LMFDB - Embedded newform 27.3.f.a.5.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,3,Mod(2,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.2"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, 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:	$0.735696713773$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	27.5
Dual form			27.3.f.a.11.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24712 - 1.48626i) q^{2} +(2.80515 + 1.06355i) q^{3} +(0.0409354 - 0.232156i) q^{4} +(-1.47839 - 4.06185i) q^{5} +(-1.91764 - 5.49555i) q^{6} +(1.54363 + 8.75434i) q^{7} +(-7.11704 + 4.10903i) q^{8} +(6.73771 + 5.96685i) q^{9} +(-4.19322 + 7.26288i) q^{10} +(-2.52275 + 6.93119i) q^{11} +(0.361741 - 0.607696i) q^{12} +(-12.4164 - 10.4186i) q^{13} +(11.0861 - 13.2119i) q^{14} +(0.172883 - 12.9664i) q^{15} +(14.0968 + 5.13081i) q^{16} +(9.06825 + 5.23555i) q^{17} +(0.465550 - 17.4553i) q^{18} +(-8.63742 - 14.9604i) q^{19} +(-1.00350 + 0.176945i) q^{20} +(-4.98060 + 26.1989i) q^{21} +(13.4477 - 4.89456i) q^{22} +(12.9785 + 2.28846i) q^{23} +(-24.3345 + 3.95708i) q^{24} +(4.83813 - 4.05967i) q^{25} +31.4473i q^{26} +(12.5542 + 23.9038i) q^{27} +2.09556 q^{28} +(-26.8925 - 32.0493i) q^{29} +(-19.4871 + 15.9137i) q^{30} +(6.43612 - 36.5011i) q^{31} +(1.28832 + 3.53963i) q^{32} +(-14.4484 + 16.7599i) q^{33} +(-3.52779 - 20.0071i) q^{34} +(33.2767 - 19.2123i) q^{35} +(1.66105 - 1.31995i) q^{36} +(-31.9875 + 55.4041i) q^{37} +(-11.4632 + 31.4949i) q^{38} +(-23.7492 - 42.4314i) q^{39} +(27.2120 + 22.8336i) q^{40} +(-16.3590 + 19.4958i) q^{41} +(45.1498 - 25.2707i) q^{42} +(-2.32975 - 0.847961i) q^{43} +(1.50585 + 0.869403i) q^{44} +(14.2755 - 36.1889i) q^{45} +(-12.7845 - 22.1433i) q^{46} +(45.9670 - 8.10521i) q^{47} +(34.0867 + 29.3853i) q^{48} +(-28.2107 + 10.2679i) q^{49} +(-12.0674 - 2.12781i) q^{50} +(19.8695 + 24.3311i) q^{51} +(-2.92703 + 2.45607i) q^{52} -50.7217i q^{53} +(19.8706 - 48.4696i) q^{54} +31.8831 q^{55} +(-46.9579 - 55.9622i) q^{56} +(-8.31801 - 51.1526i) q^{57} +(-14.0953 + 79.9384i) q^{58} +(1.43303 + 3.93723i) q^{59} +(-3.00316 - 0.570923i) q^{60} +(6.31465 + 35.8121i) q^{61} +(-62.2766 + 35.9554i) q^{62} +(-41.8353 + 68.1948i) q^{63} +(33.6571 - 58.2957i) q^{64} +(-23.9626 + 65.8366i) q^{65} +(42.9284 + 0.572369i) q^{66} +(13.2595 + 11.1260i) q^{67} +(1.58668 - 1.89093i) q^{68} +(33.9727 + 20.2228i) q^{69} +(-70.0545 - 25.4977i) q^{70} +(-51.5041 - 29.7359i) q^{71} +(-72.4705 - 14.7809i) q^{72} +(26.3451 + 45.6310i) q^{73} +(122.237 - 21.5537i) q^{74} +(17.8893 - 6.24237i) q^{75} +(-3.82674 + 1.39282i) q^{76} +(-64.5722 - 11.3858i) q^{77} +(-33.4459 + 88.2143i) q^{78} +(-1.19477 + 1.00253i) q^{79} -64.8443i q^{80} +(9.79348 + 80.4058i) q^{81} +49.3774 q^{82} +(72.6820 + 86.6190i) q^{83} +(5.87837 + 2.22874i) q^{84} +(7.85961 - 44.5741i) q^{85} +(1.64519 + 4.52012i) q^{86} +(-41.3514 - 118.505i) q^{87} +(-10.5259 - 59.6956i) q^{88} +(41.4518 - 23.9322i) q^{89} +(-71.5892 + 23.9148i) q^{90} +(72.0419 - 124.780i) q^{91} +(1.06256 - 2.91936i) q^{92} +(56.8751 - 95.5457i) q^{93} +(-69.3726 - 58.2105i) q^{94} +(-47.9976 + 57.2013i) q^{95} +(-0.150656 + 11.2994i) q^{96} +(34.5497 + 12.5750i) q^{97} +(50.4428 + 29.1232i) q^{98} +(-58.3549 + 31.6475i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20}+ \cdots + 513 q^{99}+O(q^{100}) $ 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8 - 3 * q^10 - 6 * q^11 - 15 * q^12 - 6 * q^13 - 15 * q^14 - 9 * q^15 - 18 * q^16 - 9 * q^17 + 63 * q^18 - 3 * q^19 + 213 * q^20 + 132 * q^21 - 42 * q^22 + 120 * q^23 + 144 * q^24 - 15 * q^25 - 90 * q^27 - 12 * q^28 - 168 * q^29 - 243 * q^30 + 39 * q^31 - 360 * q^32 - 207 * q^33 + 54 * q^34 - 252 * q^35 - 360 * q^36 - 3 * q^37 - 84 * q^38 + 15 * q^39 - 33 * q^40 + 228 * q^41 + 486 * q^42 - 96 * q^43 + 639 * q^44 + 477 * q^45 - 3 * q^46 + 399 * q^47 + 453 * q^48 - 78 * q^49 + 303 * q^50 + 36 * q^51 - 9 * q^52 - 54 * q^54 - 12 * q^55 - 393 * q^56 - 192 * q^57 + 129 * q^58 - 474 * q^59 - 846 * q^60 + 138 * q^61 - 900 * q^62 - 585 * q^63 - 51 * q^64 - 411 * q^65 - 423 * q^66 + 354 * q^67 + 99 * q^68 + 99 * q^69 + 489 * q^70 + 315 * q^71 + 720 * q^72 - 66 * q^73 + 321 * q^74 + 255 * q^75 + 258 * q^76 + 201 * q^77 + 180 * q^78 + 30 * q^79 + 36 * q^81 - 12 * q^82 - 33 * q^83 - 588 * q^84 - 261 * q^85 - 258 * q^86 - 279 * q^87 - 642 * q^88 + 72 * q^89 + 288 * q^90 + 96 * q^91 - 3 * q^92 + 591 * q^93 - 861 * q^94 + 681 * q^95 + 270 * q^96 - 582 * q^97 + 882 * q^98 + 513 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−1.24712	−	1.48626i	−0.623559	−	0.743128i	0.358119	−	0.933676i	$-0.383418\pi$
$2$	−1.24712	−	1.48626i	−0.623559	−	0.743128i	−0.981678	+	0.190547i	$0.938974\pi$
$3$	2.80515	+	1.06355i	0.935049	+	0.354518i
$3$	2.80515	+	1.06355i	0.935049	+	0.354518i
$4$	0.0409354	−	0.232156i	0.0102339	−	0.0580391i
$5$	−1.47839	−	4.06185i	−0.295679	−	0.812370i	−0.995209	−	0.0977676i	$-0.968830\pi$
$5$	−1.47839	−	4.06185i	−0.295679	−	0.812370i	0.699531	−	0.714602i	$-0.253392\pi$
$6$	−1.91764	−	5.49555i	−0.319606	−	0.915924i
$7$	1.54363	+	8.75434i	0.220518	+	1.25062i	0.871070	+	0.491158i	$0.163426\pi$
$7$	1.54363	+	8.75434i	0.220518	+	1.25062i	−0.650552	+	0.759462i	$0.725463\pi$
$8$	−7.11704	+	4.10903i	−0.889630	+	0.513628i
$9$	6.73771	+	5.96685i	0.748634	+	0.662983i
$10$	−4.19322	+	7.26288i	−0.419322	+	0.726288i
$11$	−2.52275	+	6.93119i	−0.229341	+	0.630108i	−0.999974	−	0.00717020i	$-0.997718\pi$
$11$	−2.52275	+	6.93119i	−0.229341	+	0.630108i	0.770634	+	0.637278i	$0.219940\pi$
$12$	0.361741	−	0.607696i	0.0301450	−	0.0506413i
$13$	−12.4164	−	10.4186i	−0.955111	−	0.801434i	0.0250395	−	0.999686i	$-0.492029\pi$
$13$	−12.4164	−	10.4186i	−0.955111	−	0.801434i	−0.980151	+	0.198253i	$0.936473\pi$
$14$	11.0861	−	13.2119i	0.791865	−	0.943708i
$15$	0.172883	−	12.9664i	0.0115255	−	0.864429i
$16$	14.0968	+	5.13081i	0.881049	+	0.320675i
$17$	9.06825	+	5.23555i	0.533426	+	0.307974i	0.742411	−	0.669945i	$-0.233682\pi$
$17$	9.06825	+	5.23555i	0.533426	+	0.307974i	−0.208984	+	0.977919i	$0.567016\pi$
$18$	0.465550	−	17.4553i	0.0258639	−	0.969740i
$19$	−8.63742	−	14.9604i	−0.454601	−	0.787392i	0.544064	−	0.839044i	$-0.316885\pi$
$19$	−8.63742	−	14.9604i	−0.454601	−	0.787392i	−0.998665	+	0.0516517i	$0.983551\pi$
$20$	−1.00350	+	0.176945i	−0.0501752	+	0.00884723i
$21$	−4.98060	+	26.1989i	−0.237172	+	1.24757i
$22$	13.4477	−	4.89456i	0.611259	−	0.222480i
$23$	12.9785	+	2.28846i	0.564282	+	0.0994981i	0.448510	−	0.893778i	$-0.351955\pi$
$23$	12.9785	+	2.28846i	0.564282	+	0.0994981i	0.115772	+	0.993276i	$0.463066\pi$
$24$	−24.3345	+	3.95708i	−1.01394	+	0.164878i
$25$	4.83813	−	4.05967i	0.193525	−	0.162387i
$26$			31.4473i			1.20951i
$27$	12.5542	+	23.9038i	0.464971	+	0.885326i
$28$	2.09556			0.0748416
$29$	−26.8925	−	32.0493i	−0.927329	−	1.10515i	−0.994217	−	0.107387i	$-0.965752\pi$
$29$	−26.8925	−	32.0493i	−0.927329	−	1.10515i	0.0668885	−	0.997760i	$-0.478693\pi$
$30$	−19.4871	+	15.9137i	−0.649569	+	0.530458i
$31$	6.43612	−	36.5011i	0.207617	−	1.17745i	−0.685651	−	0.727930i	$-0.740483\pi$
$31$	6.43612	−	36.5011i	0.207617	−	1.17745i	0.893268	−	0.449524i	$-0.148406\pi$
$32$	1.28832	+	3.53963i	0.0402600	+	0.110613i
$33$	−14.4484	+	16.7599i	−0.437829	+	0.507877i
$34$	−3.52779	−	20.0071i	−0.103759	−	0.588444i
$35$	33.2767	−	19.2123i	0.950764	−	0.548924i
$36$	1.66105	−	1.31995i	0.0461404	−	0.0366652i
$37$	−31.9875	+	55.4041i	−0.864528	+	1.49741i	0.00298644	+	0.999996i	$0.499049\pi$
$37$	−31.9875	+	55.4041i	−0.864528	+	1.49741i	−0.867515	+	0.497411i	$0.834284\pi$
$38$	−11.4632	+	31.4949i	−0.301663	+	0.828812i
$39$	−23.7492	−	42.4314i	−0.608954	−	1.08798i
$40$	27.2120	+	22.8336i	0.680301	+	0.570840i
$41$	−16.3590	+	19.4958i	−0.398999	+	0.475508i	−0.927714	−	0.373291i	$-0.878229\pi$
$41$	−16.3590	+	19.4958i	−0.398999	+	0.475508i	0.528715	+	0.848799i	$0.322674\pi$
$42$	45.1498	−	25.2707i	1.07499	−	0.601684i
$43$	−2.32975	−	0.847961i	−0.0541803	−	0.0197200i	0.314788	−	0.949162i	$-0.398067\pi$
$43$	−2.32975	−	0.847961i	−0.0541803	−	0.0197200i	−0.368968	+	0.929442i	$0.620289\pi$
$44$	1.50585	+	0.869403i	0.0342239	+	0.0197592i
$45$	14.2755	−	36.1889i	0.317232	−	0.804198i
$46$	−12.7845	−	22.1433i	−0.277923	−	0.481377i
$47$	45.9670	−	8.10521i	0.978020	−	0.172451i	0.338282	−	0.941045i	$-0.390154\pi$
$47$	45.9670	−	8.10521i	0.978020	−	0.172451i	0.639738	+	0.768593i	$0.279043\pi$
$48$	34.0867	+	29.3853i	0.710139	+	0.612195i
$49$	−28.2107	+	10.2679i	−0.575729	+	0.209548i
$50$	−12.0674	−	2.12781i	−0.241349	−	0.0425563i
$51$	19.8695	+	24.3311i	0.389598	+	0.477080i
$52$	−2.92703	+	2.45607i	−0.0562890	+	0.0472320i
$53$		−	50.7217i		−	0.957013i	−0.878084	−	0.478507i	$-0.841178\pi$
$53$		−	50.7217i		−	0.957013i	0.878084	−	0.478507i	$-0.158822\pi$
$54$	19.8706	−	48.4696i	0.367974	−	0.897586i
$55$	31.8831			0.579692
$56$	−46.9579	−	55.9622i	−0.838533	−	0.999325i
$57$	−8.31801	−	51.1526i	−0.145930	−	0.897414i
$58$	−14.0953	+	79.9384i	−0.243022	+	1.37825i
$59$	1.43303	+	3.93723i	0.0242887	+	0.0667327i	0.951244	−	0.308438i	$-0.0998063\pi$
$59$	1.43303	+	3.93723i	0.0242887	+	0.0667327i	−0.926956	+	0.375171i	$0.877584\pi$
$60$	−3.00316	−	0.570923i	−0.0500527	−	0.00951538i
$61$	6.31465	+	35.8121i	0.103519	+	0.587084i	0.991802	+	0.127787i	$0.0407875\pi$
$61$	6.31465	+	35.8121i	0.103519	+	0.587084i	−0.888283	+	0.459297i	$0.848101\pi$
$62$	−62.2766	+	35.9554i	−1.00446	+	0.579926i
$63$	−41.8353	+	68.1948i	−0.664052	+	1.08246i
$64$	33.6571	−	58.2957i	0.525892	−	0.910871i
$65$	−23.9626	+	65.8366i	−0.368655	+	1.01287i
$66$	42.9284	+	0.572369i	0.650430	+	0.00867225i
$67$	13.2595	+	11.1260i	0.197902	+	0.166060i	0.736354	−	0.676597i	$-0.236546\pi$
$67$	13.2595	+	11.1260i	0.197902	+	0.166060i	−0.538451	+	0.842657i	$0.680990\pi$
$68$	1.58668	−	1.89093i	0.0233335	−	0.0278078i
$69$	33.9727	+	20.2228i	0.492358	+	0.293084i
$70$	−70.0545	−	25.4977i	−1.00078	−	0.364253i
$71$	−51.5041	−	29.7359i	−0.725410	−	0.418815i	0.0913309	−	0.995821i	$-0.470888\pi$
$71$	−51.5041	−	29.7359i	−0.725410	−	0.418815i	−0.816740	+	0.577005i	$0.804221\pi$
$72$	−72.4705	−	14.7809i	−1.00653	−	0.205290i
$73$	26.3451	+	45.6310i	0.360892	+	0.625083i	0.988108	−	0.153762i	$-0.0491391\pi$
$73$	26.3451	+	45.6310i	0.360892	+	0.625083i	−0.627216	+	0.778845i	$0.715806\pi$
$74$	122.237	−	21.5537i	1.65185	−	0.291266i
$75$	17.8893	−	6.24237i	0.238525	−	0.0832316i
$76$	−3.82674	+	1.39282i	−0.0503518	+	0.0183266i
$77$	−64.5722	−	11.3858i	−0.838600	−	0.147868i
$78$	−33.4459	+	88.2143i	−0.428793	+	1.13095i
$79$	−1.19477	+	1.00253i	−0.0151237	+	0.0126903i	−0.650318	−	0.759662i	$-0.725364\pi$
$79$	−1.19477	+	1.00253i	−0.0151237	+	0.0126903i	0.635194	+	0.772352i	$0.280920\pi$
$80$		−	64.8443i		−	0.810554i
$81$	9.79348	+	80.4058i	0.120907	+	0.992664i
$82$	49.3774			0.602163
$83$	72.6820	+	86.6190i	0.875686	+	1.04360i	0.998689	+	0.0511958i	$0.0163033\pi$
$83$	72.6820	+	86.6190i	0.875686	+	1.04360i	−0.123002	+	0.992406i	$0.539252\pi$
$84$	5.87837	+	2.22874i	0.0699806	+	0.0265327i
$85$	7.85961	−	44.5741i	0.0924660	−	0.524401i
$86$	1.64519	+	4.52012i	0.0191301	+	0.0525595i
$87$	−41.3514	−	118.505i	−0.475304	−	1.36212i
$88$	−10.5259	−	59.6956i	−0.119613	−	0.678359i
$89$	41.4518	−	23.9322i	0.465750	−	0.268901i	−0.248709	−	0.968578i	$-0.580006\pi$
$89$	41.4518	−	23.9322i	0.465750	−	0.268901i	0.714459	+	0.699677i	$0.246673\pi$
$90$	−71.5892	+	23.9148i	−0.795436	+	0.265720i
$91$	72.0419	−	124.780i	0.791670	−	1.37121i
$92$	1.06256	−	2.91936i	0.0115496	−	0.0317322i
$93$	56.8751	−	95.5457i	0.611560	−	1.02737i
$94$	−69.3726	−	58.2105i	−0.738007	−	0.619261i
$95$	−47.9976	+	57.2013i	−0.505238	+	0.602119i
$96$	−0.150656	+	11.2994i	−0.00156933	+	0.117702i
$97$	34.5497	+	12.5750i	0.356182	+	0.129640i	0.513913	−	0.857843i	$-0.328196\pi$
$97$	34.5497	+	12.5750i	0.356182	+	0.129640i	−0.157731	+	0.987482i	$0.550418\pi$
$98$	50.4428	+	29.1232i	0.514722	+	0.297175i
$99$	−58.3549	+	31.6475i	−0.589443	+	0.319672i
$100$	−0.744428	−	1.28939i	−0.00744428	−	0.0128939i
$101$	84.0022	−	14.8119i	0.831705	−	0.146652i	0.258445	−	0.966026i	$-0.416790\pi$
$101$	84.0022	−	14.8119i	0.831705	−	0.146652i	0.573260	+	0.819374i	$0.305679\pi$
$102$	11.3826	−	59.8749i	0.111594	−	0.587008i
$103$	−21.8401	+	7.94915i	−0.212040	+	0.0771762i	−0.445856	−	0.895105i	$-0.647101\pi$
$103$	−21.8401	+	7.94915i	−0.212040	+	0.0771762i	0.233816	+	0.972281i	$0.424879\pi$
$104$	131.179	+	23.1304i	1.26134	+	0.222407i
$105$	113.779	−	18.5019i	1.08361	−	0.176208i
$106$	−75.3855	+	63.2559i	−0.711184	+	0.596754i
$107$			95.7625i			0.894977i	0.894290	+	0.447488i	$0.147681\pi$
$107$			95.7625i			0.894977i	−0.894290	+	0.447488i	$0.852319\pi$
$108$	6.06333	−	1.93603i	0.0561420	−	0.0179262i
$109$	−102.160			−0.937249			−0.468625	−	0.883397i	$-0.655250\pi$
$109$	−102.160			−0.937249			−0.468625	+	0.883397i	$0.655250\pi$
$110$	−39.7619	−	47.3864i	−0.361472	−	0.430786i
$111$	−148.655	+	121.396i	−1.33923	+	1.09366i
$112$	−23.1567	+	131.328i	−0.206756	+	1.17257i
$113$	5.57835	+	15.3264i	0.0493660	+	0.135632i	0.961925	−	0.273312i	$-0.0881193\pi$
$113$	5.57835	+	15.3264i	0.0493660	+	0.135632i	−0.912559	+	0.408944i	$0.865897\pi$
$114$	−65.6524	+	76.1560i	−0.575898	+	0.668035i
$115$	−9.89192	−	56.0999i	−0.0860167	−	0.487825i
$116$	−8.54130	+	4.93132i	−0.0736319	+	0.0425114i
$117$	−21.4920	−	144.285i	−0.183692	−	1.23320i
$118$	4.06457	−	7.04005i	0.0344455	−	0.0596614i
$119$	−31.8358	+	87.4682i	−0.267528	+	0.735027i
$120$	52.0490	+	92.9931i	0.433742	+	0.774942i
$121$	51.0142	+	42.8060i	0.421605	+	0.353769i
$122$	45.3509	−	54.0471i	0.371729	−	0.443009i
$123$	−66.6242	+	37.2901i	−0.541660	+	0.303172i
$124$	−8.21049	−	2.98837i	−0.0662136	−	0.0240998i
$125$	−117.228	−	67.6816i	−0.937824	−	0.541453i
$126$	153.529	−	22.8689i	1.21848	−	0.181499i
$127$	40.7309	+	70.5479i	0.320715	+	0.555495i	0.980636	−	0.195840i	$-0.0627433\pi$
$127$	40.7309	+	70.5479i	0.320715	+	0.555495i	−0.659920	+	0.751336i	$0.729410\pi$
$128$	−113.779	+	20.0622i	−0.888895	+	0.156736i
$129$	−5.63345	−	4.85647i	−0.0436702	−	0.0376471i
$130$	127.734	−	46.4915i	0.982571	−	0.357627i
$131$	−143.243	−	25.2576i	−1.09346	−	0.192806i	−0.402298	−	0.915509i	$-0.631788\pi$
$131$	−143.243	−	25.2576i	−1.09346	−	0.192806i	−0.691159	+	0.722703i	$0.742899\pi$
$132$	3.29948	+	4.04036i	0.0249960	+	0.0306088i
$133$	117.636	−	98.7082i	0.884480	−	0.742167i
$134$		−	33.5824i		−	0.250615i
$135$	78.5336	−	86.3325i	0.581730	−	0.639500i
$136$	−86.0521			−0.632736
$137$	−120.843	−	144.016i	−0.882069	−	1.05121i	−0.998317	−	0.0579889i	$-0.981531\pi$
$137$	−120.843	−	144.016i	−0.882069	−	1.05121i	0.116248	−	0.993220i	$-0.462913\pi$
$138$	−12.3117	−	75.7123i	−0.0892152	−	0.548640i
$139$	15.2570	−	86.5267i	0.109762	−	0.622494i	−0.879448	−	0.475995i	$-0.842088\pi$
$139$	15.2570	−	86.5267i	0.109762	−	0.622494i	0.989211	−	0.146500i	$-0.0468007\pi$
$140$	−3.09807	−	8.51187i	−0.0221291	−	0.0607991i
$141$	137.564	+	26.1520i	0.975634	+	0.185475i
$142$	20.0365	+	113.632i	0.141102	+	0.800229i
$143$	103.537	−	59.7772i	0.724036	−	0.418022i
$144$	64.3653	+	118.683i	0.446981	+	0.824189i
$145$	−90.4216	+	156.615i	−0.623597	+	1.08010i
$146$	34.9640	−	96.0629i	0.239480	−	0.657965i
$147$	−90.0557	−	1.20072i	−0.612624	−	0.00816818i
$148$	11.5530	+	9.69410i	0.0780607	+	0.0655007i
$149$	40.4096	−	48.1582i	0.271205	−	0.323210i	−0.613202	−	0.789926i	$-0.710119\pi$
$149$	40.4096	−	48.1582i	0.271205	−	0.323210i	0.884407	+	0.466717i	$0.154563\pi$
$150$	−31.5879	−	18.8032i	−0.210586	−	0.125355i
$151$	108.435	+	39.4672i	0.718114	+	0.261372i	0.675125	−	0.737703i	$-0.264090\pi$
$151$	108.435	+	39.4672i	0.718114	+	0.261372i	0.0429892	+	0.999076i	$0.486312\pi$
$152$	122.946	+	70.9828i	0.808854	+	0.466992i
$153$	29.8595	+	89.3845i	0.195160	+	0.584212i
$154$	63.6068	+	110.170i	0.413031	+	0.715391i
$155$	−157.777	+	27.8203i	−1.01792	+	0.179486i
$156$	−10.8229	+	3.77658i	−0.0693775	+	0.0242089i
$157$	−49.1767	+	17.8989i	−0.313228	+	0.114006i	−0.493850	−	0.869547i	$-0.664411\pi$
$157$	−49.1767	+	17.8989i	−0.313228	+	0.114006i	0.180623	+	0.983552i	$0.442189\pi$
$158$	2.98004	+	0.525462i	0.0188610	+	0.00332571i
$159$	53.9452	−	142.282i	0.339278	−	0.894855i
$160$	12.4728	−	10.4659i	0.0779549	−	0.0654120i
$161$			117.151i			0.727643i
$162$	107.290	−	114.831i	0.662284	−	0.708834i
$163$	−251.388			−1.54226			−0.771128	−	0.636681i	$-0.780307\pi$
$163$	−251.388			−1.54226			−0.771128	+	0.636681i	$0.780307\pi$
$164$	3.85642	+	4.59591i	0.0235148	+	0.0280238i
$165$	89.4367	+	33.9093i	0.542041	+	0.205511i
$166$	38.0951	−	216.048i	0.229489	−	1.30149i
$167$	−2.89515	−	7.95437i	−0.0173363	−	0.0476310i	0.930723	−	0.365726i	$-0.119179\pi$
$167$	−2.89515	−	7.95437i	−0.0173363	−	0.0476310i	−0.948059	+	0.318095i	$0.896957\pi$
$168$	−72.2050	−	206.924i	−0.429792	−	1.23169i
$169$	16.2736	+	92.2924i	0.0962937	+	0.546109i
$170$	−76.0504	+	43.9077i	−0.447355	+	0.258281i
$171$	31.0703	−	152.337i	0.181697	−	0.890861i
$172$	−0.292229	+	0.506155i	−0.00169901	+	0.00294276i
$173$	66.7138	−	183.295i	0.385629	−	1.05951i	−0.583319	−	0.812243i	$-0.698246\pi$
$173$	66.7138	−	183.295i	0.385629	−	1.05951i	0.968948	−	0.247264i	$-0.0795316\pi$
$174$	−124.558	+	209.248i	−0.715852	+	1.20257i
$175$	43.0080	+	36.0880i	0.245760	+	0.206217i
$176$	−71.1252	+	84.7637i	−0.404120	+	0.481612i
$177$	−0.167579	+	12.5686i	−0.000946772	+	0.0710092i
$178$	−87.2646	−	31.7617i	−0.490251	−	0.178437i
$179$	183.204	+	105.773i	1.02349	+	0.590910i	0.915112	−	0.403200i	$-0.132102\pi$
$179$	183.204	+	105.773i	1.02349	+	0.590910i	0.108374	+	0.994110i	$0.465436\pi$
$180$	−7.81711	−	4.79555i	−0.0434284	−	0.0266419i
$181$	−43.8874	−	76.0153i	−0.242472	−	0.419974i	0.718946	−	0.695066i	$-0.244625\pi$
$181$	−43.8874	−	76.0153i	−0.242472	−	0.419974i	−0.961418	+	0.275092i	$0.911292\pi$
$182$	−275.300	+	48.5429i	−1.51264	+	0.266719i
$183$	−20.3746	+	107.174i	−0.111337	+	0.585652i
$184$	−101.772	+	37.0419i	−0.553107	+	0.201315i
$185$	272.333	+	48.0197i	1.47207	+	0.259566i
$186$	−212.935	+	34.6258i	−1.14481	+	0.186160i
$187$	−59.1655	+	49.6458i	−0.316393	+	0.265485i
$188$		−	11.0033i		−	0.0585283i
$189$	−189.883	+	146.802i	−1.00467	+	0.776732i
$190$	144.874			0.762497
$191$	206.497	+	246.093i	1.08113	+	1.28845i	0.955056	+	0.296426i	$0.0957947\pi$
$191$	206.497	+	246.093i	1.08113	+	1.28845i	0.126079	+	0.992020i	$0.459761\pi$
$192$	156.414	−	127.732i	0.814654	−	0.665271i
$193$	10.7145	−	60.7650i	0.0555156	−	0.314845i	−0.944387	−	0.328838i	$-0.893343\pi$
$193$	10.7145	−	60.7650i	0.0555156	−	0.314845i	0.999902	+	0.0139930i	$0.00445425\pi$
$194$	−24.3977	−	67.0322i	−0.125762	−	0.345527i
$195$	−137.239	+	159.196i	−0.703791	+	0.816389i
$196$	1.22893	+	6.96962i	0.00627006	+	0.0355593i
$197$	−194.174	+	112.106i	−0.985652	+	0.569067i	−0.903972	−	0.427592i	$-0.859362\pi$
$197$	−194.174	+	112.106i	−0.985652	+	0.569067i	−0.0816805	+	0.996659i	$0.526029\pi$
$198$	119.812	+	47.2622i	0.605110	+	0.238698i
$199$	2.60375	−	4.50982i	0.0130842	−	0.0226624i	−0.859409	−	0.511288i	$-0.829168\pi$
$199$	2.60375	−	4.50982i	0.0130842	−	0.0226624i	0.872493	+	0.488626i	$0.162502\pi$
$200$	−17.7519	+	48.7729i	−0.0887593	+	0.243864i
$201$	25.3617	+	45.3123i	0.126177	+	0.225434i
$202$	−126.775	−	106.377i	−0.627598	−	0.526617i
$203$	239.058	−	284.898i	1.17763	−	1.40344i
$204$	6.46198	−	3.61682i	0.0316764	−	0.0177295i
$205$	103.374	+	37.6251i	0.504264	+	0.183537i
$206$	39.0517	+	22.5465i	0.189571	+	0.109449i
$207$	73.7904	+	92.8596i	0.356475	+	0.448597i
$208$	−121.576	−	210.576i	−0.584499	−	1.01238i
$209$	125.484	−	22.1262i	0.600400	−	0.105867i
$210$	−169.395	−	146.032i	−0.806642	−	0.695388i
$211$	21.6633	−	7.88481i	0.102670	−	0.0373688i	−0.290174	−	0.956974i	$-0.593713\pi$
$211$	21.6633	−	7.88481i	0.102670	−	0.0373688i	0.392844	+	0.919605i	$0.371491\pi$
$212$	−11.7754	−	2.07631i	−0.0555442	−	0.00979394i
$213$	−112.851	−	138.191i	−0.529816	−	0.648784i
$214$	142.328	−	119.427i	0.665083	−	0.558071i
$215$			10.7167i			0.0498452i
$216$	−187.570	−	118.539i	−0.868381	−	0.548791i
$217$	329.478			1.51833
$218$	127.406	+	151.836i	0.584430	+	0.696497i
$219$	25.3709	+	156.021i	0.115849	+	0.712426i
$220$	1.30515	−	7.40186i	0.00593249	−	0.0336448i
$221$	−58.0481	−	159.486i	−0.262661	−	0.721655i
$222$	365.816	+	69.5442i	1.64782	+	0.313262i
$223$	−32.6616	−	185.233i	−0.146464	−	0.830641i	−0.966180	−	0.257870i	$-0.916979\pi$
$223$	−32.6616	−	185.233i	−0.146464	−	0.830641i	0.819715	−	0.572771i	$-0.194132\pi$
$224$	−28.9984	+	16.7422i	−0.129457	+	0.0747421i
$225$	56.8213	+	1.51548i	0.252539	+	0.00673546i
$226$	15.8221	−	27.4047i	0.0700093	−	0.121260i
$227$	42.9222	−	117.928i	0.189085	−	0.519505i	−0.808536	−	0.588446i	$-0.799740\pi$
$227$	42.9222	−	117.928i	0.189085	−	0.519505i	0.997621	+	0.0689410i	$0.0219620\pi$
$228$	−12.2159	−	0.162876i	−0.0535785	−	0.000714368i
$229$	−100.359	−	84.2111i	−0.438248	−	0.367734i	0.396805	−	0.917903i	$-0.370119\pi$
$229$	−100.359	−	84.2111i	−0.438248	−	0.367734i	−0.835053	+	0.550169i	$0.814563\pi$
$230$	−71.0425	+	84.6651i	−0.308880	+	0.368109i
$231$	−169.025	−	100.615i	−0.731710	−	0.435562i
$232$	323.087	+	117.594i	1.39261	+	0.506870i
$233$	−352.009	−	203.233i	−1.51077	−	0.872243i	−0.999921	−	0.0125723i	$-0.995998\pi$
$233$	−352.009	−	203.233i	−1.51077	−	0.872243i	−0.510848	−	0.859671i	$-0.670669\pi$
$234$	−187.641	+	211.883i	−0.801886	+	0.905482i
$235$	−100.879	−	174.728i	−0.429274	−	0.743524i
$236$	0.972715	−	0.171516i	0.00412167	−	0.000726762i
$237$	−4.41776	+	1.54155i	−0.0186403	+	0.00650442i
$238$	169.703	−	61.7670i	0.713039	−	0.259525i
$239$	−189.404	−	33.3970i	−0.792484	−	0.139736i	−0.237270	−	0.971444i	$-0.576253\pi$
$239$	−189.404	−	33.3970i	−0.792484	−	0.139736i	−0.555214	+	0.831707i	$0.687364\pi$
$240$	68.9654	−	181.898i	0.287356	−	0.757908i
$241$	−265.638	+	222.896i	−1.10223	+	0.924881i	−0.997573	−	0.0696270i	$-0.977819\pi$
$241$	−265.638	+	222.896i	−1.10223	+	0.924881i	−0.104658	+	0.994508i	$0.533375\pi$
$242$		−	129.204i		−	0.533903i
$243$	−58.0436	+	235.966i	−0.238863	+	0.971053i
$244$	8.57251			0.0351332
$245$	83.4131	+	99.4079i	0.340462	+	0.405746i
$246$	138.511	+	52.5155i	0.563052	+	0.213477i
$247$	−48.6214	+	275.746i	−0.196848	+	1.11638i
$248$	104.178	+	286.226i	0.420071	+	1.15414i
$249$	111.760	+	320.280i	0.448834	+	1.28627i
$250$	45.6048	+	258.638i	0.182419	+	1.03455i
$251$	370.198	−	213.734i	1.47489	−	0.851530i	0.475294	−	0.879827i	$-0.342342\pi$
$251$	370.198	−	213.734i	1.47489	−	0.851530i	0.999600	+	0.0282966i	$0.00900829\pi$
$252$	14.1193	+	12.5039i	0.0560290	+	0.0496187i
$253$	−48.6032	+	84.1831i	−0.192107	+	0.332740i
$254$	54.0562	−	148.518i	0.212820	−	0.584717i
$255$	69.4542	−	116.678i	0.272370	−	0.457560i
$256$	−34.5496	−	28.9906i	−0.134960	−	0.113245i
$257$	−182.597	+	217.611i	−0.710495	+	0.846735i	−0.993671	−	0.112333i	$-0.964168\pi$
$257$	−182.597	+	217.611i	−0.710495	+	0.846735i	0.283176	+	0.959068i	$0.408612\pi$
$258$	−0.192388	+	14.4293i	−0.000745690	+	0.0559277i
$259$	−534.403	−	194.507i	−2.06333	−	0.750991i
$260$	14.3035	+	8.25811i	0.0550133	+	0.0317620i
$261$	10.0390	−	376.402i	0.0384636	−	1.44215i
$262$	141.101	+	244.395i	0.538555	+	0.932805i
$263$	−341.187	+	60.1605i	−1.29729	+	0.228747i	−0.779306	−	0.626643i	$-0.784428\pi$
$263$	−341.187	+	60.1605i	−1.29729	+	0.228747i	−0.517983	+	0.855391i	$0.673317\pi$
$264$	33.9626	−	178.650i	0.128646	−	0.676704i
$265$	−206.024	+	74.9866i	−0.777449	+	0.282968i
$266$	−293.412	−	51.7364i	−1.10305	−	0.194498i
$267$	141.732	−	23.0472i	0.530830	−	0.0863191i
$268$	3.12576	−	2.62282i	0.0116633	−	0.00978665i
$269$			297.900i			1.10743i	0.832705	+	0.553717i	$0.186791\pi$
$269$			297.900i			1.10743i	−0.832705	+	0.553717i	$0.813209\pi$
$270$	−226.253	−	9.05425i	−0.837974	−	0.0335343i
$271$	368.678			1.36044			0.680218	−	0.733010i	$-0.261885\pi$
$271$	368.678			1.36044			0.680218	+	0.733010i	$0.261885\pi$
$272$	100.970	+	120.332i	0.371215	+	0.442397i
$273$	334.799	−	273.407i	1.22637	−	1.00149i
$274$	−63.3382	+	359.209i	−0.231161	+	1.31098i
$275$	15.9330	+	43.7755i	0.0579381	+	0.159184i
$276$	6.08553	−	7.05914i	0.0220490	−	0.0255766i
$277$	−49.1193	−	278.569i	−0.177326	−	1.00566i	−0.935425	−	0.353525i	$-0.884983\pi$
$277$	−49.1193	−	278.569i	−0.177326	−	1.00566i	0.758099	−	0.652139i	$-0.226128\pi$
$278$	−147.628	+	85.2331i	−0.531036	+	0.306594i
$279$	261.161	−	207.530i	0.936061	−	0.743836i
$280$	−157.888	+	273.470i	−0.563886	+	0.976678i
$281$	96.1506	−	264.172i	0.342173	−	0.940112i	−0.642590	−	0.766210i	$-0.722140\pi$
$281$	96.1506	−	264.172i	0.342173	−	0.940112i	0.984763	−	0.173902i	$-0.0556377\pi$
$282$	−132.690	−	237.071i	−0.470534	−	0.840676i
$283$	334.168	+	280.400i	1.18081	+	0.990814i	0.999973	+	0.00730054i	$0.00232386\pi$
$283$	334.168	+	280.400i	1.18081	+	0.990814i	0.180833	+	0.983514i	$0.442121\pi$
$284$	−9.01172	+	10.7397i	−0.0317314	+	0.0378160i
$285$	−195.477	+	109.410i	−0.685884	+	0.383895i
$286$	−217.967	−	79.3336i	−0.762123	−	0.277390i
$287$	−195.925	−	113.118i	−0.682667	−	0.394138i
$288$	−12.4401	+	31.5362i	−0.0431948	+	0.109501i
$289$	−89.6779	−	155.327i	−0.310304	−	0.537463i
$290$	345.536	−	60.9274i	1.19150	−	0.210094i
$291$	83.5427	+	72.0203i	0.287088	+	0.247492i
$292$	11.6720	−	4.24826i	0.0399726	−	0.0145488i
$293$	363.553	+	64.1042i	1.24080	+	0.218786i	0.755256	−	0.655429i	$-0.227512\pi$
$293$	363.553	+	64.1042i	1.24080	+	0.218786i	0.485539	+	0.874215i	$0.338623\pi$
$294$	110.525	+	135.343i	0.375937	+	0.460352i
$295$	13.8739	−	11.6415i	0.0470300	−	0.0394629i
$296$		−	525.751i		−	1.77619i
$297$	−197.353	+	26.7124i	−0.664488	+	0.0899408i
$298$	−121.971			−0.409299
$299$	−137.304	−	163.633i	−0.459211	−	0.547266i
$300$	−0.716899	−	4.40866i	−0.00238966	−	0.0146955i
$301$	3.82707	−	21.7044i	0.0127145	−	0.0721076i
$302$	−76.5731	−	210.383i	−0.253553	−	0.696632i
$303$	251.392	+	47.7913i	0.829676	+	0.157727i
$304$	−45.0006	−	255.211i	−0.148028	−	0.839510i
$305$	136.128	−	78.5936i	0.446321	−	0.257684i
$306$	95.6100	−	155.852i	0.312451	−	0.509320i
$307$	183.104	−	317.145i	0.596429	−	1.03304i	−0.396915	−	0.917855i	$-0.629919\pi$
$307$	183.104	−	317.145i	0.596429	−	1.03304i	0.993344	−	0.115189i	$-0.0367475\pi$
$308$	−5.28658	+	14.5248i	−0.0171642	+	0.0471583i
$309$	−69.7191	−	0.929571i	−0.225628	−	0.00300832i
$310$	238.115	+	199.802i	0.768112	+	0.644522i
$311$	−306.742	+	365.561i	−0.986308	+	1.17544i	−0.00181732	+	0.999998i	$0.500578\pi$
$311$	−306.742	+	365.561i	−0.986308	+	1.17544i	−0.984491	+	0.175438i	$0.943866\pi$
$312$	343.376	+	204.400i	1.10056	+	0.655128i
$313$	95.0647	+	34.6007i	0.303721	+	0.110545i	0.489385	−	0.872068i	$-0.337221\pi$
$313$	95.0647	+	34.6007i	0.303721	+	0.110545i	−0.185664	+	0.982613i	$0.559444\pi$
$314$	87.9315	+	50.7673i	0.280037	+	0.161679i
$315$	338.846	+	69.1100i	1.07570	+	0.219397i
$316$	0.183836	+	0.318413i	0.000581759	+	0.00100764i
$317$	−364.896	+	64.3410i	−1.15109	+	0.202968i	−0.716452	−	0.697636i	$-0.754235\pi$
$317$	−364.896	+	64.3410i	−1.15109	+	0.202968i	−0.434639	+	0.900605i	$0.643124\pi$
$318$	−278.743	+	97.2658i	−0.876552	+	0.305867i
$319$	289.983	−	105.545i	0.909037	−	0.330862i
$320$	−286.547	−	50.5260i	−0.895459	−	0.157894i
$321$	−101.848	+	268.628i	−0.317285	+	0.836847i
$322$	174.116	−	146.101i	0.540732	−	0.453728i
$323$		−	180.887i		−	0.560021i
$324$	19.0676	+	1.01783i	0.0588507	+	0.00314144i
$325$	−102.369			−0.314980
$326$	313.510	+	373.627i	0.961687	+	1.14609i
$327$	−286.574	−	108.653i	−0.876374	−	0.332271i
$328$	36.3185	−	205.972i	0.110727	−	0.627964i
$329$	141.912	+	389.899i	0.431342	+	1.18510i
$330$	−61.1401	−	175.215i	−0.185273	−	0.530954i
$331$	61.9327	+	351.238i	0.187108	+	1.06114i	0.923217	+	0.384279i	$0.125550\pi$
$331$	61.9327	+	351.238i	0.187108	+	1.06114i	−0.736109	+	0.676863i	$0.763339\pi$
$332$	23.0844	−	13.3278i	0.0695314	−	0.0401440i
$333$	−546.110	+	182.432i	−1.63997	+	0.547843i
$334$	−8.21164	+	14.2230i	−0.0245857	+	0.0425838i
$335$	25.5895	−	70.3066i	0.0763866	−	0.209870i
$336$	−204.632	+	343.766i	−0.609024	+	1.02311i
$337$	−307.364	−	257.909i	−0.912059	−	0.765309i	0.0604502	−	0.998171i	$-0.480746\pi$
$337$	−307.364	−	257.909i	−0.912059	−	0.765309i	−0.972510	+	0.232862i	$0.925191\pi$
$338$	116.875	−	139.286i	0.345784	−	0.412090i
$339$	−0.652331	+	48.9257i	−0.00192428	+	0.144324i
$340$	−10.0264	−	3.64932i	−0.0294895	−	0.0107333i
$341$	236.759	+	136.693i	0.694308	+	0.400859i
$342$	−265.161	+	143.804i	−0.775323	+	0.420480i
$343$	84.3548	+	146.107i	0.245932	+	0.425967i
$344$	20.0652	−	3.53804i	0.0583292	−	0.0102850i
$345$	31.9169	−	167.889i	0.0925127	−	0.486635i
$346$	−355.623	+	129.436i	−1.02781	+	0.374093i
$347$	56.4104	+	9.94668i	0.162566	+	0.0286648i	0.254339	−	0.967115i	$-0.418142\pi$
$347$	56.4104	+	9.94668i	0.162566	+	0.0286648i	−0.0917726	+	0.995780i	$0.529253\pi$
$348$	−29.2043	+	4.74896i	−0.0839205	+	0.0136464i
$349$	287.357	−	241.121i	0.823371	−	0.690890i	−0.130388	−	0.991463i	$-0.541622\pi$
$349$	287.357	−	241.121i	0.823371	−	0.690890i	0.953759	+	0.300573i	$0.0971778\pi$
$350$		−	108.927i		−	0.311220i
$351$	93.1662	−	427.598i	0.265431	−	1.21823i
$352$	−27.7839			−0.0789316
$353$	−141.432	−	168.552i	−0.400658	−	0.477485i	0.527563	−	0.849516i	$-0.323106\pi$
$353$	−141.432	−	168.552i	−0.400658	−	0.477485i	−0.928220	+	0.372031i	$0.878662\pi$
$354$	18.8892	−	15.4255i	0.0533593	−	0.0435748i
$355$	−44.6395	+	253.163i	−0.125745	+	0.713136i
$356$	−3.85917	−	10.6030i	−0.0108404	−	0.0297836i
$357$	−182.331	+	211.502i	−0.510732	+	0.592443i
$358$	−71.2712	−	404.199i	−0.199082	−	1.12905i
$359$	−174.426	+	100.705i	−0.485866	+	0.280515i	−0.722858	−	0.690997i	$-0.757172\pi$
$359$	−174.426	+	100.705i	−0.485866	+	0.280515i	0.236992	+	0.971512i	$0.423838\pi$
$360$	47.1022	+	316.216i	0.130839	+	0.878379i
$361$	31.2901	−	54.1960i	0.0866761	−	0.150127i
$362$	−58.2454	+	160.028i	−0.160899	+	0.442066i
$363$	97.5760	+	174.334i	0.268804	+	0.480258i
$364$	−26.0195	−	21.8329i	−0.0714821	−	0.0599806i
$365$	146.398	−	174.470i	0.401091	−	0.478001i
$366$	184.698	−	103.377i	0.504640	−	0.282451i
$367$	−149.564	−	54.4369i	−0.407532	−	0.148330i	0.130116	−	0.991499i	$-0.458465\pi$
$367$	−149.564	−	54.4369i	−0.407532	−	0.148330i	−0.537648	+	0.843169i	$0.680687\pi$
$368$	171.213	+	98.8500i	0.465253	+	0.268614i
$369$	−226.551	+	33.7460i	−0.613958	+	0.0914525i
$370$	−268.262	−	464.643i	−0.725032	−	1.25579i
$371$	444.035	−	78.2954i	1.19686	−	0.211039i
$372$	−19.8533	−	17.1151i	−0.0533692	−	0.0460084i
$373$	48.5332	−	17.6646i	0.130116	−	0.0473583i	−0.276142	−	0.961117i	$-0.589056\pi$
$373$	48.5332	−	17.6646i	0.130116	−	0.0473583i	0.406257	+	0.913759i	$0.366834\pi$
$374$	147.573	+	26.0211i	0.394579	+	0.0695750i
$375$	−256.859	−	314.535i	−0.684957	−	0.838760i
$376$	−293.844	+	246.565i	−0.781501	+	0.655757i
$377$			678.122i			1.79873i
$378$	454.992	+	99.1350i	1.20368	+	0.262262i
$379$	147.231			0.388472			0.194236	−	0.980955i	$-0.437777\pi$
$379$	147.231			0.388472			0.194236	+	0.980955i	$0.437777\pi$
$380$	11.3148	+	13.4845i	0.0297759	+	0.0354855i
$381$	39.2246	+	241.217i	0.102952	+	0.633115i
$382$	108.232	−	613.814i	0.283330	−	1.60684i
$383$	−38.8997	−	106.876i	−0.101566	−	0.279049i	0.878494	−	0.477754i	$-0.158549\pi$
$383$	−38.8997	−	106.876i	−0.101566	−	0.279049i	−0.980059	+	0.198704i	$0.936327\pi$
$384$	−340.503	−	64.7320i	−0.886726	−	0.168573i
$385$	49.2155	+	279.115i	0.127833	+	0.724975i
$386$	−103.675	+	59.8566i	−0.268587	+	0.155069i
$387$	−10.6375	−	19.6146i	−0.0274872	−	0.0506837i
$388$	4.33368	−	7.50616i	0.0111693	−	0.0193458i
$389$	−123.951	+	340.552i	−0.318639	+	0.875454i	0.672195	+	0.740374i	$0.265351\pi$
$389$	−123.951	+	340.552i	−0.318639	+	0.875454i	−0.990835	+	0.135080i	$0.956871\pi$
$390$	407.760	+	5.43670i	1.04554	+	0.0139403i
$391$	105.711	+	88.7018i	0.270360	+	0.226859i
$392$	158.586	−	188.996i	0.404556	−	0.482132i
$393$	−374.955	−	223.198i	−0.954083	−	0.567933i
$394$	408.776	+	148.782i	1.03750	+	0.377620i
$395$	5.83848	+	3.37085i	0.0147810	+	0.00853379i
$396$	4.95839	+	14.8430i	0.0125212	+	0.0374822i
$397$	368.516	+	638.289i	0.928252	+	1.60778i	0.786246	+	0.617914i	$0.212022\pi$
$397$	368.516	+	638.289i	0.928252	+	1.60778i	0.142006	+	0.989866i	$0.454645\pi$
$398$	−9.94994	+	1.75444i	−0.0249998	+	0.00440815i
$399$	434.967	−	151.779i	1.09014	−	0.380399i
$400$	89.0314	−	32.4048i	0.222579	−	0.0810119i
$401$	217.940	+	38.4287i	0.543491	+	0.0958322i	0.438652	−	0.898657i	$-0.355456\pi$
$401$	217.940	+	38.4287i	0.543491	+	0.0958322i	0.104839	+	0.994489i	$0.466567\pi$
$402$	35.7167	−	94.2037i	0.0888475	−	0.234337i
$403$	−460.205	+	386.158i	−1.14195	+	0.958208i
$404$		−	20.1080i		−	0.0497722i
$405$	312.118	−	158.651i	0.770661	−	0.391731i
$406$	−721.566			−1.77726
$407$	−303.320	−	361.482i	−0.745257	−	0.888163i
$408$	−241.389	−	91.5210i	−0.591640	−	0.224316i
$409$	77.3060	−	438.424i	0.189012	−	1.07194i	−0.731679	−	0.681650i	$-0.761263\pi$
$409$	77.3060	−	438.424i	0.189012	−	1.07194i	0.920691	−	0.390292i	$-0.127626\pi$
$410$	−72.9992	−	200.564i	−0.178047	−	0.489179i
$411$	−185.816	−	532.509i	−0.452106	−	1.29564i
$412$	0.951411	+	5.39572i	0.00230925	+	0.0130964i
$413$	−32.2558	+	18.6229i	−0.0781012	+	0.0450917i
$414$	45.9879	−	225.478i	0.111082	−	0.544634i
$415$	244.381	−	423.280i	0.588870	−	1.01995i
$416$	20.8817	−	57.3721i	0.0501965	−	0.137914i
$417$	134.824	−	226.494i	0.323318	−	0.543150i
$418$	−189.378	−	158.907i	−0.453058	−	0.380161i
$419$	371.014	−	442.157i	0.885475	−	1.05527i	−0.112624	−	0.993638i	$-0.535926\pi$
$419$	371.014	−	442.157i	0.885475	−	1.05527i	0.998099	−	0.0616300i	$-0.0196299\pi$
$420$	0.362287	−	27.1720i	0.000862589	−	0.0646953i
$421$	315.735	+	114.918i	0.749964	+	0.272964i	0.688591	−	0.725150i	$-0.258230\pi$
$421$	315.735	+	114.918i	0.749964	+	0.272964i	0.0613732	+	0.998115i	$0.480452\pi$
$422$	−38.7356	−	22.3640i	−0.0917905	−	0.0529953i
$423$	358.075	+	219.667i	0.846512	+	0.519308i
$424$	208.417	+	360.989i	0.491549	+	0.851388i
$425$	65.1280	−	11.4838i	0.153242	−	0.0270207i
$426$	−64.6489	+	340.066i	−0.151758	+	0.798276i
$427$	−303.764	+	110.561i	−0.711392	+	0.258925i
$428$	22.2319	+	3.92008i	0.0519436	+	0.00915906i
$429$	354.013	−	57.5666i	0.825205	−	0.134188i
$430$	15.9278	−	13.3650i	0.0370414	−	0.0310814i
$431$			113.799i			0.264034i	0.991247	+	0.132017i	$0.0421454\pi$
$431$			113.799i			0.264034i	−0.991247	+	0.132017i	$0.957855\pi$
$432$	54.3282	+	401.380i	0.125760	+	0.929120i
$433$	−204.214			−0.471625			−0.235812	−	0.971799i	$-0.575775\pi$
$433$	−204.214			−0.471625			−0.235812	+	0.971799i	$0.575775\pi$
$434$	−410.897	−	489.689i	−0.946768	−	1.12831i
$435$	−420.214	+	343.160i	−0.966010	+	0.788873i
$436$	−4.18197	+	23.7171i	−0.00959168	+	0.0543971i
$437$	−77.8642	−	213.930i	−0.178179	−	0.489543i
$438$	200.247	−	232.284i	0.457185	−	0.530330i
$439$	70.1264	+	397.706i	0.159741	+	0.905937i	0.954322	+	0.298779i	$0.0965794\pi$
$439$	70.1264	+	397.706i	0.159741	+	0.905937i	−0.794581	+	0.607158i	$0.792309\pi$
$440$	−226.913	+	131.008i	−0.515712	+	0.297746i
$441$	−251.343	−	99.1472i	−0.569938	−	0.224824i
$442$	−164.644	+	285.172i	−0.372498	+	0.645185i
$443$	−226.287	+	621.719i	−0.510806	+	1.40343i	0.369593	+	0.929194i	$0.379497\pi$
$443$	−226.287	+	621.719i	−0.510806	+	1.40343i	−0.880399	+	0.474234i	$0.842725\pi$
$444$	22.0976	+	39.4806i	0.0497694	+	0.0889203i
$445$	−158.491	−	132.990i	−0.356160	−	0.298853i
$446$	−234.571	+	279.551i	−0.525944	+	0.626796i
$447$	164.574	−	92.1133i	0.368174	−	0.206070i
$448$	562.295	+	204.659i	1.25512	+	0.456827i
$449$	−403.851	−	233.164i	−0.899446	−	0.519295i	−0.0224253	−	0.999749i	$-0.507139\pi$
$449$	−403.851	−	233.164i	−0.899446	−	0.519295i	−0.877020	+	0.480453i	$0.840472\pi$
$450$	−68.6105	−	86.3411i	−0.152468	−	0.191869i
$451$	−93.8599	−	162.570i	−0.208115	−	0.360466i
$452$	3.78647	−	0.667658i	0.00837716	−	0.00147712i
$453$	262.201	+	226.038i	0.578811	+	0.498980i
$454$	−228.800	+	83.2764i	−0.503965	+	0.183428i
$455$	−613.345	−	108.149i	−1.34801	−	0.237691i
$456$	269.387	+	329.876i	0.590761	+	0.723413i
$457$	654.268	−	548.996i	1.43166	−	1.20130i	0.486935	−	0.873438i	$-0.338115\pi$
$457$	654.268	−	548.996i	1.43166	−	1.20130i	0.944724	−	0.327866i	$-0.106330\pi$
$458$			254.180i			0.554979i
$459$	−11.3049	+	282.494i	−0.0246294	+	0.615455i
$460$	−13.4289			−0.0291932
$461$	−52.6518	−	62.7480i	−0.114212	−	0.136113i	0.705909	−	0.708302i	$-0.250539\pi$
$461$	−52.6518	−	62.7480i	−0.114212	−	0.136113i	−0.820121	+	0.572190i	$0.806094\pi$
$462$	61.2547	+	376.693i	0.132586	+	0.815353i
$463$	−113.673	+	644.671i	−0.245514	+	1.39238i	0.573783	+	0.819007i	$0.305475\pi$
$463$	−113.673	+	644.671i	−0.245514	+	1.39238i	−0.819297	+	0.573370i	$0.805636\pi$
$464$	−214.659	−	589.772i	−0.462628	−	1.27106i
$465$	−472.176	−	89.7640i	−1.01543	−	0.193041i
$466$	136.941	+	776.631i	0.293865	+	1.66659i
$467$	113.391	−	65.4664i	0.242808	−	0.140185i	−0.373659	−	0.927566i	$-0.621897\pi$
$467$	113.391	−	65.4664i	0.242808	−	0.140185i	0.616466	+	0.787381i	$0.288564\pi$
$468$	−34.3764	−	0.916852i	−0.0734539	−	0.00195908i
$469$	−76.9332	+	133.252i	−0.164037	+	0.284120i
$470$	−133.883	+	367.839i	−0.284856	+	0.782637i
$471$	−156.984	−	2.09309i	−0.333300	−	0.00444393i
$472$	−26.3772	−	22.1331i	−0.0558838	−	0.0468921i
$473$	11.7548	−	14.0088i	0.0248515	−	0.0296169i
$474$	7.80060	+	4.64343i	0.0164570	+	0.00979626i
$475$	−102.523	−	37.3155i	−0.215839	−	0.0785589i
$476$	19.0031	+	10.9714i	0.0399225	+	0.0230493i
$477$	302.649	−	341.748i	0.634484	−	0.716453i
$478$	186.572	+	323.152i	0.390318	+	0.676051i
$479$	−155.272	+	27.3786i	−0.324158	+	0.0571578i	−0.333359	−	0.942800i	$-0.608182\pi$
$479$	−155.272	+	27.3786i	−0.324158	+	0.0571578i	0.00920134	+	0.999958i	$0.497071\pi$
$480$	46.1191	−	16.0930i	0.0960814	−	0.0335270i
$481$	974.406	−	354.655i	2.02579	−	0.737328i
$482$	662.563	+	116.828i	1.37461	+	0.242381i
$483$	−124.596	+	328.625i	−0.257962	+	0.680382i
$484$	12.0260	−	10.0910i	0.0248471	−	0.0208492i
$485$		−	158.926i		−	0.327683i
$486$	423.093	−	208.010i	0.870562	−	0.428003i
$487$	−698.201			−1.43368			−0.716839	−	0.697239i	$-0.754412\pi$
$487$	−698.201			−1.43368			−0.716839	+	0.697239i	$0.754412\pi$
$488$	−192.095	−	228.930i	−0.393637	−	0.469118i
$489$	−705.179	−	267.364i	−1.44208	−	0.546757i
$490$	43.7197	−	247.947i	0.0892238	−	0.506013i
$491$	14.4407	+	39.6755i	0.0294108	+	0.0808056i	0.953529	−	0.301301i	$-0.0974209\pi$
$491$	14.4407	+	39.6755i	0.0294108	+	0.0808056i	−0.924118	+	0.382107i	$0.875199\pi$
$492$	5.92985	+	16.9937i	0.0120525	+	0.0345401i
$493$	−76.0724	−	431.428i	−0.154305	−	0.875108i
$494$	470.466	−	271.623i	0.952359	−	0.549845i
$495$	214.819	+	190.241i	0.433978	+	0.384326i
$496$	278.009	−	481.525i	0.560501	−	0.970816i
$497$	180.815	−	496.785i	0.363813	−	0.999568i
$498$	336.641	−	565.531i	0.675986	−	1.13560i
$499$	−367.980	−	308.772i	−0.737435	−	0.618781i	0.194713	−	0.980860i	$-0.437623\pi$
$499$	−367.980	−	308.772i	−0.737435	−	0.618781i	−0.932147	+	0.362079i	$0.882067\pi$
$500$	−20.5115	+	24.4446i	−0.0410230	+	0.0488893i
$501$	0.338559	−	25.3923i	0.000675766	−	0.0506833i
$502$	−779.345	−	283.658i	−1.55248	−	0.565056i
$503$	73.7969	+	42.6067i	0.146714	+	0.0847051i	0.571560	−	0.820560i	$-0.306339\pi$
$503$	73.7969	+	42.6067i	0.146714	+	0.0847051i	−0.424846	+	0.905266i	$0.639672\pi$
$504$	17.5294	−	657.248i	0.0347806	−	1.30406i
$505$	−184.352	−	319.307i	−0.365053	−	0.632290i
$506$	185.732	−	32.7495i	0.367059	−	0.0647223i
$507$	−52.5079	+	276.202i	−0.103566	+	0.544777i
$508$	18.0455	−	6.56802i	0.0355226	−	0.0129292i
$509$	391.247	+	68.9874i	0.768658	+	0.135535i	0.544208	−	0.838950i	$-0.316830\pi$
$509$	391.247	+	68.9874i	0.768658	+	0.135535i	0.224450	+	0.974486i	$0.427941\pi$
$510$	−260.031	+	42.2840i	−0.509864	+	0.0829098i
$511$	−358.803	+	301.071i	−0.702158	+	0.589180i
$512$			549.639i			1.07351i
$513$	249.175	−	394.284i	0.485722	−	0.768584i
$514$	551.146			1.07227
$515$	64.5765	+	76.9593i	0.125391	+	0.149435i
$516$	−1.35807	+	1.10904i	−0.00263192	+	0.00214930i
$517$	−59.7842	+	339.053i	−0.115637	+	0.655809i
$518$	377.376	+	1036.83i	0.728525	+	2.00161i
$519$	382.086	−	443.215i	0.736196	−	0.853979i
$520$	−99.9817	−	567.025i	−0.192273	−	1.09043i
$521$	−19.7109	+	11.3801i	−0.0378328	+	0.0218428i	−0.518797	−	0.854897i	$-0.673620\pi$
$521$	−19.7109	+	11.3801i	−0.0378328	+	0.0218428i	0.480964	+	0.876740i	$0.340287\pi$
$522$	−571.950	+	454.497i	−1.09569	+	0.870685i
$523$	−380.270	+	658.647i	−0.727093	+	1.25936i	0.231013	+	0.972951i	$0.425796\pi$
$523$	−380.270	+	658.647i	−0.727093	+	1.25936i	−0.958107	+	0.286412i	$0.907537\pi$
$524$	−11.7274	+	32.2208i	−0.0223806	+	0.0614901i
$525$	82.2623	+	146.973i	0.156690	+	0.279949i
$526$	514.914	+	432.065i	0.978925	+	0.821415i
$527$	249.468	−	297.304i	0.473373	−	0.564144i
$528$	−289.667	+	162.129i	−0.548613	+	0.307063i
$529$	−333.893	−	121.527i	−0.631178	−	0.229730i
$530$	368.385	+	212.687i	0.695067	+	0.401297i
$531$	−13.8375	+	35.0786i	−0.0260593	+	0.0660614i
$532$	−18.1003	−	31.3506i	−0.0340231	−	0.0589297i
$533$	406.240	−	71.6311i	0.762177	−	0.134392i
$534$	−211.010	−	181.907i	−0.395150	−	0.340650i
$535$	388.973	−	141.575i	0.727052	−	0.264625i
$536$	−140.085	−	24.7008i	−0.261353	−	0.0460836i
$537$	401.419	+	491.556i	0.747522	+	0.915374i
$538$	442.755	−	371.516i	0.822966	−	0.690550i
$539$		−	221.437i		−	0.410830i
$540$	−16.8278	−	21.7661i	−0.0311627	−	0.0403077i
$541$	−158.844			−0.293612			−0.146806	−	0.989165i	$-0.546899\pi$
$541$	−158.844			−0.293612			−0.146806	+	0.989165i	$0.546899\pi$
$542$	−459.785	−	547.950i	−0.848312	−	1.01098i
$543$	−42.2645	−	259.911i	−0.0778352	−	0.478657i
$544$	−6.84912	+	38.8433i	−0.0125903	+	0.0714031i
$545$	151.033	+	414.959i	0.277124	+	0.761393i
$546$	−823.886	−	156.627i	−1.50895	−	0.286862i
$547$	−114.270	−	648.057i	−0.208903	−	1.18475i	−0.891179	−	0.453653i	$-0.850121\pi$
$547$	−114.270	−	648.057i	−0.208903	−	1.18475i	0.682276	−	0.731095i	$-0.260990\pi$
$548$	−38.3809	+	22.1592i	−0.0700382	+	0.0404366i
$549$	−171.139	+	278.970i	−0.311729	+	0.508143i
$550$	45.1914	−	78.2737i	0.0821661	−	0.142316i
$551$	−247.189	+	679.147i	−0.448620	+	1.23257i
$552$	−324.881	−	4.33167i	−0.588552	−	0.00784723i
$553$	−10.6208	−	8.91190i	−0.0192058	−	0.0161155i
$554$	−352.768	+	420.412i	−0.636765	+	0.758867i
$555$	712.863	+	424.343i	1.28444	+	0.764582i
$556$	−19.4632	−	7.08401i	−0.0350057	−	0.0127410i
$557$	817.907	+	472.219i	1.46842	+	0.847790i	0.999374	−	0.0353864i	$-0.0112662\pi$
$557$	817.907	+	472.219i	1.46842	+	0.847790i	0.469041	+	0.883176i	$0.344600\pi$
$558$	−634.142	−	129.338i	−1.13645	−	0.231788i
$559$	20.0927	+	34.8015i	0.0359439	+	0.0622567i
$560$	567.669	−	100.095i	1.01370	−	0.178742i
$561$	−218.769	+	76.3380i	−0.389962	+	0.136075i
$562$	−512.538	+	186.549i	−0.911989	+	0.331937i
$563$	−1042.20	−	183.769i	−1.85116	−	0.326410i	−0.866269	−	0.499577i	$-0.833489\pi$
$563$	−1042.20	−	183.769i	−1.85116	−	0.326410i	−0.984892	+	0.173168i	$0.944600\pi$
$564$	11.7026	−	30.8659i	0.0207493	−	0.0547268i
$565$	54.0066	−	45.3169i	0.0955868	−	0.0802069i
$566$		−	846.352i		−	1.49532i
$567$	−688.782	+	209.852i	−1.21478	+	0.370109i
$568$	488.742			0.860462
$569$	114.850	+	136.873i	0.201845	+	0.240550i	0.857466	−	0.514540i	$-0.172037\pi$
$569$	114.850	+	136.873i	0.201845	+	0.240550i	−0.655621	+	0.755090i	$0.727593\pi$
$570$	406.394	+	154.082i	0.712973	+	0.270319i
$571$	104.611	−	593.280i	0.183207	−	1.03902i	−0.745030	−	0.667030i	$-0.767565\pi$
$571$	104.611	−	593.280i	0.183207	−	1.03902i	0.928237	−	0.371988i	$-0.121324\pi$
$572$	−9.63932	−	26.4838i	−0.0168520	−	0.0463004i
$573$	317.521	+	909.948i	0.554137	+	1.58804i
$574$	76.2202	+	432.266i	0.132788	+	0.753077i
$575$	72.0819	−	41.6165i	0.125360	−	0.0723766i
$576$	574.613	−	191.953i	0.997593	−	0.333252i
$577$	87.1430	−	150.936i	0.151028	−	0.261588i	−0.780578	−	0.625059i	$-0.785075\pi$
$577$	87.1430	−	150.936i	0.151028	−	0.261588i	0.931606	+	0.363471i	$0.118408\pi$
$578$	−119.017	+	326.995i	−0.205911	+	0.565736i
$579$	94.6826	−	159.059i	0.163528	−	0.274714i
$580$	32.6577	+	27.4031i	0.0563064	+	0.0472466i
$581$	−646.098	+	769.990i	−1.11205	+	1.32528i
$582$	2.85307	−	213.984i	0.00490218	−	0.367670i
$583$	351.562	+	127.958i	0.603022	+	0.219482i
$584$	−374.998	−	216.505i	−0.642121	−	0.370728i
$585$	−554.290	+	300.607i	−0.947504	+	0.513858i
$586$	−358.118	−	620.279i	−0.611123	−	1.05850i
$587$	1005.60	−	177.314i	1.71311	−	0.302068i	0.770867	−	0.636996i	$-0.219823\pi$
$587$	1005.60	−	177.314i	1.71311	−	0.302068i	0.942244	+	0.334928i	$0.108712\pi$
$588$	−3.96523	+	20.8579i	−0.00674358	+	0.0354725i
$589$	−601.664	+	218.988i	−1.02150	+	0.371796i
$590$	−34.6046	−	6.10173i	−0.0586519	−	0.0103419i
$591$	−663.916	+	107.960i	−1.12338	+	0.182674i
$592$	−735.189	+	616.897i	−1.24187	+	1.04206i
$593$		−	848.172i		−	1.43031i	−0.698967	−	0.715153i	$-0.746357\pi$
$593$		−	848.172i		−	1.43031i	0.698967	−	0.715153i	$-0.253643\pi$
$594$	285.824	+	260.004i	0.481185	+	0.437716i
$595$	402.349			0.676216
$596$	−9.52606	−	11.3527i	−0.0159833	−	0.0190482i
$597$	12.1003	−	9.88150i	0.0202686	−	0.0165519i
$598$	−71.9658	+	408.138i	−0.120344	+	0.682505i
$599$	−108.727	−	298.725i	−0.181514	−	0.498706i	0.815248	−	0.579112i	$-0.196601\pi$
$599$	−108.727	−	298.725i	−0.181514	−	0.498706i	−0.996762	+	0.0804060i	$0.974378\pi$
$600$	−101.669	+	117.935i	−0.169449	+	0.196558i
$601$	−94.5670	−	536.316i	−0.157349	−	0.892372i	−0.956606	−	0.291383i	$-0.905885\pi$
$601$	−94.5670	−	536.316i	−0.157349	−	0.892372i	0.799257	−	0.600989i	$-0.205227\pi$
$602$	−37.0311	+	21.3799i	−0.0615134	+	0.0355148i
$603$	22.9512	+	154.081i	0.0380617	+	0.255524i
$604$	13.6014	−	23.5583i	0.0225189	−	0.0390039i
$605$	98.4526	−	270.496i	0.162732	−	0.447101i
$606$	−242.485	−	433.234i	−0.400140	−	0.714908i
$607$	326.292	+	273.792i	0.537549	+	0.451057i	0.870699	−	0.491817i	$-0.163667\pi$
$607$	326.292	+	273.792i	0.537549	+	0.451057i	−0.333150	+	0.942874i	$0.608111\pi$
$608$	41.8266	−	49.8470i	0.0687938	−	0.0819853i
$609$	973.598	−	544.931i	1.59868	−	0.894797i
$610$	−286.578	−	104.306i	−0.469800	−	0.170993i
$611$	−655.192	−	378.275i	−1.07233	−	0.619108i
$612$	21.9735	−	3.27307i	0.0359044	−	0.00534816i
$613$	−43.8571	−	75.9627i	−0.0715450	−	0.123920i	0.828034	−	0.560679i	$-0.189460\pi$
$613$	−43.8571	−	75.9627i	−0.0715450	−	0.123920i	−0.899579	+	0.436759i	$0.856126\pi$
$614$	−699.710	+	123.378i	−1.13959	+	0.200941i
$615$	249.964	+	215.488i	0.406445	+	0.350387i
$616$	506.348	−	184.295i	0.821993	−	0.299181i
$617$	679.824	+	119.871i	1.10182	+	0.194281i	0.694846	−	0.719159i	$-0.255472\pi$
$617$	679.824	+	119.871i	1.10182	+	0.194281i	0.406975	+	0.913439i	$0.366584\pi$
$618$	85.5663	+	104.780i	0.138457	+	0.169546i
$619$	531.346	−	445.852i	0.858393	−	0.720278i	−0.103228	−	0.994658i	$-0.532917\pi$
$619$	531.346	−	445.852i	0.858393	−	0.720278i	0.961621	+	0.274380i	$0.0884727\pi$
$620$			37.7678i			0.0609158i
$621$	108.232	+	338.965i	0.174286	+	0.545837i
$622$	925.860			1.48852
$623$	273.497	+	325.941i	0.438999	+	0.523179i
$624$	−117.080	−	719.998i	−0.187628	−	1.15384i
$625$	−74.1857	+	420.728i	−0.118697	+	0.673165i
$626$	−67.1313	−	184.442i	−0.107239	−	0.294635i
$627$	375.533	+	71.3914i	0.598936	+	0.113862i
$628$	2.14227	+	12.1494i	0.00341125	+	0.0193462i
$629$	−580.142	+	334.945i	−0.922324	+	0.532504i
$630$	−319.866	−	589.801i	−0.507723	−	0.936191i
$631$	−58.9015	+	102.020i	−0.0933463	+	0.161681i	−0.908917	−	0.416977i	$-0.863090\pi$
$631$	−58.9015	+	102.020i	−0.0933463	+	0.161681i	0.815571	+	0.578657i	$0.196423\pi$
$632$	4.38381	−	12.0444i	0.00693640	−	0.0190576i
$633$	69.1548	+	0.922048i	0.109249	+	0.00145663i
$634$	550.695	+	462.088i	0.868604	+	0.728846i
$635$	226.339	−	269.740i	0.356439	−	0.424788i
$636$	−30.8234	−	18.3481i	−0.0484644	−	0.0288492i
$637$	457.254	+	166.427i	0.717825	+	0.261267i
$638$	−518.510	−	299.362i	−0.812711	−	0.469219i
$639$	−169.590	−	507.669i	−0.265399	−	0.794474i
$640$	249.699	+	432.491i	0.390155	+	0.675768i
$641$	361.107	−	63.6729i	0.563349	−	0.0993337i	0.115281	−	0.993333i	$-0.463223\pi$
$641$	361.107	−	63.6729i	0.563349	−	0.0993337i	0.448068	+	0.893999i	$0.352112\pi$
$642$	526.267	−	183.638i	0.819731	−	0.286040i
$643$	−902.678	+	328.548i	−1.40385	+	0.510961i	−0.929320	−	0.369276i	$-0.879606\pi$
$643$	−902.678	+	328.548i	−1.40385	+	0.510961i	−0.474534	+	0.880237i	$0.657383\pi$
$644$	27.1973	+	4.79561i	0.0422318	+	0.00744660i
$645$	−11.3978	+	30.0620i	−0.0176710	+	0.0466078i
$646$	−268.844	+	225.587i	−0.416167	+	0.349206i
$647$			181.832i			0.281039i	0.990078	+	0.140519i	$0.0448772\pi$
$647$			181.832i			0.281039i	−0.990078	+	0.140519i	$0.955123\pi$
$648$	−400.090	−	532.010i	−0.617423	−	0.821003i
$649$	−30.9049			−0.0476192
$650$	127.666	+	152.146i	0.196409	+	0.234071i
$651$	924.234	+	350.417i	1.41971	+	0.538275i
$652$	−10.2907	+	58.3612i	−0.0157832	+	0.0895111i
$653$	−301.244	−	827.662i	−0.461324	−	1.26748i	−0.924491	−	0.381205i	$-0.875509\pi$
$653$	−301.244	−	827.662i	−0.461324	−	1.26748i	0.463167	−	0.886271i	$-0.346713\pi$
$654$	195.906	+	561.426i	0.299551	+	0.858449i
$655$	109.177	+	619.171i	0.166682	+	0.945300i
$656$	−330.638	+	190.894i	−0.504021	+	0.290997i
$657$	−94.7678	+	464.646i	−0.144243	+	0.707224i
$658$	402.509	−	697.167i	0.611717	−	1.05952i
$659$	−21.8046	+	59.9077i	−0.0330874	+	0.0909070i	−0.955136	−	0.296166i	$-0.904292\pi$
$659$	−21.8046	+	59.9077i	−0.0330874	+	0.0909070i	0.922049	+	0.387073i	$0.126514\pi$
$660$	11.5334	−	19.3752i	0.0174748	−	0.0293564i
$661$	−351.302	−	294.777i	−0.531471	−	0.445957i	0.337138	−	0.941455i	$-0.390541\pi$
$661$	−351.302	−	294.777i	−0.531471	−	0.445957i	−0.868609	+	0.495498i	$0.834985\pi$
$662$	444.792	−	530.083i	0.671892	−	0.800730i
$663$	6.78813	−	509.118i	0.0102385	−	0.767901i
$664$	−873.200	−	317.819i	−1.31506	−	0.478643i
$665$	−574.850	−	331.890i	−0.864436	−	0.499082i
$666$	952.204	+	584.147i	1.42974	+	0.877097i
$667$	−275.681	−	477.493i	−0.413315	−	0.715882i
$668$	−1.96517	+	0.346513i	−0.00294187	+	0.000518732i
$669$	105.385	−	554.343i	0.157526	−	0.828615i
$670$	−136.407	+	49.6480i	−0.203592	+	0.0741015i
$671$	−264.151	−	46.5770i	−0.393668	−	0.0694142i
$672$	−99.1511	+	16.1231i	−0.147546	+	0.0239927i
$673$	−840.742	+	705.467i	−1.24925	+	1.04824i	−0.252503	+	0.967596i	$0.581254\pi$
$673$	−840.742	+	705.467i	−1.24925	+	1.04824i	−0.996743	+	0.0806456i	$0.974302\pi$
$674$			778.465i			1.15499i
$675$	157.780	+	64.6836i	0.233749	+	0.0958276i
$676$	22.0924			0.0326811
$677$	315.404	+	375.883i	0.465884	+	0.555219i	0.946915	−	0.321485i	$-0.104182\pi$
$677$	315.404	+	375.883i	0.465884	+	0.555219i	−0.481031	+	0.876704i	$0.659737\pi$
$678$	73.5297	−	60.0466i	0.108451	−	0.0885643i
$679$	−56.7545	+	321.871i	−0.0835854	+	0.474036i
$680$	127.219	+	349.531i	0.187087	+	0.514016i
$681$	245.825	−	285.155i	0.360977	−	0.418729i
$682$	−92.1056	−	522.357i	−0.135052	−	0.765919i
$683$	684.465	−	395.176i	1.00215	−	0.578589i	0.0932631	−	0.995642i	$-0.470270\pi$
$683$	684.465	−	395.176i	1.00215	−	0.578589i	0.908882	+	0.417053i	$0.136937\pi$
$684$	−34.0942	−	13.4492i	−0.0498453	−	0.0196625i
$685$	−406.316	+	703.760i	−0.593162	+	1.02739i
$686$	111.952	−	307.585i	0.163195	−	0.448375i
$687$	−191.959	−	342.962i	−0.279416	−	0.499216i
$688$	−28.4913	−	23.9070i	−0.0414118	−	0.0347486i
$689$	−528.451	+	629.783i	−0.766983	+	0.914054i
$690$	−289.330	+	161.941i	−0.419319	+	0.234697i
$691$	202.870	+	73.8387i	0.293589	+	0.106858i	0.484616	−	0.874727i	$-0.338959\pi$
$691$	202.870	+	73.8387i	0.293589	+	0.106858i	−0.191027	+	0.981585i	$0.561182\pi$
$692$	−39.8221	−	22.9913i	−0.0575464	−	0.0332244i
$693$	−367.131	−	462.007i	−0.529771	−	0.666676i
$694$	−55.5671	−	96.2451i	−0.0800679	−	0.138682i
$695$	−374.014	+	65.9488i	−0.538150	+	0.0948904i
$696$	781.239	+	673.488i	1.12247	+	0.967655i
$697$	−250.419	+	91.1449i	−0.359281	+	0.130767i
$698$	−716.735	−	126.380i	−1.02684	−	0.181060i
$699$	−771.289	−	944.478i	−1.10342	−	1.35118i
$700$	10.1386	−	8.50730i	0.0144837	−	0.0121533i
$701$		−	503.242i		−	0.717891i	−0.933358	−	0.358946i	$-0.883136\pi$
$701$		−	503.242i		−	0.717891i	0.933358	−	0.358946i	$-0.116864\pi$
$702$	−751.710	+	394.796i	−1.07081	+	0.562388i
$703$	1105.16			1.57206
$704$	319.151	+	380.349i	0.453339	+	0.540268i
$705$	−97.1489	−	597.429i	−0.137800	−	0.847417i
$706$	−74.1294	+	420.409i	−0.104999	+	0.595480i
$707$	259.336	+	712.520i	0.366812	+	1.00781i
$708$	2.91103	+	0.553406i	0.00411162	+	0.000781647i
$709$	223.809	+	1269.28i	0.315668	+	1.79024i	0.568447	+	0.822720i	$0.307544\pi$
$709$	223.809	+	1269.28i	0.315668	+	1.79024i	−0.252779	+	0.967524i	$0.581345\pi$
$710$	431.936	−	249.379i	0.608361	−	0.351237i
$711$	−14.0320	−	0.374246i	−0.0197356	−	0.000526366i
$712$	−196.676	+	340.653i	−0.276230	+	0.478445i
$713$	167.062	−	459.000i	0.234309	−	0.643758i
$714$	541.735	+	7.22301i	0.758733	+	0.0101163i
$715$	−395.874	−	332.178i	−0.553671	−	0.464585i
$716$	32.0554	−	38.2021i	0.0447701	−	0.0533549i
$717$	−495.786	−	295.124i	−0.691473	−	0.411610i
$718$	367.203	+	133.651i	0.511424	+	0.186143i
$719$	497.326	+	287.131i	0.691691	+	0.399348i	0.804245	−	0.594298i	$-0.202570\pi$
$719$	497.326	+	287.131i	0.691691	+	0.399348i	−0.112554	+	0.993646i	$0.535903\pi$
$720$	386.916	−	436.902i	0.537384	−	0.606809i
$721$	−103.302	−	178.925i	−0.143277	−	0.248162i
$722$	−119.572	+	21.0837i	−0.165612	+	0.0292018i
$723$	−982.215	+	342.738i	−1.35853	+	0.474049i
$724$	−19.4440	+	7.07703i	−0.0268563	+	0.00977491i
$725$	−260.219	−	45.8836i	−0.358923	−	0.0632878i
$726$	137.416	−	362.437i	0.189278	−	0.499225i
$727$	427.936	−	359.081i	0.588633	−	0.493922i	−0.299136	−	0.954210i	$-0.596699\pi$
$727$	427.936	−	359.081i	0.588633	−	0.493922i	0.887769	+	0.460289i	$0.152254\pi$
$728$			1184.09i			1.62650i
$729$	−413.783	+	600.187i	−0.567604	+	0.823302i
$730$	−441.884			−0.605320
$731$	−16.6872	−	19.8871i	−0.0228279	−	0.0272053i
$732$	24.0472	+	9.11732i	0.0328513	+	0.0124554i
$733$	195.824	−	1110.57i	0.267155	−	1.51511i	−0.495674	−	0.868509i	$-0.665079\pi$
$733$	195.824	−	1110.57i	0.267155	−	1.51511i	0.762829	−	0.646601i	$-0.223810\pi$
$734$	105.617	+	290.180i	0.143892	+	0.395341i
$735$	128.261	+	367.568i	0.174504	+	0.500093i
$736$	8.62014	+	48.8872i	0.0117121	+	0.0664229i
$737$	−110.567	+	63.8358i	−0.150023	+	0.0866157i
$738$	332.690	+	294.627i	0.450800	+	0.399224i
$739$	−163.517	+	283.219i	−0.221268	+	0.383247i	−0.955193	−	0.295983i	$-0.904353\pi$
$739$	−163.517	+	283.219i	−0.221268	+	0.383247i	0.733926	+	0.679230i	$0.237686\pi$
$740$	22.2962	−	61.2582i	0.0301299	−	0.0827813i
$741$	−429.660	+	721.796i	−0.579839	+	0.974084i
$742$	−670.131	−	562.307i	−0.903141	−	0.757826i
$743$	239.908	−	285.911i	0.322891	−	0.384806i	−0.580043	−	0.814586i	$-0.696964\pi$
$743$	239.908	−	285.911i	0.322891	−	0.384806i	0.902934	+	0.429780i	$0.141409\pi$
$744$	−12.1825	+	913.704i	−0.0163743	+	1.22810i
$745$	−255.353	−	92.9408i	−0.342755	−	0.124753i
$746$	−86.7808	−	50.1029i	−0.116328	−	0.0671621i
$747$	−27.1322	+	1017.30i	−0.0363216	+	1.36184i
$748$	9.10361	+	15.7679i	0.0121706	+	0.0210801i
$749$	−838.337	+	147.821i	−1.11928	+	0.197358i
$750$	−147.147	+	774.020i	−0.196196	+	1.03203i
$751$	1084.18	−	394.608i	1.44364	−	0.525443i	0.502835	−	0.864383i	$-0.332290\pi$
$751$	1084.18	−	394.608i	1.44364	−	0.525443i	0.940808	+	0.338940i	$0.110068\pi$
$752$	689.572	+	121.590i	0.916984	+	0.161689i
$753$	1265.78	−	205.830i	1.68098	−	0.273347i
$754$	1007.86	−	845.698i	1.33669	−	1.12161i
$755$		−	498.796i		−	0.660657i
$756$	26.3082	+	50.0920i	0.0347992	+	0.0662592i
$757$	−372.849			−0.492535			−0.246268	−	0.969202i	$-0.579204\pi$
$757$	−372.849			−0.492535			−0.246268	+	0.969202i	$0.579204\pi$
$758$	−183.614	−	218.823i	−0.242235	−	0.288685i
$759$	−225.872	+	184.454i	−0.297592	+	0.243023i
$760$	106.559	−	604.328i	0.140210	−	0.795168i
$761$	−395.241	−	1085.91i	−0.519370	−	1.42696i	−0.871216	−	0.490900i	$-0.836668\pi$
$761$	−395.241	−	1085.91i	−0.519370	−	1.42696i	0.351846	−	0.936058i	$-0.385554\pi$
$762$	309.592	−	359.124i	0.406289	−	0.471291i
$763$	−157.697	−	894.345i	−0.206680	−	1.17214i
$764$	65.5851	−	37.8656i	0.0858444	−	0.0495623i
$765$	318.922	−	253.430i	0.416892	−	0.331281i
$766$	−110.333	+	191.102i	−0.144037	+	0.249480i
$767$	23.2274	−	63.8167i	0.0302834	−	0.0832030i
$768$	−66.0838	−	118.068i	−0.0860467	−	0.153735i
$769$	813.852	+	682.903i	1.05833	+	0.888041i	0.993944	−	0.109885i	$-0.0350482\pi$
$769$	813.852	+	682.903i	1.05833	+	0.888041i	0.0643812	+	0.997925i	$0.479493\pi$
$770$	353.459	−	421.236i	0.459038	−	0.547060i
$771$	−743.653	+	416.229i	−0.964530	+	0.539856i
$772$	−13.6684	−	4.97488i	−0.0177052	−	0.00644415i
$773$	808.848	+	466.989i	1.04638	+	0.604125i	0.921632	−	0.388064i	$-0.126856\pi$
$773$	808.848	+	466.989i	1.04638	+	0.604125i	0.124743	+	0.992189i	$0.460189\pi$
$774$	−15.8861	+	40.2718i	−0.0205246	+	0.0520308i
$775$	−117.044	−	202.725i	−0.151024	−	0.261581i
$776$	−297.563	+	52.4683i	−0.383457	+	0.0676138i
$777$	−1292.21	−	1113.99i	−1.66308	−	1.43370i
$778$	660.728	−	240.485i	0.849265	−	0.309107i
$779$	432.966	+	76.3435i	0.555797	+	0.0980020i
$780$	31.3404	+	38.3777i	0.0401800	+	0.0492022i
$781$	336.037	−	281.968i	0.430265	−	0.361035i
$782$		−	267.735i		−	0.342372i
$783$	428.485	−	1045.19i	0.547235	−	1.33485i
$784$	−450.363			−0.574443
$785$	145.405	+	173.287i	0.185229	+	0.220748i
$786$	135.883	+	835.632i	0.172880	+	1.06315i
$787$	142.512	−	808.227i	0.181083	−	1.02697i	−0.749803	−	0.661661i	$-0.769852\pi$
$787$	142.512	−	808.227i	0.181083	−	1.02697i	0.930886	−	0.365310i	$-0.119037\pi$
$788$	18.0776	+	49.6677i	0.0229411	+	0.0630301i
$789$	−1021.06	−	194.111i	−1.29412	−	0.246022i
$790$	−2.27132	−	12.8813i	−0.00287509	−	0.0163055i
$791$	−125.562	+	72.4931i	−0.158738	+	0.0916473i
$792$	285.274	−	465.019i	0.360194	−	0.587145i
$793$	294.708	−	510.450i	0.371637	−	0.643694i
$794$	489.078	−	1343.73i	0.615967	−	1.69236i
$795$	−657.680	−	8.76891i	−0.827270	−	0.0110301i
$796$	−0.940399	−	0.789088i	−0.00118141	−	0.000991317i
$797$	22.0398	−	26.2660i	0.0276534	−	0.0329561i	−0.752040	−	0.659117i	$-0.770930\pi$
$797$	22.0398	−	26.2660i	0.0276534	−	0.0329561i	0.779694	+	0.626161i	$0.215375\pi$
$798$	−768.038	−	457.187i	−0.962454	−	0.572916i
$799$	459.275	+	167.162i	0.574812	+	0.209215i
$800$	20.6028	+	11.8950i	0.0257535	+	0.0148688i
$801$	422.090	+	86.0882i	0.526954	+	0.107476i
$802$	−214.682	−	371.840i	−0.267683	−	0.463641i
$803$	−382.739	+	67.4873i	−0.476637	+	0.0840439i
$804$	11.5577	−	4.03299i	0.0143753	−	0.00501616i
$805$	475.848	−	173.195i	0.591116	−	0.215148i
$806$	1147.86	+	202.399i	1.42414	+	0.251115i
$807$	−316.832	+	835.653i	−0.392605	+	1.03551i
$808$	−536.985	+	450.584i	−0.664585	+	0.557653i
$809$			521.511i			0.644636i	0.946631	+	0.322318i	$0.104462\pi$
$809$			521.511i			0.644636i	−0.946631	+	0.322318i	$0.895538\pi$
$810$	−625.043	−	266.031i	−0.771659	−	0.328433i
$811$	−684.645			−0.844199			−0.422099	−	0.906550i	$-0.638707\pi$
$811$	−684.645			−0.844199			−0.422099	+	0.906550i	$0.638707\pi$
$812$	−56.3550	−	67.1613i	−0.0694028	−	0.0827110i
$813$	1034.20	+	392.109i	1.27207	+	0.482298i
$814$	−158.980	+	901.622i	−0.195307	+	1.10764i
$815$	371.650	+	1021.10i	0.456012	+	1.25288i
$816$	155.258	+	444.936i	0.190267	+	0.545265i
$817$	7.43718	+	42.1783i	0.00910303	+	0.0516259i
$818$	−748.021	+	431.870i	−0.914451	+	0.527958i
$819$	1229.94	−	410.870i	1.50176	−	0.501673i
$820$	12.9666	−	22.4588i	0.0158129	−	0.0273887i
$821$	−463.561	+	1273.62i	−0.564630	+	1.55131i	0.248140	+	0.968724i	$0.420181\pi$
$821$	−463.561	+	1273.62i	−0.564630	+	1.55131i	−0.812770	+	0.582585i	$0.802041\pi$
$822$	−559.711	+	940.271i	−0.680913	+	1.14388i
$823$	−498.544	−	418.328i	−0.605765	−	0.508297i	0.287528	−	0.957772i	$-0.407167\pi$
$823$	−498.544	−	418.328i	−0.605765	−	0.508297i	−0.893293	+	0.449475i	$0.851611\pi$
$824$	122.774	−	146.316i	0.148997	−	0.177568i
$825$	−1.86320	+	139.742i	−0.00225842	+	0.169385i
$826$	67.9051	+	24.7154i	0.0822096	+	0.0299218i
$827$	1042.15	+	601.688i	1.26016	+	0.727555i	0.973106	−	0.230359i	$-0.0739900\pi$
$827$	1042.15	+	601.688i	1.26016	+	0.727555i	0.287056	+	0.957914i	$0.407323\pi$
$828$	24.5786	−	13.3297i	0.0296843	−	0.0160986i
$829$	753.210	+	1304.60i	0.908577	+	1.57370i	0.816043	+	0.577992i	$0.196163\pi$
$829$	753.210	+	1304.60i	0.908577	+	1.57370i	0.0925344	+	0.995709i	$0.470503\pi$
$830$	−933.875	+	164.667i	−1.12515	+	0.198394i
$831$	158.486	−	833.669i	0.190718	−	1.00321i
$832$	−1025.26	+	373.165i	−1.23229	+	0.448516i
$833$	−309.580	−	54.5873i	−0.371645	−	0.0655310i
$834$	−504.769	+	82.0812i	−0.605238	+	0.0984188i
$835$	−28.0293	+	23.5194i	−0.0335680	+	0.0281669i
$836$		−	30.0376i		−	0.0359301i
$837$	953.315	−	304.395i	1.13897	−	0.363673i
$838$	−1119.86			−1.33635
$839$	38.2178	+	45.5462i	0.0455516	+	0.0542863i	0.788339	−	0.615241i	$-0.210941\pi$
$839$	38.2178	+	45.5462i	0.0455516	+	0.0542863i	−0.742788	+	0.669527i	$0.766497\pi$
$840$	−733.749	+	599.202i	−0.873511	+	0.713335i
$841$	−157.909	+	895.549i	−0.187764	+	1.06486i
$842$	−222.961	−	612.579i	−0.264799	−	0.727529i
$843$	550.677	−	638.779i	0.653235	−	0.757745i
$844$	−0.943711	−	5.35205i	−0.00111814	−	0.00634129i
$845$	350.819	−	202.546i	0.415171	−	0.239699i
$846$	−120.079	−	806.142i	−0.141938	−	0.952886i
$847$	−295.992	+	512.672i	−0.349459	+	0.605280i
$848$	260.243	−	715.013i	0.306891	−	0.843175i
$849$	639.171	+	1141.97i	0.752851	+	1.34508i
$850$	−98.2901	−	82.4752i	−0.115635	−	0.0970297i
$851$	−541.940	+	645.858i	−0.636827	+	0.758941i
$852$	−36.7015	+	20.5421i	−0.0430769	+	0.0241105i
$853$	330.344	+	120.235i	0.387273	+	0.140956i	0.528316	−	0.849048i	$-0.322823\pi$
$853$	330.344	+	120.235i	0.387273	+	0.140956i	−0.141043	+	0.990003i	$0.545046\pi$
$854$	543.152	+	313.589i	0.636009	+	0.367200i
$855$	−664.705	+	99.0115i	−0.777433	+	0.115803i
$856$	−393.491	−	681.546i	−0.459685	−	0.796198i
$857$	−1219.40	+	215.013i	−1.42287	+	0.250890i	−0.831507	−	0.555515i	$-0.812521\pi$
$857$	−1219.40	+	215.013i	−1.42287	+	0.250890i	−0.591363	+	0.806405i	$0.701410\pi$
$858$	−527.055	−	454.362i	−0.614283	−	0.529560i
$859$	249.859	−	90.9414i	0.290872	−	0.105869i	−0.192463	−	0.981304i	$-0.561647\pi$
$859$	249.859	−	90.9414i	0.290872	−	0.105869i	0.483335	+	0.875435i	$0.339425\pi$
$860$	2.48796	+	0.438694i	0.00289297	+	0.000510109i
$861$	−429.293	−	525.688i	−0.498598	−	0.610556i
$862$	169.134	−	141.921i	0.196211	−	0.164641i
$863$			297.514i			0.344744i	0.985032	+	0.172372i	$0.0551431\pi$
$863$			297.514i			0.344744i	−0.985032	+	0.172372i	$0.944857\pi$
$864$	−68.4367	+	75.2329i	−0.0792091	+	0.0870752i
$865$	−843.145			−0.974734
$866$	254.678	+	303.514i	0.294086	+	0.350478i
$867$	−86.3617	−	531.092i	−0.0996098	−	0.612563i
$868$	13.4873	−	76.4904i	0.0155384	−	0.0881225i
$869$	−3.93463	−	10.8103i	−0.00452777	−	0.0124400i
$870$	1034.08	+	196.586i	1.18860	+	0.225961i
$871$	−48.7176	−	276.291i	−0.0559329	−	0.317211i
$872$	727.078	−	419.779i	0.833805	−	0.481398i
$873$	157.752	+	290.880i	0.180701	+	0.333195i
$874$	−220.849	+	382.522i	−0.252688	+	0.437669i
$875$	411.552	−	1130.73i	0.470345	−	1.29226i
$876$	37.2599	+	0.496790i	0.0425341	+	0.000567112i
$877$	−276.515	−	232.024i	−0.315296	−	0.264565i	0.471381	−	0.881930i	$-0.343756\pi$
$877$	−276.515	−	232.024i	−0.315296	−	0.264565i	−0.786677	+	0.617365i	$0.788200\pi$
$878$	503.638	−	600.213i	0.573620	−	0.683613i
$879$	951.642	+	566.480i	1.08264	+	0.644459i
$880$	449.448	+	163.586i	0.510737	+	0.185893i
$881$	−782.766	−	451.930i	−0.888497	−	0.512974i	−0.0150464	−	0.999887i	$-0.504790\pi$
$881$	−782.766	−	451.930i	−0.888497	−	0.512974i	−0.873451	+	0.486913i	$0.838123\pi$
$882$	166.096	+	497.208i	0.188317	+	0.563728i
$883$	462.202	+	800.558i	0.523445	+	0.906634i	0.999628	+	0.0272872i	$0.00868687\pi$
$883$	462.202	+	800.558i	0.523445	+	0.906634i	−0.476182	+	0.879347i	$0.657980\pi$
$884$	−39.4019	+	6.94761i	−0.0445722	+	0.00785929i
$885$	51.2996	−	17.9007i	0.0579656	−	0.0202268i
$886$	1206.24	−	439.036i	1.36144	−	0.495525i
$887$	275.138	+	48.5142i	0.310189	+	0.0546947i	0.326576	−	0.945171i	$-0.394105\pi$
$887$	275.138	+	48.5142i	0.310189	+	0.0546947i	−0.0163867	+	0.999866i	$0.505216\pi$
$888$	559.164	−	1474.81i	0.629689	−	1.66082i
$889$	−554.727	+	465.471i	−0.623990	+	0.523590i
$890$			401.412i			0.451025i
$891$	−582.014	−	134.963i	−0.653215	−	0.151474i
$892$	−44.3400			−0.0497086
$893$	−518.293	−	617.678i	−0.580396	−	0.691689i
$894$	−342.147	−	129.723i	−0.382714	−	0.145104i
$895$	158.786	−	900.521i	0.177415	−	1.00617i
$896$	−351.263	−	965.087i	−0.392035	−	1.07711i
$897$	−211.126	−	605.044i	−0.235369	−	0.674519i
$898$	157.109	+	891.009i	0.174954	+	0.992215i
$899$	−1342.92	+	775.333i	−1.49379	+	0.862440i
$900$	2.67783	−	13.1294i	0.00297537	−	0.0145882i
$901$	265.556	−	459.957i	0.294735	−	0.510496i
$902$	−124.567	+	342.244i	−0.138100	+	0.379428i
$903$	33.8193	−	56.8137i	0.0374521	−	0.0629166i
$904$	−102.678	−	86.1571i	−0.113582	−	0.0953065i
$905$	−243.880	+	290.645i	−0.269480	+	0.321154i
$906$	8.95444	−	671.595i	0.00988349	−	0.741274i
$907$	555.388	+	202.145i	0.612335	+	0.222872i	0.629525	−	0.776981i	$-0.283250\pi$
$907$	555.388	+	202.145i	0.612335	+	0.222872i	−0.0171896	+	0.999852i	$0.505472\pi$
$908$	−25.6206	−	14.7921i	−0.0282166	−	0.0162908i
$909$	654.362	+	401.430i	0.719871	+	0.441617i
$910$	604.176	+	1046.46i	0.663930	+	1.14996i
$911$	−372.493	+	65.6805i	−0.408883	+	0.0720972i	−0.374307	−	0.927305i	$-0.622119\pi$
$911$	−372.493	+	65.6805i	−0.408883	+	0.0720972i	−0.0345765	+	0.999402i	$0.511008\pi$
$912$	145.197	−	763.765i	0.159207	−	0.837462i
$913$	−783.731	+	285.255i	−0.858413	+	0.312437i
$914$	−1631.90	−	287.748i	−1.78545	−	0.314823i
$915$	465.448	−	75.6872i	0.508686	−	0.0827182i
$916$	−23.6584	+	19.8517i	−0.0258279	+	0.0216722i
$917$		−	1292.98i		−	1.41002i
$918$	433.957	−	335.501i	0.472720	−	0.365470i
$919$	86.9159			0.0945766			0.0472883	−	0.998881i	$-0.484942\pi$
$919$	86.9159			0.0945766			0.0472883	+	0.998881i	$0.484942\pi$
$920$	300.917	+	358.619i	0.327084	+	0.389803i
$921$	850.933	−	694.898i	0.923923	−	0.754503i
$922$	−27.5966	+	156.508i	−0.0299313	+	0.169749i
$923$	329.690	+	905.816i	0.357194	+	0.981383i
$924$	−30.2775	+	35.1215i	−0.0327678	+	0.0380103i
$925$	70.1624	+	397.911i	0.0758513	+	0.430174i
$926$	1099.91	−	635.033i	1.18781	−	0.685781i
$927$	−194.584	−	76.7575i	−0.209907	−	0.0828020i
$928$	78.7963	−	136.479i	0.0849098	−	0.147068i
$929$	231.271	−	635.412i	0.248946	−	0.683975i	−0.750779	−	0.660553i	$-0.770322\pi$
$929$	231.271	−	635.412i	0.248946	−	0.683975i	0.999726	−	0.0234215i	$-0.00745597\pi$
$930$	455.447	+	813.721i	0.489728	+	0.874969i
$931$	397.280	+	333.357i	0.426724	+	0.358064i
$932$	−61.5914	+	73.4018i	−0.0660852	+	0.0787573i
$933$	−1249.25	+	699.215i	−1.33896	+	0.749427i
$934$	−238.712	−	86.8841i	−0.255580	−	0.0930236i
$935$	289.124	+	166.926i	0.309223	+	0.178530i
$936$	745.830	+	938.570i	0.796827	+	1.00275i
$937$	168.348	+	291.587i	0.179667	+	0.311192i	0.941766	−	0.336268i	$-0.109165\pi$
$937$	168.348	+	291.587i	0.179667	+	0.311192i	−0.762100	+	0.647460i	$0.775831\pi$
$938$	293.992	−	51.8387i	0.313424	−	0.0552651i
$939$	229.871	+	198.167i	0.244804	+	0.211040i
$940$	−44.6938	+	16.2672i	−0.0475466	+	0.0173055i
$941$	232.277	+	40.9567i	0.246841	+	0.0435247i	0.295699	−	0.955281i	$-0.404447\pi$
$941$	232.277	+	40.9567i	0.246841	+	0.0435247i	−0.0488587	+	0.998806i	$0.515558\pi$
$942$	192.667	+	235.930i	0.204530	+	0.250456i
$943$	−256.930	+	215.590i	−0.272460	+	0.228621i
$944$			62.8549i			0.0665836i
$945$	877.011	+	554.245i	0.928054	+	0.586502i
$946$	−35.4802			−0.0375055
$947$	411.104	+	489.935i	0.434112	+	0.517355i	0.938104	−	0.346354i	$-0.112580\pi$
$947$	411.104	+	489.935i	0.434112	+	0.517355i	−0.503992	+	0.863708i	$0.668136\pi$
$948$	0.177038	+	1.08871i	0.000186748	+	0.00114843i
$949$	148.301	−	841.055i	0.156271	−	0.886254i
$950$	72.3984	+	198.913i	0.0762088	+	0.209382i
$951$	−1092.02	−	207.600i	−1.14828	−	0.218297i
$952$	−132.832	−	753.330i	−0.139530	−	0.791313i
$953$	−742.976	+	428.957i	−0.779618	+	0.450112i	−0.836295	−	0.548280i	$-0.815283\pi$
$953$	−742.976	+	428.957i	−0.779618	+	0.450112i	0.0566772	+	0.998393i	$0.481949\pi$
$954$	−885.364	−	23.6135i	−0.928055	−	0.0247521i
$955$	694.310	−	1202.58i	0.727027	−	1.25925i
$956$	−15.5066	+	42.6041i	−0.0162203	+	0.0445650i
$957$	925.697	+	12.3424i	0.967291	+	0.0128970i
$958$	234.334	+	196.629i	0.244607	+	0.205250i
$959$	1074.22	−	1280.21i	1.12015	−	1.33494i
$960$	−750.070	−	446.491i	−0.781322	−	0.465094i
$961$	−387.860	−	141.169i	−0.403600	−	0.146898i
$962$	−1742.31	−	1005.92i	−1.81113	−	1.04566i
$963$	−571.400	+	645.220i	−0.593354	+	0.670010i
$964$	40.8728	+	70.7938i	0.0423992	+	0.0734376i
$965$	−262.659	+	46.3138i	−0.272185	+	0.0479936i
$966$	643.806	−	224.652i	0.666466	−	0.232559i
$967$	−538.010	+	195.820i	−0.556371	+	0.202502i	−0.604875	−	0.796321i	$-0.706777\pi$
$967$	−538.010	+	195.820i	−0.556371	+	0.202502i	0.0485042	+	0.998823i	$0.484555\pi$
$968$	−538.962	−	95.0335i	−0.556779	−	0.0981751i
$969$	192.383	−	507.414i	0.198537	−	0.523647i
$970$	−236.205	+	198.200i	−0.243511	+	0.204330i
$971$			140.513i			0.144710i	0.997379	+	0.0723548i	$0.0230514\pi$
$971$			140.513i			0.144710i	−0.997379	+	0.0723548i	$0.976949\pi$
$972$	52.4050	+	23.1346i	0.0539146	+	0.0238010i
$973$	781.035			0.802708
$974$	870.739	+	1037.71i	0.893983	+	1.06541i
$975$	−287.159	−	108.874i	−0.294522	−	0.111666i
$976$	−94.7290	+	537.235i	−0.0970584	+	0.550446i
$977$	−528.635	−	1452.41i	−0.541079	−	1.48660i	−0.845453	−	0.534050i	$-0.820669\pi$
$977$	−528.635	−	1452.41i	−0.541079	−	1.48660i	0.304373	−	0.952553i	$-0.401553\pi$
$978$	482.070	+	1381.51i	0.492914	+	1.41259i
$979$	61.3063	+	347.685i	0.0626213	+	0.355143i
$980$	26.4927	−	15.2956i	0.0270334	−	0.0156077i
$981$	−688.326	−	609.574i	−0.701657	−	0.621380i
$982$	40.9588	−	70.9427i	0.0417095	−	0.0722430i
$983$	359.214	−	986.932i	0.365426	−	1.00400i	−0.611654	−	0.791126i	$-0.709495\pi$
$983$	359.214	−	986.932i	0.365426	−	1.00400i	0.977080	−	0.212874i	$-0.0682824\pi$
$984$	320.941	−	539.156i	0.326159	−	0.547923i
$985$	742.423	+	622.967i	0.753729	+	0.632454i
$986$	−546.342	+	651.105i	−0.554099	+	0.660350i
$987$	−16.5951	+	1244.65i	−0.0168137	+	1.26105i
$988$	62.0258	+	22.5755i	0.0627791	+	0.0228497i
$989$	−28.2961	−	16.3368i	−0.0286109	−	0.0165185i
$990$	14.8432	−	556.529i	0.0149931	−	0.562151i
$991$	−255.730	−	442.938i	−0.258053	−	0.446961i	0.707667	−	0.706546i	$-0.249748\pi$
$991$	−255.730	−	442.938i	−0.258053	−	0.446961i	−0.965720	+	0.259585i	$0.916414\pi$
$992$	137.492	−	24.2435i	0.138601	−	0.0244390i
$993$	−199.830	+	1051.14i	−0.201238	+	1.05855i
$994$	−963.848	+	350.812i	−0.969666	+	0.352930i
$995$	−22.1676	−	3.90874i	−0.0222790	−	0.00392839i
$996$	78.9300	−	12.8349i	0.0792470	−	0.0128865i
$997$	250.278	−	210.008i	0.251031	−	0.210640i	−0.508585	−	0.861012i	$-0.669831\pi$
$997$	250.278	−	210.008i	0.251031	−	0.210640i	0.759616	+	0.650371i	$0.225387\pi$
$998$			931.987i			0.933855i
$999$	−1725.95	−	69.0694i	−1.72767	−	0.0691385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.3.f.a.5.2	✓	30
3.2	odd	2		81.3.f.a.44.4		30
4.3	odd	2		432.3.bc.a.113.1		30
9.2	odd	6		243.3.f.a.53.4		30
9.4	even	3		243.3.f.c.215.4		30
9.5	odd	6		243.3.f.b.215.2		30
9.7	even	3		243.3.f.d.53.2		30
27.2	odd	18		243.3.f.d.188.2		30
27.4	even	9		729.3.b.a.728.9		30
27.7	even	9		243.3.f.b.26.2		30
27.11	odd	18	inner	27.3.f.a.11.2	yes	30
27.16	even	9		81.3.f.a.35.4		30
27.20	odd	18		243.3.f.c.26.4		30
27.23	odd	18		729.3.b.a.728.22		30
27.25	even	9		243.3.f.a.188.4		30
108.11	even	18		432.3.bc.a.65.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.5.2	✓	30	1.1	even	1	trivial
27.3.f.a.11.2	yes	30	27.11	odd	18	inner
81.3.f.a.35.4		30	27.16	even	9
81.3.f.a.44.4		30	3.2	odd	2
243.3.f.a.53.4		30	9.2	odd	6
243.3.f.a.188.4		30	27.25	even	9
243.3.f.b.26.2		30	27.7	even	9
243.3.f.b.215.2		30	9.5	odd	6
243.3.f.c.26.4		30	27.20	odd	18
243.3.f.c.215.4		30	9.4	even	3
243.3.f.d.53.2		30	9.7	even	3
243.3.f.d.188.2		30	27.2	odd	18
432.3.bc.a.65.1		30	108.11	even	18
432.3.bc.a.113.1		30	4.3	odd	2
729.3.b.a.728.9		30	27.4	even	9
729.3.b.a.728.22		30	27.23	odd	18

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24712 - 1.48626i) q^{2} +(2.80515 + 1.06355i) q^{3} +(0.0409354 - 0.232156i) q^{4} +(-1.47839 - 4.06185i) q^{5} +(-1.91764 - 5.49555i) q^{6} +(1.54363 + 8.75434i) q^{7} +(-7.11704 + 4.10903i) q^{8} +(6.73771 + 5.96685i) q^{9} +(-4.19322 + 7.26288i) q^{10} +(-2.52275 + 6.93119i) q^{11} +(0.361741 - 0.607696i) q^{12} +(-12.4164 - 10.4186i) q^{13} +(11.0861 - 13.2119i) q^{14} +(0.172883 - 12.9664i) q^{15} +(14.0968 + 5.13081i) q^{16} +(9.06825 + 5.23555i) q^{17} +(0.465550 - 17.4553i) q^{18} +(-8.63742 - 14.9604i) q^{19} +(-1.00350 + 0.176945i) q^{20} +(-4.98060 + 26.1989i) q^{21} +(13.4477 - 4.89456i) q^{22} +(12.9785 + 2.28846i) q^{23} +(-24.3345 + 3.95708i) q^{24} +(4.83813 - 4.05967i) q^{25} +31.4473i q^{26} +(12.5542 + 23.9038i) q^{27} +2.09556 q^{28} +(-26.8925 - 32.0493i) q^{29} +(-19.4871 + 15.9137i) q^{30} +(6.43612 - 36.5011i) q^{31} +(1.28832 + 3.53963i) q^{32} +(-14.4484 + 16.7599i) q^{33} +(-3.52779 - 20.0071i) q^{34} +(33.2767 - 19.2123i) q^{35} +(1.66105 - 1.31995i) q^{36} +(-31.9875 + 55.4041i) q^{37} +(-11.4632 + 31.4949i) q^{38} +(-23.7492 - 42.4314i) q^{39} +(27.2120 + 22.8336i) q^{40} +(-16.3590 + 19.4958i) q^{41} +(45.1498 - 25.2707i) q^{42} +(-2.32975 - 0.847961i) q^{43} +(1.50585 + 0.869403i) q^{44} +(14.2755 - 36.1889i) q^{45} +(-12.7845 - 22.1433i) q^{46} +(45.9670 - 8.10521i) q^{47} +(34.0867 + 29.3853i) q^{48} +(-28.2107 + 10.2679i) q^{49} +(-12.0674 - 2.12781i) q^{50} +(19.8695 + 24.3311i) q^{51} +(-2.92703 + 2.45607i) q^{52} -50.7217i q^{53} +(19.8706 - 48.4696i) q^{54} +31.8831 q^{55} +(-46.9579 - 55.9622i) q^{56} +(-8.31801 - 51.1526i) q^{57} +(-14.0953 + 79.9384i) q^{58} +(1.43303 + 3.93723i) q^{59} +(-3.00316 - 0.570923i) q^{60} +(6.31465 + 35.8121i) q^{61} +(-62.2766 + 35.9554i) q^{62} +(-41.8353 + 68.1948i) q^{63} +(33.6571 - 58.2957i) q^{64} +(-23.9626 + 65.8366i) q^{65} +(42.9284 + 0.572369i) q^{66} +(13.2595 + 11.1260i) q^{67} +(1.58668 - 1.89093i) q^{68} +(33.9727 + 20.2228i) q^{69} +(-70.0545 - 25.4977i) q^{70} +(-51.5041 - 29.7359i) q^{71} +(-72.4705 - 14.7809i) q^{72} +(26.3451 + 45.6310i) q^{73} +(122.237 - 21.5537i) q^{74} +(17.8893 - 6.24237i) q^{75} +(-3.82674 + 1.39282i) q^{76} +(-64.5722 - 11.3858i) q^{77} +(-33.4459 + 88.2143i) q^{78} +(-1.19477 + 1.00253i) q^{79} -64.8443i q^{80} +(9.79348 + 80.4058i) q^{81} +49.3774 q^{82} +(72.6820 + 86.6190i) q^{83} +(5.87837 + 2.22874i) q^{84} +(7.85961 - 44.5741i) q^{85} +(1.64519 + 4.52012i) q^{86} +(-41.3514 - 118.505i) q^{87} +(-10.5259 - 59.6956i) q^{88} +(41.4518 - 23.9322i) q^{89} +(-71.5892 + 23.9148i) q^{90} +(72.0419 - 124.780i) q^{91} +(1.06256 - 2.91936i) q^{92} +(56.8751 - 95.5457i) q^{93} +(-69.3726 - 58.2105i) q^{94} +(-47.9976 + 57.2013i) q^{95} +(-0.150656 + 11.2994i) q^{96} +(34.5497 + 12.5750i) q^{97} +(50.4428 + 29.1232i) q^{98} +(-58.3549 + 31.6475i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20}+ \cdots + 513 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8 - 3 * q^10 - 6 * q^11 - 15 * q^12 - 6 * q^13 - 15 * q^14 - 9 * q^15 - 18 * q^16 - 9 * q^17 + 63 * q^18 - 3 * q^19 + 213 * q^20 + 132 * q^21 - 42 * q^22 + 120 * q^23 + 144 * q^24 - 15 * q^25 - 90 * q^27 - 12 * q^28 - 168 * q^29 - 243 * q^30 + 39 * q^31 - 360 * q^32 - 207 * q^33 + 54 * q^34 - 252 * q^35 - 360 * q^36 - 3 * q^37 - 84 * q^38 + 15 * q^39 - 33 * q^40 + 228 * q^41 + 486 * q^42 - 96 * q^43 + 639 * q^44 + 477 * q^45 - 3 * q^46 + 399 * q^47 + 453 * q^48 - 78 * q^49 + 303 * q^50 + 36 * q^51 - 9 * q^52 - 54 * q^54 - 12 * q^55 - 393 * q^56 - 192 * q^57 + 129 * q^58 - 474 * q^59 - 846 * q^60 + 138 * q^61 - 900 * q^62 - 585 * q^63 - 51 * q^64 - 411 * q^65 - 423 * q^66 + 354 * q^67 + 99 * q^68 + 99 * q^69 + 489 * q^70 + 315 * q^71 + 720 * q^72 - 66 * q^73 + 321 * q^74 + 255 * q^75 + 258 * q^76 + 201 * q^77 + 180 * q^78 + 30 * q^79 + 36 * q^81 - 12 * q^82 - 33 * q^83 - 588 * q^84 - 261 * q^85 - 258 * q^86 - 279 * q^87 - 642 * q^88 + 72 * q^89 + 288 * q^90 + 96 * q^91 - 3 * q^92 + 591 * q^93 - 861 * q^94 + 681 * q^95 + 270 * q^96 - 582 * q^97 + 882 * q^98 + 513 * q^99

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