LMFDB - Embedded newform 51.3.f.a.38.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,3,Mod(38,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.38"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.38964934824$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 62 x^{18} + 1545 x^{16} + 20120 x^{14} + 149608 x^{12} + 655792 x^{10} + 1690896 x^{8} + \cdots + 36864 $ x^20 + 62x^18 + 1545x^16 + 20120x^14 + 149608x^12 + 655792x^10 + 1690896x^8 + 2476352x^6 + 1880640x^4 + 593152*x^2 + 36864
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.7
Root			$0.284142i$ of defining polynomial
Character	$\chi$	$=$	51.38
Dual form			51.3.f.a.47.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.28414 q^{2} +(2.92586 - 0.662833i) q^{3} -2.35098 q^{4} +(2.50753 + 2.50753i) q^{5} +(3.75722 - 0.851171i) q^{6} +(-3.77510 - 3.77510i) q^{7} -8.15556 q^{8} +(8.12131 - 3.87871i) q^{9} +(3.22003 + 3.22003i) q^{10} +(-8.31510 + 8.31510i) q^{11} +(-6.87863 + 1.55831i) q^{12} +3.14376 q^{13} +(-4.84777 - 4.84777i) q^{14} +(8.99877 + 5.67462i) q^{15} -1.06899 q^{16} +(-9.78386 - 13.9024i) q^{17} +(10.4289 - 4.98082i) q^{18} +12.4867i q^{19} +(-5.89516 - 5.89516i) q^{20} +(-13.5477 - 8.54316i) q^{21} +(-10.6778 + 10.6778i) q^{22} +(-12.7032 + 12.7032i) q^{23} +(-23.8620 + 5.40577i) q^{24} -12.4245i q^{25} +4.03704 q^{26} +(21.1909 - 16.7316i) q^{27} +(8.87518 + 8.87518i) q^{28} +(27.7634 + 27.7634i) q^{29} +(11.5557 + 7.28702i) q^{30} +(38.3677 - 38.3677i) q^{31} +31.2495 q^{32} +(-18.8173 + 29.8403i) q^{33} +(-12.5639 - 17.8526i) q^{34} -18.9324i q^{35} +(-19.0930 + 9.11876i) q^{36} +(9.59085 - 9.59085i) q^{37} +16.0348i q^{38} +(9.19820 - 2.08379i) q^{39} +(-20.4504 - 20.4504i) q^{40} +(19.4127 - 19.4127i) q^{41} +(-17.3971 - 10.9706i) q^{42} +76.3223i q^{43} +(19.5486 - 19.5486i) q^{44} +(30.0905 + 10.6385i) q^{45} +(-16.3127 + 16.3127i) q^{46} +4.62947i q^{47} +(-3.12770 + 0.708559i) q^{48} -20.4972i q^{49} -15.9549i q^{50} +(-37.8411 - 34.1913i) q^{51} -7.39092 q^{52} -11.0714 q^{53} +(27.2121 - 21.4858i) q^{54} -41.7008 q^{55} +(30.7881 + 30.7881i) q^{56} +(8.27662 + 36.5345i) q^{57} +(35.6521 + 35.6521i) q^{58} -90.6793 q^{59} +(-21.1559 - 13.3409i) q^{60} +(0.602631 + 0.602631i) q^{61} +(49.2696 - 49.2696i) q^{62} +(-45.3013 - 16.0162i) q^{63} +44.4048 q^{64} +(7.88309 + 7.88309i) q^{65} +(-24.1641 + 38.3193i) q^{66} -122.226 q^{67} +(23.0016 + 32.6842i) q^{68} +(-28.7477 + 45.5879i) q^{69} -24.3119i q^{70} +(-64.8440 - 64.8440i) q^{71} +(-66.2338 + 31.6331i) q^{72} +(-0.537311 + 0.537311i) q^{73} +(12.3160 - 12.3160i) q^{74} +(-8.23539 - 36.3525i) q^{75} -29.3561i q^{76} +62.7807 q^{77} +(11.8118 - 2.67588i) q^{78} +(90.5467 + 90.5467i) q^{79} +(-2.68052 - 2.68052i) q^{80} +(50.9112 - 63.0004i) q^{81} +(24.9287 - 24.9287i) q^{82} -24.5241 q^{83} +(31.8503 + 20.0848i) q^{84} +(10.3273 - 59.3941i) q^{85} +98.0086i q^{86} +(99.6341 + 62.8292i) q^{87} +(67.8143 - 67.8143i) q^{88} +36.2481i q^{89} +(38.6404 + 13.6613i) q^{90} +(-11.8680 - 11.8680i) q^{91} +(29.8650 - 29.8650i) q^{92} +(86.8272 - 137.690i) q^{93} +5.94489i q^{94} +(-31.3110 + 31.3110i) q^{95} +(91.4317 - 20.7132i) q^{96} +(8.31577 - 8.31577i) q^{97} -26.3213i q^{98} +(-35.2776 + 99.7814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 24 q^{4} - 2 q^{6} - 4 q^{7} - 16 q^{10} - 42 q^{12} - 12 q^{13} - 64 q^{16} - 4 q^{18} + 88 q^{21} - 40 q^{22} - 82 q^{24} + 54 q^{27} - 160 q^{28} + 48 q^{31} + 264 q^{33} + 152 q^{34}+ \cdots - 864 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 24 * q^4 - 2 * q^6 - 4 * q^7 - 16 * q^10 - 42 * q^12 - 12 * q^13 - 64 * q^16 - 4 * q^18 + 88 * q^21 - 40 * q^22 - 82 * q^24 + 54 * q^27 - 160 * q^28 + 48 * q^31 + 264 * q^33 + 152 * q^34 + 32 * q^37 + 56 * q^39 + 52 * q^40 + 64 * q^45 + 388 * q^46 - 230 * q^48 - 298 * q^51 + 64 * q^52 - 254 * q^54 - 204 * q^55 - 24 * q^57 + 396 * q^58 - 336 * q^61 - 400 * q^63 - 480 * q^64 - 408 * q^67 - 132 * q^69 + 276 * q^72 - 88 * q^73 - 358 * q^75 + 380 * q^78 - 172 * q^79 + 388 * q^81 + 372 * q^82 + 1320 * q^84 + 648 * q^85 - 156 * q^88 + 672 * q^90 - 124 * q^91 + 194 * q^96 + 688 * q^97 - 864 * q^99

Character values

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

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.28414			0.642071			0.321036	−	0.947067i	$-0.395969\pi$
$2$	1.28414			0.642071			0.321036	+	0.947067i	$0.395969\pi$
$3$	2.92586	−	0.662833i	0.975286	−	0.220944i
$3$	2.92586	−	0.662833i	0.975286	−	0.220944i
$4$	−2.35098			−0.587745
$5$	2.50753	+	2.50753i	0.501507	+	0.501507i	0.911906	−	0.410399i	$-0.134611\pi$
$5$	2.50753	+	2.50753i	0.501507	+	0.501507i	−0.410399	+	0.911906i	$0.634611\pi$
$6$	3.75722	−	0.851171i	0.626203	−	0.141862i
$7$	−3.77510	−	3.77510i	−0.539300	−	0.539300i	0.384023	−	0.923323i	$-0.374538\pi$
$7$	−3.77510	−	3.77510i	−0.539300	−	0.539300i	−0.923323	+	0.384023i	$0.874538\pi$
$8$	−8.15556			−1.01945
$9$	8.12131	−	3.87871i	0.902367	−	0.430968i
$10$	3.22003	+	3.22003i	0.322003	+	0.322003i
$11$	−8.31510	+	8.31510i	−0.755919	+	0.755919i	−0.975577	−	0.219658i	$-0.929506\pi$
$11$	−8.31510	+	8.31510i	−0.755919	+	0.755919i	0.219658	+	0.975577i	$0.429506\pi$
$12$	−6.87863	+	1.55831i	−0.573219	+	0.129859i
$13$	3.14376			0.241828			0.120914	−	0.992663i	$-0.461417\pi$
$13$	3.14376			0.241828			0.120914	+	0.992663i	$0.461417\pi$
$14$	−4.84777	−	4.84777i	−0.346269	−	0.346269i
$15$	8.99877	+	5.67462i	0.599918	+	0.378308i
$16$	−1.06899			−0.0668116
$17$	−9.78386	−	13.9024i	−0.575521	−	0.817787i
$17$	−9.78386	−	13.9024i	−0.575521	−	0.817787i
$18$	10.4289	−	4.98082i	0.579384	−	0.276712i
$19$			12.4867i			0.657197i	0.944470	+	0.328599i	$0.106576\pi$
$19$			12.4867i			0.657197i	−0.944470	+	0.328599i	$0.893424\pi$
$20$	−5.89516	−	5.89516i	−0.294758	−	0.294758i
$21$	−13.5477	−	8.54316i	−0.645127	−	0.406817i
$22$	−10.6778	+	10.6778i	−0.485353	+	0.485353i
$23$	−12.7032	+	12.7032i	−0.552313	+	0.552313i	−0.927108	−	0.374795i	$-0.877713\pi$
$23$	−12.7032	+	12.7032i	−0.552313	+	0.552313i	0.374795	+	0.927108i	$0.377713\pi$
$24$	−23.8620	+	5.40577i	−0.994251	+	0.225240i
$25$		−	12.4245i		−	0.496982i
$26$	4.03704			0.155271
$27$	21.1909	−	16.7316i	0.784847	−	0.619690i
$28$	8.87518	+	8.87518i	0.316971	+	0.316971i
$29$	27.7634	+	27.7634i	0.957357	+	0.957357i	0.999127	−	0.0417701i	$-0.0132997\pi$
$29$	27.7634	+	27.7634i	0.957357	+	0.957357i	−0.0417701	+	0.999127i	$0.513300\pi$
$30$	11.5557	+	7.28702i	0.385190	+	0.242901i
$31$	38.3677	−	38.3677i	1.23767	−	1.23767i	0.276717	−	0.960951i	$-0.410754\pi$
$31$	38.3677	−	38.3677i	1.23767	−	1.23767i	0.960951	−	0.276717i	$-0.0892464\pi$
$32$	31.2495			0.976547
$33$	−18.8173	+	29.8403i	−0.570221	+	0.904253i
$34$	−12.5639	−	17.8526i	−0.369525	−	0.525077i
$35$		−	18.9324i		−	0.540926i
$36$	−19.0930	+	9.11876i	−0.530362	+	0.253299i
$37$	9.59085	−	9.59085i	0.259212	−	0.259212i	−0.565521	−	0.824734i	$-0.691325\pi$
$37$	9.59085	−	9.59085i	0.259212	−	0.259212i	0.824734	+	0.565521i	$0.191325\pi$
$38$			16.0348i			0.421967i
$39$	9.19820	−	2.08379i	0.235851	−	0.0534305i
$40$	−20.4504	−	20.4504i	−0.511259	−	0.511259i
$41$	19.4127	−	19.4127i	0.473481	−	0.473481i	−0.429558	−	0.903039i	$-0.641331\pi$
$41$	19.4127	−	19.4127i	0.473481	−	0.473481i	0.903039	+	0.429558i	$0.141331\pi$
$42$	−17.3971	−	10.9706i	−0.414218	−	0.261205i
$43$			76.3223i			1.77494i	0.460869	+	0.887468i	$0.347538\pi$
$43$			76.3223i			1.77494i	−0.460869	+	0.887468i	$0.652462\pi$
$44$	19.5486	−	19.5486i	0.444287	−	0.444287i
$45$	30.0905	+	10.6385i	0.668677	+	0.236410i
$46$	−16.3127	+	16.3127i	−0.354624	+	0.354624i
$47$			4.62947i			0.0984993i	0.998787	+	0.0492496i	$0.0156830\pi$
$47$			4.62947i			0.0984993i	−0.998787	+	0.0492496i	$0.984317\pi$
$48$	−3.12770	+	0.708559i	−0.0651605	+	0.0147616i
$49$		−	20.4972i		−	0.418311i
$50$		−	15.9549i		−	0.319098i
$51$	−37.8411	−	34.1913i	−0.741983	−	0.670419i
$52$	−7.39092			−0.142133
$53$	−11.0714			−0.208895			−0.104447	−	0.994530i	$-0.533307\pi$
$53$	−11.0714			−0.208895			−0.104447	+	0.994530i	$0.533307\pi$
$54$	27.2121	−	21.4858i	0.503927	−	0.397885i
$55$	−41.7008			−0.758197
$56$	30.7881	+	30.7881i	0.549787	+	0.549787i
$57$	8.27662	+	36.5345i	0.145204	+	0.640956i
$58$	35.6521	+	35.6521i	0.614691	+	0.614691i
$59$	−90.6793			−1.53694			−0.768469	−	0.639887i	$-0.778981\pi$
$59$	−90.6793			−1.53694			−0.768469	+	0.639887i	$0.778981\pi$
$60$	−21.1559	−	13.3409i	−0.352599	−	0.222348i
$61$	0.602631	+	0.602631i	0.00987920	+	0.00987920i	0.712029	−	0.702150i	$-0.247776\pi$
$61$	0.602631	+	0.602631i	0.00987920	+	0.00987920i	−0.702150	+	0.712029i	$0.747776\pi$
$62$	49.2696	−	49.2696i	0.794671	−	0.794671i
$63$	−45.3013	−	16.0162i	−0.719068	−	0.254226i
$64$	44.4048			0.693824
$65$	7.88309	+	7.88309i	0.121278	+	0.121278i
$66$	−24.1641	+	38.3193i	−0.366123	+	0.580595i
$67$	−122.226			−1.82428			−0.912138	−	0.409884i	$-0.865569\pi$
$67$	−122.226			−1.82428			−0.912138	+	0.409884i	$0.865569\pi$
$68$	23.0016	+	32.6842i	0.338259	+	0.480650i
$69$	−28.7477	+	45.5879i	−0.416633	+	0.660694i
$70$		−	24.3119i		−	0.347313i
$71$	−64.8440	−	64.8440i	−0.913296	−	0.913296i	0.0832343	−	0.996530i	$-0.473475\pi$
$71$	−64.8440	−	64.8440i	−0.913296	−	0.913296i	−0.996530	+	0.0832343i	$0.973475\pi$
$72$	−66.2338	+	31.6331i	−0.919914	+	0.439348i
$73$	−0.537311	+	0.537311i	−0.00736043	+	0.00736043i	−0.710777	−	0.703417i	$-0.751657\pi$
$73$	−0.537311	+	0.537311i	−0.00736043	+	0.00736043i	0.703417	+	0.710777i	$0.251657\pi$
$74$	12.3160	−	12.3160i	0.166433	−	0.166433i
$75$	−8.23539	−	36.3525i	−0.109805	−	0.484699i
$76$		−	29.3561i		−	0.386264i
$77$	62.7807			0.815334
$78$	11.8118	−	2.67588i	0.151433	−	0.0343062i
$79$	90.5467	+	90.5467i	1.14616	+	1.14616i	0.987301	+	0.158860i	$0.0507819\pi$
$79$	90.5467	+	90.5467i	1.14616	+	1.14616i	0.158860	+	0.987301i	$0.449218\pi$
$80$	−2.68052	−	2.68052i	−0.0335065	−	0.0335065i
$81$	50.9112	−	63.0004i	0.628534	−	0.777782i
$82$	24.9287	−	24.9287i	0.304008	−	0.304008i
$83$	−24.5241			−0.295471			−0.147735	−	0.989027i	$-0.547198\pi$
$83$	−24.5241			−0.295471			−0.147735	+	0.989027i	$0.547198\pi$
$84$	31.8503	+	20.0848i	0.379170	+	0.239104i
$85$	10.3273	−	59.3941i	0.121498	−	0.698754i
$86$			98.0086i			1.13964i
$87$	99.6341	+	62.8292i	1.14522	+	0.722175i
$88$	67.8143	−	67.8143i	0.770617	−	0.770617i
$89$			36.2481i			0.407282i	0.979046	+	0.203641i	$0.0652775\pi$
$89$			36.2481i			0.407282i	−0.979046	+	0.203641i	$0.934722\pi$
$90$	38.6404	+	13.6613i	0.429338	+	0.151792i
$91$	−11.8680	−	11.8680i	−0.130418	−	0.130418i
$92$	29.8650	−	29.8650i	0.324619	−	0.324619i
$93$	86.8272	−	137.690i	0.933626	−	1.48054i
$94$			5.94489i			0.0632435i
$95$	−31.3110	+	31.3110i	−0.329589	+	0.329589i
$96$	91.4317	−	20.7132i	0.952413	−	0.215762i
$97$	8.31577	−	8.31577i	0.0857296	−	0.0857296i	−0.662942	−	0.748671i	$-0.730692\pi$
$97$	8.31577	−	8.31577i	0.0857296	−	0.0857296i	0.748671	+	0.662942i	$0.230692\pi$
$98$		−	26.3213i		−	0.268585i
$99$	−35.2776	+	99.7814i	−0.356340	+	1.00789i
$100$			29.2098i			0.292098i
$101$			173.133i			1.71419i	0.515159	+	0.857095i	$0.327733\pi$
$101$			173.133i			1.71419i	−0.515159	+	0.857095i	$0.672267\pi$
$102$	−48.5934	−	43.9066i	−0.476406	−	0.430456i
$103$	0.780246			0.00757521			0.00378760	−	0.999993i	$-0.498794\pi$
$103$	0.780246			0.00757521			0.00378760	+	0.999993i	$0.498794\pi$
$104$	−25.6391			−0.246530
$105$	−12.5490	−	55.3935i	−0.119514	−	0.527557i
$106$	−14.2173			−0.134125
$107$	−127.556	−	127.556i	−1.19211	−	1.19211i	−0.976474	−	0.215636i	$-0.930818\pi$
$107$	−127.556	−	127.556i	−1.19211	−	1.19211i	−0.215636	−	0.976474i	$-0.569182\pi$
$108$	−49.8193	+	39.3357i	−0.461290	+	0.364219i
$109$	37.4643	+	37.4643i	0.343709	+	0.343709i	0.857760	−	0.514051i	$-0.171856\pi$
$109$	37.4643	+	37.4643i	0.343709	+	0.343709i	−0.514051	+	0.857760i	$0.671856\pi$
$110$	−53.5498			−0.486816
$111$	21.7043	−	34.4186i	0.195535	−	0.310078i
$112$	4.03553	+	4.03553i	0.0360315	+	0.0360315i
$113$	17.2064	−	17.2064i	0.152269	−	0.152269i	−0.626862	−	0.779131i	$-0.715661\pi$
$113$	17.2064	−	17.2064i	0.152269	−	0.152269i	0.779131	+	0.626862i	$0.215661\pi$
$114$	10.6284	+	46.9155i	0.0932312	+	0.411539i
$115$	−63.7074			−0.553978
$116$	−65.2711	−	65.2711i	−0.562682	−	0.562682i
$117$	25.5315	−	12.1937i	0.218218	−	0.104220i
$118$	−116.445			−0.986823
$119$	−15.5478	+	89.4179i	−0.130654	+	0.751411i
$120$	−73.3900	−	46.2797i	−0.611583	−	0.385664i
$121$		−	17.2819i		−	0.142826i
$122$	0.773864	+	0.773864i	0.00634315	+	0.00634315i
$123$	43.9315	−	69.6663i	0.357167	−	0.566392i
$124$	−90.2017	+	90.2017i	−0.727433	+	0.727433i
$125$	93.8433	−	93.8433i	0.750747	−	0.750747i
$126$	−58.1733	−	20.5671i	−0.461693	−	0.163231i
$127$		−	20.7584i		−	0.163452i	−0.996655	−	0.0817260i	$-0.973957\pi$
$127$		−	20.7584i		−	0.163452i	0.996655	−	0.0817260i	$-0.0260432\pi$
$128$	−67.9760			−0.531063
$129$	50.5889	+	223.308i	0.392162	+	1.73107i
$130$	10.1230	+	10.1230i	0.0778693	+	0.0778693i
$131$	79.5242	+	79.5242i	0.607055	+	0.607055i	0.942175	−	0.335120i	$-0.108777\pi$
$131$	79.5242	+	79.5242i	0.607055	+	0.607055i	−0.335120	+	0.942175i	$0.608777\pi$
$132$	44.2391	−	70.1540i	0.335144	−	0.531470i
$133$	47.1387	−	47.1387i	0.354427	−	0.354427i
$134$	−156.956			−1.17131
$135$	95.0920	+	11.1817i	0.704385	+	0.0828274i
$136$	79.7928	+	113.382i	0.586712	+	0.833689i
$137$		−	169.532i		−	1.23746i	−0.785602	−	0.618732i	$-0.787647\pi$
$137$		−	169.532i		−	1.23746i	0.785602	−	0.618732i	$-0.212353\pi$
$138$	−36.9161	+	58.5413i	−0.267508	+	0.424212i
$139$	20.3389	−	20.3389i	0.146323	−	0.146323i	−0.630150	−	0.776473i	$-0.717007\pi$
$139$	20.3389	−	20.3389i	0.146323	−	0.146323i	0.776473	+	0.630150i	$0.217007\pi$
$140$			44.5097i			0.317926i
$141$	3.06856	+	13.5452i	0.0217628	+	0.0960650i
$142$	−83.2689	−	83.2689i	−0.586401	−	0.586401i
$143$	−26.1407	+	26.1407i	−0.182802	+	0.182802i
$144$	−8.68156	+	4.14629i	−0.0602886	+	0.0287937i
$145$			139.235i			0.960243i
$146$	−0.689984	+	0.689984i	−0.00472592	+	0.00472592i
$147$	−13.5862	−	59.9720i	−0.0924233	−	0.407973i
$148$	−22.5479	+	22.5479i	−0.152351	+	0.152351i
$149$			27.3025i			0.183238i	0.995794	+	0.0916190i	$0.0292042\pi$
$149$			27.3025i			0.183238i	−0.995794	+	0.0916190i	$0.970796\pi$
$150$	−10.5754	−	46.6817i	−0.0705027	−	0.311211i
$151$		−	132.262i		−	0.875909i	−0.898997	−	0.437954i	$-0.855703\pi$
$151$		−	132.262i		−	0.875909i	0.898997	−	0.437954i	$-0.144297\pi$
$152$		−	101.836i		−	0.669976i
$153$	−133.381	−	74.9567i	−0.871771	−	0.489913i
$154$	80.6194			0.523502
$155$	192.417			1.24140
$156$	−21.6248	+	4.89894i	−0.138620	+	0.0314035i
$157$	41.4444			0.263977			0.131989	−	0.991251i	$-0.457864\pi$
$157$	41.4444			0.263977			0.131989	+	0.991251i	$0.457864\pi$
$158$	116.275	+	116.275i	0.735917	+	0.735917i
$159$	−32.3934	+	7.33850i	−0.203732	+	0.0461541i
$160$	78.3592	+	78.3592i	0.489745	+	0.489745i
$161$	95.9117			0.595725
$162$	65.3773	−	80.9015i	0.403563	−	0.499392i
$163$	−38.1113	−	38.1113i	−0.233812	−	0.233812i	0.580470	−	0.814282i	$-0.302869\pi$
$163$	−38.1113	−	38.1113i	−0.233812	−	0.233812i	−0.814282	+	0.580470i	$0.802869\pi$
$164$	−45.6389	+	45.6389i	−0.278286	+	0.278286i
$165$	−122.011	+	27.6407i	−0.739459	+	0.167519i
$166$	−31.4924			−0.189713
$167$	−38.0861	−	38.0861i	−0.228060	−	0.228060i	0.583822	−	0.811882i	$-0.301557\pi$
$167$	−38.0861	−	38.0861i	−0.228060	−	0.228060i	−0.811882	+	0.583822i	$0.801557\pi$
$168$	110.489	+	69.6742i	0.657672	+	0.414728i
$169$	−159.117			−0.941519
$170$	13.2618	−	76.2704i	0.0780104	−	0.448650i
$171$	48.4325	+	101.409i	0.283231	+	0.593033i
$172$		−	179.432i		−	1.04321i
$173$	150.781	+	150.781i	0.871565	+	0.871565i	0.992643	−	0.121078i	$-0.0386350\pi$
$173$	150.781	+	150.781i	0.871565	+	0.871565i	−0.121078	+	0.992643i	$0.538635\pi$
$174$	127.944	+	80.6817i	0.735313	+	0.463688i
$175$	−46.9039	+	46.9039i	−0.268022	+	0.268022i
$176$	8.88873	−	8.88873i	0.0505041	−	0.0505041i
$177$	−265.315	+	60.1052i	−1.49895	+	0.339577i
$178$			46.5477i			0.261504i
$179$	115.141			0.643248			0.321624	−	0.946867i	$-0.395771\pi$
$179$	115.141			0.643248			0.321624	+	0.946867i	$0.395771\pi$
$180$	−70.7420	−	25.0108i	−0.393011	−	0.138949i
$181$	−148.256	−	148.256i	−0.819095	−	0.819095i	0.166882	−	0.985977i	$-0.446630\pi$
$181$	−148.256	−	148.256i	−0.819095	−	0.819095i	−0.985977	+	0.166882i	$0.946630\pi$
$182$	−15.2402	−	15.2402i	−0.0837375	−	0.0837375i
$183$	2.16266	+	1.36377i	0.0118178	+	0.00745230i
$184$	103.602	−	103.602i	0.563053	−	0.563053i
$185$	48.0988			0.259993
$186$	111.498	−	176.813i	0.599454	−	0.950610i
$187$	196.954	+	34.2459i	1.05323	+	0.183133i
$188$		−	10.8838i		−	0.0578924i
$189$	−143.161	−	16.8341i	−0.757467	−	0.0890692i
$190$	−40.2077	+	40.2077i	−0.211620	+	0.211620i
$191$			117.726i			0.616366i	0.951327	+	0.308183i	$0.0997209\pi$
$191$			117.726i			0.616366i	−0.951327	+	0.308183i	$0.900279\pi$
$192$	129.922	−	29.4329i	0.676678	−	0.153296i
$193$	149.549	+	149.549i	0.774867	+	0.774867i	0.978953	−	0.204086i	$-0.0654223\pi$
$193$	149.549	+	149.549i	0.774867	+	0.774867i	−0.204086	+	0.978953i	$0.565422\pi$
$194$	10.6786	−	10.6786i	0.0550445	−	0.0550445i
$195$	28.2900	+	17.8396i	0.145077	+	0.0914854i
$196$			48.1885i			0.245860i
$197$	226.468	−	226.468i	1.14958	−	1.14958i	0.162950	−	0.986634i	$-0.447899\pi$
$197$	226.468	−	226.468i	1.14958	−	1.14958i	0.986634	−	0.162950i	$-0.0521009\pi$
$198$	−45.3015	+	128.133i	−0.228795	+	0.647139i
$199$	264.902	−	264.902i	1.33116	−	1.33116i	0.426834	−	0.904330i	$-0.359629\pi$
$199$	264.902	−	264.902i	1.33116	−	1.33116i	0.904330	−	0.426834i	$-0.140371\pi$
$200$			101.329i			0.506645i
$201$	−357.617	+	81.0157i	−1.77919	+	0.403063i
$202$			222.328i			1.10063i
$203$		−	209.619i		−	1.03261i
$204$	88.9637	+	80.3831i	0.436097	+	0.394035i
$205$	97.3561			0.474908
$206$	1.00195			0.00486382
$207$	−53.8946	+	152.439i	−0.260360	+	0.736418i
$208$	−3.36064			−0.0161569
$209$	−103.829	−	103.829i	−0.496788	−	0.496788i
$210$	−16.1147	−	71.1332i	−0.0767367	−	0.338729i
$211$	30.9868	+	30.9868i	0.146857	+	0.146857i	0.776712	−	0.629855i	$-0.216886\pi$
$211$	30.9868	+	30.9868i	0.146857	+	0.146857i	−0.629855	+	0.776712i	$0.716886\pi$
$212$	26.0287			0.122777
$213$	−232.705	−	146.744i	−1.09251	−	0.688938i
$214$	−163.800	−	163.800i	−0.765419	−	0.765419i
$215$	−191.381	+	191.381i	−0.890143	+	0.890143i
$216$	−172.823	+	136.456i	−0.800108	+	0.631740i
$217$	−289.684			−1.33495
$218$	48.1095	+	48.1095i	0.220686	+	0.220686i
$219$	−1.21595	+	1.92825i	−0.00555228	+	0.00880477i
$220$	98.0377			0.445626
$221$	−30.7581	−	43.7058i	−0.139177	−	0.197764i
$222$	27.8715	−	44.1984i	0.125547	−	0.199092i
$223$			144.813i			0.649386i	0.945819	+	0.324693i	$0.105261\pi$
$223$			144.813i			0.649386i	−0.945819	+	0.324693i	$0.894739\pi$
$224$	−117.970	−	117.970i	−0.526652	−	0.526652i
$225$	−48.1912	−	100.903i	−0.214183	−	0.448460i
$226$	22.0955	−	22.0955i	0.0977676	−	0.0977676i
$227$	−139.620	+	139.620i	−0.615064	+	0.615064i	−0.944261	−	0.329197i	$-0.893222\pi$
$227$	−139.620	+	139.620i	−0.615064	+	0.615064i	0.329197	+	0.944261i	$0.393222\pi$
$228$	−19.4582	−	85.8918i	−0.0853428	−	0.376718i
$229$			327.781i			1.43136i	0.698429	+	0.715680i	$0.253883\pi$
$229$			327.781i			1.43136i	−0.698429	+	0.715680i	$0.746117\pi$
$230$	−81.8094			−0.355693
$231$	183.688	−	41.6131i	0.795184	−	0.180143i
$232$	−226.426	−	226.426i	−0.975973	−	0.975973i
$233$	−169.516	−	169.516i	−0.727537	−	0.727537i	0.242592	−	0.970128i	$-0.422002\pi$
$233$	−169.516	−	169.516i	−0.727537	−	0.727537i	−0.970128	+	0.242592i	$0.922002\pi$
$234$	32.7860	−	15.6585i	0.140111	−	0.0669167i
$235$	−11.6085	+	11.6085i	−0.0493981	+	0.0493981i
$236$	213.185			0.903327
$237$	324.944	+	204.910i	1.37107	+	0.864598i
$238$	−19.9656	+	114.825i	−0.0838892	+	0.482460i
$239$		−	213.706i		−	0.894166i	−0.894492	−	0.447083i	$-0.852463\pi$
$239$		−	213.706i		−	0.894166i	0.894492	−	0.447083i	$-0.147537\pi$
$240$	−9.61956	−	6.06609i	−0.0400815	−	0.0252754i
$241$	−138.841	+	138.841i	−0.576105	+	0.576105i	−0.933828	−	0.357723i	$-0.883553\pi$
$241$	−138.841	+	138.841i	−0.576105	+	0.576105i	0.357723	+	0.933828i	$0.383553\pi$
$242$		−	22.1924i		−	0.0917042i
$243$	107.200	−	218.076i	0.441154	−	0.897432i
$244$	−1.41677	−	1.41677i	−0.00580644	−	0.00580644i
$245$	51.3975	−	51.3975i	0.209786	−	0.209786i
$246$	56.4143	−	89.4614i	0.229326	−	0.363664i
$247$			39.2554i			0.158929i
$248$	−312.910	+	312.910i	−1.26173	+	1.26173i
$249$	−71.7540	+	16.2554i	−0.288169	+	0.0652826i
$250$	120.508	−	120.508i	0.482033	−	0.482033i
$251$			292.094i			1.16372i	0.813289	+	0.581860i	$0.197675\pi$
$251$			292.094i			1.16372i	−0.813289	+	0.581860i	$0.802325\pi$
$252$	106.502	+	37.6538i	0.422628	+	0.149420i
$253$		−	211.257i		−	0.835007i
$254$		−	26.6568i		−	0.104948i
$255$	−9.15198	−	180.624i	−0.0358901	−	0.708329i
$256$	−264.910			−1.03480
$257$	−288.943			−1.12429			−0.562145	−	0.827039i	$-0.690024\pi$
$257$	−288.943			−1.12429			−0.562145	+	0.827039i	$0.690024\pi$
$258$	64.9633	+	286.759i	0.251796	+	1.11147i
$259$	−72.4129			−0.279586
$260$	−18.5330	−	18.5330i	−0.0712807	−	0.0712807i
$261$	333.161	+	117.789i	1.27648	+	0.451298i
$262$	102.120	+	102.120i	0.389772	+	0.389772i
$263$	104.513			0.397390			0.198695	−	0.980061i	$-0.436330\pi$
$263$	104.513			0.397390			0.198695	+	0.980061i	$0.436330\pi$
$264$	153.466	−	243.365i	0.581309	−	0.921836i
$265$	−27.7620	−	27.7620i	−0.104762	−	0.104762i
$266$	60.5329	−	60.5329i	0.227567	−	0.227567i
$267$	24.0264	+	106.057i	0.0899866	+	0.397217i
$268$	287.352			1.07221
$269$	181.700	+	181.700i	0.675464	+	0.675464i	0.958970	−	0.283507i	$-0.0914978\pi$
$269$	181.700	+	181.700i	0.675464	+	0.675464i	−0.283507	+	0.958970i	$0.591498\pi$
$270$	122.112	+	14.3589i	0.452265	+	0.0531811i
$271$	138.854			0.512375			0.256188	−	0.966627i	$-0.417534\pi$
$271$	138.854			0.512375			0.256188	+	0.966627i	$0.417534\pi$
$272$	10.4588	+	14.8614i	0.0384515	+	0.0546377i
$273$	−42.5907	−	26.8576i	−0.156010	−	0.0983797i
$274$		−	217.704i		−	0.794539i
$275$	103.311	+	103.311i	0.375678	+	0.375678i
$276$	67.5852	−	107.176i	0.244874	−	0.388319i
$277$	89.7588	−	89.7588i	0.324039	−	0.324039i	−0.526275	−	0.850314i	$-0.676412\pi$
$277$	89.7588	−	89.7588i	0.324039	−	0.324039i	0.850314	+	0.526275i	$0.176412\pi$
$278$	26.1180	−	26.1180i	0.0939498	−	0.0939498i
$279$	162.779	−	460.413i	0.583436	−	1.65023i
$280$			154.404i			0.551444i
$281$	−159.678			−0.568248			−0.284124	−	0.958788i	$-0.591703\pi$
$281$	−159.678			−0.568248			−0.284124	+	0.958788i	$0.591703\pi$
$282$	3.94047	+	17.3939i	0.0139733	+	0.0616806i
$283$	−89.8931	−	89.8931i	−0.317644	−	0.317644i	0.530218	−	0.847861i	$-0.322110\pi$
$283$	−89.8931	−	89.8931i	−0.317644	−	0.317644i	−0.847861	+	0.530218i	$0.822110\pi$
$284$	152.447	+	152.447i	0.536785	+	0.536785i
$285$	−70.8575	+	112.365i	−0.248623	+	0.394264i
$286$	−33.5684	+	33.5684i	−0.117372	+	0.117372i
$287$	−146.570			−0.510697
$288$	253.787	−	121.208i	0.881204	−	0.420860i
$289$	−97.5523	+	272.038i	−0.337551	+	0.941307i
$290$			178.798i			0.616544i
$291$	18.8188	−	29.8427i	0.0646694	−	0.102552i
$292$	1.26321	−	1.26321i	0.00432605	−	0.00432605i
$293$		−	447.233i		−	1.52639i	−0.646166	−	0.763197i	$-0.723629\pi$
$293$		−	447.233i		−	1.52639i	0.646166	−	0.763197i	$-0.276371\pi$
$294$	−17.4466	−	77.0126i	−0.0593423	−	0.261947i
$295$	−227.382	−	227.382i	−0.770785	−	0.770785i
$296$	−78.2188	+	78.2188i	−0.264253	+	0.264253i
$297$	−37.0790	+	315.329i	−0.124845	+	1.06172i
$298$			35.0603i			0.117652i
$299$	−39.9358	+	39.9358i	−0.133565	+	0.133565i
$300$	19.3612	+	85.4638i	0.0645374	+	0.284879i
$301$	288.124	−	288.124i	0.957223	−	0.957223i
$302$		−	169.844i		−	0.562396i
$303$	114.758	+	506.563i	0.378740	+	1.67183i
$304$		−	13.3482i		−	0.0439084i
$305$			3.02224i			0.00990897i
$306$	−171.280	−	96.2551i	−0.559739	−	0.314559i
$307$	234.122			0.762612			0.381306	−	0.924449i	$-0.375474\pi$
$307$	234.122			0.762612			0.381306	+	0.924449i	$0.375474\pi$
$308$	−147.596			−0.479208
$309$	2.28289	−	0.517173i	0.00738800	−	0.00167370i
$310$	247.091			0.797066
$311$	163.527	+	163.527i	0.525811	+	0.525811i	0.919321	−	0.393510i	$-0.128739\pi$
$311$	163.527	+	163.527i	0.525811	+	0.525811i	−0.393510	+	0.919321i	$0.628739\pi$
$312$	−75.0165	+	16.9945i	−0.240438	+	0.0544694i
$313$	192.302	+	192.302i	0.614384	+	0.614384i	0.944085	−	0.329701i	$-0.106948\pi$
$313$	192.302	+	192.302i	0.614384	+	0.614384i	−0.329701	+	0.944085i	$0.606948\pi$
$314$	53.2205			0.169492
$315$	−73.4333	−	153.756i	−0.233121	−	0.488114i
$316$	−212.873	−	212.873i	−0.673650	−	0.673650i
$317$	−45.9466	+	45.9466i	−0.144942	+	0.144942i	−0.775854	−	0.630912i	$-0.782681\pi$
$317$	−45.9466	+	45.9466i	−0.144942	+	0.144942i	0.630912	+	0.775854i	$0.282681\pi$
$318$	−41.5978	+	9.42368i	−0.130811	+	0.0296342i
$319$	−461.710			−1.44737
$320$	111.346	+	111.346i	0.347958	+	0.347958i
$321$	−457.758	−	288.662i	−1.42604	−	0.899259i
$322$	123.164			0.382498
$323$	173.596	−	122.169i	0.537447	−	0.378231i
$324$	−119.691	+	148.113i	−0.369417	+	0.457137i
$325$		−	39.0598i		−	0.120184i
$326$	−48.9403	−	48.9403i	−0.150124	−	0.150124i
$327$	134.448	+	84.7827i	0.411155	+	0.259274i
$328$	−158.322	+	158.322i	−0.482688	+	0.482688i
$329$	17.4767	−	17.4767i	0.0531207	−	0.0531207i
$330$	−156.679	+	35.4945i	−0.474785	+	0.107559i
$331$			386.026i			1.16624i	0.812386	+	0.583121i	$0.198168\pi$
$331$			386.026i			1.16624i	−0.812386	+	0.583121i	$0.801832\pi$
$332$	57.6556			0.173661
$333$	40.6901	−	115.090i	0.122192	−	0.345617i
$334$	−48.9080	−	48.9080i	−0.146431	−	0.146431i
$335$	−306.487	−	306.487i	−0.914887	−	0.914887i
$336$	14.4823	+	9.13251i	0.0431020	+	0.0271801i
$337$	281.585	−	281.585i	0.835563	−	0.835563i	−0.152708	−	0.988271i	$-0.548799\pi$
$337$	281.585	−	281.585i	0.835563	−	0.835563i	0.988271	+	0.152708i	$0.0487994\pi$
$338$	−204.329			−0.604522
$339$	38.9386	−	61.7485i	0.114863	−	0.182149i
$340$	−24.2794	+	139.634i	−0.0714099	+	0.410689i
$341$			638.063i			1.87115i
$342$	62.1942	+	130.223i	0.181854	+	0.380770i
$343$	−262.359	+	262.359i	−0.764895	+	0.764895i
$344$		−	622.451i		−	1.80945i
$345$	−186.399	+	42.2274i	−0.540287	+	0.122398i
$346$	193.624	+	193.624i	0.559607	+	0.559607i
$347$	−65.8162	+	65.8162i	−0.189672	+	0.189672i	−0.795554	−	0.605882i	$-0.792820\pi$
$347$	−65.8162	+	65.8162i	−0.189672	+	0.189672i	0.605882	+	0.795554i	$0.292820\pi$
$348$	−234.238	−	147.710i	−0.673097	−	0.424454i
$349$		−	134.299i		−	0.384812i	−0.981315	−	0.192406i	$-0.938371\pi$
$349$		−	134.299i		−	0.384812i	0.981315	−	0.192406i	$-0.0616290\pi$
$350$	−60.2313	+	60.2313i	−0.172089	+	0.172089i
$351$	66.6190	−	52.6002i	0.189798	−	0.149858i
$352$	−259.843	+	259.843i	−0.738190	+	0.738190i
$353$		−	205.257i		−	0.581464i	−0.956805	−	0.290732i	$-0.906101\pi$
$353$		−	205.257i		−	0.581464i	0.956805	−	0.290732i	$-0.0938988\pi$
$354$	−340.702	+	77.1836i	−0.962435	+	0.218033i
$355$		−	325.197i		−	0.916048i
$356$		−	85.2185i		−	0.239378i
$357$	13.7783	+	271.930i	0.0385948	+	0.761709i
$358$	147.858			0.413011
$359$	108.031			0.300921			0.150461	−	0.988616i	$-0.451924\pi$
$359$	108.031			0.300921			0.150461	+	0.988616i	$0.451924\pi$
$360$	−245.405	−	86.7626i	−0.681679	−	0.241007i
$361$	205.081			0.568092
$362$	−190.382	−	190.382i	−0.525917	−	0.525917i
$363$	−11.4550	−	50.5644i	−0.0315565	−	0.139296i
$364$	27.9015	+	27.9015i	0.0766524	+	0.0766524i
$365$	−2.69465			−0.00738261
$366$	2.77716	+	1.75127i	0.00758787	+	0.00478490i
$367$	−37.3027	−	37.3027i	−0.101642	−	0.101642i	0.654457	−	0.756099i	$-0.272897\pi$
$367$	−37.3027	−	37.3027i	−0.101642	−	0.101642i	−0.756099	+	0.654457i	$0.772897\pi$
$368$	13.5795	−	13.5795i	0.0369009	−	0.0369009i
$369$	82.3603	−	232.953i	0.223199	−	0.631309i
$370$	61.7657			0.166934
$371$	41.7958	+	41.7958i	0.112657	+	0.112657i
$372$	−204.129	+	323.706i	−0.548733	+	0.870178i
$373$	−597.865			−1.60286			−0.801428	−	0.598092i	$-0.795926\pi$
$373$	−597.865			−1.60286			−0.801428	+	0.598092i	$0.795926\pi$
$374$	252.916	+	43.9767i	0.676247	+	0.117585i
$375$	212.370	−	336.775i	0.566320	−	0.898066i
$376$		−	37.7559i		−	0.100415i
$377$	87.2814	+	87.2814i	0.231516	+	0.231516i
$378$	−183.839	−	21.6174i	−0.486348	−	0.0571888i
$379$	170.986	−	170.986i	0.451151	−	0.451151i	−0.444585	−	0.895736i	$-0.646649\pi$
$379$	170.986	−	170.986i	0.451151	−	0.451151i	0.895736	+	0.444585i	$0.146649\pi$
$380$	73.6114	−	73.6114i	0.193714	−	0.193714i
$381$	−13.7594	−	60.7362i	−0.0361138	−	0.159413i
$382$			151.177i			0.395751i
$383$	−145.744			−0.380533			−0.190266	−	0.981732i	$-0.560935\pi$
$383$	−145.744			−0.380533			−0.190266	+	0.981732i	$0.560935\pi$
$384$	−198.888	+	45.0567i	−0.517938	+	0.117335i
$385$	157.425	+	157.425i	0.408896	+	0.408896i
$386$	192.043	+	192.043i	0.497520	+	0.497520i
$387$	296.032	+	619.836i	0.764940	+	1.60164i
$388$	−19.5502	+	19.5502i	−0.0503871	+	0.0503871i
$389$	431.129			1.10830			0.554150	−	0.832417i	$-0.313043\pi$
$389$	431.129			1.10830			0.554150	+	0.832417i	$0.313043\pi$
$390$	36.3284	+	22.9086i	0.0931497	+	0.0587401i
$391$	300.891	+	52.3184i	0.769542	+	0.133807i
$392$			167.166i			0.426445i
$393$	285.388	+	179.965i	0.726178	+	0.457927i
$394$	290.817	−	290.817i	0.738115	−	0.738115i
$395$			454.098i			1.14962i
$396$	82.9369	−	234.584i	0.209437	−	0.592384i
$397$	33.7419	+	33.7419i	0.0849922	+	0.0849922i	0.748325	−	0.663333i	$-0.230858\pi$
$397$	33.7419	+	33.7419i	0.0849922	+	0.0849922i	−0.663333	+	0.748325i	$0.730858\pi$
$398$	340.171	−	340.171i	0.854702	−	0.854702i
$399$	106.676	−	169.166i	0.267359	−	0.423976i
$400$			13.2817i			0.0332041i
$401$	290.697	−	290.697i	0.724930	−	0.724930i	−0.244675	−	0.969605i	$-0.578681\pi$
$401$	290.697	−	290.697i	0.724930	−	0.724930i	0.969605	+	0.244675i	$0.0786813\pi$
$402$	−459.232	+	104.036i	−1.14237	+	0.258795i
$403$	120.619	−	120.619i	0.299303	−	0.299303i
$404$		−	407.032i		−	1.00751i
$405$	285.637	−	30.3140i	0.705277	−	0.0748493i
$406$		−	269.181i		−	0.663006i
$407$			159.498i			0.391887i
$408$	308.616	+	278.850i	0.756411	+	0.683455i
$409$	−144.942			−0.354382			−0.177191	−	0.984176i	$-0.556701\pi$
$409$	−144.942			−0.354382			−0.177191	+	0.984176i	$0.556701\pi$
$410$	125.019			0.304925
$411$	−112.372	−	496.028i	−0.273410	−	1.20688i
$412$	−1.83434			−0.00445229
$413$	342.324	+	342.324i	0.828871	+	0.828871i
$414$	−69.2083	+	195.753i	−0.167170	+	0.472833i
$415$	−61.4950	−	61.4950i	−0.148181	−	0.148181i
$416$	98.2410			0.236156
$417$	46.0275	−	72.9901i	0.110378	−	0.175036i
$418$	−133.331	−	133.331i	−0.318973	−	0.318973i
$419$	240.532	−	240.532i	0.574061	−	0.574061i	−0.359200	−	0.933261i	$-0.616950\pi$
$419$	240.532	−	240.532i	0.574061	−	0.574061i	0.933261	+	0.359200i	$0.116950\pi$
$420$	29.5025	+	130.229i	0.0702439	+	0.310069i
$421$	−385.932			−0.916704			−0.458352	−	0.888771i	$-0.651560\pi$
$421$	−385.932			−0.916704			−0.458352	+	0.888771i	$0.651560\pi$
$422$	39.7915	+	39.7915i	0.0942926	+	0.0942926i
$423$	17.9564	+	37.5973i	0.0424500	+	0.0888825i
$424$	90.2937			0.212957
$425$	−172.731	+	121.560i	−0.406425	+	0.286023i
$426$	−298.826	−	188.440i	−0.701471	−	0.442347i
$427$		−	4.54999i		−	0.0106557i
$428$	299.881	+	299.881i	0.700656	+	0.700656i
$429$	−59.1571	+	93.8109i	−0.137895	+	0.218674i
$430$	−245.760	+	245.760i	−0.571535	+	0.571535i
$431$	−166.296	+	166.296i	−0.385838	+	0.385838i	−0.873200	−	0.487362i	$-0.837959\pi$
$431$	−166.296	+	166.296i	−0.385838	+	0.385838i	0.487362	+	0.873200i	$0.337959\pi$
$432$	−22.6527	+	17.8859i	−0.0524369	+	0.0414025i
$433$		−	476.462i		−	1.10037i	−0.835041	−	0.550187i	$-0.814556\pi$
$433$		−	476.462i		−	1.10037i	0.835041	−	0.550187i	$-0.185444\pi$
$434$	−371.996			−0.857133
$435$	92.2896	+	407.383i	0.212160	+	0.936512i
$436$	−88.0777	−	88.0777i	−0.202013	−	0.202013i
$437$	−158.622	−	158.622i	−0.362979	−	0.362979i
$438$	−1.56145	+	2.47614i	−0.00356496	+	0.00565329i
$439$	−256.092	+	256.092i	−0.583352	+	0.583352i	−0.935823	−	0.352471i	$-0.885342\pi$
$439$	−256.092	+	256.092i	−0.583352	+	0.583352i	0.352471	+	0.935823i	$0.385342\pi$
$440$	340.094			0.772940
$441$	−79.5028	−	166.464i	−0.180278	−	0.377470i
$442$	−39.4978	−	56.1244i	−0.0893615	−	0.126978i
$443$		−	838.977i		−	1.89385i	−0.321448	−	0.946927i	$-0.604170\pi$
$443$		−	838.977i		−	1.89385i	0.321448	−	0.946927i	$-0.395830\pi$
$444$	−51.0265	+	80.9174i	−0.114924	+	0.182246i
$445$	−90.8934	+	90.8934i	−0.204255	+	0.204255i
$446$			185.961i			0.416952i
$447$	18.0970	+	79.8832i	0.0404854	+	0.178710i
$448$	−167.632	−	167.632i	−0.374180	−	0.374180i
$449$	−491.600	+	491.600i	−1.09488	+	1.09488i	−0.0998774	+	0.995000i	$0.531845\pi$
$449$	−491.600	+	491.600i	−1.09488	+	1.09488i	−0.995000	+	0.0998774i	$0.968155\pi$
$450$	−61.8843	−	129.574i	−0.137521	−	0.287943i
$451$			322.837i			0.715826i
$452$	−40.4519	+	40.4519i	−0.0894953	+	0.0894953i
$453$	−87.6677	−	386.981i	−0.193527	−	0.854262i
$454$	−179.291	+	179.291i	−0.394915	+	0.394915i
$455$		−	59.5189i		−	0.130811i
$456$	−67.5005	−	297.959i	−0.148027	−	0.653419i
$457$			473.298i			1.03566i	0.855483	+	0.517832i	$0.173261\pi$
$457$			473.298i			1.03566i	−0.855483	+	0.517832i	$0.826739\pi$
$458$			420.918i			0.919035i
$459$	−439.938	−	130.904i	−0.958470	−	0.285193i
$460$	149.775			0.325597
$461$	−142.935			−0.310055			−0.155027	−	0.987910i	$-0.549547\pi$
$461$	−142.935			−0.310055			−0.155027	+	0.987910i	$0.549547\pi$
$462$	235.881	−	53.4371i	0.510565	−	0.115665i
$463$	36.4646			0.0787572			0.0393786	−	0.999224i	$-0.487462\pi$
$463$	36.4646			0.0787572			0.0393786	+	0.999224i	$0.487462\pi$
$464$	−29.6786	−	29.6786i	−0.0639626	−	0.0639626i
$465$	562.984	−	127.540i	1.21072	−	0.274280i
$466$	−217.683	−	217.683i	−0.467130	−	0.467130i
$467$	342.979			0.734430			0.367215	−	0.930136i	$-0.380311\pi$
$467$	342.979			0.734430			0.367215	+	0.930136i	$0.380311\pi$
$468$	−60.0239	+	28.6672i	−0.128256	+	0.0612547i
$469$	461.417	+	461.417i	0.983832	+	0.983832i
$470$	−14.9070	+	14.9070i	−0.0317171	+	0.0317171i
$471$	121.261	−	27.4707i	0.257453	−	0.0583242i
$472$	739.541			1.56682
$473$	−634.627	−	634.627i	−1.34171	−	1.34171i
$474$	417.275	+	263.133i	0.880327	+	0.555133i
$475$	155.142			0.326615
$476$	36.5526	−	210.220i	0.0767913	−	0.441638i
$477$	−89.9144	+	42.9428i	−0.188500	+	0.0900269i
$478$		−	274.429i		−	0.574118i
$479$	−255.653	−	255.653i	−0.533723	−	0.533723i	0.387955	−	0.921678i	$-0.373181\pi$
$479$	−255.653	−	255.653i	−0.533723	−	0.533723i	−0.921678	+	0.387955i	$0.873181\pi$
$480$	281.207	+	177.329i	0.585848	+	0.369436i
$481$	30.1513	−	30.1513i	0.0626847	−	0.0626847i
$482$	−178.292	+	178.292i	−0.369901	+	0.369901i
$483$	280.624	−	63.5734i	0.581003	−	0.131622i
$484$			40.6294i			0.0839450i
$485$	41.7042			0.0859880
$486$	137.661	−	280.040i	0.283252	−	0.576215i
$487$	256.394	+	256.394i	0.526477	+	0.526477i	0.919520	−	0.393043i	$-0.128578\pi$
$487$	256.394	+	256.394i	0.526477	+	0.526477i	−0.393043	+	0.919520i	$0.628578\pi$
$488$	−4.91479	−	4.91479i	−0.0100713	−	0.0100713i
$489$	−136.770	−	86.2469i	−0.279693	−	0.176374i
$490$	66.0017	−	66.0017i	0.134697	−	0.134697i
$491$	−741.566			−1.51032			−0.755158	−	0.655542i	$-0.772440\pi$
$491$	−741.566			−1.51032			−0.755158	+	0.655542i	$0.772440\pi$
$492$	−103.282	+	163.784i	−0.209923	+	0.332894i
$493$	114.344	−	657.609i	0.231935	−	1.33389i
$494$			50.4095i			0.102043i
$495$	−338.665	+	161.745i	−0.684172	+	0.326758i
$496$	−41.0145	+	41.0145i	−0.0826906	+	0.0826906i
$497$			489.585i			0.985081i
$498$	−92.1424	+	20.8742i	−0.185025	+	0.0419161i
$499$	−182.719	−	182.719i	−0.366170	−	0.366170i	0.499908	−	0.866079i	$-0.333367\pi$
$499$	−182.719	−	182.719i	−0.366170	−	0.366170i	−0.866079	+	0.499908i	$0.833367\pi$
$500$	−220.624	+	220.624i	−0.441247	+	0.441247i
$501$	−136.679	−	86.1899i	−0.272813	−	0.172036i
$502$			375.090i			0.747191i
$503$	−286.319	+	286.319i	−0.569222	+	0.569222i	−0.931911	−	0.362688i	$-0.881859\pi$
$503$	−286.319	+	286.319i	−0.569222	+	0.569222i	0.362688	+	0.931911i	$0.381859\pi$
$504$	369.457	+	130.621i	0.733050	+	0.259169i
$505$	−434.137	+	434.137i	−0.859678	+	0.859678i
$506$		−	271.284i		−	0.536134i
$507$	−465.553	+	105.468i	−0.918251	+	0.208023i
$508$			48.8026i			0.0960681i
$509$		−	385.256i		−	0.756887i	−0.925624	−	0.378444i	$-0.876459\pi$
$509$		−	385.256i		−	0.756887i	0.925624	−	0.378444i	$-0.123541\pi$
$510$	−11.7524	−	231.947i	−0.0230440	−	0.454798i
$511$	4.05681			0.00793896
$512$	−68.2780			−0.133355
$513$	208.924	+	264.605i	0.407258	+	0.515799i
$514$	−371.044			−0.721875
$515$	1.95649	+	1.95649i	0.00379902	+	0.00379902i
$516$	−118.933	−	524.993i	−0.230491	−	1.01743i
$517$	−38.4945	−	38.4945i	−0.0744574	−	0.0744574i
$518$	−92.9884			−0.179514
$519$	541.106	+	341.221i	1.04259	+	0.657459i
$520$	−64.2910	−	64.2910i	−0.123637	−	0.123637i
$521$	−12.5129	+	12.5129i	−0.0240170	+	0.0240170i	−0.719013	−	0.694996i	$-0.755406\pi$
$521$	−12.5129	+	12.5129i	−0.0240170	+	0.0240170i	0.694996	+	0.719013i	$0.255406\pi$
$522$	427.826	+	151.257i	0.819590	+	0.289765i
$523$	−9.61347			−0.0183814			−0.00919070	−	0.999958i	$-0.502926\pi$
$523$	−9.61347			−0.0183814			−0.00919070	+	0.999958i	$0.502926\pi$
$524$	−186.960	−	186.960i	−0.356793	−	0.356793i
$525$	−106.145	+	168.324i	−0.202181	+	0.320616i
$526$	134.210			0.255152
$527$	−908.787	−	158.018i	−1.72445	−	0.299845i
$528$	20.1154	−	31.8989i	0.0380974	−	0.0604146i
$529$			206.257i			0.389900i
$530$	−35.6503	−	35.6503i	−0.0672648	−	0.0672648i
$531$	−736.434	+	351.719i	−1.38688	+	0.662371i
$532$	−110.822	+	110.822i	−0.208312	+	0.208312i
$533$	61.0290	−	61.0290i	0.114501	−	0.114501i
$534$	30.8533	+	136.192i	0.0577778	+	0.255041i
$535$		−	639.701i		−	1.19570i
$536$	996.825			1.85975
$537$	336.888	−	76.3195i	0.627351	−	0.142122i
$538$	233.328	+	233.328i	0.433696	+	0.433696i
$539$	170.436	+	170.436i	0.316209	+	0.316209i
$540$	−223.559	−	26.2879i	−0.413998	−	0.0486813i
$541$	324.234	−	324.234i	0.599323	−	0.599323i	−0.340809	−	0.940132i	$-0.610701\pi$
$541$	324.234	−	324.234i	0.599323	−	0.599323i	0.940132	+	0.340809i	$0.110701\pi$
$542$	178.308			0.328981
$543$	−532.046	−	335.508i	−0.979826	−	0.617878i
$544$	−305.741	−	434.443i	−0.562023	−	0.798608i
$545$			187.886i			0.344745i
$546$	−54.6925	−	34.4890i	−0.100169	−	0.0631667i
$547$	262.759	−	262.759i	0.480364	−	0.480364i	−0.424884	−	0.905248i	$-0.639685\pi$
$547$	262.759	−	262.759i	0.480364	−	0.480364i	0.905248	+	0.424884i	$0.139685\pi$
$548$			398.567i			0.727312i
$549$	7.23158	+	2.55672i	0.0131723	+	0.00465705i
$550$	132.666	+	132.666i	0.241212	+	0.241212i
$551$	−346.674	+	346.674i	−0.629173	+	0.629173i
$552$	234.453	−	371.795i	0.424735	−	0.673541i
$553$		−	683.646i		−	1.23625i
$554$	115.263	−	115.263i	0.208056	−	0.208056i
$555$	140.730	−	31.8814i	0.253568	−	0.0574440i
$556$	−47.8163	+	47.8163i	−0.0860006	+	0.0860006i
$557$			413.538i			0.742439i	0.928545	+	0.371219i	$0.121060\pi$
$557$			413.538i			0.742439i	−0.928545	+	0.371219i	$0.878940\pi$
$558$	209.031	−	591.236i	0.374608	−	1.05956i
$559$			239.939i			0.429229i
$560$			20.2385i			0.0361401i
$561$	598.958	−	30.3484i	1.06766	−	0.0540969i
$562$	−205.049			−0.364856
$563$	560.023			0.994713			0.497356	−	0.867546i	$-0.334304\pi$
$563$	560.023			0.994713			0.497356	+	0.867546i	$0.334304\pi$
$564$	−7.21412	−	31.8444i	−0.0127910	−	0.0564617i
$565$	86.2913			0.152728
$566$	−115.436	−	115.436i	−0.203950	−	0.203950i
$567$	−430.028	+	45.6378i	−0.758427	+	0.0804899i
$568$	528.839	+	528.839i	0.931055	+	0.931055i
$569$	21.2798			0.0373985			0.0186993	−	0.999825i	$-0.494047\pi$
$569$	21.2798			0.0373985			0.0186993	+	0.999825i	$0.494047\pi$
$570$	−90.9912	+	144.293i	−0.159634	+	0.253146i
$571$	493.008	+	493.008i	0.863411	+	0.863411i	0.991733	−	0.128322i	$-0.0409590\pi$
$571$	493.008	+	493.008i	0.863411	+	0.863411i	−0.128322	+	0.991733i	$0.540959\pi$
$572$	61.4562	−	61.4562i	0.107441	−	0.107441i
$573$	78.0325	+	344.449i	0.136182	+	0.601133i
$574$	−188.217			−0.327904
$575$	157.831	+	157.831i	0.274489	+	0.274489i
$576$	360.625	−	172.233i	0.626084	−	0.299016i
$577$	−472.279			−0.818508			−0.409254	−	0.912421i	$-0.634211\pi$
$577$	−472.279			−0.818508			−0.409254	+	0.912421i	$0.634211\pi$
$578$	−125.271	+	349.335i	−0.216732	+	0.604386i
$579$	536.686	+	338.434i	0.926919	+	0.584515i
$580$		−	327.339i		−	0.564377i
$581$	92.5809	+	92.5809i	0.159348	+	0.159348i
$582$	24.1660	−	38.3223i	0.0415224	−	0.0658459i
$583$	92.0601	−	92.0601i	0.157907	−	0.157907i
$584$	4.38208	−	4.38208i	0.00750355	−	0.00750355i
$585$	94.5972	+	33.4448i	0.161705	+	0.0571706i
$586$		−	574.311i		−	0.980053i
$587$	483.706			0.824031			0.412015	−	0.911177i	$-0.364825\pi$
$587$	483.706			0.824031			0.412015	+	0.911177i	$0.364825\pi$
$588$	31.9409	+	140.993i	0.0543213	+	0.239784i
$589$	479.088	+	479.088i	0.813392	+	0.813392i
$590$	−291.990	−	291.990i	−0.494899	−	0.494899i
$591$	512.503	−	812.724i	0.867180	−	1.37517i
$592$	−10.2525	+	10.2525i	−0.0173184	+	0.0173184i
$593$	599.472			1.01091			0.505457	−	0.862852i	$-0.331324\pi$
$593$	599.472			1.01091			0.505457	+	0.862852i	$0.331324\pi$
$594$	−47.6148	+	404.928i	−0.0801595	+	0.681697i
$595$	−263.205	+	185.232i	−0.442362	+	0.311314i
$596$		−	64.1875i		−	0.107697i
$597$	599.480	−	950.650i	1.00415	−	1.59238i
$598$	−51.2833	+	51.2833i	−0.0857580	+	0.0857580i
$599$		−	384.650i		−	0.642153i	−0.947053	−	0.321077i	$-0.895955\pi$
$599$		−	384.650i		−	0.642153i	0.947053	−	0.321077i	$-0.104045\pi$
$600$	67.1642	+	296.475i	0.111940	+	0.494124i
$601$	−194.467	−	194.467i	−0.323572	−	0.323572i	0.526563	−	0.850136i	$-0.323480\pi$
$601$	−194.467	−	194.467i	−0.323572	−	0.323572i	−0.850136	+	0.526563i	$0.823480\pi$
$602$	369.993	−	369.993i	0.614606	−	0.614606i
$603$	−992.639	+	474.081i	−1.64617	+	0.786204i
$604$			310.946i			0.514811i
$605$	43.3350	−	43.3350i	0.0716280	−	0.0716280i
$606$	147.366	+	650.499i	0.243178	+	1.07343i
$607$	−110.888	+	110.888i	−0.182682	+	0.182682i	−0.792523	−	0.609842i	$-0.791233\pi$
$607$	−110.888	+	110.888i	−0.182682	+	0.182682i	0.609842	+	0.792523i	$0.291233\pi$
$608$			390.205i			0.641784i
$609$	−138.942	−	613.316i	−0.228148	−	1.00709i
$610$			3.88098i			0.00636227i
$611$			14.5539i			0.0238199i
$612$	313.576	+	176.222i	0.512379	+	0.287944i
$613$	−342.714			−0.559076			−0.279538	−	0.960135i	$-0.590181\pi$
$613$	−342.714			−0.559076			−0.279538	+	0.960135i	$0.590181\pi$
$614$	300.646			0.489651
$615$	284.850	−	64.5308i	0.463171	−	0.104928i
$616$	−512.012			−0.831188
$617$	−167.602	−	167.602i	−0.271639	−	0.271639i	0.558121	−	0.829760i	$-0.311523\pi$
$617$	−167.602	−	167.602i	−0.271639	−	0.271639i	−0.829760	+	0.558121i	$0.811523\pi$
$618$	2.93156	−	0.664123i	0.00474362	−	0.00107463i
$619$	−467.825	−	467.825i	−0.755776	−	0.755776i	0.219775	−	0.975551i	$-0.429468\pi$
$619$	−467.825	−	467.825i	−0.755776	−	0.755776i	−0.975551	+	0.219775i	$0.929468\pi$
$620$	−452.368			−0.729625
$621$	−56.6466	+	481.737i	−0.0912184	+	0.775744i
$622$	209.992	+	209.992i	0.337608	+	0.337608i
$623$	136.840	−	136.840i	0.219647	−	0.219647i
$624$	−9.83275	+	2.22754i	−0.0157576	+	0.00356977i
$625$	160.017			0.256028
$626$	246.944	+	246.944i	0.394479	+	0.394479i
$627$	−372.609	−	234.967i	−0.594273	−	0.374748i
$628$	−97.4349			−0.155151
$629$	−227.171	−	39.5001i	−0.361162	−	0.0627983i
$630$	−94.2988	−	197.444i	−0.149681	−	0.313404i
$631$			509.287i			0.807110i	0.914955	+	0.403555i	$0.132226\pi$
$631$			509.287i			0.807110i	−0.914955	+	0.403555i	$0.867774\pi$
$632$	−738.459	−	738.459i	−1.16845	−	1.16845i
$633$	111.202	+	70.1240i	0.175675	+	0.110780i
$634$	−59.0020	+	59.0020i	−0.0930631	+	0.0930631i
$635$	52.0524	−	52.0524i	0.0819723	−	0.0819723i
$636$	76.1563	−	17.2527i	0.119743	−	0.0271268i
$637$		−	64.4384i		−	0.101159i
$638$	−592.902			−0.929313
$639$	−778.129	−	275.107i	−1.21773	−	0.430527i
$640$	−170.452	−	170.452i	−0.266332	−	0.266332i
$641$	320.062	+	320.062i	0.499317	+	0.499317i	0.911225	−	0.411909i	$-0.135138\pi$
$641$	320.062	+	320.062i	0.499317	+	0.499317i	−0.411909	+	0.911225i	$0.635138\pi$
$642$	−587.827	−	370.683i	−0.915618	−	0.577388i
$643$	−323.732	+	323.732i	−0.503471	+	0.503471i	−0.912515	−	0.409044i	$-0.865862\pi$
$643$	−323.732	+	323.732i	−0.503471	+	0.503471i	0.409044	+	0.912515i	$0.365862\pi$
$644$	−225.486			−0.350134
$645$	−433.100	+	686.806i	−0.671472	+	1.06482i
$646$	222.921	−	156.882i	0.345079	−	0.242851i
$647$		−	199.285i		−	0.308014i	−0.988070	−	0.154007i	$-0.950782\pi$
$647$		−	199.285i		−	0.308014i	0.988070	−	0.154007i	$-0.0492179\pi$
$648$	−415.210	+	513.803i	−0.640755	+	0.792906i
$649$	754.008	−	754.008i	1.16180	−	1.16180i
$650$		−	50.1583i		−	0.0771667i
$651$	−847.575	+	192.012i	−1.30196	+	0.294949i
$652$	89.5989	+	89.5989i	0.137422	+	0.137422i
$653$	544.966	−	544.966i	0.834557	−	0.834557i	−0.153579	−	0.988136i	$-0.549080\pi$
$653$	544.966	−	544.966i	0.834557	−	0.834557i	0.988136	+	0.153579i	$0.0490801\pi$
$654$	172.650	+	108.873i	0.263991	+	0.166473i
$655$			398.819i			0.608884i
$656$	−20.7519	+	20.7519i	−0.0316340	+	0.0316340i
$657$	−2.27960	+	6.44775i	−0.00346970	+	0.00981392i
$658$	22.4426	−	22.4426i	0.0341073	−	0.0341073i
$659$		−	301.152i		−	0.456983i	−0.973546	−	0.228492i	$-0.926621\pi$
$659$		−	301.152i		−	0.456983i	0.973546	−	0.228492i	$-0.0733793\pi$
$660$	286.845	−	64.9826i	0.434613	−	0.0984585i
$661$			616.135i			0.932125i	0.884752	+	0.466062i	$0.154328\pi$
$661$			616.135i			0.932125i	−0.884752	+	0.466062i	$0.845672\pi$
$662$			495.712i			0.748810i
$663$	−118.964	−	107.489i	−0.179432	−	0.162126i
$664$	200.008			0.301216
$665$	236.404			0.355495
$666$	52.2519	−	147.792i	0.0784563	−	0.221910i
$667$	−705.367			−1.05752
$668$	89.5396	+	89.5396i	0.134041	+	0.134041i
$669$	95.9868	+	423.703i	0.143478	+	0.633337i
$670$	−393.573	−	393.573i	−0.587423	−	0.587423i
$671$	−10.0219			−0.0149357
$672$	−423.358	−	266.969i	−0.629997	−	0.397276i
$673$	−172.202	−	172.202i	−0.255872	−	0.255872i	0.567501	−	0.823373i	$-0.307910\pi$
$673$	−172.202	−	172.202i	−0.255872	−	0.255872i	−0.823373	+	0.567501i	$0.807910\pi$
$674$	361.595	−	361.595i	0.536491	−	0.536491i
$675$	−207.883	−	263.287i	−0.307974	−	0.390054i
$676$	374.080			0.553373
$677$	173.154	+	173.154i	0.255766	+	0.255766i	0.823330	−	0.567563i	$-0.192114\pi$
$677$	173.154	+	173.154i	0.255766	+	0.255766i	−0.567563	+	0.823330i	$0.692114\pi$
$678$	50.0026	−	79.2938i	0.0737502	−	0.116953i
$679$	−62.7857			−0.0924680
$680$	−84.2252	+	484.392i	−0.123861	+	0.712341i
$681$	−315.963	+	501.052i	−0.463969	+	0.735759i
$682$			819.364i			1.20141i
$683$	−64.4148	−	64.4148i	−0.0943116	−	0.0943116i	0.658377	−	0.752688i	$-0.271243\pi$
$683$	−64.4148	−	64.4148i	−0.0943116	−	0.0943116i	−0.752688	+	0.658377i	$0.771243\pi$
$684$	−113.864	−	238.410i	−0.166467	−	0.348552i
$685$	425.108	−	425.108i	0.620596	−	0.620596i
$686$	−336.906	+	336.906i	−0.491117	+	0.491117i
$687$	217.264	+	959.042i	0.316251	+	1.39599i
$688$		−	81.5874i		−	0.118586i
$689$	−34.8059			−0.0505166
$690$	−239.363	+	54.2259i	−0.346903	+	0.0785883i
$691$	77.0550	+	77.0550i	0.111512	+	0.111512i	0.760661	−	0.649149i	$-0.224875\pi$
$691$	77.0550	+	77.0550i	0.111512	+	0.111512i	−0.649149	+	0.760661i	$0.724875\pi$
$692$	−354.482	−	354.482i	−0.512258	−	0.512258i
$693$	509.861	−	243.508i	0.735731	−	0.351383i
$694$	−84.5173	+	84.5173i	−0.121783	+	0.121783i
$695$	102.001			0.146764
$696$	−812.572	−	512.408i	−1.16749	−	0.736218i
$697$	−459.814	−	79.9517i	−0.659705	−	0.114708i
$698$		−	172.459i		−	0.247077i
$699$	−608.341	−	383.619i	−0.870302	−	0.548812i
$700$	110.270	−	110.270i	0.157529	−	0.157529i
$701$		−	62.9959i		−	0.0898657i	−0.998990	−	0.0449329i	$-0.985693\pi$
$701$		−	62.9959i		−	0.0898657i	0.998990	−	0.0449329i	$-0.0143074\pi$
$702$	85.5483	−	67.5462i	0.121864	−	0.0962197i
$703$	119.759	+	119.759i	0.170354	+	0.170354i
$704$	−369.230	+	369.230i	−0.524475	+	0.524475i
$705$	−26.2705	+	41.6595i	−0.0372631	+	0.0590915i
$706$		−	263.579i		−	0.373341i
$707$	653.595	−	653.595i	0.924463	−	0.924463i
$708$	623.750	−	141.306i	0.881002	−	0.199585i
$709$	106.504	−	106.504i	0.150217	−	0.150217i	−0.627998	−	0.778215i	$-0.716125\pi$
$709$	106.504	−	106.504i	0.150217	−	0.150217i	0.778215	+	0.627998i	$0.216125\pi$
$710$		−	417.599i		−	0.588168i
$711$	1086.56	+	384.153i	1.52822	+	0.540300i
$712$		−	295.624i		−	0.415202i
$713$			974.786i			1.36716i
$714$	17.6933	+	349.197i	0.0247806	+	0.489071i
$715$	−131.097			−0.183353
$716$	−270.695			−0.378066
$717$	−141.651	−	625.273i	−0.197561	−	0.872068i
$718$	138.727			0.193213
$719$	369.667	+	369.667i	0.514141	+	0.514141i	0.915792	−	0.401652i	$-0.131564\pi$
$719$	369.667	+	369.667i	0.514141	+	0.514141i	−0.401652	+	0.915792i	$0.631564\pi$
$720$	−32.1663	−	11.3724i	−0.0446754	−	0.0157949i
$721$	−2.94551	−	2.94551i	−0.00408531	−	0.00408531i
$722$	263.353			0.364755
$723$	−314.202	+	498.259i	−0.434580	+	0.689155i
$724$	348.547	+	348.547i	0.481419	+	0.481419i
$725$	344.947	−	344.947i	0.475789	−	0.475789i
$726$	−14.7099	−	64.9319i	−0.0202615	−	0.0894379i
$727$	1237.79			1.70260			0.851299	−	0.524681i	$-0.175815\pi$
$727$	1237.79			1.70260			0.851299	+	0.524681i	$0.175815\pi$
$728$	96.7903	+	96.7903i	0.132954	+	0.132954i
$729$	169.105	−	709.115i	0.231969	−	0.972723i
$730$	−3.46032			−0.00474016
$731$	1061.06	−	746.726i	1.45152	−	1.02151i
$732$	−5.08436	−	3.20619i	−0.00694585	−	0.00438005i
$733$			1157.96i			1.57975i	0.613265	+	0.789877i	$0.289856\pi$
$733$			1157.96i			1.57975i	−0.613265	+	0.789877i	$0.710144\pi$
$734$	−47.9020	−	47.9020i	−0.0652616	−	0.0652616i
$735$	116.314	−	184.450i	0.158250	−	0.250952i
$736$	−396.969	+	396.969i	−0.539360	+	0.539360i
$737$	1016.33	−	1016.33i	1.37900	−	1.37900i
$738$	105.762	−	299.145i	0.143309	−	0.405345i
$739$		−	1133.08i		−	1.53326i	−0.642090	−	0.766629i	$-0.721933\pi$
$739$		−	1133.08i		−	1.53326i	0.642090	−	0.766629i	$-0.278067\pi$
$740$	−113.079			−0.152810
$741$	26.0197	+	114.856i	0.0351143	+	0.155001i
$742$	53.6717	+	53.6717i	0.0723338	+	0.0723338i
$743$	648.289	+	648.289i	0.872529	+	0.872529i	0.992748	−	0.120218i	$-0.0383594\pi$
$743$	648.289	+	648.289i	0.872529	+	0.872529i	−0.120218	+	0.992748i	$0.538359\pi$
$744$	−708.124	+	1122.94i	−0.951780	+	1.50933i
$745$	−68.4619	+	68.4619i	−0.0918952	+	0.0918952i
$746$	−767.744			−1.02915
$747$	−199.168	+	95.1218i	−0.266623	+	0.127338i
$748$	−463.033	−	80.5115i	−0.619029	−	0.107636i
$749$			963.072i			1.28581i
$750$	272.713	−	432.467i	0.363618	−	0.576622i
$751$	−281.063	+	281.063i	−0.374251	+	0.374251i	−0.869023	−	0.494772i	$-0.835252\pi$
$751$	−281.063	+	281.063i	−0.374251	+	0.374251i	0.494772	+	0.869023i	$0.335252\pi$
$752$		−	4.94883i		−	0.00658090i
$753$	193.609	+	854.626i	0.257117	+	1.13496i
$754$	112.082	+	112.082i	0.148649	+	0.148649i
$755$	331.652	−	331.652i	0.439274	−	0.439274i
$756$	336.569	+	39.5766i	0.445197	+	0.0523499i
$757$		−	925.770i		−	1.22295i	−0.791265	−	0.611473i	$-0.790577\pi$
$757$		−	925.770i		−	1.22295i	0.791265	−	0.611473i	$-0.209423\pi$
$758$	219.571	−	219.571i	0.289671	−	0.289671i
$759$	−140.028	−	618.108i	−0.184490	−	0.814371i
$760$	255.358	−	255.358i	0.335998	−	0.335998i
$761$			635.394i			0.834946i	0.908689	+	0.417473i	$0.137084\pi$
$761$			635.394i			0.834946i	−0.908689	+	0.417473i	$0.862916\pi$
$762$	−17.6690	−	77.9939i	−0.0231876	−	0.102354i
$763$		−	282.863i		−	0.370725i
$764$		−	276.771i		−	0.362266i
$765$	−146.501	−	522.414i	−0.191504	−	0.682894i
$766$	−187.156			−0.244329
$767$	−285.074			−0.371674
$768$	−775.089	+	175.591i	−1.00923	+	0.228634i
$769$	896.298			1.16554			0.582768	−	0.812638i	$-0.301969\pi$
$769$	896.298			1.16554			0.582768	+	0.812638i	$0.301969\pi$
$770$	202.156	+	202.156i	0.262540	+	0.262540i
$771$	−845.406	+	191.521i	−1.09651	+	0.248405i
$772$	−351.587	−	351.587i	−0.455424	−	0.455424i
$773$	−1439.24			−1.86189			−0.930946	−	0.365158i	$-0.881015\pi$
$773$	−1439.24			−1.86189			−0.930946	+	0.365158i	$0.881015\pi$
$774$	380.147	+	795.958i	0.491146	+	1.02837i
$775$	−476.701	−	476.701i	−0.615098	−	0.615098i
$776$	−67.8198	+	67.8198i	−0.0873966	+	0.0873966i
$777$	−211.870	+	47.9976i	−0.272677	+	0.0617730i
$778$	553.631			0.711608
$779$	242.402	+	242.402i	0.311170	+	0.311170i
$780$	−66.5092	−	41.9406i	−0.0852682	−	0.0537700i
$781$	1078.37			1.38075
$782$	386.387	+	67.1843i	0.494101	+	0.0859134i
$783$	1052.86	+	123.803i	1.34464	+	0.158114i
$784$			21.9112i			0.0279480i
$785$	103.923	+	103.923i	0.132386	+	0.132386i
$786$	366.479	+	231.101i	0.466258	+	0.294022i
$787$	612.451	−	612.451i	0.778210	−	0.778210i	−0.201316	−	0.979526i	$-0.564522\pi$
$787$	612.451	−	612.451i	0.778210	−	0.778210i	0.979526	+	0.201316i	$0.0645219\pi$
$788$	−532.422	+	532.422i	−0.675662	+	0.675662i
$789$	305.792	−	69.2749i	0.387569	−	0.0878009i
$790$			583.127i			0.738135i
$791$	−129.912			−0.164237
$792$	287.709	−	813.773i	0.363269	−	1.02749i
$793$	1.89453	+	1.89453i	0.00238906	+	0.00238906i
$794$	43.3294	+	43.3294i	0.0545711	+	0.0545711i
$795$	−99.6292	−	62.8261i	−0.125320	−	0.0790266i
$796$	−622.778	+	622.778i	−0.782385	+	0.782385i
$797$	−1078.44			−1.35313			−0.676565	−	0.736383i	$-0.736532\pi$
$797$	−1078.44			−1.35313			−0.676565	+	0.736383i	$0.736532\pi$
$798$	136.987	−	217.234i	0.171663	−	0.272223i
$799$	64.3606	−	45.2940i	0.0805514	−	0.0566884i
$800$		−	388.261i		−	0.485326i
$801$	140.596	+	294.382i	0.175525	+	0.367518i
$802$	373.296	−	373.296i	0.465457	−	0.465457i
$803$		−	8.93560i		−	0.0111278i
$804$	840.751	−	190.466i	1.04571	−	0.236898i
$805$	240.502	+	240.502i	0.298760	+	0.298760i
$806$	154.892	−	154.892i	0.192174	−	0.192174i
$807$	652.064	+	411.191i	0.808010	+	0.509531i
$808$		−	1412.00i		−	1.74752i
$809$	−729.425	+	729.425i	−0.901638	+	0.901638i	−0.995578	−	0.0939397i	$-0.970054\pi$
$809$	−729.425	+	729.425i	−0.901638	+	0.901638i	0.0939397	+	0.995578i	$0.470054\pi$
$810$	366.799	−	38.9275i	0.452838	−	0.0480586i
$811$	−1047.79	+	1047.79i	−1.29198	+	1.29198i	−0.358414	+	0.933563i	$0.616682\pi$
$811$	−1047.79	+	1047.79i	−1.29198	+	1.29198i	−0.933563	+	0.358414i	$0.883318\pi$
$812$			492.810i			0.606909i
$813$	406.266	−	92.0367i	0.499712	−	0.113206i
$814$			204.818i			0.251619i
$815$		−	191.131i		−	0.234516i
$816$	40.4516	+	36.5501i	0.0495731	+	0.0447917i
$817$	−953.017			−1.16648
$818$	−186.127			−0.227539
$819$	−142.416	−	50.3512i	−0.173891	−	0.0614789i
$820$	−228.882			−0.279125
$821$	−519.199	−	519.199i	−0.632398	−	0.632398i	0.316271	−	0.948669i	$-0.397569\pi$
$821$	−519.199	−	519.199i	−0.632398	−	0.632398i	−0.948669	+	0.316271i	$0.897569\pi$
$822$	−144.301	−	636.971i	−0.175549	−	0.774903i
$823$	−604.984	−	604.984i	−0.735096	−	0.735096i	0.236528	−	0.971625i	$-0.423990\pi$
$823$	−604.984	−	604.984i	−0.735096	−	0.735096i	−0.971625	+	0.236528i	$0.923990\pi$
$824$	−6.36334			−0.00772251
$825$	370.753	+	233.796i	0.449397	+	0.283389i
$826$	439.592	+	439.592i	0.532194	+	0.532194i
$827$	−561.485	+	561.485i	−0.678942	+	0.678942i	−0.959761	−	0.280819i	$-0.909394\pi$
$827$	−561.485	+	561.485i	−0.678942	+	0.678942i	0.280819	+	0.959761i	$0.409394\pi$
$828$	126.705	−	358.380i	0.153025	−	0.432826i
$829$	−1296.79			−1.56428			−0.782142	−	0.623100i	$-0.785873\pi$
$829$	−1296.79			−1.56428			−0.782142	+	0.623100i	$0.785873\pi$
$830$	−78.9683	−	78.9683i	−0.0951426	−	0.0951426i
$831$	203.127	−	322.117i	0.244436	−	0.387626i
$832$	139.598			0.167786
$833$	−284.960	+	200.542i	−0.342089	+	0.240747i
$834$	59.1058	−	93.7296i	0.0708703	−	0.112386i
$835$		−	191.004i		−	0.228748i
$836$	244.099	+	244.099i	0.291984	+	0.291984i
$837$	171.091	−	1455.00i	0.204410	−	1.73835i
$838$	308.877	−	308.877i	0.368588	−	0.368588i
$839$	−190.252	+	190.252i	−0.226760	+	0.226760i	−0.811338	−	0.584578i	$-0.801260\pi$
$839$	−190.252	+	190.252i	−0.226760	+	0.226760i	0.584578	+	0.811338i	$0.301260\pi$
$840$	102.344	+	451.765i	0.121838	+	0.537816i
$841$			700.608i			0.833065i
$842$	−495.592			−0.588589
$843$	−467.194	+	105.840i	−0.554204	+	0.125551i
$844$	−72.8493	−	72.8493i	−0.0863144	−	0.0863144i
$845$	−398.991	−	398.991i	−0.472178	−	0.472178i
$846$	23.0585	+	48.2803i	0.0272559	+	0.0570689i
$847$	−65.2409	+	65.2409i	−0.0770259	+	0.0770259i
$848$	11.8352			0.0139566
$849$	−322.599	−	203.431i	−0.379975	−	0.239612i
$850$	−221.811	+	156.100i	−0.260954	+	0.183647i
$851$			243.669i			0.286333i
$852$	547.085	+	344.991i	0.642118	+	0.404919i
$853$	−917.286	+	917.286i	−1.07537	+	1.07537i	−0.0784467	+	0.996918i	$0.524996\pi$
$853$	−917.286	+	917.286i	−1.07537	+	1.07537i	−0.996918	+	0.0784467i	$0.975004\pi$
$854$		−	5.84283i		−	0.00684172i
$855$	−132.840	+	375.732i	−0.155368	+	0.439453i
$856$	1040.29	+	1040.29i	1.21529	+	1.21529i
$857$	441.619	−	441.619i	0.515308	−	0.515308i	−0.400840	−	0.916148i	$-0.631282\pi$
$857$	441.619	−	441.619i	0.515308	−	0.515308i	0.916148	+	0.400840i	$0.131282\pi$
$858$	−75.9662	+	120.467i	−0.0885386	+	0.140404i
$859$			862.976i			1.00463i	0.864685	+	0.502314i	$0.167518\pi$
$859$			862.976i			1.00463i	−0.864685	+	0.502314i	$0.832482\pi$
$860$	449.932	−	449.932i	0.523177	−	0.523177i
$861$	−428.843	+	97.1513i	−0.498076	+	0.112835i
$862$	−213.548	+	213.548i	−0.247735	+	0.247735i
$863$		−	1097.07i		−	1.27122i	−0.772009	−	0.635612i	$-0.780748\pi$
$863$		−	1097.07i		−	1.27122i	0.772009	−	0.635612i	$-0.219252\pi$
$864$	662.204	−	522.855i	0.766440	−	0.605156i
$865$			756.176i			0.874192i
$866$		−	611.845i		−	0.706519i
$867$	−105.109	+	860.605i	−0.121233	+	0.992624i
$868$	681.041			0.784609
$869$	−1505.81			−1.73281
$870$	118.513	+	523.137i	0.136222	+	0.601307i
$871$	−384.251			−0.441161
$872$	−305.542	−	305.542i	−0.350393	−	0.350393i
$873$	35.2805	−	99.7894i	0.0404129	−	0.114306i
$874$	−203.693	−	203.693i	−0.233058	−	0.233058i
$875$	−708.536			−0.809756
$876$	2.85867	−	4.53326i	0.00326333	−	0.00517496i
$877$	−718.746	−	718.746i	−0.819551	−	0.819551i	0.166492	−	0.986043i	$-0.446756\pi$
$877$	−718.746	−	718.746i	−0.819551	−	0.819551i	−0.986043	+	0.166492i	$0.946756\pi$
$878$	−328.858	+	328.858i	−0.374553	+	0.374553i
$879$	−296.441	−	1308.54i	−0.337248	−	1.48867i
$880$	44.5776			0.0506564
$881$	−776.835	−	776.835i	−0.881765	−	0.881765i	0.111949	−	0.993714i	$-0.464291\pi$
$881$	−776.835	−	776.835i	−0.881765	−	0.881765i	−0.993714	+	0.111949i	$0.964291\pi$
$882$	−102.093	−	213.764i	−0.115752	−	0.242362i
$883$	1248.37			1.41379			0.706894	−	0.707320i	$-0.250096\pi$
$883$	1248.37			1.41379			0.706894	+	0.707320i	$0.250096\pi$
$884$	72.3117	+	102.751i	0.0818005	+	0.116235i
$885$	−816.002	−	514.571i	−0.922037	−	0.581436i
$886$		−	1077.37i		−	1.21599i
$887$	618.774	+	618.774i	0.697603	+	0.697603i	0.963893	−	0.266290i	$-0.0857980\pi$
$887$	618.774	+	618.774i	0.697603	+	0.697603i	−0.266290	+	0.963893i	$0.585798\pi$
$888$	−177.011	+	280.703i	−0.199337	+	0.316107i
$889$	−78.3651	+	78.3651i	−0.0881497	+	0.0881497i
$890$	−116.720	+	116.720i	−0.131146	+	0.131146i
$891$	100.523	+	947.187i	0.112820	+	1.06306i
$892$		−	340.452i		−	0.381673i
$893$	−57.8070			−0.0647335
$894$	23.2391	+	102.581i	0.0259945	+	0.114744i
$895$	288.721	+	288.721i	0.322594	+	0.322594i
$896$	256.616	+	256.616i	0.286402	+	0.286402i
$897$	−90.3759	+	143.317i	−0.100753	+	0.159774i
$898$	−631.284	+	631.284i	−0.702989	+	0.702989i
$899$	2130.43			2.36978
$900$	113.296	+	237.222i	0.125885	+	0.263580i
$901$	108.321	+	153.919i	0.120223	+	0.170831i
$902$			414.569i			0.459611i
$903$	652.033	−	1033.99i	0.722074	−	1.14506i
$904$	−140.328	+	140.328i	−0.155230	+	0.155230i
$905$		−	743.515i		−	0.821564i
$906$	−112.578	−	496.938i	−0.124258	−	0.548497i
$907$	−590.082	−	590.082i	−0.650586	−	0.650586i	0.302548	−	0.953134i	$-0.402163\pi$
$907$	−590.082	−	590.082i	−0.650586	−	0.650586i	−0.953134	+	0.302548i	$0.902163\pi$
$908$	328.243	−	328.243i	0.361501	−	0.361501i
$909$	671.533	+	1406.07i	0.738760	+	1.54683i
$910$		−	76.4308i		−	0.0839899i
$911$	−144.447	+	144.447i	−0.158559	+	0.158559i	−0.781928	−	0.623369i	$-0.785764\pi$
$911$	−144.447	+	144.447i	−0.158559	+	0.158559i	0.623369	+	0.781928i	$0.285764\pi$
$912$	−8.84759	−	39.0548i	−0.00970131	−	0.0428233i
$913$	203.920	−	203.920i	0.223352	−	0.223352i
$914$			607.782i			0.664970i
$915$	2.00324	+	8.84264i	0.00218933	+	0.00966409i
$916$		−	770.607i		−	0.841274i
$917$		−	600.424i		−	0.654770i
$918$	−564.943	−	168.099i	−0.615406	−	0.183114i
$919$	1027.79			1.11838			0.559192	−	0.829038i	$-0.311112\pi$
$919$	1027.79			1.11838			0.559192	+	0.829038i	$0.311112\pi$
$920$	519.570			0.564750
$921$	685.008	−	155.184i	0.743765	−	0.168495i
$922$	−183.549			−0.199077
$923$	−203.854	−	203.854i	−0.220860	−	0.220860i
$924$	−431.845	+	97.8315i	−0.467365	+	0.105878i
$925$	−119.162	−	119.162i	−0.128824	−	0.128824i
$926$	46.8257			0.0505677
$927$	6.33662	−	3.02635i	0.00683562	−	0.00326467i
$928$	867.591	+	867.591i	0.934904	+	0.934904i
$929$	−1155.88	+	1155.88i	−1.24422	+	1.24422i	−0.285986	+	0.958234i	$0.592321\pi$
$929$	−1155.88	+	1155.88i	−1.24422	+	1.24422i	−0.958234	+	0.285986i	$0.907679\pi$
$930$	722.952	−	163.780i	0.777368	−	0.176107i
$931$	255.944			0.274913
$932$	398.529	+	398.529i	0.427606	+	0.427606i
$933$	586.849	+	370.066i	0.628991	+	0.396641i
$934$	440.434			0.471556
$935$	407.995	+	579.741i	0.436358	+	0.620043i
$936$	−208.223	+	99.4468i	−0.222461	+	0.106247i
$937$		−	31.1301i		−	0.0332231i	−0.999862	−	0.0166116i	$-0.994712\pi$
$937$		−	31.1301i		−	0.0332231i	0.999862	−	0.0166116i	$-0.00528787\pi$
$938$	592.525	+	592.525i	0.631690	+	0.631690i
$939$	690.114	+	435.185i	0.734945	+	0.463456i
$940$	27.2914	−	27.2914i	0.0290335	−	0.0290335i
$941$	39.4081	−	39.4081i	0.0418790	−	0.0418790i	−0.685857	−	0.727736i	$-0.740573\pi$
$941$	39.4081	−	39.4081i	0.0418790	−	0.0418790i	0.727736	+	0.685857i	$0.240573\pi$
$942$	155.716	−	35.2763i	0.165303	−	0.0374483i
$943$			493.207i			0.523019i
$944$	96.9349			0.102685
$945$	−316.770	−	401.194i	−0.335206	−	0.424544i
$946$	−814.952	−	814.952i	−0.861471	−	0.861471i
$947$	320.688	+	320.688i	0.338636	+	0.338636i	0.855854	−	0.517218i	$-0.173032\pi$
$947$	320.688	+	320.688i	0.338636	+	0.338636i	−0.517218	+	0.855854i	$0.673032\pi$
$948$	−763.937	−	481.738i	−0.805841	−	0.508163i
$949$	−1.68918	+	1.68918i	−0.00177996	+	0.00177996i
$950$	199.225			0.209710
$951$	−103.978	+	164.888i	−0.109336	+	0.173384i
$952$	126.801	−	729.253i	0.133195	−	0.766022i
$953$		−	1053.19i		−	1.10513i	−0.833471	−	0.552563i	$-0.813650\pi$
$953$		−	1053.19i		−	1.10513i	0.833471	−	0.552563i	$-0.186350\pi$
$954$	−115.463	+	55.1447i	−0.121030	+	0.0578037i
$955$	−295.202	+	295.202i	−0.309112	+	0.309112i
$956$			502.417i			0.525541i
$957$	−1350.90	+	306.037i	−1.41160	+	0.319788i
$958$	−328.295	−	328.295i	−0.342688	−	0.342688i
$959$	−640.002	+	640.002i	−0.667364	+	0.667364i
$960$	399.588	+	251.980i	0.416238	+	0.262479i
$961$		−	1983.16i		−	2.06365i
$962$	38.7186	−	38.7186i	0.0402480	−	0.0402480i
$963$	−1530.67	−	541.168i	−1.58948	−	0.561960i
$964$	326.413	−	326.413i	0.338603	−	0.338603i
$965$			750.000i			0.777202i
$966$	360.362	−	81.6373i	0.373045	−	0.0845107i
$967$			244.702i			0.253053i	0.991963	+	0.126527i	$0.0403829\pi$
$967$			244.702i			0.253053i	−0.991963	+	0.126527i	$0.959617\pi$
$968$			140.944i			0.145603i
$969$	426.939	−	472.513i	0.440597	−	0.487629i
$970$	53.5541			0.0552104
$971$	260.440			0.268218			0.134109	−	0.990967i	$-0.457183\pi$
$971$	260.440			0.268218			0.134109	+	0.990967i	$0.457183\pi$
$972$	−252.026	+	512.692i	−0.259286	+	0.527461i
$973$	−153.563			−0.157824
$974$	329.247	+	329.247i	0.338036	+	0.338036i
$975$	−25.8901	−	114.283i	−0.0265539	−	0.117214i
$976$	−0.644204	−	0.644204i	−0.000660045	−	0.000660045i
$977$	1661.77			1.70089			0.850447	−	0.526060i	$-0.176331\pi$
$977$	1661.77			1.70089			0.850447	+	0.526060i	$0.176331\pi$
$978$	−175.632	−	110.753i	−0.179583	−	0.113245i
$979$	−301.407	−	301.407i	−0.307872	−	0.307872i
$980$	−120.834	+	120.834i	−0.123300	+	0.123300i
$981$	449.572	+	158.946i	0.458279	+	0.162024i
$982$	−952.276			−0.969731
$983$	62.7039	+	62.7039i	0.0637883	+	0.0637883i	0.738281	−	0.674493i	$-0.235638\pi$
$983$	62.7039	+	62.7039i	0.0637883	+	0.0637883i	−0.674493	+	0.738281i	$0.735638\pi$
$984$	−358.286	+	568.167i	−0.364112	+	0.577406i
$985$	1135.75			1.15305
$986$	146.834	−	844.464i	0.148919	−	0.856454i
$987$	39.5503	−	62.7185i	0.0400712	−	0.0635446i
$988$		−	92.2885i		−	0.0934094i
$989$	−969.537	−	969.537i	−0.980320	−	0.980320i
$990$	−434.894	+	207.704i	−0.439287	+	0.209802i
$991$	703.801	−	703.801i	0.710193	−	0.710193i	−0.256383	−	0.966575i	$-0.582531\pi$
$991$	703.801	−	703.801i	0.710193	−	0.710193i	0.966575	+	0.256383i	$0.0825308\pi$
$992$	1198.97	−	1198.97i	1.20864	−	1.20864i
$993$	255.870	+	1129.46i	0.257674	+	1.13742i
$994$			628.697i			0.632492i
$995$	1328.50			1.33518
$996$	168.692	−	38.2160i	0.169370	−	0.0383695i
$997$	−251.502	−	251.502i	−0.252259	−	0.252259i	0.569637	−	0.821896i	$-0.307084\pi$
$997$	−251.502	−	251.502i	−0.252259	−	0.252259i	−0.821896	+	0.569637i	$0.807084\pi$
$998$	−234.637	−	234.637i	−0.235108	−	0.235108i
$999$	42.7679	−	363.709i	0.0428107	−	0.364073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.3.f.a.38.7	yes	20
3.2	odd	2	inner	51.3.f.a.38.4	✓	20
17.13	even	4	inner	51.3.f.a.47.4	yes	20
51.47	odd	4	inner	51.3.f.a.47.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.3.f.a.38.4	✓	20	3.2	odd	2	inner
51.3.f.a.38.7	yes	20	1.1	even	1	trivial
51.3.f.a.47.4	yes	20	17.13	even	4	inner
51.3.f.a.47.7	yes	20	51.47	odd	4	inner

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.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.28414 q^{2} +(2.92586 - 0.662833i) q^{3} -2.35098 q^{4} +(2.50753 + 2.50753i) q^{5} +(3.75722 - 0.851171i) q^{6} +(-3.77510 - 3.77510i) q^{7} -8.15556 q^{8} +(8.12131 - 3.87871i) q^{9} +(3.22003 + 3.22003i) q^{10} +(-8.31510 + 8.31510i) q^{11} +(-6.87863 + 1.55831i) q^{12} +3.14376 q^{13} +(-4.84777 - 4.84777i) q^{14} +(8.99877 + 5.67462i) q^{15} -1.06899 q^{16} +(-9.78386 - 13.9024i) q^{17} +(10.4289 - 4.98082i) q^{18} +12.4867i q^{19} +(-5.89516 - 5.89516i) q^{20} +(-13.5477 - 8.54316i) q^{21} +(-10.6778 + 10.6778i) q^{22} +(-12.7032 + 12.7032i) q^{23} +(-23.8620 + 5.40577i) q^{24} -12.4245i q^{25} +4.03704 q^{26} +(21.1909 - 16.7316i) q^{27} +(8.87518 + 8.87518i) q^{28} +(27.7634 + 27.7634i) q^{29} +(11.5557 + 7.28702i) q^{30} +(38.3677 - 38.3677i) q^{31} +31.2495 q^{32} +(-18.8173 + 29.8403i) q^{33} +(-12.5639 - 17.8526i) q^{34} -18.9324i q^{35} +(-19.0930 + 9.11876i) q^{36} +(9.59085 - 9.59085i) q^{37} +16.0348i q^{38} +(9.19820 - 2.08379i) q^{39} +(-20.4504 - 20.4504i) q^{40} +(19.4127 - 19.4127i) q^{41} +(-17.3971 - 10.9706i) q^{42} +76.3223i q^{43} +(19.5486 - 19.5486i) q^{44} +(30.0905 + 10.6385i) q^{45} +(-16.3127 + 16.3127i) q^{46} +4.62947i q^{47} +(-3.12770 + 0.708559i) q^{48} -20.4972i q^{49} -15.9549i q^{50} +(-37.8411 - 34.1913i) q^{51} -7.39092 q^{52} -11.0714 q^{53} +(27.2121 - 21.4858i) q^{54} -41.7008 q^{55} +(30.7881 + 30.7881i) q^{56} +(8.27662 + 36.5345i) q^{57} +(35.6521 + 35.6521i) q^{58} -90.6793 q^{59} +(-21.1559 - 13.3409i) q^{60} +(0.602631 + 0.602631i) q^{61} +(49.2696 - 49.2696i) q^{62} +(-45.3013 - 16.0162i) q^{63} +44.4048 q^{64} +(7.88309 + 7.88309i) q^{65} +(-24.1641 + 38.3193i) q^{66} -122.226 q^{67} +(23.0016 + 32.6842i) q^{68} +(-28.7477 + 45.5879i) q^{69} -24.3119i q^{70} +(-64.8440 - 64.8440i) q^{71} +(-66.2338 + 31.6331i) q^{72} +(-0.537311 + 0.537311i) q^{73} +(12.3160 - 12.3160i) q^{74} +(-8.23539 - 36.3525i) q^{75} -29.3561i q^{76} +62.7807 q^{77} +(11.8118 - 2.67588i) q^{78} +(90.5467 + 90.5467i) q^{79} +(-2.68052 - 2.68052i) q^{80} +(50.9112 - 63.0004i) q^{81} +(24.9287 - 24.9287i) q^{82} -24.5241 q^{83} +(31.8503 + 20.0848i) q^{84} +(10.3273 - 59.3941i) q^{85} +98.0086i q^{86} +(99.6341 + 62.8292i) q^{87} +(67.8143 - 67.8143i) q^{88} +36.2481i q^{89} +(38.6404 + 13.6613i) q^{90} +(-11.8680 - 11.8680i) q^{91} +(29.8650 - 29.8650i) q^{92} +(86.8272 - 137.690i) q^{93} +5.94489i q^{94} +(-31.3110 + 31.3110i) q^{95} +(91.4317 - 20.7132i) q^{96} +(8.31577 - 8.31577i) q^{97} -26.3213i q^{98} +(-35.2776 + 99.7814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 24 q^{4} - 2 q^{6} - 4 q^{7} - 16 q^{10} - 42 q^{12} - 12 q^{13} - 64 q^{16} - 4 q^{18} + 88 q^{21} - 40 q^{22} - 82 q^{24} + 54 q^{27} - 160 q^{28} + 48 q^{31} + 264 q^{33} + 152 q^{34}+ \cdots - 864 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 24 * q^4 - 2 * q^6 - 4 * q^7 - 16 * q^10 - 42 * q^12 - 12 * q^13 - 64 * q^16 - 4 * q^18 + 88 * q^21 - 40 * q^22 - 82 * q^24 + 54 * q^27 - 160 * q^28 + 48 * q^31 + 264 * q^33 + 152 * q^34 + 32 * q^37 + 56 * q^39 + 52 * q^40 + 64 * q^45 + 388 * q^46 - 230 * q^48 - 298 * q^51 + 64 * q^52 - 254 * q^54 - 204 * q^55 - 24 * q^57 + 396 * q^58 - 336 * q^61 - 400 * q^63 - 480 * q^64 - 408 * q^67 - 132 * q^69 + 276 * q^72 - 88 * q^73 - 358 * q^75 + 380 * q^78 - 172 * q^79 + 388 * q^81 + 372 * q^82 + 1320 * q^84 + 648 * q^85 - 156 * q^88 + 672 * q^90 - 124 * q^91 + 194 * q^96 + 688 * q^97 - 864 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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