LMFDB - Embedded newform 63.4.g.a.16.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,4,Mod(4,63)] 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("63.4"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.18
Character	$\chi$	$=$	63.16
Dual form			63.4.g.a.4.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.68671 + 2.92146i) q^{2} +(0.0520064 + 5.19589i) q^{3} +(-1.68996 + 2.92710i) q^{4} -9.74532 q^{5} +(-15.0919 + 8.91589i) q^{6} +(0.158327 + 18.5196i) q^{7} +15.5854 q^{8} +(-26.9946 + 0.540440i) q^{9} +(-16.4375 - 28.4706i) q^{10} +38.9123 q^{11} +(-15.2968 - 8.62865i) q^{12} +(-31.2817 - 54.1816i) q^{13} +(-53.8372 + 31.6997i) q^{14} +(-0.506819 - 50.6356i) q^{15} +(39.8078 + 68.9491i) q^{16} +(63.3614 + 109.745i) q^{17} +(-47.1109 - 77.9521i) q^{18} +(22.7332 - 39.3751i) q^{19} +(16.4692 - 28.5256i) q^{20} +(-96.2175 + 1.78579i) q^{21} +(65.6337 + 113.681i) q^{22} +153.865 q^{23} +(0.810542 + 80.9801i) q^{24} -30.0287 q^{25} +(105.526 - 182.777i) q^{26} +(-4.21196 - 140.233i) q^{27} +(-54.4763 - 30.8340i) q^{28} +(27.4655 - 47.5716i) q^{29} +(147.075 - 86.8882i) q^{30} +(-54.8509 + 95.0045i) q^{31} +(-71.9464 + 124.615i) q^{32} +(2.02369 + 202.184i) q^{33} +(-213.744 + 370.216i) q^{34} +(-1.54295 - 180.479i) q^{35} +(44.0380 - 79.9293i) q^{36} +(144.482 - 250.249i) q^{37} +153.377 q^{38} +(279.895 - 165.354i) q^{39} -151.885 q^{40} +(-11.3009 - 19.5738i) q^{41} +(-167.508 - 278.084i) q^{42} +(23.9450 - 41.4740i) q^{43} +(-65.7604 + 113.900i) q^{44} +(263.071 - 5.26676i) q^{45} +(259.525 + 449.510i) q^{46} +(-193.385 - 334.953i) q^{47} +(-356.182 + 210.423i) q^{48} +(-342.950 + 5.86430i) q^{49} +(-50.6496 - 87.7278i) q^{50} +(-566.929 + 334.926i) q^{51} +211.460 q^{52} +(-133.617 - 231.431i) q^{53} +(402.581 - 248.837i) q^{54} -379.213 q^{55} +(2.46759 + 288.635i) q^{56} +(205.771 + 116.072i) q^{57} +185.305 q^{58} +(-193.371 + 334.929i) q^{59} +(149.072 + 84.0889i) q^{60} +(-17.8409 - 30.9013i) q^{61} -370.070 q^{62} +(-14.2827 - 499.843i) q^{63} +151.514 q^{64} +(304.851 + 528.017i) q^{65} +(-587.260 + 346.938i) q^{66} +(-17.8513 + 30.9194i) q^{67} -428.314 q^{68} +(8.00195 + 799.465i) q^{69} +(524.661 - 308.923i) q^{70} -146.355 q^{71} +(-420.722 + 8.42297i) q^{72} +(-364.856 - 631.948i) q^{73} +974.792 q^{74} +(-1.56169 - 156.026i) q^{75} +(76.8367 + 133.085i) q^{76} +(6.16087 + 720.640i) q^{77} +(955.177 + 538.798i) q^{78} +(-250.675 - 434.183i) q^{79} +(-387.939 - 671.931i) q^{80} +(728.416 - 29.1779i) q^{81} +(38.1227 - 66.0304i) q^{82} +(169.622 - 293.794i) q^{83} +(157.377 - 284.657i) q^{84} +(-617.477 - 1069.50i) q^{85} +161.553 q^{86} +(248.605 + 140.234i) q^{87} +606.465 q^{88} +(-104.209 + 180.495i) q^{89} +(459.110 + 759.669i) q^{90} +(998.467 - 587.903i) q^{91} +(-260.026 + 450.378i) q^{92} +(-496.486 - 280.058i) q^{93} +(652.368 - 1129.94i) q^{94} +(-221.543 + 383.723i) q^{95} +(-651.227 - 367.345i) q^{96} +(-56.7013 + 98.2095i) q^{97} +(-595.588 - 992.024i) q^{98} +(-1050.42 + 21.0297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{3} - 79 q^{4} + 38 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} - 31 q^{9} - 18 q^{10} - 10 q^{11} - 41 q^{12} - 14 q^{13} - 79 q^{14} + 119 q^{15} - 247 q^{16} - 162 q^{17} + 157 q^{18} + 58 q^{19}+ \cdots - 5395 q^{99}+O(q^{100}) $ 44 * q + q^2 - q^3 - 79 * q^4 + 38 * q^5 - 20 * q^6 - 7 * q^7 - 24 * q^8 - 31 * q^9 - 18 * q^10 - 10 * q^11 - 41 * q^12 - 14 * q^13 - 79 * q^14 + 119 * q^15 - 247 * q^16 - 162 * q^17 + 157 * q^18 + 58 * q^19 - 362 * q^20 + 166 * q^21 - 18 * q^22 + 186 * q^23 + 414 * q^24 + 698 * q^25 - 266 * q^26 + 272 * q^27 - 172 * q^28 + 248 * q^29 + 616 * q^30 + 61 * q^31 - 163 * q^32 + 23 * q^33 + 6 * q^34 + 289 * q^35 - 806 * q^36 - 86 * q^37 + 1522 * q^38 - 565 * q^39 + 36 * q^40 - 692 * q^41 + 395 * q^42 - 86 * q^43 - 443 * q^44 - 1483 * q^45 - 270 * q^46 - 1005 * q^47 - 1013 * q^48 - 277 * q^49 + 239 * q^50 - 1719 * q^51 + 670 * q^52 + 258 * q^53 + 910 * q^54 - 870 * q^55 + 714 * q^56 + 566 * q^57 - 474 * q^58 - 1665 * q^59 + 4 * q^60 + 439 * q^61 + 1812 * q^62 + 493 * q^63 + 872 * q^64 - 613 * q^65 + 3073 * q^66 + 295 * q^67 + 2748 * q^68 + 1389 * q^69 - 1044 * q^70 + 636 * q^71 + 981 * q^72 - 338 * q^73 - 2238 * q^74 - 1064 * q^75 + 1006 * q^76 - 2909 * q^77 + 157 * q^78 + 133 * q^79 - 4817 * q^80 + 1325 * q^81 + 6 * q^82 - 1356 * q^83 - 7081 * q^84 + 483 * q^85 + 6686 * q^86 + 2774 * q^87 - 738 * q^88 - 2200 * q^89 + 2665 * q^90 + 1552 * q^91 - 396 * q^92 + 4365 * q^93 - 1191 * q^94 + 3083 * q^95 - 1468 * q^96 - 266 * q^97 + 3601 * q^98 - 5395 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.68671	+	2.92146i	0.596341	+	1.03289i	0.993356	+	0.115081i	$0.0367128\pi$
$2$	1.68671	+	2.92146i	0.596341	+	1.03289i	−0.397015	+	0.917812i	$0.629954\pi$
$3$	0.0520064	+	5.19589i	0.0100086	+	0.999950i
$3$	0.0520064	+	5.19589i	0.0100086	+	0.999950i
$4$	−1.68996	+	2.92710i	−0.211246	+	0.365888i
$5$	−9.74532			−0.871648			−0.435824	−	0.900032i	$-0.643543\pi$
$5$	−9.74532			−0.871648			−0.435824	+	0.900032i	$0.643543\pi$
$6$	−15.0919	+	8.91589i	−1.02687	+	0.606649i
$7$	0.158327	+	18.5196i	0.00854886	+	0.999963i
$7$	0.158327	+	18.5196i	0.00854886	+	0.999963i
$8$	15.5854			0.688785
$9$	−26.9946	+	0.540440i	−0.999800	+	0.0200163i
$10$	−16.4375	−	28.4706i	−0.519800	−	0.900319i
$11$	38.9123			1.06659			0.533296	−	0.845929i	$-0.320953\pi$
$11$	38.9123			1.06659			0.533296	+	0.845929i	$0.320953\pi$
$12$	−15.2968	−	8.62865i	−0.367984	−	0.207573i
$13$	−31.2817	−	54.1816i	−0.667384	−	1.15594i	−0.978633	−	0.205615i	$-0.934081\pi$
$13$	−31.2817	−	54.1816i	−0.667384	−	1.15594i	0.311249	−	0.950328i	$-0.399253\pi$
$14$	−53.8372	+	31.6997i	−1.02776	+	0.605149i
$15$	−0.506819	−	50.6356i	−0.00872401	−	0.871604i
$16$	39.8078	+	68.9491i	0.621996	+	1.07733i
$17$	63.3614	+	109.745i	0.903964	+	1.56571i	0.822302	+	0.569051i	$0.192689\pi$
$17$	63.3614	+	109.745i	0.903964	+	1.56571i	0.0816621	+	0.996660i	$0.473977\pi$
$18$	−47.1109	−	77.9521i	−0.616896	−	1.02075i
$19$	22.7332	−	39.3751i	0.274493	−	0.475435i	−0.695514	−	0.718512i	$-0.744823\pi$
$19$	22.7332	−	39.3751i	0.274493	−	0.475435i	0.970007	+	0.243077i	$0.0781568\pi$
$20$	16.4692	−	28.5256i	0.184132	−	0.318926i
$21$	−96.2175	+	1.78579i	−0.999828	+	0.0185567i
$22$	65.6337	+	113.681i	0.636052	+	1.10167i
$23$	153.865			1.39491			0.697457	−	0.716627i	$-0.254315\pi$
$23$	153.865			1.39491			0.697457	+	0.716627i	$0.254315\pi$
$24$	0.810542	+	80.9801i	0.00689380	+	0.688750i
$25$	−30.0287			−0.240230
$26$	105.526	−	182.777i	0.795977	−	1.37867i
$27$	−4.21196	−	140.233i	−0.0300219	−	0.999549i
$28$	−54.4763	−	30.8340i	−0.367681	−	0.208110i
$29$	27.4655	−	47.5716i	0.175869	−	0.304615i	−0.764592	−	0.644514i	$-0.777060\pi$
$29$	27.4655	−	47.5716i	0.175869	−	0.304615i	0.940462	+	0.339899i	$0.110393\pi$
$30$	147.075	−	86.8882i	0.895072	−	0.528785i
$31$	−54.8509	+	95.0045i	−0.317791	+	0.550430i	−0.980027	−	0.198866i	$-0.936274\pi$
$31$	−54.8509	+	95.0045i	−0.317791	+	0.550430i	0.662236	+	0.749295i	$0.269608\pi$
$32$	−71.9464	+	124.615i	−0.397452	+	0.688406i
$33$	2.02369	+	202.184i	0.0106751	+	1.06654i
$34$	−213.744	+	370.216i	−1.07814	+	1.86740i
$35$	−1.54295	−	180.479i	−0.00745159	−	0.871616i
$36$	44.0380	−	79.9293i	0.203880	−	0.370043i
$37$	144.482	−	250.249i	0.641962	−	1.11191i	−0.343032	−	0.939324i	$-0.611454\pi$
$37$	144.482	−	250.249i	0.641962	−	1.11191i	0.984994	−	0.172588i	$-0.0552129\pi$
$38$	153.377			0.654765
$39$	279.895	−	165.354i	1.14921	−	0.678920i
$40$	−151.885			−0.600378
$41$	−11.3009	−	19.5738i	−0.0430465	−	0.0745587i	0.843699	−	0.536816i	$-0.180373\pi$
$41$	−11.3009	−	19.5738i	−0.0430465	−	0.0745587i	−0.886746	+	0.462257i	$0.847040\pi$
$42$	−167.508	−	278.084i	−0.615406	−	1.02165i
$43$	23.9450	−	41.4740i	0.0849204	−	0.147086i	−0.820437	−	0.571737i	$-0.806270\pi$
$43$	23.9450	−	41.4740i	0.0849204	−	0.147086i	0.905357	+	0.424651i	$0.139603\pi$
$44$	−65.7604	+	113.900i	−0.225313	+	0.390253i
$45$	263.071	−	5.26676i	0.871473	−	0.0174472i
$46$	259.525	+	449.510i	0.831845	+	1.44080i
$47$	−193.385	−	334.953i	−0.600173	−	1.03953i	−0.992794	−	0.119830i	$-0.961765\pi$
$47$	−193.385	−	334.953i	−0.600173	−	1.03953i	0.392622	−	0.919700i	$-0.371568\pi$
$48$	−356.182	+	210.423i	−1.07105	+	0.632748i
$49$	−342.950	+	5.86430i	−0.999854	+	0.0170971i
$50$	−50.6496	−	87.7278i	−0.143259	−	0.248132i
$51$	−566.929	+	334.926i	−1.55659	+	0.919589i
$52$	211.460			0.563928
$53$	−133.617	−	231.431i	−0.346296	−	0.599802i	0.639293	−	0.768964i	$-0.279227\pi$
$53$	−133.617	−	231.431i	−0.346296	−	0.599802i	−0.985588	+	0.169162i	$0.945894\pi$
$54$	402.581	−	248.837i	1.01452	−	0.627082i
$55$	−379.213			−0.929692
$56$	2.46759	+	288.635i	0.00588832	+	0.688759i
$57$	205.771	+	116.072i	0.478159	+	0.269720i
$58$	185.305			0.419513
$59$	−193.371	+	334.929i	−0.426691	+	0.739051i	−0.996577	−	0.0826735i	$-0.973654\pi$
$59$	−193.371	+	334.929i	−0.426691	+	0.739051i	0.569886	+	0.821724i	$0.306987\pi$
$60$	149.072	+	84.0889i	0.320753	+	0.180931i
$61$	−17.8409	−	30.9013i	−0.0374473	−	0.0648607i	0.846694	−	0.532080i	$-0.178589\pi$
$61$	−17.8409	−	30.9013i	−0.0374473	−	0.0648607i	−0.884142	+	0.467219i	$0.845256\pi$
$62$	−370.070			−0.758047
$63$	−14.2827	−	499.843i	−0.0285627	−	0.999592i
$64$	151.514			0.295925
$65$	304.851	+	528.017i	0.581724	+	1.00758i
$66$	−587.260	+	346.938i	−1.09525	+	0.647047i
$67$	−17.8513	+	30.9194i	−0.0325506	+	0.0563792i	−0.881842	−	0.471545i	$-0.843696\pi$
$67$	−17.8513	+	30.9194i	−0.0325506	+	0.0563792i	0.849291	+	0.527925i	$0.177030\pi$
$68$	−428.314			−0.763834
$69$	8.00195	+	799.465i	0.0139612	+	1.39484i
$70$	524.661	−	308.923i	0.895843	−	0.527477i
$71$	−146.355			−0.244636			−0.122318	−	0.992491i	$-0.539033\pi$
$71$	−146.355			−0.244636			−0.122318	+	0.992491i	$0.539033\pi$
$72$	−420.722	+	8.42297i	−0.688647	+	0.0137869i
$73$	−364.856	−	631.948i	−0.584974	−	1.01320i	−0.994879	−	0.101076i	$-0.967771\pi$
$73$	−364.856	−	631.948i	−0.584974	−	1.01320i	0.409905	−	0.912128i	$-0.365562\pi$
$74$	974.792			1.53131
$75$	−1.56169	−	156.026i	−0.00240437	−	0.240218i
$76$	76.8367	+	133.085i	0.115971	+	0.200867i
$77$	6.16087	+	720.640i	0.00911814	+	1.06655i
$78$	955.177	+	538.798i	1.38657	+	0.782139i
$79$	−250.675	−	434.183i	−0.357002	−	0.618346i	0.630456	−	0.776225i	$-0.282868\pi$
$79$	−250.675	−	434.183i	−0.357002	−	0.618346i	−0.987459	+	0.157879i	$0.949535\pi$
$80$	−387.939	−	671.931i	−0.542162	−	0.939052i
$81$	728.416	−	29.1779i	0.999199	−	0.0400245i
$82$	38.1227	−	66.0304i	0.0513408	−	0.0889249i
$83$	169.622	−	293.794i	0.224319	−	0.388532i	−0.731796	−	0.681524i	$-0.761318\pi$
$83$	169.622	−	293.794i	0.224319	−	0.388532i	0.956115	+	0.292992i	$0.0946510\pi$
$84$	157.377	−	284.657i	0.204420	−	0.369745i
$85$	−617.477	−	1069.50i	−0.787938	−	1.36475i
$86$	161.553			0.202566
$87$	248.605	+	140.234i	0.306360	+	0.172812i
$88$	606.465			0.734652
$89$	−104.209	+	180.495i	−0.124113	+	0.214971i	−0.921386	−	0.388649i	$-0.872942\pi$
$89$	−104.209	+	180.495i	−0.124113	+	0.214971i	0.797273	+	0.603619i	$0.206275\pi$
$90$	459.110	+	759.669i	0.537717	+	0.889735i
$91$	998.467	−	587.903i	1.15020	−	0.677242i
$92$	−260.026	+	450.378i	−0.294669	+	0.510382i
$93$	−496.486	−	280.058i	−0.553583	−	0.312266i
$94$	652.368	−	1129.94i	0.715816	−	1.23983i
$95$	−221.543	+	383.723i	−0.239261	+	0.414412i
$96$	−651.227	−	367.345i	−0.692350	−	0.390542i
$97$	−56.7013	+	98.2095i	−0.0593520	+	0.102801i	−0.894175	−	0.447718i	$-0.852237\pi$
$97$	−56.7013	+	98.2095i	−0.0593520	+	0.102801i	0.834823	+	0.550519i	$0.185570\pi$
$98$	−595.588	−	992.024i	−0.613913	−	1.02255i
$99$	−1050.42	+	21.0297i	−1.06638	+	0.0213492i
$100$	50.7475	−	87.8972i	0.0507475	−	0.0878972i
$101$	1078.01			1.06204			0.531019	−	0.847360i	$-0.321809\pi$
$101$	1078.01			1.06204			0.531019	+	0.847360i	$0.321809\pi$
$102$	−1934.72	−	1091.34i	−1.87809	−	1.05940i
$103$	1710.37			1.63619			0.818097	−	0.575080i	$-0.195029\pi$
$103$	1710.37			1.63619			0.818097	+	0.575080i	$0.195029\pi$
$104$	−487.539	−	844.442i	−0.459684	−	0.796196i
$105$	937.671	−	17.4031i	0.871498	−	0.0161749i
$106$	450.745	−	780.713i	0.413021	−	0.715373i
$107$	−410.398	+	710.830i	−0.370791	+	0.642229i	−0.989687	−	0.143244i	$-0.954247\pi$
$107$	−410.398	+	710.830i	−0.370791	+	0.642229i	0.618896	+	0.785473i	$0.287580\pi$
$108$	417.594	+	224.660i	0.372065	+	0.200166i
$109$	1064.55	+	1843.85i	0.935460	+	1.62026i	0.773812	+	0.633416i	$0.218348\pi$
$109$	1064.55	+	1843.85i	0.935460	+	1.62026i	0.161648	+	0.986848i	$0.448319\pi$
$110$	−639.621	−	1107.86i	−0.554414	−	0.960273i
$111$	1307.78	+	737.696i	1.11828	+	0.630802i
$112$	−1270.61	+	748.140i	−1.07197	+	0.631183i
$113$	203.179	+	351.917i	0.169146	+	0.292970i	0.938120	−	0.346311i	$-0.112566\pi$
$113$	203.179	+	351.917i	0.169146	+	0.292970i	−0.768974	+	0.639280i	$0.779232\pi$
$114$	7.97660	+	796.932i	0.00655331	+	0.654732i
$115$	−1499.46			−1.21587
$116$	92.8314	+	160.789i	0.0743033	+	0.128697i
$117$	873.719	+	1445.70i	0.690388	+	1.14235i
$118$	−1304.64			−1.01781
$119$	−2022.40	+	1190.80i	−1.55793	+	0.917316i
$120$	−7.89899	−	789.178i	−0.00600897	−	0.600348i
$121$	183.168			0.137617
$122$	60.1846	−	104.243i	0.0446628	−	0.0773582i
$123$	101.115	−	59.7363i	0.0741242	−	0.0437906i
$124$	−185.392	−	321.109i	−0.134264	−	0.232552i
$125$	1510.80			1.08104
$126$	1436.18	−	884.815i	1.01544	−	0.625600i
$127$	−2300.05			−1.60706			−0.803529	−	0.595266i	$-0.797047\pi$
$127$	−2300.05			−1.60706			−0.803529	+	0.595266i	$0.797047\pi$
$128$	831.131	+	1439.56i	0.573924	+	0.994066i
$129$	216.739	+	122.259i	0.147929	+	0.0834440i
$130$	−1028.39	+	1781.22i	−0.693812	+	1.20172i
$131$	−583.702			−0.389300			−0.194650	−	0.980873i	$-0.562357\pi$
$131$	−583.702			−0.389300			−0.194650	+	0.980873i	$0.562357\pi$
$132$	−595.234	−	335.761i	−0.392489	−	0.221395i
$133$	732.810	+	414.776i	0.477764	+	0.270418i
$134$	−120.440			−0.0776449
$135$	41.0469	+	1366.61i	0.0261685	+	0.871255i
$136$	987.513	+	1710.42i	0.622636	+	1.07844i
$137$	−168.798			−0.105266			−0.0526328	−	0.998614i	$-0.516761\pi$
$137$	−168.798			−0.105266			−0.0526328	+	0.998614i	$0.516761\pi$
$138$	−2322.11	+	1371.84i	−1.43240	+	0.846223i
$139$	671.306	+	1162.74i	0.409636	+	0.709511i	0.994849	−	0.101369i	$-0.0323223\pi$
$139$	671.306	+	1162.74i	0.409636	+	0.709511i	−0.585213	+	0.810880i	$0.698989\pi$
$140$	530.889	+	300.487i	0.320488	+	0.181399i
$141$	1730.32	−	1022.23i	1.03347	−	0.610547i
$142$	−246.858	−	427.571i	−0.145887	−	0.252683i
$143$	−1217.24	−	2108.33i	−0.711826	−	1.23292i
$144$	−1111.86	−	1839.74i	−0.643436	−	1.06466i
$145$	−267.660	+	463.601i	−0.153296	+	0.265517i
$146$	1230.81	−	2131.82i	0.697688	−	1.20843i
$147$	−48.3059	−	1781.63i	−0.0271034	−	0.999633i
$148$	488.337	+	845.825i	0.271223	+	0.469773i
$149$	−721.359			−0.396618			−0.198309	−	0.980140i	$-0.563545\pi$
$149$	−721.359			−0.396618			−0.198309	+	0.980140i	$0.563545\pi$
$150$	453.190	−	267.733i	0.246685	−	0.145735i
$151$	−2867.01			−1.54513			−0.772563	−	0.634938i	$-0.781026\pi$
$151$	−2867.01			−1.54513			−0.772563	+	0.634938i	$0.781026\pi$
$152$	354.307	−	613.677i	0.189066	−	0.327472i
$153$	−1769.72	−	2928.28i	−0.935123	−	1.54730i
$154$	−2094.93	+	1233.51i	−1.09620	+	0.645447i
$155$	534.540	−	925.850i	0.277002	−	0.479781i
$156$	10.9973	+	1098.72i	0.00564415	+	0.563899i
$157$	375.097	−	649.686i	0.190675	−	0.330259i	−0.754799	−	0.655956i	$-0.772266\pi$
$157$	375.097	−	649.686i	0.190675	−	0.330259i	0.945474	+	0.325697i	$0.105599\pi$
$158$	845.632	−	1464.68i	0.425790	−	0.737491i
$159$	1195.54	−	706.294i	0.596306	−	0.352282i
$160$	701.141	−	1214.41i	0.346438	−	0.600048i
$161$	24.3610	+	2849.51i	0.0119249	+	1.39486i
$162$	1313.87	+	2078.83i	0.637204	+	1.00820i
$163$	1400.06	−	2424.98i	0.672769	−	1.16527i	−0.304347	−	0.952561i	$-0.598438\pi$
$163$	1400.06	−	2424.98i	0.672769	−	1.16527i	0.977116	−	0.212709i	$-0.0682285\pi$
$164$	76.3926			0.0363735
$165$	−19.7215	−	1970.35i	−0.00930495	−	0.929646i
$166$	1144.41			0.535082
$167$	−0.0790177	−	0.136863i	−3.66142e−5	−	6.34176e-5i	0.866007	−	0.500032i	$-0.166678\pi$
$167$	−0.0790177	−	0.136863i	−3.66142e−5	−	6.34176e-5i	−0.866044	+	0.499968i	$0.833345\pi$
$168$	−1499.59	+	27.8322i	−0.688666	+	0.0127816i
$169$	−858.594	+	1487.13i	−0.390803	+	0.676890i
$170$	2083.01	−	3607.87i	0.939760	−	1.62771i
$171$	−592.394	+	1075.20i	−0.264921	+	0.480834i
$172$	80.9324	+	140.179i	0.0358781	+	0.0621427i
$173$	−631.310	−	1093.46i	−0.277443	−	0.480545i	0.693306	−	0.720644i	$-0.256154\pi$
$173$	−631.310	−	1093.46i	−0.277443	−	0.480545i	−0.970748	+	0.240099i	$0.922820\pi$
$174$	9.63705	+	962.825i	0.00419875	+	0.419492i
$175$	−4.75436	−	556.119i	−0.00205369	−	0.240221i
$176$	1549.01	+	2682.97i	0.663416	+	1.14907i
$177$	−1750.31	−	987.317i	−0.743284	−	0.419273i
$178$	−703.078			−0.296056
$179$	1457.18	+	2523.91i	0.608462	+	1.05389i	0.991494	+	0.130152i	$0.0415465\pi$
$179$	1457.18	+	2523.91i	0.608462	+	1.05389i	−0.383032	+	0.923735i	$0.625120\pi$
$180$	−429.164	+	778.937i	−0.177711	+	0.322547i
$181$	870.971			0.357673			0.178836	−	0.983879i	$-0.442767\pi$
$181$	870.971			0.357673			0.178836	+	0.983879i	$0.442767\pi$
$182$	3401.66	+	1925.36i	1.38543	+	0.784162i
$183$	159.632	−	94.3062i	0.0644827	−	0.0380946i
$184$	2398.05			0.960795
$185$	−1408.02	+	2438.76i	−0.559565	+	0.969196i
$186$	−19.2460	−	1922.84i	−0.00758702	−	0.758009i
$187$	2465.54	+	4270.44i	0.964160	+	1.66997i
$188$	1307.26			0.507135
$189$	2596.39	−	100.206i	0.999256	−	0.0385658i
$190$	−1494.71			−0.570725
$191$	−1588.84	−	2751.95i	−0.601907	−	1.04253i	−0.992532	−	0.121983i	$-0.961075\pi$
$191$	−1588.84	−	2751.95i	−0.601907	−	1.04253i	0.390625	−	0.920550i	$-0.372259\pi$
$192$	7.87969	+	787.249i	0.00296181	+	0.295911i
$193$	851.492	−	1474.83i	0.317574	−	0.550054i	−0.662407	−	0.749144i	$-0.730465\pi$
$193$	851.492	−	1474.83i	0.317574	−	0.550054i	0.979981	+	0.199090i	$0.0637985\pi$
$194$	−382.554			−0.141576
$195$	−2727.66	+	1611.43i	−1.00170	+	0.591779i
$196$	562.408	−	1013.76i	0.204959	−	0.369446i
$197$	254.870			0.0921763			0.0460881	−	0.998937i	$-0.485324\pi$
$197$	254.870			0.0921763			0.0460881	+	0.998937i	$0.485324\pi$
$198$	−1833.19	−	3033.30i	−0.657976	−	1.08872i
$199$	−386.703	−	669.790i	−0.137752	−	0.238594i	0.788893	−	0.614530i	$-0.210654\pi$
$199$	−386.703	−	669.790i	−0.137752	−	0.238594i	−0.926645	+	0.375937i	$0.877321\pi$
$200$	−468.010			−0.165466
$201$	−161.582	−	91.1456i	−0.0567022	−	0.0319846i
$202$	1818.28	+	3149.36i	0.633337	+	1.09697i
$203$	885.355	+	501.118i	0.306107	+	0.173259i
$204$	−22.2751	−	2225.47i	−0.00764494	−	0.763795i
$205$	110.131	+	190.753i	0.0375214	+	0.0649890i
$206$	2884.90	+	4996.79i	0.975730	+	1.69001i
$207$	−4153.52	+	83.1546i	−1.39463	+	0.0279210i
$208$	2490.51	−	4313.69i	0.830221	−	1.43798i
$209$	884.602	−	1532.18i	0.292771	−	0.507095i
$210$	1632.42	+	2710.02i	0.536417	+	0.890519i
$211$	−1834.55	−	3177.54i	−0.598558	−	1.03673i	−0.993034	−	0.117827i	$-0.962407\pi$
$211$	−1834.55	−	3177.54i	−0.598558	−	1.03673i	0.394476	−	0.918906i	$-0.370926\pi$
$212$	903.230			0.292614
$213$	−7.61141	−	760.445i	−0.00244847	−	0.244624i
$214$	−2768.88			−0.884472
$215$	−233.352	+	404.177i	−0.0740207	+	0.128208i
$216$	−65.6451	−	2185.59i	−0.0206786	−	0.688474i
$217$	−1768.13	−	1000.77i	−0.553126	−	0.313074i
$218$	−3591.16	+	6220.07i	−1.11571	+	1.93246i
$219$	3264.56	−	1928.62i	1.00730	−	0.595086i
$220$	640.857	−	1110.00i	0.196393	−	0.340163i
$221$	3964.11	−	6866.03i	1.20658	−	2.08986i
$222$	50.6955	+	5064.91i	0.0153264	+	1.53124i
$223$	1002.18	−	1735.83i	0.300947	−	0.521256i	−0.675404	−	0.737448i	$-0.736031\pi$
$223$	1002.18	−	1735.83i	0.300947	−	0.521256i	0.976351	+	0.216192i	$0.0693639\pi$
$224$	−2319.21	−	1312.69i	−0.691779	−	0.391552i
$225$	810.613	−	16.2287i	0.240182	−	0.00480850i
$226$	−685.409	+	1187.16i	−0.201738	+	0.349420i
$227$	−3396.02			−0.992958			−0.496479	−	0.868049i	$-0.665374\pi$
$227$	−3396.02			−0.992958			−0.496479	+	0.868049i	$0.665374\pi$
$228$	−687.500	+	406.157i	−0.199696	+	0.117975i
$229$	−5153.79			−1.48721			−0.743606	−	0.668618i	$-0.766886\pi$
$229$	−5153.79			−1.48721			−0.743606	+	0.668618i	$0.766886\pi$
$230$	−2529.15	−	4380.62i	−0.725076	−	1.25587i
$231$	−3744.05	+	69.4891i	−1.06641	+	0.0197924i
$232$	428.061	−	741.424i	0.121136	−	0.209814i
$233$	−3053.12	+	5288.16i	−0.858441	+	1.48686i	0.0149746	+	0.999888i	$0.495233\pi$
$233$	−3053.12	+	5288.16i	−0.858441	+	1.48686i	−0.873416	+	0.486976i	$0.838100\pi$
$234$	−2749.86	+	4991.02i	−0.768222	+	1.39433i
$235$	1884.60	+	3264.22i	0.523139	+	0.906104i
$236$	−653.581	−	1132.03i	−0.180273	−	0.312242i
$237$	2242.93	−	1325.06i	0.614742	−	0.363173i
$238$	−6890.08	−	3899.84i	−1.87655	−	1.06214i
$239$	−1301.70	−	2254.62i	−0.352302	−	0.610205i	0.634350	−	0.773046i	$-0.281268\pi$
$239$	−1301.70	−	2254.62i	−0.352302	−	0.610205i	−0.986652	+	0.162840i	$0.947934\pi$
$240$	3471.10	−	2050.64i	0.933578	−	0.551533i
$241$	2322.27			0.620707			0.310354	−	0.950621i	$-0.399553\pi$
$241$	2322.27			0.620707			0.310354	+	0.950621i	$0.399553\pi$
$242$	308.950	+	535.118i	0.0820665	+	0.142143i
$243$	189.487	+	3783.25i	0.0500232	+	0.998748i
$244$	120.602			0.0316423
$245$	3342.16	−	57.1495i	0.871521	−	0.0149026i
$246$	345.070	+	194.647i	0.0894343	+	0.0504482i
$247$	−2844.54			−0.732768
$248$	−854.874	+	1480.69i	−0.218889	+	0.379127i
$249$	1535.35	+	866.060i	0.390757	+	0.220419i
$250$	2548.29	+	4413.76i	0.644671	+	1.11660i
$251$	−476.889			−0.119924			−0.0599621	−	0.998201i	$-0.519098\pi$
$251$	−476.889			−0.119924			−0.0599621	+	0.998201i	$0.519098\pi$
$252$	1487.23	+	802.910i	0.371773	+	0.200709i
$253$	5987.23			1.48780
$254$	−3879.51	−	6719.51i	−0.958354	−	1.65992i
$255$	5524.90	−	3263.96i	1.35679	−	0.801558i
$256$	−2197.69	+	3806.52i	−0.536546	+	0.929326i
$257$	3736.85			0.906997			0.453499	−	0.891257i	$-0.350176\pi$
$257$	3736.85			0.906997			0.453499	+	0.891257i	$0.350176\pi$
$258$	8.40179	+	839.411i	0.00202741	+	0.202556i
$259$	4657.39	+	2636.12i	1.11736	+	0.632433i
$260$	−2060.75			−0.491546
$261$	−715.710	+	1299.02i	−0.169737	+	0.308074i
$262$	−984.535	−	1705.26i	−0.232156	−	0.402105i
$263$	1009.13			0.236600			0.118300	−	0.992978i	$-0.462256\pi$
$263$	1009.13			0.236600			0.118300	+	0.992978i	$0.462256\pi$
$264$	31.5400	+	3151.12i	0.00735286	+	0.734615i
$265$	1302.14	+	2255.37i	0.301848	+	0.522816i
$266$	24.2838	+	2840.48i	0.00559749	+	0.654741i
$267$	−943.251	−	532.070i	−0.216202	−	0.121956i
$268$	−60.3362	−	104.505i	−0.0137523	−	0.0238197i
$269$	−4069.36	−	7048.33i	−0.922354	−	1.59756i	−0.795763	−	0.605608i	$-0.792930\pi$
$269$	−4069.36	−	7048.33i	−0.922354	−	1.59756i	−0.126591	−	0.991955i	$-0.540403\pi$
$270$	−3923.28	+	2425.00i	−0.884308	+	0.546595i
$271$	3384.69	−	5862.46i	0.758692	−	1.31409i	−0.184826	−	0.982771i	$-0.559172\pi$
$271$	3384.69	−	5862.46i	0.758692	−	1.31409i	0.943518	−	0.331321i	$-0.107494\pi$
$272$	−5044.55	+	8737.41i	−1.12452	+	1.94773i
$273$	3106.61	+	5157.35i	0.688720	+	1.14336i
$274$	−284.713	−	493.137i	−0.0627742	−	0.108728i
$275$	−1168.49			−0.256227
$276$	−2353.64	−	1327.64i	−0.513306	−	0.289546i
$277$	−6519.00			−1.41404			−0.707019	−	0.707194i	$-0.749961\pi$
$277$	−6519.00			−1.41404			−0.707019	+	0.707194i	$0.749961\pi$
$278$	−2264.59	+	3922.39i	−0.488566	+	0.846221i
$279$	1429.33	−	2594.25i	0.306709	−	0.556680i
$280$	−24.0475	−	2812.84i	−0.00513254	−	0.600356i
$281$	−3138.53	+	5436.10i	−0.666296	+	1.15406i	0.312636	+	0.949873i	$0.398788\pi$
$281$	−3138.53	+	5436.10i	−0.666296	+	1.15406i	−0.978932	+	0.204185i	$0.934545\pi$
$282$	5904.95	+	3330.87i	1.24693	+	0.703371i
$283$	−403.166	+	698.304i	−0.0846845	+	0.146678i	−0.905257	−	0.424865i	$-0.860322\pi$
$283$	−403.166	+	698.304i	−0.0846845	+	0.146678i	0.820572	+	0.571543i	$0.193655\pi$
$284$	247.335	−	428.397i	0.0516783	−	0.0895094i
$285$	−2005.31	−	1131.16i	−0.416786	−	0.235101i
$286$	4106.27	−	7112.27i	0.848982	−	1.47048i
$287$	360.709	−	212.387i	0.0741880	−	0.0436823i
$288$	1874.82	−	3402.81i	0.383593	−	0.696224i
$289$	−5572.82	+	9652.42i	−1.13430	+	1.96467i
$290$	−1805.86			−0.365668
$291$	−513.235	−	289.506i	−0.103390	−	0.0583201i
$292$	2466.37			0.494293
$293$	3084.92	+	5343.24i	0.615095	+	1.06538i	0.990368	+	0.138462i	$0.0442158\pi$
$293$	3084.92	+	5343.24i	0.615095	+	1.06538i	−0.375272	+	0.926915i	$0.622451\pi$
$294$	5123.48	−	3146.21i	1.01635	−	0.624117i
$295$	1884.46	−	3263.99i	0.371924	−	0.644192i
$296$	2251.80	−	3900.24i	0.442174	−	0.765868i
$297$	−163.897	−	5456.78i	−0.0320211	−	1.06611i
$298$	−1216.72	−	2107.42i	−0.236519	−	0.409664i
$299$	−4813.16	−	8336.63i	−0.930943	−	1.61244i
$300$	459.343	+	259.107i	0.0884007	+	0.0498652i
$301$	771.871	+	436.885i	0.147807	+	0.0836599i
$302$	−4835.81	−	8375.87i	−0.921423	−	1.59595i
$303$	56.0633	+	5601.21i	0.0106296	+	1.06198i
$304$	3619.84			0.682933
$305$	173.865	+	301.143i	0.0326409	+	0.0565357i
$306$	5569.86	−	10109.3i	1.04055	−	1.88860i
$307$	4381.77			0.814596			0.407298	−	0.913295i	$-0.366471\pi$
$307$	4381.77			0.814596			0.407298	+	0.913295i	$0.366471\pi$
$308$	−2119.80	−	1199.82i	−0.392165	−	0.221968i
$309$	88.9504	+	8886.91i	0.0163761	+	1.63611i
$310$	3606.45			0.660750
$311$	4231.30	−	7328.83i	0.771495	−	1.33627i	−0.165248	−	0.986252i	$-0.552843\pi$
$311$	4231.30	−	7328.83i	0.771495	−	1.33627i	0.936743	−	0.350017i	$-0.113824\pi$
$312$	4362.27	−	2577.12i	0.791555	−	0.467630i
$313$	−2910.23	−	5040.67i	−0.525547	−	0.910273i	−0.999557	−	0.0297543i	$-0.990528\pi$
$313$	−2910.23	−	5040.67i	−0.525547	−	0.910273i	0.474011	−	0.880519i	$-0.342806\pi$
$314$	2530.71			0.454829
$315$	139.189	+	4871.13i	0.0248966	+	0.871292i
$316$	1694.53			0.301661
$317$	3207.59	+	5555.71i	0.568316	+	0.984353i	0.996733	+	0.0807714i	$0.0257384\pi$
$317$	3207.59	+	5555.71i	0.568316	+	0.984353i	−0.428416	+	0.903582i	$0.640928\pi$
$318$	4079.94	+	2301.42i	0.719471	+	0.405840i
$319$	1068.75	−	1851.12i	0.187581	−	0.324900i
$320$	−1476.55			−0.257943
$321$	−3714.74	−	2095.41i	−0.645908	−	0.364345i
$322$	−8283.65	+	4877.46i	−1.43363	+	0.844131i
$323$	5761.63			0.992526
$324$	−1145.59	+	2181.46i	−0.196432	+	0.374050i
$325$	939.350	+	1627.00i	0.160325	+	0.277692i
$326$	9445.98			1.60480
$327$	−9525.08	+	5627.16i	−1.61082	+	0.951630i
$328$	−176.130	−	305.065i	−0.0296498	−	0.0513549i
$329$	6172.57	−	3634.44i	1.03436	−	0.609038i
$330$	5723.04	−	3381.02i	0.954676	−	0.563997i
$331$	414.418	+	717.794i	0.0688172	+	0.119195i	0.898381	−	0.439217i	$-0.144744\pi$
$331$	414.418	+	717.794i	0.0688172	+	0.119195i	−0.829564	+	0.558412i	$0.811411\pi$
$332$	573.311	+	993.004i	0.0947727	+	0.164151i
$333$	−3764.97	+	6833.46i	−0.619578	+	1.12454i
$334$	0.266559	−	0.461694i	4.36691e−5	−	7.56371e-5i
$335$	173.967	−	301.320i	0.0283726	−	0.0491428i
$336$	−3953.33	−	6563.02i	−0.641881	−	1.06560i
$337$	−2906.88	−	5034.86i	−0.469875	−	0.813847i	0.529532	−	0.848290i	$-0.322368\pi$
$337$	−2906.88	−	5034.86i	−0.469875	−	0.813847i	−0.999407	+	0.0344432i	$0.989034\pi$
$338$	−5792.79			−0.932207
$339$	−1817.96	+	1074.00i	−0.291262	+	0.172070i
$340$	4174.06			0.665794
$341$	−2134.37	+	3696.85i	−0.338953	+	0.587083i
$342$	−4140.36	+	82.8911i	−0.654634	+	0.0131060i
$343$	−162.903	−	6350.36i	−0.0256441	−	0.999671i
$344$	373.193	−	646.389i	0.0584919	−	0.101311i
$345$	−77.9816	−	7791.04i	−0.0121692	−	1.21581i
$346$	2129.67	−	3688.70i	0.330901	−	0.573137i
$347$	−1661.46	+	2877.74i	−0.257038	+	0.445202i	−0.965447	−	0.260600i	$-0.916080\pi$
$347$	−1661.46	+	2877.74i	−0.257038	+	0.445202i	0.708409	+	0.705802i	$0.249413\pi$
$348$	−830.613	+	490.704i	−0.127947	+	0.0755877i
$349$	−376.201	+	651.599i	−0.0577008	+	0.0999407i	−0.893433	−	0.449197i	$-0.851710\pi$
$349$	−376.201	+	651.599i	−0.0577008	+	0.0999407i	0.835732	+	0.549137i	$0.185044\pi$
$350$	1616.66	−	951.900i	0.246898	−	0.145375i
$351$	−7466.28	+	4614.94i	−1.13539	+	0.701787i
$352$	−2799.60	+	4849.05i	−0.423918	+	0.734248i
$353$	−2213.65			−0.333770			−0.166885	−	0.985976i	$-0.553371\pi$
$353$	−2213.65			−0.333770			−0.166885	+	0.985976i	$0.553371\pi$
$354$	−67.8498	−	6778.78i	−0.0101869	−	1.01776i
$355$	1426.28			0.213236
$356$	−352.218	−	610.060i	−0.0524368	−	0.0908233i
$357$	−6292.45	−	10446.3i	−0.932863	−	1.54867i
$358$	−4915.67	+	8514.19i	−0.725702	+	1.25695i
$359$	−435.090	+	753.599i	−0.0639643	+	0.110789i	−0.896234	−	0.443581i	$-0.853708\pi$
$359$	−435.090	+	753.599i	−0.0639643	+	0.110789i	0.832270	+	0.554371i	$0.187041\pi$
$360$	4100.07	−	82.0846i	0.600257	−	0.0120173i
$361$	2395.90	+	4149.82i	0.349308	+	0.605018i
$362$	1469.07	+	2544.51i	0.213295	+	0.369438i
$363$	9.52590	+	951.720i	0.00137736	+	0.137610i
$364$	33.4799	+	3916.15i	0.00482094	+	0.563907i
$365$	3555.63	+	6158.54i	0.509892	+	0.883158i
$366$	544.764	+	307.292i	0.0778014	+	0.0438863i
$367$	−2528.67			−0.359660			−0.179830	−	0.983698i	$-0.557555\pi$
$367$	−2528.67			−0.359660			−0.179830	+	0.983698i	$0.557555\pi$
$368$	6125.01	+	10608.8i	0.867631	+	1.50278i
$369$	315.642	+	522.278i	0.0445303	+	0.0736822i
$370$	−9499.66			−1.33477
$371$	4264.85	−	2511.17i	0.596819	−	0.351411i
$372$	1658.80	−	979.977i	0.231196	−	0.136585i
$373$	5370.58			0.745518			0.372759	−	0.927928i	$-0.378412\pi$
$373$	5370.58			0.745518			0.372759	+	0.927928i	$0.378412\pi$
$374$	−8317.28	+	14406.0i	−1.14994	+	1.99175i
$375$	78.5715	+	7849.98i	0.0108198	+	1.08099i
$376$	−3013.99	−	5220.38i	−0.413390	−	0.716012i
$377$	−3436.67			−0.469490
$378$	4672.10	+	7416.23i	0.635732	+	1.00913i
$379$	−9923.53			−1.34495			−0.672477	−	0.740118i	$-0.734770\pi$
$379$	−9923.53			−1.34495			−0.672477	+	0.740118i	$0.734770\pi$
$380$	−748.798	−	1296.96i	−0.101086	−	0.175085i
$381$	−119.617	−	11950.8i	−0.0160845	−	1.60698i
$382$	5359.81	−	9283.46i	0.717884	−	1.24341i
$383$	11187.6			1.49259			0.746295	−	0.665616i	$-0.231831\pi$
$383$	11187.6			1.49259			0.746295	+	0.665616i	$0.231831\pi$
$384$	−7436.58	+	4393.33i	−0.988272	+	0.583845i
$385$	−60.0397	−	7022.87i	−0.00794781	−	0.929658i
$386$	5744.87			0.757529
$387$	−623.971	+	1132.51i	−0.0819593	+	0.148757i
$388$	−191.646	−	331.941i	−0.0250757	−	0.0434324i
$389$	−1683.37			−0.219410			−0.109705	−	0.993964i	$-0.534991\pi$
$389$	−1683.37			−0.219410			−0.109705	+	0.993964i	$0.534991\pi$
$390$	−9308.51	−	5250.76i	−1.20860	−	0.681750i
$391$	9749.08	+	16885.9i	1.26095	+	2.18403i
$392$	−5345.02	+	91.3976i	−0.688684	+	0.0117762i
$393$	−30.3563	−	3032.85i	−0.00389636	−	0.389280i
$394$	429.891	+	744.593i	0.0549685	+	0.0952083i
$395$	2442.91	+	4231.25i	0.311180	+	0.538980i
$396$	1713.62	−	3110.23i	0.217456	−	0.394685i
$397$	−1775.41	+	3075.09i	−0.224446	+	0.388752i	−0.956153	−	0.292867i	$-0.905391\pi$
$397$	−1775.41	+	3075.09i	−0.224446	+	0.388752i	0.731707	+	0.681619i	$0.238724\pi$
$398$	1304.51	−	2259.48i	0.164295	−	0.284566i
$399$	−2117.02	+	3829.17i	−0.265623	+	0.480447i
$400$	−1195.38	−	2070.45i	−0.149422	−	0.258806i
$401$	−3801.66			−0.473431			−0.236716	−	0.971579i	$-0.576071\pi$
$401$	−3801.66			−0.473431			−0.236716	+	0.971579i	$0.576071\pi$
$402$	−6.26365	−	625.793i	−0.000777120	−	0.0776411i
$403$	6863.32			0.848354
$404$	−1821.80	+	3155.44i	−0.224351	+	0.388587i
$405$	−7098.65	+	284.348i	−0.870950	+	0.0348873i
$406$	29.3388	+	3431.77i	0.00358636	+	0.419498i
$407$	5622.11	−	9737.78i	0.684712	−	1.18596i
$408$	−8835.82	+	5219.97i	−1.07215	+	0.633399i
$409$	−6622.39	+	11470.3i	−0.800626	+	1.38673i	0.118578	+	0.992945i	$0.462166\pi$
$409$	−6622.39	+	11470.3i	−0.800626	+	1.38673i	−0.919204	+	0.393781i	$0.871167\pi$
$410$	−371.518	+	643.488i	−0.0447511	+	0.0775112i
$411$	−8.77858	−	877.056i	−0.00105357	−	0.105260i
$412$	−2890.47	+	5006.44i	−0.345639	+	0.598664i
$413$	−6233.35	−	3528.12i	−0.742671	−	0.420357i
$414$	−7248.70	−	11994.1i	−0.860517	−	1.42386i
$415$	−1653.02	+	2863.12i	−0.195527	+	0.338663i
$416$	9002.44			1.06101
$417$	−6006.54	+	3548.50i	−0.705376	+	0.416717i
$418$	5968.26			0.698367
$419$	1435.52	+	2486.39i	0.167374	+	0.289900i	0.937496	−	0.347997i	$-0.113138\pi$
$419$	1435.52	+	2486.39i	0.167374	+	0.289900i	−0.770122	+	0.637897i	$0.779805\pi$
$420$	−1533.69	+	2774.07i	−0.178182	+	0.322288i
$421$	−441.098	+	764.004i	−0.0510637	+	0.0884449i	−0.890427	−	0.455125i	$-0.849594\pi$
$421$	−441.098	+	764.004i	−0.0510637	+	0.0884449i	0.839364	+	0.543570i	$0.182928\pi$
$422$	6188.70	−	10719.1i	0.713890	−	1.23649i
$423$	5401.37	+	8937.40i	0.620860	+	1.02731i
$424$	−2082.47	−	3606.95i	−0.238523	−	0.413134i
$425$	−1902.66	−	3295.50i	−0.217159	−	0.376130i
$426$	2208.77	−	1304.89i	0.251210	−	0.148408i
$427$	569.454	−	335.298i	0.0645382	−	0.0380005i
$428$	−1387.12	−	2402.55i	−0.156656	−	0.271336i
$429$	10891.3	−	6434.32i	1.22573	−	0.724130i
$430$	−1574.38			−0.176566
$431$	−4337.40	−	7512.59i	−0.484745	−	0.839603i	0.515102	−	0.857129i	$-0.327754\pi$
$431$	−4337.40	−	7512.59i	−0.484745	−	0.839603i	−0.999846	+	0.0175265i	$0.994421\pi$
$432$	9501.26	−	5872.77i	1.05817	−	0.654059i
$433$	−10521.0			−1.16769			−0.583843	−	0.811866i	$-0.698452\pi$
$433$	−10521.0			−1.16769			−0.583843	+	0.811866i	$0.698452\pi$
$434$	−58.5920	−	6853.54i	−0.00648043	−	0.758019i
$435$	−2422.74	−	1366.62i	−0.267038	−	0.150631i
$436$	−7196.19			−0.790447
$437$	3497.84	−	6058.44i	0.382894	−	0.663191i
$438$	11140.7	+	6284.28i	1.21535	+	0.685559i
$439$	5603.51	+	9705.56i	0.609205	+	1.05517i	0.991372	+	0.131080i	$0.0418445\pi$
$439$	5603.51	+	9705.56i	0.609205	+	1.05517i	−0.382167	+	0.924093i	$0.624822\pi$
$440$	−5910.19			−0.640358
$441$	9254.62	−	343.648i	0.999311	−	0.0371070i
$442$	26745.2			2.87814
$443$	1280.39	+	2217.70i	0.137321	+	0.237847i	0.926482	−	0.376340i	$-0.122817\pi$
$443$	1280.39	+	2217.70i	0.137321	+	0.237847i	−0.789161	+	0.614187i	$0.789484\pi$
$444$	−4369.42	+	2581.34i	−0.467035	+	0.275912i
$445$	1015.55	−	1758.98i	0.108183	−	0.187379i
$446$	6761.57			0.717869
$447$	−37.5153	−	3748.10i	−0.00396960	−	0.396598i
$448$	23.9887	+	2805.97i	0.00252982	+	0.295915i
$449$	10296.7			1.08225			0.541126	−	0.840941i	$-0.317998\pi$
$449$	10296.7			1.08225			0.541126	+	0.840941i	$0.317998\pi$
$450$	1414.68	+	2340.80i	0.148197	+	0.245214i
$451$	−439.745	−	761.660i	−0.0459130	−	0.0795237i
$452$	−1373.46			−0.142926
$453$	−149.103	−	14896.7i	−0.0154646	−	1.54505i
$454$	−5728.08	−	9921.33i	−0.592142	−	1.02562i
$455$	−9730.38	+	5729.30i	−1.00257	+	0.590316i
$456$	3207.03	+	1809.02i	0.329348	+	0.185779i
$457$	−7182.41	−	12440.3i	−0.735184	−	1.27338i	−0.954643	−	0.297754i	$-0.903762\pi$
$457$	−7182.41	−	12440.3i	−0.735184	−	1.27338i	0.219459	−	0.975622i	$-0.429571\pi$
$458$	−8692.93	−	15056.6i	−0.886886	−	1.53613i
$459$	15123.0	−	9347.59i	1.53787	−	0.950562i
$460$	2534.04	−	4389.08i	0.256848	−	0.444874i
$461$	−2747.56	+	4758.92i	−0.277585	+	0.480792i	−0.970784	−	0.239955i	$-0.922867\pi$
$461$	−2747.56	+	4758.92i	−0.277585	+	0.480792i	0.693199	+	0.720746i	$0.256201\pi$
$462$	−6518.12	−	10820.9i	−0.656386	−	1.08968i
$463$	3667.94	+	6353.05i	0.368172	+	0.637692i	0.989280	−	0.146033i	$-0.0466506\pi$
$463$	3667.94	+	6353.05i	0.368172	+	0.637692i	−0.621108	+	0.783725i	$0.713317\pi$
$464$	4373.36			0.437561
$465$	4838.42	+	2729.26i	0.482529	+	0.272186i
$466$	−20598.9			−2.04769
$467$	1503.29	−	2603.77i	0.148959	−	0.258004i	−0.781884	−	0.623424i	$-0.785741\pi$
$467$	1503.29	−	2603.77i	0.148959	−	0.258004i	0.930843	+	0.365420i	$0.119074\pi$
$468$	−5708.28	+	114.281i	−0.563815	+	0.0112877i
$469$	−575.441	−	325.704i	−0.0566554	−	0.0320674i
$470$	−6357.54	+	11011.6i	−0.623939	+	1.08069i
$471$	3395.21	+	1915.17i	0.332151	+	0.187360i
$472$	−3013.77	+	5220.00i	−0.293898	+	0.509047i
$473$	931.755	−	1613.85i	0.0905754	−	0.156881i
$474$	7654.29	+	4317.64i	0.741715	+	0.418388i
$475$	−682.649	+	1182.38i	−0.0659413	+	0.114214i
$476$	−67.8137	−	7932.19i	−0.00652990	−	0.763806i
$477$	3732.00	+	6175.17i	0.358232	+	0.592750i
$478$	4391.19	−	7605.76i	0.420185	−	0.727781i
$479$	10603.8			1.01148			0.505740	−	0.862686i	$-0.331219\pi$
$479$	10603.8			1.01148			0.505740	+	0.862686i	$0.331219\pi$
$480$	6346.42	+	3579.90i	0.603485	+	0.340415i
$481$	−18078.5			−1.71374
$482$	3916.99	+	6784.42i	0.370153	+	0.641124i
$483$	−14804.5	+	274.770i	−1.39467	+	0.0258850i
$484$	−309.547	+	536.151i	−0.0290709	+	0.0503523i
$485$	552.572	−	957.083i	0.0517340	−	0.0896060i
$486$	−10733.0	+	6934.82i	−1.00177	+	0.647263i
$487$	7160.77	+	12402.8i	0.666294	+	1.15406i	0.978933	+	0.204183i	$0.0654538\pi$
$487$	7160.77	+	12402.8i	0.666294	+	1.15406i	−0.312638	+	0.949872i	$0.601213\pi$
$488$	−278.057	−	481.609i	−0.0257932	−	0.0446751i
$489$	12672.7	+	7148.46i	1.17194	+	0.661072i
$490$	5804.20	+	9667.59i	0.535116	+	0.891301i
$491$	−2111.73	−	3657.62i	−0.194096	−	0.336184i	0.752508	−	0.658583i	$-0.228844\pi$
$491$	−2111.73	−	3657.62i	−0.194096	−	0.336184i	−0.946604	+	0.322399i	$0.895511\pi$
$492$	3.97291	+	396.928i	0.000364050	+	0.0363717i
$493$	6961.01			0.635919
$494$	−4797.91	−	8310.22i	−0.436980	−	0.756871i
$495$	10236.7	−	204.942i	0.929506	−	0.0186090i
$496$	−8733.96			−0.790658
$497$	−23.1720	−	2710.44i	−0.00209136	−	0.244627i
$498$	59.5168	+	5946.25i	0.00535545	+	0.535055i
$499$	18697.4			1.67738			0.838690	−	0.544610i	$-0.183322\pi$
$499$	18697.4			1.67738			0.838690	+	0.544610i	$0.183322\pi$
$500$	−2553.21	+	4422.28i	−0.228366	+	0.395541i
$501$	0.707014	−	0.417685i	6.30480e−5	−	3.72471e-5i
$502$	−804.372	−	1393.21i	−0.0715157	−	0.123869i
$503$	−7096.25			−0.629038			−0.314519	−	0.949251i	$-0.601843\pi$
$503$	−7096.25			−0.629038			−0.314519	+	0.949251i	$0.601843\pi$
$504$	−222.602	−	7790.26i	−0.0196735	−	0.688504i
$505$	−10505.5			−0.925723
$506$	10098.7	+	17491.5i	0.887238	+	1.53674i
$507$	−7771.61	−	4383.82i	−0.680768	−	0.384008i
$508$	3887.00	−	6732.48i	0.339484	−	0.588003i
$509$	−6419.73			−0.559037			−0.279518	−	0.960140i	$-0.590175\pi$
$509$	−6419.73			−0.559037			−0.279518	+	0.960140i	$0.590175\pi$
$510$	18854.4	+	10635.4i	1.63704	+	0.923422i
$511$	11645.7	−	6857.03i	1.00817	−	0.593614i
$512$	−1529.38			−0.132011
$513$	−5617.44	−	3022.10i	−0.483462	−	0.260095i
$514$	6302.97	+	10917.1i	0.540880	+	0.936831i
$515$	−16668.1			−1.42619
$516$	−724.146	+	427.806i	−0.0617805	+	0.0364983i
$517$	−7525.06	−	13033.8i	−0.640139	−	1.10875i
$518$	154.336	+	18052.7i	0.0130910	+	1.53126i
$519$	5648.67	−	3337.08i	0.477744	−	0.282238i
$520$	4751.22	+	8229.36i	0.400682	+	0.694002i
$521$	4877.13	+	8447.45i	0.410117	+	0.710344i	0.994902	−	0.100844i	$-0.0321544\pi$
$521$	4877.13	+	8447.45i	0.410117	+	0.710344i	−0.584785	+	0.811188i	$0.698821\pi$
$522$	−5002.23	+	100.146i	−0.419429	+	0.00839709i
$523$	−2134.28	+	3696.68i	−0.178443	+	0.309072i	−0.941347	−	0.337439i	$-0.890439\pi$
$523$	−2134.28	+	3696.68i	−0.178443	+	0.309072i	0.762905	+	0.646511i	$0.223773\pi$
$524$	986.436	−	1708.56i	0.0822379	−	0.142440i
$525$	2889.29	−	53.6249i	0.240188	−	0.00445787i
$526$	1702.11	+	2948.15i	0.141094	+	0.244383i
$527$	−13901.7			−1.14909
$528$	−13859.8	+	8188.03i	−1.14237	+	0.674883i
$529$	11507.4			0.945784
$530$	−4392.65	+	7608.30i	−0.360009	+	0.623553i
$531$	5038.96	−	9145.76i	0.411813	−	0.747443i
$532$	−2452.51	+	1444.05i	−0.199868	+	0.117684i
$533$	−707.025	+	1224.60i	−0.0574571	+	0.0995186i
$534$	−36.5646	−	3653.12i	−0.00296312	−	0.296041i
$535$	3999.46	−	6927.26i	0.323199	−	0.559798i
$536$	−278.220	+	481.892i	−0.0224203	+	0.0388331i
$537$	−13038.2	+	7702.60i	−1.04774	+	0.618979i
$538$	13727.6	−	23777.0i	1.10007	−	1.90539i
$539$	−13345.0	+	228.194i	−1.06644	+	0.0182356i
$540$	−4069.59	−	2189.38i	−0.324310	−	0.174474i
$541$	10185.3	−	17641.4i	0.809426	−	1.40197i	−0.103836	−	0.994594i	$-0.533112\pi$
$541$	10185.3	−	17641.4i	0.809426	−	1.40197i	0.913262	−	0.407373i	$-0.133555\pi$
$542$	22835.9			1.80976
$543$	45.2961	+	4525.47i	0.00357982	+	0.357655i
$544$	−18234.5			−1.43713
$545$	−10374.4	−	17968.9i	−0.815392	−	1.41230i
$546$	−9827.08	+	17774.8i	−0.770256	+	1.39321i
$547$	−1046.82	+	1813.14i	−0.0818258	+	0.141726i	−0.904034	−	0.427460i	$-0.859408\pi$
$547$	−1046.82	+	1813.14i	−0.0818258	+	0.141726i	0.822208	+	0.569187i	$0.192742\pi$
$548$	285.263	−	494.089i	0.0222369	−	0.0385154i
$549$	498.307	+	824.525i	0.0387381	+	0.0640981i
$550$	−1970.89	−	3413.69i	−0.152799	−	0.264655i
$551$	−1248.76	−	2162.91i	−0.0965498	−	0.167229i
$552$	124.714	+	12460.0i	0.00961625	+	0.960747i
$553$	8001.19	−	4711.15i	0.615272	−	0.362275i
$554$	−10995.6	−	19045.0i	−0.843249	−	1.46055i
$555$	−12744.8	−	7189.08i	−0.974748	−	0.549837i
$556$	−4537.94			−0.346135
$557$	844.740	+	1463.13i	0.0642599	+	0.111301i	0.896365	−	0.443316i	$-0.146198\pi$
$557$	844.740	+	1463.13i	0.0642599	+	0.111301i	−0.832106	+	0.554617i	$0.812865\pi$
$558$	9989.88	−	200.000i	0.757895	−	0.0151733i
$559$	−2996.16			−0.226698
$560$	12382.5	−	7290.86i	0.934383	−	0.550170i
$561$	−22060.5	+	13032.8i	−1.66024	+	0.980826i
$562$	−21175.1			−1.58936
$563$	−6454.60	+	11179.7i	−0.483178	+	0.836888i	−0.999813	−	0.0193169i	$-0.993851\pi$
$563$	−6454.60	+	11179.7i	−0.483178	+	0.836888i	0.516636	+	0.856205i	$0.327184\pi$
$564$	67.9857	+	6792.36i	0.00507574	+	0.507110i
$565$	−1980.05	−	3429.55i	−0.147436	−	0.255367i
$566$	−2720.09			−0.202004
$567$	655.690	+	13485.3i	0.0485651	+	0.998820i
$568$	−2281.01			−0.168501
$569$	13211.4	+	22882.8i	0.973377	+	1.68594i	0.685191	+	0.728363i	$0.259719\pi$
$569$	13211.4	+	22882.8i	0.973377	+	1.68594i	0.288185	+	0.957575i	$0.406948\pi$
$570$	−77.7345	−	7766.35i	−0.00571218	−	0.570696i
$571$	6392.78	−	11072.6i	0.468528	−	0.811515i	−0.530825	−	0.847482i	$-0.678118\pi$
$571$	6392.78	−	11072.6i	0.468528	−	0.811515i	0.999353	+	0.0359669i	$0.0114511\pi$
$572$	8228.40			0.601480
$573$	14216.2	−	8398.54i	1.03646	−	0.612311i
$574$	1228.89	+	695.562i	0.0893606	+	0.0505787i
$575$	−4620.36			−0.335100
$576$	−4090.05	+	81.8841i	−0.295866	+	0.00592333i
$577$	−2294.12	−	3973.54i	−0.165521	−	0.286691i	0.771319	−	0.636449i	$-0.219597\pi$
$577$	−2294.12	−	3973.54i	−0.165521	−	0.286691i	−0.936840	+	0.349758i	$0.886264\pi$
$578$	−37598.9			−2.70572
$579$	7707.33	+	4347.56i	0.553205	+	0.312053i
$580$	−904.672	−	1566.94i	−0.0647663	−	0.112179i
$581$	5467.81	+	3094.82i	0.390435	+	0.220989i
$582$	−19.8953	−	1987.71i	−0.00141698	−	0.141569i
$583$	−5199.34	−	9005.52i	−0.369356	−	0.639743i
$584$	−5686.43	−	9849.18i	−0.402921	−	0.697880i
$585$	−8514.68	−	14088.8i	−0.601775	−	0.995730i
$586$	−10406.7	+	18025.0i	−0.733613	+	1.27066i
$587$	10298.2	−	17837.0i	0.724111	−	1.25420i	−0.235228	−	0.971940i	$-0.575584\pi$
$587$	10298.2	−	17837.0i	0.724111	−	1.25420i	0.959339	−	0.282256i	$-0.0910829\pi$
$588$	5296.64	+	2869.49i	0.371479	+	0.201251i
$589$	2493.88	+	4319.52i	0.174462	+	0.302178i
$590$	12714.2			0.887175
$591$	13.2549	+	1324.28i	0.000922559	+	0.0921717i
$592$	23005.9			1.59719
$593$	−3894.55	+	6745.56i	−0.269697	+	0.467128i	−0.968783	−	0.247909i	$-0.920257\pi$
$593$	−3894.55	+	6745.56i	−0.269697	+	0.467128i	0.699087	+	0.715037i	$0.253590\pi$
$594$	15665.3	−	9682.82i	1.08208	−	0.668840i
$595$	19709.0	−	11604.7i	1.35796	−	0.799577i
$596$	1219.07	−	2111.49i	0.0837837	−	0.145118i
$597$	3460.04	−	2044.10i	0.237203	−	0.140133i
$598$	16236.8	−	28122.9i	1.11032	−	1.92313i
$599$	−10937.0	+	18943.4i	−0.746031	+	1.29216i	0.203681	+	0.979037i	$0.434709\pi$
$599$	−10937.0	+	18943.4i	−0.746031	+	1.29216i	−0.949712	+	0.313126i	$0.898624\pi$
$600$	−24.3395	−	2431.73i	−0.00165609	−	0.165458i
$601$	−13992.6	+	24235.9i	−0.949702	+	1.64493i	−0.203650	+	0.979044i	$0.565281\pi$
$601$	−13992.6	+	24235.9i	−0.949702	+	1.64493i	−0.746052	+	0.665888i	$0.768053\pi$
$602$	25.5782	+	2991.89i	0.00173171	+	0.202559i
$603$	465.179	−	844.304i	0.0314155	−	0.0570195i
$604$	4845.15	−	8392.04i	0.326401	−	0.565343i
$605$	−1785.03			−0.119953
$606$	−16269.2	+	9611.40i	−1.09058	+	0.644284i
$607$	−4683.46			−0.313172			−0.156586	−	0.987664i	$-0.550049\pi$
$607$	−4683.46			−0.313172			−0.156586	+	0.987664i	$0.550049\pi$
$608$	3271.15	+	5665.80i	0.218195	+	0.377925i
$609$	−2557.71	+	4626.27i	−0.170187	+	0.307826i
$610$	−586.518	+	1015.88i	−0.0389302	+	0.0674291i
$611$	−12098.8	+	20955.8i	−0.801091	+	1.38753i
$612$	11562.2	−	231.478i	0.763681	−	0.0152891i
$613$	−13144.7	−	22767.2i	−0.866082	−	1.50010i	−0.865968	−	0.500099i	$-0.833297\pi$
$613$	−13144.7	−	22767.2i	−0.866082	−	1.50010i	−0.000113990	−	1.00000i	$-0.500036\pi$
$614$	7390.77	+	12801.2i	0.485777	+	0.841391i
$615$	−985.403	+	582.150i	−0.0646102	+	0.0381700i
$616$	96.0197	+	11231.5i	0.00628043	+	0.734625i
$617$	−215.459	−	373.186i	−0.0140584	−	0.0243499i	0.858911	−	0.512126i	$-0.171142\pi$
$617$	−215.459	−	373.186i	−0.0140584	−	0.0243499i	−0.872969	+	0.487776i	$0.837808\pi$
$618$	−25812.8	+	15249.5i	−1.68016	+	0.992596i
$619$	−17378.1			−1.12841			−0.564205	−	0.825635i	$-0.690817\pi$
$619$	−17378.1			−1.12841			−0.564205	+	0.825635i	$0.690817\pi$
$620$	1806.71	+	3129.31i	0.117031	+	0.202703i
$621$	−648.072	−	21576.9i	−0.0418780	−	1.39428i
$622$	28547.9			1.84030
$623$	−3359.19	−	1901.32i	−0.216024	−	0.122271i
$624$	22543.0	+	12716.1i	1.44622	+	0.815787i
$625$	−10969.7			−0.702060
$626$	9817.42	−	17004.3i	0.626810	−	1.08567i
$627$	8007.03	+	4516.62i	0.510000	+	0.287681i
$628$	1267.80	+	2195.89i	0.0805585	+	0.139531i
$629$	36618.2			2.32124
$630$	−13996.1	+	8622.81i	−0.885105	+	0.545303i
$631$	−176.931			−0.0111625			−0.00558123	−	0.999984i	$-0.501777\pi$
$631$	−176.931			−0.0111625			−0.00558123	+	0.999984i	$0.501777\pi$
$632$	−3906.88	−	6766.92i	−0.245898	−	0.425907i
$633$	16414.7	−	9697.38i	1.03069	−	0.608904i
$634$	−10820.5	+	18741.7i	−0.677821	+	1.17402i
$635$	22414.7			1.40079
$636$	46.9738	+	4693.09i	0.00292867	+	0.292599i
$637$	11045.8	+	18398.1i	0.687050	+	1.14436i
$638$	7210.65			0.447449
$639$	3950.80	−	79.0961i	0.244587	−	0.00489670i
$640$	−8099.64	−	14029.0i	−0.500260	−	0.866475i
$641$	−21029.9			−1.29583			−0.647917	−	0.761711i	$-0.724360\pi$
$641$	−21029.9			−1.29583			−0.647917	+	0.761711i	$0.724360\pi$
$642$	−144.000	−	14386.8i	−0.00885236	−	0.884428i
$643$	−6304.53	−	10919.8i	−0.386666	−	0.669725i	0.605333	−	0.795973i	$-0.293040\pi$
$643$	−6304.53	−	10919.8i	−0.386666	−	0.669725i	−0.991999	+	0.126247i	$0.959707\pi$
$644$	−8381.99	−	4744.27i	−0.512883	−	0.290295i
$645$	−2112.20	−	1191.45i	−0.128942	−	0.0727338i
$646$	9718.19	+	16832.4i	0.591884	+	1.02517i
$647$	−5084.38	−	8806.41i	−0.308945	−	0.535109i	0.669187	−	0.743094i	$-0.266643\pi$
$647$	−5084.38	−	8806.41i	−0.308945	−	0.535109i	−0.978132	+	0.207985i	$0.933309\pi$
$648$	11352.7	−	454.750i	0.688233	−	0.0275683i
$649$	−7524.52	+	13032.8i	−0.455105	+	0.788265i
$650$	−3168.82	+	5488.55i	−0.191217	+	0.331198i
$651$	5107.96	−	9239.05i	0.307522	−	0.556232i
$652$	4732.11	+	8196.26i	0.284239	+	0.492316i
$653$	17327.5			1.03841			0.519203	−	0.854651i	$-0.326229\pi$
$653$	17327.5			1.03841			0.519203	+	0.854651i	$0.326229\pi$
$654$	−32505.6	−	18335.8i	−1.94353	−	1.09631i
$655$	5688.36			0.339333
$656$	899.728	−	1558.38i	0.0535495	−	0.0927505i
$657$	10190.7	+	16862.0i	0.605137	+	1.00129i
$658$	21029.2	+	11902.7i	1.24590	+	0.705190i
$659$	7431.15	−	12871.1i	0.439266	−	0.760831i	−0.558367	−	0.829594i	$-0.688572\pi$
$659$	7431.15	−	12871.1i	0.439266	−	0.760831i	0.997633	+	0.0687629i	$0.0219052\pi$
$660$	5800.75	+	3272.09i	0.342112	+	0.192979i
$661$	−15644.7	+	27097.4i	−0.920588	+	1.59451i	−0.122081	+	0.992520i	$0.538957\pi$
$661$	−15644.7	+	27097.4i	−0.920588	+	1.59451i	−0.798507	+	0.601985i	$0.794377\pi$
$662$	−1398.01	+	2421.42i	−0.0820771	+	0.142162i
$663$	35881.3	+	20240.0i	2.10183	+	1.18561i
$664$	2643.63	−	4578.91i	0.154507	−	0.267615i
$665$	−7141.47	−	4042.12i	−0.416442	−	0.235709i
$666$	−26314.1	+	526.816i	−1.53101	+	0.0306512i
$667$	4225.97	−	7319.60i	0.245323	−	0.424911i
$668$	0.534148			3.09383e−5
$669$	9071.33	+	5116.97i	0.524242	+	0.295715i
$670$	1173.73			0.0676791
$671$	−694.229	−	1202.44i	−0.0399410	−	0.0691798i
$672$	6699.97	−	12118.6i	0.384609	−	0.695663i
$673$	2162.02	−	3744.73i	0.123833	−	0.214485i	−0.797443	−	0.603394i	$-0.793815\pi$
$673$	2162.02	−	3744.73i	0.123833	−	0.214485i	0.921276	+	0.388909i	$0.127148\pi$
$674$	9806.11	−	16984.7i	0.560411	−	0.970661i
$675$	126.480	+	4211.01i	0.00721215	+	0.240121i
$676$	−2901.99	−	5026.39i	−0.165111	−	0.285980i
$677$	2404.70	+	4165.07i	0.136514	+	0.236450i	0.926175	−	0.377094i	$-0.123077\pi$
$677$	2404.70	+	4165.07i	0.136514	+	0.236450i	−0.789661	+	0.613544i	$0.789743\pi$
$678$	−6204.02	−	3499.57i	−0.351421	−	0.198230i
$679$	−1827.78	−	1034.53i	−0.103304	−	0.0584710i
$680$	−9623.63	−	16668.6i	−0.542720	−	0.940018i
$681$	−176.615	−	17645.3i	−0.00993816	−	0.992908i
$682$	−14400.3			−0.808526
$683$	−13158.2	−	22790.8i	−0.737169	−	1.27681i	−0.953765	−	0.300553i	$-0.902829\pi$
$683$	−13158.2	−	22790.8i	−0.737169	−	1.27681i	0.216596	−	0.976261i	$-0.430504\pi$
$684$	−2146.10	−	3551.05i	−0.119968	−	0.198506i
$685$	1644.99			0.0917545
$686$	18277.6	−	11187.1i	1.01726	−	0.622633i
$687$	−268.030	−	26778.5i	−0.0148850	−	1.48714i
$688$	3812.79			0.211281
$689$	−8359.53	+	14479.1i	−0.462224	+	0.800596i
$690$	22629.7	−	13369.0i	1.24855	−	0.737609i
$691$	−1095.59	−	1897.63i	−0.0603161	−	0.104470i	0.834291	−	0.551325i	$-0.185878\pi$
$691$	−1095.59	−	1897.63i	−0.0603161	−	0.104470i	−0.894607	+	0.446854i	$0.852544\pi$
$692$	4267.56			0.234434
$693$	−555.772	−	19450.0i	−0.0304647	−	1.06616i
$694$	−11209.6			−0.613128
$695$	−6542.10	−	11331.2i	−0.357059	−	0.618444i
$696$	3874.62	+	2185.60i	0.211016	+	0.119030i
$697$	1432.08	−	2480.44i	0.0778250	−	0.134797i
$698$	−2538.16			−0.137637
$699$	−27635.5	−	15588.7i	−1.49538	−	0.843517i
$700$	1635.85	+	925.905i	0.0883278	+	0.0499942i
$701$	7938.38			0.427715			0.213858	−	0.976865i	$-0.431397\pi$
$701$	7938.38			0.427715			0.213858	+	0.976865i	$0.431397\pi$
$702$	−26075.8	−	14028.4i	−1.40195	−	0.754228i
$703$	−6569.06	−	11377.9i	−0.352428	−	0.610423i
$704$	5895.75			0.315631
$705$	−16862.5	+	9961.94i	−0.900823	+	0.532182i
$706$	−3733.79	−	6467.11i	−0.199041	−	0.344749i
$707$	170.678	+	19964.3i	0.00907921	+	1.06200i
$708$	5847.94	−	3454.81i	0.310422	−	0.183389i
$709$	−11439.3	−	19813.4i	−0.605940	−	1.04952i	−0.991902	−	0.127004i	$-0.959464\pi$
$709$	−11439.3	−	19813.4i	−0.605940	−	1.04952i	0.385962	−	0.922515i	$-0.373870\pi$
$710$	2405.71	+	4166.82i	0.127162	+	0.220251i
$711$	7001.53	+	11585.1i	0.369308	+	0.611077i
$712$	−1624.14	+	2813.09i	−0.0854875	+	0.148069i
$713$	−8439.62	+	14617.8i	−0.443291	+	0.767802i
$714$	19904.8	−	36002.9i	1.04330	−	1.88708i
$715$	11862.4	+	20546.3i	0.620462	+	1.07467i
$716$	−9850.32			−0.514139
$717$	11647.1	−	6880.77i	0.606649	−	0.358392i
$718$	−2935.48			−0.152578
$719$	−5773.81	+	10000.5i	−0.299481	+	0.518716i	−0.976017	−	0.217693i	$-0.930147\pi$
$719$	−5773.81	+	10000.5i	−0.299481	+	0.518716i	0.676536	+	0.736409i	$0.263480\pi$
$720$	10835.4	+	17928.8i	0.560849	+	0.928012i
$721$	270.798	+	31675.4i	0.0139876	+	1.63613i
$722$	−8082.37	+	13999.1i	−0.416613	+	0.721595i
$723$	120.773	+	12066.3i	0.00621244	+	0.620676i
$724$	−1471.91	+	2549.42i	−0.0755568	+	0.130868i
$725$	−824.753	+	1428.51i	−0.0422491	+	0.0731775i
$726$	−2764.35	+	1633.10i	−0.141315	+	0.0834850i
$727$	−9053.60	+	15681.3i	−0.461870	+	0.799982i	−0.999054	−	0.0434827i	$-0.986155\pi$
$727$	−9053.60	+	15681.3i	−0.461870	+	0.799982i	0.537184	+	0.843465i	$0.319488\pi$
$728$	15561.5	−	9162.71i	0.792237	−	0.466474i
$729$	−19647.5	+	1181.31i	−0.998197	+	0.0600168i
$730$	−11994.6	+	20775.3i	−0.608139	+	1.05333i
$731$	6068.75			0.307060
$732$	6.27206	+	626.633i	0.000316697	+	0.0316408i
$733$	23101.1			1.16406			0.582032	−	0.813166i	$-0.302258\pi$
$733$	23101.1			1.16406			0.582032	+	0.813166i	$0.302258\pi$
$734$	−4265.12	−	7387.41i	−0.214480	−	0.371491i
$735$	470.756	+	17362.5i	0.0236246	+	0.871328i
$736$	−11070.0	+	19173.8i	−0.554411	+	0.960267i
$737$	−694.636	+	1203.15i	−0.0347181	+	0.0601336i
$738$	−993.421	+	1803.07i	−0.0495506	+	0.0899347i
$739$	−5479.70	−	9491.12i	−0.272766	−	0.472444i	0.696803	−	0.717262i	$-0.254605\pi$
$739$	−5479.70	−	9491.12i	−0.272766	−	0.472444i	−0.969569	+	0.244818i	$0.921272\pi$
$740$	−4759.00	−	8242.84i	−0.236411	−	0.409477i
$741$	−147.934	−	14779.9i	−0.00733401	−	0.732731i
$742$	14529.8	+	8224.00i	0.718878	+	0.406890i
$743$	−2774.77	−	4806.05i	−0.137008	−	0.237304i	0.789355	−	0.613937i	$-0.210415\pi$
$743$	−2774.77	−	4806.05i	−0.137008	−	0.237304i	−0.926363	+	0.376633i	$0.877082\pi$
$744$	−7737.94	−	4364.83i	−0.381299	−	0.215084i
$745$	7029.87			0.345711
$746$	9058.60	+	15690.0i	0.444583	+	0.770040i
$747$	−4420.11	+	8022.53i	−0.216497	+	0.392944i
$748$	−16666.7			−0.814698
$749$	−13229.2	−	7487.85i	−0.645375	−	0.365287i
$750$	−22800.9	+	13470.2i	−1.11009	+	0.655814i
$751$	−16603.6			−0.806754			−0.403377	−	0.915034i	$-0.632164\pi$
$751$	−16603.6			−0.806754			−0.403377	+	0.915034i	$0.632164\pi$
$752$	15396.5	−	26667.4i	0.746610	−	1.29317i
$753$	−24.8013	−	2477.86i	−0.00120028	−	0.119918i
$754$	−5796.66	−	10040.1i	−0.279976	−	0.484933i
$755$	27939.9			1.34681
$756$	−4094.49	+	7769.24i	−0.196978	+	0.373763i
$757$	2336.31			0.112172			0.0560862	−	0.998426i	$-0.482138\pi$
$757$	2336.31			0.112172			0.0560862	+	0.998426i	$0.482138\pi$
$758$	−16738.1	−	28991.2i	−0.802052	−	1.38919i
$759$	311.375	+	31109.0i	0.0148909	+	1.48773i
$760$	−3452.83	+	5980.48i	−0.164799	+	0.285441i
$761$	10068.8			0.479625			0.239812	−	0.970819i	$-0.422914\pi$
$761$	10068.8			0.479625			0.239812	+	0.970819i	$0.422914\pi$
$762$	34712.1	−	20507.0i	1.65024	−	0.974920i
$763$	−33978.8	+	20006.9i	−1.61221	+	0.949277i
$764$	10740.3			0.508601
$765$	17246.5	+	28537.0i	0.815098	+	1.34870i
$766$	18870.3	+	32684.3i	0.890093	+	1.54169i
$767$	24195.9			1.13907
$768$	−19892.6	−	11221.0i	−0.934649	−	0.527218i
$769$	−1220.38	−	2113.76i	−0.0572277	−	0.0991213i	0.835992	−	0.548741i	$-0.184893\pi$
$769$	−1220.38	−	2113.76i	−0.0572277	−	0.0991213i	−0.893220	+	0.449620i	$0.851559\pi$
$770$	20415.8	−	12020.9i	0.955498	−	0.562603i
$771$	194.340	+	19416.3i	0.00907781	+	0.906952i
$772$	2877.98	+	4984.81i	0.134172	+	0.232393i
$773$	5436.01	+	9415.44i	0.252936	+	0.438098i	0.964333	−	0.264692i	$-0.0852704\pi$
$773$	5436.01	+	9415.44i	0.252936	+	0.438098i	−0.711397	+	0.702791i	$0.751937\pi$
$774$	−4361.05	+	87.3095i	−0.202526	+	0.00405462i
$775$	1647.10	−	2852.86i	0.0763428	−	0.132230i
$776$	−883.713	+	1530.64i	−0.0408807	+	0.0708075i
$777$	−13454.8	+	24336.4i	−0.621219	+	1.12363i
$778$	−2839.35	−	4917.91i	−0.130843	−	0.226627i
$779$	−1027.63			−0.0472638
$780$	−107.172	−	10707.4i	−0.00491971	−	0.491522i
$781$	−5695.01			−0.260927
$782$	−32887.7	+	56963.2i	−1.50391	+	2.60486i
$783$	−6786.79	−	3651.20i	−0.309758	−	0.166645i
$784$	−14056.4	−	23412.6i	−0.640324	−	1.06654i
$785$	−3655.44	+	6331.40i	−0.166201	+	0.287869i
$786$	8809.17	−	5204.22i	0.399762	−	0.236168i
$787$	−9740.91	+	16871.7i	−0.441202	+	0.764184i	−0.997779	−	0.0666120i	$-0.978781\pi$
$787$	−9740.91	+	16871.7i	−0.441202	+	0.764184i	0.556577	+	0.830796i	$0.312114\pi$
$788$	−430.721	+	746.031i	−0.0194718	+	0.0337262i
$789$	52.4814	+	5243.35i	0.00236805	+	0.236588i
$790$	−8240.96	+	14273.8i	−0.371139	+	0.642832i
$791$	−6485.19	+	3818.52i	−0.291513	+	0.171645i
$792$	−16371.3	+	327.757i	−0.734504	+	0.0147050i
$793$	−1116.19	+	1933.29i	−0.0499835	+	0.0865740i
$794$	−11978.4			−0.535385
$795$	−11650.9	+	6883.06i	−0.519769	+	0.307066i
$796$	2614.06			0.116398
$797$	1644.31	+	2848.02i	0.0730794	+	0.126577i	0.900249	−	0.435374i	$-0.143384\pi$
$797$	1644.31	+	2848.02i	0.0730794	+	0.126577i	−0.827170	+	0.561952i	$0.810051\pi$
$798$	−14757.6	+	273.899i	−0.654652	+	0.0121503i
$799$	24506.3	−	42446.1i	1.08507	−	1.87939i
$800$	2160.46	−	3742.02i	0.0954797	−	0.165376i
$801$	2715.52	−	4928.70i	0.119786	−	0.217412i
$802$	−6412.29	−	11106.4i	−0.282327	−	0.489004i
$803$	−14197.4	−	24590.6i	−0.623928	−	1.08068i
$804$	539.861	−	318.936i	0.0236809	−	0.0139900i
$805$	−237.405	−	27769.4i	−0.0103943	−	1.21583i
$806$	11576.4	+	20050.9i	0.505908	+	0.876259i
$807$	36410.8	−	21510.5i	1.58825	−	0.938297i
$808$	16801.2			0.731515
$809$	14785.3	+	25608.8i	0.642549	+	1.11293i	0.984862	+	0.173341i	$0.0554562\pi$
$809$	14785.3	+	25608.8i	0.642549	+	1.11293i	−0.342313	+	0.939586i	$0.611210\pi$
$810$	−12804.1	−	20258.8i	−0.555418	−	0.878793i
$811$	−1910.74			−0.0827313			−0.0413656	−	0.999144i	$-0.513171\pi$
$811$	−1910.74			−0.0827313			−0.0413656	+	0.999144i	$0.513171\pi$
$812$	−2963.04	+	1744.66i	−0.128057	+	0.0754008i
$813$	30636.7	+	17281.6i	1.32162	+	0.745501i
$814$	37931.4			1.63329
$815$	−13644.1	+	23632.2i	−0.586418	+	1.01571i
$816$	−45661.0	−	25756.5i	−1.95889	−	1.10497i
$817$	−1088.69	−	1885.67i	−0.0466201	−	0.0807483i
$818$	−44680.1			−1.90979
$819$	−26635.5	+	16409.8i	−1.13641	+	0.700129i
$820$	−744.471			−0.0317049
$821$	16782.8	+	29068.7i	0.713428	+	1.23569i	0.963563	+	0.267482i	$0.0861917\pi$
$821$	16782.8	+	29068.7i	0.713428	+	1.23569i	−0.250135	+	0.968211i	$0.580475\pi$
$822$	2547.48	−	1504.98i	0.108094	−	0.0638593i
$823$	19668.3	−	34066.5i	0.833042	−	1.44287i	−0.0625721	−	0.998040i	$-0.519930\pi$
$823$	19668.3	−	34066.5i	0.833042	−	1.44287i	0.895614	−	0.444831i	$-0.146736\pi$
$824$	26656.9			1.12699
$825$	−60.7688	−	6071.33i	−0.00256448	−	0.256214i
$826$	−206.560	−	24161.4i	−0.00870114	−	1.01778i
$827$	36017.5			1.51445			0.757226	−	0.653153i	$-0.226554\pi$
$827$	36017.5			1.51445			0.757226	+	0.653153i	$0.226554\pi$
$828$	6775.89	−	12298.3i	0.284394	−	0.516178i
$829$	−1351.86	−	2341.49i	−0.0566369	−	0.0980980i	0.836317	−	0.548246i	$-0.184704\pi$
$829$	−1351.86	−	2341.49i	−0.0566369	−	0.0980980i	−0.892954	+	0.450148i	$0.851371\pi$
$830$	−11152.7			−0.466403
$831$	−339.030	−	33872.0i	−0.0141526	−	1.41397i
$832$	−4739.61	−	8209.25i	−0.197496	−	0.342073i
$833$	−22373.3	−	37265.5i	−0.930601	−	1.55003i
$834$	−20498.1	−	11562.6i	−0.851069	−	0.480072i
$835$	0.770052	+	1.33377i	3.19147e−5	+	5.52779e-5i
$836$	2989.89	+	5178.65i	0.123693	+	0.214243i
$837$	13553.8	+	7291.74i	0.559722	+	0.301123i
$838$	−4842.59	+	8387.62i	−0.199624	+	0.345758i
$839$	−14788.7	+	25614.8i	−0.608537	+	1.05402i	0.382945	+	0.923771i	$0.374910\pi$
$839$	−14788.7	+	25614.8i	−0.608537	+	1.05402i	−0.991482	+	0.130245i	$0.958424\pi$
$840$	14614.0	−	271.234i	0.600274	−	0.0111410i
$841$	10685.8	+	18508.3i	0.438140	+	0.758880i
$842$	−2976.01			−0.121805
$843$	−28408.6	−	16024.8i	−1.16067	−	0.654712i
$844$	12401.3			0.505771
$845$	8367.27	−	14492.5i	0.340642	−	0.590010i
$846$	−16999.8	+	30854.7i	−0.690855	+	1.25391i
$847$	29.0004	+	3392.19i	0.00117647	+	0.137612i
$848$	10638.0	−	18425.5i	0.430789	−	0.746149i
$849$	−3649.28	−	2058.49i	−0.147518	−	0.0832123i
$850$	6418.46	−	11117.1i	0.259002	−	0.448604i
$851$	22230.6	−	38504.5i	0.895482	−	1.55102i
$852$	2238.77	+	1262.85i	0.0900221	+	0.0507798i
$853$	1776.98	−	3077.82i	0.0713279	−	0.123544i	−0.828156	−	0.560498i	$-0.810610\pi$
$853$	1776.98	−	3077.82i	0.0713279	−	0.123544i	0.899484	+	0.436955i	$0.143943\pi$
$854$	1940.06	+	1098.09i	0.0777372	+	0.0439998i
$855$	5773.07	−	10478.2i	0.230918	−	0.419118i
$856$	−6396.22	+	11078.6i	−0.255395	+	0.442357i
$857$	13277.7			0.529237			0.264619	−	0.964353i	$-0.414754\pi$
$857$	13277.7			0.529237			0.264619	+	0.964353i	$0.414754\pi$
$858$	37168.1	+	20965.9i	1.47890	+	0.834222i
$859$	36198.1			1.43779			0.718896	−	0.695117i	$-0.244648\pi$
$859$	36198.1			1.43779			0.718896	+	0.695117i	$0.244648\pi$
$860$	−788.712	−	1366.09i	−0.0312731	−	0.0541666i
$861$	1122.30	+	1863.16i	0.0444227	+	0.0737471i
$862$	14631.8	−	25343.1i	0.578147	−	1.00138i
$863$	8941.47	−	15487.1i	0.352689	−	0.610876i	−0.634030	−	0.773308i	$-0.718601\pi$
$863$	8941.47	−	15487.1i	0.352689	−	0.610876i	0.986720	+	0.162432i	$0.0519339\pi$
$864$	17778.1	+	9564.38i	0.700028	+	0.376605i
$865$	6152.32	+	10656.1i	0.241832	+	0.418866i
$866$	−17745.9	−	30736.8i	−0.696340	−	1.20610i
$867$	−50442.7	−	28453.8i	−1.97592	−	1.11458i
$868$	5917.45	−	3484.23i	0.231395	−	0.136247i
$869$	−9754.36	−	16895.0i	−0.380776	−	0.659523i
$870$	−93.9162	−	9383.04i	−0.00365984	−	0.365649i
$871$	2233.68			0.0868949
$872$	16591.4	+	28737.2i	0.644330	+	1.11601i
$873$	1477.55	−	2681.77i	0.0572824	−	0.103968i
$874$	23599.3			0.913341
$875$	239.201	+	27979.5i	0.00924169	+	1.08100i
$876$	128.267	+	12815.0i	0.00494720	+	0.494268i
$877$	−10938.4			−0.421166			−0.210583	−	0.977576i	$-0.567536\pi$
$877$	−10938.4			−0.421166			−0.210583	+	0.977576i	$0.567536\pi$
$878$	−18903.0	+	32740.9i	−0.726587	+	1.25849i
$879$	−27602.5	+	16306.8i	−1.05917	+	0.625727i
$880$	−15095.6	−	26146.4i	−0.578265	−	1.00158i
$881$	−16145.8			−0.617442			−0.308721	−	0.951153i	$-0.599901\pi$
$881$	−16145.8			−0.617442			−0.308721	+	0.951153i	$0.599901\pi$
$882$	16613.8	+	26457.4i	0.634258	+	1.01005i
$883$	−36343.7			−1.38512			−0.692562	−	0.721359i	$-0.743518\pi$
$883$	−36343.7			−1.38512			−0.692562	+	0.721359i	$0.743518\pi$
$884$	13398.4	+	23206.7i	0.509770	+	0.882948i
$885$	17057.3	+	9621.72i	0.647882	+	0.365458i
$886$	−4319.29	+	7481.23i	−0.163780	+	0.283676i
$887$	24675.6			0.934077			0.467038	−	0.884237i	$-0.345321\pi$
$887$	24675.6			0.934077			0.467038	+	0.884237i	$0.345321\pi$
$888$	20382.3	+	11497.3i	0.770255	+	0.434486i
$889$	−364.160	−	42595.9i	−0.0137385	−	1.60700i
$890$	6851.72			0.258057
$891$	28344.3	−	1135.38i	1.06574	−	0.0426898i
$892$	3387.31	+	5867.00i	0.127148	+	0.220226i
$893$	−17585.1			−0.658972
$894$	10886.7	−	6431.55i	0.407276	−	0.240608i
$895$	−14200.7	−	24596.3i	−0.530365	−	0.918618i
$896$	−26528.5	+	15620.1i	−0.989123	+	0.582401i
$897$	43065.9	−	25442.2i	1.60304	−	0.947035i
$898$	17367.5	+	30081.4i	0.645392	+	1.11785i
$899$	3013.01	+	5218.69i	0.111779	+	0.193608i
$900$	−1322.40	+	2400.17i	−0.0489779	+	0.0888953i
$901$	16932.3	−	29327.6i	0.626078	−	1.08440i
$902$	1483.44	−	2569.40i	0.0547597	−	0.0948465i
$903$	−2229.86	+	4033.28i	−0.0821764	+	0.148637i
$904$	3166.64	+	5484.78i	0.116505	+	0.201793i
$905$	−8487.89			−0.311765
$906$	43268.6	−	25561.9i	1.58665	−	0.937350i
$907$	−16901.6			−0.618753			−0.309377	−	0.950940i	$-0.600120\pi$
$907$	−16901.6			−0.618753			−0.309377	+	0.950940i	$0.600120\pi$
$908$	5739.15	−	9940.49i	0.209758	−	0.363311i
$909$	−29100.4	+	582.598i	−1.06182	+	0.0212580i
$910$	−33150.3	−	18763.3i	−1.20760	−	0.683513i
$911$	−17861.1	+	30936.3i	−0.649576	+	1.12510i	0.333649	+	0.942698i	$0.391720\pi$
$911$	−17861.1	+	30936.3i	−0.649576	+	1.12510i	−0.983224	+	0.182401i	$0.941613\pi$
$912$	188.255	+	18808.3i	0.00683524	+	0.682899i
$913$	6600.39	−	11432.2i	0.239256	−	0.414404i
$914$	24229.3	−	41966.3i	0.876841	−	1.51873i
$915$	−1555.66	+	919.045i	−0.0562062	+	0.0332051i
$916$	8709.71	−	15085.7i	0.314167	−	0.544153i
$917$	−92.4158	−	10809.9i	−0.00332807	−	0.389286i
$918$	52816.7	+	28414.6i	1.89892	+	1.02159i
$919$	−706.061	+	1222.93i	−0.0253436	+	0.0438965i	−0.878419	−	0.477891i	$-0.841401\pi$
$919$	−706.061	+	1222.93i	−0.0253436	+	0.0438965i	0.853075	+	0.521788i	$0.174735\pi$
$920$	−23369.7			−0.837475
$921$	227.880	+	22767.2i	0.00815300	+	0.814555i
$922$	−18537.4			−0.662142
$923$	4578.24	+	7929.75i	0.163266	+	0.282785i
$924$	6123.90	−	11076.6i	0.218032	−	0.394367i
$925$	−4338.59	+	7514.66i	−0.154218	+	0.267114i
$926$	−12373.5	+	21431.5i	−0.439112	+	0.760564i
$927$	−46170.8	+	924.353i	−1.63587	+	0.0327505i
$928$	3952.09	+	6845.22i	0.139799	+	0.242139i
$929$	6295.72	+	10904.5i	0.222342	+	0.385108i	0.955519	−	0.294930i	$-0.0952964\pi$
$929$	6295.72	+	10904.5i	0.222342	+	0.385108i	−0.733177	+	0.680038i	$0.761963\pi$
$930$	187.558	+	18738.7i	0.00661321	+	0.660717i
$931$	−7565.45	+	13637.0i	−0.266324	+	0.480059i
$932$	−10319.3	−	17873.6i	−0.362684	−	0.628187i
$933$	38299.8	+	21604.2i	1.34392	+	0.758082i
$934$	10142.4			0.355321
$935$	−24027.4	−	41616.8i	−0.840408	−	1.45563i
$936$	13617.3	+	22531.9i	0.475529	+	0.786835i
$937$	48310.9			1.68436			0.842182	−	0.539193i	$-0.181271\pi$
$937$	48310.9			1.68436			0.842182	+	0.539193i	$0.181271\pi$
$938$	−19.0689	−	2230.50i	−0.000663776	−	0.0776421i
$939$	26039.4	−	15383.4i	0.904968	−	0.534631i
$940$	−12739.6			−0.442044
$941$	10507.2	−	18199.0i	0.364000	−	0.630467i	−0.624615	−	0.780933i	$-0.714744\pi$
$941$	10507.2	−	18199.0i	0.364000	−	0.630467i	0.988615	+	0.150466i	$0.0480773\pi$
$942$	131.613	+	13149.3i	0.00455222	+	0.454807i
$943$	−1738.81	−	3011.71i	−0.0600462	−	0.104003i
$944$	−30790.7			−1.06160
$945$	−25302.6	+	976.543i	−0.871000	+	0.0336158i
$946$	6286.39			0.216055
$947$	−25990.5	−	45016.9i	−0.891845	−	1.54472i	−0.837661	−	0.546190i	$-0.816077\pi$
$947$	−25990.5	−	45016.9i	−0.891845	−	1.54472i	−0.0541843	−	0.998531i	$-0.517256\pi$
$948$	88.1265	+	8804.60i	0.00301921	+	0.301646i
$949$	−22826.6	+	39536.9i	−0.780805	+	1.35239i
$950$	−4605.72			−0.157294
$951$	−28700.1	+	16955.2i	−0.978616	+	0.578140i
$952$	−31520.0	+	18559.1i	−1.07308	+	0.631833i
$953$	−26692.5			−0.907296			−0.453648	−	0.891181i	$-0.649878\pi$
$953$	−26692.5			−0.907296			−0.453648	+	0.891181i	$0.649878\pi$
$954$	−11745.7	+	21318.6i	−0.398619	+	0.723497i
$955$	15483.7	+	26818.6i	0.524651	+	0.908722i
$956$	8799.33			0.297689
$957$	9673.81	+	5456.82i	0.326761	+	0.184320i
$958$	17885.5	+	30978.6i	0.603187	+	1.04475i
$959$	−26.7253	−	3126.07i	−0.000899900	−	0.105262i
$960$	−76.7901	−	7672.00i	−0.00258166	−	0.257930i
$961$	8878.26	+	15377.6i	0.298018	+	0.516183i
$962$	−30493.2	−	52815.8i	−1.02197	−	1.77011i
$963$	10694.4	−	19410.4i	0.357862	−	0.649522i
$964$	−3924.55	+	6797.52i	−0.131122	+	0.227109i
$965$	−8298.07	+	14372.7i	−0.276813	+	0.479454i
$966$	−25773.6	−	42787.3i	−0.858438	−	1.42511i
$967$	−17421.6	−	30175.0i	−0.579359	−	1.00348i	−0.995553	−	0.0942029i	$-0.969970\pi$
$967$	−17421.6	−	30175.0i	−0.579359	−	1.00348i	0.416194	−	0.909276i	$-0.363364\pi$
$968$	2854.75			0.0947882
$969$	299.642	+	29936.8i	0.00993383	+	0.992476i
$970$	3728.11			0.123405
$971$	−3963.58	+	6865.13i	−0.130996	+	0.226892i	−0.924061	−	0.382245i	$-0.875151\pi$
$971$	−3963.58	+	6865.13i	−0.130996	+	0.226892i	0.793065	+	0.609138i	$0.208484\pi$
$972$	−11394.2	−	5838.91i	−0.375997	−	0.192678i
$973$	−21427.1	+	12616.4i	−0.705983	+	0.415687i
$974$	−24156.2	+	41839.8i	−0.794677	+	1.37642i
$975$	−8404.87	+	4965.38i	−0.276073	+	0.163097i
$976$	1420.41	−	2460.22i	0.0465842	−	0.0806862i
$977$	3122.04	−	5407.52i	0.102234	−	0.177075i	−0.810371	−	0.585918i	$-0.800734\pi$
$977$	3122.04	−	5407.52i	0.102234	−	0.177075i	0.912605	+	0.408843i	$0.134068\pi$
$978$	491.252	+	49080.3i	0.0160619	+	1.60472i
$979$	−4055.00	+	7023.47i	−0.132378	+	0.229286i
$980$	−5480.84	+	9879.42i	−0.178652	+	0.322027i
$981$	−29733.5	−	49198.7i	−0.967704	−	1.60122i
$982$	7123.74	−	12338.7i	0.231495	−	0.400961i
$983$	8380.12			0.271907			0.135953	−	0.990715i	$-0.456590\pi$
$983$	8380.12			0.271907			0.135953	+	0.990715i	$0.456590\pi$
$984$	1575.93	−	931.015i	0.0510556	−	0.0301623i
$985$	−2483.79			−0.0803453
$986$	11741.2	+	20336.3i	0.379225	+	0.656836i
$987$	19205.2	+	31883.0i	0.619360	+	1.02821i
$988$	4807.17	−	8326.26i	0.154794	−	0.268111i
$989$	3684.29	−	6381.38i	0.118457	−	0.205173i
$990$	17865.0	+	29560.5i	0.573524	+	0.948983i
$991$	4971.94	+	8611.66i	0.159373	+	0.276043i	0.934643	−	0.355588i	$-0.115719\pi$
$991$	4971.94	+	8611.66i	0.159373	+	0.276043i	−0.775269	+	0.631631i	$0.782386\pi$
$992$	−7892.65	−	13670.5i	−0.252613	−	0.437538i
$993$	−3708.03	+	2190.60i	−0.118500	+	0.0700067i
$994$	7879.35	−	4639.41i	0.251426	−	0.148041i
$995$	3768.55	+	6527.32i	0.120071	+	0.207970i
$996$	−5129.73	+	3030.51i	−0.163194	+	0.0964109i
$997$	34946.8			1.11011			0.555053	−	0.831815i	$-0.312698\pi$
$997$	34946.8			1.11011			0.555053	+	0.831815i	$0.312698\pi$
$998$	31537.1	+	54623.9i	1.00029	+	1.73255i
$999$	−35701.7	−	19207.0i	−1.13068	−	0.608291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.g.a.16.18	yes	44
3.2	odd	2		189.4.g.a.100.5		44
7.4	even	3		63.4.h.a.25.5	yes	44
9.4	even	3		63.4.h.a.58.5	yes	44
9.5	odd	6		189.4.h.a.37.18		44
21.11	odd	6		189.4.h.a.46.18		44
63.4	even	3	inner	63.4.g.a.4.18	✓	44
63.32	odd	6		189.4.g.a.172.5		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.18	✓	44	63.4	even	3	inner
63.4.g.a.16.18	yes	44	1.1	even	1	trivial
63.4.h.a.25.5	yes	44	7.4	even	3
63.4.h.a.58.5	yes	44	9.4	even	3
189.4.g.a.100.5		44	3.2	odd	2
189.4.g.a.172.5		44	63.32	odd	6
189.4.h.a.37.18		44	9.5	odd	6
189.4.h.a.46.18		44	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68671 + 2.92146i) q^{2} +(0.0520064 + 5.19589i) q^{3} +(-1.68996 + 2.92710i) q^{4} -9.74532 q^{5} +(-15.0919 + 8.91589i) q^{6} +(0.158327 + 18.5196i) q^{7} +15.5854 q^{8} +(-26.9946 + 0.540440i) q^{9} +(-16.4375 - 28.4706i) q^{10} +38.9123 q^{11} +(-15.2968 - 8.62865i) q^{12} +(-31.2817 - 54.1816i) q^{13} +(-53.8372 + 31.6997i) q^{14} +(-0.506819 - 50.6356i) q^{15} +(39.8078 + 68.9491i) q^{16} +(63.3614 + 109.745i) q^{17} +(-47.1109 - 77.9521i) q^{18} +(22.7332 - 39.3751i) q^{19} +(16.4692 - 28.5256i) q^{20} +(-96.2175 + 1.78579i) q^{21} +(65.6337 + 113.681i) q^{22} +153.865 q^{23} +(0.810542 + 80.9801i) q^{24} -30.0287 q^{25} +(105.526 - 182.777i) q^{26} +(-4.21196 - 140.233i) q^{27} +(-54.4763 - 30.8340i) q^{28} +(27.4655 - 47.5716i) q^{29} +(147.075 - 86.8882i) q^{30} +(-54.8509 + 95.0045i) q^{31} +(-71.9464 + 124.615i) q^{32} +(2.02369 + 202.184i) q^{33} +(-213.744 + 370.216i) q^{34} +(-1.54295 - 180.479i) q^{35} +(44.0380 - 79.9293i) q^{36} +(144.482 - 250.249i) q^{37} +153.377 q^{38} +(279.895 - 165.354i) q^{39} -151.885 q^{40} +(-11.3009 - 19.5738i) q^{41} +(-167.508 - 278.084i) q^{42} +(23.9450 - 41.4740i) q^{43} +(-65.7604 + 113.900i) q^{44} +(263.071 - 5.26676i) q^{45} +(259.525 + 449.510i) q^{46} +(-193.385 - 334.953i) q^{47} +(-356.182 + 210.423i) q^{48} +(-342.950 + 5.86430i) q^{49} +(-50.6496 - 87.7278i) q^{50} +(-566.929 + 334.926i) q^{51} +211.460 q^{52} +(-133.617 - 231.431i) q^{53} +(402.581 - 248.837i) q^{54} -379.213 q^{55} +(2.46759 + 288.635i) q^{56} +(205.771 + 116.072i) q^{57} +185.305 q^{58} +(-193.371 + 334.929i) q^{59} +(149.072 + 84.0889i) q^{60} +(-17.8409 - 30.9013i) q^{61} -370.070 q^{62} +(-14.2827 - 499.843i) q^{63} +151.514 q^{64} +(304.851 + 528.017i) q^{65} +(-587.260 + 346.938i) q^{66} +(-17.8513 + 30.9194i) q^{67} -428.314 q^{68} +(8.00195 + 799.465i) q^{69} +(524.661 - 308.923i) q^{70} -146.355 q^{71} +(-420.722 + 8.42297i) q^{72} +(-364.856 - 631.948i) q^{73} +974.792 q^{74} +(-1.56169 - 156.026i) q^{75} +(76.8367 + 133.085i) q^{76} +(6.16087 + 720.640i) q^{77} +(955.177 + 538.798i) q^{78} +(-250.675 - 434.183i) q^{79} +(-387.939 - 671.931i) q^{80} +(728.416 - 29.1779i) q^{81} +(38.1227 - 66.0304i) q^{82} +(169.622 - 293.794i) q^{83} +(157.377 - 284.657i) q^{84} +(-617.477 - 1069.50i) q^{85} +161.553 q^{86} +(248.605 + 140.234i) q^{87} +606.465 q^{88} +(-104.209 + 180.495i) q^{89} +(459.110 + 759.669i) q^{90} +(998.467 - 587.903i) q^{91} +(-260.026 + 450.378i) q^{92} +(-496.486 - 280.058i) q^{93} +(652.368 - 1129.94i) q^{94} +(-221.543 + 383.723i) q^{95} +(-651.227 - 367.345i) q^{96} +(-56.7013 + 98.2095i) q^{97} +(-595.588 - 992.024i) q^{98} +(-1050.42 + 21.0297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{3} - 79 q^{4} + 38 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} - 31 q^{9} - 18 q^{10} - 10 q^{11} - 41 q^{12} - 14 q^{13} - 79 q^{14} + 119 q^{15} - 247 q^{16} - 162 q^{17} + 157 q^{18} + 58 q^{19}+ \cdots - 5395 q^{99}+O(q^{100}) \) 44 * q + q^2 - q^3 - 79 * q^4 + 38 * q^5 - 20 * q^6 - 7 * q^7 - 24 * q^8 - 31 * q^9 - 18 * q^10 - 10 * q^11 - 41 * q^12 - 14 * q^13 - 79 * q^14 + 119 * q^15 - 247 * q^16 - 162 * q^17 + 157 * q^18 + 58 * q^19 - 362 * q^20 + 166 * q^21 - 18 * q^22 + 186 * q^23 + 414 * q^24 + 698 * q^25 - 266 * q^26 + 272 * q^27 - 172 * q^28 + 248 * q^29 + 616 * q^30 + 61 * q^31 - 163 * q^32 + 23 * q^33 + 6 * q^34 + 289 * q^35 - 806 * q^36 - 86 * q^37 + 1522 * q^38 - 565 * q^39 + 36 * q^40 - 692 * q^41 + 395 * q^42 - 86 * q^43 - 443 * q^44 - 1483 * q^45 - 270 * q^46 - 1005 * q^47 - 1013 * q^48 - 277 * q^49 + 239 * q^50 - 1719 * q^51 + 670 * q^52 + 258 * q^53 + 910 * q^54 - 870 * q^55 + 714 * q^56 + 566 * q^57 - 474 * q^58 - 1665 * q^59 + 4 * q^60 + 439 * q^61 + 1812 * q^62 + 493 * q^63 + 872 * q^64 - 613 * q^65 + 3073 * q^66 + 295 * q^67 + 2748 * q^68 + 1389 * q^69 - 1044 * q^70 + 636 * q^71 + 981 * q^72 - 338 * q^73 - 2238 * q^74 - 1064 * q^75 + 1006 * q^76 - 2909 * q^77 + 157 * q^78 + 133 * q^79 - 4817 * q^80 + 1325 * q^81 + 6 * q^82 - 1356 * q^83 - 7081 * q^84 + 483 * q^85 + 6686 * q^86 + 2774 * q^87 - 738 * q^88 - 2200 * q^89 + 2665 * q^90 + 1552 * q^91 - 396 * q^92 + 4365 * q^93 - 1191 * q^94 + 3083 * q^95 - 1468 * q^96 - 266 * q^97 + 3601 * q^98 - 5395 * q^99

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