LMFDB - Embedded newform 105.3.w.a.38.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,3,Mod(17,105)] 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("105.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.w (of order $12$, degree $4$, 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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			38.4
Character	$\chi$	$=$	105.38
Dual form			105.3.w.a.47.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.810462 + 3.02468i) q^{2} +(2.92544 - 0.664693i) q^{3} +(-5.02776 - 2.90278i) q^{4} +(4.98450 - 0.393384i) q^{5} +(-0.360468 + 9.38723i) q^{6} +(-3.66357 + 5.96475i) q^{7} +(3.99791 - 3.99791i) q^{8} +(8.11637 - 3.88904i) q^{9} +(-2.84988 + 15.3954i) q^{10} +(10.3392 + 5.96936i) q^{11} +(-16.6379 - 5.14998i) q^{12} +(-7.11430 + 7.11430i) q^{13} +(-15.0723 - 15.9153i) q^{14} +(14.3204 - 4.46398i) q^{15} +(-2.75886 - 4.77849i) q^{16} +(-0.811768 - 3.02956i) q^{17} +(5.18510 + 27.7014i) q^{18} +(-17.2142 - 29.8159i) q^{19} +(-26.2028 - 12.4911i) q^{20} +(-6.75280 + 19.8847i) q^{21} +(-26.4350 + 26.4350i) q^{22} +(-9.38391 - 2.51441i) q^{23} +(9.03824 - 14.3530i) q^{24} +(24.6905 - 3.92165i) q^{25} +(-15.7526 - 27.2844i) q^{26} +(21.1589 - 16.7720i) q^{27} +(35.7339 - 19.3548i) q^{28} +26.5784 q^{29} +(1.89604 + 46.9325i) q^{30} +(0.677558 + 0.391188i) q^{31} +(38.5343 - 10.3252i) q^{32} +(34.2146 + 10.5906i) q^{33} +9.82137 q^{34} +(-15.9146 + 31.1725i) q^{35} +(-52.0962 - 4.00687i) q^{36} +(28.4517 + 7.62362i) q^{37} +(104.135 - 27.9030i) q^{38} +(-16.0836 + 25.5412i) q^{39} +(18.3549 - 21.5003i) q^{40} -43.0909 q^{41} +(-54.6719 - 36.5408i) q^{42} +(-40.7104 - 40.7104i) q^{43} +(-34.6554 - 60.0250i) q^{44} +(38.9261 - 22.5778i) q^{45} +(15.2106 - 26.3455i) q^{46} +(28.9750 + 7.76382i) q^{47} +(-11.2471 - 12.1454i) q^{48} +(-22.1566 - 43.7045i) q^{49} +(-8.14895 + 77.8593i) q^{50} +(-4.38851 - 8.32321i) q^{51} +(56.4202 - 15.1177i) q^{52} +(-4.59967 - 17.1662i) q^{53} +(33.5816 + 77.5921i) q^{54} +(53.8841 + 25.6870i) q^{55} +(9.19994 + 38.4931i) q^{56} +(-70.1776 - 75.7825i) q^{57} +(-21.5408 + 80.3912i) q^{58} +(-62.8463 - 36.2843i) q^{59} +(-84.9573 - 19.1250i) q^{60} +(21.4620 - 12.3911i) q^{61} +(-1.73236 + 1.73236i) q^{62} +(-6.53769 + 62.6599i) q^{63} +102.852i q^{64} +(-32.6626 + 38.2599i) q^{65} +(-59.7627 + 94.9050i) q^{66} +(15.0622 + 56.2130i) q^{67} +(-4.71277 + 17.5883i) q^{68} +(-29.1233 - 1.11833i) q^{69} +(-81.3888 - 73.4008i) q^{70} -43.6004i q^{71} +(16.9005 - 47.9965i) q^{72} +(0.0891230 + 0.332612i) q^{73} +(-46.1180 + 79.8788i) q^{74} +(69.6238 - 27.8841i) q^{75} +199.877i q^{76} +(-73.4842 + 39.8018i) q^{77} +(-64.2191 - 69.3480i) q^{78} +(-66.7293 + 38.5262i) q^{79} +(-15.6313 - 22.7331i) q^{80} +(50.7508 - 63.1297i) q^{81} +(34.9235 - 130.336i) q^{82} +(76.7710 + 76.7710i) q^{83} +(91.6722 - 80.3734i) q^{84} +(-5.23804 - 14.7815i) q^{85} +(156.130 - 90.1420i) q^{86} +(77.7534 - 17.6665i) q^{87} +(65.2002 - 17.4703i) q^{88} +(56.8471 - 32.8207i) q^{89} +(36.7424 + 136.038i) q^{90} +(-16.3713 - 68.4987i) q^{91} +(39.8813 + 39.8813i) q^{92} +(2.24217 + 0.694029i) q^{93} +(-46.9662 + 81.3479i) q^{94} +(-97.5335 - 141.846i) q^{95} +(105.867 - 55.8194i) q^{96} +(-53.5343 - 53.5343i) q^{97} +(150.149 - 31.5958i) q^{98} +(107.132 + 8.23984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) $ 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.810462	+	3.02468i	−0.405231	+	1.51234i	0.398399	+	0.917212i	$0.369566\pi$
$2$	−0.810462	+	3.02468i	−0.405231	+	1.51234i	−0.803630	+	0.595130i	$0.797101\pi$
$3$	2.92544	−	0.664693i	0.975146	−	0.221564i
$3$	2.92544	−	0.664693i	0.975146	−	0.221564i
$4$	−5.02776	−	2.90278i	−1.25694	−	0.725695i
$5$	4.98450	−	0.393384i	0.996900	−	0.0786768i
$5$	4.98450	−	0.393384i	0.996900	−	0.0786768i
$6$	−0.360468	+	9.38723i	−0.0600779	+	1.56454i
$7$	−3.66357	+	5.96475i	−0.523367	+	0.852108i
$7$	−3.66357	+	5.96475i	−0.523367	+	0.852108i
$8$	3.99791	−	3.99791i	0.499738	−	0.499738i
$9$	8.11637	−	3.88904i	0.901818	−	0.432115i
$10$	−2.84988	+	15.3954i	−0.284988	+	1.53954i
$11$	10.3392	+	5.96936i	0.939930	+	0.542669i	0.889938	−	0.456081i	$-0.150747\pi$
$11$	10.3392	+	5.96936i	0.939930	+	0.542669i	0.0499915	+	0.998750i	$0.484081\pi$
$12$	−16.6379	−	5.14998i	−1.38649	−	0.429165i
$13$	−7.11430	+	7.11430i	−0.547254	+	0.547254i	−0.925645	−	0.378392i	$-0.876477\pi$
$13$	−7.11430	+	7.11430i	−0.547254	+	0.547254i	0.378392	+	0.925645i	$0.376477\pi$
$14$	−15.0723	−	15.9153i	−1.07659	−	1.13681i
$15$	14.3204	−	4.46398i	0.954691	−	0.297599i
$16$	−2.75886	−	4.77849i	−0.172429	−	0.298656i
$17$	−0.811768	−	3.02956i	−0.0477511	−	0.178209i	0.937932	−	0.346820i	$-0.112739\pi$
$17$	−0.811768	−	3.02956i	−0.0477511	−	0.178209i	−0.985683	+	0.168611i	$0.946072\pi$
$18$	5.18510	+	27.7014i	0.288061	+	1.53896i
$19$	−17.2142	−	29.8159i	−0.906013	−	1.56926i	−0.819552	−	0.573005i	$-0.805778\pi$
$19$	−17.2142	−	29.8159i	−0.906013	−	1.56926i	−0.0864609	−	0.996255i	$-0.527556\pi$
$20$	−26.2028	−	12.4911i	−1.31014	−	0.624553i
$21$	−6.75280	+	19.8847i	−0.321562	+	0.946889i
$22$	−26.4350	+	26.4350i	−1.20159	+	1.20159i
$23$	−9.38391	−	2.51441i	−0.407996	−	0.109322i	0.0489831	−	0.998800i	$-0.484402\pi$
$23$	−9.38391	−	2.51441i	−0.407996	−	0.109322i	−0.456979	+	0.889477i	$0.651069\pi$
$24$	9.03824	−	14.3530i	0.376594	−	0.598042i
$25$	24.6905	−	3.92165i	0.987620	−	0.156866i
$26$	−15.7526	−	27.2844i	−0.605870	−	1.04940i
$27$	21.1589	−	16.7720i	0.783663	−	0.621186i
$28$	35.7339	−	19.3548i	1.27621	−	0.691244i
$29$	26.5784			0.916496			0.458248	−	0.888824i	$-0.348477\pi$
$29$	26.5784			0.916496			0.458248	+	0.888824i	$0.348477\pi$
$30$	1.89604	+	46.9325i	0.0632012	+	1.56442i
$31$	0.677558	+	0.391188i	0.0218567	+	0.0126190i	0.510889	−	0.859647i	$-0.329316\pi$
$31$	0.677558	+	0.391188i	0.0218567	+	0.0126190i	−0.489032	+	0.872266i	$0.662650\pi$
$32$	38.5343	−	10.3252i	1.20420	−	0.322664i
$33$	34.2146	+	10.5906i	1.03680	+	0.320926i
$34$	9.82137			0.288864
$35$	−15.9146	+	31.1725i	−0.454703	+	0.890643i
$36$	−52.0962	−	4.00687i	−1.44712	−	0.111302i
$37$	28.4517	+	7.62362i	0.768965	+	0.206044i	0.621914	−	0.783085i	$-0.286355\pi$
$37$	28.4517	+	7.62362i	0.768965	+	0.206044i	0.147051	+	0.989129i	$0.453022\pi$
$38$	104.135	−	27.9030i	2.74040	−	0.734288i
$39$	−16.0836	+	25.5412i	−0.412400	+	0.654904i
$40$	18.3549	−	21.5003i	0.458871	−	0.537507i
$41$	−43.0909			−1.05100			−0.525499	−	0.850794i	$-0.676121\pi$
$41$	−43.0909			−1.05100			−0.525499	+	0.850794i	$0.676121\pi$
$42$	−54.6719	−	36.5408i	−1.30171	−	0.870020i
$43$	−40.7104	−	40.7104i	−0.946754	−	0.946754i	0.0518979	−	0.998652i	$-0.483473\pi$
$43$	−40.7104	−	40.7104i	−0.946754	−	0.946754i	−0.998652	+	0.0518979i	$0.983473\pi$
$44$	−34.6554	−	60.0250i	−0.787624	−	1.36420i
$45$	38.9261	−	22.5778i	0.865025	−	0.501728i
$46$	15.2106	−	26.3455i	0.330665	−	0.572729i
$47$	28.9750	+	7.76382i	0.616489	+	0.165188i	0.553531	−	0.832828i	$-0.313280\pi$
$47$	28.9750	+	7.76382i	0.616489	+	0.165188i	0.0629579	+	0.998016i	$0.479947\pi$
$48$	−11.2471	−	12.1454i	−0.234315	−	0.253029i
$49$	−22.1566	−	43.7045i	−0.452175	−	0.891929i
$50$	−8.14895	+	77.8593i	−0.162979	+	1.55719i
$51$	−4.38851	−	8.32321i	−0.0860491	−	0.163200i
$52$	56.4202	−	15.1177i	1.08500	−	0.290726i
$53$	−4.59967	−	17.1662i	−0.0867863	−	0.323891i	0.908860	−	0.417101i	$-0.136954\pi$
$53$	−4.59967	−	17.1662i	−0.0867863	−	0.323891i	−0.995646	+	0.0932100i	$0.970287\pi$
$54$	33.5816	+	77.5921i	0.621881	+	1.43689i
$55$	53.8841	+	25.6870i	0.979712	+	0.467036i
$56$	9.19994	+	38.4931i	0.164285	+	0.687377i
$57$	−70.1776	−	75.7825i	−1.23119	−	1.32952i
$58$	−21.5408	+	80.3912i	−0.371392	+	1.38606i
$59$	−62.8463	−	36.2843i	−1.06519	−	0.614988i	−0.138328	−	0.990387i	$-0.544173\pi$
$59$	−62.8463	−	36.2843i	−1.06519	−	0.614988i	−0.926864	+	0.375398i	$0.877506\pi$
$60$	−84.9573	−	19.1250i	−1.41596	−	0.318750i
$61$	21.4620	−	12.3911i	0.351836	−	0.203132i	−0.313658	−	0.949536i	$-0.601554\pi$
$61$	21.4620	−	12.3911i	0.351836	−	0.203132i	0.665494	+	0.746404i	$0.268221\pi$
$62$	−1.73236	+	1.73236i	−0.0279412	+	0.0279412i
$63$	−6.53769	+	62.6599i	−0.103773	+	0.994601i
$64$			102.852i			1.60705i
$65$	−32.6626	+	38.2599i	−0.502501	+	0.588613i
$66$	−59.7627	+	94.9050i	−0.905495	+	1.43795i
$67$	15.0622	+	56.2130i	0.224809	+	0.839000i	0.982481	+	0.186364i	$0.0596702\pi$
$67$	15.0622	+	56.2130i	0.224809	+	0.839000i	−0.757672	+	0.652636i	$0.773663\pi$
$68$	−4.71277	+	17.5883i	−0.0693054	+	0.258651i
$69$	−29.1233	−	1.11833i	−0.422077	−	0.0162077i
$70$	−81.3888	−	73.4008i	−1.16270	−	1.04858i
$71$		−	43.6004i		−	0.614091i	−0.951695	−	0.307045i	$-0.900660\pi$
$71$		−	43.6004i		−	0.614091i	0.951695	−	0.307045i	$-0.0993403\pi$
$72$	16.9005	−	47.9965i	0.234729	−	0.666618i
$73$	0.0891230	+	0.332612i	0.00122086	+	0.00455632i	0.966534	−	0.256540i	$-0.0825826\pi$
$73$	0.0891230	+	0.332612i	0.00122086	+	0.00455632i	−0.965313	+	0.261096i	$0.915916\pi$
$74$	−46.1180	+	79.8788i	−0.623217	+	1.07944i
$75$	69.6238	−	27.8841i	0.928317	−	0.371789i
$76$			199.877i			2.62996i
$77$	−73.4842	+	39.8018i	−0.954340	+	0.516907i
$78$	−64.2191	−	69.3480i	−0.823321	−	0.889077i
$79$	−66.7293	+	38.5262i	−0.844674	+	0.487673i	−0.858850	−	0.512227i	$-0.828821\pi$
$79$	−66.7293	+	38.5262i	−0.844674	+	0.487673i	0.0141761	+	0.999900i	$0.495487\pi$
$80$	−15.6313	−	22.7331i	−0.195392	−	0.284164i
$81$	50.7508	−	63.1297i	0.626553	−	0.779379i
$82$	34.9235	−	130.336i	0.425897	−	1.58947i
$83$	76.7710	+	76.7710i	0.924952	+	0.924952i	0.997374	−	0.0724223i	$-0.0230729\pi$
$83$	76.7710	+	76.7710i	0.924952	+	0.924952i	−0.0724223	+	0.997374i	$0.523073\pi$
$84$	91.6722	−	80.3734i	1.09134	−	0.956827i
$85$	−5.23804	−	14.7815i	−0.0616240	−	0.173900i
$86$	156.130	−	90.1420i	1.81547	−	1.04816i
$87$	77.7534	−	17.6665i	0.893717	−	0.203063i
$88$	65.2002	−	17.4703i	0.740911	−	0.198527i
$89$	56.8471	−	32.8207i	0.638731	−	0.368772i	−0.145394	−	0.989374i	$-0.546445\pi$
$89$	56.8471	−	32.8207i	0.638731	−	0.368772i	0.784126	+	0.620602i	$0.213112\pi$
$90$	36.7424	+	136.038i	0.408249	+	1.51153i
$91$	−16.3713	−	68.4987i	−0.179905	−	0.752733i
$92$	39.8813	+	39.8813i	0.433492	+	0.433492i
$93$	2.24217	+	0.694029i	0.0241094	+	0.00746268i
$94$	−46.9662	+	81.3479i	−0.499641	+	0.865403i
$95$	−97.5335	−	141.846i	−1.02667	−	1.49311i
$96$	105.867	−	55.8194i	1.10278	−	0.581452i
$97$	−53.5343	−	53.5343i	−0.551900	−	0.551900i	0.375089	−	0.926989i	$-0.377612\pi$
$97$	−53.5343	−	53.5343i	−0.551900	−	0.551900i	−0.926989	+	0.375089i	$0.877612\pi$
$98$	150.149	−	31.5958i	1.53214	−	0.322406i
$99$	107.132	+	8.23984i	1.08214	+	0.0832307i
$100$	−135.522	−	51.9540i	−1.35522	−	0.519540i
$101$	−11.5407	+	19.9891i	−0.114264	+	0.197912i	−0.917485	−	0.397769i	$-0.869784\pi$
$101$	−11.5407	+	19.9891i	−0.114264	+	0.197912i	0.803221	+	0.595681i	$0.203118\pi$
$102$	28.7318	−	6.52820i	0.281684	−	0.0640019i
$103$	−158.852	−	42.5642i	−1.54225	−	0.413245i	−0.615259	−	0.788325i	$-0.710948\pi$
$103$	−158.852	−	42.5642i	−1.54225	−	0.413245i	−0.926992	+	0.375081i	$0.877615\pi$
$104$			56.8846i			0.546967i
$105$	−25.8370	+	101.772i	−0.246067	+	0.969253i
$106$	55.6502			0.525002
$107$	−22.3609	+	83.4520i	−0.208980	+	0.779925i	0.779219	+	0.626752i	$0.215616\pi$
$107$	−22.3609	+	83.4520i	−0.208980	+	0.779925i	−0.988199	+	0.153173i	$0.951051\pi$
$108$	−155.067	+	22.9061i	−1.43581	+	0.212094i
$109$	88.6816	+	51.2003i	0.813593	+	0.469728i	0.848202	−	0.529673i	$-0.177685\pi$
$109$	88.6816	+	51.2003i	0.813593	+	0.469728i	−0.0346094	+	0.999401i	$0.511019\pi$
$110$	−121.366	+	142.164i	−1.10333	+	1.29240i
$111$	88.3011	+	3.39074i	0.795505	+	0.0305472i
$112$	38.6098	+	1.05038i	0.344730	+	0.00937837i
$113$	−88.2611	+	88.2611i	−0.781072	+	0.781072i	−0.980012	−	0.198940i	$-0.936250\pi$
$113$	−88.2611	+	88.2611i	−0.781072	+	0.781072i	0.198940	+	0.980012i	$0.436250\pi$
$114$	286.094	−	150.846i	2.50960	−	1.32321i
$115$	−47.7632	−	8.84160i	−0.415332	−	0.0768835i
$116$	−133.630	−	77.1512i	−1.15198	−	0.665096i
$117$	−30.0745	+	85.4100i	−0.257047	+	0.730000i
$118$	160.683	−	160.683i	1.36172	−	1.36172i
$119$	21.0445	+	6.25700i	0.176845	+	0.0525798i
$120$	39.4049	−	75.0981i	0.328374	−	0.625817i
$121$	10.7664	+	18.6480i	0.0889787	+	0.154116i
$122$	20.0850	+	74.9582i	0.164631	+	0.614411i
$123$	−126.060	+	28.6422i	−1.02488	+	0.232864i
$124$	−2.27107	−	3.93360i	−0.0183151	−	0.0317226i
$125$	121.527	−	29.2603i	0.972217	−	0.234082i
$126$	−184.228	−	70.5579i	−1.46212	−	0.559983i
$127$	−139.976	+	139.976i	−1.10217	+	1.10217i	−0.108021	+	0.994149i	$0.534451\pi$
$127$	−139.976	+	139.976i	−1.10217	+	1.10217i	−0.994149	+	0.108021i	$0.965549\pi$
$128$	−156.956	−	42.0562i	−1.22622	−	0.328564i
$129$	−146.156	−	92.0359i	−1.13299	−	0.713457i
$130$	−89.2522	−	129.802i	−0.686556	−	0.998477i
$131$	90.9080	+	157.457i	0.693954	+	1.20196i	0.970532	+	0.240972i	$0.0774663\pi$
$131$	90.9080	+	157.457i	0.693954	+	1.20196i	−0.276578	+	0.960991i	$0.589200\pi$
$132$	−141.281	−	152.564i	−1.07031	−	1.15579i
$133$	240.910	+	6.55395i	1.81136	+	0.0492778i
$134$	−182.234			−1.35995
$135$	98.8687	−	91.9238i	0.732361	−	0.680917i
$136$	−15.3573	−	8.86653i	−0.112921	−	0.0651950i
$137$	105.189	−	28.1852i	0.767800	−	0.205731i	0.146401	−	0.989225i	$-0.453231\pi$
$137$	105.189	−	28.1852i	0.767800	−	0.205731i	0.621399	+	0.783494i	$0.286564\pi$
$138$	26.9859	−	87.1825i	0.195550	−	0.631758i
$139$	−181.388			−1.30495			−0.652475	−	0.757810i	$-0.726269\pi$
$139$	−181.388			−1.30495			−0.652475	+	0.757810i	$0.726269\pi$
$140$	170.502	−	110.531i	1.21787	−	0.789510i
$141$	89.9251	+	3.45310i	0.637766	+	0.0244901i
$142$	131.878	+	35.3365i	0.928715	+	0.248848i
$143$	−116.024	+	31.0886i	−0.811357	+	0.217403i
$144$	−40.9757	−	28.0547i	−0.284553	−	0.194824i
$145$	132.480	−	10.4555i	0.913655	−	0.0721070i
$146$	−1.07828			−0.00738545
$147$	−93.8678	−	113.128i	−0.638556	−	0.769575i
$148$	−120.919	−	120.919i	−0.817019	−	0.817019i
$149$	103.679	+	179.578i	0.695834	+	1.20522i	0.969899	+	0.243508i	$0.0782983\pi$
$149$	103.679	+	179.578i	0.695834	+	1.20522i	−0.274065	+	0.961711i	$0.588368\pi$
$150$	27.9133	+	233.189i	0.186089	+	1.55459i
$151$	8.73623	−	15.1316i	0.0578558	−	0.100209i	−0.835647	−	0.549267i	$-0.814907\pi$
$151$	8.73623	−	15.1316i	0.0578558	−	0.100209i	0.893503	+	0.449058i	$0.148240\pi$
$152$	−188.022	−	50.3804i	−1.23699	−	0.331450i
$153$	−18.3707	−	21.4320i	−0.120070	−	0.140079i
$154$	−60.8318	−	254.524i	−0.395012	−	1.65275i
$155$	3.53118	+	1.68334i	0.0227818	+	0.0108602i
$156$	155.005	−	81.7282i	0.993622	−	0.523898i
$157$	109.761	−	29.4104i	0.699116	−	0.187327i	0.108281	−	0.994120i	$-0.465465\pi$
$157$	109.761	−	29.4104i	0.699116	−	0.187327i	0.590834	+	0.806793i	$0.298799\pi$
$158$	−62.4479	−	233.059i	−0.395240	−	1.47506i
$159$	−24.8663	−	47.1613i	−0.156392	−	0.296612i
$160$	188.013	−	66.6250i	1.17508	−	0.416406i
$161$	49.3764	−	46.7610i	0.306686	−	0.290441i
$162$	149.816	+	204.669i	0.924789	+	1.26339i
$163$	−45.5539	+	170.009i	−0.279472	+	1.04300i	0.673313	+	0.739357i	$0.264870\pi$
$163$	−45.5539	+	170.009i	−0.279472	+	1.04300i	−0.952785	+	0.303645i	$0.901796\pi$
$164$	216.651	+	125.083i	1.32104	+	0.762704i
$165$	174.709	+	39.3292i	1.05884	+	0.238359i
$166$	−294.428	+	169.988i	−1.77366	+	1.02402i
$167$	−23.5359	+	23.5359i	−0.140933	+	0.140933i	−0.774053	−	0.633120i	$-0.781774\pi$
$167$	−23.5359	+	23.5359i	−0.140933	+	0.140933i	0.633120	+	0.774053i	$0.281774\pi$
$168$	52.5000	+	106.494i	0.312500	+	0.633893i
$169$			67.7736i			0.401027i
$170$	48.9546	−	3.86357i	0.287968	−	0.0227269i
$171$	−255.672	−	175.050i	−1.49516	−	1.02369i
$172$	86.5090	+	322.856i	0.502959	+	1.87707i
$173$	8.24173	−	30.7585i	0.0476400	−	0.177795i	−0.938006	−	0.346618i	$-0.887330\pi$
$173$	8.24173	−	30.7585i	0.0476400	−	0.177795i	0.985646	+	0.168823i	$0.0539966\pi$
$174$	−9.58065	+	249.497i	−0.0550612	+	1.43389i
$175$	−67.0636	+	161.640i	−0.383221	+	0.923657i
$176$		−	65.8745i		−	0.374287i
$177$	−207.971	−	64.3740i	−1.17498	−	0.363695i
$178$	53.1998	+	198.544i	0.298875	+	1.11542i
$179$	−13.1960	+	22.8561i	−0.0737207	+	0.127688i	−0.900529	−	0.434795i	$-0.856821\pi$
$179$	−13.1960	+	22.8561i	−0.0737207	+	0.127688i	0.826809	+	0.562483i	$0.190154\pi$
$180$	−261.250	+	0.521559i	−1.45139	+	0.00289755i
$181$			32.4648i			0.179364i	0.995970	+	0.0896818i	$0.0285850\pi$
$181$			32.4648i			0.179364i	−0.995970	+	0.0896818i	$0.971415\pi$
$182$	220.455	+	5.99747i	1.21129	+	0.0329531i
$183$	54.5494	−	50.5150i	0.298084	−	0.276038i
$184$	−47.5684	+	27.4636i	−0.258524	+	0.149259i
$185$	144.817	+	26.8075i	0.782793	+	0.144905i
$186$	−3.91641	+	6.21939i	−0.0210560	+	0.0334376i
$187$	9.69147	−	36.1690i	0.0518260	−	0.193417i
$188$	−123.143	−	123.143i	−0.655014	−	0.655014i
$189$	22.5240	+	187.653i	0.119174	+	0.992873i
$190$	508.086	−	180.048i	2.67414	−	0.947619i
$191$	−283.840	+	163.875i	−1.48607	+	0.857985i	−0.999874	−	0.0158629i	$-0.994950\pi$
$191$	−283.840	+	163.875i	−1.48607	+	0.857985i	−0.486199	+	0.873848i	$0.661617\pi$
$192$	68.3647	+	300.886i	0.356066	+	1.56711i
$193$	68.7422	−	18.4194i	0.356177	−	0.0954373i	−0.0762936	−	0.997085i	$-0.524309\pi$
$193$	68.7422	−	18.4194i	0.356177	−	0.0954373i	0.432471	+	0.901648i	$0.357642\pi$
$194$	205.312	−	118.537i	1.05831	−	0.611015i
$195$	−70.1212	+	133.637i	−0.359596	+	0.685320i
$196$	−15.4667	+	284.052i	−0.0789115	+	1.44924i
$197$	−63.4729	−	63.4729i	−0.322198	−	0.322198i	0.527412	−	0.849610i	$-0.323162\pi$
$197$	−63.4729	−	63.4729i	−0.322198	−	0.322198i	−0.849610	+	0.527412i	$0.823162\pi$
$198$	−111.749	+	317.362i	−0.564390	+	1.60284i
$199$	149.531	−	258.996i	0.751413	−	1.30149i	−0.195725	−	0.980659i	$-0.562706\pi$
$199$	149.531	−	258.996i	0.751413	−	1.30149i	0.947138	−	0.320826i	$-0.103961\pi$
$200$	83.0319	−	114.389i	0.415160	−	0.571944i
$201$	81.4280	+	154.436i	0.405114	+	0.768337i
$202$	−51.1074	−	51.1074i	−0.253007	−	0.253007i
$203$	−97.3717	+	158.534i	−0.479663	+	0.780953i
$204$	−2.09609	+	54.5860i	−0.0102749	+	0.267578i
$205$	−214.787	+	16.9513i	−1.04774	+	0.0826892i
$206$	257.487	−	445.980i	1.24993	−	2.16495i
$207$	−85.9419	+	16.0865i	−0.415178	+	0.0777125i
$208$	53.6230	+	14.3682i	0.257803	+	0.0690780i
$209$		−	411.032i		−	1.96666i
$210$	−286.887	−	160.631i	−1.36613	−	0.764908i
$211$	151.609			0.718525			0.359263	−	0.933236i	$-0.383028\pi$
$211$	151.609			0.718525			0.359263	+	0.933236i	$0.383028\pi$
$212$	−26.7037	+	99.6595i	−0.125961	+	0.470092i
$213$	−28.9809	−	127.550i	−0.136061	−	0.598828i
$214$	−234.293	−	135.269i	−1.09483	−	0.632099i
$215$	−218.936	−	186.906i	−1.01831	−	0.869332i
$216$	17.5383	−	151.644i	0.0811959	−	0.702057i
$217$	−4.81562	+	2.60832i	−0.0221918	+	0.0120199i
$218$	−226.738	+	226.738i	−1.04008	+	1.04008i
$219$	0.481808	+	0.913795i	0.00220004	+	0.00417258i
$220$	−196.353	−	285.562i	−0.892514	−	1.29801i
$221$	27.3283	+	15.7780i	0.123658	+	0.0713938i
$222$	−81.8206	+	264.335i	−0.368561	+	1.19070i
$223$	24.9405	−	24.9405i	0.111841	−	0.111841i	−0.648972	−	0.760813i	$-0.724801\pi$
$223$	24.9405	−	24.9405i	0.111841	−	0.111841i	0.760813	+	0.648972i	$0.224801\pi$
$224$	−79.5856	+	267.675i	−0.355293	+	1.19498i
$225$	185.146	−	127.852i	0.822870	−	0.568230i
$226$	−195.430	−	338.494i	−0.864734	−	1.49776i
$227$	−84.5475	−	315.536i	−0.372456	−	1.39003i	−0.857026	−	0.515273i	$-0.827691\pi$
$227$	−84.5475	−	315.536i	−0.372456	−	1.39003i	0.484570	−	0.874752i	$-0.338976\pi$
$228$	132.857	+	584.726i	0.582704	+	2.56459i
$229$	76.9204	+	133.230i	0.335897	+	0.581790i	0.983657	−	0.180054i	$-0.0576273\pi$
$229$	76.9204	+	133.230i	0.335897	+	0.581790i	−0.647760	+	0.761845i	$0.724294\pi$
$230$	65.4533	−	137.303i	0.284580	−	0.596969i
$231$	−188.517	+	165.282i	−0.816092	+	0.715507i
$232$	106.258	−	106.258i	0.458008	−	0.458008i
$233$	−50.7709	−	13.6040i	−0.217901	−	0.0583864i	0.148217	−	0.988955i	$-0.452647\pi$
$233$	−50.7709	−	13.6040i	−0.217901	−	0.0583864i	−0.366118	+	0.930569i	$0.619313\pi$
$234$	−233.964	−	160.187i	−0.999846	−	0.684561i
$235$	147.480	+	27.3005i	0.627575	+	0.116172i
$236$	210.651	+	364.858i	0.892588	+	1.54601i
$237$	−169.604	+	157.060i	−0.715629	+	0.662702i
$238$	−35.9812	+	58.5820i	−0.151182	+	0.246143i
$239$	127.602			0.533902			0.266951	−	0.963710i	$-0.413984\pi$
$239$	127.602			0.533902			0.266951	+	0.963710i	$0.413984\pi$
$240$	−60.8390	−	56.1142i	−0.253496	−	0.233809i
$241$	115.480	+	66.6725i	0.479171	+	0.276650i	0.720071	−	0.693900i	$-0.244109\pi$
$241$	115.480	+	66.6725i	0.479171	+	0.276650i	−0.240900	+	0.970550i	$0.577443\pi$
$242$	−65.1300	+	17.4515i	−0.269132	+	0.0721138i
$243$	106.506	−	218.416i	0.438298	−	0.898830i
$244$	−143.874			−0.589649
$245$	−127.632	−	209.129i	−0.520947	−	0.853589i
$246$	15.5329	−	404.504i	0.0631418	−	1.64433i
$247$	334.587	+	89.6522i	1.35460	+	0.362964i
$248$	4.27275	−	1.14488i	0.0172288	−	0.00461645i
$249$	275.618	+	173.560i	1.10690	+	0.697026i
$250$	−9.98985	+	391.295i	−0.0399594	+	1.56518i
$251$	−264.593			−1.05416			−0.527078	−	0.849817i	$-0.676712\pi$
$251$	−264.593			−1.05416			−0.527078	+	0.849817i	$0.676712\pi$
$252$	214.758	−	296.061i	0.852213	−	1.17485i
$253$	−82.0130	−	82.0130i	−0.324162	−	0.324162i
$254$	−309.937	−	536.826i	−1.22022	−	2.11349i
$255$	−25.1487	−	39.7607i	−0.0986225	−	0.155924i
$256$	48.7104	−	84.3689i	0.190275	−	0.329566i
$257$	−138.397	−	37.0832i	−0.538508	−	0.144293i	−0.0206937	−	0.999786i	$-0.506587\pi$
$257$	−138.397	−	37.0832i	−0.538508	−	0.144293i	−0.517814	+	0.855493i	$0.673254\pi$
$258$	396.833	−	367.483i	1.53811	−	1.42435i
$259$	−149.708	+	141.778i	−0.578022	+	0.547405i
$260$	275.279	−	97.5493i	1.05877	−	0.375189i
$261$	215.720	−	103.364i	0.826513	−	0.396032i
$262$	−549.936	+	147.355i	−2.09899	+	0.562423i
$263$	94.0103	+	350.851i	0.357454	+	1.33403i	0.877369	+	0.479817i	$0.159297\pi$
$263$	94.0103	+	350.851i	0.357454	+	1.33403i	−0.519915	+	0.854218i	$0.674036\pi$
$264$	179.127	−	94.4465i	0.678510	−	0.357752i
$265$	−29.6800	−	83.7556i	−0.112000	−	0.316059i
$266$	−215.072	+	723.366i	−0.808542	+	2.71942i
$267$	144.487	−	133.801i	0.541149	−	0.501126i
$268$	87.4446	−	326.348i	0.326286	−	1.21772i
$269$	454.286	+	262.282i	1.68879	+	0.975026i	0.955443	+	0.295176i	$0.0953782\pi$
$269$	454.286	+	262.282i	1.68879	+	0.975026i	0.733351	+	0.679850i	$0.237955\pi$
$270$	197.911	+	373.547i	0.733004	+	1.38351i
$271$	81.8541	−	47.2585i	0.302045	−	0.174386i	−0.341316	−	0.939948i	$-0.610873\pi$
$271$	81.8541	−	47.2585i	0.302045	−	0.174386i	0.643361	+	0.765563i	$0.277539\pi$
$272$	−12.2372	+	12.2372i	−0.0449896	+	0.0449896i
$273$	−93.4239	−	189.507i	−0.342212	−	0.694164i
$274$			341.005i			1.24454i
$275$	278.690	+	106.840i	1.01342	+	0.388507i
$276$	143.179	+	90.1613i	0.518764	+	0.326672i
$277$	−68.9893	−	257.471i	−0.249059	−	0.929500i	−0.971300	−	0.237858i	$-0.923555\pi$
$277$	−68.9893	−	257.471i	−0.249059	−	0.929500i	0.722241	−	0.691641i	$-0.243112\pi$
$278$	147.008	−	548.642i	0.528806	−	1.97353i
$279$	7.02066	+	0.539980i	0.0251636	+	0.00193541i
$280$	60.9997	+	188.250i	0.217856	+	0.672321i
$281$			104.628i			0.372343i	0.982517	+	0.186171i	$0.0596079\pi$
$281$			104.628i			0.372343i	−0.982517	+	0.186171i	$0.940392\pi$
$282$	−83.3254	+	269.196i	−0.295480	+	0.954597i
$283$	−24.7817	−	92.4866i	−0.0875679	−	0.326808i	0.908220	−	0.418493i	$-0.137441\pi$
$283$	−24.7817	−	92.4866i	−0.0875679	−	0.326808i	−0.995788	+	0.0916849i	$0.970775\pi$
$284$	−126.562	+	219.213i	−0.445643	+	0.771875i
$285$	−379.612	−	350.131i	−1.33197	−	1.22853i
$286$		−	376.132i		−	1.31515i
$287$	157.866	−	257.027i	0.550057	−	0.895563i
$288$	272.604	−	233.665i	0.946540	−	0.811337i
$289$	241.762	−	139.581i	0.836547	−	0.482981i
$290$	−75.7453	+	409.184i	−0.261191	+	1.41098i
$291$	−192.195	−	121.027i	−0.660464	−	0.415902i
$292$	0.517409	−	1.93100i	0.00177195	−	0.00661300i
$293$	−43.5663	−	43.5663i	−0.148690	−	0.148690i	0.628842	−	0.777533i	$-0.283529\pi$
$293$	−43.5663	−	43.5663i	−0.148690	−	0.148690i	−0.777533	+	0.628842i	$0.783529\pi$
$294$	418.251	−	192.235i	1.42262	−	0.653860i
$295$	−327.531	−	156.136i	−1.11027	−	0.529276i
$296$	144.226	−	83.2688i	0.487249	−	0.281314i
$297$	318.885	−	47.1048i	1.07369	−	0.158602i
$298$	−627.194	+	168.056i	−2.10468	+	0.563946i
$299$	84.6482	−	48.8716i	0.283104	−	0.163450i
$300$	−430.993	−	61.9077i	−1.43664	−	0.206359i
$301$	391.973	−	93.6824i	1.30224	−	0.311237i
$302$	38.6879	+	38.6879i	0.128106	+	0.128106i
$303$	−20.4750	+	66.1479i	−0.0675743	+	0.218310i
$304$	−94.9835	+	164.516i	−0.312446	+	0.541172i
$305$	102.103	−	70.2062i	0.334763	−	0.230184i
$306$	79.7138	−	38.1957i	0.260503	−	0.124822i
$307$	−341.970	−	341.970i	−1.11391	−	1.11391i	−0.992617	−	0.121293i	$-0.961296\pi$
$307$	−341.970	−	341.970i	−1.11391	−	1.11391i	−0.121293	−	0.992617i	$-0.538704\pi$
$308$	484.997	+	13.1943i	1.57466	+	0.0428387i
$309$	−493.003	−	18.9312i	−1.59548	−	0.0612661i
$310$	−7.95345	+	9.31641i	−0.0256563	+	0.0300529i
$311$	157.476	−	272.756i	0.506353	−	0.877029i	−0.493620	−	0.869678i	$-0.664327\pi$
$311$	157.476	−	272.756i	0.506353	−	0.877029i	0.999973	−	0.00735136i	$-0.00234003\pi$
$312$	37.8108	+	166.412i	0.121188	+	0.533373i
$313$	−288.498	−	77.3027i	−0.921717	−	0.246973i	−0.233398	−	0.972381i	$-0.574985\pi$
$313$	−288.498	−	77.3027i	−0.921717	−	0.246973i	−0.688319	+	0.725408i	$0.741651\pi$
$314$			355.829i			1.13321i
$315$	−7.93774	+	314.900i	−0.0251992	+	0.999682i
$316$	447.332			1.41561
$317$	30.6907	−	114.539i	0.0968162	−	0.361323i	−0.900472	−	0.434913i	$-0.856779\pi$
$317$	30.6907	−	114.539i	0.0968162	−	0.361323i	0.997289	+	0.0735902i	$0.0234457\pi$
$318$	162.801	−	36.9903i	0.511954	−	0.116322i
$319$	274.800	+	158.656i	0.861442	+	0.497354i
$320$	40.4602	+	512.663i	0.126438	+	1.60207i
$321$	−9.94542	+	258.997i	−0.0309826	+	0.806843i
$322$	101.420	+	187.246i	0.314967	+	0.581509i
$323$	−76.3552	+	76.3552i	−0.236394	+	0.236394i
$324$	−438.414	+	170.083i	−1.35313	+	0.524946i
$325$	−147.756	+	203.555i	−0.454633	+	0.626324i
$326$	−477.305	−	275.572i	−1.46413	−	0.845313i
$327$	293.465	+	90.8373i	0.897446	+	0.277790i
$328$	−172.273	+	172.273i	−0.525224	+	0.525224i
$329$	−152.461	+	144.385i	−0.463408	+	0.438861i
$330$	−260.553	+	496.564i	−0.789555	+	1.50474i
$331$	97.3575	+	168.628i	0.294131	+	0.509450i	0.974782	−	0.223157i	$-0.0716363\pi$
$331$	97.3575	+	168.628i	0.294131	+	0.509450i	−0.680651	+	0.732608i	$0.738303\pi$
$332$	−163.137	−	608.835i	−0.491376	−	1.83384i
$333$	260.573	−	48.7737i	0.782502	−	0.146468i
$334$	−52.1136	−	90.2634i	−0.156029	−	0.270250i
$335$	97.1910	+	274.268i	0.290122	+	0.818712i
$336$	113.649	−	22.5909i	0.338240	−	0.0672347i
$337$	−76.8819	+	76.8819i	−0.228136	+	0.228136i	−0.811914	−	0.583777i	$-0.801574\pi$
$337$	−76.8819	+	76.8819i	−0.228136	+	0.228136i	0.583777	+	0.811914i	$0.301574\pi$
$338$	−204.994	−	54.9279i	−0.606490	−	0.162509i
$339$	−199.536	+	316.869i	−0.588601	+	0.934717i
$340$	−16.5718	+	89.5228i	−0.0487407	+	0.263302i
$341$	4.67029	+	8.08917i	0.0136959	+	0.0237219i
$342$	736.684	−	631.457i	2.15405	−	1.84636i
$343$	341.859	+	27.9559i	0.996673	+	0.0815042i
$344$	−325.513			−0.946259
$345$	−145.605	+	5.88235i	−0.422044	+	0.0170503i
$346$	86.3553	+	49.8572i	0.249582	+	0.144096i
$347$	123.182	−	33.0067i	0.354993	−	0.0951200i	−0.0769154	−	0.997038i	$-0.524507\pi$
$347$	123.182	−	33.0067i	0.354993	−	0.0951200i	0.431908	+	0.901918i	$0.357840\pi$
$348$	−442.207	−	136.878i	−1.27071	−	0.393328i
$349$	51.0844			0.146374			0.0731869	−	0.997318i	$-0.476683\pi$
$349$	51.0844			0.146374			0.0731869	+	0.997318i	$0.476683\pi$
$350$	−434.557	−	333.849i	−1.24159	−	0.953855i
$351$	−31.2095	+	269.852i	−0.0889161	+	0.768809i
$352$	460.050	+	123.270i	1.30696	+	0.350199i
$353$	−83.7097	+	22.4299i	−0.237138	+	0.0635409i	−0.375431	−	0.926850i	$-0.622505\pi$
$353$	−83.7097	+	22.4299i	−0.237138	+	0.0635409i	0.138293	+	0.990391i	$0.455839\pi$
$354$	363.263	−	576.873i	1.02617	−	1.62959i
$355$	−17.1517	−	217.326i	−0.0483147	−	0.612187i
$356$	−381.085			−1.07046
$357$	65.7235	+	4.31628i	0.184099	+	0.0120904i
$358$	−58.4378	−	58.4378i	−0.163234	−	0.163234i
$359$	−289.434	−	501.315i	−0.806224	−	1.39642i	−0.915462	−	0.402405i	$-0.868174\pi$
$359$	−289.434	−	501.315i	−0.806224	−	1.39642i	0.109238	−	0.994016i	$-0.465159\pi$
$360$	65.3593	−	245.887i	0.181554	−	0.683019i
$361$	−412.160	+	713.883i	−1.14172	+	1.97751i
$362$	−98.1958	−	26.3115i	−0.271259	−	0.0726837i
$363$	43.8917	+	47.3972i	0.120914	+	0.130571i
$364$	−116.525	+	391.918i	−0.320125	+	1.07670i
$365$	0.575078	+	1.62284i	0.00157556	+	0.00444615i
$366$	108.582	+	205.935i	0.296671	+	0.562664i
$367$	290.131	−	77.7404i	0.790548	−	0.211827i	0.159118	−	0.987260i	$-0.449135\pi$
$367$	290.131	−	77.7404i	0.790548	−	0.211827i	0.631430	+	0.775433i	$0.282468\pi$
$368$	13.8738	+	51.7778i	0.0377006	+	0.140701i
$369$	−349.742	+	167.582i	−0.947809	+	0.454152i
$370$	−198.452	+	416.298i	−0.536358	+	1.12513i
$371$	119.243	+	35.4536i	0.321411	+	0.0955624i
$372$	−9.25851	−	9.99795i	−0.0248885	−	0.0268762i
$373$	122.982	−	458.973i	0.329709	−	1.23049i	−0.579783	−	0.814771i	$-0.696863\pi$
$373$	122.982	−	458.973i	0.329709	−	1.23049i	0.909492	−	0.415721i	$-0.136471\pi$
$374$	101.545	+	58.6272i	0.271512	+	0.156757i
$375$	336.071	−	166.377i	0.896189	−	0.443673i
$376$	146.878	−	84.8003i	0.390634	−	0.225533i
$377$	−189.086	+	189.086i	−0.501556	+	0.501556i
$378$	−585.846	−	83.9577i	−1.54986	−	0.222110i
$379$		−	497.374i		−	1.31233i	−0.754617	−	0.656166i	$-0.772177\pi$
$379$		−	497.374i		−	1.31233i	0.754617	−	0.656166i	$-0.227823\pi$
$380$	78.6283	+	996.285i	0.206917	+	2.62180i
$381$	−316.449	+	502.530i	−0.830574	+	1.31898i
$382$	−265.629	−	991.341i	−0.695364	−	2.59513i
$383$	−153.392	+	572.466i	−0.400501	+	1.49469i	0.411705	+	0.911317i	$0.364934\pi$
$383$	−153.392	+	572.466i	−0.400501	+	1.49469i	−0.812205	+	0.583372i	$0.801733\pi$
$384$	−487.119	−	18.7053i	−1.26854	−	0.0487116i
$385$	−350.625	+	227.300i	−0.910713	+	0.590389i
$386$			222.851i			0.577335i
$387$	−488.745	−	172.096i	−1.26291	−	0.444694i
$388$	113.759	+	424.556i	0.293194	+	1.09422i
$389$	39.0172	−	67.5798i	0.100301	−	0.173727i	−0.811507	−	0.584342i	$-0.801353\pi$
$389$	39.0172	−	67.5798i	0.100301	−	0.173727i	0.911809	+	0.410615i	$0.134686\pi$
$390$	−347.380	−	320.402i	−0.890719	−	0.821545i
$391$			30.4702i			0.0779290i
$392$	−263.307	−	86.1468i	−0.671700	−	0.219762i
$393$	370.606	+	400.205i	0.943019	+	1.01833i
$394$	243.428	−	140.543i	0.617837	−	0.356709i
$395$	−317.456	+	218.284i	−0.803687	+	0.552617i
$396$	−514.716	−	352.408i	−1.29979	−	0.889920i
$397$	−89.7734	+	335.039i	−0.226129	+	0.843927i	0.755819	+	0.654780i	$0.227239\pi$
$397$	−89.7734	+	335.039i	−0.226129	+	0.843927i	−0.981949	+	0.189146i	$0.939428\pi$
$398$	662.190	+	662.190i	1.66379	+	1.66379i
$399$	709.124	−	140.958i	1.77725	−	0.353279i
$400$	−86.8572	−	107.164i	−0.217143	−	0.267910i
$401$	635.125	−	366.690i	1.58385	−	0.914438i	0.589563	−	0.807722i	$-0.299300\pi$
$401$	635.125	−	366.690i	1.58385	−	0.914438i	0.994290	−	0.106716i	$-0.0340335\pi$
$402$	−533.114	+	121.130i	−1.32615	+	0.301317i
$403$	−7.60338	+	2.03732i	−0.0188670	+	0.00505538i
$404$	116.048	−	67.0003i	0.287247	−	0.165842i
$405$	228.133	−	334.635i	0.563292	−	0.826258i
$406$	−400.598	−	423.004i	−0.986694	−	1.04188i
$407$	248.661	+	248.661i	0.610960	+	0.610960i
$408$	−50.8203	−	15.7306i	−0.124559	−	0.0385554i
$409$	237.092	−	410.656i	0.579687	−	1.00405i	−0.415828	−	0.909443i	$-0.636508\pi$
$409$	237.092	−	410.656i	0.579687	−	1.00405i	0.995515	−	0.0946043i	$-0.0301586\pi$
$410$	122.804	−	663.400i	0.299522	−	1.61805i
$411$	288.988	−	152.372i	0.703134	−	0.370735i
$412$	675.115	+	675.115i	1.63863	+	1.63863i
$413$	446.668	−	241.933i	1.08152	−	0.585793i
$414$	20.9960	−	272.984i	0.0507151	−	0.659383i
$415$	412.866	+	352.465i	0.994857	+	0.849312i
$416$	−200.688	+	347.602i	−0.482423	+	0.835581i
$417$	−530.640	+	120.567i	−1.27252	+	0.289131i
$418$	1243.24	+	333.125i	2.97426	+	0.796951i
$419$		−	124.867i		−	0.298012i	−0.988836	−	0.149006i	$-0.952393\pi$
$419$		−	124.867i		−	0.298012i	0.988836	−	0.149006i	$-0.0476073\pi$
$420$	425.323	−	436.684i	1.01267	−	1.03972i
$421$	−385.564			−0.915829			−0.457914	−	0.888996i	$-0.651403\pi$
$421$	−385.564			−0.915829			−0.457914	+	0.888996i	$0.651403\pi$
$422$	−122.873	+	458.569i	−0.291169	+	1.08666i
$423$	265.365	−	49.6708i	0.627341	−	0.117425i
$424$	−87.0180	−	50.2399i	−0.205231	−	0.118490i
$425$	−31.9238	−	71.6179i	−0.0751149	−	0.168513i
$426$	409.287	+	15.7165i	0.960769	+	0.0368933i
$427$	−4.71764	+	173.411i	−0.0110483	+	0.406115i
$428$	354.668	−	354.668i	0.828664	−	0.828664i
$429$	−318.757	+	168.068i	−0.743023	+	0.391767i
$430$	742.772	−	510.732i	1.72738	−	1.18775i
$431$	143.931	+	83.0986i	0.333947	+	0.192804i	0.657592	−	0.753374i	$-0.271575\pi$
$431$	143.931	+	83.0986i	0.333947	+	0.192804i	−0.323645	+	0.946178i	$0.604908\pi$
$432$	−138.519	−	54.8359i	−0.320647	−	0.126935i
$433$	−223.442	+	223.442i	−0.516033	+	0.516033i	−0.916369	−	0.400335i	$-0.868894\pi$
$433$	−223.442	+	223.442i	−0.516033	+	0.516033i	0.400335	+	0.916369i	$0.368894\pi$
$434$	−3.98648	−	16.6797i	−0.00918543	−	0.0384324i
$435$	380.612	−	118.646i	0.874971	−	0.272748i
$436$	−297.247	−	514.846i	−0.681758	−	1.18084i
$437$	86.5674	+	323.074i	0.198095	+	0.739299i
$438$	−3.15443	+	0.716722i	−0.00720189	+	0.00163635i
$439$	160.351	+	277.735i	0.365263	+	0.632655i	0.988818	−	0.149125i	$-0.0476456\pi$
$439$	160.351	+	277.735i	0.365263	+	0.632655i	−0.623555	+	0.781779i	$0.714312\pi$
$440$	318.118	−	112.730i	0.722995	−	0.256204i
$441$	−349.799	−	268.554i	−0.793196	−	0.608967i
$442$	−69.8721	+	69.8721i	−0.158082	+	0.158082i
$443$	356.801	+	95.6047i	0.805421	+	0.215812i	0.637963	−	0.770067i	$-0.279777\pi$
$443$	356.801	+	95.6047i	0.805421	+	0.215812i	0.167458	+	0.985879i	$0.446444\pi$
$444$	−434.114	−	273.366i	−0.977735	−	0.615690i
$445$	270.443	−	185.957i	0.607738	−	0.417882i
$446$	55.2238	+	95.6505i	0.123820	+	0.214463i
$447$	422.671	+	456.428i	0.945573	+	1.02109i
$448$	−613.484	−	376.803i	−1.36938	−	0.841079i
$449$	40.2211			0.0895793			0.0447897	−	0.998996i	$-0.485738\pi$
$449$	40.2211			0.0895793			0.0447897	+	0.998996i	$0.485738\pi$
$450$	236.658	+	663.626i	0.525906	+	1.47472i
$451$	−445.527	−	257.225i	−0.987864	−	0.570344i
$452$	699.959	−	187.553i	1.54858	−	0.414941i
$453$	15.4994	−	50.0735i	0.0342151	−	0.110537i
$454$	1022.92			2.25312
$455$	−108.549	−	334.992i	−0.238570	−	0.736245i
$456$	−583.535	−	22.4076i	−1.27968	−	0.0491395i
$457$	−803.200	−	215.217i	−1.75755	−	0.470934i	−0.771338	−	0.636425i	$-0.780412\pi$
$457$	−803.200	−	215.217i	−1.75755	−	0.470934i	−0.986211	+	0.165491i	$0.947079\pi$
$458$	−465.320	+	124.682i	−1.01598	+	0.272231i
$459$	−67.9880	−	50.4872i	−0.148122	−	0.109994i
$460$	214.477	+	183.100i	0.466254	+	0.398043i
$461$	−100.425			−0.217841			−0.108920	−	0.994050i	$-0.534739\pi$
$461$	−100.425			−0.217841			−0.108920	+	0.994050i	$0.534739\pi$
$462$	−347.140	−	704.160i	−0.751386	−	1.52416i
$463$	155.475	+	155.475i	0.335799	+	0.335799i	0.854784	−	0.518984i	$-0.173690\pi$
$463$	155.475	+	155.475i	0.335799	+	0.335799i	−0.518984	+	0.854784i	$0.673690\pi$
$464$	−73.3261	−	127.005i	−0.158030	−	0.273717i
$465$	11.4491	+	2.57735i	0.0246218	+	0.00554269i
$466$	82.2957	−	142.540i	0.176600	−	0.305881i
$467$	−363.036	−	97.2752i	−0.777379	−	0.208298i	−0.151750	−	0.988419i	$-0.548491\pi$
$467$	−363.036	−	97.2752i	−0.777379	−	0.208298i	−0.625629	+	0.780121i	$0.715158\pi$
$468$	399.134	−	342.121i	0.852849	−	0.731029i
$469$	−390.478	−	116.097i	−0.832576	−	0.247543i
$470$	−202.102	+	423.954i	−0.430005	+	0.902031i
$471$	301.551	−	158.996i	0.640235	−	0.337571i
$472$	−396.315	+	106.192i	−0.839650	+	0.224984i
$473$	−177.899	−	663.930i	−0.376109	−	1.40366i
$474$	−337.600	−	640.290i	−0.712237	−	1.35082i
$475$	−541.956	−	668.662i	−1.14096	−	1.40771i
$476$	−87.6443	−	92.5463i	−0.184127	−	0.194425i
$477$	−104.093	−	121.439i	−0.218224	−	0.254589i
$478$	−103.417	+	385.957i	−0.216353	+	0.807442i
$479$	−79.5325	−	45.9181i	−0.166039	−	0.0958625i	0.414678	−	0.909968i	$-0.363894\pi$
$479$	−79.5325	−	45.9181i	−0.166039	−	0.0958625i	−0.580717	+	0.814106i	$0.697228\pi$
$480$	505.734	−	319.878i	1.05361	−	0.666413i
$481$	−256.651	+	148.177i	−0.533577	+	0.308061i
$482$	−295.256	+	295.256i	−0.612564	+	0.612564i
$483$	113.366	−	169.617i	0.234712	−	0.351173i
$484$		−	125.010i		−	0.258286i
$485$	−287.901	−	245.782i	−0.593611	−	0.506768i
$486$	574.319	+	499.166i	1.18173	+	1.02709i
$487$	11.2537	+	41.9994i	0.0231082	+	0.0862411i	0.976517	−	0.215440i	$-0.0691187\pi$
$487$	11.2537	+	41.9994i	0.0231082	+	0.0862411i	−0.953409	+	0.301682i	$0.902452\pi$
$488$	36.2646	−	135.341i	0.0743127	−	0.277339i
$489$	−20.2609	+	527.631i	−0.0414334	+	1.07900i
$490$	735.991	−	216.556i	1.50202	−	0.441950i
$491$		−	147.820i		−	0.301059i	−0.988605	−	0.150530i	$-0.951902\pi$
$491$		−	147.820i		−	0.301059i	0.988605	−	0.150530i	$-0.0480979\pi$
$492$	716.940	+	221.917i	1.45720	+	0.451051i
$493$	−21.5755	−	80.5208i	−0.0437637	−	0.163328i
$494$	−542.339	+	939.359i	−1.09785	+	1.90154i
$495$	537.241	−	1.07255i	1.08534	−	0.00216676i
$496$		−	4.31694i		−	0.00870351i
$497$	260.066	+	159.733i	0.523271	+	0.321395i
$498$	−748.340	+	692.994i	−1.50269	+	1.39155i
$499$	−285.561	+	164.869i	−0.572267	+	0.330399i	−0.758054	−	0.652191i	$-0.773850\pi$
$499$	−285.561	+	164.869i	−0.572267	+	0.330399i	0.185787	+	0.982590i	$0.440517\pi$
$500$	−695.945	−	205.652i	−1.39189	−	0.411305i
$501$	−53.2085	+	84.4968i	−0.106205	+	0.168656i
$502$	214.442	−	800.310i	0.427176	−	1.59424i
$503$	202.943	+	202.943i	0.403465	+	0.403465i	0.879452	−	0.475987i	$-0.157909\pi$
$503$	202.943	+	202.943i	0.403465	+	0.403465i	−0.475987	+	0.879452i	$0.657909\pi$
$504$	224.371	+	276.645i	0.445181	+	0.548900i
$505$	−49.6613	+	104.176i	−0.0983392	+	0.206288i
$506$	314.532	−	181.595i	0.621604	−	0.358883i
$507$	45.0487	+	198.267i	0.0888534	+	0.391060i
$508$	1110.08	−	297.445i	2.18520	−	0.585523i
$509$	−391.137	+	225.823i	−0.768442	+	0.443660i	−0.832319	−	0.554297i	$-0.812987\pi$
$509$	−391.137	+	225.823i	−0.768442	+	0.443660i	0.0638764	+	0.997958i	$0.479654\pi$
$510$	140.646	−	43.8424i	0.275776	−	0.0859656i
$511$	−2.31045	−	0.686948i	−0.00452144	−	0.00134432i
$512$	−243.887	−	243.887i	−0.476343	−	0.476343i
$513$	−864.308	−	342.155i	−1.68481	−	0.666969i
$514$	224.330	−	388.551i	0.436440	−	0.755936i
$515$	−808.541	−	149.672i	−1.56998	−	0.290624i
$516$	467.677	+	886.992i	0.906350	+	1.71898i
$517$	253.234	+	253.234i	0.489814	+	0.489814i
$518$	−307.501	−	567.724i	−0.593631	−	1.09599i
$519$	3.66566	−	95.4604i	0.00706293	−	0.183931i
$520$	22.3775	+	283.541i	0.0430337	+	0.545272i
$521$	79.6615	−	137.978i	0.152901	−	0.264833i	−0.779392	−	0.626537i	$-0.784472\pi$
$521$	79.6615	−	137.978i	0.152901	−	0.264833i	0.932293	+	0.361704i	$0.117805\pi$
$522$	137.812	+	736.257i	0.264007	+	1.41045i
$523$	229.189	+	61.4111i	0.438221	+	0.117421i	0.471183	−	0.882036i	$-0.343827\pi$
$523$	229.189	+	61.4111i	0.438221	+	0.117421i	−0.0329618	+	0.999457i	$0.510494\pi$
$524$		−	1055.54i		−	2.01440i
$525$	−88.7494	+	517.444i	−0.169046	+	0.985608i
$526$	−1137.41			−2.16237
$527$	0.635109	−	2.37026i	0.00120514	−	0.00449764i
$528$	−43.7864	−	192.712i	−0.0829287	−	0.364984i
$529$	−376.392	−	217.310i	−0.711516	−	0.410794i
$530$	277.389	−	21.8919i	0.523375	−	0.0413055i
$531$	−651.194	−	50.0853i	−1.22635	−	0.0943226i
$532$	−1192.21	−	732.261i	−2.24100	−	1.37643i
$533$	306.561	−	306.561i	0.575162	−	0.575162i
$534$	287.604	+	545.467i	0.538584	+	1.02147i
$535$	−78.6292	+	424.763i	−0.146970	+	0.793950i
$536$	284.952	+	164.517i	0.531626	+	0.306935i
$537$	−23.4118	+	75.6355i	−0.0435973	+	0.140848i
$538$	−1161.50	+	1161.50i	−2.15892	+	2.15892i
$539$	31.8061	−	584.132i	0.0590094	−	1.08373i
$540$	−763.923	+	175.177i	−1.41467	+	0.324401i
$541$	337.537	+	584.631i	0.623913	+	1.08065i	0.988750	+	0.149578i	$0.0477914\pi$
$541$	337.537	+	584.631i	0.623913	+	1.08065i	−0.364837	+	0.931071i	$0.618875\pi$
$542$	76.6024	+	285.884i	0.141333	+	0.527461i
$543$	21.5791	+	94.9738i	0.0397406	+	0.174906i
$544$	−62.5619	−	108.360i	−0.115004	−	0.199192i
$545$	462.175	+	220.322i	0.848027	+	0.404261i
$546$	648.914	−	128.990i	1.18849	−	0.236245i
$547$	−734.930	+	734.930i	−1.34356	+	1.34356i	−0.451081	+	0.892483i	$0.648961\pi$
$547$	−734.930	+	734.930i	−1.34356	+	1.34356i	−0.892483	+	0.451081i	$0.851039\pi$
$548$	−610.679	−	163.631i	−1.11438	−	0.298596i
$549$	126.004	−	184.037i	0.229515	−	0.335222i
$550$	−549.024	+	756.361i	−0.998225	+	1.37520i
$551$	−457.527	−	792.460i	−0.830357	−	1.43822i
$552$	−120.903	+	111.961i	−0.219028	+	0.202829i
$553$	14.6680	−	539.167i	0.0265244	−	0.974985i
$554$	834.683			1.50665
$555$	441.471	−	17.8351i	0.795443	−	0.0321353i
$556$	911.976	+	526.530i	1.64025	+	0.946996i
$557$	703.308	−	188.451i	1.26267	−	0.338332i	0.435452	−	0.900212i	$-0.356588\pi$
$557$	703.308	−	188.451i	1.26267	−	0.338332i	0.827219	+	0.561880i	$0.189922\pi$
$558$	−7.32324	+	20.7976i	−0.0131241	+	0.0372717i
$559$	579.252			1.03623
$560$	192.864	−	9.95288i	0.344400	−	0.0177730i
$561$	4.31046	−	112.252i	0.00768352	−	0.200093i
$562$	−316.467	−	84.7972i	−0.563109	−	0.150885i
$563$	−59.9668	+	16.0681i	−0.106513	+	0.0285401i	−0.311682	−	0.950187i	$-0.600892\pi$
$563$	−59.9668	+	16.0681i	−0.106513	+	0.0285401i	0.205169	+	0.978727i	$0.434226\pi$
$564$	−442.098	−	278.394i	−0.783862	−	0.493606i
$565$	−405.217	+	474.658i	−0.717199	+	0.840103i
$566$	299.827			0.529730
$567$	190.624	+	533.996i	0.336198	+	0.941791i
$568$	−174.311	−	174.311i	−0.306885	−	0.306885i
$569$	362.028	+	627.052i	0.636254	+	1.10202i	0.986248	+	0.165272i	$0.0528502\pi$
$569$	362.028	+	627.052i	0.636254	+	1.10202i	−0.349994	+	0.936752i	$0.613816\pi$
$570$	1366.70	−	864.439i	2.39771	−	1.51656i
$571$	238.498	−	413.091i	0.417685	−	0.723451i	−0.578021	−	0.816022i	$-0.696175\pi$
$571$	238.498	−	413.091i	0.417685	−	0.723451i	0.995706	+	0.0925704i	$0.0295083\pi$
$572$	673.585	+	180.486i	1.17760	+	0.315536i
$573$	−721.430	+	668.073i	−1.25904	+	1.16592i
$574$	649.480	+	685.806i	1.13150	+	1.19478i
$575$	−241.554	−	25.2817i	−0.420094	−	0.0439681i
$576$	399.993	+	834.780i	0.694433	+	1.44927i
$577$	245.418	−	65.7596i	0.425335	−	0.113968i	−0.0398006	−	0.999208i	$-0.512672\pi$
$577$	245.418	−	65.7596i	0.425335	−	0.113968i	0.465135	+	0.885240i	$0.346006\pi$
$578$	226.251	+	844.379i	0.391437	+	1.46086i
$579$	188.858	−	99.5773i	0.326179	−	0.171981i
$580$	−696.428	−	331.992i	−1.20074	−	0.572401i
$581$	−739.176	+	176.664i	−1.27225	+	0.304070i
$582$	521.836	−	483.241i	0.896626	−	0.830312i
$583$	54.9142	−	204.943i	0.0941924	−	0.351531i
$584$	1.68606	+	0.973445i	0.00288708	+	0.00166686i
$585$	−116.307	+	437.557i	−0.198816	+	0.747961i
$586$	167.083	−	96.4655i	0.285125	−	0.164617i
$587$	324.936	−	324.936i	0.553554	−	0.553554i	−0.373911	−	0.927465i	$-0.621983\pi$
$587$	324.936	−	324.936i	0.553554	−	0.553554i	0.927465	+	0.373911i	$0.121983\pi$
$588$	143.560	+	841.256i	0.244150	+	1.43071i
$589$		−	26.9361i		−	0.0457318i
$590$	737.715	−	864.135i	1.25036	−	1.46464i
$591$	−227.876	−	143.496i	−0.385577	−	0.242802i
$592$	−42.0650	−	156.989i	−0.0710558	−	0.265184i
$593$	165.267	−	616.787i	0.278697	−	1.04011i	−0.674626	−	0.738160i	$-0.735695\pi$
$593$	165.267	−	616.787i	0.278697	−	1.04011i	0.953323	−	0.301952i	$-0.0976383\pi$
$594$	−115.967	+	1002.70i	−0.195230	+	1.68805i
$595$	107.358	+	22.9094i	0.180434	+	0.0385032i
$596$		−	1203.83i		−	2.01985i
$597$	265.291	−	857.068i	0.444374	−	1.43562i
$598$	79.2172	+	295.642i	0.132470	+	0.494385i
$599$	−342.953	+	594.012i	−0.572542	+	0.991672i	0.423762	+	0.905774i	$0.360709\pi$
$599$	−342.953	+	594.012i	−0.572542	+	0.991672i	−0.996304	+	0.0858986i	$0.972624\pi$
$600$	166.871	−	389.828i	0.278119	−	0.649713i
$601$		−	491.319i		−	0.817502i	−0.912646	−	0.408751i	$-0.865964\pi$
$601$		−	491.319i		−	0.817502i	0.912646	−	0.408751i	$-0.134036\pi$
$602$	−34.3196	+	1261.52i	−0.0570093	+	2.09555i
$603$	340.865	+	397.668i	0.565282	+	0.659482i
$604$	−87.8474	+	50.7187i	−0.145443	+	0.0839714i
$605$	61.0011	+	88.7156i	0.100828	+	0.146637i
$606$	−183.482	−	115.541i	−0.302776	−	0.190661i
$607$	161.749	−	603.657i	0.266473	−	0.994493i	−0.694869	−	0.719136i	$-0.744538\pi$
$607$	161.749	−	603.657i	0.266473	−	0.994493i	0.961342	−	0.275356i	$-0.0887957\pi$
$608$	−971.197	−	971.197i	−1.59736	−	1.59736i
$609$	−179.479	+	528.502i	−0.294710	+	0.867820i
$610$	129.601	+	365.728i	0.212461	+	0.599554i
$611$	−261.371	+	150.902i	−0.427775	+	0.246976i
$612$	30.1510	+	161.081i	0.0492663	+	0.263204i
$613$	−926.155	+	248.162i	−1.51086	+	0.404833i	−0.916719	−	0.399531i	$-0.869173\pi$
$613$	−926.155	+	248.162i	−1.51086	+	0.404833i	−0.594137	+	0.804364i	$0.702506\pi$
$614$	1311.51	−	757.198i	2.13600	−	1.23322i
$615$	−617.078	+	192.357i	−1.00338	+	0.312776i
$616$	−134.659	+	452.907i	−0.218602	+	0.735238i
$617$	519.079	+	519.079i	0.841294	+	0.841294i	0.989027	−	0.147733i	$-0.0471976\pi$
$617$	519.079	+	519.079i	0.841294	+	0.841294i	−0.147733	+	0.989027i	$0.547198\pi$
$618$	456.821	−	1475.84i	0.739193	−	2.38808i
$619$	−370.531	+	641.779i	−0.598597	+	1.03680i	0.394432	+	0.918925i	$0.370941\pi$
$619$	−370.531	+	641.779i	−0.598597	+	1.03680i	−0.993029	+	0.117874i	$0.962392\pi$
$620$	−12.8676	−	18.7137i	−0.0207541	−	0.0301833i
$621$	−240.725	+	104.185i	−0.387641	+	0.167770i
$622$	697.373	+	697.373i	1.12118	+	1.12118i
$623$	−12.4958	+	459.320i	−0.0200574	+	0.737271i
$624$	166.421	+	6.39053i	0.266700	+	0.0102412i
$625$	594.241	−	193.655i	0.950786	−	0.309848i
$626$	467.632	−	809.963i	0.747016	−	1.29387i
$627$	−273.210	−	1202.45i	−0.435742	−	1.91778i
$628$	−637.225	−	170.744i	−1.01469	−	0.271885i
$629$		−	92.3848i		−	0.146876i
$630$	−946.040	−	279.223i	−1.50165	−	0.443212i
$631$	1132.04			1.79404			0.897022	−	0.441985i	$-0.145726\pi$
$631$	1132.04			1.79404			0.897022	+	0.441985i	$0.145726\pi$
$632$	−112.753	+	420.801i	−0.178407	+	0.665825i
$633$	443.522	−	100.773i	0.700667	−	0.159200i
$634$	321.572	+	185.660i	0.507211	+	0.292838i
$635$	−642.644	+	752.772i	−1.01204	+	1.18547i
$636$	−11.8769	+	309.297i	−0.0186744	+	0.486317i
$637$	468.555	+	153.299i	0.735566	+	0.240657i
$638$	−702.599	+	702.599i	−1.10125	+	1.10125i
$639$	−169.564	−	353.877i	−0.265358	−	0.553798i
$640$	−798.891	−	147.885i	−1.24827	−	0.231071i
$641$	715.066	+	412.844i	1.11555	+	0.644062i	0.940261	−	0.340455i	$-0.110581\pi$
$641$	715.066	+	412.844i	1.11555	+	0.644062i	0.175287	+	0.984517i	$0.443915\pi$
$642$	−775.323	−	239.989i	−1.20767	−	0.373814i
$643$	−40.3544	+	40.3544i	−0.0627595	+	0.0627595i	−0.737790	−	0.675030i	$-0.764130\pi$
$643$	−40.3544	+	40.3544i	−0.0627595	+	0.0627595i	0.675030	+	0.737790i	$0.264130\pi$
$644$	−383.990	+	91.7743i	−0.596257	+	0.142507i
$645$	−764.719	−	401.258i	−1.18561	−	0.622105i
$646$	−169.067	−	292.833i	−0.261714	−	0.453302i
$647$	127.152	+	474.537i	0.196525	+	0.733442i	0.991867	+	0.127281i	$0.0406249\pi$
$647$	127.152	+	474.537i	0.196525	+	0.733442i	−0.795342	+	0.606162i	$0.792708\pi$
$648$	−49.4897	−	455.284i	−0.0763730	−	0.702598i
$649$	−433.188	−	750.304i	−0.667470	−	1.15609i
$650$	−495.940	−	611.888i	−0.762984	−	0.941366i
$651$	−12.3541	+	10.8314i	−0.0189771	+	0.0166381i
$652$	722.534	−	722.534i	1.10818	−	1.10818i
$653$	−423.092	−	113.367i	−0.647921	−	0.173610i	−0.0801323	−	0.996784i	$-0.525534\pi$
$653$	−423.092	−	113.367i	−0.647921	−	0.173610i	−0.567789	+	0.823174i	$0.692201\pi$
$654$	−512.596	+	814.018i	−0.783786	+	1.24468i
$655$	515.072	+	749.084i	0.786370	+	1.14364i
$656$	118.882	+	205.910i	0.181222	+	0.313886i
$657$	2.01689	+	2.35299i	0.00306985	+	0.00358142i
$658$	−313.156	−	578.165i	−0.475921	−	0.878671i
$659$	−777.010			−1.17907			−0.589537	−	0.807741i	$-0.700690\pi$
$659$	−777.010			−1.17907			−0.589537	+	0.807741i	$0.700690\pi$
$660$	−764.229	−	704.878i	−1.15792	−	1.06800i
$661$	8.95181	+	5.16833i	0.0135428	+	0.00781896i	0.506756	−	0.862089i	$-0.330844\pi$
$661$	8.95181	+	5.16833i	0.0135428	+	0.00781896i	−0.493213	+	0.869908i	$0.664178\pi$
$662$	−588.951	+	157.809i	−0.889654	+	0.238382i
$663$	90.4349	+	27.9927i	0.136403	+	0.0422212i
$664$	613.847			0.924468
$665$	1203.40	−	62.1021i	1.80962	−	0.0933867i
$666$	−63.6594	+	827.680i	−0.0955846	+	1.24276i
$667$	−249.409	−	66.8290i	−0.373927	−	0.100193i
$668$	186.652	−	50.0133i	0.279419	−	0.0748702i
$669$	56.3841	−	89.5397i	0.0842812	−	0.133841i
$670$	−908.345	+	71.6879i	−1.35574	+	0.106997i
$671$	295.867			0.440935
$672$	−54.9007	+	835.967i	−0.0816975	+	1.24400i
$673$	179.773	+	179.773i	0.267121	+	0.267121i	0.827939	−	0.560818i	$-0.189513\pi$
$673$	179.773	+	179.773i	0.267121	+	0.267121i	−0.560818	+	0.827939i	$0.689513\pi$
$674$	−170.234	−	294.853i	−0.252572	−	0.437468i
$675$	456.650	−	497.087i	0.676518	−	0.736426i
$676$	196.732	−	340.749i	0.291023	−	0.504067i
$677$	−586.770	−	157.225i	−0.866721	−	0.232237i	−0.202052	−	0.979375i	$-0.564761\pi$
$677$	−586.770	−	157.225i	−0.866721	−	0.232237i	−0.664669	+	0.747138i	$0.731428\pi$
$678$	−796.712	−	860.343i	−1.17509	−	1.26894i
$679$	515.445	−	123.192i	0.759124	−	0.181432i
$680$	−80.0363	−	38.1539i	−0.117700	−	0.0561087i
$681$	−457.073	−	866.882i	−0.671179	−	1.27295i
$682$	−28.2523	+	7.57018i	−0.0414256	+	0.0111000i
$683$	−50.3773	−	188.011i	−0.0737589	−	0.275272i	0.919190	−	0.393814i	$-0.128845\pi$
$683$	−50.3773	−	188.011i	−0.0737589	−	0.275272i	−0.992949	+	0.118542i	$0.962178\pi$
$684$	777.327	+	1622.27i	1.13644	+	2.37174i
$685$	513.225	−	181.869i	0.749234	−	0.265502i
$686$	−361.621	+	1011.36i	−0.527145	+	1.47428i
$687$	313.583	+	338.628i	0.456452	+	0.492908i
$688$	−82.2199	+	306.849i	−0.119506	+	0.446001i
$689$	154.849	+	89.4021i	0.224745	+	0.129756i
$690$	100.215	−	445.177i	0.145239	−	0.645185i
$691$	853.990	−	493.052i	1.23588	−	0.713533i	0.267627	−	0.963523i	$-0.413760\pi$
$691$	853.990	−	493.052i	1.23588	−	0.713533i	0.968249	+	0.249989i	$0.0804271\pi$
$692$	−130.723	+	130.723i	−0.188906	+	0.188906i
$693$	−441.634	+	608.829i	−0.637278	+	0.878541i
$694$			399.339i			0.575416i
$695$	−904.129	+	71.3552i	−1.30091	+	0.102669i
$696$	240.222	−	381.480i	0.345146	−	0.548103i
$697$	34.9798	+	130.547i	0.0501863	+	0.187298i
$698$	−41.4020	+	154.514i	−0.0593152	+	0.221367i
$699$	−157.570	−	6.05064i	−0.225421	−	0.00865613i
$700$	806.385	−	618.016i	1.15198	−	0.882880i
$701$		−	693.931i		−	0.989917i	−0.868917	−	0.494958i	$-0.835183\pi$
$701$		−	693.931i		−	0.989917i	0.868917	−	0.494958i	$-0.164817\pi$
$702$	−790.922	−	313.103i	−1.12667	−	0.446016i
$703$	−262.470	−	979.550i	−0.373356	−	1.39338i
$704$	−613.957	+	1063.41i	−0.872098	+	1.51052i
$705$	449.590	−	18.1631i	0.637716	−	0.0257633i
$706$		−	271.374i		−	0.384382i
$707$	−76.9499	−	142.069i	−0.108840	−	0.200946i
$708$	858.764	+	927.350i	1.21294	+	1.30982i
$709$	−281.100	+	162.293i	−0.396473	+	0.228904i	−0.684961	−	0.728580i	$-0.740181\pi$
$709$	−281.100	+	162.293i	−0.396473	+	0.228904i	0.288488	+	0.957484i	$0.406848\pi$
$710$	671.245	+	124.256i	0.945415	+	0.175009i
$711$	−391.769	+	572.205i	−0.551012	+	0.804789i
$712$	96.0553	−	358.483i	0.134909	−	0.503488i
$713$	−5.37454	−	5.37454i	−0.00753792	−	0.00753792i
$714$	−66.3217	+	195.295i	−0.0928876	+	0.273522i
$715$	−566.092	+	200.603i	−0.791738	+	0.280564i
$716$	132.693	−	76.6102i	0.185325	−	0.106997i
$717$	373.293	−	84.8165i	0.520632	−	0.118294i
$718$	1750.89	−	469.151i	2.43857	−	0.653413i
$719$	529.025	−	305.433i	0.735779	−	0.424802i	−0.0847533	−	0.996402i	$-0.527010\pi$
$719$	529.025	−	305.433i	0.735779	−	0.424802i	0.820533	+	0.571600i	$0.193677\pi$
$720$	−215.279	−	123.719i	−0.298999	−	0.171832i
$721$	835.849	−	791.575i	1.15929	−	1.09789i
$722$	−1825.23	−	1825.23i	−2.52802	−	2.52802i
$723$	382.147	+	118.287i	0.528557	+	0.163606i
$724$	94.2382	−	163.225i	0.130163	−	0.225449i
$725$	656.234	−	104.231i	0.905150	−	0.143767i
$726$	−178.934	+	94.3449i	−0.246465	+	0.129952i
$727$	−104.280	−	104.280i	−0.143439	−	0.143439i	0.631741	−	0.775180i	$-0.282341\pi$
$727$	−104.280	−	104.280i	−0.143439	−	0.143439i	−0.775180	+	0.631741i	$0.782341\pi$
$728$	−339.303	−	208.400i	−0.466075	−	0.286264i
$729$	166.398	−	709.755i	0.228256	−	0.973601i
$730$	−5.37467	+	0.424177i	−0.00736256	+	0.000581064i
$731$	−90.2873	+	156.382i	−0.123512	+	0.213929i
$732$	−420.895	+	95.6323i	−0.574993	+	0.130645i
$733$	−34.7645	−	9.31513i	−0.0474277	−	0.0127082i	0.235027	−	0.971989i	$-0.424482\pi$
$733$	−34.7645	−	9.31513i	−0.0474277	−	0.0127082i	−0.282455	+	0.959281i	$0.591149\pi$
$734$			940.560i			1.28142i
$735$	−512.387	−	526.958i	−0.697125	−	0.716950i
$736$	−387.565			−0.526582
$737$	−179.824	+	671.111i	−0.243994	+	0.910598i
$738$	−223.431	−	1193.68i	−0.302752	−	1.61745i
$739$	235.115	+	135.743i	0.318152	+	0.183685i	0.650569	−	0.759447i	$-0.274531\pi$
$739$	235.115	+	135.743i	0.318152	+	0.183685i	−0.332416	+	0.943133i	$0.607864\pi$
$740$	−650.287	−	555.152i	−0.878767	−	0.750206i
$741$	1038.40	+	39.8745i	1.40135	+	0.0538117i
$742$	−203.878	+	331.940i	−0.274769	+	0.447358i
$743$	389.786	−	389.786i	0.524611	−	0.524611i	−0.394349	−	0.918961i	$-0.629030\pi$
$743$	389.786	−	389.786i	0.524611	−	0.524611i	0.918961	+	0.394349i	$0.129030\pi$
$744$	11.7387	−	6.18934i	0.0157778	−	0.00831901i
$745$	587.432	+	854.319i	0.788500	+	1.14674i
$746$	1288.58	+	743.960i	1.72732	+	0.997266i
$747$	921.667	+	324.536i	1.23382	+	0.434453i
$748$	−153.717	+	153.717i	−0.205504	+	0.205504i
$749$	−415.850	−	439.109i	−0.555207	−	0.586261i
$750$	230.867	+	1151.35i	0.307822	+	1.53513i
$751$	515.279	+	892.489i	0.686124	+	1.18840i	0.973082	+	0.230458i	$0.0740225\pi$
$751$	515.279	+	892.489i	0.686124	+	1.18840i	−0.286958	+	0.957943i	$0.592644\pi$
$752$	−42.8387	−	159.876i	−0.0569663	−	0.212601i
$753$	−774.050	+	175.873i	−1.02796	+	0.233563i
$754$	−418.679	−	725.174i	−0.555278	−	0.961769i
$755$	37.5932	−	78.8602i	0.0497924	−	0.104451i
$756$	431.470	−	1008.86i	0.570728	−	1.33447i
$757$	770.070	−	770.070i	1.01727	−	1.01727i	0.0174177	−	0.999848i	$-0.494455\pi$
$757$	770.070	−	770.070i	1.01727	−	1.01727i	0.999848	−	0.0174177i	$-0.00554450\pi$
$758$	1504.40	+	403.102i	1.98469	+	0.531797i
$759$	−294.437	−	185.410i	−0.387928	−	0.244282i
$760$	−957.016	−	177.156i	−1.25923	−	0.233100i
$761$	198.598	+	343.982i	0.260970	+	0.452013i	0.966500	−	0.256667i	$-0.0826244\pi$
$761$	198.598	+	343.982i	0.260970	+	0.452013i	−0.705530	+	0.708680i	$0.749291\pi$
$762$	−1263.53	−	1364.44i	−1.65817	−	1.79060i
$763$	−630.288	+	341.388i	−0.826066	+	0.447429i
$764$	1902.77			2.49054
$765$	−99.9997	−	99.6012i	−0.130719	−	0.130198i
$766$	−1607.21	−	927.923i	−2.09819	−	1.21139i
$767$	705.244	−	188.970i	0.919484	−	0.246375i
$768$	86.4198	−	279.193i	0.112526	−	0.363533i
$769$	548.417			0.713156			0.356578	−	0.934266i	$-0.383943\pi$
$769$	548.417			0.713156			0.356578	+	0.934266i	$0.383943\pi$
$770$	−403.342	−	1244.75i	−0.523821	−	1.61655i
$771$	−429.519	−	16.4934i	−0.557094	−	0.0213923i
$772$	−399.087	−	106.935i	−0.516952	−	0.138517i
$773$	−527.718	+	141.402i	−0.682688	+	0.182926i	−0.583463	−	0.812139i	$-0.698303\pi$
$773$	−527.718	+	141.402i	−0.682688	+	0.182926i	−0.0992245	+	0.995065i	$0.531636\pi$
$774$	916.646	−	1338.82i	1.18430	−	1.72974i
$775$	18.2634	+	7.00149i	0.0235656	+	0.00903418i
$776$	−428.050			−0.551611
$777$	−343.722	+	514.272i	−0.442370	+	0.661869i
$778$	172.785	+	172.785i	0.222089	+	0.222089i
$779$	741.777	+	1284.80i	0.952217	+	1.64929i
$780$	740.473	−	468.351i	0.949324	−	0.600450i
$781$	260.267	−	450.795i	0.333248	−	0.577202i
$782$	−92.1628	−	24.6950i	−0.117855	−	0.0315792i
$783$	562.369	−	445.773i	0.718224	−	0.569315i
$784$	−147.715	+	226.450i	−0.188412	+	0.288839i
$785$	535.535	−	189.775i	0.682210	−	0.241751i
$786$	−1510.86	+	796.616i	−1.92221	+	1.01351i
$787$	929.410	−	249.035i	1.18095	−	0.316435i	0.385649	−	0.922646i	$-0.373978\pi$
$787$	929.410	−	249.035i	1.18095	−	0.316435i	0.795305	+	0.606210i	$0.207311\pi$
$788$	134.879	+	503.375i	0.171166	+	0.638800i
$789$	508.230	+	963.905i	0.644144	+	1.22168i
$790$	−402.953	−	1137.12i	−0.510068	−	1.43939i
$791$	−203.105	−	849.807i	−0.256771	−	1.07434i
$792$	461.246	−	395.362i	0.582381	−	0.499194i
$793$	−64.5331	+	240.841i	−0.0813784	+	0.303708i
$794$	−940.629	−	543.072i	−1.18467	−	0.683970i
$795$	−142.499	−	225.294i	−0.179244	−	0.283388i
$796$	−1503.61	+	868.112i	−1.88896	+	1.09059i
$797$	−673.373	+	673.373i	−0.844885	+	0.844885i	−0.989490	−	0.144605i	$-0.953809\pi$
$797$	−673.373	+	673.373i	−0.844885	+	0.844885i	0.144605	+	0.989490i	$0.453809\pi$
$798$	−148.364	+	2259.12i	−0.185920	+	2.83097i
$799$		−	94.0839i		−	0.117752i
$800$	910.940	−	406.054i	1.13868	−	0.507567i
$801$	333.751	−	487.465i	0.416668	−	0.608571i
$802$	594.376	+	2218.24i	0.741117	+	2.76589i
$803$	−1.06401	+	3.97095i	−0.00132505	+	0.00494515i
$804$	38.8926	−	1012.83i	0.0483739	−	1.25974i
$805$	227.722	−	252.504i	0.282884	−	0.313670i
$806$		−	24.6490i		−	0.0305819i
$807$	1503.32	+	465.329i	1.86285	+	0.576616i
$808$	33.7759	+	126.053i	0.0418018	+	0.156007i
$809$	−247.264	+	428.274i	−0.305641	+	0.529386i	−0.977404	−	0.211380i	$-0.932204\pi$
$809$	−247.264	+	428.274i	−0.305641	+	0.529386i	0.671763	+	0.740767i	$0.265538\pi$
$810$	827.270	+	961.239i	1.02132	+	1.18671i
$811$		−	809.347i		−	0.997962i	−0.866613	−	0.498981i	$-0.833708\pi$
$811$		−	809.347i		−	0.997962i	0.866613	−	0.498981i	$-0.166292\pi$
$812$	949.749	−	514.420i	1.16964	−	0.633522i
$813$	208.047	−	192.660i	0.255900	−	0.236974i
$814$	−953.650	+	550.590i	−1.17156	+	0.676401i
$815$	−160.184	+	865.332i	−0.196545	+	1.06176i
$816$	−27.6651	+	43.9330i	−0.0339033	+	0.0538395i
$817$	−513.021	+	1914.62i	−0.627932	+	2.34348i
$818$	1049.95	+	1049.95i	1.28356	+	1.28356i
$819$	−399.270	−	492.292i	−0.487509	−	0.601089i
$820$	1129.10	+	538.251i	1.37695	+	0.656404i
$821$	−827.948	+	478.016i	−1.00846	+	0.582236i	−0.910741	−	0.412978i	$-0.864489\pi$
$821$	−827.948	+	478.016i	−1.00846	+	0.582236i	−0.0977213	+	0.995214i	$0.531155\pi$
$822$	226.664	+	997.589i	0.275747	+	1.21361i
$823$	−256.679	+	68.7769i	−0.311882	+	0.0835686i	−0.411365	−	0.911471i	$-0.634948\pi$
$823$	−256.679	+	68.7769i	−0.311882	+	0.0835686i	0.0994828	+	0.995039i	$0.468281\pi$
$824$	−805.243	+	464.907i	−0.977236	+	0.564208i
$825$	886.307	+	127.309i	1.07431	+	0.154314i
$826$	369.762	+	1547.11i	0.447654	+	1.87301i
$827$	775.831	+	775.831i	0.938127	+	0.938127i	0.998194	−	0.0600672i	$-0.0191315\pi$
$827$	775.831	+	775.831i	0.938127	+	0.938127i	−0.0600672	+	0.998194i	$0.519131\pi$
$828$	478.791	+	168.591i	0.578250	+	0.203613i
$829$	−660.449	+	1143.93i	−0.796682	+	1.37989i	0.125084	+	0.992146i	$0.460080\pi$
$829$	−660.449	+	1143.93i	−0.796682	+	1.37989i	−0.921766	+	0.387747i	$0.873253\pi$
$830$	−1400.71	+	963.129i	−1.68760	+	1.16040i
$831$	−372.963	−	707.360i	−0.448813	−	0.851215i
$832$	−731.716	−	731.716i	−0.879466	−	0.879466i
$833$	−114.420	+	102.603i	−0.137358	+	0.123172i
$834$	65.3845	−	1702.73i	0.0783987	−	2.04165i
$835$	−108.056	+	126.573i	−0.129408	+	0.151585i
$836$	−1193.13	+	2066.57i	−1.42719	+	2.47197i
$837$	20.8974	−	3.08691i	0.0249670	−	0.00368806i
$838$	377.683	+	101.200i	0.450696	+	0.120764i
$839$		−	1167.63i		−	1.39169i	−0.718193	−	0.695843i	$-0.755031\pi$
$839$		−	1167.63i		−	1.39169i	0.718193	−	0.695843i	$-0.244969\pi$
$840$	303.579	+	510.167i	0.361404	+	0.607342i
$841$	−134.589			−0.160035
$842$	312.485	−	1166.21i	0.371122	−	1.38505i
$843$	69.5457	+	306.083i	0.0824979	+	0.363088i
$844$	−762.253	−	440.087i	−0.903143	−	0.521430i
$845$	26.6611	+	337.818i	0.0315516	+	0.399784i
$846$	−64.8301	+	842.903i	−0.0766314	+	0.996339i
$847$	−150.674	−	4.09908i	−0.177892	−	0.00483953i
$848$	−69.3387	+	69.3387i	−0.0817674	+	0.0817674i
$849$	−133.973	−	254.091i	−0.157800	−	0.299283i
$850$	242.494	−	38.5159i	0.285288	−	0.0453129i
$851$	−247.819	−	143.079i	−0.291210	−	0.168130i
$852$	−224.541	+	725.418i	−0.263546	+	0.851430i
$853$	−196.296	+	196.296i	−0.230124	+	0.230124i	−0.812744	−	0.582621i	$-0.802027\pi$
$853$	−196.296	+	196.296i	−0.230124	+	0.230124i	0.582621	+	0.812744i	$0.302027\pi$
$854$	−520.690	−	154.812i	−0.609707	−	0.181279i
$855$	−1343.26	−	771.961i	−1.57107	−	0.902878i
$856$	244.237	+	423.030i	0.285323	+	0.494194i
$857$	−279.112	−	1041.66i	−0.325684	−	1.21547i	−0.913622	−	0.406564i	$-0.866727\pi$
$857$	−279.112	−	1041.66i	−0.325684	−	1.21547i	0.587938	−	0.808906i	$-0.299940\pi$
$858$	−250.013	−	1100.35i	−0.291390	−	1.28246i
$859$	−380.060	−	658.283i	−0.442444	−	0.766336i	0.555426	−	0.831566i	$-0.312555\pi$
$859$	−380.060	−	658.283i	−0.442444	−	0.766336i	−0.997870	+	0.0652300i	$0.979222\pi$
$860$	558.210	+	1575.24i	0.649082	+	1.83168i
$861$	290.984	−	856.848i	0.337961	−	0.995178i
$862$	−367.997	+	367.997i	−0.426911	+	0.426911i
$863$	195.907	+	52.4932i	0.227007	+	0.0608264i	0.370530	−	0.928821i	$-0.379176\pi$
$863$	195.907	+	52.4932i	0.227007	+	0.0608264i	−0.143522	+	0.989647i	$0.545843\pi$
$864$	642.169	−	864.770i	0.743251	−	1.00089i
$865$	28.9810	−	156.558i	0.0335040	−	0.180992i
$866$	−494.751	−	856.934i	−0.571306	−	0.989531i
$867$	614.481	−	569.034i	0.708744	−	0.656326i
$868$	31.7832	+	0.864660i	0.0366166	+	0.000996152i
$869$	−919.905			−1.05858
$870$	50.3936	+	1247.39i	0.0579237	+	1.43378i
$871$	−507.073	−	292.759i	−0.582173	−	0.336118i
$872$	559.235	−	149.847i	0.641324	−	0.171842i
$873$	−642.701	−	226.307i	−0.736198	−	0.259229i
$874$	−1047.36			−1.19835
$875$	−270.692	+	832.076i	−0.309362	+	0.950944i
$876$	0.230127	−	5.99293i	0.000262702	−	0.00684124i
$877$	−1269.66	−	340.203i	−1.44773	−	0.387917i	−0.552495	−	0.833516i	$-0.686324\pi$
$877$	−1269.66	−	340.203i	−1.44773	−	0.387917i	−0.895233	+	0.445599i	$0.852991\pi$
$878$	−970.019	+	259.916i	−1.10481	+	0.296032i
$879$	−156.409	−	98.4923i	−0.177939	−	0.112050i
$880$	−25.9140	−	328.352i	−0.0294477	−	0.373127i
$881$	−175.429			−0.199125			−0.0995623	−	0.995031i	$-0.531744\pi$
$881$	−175.429			−0.199125			−0.0995623	+	0.995031i	$0.531744\pi$
$882$	1095.79	−	840.380i	1.24239	−	0.952811i
$883$	21.1868	+	21.1868i	0.0239941	+	0.0239941i	0.719002	−	0.695008i	$-0.244599\pi$
$883$	21.1868	+	21.1868i	0.0239941	+	0.0239941i	−0.695008	+	0.719002i	$0.744599\pi$
$884$	−91.6003	−	158.656i	−0.103620	−	0.179475i
$885$	−1061.95	−	239.060i	−1.19995	−	0.270124i
$886$	−578.348	+	1001.73i	−0.652763	+	1.13062i
$887$	−595.560	−	159.580i	−0.671431	−	0.179909i	−0.0930318	−	0.995663i	$-0.529656\pi$
$887$	−595.560	−	159.580i	−0.671431	−	0.179909i	−0.578399	+	0.815754i	$0.696322\pi$
$888$	366.575	−	339.464i	0.412810	−	0.382279i
$889$	−322.110	−	1347.73i	−0.362328	−	1.51601i
$890$	343.279	+	968.716i	0.385706	+	1.08845i
$891$	901.568	−	349.763i	1.01186	−	0.392551i
$892$	−197.792	+	52.9981i	−0.221740	+	0.0594150i
$893$	−267.297	−	997.565i	−0.299324	−	1.11709i
$894$	−1723.11	+	908.529i	−1.92742	+	1.01625i
$895$	−56.7842	+	119.118i	−0.0634461	+	0.133092i
$896$	825.873	−	782.128i	0.921733	−	0.872910i
$897$	215.148	−	199.236i	0.239853	−	0.222114i
$898$	−32.5977	+	121.656i	−0.0363003	+	0.135475i
$899$	18.0084	+	10.3972i	0.0200316	+	0.0115652i
$900$	−1301.99	+	105.371i	−1.44666	+	0.117079i
$901$	−48.2722	+	27.8700i	−0.0535763	+	0.0309323i
$902$	1139.11	−	1139.11i	1.26287	−	1.26287i
$903$	1084.42	−	534.604i	1.20091	−	0.592031i
$904$			705.720i			0.780663i
$905$	12.7711	+	161.821i	0.0141118	+	0.178808i
$906$	138.895	+	87.4635i	0.153305	+	0.0965381i
$907$	−335.284	−	1251.30i	−0.369663	−	1.37960i	−0.860988	−	0.508625i	$-0.830154\pi$
$907$	−335.284	−	1251.30i	−0.369663	−	1.37960i	0.491325	−	0.870976i	$-0.336513\pi$
$908$	−490.846	+	1831.86i	−0.540579	+	2.01747i
$909$	−15.9303	+	207.121i	−0.0175251	+	0.227856i
$910$	1101.22	−	56.8292i	1.21013	−	0.0624497i
$911$			1273.56i			1.39798i	0.715132	+	0.698989i	$0.246366\pi$
$911$			1273.56i			1.39798i	−0.715132	+	0.698989i	$0.753634\pi$
$912$	−168.515	+	544.417i	−0.184776	+	0.596948i
$913$	335.479	+	1252.03i	0.367447	+	1.37133i
$914$	1301.93	−	2255.00i	1.42443	−	2.46718i
$915$	252.030	−	273.251i	0.275442	−	0.298635i
$916$		−	893.132i		−	0.975034i
$917$	−1272.24	−	34.6112i	−1.38739	−	0.0377440i
$918$	207.809	−	164.724i	0.226372	−	0.179438i
$919$	908.766	−	524.676i	0.988864	−	0.570921i	0.0839294	−	0.996472i	$-0.473253\pi$
$919$	908.766	−	524.676i	0.988864	−	0.570921i	0.904935	+	0.425551i	$0.139920\pi$
$920$	−226.301	+	155.605i	−0.245979	+	0.169136i
$921$	−1227.72	−	773.107i	−1.33303	−	0.839422i
$922$	81.3902	−	303.752i	0.0882757	−	0.329449i
$923$	310.186	+	310.186i	0.336063	+	0.336063i
$924$	1427.60	−	283.775i	1.54502	−	0.307116i
$925$	732.384	+	76.6532i	0.791767	+	0.0828683i
$926$	−596.269	+	344.256i	−0.643919	+	0.371767i
$927$	−1454.83	+	272.314i	−1.56940	+	0.293758i
$928$	1024.18	−	274.428i	1.10364	−	0.295720i
$929$	−244.701	+	141.278i	−0.263403	+	0.152076i	−0.625886	−	0.779915i	$-0.715262\pi$
$929$	−244.701	+	141.278i	−0.263403	+	0.152076i	0.362483	+	0.931990i	$0.381929\pi$
$930$	−17.0748	+	32.5412i	−0.0183600	+	0.0349905i
$931$	−921.683	+	1412.96i	−0.989993	+	1.51768i
$932$	215.775	+	215.775i	0.231518	+	0.231518i
$933$	279.386	−	902.604i	0.299450	−	0.967421i
$934$	588.453	−	1019.23i	0.630036	−	1.09125i
$935$	34.0788	−	184.097i	0.0364479	−	0.196895i
$936$	221.226	+	461.696i	0.236353	+	0.493265i
$937$	271.472	+	271.472i	0.289725	+	0.289725i	0.836971	−	0.547247i	$-0.184324\pi$
$937$	271.472	+	271.472i	0.289725	+	0.289725i	−0.547247	+	0.836971i	$0.684324\pi$
$938$	667.626	−	1086.98i	0.711754	−	1.15883i
$939$	−895.364	−	34.3818i	−0.953529	−	0.0366153i
$940$	−662.247	−	565.362i	−0.704518	−	0.601449i
$941$	244.200	−	422.967i	0.259511	−	0.449486i	−0.706600	−	0.707613i	$-0.749772\pi$
$941$	244.200	−	422.967i	0.259511	−	0.449486i	0.966111	+	0.258127i	$0.0831053\pi$
$942$	236.517	+	1040.95i	0.251080	+	1.10505i
$943$	404.361	+	108.348i	0.428803	+	0.114897i
$944$			400.414i			0.424167i
$945$	186.091	+	926.496i	0.196921	+	0.980419i
$946$	2152.36			2.27522
$947$	295.191	−	1101.67i	0.311711	−	1.16332i	−0.615301	−	0.788292i	$-0.710966\pi$
$947$	295.191	−	1101.67i	0.311711	−	1.16332i	0.927013	−	0.375030i	$-0.122368\pi$
$948$	1308.64	−	297.338i	1.38042	−	0.313648i
$949$	−3.00034	−	1.73225i	−0.00316159	−	0.00182534i
$950$	2461.73	−	1097.32i	2.59129	−	1.15507i
$951$	13.6503	−	355.478i	0.0143536	−	0.373794i
$952$	109.149	−	59.1193i	0.114652	−	0.0621001i
$953$	354.436	−	354.436i	0.371916	−	0.371916i	−0.496258	−	0.868175i	$-0.665293\pi$
$953$	354.436	−	354.436i	0.371916	−	0.371916i	0.868175	+	0.496258i	$0.165293\pi$
$954$	451.678	−	216.426i	0.473457	−	0.226861i
$955$	−1350.34	+	928.494i	−1.41396	+	0.972245i
$956$	−641.555	−	370.402i	−0.671082	−	0.387450i
$957$	909.368	+	281.480i	0.950227	+	0.294128i
$958$	203.346	−	203.346i	0.212261	−	0.212261i
$959$	−217.248	+	730.682i	−0.226536	+	0.761921i
$960$	459.128	+	1472.87i	0.478258	+	1.53424i
$961$	−480.194	−	831.720i	−0.499682	−	0.865474i
$962$	−240.184	−	896.379i	−0.249671	−	0.931787i
$963$	143.059	+	764.289i	0.148555	+	0.793655i
$964$	−387.071	−	670.427i	−0.401526	−	0.695464i
$965$	335.399	−	118.854i	0.347564	−	0.123164i
$966$	421.158	+	480.364i	0.435981	+	0.497271i
$967$	−563.373	+	563.373i	−0.582599	+	0.582599i	−0.935617	−	0.353018i	$-0.885155\pi$
$967$	−563.373	+	563.373i	−0.582599	+	0.582599i	0.353018	+	0.935617i	$0.385155\pi$
$968$	117.596	+	31.5098i	0.121484	+	0.0325514i
$969$	−172.620	+	274.125i	−0.178142	+	0.282895i
$970$	976.746	−	671.613i	1.00696	−	0.692385i
$971$	673.469	+	1166.48i	0.693583	+	1.20132i	0.970656	+	0.240472i	$0.0773021\pi$
$971$	673.469	+	1166.48i	0.693583	+	1.20132i	−0.277073	+	0.960849i	$0.589365\pi$
$972$	−1169.50	+	788.977i	−1.20319	+	0.811705i
$973$	664.527	−	1081.94i	0.682968	−	1.11196i
$974$	−136.156			−0.139790
$975$	−296.948	+	693.700i	−0.304562	+	0.711488i
$976$	−118.421	−	68.3706i	−0.121333	−	0.0700518i
$977$	−1443.22	+	386.710i	−1.47720	+	0.395814i	−0.905393	−	0.424575i	$-0.860423\pi$
$977$	−1443.22	+	386.710i	−1.47720	+	0.395814i	−0.571806	+	0.820389i	$0.693757\pi$
$978$	−1579.50	−	488.908i	−1.61503	−	0.499906i
$979$	783.673			0.800483
$980$	34.6478	+	1421.94i	0.0353549	+	1.45096i
$981$	918.892	+	70.6747i	0.936689	+	0.0720436i
$982$	447.109	+	119.803i	0.455305	+	0.121999i
$983$	52.0708	−	13.9523i	0.0529713	−	0.0141936i	−0.232236	−	0.972659i	$-0.574604\pi$
$983$	52.0708	−	13.9523i	0.0529713	−	0.0141936i	0.285207	+	0.958466i	$0.407938\pi$
$984$	−389.466	+	618.484i	−0.395799	+	0.628541i
$985$	−341.350	−	291.412i	−0.346548	−	0.295849i
$986$	261.036			0.264743
$987$	−350.043	+	523.730i	−0.354654	+	0.530628i
$988$	−1421.98	−	1421.98i	−1.43925	−	1.43925i
$989$	279.660	+	484.386i	0.282771	+	0.489773i
$990$	−432.169	+	1625.85i	−0.436534	+	1.64228i
$991$	−448.670	+	777.120i	−0.452745	+	0.784177i	−0.998555	−	0.0537313i	$-0.982889\pi$
$991$	−448.670	+	777.120i	−0.452745	+	0.784177i	0.545810	+	0.837909i	$0.316222\pi$
$992$	30.1484	+	8.07824i	0.0303915	+	0.00814338i
$993$	396.899	+	428.598i	0.399697	+	0.431619i
$994$	−693.916	+	657.160i	−0.698104	+	0.661126i
$995$	643.453	−	1349.79i	0.646687	−	1.35657i
$996$	−881.936	−	1672.67i	−0.885478	−	1.67939i
$997$	843.351	−	225.975i	0.845889	−	0.226655i	0.190256	−	0.981735i	$-0.439068\pi$
$997$	843.351	−	225.975i	0.845889	−	0.226655i	0.655634	+	0.755079i	$0.272402\pi$
$998$	−267.240	−	997.353i	−0.267775	−	0.999351i
$999$	729.871	−	315.886i	0.730601	−	0.316202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.38.4	yes	112
3.2	odd	2	inner	105.3.w.a.38.25	yes	112
5.2	odd	4	inner	105.3.w.a.17.4	✓	112
7.5	odd	6	inner	105.3.w.a.68.25	yes	112
15.2	even	4	inner	105.3.w.a.17.25	yes	112
21.5	even	6	inner	105.3.w.a.68.4	yes	112
35.12	even	12	inner	105.3.w.a.47.25	yes	112
105.47	odd	12	inner	105.3.w.a.47.4	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.4	✓	112	5.2	odd	4	inner
105.3.w.a.17.25	yes	112	15.2	even	4	inner
105.3.w.a.38.4	yes	112	1.1	even	1	trivial
105.3.w.a.38.25	yes	112	3.2	odd	2	inner
105.3.w.a.47.4	yes	112	105.47	odd	12	inner
105.3.w.a.47.25	yes	112	35.12	even	12	inner
105.3.w.a.68.4	yes	112	21.5	even	6	inner
105.3.w.a.68.25	yes	112	7.5	odd	6	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.810462 + 3.02468i) q^{2} +(2.92544 - 0.664693i) q^{3} +(-5.02776 - 2.90278i) q^{4} +(4.98450 - 0.393384i) q^{5} +(-0.360468 + 9.38723i) q^{6} +(-3.66357 + 5.96475i) q^{7} +(3.99791 - 3.99791i) q^{8} +(8.11637 - 3.88904i) q^{9} +(-2.84988 + 15.3954i) q^{10} +(10.3392 + 5.96936i) q^{11} +(-16.6379 - 5.14998i) q^{12} +(-7.11430 + 7.11430i) q^{13} +(-15.0723 - 15.9153i) q^{14} +(14.3204 - 4.46398i) q^{15} +(-2.75886 - 4.77849i) q^{16} +(-0.811768 - 3.02956i) q^{17} +(5.18510 + 27.7014i) q^{18} +(-17.2142 - 29.8159i) q^{19} +(-26.2028 - 12.4911i) q^{20} +(-6.75280 + 19.8847i) q^{21} +(-26.4350 + 26.4350i) q^{22} +(-9.38391 - 2.51441i) q^{23} +(9.03824 - 14.3530i) q^{24} +(24.6905 - 3.92165i) q^{25} +(-15.7526 - 27.2844i) q^{26} +(21.1589 - 16.7720i) q^{27} +(35.7339 - 19.3548i) q^{28} +26.5784 q^{29} +(1.89604 + 46.9325i) q^{30} +(0.677558 + 0.391188i) q^{31} +(38.5343 - 10.3252i) q^{32} +(34.2146 + 10.5906i) q^{33} +9.82137 q^{34} +(-15.9146 + 31.1725i) q^{35} +(-52.0962 - 4.00687i) q^{36} +(28.4517 + 7.62362i) q^{37} +(104.135 - 27.9030i) q^{38} +(-16.0836 + 25.5412i) q^{39} +(18.3549 - 21.5003i) q^{40} -43.0909 q^{41} +(-54.6719 - 36.5408i) q^{42} +(-40.7104 - 40.7104i) q^{43} +(-34.6554 - 60.0250i) q^{44} +(38.9261 - 22.5778i) q^{45} +(15.2106 - 26.3455i) q^{46} +(28.9750 + 7.76382i) q^{47} +(-11.2471 - 12.1454i) q^{48} +(-22.1566 - 43.7045i) q^{49} +(-8.14895 + 77.8593i) q^{50} +(-4.38851 - 8.32321i) q^{51} +(56.4202 - 15.1177i) q^{52} +(-4.59967 - 17.1662i) q^{53} +(33.5816 + 77.5921i) q^{54} +(53.8841 + 25.6870i) q^{55} +(9.19994 + 38.4931i) q^{56} +(-70.1776 - 75.7825i) q^{57} +(-21.5408 + 80.3912i) q^{58} +(-62.8463 - 36.2843i) q^{59} +(-84.9573 - 19.1250i) q^{60} +(21.4620 - 12.3911i) q^{61} +(-1.73236 + 1.73236i) q^{62} +(-6.53769 + 62.6599i) q^{63} +102.852i q^{64} +(-32.6626 + 38.2599i) q^{65} +(-59.7627 + 94.9050i) q^{66} +(15.0622 + 56.2130i) q^{67} +(-4.71277 + 17.5883i) q^{68} +(-29.1233 - 1.11833i) q^{69} +(-81.3888 - 73.4008i) q^{70} -43.6004i q^{71} +(16.9005 - 47.9965i) q^{72} +(0.0891230 + 0.332612i) q^{73} +(-46.1180 + 79.8788i) q^{74} +(69.6238 - 27.8841i) q^{75} +199.877i q^{76} +(-73.4842 + 39.8018i) q^{77} +(-64.2191 - 69.3480i) q^{78} +(-66.7293 + 38.5262i) q^{79} +(-15.6313 - 22.7331i) q^{80} +(50.7508 - 63.1297i) q^{81} +(34.9235 - 130.336i) q^{82} +(76.7710 + 76.7710i) q^{83} +(91.6722 - 80.3734i) q^{84} +(-5.23804 - 14.7815i) q^{85} +(156.130 - 90.1420i) q^{86} +(77.7534 - 17.6665i) q^{87} +(65.2002 - 17.4703i) q^{88} +(56.8471 - 32.8207i) q^{89} +(36.7424 + 136.038i) q^{90} +(-16.3713 - 68.4987i) q^{91} +(39.8813 + 39.8813i) q^{92} +(2.24217 + 0.694029i) q^{93} +(-46.9662 + 81.3479i) q^{94} +(-97.5335 - 141.846i) q^{95} +(105.867 - 55.8194i) q^{96} +(-53.5343 - 53.5343i) q^{97} +(150.149 - 31.5958i) q^{98} +(107.132 + 8.23984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) \) 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Introduction

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