LMFDB - Embedded newform 220.3.w.a.7.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,3,Mod(7,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 5, 14])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.18
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.48321 + 1.34167i) q^{2} +(2.40882 - 1.22736i) q^{3} +(0.399834 - 3.97997i) q^{4} +(-4.64336 - 1.85452i) q^{5} +(-1.92608 + 5.05228i) q^{6} +(-0.118689 + 0.232940i) q^{7} +(4.74677 + 6.43958i) q^{8} +(-0.994045 + 1.36819i) q^{9} +(9.37524 - 3.47922i) q^{10} +(6.29422 - 9.02124i) q^{11} +(-3.92171 - 10.0778i) q^{12} +(-0.636813 - 4.02068i) q^{13} +(-0.136488 - 0.504740i) q^{14} +(-13.4612 + 1.23185i) q^{15} +(-15.6803 - 3.18265i) q^{16} +(4.69785 - 29.6611i) q^{17} +(-0.361277 - 3.36299i) q^{18} +(-22.0109 - 7.15178i) q^{19} +(-9.23749 + 17.7389i) q^{20} +0.706783i q^{21} +(2.76788 + 21.8252i) q^{22} +(-25.1629 - 25.1629i) q^{23} +(19.3378 + 9.68582i) q^{24} +(18.1215 + 17.2224i) q^{25} +(6.33896 + 5.10912i) q^{26} +(-4.52149 + 28.5476i) q^{27} +(0.879636 + 0.565514i) q^{28} +(-14.7711 - 45.4607i) q^{29} +(18.3130 - 19.8876i) q^{30} +(-15.0900 + 20.7696i) q^{31} +(27.5272 - 16.3172i) q^{32} +(4.08939 - 29.4558i) q^{33} +(32.8275 + 50.2966i) q^{34} +(0.983104 - 0.861511i) q^{35} +(5.04788 + 4.50331i) q^{36} +(16.1966 - 31.7877i) q^{37} +(42.2422 - 18.9238i) q^{38} +(-6.46877 - 8.90350i) q^{39} +(-10.0986 - 38.7042i) q^{40} +(49.9808 + 16.2397i) q^{41} +(-0.948271 - 1.04831i) q^{42} +(4.30965 - 4.30965i) q^{43} +(-33.3876 - 28.6578i) q^{44} +(7.15303 - 4.50950i) q^{45} +(71.0824 + 3.56156i) q^{46} +(1.77867 + 3.49084i) q^{47} +(-41.6772 + 11.5788i) q^{48} +(28.7613 + 39.5865i) q^{49} +(-49.9848 - 1.23130i) q^{50} +(-25.0884 - 77.2142i) q^{51} +(-16.2568 + 0.926890i) q^{52} +(-39.3423 + 6.23122i) q^{53} +(-31.5951 - 48.4084i) q^{54} +(-45.9564 + 30.2161i) q^{55} +(-2.06342 + 0.341406i) q^{56} +(-61.7982 + 9.78787i) q^{57} +(82.9019 + 47.6099i) q^{58} +(11.9586 + 36.8047i) q^{59} +(-0.479522 + 54.0676i) q^{60} +(50.3282 + 69.2708i) q^{61} +(-5.48431 - 51.0514i) q^{62} +(-0.200723 - 0.393940i) q^{63} +(-18.9363 + 61.1344i) q^{64} +(-4.49947 + 19.8504i) q^{65} +(33.4546 + 49.1758i) q^{66} +(45.0546 - 45.0546i) q^{67} +(-116.172 - 30.5568i) q^{68} +(-91.4969 - 29.7292i) q^{69} +(-0.302287 + 2.59681i) q^{70} +(32.7548 + 45.0831i) q^{71} +(-13.5290 + 0.0932312i) q^{72} +(4.51537 - 8.86192i) q^{73} +(18.6256 + 68.8785i) q^{74} +(64.7895 + 19.2441i) q^{75} +(-37.2646 + 84.7432i) q^{76} +(1.35435 + 2.53689i) q^{77} +(21.5401 + 4.52681i) q^{78} +(-61.1887 + 84.2190i) q^{79} +(66.9068 + 43.8575i) q^{80} +(19.4432 + 59.8399i) q^{81} +(-95.9205 + 42.9708i) q^{82} +(14.1953 - 89.6254i) q^{83} +(2.81297 + 0.282596i) q^{84} +(-76.8208 + 129.015i) q^{85} +(-0.609987 + 12.1743i) q^{86} +(-91.3773 - 91.3773i) q^{87} +(87.9702 - 2.28961i) q^{88} +15.7814i q^{89} +(-4.55919 + 16.2856i) q^{90} +(1.01216 + 0.328870i) q^{91} +(-110.209 + 90.0866i) q^{92} +(-10.8574 + 68.5509i) q^{93} +(-7.32171 - 2.79126i) q^{94} +(88.9414 + 74.0279i) q^{95} +(46.2812 - 73.0910i) q^{96} +(-22.3539 - 141.137i) q^{97} +(-95.7712 - 20.1270i) q^{98} +(6.08599 + 17.5792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.48321	+	1.34167i	−0.741606	+	0.670836i
$2$	−1.48321	+	1.34167i	−0.741606	+	0.670836i
$3$	2.40882	−	1.22736i	0.802941	−	0.409119i	−0.00382307	−	0.999993i	$-0.501217\pi$
$3$	2.40882	−	1.22736i	0.802941	−	0.409119i	0.806764	+	0.590874i	$0.201217\pi$
$4$	0.399834	−	3.97997i	0.0999585	−	0.994992i
$5$	−4.64336	−	1.85452i	−0.928671	−	0.370904i
$5$	−4.64336	−	1.85452i	−0.928671	−	0.370904i
$6$	−1.92608	+	5.05228i	−0.321014	+	0.842046i
$7$	−0.118689	+	0.232940i	−0.0169555	+	0.0332771i	−0.899329	−	0.437273i	$-0.855944\pi$
$7$	−0.118689	+	0.232940i	−0.0169555	+	0.0332771i	0.882373	+	0.470550i	$0.155944\pi$
$8$	4.74677	+	6.43958i	0.593346	+	0.804947i
$9$	−0.994045	+	1.36819i	−0.110449	+	0.152021i
$10$	9.37524	−	3.47922i	0.937524	−	0.347922i
$11$	6.29422	−	9.02124i	0.572202	−	0.820113i
$11$	6.29422	−	9.02124i	0.572202	−	0.820113i
$12$	−3.92171	−	10.0778i	−0.326809	−	0.839814i
$13$	−0.636813	−	4.02068i	−0.0489856	−	0.309283i	−1.00000		0.000136283i	$-0.999957\pi$
$13$	−0.636813	−	4.02068i	−0.0489856	−	0.309283i	0.951014	−	0.309147i	$-0.100043\pi$
$14$	−0.136488	−	0.504740i	−0.00974915	−	0.0360529i
$15$	−13.4612	+	1.23185i	−0.897412	+	0.0821232i
$16$	−15.6803	−	3.18265i	−0.980017	−	0.198916i
$17$	4.69785	−	29.6611i	0.276344	−	1.74477i	−0.324941	−	0.945734i	$-0.605344\pi$
$17$	4.69785	−	29.6611i	0.276344	−	1.74477i	0.601285	−	0.799035i	$-0.294656\pi$
$18$	−0.361277	−	3.36299i	−0.0200709	−	0.186833i
$19$	−22.0109	−	7.15178i	−1.15847	−	0.376410i	−0.334142	−	0.942523i	$-0.608446\pi$
$19$	−22.0109	−	7.15178i	−1.15847	−	0.376410i	−0.824327	+	0.566113i	$0.808446\pi$
$20$	−9.23749	+	17.7389i	−0.461875	+	0.886945i
$21$			0.706783i			0.0336564i
$22$	2.76788	+	21.8252i	0.125813	+	0.992054i
$23$	−25.1629	−	25.1629i	−1.09404	−	1.09404i	−0.995093	−	0.0989481i	$-0.968452\pi$
$23$	−25.1629	−	25.1629i	−1.09404	−	1.09404i	−0.0989481	−	0.995093i	$-0.531548\pi$
$24$	19.3378	+	9.68582i	0.805741	+	0.403576i
$25$	18.1215	+	17.2224i	0.724861	+	0.688895i
$26$	6.33896	+	5.10912i	0.243806	+	0.196505i
$27$	−4.52149	+	28.5476i	−0.167463	+	1.05732i
$28$	0.879636	+	0.565514i	0.0314156	+	0.0201969i
$29$	−14.7711	−	45.4607i	−0.509347	−	1.56761i	−0.793337	−	0.608782i	$-0.791658\pi$
$29$	−14.7711	−	45.4607i	−0.509347	−	1.56761i	0.283990	−	0.958827i	$-0.408342\pi$
$30$	18.3130	−	19.8876i	0.610435	−	0.662919i
$31$	−15.0900	+	20.7696i	−0.486773	+	0.669986i	−0.979789	−	0.200035i	$-0.935894\pi$
$31$	−15.0900	+	20.7696i	−0.486773	+	0.669986i	0.493016	+	0.870020i	$0.335894\pi$
$32$	27.5272	−	16.3172i	0.860226	−	0.509913i
$33$	4.08939	−	29.4558i	0.123921	−	0.892601i
$34$	32.8275	+	50.2966i	0.965515	+	1.47931i
$35$	0.983104	−	0.861511i	0.0280887	−	0.0246146i
$36$	5.04788	+	4.50331i	0.140219	+	0.125092i
$37$	16.1966	−	31.7877i	0.437747	−	0.859127i	−0.561746	−	0.827309i	$-0.689870\pi$
$37$	16.1966	−	31.7877i	0.437747	−	0.859127i	0.999494	−	0.0318179i	$-0.0101297\pi$
$38$	42.2422	−	18.9238i	1.11164	−	0.497995i
$39$	−6.46877	−	8.90350i	−0.165866	−	0.228295i
$40$	−10.0986	−	38.7042i	−0.252466	−	0.967606i
$41$	49.9808	+	16.2397i	1.21904	+	0.396091i	0.846733	−	0.532017i	$-0.178566\pi$
$41$	49.9808	+	16.2397i	1.21904	+	0.396091i	0.372310	+	0.928108i	$0.378566\pi$
$42$	−0.948271	−	1.04831i	−0.0225779	−	0.0249597i
$43$	4.30965	−	4.30965i	0.100224	−	0.100224i	−0.655217	−	0.755441i	$-0.727423\pi$
$43$	4.30965	−	4.30965i	0.100224	−	0.100224i	0.755441	+	0.655217i	$0.227423\pi$
$44$	−33.3876	−	28.6578i	−0.758809	−	0.651313i
$45$	7.15303	−	4.50950i	0.158956	−	0.100211i
$46$	71.0824	+	3.56156i	1.54527	+	0.0774253i
$47$	1.77867	+	3.49084i	0.0378441	+	0.0742732i	0.909154	−	0.416459i	$-0.136729\pi$
$47$	1.77867	+	3.49084i	0.0378441	+	0.0742732i	−0.871310	+	0.490733i	$0.836729\pi$
$48$	−41.6772	+	11.5788i	−0.868276	+	0.241226i
$49$	28.7613	+	39.5865i	0.586965	+	0.807889i
$50$	−49.9848	−	1.23130i	−0.999697	−	0.0246260i
$51$	−25.0884	−	77.2142i	−0.491930	−	1.51400i
$52$	−16.2568	+	0.926890i	−0.312630	+	0.0178248i
$53$	−39.3423	+	6.23122i	−0.742308	+	0.117570i	−0.516123	−	0.856514i	$-0.672625\pi$
$53$	−39.3423	+	6.23122i	−0.742308	+	0.117570i	−0.226185	+	0.974084i	$0.572625\pi$
$54$	−31.5951	−	48.4084i	−0.585095	−	0.896453i
$55$	−45.9564	+	30.2161i	−0.835570	+	0.549383i
$56$	−2.06342	+	0.341406i	−0.0368468	+	0.00609653i
$57$	−61.7982	+	9.78787i	−1.08418	+	0.171717i
$58$	82.9019	+	47.6099i	1.42934	+	0.820860i
$59$	11.9586	+	36.8047i	0.202688	+	0.623809i	0.999800	+	0.0199783i	$0.00635972\pi$
$59$	11.9586	+	36.8047i	0.202688	+	0.623809i	−0.797113	+	0.603831i	$0.793640\pi$
$60$	−0.479522	+	54.0676i	−0.00799204	+	0.901126i
$61$	50.3282	+	69.2708i	0.825052	+	1.13559i	0.988824	+	0.149089i	$0.0476340\pi$
$61$	50.3282	+	69.2708i	0.825052	+	1.13559i	−0.163772	+	0.986498i	$0.552366\pi$
$62$	−5.48431	−	51.0514i	−0.0884566	−	0.823410i
$63$	−0.200723	−	0.393940i	−0.00318607	−	0.00625302i
$64$	−18.9363	+	61.1344i	−0.295880	+	0.955225i
$65$	−4.49947	+	19.8504i	−0.0692226	+	0.305391i
$66$	33.4546	+	49.1758i	0.506888	+	0.745088i
$67$	45.0546	−	45.0546i	0.672457	−	0.672457i	−0.285825	−	0.958282i	$-0.592268\pi$
$67$	45.0546	−	45.0546i	0.672457	−	0.672457i	0.958282	+	0.285825i	$0.0922676\pi$
$68$	−116.172	−	30.5568i	−1.70841	−	0.449365i
$69$	−91.4969	−	29.7292i	−1.32604	−	0.430857i
$70$	−0.302287	+	2.59681i	−0.00431838	+	0.0370972i
$71$	32.7548	+	45.0831i	0.461335	+	0.634974i	0.974785	−	0.223146i	$-0.0716327\pi$
$71$	32.7548	+	45.0831i	0.461335	+	0.634974i	−0.513450	+	0.858120i	$0.671633\pi$
$72$	−13.5290	+	0.0932312i	−0.187903	+	0.00129488i
$73$	4.51537	−	8.86192i	0.0618544	−	0.121396i	−0.858009	−	0.513634i	$-0.828299\pi$
$73$	4.51537	−	8.86192i	0.0618544	−	0.121396i	0.919864	+	0.392238i	$0.128299\pi$
$74$	18.6256	+	68.8785i	0.251698	+	0.930790i
$75$	64.7895	+	19.2441i	0.863860	+	0.256588i
$76$	−37.2646	+	84.7432i	−0.490323	+	1.11504i
$77$	1.35435	+	2.53689i	0.0175890	+	0.0329467i
$78$	21.5401	+	4.52681i	0.276156	+	0.0580360i
$79$	−61.1887	+	84.2190i	−0.774540	+	1.06606i	0.221323	+	0.975201i	$0.428963\pi$
$79$	−61.1887	+	84.2190i	−0.774540	+	1.06606i	−0.995863	+	0.0908629i	$0.971037\pi$
$80$	66.9068	+	43.8575i	0.836335	+	0.548219i
$81$	19.4432	+	59.8399i	0.240039	+	0.738764i
$82$	−95.9205	+	42.9708i	−1.16976	+	0.524034i
$83$	14.1953	−	89.6254i	0.171027	−	1.07982i	−0.741543	−	0.670905i	$-0.765906\pi$
$83$	14.1953	−	89.6254i	0.171027	−	1.07982i	0.912571	−	0.408919i	$-0.134094\pi$
$84$	2.81297	+	0.282596i	0.0334878	+	0.00336424i
$85$	−76.8208	+	129.015i	−0.903774	+	1.51782i
$86$	−0.609987	+	12.1743i	−0.00709288	+	0.141561i
$87$	−91.3773	−	91.3773i	−1.05031	−	1.05031i
$88$	87.9702	−	2.28961i	0.999661	−	0.0260183i
$89$			15.7814i			0.177319i	0.996062	+	0.0886595i	$0.0282583\pi$
$89$			15.7814i			0.177319i	−0.996062	+	0.0886595i	$0.971742\pi$
$90$	−4.55919	+	16.2856i	−0.0506577	+	0.180951i
$91$	1.01216	+	0.328870i	0.0111226	+	0.00361395i
$92$	−110.209	+	90.0866i	−1.19792	+	0.979203i
$93$	−10.8574	+	68.5509i	−0.116746	+	0.737107i
$94$	−7.32171	−	2.79126i	−0.0778905	−	0.0296943i
$95$	88.9414	+	74.0279i	0.936226	+	0.779241i
$96$	46.2812	−	73.0910i	0.482095	−	0.761365i
$97$	−22.3539	−	141.137i	−0.230453	−	1.45502i	−0.783251	−	0.621705i	$-0.786440\pi$
$97$	−22.3539	−	141.137i	−0.230453	−	1.45502i	0.552799	−	0.833315i	$-0.313560\pi$
$98$	−95.7712	−	20.1270i	−0.977258	−	0.205377i
$99$	6.08599	+	17.5792i	0.0614746	+	0.177567i
$100$	75.7901	−	65.2370i	0.757901	−	0.652370i
$101$	84.9980	−	116.990i	0.841564	−	1.15831i	−0.144095	−	0.989564i	$-0.546027\pi$
$101$	84.9980	−	116.990i	0.841564	−	1.15831i	0.985659	−	0.168750i	$-0.0539729\pi$
$102$	140.808	+	80.8646i	1.38047	+	0.792790i
$103$	−23.9681	+	47.0400i	−0.232700	+	0.456699i	−0.977598	−	0.210479i	$-0.932498\pi$
$103$	−23.9681	+	47.0400i	−0.232700	+	0.456699i	0.744899	+	0.667178i	$0.232498\pi$
$104$	22.8687	−	23.1860i	0.219891	−	0.222943i
$105$	1.31074	−	3.28185i	0.0124833	−	0.0312557i
$106$	49.9928	−	62.0267i	0.471630	−	0.585158i
$107$	34.5441	−	17.6011i	0.322842	−	0.164496i	−0.285057	−	0.958511i	$-0.592013\pi$
$107$	34.5441	−	17.6011i	0.322842	−	0.164496i	0.607899	+	0.794014i	$0.292013\pi$
$108$	111.811	+	29.4097i	1.03528	+	0.272312i
$109$	−16.3137			−0.149667			−0.0748337	−	0.997196i	$-0.523843\pi$
$109$	−16.3137			−0.149667			−0.0748337	+	0.997196i	$0.523843\pi$
$110$	27.6230	−	106.475i	0.251118	−	0.967957i
$111$		−	96.4500i		−	0.868919i
$112$	2.60244	−	3.27481i	0.0232360	−	0.0292394i
$113$	6.99939	+	13.7371i	0.0619415	+	0.121567i	0.919902	−	0.392149i	$-0.128268\pi$
$113$	6.99939	+	13.7371i	0.0619415	+	0.121567i	−0.857960	+	0.513716i	$0.828268\pi$
$114$	78.5277	−	97.4304i	0.688839	−	0.854652i
$115$	70.1754	+	163.506i	0.610221	+	1.42179i
$116$	−186.838	+	40.6116i	−1.61067	+	0.350100i
$117$	6.13405	+	3.12546i	0.0524278	+	0.0267133i
$118$	−67.1170	−	38.5447i	−0.568788	−	0.326650i
$119$	6.35166	+	4.61475i	0.0533753	+	0.0387794i
$120$	−71.8297	−	80.8370i	−0.598581	−	0.673642i
$121$	−41.7655	−	113.563i	−0.345170	−	0.938540i
$122$	−167.586	−	35.2194i	−1.37366	−	0.288683i
$123$	140.327	−	22.2256i	1.14087	−	0.180696i
$124$	76.6286	+	68.3619i	0.617973	+	0.551306i
$125$	−52.2055	−	113.576i	−0.417644	−	0.908611i
$126$	0.826253	+	0.314993i	0.00655756	+	0.00249995i
$127$	−63.2375	−	10.0158i	−0.497933	−	0.0788649i	−0.0975836	−	0.995227i	$-0.531111\pi$
$127$	−63.2375	−	10.0158i	−0.497933	−	0.0788649i	−0.400350	+	0.916362i	$0.631111\pi$
$128$	−53.9357	−	116.082i	−0.421373	−	0.906888i
$129$	5.09170	−	15.6706i	0.0394706	−	0.121478i
$130$	−19.9591	−	35.4792i	−0.153531	−	0.272917i
$131$	−183.238			−1.39877			−0.699383	−	0.714747i	$-0.746542\pi$
$131$	−183.238			−1.39877			−0.699383	+	0.714747i	$0.746542\pi$
$132$	−115.598	−	28.0531i	−0.875743	−	0.212523i
$133$	4.27838	−	4.27838i	0.0321683	−	0.0321683i
$134$	−6.37703	+	127.274i	−0.0475898	+	0.949806i
$135$	73.9369	−	124.171i	0.547681	−	0.919788i
$136$	213.304	−	110.542i	1.56841	−	0.812810i
$137$	104.651	+	16.5752i	0.763879	+	0.120987i	0.526204	−	0.850358i	$-0.323615\pi$
$137$	104.651	+	16.5752i	0.763879	+	0.120987i	0.237675	+	0.971345i	$0.423615\pi$
$138$	175.596	−	78.6642i	1.27244	−	0.570031i
$139$	224.699	−	73.0090i	1.61654	−	0.525244i	0.645415	−	0.763832i	$-0.276684\pi$
$139$	224.699	−	73.0090i	1.61654	−	0.525244i	0.971121	+	0.238587i	$0.0766843\pi$
$140$	−3.03571	−	4.25718i	−0.0216836	−	0.0304085i
$141$	8.56901	+	6.22575i	0.0607731	+	0.0441542i
$142$	−109.069	−	22.9216i	−0.768092	−	0.161420i
$143$	−40.2797	−	19.5622i	−0.281676	−	0.136799i
$144$	19.9413	−	18.2898i	0.138482	−	0.127013i
$145$	−15.7203	+	238.483i	−0.108416	+	1.64471i
$146$	5.19253	+	19.2022i	0.0355653	+	0.131522i
$147$	117.868	+	60.0566i	0.801821	+	0.408548i
$148$	−120.038	−	77.1719i	−0.811068	−	0.521432i
$149$	23.0847	−	16.7721i	0.154931	−	0.112564i	−0.507619	−	0.861582i	$-0.669474\pi$
$149$	23.0847	−	16.7721i	0.154931	−	0.112564i	0.662550	+	0.749018i	$0.269474\pi$
$150$	−121.916	+	58.3832i	−0.812772	+	0.389221i
$151$	9.30741	−	28.6453i	0.0616385	−	0.189704i	−0.915496	−	0.402328i	$-0.868201\pi$
$151$	9.30741	−	28.6453i	0.0616385	−	0.189704i	0.977134	+	0.212624i	$0.0682011\pi$
$152$	−58.4263	−	175.689i	−0.384384	−	1.15585i
$153$	35.9120	+	35.9120i	0.234719	+	0.234719i
$154$	−5.41247	−	1.94565i	−0.0351459	−	0.0126341i
$155$	108.586	−	68.4558i	0.700552	−	0.441650i
$156$	−38.0221	+	22.1856i	−0.243731	+	0.142215i
$157$	18.1367	−	9.24111i	0.115520	−	0.0588606i	−0.395275	−	0.918563i	$-0.629351\pi$
$157$	18.1367	−	9.24111i	0.115520	−	0.0588606i	0.510796	+	0.859702i	$0.329351\pi$
$158$	−22.2385	−	207.010i	−0.140750	−	1.31019i
$159$	−87.1208	+	63.2970i	−0.547930	+	0.398094i
$160$	−158.079	+	24.7169i	−0.987996	+	0.154481i
$161$	8.84800	−	2.87489i	0.0549565	−	0.0178565i
$162$	−109.124	−	62.6689i	−0.673604	−	0.386845i
$163$	31.5130	+	198.965i	0.193331	+	1.22065i	0.873219	+	0.487329i	$0.162029\pi$
$163$	31.5130	+	198.965i	0.193331	+	1.22065i	−0.679887	+	0.733317i	$0.737971\pi$
$164$	84.6176	−	192.429i	0.515961	−	1.17335i
$165$	−73.6148	+	129.190i	−0.446151	+	0.782970i
$166$	99.1933	+	151.979i	0.597550	+	0.915535i
$167$	0.639994	+	4.04076i	0.00383230	+	0.0241962i	0.989530	−	0.144325i	$-0.0461010\pi$
$167$	0.639994	+	4.04076i	0.00383230	+	0.0241962i	−0.985698	+	0.168521i	$0.946101\pi$
$168$	−4.55139	+	3.35494i	−0.0270916	+	0.0199699i
$169$	144.968	−	47.1030i	0.857800	−	0.278716i
$170$	−59.1538	−	294.424i	−0.347964	−	1.73191i
$171$	31.6648	−	23.0058i	0.185174	−	0.134537i
$172$	−15.4291	−	18.8754i	−0.0897041	−	0.109741i
$173$	46.1040	−	23.4912i	0.266497	−	0.135787i	−0.315636	−	0.948880i	$-0.602218\pi$
$173$	46.1040	−	23.4912i	0.266497	−	0.135787i	0.582134	+	0.813093i	$0.302218\pi$
$174$	258.130	+	12.9335i	1.48351	+	0.0743307i
$175$	−6.16259	+	2.17712i	−0.0352148	+	0.0124407i
$176$	−127.407	+	121.423i	−0.723901	+	0.689904i
$177$	73.9786	+	73.9786i	0.417958	+	0.417958i
$178$	−21.1735	−	23.4072i	−0.118952	−	0.131501i
$179$	−92.5331	+	284.788i	−0.516945	+	1.59099i	0.262771	+	0.964858i	$0.415364\pi$
$179$	−92.5331	+	284.788i	−0.516945	+	1.59099i	−0.779716	+	0.626134i	$0.784636\pi$
$180$	−15.0876	−	30.2719i	−0.0838201	−	0.168177i
$181$	−41.4561	+	30.1196i	−0.229039	+	0.166407i	−0.696386	−	0.717667i	$-0.745210\pi$
$181$	−41.4561	+	30.1196i	−0.229039	+	0.166407i	0.467347	+	0.884074i	$0.345210\pi$
$182$	−1.94248	+	0.870199i	−0.0106730	+	0.00478131i
$183$	206.252	+	105.090i	1.12706	+	0.574265i
$184$	42.5960	−	281.481i	0.231500	−	1.52979i
$185$	−134.158	+	117.565i	−0.725177	+	0.635485i
$186$	−75.8690	−	116.243i	−0.407898	−	0.624960i
$187$	−238.010	−	229.074i	−1.27278	−	1.22499i
$188$	14.6046	−	5.68330i	0.0776840	−	0.0302303i
$189$	−6.11321	−	4.44151i	−0.0323450	−	0.0235000i
$190$	−231.240	+	9.53113i	−1.21705	+	0.0501638i
$191$	−22.7883	+	7.40436i	−0.119310	+	0.0387663i	−0.368064	−	0.929801i	$-0.619979\pi$
$191$	−22.7883	+	7.40436i	−0.119310	+	0.0387663i	0.248753	+	0.968567i	$0.419979\pi$
$192$	29.4194	+	170.504i	0.153226	+	0.888039i
$193$	227.586	+	36.0460i	1.17920	+	0.186767i	0.715104	−	0.699018i	$-0.246379\pi$
$193$	227.586	+	36.0460i	1.17920	+	0.186767i	0.464096	+	0.885785i	$0.346379\pi$
$194$	222.515	+	179.344i	1.14698	+	0.924456i
$195$	13.5251	+	53.3386i	0.0693596	+	0.273531i
$196$	169.053	−	98.6410i	0.862514	−	0.503270i
$197$	−7.47757	+	7.47757i	−0.0379572	+	0.0379572i	−0.725831	−	0.687873i	$-0.758544\pi$
$197$	−7.47757	+	7.47757i	−0.0379572	+	0.0379572i	0.687873	+	0.725831i	$0.258544\pi$
$198$	−32.6123	−	17.9082i	−0.164709	−	0.0904457i
$199$	−311.254			−1.56409			−0.782046	−	0.623221i	$-0.785824\pi$
$199$	−311.254			−1.56409			−0.782046	+	0.623221i	$0.785824\pi$
$200$	−24.8862	+	198.446i	−0.124431	+	0.992228i
$201$	53.2305	−	163.827i	0.264828	−	0.815058i
$202$	30.8917	+	287.560i	0.152929	+	1.42356i
$203$	12.3427	+	1.95490i	0.0608017	+	0.00963005i
$204$	−317.341	+	68.9782i	−1.55559	+	0.338128i
$205$	−201.962	−	168.097i	−0.985179	−	0.819986i
$206$	−27.5625	−	101.928i	−0.133799	−	0.494794i
$207$	59.4406	−	9.41447i	0.287153	−	0.0454805i
$208$	−2.81102	+	65.0720i	−0.0135145	+	0.312846i
$209$	−203.060	+	153.551i	−0.971577	+	0.734693i
$210$	2.45905	+	6.62626i	0.0117098	+	0.0315536i
$211$	10.3525	+	7.52157i	0.0490642	+	0.0356472i	0.612047	−	0.790821i	$-0.290346\pi$
$211$	10.3525	+	7.52157i	0.0490642	+	0.0356472i	−0.562983	+	0.826469i	$0.690346\pi$
$212$	9.06962	+	159.073i	0.0427812	+	0.750343i
$213$	134.234	+	68.3954i	0.630205	+	0.321105i
$214$	−27.6213	+	72.4530i	−0.129072	+	0.338566i
$215$	−28.0036	+	12.0189i	−0.130249	+	0.0559019i
$216$	−205.297	+	106.392i	−0.950448	+	0.492557i
$217$	−3.04704	−	5.98016i	−0.0140417	−	0.0275583i
$218$	24.1967	−	21.8877i	0.110994	−	0.100402i
$219$		−	26.8888i		−	0.122780i
$220$	101.884	+	194.986i	0.463109	+	0.886301i
$221$	−122.249			−0.553164
$222$	129.404	+	143.056i	0.582902	+	0.644396i
$223$	112.164	−	57.1506i	0.502979	−	0.256281i	−0.184042	−	0.982918i	$-0.558918\pi$
$223$	112.164	−	57.1506i	0.502979	−	0.256281i	0.687021	+	0.726638i	$0.258918\pi$
$224$	0.533758	+	8.34885i	0.00238285	+	0.0372717i
$225$	−41.5770	+	7.67378i	−0.184787	+	0.0341057i
$226$	−28.8122	−	10.9841i	−0.127488	−	0.0486023i
$227$	134.651	−	264.267i	0.593175	−	1.16417i	−0.378001	−	0.925805i	$-0.623388\pi$
$227$	134.651	−	264.267i	0.593175	−	1.16417i	0.971176	−	0.238365i	$-0.0766116\pi$
$228$	14.2464	+	249.868i	0.0624841	+	1.09591i
$229$	30.6482	−	42.1836i	0.133835	−	0.184208i	−0.736840	−	0.676068i	$-0.763683\pi$
$229$	30.6482	−	42.1836i	0.133835	−	0.184208i	0.870675	+	0.491860i	$0.163683\pi$
$230$	−323.456	−	148.361i	−1.40633	−	0.645048i
$231$	6.37606	+	4.44865i	0.0276020	+	0.0192582i
$232$	222.633	−	310.911i	0.959624	−	1.34013i
$233$	5.07822	+	32.0626i	0.0217949	+	0.137608i	0.996186	−	0.0872505i	$-0.0278081\pi$
$233$	5.07822	+	32.0626i	0.0217949	+	0.137608i	−0.974391	+	0.224858i	$0.927808\pi$
$234$	−13.2914	+	3.59417i	−0.0568010	+	0.0153597i
$235$	−1.78518	−	19.5078i	−0.00759651	−	0.0830119i
$236$	151.263	−	32.8790i	0.640945	−	0.139318i
$237$	−44.0260	+	277.969i	−0.185764	+	1.17286i
$238$	−15.6123	+	1.67719i	−0.0655980	+	0.00704701i
$239$	−242.479	−	78.7861i	−1.01456	−	0.329649i	−0.245888	−	0.969298i	$-0.579080\pi$
$239$	−242.479	−	78.7861i	−1.01456	−	0.329649i	−0.768667	+	0.639649i	$0.779080\pi$
$240$	214.995	+	23.5265i	0.895814	+	0.0980272i
$241$		−	55.0838i		−	0.228564i	−0.993448	−	0.114282i	$-0.963543\pi$
$241$		−	55.0838i		−	0.228564i	0.993448	−	0.114282i	$-0.0364567\pi$
$242$	214.312	+	112.403i	0.885586	+	0.464475i
$243$	−63.6602	−	63.6602i	−0.261976	−	0.261976i
$244$	295.818	−	172.608i	1.21237	−	0.707409i
$245$	−60.1350	−	237.153i	−0.245449	−	0.967971i
$246$	−178.315	+	221.238i	−0.724857	+	0.899340i
$247$	−14.7382	+	93.0531i	−0.0596687	+	0.376733i
$248$	−205.376	+	1.41528i	−0.828128	+	0.00570679i
$249$	−75.8084	−	233.314i	−0.304452	−	0.937006i
$250$	229.814	+	98.4152i	0.919256	+	0.393661i
$251$	210.055	−	289.115i	0.836871	−	1.15185i	−0.149734	−	0.988726i	$-0.547842\pi$
$251$	210.055	−	289.115i	0.836871	−	1.15185i	0.986605	−	0.163128i	$-0.0521583\pi$
$252$	−1.64813	+	0.641359i	−0.00654018	+	0.00254507i
$253$	−385.382	+	68.6198i	−1.52325	+	0.271224i
$254$	107.233	−	69.9884i	0.422176	−	0.275545i
$255$	−26.7007	+	405.060i	−0.104709	+	1.58847i
$256$	235.741	+	99.8096i	0.920865	+	0.389881i
$257$	−43.4164	+	85.2094i	−0.168935	+	0.331554i	−0.959916	−	0.280286i	$-0.909571\pi$
$257$	−43.4164	+	85.2094i	−0.168935	+	0.331554i	0.790981	+	0.611841i	$0.209571\pi$
$258$	13.4728	+	30.0743i	0.0522201	+	0.116567i
$259$	5.48226	+	7.54568i	0.0211670	+	0.0291339i
$260$	77.2050	+	25.8446i	0.296942	+	0.0994024i
$261$	76.8817	+	24.9804i	0.294566	+	0.0957103i
$262$	271.781	−	245.846i	1.03733	−	0.938342i
$263$	−86.6193	+	86.6193i	−0.329351	+	0.329351i	−0.852340	−	0.522989i	$-0.824817\pi$
$263$	−86.6193	+	86.6193i	−0.329351	+	0.329351i	0.522989	+	0.852340i	$0.324817\pi$
$264$	209.094	−	113.486i	0.792024	−	0.429871i
$265$	194.236	+	44.0274i	0.732968	+	0.166141i
$266$	−0.605562	+	12.0859i	−0.00227655	+	0.0454358i
$267$	19.3694	+	38.0146i	0.0725446	+	0.142377i
$268$	−161.301	−	197.330i	−0.601871	−	0.736307i
$269$	45.3303	+	62.3919i	0.168514	+	0.231940i	0.884919	−	0.465745i	$-0.154214\pi$
$269$	45.3303	+	62.3919i	0.168514	+	0.231940i	−0.716405	+	0.697685i	$0.754214\pi$
$270$	56.9331	+	283.371i	0.210863	+	1.04952i
$271$	9.80192	+	30.1672i	0.0361694	+	0.111318i	0.967511	−	0.252828i	$-0.0813608\pi$
$271$	9.80192	+	30.1672i	0.0361694	+	0.111318i	−0.931342	+	0.364146i	$0.881361\pi$
$272$	−168.064	+	450.142i	−0.617884	+	1.65493i
$273$	2.84175	−	0.450089i	0.0104093	−	0.00164868i
$274$	−177.459	+	115.823i	−0.647659	+	0.422713i
$275$	269.428	−	55.0771i	0.979739	−	0.200280i
$276$	−154.905	+	352.268i	−0.561249	+	1.27633i
$277$	369.430	−	58.5120i	1.33368	−	0.211235i	0.551443	−	0.834212i	$-0.314077\pi$
$277$	369.430	−	58.5120i	1.33368	−	0.211235i	0.782240	+	0.622978i	$0.214077\pi$
$278$	−235.321	+	409.759i	−0.846480	+	1.47395i
$279$	−13.4165	−	41.2917i	−0.0480878	−	0.147999i
$280$	10.2143	+	2.24138i	0.0364798	+	0.00800494i
$281$	−148.433	−	204.301i	−0.528231	−	0.727048i	0.458628	−	0.888628i	$-0.348341\pi$
$281$	−148.433	−	204.301i	−0.528231	−	0.727048i	−0.986860	+	0.161580i	$0.948341\pi$
$282$	−21.0626	+	2.26269i	−0.0746899	+	0.00802373i
$283$	−5.59113	−	10.9732i	−0.0197567	−	0.0387746i	0.880917	−	0.473270i	$-0.156927\pi$
$283$	−5.59113	−	10.9732i	−0.0197567	−	0.0387746i	−0.900674	+	0.434496i	$0.856927\pi$
$284$	192.526	−	112.337i	0.677908	−	0.395554i
$285$	305.103	+	69.1573i	1.07054	+	0.242657i
$286$	85.9894	−	25.0273i	0.300662	−	0.0875081i
$287$	−9.71503	+	9.71503i	−0.0338503	+	0.0338503i
$288$	−5.03831	+	53.8824i	−0.0174941	+	0.187092i
$289$	−582.854	−	189.381i	−2.01680	−	0.655297i
$290$	−296.650	−	374.813i	−1.02293	−	1.29246i
$291$	−227.072	−	312.538i	−0.780316	−	1.07401i
$292$	−33.4647	−	21.5143i	−0.114605	−	0.0736792i
$293$	179.659	−	352.601i	0.613170	−	1.20341i	−0.350561	−	0.936540i	$-0.614009\pi$
$293$	179.659	−	352.601i	0.613170	−	1.20341i	0.963731	−	0.266875i	$-0.0859910\pi$
$294$	−255.399	+	69.0631i	−0.868704	+	0.234909i
$295$	12.7271	−	193.075i	0.0431427	−	0.654491i
$296$	281.581	−	46.5894i	0.951288	−	0.157397i
$297$	229.075	+	220.474i	0.771297	+	0.742337i
$298$	−11.7370	+	55.8487i	−0.0393858	+	0.187412i
$299$	−85.1480	+	117.196i	−0.284776	+	0.391960i
$300$	102.496	−	250.166i	0.341653	−	0.833886i
$301$	0.492381	+	1.51539i	0.00163582	+	0.00503453i
$302$	24.6277	+	54.9745i	0.0815486	+	0.182035i
$303$	61.1570	−	386.130i	0.201838	−	1.27436i
$304$	322.375	+	182.195i	1.06045	+	0.599325i
$305$	−105.228	−	414.984i	−0.345009	−	1.36060i
$306$	−101.447	−	5.08298i	−0.331527	−	0.0166110i
$307$	206.158	+	206.158i	0.671526	+	0.671526i	0.958068	−	0.286542i	$-0.0925058\pi$
$307$	206.158	+	206.158i	0.671526	+	0.671526i	−0.286542	+	0.958068i	$0.592506\pi$
$308$	10.6383	−	4.37594i	0.0345398	−	0.0142076i
$309$			142.728i			0.461904i
$310$	−69.2102	+	247.221i	−0.223259	+	0.797486i
$311$	−88.9741	−	28.9094i	−0.286090	−	0.0929564i	0.162456	−	0.986716i	$-0.448058\pi$
$311$	−88.9741	−	28.9094i	−0.286090	−	0.0929564i	−0.448547	+	0.893759i	$0.648058\pi$
$312$	26.6290	−	83.9191i	0.0853494	−	0.268971i
$313$	3.80615	−	24.0311i	0.0121602	−	0.0767766i	−0.980862	−	0.194705i	$-0.937625\pi$
$313$	3.80615	−	24.0311i	0.0121602	−	0.0767766i	0.993022	+	0.117928i	$0.0376252\pi$
$314$	−14.5020	+	38.0400i	−0.0461848	+	0.121147i
$315$	0.201457	+	2.20145i	0.000639547	+	0.00698873i
$316$	310.724	+	277.203i	0.983302	+	0.877223i
$317$	20.7094	+	130.754i	0.0653292	+	0.412472i	0.998581	+	0.0532500i	$0.0169580\pi$
$317$	20.7094	+	130.754i	0.0653292	+	0.412472i	−0.933252	+	0.359222i	$0.883042\pi$
$318$	44.2948	−	210.770i	0.139292	−	0.662800i
$319$	−503.084	−	152.886i	−1.57707	−	0.479267i
$320$	201.303	−	248.751i	0.629072	−	0.777347i
$321$	61.6078	−	84.7959i	0.191925	−	0.264162i
$322$	−9.26630	+	16.1352i	−0.0287773	+	0.0501093i
$323$	−315.534	+	619.269i	−0.976884	+	1.91724i
$324$	245.935	−	53.4571i	0.759058	−	0.164991i
$325$	57.7056	−	83.8282i	0.177556	−	0.257933i
$326$	−313.686	−	252.827i	−0.962228	−	0.775544i
$327$	−39.2969	+	20.0228i	−0.120174	+	0.0612317i
$328$	132.670	+	398.941i	0.404482	+	1.21628i
$329$	−1.02426			−0.00311326
$330$	−64.1442	−	290.383i	−0.194376	−	0.879949i
$331$			330.941i			0.999822i	0.866077	+	0.499911i	$0.166634\pi$
$331$			330.941i			0.999822i	−0.866077	+	0.499911i	$0.833366\pi$
$332$	−351.030	−	92.3320i	−1.05732	−	0.278108i
$333$	27.3913	+	53.7584i	0.0822561	+	0.161437i
$334$	−6.37062	−	5.13465i	−0.0190737	−	0.0153732i
$335$	−292.759	+	125.650i	−0.873908	+	0.375075i
$336$	2.24945	−	11.0826i	0.00669478	−	0.0329838i
$337$	−251.656	−	128.225i	−0.746753	−	0.380489i	0.0388303	−	0.999246i	$-0.487637\pi$
$337$	−251.656	−	128.225i	−0.746753	−	0.380489i	−0.785583	+	0.618756i	$0.787637\pi$
$338$	−151.822	+	264.364i	−0.449177	+	0.782141i
$339$	33.7206	+	24.4995i	0.0994708	+	0.0722698i
$340$	482.759	+	357.329i	1.41988	+	1.05097i
$341$	92.3875	+	266.858i	0.270931	+	0.782576i
$342$	−16.0993	+	76.6063i	−0.0470741	+	0.223995i
$343$	−25.2875	+	4.00514i	−0.0737244	+	0.0116768i
$344$	48.2092	+	7.29541i	0.140143	+	0.0212076i
$345$	369.720	+	307.726i	1.07165	+	0.891959i
$346$	−36.8646	+	96.6989i	−0.106545	+	0.279477i
$347$	238.755	+	37.8151i	0.688054	+	0.108977i	0.490665	−	0.871348i	$-0.336754\pi$
$347$	238.755	+	37.8151i	0.688054	+	0.108977i	0.197389	+	0.980325i	$0.436754\pi$
$348$	−400.215	+	327.143i	−1.15004	+	0.940066i
$349$	171.175	−	526.823i	0.490474	−	1.50952i	−0.333420	−	0.942778i	$-0.608203\pi$
$349$	171.175	−	526.823i	0.490474	−	1.50952i	0.823894	−	0.566744i	$-0.191797\pi$
$350$	6.21945	−	11.4973i	0.0177699	−	0.0328494i
$351$	117.660			0.335213
$352$	26.0609	−	351.034i	0.0740367	−	0.997256i
$353$	−162.563	+	162.563i	−0.460518	+	0.460518i	−0.898825	−	0.438307i	$-0.855578\pi$
$353$	−162.563	+	162.563i	−0.460518	+	0.460518i	0.438307	+	0.898825i	$0.355578\pi$
$354$	−208.981	−	10.4709i	−0.590342	−	0.0295789i
$355$	−68.4848	−	270.081i	−0.192915	−	0.760793i
$356$	62.8094	+	6.30994i	0.176431	+	0.0177245i
$357$	20.9640	+	3.32036i	0.0587226	+	0.00930074i
$358$	−244.845	−	546.549i	−0.683925	−	1.52667i
$359$	287.976	−	93.5692i	0.802163	−	0.260638i	0.120888	−	0.992666i	$-0.461426\pi$
$359$	287.976	−	93.5692i	0.802163	−	0.260638i	0.681275	+	0.732028i	$0.261426\pi$
$360$	62.9931	+	24.6569i	0.174981	+	0.0684915i
$361$	141.277	+	102.644i	0.391350	+	0.284333i
$362$	21.0775	−	100.294i	0.0582252	−	0.277056i
$363$	−239.988	−	222.293i	−0.661125	−	0.612377i
$364$	1.71359	−	3.89686i	0.00470765	−	0.0107057i
$365$	−37.4011	+	32.7752i	−0.102469	+	0.0897951i
$366$	−446.912	+	120.851i	−1.22107	+	0.330193i
$367$	−362.988	−	184.952i	−0.989069	−	0.503956i	−0.116891	−	0.993145i	$-0.537293\pi$
$367$	−362.988	−	184.952i	−0.989069	−	0.503956i	−0.872178	+	0.489189i	$0.837293\pi$
$368$	314.477	+	474.646i	0.854556	+	1.28980i
$369$	−71.9021	+	52.2399i	−0.194857	+	0.141572i
$370$	41.2510	−	354.369i	0.111489	−	0.957754i
$371$	3.21799	−	9.90397i	0.00867384	−	0.0266953i
$372$	268.489	+	70.6211i	0.721745	+	0.189842i
$373$	259.854	+	259.854i	0.696659	+	0.696659i	0.963688	−	0.267029i	$-0.0860421\pi$
$373$	259.854	+	259.854i	0.696659	+	0.696659i	−0.267029	+	0.963688i	$0.586042\pi$
$374$	660.362	+	20.4333i	1.76567	+	0.0546345i
$375$	−265.152	−	209.511i	−0.707073	−	0.558695i
$376$	−14.0366	+	28.0241i	−0.0373314	+	0.0745322i
$377$	−173.376	+	88.3396i	−0.459884	+	0.234323i
$378$	15.0262	−	1.61423i	0.0397519	−	0.00427044i
$379$	94.3847	−	68.5745i	0.249036	−	0.180935i	−0.456263	−	0.889845i	$-0.650813\pi$
$379$	94.3847	−	68.5745i	0.249036	−	0.180935i	0.705300	+	0.708909i	$0.250813\pi$
$380$	330.190	−	324.385i	0.868922	−	0.853645i
$381$	−164.621	+	53.4886i	−0.432076	+	0.140390i
$382$	23.8656	−	41.5566i	0.0624754	−	0.108787i
$383$	−35.1135	−	221.698i	−0.0916802	−	0.578846i	−0.990172	−	0.139856i	$-0.955336\pi$
$383$	−35.1135	−	221.698i	−0.0916802	−	0.578846i	0.898492	−	0.438991i	$-0.144664\pi$
$384$	−272.395	−	213.422i	−0.709362	−	0.555786i
$385$	−1.58402	−	14.2914i	−0.00411434	−	0.0371204i
$386$	−385.920	+	251.881i	−0.999792	+	0.652543i
$387$	1.61241	+	10.1804i	0.00416644	+	0.0263059i
$388$	−570.658	+	32.5364i	−1.47077	+	0.0838567i
$389$	546.922	−	177.706i	1.40597	−	0.456827i	0.494852	−	0.868977i	$-0.335222\pi$
$389$	546.922	−	177.706i	1.40597	−	0.456827i	0.911116	+	0.412150i	$0.135222\pi$
$390$	−91.6235	−	60.9662i	−0.234932	−	0.156324i
$391$	−864.571	+	628.148i	−2.21118	+	1.60652i
$392$	−118.397	+	373.119i	−0.302034	+	0.951834i
$393$	−441.389	+	224.899i	−1.12313	+	0.572261i
$394$	1.05837	−	21.1233i	0.00268623	−	0.0536123i
$395$	440.307	−	277.583i	1.11470	−	0.702743i
$396$	72.3979	−	17.1933i	0.182823	−	0.0434174i
$397$	−277.982	−	277.982i	−0.700207	−	0.700207i	0.264248	−	0.964455i	$-0.414876\pi$
$397$	−277.982	−	277.982i	−0.700207	−	0.700207i	−0.964455	+	0.264248i	$0.914876\pi$
$398$	461.656	−	417.601i	1.15994	−	1.04925i
$399$	5.05476	−	15.5570i	0.0126686	−	0.0389899i
$400$	−229.337	−	327.726i	−0.573344	−	0.819315i
$401$	−266.732	+	193.792i	−0.665167	+	0.483272i	−0.868404	−	0.495857i	$-0.834854\pi$
$401$	−266.732	+	193.792i	−0.665167	+	0.483272i	0.203237	+	0.979130i	$0.434854\pi$
$402$	140.849	+	314.407i	0.350372	+	0.782108i
$403$	93.1171	+	47.4456i	0.231060	+	0.117731i
$404$	−431.630	−	385.066i	−1.06839	−	0.953132i
$405$	20.6927	−	313.916i	0.0510930	−	0.775101i
$406$	−20.9297	+	13.6604i	−0.0515511	+	0.0336463i
$407$	−184.819	−	346.193i	−0.454101	−	0.850597i
$408$	378.138	−	528.077i	0.926809	−	1.29431i
$409$	−197.724	−	143.655i	−0.483433	−	0.351235i	0.319220	−	0.947681i	$-0.396579\pi$
$409$	−197.724	−	143.655i	−0.483433	−	0.351235i	−0.802653	+	0.596446i	$0.796579\pi$
$410$	525.083	−	21.6426i	1.28069	−	0.0527868i
$411$	272.430	−	88.5180i	0.662848	−	0.215372i
$412$	177.634	+	114.200i	0.431151	+	0.277185i
$413$	−9.99263	−	1.58268i	−0.0241952	−	0.00383215i
$414$	−75.5319	+	93.7135i	−0.182444	+	0.226361i
$415$	−232.126	+	389.837i	−0.559339	+	0.939367i
$416$	−83.1360	−	100.287i	−0.199846	−	0.241075i
$417$	451.651	−	451.651i	1.08310	−	1.08310i
$418$	95.1654	−	500.188i	0.227668	−	1.19662i
$419$	−478.038			−1.14090			−0.570451	−	0.821332i	$-0.693232\pi$
$419$	−478.038			−1.14090			−0.570451	+	0.821332i	$0.693232\pi$
$420$	−12.5376	−	6.52891i	−0.0298513	−	0.0155450i
$421$	86.2908	−	265.576i	0.204966	−	0.630821i	−0.794748	−	0.606939i	$-0.792397\pi$
$421$	86.2908	−	265.576i	0.204966	−	0.630821i	0.999715	−	0.0238825i	$-0.00760274\pi$
$422$	−25.4465	+	2.73365i	−0.0602997	+	0.00647783i
$423$	−6.54419	−	1.03650i	−0.0154709	−	0.00245035i
$424$	−226.875	−	223.770i	−0.535084	−	0.527759i
$425$	595.967	−	456.596i	1.40227	−	1.07434i
$426$	−290.861	+	78.6525i	−0.682772	+	0.184630i
$427$	−22.1093	+	3.50177i	−0.0517782	+	0.00820086i
$428$	−56.2399	−	144.522i	−0.131402	−	0.337668i
$429$	−121.037	+	2.31573i	−0.282136	+	0.00539797i
$430$	25.4098	−	55.3982i	0.0590925	−	0.128833i
$431$	115.362	+	83.8154i	0.267661	+	0.194467i	0.713518	−	0.700637i	$-0.247101\pi$
$431$	115.362	+	83.8154i	0.267661	+	0.194467i	−0.445856	+	0.895104i	$0.647101\pi$
$432$	161.755	−	433.243i	0.374433	−	1.00288i
$433$	−312.649	−	159.303i	−0.722054	−	0.367905i	0.0540261	−	0.998540i	$-0.482795\pi$
$433$	−312.649	−	159.303i	−0.722054	−	0.367905i	−0.776080	+	0.630635i	$0.782795\pi$
$434$	12.5428	+	4.78171i	0.0289005	+	0.0110178i
$435$	254.837	+	593.759i	0.585831	+	1.36496i
$436$	−6.52279	+	64.9282i	−0.0149605	+	0.148918i
$437$	373.900	+	733.819i	0.855605	+	1.67922i
$438$	36.0759	+	39.8817i	0.0823650	+	0.0910541i
$439$			371.749i			0.846809i	0.905941	+	0.423405i	$0.139165\pi$
$439$			371.749i			0.846809i	−0.905941	+	0.423405i	$0.860835\pi$
$440$	−412.723	−	152.511i	−0.938007	−	0.346616i
$441$	−82.7517			−0.187646
$442$	181.322	−	164.018i	0.410230	−	0.371082i
$443$	631.406	−	321.718i	1.42530	−	0.726225i	0.440147	−	0.897926i	$-0.354926\pi$
$443$	631.406	−	321.718i	1.42530	−	0.726225i	0.985149	+	0.171701i	$0.0549262\pi$
$444$	−383.868	−	38.5640i	−0.864567	−	0.0868558i
$445$	29.2669	−	73.2787i	0.0657683	−	0.164671i
$446$	−89.6861	+	235.254i	−0.201090	+	0.527476i
$447$	35.0218	−	68.7341i	0.0783485	−	0.153768i
$448$	−11.9931	−	11.6670i	−0.0267703	−	0.0260424i
$449$	−10.8111	+	14.8802i	−0.0240781	+	0.0331407i	−0.820886	−	0.571092i	$-0.806520\pi$
$449$	−10.8111	+	14.8802i	−0.0240781	+	0.0331407i	0.796808	+	0.604232i	$0.206520\pi$
$450$	51.3718	−	67.1645i	0.114160	−	0.149255i
$451$	461.093	−	348.672i	1.02238	−	0.773109i
$452$	57.4717	−	22.3648i	0.127150	−	0.0494797i
$453$	−12.7380	−	80.4249i	−0.0281193	−	0.177538i
$454$	154.844	+	572.620i	0.341066	+	1.26128i
$455$	−4.08991	−	3.40412i	−0.00898882	−	0.00748159i
$456$	−356.372	−	351.493i	−0.781516	−	0.770819i
$457$	68.7689	−	434.189i	0.150479	−	0.950086i	−0.790706	−	0.612196i	$-0.790287\pi$
$457$	68.7689	−	434.189i	0.150479	−	0.950086i	0.941185	−	0.337891i	$-0.109713\pi$
$458$	11.1388	+	103.687i	0.0243206	+	0.226391i
$459$	825.510	+	268.225i	1.79850	+	0.584367i
$460$	678.805	−	213.920i	1.47566	−	0.465045i
$461$			518.031i			1.12371i	0.827235	+	0.561856i	$0.189912\pi$
$461$			518.031i			1.12371i	−0.827235	+	0.561856i	$0.810088\pi$
$462$	−15.4257	+	1.95629i	−0.0333889	+	0.00423439i
$463$	636.948	+	636.948i	1.37570	+	1.37570i	0.851750	+	0.523949i	$0.175542\pi$
$463$	636.948	+	636.948i	1.37570	+	1.37570i	0.523949	+	0.851750i	$0.324458\pi$
$464$	86.9288	+	759.847i	0.187347	+	1.63760i
$465$	177.544	−	298.171i	0.381814	−	0.641228i
$466$	−50.5496	−	40.7424i	−0.108476	−	0.0874299i
$467$	57.4408	−	362.667i	0.123000	−	0.776588i	−0.846661	−	0.532133i	$-0.821391\pi$
$467$	57.4408	−	362.667i	0.123000	−	0.776588i	0.969660	−	0.244456i	$-0.0786093\pi$
$468$	14.8918	−	23.1637i	0.0318201	−	0.0494950i
$469$	5.14753	+	15.8425i	0.0109755	+	0.0337793i
$470$	28.8208	+	26.5391i	0.0613210	+	0.0564661i
$471$	32.3460	−	44.5204i	0.0686751	−	0.0945231i
$472$	−180.242	+	251.712i	−0.381869	+	0.533288i
$473$	−11.7525	−	66.0042i	−0.0248467	−	0.139544i
$474$	−307.643	−	471.355i	−0.649037	−	0.994420i
$475$	−275.701	−	508.682i	−0.580422	−	1.07091i
$476$	20.9062	−	23.4342i	0.0439205	−	0.0492316i
$477$	30.5826	−	60.0217i	0.0641145	−	0.125832i
$478$	465.352	−	208.470i	0.973540	−	0.436130i
$479$	51.8442	+	71.3574i	0.108234	+	0.148972i	0.859698	−	0.510803i	$-0.170652\pi$
$479$	51.8442	+	71.3574i	0.108234	+	0.148972i	−0.751464	+	0.659774i	$0.770652\pi$
$480$	−350.449	+	253.558i	−0.730101	+	0.528247i
$481$	−138.122	−	44.8787i	−0.287157	−	0.0933029i
$482$	73.9044	+	81.7010i	0.153329	+	0.169504i
$483$	17.7847	−	17.7847i	0.0368214	−	0.0368214i
$484$	−468.678	+	120.819i	−0.968342	+	0.249626i
$485$	−157.944	+	696.805i	−0.325658	+	1.43671i
$486$	179.833	+	9.01046i	0.370026	+	0.0185400i
$487$	189.407	+	371.733i	0.388927	+	0.763312i	0.999592	−	0.0285770i	$-0.00909759\pi$
$487$	189.407	+	371.733i	0.388927	+	0.763312i	−0.610664	+	0.791889i	$0.709098\pi$
$488$	−207.178	+	652.905i	−0.424546	+	1.33792i
$489$	320.110	+	440.594i	0.654623	+	0.901011i
$490$	407.374	+	271.066i	0.831376	+	0.553197i
$491$	3.50929	+	10.8005i	0.00714722	+	0.0219969i	0.954567	−	0.297998i	$-0.0963188\pi$
$491$	3.50929	+	10.8005i	0.00714722	+	0.0219969i	−0.947419	+	0.319995i	$0.896319\pi$
$492$	−32.3496	−	567.382i	−0.0657513	−	1.15322i
$493$	−1417.80	+	224.558i	−2.87587	+	0.455493i
$494$	−102.987	−	157.791i	−0.208476	−	0.319416i
$495$	4.34149	−	92.9130i	0.00877070	−	0.187703i
$496$	302.717	−	277.646i	0.610316	−	0.559770i
$497$	−14.3893	+	2.27904i	−0.0289522	+	0.00458559i
$498$	425.471	+	244.345i	0.854360	+	0.490652i
$499$	25.3376	+	77.9810i	0.0507767	+	0.156275i	0.973230	−	0.229835i	$-0.0738187\pi$
$499$	25.3376	+	77.9810i	0.0507767	+	0.156275i	−0.922453	+	0.386110i	$0.873819\pi$
$500$	−472.904	+	162.364i	−0.945807	+	0.324729i
$501$	6.50109	+	8.94798i	0.0129762	+	0.0178602i
$502$	76.3425	+	710.644i	0.152077	+	1.41562i
$503$	−312.391	−	613.102i	−0.621056	−	1.21889i	−0.960504	−	0.278266i	$-0.910240\pi$
$503$	−312.391	−	613.102i	−0.621056	−	1.21889i	0.339448	−	0.940625i	$-0.389760\pi$
$504$	1.58403	−	3.16251i	0.00314291	−	0.00627483i
$505$	−611.635	+	385.594i	−1.21116	+	0.763553i
$506$	479.538	−	618.834i	0.947703	−	1.22299i
$507$	291.391	−	291.391i	0.574735	−	0.574735i
$508$	−65.1472	+	247.679i	−0.128243	+	0.487556i
$509$	610.099	+	198.233i	1.19862	+	0.389456i	0.839254	−	0.543740i	$-0.182992\pi$
$509$	610.099	+	198.233i	1.19862	+	0.389456i	0.359368	+	0.933196i	$0.382992\pi$
$510$	−503.855	−	636.613i	−0.987951	−	1.24826i
$511$	1.52837	+	2.10362i	0.00299093	+	0.00411667i
$512$	−483.566	+	168.249i	−0.944465	+	0.328611i
$513$	303.688	−	596.021i	0.591985	−	1.16184i
$514$	−49.9274	−	184.634i	−0.0971350	−	0.359210i
$515$	198.529	−	173.974i	0.385493	−	0.337814i
$516$	−60.3328	−	26.5305i	−0.116924	−	0.0514156i
$517$	42.6870	+	5.92630i	0.0825668	+	0.0114629i
$518$	−18.2552	−	3.83645i	−0.0352417	−	0.00740628i
$519$	82.2244	−	113.172i	0.158429	−	0.218058i
$520$	−149.186	+	65.2507i	−0.286897	+	0.125482i
$521$	97.7205	+	300.753i	0.187563	+	0.577261i	0.999983	−	0.00581228i	$-0.00185012\pi$
$521$	97.7205	+	300.753i	0.187563	+	0.577261i	−0.812420	+	0.583073i	$0.801850\pi$
$522$	−147.547	+	66.0988i	−0.282658	+	0.126626i
$523$	−14.8497	+	93.7574i	−0.0283933	+	0.179269i	−0.997809	−	0.0661547i	$-0.978927\pi$
$523$	−14.8497	+	93.7574i	−0.0283933	+	0.179269i	0.969416	+	0.245423i	$0.0789269\pi$
$524$	−73.2649	+	729.282i	−0.139819	+	1.39176i
$525$	−12.1725	+	12.8080i	−0.0231857	+	0.0243962i
$526$	12.2601	−	244.690i	0.0233082	−	0.465189i
$527$	545.157	+	545.157i	1.03445	+	1.03445i
$528$	−157.870	+	448.860i	−0.298997	+	0.850114i
$529$			737.347i			1.39385i
$530$	−347.164	+	195.300i	−0.655027	+	0.368490i
$531$	−62.2431	−	20.2240i	−0.117219	−	0.0380866i
$532$	−15.3172	−	18.7384i	−0.0287917	−	0.0352226i
$533$	33.4664	−	211.298i	0.0627887	−	0.396432i
$534$	−79.7320	−	30.3963i	−0.149311	−	0.0569219i
$535$	−193.042	+	17.6655i	−0.360827	+	0.0330197i
$536$	503.996	+	76.2688i	0.940292	+	0.142293i
$537$	126.640	+	799.574i	0.235829	+	1.48896i
$538$	−150.944	−	31.7219i	−0.280565	−	0.0589627i
$539$	538.150	−	10.2961i	0.998422	−	0.0191023i
$540$	−464.635	−	343.914i	−0.860436	−	0.636878i
$541$	53.7552	−	73.9877i	0.0993626	−	0.136761i	−0.756441	−	0.654062i	$-0.773063\pi$
$541$	53.7552	−	73.9877i	0.0993626	−	0.136761i	0.855803	+	0.517301i	$0.173063\pi$
$542$	−55.0128	−	31.5934i	−0.101500	−	0.0582904i
$543$	−62.8928	+	123.434i	−0.115825	+	0.227319i
$544$	−354.667	−	893.143i	−0.651962	−	1.64181i
$545$	75.7505	+	30.2541i	0.138992	+	0.0555122i
$546$	−3.61104	+	4.48027i	−0.00661363	+	0.00820562i
$547$	−273.634	+	139.424i	−0.500245	+	0.254888i	−0.685858	−	0.727735i	$-0.740573\pi$
$547$	−273.634	+	139.424i	−0.500245	+	0.254888i	0.185613	+	0.982623i	$0.440573\pi$
$548$	107.812	−	409.882i	0.196737	−	0.747960i
$549$	−144.804			−0.263759
$550$	−325.724	+	443.175i	−0.592225	+	0.805773i
$551$			1106.27i			2.00775i
$552$	−242.872	−	730.319i	−0.439985	−	1.32304i
$553$	−12.3555	−	24.2491i	−0.0223427	−	0.0438501i
$554$	−469.439	+	582.440i	−0.847363	+	1.05134i
$555$	−178.868	+	447.852i	−0.322285	+	0.806940i
$556$	−200.731	−	923.484i	−0.361027	−	1.66094i
$557$	−490.021	−	249.678i	−0.879751	−	0.448255i	−0.0450664	−	0.998984i	$-0.514350\pi$
$557$	−490.021	−	249.678i	−0.879751	−	0.448255i	−0.834684	+	0.550729i	$0.814350\pi$
$558$	75.2994	+	43.2438i	0.134945	+	0.0774979i
$559$	−20.0721	−	14.5833i	−0.0359072	−	0.0260881i
$560$	−18.1572	+	10.3798i	−0.0324236	+	0.0185354i
$561$	−854.480	−	259.675i	−1.52314	−	0.462878i
$562$	494.262	+	103.873i	0.879470	+	0.184827i
$563$	104.018	−	16.4749i	0.184757	−	0.0292626i	−0.0633702	−	0.997990i	$-0.520185\pi$
$563$	104.018	−	16.4749i	0.184757	−	0.0292626i	0.248127	+	0.968727i	$0.420185\pi$
$564$	28.2044	−	31.6151i	0.0500079	−	0.0560551i
$565$	−7.02501	−	76.7667i	−0.0124336	−	0.135870i
$566$	23.0153	+	8.77414i	0.0406631	+	0.0155020i
$567$	−16.2468	−	2.57324i	−0.0286539	−	0.00453833i
$568$	−134.837	+	424.926i	−0.237389	+	0.748110i
$569$	−158.054	+	486.440i	−0.277775	+	0.854903i	0.710697	+	0.703498i	$0.248380\pi$
$569$	−158.054	+	486.440i	−0.277775	+	0.854903i	−0.988472	+	0.151405i	$0.951620\pi$
$570$	−545.318	+	306.773i	−0.956699	+	0.538198i
$571$	−627.155			−1.09834			−0.549172	−	0.835709i	$-0.685057\pi$
$571$	−627.155			−1.09834			−0.549172	+	0.835709i	$0.685057\pi$
$572$	−93.9621	+	152.490i	−0.164269	+	0.266592i
$573$	−45.8051	+	45.8051i	−0.0799391	+	0.0799391i
$574$	1.37507	−	27.4438i	0.00239558	−	0.0478115i
$575$	−22.6251	−	889.356i	−0.0393480	−	1.54671i
$576$	−64.8196	−	86.6788i	−0.112534	−	0.150484i
$577$	−369.214	−	58.4778i	−0.639886	−	0.101348i	−0.171943	−	0.985107i	$-0.555005\pi$
$577$	−369.214	−	58.4778i	−0.639886	−	0.101348i	−0.467942	+	0.883759i	$0.655005\pi$
$578$	1118.58	−	501.107i	1.93526	−	0.866967i
$579$	592.455	−	192.500i	1.02324	−	0.332470i
$580$	942.870	+	157.920i	1.62564	+	0.272276i
$581$	19.1925	+	13.9442i	0.0330335	+	0.0240003i
$582$	756.119	+	158.904i	1.29917	+	0.273030i
$583$	−191.416	+	394.137i	−0.328330	+	0.676050i
$584$	78.5004	−	12.9884i	0.134419	−	0.0222404i
$585$	−22.6864	−	25.8883i	−0.0387801	−	0.0442535i
$586$	206.602	+	764.025i	0.352563	+	1.30380i
$587$	826.097	+	420.918i	1.40732	+	0.717066i	0.982159	−	0.188051i	$-0.0602171\pi$
$587$	826.097	+	420.918i	1.40732	+	0.717066i	0.425162	+	0.905117i	$0.360217\pi$
$588$	286.151	−	445.097i	0.486651	−	0.756967i
$589$	480.683	−	349.237i	0.816101	−	0.592932i
$590$	240.166	+	303.447i	0.407061	+	0.514316i
$591$	−8.83449	+	27.1898i	−0.0149484	+	0.0460064i
$592$	−355.137	+	446.892i	−0.599894	+	0.754884i
$593$	390.551	+	390.551i	0.658602	+	0.658602i	0.955049	−	0.296447i	$-0.0958019\pi$
$593$	390.551	+	390.551i	0.658602	+	0.658602i	−0.296447	+	0.955049i	$0.595802\pi$
$594$	−635.571	−	19.6662i	−1.06998	−	0.0331081i
$595$	−20.9349	−	33.2072i	−0.0351847	−	0.0558104i
$596$	−57.5221	−	98.5826i	−0.0965137	−	0.165407i
$597$	−749.756	+	382.020i	−1.25587	+	0.639899i
$598$	−30.9463	−	288.067i	−0.0517496	−	0.481718i
$599$	555.361	−	403.493i	0.927147	−	0.673612i	−0.0181456	−	0.999835i	$-0.505776\pi$
$599$	555.361	−	403.493i	0.927147	−	0.673612i	0.945293	+	0.326224i	$0.105776\pi$
$600$	183.617	+	508.565i	0.306029	+	0.847608i
$601$	487.260	−	158.320i	0.810749	−	0.263428i	0.125834	−	0.992051i	$-0.459839\pi$
$601$	487.260	−	158.320i	0.810749	−	0.263428i	0.684915	+	0.728623i	$0.259839\pi$
$602$	−2.76347	−	1.58704i	−0.00459048	−	0.00263627i
$603$	16.8568	+	106.429i	0.0279548	+	0.176500i
$604$	−110.286	−	48.4965i	−0.182592	−	0.0802923i
$605$	−16.6731	+	604.770i	−0.0275589	+	0.999620i
$606$	427.351	+	654.765i	0.705200	+	1.08047i
$607$	−79.9289	−	504.651i	−0.131679	−	0.831386i	−0.961790	−	0.273788i	$-0.911723\pi$
$607$	−79.9289	−	504.651i	−0.131679	−	0.831386i	0.830111	−	0.557598i	$-0.188277\pi$
$608$	−722.597	+	162.288i	−1.18848	+	0.266922i
$609$	32.1309	−	10.4399i	0.0527600	−	0.0171428i
$610$	712.847	+	474.327i	1.16860	+	0.777586i
$611$	12.9029	−	9.37447i	0.0211176	−	0.0153428i
$612$	157.287	−	128.570i	0.257005	−	0.210081i
$613$	186.867	−	95.2135i	0.304840	−	0.155324i	−0.294878	−	0.955535i	$-0.595279\pi$
$613$	186.867	−	95.2135i	0.304840	−	0.155324i	0.599719	+	0.800211i	$0.295279\pi$
$614$	−582.373	−	29.1796i	−0.948491	−	0.0475239i
$615$	−692.805	−	157.037i	−1.12651	−	0.255345i
$616$	−9.90772	+	20.7635i	−0.0160840	+	0.0337070i
$617$	−359.894	−	359.894i	−0.583296	−	0.583296i	0.352511	−	0.935808i	$-0.385328\pi$
$617$	−359.894	−	359.894i	−0.583296	−	0.583296i	−0.935808	+	0.352511i	$0.885328\pi$
$618$	−191.495	−	211.696i	−0.309862	−	0.342551i
$619$	353.068	−	1086.63i	0.570385	−	1.75546i	−0.0809973	−	0.996714i	$-0.525811\pi$
$619$	353.068	−	1086.63i	0.570385	−	1.75546i	0.651382	−	0.758750i	$-0.274189\pi$
$620$	−229.036	−	459.538i	−0.369412	−	0.741190i
$621$	832.115	−	604.567i	1.33996	−	0.973537i
$622$	170.754	−	76.4952i	0.274525	−	0.122983i
$623$	−3.67611	−	1.87307i	−0.00590066	−	0.00300654i
$624$	73.0953	+	160.197i	0.117140	+	0.256726i
$625$	31.7792	+	624.192i	0.0508467	+	0.998706i
$626$	26.5965	+	40.7498i	0.0424864	+	0.0650955i
$627$	−300.673	+	619.103i	−0.479542	+	0.987405i
$628$	−29.5276	−	75.8784i	−0.0470185	−	0.120825i
$629$	−866.768	−	629.744i	−1.37801	−	1.00118i
$630$	−3.25243	−	2.99493i	−0.00516258	−	0.00475385i
$631$	944.582	−	306.913i	1.49696	−	0.486392i	0.557831	−	0.829955i	$-0.311634\pi$
$631$	944.582	−	306.913i	1.49696	−	0.486392i	0.939130	+	0.343563i	$0.111634\pi$
$632$	−832.784	+	5.73887i	−1.31770	+	0.00908050i
$633$	34.1691	+	5.41185i	0.0539796	+	0.00854953i
$634$	−206.145	−	166.150i	−0.325150	−	0.262067i
$635$	275.060	+	163.782i	0.433165	+	0.257925i
$636$	217.086	+	372.046i	0.341330	+	0.584978i
$637$	140.849	−	140.849i	0.221113	−	0.221113i
$638$	951.303	−	448.211i	1.49107	−	0.702525i
$639$	−94.2418			−0.147483
$640$	35.1671	+	639.033i	0.0549486	+	0.998489i
$641$	−320.214	+	985.517i	−0.499554	+	1.53747i	0.310184	+	0.950677i	$0.399609\pi$
$641$	−320.214	+	985.517i	−0.499554	+	1.53747i	−0.809738	+	0.586792i	$0.800391\pi$
$642$	22.3908	+	208.428i	0.0348766	+	0.324654i
$643$	−891.746	−	141.239i	−1.38685	−	0.219656i	−0.582028	−	0.813169i	$-0.697741\pi$
$643$	−891.746	−	141.239i	−1.38685	−	0.219656i	−0.804825	+	0.593513i	$0.797741\pi$
$644$	−7.90423	−	36.3642i	−0.0122737	−	0.0564662i
$645$	−52.7041	+	63.3218i	−0.0817118	+	0.0981733i
$646$	−362.853	−	1341.85i	−0.561692	−	2.07717i
$647$	−977.200	+	154.773i	−1.51035	+	0.239217i	−0.856002	−	0.516973i	$-0.827059\pi$
$647$	−977.200	+	154.773i	−1.51035	+	0.239217i	−0.654353	+	0.756189i	$0.727059\pi$
$648$	−293.052	+	409.252i	−0.452240	+	0.631562i
$649$	407.294	+	123.776i	0.627572	+	0.190718i
$650$	26.8803	+	201.757i	0.0413543	+	0.310395i
$651$	−14.6796	−	10.6653i	−0.0225493	−	0.0163830i
$652$	804.475	−	45.8676i	1.23386	−	0.0703491i
$653$	1102.90	+	561.957i	1.68898	+	0.860578i	0.989261	+	0.146159i	$0.0466912\pi$
$653$	1102.90	+	561.957i	1.68898	+	0.860578i	0.699718	+	0.714419i	$0.253309\pi$
$654$	31.4217	−	82.4216i	0.0480453	−	0.126027i
$655$	850.841	+	339.819i	1.29899	+	0.518807i
$656$	−732.026	−	413.715i	−1.11589	−	0.630663i
$657$	7.63626	+	14.9870i	0.0116229	+	0.0228113i
$658$	1.51920	−	1.37422i	0.00230881	−	0.00208849i
$659$			208.811i			0.316860i	0.987370	+	0.158430i	$0.0506433\pi$
$659$			208.811i			0.316860i	−0.987370	+	0.158430i	$0.949357\pi$
$660$	484.738	+	344.639i	0.734452	+	0.522181i
$661$	109.752			0.166040			0.0830200	−	0.996548i	$-0.473543\pi$
$661$	109.752			0.166040			0.0830200	+	0.996548i	$0.473543\pi$
$662$	−444.014	−	490.856i	−0.670716	−	0.741474i
$663$	−294.477	+	150.043i	−0.444158	+	0.226310i
$664$	644.532	−	334.020i	0.970680	−	0.503042i
$665$	−27.8004	+	11.9317i	−0.0418051	+	0.0179424i
$666$	−112.753	−	42.9850i	−0.169299	−	0.0645421i
$667$	−772.241	+	1515.61i	−1.15778	+	2.27228i
$668$	16.3380	−	0.931520i	0.0244581	−	0.00139449i
$669$	200.040	−	275.331i	0.299013	−	0.411556i
$670$	265.643	−	579.152i	0.396482	−	0.864406i
$671$	941.685	−	18.0168i	1.40341	−	0.0268506i
$672$	11.5327	+	19.4558i	0.0171618	+	0.0289521i
$673$	142.691	+	900.918i	0.212023	+	1.33866i	0.832321	+	0.554294i	$0.187012\pi$
$673$	142.691	+	900.918i	0.212023	+	1.33866i	−0.620298	+	0.784366i	$0.712988\pi$
$674$	545.294	−	147.455i	0.809042	−	0.218775i
$675$	−573.593	+	439.455i	−0.849768	+	0.651044i
$676$	−129.505	−	595.802i	−0.191576	−	0.881364i
$677$	−69.4858	+	438.716i	−0.102638	+	0.648030i	0.881710	+	0.471792i	$0.156393\pi$
$677$	−69.4858	+	438.716i	−0.102638	+	0.648030i	−0.984348	+	0.176238i	$0.943607\pi$
$678$	−82.8850	+	8.90410i	−0.122249	+	0.0131329i
$679$	35.5295	+	11.5442i	0.0523263	+	0.0170018i
$680$	−1195.45	+	117.709i	−1.75802	+	0.173102i
$681$		−	801.836i		−	1.17744i
$682$	−495.067	−	271.854i	−0.725904	−	0.398612i
$683$	−839.835	−	839.835i	−1.22963	−	1.22963i	−0.964105	−	0.265522i	$-0.914456\pi$
$683$	−839.835	−	839.835i	−1.22963	−	1.22963i	−0.265522	−	0.964105i	$-0.585544\pi$
$684$	−78.9017	−	135.223i	−0.115353	−	0.197695i
$685$	−455.195	−	271.042i	−0.664518	−	0.395682i
$686$	32.1331	−	39.8680i	0.0468412	−	0.0581166i
$687$	22.0517	−	139.229i	0.0320986	−	0.202663i
$688$	−81.2925	+	53.8603i	−0.118158	+	0.0782853i
$689$	50.1074	+	154.215i	0.0727248	+	0.223824i
$690$	−961.240	+	39.6199i	−1.39310	+	0.0574201i
$691$	68.3233	−	94.0389i	0.0988759	−	0.136091i	−0.756712	−	0.653748i	$-0.773196\pi$
$691$	68.3233	−	94.0389i	0.0988759	−	0.136091i	0.855588	+	0.517657i	$0.173196\pi$
$692$	−75.0602	−	192.885i	−0.108468	−	0.278736i
$693$	−4.81722	−	0.668781i	−0.00695126	−	0.000965052i
$694$	−404.859	+	264.243i	−0.583371	+	0.380754i
$695$	−1178.75	−	77.7008i	−1.69605	−	0.111800i
$696$	154.684	−	1022.18i	0.222248	−	1.46865i
$697$	716.490	−	1406.19i	1.02796	−	2.01749i
$698$	452.935	+	1011.05i	0.648904	+	1.44850i
$699$	51.5848	+	71.0004i	0.0737980	+	0.101574i
$700$	6.20085	+	25.3974i	0.00885835	+	0.0362820i
$701$	−620.160	−	201.502i	−0.884678	−	0.287449i	−0.168780	−	0.985654i	$-0.553983\pi$
$701$	−620.160	−	201.502i	−0.884678	−	0.287449i	−0.715899	+	0.698204i	$0.753983\pi$
$702$	−174.515	+	157.861i	−0.248596	+	0.224873i
$703$	−583.842	+	583.842i	−0.830501	+	0.830501i
$704$	432.318	+	555.623i	0.614089	+	0.789237i
$705$	−28.2432	−	44.7997i	−0.0400613	−	0.0635457i
$706$	23.0091	−	459.221i	0.0325908	−	0.650454i
$707$	17.1632	+	33.6847i	0.0242761	+	0.0476446i
$708$	324.012	−	264.853i	0.457644	−	0.374087i
$709$	666.474	+	917.322i	0.940019	+	1.29383i	0.955821	+	0.293950i	$0.0949700\pi$
$709$	666.474	+	917.322i	0.940019	+	1.29383i	−0.0158017	+	0.999875i	$0.505030\pi$
$710$	463.938	+	308.704i	0.653434	+	0.434794i
$711$	−54.4029	−	167.435i	−0.0765160	−	0.235492i
$712$	−101.626	+	74.9107i	−0.142733	+	0.105212i
$713$	902.331	−	142.915i	1.26554	−	0.200442i
$714$	−35.5488	+	23.2019i	−0.0497883	+	0.0324957i
$715$	150.755	+	165.534i	0.210846	+	0.231516i
$716$	1096.45	+	482.146i	1.53135	+	0.673389i
$717$	−680.787	+	107.826i	−0.949493	+	0.150385i
$718$	−301.591	+	525.153i	−0.420043	+	0.731411i
$719$	−157.762	−	485.542i	−0.219419	−	0.675302i	−0.998810	−	0.0487648i	$-0.984472\pi$
$719$	−157.762	−	485.542i	−0.219419	−	0.675302i	0.779391	−	0.626538i	$-0.215528\pi$
$720$	−126.514	+	47.9445i	−0.175713	+	0.0665896i
$721$	−8.11274	−	11.1662i	−0.0112521	−	0.0154871i
$722$	−347.259	+	37.3051i	−0.480968	+	0.0516690i
$723$	−67.6075	−	132.687i	−0.0935097	−	0.183523i
$724$	103.299	+	177.037i	0.142679	+	0.244526i
$725$	515.267	−	1078.21i	0.710713	−	1.48719i
$726$	654.198	+	7.72157i	0.901099	+	0.0106358i
$727$	687.504	−	687.504i	0.945672	−	0.945672i	−0.0529261	−	0.998598i	$-0.516855\pi$
$727$	687.504	−	687.504i	0.945672	−	0.945672i	0.998598	+	0.0529261i	$0.0168548\pi$
$728$	2.68670	+	8.07894i	0.00369052	+	0.0110974i
$729$	−770.039	−	250.201i	−1.05629	−	0.343211i
$730$	11.5001	−	98.7925i	0.0157536	−	0.135332i
$731$	−107.583	−	148.075i	−0.147172	−	0.202565i
$732$	500.723	−	778.856i	0.684048	−	1.06401i
$733$	238.263	−	467.618i	0.325052	−	0.637951i	−0.669428	−	0.742877i	$-0.733461\pi$
$733$	238.263	−	467.618i	0.325052	−	0.637951i	0.994480	+	0.104926i	$0.0334606\pi$
$734$	786.533	−	212.689i	1.07157	−	0.289766i
$735$	−435.926	−	497.452i	−0.593096	−	0.676805i
$736$	−1103.26	−	282.077i	−1.49899	−	0.383256i
$737$	−122.865	−	690.032i	−0.166709	−	0.936271i
$738$	36.5572	−	173.952i	0.0495355	−	0.235707i
$739$	555.216	−	764.189i	0.751307	−	1.03408i	−0.246581	−	0.969122i	$-0.579307\pi$
$739$	555.216	−	764.189i	0.751307	−	1.03408i	0.997888	−	0.0649628i	$-0.0206929\pi$
$740$	414.263	+	580.950i	0.559815	+	0.785067i
$741$	78.7077	+	242.238i	0.106218	+	0.326906i
$742$	8.51490	+	19.0072i	0.0114756	+	0.0256161i
$743$	47.8436	−	302.073i	0.0643925	−	0.406558i	−0.934347	−	0.356365i	$-0.884016\pi$
$743$	47.8436	−	302.073i	0.0643925	−	0.406558i	0.998740	−	0.0501937i	$-0.0159839\pi$
$744$	−492.977	+	255.478i	−0.662603	+	0.343385i
$745$	−138.295	+	35.0675i	−0.185631	+	0.0470705i
$746$	−734.057	−	36.7797i	−0.983990	−	0.0493026i
$747$	108.513	+	108.513i	0.145266	+	0.145266i
$748$	−1006.87	+	855.682i	−1.34608	+	1.14396i
$749$			10.1357i			0.0135324i
$750$	674.372	−	44.9990i	0.899162	−	0.0599986i
$751$	413.712	+	134.423i	0.550882	+	0.178992i	0.571214	−	0.820801i	$-0.306472\pi$
$751$	413.712	+	134.423i	0.550882	+	0.178992i	−0.0203325	+	0.999793i	$0.506472\pi$
$752$	−16.7799	−	60.3982i	−0.0223137	−	0.0803167i
$753$	151.137	−	954.240i	0.200713	−	1.26725i
$754$	138.631	−	363.641i	0.183861	−	0.482282i
$755$	−96.3408	+	115.749i	−0.127604	+	0.153311i
$756$	−20.1213	+	22.5545i	−0.0266155	+	0.0298340i
$757$	−121.827	−	769.187i	−0.160934	−	1.01610i	−0.927470	−	0.373897i	$-0.878021\pi$
$757$	−121.827	−	769.187i	−0.160934	−	1.01610i	0.766536	−	0.642201i	$-0.221979\pi$
$758$	−47.9880	+	228.344i	−0.0633087	+	0.301245i
$759$	−844.096	+	638.294i	−1.11212	+	0.840967i
$760$	−54.5241	+	924.139i	−0.0717422	+	1.21597i
$761$	449.036	−	618.045i	0.590060	−	0.812148i	−0.404693	−	0.914453i	$-0.632622\pi$
$761$	449.036	−	618.045i	0.590060	−	0.812148i	0.994753	+	0.102304i	$0.0326216\pi$
$762$	172.404	−	300.202i	0.226251	−	0.393966i
$763$	1.93626	−	3.80012i	0.00253769	−	0.00498049i
$764$	20.3576	+	93.6570i	0.0266460	+	0.122588i
$765$	−100.153	−	233.351i	−0.130919	−	0.305035i
$766$	349.527	+	281.714i	0.456301	+	0.367773i
$767$	140.365	−	71.5193i	0.183005	−	0.0932455i
$768$	690.361	−	48.9151i	0.898908	−	0.0636915i
$769$	452.899			0.588946			0.294473	−	0.955660i	$-0.404856\pi$
$769$	452.899			0.588946			0.294473	+	0.955660i	$0.404856\pi$
$770$	21.5238	+	19.0719i	0.0279529	+	0.0247687i
$771$			258.542i			0.335333i
$772$	234.459	−	891.371i	0.303703	−	1.15463i
$773$	−601.603	−	1180.71i	−0.778271	−	1.52744i	−0.848072	−	0.529881i	$-0.822237\pi$
$773$	−601.603	−	1180.71i	−0.778271	−	1.52744i	0.0698013	−	0.997561i	$-0.477763\pi$
$774$	−16.0503	−	12.9363i	−0.0207368	−	0.0167136i
$775$	−631.154	+	116.491i	−0.814393	+	0.150311i
$776$	802.754	−	813.894i	1.03448	−	1.04883i
$777$	22.4670	+	11.4475i	0.0289151	+	0.0147330i
$778$	−572.778	+	997.364i	−0.736218	+	1.28196i
$779$	−983.980	−	714.903i	−1.26313	−	0.917719i
$780$	217.694	−	32.5029i	0.279094	−	0.0416704i
$781$	612.872	−	11.7258i	0.784727	−	0.0150138i
$782$	439.574	−	2091.65i	0.562115	−	2.67474i
$783$	1364.58	−	216.128i	1.74276	−	0.276026i
$784$	−324.995	−	712.265i	−0.414534	−	0.908501i
$785$	−101.353	+	9.27493i	−0.129112	+	0.0118152i
$786$	352.933	−	925.771i	0.449024	−	1.17783i
$787$	−1398.16	−	221.447i	−1.77657	−	0.281381i	−0.819891	−	0.572519i	$-0.805966\pi$
$787$	−1398.16	−	221.447i	−1.77657	−	0.281381i	−0.956681	+	0.291138i	$0.905966\pi$
$788$	26.7707	+	32.7502i	0.0339729	+	0.0415612i
$789$	−102.338	+	314.963i	−0.129706	+	0.399193i
$790$	−280.642	+	1002.46i	−0.355243	+	1.26894i
$791$	−4.03066			−0.00509565
$792$	−84.3137	+	122.636i	−0.106457	+	0.154843i
$793$	246.466	−	246.466i	0.310802	−	0.310802i
$794$	785.267	+	39.3456i	0.989001	+	0.0495536i
$795$	521.918	−	132.343i	0.656501	−	0.166470i
$796$	−124.450	+	1238.78i	−0.156344	+	1.55626i
$797$	−276.563	−	43.8033i	−0.347005	−	0.0549603i	−0.0195008	−	0.999810i	$-0.506208\pi$
$797$	−276.563	−	43.8033i	−0.347005	−	0.0549603i	−0.327505	+	0.944850i	$0.606208\pi$
$798$	13.3750	+	29.8561i	0.0167607	+	0.0374136i
$799$	111.898	−	36.3579i	0.140048	−	0.0455042i
$800$	779.857	+	178.391i	0.974821	+	0.222989i
$801$	−21.5919	−	15.6874i	−0.0269561	−	0.0195848i
$802$	135.615	−	645.302i	0.169095	−	0.804615i
$803$	−51.5247	−	96.5131i	−0.0641653	−	0.120191i
$804$	−630.741	−	277.359i	−0.784504	−	0.344974i
$805$	−46.4160	−	3.05964i	−0.0576596	−	0.00380080i
$806$	−201.769	+	54.5608i	−0.250334	+	0.0676934i
$807$	185.770	+	94.6545i	0.230198	+	0.117292i
$808$	1156.83	−	7.97194i	1.43172	−	0.00986626i
$809$	810.194	−	588.640i	1.00148	−	0.727615i	0.0390715	−	0.999236i	$-0.487560\pi$
$809$	810.194	−	588.640i	1.00148	−	0.727615i	0.962404	+	0.271622i	$0.0875600\pi$
$810$	390.480	+	493.366i	0.482075	+	0.609094i
$811$	20.1456	−	62.0019i	0.0248405	−	0.0764511i	−0.937868	−	0.346993i	$-0.887203\pi$
$811$	20.1456	−	62.0019i	0.0248405	−	0.0764511i	0.962708	+	0.270542i	$0.0872028\pi$
$812$	12.7155	−	48.3421i	0.0156595	−	0.0595346i
$813$	60.6370	+	60.6370i	0.0745842	+	0.0745842i
$814$	738.603	+	265.510i	0.907375	+	0.326180i
$815$	222.659	−	982.308i	0.273201	−	1.20529i
$816$	147.647	+	1290.59i	0.180940	+	1.58160i
$817$	−125.681	+	64.0376i	−0.153832	+	0.0783814i
$818$	486.004	−	52.2101i	0.594138	−	0.0638265i
$819$	−1.45608	+	1.05791i	−0.00177788	+	0.00129171i
$820$	−749.772	+	736.590i	−0.914356	+	0.898280i
$821$	−387.721	+	125.978i	−0.472255	+	0.153445i	−0.535468	−	0.844555i	$-0.679865\pi$
$821$	−387.721	+	125.978i	−0.472255	+	0.153445i	0.0632140	+	0.998000i	$0.479865\pi$
$822$	−285.310	+	496.803i	−0.347092	+	0.604383i
$823$	8.66948	+	54.7369i	0.0105340	+	0.0665090i	0.992395	−	0.123091i	$-0.0392808\pi$
$823$	8.66948	+	54.7369i	0.0105340	+	0.0665090i	−0.981861	+	0.189600i	$0.939281\pi$
$824$	−416.689	+	68.9437i	−0.505690	+	0.0836696i
$825$	581.405	−	463.355i	0.704734	−	0.561643i
$826$	16.9446	−	11.0594i	0.0205141	−	0.0133891i
$827$	176.337	+	1113.35i	0.213225	+	1.34625i	0.829406	+	0.558646i	$0.188679\pi$
$827$	176.337	+	1113.35i	0.213225	+	1.34625i	−0.616181	+	0.787604i	$0.711321\pi$
$828$	−13.7029	−	240.336i	−0.0165494	−	0.290261i
$829$	−931.441	+	302.643i	−1.12357	+	0.365070i	−0.811130	−	0.584866i	$-0.801147\pi$
$829$	−931.441	+	302.643i	−1.12357	+	0.365070i	−0.312442	+	0.949937i	$0.601147\pi$
$830$	−178.742	−	889.648i	−0.215352	−	1.07186i
$831$	818.077	−	594.367i	0.984448	−	0.715244i
$832$	257.861	+	37.2058i	0.309929	+	0.0447185i
$833$	1309.30	−	667.119i	1.57178	−	0.800864i
$834$	−63.9267	+	1275.86i	−0.0766507	+	1.52981i
$835$	4.52195	−	19.9496i	0.00541551	−	0.0238917i
$836$	529.937	+	869.565i	0.633896	+	1.04015i
$837$	−524.691	−	524.691i	−0.626871	−	0.626871i
$838$	709.032	−	641.370i	0.846100	−	0.765358i
$839$	−224.793	+	691.841i	−0.267929	+	0.824602i	0.723075	+	0.690770i	$0.242728\pi$
$839$	−224.793	+	691.841i	−0.267929	+	0.824602i	−0.991004	+	0.133832i	$0.957272\pi$
$840$	27.3555	−	7.13754i	0.0325661	−	0.00849708i
$841$	−1168.11	+	848.678i	−1.38895	+	1.00913i
$842$	228.328	+	509.679i	0.271173	+	0.605320i
$843$	−608.298	−	309.944i	−0.721588	−	0.367667i
$844$	34.0749	−	38.1954i	0.0403731	−	0.0452552i
$845$	−760.493	−	50.1301i	−0.899991	−	0.0593255i
$846$	11.0971	−	7.24281i	0.0131171	−	0.00856124i
$847$	31.4105	+	3.74984i	0.0370844	+	0.00442720i
$848$	636.730	+	27.5059i	0.750861	+	0.0324362i
$849$	−26.9361	−	19.5702i	−0.0317269	−	0.0230509i
$850$	−271.343	+	1476.82i	−0.319227	+	1.73743i
$851$	−1207.43	+	392.317i	−1.41883	+	0.461007i
$852$	325.883	−	506.898i	0.382491	−	0.594951i
$853$	−346.935	−	54.9491i	−0.406723	−	0.0644186i	−0.0502788	−	0.998735i	$-0.516011\pi$
$853$	−346.935	−	54.9491i	−0.406723	−	0.0644186i	−0.356444	+	0.934317i	$0.616011\pi$
$854$	28.0945	−	34.8573i	0.0328976	−	0.0408165i
$855$	−189.696	+	48.1013i	−0.221866	+	0.0562588i
$856$	277.317	+	138.901i	0.323968	+	0.162268i
$857$	−526.108	+	526.108i	−0.613895	+	0.613895i	−0.943959	−	0.330064i	$-0.892930\pi$
$857$	−526.108	+	526.108i	−0.613895	+	0.613895i	0.330064	+	0.943959i	$0.392930\pi$
$858$	176.416	−	165.826i	0.205613	−	0.193270i
$859$	−661.754			−0.770377			−0.385189	−	0.922838i	$-0.625864\pi$
$859$	−661.754			−0.770377			−0.385189	+	0.922838i	$0.625864\pi$
$860$	36.6381	+	116.259i	0.0426024	+	0.135185i
$861$	−11.4780	+	35.3256i	−0.0133310	+	0.0410286i
$862$	−283.559	+	30.4620i	−0.328955	+	0.0353387i
$863$	636.261	+	100.774i	0.737266	+	0.116771i	0.513764	−	0.857932i	$-0.328251\pi$
$863$	636.261	+	100.774i	0.737266	+	0.116771i	0.223503	+	0.974703i	$0.428251\pi$
$864$	341.353	+	859.614i	0.395084	+	0.994923i
$865$	−257.642	+	23.5771i	−0.297852	+	0.0272568i
$866$	677.457	−	183.193i	0.782283	−	0.211539i
$867$	−1636.43	+	259.185i	−1.88746	+	0.298945i
$868$	−25.0191	+	9.73606i	−0.0288239	+	0.0112167i
$869$	374.625	+	1082.09i	0.431099	+	1.24521i
$870$	−1174.61	−	538.763i	−1.35012	−	0.619267i
$871$	−209.841	−	152.459i	−0.240920	−	0.175039i
$872$	−77.4376	−	105.054i	−0.0888046	−	0.120474i
$873$	215.322	+	109.712i	0.246646	+	0.125673i
$874$	−1539.12	−	586.759i	−1.76100	−	0.671349i
$875$	32.6526	+	1.31950i	0.0373173	+	0.00150800i
$876$	−107.016	−	10.7510i	−0.122165	−	0.0122729i
$877$	282.283	+	554.012i	0.321874	+	0.631713i	0.994080	−	0.108651i	$-0.0346532\pi$
$877$	282.283	+	554.012i	0.321874	+	0.631713i	−0.672206	+	0.740364i	$0.734653\pi$
$878$	−498.766	−	551.383i	−0.568070	−	0.627999i
$879$		−	1069.86i		−	1.21713i
$880$	816.775	−	327.533i	0.928154	−	0.372197i
$881$	328.268			0.372609			0.186304	−	0.982492i	$-0.440349\pi$
$881$	328.268			0.372609			0.186304	+	0.982492i	$0.440349\pi$
$882$	122.738	−	111.026i	0.139159	−	0.125879i
$883$	−1075.50	+	547.994i	−1.21801	+	0.620605i	−0.940393	−	0.340088i	$-0.889543\pi$
$883$	−1075.50	+	547.994i	−1.21801	+	0.620605i	−0.277612	+	0.960693i	$0.589543\pi$
$884$	−48.8794	+	486.548i	−0.0552934	+	0.550394i
$885$	−206.314	−	480.704i	−0.233124	−	0.543168i
$886$	−504.870	+	1324.32i	−0.569831	+	1.49471i
$887$	206.041	−	404.377i	0.232289	−	0.455893i	−0.745211	−	0.666829i	$-0.767651\pi$
$887$	206.041	−	404.377i	0.232289	−	0.455893i	0.977500	+	0.210936i	$0.0676511\pi$
$888$	621.098	−	457.826i	0.699434	−	0.515570i
$889$	9.83866	−	13.5418i	0.0110671	−	0.0152326i
$890$	54.9069	+	147.954i	0.0616932	+	0.166241i
$891$	662.210	+	201.244i	0.743221	+	0.225863i
$892$	−182.610	−	469.261i	−0.204720	−	0.526077i
$893$	−14.1845	−	89.5572i	−0.0158841	−	0.100288i
$894$	40.2739	+	148.935i	0.0450491	+	0.166594i
$895$	957.808	−	1150.77i	1.07018	−	1.28577i
$896$	33.4416	+	1.21382i	0.0373232	+	0.00135470i
$897$	−61.2649	+	386.812i	−0.0682998	+	0.431228i
$898$	−3.92919	−	36.5754i	−0.00437549	−	0.0407298i
$899$	1167.09	+	379.211i	1.29821	+	0.421815i
$900$	13.9175	+	168.543i	0.0154639	+	0.187270i
$901$			1196.21i			1.32765i
$902$	−216.095	+	1135.79i	−0.239573	+	1.25919i
$903$	3.04599	+	3.04599i	0.00337319	+	0.00337319i
$904$	−55.2365	+	110.280i	−0.0611024	+	0.121991i
$905$	248.353	−	62.9750i	0.274423	−	0.0695856i
$906$	126.797	+	102.197i	0.139953	+	0.112800i
$907$	−90.4755	+	571.240i	−0.0997524	+	0.629812i	0.886266	+	0.463176i	$0.153290\pi$
$907$	−90.4755	+	571.240i	−0.0997524	+	0.629812i	−0.986019	+	0.166636i	$0.946710\pi$
$908$	−997.935	−	641.568i	−1.09905	−	0.706572i
$909$	75.5718	+	232.586i	0.0831372	+	0.255870i
$910$	10.6334	−	0.438283i	0.0116851	−	0.000481629i
$911$	−637.032	+	876.800i	−0.699267	+	0.962459i	0.300695	+	0.953720i	$0.402782\pi$
$911$	−637.032	+	876.800i	−0.699267	+	0.962459i	−0.999962	+	0.00873830i	$0.997218\pi$
$912$	1000.16	+	43.2057i	1.09667	+	0.0473746i
$913$	−719.184	−	692.181i	−0.787715	−	0.758139i
$914$	480.541	+	736.260i	0.525756	+	0.805536i
$915$	−762.808	−	870.470i	−0.833670	−	0.951333i
$916$	−155.635	−	138.845i	−0.169908	−	0.151578i
$917$	21.7483	−	42.6835i	0.0237168	−	0.0465469i
$918$	−1584.28	+	709.730i	−1.72579	+	0.773126i
$919$	862.669	+	1187.36i	0.938704	+	1.29202i	0.956366	+	0.292171i	$0.0943776\pi$
$919$	862.669	+	1187.36i	0.938704	+	1.29202i	−0.0176622	+	0.999844i	$0.505622\pi$
$920$	−719.801	+	1228.02i	−0.782392	+	1.33481i
$921$	749.629	+	243.569i	0.813929	+	0.264462i
$922$	−695.028	−	768.350i	−0.753826	−	0.833351i
$923$	160.406	−	160.406i	0.173788	−	0.173788i
$924$	20.2549	−	23.5978i	0.0219208	−	0.0255387i
$925$	840.968	−	297.097i	0.909155	−	0.321186i
$926$	−1799.31	−	90.1537i	−1.94309	−	0.0973582i
$927$	−40.5341	−	79.5526i	−0.0437261	−	0.0858173i
$928$	−1148.40	−	1010.38i	−1.23750	−	1.08878i
$929$	−237.866	−	327.394i	−0.256045	−	0.352416i	0.661572	−	0.749882i	$-0.269890\pi$
$929$	−237.866	−	327.394i	−0.256045	−	0.352416i	−0.917617	+	0.397466i	$0.869890\pi$
$930$	136.713	+	680.456i	0.147003	+	0.731674i
$931$	−349.948	−	1077.03i	−0.375884	−	1.15685i
$932$	129.639	−	7.39142i	0.139097	−	0.00793071i
$933$	−249.805	+	39.5652i	−0.267744	+	0.0424065i
$934$	401.383	+	614.978i	0.429746	+	0.658435i
$935$	680.345	+	1505.07i	0.727642	+	1.60970i
$936$	8.99032	+	54.3365i	0.00960504	+	0.0580518i
$937$	−266.894	+	42.2719i	−0.284839	+	0.0451141i	−0.297219	−	0.954809i	$-0.596059\pi$
$937$	−266.894	+	42.2719i	−0.284839	+	0.0451141i	0.0123800	+	0.999923i	$0.496059\pi$
$938$	−28.8903	−	16.5914i	−0.0307999	−	0.0176881i
$939$	−20.3264	−	62.5581i	−0.0216468	−	0.0666220i
$940$	−78.3541	−	0.694918i	−0.0833554	−	0.000739275i
$941$	112.348	+	154.634i	0.119392	+	0.164329i	0.864530	−	0.502581i	$-0.167616\pi$
$941$	112.348	+	154.634i	0.119392	+	0.164329i	−0.745138	+	0.666911i	$0.767616\pi$
$942$	11.7558	+	109.431i	0.0124797	+	0.116169i
$943$	−849.024	−	1666.30i	−0.900343	−	1.76702i
$944$	−70.3771	−	615.168i	−0.0745520	−	0.651661i
$945$	20.1490	+	31.9606i	0.0213216	+	0.0338207i
$946$	105.987	+	82.1303i	0.112037	+	0.0868185i
$947$	222.651	−	222.651i	0.235112	−	0.235112i	−0.579711	−	0.814823i	$-0.696834\pi$
$947$	222.651	−	222.651i	0.235112	−	0.235112i	0.814823	+	0.579711i	$0.196834\pi$
$948$	1088.70	+	286.363i	1.14842	+	0.302071i
$949$	−38.5064	−	12.5115i	−0.0405757	−	0.0131838i
$950$	1091.41	+	384.583i	1.14885	+	0.404824i
$951$	210.367	+	289.545i	0.221206	+	0.304463i
$952$	0.432816	+	62.8071i	0.000454639	+	0.0659739i
$953$	−739.244	+	1450.85i	−0.775702	+	1.52240i	0.0752547	+	0.997164i	$0.476023\pi$
$953$	−739.244	+	1450.85i	−0.775702	+	1.52240i	−0.850956	+	0.525236i	$0.823977\pi$
$954$	35.1690	+	130.057i	0.0368648	+	0.136328i
$955$	119.546	+	7.88019i	0.125179	+	0.00825151i
$956$	−410.517	+	933.556i	−0.429411	+	0.976523i
$957$	−1399.49	+	249.188i	−1.46237	+	0.260384i
$958$	−172.634	−	36.2803i	−0.180203	−	0.0378708i
$959$	−16.2820	+	22.4102i	−0.0169781	+	0.0233683i
$960$	179.597	−	846.268i	0.187080	−	0.881529i
$961$	93.2980	+	287.142i	0.0970843	+	0.298795i
$962$	265.077	−	118.750i	0.275548	−	0.123441i
$963$	−10.2568	+	64.7590i	−0.0106509	+	0.0672472i
$964$	−219.232	−	22.0244i	−0.227419	−	0.0228469i
$965$	−989.914	−	589.437i	−1.02582	−	0.610815i
$966$	−2.51725	+	50.2398i	−0.00260585	+	0.0520081i
$967$	845.499	+	845.499i	0.874353	+	0.874353i	0.992943	−	0.118590i	$-0.0378376\pi$
$967$	845.499	+	845.499i	0.874353	+	0.874353i	−0.118590	+	0.992943i	$0.537838\pi$
$968$	533.049	−	808.012i	0.550670	−	0.834723i
$969$			1878.98i			1.93909i
$970$	−700.619	−	1245.42i	−0.722288	−	1.28394i
$971$	−138.975	−	45.1558i	−0.143126	−	0.0465045i	0.236578	−	0.971613i	$-0.423974\pi$
$971$	−138.975	−	45.1558i	−0.143126	−	0.0465045i	−0.379704	+	0.925108i	$0.623974\pi$
$972$	−278.819	+	227.912i	−0.286851	+	0.234477i
$973$	−9.66248	+	61.0065i	−0.00993061	+	0.0626994i
$974$	−779.675	−	297.236i	−0.800488	−	0.305171i
$975$	36.1155	−	272.753i	0.0370415	−	0.279746i
$976$	−568.695	−	1246.36i	−0.582679	−	1.27701i
$977$	201.901	+	1274.75i	0.206654	+	1.30476i	0.844899	+	0.534926i	$0.179661\pi$
$977$	201.901	+	1274.75i	0.206654	+	1.30476i	−0.638245	+	0.769833i	$0.720339\pi$
$978$	−1065.92	−	224.011i	−1.08990	−	0.229050i
$979$	142.368	+	99.3316i	0.145422	+	0.101462i
$980$	−967.904	+	144.514i	−0.987657	+	0.147463i
$981$	16.2166	−	22.3202i	0.0165307	−	0.0227525i
$982$	−19.6957	−	11.3111i	−0.0200567	−	0.0115184i
$983$	−858.908	+	1685.70i	−0.873762	+	1.71485i	−0.194576	+	0.980888i	$0.562333\pi$
$983$	−858.908	+	1685.70i	−0.873762	+	1.71485i	−0.679186	+	0.733966i	$0.737667\pi$
$984$	809.222	+	798.146i	0.822380	+	0.811124i
$985$	48.5883	−	20.8537i	0.0493282	−	0.0211713i
$986$	1801.62	−	2235.30i	1.82720	−	2.26703i
$987$	−2.46727	+	1.25714i	−0.00249976	+	0.00127369i
$988$	364.456	+	95.8632i	0.368882	+	0.0970276i
$989$	−216.887			−0.219299
$990$	118.219	+	143.634i	0.119413	+	0.145085i
$991$		−	204.299i		−	0.206154i	−0.994673	−	0.103077i	$-0.967131\pi$
$991$		−	204.299i		−	0.206154i	0.994673	−	0.103077i	$-0.0328688\pi$
$992$	−76.4834	+	817.954i	−0.0771002	+	0.824551i
$993$	406.183	+	797.178i	0.409046	+	0.802798i
$994$	18.2846	−	22.6860i	0.0183950	−	0.0228229i
$995$	1445.26	+	577.227i	1.45253	+	0.580127i
$996$	−958.894	+	208.428i	−0.962745	+	0.209265i
$997$	1335.75	+	680.597i	1.33977	+	0.682645i	0.969226	−	0.246172i	$-0.0791728\pi$
$997$	1335.75	+	680.597i	1.33977	+	0.682645i	0.370540	+	0.928817i	$0.379173\pi$
$998$	−142.206	−	81.6676i	−0.142491	−	0.0818313i
$999$	834.229	+	606.103i	0.835064	+	0.606709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.w.a.7.18	yes	544
4.3	odd	2	inner	220.3.w.a.7.10	✓	544
5.3	odd	4	inner	220.3.w.a.183.51	yes	544
11.8	odd	10	inner	220.3.w.a.107.26	yes	544
20.3	even	4	inner	220.3.w.a.183.26	yes	544
44.19	even	10	inner	220.3.w.a.107.51	yes	544
55.8	even	20	inner	220.3.w.a.63.10	yes	544
220.63	odd	20	inner	220.3.w.a.63.18	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.w.a.7.10	✓	544	4.3	odd	2	inner
220.3.w.a.7.18	yes	544	1.1	even	1	trivial
220.3.w.a.63.10	yes	544	55.8	even	20	inner
220.3.w.a.63.18	yes	544	220.63	odd	20	inner
220.3.w.a.107.26	yes	544	11.8	odd	10	inner
220.3.w.a.107.51	yes	544	44.19	even	10	inner
220.3.w.a.183.26	yes	544	20.3	even	4	inner
220.3.w.a.183.51	yes	544	5.3	odd	4	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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48321 + 1.34167i) q^{2} +(2.40882 - 1.22736i) q^{3} +(0.399834 - 3.97997i) q^{4} +(-4.64336 - 1.85452i) q^{5} +(-1.92608 + 5.05228i) q^{6} +(-0.118689 + 0.232940i) q^{7} +(4.74677 + 6.43958i) q^{8} +(-0.994045 + 1.36819i) q^{9} +(9.37524 - 3.47922i) q^{10} +(6.29422 - 9.02124i) q^{11} +(-3.92171 - 10.0778i) q^{12} +(-0.636813 - 4.02068i) q^{13} +(-0.136488 - 0.504740i) q^{14} +(-13.4612 + 1.23185i) q^{15} +(-15.6803 - 3.18265i) q^{16} +(4.69785 - 29.6611i) q^{17} +(-0.361277 - 3.36299i) q^{18} +(-22.0109 - 7.15178i) q^{19} +(-9.23749 + 17.7389i) q^{20} +0.706783i q^{21} +(2.76788 + 21.8252i) q^{22} +(-25.1629 - 25.1629i) q^{23} +(19.3378 + 9.68582i) q^{24} +(18.1215 + 17.2224i) q^{25} +(6.33896 + 5.10912i) q^{26} +(-4.52149 + 28.5476i) q^{27} +(0.879636 + 0.565514i) q^{28} +(-14.7711 - 45.4607i) q^{29} +(18.3130 - 19.8876i) q^{30} +(-15.0900 + 20.7696i) q^{31} +(27.5272 - 16.3172i) q^{32} +(4.08939 - 29.4558i) q^{33} +(32.8275 + 50.2966i) q^{34} +(0.983104 - 0.861511i) q^{35} +(5.04788 + 4.50331i) q^{36} +(16.1966 - 31.7877i) q^{37} +(42.2422 - 18.9238i) q^{38} +(-6.46877 - 8.90350i) q^{39} +(-10.0986 - 38.7042i) q^{40} +(49.9808 + 16.2397i) q^{41} +(-0.948271 - 1.04831i) q^{42} +(4.30965 - 4.30965i) q^{43} +(-33.3876 - 28.6578i) q^{44} +(7.15303 - 4.50950i) q^{45} +(71.0824 + 3.56156i) q^{46} +(1.77867 + 3.49084i) q^{47} +(-41.6772 + 11.5788i) q^{48} +(28.7613 + 39.5865i) q^{49} +(-49.9848 - 1.23130i) q^{50} +(-25.0884 - 77.2142i) q^{51} +(-16.2568 + 0.926890i) q^{52} +(-39.3423 + 6.23122i) q^{53} +(-31.5951 - 48.4084i) q^{54} +(-45.9564 + 30.2161i) q^{55} +(-2.06342 + 0.341406i) q^{56} +(-61.7982 + 9.78787i) q^{57} +(82.9019 + 47.6099i) q^{58} +(11.9586 + 36.8047i) q^{59} +(-0.479522 + 54.0676i) q^{60} +(50.3282 + 69.2708i) q^{61} +(-5.48431 - 51.0514i) q^{62} +(-0.200723 - 0.393940i) q^{63} +(-18.9363 + 61.1344i) q^{64} +(-4.49947 + 19.8504i) q^{65} +(33.4546 + 49.1758i) q^{66} +(45.0546 - 45.0546i) q^{67} +(-116.172 - 30.5568i) q^{68} +(-91.4969 - 29.7292i) q^{69} +(-0.302287 + 2.59681i) q^{70} +(32.7548 + 45.0831i) q^{71} +(-13.5290 + 0.0932312i) q^{72} +(4.51537 - 8.86192i) q^{73} +(18.6256 + 68.8785i) q^{74} +(64.7895 + 19.2441i) q^{75} +(-37.2646 + 84.7432i) q^{76} +(1.35435 + 2.53689i) q^{77} +(21.5401 + 4.52681i) q^{78} +(-61.1887 + 84.2190i) q^{79} +(66.9068 + 43.8575i) q^{80} +(19.4432 + 59.8399i) q^{81} +(-95.9205 + 42.9708i) q^{82} +(14.1953 - 89.6254i) q^{83} +(2.81297 + 0.282596i) q^{84} +(-76.8208 + 129.015i) q^{85} +(-0.609987 + 12.1743i) q^{86} +(-91.3773 - 91.3773i) q^{87} +(87.9702 - 2.28961i) q^{88} +15.7814i q^{89} +(-4.55919 + 16.2856i) q^{90} +(1.01216 + 0.328870i) q^{91} +(-110.209 + 90.0866i) q^{92} +(-10.8574 + 68.5509i) q^{93} +(-7.32171 - 2.79126i) q^{94} +(88.9414 + 74.0279i) q^{95} +(46.2812 - 73.0910i) q^{96} +(-22.3539 - 141.137i) q^{97} +(-95.7712 - 20.1270i) q^{98} +(6.08599 + 17.5792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Introduction

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