LMFDB - Embedded newform 126.3.o.a.13.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(13,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.13"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.o (of order $6$, degree $2$, 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:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	126.13
Dual form			126.3.o.a.97.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 1.22474i) q^{2} +(1.92058 + 2.30464i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.19747 + 0.691358i) q^{5} +(1.46454 - 3.98185i) q^{6} +(2.27133 - 6.62126i) q^{7} +2.82843 q^{8} +(-1.62273 + 8.85250i) q^{9} -1.95546i q^{10} +(8.18564 + 14.1779i) q^{11} +(-5.91234 + 1.02190i) q^{12} +(16.0710 + 9.27862i) q^{13} +(-9.71543 + 1.90013i) q^{14} +(0.706502 + 4.08754i) q^{15} +(-2.00000 - 3.46410i) q^{16} +1.67115i q^{17} +(11.9895 - 4.27223i) q^{18} -28.9316i q^{19} +(-2.39494 + 1.38272i) q^{20} +(19.6219 - 7.48206i) q^{21} +(11.5762 - 20.0506i) q^{22} +(-12.2584 + 21.2321i) q^{23} +(5.43223 + 6.51851i) q^{24} +(-11.5440 - 19.9949i) q^{25} -26.2439i q^{26} +(-23.5184 + 13.2621i) q^{27} +(9.19702 + 10.5553i) q^{28} +(-20.7008 - 35.8548i) q^{29} +(4.50662 - 3.75561i) q^{30} +(37.2581 + 21.5110i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-16.9539 + 46.0948i) q^{33} +(2.04673 - 1.18168i) q^{34} +(7.29751 - 6.35844i) q^{35} +(-13.7102 - 11.6632i) q^{36} -18.5784 q^{37} +(-35.4339 + 20.4578i) q^{38} +(9.48187 + 54.8583i) q^{39} +(3.38695 + 1.95546i) q^{40} +(-9.80630 - 5.66167i) q^{41} +(-23.0384 - 18.7412i) q^{42} +(-28.9639 - 50.1669i) q^{43} -32.7425 q^{44} +(-8.06342 + 9.47869i) q^{45} +34.6719 q^{46} +(-11.2382 + 6.48838i) q^{47} +(4.14234 - 11.2624i) q^{48} +(-38.6821 - 30.0782i) q^{49} +(-16.3257 + 28.2770i) q^{50} +(-3.85139 + 3.20957i) q^{51} +(-32.1421 + 18.5572i) q^{52} -45.2169 q^{53} +(32.8728 + 19.4263i) q^{54} +22.6368i q^{55} +(6.42430 - 18.7277i) q^{56} +(66.6770 - 55.5656i) q^{57} +(-29.2753 + 50.7063i) q^{58} +(-21.6394 - 12.4935i) q^{59} +(-7.78633 - 2.86384i) q^{60} +(13.9412 - 8.04896i) q^{61} -60.8422i q^{62} +(54.9289 + 30.8515i) q^{63} +8.00000 q^{64} +(12.8297 + 22.2217i) q^{65} +(68.4426 - 11.8298i) q^{66} +(-22.1391 + 38.3460i) q^{67} +(-2.89451 - 1.67115i) q^{68} +(-72.4756 + 12.5269i) q^{69} +(-12.9476 - 4.44149i) q^{70} +80.7195 q^{71} +(-4.58978 + 25.0386i) q^{72} -79.4212i q^{73} +(13.1369 + 22.7538i) q^{74} +(23.9097 - 65.0067i) q^{75} +(50.1111 + 28.9316i) q^{76} +(112.468 - 21.9964i) q^{77} +(60.4828 - 50.4036i) q^{78} +(19.6156 + 33.9751i) q^{79} -5.53087i q^{80} +(-75.7335 - 28.7305i) q^{81} +16.0136i q^{82} +(100.367 - 57.9469i) q^{83} +(-6.66258 + 41.4682i) q^{84} +(-1.15536 + 2.00114i) q^{85} +(-40.9611 + 70.9467i) q^{86} +(42.8749 - 116.570i) q^{87} +(23.1525 + 40.1013i) q^{88} +30.2467i q^{89} +(17.3107 + 3.17318i) q^{90} +(97.9389 - 85.3357i) q^{91} +(-24.5167 - 42.4642i) q^{92} +(21.9822 + 127.180i) q^{93} +(15.8932 + 9.17596i) q^{94} +(20.0021 - 34.6447i) q^{95} +(-16.7226 + 2.89038i) q^{96} +(-71.7067 + 41.3999i) q^{97} +(-9.48569 + 68.6442i) q^{98} +(-138.793 + 49.4563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$	1.92058	+	2.30464i	0.640194	+	0.768213i
$3$	1.92058	+	2.30464i	0.640194	+	0.768213i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	1.19747	+	0.691358i	0.239494	+	0.138272i	0.614944	−	0.788571i	$-0.289179\pi$
$5$	1.19747	+	0.691358i	0.239494	+	0.138272i	−0.375450	+	0.926842i	$0.622512\pi$
$6$	1.46454	−	3.98185i	0.244090	−	0.663642i
$7$	2.27133	−	6.62126i	0.324476	−	0.945894i
$7$	2.27133	−	6.62126i	0.324476	−	0.945894i
$8$	2.82843			0.353553
$9$	−1.62273	+	8.85250i	−0.180304	+	0.983611i
$10$		−	1.95546i		−	0.195546i
$11$	8.18564	+	14.1779i	0.744149	+	1.28890i	0.950591	+	0.310445i	$0.100478\pi$
$11$	8.18564	+	14.1779i	0.744149	+	1.28890i	−0.206443	+	0.978459i	$0.566189\pi$
$12$	−5.91234	+	1.02190i	−0.492695	+	0.0851587i
$13$	16.0710	+	9.27862i	1.23623	+	0.713740i	0.968322	−	0.249703i	$-0.0803330\pi$
$13$	16.0710	+	9.27862i	1.23623	+	0.713740i	0.267912	+	0.963443i	$0.413666\pi$
$14$	−9.71543	+	1.90013i	−0.693959	+	0.135724i
$15$	0.706502	+	4.08754i	0.0471002	+	0.272503i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$			1.67115i			0.0983028i	0.998791	+	0.0491514i	$0.0156517\pi$
$17$			1.67115i			0.0983028i	−0.998791	+	0.0491514i	$0.984348\pi$
$18$	11.9895	−	4.27223i	0.666083	−	0.237346i
$19$		−	28.9316i		−	1.52272i	−0.648330	−	0.761359i	$-0.724532\pi$
$19$		−	28.9316i		−	1.52272i	0.648330	−	0.761359i	$-0.275468\pi$
$20$	−2.39494	+	1.38272i	−0.119747	+	0.0691358i
$21$	19.6219	−	7.48206i	0.934376	−	0.356289i
$22$	11.5762	−	20.0506i	0.526193	−	0.911392i
$23$	−12.2584	+	21.2321i	−0.532972	+	0.923135i	0.466286	+	0.884634i	$0.345592\pi$
$23$	−12.2584	+	21.2321i	−0.532972	+	0.923135i	−0.999259	+	0.0385014i	$0.987742\pi$
$24$	5.43223	+	6.51851i	0.226343	+	0.271604i
$25$	−11.5440	−	19.9949i	−0.461762	−	0.799795i
$26$		−	26.2439i		−	1.00938i
$27$	−23.5184	+	13.2621i	−0.871052	+	0.491190i
$28$	9.19702	+	10.5553i	0.328465	+	0.376976i
$29$	−20.7008	−	35.8548i	−0.713820	−	1.23637i	−0.963413	−	0.268021i	$-0.913630\pi$
$29$	−20.7008	−	35.8548i	−0.713820	−	1.23637i	0.249593	−	0.968351i	$-0.419703\pi$
$30$	4.50662	−	3.75561i	0.150221	−	0.125187i
$31$	37.2581	+	21.5110i	1.20187	+	0.693903i	0.960972	−	0.276647i	$-0.0892231\pi$
$31$	37.2581	+	21.5110i	1.20187	+	0.693903i	0.240903	+	0.970549i	$0.422556\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$	−16.9539	+	46.0948i	−0.513753	+	1.39681i
$34$	2.04673	−	1.18168i	0.0601979	−	0.0347553i
$35$	7.29751	−	6.35844i	0.208500	−	0.181670i
$36$	−13.7102	−	11.6632i	−0.380840	−	0.323976i
$37$	−18.5784			−0.502118			−0.251059	−	0.967972i	$-0.580779\pi$
$37$	−18.5784			−0.502118			−0.251059	+	0.967972i	$0.580779\pi$
$38$	−35.4339	+	20.4578i	−0.932471	+	0.538362i
$39$	9.48187	+	54.8583i	0.243125	+	1.40662i
$40$	3.38695	+	1.95546i	0.0846738	+	0.0488864i
$41$	−9.80630	−	5.66167i	−0.239178	−	0.138090i	0.375621	−	0.926773i	$-0.377430\pi$
$41$	−9.80630	−	5.66167i	−0.239178	−	0.138090i	−0.614799	+	0.788684i	$0.710763\pi$
$42$	−23.0384	−	18.7412i	−0.548533	−	0.446219i
$43$	−28.9639	−	50.1669i	−0.673578	−	1.16667i	−0.976882	−	0.213778i	$-0.931423\pi$
$43$	−28.9639	−	50.1669i	−0.673578	−	1.16667i	0.303304	−	0.952894i	$-0.401910\pi$
$44$	−32.7425			−0.744149
$45$	−8.06342	+	9.47869i	−0.179187	+	0.210638i
$46$	34.6719			0.753737
$47$	−11.2382	+	6.48838i	−0.239111	+	0.138051i	−0.614768	−	0.788708i	$-0.710750\pi$
$47$	−11.2382	+	6.48838i	−0.239111	+	0.138051i	0.375657	+	0.926759i	$0.377417\pi$
$48$	4.14234	−	11.2624i	0.0862988	−	0.234633i
$49$	−38.6821	−	30.0782i	−0.789431	−	0.613840i
$50$	−16.3257	+	28.2770i	−0.326515	+	0.565541i
$51$	−3.85139	+	3.20957i	−0.0755175	+	0.0629328i
$52$	−32.1421	+	18.5572i	−0.618117	+	0.356870i
$53$	−45.2169			−0.853148			−0.426574	−	0.904453i	$-0.640280\pi$
$53$	−45.2169			−0.853148			−0.426574	+	0.904453i	$0.640280\pi$
$54$	32.8728	+	19.4263i	0.608755	+	0.359747i
$55$			22.6368i			0.411579i
$56$	6.42430	−	18.7277i	0.114720	−	0.334424i
$57$	66.6770	−	55.5656i	1.16977	−	0.974835i
$58$	−29.2753	+	50.7063i	−0.504747	+	0.874247i
$59$	−21.6394	−	12.4935i	−0.366769	−	0.211754i	0.305277	−	0.952264i	$-0.401251\pi$
$59$	−21.6394	−	12.4935i	−0.366769	−	0.211754i	−0.672046	+	0.740509i	$0.734584\pi$
$60$	−7.78633	−	2.86384i	−0.129772	−	0.0477307i
$61$	13.9412	−	8.04896i	0.228544	−	0.131950i	−0.381356	−	0.924428i	$-0.624543\pi$
$61$	13.9412	−	8.04896i	0.228544	−	0.131950i	0.609900	+	0.792478i	$0.291209\pi$
$62$		−	60.8422i		−	0.981327i
$63$	54.9289	+	30.8515i	0.871887	+	0.489706i
$64$	8.00000			0.125000
$65$	12.8297	+	22.2217i	0.197380	+	0.341872i
$66$	68.4426	−	11.8298i	1.03701	−	0.179240i
$67$	−22.1391	+	38.3460i	−0.330434	+	0.572329i	−0.982597	−	0.185750i	$-0.940529\pi$
$67$	−22.1391	+	38.3460i	−0.330434	+	0.572329i	0.652163	+	0.758079i	$0.273862\pi$
$68$	−2.89451	−	1.67115i	−0.0425663	−	0.0245757i
$69$	−72.4756	+	12.5269i	−1.05037	+	0.181549i
$70$	−12.9476	−	4.44149i	−0.184965	−	0.0634499i
$71$	80.7195			1.13690			0.568448	−	0.822720i	$-0.307544\pi$
$71$	80.7195			1.13690			0.568448	+	0.822720i	$0.307544\pi$
$72$	−4.58978	+	25.0386i	−0.0637469	+	0.347759i
$73$		−	79.4212i		−	1.08796i	−0.839098	−	0.543981i	$-0.816917\pi$
$73$		−	79.4212i		−	1.08796i	0.839098	−	0.543981i	$-0.183083\pi$
$74$	13.1369	+	22.7538i	0.177526	+	0.307483i
$75$	23.9097	−	65.0067i	0.318796	−	0.866756i
$76$	50.1111	+	28.9316i	0.659356	+	0.380680i
$77$	112.468	−	21.9964i	1.46062	−	0.285668i
$78$	60.4828	−	50.4036i	0.775420	−	0.646200i
$79$	19.6156	+	33.9751i	0.248298	+	0.430065i	0.963054	−	0.269309i	$-0.0867954\pi$
$79$	19.6156	+	33.9751i	0.248298	+	0.430065i	−0.714756	+	0.699374i	$0.753462\pi$
$80$		−	5.53087i		−	0.0691358i
$81$	−75.7335	−	28.7305i	−0.934981	−	0.354697i
$82$			16.0136i			0.195288i
$83$	100.367	−	57.9469i	1.20924	−	0.698155i	0.246646	−	0.969106i	$-0.420671\pi$
$83$	100.367	−	57.9469i	1.20924	−	0.698155i	0.962593	+	0.270951i	$0.0873380\pi$
$84$	−6.66258	+	41.4682i	−0.0793165	+	0.493669i
$85$	−1.15536	+	2.00114i	−0.0135925	+	0.0235429i
$86$	−40.9611	+	70.9467i	−0.476292	+	0.824961i
$87$	42.8749	−	116.570i	0.492814	−	1.33988i
$88$	23.1525	+	40.1013i	0.263096	+	0.455696i
$89$			30.2467i			0.339850i	0.985457	+	0.169925i	$0.0543526\pi$
$89$			30.2467i			0.339850i	−0.985457	+	0.169925i	$0.945647\pi$
$90$	17.3107	+	3.17318i	0.192341	+	0.0352576i
$91$	97.9389	−	85.3357i	1.07625	−	0.937755i
$92$	−24.5167	−	42.4642i	−0.266486	−	0.461568i
$93$	21.9822	+	127.180i	0.236368	+	1.36753i
$94$	15.8932	+	9.17596i	0.169077	+	0.0976166i
$95$	20.0021	−	34.6447i	0.210549	−	0.364681i
$96$	−16.7226	+	2.89038i	−0.174194	+	0.0301082i
$97$	−71.7067	+	41.3999i	−0.739244	+	0.426803i	−0.821794	−	0.569784i	$-0.807027\pi$
$97$	−71.7067	+	41.3999i	−0.739244	+	0.426803i	0.0825504	+	0.996587i	$0.473693\pi$
$98$	−9.48569	+	68.6442i	−0.0967927	+	0.700451i
$99$	−138.793	+	49.4563i	−1.40195	+	0.499559i
$100$	46.1762			0.461762
$101$	−113.621	+	65.5988i	−1.12496	+	0.649493i	−0.942661	−	0.333751i	$-0.891686\pi$
$101$	−113.621	+	65.5988i	−1.12496	+	0.649493i	−0.182294	+	0.983244i	$0.558352\pi$
$102$	6.65425	+	2.44746i	0.0652378	+	0.0239947i
$103$	14.8104	+	8.55080i	0.143790	+	0.0830174i	0.570169	−	0.821527i	$-0.306878\pi$
$103$	14.8104	+	8.55080i	0.143790	+	0.0830174i	−0.426379	+	0.904545i	$0.640211\pi$
$104$	45.4558	+	26.2439i	0.437075	+	0.252345i
$105$	28.6694	+	4.60623i	0.273042	+	0.0438689i
$106$	31.9732	+	55.3791i	0.301633	+	0.522445i
$107$	19.9716			0.186650			0.0933252	−	0.995636i	$-0.470250\pi$
$107$	19.9716			0.186650			0.0933252	+	0.995636i	$0.470250\pi$
$108$	0.547726	−	53.9972i	0.00507154	−	0.499974i
$109$	−97.1390			−0.891184			−0.445592	−	0.895236i	$-0.647007\pi$
$109$	−97.1390			−0.891184			−0.445592	+	0.895236i	$0.647007\pi$
$110$	27.7243	−	16.0067i	0.252040	−	0.145515i
$111$	−35.6813	−	42.8165i	−0.321453	−	0.385734i
$112$	−27.4794	+	5.37439i	−0.245352	+	0.0479856i
$113$	39.7264	−	68.8081i	0.351561	−	0.608921i	−0.634962	−	0.772543i	$-0.718984\pi$
$113$	39.7264	−	68.8081i	0.351561	−	0.608921i	0.986523	+	0.163622i	$0.0523177\pi$
$114$	−115.201	−	42.3716i	−1.01054	−	0.371680i
$115$	−29.3580	+	16.9498i	−0.255287	+	0.147390i
$116$	82.8031			0.713820
$117$	−108.218	+	127.212i	−0.924940	+	1.08728i
$118$			35.3370i			0.299466i
$119$	11.0651	+	3.79573i	0.0929840	+	0.0318969i
$120$	1.99829	+	11.5613i	0.0166524	+	0.0963443i
$121$	−73.5093	+	127.322i	−0.607515	+	1.05225i
$122$	−19.7158	−	11.3829i	−0.161605	−	0.0933028i
$123$	−5.78569	−	33.4737i	−0.0470381	−	0.272144i
$124$	−74.5162	+	43.0220i	−0.600937	+	0.346951i
$125$		−	66.4922i		−	0.531938i
$126$	−1.05539	−	89.0892i	−0.00837614	−	0.707057i
$127$	69.1372			0.544388			0.272194	−	0.962242i	$-0.412251\pi$
$127$	69.1372			0.544388			0.272194	+	0.962242i	$0.412251\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$	59.9891	−	163.101i	0.465032	−	1.26435i
$130$	18.1439	−	31.4262i	0.139569	−	0.241740i
$131$	101.978	+	58.8770i	0.778458	+	0.449443i	0.835883	−	0.548907i	$-0.184956\pi$
$131$	101.978	+	58.8770i	0.778458	+	0.449443i	−0.0574258	+	0.998350i	$0.518289\pi$
$132$	−62.8847	−	75.4598i	−0.476400	−	0.571665i
$133$	−191.564	−	65.7134i	−1.44033	−	0.494086i
$134$	62.6188			0.467305
$135$	−37.3314	−	0.378675i	−0.276529	−	0.00280500i
$136$			4.72672i			0.0347553i
$137$	−0.955894	−	1.65566i	−0.00697733	−	0.0120851i	0.862516	−	0.506030i	$-0.168888\pi$
$137$	−0.955894	−	1.65566i	−0.00697733	−	0.0120851i	−0.869493	+	0.493945i	$0.835554\pi$
$138$	66.5902	+	79.9063i	0.482538	+	0.579031i
$139$	217.488	+	125.566i	1.56466	+	0.903356i	0.996775	+	0.0802469i	$0.0255709\pi$
$139$	217.488	+	125.566i	1.56466	+	0.903356i	0.567883	+	0.823109i	$0.307762\pi$
$140$	3.71563	+	18.9981i	0.0265402	+	0.135701i
$141$	−36.5373	−	13.4386i	−0.259130	−	0.0953089i
$142$	−57.0773	−	98.8609i	−0.401953	−	0.696203i
$143$			303.806i			2.12452i
$144$	33.9114	−	12.0837i	0.235496	−	0.0839145i
$145$		−	57.2466i		−	0.394804i
$146$	−97.2707	+	56.1592i	−0.666237	+	0.384652i
$147$	−4.97281	−	146.916i	−0.0338286	−	0.999428i
$148$	18.5784	−	32.1787i	0.125530	−	0.217424i
$149$	78.1129	−	135.295i	0.524248	−	0.908023i	−0.475354	−	0.879795i	$-0.657680\pi$
$149$	78.1129	−	135.295i	0.524248	−	0.908023i	0.999601	−	0.0282288i	$-0.00898670\pi$
$150$	−96.5233	+	16.6834i	−0.643489	+	0.111222i
$151$	−13.5376	−	23.4479i	−0.0896532	−	0.155284i	0.817711	−	0.575628i	$-0.195243\pi$
$151$	−13.5376	−	23.4479i	−0.0896532	−	0.155284i	−0.907365	+	0.420345i	$0.861909\pi$
$152$		−	81.8311i		−	0.538362i
$153$	−14.7938	−	2.71182i	−0.0966917	−	0.0177243i
$154$	−106.467	−	122.191i	−0.691344	−	0.793448i
$155$	29.7436	+	51.5174i	0.191894	+	0.332370i
$156$	−104.499	−	38.4353i	−0.669867	−	0.246380i
$157$	−129.709	−	74.8877i	−0.826174	−	0.476992i	0.0263672	−	0.999652i	$-0.491606\pi$
$157$	−129.709	−	74.8877i	−0.826174	−	0.476992i	−0.852541	+	0.522661i	$0.824939\pi$
$158$	27.7406	−	48.0481i	0.175573	−	0.304102i
$159$	−86.8427	−	104.209i	−0.546180	−	0.655400i
$160$	−6.77390	+	3.91091i	−0.0423369	+	0.0244432i
$161$	112.740	+	129.391i	0.700251	+	0.803671i
$162$	18.3642	+	113.070i	0.113359	+	0.697961i
$163$	105.699			0.648463			0.324231	−	0.945978i	$-0.394894\pi$
$163$	105.699			0.648463			0.324231	+	0.945978i	$0.394894\pi$
$164$	19.6126	−	11.3233i	0.119589	−	0.0690448i
$165$	−52.1698	+	43.4759i	−0.316180	+	0.263490i
$166$	−141.940	−	81.9492i	−0.855062	−	0.493670i
$167$	−224.477	−	129.602i	−1.34417	−	0.776060i	−0.356758	−	0.934197i	$-0.616118\pi$
$167$	−224.477	−	129.602i	−1.34417	−	0.776060i	−0.987417	+	0.158137i	$0.949451\pi$
$168$	55.4991	−	21.1625i	0.330352	−	0.125967i
$169$	87.6857	+	151.876i	0.518851	+	0.898676i
$170$	3.26786			0.0192227
$171$	256.117	+	46.9483i	1.49776	+	0.274552i
$172$	115.855			0.673578
$173$	204.267	−	117.933i	1.18073	−	0.681696i	0.224548	−	0.974463i	$-0.427909\pi$
$173$	204.267	−	117.933i	1.18073	−	0.681696i	0.956184	+	0.292767i	$0.0945760\pi$
$174$	−173.085	+	29.9166i	−0.994744	+	0.171934i
$175$	−158.612	+	31.0211i	−0.906352	+	0.177263i
$176$	32.7425	−	56.7118i	0.186037	−	0.322226i
$177$	−12.7672	−	73.8658i	−0.0721310	−	0.417321i
$178$	37.0445	−	21.3876i	0.208115	−	0.120155i
$179$	−238.022			−1.32973			−0.664865	−	0.746963i	$-0.731511\pi$
$179$	−238.022			−1.32973			−0.664865	+	0.746963i	$0.731511\pi$
$180$	−8.35416	−	23.4449i	−0.0464120	−	0.130250i
$181$			163.801i			0.904980i	0.891770	+	0.452490i	$0.149464\pi$
$181$			163.801i			0.904980i	−0.891770	+	0.452490i	$0.850536\pi$
$182$	−173.768	−	59.6086i	−0.954768	−	0.327520i
$183$	45.3252	+	16.6708i	0.247678	+	0.0910971i
$184$	−34.6719	+	60.0535i	−0.188434	+	0.326378i
$185$	−22.2470	−	12.8443i	−0.120254	−	0.0694287i
$186$	140.219	−	116.853i	0.753868	−	0.628239i
$187$	−23.6934	+	13.6794i	−0.126703	+	0.0731519i
$188$		−	25.9535i		−	0.138051i
$189$	34.3939	+	185.844i	0.181978	+	0.983303i
$190$	−56.5746			−0.297761
$191$	126.758	+	219.552i	0.663656	+	1.14949i	0.979648	+	0.200724i	$0.0643294\pi$
$191$	126.758	+	219.552i	0.663656	+	1.14949i	−0.315992	+	0.948762i	$0.602337\pi$
$192$	15.3647	+	18.4371i	0.0800242	+	0.0960267i
$193$	−15.5656	+	26.9604i	−0.0806507	+	0.139691i	−0.903530	−	0.428526i	$-0.859033\pi$
$193$	−15.5656	+	26.9604i	−0.0806507	+	0.139691i	0.822879	+	0.568217i	$0.192366\pi$
$194$	101.409	+	58.5482i	0.522724	+	0.301795i
$195$	−26.5725	+	72.2465i	−0.136269	+	0.370495i
$196$	90.7790	−	36.9212i	0.463158	−	0.188374i
$197$	−197.604			−1.00307			−0.501533	−	0.865138i	$-0.667230\pi$
$197$	−197.604			−1.00307			−0.501533	+	0.865138i	$0.667230\pi$
$198$	158.713	+	135.015i	0.801581	+	0.681896i
$199$			161.524i			0.811680i	0.913944	+	0.405840i	$0.133021\pi$
$199$			161.524i			0.811680i	−0.913944	+	0.405840i	$0.866979\pi$
$200$	−32.6515	−	56.5541i	−0.163257	−	0.282770i
$201$	−130.894	+	22.6241i	−0.651213	+	0.112557i
$202$	160.684	+	92.7708i	0.795464	+	0.459261i
$203$	−284.422	+	55.6270i	−1.40109	+	0.274025i
$204$	−1.70775	−	9.88038i	−0.00837134	−	0.0484332i
$205$	−7.82849	−	13.5593i	−0.0381877	−	0.0661431i
$206$		−	24.1853i		−	0.117404i
$207$	−168.065	−	142.971i	−0.811909	−	0.690682i
$208$		−	74.2290i		−	0.356870i
$209$	410.191	−	236.824i	1.96264	−	1.13313i
$210$	−14.6308	−	38.3698i	−0.0696707	−	0.182713i
$211$	−7.20535	+	12.4800i	−0.0341486	+	0.0591470i	−0.882595	−	0.470135i	$-0.844205\pi$
$211$	−7.20535	+	12.4800i	−0.0341486	+	0.0591470i	0.848446	+	0.529282i	$0.177539\pi$
$212$	45.2169	−	78.3179i	0.213287	−	0.369424i
$213$	155.028	+	186.030i	0.727833	+	0.873378i
$214$	−14.1221	−	24.4601i	−0.0659909	−	0.114300i
$215$		−	80.0976i		−	0.372547i
$216$	−66.5201	+	37.5110i	−0.307964	+	0.173662i
$217$	227.055	−	197.837i	1.04634	−	0.911691i
$218$	68.6877	+	118.971i	0.315081	+	0.545736i
$219$	183.037	−	152.535i	0.835786	−	0.696506i
$220$	−39.2081	−	22.6368i	−0.178219	−	0.102895i
$221$	−15.5059	+	26.8571i	−0.0701626	+	0.121525i
$222$	−27.2088	+	73.9763i	−0.122562	+	0.333226i
$223$	162.482	−	93.8091i	0.728619	−	0.420668i	−0.0892977	−	0.996005i	$-0.528462\pi$
$223$	162.482	−	93.8091i	0.728619	−	0.420668i	0.817917	+	0.575337i	$0.195129\pi$
$224$	26.0131	+	29.8550i	0.116130	+	0.133281i
$225$	195.738	−	69.7473i	0.869945	−	0.309988i
$226$	−112.363			−0.497182
$227$	−239.150	+	138.073i	−1.05352	+	0.608252i	−0.923634	−	0.383276i	$-0.874796\pi$
$227$	−239.150	+	138.073i	−1.05352	+	0.608252i	−0.129890	+	0.991528i	$0.541462\pi$
$228$	29.5654	+	171.054i	0.129673	+	0.750235i
$229$	312.831	+	180.613i	1.36607	+	0.788703i	0.990424	−	0.138059i	$-0.0440864\pi$
$229$	312.831	+	180.613i	1.36607	+	0.788703i	0.375649	+	0.926762i	$0.377420\pi$
$230$	41.5185	+	23.9707i	0.180515	+	0.104220i
$231$	266.698	+	216.953i	1.15454	+	0.939189i
$232$	−58.5506	−	101.413i	−0.252373	−	0.437123i
$233$	−313.585			−1.34586			−0.672929	−	0.739707i	$-0.734964\pi$
$233$	−313.585			−1.34586			−0.672929	+	0.739707i	$0.734964\pi$
$234$	232.324	+	42.5868i	0.992839	+	0.181995i
$235$	−17.9432			−0.0763540
$236$	43.2788	−	24.9870i	0.183385	−	0.105877i
$237$	−40.6272	+	110.459i	−0.171423	+	0.466071i
$238$	−3.17540	−	16.2359i	−0.0133420	−	0.0682181i
$239$	−200.689	+	347.604i	−0.839705	+	1.45441i	0.0504372	+	0.998727i	$0.483939\pi$
$239$	−200.689	+	347.604i	−0.839705	+	1.45441i	−0.890142	+	0.455684i	$0.849395\pi$
$240$	12.7467	−	10.6225i	0.0531111	−	0.0442603i
$241$	86.1192	−	49.7209i	0.357341	−	0.206311i	−0.310573	−	0.950550i	$-0.600521\pi$
$241$	86.1192	−	49.7209i	0.357341	−	0.206311i	0.667914	+	0.744239i	$0.267188\pi$
$242$	207.916			0.859156
$243$	−79.2389	−	229.718i	−0.326086	−	0.945340i
$244$			32.1958i			0.131950i
$245$	−25.5258	−	62.7608i	−0.104187	−	0.256167i
$246$	−36.9056	+	30.7555i	−0.150023	+	0.125022i
$247$	268.446	−	464.962i	1.08683	−	1.88244i
$248$	105.382	+	60.8422i	0.424927	+	0.245332i
$249$	326.309	+	120.018i	1.31048	+	0.482000i
$250$	−81.4360	+	47.0171i	−0.325744	+	0.188068i
$251$		−	450.528i		−	1.79493i	−0.441082	−	0.897467i	$-0.645405\pi$
$251$		−	450.528i		−	1.79493i	0.441082	−	0.897467i	$-0.354595\pi$
$252$	−108.365	+	64.2882i	−0.430021	+	0.255112i
$253$	−401.370			−1.58644
$254$	−48.8874	−	84.6755i	−0.192470	−	0.333368i
$255$	−6.83088	+	1.18067i	−0.0267878	+	0.00463008i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−318.600	−	183.944i	−1.23969	−	0.715734i	−0.270657	−	0.962676i	$-0.587241\pi$
$257$	−318.600	−	183.944i	−1.23969	−	0.715734i	−0.969030	+	0.246942i	$0.920574\pi$
$258$	−242.176	+	41.8583i	−0.938665	+	0.162242i
$259$	−42.1977	+	123.012i	−0.162925	+	0.474950i
$260$	−51.3188			−0.197380
$261$	350.996	−	125.071i	1.34481	−	0.479199i
$262$		−	166.529i		−	0.635608i
$263$	18.9724	+	32.8612i	0.0721385	+	0.124947i	0.899838	−	0.436224i	$-0.143684\pi$
$263$	18.9724	+	32.8612i	0.0721385	+	0.124947i	−0.827700	+	0.561171i	$0.810351\pi$
$264$	−47.9528	+	130.376i	−0.181639	+	0.493848i
$265$	−54.1457	−	31.2611i	−0.204324	−	0.117966i
$266$	54.9740	+	281.083i	0.206669	+	1.05670i
$267$	−69.7077	+	58.0912i	−0.261078	+	0.217570i
$268$	−44.2782	−	76.6921i	−0.165217	−	0.286165i
$269$		−	25.3987i		−	0.0944190i	−0.998885	−	0.0472095i	$-0.984967\pi$
$269$		−	25.3987i		−	0.0944190i	0.998885	−	0.0472095i	$-0.0150328\pi$
$270$	25.9335	+	45.9892i	0.0960501	+	0.170331i
$271$			171.660i			0.633432i	0.948520	+	0.316716i	$0.102580\pi$
$271$			171.660i			0.633432i	−0.948520	+	0.316716i	$0.897420\pi$
$272$	5.78902	−	3.34229i	0.0212832	−	0.0122878i
$273$	384.768	+	61.8196i	1.40941	+	0.226445i
$274$	−1.35184	+	2.34145i	−0.00493372	+	0.00854545i
$275$	188.991	−	327.342i	0.687239	−	1.19033i
$276$	50.7784	−	138.058i	0.183980	−	0.500211i
$277$	95.0147	+	164.570i	0.343013	+	0.594117i	0.984991	−	0.172607i	$-0.0552191\pi$
$277$	95.0147	+	164.570i	0.343013	+	0.594117i	−0.641977	+	0.766724i	$0.721886\pi$
$278$		−	355.156i		−	1.27754i
$279$	−250.886	+	294.921i	−0.899233	+	1.05706i
$280$	20.6405	−	17.9844i	0.0737160	−	0.0642299i
$281$	−52.1486	−	90.3240i	−0.185582	−	0.321438i	0.758190	−	0.652033i	$-0.226084\pi$
$281$	−52.1486	−	90.3240i	−0.185582	−	0.321438i	−0.943773	+	0.330595i	$0.892750\pi$
$282$	9.37696	+	54.2513i	0.0332516	+	0.192381i
$283$	−131.374	−	75.8486i	−0.464218	−	0.268016i	0.249598	−	0.968349i	$-0.419701\pi$
$283$	−131.374	−	75.8486i	−0.464218	−	0.268016i	−0.713816	+	0.700333i	$0.753035\pi$
$284$	−80.7195	+	139.810i	−0.284224	+	0.492290i
$285$	118.259	−	20.4403i	0.414945	−	0.0717203i
$286$	372.085	−	214.823i	1.30100	−	0.751130i
$287$	−59.7608	+	52.0705i	−0.208226	+	0.181430i
$288$	−38.7784	−	32.9884i	−0.134647	−	0.114543i
$289$	286.207			0.990337
$290$	−70.1125	+	40.4795i	−0.241767	+	0.139584i
$291$	−233.130	−	85.7462i	−0.801135	−	0.294661i
$292$	137.561	+	79.4212i	0.471101	+	0.271990i
$293$	−51.7663	−	29.8873i	−0.176677	−	0.102004i	0.409054	−	0.912510i	$-0.365859\pi$
$293$	−51.7663	−	29.8873i	−0.176677	−	0.102004i	−0.585730	+	0.810506i	$0.699192\pi$
$294$	−176.418	+	109.976i	−0.600062	+	0.374067i
$295$	−17.2750	−	29.9212i	−0.0585593	−	0.101428i
$296$	−52.5476			−0.177526
$297$	−380.543	−	224.884i	−1.28129	−	0.757184i
$298$	−220.937			−0.741398
$299$	−394.010	+	227.482i	−1.31776	+	0.760808i
$300$	88.6851	+	106.419i	0.295617	+	0.354732i
$301$	−397.954	+	77.8315i	−1.32211	+	0.258576i
$302$	−19.1451	+	33.1603i	−0.0633944	+	0.109802i
$303$	−369.399	−	135.866i	−1.21914	−	0.448404i
$304$	−100.222	+	57.8633i	−0.329678	+	0.190340i
$305$	22.2589			0.0729798
$306$	7.13952	+	20.0362i	0.0233318	+	0.0654778i
$307$			474.281i			1.54489i	0.635082	+	0.772445i	$0.280967\pi$
$307$			474.281i			1.54489i	−0.635082	+	0.772445i	$0.719033\pi$
$308$	−74.3692	+	216.797i	−0.241458	+	0.703886i
$309$	8.73810	+	50.5552i	0.0282786	+	0.163609i
$310$	42.0638	−	72.8566i	0.135690	−	0.235021i
$311$	−90.5502	−	52.2792i	−0.291158	−	0.168100i	0.347306	−	0.937752i	$-0.387097\pi$
$311$	−90.5502	−	52.2792i	−0.291158	−	0.168100i	−0.638464	+	0.769652i	$0.720430\pi$
$312$	26.8188	+	155.163i	0.0859576	+	0.497317i
$313$	249.488	−	144.042i	0.797087	−	0.460198i	−0.0453645	−	0.998970i	$-0.514445\pi$
$313$	249.488	−	144.042i	0.797087	−	0.460198i	0.842452	+	0.538772i	$0.181112\pi$
$314$			211.814i			0.674568i
$315$	44.4462	+	74.9192i	0.141099	+	0.237839i
$316$	−78.4622			−0.248298
$317$	61.7440	+	106.944i	0.194776	+	0.337362i	0.946827	−	0.321743i	$-0.104269\pi$
$317$	61.7440	+	106.944i	0.194776	+	0.337362i	−0.752051	+	0.659105i	$0.770935\pi$
$318$	−66.2219	+	180.047i	−0.208245	+	0.566185i
$319$	338.898	−	586.989i	1.06238	−	1.84009i
$320$	9.57974	+	5.53087i	0.0299367	+	0.0172840i
$321$	38.3571	+	46.0273i	0.119492	+	0.143387i
$322$	78.7514	−	229.572i	0.244570	−	0.712955i
$323$	48.3490			0.149687
$324$	125.496	−	102.444i	0.387334	−	0.316184i
$325$		−	428.452i		−	1.31831i
$326$	−74.7408	−	129.455i	−0.229266	−	0.397101i
$327$	−186.563	−	223.871i	−0.570530	−	0.684619i
$328$	−27.7364	−	16.0136i	−0.0845622	−	0.0488220i
$329$	17.4355	+	89.1483i	0.0529956	+	0.270968i
$330$	90.1365	+	33.1525i	0.273141	+	0.100462i
$331$	−200.090	−	346.566i	−0.604502	−	1.04703i	−0.992130	−	0.125212i	$-0.960039\pi$
$331$	−200.090	−	346.566i	−0.604502	−	1.04703i	0.387628	−	0.921816i	$-0.373294\pi$
$332$			231.787i			0.698155i
$333$	30.1477	−	164.465i	0.0905337	−	0.493889i
$334$			366.570i			1.09751i
$335$	−53.0217	+	30.6121i	−0.158274	+	0.0913794i
$336$	−65.1624	−	53.0081i	−0.193936	−	0.157762i
$337$	172.186	−	298.235i	0.510937	−	0.884969i	−0.488982	−	0.872294i	$-0.662632\pi$
$337$	172.186	−	298.235i	0.510937	−	0.884969i	0.999920	−	0.0126757i	$-0.00403491\pi$
$338$	124.006	−	214.785i	0.366883	−	0.635460i
$339$	234.876	−	40.5966i	0.692849	−	0.119754i
$340$	−2.31072	−	4.00229i	−0.00679624	−	0.0117714i
$341$			704.324i			2.06547i
$342$	−123.603	−	346.876i	−0.361411	−	1.01426i
$343$	−287.015	+	187.807i	−0.836779	+	0.547541i
$344$	−81.9221	−	141.893i	−0.238146	−	0.412481i
$345$	−95.4477	−	35.1061i	−0.276660	−	0.101757i
$346$	−288.877	−	166.783i	−0.834904	−	0.482032i
$347$	−45.1558	+	78.2121i	−0.130132	+	0.225395i	−0.923727	−	0.383051i	$-0.874873\pi$
$347$	−45.1558	+	78.2121i	−0.130132	+	0.225395i	0.793595	+	0.608446i	$0.208207\pi$
$348$	159.030	+	190.831i	0.456983	+	0.548366i
$349$	−128.101	+	73.9590i	−0.367051	+	0.211917i	−0.672169	−	0.740397i	$-0.734637\pi$
$349$	−128.101	+	73.9590i	−0.367051	+	0.211917i	0.305118	+	0.952314i	$0.401304\pi$
$350$	150.148	+	172.324i	0.428995	+	0.492353i
$351$	−501.020	−	5.08215i	−1.42741	−	0.0144791i
$352$	−92.6099			−0.263096
$353$	304.978	−	176.079i	0.863960	−	0.498808i	−0.00137625	−	0.999999i	$-0.500438\pi$
$353$	304.978	−	176.079i	0.863960	−	0.498808i	0.865336	+	0.501191i	$0.167105\pi$
$354$	−81.4390	+	67.8676i	−0.230054	+	0.191716i
$355$	96.6591	+	55.8061i	0.272279	+	0.157200i
$356$	−52.3888	−	30.2467i	−0.147160	−	0.0849626i
$357$	12.5036	+	32.7911i	0.0350242	+	0.0918517i
$358$	168.307	+	291.516i	0.470131	+	0.814290i
$359$	122.724			0.341850			0.170925	−	0.985284i	$-0.445324\pi$
$359$	122.724			0.341850			0.170925	+	0.985284i	$0.445324\pi$
$360$	−22.8068	+	26.8098i	−0.0633522	+	0.0744716i
$361$	−476.040			−1.31867
$362$	200.615	−	115.825i	0.554185	−	0.319959i
$363$	−434.612	+	75.1195i	−1.19728	+	0.206941i
$364$	49.8669	+	254.971i	0.136997	+	0.700469i
$365$	54.9085	−	95.1043i	0.150434	−	0.260560i
$366$	−11.6323	−	67.2998i	−0.0317822	−	0.183879i
$367$	43.4804	−	25.1034i	0.118475	−	0.0684017i	−0.439591	−	0.898198i	$-0.644877\pi$
$367$	43.4804	−	25.1034i	0.118475	−	0.0684017i	0.558067	+	0.829796i	$0.311543\pi$
$368$	98.0669			0.266486
$369$	66.0329	−	77.6229i	0.178951	−	0.210360i
$370$			36.3292i			0.0981870i
$371$	−102.703	+	299.392i	−0.276826	+	0.806988i
$372$	−242.265	−	89.1059i	−0.651249	−	0.239532i
$373$	−264.093	+	457.423i	−0.708025	+	1.22634i	0.257564	+	0.966261i	$0.417080\pi$
$373$	−264.093	+	457.423i	−0.708025	+	1.22634i	−0.965589	+	0.260074i	$0.916253\pi$
$374$	33.5076	+	19.3456i	0.0895924	+	0.0517262i
$375$	153.241	−	127.704i	0.408642	−	0.340543i
$376$	−31.7865	+	18.3519i	−0.0845384	+	0.0488083i
$377$		−	768.299i		−	2.03793i
$378$	203.292	−	173.535i	0.537808	−	0.459088i
$379$	122.654			0.323624			0.161812	−	0.986822i	$-0.448266\pi$
$379$	122.654			0.323624			0.161812	+	0.986822i	$0.448266\pi$
$380$	40.0043	+	69.2894i	0.105274	+	0.182341i
$381$	132.784	+	159.336i	0.348514	+	0.418206i
$382$	179.263	−	310.493i	0.469276	−	0.812809i
$383$	205.357	+	118.563i	0.536180	+	0.309563i	0.743529	−	0.668703i	$-0.233150\pi$
$383$	205.357	+	118.563i	0.536180	+	0.309563i	−0.207350	+	0.978267i	$0.566484\pi$
$384$	11.7163	−	31.8548i	0.0305112	−	0.0829552i
$385$	149.884	+	51.4158i	0.389310	+	0.133547i
$386$	44.0261			0.114057
$387$	491.103	−	174.995i	1.26900	−	0.452184i
$388$		−	165.599i		−	0.426803i
$389$	86.2568	+	149.401i	0.221740	+	0.384065i	0.955336	−	0.295520i	$-0.0954931\pi$
$389$	86.2568	+	149.401i	0.221740	+	0.384065i	−0.733596	+	0.679585i	$0.762160\pi$
$390$	107.273	−	18.5414i	0.275059	−	0.0475420i
$391$	−35.4820	−	20.4855i	−0.0907468	−	0.0523927i
$392$	−109.409	−	85.0739i	−0.279106	−	0.217025i
$393$	60.1667	+	348.101i	0.153096	+	0.885752i
$394$	139.727	+	242.015i	0.354637	+	0.614250i
$395$			54.2455i			0.137330i
$396$	53.1324	−	289.853i	0.134173	−	0.731953i
$397$			188.846i			0.475683i	0.971304	+	0.237842i	$0.0764400\pi$
$397$			188.846i			0.475683i	−0.971304	+	0.237842i	$0.923560\pi$
$398$	197.826	−	114.215i	0.497051	−	0.286972i
$399$	−216.468	−	567.694i	−0.542527	−	1.42279i
$400$	−46.1762	+	79.9795i	−0.115440	+	0.199949i
$401$	−32.5064	+	56.3028i	−0.0810634	+	0.140406i	−0.903707	−	0.428151i	$-0.859165\pi$
$401$	−32.5064	+	56.3028i	−0.0810634	+	0.140406i	0.822644	+	0.568557i	$0.192498\pi$
$402$	120.265	+	144.314i	0.299166	+	0.358990i
$403$	399.185	+	691.408i	0.990533	+	1.71565i
$404$		−	262.395i		−	0.649493i
$405$	−70.8253	−	86.7628i	−0.174877	−	0.214229i
$406$	269.246	+	309.010i	0.663167	+	0.761109i
$407$	−152.076	−	263.403i	−0.373651	−	0.647182i
$408$	−10.8934	+	9.07805i	−0.0266995	+	0.0222501i
$409$	−380.954	−	219.944i	−0.931427	−	0.537760i	−0.0441644	−	0.999024i	$-0.514063\pi$
$409$	−380.954	−	219.944i	−0.931427	−	0.537760i	−0.887263	+	0.461265i	$0.847396\pi$
$410$	−11.0712	+	19.1758i	−0.0270028	+	0.0467702i
$411$	1.97982	−	5.38282i	0.00481708	−	0.0130969i
$412$	−29.6208	+	17.1016i	−0.0718952	+	0.0415087i
$413$	−131.873	+	114.903i	−0.319305	+	0.278216i
$414$	−56.2632	+	306.933i	−0.135901	+	0.741384i
$415$	160.248			0.386140
$416$	−90.9116	+	52.4878i	−0.218537	+	0.126173i
$417$	128.317	+	742.391i	0.307715	+	1.78031i
$418$	−580.098	−	334.920i	−1.38779	−	0.801243i
$419$	530.898	+	306.514i	1.26706	+	0.731537i	0.974430	−	0.224689i	$-0.0721367\pi$
$419$	530.898	+	306.514i	1.26706	+	0.731537i	0.292629	+	0.956226i	$0.405470\pi$
$420$	−36.6476	+	45.0506i	−0.0872562	+	0.107263i
$421$	157.202	+	272.282i	0.373402	+	0.646750i	0.990086	−	0.140460i	$-0.0448580\pi$
$421$	157.202	+	272.282i	0.373402	+	0.646750i	−0.616685	+	0.787210i	$0.711525\pi$
$422$	20.3798			0.0482934
$423$	−39.2018	−	110.015i	−0.0926756	−	0.260083i
$424$	−127.893			−0.301633
$425$	33.4144	−	19.2918i	0.0786221	−	0.0453925i
$426$	118.217	−	321.413i	0.277505	−	0.754491i
$427$	−21.6291	−	110.590i	−0.0506536	−	0.258993i
$428$	−19.9716	+	34.5918i	−0.0466626	+	0.0808220i
$429$	−700.163	+	583.484i	−1.63208	+	1.36010i
$430$	−98.0991	+	56.6376i	−0.228138	+	0.131715i
$431$	545.839			1.26645			0.633224	−	0.773968i	$-0.281731\pi$
$431$	545.839			1.26645			0.633224	+	0.773968i	$0.281731\pi$
$432$	92.9782	+	54.9459i	0.215227	+	0.127190i
$433$			243.306i			0.561908i	0.959721	+	0.280954i	$0.0906509\pi$
$433$			243.306i			0.561908i	−0.959721	+	0.280954i	$0.909349\pi$
$434$	−402.852	−	138.193i	−0.928231	−	0.318417i
$435$	131.933	−	109.947i	0.303294	−	0.252751i
$436$	97.1390	−	168.250i	0.222796	−	0.385894i
$437$	614.280	+	354.655i	1.40568	+	0.811567i
$438$	−316.243	−	116.315i	−0.722016	−	0.265560i
$439$	680.738	−	393.024i	1.55066	−	0.895271i	0.552567	−	0.833469i	$-0.313648\pi$
$439$	680.738	−	393.024i	1.55066	−	0.895271i	0.998088	−	0.0618024i	$-0.0196849\pi$
$440$			64.0266i			0.145515i
$441$	329.038	−	293.624i	0.746117	−	0.665815i
$442$	43.8574			0.0992250
$443$	−272.893	−	472.665i	−0.616011	−	1.06696i	−0.990206	−	0.139613i	$-0.955414\pi$
$443$	−272.893	−	472.665i	−0.616011	−	1.06696i	0.374195	−	0.927350i	$-0.377919\pi$
$444$	109.842	−	18.9853i	0.247391	−	0.0427597i
$445$	−20.9113	+	36.2194i	−0.0469917	+	0.0813920i
$446$	−229.784	−	132.666i	−0.515211	−	0.297457i
$447$	461.830	−	79.8239i	1.03318	−	0.178577i
$448$	18.1707	−	52.9701i	0.0405595	−	0.118237i
$449$	789.261			1.75782			0.878910	−	0.476987i	$-0.158271\pi$
$449$	789.261			1.75782			0.878910	+	0.476987i	$0.158271\pi$
$450$	−223.830	−	190.410i	−0.497400	−	0.423133i
$451$		−	185.378i		−	0.411037i
$452$	79.4528	+	137.616i	0.175780	+	0.304461i
$453$	28.0388	−	76.2329i	0.0618957	−	0.168284i
$454$	338.209	+	195.265i	0.744954	+	0.430099i
$455$	176.276	−	34.4759i	0.387420	−	0.0757713i
$456$	188.591	−	157.163i	0.413577	−	0.344656i
$457$	44.1193	+	76.4168i	0.0965411	+	0.167214i	0.910251	−	0.414057i	$-0.135889\pi$
$457$	44.1193	+	76.4168i	0.0965411	+	0.167214i	−0.813710	+	0.581272i	$0.802555\pi$
$458$		−	510.851i		−	1.11539i
$459$	−22.1630	−	39.3027i	−0.0482853	−	0.0856268i
$460$		−	67.7994i		−	0.147390i
$461$	−24.0627	+	13.8926i	−0.0521967	+	0.0301358i	−0.525871	−	0.850564i	$-0.676261\pi$
$461$	−24.0627	+	13.8926i	−0.0521967	+	0.0301358i	0.473675	+	0.880700i	$0.342927\pi$
$462$	77.1277	−	480.046i	0.166943	−	1.03906i
$463$	−233.432	+	404.317i	−0.504174	+	0.873254i	0.495815	+	0.868428i	$0.334870\pi$
$463$	−233.432	+	404.317i	−0.504174	+	0.873254i	−0.999988	+	0.00482604i	$0.998464\pi$
$464$	−82.8031	+	143.419i	−0.178455	+	0.309093i
$465$	−61.6041	+	167.492i	−0.132482	+	0.360197i
$466$	221.738	+	384.062i	0.475833	+	0.824167i
$467$		−	163.433i		−	0.349963i	−0.984572	−	0.174981i	$-0.944014\pi$
$467$		−	163.433i		−	0.349963i	0.984572	−	0.174981i	$-0.0559865\pi$
$468$	−112.120	−	314.651i	−0.239573	−	0.672332i
$469$	203.614	+	233.685i	0.434145	+	0.498263i
$470$	12.6878	+	21.9758i	0.0269952	+	0.0467571i
$471$	−76.5281	−	442.761i	−0.162480	−	0.940045i
$472$	−61.2055	−	35.3370i	−0.129673	−	0.0748665i
$473$	474.175	−	821.296i	1.00248	−	1.73635i
$474$	164.012	−	28.3482i	0.346016	−	0.0598064i
$475$	−578.485	+	333.988i	−1.21786	+	0.703133i
$476$	−17.6395	+	15.3696i	−0.0370578	+	0.0322890i
$477$	73.3749	−	400.282i	0.153826	−	0.839166i
$478$	567.635			1.18752
$479$	194.691	−	112.405i	0.406454	−	0.234666i	−0.282811	−	0.959176i	$-0.591267\pi$
$479$	194.691	−	112.405i	0.406454	−	0.234666i	0.689265	+	0.724509i	$0.257934\pi$
$480$	−22.0231	−	8.10017i	−0.0458814	−	0.0168754i
$481$	−298.574	−	172.382i	−0.620736	−	0.358382i
$482$	−121.791	−	70.3160i	−0.252678	−	0.145884i
$483$	−81.6724	+	508.332i	−0.169094	+	1.05245i
$484$	−147.019	−	254.644i	−0.303758	−	0.526123i
$485$	−114.489			−0.236059
$486$	−225.315	+	259.482i	−0.463611	+	0.533914i
$487$	−350.781			−0.720290			−0.360145	−	0.932896i	$-0.617273\pi$
$487$	−350.781			−0.720290			−0.360145	+	0.932896i	$0.617273\pi$
$488$	39.4317	−	22.7659i	0.0808026	−	0.0466514i
$489$	203.004	+	243.599i	0.415142	+	0.498158i
$490$	−58.8165	+	75.6412i	−0.120034	+	0.154370i
$491$	−367.144	+	635.912i	−0.747748	+	1.29514i	0.201152	+	0.979560i	$0.435531\pi$
$491$	−367.144	+	635.912i	−0.747748	+	1.29514i	−0.948900	+	0.315577i	$0.897802\pi$
$492$	63.7638	+	23.4526i	0.129601	+	0.0476679i
$493$	59.9186	−	34.5940i	0.121539	−	0.0701704i
$494$	−759.280			−1.53700
$495$	−200.393	−	36.7335i	−0.404833	−	0.0742091i
$496$		−	172.088i		−	0.346951i
$497$	183.341	−	534.465i	0.368895	−	1.07538i
$498$	−83.7443	−	484.511i	−0.168161	−	0.972914i
$499$	−467.575	+	809.863i	−0.937024	+	1.62297i	−0.166039	+	0.986119i	$0.553098\pi$
$499$	−467.575	+	809.863i	−0.937024	+	1.62297i	−0.770985	+	0.636854i	$0.780236\pi$
$500$	115.168	+	66.4922i	0.230336	+	0.132984i
$501$	−132.441	−	766.250i	−0.264353	−	1.52944i
$502$	−551.782	+	318.572i	−1.09917	+	0.634605i
$503$			670.586i			1.33317i	0.745427	+	0.666587i	$0.232245\pi$
$503$			670.586i			1.33317i	−0.745427	+	0.666587i	$0.767755\pi$
$504$	155.362	+	87.2612i	0.308259	+	0.173137i
$505$	−181.409			−0.359226
$506$	283.812	+	491.576i	0.560892	+	0.971494i
$507$	−181.612	+	493.775i	−0.358210	+	0.973915i
$508$	−69.1372	+	119.749i	−0.136097	+	0.235727i
$509$	−6.41553	−	3.70401i	−0.0126042	−	0.00727703i	0.493685	−	0.869641i	$-0.335650\pi$
$509$	−6.41553	−	3.70401i	−0.0126042	−	0.00727703i	−0.506289	+	0.862364i	$0.668983\pi$
$510$	6.27618	+	7.53123i	0.0123062	+	0.0147671i
$511$	−525.868	−	180.392i	−1.02910	−	0.353017i
$512$	22.6274			0.0441942
$513$	383.695	+	680.426i	0.747944	+	1.32637i
$514$			520.271i			1.01220i
$515$	11.8233	+	20.4786i	0.0229579	+	0.0397643i
$516$	222.510	+	267.005i	0.431221	+	0.517452i
$517$	−183.984	−	106.223i	−0.355868	−	0.205461i
$518$	180.497	−	35.3014i	0.348449	−	0.0681494i
$519$	664.105	+	244.260i	1.27959	+	0.470637i
$520$	36.2879	+	62.8525i	0.0697844	+	0.120870i
$521$			855.964i			1.64292i	0.570263	+	0.821462i	$0.306841\pi$
$521$			855.964i			1.64292i	−0.570263	+	0.821462i	$0.693159\pi$
$522$	−401.372	−	341.442i	−0.768911	−	0.654104i
$523$		−	26.4383i		−	0.0505512i	−0.999681	−	0.0252756i	$-0.991954\pi$
$523$		−	26.4383i		−	0.0505512i	0.999681	−	0.0252756i	$-0.00804633\pi$
$524$	−203.956	+	117.754i	−0.389229	+	0.224721i
$525$	−376.119	−	305.964i	−0.716417	−	0.582789i
$526$	26.8310	−	46.4727i	0.0510096	−	0.0883512i
$527$	−35.9480	+	62.2638i	−0.0682125	+	0.118148i
$528$	193.585	−	33.4598i	0.366638	−	0.0633708i
$529$	−36.0351	−	62.4147i	−0.0681194	−	0.117986i
$530$			88.4196i			0.166829i
$531$	145.714	−	171.289i	0.274414	−	0.322578i
$532$	305.383	−	266.085i	0.574028	−	0.500160i
$533$	−105.065	−	181.978i	−0.197120	−	0.341422i
$534$	120.438	+	44.2975i	0.225539	+	0.0829541i
$535$	23.9153	+	13.8075i	0.0447016	+	0.0258085i
$536$	−62.6188	+	108.459i	−0.116826	+	0.202349i
$537$	−457.140	−	548.554i	−0.851285	−	1.02152i
$538$	−31.1069	+	17.9596i	−0.0578196	+	0.0333822i
$539$	109.809	−	794.641i	0.203727	−	1.47429i
$540$	37.9873	−	64.2813i	0.0703469	−	0.119039i
$541$	−607.504			−1.12293			−0.561464	−	0.827501i	$-0.689762\pi$
$541$	−607.504			−1.12293			−0.561464	+	0.827501i	$0.689762\pi$
$542$	210.240	−	121.382i	0.387896	−	0.223952i
$543$	−377.503	+	314.594i	−0.695217	+	0.579362i
$544$	−8.18691	−	4.72672i	−0.0150495	−	0.00868882i
$545$	−116.321	−	67.1579i	−0.213433	−	0.123225i
$546$	−196.359	−	514.955i	−0.359631	−	0.943142i
$547$	123.324	+	213.603i	0.225455	+	0.390499i	0.956456	−	0.291877i	$-0.0942799\pi$
$547$	123.324	+	213.603i	0.225455	+	0.390499i	−0.731001	+	0.682376i	$0.760947\pi$
$548$	3.82358			0.00697733
$549$	48.6305	+	136.476i	0.0885802	+	0.248590i
$550$	−534.547			−0.971903
$551$	−1037.34	+	598.907i	−1.88265	+	1.08695i
$552$	−204.992	+	35.4314i	−0.371362	+	0.0641873i
$553$	269.512	−	52.7108i	0.487363	−	0.0953179i
$554$	134.371	−	232.738i	0.242547	−	0.420104i
$555$	−13.1257	−	75.9399i	−0.0236498	−	0.136829i
$556$	−434.975	+	251.133i	−0.782329	+	0.451678i
$557$	−947.646			−1.70134			−0.850670	−	0.525700i	$-0.823803\pi$
$557$	−947.646			−1.70134			−0.850670	+	0.525700i	$0.823803\pi$
$558$	538.606	+	98.7307i	0.965244	+	0.176937i
$559$		−	1074.98i		−	1.92304i
$560$	−36.6213	−	12.5624i	−0.0653952	−	0.0224329i
$561$	−77.0312	−	28.3324i	−0.137311	−	0.0505034i
$562$	−73.7493	+	127.737i	−0.131226	+	0.227291i
$563$	−157.042	−	90.6681i	−0.278937	−	0.161045i	0.354005	−	0.935244i	$-0.384820\pi$
$563$	−157.042	−	90.6681i	−0.278937	−	0.161045i	−0.632942	+	0.774199i	$0.718153\pi$
$564$	59.8136	−	49.8459i	0.106052	−	0.0883792i
$565$	95.1421	−	54.9303i	0.168393	−	0.0972218i
$566$			214.532i			0.379032i
$567$	−362.248	+	436.194i	−0.638885	+	0.769302i
$568$	228.309			0.401953
$569$	289.027	+	500.610i	0.507957	+	0.879807i	0.999958	+	0.00921190i	$0.00293228\pi$
$569$	289.027	+	500.610i	0.507957	+	0.879807i	−0.492001	+	0.870595i	$0.663734\pi$
$570$	−108.656	−	130.384i	−0.190625	−	0.228744i
$571$	376.525	−	652.160i	0.659413	−	1.14214i	−0.321355	−	0.946959i	$-0.604138\pi$
$571$	376.525	−	652.160i	0.659413	−	1.14214i	0.980768	−	0.195178i	$-0.0625284\pi$
$572$	−526.207	−	303.806i	−0.919943	−	0.531129i
$573$	−262.538	+	713.799i	−0.458182	+	1.24572i
$574$	106.030	+	36.3723i	0.184722	+	0.0633663i
$575$	566.045			0.984426
$576$	−12.9819	+	70.8200i	−0.0225379	+	0.122951i
$577$			11.7220i			0.0203154i	0.999948	+	0.0101577i	$0.00323335\pi$
$577$			11.7220i			0.0203154i	−0.999948	+	0.0101577i	$0.996767\pi$
$578$	−202.379	−	350.531i	−0.350137	−	0.606455i
$579$	−92.0290	+	15.9065i	−0.158945	+	0.0274725i
$580$	99.1540	+	57.2466i	0.170955	+	0.0987010i
$581$	−155.714	−	796.172i	−0.268011	−	1.37035i
$582$	59.8307	+	346.157i	0.102802	+	0.594771i
$583$	−370.129	−	641.082i	−0.634869	−	1.09963i
$584$		−	224.637i		−	0.384652i
$585$	−217.537	+	77.5151i	−0.371858	+	0.132504i
$586$			84.5340i			0.144256i
$587$	536.412	−	309.697i	0.913819	−	0.527594i	0.0321610	−	0.999483i	$-0.489761\pi$
$587$	536.412	−	309.697i	0.913819	−	0.527594i	0.881658	+	0.471889i	$0.156428\pi$
$588$	259.439	+	138.303i	0.441222	+	0.235209i
$589$	622.348	−	1077.94i	1.05662	−	1.83012i
$590$	−24.4305	+	42.3149i	−0.0414077	+	0.0717202i
$591$	−379.515	−	455.406i	−0.642157	−	0.770569i
$592$	37.1567	+	64.3574i	0.0627648	+	0.108712i
$593$			242.416i			0.408797i	0.978888	+	0.204398i	$0.0655238\pi$
$593$			242.416i			0.408797i	−0.978888	+	0.204398i	$0.934476\pi$
$594$	−6.34061	+	625.085i	−0.0106744	+	1.05233i
$595$	10.6259	+	12.1952i	0.0178586	+	0.0204961i
$596$	156.226	+	270.591i	0.262124	+	0.454012i
$597$	−372.256	+	310.221i	−0.623544	+	0.519633i
$598$	557.214	+	321.708i	0.931796	+	0.537972i
$599$	49.1263	−	85.0892i	0.0820139	−	0.142052i	−0.822101	−	0.569342i	$-0.807198\pi$
$599$	49.1263	−	85.0892i	0.0820139	−	0.142052i	0.904115	+	0.427290i	$0.140531\pi$
$600$	67.6269	−	183.867i	0.112711	−	0.306444i
$601$	128.939	−	74.4429i	0.214541	−	0.123865i	−0.388879	−	0.921289i	$-0.627138\pi$
$601$	128.939	−	74.4429i	0.214541	−	0.123865i	0.603420	+	0.797424i	$0.293804\pi$
$602$	376.720	+	432.357i	0.625781	+	0.718201i
$603$	−303.533	−	258.212i	−0.503371	−	0.428212i
$604$	54.1505			0.0896532
$605$	−176.050	+	101.643i	−0.290992	+	0.168004i
$606$	94.8029	+	548.492i	0.156440	+	0.905102i
$607$	1034.74	+	597.407i	1.70468	+	0.984196i	0.940879	+	0.338742i	$0.110002\pi$
$607$	1034.74	+	597.407i	1.70468	+	0.984196i	0.763799	+	0.645454i	$0.223332\pi$
$608$	141.736	+	81.8311i	0.233118	+	0.134591i
$609$	−674.456	−	548.654i	−1.10748	−	0.900910i
$610$	−15.7394	−	27.2614i	−0.0258023	−	0.0446908i
$611$	−240.813			−0.394129
$612$	19.4908	−	22.9118i	0.0318478	−	0.0374376i
$613$	333.307			0.543731			0.271866	−	0.962335i	$-0.412359\pi$
$613$	333.307			0.543731			0.271866	+	0.962335i	$0.412359\pi$
$614$	580.874	−	335.368i	0.946048	−	0.546201i
$615$	16.2141	−	44.0837i	0.0263645	−	0.0716807i
$616$	318.108	−	62.2152i	0.516409	−	0.100999i
$617$	180.741	−	313.053i	0.292935	−	0.507379i	−0.681567	−	0.731756i	$-0.738701\pi$
$617$	180.741	−	313.053i	0.292935	−	0.507379i	0.974502	+	0.224377i	$0.0720346\pi$
$618$	55.7384	−	46.4498i	0.0901916	−	0.0751616i
$619$	161.200	−	93.0688i	0.260420	−	0.150353i	−0.364106	−	0.931357i	$-0.618626\pi$
$619$	161.200	−	93.0688i	0.260420	−	0.150353i	0.624526	+	0.781004i	$0.285292\pi$
$620$	−118.974			−0.191894
$621$	6.71423	−	661.918i	0.0108120	−	1.06589i
$622$			147.868i			0.237730i
$623$	200.271	+	68.7003i	0.321462	+	0.110273i
$624$	171.071	−	142.563i	0.274152	−	0.228466i
$625$	−242.631	+	420.250i	−0.388210	+	0.672399i
$626$	−352.830	−	203.706i	−0.563626	−	0.325409i
$627$	1333.60	+	490.503i	2.12695	+	0.782302i
$628$	259.418	−	149.775i	0.413087	−	0.238496i
$629$		−	31.0472i		−	0.0493596i
$630$	60.3288	−	107.411i	0.0957599	−	0.170494i
$631$	72.1705			0.114375			0.0571874	−	0.998363i	$-0.481787\pi$
$631$	72.1705			0.114375			0.0571874	+	0.998363i	$0.481787\pi$
$632$	55.4812	+	96.0962i	0.0877866	+	0.152051i
$633$	−42.6004	+	7.36318i	−0.0672992	+	0.0116322i
$634$	87.3192	−	151.241i	0.137727	−	0.238551i
$635$	82.7896	+	47.7986i	0.130377	+	0.0752734i
$636$	267.337	−	46.2073i	0.420342	−	0.0726530i
$637$	−342.578	−	842.304i	−0.537799	−	1.32230i
$638$	−958.548			−1.50243
$639$	−130.986	+	714.570i	−0.204986	+	1.11826i
$640$		−	15.6437i		−	0.0244432i
$641$	441.291	+	764.339i	0.688442	+	1.19242i	0.972342	+	0.233563i	$0.0750384\pi$
$641$	441.291	+	764.339i	0.688442	+	1.19242i	−0.283900	+	0.958854i	$0.591628\pi$
$642$	29.2492	−	79.5239i	0.0455595	−	0.123869i
$643$	−889.475	−	513.539i	−1.38332	−	0.798660i	−0.390769	−	0.920489i	$-0.627791\pi$
$643$	−889.475	−	513.539i	−1.38332	−	0.798660i	−0.992551	+	0.121828i	$0.961124\pi$
$644$	−336.852	+	65.8812i	−0.523063	+	0.102300i
$645$	184.596	−	153.834i	0.286196	−	0.238502i
$646$	−34.1879	−	59.2152i	−0.0529225	−	0.0916644i
$647$		−	1016.79i		−	1.57154i	−0.618516	−	0.785772i	$-0.712266\pi$
$647$		−	1016.79i		−	1.57154i	0.618516	−	0.785772i	$-0.287734\pi$
$648$	−214.207	−	81.2620i	−0.330566	−	0.125404i
$649$		−	409.069i		−	0.630307i
$650$	−524.744	+	302.961i	−0.807298	+	0.466094i
$651$	892.021	+	143.319i	1.37023	+	0.220152i
$652$	−105.699	+	183.077i	−0.162116	+	0.280793i
$653$	−382.857	+	663.127i	−0.586304	+	1.01551i	0.408407	+	0.912800i	$0.366084\pi$
$653$	−382.857	+	663.127i	−0.586304	+	1.01551i	−0.994711	+	0.102709i	$0.967249\pi$
$654$	−142.264	+	386.793i	−0.217529	+	0.591427i
$655$	81.4102	+	141.007i	0.124290	+	0.215277i
$656$			45.2934i			0.0690448i
$657$	703.076	+	128.879i	1.07013	+	0.196163i
$658$	96.8552	−	84.3915i	0.147196	−	0.128255i
$659$	−454.791	−	787.721i	−0.690123	−	1.19533i	−0.971797	−	0.235818i	$-0.924223\pi$
$659$	−454.791	−	787.721i	−0.690123	−	1.19533i	0.281674	−	0.959510i	$-0.409110\pi$
$660$	−23.1327	−	133.837i	−0.0350495	−	0.202783i
$661$	623.505	+	359.981i	0.943275	+	0.544600i	0.890985	−	0.454032i	$-0.150015\pi$
$661$	623.505	+	359.981i	0.943275	+	0.544600i	0.0522895	+	0.998632i	$0.483348\pi$
$662$	−282.970	+	490.119i	−0.427447	+	0.740360i
$663$	−91.6763	+	15.8456i	−0.138275	+	0.0238998i
$664$	283.880	−	163.898i	0.427531	−	0.246835i
$665$	−183.960	−	211.129i	−0.276632	−	0.317487i
$666$	−222.745	+	79.3711i	−0.334452	+	0.119176i
$667$	1015.03			1.52179
$668$	448.954	−	259.204i	0.672087	−	0.388030i
$669$	528.256	+	194.295i	0.789621	+	0.290426i
$670$	74.9840	+	43.2921i	0.111916	+	0.0646150i
$671$	228.235	+	131.772i	0.340142	+	0.196381i
$672$	−18.8446	+	117.290i	−0.0280426	+	0.174538i
$673$	−454.142	−	786.597i	−0.674803	−	1.16879i	−0.976527	−	0.215397i	$-0.930895\pi$
$673$	−454.142	−	786.597i	−0.674803	−	1.16879i	0.301724	−	0.953395i	$-0.402438\pi$
$674$	−487.015			−0.722574
$675$	536.672	+	317.149i	0.795070	+	0.469851i
$676$	−350.743			−0.518851
$677$	127.233	−	73.4577i	0.187936	−	0.108505i	−0.403080	−	0.915165i	$-0.632060\pi$
$677$	127.233	−	73.4577i	0.187936	−	0.108505i	0.591016	+	0.806660i	$0.298727\pi$
$678$	−215.803	−	258.957i	−0.318293	−	0.381942i
$679$	111.249	+	568.821i	0.163843	+	0.837734i
$680$	−3.26786	+	5.66009i	−0.00480567	+	0.00832366i
$681$	−777.516	−	285.974i	−1.14173	−	0.419932i
$682$	862.618	−	498.033i	1.26484	−	0.730253i
$683$	532.770			0.780044			0.390022	−	0.920805i	$-0.372467\pi$
$683$	532.770			0.780044			0.390022	+	0.920805i	$0.372467\pi$
$684$	−337.434	+	396.660i	−0.493325	+	0.579912i
$685$		−	2.64346i		−	0.00385907i
$686$	432.966	+	218.721i	0.631145	+	0.318835i
$687$	184.569	+	1067.84i	0.268660	+	1.55436i
$688$	−115.855	+	200.667i	−0.168394	+	0.291668i
$689$	−726.682	−	419.550i	−1.05469	−	0.608926i
$690$	24.4958	+	141.723i	0.0355011	+	0.205395i
$691$	33.7657	−	19.4946i	0.0488650	−	0.0282122i	−0.475368	−	0.879787i	$-0.657685\pi$
$691$	33.7657	−	19.4946i	0.0488650	−	0.0282122i	0.524233	+	0.851575i	$0.324352\pi$
$692$			471.734i			0.681696i
$693$	12.2175	+	1031.32i	0.0176298	+	1.48819i
$694$	127.720			0.184034
$695$	173.623	+	300.724i	0.249817	+	0.432696i
$696$	121.268	−	329.709i	0.174236	−	0.473720i
$697$	9.46148	−	16.3878i	0.0135746	−	0.0235119i
$698$	181.162	+	104.594i	0.259544	+	0.149848i
$699$	−602.266	−	722.701i	−0.861610	−	1.03391i
$700$	104.881	−	305.744i	0.149831	−	0.436778i
$701$	508.129			0.724863			0.362432	−	0.932010i	$-0.381947\pi$
$701$	508.129			0.724863			0.362432	+	0.932010i	$0.381947\pi$
$702$	348.050	+	617.215i	0.495798	+	0.879224i
$703$			537.503i			0.764584i
$704$	65.4851	+	113.424i	0.0930186	+	0.161113i
$705$	−34.4614	−	41.3526i	−0.0488814	−	0.0586562i
$706$	−431.304	−	249.013i	−0.610912	−	0.352710i
$707$	176.277	+	901.308i	0.249331	+	1.27483i
$708$	140.707	+	51.7524i	0.198738	+	0.0730967i
$709$	−303.884	−	526.343i	−0.428609	−	0.742373i	0.568140	−	0.822932i	$-0.307663\pi$
$709$	−303.884	−	526.343i	−0.428609	−	0.742373i	−0.996750	+	0.0805582i	$0.974330\pi$
$710$		−	157.844i		−	0.222315i
$711$	−332.596	+	118.514i	−0.467786	+	0.166687i
$712$			85.5506i			0.120155i
$713$	−913.447	+	527.379i	−1.28113	+	0.739662i
$714$	31.3193	−	38.5005i	0.0438646	−	0.0539223i
$715$	−210.039	+	363.798i	−0.293760	+	0.508808i
$716$	238.022	−	412.266i	0.332433	−	0.575790i
$717$	−1186.54	+	205.085i	−1.65487	+	0.286033i
$718$	−86.7791	−	150.306i	−0.120862	−	0.209340i
$719$			313.462i			0.435969i	0.975952	+	0.217985i	$0.0699483\pi$
$719$			313.462i			0.435969i	−0.975952	+	0.217985i	$0.930052\pi$
$720$	48.9620	+	8.97512i	0.0680028	+	0.0124654i
$721$	90.2564	−	78.6419i	0.125182	−	0.109073i
$722$	336.611	+	583.028i	0.466221	+	0.807518i
$723$	279.988	+	102.981i	0.387258	+	0.142435i
$724$	−283.712	−	163.801i	−0.391868	−	0.226245i
$725$	−477.941	+	827.819i	−0.659229	+	1.14182i
$726$	399.319	+	479.171i	0.550026	+	0.660015i
$727$	631.488	−	364.589i	0.868621	−	0.501499i	0.00173131	−	0.999999i	$-0.499449\pi$
$727$	631.488	−	364.589i	0.868621	−	0.501499i	0.866890	+	0.498500i	$0.166116\pi$
$728$	277.013	−	241.366i	0.380512	−	0.331546i
$729$	377.232	−	623.809i	0.517465	−	0.855705i
$730$	−155.305			−0.212746
$731$	83.8362	−	48.4029i	0.114687	−	0.0662146i
$732$	−74.1998	+	61.8347i	−0.101366	+	0.0844736i
$733$	299.131	+	172.703i	0.408092	+	0.235612i	0.689969	−	0.723838i	$-0.257624\pi$
$733$	299.131	+	172.703i	0.408092	+	0.235612i	−0.281878	+	0.959450i	$0.590957\pi$
$734$	−61.4906	−	35.5016i	−0.0837746	−	0.0483673i
$735$	95.6167	−	179.365i	0.130091	−	0.244034i
$736$	−69.3438	−	120.107i	−0.0942171	−	0.163189i
$737$	−724.891			−0.983569
$738$	−141.761	−	25.9858i	−0.192088	−	0.0352111i
$739$	−1005.34			−1.36041			−0.680203	−	0.733024i	$-0.738108\pi$
$739$	−1005.34			−1.36041			−0.680203	+	0.733024i	$0.738108\pi$
$740$	44.4940	−	25.6886i	0.0601270	−	0.0347144i
$741$	1587.14	−	274.326i	2.14189	−	0.370211i
$742$	439.301	−	85.9181i	0.592050	−	0.115793i
$743$	69.5157	−	120.405i	0.0935609	−	0.162052i	−0.815446	−	0.578833i	$-0.803508\pi$
$743$	69.5157	−	120.405i	0.0935609	−	0.162052i	0.909007	+	0.416781i	$0.136842\pi$
$744$	62.1750	+	359.720i	0.0835685	+	0.483494i
$745$	187.075	−	108.008i	0.251108	−	0.144977i
$746$	746.969			1.00130
$747$	350.106	+	982.530i	0.468683	+	1.31530i
$748$		−	54.7176i		−	0.0731519i
$749$	45.3621	−	132.237i	0.0605636	−	0.176552i
$750$	−264.762	−	97.3805i	−0.353016	−	0.129841i
$751$	−17.8265	+	30.8765i	−0.0237371	+	0.0411138i	−0.877650	−	0.479302i	$-0.840890\pi$
$751$	−17.8265	+	30.8765i	−0.0237371	+	0.0411138i	0.853913	+	0.520416i	$0.174223\pi$
$752$	44.9528	+	25.9535i	0.0597777	+	0.0345127i
$753$	1038.31	−	865.276i	1.37889	−	1.14911i
$754$	−940.970	+	543.269i	−1.24797	+	0.720516i
$755$		−	37.4374i		−	0.0495860i
$756$	−356.285	−	126.272i	−0.471277	−	0.167027i
$757$	719.557			0.950538			0.475269	−	0.879841i	$-0.342351\pi$
$757$	719.557			0.950538			0.475269	+	0.879841i	$0.342351\pi$
$758$	−86.7292	−	150.219i	−0.114418	−	0.198179i
$759$	−770.864	−	925.014i	−1.01563	−	1.21873i
$760$	56.5746	−	97.9901i	0.0744402	−	0.128934i
$761$	161.236	+	93.0898i	0.211874	+	0.122326i	0.602182	−	0.798359i	$-0.294298\pi$
$761$	161.236	+	93.0898i	0.211874	+	0.122326i	−0.390308	+	0.920684i	$0.627631\pi$
$762$	101.254	−	275.294i	0.132880	−	0.361278i
$763$	−220.635	+	643.183i	−0.289168	+	0.842965i
$764$	−507.033			−0.663656
$765$	−15.8403	−	13.4752i	−0.0207063	−	0.0176146i
$766$		−	335.346i		−	0.437789i
$767$	−231.845	−	401.568i	−0.302275	−	0.523556i
$768$	−47.2987	+	8.17524i	−0.0615868	+	0.0106448i
$769$	53.0824	+	30.6472i	0.0690279	+	0.0398533i	0.534117	−	0.845411i	$-0.320644\pi$
$769$	53.0824	+	30.6472i	0.0690279	+	0.0398533i	−0.465089	+	0.885264i	$0.653978\pi$
$770$	−43.0130	−	219.926i	−0.0558610	−	0.285619i
$771$	−187.973	−	1087.54i	−0.243804	−	1.41055i
$772$	−31.1312	−	53.9208i	−0.0403254	−	0.0698456i
$773$		−	484.245i		−	0.626449i	−0.949679	−	0.313225i	$-0.898591\pi$
$773$		−	484.245i		−	0.626449i	0.949679	−	0.313225i	$-0.101409\pi$
$774$	−561.586	−	477.735i	−0.725564	−	0.617229i
$775$		−	993.295i		−	1.28167i
$776$	−202.817	+	117.096i	−0.261362	+	0.150898i
$777$	−364.543	+	139.005i	−0.469167	+	0.178899i
$778$	121.986	−	211.285i	0.156794	−	0.271575i
$779$	−163.801	+	283.712i	−0.210271	+	0.364201i
$780$	−98.5620	−	118.271i	−0.126362	−	0.151630i
$781$	660.741	+	1144.44i	0.846019	+	1.46535i
$782$			57.9418i			0.0740944i
$783$	962.360	+	568.711i	1.22907	+	0.726324i
$784$	−26.8296	+	194.155i	−0.0342214	+	0.247647i
$785$	−103.548	−	179.351i	−0.131909	−	0.228473i
$786$	383.790	−	319.833i	0.488283	−	0.406912i
$787$	588.211	+	339.604i	0.747409	+	0.431517i	0.824757	−	0.565487i	$-0.191312\pi$
$787$	588.211	+	339.604i	0.747409	+	0.431517i	−0.0773479	+	0.997004i	$0.524645\pi$
$788$	197.604	−	342.260i	0.250767	−	0.434340i
$789$	−39.2951	+	106.837i	−0.0498037	+	0.135408i
$790$	66.4369	−	38.3574i	0.0840973	−	0.0485536i
$791$	−365.364	−	419.325i	−0.461902	−	0.530120i
$792$	−392.567	+	139.884i	−0.495665	+	0.176621i
$793$	298.733			0.376712
$794$	231.289	−	133.535i	0.291295	−	0.168179i
$795$	−31.9458	−	184.826i	−0.0401834	−	0.232485i
$796$	−279.768	−	161.524i	−0.351468	−	0.202920i
$797$	−1282.65	−	740.541i	−1.60935	−	0.929160i	−0.989515	−	0.144430i	$-0.953865\pi$
$797$	−1282.65	−	740.541i	−1.60935	−	0.929160i	−0.619838	−	0.784730i	$-0.712802\pi$
$798$	−542.214	+	666.539i	−0.679466	+	0.835261i
$799$	−10.8430	−	18.7807i	−0.0135708	−	0.0235053i
$800$	130.606			0.163257
$801$	−267.759	−	49.0823i	−0.334281	−	0.0612763i
$802$	91.9421			0.114641
$803$	1126.03	−	650.113i	1.40228	−	0.809605i
$804$	91.7078	−	249.339i	0.114064	−	0.310123i
$805$	45.5475	+	232.886i	0.0565808	+	0.289299i
$806$	564.532	−	977.799i	0.700412	−	1.21315i
$807$	58.5349	−	48.7803i	0.0725340	−	0.0604465i
$808$	−321.367	+	185.542i	−0.397732	+	0.229631i
$809$	−178.357			−0.220466			−0.110233	−	0.993906i	$-0.535160\pi$
$809$	−178.357			−0.220466			−0.110233	+	0.993906i	$0.535160\pi$
$810$	−56.1812	+	148.094i	−0.0693595	+	0.182832i
$811$		−	1087.09i		−	1.34043i	−0.742166	−	0.670216i	$-0.766201\pi$
$811$		−	1087.09i		−	1.34043i	0.742166	−	0.670216i	$-0.233799\pi$
$812$	188.073	−	548.261i	0.231617	−	0.675198i
$813$	−395.615	+	329.687i	−0.486611	+	0.405519i
$814$	−215.068	+	372.508i	−0.264211	+	0.457627i
$815$	126.572	+	73.0762i	0.155303	+	0.0896641i
$816$	18.8211	+	6.92247i	0.0230650	+	0.00848341i
$817$	−1451.41	+	837.972i	−1.77651	+	1.02567i
$818$			622.095i			0.760507i
$819$	596.506	+	1005.48i	0.728334	+	1.22769i
$820$	31.3139			0.0381877
$821$	−363.136	−	628.969i	−0.442309	−	0.766102i	0.555551	−	0.831482i	$-0.312507\pi$
$821$	−363.136	−	628.969i	−0.442309	−	0.766102i	−0.997860	+	0.0653806i	$0.979174\pi$
$822$	−7.99252	+	1.38145i	−0.00972326	+	0.00168060i
$823$	377.864	−	654.480i	0.459130	−	0.795237i	−0.539785	−	0.841803i	$-0.681494\pi$
$823$	377.864	−	654.480i	0.459130	−	0.795237i	0.998915	+	0.0465659i	$0.0148277\pi$
$824$	41.8902	+	24.1853i	0.0508376	+	0.0293511i
$825$	1117.38	−	193.131i	1.35440	−	0.234098i
$826$	233.975	+	80.2620i	0.283263	+	0.0971695i
$827$	−890.828			−1.07718			−0.538590	−	0.842568i	$-0.681043\pi$
$827$	−890.828			−1.07718			−0.538590	+	0.842568i	$0.681043\pi$
$828$	415.699	−	148.126i	0.502052	−	0.178896i
$829$			1129.80i			1.36285i	0.731888	+	0.681425i	$0.238640\pi$
$829$			1129.80i			1.36285i	−0.731888	+	0.681425i	$0.761360\pi$
$830$	−113.313	−	196.263i	−0.136521	−	0.236462i
$831$	−196.792	+	535.045i	−0.236813	+	0.643857i
$832$	128.568	+	74.2290i	0.154529	+	0.0892175i
$833$	50.2650	−	64.6435i	0.0603421	−	0.0776032i
$834$	818.506	−	682.105i	0.981422	−	0.817872i
$835$	−179.203	−	310.388i	−0.214614	−	0.371723i
$836$			947.296i			1.13313i
$837$	−1161.53	−	11.7821i	−1.38773	−	0.0140766i
$838$		−	866.952i		−	1.03455i
$839$	−819.430	+	473.098i	−0.976674	+	0.563883i	−0.901264	−	0.433269i	$-0.857360\pi$
$839$	−819.430	+	473.098i	−0.976674	+	0.563883i	−0.0754099	+	0.997153i	$0.524027\pi$
$840$	81.0892	+	13.0284i	0.0965348	+	0.0155100i
$841$	−436.544	+	756.116i	−0.519077	+	0.899068i
$842$	222.317	−	385.065i	0.264035	−	0.457322i
$843$	108.009	−	293.658i	0.128124	−	0.348349i
$844$	−14.4107	−	24.9600i	−0.0170743	−	0.0295735i
$845$			242.489i			0.286969i
$846$	−107.021	+	125.805i	−0.126502	+	0.148705i
$847$	676.067	+	775.914i	0.798190	+	0.916074i
$848$	90.4337	+	156.636i	0.106644	+	0.184712i
$849$	−77.5100	−	448.442i	−0.0912957	−	0.528200i
$850$	−47.2551	−	27.2827i	−0.0555942	−	0.0320973i
$851$	227.740	−	394.458i	0.267615	−	0.463523i
$852$	−477.241	+	82.4877i	−0.560142	+	0.0968165i
$853$	−1435.45	+	828.756i	−1.68282	+	0.971578i	−0.723052	+	0.690793i	$0.757261\pi$
$853$	−1435.45	+	828.756i	−1.68282	+	0.971578i	−0.959771	+	0.280785i	$0.909405\pi$
$854$	−120.151	+	104.689i	−0.140692	+	0.122587i
$855$	274.234	+	233.288i	0.320742	+	0.272851i
$856$	56.4882			0.0659909
$857$	−62.7927	+	36.2534i	−0.0732704	+	0.0423027i	−0.536188	−	0.844099i	$-0.680136\pi$
$857$	−62.7927	+	36.2534i	−0.0732704	+	0.0423027i	0.462917	+	0.886402i	$0.346803\pi$
$858$	1209.71	+	444.936i	1.40992	+	0.518573i
$859$	−1065.06	−	614.911i	−1.23988	−	0.715845i	−0.270811	−	0.962633i	$-0.587292\pi$
$859$	−1065.06	−	614.911i	−1.23988	−	0.715845i	−0.969070	+	0.246787i	$0.920625\pi$
$860$	138.733	+	80.0976i	0.161318	+	0.0931368i
$861$	−234.779	−	37.7214i	−0.272682	−	0.0438111i
$862$	−385.967	−	668.514i	−0.447757	−	0.775538i
$863$	1190.72			1.37974			0.689871	−	0.723932i	$-0.257667\pi$
$863$	1190.72			1.37974			0.689871	+	0.723932i	$0.257667\pi$
$864$	1.54920	−	152.727i	0.00179306	−	0.176768i
$865$	326.137			0.377037
$866$	297.988	−	172.044i	0.344097	−	0.198665i
$867$	549.684	+	659.605i	0.634007	+	0.760790i
$868$	115.608	+	591.108i	0.133189	+	0.681000i
$869$	−321.132	+	556.216i	−0.369542	+	0.640065i
$870$	−227.947	−	83.8399i	−0.262008	−	0.0963677i
$871$	−711.597	+	410.841i	−0.816989	+	0.471689i
$872$	−274.751			−0.315081
$873$	−250.131	−	701.964i	−0.286519	−	0.804082i
$874$		−	1003.12i		−	1.14773i
$875$	−440.262	−	151.026i	−0.503157	−	0.172601i
$876$	81.1609	+	469.565i	0.0926494	+	0.536033i
$877$	−315.330	+	546.168i	−0.359556	+	0.622769i	−0.987887	−	0.155177i	$-0.950405\pi$
$877$	−315.330	+	546.168i	−0.359556	+	0.622769i	0.628331	+	0.777946i	$0.283738\pi$
$878$	−962.708	−	555.820i	−1.09648	−	0.633052i
$879$	−30.5420	−	176.704i	−0.0347463	−	0.201028i
$880$	78.4163	−	45.2737i	0.0891094	−	0.0514474i
$881$			1025.23i			1.16372i	0.813290	+	0.581858i	$0.197674\pi$
$881$			1025.23i			1.16372i	−0.813290	+	0.581858i	$0.802326\pi$
$882$	−592.280	−	195.363i	−0.671519	−	0.221500i
$883$	−571.513			−0.647241			−0.323620	−	0.946187i	$-0.604900\pi$
$883$	−571.513			−0.647241			−0.323620	+	0.946187i	$0.604900\pi$
$884$	−31.0119	−	53.7142i	−0.0350813	−	0.0607626i
$885$	35.7795	−	97.2787i	0.0404288	−	0.109919i
$886$	−385.929	+	668.449i	−0.435586	+	0.754457i
$887$	895.056	+	516.761i	1.00908	+	0.582594i	0.910923	−	0.412577i	$-0.135371\pi$
$887$	895.056	+	516.761i	1.00908	+	0.582594i	0.0981594	+	0.995171i	$0.468705\pi$
$888$	−100.922	−	121.103i	−0.113651	−	0.136378i
$889$	157.034	−	457.775i	0.176641	−	0.514933i
$890$	59.1461			0.0664563
$891$	−212.588	−	1308.92i	−0.238595	−	1.46905i
$892$			375.236i			0.420668i
$893$	187.720	+	325.140i	0.210212	+	0.364098i
$894$	−424.327	−	509.179i	−0.474638	−	0.569552i
$895$	−285.023	−	164.558i	−0.318462	−	0.183864i
$896$	−77.7234	+	15.2011i	−0.0867449	+	0.0169655i
$897$	−1280.99	−	471.154i	−1.42808	−	0.525255i
$898$	−558.092	−	966.644i	−0.621483	−	1.07644i
$899$		−	1781.18i		−	1.98129i
$900$	−74.9316	+	408.775i	−0.0832573	+	0.454194i
$901$		−	75.5640i		−	0.0838668i
$902$	−227.040	+	131.082i	−0.251708	+	0.145323i
$903$	−943.677	−	767.660i	−1.04505	−	0.850121i
$904$	112.363	−	194.619i	0.124296	−	0.215286i
$905$	−113.245	+	196.147i	−0.125133	+	0.216737i
$906$	−113.192	+	19.5645i	−0.124936	+	0.0215943i
$907$	465.692	+	806.603i	0.513442	+	0.889308i	0.999878	+	0.0155921i	$0.00496331\pi$
$907$	465.692	+	806.603i	0.513442	+	0.889308i	−0.486436	+	0.873716i	$0.661703\pi$
$908$		−	552.293i		−	0.608252i
$909$	−396.338	−	1112.27i	−0.436015	−	1.22362i
$910$	−166.870	−	191.515i	−0.183374	−	0.210456i
$911$	624.813	+	1082.21i	0.685854	+	1.18793i	0.973168	+	0.230097i	$0.0739044\pi$
$911$	624.813	+	1082.21i	0.685854	+	1.18793i	−0.287314	+	0.957836i	$0.592762\pi$
$912$	−325.839	−	119.845i	−0.357280	−	0.131409i
$913$	1643.13	+	948.664i	1.79971	+	1.03906i
$914$	62.3941	−	108.070i	0.0682648	−	0.118238i
$915$	42.7499	+	51.2986i	0.0467212	+	0.0560641i
$916$	−625.662	+	361.226i	−0.683037	+	0.394351i
$917$	621.466	−	541.493i	0.677716	−	0.590505i
$918$	−32.4642	+	54.9352i	−0.0353641	+	0.0598423i
$919$	659.705			0.717851			0.358925	−	0.933366i	$-0.383143\pi$
$919$	659.705			0.717851			0.358925	+	0.933366i	$0.383143\pi$
$920$	−83.0370	+	47.9414i	−0.0902576	+	0.0521102i
$921$	−1093.05	+	910.896i	−1.18681	+	0.989029i
$922$	34.0297	+	19.6471i	0.0369086	+	0.0213092i
$923$	1297.25	+	748.966i	1.40547	+	0.811448i
$924$	−642.471	+	244.982i	−0.695315	+	0.265132i
$925$	214.470	+	371.472i	0.231859	+	0.401592i
$926$	660.247			0.713009
$927$	−99.7292	+	117.234i	−0.107583	+	0.126465i
$928$	234.202			0.252373
$929$	−1038.59	+	599.631i	−1.11797	+	0.645458i	−0.940881	−	0.338737i	$-0.890000\pi$
$929$	−1038.59	+	599.631i	−1.11797	+	0.645458i	−0.177085	+	0.984196i	$0.556667\pi$
$930$	248.695	−	42.9852i	0.267414	−	0.0462206i
$931$	−870.210	+	1119.14i	−0.934705	+	1.20208i
$932$	313.585	−	543.145i	0.336465	−	0.582774i
$933$	−53.4243	−	309.092i	−0.0572608	−	0.331288i
$934$	−200.163	+	115.564i	−0.214307	+	0.123730i
$935$	−37.8295			−0.0404593
$936$	−306.087	+	359.811i	−0.327016	+	0.384413i
$937$			651.336i			0.695130i	0.937656	+	0.347565i	$0.112991\pi$
$937$			651.336i			0.695130i	−0.937656	+	0.347565i	$0.887009\pi$
$938$	142.228	−	414.615i	0.151629	−	0.442021i
$939$	811.128	+	298.336i	0.863821	+	0.317717i
$940$	17.9432	−	31.0785i	0.0190885	−	0.0330623i
$941$	1262.91	+	729.141i	1.34209	+	0.774858i	0.987114	−	0.160016i	$-0.0511546\pi$
$941$	1262.91	+	729.141i	1.34209	+	0.774858i	0.354979	+	0.934874i	$0.384488\pi$
$942$	−488.156	+	406.807i	−0.518212	+	0.431854i
$943$	240.419	−	138.806i	0.254951	−	0.147196i
$944$			99.9481i			0.105877i
$945$	−87.2994	+	246.321i	−0.0923803	+	0.260657i
$946$	−1341.17			−1.41773
$947$	−817.000	−	1415.09i	−0.862724	−	1.49428i	−0.869289	−	0.494304i	$-0.835423\pi$
$947$	−817.000	−	1415.09i	−0.862724	−	1.49428i	0.00656479	−	0.999978i	$-0.497910\pi$
$948$	−150.693	−	180.827i	−0.158959	−	0.190746i
$949$	736.919	−	1276.38i	0.776522	−	1.34498i
$950$	818.101	+	472.331i	0.861159	+	0.497190i
$951$	−127.882	+	347.692i	−0.134472	+	0.365606i
$952$	31.2968	+	10.7359i	0.0328748	+	0.0112773i
$953$	−1002.99			−1.05245			−0.526226	−	0.850345i	$-0.676393\pi$
$953$	−1002.99			−1.05245			−0.526226	+	0.850345i	$0.676393\pi$
$954$	−542.127	+	193.177i	−0.568268	+	0.202491i
$955$			350.542i			0.367059i
$956$	−401.379	−	695.208i	−0.419852	−	0.727205i
$957$	2003.68	−	346.322i	2.09371	−	0.361882i
$958$	−275.335	−	158.965i	−0.287406	−	0.165934i
$959$	−13.1337	+	2.56867i	−0.0136952	+	0.00267849i
$960$	5.65202	+	32.7003i	0.00588752	+	0.0340629i
$961$	444.945	+	770.667i	0.463002	+	0.801943i
$962$			487.569i			0.506829i
$963$	−32.4086	+	176.799i	−0.0336537	+	0.183591i
$964$			198.884i			0.206311i
$965$	−37.2786	+	21.5228i	−0.0386307	+	0.0223034i
$966$	680.328	−	259.417i	0.704274	−	0.268548i
$967$	−337.799	+	585.086i	−0.349327	+	0.605052i	−0.986130	−	0.165974i	$-0.946923\pi$
$967$	−337.799	+	585.086i	−0.349327	+	0.605052i	0.636803	+	0.771027i	$0.280256\pi$
$968$	−207.916	+	360.121i	−0.214789	+	0.372025i
$969$	92.8583	+	111.427i	0.0958290	+	0.114992i
$970$	80.9556	+	140.219i	0.0834594	+	0.144556i
$971$			103.021i			0.106098i	0.998592	+	0.0530489i	$0.0168939\pi$
$971$			103.021i			0.106098i	−0.998592	+	0.0530489i	$0.983106\pi$
$972$	477.122	+	92.4718i	0.490866	+	0.0951356i
$973$	1325.39	−	1154.84i	1.36217	−	1.18688i
$974$	248.040	+	429.617i	0.254661	+	0.441086i
$975$	987.427	−	822.876i	1.01275	−	0.843976i
$976$	−55.7648	−	32.1958i	−0.0571361	−	0.0329875i
$977$	145.091	−	251.306i	0.148507	−	0.257222i	−0.782169	−	0.623067i	$-0.785887\pi$
$977$	145.091	−	251.306i	0.148507	−	0.257222i	0.930676	+	0.365845i	$0.119220\pi$
$978$	154.801	−	420.879i	0.158283	−	0.430347i
$979$	−428.836	+	247.588i	−0.438034	+	0.252899i
$980$	134.231	+	18.5489i	0.136970	+	0.0189274i
$981$	157.631	−	859.923i	0.160684	−	0.876578i
$982$	1038.44			1.05747
$983$	−619.095	+	357.435i	−0.629802	+	0.363616i	−0.780675	−	0.624937i	$-0.785125\pi$
$983$	−619.095	+	357.435i	−0.629802	+	0.363616i	0.150873	+	0.988553i	$0.451791\pi$
$984$	−16.3644	−	94.6779i	−0.0166305	−	0.0962174i
$985$	−236.624	−	136.615i	−0.240228	−	0.138696i
$986$	−84.7377	−	48.9233i	−0.0859409	−	0.0496180i
$987$	−171.968	+	211.399i	−0.174234	+	0.214184i
$988$	536.892	+	929.924i	0.543413	+	0.941218i
$989$	1420.20			1.43599
$990$	96.7097	+	271.404i	0.0976866	+	0.274146i
$991$	−1129.26			−1.13951			−0.569756	−	0.821814i	$-0.692962\pi$
$991$	−1129.26			−1.13951			−0.569756	+	0.821814i	$0.692962\pi$
$992$	−210.764	+	121.684i	−0.212463	+	0.122666i
$993$	414.421	−	1126.74i	0.417342	−	1.13469i
$994$	−784.225	+	153.378i	−0.788959	+	0.154304i
$995$	−111.671	+	193.420i	−0.112232	+	0.194392i
$996$	−534.187	+	445.167i	−0.536332	+	0.446954i
$997$	352.564	−	203.553i	0.353625	−	0.204166i	−0.312656	−	0.949867i	$-0.601219\pi$
$997$	352.564	−	203.553i	0.353625	−	0.204166i	0.666281	+	0.745701i	$0.267885\pi$
$998$	1322.50			1.32515
$999$	436.934	−	246.389i	0.437371	−	0.246635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.o.a.13.6	yes	32
3.2	odd	2		378.3.o.a.307.12		32
7.6	odd	2	inner	126.3.o.a.13.3	✓	32
9.2	odd	6		378.3.o.a.181.13		32
9.4	even	3		1134.3.c.e.811.12		16
9.5	odd	6		1134.3.c.d.811.5		16
9.7	even	3	inner	126.3.o.a.97.3	yes	32
21.20	even	2		378.3.o.a.307.13		32
63.13	odd	6		1134.3.c.e.811.13		16
63.20	even	6		378.3.o.a.181.12		32
63.34	odd	6	inner	126.3.o.a.97.6	yes	32
63.41	even	6		1134.3.c.d.811.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.o.a.13.3	✓	32	7.6	odd	2	inner
126.3.o.a.13.6	yes	32	1.1	even	1	trivial
126.3.o.a.97.3	yes	32	9.7	even	3	inner
126.3.o.a.97.6	yes	32	63.34	odd	6	inner
378.3.o.a.181.12		32	63.20	even	6
378.3.o.a.181.13		32	9.2	odd	6
378.3.o.a.307.12		32	3.2	odd	2
378.3.o.a.307.13		32	21.20	even	2
1134.3.c.d.811.4		16	63.41	even	6
1134.3.c.d.811.5		16	9.5	odd	6
1134.3.c.e.811.12		16	9.4	even	3
1134.3.c.e.811.13		16	63.13	odd	6

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(1.92058 + 2.30464i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.19747 + 0.691358i) q^{5} +(1.46454 - 3.98185i) q^{6} +(2.27133 - 6.62126i) q^{7} +2.82843 q^{8} +(-1.62273 + 8.85250i) q^{9} -1.95546i q^{10} +(8.18564 + 14.1779i) q^{11} +(-5.91234 + 1.02190i) q^{12} +(16.0710 + 9.27862i) q^{13} +(-9.71543 + 1.90013i) q^{14} +(0.706502 + 4.08754i) q^{15} +(-2.00000 - 3.46410i) q^{16} +1.67115i q^{17} +(11.9895 - 4.27223i) q^{18} -28.9316i q^{19} +(-2.39494 + 1.38272i) q^{20} +(19.6219 - 7.48206i) q^{21} +(11.5762 - 20.0506i) q^{22} +(-12.2584 + 21.2321i) q^{23} +(5.43223 + 6.51851i) q^{24} +(-11.5440 - 19.9949i) q^{25} -26.2439i q^{26} +(-23.5184 + 13.2621i) q^{27} +(9.19702 + 10.5553i) q^{28} +(-20.7008 - 35.8548i) q^{29} +(4.50662 - 3.75561i) q^{30} +(37.2581 + 21.5110i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-16.9539 + 46.0948i) q^{33} +(2.04673 - 1.18168i) q^{34} +(7.29751 - 6.35844i) q^{35} +(-13.7102 - 11.6632i) q^{36} -18.5784 q^{37} +(-35.4339 + 20.4578i) q^{38} +(9.48187 + 54.8583i) q^{39} +(3.38695 + 1.95546i) q^{40} +(-9.80630 - 5.66167i) q^{41} +(-23.0384 - 18.7412i) q^{42} +(-28.9639 - 50.1669i) q^{43} -32.7425 q^{44} +(-8.06342 + 9.47869i) q^{45} +34.6719 q^{46} +(-11.2382 + 6.48838i) q^{47} +(4.14234 - 11.2624i) q^{48} +(-38.6821 - 30.0782i) q^{49} +(-16.3257 + 28.2770i) q^{50} +(-3.85139 + 3.20957i) q^{51} +(-32.1421 + 18.5572i) q^{52} -45.2169 q^{53} +(32.8728 + 19.4263i) q^{54} +22.6368i q^{55} +(6.42430 - 18.7277i) q^{56} +(66.6770 - 55.5656i) q^{57} +(-29.2753 + 50.7063i) q^{58} +(-21.6394 - 12.4935i) q^{59} +(-7.78633 - 2.86384i) q^{60} +(13.9412 - 8.04896i) q^{61} -60.8422i q^{62} +(54.9289 + 30.8515i) q^{63} +8.00000 q^{64} +(12.8297 + 22.2217i) q^{65} +(68.4426 - 11.8298i) q^{66} +(-22.1391 + 38.3460i) q^{67} +(-2.89451 - 1.67115i) q^{68} +(-72.4756 + 12.5269i) q^{69} +(-12.9476 - 4.44149i) q^{70} +80.7195 q^{71} +(-4.58978 + 25.0386i) q^{72} -79.4212i q^{73} +(13.1369 + 22.7538i) q^{74} +(23.9097 - 65.0067i) q^{75} +(50.1111 + 28.9316i) q^{76} +(112.468 - 21.9964i) q^{77} +(60.4828 - 50.4036i) q^{78} +(19.6156 + 33.9751i) q^{79} -5.53087i q^{80} +(-75.7335 - 28.7305i) q^{81} +16.0136i q^{82} +(100.367 - 57.9469i) q^{83} +(-6.66258 + 41.4682i) q^{84} +(-1.15536 + 2.00114i) q^{85} +(-40.9611 + 70.9467i) q^{86} +(42.8749 - 116.570i) q^{87} +(23.1525 + 40.1013i) q^{88} +30.2467i q^{89} +(17.3107 + 3.17318i) q^{90} +(97.9389 - 85.3357i) q^{91} +(-24.5167 - 42.4642i) q^{92} +(21.9822 + 127.180i) q^{93} +(15.8932 + 9.17596i) q^{94} +(20.0021 - 34.6447i) q^{95} +(-16.7226 + 2.89038i) q^{96} +(-71.7067 + 41.3999i) q^{97} +(-9.48569 + 68.6442i) q^{98} +(-138.793 + 49.4563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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