LMFDB - Embedded newform 105.3.w.a.47.16

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			47.16
Character	$\chi$	$=$	105.47
Dual form			105.3.w.a.38.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0433902 + 0.161935i) q^{2} +(-2.98075 - 0.339350i) 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} +(8.76968 + 2.02303i) q^{9} +(-0.652953 + 0.525633i) q^{10} +(13.2452 - 7.64711i) q^{11} +(-10.9270 + 4.75232i) q^{12} +(11.7128 + 11.7128i) q^{13} +(1.10377 - 0.398585i) q^{14} +(-4.47046 - 14.3183i) q^{15} +(7.83176 - 13.5650i) q^{16} +(3.95586 - 14.7635i) q^{17} +(0.0529196 + 1.50789i) 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} +(-32.0900 + 8.59850i) q^{23} +(-2.49618 - 3.13757i) q^{24} +(-16.8354 + 18.4816i) q^{25} +(-1.38849 + 2.40493i) q^{26} +(-25.4537 - 9.00614i) q^{27} +(-15.8897 - 22.8153i) q^{28} +6.89705 q^{29} +(2.12466 - 1.34520i) q^{30} +(-31.4348 + 18.1489i) q^{31} +(7.70017 + 2.06325i) q^{32} +(-42.0756 + 18.2993i) 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} +(-30.9381 - 38.8876i) q^{39} +(-2.41276 + 6.23153i) q^{40} +17.4740 q^{41} +(-3.42531 + 0.813516i) q^{42} +(33.7982 - 33.7982i) q^{43} +(30.3735 - 52.6085i) q^{44} +(8.46636 + 44.1964i) q^{45} +(-2.78479 - 4.82340i) q^{46} +(10.9049 - 2.92196i) q^{47} +(-27.9478 + 37.7761i) q^{48} +(-48.2979 + 8.26495i) q^{49} +(-3.72330 - 1.92431i) q^{50} +(-16.8014 + 42.6637i) q^{51} +(63.5502 + 17.0282i) q^{52} +(-19.8572 + 74.1079i) q^{53} +(0.353964 - 4.51261i) q^{54} +(61.7362 + 45.1272i) q^{55} +(6.03151 - 7.15133i) q^{56} +(16.7725 - 22.6708i) q^{57} +(0.299265 + 1.11687i) q^{58} +(-4.43046 + 2.55793i) q^{59} +(-43.8128 - 40.3736i) q^{60} +(-51.8761 - 29.9507i) q^{61} +(-4.30289 - 4.30289i) q^{62} +(8.91455 - 62.3661i) q^{63} -61.3176i q^{64} +(-29.9042 + 77.2349i) q^{65} +(-4.78896 - 6.01947i) 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} +(6.37574 + 10.1994i) q^{72} +(-19.6391 + 73.2942i) q^{73} +(-1.46480 - 2.53712i) q^{74} +(56.4538 - 49.3758i) q^{75} +37.3368i q^{76} +(-61.1852 - 87.8528i) q^{77} +(4.95483 - 6.69729i) q^{78} +(26.3396 + 15.2072i) q^{79} +(77.8646 + 8.41157i) q^{80} +(72.8147 + 35.4827i) q^{81} +(0.758201 + 2.82965i) 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} +(-20.5584 - 2.34052i) q^{87} +(19.7437 + 5.29031i) q^{88} +(-33.2788 - 19.2135i) q^{89} +(-6.78956 + 3.28869i) q^{90} +(74.7558 - 88.6350i) q^{91} +(-93.3059 + 93.3059i) q^{92} +(99.8579 - 43.4298i) q^{93} +(0.946333 + 1.63910i) q^{94} +(-46.7294 - 5.04808i) q^{95} +(-22.2521 - 8.76308i) 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.0433902	+	0.161935i	0.0216951	+	0.0809673i	0.975925	−	0.218108i	$-0.0699885\pi$
$2$	0.0433902	+	0.161935i	0.0216951	+	0.0809673i	−0.954230	+	0.299075i	$0.903322\pi$
$3$	−2.98075	−	0.339350i	−0.993582	−	0.113117i
$3$	−2.98075	−	0.339350i	−0.993582	−	0.113117i
$4$	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
$9$	8.76968	+	2.02303i	0.974409	+	0.224781i
$10$	−0.652953	+	0.525633i	−0.0652953	+	0.0525633i
$11$	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	$0.0886528\pi$
$12$	−10.9270	+	4.75232i	−0.910582	+	0.396027i
$13$	11.7128	+	11.7128i	0.900984	+	0.900984i	0.995521	−	0.0945369i	$-0.0301370\pi$
$13$	11.7128	+	11.7128i	0.900984	+	0.900984i	−0.0945369	+	0.995521i	$0.530137\pi$
$14$	1.10377	−	0.398585i	0.0788405	−	0.0284703i
$15$	−4.47046	−	14.3183i	−0.298030	−	0.954556i
$16$	7.83176	−	13.5650i	0.489485	−	0.847813i
$17$	3.95586	−	14.7635i	0.232697	−	0.868439i	−0.746476	−	0.665412i	$-0.768256\pi$
$17$	3.95586	−	14.7635i	0.232697	−	0.868439i	0.979173	−	0.203026i	$-0.0650776\pi$
$18$	0.0529196	+	1.50789i	0.00293998	+	0.0837719i
$19$	−4.70012	+	8.14085i	−0.247375	+	0.428466i	−0.962797	−	0.270227i	$-0.912901\pi$
$19$	−4.70012	+	8.14085i	−0.247375	+	0.428466i	0.715422	+	0.698693i	$0.246235\pi$
$20$	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
$23$	−32.0900	+	8.59850i	−1.39522	+	0.373848i	−0.876626	−	0.481173i	$-0.840211\pi$
$23$	−32.0900	+	8.59850i	−1.39522	+	0.373848i	−0.518594	+	0.855021i	$0.673544\pi$
$24$	−2.49618	−	3.13757i	−0.104007	−	0.130732i
$25$	−16.8354	+	18.4816i	−0.673416	+	0.739263i
$26$	−1.38849	+	2.40493i	−0.0534033	+	0.0924972i
$27$	−25.4537	−	9.00614i	−0.942729	−	0.333561i
$28$	−15.8897	−	22.8153i	−0.567491	−	0.814832i
$29$	6.89705			0.237829			0.118915	−	0.992904i	$-0.462059\pi$
$29$	6.89705			0.237829			0.118915	+	0.992904i	$0.462059\pi$
$30$	2.12466	−	1.34520i	0.0708220	−	0.0448399i
$31$	−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	$0.532414\pi$
$32$	7.70017	+	2.06325i	0.240630	+	0.0644767i
$33$	−42.0756	+	18.2993i	−1.27502	+	0.554525i
$34$	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	−0.479599	−	0.877488i	$-0.659218\pi$
$37$	−16.8794	+	4.52283i	−0.456201	+	0.122239i	0.0233986	+	0.999726i	$0.492551\pi$
$38$	−1.52222	−	0.407879i	−0.0400585	−	0.0107337i
$39$	−30.9381	−	38.8876i	−0.793285	−	0.997118i
$40$	−2.41276	+	6.23153i	−0.0603189	+	0.155788i
$41$	17.4740			0.426195			0.213098	−	0.977031i	$-0.431645\pi$
$41$	17.4740			0.426195			0.213098	+	0.977031i	$0.431645\pi$
$42$	−3.42531	+	0.813516i	−0.0815549	+	0.0193694i
$43$	33.7982	−	33.7982i	0.786004	−	0.786004i	−0.194832	−	0.980837i	$-0.562416\pi$
$43$	33.7982	−	33.7982i	0.786004	−	0.786004i	0.980837	+	0.194832i	$0.0624163\pi$
$44$	30.3735	−	52.6085i	0.690307	−	1.19565i
$45$	8.46636	+	44.1964i	0.188141	+	0.982142i
$46$	−2.78479	−	4.82340i	−0.0605389	−	0.104856i
$47$	10.9049	−	2.92196i	0.232019	−	0.0621694i	−0.140936	−	0.990019i	$-0.545011\pi$
$47$	10.9049	−	2.92196i	0.232019	−	0.0621694i	0.372955	+	0.927849i	$0.378344\pi$
$48$	−27.9478	+	37.7761i	−0.582245	+	0.787003i
$49$	−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
$52$	63.5502	+	17.0282i	1.22212	+	0.327466i
$53$	−19.8572	+	74.1079i	−0.374663	+	1.39826i	0.479173	+	0.877721i	$0.340937\pi$
$53$	−19.8572	+	74.1079i	−0.374663	+	1.39826i	−0.853836	+	0.520542i	$0.825730\pi$
$54$	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
$57$	16.7725	−	22.6708i	0.294254	−	0.397734i
$58$	0.299265	+	1.11687i	0.00515974	+	0.0192564i
$59$	−4.43046	+	2.55793i	−0.0750925	+	0.0433547i	−0.537076	−	0.843534i	$-0.680471\pi$
$59$	−4.43046	+	2.55793i	−0.0750925	+	0.0433547i	0.461984	+	0.886888i	$0.347138\pi$
$60$	−43.8128	−	40.3736i	−0.730213	−	0.672893i
$61$	−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
$63$	8.91455	−	62.3661i	0.141501	−	0.989938i
$64$		−	61.3176i		−	0.958088i
$65$	−29.9042	+	77.2349i	−0.460064	+	1.18823i
$66$	−4.78896	−	6.01947i	−0.0725600	−	0.0912041i
$67$	17.5487	−	65.4926i	0.261921	−	0.977502i	−0.702187	−	0.711992i	$-0.747793\pi$
$67$	17.5487	−	65.4926i	0.261921	−	0.977502i	0.964108	−	0.265510i	$-0.0855402\pi$
$68$	−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	$0.883325\pi$
$72$	6.37574	+	10.1994i	0.0885519	+	0.141658i
$73$	−19.6391	+	73.2942i	−0.269029	+	1.00403i	0.690709	+	0.723133i	$0.257299\pi$
$73$	−19.6391	+	73.2942i	−0.269029	+	1.00403i	−0.959738	+	0.280897i	$0.909368\pi$
$74$	−1.46480	−	2.53712i	−0.0197947	−	0.0342854i
$75$	56.4538	−	49.3758i	0.752717	−	0.658344i
$76$			37.3368i			0.491274i
$77$	−61.1852	−	87.8528i	−0.794613	−	1.14095i
$78$	4.95483	−	6.69729i	0.0635235	−	0.0858627i
$79$	26.3396	+	15.2072i	0.333412	+	0.192496i	0.657355	−	0.753581i	$-0.271675\pi$
$79$	26.3396	+	15.2072i	0.333412	+	0.192496i	−0.323943	+	0.946077i	$0.605009\pi$
$80$	77.8646	+	8.41157i	0.973307	+	0.105145i
$81$	72.8147	+	35.4827i	0.898947	+	0.438058i
$82$	0.758201	+	2.82965i	0.00924636	+	0.0345079i
$83$	−10.9693	+	10.9693i	−0.132160	+	0.132160i	−0.770092	−	0.637932i	$-0.779790\pi$
$83$	−10.9693	+	10.9693i	−0.132160	+	0.132160i	0.637932	+	0.770092i	$0.279790\pi$
$84$	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
$87$	−20.5584	−	2.34052i	−0.236303	−	0.0269025i
$88$	19.7437	+	5.29031i	0.224360	+	0.0601171i
$89$	−33.2788	−	19.2135i	−0.373919	−	0.215882i	0.301250	−	0.953545i	$-0.402596\pi$
$89$	−33.2788	−	19.2135i	−0.373919	−	0.215882i	−0.675169	+	0.737663i	$0.735929\pi$
$90$	−6.78956	+	3.28869i	−0.0754396	+	0.0365410i
$91$	74.7558	−	88.6350i	0.821492	−	0.974011i
$92$	−93.3059	+	93.3059i	−1.01419	+	1.01419i
$93$	99.8579	−	43.4298i	1.07374	−	0.466987i
$94$	0.946333	+	1.63910i	0.0100674	+	0.0174372i
$95$	−46.7294	−	5.04808i	−0.491888	−	0.0531377i
$96$	−22.2521	−	8.76308i	−0.231792	−	0.0912821i
$97$	17.8473	−	17.8473i	0.183992	−	0.183992i	−0.609101	−	0.793093i	$-0.708469\pi$
$97$	17.8473	−	17.8473i	0.183992	−	0.183992i	0.793093	+	0.609101i	$0.208469\pi$
$98$	−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	−0.995559	−	0.0941439i	$-0.969989\pi$
$101$	−58.5103	−	101.343i	−0.579310	−	1.00339i	0.416248	−	0.909251i	$-0.363345\pi$
$102$	−7.63774	−	0.869537i	−0.0748798	−	0.00852487i
$103$	−12.9566	+	3.47170i	−0.125792	+	0.0337058i	−0.321166	−	0.947023i	$-0.604075\pi$
$103$	−12.9566	+	3.47170i	−0.125792	+	0.0337058i	0.195374	+	0.980729i	$0.437408\pi$
$104$			22.1377i			0.212863i
$105$	−97.2201	+	39.6642i	−0.925906	+	0.377755i
$106$	−12.8622			−0.121342
$107$	4.54048	+	16.9453i	0.0424344	+	0.158367i	0.983892	−	0.178764i	$-0.0572100\pi$
$107$	4.54048	+	16.9453i	0.0424344	+	0.158367i	−0.941458	+	0.337132i	$0.890543\pi$
$108$	−105.440	+	19.5707i	−0.976299	+	0.181210i
$109$	−145.191	+	83.8258i	−1.33202	+	0.769044i	−0.985610	−	0.169038i	$-0.945934\pi$
$109$	−145.191	+	83.8258i	−1.33202	+	0.769044i	−0.346414	+	0.938082i	$0.612601\pi$
$110$	−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	$-0.299149\pi$
$113$	−24.5772	−	24.5772i	−0.217497	−	0.217497i	−0.807443	+	0.589946i	$0.799149\pi$
$114$	4.39895	+	1.73235i	0.0385873	+	0.0151961i
$115$	−104.163	−	129.394i	−0.905765	−	1.12516i
$116$	23.7242	−	13.6972i	0.204519	−	0.118079i
$117$	79.0221	+	126.413i	0.675403	+	1.08045i
$118$	−0.606455	−	0.606455i	−0.00513945	−	0.00513945i
$119$	−105.317	−	18.8446i	−0.885018	−	0.158358i
$120$	9.30648	−	17.7558i	0.0775540	−	0.147965i
$121$	56.4565	−	97.7856i	0.466583	−	0.808145i
$122$	2.59913	−	9.70009i	0.0213044	−	0.0795090i
$123$	−52.0856	−	5.92981i	−0.423460	−	0.0482098i
$124$	−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	0.671972	−	0.740577i	$-0.265448\pi$
$127$	−8.71278	−	8.71278i	−0.0686046	−	0.0686046i	−0.740577	+	0.671972i	$0.765448\pi$
$128$	40.7301	−	10.9136i	0.318204	−	0.0852625i
$129$	−112.213	+	89.2743i	−0.869870	+	0.692049i
$130$	−13.8045	−	1.49128i	−0.106189	−	0.0114714i
$131$	−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	$0.936509\pi$
$132$	−108.388	+	146.505i	−0.821124	+	1.10989i
$133$	59.5662	+	27.9595i	0.447866	+	0.210222i
$134$	11.3670			0.0848280
$135$	−10.2380	−	134.611i	−0.0758370	−	0.997120i
$136$	17.6902	−	10.2134i	0.130075	−	0.0750987i
$137$	137.450	+	36.8296i	1.00328	+	0.268829i	0.722820	−	0.691036i	$-0.242845\pi$
$137$	137.450	+	36.8296i	1.00328	+	0.268829i	0.280463	+	0.959865i	$0.409512\pi$
$138$	6.66393	+	15.3223i	0.0482893	+	0.111031i
$139$	−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
$144$	96.1245	−	103.117i	0.667531	−	0.716090i
$145$	13.9353	+	31.5443i	0.0961054	+	0.217547i
$146$	−12.7210			−0.0871302
$147$	146.769	−	8.24580i	0.998425	−	0.0560939i
$148$	−49.0791	+	49.0791i	−0.331616	+	0.331616i
$149$	−35.1442	+	60.8716i	−0.235867	+	0.408534i	−0.959524	−	0.281625i	$-0.909126\pi$
$149$	−35.1442	+	60.8716i	−0.235867	+	0.408534i	0.723657	+	0.690160i	$0.242460\pi$
$150$	10.4452	+	6.99939i	0.0696346	+	0.0466626i
$151$	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	$0.721892\pi$
$152$	−12.1350	+	3.25157i	−0.0798356	+	0.0213919i
$153$	64.5586	−	121.468i	0.421951	−	0.793908i
$154$	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
$157$	114.747	+	30.7462i	0.730869	+	0.195836i	0.605016	−	0.796213i	$-0.293167\pi$
$157$	114.747	+	30.7462i	0.730869	+	0.195836i	0.125853	+	0.992049i	$0.459833\pi$
$158$	−1.31968	+	4.92513i	−0.00835243	+	0.0311717i
$159$	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
$162$	−2.58643	+	13.3308i	−0.0159656	+	0.0822890i
$163$	5.96176	+	22.2496i	0.0365752	+	0.136501i	0.981799	−	0.189922i	$-0.0608235\pi$
$163$	5.96176	+	22.2496i	0.0365752	+	0.136501i	−0.945224	+	0.326422i	$0.894157\pi$
$164$	60.1064	−	34.7025i	0.366503	−	0.211600i
$165$	−168.706	−	155.463i	−1.02246	−	0.942200i
$166$	−2.25227	−	1.30035i	−0.0135679	−	0.00783342i
$167$	55.5957	+	55.5957i	0.332908	+	0.332908i	0.853690	−	0.520782i	$-0.174359\pi$
$167$	55.5957	+	55.5957i	0.332908	+	0.332908i	−0.520782	+	0.853690i	$0.674359\pi$
$168$	−20.4052	+	19.2695i	−0.121460	+	0.114699i
$169$			105.379i			0.623546i
$170$	5.17717	+	11.7192i	0.0304539	+	0.0689363i
$171$	−57.6878	+	61.8842i	−0.337356	+	0.361896i
$172$	49.1363	−	183.379i	0.285676	−	1.06616i
$173$	−52.0348	−	194.196i	−0.300779	−	1.12252i	−0.936518	−	0.350619i	$-0.885971\pi$
$173$	−52.0348	−	194.196i	−0.300779	−	1.12252i	0.635739	−	0.771904i	$-0.280695\pi$
$174$	−0.513021	−	3.43066i	−0.00294840	−	0.0197165i
$175$	138.882	+	106.475i	0.793609	+	0.608429i
$176$		−	239.561i		−	1.36114i
$177$	14.0741	−	6.12105i	0.0795147	−	0.0345822i
$178$	1.66736	−	6.22267i	0.00936719	−	0.0349588i
$179$	167.017	+	289.281i	0.933053	+	1.61610i	0.778069	+	0.628179i	$0.216199\pi$
$179$	167.017	+	289.281i	0.933053	+	1.61610i	0.154984	+	0.987917i	$0.450467\pi$
$180$	116.894	+	135.211i	0.649411	+	0.751174i
$181$		−	200.663i		−	1.10864i	−0.832304	−	0.554319i	$-0.812979\pi$
$181$		−	200.663i		−	1.10864i	0.832304	−	0.554319i	$-0.187021\pi$
$182$	17.5967	+	8.25965i	0.0966853	+	0.0453827i
$183$	144.466	+	106.879i	0.789429	+	0.584041i
$184$	−38.4516	−	22.2000i	−0.208976	−	0.120652i
$185$	−54.7899	−	68.0613i	−0.296162	−	0.367899i
$186$	11.3656	+	14.2860i	0.0611056	+	0.0768065i
$187$	−60.5017	−	225.795i	−0.323539	−	1.20746i
$188$	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	$0.970403\pi$
$192$	−20.8082	+	182.772i	−0.108376	+	0.951939i
$193$	191.908	+	51.4216i	0.994342	+	0.266433i	0.719073	−	0.694934i	$-0.244567\pi$
$193$	191.908	+	51.4216i	0.994342	+	0.266433i	0.275269	+	0.961367i	$0.411233\pi$
$194$	3.66449	+	2.11569i	0.0188891	+	0.0109056i
$195$	115.346	−	220.069i	0.591520	−	1.12856i
$196$	−149.720	+	124.347i	−0.763876	+	0.634422i
$197$	43.4334	−	43.4334i	0.220474	−	0.220474i	−0.588224	−	0.808698i	$-0.700173\pi$
$197$	43.4334	−	43.4334i	0.220474	−	0.220474i	0.808698	+	0.588224i	$0.200173\pi$
$198$	12.2320	+	19.5677i	0.0617776	+	0.0988265i
$199$	−110.179	−	190.836i	−0.553666	−	0.958977i	−0.998006	−	0.0631192i	$-0.979895\pi$
$199$	−110.179	−	190.836i	−0.553666	−	0.958977i	0.444340	−	0.895858i	$-0.353438\pi$
$200$	−33.3754	+	1.55568i	−0.166877	+	0.00777838i
$201$	−74.5331	+	189.262i	−0.370811	+	0.941600i
$202$	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
$207$	−298.815	+	10.4869i	−1.44355	+	0.0506614i
$208$	250.616	−	67.1524i	1.20488	−	0.322848i
$209$			143.769i			0.687892i
$210$	−10.6414	−	14.0223i	−0.0506734	−	0.0667726i
$211$	−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
$213$	17.2701	−	151.695i	0.0810802	−	0.712183i
$214$	−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
$219$	83.4117	−	211.807i	0.380875	−	0.967155i
$220$	301.978	+	32.6221i	1.37263	+	0.148282i
$221$	219.256	−	126.587i	0.992106	−	0.572793i
$222$	3.50524	+	8.05958i	0.0157894	+	0.0363044i
$223$	−129.563	−	129.563i	−0.581002	−	0.581002i	0.354177	−	0.935179i	$-0.384761\pi$
$223$	−129.563	−	129.563i	−0.581002	−	0.581002i	−0.935179	+	0.354177i	$0.884761\pi$
$224$	9.82875	−	54.9302i	0.0438784	−	0.245224i
$225$	−185.030	+	128.019i	−0.822356	+	0.568974i
$226$	2.91348	−	5.04630i	0.0128915	−	0.0223288i
$227$	28.2785	−	105.537i	0.124575	−	0.464920i	−0.875249	−	0.483672i	$-0.839303\pi$
$227$	28.2785	−	105.537i	0.124575	−	0.464920i	0.999824	+	0.0187523i	$0.00596938\pi$
$228$	12.6702	−	111.291i	0.0555713	−	0.488120i
$229$	77.7730	−	134.707i	0.339620	−	0.588239i	−0.644741	−	0.764401i	$-0.723035\pi$
$229$	77.7730	−	134.707i	0.339620	−	0.588239i	0.984361	+	0.176162i	$0.0563681\pi$
$230$	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
$233$	349.029	−	93.5221i	1.49798	−	0.401382i	0.585557	−	0.810632i	$-0.300876\pi$
$233$	349.029	−	93.5221i	1.49798	−	0.401382i	0.912423	+	0.409249i	$0.134209\pi$
$234$	−17.0418	+	18.2815i	−0.0728283	+	0.0781261i
$235$	35.3969	+	43.9708i	0.150625	+	0.187110i
$236$	−10.1598	+	17.5973i	−0.0430500	+	0.0745649i
$237$	−73.3510	−	54.2670i	−0.309498	−	0.228975i
$238$	−1.51815	−	17.8721i	−0.00637876	−	0.0750931i
$239$	−309.068			−1.29317			−0.646586	−	0.762841i	$-0.723804\pi$
$239$	−309.068			−1.29317			−0.646586	+	0.762841i	$0.723804\pi$
$240$	−229.240	−	51.4961i	−0.955167	−	0.214567i
$241$	−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	$0.436481\pi$
$242$	18.2845	+	4.89932i	0.0755559	+	0.0202451i
$243$	−205.001	−	130.475i	−0.843625	−	0.536933i
$244$	−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
$249$	36.4191	−	28.9742i	0.146261	−	0.116362i
$250$	1.27821	−	20.9169i	0.00511283	−	0.0836674i
$251$	188.250			0.750001			0.375001	−	0.927025i	$-0.377643\pi$
$251$	188.250			0.750001			0.375001	+	0.927025i	$0.377643\pi$
$252$	−93.1918	−	232.228i	−0.369809	−	0.921541i
$253$	−359.285	+	359.285i	−1.42010	+	1.42010i
$254$	1.03285	−	1.78895i	0.00406634	−	0.00704311i
$255$	−229.073	+	9.35806i	−0.898324	+	0.0366983i
$256$	−119.101	−	206.288i	−0.465237	−	0.805814i
$257$	177.882	−	47.6632i	0.692146	−	0.185460i	0.104436	−	0.994532i	$-0.466696\pi$
$257$	177.882	−	47.6632i	0.692146	−	0.185460i	0.587710	+	0.809072i	$0.300030\pi$
$258$	−19.3256	−	14.2976i	−0.0749053	−	0.0554169i
$259$	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
$262$	−28.0731	−	7.52217i	−0.107149	−	0.0287106i
$263$	−71.4527	+	266.665i	−0.271683	+	1.01394i	0.686348	+	0.727273i	$0.259213\pi$
$263$	−71.4527	+	266.665i	−0.271683	+	1.01394i	−0.958031	+	0.286663i	$0.907454\pi$
$264$	−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
$267$	92.6756	+	68.5638i	0.347100	+	0.256793i
$268$	−69.7016	−	260.130i	−0.260080	−	0.970633i
$269$	441.194	−	254.723i	1.64012	−	0.946926i	0.659337	−	0.751848i	$-0.270837\pi$
$269$	441.194	−	254.723i	1.64012	−	0.946926i	0.980788	−	0.195079i	$-0.0624963\pi$
$270$	21.3540	−	7.49870i	0.0790888	−	0.0277730i
$271$	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
$273$	−252.906	+	238.830i	−0.926396	+	0.874835i
$274$			23.8559i			0.0870654i
$275$	−81.6573	+	373.534i	−0.296936	+	1.35831i
$276$	309.785	−	246.458i	1.12241	−	0.892963i
$277$	−77.5629	+	289.469i	−0.280011	+	1.04501i	0.672398	+	0.740190i	$0.265264\pi$
$277$	−77.5629	+	289.469i	−0.280011	+	1.04501i	−0.952409	+	0.304824i	$0.901402\pi$
$278$	−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	$-0.0264637\pi$
$282$	−2.26455	−	5.20687i	−0.00803032	−	0.0184641i
$283$	30.3772	−	113.369i	0.107340	−	0.400598i	−0.891260	−	0.453492i	$-0.850178\pi$
$283$	30.3772	−	113.369i	0.107340	−	0.400598i	0.998600	+	0.0528940i	$0.0168446\pi$
$284$	101.068	+	175.055i	0.355874	+	0.616391i
$285$	137.575	+	30.9047i	0.482720	+	0.108437i
$286$			42.4716i			0.148502i
$287$	−10.3530	−	121.879i	−0.0360732	−	0.424666i
$288$	63.3540	+	33.6718i	0.219979	+	0.116916i
$289$	47.9705	+	27.6958i	0.165988	+	0.0958332i
$290$	−4.50345	+	3.62532i	−0.0155291	+	0.0125011i
$291$	−59.2546	+	47.1417i	−0.203624	+	0.161999i
$292$	78.0046	+	291.117i	0.267139	+	0.996976i
$293$	−197.170	+	197.170i	−0.672934	+	0.672934i	−0.958391	−	0.285458i	$-0.907854\pi$
$293$	−197.170	+	197.170i	−0.672934	+	0.672934i	0.285458	+	0.958391i	$0.407854\pi$
$294$	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
$297$	−406.009	+	75.3591i	−1.36704	+	0.253734i
$298$	−11.3821	−	3.04983i	−0.0381951	−	0.0102343i
$299$	−476.577	−	275.152i	−1.59390	−	0.920240i
$300$	96.1299	−	281.955i	0.320433	−	0.939851i
$301$	−255.763	−	215.714i	−0.849711	−	0.716656i
$302$	−12.2794	+	12.2794i	−0.0406602	+	0.0406602i
$303$	140.014	+	321.933i	0.462091	+	1.06248i
$304$	73.6205	+	127.514i	0.242173	+	0.419455i
$305$	32.1680	−	297.774i	0.105469	−	0.976309i
$306$	22.4711	+	5.18374i	0.0734349	+	0.0169403i
$307$	266.516	−	266.516i	0.868131	−	0.868131i	−0.124134	−	0.992265i	$-0.539615\pi$
$307$	266.516	−	266.516i	0.868131	−	0.868131i	0.992265	+	0.124134i	$0.0396153\pi$
$308$	−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	$-0.0497864\pi$
$311$	111.647	+	193.379i	0.358994	+	0.621796i	−0.628799	+	0.777568i	$0.716453\pi$
$312$	7.51244	−	65.9869i	0.0240783	−	0.211496i
$313$	380.906	−	102.063i	1.21695	−	0.326081i	0.407465	−	0.913221i	$-0.366413\pi$
$313$	380.906	−	102.063i	1.21695	−	0.326081i	0.809486	+	0.587140i	$0.199746\pi$
$314$			19.9155i			0.0634252i
$315$	303.248	−	85.2373i	0.962693	−	0.270595i
$316$	120.802			0.382286
$317$	−31.0406	−	115.845i	−0.0979200	−	0.365442i	0.899526	−	0.436867i	$-0.143912\pi$
$317$	−31.0406	−	115.845i	−0.0979200	−	0.365442i	−0.997446	+	0.0714248i	$0.977245\pi$
$318$	38.3391	+	4.36480i	0.120563	+	0.0137258i
$319$	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
$324$	320.932	−	22.5540i	0.990531	−	0.0696112i
$325$	−413.661	+	19.2813i	−1.27280	+	0.0593272i
$326$	−3.34430	+	1.93083i	−0.0102586	+	0.00592279i
$327$	461.222	−	200.593i	1.41047	−	0.613434i
$328$	16.5133	+	16.5133i	0.0503455	+	0.0503455i
$329$	−26.8413	−	74.3292i	−0.0815844	−	0.225925i
$330$	17.8546	−	34.0649i	0.0541050	−	0.103227i
$331$	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	$0.0484363\pi$
$332$	−15.9473	+	59.5162i	−0.0480341	+	0.179266i
$333$	−157.177	+	5.51614i	−0.472003	+	0.0165650i
$334$	−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	0.424741	−	0.905315i	$-0.360365\pi$
$337$	−161.954	−	161.954i	−0.480574	−	0.480574i	−0.905315	+	0.424741i	$0.860365\pi$
$338$	−17.0645	+	4.57243i	−0.0504868	+	0.0135279i
$339$	64.9180	+	81.5985i	0.191499	+	0.240704i
$340$	236.444	−	190.339i	0.695424	−	0.559822i
$341$	−277.573	+	480.770i	−0.813996	+	1.40988i
$342$	−12.5243	−	6.65648i	−0.0366207	−	0.0194634i
$343$	86.2626	+	331.976i	0.251495	+	0.967859i
$344$	63.8801			0.185698
$345$	266.573	+	421.037i	0.772677	+	1.22040i
$346$	29.1893	−	16.8525i	0.0843622	−	0.0487065i
$347$	−651.282	−	174.511i	−1.87689	−	0.502912i	−0.999742	−	0.0226990i	$-0.992774\pi$
$347$	−651.282	−	174.511i	−1.87689	−	0.502912i	−0.877152	−	0.480213i	$-0.840559\pi$
$348$	−75.3640	+	32.7770i	−0.216563	+	0.0941867i
$349$	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	$-0.575092\pi$
$353$	−325.569	−	87.2361i	−0.922293	−	0.247128i	−0.688565	+	0.725174i	$0.741759\pi$
$354$	1.60189	+	2.01349i	0.00452510	+	0.00568782i
$355$	−232.757	+	102.825i	−0.655655	+	0.289648i
$356$	−152.628			−0.428731
$357$	307.529	+	91.9103i	0.861425	+	0.257452i
$358$	−39.5977	+	39.5977i	−0.110608	+	0.110608i
$359$	153.677	−	266.177i	0.428070	−	0.741439i	−0.568631	−	0.822592i	$-0.692527\pi$
$359$	153.677	−	266.177i	0.428070	−	0.741439i	0.996702	+	0.0811531i	$0.0258603\pi$
$360$	−33.7657	+	49.7675i	−0.0937936	+	0.138243i
$361$	136.318	+	236.109i	0.377611	+	0.654042i
$362$	32.4943	−	8.70683i	0.0897634	−	0.0240520i
$363$	−201.466	+	272.315i	−0.555003	+	0.750180i
$364$	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
$367$	−92.7994	−	24.8655i	−0.252859	−	0.0677535i	0.130163	−	0.991493i	$-0.458450\pi$
$367$	−92.7994	−	24.8655i	−0.252859	−	0.0677535i	−0.383022	+	0.923739i	$0.625117\pi$
$368$	−134.683	+	502.643i	−0.365986	+	1.36588i
$369$	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
$372$	257.238	−	347.700i	0.691500	−	0.934679i
$373$	−7.69678	−	28.7248i	−0.0206348	−	0.0770101i	0.954841	−	0.297118i	$-0.0960256\pi$
$373$	−7.69678	−	28.7248i	−0.0206348	−	0.0770101i	−0.975475	+	0.220108i	$0.929359\pi$
$374$	33.9389	−	19.5946i	0.0907457	−	0.0523921i
$375$	339.888	+	158.434i	0.906367	+	0.422491i
$376$	13.0667	+	7.54407i	0.0347519	+	0.0200640i
$377$	80.7838	+	80.7838i	0.214281	+	0.214281i
$378$	−31.6846	+	0.204770i	−0.0838217	+	0.000541719i
$379$		−	227.162i		−	0.599373i	−0.954038	−	0.299686i	$-0.903118\pi$
$379$		−	227.162i		−	0.599373i	0.954038	−	0.299686i	$-0.0968821\pi$
$380$	−170.763	+	75.4378i	−0.449376	+	0.198521i
$381$	23.0139	+	28.9273i	0.0604039	+	0.0759246i
$382$	13.5230	−	50.4683i	0.0354004	−	0.132116i
$383$	14.1699	+	52.8830i	0.0369973	+	0.138076i	0.981954	−	0.189119i	$-0.0605633\pi$
$383$	14.1699	+	52.8830i	0.0369973	+	0.138076i	−0.944957	+	0.327195i	$0.893897\pi$
$384$	−125.110	+	18.7089i	−0.325806	+	0.0487211i
$385$	278.180	−	457.340i	0.722545	−	1.18790i
$386$			33.3077i			0.0862895i
$387$	364.774	−	228.024i	0.942569	−	0.589211i
$388$	25.9466	−	96.8340i	0.0668727	−	0.249572i
$389$	104.326	+	180.698i	0.268190	+	0.464519i	0.968394	−	0.249424i	$-0.0802411\pi$
$389$	104.326	+	180.698i	0.268190	+	0.464519i	−0.700204	+	0.713942i	$0.746908\pi$
$390$	40.6417	+	9.12969i	0.104210	+	0.0234095i
$391$			507.774i			1.29866i
$392$	−53.4532	−	37.8321i	−0.136360	−	0.0965104i
$393$	309.321	−	418.099i	0.787076	−	1.06387i
$394$	8.91794	+	5.14878i	0.0226344	+	0.0130680i
$395$	−16.3330	+	151.192i	−0.0413493	+	0.382764i
$396$	372.795	−	399.913i	0.941401	−	1.00988i
$397$	−74.2885	−	277.248i	−0.187125	−	0.698359i	−0.994166	−	0.107864i	$-0.965599\pi$
$397$	−74.2885	−	277.248i	−0.187125	−	0.698359i	0.807041	−	0.590495i	$-0.201068\pi$
$398$	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	$0.970878\pi$
$402$	−33.8820	−	3.85738i	−0.0842836	−	0.00959547i
$403$	−580.763	−	155.615i	−1.44110	−	0.386141i
$404$	−402.523	−	232.397i	−0.996345	−	0.575240i
$405$	−15.1635	+	404.716i	−0.0374407	+	0.999299i
$406$	7.61273	−	2.74906i	0.0187506	−	0.00677108i
$407$	−188.985	+	188.985i	−0.464335	+	0.464335i
$408$	−56.1958	+	24.4405i	−0.137735	+	0.0599031i
$409$	235.407	+	407.738i	0.575568	+	0.996914i	0.995980	+	0.0895799i	$0.0285524\pi$
$409$	235.407	+	407.738i	0.575568	+	0.996914i	−0.420411	+	0.907334i	$0.638114\pi$
$410$	−11.4097	+	9.18491i	−0.0278286	+	0.0224022i
$411$	−397.205	−	156.423i	−0.966435	−	0.380592i
$412$	−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
$417$	153.863	+	17.5169i	0.368976	+	0.0420070i
$418$	−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	$-0.244463\pi$
$420$	−255.643	+	329.509i	−0.608674	+	0.784546i
$421$	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
$423$	101.544	−	3.56369i	0.240056	−	0.00842479i
$424$	−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
$429$	−707.159	−	278.486i	−1.64839	−	0.649152i
$430$	−4.30320	+	39.8341i	−0.0100074	+	0.0926374i
$431$	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	$0.177970\pi$
$432$	−321.515	+	274.745i	−0.744249	+	0.635985i
$433$	−23.1671	−	23.1671i	−0.0535036	−	0.0535036i	0.679849	−	0.733352i	$-0.262045\pi$
$433$	−23.1671	−	23.1671i	−0.0535036	−	0.0535036i	−0.733352	+	0.679849i	$0.762045\pi$
$434$	−27.4628	+	32.5615i	−0.0632783	+	0.0750266i
$435$	−30.8330	−	98.7544i	−0.0708804	−	0.227022i
$436$	−332.947	+	576.682i	−0.763640	+	1.32266i
$437$	80.8280	−	301.654i	0.184961	−	0.690284i
$438$	37.9181	+	4.31688i	0.0865710	+	0.00985589i
$439$	−252.925	+	438.079i	−0.576139	+	0.997902i	0.419778	+	0.907627i	$0.362108\pi$
$439$	−252.925	+	438.079i	−0.576139	+	0.997902i	−0.995917	+	0.0902749i	$0.971225\pi$
$440$	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
$443$	−121.349	+	32.5153i	−0.273925	+	0.0733979i	−0.393166	−	0.919467i	$-0.628620\pi$
$443$	−121.349	+	32.5153i	−0.273925	+	0.0733979i	0.119242	+	0.992865i	$0.461954\pi$
$444$	162.947	−	129.637i	0.366998	−	0.291976i
$445$	20.6360	−	191.024i	0.0463730	−	0.429267i
$446$	15.3590	−	26.6026i	0.0344372	−	0.0596470i
$447$	125.413	−	169.517i	0.280566	−	0.379232i
$448$	−427.683	+	36.3295i	−0.954650	+	0.0810926i
$449$	550.812			1.22675			0.613376	−	0.789791i	$-0.289811\pi$
$449$	550.812			1.22675			0.613376	+	0.789791i	$0.289811\pi$
$450$	−28.7592	−	24.4080i	−0.0639093	−	0.0542400i
$451$	231.446	−	133.626i	0.513185	−	0.296287i
$452$	−133.349	−	35.7306i	−0.295019	−	0.0790501i
$453$	−123.938	−	284.969i	−0.273593	−	0.629071i
$454$	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	−0.493078	−	0.869985i	$-0.664128\pi$
$457$	−221.692	+	59.4023i	−0.485104	+	0.129983i	0.00797430	+	0.999968i	$0.497462\pi$
$458$	25.1883	+	6.74918i	0.0549962	+	0.0147362i
$459$	−233.653	+	340.157i	−0.509047	+	0.741083i
$460$	−615.265	−	238.221i	−1.33753	−	0.517872i
$461$	532.899			1.15596			0.577982	−	0.816050i	$-0.303840\pi$
$461$	532.899			1.15596			0.577982	+	0.816050i	$0.303840\pi$
$462$	−39.1478	+	36.9689i	−0.0847354	+	0.0800192i
$463$	405.296	−	405.296i	0.875369	−	0.875369i	−0.117682	−	0.993051i	$-0.537546\pi$
$463$	405.296	−	405.296i	0.875369	−	0.875369i	0.993051	+	0.117682i	$0.0375463\pi$
$464$	54.0161	−	93.5586i	0.116414	−	0.201635i
$465$	400.390	+	368.960i	0.861053	+	0.793463i
$466$	30.2889	+	52.4619i	0.0649977	+	0.112579i
$467$	−250.251	+	67.0547i	−0.535870	+	0.143586i	−0.516598	−	0.856228i	$-0.672802\pi$
$467$	−250.251	+	67.0547i	−0.535870	+	0.143586i	−0.0192726	+	0.999814i	$0.506135\pi$
$468$	522.867	+	277.896i	1.11724	+	0.593796i
$469$	−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
$472$	−6.60418	−	1.76958i	−0.0139919	−	0.00374912i
$473$	189.205	−	706.121i	0.400010	−	1.49286i
$474$	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
$477$	−324.064	+	609.731i	−0.679379	+	1.27826i
$478$	−13.4105	−	50.0488i	−0.0280555	−	0.104705i
$479$	−525.786	+	303.563i	−1.09767	+	0.633742i	−0.935609	−	0.353038i	$-0.885149\pi$
$479$	−525.786	+	303.563i	−1.09767	+	0.633742i	−0.162065	+	0.986780i	$0.551815\pi$
$480$	−4.88088	−	119.477i	−0.0101685	−	0.248911i
$481$	−250.680	−	144.730i	−0.521165	−	0.300895i
$482$	−18.1932	−	18.1932i	−0.0377453	−	0.0377453i
$483$	−161.212	−	678.782i	−0.333772	−	1.40535i
$484$		−	448.479i		−	0.926609i
$485$	117.686	+	45.5662i	0.242651	+	0.0939509i
$486$	12.2333	−	38.8581i	0.0251714	−	0.0799548i
$487$	−141.304	+	527.352i	−0.290151	+	1.08286i	0.654841	+	0.755767i	$0.272736\pi$
$487$	−141.304	+	527.352i	−0.290151	+	1.08286i	−0.944992	+	0.327093i	$0.893931\pi$
$488$	−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	$-0.0437428\pi$
$492$	−190.938	+	83.0421i	−0.388086	+	0.168785i
$493$	27.2837	−	101.824i	0.0553423	−	0.206540i
$494$	−13.0521	−	22.6069i	−0.0264213	−	0.0457630i
$495$	450.113	+	520.646i	0.909319	+	1.05181i
$496$			568.551i			1.14627i
$497$	354.963	−	30.1523i	0.714212	−	0.0606686i
$498$	6.27216	+	4.64031i	0.0125947	+	0.00931790i
$499$	449.573	+	259.561i	0.900948	+	0.520162i	0.877508	−	0.479563i	$-0.159205\pi$
$499$	449.573	+	259.561i	0.900948	+	0.520162i	0.0234401	+	0.999725i	$0.492538\pi$
$500$	−486.514	+	99.0096i	−0.973029	+	0.198019i
$501$	−146.850	−	184.583i	−0.293114	−	0.368429i
$502$	8.16822	+	30.4842i	0.0162714	+	0.0607255i
$503$	−197.863	+	197.863i	−0.393366	+	0.393366i	−0.875885	−	0.482519i	$-0.839722\pi$
$503$	−197.863	+	197.863i	−0.393366	+	0.393366i	0.482519	+	0.875885i	$0.339722\pi$
$504$	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
$507$	35.7605	−	314.109i	0.0705335	−	0.619544i
$508$	−47.2730	−	12.6668i	−0.0930571	−	0.0249346i
$509$	540.522	+	312.071i	1.06193	+	0.613106i	0.925966	−	0.377608i	$-0.123253\pi$
$509$	540.522	+	312.071i	1.06193	+	0.613106i	0.135965	+	0.990714i	$0.456587\pi$
$510$	−11.4549	−	36.6887i	−0.0224606	−	0.0719387i
$511$	522.854	+	93.5553i	1.02320	+	0.183083i
$512$	147.503	−	147.503i	0.288093	−	0.288093i
$513$	192.953	−	164.885i	0.376127	−	0.321413i
$514$	15.4366	+	26.7370i	0.0300324	+	0.0520176i
$515$	−42.0564	−	52.2435i	−0.0816630	−	0.101444i
$516$	−208.692	+	529.932i	−0.404443	+	1.02700i
$517$	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	−0.990851	−	0.134962i	$-0.956909\pi$
$521$	−319.011	−	552.544i	−0.612306	−	1.06054i	0.378545	−	0.925583i	$-0.376424\pi$
$522$	0.364990	+	10.4000i	0.000699214	+	0.0199234i
$523$	−698.967	+	187.288i	−1.33646	+	0.358103i	−0.855119	−	0.518432i	$-0.826516\pi$
$523$	−698.967	+	187.288i	−1.33646	+	0.358103i	−0.481339	+	0.876535i	$0.659849\pi$
$524$			688.571i			1.31407i
$525$	−377.838	−	364.504i	−0.719692	−	0.694294i
$526$	−46.2827			−0.0879898
$527$	143.589	+	535.880i	0.272464	+	1.01685i
$528$	−81.2952	+	714.071i	−0.153968	+	1.35241i
$529$	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
$534$	−7.08164	+	17.9824i	−0.0132615	+	0.0336749i
$535$	−68.3269	+	55.0037i	−0.127714	+	0.102811i
$536$	78.4759	−	45.3081i	0.146410	−	0.0845300i
$537$	−399.666	−	918.950i	−0.744257	−	1.71127i
$538$	60.3920	+	60.3920i	0.112253	+	0.112253i
$539$	−576.512	+	478.810i	−1.06960	+	0.888331i
$540$	−302.547	−	442.698i	−0.560272	−	0.819812i
$541$	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	$0.00451647\pi$
$542$	−8.69232	+	32.4402i	−0.0160375	+	0.0598527i
$543$	−68.0952	+	598.126i	−0.125405	+	1.10152i
$544$	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	0.503278	−	0.864125i	$-0.332127\pi$
$547$	−197.383	−	197.383i	−0.360847	−	0.360847i	−0.864125	+	0.503278i	$0.832127\pi$
$548$	545.936	−	146.283i	0.996234	−	0.266940i
$549$	−394.345	−	367.605i	−0.718298	−	0.669590i
$550$	−64.0312	+	2.98459i	−0.116420	+	0.00542653i
$551$	−32.4170	+	56.1479i	−0.0588330	+	0.101902i
$552$	107.081	+	79.2212i	0.193987	+	0.143517i
$553$	90.4625	−	192.725i	0.163585	−	0.348509i
$554$	−50.2405			−0.0906867
$555$	140.218	+	221.466i	0.252645	+	0.399039i
$556$	−177.557	+	102.513i	−0.319347	+	0.184375i
$557$	490.865	+	131.527i	0.881265	+	0.236134i	0.670953	−	0.741500i	$-0.265885\pi$
$557$	490.865	+	131.527i	0.881265	+	0.236134i	0.210312	+	0.977634i	$0.432552\pi$
$558$	−29.0301	−	46.4399i	−0.0520253	−	0.0832256i
$559$	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	$-0.244468\pi$
$563$	560.102	+	150.079i	0.994853	+	0.266570i	0.275565	+	0.961282i	$0.411135\pi$
$564$	−105.272	+	83.7518i	−0.186652	+	0.148496i
$565$	62.7484	−	162.063i	0.111059	−	0.286838i
$566$	19.6765			0.0347641
$567$	204.346	−	528.897i	0.360399	−	0.932798i
$568$	−48.0938	+	48.0938i	−0.0846721	+	0.0846721i
$569$	150.720	−	261.055i	0.264886	−	0.458795i	−0.702648	−	0.711538i	$-0.747999\pi$
$569$	150.720	−	261.055i	0.264886	−	0.458795i	0.967534	+	0.252742i	$0.0813324\pi$
$570$	0.964887	+	23.6191i	0.00169278	+	0.0414371i
$571$	−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	$-0.389573\pi$
$572$	971.951	−	260.433i	1.69922	−	0.455303i
$573$	751.636	+	556.080i	1.31176	+	0.970471i
$574$	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
$577$	−26.0811	−	6.98842i	−0.0452013	−	0.0121116i	0.236148	−	0.971717i	$-0.424115\pi$
$577$	−26.0811	−	6.98842i	−0.0452013	−	0.0121116i	−0.281349	+	0.959606i	$0.590782\pi$
$578$	−2.40345	+	8.96981i	−0.00415822	+	0.0155187i
$579$	−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
$582$	−10.2049	−	7.54988i	−0.0175343	−	0.0129723i
$583$	303.700	+	1133.42i	0.520926	+	1.94412i
$584$	−87.8241	+	50.7053i	−0.150384	+	0.0868241i
$585$	−418.499	+	616.828i	−0.715382	+	1.05441i
$586$	−40.4838	−	23.3733i	−0.0690850	−	0.0398862i
$587$	312.326	+	312.326i	0.532072	+	0.532072i	0.921188	−	0.389117i	$-0.127220\pi$
$587$	312.326	+	312.326i	0.532072	+	0.532072i	−0.389117	+	0.921188i	$0.627220\pi$
$588$	488.473	−	319.838i	0.830737	−	0.543943i
$589$		−	341.208i		−	0.579300i
$590$	1.54835	−	3.99900i	0.00262432	−	0.00677796i
$591$	−144.203	+	114.725i	−0.243998	+	0.194120i
$592$	−70.8434	+	264.391i	−0.119668	+	0.446607i
$593$	−222.299	−	829.633i	−0.374873	−	1.39904i	−0.853531	−	0.521042i	$-0.825543\pi$
$593$	−222.299	−	829.633i	−0.374873	−	1.39904i	0.478658	−	0.878001i	$-0.341123\pi$
$594$	−29.8201	−	62.4771i	−0.0502021	−	0.105180i
$595$	−126.603	−	519.752i	−0.212778	−	0.873533i
$596$			279.178i			0.468420i
$597$	263.657	+	606.224i	0.441636	+	1.01545i
$598$	23.8778	−	89.1131i	0.0399294	−	0.149019i
$599$	−202.842	−	351.333i	−0.338634	−	0.586532i	0.645542	−	0.763725i	$-0.276632\pi$
$599$	−202.842	−	351.333i	−0.338634	−	0.586532i	−0.984176	+	0.177193i	$0.943298\pi$
$600$	100.011	+	6.68886i	0.166686	+	0.0111481i
$601$			207.421i			0.345127i	0.984998	+	0.172563i	$0.0552050\pi$
$601$			207.421i			0.345127i	−0.984998	+	0.172563i	$0.944795\pi$
$602$	23.8339	−	50.7767i	0.0395911	−	0.0843467i
$603$	286.390	−	538.848i	0.474942	−	0.893612i
$604$	356.306	+	205.714i	0.589911	+	0.340585i
$605$	561.300	+	60.6361i	0.927768	+	0.100225i
$606$	−46.0568	+	36.6418i	−0.0760013	+	0.0604650i
$607$	306.916	+	1145.43i	0.505628	+	1.88703i	0.459678	+	0.888086i	$0.347965\pi$
$607$	306.916	+	1145.43i	0.505628	+	1.88703i	0.0459504	+	0.998944i	$0.485368\pi$
$608$	−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
$612$	−19.1630	−	546.031i	−0.0313121	−	0.892207i
$613$	373.703	+	100.133i	0.609630	+	0.163350i	0.550409	−	0.834895i	$-0.314472\pi$
$613$	373.703	+	100.133i	0.609630	+	0.163350i	0.0592208	+	0.998245i	$0.481138\pi$
$614$	54.7224	+	31.5940i	0.0891244	+	0.0514560i
$615$	−78.1168	−	250.199i	−0.127019	−	0.406827i
$616$	25.2015	−	140.844i	0.0409115	−	0.228643i
$617$	81.5983	−	81.5983i	0.132250	−	0.132250i	−0.637883	−	0.770133i	$-0.720190\pi$
$617$	81.5983	−	81.5983i	0.132250	−	0.132250i	0.770133	+	0.637883i	$0.220190\pi$
$618$	2.69060	+	6.18649i	0.00435372	+	0.0100105i
$619$	91.0832	+	157.761i	0.147146	+	0.254864i	0.930171	−	0.367125i	$-0.119658\pi$
$619$	91.0832	+	157.761i	0.147146	+	0.254864i	−0.783026	+	0.621989i	$0.786325\pi$
$620$	−716.684	−	77.4221i	−1.15594	−	0.124874i
$621$	894.249	+	70.1440i	1.44001	+	0.112953i
$622$	−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
$627$	48.7882	−	428.540i	0.0778121	−	0.683477i
$628$	455.761	−	122.121i	0.725734	−	0.194460i
$629$			267.090i			0.424627i
$630$	26.9609	+	45.4079i	0.0427950	+	0.0720761i
$631$	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
$633$	175.263	+	19.9532i	0.276876	+	0.0315216i
$634$	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
$639$	−102.955	+	446.304i	−0.161120	+	0.698441i
$640$	132.208	+	164.232i	0.206575	+	0.256613i
$641$	−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	$0.429210\pi$
$642$	8.09103	−	3.51892i	0.0126028	−	0.00548118i
$643$	−548.817	−	548.817i	−0.853526	−	0.853526i	0.137039	−	0.990566i	$-0.456241\pi$
$643$	−548.817	−	548.817i	−0.853526	−	0.853526i	−0.990566	+	0.137039i	$0.956241\pi$
$644$	706.080	+	595.516i	1.09640	+	0.924714i
$645$	−635.027	−	332.841i	−0.984538	−	0.516032i
$646$	−12.0434	+	20.8598i	−0.0186430	+	0.0322907i
$647$	−316.824	+	1182.40i	−0.489681	+	1.82751i	0.0683064	+	0.997664i	$0.478240\pi$
$647$	−316.824	+	1182.40i	−0.489681	+	1.82751i	−0.557987	+	0.829849i	$0.688426\pi$
$648$	35.2796	+	102.343i	0.0544438	+	0.157937i
$649$	−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
$653$	44.7631	−	11.9942i	0.0685499	−	0.0183679i	−0.224381	−	0.974501i	$-0.572036\pi$
$653$	44.7631	−	11.9942i	0.0685499	−	0.0183679i	0.292931	+	0.956134i	$0.405369\pi$
$654$	52.4955	+	65.9841i	0.0802683	+	0.100893i
$655$	−861.791	−	93.0976i	−1.31571	−	0.142134i
$656$	136.852	−	237.035i	0.208616	−	0.361334i
$657$	−320.506	+	603.037i	−0.487832	+	0.917864i
$658$	10.8718	−	7.57169i	0.0165225	−	0.0115071i
$659$	1102.69			1.67328			0.836642	−	0.547750i	$-0.184516\pi$
$659$	1102.69			1.67328			0.836642	+	0.547750i	$0.184516\pi$
$660$	−889.050	−	199.715i	−1.34704	−	0.302598i
$661$	−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	$0.433925\pi$
$662$	38.9085	+	10.4255i	0.0587741	+	0.0157485i
$663$	−696.502	+	302.920i	−1.05053	+	0.456893i
$664$	−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
$669$	342.228	+	430.163i	0.511552	+	0.642994i
$670$	22.9666	+	51.9878i	0.0342785	+	0.0775937i
$671$	−916.144			−1.36534
$672$	−47.9376	+	160.397i	−0.0713357	+	0.238687i
$673$	−747.970	+	747.970i	−1.11140	+	1.11140i	−0.118435	+	0.992962i	$0.537788\pi$
$673$	−747.970	+	747.970i	−1.11140	+	1.11140i	−0.992962	+	0.118435i	$0.962212\pi$
$674$	19.1987	−	33.2531i	0.0284847	−	0.0493369i
$675$	594.971	−	318.802i	0.881438	−	0.472300i
$676$	209.278	+	362.480i	0.309582	+	0.536212i
$677$	−222.162	+	59.5281i	−0.328156	+	0.0879292i	−0.419136	−	0.907924i	$-0.637667\pi$
$677$	−222.162	+	59.5281i	−0.328156	+	0.0879292i	0.0909796	+	0.995853i	$0.471000\pi$
$678$	−10.3968	+	14.0530i	−0.0153345	+	0.0207272i
$679$	−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
$682$	−89.8972	−	24.0879i	−0.131814	−	0.0353195i
$683$	41.9067	−	156.398i	0.0613568	−	0.228987i	−0.928438	−	0.371488i	$-0.878848\pi$
$683$	41.9067	−	156.398i	0.0613568	−	0.228987i	0.989795	+	0.142501i	$0.0455145\pi$
$684$	−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
$687$	−277.534	+	375.134i	−0.403980	+	0.546047i
$688$	−193.773	−	723.172i	−0.281647	−	1.05112i
$689$	−1100.59	+	635.428i	−1.59738	+	0.922247i
$690$	−56.6138	+	61.4363i	−0.0820489	+	0.0890382i
$691$	−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
$693$	−358.845	−	894.221i	−0.517815	−	1.29036i
$694$		−	113.037i		−	0.162878i
$695$	−104.295	−	236.084i	−0.150064	−	0.339689i
$696$	−17.2163	−	21.6400i	−0.0247360	−	0.0310919i
$697$	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	$-0.186086\pi$
$702$	57.0012	−	48.7093i	0.0811982	−	0.0693865i
$703$	42.5157	−	158.671i	0.0604775	−	0.225705i
$704$	−468.903	−	812.163i	−0.666055	−	1.15364i
$705$	−90.5876	−	143.078i	−0.128493	−	0.202947i
$706$		−	56.5061i		−	0.0800370i
$707$	−672.188	+	468.146i	−0.950762	+	0.662159i
$708$	36.2554	−	49.0053i	0.0512083	−	0.0692166i
$709$	−767.065	−	442.865i	−1.08190	−	0.624633i	−0.150489	−	0.988612i	$-0.548085\pi$
$709$	−767.065	−	442.865i	−1.08190	−	0.624633i	−0.931407	+	0.363978i	$0.881418\pi$
$710$	−26.7503	−	33.2299i	−0.0376765	−	0.0468026i
$711$	200.225	+	186.648i	0.281611	+	0.262514i
$712$	−13.2920	−	49.6065i	−0.0186686	−	0.0696720i
$713$	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
$717$	921.253	+	104.882i	1.28487	+	0.146279i
$718$	49.7713	+	13.3362i	0.0693193	+	0.0185741i
$719$	428.934	+	247.645i	0.596570	+	0.344430i	0.767691	−	0.640820i	$-0.221406\pi$
$719$	428.934	+	247.645i	0.596570	+	0.344430i	−0.171121	+	0.985250i	$0.554739\pi$
$720$	665.831	+	231.289i	0.924765	+	0.321235i
$721$	31.8912	+	88.3135i	0.0442319	+	0.122488i
$722$	−32.3194	+	32.3194i	−0.0447637	+	0.0447637i
$723$	422.213	−	183.627i	0.583974	−	0.253980i
$724$	−398.507	−	690.234i	−0.550424	−	0.953362i
$725$	−116.115	+	127.468i	−0.160158	+	0.175819i
$726$	−52.8389	−	20.8085i	−0.0727809	−	0.0286618i
$727$	−242.067	+	242.067i	−0.332967	+	0.332967i	−0.853712	−	0.520745i	$-0.825654\pi$
$727$	−242.067	+	242.067i	−0.332967	+	0.332967i	0.520745	+	0.853712i	$0.325654\pi$
$728$	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
$732$	709.184	+	80.7388i	0.968831	+	0.110299i
$733$	1122.76	−	300.842i	1.53173	−	0.410425i	0.608145	−	0.793826i	$-0.291914\pi$
$733$	1122.76	−	300.842i	1.53173	−	0.410425i	0.923582	+	0.383401i	$0.125247\pi$
$734$		−	16.1063i		−	0.0219432i
$735$	334.254	+	654.598i	0.454768	+	0.890610i
$736$	−264.840			−0.359836
$737$	−268.393	−	1001.66i	−0.364170	−	1.35910i
$738$	0.924718	+	26.3490i	0.00125301	+	0.0357032i
$739$	−377.355	+	217.866i	−0.510629	+	0.294812i	−0.733092	−	0.680129i	$-0.761924\pi$
$739$	−377.355	+	217.866i	−0.510629	+	0.294812i	0.222463	+	0.974941i	$0.428590\pi$
$740$	−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	$-0.329344\pi$
$743$	−259.217	−	259.217i	−0.348878	−	0.348878i	−0.859692	+	0.510813i	$0.829344\pi$
$744$	135.410	+	53.3258i	0.182003	+	0.0716745i
$745$	−349.410	−	37.7461i	−0.469006	−	0.0506659i
$746$	4.31757	−	2.49275i	0.00578762	−	0.00334149i
$747$	−118.388	+	74.0060i	−0.158485	+	0.0990710i
$748$	−656.529	−	656.529i	−0.877713	−	0.877713i
$749$	115.501	−	41.7090i	0.154207	−	0.0556863i
$750$	−10.9081	+	61.9140i	−0.0145442	+	0.0825521i
$751$	−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	$0.308272\pi$
$752$	45.7682	−	170.809i	0.0608620	−	0.227140i
$753$	−561.126	−	63.8828i	−0.745187	−	0.0848377i
$754$	−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	0.528955	−	0.848650i	$-0.322584\pi$
$757$	−242.009	−	242.009i	−0.319695	−	0.319695i	−0.848650	+	0.528955i	$0.822584\pi$
$758$	36.7854	−	9.85663i	0.0485296	−	0.0130035i
$759$	1192.86	−	949.013i	1.57162	−	1.25035i
$760$	−39.3897	−	48.9309i	−0.0518286	−	0.0643827i
$761$	−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	$0.325275\pi$
$762$	−3.68574	+	4.98190i	−0.00483693	+	0.00653793i
$763$	670.698	+	963.022i	0.879027	+	1.26215i
$764$	−1237.88			−1.62026
$765$	685.983	+	49.8419i	0.896710	+	0.0651528i
$766$	−7.94874	+	4.58921i	−0.0103769	+	0.00599113i
$767$	−81.8535	−	21.9326i	−0.106719	−	0.0285953i
$768$	285.005	+	655.310i	0.371100	+	0.853269i
$769$	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	$-0.652919\pi$
$773$	−1009.36	−	270.458i	−1.30577	−	0.349881i	−0.843630	+	0.536925i	$0.819586\pi$
$774$	52.7527	+	49.1755i	0.0681559	+	0.0635342i
$775$	193.797	−	886.508i	0.250061	−	1.14388i
$776$	33.7321			0.0434692
$777$	−84.7977	−	357.041i	−0.109135	−	0.459512i
$778$	−24.7345	+	24.7345i	−0.0317924	+	0.0317924i
$779$	−82.1300	+	142.253i	−0.105430	+	0.182610i
$780$	−40.2824	−	986.058i	−0.0516441	−	1.26418i
$781$	389.174	+	674.069i	0.498302	+	0.863085i
$782$	−82.2262	+	22.0324i	−0.105149	+	0.0281745i
$783$	−175.555	−	62.1158i	−0.224209	−	0.0793305i
$784$	−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
$787$	864.548	+	231.655i	1.09854	+	0.294352i	0.762169	−	0.647379i	$-0.224135\pi$
$787$	864.548	+	231.655i	1.09854	+	0.294352i	0.336368	+	0.941731i	$0.390801\pi$
$788$	63.1440	−	235.657i	0.0801320	−	0.299057i
$789$	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
$792$	162.443	+	86.3364i	0.205105	+	0.109011i
$793$	−256.808	−	958.420i	−0.323843	−	1.20860i
$794$	41.6727	−	24.0598i	0.0524845	−	0.0303020i
$795$	1149.87	−	46.9745i	1.44638	−	0.0590875i
$796$	−757.982	−	437.621i	−0.952239	−	0.549776i
$797$	337.006	+	337.006i	0.422843	+	0.422843i	0.886181	−	0.463338i	$-0.153349\pi$
$797$	337.006	+	337.006i	0.422843	+	0.422843i	−0.463338	+	0.886181i	$0.653349\pi$
$798$	9.47665	−	31.7085i	0.0118755	−	0.0397350i
$799$		−	172.553i		−	0.215961i
$800$	−167.768	+	107.576i	−0.209710	+	0.134469i
$801$	−252.975	−	235.821i	−0.315824	−	0.294408i
$802$	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
$807$	−1401.53	+	609.546i	−1.73671	+	0.755323i
$808$	40.4777	−	151.065i	0.0500962	−	0.186962i
$809$	−306.932	−	531.622i	−0.379397	−	0.657134i	0.611578	−	0.791184i	$-0.290535\pi$
$809$	−306.932	−	531.622i	−0.379397	−	0.657134i	−0.990975	+	0.134050i	$0.957202\pi$
$810$	−66.1955	+	15.1052i	−0.0817228	+	0.0186484i
$811$		−	585.506i		−	0.721955i	−0.932574	−	0.360978i	$-0.882443\pi$
$811$		−	585.506i		−	0.721955i	0.932574	−	0.360978i	$-0.117557\pi$
$812$	−109.592	−	157.358i	−0.134966	−	0.193791i
$813$	−483.139	−	357.439i	−0.594266	−	0.439654i
$814$	−38.8032	−	22.4030i	−0.0476698	−	0.0275222i
$815$	−89.7149	+	72.2212i	−0.110080	+	0.0886150i
$816$	447.149	+	562.043i	0.547976	+	0.688778i
$817$	116.290	+	434.002i	0.142338	+	0.531214i
$818$	−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	$0.834901\pi$
$822$	8.09551	−	71.1084i	0.00984855	−	0.0865066i
$823$	1366.00	+	366.018i	1.65978	+	0.444737i	0.962327	−	0.271893i	$-0.0876498\pi$
$823$	1366.00	+	366.018i	1.65978	+	0.444737i	0.697453	+	0.716630i	$0.254316\pi$
$824$	−15.5251	−	8.96340i	−0.0188411	−	0.0108779i
$825$	370.159	−	1085.70i	0.448677	−	1.31600i
$826$	−3.87064	+	4.58926i	−0.00468600	+	0.00555601i
$827$	16.4891	−	16.4891i	0.0199384	−	0.0199384i	−0.697067	−	0.717006i	$-0.745512\pi$
$827$	16.4891	−	16.4891i	0.0199384	−	0.0199384i	0.717006	+	0.697067i	$0.245512\pi$
$828$	−1007.02	+	629.502i	−1.21621	+	0.760269i
$829$	537.538	+	931.043i	0.648417	+	1.12309i	0.983501	+	0.180903i	$0.0579021\pi$
$829$	537.538	+	931.043i	0.648417	+	1.12309i	−0.335083	+	0.942188i	$0.608765\pi$
$830$	1.39662	−	12.9283i	0.00168267	−	0.0155762i
$831$	329.427	−	836.512i	0.396422	−	1.00663i
$832$	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
$837$	963.582	−	178.850i	1.15123	−	0.213679i
$838$	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	$-0.301797\pi$
$840$	−129.359	−	54.3916i	−0.153999	−	0.0647519i
$841$	−793.431			−0.943437
$842$	15.6284	+	58.3259i	0.0185610	+	0.0692707i
$843$	−15.8374	+	139.111i	−0.0187870	+	0.165019i
$844$	−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
$849$	−129.019	+	327.617i	−0.151965	+	0.385885i
$850$	−43.1384	+	47.3565i	−0.0507510	+	0.0557135i
$851$	502.772	−	290.276i	0.590801	−	0.341099i
$852$	−241.853	−	556.092i	−0.283865	−	0.652690i
$853$	−886.732	−	886.732i	−1.03955	−	1.03955i	−0.999185	−	0.0403603i	$-0.987149\pi$
$853$	−886.732	−	886.732i	−1.03955	−	1.03955i	−0.0403603	−	0.999185i	$-0.512851\pi$
$854$	−69.1969	−	12.3815i	−0.0810268	−	0.0144983i
$855$	−399.589	−	138.805i	−0.467356	−	0.162345i
$856$	−11.7228	+	20.3045i	−0.0136949	+	0.0237203i
$857$	40.8768	−	152.554i	0.0476975	−	0.178010i	−0.937968	−	0.346723i	$-0.887294\pi$
$857$	40.8768	−	152.554i	0.0476975	−	0.178010i	0.985665	+	0.168713i	$0.0539612\pi$
$858$	14.4127	−	126.597i	0.0167981	−	0.147549i
$859$	598.502	−	1036.64i	0.696743	−	1.20679i	−0.272847	−	0.962058i	$-0.587965\pi$
$859$	598.502	−	1036.64i	0.696743	−	1.20679i	0.969590	−	0.244737i	$-0.0787015\pi$
$860$	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
$863$	−1543.44	+	413.564i	−1.78846	+	0.479217i	−0.992083	−	0.125582i	$-0.959920\pi$
$863$	−1543.44	+	413.564i	−1.78846	+	0.479217i	−0.796378	+	0.604799i	$0.793254\pi$
$864$	−177.416	−	121.866i	−0.205342	−	0.141049i
$865$	783.040	−	630.354i	0.905248	−	0.728733i
$866$	2.74632	−	4.75677i	0.00317127	−	0.00549281i
$867$	−133.589	−	98.8329i	−0.154082	−	0.113994i
$868$	913.562	+	428.813i	1.05249	+	0.494024i
$869$	465.163			0.535286
$870$	14.6539	−	9.27790i	0.0168436	−	0.0106642i
$871$	972.646	−	561.557i	1.11670	−	0.644727i
$872$	−216.426	−	57.9911i	−0.248195	−	0.0665035i
$873$	192.620	−	120.409i	0.220642	−	0.137926i
$874$	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	−0.0214786	−	0.999769i	$-0.506837\pi$
$877$	403.249	−	108.050i	0.459805	−	0.123204i	0.481284	+	0.876565i	$0.340171\pi$
$878$	−81.9146	−	21.9489i	−0.0932968	−	0.0249988i
$879$	654.622	−	520.803i	0.744735	−	0.592494i
$880$	1095.65	−	484.026i	1.24506	−	0.550030i
$881$	276.453			0.313795			0.156898	−	0.987615i	$-0.449851\pi$
$881$	276.453			0.313795			0.156898	+	0.987615i	$0.449851\pi$
$882$	−15.0186	−	72.3908i	−0.0170279	−	0.0820757i
$883$	−982.011	+	982.011i	−1.11213	+	1.11213i	−0.119269	+	0.992862i	$0.538055\pi$
$883$	−982.011	+	982.011i	−1.11213	+	1.11213i	−0.992862	+	0.119269i	$0.961945\pi$
$884$	502.791	−	870.860i	0.568768	−	0.985135i
$885$	56.4314	+	52.0017i	0.0637643	+	0.0587590i
$886$	−10.5307	−	18.2397i	−0.0118857	−	0.0205866i
$887$	−1006.64	+	269.729i	−1.13489	+	0.304092i	−0.776893	−	0.629633i	$-0.783205\pi$
$887$	−1006.64	+	269.729i	−1.13489	+	0.304092i	−0.357993	+	0.933724i	$0.616539\pi$
$888$	56.3247	+	41.6705i	0.0634288	+	0.0469263i
$889$	−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
$892$	−702.973	−	188.361i	−0.788087	−	0.211167i
$893$	−27.4672	+	102.509i	−0.0307583	+	0.114792i
$894$	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
$897$	1327.18	+	981.883i	1.47958	+	1.09463i
$898$	23.8999	+	89.1955i	0.0266145	+	0.0993268i
$899$	−216.807	+	125.174i	−0.241165	+	0.139237i
$900$	−382.220	+	807.815i	−0.424689	+	0.897572i
$901$	1015.54	+	586.320i	1.12712	+	0.650744i
$902$	31.6811	+	31.6811i	0.0351232	+	0.0351232i
$903$	689.162	+	729.780i	0.763192	+	0.808173i
$904$		−	46.4520i		−	0.0513849i
$905$	917.752	−	405.434i	1.01409	−	0.447994i
$906$	40.7687	−	32.4347i	0.0449985	−	0.0357999i
$907$	393.840	−	1469.83i	0.434222	−	1.62054i	−0.308698	−	0.951160i	$-0.599893\pi$
$907$	393.840	−	1469.83i	0.434222	−	1.62054i	0.742921	−	0.669380i	$-0.233440\pi$
$908$	−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	$0.639942\pi$
$912$	−176.172	−	405.071i	−0.193171	−	0.444157i
$913$	−61.4069	+	229.174i	−0.0672584	+	0.251012i
$914$	−19.2386	−	33.3222i	−0.0210488	−	0.0364575i
$915$	−196.934	+	876.673i	−0.215229	+	0.958112i
$916$		−	617.813i		−	0.674468i
$917$	1098.53	+	515.634i	1.19796	+	0.562305i
$918$	−65.2214	−	23.0770i	−0.0710473	−	0.0251383i
$919$	415.979	+	240.166i	0.452643	+	0.261334i	0.708946	−	0.705263i	$-0.249171\pi$
$919$	415.979	+	240.166i	0.452643	+	0.261334i	−0.256303	+	0.966597i	$0.582504\pi$
$920$	23.8436	−	220.716i	0.0259169	−	0.239909i
$921$	−884.860	+	703.975i	−0.960760	+	0.764359i
$922$	23.1226	+	86.2948i	0.0250788	+	0.0935952i
$923$	−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
$927$	−120.648	+	4.23416i	−0.130149	+	0.00456759i
$928$	53.1084	+	14.2304i	0.0572289	+	0.0153344i
$929$	804.028	+	464.206i	0.865477	+	0.499683i	0.865842	−	0.500317i	$-0.166783\pi$
$929$	804.028	+	464.206i	0.865477	+	0.499683i	−0.000365893		1.00000i	$0.500116\pi$
$930$	−42.3744	+	80.8462i	−0.0455639	+	0.0869314i
$931$	159.722	−	432.033i	0.171560	−	0.464052i
$932$	1014.85	−	1014.85i	1.08889	−	1.08889i
$933$	−267.169	−	614.300i	−0.286355	−	0.658414i
$934$	−21.7169	−	37.6148i	−0.0232515	−	0.0402728i
$935$	910.454	−	732.923i	0.973747	−	0.783875i
$936$	−44.7853	+	194.141i	−0.0478476	+	0.207415i
$937$	−723.582	+	723.582i	−0.772232	+	0.772232i	−0.978496	−	0.206264i	$-0.933869\pi$
$937$	−723.582	+	723.582i	−0.772232	+	0.772232i	0.206264	+	0.978496i	$0.433869\pi$
$938$	−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	0.899779	+	0.436347i	$0.143728\pi$
$941$	778.938	+	1349.16i	0.827777	+	1.43375i	−0.0720018	+	0.997405i	$0.522939\pi$
$942$	6.75833	−	59.3631i	0.00717445	−	0.0630181i
$943$	−560.742	+	150.250i	−0.594636	+	0.159332i
$944$			80.1322i			0.0848858i
$945$	−932.832	+	151.163i	−0.987123	+	0.159961i
$946$	122.555			0.129551
$947$	−361.534	−	1349.26i	−0.381768	−	1.42478i	−0.843199	−	0.537601i	$-0.819331\pi$
$947$	−361.534	−	1349.26i	−0.381768	−	1.42478i	0.461432	−	0.887176i	$-0.347336\pi$
$948$	−360.081	−	40.9943i	−0.379833	−	0.0432430i
$949$	−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	−0.975813	−	0.218607i	$-0.929849\pi$
$953$	−1138.28	−	1138.28i	−1.19442	−	1.19442i	−0.218607	−	0.975813i	$-0.570151\pi$
$954$	−112.798	−	26.0207i	−0.118237	−	0.0272754i
$955$	167.366	−	1549.28i	0.175252	−	1.62228i
$956$	−1063.12	+	613.793i	−1.11205	+	0.642043i
$957$	−290.197	+	126.211i	−0.303236	+	0.131882i
$958$	−71.9712	−	71.9712i	−0.0751265	−	0.0751265i
$959$	175.446	−	980.517i	0.182946	−	1.02244i
$960$	−877.967	+	274.118i	−0.914549	+	0.285539i
$961$	178.263	−	308.761i	0.185497	−	0.321291i
$962$	12.5598	−	46.8737i	0.0130559	−	0.0487252i
$963$	5.53766	+	157.790i	0.00575043	+	0.163853i
$964$	−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	0.345060	−	0.938581i	$-0.387859\pi$
$967$	−573.934	−	573.934i	−0.593521	−	0.593521i	−0.938581	+	0.345060i	$0.887859\pi$
$968$	145.762	−	39.0569i	0.150581	−	0.0403480i
$969$	−268.350	−	337.302i	−0.276935	−	0.348093i
$970$	−2.27232	+	21.0345i	−0.00234260	+	0.0216851i
$971$	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	$-0.215142\pi$
$972$	−964.270	−	41.6805i	−0.992047	−	0.0428812i
$973$	30.5832	+	360.037i	0.0314319	+	0.370027i
$974$	−91.5278			−0.0939710
$975$	1239.56	+	82.9031i	1.27134	+	0.0850288i
$976$	−812.562	+	469.133i	−0.832543	+	0.480669i
$977$	−817.894	−	219.154i	−0.837148	−	0.224313i	−0.185319	−	0.982678i	$-0.559332\pi$
$977$	−817.894	−	219.154i	−0.837148	−	0.224313i	−0.651830	+	0.758365i	$0.725998\pi$
$978$	10.6237	−	4.62042i	0.0108627	−	0.00472436i
$979$	−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	$-0.527746\pi$
$983$	−649.321	−	173.985i	−0.660551	−	0.176994i	−0.573494	+	0.819209i	$0.694413\pi$
$984$	−43.6182	−	54.8258i	−0.0443275	−	0.0557173i
$985$	286.402	+	110.890i	0.290763	+	0.112579i
$986$	17.6727			0.0179237
$987$	54.7833	+	230.665i	0.0555049	+	0.233703i
$988$	−437.318	+	437.318i	−0.442630	+	0.442630i
$989$	−793.971	+	1375.20i	−0.802802	+	1.39049i
$990$	−64.7801	+	95.4798i	−0.0654344	+	0.0964442i
$991$	−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	$0.955957\pi$
$992$	−279.499	+	74.8914i	−0.281753	+	0.0754954i
$993$	−428.709	+	579.472i	−0.431731	+	0.583557i
$994$	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
$997$	525.982	+	140.936i	0.527564	+	0.141360i	0.512763	−	0.858530i	$-0.328622\pi$
$997$	525.982	+	140.936i	0.527564	+	0.141360i	0.0148011	+	0.999890i	$0.495288\pi$
$998$	−22.5248	+	84.0638i	−0.0225700	+	0.0842323i
$999$	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.47.16	yes	112
3.2	odd	2	inner	105.3.w.a.47.13	yes	112
5.3	odd	4	inner	105.3.w.a.68.16	yes	112
7.3	odd	6	inner	105.3.w.a.17.13	✓	112
15.8	even	4	inner	105.3.w.a.68.13	yes	112
21.17	even	6	inner	105.3.w.a.17.16	yes	112
35.3	even	12	inner	105.3.w.a.38.13	yes	112
105.38	odd	12	inner	105.3.w.a.38.16	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.13	✓	112	7.3	odd	6	inner
105.3.w.a.17.16	yes	112	21.17	even	6	inner
105.3.w.a.38.13	yes	112	35.3	even	12	inner
105.3.w.a.38.16	yes	112	105.38	odd	12	inner
105.3.w.a.47.13	yes	112	3.2	odd	2	inner
105.3.w.a.47.16	yes	112	1.1	even	1	trivial
105.3.w.a.68.13	yes	112	15.8	even	4	inner
105.3.w.a.68.16	yes	112	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0433902 + 0.161935i) q^{2} +(-2.98075 - 0.339350i) 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} +(8.76968 + 2.02303i) q^{9} +(-0.652953 + 0.525633i) q^{10} +(13.2452 - 7.64711i) q^{11} +(-10.9270 + 4.75232i) q^{12} +(11.7128 + 11.7128i) q^{13} +(1.10377 - 0.398585i) q^{14} +(-4.47046 - 14.3183i) q^{15} +(7.83176 - 13.5650i) q^{16} +(3.95586 - 14.7635i) q^{17} +(0.0529196 + 1.50789i) 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} +(-32.0900 + 8.59850i) q^{23} +(-2.49618 - 3.13757i) q^{24} +(-16.8354 + 18.4816i) q^{25} +(-1.38849 + 2.40493i) q^{26} +(-25.4537 - 9.00614i) q^{27} +(-15.8897 - 22.8153i) q^{28} +6.89705 q^{29} +(2.12466 - 1.34520i) q^{30} +(-31.4348 + 18.1489i) q^{31} +(7.70017 + 2.06325i) q^{32} +(-42.0756 + 18.2993i) 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} +(-30.9381 - 38.8876i) q^{39} +(-2.41276 + 6.23153i) q^{40} +17.4740 q^{41} +(-3.42531 + 0.813516i) q^{42} +(33.7982 - 33.7982i) q^{43} +(30.3735 - 52.6085i) q^{44} +(8.46636 + 44.1964i) q^{45} +(-2.78479 - 4.82340i) q^{46} +(10.9049 - 2.92196i) q^{47} +(-27.9478 + 37.7761i) q^{48} +(-48.2979 + 8.26495i) q^{49} +(-3.72330 - 1.92431i) q^{50} +(-16.8014 + 42.6637i) q^{51} +(63.5502 + 17.0282i) q^{52} +(-19.8572 + 74.1079i) q^{53} +(0.353964 - 4.51261i) q^{54} +(61.7362 + 45.1272i) q^{55} +(6.03151 - 7.15133i) q^{56} +(16.7725 - 22.6708i) q^{57} +(0.299265 + 1.11687i) q^{58} +(-4.43046 + 2.55793i) q^{59} +(-43.8128 - 40.3736i) q^{60} +(-51.8761 - 29.9507i) q^{61} +(-4.30289 - 4.30289i) q^{62} +(8.91455 - 62.3661i) q^{63} -61.3176i q^{64} +(-29.9042 + 77.2349i) q^{65} +(-4.78896 - 6.01947i) 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} +(6.37574 + 10.1994i) q^{72} +(-19.6391 + 73.2942i) q^{73} +(-1.46480 - 2.53712i) q^{74} +(56.4538 - 49.3758i) q^{75} +37.3368i q^{76} +(-61.1852 - 87.8528i) q^{77} +(4.95483 - 6.69729i) q^{78} +(26.3396 + 15.2072i) q^{79} +(77.8646 + 8.41157i) q^{80} +(72.8147 + 35.4827i) q^{81} +(0.758201 + 2.82965i) 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} +(-20.5584 - 2.34052i) q^{87} +(19.7437 + 5.29031i) q^{88} +(-33.2788 - 19.2135i) q^{89} +(-6.78956 + 3.28869i) q^{90} +(74.7558 - 88.6350i) q^{91} +(-93.3059 + 93.3059i) q^{92} +(99.8579 - 43.4298i) q^{93} +(0.946333 + 1.63910i) q^{94} +(-46.7294 - 5.04808i) q^{95} +(-22.2521 - 8.76308i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more