LMFDB - Embedded newform 363.3.h.q.269.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			269.6
Character	$\chi$	$=$	363.269
Dual form			363.3.h.q.251.6

$q$-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} +(-0.440492 + 2.96748i) q^{3} +(6.67952 - 4.85296i) q^{4} +(7.51264 + 2.44100i) q^{5} +(1.74370 + 10.3570i) q^{6} +(-1.46803 + 1.06658i) q^{7} +(8.75863 - 12.0552i) q^{8} +(-8.61193 - 2.61430i) q^{9} +27.6545 q^{10} +(11.4588 + 21.9591i) q^{12} +(0.0219178 + 0.0674561i) q^{13} +(-3.73401 + 5.13943i) q^{14} +(-10.5529 + 21.2184i) q^{15} +(5.91516 - 18.2050i) q^{16} +(3.48121 + 1.13111i) q^{17} +(-31.5022 + 0.612250i) q^{18} +(-21.2992 - 15.4748i) q^{19} +(62.0269 - 20.1538i) q^{20} +(-2.51842 - 4.82617i) q^{21} -6.84236i q^{23} +(31.9156 + 31.3013i) q^{24} +(30.2558 + 21.9821i) q^{25} +(0.145953 + 0.200887i) q^{26} +(11.5514 - 24.4042i) q^{27} +(-4.62964 + 14.2486i) q^{28} +(-17.7569 - 24.4403i) q^{29} +(-12.1816 + 82.0644i) q^{30} +(13.0523 + 40.1709i) q^{31} -7.40958i q^{32} +12.8146 q^{34} +(-13.6323 + 4.42940i) q^{35} +(-70.2107 + 24.3311i) q^{36} +(-2.99344 + 2.17486i) q^{37} +(-87.6582 - 28.4819i) q^{38} +(-0.209829 + 0.0353269i) q^{39} +(95.2272 - 69.1866i) q^{40} +(41.7768 - 57.5009i) q^{41} +(-13.6064 - 13.3445i) q^{42} -13.8601 q^{43} +(-58.3168 - 40.6621i) q^{45} +(-7.40233 - 22.7820i) q^{46} +(16.0807 - 22.1332i) q^{47} +(51.4174 + 25.5723i) q^{48} +(-14.1243 + 43.4702i) q^{49} +(124.520 + 40.4589i) q^{50} +(-4.89001 + 9.83219i) q^{51} +(0.473762 + 0.344208i) q^{52} +(20.6619 - 6.71345i) q^{53} +(12.0596 - 93.7520i) q^{54} +27.0392i q^{56} +(55.3033 - 56.3886i) q^{57} +(-85.5633 - 62.1654i) q^{58} +(-46.9059 - 64.5605i) q^{59} +(32.4837 + 192.942i) q^{60} +(24.4640 - 75.2925i) q^{61} +(86.9169 + 119.631i) q^{62} +(15.4309 - 5.34749i) q^{63} +(15.6447 + 48.1493i) q^{64} +0.560274i q^{65} -101.689 q^{67} +(28.7421 - 9.33887i) q^{68} +(20.3046 + 3.01400i) q^{69} +(-40.5976 + 29.4959i) q^{70} +(44.1378 + 14.3412i) q^{71} +(-106.945 + 80.9210i) q^{72} +(-93.4412 + 67.8890i) q^{73} +(-7.61398 + 10.4797i) q^{74} +(-78.5590 + 80.1006i) q^{75} -217.367 q^{76} +(-0.660422 + 0.344625i) q^{78} +(19.4337 + 59.8107i) q^{79} +(88.8769 - 122.329i) q^{80} +(67.3308 + 45.0284i) q^{81} +(76.8918 - 236.649i) q^{82} +(-80.3644 - 26.1120i) q^{83} +(-40.2431 - 20.0147i) q^{84} +(23.3920 + 16.9953i) q^{85} +(-46.1481 + 14.9944i) q^{86} +(80.3481 - 41.9277i) q^{87} +45.3523i q^{89} +(-238.159 - 72.2974i) q^{90} +(-0.104124 - 0.0756502i) q^{91} +(-33.2057 - 45.7037i) q^{92} +(-124.956 + 21.0376i) q^{93} +(29.5971 - 91.0905i) q^{94} +(-122.239 - 168.248i) q^{95} +(21.9878 + 3.26386i) 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	0.682914	−	0.730498i	$-0.260712\pi$
$2$	3.32956	−	1.08184i	1.66478	−	0.540920i	0.981866	+	0.189579i	$0.0607122\pi$
$3$	−0.440492	+	2.96748i	−0.146831	+	0.989162i
$3$	−0.440492	+	2.96748i	−0.146831	+	0.989162i
$4$	6.67952	−	4.85296i	1.66988	−	1.21324i
$5$	7.51264	+	2.44100i	1.50253	+	0.488201i	0.940754	−	0.339090i	$-0.110119\pi$
$5$	7.51264	+	2.44100i	1.50253	+	0.488201i	0.561773	+	0.827291i	$0.310119\pi$
$6$	1.74370	+	10.3570i	0.290617	+	1.72616i
$7$	−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
$9$	−8.61193	−	2.61430i	−0.956882	−	0.290478i
$10$	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
$15$	−10.5529	+	21.2184i	−0.703526	+	1.41456i
$16$	5.91516	−	18.2050i	0.369697	−	1.13781i
$17$	3.48121	+	1.13111i	0.204777	+	0.0665361i	0.409610	−	0.912261i	$-0.365665\pi$
$17$	3.48121	+	1.13111i	0.204777	+	0.0665361i	−0.204832	+	0.978797i	$0.565665\pi$
$18$	−31.5022	+	0.612250i	−1.75012	+	0.0340139i
$19$	−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	$-0.952476\pi$
$23$		−	6.84236i		−	0.297494i	0.988875	−	0.148747i	$-0.0475240\pi$
$24$	31.9156	+	31.3013i	1.32982	+	1.30422i
$25$	30.2558	+	21.9821i	1.21023	+	0.879284i
$26$	0.145953	+	0.200887i	0.00561359	+	0.00772644i
$27$	11.5514	−	24.4042i	0.427829	−	0.903860i
$28$	−4.62964	+	14.2486i	−0.165344	+	0.508877i
$29$	−17.7569	−	24.4403i	−0.612308	−	0.842770i	0.384457	−	0.923143i	$-0.374389\pi$
$29$	−17.7569	−	24.4403i	−0.612308	−	0.842770i	−0.996765	+	0.0803733i	$0.974389\pi$
$30$	−12.1816	+	82.0644i	−0.406053	+	2.73548i
$31$	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
$36$	−70.2107	+	24.3311i	−1.95030	+	0.675863i
$37$	−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
$39$	−0.209829	+	0.0353269i	−0.00538024	+	0.000905819i
$40$	95.2272	−	69.1866i	2.38068	−	1.72967i
$41$	41.7768	−	57.5009i	1.01895	−	1.40246i	0.106008	−	0.994365i	$-0.466193\pi$
$41$	41.7768	−	57.5009i	1.01895	−	1.40246i	0.912939	−	0.408096i	$-0.133807\pi$
$42$	−13.6064	−	13.3445i	−0.323961	−	0.317726i
$43$	−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	$-0.705997\pi$
$47$	16.0807	−	22.1332i	0.342143	−	0.470919i	0.945066	+	0.326880i	$0.105997\pi$
$48$	51.4174	+	25.5723i	1.07120	+	0.532756i
$49$	−14.1243	+	43.4702i	−0.288252	+	0.887147i
$50$	124.520	+	40.4589i	2.49039	+	0.809177i
$51$	−4.89001	+	9.83219i	−0.0958825	+	0.192788i
$52$	0.473762	+	0.344208i	0.00911081	+	0.00661939i
$53$	20.6619	−	6.71345i	0.389846	−	0.126669i	−0.107534	−	0.994201i	$-0.534295\pi$
$53$	20.6619	−	6.71345i	0.389846	−	0.126669i	0.497380	+	0.867533i	$0.334295\pi$
$54$	12.0596	−	93.7520i	0.223326	−	1.73615i
$55$		0			0
$56$			27.0392i			0.482843i
$57$	55.3033	−	56.3886i	0.970233	−	0.989273i
$58$	−85.5633	−	62.1654i	−1.47523	−	1.07182i
$59$	−46.9059	−	64.5605i	−0.795016	−	1.09425i	−0.993465	−	0.114134i	$-0.963591\pi$
$59$	−46.9059	−	64.5605i	−0.795016	−	1.09425i	0.198450	−	0.980111i	$-0.436409\pi$
$60$	32.4837	+	192.942i	0.541394	+	3.21569i
$61$	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
$63$	15.4309	−	5.34749i	0.244936	−	0.0848807i
$64$	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
$69$	20.3046	+	3.01400i	0.294269	+	0.0436812i
$70$	−40.5976	+	29.4959i	−0.579966	+	0.421370i
$71$	44.1378	+	14.3412i	0.621659	+	0.201989i	0.602877	−	0.797834i	$-0.294021\pi$
$71$	44.1378	+	14.3412i	0.621659	+	0.201989i	0.0187823	+	0.999824i	$0.494021\pi$
$72$	−106.945	+	80.9210i	−1.48534	+	1.12390i
$73$	−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
$75$	−78.5590	+	80.1006i	−1.04745	+	1.06801i
$76$	−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
$81$	67.3308	+	45.0284i	0.831245	+	0.555907i
$82$	76.8918	−	236.649i	0.937705	−	2.88596i
$83$	−80.3644	−	26.1120i	−0.968246	−	0.314602i	−0.218138	−	0.975918i	$-0.569998\pi$
$83$	−80.3644	−	26.1120i	−0.968246	−	0.314602i	−0.750108	+	0.661316i	$0.769998\pi$
$84$	−40.2431	−	20.0147i	−0.479084	−	0.238271i
$85$	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	$0.917994\pi$
$90$	−238.159	−	72.2974i	−2.64621	−	0.803304i
$91$	−0.104124	−	0.0756502i	−0.00114422	−	0.000831321i
$92$	−33.2057	−	45.7037i	−0.360931	−	0.496779i
$93$	−124.956	+	21.0376i	−1.34361	+	0.226211i
$94$	29.5971	−	91.0905i	0.314863	−	0.969048i
$95$	−122.239	−	168.248i	−1.28673	−	1.77103i
$96$	21.9878	+	3.26386i	0.229040	+	0.0339985i
$97$	−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	−0.0348128	−	0.999394i	$-0.511083\pi$
$101$	52.9697	−	17.2109i	0.524452	−	0.170405i	0.559265	+	0.828989i	$0.311083\pi$
$102$	−5.64472	+	38.0271i	−0.0553403	+	0.372815i
$103$	−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
$105$	−7.13927	−	42.4048i	−0.0679931	−	0.403855i
$106$	61.5320	−	44.7056i	0.580491	−	0.421751i
$107$	−34.1736	+	47.0359i	−0.319379	+	0.439588i	−0.938278	−	0.345883i	$-0.887579\pi$
$107$	−34.1736	+	47.0359i	−0.319379	+	0.439588i	0.618898	+	0.785471i	$0.287579\pi$
$108$	−41.2748	−	219.067i	−0.382174	−	2.02840i
$109$	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	$-0.874200\pi$
$113$	−30.6859	+	42.2355i	−0.271557	+	0.373766i	0.651358	+	0.758771i	$0.274200\pi$
$114$	123.132	−	247.578i	1.08011	−	2.17174i
$115$	16.7022	−	51.4041i	0.145237	−	0.446993i
$116$	−237.216	−	77.0761i	−2.04496	−	0.664449i
$117$	−0.0124040	−	0.638227i	−0.000106017	−	0.00545493i
$118$	−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
$123$	152.231	+	149.301i	1.23765	+	1.21383i
$124$	282.131	+	204.980i	2.27525	+	1.65306i
$125$	57.5656	+	79.2323i	0.460525	+	0.633858i
$126$	45.5931	−	34.4986i	0.361850	−	0.273798i
$127$	−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
$129$	6.10527	−	41.1297i	0.0473277	−	0.318835i
$130$	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
$135$	146.352	−	155.143i	1.08409	−	1.14921i
$136$	44.1264	−	32.0597i	0.324459	−	0.235733i
$137$	157.356	+	51.1281i	1.14858	+	0.373198i	0.820610	−	0.571489i	$-0.193634\pi$
$137$	157.356	+	51.1281i	1.14858	+	0.373198i	0.327974	+	0.944687i	$0.393634\pi$
$138$	70.8660	−	11.9310i	0.513522	−	0.0864566i
$139$	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
$141$	58.5965	+	57.4687i	0.415578	+	0.407580i
$142$	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
$147$	−122.776	−	61.0620i	−0.835208	−	0.415388i
$148$	−9.44023	+	29.0541i	−0.0637854	+	0.196311i
$149$	29.0495	+	9.43876i	0.194963	+	0.0633474i	0.404871	−	0.914374i	$-0.367316\pi$
$149$	29.0495	+	9.43876i	0.194963	+	0.0633474i	−0.209908	+	0.977721i	$0.567316\pi$
$150$	−174.911	+	351.688i	−1.16607	+	2.34459i
$151$	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
$156$	−1.23012	+	1.25426i	−0.00788539	+	0.00804013i
$157$	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
$159$	10.8207	+	64.2710i	0.0680546	+	0.404220i
$160$	18.0868	−	55.6655i	0.113043	−	0.347909i
$161$	7.29795	+	10.0448i	0.0453289	+	0.0623899i
$162$	272.896	+	77.0837i	1.68454	+	0.475825i
$163$	−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	−0.424427	−	0.905462i	$-0.639524\pi$
$167$	−39.3415	+	12.7828i	−0.235578	+	0.0765439i	0.188849	+	0.982006i	$0.439524\pi$
$168$	−80.2385	−	11.9105i	−0.477610	−	0.0708961i
$169$	136.720	−	99.3328i	0.808993	−	0.587768i
$170$	96.2713	+	31.2804i	0.566302	+	0.184003i
$171$	142.972	+	188.950i	0.836091	+	1.10497i
$172$	−92.5791	+	67.2626i	−0.538250	+	0.391062i
$173$	121.574	−	167.332i	0.702740	−	0.967238i	−0.297183	−	0.954820i	$-0.596047\pi$
$173$	121.574	−	167.332i	0.702740	−	0.967238i	0.999923	−	0.0124175i	$-0.00395273\pi$
$174$	222.165	−	226.524i	1.27681	−	1.30186i
$175$	−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	$-0.673756\pi$
$179$	81.2859	−	111.880i	0.454111	−	0.625030i	0.973275	+	0.229645i	$0.0737564\pi$
$180$	−586.860	+	11.4057i	−3.26033	+	0.0633650i
$181$	−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
$183$	212.653	+	105.762i	1.16204	+	0.577936i
$184$	−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
$189$	9.07139	+	48.1466i	0.0479968	+	0.254744i
$190$	−589.020	−	427.948i	−3.10011	−	2.25236i
$191$	14.2774	+	19.6512i	0.0747508	+	0.102886i	0.844755	−	0.535153i	$-0.179746\pi$
$191$	14.2774	+	19.6512i	0.0747508	+	0.102886i	−0.770004	+	0.638039i	$0.779746\pi$
$192$	−149.774	+	25.2159i	−0.780071	+	0.131333i
$193$	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
$195$	−1.66261	−	0.246796i	−0.00852618	−	0.00126562i
$196$	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
$201$	44.7932	−	301.761i	0.222852	−	1.50130i
$202$	157.746	−	114.609i	0.780922	−	0.567373i
$203$	52.1353	+	16.9398i	0.256824	+	0.0834473i
$204$	15.0523	+	89.4054i	0.0737858	+	0.438262i
$205$	454.214	−	330.006i	2.21568	−	1.60978i
$206$	−268.496	+	369.553i	−1.30338	+	1.79395i
$207$	−17.8880	+	58.9259i	−0.0864155	+	0.284666i
$208$	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
$213$	−61.9997	+	124.661i	−0.291079	+	0.585263i
$214$	−62.8977	+	193.579i	−0.293915	+	0.904576i
$215$	−104.126	−	33.8326i	−0.484307	−	0.157361i
$216$	−193.024	−	353.002i	−0.893628	−	1.63427i
$217$	−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
$222$	−27.7446	−	27.2106i	−0.124976	−	0.122570i
$223$	−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
$225$	−203.093	−	268.406i	−0.902635	−	1.19292i
$226$	−56.4785	+	173.823i	−0.249905	+	0.769128i
$227$	−28.0418	−	38.5962i	−0.123532	−	0.170027i	0.742772	−	0.669545i	$-0.233511\pi$
$227$	−28.0418	−	38.5962i	−0.123532	−	0.170027i	−0.866304	+	0.499517i	$0.833511\pi$
$228$	95.7483	−	645.033i	0.419949	−	2.82909i
$229$	−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	0.0948641	−	0.995490i	$-0.469758\pi$
$233$	176.322	−	57.2904i	0.756745	−	0.245881i	0.661881	+	0.749609i	$0.269758\pi$
$234$	−0.731759	−	2.11160i	−0.00312718	−	0.00902391i
$235$	174.836	−	127.026i	0.743981	−	0.540534i
$236$	−626.618	−	203.601i	−2.65516	−	0.862715i
$237$	−186.048	+	31.3231i	−0.785012	+	0.132165i
$238$	−18.8122	+	13.6678i	−0.0790427	+	0.0574279i
$239$	−206.294	+	283.939i	−0.863154	+	1.18803i	0.117655	+	0.993055i	$0.462462\pi$
$239$	−206.294	+	283.939i	−0.863154	+	1.18803i	−0.980808	+	0.194975i	$0.937538\pi$
$240$	323.859	+	317.625i	1.34941	+	1.32344i
$241$	−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
$246$	668.381	+	332.417i	2.71700	+	1.35129i
$247$	0.577036	−	1.77593i	0.00233618	−	0.00719002i
$248$	598.589	+	194.493i	2.41367	+	0.784247i
$249$	112.887	−	226.978i	0.453360	−	0.911558i
$250$	277.385	+	201.532i	1.10954	+	0.806128i
$251$	132.205	−	42.9562i	0.526715	−	0.171140i	−0.0335755	−	0.999436i	$-0.510689\pi$
$251$	132.205	−	42.9562i	0.526715	−	0.171140i	0.560291	+	0.828296i	$0.310689\pi$
$252$	77.1202	−	110.604i	0.306032	−	0.438906i
$253$		0			0
$254$			204.706i			0.805930i
$255$	−60.7373	+	61.9292i	−0.238185	+	0.242859i
$256$	422.110	+	306.681i	1.64887	+	1.19797i
$257$	251.203	+	345.752i	0.977445	+	1.34534i	0.938194	+	0.346109i	$0.112497\pi$
$257$	251.203	+	345.752i	0.977445	+	1.34534i	0.0392507	+	0.999229i	$0.487503\pi$
$258$	−24.1679	−	143.549i	−0.0936740	−	0.556391i
$259$	2.07478	−	6.38551i	0.00801072	−	0.0246545i
$260$	2.71899	+	3.74237i	0.0104576	+	0.0143937i
$261$	89.0271	+	256.900i	0.341100	+	0.984293i
$262$	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
$267$	−134.582	−	19.9773i	−0.504054	−	0.0748214i
$268$	−679.235	+	493.493i	−2.53446	+	1.84139i
$269$	326.260	+	106.008i	1.21286	+	0.394083i	0.844478	−	0.535590i	$-0.179911\pi$
$269$	326.260	+	106.008i	1.21286	+	0.394083i	0.368385	+	0.929673i	$0.379911\pi$
$270$	319.448	−	674.887i	1.18314	−	2.49958i
$271$	−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
$273$	0.270356	−	0.275662i	0.000990316	−	0.00100975i
$274$	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
$279$	−7.38675	−	380.072i	−0.0264758	−	1.36226i
$280$	−66.0028	+	203.136i	−0.235724	+	0.725485i
$281$	−368.065	−	119.591i	−1.30984	−	0.425593i	−0.430845	−	0.902426i	$-0.641785\pi$
$281$	−368.065	−	119.591i	−1.30984	−	0.425593i	−0.878994	+	0.476833i	$0.841785\pi$
$282$	257.272	+	127.954i	0.912314	+	0.453736i
$283$	−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
$288$	−19.3709	+	63.8108i	−0.0672600	+	0.221565i
$289$	−222.967	−	161.995i	−0.771510	−	0.560535i
$290$	−491.060	−	675.886i	−1.69331	−	2.33064i
$291$	284.792	−	47.9477i	0.978668	−	0.164769i
$292$	−294.680	+	906.933i	−1.00918	+	3.10593i
$293$	260.247	+	358.200i	0.888216	+	1.22252i	0.974077	+	0.226217i	$0.0726358\pi$
$293$	260.247	+	358.200i	0.888216	+	1.22252i	−0.0858612	+	0.996307i	$0.527364\pi$
$294$	−474.848	−	70.4861i	−1.61513	−	0.239749i
$295$	−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
$300$	−136.012	+	916.278i	−0.453372	+	3.05426i
$301$	20.3471	−	14.7830i	0.0675982	−	0.0491130i
$302$	550.299	+	178.803i	1.82218	+	0.592062i
$303$	27.7404	+	164.768i	0.0915523	+	0.543788i
$304$	−407.706	+	296.216i	−1.34114	+	0.974395i
$305$	367.579	−	505.929i	1.20518	−	1.65878i
$306$	−110.358	−	33.5012i	−0.360648	−	0.109481i
$307$	−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	$-0.860236\pi$
$311$	−68.7732	+	94.6582i	−0.221136	+	0.304367i	0.684007	+	0.729476i	$0.260236\pi$
$312$	−1.41194	+	2.83896i	−0.00452546	+	0.00909922i
$313$	−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
$315$	128.980	−	2.50675i	0.409461	−	0.00795793i
$316$	420.067	+	305.196i	1.32933	+	0.965811i
$317$	64.2560	−	20.8781i	0.202700	−	0.0658614i	−0.205907	−	0.978572i	$-0.566014\pi$
$317$	64.2560	−	20.8781i	0.202700	−	0.0658614i	0.408608	+	0.912710i	$0.366014\pi$
$318$	105.559	+	202.288i	0.331946	+	0.636125i
$319$		0			0
$320$			399.917i			1.24974i
$321$	−124.525	−	122.129i	−0.387929	−	0.380463i
$322$	35.1658	+	25.5495i	0.109211	+	0.0793461i
$323$	−56.6433	−	77.9628i	−0.175366	−	0.241371i
$324$	668.259	−	25.9852i	2.06253	−	0.0802013i
$325$	−0.819687	+	2.52274i	−0.00252211	+	0.00776226i
$326$	−179.878	−	247.580i	−0.551772	−	0.759448i
$327$	−21.5890	+	145.440i	−0.0660214	+	0.444770i
$328$	−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
$333$	31.4650	−	10.9040i	0.0944896	−	0.0327447i
$334$	−117.161	+	85.1224i	−0.350781	+	0.254857i
$335$	−763.953	−	248.223i	−2.28046	−	0.740966i
$336$	−102.757	+	17.3002i	−0.305825	+	0.0514888i
$337$	−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
$339$	−111.816	−	109.664i	−0.329842	−	0.323494i
$340$	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
$345$	145.184	+	72.2067i	0.420823	+	0.209295i
$346$	223.761	−	688.666i	0.646708	−	1.99036i
$347$	368.981	+	119.889i	1.06335	+	0.345502i	0.787893	−	0.615812i	$-0.211172\pi$
$347$	368.981	+	119.889i	1.06335	+	0.345502i	0.275454	+	0.961314i	$0.411172\pi$
$348$	333.214	−	669.983i	0.957510	−	1.92524i
$349$	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	$-0.858077\pi$
$353$		−	304.454i		−	0.862476i	0.902238	−	0.431238i	$-0.141923\pi$
$354$	586.860	−	598.377i	1.65780	−	1.69033i
$355$	296.584	+	215.481i	0.835448	+	0.606989i
$356$	220.093	+	302.932i	0.618239	+	0.850932i
$357$	−3.30820	−	19.6495i	−0.00926667	−	0.0550407i
$358$	149.610	−	460.451i	0.417904	−	1.28618i
$359$	−178.166	−	245.224i	−0.496284	−	0.683076i	0.485248	−	0.874377i	$-0.338730\pi$
$359$	−178.166	−	245.224i	−0.496284	−	0.683076i	−0.981532	+	0.191301i	$0.938730\pi$
$360$	−1000.97	+	346.878i	−2.78046	+	0.963549i
$361$	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
$366$	822.459	+	122.085i	2.24716	+	0.333567i
$367$	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
$369$	−510.104	+	385.977i	−1.38240	+	1.04601i
$370$	−82.7822	+	60.1448i	−0.223736	+	0.162553i
$371$	−23.1717	+	31.8932i	−0.0624575	+	0.0859654i
$372$	−732.551	+	746.927i	−1.96922	+	2.00787i
$373$	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
$378$	82.2906	+	150.493i	0.217700	+	0.398130i
$379$	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
$381$	−157.064	−	78.1153i	−0.412242	−	0.205027i
$382$	68.7969	+	49.9839i	0.180097	+	0.130848i
$383$	499.215	−	162.205i	1.30343	−	0.423511i	0.426659	−	0.904413i	$-0.359691\pi$
$383$	499.215	−	162.205i	1.30343	−	0.423511i	0.876775	+	0.480901i	$0.159691\pi$
$384$	−550.229	+	287.123i	−1.43289	+	0.747717i
$385$		0			0
$386$		−	706.528i		−	1.83038i
$387$	119.363	+	36.2346i	0.308430	+	0.0936294i
$388$	−643.016	−	467.179i	−1.65726	−	1.20407i
$389$	−219.197	−	301.699i	−0.563489	−	0.775576i	0.428276	−	0.903648i	$-0.359121\pi$
$389$	−219.197	−	301.699i	−0.563489	−	0.775576i	−0.991765	+	0.128072i	$0.959121\pi$
$390$	−5.80274	+	0.976950i	−0.0148788	+	0.00250500i
$391$	7.73949	−	23.8197i	0.0197941	−	0.0609199i
$392$	400.333	+	551.011i	1.02126	+	1.40564i
$393$	−438.247	−	65.0530i	−1.11513	−	0.165529i
$394$	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
$399$	−21.0436	+	141.766i	−0.0527409	+	0.355302i
$400$	579.152	−	420.778i	1.44788	−	1.05195i
$401$	86.3473	+	28.0559i	0.215330	+	0.0699649i	0.414695	−	0.909960i	$-0.363888\pi$
$401$	86.3473	+	28.0559i	0.215330	+	0.0699649i	−0.199366	+	0.979925i	$0.563888\pi$
$402$	−177.315	−	1053.19i	−0.441083	−	2.61988i
$403$	−2.42369	+	1.76092i	−0.00601412	+	0.00436952i
$404$	270.288	−	372.020i	0.669031	−	0.920842i
$405$	395.917	+	502.637i	0.977574	+	1.24108i
$406$	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
$411$	−221.036	+	444.430i	−0.537800	+	1.08134i
$412$	−332.896	+	1024.55i	−0.808000	+	2.48677i
$413$	137.718	+	44.7474i	0.333459	+	0.108347i
$414$	4.18923	+	215.549i	0.0101189	+	0.520651i
$415$	−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	$-0.115890\pi$
$420$	−253.475	−	248.597i	−0.603513	−	0.591897i
$421$	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
$423$	−196.349	+	148.570i	−0.464182	+	0.351229i
$424$	100.037	−	307.884i	0.235937	−	0.726141i
$425$	80.4625	+	110.747i	0.189323	+	0.260581i
$426$	−71.5686	+	482.140i	−0.168001	+	1.13178i
$427$	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	$-0.359519\pi$
$431$	562.102	−	182.638i	1.30418	−	0.423754i	0.877034	+	0.480428i	$0.159519\pi$
$432$	−375.950	−	354.648i	−0.870254	−	0.820944i
$433$	−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
$435$	705.971	−	118.857i	1.62292	−	0.273236i
$436$	327.371	−	237.849i	0.750851	−	0.545526i
$437$	−105.884	+	145.737i	−0.242297	+	0.333494i
$438$	−866.057	−	849.389i	−1.97730	−	1.93924i
$439$	−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	$-0.838797\pi$
$443$	−63.3171	+	87.1485i	−0.142928	+	0.196723i	0.731551	+	0.681786i	$0.238797\pi$
$444$	−82.0591	−	40.8118i	−0.184818	−	0.0919185i
$445$	−110.705	+	340.716i	−0.248776	+	0.765653i
$446$	−413.729	−	134.429i	−0.927643	−	0.301409i
$447$	−40.8055	+	82.0463i	−0.0912874	+	0.183549i
$448$	−74.3221	−	53.9982i	−0.165898	−	0.120532i
$449$	−213.489	+	69.3667i	−0.475476	+	0.154491i	−0.536945	−	0.843618i	$-0.680422\pi$
$449$	−213.489	+	69.3667i	−0.475476	+	0.154491i	0.0614686	+	0.998109i	$0.480422\pi$
$450$	−966.582	−	673.961i	−2.14796	−	1.49769i
$451$		0			0
$452$			431.031i			0.953608i
$453$	−347.182	+	353.995i	−0.766406	+	0.781445i
$454$	−135.122	−	98.1716i	−0.297625	−	0.216237i
$455$	−0.597580	−	0.822498i	−0.00131336	−	0.00180769i
$456$	−195.395	−	1160.58i	−0.428499	−	2.54513i
$457$	−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
$459$	67.8168	−	71.8902i	0.147749	−	0.156624i
$460$	−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
$465$	−990.101	−	146.970i	−2.12925	−	0.316064i
$466$	525.094	−	381.503i	1.12681	−	0.818677i
$467$	305.347	+	99.2132i	0.653847	+	0.212448i	0.617110	−	0.786877i	$-0.288303\pi$
$467$	305.347	+	99.2132i	0.653847	+	0.212448i	0.0367376	+	0.999325i	$0.488303\pi$
$468$	−3.18014	−	4.20286i	−0.00679518	−	0.00898046i
$469$	149.282	−	108.460i	0.318299	−	0.231258i
$470$	444.704	−	612.083i	0.946180	−	1.30230i
$471$	−443.491	+	452.194i	−0.941594	+	0.960072i
$472$	−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
$477$	−195.490	+	3.79937i	−0.409831	+	0.00796513i
$478$	−379.691	+	1168.57i	−0.794332	+	2.44470i
$479$	412.015	+	133.872i	0.860157	+	0.279482i	0.705694	−	0.708517i	$-0.250635\pi$
$479$	412.015	+	133.872i	0.860157	+	0.279482i	0.154463	+	0.987999i	$0.450635\pi$
$480$	157.219	+	78.1925i	0.327540	+	0.162901i
$481$	−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
$486$	−348.953	+	775.859i	−0.718010	+	1.59642i
$487$	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
$489$	258.601	−	43.5380i	0.528836	−	0.0890349i
$490$	−390.602	+	1202.15i	−0.797147	+	2.45337i
$491$	262.378	+	361.133i	0.534375	+	0.735505i	0.987789	−	0.155795i	$-0.0497941\pi$
$491$	262.378	+	361.133i	0.534375	+	0.735505i	−0.453414	+	0.891300i	$0.649794\pi$
$492$	1741.38	+	258.489i	3.53939	+	0.525385i
$493$	−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
$498$	130.309	−	877.862i	0.261665	−	1.76278i
$499$	−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
$501$	−20.6033	−	122.376i	−0.0411243	−	0.244264i
$502$	393.714	−	286.050i	0.784292	−	0.569821i
$503$	−573.691	+	789.618i	−1.14054	+	1.56982i	−0.374242	+	0.927331i	$0.622097\pi$
$503$	−573.691	+	789.618i	−1.14054	+	1.56982i	−0.766297	+	0.642487i	$0.777903\pi$
$504$	70.6887	−	232.860i	0.140255	−	0.462024i
$505$	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	$-0.902332\pi$
$509$	−189.070	+	260.232i	−0.371454	+	0.511262i	0.581842	+	0.813302i	$0.302332\pi$
$510$	−135.231	+	271.905i	−0.265159	+	0.533147i
$511$	64.7649	−	199.326i	0.126742	−	0.390070i
$512$	950.204	+	308.740i	1.85587	+	0.603007i
$513$	−623.685	+	341.035i	−1.21576	+	0.664786i
$514$	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
$519$	443.003	+	434.477i	0.853571	+	0.837143i
$520$	6.75423	+	4.90723i	0.0129889	+	0.00943699i
$521$	−180.087	−	247.868i	−0.345656	−	0.475755i	0.600426	−	0.799680i	$-0.294998\pi$
$521$	−180.087	−	247.868i	−0.345656	−	0.475755i	−0.946083	+	0.323925i	$0.894998\pi$
$522$	574.346	+	759.052i	1.10028	+	1.45412i
$523$	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
$525$	29.8927	−	201.380i	0.0569385	−	0.383581i
$526$	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
$531$	235.170	+	678.617i	0.442881	+	1.27800i
$532$	319.101	−	231.840i	0.599814	−	0.435790i
$533$	4.79444	+	1.55781i	0.00899520	+	0.00292272i
$534$	−469.712	+	79.0808i	−0.879611	+	0.148091i
$535$	−371.549	+	269.946i	−0.694484	+	0.504572i
$536$	−890.657	+	1225.88i	−1.66167	+	2.28710i
$537$	296.198	+	290.497i	0.551579	+	0.540963i
$538$	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
$543$	−166.355	−	82.7359i	−0.306362	−	0.152368i
$544$	8.38108	−	25.7943i	0.0154064	−	0.0474160i
$545$	368.203	+	119.636i	0.675602	+	0.219516i
$546$	0.601946	−	1.21031i	0.00110246	−	0.00221669i
$547$	−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
$552$	214.175	−	218.378i	0.387998	−	0.395612i
$553$	−92.3224	−	67.0762i	−0.166948	−	0.121295i
$554$	1022.71	+	1407.64i	1.84604	+	2.54086i
$555$	−14.5576	−	86.4670i	−0.0262299	−	0.155796i
$556$	132.916	−	409.073i	0.239057	−	0.735743i
$557$	−238.714	−	328.561i	−0.428570	−	0.589876i	0.539054	−	0.842271i	$-0.318782\pi$
$557$	−238.714	−	328.561i	−0.428570	−	0.589876i	−0.967624	+	0.252395i	$0.918782\pi$
$558$	−435.771	−	1257.48i	−0.780952	−	2.25355i
$559$	−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	$-0.692397\pi$
$563$	−306.504	+	99.5891i	−0.544412	+	0.176890i	0.0238835	+	0.999715i	$0.492397\pi$
$564$	670.290	+	99.4974i	1.18846	+	0.176414i
$565$	−333.629	+	242.396i	−0.590494	+	0.429019i
$566$	−738.347	−	239.903i	−1.30450	−	0.423857i
$567$	−146.870	+	5.71104i	−0.259030	+	0.0100724i
$568$	559.473	−	406.481i	0.984988	−	0.715636i
$569$	256.283	−	352.744i	0.450410	−	0.619936i	−0.522075	−	0.852899i	$-0.674842\pi$
$569$	256.283	−	352.744i	0.450410	−	0.619936i	0.972486	+	0.232963i	$0.0748421\pi$
$570$	1529.39	−	1559.40i	2.68314	−	2.73579i
$571$	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
$576$	−8.85384	−	455.559i	−0.0153713	−	0.790900i
$577$	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
$579$	542.095	+	269.609i	0.936260	+	0.465646i
$580$	−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
$585$	1.46473	−	4.82505i	0.00250381	−	0.00824794i
$586$	1254.02	+	911.101i	2.13997	+	1.55478i
$587$	−358.686	−	493.689i	−0.611050	−	0.841038i	0.385613	−	0.922660i	$-0.373990\pi$
$587$	−358.686	−	493.689i	−0.611050	−	0.841038i	−0.996663	+	0.0816225i	$0.973990\pi$
$588$	−1116.41	+	187.960i	−1.89866	+	0.319659i
$589$	343.632	−	1057.59i	0.583416	−	1.79557i
$590$	−1297.16	−	1785.39i	−2.19858	−	3.02609i
$591$	−192.616	−	28.5918i	−0.325915	−	0.0483786i
$592$	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
$597$	−60.0229	+	404.359i	−0.100541	+	0.677319i
$598$	1.37454	−	0.998665i	0.00229857	−	0.00167001i
$599$	−1090.50	−	354.326i	−1.82054	−	0.591529i	−0.999795	−	0.0202344i	$-0.993559\pi$
$599$	−1090.50	−	354.326i	−1.82054	−	0.591529i	−0.820745	−	0.571295i	$-0.806441\pi$
$600$	277.562	+	1648.62i	0.462603	+	2.74770i
$601$	−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
$603$	875.740	+	265.846i	1.45231	+	0.440873i
$604$	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
$609$	−73.2338	+	147.249i	−0.120253	+	0.241788i
$610$	676.541	−	2082.18i	1.10908	−	3.41341i
$611$	1.84547	+	0.599630i	0.00302041	+	0.000981391i
$612$	−271.940	+	5.28518i	−0.444346	+	0.00863592i
$613$	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	$-0.920309\pi$
$617$		−	305.723i		−	0.495499i	0.968824	−	0.247749i	$-0.0796910\pi$
$618$	−978.372	−	959.542i	−1.58313	−	1.55266i
$619$	−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
$621$	−166.982	−	79.0388i	−0.268893	−	0.127277i
$622$	−126.579	+	389.572i	−0.203504	+	0.626321i
$623$	−48.3721	−	66.5785i	−0.0776438	−	0.106868i
$624$	−0.598048	+	4.02891i	−0.000958411	+	0.00645658i
$625$	−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
$630$	426.736	−	147.882i	0.677358	−	0.234734i
$631$	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
$633$	3.67413	−	0.618578i	0.00580432	−	0.000977216i
$634$	191.358	−	139.029i	0.301826	−	0.219289i
$635$	−271.491	+	373.675i	−0.427545	+	0.588465i
$636$	384.181	+	376.787i	0.604059	+	0.592433i
$637$	−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	$-0.728686\pi$
$641$	167.415	−	230.427i	0.261178	−	0.359481i	0.919387	+	0.393355i	$0.128686\pi$
$642$	−546.738	−	271.918i	−0.851616	−	0.423548i
$643$	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
$645$	146.264	−	294.090i	0.226767	−	0.455953i
$646$	−272.940	−	198.303i	−0.422509	−	0.306970i
$647$	264.676	−	85.9983i	0.409081	−	0.132919i	−0.0972452	−	0.995260i	$-0.531003\pi$
$647$	264.676	−	85.9983i	0.409081	−	0.132919i	0.506326	+	0.862342i	$0.331003\pi$
$648$	1132.55	−	417.300i	1.74777	−	0.643982i
$649$		0			0
$650$			9.28637i			0.0142867i
$651$	161.000	−	164.160i	0.247312	−	0.252166i
$652$	−583.879	−	424.213i	−0.895521	−	0.650634i
$653$	−351.286	−	483.504i	−0.537957	−	0.740435i	0.450360	−	0.892847i	$-0.351296\pi$
$653$	−351.286	−	483.504i	−0.537957	−	0.740435i	−0.988317	+	0.152412i	$0.951296\pi$
$654$	85.4608	+	507.607i	0.130674	+	0.776157i
$655$	−360.494	+	1109.49i	−0.550373	+	1.69387i
$656$	−799.686	−	1100.67i	−1.21903	−	1.67786i
$657$	982.192	−	340.372i	1.49497	−	0.518070i
$658$	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
$663$	−0.770419	−	0.114361i	−0.00116202	−	0.000172490i
$664$	−1018.67	+	740.105i	−1.53414	+	1.11462i
$665$	358.901	+	116.614i	0.539701	+	0.175360i
$666$	92.9683	−	70.3456i	0.139592	−	0.105624i
$667$	−167.229	+	121.499i	−0.250719	+	0.182158i
$668$	−200.748	+	276.306i	−0.300521	+	0.413632i
$669$	261.020	−	266.142i	0.390165	−	0.397821i
$670$	−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
$675$	885.952	−	484.444i	1.31252	−	0.717695i
$676$	431.165	−	1326.99i	0.637819	−	1.96300i
$677$	−775.510	−	251.979i	−1.14551	−	0.372199i	−0.326060	−	0.945349i	$-0.605721\pi$
$677$	−775.510	−	251.979i	−1.14551	−	0.372199i	−0.819450	+	0.573150i	$0.805721\pi$
$678$	−490.939	−	244.167i	−0.724098	−	0.360128i
$679$	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	$-0.0223662\pi$
$684$	1871.95	+	568.264i	2.73677	+	0.830795i
$685$	1057.35	+	768.213i	1.54358	+	1.12148i
$686$	−353.638	−	486.741i	−0.515508	−	0.709535i
$687$	216.574	−	36.4625i	0.315246	−	0.0530749i
$688$	−81.9849	+	252.323i	−0.119164	+	0.366749i
$689$	0.905725	+	1.24662i	0.00131455	+	0.00180932i
$690$	561.514	+	83.3508i	0.813789	+	0.120798i
$691$	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
$696$	198.292	−	1335.84i	0.284902	−	1.91931i
$697$	210.474	−	152.918i	0.301971	−	0.219395i
$698$	1505.08	+	489.029i	2.15627	+	0.700615i
$699$	92.3401	+	548.468i	0.132103	+	0.784646i
$700$	−453.287	+	329.332i	−0.647552	+	0.470474i
$701$	−437.413	+	602.048i	−0.623985	+	0.858841i	−0.997635	−	0.0687283i	$-0.978106\pi$
$701$	−437.413	+	602.048i	−0.623985	+	0.858841i	0.373651	+	0.927569i	$0.378106\pi$
$702$	6.58846	−	1.24134i	0.00938528	−	0.00176830i
$703$	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
$708$	880.202	−	1769.80i	1.24322	−	2.49971i
$709$	−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
$711$	−10.9982	−	565.892i	−0.0154686	−	0.795910i
$712$	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
$717$	−751.714	−	737.246i	−1.04842	−	1.02824i
$718$	−858.508	−	623.742i	−1.19569	−	0.868722i
$719$	287.294	+	395.426i	0.399574	+	0.549967i	0.960637	−	0.277806i	$-0.0896074\pi$
$719$	287.294	+	395.426i	0.399574	+	0.549967i	−0.561063	+	0.827773i	$0.689607\pi$
$720$	−1085.21	+	821.134i	−1.50723	+	1.14046i
$721$	73.1640	−	225.176i	0.101476	−	0.312310i
$722$	683.441	+	940.676i	0.946594	+	1.30288i
$723$	77.3096	−	520.816i	0.106929	−	0.720355i
$724$	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
$729$	−462.131	−	563.805i	−0.633924	−	0.773395i
$730$	−2584.07	+	1877.44i	−3.53983	+	2.57184i
$731$	−48.2500	−	15.6774i	−0.0660055	−	0.0214465i
$732$	1933.68	−	325.555i	2.64164	−	0.444747i
$733$	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
$735$	−773.316	−	758.432i	−1.05213	−	1.03188i
$736$	−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
$741$	5.01588	+	2.49463i	0.00676907	+	0.00336657i
$742$	−42.6484	+	131.258i	−0.0574776	+	0.176898i
$743$	690.050	+	224.211i	0.928734	+	0.301764i	0.734045	−	0.679101i	$-0.237630\pi$
$743$	690.050	+	224.211i	0.928734	+	0.301764i	0.194689	+	0.980865i	$0.437630\pi$
$744$	−840.829	+	1690.63i	−1.13015	+	2.27235i
$745$	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
$750$	−720.229	+	734.362i	−0.960305	+	0.979150i
$751$	−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
$753$	69.2364	+	411.240i	0.0919474	+	0.546135i
$754$	2.31807	−	7.13429i	0.00307437	−	0.00946192i
$755$	767.390	+	1056.22i	1.01641	+	1.39897i
$756$	294.246	+	277.573i	0.389214	+	0.367160i
$757$	−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	−0.380993	−	0.924578i	$-0.624418\pi$
$761$	−110.930	+	36.0434i	−0.145769	+	0.0473632i	0.235224	+	0.971941i	$0.424418\pi$
$762$	−607.463	−	90.1714i	−0.797195	−	0.118335i
$763$	−71.9498	+	52.2746i	−0.0942985	+	0.0685119i
$764$	190.733	+	61.9728i	0.249650	+	0.0811162i
$765$	−157.020	−	207.516i	−0.205254	−	0.271263i
$766$	1486.69	−	1080.14i	1.94084	−	1.41011i
$767$	3.32692	−	4.57911i	0.00433758	−	0.00597016i
$768$	−1096.01	+	1117.51i	−1.42709	+	1.45510i
$769$	−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	$-0.527311\pi$
$773$	686.689	−	945.147i	0.888343	−	1.22270i	0.974039	−	0.226378i	$-0.0726885\pi$
$774$	436.625	−	8.48586i	0.564115	−	0.0109636i
$775$	−488.133	+	1502.32i	−0.629849	+	1.93848i
$776$	−1364.27	−	443.278i	−1.75808	−	0.571234i
$777$	18.0350	+	8.96963i	0.0232110	+	0.0115439i
$778$	−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
$783$	−801.564	+	151.024i	−1.02371	+	0.192879i
$784$	707.827	+	514.266i	0.902841	+	0.655952i
$785$	980.267	+	1349.22i	1.24875	+	1.71875i
$786$	−1529.55	+	257.515i	−1.94599	+	0.327627i
$787$	−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
$789$	−598.359	−	88.8200i	−0.758376	−	0.112573i
$790$	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
$795$	−75.5939	+	509.258i	−0.0950867	+	0.640576i
$796$	910.174	−	661.280i	1.14344	−	0.830754i
$797$	−61.7682	−	20.0697i	−0.0775009	−	0.0251816i	0.270010	−	0.962858i	$-0.412973\pi$
$797$	−61.7682	−	20.0697i	−0.0775009	−	0.0251816i	−0.347511	+	0.937676i	$0.612973\pi$
$798$	83.3018	+	494.783i	0.104388	+	0.620029i
$799$	81.0155	−	58.8612i	0.101396	−	0.0736686i
$800$	162.878	−	224.183i	0.203598	−	0.280228i
$801$	118.565	−	390.571i	0.148021	−	0.487605i
$802$	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
$807$	−458.293	+	921.477i	−0.567897	+	1.14185i
$808$	256.461	−	789.304i	0.317402	−	0.976862i
$809$	−610.865	−	198.482i	−0.755087	−	0.245343i	−0.0939183	−	0.995580i	$-0.529939\pi$
$809$	−610.865	−	198.482i	−0.755087	−	0.245343i	−0.661169	+	0.750237i	$0.729939\pi$
$810$	1862.00	+	1245.24i	2.29877	+	1.53733i
$811$	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
$816$	150.070	+	147.181i	0.183909	+	0.180369i
$817$	295.210	+	214.482i	0.361334	+	0.262524i
$818$	−1131.62	−	1557.54i	−1.38340	−	1.90409i
$819$	0.698933	+	0.923705i	0.000853398	+	0.00112785i
$820$	1432.43	−	4408.56i	1.74687	−	5.37630i
$821$	−532.043	−	732.295i	−0.648043	−	0.891955i	0.350969	−	0.936387i	$-0.385852\pi$
$821$	−532.043	−	732.295i	−0.648043	−	0.891955i	−0.999012	+	0.0444321i	$0.985852\pi$
$822$	−255.150	+	1718.88i	−0.310401	+	2.09110i
$823$	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	0.264156	−	0.964480i	$-0.414907\pi$
$827$	864.024	−	280.738i	1.04477	−	0.339466i	0.780613	+	0.625014i	$0.214907\pi$
$828$	166.482	+	480.407i	0.201065	+	0.580202i
$829$	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
$831$	−1470.29	+	247.539i	−1.76931	+	0.297881i
$832$	−2.90507	+	2.11065i	−0.00349167	+	0.00253684i
$833$	−98.3395	+	135.353i	−0.118055	+	0.162488i
$834$	390.636	+	383.118i	0.468389	+	0.459374i
$835$	−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	$-0.591092\pi$
$839$	601.835	−	828.355i	0.717325	−	0.987313i	0.999608	−	0.0279817i	$-0.00890801\pi$
$840$	−573.729	−	285.342i	−0.683010	−	0.339693i
$841$	−22.1373	+	68.1317i	−0.0263226	+	0.0810127i
$842$	408.204	+	132.634i	0.484803	+	0.157522i
$843$	517.015	−	1039.55i	0.613304	−	1.23315i
$844$	−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
$849$	465.821	−	474.962i	0.548670	−	0.559437i
$850$	387.715	+	281.692i	0.456136	+	0.331402i
$851$	14.8812	+	20.4822i	0.0174867	+	0.0240684i
$852$	190.846	+	1133.56i	0.223998	+	1.33047i
$853$	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
$855$	612.865	+	1768.51i	0.716801	+	2.06843i
$856$	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
$861$	−382.721	−	56.8108i	−0.444507	−	0.0659824i
$862$	1673.97	−	1216.21i	1.94196	−	1.41091i
$863$	442.630	+	143.819i	0.512897	+	0.166650i	0.554019	−	0.832504i	$-0.313093\pi$
$863$	442.630	+	143.819i	0.512897	+	0.166650i	−0.0411222	+	0.999154i	$0.513093\pi$
$864$	−180.825	−	85.5909i	−0.209288	−	0.0990636i
$865$	1321.80	−	960.343i	1.52809	−	1.11022i
$866$	−1321.78	+	1819.28i	−1.52631	+	2.10078i
$867$	578.932	−	590.292i	0.667741	−	0.680845i
$868$	−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
$873$	16.8354	+	866.237i	0.0192846	+	0.992254i
$874$	−194.883	+	599.789i	−0.222979	+	0.686257i
$875$	−169.016	−	54.9166i	−0.193161	−	0.0627618i
$876$	−2561.51	−	1273.96i	−2.92409	−	1.45429i
$877$	−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	$-0.888096\pi$
$881$		−	606.759i		−	0.688717i	0.938838	−	0.344358i	$-0.111904\pi$
$882$	418.333	−	1378.06i	0.474300	−	1.56242i
$883$	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
$885$	1864.86	−	313.969i	2.10719	−	0.354767i
$886$	−116.537	+	358.665i	−0.131532	+	0.404814i
$887$	6.70027	+	9.22213i	0.00755386	+	0.0103970i	0.812777	−	0.582575i	$-0.197955\pi$
$887$	6.70027	+	9.22213i	0.00755386	+	0.0103970i	−0.805223	+	0.592972i	$0.797955\pi$
$888$	−163.613	−	24.2866i	−0.184249	−	0.0273498i
$889$	−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
$894$	−47.1032	+	317.323i	−0.0526882	+	0.354948i
$895$	883.772	−	642.098i	0.987454	−	0.717428i
$896$	−357.026	−	116.005i	−0.398467	−	0.129470i
$897$	0.241720	+	1.43573i	0.000269475	+	0.00160059i
$898$	−635.780	+	461.921i	−0.707995	+	0.514389i
$899$	750.020	−	1032.31i	0.834283	−	1.14829i
$900$	−2659.13	−	807.225i	−2.95459	−	0.896917i
$901$	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
$906$	−772.997	+	1554.24i	−0.853197	+	1.71550i
$907$	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
$909$	−501.166	+	9.74022i	−0.551337	+	0.0107153i
$910$	−2.87949	−	2.09207i	−0.00316427	−	0.00229898i
$911$	575.802	−	187.089i	0.632055	−	0.205367i	0.0245695	−	0.999698i	$-0.492178\pi$
$911$	575.802	−	187.089i	0.632055	−	0.205367i	0.607485	+	0.794331i	$0.292178\pi$
$912$	−699.425	−	1340.34i	−0.766914	−	1.46967i
$913$		0			0
$914$			249.573i			0.273056i
$915$	1339.42	+	1313.64i	1.46385	+	1.43567i
$916$	−488.990	−	355.272i	−0.533832	−	0.387852i
$917$	−157.516	−	216.803i	−0.171773	−	0.236426i
$918$	148.026	−	312.730i	0.161249	−	0.340664i
$919$	−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
$921$	143.118	−	964.153i	0.155394	−	1.04685i
$922$	−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
$927$	1109.57	−	384.513i	1.19695	−	0.414793i
$928$	−181.092	+	131.571i	−0.195143	+	0.141780i
$929$	−1589.96	−	516.611i	−1.71148	−	0.556093i	−0.720900	−	0.693039i	$-0.756271\pi$
$929$	−1589.96	−	516.611i	−1.71148	−	0.556093i	−0.990579	+	0.136946i	$0.956271\pi$
$930$	−3455.60	+	581.785i	−3.71570	+	0.625576i
$931$	973.529	−	707.310i	1.04568	−	0.759732i
$932$	899.717	−	1238.35i	0.965361	−	1.32871i
$933$	−250.603	−	245.780i	−0.268599	−	0.263429i
$934$	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
$939$	−392.378	−	195.148i	−0.417868	−	0.207825i
$940$	551.369	−	1696.94i	0.586563	−	1.80526i
$941$	335.079	+	108.874i	0.356088	+	0.115700i	0.481598	−	0.876392i	$-0.340057\pi$
$941$	335.079	+	108.874i	0.356088	+	0.115700i	−0.125510	+	0.992092i	$0.540057\pi$
$942$	−987.428	+	1985.39i	−1.04823	+	2.10764i
$943$	−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	$0.698877\pi$
$948$	−1090.70	+	1112.11i	−1.15053	+	1.17311i
$949$	−6.62755	−	4.81520i	−0.00698372	−	0.00507397i
$950$	−2026.08	−	2788.65i	−2.13271	−	2.93543i
$951$	33.6511	+	199.875i	0.0353849	+	0.210174i
$952$	−30.5844	+	94.1292i	−0.0321265	+	0.0988752i
$953$	527.449	+	725.972i	0.553462	+	0.761775i	0.990477	−	0.137679i	$-0.0439643\pi$
$953$	527.449	+	725.972i	0.553462	+	0.761775i	−0.437015	+	0.899454i	$0.643964\pi$
$954$	−646.784	+	224.139i	−0.677971	+	0.234946i
$955$	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
$960$	−1186.75	−	176.160i	−1.23620	−	0.183500i
$961$	−665.871	+	483.784i	−0.692894	+	0.503417i
$962$	−0.873804	−	0.283916i	−0.000908320	−	0.000295131i
$963$	417.267	−	315.730i	0.433299	−	0.327861i
$964$	−1172.31	+	851.731i	−1.21609	+	0.883539i
$965$	937.030	−	1289.71i	0.971015	−	1.33649i
$966$	−91.3079	+	93.0997i	−0.0945216	+	0.0963765i
$967$	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	$-0.519382\pi$
$971$	880.936	−	1212.50i	0.907246	−	1.24872i	0.968099	−	0.250570i	$-0.0806180\pi$
$972$	−217.252	+	1994.49i	−0.223510	+	2.05195i
$973$	−29.2123	+	89.9063i	−0.0300229	+	0.0924011i
$974$	1173.86	+	381.410i	1.20519	+	0.391591i
$975$	−7.12512	−	3.54365i	−0.00730781	−	0.00363451i
$976$	−1225.99	−	890.734i	−1.25614	−	0.912638i
$977$	−53.6767	+	17.4406i	−0.0549404	+	0.0178512i	−0.336358	−	0.941734i	$-0.609195\pi$
$977$	−53.6767	+	17.4406i	−0.0549404	+	0.0178512i	0.281418	+	0.959585i	$0.409195\pi$
$978$	813.925	−	424.727i	0.832234	−	0.434281i
$979$		0			0
$980$			2980.98i			3.04182i
$981$	−422.081	−	128.130i	−0.430256	−	0.130612i
$982$	1264.29	+	918.562i	1.28747	+	0.935399i
$983$	27.9524	+	38.4732i	0.0284358	+	0.0391385i	0.822998	−	0.568044i	$-0.192300\pi$
$983$	27.9524	+	38.4732i	0.0284358	+	0.0391385i	−0.794562	+	0.607183i	$0.792300\pi$
$984$	3133.19	−	527.504i	3.18413	−	0.536081i
$985$	−158.443	+	487.636i	−0.160855	+	0.495062i
$986$	−227.548	−	313.192i	−0.230779	−	0.317639i
$987$	−147.317	−	21.8676i	−0.149257	−	0.0221556i
$988$	−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
$993$	−133.674	+	900.529i	−0.134616	+	0.906877i
$994$	−238.517	+	173.293i	−0.239957	+	0.174339i
$995$	1023.70	+	332.619i	1.02884	+	0.334291i
$996$	−347.485	−	2063.94i	−0.348881	−	2.07223i
$997$	−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
$999$	18.4974	+	98.1751i	0.0185159	+	0.0982734i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.j.122.1	✓	6	11.3	even	5
363.3.b.j.122.6	yes	6	33.14	odd	10
363.3.b.k.122.1	yes	6	33.8	even	10
363.3.b.k.122.6	yes	6	11.8	odd	10
363.3.h.p.245.1		24	11.7	odd	10
363.3.h.p.245.6		24	33.29	even	10
363.3.h.p.251.1		24	33.2	even	10
363.3.h.p.251.6		24	11.2	odd	10
363.3.h.p.269.1		24	11.10	odd	2
363.3.h.p.269.6		24	33.32	even	2
363.3.h.p.323.1		24	33.17	even	10
363.3.h.p.323.6		24	11.6	odd	10
363.3.h.q.245.1		24	33.26	odd	10	inner
363.3.h.q.245.6		24	11.4	even	5	inner
363.3.h.q.251.1		24	11.9	even	5	inner
363.3.h.q.251.6		24	33.20	odd	10	inner
363.3.h.q.269.1		24	3.2	odd	2	inner
363.3.h.q.269.6		24	1.1	even	1	trivial
363.3.h.q.323.1		24	11.5	even	5	inner
363.3.h.q.323.6		24	33.5	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} +(-0.440492 + 2.96748i) q^{3} +(6.67952 - 4.85296i) q^{4} +(7.51264 + 2.44100i) q^{5} +(1.74370 + 10.3570i) q^{6} +(-1.46803 + 1.06658i) q^{7} +(8.75863 - 12.0552i) q^{8} +(-8.61193 - 2.61430i) q^{9} +27.6545 q^{10} +(11.4588 + 21.9591i) q^{12} +(0.0219178 + 0.0674561i) q^{13} +(-3.73401 + 5.13943i) q^{14} +(-10.5529 + 21.2184i) q^{15} +(5.91516 - 18.2050i) q^{16} +(3.48121 + 1.13111i) q^{17} +(-31.5022 + 0.612250i) q^{18} +(-21.2992 - 15.4748i) q^{19} +(62.0269 - 20.1538i) q^{20} +(-2.51842 - 4.82617i) q^{21} -6.84236i q^{23} +(31.9156 + 31.3013i) q^{24} +(30.2558 + 21.9821i) q^{25} +(0.145953 + 0.200887i) q^{26} +(11.5514 - 24.4042i) q^{27} +(-4.62964 + 14.2486i) q^{28} +(-17.7569 - 24.4403i) q^{29} +(-12.1816 + 82.0644i) q^{30} +(13.0523 + 40.1709i) q^{31} -7.40958i q^{32} +12.8146 q^{34} +(-13.6323 + 4.42940i) q^{35} +(-70.2107 + 24.3311i) q^{36} +(-2.99344 + 2.17486i) q^{37} +(-87.6582 - 28.4819i) q^{38} +(-0.209829 + 0.0353269i) q^{39} +(95.2272 - 69.1866i) q^{40} +(41.7768 - 57.5009i) q^{41} +(-13.6064 - 13.3445i) q^{42} -13.8601 q^{43} +(-58.3168 - 40.6621i) q^{45} +(-7.40233 - 22.7820i) q^{46} +(16.0807 - 22.1332i) q^{47} +(51.4174 + 25.5723i) q^{48} +(-14.1243 + 43.4702i) q^{49} +(124.520 + 40.4589i) q^{50} +(-4.89001 + 9.83219i) q^{51} +(0.473762 + 0.344208i) q^{52} +(20.6619 - 6.71345i) q^{53} +(12.0596 - 93.7520i) q^{54} +27.0392i q^{56} +(55.3033 - 56.3886i) q^{57} +(-85.5633 - 62.1654i) q^{58} +(-46.9059 - 64.5605i) q^{59} +(32.4837 + 192.942i) q^{60} +(24.4640 - 75.2925i) q^{61} +(86.9169 + 119.631i) q^{62} +(15.4309 - 5.34749i) q^{63} +(15.6447 + 48.1493i) q^{64} +0.560274i q^{65} -101.689 q^{67} +(28.7421 - 9.33887i) q^{68} +(20.3046 + 3.01400i) q^{69} +(-40.5976 + 29.4959i) q^{70} +(44.1378 + 14.3412i) q^{71} +(-106.945 + 80.9210i) q^{72} +(-93.4412 + 67.8890i) q^{73} +(-7.61398 + 10.4797i) q^{74} +(-78.5590 + 80.1006i) q^{75} -217.367 q^{76} +(-0.660422 + 0.344625i) q^{78} +(19.4337 + 59.8107i) q^{79} +(88.8769 - 122.329i) q^{80} +(67.3308 + 45.0284i) q^{81} +(76.8918 - 236.649i) q^{82} +(-80.3644 - 26.1120i) q^{83} +(-40.2431 - 20.0147i) q^{84} +(23.3920 + 16.9953i) q^{85} +(-46.1481 + 14.9944i) q^{86} +(80.3481 - 41.9277i) q^{87} +45.3523i q^{89} +(-238.159 - 72.2974i) q^{90} +(-0.104124 - 0.0756502i) q^{91} +(-33.2057 - 45.7037i) q^{92} +(-124.956 + 21.0376i) q^{93} +(29.5971 - 91.0905i) q^{94} +(-122.239 - 168.248i) q^{95} +(21.9878 + 3.26386i) 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

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