LMFDB - Embedded newform 27.3.f.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,3,Mod(2,27)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			11.2
Character	$\chi$	$=$	27.11
Dual form			27.3.f.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24712 + 1.48626i) q^{2} +(2.80515 - 1.06355i) q^{3} +(0.0409354 + 0.232156i) q^{4} +(-1.47839 + 4.06185i) q^{5} +(-1.91764 + 5.49555i) q^{6} +(1.54363 - 8.75434i) q^{7} +(-7.11704 - 4.10903i) q^{8} +(6.73771 - 5.96685i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8	\( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20} + 132 q^{21} - 42 q^{22} + 120 q^{23} + 144 q^{24} - 15 q^{25} - 90 q^{27} - 12 q^{28} - 168 q^{29} - 243 q^{30} + 39 q^{31} - 360 q^{32} - 207 q^{33} + 54 q^{34} - 252 q^{35} - 360 q^{36} - 3 q^{37} - 84 q^{38} + 15 q^{39} - 33 q^{40} + 228 q^{41} + 486 q^{42} - 96 q^{43} + 639 q^{44} + 477 q^{45} - 3 q^{46} + 399 q^{47} + 453 q^{48} - 78 q^{49} + 303 q^{50} + 36 q^{51} - 9 q^{52} - 54 q^{54} - 12 q^{55} - 393 q^{56} - 192 q^{57} + 129 q^{58} - 474 q^{59} - 846 q^{60} + 138 q^{61} - 900 q^{62} - 585 q^{63} - 51 q^{64} - 411 q^{65} - 423 q^{66} + 354 q^{67} + 99 q^{68} + 99 q^{69} + 489 q^{70} + 315 q^{71} + 720 q^{72} - 66 q^{73} + 321 q^{74} + 255 q^{75} + 258 q^{76} + 201 q^{77} + 180 q^{78} + 30 q^{79} + 36 q^{81} - 12 q^{82} - 33 q^{83} - 588 q^{84} - 261 q^{85} - 258 q^{86} - 279 q^{87} - 642 q^{88} + 72 q^{89} + 288 q^{90} + 96 q^{91} - 3 q^{92} + 591 q^{93} - 861 q^{94} + 681 q^{95} + 270 q^{96} - 582 q^{97} + 882 q^{98} + 513 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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	−0.981678	−	0.190547i	$-0.938974\pi$
$2$	−1.24712	+	1.48626i	−0.623559	+	0.743128i	0.358119	+	0.933676i	$0.383418\pi$
$3$	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	0.699531	+	0.714602i	$0.253392\pi$
$5$	−1.47839	+	4.06185i	−0.295679	+	0.812370i	−0.995209	+	0.0977676i	$0.968830\pi$
$6$	−1.91764	+	5.49555i	−0.319606	+	0.915924i
$7$	1.54363	−	8.75434i	0.220518	−	1.25062i	−0.650552	−	0.759462i	$-0.725463\pi$
$7$	1.54363	−	8.75434i	0.220518	−	1.25062i	0.871070	−	0.491158i	$-0.163426\pi$
$8$	−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	0.770634	−	0.637278i	$-0.219940\pi$
$11$	−2.52275	−	6.93119i	−0.229341	−	0.630108i	−0.999974	+	0.00717020i	$0.997718\pi$
$12$	0.361741	+	0.607696i	0.0301450	+	0.0506413i
$13$	−12.4164	+	10.4186i	−0.955111	+	0.801434i	−0.980151	−	0.198253i	$-0.936473\pi$
$13$	−12.4164	+	10.4186i	−0.955111	+	0.801434i	0.0250395	+	0.999686i	$0.492029\pi$
$14$	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	−0.208984	−	0.977919i	$-0.567016\pi$
$17$	9.06825	−	5.23555i	0.533426	−	0.307974i	0.742411	+	0.669945i	$0.233682\pi$
$18$	0.465550	+	17.4553i	0.0258639	+	0.969740i
$19$	−8.63742	+	14.9604i	−0.454601	+	0.787392i	−0.998665	−	0.0516517i	$-0.983551\pi$
$19$	−8.63742	+	14.9604i	−0.454601	+	0.787392i	0.544064	+	0.839044i	$0.316885\pi$
$20$	−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	0.115772	−	0.993276i	$-0.463066\pi$
$23$	12.9785	−	2.28846i	0.564282	−	0.0994981i	0.448510	+	0.893778i	$0.351955\pi$
$24$	−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	0.0668885	+	0.997760i	$0.478693\pi$
$29$	−26.8925	+	32.0493i	−0.927329	+	1.10515i	−0.994217	+	0.107387i	$0.965752\pi$
$30$	−19.4871	−	15.9137i	−0.649569	−	0.530458i
$31$	6.43612	+	36.5011i	0.207617	+	1.17745i	0.893268	+	0.449524i	$0.148406\pi$
$31$	6.43612	+	36.5011i	0.207617	+	1.17745i	−0.685651	+	0.727930i	$0.740483\pi$
$32$	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	−0.867515	−	0.497411i	$-0.834284\pi$
$37$	−31.9875	−	55.4041i	−0.864528	−	1.49741i	0.00298644	−	0.999996i	$-0.499049\pi$
$38$	−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	0.528715	−	0.848799i	$-0.322674\pi$
$41$	−16.3590	−	19.4958i	−0.398999	−	0.475508i	−0.927714	+	0.373291i	$0.878229\pi$
$42$	45.1498	+	25.2707i	1.07499	+	0.601684i
$43$	−2.32975	+	0.847961i	−0.0541803	+	0.0197200i	−0.368968	−	0.929442i	$-0.620289\pi$
$43$	−2.32975	+	0.847961i	−0.0541803	+	0.0197200i	0.314788	+	0.949162i	$0.398067\pi$
$44$	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	0.639738	−	0.768593i	$-0.279043\pi$
$47$	45.9670	+	8.10521i	0.978020	+	0.172451i	0.338282	+	0.941045i	$0.390154\pi$
$48$	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	$0.158822\pi$
$53$			50.7217i			0.957013i	−0.878084	+	0.478507i	$0.841178\pi$
$54$	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	−0.926956	−	0.375171i	$-0.877584\pi$
$59$	1.43303	−	3.93723i	0.0242887	−	0.0667327i	0.951244	+	0.308438i	$0.0998063\pi$
$60$	−3.00316	+	0.570923i	−0.0500527	+	0.00951538i
$61$	6.31465	−	35.8121i	0.103519	−	0.587084i	−0.888283	−	0.459297i	$-0.848101\pi$
$61$	6.31465	−	35.8121i	0.103519	−	0.587084i	0.991802	−	0.127787i	$-0.0407875\pi$
$62$	−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	−0.538451	−	0.842657i	$-0.680990\pi$
$67$	13.2595	−	11.1260i	0.197902	−	0.166060i	0.736354	+	0.676597i	$0.236546\pi$
$68$	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	−0.816740	−	0.577005i	$-0.804221\pi$
$71$	−51.5041	+	29.7359i	−0.725410	+	0.418815i	0.0913309	+	0.995821i	$0.470888\pi$
$72$	−72.4705	+	14.7809i	−1.00653	+	0.205290i
$73$	26.3451	−	45.6310i	0.360892	−	0.625083i	−0.627216	−	0.778845i	$-0.715806\pi$
$73$	26.3451	−	45.6310i	0.360892	−	0.625083i	0.988108	+	0.153762i	$0.0491391\pi$
$74$	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	0.635194	−	0.772352i	$-0.280920\pi$
$79$	−1.19477	−	1.00253i	−0.0151237	−	0.0126903i	−0.650318	+	0.759662i	$0.725364\pi$
$80$			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	−0.123002	−	0.992406i	$-0.539252\pi$
$83$	72.6820	−	86.6190i	0.875686	−	1.04360i	0.998689	−	0.0511958i	$-0.0163033\pi$
$84$	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	0.714459	−	0.699677i	$-0.246673\pi$
$89$	41.4518	+	23.9322i	0.465750	+	0.268901i	−0.248709	+	0.968578i	$0.580006\pi$
$90$	−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	−0.157731	−	0.987482i	$-0.550418\pi$
$97$	34.5497	−	12.5750i	0.356182	−	0.129640i	0.513913	+	0.857843i	$0.328196\pi$
$98$	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	0.573260	−	0.819374i	$-0.305679\pi$
$101$	84.0022	+	14.8119i	0.831705	+	0.146652i	0.258445	+	0.966026i	$0.416790\pi$
$102$	11.3826	+	59.8749i	0.111594	+	0.587008i
$103$	−21.8401	−	7.94915i	−0.212040	−	0.0771762i	0.233816	−	0.972281i	$-0.424879\pi$
$103$	−21.8401	−	7.94915i	−0.212040	−	0.0771762i	−0.445856	+	0.895105i	$0.647101\pi$
$104$	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	$-0.852319\pi$
$107$		−	95.7625i		−	0.894977i	0.894290	−	0.447488i	$-0.147681\pi$
$108$	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	−0.912559	−	0.408944i	$-0.865897\pi$
$113$	5.57835	−	15.3264i	0.0493660	−	0.135632i	0.961925	+	0.273312i	$0.0881193\pi$
$114$	−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	−0.659920	−	0.751336i	$-0.729410\pi$
$127$	40.7309	−	70.5479i	0.320715	−	0.555495i	0.980636	+	0.195840i	$0.0627433\pi$
$128$	−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	−0.691159	−	0.722703i	$-0.742899\pi$
$131$	−143.243	+	25.2576i	−1.09346	+	0.192806i	−0.402298	+	0.915509i	$0.631788\pi$
$132$	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	0.116248	+	0.993220i	$0.462913\pi$
$137$	−120.843	+	144.016i	−0.882069	+	1.05121i	−0.998317	+	0.0579889i	$0.981531\pi$
$138$	−12.3117	+	75.7123i	−0.0892152	+	0.548640i
$139$	15.2570	+	86.5267i	0.109762	+	0.622494i	0.989211	+	0.146500i	$0.0468007\pi$
$139$	15.2570	+	86.5267i	0.109762	+	0.622494i	−0.879448	+	0.475995i	$0.842088\pi$
$140$	−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	0.884407	−	0.466717i	$-0.154563\pi$
$149$	40.4096	+	48.1582i	0.271205	+	0.323210i	−0.613202	+	0.789926i	$0.710119\pi$
$150$	−31.5879	+	18.8032i	−0.210586	+	0.125355i
$151$	108.435	−	39.4672i	0.718114	−	0.261372i	0.0429892	−	0.999076i	$-0.486312\pi$
$151$	108.435	−	39.4672i	0.718114	−	0.261372i	0.675125	+	0.737703i	$0.264090\pi$
$152$	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	0.180623	−	0.983552i	$-0.442189\pi$
$157$	−49.1767	−	17.8989i	−0.313228	−	0.114006i	−0.493850	+	0.869547i	$0.664411\pi$
$158$	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	−0.948059	−	0.318095i	$-0.896957\pi$
$167$	−2.89515	+	7.95437i	−0.0173363	+	0.0476310i	0.930723	+	0.365726i	$0.119179\pi$
$168$	−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	0.968948	+	0.247264i	$0.0795316\pi$
$173$	66.7138	+	183.295i	0.385629	+	1.05951i	−0.583319	+	0.812243i	$0.698246\pi$
$174$	−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	0.108374	−	0.994110i	$-0.465436\pi$
$179$	183.204	−	105.773i	1.02349	−	0.590910i	0.915112	+	0.403200i	$0.132102\pi$
$180$	−7.81711	+	4.79555i	−0.0434284	+	0.0266419i
$181$	−43.8874	+	76.0153i	−0.242472	+	0.419974i	−0.961418	−	0.275092i	$-0.911292\pi$
$181$	−43.8874	+	76.0153i	−0.242472	+	0.419974i	0.718946	+	0.695066i	$0.244625\pi$
$182$	−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	0.126079	−	0.992020i	$-0.459761\pi$
$191$	206.497	−	246.093i	1.08113	−	1.28845i	0.955056	−	0.296426i	$-0.0957947\pi$
$192$	156.414	+	127.732i	0.814654	+	0.665271i
$193$	10.7145	+	60.7650i	0.0555156	+	0.314845i	0.999902	−	0.0139930i	$-0.00445425\pi$
$193$	10.7145	+	60.7650i	0.0555156	+	0.314845i	−0.944387	+	0.328838i	$0.893343\pi$
$194$	−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	−0.0816805	−	0.996659i	$-0.526029\pi$
$197$	−194.174	−	112.106i	−0.985652	−	0.569067i	−0.903972	+	0.427592i	$0.859362\pi$
$198$	119.812	−	47.2622i	0.605110	−	0.238698i
$199$	2.60375	+	4.50982i	0.0130842	+	0.0226624i	0.872493	−	0.488626i	$-0.162502\pi$
$199$	2.60375	+	4.50982i	0.0130842	+	0.0226624i	−0.859409	+	0.511288i	$0.829168\pi$
$200$	−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	0.392844	−	0.919605i	$-0.371491\pi$
$211$	21.6633	+	7.88481i	0.102670	+	0.0373688i	−0.290174	+	0.956974i	$0.593713\pi$
$212$	−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	0.819715	+	0.572771i	$0.194132\pi$
$223$	−32.6616	+	185.233i	−0.146464	+	0.830641i	−0.966180	+	0.257870i	$0.916979\pi$
$224$	−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	0.997621	−	0.0689410i	$-0.0219620\pi$
$227$	42.9222	+	117.928i	0.189085	+	0.519505i	−0.808536	+	0.588446i	$0.799740\pi$
$228$	−12.2159	+	0.162876i	−0.0535785	+	0.000714368i
$229$	−100.359	+	84.2111i	−0.438248	+	0.367734i	−0.835053	−	0.550169i	$-0.814563\pi$
$229$	−100.359	+	84.2111i	−0.438248	+	0.367734i	0.396805	+	0.917903i	$0.370119\pi$
$230$	−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	−0.510848	+	0.859671i	$0.670669\pi$
$233$	−352.009	+	203.233i	−1.51077	+	0.872243i	−0.999921	+	0.0125723i	$0.995998\pi$
$234$	−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	−0.555214	−	0.831707i	$-0.687364\pi$
$239$	−189.404	+	33.3970i	−0.792484	+	0.139736i	−0.237270	+	0.971444i	$0.576253\pi$
$240$	68.9654	+	181.898i	0.287356	+	0.757908i
$241$	−265.638	−	222.896i	−1.10223	−	0.924881i	−0.104658	−	0.994508i	$-0.533375\pi$
$241$	−265.638	−	222.896i	−1.10223	−	0.924881i	−0.997573	+	0.0696270i	$0.977819\pi$
$242$			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	0.999600	−	0.0282966i	$-0.00900829\pi$
$251$	370.198	+	213.734i	1.47489	+	0.851530i	0.475294	+	0.879827i	$0.342342\pi$
$252$	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	0.283176	−	0.959068i	$-0.408612\pi$
$257$	−182.597	−	217.611i	−0.710495	−	0.846735i	−0.993671	+	0.112333i	$0.964168\pi$
$258$	−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	−0.517983	−	0.855391i	$-0.673317\pi$
$263$	−341.187	−	60.1605i	−1.29729	−	0.228747i	−0.779306	+	0.626643i	$0.784428\pi$
$264$	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	$-0.813209\pi$
$269$		−	297.900i		−	1.10743i	0.832705	−	0.553717i	$-0.186791\pi$
$270$	−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	0.758099	+	0.652139i	$0.226128\pi$
$277$	−49.1193	+	278.569i	−0.177326	+	1.00566i	−0.935425	+	0.353525i	$0.884983\pi$
$278$	−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	0.984763	+	0.173902i	$0.0556377\pi$
$281$	96.1506	+	264.172i	0.342173	+	0.940112i	−0.642590	+	0.766210i	$0.722140\pi$
$282$	−132.690	+	237.071i	−0.470534	+	0.840676i
$283$	334.168	−	280.400i	1.18081	−	0.990814i	0.180833	−	0.983514i	$-0.442121\pi$
$283$	334.168	−	280.400i	1.18081	−	0.990814i	0.999973	−	0.00730054i	$-0.00232386\pi$
$284$	−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	0.485539	−	0.874215i	$-0.338623\pi$
$293$	363.553	−	64.1042i	1.24080	−	0.218786i	0.755256	+	0.655429i	$0.227512\pi$
$294$	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	0.993344	+	0.115189i	$0.0367475\pi$
$307$	183.104	+	317.145i	0.596429	+	1.03304i	−0.396915	+	0.917855i	$0.629919\pi$
$308$	−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	−0.984491	−	0.175438i	$-0.943866\pi$
$311$	−306.742	−	365.561i	−0.986308	−	1.17544i	−0.00181732	−	0.999998i	$-0.500578\pi$
$312$	343.376	−	204.400i	1.10056	−	0.655128i
$313$	95.0647	−	34.6007i	0.303721	−	0.110545i	−0.185664	−	0.982613i	$-0.559444\pi$
$313$	95.0647	−	34.6007i	0.303721	−	0.110545i	0.489385	+	0.872068i	$0.337221\pi$
$314$	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	−0.434639	−	0.900605i	$-0.643124\pi$
$317$	−364.896	−	64.3410i	−1.15109	−	0.202968i	−0.716452	+	0.697636i	$0.754235\pi$
$318$	−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	−0.736109	−	0.676863i	$-0.763339\pi$
$331$	61.9327	−	351.238i	0.187108	−	1.06114i	0.923217	−	0.384279i	$-0.125550\pi$
$332$	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	−0.972510	−	0.232862i	$-0.925191\pi$
$337$	−307.364	+	257.909i	−0.912059	+	0.765309i	0.0604502	+	0.998171i	$0.480746\pi$
$338$	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	−0.0917726	−	0.995780i	$-0.529253\pi$
$347$	56.4104	−	9.94668i	0.162566	−	0.0286648i	0.254339	+	0.967115i	$0.418142\pi$
$348$	−29.2043	−	4.74896i	−0.0839205	−	0.0136464i
$349$	287.357	+	241.121i	0.823371	+	0.690890i	0.953759	−	0.300573i	$-0.0971778\pi$
$349$	287.357	+	241.121i	0.823371	+	0.690890i	−0.130388	+	0.991463i	$0.541622\pi$
$350$			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	−0.928220	−	0.372031i	$-0.878662\pi$
$353$	−141.432	+	168.552i	−0.400658	+	0.477485i	0.527563	+	0.849516i	$0.323106\pi$
$354$	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	0.236992	−	0.971512i	$-0.423838\pi$
$359$	−174.426	−	100.705i	−0.485866	−	0.280515i	−0.722858	+	0.690997i	$0.757172\pi$
$360$	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	−0.537648	−	0.843169i	$-0.680687\pi$
$367$	−149.564	+	54.4369i	−0.407532	+	0.148330i	0.130116	+	0.991499i	$0.458465\pi$
$368$	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	0.406257	−	0.913759i	$-0.366834\pi$
$373$	48.5332	+	17.6646i	0.130116	+	0.0473583i	−0.276142	+	0.961117i	$0.589056\pi$
$374$	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	−0.980059	−	0.198704i	$-0.936327\pi$
$383$	−38.8997	+	106.876i	−0.101566	+	0.279049i	0.878494	+	0.477754i	$0.158549\pi$
$384$	−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	−0.990835	−	0.135080i	$-0.956871\pi$
$389$	−123.951	−	340.552i	−0.318639	−	0.875454i	0.672195	−	0.740374i	$-0.265351\pi$
$390$	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	0.142006	−	0.989866i	$-0.454645\pi$
$397$	368.516	−	638.289i	0.928252	−	1.60778i	0.786246	−	0.617914i	$-0.212022\pi$
$398$	−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	0.104839	−	0.994489i	$-0.466567\pi$
$401$	217.940	−	38.4287i	0.543491	−	0.0958322i	0.438652	+	0.898657i	$0.355456\pi$
$402$	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	0.920691	+	0.390292i	$0.127626\pi$
$409$	77.3060	+	438.424i	0.189012	+	1.07194i	−0.731679	+	0.681650i	$0.761263\pi$
$410$	−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	0.998099	+	0.0616300i	$0.0196299\pi$
$419$	371.014	+	442.157i	0.885475	+	1.05527i	−0.112624	+	0.993638i	$0.535926\pi$
$420$	0.362287	+	27.1720i	0.000862589	+	0.0646953i
$421$	315.735	−	114.918i	0.749964	−	0.272964i	0.0613732	−	0.998115i	$-0.480452\pi$
$421$	315.735	−	114.918i	0.749964	−	0.272964i	0.688591	+	0.725150i	$0.258230\pi$
$422$	−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	$-0.957855\pi$
$431$		−	113.799i		−	0.264034i	0.991247	−	0.132017i	$-0.0421454\pi$
$432$	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	−0.794581	−	0.607158i	$-0.792309\pi$
$439$	70.1264	−	397.706i	0.159741	−	0.905937i	0.954322	−	0.298779i	$-0.0965794\pi$
$440$	−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	−0.880399	−	0.474234i	$-0.842725\pi$
$443$	−226.287	−	621.719i	−0.510806	−	1.40343i	0.369593	−	0.929194i	$-0.379497\pi$
$444$	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	−0.877020	−	0.480453i	$-0.840472\pi$
$449$	−403.851	+	233.164i	−0.899446	+	0.519295i	−0.0224253	+	0.999749i	$0.507139\pi$
$450$	−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	0.944724	+	0.327866i	$0.106330\pi$
$457$	654.268	+	548.996i	1.43166	+	1.20130i	0.486935	+	0.873438i	$0.338115\pi$
$458$		−	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	−0.820121	−	0.572190i	$-0.806094\pi$
$461$	−52.6518	+	62.7480i	−0.114212	+	0.136113i	0.705909	+	0.708302i	$0.250539\pi$
$462$	61.2547	−	376.693i	0.132586	−	0.815353i
$463$	−113.673	−	644.671i	−0.245514	−	1.39238i	−0.819297	−	0.573370i	$-0.805636\pi$
$463$	−113.673	−	644.671i	−0.245514	−	1.39238i	0.573783	−	0.819007i	$-0.305475\pi$
$464$	−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	0.616466	−	0.787381i	$-0.288564\pi$
$467$	113.391	+	65.4664i	0.242808	+	0.140185i	−0.373659	+	0.927566i	$0.621897\pi$
$468$	−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	0.00920134	−	0.999958i	$-0.497071\pi$
$479$	−155.272	−	27.3786i	−0.324158	−	0.0571578i	−0.333359	+	0.942800i	$0.608182\pi$
$480$	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	−0.924118	−	0.382107i	$-0.875199\pi$
$491$	14.4407	−	39.6755i	0.0294108	−	0.0808056i	0.953529	+	0.301301i	$0.0974209\pi$
$492$	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	−0.932147	−	0.362079i	$-0.882067\pi$
$499$	−367.980	+	308.772i	−0.737435	+	0.618781i	0.194713	+	0.980860i	$0.437623\pi$
$500$	−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	−0.424846	−	0.905266i	$-0.639672\pi$
$503$	73.7969	−	42.6067i	0.146714	−	0.0847051i	0.571560	+	0.820560i	$0.306339\pi$
$504$	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	0.224450	−	0.974486i	$-0.427941\pi$
$509$	391.247	−	68.9874i	0.768658	−	0.135535i	0.544208	+	0.838950i	$0.316830\pi$
$510$	−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	0.480964	−	0.876740i	$-0.340287\pi$
$521$	−19.7109	−	11.3801i	−0.0378328	−	0.0218428i	−0.518797	+	0.854897i	$0.673620\pi$
$522$	−571.950	−	454.497i	−1.09569	−	0.870685i
$523$	−380.270	−	658.647i	−0.727093	−	1.25936i	−0.958107	−	0.286412i	$-0.907537\pi$
$523$	−380.270	−	658.647i	−0.727093	−	1.25936i	0.231013	−	0.972951i	$-0.425796\pi$
$524$	−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	0.682276	+	0.731095i	$0.260990\pi$
$547$	−114.270	+	648.057i	−0.208903	+	1.18475i	−0.891179	+	0.453653i	$0.850121\pi$
$548$	−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	0.469041	−	0.883176i	$-0.344600\pi$
$557$	817.907	−	472.219i	1.46842	−	0.847790i	0.999374	+	0.0353864i	$0.0112662\pi$
$558$	−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	−0.984892	−	0.173168i	$-0.944600\pi$
$563$	−1042.20	+	183.769i	−1.85116	+	0.326410i	−0.866269	+	0.499577i	$0.833489\pi$
$564$	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	−0.655621	−	0.755090i	$-0.727593\pi$
$569$	114.850	−	136.873i	0.201845	−	0.240550i	0.857466	+	0.514540i	$0.172037\pi$
$570$	406.394	−	154.082i	0.712973	−	0.270319i
$571$	104.611	+	593.280i	0.183207	+	1.03902i	0.928237	+	0.371988i	$0.121324\pi$
$571$	104.611	+	593.280i	0.183207	+	1.03902i	−0.745030	+	0.667030i	$0.767565\pi$
$572$	−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	0.931606	−	0.363471i	$-0.118408\pi$
$577$	87.1430	+	150.936i	0.151028	+	0.261588i	−0.780578	+	0.625059i	$0.785075\pi$
$578$	−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	0.942244	−	0.334928i	$-0.108712\pi$
$587$	1005.60	+	177.314i	1.71311	+	0.302068i	0.770867	+	0.636996i	$0.219823\pi$
$588$	−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	$0.253643\pi$
$593$			848.172i			1.43031i	−0.698967	+	0.715153i	$0.746357\pi$
$594$	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	−0.996762	−	0.0804060i	$-0.974378\pi$
$599$	−108.727	+	298.725i	−0.181514	+	0.498706i	0.815248	+	0.579112i	$0.196601\pi$
$600$	−101.669	−	117.935i	−0.169449	−	0.196558i
$601$	−94.5670	+	536.316i	−0.157349	+	0.892372i	0.799257	+	0.600989i	$0.205227\pi$
$601$	−94.5670	+	536.316i	−0.157349	+	0.892372i	−0.956606	+	0.291383i	$0.905885\pi$
$602$	−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	−0.333150	−	0.942874i	$-0.608111\pi$
$607$	326.292	−	273.792i	0.537549	−	0.451057i	0.870699	+	0.491817i	$0.163667\pi$
$608$	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	−0.899579	−	0.436759i	$-0.856126\pi$
$613$	−43.8571	+	75.9627i	−0.0715450	+	0.123920i	0.828034	+	0.560679i	$0.189460\pi$
$614$	−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	0.406975	−	0.913439i	$-0.366584\pi$
$617$	679.824	−	119.871i	1.10182	−	0.194281i	0.694846	+	0.719159i	$0.255472\pi$
$618$	85.5663	−	104.780i	0.138457	−	0.169546i
$619$	531.346	+	445.852i	0.858393	+	0.720278i	0.961621	−	0.274380i	$-0.0884727\pi$
$619$	531.346	+	445.852i	0.858393	+	0.720278i	−0.103228	+	0.994658i	$0.532917\pi$
$620$		−	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	0.815571	−	0.578657i	$-0.196423\pi$
$631$	−58.9015	−	102.020i	−0.0933463	−	0.161681i	−0.908917	+	0.416977i	$0.863090\pi$
$632$	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	0.448068	−	0.893999i	$-0.352112\pi$
$641$	361.107	+	63.6729i	0.563349	+	0.0993337i	0.115281	+	0.993333i	$0.463223\pi$
$642$	526.267	+	183.638i	0.819731	+	0.286040i
$643$	−902.678	−	328.548i	−1.40385	−	0.510961i	−0.474534	−	0.880237i	$-0.657383\pi$
$643$	−902.678	−	328.548i	−1.40385	−	0.510961i	−0.929320	+	0.369276i	$0.879606\pi$
$644$	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	$-0.955123\pi$
$647$		−	181.832i		−	0.281039i	0.990078	−	0.140519i	$-0.0448772\pi$
$648$	−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	0.463167	+	0.886271i	$0.346713\pi$
$653$	−301.244	+	827.662i	−0.461324	+	1.26748i	−0.924491	+	0.381205i	$0.875509\pi$
$654$	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	0.922049	−	0.387073i	$-0.126514\pi$
$659$	−21.8046	−	59.9077i	−0.0330874	−	0.0909070i	−0.955136	+	0.296166i	$0.904292\pi$
$660$	11.5334	+	19.3752i	0.0174748	+	0.0293564i
$661$	−351.302	+	294.777i	−0.531471	+	0.445957i	−0.868609	−	0.495498i	$-0.834985\pi$
$661$	−351.302	+	294.777i	−0.531471	+	0.445957i	0.337138	+	0.941455i	$0.390541\pi$
$662$	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	−0.996743	−	0.0806456i	$-0.974302\pi$
$673$	−840.742	−	705.467i	−1.24925	−	1.04824i	−0.252503	−	0.967596i	$-0.581254\pi$
$674$		−	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	−0.481031	−	0.876704i	$-0.659737\pi$
$677$	315.404	−	375.883i	0.465884	−	0.555219i	0.946915	+	0.321485i	$0.104182\pi$
$678$	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	0.908882	−	0.417053i	$-0.136937\pi$
$683$	684.465	+	395.176i	1.00215	+	0.578589i	0.0932631	+	0.995642i	$0.470270\pi$
$684$	−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	−0.191027	−	0.981585i	$-0.561182\pi$
$691$	202.870	−	73.8387i	0.293589	−	0.106858i	0.484616	+	0.874727i	$0.338959\pi$
$692$	−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	$0.116864\pi$
$701$			503.242i			0.717891i	−0.933358	+	0.358946i	$0.883136\pi$
$702$	−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	−0.252779	−	0.967524i	$-0.581345\pi$
$709$	223.809	−	1269.28i	0.315668	−	1.79024i	0.568447	−	0.822720i	$-0.307544\pi$
$710$	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	−0.112554	−	0.993646i	$-0.535903\pi$
$719$	497.326	−	287.131i	0.691691	−	0.399348i	0.804245	+	0.594298i	$0.202570\pi$
$720$	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	0.887769	−	0.460289i	$-0.152254\pi$
$727$	427.936	+	359.081i	0.588633	+	0.493922i	−0.299136	+	0.954210i	$0.596699\pi$
$728$		−	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	0.762829	+	0.646601i	$0.223810\pi$
$733$	195.824	+	1110.57i	0.267155	+	1.51511i	−0.495674	+	0.868509i	$0.665079\pi$
$734$	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	0.733926	−	0.679230i	$-0.237686\pi$
$739$	−163.517	−	283.219i	−0.221268	−	0.383247i	−0.955193	+	0.295983i	$0.904353\pi$
$740$	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	0.902934	−	0.429780i	$-0.141409\pi$
$743$	239.908	+	285.911i	0.322891	+	0.384806i	−0.580043	+	0.814586i	$0.696964\pi$
$744$	−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	0.940808	−	0.338940i	$-0.110068\pi$
$751$	1084.18	+	394.608i	1.44364	+	0.525443i	0.502835	+	0.864383i	$0.332290\pi$
$752$	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	0.351846	+	0.936058i	$0.385554\pi$
$761$	−395.241	+	1085.91i	−0.519370	+	1.42696i	−0.871216	+	0.490900i	$0.836668\pi$
$762$	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	0.0643812	−	0.997925i	$-0.479493\pi$
$769$	813.852	−	682.903i	1.05833	−	0.888041i	0.993944	+	0.109885i	$0.0350482\pi$
$770$	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	0.124743	−	0.992189i	$-0.460189\pi$
$773$	808.848	−	466.989i	1.04638	−	0.604125i	0.921632	+	0.388064i	$0.126856\pi$
$774$	−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	0.930886	+	0.365310i	$0.119037\pi$
$787$	142.512	+	808.227i	0.181083	+	1.02697i	−0.749803	+	0.661661i	$0.769852\pi$
$788$	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	0.779694	−	0.626161i	$-0.215375\pi$
$797$	22.0398	+	26.2660i	0.0276534	+	0.0329561i	−0.752040	+	0.659117i	$0.770930\pi$
$798$	−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	$-0.895538\pi$
$809$		−	521.511i		−	0.644636i	0.946631	−	0.322318i	$-0.104462\pi$
$810$	−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	−0.812770	−	0.582585i	$-0.802041\pi$
$821$	−463.561	−	1273.62i	−0.564630	−	1.55131i	0.248140	−	0.968724i	$-0.420181\pi$
$822$	−559.711	−	940.271i	−0.680913	−	1.14388i
$823$	−498.544	+	418.328i	−0.605765	+	0.508297i	−0.893293	−	0.449475i	$-0.851611\pi$
$823$	−498.544	+	418.328i	−0.605765	+	0.508297i	0.287528	+	0.957772i	$0.407167\pi$
$824$	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	0.287056	−	0.957914i	$-0.407323\pi$
$827$	1042.15	−	601.688i	1.26016	−	0.727555i	0.973106	+	0.230359i	$0.0739900\pi$
$828$	24.5786	+	13.3297i	0.0296843	+	0.0160986i
$829$	753.210	−	1304.60i	0.908577	−	1.57370i	0.0925344	−	0.995709i	$-0.470503\pi$
$829$	753.210	−	1304.60i	0.908577	−	1.57370i	0.816043	−	0.577992i	$-0.196163\pi$
$830$	−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	−0.742788	−	0.669527i	$-0.766497\pi$
$839$	38.2178	−	45.5462i	0.0455516	−	0.0542863i	0.788339	+	0.615241i	$0.210941\pi$
$840$	−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	−0.141043	−	0.990003i	$-0.545046\pi$
$853$	330.344	−	120.235i	0.387273	−	0.140956i	0.528316	+	0.849048i	$0.322823\pi$
$854$	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	−0.591363	−	0.806405i	$-0.701410\pi$
$857$	−1219.40	−	215.013i	−1.42287	−	0.250890i	−0.831507	+	0.555515i	$0.812521\pi$
$858$	−527.055	+	454.362i	−0.614283	+	0.529560i
$859$	249.859	+	90.9414i	0.290872	+	0.105869i	0.483335	−	0.875435i	$-0.339425\pi$
$859$	249.859	+	90.9414i	0.290872	+	0.105869i	−0.192463	+	0.981304i	$0.561647\pi$
$860$	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	$-0.944857\pi$
$863$		−	297.514i		−	0.344744i	0.985032	−	0.172372i	$-0.0551431\pi$
$864$	−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	−0.786677	−	0.617365i	$-0.788200\pi$
$877$	−276.515	+	232.024i	−0.315296	+	0.264565i	0.471381	+	0.881930i	$0.343756\pi$
$878$	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	−0.873451	−	0.486913i	$-0.838123\pi$
$881$	−782.766	+	451.930i	−0.888497	+	0.512974i	−0.0150464	+	0.999887i	$0.504790\pi$
$882$	166.096	−	497.208i	0.188317	−	0.563728i
$883$	462.202	−	800.558i	0.523445	−	0.906634i	−0.476182	−	0.879347i	$-0.657980\pi$
$883$	462.202	−	800.558i	0.523445	−	0.906634i	0.999628	−	0.0272872i	$-0.00868687\pi$
$884$	−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	−0.0163867	−	0.999866i	$-0.505216\pi$
$887$	275.138	−	48.5142i	0.310189	−	0.0546947i	0.326576	+	0.945171i	$0.394105\pi$
$888$	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	−0.0171896	−	0.999852i	$-0.505472\pi$
$907$	555.388	−	202.145i	0.612335	−	0.222872i	0.629525	+	0.776981i	$0.283250\pi$
$908$	−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	−0.0345765	−	0.999402i	$-0.511008\pi$
$911$	−372.493	−	65.6805i	−0.408883	−	0.0720972i	−0.374307	+	0.927305i	$0.622119\pi$
$912$	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	0.999726	+	0.0234215i	$0.00745597\pi$
$929$	231.271	+	635.412i	0.248946	+	0.683975i	−0.750779	+	0.660553i	$0.770322\pi$
$930$	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	−0.762100	−	0.647460i	$-0.775831\pi$
$937$	168.348	−	291.587i	0.179667	−	0.311192i	0.941766	+	0.336268i	$0.109165\pi$
$938$	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	−0.0488587	−	0.998806i	$-0.515558\pi$
$941$	232.277	−	40.9567i	0.246841	−	0.0435247i	0.295699	+	0.955281i	$0.404447\pi$
$942$	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	−0.503992	−	0.863708i	$-0.668136\pi$
$947$	411.104	−	489.935i	0.434112	−	0.517355i	0.938104	+	0.346354i	$0.112580\pi$
$948$	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	0.0566772	−	0.998393i	$-0.481949\pi$
$953$	−742.976	−	428.957i	−0.779618	−	0.450112i	−0.836295	+	0.548280i	$0.815283\pi$
$954$	−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	0.0485042	−	0.998823i	$-0.484555\pi$
$967$	−538.010	−	195.820i	−0.556371	−	0.202502i	−0.604875	+	0.796321i	$0.706777\pi$
$968$	−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	$-0.976949\pi$
$971$		−	140.513i		−	0.144710i	0.997379	−	0.0723548i	$-0.0230514\pi$
$972$	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	0.304373	+	0.952553i	$0.401553\pi$
$977$	−528.635	+	1452.41i	−0.541079	+	1.48660i	−0.845453	+	0.534050i	$0.820669\pi$
$978$	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	0.977080	+	0.212874i	$0.0682824\pi$
$983$	359.214	+	986.932i	0.365426	+	1.00400i	−0.611654	+	0.791126i	$0.709495\pi$
$984$	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	−0.965720	−	0.259585i	$-0.916414\pi$
$991$	−255.730	+	442.938i	−0.258053	+	0.446961i	0.707667	+	0.706546i	$0.249748\pi$
$992$	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	0.759616	−	0.650371i	$-0.225387\pi$
$997$	250.278	+	210.008i	0.251031	+	0.210640i	−0.508585	+	0.861012i	$0.669831\pi$
$998$		−	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.11.2	yes	30
3.2	odd	2		81.3.f.a.35.4		30
4.3	odd	2		432.3.bc.a.65.1		30
9.2	odd	6		243.3.f.b.26.2		30
9.4	even	3		243.3.f.d.188.2		30
9.5	odd	6		243.3.f.a.188.4		30
9.7	even	3		243.3.f.c.26.4		30
27.4	even	9		243.3.f.b.215.2		30
27.5	odd	18	inner	27.3.f.a.5.2	✓	30
27.7	even	9		729.3.b.a.728.22		30
27.13	even	9		243.3.f.a.53.4		30
27.14	odd	18		243.3.f.d.53.2		30
27.20	odd	18		729.3.b.a.728.9		30
27.22	even	9		81.3.f.a.44.4		30
27.23	odd	18		243.3.f.c.215.4		30
108.59	even	18		432.3.bc.a.113.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.5.2	✓	30	27.5	odd	18	inner
27.3.f.a.11.2	yes	30	1.1	even	1	trivial
81.3.f.a.35.4		30	3.2	odd	2
81.3.f.a.44.4		30	27.22	even	9
243.3.f.a.53.4		30	27.13	even	9
243.3.f.a.188.4		30	9.5	odd	6
243.3.f.b.26.2		30	9.2	odd	6
243.3.f.b.215.2		30	27.4	even	9
243.3.f.c.26.4		30	9.7	even	3
243.3.f.c.215.4		30	27.23	odd	18
243.3.f.d.53.2		30	27.14	odd	18
243.3.f.d.188.2		30	9.4	even	3
432.3.bc.a.65.1		30	4.3	odd	2
432.3.bc.a.113.1		30	108.59	even	18
729.3.b.a.728.9		30	27.20	odd	18
729.3.b.a.728.22		30	27.7	even	9

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.24712 + 1.48626i) q^{2} +(2.80515 - 1.06355i) q^{3} +(0.0409354 + 0.232156i) q^{4} +(-1.47839 + 4.06185i) q^{5} +(-1.91764 + 5.49555i) q^{6} +(1.54363 - 8.75434i) q^{7} +(-7.11704 - 4.10903i) q^{8} +(6.73771 - 5.96685i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8}+O(q^{10}) \) 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8	\( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20} + 132 q^{21} - 42 q^{22} + 120 q^{23} + 144 q^{24} - 15 q^{25} - 90 q^{27} - 12 q^{28} - 168 q^{29} - 243 q^{30} + 39 q^{31} - 360 q^{32} - 207 q^{33} + 54 q^{34} - 252 q^{35} - 360 q^{36} - 3 q^{37} - 84 q^{38} + 15 q^{39} - 33 q^{40} + 228 q^{41} + 486 q^{42} - 96 q^{43} + 639 q^{44} + 477 q^{45} - 3 q^{46} + 399 q^{47} + 453 q^{48} - 78 q^{49} + 303 q^{50} + 36 q^{51} - 9 q^{52} - 54 q^{54} - 12 q^{55} - 393 q^{56} - 192 q^{57} + 129 q^{58} - 474 q^{59} - 846 q^{60} + 138 q^{61} - 900 q^{62} - 585 q^{63} - 51 q^{64} - 411 q^{65} - 423 q^{66} + 354 q^{67} + 99 q^{68} + 99 q^{69} + 489 q^{70} + 315 q^{71} + 720 q^{72} - 66 q^{73} + 321 q^{74} + 255 q^{75} + 258 q^{76} + 201 q^{77} + 180 q^{78} + 30 q^{79} + 36 q^{81} - 12 q^{82} - 33 q^{83} - 588 q^{84} - 261 q^{85} - 258 q^{86} - 279 q^{87} - 642 q^{88} + 72 q^{89} + 288 q^{90} + 96 q^{91} - 3 q^{92} + 591 q^{93} - 861 q^{94} + 681 q^{95} + 270 q^{96} - 582 q^{97} + 882 q^{98} + 513 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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