LMFDB - Embedded newform 363.3.h.q.251.1

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			251.1
Character	$\chi$	$=$	363.251
Dual form			363.3.h.q.269.1

$q$-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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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	−0.682914	−	0.730498i	$-0.739288\pi$
$2$	−3.32956	−	1.08184i	−1.66478	−	0.540920i	−0.981866	+	0.189579i	$0.939288\pi$
$3$	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	−0.940754	−	0.339090i	$-0.889881\pi$
$5$	−7.51264	+	2.44100i	−1.50253	+	0.488201i	−0.561773	+	0.827291i	$0.689881\pi$
$6$	−7.49835	−	7.35404i	−1.24973	−	1.22567i
$7$	−1.46803	−	1.06658i	−0.209718	−	0.152369i	0.477968	−	0.878377i	$-0.341374\pi$
$7$	−1.46803	−	1.06658i	−0.209718	−	0.152369i	−0.687686	+	0.726008i	$0.741374\pi$
$8$	−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	−0.950210	−	0.311610i	$-0.899132\pi$
$13$	0.0219178	−	0.0674561i	0.00168599	−	0.00518893i	0.951896	+	0.306421i	$0.0991317\pi$
$14$	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	−0.409610	−	0.912261i	$-0.634335\pi$
$17$	−3.48121	+	1.13111i	−0.204777	+	0.0665361i	0.204832	+	0.978797i	$0.434335\pi$
$18$	−10.3170	−	29.7712i	−0.573167	−	1.65395i
$19$	−21.2992	+	15.4748i	−1.12101	+	0.814462i	−0.984362	−	0.176157i	$-0.943633\pi$
$19$	−21.2992	+	15.4748i	−1.12101	+	0.814462i	−0.136649	+	0.990620i	$0.543633\pi$
$20$	−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	$-0.952476\pi$
$23$		−	6.84236i		−	0.297494i	0.988875	−	0.148747i	$-0.0475240\pi$
$24$	−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	−0.384457	−	0.923143i	$-0.625611\pi$
$29$	17.7569	−	24.4403i	0.612308	−	0.842770i	0.996765	+	0.0803733i	$0.0256112\pi$
$30$	74.2836	+	36.9447i	2.47612	+	1.23149i
$31$	13.0523	−	40.1709i	0.421042	−	1.29583i	−0.485691	−	0.874131i	$-0.661432\pi$
$31$	13.0523	−	40.1709i	0.421042	−	1.29583i	0.906733	−	0.421704i	$-0.138568\pi$
$32$		−	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	0.546598	−	0.837395i	$-0.315923\pi$
$37$	−2.99344	−	2.17486i	−0.0809037	−	0.0587800i	−0.627502	+	0.778615i	$0.715923\pi$
$38$	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	−0.912939	−	0.408096i	$-0.866193\pi$
$41$	−41.7768	−	57.5009i	−1.01895	−	1.40246i	−0.106008	−	0.994365i	$-0.533807\pi$
$42$	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	0.602923	−	0.797799i	$-0.294003\pi$
$47$	−16.0807	−	22.1332i	−0.342143	−	0.470919i	−0.945066	+	0.326880i	$0.894003\pi$
$48$	−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	0.107534	−	0.994201i	$-0.465705\pi$
$53$	−20.6619	−	6.71345i	−0.389846	−	0.126669i	−0.497380	+	0.867533i	$0.665705\pi$
$54$	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	−0.198450	−	0.980111i	$-0.563591\pi$
$59$	46.9059	−	64.5605i	0.795016	−	1.09425i	0.993465	−	0.114134i	$-0.0364093\pi$
$60$	−139.688	−	137.000i	−2.32813	−	2.28333i
$61$	24.4640	+	75.2925i	0.401050	+	1.23430i	0.924149	+	0.382032i	$0.124776\pi$
$61$	24.4640	+	75.2925i	0.401050	+	1.23430i	−0.523100	+	0.852272i	$0.675224\pi$
$62$	−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	−0.602877	−	0.797834i	$-0.705979\pi$
$71$	−44.1378	+	14.3412i	−0.621659	+	0.201989i	−0.0187823	+	0.999824i	$0.505979\pi$
$72$	38.9559	−	128.327i	0.541054	−	1.78232i
$73$	−93.4412	−	67.8890i	−1.28002	−	0.929987i	−0.280463	−	0.959865i	$-0.590488\pi$
$73$	−93.4412	−	67.8890i	−1.28002	−	0.929987i	−0.999554	+	0.0298780i	$0.990488\pi$
$74$	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	−0.749475	−	0.662033i	$-0.769694\pi$
$79$	19.4337	−	59.8107i	0.245996	−	0.757098i	0.995471	−	0.0950654i	$-0.0303060\pi$
$80$	−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	0.218138	−	0.975918i	$-0.430002\pi$
$83$	80.3644	−	26.1120i	0.968246	−	0.314602i	0.750108	+	0.661316i	$0.230002\pi$
$84$	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	$0.0820058\pi$
$89$			45.3523i			0.509577i	−0.966997	+	0.254788i	$0.917994\pi$
$90$	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	0.672363	+	0.740221i	$0.265279\pi$
$97$	−29.7481	+	91.5551i	−0.306681	+	0.943867i	−0.979045	+	0.203646i	$0.934721\pi$
$98$			160.017i			1.63283i
$99$		0			0
$100$	308.772			3.08772
$101$	−52.9697	−	17.2109i	−0.524452	−	0.170405i	0.0348128	−	0.999394i	$-0.488917\pi$
$101$	−52.9697	−	17.2109i	−0.524452	−	0.170405i	−0.559265	+	0.828989i	$0.688917\pi$
$102$	34.4216	+	17.1195i	0.337467	+	0.167838i
$103$	−105.559	−	76.6932i	−1.02485	−	0.744594i	−0.0575756	−	0.998341i	$-0.518337\pi$
$103$	−105.559	−	76.6932i	−1.02485	−	0.744594i	−0.967271	+	0.253747i	$0.918337\pi$
$104$	−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	0.938278	−	0.345883i	$-0.112421\pi$
$107$	34.1736	+	47.0359i	0.319379	+	0.439588i	−0.618898	+	0.785471i	$0.712421\pi$
$108$	−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	0.922915	−	0.385005i	$-0.125800\pi$
$113$	30.6859	+	42.2355i	0.271557	+	0.373766i	−0.651358	+	0.758771i	$0.725800\pi$
$114$	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	0.854375	−	0.519656i	$-0.173940\pi$
$127$	−18.0690	−	55.6105i	−0.142275	−	0.437878i	−0.996651	+	0.0817783i	$0.973940\pi$
$128$	−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	$0.190613\pi$
$131$			147.683i			1.12735i	−0.825997	+	0.563675i	$0.809387\pi$
$132$		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	−0.820610	−	0.571489i	$-0.806366\pi$
$137$	−157.356	+	51.1281i	−1.14858	+	0.373198i	−0.327974	+	0.944687i	$0.606366\pi$
$138$	−50.3189	+	51.3064i	−0.364630	+	0.371786i
$139$	42.1468	+	30.6214i	0.303214	+	0.220298i	0.728979	−	0.684536i	$-0.239995\pi$
$139$	42.1468	+	30.6214i	0.303214	+	0.220298i	−0.425765	+	0.904834i	$0.639995\pi$
$140$	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	−0.404871	−	0.914374i	$-0.632684\pi$
$149$	−29.0495	+	9.43876i	−0.194963	+	0.0633474i	0.209908	+	0.977721i	$0.432684\pi$
$150$	−388.526	−	57.6725i	−2.59017	−	0.384483i
$151$	133.712	−	97.1472i	0.885508	−	0.643359i	−0.0491952	−	0.998789i	$-0.515666\pi$
$151$	133.712	−	97.1472i	0.885508	−	0.643359i	0.934703	+	0.355430i	$0.115666\pi$
$152$	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	0.108874	−	0.994056i	$-0.465275\pi$
$157$	170.804	−	124.096i	1.08792	−	0.790421i	0.979047	+	0.203634i	$0.0652754\pi$
$158$	−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	−0.999089	−	0.0426855i	$-0.986409\pi$
$163$	−27.0122	+	83.1350i	−0.165719	+	0.510031i	0.833370	+	0.552716i	$0.186409\pi$
$164$		−	586.820i		−	3.57817i
$165$		0			0
$166$	−295.827			−1.78209
$167$	39.3415	+	12.7828i	0.235578	+	0.0765439i	0.424427	−	0.905462i	$-0.360476\pi$
$167$	39.3415	+	12.7828i	0.235578	+	0.0765439i	−0.188849	+	0.982006i	$0.560476\pi$
$168$	−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	−0.999923	−	0.0124175i	$-0.996047\pi$
$173$	−121.574	−	167.332i	−0.702740	−	0.967238i	0.297183	−	0.954820i	$-0.403953\pi$
$174$	−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	0.519164	−	0.854675i	$-0.326244\pi$
$179$	−81.2859	−	111.880i	−0.454111	−	0.625030i	−0.973275	+	0.229645i	$0.926244\pi$
$180$	−192.197	−	554.612i	−1.06776	−	3.08118i
$181$	−19.1377	−	58.8999i	−0.105733	−	0.325414i	0.884168	−	0.467168i	$-0.154726\pi$
$181$	−19.1377	−	58.8999i	−0.105733	−	0.325414i	−0.989902	+	0.141754i	$0.954726\pi$
$182$	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	−0.844755	−	0.535153i	$-0.820254\pi$
$191$	−14.2774	+	19.6512i	−0.0747508	+	0.102886i	0.770004	+	0.638039i	$0.220254\pi$
$192$	106.348	−	108.435i	0.553895	−	0.564765i
$193$	62.3636	+	191.935i	0.323127	+	0.994484i	0.972279	+	0.233825i	$0.0751241\pi$
$193$	62.3636	+	191.935i	0.323127	+	0.994484i	−0.649151	+	0.760659i	$0.724876\pi$
$194$	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	$0.0526795\pi$
$197$			64.9088i			0.329486i	−0.986337	+	0.164743i	$0.947320\pi$
$198$		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	−0.951962	−	0.306217i	$-0.900937\pi$
$211$	−0.383783	+	1.18116i	−0.00181888	+	0.00559793i	0.950143	+	0.311815i	$0.100937\pi$
$212$	−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	−0.789911	−	0.613222i	$-0.789873\pi$
$223$	−100.528	+	73.0378i	−0.450798	+	0.327524i	0.339113	+	0.940746i	$0.389873\pi$
$224$	−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	−0.742772	−	0.669545i	$-0.766489\pi$
$227$	28.0418	−	38.5962i	0.123532	−	0.170027i	0.866304	+	0.499517i	$0.166489\pi$
$228$	−583.875	−	290.388i	−2.56086	−	1.27363i
$229$	−22.6223	+	69.6244i	−0.0987874	+	0.304037i	−0.988222	−	0.153026i	$-0.951098\pi$
$229$	−22.6223	+	69.6244i	−0.0987874	+	0.304037i	0.889435	+	0.457062i	$0.151098\pi$
$230$		−	189.222i		−	0.822706i
$231$		0			0
$232$	−450.160			−1.94034
$233$	−176.322	−	57.2904i	−0.756745	−	0.245881i	−0.0948641	−	0.995490i	$-0.530242\pi$
$233$	−176.322	−	57.2904i	−0.756745	−	0.245881i	−0.661881	+	0.749609i	$0.730242\pi$
$234$	−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	0.980808	+	0.194975i	$0.0624624\pi$
$239$	206.294	+	283.939i	0.863154	+	1.18803i	−0.117655	+	0.993055i	$0.537538\pi$
$240$	−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	0.0335755	−	0.999436i	$-0.489311\pi$
$251$	−132.205	−	42.9562i	−0.526715	−	0.171140i	−0.560291	+	0.828296i	$0.689311\pi$
$252$	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	−0.0392507	+	0.999229i	$0.512497\pi$
$257$	−251.203	+	345.752i	−0.977445	+	1.34534i	−0.938194	+	0.346109i	$0.887503\pi$
$258$	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	$0.125227\pi$
$263$			201.638i			0.766686i	−0.923606	+	0.383343i	$0.874773\pi$
$264$		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	−0.844478	−	0.535590i	$-0.820089\pi$
$269$	−326.260	+	106.008i	−1.21286	+	0.394083i	−0.368385	+	0.929673i	$0.620089\pi$
$270$	138.250	+	733.762i	0.512035	+	2.71764i
$271$	−329.745	−	239.574i	−1.21677	−	0.884035i	−0.220942	−	0.975287i	$-0.570913\pi$
$271$	−329.745	−	239.574i	−1.21677	−	0.884035i	−0.995828	+	0.0912517i	$0.970913\pi$
$272$	−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	−0.142975	−	0.989726i	$-0.545667\pi$
$277$	153.580	−	472.671i	0.554441	−	1.70639i	0.697416	−	0.716667i	$-0.254333\pi$
$278$	−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	0.430845	−	0.902426i	$-0.358215\pi$
$281$	368.065	−	119.591i	1.30984	−	0.425593i	0.878994	+	0.476833i	$0.158215\pi$
$282$	−42.1895	+	284.220i	−0.149608	+	1.00787i
$283$	−179.404	+	130.344i	−0.633935	+	0.460581i	−0.857761	−	0.514048i	$-0.828145\pi$
$283$	−179.404	+	130.344i	−0.633935	+	0.460581i	0.223826	+	0.974629i	$0.428145\pi$
$284$	−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	0.0858612	+	0.996307i	$0.472636\pi$
$293$	−260.247	+	358.200i	−0.888216	+	1.22252i	−0.974077	+	0.226217i	$0.927364\pi$
$294$	−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	0.905142	−	0.425109i	$-0.139764\pi$
$311$	68.7732	+	94.6582i	0.221136	+	0.304367i	−0.684007	+	0.729476i	$0.739764\pi$
$312$	−3.13632	−	0.465554i	−0.0100523	−	0.00149216i
$313$	−45.1399	−	138.926i	−0.144217	−	0.443854i	0.852693	−	0.522413i	$-0.174968\pi$
$313$	−45.1399	−	138.926i	−0.144217	−	0.443854i	−0.996909	+	0.0785593i	$0.974968\pi$
$314$	−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	0.205907	−	0.978572i	$-0.433986\pi$
$317$	−64.2560	−	20.8781i	−0.202700	−	0.0658614i	−0.408608	+	0.912710i	$0.633986\pi$
$318$	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	−0.999659	−	0.0261175i	$-0.991686\pi$
$337$	−449.359	−	326.478i	−1.33341	−	0.968779i	−0.333751	−	0.942661i	$-0.608314\pi$
$338$	−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	−0.787893	−	0.615812i	$-0.788828\pi$
$347$	−368.981	+	119.889i	−1.06335	+	0.345502i	−0.275454	+	0.961314i	$0.588828\pi$
$348$	740.160	+	109.869i	2.12690	+	0.315715i
$349$	365.704	−	265.700i	1.04786	−	0.761317i	0.0760578	−	0.997103i	$-0.475767\pi$
$349$	365.704	−	265.700i	1.04786	−	0.761317i	0.971805	+	0.235787i	$0.0757667\pi$
$350$	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	$-0.858077\pi$
$353$		−	304.454i		−	0.862476i	0.902238	−	0.431238i	$-0.141923\pi$
$354$	−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	−0.485248	−	0.874377i	$-0.661270\pi$
$359$	178.166	−	245.224i	0.496284	−	0.683076i	0.981532	+	0.191301i	$0.0612705\pi$
$360$	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	0.944953	−	0.327205i	$-0.106107\pi$
$367$	339.757	+	246.848i	0.925770	+	0.672611i	−0.0191838	+	0.999816i	$0.506107\pi$
$368$	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	0.976227	−	0.216752i	$-0.0695463\pi$
$379$	22.3758	+	68.8656i	0.0590390	+	0.181703i	−0.917188	+	0.398455i	$0.869546\pi$
$380$	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	−0.426659	−	0.904413i	$-0.640309\pi$
$383$	−499.215	−	162.205i	−1.30343	−	0.423511i	−0.876775	+	0.480901i	$0.840309\pi$
$384$	−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	−0.428276	−	0.903648i	$-0.640879\pi$
$389$	219.197	−	301.699i	0.563489	−	0.775576i	0.991765	+	0.128072i	$0.0408788\pi$
$390$	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	−0.414695	−	0.909960i	$-0.636112\pi$
$401$	−86.3473	+	28.0559i	−0.215330	+	0.0699649i	0.199366	+	0.979925i	$0.436112\pi$
$402$	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	0.496321	+	0.868139i	$0.334684\pi$
$409$	−169.936	+	523.008i	−0.415490	+	1.27875i	−0.911812	+	0.410609i	$0.865316\pi$
$410$	−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	$-0.884110\pi$
$419$		−	298.402i		−	0.712176i	0.934452	−	0.356088i	$-0.115890\pi$
$420$	58.9443	+	350.108i	0.140344	+	0.833591i
$421$	99.1856	−	72.0626i	0.235595	−	0.171170i	−0.463723	−	0.885980i	$-0.653487\pi$
$421$	99.1856	−	72.0626i	0.235595	−	0.171170i	0.699319	+	0.714810i	$0.253487\pi$
$422$	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	−0.427147	−	0.904182i	$-0.640481\pi$
$431$	−562.102	−	182.638i	−1.30418	−	0.423754i	−0.877034	+	0.480428i	$0.840481\pi$
$432$	−453.465	+	247.957i	−1.04969	+	0.573976i
$433$	−519.659	−	377.554i	−1.20014	−	0.871950i	−0.205838	−	0.978586i	$-0.565992\pi$
$433$	−519.659	−	377.554i	−1.20014	−	0.871950i	−0.994298	+	0.106636i	$0.965992\pi$
$434$	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	0.874479	−	0.485063i	$-0.161203\pi$
$443$	63.3171	+	87.1485i	0.142928	+	0.196723i	−0.731551	+	0.681786i	$0.761203\pi$
$444$	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	0.536945	−	0.843618i	$-0.319578\pi$
$449$	213.489	+	69.3667i	0.475476	+	0.154491i	−0.0614686	+	0.998109i	$0.519578\pi$
$450$	−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	0.924057	−	0.382254i	$-0.124852\pi$
$457$	−22.0293	−	67.7991i	−0.0482041	−	0.148357i	−0.972261	+	0.233897i	$0.924852\pi$
$458$	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	$-0.600376\pi$
$461$		−	876.537i		−	1.90138i	0.310141	−	0.950691i	$-0.399624\pi$
$462$		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	−0.617110	−	0.786877i	$-0.711697\pi$
$467$	−305.347	+	99.2132i	−0.653847	+	0.212448i	−0.0367376	+	0.999325i	$0.511697\pi$
$468$	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	−0.705694	−	0.708517i	$-0.749365\pi$
$479$	−412.015	+	133.872i	−0.860157	+	0.279482i	−0.154463	+	0.987999i	$0.549365\pi$
$480$	−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	−0.255090	−	0.966917i	$-0.582105\pi$
$487$	285.224	−	207.228i	0.585676	−	0.425519i	0.840766	+	0.541399i	$0.182105\pi$
$488$	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	−0.987789	−	0.155795i	$-0.950206\pi$
$491$	−262.378	+	361.133i	−0.534375	+	0.735505i	0.453414	+	0.891300i	$0.350206\pi$
$492$	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	0.512632	−	0.858608i	$-0.328671\pi$
$499$	−72.6250	−	52.7651i	−0.145541	−	0.105742i	−0.658173	+	0.752867i	$0.728671\pi$
$500$	−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	0.766297	+	0.642487i	$0.222097\pi$
$503$	573.691	+	789.618i	1.14054	+	1.56982i	0.374242	+	0.927331i	$0.377903\pi$
$504$	−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	0.953295	−	0.302040i	$-0.0976676\pi$
$509$	189.070	+	260.232i	0.371454	+	0.511262i	−0.581842	+	0.813302i	$0.697668\pi$
$510$	−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	−0.600426	−	0.799680i	$-0.705002\pi$
$521$	180.087	−	247.868i	0.345656	−	0.475755i	0.946083	+	0.323925i	$0.105002\pi$
$522$	−910.816	−	276.494i	−1.74486	−	0.529682i
$523$	207.538	+	638.736i	0.396822	+	1.22129i	0.927533	+	0.373740i	$0.121925\pi$
$523$	207.538	+	638.736i	0.396822	+	1.22129i	−0.530711	+	0.847553i	$0.678075\pi$
$524$	−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	−0.989767	−	0.142690i	$-0.954425\pi$
$541$	−56.8905	+	175.091i	−0.105158	+	0.323643i	0.884610	+	0.466332i	$0.154425\pi$
$542$	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	−0.937934	−	0.346812i	$-0.887264\pi$
$547$	−491.170	+	356.856i	−0.897934	+	0.652387i	0.0400006	+	0.999200i	$0.487264\pi$
$548$	−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	−0.539054	−	0.842271i	$-0.681218\pi$
$557$	238.714	−	328.561i	0.428570	−	0.589876i	0.967624	+	0.252395i	$0.0812182\pi$
$558$	−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	0.568295	−	0.822825i	$-0.307603\pi$
$563$	306.504	+	99.5891i	0.544412	+	0.176890i	−0.0238835	+	0.999715i	$0.507603\pi$
$564$	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	0.522075	−	0.852899i	$-0.325158\pi$
$569$	−256.283	−	352.744i	−0.450410	−	0.619936i	−0.972486	+	0.232963i	$0.925158\pi$
$570$	−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	0.878103	+	0.478472i	$0.158809\pi$
$577$	259.039	+	797.241i	0.448942	+	1.38170i	−0.429161	+	0.903228i	$0.641191\pi$
$578$	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	−0.385613	−	0.922660i	$-0.626010\pi$
$587$	358.686	−	493.689i	0.611050	−	0.841038i	0.996663	+	0.0816225i	$0.0260102\pi$
$588$	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	$-0.822845\pi$
$593$		−	626.517i		−	1.05652i	0.849083	−	0.528260i	$-0.177155\pi$
$594$		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	0.820745	−	0.571295i	$-0.193559\pi$
$599$	1090.50	−	354.326i	1.82054	−	0.591529i	0.999795	−	0.0202344i	$-0.00644123\pi$
$600$	−1193.58	−	1170.61i	−1.98931	−	1.95102i
$601$	−494.787	−	359.484i	−0.823273	−	0.598143i	0.0943748	−	0.995537i	$-0.469915\pi$
$601$	−494.787	−	359.484i	−0.823273	−	0.598143i	−0.917648	+	0.397394i	$0.869915\pi$
$602$	−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	−0.975428	−	0.220320i	$-0.929290\pi$
$607$	−34.4711	+	106.091i	−0.0567893	+	0.174780i	0.918638	+	0.395099i	$0.129290\pi$
$608$	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	0.00343063	−	0.999994i	$-0.498908\pi$
$613$	585.747	−	425.570i	0.955542	−	0.694242i	0.952111	+	0.305752i	$0.0989080\pi$
$614$	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	$-0.920309\pi$
$617$		−	305.723i		−	0.495499i	0.968824	−	0.247749i	$-0.0796910\pi$
$618$	227.515	+	1351.36i	0.368147	+	2.18666i
$619$	−801.760	+	582.513i	−1.29525	+	0.941054i	−0.999897	−	0.0143342i	$-0.995437\pi$
$619$	−801.760	+	582.513i	−1.29525	+	0.941054i	−0.295353	+	0.955388i	$0.595437\pi$
$620$	−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	0.877619	−	0.479358i	$-0.159131\pi$
$631$	437.234	+	317.669i	0.692922	+	0.503437i	−0.184698	+	0.982795i	$0.559131\pi$
$632$	−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	0.658209	−	0.752835i	$-0.271314\pi$
$641$	−167.415	−	230.427i	−0.261178	−	0.359481i	−0.919387	+	0.393355i	$0.871314\pi$
$642$	89.6582	−	604.006i	0.139655	−	0.940819i
$643$	50.1585	+	154.372i	0.0780071	+	0.240081i	0.982454	−	0.186505i	$-0.0597161\pi$
$643$	50.1585	+	154.372i	0.0780071	+	0.240081i	−0.904447	+	0.426586i	$0.859716\pi$
$644$	−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	0.0972452	−	0.995260i	$-0.468997\pi$
$647$	−264.676	−	85.9983i	−0.409081	−	0.132919i	−0.506326	+	0.862342i	$0.668997\pi$
$648$	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	−0.450360	−	0.892847i	$-0.648704\pi$
$653$	351.286	−	483.504i	0.537957	−	0.740435i	0.988317	+	0.152412i	$0.0487042\pi$
$654$	−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	$-0.954620\pi$
$659$		−	187.267i		−	0.284169i	0.989855	−	0.142085i	$-0.0453805\pi$
$660$		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	−0.705294	−	0.708915i	$-0.749185\pi$
$673$	189.780	−	584.082i	0.281991	−	0.867878i	0.987285	−	0.158963i	$-0.0508151\pi$
$674$	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	0.326060	−	0.945349i	$-0.394279\pi$
$677$	775.510	−	251.979i	1.14551	−	0.372199i	0.819450	+	0.573150i	$0.194279\pi$
$678$	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	$-0.977634\pi$
$683$		−	95.9038i		−	0.140416i	0.997532	−	0.0702078i	$-0.0223662\pi$
$684$	−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	−0.862721	−	0.505680i	$-0.831242\pi$
$691$	91.5341	−	281.713i	0.132466	−	0.407689i	0.995187	+	0.0979912i	$0.0312417\pi$
$692$		−	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	0.997635	−	0.0687283i	$-0.0218942\pi$
$701$	437.413	+	602.048i	0.623985	+	0.858841i	−0.373651	+	0.927569i	$0.621894\pi$
$702$	−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	−0.962484	−	0.271337i	$-0.912534\pi$
$709$	−243.404	−	749.120i	−0.343306	−	1.05659i	0.619179	−	0.785250i	$-0.287466\pi$
$710$	−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	−0.960637	−	0.277806i	$-0.910393\pi$
$719$	−287.294	+	395.426i	−0.399574	+	0.549967i	0.561063	+	0.827773i	$0.310393\pi$
$720$	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	0.788959	−	0.614446i	$-0.210620\pi$
$733$	328.669	+	238.792i	0.448388	+	0.325773i	−0.340571	+	0.940219i	$0.610620\pi$
$734$	−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	−0.545426	−	0.838159i	$-0.683632\pi$
$739$	287.094	−	883.586i	0.388490	−	1.19565i	0.933916	−	0.357492i	$-0.116368\pi$
$740$	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	−0.734045	−	0.679101i	$-0.762370\pi$
$743$	−690.050	+	224.211i	−0.928734	+	0.301764i	−0.194689	+	0.980865i	$0.562370\pi$
$744$	−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	−0.992737	−	0.120308i	$-0.961612\pi$
$751$	−890.002	+	646.624i	−1.18509	+	0.861018i	−0.192352	+	0.981326i	$0.561612\pi$
$752$	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	0.268646	+	0.963239i	$0.413424\pi$
$757$	−389.757	+	1199.55i	−0.514871	+	1.58461i	−0.783517	+	0.621370i	$0.786576\pi$
$758$		−	253.499i		−	0.334431i
$759$		0			0
$760$	−3098.91			−4.07752
$761$	110.930	+	36.0434i	0.145769	+	0.0473632i	0.380993	−	0.924578i	$-0.375582\pi$
$761$	110.930	+	36.0434i	0.145769	+	0.0473632i	−0.235224	+	0.971941i	$0.575582\pi$
$762$	−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	−0.974039	−	0.226378i	$-0.927311\pi$
$773$	−686.689	−	945.147i	−0.888343	−	1.22270i	0.0856964	−	0.996321i	$-0.472689\pi$
$774$	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	−0.893498	−	0.449068i	$-0.851756\pi$
$787$	−342.029	−	1052.66i	−0.434598	−	1.33756i	0.458899	−	0.888488i	$-0.348244\pi$
$788$	−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	−0.270010	−	0.962858i	$-0.587027\pi$
$797$	61.7682	−	20.0697i	0.0775009	−	0.0251816i	0.347511	+	0.937676i	$0.387027\pi$
$798$	−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	0.0939183	−	0.995580i	$-0.470061\pi$
$809$	610.865	−	198.482i	0.755087	−	0.245343i	0.661169	+	0.750237i	$0.270061\pi$
$810$	−608.904	+	2155.67i	−0.751733	+	2.66132i
$811$	73.8187	−	53.6324i	0.0910218	−	0.0661312i	−0.541344	−	0.840802i	$-0.682084\pi$
$811$	73.8187	−	53.6324i	0.0910218	−	0.0661312i	0.632365	+	0.774670i	$0.282084\pi$
$812$	−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	−0.350969	−	0.936387i	$-0.614148\pi$
$821$	532.043	−	732.295i	0.648043	−	0.891955i	0.999012	+	0.0444321i	$0.0141478\pi$
$822$	1555.91	+	773.826i	1.89283	+	0.941394i
$823$	193.305	−	594.932i	0.234879	−	0.722883i	−0.762259	−	0.647273i	$-0.775910\pi$
$823$	193.305	−	594.932i	0.234879	−	0.722883i	0.997137	−	0.0756101i	$-0.0240904\pi$
$824$			1944.27i			2.35955i
$825$		0			0
$826$	506.951			0.613742
$827$	−864.024	−	280.738i	−1.04477	−	0.339466i	−0.264156	−	0.964480i	$-0.585093\pi$
$827$	−864.024	−	280.738i	−1.04477	−	0.339466i	−0.780613	+	0.625014i	$0.785093\pi$
$828$	508.340	−	9.87965i	0.613937	−	0.0119319i
$829$	474.666	+	344.865i	0.572577	+	0.416001i	0.836040	−	0.548668i	$-0.184865\pi$
$829$	474.666	+	344.865i	0.572577	+	0.416001i	−0.263464	+	0.964669i	$0.584865\pi$
$830$	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	−0.999608	−	0.0279817i	$-0.991092\pi$
$839$	−601.835	−	828.355i	−0.717325	−	0.987313i	0.282284	−	0.959331i	$-0.408908\pi$
$840$	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	0.996751	−	0.0805454i	$-0.0256662\pi$
$853$	121.995	+	375.463i	0.143019	+	0.440168i	−0.853732	+	0.520713i	$0.825666\pi$
$854$	−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	$0.000249801\pi$
$857$			1.34510i			0.00156955i	−1.00000		0.000784774i	$0.999750\pi$
$858$		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	−0.554019	−	0.832504i	$-0.686907\pi$
$863$	−442.630	+	143.819i	−0.512897	+	0.166650i	0.0411222	+	0.999154i	$0.486907\pi$
$864$	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	−0.801541	−	0.597939i	$-0.795986\pi$
$877$	−421.449	+	306.200i	−0.480557	+	0.349145i	0.320984	+	0.947085i	$0.395986\pi$
$878$	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	$-0.888096\pi$
$881$		−	606.759i		−	0.688717i	0.938838	−	0.344358i	$-0.111904\pi$
$882$	−1148.44	+	868.980i	−1.30209	+	0.985238i
$883$	90.4194	−	65.6935i	0.102400	−	0.0743981i	−0.535407	−	0.844594i	$-0.679842\pi$
$883$	90.4194	−	65.6935i	0.102400	−	0.0743981i	0.637807	+	0.770196i	$0.279842\pi$
$884$	−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	−0.812777	−	0.582575i	$-0.802045\pi$
$887$	−6.70027	+	9.22213i	−0.00755386	+	0.0103970i	0.805223	+	0.592972i	$0.202045\pi$
$888$	−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	0.724458	+	0.689319i	$0.242090\pi$
$907$	492.982	+	1517.24i	0.543531	+	1.67282i	−0.180927	+	0.983496i	$0.557910\pi$
$908$	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	−0.0245695	−	0.999698i	$-0.507822\pi$
$911$	−575.802	−	187.089i	−0.632055	−	0.205367i	−0.607485	+	0.794331i	$0.707822\pi$
$912$	−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	0.870049	−	0.492965i	$-0.164087\pi$
$919$	−113.582	−	349.570i	−0.123593	−	0.380381i	−0.993642	+	0.112585i	$0.964087\pi$
$920$	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	0.720900	−	0.693039i	$-0.243729\pi$
$929$	1589.96	−	516.611i	1.71148	−	0.556093i	0.990579	+	0.136946i	$0.0437286\pi$
$930$	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	−0.639011	−	0.769197i	$-0.720656\pi$
$937$	309.287	−	951.889i	0.330083	−	1.01589i	0.969094	−	0.246692i	$-0.0793437\pi$
$938$	−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	−0.481598	−	0.876392i	$-0.659943\pi$
$941$	−335.079	+	108.874i	−0.356088	+	0.115700i	0.125510	+	0.992092i	$0.459943\pi$
$942$	−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	$0.301123\pi$
$947$			1536.20i			1.62217i	−0.584927	+	0.811086i	$0.698877\pi$
$948$	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	−0.990477	−	0.137679i	$-0.956036\pi$
$953$	−527.449	+	725.972i	−0.553462	+	0.761775i	0.437015	+	0.899454i	$0.356036\pi$
$954$	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	−0.968099	−	0.250570i	$-0.919382\pi$
$971$	−880.936	−	1212.50i	−0.907246	−	1.24872i	0.0608528	−	0.998147i	$-0.480618\pi$
$972$	−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	0.336358	−	0.941734i	$-0.390805\pi$
$977$	53.6767	+	17.4406i	0.0549404	+	0.0178512i	−0.281418	+	0.959585i	$0.590805\pi$
$978$	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	−0.822998	−	0.568044i	$-0.807700\pi$
$983$	−27.9524	+	38.4732i	−0.0284358	+	0.0391385i	0.794562	+	0.607183i	$0.207700\pi$
$984$	−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	0.288070	−	0.957609i	$-0.406987\pi$
$997$	−532.052	−	386.558i	−0.533653	−	0.387721i	−0.821722	+	0.569888i	$0.806987\pi$
$998$	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.251.1		24
3.2	odd	2	inner	363.3.h.q.251.6		24
11.2	odd	10		363.3.h.p.245.1		24
11.3	even	5	inner	363.3.h.q.323.1		24
11.4	even	5		363.3.b.j.122.1	✓	6
11.5	even	5	inner	363.3.h.q.269.6		24
11.6	odd	10		363.3.h.p.269.1		24
11.7	odd	10		363.3.b.k.122.6	yes	6
11.8	odd	10		363.3.h.p.323.6		24
11.9	even	5	inner	363.3.h.q.245.6		24
11.10	odd	2		363.3.h.p.251.6		24
33.2	even	10		363.3.h.p.245.6		24
33.5	odd	10	inner	363.3.h.q.269.1		24
33.8	even	10		363.3.h.p.323.1		24
33.14	odd	10	inner	363.3.h.q.323.6		24
33.17	even	10		363.3.h.p.269.6		24
33.20	odd	10	inner	363.3.h.q.245.1		24
33.26	odd	10		363.3.b.j.122.6	yes	6
33.29	even	10		363.3.b.k.122.1	yes	6
33.32	even	2		363.3.h.p.251.1		24

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

Fields

Representations

Groups

Database

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