LMFDB - Embedded newform 105.3.w.a.38.13

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			38.13
Character	$\chi$	$=$	105.38
Dual form			105.3.w.a.47.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0433902 + 0.161935i) q^{2} +(2.75108 - 1.19649i) q^{3} +(3.43976 + 1.98595i) q^{4} +(-2.02047 + 4.57359i) q^{5} +(0.0743827 + 0.497410i) q^{6} +(-0.592480 + 6.97488i) q^{7} +(-0.945023 + 0.945023i) q^{8} +(6.13684 - 6.58325i) q^{9} +(-0.652953 - 0.525633i) q^{10} +(-13.2452 - 7.64711i) q^{11} +(11.8392 + 1.34786i) 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} +(-3.95586 - 14.7635i) q^{17} +(0.799777 + 1.27942i) q^{18} +(-4.70012 - 8.14085i) q^{19} +(-16.0328 + 11.7195i) q^{20} +(6.71540 + 19.8973i) q^{21} +(1.81304 - 1.81304i) q^{22} +(32.0900 + 8.59850i) q^{23} +(-1.46912 + 3.73054i) q^{24} +(-16.8354 - 18.4816i) q^{25} +(1.38849 + 2.40493i) q^{26} +(9.00614 - 25.4537i) q^{27} +(-15.8897 + 22.8153i) q^{28} -6.89705 q^{29} +(-2.42524 - 0.664806i) q^{30} +(-31.4348 - 18.1489i) q^{31} +(-7.70017 + 2.06325i) q^{32} +(-45.5882 - 5.19010i) q^{33} +2.56236 q^{34} +(-30.7031 - 16.8023i) q^{35} +(34.1833 - 10.4574i) q^{36} +(-16.8794 - 4.52283i) q^{37} +(1.52222 - 0.407879i) q^{38} +(18.2086 - 46.2370i) q^{39} +(-2.41276 - 6.23153i) q^{40} -17.4740 q^{41} +(-3.51345 + 0.224105i) q^{42} +(33.7982 + 33.7982i) q^{43} +(-30.3735 - 52.6085i) q^{44} +(17.7098 + 41.3686i) q^{45} +(-2.78479 + 4.82340i) q^{46} +(-10.9049 - 2.92196i) q^{47} +(37.7761 + 27.9478i) q^{48} +(-48.2979 - 8.26495i) q^{49} +(3.72330 - 1.92431i) q^{50} +(-28.5471 - 35.8823i) q^{51} +(63.5502 - 17.0282i) q^{52} +(19.8572 + 74.1079i) q^{53} +(3.73105 + 2.56285i) q^{54} +(61.7362 - 45.1272i) q^{55} +(-6.03151 - 7.15133i) q^{56} +(-22.6708 - 16.7725i) q^{57} +(0.299265 - 1.11687i) q^{58} +(4.43046 + 2.55793i) q^{59} +(-30.0853 + 51.4243i) q^{60} +(-51.8761 + 29.9507i) q^{61} +(4.30289 - 4.30289i) q^{62} +(42.2814 + 46.7042i) q^{63} +61.3176i q^{64} +(29.9042 + 77.2349i) q^{65} +(2.81854 - 7.15710i) q^{66} +(17.5487 + 65.4926i) q^{67} +(15.7122 - 58.6389i) q^{68} +(98.5701 - 14.7402i) q^{69} +(4.05309 - 4.24284i) q^{70} +50.8917i q^{71} +(0.421870 + 12.0208i) q^{72} +(-19.6391 - 73.2942i) q^{73} +(1.46480 - 2.53712i) q^{74} +(-68.4285 - 30.7009i) q^{75} -37.3368i q^{76} +(61.1852 - 87.8528i) q^{77} +(6.69729 + 4.95483i) q^{78} +(26.3396 - 15.2072i) q^{79} +(-77.8646 + 8.41157i) q^{80} +(-5.67841 - 80.8007i) q^{81} +(0.758201 - 2.82965i) q^{82} +(10.9693 + 10.9693i) q^{83} +(-16.4157 + 81.7785i) q^{84} +(75.5146 + 11.7367i) q^{85} +(-6.93960 + 4.00658i) q^{86} +(-18.9743 + 8.25223i) q^{87} +(19.7437 - 5.29031i) 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} +(-108.194 - 12.3176i) q^{93} +(0.946333 - 1.63910i) q^{94} +(46.7294 - 5.04808i) q^{95} +(-18.7151 + 14.8893i) q^{96} +(17.8473 + 17.8473i) q^{97} +(3.43404 - 7.46249i) 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.0433902	+	0.161935i	−0.0216951	+	0.0809673i	−0.975925	−	0.218108i	$-0.930011\pi$
$2$	−0.0433902	+	0.161935i	−0.0216951	+	0.0809673i	0.954230	+	0.299075i	$0.0966782\pi$
$3$	2.75108	−	1.19649i	0.917025	−	0.398829i
$3$	2.75108	−	1.19649i	0.917025	−	0.398829i
$4$	3.43976	+	1.98595i	0.859940	+	0.496487i
$5$	−2.02047	+	4.57359i	−0.404094	+	0.914718i
$5$	−2.02047	+	4.57359i	−0.404094	+	0.914718i
$6$	0.0743827	+	0.497410i	0.0123971	+	0.0829017i
$7$	−0.592480	+	6.97488i	−0.0846400	+	0.996412i
$7$	−0.592480	+	6.97488i	−0.0846400	+	0.996412i
$8$	−0.945023	+	0.945023i	−0.118128	+	0.118128i
$9$	6.13684	−	6.58325i	0.681871	−	0.731472i
$10$	−0.652953	−	0.525633i	−0.0652953	−	0.0525633i
$11$	−13.2452	−	7.64711i	−1.20411	−	0.695192i	−0.242641	−	0.970116i	$-0.578014\pi$
$11$	−13.2452	−	7.64711i	−1.20411	−	0.695192i	−0.961466	+	0.274924i	$0.911347\pi$
$12$	11.8392	+	1.34786i	0.986600	+	0.112322i
$13$	11.7128	−	11.7128i	0.900984	−	0.900984i	−0.0945369	−	0.995521i	$-0.530137\pi$
$13$	11.7128	−	11.7128i	0.900984	−	0.900984i	0.995521	+	0.0945369i	$0.0301370\pi$
$14$	−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
$17$	−3.95586	−	14.7635i	−0.232697	−	0.868439i	−0.979173	−	0.203026i	$-0.934922\pi$
$17$	−3.95586	−	14.7635i	−0.232697	−	0.868439i	0.746476	−	0.665412i	$-0.231744\pi$
$18$	0.799777	+	1.27942i	0.0444321	+	0.0710786i
$19$	−4.70012	−	8.14085i	−0.247375	−	0.428466i	0.715422	−	0.698693i	$-0.246235\pi$
$19$	−4.70012	−	8.14085i	−0.247375	−	0.428466i	−0.962797	+	0.270227i	$0.912901\pi$
$20$	−16.0328	+	11.7195i	−0.801642	+	0.585975i
$21$	6.71540	+	19.8973i	0.319781	+	0.947492i
$22$	1.81304	−	1.81304i	0.0824110	−	0.0824110i
$23$	32.0900	+	8.59850i	1.39522	+	0.373848i	0.876626	−	0.481173i	$-0.159789\pi$
$23$	32.0900	+	8.59850i	1.39522	+	0.373848i	0.518594	+	0.855021i	$0.326456\pi$
$24$	−1.46912	+	3.73054i	−0.0612134	+	0.155439i
$25$	−16.8354	−	18.4816i	−0.673416	−	0.739263i
$26$	1.38849	+	2.40493i	0.0534033	+	0.0924972i
$27$	9.00614	−	25.4537i	0.333561	−	0.942729i
$28$	−15.8897	+	22.8153i	−0.567491	+	0.814832i
$29$	−6.89705			−0.237829			−0.118915	−	0.992904i	$-0.537941\pi$
$29$	−6.89705			−0.237829			−0.118915	+	0.992904i	$0.537941\pi$
$30$	−2.42524	−	0.664806i	−0.0808412	−	0.0221602i
$31$	−31.4348	−	18.1489i	−1.01402	−	0.585447i	−0.101657	−	0.994819i	$-0.532414\pi$
$31$	−31.4348	−	18.1489i	−1.01402	−	0.585447i	−0.912368	+	0.409372i	$0.865748\pi$
$32$	−7.70017	+	2.06325i	−0.240630	+	0.0644767i
$33$	−45.5882	−	5.19010i	−1.38146	−	0.157276i
$34$	2.56236			0.0753635
$35$	−30.7031	−	16.8023i	−0.877233	−	0.480065i
$36$	34.1833	−	10.4574i	0.949535	−	0.290483i
$37$	−16.8794	−	4.52283i	−0.456201	−	0.122239i	0.0233986	−	0.999726i	$-0.492551\pi$
$37$	−16.8794	−	4.52283i	−0.456201	−	0.122239i	−0.479599	+	0.877488i	$0.659218\pi$
$38$	1.52222	−	0.407879i	0.0400585	−	0.0107337i
$39$	18.2086	−	46.2370i	0.466887	−	1.18556i
$40$	−2.41276	−	6.23153i	−0.0603189	−	0.155788i
$41$	−17.4740			−0.426195			−0.213098	−	0.977031i	$-0.568355\pi$
$41$	−17.4740			−0.426195			−0.213098	+	0.977031i	$0.568355\pi$
$42$	−3.51345	+	0.224105i	−0.0836535	+	0.00533583i
$43$	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
$45$	17.7098	+	41.3686i	0.393551	+	0.919303i
$46$	−2.78479	+	4.82340i	−0.0605389	+	0.104856i
$47$	−10.9049	−	2.92196i	−0.232019	−	0.0621694i	0.140936	−	0.990019i	$-0.454989\pi$
$47$	−10.9049	−	2.92196i	−0.232019	−	0.0621694i	−0.372955	+	0.927849i	$0.621656\pi$
$48$	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
$51$	−28.5471	−	35.8823i	−0.559748	−	0.703574i
$52$	63.5502	−	17.0282i	1.22212	−	0.327466i
$53$	19.8572	+	74.1079i	0.374663	+	1.39826i	0.853836	+	0.520542i	$0.174270\pi$
$53$	19.8572	+	74.1079i	0.374663	+	1.39826i	−0.479173	+	0.877721i	$0.659063\pi$
$54$	3.73105	+	2.56285i	0.0690935	+	0.0474601i
$55$	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
$58$	0.299265	−	1.11687i	0.00515974	−	0.0192564i
$59$	4.43046	+	2.55793i	0.0750925	+	0.0433547i	0.537076	−	0.843534i	$-0.319529\pi$
$59$	4.43046	+	2.55793i	0.0750925	+	0.0433547i	−0.461984	+	0.886888i	$0.652862\pi$
$60$	−30.0853	+	51.4243i	−0.501422	+	0.857072i
$61$	−51.8761	+	29.9507i	−0.850427	+	0.490994i	−0.860795	−	0.508952i	$-0.830033\pi$
$61$	−51.8761	+	29.9507i	−0.850427	+	0.490994i	0.0103677	+	0.999946i	$0.496700\pi$
$62$	4.30289	−	4.30289i	0.0694015	−	0.0694015i
$63$	42.2814	+	46.7042i	0.671134	+	0.741336i
$64$			61.3176i			0.958088i
$65$	29.9042	+	77.2349i	0.460064	+	1.18823i
$66$	2.81854	−	7.15710i	0.0427051	−	0.108441i
$67$	17.5487	+	65.4926i	0.261921	+	0.977502i	0.964108	+	0.265510i	$0.0855402\pi$
$67$	17.5487	+	65.4926i	0.261921	+	0.977502i	−0.702187	+	0.711992i	$0.747793\pi$
$68$	15.7122	−	58.6389i	0.231062	−	0.862337i
$69$	98.5701	−	14.7402i	1.42855	−	0.213626i
$70$	4.05309	−	4.24284i	0.0579013	−	0.0606121i
$71$			50.8917i			0.716784i	0.933571	+	0.358392i	$0.116675\pi$
$71$			50.8917i			0.716784i	−0.933571	+	0.358392i	$0.883325\pi$
$72$	0.421870	+	12.0208i	0.00585930	+	0.166955i
$73$	−19.6391	−	73.2942i	−0.269029	−	1.00403i	−0.959738	−	0.280897i	$-0.909368\pi$
$73$	−19.6391	−	73.2942i	−0.269029	−	1.00403i	0.690709	−	0.723133i	$-0.257299\pi$
$74$	1.46480	−	2.53712i	0.0197947	−	0.0342854i
$75$	−68.4285	−	30.7009i	−0.912379	−	0.409345i
$76$		−	37.3368i		−	0.491274i
$77$	61.1852	−	87.8528i	0.794613	−	1.14095i
$78$	6.69729	+	4.95483i	0.0858627	+	0.0635235i
$79$	26.3396	−	15.2072i	0.333412	−	0.192496i	−0.323943	−	0.946077i	$-0.605009\pi$
$79$	26.3396	−	15.2072i	0.333412	−	0.192496i	0.657355	+	0.753581i	$0.271675\pi$
$80$	−77.8646	+	8.41157i	−0.973307	+	0.105145i
$81$	−5.67841	−	80.8007i	−0.0701038	−	0.997540i
$82$	0.758201	−	2.82965i	0.00924636	−	0.0345079i
$83$	10.9693	+	10.9693i	0.132160	+	0.132160i	0.770092	−	0.637932i	$-0.220210\pi$
$83$	10.9693	+	10.9693i	0.132160	+	0.132160i	−0.637932	+	0.770092i	$0.720210\pi$
$84$	−16.4157	+	81.7785i	−0.195425	+	0.973553i
$85$	75.5146	+	11.7367i	0.888408	+	0.138078i
$86$	−6.93960	+	4.00658i	−0.0806931	+	0.0465882i
$87$	−18.9743	+	8.25223i	−0.218096	+	0.0948532i
$88$	19.7437	−	5.29031i	0.224360	−	0.0601171i
$89$	33.2788	−	19.2135i	0.373919	−	0.215882i	−0.301250	−	0.953545i	$-0.597404\pi$
$89$	33.2788	−	19.2135i	0.373919	−	0.215882i	0.675169	+	0.737663i	$0.264071\pi$
$90$	−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
$93$	−108.194	−	12.3176i	−1.16338	−	0.132448i
$94$	0.946333	−	1.63910i	0.0100674	−	0.0174372i
$95$	46.7294	−	5.04808i	0.491888	−	0.0531377i
$96$	−18.7151	+	14.8893i	−0.194949	+	0.155097i
$97$	17.8473	+	17.8473i	0.183992	+	0.183992i	0.793093	−	0.609101i	$-0.208469\pi$
$97$	17.8473	+	17.8473i	0.183992	+	0.183992i	−0.609101	+	0.793093i	$0.708469\pi$
$98$	3.43404	−	7.46249i	0.0350412	−	0.0761478i
$99$	−131.626	+	40.2673i	−1.32956	+	0.406740i
$100$	−21.2063	−	97.0065i	−0.212063	−	0.970065i
$101$	58.5103	−	101.343i	0.579310	−	1.00339i	−0.416248	−	0.909251i	$-0.636655\pi$
$101$	58.5103	−	101.343i	0.579310	−	1.00339i	0.995559	−	0.0941439i	$-0.0300114\pi$
$102$	7.04924	−	3.06583i	0.0691102	−	0.0300571i
$103$	−12.9566	−	3.47170i	−0.125792	−	0.0337058i	0.195374	−	0.980729i	$-0.437408\pi$
$103$	−12.9566	−	3.47170i	−0.125792	−	0.0337058i	−0.321166	+	0.947023i	$0.604075\pi$
$104$			22.1377i			0.212863i
$105$	−104.570	−	9.48848i	−0.995909	−	0.0903665i
$106$	−12.8622			−0.121342
$107$	−4.54048	+	16.9453i	−0.0424344	+	0.158367i	−0.983892	−	0.178764i	$-0.942790\pi$
$107$	−4.54048	+	16.9453i	−0.0424344	+	0.158367i	0.941458	+	0.337132i	$0.109457\pi$
$108$	81.5286	−	69.6688i	0.754895	−	0.645082i
$109$	−145.191	−	83.8258i	−1.33202	−	0.769044i	−0.346414	−	0.938082i	$-0.612601\pi$
$109$	−145.191	−	83.8258i	−1.33202	−	0.769044i	−0.985610	+	0.169038i	$0.945934\pi$
$110$	4.62891	+	11.9553i	0.0420810	+	0.108685i
$111$	−51.8481	+	7.75336i	−0.467100	+	0.0698501i
$112$	−99.2545	+	46.5886i	−0.886201	+	0.415970i
$113$	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	$0.200851\pi$
$114$	3.69973	−	2.94343i	0.0324538	−	0.0258195i
$115$	−104.163	+	129.394i	−0.905765	+	1.12516i
$116$	−23.7242	−	13.6972i	−0.204519	−	0.118079i
$117$	−5.22874	−	148.988i	−0.0446901	−	1.27340i
$118$	−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
$122$	−2.59913	−	9.70009i	−0.0213044	−	0.0795090i
$123$	−48.0723	+	20.9074i	−0.390832	+	0.169979i
$124$	−72.0854	−	124.856i	−0.581334	−	1.00690i
$125$	118.543	−	39.6567i	0.948341	−	0.317254i
$126$	−9.39762	+	4.82032i	−0.0745843	+	0.0382565i
$127$	−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	$0.265448\pi$
$128$	−40.7301	−	10.9136i	−0.318204	−	0.0852625i
$129$	133.420	+	52.5423i	1.03427	+	0.407305i
$130$	−13.8045	+	1.49128i	−0.106189	+	0.0114714i
$131$	86.6805	+	150.135i	0.661683	+	1.14607i	0.980173	+	0.198142i	$0.0634909\pi$
$131$	86.6805	+	150.135i	0.661683	+	1.14607i	−0.318490	+	0.947926i	$0.603176\pi$
$132$	−146.505	−	108.388i	−1.10989	−	0.821124i
$133$	59.5662	−	27.9595i	0.447866	−	0.210222i
$134$	−11.3670			−0.0848280
$135$	98.2180	+	92.6187i	0.727541	+	0.686065i
$136$	17.6902	+	10.2134i	0.130075	+	0.0750987i
$137$	−137.450	+	36.8296i	−1.00328	+	0.268829i	−0.722820	−	0.691036i	$-0.757155\pi$
$137$	−137.450	+	36.8296i	−1.00328	+	0.268829i	−0.280463	+	0.959865i	$0.590488\pi$
$138$	−1.89004	+	16.6015i	−0.0136959	+	0.120301i
$139$	−51.6190			−0.371360			−0.185680	−	0.982610i	$-0.559449\pi$
$139$	−51.6190			−0.371360			−0.185680	+	0.982610i	$0.559449\pi$
$140$	−72.2430	−	118.771i	−0.516022	−	0.848362i
$141$	−33.4963	+	5.00904i	−0.237563	+	0.0355251i
$142$	−8.24112	−	2.20820i	−0.0580360	−	0.0155507i
$143$	−244.707	+	65.5691i	−1.71124	+	0.458525i
$144$	137.364	+	31.6878i	0.953918	+	0.220054i
$145$	13.9353	−	31.5443i	0.0961054	−	0.217547i
$146$	12.7210			0.0871302
$147$	−142.760	+	35.0503i	−0.971158	+	0.238438i
$148$	−49.0791	−	49.0791i	−0.331616	−	0.331616i
$149$	35.1442	+	60.8716i	0.235867	+	0.408534i	0.959524	−	0.281625i	$-0.0908736\pi$
$149$	35.1442	+	60.8716i	0.235867	+	0.408534i	−0.723657	+	0.690160i	$0.757540\pi$
$150$	7.94066	−	9.74881i	0.0529378	−	0.0649921i
$151$	51.7923	−	89.7069i	0.342995	−	0.594086i	−0.641992	−	0.766711i	$-0.721892\pi$
$151$	51.7923	−	89.7069i	0.342995	−	0.594086i	0.984987	+	0.172626i	$0.0552251\pi$
$152$	12.1350	+	3.25157i	0.0798356	+	0.0213919i
$153$	−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
$156$	154.457	−	122.883i	0.990112	−	0.787711i
$157$	114.747	−	30.7462i	0.730869	−	0.195836i	0.125853	−	0.992049i	$-0.459833\pi$
$157$	114.747	−	30.7462i	0.730869	−	0.195836i	0.605016	+	0.796213i	$0.293167\pi$
$158$	1.31968	+	4.92513i	0.00835243	+	0.0311717i
$159$	143.298	+	180.118i	0.901243	+	1.13282i
$160$	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
$163$	5.96176	−	22.2496i	0.0365752	−	0.136501i	−0.945224	−	0.326422i	$-0.894157\pi$
$163$	5.96176	−	22.2496i	0.0365752	−	0.136501i	0.981799	+	0.189922i	$0.0608235\pi$
$164$	−60.1064	−	34.7025i	−0.366503	−	0.211600i
$165$	115.847	−	198.015i	0.702102	−	1.20009i
$166$	−2.25227	+	1.30035i	−0.0135679	+	0.00783342i
$167$	−55.5957	+	55.5957i	−0.332908	+	0.332908i	−0.853690	−	0.520782i	$-0.825641\pi$
$167$	−55.5957	+	55.5957i	−0.332908	+	0.332908i	0.520782	+	0.853690i	$0.325641\pi$
$168$	−25.1496	−	12.4572i	−0.149700	−	0.0741501i
$169$		−	105.379i		−	0.623546i
$170$	−5.17717	+	11.7192i	−0.0304539	+	0.0689363i
$171$	−82.4372	−	19.0170i	−0.482089	−	0.111211i
$172$	49.1363	+	183.379i	0.285676	+	1.06616i
$173$	52.0348	−	194.196i	0.300779	−	1.12252i	−0.635739	−	0.771904i	$-0.719305\pi$
$173$	52.0348	−	194.196i	0.300779	−	1.12252i	0.936518	−	0.350619i	$-0.114029\pi$
$174$	−0.513021	−	3.43066i	−0.00294840	−	0.0197165i
$175$	138.882	−	106.475i	0.793609	−	0.608429i
$176$		−	239.561i		−	1.36114i
$177$	15.2490	+	1.73606i	0.0861528	+	0.00980828i
$178$	1.66736	+	6.22267i	0.00936719	+	0.0349588i
$179$	−167.017	+	289.281i	−0.933053	+	1.61610i	−0.154984	+	0.987917i	$0.549533\pi$
$179$	−167.017	+	289.281i	−0.933053	+	1.61610i	−0.778069	+	0.628179i	$0.783801\pi$
$180$	−21.2385	+	177.469i	−0.117992	+	0.985938i
$181$			200.663i			1.10864i	0.832304	+	0.554319i	$0.187021\pi$
$181$			200.663i			1.10864i	−0.832304	+	0.554319i	$0.812979\pi$
$182$	−17.5967	+	8.25965i	−0.0966853	+	0.0453827i
$183$	−106.879	+	144.466i	−0.584041	+	0.789429i
$184$	−38.4516	+	22.2000i	−0.208976	+	0.120652i
$185$	54.7899	−	68.0613i	0.296162	−	0.367899i
$186$	6.68923	−	16.9859i	0.0359636	−	0.0913222i
$187$	−60.5017	+	225.795i	−0.323539	+	1.20746i
$188$	−31.7074	−	31.7074i	−0.168656	−	0.168656i
$189$	172.200	+	77.8975i	0.911113	+	0.412156i
$190$	−1.21014	+	7.78613i	−0.00636915	+	0.0409797i
$191$	269.905	−	155.829i	1.41311	−	0.815861i	0.417432	−	0.908708i	$-0.362930\pi$
$191$	269.905	−	155.829i	1.41311	−	0.815861i	0.995680	+	0.0928471i	$0.0295968\pi$
$192$	73.3657	+	168.690i	0.382113	+	0.878591i
$193$	191.908	−	51.4216i	0.994342	−	0.266433i	0.275269	−	0.961367i	$-0.411233\pi$
$193$	191.908	−	51.4216i	0.994342	−	0.266433i	0.719073	+	0.694934i	$0.244567\pi$
$194$	−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	$0.799827\pi$
$198$	−0.809365	−	23.0621i	−0.00408770	−	0.116475i
$199$	−110.179	+	190.836i	−0.553666	+	0.958977i	0.444340	+	0.895858i	$0.353438\pi$
$199$	−110.179	+	190.836i	−0.553666	+	0.958977i	−0.998006	+	0.0631192i	$0.979895\pi$
$200$	33.3754	+	1.55568i	0.166877	+	0.00777838i
$201$	126.639	+	159.178i	0.630044	+	0.791932i
$202$	13.8721	+	13.8721i	0.0686739	+	0.0686739i
$203$	4.08636	−	48.1061i	0.0201299	−	0.236976i
$204$	−26.9351	−	180.120i	−0.132035	−	0.882939i
$205$	35.3057	−	79.9189i	0.172223	−	0.389848i
$206$	1.12438	−	1.94748i	0.00545813	−	0.00945377i
$207$	253.538	−	158.489i	1.22482	−	0.765648i
$208$	250.616	+	67.1524i	1.20488	+	0.322848i
$209$			143.769i			0.687892i
$210$	6.07385	−	16.5219i	0.0289231	−	0.0786755i
$211$	−58.7982			−0.278665			−0.139332	−	0.990246i	$-0.544496\pi$
$211$	−58.7982			−0.278665			−0.139332	+	0.990246i	$0.544496\pi$
$212$	−78.8705	+	294.349i	−0.372031	+	1.38844i
$213$	60.8912	+	140.007i	0.285874	+	0.657309i
$214$	−2.54702	−	1.47052i	−0.0119019	−	0.00687159i
$215$	−222.867	+	86.2908i	−1.03659	+	0.401352i
$216$	15.5433	+	32.5653i	0.0719597	+	0.150765i
$217$	145.211	−	208.501i	0.669174	−	0.960834i
$218$	19.8741	−	19.8741i	0.0911658	−	0.0911658i
$219$	−141.724	−	178.140i	−0.647143	−	0.813425i
$220$	301.978	−	32.6221i	1.37263	−	0.148282i
$221$	−219.256	−	126.587i	−0.992106	−	0.572793i
$222$	0.994163	−	8.73242i	0.00447821	−	0.0393352i
$223$	−129.563	+	129.563i	−0.581002	+	0.581002i	−0.935179	−	0.354177i	$-0.884761\pi$
$223$	−129.563	+	129.563i	−0.581002	+	0.581002i	0.354177	+	0.935179i	$0.384761\pi$
$224$	−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
$227$	−28.2785	−	105.537i	−0.124575	−	0.464920i	0.875249	−	0.483672i	$-0.160697\pi$
$227$	−28.2785	−	105.537i	−0.124575	−	0.464920i	−0.999824	+	0.0187523i	$0.994031\pi$
$228$	−44.6730	−	102.716i	−0.195934	−	0.450510i
$229$	77.7730	+	134.707i	0.339620	+	0.588239i	0.984361	−	0.176162i	$-0.0563681\pi$
$229$	77.7730	+	134.707i	0.339620	+	0.588239i	−0.644741	+	0.764401i	$0.723035\pi$
$230$	−16.4336	−	22.4820i	−0.0714506	−	0.0977478i
$231$	63.2104	−	314.897i	0.273638	−	1.36319i
$232$	6.51787	−	6.51787i	0.0280943	−	0.0280943i
$233$	−349.029	−	93.5221i	−1.49798	−	0.401382i	−0.585557	−	0.810632i	$-0.699124\pi$
$233$	−349.029	−	93.5221i	−1.49798	−	0.401382i	−0.912423	+	0.409249i	$0.865791\pi$
$234$	24.3532	+	5.61790i	0.104073	+	0.0240081i
$235$	35.3969	−	43.9708i	0.150625	−	0.187110i
$236$	10.1598	+	17.5973i	0.0430500	+	0.0745649i
$237$	54.2670	−	73.3510i	0.228975	−	0.309498i
$238$	−1.51815	+	17.8721i	−0.00637876	+	0.0750931i
$239$	309.068			1.29317			0.646586	−	0.762841i	$-0.276196\pi$
$239$	309.068			1.29317			0.646586	+	0.762841i	$0.276196\pi$
$240$	−204.147	+	116.305i	−0.850613	+	0.484603i
$241$	−132.911	−	76.7360i	−0.551497	−	0.318407i	0.198229	−	0.980156i	$-0.436481\pi$
$241$	−132.911	−	76.7360i	−0.551497	−	0.318407i	−0.749725	+	0.661749i	$0.769814\pi$
$242$	−18.2845	+	4.89932i	−0.0755559	+	0.0202451i
$243$	−112.299	−	215.495i	−0.462135	−	0.886810i
$244$	−237.922			−0.975089
$245$	135.385	−	204.196i	0.552592	−	0.833452i
$246$	−1.29976	−	8.69175i	−0.00528359	−	0.0353323i
$247$	−150.404	−	40.3006i	−0.608922	−	0.163160i
$248$	46.8577	−	12.5555i	0.188942	−	0.0506269i
$249$	43.3020	+	17.0528i	0.173904	+	0.0684849i
$250$	1.27821	+	20.9169i	0.00511283	+	0.0836674i
$251$	−188.250			−0.750001			−0.375001	−	0.927025i	$-0.622357\pi$
$251$	−188.250			−0.750001			−0.375001	+	0.927025i	$0.622357\pi$
$252$	52.6861	+	244.620i	0.209072	+	0.970714i
$253$	−359.285	−	359.285i	−1.42010	−	1.42010i
$254$	−1.03285	−	1.78895i	−0.00406634	−	0.00704311i
$255$	221.789	−	58.0638i	0.869762	−	0.227701i
$256$	−119.101	+	206.288i	−0.465237	+	0.805814i
$257$	−177.882	−	47.6632i	−0.692146	−	0.185460i	−0.104436	−	0.994532i	$-0.533304\pi$
$257$	−177.882	−	47.6632i	−0.692146	−	0.185460i	−0.587710	+	0.809072i	$0.699970\pi$
$258$	−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
$261$	−42.3261	+	45.4050i	−0.162169	+	0.173966i
$262$	−28.0731	+	7.52217i	−0.107149	+	0.0287106i
$263$	71.4527	+	266.665i	0.271683	+	1.01394i	0.958031	+	0.286663i	$0.0925460\pi$
$263$	71.4527	+	266.665i	0.271683	+	1.01394i	−0.686348	+	0.727273i	$0.740787\pi$
$264$	47.9866	−	38.1771i	0.181767	−	0.144610i
$265$	−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
$268$	−69.7016	+	260.130i	−0.260080	+	0.970633i
$269$	−441.194	−	254.723i	−1.64012	−	0.946926i	−0.980788	−	0.195079i	$-0.937504\pi$
$269$	−441.194	−	254.723i	−1.64012	−	0.946926i	−0.659337	−	0.751848i	$-0.729163\pi$
$270$	−19.2599	+	11.8861i	−0.0713329	+	0.0440227i
$271$	173.490	−	100.164i	0.640184	−	0.369611i	−0.144501	−	0.989505i	$-0.546158\pi$
$271$	173.490	−	100.164i	0.640184	−	0.369611i	0.784686	+	0.619894i	$0.212824\pi$
$272$	169.285	−	169.285i	0.622372	−	0.622372i
$273$	311.709	+	154.397i	1.14179	+	0.565558i
$274$		−	23.8559i		−	0.0870654i
$275$	81.6573	+	373.534i	0.296936	+	1.35831i
$276$	368.331	+	145.052i	1.33453	+	0.525552i
$277$	−77.5629	−	289.469i	−0.280011	−	1.04501i	−0.952409	−	0.304824i	$-0.901402\pi$
$277$	−77.5629	−	289.469i	−0.280011	−	1.04501i	0.672398	−	0.740190i	$-0.265264\pi$
$278$	2.23976	−	8.35890i	0.00805669	−	0.0300680i
$279$	−312.389	+	95.5663i	−1.11967	+	0.342531i
$280$	44.8937	−	13.1366i	0.160335	−	0.0469165i
$281$		−	46.6699i		−	0.166085i	−0.996546	−	0.0830425i	$-0.973536\pi$
$281$		−	46.6699i		−	0.166085i	0.996546	−	0.0830425i	$-0.0264637\pi$
$282$	0.642276	−	5.64155i	0.00227758	−	0.0200055i
$283$	30.3772	+	113.369i	0.107340	+	0.400598i	0.998600	−	0.0528940i	$-0.0168446\pi$
$283$	30.3772	+	113.369i	0.107340	+	0.400598i	−0.891260	+	0.453492i	$0.850178\pi$
$284$	−101.068	+	175.055i	−0.355874	+	0.616391i
$285$	122.516	−	69.7987i	0.429881	−	0.244908i
$286$		−	42.4716i		−	0.148502i
$287$	10.3530	−	121.879i	0.0360732	−	0.424666i
$288$	−33.6718	+	63.3540i	−0.116916	+	0.219979i
$289$	47.9705	−	27.6958i	0.165988	−	0.0958332i
$290$	4.50345	+	3.62532i	0.0155291	+	0.0125011i
$291$	70.4532	+	27.7452i	0.242107	+	0.0953442i
$292$	78.0046	−	291.117i	0.267139	−	0.996976i
$293$	197.170	+	197.170i	0.672934	+	0.672934i	0.958391	−	0.285458i	$-0.0921456\pi$
$293$	197.170	+	197.170i	0.672934	+	0.672934i	−0.285458	+	0.958391i	$0.592146\pi$
$294$	0.518540	−	24.6386i	0.00176374	−	0.0838049i
$295$	−20.6505	+	15.0949i	−0.0700017	+	0.0511691i
$296$	20.2256	−	11.6773i	0.0683298	−	0.0394502i
$297$	−313.935	+	268.268i	−1.05702	+	0.903258i
$298$	−11.3821	+	3.04983i	−0.0381951	+	0.0102343i
$299$	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
$303$	39.7110	−	348.809i	0.131059	−	1.15118i
$304$	73.6205	−	127.514i	0.242173	−	0.419455i
$305$	−32.1680	−	297.774i	−0.105469	−	0.976309i
$306$	15.7248	−	16.8687i	0.0513882	−	0.0551263i
$307$	266.516	+	266.516i	0.868131	+	0.868131i	0.992265	−	0.124134i	$-0.0396153\pi$
$307$	266.516	+	266.516i	0.868131	+	0.868131i	−0.124134	+	0.992265i	$0.539615\pi$
$308$	384.933	−	180.682i	1.24978	−	0.586630i
$309$	−39.7983	+	5.95144i	−0.128797	+	0.0192603i
$310$	10.9858	+	28.3735i	0.0354380	+	0.0915274i
$311$	−111.647	+	193.379i	−0.358994	+	0.621796i	−0.987793	−	0.155772i	$-0.950214\pi$
$311$	−111.647	+	193.379i	−0.358994	+	0.621796i	0.628799	+	0.777568i	$0.283547\pi$
$312$	26.4875	+	60.9026i	0.0848958	+	0.195200i
$313$	380.906	+	102.063i	1.21695	+	0.326081i	0.809486	−	0.587140i	$-0.199746\pi$
$313$	380.906	+	102.063i	1.21695	+	0.326081i	0.407465	+	0.913221i	$0.366413\pi$
$314$			19.9155i			0.0634252i
$315$	−299.034	+	99.0136i	−0.949314	+	0.314329i
$316$	120.802			0.382286
$317$	31.0406	−	115.845i	0.0979200	−	0.365442i	−0.899526	−	0.436867i	$-0.856088\pi$
$317$	31.0406	−	115.845i	0.0979200	−	0.365442i	0.997446	+	0.0714248i	$0.0227546\pi$
$318$	−35.3850	+	15.3895i	−0.111274	+	0.0483946i
$319$	91.3527	+	52.7425i	0.286372	+	0.165337i
$320$	−280.442	−	123.890i	−0.876380	−	0.387158i
$321$	7.78362	+	52.0504i	0.0242480	+	0.162151i
$322$	−31.9927	−	22.2813i	−0.0993561	−	0.0691967i
$323$	−101.594	+	101.594i	−0.314533	+	0.314533i
$324$	140.934	−	289.212i	0.434980	−	0.892630i
$325$	−413.661	−	19.2813i	−1.27280	−	0.0593272i
$326$	3.34430	+	1.93083i	0.0102586	+	0.00592279i
$327$	−499.727	−	56.8926i	−1.52822	−	0.173984i
$328$	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	0.988445	−	0.151581i	$-0.0484363\pi$
$331$	120.136	+	208.082i	0.362950	+	0.628648i	−0.625495	+	0.780228i	$0.715103\pi$
$332$	15.9473	+	59.5162i	0.0480341	+	0.179266i
$333$	−133.361	+	83.3657i	−0.400484	+	0.250347i
$334$	−6.59055	−	11.4152i	−0.0197322	−	0.0341772i
$335$	−334.993	−	52.0653i	−0.999978	−	0.155419i
$336$	−217.314	+	246.925i	−0.646768	+	0.734897i
$337$	−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	$0.360365\pi$
$338$	17.0645	+	4.57243i	0.0504868	+	0.0135279i
$339$	38.2074	−	97.0199i	0.112706	−	0.286194i
$340$	236.444	+	190.339i	0.695424	+	0.559822i
$341$	277.573	+	480.770i	0.813996	+	1.40988i
$342$	6.65648	−	12.5243i	0.0194634	−	0.0366207i
$343$	86.2626	−	331.976i	0.251495	−	0.967859i
$344$	−63.8801			−0.185698
$345$	−131.742	+	480.601i	−0.381862	+	1.39305i
$346$	29.1893	+	16.8525i	0.0843622	+	0.0487065i
$347$	651.282	−	174.511i	1.87689	−	0.502912i	0.877152	−	0.480213i	$-0.159441\pi$
$347$	651.282	−	174.511i	1.87689	−	0.502912i	0.999742	−	0.0226990i	$-0.00722594\pi$
$348$	−81.6556	−	9.29628i	−0.234643	−	0.0267135i
$349$	513.119			1.47025			0.735127	−	0.677929i	$-0.237122\pi$
$349$	513.119			1.47025			0.735127	+	0.677929i	$0.237122\pi$
$350$	11.2159	+	27.1097i	0.0320454	+	0.0774563i
$351$	−192.647	−	403.621i	−0.548851	−	1.14992i
$352$	117.768	+	31.5558i	0.334568	+	0.0896473i
$353$	325.569	−	87.2361i	0.922293	−	0.247128i	0.233728	−	0.972302i	$-0.424908\pi$
$353$	325.569	−	87.2361i	0.922293	−	0.247128i	0.688565	+	0.725174i	$0.258241\pi$
$354$	−0.942788	+	2.39402i	−0.00266324	+	0.00676277i
$355$	−232.757	−	102.825i	−0.655655	−	0.289648i
$356$	152.628			0.428731
$357$	267.188	−	177.853i	0.748426	−	0.498189i
$358$	−39.5977	−	39.5977i	−0.110608	−	0.110608i
$359$	−153.677	−	266.177i	−0.428070	−	0.741439i	0.568631	−	0.822592i	$-0.307473\pi$
$359$	−153.677	−	266.177i	−0.428070	−	0.741439i	−0.996702	+	0.0811531i	$0.974140\pi$
$360$	−55.8304	−	22.3581i	−0.155085	−	0.0621060i
$361$	136.318	−	236.109i	0.377611	−	0.654042i
$362$	−32.4943	−	8.70683i	−0.0897634	−	0.0240520i
$363$	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
$366$	−18.7564	−	23.5759i	−0.0512471	−	0.0644149i
$367$	−92.7994	+	24.8655i	−0.252859	+	0.0677535i	−0.383022	−	0.923739i	$-0.625117\pi$
$367$	−92.7994	+	24.8655i	−0.252859	+	0.0677535i	0.130163	+	0.991493i	$0.458450\pi$
$368$	134.683	+	502.643i	0.365986	+	1.36588i
$369$	−107.235	+	115.036i	−0.290610	+	0.311750i
$370$	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
$373$	−7.69678	+	28.7248i	−0.0206348	+	0.0770101i	−0.975475	−	0.220108i	$-0.929359\pi$
$373$	−7.69678	+	28.7248i	−0.0206348	+	0.0770101i	0.954841	+	0.297118i	$0.0960256\pi$
$374$	−33.9389	−	19.5946i	−0.0907457	−	0.0523921i
$375$	278.671	−	250.933i	0.743122	−	0.669156i
$376$	13.0667	−	7.54407i	0.0347519	−	0.0200640i
$377$	−80.7838	+	80.7838i	−0.214281	+	0.214281i
$378$	−20.0861	+	24.5052i	−0.0531379	+	0.0648286i
$379$			227.162i			0.599373i	0.954038	+	0.299686i	$0.0968821\pi$
$379$			227.162i			0.599373i	−0.954038	+	0.299686i	$0.903118\pi$
$380$	170.763	+	75.4378i	0.449376	+	0.198521i
$381$	−13.5448	+	34.3942i	−0.0355506	+	0.0902736i
$382$	13.5230	+	50.4683i	0.0354004	+	0.132116i
$383$	−14.1699	+	52.8830i	−0.0369973	+	0.138076i	−0.981954	−	0.189119i	$-0.939437\pi$
$383$	−14.1699	+	52.8830i	−0.0369973	+	0.138076i	0.944957	+	0.327195i	$0.106103\pi$
$384$	−125.110	+	18.7089i	−0.325806	+	0.0487211i
$385$	278.180	+	457.340i	0.722545	+	1.18790i
$386$			33.3077i			0.0862895i
$387$	429.916	−	15.0879i	1.11089	−	0.0389869i
$388$	25.9466	+	96.8340i	0.0668727	+	0.249572i
$389$	−104.326	+	180.698i	−0.268190	+	0.464519i	−0.968394	−	0.249424i	$-0.919759\pi$
$389$	−104.326	+	180.698i	−0.268190	+	0.464519i	0.700204	+	0.713942i	$0.253092\pi$
$390$	−36.1930	+	20.6196i	−0.0928027	+	0.0528707i
$391$		−	507.774i		−	1.29866i
$392$	53.4532	−	37.8321i	0.136360	−	0.0965104i
$393$	418.099	+	309.321i	1.06387	+	0.787076i
$394$	8.91794	−	5.14878i	0.0226344	−	0.0130680i
$395$	16.3330	+	151.192i	0.0413493	+	0.382764i
$396$	−532.732	−	122.893i	−1.34528	−	0.310336i
$397$	−74.2885	+	277.248i	−0.187125	+	0.698359i	0.807041	+	0.590495i	$0.201068\pi$
$397$	−74.2885	+	277.248i	−0.187125	+	0.698359i	−0.994166	+	0.107864i	$0.965599\pi$
$398$	−26.1223	−	26.1223i	−0.0656339	−	0.0656339i
$399$	130.418	−	148.189i	0.326862	−	0.371401i
$400$	118.852	−	373.116i	0.297130	−	0.932790i
$401$	567.257	−	327.506i	1.41461	−	0.816723i	0.418788	−	0.908084i	$-0.362455\pi$
$401$	567.257	−	327.506i	1.41461	−	0.816723i	0.995818	+	0.0913615i	$0.0291219\pi$
$402$	−31.2714	+	13.6004i	−0.0777895	+	0.0338319i
$403$	−580.763	+	155.615i	−1.44110	+	0.386141i
$404$	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
$408$	60.8872	+	6.93186i	0.149233	+	0.0169898i
$409$	235.407	−	407.738i	0.575568	−	0.996914i	−0.420411	−	0.907334i	$-0.638114\pi$
$409$	235.407	−	407.738i	0.575568	−	0.996914i	0.995980	−	0.0895799i	$-0.0285524\pi$
$410$	11.4097	+	9.18491i	0.0278286	+	0.0224022i
$411$	−334.069	+	265.778i	−0.812819	+	0.646661i
$412$	−37.6728	−	37.6728i	−0.0914389	−	0.0914389i
$413$	−20.4662	+	29.3864i	−0.0495549	+	0.0711535i
$414$	14.6638	+	47.9334i	0.0354199	+	0.115781i
$415$	−72.3322	+	28.0059i	−0.174294	+	0.0674841i
$416$	−66.0240	+	114.357i	−0.158712	+	0.274897i
$417$	−142.008	+	61.7615i	−0.340546	+	0.148109i
$418$	−23.2812	−	6.23819i	−0.0556967	−	0.0149239i
$419$		−	582.158i		−	1.38940i	−0.719300	−	0.694699i	$-0.755537\pi$
$419$		−	582.158i		−	1.38940i	0.719300	−	0.694699i	$-0.244463\pi$
$420$	−340.854	−	240.309i	−0.811556	−	0.572165i
$421$	360.182			0.855540			0.427770	−	0.903888i	$-0.359299\pi$
$421$	360.182			0.855540			0.427770	+	0.903888i	$0.359299\pi$
$422$	2.55127	−	9.52147i	0.00604566	−	0.0225627i
$423$	−86.1577	+	53.8581i	−0.203682	+	0.127324i
$424$	−88.7991	−	51.2682i	−0.209432	−	0.120916i
$425$	−206.254	+	321.659i	−0.485303	+	0.756845i
$426$	−25.3140	+	3.78546i	−0.0594226	+	0.00888605i
$427$	−178.167	−	379.575i	−0.417252	−	0.888933i
$428$	−49.2706	+	49.2706i	−0.115118	+	0.115118i
$429$	−594.755	+	473.174i	−1.38638	+	1.10297i
$430$	−4.30320	−	39.8341i	−0.0100074	−	0.0926374i
$431$	−350.070	−	202.113i	−0.812227	−	0.468939i	0.0355017	−	0.999370i	$-0.488697\pi$
$431$	−350.070	−	202.113i	−0.812227	−	0.468939i	−0.847729	+	0.530430i	$0.822030\pi$
$432$	415.813	−	77.1787i	0.962531	−	0.178654i
$433$	−23.1671	+	23.1671i	−0.0535036	+	0.0535036i	−0.733352	−	0.679849i	$-0.762045\pi$
$433$	−23.1671	+	23.1671i	−0.0535036	+	0.0535036i	0.679849	+	0.733352i	$0.262045\pi$
$434$	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
$437$	−80.8280	−	301.654i	−0.184961	−	0.690284i
$438$	34.9965	−	15.2205i	0.0799006	−	0.0347501i
$439$	−252.925	−	438.079i	−0.576139	−	0.997902i	−0.995917	−	0.0902749i	$-0.971225\pi$
$439$	−252.925	−	438.079i	−0.576139	−	0.997902i	0.419778	−	0.907627i	$-0.362108\pi$
$440$	−15.6958	+	100.988i	−0.0356724	+	0.229519i
$441$	−350.807	+	267.237i	−0.795481	+	0.605979i
$442$	30.0124	−	30.0124i	0.0679013	−	0.0679013i
$443$	121.349	+	32.5153i	0.273925	+	0.0733979i	0.393166	−	0.919467i	$-0.371380\pi$
$443$	121.349	+	32.5153i	0.273925	+	0.0733979i	−0.119242	+	0.992865i	$0.538046\pi$
$444$	−193.743	−	76.2979i	−0.436358	−	0.171842i
$445$	20.6360	+	191.024i	0.0463730	+	0.429267i
$446$	−15.3590	−	26.6026i	−0.0344372	−	0.0596470i
$447$	169.517	+	125.413i	0.379232	+	0.280566i
$448$	−427.683	−	36.3295i	−0.954650	−	0.0810926i
$449$	−550.812			−1.22675			−0.613376	−	0.789791i	$-0.710189\pi$
$449$	−550.812			−1.22675			−0.613376	+	0.789791i	$0.710189\pi$
$450$	10.1810	−	36.3206i	0.0226245	−	0.0807125i
$451$	231.446	+	133.626i	0.513185	+	0.296287i
$452$	133.349	−	35.7306i	0.295019	−	0.0790501i
$453$	35.1515	−	308.759i	0.0775971	−	0.681588i
$454$	18.3171			0.0403460
$455$	−556.422	+	162.818i	−1.22290	+	0.357841i
$456$	37.2748	−	5.57407i	0.0817430	−	0.0122238i
$457$	−221.692	−	59.4023i	−0.485104	−	0.129983i	0.00797430	−	0.999968i	$-0.497462\pi$
$457$	−221.692	−	59.4023i	−0.485104	−	0.129983i	−0.493078	+	0.869985i	$0.664128\pi$
$458$	−25.1883	+	6.74918i	−0.0549962	+	0.0147362i
$459$	−411.411	−	32.2707i	−0.896321	−	0.0703065i
$460$	−615.265	+	238.221i	−1.33753	+	0.517872i
$461$	−532.899			−1.15596			−0.577982	−	0.816050i	$-0.696160\pi$
$461$	−532.899			−1.15596			−0.577982	+	0.816050i	$0.696160\pi$
$462$	48.2500	+	23.8994i	0.104437	+	0.0517303i
$463$	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
$465$	274.939	−	469.949i	0.591267	−	1.01064i
$466$	30.2889	−	52.4619i	0.0649977	−	0.112579i
$467$	250.251	+	67.0547i	0.535870	+	0.143586i	0.516598	−	0.856228i	$-0.327198\pi$
$467$	250.251	+	67.0547i	0.535870	+	0.143586i	0.0192726	+	0.999814i	$0.493865\pi$
$468$	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
$471$	278.889	−	221.878i	0.592121	−	0.471078i
$472$	−6.60418	+	1.76958i	−0.0139919	+	0.00374912i
$473$	−189.205	−	706.121i	−0.400010	−	1.49286i
$474$	9.52340	+	11.9704i	0.0200916	+	0.0252541i
$475$	−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
$478$	−13.4105	+	50.0488i	−0.0280555	+	0.104705i
$479$	525.786	+	303.563i	1.09767	+	0.633742i	0.935609	−	0.353038i	$-0.114851\pi$
$479$	525.786	+	303.563i	1.09767	+	0.633742i	0.162065	+	0.986780i	$0.448185\pi$
$480$	−30.2843	−	115.678i	−0.0630923	−	0.240997i
$481$	−250.680	+	144.730i	−0.521165	+	0.300895i
$482$	18.1932	−	18.1932i	0.0377453	−	0.0377453i
$483$	44.4102	+	696.248i	0.0919465	+	1.44151i
$484$			448.479i			0.926609i
$485$	−117.686	+	45.5662i	−0.242651	+	0.0939509i
$486$	39.7687	−	8.83467i	0.0818286	−	0.0181783i
$487$	−141.304	−	527.352i	−0.290151	−	1.08286i	−0.944992	−	0.327093i	$-0.893931\pi$
$487$	−141.304	−	527.352i	−0.290151	−	1.08286i	0.654841	−	0.755767i	$-0.272736\pi$
$488$	20.7200	−	77.3281i	0.0424590	−	0.158459i
$489$	−10.2201	−	68.3435i	−0.0209000	−	0.139762i
$490$	27.1920	+	30.7836i	0.0554938	+	0.0628237i
$491$		−	134.524i		−	0.273980i	−0.990572	−	0.136990i	$-0.956257\pi$
$491$		−	134.524i		−	0.273980i	0.990572	−	0.136990i	$-0.0437428\pi$
$492$	−206.878	−	23.5526i	−0.420485	−	0.0478711i
$493$	27.2837	+	101.824i	0.0553423	+	0.206540i
$494$	13.0521	−	22.6069i	0.0264213	−	0.0457630i
$495$	81.7811	−	683.364i	0.165214	−	1.38053i
$496$		−	568.551i		−	1.14627i
$497$	−354.963	−	30.1523i	−0.714212	−	0.0606686i
$498$	−4.64031	+	6.27216i	−0.00931790	+	0.0125947i
$499$	449.573	−	259.561i	0.900948	−	0.520162i	0.0234401	−	0.999725i	$-0.492538\pi$
$499$	449.573	−	259.561i	0.900948	−	0.520162i	0.877508	+	0.479563i	$0.159205\pi$
$500$	486.514	+	99.0096i	0.973029	+	0.198019i
$501$	−86.4285	+	219.467i	−0.172512	+	0.438059i
$502$	8.16822	−	30.4842i	0.0162714	−	0.0607255i
$503$	197.863	+	197.863i	0.393366	+	0.393366i	0.875885	−	0.482519i	$-0.160278\pi$
$503$	197.863	+	197.863i	0.393366	+	0.393366i	−0.482519	+	0.875885i	$0.660278\pi$
$504$	−84.0934	−	4.17957i	−0.166852	−	0.00829281i
$505$	345.282	+	472.362i	0.683727	+	0.935371i
$506$	73.7701	−	42.5912i	0.145791	−	0.0841723i
$507$	−126.085	−	289.906i	−0.248688	−	0.571808i
$508$	−47.2730	+	12.6668i	−0.0930571	+	0.0249346i
$509$	−540.522	+	312.071i	−1.06193	+	0.613106i	−0.925966	−	0.377608i	$-0.876747\pi$
$509$	−540.522	+	312.071i	−1.06193	+	0.613106i	−0.135965	+	0.990714i	$0.543413\pi$
$510$	−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
$513$	−249.545	+	46.3178i	−0.486442	+	0.0902880i
$514$	15.4366	−	26.7370i	0.0300324	−	0.0520176i
$515$	42.0564	−	52.2435i	0.0816630	−	0.101444i
$516$	354.588	+	445.699i	0.687187	+	0.863758i
$517$	122.093	+	122.093i	0.236156	+	0.236156i
$518$	16.8282	+	11.7200i	0.0324869	+	0.0226255i
$519$	−89.2018	−	596.508i	−0.171873	−	1.14934i
$520$	−101.249	−	44.7286i	−0.194709	−	0.0860165i
$521$	319.011	−	552.544i	0.612306	−	1.06054i	−0.378545	−	0.925583i	$-0.623576\pi$
$521$	319.011	−	552.544i	0.612306	−	1.06054i	0.990851	−	0.134962i	$-0.0430911\pi$
$522$	−5.51610	−	8.82419i	−0.0105672	−	0.0169046i
$523$	−698.967	−	187.288i	−1.33646	−	0.358103i	−0.481339	−	0.876535i	$-0.659849\pi$
$523$	−698.967	−	187.288i	−1.33646	−	0.358103i	−0.855119	+	0.518432i	$0.826516\pi$
$524$			688.571i			1.31407i
$525$	254.678	−	459.091i	0.485100	−	0.874459i
$526$	−46.2827			−0.0879898
$527$	−143.589	+	535.880i	−0.272464	+	1.01685i
$528$	−286.632	−	659.051i	−0.542864	−	1.24820i
$529$	497.709	+	287.353i	0.940849	+	0.543200i
$530$	25.9878	−	58.8266i	0.0490335	−	0.110994i
$531$	44.0285	−	13.4692i	0.0829161	−	0.0253658i
$532$	260.420	+	22.1213i	0.489511	+	0.0415814i
$533$	−204.670	+	204.670i	−0.383995	+	0.383995i
$534$	12.0324	+	15.1241i	0.0225325	+	0.0283222i
$535$	−68.3269	−	55.0037i	−0.127714	−	0.102811i
$536$	−78.4759	−	45.3081i	−0.146410	−	0.0845300i
$537$	−113.354	+	995.668i	−0.211088	+	1.85413i
$538$	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	0.999899	−	0.0141884i	$-0.00451647\pi$
$541$	263.825	+	456.959i	0.487662	+	0.844656i	−0.512237	+	0.858844i	$0.671183\pi$
$542$	8.69232	+	32.4402i	0.0160375	+	0.0598527i
$543$	240.091	+	552.040i	0.442157	+	1.01665i
$544$	60.9215	+	105.519i	0.111988	+	0.193969i
$545$	676.738	−	494.674i	1.24172	−	0.907659i
$546$	−38.5274	+	43.7772i	−0.0705630	+	0.0801780i
$547$	−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	$0.332127\pi$
$548$	−545.936	−	146.283i	−0.996234	−	0.266940i
$549$	−121.182	+	525.316i	−0.220733	+	0.956859i
$550$	−64.0312	−	2.98459i	−0.116420	−	0.00542653i
$551$	32.4170	+	56.1479i	0.0588330	+	0.101902i
$552$	−79.2212	+	107.081i	−0.143517	+	0.193987i
$553$	90.4625	+	192.725i	0.163585	+	0.348509i
$554$	50.2405			0.0906867
$555$	69.2968	−	252.797i	0.124859	−	0.455491i
$556$	−177.557	−	102.513i	−0.319347	−	0.184375i
$557$	−490.865	+	131.527i	−0.881265	+	0.236134i	−0.670953	−	0.741500i	$-0.734115\pi$
$557$	−490.865	+	131.527i	−0.881265	+	0.236134i	−0.210312	+	0.977634i	$0.567448\pi$
$558$	−1.92086	−	54.7332i	−0.00344241	−	0.0980881i
$559$	791.743			1.41636
$560$	−12.5365	−	548.080i	−0.0223866	−	0.978714i
$561$	103.716	+	693.570i	0.184878	+	1.23631i
$562$	7.55747	+	2.02502i	0.0134474	+	0.00360323i
$563$	−560.102	+	150.079i	−0.994853	+	0.266570i	−0.719288	−	0.694712i	$-0.755532\pi$
$563$	−560.102	+	150.079i	−0.994853	+	0.266570i	−0.275565	+	0.961282i	$0.588865\pi$
$564$	−125.167	−	49.2920i	−0.221927	−	0.0873972i
$565$	62.7484	+	162.063i	0.111059	+	0.286838i
$566$	−19.6765			−0.0347641
$567$	566.940	+	8.26659i	0.999894	+	0.0145795i
$568$	−48.0938	−	48.0938i	−0.0846721	−	0.0846721i
$569$	−150.720	−	261.055i	−0.264886	−	0.458795i	0.702648	−	0.711538i	$-0.252001\pi$
$569$	−150.720	−	261.055i	−0.264886	−	0.458795i	−0.967534	+	0.252742i	$0.918668\pi$
$570$	5.98682	+	22.8682i	0.0105032	+	0.0401196i
$571$	−367.971	+	637.344i	−0.644432	+	1.11619i	0.340000	+	0.940425i	$0.389573\pi$
$571$	−367.971	+	637.344i	−0.644432	+	1.11619i	−0.984432	+	0.175764i	$0.943760\pi$
$572$	−971.951	−	260.433i	−1.69922	−	0.455303i
$573$	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
$576$	403.670	+	376.297i	0.700815	+	0.653293i
$577$	−26.0811	+	6.98842i	−0.0452013	+	0.0121116i	−0.281349	−	0.959606i	$-0.590782\pi$
$577$	−26.0811	+	6.98842i	−0.0452013	+	0.0121116i	0.236148	+	0.971717i	$0.424115\pi$
$578$	2.40345	+	8.96981i	0.00415822	+	0.0155187i
$579$	466.428	−	371.080i	0.805576	−	0.640898i
$580$	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
$583$	303.700	−	1133.42i	0.520926	−	1.94412i
$584$	87.8241	+	50.7053i	0.150384	+	0.0868241i
$585$	691.974	+	277.111i	1.18286	+	0.473695i
$586$	−40.4838	+	23.3733i	−0.0690850	+	0.0398862i
$587$	−312.326	+	312.326i	−0.532072	+	0.532072i	−0.921188	−	0.389117i	$-0.872780\pi$
$587$	−312.326	+	312.326i	−0.532072	+	0.532072i	0.389117	+	0.921188i	$0.372780\pi$
$588$	−560.669	−	162.949i	−0.953519	−	0.277125i
$589$			341.208i			0.579300i
$590$	−1.54835	−	3.99900i	−0.00262432	−	0.00677796i
$591$	−171.456	−	67.5210i	−0.290111	−	0.114249i
$592$	−70.8434	−	264.391i	−0.119668	−	0.446607i
$593$	222.299	−	829.633i	0.374873	−	1.39904i	−0.478658	−	0.878001i	$-0.658877\pi$
$593$	222.299	−	829.633i	0.374873	−	1.39904i	0.853531	−	0.521042i	$-0.174457\pi$
$594$	−29.8201	−	62.4771i	−0.0502021	−	0.105180i
$595$	−126.603	+	519.752i	−0.212778	+	0.873533i
$596$			279.178i			0.468420i
$597$	−74.7789	+	656.834i	−0.125258	+	1.10022i
$598$	23.8778	+	89.1131i	0.0399294	+	0.149019i
$599$	202.842	−	351.333i	0.338634	−	0.586532i	−0.645542	−	0.763725i	$-0.723368\pi$
$599$	202.842	−	351.333i	0.338634	−	0.586532i	0.984176	+	0.177193i	$0.0567017\pi$
$600$	93.6795	−	35.6534i	0.156133	−	0.0594223i
$601$		−	207.421i		−	0.345127i	−0.984998	−	0.172563i	$-0.944795\pi$
$601$		−	207.421i		−	0.345127i	0.984998	−	0.172563i	$-0.0552050\pi$
$602$	−23.8339	−	50.7767i	−0.0395911	−	0.0843467i
$603$	538.848	+	286.390i	0.893612	+	0.474942i
$604$	356.306	−	205.714i	0.589911	−	0.340585i
$605$	−561.300	+	60.6361i	−0.927768	+	0.100225i
$606$	54.7611	+	21.5655i	0.0903649	+	0.0355866i
$607$	306.916	−	1145.43i	0.505628	−	1.88703i	0.0459504	−	0.998944i	$-0.485368\pi$
$607$	306.916	−	1145.43i	0.505628	−	1.88703i	0.459678	−	0.888086i	$-0.347965\pi$
$608$	52.9884	+	52.9884i	0.0871519	+	0.0871519i
$609$	−46.3164	−	137.233i	−0.0760532	−	0.225341i
$610$	49.6157	+	7.71138i	0.0813372	+	0.0126416i
$611$	−161.951	+	93.5026i	−0.265059	+	0.153032i
$612$	−289.611	−	463.295i	−0.473221	−	0.757018i
$613$	373.703	−	100.133i	0.609630	−	0.163350i	0.0592208	−	0.998245i	$-0.481138\pi$
$613$	373.703	−	100.133i	0.609630	−	0.163350i	0.550409	+	0.834895i	$0.314472\pi$
$614$	−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	$0.779810\pi$
$618$	0.763114	−	6.70295i	0.00123481	−	0.0108462i
$619$	91.0832	−	157.761i	0.147146	−	0.254864i	−0.783026	−	0.621989i	$-0.786325\pi$
$619$	91.0832	−	157.761i	0.147146	−	0.254864i	0.930171	+	0.367125i	$0.119658\pi$
$620$	716.684	−	77.4221i	1.15594	−	0.124874i
$621$	507.871	−	739.370i	0.817827	−	1.19061i
$622$	−26.4703	−	26.4703i	−0.0425567	−	0.0425567i
$623$	114.295	+	243.500i	0.183459	+	0.390850i
$624$	769.811	−	115.117i	1.23367	−	0.184483i
$625$	−58.1380	+	622.290i	−0.0930209	+	0.995664i
$626$	−33.0552	+	57.2532i	−0.0528038	+	0.0914588i
$627$	172.018	+	395.521i	0.274351	+	0.630814i
$628$	455.761	+	122.121i	0.725734	+	0.194460i
$629$			267.090i			0.424627i
$630$	−3.05856	−	52.7201i	−0.00485486	−	0.0836828i
$631$	508.007			0.805082			0.402541	−	0.915402i	$-0.368127\pi$
$631$	508.007			0.805082			0.402541	+	0.915402i	$0.368127\pi$
$632$	−10.5204	+	39.2626i	−0.0166462	+	0.0621244i
$633$	−161.758	+	70.3513i	−0.255543	+	0.111140i
$634$	17.4125	+	10.0531i	0.0274645	+	0.0158566i
$635$	−22.2448	−	57.4526i	−0.0350311	−	0.0904765i
$636$	135.206	+	904.144i	0.212587	+	1.42161i
$637$	−662.510	+	468.898i	−1.04005	+	0.736104i
$638$	−12.5046	+	12.5046i	−0.0195998	+	0.0195998i
$639$	335.033	+	312.314i	0.524308	+	0.488754i
$640$	132.208	−	164.232i	0.206575	−	0.256613i
$641$	329.378	+	190.166i	0.513850	+	0.296671i	0.734415	−	0.678701i	$-0.237457\pi$
$641$	329.378	+	190.166i	0.513850	+	0.296671i	−0.220565	+	0.975372i	$0.570790\pi$
$642$	−8.76649	−	0.998043i	−0.0136550	−	0.00155458i
$643$	−548.817	+	548.817i	−0.853526	+	0.853526i	−0.990566	−	0.137039i	$-0.956241\pi$
$643$	−548.817	+	548.817i	−0.853526	+	0.853526i	0.137039	+	0.990566i	$0.456241\pi$
$644$	−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
$647$	316.824	+	1182.40i	0.489681	+	1.82751i	0.557987	+	0.829849i	$0.311574\pi$
$647$	316.824	+	1182.40i	0.489681	+	1.82751i	−0.0683064	+	0.997664i	$0.521760\pi$
$648$	81.7247	+	70.9923i	0.126118	+	0.109556i
$649$	−39.1215	−	67.7604i	−0.0602796	−	0.104407i
$650$	21.0712	−	66.1494i	0.0324172	−	0.101768i
$651$	150.017	−	747.345i	0.230441	−	1.14799i
$652$	64.6935	−	64.6935i	0.0992232	−	0.0992232i
$653$	−44.7631	−	11.9942i	−0.0685499	−	0.0183679i	0.224381	−	0.974501i	$-0.427964\pi$
$653$	−44.7631	−	11.9942i	−0.0685499	−	0.0183679i	−0.292931	+	0.956134i	$0.594631\pi$
$654$	30.8961	−	78.4544i	0.0472418	−	0.119961i
$655$	−861.791	+	93.0976i	−1.31571	+	0.142134i
$656$	−136.852	−	237.035i	−0.208616	−	0.361334i
$657$	−603.037	−	320.506i	−0.917864	−	0.487832i
$658$	10.8718	+	7.57169i	0.0165225	+	0.0115071i
$659$	−1102.69			−1.67328			−0.836642	−	0.547750i	$-0.815484\pi$
$659$	−1102.69			−1.67328			−0.836642	+	0.547750i	$0.815484\pi$
$660$	791.733	−	451.059i	1.19960	−	0.683422i
$661$	−355.813	−	205.429i	−0.538295	−	0.310785i	0.206093	−	0.978532i	$-0.433925\pi$
$661$	−355.813	−	205.429i	−0.538295	−	0.310785i	−0.744388	+	0.667748i	$0.767258\pi$
$662$	−38.9085	+	10.4255i	−0.0587741	+	0.0157485i
$663$	−754.649	−	85.9148i	−1.13823	−	0.129585i
$664$	−20.7325			−0.0312236
$665$	7.52359	+	328.923i	0.0113137	+	0.494620i
$666$	−7.71320	−	25.2131i	−0.0115814	−	0.0378574i
$667$	−221.327	−	59.3043i	−0.331824	−	0.0889120i
$668$	−301.646	+	80.8258i	−0.451566	+	0.120997i
$669$	−201.418	+	511.460i	−0.301073	+	0.764514i
$670$	22.9666	−	51.9878i	0.0342785	−	0.0775937i
$671$	916.144			1.36534
$672$	−92.7629	−	139.357i	−0.138040	−	0.207377i
$673$	−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
$675$	−622.046	+	262.075i	−0.921550	+	0.388260i
$676$	209.278	−	362.480i	0.309582	−	0.536212i
$677$	222.162	+	59.5281i	0.328156	+	0.0879292i	0.419136	−	0.907924i	$-0.362333\pi$
$677$	222.162	+	59.5281i	0.328156	+	0.0879292i	−0.0909796	+	0.995853i	$0.529000\pi$
$678$	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
$681$	−204.070	−	256.505i	−0.299662	−	0.376659i
$682$	−89.8972	+	24.0879i	−0.131814	+	0.0353195i
$683$	−41.9067	−	156.398i	−0.0613568	−	0.228987i	0.928438	−	0.371488i	$-0.121152\pi$
$683$	−41.9067	−	156.398i	−0.0613568	−	0.228987i	−0.989795	+	0.142501i	$0.954486\pi$
$684$	−245.797	−	229.130i	−0.359353	−	0.334985i
$685$	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
$688$	−193.773	+	723.172i	−0.281647	+	1.05112i
$689$	1100.59	+	635.428i	1.59738	+	0.922247i
$690$	−72.1096	−	42.1871i	−0.104507	−	0.0611407i
$691$	−316.769	+	182.886i	−0.458421	+	0.264669i	−0.711380	−	0.702808i	$-0.751929\pi$
$691$	−316.769	+	182.886i	−0.458421	+	0.264669i	0.252959	+	0.967477i	$0.418596\pi$
$692$	564.651	−	564.651i	0.815970	−	0.815970i
$693$	−202.874	−	941.936i	−0.292747	−	1.35921i
$694$			113.037i			0.162878i
$695$	104.295	−	236.084i	0.150064	−	0.339689i
$696$	10.1326	−	25.7297i	0.0145584	−	0.0369680i
$697$	69.1247	+	257.977i	0.0991746	+	0.370124i
$698$	−22.2643	+	83.0916i	−0.0318973	+	0.119042i
$699$	−1072.10	+	160.322i	−1.53377	+	0.229360i
$700$	689.173	−	90.4373i	0.984533	−	0.129196i
$701$		−	773.724i		−	1.10374i	−0.833929	−	0.551872i	$-0.813914\pi$
$701$		−	773.724i		−	1.10374i	0.833929	−	0.551872i	$-0.186086\pi$
$702$	73.7191	−	13.6829i	0.105013	−	0.0194914i
$703$	42.5157	+	158.671i	0.0604775	+	0.225705i
$704$	468.903	−	812.163i	0.666055	−	1.15364i
$705$	44.7690	−	163.319i	0.0635021	−	0.231658i
$706$			56.5061i			0.0800370i
$707$	672.188	+	468.146i	0.950762	+	0.662159i
$708$	49.0053	+	36.2554i	0.0692166	+	0.0512083i
$709$	−767.065	+	442.865i	−1.08190	+	0.624633i	−0.931407	−	0.363978i	$-0.881418\pi$
$709$	−767.065	+	442.865i	−1.08190	+	0.624633i	−0.150489	+	0.988612i	$0.548085\pi$
$710$	26.7503	−	33.2299i	0.0376765	−	0.0468026i
$711$	61.5292	−	266.724i	0.0865389	−	0.375139i
$712$	−13.2920	+	49.6065i	−0.0186686	+	0.0696720i
$713$	−852.690	−	852.690i	−1.19592	−	1.19592i
$714$	17.2073	+	50.9841i	0.0240998	+	0.0714063i
$715$	194.537	−	1251.67i	0.272080	−	1.75059i
$716$	−1148.99	+	663.372i	−1.60474	+	0.926497i
$717$	850.270	−	369.796i	1.18587	−	0.515754i
$718$	49.7713	−	13.3362i	0.0693193	−	0.0185741i
$719$	−428.934	+	247.645i	−0.596570	+	0.344430i	−0.767691	−	0.640820i	$-0.778594\pi$
$719$	−428.934	+	247.645i	−0.596570	+	0.344430i	0.171121	+	0.985250i	$0.445261\pi$
$720$	−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
$723$	−457.461	−	52.0808i	−0.632726	−	0.0720343i
$724$	−398.507	+	690.234i	−0.550424	+	0.953362i
$725$	116.115	+	127.468i	0.160158	+	0.175819i
$726$	−44.4401	+	35.3556i	−0.0612123	+	0.0486992i
$727$	−242.067	−	242.067i	−0.332967	−	0.332967i	0.520745	−	0.853712i	$-0.325654\pi$
$727$	−242.067	−	242.067i	−0.332967	−	0.332967i	−0.853712	+	0.520745i	$0.825654\pi$
$728$	−154.408	−	13.1162i	−0.212099	−	0.0180167i
$729$	−566.779	−	458.479i	−0.777475	−	0.628914i
$730$	−25.7024	+	58.1807i	−0.0352088	+	0.0796996i
$731$	365.277	−	632.679i	0.499695	−	0.865498i
$732$	−654.541	+	284.670i	−0.894181	+	0.388894i
$733$	1122.76	+	300.842i	1.53173	+	0.410425i	0.923582	−	0.383401i	$-0.125247\pi$
$733$	1122.76	+	300.842i	1.53173	+	0.410425i	0.608145	+	0.793826i	$0.291914\pi$
$734$		−	16.1063i		−	0.0219432i
$735$	128.137	−	723.744i	0.174336	−	0.984686i
$736$	−264.840			−0.359836
$737$	268.393	−	1001.66i	0.364170	−	1.35910i
$738$	−13.9753	−	22.3565i	−0.0189367	−	0.0302934i
$739$	−377.355	−	217.866i	−0.510629	−	0.294812i	0.222463	−	0.974941i	$-0.428590\pi$
$739$	−377.355	−	217.866i	−0.510629	−	0.294812i	−0.733092	+	0.680129i	$0.761924\pi$
$740$	323.630	−	125.305i	0.437338	−	0.169331i
$741$	−461.991	+	69.0862i	−0.623470	+	0.0932337i
$742$	7.62062	−	89.7126i	0.0102704	−	0.120906i
$743$	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	$0.170656\pi$
$744$	113.887	−	90.6056i	0.153073	−	0.121782i
$745$	−349.410	+	37.7461i	−0.469006	+	0.0506659i
$746$	−4.31757	−	2.49275i	−0.00578762	−	0.00334149i
$747$	139.530	−	4.89683i	0.186788	−	0.00655533i
$748$	−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	0.566564	−	0.824018i	$-0.308272\pi$
$751$	−323.184	−	559.771i	−0.430338	−	0.745368i	−0.996902	+	0.0786500i	$0.974939\pi$
$752$	−45.7682	−	170.809i	−0.0608620	−	0.227140i
$753$	−517.891	+	225.239i	−0.687770	+	0.299122i
$754$	−9.57646	−	16.5869i	−0.0127009	−	0.0219986i
$755$	305.638	+	418.127i	0.404818	+	0.553810i
$756$	437.628	+	609.930i	0.578873	+	0.806786i
$757$	−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	$0.322584\pi$
$758$	−36.7854	−	9.85663i	−0.0485296	−	0.0130035i
$759$	−1418.30	−	558.540i	−1.86864	−	0.735890i
$760$	−39.3897	+	48.9309i	−0.0518286	+	0.0643827i
$761$	363.696	+	629.940i	0.477919	+	0.827779i	0.999680	−	0.0253124i	$-0.00805805\pi$
$761$	363.696	+	629.940i	0.477919	+	0.827779i	−0.521761	+	0.853092i	$0.674725\pi$
$762$	−4.98190	−	3.68574i	−0.00653793	−	0.00483693i
$763$	670.698	−	963.022i	0.879027	−	1.26215i
$764$	1237.88			1.62026
$765$	540.687	−	425.106i	0.706780	−	0.555694i
$766$	−7.94874	−	4.58921i	−0.0103769	−	0.00599113i
$767$	81.8535	−	21.9326i	0.106719	−	0.0285953i
$768$	−80.8337	+	710.018i	−0.105252	+	0.924502i
$769$	386.196			0.502205			0.251103	−	0.967960i	$-0.419207\pi$
$769$	386.196			0.502205			0.251103	+	0.967960i	$0.419207\pi$
$770$	−86.1294	+	25.2028i	−0.111856	+	0.0327310i
$771$	−546.394	+	81.7078i	−0.708682	+	0.105976i
$772$	762.238	+	204.241i	0.987355	+	0.264561i
$773$	1009.36	−	270.458i	1.30577	−	0.349881i	0.462143	−	0.886806i	$-0.347081\pi$
$773$	1009.36	−	270.458i	1.30577	−	0.349881i	0.843630	+	0.536925i	$0.180414\pi$
$774$	−16.2109	+	70.2729i	−0.0209443	+	0.0907919i
$775$	193.797	+	886.508i	0.250061	+	1.14388i
$776$	−33.7321			−0.0434692
$777$	−23.3598	−	366.228i	−0.0300641	−	0.471336i
$778$	−24.7345	−	24.7345i	−0.0317924	−	0.0317924i
$779$	82.1300	+	142.253i	0.105430	+	0.182610i
$780$	249.939	+	954.706i	0.320435	+	1.22398i
$781$	389.174	−	674.069i	0.498302	−	0.863085i
$782$	82.2262	+	22.0324i	0.105149	+	0.0281745i
$783$	−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
$786$	−68.2311	+	54.2832i	−0.0868081	+	0.0690626i
$787$	864.548	−	231.655i	1.09854	−	0.294352i	0.336368	−	0.941731i	$-0.390801\pi$
$787$	864.548	−	231.655i	1.09854	−	0.294352i	0.762169	+	0.647379i	$0.224135\pi$
$788$	−63.1440	−	235.657i	−0.0801320	−	0.299057i
$789$	515.633	+	648.124i	0.653528	+	0.821450i
$790$	−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
$793$	−256.808	+	958.420i	−0.323843	+	1.20860i
$794$	−41.6727	−	24.0598i	−0.0524845	−	0.0303020i
$795$	−1113.31	+	291.462i	−1.40039	+	0.366619i
$796$	−757.982	+	437.621i	−0.952239	+	0.549776i
$797$	−337.006	+	337.006i	−0.422843	+	0.422843i	−0.886181	−	0.463338i	$-0.846651\pi$
$797$	−337.006	+	337.006i	−0.422843	+	0.422843i	0.463338	+	0.886181i	$0.346651\pi$
$798$	18.3380	+	27.5491i	0.0229800	+	0.0345227i
$799$			172.553i			0.215961i
$800$	167.768	+	107.576i	0.209710	+	0.134469i
$801$	77.7392	−	336.993i	0.0970527	−	0.420716i
$802$	28.4211	+	106.069i	0.0354378	+	0.132256i
$803$	−300.365	+	1120.98i	−0.374054	+	1.39599i
$804$	119.487	+	799.034i	0.148616	+	0.993823i
$805$	−840.791	−	803.187i	−1.04446	−	0.997748i
$806$		−	100.798i		−	0.125059i
$807$	−1518.53	−	172.881i	−1.88170	−	0.214226i
$808$	40.4777	+	151.065i	0.0500962	+	0.186962i
$809$	306.932	−	531.622i	0.379397	−	0.657134i	−0.611578	−	0.791184i	$-0.709465\pi$
$809$	306.932	−	531.622i	0.379397	−	0.657134i	0.990975	+	0.134050i	$0.0427982\pi$
$810$	−38.7638	+	55.7438i	−0.0478565	+	0.0688196i
$811$			585.506i			0.721955i	0.932574	+	0.360978i	$0.117557\pi$
$811$			585.506i			0.721955i	−0.932574	+	0.360978i	$0.882443\pi$
$812$	109.592	−	157.358i	0.134966	−	0.193791i
$813$	357.439	−	483.139i	0.439654	−	0.594266i
$814$	−38.8032	+	22.4030i	−0.0476698	+	0.0275222i
$815$	89.7149	+	72.2212i	0.110080	+	0.0886150i
$816$	263.169	−	668.264i	0.322511	−	0.818950i
$817$	116.290	−	434.002i	0.142338	−	0.531214i
$818$	55.8124	+	55.8124i	0.0682303	+	0.0682303i
$819$	1042.27	+	51.8025i	1.27261	+	0.0632509i
$820$	280.158	−	204.787i	0.341656	−	0.249740i
$821$	717.063	−	413.997i	0.873402	−	0.504259i	0.00492484	−	0.999988i	$-0.498432\pi$
$821$	717.063	−	413.997i	0.873402	−	0.504259i	0.868477	+	0.495729i	$0.165099\pi$
$822$	−28.5433	−	65.6294i	−0.0347242	−	0.0798412i
$823$	1366.00	−	366.018i	1.65978	−	0.444737i	0.697453	−	0.716630i	$-0.254316\pi$
$823$	1366.00	−	366.018i	1.65978	−	0.444737i	0.962327	+	0.271893i	$0.0876498\pi$
$824$	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	$0.754488\pi$
$828$	1186.86	−	41.6529i	1.43341	−	0.0503055i
$829$	537.538	−	931.043i	0.648417	−	1.12309i	−0.335083	−	0.942188i	$-0.608765\pi$
$829$	537.538	−	931.043i	0.648417	−	1.12309i	0.983501	−	0.180903i	$-0.0579021\pi$
$830$	−1.39662	−	12.9283i	−0.00168267	−	0.0155762i
$831$	−559.727	−	703.548i	−0.673558	−	0.846628i
$832$	718.201	+	718.201i	0.863223	+	0.863223i
$833$	69.0404	+	745.739i	0.0828817	+	0.895245i
$834$	−3.83956	−	25.6758i	−0.00460379	−	0.0307864i
$835$	−141.942	−	366.601i	−0.169991	−	0.439043i
$836$	−285.518	+	494.532i	−0.341529	+	0.591546i
$837$	−745.061	+	636.679i	−0.890157	+	0.760668i
$838$	94.2715	+	25.2600i	0.112496	+	0.0301432i
$839$		−	1363.08i		−	1.62464i	−0.583209	−	0.812322i	$-0.698203\pi$
$839$		−	1363.08i		−	1.62464i	0.583209	−	0.812322i	$-0.301797\pi$
$840$	107.788	−	89.8546i	0.128319	−	0.106970i
$841$	−793.431			−0.943437
$842$	−15.6284	+	58.3259i	−0.0185610	+	0.0692707i
$843$	−55.8399	−	128.392i	−0.0662395	−	0.152304i
$844$	−202.252	−	116.770i	−0.239635	−	0.138353i
$845$	481.961	+	212.916i	0.570368	+	0.251971i
$846$	−4.98309	−	16.2888i	−0.00589018	−	0.0192539i
$847$	−715.492	+	335.842i	−0.844737	+	0.396507i
$848$	−849.758	+	849.758i	−1.00207	+	1.00207i
$849$	219.215	+	275.542i	0.258204	+	0.324549i
$850$	−43.1384	−	47.3565i	−0.0507510	−	0.0557135i
$851$	−502.772	−	290.276i	−0.590801	−	0.341099i
$852$	−68.5950	+	602.517i	−0.0805105	+	0.707179i
$853$	−886.732	+	886.732i	−1.03955	+	1.03955i	−0.0403603	+	0.999185i	$0.512851\pi$
$853$	−886.732	+	886.732i	−1.03955	+	1.03955i	−0.999185	+	0.0403603i	$0.987149\pi$
$854$	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
$857$	−40.8768	−	152.554i	−0.0476975	−	0.178010i	0.937968	−	0.346723i	$-0.112706\pi$
$857$	−40.8768	−	152.554i	−0.0476975	−	0.178010i	−0.985665	+	0.168713i	$0.946039\pi$
$858$	−50.8167	−	116.843i	−0.0592269	−	0.136180i
$859$	598.502	+	1036.64i	0.696743	+	1.20679i	0.969590	+	0.244737i	$0.0787015\pi$
$859$	598.502	+	1036.64i	0.696743	+	1.20679i	−0.272847	+	0.962058i	$0.587965\pi$
$860$	−937.979	−	145.783i	−1.09067	−	0.169515i
$861$	−117.345	−	347.686i	−0.136289	−	0.403817i
$862$	47.9187	−	47.9187i	0.0555901	−	0.0555901i
$863$	1543.44	+	413.564i	1.78846	+	0.479217i	0.992083	−	0.125582i	$-0.0400797\pi$
$863$	1543.44	+	413.564i	1.78846	+	0.479217i	0.796378	+	0.604799i	$0.206746\pi$
$864$	−16.8314	+	214.579i	−0.0194808	+	0.248356i
$865$	783.040	+	630.354i	0.905248	+	0.728733i
$866$	−2.74632	−	4.75677i	−0.00317127	−	0.00549281i
$867$	98.8329	−	133.589i	0.113994	−	0.154082i
$868$	913.562	−	428.813i	1.05249	−	0.494024i
$869$	−465.163			−0.535286
$870$	16.7270	+	4.58520i	0.0192264	+	0.00527035i
$871$	972.646	+	561.557i	1.11670	+	0.644727i
$872$	216.426	−	57.9911i	0.248195	−	0.0665035i
$873$	227.019	−	7.96724i	0.260044	−	0.00912628i
$874$	52.3554			0.0599032
$875$	206.367	+	850.316i	0.235848	+	0.971790i
$876$	−133.721	−	894.216i	−0.152650	−	1.02079i
$877$	403.249	+	108.050i	0.459805	+	0.123204i	0.481284	−	0.876565i	$-0.340171\pi$
$877$	403.249	+	108.050i	0.459805	+	0.123204i	−0.0214786	+	0.999769i	$0.506837\pi$
$878$	81.9146	−	21.9489i	0.0932968	−	0.0249988i
$879$	778.339	+	306.518i	0.885483	+	0.348712i
$880$	1095.65	+	484.026i	1.24506	+	0.550030i
$881$	−276.453			−0.313795			−0.156898	−	0.987615i	$-0.550149\pi$
$881$	−276.453			−0.313795			−0.156898	+	0.987615i	$0.550149\pi$
$882$	−28.0533	−	68.4032i	−0.0318064	−	0.0775547i
$883$	−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
$885$	−38.7503	+	66.2352i	−0.0437856	+	0.0748420i
$886$	−10.5307	+	18.2397i	−0.0118857	+	0.0205866i
$887$	1006.64	+	269.729i	1.13489	+	0.304092i	0.776893	−	0.629633i	$-0.216795\pi$
$887$	1006.64	+	269.729i	1.13489	+	0.304092i	0.357993	+	0.933724i	$0.383461\pi$
$888$	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
$891$	−542.680	+	1113.64i	−0.609069	+	1.24988i
$892$	−702.973	+	188.361i	−0.788087	+	0.211167i
$893$	27.4672	+	102.509i	0.0307583	+	0.114792i
$894$	−27.6640	+	22.0089i	−0.0309441	+	0.0246185i
$895$	−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
$898$	23.8999	−	89.1955i	0.0266145	−	0.0993268i
$899$	216.807	+	125.174i	0.241165	+	0.139237i
$900$	−768.758	−	455.707i	−0.854176	−	0.506341i
$901$	1015.54	−	586.320i	1.12712	−	0.650744i
$902$	−31.6811	+	31.6811i	−0.0351232	+	0.0351232i
$903$	−445.525	+	899.461i	−0.493383	+	0.996081i
$904$			46.4520i			0.0513849i
$905$	−917.752	−	405.434i	−1.01409	−	0.447994i
$906$	48.4736	+	19.0894i	0.0535029	+	0.0210700i
$907$	393.840	+	1469.83i	0.434222	+	1.62054i	0.742921	+	0.669380i	$0.233440\pi$
$907$	393.840	+	1469.83i	0.434222	+	1.62054i	−0.308698	+	0.951160i	$0.599893\pi$
$908$	112.319	−	419.181i	0.123700	−	0.461653i
$909$	−308.097	−	1007.11i	−0.338941	−	1.10794i
$910$	−2.22258	−	97.1686i	−0.00244239	−	0.106779i
$911$			1648.74i			1.80981i	0.425616	+	0.904904i	$0.360058\pi$
$911$			1648.74i			1.80981i	−0.425616	+	0.904904i	$0.639942\pi$
$912$	49.9663	−	438.888i	0.0547876	−	0.481237i
$913$	−61.4069	−	229.174i	−0.0672584	−	0.251012i
$914$	19.2386	−	33.3222i	0.0210488	−	0.0364575i
$915$	−444.779	−	780.711i	−0.486098	−	0.853236i
$916$			617.813i			0.674468i
$917$	−1098.53	+	515.634i	−1.19796	+	0.562305i
$918$	23.0770	−	65.2214i	0.0251383	−	0.0710473i
$919$	415.979	−	240.166i	0.452643	−	0.261334i	−0.256303	−	0.966597i	$-0.582504\pi$
$919$	415.979	−	240.166i	0.452643	−	0.261334i	0.708946	+	0.705263i	$0.249171\pi$
$920$	−23.8436	−	220.716i	−0.0259169	−	0.239909i
$921$	1052.09	+	414.324i	1.14233	+	0.449863i
$922$	23.1226	−	86.2948i	0.0250788	−	0.0935952i
$923$	596.084	+	596.084i	0.645811	+	0.645811i
$924$	842.797	−	957.638i	0.912118	−	1.03640i
$925$	200.583	+	388.102i	0.216847	+	0.419570i
$926$	−83.2173	+	48.0455i	−0.0898675	+	0.0518850i
$927$	−102.367	+	63.9910i	−0.110429	+	0.0690302i
$928$	53.1084	−	14.2304i	0.0572289	−	0.0153344i
$929$	−804.028	+	464.206i	−0.865477	+	0.499683i	−0.865842	−	0.500317i	$-0.833217\pi$
$929$	−804.028	+	464.206i	−0.865477	+	0.499683i	0.000365893		1.00000i	$0.499884\pi$
$930$	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
$933$	−75.7750	+	665.584i	−0.0812165	+	0.713380i
$934$	−21.7169	+	37.6148i	−0.0232515	+	0.0402728i
$935$	−910.454	−	732.923i	−0.973747	−	0.783875i
$936$	145.738	+	135.856i	0.155703	+	0.145145i
$937$	−723.582	−	723.582i	−0.772232	−	0.772232i	0.206264	−	0.978496i	$-0.433869\pi$
$937$	−723.582	−	723.582i	−0.772232	−	0.772232i	−0.978496	+	0.206264i	$0.933869\pi$
$938$	6.73469	−	79.2832i	0.00717984	−	0.0845236i
$939$	1170.02	−	174.964i	1.24603	−	0.186331i
$940$	209.081	−	80.9528i	0.222426	−	0.0861200i
$941$	−778.938	+	1349.16i	−0.827777	+	1.43375i	0.0720018	+	0.997405i	$0.477061\pi$
$941$	−778.938	+	1349.16i	−0.827777	+	1.43375i	−0.899779	+	0.436347i	$0.856272\pi$
$942$	23.8286	+	54.7891i	0.0252958	+	0.0581625i
$943$	−560.742	−	150.250i	−0.594636	−	0.159332i
$944$			80.1322i			0.0848858i
$945$	−704.197	+	630.184i	−0.745182	+	0.666861i
$946$	122.555			0.129551
$947$	361.534	−	1349.26i	0.381768	−	1.42478i	−0.461432	−	0.887176i	$-0.652664\pi$
$947$	361.534	−	1349.26i	0.381768	−	1.42478i	0.843199	−	0.537601i	$-0.180669\pi$
$948$	332.337	−	144.539i	0.350566	−	0.152467i
$949$	−1088.51	−	628.451i	−1.14701	−	0.662225i
$950$	−33.1655	−	21.2663i	−0.0349111	−	0.0223856i
$951$	−53.2121	−	355.839i	−0.0559539	−	0.374173i
$952$	−81.7185	+	117.336i	−0.0858388	+	0.123252i
$953$	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	$-0.0701513\pi$
$954$	−78.9335	+	84.6753i	−0.0827395	+	0.0887582i
$955$	167.366	+	1549.28i	0.175252	+	1.62228i
$956$	1063.12	+	613.793i	1.11205	+	0.642043i
$957$	314.424	+	35.7964i	0.328552	+	0.0374048i
$958$	−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
$962$	−12.5598	−	46.8737i	−0.0130559	−	0.0487252i
$963$	83.6910	+	133.882i	0.0869065	+	0.139026i
$964$	−304.787	−	527.907i	−0.316170	−	0.547622i
$965$	−152.563	+	981.604i	−0.158096	+	1.01721i
$966$	−114.674	−	23.0188i	−0.118710	−	0.0238290i
$967$	−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	$0.387859\pi$
$968$	−145.762	−	39.0569i	−0.150581	−	0.0403480i
$969$	−157.937	+	401.049i	−0.162990	+	0.413879i
$970$	−2.27232	−	21.0345i	−0.00234260	−	0.0216851i
$971$	−904.830	−	1567.21i	−0.931853	−	1.61402i	−0.780151	−	0.625591i	$-0.784858\pi$
$971$	−904.830	−	1567.21i	−0.931853	−	1.61402i	−0.151703	−	0.988426i	$-0.548476\pi$
$972$	41.6805	−	964.270i	0.0428812	−	0.992047i
$973$	30.5832	−	360.037i	0.0314319	−	0.370027i
$974$	91.5278			0.0939710
$975$	−1161.08	+	441.895i	−1.19085	+	0.453226i
$976$	−812.562	−	469.133i	−0.832543	−	0.480669i
$977$	817.894	−	219.154i	0.837148	−	0.224313i	0.185319	−	0.982678i	$-0.440668\pi$
$977$	817.894	−	219.154i	0.837148	−	0.224313i	0.651830	+	0.758365i	$0.274002\pi$
$978$	11.5106	+	1.31045i	0.0117696	+	0.00133993i
$979$	−587.712			−0.600319
$980$	871.214	−	433.517i	0.888994	−	0.442365i
$981$	−1442.86	+	441.400i	−1.47080	+	0.449949i
$982$	21.7841	+	5.83703i	0.0221834	+	0.00594402i
$983$	649.321	−	173.985i	0.660551	−	0.176994i	0.0870561	−	0.996203i	$-0.472254\pi$
$983$	649.321	−	173.985i	0.660551	−	0.176994i	0.573494	+	0.819209i	$0.305587\pi$
$984$	25.6715	−	65.1874i	0.0260889	−	0.0662474i
$985$	286.402	−	110.890i	0.290763	−	0.112579i
$986$	−17.6727			−0.0179237
$987$	−15.0916	−	236.601i	−0.0152903	−	0.239717i
$988$	−437.318	−	437.318i	−0.442630	−	0.442630i
$989$	793.971	+	1375.20i	0.802802	+	1.39049i
$990$	107.112	+	42.8945i	0.108194	+	0.0433278i
$991$	−372.392	+	645.003i	−0.375774	+	0.650860i	−0.990443	−	0.137925i	$-0.955957\pi$
$991$	−372.392	+	645.003i	−0.375774	+	0.650860i	0.614668	+	0.788786i	$0.289290\pi$
$992$	279.499	+	74.8914i	0.281753	+	0.0754954i
$993$	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
$996$	115.083	+	144.653i	0.115545	+	0.145234i
$997$	525.982	−	140.936i	0.527564	−	0.141360i	0.0148011	−	0.999890i	$-0.495288\pi$
$997$	525.982	−	140.936i	0.527564	−	0.141360i	0.512763	+	0.858530i	$0.328622\pi$
$998$	22.5248	+	84.0638i	0.0225700	+	0.0842323i
$999$	−267.141	+	388.910i	−0.267409	+	0.389300i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.13	✓	112	5.2	odd	4	inner
105.3.w.a.17.16	yes	112	15.2	even	4	inner
105.3.w.a.38.13	yes	112	1.1	even	1	trivial
105.3.w.a.38.16	yes	112	3.2	odd	2	inner
105.3.w.a.47.13	yes	112	105.47	odd	12	inner
105.3.w.a.47.16	yes	112	35.12	even	12	inner
105.3.w.a.68.13	yes	112	21.5	even	6	inner
105.3.w.a.68.16	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+(-0.0433902 + 0.161935i) q^{2} +(2.75108 - 1.19649i) q^{3} +(3.43976 + 1.98595i) q^{4} +(-2.02047 + 4.57359i) q^{5} +(0.0743827 + 0.497410i) q^{6} +(-0.592480 + 6.97488i) q^{7} +(-0.945023 + 0.945023i) q^{8} +(6.13684 - 6.58325i) q^{9} +(-0.652953 - 0.525633i) q^{10} +(-13.2452 - 7.64711i) q^{11} +(11.8392 + 1.34786i) 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} +(-3.95586 - 14.7635i) q^{17} +(0.799777 + 1.27942i) q^{18} +(-4.70012 - 8.14085i) q^{19} +(-16.0328 + 11.7195i) q^{20} +(6.71540 + 19.8973i) q^{21} +(1.81304 - 1.81304i) q^{22} +(32.0900 + 8.59850i) q^{23} +(-1.46912 + 3.73054i) q^{24} +(-16.8354 - 18.4816i) q^{25} +(1.38849 + 2.40493i) q^{26} +(9.00614 - 25.4537i) q^{27} +(-15.8897 + 22.8153i) q^{28} -6.89705 q^{29} +(-2.42524 - 0.664806i) q^{30} +(-31.4348 - 18.1489i) q^{31} +(-7.70017 + 2.06325i) q^{32} +(-45.5882 - 5.19010i) q^{33} +2.56236 q^{34} +(-30.7031 - 16.8023i) q^{35} +(34.1833 - 10.4574i) q^{36} +(-16.8794 - 4.52283i) q^{37} +(1.52222 - 0.407879i) q^{38} +(18.2086 - 46.2370i) q^{39} +(-2.41276 - 6.23153i) q^{40} -17.4740 q^{41} +(-3.51345 + 0.224105i) q^{42} +(33.7982 + 33.7982i) q^{43} +(-30.3735 - 52.6085i) q^{44} +(17.7098 + 41.3686i) q^{45} +(-2.78479 + 4.82340i) q^{46} +(-10.9049 - 2.92196i) q^{47} +(37.7761 + 27.9478i) q^{48} +(-48.2979 - 8.26495i) q^{49} +(3.72330 - 1.92431i) q^{50} +(-28.5471 - 35.8823i) q^{51} +(63.5502 - 17.0282i) q^{52} +(19.8572 + 74.1079i) q^{53} +(3.73105 + 2.56285i) q^{54} +(61.7362 - 45.1272i) q^{55} +(-6.03151 - 7.15133i) q^{56} +(-22.6708 - 16.7725i) q^{57} +(0.299265 - 1.11687i) q^{58} +(4.43046 + 2.55793i) q^{59} +(-30.0853 + 51.4243i) q^{60} +(-51.8761 + 29.9507i) q^{61} +(4.30289 - 4.30289i) q^{62} +(42.2814 + 46.7042i) q^{63} +61.3176i q^{64} +(29.9042 + 77.2349i) q^{65} +(2.81854 - 7.15710i) q^{66} +(17.5487 + 65.4926i) q^{67} +(15.7122 - 58.6389i) q^{68} +(98.5701 - 14.7402i) q^{69} +(4.05309 - 4.24284i) q^{70} +50.8917i q^{71} +(0.421870 + 12.0208i) q^{72} +(-19.6391 - 73.2942i) q^{73} +(1.46480 - 2.53712i) q^{74} +(-68.4285 - 30.7009i) q^{75} -37.3368i q^{76} +(61.1852 - 87.8528i) q^{77} +(6.69729 + 4.95483i) q^{78} +(26.3396 - 15.2072i) q^{79} +(-77.8646 + 8.41157i) q^{80} +(-5.67841 - 80.8007i) q^{81} +(0.758201 - 2.82965i) q^{82} +(10.9693 + 10.9693i) q^{83} +(-16.4157 + 81.7785i) q^{84} +(75.5146 + 11.7367i) q^{85} +(-6.93960 + 4.00658i) q^{86} +(-18.9743 + 8.25223i) q^{87} +(19.7437 - 5.29031i) 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} +(-108.194 - 12.3176i) q^{93} +(0.946333 - 1.63910i) q^{94} +(46.7294 - 5.04808i) q^{95} +(-18.7151 + 14.8893i) q^{96} +(17.8473 + 17.8473i) q^{97} +(3.43404 - 7.46249i) 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

Introduction

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