LMFDB - Embedded newform 80.3.r.a.11.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,3,Mod(11,80)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("80.11"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	80.r (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17984211488$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	80.11
Dual form			80.3.r.a.51.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96150 - 0.390534i) q^{2} +(3.81615 + 3.81615i) q^{3} +(3.69497 + 1.53206i) q^{4} +(1.58114 + 1.58114i) q^{5} +(-5.99504 - 8.97572i) q^{6} -7.06228 q^{7} +(-6.64935 - 4.44816i) q^{8} +20.1260i q^{9} +(-2.48392 - 3.71889i) q^{10} +(10.3638 - 10.3638i) q^{11} +(8.25396 + 19.9471i) q^{12} +(-5.72609 + 5.72609i) q^{13} +(13.8527 + 2.75806i) q^{14} +12.0677i q^{15} +(11.3056 + 11.3219i) q^{16} +20.9484 q^{17} +(7.85989 - 39.4772i) q^{18} +(-7.58079 - 7.58079i) q^{19} +(3.41985 + 8.26466i) q^{20} +(-26.9507 - 26.9507i) q^{21} +(-24.3759 + 16.2811i) q^{22} -13.7305 q^{23} +(-8.40010 - 42.3498i) q^{24} +5.00000i q^{25} +(13.4680 - 8.99549i) q^{26} +(-42.4585 + 42.4585i) q^{27} +(-26.0949 - 10.8199i) q^{28} +(32.5485 - 32.5485i) q^{29} +(4.71286 - 23.6709i) q^{30} -26.0923i q^{31} +(-17.7543 - 26.6230i) q^{32} +79.0994 q^{33} +(-41.0902 - 8.18104i) q^{34} +(-11.1664 - 11.1664i) q^{35} +(-30.8344 + 74.3649i) q^{36} +(19.6248 + 19.6248i) q^{37} +(11.9092 + 17.8303i) q^{38} -43.7032 q^{39} +(-3.48040 - 17.5467i) q^{40} -28.8892i q^{41} +(42.3387 + 63.3890i) q^{42} +(1.30688 - 1.30688i) q^{43} +(54.1717 - 22.4158i) q^{44} +(-31.8220 + 31.8220i) q^{45} +(26.9324 + 5.36222i) q^{46} -25.9157i q^{47} +(-0.0622149 + 86.3496i) q^{48} +0.875810 q^{49} +(1.95267 - 9.80750i) q^{50} +(79.9421 + 79.9421i) q^{51} +(-29.9304 + 12.3850i) q^{52} +(-8.62769 - 8.62769i) q^{53} +(99.8639 - 66.7009i) q^{54} +32.7731 q^{55} +(46.9596 + 31.4141i) q^{56} -57.8589i q^{57} +(-76.5552 + 51.1326i) q^{58} +(-43.8075 + 43.8075i) q^{59} +(-18.4885 + 44.5898i) q^{60} +(-26.3726 + 26.3726i) q^{61} +(-10.1899 + 51.1800i) q^{62} -142.136i q^{63} +(24.4278 + 59.1547i) q^{64} -18.1075 q^{65} +(-155.153 - 30.8910i) q^{66} +(-62.9542 - 62.9542i) q^{67} +(77.4035 + 32.0942i) q^{68} +(-52.3976 - 52.3976i) q^{69} +(17.5421 + 26.2639i) q^{70} +67.9581 q^{71} +(89.5236 - 133.825i) q^{72} +14.0243i q^{73} +(-30.8300 - 46.1583i) q^{74} +(-19.0808 + 19.0808i) q^{75} +(-16.3965 - 39.6251i) q^{76} +(-73.1918 + 73.1918i) q^{77} +(85.7239 + 17.0676i) q^{78} -11.0029i q^{79} +(-0.0257774 + 35.7771i) q^{80} -142.922 q^{81} +(-11.2822 + 56.6662i) q^{82} +(-70.2950 - 70.2950i) q^{83} +(-58.2918 - 140.872i) q^{84} +(33.1223 + 33.1223i) q^{85} +(-3.07383 + 2.05307i) q^{86} +248.420 q^{87} +(-115.012 + 22.8127i) q^{88} +161.754i q^{89} +(74.8465 - 49.9913i) q^{90} +(40.4393 - 40.4393i) q^{91} +(-50.7337 - 21.0360i) q^{92} +(99.5721 - 99.5721i) q^{93} +(-10.1210 + 50.8337i) q^{94} -23.9726i q^{95} +(33.8445 - 169.350i) q^{96} +125.858 q^{97} +(-1.71790 - 0.342034i) q^{98} +(208.581 + 208.581i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} + 12 q^{6} - 20 q^{10} + 32 q^{11} - 60 q^{12} - 36 q^{14} + 48 q^{16} + 160 q^{18} - 32 q^{19} + 40 q^{20} - 12 q^{22} - 128 q^{23} - 120 q^{24} - 48 q^{26} - 96 q^{27} - 180 q^{28} + 32 q^{29}+ \cdots + 608 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 + 12 * q^6 - 20 * q^10 + 32 * q^11 - 60 * q^12 - 36 * q^14 + 48 * q^16 + 160 * q^18 - 32 * q^19 + 40 * q^20 - 12 * q^22 - 128 * q^23 - 120 * q^24 - 48 * q^26 - 96 * q^27 - 180 * q^28 + 32 * q^29 - 160 * q^32 + 16 * q^34 - 84 * q^36 - 96 * q^37 + 140 * q^38 + 384 * q^39 + 20 * q^42 + 96 * q^43 + 8 * q^44 + 36 * q^46 + 280 * q^48 + 224 * q^49 + 20 * q^50 - 256 * q^51 - 104 * q^52 - 160 * q^53 + 192 * q^54 + 304 * q^56 - 4 * q^58 - 352 * q^59 - 140 * q^60 - 32 * q^61 + 552 * q^62 + 240 * q^64 - 576 * q^66 + 160 * q^67 + 16 * q^68 + 96 * q^69 - 120 * q^70 + 256 * q^71 + 568 * q^72 + 136 * q^74 + 512 * q^76 + 224 * q^77 - 208 * q^78 - 240 * q^80 - 288 * q^81 - 196 * q^82 - 480 * q^83 - 736 * q^84 + 160 * q^85 - 188 * q^86 - 320 * q^88 - 180 * q^90 - 384 * q^91 + 28 * q^92 + 96 * q^93 - 604 * q^94 + 232 * q^96 + 20 * q^98 + 608 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.96150	−	0.390534i	−0.980750	−	0.195267i
$2$	−1.96150	−	0.390534i	−0.980750	−	0.195267i
$3$	3.81615	+	3.81615i	1.27205	+	1.27205i	0.945011	+	0.327039i	$0.106051\pi$
$3$	3.81615	+	3.81615i	1.27205	+	1.27205i	0.327039	+	0.945011i	$0.393949\pi$
$4$	3.69497	+	1.53206i	0.923742	+	0.383016i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$6$	−5.99504	−	8.97572i	−0.999174	−	1.49595i
$7$	−7.06228			−1.00890			−0.504449	−	0.863442i	$-0.668304\pi$
$7$	−7.06228			−1.00890			−0.504449	+	0.863442i	$0.668304\pi$
$8$	−6.64935	−	4.44816i	−0.831169	−	0.556019i
$9$			20.1260i			2.23622i
$10$	−2.48392	−	3.71889i	−0.248392	−	0.371889i
$11$	10.3638	−	10.3638i	0.942161	−	0.942161i	−0.0562558	−	0.998416i	$-0.517916\pi$
$11$	10.3638	−	10.3638i	0.942161	−	0.942161i	0.998416	+	0.0562558i	$0.0179162\pi$
$12$	8.25396	+	19.9471i	0.687830	+	1.66226i
$13$	−5.72609	+	5.72609i	−0.440468	+	0.440468i	−0.892169	−	0.451701i	$-0.850817\pi$
$13$	−5.72609	+	5.72609i	−0.440468	+	0.440468i	0.451701	+	0.892169i	$0.350817\pi$
$14$	13.8527	+	2.75806i	0.989476	+	0.197004i
$15$			12.0677i			0.804515i
$16$	11.3056	+	11.3219i	0.706597	+	0.707616i
$17$	20.9484			1.23226			0.616128	−	0.787646i	$-0.288700\pi$
$17$	20.9484			1.23226			0.616128	+	0.787646i	$0.288700\pi$
$18$	7.85989	−	39.4772i	0.436661	−	2.19318i
$19$	−7.58079	−	7.58079i	−0.398989	−	0.398989i	0.478887	−	0.877876i	$-0.341040\pi$
$19$	−7.58079	−	7.58079i	−0.398989	−	0.398989i	−0.877876	+	0.478887i	$0.841040\pi$
$20$	3.41985	+	8.26466i	0.170992	+	0.413233i
$21$	−26.9507	−	26.9507i	−1.28337	−	1.28337i
$22$	−24.3759	+	16.2811i	−1.10800	+	0.740051i
$23$	−13.7305			−0.596978			−0.298489	−	0.954413i	$-0.596483\pi$
$23$	−13.7305			−0.596978			−0.298489	+	0.954413i	$0.596483\pi$
$24$	−8.40010	−	42.3498i	−0.350004	−	1.76457i
$25$			5.00000i			0.200000i
$26$	13.4680	−	8.99549i	0.517998	−	0.345981i
$27$	−42.4585	+	42.4585i	−1.57254	+	1.57254i
$28$	−26.0949	−	10.8199i	−0.931960	−	0.386424i
$29$	32.5485	−	32.5485i	1.12236	−	1.12236i	0.130976	−	0.991386i	$-0.458189\pi$
$29$	32.5485	−	32.5485i	1.12236	−	1.12236i	0.991386	−	0.130976i	$-0.0418111\pi$
$30$	4.71286	−	23.6709i	0.157095	−	0.789028i
$31$		−	26.0923i		−	0.841687i	−0.907133	−	0.420843i	$-0.861734\pi$
$31$		−	26.0923i		−	0.841687i	0.907133	−	0.420843i	$-0.138266\pi$
$32$	−17.7543	−	26.6230i	−0.554821	−	0.831970i
$33$	79.0994			2.39695
$34$	−41.0902	−	8.18104i	−1.20854	−	0.240619i
$35$	−11.1664	−	11.1664i	−0.319041	−	0.319041i
$36$	−30.8344	+	74.3649i	−0.856510	+	2.06569i
$37$	19.6248	+	19.6248i	0.530401	+	0.530401i	0.920692	−	0.390290i	$-0.127625\pi$
$37$	19.6248	+	19.6248i	0.530401	+	0.530401i	−0.390290	+	0.920692i	$0.627625\pi$
$38$	11.9092	+	17.8303i	0.313399	+	0.469218i
$39$	−43.7032			−1.12060
$40$	−3.48040	−	17.5467i	−0.0870100	−	0.438668i
$41$		−	28.8892i		−	0.704614i	−0.935884	−	0.352307i	$-0.885397\pi$
$41$		−	28.8892i		−	0.704614i	0.935884	−	0.352307i	$-0.114603\pi$
$42$	42.3387	+	63.3890i	1.00806	+	1.50926i
$43$	1.30688	−	1.30688i	0.0303926	−	0.0303926i	−0.691747	−	0.722140i	$-0.743159\pi$
$43$	1.30688	−	1.30688i	0.0303926	−	0.0303926i	0.722140	+	0.691747i	$0.243159\pi$
$44$	54.1717	−	22.4158i	1.23118	−	0.509450i
$45$	−31.8220	+	31.8220i	−0.707156	+	0.707156i
$46$	26.9324	+	5.36222i	0.585486	+	0.116570i
$47$		−	25.9157i		−	0.551398i	−0.961244	−	0.275699i	$-0.911091\pi$
$47$		−	25.9157i		−	0.551398i	0.961244	−	0.275699i	$-0.0889093\pi$
$48$	−0.0622149	+	86.3496i	−0.00129614	+	1.79895i
$49$	0.875810			0.0178737
$50$	1.95267	−	9.80750i	0.0390534	−	0.196150i
$51$	79.9421	+	79.9421i	1.56749	+	1.56749i
$52$	−29.9304	+	12.3850i	−0.575586	+	0.238172i
$53$	−8.62769	−	8.62769i	−0.162787	−	0.162787i	0.621013	−	0.783800i	$-0.286721\pi$
$53$	−8.62769	−	8.62769i	−0.162787	−	0.162787i	−0.783800	+	0.621013i	$0.786721\pi$
$54$	99.8639	−	66.7009i	1.84933	−	1.23520i
$55$	32.7731			0.595875
$56$	46.9596	+	31.4141i	0.838564	+	0.560967i
$57$		−	57.8589i		−	1.01507i
$58$	−76.5552	+	51.1326i	−1.31992	+	0.881596i
$59$	−43.8075	+	43.8075i	−0.742500	+	0.742500i	−0.973058	−	0.230558i	$-0.925945\pi$
$59$	−43.8075	+	43.8075i	−0.742500	+	0.742500i	0.230558	+	0.973058i	$0.425945\pi$
$60$	−18.4885	+	44.5898i	−0.308142	+	0.743164i
$61$	−26.3726	+	26.3726i	−0.432338	+	0.432338i	−0.889423	−	0.457085i	$-0.848894\pi$
$61$	−26.3726	+	26.3726i	−0.432338	+	0.432338i	0.457085	+	0.889423i	$0.348894\pi$
$62$	−10.1899	+	51.1800i	−0.164354	+	0.825484i
$63$		−	142.136i		−	2.25612i
$64$	24.4278	+	59.1547i	0.381685	+	0.924293i
$65$	−18.1075			−0.278577
$66$	−155.153	−	30.8910i	−2.35081	−	0.468045i
$67$	−62.9542	−	62.9542i	−0.939615	−	0.939615i	0.0586632	−	0.998278i	$-0.481316\pi$
$67$	−62.9542	−	62.9542i	−0.939615	−	0.939615i	−0.998278	+	0.0586632i	$0.981316\pi$
$68$	77.4035	+	32.0942i	1.13829	+	0.471974i
$69$	−52.3976	−	52.3976i	−0.759386	−	0.759386i
$70$	17.5421	+	26.2639i	0.250602	+	0.375198i
$71$	67.9581			0.957156			0.478578	−	0.878045i	$-0.341152\pi$
$71$	67.9581			0.957156			0.478578	+	0.878045i	$0.341152\pi$
$72$	89.5236	−	133.825i	1.24338	−	1.85868i
$73$			14.0243i			0.192113i	0.995376	+	0.0960566i	$0.0306230\pi$
$73$			14.0243i			0.192113i	−0.995376	+	0.0960566i	$0.969377\pi$
$74$	−30.8300	−	46.1583i	−0.416621	−	0.623761i
$75$	−19.0808	+	19.0808i	−0.254410	+	0.254410i
$76$	−16.3965	−	39.6251i	−0.215744	−	0.521382i
$77$	−73.1918	+	73.1918i	−0.950543	+	0.950543i
$78$	85.7239	+	17.0676i	1.09902	+	0.218815i
$79$		−	11.0029i		−	0.139277i	−0.997572	−	0.0696384i	$-0.977815\pi$
$79$		−	11.0029i		−	0.139277i	0.997572	−	0.0696384i	$-0.0221845\pi$
$80$	−0.0257774	+	35.7771i	−0.000322218	+	0.447213i
$81$	−142.922			−1.76447
$82$	−11.2822	+	56.6662i	−0.137588	+	0.691051i
$83$	−70.2950	−	70.2950i	−0.846928	−	0.846928i	0.142821	−	0.989749i	$-0.454383\pi$
$83$	−70.2950	−	70.2950i	−0.846928	−	0.846928i	−0.989749	+	0.142821i	$0.954383\pi$
$84$	−58.2918	−	140.872i	−0.693950	−	1.67705i
$85$	33.1223	+	33.1223i	0.389674	+	0.389674i
$86$	−3.07383	+	2.05307i	−0.0357422	+	0.0238729i
$87$	248.420			2.85540
$88$	−115.012	+	22.8127i	−1.30695	+	0.259235i
$89$			161.754i			1.81746i	0.417388	+	0.908728i	$0.362946\pi$
$89$			161.754i			1.81746i	−0.417388	+	0.908728i	$0.637054\pi$
$90$	74.8465	−	49.9913i	0.831627	−	0.555459i
$91$	40.4393	−	40.4393i	0.444387	−	0.444387i
$92$	−50.7337	−	21.0360i	−0.551453	−	0.228652i
$93$	99.5721	−	99.5721i	1.07067	−	1.07067i
$94$	−10.1210	+	50.8337i	−0.107670	+	0.540784i
$95$		−	23.9726i		−	0.252343i
$96$	33.8445	−	169.350i	0.352547	−	1.76407i
$97$	125.858			1.29750			0.648752	−	0.761000i	$-0.275291\pi$
$97$	125.858			1.29750			0.648752	+	0.761000i	$0.275291\pi$
$98$	−1.71790	−	0.342034i	−0.0175296	−	0.00349014i
$99$	208.581	+	208.581i	2.10688	+	2.10688i
$100$	−7.66032	+	18.4748i	−0.0766032	+	0.184748i
$101$	35.9589	+	35.9589i	0.356029	+	0.356029i	0.862347	−	0.506318i	$-0.168994\pi$
$101$	35.9589	+	35.9589i	0.356029	+	0.356029i	−0.506318	+	0.862347i	$0.668994\pi$
$102$	−125.586	−	188.026i	−1.23124	−	1.84340i
$103$	−52.9240			−0.513826			−0.256913	−	0.966435i	$-0.582705\pi$
$103$	−52.9240			−0.513826			−0.256913	+	0.966435i	$0.582705\pi$
$104$	63.5453	−	12.6043i	0.611013	−	0.121195i
$105$		−	85.2257i		−	0.811673i
$106$	13.5538	+	20.2926i	0.127866	+	0.191440i
$107$	−105.376	+	105.376i	−0.984824	+	0.984824i	−0.999887	−	0.0150622i	$-0.995205\pi$
$107$	−105.376	+	105.376i	−0.984824	+	0.984824i	0.0150622	+	0.999887i	$0.495205\pi$
$108$	−221.932	+	91.8336i	−2.05493	+	0.850311i
$109$	−126.083	+	126.083i	−1.15672	+	1.15672i	−0.171548	+	0.985176i	$0.554877\pi$
$109$	−126.083	+	126.083i	−1.15672	+	1.15672i	−0.985176	+	0.171548i	$0.945123\pi$
$110$	−64.2845	−	12.7990i	−0.584404	−	0.116355i
$111$			149.783i			1.34939i
$112$	−79.8430	−	79.9581i	−0.712884	−	0.713912i
$113$	−63.3329			−0.560468			−0.280234	−	0.959932i	$-0.590412\pi$
$113$	−63.3329			−0.560468			−0.280234	+	0.959932i	$0.590412\pi$
$114$	−22.5959	+	113.490i	−0.198209	+	0.995529i
$115$	−21.7098	−	21.7098i	−0.188781	−	0.188781i
$116$	170.132	−	70.3992i	1.46665	−	0.606889i
$117$	−115.243	−	115.243i	−0.984986	−	0.984986i
$118$	103.037	−	68.8201i	0.873193	−	0.583221i
$119$	−147.943			−1.24322
$120$	53.6791	−	80.2426i	0.447326	−	0.668688i
$121$		−	93.8153i		−	0.775333i
$122$	62.0293	−	41.4305i	0.508437	−	0.339594i
$123$	110.245	−	110.245i	0.896305	−	0.896305i
$124$	39.9751	−	96.4101i	0.322380	−	0.777501i
$125$	−7.90569	+	7.90569i	−0.0632456	+	0.0632456i
$126$	−55.5088	+	278.799i	−0.440546	+	2.21269i
$127$			108.702i			0.855922i	0.903797	+	0.427961i	$0.140768\pi$
$127$			108.702i			0.855922i	−0.903797	+	0.427961i	$0.859232\pi$
$128$	−24.8133	−	125.572i	−0.193854	−	0.981030i
$129$	9.97452			0.0773219
$130$	35.5178	+	7.07159i	0.273214	+	0.0543968i
$131$	−0.204051	−	0.204051i	−0.00155764	−	0.00155764i	0.706328	−	0.707885i	$-0.250351\pi$
$131$	−0.204051	−	0.204051i	−0.00155764	−	0.00155764i	−0.707885	+	0.706328i	$0.750351\pi$
$132$	292.270	+	121.185i	2.21416	+	0.918071i
$133$	53.5377	+	53.5377i	0.402539	+	0.402539i
$134$	98.8989	+	148.070i	0.738051	+	1.10500i
$135$	−134.266			−0.994560
$136$	−139.293	−	93.1815i	−1.02421	−	0.685158i
$137$		−	131.227i		−	0.957862i	−0.877853	−	0.478931i	$-0.841024\pi$
$137$		−	131.227i		−	0.957862i	0.877853	−	0.478931i	$-0.158976\pi$
$138$	82.3149	+	123.241i	0.596485	+	0.893050i
$139$	74.4886	−	74.4886i	0.535889	−	0.535889i	−0.386429	−	0.922319i	$-0.626292\pi$
$139$	74.4886	−	74.4886i	0.535889	−	0.535889i	0.922319	+	0.386429i	$0.126292\pi$
$140$	−24.1519	−	58.3674i	−0.172514	−	0.416910i
$141$	98.8982	−	98.8982i	0.701406	−	0.701406i
$142$	−133.300	−	26.5399i	−0.938731	−	0.186901i
$143$			118.688i			0.829984i
$144$	−227.864	+	227.536i	−1.58239	+	1.58011i
$145$	102.927			0.709844
$146$	5.47695	−	27.5086i	0.0375134	−	0.188415i
$147$	3.34222	+	3.34222i	0.0227362	+	0.0227362i
$148$	42.4466	+	102.580i	0.286801	+	0.693106i
$149$	−139.785	−	139.785i	−0.938157	−	0.938157i	0.0600393	−	0.998196i	$-0.480877\pi$
$149$	−139.785	−	139.785i	−0.938157	−	0.938157i	−0.998196	+	0.0600393i	$0.980877\pi$
$150$	44.8786	−	29.9752i	0.299191	−	0.199835i
$151$	−176.707			−1.17024			−0.585121	−	0.810946i	$-0.698953\pi$
$151$	−176.707			−1.17024			−0.585121	+	0.810946i	$0.698953\pi$
$152$	16.6868	+	84.1279i	0.109782	+	0.553473i
$153$			421.607i			2.75560i
$154$	172.150	−	114.982i	1.11786	−	0.746636i
$155$	41.2555	−	41.2555i	0.266165	−	0.266165i
$156$	−161.482	−	66.9562i	−1.03514	−	0.429206i
$157$	−9.60929	+	9.60929i	−0.0612057	+	0.0612057i	−0.737047	−	0.675841i	$-0.763780\pi$
$157$	−9.60929	+	9.60929i	−0.0612057	+	0.0612057i	0.675841	+	0.737047i	$0.263780\pi$
$158$	−4.29699	+	21.5821i	−0.0271962	+	0.136596i
$159$		−	65.8491i		−	0.414145i
$160$	14.0227	−	70.1667i	0.0876420	−	0.438542i
$161$	96.9686			0.602289
$162$	280.342	+	55.8160i	1.73051	+	0.344543i
$163$	51.3986	+	51.3986i	0.315329	+	0.315329i	0.846970	−	0.531641i	$-0.178424\pi$
$163$	51.3986	+	51.3986i	0.315329	+	0.315329i	−0.531641	+	0.846970i	$0.678424\pi$
$164$	44.2601	−	106.745i	0.269879	−	0.650882i
$165$	125.067	+	125.067i	0.757982	+	0.757982i
$166$	110.431	+	165.336i	0.665248	+	0.996002i
$167$	209.405			1.25392			0.626961	−	0.779050i	$-0.284298\pi$
$167$	209.405			1.25392			0.626961	+	0.779050i	$0.284298\pi$
$168$	59.3239	+	299.086i	0.353118	+	1.78027i
$169$			103.424i			0.611975i
$170$	−52.0339	−	77.9047i	−0.306082	−	0.458263i
$171$	152.571	−	152.571i	0.892229	−	0.892229i
$172$	6.83112	−	2.82666i	0.0397158	−	0.0164341i
$173$	−10.8022	+	10.8022i	−0.0624404	+	0.0624404i	−0.737637	−	0.675197i	$-0.764059\pi$
$173$	−10.8022	+	10.8022i	−0.0624404	+	0.0624404i	0.675197	+	0.737637i	$0.264059\pi$
$174$	−487.276	−	97.0164i	−2.80043	−	0.557565i
$175$		−	35.3114i		−	0.201779i
$176$	234.505	+	0.168961i	1.33242	+	0.000960006i
$177$	−334.352			−1.88899
$178$	63.1703	−	317.280i	0.354889	−	1.78247i
$179$	−213.052	−	213.052i	−1.19024	−	1.19024i	−0.977001	−	0.213234i	$-0.931600\pi$
$179$	−213.052	−	213.052i	−1.19024	−	1.19024i	−0.213234	−	0.977001i	$-0.568400\pi$
$180$	−166.335	+	68.8279i	−0.924081	+	0.382377i
$181$	−27.5517	−	27.5517i	−0.152219	−	0.152219i	0.626889	−	0.779108i	$-0.284328\pi$
$181$	−27.5517	−	27.5517i	−0.152219	−	0.152219i	−0.779108	+	0.626889i	$0.784328\pi$
$182$	−95.1145	+	63.5287i	−0.522607	+	0.349059i
$183$	−201.284			−1.09991
$184$	91.2989	+	61.0753i	0.496190	+	0.331931i
$185$			62.0592i			0.335455i
$186$	−234.197	+	156.424i	−1.25912	+	0.840991i
$187$	217.104	−	217.104i	1.16098	−	1.16098i
$188$	39.7045	−	95.7576i	0.211194	−	0.509349i
$189$	299.854	−	299.854i	1.58653	−	1.58653i
$190$	−9.36211	+	47.0222i	−0.0492742	+	0.247485i
$191$			285.029i			1.49230i	0.665778	+	0.746150i	$0.268100\pi$
$191$			285.029i			1.49230i	−0.665778	+	0.746150i	$0.731900\pi$
$192$	−132.523	+	318.964i	−0.690224	+	1.66127i
$193$	17.4519			0.0904245			0.0452123	−	0.998977i	$-0.485604\pi$
$193$	17.4519			0.0904245			0.0452123	+	0.998977i	$0.485604\pi$
$194$	−246.870	−	49.1518i	−1.27253	−	0.253360i
$195$	−69.1009	−	69.1009i	−0.354364	−	0.354364i
$196$	3.23609	+	1.34180i	0.0165107	+	0.00684591i
$197$	−92.3883	−	92.3883i	−0.468976	−	0.468976i	0.432607	−	0.901583i	$-0.357594\pi$
$197$	−92.3883	−	92.3883i	−0.468976	−	0.468976i	−0.901583	+	0.432607i	$0.857594\pi$
$198$	−327.674	−	490.590i	−1.65492	−	2.47773i
$199$	296.441			1.48965			0.744826	−	0.667258i	$-0.232532\pi$
$199$	296.441			1.48965			0.744826	+	0.667258i	$0.232532\pi$
$200$	22.2408	−	33.2468i	0.111204	−	0.166234i
$201$		−	480.485i		−	2.39047i
$202$	−56.4902	−	84.5765i	−0.279654	−	0.418696i
$203$	−229.867	+	229.867i	−1.13235	+	1.13235i
$204$	172.907	+	417.860i	0.847582	+	2.04833i
$205$	45.6778	−	45.6778i	0.222819	−	0.222819i
$206$	103.811	+	20.6686i	0.503935	+	0.100333i
$207$		−	276.340i		−	1.33498i
$208$	−129.567	−	0.0933528i	−0.622916	−	0.000448812i
$209$	−157.131			−0.751824
$210$	−33.2835	+	167.170i	−0.158493	+	0.796049i
$211$	−170.896	−	170.896i	−0.809932	−	0.809932i	0.174692	−	0.984623i	$-0.444107\pi$
$211$	−170.896	−	170.896i	−0.809932	−	0.809932i	−0.984623	+	0.174692i	$0.944107\pi$
$212$	−18.6608	−	45.0972i	−0.0880229	−	0.212723i
$213$	259.338	+	259.338i	1.21755	+	1.21755i
$214$	247.848	−	165.542i	1.15817	−	0.773563i
$215$	4.13272			0.0192220
$216$	471.184	−	93.4596i	2.18141	−	0.432684i
$217$			184.271i			0.849175i
$218$	296.551	−	198.072i	1.36033	−	0.908587i
$219$	−53.5187	+	53.5187i	−0.244378	+	0.244378i
$220$	121.096	+	50.2105i	0.550434	+	0.228230i
$221$	−119.952	+	119.952i	−0.542770	+	0.542770i
$222$	58.4953	−	293.799i	0.263492	−	1.32342i
$223$		−	231.463i		−	1.03795i	−0.854789	−	0.518975i	$-0.826314\pi$
$223$		−	231.463i		−	1.03795i	0.854789	−	0.518975i	$-0.173686\pi$
$224$	125.386	+	188.019i	0.559758	+	0.839372i
$225$	−100.630			−0.447245
$226$	124.227	+	24.7336i	0.549679	+	0.109441i
$227$	15.9457	+	15.9457i	0.0702453	+	0.0702453i	0.741357	−	0.671111i	$-0.234183\pi$
$227$	15.9457	+	15.9457i	0.0702453	+	0.0702453i	−0.671111	+	0.741357i	$0.734183\pi$
$228$	88.6436	−	213.787i	0.388788	−	0.937661i
$229$	245.622	+	245.622i	1.07258	+	1.07258i	0.997151	+	0.0754331i	$0.0240339\pi$
$229$	245.622	+	245.622i	1.07258	+	1.07258i	0.0754331	+	0.997151i	$0.475966\pi$
$230$	34.1054	+	51.0622i	0.148284	+	0.222010i
$231$	−558.622			−2.41828
$232$	−361.207	+	71.6457i	−1.55693	+	0.308818i
$233$		−	343.876i		−	1.47586i	−0.674876	−	0.737931i	$-0.735803\pi$
$233$		−	343.876i		−	1.47586i	0.674876	−	0.737931i	$-0.264197\pi$
$234$	181.043	+	271.056i	0.773690	+	1.15836i
$235$	40.9763	−	40.9763i	0.174367	−	0.174367i
$236$	−228.983	+	94.7513i	−0.970268	+	0.401489i
$237$	41.9886	−	41.9886i	0.177167	−	0.177167i
$238$	290.191	+	57.7768i	1.21929	+	0.242760i
$239$			257.404i			1.07700i	0.842624	+	0.538502i	$0.181009\pi$
$239$			257.404i			1.07700i	−0.842624	+	0.538502i	$0.818991\pi$
$240$	−136.629	+	136.432i	−0.569288	+	0.568468i
$241$	−181.726			−0.754051			−0.377025	−	0.926203i	$-0.623053\pi$
$241$	−181.726			−0.754051			−0.377025	+	0.926203i	$0.623053\pi$
$242$	−36.6381	+	184.019i	−0.151397	+	0.760408i
$243$	−163.286	−	163.286i	−0.671958	−	0.671958i
$244$	−137.851	+	57.0414i	−0.564961	+	0.233776i
$245$	1.38478	+	1.38478i	0.00565215	+	0.00565215i
$246$	−259.301	+	173.192i	−1.05407	+	0.704032i
$247$	86.8166			0.351484
$248$	−116.063	+	173.497i	−0.467994	+	0.699584i
$249$		−	536.513i		−	2.15467i
$250$	18.5945	−	12.4196i	0.0743779	−	0.0496783i
$251$	50.3743	−	50.3743i	0.200695	−	0.200695i	−0.599603	−	0.800298i	$-0.704675\pi$
$251$	50.3743	−	50.3743i	0.200695	−	0.200695i	0.800298	+	0.599603i	$0.204675\pi$
$252$	217.761	−	525.186i	0.864130	−	2.08407i
$253$	−142.300	+	142.300i	−0.562449	+	0.562449i
$254$	42.4518	−	213.219i	0.167133	−	0.839445i
$255$			252.799i			0.991369i
$256$	−0.368896	+	256.000i	−0.00144100	+	0.999999i
$257$	196.964			0.766398			0.383199	−	0.923666i	$-0.374822\pi$
$257$	196.964			0.766398			0.383199	+	0.923666i	$0.374822\pi$
$258$	−19.5650	−	3.89539i	−0.0758334	−	0.0150984i
$259$	−138.596	−	138.596i	−0.535120	−	0.535120i
$260$	−66.9065	−	27.7418i	−0.257333	−	0.106699i
$261$	655.071	+	655.071i	2.50985	+	2.50985i
$262$	0.320557	+	0.479934i	0.00122350	+	0.00183181i
$263$	44.0635			0.167542			0.0837709	−	0.996485i	$-0.473304\pi$
$263$	44.0635			0.167542			0.0837709	+	0.996485i	$0.473304\pi$
$264$	−525.960	−	351.846i	−1.99227	−	1.33275i
$265$		−	27.2832i		−	0.102955i
$266$	−84.1059	−	125.923i	−0.316188	−	0.473393i
$267$	−617.276	+	617.276i	−2.31190	+	2.31190i
$268$	−136.164	−	329.063i	−0.508073	−	1.22785i
$269$	121.781	−	121.781i	0.452717	−	0.452717i	−0.443538	−	0.896255i	$-0.646277\pi$
$269$	121.781	−	121.781i	0.452717	−	0.452717i	0.896255	+	0.443538i	$0.146277\pi$
$270$	263.362	+	52.4353i	0.975415	+	0.194205i
$271$			225.635i			0.832602i	0.909227	+	0.416301i	$0.136674\pi$
$271$			225.635i			0.832602i	−0.909227	+	0.416301i	$0.863326\pi$
$272$	236.833	+	237.174i	0.870709	+	0.871964i
$273$	308.645			1.13057
$274$	−51.2486	+	257.402i	−0.187039	+	0.939423i
$275$	51.8188	+	51.8188i	0.188432	+	0.188432i
$276$	−113.331	−	273.884i	−0.410619	−	0.992333i
$277$	−25.3569	−	25.3569i	−0.0915410	−	0.0915410i	0.659853	−	0.751394i	$-0.270618\pi$
$277$	−25.3569	−	25.3569i	−0.0915410	−	0.0915410i	−0.751394	+	0.659853i	$0.770618\pi$
$278$	−175.200	+	117.019i	−0.630215	+	0.420932i
$279$	525.134			1.88220
$280$	24.5796	+	123.920i	0.0877842	+	0.442571i
$281$			230.379i			0.819854i	0.912118	+	0.409927i	$0.134446\pi$
$281$			230.379i			0.819854i	−0.912118	+	0.409927i	$0.865554\pi$
$282$	−232.612	+	155.366i	−0.824865	+	0.550942i
$283$	−72.1310	+	72.1310i	−0.254880	+	0.254880i	−0.822968	−	0.568088i	$-0.807683\pi$
$283$	−72.1310	+	72.1310i	−0.254880	+	0.254880i	0.568088	+	0.822968i	$0.307683\pi$
$284$	251.103	+	104.116i	0.884165	+	0.366606i
$285$	91.4830	−	91.4830i	0.320993	−	0.320993i
$286$	46.3516	−	232.806i	0.162068	−	0.814007i
$287$			204.024i			0.710884i
$288$	535.815	−	357.323i	1.86047	−	1.24070i
$289$	149.833			0.518455
$290$	−201.892	−	40.1966i	−0.696179	−	0.138609i
$291$	480.293	+	480.293i	1.65049	+	1.65049i
$292$	−21.4861	+	51.8192i	−0.0735825	+	0.177463i
$293$	−240.920	−	240.920i	−0.822254	−	0.822254i	0.164177	−	0.986431i	$-0.447503\pi$
$293$	−240.920	−	240.920i	−0.822254	−	0.822254i	−0.986431	+	0.164177i	$0.947503\pi$
$294$	−5.25052	−	7.86102i	−0.0178589	−	0.0267382i
$295$	−138.531			−0.469598
$296$	−43.1982	−	217.787i	−0.145940	−	0.735767i
$297$			880.060i			2.96317i
$298$	219.598	+	328.780i	0.736906	+	1.10329i
$299$	78.6220	−	78.6220i	0.262950	−	0.262950i
$300$	−99.7357	+	41.2698i	−0.332452	+	0.137566i
$301$	−9.22957	+	9.22957i	−0.0306630	+	0.0306630i
$302$	346.610	+	69.0099i	1.14772	+	0.228510i
$303$			274.449i			0.905772i
$304$	0.123590	−	171.534i	0.000406547	−	0.564256i
$305$	−83.3976			−0.273435
$306$	164.652	−	826.982i	0.538078	−	2.70255i
$307$	270.295	+	270.295i	0.880439	+	0.880439i	0.993579	−	0.113140i	$-0.0360909\pi$
$307$	270.295	+	270.295i	0.880439	+	0.880439i	−0.113140	+	0.993579i	$0.536091\pi$
$308$	−382.576	+	158.307i	−1.24213	+	0.513983i
$309$	−201.966	−	201.966i	−0.653612	−	0.653612i
$310$	−97.0344	+	64.8110i	−0.313014	+	0.209068i
$311$	542.105			1.74310			0.871552	−	0.490303i	$-0.163114\pi$
$311$	542.105			1.74310			0.871552	+	0.490303i	$0.163114\pi$
$312$	290.598	+	194.399i	0.931405	+	0.623073i
$313$		−	149.812i		−	0.478633i	−0.970942	−	0.239316i	$-0.923077\pi$
$313$		−	149.812i		−	0.478633i	0.970942	−	0.239316i	$-0.0769233\pi$
$314$	22.6014	−	15.0959i	0.0719789	−	0.0480760i
$315$	224.736	−	224.736i	0.713448	−	0.713448i
$316$	16.8571	−	40.6552i	0.0533453	−	0.128656i
$317$	419.328	−	419.328i	1.32280	−	1.32280i	0.411304	−	0.911498i	$-0.365073\pi$
$317$	419.328	−	419.328i	1.32280	−	1.32280i	0.911498	−	0.411304i	$-0.134927\pi$
$318$	−25.7163	+	129.163i	−0.0808689	+	0.406173i
$319$		−	674.650i		−	2.11489i
$320$	−54.9081	+	132.156i	−0.171588	+	0.412986i
$321$	−804.263			−2.50549
$322$	−190.204	−	37.8695i	−0.590695	−	0.117607i
$323$	−158.805	−	158.805i	−0.491657	−	0.491657i
$324$	−528.093	−	218.966i	−1.62992	−	0.675821i
$325$	−28.6304	−	28.6304i	−0.0880937	−	0.0880937i
$326$	−80.7455	−	120.891i	−0.247686	−	0.370832i
$327$	−962.302			−2.94282
$328$	−128.504	+	192.094i	−0.391779	+	0.585654i
$329$			183.024i			0.556304i
$330$	−196.476	−	294.162i	−0.595382	−	0.891400i
$331$	106.842	−	106.842i	0.322785	−	0.322785i	−0.527050	−	0.849835i	$-0.676702\pi$
$331$	106.842	−	106.842i	0.322785	−	0.322785i	0.849835	+	0.527050i	$0.176702\pi$
$332$	−152.041	−	367.434i	−0.457955	−	1.10673i
$333$	−394.970	+	394.970i	−1.18610	+	1.18610i
$334$	−410.748	−	81.7798i	−1.22978	−	0.244850i
$335$		−	199.079i		−	0.594264i
$336$	0.439379	−	609.825i	0.00130768	−	1.81496i
$337$	291.677			0.865510			0.432755	−	0.901512i	$-0.357542\pi$
$337$	291.677			0.865510			0.432755	+	0.901512i	$0.357542\pi$
$338$	40.3905	−	202.866i	0.119499	−	0.600195i
$339$	−241.688	−	241.688i	−0.712943	−	0.712943i
$340$	71.6402	+	173.131i	0.210706	+	0.509209i
$341$	−270.414	−	270.414i	−0.793004	−	0.793004i
$342$	−358.853	+	239.684i	−1.04928	+	0.700831i
$343$	339.867			0.990865
$344$	−14.5031	+	2.87671i	−0.0421603	+	0.00836252i
$345$		−	165.696i		−	0.480278i
$346$	25.4071	−	16.9699i	0.0734310	−	0.0490459i
$347$	262.829	−	262.829i	0.757433	−	0.757433i	−0.218422	−	0.975854i	$-0.570091\pi$
$347$	262.829	−	262.829i	0.757433	−	0.757433i	0.975854	+	0.218422i	$0.0700909\pi$
$348$	917.903	+	380.595i	2.63765	+	1.09366i
$349$	−429.583	+	429.583i	−1.23090	+	1.23090i	−0.267277	+	0.963620i	$0.586124\pi$
$349$	−429.583	+	429.583i	−1.23090	+	1.23090i	−0.963620	+	0.267277i	$0.913876\pi$
$350$	−13.7903	+	69.2633i	−0.0394009	+	0.197895i
$351$		−	486.243i		−	1.38531i
$352$	−459.916	−	91.9137i	−1.30658	−	0.261118i
$353$	−240.396			−0.681008			−0.340504	−	0.940243i	$-0.610598\pi$
$353$	−240.396			−0.681008			−0.340504	+	0.940243i	$0.610598\pi$
$354$	655.832	+	130.576i	1.85263	+	0.368858i
$355$	107.451	+	107.451i	0.302679	+	0.302679i
$356$	−247.817	+	597.674i	−0.696115	+	1.67886i
$357$	−564.573	−	564.573i	−1.58144	−	1.58144i
$358$	334.698	+	501.106i	0.934910	+	1.39974i
$359$	57.3483			0.159744			0.0798722	−	0.996805i	$-0.474549\pi$
$359$	57.3483			0.159744			0.0798722	+	0.996805i	$0.474549\pi$
$360$	353.145	−	70.0466i	0.980959	−	0.194574i
$361$		−	246.063i		−	0.681615i
$362$	43.2828	+	64.8025i	0.119566	+	0.179013i
$363$	358.013	−	358.013i	0.986263	−	0.986263i
$364$	211.377	−	87.4661i	0.580707	−	0.240292i
$365$	−22.1743	+	22.1743i	−0.0607515	+	0.0607515i
$366$	394.818	+	78.6082i	1.07874	+	0.214777i
$367$		−	67.9139i		−	0.185052i	−0.995710	−	0.0925258i	$-0.970506\pi$
$367$		−	67.9139i		−	0.185052i	0.995710	−	0.0925258i	$-0.0294941\pi$
$368$	−155.231	−	155.455i	−0.421823	−	0.422431i
$369$	581.424			1.57568
$370$	24.2362	−	121.729i	0.0655033	−	0.328998i
$371$	60.9312	+	60.9312i	0.164235	+	0.164235i
$372$	520.466	−	215.365i	1.39910	−	0.578937i
$373$	23.4566	+	23.4566i	0.0628862	+	0.0628862i	0.737850	−	0.674964i	$-0.235841\pi$
$373$	23.4566	+	23.4566i	0.0628862	+	0.0628862i	−0.674964	+	0.737850i	$0.735841\pi$
$374$	−510.636	+	341.063i	−1.36534	+	0.911933i
$375$	−60.3386			−0.160903
$376$	−115.277	+	172.323i	−0.306588	+	0.458305i
$377$			372.751i			0.988730i
$378$	−705.267	+	471.061i	−1.86579	+	1.24619i
$379$	−200.977	+	200.977i	−0.530283	+	0.530283i	−0.920657	−	0.390374i	$-0.872346\pi$
$379$	−200.977	+	200.977i	−0.530283	+	0.530283i	0.390374	+	0.920657i	$0.372346\pi$
$380$	36.7275	−	88.5779i	0.0966514	−	0.233100i
$381$	−414.823	+	414.823i	−1.08878	+	1.08878i
$382$	111.314	−	559.085i	0.291397	−	1.46357i
$383$			128.871i			0.336479i	0.985746	+	0.168239i	$0.0538082\pi$
$383$			128.871i			0.336479i	−0.985746	+	0.168239i	$0.946192\pi$
$384$	384.510	−	573.892i	1.00133	−	1.49451i
$385$	−231.453			−0.601176
$386$	−34.2320	−	6.81557i	−0.0886839	−	0.0176569i
$387$	26.3023	+	26.3023i	0.0679647	+	0.0679647i
$388$	465.041	+	192.823i	1.19856	+	0.496965i
$389$	−104.010	−	104.010i	−0.267379	−	0.267379i	0.560664	−	0.828043i	$-0.310546\pi$
$389$	−104.010	−	104.010i	−0.267379	−	0.267379i	−0.828043	+	0.560664i	$0.810546\pi$
$390$	108.555	+	162.528i	0.278347	+	0.416738i
$391$	−287.631			−0.735629
$392$	−5.82357	−	3.89574i	−0.0148560	−	0.00993811i
$393$		−	1.55738i		−	0.00396279i
$394$	145.139	+	217.300i	0.368373	+	0.551524i
$395$	17.3971	−	17.3971i	0.0440432	−	0.0440432i
$396$	451.141	+	1090.26i	1.13924	+	2.75318i
$397$	87.2509	−	87.2509i	0.219776	−	0.219776i	−0.588628	−	0.808404i	$-0.700332\pi$
$397$	87.2509	−	87.2509i	0.219776	−	0.219776i	0.808404	+	0.588628i	$0.200332\pi$
$398$	−581.469	−	115.770i	−1.46098	−	0.290880i
$399$			408.616i			1.02410i
$400$	−56.6093	+	56.5278i	−0.141523	+	0.141319i
$401$	416.906			1.03967			0.519833	−	0.854268i	$-0.325994\pi$
$401$	416.906			1.03967			0.519833	+	0.854268i	$0.325994\pi$
$402$	−187.646	+	942.472i	−0.466781	+	2.34446i
$403$	149.407	+	149.407i	0.370736	+	0.370736i
$404$	77.7755	+	187.958i	0.192514	+	0.465243i
$405$	−225.980	−	225.980i	−0.557975	−	0.557975i
$406$	540.654	−	361.113i	1.33166	−	0.889440i
$407$	406.775			0.999446
$408$	−175.968	−	887.158i	−0.431295	−	2.17441i
$409$		−	364.415i		−	0.890990i	−0.895284	−	0.445495i	$-0.853028\pi$
$409$		−	364.415i		−	0.890990i	0.895284	−	0.445495i	$-0.146972\pi$
$410$	−107.436	+	71.7583i	−0.262039	+	0.175020i
$411$	500.782	−	500.782i	1.21845	−	1.21845i
$412$	−195.553	−	81.0831i	−0.474642	−	0.196804i
$413$	309.381	−	309.381i	0.749106	−	0.749106i
$414$	−107.920	+	542.041i	−0.260677	+	1.30928i
$415$		−	222.292i		−	0.535644i
$416$	254.108	+	50.7833i	0.610838	+	0.122075i
$417$	568.520			1.36336
$418$	308.213	+	61.3651i	0.737351	+	0.146806i
$419$	206.623	+	206.623i	0.493134	+	0.493134i	0.909292	−	0.416159i	$-0.136624\pi$
$419$	206.623	+	206.623i	0.493134	+	0.493134i	−0.416159	+	0.909292i	$0.636624\pi$
$420$	130.571	−	314.906i	0.310884	−	0.749776i
$421$	−262.161	−	262.161i	−0.622710	−	0.622710i	0.323513	−	0.946224i	$-0.395136\pi$
$421$	−262.161	−	262.161i	−0.622710	−	0.622710i	−0.946224	+	0.323513i	$0.895136\pi$
$422$	268.471	+	401.952i	0.636188	+	0.952493i
$423$	521.580			1.23305
$424$	18.9913	+	95.7459i	0.0447907	+	0.225816i
$425$			104.742i			0.246451i
$426$	−407.412	−	609.973i	−0.956366	−	1.43186i
$427$	186.251	−	186.251i	0.436185	−	0.436185i
$428$	−550.805	+	227.918i	−1.28693	+	0.532520i
$429$	−452.930	+	452.930i	−1.05578	+	1.05578i
$430$	−8.10634	−	1.61397i	−0.0188520	−	0.00375342i
$431$			272.447i			0.632128i	0.948738	+	0.316064i	$0.102361\pi$
$431$			272.447i			0.632128i	−0.948738	+	0.316064i	$0.897639\pi$
$432$	−960.726	−	0.692204i	−2.22390	−	0.00160232i
$433$	−477.786			−1.10343			−0.551716	−	0.834032i	$-0.686027\pi$
$433$	−477.786			−1.10343			−0.551716	+	0.834032i	$0.686027\pi$
$434$	71.9641	−	361.448i	0.165816	−	0.832829i
$435$	392.786	+	392.786i	0.902957	+	0.902957i
$436$	−659.039	+	272.705i	−1.51156	+	0.625470i
$437$	104.088	+	104.088i	0.238188	+	0.238188i
$438$	125.878	−	84.0761i	0.287392	−	0.191955i
$439$	−304.402			−0.693398			−0.346699	−	0.937977i	$-0.612697\pi$
$439$	−304.402			−0.693398			−0.346699	+	0.937977i	$0.612697\pi$
$440$	−217.920	−	145.780i	−0.495273	−	0.331318i
$441$			17.6266i			0.0399695i
$442$	282.132	−	188.441i	0.638307	−	0.426337i
$443$	−541.093	+	541.093i	−1.22143	+	1.22143i	−0.254304	+	0.967124i	$0.581846\pi$
$443$	−541.093	+	541.093i	−1.22143	+	1.22143i	−0.967124	+	0.254304i	$0.918154\pi$
$444$	−229.477	+	553.442i	−0.516840	+	1.24649i
$445$	−255.755	+	255.755i	−0.574730	+	0.574730i
$446$	−90.3941	+	454.014i	−0.202677	+	1.01797i
$447$		−	1066.88i		−	2.38676i
$448$	−172.516	−	417.767i	−0.385081	−	0.932516i
$449$	467.626			1.04148			0.520742	−	0.853714i	$-0.325656\pi$
$449$	467.626			1.04148			0.520742	+	0.853714i	$0.325656\pi$
$450$	197.386	+	39.2995i	0.438635	+	0.0873321i
$451$	−299.401	−	299.401i	−0.663860	−	0.663860i
$452$	−234.013	−	97.0301i	−0.517727	−	0.214668i
$453$	−674.339	−	674.339i	−1.48861	−	1.48861i
$454$	−25.0501	−	37.5048i	−0.0551765	−	0.0826097i
$455$	127.880			0.281055
$456$	−257.365	+	384.724i	−0.564398	+	0.843694i
$457$			388.024i			0.849069i	0.905412	+	0.424534i	$0.139562\pi$
$457$			388.024i			0.849069i	−0.905412	+	0.424534i	$0.860438\pi$
$458$	−385.863	−	577.711i	−0.842497	−	1.26138i
$459$	−889.436	+	889.436i	−1.93777	+	1.93777i
$460$	−46.9562	−	113.478i	−0.102079	−	0.246691i
$461$	513.706	−	513.706i	1.11433	−	1.11433i	0.121772	−	0.992558i	$-0.461142\pi$
$461$	513.706	−	513.706i	1.11433	−	1.11433i	0.992558	−	0.121772i	$-0.0388576\pi$
$462$	1095.74	+	218.161i	2.37173	+	0.472210i
$463$			338.087i			0.730209i	0.930967	+	0.365105i	$0.118967\pi$
$463$			338.087i			0.730209i	−0.930967	+	0.365105i	$0.881033\pi$
$464$	736.488	+	0.530640i	1.58726	+	0.00114362i
$465$	314.875			0.677150
$466$	−134.295	+	674.513i	−0.288187	+	1.44745i
$467$	−368.745	−	368.745i	−0.789604	−	0.789604i	0.191825	−	0.981429i	$-0.438559\pi$
$467$	−368.745	−	368.745i	−0.789604	−	0.789604i	−0.981429	+	0.191825i	$0.938559\pi$
$468$	−249.260	−	602.381i	−0.532607	−	1.28714i
$469$	444.600	+	444.600i	0.947975	+	0.947975i
$470$	−96.3777	+	64.3724i	−0.205059	+	0.136963i
$471$	−73.3410			−0.155713
$472$	486.154	−	96.4290i	1.02999	−	0.204299i
$473$		−	27.0884i		−	0.0572694i
$474$	−98.7586	+	65.9626i	−0.208351	+	0.139162i
$475$	37.9040	−	37.9040i	0.0797978	−	0.0797978i
$476$	−546.645	−	226.658i	−1.14841	−	0.476173i
$477$	173.641	−	173.641i	0.364027	−	0.364027i
$478$	100.525	−	504.898i	0.210303	−	1.05627i
$479$		−	448.127i		−	0.935547i	−0.883848	−	0.467773i	$-0.845056\pi$
$479$		−	448.127i		−	0.935547i	0.883848	−	0.467773i	$-0.154944\pi$
$480$	321.279	−	214.254i	0.669332	−	0.446362i
$481$	−224.747			−0.467250
$482$	356.456	+	70.9703i	0.739536	+	0.147241i
$483$	370.047	+	370.047i	0.766142	+	0.766142i
$484$	143.731	−	346.644i	0.296965	−	0.716208i
$485$	198.999	+	198.999i	0.410307	+	0.410307i
$486$	256.516	+	384.054i	0.527811	+	0.790234i
$487$	−333.697			−0.685210			−0.342605	−	0.939480i	$-0.611309\pi$
$487$	−333.697			−0.685210			−0.342605	+	0.939480i	$0.611309\pi$
$488$	292.671	−	58.0514i	0.599735	−	0.118958i
$489$			392.290i			0.802229i
$490$	−2.17544	−	3.25704i	−0.00443967	−	0.00664703i
$491$	−118.839	+	118.839i	−0.242034	+	0.242034i	−0.817691	−	0.575657i	$-0.804746\pi$
$491$	−118.839	+	118.839i	−0.242034	+	0.242034i	0.575657	+	0.817691i	$0.304746\pi$
$492$	576.257	−	238.450i	1.17125	−	0.484655i
$493$	681.837	−	681.837i	1.38304	−	1.38304i
$494$	−170.291	−	33.9048i	−0.344718	−	0.0686333i
$495$			659.592i			1.33251i
$496$	295.413	−	294.988i	0.595591	−	0.594733i
$497$	−479.939			−0.965672
$498$	−209.526	+	1052.37i	−0.420736	+	2.11319i
$499$	148.915	+	148.915i	0.298427	+	0.298427i	0.840398	−	0.541970i	$-0.182321\pi$
$499$	148.915	+	148.915i	0.298427	+	0.298427i	−0.541970	+	0.840398i	$0.682321\pi$
$500$	−41.3233	+	17.0992i	−0.0826466	+	0.0341985i
$501$	799.121	+	799.121i	1.59505	+	1.59505i
$502$	−118.482	+	79.1364i	−0.236020	+	0.157642i
$503$	347.840			0.691530			0.345765	−	0.938321i	$-0.387619\pi$
$503$	347.840			0.691530			0.345765	+	0.938321i	$0.387619\pi$
$504$	−632.241	+	945.109i	−1.25445	+	1.87522i
$505$			113.712i			0.225172i
$506$	334.693	−	223.548i	0.661449	−	0.441794i
$507$	−394.681	+	394.681i	−0.778463	+	0.778463i
$508$	−166.539	+	401.650i	−0.327832	+	0.790650i
$509$	129.882	−	129.882i	0.255171	−	0.255171i	−0.567916	−	0.823087i	$-0.692250\pi$
$509$	129.882	−	129.882i	0.255171	−	0.255171i	0.823087	+	0.567916i	$0.192250\pi$
$510$	98.7266	−	495.865i	0.193582	−	0.972285i
$511$		−	99.0433i		−	0.193823i
$512$	100.700	−	501.999i	0.196680	−	0.980468i
$513$	643.739			1.25485
$514$	−386.346	−	76.9213i	−0.751645	−	0.149652i
$515$	−83.6802	−	83.6802i	−0.162486	−	0.162486i
$516$	36.8555	+	15.2816i	0.0714254	+	0.0296155i
$517$	−268.584	−	268.584i	−0.519505	−	0.519505i
$518$	217.730	+	325.983i	0.420328	+	0.629311i
$519$	−82.4456			−0.158855
$520$	120.403	+	80.5449i	0.231544	+	0.154894i
$521$		−	240.395i		−	0.461411i	−0.973024	−	0.230706i	$-0.925897\pi$
$521$		−	240.395i		−	0.461411i	0.973024	−	0.230706i	$-0.0741034\pi$
$522$	−1029.09	−	1540.75i	−1.97145	−	2.95163i
$523$	−501.537	+	501.537i	−0.958962	+	0.958962i	−0.999191	−	0.0402281i	$-0.987192\pi$
$523$	−501.537	+	501.537i	−0.958962	+	0.958962i	0.0402281	+	0.999191i	$0.487192\pi$
$524$	−0.441342	−	1.06658i	−0.000842255	−	0.00203546i
$525$	134.754	−	134.754i	0.256674	−	0.256674i
$526$	−86.4305	−	17.2083i	−0.164317	−	0.0327154i
$527$		−	546.590i		−	1.03717i
$528$	894.262	+	895.552i	1.69368	+	1.69612i
$529$	−340.474			−0.643618
$530$	−10.6550	+	53.5159i	−0.0201038	+	0.100973i
$531$	−881.670	−	881.670i	−1.66040	−	1.66040i
$532$	115.797	+	279.843i	0.217663	+	0.526021i
$533$	165.422	+	165.422i	0.310360	+	0.310360i
$534$	1451.85	−	969.720i	2.71883	−	1.81596i
$535$	−333.229			−0.622858
$536$	138.575	+	698.635i	0.258535	+	1.30342i
$537$		−	1626.08i		−	3.02808i
$538$	−286.433	+	191.314i	−0.532403	+	0.355602i
$539$	9.07669	−	9.07669i	0.0168399	−	0.0168399i
$540$	−496.107	−	205.704i	−0.918717	−	0.380933i
$541$	−675.194	+	675.194i	−1.24805	+	1.24805i	−0.291467	+	0.956581i	$0.594143\pi$
$541$	−675.194	+	675.194i	−1.24805	+	1.24805i	−0.956581	+	0.291467i	$0.905857\pi$
$542$	88.1182	−	442.583i	0.162580	−	0.816574i
$543$		−	210.283i		−	0.387261i
$544$	−371.923	−	557.709i	−0.683682	−	1.02520i
$545$	−398.709			−0.731576
$546$	−605.406	−	120.536i	−1.10880	−	0.220762i
$547$	324.268	+	324.268i	0.592811	+	0.592811i	0.938390	−	0.345579i	$-0.112317\pi$
$547$	324.268	+	324.268i	0.592811	+	0.592811i	−0.345579	+	0.938390i	$0.612317\pi$
$548$	201.048	−	484.880i	0.366877	−	0.884817i
$549$	−530.776	−	530.776i	−0.966805	−	0.966805i
$550$	−81.4056	−	121.880i	−0.148010	−	0.221599i
$551$	−493.487			−0.895620
$552$	115.338	+	581.483i	0.208945	+	1.05341i
$553$			77.7053i			0.140516i
$554$	39.8348	+	59.6402i	0.0719039	+	0.107654i
$555$	−236.827	+	236.827i	−0.426716	+	0.426716i
$556$	389.354	−	161.112i	0.700278	−	0.289769i
$557$	−454.039	+	454.039i	−0.815151	+	0.815151i	−0.985401	−	0.170250i	$-0.945543\pi$
$557$	−454.039	+	454.039i	−0.815151	+	0.815151i	0.170250	+	0.985401i	$0.445543\pi$
$558$	−1030.05	−	205.082i	−1.84597	−	0.367531i
$559$			14.9667i			0.0267740i
$560$	0.182047	−	252.668i	0.000325084	−	0.451192i
$561$	1657.00			2.95366
$562$	89.9708	−	451.888i	0.160090	−	0.804072i
$563$	530.844	+	530.844i	0.942885	+	0.942885i	0.998455	−	0.0555697i	$-0.0176975\pi$
$563$	530.844	+	530.844i	0.942885	+	0.942885i	−0.0555697	+	0.998455i	$0.517698\pi$
$564$	516.944	−	213.907i	0.916567	−	0.379268i
$565$	−100.138	−	100.138i	−0.177235	−	0.177235i
$566$	169.654	−	113.315i	0.299743	−	0.200204i
$567$	1009.36			1.78017
$568$	−451.877	−	302.288i	−0.795559	−	0.532197i
$569$			444.904i			0.781906i	0.920411	+	0.390953i	$0.127854\pi$
$569$			444.904i			0.781906i	−0.920411	+	0.390953i	$0.872146\pi$
$570$	−215.171	+	143.717i	−0.377493	+	0.252134i
$571$	−144.285	+	144.285i	−0.252688	+	0.252688i	−0.822072	−	0.569384i	$-0.807182\pi$
$571$	−144.285	+	144.285i	−0.252688	+	0.252688i	0.569384	+	0.822072i	$0.307182\pi$
$572$	−181.837	+	438.547i	−0.317897	+	0.766691i
$573$	−1087.71	+	1087.71i	−1.89828	+	1.89828i
$574$	79.6781	−	400.192i	0.138812	−	0.697199i
$575$		−	68.6524i		−	0.119396i
$576$	−1190.55	+	491.635i	−2.06692	+	0.853532i
$577$	572.779			0.992685			0.496343	−	0.868127i	$-0.334676\pi$
$577$	572.779			0.992685			0.496343	+	0.868127i	$0.334676\pi$
$578$	−293.898	−	58.5150i	−0.508475	−	0.101237i
$579$	66.5992	+	66.5992i	0.115025	+	0.115025i
$580$	380.313	+	157.691i	0.655712	+	0.271882i
$581$	496.443	+	496.443i	0.854463	+	0.854463i
$582$	−754.524	−	1129.67i	−1.29643	−	1.94101i
$583$	−178.831			−0.306742
$584$	62.3821	−	93.2523i	0.106819	−	0.159679i
$585$		−	364.431i		−	0.622960i
$586$	378.478	+	566.653i	0.645866	+	0.966984i
$587$	−44.1122	+	44.1122i	−0.0751486	+	0.0751486i	−0.743682	−	0.668533i	$-0.766922\pi$
$587$	−44.1122	+	44.1122i	−0.0751486	+	0.0751486i	0.668533	+	0.743682i	$0.266922\pi$
$588$	7.22890	+	17.4699i	0.0122940	+	0.0297107i
$589$	−197.800	+	197.800i	−0.335824	+	0.335824i
$590$	271.730	+	54.1013i	0.460559	+	0.0916970i
$591$		−	705.135i		−	1.19312i
$592$	−0.319945	+	444.060i	−0.000540448	+	0.750101i
$593$	−463.508			−0.781632			−0.390816	−	0.920469i	$-0.627807\pi$
$593$	−463.508			−0.781632			−0.390816	+	0.920469i	$0.627807\pi$
$594$	343.694	−	1726.24i	0.578609	−	2.90613i
$595$	−233.919	−	233.919i	−0.393141	−	0.393141i
$596$	−302.342	−	730.662i	−0.507285	−	1.22594i
$597$	1131.26	+	1131.26i	1.89491	+	1.89491i
$598$	−184.922	+	123.513i	−0.309233	+	0.206543i
$599$	441.512			0.737082			0.368541	−	0.929612i	$-0.379857\pi$
$599$	441.512			0.737082			0.368541	+	0.929612i	$0.379857\pi$
$600$	211.749	−	42.0005i	0.352915	−	0.0700009i
$601$			403.814i			0.671904i	0.941879	+	0.335952i	$0.109058\pi$
$601$			403.814i			0.671904i	−0.941879	+	0.335952i	$0.890942\pi$
$602$	21.7083	−	14.4993i	0.0360602	−	0.0240853i
$603$	1267.02	−	1267.02i	2.10119	−	2.10119i
$604$	−652.925	−	270.726i	−1.08100	−	0.448222i
$605$	148.335	−	148.335i	0.245182	−	0.245182i
$606$	107.182	−	538.332i	0.176867	−	0.888336i
$607$			789.688i			1.30097i	0.759520	+	0.650484i	$0.225434\pi$
$607$			789.688i			1.30097i	−0.759520	+	0.650484i	$0.774566\pi$
$608$	−67.2322	+	336.415i	−0.110579	+	0.553315i
$609$	−1754.41			−2.88081
$610$	163.584	+	32.5696i	0.268171	+	0.0533928i
$611$	148.396	+	148.396i	0.242873	+	0.242873i
$612$	−645.929	+	1557.82i	−1.05544	+	2.54546i
$613$	664.045	+	664.045i	1.08327	+	1.08327i	0.996202	+	0.0870678i	$0.0277497\pi$
$613$	664.045	+	664.045i	1.08327	+	1.08327i	0.0870678	+	0.996202i	$0.472250\pi$
$614$	−424.624	−	635.743i	−0.691570	−	1.03541i
$615$	348.627			0.566873
$616$	812.247	−	161.110i	1.31858	−	0.261542i
$617$			934.518i			1.51462i	0.653058	+	0.757308i	$0.273486\pi$
$617$			934.518i			1.51462i	−0.653058	+	0.757308i	$0.726514\pi$
$618$	317.282	+	475.031i	0.513401	+	0.768659i
$619$	496.720	−	496.720i	0.802455	−	0.802455i	−0.181024	−	0.983479i	$-0.557941\pi$
$619$	496.720	−	496.720i	0.802455	−	0.802455i	0.983479	+	0.181024i	$0.0579411\pi$
$620$	215.644	−	89.2316i	0.347813	−	0.143922i
$621$	582.976	−	582.976i	0.938770	−	0.938770i
$622$	−1063.34	−	211.711i	−1.70955	−	0.340371i
$623$		−	1142.35i		−	1.83363i
$624$	−494.089	−	494.802i	−0.791810	−	0.792952i
$625$	−25.0000			−0.0400000
$626$	−58.5067	+	293.856i	−0.0934612	+	0.469419i
$627$	−599.636	−	599.636i	−0.956358	−	0.956358i
$628$	−50.2281	+	20.7840i	−0.0799810	+	0.0330955i
$629$	411.108	+	411.108i	0.653590	+	0.653590i
$630$	−528.587	+	353.053i	−0.839027	+	0.560401i
$631$	−767.372			−1.21612			−0.608060	−	0.793891i	$-0.708052\pi$
$631$	−767.372			−1.21612			−0.608060	+	0.793891i	$0.708052\pi$
$632$	−48.9424	+	73.1619i	−0.0774406	+	0.115763i
$633$		−	1304.33i		−	2.06055i
$634$	−986.275	+	658.751i	−1.55564	+	1.03904i
$635$	−171.873	+	171.873i	−0.270666	+	0.270666i
$636$	100.885	−	243.310i	0.158624	−	0.382563i
$637$	−5.01497	+	5.01497i	−0.00787279	+	0.00787279i
$638$	−263.474	+	1323.33i	−0.412968	+	2.07418i
$639$			1367.73i			2.14041i
$640$	159.313	−	237.780i	0.248927	−	0.371531i
$641$	670.734			1.04639			0.523193	−	0.852214i	$-0.324741\pi$
$641$	670.734			1.04639			0.523193	+	0.852214i	$0.324741\pi$
$642$	1577.56	+	314.092i	2.45726	+	0.489240i
$643$	329.050	+	329.050i	0.511743	+	0.511743i	0.915060	−	0.403317i	$-0.132143\pi$
$643$	329.050	+	329.050i	0.511743	+	0.511743i	−0.403317	+	0.915060i	$0.632143\pi$
$644$	358.296	+	148.562i	0.556360	+	0.230687i
$645$	15.7711	+	15.7711i	0.0244513	+	0.0244513i
$646$	249.478	+	373.515i	0.386188	+	0.578197i
$647$	576.907			0.891664			0.445832	−	0.895117i	$-0.352908\pi$
$647$	576.907			0.891664			0.445832	+	0.895117i	$0.352908\pi$
$648$	950.340	+	635.740i	1.46657	+	0.981080i
$649$			908.021i			1.39911i
$650$	44.9775	+	67.3398i	0.0691961	+	0.103600i
$651$	−703.206	+	703.206i	−1.08019	+	1.08019i
$652$	111.170	+	268.662i	0.170506	+	0.412059i
$653$	905.010	−	905.010i	1.38593	−	1.38593i	0.552243	−	0.833683i	$-0.313772\pi$
$653$	905.010	−	905.010i	1.38593	−	1.38593i	0.833683	−	0.552243i	$-0.186228\pi$
$654$	1887.56	+	375.812i	2.88617	+	0.574636i
$655$		−	0.645265i		−	0.000985138i
$656$	327.079	−	326.608i	0.498596	−	0.497879i
$657$	−282.253			−0.429608
$658$	71.4771	−	359.002i	0.108628	−	0.545595i
$659$	−420.842	−	420.842i	−0.638606	−	0.638606i	0.311605	−	0.950212i	$-0.399133\pi$
$659$	−420.842	−	420.842i	−0.638606	−	0.638606i	−0.950212	+	0.311605i	$0.899133\pi$
$660$	270.508	+	653.730i	0.409860	+	0.990500i
$661$	−661.814	−	661.814i	−1.00123	−	1.00123i	−0.999999	−	0.00123192i	$-0.999608\pi$
$661$	−661.814	−	661.814i	−1.00123	−	1.00123i	−0.00123192	−	0.999999i	$-0.500392\pi$
$662$	−251.296	+	167.845i	−0.379601	+	0.253542i
$663$	−915.511			−1.38086
$664$	154.733	+	780.100i	0.233032	+	1.17485i
$665$			169.301i			0.254588i
$666$	928.983	−	620.484i	1.39487	−	0.931658i
$667$	−446.907	+	446.907i	−0.670025	+	0.670025i
$668$	773.745	+	320.822i	1.15830	+	0.480273i
$669$	883.297	−	883.297i	1.32032	−	1.32032i
$670$	−77.7470	+	390.493i	−0.116040	+	0.582825i
$671$			546.640i			0.814664i
$672$	−239.019	+	1196.00i	−0.355683	+	1.77976i
$673$	−469.242			−0.697240			−0.348620	−	0.937264i	$-0.613350\pi$
$673$	−469.242			−0.697240			−0.348620	+	0.937264i	$0.613350\pi$
$674$	−572.124	−	113.910i	−0.848849	−	0.169005i
$675$	−212.293	−	212.293i	−0.314508	−	0.314508i
$676$	−158.452	+	382.147i	−0.234396	+	0.565307i
$677$	−656.674	−	656.674i	−0.969977	−	0.969977i	0.0295853	−	0.999562i	$-0.490581\pi$
$677$	−656.674	−	656.674i	−0.969977	−	0.969977i	−0.999562	+	0.0295853i	$0.990581\pi$
$678$	379.683	+	568.458i	0.560005	+	0.838433i
$679$	−888.844			−1.30905
$680$	−72.9087	−	367.575i	−0.107219	−	0.540551i
$681$			121.702i			0.178711i
$682$	424.812	+	636.024i	0.622891	+	0.932586i
$683$	−21.1806	+	21.1806i	−0.0310111	+	0.0310111i	−0.722442	−	0.691431i	$-0.756981\pi$
$683$	−21.1806	+	21.1806i	−0.0310111	+	0.0310111i	0.691431	+	0.722442i	$0.256981\pi$
$684$	797.494	−	329.996i	1.16593	−	0.482451i
$685$	207.488	−	207.488i	0.302902	−	0.302902i
$686$	−666.648	−	132.729i	−0.971791	−	0.193483i
$687$			1874.66i			2.72876i
$688$	29.5714	+	0.0213062i	0.0429816	+	3.09683e-5i
$689$	98.8059			0.143405
$690$	−64.7098	+	325.012i	−0.0937824	+	0.471032i
$691$	−117.463	−	117.463i	−0.169990	−	0.169990i	0.616985	−	0.786975i	$-0.288354\pi$
$691$	−117.463	−	117.463i	−0.169990	−	0.169990i	−0.786975	+	0.616985i	$0.788354\pi$
$692$	−56.4634	+	23.3641i	−0.0815945	+	0.0337631i
$693$	−1473.06	−	1473.06i	−2.12563	−	2.12563i
$694$	−618.183	+	412.896i	−0.890754	+	0.594950i
$695$	235.554			0.338926
$696$	−1651.83	−	1105.01i	−2.37332	−	1.58766i
$697$		−	605.181i		−	0.868265i
$698$	1010.39	−	674.860i	1.44756	−	0.966849i
$699$	1312.28	−	1312.28i	1.87737	−	1.87737i
$700$	54.0994	−	130.474i	0.0772848	−	0.186392i
$701$	475.012	−	475.012i	0.677620	−	0.677620i	−0.281841	−	0.959461i	$-0.590945\pi$
$701$	475.012	−	475.012i	0.677620	−	0.677620i	0.959461	+	0.281841i	$0.0909450\pi$
$702$	−189.894	+	953.765i	−0.270505	+	1.35864i
$703$		−	297.544i		−	0.423249i
$704$	866.230	+	359.902i	1.23044	+	0.511224i
$705$	312.744			0.443608
$706$	471.536	+	93.8827i	0.667898	+	0.132978i
$707$	−253.952	−	253.952i	−0.359196	−	0.359196i
$708$	−1235.42	−	512.249i	−1.74494	−	0.723516i
$709$	−459.941	−	459.941i	−0.648718	−	0.648718i	0.303965	−	0.952683i	$-0.401689\pi$
$709$	−459.941	−	459.941i	−0.648718	−	0.648718i	−0.952683	+	0.303965i	$0.901689\pi$
$710$	−168.802	−	252.729i	−0.237750	−	0.355956i
$711$	221.444			0.311454
$712$	719.505	−	1075.56i	1.01054	−	1.51061i
$713$			358.260i			0.502468i
$714$	886.926	+	1327.90i	1.24219	+	1.85980i
$715$	−187.662	+	187.662i	−0.262464	+	0.262464i
$716$	−460.811	−	1113.63i	−0.643591	−	1.55535i
$717$	−982.292	+	982.292i	−1.37000	+	1.37000i
$718$	−112.489	−	22.3964i	−0.156669	−	0.0311928i
$719$			79.4499i			0.110501i	0.998473	+	0.0552503i	$0.0175957\pi$
$719$			79.4499i			0.110501i	−0.998473	+	0.0552503i	$0.982404\pi$
$720$	−720.050	−	0.518796i	−1.00007	−	0.000720550i
$721$	373.764			0.518397
$722$	−96.0960	+	482.653i	−0.133097	+	0.668494i
$723$	−693.495	−	693.495i	−0.959191	−	0.959191i
$724$	−59.5916	−	144.014i	−0.0823089	−	0.198914i
$725$	162.742	+	162.742i	0.224472	+	0.224472i
$726$	−842.060	+	562.427i	−1.15986	+	0.774693i
$727$	−645.074			−0.887310			−0.443655	−	0.896198i	$-0.646318\pi$
$727$	−645.074			−0.887310			−0.443655	+	0.896198i	$0.646318\pi$
$728$	−448.775	+	89.0148i	−0.616449	+	0.122273i
$729$			40.0535i			0.0549431i
$730$	52.1547	−	34.8351i	0.0714449	−	0.0477193i
$731$	27.3770	−	27.3770i	0.0374515	−	0.0374515i
$732$	−743.737	−	308.380i	−1.01603	−	0.421284i
$733$	673.917	−	673.917i	0.919396	−	0.919396i	−0.0775895	−	0.996985i	$-0.524722\pi$
$733$	673.917	−	673.917i	0.919396	−	0.919396i	0.996985	+	0.0775895i	$0.0247224\pi$
$734$	−26.5227	+	133.213i	−0.0361345	+	0.181489i
$735$			10.5690i			0.0143796i
$736$	243.775	+	365.547i	0.331216	+	0.496667i
$737$	−1304.88			−1.77054
$738$	−1140.46	−	227.066i	−1.54534	−	0.307677i
$739$	489.699	+	489.699i	0.662651	+	0.662651i	0.956004	−	0.293353i	$-0.0947711\pi$
$739$	489.699	+	489.699i	0.662651	+	0.662651i	−0.293353	+	0.956004i	$0.594771\pi$
$740$	−95.0788	+	229.307i	−0.128485	+	0.309874i
$741$	331.305	+	331.305i	0.447106	+	0.447106i
$742$	−95.7208	−	143.312i	−0.129004	−	0.193143i
$743$	−444.077			−0.597681			−0.298840	−	0.954303i	$-0.596600\pi$
$743$	−444.077			−0.597681			−0.298840	+	0.954303i	$0.596600\pi$
$744$	−1105.00	+	219.178i	−1.48522	+	0.294594i
$745$		−	442.040i		−	0.593342i
$746$	−36.8495	−	55.1706i	−0.0493961	−	0.0739553i
$747$	1414.76	−	1414.76i	1.89392	−	1.89392i
$748$	1134.81	−	469.574i	1.51712	−	0.627773i
$749$	744.196	−	744.196i	0.993587	−	0.993587i
$750$	118.354	+	23.5643i	0.157806	+	0.0314190i
$751$		−	739.796i		−	0.985081i	−0.870289	−	0.492541i	$-0.836068\pi$
$751$		−	739.796i		−	0.985081i	0.870289	−	0.492541i	$-0.163932\pi$
$752$	293.414	−	292.991i	0.390178	−	0.389616i
$753$	384.472			0.510587
$754$	145.572	−	731.151i	0.193066	−	0.969697i
$755$	−279.398	−	279.398i	−0.370063	−	0.370063i
$756$	1567.35	−	648.555i	2.07321	−	0.857877i
$757$	705.538	+	705.538i	0.932019	+	0.932019i	0.997832	−	0.0658133i	$-0.0209642\pi$
$757$	705.538	+	705.538i	0.932019	+	0.932019i	−0.0658133	+	0.997832i	$0.520964\pi$
$758$	472.705	−	315.729i	0.623622	−	0.416528i
$759$	−1086.07			−1.43093
$760$	−106.634	+	159.402i	−0.140308	+	0.209740i
$761$			1439.41i			1.89148i	0.324929	+	0.945738i	$0.394660\pi$
$761$			1439.41i			1.89148i	−0.324929	+	0.945738i	$0.605340\pi$
$762$	975.679	−	651.673i	1.28042	−	0.855215i
$763$	890.433	−	890.433i	1.16702	−	1.16702i
$764$	−436.683	+	1053.17i	−0.571575	+	1.37850i
$765$	−666.619	+	666.619i	−0.871397	+	0.871397i
$766$	50.3287	−	252.781i	0.0657032	−	0.330002i
$767$		−	501.691i		−	0.654096i
$768$	−978.341	+	975.526i	−1.27388	+	1.27022i
$769$	994.407			1.29312			0.646558	−	0.762865i	$-0.276208\pi$
$769$	994.407			1.29312			0.646558	+	0.762865i	$0.276208\pi$
$770$	453.995	+	90.3902i	0.589604	+	0.117390i
$771$	751.645	+	751.645i	0.974897	+	0.974897i
$772$	64.4843	+	26.7375i	0.0835289	+	0.0346341i
$773$	−506.461	−	506.461i	−0.655188	−	0.655188i	0.299049	−	0.954238i	$-0.403331\pi$
$773$	−506.461	−	506.461i	−0.655188	−	0.655188i	−0.954238	+	0.299049i	$0.903331\pi$
$774$	−41.3201	−	61.8640i	−0.0533851	−	0.0799276i
$775$	130.461			0.168337
$776$	−836.874	−	559.836i	−1.07845	−	0.721438i
$777$		−	1057.81i		−	1.36140i
$778$	163.397	+	244.636i	0.210022	+	0.314442i
$779$	−219.003	+	219.003i	−0.281134	+	0.281134i
$780$	−149.458	−	361.193i	−0.191613	−	0.463067i
$781$	704.302	−	704.302i	0.901795	−	0.901795i
$782$	564.188	+	112.330i	0.721469	+	0.143644i
$783$			2763.92i			3.52991i
$784$	9.90152	+	9.91579i	0.0126295	+	0.0126477i
$785$	−30.3873			−0.0387099
$786$	−0.608208	+	3.05479i	−0.000773802	+	0.00388651i
$787$	−168.801	−	168.801i	−0.214487	−	0.214487i	0.591684	−	0.806170i	$-0.298463\pi$
$787$	−168.801	−	168.801i	−0.214487	−	0.214487i	−0.806170	+	0.591684i	$0.798463\pi$
$788$	−199.827	−	482.916i	−0.253587	−	0.612838i
$789$	168.153	+	168.153i	0.213122	+	0.213122i
$790$	−40.9185	+	27.3302i	−0.0517955	+	0.0345952i
$791$	447.274			0.565454
$792$	−459.129	−	2314.73i	−0.579708	−	2.92264i
$793$		−	302.024i		−	0.380863i
$794$	−205.217	+	137.068i	−0.258460	+	0.172630i
$795$	104.117	−	104.117i	0.130964	−	0.130964i
$796$	1095.34	+	454.167i	1.37605	+	0.570561i
$797$	−994.677	+	994.677i	−1.24803	+	1.24803i	−0.291435	+	0.956591i	$0.594133\pi$
$797$	−994.677	+	994.677i	−1.24803	+	1.24803i	−0.956591	+	0.291435i	$0.905867\pi$
$798$	159.578	−	801.500i	0.199973	−	1.00439i
$799$		−	542.891i		−	0.679463i
$800$	133.115	−	88.7714i	0.166394	−	0.110964i
$801$	−3255.46			−4.06424
$802$	−817.761	−	162.816i	−1.01965	−	0.203012i
$803$	145.344	+	145.344i	0.181002	+	0.181002i
$804$	736.135	−	1775.38i	0.915590	−	2.20818i
$805$	153.321	+	153.321i	0.190461	+	0.190461i
$806$	−234.713	−	351.410i	−0.291207	−	0.435992i
$807$	929.468			1.15176
$808$	−79.1526	−	399.054i	−0.0979612	−	0.493879i
$809$		−	219.139i		−	0.270876i	−0.990786	−	0.135438i	$-0.956756\pi$
$809$		−	219.139i		−	0.270876i	0.990786	−	0.135438i	$-0.0432441\pi$
$810$	355.007	+	531.512i	0.438280	+	0.656188i
$811$	942.641	−	942.641i	1.16232	−	1.16232i	0.178352	−	0.983967i	$-0.442923\pi$
$811$	942.641	−	942.641i	1.16232	−	1.16232i	0.983967	−	0.178352i	$-0.0570767\pi$
$812$	−1201.52	+	497.179i	−1.47970	+	0.612289i
$813$	−861.057	+	861.057i	−1.05911	+	1.05911i
$814$	−797.889	−	158.859i	−0.980207	−	0.195159i
$815$			162.537i			0.199432i
$816$	−1.30330	+	1808.88i	−0.00159718	+	2.21677i
$817$	−19.8144			−0.0242526
$818$	−142.316	+	714.800i	−0.173981	+	0.873839i
$819$	813.881	+	813.881i	0.993749	+	0.993749i
$820$	238.759	−	98.7966i	0.291170	−	0.120484i
$821$	−476.861	−	476.861i	−0.580830	−	0.580830i	0.354301	−	0.935131i	$-0.384719\pi$
$821$	−476.861	−	476.861i	−0.580830	−	0.580830i	−0.935131	+	0.354301i	$0.884719\pi$
$822$	−1177.86	+	786.712i	−1.43292	+	0.957070i
$823$	1372.74			1.66797			0.833985	−	0.551788i	$-0.186054\pi$
$823$	1372.74			1.66797			0.833985	+	0.551788i	$0.186054\pi$
$824$	351.911	+	235.414i	0.427076	+	0.285697i
$825$			395.497i			0.479390i
$826$	−727.674	+	486.027i	−0.880962	+	0.588410i
$827$	171.863	−	171.863i	0.207815	−	0.207815i	−0.595523	−	0.803338i	$-0.703055\pi$
$827$	171.863	−	171.863i	0.207815	−	0.207815i	0.803338	+	0.595523i	$0.203055\pi$
$828$	423.371	−	1021.07i	0.511317	−	1.23317i
$829$	100.485	−	100.485i	0.121212	−	0.121212i	−0.643899	−	0.765111i	$-0.722684\pi$
$829$	100.485	−	100.485i	0.121212	−	0.121212i	0.765111	+	0.643899i	$0.222684\pi$
$830$	−86.8127	+	436.026i	−0.104594	+	0.525333i
$831$		−	193.531i		−	0.232889i
$832$	−478.601	−	198.849i	−0.575242	−	0.239002i
$833$	18.3468			0.0220249
$834$	−1115.15	−	222.026i	−1.33711	−	0.266219i
$835$	331.099	+	331.099i	0.396525	+	0.396525i
$836$	−580.594	−	240.735i	−0.694491	−	0.287961i
$837$	1107.84	+	1107.84i	1.32358	+	1.32358i
$838$	−324.598	−	485.984i	−0.387348	−	0.579933i
$839$	−519.265			−0.618909			−0.309455	−	0.950914i	$-0.600147\pi$
$839$	−519.265			−0.618909			−0.309455	+	0.950914i	$0.600147\pi$
$840$	−379.097	+	566.696i	−0.451306	+	0.674638i
$841$		−	1277.81i		−	1.51939i
$842$	411.846	+	616.612i	0.489128	+	0.732318i
$843$	−879.161	+	879.161i	−1.04290	+	1.04290i
$844$	−369.630	−	893.277i	−0.437951	−	1.05838i
$845$	−163.527	+	163.527i	−0.193524	+	0.193524i
$846$	−1023.08	−	203.695i	−1.20931	−	0.240774i
$847$			662.550i			0.782232i
$848$	0.140658	−	195.222i	0.000165870	−	0.230215i
$849$	−550.525			−0.648440
$850$	40.9052	−	205.451i	0.0481238	−	0.241707i
$851$	−269.459	−	269.459i	−0.316638	−	0.316638i
$852$	560.923	+	1355.57i	0.658361	+	1.59104i
$853$	989.103	+	989.103i	1.15956	+	1.15956i	0.984571	+	0.174987i	$0.0559885\pi$
$853$	989.103	+	989.103i	1.15956	+	1.15956i	0.174987	+	0.984571i	$0.444012\pi$
$854$	−438.069	+	292.594i	−0.512961	+	0.342616i
$855$	482.472			0.564295
$856$	1169.41	−	231.954i	1.36614	−	0.270974i
$857$		−	271.282i		−	0.316549i	−0.987395	−	0.158274i	$-0.949407\pi$
$857$		−	271.282i		−	0.316549i	0.987395	−	0.158274i	$-0.0505931\pi$
$858$	1065.31	−	711.538i	1.24162	−	0.829298i
$859$	397.195	−	397.195i	0.462393	−	0.462393i	−0.437046	−	0.899439i	$-0.643975\pi$
$859$	397.195	−	397.195i	0.462393	−	0.462393i	0.899439	+	0.437046i	$0.143975\pi$
$860$	15.2703	+	6.33160i	0.0177561	+	0.00736233i
$861$	−778.585	+	778.585i	−0.904280	+	0.904280i
$862$	106.400	−	534.405i	0.123434	−	0.619960i
$863$			84.9753i			0.0984649i	0.998787	+	0.0492325i	$0.0156775\pi$
$863$			84.9753i			0.0984649i	−0.998787	+	0.0492325i	$0.984322\pi$
$864$	1884.19	+	376.554i	2.18078	+	0.435826i
$865$	−34.1595			−0.0394908
$866$	937.177	+	186.592i	1.08219	+	0.215464i
$867$	571.787	+	571.787i	0.659500	+	0.659500i
$868$	−282.315	+	680.875i	−0.325248	+	0.784419i
$869$	−114.031	−	114.031i	−0.131221	−	0.131221i
$870$	−617.054	−	923.847i	−0.709257	−	1.06189i
$871$	720.963			0.827741
$872$	1399.21	−	277.533i	1.60459	−	0.318272i
$873$			2533.02i			2.90151i
$874$	−163.519	−	244.819i	−0.187092	−	0.280113i
$875$	55.8322	−	55.8322i	0.0638083	−	0.0638083i
$876$	−279.744	+	115.756i	−0.319342	+	0.132141i
$877$	264.532	−	264.532i	0.301633	−	0.301633i	−0.540020	−	0.841652i	$-0.681583\pi$
$877$	264.532	−	264.532i	0.301633	−	0.301633i	0.841652	+	0.540020i	$0.181583\pi$
$878$	597.084	+	118.879i	0.680050	+	0.135398i
$879$		−	1838.78i		−	2.09190i
$880$	370.518	+	371.052i	0.421043	+	0.421651i
$881$	−199.022			−0.225905			−0.112952	−	0.993600i	$-0.536031\pi$
$881$	−199.022			−0.225905			−0.112952	+	0.993600i	$0.536031\pi$
$882$	6.88377	−	34.5745i	0.00780473	−	0.0392001i
$883$	403.210	+	403.210i	0.456636	+	0.456636i	0.897550	−	0.440913i	$-0.145345\pi$
$883$	403.210	+	403.210i	0.456636	+	0.456636i	−0.440913	+	0.897550i	$0.645345\pi$
$884$	−626.994	+	259.445i	−0.709269	+	0.293489i
$885$	−528.657	−	528.657i	−0.597353	−	0.597353i
$886$	1272.67	−	850.038i	1.43642	−	0.959411i
$887$	−794.907			−0.896174			−0.448087	−	0.893990i	$-0.647895\pi$
$887$	−794.907			−0.896174			−0.448087	+	0.893990i	$0.647895\pi$
$888$	666.257	−	995.959i	0.750289	−	1.12157i
$889$		−	767.684i		−	0.863537i
$890$	601.544	−	401.782i	0.675893	−	0.451441i
$891$	−1481.21	+	1481.21i	−1.66242	+	1.66242i
$892$	354.616	−	855.247i	0.397552	−	0.958798i
$893$	−196.462	+	196.462i	−0.220002	+	0.220002i
$894$	−416.654	+	2092.69i	−0.466056	+	2.34082i
$895$		−	673.730i		−	0.752771i
$896$	175.238	+	886.824i	0.195578	+	0.989759i
$897$	600.067			0.668971
$898$	−917.248	−	182.624i	−1.02143	−	0.203367i
$899$	−849.264	−	849.264i	−0.944677	−	0.944677i
$900$	−371.825	−	154.172i	−0.413138	−	0.171302i
$901$	−180.736	−	180.736i	−0.200595	−	0.200595i
$902$	470.349	+	704.201i	0.521451	+	0.780711i
$903$	−70.4429			−0.0780098
$904$	421.123	+	281.714i	0.465844	+	0.311631i
$905$		−	87.1261i		−	0.0962720i
$906$	1059.36	+	1586.07i	1.16928	+	1.75063i
$907$	−779.778	+	779.778i	−0.859733	+	0.859733i	−0.991306	−	0.131573i	$-0.957997\pi$
$907$	−779.778	+	779.778i	−0.859733	+	0.859733i	0.131573	+	0.991306i	$0.457997\pi$
$908$	34.4890	+	83.3486i	0.0379834	+	0.0917937i
$909$	−723.709	+	723.709i	−0.796159	+	0.796159i
$910$	−250.837	−	49.9415i	−0.275645	−	0.0548808i
$911$			491.368i			0.539372i	0.962948	+	0.269686i	$0.0869199\pi$
$911$			491.368i			0.539372i	−0.962948	+	0.269686i	$0.913080\pi$
$912$	655.070	−	654.127i	0.718279	−	0.717244i
$913$	−1457.04			−1.59588
$914$	151.537	−	761.110i	0.165795	−	0.832724i
$915$	−318.258	−	318.258i	−0.347823	−	0.347823i
$916$	531.256	+	1283.87i	0.579973	+	1.40161i
$917$	1.44106	+	1.44106i	0.00157150	+	0.00157150i
$918$	2091.98	−	1397.27i	2.27885	−	1.52209i
$919$	1434.03			1.56042			0.780212	−	0.625515i	$-0.215111\pi$
$919$	1434.03			1.56042			0.780212	+	0.625515i	$0.215111\pi$
$920$	47.7876	+	240.925i	0.0519430	+	0.261875i
$921$			2062.97i			2.23993i
$922$	−1208.25	+	807.015i	−1.31047	+	0.875287i
$923$	−389.134	+	389.134i	−0.421597	+	0.421597i
$924$	−2064.09	−	855.845i	−2.23386	−	0.926240i
$925$	−98.1242	+	98.1242i	−0.106080	+	0.106080i
$926$	132.034	−	663.157i	0.142586	−	0.716153i
$927$		−	1065.15i		−	1.14903i
$928$	−1444.41	−	288.664i	−1.55648	−	0.311061i
$929$	429.452			0.462273			0.231137	−	0.972921i	$-0.425756\pi$
$929$	429.452			0.462273			0.231137	+	0.972921i	$0.425756\pi$
$930$	−617.627	−	122.969i	−0.664115	−	0.132225i
$931$	−6.63934	−	6.63934i	−0.00713140	−	0.00713140i
$932$	526.840	−	1270.61i	0.565279	−	1.36332i
$933$	2068.76	+	2068.76i	2.21732	+	2.21732i
$934$	579.286	+	867.301i	0.620221	+	0.928588i
$935$	686.543			0.734270
$936$	253.673	+	1278.91i	0.271019	+	1.36636i
$937$		−	1739.01i		−	1.85594i	−0.372660	−	0.927968i	$-0.621554\pi$
$937$		−	1739.01i		−	1.85594i	0.372660	−	0.927968i	$-0.378446\pi$
$938$	−698.452	−	1045.71i	−0.744618	−	1.11483i
$939$	571.705	−	571.705i	0.608845	−	0.608845i
$940$	214.185	−	88.6277i	0.227856	−	0.0942848i
$941$	−732.880	+	732.880i	−0.778831	+	0.778831i	−0.979632	−	0.200801i	$-0.935645\pi$
$941$	−732.880	+	732.880i	−0.778831	+	0.778831i	0.200801	+	0.979632i	$0.435645\pi$
$942$	143.858	+	28.6422i	0.152716	+	0.0304057i
$943$			396.663i			0.420639i
$944$	−991.250	−	0.714196i	−1.05005	−	0.000756564i
$945$	948.222			1.00341
$946$	−10.5790	+	53.1340i	−0.0111828	+	0.0561670i
$947$	−1044.83	−	1044.83i	−1.10330	−	1.10330i	−0.994009	−	0.109296i	$-0.965140\pi$
$947$	−1044.83	−	1044.83i	−1.10330	−	1.10330i	−0.109296	−	0.994009i	$-0.534860\pi$
$948$	219.476	−	90.8172i	0.231514	−	0.0957987i
$949$	−80.3042	−	80.3042i	−0.0846198	−	0.0846198i
$950$	−89.1514	+	59.5459i	−0.0938436	+	0.0626799i
$951$	3200.44			3.36534
$952$	983.726	+	658.074i	1.03333	+	0.691254i
$953$			759.754i			0.797224i	0.917120	+	0.398612i	$0.130508\pi$
$953$			759.754i			0.797224i	−0.917120	+	0.398612i	$0.869492\pi$
$954$	−408.410	+	272.784i	−0.428102	+	0.285937i
$955$	−450.671	+	450.671i	−0.471907	+	0.471907i
$956$	−394.359	+	951.099i	−0.412510	+	0.994873i
$957$	2574.57	−	2574.57i	2.69025	−	2.69025i
$958$	−175.009	+	879.001i	−0.182681	+	0.917538i
$959$			926.762i			0.966384i
$960$	−713.863	+	294.788i	−0.743607	+	0.307071i
$961$	280.193			0.291564
$962$	440.842	+	87.7714i	0.458256	+	0.0912385i
$963$	−2120.80	−	2120.80i	−2.20229	−	2.20229i
$964$	−671.473	−	278.416i	−0.696548	−	0.288814i
$965$	27.5939	+	27.5939i	0.0285947	+	0.0285947i
$966$	−581.331	−	870.362i	−0.601792	−	0.900996i
$967$	−44.4105			−0.0459260			−0.0229630	−	0.999736i	$-0.507310\pi$
$967$	−44.4105			−0.0459260			−0.0229630	+	0.999736i	$0.507310\pi$
$968$	−417.305	+	623.811i	−0.431100	+	0.644433i
$969$		−	1212.05i		−	1.25082i
$970$	−312.621	−	468.052i	−0.322289	−	0.482528i
$971$	519.035	−	519.035i	0.534537	−	0.534537i	−0.387382	−	0.921919i	$-0.626621\pi$
$971$	519.035	−	519.035i	0.534537	−	0.534537i	0.921919	+	0.387382i	$0.126621\pi$
$972$	−353.171	−	853.500i	−0.363345	−	0.878086i
$973$	−526.060	+	526.060i	−0.540657	+	0.540657i
$974$	654.547	+	130.320i	0.672020	+	0.133799i
$975$		−	218.516i		−	0.224119i
$976$	−596.745	−	0.429955i	−0.611419	−	0.000440527i
$977$	−797.585			−0.816361			−0.408181	−	0.912901i	$-0.633837\pi$
$977$	−797.585			−0.816361			−0.408181	+	0.912901i	$0.633837\pi$
$978$	153.202	−	769.477i	0.156649	−	0.786786i
$979$	1676.38	+	1676.38i	1.71234	+	1.71234i
$980$	2.99514	+	7.23827i	0.00305626	+	0.00738599i
$981$	−2537.55	−	2537.55i	−2.58669	−	2.58669i
$982$	279.512	−	186.691i	0.284636	−	0.190113i
$983$	−1432.42			−1.45720			−0.728599	−	0.684941i	$-0.759828\pi$
$983$	−1432.42			−1.45720			−0.728599	+	0.684941i	$0.759828\pi$
$984$	−1223.45	+	242.672i	−1.24334	+	0.246618i
$985$		−	292.157i		−	0.296606i
$986$	−1603.70	+	1071.14i	−1.62647	+	1.08635i
$987$	−698.447	+	698.447i	−0.707646	+	0.707646i
$988$	320.784	+	133.009i	0.324681	+	0.134624i
$989$	−17.9441	+	17.9441i	−0.0181437	+	0.0181437i
$990$	257.593	−	1293.79i	0.260195	−	1.30686i
$991$			1885.38i			1.90250i	0.308424	+	0.951249i	$0.400198\pi$
$991$			1885.38i			1.90250i	−0.308424	+	0.951249i	$0.599802\pi$
$992$	−694.656	+	463.250i	−0.700258	+	0.466986i
$993$	815.449			0.821197
$994$	941.401	+	187.433i	0.947083	+	0.188564i
$995$	468.714	+	468.714i	0.471070	+	0.471070i
$996$	821.972	−	1982.40i	0.825273	−	1.99036i
$997$	396.902	+	396.902i	0.398096	+	0.398096i	0.877561	−	0.479465i	$-0.159169\pi$
$997$	396.902	+	396.902i	0.398096	+	0.398096i	−0.479465	+	0.877561i	$0.659169\pi$
$998$	−233.941	−	350.254i	−0.234410	−	0.350956i
$999$	−1666.48			−1.66815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.r.a.11.2	✓	32
4.3	odd	2		320.3.r.a.271.1		32
5.2	odd	4		400.3.k.h.299.9		32
5.3	odd	4		400.3.k.g.299.8		32
5.4	even	2		400.3.r.f.251.15		32
8.3	odd	2		640.3.r.b.31.16		32
8.5	even	2		640.3.r.a.31.1		32
16.3	odd	4	inner	80.3.r.a.51.2	yes	32
16.5	even	4		640.3.r.b.351.16		32
16.11	odd	4		640.3.r.a.351.1		32
16.13	even	4		320.3.r.a.111.1		32
80.3	even	4		400.3.k.h.99.9		32
80.19	odd	4		400.3.r.f.51.15		32
80.67	even	4		400.3.k.g.99.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.2	✓	32	1.1	even	1	trivial
80.3.r.a.51.2	yes	32	16.3	odd	4	inner
320.3.r.a.111.1		32	16.13	even	4
320.3.r.a.271.1		32	4.3	odd	2
400.3.k.g.99.8		32	80.67	even	4
400.3.k.g.299.8		32	5.3	odd	4
400.3.k.h.99.9		32	80.3	even	4
400.3.k.h.299.9		32	5.2	odd	4
400.3.r.f.51.15		32	80.19	odd	4
400.3.r.f.251.15		32	5.4	even	2
640.3.r.a.31.1		32	8.5	even	2
640.3.r.a.351.1		32	16.11	odd	4
640.3.r.b.31.16		32	8.3	odd	2
640.3.r.b.351.16		32	16.5	even	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	80.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96150 - 0.390534i) q^{2} +(3.81615 + 3.81615i) q^{3} +(3.69497 + 1.53206i) q^{4} +(1.58114 + 1.58114i) q^{5} +(-5.99504 - 8.97572i) q^{6} -7.06228 q^{7} +(-6.64935 - 4.44816i) q^{8} +20.1260i q^{9} +(-2.48392 - 3.71889i) q^{10} +(10.3638 - 10.3638i) q^{11} +(8.25396 + 19.9471i) q^{12} +(-5.72609 + 5.72609i) q^{13} +(13.8527 + 2.75806i) q^{14} +12.0677i q^{15} +(11.3056 + 11.3219i) q^{16} +20.9484 q^{17} +(7.85989 - 39.4772i) q^{18} +(-7.58079 - 7.58079i) q^{19} +(3.41985 + 8.26466i) q^{20} +(-26.9507 - 26.9507i) q^{21} +(-24.3759 + 16.2811i) q^{22} -13.7305 q^{23} +(-8.40010 - 42.3498i) q^{24} +5.00000i q^{25} +(13.4680 - 8.99549i) q^{26} +(-42.4585 + 42.4585i) q^{27} +(-26.0949 - 10.8199i) q^{28} +(32.5485 - 32.5485i) q^{29} +(4.71286 - 23.6709i) q^{30} -26.0923i q^{31} +(-17.7543 - 26.6230i) q^{32} +79.0994 q^{33} +(-41.0902 - 8.18104i) q^{34} +(-11.1664 - 11.1664i) q^{35} +(-30.8344 + 74.3649i) q^{36} +(19.6248 + 19.6248i) q^{37} +(11.9092 + 17.8303i) q^{38} -43.7032 q^{39} +(-3.48040 - 17.5467i) q^{40} -28.8892i q^{41} +(42.3387 + 63.3890i) q^{42} +(1.30688 - 1.30688i) q^{43} +(54.1717 - 22.4158i) q^{44} +(-31.8220 + 31.8220i) q^{45} +(26.9324 + 5.36222i) q^{46} -25.9157i q^{47} +(-0.0622149 + 86.3496i) q^{48} +0.875810 q^{49} +(1.95267 - 9.80750i) q^{50} +(79.9421 + 79.9421i) q^{51} +(-29.9304 + 12.3850i) q^{52} +(-8.62769 - 8.62769i) q^{53} +(99.8639 - 66.7009i) q^{54} +32.7731 q^{55} +(46.9596 + 31.4141i) q^{56} -57.8589i q^{57} +(-76.5552 + 51.1326i) q^{58} +(-43.8075 + 43.8075i) q^{59} +(-18.4885 + 44.5898i) q^{60} +(-26.3726 + 26.3726i) q^{61} +(-10.1899 + 51.1800i) q^{62} -142.136i q^{63} +(24.4278 + 59.1547i) q^{64} -18.1075 q^{65} +(-155.153 - 30.8910i) q^{66} +(-62.9542 - 62.9542i) q^{67} +(77.4035 + 32.0942i) q^{68} +(-52.3976 - 52.3976i) q^{69} +(17.5421 + 26.2639i) q^{70} +67.9581 q^{71} +(89.5236 - 133.825i) q^{72} +14.0243i q^{73} +(-30.8300 - 46.1583i) q^{74} +(-19.0808 + 19.0808i) q^{75} +(-16.3965 - 39.6251i) q^{76} +(-73.1918 + 73.1918i) q^{77} +(85.7239 + 17.0676i) q^{78} -11.0029i q^{79} +(-0.0257774 + 35.7771i) q^{80} -142.922 q^{81} +(-11.2822 + 56.6662i) q^{82} +(-70.2950 - 70.2950i) q^{83} +(-58.2918 - 140.872i) q^{84} +(33.1223 + 33.1223i) q^{85} +(-3.07383 + 2.05307i) q^{86} +248.420 q^{87} +(-115.012 + 22.8127i) q^{88} +161.754i q^{89} +(74.8465 - 49.9913i) q^{90} +(40.4393 - 40.4393i) q^{91} +(-50.7337 - 21.0360i) q^{92} +(99.5721 - 99.5721i) q^{93} +(-10.1210 + 50.8337i) q^{94} -23.9726i q^{95} +(33.8445 - 169.350i) q^{96} +125.858 q^{97} +(-1.71790 - 0.342034i) q^{98} +(208.581 + 208.581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} + 12 q^{6} - 20 q^{10} + 32 q^{11} - 60 q^{12} - 36 q^{14} + 48 q^{16} + 160 q^{18} - 32 q^{19} + 40 q^{20} - 12 q^{22} - 128 q^{23} - 120 q^{24} - 48 q^{26} - 96 q^{27} - 180 q^{28} + 32 q^{29}+ \cdots + 608 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 + 12 * q^6 - 20 * q^10 + 32 * q^11 - 60 * q^12 - 36 * q^14 + 48 * q^16 + 160 * q^18 - 32 * q^19 + 40 * q^20 - 12 * q^22 - 128 * q^23 - 120 * q^24 - 48 * q^26 - 96 * q^27 - 180 * q^28 + 32 * q^29 - 160 * q^32 + 16 * q^34 - 84 * q^36 - 96 * q^37 + 140 * q^38 + 384 * q^39 + 20 * q^42 + 96 * q^43 + 8 * q^44 + 36 * q^46 + 280 * q^48 + 224 * q^49 + 20 * q^50 - 256 * q^51 - 104 * q^52 - 160 * q^53 + 192 * q^54 + 304 * q^56 - 4 * q^58 - 352 * q^59 - 140 * q^60 - 32 * q^61 + 552 * q^62 + 240 * q^64 - 576 * q^66 + 160 * q^67 + 16 * q^68 + 96 * q^69 - 120 * q^70 + 256 * q^71 + 568 * q^72 + 136 * q^74 + 512 * q^76 + 224 * q^77 - 208 * q^78 - 240 * q^80 - 288 * q^81 - 196 * q^82 - 480 * q^83 - 736 * q^84 + 160 * q^85 - 188 * q^86 - 320 * q^88 - 180 * q^90 - 384 * q^91 + 28 * q^92 + 96 * q^93 - 604 * q^94 + 232 * q^96 + 20 * q^98 + 608 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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