LMFDB - Embedded newform 105.3.w.a.68.16

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			68.16
Character	$\chi$	$=$	105.68
Dual form			105.3.w.a.17.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.161935 - 0.0433902i) q^{2} +(0.339350 - 2.98075i) q^{3} +(-3.43976 + 1.98595i) q^{4} +(-4.97108 + 0.537016i) q^{5} +(-0.0743827 - 0.497410i) q^{6} +(-6.97488 + 0.592480i) q^{7} +(-0.945023 + 0.945023i) q^{8} +(-8.76968 - 2.02303i) q^{9} +(-0.781688 + 0.302658i) q^{10} +(13.2452 - 7.64711i) q^{11} +(4.75232 + 10.9270i) q^{12} +(-11.7128 + 11.7128i) q^{13} +(-1.10377 + 0.398585i) q^{14} +(-0.0862278 + 14.9998i) q^{15} +(7.83176 - 13.5650i) q^{16} +(-14.7635 - 3.95586i) q^{17} +(-1.50789 + 0.0529196i) q^{18} +(4.70012 - 8.14085i) q^{19} +(16.0328 - 11.7195i) q^{20} +(-0.600896 + 20.9914i) q^{21} +(1.81304 - 1.81304i) q^{22} +(-8.59850 - 32.0900i) q^{23} +(2.49618 + 3.13757i) q^{24} +(24.4232 - 5.33910i) q^{25} +(-1.38849 + 2.40493i) q^{26} +(-9.00614 + 25.4537i) q^{27} +(22.8153 - 15.8897i) q^{28} -6.89705 q^{29} +(0.636879 + 2.43272i) q^{30} +(-31.4348 + 18.1489i) q^{31} +(2.06325 - 7.70017i) q^{32} +(-18.2993 - 42.0756i) q^{33} -2.56236 q^{34} +(34.3545 - 6.69089i) q^{35} +(34.1833 - 10.4574i) q^{36} +(4.52283 + 16.8794i) q^{37} +(0.407879 - 1.52222i) q^{38} +(30.9381 + 38.8876i) q^{39} +(4.19029 - 5.20527i) q^{40} +17.4740 q^{41} +(0.813516 + 3.42531i) q^{42} +(33.7982 + 33.7982i) q^{43} +(-30.3735 + 52.6085i) q^{44} +(44.6812 + 5.34719i) q^{45} +(-2.78479 - 4.82340i) q^{46} +(-2.92196 - 10.9049i) q^{47} +(-37.7761 - 27.9478i) q^{48} +(48.2979 - 8.26495i) q^{49} +(3.72330 - 1.92431i) q^{50} +(-16.8014 + 42.6637i) q^{51} +(17.0282 - 63.5502i) q^{52} +(-74.1079 - 19.8572i) q^{53} +(-0.353964 + 4.51261i) q^{54} +(-61.7362 + 45.1272i) q^{55} +(6.03151 - 7.15133i) q^{56} +(-22.6708 - 16.7725i) q^{57} +(-1.11687 + 0.299265i) q^{58} +(4.43046 - 2.55793i) q^{59} +(-29.4921 - 51.7668i) q^{60} +(-51.8761 - 29.9507i) q^{61} +(-4.30289 + 4.30289i) q^{62} +(62.3661 + 8.91455i) q^{63} +61.3176i q^{64} +(51.9353 - 64.5152i) q^{65} +(-4.78896 - 6.01947i) q^{66} +(-65.4926 - 17.5487i) q^{67} +(58.6389 - 15.7122i) q^{68} +(-98.5701 + 14.7402i) q^{69} +(5.27286 - 2.57414i) q^{70} +50.8917i q^{71} +(10.1994 - 6.37574i) q^{72} +(-73.2942 - 19.6391i) q^{73} +(1.46480 + 2.53712i) q^{74} +(-7.62646 - 74.6112i) q^{75} +37.3368i q^{76} +(-87.8528 + 61.1852i) q^{77} +(6.69729 + 4.95483i) q^{78} +(-26.3396 - 15.2072i) q^{79} +(-31.6477 + 71.6385i) q^{80} +(72.8147 + 35.4827i) q^{81} +(2.82965 - 0.758201i) q^{82} +(-10.9693 - 10.9693i) q^{83} +(-39.6209 - 73.3988i) q^{84} +(75.5146 + 11.7367i) q^{85} +(6.93960 + 4.00658i) q^{86} +(-2.34052 + 20.5584i) q^{87} +(-5.29031 + 19.7437i) q^{88} +(33.2788 + 19.2135i) q^{89} +(7.46744 - 1.07283i) q^{90} +(74.7558 - 88.6350i) q^{91} +(93.3059 + 93.3059i) q^{92} +(43.4298 + 99.8579i) q^{93} +(-0.946333 - 1.63910i) q^{94} +(-18.9929 + 42.9929i) q^{95} +(-22.2521 - 8.76308i) q^{96} +(-17.8473 - 17.8473i) q^{97} +(7.46249 - 3.43404i) q^{98} +(-131.626 + 40.2673i) 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.161935	−	0.0433902i	0.0809673	−	0.0216951i	−0.218108	−	0.975925i	$-0.569989\pi$
$2$	0.161935	−	0.0433902i	0.0809673	−	0.0216951i	0.299075	+	0.954230i	$0.403322\pi$
$3$	0.339350	−	2.98075i	0.113117	−	0.993582i
$3$	0.339350	−	2.98075i	0.113117	−	0.993582i
$4$	−3.43976	+	1.98595i	−0.859940	+	0.496487i
$5$	−4.97108	+	0.537016i	−0.994216	+	0.107403i
$5$	−4.97108	+	0.537016i	−0.994216	+	0.107403i
$6$	−0.0743827	−	0.497410i	−0.0123971	−	0.0829017i
$7$	−6.97488	+	0.592480i	−0.996412	+	0.0846400i
$7$	−6.97488	+	0.592480i	−0.996412	+	0.0846400i
$8$	−0.945023	+	0.945023i	−0.118128	+	0.118128i
$9$	−8.76968	−	2.02303i	−0.974409	−	0.224781i
$10$	−0.781688	+	0.302658i	−0.0781688	+	0.0302658i
$11$	13.2452	−	7.64711i	1.20411	−	0.695192i	0.242641	−	0.970116i	$-0.421986\pi$
$11$	13.2452	−	7.64711i	1.20411	−	0.695192i	0.961466	+	0.274924i	$0.0886528\pi$
$12$	4.75232	+	10.9270i	0.396027	+	0.910582i
$13$	−11.7128	+	11.7128i	−0.900984	+	0.900984i	−0.995521	−	0.0945369i	$-0.969863\pi$
$13$	−11.7128	+	11.7128i	−0.900984	+	0.900984i	0.0945369	+	0.995521i	$0.469863\pi$
$14$	−1.10377	+	0.398585i	−0.0788405	+	0.0284703i
$15$	−0.0862278	+	14.9998i	−0.00574852	+	0.999983i
$16$	7.83176	−	13.5650i	0.489485	−	0.847813i
$17$	−14.7635	−	3.95586i	−0.868439	−	0.232697i	−0.203026	−	0.979173i	$-0.565078\pi$
$17$	−14.7635	−	3.95586i	−0.868439	−	0.232697i	−0.665412	+	0.746476i	$0.731744\pi$
$18$	−1.50789	+	0.0529196i	−0.0837719	+	0.00293998i
$19$	4.70012	−	8.14085i	0.247375	−	0.428466i	−0.715422	−	0.698693i	$-0.753765\pi$
$19$	4.70012	−	8.14085i	0.247375	−	0.428466i	0.962797	+	0.270227i	$0.0870987\pi$
$20$	16.0328	−	11.7195i	0.801642	−	0.585975i
$21$	−0.600896	+	20.9914i	−0.0286141	+	0.999591i
$22$	1.81304	−	1.81304i	0.0824110	−	0.0824110i
$23$	−8.59850	−	32.0900i	−0.373848	−	1.39522i	−0.855021	−	0.518594i	$-0.826456\pi$
$23$	−8.59850	−	32.0900i	−0.373848	−	1.39522i	0.481173	−	0.876626i	$-0.340211\pi$
$24$	2.49618	+	3.13757i	0.104007	+	0.130732i
$25$	24.4232	−	5.33910i	0.976929	−	0.213564i
$26$	−1.38849	+	2.40493i	−0.0534033	+	0.0924972i
$27$	−9.00614	+	25.4537i	−0.333561	+	0.942729i
$28$	22.8153	−	15.8897i	0.814832	−	0.567491i
$29$	−6.89705			−0.237829			−0.118915	−	0.992904i	$-0.537941\pi$
$29$	−6.89705			−0.237829			−0.118915	+	0.992904i	$0.537941\pi$
$30$	0.636879	+	2.43272i	0.0212293	+	0.0810906i
$31$	−31.4348	+	18.1489i	−1.01402	+	0.585447i	−0.912368	−	0.409372i	$-0.865748\pi$
$31$	−31.4348	+	18.1489i	−1.01402	+	0.585447i	−0.101657	+	0.994819i	$0.532414\pi$
$32$	2.06325	−	7.70017i	0.0644767	−	0.240630i
$33$	−18.2993	−	42.0756i	−0.554525	−	1.27502i
$34$	−2.56236			−0.0753635
$35$	34.3545	−	6.69089i	0.981557	−	0.191168i
$36$	34.1833	−	10.4574i	0.949535	−	0.290483i
$37$	4.52283	+	16.8794i	0.122239	+	0.456201i	0.999726	−	0.0233986i	$-0.00744868\pi$
$37$	4.52283	+	16.8794i	0.122239	+	0.456201i	−0.877488	+	0.479599i	$0.840782\pi$
$38$	0.407879	−	1.52222i	0.0107337	−	0.0400585i
$39$	30.9381	+	38.8876i	0.793285	+	0.997118i
$40$	4.19029	−	5.20527i	0.104757	−	0.130132i
$41$	17.4740			0.426195			0.213098	−	0.977031i	$-0.431645\pi$
$41$	17.4740			0.426195			0.213098	+	0.977031i	$0.431645\pi$
$42$	0.813516	+	3.42531i	0.0193694	+	0.0815549i
$43$	33.7982	+	33.7982i	0.786004	+	0.786004i	0.980837	−	0.194832i	$-0.0624163\pi$
$43$	33.7982	+	33.7982i	0.786004	+	0.786004i	−0.194832	+	0.980837i	$0.562416\pi$
$44$	−30.3735	+	52.6085i	−0.690307	+	1.19565i
$45$	44.6812	+	5.34719i	0.992915	+	0.118826i
$46$	−2.78479	−	4.82340i	−0.0605389	−	0.104856i
$47$	−2.92196	−	10.9049i	−0.0621694	−	0.232019i	0.927849	−	0.372955i	$-0.121656\pi$
$47$	−2.92196	−	10.9049i	−0.0621694	−	0.232019i	−0.990019	+	0.140936i	$0.954989\pi$
$48$	−37.7761	−	27.9478i	−0.787003	−	0.582245i
$49$	48.2979	−	8.26495i	0.985672	−	0.168673i
$50$	3.72330	−	1.92431i	0.0744660	−	0.0384863i
$51$	−16.8014	+	42.6637i	−0.329439	+	0.836543i
$52$	17.0282	−	63.5502i	0.327466	−	1.22212i
$53$	−74.1079	−	19.8572i	−1.39826	−	0.374663i	−0.520542	−	0.853836i	$-0.674270\pi$
$53$	−74.1079	−	19.8572i	−1.39826	−	0.374663i	−0.877721	+	0.479173i	$0.840937\pi$
$54$	−0.353964	+	4.51261i	−0.00655489	+	0.0835668i
$55$	−61.7362	+	45.1272i	−1.12248	+	0.820495i
$56$	6.03151	−	7.15133i	0.107706	−	0.127702i
$57$	−22.6708	−	16.7725i	−0.397734	−	0.294254i
$58$	−1.11687	+	0.299265i	−0.0192564	+	0.00515974i
$59$	4.43046	−	2.55793i	0.0750925	−	0.0433547i	−0.461984	−	0.886888i	$-0.652862\pi$
$59$	4.43046	−	2.55793i	0.0750925	−	0.0433547i	0.537076	+	0.843534i	$0.319529\pi$
$60$	−29.4921	−	51.7668i	−0.491535	−	0.862780i
$61$	−51.8761	−	29.9507i	−0.850427	−	0.490994i	0.0103677	−	0.999946i	$-0.496700\pi$
$61$	−51.8761	−	29.9507i	−0.850427	−	0.490994i	−0.860795	+	0.508952i	$0.830033\pi$
$62$	−4.30289	+	4.30289i	−0.0694015	+	0.0694015i
$63$	62.3661	+	8.91455i	0.989938	+	0.141501i
$64$			61.3176i			0.958088i
$65$	51.9353	−	64.5152i	0.799004	−	0.992541i
$66$	−4.78896	−	6.01947i	−0.0725600	−	0.0912041i
$67$	−65.4926	−	17.5487i	−0.977502	−	0.261921i	−0.265510	−	0.964108i	$-0.585540\pi$
$67$	−65.4926	−	17.5487i	−0.977502	−	0.261921i	−0.711992	+	0.702187i	$0.752207\pi$
$68$	58.6389	−	15.7122i	0.862337	−	0.231062i
$69$	−98.5701	+	14.7402i	−1.42855	+	0.213626i
$70$	5.27286	−	2.57414i	0.0753266	−	0.0367734i
$71$			50.8917i			0.716784i	0.933571	+	0.358392i	$0.116675\pi$
$71$			50.8917i			0.716784i	−0.933571	+	0.358392i	$0.883325\pi$
$72$	10.1994	−	6.37574i	0.141658	−	0.0885519i
$73$	−73.2942	−	19.6391i	−1.00403	−	0.269029i	−0.280897	−	0.959738i	$-0.590632\pi$
$73$	−73.2942	−	19.6391i	−1.00403	−	0.269029i	−0.723133	+	0.690709i	$0.757299\pi$
$74$	1.46480	+	2.53712i	0.0197947	+	0.0342854i
$75$	−7.62646	−	74.6112i	−0.101686	−	0.994817i
$76$			37.3368i			0.491274i
$77$	−87.8528	+	61.1852i	−1.14095	+	0.794613i
$78$	6.69729	+	4.95483i	0.0858627	+	0.0635235i
$79$	−26.3396	−	15.2072i	−0.333412	−	0.192496i	0.323943	−	0.946077i	$-0.394991\pi$
$79$	−26.3396	−	15.2072i	−0.333412	−	0.192496i	−0.657355	+	0.753581i	$0.728325\pi$
$80$	−31.6477	+	71.6385i	−0.395596	+	0.895481i
$81$	72.8147	+	35.4827i	0.898947	+	0.438058i
$82$	2.82965	−	0.758201i	0.0345079	−	0.00924636i
$83$	−10.9693	−	10.9693i	−0.132160	−	0.132160i	0.637932	−	0.770092i	$-0.279790\pi$
$83$	−10.9693	−	10.9693i	−0.132160	−	0.132160i	−0.770092	+	0.637932i	$0.779790\pi$
$84$	−39.6209	−	73.3988i	−0.471677	−	0.873795i
$85$	75.5146	+	11.7367i	0.888408	+	0.138078i
$86$	6.93960	+	4.00658i	0.0806931	+	0.0465882i
$87$	−2.34052	+	20.5584i	−0.0269025	+	0.236303i
$88$	−5.29031	+	19.7437i	−0.0601171	+	0.224360i
$89$	33.2788	+	19.2135i	0.373919	+	0.215882i	0.675169	−	0.737663i	$-0.264071\pi$
$89$	33.2788	+	19.2135i	0.373919	+	0.215882i	−0.301250	+	0.953545i	$0.597404\pi$
$90$	7.46744	−	1.07283i	0.0829716	−	0.0119203i
$91$	74.7558	−	88.6350i	0.821492	−	0.974011i
$92$	93.3059	+	93.3059i	1.01419	+	1.01419i
$93$	43.4298	+	99.8579i	0.466987	+	1.07374i
$94$	−0.946333	−	1.63910i	−0.0100674	−	0.0174372i
$95$	−18.9929	+	42.9929i	−0.199925	+	0.452556i
$96$	−22.2521	−	8.76308i	−0.231792	−	0.0912821i
$97$	−17.8473	−	17.8473i	−0.183992	−	0.183992i	0.609101	−	0.793093i	$-0.291531\pi$
$97$	−17.8473	−	17.8473i	−0.183992	−	0.183992i	−0.793093	+	0.609101i	$0.791531\pi$
$98$	7.46249	−	3.43404i	0.0761478	−	0.0350412i
$99$	−131.626	+	40.2673i	−1.32956	+	0.406740i
$100$	−73.4069	+	66.8685i	−0.734069	+	0.668685i
$101$	−58.5103	−	101.343i	−0.579310	−	1.00339i	−0.995559	−	0.0941439i	$-0.969989\pi$
$101$	−58.5103	−	101.343i	−0.579310	−	1.00339i	0.416248	−	0.909251i	$-0.363345\pi$
$102$	−0.869537	+	7.63774i	−0.00852487	+	0.0748798i
$103$	−3.47170	−	12.9566i	−0.0337058	−	0.125792i	0.947023	−	0.321166i	$-0.104075\pi$
$103$	−3.47170	−	12.9566i	−0.0337058	−	0.125792i	−0.980729	+	0.195374i	$0.937408\pi$
$104$		−	22.1377i		−	0.212863i
$105$	−8.28562	−	104.673i	−0.0789107	−	0.996882i
$106$	−12.8622			−0.121342
$107$	16.9453	−	4.54048i	0.158367	−	0.0424344i	−0.178764	−	0.983892i	$-0.557210\pi$
$107$	16.9453	−	4.54048i	0.158367	−	0.0424344i	0.337132	+	0.941458i	$0.390543\pi$
$108$	−19.5707	−	105.440i	−0.181210	−	0.976299i
$109$	145.191	−	83.8258i	1.33202	−	0.769044i	0.346414	−	0.938082i	$-0.387399\pi$
$109$	145.191	−	83.8258i	1.33202	−	0.769044i	0.985610	+	0.169038i	$0.0540660\pi$
$110$	−8.03914	+	9.98641i	−0.0730831	+	0.0907855i
$111$	51.8481	−	7.75336i	0.467100	−	0.0698501i
$112$	−46.5886	+	99.2545i	−0.415970	+	0.886201i
$113$	24.5772	−	24.5772i	0.217497	−	0.217497i	−0.589946	−	0.807443i	$-0.700851\pi$
$113$	24.5772	−	24.5772i	0.217497	−	0.217497i	0.807443	+	0.589946i	$0.200851\pi$
$114$	−4.39895	−	1.73235i	−0.0385873	−	0.0151961i
$115$	59.9767	+	154.905i	0.521536	+	1.34700i
$116$	23.7242	−	13.6972i	0.204519	−	0.118079i
$117$	126.413	−	79.0221i	1.08045	−	0.675403i
$118$	0.606455	−	0.606455i	0.00513945	−	0.00513945i
$119$	105.317	+	18.8446i	0.885018	+	0.158358i
$120$	−14.0936	−	14.2566i	−0.117447	−	0.118805i
$121$	56.4565	−	97.7856i	0.466583	−	0.808145i
$122$	−9.70009	−	2.59913i	−0.0795090	−	0.0213044i
$123$	5.92981	−	52.0856i	0.0482098	−	0.423460i
$124$	72.0854	−	124.856i	0.581334	−	1.00690i
$125$	−118.543	+	39.6567i	−0.948341	+	0.317254i
$126$	10.4860	−	1.26251i	0.0832225	−	0.0100199i
$127$	−8.71278	+	8.71278i	−0.0686046	+	0.0686046i	−0.740577	−	0.671972i	$-0.765448\pi$
$127$	−8.71278	+	8.71278i	−0.0686046	+	0.0686046i	0.671972	+	0.740577i	$0.265448\pi$
$128$	10.9136	+	40.7301i	0.0852625	+	0.318204i
$129$	112.213	−	89.2743i	0.869870	−	0.692049i
$130$	5.61078	−	12.7007i	0.0431599	−	0.0976979i
$131$	−86.6805	+	150.135i	−0.661683	+	1.14607i	0.318490	+	0.947926i	$0.396824\pi$
$131$	−86.6805	+	150.135i	−0.661683	+	1.14607i	−0.980173	+	0.198142i	$0.936509\pi$
$132$	146.505	+	108.388i	1.10989	+	0.821124i
$133$	−27.9595	+	59.5662i	−0.210222	+	0.447866i
$134$	−11.3670			−0.0848280
$135$	31.1012	−	131.369i	0.230379	−	0.973101i
$136$	17.6902	−	10.2134i	0.130075	−	0.0750987i
$137$	36.8296	−	137.450i	0.268829	−	1.00328i	−0.691036	−	0.722820i	$-0.742845\pi$
$137$	36.8296	−	137.450i	0.268829	−	1.00328i	0.959865	−	0.280463i	$-0.0904880\pi$
$138$	−15.3223	+	6.66393i	−0.111031	+	0.0482893i
$139$	51.6190			0.371360			0.185680	−	0.982610i	$-0.440551\pi$
$139$	51.6190			0.371360			0.185680	+	0.982610i	$0.440551\pi$
$140$	−104.884	+	91.2413i	−0.749168	+	0.651724i
$141$	−33.4963	+	5.00904i	−0.237563	+	0.0355251i
$142$	2.20820	+	8.24112i	0.0155507	+	0.0580360i
$143$	−65.5691	+	244.707i	−0.458525	+	1.71124i
$144$	−96.1245	+	103.117i	−0.667531	+	0.716090i
$145$	34.2858	−	3.70383i	0.236454	−	0.0255436i
$146$	−12.7210			−0.0871302
$147$	−8.24580	−	146.769i	−0.0560939	−	0.998425i
$148$	−49.0791	−	49.0791i	−0.331616	−	0.331616i
$149$	35.1442	−	60.8716i	0.235867	−	0.408534i	−0.723657	−	0.690160i	$-0.757540\pi$
$149$	35.1442	−	60.8716i	0.235867	−	0.408534i	0.959524	+	0.281625i	$0.0908736\pi$
$150$	−4.47239	−	11.7512i	−0.0298159	−	0.0783415i
$151$	51.7923	+	89.7069i	0.342995	+	0.594086i	0.984987	−	0.172626i	$-0.0552251\pi$
$151$	51.7923	+	89.7069i	0.342995	+	0.594086i	−0.641992	+	0.766711i	$0.721892\pi$
$152$	3.25157	+	12.1350i	0.0213919	+	0.0798356i
$153$	121.468	+	64.5586i	0.793908	+	0.421951i
$154$	−11.5716	+	13.7199i	−0.0751400	+	0.0890906i
$155$	146.518	−	107.100i	0.945280	−	0.690971i
$156$	−183.649	−	72.3226i	−1.17723	−	0.463606i
$157$	30.7462	−	114.747i	0.195836	−	0.730869i	−0.796213	−	0.605016i	$-0.793167\pi$
$157$	30.7462	−	114.747i	0.195836	−	0.730869i	0.992049	−	0.125853i	$-0.0401668\pi$
$158$	−4.92513	−	1.31968i	−0.0311717	−	0.00835243i
$159$	−84.3377	+	214.158i	−0.530425	+	1.34691i
$160$	−6.12148	+	39.3861i	−0.0382592	+	0.246163i
$161$	78.9862	+	218.730i	0.490598	+	1.35857i
$162$	13.3308	+	2.58643i	0.0822890	+	0.0159656i
$163$	−22.2496	+	5.96176i	−0.136501	+	0.0365752i	−0.326422	−	0.945224i	$-0.605843\pi$
$163$	−22.2496	+	5.96176i	−0.136501	+	0.0365752i	0.189922	+	0.981799i	$0.439177\pi$
$164$	−60.1064	+	34.7025i	−0.366503	+	0.211600i
$165$	113.563	+	199.334i	0.688258	+	1.20808i
$166$	−2.25227	−	1.30035i	−0.0135679	−	0.00783342i
$167$	55.5957	−	55.5957i	0.332908	−	0.332908i	−0.520782	−	0.853690i	$-0.674359\pi$
$167$	55.5957	−	55.5957i	0.332908	−	0.332908i	0.853690	+	0.520782i	$0.174359\pi$
$168$	−19.2695	−	20.4052i	−0.114699	−	0.121460i
$169$		−	105.379i		−	0.623546i
$170$	12.7377	−	1.37603i	0.0749276	−	0.00809428i
$171$	−57.6878	+	61.8842i	−0.337356	+	0.361896i
$172$	−183.379	−	49.1363i	−1.06616	−	0.285676i
$173$	194.196	−	52.0348i	1.12252	−	0.300779i	0.350619	−	0.936518i	$-0.385971\pi$
$173$	194.196	−	52.0348i	1.12252	−	0.300779i	0.771904	+	0.635739i	$0.219305\pi$
$174$	0.513021	+	3.43066i	0.00294840	+	0.0197165i
$175$	−167.186	+	51.7098i	−0.955347	+	0.295485i
$176$		−	239.561i		−	1.36114i
$177$	−6.12105	−	14.0741i	−0.0345822	−	0.0795147i
$178$	6.22267	+	1.66736i	0.0349588	+	0.00936719i
$179$	−167.017	−	289.281i	−0.933053	−	1.61610i	−0.778069	−	0.628179i	$-0.783801\pi$
$179$	−167.017	−	289.281i	−0.933053	−	1.61610i	−0.154984	−	0.987917i	$-0.549533\pi$
$180$	−164.312	+	70.3414i	−0.912844	+	0.390786i
$181$		−	200.663i		−	1.10864i	−0.832304	−	0.554319i	$-0.812979\pi$
$181$		−	200.663i		−	1.10864i	0.832304	−	0.554319i	$-0.187021\pi$
$182$	8.25965	−	17.5967i	0.0453827	−	0.0966853i
$183$	−106.879	+	144.466i	−0.584041	+	0.789429i
$184$	38.4516	+	22.2000i	0.208976	+	0.120652i
$185$	−31.5479	−	81.4801i	−0.170529	−	0.440433i
$186$	11.3656	+	14.2860i	0.0611056	+	0.0768065i
$187$	−225.795	+	60.5017i	−1.20746	+	0.323539i
$188$	31.7074	+	31.7074i	0.168656	+	0.168656i
$189$	47.7360	−	182.872i	0.252571	−	0.967578i
$190$	−1.21014	+	7.78613i	−0.00636915	+	0.0409797i
$191$	−269.905	−	155.829i	−1.41311	−	0.815861i	−0.417432	−	0.908708i	$-0.637070\pi$
$191$	−269.905	−	155.829i	−1.41311	−	0.815861i	−0.995680	+	0.0928471i	$0.970403\pi$
$192$	182.772	+	20.8082i	0.951939	+	0.108376i
$193$	−51.4216	+	191.908i	−0.266433	+	0.994342i	0.694934	+	0.719073i	$0.255433\pi$
$193$	−51.4216	+	191.908i	−0.266433	+	0.994342i	−0.961367	+	0.275269i	$0.911233\pi$
$194$	−3.66449	−	2.11569i	−0.0188891	−	0.0109056i
$195$	−174.679	−	176.699i	−0.895790	−	0.906149i
$196$	−149.720	+	124.347i	−0.763876	+	0.634422i
$197$	−43.4334	−	43.4334i	−0.220474	−	0.220474i	0.588224	−	0.808698i	$-0.299827\pi$
$197$	−43.4334	−	43.4334i	−0.220474	−	0.220474i	−0.808698	+	0.588224i	$0.799827\pi$
$198$	−19.5677	+	12.2320i	−0.0988265	+	0.0617776i
$199$	110.179	+	190.836i	0.553666	+	0.958977i	0.998006	+	0.0631192i	$0.0201048\pi$
$199$	110.179	+	190.836i	0.553666	+	0.958977i	−0.444340	+	0.895858i	$0.646562\pi$
$200$	−18.0349	+	28.1261i	−0.0901747	+	0.140630i
$201$	−74.5331	+	189.262i	−0.370811	+	0.941600i
$202$	−13.8721	−	13.8721i	−0.0686739	−	0.0686739i
$203$	48.1061	−	4.08636i	0.236976	−	0.0201299i
$204$	−26.9351	−	180.120i	−0.132035	−	0.882939i
$205$	−86.8647	+	9.38383i	−0.423730	+	0.0457748i
$206$	−1.12438	−	1.94748i	−0.00545813	−	0.00945377i
$207$	10.4869	+	298.815i	0.0506614	+	1.44355i
$208$	67.1524	+	250.616i	0.322848	+	1.20488i
$209$		−	143.769i		−	0.687892i
$210$	−5.88350	−	16.5906i	−0.0280166	−	0.0790028i
$211$	−58.7982			−0.278665			−0.139332	−	0.990246i	$-0.544496\pi$
$211$	−58.7982			−0.278665			−0.139332	+	0.990246i	$0.544496\pi$
$212$	294.349	−	78.8705i	1.38844	−	0.372031i
$213$	151.695	+	17.2701i	0.712183	+	0.0810802i
$214$	2.54702	−	1.47052i	0.0119019	−	0.00687159i
$215$	−186.164	−	149.863i	−0.865877	−	0.697038i
$216$	−15.5433	−	32.5653i	−0.0719597	−	0.150765i
$217$	208.501	−	145.211i	0.960834	−	0.669174i
$218$	19.8741	−	19.8741i	0.0911658	−	0.0911658i
$219$	−83.4117	+	211.807i	−0.380875	+	0.967155i
$220$	122.737	−	277.832i	0.557898	−	1.26287i
$221$	219.256	−	126.587i	0.992106	−	0.572793i
$222$	8.05958	−	3.50524i	0.0363044	−	0.0157894i
$223$	129.563	−	129.563i	0.581002	−	0.581002i	−0.354177	−	0.935179i	$-0.615239\pi$
$223$	129.563	−	129.563i	0.581002	−	0.581002i	0.935179	+	0.354177i	$0.115239\pi$
$224$	−9.82875	+	54.9302i	−0.0438784	+	0.245224i
$225$	−224.985	−	2.58679i	−0.999934	−	0.0114969i
$226$	2.91348	−	5.04630i	0.0128915	−	0.0223288i
$227$	−105.537	−	28.2785i	−0.464920	−	0.124575i	0.0187523	−	0.999824i	$-0.494031\pi$
$227$	−105.537	−	28.2785i	−0.464920	−	0.124575i	−0.483672	+	0.875249i	$0.660697\pi$
$228$	111.291	+	12.6702i	0.488120	+	0.0555713i
$229$	−77.7730	+	134.707i	−0.339620	+	0.588239i	−0.984361	−	0.176162i	$-0.943632\pi$
$229$	−77.7730	+	134.707i	−0.339620	+	0.588239i	0.644741	+	0.764401i	$0.276965\pi$
$230$	16.4336	+	22.4820i	0.0714506	+	0.0977478i
$231$	152.565	+	282.630i	0.660453	+	1.22351i
$232$	6.51787	−	6.51787i	0.0280943	−	0.0280943i
$233$	93.5221	+	349.029i	0.401382	+	1.49798i	0.810632	+	0.585557i	$0.199124\pi$
$233$	93.5221	+	349.029i	0.401382	+	1.49798i	−0.409249	+	0.912423i	$0.634209\pi$
$234$	17.0418	−	18.2815i	0.0728283	−	0.0781261i
$235$	20.3814	+	52.6400i	0.0867294	+	0.224000i
$236$	−10.1598	+	17.5973i	−0.0430500	+	0.0745649i
$237$	−54.2670	+	73.3510i	−0.228975	+	0.309498i
$238$	17.8721	−	1.51815i	0.0750931	−	0.00637876i
$239$	309.068			1.29317			0.646586	−	0.762841i	$-0.276196\pi$
$239$	309.068			1.29317			0.646586	+	0.762841i	$0.276196\pi$
$240$	202.796	+	118.644i	0.844985	+	0.494351i
$241$	−132.911	+	76.7360i	−0.551497	+	0.318407i	−0.749725	−	0.661749i	$-0.769814\pi$
$241$	−132.911	+	76.7360i	−0.551497	+	0.318407i	0.198229	+	0.980156i	$0.436481\pi$
$242$	4.89932	−	18.2845i	0.0202451	−	0.0755559i
$243$	130.475	−	205.001i	0.536933	−	0.843625i
$244$	237.922			0.975089
$245$	−235.654	+	67.0225i	−0.961855	+	0.273561i
$246$	−1.29976	−	8.69175i	−0.00528359	−	0.0353323i
$247$	40.3006	+	150.404i	0.163160	+	0.608922i
$248$	12.5555	−	46.8577i	0.0506269	−	0.188942i
$249$	−36.4191	+	28.9742i	−0.146261	+	0.116362i
$250$	−17.4754	+	11.5654i	−0.0699017	+	0.0462615i
$251$	188.250			0.750001			0.375001	−	0.927025i	$-0.377643\pi$
$251$	188.250			0.750001			0.375001	+	0.927025i	$0.377643\pi$
$252$	−232.228	+	93.1918i	−0.921541	+	0.369809i
$253$	−359.285	−	359.285i	−1.42010	−	1.42010i
$254$	−1.03285	+	1.78895i	−0.00406634	+	0.00704311i
$255$	60.6099	−	221.107i	0.237686	−	0.867087i
$256$	−119.101	−	206.288i	−0.465237	−	0.805814i
$257$	−47.6632	−	177.882i	−0.185460	−	0.692146i	−0.994532	−	0.104436i	$-0.966696\pi$
$257$	−47.6632	−	177.882i	−0.185460	−	0.692146i	0.809072	−	0.587710i	$-0.199970\pi$
$258$	14.2976	−	19.3256i	0.0554169	−	0.0749053i
$259$	−41.5469	−	115.052i	−0.160413	−	0.444217i
$260$	−50.5212	+	325.058i	−0.194312	+	1.25022i
$261$	60.4850	+	13.9530i	0.231743	+	0.0534596i
$262$	−7.52217	+	28.0731i	−0.0287106	+	0.107149i
$263$	−266.665	−	71.4527i	−1.01394	−	0.271683i	−0.286663	−	0.958031i	$-0.592546\pi$
$263$	−266.665	−	71.4527i	−1.01394	−	0.271683i	−0.727273	+	0.686348i	$0.759213\pi$
$264$	57.0556	+	22.4691i	0.216120	+	0.0851101i
$265$	379.060	+	58.9143i	1.43041	+	0.222318i
$266$	−1.94302	+	10.8590i	−0.00730458	+	0.0408233i
$267$	68.5638	−	92.6756i	0.256793	−	0.347100i
$268$	260.130	−	69.7016i	0.970633	−	0.260080i
$269$	−441.194	+	254.723i	−1.64012	+	0.946926i	−0.659337	+	0.751848i	$0.729163\pi$
$269$	−441.194	+	254.723i	−1.64012	+	0.946926i	−0.980788	+	0.195079i	$0.937504\pi$
$270$	−0.663759	−	22.6226i	−0.00245837	−	0.0837874i
$271$	173.490	+	100.164i	0.640184	+	0.369611i	0.784686	−	0.619894i	$-0.212824\pi$
$271$	173.490	+	100.164i	0.640184	+	0.369611i	−0.144501	+	0.989505i	$0.546158\pi$
$272$	−169.285	+	169.285i	−0.622372	+	0.622372i
$273$	−238.830	−	252.906i	−0.874835	−	0.926396i
$274$		−	23.8559i		−	0.0870654i
$275$	282.661	−	257.484i	1.02786	−	0.936307i
$276$	309.785	−	246.458i	1.12241	−	0.892963i
$277$	289.469	+	77.5629i	1.04501	+	0.280011i	0.740190	−	0.672398i	$-0.234736\pi$
$277$	289.469	+	77.5629i	1.04501	+	0.280011i	0.304824	+	0.952409i	$0.401402\pi$
$278$	8.35890	−	2.23976i	0.0300680	−	0.00805669i
$279$	312.389	−	95.5663i	1.11967	−	0.342531i
$280$	−26.1427	+	38.7888i	−0.0933670	+	0.138532i
$281$		−	46.6699i		−	0.166085i	−0.996546	−	0.0830425i	$-0.973536\pi$
$281$		−	46.6699i		−	0.166085i	0.996546	−	0.0830425i	$-0.0264637\pi$
$282$	−5.20687	+	2.26455i	−0.0184641	+	0.00803032i
$283$	113.369	+	30.3772i	0.400598	+	0.107340i	0.453492	−	0.891260i	$-0.350178\pi$
$283$	113.369	+	30.3772i	0.400598	+	0.107340i	−0.0528940	+	0.998600i	$0.516845\pi$
$284$	−101.068	−	175.055i	−0.355874	−	0.616391i
$285$	121.705	+	71.2027i	0.427037	+	0.249834i
$286$			42.4716i			0.148502i
$287$	−121.879	+	10.3530i	−0.424666	+	0.0360732i
$288$	−33.6718	+	63.3540i	−0.116916	+	0.219979i
$289$	−47.9705	−	27.6958i	−0.165988	−	0.0958332i
$290$	5.39134	−	2.08745i	0.0185908	−	0.00719809i
$291$	−59.2546	+	47.1417i	−0.203624	+	0.161999i
$292$	291.117	−	78.0046i	0.996976	−	0.267139i
$293$	−197.170	−	197.170i	−0.672934	−	0.672934i	0.285458	−	0.958391i	$-0.407854\pi$
$293$	−197.170	−	197.170i	−0.672934	−	0.672934i	−0.958391	+	0.285458i	$0.907854\pi$
$294$	−7.70360	−	23.4091i	−0.0262027	−	0.0796228i
$295$	−20.6505	+	15.0949i	−0.0700017	+	0.0511691i
$296$	−20.2256	−	11.6773i	−0.0683298	−	0.0394502i
$297$	75.3591	+	406.009i	0.253734	+	1.36704i
$298$	3.04983	−	11.3821i	0.0102343	−	0.0381951i
$299$	476.577	+	275.152i	1.59390	+	0.920240i
$300$	174.407	+	241.499i	0.581357	+	0.804997i
$301$	−255.763	−	215.714i	−0.849711	−	0.716656i
$302$	12.2794	+	12.2794i	0.0406602	+	0.0406602i
$303$	−321.933	+	140.014i	−1.06248	+	0.462091i
$304$	−73.6205	−	127.514i	−0.242173	−	0.419455i
$305$	273.964	+	121.029i	0.898242	+	0.396816i
$306$	22.4711	+	5.18374i	0.0734349	+	0.0169403i
$307$	−266.516	−	266.516i	−0.868131	−	0.868131i	0.124134	−	0.992265i	$-0.460385\pi$
$307$	−266.516	−	266.516i	−0.868131	−	0.868131i	−0.992265	+	0.124134i	$0.960385\pi$
$308$	180.682	−	384.933i	0.586630	−	1.24978i
$309$	−39.7983	+	5.95144i	−0.128797	+	0.0192603i
$310$	19.0793	−	23.7007i	0.0615461	−	0.0764540i
$311$	111.647	+	193.379i	0.358994	+	0.621796i	0.987793	−	0.155772i	$-0.0497864\pi$
$311$	111.647	+	193.379i	0.358994	+	0.621796i	−0.628799	+	0.777568i	$0.716453\pi$
$312$	−65.9869	−	7.51244i	−0.211496	−	0.0240783i
$313$	102.063	+	380.906i	0.326081	+	1.21695i	0.913221	+	0.407465i	$0.133587\pi$
$313$	102.063	+	380.906i	0.326081	+	1.21695i	−0.587140	+	0.809486i	$0.699746\pi$
$314$		−	19.9155i		−	0.0634252i
$315$	−314.814	−	10.8233i	−0.999410	−	0.0343598i
$316$	120.802			0.382286
$317$	−115.845	+	31.0406i	−0.365442	+	0.0979200i	−0.436867	−	0.899526i	$-0.643912\pi$
$317$	−115.845	+	31.0406i	−0.365442	+	0.0979200i	0.0714248	+	0.997446i	$0.477245\pi$
$318$	−4.36480	+	38.3391i	−0.0137258	+	0.120563i
$319$	−91.3527	+	52.7425i	−0.286372	+	0.165337i
$320$	−32.9286	−	304.815i	−0.102902	−	0.952546i
$321$	−7.78362	−	52.0504i	−0.0242480	−	0.162151i
$322$	22.2813	+	31.9927i	0.0691967	+	0.0993561i
$323$	−101.594	+	101.594i	−0.314533	+	0.314533i
$324$	−320.932	+	22.5540i	−0.990531	+	0.0696112i
$325$	−223.529	+	348.600i	−0.687780	+	1.07262i
$326$	−3.34430	+	1.93083i	−0.0102586	+	0.00592279i
$327$	−200.593	−	461.222i	−0.613434	−	1.41047i
$328$	−16.5133	+	16.5133i	−0.0503455	+	0.0503455i
$329$	26.8413	+	74.3292i	0.0815844	+	0.225925i
$330$	27.0389	+	27.3515i	0.0819359	+	0.0828834i
$331$	120.136	−	208.082i	0.362950	−	0.628648i	−0.625495	−	0.780228i	$-0.715103\pi$
$331$	120.136	−	208.082i	0.362950	−	0.628648i	0.988445	+	0.151581i	$0.0484363\pi$
$332$	59.5162	+	15.9473i	0.179266	+	0.0480341i
$333$	−5.51614	−	157.177i	−0.0165650	−	0.472003i
$334$	6.59055	−	11.4152i	0.0197322	−	0.0341772i
$335$	334.993	+	52.0653i	0.999978	+	0.155419i
$336$	280.042	+	172.551i	0.833460	+	0.513544i
$337$	−161.954	+	161.954i	−0.480574	+	0.480574i	−0.905315	−	0.424741i	$-0.860365\pi$
$337$	−161.954	+	161.954i	−0.480574	+	0.480574i	0.424741	+	0.905315i	$0.360365\pi$
$338$	−4.57243	−	17.0645i	−0.0135279	−	0.0504868i
$339$	−64.9180	−	81.5985i	−0.191499	−	0.240704i
$340$	−283.061	+	109.597i	−0.832532	+	0.322344i
$341$	−277.573	+	480.770i	−0.813996	+	1.40988i
$342$	−6.65648	+	12.5243i	−0.0194634	+	0.0366207i
$343$	−331.976	+	86.2626i	−0.967859	+	0.251495i
$344$	−63.8801			−0.185698
$345$	482.084	−	126.208i	1.39735	−	0.365821i
$346$	29.1893	−	16.8525i	0.0843622	−	0.0487065i
$347$	−174.511	+	651.282i	−0.502912	+	1.87689i	−0.0226990	+	0.999742i	$0.507226\pi$
$347$	−174.511	+	651.282i	−0.502912	+	1.87689i	−0.480213	+	0.877152i	$0.659441\pi$
$348$	−32.7770	−	75.3640i	−0.0941867	−	0.216563i
$349$	−513.119			−1.47025			−0.735127	−	0.677929i	$-0.762878\pi$
$349$	−513.119			−1.47025			−0.735127	+	0.677929i	$0.762878\pi$
$350$	−24.8295	+	15.6278i	−0.0709413	+	0.0446510i
$351$	−192.647	−	403.621i	−0.548851	−	1.14992i
$352$	−31.5558	−	117.768i	−0.0896473	−	0.334568i
$353$	87.2361	−	325.569i	0.247128	−	0.922293i	−0.725174	−	0.688565i	$-0.758241\pi$
$353$	87.2361	−	325.569i	0.247128	−	0.922293i	0.972302	−	0.233728i	$-0.0750925\pi$
$354$	−1.60189	−	2.01349i	−0.00452510	−	0.00568782i
$355$	−27.3296	−	252.986i	−0.0769849	−	0.712638i
$356$	−152.628			−0.428731
$357$	91.9103	−	307.529i	0.257452	−	0.861425i
$358$	−39.5977	−	39.5977i	−0.110608	−	0.110608i
$359$	−153.677	+	266.177i	−0.428070	+	0.741439i	−0.996702	−	0.0811531i	$-0.974140\pi$
$359$	−153.677	+	266.177i	−0.428070	+	0.741439i	0.568631	+	0.822592i	$0.307473\pi$
$360$	−47.2779	+	37.1715i	−0.131328	+	0.103254i
$361$	136.318	+	236.109i	0.377611	+	0.654042i
$362$	−8.70683	−	32.4943i	−0.0240520	−	0.0897634i
$363$	−272.315	−	201.466i	−0.750180	−	0.555003i
$364$	−81.1177	+	453.344i	−0.222851	+	1.24545i
$365$	374.898	+	58.2675i	1.02712	+	0.159637i
$366$	−11.0391	+	28.0315i	−0.0301614	+	0.0765888i
$367$	−24.8655	+	92.7994i	−0.0677535	+	0.252859i	−0.991493	−	0.130163i	$-0.958450\pi$
$367$	−24.8655	+	92.7994i	−0.0677535	+	0.252859i	0.923739	+	0.383022i	$0.125117\pi$
$368$	−502.643	−	134.683i	−1.36588	−	0.365986i
$369$	−153.242	−	35.3505i	−0.415289	−	0.0958008i
$370$	−8.64413	−	11.8256i	−0.0233625	−	0.0319610i
$371$	528.659	+	94.5939i	1.42496	+	0.254970i
$372$	−347.700	−	257.238i	−0.934679	−	0.691500i
$373$	28.7248	−	7.69678i	0.0770101	−	0.0206348i	−0.220108	−	0.975475i	$-0.570641\pi$
$373$	28.7248	−	7.69678i	0.0770101	−	0.0206348i	0.297118	+	0.954841i	$0.403974\pi$
$374$	−33.9389	+	19.5946i	−0.0907457	+	0.0523921i
$375$	77.9792	+	366.803i	0.207945	+	0.978141i
$376$	13.0667	+	7.54407i	0.0347519	+	0.0200640i
$377$	80.7838	−	80.7838i	0.214281	−	0.214281i
$378$	−0.204770	−	31.6846i	−0.000541719	−	0.0838217i
$379$			227.162i			0.599373i	0.954038	+	0.299686i	$0.0968821\pi$
$379$			227.162i			0.599373i	−0.954038	+	0.299686i	$0.903118\pi$
$380$	−20.0505	−	185.604i	−0.0527644	−	0.488432i
$381$	23.0139	+	28.9273i	0.0604039	+	0.0759246i
$382$	−50.4683	−	13.5230i	−0.132116	−	0.0354004i
$383$	−52.8830	+	14.1699i	−0.138076	+	0.0369973i	−0.327195	−	0.944957i	$-0.606103\pi$
$383$	−52.8830	+	14.1699i	−0.138076	+	0.0369973i	0.189119	+	0.981954i	$0.439437\pi$
$384$	125.110	−	18.7089i	0.325806	−	0.0487211i
$385$	403.866	−	351.335i	1.04900	−	0.912557i
$386$			33.3077i			0.0862895i
$387$	−228.024	−	364.774i	−0.589211	−	0.942569i
$388$	96.8340	+	25.9466i	0.249572	+	0.0668727i
$389$	−104.326	−	180.698i	−0.268190	−	0.464519i	0.700204	−	0.713942i	$-0.253092\pi$
$389$	−104.326	−	180.698i	−0.268190	−	0.464519i	−0.968394	+	0.249424i	$0.919759\pi$
$390$	−35.9536	−	21.0343i	−0.0921887	−	0.0539341i
$391$			507.774i			1.29866i
$392$	−37.8321	+	53.4532i	−0.0965104	+	0.136360i
$393$	418.099	+	309.321i	1.06387	+	0.787076i
$394$	−8.91794	−	5.14878i	−0.0226344	−	0.0130680i
$395$	139.103	+	61.4512i	0.352158	+	0.155573i
$396$	372.795	−	399.913i	0.941401	−	1.00988i
$397$	−277.248	+	74.2885i	−0.698359	+	0.187125i	−0.590495	−	0.807041i	$-0.701068\pi$
$397$	−277.248	+	74.2885i	−0.698359	+	0.187125i	−0.107864	+	0.994166i	$0.534401\pi$
$398$	26.1223	+	26.1223i	0.0656339	+	0.0656339i
$399$	168.064	+	103.554i	0.421212	+	0.259534i
$400$	118.852	−	373.116i	0.297130	−	0.932790i
$401$	−567.257	−	327.506i	−1.41461	−	0.816723i	−0.418788	−	0.908084i	$-0.637545\pi$
$401$	−567.257	−	327.506i	−1.41461	−	0.816723i	−0.995818	+	0.0913615i	$0.970878\pi$
$402$	−3.85738	+	33.8820i	−0.00959547	+	0.0842836i
$403$	155.615	−	580.763i	0.386141	−	1.44110i
$404$	402.523	+	232.397i	0.996345	+	0.575240i
$405$	−381.022	−	137.285i	−0.940796	−	0.338974i
$406$	7.61273	−	2.74906i	0.0187506	−	0.00677108i
$407$	188.985	+	188.985i	0.464335	+	0.464335i
$408$	−24.4405	−	56.1958i	−0.0599031	−	0.137735i
$409$	−235.407	−	407.738i	−0.575568	−	0.996914i	−0.995980	−	0.0895799i	$-0.971448\pi$
$409$	−235.407	−	407.738i	−0.575568	−	0.996914i	0.420411	−	0.907334i	$-0.361886\pi$
$410$	−13.6592	+	5.28864i	−0.0333152	+	0.0128991i
$411$	−397.205	−	156.423i	−0.966435	−	0.380592i
$412$	37.6728	+	37.6728i	0.0914389	+	0.0914389i
$413$	−29.3864	+	20.4662i	−0.0711535	+	0.0495549i
$414$	14.6638	+	47.9334i	0.0354199	+	0.115781i
$415$	60.4199	+	48.6385i	0.145590	+	0.117201i
$416$	66.0240	+	114.357i	0.158712	+	0.274897i
$417$	17.5169	−	153.863i	0.0420070	−	0.368976i
$418$	−6.23819	−	23.2812i	−0.0149239	−	0.0556967i
$419$			582.158i			1.38940i	0.719300	+	0.694699i	$0.244463\pi$
$419$			582.158i			1.38940i	−0.719300	+	0.694699i	$0.755537\pi$
$420$	236.375	+	343.594i	0.562797	+	0.818081i
$421$	360.182			0.855540			0.427770	−	0.903888i	$-0.359299\pi$
$421$	360.182			0.855540			0.427770	+	0.903888i	$0.359299\pi$
$422$	−9.52147	+	2.55127i	−0.0225627	+	0.00604566i
$423$	3.56369	+	101.544i	0.00842479	+	0.240056i
$424$	88.7991	−	51.2682i	0.209432	−	0.120916i
$425$	−381.692	−	17.7912i	−0.898099	−	0.0418617i
$426$	25.3140	−	3.78546i	0.0594226	−	0.00888605i
$427$	379.575	+	178.167i	0.888933	+	0.417252i
$428$	−49.2706	+	49.2706i	−0.115118	+	0.115118i
$429$	707.159	+	278.486i	1.64839	+	0.649152i
$430$	−36.6489	−	16.1904i	−0.0852300	−	0.0376520i
$431$	350.070	−	202.113i	0.812227	−	0.468939i	−0.0355017	−	0.999370i	$-0.511303\pi$
$431$	350.070	−	202.113i	0.812227	−	0.468939i	0.847729	+	0.530430i	$0.177970\pi$
$432$	274.745	+	321.515i	0.635985	+	0.744249i
$433$	23.1671	−	23.1671i	0.0535036	−	0.0535036i	−0.679849	−	0.733352i	$-0.737955\pi$
$433$	23.1671	−	23.1671i	0.0535036	−	0.0535036i	0.733352	+	0.679849i	$0.237955\pi$
$434$	27.4628	−	32.5615i	0.0632783	−	0.0750266i
$435$	0.594718	−	103.454i	0.00136717	−	0.237825i
$436$	−332.947	+	576.682i	−0.763640	+	1.32266i
$437$	−301.654	−	80.8280i	−0.690284	−	0.184961i
$438$	−4.31688	+	37.9181i	−0.00985589	+	0.0865710i
$439$	252.925	−	438.079i	0.576139	−	0.997902i	−0.419778	−	0.907627i	$-0.637892\pi$
$439$	252.925	−	438.079i	0.576139	−	0.997902i	0.995917	−	0.0902749i	$-0.0287746\pi$
$440$	15.6958	−	100.988i	0.0356724	−	0.229519i
$441$	−440.278	−	25.2273i	−0.998362	−	0.0572048i
$442$	30.0124	−	30.0124i	0.0679013	−	0.0679013i
$443$	−32.5153	−	121.349i	−0.0733979	−	0.273925i	0.919467	−	0.393166i	$-0.128620\pi$
$443$	−32.5153	−	121.349i	−0.0733979	−	0.273925i	−0.992865	+	0.119242i	$0.961954\pi$
$444$	−162.947	+	129.637i	−0.366998	+	0.291976i
$445$	−175.750	−	77.6407i	−0.394943	−	0.174474i
$446$	15.3590	−	26.6026i	0.0344372	−	0.0596470i
$447$	−169.517	−	125.413i	−0.379232	−	0.280566i
$448$	−36.3295	−	427.683i	−0.0810926	−	0.954650i
$449$	−550.812			−1.22675			−0.613376	−	0.789791i	$-0.710189\pi$
$449$	−550.812			−1.22675			−0.613376	+	0.789791i	$0.710189\pi$
$450$	−36.5451	+	9.34327i	−0.0812113	+	0.0207628i
$451$	231.446	−	133.626i	0.513185	−	0.296287i
$452$	−35.7306	+	133.349i	−0.0790501	+	0.295019i
$453$	284.969	−	123.938i	0.629071	−	0.273593i
$454$	−18.3171			−0.0403460
$455$	−324.018	+	480.756i	−0.712128	+	1.05661i
$456$	37.2748	−	5.57407i	0.0817430	−	0.0122238i
$457$	59.4023	+	221.692i	0.129983	+	0.485104i	0.999968	−	0.00797430i	$-0.00253833\pi$
$457$	59.4023	+	221.692i	0.129983	+	0.485104i	−0.869985	+	0.493078i	$0.835872\pi$
$458$	−6.74918	+	25.1883i	−0.0147362	+	0.0549962i
$459$	233.653	−	340.157i	0.509047	−	0.741083i
$460$	−513.938	−	413.724i	−1.11726	−	0.899400i
$461$	532.899			1.15596			0.577982	−	0.816050i	$-0.303840\pi$
$461$	532.899			1.15596			0.577982	+	0.816050i	$0.303840\pi$
$462$	36.9689	+	39.1478i	0.0800192	+	0.0847354i
$463$	405.296	+	405.296i	0.875369	+	0.875369i	0.993051	−	0.117682i	$-0.0375463\pi$
$463$	405.296	+	405.296i	0.875369	+	0.875369i	−0.117682	+	0.993051i	$0.537546\pi$
$464$	−54.0161	+	93.5586i	−0.116414	+	0.201635i
$465$	−269.518	−	473.079i	−0.579609	−	1.01737i
$466$	30.2889	+	52.4619i	0.0649977	+	0.112579i
$467$	67.0547	+	250.251i	0.143586	+	0.535870i	0.999814	+	0.0192726i	$0.00613504\pi$
$467$	67.0547	+	250.251i	0.143586	+	0.535870i	−0.856228	+	0.516598i	$0.827198\pi$
$468$	−277.896	+	522.867i	−0.593796	+	1.11724i
$469$	467.200	+	83.5970i	0.996163	+	0.178245i
$470$	5.58452	+	7.63988i	0.0118819	+	0.0162551i
$471$	−331.596	−	130.586i	−0.704026	−	0.277253i
$472$	−1.76958	+	6.60418i	−0.00374912	+	0.0139919i
$473$	706.121	+	189.205i	1.49286	+	0.400010i
$474$	−5.60499	+	14.2327i	−0.0118249	+	0.0300268i
$475$	71.3274	−	223.920i	0.150163	−	0.471411i
$476$	−399.690	+	144.333i	−0.839685	+	0.303221i
$477$	609.731	+	324.064i	1.27826	+	0.679379i
$478$	50.0488	−	13.4105i	0.104705	−	0.0280555i
$479$	525.786	−	303.563i	1.09767	−	0.633742i	0.162065	−	0.986780i	$-0.448185\pi$
$479$	525.786	−	303.563i	1.09767	−	0.633742i	0.935609	+	0.353038i	$0.114851\pi$
$480$	115.323	+	31.6123i	0.240256	+	0.0658589i
$481$	−250.680	−	144.730i	−0.521165	−	0.300895i
$482$	−18.1932	+	18.1932i	−0.0377453	+	0.0377453i
$483$	678.782	−	161.212i	1.40535	−	0.333772i
$484$			448.479i			0.926609i
$485$	98.3044	+	79.1359i	0.202689	+	0.163167i
$486$	12.2333	−	38.8581i	0.0251714	−	0.0799548i
$487$	527.352	+	141.304i	1.08286	+	0.290151i	0.755767	−	0.654841i	$-0.227264\pi$
$487$	527.352	+	141.304i	1.08286	+	0.290151i	0.327093	+	0.944992i	$0.393931\pi$
$488$	77.3281	−	20.7200i	0.158459	−	0.0424590i
$489$	10.2201	+	68.3435i	0.0209000	+	0.139762i
$490$	−35.2525	+	21.0784i	−0.0719438	+	0.0430170i
$491$		−	134.524i		−	0.273980i	−0.990572	−	0.136990i	$-0.956257\pi$
$491$		−	134.524i		−	0.273980i	0.990572	−	0.136990i	$-0.0437428\pi$
$492$	83.0421	+	190.938i	0.168785	+	0.388086i
$493$	101.824	+	27.2837i	0.206540	+	0.0553423i
$494$	13.0521	+	22.6069i	0.0264213	+	0.0457630i
$495$	632.701	−	270.857i	1.27818	−	0.547186i
$496$			568.551i			1.14627i
$497$	−30.1523	−	354.963i	−0.0606686	−	0.714212i
$498$	−4.64031	+	6.27216i	−0.00931790	+	0.0125947i
$499$	−449.573	−	259.561i	−0.900948	−	0.520162i	−0.0234401	−	0.999725i	$-0.507462\pi$
$499$	−449.573	−	259.561i	−0.900948	−	0.520162i	−0.877508	+	0.479563i	$0.840795\pi$
$500$	329.002	−	371.829i	0.658004	−	0.743658i
$501$	−146.850	−	184.583i	−0.293114	−	0.368429i
$502$	30.4842	−	8.16822i	0.0607255	−	0.0162714i
$503$	−197.863	−	197.863i	−0.393366	−	0.393366i	0.482519	−	0.875885i	$-0.339722\pi$
$503$	−197.863	−	197.863i	−0.393366	−	0.393366i	−0.875885	+	0.482519i	$0.839722\pi$
$504$	−67.3618	+	50.5129i	−0.133654	+	0.100224i
$505$	345.282	+	472.362i	0.683727	+	0.935371i
$506$	−73.7701	−	42.5912i	−0.145791	−	0.0841723i
$507$	−314.109	−	35.7605i	−0.619544	−	0.0705335i
$508$	12.6668	−	47.2730i	0.0249346	−	0.0930571i
$509$	−540.522	−	312.071i	−1.06193	−	0.613106i	−0.135965	−	0.990714i	$-0.543413\pi$
$509$	−540.522	−	312.071i	−1.06193	−	0.613106i	−0.925966	+	0.377608i	$0.876747\pi$
$510$	0.220947	−	38.4347i	0.000433229	−	0.0753623i
$511$	522.854	+	93.5553i	1.02320	+	0.183083i
$512$	−147.503	−	147.503i	−0.288093	−	0.288093i
$513$	164.885	+	192.953i	0.321413	+	0.376127i
$514$	−15.4366	−	26.7370i	−0.0300324	−	0.0520176i
$515$	24.2160	+	62.5437i	0.0470213	+	0.121444i
$516$	−208.692	+	529.932i	−0.404443	+	1.02700i
$517$	−122.093	−	122.093i	−0.236156	−	0.236156i
$518$	−11.7200	−	16.8282i	−0.0226255	−	0.0324869i
$519$	−89.2018	−	596.508i	−0.171873	−	1.14934i
$520$	11.8883	+	110.048i	0.0228621	+	0.211631i
$521$	−319.011	−	552.544i	−0.612306	−	1.06054i	−0.990851	−	0.134962i	$-0.956909\pi$
$521$	−319.011	−	552.544i	−0.612306	−	1.06054i	0.378545	−	0.925583i	$-0.376424\pi$
$522$	10.4000	−	0.364990i	0.0199234	−	0.000699214i
$523$	−187.288	−	698.967i	−0.358103	−	1.33646i	−0.876535	−	0.481339i	$-0.840151\pi$
$523$	−187.288	−	698.967i	−0.358103	−	1.33646i	0.518432	−	0.855119i	$-0.326516\pi$
$524$		−	688.571i		−	1.31407i
$525$	97.3993	+	515.886i	0.185523	+	0.982640i
$526$	−46.2827			−0.0879898
$527$	535.880	−	143.589i	1.01685	−	0.272464i
$528$	−714.071	−	81.2952i	−1.35241	−	0.153968i
$529$	−497.709	+	287.353i	−0.940849	+	0.543200i
$530$	63.9392	−	6.90723i	0.120640	−	0.0130325i
$531$	−44.0285	+	13.4692i	−0.0829161	+	0.0253658i
$532$	−22.1213	−	260.420i	−0.0415814	−	0.489511i
$533$	−204.670	+	204.670i	−0.383995	+	0.383995i
$534$	7.08164	−	17.9824i	0.0132615	−	0.0336749i
$535$	−81.7981	+	31.6710i	−0.152894	+	0.0591981i
$536$	78.4759	−	45.3081i	0.146410	−	0.0845300i
$537$	−918.950	+	399.666i	−1.71127	+	0.744257i
$538$	−60.3920	+	60.3920i	−0.112253	+	0.112253i
$539$	576.512	−	478.810i	1.06960	−	0.888331i
$540$	153.911	+	513.642i	0.285019	+	0.951189i
$541$	263.825	−	456.959i	0.487662	−	0.844656i	−0.512237	−	0.858844i	$-0.671183\pi$
$541$	263.825	−	456.959i	0.487662	−	0.844656i	0.999899	+	0.0141884i	$0.00451647\pi$
$542$	32.4402	+	8.69232i	0.0598527	+	0.0160375i
$543$	−598.126	−	68.0952i	−1.10152	−	0.125405i
$544$	−60.9215	+	105.519i	−0.111988	+	0.193969i
$545$	−676.738	+	494.674i	−1.24172	+	0.907659i
$546$	−49.6485	−	30.5914i	−0.0909313	−	0.0560281i
$547$	−197.383	+	197.383i	−0.360847	+	0.360847i	−0.864125	−	0.503278i	$-0.832127\pi$
$547$	−197.383	+	197.383i	−0.360847	+	0.360847i	0.503278	+	0.864125i	$0.332127\pi$
$548$	146.283	+	545.936i	0.266940	+	0.996234i
$549$	394.345	+	367.605i	0.718298	+	0.669590i
$550$	34.6003	−	53.9604i	0.0629097	−	0.0981097i
$551$	−32.4170	+	56.1479i	−0.0588330	+	0.101902i
$552$	79.2212	−	107.081i	0.143517	−	0.193987i
$553$	192.725	+	90.4625i	0.348509	+	0.163585i
$554$	50.2405			0.0906867
$555$	−253.577	+	66.3858i	−0.456896	+	0.119614i
$556$	−177.557	+	102.513i	−0.319347	+	0.184375i
$557$	131.527	−	490.865i	0.236134	−	0.881265i	−0.741500	−	0.670953i	$-0.765885\pi$
$557$	131.527	−	490.865i	0.236134	−	0.881265i	0.977634	−	0.210312i	$-0.0674480\pi$
$558$	46.4399	−	29.0301i	0.0832256	−	0.0520253i
$559$	−791.743			−1.41636
$560$	178.294	−	518.421i	0.318383	−	0.925751i
$561$	103.716	+	693.570i	0.184878	+	1.23631i
$562$	−2.02502	−	7.55747i	−0.00360323	−	0.0134474i
$563$	−150.079	+	560.102i	−0.266570	+	0.994853i	0.694712	+	0.719288i	$0.255532\pi$
$563$	−150.079	+	560.102i	−0.266570	+	0.994853i	−0.961282	+	0.275565i	$0.911135\pi$
$564$	105.272	−	83.7518i	0.186652	−	0.148496i
$565$	−108.977	+	135.373i	−0.192879	+	0.239599i
$566$	19.6765			0.0347641
$567$	−528.897	−	204.346i	−0.932798	−	0.360399i
$568$	−48.0938	−	48.0938i	−0.0846721	−	0.0846721i
$569$	−150.720	+	261.055i	−0.264886	+	0.458795i	−0.967534	−	0.252742i	$-0.918668\pi$
$569$	−150.720	+	261.055i	−0.264886	+	0.458795i	0.702648	+	0.711538i	$0.252001\pi$
$570$	22.7978	+	6.24934i	0.0399962	+	0.0109638i
$571$	−367.971	−	637.344i	−0.644432	−	1.11619i	−0.984432	−	0.175764i	$-0.943760\pi$
$571$	−367.971	−	637.344i	−0.644432	−	1.11619i	0.340000	−	0.940425i	$-0.389573\pi$
$572$	−260.433	−	971.951i	−0.455303	−	1.69922i
$573$	−556.080	+	751.636i	−0.970471	+	1.31176i
$574$	−19.2872	+	6.96487i	−0.0336014	+	0.0121339i
$575$	−381.335	−	737.834i	−0.663191	−	1.28319i
$576$	124.048	−	537.736i	0.215360	−	0.933570i
$577$	−6.98842	+	26.0811i	−0.0121116	+	0.0452013i	−0.971717	−	0.236148i	$-0.924115\pi$
$577$	−6.98842	+	26.0811i	−0.0121116	+	0.0452013i	0.959606	+	0.281349i	$0.0907818\pi$
$578$	−8.96981	−	2.40345i	−0.0155187	−	0.00415822i
$579$	554.579	+	218.399i	0.957822	+	0.377200i
$580$	−110.579	+	80.8300i	−0.190654	+	0.139362i
$581$	83.0086	+	70.0105i	0.142872	+	0.120500i
$582$	−7.54988	+	10.2049i	−0.0129723	+	0.0175343i
$583$	−1133.42	+	303.700i	−1.94412	+	0.520926i
$584$	87.8241	−	50.7053i	0.150384	−	0.0868241i
$585$	−585.972	+	460.711i	−1.00166	+	0.787540i
$586$	−40.4838	−	23.3733i	−0.0690850	−	0.0398862i
$587$	312.326	−	312.326i	0.532072	−	0.532072i	−0.389117	−	0.921188i	$-0.627220\pi$
$587$	312.326	−	312.326i	0.532072	−	0.532072i	0.921188	+	0.389117i	$0.127220\pi$
$588$	319.838	+	488.473i	0.543943	+	0.830737i
$589$			341.208i			0.579300i
$590$	−2.68906	+	3.34041i	−0.00455773	+	0.00566171i
$591$	−144.203	+	114.725i	−0.243998	+	0.194120i
$592$	264.391	+	70.8434i	0.446607	+	0.119668i
$593$	829.633	−	222.299i	1.39904	−	0.374873i	0.521042	−	0.853531i	$-0.325543\pi$
$593$	829.633	−	222.299i	1.39904	−	0.374873i	0.878001	+	0.478658i	$0.158877\pi$
$594$	29.8201	+	62.4771i	0.0502021	+	0.105180i
$595$	−533.659	−	37.1209i	−0.896907	−	0.0623880i
$596$			279.178i			0.468420i
$597$	606.224	−	263.657i	1.01545	−	0.441636i
$598$	89.1131	+	23.8778i	0.149019	+	0.0399294i
$599$	202.842	+	351.333i	0.338634	+	0.586532i	0.984176	−	0.177193i	$-0.0567017\pi$
$599$	202.842	+	351.333i	0.338634	+	0.586532i	−0.645542	+	0.763725i	$0.723368\pi$
$600$	77.7165	+	63.3021i	0.129527	+	0.105504i
$601$			207.421i			0.345127i	0.984998	+	0.172563i	$0.0552050\pi$
$601$			207.421i			0.345127i	−0.984998	+	0.172563i	$0.944795\pi$
$602$	−50.7767	−	23.8339i	−0.0843467	−	0.0395911i
$603$	538.848	+	286.390i	0.893612	+	0.474942i
$604$	−356.306	−	205.714i	−0.589911	−	0.340585i
$605$	−228.137	+	516.418i	−0.377087	+	0.853583i
$606$	−46.0568	+	36.6418i	−0.0760013	+	0.0604650i
$607$	1145.43	−	306.916i	1.88703	−	0.505628i	0.888086	−	0.459678i	$-0.152035\pi$
$607$	1145.43	−	306.916i	1.88703	−	0.505628i	0.998944	−	0.0459504i	$-0.0146316\pi$
$608$	−52.9884	−	52.9884i	−0.0871519	−	0.0871519i
$609$	4.14441	−	144.779i	0.00680527	−	0.237732i
$610$	49.6157	+	7.71138i	0.0813372	+	0.0126416i
$611$	161.951	+	93.5026i	0.265059	+	0.153032i
$612$	−546.031	+	19.1630i	−0.892207	+	0.0313121i
$613$	−100.133	+	373.703i	−0.163350	+	0.609630i	0.834895	+	0.550409i	$0.185528\pi$
$613$	−100.133	+	373.703i	−0.163350	+	0.609630i	−0.998245	+	0.0592208i	$0.981138\pi$
$614$	−54.7224	−	31.5940i	−0.0891244	−	0.0514560i
$615$	−1.50675	+	262.106i	−0.00244999	+	0.426188i
$616$	25.2015	−	140.844i	0.0409115	−	0.228643i
$617$	−81.5983	−	81.5983i	−0.132250	−	0.132250i	0.637883	−	0.770133i	$-0.279810\pi$
$617$	−81.5983	−	81.5983i	−0.132250	−	0.132250i	−0.770133	+	0.637883i	$0.779810\pi$
$618$	−6.18649	+	2.69060i	−0.0100105	+	0.00435372i
$619$	−91.0832	−	157.761i	−0.147146	−	0.254864i	0.783026	−	0.621989i	$-0.213675\pi$
$619$	−91.0832	−	157.761i	−0.147146	−	0.254864i	−0.930171	+	0.367125i	$0.880342\pi$
$620$	−291.293	+	659.378i	−0.469827	+	1.06351i
$621$	894.249	+	70.1440i	1.44001	+	0.112953i
$622$	26.4703	+	26.4703i	0.0425567	+	0.0425567i
$623$	−243.500	−	114.295i	−0.390850	−	0.183459i
$624$	769.811	−	115.117i	1.23367	−	0.184483i
$625$	567.988	−	260.796i	0.908781	−	0.417274i
$626$	33.0552	+	57.2532i	0.0528038	+	0.0914588i
$627$	−428.540	−	48.7882i	−0.683477	−	0.0778121i
$628$	122.121	+	455.761i	0.194460	+	0.725734i
$629$		−	267.090i		−	0.424627i
$630$	−51.4489	+	11.9072i	−0.0816649	+	0.0189003i
$631$	508.007			0.805082			0.402541	−	0.915402i	$-0.368127\pi$
$631$	508.007			0.805082			0.402541	+	0.915402i	$0.368127\pi$
$632$	39.2626	−	10.5204i	0.0621244	−	0.0166462i
$633$	−19.9532	+	175.263i	−0.0315216	+	0.276876i
$634$	−17.4125	+	10.0531i	−0.0274645	+	0.0158566i
$635$	38.6330	−	47.9908i	0.0608394	−	0.0755761i
$636$	−135.206	−	904.144i	−0.212587	−	1.42161i
$637$	−468.898	+	662.510i	−0.736104	+	1.04005i
$638$	−12.5046	+	12.5046i	−0.0195998	+	0.0195998i
$639$	102.955	−	446.304i	0.161120	−	0.698441i
$640$	−76.1251	−	196.612i	−0.118945	−	0.307206i
$641$	−329.378	+	190.166i	−0.513850	+	0.296671i	−0.734415	−	0.678701i	$-0.762543\pi$
$641$	−329.378	+	190.166i	−0.513850	+	0.296671i	0.220565	+	0.975372i	$0.429210\pi$
$642$	−3.51892	−	8.09103i	−0.00548118	−	0.0126028i
$643$	548.817	−	548.817i	0.853526	−	0.853526i	−0.137039	−	0.990566i	$-0.543759\pi$
$643$	548.817	−	548.817i	0.853526	−	0.853526i	0.990566	+	0.137039i	$0.0437587\pi$
$644$	−706.080	−	595.516i	−1.09640	−	0.924714i
$645$	−509.879	+	504.050i	−0.790510	+	0.781473i
$646$	−12.0434	+	20.8598i	−0.0186430	+	0.0322907i
$647$	1182.40	+	316.824i	1.82751	+	0.489681i	0.997664	−	0.0683064i	$-0.0217596\pi$
$647$	1182.40	+	316.824i	1.82751	+	0.489681i	0.829849	+	0.557987i	$0.188426\pi$
$648$	−102.343	+	35.2796i	−0.157937	+	0.0544438i
$649$	39.1215	−	67.7604i	0.0602796	−	0.104407i
$650$	−21.0712	+	66.1494i	−0.0324172	+	0.101768i
$651$	−362.081	−	670.765i	−0.556192	−	1.03036i
$652$	64.6935	−	64.6935i	0.0992232	−	0.0992232i
$653$	11.9942	+	44.7631i	0.0183679	+	0.0685499i	0.974501	−	0.224381i	$-0.0720360\pi$
$653$	11.9942	+	44.7631i	0.0183679	+	0.0685499i	−0.956134	+	0.292931i	$0.905369\pi$
$654$	−52.4955	−	65.9841i	−0.0802683	−	0.100893i
$655$	350.270	−	792.882i	0.534764	−	1.21051i
$656$	136.852	−	237.035i	0.208616	−	0.361334i
$657$	603.037	+	320.506i	0.917864	+	0.487832i
$658$	7.57169	+	10.8718i	0.0115071	+	0.0165225i
$659$	−1102.69			−1.67328			−0.836642	−	0.547750i	$-0.815484\pi$
$659$	−1102.69			−1.67328			−0.836642	+	0.547750i	$0.815484\pi$
$660$	−786.495	−	460.131i	−1.19166	−	0.697169i
$661$	−355.813	+	205.429i	−0.538295	+	0.310785i	−0.744388	−	0.667748i	$-0.767258\pi$
$661$	−355.813	+	205.429i	−0.538295	+	0.310785i	0.206093	+	0.978532i	$0.433925\pi$
$662$	10.4255	−	38.9085i	0.0157485	−	0.0587741i
$663$	−302.920	−	696.502i	−0.456893	−	1.05053i
$664$	20.7325			0.0312236
$665$	107.001	−	311.123i	0.160904	−	0.467854i
$666$	−7.71320	−	25.2131i	−0.0115814	−	0.0378574i
$667$	59.3043	+	221.327i	0.0889120	+	0.331824i
$668$	−80.8258	+	301.646i	−0.120997	+	0.451566i
$669$	−342.228	−	430.163i	−0.511552	−	0.642994i
$670$	56.5060	−	6.10424i	0.0843374	−	0.00911081i
$671$	−916.144			−1.36534
$672$	160.397	+	47.9376i	0.238687	+	0.0713357i
$673$	−747.970	−	747.970i	−1.11140	−	1.11140i	−0.992962	−	0.118435i	$-0.962212\pi$
$673$	−747.970	−	747.970i	−1.11140	−	1.11140i	−0.118435	−	0.992962i	$-0.537788\pi$
$674$	−19.1987	+	33.2531i	−0.0284847	+	0.0493369i
$675$	−84.0593	+	669.745i	−0.124532	+	0.992216i
$676$	209.278	+	362.480i	0.309582	+	0.536212i
$677$	59.5281	+	222.162i	0.0879292	+	0.328156i	0.995853	−	0.0909796i	$-0.0289998\pi$
$677$	59.5281	+	222.162i	0.0879292	+	0.328156i	−0.907924	+	0.419136i	$0.862333\pi$
$678$	−14.0530	−	10.3968i	−0.0207272	−	0.0153345i
$679$	135.057	+	113.908i	0.198905	+	0.167759i
$680$	−82.4545	+	60.2717i	−0.121257	+	0.0886348i
$681$	−120.105	+	304.982i	−0.176366	+	0.447844i
$682$	−24.0879	+	89.8972i	−0.0353195	+	0.131814i
$683$	156.398	+	41.9067i	0.228987	+	0.0613568i	0.371488	−	0.928438i	$-0.378848\pi$
$683$	156.398	+	41.9067i	0.228987	+	0.0613568i	−0.142501	+	0.989795i	$0.545514\pi$
$684$	75.5335	−	327.432i	0.110429	−	0.478701i
$685$	−109.270	+	703.052i	−0.159518	+	1.02635i
$686$	−50.0154	+	28.3734i	−0.0729087	+	0.0413606i
$687$	375.134	+	277.534i	0.546047	+	0.403980i
$688$	723.172	−	193.773i	1.05112	−	0.281647i
$689$	1100.59	−	635.428i	1.59738	−	0.922247i
$690$	72.5899	−	41.3552i	0.105203	−	0.0599351i
$691$	−316.769	−	182.886i	−0.458421	−	0.264669i	0.252959	−	0.967477i	$-0.418596\pi$
$691$	−316.769	−	182.886i	−0.458421	−	0.264669i	−0.711380	+	0.702808i	$0.751929\pi$
$692$	−564.651	+	564.651i	−0.815970	+	0.815970i
$693$	894.221	−	358.845i	1.29036	−	0.517815i
$694$			113.037i			0.162878i
$695$	−256.602	+	27.7202i	−0.369212	+	0.0398852i
$696$	−17.2163	−	21.6400i	−0.0247360	−	0.0310919i
$697$	−257.977	−	69.1247i	−0.370124	−	0.0991746i
$698$	−83.0916	+	22.2643i	−0.119042	+	0.0318973i
$699$	1072.10	−	160.322i	1.53377	−	0.229360i
$700$	472.386	−	509.892i	0.674838	−	0.728417i
$701$		−	773.724i		−	1.10374i	−0.833929	−	0.551872i	$-0.813914\pi$
$701$		−	773.724i		−	1.10374i	0.833929	−	0.551872i	$-0.186086\pi$
$702$	−48.7093	−	57.0012i	−0.0693865	−	0.0811982i
$703$	158.671	+	42.5157i	0.225705	+	0.0604775i
$704$	468.903	+	812.163i	0.666055	+	1.15364i
$705$	163.823	−	42.8884i	0.232373	−	0.0608346i
$706$		−	56.5061i		−	0.0800370i
$707$	468.146	+	672.188i	0.662159	+	0.950762i
$708$	49.0053	+	36.2554i	0.0692166	+	0.0512083i
$709$	767.065	+	442.865i	1.08190	+	0.624633i	0.931407	−	0.363978i	$-0.118582\pi$
$709$	767.065	+	442.865i	1.08190	+	0.624633i	0.150489	+	0.988612i	$0.451915\pi$
$710$	−15.4027	−	39.7814i	−0.0216940	−	0.0560301i
$711$	200.225	+	186.648i	0.281611	+	0.262514i
$712$	−49.6065	+	13.2920i	−0.0696720	+	0.0186686i
$713$	852.690	+	852.690i	1.19592	+	1.19592i
$714$	1.53971	−	53.7875i	0.00215646	−	0.0753326i
$715$	194.537	−	1251.67i	0.272080	−	1.75059i
$716$	1148.99	+	663.372i	1.60474	+	0.926497i
$717$	104.882	−	921.253i	0.146279	−	1.28487i
$718$	−13.3362	+	49.7713i	−0.0185741	+	0.0693193i
$719$	−428.934	−	247.645i	−0.596570	−	0.344430i	0.171121	−	0.985250i	$-0.445261\pi$
$719$	−428.934	−	247.645i	−0.596570	−	0.344430i	−0.767691	+	0.640820i	$0.778594\pi$
$720$	422.467	−	564.223i	0.586760	−	0.783643i
$721$	31.8912	+	88.3135i	0.0442319	+	0.122488i
$722$	32.3194	+	32.3194i	0.0447637	+	0.0447637i
$723$	183.627	+	422.213i	0.253980	+	0.583974i
$724$	398.507	+	690.234i	0.550424	+	0.953362i
$725$	−168.448	+	36.8240i	−0.232342	+	0.0507918i
$726$	−52.8389	−	20.8085i	−0.0727809	−	0.0286618i
$727$	242.067	+	242.067i	0.332967	+	0.332967i	0.853712	−	0.520745i	$-0.174346\pi$
$727$	242.067	+	242.067i	0.332967	+	0.332967i	−0.520745	+	0.853712i	$0.674346\pi$
$728$	13.1162	+	154.408i	0.0180167	+	0.212099i
$729$	−566.779	−	458.479i	−0.777475	−	0.628914i
$730$	63.2372	−	6.83139i	0.0866262	−	0.00935807i
$731$	−365.277	−	632.679i	−0.499695	−	0.865498i
$732$	80.7388	−	709.184i	0.110299	−	0.968831i
$733$	300.842	+	1122.76i	0.410425	+	1.53173i	0.793826	+	0.608145i	$0.208086\pi$
$733$	300.842	+	1122.76i	0.410425	+	1.53173i	−0.383401	+	0.923582i	$0.625247\pi$
$734$			16.1063i			0.0219432i
$735$	119.808	+	725.170i	0.163004	+	0.986625i
$736$	−264.840			−0.359836
$737$	−1001.66	+	268.393i	−1.35910	+	0.364170i
$738$	−26.3490	+	0.924718i	−0.0357032	+	0.00125301i
$739$	377.355	−	217.866i	0.510629	−	0.294812i	−0.222463	−	0.974941i	$-0.571410\pi$
$739$	377.355	−	217.866i	0.510629	−	0.294812i	0.733092	+	0.680129i	$0.238076\pi$
$740$	270.332	+	217.620i	0.365314	+	0.294081i
$741$	461.991	−	69.0862i	0.623470	−	0.0932337i
$742$	89.7126	−	7.62062i	0.120906	−	0.0102704i
$743$	259.217	−	259.217i	0.348878	−	0.348878i	−0.510813	−	0.859692i	$-0.670656\pi$
$743$	259.217	−	259.217i	0.348878	−	0.348878i	0.859692	+	0.510813i	$0.170656\pi$
$744$	−135.410	−	53.3258i	−0.182003	−	0.0716745i
$745$	−142.016	+	321.471i	−0.190625	+	0.431504i
$746$	4.31757	−	2.49275i	0.00578762	−	0.00334149i
$747$	74.0060	+	118.388i	0.0990710	+	0.158485i
$748$	656.529	−	656.529i	0.877713	−	0.877713i
$749$	−115.501	+	41.7090i	−0.154207	+	0.0556863i
$750$	28.5432	+	56.0145i	0.0380576	+	0.0746860i
$751$	−323.184	+	559.771i	−0.430338	+	0.745368i	−0.996902	−	0.0786500i	$-0.974939\pi$
$751$	−323.184	+	559.771i	−0.430338	+	0.745368i	0.566564	+	0.824018i	$0.308272\pi$
$752$	−170.809	−	45.7682i	−0.227140	−	0.0608620i
$753$	63.8828	−	561.126i	0.0848377	−	0.745187i
$754$	9.57646	−	16.5869i	0.0127009	−	0.0219986i
$755$	−305.638	−	418.127i	−0.404818	−	0.553810i
$756$	198.974	+	723.838i	0.263194	+	0.957458i
$757$	−242.009	+	242.009i	−0.319695	+	0.319695i	−0.848650	−	0.528955i	$-0.822584\pi$
$757$	−242.009	+	242.009i	−0.319695	+	0.319695i	0.528955	+	0.848650i	$0.322584\pi$
$758$	9.85663	+	36.7854i	0.0130035	+	0.0485296i
$759$	−1192.86	+	949.013i	−1.57162	+	1.25035i
$760$	−22.6805	−	58.5780i	−0.0298428	−	0.0770763i
$761$	−363.696	+	629.940i	−0.477919	+	0.827779i	−0.999680	−	0.0253124i	$-0.991942\pi$
$761$	−363.696	+	629.940i	−0.477919	+	0.827779i	0.521761	+	0.853092i	$0.325275\pi$
$762$	4.98190	+	3.68574i	0.00653793	+	0.00483693i
$763$	−963.022	+	670.698i	−1.26215	+	0.879027i
$764$	1237.88			1.62026
$765$	−638.496	−	255.695i	−0.834635	−	0.334242i
$766$	−7.94874	+	4.58921i	−0.0103769	+	0.00599113i
$767$	−21.9326	+	81.8535i	−0.0285953	+	0.106719i
$768$	−655.310	+	285.005i	−0.853269	+	0.371100i
$769$	−386.196			−0.502205			−0.251103	−	0.967960i	$-0.580793\pi$
$769$	−386.196			−0.502205			−0.251103	+	0.967960i	$0.580793\pi$
$770$	50.1553	−	74.4170i	0.0651368	−	0.0966455i
$771$	−546.394	+	81.7078i	−0.708682	+	0.105976i
$772$	−204.241	−	762.238i	−0.264561	−	0.987355i
$773$	270.458	−	1009.36i	0.349881	−	1.30577i	−0.536925	−	0.843630i	$-0.680414\pi$
$773$	270.458	−	1009.36i	0.349881	−	1.30577i	0.886806	−	0.462143i	$-0.152919\pi$
$774$	−52.7527	−	49.1755i	−0.0681559	−	0.0635342i
$775$	−670.840	+	611.087i	−0.865600	+	0.788500i
$776$	33.7321			0.0434692
$777$	−357.041	+	84.7977i	−0.459512	+	0.109135i
$778$	−24.7345	−	24.7345i	−0.0317924	−	0.0317924i
$779$	82.1300	−	142.253i	0.105430	−	0.182610i
$780$	951.769	+	260.899i	1.22022	+	0.334486i
$781$	389.174	+	674.069i	0.498302	+	0.863085i
$782$	22.0324	+	82.2262i	0.0281745	+	0.105149i
$783$	62.1158	−	175.555i	0.0793305	−	0.224209i
$784$	266.144	−	719.891i	0.339469	−	0.918228i
$785$	−91.2212	+	586.925i	−0.116205	+	0.747675i
$786$	81.1262	+	31.9483i	0.103214	+	0.0406467i
$787$	231.655	−	864.548i	0.294352	−	1.09854i	−0.647379	−	0.762169i	$-0.724135\pi$
$787$	231.655	−	864.548i	0.294352	−	1.09854i	0.941731	−	0.336368i	$-0.109199\pi$
$788$	235.657	+	63.1440i	0.299057	+	0.0801320i
$789$	−303.475	+	770.614i	−0.384633	+	0.976697i
$790$	25.1919	+	3.91538i	0.0318885	+	0.00495618i
$791$	−156.861	+	185.984i	−0.198308	+	0.235126i
$792$	86.3364	−	162.443i	0.109011	−	0.205105i
$793$	958.420	−	256.808i	1.20860	−	0.323843i
$794$	−41.6727	+	24.0598i	−0.0524845	+	0.0303020i
$795$	304.243	−	1109.89i	0.382695	−	1.39609i
$796$	−757.982	−	437.621i	−0.952239	−	0.549776i
$797$	337.006	−	337.006i	0.422843	−	0.422843i	−0.463338	−	0.886181i	$-0.653349\pi$
$797$	337.006	−	337.006i	0.422843	−	0.422843i	0.886181	+	0.463338i	$0.153349\pi$
$798$	31.7085	+	9.47665i	0.0397350	+	0.0118755i
$799$			172.553i			0.215961i
$800$	9.27936	−	199.079i	0.0115992	−	0.248849i
$801$	−252.975	−	235.821i	−0.315824	−	0.294408i
$802$	−106.069	−	28.4211i	−0.132256	−	0.0354378i
$803$	−1120.98	+	300.365i	−1.39599	+	0.374054i
$804$	−119.487	−	799.034i	−0.148616	−	0.993823i
$805$	−510.108	−	1044.91i	−0.633675	−	1.29802i
$806$		−	100.798i		−	0.125059i
$807$	609.546	+	1401.53i	0.755323	+	1.73671i
$808$	151.065	+	40.4777i	0.186962	+	0.0500962i
$809$	306.932	+	531.622i	0.379397	+	0.657134i	0.990975	−	0.134050i	$-0.0427982\pi$
$809$	306.932	+	531.622i	0.379397	+	0.657134i	−0.611578	+	0.791184i	$0.709465\pi$
$810$	−67.6575	−	5.69849i	−0.0835277	−	0.00703517i
$811$		−	585.506i		−	0.721955i	−0.932574	−	0.360978i	$-0.882443\pi$
$811$		−	585.506i		−	0.721955i	0.932574	−	0.360978i	$-0.117557\pi$
$812$	−157.358	+	109.592i	−0.193791	+	0.134966i
$813$	357.439	−	483.139i	0.439654	−	0.594266i
$814$	38.8032	+	22.4030i	0.0476698	+	0.0275222i
$815$	107.403	−	41.5848i	0.131783	−	0.0510243i
$816$	447.149	+	562.043i	0.547976	+	0.688778i
$817$	434.002	−	116.290i	0.531214	−	0.142338i
$818$	−55.8124	−	55.8124i	−0.0682303	−	0.0682303i
$819$	−834.896	+	626.067i	−1.01941	+	0.764429i
$820$	280.158	−	204.787i	0.341656	−	0.249740i
$821$	−717.063	−	413.997i	−0.873402	−	0.504259i	−0.00492484	−	0.999988i	$-0.501568\pi$
$821$	−717.063	−	413.997i	−0.873402	−	0.504259i	−0.868477	+	0.495729i	$0.834901\pi$
$822$	−71.1084	−	8.09551i	−0.0865066	−	0.00984855i
$823$	−366.018	+	1366.00i	−0.444737	+	1.65978i	0.271893	+	0.962327i	$0.412350\pi$
$823$	−366.018	+	1366.00i	−0.444737	+	1.65978i	−0.716630	+	0.697453i	$0.754316\pi$
$824$	15.5251	+	8.96340i	0.0188411	+	0.0108779i
$825$	−671.574	−	929.919i	−0.814029	−	1.12717i
$826$	−3.87064	+	4.58926i	−0.00468600	+	0.00555601i
$827$	−16.4891	−	16.4891i	−0.0199384	−	0.0199384i	0.697067	−	0.717006i	$-0.254488\pi$
$827$	−16.4891	−	16.4891i	−0.0199384	−	0.0199384i	−0.717006	+	0.697067i	$0.754488\pi$
$828$	−629.502	−	1007.02i	−0.760269	−	1.21621i
$829$	−537.538	−	931.043i	−0.648417	−	1.12309i	−0.983501	−	0.180903i	$-0.942098\pi$
$829$	−537.538	−	931.043i	−0.648417	−	1.12309i	0.335083	−	0.942188i	$-0.391235\pi$
$830$	11.8945	+	5.25462i	0.0143307	+	0.00633087i
$831$	329.427	−	836.512i	0.396422	−	1.00663i
$832$	−718.201	−	718.201i	−0.863223	−	0.863223i
$833$	−745.739	−	69.0404i	−0.895245	−	0.0828817i
$834$	−3.83956	−	25.6758i	−0.00460379	−	0.0307864i
$835$	−246.515	+	306.226i	−0.295227	+	0.366738i
$836$	285.518	+	494.532i	0.341529	+	0.591546i
$837$	−178.850	−	963.582i	−0.213679	−	1.15123i
$838$	25.2600	+	94.2715i	0.0301432	+	0.112496i
$839$			1363.08i			1.62464i	0.583209	+	0.812322i	$0.301797\pi$
$839$			1363.08i			1.62464i	−0.583209	+	0.812322i	$0.698203\pi$
$840$	106.748	+	91.0879i	0.127081	+	0.108438i
$841$	−793.431			−0.943437
$842$	58.3259	−	15.6284i	0.0692707	−	0.0185610i
$843$	−139.111	−	15.8374i	−0.165019	−	0.0187870i
$844$	202.252	−	116.770i	0.239635	−	0.138353i
$845$	56.5904	+	523.849i	0.0669709	+	0.619939i
$846$	4.98309	+	16.2888i	0.00589018	+	0.0192539i
$847$	−335.842	+	715.492i	−0.396507	+	0.844737i
$848$	−849.758	+	849.758i	−1.00207	+	1.00207i
$849$	129.019	−	327.617i	0.151965	−	0.385885i
$850$	−62.5811	+	13.6807i	−0.0736248	+	0.0160949i
$851$	502.772	−	290.276i	0.590801	−	0.341099i
$852$	−556.092	+	241.853i	−0.652690	+	0.283865i
$853$	886.732	−	886.732i	1.03955	−	1.03955i	0.0403603	−	0.999185i	$-0.487149\pi$
$853$	886.732	−	886.732i	1.03955	−	1.03955i	0.999185	−	0.0403603i	$-0.0128506\pi$
$854$	69.1969	+	12.3815i	0.0810268	+	0.0144983i
$855$	253.538	−	338.610i	0.296535	−	0.396036i
$856$	−11.7228	+	20.3045i	−0.0136949	+	0.0237203i
$857$	−152.554	−	40.8768i	−0.178010	−	0.0476975i	0.168713	−	0.985665i	$-0.446039\pi$
$857$	−152.554	−	40.8768i	−0.178010	−	0.0476975i	−0.346723	+	0.937968i	$0.612706\pi$
$858$	126.597	+	14.4127i	0.147549	+	0.0167981i
$859$	−598.502	+	1036.64i	−0.696743	+	1.20679i	0.272847	+	0.962058i	$0.412035\pi$
$859$	−598.502	+	1036.64i	−0.696743	+	1.20679i	−0.969590	+	0.244737i	$0.921298\pi$
$860$	937.979	+	145.783i	1.09067	+	0.169515i
$861$	−10.5001	+	366.804i	−0.0121952	+	0.426021i
$862$	47.9187	−	47.9187i	0.0555901	−	0.0555901i
$863$	−413.564	−	1543.44i	−0.479217	−	1.78846i	−0.604799	−	0.796378i	$-0.706746\pi$
$863$	−413.564	−	1543.44i	−0.479217	−	1.78846i	0.125582	−	0.992083i	$-0.459920\pi$
$864$	177.416	+	121.866i	0.205342	+	0.141049i
$865$	−937.422	+	362.956i	−1.08373	+	0.419602i
$866$	2.74632	−	4.75677i	0.00317127	−	0.00549281i
$867$	−98.8329	+	133.589i	−0.113994	+	0.154082i
$868$	−428.813	+	913.562i	−0.494024	+	1.05249i
$869$	−465.163			−0.535286
$870$	−4.39259	−	16.7786i	−0.00504895	−	0.0192857i
$871$	972.646	−	561.557i	1.11670	−	0.644727i
$872$	−57.9911	+	216.426i	−0.0665035	+	0.248195i
$873$	120.409	+	192.620i	0.137926	+	0.220642i
$874$	−52.3554			−0.0599032
$875$	803.325	−	346.835i	0.918085	−	0.396383i
$876$	−133.721	−	894.216i	−0.152650	−	1.02079i
$877$	−108.050	−	403.249i	−0.123204	−	0.459805i	0.876565	−	0.481284i	$-0.159829\pi$
$877$	−108.050	−	403.249i	−0.123204	−	0.459805i	−0.999769	+	0.0214786i	$0.993163\pi$
$878$	21.9489	−	81.9146i	0.0249988	−	0.0932968i
$879$	−654.622	+	520.803i	−0.744735	+	0.592494i
$880$	128.648	+	1190.88i	0.146191	+	1.35327i
$881$	276.453			0.313795			0.156898	−	0.987615i	$-0.449851\pi$
$881$	276.453			0.313795			0.156898	+	0.987615i	$0.449851\pi$
$882$	−72.3908	+	15.0186i	−0.0820757	+	0.0170279i
$883$	−982.011	−	982.011i	−1.11213	−	1.11213i	−0.992862	−	0.119269i	$-0.961945\pi$
$883$	−982.011	−	982.011i	−1.11213	−	1.11213i	−0.119269	−	0.992862i	$-0.538055\pi$
$884$	−502.791	+	870.860i	−0.568768	+	0.985135i
$885$	37.9862	+	66.6763i	0.0429223	+	0.0753405i
$886$	−10.5307	−	18.2397i	−0.0118857	−	0.0205866i
$887$	269.729	+	1006.64i	0.304092	+	1.13489i	0.933724	+	0.357993i	$0.116539\pi$
$887$	269.729	+	1006.64i	0.304092	+	1.13489i	−0.629633	+	0.776893i	$0.716795\pi$
$888$	−41.6705	+	56.3247i	−0.0469263	+	0.0634288i
$889$	55.6085	−	65.9327i	0.0625517	−	0.0741651i
$890$	−31.8288	−	4.94690i	−0.0357627	−	0.00555831i
$891$	1235.78	−	86.8468i	1.38696	−	0.0974711i
$892$	−188.361	+	702.973i	−0.211167	+	0.788087i
$893$	−102.509	−	27.4672i	−0.114792	−	0.0307583i
$894$	−32.8923	−	12.9533i	−0.0367923	−	0.0144892i
$895$	985.601	+	1348.35i	1.10123	+	1.50653i
$896$	−100.253	−	277.622i	−0.111889	−	0.309846i
$897$	981.883	−	1327.18i	1.09463	−	1.47958i
$898$	−89.1955	+	23.8999i	−0.0993268	+	0.0266145i
$899$	216.807	−	125.174i	0.241165	−	0.139237i
$900$	779.032	−	437.911i	0.865592	−	0.486567i
$901$	1015.54	+	586.320i	1.12712	+	0.650744i
$902$	31.6811	−	31.6811i	0.0351232	−	0.0351232i
$903$	−729.780	+	689.162i	−0.808173	+	0.763192i
$904$			46.4520i			0.0513849i
$905$	107.759	+	997.513i	0.119071	+	1.10222i
$906$	40.7687	−	32.4347i	0.0449985	−	0.0357999i
$907$	−1469.83	−	393.840i	−1.62054	−	0.434222i	−0.669380	−	0.742921i	$-0.733440\pi$
$907$	−1469.83	−	393.840i	−1.62054	−	0.434222i	−0.951160	+	0.308698i	$0.900107\pi$
$908$	419.181	−	112.319i	0.461653	−	0.123700i
$909$	308.097	+	1007.11i	0.338941	+	1.10794i
$910$	−31.6096	+	91.9103i	−0.0347359	+	0.101000i
$911$			1648.74i			1.80981i	0.425616	+	0.904904i	$0.360058\pi$
$911$			1648.74i			1.80981i	−0.425616	+	0.904904i	$0.639942\pi$
$912$	−405.071	+	176.172i	−0.444157	+	0.193171i
$913$	−229.174	−	61.4069i	−0.251012	−	0.0672584i
$914$	19.2386	+	33.3222i	0.0210488	+	0.0364575i
$915$	453.726	−	775.546i	0.495875	−	0.847591i
$916$		−	617.813i		−	0.674468i
$917$	515.634	−	1098.53i	0.562305	−	1.19796i
$918$	23.0770	−	65.2214i	0.0251383	−	0.0710473i
$919$	−415.979	−	240.166i	−0.452643	−	0.261334i	0.256303	−	0.966597i	$-0.417496\pi$
$919$	−415.979	−	240.166i	−0.452643	−	0.261334i	−0.708946	+	0.705263i	$0.750829\pi$
$920$	−203.068	−	89.7090i	−0.220726	−	0.0975098i
$921$	−884.860	+	703.975i	−0.960760	+	0.764359i
$922$	86.2948	−	23.1226i	0.0935952	−	0.0250788i
$923$	−596.084	−	596.084i	−0.645811	−	0.645811i
$924$	−1086.07	−	669.195i	−1.17540	−	0.724237i
$925$	200.583	+	388.102i	0.216847	+	0.419570i
$926$	83.2173	+	48.0455i	0.0898675	+	0.0518850i
$927$	4.23416	+	120.648i	0.00456759	+	0.130149i
$928$	−14.2304	+	53.1084i	−0.0153344	+	0.0572289i
$929$	−804.028	−	464.206i	−0.865477	−	0.499683i	0.000365893	−	1.00000i	$-0.499884\pi$
$929$	−804.028	−	464.206i	−0.865477	−	0.499683i	−0.865842	+	0.500317i	$0.833217\pi$
$930$	−64.1713	−	64.9133i	−0.0690014	−	0.0697993i
$931$	159.722	−	432.033i	0.171560	−	0.464052i
$932$	−1014.85	−	1014.85i	−1.08889	−	1.08889i
$933$	614.300	−	267.169i	0.658414	−	0.286355i
$934$	21.7169	+	37.6148i	0.0232515	+	0.0402728i
$935$	1089.96	−	422.015i	1.16573	−	0.451352i
$936$	−44.7853	+	194.141i	−0.0478476	+	0.207415i
$937$	723.582	+	723.582i	0.772232	+	0.772232i	0.978496	−	0.206264i	$-0.0661306\pi$
$937$	723.582	+	723.582i	0.772232	+	0.772232i	−0.206264	+	0.978496i	$0.566131\pi$
$938$	79.2832	−	6.73469i	0.0845236	−	0.00717984i
$939$	1170.02	−	174.964i	1.24603	−	0.186331i
$940$	−174.647	−	140.593i	−0.185795	−	0.149567i
$941$	778.938	+	1349.16i	0.827777	+	1.43375i	0.899779	+	0.436347i	$0.143728\pi$
$941$	778.938	+	1349.16i	0.827777	+	1.43375i	−0.0720018	+	0.997405i	$0.522939\pi$
$942$	−59.3631	−	6.75833i	−0.0630181	−	0.00717445i
$943$	−150.250	−	560.742i	−0.159332	−	0.594636i
$944$		−	80.1322i		−	0.0848858i
$945$	−139.094	+	934.707i	−0.147189	+	0.989108i
$946$	122.555			0.129551
$947$	−1349.26	+	361.534i	−1.42478	+	0.381768i	−0.887176	−	0.461432i	$-0.847336\pi$
$947$	−1349.26	+	361.534i	−1.42478	+	0.381768i	−0.537601	+	0.843199i	$0.680669\pi$
$948$	40.9943	−	360.081i	0.0432430	−	0.379833i
$949$	1088.51	−	628.451i	1.14701	−	0.662225i
$950$	1.83441	−	39.3553i	0.00193096	−	0.0414267i
$951$	53.2121	+	355.839i	0.0559539	+	0.374173i
$952$	−117.336	+	81.7185i	−0.123252	+	0.0858388i
$953$	1138.28	−	1138.28i	1.19442	−	1.19442i	0.218607	−	0.975813i	$-0.429849\pi$
$953$	1138.28	−	1138.28i	1.19442	−	1.19442i	0.975813	−	0.218607i	$-0.0701513\pi$
$954$	112.798	+	26.0207i	0.118237	+	0.0272754i
$955$	1425.40	+	629.697i	1.49256	+	0.659369i
$956$	−1063.12	+	613.793i	−1.11205	+	0.642043i
$957$	126.211	+	290.197i	0.131882	+	0.303236i
$958$	71.9712	−	71.9712i	0.0751265	−	0.0751265i
$959$	−175.446	+	980.517i	−0.182946	+	1.02244i
$960$	−919.750	−	5.28729i	−0.958072	−	0.00550759i
$961$	178.263	−	308.761i	0.185497	−	0.321291i
$962$	−46.8737	−	12.5598i	−0.0487252	−	0.0130559i
$963$	−157.790	+	5.53766i	−0.163853	+	0.00575043i
$964$	304.787	−	527.907i	0.316170	−	0.547622i
$965$	152.563	−	981.604i	0.158096	−	1.01721i
$966$	102.923	−	55.5583i	0.106546	−	0.0575137i
$967$	−573.934	+	573.934i	−0.593521	+	0.593521i	−0.938581	−	0.345060i	$-0.887859\pi$
$967$	−573.934	+	573.934i	−0.593521	+	0.593521i	0.345060	+	0.938581i	$0.387859\pi$
$968$	39.0569	+	145.762i	0.0403480	+	0.150581i
$969$	268.350	+	337.302i	0.276935	+	0.348093i
$970$	19.3526	+	8.54938i	0.0199511	+	0.00881379i
$971$	904.830	−	1567.21i	0.931853	−	1.61402i	0.151703	−	0.988426i	$-0.451524\pi$
$971$	904.830	−	1567.21i	0.931853	−	1.61402i	0.780151	−	0.625591i	$-0.215142\pi$
$972$	−41.6805	+	964.270i	−0.0428812	+	0.992047i
$973$	−360.037	+	30.5832i	−0.370027	+	0.0314319i
$974$	91.5278			0.0939710
$975$	963.234	+	784.579i	0.987932	+	0.804697i
$976$	−812.562	+	469.133i	−0.832543	+	0.480669i
$977$	−219.154	+	817.894i	−0.224313	+	0.837148i	0.758365	+	0.651830i	$0.225998\pi$
$977$	−219.154	+	817.894i	−0.224313	+	0.837148i	−0.982678	+	0.185319i	$0.940668\pi$
$978$	4.62042	+	10.6237i	0.00472436	+	0.0108627i
$979$	587.712			0.600319
$980$	677.492	−	698.539i	0.691318	−	0.712794i
$981$	−1442.86	+	441.400i	−1.47080	+	0.449949i
$982$	−5.83703	−	21.7841i	−0.00594402	−	0.0221834i
$983$	173.985	−	649.321i	0.176994	−	0.660551i	−0.819209	−	0.573494i	$-0.805587\pi$
$983$	173.985	−	649.321i	0.176994	−	0.660551i	0.996203	−	0.0870561i	$-0.0277459\pi$
$984$	43.6182	+	54.8258i	0.0443275	+	0.0557173i
$985$	239.235	+	192.586i	0.242878	+	0.195519i
$986$	17.6727			0.0179237
$987$	230.665	−	54.7833i	0.233703	−	0.0555049i
$988$	−437.318	−	437.318i	−0.442630	−	0.442630i
$989$	793.971	−	1375.20i	0.802802	−	1.39049i
$990$	90.7036	−	71.3142i	0.0916198	−	0.0720345i
$991$	−372.392	−	645.003i	−0.375774	−	0.650860i	0.614668	−	0.788786i	$-0.289290\pi$
$991$	−372.392	−	645.003i	−0.375774	−	0.650860i	−0.990443	+	0.137925i	$0.955957\pi$
$992$	74.8914	+	279.499i	0.0754954	+	0.281753i
$993$	−579.472	−	428.709i	−0.583557	−	0.431731i
$994$	−20.2846	−	56.1725i	−0.0204071	−	0.0565116i
$995$	−650.193	−	889.495i	−0.653460	−	0.893965i
$996$	67.7317	−	171.991i	0.0680037	−	0.172682i
$997$	140.936	−	525.982i	0.141360	−	0.527564i	−0.858530	−	0.512763i	$-0.828622\pi$
$997$	140.936	−	525.982i	0.141360	−	0.527564i	0.999890	−	0.0148011i	$-0.00471150\pi$
$998$	−84.0638	−	22.5248i	−0.0842323	−	0.0225700i
$999$	−470.377	−	36.8959i	−0.470848	−	0.0369328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.68.16	yes	112
3.2	odd	2	inner	105.3.w.a.68.13	yes	112
5.2	odd	4	inner	105.3.w.a.47.16	yes	112
7.3	odd	6	inner	105.3.w.a.38.13	yes	112
15.2	even	4	inner	105.3.w.a.47.13	yes	112
21.17	even	6	inner	105.3.w.a.38.16	yes	112
35.17	even	12	inner	105.3.w.a.17.13	✓	112
105.17	odd	12	inner	105.3.w.a.17.16	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.13	✓	112	35.17	even	12	inner
105.3.w.a.17.16	yes	112	105.17	odd	12	inner
105.3.w.a.38.13	yes	112	7.3	odd	6	inner
105.3.w.a.38.16	yes	112	21.17	even	6	inner
105.3.w.a.47.13	yes	112	15.2	even	4	inner
105.3.w.a.47.16	yes	112	5.2	odd	4	inner
105.3.w.a.68.13	yes	112	3.2	odd	2	inner
105.3.w.a.68.16	yes	112	1.1	even	1	trivial

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+(0.161935 - 0.0433902i) q^{2} +(0.339350 - 2.98075i) q^{3} +(-3.43976 + 1.98595i) q^{4} +(-4.97108 + 0.537016i) q^{5} +(-0.0743827 - 0.497410i) q^{6} +(-6.97488 + 0.592480i) q^{7} +(-0.945023 + 0.945023i) q^{8} +(-8.76968 - 2.02303i) q^{9} +(-0.781688 + 0.302658i) q^{10} +(13.2452 - 7.64711i) q^{11} +(4.75232 + 10.9270i) q^{12} +(-11.7128 + 11.7128i) q^{13} +(-1.10377 + 0.398585i) q^{14} +(-0.0862278 + 14.9998i) q^{15} +(7.83176 - 13.5650i) q^{16} +(-14.7635 - 3.95586i) q^{17} +(-1.50789 + 0.0529196i) q^{18} +(4.70012 - 8.14085i) q^{19} +(16.0328 - 11.7195i) q^{20} +(-0.600896 + 20.9914i) q^{21} +(1.81304 - 1.81304i) q^{22} +(-8.59850 - 32.0900i) q^{23} +(2.49618 + 3.13757i) q^{24} +(24.4232 - 5.33910i) q^{25} +(-1.38849 + 2.40493i) q^{26} +(-9.00614 + 25.4537i) q^{27} +(22.8153 - 15.8897i) q^{28} -6.89705 q^{29} +(0.636879 + 2.43272i) q^{30} +(-31.4348 + 18.1489i) q^{31} +(2.06325 - 7.70017i) q^{32} +(-18.2993 - 42.0756i) q^{33} -2.56236 q^{34} +(34.3545 - 6.69089i) q^{35} +(34.1833 - 10.4574i) q^{36} +(4.52283 + 16.8794i) q^{37} +(0.407879 - 1.52222i) q^{38} +(30.9381 + 38.8876i) q^{39} +(4.19029 - 5.20527i) q^{40} +17.4740 q^{41} +(0.813516 + 3.42531i) q^{42} +(33.7982 + 33.7982i) q^{43} +(-30.3735 + 52.6085i) q^{44} +(44.6812 + 5.34719i) q^{45} +(-2.78479 - 4.82340i) q^{46} +(-2.92196 - 10.9049i) q^{47} +(-37.7761 - 27.9478i) q^{48} +(48.2979 - 8.26495i) q^{49} +(3.72330 - 1.92431i) q^{50} +(-16.8014 + 42.6637i) q^{51} +(17.0282 - 63.5502i) q^{52} +(-74.1079 - 19.8572i) q^{53} +(-0.353964 + 4.51261i) q^{54} +(-61.7362 + 45.1272i) q^{55} +(6.03151 - 7.15133i) q^{56} +(-22.6708 - 16.7725i) q^{57} +(-1.11687 + 0.299265i) q^{58} +(4.43046 - 2.55793i) q^{59} +(-29.4921 - 51.7668i) q^{60} +(-51.8761 - 29.9507i) q^{61} +(-4.30289 + 4.30289i) q^{62} +(62.3661 + 8.91455i) q^{63} +61.3176i q^{64} +(51.9353 - 64.5152i) q^{65} +(-4.78896 - 6.01947i) q^{66} +(-65.4926 - 17.5487i) q^{67} +(58.6389 - 15.7122i) q^{68} +(-98.5701 + 14.7402i) q^{69} +(5.27286 - 2.57414i) q^{70} +50.8917i q^{71} +(10.1994 - 6.37574i) q^{72} +(-73.2942 - 19.6391i) q^{73} +(1.46480 + 2.53712i) q^{74} +(-7.62646 - 74.6112i) q^{75} +37.3368i q^{76} +(-87.8528 + 61.1852i) q^{77} +(6.69729 + 4.95483i) q^{78} +(-26.3396 - 15.2072i) q^{79} +(-31.6477 + 71.6385i) q^{80} +(72.8147 + 35.4827i) q^{81} +(2.82965 - 0.758201i) q^{82} +(-10.9693 - 10.9693i) q^{83} +(-39.6209 - 73.3988i) q^{84} +(75.5146 + 11.7367i) q^{85} +(6.93960 + 4.00658i) q^{86} +(-2.34052 + 20.5584i) q^{87} +(-5.29031 + 19.7437i) q^{88} +(33.2788 + 19.2135i) q^{89} +(7.46744 - 1.07283i) q^{90} +(74.7558 - 88.6350i) q^{91} +(93.3059 + 93.3059i) q^{92} +(43.4298 + 99.8579i) q^{93} +(-0.946333 - 1.63910i) q^{94} +(-18.9929 + 42.9929i) q^{95} +(-22.2521 - 8.76308i) q^{96} +(-17.8473 - 17.8473i) q^{97} +(7.46249 - 3.43404i) q^{98} +(-131.626 + 40.2673i) 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

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