0.840128i	$-0.682480\pi$
$439$	−476.217			−1.08478			−0.542388	+	0.840128i	$0.682480\pi$
$440$		0			0
$441$	235.282	+	337.437i	0.533520	+	0.765164i
$442$	0.280868	+	0.864421i	0.000635447	+	0.00195570i
$443$	63.3171	−	87.1485i	0.142928	−	0.196723i	−0.731551	−	0.681786i	$-0.761203\pi$
$443$	63.3171	−	87.1485i	0.142928	−	0.196723i	0.874479	+	0.485063i	$0.161203\pi$
$444$	13.4567	+	90.6544i	0.0303078	+	0.204177i
$445$	−110.705	+	340.716i	−0.248776	+	0.765653i
$446$	413.729	+	134.429i	0.927643	+	0.301409i
$447$	−90.6403	+	13.4546i	−0.202775	+	0.0300997i
$448$	−74.3221	−	53.9982i	−0.165898	−	0.120532i
$449$	213.489	−	69.3667i	0.475476	−	0.154491i	−0.0614686	−	0.998109i	$-0.519578\pi$
$449$	213.489	−	69.3667i	0.475476	−	0.154491i	0.536945	+	0.843618i	$0.319578\pi$
$450$	−966.582	+	673.961i	−2.14796	+	1.49769i
$451$		0			0
$452$		−	431.031i		−	0.953608i
$453$	488.949	+	82.3195i	1.07936	+	0.181721i
$454$	−135.122	−	98.1716i	−0.297625	−	0.216237i
$455$	0.597580	+	0.822498i	0.00131336	+	0.00180769i
$456$	840.250	−	824.078i	1.84265	−	1.80719i
$457$	−22.0293	+	67.7991i	−0.0482041	+	0.148357i	−0.972261	−	0.233897i	$-0.924852\pi$
$457$	−22.0293	+	67.7991i	−0.0482041	+	0.148357i	0.924057	+	0.382254i	$0.124852\pi$
$458$	150.645	+	207.345i	0.328919	+	0.452718i
$459$	−47.4152	+	86.7129i	−0.103301	+	0.188917i
$460$	−137.899	−	424.410i	−0.299781	−	0.922631i
$461$			876.537i			1.90138i	0.310141	+	0.950691i	$0.399624\pi$
$461$			876.537i			1.90138i	−0.310141	+	0.950691i	$0.600376\pi$
$462$		0			0
$463$	−824.691			−1.78119			−0.890595	−	0.454797i	$-0.849712\pi$
$463$	−824.691			−1.78119			−0.890595	+	0.454797i	$0.849712\pi$
$464$	549.971	−	178.696i	1.18528	−	0.385121i
$465$	−445.735	−	896.226i	−0.958570	−	1.92737i
$466$	525.094	−	381.503i	1.12681	−	0.818677i
$467$	−305.347	−	99.2132i	−0.653847	−	0.212448i	−0.0367376	−	0.999325i	$-0.511697\pi$
$467$	−305.347	−	99.2132i	−0.653847	−	0.212448i	−0.617110	+	0.786877i	$0.711697\pi$
$468$	5.04317	−	1.53094i	0.0107760	−	0.00327124i
$469$	149.282	−	108.460i	0.318299	−	0.231258i
$470$	−444.704	+	612.083i	−0.946180	+	1.30230i
$471$	624.585	+	105.155i	1.32608	+	0.223259i
$472$	−1189.12			−2.51933
$473$		0			0
$474$	−585.571	−	305.566i	−1.23538	−	0.644654i
$475$	−304.256	−	936.403i	−0.640539	−	1.97138i
$476$	32.2335	−	44.3656i	0.0677174	−	0.0932050i
$477$	−64.0230	+	184.748i	−0.134220	+	0.387311i
$478$	−379.691	+	1168.57i	−0.794332	+	2.44470i
$479$	−412.015	−	133.872i	−0.860157	−	0.279482i	−0.154463	−	0.987999i	$-0.549365\pi$
$479$	−412.015	−	133.872i	−0.860157	−	0.279482i	−0.705694	+	0.708517i	$0.749365\pi$
$480$	−25.7820	−	173.687i	−0.0537126	−	0.361849i
$481$	−0.212317	−	0.154257i	−0.000441408	−	0.000320701i
$482$	584.363	−	189.871i	1.21237	−	0.393924i
$483$	−33.0224	−	17.2319i	−0.0683694	−	0.0356769i
$484$		0			0
$485$			760.436i			1.56791i
$486$	738.347	+	422.574i	1.51923	+	0.869493i
$487$	285.224	+	207.228i	0.585676	+	0.425519i	0.840766	−	0.541399i	$-0.182105\pi$
$487$	285.224	+	207.228i	0.585676	+	0.425519i	−0.255090	+	0.966917i	$0.582105\pi$
$488$	693.396	+	954.378i	1.42089	+	1.95569i
$489$	−183.621	−	187.225i	−0.375504	−	0.382872i
$490$	−390.602	+	1202.15i	−0.797147	+	2.45337i
$491$	−262.378	−	361.133i	−0.534375	−	0.735505i	0.453414	−	0.891300i	$-0.350206\pi$
$491$	−262.378	−	361.133i	−0.534375	−	0.735505i	−0.987789	+	0.155795i	$0.950206\pi$
$492$	783.954	+	1576.27i	1.59340	+	3.20381i
$493$	−34.1708	−	105.167i	−0.0693120	−	0.213321i
$494$			6.53734i			0.0132335i
$495$		0			0
$496$	808.517			1.63007
$497$	80.0917	−	26.0234i	0.161150	−	0.0523609i
$498$	−794.629	+	395.206i	−1.59564	+	0.793586i
$499$	−72.6250	+	52.7651i	−0.145541	+	0.105742i	−0.658173	−	0.752867i	$-0.728671\pi$
$499$	−72.6250	+	52.7651i	−0.145541	+	0.105742i	0.512632	+	0.858608i	$0.328671\pi$
$500$	−769.022	−	249.870i	−1.53804	−	0.499741i
$501$	88.5992	−	86.8940i	0.176845	−	0.173441i
$502$	393.714	−	286.050i	0.784292	−	0.569821i
$503$	573.691	−	789.618i	1.14054	−	1.56982i	0.374242	−	0.927331i	$-0.377903\pi$
$503$	573.691	−	789.618i	1.14054	−	1.56982i	0.766297	−	0.642487i	$-0.222097\pi$
$504$	−194.060	−	146.838i	−0.385040	−	0.291345i
$505$	439.954			0.871195
$506$		0			0
$507$	234.545	−	449.469i	0.462612	−	0.886527i
$508$	149.184	+	459.140i	0.293668	+	0.903818i
$509$	189.070	−	260.232i	0.371454	−	0.511262i	−0.581842	−	0.813302i	$-0.697668\pi$
$509$	189.070	−	260.232i	0.371454	−	0.511262i	0.953295	+	0.302040i	$0.0976676\pi$
$510$	−300.386	+	44.5890i	−0.588991	+	0.0874295i
$511$	64.7649	−	199.326i	0.126742	−	0.390070i
$512$	−950.204	−	308.740i	−1.85587	−	0.603007i
$513$	−517.073	+	487.774i	−1.00794	+	0.950827i
$514$	1210.44	+	879.440i	2.35495	+	1.71097i
$515$	980.236	−	318.498i	1.90337	−	0.618443i
$516$	−158.821	+	304.356i	−0.307792	+	0.589836i
$517$		0			0
$518$			23.5055i			0.0453774i
$519$	−103.018	+	611.890i	−0.198493	+	1.17898i
$520$	6.75423	+	4.90723i	0.0129889	+	0.00943699i
$521$	180.087	+	247.868i	0.345656	+	0.475755i	0.946083	−	0.323925i	$-0.105002\pi$
$521$	180.087	+	247.868i	0.345656	+	0.475755i	−0.600426	+	0.799680i	$0.705002\pi$
$522$	−910.816	+	276.494i	−1.74486	+	0.529682i
$523$	207.538	−	638.736i	0.396822	−	1.22129i	−0.530711	−	0.847553i	$-0.678075\pi$
$523$	207.538	−	638.736i	0.396822	−	1.22129i	0.927533	−	0.373740i	$-0.121925\pi$
$524$	−716.699	−	986.451i	−1.36775	−	1.88254i
$525$	−182.286	+	90.6594i	−0.347212	+	0.172685i
$526$	218.140	+	671.367i	0.414715	+	1.27636i
$527$		−	154.607i		−	0.293372i
$528$		0			0
$529$	482.182			0.911497
$530$	−571.394	+	185.657i	−1.07810	+	0.350297i
$531$	718.074	+	13.9559i	1.35231	+	0.0262823i
$532$	319.101	−	231.840i	0.599814	−	0.435790i
$533$	−4.79444	−	1.55781i	−0.00899520	−	0.00292272i
$534$	333.523	+	340.068i	0.624574	+	0.636831i
$535$	−371.549	+	269.946i	−0.694484	+	0.504572i
$536$	890.657	−	1225.88i	1.66167	−	2.28710i
$537$	−68.8791	+	409.118i	−0.128267	+	0.761858i
$538$	1200.99			2.23232
$539$		0			0
$540$	224.661	+	1746.52i	0.416038	+	3.23430i
$541$	−56.8905	−	175.091i	−0.105158	−	0.323643i	0.884610	−	0.466332i	$-0.154425\pi$
$541$	−56.8905	−	175.091i	−0.105158	−	0.323643i	−0.989767	+	0.142690i	$0.954425\pi$
$542$	838.725	−	1154.41i	1.54746	−	2.12990i
$543$	27.2801	+	183.779i	0.0502396	+	0.338452i
$544$	8.38108	−	25.7943i	0.0154064	−	0.0474160i
$545$	−368.203	−	119.636i	−0.675602	−	0.219516i
$546$	1.33709	−	0.198477i	0.00244888	−	0.000363510i
$547$	−491.170	−	356.856i	−0.897934	−	0.652387i	0.0400006	−	0.999200i	$-0.487264\pi$
$547$	−491.170	−	356.856i	−0.897934	−	0.652387i	−0.937934	+	0.346812i	$0.887264\pi$
$548$	−1299.19	+	422.131i	−2.37078	+	0.770312i
$549$	−407.520	−	584.458i	−0.742295	−	1.06459i
$550$		0			0
$551$		−	795.344i		−	1.44346i
$552$	−301.630	−	50.7825i	−0.546432	−	0.0919973i
$553$	−92.3224	−	67.0762i	−0.166948	−	0.121295i
$554$	−1022.71	−	1407.64i	−1.84604	−	2.54086i
$555$	62.6014	−	61.3965i	0.112795	−	0.110624i
$556$	132.916	−	409.073i	0.239057	−	0.735743i
$557$	238.714	+	328.561i	0.428570	+	0.589876i	0.967624	−	0.252395i	$-0.0812182\pi$
$557$	238.714	+	328.561i	0.428570	+	0.589876i	−0.539054	+	0.842271i	$0.681218\pi$
$558$	−1330.60	−	25.8603i	−2.38458	−	0.0463446i
$559$	−0.303784	−	0.934950i	−0.000543441	−	0.00167254i
$560$		−	274.376i		−	0.489958i
$561$		0			0
$562$	−1354.87			−2.41081
$563$	306.504	−	99.5891i	0.544412	−	0.176890i	−0.0238835	−	0.999715i	$-0.507603\pi$
$563$	306.504	−	99.5891i	0.544412	−	0.176890i	0.568295	+	0.822825i	$0.307603\pi$
$564$	301.759	+	606.737i	0.535033	+	1.07578i
$565$	−333.629	+	242.396i	−0.590494	+	0.429019i
$566$	738.347	+	239.903i	1.30450	+	0.423857i
$567$	115.464	+	90.9485i	0.203640	+	0.160403i
$568$	559.473	−	406.481i	0.984988	−	0.715636i
$569$	−256.283	+	352.744i	−0.450410	+	0.619936i	−0.972486	−	0.232963i	$-0.925158\pi$
$569$	−256.283	+	352.744i	−0.450410	+	0.619936i	0.522075	+	0.852899i	$0.325158\pi$
$570$	−2153.89	−	362.630i	−3.77876	−	0.636193i
$571$	155.637			0.272569			0.136284	−	0.990670i	$-0.456484\pi$
$571$	155.637			0.272569			0.136284	+	0.990670i	$0.456484\pi$
$572$		0			0
$573$	−64.6036	−	33.7118i	−0.112746	−	0.0588339i
$574$	139.526	+	429.418i	0.243077	+	0.748115i
$575$	−150.409	+	207.021i	−0.261582	+	0.360036i
$576$	430.526	+	149.196i	0.747441	+	0.259021i
$577$	259.039	−	797.241i	0.448942	−	1.38170i	−0.429161	−	0.903228i	$-0.641191\pi$
$577$	259.039	−	797.241i	0.448942	−	1.38170i	0.878103	−	0.478472i	$-0.158809\pi$
$578$	917.633	+	298.157i	1.58760	+	0.515842i
$579$	−88.8968	−	598.876i	−0.153535	−	1.03433i
$580$	−1593.97	−	1158.09i	−2.74823	−	1.99670i
$581$	−145.828	+	47.3823i	−0.250994	+	0.0815531i
$582$	896.361	+	467.744i	1.54014	+	0.803684i
$583$		0			0
$584$		−	1721.07i		−	2.94704i
$585$	−4.02108	−	3.04260i	−0.00687364	−	0.00520102i
$586$	1254.02	+	911.101i	2.13997	+	1.55478i
$587$	358.686	+	493.689i	0.611050	+	0.841038i	0.996663	−	0.0816225i	$-0.0260102\pi$
$587$	358.686	+	493.689i	0.611050	+	0.841038i	−0.385613	+	0.922660i	$0.626010\pi$
$588$	792.718	+	808.274i	1.34816	+	1.37462i
$589$	343.632	−	1057.59i	0.583416	−	1.79557i
$590$	1297.16	+	1785.39i	2.19858	+	3.02609i
$591$	−86.7139	−	174.353i	−0.146724	−	0.295014i
$592$	21.8866	+	67.3601i	0.0369707	+	0.113784i
$593$			626.517i			1.05652i	0.849083	+	0.528260i	$0.177155\pi$
$593$			626.517i			1.05652i	−0.849083	+	0.528260i	$0.822845\pi$
$594$		0			0
$595$	−52.4671			−0.0881799
$596$	−239.843	+	77.9297i	−0.402421	+	0.130755i
$597$	366.021	−	182.039i	0.613100	−	0.304923i
$598$	1.37454	−	0.998665i	0.00229857	−	0.00167001i
$599$	1090.50	+	354.326i	1.82054	+	0.591529i	0.999795	+	0.0202344i	$0.00644123\pi$
$599$	1090.50	+	354.326i	1.82054	+	0.591529i	0.820745	+	0.571295i	$0.193559\pi$
$600$	−1193.58	+	1170.61i	−1.98931	+	1.95102i
$601$	−494.787	+	359.484i	−0.823273	+	0.598143i	−0.917648	−	0.397394i	$-0.869915\pi$
$601$	−494.787	+	359.484i	−0.823273	+	0.598143i	0.0943748	+	0.995537i	$0.469915\pi$
$602$	−51.7539	+	71.2331i	−0.0859699	+	0.118327i
$603$	−552.228	+	729.821i	−0.915801	+	1.21032i
$604$	1364.58			2.25924
$605$		0			0
$606$	270.616	−	518.594i	0.446560	−	0.855766i
$607$	−34.4711	−	106.091i	−0.0567893	−	0.174780i	0.918638	−	0.395099i	$-0.129290\pi$
$607$	−34.4711	−	106.091i	−0.0567893	−	0.174780i	−0.975428	+	0.220320i	$0.929290\pi$
$608$	114.662	−	157.818i	0.188588	−	0.259569i
$609$	−162.673	+	24.1470i	−0.267114	+	0.0396503i
$610$	676.541	−	2082.18i	1.10908	−	3.41341i
$611$	−1.84547	−	0.599630i	−0.00302041	−	0.000981391i
$612$	−89.0604	+	256.997i	−0.145524	+	0.419929i
$613$	585.747	+	425.570i	0.955542	+	0.694242i	0.952111	−	0.305752i	$-0.0989080\pi$
$613$	585.747	+	425.570i	0.955542	+	0.694242i	0.00343063	+	0.999994i	$0.498908\pi$
$614$	1081.79	−	351.496i	1.76188	−	0.572469i
$615$	779.210	−	1493.24i	1.26701	−	2.42803i
$616$		0			0
$617$			305.723i			0.495499i	0.968824	+	0.247749i	$0.0796910\pi$
$617$			305.723i			0.495499i	−0.968824	+	0.247749i	$0.920309\pi$
$618$	227.515	−	1351.36i	0.368147	−	2.18666i
$619$	−801.760	−	582.513i	−1.29525	−	0.941054i	−0.295353	−	0.955388i	$-0.595437\pi$
$619$	−801.760	−	582.513i	−1.29525	−	0.941054i	−0.999897	+	0.0143342i	$0.995437\pi$
$620$	−1619.19	−	2228.62i	−2.61160	−	3.59455i
$621$	181.549	+	34.2060i	0.292350	+	0.0550822i
$622$	−126.579	+	389.572i	−0.203504	+	0.626321i
$623$	48.3721	+	66.5785i	0.0776438	+	0.106868i
$624$	3.64691	−	1.81378i	0.00584441	−	0.00290670i
$625$	−49.8536	−	153.434i	−0.0797658	−	0.245494i
$626$		−	511.397i		−	0.816928i
$627$		0			0
$628$	1743.12			2.77567
$629$	12.8808	−	4.18523i	0.0204782	−	0.00665378i
$630$	−8.77589	+	451.548i	−0.0139300	+	0.716742i
$631$	437.234	−	317.669i	0.692922	−	0.503437i	−0.184698	−	0.982795i	$-0.559131\pi$
$631$	437.234	−	317.669i	0.692922	−	0.503437i	0.877619	+	0.479358i	$0.159131\pi$
$632$	−891.244	−	289.583i	−1.41020	−	0.458200i
$633$	−2.60885	−	2.66004i	−0.00412140	−	0.00420228i
$634$	191.358	−	139.029i	0.301826	−	0.219289i
$635$	271.491	−	373.675i	0.427545	−	0.588465i
$636$	−89.3392	+	530.643i	−0.140470	+	0.834345i
$637$	−3.24190			−0.00508933
$638$		0			0
$639$	−342.619	+	238.895i	−0.536181	+	0.373858i
$640$	504.993	+	1554.21i	0.789052	+	2.42845i
$641$	−167.415	+	230.427i	−0.261178	+	0.359481i	−0.919387	−	0.393355i	$-0.871314\pi$
$641$	−167.415	+	230.427i	−0.261178	+	0.359481i	0.658209	+	0.752835i	$0.271314\pi$
$642$	89.6582	+	604.006i	0.139655	+	0.940819i
$643$	50.1585	−	154.372i	0.0780071	−	0.240081i	−0.904447	−	0.426586i	$-0.859716\pi$
$643$	50.1585	−	154.372i	0.0780071	−	0.240081i	0.982454	+	0.186505i	$0.0597161\pi$
$644$	−97.4937	−	31.6776i	−0.151388	−	0.0491889i
$645$	324.894	−	48.2271i	0.503712	−	0.0747707i
$646$	−272.940	−	198.303i	−0.422509	−	0.306970i
$647$	−264.676	+	85.9983i	−0.409081	+	0.132919i	−0.506326	−	0.862342i	$-0.668997\pi$
$647$	−264.676	+	85.9983i	−0.409081	+	0.132919i	0.0972452	+	0.995260i	$0.468997\pi$
$648$	1132.55	+	417.300i	1.74777	+	0.643982i
$649$		0			0
$650$		−	9.28637i		−	0.0142867i
$651$	−226.743	−	38.1745i	−0.348299	−	0.0586397i
$652$	−583.879	−	424.213i	−0.895521	−	0.650634i
$653$	351.286	+	483.504i	0.537957	+	0.740435i	0.988317	−	0.152412i	$-0.0487042\pi$
$653$	351.286	+	483.504i	0.537957	+	0.740435i	−0.450360	+	0.892847i	$0.648704\pi$
$654$	−367.503	+	360.430i	−0.561931	+	0.551116i
$655$	−360.494	+	1109.49i	−0.550373	+	1.69387i
$656$	799.686	+	1100.67i	1.21903	+	1.67786i
$657$	−20.1990	+	1039.30i	−0.0307442	+	1.58189i
$658$	53.7064	+	165.291i	0.0816206	+	0.251202i
$659$			187.267i			0.284169i	0.989855	+	0.142085i	$0.0453805\pi$
$659$			187.267i			0.284169i	−0.989855	+	0.142085i	$0.954620\pi$
$660$		0			0
$661$	218.982			0.331289			0.165645	−	0.986186i	$-0.447030\pi$
$661$	218.982			0.331289			0.165645	+	0.986186i	$0.447030\pi$
$662$	−1010.41	+	328.301i	−1.52629	+	0.495923i
$663$	−0.346836	−	0.697373i	−0.000523131	−	0.00105184i
$664$	−1018.67	+	740.105i	−1.53414	+	1.11462i
$665$	−358.901	−	116.614i	−0.539701	−	0.175360i
$666$	−33.8648	−	111.556i	−0.0508481	−	0.167502i
$667$	−167.229	+	121.499i	−0.250719	+	0.182158i
$668$	200.748	−	276.306i	0.300521	−	0.413632i
$669$	−367.604	−	61.8899i	−0.549483	−	0.0925111i
$670$	−2812.17			−4.19726
$671$		0			0
$672$	−35.7599	−	18.6604i	−0.0532141	−	0.0277685i
$673$	189.780	+	584.082i	0.281991	+	0.867878i	0.987285	+	0.158963i	$0.0508151\pi$
$673$	189.780	+	584.082i	0.281991	+	0.867878i	−0.705294	+	0.708915i	$0.749185\pi$
$674$	1142.97	−	1573.16i	1.69580	−	2.33407i
$675$	734.508	−	692.889i	1.08816	−	1.02650i
$676$	431.165	−	1326.99i	0.637819	−	1.96300i
$677$	775.510	+	251.979i	1.14551	+	0.372199i	0.819450	−	0.573150i	$-0.194279\pi$
$677$	775.510	+	251.979i	1.14551	+	0.372199i	0.326060	+	0.945349i	$0.394279\pi$
$678$	80.5079	+	542.362i	0.118743	+	0.799944i
$679$	141.322	+	102.677i	0.208133	+	0.151217i
$680$	−409.764	+	133.140i	−0.602594	+	0.195795i
$681$	126.886	+	66.2122i	0.186323	+	0.0972279i
$682$		0			0
$683$			95.9038i			0.140416i	0.997532	+	0.0702078i	$0.0223662\pi$
$683$			95.9038i			0.140416i	−0.997532	+	0.0702078i	$0.977634\pi$
$684$	−1180.42	+	1560.04i	−1.72576	+	2.28076i
$685$	1057.35	+	768.213i	1.54358	+	1.12148i
$686$	353.638	+	486.741i	0.515508	+	0.709535i
$687$	−153.780	−	156.798i	−0.223843	−	0.228236i
$688$	−81.9849	+	252.323i	−0.119164	+	0.366749i
$689$	−0.905725	−	1.24662i	−0.00131455	−	0.00180932i
$690$	252.789	+	508.275i	0.366361	+	0.736630i
$691$	91.5341	+	281.713i	0.132466	+	0.407689i	0.995187	−	0.0979912i	$-0.0312417\pi$
$691$	91.5341	+	281.713i	0.132466	+	0.407689i	−0.862721	+	0.505680i	$0.831242\pi$
$692$			1707.69i			2.46776i
$693$		0			0
$694$	1358.25			1.95713
$695$	−391.381	+	127.167i	−0.563138	+	0.182974i
$696$	−1209.19	+	601.384i	−1.73734	+	0.864058i
$697$	210.474	−	152.918i	0.301971	−	0.219395i
$698$	−1505.08	−	489.029i	−2.15627	−	0.700615i
$699$	−397.086	+	389.444i	−0.568077	+	0.557144i
$700$	−453.287	+	329.332i	−0.647552	+	0.470474i
$701$	437.413	−	602.048i	0.623985	−	0.858841i	−0.373651	−	0.927569i	$-0.621894\pi$
$701$	437.413	−	602.048i	0.623985	−	0.858841i	0.997635	+	0.0687283i	$0.0218942\pi$
$702$	−6.05982	+	2.86833i	−0.00863223	+	0.00408594i
$703$	97.4133			0.138568
$704$		0			0
$705$	299.933	−	574.776i	0.425436	−	0.815285i
$706$	−329.371	−	1013.70i	−0.466530	−	1.43583i
$707$	59.4041	−	81.7627i	0.0840227	−	0.115647i
$708$	1955.17	−	290.225i	2.76154	−	0.409922i
$709$	−243.404	+	749.120i	−0.343306	+	1.05659i	0.619179	+	0.785250i	$0.287466\pi$
$709$	−243.404	+	749.120i	−0.343306	+	1.05659i	−0.962484	+	0.271337i	$0.912534\pi$
$710$	−1220.61	−	396.600i	−1.71917	−	0.558592i
$711$	534.796	+	185.330i	0.752175	+	0.260661i
$712$	546.732	+	397.224i	0.767882	+	0.557899i
$713$	−274.864	+	89.3086i	−0.385503	+	0.125257i
$714$	−32.2725	+	61.8454i	−0.0451996	+	0.0866182i
$715$		0			0
$716$			1141.78i			1.59467i
$717$	174.807	−	1038.29i	0.243803	−	1.44810i
$718$	−858.508	−	623.742i	−1.19569	−	0.868722i
$719$	−287.294	−	395.426i	−0.399574	−	0.549967i	0.561063	−	0.827773i	$-0.310393\pi$
$719$	−287.294	−	395.426i	−0.399574	−	0.549967i	−0.960637	+	0.277806i	$0.910393\pi$
$720$	395.299	+	1302.18i	0.549027	+	1.80858i
$721$	73.1640	−	225.176i	0.101476	−	0.312310i
$722$	−683.441	−	940.676i	−0.946594	−	1.30288i
$723$	−471.436	+	234.467i	−0.652055	+	0.324297i
$724$	158.008	+	486.298i	0.218243	+	0.671683i
$725$			1129.80i			1.55834i
$726$		0			0
$727$	270.772			0.372452			0.186226	−	0.982507i	$-0.440374\pi$
$727$	270.772			0.372452			0.186226	+	0.982507i	$0.440374\pi$
$728$	1.82396	−	0.592640i	0.00250544	−	0.000814066i
$729$	−679.017	−	265.287i	−0.931436	−	0.363905i
$730$	−2584.07	+	1877.44i	−3.53983	+	2.57184i
$731$	48.2500	+	15.6774i	0.0660055	+	0.0214465i
$732$	−1373.03	−	1399.97i	−1.87572	−	1.91253i
$733$	328.669	−	238.792i	0.448388	−	0.325773i	−0.340571	−	0.940219i	$-0.610620\pi$
$733$	328.669	−	238.792i	0.448388	−	0.325773i	0.788959	+	0.614446i	$0.210620\pi$
$734$	−864.192	+	1189.46i	−1.17737	+	1.62052i
$735$	179.830	−	1068.13i	0.244667	−	1.45324i
$736$	−50.6990			−0.0688845
$737$		0			0
$738$	−1280.86	−	1836.98i	−1.73558	−	2.48914i
$739$	287.094	+	883.586i	0.388490	+	1.19565i	0.933916	+	0.357492i	$0.116368\pi$
$739$	287.094	+	883.586i	0.388490	+	1.19565i	−0.545426	+	0.838159i	$0.683632\pi$
$740$	141.842	−	195.229i	0.191678	−	0.263823i
$741$	−0.822542	−	5.54127i	−0.00111004	−	0.00747809i
$742$	−42.6484	+	131.258i	−0.0574776	+	0.176898i
$743$	−690.050	−	224.211i	−0.928734	−	0.301764i	−0.194689	−	0.980865i	$-0.562370\pi$
$743$	−690.050	−	224.211i	−0.928734	−	0.301764i	−0.734045	+	0.679101i	$0.762370\pi$
$744$	−1867.72	+	277.243i	−2.51037	+	0.372638i
$745$	195.198	+	141.820i	0.262011	+	0.190362i
$746$	−661.901	+	215.065i	−0.887267	+	0.288290i
$747$	623.828	−	434.972i	0.835111	−	0.582291i
$748$		0			0
$749$			105.499i			0.140853i
$750$	1014.32	+	170.772i	1.35243	+	0.227696i
$751$	−890.002	−	646.624i	−1.18509	−	0.861018i	−0.192352	−	0.981326i	$-0.561612\pi$
$751$	−890.002	−	646.624i	−1.18509	−	0.861018i	−0.992737	+	0.120308i	$0.961612\pi$
$752$	307.814	+	423.670i	0.409328	+	0.563391i
$753$	−297.734	+	292.004i	−0.395397	+	0.387787i
$754$	2.31807	−	7.13429i	0.00307437	−	0.00946192i
$755$	−767.390	−	1056.22i	−1.01641	−	1.39897i
$756$	354.915	+	194.070i	0.469464	+	0.256706i
$757$	−389.757	−	1199.55i	−0.514871	−	1.58461i	−0.783517	−	0.621370i	$-0.786576\pi$
$757$	−389.757	−	1199.55i	−0.514871	−	1.58461i	0.268646	−	0.963239i	$-0.413424\pi$
$758$			253.499i			0.334431i
$759$		0			0
$760$	−3098.91			−4.07752
$761$	110.930	−	36.0434i	0.145769	−	0.0473632i	−0.235224	−	0.971941i	$-0.575582\pi$
$761$	110.930	−	36.0434i	0.145769	−	0.0473632i	0.380993	+	0.924578i	$0.375582\pi$
$762$	−273.474	−	549.867i	−0.358890	−	0.721610i
$763$	−71.9498	+	52.2746i	−0.0942985	+	0.0685119i
$764$	−190.733	−	61.9728i	−0.249650	−	0.0811162i
$765$	249.007	−	75.5903i	0.325499	−	0.0988109i
$766$	1486.69	−	1080.14i	1.94084	−	1.41011i
$767$	−3.32692	+	4.57911i	−0.00433758	+	0.00597016i
$768$	1543.55	+	259.872i	2.00983	+	0.338375i
$769$	−1252.94			−1.62930			−0.814652	−	0.579949i	$-0.803072\pi$
$769$	−1252.94			−1.62930			−0.814652	+	0.579949i	$0.803072\pi$
$770$		0			0
$771$	−1136.67	−	593.142i	−1.47428	−	0.769315i
$772$	−514.895	−	1584.68i	−0.666963	−	2.05270i
$773$	−686.689	+	945.147i	−0.888343	+	1.22270i	0.0856964	+	0.996321i	$0.472689\pi$
$773$	−686.689	+	945.147i	−0.888343	+	1.22270i	−0.974039	+	0.226378i	$0.927311\pi$
$774$	142.995	−	412.632i	0.184748	−	0.533117i
$775$	−488.133	+	1502.32i	−0.629849	+	1.93848i
$776$	1364.27	+	443.278i	1.75808	+	0.571234i
$777$	−2.95751	−	19.9241i	−0.00380632	−	0.0256423i
$778$	−1056.22	−	767.389i	−1.35761	−	0.986361i
$779$	1779.63	−	578.236i	2.28450	−	0.742280i
$780$	−12.3031	−	6.42008i	−0.0157732	−	0.00823087i
$781$		0			0
$782$			87.6820i			0.112125i
$783$	737.249	−	348.966i	0.941569	−	0.445679i
$784$	707.827	+	514.266i	0.902841	+	0.655952i
$785$	−980.267	−	1349.22i	−1.24875	−	1.71875i
$786$	1086.06	+	1107.38i	1.38176	+	1.40888i
$787$	−342.029	+	1052.66i	−0.434598	+	1.33756i	0.458899	+	0.888488i	$0.348244\pi$
$787$	−342.029	+	1052.66i	−0.434598	+	1.33756i	−0.893498	+	0.449068i	$0.851756\pi$
$788$	−315.000	−	433.560i	−0.399746	−	0.550203i
$789$	−269.376	−	541.626i	−0.341414	−	0.686472i
$790$	537.430	+	1654.04i	0.680291	+	2.09372i
$791$			94.7321i			0.119762i
$792$		0			0
$793$	5.61513			0.00708088
$794$	614.584	−	199.690i	0.774035	−	0.251499i
$795$	460.973	−	229.263i	0.579840	−	0.288382i
$796$	910.174	−	661.280i	1.14344	−	0.830754i
$797$	61.7682	+	20.0697i	0.0775009	+	0.0251816i	0.347511	−	0.937676i	$-0.387027\pi$
$797$	61.7682	+	20.0697i	0.0775009	+	0.0251816i	−0.270010	+	0.962858i	$0.587027\pi$
$798$	−358.219	+	351.324i	−0.448896	+	0.440256i
$799$	81.0155	−	58.8612i	0.101396	−	0.0736686i
$800$	−162.878	+	224.183i	−0.203598	+	0.280228i
$801$	−325.493	−	246.288i	−0.406358	−	0.307476i
$802$	317.851			0.396322
$803$		0			0
$804$	−1165.24	+	2233.00i	−1.44930	+	2.77736i
$805$	30.3076	+	93.2771i	0.0376491	+	0.115872i
$806$	6.16480	−	8.48512i	0.00764863	−	0.0105274i
$807$	−1018.00	+	151.111i	−1.26146	+	0.187250i
$808$	256.461	−	789.304i	0.317402	−	0.976862i
$809$	610.865	+	198.482i	0.755087	+	0.245343i	0.661169	−	0.750237i	$-0.270061\pi$
$809$	610.865	+	198.482i	0.755087	+	0.245343i	0.0939183	+	0.995580i	$0.470061\pi$
$810$	−608.904	−	2155.67i	−0.751733	−	2.66132i
$811$	73.8187	+	53.6324i	0.0910218	+	0.0661312i	0.632365	−	0.774670i	$-0.282084\pi$
$811$	73.8187	+	53.6324i	0.0910218	+	0.0661312i	−0.541344	+	0.840802i	$0.682084\pi$
$812$	−430.447	+	139.861i	−0.530108	+	0.172242i
$813$	−565.681	+	1084.04i	−0.695795	+	1.33339i
$814$		0			0
$815$			690.500i			0.847239i
$816$	−34.8979	+	207.281i	−0.0427670	+	0.254021i
$817$	295.210	+	214.482i	0.361334	+	0.262524i
$818$	1131.62	+	1557.54i	1.38340	+	1.90409i
$819$	−1.10839	+	0.336471i	−0.00135334	+	0.000410831i
$820$	1432.43	−	4408.56i	1.74687	−	5.37630i
$821$	532.043	+	732.295i	0.648043	+	0.891955i	0.999012	−	0.0444321i	$-0.0141478\pi$
$821$	532.043	+	732.295i	0.648043	+	0.891955i	−0.350969	+	0.936387i	$0.614148\pi$
$822$	1555.91	−	773.826i	1.89283	−	0.941394i
$823$	193.305	+	594.932i	0.234879	+	0.722883i	0.997137	+	0.0756101i	$0.0240904\pi$
$823$	193.305	+	594.932i	0.234879	+	0.722883i	−0.762259	+	0.647273i	$0.775910\pi$
$824$		−	1944.27i		−	2.35955i
$825$		0			0
$826$	506.951			0.613742
$827$	−864.024	+	280.738i	−1.04477	+	0.339466i	−0.780613	−	0.625014i	$-0.785093\pi$
$827$	−864.024	+	280.738i	−1.04477	+	0.339466i	−0.264156	+	0.964480i	$0.585093\pi$
$828$	508.340	+	9.87965i	0.613937	+	0.0119319i
$829$	474.666	−	344.865i	0.572577	−	0.416001i	−0.263464	−	0.964669i	$-0.584865\pi$
$829$	474.666	−	344.865i	0.572577	−	0.416001i	0.836040	+	0.548668i	$0.184865\pi$
$830$	2222.44	+	722.115i	2.67764	+	0.870018i
$831$	1043.99	+	1064.48i	1.25631	+	1.28096i
$832$	−2.90507	+	2.11065i	−0.00349167	+	0.00253684i
$833$	98.3395	−	135.353i	0.118055	−	0.162488i
$834$	−90.8403	+	539.559i	−0.108921	+	0.646954i
$835$	−326.761			−0.391331
$836$		0			0
$837$	1131.11	−	145.498i	1.35139	−	0.173833i
$838$	−322.823	−	993.547i	−0.385230	−	1.18562i
$839$	−601.835	+	828.355i	−0.717325	+	0.987313i	0.282284	+	0.959331i	$0.408908\pi$
$839$	−601.835	+	828.355i	−0.717325	+	0.987313i	−0.999608	+	0.0279817i	$0.991092\pi$
$840$	94.0844	+	633.824i	0.112005	+	0.754552i
$841$	−22.1373	+	68.1317i	−0.0263226	+	0.0810127i
$842$	−408.204	−	132.634i	−0.484803	−	0.157522i
$843$	1148.44	−	170.473i	1.36232	−	0.202222i
$844$	−8.29562	−	6.02712i	−0.00982893	−	0.00714114i
$845$	−1269.60	+	412.517i	−1.50248	+	0.488186i
$846$	−493.027	−	707.090i	−0.582774	−	0.835803i
$847$		0			0
$848$			415.860i			0.490401i
$849$	−656.032	−	110.450i	−0.772712	−	0.130094i
$850$	387.715	+	281.692i	0.456136	+	0.331402i
$851$	−14.8812	−	20.4822i	−0.0174867	−	0.0240684i
$852$	−820.687	+	804.892i	−0.963247	+	0.944708i
$853$	121.995	−	375.463i	0.143019	−	0.440168i	−0.853732	−	0.520713i	$-0.825666\pi$
$853$	121.995	−	375.463i	0.143019	−	0.440168i	0.996751	+	0.0805454i	$0.0256662\pi$
$854$	−295.612	−	406.874i	−0.346149	−	0.476434i
$855$	1871.34	+	36.3697i	2.18870	+	0.0425377i
$856$	267.714	+	823.940i	0.312750	+	0.962547i
$857$		−	1.34510i		−	0.00156955i	−1.00000		0.000784774i	$-0.999750\pi$
$857$		−	1.34510i		−	0.00156955i	1.00000		0.000784774i	$-0.000249801\pi$
$858$		0			0
$859$	847.638			0.986772			0.493386	−	0.869810i	$-0.335759\pi$
$859$	847.638			0.986772			0.493386	+	0.869810i	$0.335759\pi$
$860$	859.701	−	279.334i	0.999652	−	0.324807i
$861$	−172.298	−	346.434i	−0.200113	−	0.402362i
$862$	1673.97	−	1216.21i	1.94196	−	1.41091i
$863$	−442.630	−	143.819i	−0.512897	−	0.166650i	0.0411222	−	0.999154i	$-0.486907\pi$
$863$	−442.630	−	143.819i	−0.512897	−	0.166650i	−0.554019	+	0.832504i	$0.686907\pi$
$864$	196.600	+	37.0417i	0.227546	+	0.0428723i
$865$	1321.80	−	960.343i	1.52809	−	1.11022i
$866$	1321.78	−	1819.28i	1.52631	−	2.10078i
$867$	−815.331	−	137.269i	−0.940404	−	0.158327i
$868$	−632.804			−0.729037
$869$		0			0
$870$	2221.99	+	1159.49i	2.55401	+	1.33275i
$871$	−2.22880	−	6.85955i	−0.00255890	−	0.00787549i
$872$	−429.271	+	590.840i	−0.492283	+	0.677569i
$873$	−818.638	−	283.694i	−0.937730	−	0.324964i
$874$	−194.883	+	599.789i	−0.222979	+	0.686257i
$875$	169.016	+	54.9166i	0.193161	+	0.0627618i
$876$	420.055	+	2829.81i	0.479515	+	3.23038i
$877$	−421.449	−	306.200i	−0.480557	−	0.349145i	0.320984	−	0.947085i	$-0.395986\pi$
$877$	−421.449	−	306.200i	−0.480557	−	0.349145i	−0.801541	+	0.597939i	$0.795986\pi$
$878$	1585.59	−	515.190i	1.80591	−	0.586777i
$879$	−1177.59	−	614.496i	−1.33969	−	0.699085i
$880$		0			0
$881$			606.759i			0.688717i	0.938838	+	0.344358i	$0.111904\pi$
$881$			606.759i			0.688717i	−0.938838	+	0.344358i	$0.888096\pi$
$882$	−1148.44	−	868.980i	−1.30209	−	0.985238i
$883$	90.4194	+	65.6935i	0.102400	+	0.0743981i	0.637807	−	0.770196i	$-0.279842\pi$
$883$	90.4194	+	65.6935i	0.102400	+	0.0743981i	−0.535407	+	0.844594i	$0.679842\pi$
$884$	−1.25993	−	1.73414i	−0.00142526	−	0.00196170i
$885$	−1324.16	−	1350.14i	−1.49623	−	1.52559i
$886$	−116.537	+	358.665i	−0.131532	+	0.404814i
$887$	−6.70027	−	9.22213i	−0.00755386	−	0.0103970i	0.805223	−	0.592972i	$-0.202045\pi$
$887$	−6.70027	−	9.22213i	−0.00755386	−	0.0103970i	−0.812777	+	0.582575i	$0.802045\pi$
$888$	−73.6572	−	148.100i	−0.0829473	−	0.166780i
$889$	−32.7876	−	100.910i	−0.0368814	−	0.113509i
$890$		−	1254.20i		−	1.40921i
$891$		0			0
$892$	−1025.93			−1.15014
$893$	685.012	−	222.574i	0.767091	−	0.249243i
$894$	287.237	−	142.856i	0.321294	−	0.159794i
$895$	883.772	−	642.098i	0.987454	−	0.717428i
$896$	357.026	+	116.005i	0.398467	+	0.129470i
$897$	−1.03946	+	1.01945i	−0.00115881	+	0.00113651i
$898$	−635.780	+	461.921i	−0.707995	+	0.514389i
$899$	−750.020	+	1032.31i	−0.834283	+	1.14829i
$900$	1676.80	−	2216.06i	1.86312	−	2.46228i
$901$	79.5220			0.0882597
$902$		0			0
$903$	34.9056	−	66.8914i	0.0386552	−	0.0740768i
$904$	240.392	+	739.851i	0.265920	+	0.818419i
$905$	287.550	−	395.778i	0.317735	−	0.437324i
$906$	−1717.04	+	254.876i	−1.89519	+	0.281321i
$907$	492.982	−	1517.24i	0.543531	−	1.67282i	−0.180927	−	0.983496i	$-0.557910\pi$
$907$	492.982	−	1517.24i	0.543531	−	1.67282i	0.724458	−	0.689319i	$-0.242090\pi$
$908$	374.611	+	121.719i	0.412567	+	0.134051i
$909$	−164.132	+	473.627i	−0.180563	+	0.521042i
$910$	−2.87949	−	2.09207i	−0.00316427	−	0.00229898i
$911$	−575.802	+	187.089i	−0.632055	+	0.205367i	−0.607485	−	0.794331i	$-0.707822\pi$
$911$	−575.802	+	187.089i	−0.632055	+	0.205367i	−0.0245695	+	0.999698i	$0.507822\pi$
$912$	−699.425	+	1340.34i	−0.766914	+	1.46967i
$913$		0			0
$914$		−	249.573i		−	0.273056i
$915$	−311.475	+	1850.05i	−0.340409	+	2.02191i
$916$	−488.990	−	355.272i	−0.533832	−	0.387852i
$917$	157.516	+	216.803i	0.171773	+	0.236426i
$918$	64.0622	−	340.011i	0.0697845	−	0.370383i
$919$	−113.582	+	349.570i	−0.123593	+	0.380381i	−0.993642	−	0.112585i	$-0.964087\pi$
$919$	−113.582	+	349.570i	−0.123593	+	0.380381i	0.870049	+	0.492965i	$0.164087\pi$
$920$	473.400	+	651.579i	0.514565	+	0.708238i
$921$	−872.738	+	434.053i	−0.947598	+	0.471284i
$922$	−948.272	−	2918.48i	−1.02849	−	3.16538i
$923$		−	3.29169i		−	0.00356630i
$924$		0			0
$925$	−138.377			−0.149597
$926$	2745.86	−	892.183i	2.96529	−	0.963481i
$927$	−22.8185	+	1174.08i	−0.0246154	+	1.26654i
$928$	−181.092	+	131.571i	−0.195143	+	0.141780i
$929$	1589.96	+	516.611i	1.71148	+	0.556093i	0.990579	−	0.136946i	$-0.0437286\pi$
$929$	1589.96	+	516.611i	1.71148	+	0.556093i	0.720900	+	0.693039i	$0.243729\pi$
$930$	2453.67	+	2501.82i	2.63836	+	2.69013i
$931$	973.529	−	707.310i	1.04568	−	0.759732i
$932$	−899.717	+	1238.35i	−0.965361	+	1.32871i
$933$	58.2763	−	346.140i	0.0624612	−	0.370997i
$934$	1124.00			1.20343
$935$		0			0
$936$	−7.80261	+	5.44046i	−0.00833612	+	0.00581246i
$937$	309.287	+	951.889i	0.330083	+	1.01589i	0.969094	+	0.246692i	$0.0793437\pi$
$937$	309.287	+	951.889i	0.330083	+	1.01589i	−0.639011	+	0.769197i	$0.720656\pi$
$938$	−379.708	+	522.624i	−0.404806	+	0.557168i
$939$	64.3451	+	433.477i	0.0685251	+	0.461637i
$940$	551.369	−	1696.94i	0.586563	−	1.80526i
$941$	−335.079	−	108.874i	−0.356088	−	0.115700i	0.125510	−	0.992092i	$-0.459943\pi$
$941$	−335.079	−	108.874i	−0.356088	−	0.115700i	−0.481598	+	0.876392i	$0.659943\pi$
$942$	−2193.35	+	325.580i	−2.32840	+	0.345626i
$943$	−393.442	−	285.852i	−0.417223	−	0.303131i
$944$	1452.78	−	472.036i	1.53896	−	0.500038i
$945$	−49.3760	−	383.851i	−0.0522497	−	0.406192i
$946$		0			0
$947$		−	1536.20i		−	1.62217i	−0.584927	−	0.811086i	$-0.698877\pi$
$947$		−	1536.20i		−	1.62217i	0.584927	−	0.811086i	$-0.301123\pi$
$948$	1536.08	+	258.614i	1.62033	+	0.272800i
$949$	−6.62755	−	4.81520i	−0.00698372	−	0.00507397i
$950$	2026.08	+	2788.65i	2.13271	+	2.93543i
$951$	−144.708	+	141.923i	−0.152164	+	0.149236i
$952$	−30.5844	+	94.1292i	−0.0321265	+	0.0988752i
$953$	−527.449	−	725.972i	−0.553462	−	0.761775i	0.437015	−	0.899454i	$-0.356036\pi$
$953$	−527.449	−	725.972i	−0.553462	−	0.761775i	−0.990477	+	0.137679i	$0.956036\pi$
$954$	13.3012	−	684.391i	0.0139426	−	0.717391i
$955$	59.2924	+	182.483i	0.0620863	+	0.191082i
$956$		−	2897.71i		−	3.03108i
$957$		0			0
$958$	1516.66			1.58315
$959$	285.535	−	92.7761i	0.297743	−	0.0967425i
$960$	−534.263	−	1074.23i	−0.556524	−	1.11899i
$961$	−665.871	+	483.784i	−0.692894	+	0.503417i
$962$	0.873804	+	0.283916i	0.000908320	+	0.000295131i
$963$	−151.995	−	500.694i	−0.157834	−	0.519932i
$964$	−1172.31	+	851.731i	−1.21609	+	0.883539i
$965$	−937.030	+	1289.71i	−0.971015	+	1.33649i
$966$	128.592	+	21.6498i	0.133118	+	0.0224118i
$967$	1717.58			1.77620			0.888099	−	0.459652i	$-0.152026\pi$
$967$	1717.58			1.77620			0.888099	+	0.459652i	$0.152026\pi$
$968$		0			0
$969$	256.304	+	133.746i	0.264504	+	0.138025i
$970$	−822.669	−	2531.92i	−0.848113	−	2.61022i
$971$	−880.936	+	1212.50i	−0.907246	+	1.24872i	0.0608528	+	0.998147i	$0.480618\pi$
$971$	−880.936	+	1212.50i	−0.907246	+	1.24872i	−0.968099	+	0.250570i	$0.919382\pi$
$972$	−1964.01	−	409.714i	−2.02059	−	0.421517i
$973$	−29.2123	+	89.9063i	−0.0300229	+	0.0924011i
$974$	−1173.86	−	381.410i	−1.20519	−	0.391591i
$975$	1.16843	+	7.87144i	0.00119839	+	0.00807327i
$976$	−1225.99	−	890.734i	−1.25614	−	0.912638i
$977$	53.6767	−	17.4406i	0.0549404	−	0.0178512i	−0.281418	−	0.959585i	$-0.590805\pi$
$977$	53.6767	−	17.4406i	0.0549404	−	0.0178512i	0.336358	+	0.941734i	$0.390805\pi$
$978$	813.925	+	424.727i	0.832234	+	0.434281i
$979$		0			0
$980$		−	2980.98i		−	3.04182i
$981$	266.158	−	351.752i	0.271313	−	0.358565i
$982$	1264.29	+	918.562i	1.28747	+	0.935399i
$983$	−27.9524	−	38.4732i	−0.0284358	−	0.0391385i	0.794562	−	0.607183i	$-0.207700\pi$
$983$	−27.9524	−	38.4732i	−0.0284358	−	0.0391385i	−0.822998	+	0.568044i	$0.807700\pi$
$984$	−2224.74	−	2268.40i	−2.26092	−	2.30528i
$985$	−158.443	+	487.636i	−0.160855	+	0.495062i
$986$	227.548	+	313.192i	0.230779	+	0.317639i
$987$	−66.3206	−	133.349i	−0.0671941	−	0.135105i
$988$	−4.76421	−	14.6627i	−0.00482207	−	0.0148408i
$989$		−	94.8360i		−	0.0958908i
$990$		0			0
$991$	−218.685			−0.220671			−0.110336	−	0.993894i	$-0.535193\pi$
$991$	−218.685			−0.220671			−0.110336	+	0.993894i	$0.535193\pi$
$992$	−297.649	+	96.7121i	−0.300050	+	0.0974921i
$993$	815.146	−	405.410i	0.820893	−	0.408268i
$994$	−238.517	+	173.293i	−0.239957	+	0.174339i
$995$	−1023.70	−	332.619i	−1.02884	−	0.334291i
$996$	1494.27	−	1465.52i	1.50028	−	1.47140i
$997$	−532.052	+	386.558i	−0.533653	+	0.387721i	−0.821722	−	0.569888i	$-0.806987\pi$
$997$	−532.052	+	386.558i	−0.533653	+	0.387721i	0.288070	+	0.957609i	$0.406987\pi$
$998$	184.726	−	254.253i	0.185096	−	0.254763i
$999$	42.7412	+	90.2978i	0.0427840	+	0.0903882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.q.269.1		24
3.2	odd	2	inner	363.3.h.q.269.6		24
11.2	odd	10		363.3.h.p.251.1		24
11.3	even	5		363.3.b.j.122.6	yes	6
11.4	even	5	inner	363.3.h.q.245.1		24
11.5	even	5	inner	363.3.h.q.323.6		24
11.6	odd	10		363.3.h.p.323.1		24
11.7	odd	10		363.3.h.p.245.6		24
11.8	odd	10		363.3.b.k.122.1	yes	6
11.9	even	5	inner	363.3.h.q.251.6		24
11.10	odd	2		363.3.h.p.269.6		24
33.2	even	10		363.3.h.p.251.6		24
33.5	odd	10	inner	363.3.h.q.323.1		24
33.8	even	10		363.3.b.k.122.6	yes	6
33.14	odd	10		363.3.b.j.122.1	✓	6
33.17	even	10		363.3.h.p.323.6		24
33.20	odd	10	inner	363.3.h.q.251.1		24
33.26	odd	10	inner	363.3.h.q.245.6		24
33.29	even	10		363.3.h.p.245.1		24
33.32	even	2		363.3.h.p.269.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.j.122.1	✓	6	33.14	odd	10
363.3.b.j.122.6	yes	6	11.3	even	5
363.3.b.k.122.1	yes	6	11.8	odd	10
363.3.b.k.122.6	yes	6	33.8	even	10
363.3.h.p.245.1		24	33.29	even	10
363.3.h.p.245.6		24	11.7	odd	10
363.3.h.p.251.1		24	11.2	odd	10
363.3.h.p.251.6		24	33.2	even	10
363.3.h.p.269.1		24	33.32	even	2
363.3.h.p.269.6		24	11.10	odd	2
363.3.h.p.323.1		24	11.6	odd	10
363.3.h.p.323.6		24	33.17	even	10
363.3.h.q.245.1		24	11.4	even	5	inner
363.3.h.q.245.6		24	33.26	odd	10	inner
363.3.h.q.251.1		24	33.20	odd	10	inner
363.3.h.q.251.6		24	11.9	even	5	inner
363.3.h.q.269.1		24	1.1	even	1	trivial
363.3.h.q.269.6		24	3.2	odd	2	inner
363.3.h.q.323.1		24	33.5	odd	10	inner
363.3.h.q.323.6		24	11.5	even	5	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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.32956 + 1.08184i) q^{2} +(2.68613 - 1.33594i) q^{3} +(6.67952 - 4.85296i) q^{4} +(-7.51264 - 2.44100i) q^{5} +(-7.49835 + 7.35404i) q^{6} +(-1.46803 + 1.06658i) q^{7} +(-8.75863 + 12.0552i) q^{8} +(5.43055 - 7.17698i) q^{9} +27.6545 q^{10} +(11.4588 - 21.9591i) q^{12} +(0.0219178 + 0.0674561i) q^{13} +(3.73401 - 5.13943i) q^{14} +(-23.4409 + 3.47955i) q^{15} +(5.91516 - 18.2050i) q^{16} +(-3.48121 - 1.13111i) q^{17} +(-10.3170 + 29.7712i) q^{18} +(-21.2992 - 15.4748i) q^{19} +(-62.0269 + 20.1538i) q^{20} +(-2.51842 + 4.82617i) q^{21} +6.84236i q^{23} +(-7.42179 + 44.0828i) q^{24} +(30.2558 + 21.9821i) q^{25} +(-0.145953 - 0.200887i) q^{26} +(4.99916 - 26.5332i) q^{27} +(-4.62964 + 14.2486i) q^{28} +(17.7569 + 24.4403i) q^{29} +(74.2836 - 36.9447i) q^{30} +(13.0523 + 40.1709i) q^{31} +7.40958i q^{32} +12.8146 q^{34} +(13.6323 - 4.42940i) q^{35} +(1.44390 - 74.2931i) q^{36} +(-2.99344 + 2.17486i) q^{37} +(87.6582 + 28.4819i) q^{38} +(0.148991 + 0.151915i) q^{39} +(95.2272 - 69.1866i) q^{40} +(-41.7768 + 57.5009i) q^{41} +(3.16409 - 18.7936i) q^{42} -13.8601 q^{43} +(-58.3168 + 40.6621i) q^{45} +(-7.40233 - 22.7820i) q^{46} +(-16.0807 + 22.1332i) q^{47} +(-8.43183 - 56.8032i) q^{48} +(-14.1243 + 43.4702i) q^{49} +(-124.520 - 40.4589i) q^{50} +(-10.8621 + 1.61236i) q^{51} +(0.473762 + 0.344208i) q^{52} +(-20.6619 + 6.71345i) q^{53} +(12.0596 + 93.7520i) q^{54} -27.0392i q^{56} +(-77.8857 - 13.1128i) q^{57} +(-85.5633 - 62.1654i) q^{58} +(46.9059 + 64.5605i) q^{59} +(-139.688 + 137.000i) q^{60} +(24.4640 - 75.2925i) q^{61} +(-86.9169 - 119.631i) q^{62} +(-0.317340 + 16.3282i) q^{63} +(15.6447 + 48.1493i) q^{64} -0.560274i q^{65} -101.689 q^{67} +(-28.7421 + 9.33887i) q^{68} +(9.14095 + 18.3794i) q^{69} +(-40.5976 + 29.4959i) q^{70} +(-44.1378 - 14.3412i) q^{71} +(38.9559 + 128.327i) q^{72} +(-93.4412 + 67.8890i) q^{73} +(7.61398 - 10.4797i) q^{74} +(110.638 + 18.6270i) q^{75} -217.367 q^{76} +(-0.660422 - 0.344625i) q^{78} +(19.4337 + 59.8107i) q^{79} +(-88.8769 + 122.329i) q^{80} +(-22.0182 - 77.9500i) q^{81} +(76.8918 - 236.649i) q^{82} +(80.3644 + 26.1120i) q^{83} +(6.59936 + 44.4583i) q^{84} +(23.3920 + 16.9953i) q^{85} +(46.1481 - 14.9944i) q^{86} +(80.3481 + 41.9277i) q^{87} -45.3523i q^{89} +(150.179 - 198.476i) q^{90} +(-0.104124 - 0.0756502i) q^{91} +(33.2057 + 45.7037i) q^{92} +(88.7259 + 90.4670i) q^{93} +(29.5971 - 91.0905i) q^{94} +(122.239 + 168.248i) q^{95} +(9.89872 + 19.9031i) q^{96} +(-29.7481 - 91.5551i) q^{97} -160.017i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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