LMFDB - Embedded newform 105.3.w.a.68.13

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			68.13
Character	$\chi$	$=$	105.68
Dual form			105.3.w.a.17.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.161935 + 0.0433902i) q^{2} +(-1.19649 + 2.75108i) q^{3} +(-3.43976 + 1.98595i) q^{4} +(4.97108 - 0.537016i) q^{5} +(0.0743827 - 0.497410i) q^{6} +(-6.97488 + 0.592480i) q^{7} +(0.945023 - 0.945023i) q^{8} +(-6.13684 - 6.58325i) q^{9} +(-0.781688 + 0.302658i) q^{10} +(-13.2452 + 7.64711i) q^{11} +(-1.34786 - 11.8392i) 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} +(14.7635 + 3.95586i) q^{17} +(1.27942 + 0.799777i) 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} +(8.59850 + 32.0900i) q^{23} +(1.46912 + 3.73054i) q^{24} +(24.4232 - 5.33910i) q^{25} +(1.38849 - 2.40493i) q^{26} +(25.4537 - 9.00614i) q^{27} +(22.8153 - 15.8897i) q^{28} +6.89705 q^{29} +(0.102645 - 2.51261i) q^{30} +(-31.4348 + 18.1489i) q^{31} +(-2.06325 + 7.70017i) q^{32} +(-5.19010 - 45.5882i) q^{33} -2.56236 q^{34} +(-34.3545 + 6.69089i) q^{35} +(34.1833 + 10.4574i) q^{36} +(4.52283 + 16.8794i) q^{37} +(-0.407879 + 1.52222i) q^{38} +(-18.2086 - 46.2370i) q^{39} +(4.19029 - 5.20527i) q^{40} -17.4740 q^{41} +(-0.224105 + 3.51345i) q^{42} +(33.7982 + 33.7982i) q^{43} +(30.3735 - 52.6085i) q^{44} +(-34.0420 - 29.4303i) q^{45} +(-2.78479 - 4.82340i) q^{46} +(2.92196 + 10.9049i) q^{47} +(27.9478 + 37.7761i) q^{48} +(48.2979 - 8.26495i) q^{49} +(-3.72330 + 1.92431i) q^{50} +(-28.5471 + 35.8823i) q^{51} +(17.0282 - 63.5502i) q^{52} +(74.1079 + 19.8572i) q^{53} +(-3.73105 + 2.56285i) q^{54} +(-61.7362 + 45.1272i) q^{55} +(-6.03151 + 7.15133i) q^{56} +(16.7725 + 22.6708i) q^{57} +(-1.11687 + 0.299265i) q^{58} +(-4.43046 + 2.55793i) q^{59} +(-13.0582 - 58.1298i) q^{60} +(-51.8761 - 29.9507i) q^{61} +(4.30289 - 4.30289i) q^{62} +(46.7042 + 42.2814i) q^{63} +61.3176i q^{64} +(-51.9353 + 64.5152i) q^{65} +(2.81854 + 7.15710i) q^{66} +(-65.4926 - 17.5487i) q^{67} +(-58.6389 + 15.7122i) q^{68} +(-98.5701 - 14.7402i) q^{69} +(5.27286 - 2.57414i) q^{70} -50.8917i q^{71} +(-12.0208 - 0.421870i) q^{72} +(-73.2942 - 19.6391i) q^{73} +(-1.46480 - 2.53712i) q^{74} +(-14.5338 + 73.5783i) q^{75} +37.3368i q^{76} +(87.8528 - 61.1852i) q^{77} +(4.95483 + 6.69729i) q^{78} +(-26.3396 - 15.2072i) q^{79} +(31.6477 - 71.6385i) q^{80} +(-5.67841 + 80.8007i) q^{81} +(2.82965 - 0.758201i) 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} +(-8.25223 + 18.9743i) q^{87} +(-5.29031 + 19.7437i) 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} +(-12.3176 - 108.194i) q^{93} +(-0.946333 - 1.63910i) q^{94} +(18.9929 - 42.9929i) q^{95} +(-18.7151 - 14.8893i) q^{96} +(-17.8473 - 17.8473i) q^{97} +(-7.46249 + 3.43404i) q^{98} +(131.626 + 40.2673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) $ 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.161935	+	0.0433902i	−0.0809673	+	0.0216951i	−0.299075	−	0.954230i	$-0.596678\pi$
$2$	−0.161935	+	0.0433902i	−0.0809673	+	0.0216951i	0.218108	+	0.975925i	$0.430011\pi$
$3$	−1.19649	+	2.75108i	−0.398829	+	0.917025i
$3$	−1.19649	+	2.75108i	−0.398829	+	0.917025i
$4$	−3.43976	+	1.98595i	−0.859940	+	0.496487i
$5$	4.97108	−	0.537016i	0.994216	−	0.107403i
$5$	4.97108	−	0.537016i	0.994216	−	0.107403i
$6$	0.0743827	−	0.497410i	0.0123971	−	0.0829017i
$7$	−6.97488	+	0.592480i	−0.996412	+	0.0846400i
$7$	−6.97488	+	0.592480i	−0.996412	+	0.0846400i
$8$	0.945023	−	0.945023i	0.118128	−	0.118128i
$9$	−6.13684	−	6.58325i	−0.681871	−	0.731472i
$10$	−0.781688	+	0.302658i	−0.0781688	+	0.0302658i
$11$	−13.2452	+	7.64711i	−1.20411	+	0.695192i	−0.961466	−	0.274924i	$-0.911347\pi$
$11$	−13.2452	+	7.64711i	−1.20411	+	0.695192i	−0.242641	+	0.970116i	$0.578014\pi$
$12$	−1.34786	−	11.8392i	−0.112322	−	0.986600i
$13$	−11.7128	+	11.7128i	−0.900984	+	0.900984i	−0.995521	−	0.0945369i	$-0.969863\pi$
$13$	−11.7128	+	11.7128i	−0.900984	+	0.900984i	0.0945369	+	0.995521i	$0.469863\pi$
$14$	1.10377	−	0.398585i	0.0788405	−	0.0284703i
$15$	−4.47046	+	14.3183i	−0.298030	+	0.954556i
$16$	7.83176	−	13.5650i	0.489485	−	0.847813i
$17$	14.7635	+	3.95586i	0.868439	+	0.232697i	0.665412	−	0.746476i	$-0.268256\pi$
$17$	14.7635	+	3.95586i	0.868439	+	0.232697i	0.203026	+	0.979173i	$0.434922\pi$
$18$	1.27942	+	0.799777i	0.0710786	+	0.0444321i
$19$	4.70012	−	8.14085i	0.247375	−	0.428466i	−0.715422	−	0.698693i	$-0.753765\pi$
$19$	4.70012	−	8.14085i	0.247375	−	0.428466i	0.962797	+	0.270227i	$0.0870987\pi$
$20$	−16.0328	+	11.7195i	−0.801642	+	0.585975i
$21$	6.71540	−	19.8973i	0.319781	−	0.947492i
$22$	1.81304	−	1.81304i	0.0824110	−	0.0824110i
$23$	8.59850	+	32.0900i	0.373848	+	1.39522i	0.855021	+	0.518594i	$0.173544\pi$
$23$	8.59850	+	32.0900i	0.373848	+	1.39522i	−0.481173	+	0.876626i	$0.659789\pi$
$24$	1.46912	+	3.73054i	0.0612134	+	0.155439i
$25$	24.4232	−	5.33910i	0.976929	−	0.213564i
$26$	1.38849	−	2.40493i	0.0534033	−	0.0924972i
$27$	25.4537	−	9.00614i	0.942729	−	0.333561i
$28$	22.8153	−	15.8897i	0.814832	−	0.567491i
$29$	6.89705			0.237829			0.118915	−	0.992904i	$-0.462059\pi$
$29$	6.89705			0.237829			0.118915	+	0.992904i	$0.462059\pi$
$30$	0.102645	−	2.51261i	0.00342150	−	0.0837536i
$31$	−31.4348	+	18.1489i	−1.01402	+	0.585447i	−0.912368	−	0.409372i	$-0.865748\pi$
$31$	−31.4348	+	18.1489i	−1.01402	+	0.585447i	−0.101657	+	0.994819i	$0.532414\pi$
$32$	−2.06325	+	7.70017i	−0.0644767	+	0.240630i
$33$	−5.19010	−	45.5882i	−0.157276	−	1.38146i
$34$	−2.56236			−0.0753635
$35$	−34.3545	+	6.69089i	−0.981557	+	0.191168i
$36$	34.1833	+	10.4574i	0.949535	+	0.290483i
$37$	4.52283	+	16.8794i	0.122239	+	0.456201i	0.999726	−	0.0233986i	$-0.00744868\pi$
$37$	4.52283	+	16.8794i	0.122239	+	0.456201i	−0.877488	+	0.479599i	$0.840782\pi$
$38$	−0.407879	+	1.52222i	−0.0107337	+	0.0400585i
$39$	−18.2086	−	46.2370i	−0.466887	−	1.18556i
$40$	4.19029	−	5.20527i	0.104757	−	0.130132i
$41$	−17.4740			−0.426195			−0.213098	−	0.977031i	$-0.568355\pi$
$41$	−17.4740			−0.426195			−0.213098	+	0.977031i	$0.568355\pi$
$42$	−0.224105	+	3.51345i	−0.00533583	+	0.0836535i
$43$	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
$45$	−34.0420	−	29.4303i	−0.756489	−	0.654006i
$46$	−2.78479	−	4.82340i	−0.0605389	−	0.104856i
$47$	2.92196	+	10.9049i	0.0621694	+	0.232019i	0.990019	−	0.140936i	$-0.0450112\pi$
$47$	2.92196	+	10.9049i	0.0621694	+	0.232019i	−0.927849	+	0.372955i	$0.878344\pi$
$48$	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
$51$	−28.5471	+	35.8823i	−0.559748	+	0.703574i
$52$	17.0282	−	63.5502i	0.327466	−	1.22212i
$53$	74.1079	+	19.8572i	1.39826	+	0.374663i	0.877721	−	0.479173i	$-0.159063\pi$
$53$	74.1079	+	19.8572i	1.39826	+	0.374663i	0.520542	+	0.853836i	$0.325730\pi$
$54$	−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
$57$	16.7725	+	22.6708i	0.294254	+	0.397734i
$58$	−1.11687	+	0.299265i	−0.0192564	+	0.00515974i
$59$	−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	$0.347138\pi$
$60$	−13.0582	−	58.1298i	−0.217636	−	0.968830i
$61$	−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
$63$	46.7042	+	42.2814i	0.741336	+	0.671134i
$64$			61.3176i			0.958088i
$65$	−51.9353	+	64.5152i	−0.799004	+	0.992541i
$66$	2.81854	+	7.15710i	0.0427051	+	0.108441i
$67$	−65.4926	−	17.5487i	−0.977502	−	0.261921i	−0.265510	−	0.964108i	$-0.585540\pi$
$67$	−65.4926	−	17.5487i	−0.977502	−	0.261921i	−0.711992	+	0.702187i	$0.752207\pi$
$68$	−58.6389	+	15.7122i	−0.862337	+	0.231062i
$69$	−98.5701	−	14.7402i	−1.42855	−	0.213626i
$70$	5.27286	−	2.57414i	0.0753266	−	0.0367734i
$71$		−	50.8917i		−	0.716784i	−0.933571	−	0.358392i	$-0.883325\pi$
$71$		−	50.8917i		−	0.716784i	0.933571	−	0.358392i	$-0.116675\pi$
$72$	−12.0208	−	0.421870i	−0.166955	−	0.00585930i
$73$	−73.2942	−	19.6391i	−1.00403	−	0.269029i	−0.280897	−	0.959738i	$-0.590632\pi$
$73$	−73.2942	−	19.6391i	−1.00403	−	0.269029i	−0.723133	+	0.690709i	$0.757299\pi$
$74$	−1.46480	−	2.53712i	−0.0197947	−	0.0342854i
$75$	−14.5338	+	73.5783i	−0.193784	+	0.981044i
$76$			37.3368i			0.491274i
$77$	87.8528	−	61.1852i	1.14095	−	0.794613i
$78$	4.95483	+	6.69729i	0.0635235	+	0.0858627i
$79$	−26.3396	−	15.2072i	−0.333412	−	0.192496i	0.323943	−	0.946077i	$-0.394991\pi$
$79$	−26.3396	−	15.2072i	−0.333412	−	0.192496i	−0.657355	+	0.753581i	$0.728325\pi$
$80$	31.6477	−	71.6385i	0.395596	−	0.895481i
$81$	−5.67841	+	80.8007i	−0.0701038	+	0.997540i
$82$	2.82965	−	0.758201i	0.0345079	−	0.00924636i
$83$	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
$87$	−8.25223	+	18.9743i	−0.0948532	+	0.218096i
$88$	−5.29031	+	19.7437i	−0.0601171	+	0.224360i
$89$	−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
$93$	−12.3176	−	108.194i	−0.132448	−	1.16338i
$94$	−0.946333	−	1.63910i	−0.0100674	−	0.0174372i
$95$	18.9929	−	42.9929i	0.199925	−	0.452556i
$96$	−18.7151	−	14.8893i	−0.194949	−	0.155097i
$97$	−17.8473	−	17.8473i	−0.183992	−	0.183992i	0.609101	−	0.793093i	$-0.291531\pi$
$97$	−17.8473	−	17.8473i	−0.183992	−	0.183992i	−0.793093	+	0.609101i	$0.791531\pi$
$98$	−7.46249	+	3.43404i	−0.0761478	+	0.0350412i
$99$	131.626	+	40.2673i	1.32956	+	0.406740i
$100$	−73.4069	+	66.8685i	−0.734069	+	0.668685i
$101$	58.5103	+	101.343i	0.579310	+	1.00339i	0.995559	+	0.0941439i	$0.0300114\pi$
$101$	58.5103	+	101.343i	0.579310	+	1.00339i	−0.416248	+	0.909251i	$0.636655\pi$
$102$	3.06583	−	7.04924i	0.0300571	−	0.0691102i
$103$	−3.47170	−	12.9566i	−0.0337058	−	0.125792i	0.947023	−	0.321166i	$-0.104075\pi$
$103$	−3.47170	−	12.9566i	−0.0337058	−	0.125792i	−0.980729	+	0.195374i	$0.937408\pi$
$104$			22.1377i			0.212863i
$105$	22.6976	−	102.517i	0.216167	−	0.976356i
$106$	−12.8622			−0.121342
$107$	−16.9453	+	4.54048i	−0.158367	+	0.0424344i	−0.337132	−	0.941458i	$-0.609457\pi$
$107$	−16.9453	+	4.54048i	−0.158367	+	0.0424344i	0.178764	+	0.983892i	$0.442790\pi$
$108$	−69.6688	+	81.5286i	−0.645082	+	0.754895i
$109$	145.191	−	83.8258i	1.33202	−	0.769044i	0.346414	−	0.938082i	$-0.387399\pi$
$109$	145.191	−	83.8258i	1.33202	−	0.769044i	0.985610	+	0.169038i	$0.0540660\pi$
$110$	8.03914	−	9.98641i	0.0730831	−	0.0907855i
$111$	−51.8481	−	7.75336i	−0.467100	−	0.0698501i
$112$	−46.5886	+	99.2545i	−0.415970	+	0.886201i
$113$	−24.5772	+	24.5772i	−0.217497	+	0.217497i	−0.807443	−	0.589946i	$-0.799149\pi$
$113$	−24.5772	+	24.5772i	−0.217497	+	0.217497i	0.589946	+	0.807443i	$0.299149\pi$
$114$	−3.69973	−	2.94343i	−0.0324538	−	0.0258195i
$115$	59.9767	+	154.905i	0.521536	+	1.34700i
$116$	−23.7242	+	13.6972i	−0.204519	+	0.118079i
$117$	148.988	+	5.22874i	1.27340	+	0.0446901i
$118$	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
$122$	9.70009	+	2.59913i	0.0795090	+	0.0213044i
$123$	20.9074	−	48.0723i	0.169979	−	0.390832i
$124$	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	$0.265448\pi$
$128$	−10.9136	−	40.7301i	−0.0852625	−	0.318204i
$129$	−133.420	+	52.5423i	−1.03427	+	0.407305i
$130$	5.61078	−	12.7007i	0.0431599	−	0.0976979i
$131$	86.6805	−	150.135i	0.661683	−	1.14607i	−0.318490	−	0.947926i	$-0.603176\pi$
$131$	86.6805	−	150.135i	0.661683	−	1.14607i	0.980173	−	0.198142i	$-0.0634909\pi$
$132$	108.388	+	146.505i	0.821124	+	1.10989i
$133$	−27.9595	+	59.5662i	−0.210222	+	0.447866i
$134$	11.3670			0.0848280
$135$	121.696	−	58.4393i	0.901450	−	0.432883i
$136$	17.6902	−	10.2134i	0.130075	−	0.0750987i
$137$	−36.8296	+	137.450i	−0.268829	+	1.00328i	0.691036	+	0.722820i	$0.257155\pi$
$137$	−36.8296	+	137.450i	−0.268829	+	1.00328i	−0.959865	+	0.280463i	$0.909512\pi$
$138$	16.6015	−	1.89004i	0.120301	−	0.0136959i
$139$	51.6190			0.371360			0.185680	−	0.982610i	$-0.440551\pi$
$139$	51.6190			0.371360			0.185680	+	0.982610i	$0.440551\pi$
$140$	104.884	−	91.2413i	0.749168	−	0.651724i
$141$	−33.4963	−	5.00904i	−0.237563	−	0.0355251i
$142$	2.20820	+	8.24112i	0.0155507	+	0.0580360i
$143$	65.5691	−	244.707i	0.458525	−	1.71124i
$144$	−137.364	+	31.6878i	−0.953918	+	0.220054i
$145$	34.2858	−	3.70383i	0.236454	−	0.0255436i
$146$	12.7210			0.0871302
$147$	−35.0503	+	142.760i	−0.238438	+	0.971158i
$148$	−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	$0.242460\pi$
$150$	−0.839056	−	12.5455i	−0.00559371	−	0.0836366i
$151$	51.7923	+	89.7069i	0.342995	+	0.594086i	0.984987	−	0.172626i	$-0.0552251\pi$
$151$	51.7923	+	89.7069i	0.342995	+	0.594086i	−0.641992	+	0.766711i	$0.721892\pi$
$152$	−3.25157	−	12.1350i	−0.0213919	−	0.0798356i
$153$	−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
$156$	154.457	+	122.883i	0.990112	+	0.787711i
$157$	30.7462	−	114.747i	0.195836	−	0.730869i	−0.796213	−	0.605016i	$-0.793167\pi$
$157$	30.7462	−	114.747i	0.195836	−	0.730869i	0.992049	−	0.125853i	$-0.0401668\pi$
$158$	4.92513	+	1.31968i	0.0311717	+	0.00835243i
$159$	−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
$162$	−2.58643	−	13.3308i	−0.0159656	−	0.0822890i
$163$	−22.2496	+	5.96176i	−0.136501	+	0.0365752i	−0.326422	−	0.945224i	$-0.605843\pi$
$163$	−22.2496	+	5.96176i	−0.136501	+	0.0365752i	0.189922	+	0.981799i	$0.439177\pi$
$164$	60.1064	−	34.7025i	0.366503	−	0.211600i
$165$	−50.2819	−	223.835i	−0.304739	−	1.35658i
$166$	−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	$0.325641\pi$
$168$	−12.4572	−	25.1496i	−0.0741501	−	0.149700i
$169$		−	105.379i		−	0.623546i
$170$	−12.7377	+	1.37603i	−0.0749276	+	0.00809428i
$171$	−82.4372	+	19.0170i	−0.482089	+	0.111211i
$172$	−183.379	−	49.1363i	−1.06616	−	0.285676i
$173$	−194.196	+	52.0348i	−1.12252	+	0.300779i	−0.771904	−	0.635739i	$-0.780695\pi$
$173$	−194.196	+	52.0348i	−1.12252	+	0.300779i	−0.350619	+	0.936518i	$0.614029\pi$
$174$	0.513021	−	3.43066i	0.00294840	−	0.0197165i
$175$	−167.186	+	51.7098i	−0.955347	+	0.295485i
$176$			239.561i			1.36114i
$177$	−1.73606	−	15.2490i	−0.00980828	−	0.0861528i
$178$	6.22267	+	1.66736i	0.0349588	+	0.00936719i
$179$	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	$0.450467\pi$
$180$	175.543	+	33.6275i	0.975241	+	0.186819i
$181$		−	200.663i		−	1.10864i	−0.832304	−	0.554319i	$-0.812979\pi$
$181$		−	200.663i		−	1.10864i	0.832304	−	0.554319i	$-0.187021\pi$
$182$	−8.25965	+	17.5967i	−0.0453827	+	0.0966853i
$183$	144.466	−	106.879i	0.789429	−	0.584041i
$184$	38.4516	+	22.2000i	0.208976	+	0.120652i
$185$	31.5479	+	81.4801i	0.170529	+	0.440433i
$186$	6.68923	+	16.9859i	0.0359636	+	0.0913222i
$187$	−225.795	+	60.5017i	−1.20746	+	0.323539i
$188$	−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	0.995680	−	0.0928471i	$-0.0295968\pi$
$191$	269.905	+	155.829i	1.41311	+	0.815861i	0.417432	+	0.908708i	$0.362930\pi$
$192$	−168.690	−	73.3657i	−0.878591	−	0.382113i
$193$	−51.4216	+	191.908i	−0.266433	+	0.994342i	0.694934	+	0.719073i	$0.255433\pi$
$193$	−51.4216	+	191.908i	−0.266433	+	0.994342i	−0.961367	+	0.275269i	$0.911233\pi$
$194$	3.66449	+	2.11569i	0.0188891	+	0.0109056i
$195$	−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	0.808698	−	0.588224i	$-0.200173\pi$
$197$	43.4334	+	43.4334i	0.220474	+	0.220474i	−0.588224	+	0.808698i	$0.700173\pi$
$198$	−23.0621	−	0.809365i	−0.116475	−	0.00408770i
$199$	110.179	+	190.836i	0.553666	+	0.958977i	0.998006	+	0.0631192i	$0.0201048\pi$
$199$	110.179	+	190.836i	0.553666	+	0.958977i	−0.444340	+	0.895858i	$0.646562\pi$
$200$	18.0349	−	28.1261i	0.0901747	−	0.140630i
$201$	126.639	−	159.178i	0.630044	−	0.791932i
$202$	−13.8721	−	13.8721i	−0.0686739	−	0.0686739i
$203$	−48.1061	+	4.08636i	−0.236976	+	0.0201299i
$204$	26.9351	−	180.120i	0.132035	−	0.882939i
$205$	−86.8647	+	9.38383i	−0.423730	+	0.0457748i
$206$	1.12438	+	1.94748i	0.00545813	+	0.00945377i
$207$	158.489	−	253.538i	0.765648	−	1.22482i
$208$	67.1524	+	250.616i	0.322848	+	1.20488i
$209$			143.769i			0.687892i
$210$	0.772734	+	17.5860i	0.00367969	+	0.0837427i
$211$	−58.7982			−0.278665			−0.139332	−	0.990246i	$-0.544496\pi$
$211$	−58.7982			−0.278665			−0.139332	+	0.990246i	$0.544496\pi$
$212$	−294.349	+	78.8705i	−1.38844	+	0.372031i
$213$	140.007	+	60.8912i	0.657309	+	0.285874i
$214$	2.54702	−	1.47052i	0.0119019	−	0.00687159i
$215$	186.164	+	149.863i	0.865877	+	0.697038i
$216$	15.5433	−	32.5653i	0.0719597	−	0.150765i
$217$	208.501	−	145.211i	0.960834	−	0.669174i
$218$	−19.8741	+	19.8741i	−0.0911658	+	0.0911658i
$219$	141.724	−	178.140i	0.647143	−	0.813425i
$220$	122.737	−	277.832i	0.557898	−	1.26287i
$221$	−219.256	+	126.587i	−0.992106	+	0.572793i
$222$	8.73242	−	0.994163i	0.0393352	−	0.00447821i
$223$	129.563	−	129.563i	0.581002	−	0.581002i	−0.354177	−	0.935179i	$-0.615239\pi$
$223$	129.563	−	129.563i	0.581002	−	0.581002i	0.935179	+	0.354177i	$0.115239\pi$
$224$	9.82875	−	54.9302i	0.0438784	−	0.245224i
$225$	−185.030	−	128.019i	−0.822356	−	0.568974i
$226$	2.91348	−	5.04630i	0.0128915	−	0.0223288i
$227$	105.537	+	28.2785i	0.464920	+	0.124575i	0.483672	−	0.875249i	$-0.339303\pi$
$227$	105.537	+	28.2785i	0.464920	+	0.124575i	−0.0187523	+	0.999824i	$0.505969\pi$
$228$	−102.716	−	44.6730i	−0.450510	−	0.195934i
$229$	−77.7730	+	134.707i	−0.339620	+	0.588239i	−0.984361	−	0.176162i	$-0.943632\pi$
$229$	−77.7730	+	134.707i	−0.339620	+	0.588239i	0.644741	+	0.764401i	$0.276965\pi$
$230$	−16.4336	−	22.4820i	−0.0714506	−	0.0977478i
$231$	63.2104	+	314.897i	0.273638	+	1.36319i
$232$	6.51787	−	6.51787i	0.0280943	−	0.0280943i
$233$	−93.5221	−	349.029i	−0.401382	−	1.49798i	−0.810632	−	0.585557i	$-0.800876\pi$
$233$	−93.5221	−	349.029i	−0.401382	−	1.49798i	0.409249	−	0.912423i	$-0.365791\pi$
$234$	−24.3532	+	5.61790i	−0.104073	+	0.0240081i
$235$	20.3814	+	52.6400i	0.0867294	+	0.224000i
$236$	10.1598	−	17.5973i	0.0430500	−	0.0745649i
$237$	73.3510	−	54.2670i	0.309498	−	0.228975i
$238$	17.8721	−	1.51815i	0.0750931	−	0.00637876i
$239$	−309.068			−1.29317			−0.646586	−	0.762841i	$-0.723804\pi$
$239$	−309.068			−1.29317			−0.646586	+	0.762841i	$0.723804\pi$
$240$	159.217	+	172.780i	0.663404	+	0.719915i
$241$	−132.911	+	76.7360i	−0.551497	+	0.318407i	−0.749725	−	0.661749i	$-0.769814\pi$
$241$	−132.911	+	76.7360i	−0.551497	+	0.318407i	0.198229	+	0.980156i	$0.436481\pi$
$242$	−4.89932	+	18.2845i	−0.0202451	+	0.0755559i
$243$	−215.495	−	112.299i	−0.886810	−	0.462135i
$244$	237.922			0.975089
$245$	235.654	−	67.0225i	0.961855	−	0.273561i
$246$	−1.29976	+	8.69175i	−0.00528359	+	0.0353323i
$247$	40.3006	+	150.404i	0.163160	+	0.608922i
$248$	−12.5555	+	46.8577i	−0.0506269	+	0.188942i
$249$	−43.3020	+	17.0528i	−0.173904	+	0.0684849i
$250$	−17.4754	+	11.5654i	−0.0699017	+	0.0462615i
$251$	−188.250			−0.750001			−0.375001	−	0.927025i	$-0.622357\pi$
$251$	−188.250			−0.750001			−0.375001	+	0.927025i	$0.622357\pi$
$252$	−244.620	−	52.6861i	−0.970714	−	0.209072i
$253$	−359.285	−	359.285i	−1.42010	−	1.42010i
$254$	1.03285	−	1.78895i	0.00406634	−	0.00704311i
$255$	−122.641	+	193.704i	−0.480944	+	0.759623i
$256$	−119.101	−	206.288i	−0.465237	−	0.805814i
$257$	47.6632	+	177.882i	0.185460	+	0.692146i	0.994532	+	0.104436i	$0.0333037\pi$
$257$	47.6632	+	177.882i	0.185460	+	0.692146i	−0.809072	+	0.587710i	$0.800030\pi$
$258$	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
$261$	−42.3261	−	45.4050i	−0.162169	−	0.173966i
$262$	−7.52217	+	28.0731i	−0.0287106	+	0.107149i
$263$	266.665	+	71.4527i	1.01394	+	0.271683i	0.727273	−	0.686348i	$-0.240787\pi$
$263$	266.665	+	71.4527i	1.01394	+	0.271683i	0.286663	+	0.958031i	$0.407454\pi$
$264$	−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
$267$	92.6756	−	68.5638i	0.347100	−	0.256793i
$268$	260.130	−	69.7016i	0.970633	−	0.260080i
$269$	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	$-0.0624963\pi$
$270$	−17.1711	+	14.7437i	−0.0635965	+	0.0546064i
$271$	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
$273$	154.397	+	311.709i	0.565558	+	1.14179i
$274$		−	23.8559i		−	0.0870654i
$275$	−282.661	+	257.484i	−1.02786	+	0.936307i
$276$	368.331	−	145.052i	1.33453	−	0.525552i
$277$	289.469	+	77.5629i	1.04501	+	0.280011i	0.740190	−	0.672398i	$-0.234736\pi$
$277$	289.469	+	77.5629i	1.04501	+	0.280011i	0.304824	+	0.952409i	$0.401402\pi$
$278$	−8.35890	+	2.23976i	−0.0300680	+	0.00805669i
$279$	312.389	+	95.5663i	1.11967	+	0.342531i
$280$	−26.1427	+	38.7888i	−0.0933670	+	0.138532i
$281$			46.6699i			0.166085i	0.996546	+	0.0830425i	$0.0264637\pi$
$281$			46.6699i			0.166085i	−0.996546	+	0.0830425i	$0.973536\pi$
$282$	5.64155	−	0.642276i	0.0200055	−	0.00227758i
$283$	113.369	+	30.3772i	0.400598	+	0.107340i	0.453492	−	0.891260i	$-0.350178\pi$
$283$	113.369	+	30.3772i	0.400598	+	0.107340i	−0.0528940	+	0.998600i	$0.516845\pi$
$284$	101.068	+	175.055i	0.355874	+	0.616391i
$285$	95.5518	+	103.691i	0.335270	+	0.363829i
$286$			42.4716i			0.148502i
$287$	121.879	−	10.3530i	0.424666	−	0.0360732i
$288$	63.3540	−	33.6718i	0.219979	−	0.116916i
$289$	−47.9705	−	27.6958i	−0.165988	−	0.0958332i
$290$	−5.39134	+	2.08745i	−0.0185908	+	0.00719809i
$291$	70.4532	−	27.7452i	0.242107	−	0.0953442i
$292$	291.117	−	78.0046i	0.996976	−	0.267139i
$293$	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
$297$	−268.268	+	313.935i	−0.903258	+	1.05702i
$298$	3.04983	−	11.3821i	0.0102343	−	0.0381951i
$299$	−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
$303$	−348.809	+	39.7110i	−1.15118	+	0.131059i
$304$	−73.6205	−	127.514i	−0.242173	−	0.419455i
$305$	−273.964	−	121.029i	−0.898242	−	0.396816i
$306$	15.7248	+	16.8687i	0.0513882	+	0.0551263i
$307$	−266.516	−	266.516i	−0.868131	−	0.868131i	0.124134	−	0.992265i	$-0.460385\pi$
$307$	−266.516	−	266.516i	−0.868131	−	0.868131i	−0.992265	+	0.124134i	$0.960385\pi$
$308$	−180.682	+	384.933i	−0.586630	+	1.24978i
$309$	39.7983	+	5.95144i	0.128797	+	0.0192603i
$310$	19.0793	−	23.7007i	0.0615461	−	0.0764540i
$311$	−111.647	−	193.379i	−0.358994	−	0.621796i	0.628799	−	0.777568i	$-0.283547\pi$
$311$	−111.647	−	193.379i	−0.358994	−	0.621796i	−0.987793	+	0.155772i	$0.950214\pi$
$312$	−60.9026	−	26.4875i	−0.195200	−	0.0848958i
$313$	102.063	+	380.906i	0.326081	+	1.21695i	0.913221	+	0.407465i	$0.133587\pi$
$313$	102.063	+	380.906i	0.326081	+	1.21695i	−0.587140	+	0.809486i	$0.699746\pi$
$314$			19.9155i			0.0634252i
$315$	254.876	+	185.103i	0.809130	+	0.587630i
$316$	120.802			0.382286
$317$	115.845	−	31.0406i	0.365442	−	0.0979200i	−0.0714248	−	0.997446i	$-0.522755\pi$
$317$	115.845	−	31.0406i	0.365442	−	0.0979200i	0.436867	+	0.899526i	$0.356088\pi$
$318$	15.3895	−	35.3850i	0.0483946	−	0.111274i
$319$	−91.3527	+	52.7425i	−0.286372	+	0.165337i
$320$	32.9286	+	304.815i	0.102902	+	0.952546i
$321$	7.78362	−	52.0504i	0.0242480	−	0.162151i
$322$	22.2813	+	31.9927i	0.0691967	+	0.0993561i
$323$	101.594	−	101.594i	0.314533	−	0.314533i
$324$	−140.934	−	289.212i	−0.434980	−	0.892630i
$325$	−223.529	+	348.600i	−0.687780	+	1.07262i
$326$	3.34430	−	1.93083i	0.0102586	−	0.00592279i
$327$	56.8926	+	499.727i	0.173984	+	1.52822i
$328$	−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	$0.0484363\pi$
$332$	−59.5162	−	15.9473i	−0.179266	−	0.0480341i
$333$	83.3657	−	133.361i	0.250347	−	0.400484i
$334$	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	$0.360365\pi$
$338$	4.57243	+	17.0645i	0.0135279	+	0.0504868i
$339$	−38.2074	−	97.0199i	−0.112706	−	0.286194i
$340$	−283.061	+	109.597i	−0.832532	+	0.322344i
$341$	277.573	−	480.770i	0.813996	−	1.40988i
$342$	12.5243	−	6.65648i	0.0366207	−	0.0194634i
$343$	−331.976	+	86.2626i	−0.967859	+	0.251495i
$344$	63.8801			0.185698
$345$	−497.916	−	20.3408i	−1.44323	−	0.0589589i
$346$	29.1893	−	16.8525i	0.0843622	−	0.0487065i
$347$	174.511	−	651.282i	0.502912	−	1.87689i	0.0226990	−	0.999742i	$-0.492774\pi$
$347$	174.511	−	651.282i	0.502912	−	1.87689i	0.480213	−	0.877152i	$-0.340559\pi$
$348$	−9.29628	−	81.6556i	−0.0267135	−	0.234643i
$349$	−513.119			−1.47025			−0.735127	−	0.677929i	$-0.762878\pi$
$349$	−513.119			−1.47025			−0.735127	+	0.677929i	$0.762878\pi$
$350$	24.8295	−	15.6278i	0.0709413	−	0.0446510i
$351$	−192.647	+	403.621i	−0.548851	+	1.14992i
$352$	−31.5558	−	117.768i	−0.0896473	−	0.334568i
$353$	−87.2361	+	325.569i	−0.247128	+	0.922293i	0.725174	+	0.688565i	$0.241759\pi$
$353$	−87.2361	+	325.569i	−0.247128	+	0.922293i	−0.972302	+	0.233728i	$0.924908\pi$
$354$	0.942788	+	2.39402i	0.00266324	+	0.00676277i
$355$	−27.3296	−	252.986i	−0.0769849	−	0.712638i
$356$	152.628			0.428731
$357$	177.853	−	267.188i	0.498189	−	0.748426i
$358$	−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	$0.0258603\pi$
$360$	−59.9828	+	4.35820i	−0.166619	+	0.0121061i
$361$	136.318	+	236.109i	0.377611	+	0.654042i
$362$	8.70683	+	32.4943i	0.0240520	+	0.0897634i
$363$	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
$366$	−18.7564	+	23.5759i	−0.0512471	+	0.0644149i
$367$	−24.8655	+	92.7994i	−0.0677535	+	0.252859i	−0.991493	−	0.130163i	$-0.958450\pi$
$367$	−24.8655	+	92.7994i	−0.0677535	+	0.252859i	0.923739	+	0.383022i	$0.125117\pi$
$368$	502.643	+	134.683i	1.36588	+	0.365986i
$369$	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
$372$	257.238	+	347.700i	0.691500	+	0.934679i
$373$	28.7248	−	7.69678i	0.0770101	−	0.0206348i	−0.220108	−	0.975475i	$-0.570641\pi$
$373$	28.7248	−	7.69678i	0.0770101	−	0.0206348i	0.297118	+	0.954841i	$0.403974\pi$
$374$	33.9389	−	19.5946i	0.0907457	−	0.0523921i
$375$	−32.7359	+	373.568i	−0.0872957	+	0.996182i
$376$	13.0667	+	7.54407i	0.0347519	+	0.0200640i
$377$	−80.7838	+	80.7838i	−0.214281	+	0.214281i
$378$	24.5052	−	20.0861i	0.0648286	−	0.0531379i
$379$			227.162i			0.599373i	0.954038	+	0.299686i	$0.0968821\pi$
$379$			227.162i			0.599373i	−0.954038	+	0.299686i	$0.903118\pi$
$380$	20.0505	+	185.604i	0.0527644	+	0.488432i
$381$	−13.5448	−	34.3942i	−0.0355506	−	0.0902736i
$382$	−50.4683	−	13.5230i	−0.132116	−	0.0354004i
$383$	52.8830	−	14.1699i	0.138076	−	0.0369973i	−0.189119	−	0.981954i	$-0.560563\pi$
$383$	52.8830	−	14.1699i	0.138076	−	0.0369973i	0.327195	+	0.944957i	$0.393897\pi$
$384$	125.110	+	18.7089i	0.325806	+	0.0487211i
$385$	403.866	−	351.335i	1.04900	−	0.912557i
$386$		−	33.3077i		−	0.0862895i
$387$	15.0879	−	429.916i	0.0389869	−	1.11089i
$388$	96.8340	+	25.9466i	0.249572	+	0.0668727i
$389$	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	$0.746908\pi$
$390$	28.2274	+	30.6319i	0.0723780	+	0.0785434i
$391$			507.774i			1.29866i
$392$	37.8321	−	53.4532i	0.0965104	−	0.136360i
$393$	309.321	+	418.099i	0.787076	+	1.06387i
$394$	−8.91794	−	5.14878i	−0.0226344	−	0.0130680i
$395$	−139.103	−	61.4512i	−0.352158	−	0.155573i
$396$	−532.732	+	122.893i	−1.34528	+	0.310336i
$397$	−277.248	+	74.2885i	−0.698359	+	0.187125i	−0.590495	−	0.807041i	$-0.701068\pi$
$397$	−277.248	+	74.2885i	−0.698359	+	0.187125i	−0.107864	+	0.994166i	$0.534401\pi$
$398$	−26.1223	−	26.1223i	−0.0656339	−	0.0656339i
$399$	−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	0.995818	−	0.0913615i	$-0.0291219\pi$
$401$	567.257	+	327.506i	1.41461	+	0.816723i	0.418788	+	0.908084i	$0.362455\pi$
$402$	−13.6004	+	31.2714i	−0.0338319	+	0.0777895i
$403$	155.615	−	580.763i	0.386141	−	1.44110i
$404$	−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
$408$	6.93186	+	60.8872i	0.0169898	+	0.149233i
$409$	−235.407	−	407.738i	−0.575568	−	0.996914i	−0.995980	−	0.0895799i	$-0.971448\pi$
$409$	−235.407	−	407.738i	−0.575568	−	0.996914i	0.420411	−	0.907334i	$-0.361886\pi$
$410$	13.6592	−	5.28864i	0.0333152	−	0.0128991i
$411$	−334.069	−	265.778i	−0.812819	−	0.646661i
$412$	37.6728	+	37.6728i	0.0914389	+	0.0914389i
$413$	29.3864	−	20.4662i	0.0711535	−	0.0495549i
$414$	−14.6638	+	47.9334i	−0.0354199	+	0.115781i
$415$	60.4199	+	48.6385i	0.145590	+	0.117201i
$416$	−66.0240	−	114.357i	−0.158712	−	0.274897i
$417$	−61.7615	+	142.008i	−0.148109	+	0.340546i
$418$	−6.23819	−	23.2812i	−0.0149239	−	0.0556967i
$419$		−	582.158i		−	1.38940i	−0.719300	−	0.694699i	$-0.755537\pi$
$419$		−	582.158i		−	1.38940i	0.719300	−	0.694699i	$-0.244463\pi$
$420$	125.520	+	397.712i	0.298857	+	0.946932i
$421$	360.182			0.855540			0.427770	−	0.903888i	$-0.359299\pi$
$421$	360.182			0.855540			0.427770	+	0.903888i	$0.359299\pi$
$422$	9.52147	−	2.55127i	0.0225627	−	0.00604566i
$423$	53.8581	−	86.1577i	0.127324	−	0.203682i
$424$	88.7991	−	51.2682i	0.209432	−	0.120916i
$425$	381.692	+	17.7912i	0.898099	+	0.0418617i
$426$	−25.3140	−	3.78546i	−0.0594226	−	0.00888605i
$427$	379.575	+	178.167i	0.888933	+	0.417252i
$428$	49.2706	−	49.2706i	0.115118	−	0.115118i
$429$	594.755	+	473.174i	1.38638	+	1.10297i
$430$	−36.6489	−	16.1904i	−0.0852300	−	0.0376520i
$431$	−350.070	+	202.113i	−0.812227	+	0.468939i	−0.847729	−	0.530430i	$-0.822030\pi$
$431$	−350.070	+	202.113i	−0.812227	+	0.468939i	0.0355017	+	0.999370i	$0.488697\pi$
$432$	77.1787	−	415.813i	0.178654	−	0.962531i
$433$	23.1671	−	23.1671i	0.0535036	−	0.0535036i	−0.679849	−	0.733352i	$-0.737955\pi$
$433$	23.1671	−	23.1671i	0.0535036	−	0.0535036i	0.733352	+	0.679849i	$0.237955\pi$
$434$	−27.4628	+	32.5615i	−0.0632783	+	0.0750266i
$435$	−30.8330	+	98.7544i	−0.0708804	+	0.227022i
$436$	−332.947	+	576.682i	−0.763640	+	1.32266i
$437$	301.654	+	80.8280i	0.690284	+	0.184961i
$438$	−15.2205	+	34.9965i	−0.0347501	+	0.0799006i
$439$	252.925	−	438.079i	0.576139	−	0.997902i	−0.419778	−	0.907627i	$-0.637892\pi$
$439$	252.925	−	438.079i	0.576139	−	0.997902i	0.995917	−	0.0902749i	$-0.0287746\pi$
$440$	−15.6958	+	100.988i	−0.0356724	+	0.229519i
$441$	−350.807	−	267.237i	−0.795481	−	0.605979i
$442$	30.0124	−	30.0124i	0.0679013	−	0.0679013i
$443$	32.5153	+	121.349i	0.0733979	+	0.273925i	0.992865	−	0.119242i	$-0.0380463\pi$
$443$	32.5153	+	121.349i	0.0733979	+	0.273925i	−0.919467	+	0.393166i	$0.871380\pi$
$444$	193.743	−	76.2979i	0.436358	−	0.171842i
$445$	−175.750	−	77.6407i	−0.394943	−	0.174474i
$446$	−15.3590	+	26.6026i	−0.0344372	+	0.0596470i
$447$	−125.413	−	169.517i	−0.280566	−	0.379232i
$448$	−36.3295	−	427.683i	−0.0810926	−	0.954650i
$449$	550.812			1.22675			0.613376	−	0.789791i	$-0.289811\pi$
$449$	550.812			1.22675			0.613376	+	0.789791i	$0.289811\pi$
$450$	35.5175	+	12.7022i	0.0789278	+	0.0282271i
$451$	231.446	−	133.626i	0.513185	−	0.296287i
$452$	35.7306	−	133.349i	0.0790501	−	0.295019i
$453$	−308.759	+	35.1515i	−0.681588	+	0.0775971i
$454$	−18.3171			−0.0403460
$455$	324.018	−	480.756i	0.712128	−	1.05661i
$456$	37.2748	+	5.57407i	0.0817430	+	0.0122238i
$457$	59.4023	+	221.692i	0.129983	+	0.485104i	0.999968	−	0.00797430i	$-0.00253833\pi$
$457$	59.4023	+	221.692i	0.129983	+	0.485104i	−0.869985	+	0.493078i	$0.835872\pi$
$458$	6.74918	−	25.1883i	0.0147362	−	0.0549962i
$459$	411.411	−	32.2707i	0.896321	−	0.0703065i
$460$	−513.938	−	413.724i	−1.11726	−	0.899400i
$461$	−532.899			−1.15596			−0.577982	−	0.816050i	$-0.696160\pi$
$461$	−532.899			−1.15596			−0.577982	+	0.816050i	$0.696160\pi$
$462$	−23.8994	−	48.2500i	−0.0517303	−	0.104437i
$463$	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
$465$	−119.334	−	531.228i	−0.256632	−	1.14242i
$466$	30.2889	+	52.4619i	0.0649977	+	0.112579i
$467$	−67.0547	−	250.251i	−0.143586	−	0.535870i	−0.999814	−	0.0192726i	$-0.993865\pi$
$467$	−67.0547	−	250.251i	−0.143586	−	0.535870i	0.856228	−	0.516598i	$-0.172802\pi$
$468$	−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
$471$	278.889	+	221.878i	0.592121	+	0.471078i
$472$	−1.76958	+	6.60418i	−0.00374912	+	0.0139919i
$473$	−706.121	−	189.205i	−1.49286	−	0.400010i
$474$	−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
$477$	−324.064	−	609.731i	−0.679379	−	1.27826i
$478$	50.0488	−	13.4105i	0.104705	−	0.0280555i
$479$	−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	$0.551815\pi$
$480$	−101.030	−	63.9656i	−0.210479	−	0.133262i
$481$	−250.680	−	144.730i	−0.521165	−	0.300895i
$482$	18.1932	−	18.1932i	0.0377453	−	0.0377453i
$483$	696.248	+	44.4102i	1.44151	+	0.0919465i
$484$			448.479i			0.926609i
$485$	−98.3044	−	79.1359i	−0.202689	−	0.163167i
$486$	39.7687	+	8.83467i	0.0818286	+	0.0181783i
$487$	527.352	+	141.304i	1.08286	+	0.290151i	0.755767	−	0.654841i	$-0.227264\pi$
$487$	527.352	+	141.304i	1.08286	+	0.290151i	0.327093	+	0.944992i	$0.393931\pi$
$488$	−77.3281	+	20.7200i	−0.158459	+	0.0424590i
$489$	10.2201	−	68.3435i	0.0209000	−	0.139762i
$490$	−35.2525	+	21.0784i	−0.0719438	+	0.0430170i
$491$			134.524i			0.273980i	0.990572	+	0.136990i	$0.0437428\pi$
$491$			134.524i			0.273980i	−0.990572	+	0.136990i	$0.956257\pi$
$492$	23.5526	+	206.878i	0.0478711	+	0.420485i
$493$	101.824	+	27.2837i	0.206540	+	0.0553423i
$494$	−13.0521	−	22.6069i	−0.0264213	−	0.0457630i
$495$	675.949	+	129.486i	1.36555	+	0.261588i
$496$			568.551i			1.14627i
$497$	30.1523	+	354.963i	0.0606686	+	0.714212i
$498$	6.27216	−	4.64031i	0.0125947	−	0.00931790i
$499$	−449.573	−	259.561i	−0.900948	−	0.520162i	−0.0234401	−	0.999725i	$-0.507462\pi$
$499$	−449.573	−	259.561i	−0.900948	−	0.520162i	−0.877508	+	0.479563i	$0.840795\pi$
$500$	−329.002	+	371.829i	−0.658004	+	0.743658i
$501$	−86.4285	−	219.467i	−0.172512	−	0.438059i
$502$	30.4842	−	8.16822i	0.0607255	−	0.0162714i
$503$	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
$507$	289.906	+	126.085i	0.571808	+	0.248688i
$508$	12.6668	−	47.2730i	0.0249346	−	0.0930571i
$509$	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
$513$	46.3178	−	249.545i	0.0902880	−	0.486442i
$514$	−15.4366	−	26.7370i	−0.0300324	−	0.0520176i
$515$	−24.2160	−	62.5437i	−0.0470213	−	0.121444i
$516$	354.588	−	445.699i	0.687187	−	0.863758i
$517$	−122.093	−	122.093i	−0.236156	−	0.236156i
$518$	11.7200	+	16.8282i	0.0226255	+	0.0324869i
$519$	89.2018	−	596.508i	0.171873	−	1.14934i
$520$	11.8883	+	110.048i	0.0228621	+	0.211631i
$521$	319.011	+	552.544i	0.612306	+	1.06054i	0.990851	+	0.134962i	$0.0430911\pi$
$521$	319.011	+	552.544i	0.612306	+	1.06054i	−0.378545	+	0.925583i	$0.623576\pi$
$522$	8.82419	+	5.51610i	0.0169046	+	0.0105672i
$523$	−187.288	−	698.967i	−0.358103	−	1.33646i	−0.876535	−	0.481339i	$-0.840151\pi$
$523$	−187.288	−	698.967i	−0.358103	−	1.33646i	0.518432	−	0.855119i	$-0.326516\pi$
$524$			688.571i			1.31407i
$525$	57.7779	−	521.811i	0.110053	−	0.993926i
$526$	−46.2827			−0.0879898
$527$	−535.880	+	143.589i	−1.01685	+	0.272464i
$528$	−659.051	−	286.632i	−1.24820	−	0.542864i
$529$	−497.709	+	287.353i	−0.940849	+	0.543200i
$530$	−63.9392	+	6.90723i	−0.120640	+	0.0130325i
$531$	44.0285	+	13.4692i	0.0829161	+	0.0253658i
$532$	−22.1213	−	260.420i	−0.0415814	−	0.489511i
$533$	204.670	−	204.670i	0.383995	−	0.383995i
$534$	−12.0324	+	15.1241i	−0.0225325	+	0.0283222i
$535$	−81.7981	+	31.6710i	−0.152894	+	0.0591981i
$536$	−78.4759	+	45.3081i	−0.146410	+	0.0845300i
$537$	−995.668	+	113.354i	−1.85413	+	0.211088i
$538$	−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	$0.00451647\pi$
$542$	−32.4402	−	8.69232i	−0.0598527	−	0.0160375i
$543$	552.040	+	240.091i	1.01665	+	0.442157i
$544$	−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	$0.332127\pi$
$548$	−146.283	−	545.936i	−0.266940	−	0.996234i
$549$	121.182	+	525.316i	0.220733	+	0.956859i
$550$	34.6003	−	53.9604i	0.0629097	−	0.0981097i
$551$	32.4170	−	56.1479i	0.0588330	−	0.101902i
$552$	−107.081	+	79.2212i	−0.193987	+	0.143517i
$553$	192.725	+	90.4625i	0.348509	+	0.163585i
$554$	−50.2405			−0.0906867
$555$	−261.905	−	10.6993i	−0.471900	−	0.0192780i
$556$	−177.557	+	102.513i	−0.319347	+	0.184375i
$557$	−131.527	+	490.865i	−0.236134	+	0.881265i	0.741500	+	0.670953i	$0.234115\pi$
$557$	−131.527	+	490.865i	−0.236134	+	0.881265i	−0.977634	+	0.210312i	$0.932552\pi$
$558$	−54.7332	−	1.92086i	−0.0980881	−	0.00344241i
$559$	−791.743			−1.41636
$560$	−178.294	+	518.421i	−0.318383	+	0.925751i
$561$	103.716	−	693.570i	0.184878	−	1.23631i
$562$	−2.02502	−	7.55747i	−0.00360323	−	0.0134474i
$563$	150.079	−	560.102i	0.266570	−	0.994853i	−0.694712	−	0.719288i	$-0.744468\pi$
$563$	150.079	−	560.102i	0.266570	−	0.994853i	0.961282	−	0.275565i	$-0.0888649\pi$
$564$	125.167	−	49.2920i	0.221927	−	0.0873972i
$565$	−108.977	+	135.373i	−0.192879	+	0.239599i
$566$	−19.6765			−0.0347641
$567$	−8.26659	−	566.940i	−0.0145795	−	0.999894i
$568$	−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	$0.0813324\pi$
$570$	−19.9723	−	12.6452i	−0.0350392	−	0.0221845i
$571$	−367.971	−	637.344i	−0.644432	−	1.11619i	−0.984432	−	0.175764i	$-0.943760\pi$
$571$	−367.971	−	637.344i	−0.644432	−	1.11619i	0.340000	−	0.940425i	$-0.389573\pi$
$572$	260.433	+	971.951i	0.455303	+	1.69922i
$573$	−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
$576$	403.670	−	376.297i	0.700815	−	0.653293i
$577$	−6.98842	+	26.0811i	−0.0121116	+	0.0452013i	−0.971717	−	0.236148i	$-0.924115\pi$
$577$	−6.98842	+	26.0811i	−0.0121116	+	0.0452013i	0.959606	+	0.281349i	$0.0907818\pi$
$578$	8.96981	+	2.40345i	0.0155187	+	0.00415822i
$579$	−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
$582$	−10.2049	+	7.54988i	−0.0175343	+	0.0129723i
$583$	−1133.42	+	303.700i	−1.94412	+	0.520926i
$584$	−87.8241	+	50.7053i	−0.150384	+	0.0868241i
$585$	743.438	−	54.0164i	1.27083	−	0.0923358i
$586$	−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	$0.372780\pi$
$588$	−162.949	−	560.669i	−0.277125	−	0.953519i
$589$			341.208i			0.579300i
$590$	2.68906	−	3.34041i	0.00455773	−	0.00566171i
$591$	−171.456	+	67.5210i	−0.290111	+	0.114249i
$592$	264.391	+	70.8434i	0.446607	+	0.119668i
$593$	−829.633	+	222.299i	−1.39904	+	0.374873i	−0.878001	−	0.478658i	$-0.841123\pi$
$593$	−829.633	+	222.299i	−1.39904	+	0.374873i	−0.521042	+	0.853531i	$0.674457\pi$
$594$	29.8201	−	62.4771i	0.0502021	−	0.105180i
$595$	−533.659	−	37.1209i	−0.896907	−	0.0623880i
$596$		−	279.178i		−	0.468420i
$597$	−656.834	+	74.7789i	−1.10022	+	0.125258i
$598$	89.1131	+	23.8778i	0.149019	+	0.0399294i
$599$	−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	$0.943298\pi$
$600$	55.7984	+	83.2680i	0.0929974	+	0.138780i
$601$			207.421i			0.345127i	0.984998	+	0.172563i	$0.0552050\pi$
$601$			207.421i			0.345127i	−0.984998	+	0.172563i	$0.944795\pi$
$602$	50.7767	+	23.8339i	0.0843467	+	0.0395911i
$603$	286.390	+	538.848i	0.474942	+	0.893612i
$604$	−356.306	−	205.714i	−0.589911	−	0.340585i
$605$	228.137	−	516.418i	0.377087	−	0.853583i
$606$	54.7611	−	21.5655i	0.0903649	−	0.0355866i
$607$	1145.43	−	306.916i	1.88703	−	0.505628i	0.888086	−	0.459678i	$-0.152035\pi$
$607$	1145.43	−	306.916i	1.88703	−	0.505628i	0.998944	−	0.0459504i	$-0.0146316\pi$
$608$	52.9884	+	52.9884i	0.0871519	+	0.0871519i
$609$	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
$612$	463.295	+	289.611i	0.757018	+	0.473221i
$613$	−100.133	+	373.703i	−0.163350	+	0.609630i	0.834895	+	0.550409i	$0.185528\pi$
$613$	−100.133	+	373.703i	−0.163350	+	0.609630i	−0.998245	+	0.0592208i	$0.981138\pi$
$614$	54.7224	+	31.5940i	0.0891244	+	0.0514560i
$615$	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	0.770133	−	0.637883i	$-0.220190\pi$
$617$	81.5983	+	81.5983i	0.132250	+	0.132250i	−0.637883	+	0.770133i	$0.720190\pi$
$618$	−6.70295	+	0.763114i	−0.0108462	+	0.00123481i
$619$	−91.0832	−	157.761i	−0.147146	−	0.254864i	0.783026	−	0.621989i	$-0.213675\pi$
$619$	−91.0832	−	157.761i	−0.147146	−	0.254864i	−0.930171	+	0.367125i	$0.880342\pi$
$620$	291.293	−	659.378i	0.469827	−	1.06351i
$621$	507.871	+	739.370i	0.817827	+	1.19061i
$622$	26.4703	+	26.4703i	0.0425567	+	0.0425567i
$623$	243.500	+	114.295i	0.390850	+	0.183459i
$624$	−769.811	−	115.117i	−1.23367	−	0.184483i
$625$	567.988	−	260.796i	0.908781	−	0.417274i
$626$	−33.0552	−	57.2532i	−0.0528038	−	0.0914588i
$627$	−395.521	−	172.018i	−0.630814	−	0.274351i
$628$	122.121	+	455.761i	0.194460	+	0.725734i
$629$			267.090i			0.424627i
$630$	−49.3049	−	18.9155i	−0.0782617	−	0.0300246i
$631$	508.007			0.805082			0.402541	−	0.915402i	$-0.368127\pi$
$631$	508.007			0.805082			0.402541	+	0.915402i	$0.368127\pi$
$632$	−39.2626	+	10.5204i	−0.0621244	+	0.0166462i
$633$	70.3513	−	161.758i	0.111140	−	0.255543i
$634$	−17.4125	+	10.0531i	−0.0274645	+	0.0158566i
$635$	−38.6330	+	47.9908i	−0.0608394	+	0.0755761i
$636$	135.206	−	904.144i	0.212587	−	1.42161i
$637$	−468.898	+	662.510i	−0.736104	+	1.04005i
$638$	12.5046	−	12.5046i	0.0195998	−	0.0195998i
$639$	−335.033	+	312.314i	−0.524308	+	0.488754i
$640$	−76.1251	−	196.612i	−0.118945	−	0.307206i
$641$	329.378	−	190.166i	0.513850	−	0.296671i	−0.220565	−	0.975372i	$-0.570790\pi$
$641$	329.378	−	190.166i	0.513850	−	0.296671i	0.734415	+	0.678701i	$0.237457\pi$
$642$	0.998043	+	8.76649i	0.00155458	+	0.0136550i
$643$	548.817	−	548.817i	0.853526	−	0.853526i	−0.137039	−	0.990566i	$-0.543759\pi$
$643$	548.817	−	548.817i	0.853526	−	0.853526i	0.990566	+	0.137039i	$0.0437587\pi$
$644$	706.080	+	595.516i	1.09640	+	0.924714i
$645$	−635.027	+	332.841i	−0.984538	+	0.516032i
$646$	−12.0434	+	20.8598i	−0.0186430	+	0.0322907i
$647$	−1182.40	−	316.824i	−1.82751	−	0.489681i	−0.829849	−	0.557987i	$-0.811574\pi$
$647$	−1182.40	−	316.824i	−1.82751	−	0.489681i	−0.997664	+	0.0683064i	$0.978240\pi$
$648$	70.9923	+	81.7247i	0.109556	+	0.126118i
$649$	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
$653$	−11.9942	−	44.7631i	−0.0183679	−	0.0685499i	0.956134	−	0.292931i	$-0.0946306\pi$
$653$	−11.9942	−	44.7631i	−0.0183679	−	0.0685499i	−0.974501	+	0.224381i	$0.927964\pi$
$654$	−30.8961	−	78.4544i	−0.0472418	−	0.119961i
$655$	350.270	−	792.882i	0.534764	−	1.21051i
$656$	−136.852	+	237.035i	−0.208616	+	0.361334i
$657$	320.506	+	603.037i	0.487832	+	0.917864i
$658$	7.57169	+	10.8718i	0.0115071	+	0.0165225i
$659$	1102.69			1.67328			0.836642	−	0.547750i	$-0.184516\pi$
$659$	1102.69			1.67328			0.836642	+	0.547750i	$0.184516\pi$
$660$	617.483	+	670.082i	0.935580	+	1.01528i
$661$	−355.813	+	205.429i	−0.538295	+	0.310785i	−0.744388	−	0.667748i	$-0.767258\pi$
$661$	−355.813	+	205.429i	−0.538295	+	0.310785i	0.206093	+	0.978532i	$0.433925\pi$
$662$	−10.4255	+	38.9085i	−0.0157485	+	0.0587741i
$663$	−85.9148	−	754.649i	−0.129585	−	1.13823i
$664$	20.7325			0.0312236
$665$	−107.001	+	311.123i	−0.160904	+	0.467854i
$666$	−7.71320	+	25.2131i	−0.0115814	+	0.0378574i
$667$	59.3043	+	221.327i	0.0889120	+	0.331824i
$668$	80.8258	−	301.646i	0.120997	−	0.451566i
$669$	201.418	+	511.460i	0.301073	+	0.764514i
$670$	56.5060	−	6.10424i	0.0843374	−	0.00911081i
$671$	916.144			1.36534
$672$	139.357	+	92.7629i	0.207377	+	0.138040i
$673$	−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
$675$	573.576	−	355.859i	0.849742	−	0.527198i
$676$	209.278	+	362.480i	0.309582	+	0.536212i
$677$	−59.5281	−	222.162i	−0.0879292	−	0.328156i	0.907924	−	0.419136i	$-0.137667\pi$
$677$	−59.5281	−	222.162i	−0.0879292	−	0.328156i	−0.995853	+	0.0909796i	$0.971000\pi$
$678$	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
$681$	−204.070	+	256.505i	−0.299662	+	0.376659i
$682$	−24.0879	+	89.8972i	−0.0353195	+	0.131814i
$683$	−156.398	−	41.9067i	−0.228987	−	0.0613568i	0.142501	−	0.989795i	$-0.454486\pi$
$683$	−156.398	−	41.9067i	−0.228987	−	0.0613568i	−0.371488	+	0.928438i	$0.621152\pi$
$684$	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
$687$	−277.534	−	375.134i	−0.403980	−	0.546047i
$688$	723.172	−	193.773i	1.05112	−	0.281647i
$689$	−1100.59	+	635.428i	−1.59738	+	0.922247i
$690$	81.5123	−	18.3108i	0.118134	−	0.0265374i
$691$	−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
$693$	−941.936	−	202.874i	−1.35921	−	0.292747i
$694$			113.037i			0.162878i
$695$	256.602	−	27.7202i	0.369212	−	0.0398852i
$696$	10.1326	+	25.7297i	0.0145584	+	0.0369680i
$697$	−257.977	−	69.1247i	−0.370124	−	0.0991746i
$698$	83.0916	−	22.2643i	0.119042	−	0.0318973i
$699$	1072.10	+	160.322i	1.53377	+	0.229360i
$700$	472.386	−	509.892i	0.674838	−	0.728417i
$701$			773.724i			1.10374i	0.833929	+	0.551872i	$0.186086\pi$
$701$			773.724i			1.10374i	−0.833929	+	0.551872i	$0.813914\pi$
$702$	13.6829	−	73.7191i	0.0194914	−	0.105013i
$703$	158.671	+	42.5157i	0.225705	+	0.0604775i
$704$	−468.903	−	812.163i	−0.666055	−	1.15364i
$705$	−169.203	−	6.91226i	−0.240004	−	0.00980462i
$706$		−	56.5061i		−	0.0800370i
$707$	−468.146	−	672.188i	−0.662159	−	0.950762i
$708$	36.2554	+	49.0053i	0.0512083	+	0.0692166i
$709$	767.065	+	442.865i	1.08190	+	0.624633i	0.931407	−	0.363978i	$-0.118582\pi$
$709$	767.065	+	442.865i	1.08190	+	0.624633i	0.150489	+	0.988612i	$0.451915\pi$
$710$	15.4027	+	39.7814i	0.0216940	+	0.0560301i
$711$	61.5292	+	266.724i	0.0865389	+	0.375139i
$712$	−49.6065	+	13.2920i	−0.0696720	+	0.0186686i
$713$	−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
$717$	369.796	−	850.270i	0.515754	−	1.18587i
$718$	−13.3362	+	49.7713i	−0.0185741	+	0.0693193i
$719$	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
$723$	−52.0808	−	457.461i	−0.0720343	−	0.632726i
$724$	398.507	+	690.234i	0.550424	+	0.953362i
$725$	168.448	−	36.8240i	0.232342	−	0.0507918i
$726$	−44.4401	−	35.3556i	−0.0612123	−	0.0486992i
$727$	242.067	+	242.067i	0.332967	+	0.332967i	0.853712	−	0.520745i	$-0.174346\pi$
$727$	242.067	+	242.067i	0.332967	+	0.332967i	−0.520745	+	0.853712i	$0.674346\pi$
$728$	−13.1162	−	154.408i	−0.0180167	−	0.212099i
$729$	566.779	−	458.479i	0.777475	−	0.628914i
$730$	63.2372	−	6.83139i	0.0866262	−	0.00935807i
$731$	365.277	+	632.679i	0.499695	+	0.865498i
$732$	−284.670	+	654.541i	−0.388894	+	0.894181i
$733$	300.842	+	1122.76i	0.410425	+	1.53173i	0.793826	+	0.608145i	$0.208086\pi$
$733$	300.842	+	1122.76i	0.410425	+	1.53173i	−0.383401	+	0.923582i	$0.625247\pi$
$734$		−	16.1063i		−	0.0219432i
$735$	−97.5733	+	728.495i	−0.132753	+	0.991149i
$736$	−264.840			−0.359836
$737$	1001.66	−	268.393i	1.35910	−	0.364170i
$738$	−22.3565	−	13.9753i	−0.0302934	−	0.0189367i
$739$	377.355	−	217.866i	0.510629	−	0.294812i	−0.222463	−	0.974941i	$-0.571410\pi$
$739$	377.355	−	217.866i	0.510629	−	0.294812i	0.733092	+	0.680129i	$0.238076\pi$
$740$	−270.332	−	217.620i	−0.365314	−	0.294081i
$741$	−461.991	−	69.0862i	−0.623470	−	0.0932337i
$742$	89.7126	−	7.62062i	0.120906	−	0.0102704i
$743$	−259.217	+	259.217i	−0.348878	+	0.348878i	−0.859692	−	0.510813i	$-0.829344\pi$
$743$	−259.217	+	259.217i	−0.348878	+	0.348878i	0.510813	+	0.859692i	$0.329344\pi$
$744$	−113.887	−	90.6056i	−0.153073	−	0.121782i
$745$	−142.016	+	321.471i	−0.190625	+	0.431504i
$746$	−4.31757	+	2.49275i	−0.00578762	+	0.00334149i
$747$	4.89683	−	139.530i	0.00655533	−	0.186788i
$748$	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	$0.308272\pi$
$752$	170.809	+	45.7682i	0.227140	+	0.0608620i
$753$	225.239	−	517.891i	0.299122	−	0.687770i
$754$	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	$0.322584\pi$
$758$	−9.85663	−	36.7854i	−0.0130035	−	0.0485296i
$759$	1418.30	−	558.540i	1.86864	−	0.735890i
$760$	−22.6805	−	58.5780i	−0.0298428	−	0.0770763i
$761$	363.696	−	629.940i	0.477919	−	0.827779i	−0.521761	−	0.853092i	$-0.674725\pi$
$761$	363.696	−	629.940i	0.477919	−	0.827779i	0.999680	+	0.0253124i	$0.00805805\pi$
$762$	3.68574	+	4.98190i	0.00483693	+	0.00653793i
$763$	−963.022	+	670.698i	−1.26215	+	0.879027i
$764$	−1237.88			−1.62026
$765$	−386.156	−	569.158i	−0.504779	−	0.743997i
$766$	−7.94874	+	4.58921i	−0.0103769	+	0.00599113i
$767$	21.9326	−	81.8535i	0.0285953	−	0.106719i
$768$	710.018	−	80.8337i	0.924502	−	0.105252i
$769$	−386.196			−0.502205			−0.251103	−	0.967960i	$-0.580793\pi$
$769$	−386.196			−0.502205			−0.251103	+	0.967960i	$0.580793\pi$
$770$	−50.1553	+	74.4170i	−0.0651368	+	0.0966455i
$771$	−546.394	−	81.7078i	−0.708682	−	0.105976i
$772$	−204.241	−	762.238i	−0.264561	−	0.987355i
$773$	−270.458	+	1009.36i	−0.349881	+	1.30577i	0.536925	+	0.843630i	$0.319586\pi$
$773$	−270.458	+	1009.36i	−0.349881	+	1.30577i	−0.886806	+	0.462143i	$0.847081\pi$
$774$	16.2109	+	70.2729i	0.0209443	+	0.0907919i
$775$	−670.840	+	611.087i	−0.865600	+	0.788500i
$776$	−33.7321			−0.0434692
$777$	366.228	+	23.3598i	0.471336	+	0.0300641i
$778$	−24.7345	−	24.7345i	−0.0317924	−	0.0317924i
$779$	−82.1300	+	142.253i	−0.105430	+	0.182610i
$780$	833.810	+	527.915i	1.06899	+	0.676814i
$781$	389.174	+	674.069i	0.498302	+	0.863085i
$782$	−22.0324	−	82.2262i	−0.0281745	−	0.105149i
$783$	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
$786$	−68.2311	−	54.2832i	−0.0868081	−	0.0690626i
$787$	231.655	−	864.548i	0.294352	−	1.09854i	−0.647379	−	0.762169i	$-0.724135\pi$
$787$	231.655	−	864.548i	0.294352	−	1.09854i	0.941731	−	0.336368i	$-0.109199\pi$
$788$	−235.657	−	63.1440i	−0.299057	−	0.0801320i
$789$	−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
$792$	162.443	−	86.3364i	0.205105	−	0.109011i
$793$	958.420	−	256.808i	1.20860	−	0.323843i
$794$	41.6727	−	24.0598i	0.0524845	−	0.0303020i
$795$	−615.618	+	972.332i	−0.774362	+	1.22306i
$796$	−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	$0.346651\pi$
$798$	27.5491	+	18.3380i	0.0345227	+	0.0229800i
$799$			172.553i			0.215961i
$800$	−9.27936	+	199.079i	−0.0115992	+	0.248849i
$801$	77.7392	+	336.993i	0.0970527	+	0.420716i
$802$	−106.069	−	28.4211i	−0.132256	−	0.0354378i
$803$	1120.98	−	300.365i	1.39599	−	0.374054i
$804$	−119.487	+	799.034i	−0.148616	+	0.993823i
$805$	−510.108	−	1044.91i	−0.633675	−	1.29802i
$806$			100.798i			0.125059i
$807$	172.881	+	1518.53i	0.214226	+	1.88170i
$808$	151.065	+	40.4777i	0.186962	+	0.0500962i
$809$	−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	$0.957202\pi$
$810$	−20.0162	−	64.8796i	−0.0247114	−	0.0800982i
$811$		−	585.506i		−	0.721955i	−0.932574	−	0.360978i	$-0.882443\pi$
$811$		−	585.506i		−	0.721955i	0.932574	−	0.360978i	$-0.117557\pi$
$812$	157.358	−	109.592i	0.193791	−	0.134966i
$813$	−483.139	+	357.439i	−0.594266	+	0.439654i
$814$	38.8032	+	22.4030i	0.0476698	+	0.0275222i
$815$	−107.403	+	41.5848i	−0.131783	+	0.0510243i
$816$	263.169	+	668.264i	0.322511	+	0.818950i
$817$	434.002	−	116.290i	0.531214	−	0.142338i
$818$	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	0.868477	−	0.495729i	$-0.165099\pi$
$821$	717.063	+	413.997i	0.873402	+	0.504259i	0.00492484	+	0.999988i	$0.498432\pi$
$822$	65.6294	+	28.5433i	0.0798412	+	0.0347242i
$823$	−366.018	+	1366.00i	−0.444737	+	1.65978i	0.271893	+	0.962327i	$0.412350\pi$
$823$	−366.018	+	1366.00i	−0.444737	+	1.65978i	−0.716630	+	0.697453i	$0.754316\pi$
$824$	−15.5251	−	8.96340i	−0.0188411	−	0.0108779i
$825$	−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	0.717006	−	0.697067i	$-0.245512\pi$
$827$	16.4891	+	16.4891i	0.0199384	+	0.0199384i	−0.697067	+	0.717006i	$0.745512\pi$
$828$	−41.6529	+	1186.86i	−0.0503055	+	1.43341i
$829$	−537.538	−	931.043i	−0.648417	−	1.12309i	−0.983501	−	0.180903i	$-0.942098\pi$
$829$	−537.538	−	931.043i	−0.648417	−	1.12309i	0.335083	−	0.942188i	$-0.391235\pi$
$830$	−11.8945	−	5.25462i	−0.0143307	−	0.00633087i
$831$	−559.727	+	703.548i	−0.673558	+	0.846628i
$832$	−718.201	−	718.201i	−0.863223	−	0.863223i
$833$	745.739	+	69.0404i	0.895245	+	0.0828817i
$834$	3.83956	−	25.6758i	0.00460379	−	0.0307864i
$835$	−246.515	+	306.226i	−0.295227	+	0.366738i
$836$	−285.518	−	494.532i	−0.341529	−	0.591546i
$837$	−636.679	+	745.061i	−0.760668	+	0.890157i
$838$	25.2600	+	94.2715i	0.0301432	+	0.112496i
$839$		−	1363.08i		−	1.62464i	−0.583209	−	0.812322i	$-0.698203\pi$
$839$		−	1363.08i		−	1.62464i	0.583209	−	0.812322i	$-0.301797\pi$
$840$	−75.4316	−	118.331i	−0.0897995	−	0.140870i
$841$	−793.431			−0.943437
$842$	−58.3259	+	15.6284i	−0.0692707	+	0.0185610i
$843$	−128.392	−	55.8399i	−0.152304	−	0.0662395i
$844$	202.252	−	116.770i	0.239635	−	0.138353i
$845$	−56.5904	−	523.849i	−0.0669709	−	0.619939i
$846$	−4.98309	+	16.2888i	−0.00589018	+	0.0192539i
$847$	−335.842	+	715.492i	−0.396507	+	0.844737i
$848$	849.758	−	849.758i	1.00207	−	1.00207i
$849$	−219.215	+	275.542i	−0.258204	+	0.324549i
$850$	−62.5811	+	13.6807i	−0.0736248	+	0.0160949i
$851$	−502.772	+	290.276i	−0.590801	+	0.341099i
$852$	−602.517	+	68.5950i	−0.707179	+	0.0805105i
$853$	886.732	−	886.732i	1.03955	−	1.03955i	0.0403603	−	0.999185i	$-0.487149\pi$
$853$	886.732	−	886.732i	1.03955	−	1.03955i	0.999185	−	0.0403603i	$-0.0128506\pi$
$854$	−69.1969	−	12.3815i	−0.0810268	−	0.0144983i
$855$	−399.589	+	138.805i	−0.467356	+	0.162345i
$856$	−11.7228	+	20.3045i	−0.0136949	+	0.0237203i
$857$	152.554	+	40.8768i	0.178010	+	0.0476975i	0.346723	−	0.937968i	$-0.387294\pi$
$857$	152.554	+	40.8768i	0.178010	+	0.0476975i	−0.168713	+	0.985665i	$0.553961\pi$
$858$	−116.843	−	50.8167i	−0.136180	−	0.0592269i
$859$	−598.502	+	1036.64i	−0.696743	+	1.20679i	0.272847	+	0.962058i	$0.412035\pi$
$859$	−598.502	+	1036.64i	−0.696743	+	1.20679i	−0.969590	+	0.244737i	$0.921298\pi$
$860$	−937.979	−	145.783i	−1.09067	−	0.169515i
$861$	−117.345	+	347.686i	−0.136289	+	0.403817i
$862$	47.9187	−	47.9187i	0.0555901	−	0.0555901i
$863$	413.564	+	1543.44i	0.479217	+	1.78846i	0.604799	+	0.796378i	$0.293254\pi$
$863$	413.564	+	1543.44i	0.479217	+	1.78846i	−0.125582	+	0.992083i	$0.540080\pi$
$864$	16.8314	+	214.579i	0.0194808	+	0.248356i
$865$	−937.422	+	362.956i	−1.08373	+	0.419602i
$866$	−2.74632	+	4.75677i	−0.00317127	+	0.00549281i
$867$	133.589	−	98.8329i	0.154082	−	0.113994i
$868$	−428.813	+	913.562i	−0.494024	+	1.05249i
$869$	465.163			0.535286
$870$	0.707947	−	17.3296i	0.000813732	−	0.0199191i
$871$	972.646	−	561.557i	1.11670	−	0.644727i
$872$	57.9911	−	216.426i	0.0665035	−	0.248195i
$873$	−7.96724	+	227.019i	−0.00912628	+	0.260044i
$874$	−52.3554			−0.0599032
$875$	−803.325	+	346.835i	−0.918085	+	0.396383i
$876$	−133.721	+	894.216i	−0.152650	+	1.02079i
$877$	−108.050	−	403.249i	−0.123204	−	0.459805i	0.876565	−	0.481284i	$-0.159829\pi$
$877$	−108.050	−	403.249i	−0.123204	−	0.459805i	−0.999769	+	0.0214786i	$0.993163\pi$
$878$	−21.9489	+	81.9146i	−0.0249988	+	0.0932968i
$879$	−778.339	+	306.518i	−0.885483	+	0.348712i
$880$	128.648	+	1190.88i	0.146191	+	1.35327i
$881$	−276.453			−0.313795			−0.156898	−	0.987615i	$-0.550149\pi$
$881$	−276.453			−0.313795			−0.156898	+	0.987615i	$0.550149\pi$
$882$	68.4032	+	28.0533i	0.0775547	+	0.0318064i
$883$	−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
$885$	−16.8191	−	74.8719i	−0.0190046	−	0.0846010i
$886$	−10.5307	−	18.2397i	−0.0118857	−	0.0205866i
$887$	−269.729	−	1006.64i	−0.304092	−	1.13489i	−0.933724	−	0.357993i	$-0.883461\pi$
$887$	−269.729	−	1006.64i	−0.304092	−	1.13489i	0.629633	−	0.776893i	$-0.283205\pi$
$888$	−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
$891$	−542.680	−	1113.64i	−0.609069	−	1.24988i
$892$	−188.361	+	702.973i	−0.211167	+	0.788087i
$893$	102.509	+	27.4672i	0.114792	+	0.0307583i
$894$	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
$897$	1327.18	−	981.883i	1.47958	−	1.09463i
$898$	−89.1955	+	23.8999i	−0.0993268	+	0.0266145i
$899$	−216.807	+	125.174i	−0.241165	+	0.139237i
$900$	890.698	+	72.8951i	0.989665	+	0.0809946i
$901$	1015.54	+	586.320i	1.12712	+	0.650744i
$902$	−31.6811	+	31.6811i	−0.0351232	+	0.0351232i
$903$	899.461	−	445.525i	0.996081	−	0.493383i
$904$			46.4520i			0.0513849i
$905$	−107.759	−	997.513i	−0.119071	−	1.10222i
$906$	48.4736	−	19.0894i	0.0535029	−	0.0210700i
$907$	−1469.83	−	393.840i	−1.62054	−	0.434222i	−0.669380	−	0.742921i	$-0.733440\pi$
$907$	−1469.83	−	393.840i	−1.62054	−	0.434222i	−0.951160	+	0.308698i	$0.900107\pi$
$908$	−419.181	+	112.319i	−0.461653	+	0.123700i
$909$	308.097	−	1007.11i	0.338941	−	1.10794i
$910$	−31.6096	+	91.9103i	−0.0347359	+	0.101000i
$911$		−	1648.74i		−	1.80981i	−0.425616	−	0.904904i	$-0.639942\pi$
$911$		−	1648.74i		−	1.80981i	0.425616	−	0.904904i	$-0.360058\pi$
$912$	438.888	−	49.9663i	0.481237	−	0.0547876i
$913$	−229.174	−	61.4069i	−0.251012	−	0.0672584i
$914$	−19.2386	−	33.3222i	−0.0210488	−	0.0364575i
$915$	660.754	−	608.886i	0.722135	−	0.665450i
$916$		−	617.813i		−	0.674468i
$917$	−515.634	+	1098.53i	−0.562305	+	1.19796i
$918$	−65.2214	+	23.0770i	−0.0710473	+	0.0251383i
$919$	−415.979	−	240.166i	−0.452643	−	0.261334i	0.256303	−	0.966597i	$-0.417496\pi$
$919$	−415.979	−	240.166i	−0.452643	−	0.261334i	−0.708946	+	0.705263i	$0.750829\pi$
$920$	203.068	+	89.7090i	0.220726	+	0.0975098i
$921$	1052.09	−	414.324i	1.14233	−	0.449863i
$922$	86.2948	−	23.1226i	0.0935952	−	0.0250788i
$923$	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
$927$	−63.9910	+	102.367i	−0.0690302	+	0.110429i
$928$	−14.2304	+	53.1084i	−0.0153344	+	0.0572289i
$929$	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
$933$	665.584	−	75.7750i	0.713380	−	0.0812165i
$934$	21.7169	+	37.6148i	0.0232515	+	0.0402728i
$935$	−1089.96	+	422.015i	−1.16573	+	0.451352i
$936$	145.738	−	135.856i	0.155703	−	0.145145i
$937$	723.582	+	723.582i	0.772232	+	0.772232i	0.978496	−	0.206264i	$-0.0661306\pi$
$937$	723.582	+	723.582i	0.772232	+	0.772232i	−0.206264	+	0.978496i	$0.566131\pi$
$938$	−79.2832	+	6.73469i	−0.0845236	+	0.00717984i
$939$	−1170.02	−	174.964i	−1.24603	−	0.186331i
$940$	−174.647	−	140.593i	−0.185795	−	0.149567i
$941$	−778.938	−	1349.16i	−0.827777	−	1.43375i	−0.899779	−	0.436347i	$-0.856272\pi$
$941$	−778.938	−	1349.16i	−0.827777	−	1.43375i	0.0720018	−	0.997405i	$-0.477061\pi$
$942$	−54.7891	−	23.8286i	−0.0581625	−	0.0252958i
$943$	−150.250	−	560.742i	−0.159332	−	0.594636i
$944$			80.1322i			0.0848858i
$945$	−814.189	+	479.709i	−0.861576	+	0.507629i
$946$	122.555			0.129551
$947$	1349.26	−	361.534i	1.42478	−	0.381768i	0.537601	−	0.843199i	$-0.319331\pi$
$947$	1349.26	−	361.534i	1.42478	−	0.381768i	0.887176	+	0.461432i	$0.152664\pi$
$948$	−144.539	+	332.337i	−0.152467	+	0.350566i
$949$	1088.51	−	628.451i	1.14701	−	0.662225i
$950$	−1.83441	+	39.3553i	−0.00193096	+	0.0414267i
$951$	−53.2121	+	355.839i	−0.0559539	+	0.374173i
$952$	−117.336	+	81.7185i	−0.123252	+	0.0858388i
$953$	−1138.28	+	1138.28i	−1.19442	+	1.19442i	−0.218607	+	0.975813i	$0.570151\pi$
$953$	−1138.28	+	1138.28i	−1.19442	+	1.19442i	−0.975813	+	0.218607i	$0.929849\pi$
$954$	78.9335	+	84.6753i	0.0827395	+	0.0887582i
$955$	1425.40	+	629.697i	1.49256	+	0.659369i
$956$	1063.12	−	613.793i	1.11205	−	0.642043i
$957$	−35.7964	−	314.424i	−0.0374048	−	0.328552i
$958$	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
$962$	46.8737	+	12.5598i	0.0487252	+	0.0130559i
$963$	133.882	+	83.6910i	0.139026	+	0.0869065i
$964$	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	$0.387859\pi$
$968$	−39.0569	−	145.762i	−0.0403480	−	0.150581i
$969$	157.937	+	401.049i	0.162990	+	0.413879i
$970$	19.3526	+	8.54938i	0.0199511	+	0.00881379i
$971$	−904.830	+	1567.21i	−0.931853	+	1.61402i	−0.151703	+	0.988426i	$0.548476\pi$
$971$	−904.830	+	1567.21i	−0.931853	+	1.61402i	−0.780151	+	0.625591i	$0.784858\pi$
$972$	964.270	−	41.6805i	0.992047	−	0.0428812i
$973$	−360.037	+	30.5832i	−0.370027	+	0.0314319i
$974$	−91.5278			−0.0939710
$975$	−691.577	−	1032.04i	−0.709309	−	1.05850i
$976$	−812.562	+	469.133i	−0.832543	+	0.480669i
$977$	219.154	−	817.894i	0.224313	−	0.837148i	−0.758365	−	0.651830i	$-0.774002\pi$
$977$	219.154	−	817.894i	0.224313	−	0.837148i	0.982678	−	0.185319i	$-0.0593317\pi$
$978$	1.31045	+	11.5106i	0.00133993	+	0.0117696i
$979$	587.712			0.600319
$980$	−677.492	+	698.539i	−0.691318	+	0.712794i
$981$	−1442.86	−	441.400i	−1.47080	−	0.449949i
$982$	−5.83703	−	21.7841i	−0.00594402	−	0.0221834i
$983$	−173.985	+	649.321i	−0.176994	+	0.660551i	0.819209	+	0.573494i	$0.194413\pi$
$983$	−173.985	+	649.321i	−0.176994	+	0.660551i	−0.996203	+	0.0870561i	$0.972254\pi$
$984$	−25.6715	−	65.1874i	−0.0260889	−	0.0662474i
$985$	239.235	+	192.586i	0.242878	+	0.195519i
$986$	−17.6727			−0.0179237
$987$	236.601	+	15.0916i	0.239717	+	0.0152903i
$988$	−437.318	−	437.318i	−0.442630	−	0.442630i
$989$	−793.971	+	1375.20i	−0.802802	+	1.39049i
$990$	−115.078	+	8.36129i	−0.116240	+	0.00844575i
$991$	−372.392	−	645.003i	−0.375774	−	0.650860i	0.614668	−	0.788786i	$-0.289290\pi$
$991$	−372.392	−	645.003i	−0.375774	−	0.650860i	−0.990443	+	0.137925i	$0.955957\pi$
$992$	−74.8914	−	279.499i	−0.0754954	−	0.281753i
$993$	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
$996$	115.083	−	144.653i	0.115545	−	0.145234i
$997$	140.936	−	525.982i	0.141360	−	0.527564i	−0.858530	−	0.512763i	$-0.828622\pi$
$997$	140.936	−	525.982i	0.141360	−	0.527564i	0.999890	−	0.0148011i	$-0.00471150\pi$
$998$	84.0638	+	22.5248i	0.0842323	+	0.0225700i
$999$	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.68.13	yes	112
3.2	odd	2	inner	105.3.w.a.68.16	yes	112
5.2	odd	4	inner	105.3.w.a.47.13	yes	112
7.3	odd	6	inner	105.3.w.a.38.16	yes	112
15.2	even	4	inner	105.3.w.a.47.16	yes	112
21.17	even	6	inner	105.3.w.a.38.13	yes	112
35.17	even	12	inner	105.3.w.a.17.16	yes	112
105.17	odd	12	inner	105.3.w.a.17.13	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.13	✓	112	105.17	odd	12	inner
105.3.w.a.17.16	yes	112	35.17	even	12	inner
105.3.w.a.38.13	yes	112	21.17	even	6	inner
105.3.w.a.38.16	yes	112	7.3	odd	6	inner
105.3.w.a.47.13	yes	112	5.2	odd	4	inner
105.3.w.a.47.16	yes	112	15.2	even	4	inner
105.3.w.a.68.13	yes	112	1.1	even	1	trivial
105.3.w.a.68.16	yes	112	3.2	odd	2	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+(-0.161935 + 0.0433902i) q^{2} +(-1.19649 + 2.75108i) q^{3} +(-3.43976 + 1.98595i) q^{4} +(4.97108 - 0.537016i) q^{5} +(0.0743827 - 0.497410i) q^{6} +(-6.97488 + 0.592480i) q^{7} +(0.945023 - 0.945023i) q^{8} +(-6.13684 - 6.58325i) q^{9} +(-0.781688 + 0.302658i) q^{10} +(-13.2452 + 7.64711i) q^{11} +(-1.34786 - 11.8392i) 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} +(14.7635 + 3.95586i) q^{17} +(1.27942 + 0.799777i) 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} +(8.59850 + 32.0900i) q^{23} +(1.46912 + 3.73054i) q^{24} +(24.4232 - 5.33910i) q^{25} +(1.38849 - 2.40493i) q^{26} +(25.4537 - 9.00614i) q^{27} +(22.8153 - 15.8897i) q^{28} +6.89705 q^{29} +(0.102645 - 2.51261i) q^{30} +(-31.4348 + 18.1489i) q^{31} +(-2.06325 + 7.70017i) q^{32} +(-5.19010 - 45.5882i) q^{33} -2.56236 q^{34} +(-34.3545 + 6.69089i) q^{35} +(34.1833 + 10.4574i) q^{36} +(4.52283 + 16.8794i) q^{37} +(-0.407879 + 1.52222i) q^{38} +(-18.2086 - 46.2370i) q^{39} +(4.19029 - 5.20527i) q^{40} -17.4740 q^{41} +(-0.224105 + 3.51345i) q^{42} +(33.7982 + 33.7982i) q^{43} +(30.3735 - 52.6085i) q^{44} +(-34.0420 - 29.4303i) q^{45} +(-2.78479 - 4.82340i) q^{46} +(2.92196 + 10.9049i) q^{47} +(27.9478 + 37.7761i) q^{48} +(48.2979 - 8.26495i) q^{49} +(-3.72330 + 1.92431i) q^{50} +(-28.5471 + 35.8823i) q^{51} +(17.0282 - 63.5502i) q^{52} +(74.1079 + 19.8572i) q^{53} +(-3.73105 + 2.56285i) q^{54} +(-61.7362 + 45.1272i) q^{55} +(-6.03151 + 7.15133i) q^{56} +(16.7725 + 22.6708i) q^{57} +(-1.11687 + 0.299265i) q^{58} +(-4.43046 + 2.55793i) q^{59} +(-13.0582 - 58.1298i) q^{60} +(-51.8761 - 29.9507i) q^{61} +(4.30289 - 4.30289i) q^{62} +(46.7042 + 42.2814i) q^{63} +61.3176i q^{64} +(-51.9353 + 64.5152i) q^{65} +(2.81854 + 7.15710i) q^{66} +(-65.4926 - 17.5487i) q^{67} +(-58.6389 + 15.7122i) q^{68} +(-98.5701 - 14.7402i) q^{69} +(5.27286 - 2.57414i) q^{70} -50.8917i q^{71} +(-12.0208 - 0.421870i) q^{72} +(-73.2942 - 19.6391i) q^{73} +(-1.46480 - 2.53712i) q^{74} +(-14.5338 + 73.5783i) q^{75} +37.3368i q^{76} +(87.8528 - 61.1852i) q^{77} +(4.95483 + 6.69729i) q^{78} +(-26.3396 - 15.2072i) q^{79} +(31.6477 - 71.6385i) q^{80} +(-5.67841 + 80.8007i) q^{81} +(2.82965 - 0.758201i) 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} +(-8.25223 + 18.9743i) q^{87} +(-5.29031 + 19.7437i) 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} +(-12.3176 - 108.194i) q^{93} +(-0.946333 - 1.63910i) q^{94} +(18.9929 - 42.9929i) q^{95} +(-18.7151 - 14.8893i) q^{96} +(-17.8473 - 17.8473i) q^{97} +(-7.46249 + 3.43404i) q^{98} +(131.626 + 40.2673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) \) 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Introduction

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