LMFDB - Embedded newform 51.3.j.a.40.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,3,Mod(7,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	51.j (of order $16$, degree $8$, 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:	$1.38964934824$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			40.6
Character	$\chi$	$=$	51.40
Dual form			51.3.j.a.37.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.92891 + 1.21319i) q^{2} +(-1.69877 + 0.337906i) q^{3} +(4.27824 + 4.27824i) q^{4} +(0.0817276 - 0.122314i) q^{5} +(-5.38549 - 1.07124i) q^{6} +(-2.35178 - 3.51969i) q^{7} +(2.48747 + 6.00528i) q^{8} +(2.77164 - 1.14805i) q^{9} +(0.387763 - 0.259095i) q^{10} +(2.13536 - 10.7352i) q^{11} +(-8.71339 - 5.82210i) q^{12} +(-12.2605 + 12.2605i) q^{13} +(-2.61809 - 13.1620i) q^{14} +(-0.0975057 + 0.235400i) q^{15} -3.59468i q^{16} +(-16.0231 + 5.67992i) q^{17} +9.51069 q^{18} +(30.9397 + 12.8156i) q^{19} +(0.872939 - 0.173638i) q^{20} +(5.18446 + 5.18446i) q^{21} +(19.2781 - 28.8517i) q^{22} +(-0.932603 - 0.185506i) q^{23} +(-6.25486 - 9.36106i) q^{24} +(9.55880 + 23.0770i) q^{25} +(-50.7842 + 21.0355i) q^{26} +(-4.32044 + 2.88683i) q^{27} +(4.99659 - 25.1195i) q^{28} +(-27.7735 - 18.5576i) q^{29} +(-0.571171 + 0.571171i) q^{30} +(5.12889 + 25.7847i) q^{31} +(14.3109 - 34.5496i) q^{32} +18.9581i q^{33} +(-53.8209 - 2.80312i) q^{34} -0.622712 q^{35} +(16.7694 + 6.94610i) q^{36} +(8.46626 - 1.68404i) q^{37} +(75.0717 + 75.0717i) q^{38} +(16.6849 - 24.9707i) q^{39} +(0.937825 + 0.186545i) q^{40} +(19.5445 + 29.2504i) q^{41} +(8.89505 + 21.4745i) q^{42} +(-20.6891 + 8.56969i) q^{43} +(55.0633 - 36.7921i) q^{44} +(0.0860968 - 0.432838i) q^{45} +(-2.50645 - 1.67476i) q^{46} +(35.2299 - 35.2299i) q^{47} +(1.21467 + 6.10654i) q^{48} +(11.8942 - 28.7150i) q^{49} +79.1871i q^{50} +(25.3002 - 15.0632i) q^{51} -104.907 q^{52} +(0.136939 + 0.0567219i) q^{53} +(-16.1565 + 3.21372i) q^{54} +(-1.13854 - 1.13854i) q^{55} +(15.2867 - 22.8782i) q^{56} +(-56.8899 - 11.3161i) q^{57} +(-58.8319 - 88.0482i) q^{58} +(-43.4125 - 104.807i) q^{59} +(-1.42425 + 0.589944i) q^{60} +(-82.1151 + 54.8676i) q^{61} +(-16.2597 + 81.7433i) q^{62} +(-10.5591 - 7.05534i) q^{63} +(73.6635 - 73.6635i) q^{64} +(0.497610 + 2.50165i) q^{65} +(-22.9999 + 55.5267i) q^{66} -24.5661i q^{67} +(-92.8506 - 44.2505i) q^{68} +1.64696 q^{69} +(-1.82387 - 0.755471i) q^{70} +(76.3125 - 15.1795i) q^{71} +(13.7887 + 13.7887i) q^{72} +(49.1586 - 73.5711i) q^{73} +(26.8400 + 5.33880i) q^{74} +(-24.0361 - 35.9725i) q^{75} +(77.5391 + 187.196i) q^{76} +(-42.8063 + 17.7310i) q^{77} +(79.1627 - 52.8948i) q^{78} +(5.48545 - 27.5772i) q^{79} +(-0.439680 - 0.293785i) q^{80} +(6.36396 - 6.36396i) q^{81} +(21.7576 + 109.383i) q^{82} +(-34.6160 + 83.5703i) q^{83} +44.3607i q^{84} +(-0.614793 + 2.42405i) q^{85} -70.9931 q^{86} +(53.4515 + 22.1403i) q^{87} +(69.7794 - 13.8800i) q^{88} +(-2.81464 - 2.81464i) q^{89} +(0.777286 - 1.16329i) q^{90} +(71.9871 + 14.3191i) q^{91} +(-3.19626 - 4.78354i) q^{92} +(-17.4256 - 42.0691i) q^{93} +(145.926 - 60.4445i) q^{94} +(4.09616 - 2.73697i) q^{95} +(-12.6364 + 63.5276i) q^{96} +(-12.3434 - 8.24758i) q^{97} +(69.6738 - 69.6738i) q^{98} +(-6.40608 - 32.2055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{10} - 80 q^{11} - 48 q^{13} - 64 q^{14} + 16 q^{17} + 48 q^{19} + 224 q^{20} + 192 q^{22} + 112 q^{23} - 144 q^{24} + 80 q^{25} - 368 q^{26} - 240 q^{28} - 160 q^{29} - 192 q^{30} - 64 q^{31}+ \cdots + 240 q^{99}+O(q^{100}) $ 48 * q - 48 * q^10 - 80 * q^11 - 48 * q^13 - 64 * q^14 + 16 * q^17 + 48 * q^19 + 224 * q^20 + 192 * q^22 + 112 * q^23 - 144 * q^24 + 80 * q^25 - 368 * q^26 - 240 * q^28 - 160 * q^29 - 192 * q^30 - 64 * q^31 - 80 * q^32 + 16 * q^34 + 128 * q^35 + 48 * q^36 + 128 * q^37 + 400 * q^38 + 192 * q^39 + 128 * q^40 + 320 * q^41 + 432 * q^42 - 112 * q^43 + 704 * q^44 + 96 * q^45 + 80 * q^46 - 32 * q^49 + 128 * q^52 - 336 * q^53 - 608 * q^55 - 880 * q^56 - 752 * q^58 - 512 * q^59 - 400 * q^61 - 560 * q^62 + 160 * q^64 - 240 * q^65 - 208 * q^68 - 240 * q^69 + 80 * q^70 - 160 * q^71 - 288 * q^72 + 544 * q^73 - 48 * q^74 - 288 * q^75 + 496 * q^76 + 512 * q^77 - 384 * q^78 + 608 * q^79 + 816 * q^80 + 1184 * q^82 + 976 * q^83 - 32 * q^85 + 128 * q^86 + 144 * q^87 - 448 * q^88 + 240 * q^89 + 48 * q^90 - 640 * q^91 + 1280 * q^92 + 288 * q^93 - 32 * q^94 + 704 * q^95 + 768 * q^96 + 288 * q^97 + 1008 * q^98 + 240 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{15}{16}\right)$

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 $

$2$	2.92891	+	1.21319i	1.46445	+	0.606597i	0.965587	−	0.260081i	$-0.0837493\pi$
$2$	2.92891	+	1.21319i	1.46445	+	0.606597i	0.498868	+	0.866678i	$0.333749\pi$
$3$	−1.69877	+	0.337906i	−0.566257	+	0.112635i
$3$	−1.69877	+	0.337906i	−0.566257	+	0.112635i
$4$	4.27824	+	4.27824i	1.06956	+	1.06956i
$5$	0.0817276	−	0.122314i	0.0163455	−	0.0244628i	−0.823207	−	0.567742i	$-0.807817\pi$
$5$	0.0817276	−	0.122314i	0.0163455	−	0.0244628i	0.839552	+	0.543279i	$0.182817\pi$
$6$	−5.38549	−	1.07124i	−0.897581	−	0.178540i
$7$	−2.35178	−	3.51969i	−0.335968	−	0.502812i	0.624567	−	0.780972i	$-0.285276\pi$
$7$	−2.35178	−	3.51969i	−0.335968	−	0.502812i	−0.960535	+	0.278159i	$0.910276\pi$
$8$	2.48747	+	6.00528i	0.310934	+	0.750660i
$9$	2.77164	−	1.14805i	0.307960	−	0.127561i
$10$	0.387763	−	0.259095i	0.0387763	−	0.0259095i
$11$	2.13536	−	10.7352i	0.194124	−	0.975925i	−0.753722	−	0.657194i	$-0.771743\pi$
$11$	2.13536	−	10.7352i	0.194124	−	0.975925i	0.947845	−	0.318731i	$-0.103257\pi$
$12$	−8.71339	−	5.82210i	−0.726116	−	0.485175i
$13$	−12.2605	+	12.2605i	−0.943115	+	0.943115i	−0.998467	−	0.0553516i	$-0.982372\pi$
$13$	−12.2605	+	12.2605i	−0.943115	+	0.943115i	0.0553516	+	0.998467i	$0.482372\pi$
$14$	−2.61809	−	13.1620i	−0.187006	−	0.940143i
$15$	−0.0975057	+	0.235400i	−0.00650038	+	0.0156933i
$16$		−	3.59468i		−	0.224668i
$17$	−16.0231	+	5.67992i	−0.942533	+	0.334113i
$17$	−16.0231	+	5.67992i	−0.942533	+	0.334113i
$18$	9.51069			0.528371
$19$	30.9397	+	12.8156i	1.62840	+	0.674507i	0.995052	−	0.0993562i	$-0.0316783\pi$
$19$	30.9397	+	12.8156i	1.62840	+	0.674507i	0.633353	+	0.773863i	$0.281678\pi$
$20$	0.872939	−	0.173638i	0.0436470	−	0.00868192i
$21$	5.18446	+	5.18446i	0.246879	+	0.246879i
$22$	19.2781	−	28.8517i	0.876278	−	1.31144i
$23$	−0.932603	−	0.185506i	−0.0405479	−	0.00806549i	0.174775	−	0.984608i	$-0.444080\pi$
$23$	−0.932603	−	0.185506i	−0.0405479	−	0.00806549i	−0.215323	+	0.976543i	$0.569080\pi$
$24$	−6.25486	−	9.36106i	−0.260619	−	0.390044i
$25$	9.55880	+	23.0770i	0.382352	+	0.923080i
$26$	−50.7842	+	21.0355i	−1.95324	+	0.809059i
$27$	−4.32044	+	2.88683i	−0.160016	+	0.106920i
$28$	4.99659	−	25.1195i	0.178450	−	0.897127i
$29$	−27.7735	−	18.5576i	−0.957706	−	0.639918i	−0.0246674	−	0.999696i	$-0.507853\pi$
$29$	−27.7735	−	18.5576i	−0.957706	−	0.639918i	−0.933038	+	0.359777i	$0.882853\pi$
$30$	−0.571171	+	0.571171i	−0.0190390	+	0.0190390i
$31$	5.12889	+	25.7847i	0.165448	+	0.831763i	0.970971	+	0.239198i	$0.0768846\pi$
$31$	5.12889	+	25.7847i	0.165448	+	0.831763i	−0.805523	+	0.592565i	$0.798115\pi$
$32$	14.3109	−	34.5496i	0.447216	−	1.07968i
$33$			18.9581i			0.574489i
$34$	−53.8209	−	2.80312i	−1.58297	−	0.0824448i
$35$	−0.622712			−0.0177918
$36$	16.7694	+	6.94610i	0.465816	+	0.192947i
$37$	8.46626	−	1.68404i	0.228818	−	0.0455147i	−0.0793495	−	0.996847i	$-0.525284\pi$
$37$	8.46626	−	1.68404i	0.228818	−	0.0455147i	0.308167	+	0.951332i	$0.400284\pi$
$38$	75.0717	+	75.0717i	1.97557	+	1.97557i
$39$	16.6849	−	24.9707i	0.427817	−	0.640274i
$40$	0.937825	+	0.186545i	0.0234456	+	0.00466363i
$41$	19.5445	+	29.2504i	0.476695	+	0.713424i	0.989412	−	0.145133i	$-0.0463611\pi$
$41$	19.5445	+	29.2504i	0.476695	+	0.713424i	−0.512717	+	0.858557i	$0.671361\pi$
$42$	8.89505	+	21.4745i	0.211787	+	0.511299i
$43$	−20.6891	+	8.56969i	−0.481141	+	0.199295i	−0.610053	−	0.792361i	$-0.708852\pi$
$43$	−20.6891	+	8.56969i	−0.481141	+	0.199295i	0.128911	+	0.991656i	$0.458852\pi$
$44$	55.0633	−	36.7921i	1.25144	−	0.836184i
$45$	0.0860968	−	0.432838i	0.00191326	−	0.00961861i
$46$	−2.50645	−	1.67476i	−0.0544881	−	0.0364078i
$47$	35.2299	−	35.2299i	0.749573	−	0.749573i	−0.224826	−	0.974399i	$-0.572181\pi$
$47$	35.2299	−	35.2299i	0.749573	−	0.749573i	0.974399	+	0.224826i	$0.0721813\pi$
$48$	1.21467	+	6.10654i	0.0253055	+	0.127220i
$49$	11.8942	−	28.7150i	0.242738	−	0.586021i
$50$			79.1871i			1.58374i
$51$	25.3002	−	15.0632i	0.496083	−	0.295356i
$52$	−104.907			−2.01744
$53$	0.136939	+	0.0567219i	0.00258375	+	0.00107023i	0.383975	−	0.923344i	$-0.374555\pi$
$53$	0.136939	+	0.0567219i	0.00258375	+	0.00107023i	−0.381391	+	0.924414i	$0.624555\pi$
$54$	−16.1565	+	3.21372i	−0.299194	+	0.0595133i
$55$	−1.13854	−	1.13854i	−0.0207008	−	0.0207008i
$56$	15.2867	−	22.8782i	0.272977	−	0.408539i
$57$	−56.8899	−	11.3161i	−0.998068	−	0.198528i
$58$	−58.8319	−	88.0482i	−1.01434	−	1.51807i
$59$	−43.4125	−	104.807i	−0.735805	−	1.77639i	−0.622193	−	0.782864i	$-0.713758\pi$
$59$	−43.4125	−	104.807i	−0.735805	−	1.77639i	−0.113612	−	0.993525i	$-0.536242\pi$
$60$	−1.42425	+	0.589944i	−0.0237375	+	0.00983239i
$61$	−82.1151	+	54.8676i	−1.34615	+	0.899468i	−0.999261	−	0.0384384i	$-0.987762\pi$
$61$	−82.1151	+	54.8676i	−1.34615	+	0.899468i	−0.346888	+	0.937906i	$0.612762\pi$
$62$	−16.2597	+	81.7433i	−0.262254	+	1.31844i
$63$	−10.5591	−	7.05534i	−0.167604	−	0.111989i
$64$	73.6635	−	73.6635i	1.15099	−	1.15099i
$65$	0.497610	+	2.50165i	0.00765553	+	0.0384870i
$66$	−22.9999	+	55.5267i	−0.348483	+	0.841313i
$67$		−	24.5661i		−	0.366658i	−0.983052	−	0.183329i	$-0.941313\pi$
$67$		−	24.5661i		−	0.366658i	0.983052	−	0.183329i	$-0.0586874\pi$
$68$	−92.8506	−	44.2505i	−1.36545	−	0.650742i
$69$	1.64696			0.0238690
$70$	−1.82387	−	0.755471i	−0.0260552	−	0.0107924i
$71$	76.3125	−	15.1795i	1.07482	−	0.213796i	0.374215	−	0.927342i	$-0.377912\pi$
$71$	76.3125	−	15.1795i	1.07482	−	0.213796i	0.700608	+	0.713546i	$0.252912\pi$
$72$	13.7887	+	13.7887i	0.191510	+	0.191510i
$73$	49.1586	−	73.5711i	0.673406	−	1.00782i	−0.324671	−	0.945827i	$-0.605253\pi$
$73$	49.1586	−	73.5711i	0.673406	−	1.00782i	0.998076	−	0.0619958i	$-0.0197465\pi$
$74$	26.8400	+	5.33880i	0.362702	+	0.0721460i
$75$	−24.0361	−	35.9725i	−0.320481	−	0.479634i
$76$	77.5391	+	187.196i	1.02025	+	2.46310i
$77$	−42.8063	+	17.7310i	−0.555926	+	0.230272i
$78$	79.1627	−	52.8948i	1.01491	−	0.678139i
$79$	5.48545	−	27.5772i	0.0694361	−	0.349079i	−0.930412	−	0.366516i	$-0.880551\pi$
$79$	5.48545	−	27.5772i	0.0694361	−	0.349079i	0.999848	+	0.0174369i	$0.00555062\pi$
$80$	−0.439680	−	0.293785i	−0.00549600	−	0.00367231i
$81$	6.36396	−	6.36396i	0.0785674	−	0.0785674i
$82$	21.7576	+	109.383i	0.265337	+	1.33394i
$83$	−34.6160	+	83.5703i	−0.417060	+	1.00687i	0.566135	+	0.824312i	$0.308438\pi$
$83$	−34.6160	+	83.5703i	−0.417060	+	1.00687i	−0.983195	+	0.182559i	$0.941562\pi$
$84$			44.3607i			0.528104i
$85$	−0.614793	+	2.42405i	−0.00723286	+	0.0285182i
$86$	−70.9931			−0.825501
$87$	53.4515	+	22.1403i	0.614385	+	0.254486i
$88$	69.7794	−	13.8800i	0.792948	−	0.157727i
$89$	−2.81464	−	2.81464i	−0.0316252	−	0.0316252i	0.691117	−	0.722743i	$-0.257119\pi$
$89$	−2.81464	−	2.81464i	−0.0316252	−	0.0316252i	−0.722743	+	0.691117i	$0.757119\pi$
$90$	0.777286	−	1.16329i	0.00863651	−	0.0129254i
$91$	71.9871	+	14.3191i	0.791067	+	0.157353i
$92$	−3.19626	−	4.78354i	−0.0347420	−	0.0519950i
$93$	−17.4256	−	42.0691i	−0.187372	−	0.452356i
$94$	145.926	−	60.4445i	1.55240	−	0.643027i
$95$	4.09616	−	2.73697i	0.0431175	−	0.0288102i
$96$	−12.6364	+	63.5276i	−0.131629	+	0.661746i
$97$	−12.3434	−	8.24758i	−0.127251	−	0.0850266i	0.490316	−	0.871545i	$-0.336882\pi$
$97$	−12.3434	−	8.24758i	−0.127251	−	0.0850266i	−0.617567	+	0.786518i	$0.711882\pi$
$98$	69.6738	−	69.6738i	0.710958	−	0.710958i
$99$	−6.40608	−	32.2055i	−0.0647078	−	0.325308i
$100$	−57.8341	+	139.624i	−0.578341	+	1.39624i
$101$		−	7.01636i		−	0.0694689i	−0.999397	−	0.0347345i	$-0.988941\pi$
$101$		−	7.01636i		−	0.0694689i	0.999397	−	0.0347345i	$-0.0110585\pi$
$102$	92.3766	−	13.4246i	0.905653	−	0.131613i
$103$	−127.796			−1.24074			−0.620369	−	0.784310i	$-0.713017\pi$
$103$	−127.796			−1.24074			−0.620369	+	0.784310i	$0.713017\pi$
$104$	−104.125	−	43.1301i	−1.00121	−	0.414713i
$105$	1.05784	−	0.210418i	0.0100747	−	0.00200398i
$106$	0.332267	+	0.332267i	0.00313459	+	0.00313459i
$107$	31.3619	−	46.9364i	0.293102	−	0.438658i	−0.655469	−	0.755222i	$-0.727529\pi$
$107$	31.3619	−	46.9364i	0.293102	−	0.438658i	0.948571	+	0.316564i	$0.102529\pi$
$108$	−30.8344	−	6.13335i	−0.285504	−	0.0567903i
$109$	100.780	+	150.828i	0.924585	+	1.38374i	0.923441	+	0.383740i	$0.125364\pi$
$109$	100.780	+	150.828i	0.924585	+	1.38374i	0.00114360	+	0.999999i	$0.499636\pi$
$110$	−1.95342	−	4.71597i	−0.0177583	−	0.0428724i
$111$	−13.8132	+	5.72161i	−0.124443	+	0.0515460i
$112$	−12.6522	+	8.45390i	−0.112966	+	0.0754812i
$113$	−36.3987	+	182.989i	−0.322112	+	1.61937i	0.392434	+	0.919780i	$0.371633\pi$
$113$	−36.3987	+	182.989i	−0.322112	+	1.61937i	−0.714547	+	0.699588i	$0.753367\pi$
$114$	−152.897	−	102.162i	−1.34120	−	0.896161i
$115$	−0.0989094	+	0.0989094i	−0.000860082	+	0.000860082i
$116$	−39.4275	−	198.216i	−0.339893	−	1.70876i
$117$	−19.9060	+	48.0573i	−0.170137	+	0.410747i
$118$		−	359.638i		−	3.04778i
$119$	57.6742	+	43.0382i	0.484657	+	0.361666i
$120$	−1.65618			−0.0138015
$121$	1.10523	+	0.457802i	0.00913415	+	0.00378349i
$122$	−307.073	+	61.0805i	−2.51699	+	0.500660i
$123$	−43.0855	−	43.0855i	−0.350288	−	0.350288i
$124$	−88.3704	+	132.256i	−0.712664	+	1.06658i
$125$	7.21084	+	1.43433i	0.0576867	+	0.0114746i
$126$	−22.3670	−	33.4746i	−0.177516	−	0.265672i
$127$	35.0857	+	84.7043i	0.276265	+	0.666963i	0.999726	−	0.0234023i	$-0.00744987\pi$
$127$	35.0857	+	84.7043i	0.276265	+	0.666963i	−0.723461	+	0.690365i	$0.757450\pi$
$128$	166.923	−	69.1419i	1.30409	−	0.540171i
$129$	32.2502	−	21.5489i	0.250002	−	0.167046i
$130$	−1.57754	+	7.93081i	−0.0121349	+	0.0610062i
$131$	14.9226	+	9.97096i	0.113913	+	0.0761142i	0.611222	−	0.791459i	$-0.290678\pi$
$131$	14.9226	+	9.97096i	0.113913	+	0.0761142i	−0.497309	+	0.867574i	$0.665678\pi$
$132$	−81.1075	+	81.1075i	−0.614451	+	0.614451i
$133$	−27.6563	−	139.038i	−0.207942	−	1.04539i
$134$	29.8034	−	71.9518i	0.222414	−	0.536954i
$135$			0.764384i			0.00566211i
$136$	−73.9664	−	82.0944i	−0.543870	−	0.603635i
$137$	131.421			0.959278			0.479639	−	0.877466i	$-0.340768\pi$
$137$	131.421			0.959278			0.479639	+	0.877466i	$0.340768\pi$
$138$	4.82380	+	1.99808i	0.0349551	+	0.0144789i
$139$	14.7270	−	2.92938i	0.105949	−	0.0210747i	−0.141831	−	0.989891i	$-0.545299\pi$
$139$	14.7270	−	2.92938i	0.105949	−	0.0210747i	0.247780	+	0.968816i	$0.420299\pi$
$140$	−2.66411	−	2.66411i	−0.0190294	−	0.0190294i
$141$	−47.9431	+	71.7520i	−0.340022	+	0.508879i
$142$	241.928	+	48.1225i	1.70372	+	0.338891i
$143$	105.438	+	157.799i	0.737329	+	1.10349i
$144$	−4.12688	−	9.96316i	−0.0286589	−	0.0691886i
$145$	−4.53972	+	1.88041i	−0.0313084	+	0.0129684i
$146$	233.237	−	155.844i	1.59751	−	1.06742i
$147$	−10.5024	+	52.7994i	−0.0714452	+	0.359179i
$148$	43.4255	+	29.0160i	0.293415	+	0.196054i
$149$	−10.8438	+	10.8438i	−0.0727772	+	0.0727772i	−0.742558	−	0.669781i	$-0.766388\pi$
$149$	−10.8438	+	10.8438i	−0.0727772	+	0.0727772i	0.669781	+	0.742558i	$0.266388\pi$
$150$	−26.7578	−	134.521i	−0.178386	−	0.896804i
$151$	4.56032	−	11.0096i	0.0302008	−	0.0729112i	−0.908060	−	0.418841i	$-0.862436\pi$
$151$	4.56032	−	11.0096i	0.0302008	−	0.0729112i	0.938260	+	0.345930i	$0.112436\pi$
$152$			217.680i			1.43211i
$153$	−37.8893	+	34.1380i	−0.247643	+	0.223124i
$154$	−146.887			−0.953811
$155$	3.57300	+	1.47998i	0.0230516	+	0.00954828i
$156$	178.212	−	35.4487i	1.14239	−	0.227235i
$157$	−107.166	−	107.166i	−0.682584	−	0.682584i	0.277998	−	0.960582i	$-0.410329\pi$
$157$	−107.166	−	107.166i	−0.682584	−	0.682584i	−0.960582	+	0.277998i	$0.910329\pi$
$158$	49.5229	−	74.1163i	0.313436	−	0.469090i
$159$	−0.251794	−	0.0500850i	−0.00158361	−	0.000315000i
$160$	−3.05631	−	4.57409i	−0.0191019	−	0.0285880i
$161$	1.54035	+	3.71874i	0.00956740	+	0.0230978i
$162$	26.3602	−	10.9187i	0.162717	−	0.0673997i
$163$	−234.223	+	156.503i	−1.43695	+	0.960139i	−0.438847	+	0.898562i	$0.644613\pi$
$163$	−234.223	+	156.503i	−1.43695	+	0.960139i	−0.998102	+	0.0615770i	$0.980387\pi$
$164$	−41.5242	+	208.756i	−0.253196	+	1.27290i
$165$	2.31885	+	1.54940i	0.0140536	+	0.00939033i
$166$	−202.774	+	202.774i	−1.22153	+	1.22153i
$167$	−36.9681	−	185.851i	−0.221366	−	1.11288i	−0.918342	−	0.395787i	$-0.870472\pi$
$167$	−36.9681	−	185.851i	−0.221366	−	1.11288i	0.696976	−	0.717094i	$-0.254528\pi$
$168$	−18.2379	+	44.0303i	−0.108559	+	0.262085i
$169$		−	131.640i		−	0.778933i
$170$	−4.74152	+	6.35396i	−0.0278913	+	0.0373762i
$171$	100.467			0.587524
$172$	−125.176	−	51.8496i	−0.727768	−	0.301451i
$173$	−256.810	+	51.0827i	−1.48445	+	0.295276i	−0.869753	−	0.493487i	$-0.835722\pi$
$173$	−256.810	+	51.0827i	−1.48445	+	0.295276i	−0.614698	+	0.788762i	$0.710722\pi$
$174$	129.694	+	129.694i	0.745368	+	0.745368i
$175$	58.7436	−	87.9160i	0.335678	−	0.502377i
$176$	−38.5895	−	7.67594i	−0.219259	−	0.0436133i
$177$	109.163	+	163.374i	0.616739	+	0.923015i
$178$	−4.82912	−	11.6585i	−0.0271299	−	0.0654973i
$179$	77.7596	−	32.2091i	0.434411	−	0.179939i	−0.154752	−	0.987953i	$-0.549458\pi$
$179$	77.7596	−	32.2091i	0.434411	−	0.179939i	0.589163	+	0.808014i	$0.299458\pi$
$180$	2.22013	−	1.48344i	0.0123340	−	0.00824134i
$181$	29.7920	−	149.774i	0.164597	−	0.827483i	−0.806947	−	0.590624i	$-0.798882\pi$
$181$	29.7920	−	149.774i	0.164597	−	0.827483i	0.971544	−	0.236860i	$-0.0761182\pi$
$182$	193.472	+	129.274i	1.06303	+	0.710295i
$183$	120.955	−	120.955i	0.660954	−	0.660954i
$184$	−1.20580	−	6.06198i	−0.00655328	−	0.0329456i
$185$	0.485945	−	1.17318i	0.00262673	−	0.00634149i
$186$		−	144.357i		−	0.776114i
$187$	26.7599	+	184.139i	0.143101	+	0.984701i
$188$	301.444			1.60343
$189$	20.3215	+	8.41742i	0.107521	+	0.0445366i
$190$	15.3177	−	3.04689i	0.0806197	−	0.0160363i
$191$	−213.435	−	213.435i	−1.11746	−	1.11746i	−0.992113	−	0.125347i	$-0.959996\pi$
$191$	−213.435	−	213.435i	−1.11746	−	1.11746i	−0.125347	−	0.992113i	$-0.540004\pi$
$192$	−100.246	+	150.029i	−0.522114	+	0.781399i
$193$	247.768	+	49.2841i	1.28377	+	0.255358i	0.789393	−	0.613888i	$-0.210395\pi$
$193$	247.768	+	49.2841i	1.28377	+	0.255358i	0.494379	+	0.869246i	$0.335395\pi$
$194$	−26.1467	−	39.1313i	−0.134777	−	0.201708i
$195$	−1.69065	−	4.08159i	−0.00866999	−	0.0209312i
$196$	173.736	−	71.9638i	0.886408	−	0.367162i
$197$	−272.321	+	181.959i	−1.38234	+	0.923650i	−1.00000		0.000371241i	$-0.999882\pi$
$197$	−272.321	+	181.959i	−1.38234	+	0.923650i	−0.382340	+	0.924022i	$0.624882\pi$
$198$	20.3087	−	102.099i	0.102569	−	0.515651i
$199$	27.1556	+	18.1448i	0.136460	+	0.0911800i	0.621927	−	0.783075i	$-0.286350\pi$
$199$	27.1556	+	18.1448i	0.136460	+	0.0911800i	−0.485466	+	0.874255i	$0.661350\pi$
$200$	−114.807	+	114.807i	−0.574033	+	0.574033i
$201$	8.30104	+	41.7321i	0.0412987	+	0.207622i
$202$	8.51221	−	20.5503i	0.0421396	−	0.101734i
$203$			141.397i			0.696539i
$204$	172.684	+	43.7966i	0.846492	+	0.214689i
$205$	5.17506			0.0252442
$206$	−374.303	−	155.041i	−1.81700	−	0.752628i
$207$	−2.79781	+	0.556519i	−0.0135160	+	0.00268850i
$208$	44.0726	+	44.0726i	0.211888	+	0.211888i
$209$	203.645	−	304.777i	0.974380	−	1.45826i
$210$	3.35361	+	0.667074i	0.0159696	+	0.00317654i
$211$	−167.950	−	251.355i	−0.795971	−	1.19125i	−0.978132	−	0.207986i	$-0.933309\pi$
$211$	−167.950	−	251.355i	−0.795971	−	1.19125i	0.182161	−	0.983269i	$-0.441691\pi$
$212$	0.343188	+	0.828528i	0.00161881	+	0.00390815i
$213$	−124.508	+	51.5729i	−0.584545	+	0.242126i
$214$	148.799	−	99.4243i	0.695323	−	0.464600i
$215$	−0.642675	+	3.23094i	−0.00298918	+	0.0150276i
$216$	−28.0832	−	18.7646i	−0.130015	−	0.0868731i
$217$	78.6919	−	78.6919i	0.362635	−	0.362635i
$218$	112.192	+	564.026i	0.514641	+	2.58727i
$219$	−58.6490	+	141.591i	−0.267804	+	0.646536i
$220$		−	9.74194i		−	0.0442815i
$221$	126.812	−	266.089i	0.573811	−	1.20402i
$222$	−47.3990			−0.213509
$223$	147.178	+	60.9632i	0.659992	+	0.273378i	0.687435	−	0.726246i	$-0.258737\pi$
$223$	147.178	+	60.9632i	0.659992	+	0.273378i	−0.0274431	+	0.999623i	$0.508737\pi$
$224$	−155.260	+	30.8831i	−0.693125	+	0.137871i
$225$	52.9871	+	52.9871i	0.235498	+	0.235498i
$226$	−328.609	+	491.798i	−1.45402	+	2.17610i
$227$	−120.893	−	24.0472i	−0.532569	−	0.105935i	−0.0785223	−	0.996912i	$-0.525020\pi$
$227$	−120.893	−	24.0472i	−0.532569	−	0.105935i	−0.454047	+	0.890978i	$0.650020\pi$
$228$	−194.976	−	291.802i	−0.855157	−	1.27983i
$229$	−118.603	−	286.334i	−0.517918	−	1.25037i	−0.939180	−	0.343426i	$-0.888412\pi$
$229$	−118.603	−	286.334i	−0.517918	−	1.25037i	0.421261	−	0.906939i	$-0.361588\pi$
$230$	−0.409693	+	0.169700i	−0.00178127	+	0.000737828i
$231$	66.7267	−	44.5854i	0.288860	−	0.193010i
$232$	42.3582	−	212.949i	0.182578	−	0.917884i
$233$	−34.9316	−	23.3406i	−0.149921	−	0.100174i	0.478347	−	0.878171i	$-0.341236\pi$
$233$	−34.9316	−	23.3406i	−0.149921	−	0.100174i	−0.628268	+	0.777997i	$0.716236\pi$
$234$	−116.606	+	116.606i	−0.498315	+	0.498315i
$235$	−1.42986	−	7.18837i	−0.00608450	−	0.0305888i
$236$	262.661	−	634.119i	1.11297	−	2.68694i
$237$			48.7009i			0.205489i
$238$	116.709	+	196.025i	0.490373	+	0.823635i
$239$	−69.3690			−0.290247			−0.145123	−	0.989414i	$-0.546358\pi$
$239$	−69.3690			−0.290247			−0.145123	+	0.989414i	$0.546358\pi$
$240$	0.846187	+	0.350502i	0.00352578	+	0.00146043i
$241$	327.324	−	65.1087i	1.35819	−	0.270161i	0.538334	−	0.842732i	$-0.319054\pi$
$241$	327.324	−	65.1087i	1.35819	−	0.270161i	0.819855	+	0.572571i	$0.194054\pi$
$242$	2.68172	+	2.68172i	0.0110815	+	0.0110815i
$243$	−8.66048	+	12.9613i	−0.0356398	+	0.0533388i
$244$	−586.045	−	116.572i	−2.40182	−	0.477752i
$245$	−2.54017	−	3.80164i	−0.0103680	−	0.0155169i
$246$	−73.9224	−	178.464i	−0.300498	−	0.725465i
$247$	−536.462	+	222.210i	−2.17191	+	0.899635i
$248$	−142.086	+	94.9390i	−0.572928	+	0.382818i
$249$	30.5656	−	153.664i	0.122753	−	0.617123i
$250$	19.3798	+	12.9492i	0.0775191	+	0.0517966i
$251$	31.1640	−	31.1640i	0.124159	−	0.124159i	−0.642297	−	0.766456i	$-0.722018\pi$
$251$	31.1640	−	31.1640i	0.124159	−	0.124159i	0.766456	+	0.642297i	$0.222018\pi$
$252$	−14.9898	−	75.3586i	−0.0594832	−	0.299042i
$253$	−3.98288	+	9.61553i	−0.0157426	+	0.0380060i
$254$			290.657i			1.14432i
$255$	0.225290	−	4.32565i	0.000883491	−	0.0169633i
$256$	156.082			0.609695
$257$	298.932	+	123.822i	1.16316	+	0.481797i	0.878926	−	0.476958i	$-0.158260\pi$
$257$	298.932	+	123.822i	1.16316	+	0.481797i	0.284235	+	0.958755i	$0.408260\pi$
$258$	120.601	−	23.9890i	0.467446	−	0.0929807i
$259$	−25.8381	−	25.8381i	−0.0997609	−	0.0997609i
$260$	−8.57378	+	12.8316i	−0.0329761	+	0.0493522i
$261$	−98.2831	−	19.5497i	−0.376564	−	0.0749032i
$262$	31.6102	+	47.3080i	0.120650	+	0.180565i
$263$	19.7498	+	47.6802i	0.0750943	+	0.181294i	0.956969	−	0.290190i	$-0.0937186\pi$
$263$	19.7498	+	47.6802i	0.0750943	+	0.181294i	−0.881875	+	0.471484i	$0.843719\pi$
$264$	−113.849	+	47.1578i	−0.431246	+	0.178628i
$265$	0.0181296	−	0.0121138i	6.84135e−5	−	4.57124e-5i
$266$	87.6767	−	440.781i	0.329612	−	1.65707i
$267$	5.73251	+	3.83034i	0.0214701	+	0.0143458i
$268$	105.100	−	105.100i	0.392163	−	0.392163i
$269$	76.1166	+	382.664i	0.282961	+	1.42254i	0.816783	+	0.576945i	$0.195755\pi$
$269$	76.1166	+	382.664i	0.282961	+	1.42254i	−0.533822	+	0.845597i	$0.679245\pi$
$270$	−0.927346	+	2.23881i	−0.00343462	+	0.00829190i
$271$			347.631i			1.28277i	0.767219	+	0.641385i	$0.221640\pi$
$271$			347.631i			1.28277i	−0.767219	+	0.641385i	$0.778360\pi$
$272$	20.4175	+	57.5978i	0.0750643	+	0.211757i
$273$	−127.128			−0.465670
$274$	384.921	+	159.439i	1.40482	+	0.581895i
$275$	268.147	−	53.3378i	0.975080	−	0.193955i
$276$	7.04610	+	7.04610i	0.0255293	+	0.0255293i
$277$	72.8289	−	108.996i	0.262920	−	0.393488i	−0.676397	−	0.736537i	$-0.736460\pi$
$277$	72.8289	−	108.996i	0.262920	−	0.393488i	0.939317	+	0.343049i	$0.111460\pi$
$278$	46.6879	+	9.28680i	0.167942	+	0.0334057i
$279$	43.8175	+	65.5775i	0.157052	+	0.235045i
$280$	−1.54898	−	3.73956i	−0.00553206	−	0.0133556i
$281$	−76.2945	+	31.6022i	−0.271511	+	0.112463i	−0.514285	−	0.857619i	$-0.671943\pi$
$281$	−76.2945	+	31.6022i	−0.271511	+	0.112463i	0.242774	+	0.970083i	$0.421943\pi$
$282$	−227.470	+	151.991i	−0.806632	+	0.538974i
$283$	−31.9246	+	160.496i	−0.112808	+	0.567123i	0.882496	+	0.470320i	$0.155862\pi$
$283$	−31.9246	+	160.496i	−0.112808	+	0.567123i	−0.995304	+	0.0968028i	$0.969138\pi$
$284$	391.425	+	261.542i	1.37826	+	0.920921i
$285$	−6.03359	+	6.03359i	−0.0211705	+	0.0211705i
$286$	117.377	+	590.096i	0.410411	+	2.06327i
$287$	56.9879	−	137.581i	0.198564	−	0.479376i
$288$		−	112.189i		−	0.389544i
$289$	224.477	−	182.019i	0.776737	−	0.629825i
$290$	−15.5777			−0.0537163
$291$	23.7555	+	9.83983i	0.0816339	+	0.0338139i
$292$	525.067	−	104.442i	1.79818	−	0.357679i
$293$	−81.3894	−	81.3894i	−0.277779	−	0.277779i	0.554443	−	0.832222i	$-0.312932\pi$
$293$	−81.3894	−	81.3894i	−0.277779	−	0.277779i	−0.832222	+	0.554443i	$0.812932\pi$
$294$	−94.8166	+	141.903i	−0.322505	+	0.482663i
$295$	−16.3674	−	3.25567i	−0.0554826	−	0.0110362i
$296$	31.1727	+	46.6533i	0.105313	+	0.157612i
$297$	21.7649	+	52.5451i	0.0732825	+	0.176920i
$298$	−44.9162	+	18.6049i	−0.150725	+	0.0624325i
$299$	13.7086	−	9.15978i	0.0458481	−	0.0306347i
$300$	51.0670	−	256.731i	0.170223	−	0.855771i
$301$	78.8187	+	52.6650i	0.261856	+	0.174967i
$302$	26.7135	−	26.7135i	0.0884554	−	0.0884554i
$303$	2.37087	+	11.9192i	0.00782466	+	0.0393372i
$304$	46.0681	−	111.218i	0.151540	−	0.365850i
$305$			14.5280i			0.0476329i
$306$	−152.390	+	54.0199i	−0.498008	+	0.176536i
$307$	583.110			1.89938			0.949691	−	0.313190i	$-0.101398\pi$
$307$	583.110			1.89938			0.949691	+	0.313190i	$0.101398\pi$
$308$	−258.993	−	107.278i	−0.840887	−	0.348307i
$309$	217.096	−	43.1831i	0.702576	−	0.139751i
$310$	8.66948	+	8.66948i	0.0279661	+	0.0279661i
$311$	−252.650	+	378.117i	−0.812379	+	1.21581i	0.161078	+	0.986942i	$0.448503\pi$
$311$	−252.650	+	378.117i	−0.812379	+	1.21581i	−0.973457	+	0.228869i	$0.926497\pi$
$312$	191.459	+	38.0836i	0.613651	+	0.122063i
$313$	−158.106	−	236.622i	−0.505130	−	0.755981i	0.488019	−	0.872833i	$-0.337720\pi$
$313$	−158.106	−	236.622i	−0.505130	−	0.755981i	−0.993149	+	0.116852i	$0.962720\pi$
$314$	−183.866	−	443.891i	−0.585560	−	1.41367i
$315$	−1.72593	+	0.714905i	−0.00547915	+	0.00226954i
$316$	141.450	−	94.5139i	0.447627	−	0.299095i
$317$	40.1080	−	201.636i	0.126524	−	0.636077i	−0.864527	−	0.502587i	$-0.832382\pi$
$317$	40.1080	−	201.636i	0.126524	−	0.636077i	0.991050	−	0.133490i	$-0.0426184\pi$
$318$	−0.676720	−	0.452170i	−0.00212805	−	0.00142192i
$319$	−258.526	+	258.526i	−0.810425	+	0.810425i
$320$	−2.98974	−	15.0304i	−0.00934293	−	0.0469701i
$321$	−37.4165	+	90.3315i	−0.116562	+	0.281407i
$322$			12.7606i			0.0396292i
$323$	−568.540	−	29.6109i	−1.76019	−	0.0916748i
$324$	54.4531			0.168065
$325$	−400.131	−	165.740i	−1.23117	−	0.509969i
$326$	−875.885	+	174.224i	−2.68676	+	0.534431i
$327$	−222.167	−	222.167i	−0.679410	−	0.679410i
$328$	−127.041	+	190.130i	−0.387319	+	0.579663i
$329$	−206.851	−	41.1453i	−0.628727	−	0.125062i
$330$	4.91196	+	7.35127i	0.0148847	+	0.0222766i
$331$	34.6177	+	83.5745i	0.104585	+	0.252491i	0.967506	−	0.252848i	$-0.0813674\pi$
$331$	34.6177	+	83.5745i	0.104585	+	0.252491i	−0.862921	+	0.505339i	$0.831367\pi$
$332$	−505.629	+	209.439i	−1.52298	+	0.630839i
$333$	21.5320	−	14.3873i	0.0646608	−	0.0432050i
$334$	117.197	−	589.191i	0.350890	−	1.76404i
$335$	−3.00478	−	2.00773i	−0.00896948	−	0.00599322i
$336$	18.6365	−	18.6365i	0.0554657	−	0.0554657i
$337$	−90.6560	−	455.758i	−0.269009	−	1.35240i	−0.844923	−	0.534888i	$-0.820354\pi$
$337$	−90.6560	−	455.758i	−0.269009	−	1.35240i	0.575914	−	0.817510i	$-0.304646\pi$
$338$	159.704	−	385.561i	0.472498	−	1.14071i
$339$		−	323.155i		−	0.953259i
$340$	−13.0009	+	7.74044i	−0.0382380	+	0.0227660i
$341$	287.755			0.843856
$342$	294.258	+	121.885i	0.860402	+	0.356390i
$343$	−332.476	+	66.1336i	−0.969319	+	0.192809i
$344$	−102.927	−	102.927i	−0.299206	−	0.299206i
$345$	0.134602	−	0.201446i	0.000390151	−	0.000583903i
$346$	−814.147	−	161.944i	−2.35303	−	0.468046i
$347$	164.221	+	245.774i	0.473259	+	0.708282i	0.988910	−	0.148517i	$-0.0474500\pi$
$347$	164.221	+	245.774i	0.473259	+	0.708282i	−0.515651	+	0.856799i	$0.672450\pi$
$348$	133.957	+	323.400i	0.384933	+	0.929310i
$349$	−65.4532	+	27.1116i	−0.187545	+	0.0776837i	−0.474480	−	0.880266i	$-0.657364\pi$
$349$	−65.4532	+	27.1116i	−0.187545	+	0.0776837i	0.286935	+	0.957950i	$0.407364\pi$
$350$	278.714	−	186.231i	0.796325	−	0.532087i
$351$	17.5768	−	88.3647i	0.0500765	−	0.251751i
$352$	−340.337	−	227.406i	−0.966867	−	0.646040i
$353$	55.4879	−	55.4879i	0.157189	−	0.157189i	−0.624131	−	0.781320i	$-0.714547\pi$
$353$	55.4879	−	55.4879i	0.157189	−	0.157189i	0.781320	+	0.624131i	$0.214547\pi$
$354$	121.524	+	610.942i	0.343288	+	1.72582i
$355$	4.38017	−	10.5747i	0.0123385	−	0.0297878i
$356$		−	24.0834i		−	0.0676501i
$357$	−112.518	−	53.6236i	−0.315177	−	0.150206i
$358$	266.827			0.745326
$359$	134.505	+	55.7140i	0.374667	+	0.155192i	0.562067	−	0.827091i	$-0.310006\pi$
$359$	134.505	+	55.7140i	0.374667	+	0.155192i	−0.187400	+	0.982284i	$0.560006\pi$
$360$	2.81348	−	0.559635i	0.00781521	−	0.00155454i
$361$	537.758	+	537.758i	1.48963	+	1.48963i
$362$	268.964	−	402.532i	0.742993	−	1.11197i
$363$	−2.03223	−	0.404236i	−0.00559843	−	0.00111360i
$364$	246.718	+	369.239i	0.677795	+	1.01439i
$365$	−4.98116	−	12.0256i	−0.0136470	−	0.0329468i
$366$	501.006	−	207.524i	1.36887	−	0.567004i
$367$	−164.975	+	110.233i	−0.449524	+	0.300362i	−0.759649	−	0.650334i	$-0.774629\pi$
$367$	−164.975	+	110.233i	−0.449524	+	0.300362i	0.310125	+	0.950696i	$0.399629\pi$
$368$	−0.666836	+	3.35241i	−0.00181205	+	0.00910981i
$369$	87.7511	+	58.6334i	0.237808	+	0.158898i
$370$	2.84658	−	2.84658i	0.00769345	−	0.00769345i
$371$	−0.122407	−	0.615379i	−0.000329937	−	0.00165870i
$372$	105.431	−	254.533i	0.283417	−	0.684228i
$373$			234.770i			0.629411i	0.949189	+	0.314705i	$0.101906\pi$
$373$			234.770i			0.629411i	−0.949189	+	0.314705i	$0.898094\pi$
$374$	−145.019	+	571.791i	−0.387751	+	1.52885i
$375$	−12.7342			−0.0339579
$376$	299.199	+	123.932i	0.795742	+	0.329607i
$377$	568.042	−	112.991i	1.50674	−	0.299710i
$378$	49.3077	+	49.3077i	0.130444	+	0.130444i
$379$	110.434	−	165.276i	0.291382	−	0.436084i	−0.656680	−	0.754169i	$-0.728040\pi$
$379$	110.434	−	165.276i	0.291382	−	0.436084i	0.948062	+	0.318085i	$0.103040\pi$
$380$	29.2338	+	5.81496i	0.0769309	+	0.0153025i
$381$	−88.2246	−	132.037i	−0.231561	−	0.346555i
$382$	−366.193	−	884.069i	−0.958621	−	2.31432i
$383$	175.404	−	72.6548i	0.457975	−	0.189699i	−0.141755	−	0.989902i	$-0.545275\pi$
$383$	175.404	−	72.6548i	0.457975	−	0.189699i	0.599730	+	0.800202i	$0.295275\pi$
$384$	−260.201	+	173.861i	−0.677606	+	0.452762i
$385$	−1.32971	+	6.68492i	−0.00345380	+	0.0173634i
$386$	665.899	+	444.940i	1.72513	+	1.15269i
$387$	−47.5042	+	47.5042i	−0.122750	+	0.122750i
$388$	−17.5228	−	88.0931i	−0.0451619	−	0.227044i
$389$	−111.532	+	269.263i	−0.286715	+	0.692192i	−0.999962	−	0.00872133i	$-0.997224\pi$
$389$	−111.532	+	269.263i	−0.286715	+	0.692192i	0.713247	+	0.700913i	$0.247224\pi$
$390$		−	14.0057i		−	0.0359120i
$391$	15.9968	−	2.32473i	0.0409126	−	0.00594560i
$392$	202.028			0.515378
$393$	−28.7193	−	11.8959i	−0.0730771	−	0.0302695i
$394$	−1018.36	+	202.563i	−2.58466	+	0.514120i
$395$	−2.92477	−	2.92477i	−0.00740448	−	0.00740448i
$396$	110.376	−	165.190i	0.278728	−	0.417146i
$397$	70.5719	+	14.0376i	0.177763	+	0.0353593i	0.283169	−	0.959070i	$-0.408614\pi$
$397$	70.5719	+	14.0376i	0.177763	+	0.0353593i	−0.105406	+	0.994429i	$0.533614\pi$
$398$	57.5232	+	86.0896i	0.144531	+	0.216305i
$399$	93.9633	+	226.848i	0.235497	+	0.568540i
$400$	82.9545	−	34.3609i	0.207386	−	0.0859022i
$401$	−55.7843	+	37.2739i	−0.139113	+	0.0929523i	−0.623179	−	0.782079i	$-0.714159\pi$
$401$	−55.7843	+	37.2739i	−0.139113	+	0.0929523i	0.484066	+	0.875031i	$0.339159\pi$
$402$	−26.3162	+	132.300i	−0.0654631	+	0.329105i
$403$	−379.016	−	253.250i	−0.940485	−	0.628412i
$404$	30.0177	−	30.0177i	0.0743012	−	0.0743012i
$405$	−0.258290	−	1.29851i	−0.000637754	−	0.00320620i
$406$	−171.542	+	414.140i	−0.422518	+	1.02005i
$407$		−	94.4828i		−	0.232144i
$408$	153.392	+	114.466i	0.375961	+	0.280553i
$409$	168.565			0.412140			0.206070	−	0.978537i	$-0.433932\pi$
$409$	168.565			0.412140			0.206070	+	0.978537i	$0.433932\pi$
$410$	15.1573	+	6.27835i	0.0369689	+	0.0153130i
$411$	−223.254	+	44.4080i	−0.543198	+	0.108049i
$412$	−546.742	−	546.742i	−1.32704	−	1.32704i
$413$	−266.791	+	399.281i	−0.645983	+	0.966782i
$414$	−8.86969	−	1.76429i	−0.0214244	−	0.00426157i
$415$	7.39274	+	11.0640i	0.0178138	+	0.0266603i
$416$	248.137	+	599.055i	0.596482	+	1.44004i
$417$	−24.0279	+	9.95268i	−0.0576208	+	0.0238673i
$418$	966.212	−	645.602i	2.31151	−	1.54450i
$419$	−46.8504	+	235.533i	−0.111815	+	0.562131i	0.883743	+	0.467973i	$0.155016\pi$
$419$	−46.8504	+	235.533i	−0.111815	+	0.562131i	−0.995557	+	0.0941575i	$0.969984\pi$
$420$	5.42594	+	3.62550i	0.0129189	+	0.00863213i
$421$	−392.673	+	392.673i	−0.932715	+	0.932715i	−0.997875	−	0.0651594i	$-0.979244\pi$
$421$	−392.673	+	392.673i	−0.932715	+	0.932715i	0.0651594	+	0.997875i	$0.479244\pi$
$422$	−186.968	−	939.951i	−0.443052	−	2.22737i
$423$	57.1989	−	138.090i	0.135222	−	0.326455i
$424$			0.963451i			0.00227229i
$425$	−284.237	−	315.471i	−0.668792	−	0.742285i
$426$	−427.241			−1.00291
$427$	386.233	+	159.983i	0.904527	+	0.374667i
$428$	334.979	−	66.6315i	0.782661	−	0.155681i
$429$	−232.436	−	232.436i	−0.541809	−	0.541809i
$430$	−5.80210	+	8.68345i	−0.0134932	+	0.0201941i
$431$	784.097	+	155.967i	1.81925	+	0.361871i	0.982581	−	0.185837i	$-0.0594995\pi$
$431$	784.097	+	155.967i	1.81925	+	0.361871i	0.836670	+	0.547708i	$0.184500\pi$
$432$	10.3772	+	15.5306i	0.0240214	+	0.0359505i
$433$	244.645	+	590.626i	0.565001	+	1.36403i	0.905724	+	0.423868i	$0.139328\pi$
$433$	244.645	+	590.626i	0.565001	+	1.36403i	−0.340723	+	0.940164i	$0.610672\pi$
$434$	325.950	−	135.013i	0.751037	−	0.311090i
$435$	7.07653	−	4.72839i	0.0162679	−	0.0108699i
$436$	−214.117	+	1076.44i	−0.491093	+	2.46889i
$437$	−26.4771	−	17.6914i	−0.0605882	−	0.0404838i
$438$	−343.555	+	343.555i	−0.784373	+	0.784373i
$439$	−85.0515	−	427.583i	−0.193739	−	0.973993i	−0.948206	−	0.317655i	$-0.897105\pi$
$439$	−85.0515	−	427.583i	−0.193739	−	0.973993i	0.754467	−	0.656338i	$-0.227895\pi$
$440$	4.00519	−	9.66938i	0.00910270	−	0.0219759i
$441$		−	93.2428i		−	0.211435i
$442$	694.239	−	625.504i	1.57068	−	1.41517i
$443$	67.6445			0.152696			0.0763482	−	0.997081i	$-0.475674\pi$
$443$	67.6445			0.152696			0.0763482	+	0.997081i	$0.475674\pi$
$444$	−83.5745	−	34.6177i	−0.188231	−	0.0779678i
$445$	−0.574304	+	0.114236i	−0.00129057	+	0.000256710i
$446$	357.112	+	357.112i	0.800698	+	0.800698i
$447$	14.7569	−	22.0853i	0.0330133	−	0.0494079i
$448$	−432.513	−	86.0321i	−0.965430	−	0.192036i
$449$	202.715	+	303.384i	0.451481	+	0.675689i	0.985479	−	0.169797i	$-0.0543112\pi$
$449$	202.715	+	303.384i	0.451481	+	0.675689i	−0.533998	+	0.845485i	$0.679311\pi$
$450$	90.9108	+	219.478i	0.202024	+	0.487729i
$451$	355.742	−	147.353i	0.788786	−	0.326726i
$452$	−938.592	+	627.147i	−2.07653	+	1.38749i
$453$	−4.02673	+	20.2437i	−0.00888902	+	0.0446881i
$454$	−324.911	−	217.099i	−0.715664	−	0.478191i
$455$	7.63476	−	7.63476i	0.0167797	−	0.0167797i
$456$	−73.5555	−	369.788i	−0.161306	−	0.810939i
$457$	−118.228	+	285.427i	−0.258704	+	0.624566i	−0.998853	−	0.0478763i	$-0.984755\pi$
$457$	−118.228	+	285.427i	−0.258704	+	0.624566i	0.740150	+	0.672442i	$0.234755\pi$
$458$		−	982.534i		−	2.14527i
$459$	52.8298	−	70.7956i	0.115098	−	0.154239i
$460$	−0.846317			−0.00183982
$461$	−670.150	−	277.585i	−1.45369	−	0.602137i	−0.490615	−	0.871376i	$-0.663228\pi$
$461$	−670.150	−	277.585i	−1.45369	−	0.602137i	−0.963073	+	0.269239i	$0.913228\pi$
$462$	249.527	−	49.6340i	0.540102	−	0.107433i
$463$	−293.832	−	293.832i	−0.634626	−	0.634626i	0.314598	−	0.949225i	$-0.398130\pi$
$463$	−293.832	−	293.832i	−0.634626	−	0.634626i	−0.949225	+	0.314598i	$0.898130\pi$
$464$	−66.7088	+	99.8368i	−0.143769	+	0.215165i
$465$	−6.56980	−	1.30681i	−0.0141286	−	0.00281035i
$466$	−73.9949	−	110.741i	−0.158787	−	0.237642i
$467$	−243.012	−	586.684i	−0.520369	−	1.25628i	−0.937674	−	0.347516i	$-0.887025\pi$
$467$	−243.012	−	586.684i	−0.520369	−	1.25628i	0.417305	−	0.908766i	$-0.362975\pi$
$468$	−290.764	+	120.438i	−0.621290	+	0.257347i
$469$	−86.4649	+	57.7740i	−0.184360	+	0.123185i
$470$	4.53297	−	22.7888i	0.00964462	−	0.0484868i
$471$	218.262	+	145.838i	0.463401	+	0.309634i
$472$	521.408	−	521.408i	1.10468	−	1.10468i
$473$	47.8186	+	240.400i	0.101096	+	0.508245i
$474$	−59.0837	+	142.641i	−0.124649	+	0.300930i
$475$			836.497i			1.76105i
$476$	62.6163	+	430.872i	0.131547	+	0.905194i
$477$	0.444665			0.000932211
$478$	−203.175	−	84.1580i	−0.425053	−	0.176063i
$479$	207.367	−	41.2480i	0.432918	−	0.0861127i	0.0261790	−	0.999657i	$-0.491666\pi$
$479$	207.367	−	41.2480i	0.432918	−	0.0861127i	0.406739	+	0.913545i	$0.366666\pi$
$480$	6.73757	+	6.73757i	0.0140366	+	0.0140366i
$481$	−83.1533	+	124.448i	−0.172876	+	0.258727i
$482$	1037.69	+	206.409i	2.15288	+	0.428235i
$483$	−3.87329	−	5.79679i	−0.00801923	−	0.0120016i
$484$	2.76986	+	6.68704i	0.00572286	+	0.0138162i
$485$	−2.01759	+	0.835713i	−0.00415998	+	0.00172312i
$486$	−41.0904	+	27.4557i	−0.0845481	+	0.0564932i
$487$	33.0603	−	166.205i	0.0678856	−	0.341284i	−0.931884	−	0.362757i	$-0.881836\pi$
$487$	33.0603	−	166.205i	0.0678856	−	0.341284i	0.999769	+	0.0214729i	$0.00683556\pi$
$488$	−533.754	−	356.643i	−1.09376	−	0.730826i
$489$	345.007	−	345.007i	0.705536	−	0.705536i
$490$	−2.82781	−	14.2164i	−0.00577104	−	0.0290130i
$491$	44.4743	−	107.370i	0.0905790	−	0.218677i	−0.872097	−	0.489333i	$-0.837240\pi$
$491$	44.4743	−	107.370i	0.0905790	−	0.218677i	0.962676	+	0.270656i	$0.0872404\pi$
$492$		−	368.660i		−	0.749309i
$493$	550.422	+	139.599i	1.11647	+	0.283163i
$494$	−1840.83			−3.72638
$495$	−4.46274	−	1.84853i	−0.00901564	−	0.00373440i
$496$	92.6877	−	18.4367i	0.186870	−	0.0371708i
$497$	−232.897	−	232.897i	−0.468606	−	0.468606i
$498$	275.948	−	412.985i	0.554112	−	0.829287i
$499$	594.201	+	118.194i	1.19078	+	0.236861i	0.750422	−	0.660959i	$-0.229850\pi$
$499$	594.201	+	118.194i	1.19078	+	0.236861i	0.440361	+	0.897821i	$0.354850\pi$
$500$	24.7133	+	36.9861i	0.0494266	+	0.0739722i
$501$	125.601	+	303.227i	0.250700	+	0.605243i
$502$	129.084	−	53.4685i	0.257140	−	0.106511i
$503$	256.869	−	171.635i	0.510675	−	0.341222i	−0.273388	−	0.961904i	$-0.588144\pi$
$503$	256.869	−	171.635i	0.510675	−	0.341222i	0.784062	+	0.620682i	$0.213144\pi$
$504$	16.1040	−	80.9601i	0.0319523	−	0.160635i
$505$	−0.858199	−	0.573430i	−0.00169940	−	0.00113551i
$506$	−23.3310	+	23.3310i	−0.0461087	+	0.0461087i
$507$	44.4819	+	223.626i	0.0877355	+	0.441076i
$508$	−212.280	+	512.490i	−0.417875	+	1.00884i
$509$		−	540.267i		−	1.06143i	−0.847551	−	0.530714i	$-0.821924\pi$
$509$		−	540.267i		−	1.06143i	0.847551	−	0.530714i	$-0.178076\pi$
$510$	5.90770	−	12.3961i	0.0115837	−	0.0243061i
$511$	−374.557			−0.732989
$512$	−210.543	−	87.2099i	−0.411217	−	0.170332i
$513$	−170.670	+	33.9483i	−0.332689	+	0.0661760i
$514$	725.326	+	725.326i	1.41114	+	1.41114i
$515$	−10.4445	+	15.6312i	−0.0202805	+	0.0303519i
$516$	230.166	+	45.7828i	0.446057	+	0.0887263i
$517$	−302.971	−	453.428i	−0.586017	−	0.877037i
$518$	−44.3308	−	107.024i	−0.0855807	−	0.206610i
$519$	419.000	−	173.556i	0.807322	−	0.334404i
$520$	−13.7853	+	9.21107i	−0.0265103	+	0.0177136i
$521$	−26.7745	+	134.605i	−0.0513906	+	0.258358i	−0.997936	−	0.0642116i	$-0.979547\pi$
$521$	−26.7745	+	134.605i	−0.0513906	+	0.258358i	0.946546	+	0.322570i	$0.104547\pi$
$522$	−264.145	−	176.496i	−0.506024	−	0.338115i
$523$	46.2164	−	46.2164i	0.0883678	−	0.0883678i	−0.661541	−	0.749909i	$-0.730097\pi$
$523$	46.2164	−	46.2164i	0.0883678	−	0.0883678i	0.749909	+	0.661541i	$0.230097\pi$
$524$	21.1843	+	106.501i	0.0404280	+	0.203246i
$525$	−70.0845	+	169.199i	−0.133494	+	0.322284i
$526$			163.611i			0.311048i
$527$	−228.635	−	384.018i	−0.433843	−	0.728686i
$528$	68.1485			0.129069
$529$	−487.897	−	202.094i	−0.922300	−	0.382029i
$530$	0.0677963	−	0.0134855i	0.000127917	−	2.54444e-5i
$531$	−240.647	−	240.647i	−0.453196	−	0.453196i
$532$	476.516	−	713.156i	0.895707	−	1.34052i
$533$	−598.249	−	118.999i	−1.12242	−	0.223263i
$534$	12.1431	+	18.1734i	0.0227398	+	0.0340325i
$535$	−3.17785	−	7.67200i	−0.00593990	−	0.0143402i
$536$	147.526	−	61.1074i	0.275236	−	0.114006i
$537$	−121.212	+	80.9913i	−0.225721	+	0.150822i
$538$	−241.307	+	1213.13i	−0.448526	+	2.25489i
$539$	−282.863	−	189.003i	−0.524792	−	0.350655i
$540$	−3.27022	+	3.27022i	−0.00605596	+	0.00605596i
$541$	−125.835	−	632.616i	−0.232597	−	1.16935i	−0.903761	−	0.428037i	$-0.859205\pi$
$541$	−125.835	−	632.616i	−0.232597	−	1.16935i	0.671164	−	0.741309i	$-0.265795\pi$
$542$	−421.743	+	1018.18i	−0.778124	+	1.87856i
$543$			264.499i			0.487107i
$544$	−33.0659	+	634.876i	−0.0607828	+	1.16705i
$545$	26.6848			0.0489630
$546$	−372.346	−	154.231i	−0.681953	−	0.282474i
$547$	571.637	−	113.706i	1.04504	−	0.207872i	0.357422	−	0.933943i	$-0.383656\pi$
$547$	571.637	−	113.706i	1.04504	−	0.207872i	0.687619	+	0.726071i	$0.258656\pi$
$548$	562.251	+	562.251i	1.02601	+	1.02601i
$549$	−164.603	+	246.345i	−0.299823	+	0.448716i
$550$	850.087	+	169.093i	1.54561	+	0.307442i
$551$	−621.474	−	930.102i	−1.12790	−	1.68803i
$552$	4.09677	+	9.89047i	0.00742168	+	0.0179175i
$553$	−109.964	+	45.5485i	−0.198849	+	0.0823661i
$554$	345.543	−	230.884i	0.623723	−	0.416758i
$555$	−0.429085	+	2.15716i	−0.000773127	+	0.00388677i
$556$	75.5382	+	50.4730i	0.135860	+	0.0907788i
$557$	−13.2719	+	13.2719i	−0.0238275	+	0.0238275i	−0.718920	−	0.695093i	$-0.755363\pi$
$557$	−13.2719	+	13.2719i	−0.0238275	+	0.0238275i	0.695093	+	0.718920i	$0.255363\pi$
$558$	48.7792	+	245.230i	0.0874180	+	0.439480i
$559$	148.590	−	358.727i	0.265813	−	0.641730i
$560$			2.23845i			0.00399724i
$561$	−107.681	−	303.767i	−0.191944	−	0.541475i
$562$	−261.799			−0.465835
$563$	−617.300	−	255.694i	−1.09645	−	0.454164i	−0.240197	−	0.970724i	$-0.577212\pi$
$563$	−617.300	−	255.694i	−1.09645	−	0.454164i	−0.856251	+	0.516560i	$0.827212\pi$
$564$	−512.085	+	101.860i	−0.907952	+	0.180603i
$565$	19.4073	+	19.4073i	0.0343492	+	0.0343492i
$566$	−288.217	+	431.347i	−0.509217	+	0.762097i
$567$	−37.3658	−	7.43251i	−0.0659008	−	0.0131085i
$568$	280.982	+	420.519i	0.494687	+	0.740351i
$569$	95.1359	+	229.678i	0.167198	+	0.403653i	0.985164	−	0.171614i	$-0.0548982\pi$
$569$	95.1359	+	229.678i	0.167198	+	0.403653i	−0.817966	+	0.575267i	$0.804898\pi$
$570$	−24.9918	+	10.3519i	−0.0438452	+	0.0181613i
$571$	870.543	−	581.678i	1.52459	−	1.01870i	0.540439	−	0.841383i	$-0.318258\pi$
$571$	870.543	−	581.678i	1.52459	−	1.01870i	0.984154	−	0.177317i	$-0.0567419\pi$
$572$	−224.014	+	1126.19i	−0.391632	+	1.96887i
$573$	434.698	+	290.456i	0.758635	+	0.506903i
$574$	333.825	−	333.825i	0.581576	−	0.581576i
$575$	−4.63364	−	23.2949i	−0.00805851	−	0.0405128i
$576$	119.599	−	288.738i	0.207637	−	0.501281i
$577$			166.838i			0.289147i	0.989494	+	0.144573i	$0.0461810\pi$
$577$			166.838i			0.289147i	−0.989494	+	0.144573i	$0.953819\pi$
$578$	878.298	−	260.784i	1.51955	−	0.451183i
$579$	−437.554			−0.755707
$580$	−27.4669	−	11.3772i	−0.0473567	−	0.0196158i
$581$	375.550	−	74.7016i	0.646386	−	0.128574i
$582$	57.6399	+	57.6399i	0.0990377	+	0.0990377i
$583$	0.901334	−	1.34894i	0.00154603	−	0.00231379i
$584$	564.096	+	112.206i	0.965917	+	0.192133i
$585$	4.25122	+	6.36239i	0.00726704	+	0.0108759i
$586$	−139.641	−	337.123i	−0.238295	−	0.575296i
$587$	688.139	−	285.037i	1.17230	−	0.485582i	0.290347	−	0.956921i	$-0.406229\pi$
$587$	688.139	−	285.037i	1.17230	−	0.485582i	0.881952	+	0.471339i	$0.156229\pi$
$588$	−270.821	+	180.956i	−0.460579	+	0.307749i
$589$	−171.761	+	863.499i	−0.291614	+	1.46604i
$590$	−43.9887	−	29.3923i	−0.0745572	−	0.0498175i
$591$	401.126	−	401.126i	0.678724	−	0.678724i
$592$	−6.05360	−	30.4335i	−0.0102257	−	0.0514080i
$593$	−136.332	+	329.133i	−0.229901	+	0.555031i	−0.996165	−	0.0874954i	$-0.972114\pi$
$593$	−136.332	+	329.133i	−0.229901	+	0.555031i	0.766264	+	0.642526i	$0.222114\pi$
$594$			180.305i			0.303544i
$595$	9.97776	−	3.53695i	0.0167693	−	0.00594446i
$596$	−92.7849			−0.155679
$597$	−52.2624	−	21.6478i	−0.0875417	−	0.0362610i
$598$	51.2638	−	10.1970i	0.0857253	−	0.0170518i
$599$	242.951	+	242.951i	0.405594	+	0.405594i	0.880199	−	0.474605i	$-0.157409\pi$
$599$	242.951	+	242.951i	0.405594	+	0.405594i	−0.474605	+	0.880199i	$0.657409\pi$
$600$	156.236	−	233.824i	0.260394	−	0.389707i
$601$	−81.6626	−	16.2437i	−0.135878	−	0.0270278i	0.126683	−	0.991943i	$-0.459567\pi$
$601$	−81.6626	−	16.2437i	−0.135878	−	0.0270278i	−0.262561	+	0.964915i	$0.584567\pi$
$602$	166.960	+	249.873i	0.277342	+	0.415072i
$603$	−28.2031	−	68.0883i	−0.0467713	−	0.112916i
$604$	66.6118	−	27.5915i	0.110284	−	0.0456813i
$605$	0.146324	−	0.0977703i	0.000241857	−	0.000161604i
$606$	−7.51621	+	37.7865i	−0.0124030	+	0.0623540i
$607$	374.212	+	250.040i	0.616494	+	0.411928i	0.824229	−	0.566257i	$-0.191609\pi$
$607$	374.212	+	250.040i	0.616494	+	0.411928i	−0.207735	+	0.978185i	$0.566609\pi$
$608$	885.551	−	885.551i	1.45650	−	1.45650i
$609$	−47.7791	−	240.202i	−0.0784549	−	0.394420i
$610$	−17.6253	+	42.5513i	−0.0288939	+	0.0697562i
$611$			863.873i			1.41387i
$612$	−308.150	−	16.0492i	−0.503513	−	0.0262242i
$613$	−61.7490			−0.100732			−0.0503662	−	0.998731i	$-0.516039\pi$
$613$	−61.7490			−0.100732			−0.0503662	+	0.998731i	$0.516039\pi$
$614$	1707.88	+	707.425i	2.78156	+	1.15216i
$615$	−8.79123	+	1.74868i	−0.0142947	+	0.00284339i
$616$	−212.959	−	212.959i	−0.345712	−	0.345712i
$617$	472.045	−	706.466i	0.765065	−	1.14500i	−0.220448	−	0.975399i	$-0.570752\pi$
$617$	472.045	−	706.466i	0.765065	−	1.14500i	0.985513	−	0.169602i	$-0.0542482\pi$
$618$	688.244	+	136.900i	1.11366	+	0.221521i
$619$	−194.272	−	290.748i	−0.313848	−	0.469706i	0.640689	−	0.767801i	$-0.278649\pi$
$619$	−194.272	−	290.748i	−0.313848	−	0.469706i	−0.954536	+	0.298095i	$0.903649\pi$
$620$	8.95442	+	21.6179i	0.0144426	+	0.0348675i
$621$	4.56478	−	1.89079i	0.00735069	−	0.00304476i
$622$	−1198.72	+	800.958i	−1.92720	+	1.28771i
$623$	−3.28724	+	16.5261i	−0.00527646	+	0.0265266i
$624$	−89.7616	−	59.9768i	−0.143849	−	0.0961167i
$625$	−440.794	+	440.794i	−0.705271	+	0.705271i
$626$	−176.009	−	884.857i	−0.281165	−	1.41351i
$627$	−242.961	+	586.559i	−0.387497	+	0.935501i
$628$		−	916.961i		−	1.46013i
$629$	−126.090	+	75.0712i	−0.200461	+	0.119350i
$630$	−5.92242			−0.00940067
$631$	−652.499	−	270.274i	−1.03407	−	0.428327i	−0.199891	−	0.979818i	$-0.564059\pi$
$631$	−652.499	−	270.274i	−1.03407	−	0.428327i	−0.834180	+	0.551492i	$0.814059\pi$
$632$	179.254	−	35.6558i	0.283630	−	0.0564174i
$633$	370.243	+	370.243i	0.584901	+	0.584901i
$634$	362.097	−	541.916i	0.571130	−	0.854757i
$635$	13.2280	+	2.63121i	0.0208315	+	0.00414364i
$636$	−0.862961	−	1.29151i	−0.00135686	−	0.00203068i
$637$	206.232	+	497.889i	0.323756	+	0.781616i
$638$	−1070.84	+	443.557i	−1.67843	+	0.695230i
$639$	194.084	−	129.683i	0.303730	−	0.202946i
$640$	5.18522	−	26.0679i	0.00810190	−	0.0407310i
$641$	112.788	+	75.3625i	0.175956	+	0.117570i	0.640430	−	0.768017i	$-0.278756\pi$
$641$	112.788	+	75.3625i	0.175956	+	0.117570i	−0.464473	+	0.885587i	$0.653756\pi$
$642$	−219.179	+	219.179i	−0.341401	+	0.341401i
$643$	−26.2415	−	131.925i	−0.0408111	−	0.205171i	0.955000	−	0.296606i	$-0.0958547\pi$
$643$	−26.2415	−	131.925i	−0.0408111	−	0.205171i	−0.995811	+	0.0914346i	$0.970855\pi$
$644$	−9.31967	+	22.4997i	−0.0144715	+	0.0349374i
$645$		−	5.70579i		−	0.00884619i
$646$	−1629.28	−	776.477i	−2.52210	−	1.20198i
$647$	220.979			0.341544			0.170772	−	0.985311i	$-0.445374\pi$
$647$	220.979			0.341544			0.170772	+	0.985311i	$0.445374\pi$
$648$	54.0475	+	22.3872i	0.0834067	+	0.0345482i
$649$	−1217.82	+	242.240i	−1.87646	+	0.373251i
$650$	−970.873	−	970.873i	−1.49365	−	1.49365i
$651$	−107.089	+	160.270i	−0.164499	+	0.246190i
$652$	−1671.62	−	332.505i	−2.56383	−	0.509978i
$653$	365.630	+	547.204i	0.559924	+	0.837985i	0.998145	−	0.0608819i	$-0.0193913\pi$
$653$	365.630	+	547.204i	0.559924	+	0.837985i	−0.438221	+	0.898867i	$0.644391\pi$
$654$	−381.176	−	920.239i	−0.582837	−	1.40709i
$655$	2.43918	−	1.01034i	0.00372393	−	0.00154250i
$656$	105.146	−	70.2562i	0.160283	−	0.107098i
$657$	51.7866	−	260.349i	0.0788229	−	0.396269i
$658$	−555.932	−	371.462i	−0.844881	−	0.564531i
$659$	−503.274	+	503.274i	−0.763693	+	0.763693i	−0.976988	−	0.213295i	$-0.931580\pi$
$659$	−503.274	+	503.274i	−0.763693	+	0.763693i	0.213295	+	0.976988i	$0.431580\pi$
$660$	3.29186	+	16.5493i	0.00498767	+	0.0250747i
$661$	165.181	−	398.781i	0.249895	−	0.603300i	−0.748300	−	0.663361i	$-0.769130\pi$
$661$	165.181	−	398.781i	0.249895	−	0.603300i	0.998195	+	0.0600610i	$0.0191295\pi$
$662$			286.780i			0.433203i
$663$	−125.511	+	494.875i	−0.189308	+	0.746418i
$664$	−587.969			−0.885496
$665$	−19.2665	−	7.98045i	−0.0289722	−	0.0120007i
$666$	80.5199	−	16.0164i	0.120901	−	0.0240487i
$667$	22.4591	+	22.4591i	0.0336717	+	0.0336717i
$668$	636.958	−	953.275i	0.953530	−	1.42706i
$669$	−270.622	−	53.8300i	−0.404517	−	0.0804634i
$670$	−6.36495	−	9.52583i	−0.00949993	−	0.0142177i
$671$	413.668	+	998.682i	0.616494	+	1.48835i
$672$	253.315	−	104.927i	0.376957	−	0.156141i
$673$	163.755	−	109.418i	0.243321	−	0.162582i	−0.427930	−	0.903812i	$-0.640757\pi$
$673$	163.755	−	109.418i	0.243321	−	0.162582i	0.671251	+	0.741230i	$0.265757\pi$
$674$	287.400	−	1444.86i	0.426410	−	2.14371i
$675$	−107.918	−	72.1082i	−0.159878	−	0.106827i
$676$	563.186	−	563.186i	0.833116	−	0.833116i
$677$	91.3086	+	459.039i	0.134872	+	0.678049i	0.987763	+	0.155960i	$0.0498472\pi$
$677$	91.3086	+	459.039i	0.134872	+	0.678049i	−0.852891	+	0.522089i	$0.825153\pi$
$678$	392.049	−	946.491i	0.578244	−	1.39600i
$679$			62.8413i			0.0925497i
$680$	−16.0864	+	2.33775i	−0.0236565	+	0.00343786i
$681$	213.495			0.313503
$682$	842.808	+	349.102i	1.23579	+	0.511880i
$683$	−290.137	+	57.7118i	−0.424798	+	0.0844975i	−0.402860	−	0.915262i	$-0.631984\pi$
$683$	−290.137	+	57.7118i	−0.424798	+	0.0844975i	−0.0219382	+	0.999759i	$0.506984\pi$
$684$	429.821	+	429.821i	0.628393	+	0.628393i
$685$	10.7407	−	16.0746i	0.0156799	−	0.0234666i
$686$	−1054.03	−	209.659i	−1.53648	−	0.305625i
$687$	298.234	+	446.338i	0.434110	+	0.649692i
$688$	30.8053	+	74.3706i	0.0447752	+	0.108097i
$689$	−2.37438	+	0.983500i	−0.00344612	+	0.00142743i
$690$	0.638631	−	0.426720i	0.000925553	−	0.000618434i
$691$	186.934	−	939.780i	0.270526	−	1.36003i	−0.571504	−	0.820599i	$-0.693640\pi$
$691$	186.934	−	939.780i	0.270526	−	1.36003i	0.842031	−	0.539429i	$-0.181360\pi$
$692$	−1317.24	−	880.152i	−1.90353	−	1.27190i
$693$	−98.2876	+	98.2876i	−0.141829	+	0.141829i
$694$	182.816	+	919.080i	0.263424	+	1.32432i
$695$	0.845297	−	2.04073i	0.00121625	−	0.00293630i
$696$			376.065i			0.540323i
$697$	−479.302	−	357.670i	−0.687665	−	0.513156i
$698$	−224.598			−0.321774
$699$	67.2277	+	27.8466i	0.0961769	+	0.0398378i
$700$	627.445	−	124.807i	0.896350	−	0.178295i
$701$	789.024	+	789.024i	1.12557	+	1.12557i	0.990889	+	0.134680i	$0.0430006\pi$
$701$	789.024	+	789.024i	1.12557	+	1.12557i	0.134680	+	0.990889i	$0.456999\pi$
$702$	158.685	−	237.488i	0.226046	−	0.338302i
$703$	283.525	+	56.3967i	0.403308	+	0.0802229i
$704$	−633.492	−	948.088i	−0.899847	−	1.34672i
$705$	4.85799	+	11.7282i	0.00689077	+	0.0166358i
$706$	229.836	−	95.2014i	0.325547	−	0.134846i
$707$	−24.6954	+	16.5009i	−0.0349298	+	0.0233394i
$708$	−231.927	+	1165.98i	−0.327581	+	1.64686i
$709$	732.595	+	489.504i	1.03328	+	0.690415i	0.951944	−	0.306272i	$-0.0990816\pi$
$709$	732.595	+	489.504i	1.03328	+	0.690415i	0.0813353	+	0.996687i	$0.474082\pi$
$710$	25.6582	−	25.6582i	0.0361384	−	0.0361384i
$711$	−16.4564	−	82.7317i	−0.0231454	−	0.116360i
$712$	9.90138	−	23.9040i	0.0139064	−	0.0335731i
$713$		−	24.9983i		−	0.0350607i
$714$	−264.500	−	293.565i	−0.370448	−	0.411155i
$715$	27.9182			0.0390465
$716$	470.473	+	194.876i	0.657085	+	0.272173i
$717$	117.842	−	23.4402i	0.164354	−	0.0326921i
$718$	326.362	+	326.362i	0.454544	+	0.454544i
$719$	−569.678	+	852.583i	−0.792320	+	1.18579i	0.186779	+	0.982402i	$0.440195\pi$
$719$	−569.678	+	852.583i	−0.792320	+	1.18579i	−0.979098	+	0.203388i	$0.934805\pi$
$720$	−1.55591	−	0.309491i	−0.00216099	−	0.000429848i
$721$	300.548	+	449.802i	0.416849	+	0.623858i
$722$	922.640	+	2227.45i	1.27789	+	3.08511i
$723$	−534.047	+	221.209i	−0.738654	+	0.305960i
$724$	768.229	−	513.314i	1.06109	−	0.708997i
$725$	162.773	−	818.317i	0.224515	−	1.12871i
$726$	−5.46180	−	3.64946i	−0.00752314	−	0.00502680i
$727$	325.279	−	325.279i	0.447426	−	0.447426i	−0.447072	−	0.894498i	$-0.647533\pi$
$727$	325.279	−	325.279i	0.447426	−	0.447426i	0.894498	+	0.447072i	$0.147533\pi$
$728$	93.0753	+	467.921i	0.127851	+	0.642749i
$729$	10.3325	−	24.9447i	0.0141735	−	0.0342178i
$730$		−	41.2649i		−	0.0565273i
$731$	282.827	−	254.825i	0.386904	−	0.348598i
$732$	1034.95			1.41386
$733$	219.374	+	90.8676i	0.299282	+	0.123967i	0.527271	−	0.849697i	$-0.323215\pi$
$733$	219.374	+	90.8676i	0.299282	+	0.123967i	−0.227989	+	0.973664i	$0.573215\pi$
$734$	−616.931	+	122.715i	−0.840506	+	0.167187i
$735$	5.59976	+	5.59976i	0.00761873	+	0.00761873i
$736$	−19.7556	+	29.5663i	−0.0268418	+	0.0401716i
$737$	−263.721	−	52.4574i	−0.357831	−	0.0711769i
$738$	185.881	+	278.191i	0.251872	+	0.376953i
$739$	−86.4161	−	208.627i	−0.116937	−	0.282310i	0.854564	−	0.519345i	$-0.173824\pi$
$739$	−86.4161	−	208.627i	−0.116937	−	0.282310i	−0.971501	+	0.237036i	$0.923824\pi$
$740$	7.09812	−	2.94014i	0.00959205	−	0.00397316i
$741$	836.240	−	558.757i	1.12853	−	0.754059i
$742$	0.388057	−	1.95089i	0.000522988	−	0.00262924i
$743$	−577.764	−	386.050i	−0.777610	−	0.519582i	0.102282	−	0.994755i	$-0.467385\pi$
$743$	−577.764	−	386.050i	−0.777610	−	0.519582i	−0.879892	+	0.475173i	$0.842385\pi$
$744$	209.291	−	209.291i	0.281306	−	0.281306i
$745$	0.440111	+	2.21259i	0.000590753	+	0.00296992i
$746$	−284.822	+	687.621i	−0.381799	+	0.921743i
$747$			271.368i			0.363277i
$748$	−673.306	+	902.277i	−0.900142	+	1.20625i
$749$	−238.958			−0.319035
$750$	−37.2974	−	15.4491i	−0.0497298	−	0.0205988i
$751$	246.753	−	49.0821i	0.328565	−	0.0653557i	−0.0280514	−	0.999606i	$-0.508930\pi$
$751$	246.753	−	49.0821i	0.328565	−	0.0653557i	0.356617	+	0.934251i	$0.383930\pi$
$752$	−126.640	−	126.640i	−0.168405	−	0.168405i
$753$	−42.4099	+	63.4709i	−0.0563213	+	0.0842907i
$754$	1800.82	+	358.206i	2.38836	+	0.475074i
$755$	−0.973923	−	1.45758i	−0.00128996	−	0.00193057i
$756$	50.9283	+	122.952i	0.0673655	+	0.162635i
$757$	−1268.13	+	525.275i	−1.67520	+	0.693890i	−0.999079	−	0.0429009i	$-0.986340\pi$
$757$	−1268.13	+	525.275i	−1.67520	+	0.693890i	−0.676120	+	0.736791i	$0.736340\pi$
$758$	523.963	−	350.101i	0.691244	−	0.461874i
$759$	3.51685	−	17.6804i	0.00463354	−	0.0232944i
$760$	26.6253	+	17.7905i	0.0350333	+	0.0234085i
$761$	−792.972	+	792.972i	−1.04201	+	1.04201i	−0.0429349	+	0.999078i	$0.513671\pi$
$761$	−792.972	+	792.972i	−1.04201	+	1.04201i	−0.999078	+	0.0429349i	$0.986329\pi$
$762$	−98.2148	−	493.759i	−0.128891	−	0.647978i
$763$	293.854	−	709.426i	0.385130	−	0.929785i
$764$		−	1826.25i		−	2.39038i
$765$	1.07895	+	7.42441i	0.00141039	+	0.00970511i
$766$	601.888			0.785754
$767$	1817.24	+	752.727i	2.36929	+	0.981391i
$768$	−265.147	+	52.7411i	−0.345244	+	0.0686733i
$769$	428.511	+	428.511i	0.557231	+	0.557231i	0.928518	−	0.371287i	$-0.121083\pi$
$769$	428.511	+	428.511i	0.557231	+	0.557231i	−0.371287	+	0.928518i	$0.621083\pi$
$770$	−12.0047	+	17.9663i	−0.0155905	+	0.0233329i
$771$	−549.658	−	109.334i	−0.712915	−	0.141808i
$772$	849.162	+	1270.86i	1.09995	+	1.64619i
$773$	−289.006	−	697.723i	−0.373876	−	0.902617i	−0.993086	−	0.117391i	$-0.962547\pi$
$773$	−289.006	−	697.723i	−0.373876	−	0.902617i	0.619210	−	0.785226i	$-0.287453\pi$
$774$	−196.767	+	81.5037i	−0.254221	+	0.105302i
$775$	−546.006	+	364.830i	−0.704524	+	0.470748i
$776$	18.8253	−	94.6410i	0.0242594	−	0.121960i
$777$	52.6238	+	35.1621i	0.0677269	+	0.0452537i
$778$	−653.335	+	653.335i	−0.839763	+	0.839763i
$779$	229.838	+	1155.47i	0.295042	+	1.48328i
$780$	10.2290	−	24.6950i	0.0131141	−	0.0316603i
$781$		−	851.641i		−	1.09045i
$782$	49.6736	+	12.5983i	0.0635212	+	0.0161104i
$783$	173.566			0.221668
$784$	−103.221	−	42.7557i	−0.131660	−	0.0545354i
$785$	−21.8663	+	4.34947i	−0.0278551	+	0.00554072i
$786$	−69.6842	−	69.6842i	−0.0886567	−	0.0886567i
$787$	−78.2193	+	117.063i	−0.0993892	+	0.148746i	−0.877831	−	0.478970i	$-0.841010\pi$
$787$	−78.2193	+	117.063i	−0.0993892	+	0.148746i	0.778442	+	0.627716i	$0.216010\pi$
$788$	−1943.52	−	386.590i	−2.46640	−	0.490597i
$789$	−49.6618	−	74.3241i	−0.0629427	−	0.0942004i
$790$	−5.01807	−	12.1147i	−0.00635199	−	0.0153351i
$791$	729.664	−	302.237i	0.922458	−	0.382094i
$792$	177.468	−	118.581i	0.224076	−	0.149723i
$793$	334.068	−	1679.48i	0.421272	−	2.11788i
$794$	189.668	+	126.732i	0.238877	+	0.159612i
$795$	−0.0267047	+	0.0267047i	−3.35908e−5	+	3.35908e-5i
$796$	38.5505	+	193.806i	0.0484302	+	0.243475i
$797$	−79.4807	+	191.883i	−0.0997248	+	0.240757i	−0.965866	−	0.259043i	$-0.916593\pi$
$797$	−79.4807	+	191.883i	−0.0997248	+	0.240757i	0.866141	+	0.499800i	$0.166593\pi$
$798$			778.412i			0.975453i
$799$	−364.388	+	764.595i	−0.456056	+	0.956939i
$800$	934.097			1.16762
$801$	−11.0325	−	4.56982i	−0.0137734	−	0.00570514i
$802$	−208.608	+	41.4946i	−0.260109	+	0.0517390i
$803$	−684.827	−	684.827i	−0.852836	−	0.852836i
$804$	−143.026	+	214.054i	−0.177893	+	0.266236i
$805$	0.580743	+	0.115517i	0.000721420	+	0.000143499i
$806$	−802.861	−	1201.57i	−0.996105	−	1.49078i
$807$	−258.609	−	624.338i	−0.320457	−	0.773652i
$808$	42.1352	−	17.4530i	0.0521476	−	0.0216002i
$809$	605.877	−	404.834i	0.748920	−	0.500413i	−0.121579	−	0.992582i	$-0.538796\pi$
$809$	605.877	−	404.834i	0.748920	−	0.500413i	0.870500	+	0.492169i	$0.163796\pi$
$810$	0.818839	−	4.11658i	0.00101091	−	0.00508220i
$811$	−943.587	−	630.485i	−1.16349	−	0.777417i	−0.184800	−	0.982776i	$-0.559164\pi$
$811$	−943.587	−	630.485i	−1.16349	−	0.777417i	−0.978687	+	0.205359i	$0.934164\pi$
$812$	−604.932	+	604.932i	−0.744990	+	0.744990i
$813$	−117.467	−	590.544i	−0.144485	−	0.726377i
$814$	114.626	−	276.732i	0.140818	−	0.339965i
$815$			41.4393i			0.0508458i
$816$	−54.1473	−	90.9463i	−0.0663570	−	0.111454i
$817$	−749.939			−0.917918
$818$	493.713	+	204.502i	0.603561	+	0.250003i
$819$	215.961	−	42.9574i	0.263689	−	0.0524510i
$820$	22.1401	+	22.1401i	0.0270002	+	0.0270002i
$821$	631.689	−	945.389i	0.769414	−	1.15151i	−0.215166	−	0.976577i	$-0.569029\pi$
$821$	631.689	−	945.389i	0.769414	−	1.15151i	0.984580	−	0.174932i	$-0.0559706\pi$
$822$	−707.767	−	140.784i	−0.861031	−	0.171270i
$823$	−521.180	−	780.000i	−0.633268	−	0.947753i	−0.999849	−	0.0173666i	$-0.994472\pi$
$823$	−521.180	−	780.000i	−0.633268	−	0.947753i	0.366581	−	0.930386i	$-0.380528\pi$
$824$	−317.889	−	767.451i	−0.385787	−	0.931373i
$825$	−437.497	+	181.217i	−0.530299	+	0.219657i
$826$	−1265.81	+	845.789i	−1.53246	+	1.02396i
$827$	−178.315	+	896.451i	−0.215617	+	1.08398i	0.709618	+	0.704586i	$0.248867\pi$
$827$	−178.315	+	896.451i	−0.215617	+	1.08398i	−0.925235	+	0.379394i	$0.876133\pi$
$828$	−14.3506	−	9.58878i	−0.0173317	−	0.0115807i
$829$	275.393	−	275.393i	0.332199	−	0.332199i	−0.521222	−	0.853421i	$-0.674524\pi$
$829$	275.393	−	275.393i	0.332199	−	0.332199i	0.853421	+	0.521222i	$0.174524\pi$
$830$	8.22987	+	41.3743i	0.00991550	+	0.0498486i
$831$	−86.8890	+	209.769i	−0.104560	+	0.252429i
$832$			1806.30i			2.17104i
$833$	−27.4818	+	527.661i	−0.0329914	+	0.633446i
$834$	−82.4500			−0.0988610
$835$	−25.7535	−	10.6675i	−0.0308425	−	0.0127754i
$836$	2175.15	−	432.665i	2.60186	−	0.517542i
$837$	−96.5949	−	96.5949i	−0.115406	−	0.115406i
$838$	−422.968	+	633.016i	−0.504735	+	0.755389i
$839$	−1222.45	−	243.160i	−1.45703	−	0.289821i	−0.597896	−	0.801574i	$-0.703996\pi$
$839$	−1222.45	−	243.160i	−1.45703	−	0.289821i	−0.859133	+	0.511753i	$0.828996\pi$
$840$	3.89498	+	5.82925i	0.00463688	+	0.00693958i
$841$	105.143	+	253.837i	0.125021	+	0.301827i
$842$	−1626.49	+	673.715i	−1.93170	+	0.800137i
$843$	118.928	−	79.4653i	0.141077	−	0.0942649i
$844$	356.826	−	1793.89i	0.422780	−	2.12546i
$845$	−16.1014	−	10.7586i	−0.0190549	−	0.0127321i
$846$	335.061	−	335.061i	0.396053	−	0.396053i
$847$	−0.987942	−	4.96672i	−0.00116640	−	0.00586390i
$848$	0.203897	−	0.492252i	0.000240445	−	0.000580486i
$849$		−	283.433i		−	0.333843i
$850$	−449.776	−	1268.82i	−0.529148	−	1.49273i
$851$	−8.20806			−0.00964519
$852$	−753.317	−	312.034i	−0.884175	−	0.366237i
$853$	590.983	−	117.554i	0.692829	−	0.137812i	0.163898	−	0.986477i	$-0.447593\pi$
$853$	590.983	−	117.554i	0.692829	−	0.137812i	0.528931	+	0.848665i	$0.322593\pi$
$854$	937.151	+	937.151i	1.09737	+	1.09737i
$855$	8.21090	−	12.2885i	0.00960339	−	0.0143725i
$856$	359.878	+	71.5842i	0.420418	+	0.0836264i
$857$	−104.359	−	156.184i	−0.121772	−	0.182245i	0.765575	−	0.643346i	$-0.222454\pi$
$857$	−104.359	−	156.184i	−0.121772	−	0.182245i	−0.887348	+	0.461101i	$0.847454\pi$
$858$	−398.794	−	962.775i	−0.464795	−	1.12212i
$859$	218.252	−	90.4030i	0.254077	−	0.105242i	−0.252010	−	0.967725i	$-0.581092\pi$
$859$	218.252	−	90.4030i	0.254077	−	0.105242i	0.506087	+	0.862483i	$0.331092\pi$
$860$	−16.5723	+	11.0732i	−0.0192701	+	0.0128759i
$861$	−50.3198	+	252.975i	−0.0584435	+	0.293815i
$862$	2107.33	+	1408.07i	2.44470	+	1.63350i
$863$	730.895	−	730.895i	0.846924	−	0.846924i	−0.142824	−	0.989748i	$-0.545618\pi$
$863$	730.895	−	730.895i	0.846924	−	0.846924i	0.989748	+	0.142824i	$0.0456183\pi$
$864$	37.9093	+	190.583i	0.0438765	+	0.220582i
$865$	−14.7403	+	35.5863i	−0.0170409	+	0.0411403i
$866$			2026.69i			2.34029i
$867$	−319.829	+	385.061i	−0.368892	+	0.444131i
$868$	673.326			0.775721
$869$	−284.333	−	117.775i	−0.327195	−	0.135529i
$870$	26.4630	−	5.26381i	0.0304172	−	0.00605036i
$871$	301.192	+	301.192i	0.345801	+	0.345801i
$872$	−655.076	+	980.390i	−0.751233	+	1.12430i
$873$	−43.6800	−	8.68849i	−0.0500344	−	0.00995245i
$874$	−56.0858	−	83.9383i	−0.0641714	−	0.0960393i
$875$	−11.9099	−	28.7531i	−0.0136113	−	0.0328607i
$876$	−856.677	+	354.847i	−0.977942	+	0.405077i
$877$	−391.441	+	261.552i	−0.446341	+	0.298235i	−0.758355	−	0.651842i	$-0.773996\pi$
$877$	−391.441	+	261.552i	−0.446341	+	0.298235i	0.312014	+	0.950078i	$0.398996\pi$
$878$	269.633	−	1355.54i	0.307099	−	1.54389i
$879$	165.764	+	110.760i	0.188582	+	0.126007i
$880$	−4.09271	+	4.09271i	−0.00465080	+	0.00465080i
$881$	−116.853	−	587.462i	−0.132637	−	0.666813i	−0.988696	−	0.149934i	$-0.952094\pi$
$881$	−116.853	−	587.462i	−0.132637	−	0.666813i	0.856059	−	0.516879i	$-0.172906\pi$
$882$	113.122	−	273.100i	0.128256	−	0.309637i
$883$		−	666.108i		−	0.754369i	−0.926138	−	0.377184i	$-0.876892\pi$
$883$		−	666.108i		−	0.754369i	0.926138	−	0.377184i	$-0.123108\pi$
$884$	1680.93	−	595.862i	1.90150	−	0.674052i
$885$	28.9045			0.0326604
$886$	198.125	+	82.0659i	0.223617	+	0.0926252i
$887$	572.685	−	113.914i	0.645643	−	0.128426i	0.138602	−	0.990348i	$-0.455739\pi$
$887$	572.685	−	113.914i	0.645643	−	0.128426i	0.507041	+	0.861922i	$0.330739\pi$
$888$	−68.7197	−	68.7197i	−0.0773871	−	0.0773871i
$889$	215.619	−	322.696i	0.242541	−	0.362988i
$890$	−1.82067	−	0.362155i	−0.00204570	−	0.000406915i
$891$	−54.7289	−	81.9076i	−0.0614241	−	0.0919277i
$892$	368.849	+	890.480i	0.413508	+	0.998296i
$893$	1541.50	−	638.509i	1.72620	−	0.715016i
$894$	70.0155	−	46.7829i	0.0783171	−	0.0523298i
$895$	2.41548	−	12.1435i	0.00269886	−	0.0135681i
$896$	−635.924	−	424.911i	−0.709737	−	0.474231i
$897$	−20.1926	+	20.1926i	−0.0225112	+	0.0225112i
$898$	225.669	+	1134.52i	0.251302	+	1.26338i
$899$	336.055	−	811.309i	0.373810	−	0.902458i
$900$			453.383i			0.503759i
$901$	−2.51636	−	0.131058i	−0.00279285	−	0.000145458i
$902$	1220.71			1.35333
$903$	−151.691	−	62.8324i	−0.167985	−	0.0695818i
$904$	−1189.44	+	236.594i	−1.31575	+	0.261719i
$905$	−15.8847	−	15.8847i	−0.0175521	−	0.0175521i
$906$	−36.3535	+	54.4068i	−0.0401252	+	0.0600517i
$907$	1039.96	+	206.862i	1.14660	+	0.228073i	0.731590	−	0.681745i	$-0.238779\pi$
$907$	1039.96	+	206.862i	1.14660	+	0.228073i	0.415009	+	0.909818i	$0.363779\pi$
$908$	−414.331	−	620.090i	−0.456312	−	0.682918i
$909$	−8.05513	−	19.4468i	−0.00886153	−	0.0213936i
$910$	31.6240	−	13.0991i	0.0347516	−	0.0143946i
$911$	−1302.32	+	870.182i	−1.42955	+	0.955194i	−0.430945	+	0.902378i	$0.641820\pi$
$911$	−1302.32	+	870.182i	−1.42955	+	0.955194i	−0.998604	+	0.0528157i	$0.983180\pi$
$912$	−40.6778	+	204.501i	−0.0446028	+	0.224234i
$913$	823.224	+	550.061i	0.901670	+	0.602476i
$914$	−692.556	+	692.556i	−0.757720	+	0.757720i
$915$	−4.90911	−	24.6798i	−0.00536515	−	0.0269724i
$916$	717.591	−	1732.42i	0.783397	−	1.89129i
$917$		−	75.9723i		−	0.0828488i
$918$	240.622	−	143.261i	0.262116	−	0.156058i
$919$	−1243.67			−1.35329			−0.676645	−	0.736310i	$-0.736567\pi$
$919$	−1243.67			−1.35329			−0.676645	+	0.736310i	$0.736567\pi$
$920$	−0.840013	−	0.347945i	−0.000913058	−	0.000378201i
$921$	−990.570	+	197.037i	−1.07554	+	0.213938i
$922$	−1626.04	−	1626.04i	−1.76361	−	1.76361i
$923$	−749.521	+	1121.74i	−0.812048	+	1.21532i
$924$	476.220	+	94.7260i	0.515390	+	0.102517i
$925$	119.790	+	179.278i	0.129503	+	0.193814i
$926$	−504.132	−	1217.08i	−0.544419	−	1.31434i
$927$	−354.204	+	146.716i	−0.382097	+	0.158270i
$928$	−1038.62	+	693.986i	−1.11921	+	0.747830i
$929$	−212.341	+	1067.51i	−0.228569	+	1.14909i	0.680596	+	0.732659i	$0.261721\pi$
$929$	−212.341	+	1067.51i	−0.228569	+	1.14909i	−0.909165	+	0.416435i	$0.863279\pi$
$930$	−17.6569	−	11.7980i	−0.0189859	−	0.0126860i
$931$	736.003	−	736.003i	0.790551	−	0.790551i
$932$	−49.5893	−	249.302i	−0.0532074	−	0.267492i
$933$	301.426	−	727.706i	0.323072	−	0.779964i
$934$		−	2013.16i		−	2.15542i
$935$	24.7098	+	11.7761i	0.0264276	+	0.0125948i
$936$	−338.113			−0.361232
$937$	−476.362	−	197.316i	−0.508391	−	0.210582i	0.113718	−	0.993513i	$-0.463724\pi$
$937$	−476.362	−	197.316i	−0.508391	−	0.210582i	−0.622109	+	0.782931i	$0.713724\pi$
$938$	−323.339	+	64.3161i	−0.344711	+	0.0685673i
$939$	348.541	+	348.541i	0.371184	+	0.371184i
$940$	24.6363	−	36.8709i	0.0262089	−	0.0392243i
$941$	255.677	+	50.8573i	0.271708	+	0.0540460i	0.329063	−	0.944308i	$-0.393267\pi$
$941$	255.677	+	50.8573i	0.271708	+	0.0540460i	−0.0573559	+	0.998354i	$0.518267\pi$
$942$	462.339	+	691.939i	0.490806	+	0.734543i
$943$	−12.8011	−	30.9046i	−0.0135749	−	0.0327727i
$944$	−376.748	+	156.054i	−0.399097	+	0.165311i
$945$	2.69039	−	1.79766i	0.00284698	−	0.00190229i
$946$	−151.596	+	762.123i	−0.160249	+	0.805627i
$947$	−875.169	−	584.769i	−0.924148	−	0.617496i	−0.000194452	−	1.00000i	$-0.500062\pi$
$947$	−875.169	−	584.769i	−0.924148	−	0.617496i	−0.923954	+	0.382504i	$0.875062\pi$
$948$	−208.354	+	208.354i	−0.219783	+	0.219783i
$949$	299.309	+	1504.73i	0.315394	+	1.58559i
$950$	−1014.83	+	2450.02i	−1.06825	+	2.57897i
$951$			356.087i			0.374434i
$952$	−114.994	+	453.406i	−0.120792	+	0.476267i
$953$	76.9694			0.0807653			0.0403827	−	0.999184i	$-0.487142\pi$
$953$	76.9694			0.0807653			0.0403827	+	0.999184i	$0.487142\pi$
$954$	1.30238	+	0.539465i	0.00136518	+	0.000565476i
$955$	−43.5496	+	8.66255i	−0.0456017	+	0.00907073i
$956$	−296.777	−	296.777i	−0.310437	−	0.310437i
$957$	351.818	−	526.533i	0.367626	−	0.550191i
$958$	657.402	+	130.765i	0.686224	+	0.136498i
$959$	−309.074	−	462.561i	−0.322287	−	0.482337i
$960$	10.1577	+	24.5230i	0.0105810	+	0.0255448i
$961$	249.305	−	103.266i	0.259422	−	0.107456i
$962$	−394.528	+	263.615i	−0.410112	+	0.274028i
$963$	33.0385	−	166.096i	0.0343079	−	0.172477i
$964$	1678.92	+	1121.82i	1.74162	+	1.16371i
$965$	26.2776	−	26.2776i	0.0272307	−	0.0272307i
$966$	−4.31189	−	21.6773i	−0.00446365	−	0.0224403i
$967$	−161.491	+	389.874i	−0.167002	+	0.403179i	−0.985119	−	0.171873i	$-0.945018\pi$
$967$	−161.491	+	389.874i	−0.167002	+	0.403179i	0.818117	+	0.575052i	$0.195018\pi$
$968$			7.77600i			0.00803306i
$969$	975.825	−	141.811i	1.00704	−	0.146348i
$970$	−6.92321			−0.00713733
$971$	−199.129	−	82.4820i	−0.205076	−	0.0849455i	0.277781	−	0.960644i	$-0.410401\pi$
$971$	−199.129	−	82.4820i	−0.205076	−	0.0849455i	−0.482857	+	0.875699i	$0.660401\pi$
$972$	−92.5033	+	18.4001i	−0.0951680	+	0.0189301i
$973$	−44.9451	−	44.9451i	−0.0461923	−	0.0461923i
$974$	298.470	−	446.692i	0.306437	−	0.458616i
$975$	735.735	+	146.347i	0.754600	+	0.150099i
$976$	197.231	+	295.178i	0.202081	+	0.302436i
$977$	−674.807	−	1629.13i	−0.690693	−	1.66748i	−0.743379	−	0.668870i	$-0.766778\pi$
$977$	−674.807	−	1629.13i	−0.690693	−	1.66748i	0.0526861	−	0.998611i	$-0.483222\pi$
$978$	1429.06	−	591.934i	1.46120	−	0.605250i
$979$	−36.2259	+	24.2054i	−0.0370030	+	0.0247246i
$980$	5.39685	−	27.1318i	0.00550699	−	0.0276855i
$981$	452.483	+	302.339i	0.461246	+	0.308195i
$982$	260.522	−	260.522i	0.265298	−	0.265298i
$983$	144.812	+	728.020i	0.147317	+	0.740610i	0.981851	+	0.189654i	$0.0607368\pi$
$983$	144.812	+	728.020i	0.147317	+	0.740610i	−0.834534	+	0.550956i	$0.814263\pi$
$984$	151.567	−	365.914i	0.154031	−	0.371864i
$985$			48.1798i			0.0489135i
$986$	1442.77	+	1076.64i	1.46326	+	1.09193i
$987$	365.296			0.370107
$988$	−3245.78	−	1344.45i	−3.28520	−	1.36078i
$989$	20.8844	−	4.15417i	0.0211167	−	0.00420037i
$990$	−10.8283	−	10.8283i	−0.0109377	−	0.0109377i
$991$	−153.630	+	229.924i	−0.155025	+	0.232012i	−0.900850	−	0.434131i	$-0.857056\pi$
$991$	−153.630	+	229.924i	−0.155025	+	0.232012i	0.745825	+	0.666142i	$0.232056\pi$
$992$	964.250	+	191.801i	0.972026	+	0.193348i
$993$	−87.0478	−	130.276i	−0.0876615	−	0.131195i
$994$	−399.585	−	964.684i	−0.401997	−	0.970507i
$995$	4.43873	−	1.83858i	0.00446104	−	0.00184782i
$996$	788.177	−	526.643i	0.791343	−	0.528758i
$997$	−146.304	+	735.517i	−0.146744	+	0.737731i	0.835407	+	0.549633i	$0.185232\pi$
$997$	−146.304	+	735.517i	−0.146744	+	0.737731i	−0.982150	+	0.188098i	$0.939768\pi$
$998$	1596.97	+	1067.06i	1.60017	+	1.06920i
$999$	−31.7164	+	31.7164i	−0.0317482	+	0.0317482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.3.j.a.40.6	yes	48
3.2	odd	2		153.3.p.c.91.1		48
17.3	odd	16	inner	51.3.j.a.37.6	✓	48
51.20	even	16		153.3.p.c.37.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.3.j.a.37.6	✓	48	17.3	odd	16	inner
51.3.j.a.40.6	yes	48	1.1	even	1	trivial
153.3.p.c.37.1		48	51.20	even	16
153.3.p.c.91.1		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	51.j (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.92891 + 1.21319i) q^{2} +(-1.69877 + 0.337906i) q^{3} +(4.27824 + 4.27824i) q^{4} +(0.0817276 - 0.122314i) q^{5} +(-5.38549 - 1.07124i) q^{6} +(-2.35178 - 3.51969i) q^{7} +(2.48747 + 6.00528i) q^{8} +(2.77164 - 1.14805i) q^{9} +(0.387763 - 0.259095i) q^{10} +(2.13536 - 10.7352i) q^{11} +(-8.71339 - 5.82210i) q^{12} +(-12.2605 + 12.2605i) q^{13} +(-2.61809 - 13.1620i) q^{14} +(-0.0975057 + 0.235400i) q^{15} -3.59468i q^{16} +(-16.0231 + 5.67992i) q^{17} +9.51069 q^{18} +(30.9397 + 12.8156i) q^{19} +(0.872939 - 0.173638i) q^{20} +(5.18446 + 5.18446i) q^{21} +(19.2781 - 28.8517i) q^{22} +(-0.932603 - 0.185506i) q^{23} +(-6.25486 - 9.36106i) q^{24} +(9.55880 + 23.0770i) q^{25} +(-50.7842 + 21.0355i) q^{26} +(-4.32044 + 2.88683i) q^{27} +(4.99659 - 25.1195i) q^{28} +(-27.7735 - 18.5576i) q^{29} +(-0.571171 + 0.571171i) q^{30} +(5.12889 + 25.7847i) q^{31} +(14.3109 - 34.5496i) q^{32} +18.9581i q^{33} +(-53.8209 - 2.80312i) q^{34} -0.622712 q^{35} +(16.7694 + 6.94610i) q^{36} +(8.46626 - 1.68404i) q^{37} +(75.0717 + 75.0717i) q^{38} +(16.6849 - 24.9707i) q^{39} +(0.937825 + 0.186545i) q^{40} +(19.5445 + 29.2504i) q^{41} +(8.89505 + 21.4745i) q^{42} +(-20.6891 + 8.56969i) q^{43} +(55.0633 - 36.7921i) q^{44} +(0.0860968 - 0.432838i) q^{45} +(-2.50645 - 1.67476i) q^{46} +(35.2299 - 35.2299i) q^{47} +(1.21467 + 6.10654i) q^{48} +(11.8942 - 28.7150i) q^{49} +79.1871i q^{50} +(25.3002 - 15.0632i) q^{51} -104.907 q^{52} +(0.136939 + 0.0567219i) q^{53} +(-16.1565 + 3.21372i) q^{54} +(-1.13854 - 1.13854i) q^{55} +(15.2867 - 22.8782i) q^{56} +(-56.8899 - 11.3161i) q^{57} +(-58.8319 - 88.0482i) q^{58} +(-43.4125 - 104.807i) q^{59} +(-1.42425 + 0.589944i) q^{60} +(-82.1151 + 54.8676i) q^{61} +(-16.2597 + 81.7433i) q^{62} +(-10.5591 - 7.05534i) q^{63} +(73.6635 - 73.6635i) q^{64} +(0.497610 + 2.50165i) q^{65} +(-22.9999 + 55.5267i) q^{66} -24.5661i q^{67} +(-92.8506 - 44.2505i) q^{68} +1.64696 q^{69} +(-1.82387 - 0.755471i) q^{70} +(76.3125 - 15.1795i) q^{71} +(13.7887 + 13.7887i) q^{72} +(49.1586 - 73.5711i) q^{73} +(26.8400 + 5.33880i) q^{74} +(-24.0361 - 35.9725i) q^{75} +(77.5391 + 187.196i) q^{76} +(-42.8063 + 17.7310i) q^{77} +(79.1627 - 52.8948i) q^{78} +(5.48545 - 27.5772i) q^{79} +(-0.439680 - 0.293785i) q^{80} +(6.36396 - 6.36396i) q^{81} +(21.7576 + 109.383i) q^{82} +(-34.6160 + 83.5703i) q^{83} +44.3607i q^{84} +(-0.614793 + 2.42405i) q^{85} -70.9931 q^{86} +(53.4515 + 22.1403i) q^{87} +(69.7794 - 13.8800i) q^{88} +(-2.81464 - 2.81464i) q^{89} +(0.777286 - 1.16329i) q^{90} +(71.9871 + 14.3191i) q^{91} +(-3.19626 - 4.78354i) q^{92} +(-17.4256 - 42.0691i) q^{93} +(145.926 - 60.4445i) q^{94} +(4.09616 - 2.73697i) q^{95} +(-12.6364 + 63.5276i) q^{96} +(-12.3434 - 8.24758i) q^{97} +(69.6738 - 69.6738i) q^{98} +(-6.40608 - 32.2055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{10} - 80 q^{11} - 48 q^{13} - 64 q^{14} + 16 q^{17} + 48 q^{19} + 224 q^{20} + 192 q^{22} + 112 q^{23} - 144 q^{24} + 80 q^{25} - 368 q^{26} - 240 q^{28} - 160 q^{29} - 192 q^{30} - 64 q^{31}+ \cdots + 240 q^{99}+O(q^{100}) \) 48 * q - 48 * q^10 - 80 * q^11 - 48 * q^13 - 64 * q^14 + 16 * q^17 + 48 * q^19 + 224 * q^20 + 192 * q^22 + 112 * q^23 - 144 * q^24 + 80 * q^25 - 368 * q^26 - 240 * q^28 - 160 * q^29 - 192 * q^30 - 64 * q^31 - 80 * q^32 + 16 * q^34 + 128 * q^35 + 48 * q^36 + 128 * q^37 + 400 * q^38 + 192 * q^39 + 128 * q^40 + 320 * q^41 + 432 * q^42 - 112 * q^43 + 704 * q^44 + 96 * q^45 + 80 * q^46 - 32 * q^49 + 128 * q^52 - 336 * q^53 - 608 * q^55 - 880 * q^56 - 752 * q^58 - 512 * q^59 - 400 * q^61 - 560 * q^62 + 160 * q^64 - 240 * q^65 - 208 * q^68 - 240 * q^69 + 80 * q^70 - 160 * q^71 - 288 * q^72 + 544 * q^73 - 48 * q^74 - 288 * q^75 + 496 * q^76 + 512 * q^77 - 384 * q^78 + 608 * q^79 + 816 * q^80 + 1184 * q^82 + 976 * q^83 - 32 * q^85 + 128 * q^86 + 144 * q^87 - 448 * q^88 + 240 * q^89 + 48 * q^90 - 640 * q^91 + 1280 * q^92 + 288 * q^93 - 32 * q^94 + 704 * q^95 + 768 * q^96 + 288 * q^97 + 1008 * q^98 + 240 * q^99

Introduction

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