LMFDB - Embedded newform 97.4.e.a.36.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,4,Mod(36,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.36"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	97.e (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.72318527056$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-65})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 65x^{2} + 4225 $ x^4 - 65*x^2 + 4225
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.1
Root			$-6.98212 - 4.03113i$ of defining polynomial
Character	$\chi$	$=$	97.36
Dual form			97.4.e.a.62.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(2.00000 - 3.46410i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-12.9821 - 7.49523i) q^{5} +(2.00000 + 3.46410i) q^{6} +(-31.4464 - 18.1556i) q^{7} -15.0000 q^{8} +(5.50000 + 9.52628i) q^{9} +(12.9821 - 7.49523i) q^{10} +(1.48212 + 2.56711i) q^{11} +28.0000 q^{12} +(-19.9106 - 11.4954i) q^{13} +(31.4464 - 18.1556i) q^{14} +(-51.9285 + 29.9809i) q^{15} +(-20.5000 + 35.5070i) q^{16} +(-15.3570 + 8.86635i) q^{17} -11.0000 q^{18} -143.451i q^{19} -104.933i q^{20} +(-125.785 + 72.6223i) q^{21} -2.96424 q^{22} +(-93.9285 + 54.2296i) q^{23} +(-30.0000 + 51.9615i) q^{24} +(49.8570 + 86.3548i) q^{25} +(19.9106 - 11.4954i) q^{26} +152.000 q^{27} -254.178i q^{28} +(82.9642 + 47.8994i) q^{29} -59.9618i q^{30} +(40.8927 - 70.8283i) q^{31} +(-80.5000 - 139.430i) q^{32} +11.8570 q^{33} -17.7327i q^{34} +(272.160 + 471.395i) q^{35} +(-38.5000 + 66.6840i) q^{36} +(-266.125 - 153.647i) q^{37} +(124.232 + 71.7253i) q^{38} +(-79.6424 + 45.9816i) q^{39} +(194.732 + 112.428i) q^{40} +(377.249 + 217.805i) q^{41} -145.245i q^{42} +(-47.6424 + 82.5191i) q^{43} +(-10.3748 + 17.9698i) q^{44} -164.895i q^{45} -108.459i q^{46} -133.250 q^{47} +(82.0000 + 142.028i) q^{48} +(487.749 + 844.806i) q^{49} -99.7139 q^{50} +70.9308i q^{51} -160.935i q^{52} +(-10.9106 + 18.8977i) q^{53} +(-76.0000 + 131.636i) q^{54} -44.4353i q^{55} +(471.695 + 272.333i) q^{56} +(-496.927 - 286.901i) q^{57} +(-82.9642 + 47.8994i) q^{58} +(-332.893 - 192.196i) q^{59} +(-363.499 - 209.866i) q^{60} +(313.696 - 543.337i) q^{61} +(40.8927 + 70.8283i) q^{62} -399.422i q^{63} -167.000 q^{64} +(172.321 + 298.469i) q^{65} +(-5.92848 + 10.2684i) q^{66} -615.824i q^{67} +(-107.499 - 62.0644i) q^{68} +433.837i q^{69} -544.321 q^{70} +(-251.160 + 145.007i) q^{71} +(-82.5000 - 142.894i) q^{72} +(66.3921 - 114.994i) q^{73} +(266.125 - 153.647i) q^{74} +398.856 q^{75} +(869.623 - 502.077i) q^{76} -107.635i q^{77} -91.9631i q^{78} +295.571 q^{79} +(532.267 - 307.304i) q^{80} +(155.500 - 269.334i) q^{81} +(-377.249 + 217.805i) q^{82} +(-1183.57 + 683.333i) q^{83} +(-880.498 - 508.356i) q^{84} +265.821 q^{85} +(-47.6424 - 82.5191i) q^{86} +(331.857 - 191.598i) q^{87} +(-22.2318 - 38.5066i) q^{88} -788.068 q^{89} +(142.803 + 82.4475i) q^{90} +(417.411 + 722.976i) q^{91} +(-657.499 - 379.607i) q^{92} +(-163.571 - 283.313i) q^{93} +(66.6252 - 115.398i) q^{94} +(-1075.19 + 1862.29i) q^{95} -644.000 q^{96} +(-719.284 + 628.732i) q^{97} -975.498 q^{98} +(-16.3033 + 28.2382i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 8 q^{3} + 14 q^{4} - 24 q^{5} + 8 q^{6} - 42 q^{7} - 60 q^{8} + 22 q^{9} + 24 q^{10} - 22 q^{11} + 112 q^{12} + 60 q^{13} + 42 q^{14} - 96 q^{15} - 82 q^{16} + 162 q^{17} - 44 q^{18} - 168 q^{21}+ \cdots + 242 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 8 * q^3 + 14 * q^4 - 24 * q^5 + 8 * q^6 - 42 * q^7 - 60 * q^8 + 22 * q^9 + 24 * q^10 - 22 * q^11 + 112 * q^12 + 60 * q^13 + 42 * q^14 - 96 * q^15 - 82 * q^16 + 162 * q^17 - 44 * q^18 - 168 * q^21 + 44 * q^22 - 264 * q^23 - 120 * q^24 - 24 * q^25 - 60 * q^26 + 608 * q^27 + 276 * q^29 - 4 * q^31 - 322 * q^32 - 176 * q^33 + 558 * q^35 - 154 * q^36 - 1260 * q^37 + 78 * q^38 + 240 * q^39 + 360 * q^40 + 336 * q^41 + 368 * q^43 + 154 * q^44 - 924 * q^47 + 328 * q^48 + 778 * q^49 + 48 * q^50 + 96 * q^53 - 304 * q^54 + 630 * q^56 - 312 * q^57 - 276 * q^58 - 1164 * q^59 - 672 * q^60 + 780 * q^61 - 4 * q^62 - 668 * q^64 + 410 * q^65 + 88 * q^66 + 1134 * q^68 - 1116 * q^70 - 474 * q^71 - 330 * q^72 - 684 * q^73 + 1260 * q^74 - 192 * q^75 + 546 * q^76 + 512 * q^79 + 984 * q^80 + 622 * q^81 - 336 * q^82 - 936 * q^83 - 1176 * q^84 + 784 * q^85 + 368 * q^86 + 1104 * q^87 + 330 * q^88 + 1428 * q^89 + 264 * q^90 + 1530 * q^91 - 1848 * q^92 + 16 * q^93 + 462 * q^94 - 2262 * q^95 - 2576 * q^96 - 196 * q^97 - 1556 * q^98 + 242 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.176777	+	0.306186i	−0.940775	−	0.339032i	$-0.889900\pi$
$2$	−0.500000	+	0.866025i	−0.176777	+	0.306186i	0.763998	+	0.645219i	$0.223234\pi$
$3$	2.00000	−	3.46410i	0.384900	−	0.666667i	−0.606855	−	0.794812i	$-0.707569\pi$
$3$	2.00000	−	3.46410i	0.384900	−	0.666667i	0.991755	+	0.128146i	$0.0409025\pi$
$4$	3.50000	+	6.06218i	0.437500	+	0.757772i
$5$	−12.9821	−	7.49523i	−1.16116	−	0.670394i	−0.209575	−	0.977793i	$-0.567208\pi$
$5$	−12.9821	−	7.49523i	−1.16116	−	0.670394i	−0.951581	+	0.307399i	$0.900541\pi$
$6$	2.00000	+	3.46410i	0.136083	+	0.235702i
$7$	−31.4464	−	18.1556i	−1.69794	−	0.980308i	−0.947708	−	0.319138i	$-0.896607\pi$
$7$	−31.4464	−	18.1556i	−1.69794	−	0.980308i	−0.750235	−	0.661171i	$-0.770060\pi$
$8$	−15.0000			−0.662913
$9$	5.50000	+	9.52628i	0.203704	+	0.352825i
$10$	12.9821	−	7.49523i	0.410531	−	0.237020i
$11$	1.48212	+	2.56711i	0.0406251	+	0.0703647i	0.885623	−	0.464405i	$-0.153732\pi$
$11$	1.48212	+	2.56711i	0.0406251	+	0.0703647i	−0.844998	+	0.534770i	$0.820398\pi$
$12$	28.0000			0.673575
$13$	−19.9106	−	11.4954i	−0.424785	−	0.245250i	0.272337	−	0.962202i	$-0.412203\pi$
$13$	−19.9106	−	11.4954i	−0.424785	−	0.245250i	−0.697123	+	0.716952i	$0.745537\pi$
$14$	31.4464	−	18.1556i	0.600314	−	0.346591i
$15$	−51.9285	+	29.9809i	−0.893858	+	0.516069i
$16$	−20.5000	+	35.5070i	−0.320312	+	0.554798i
$17$	−15.3570	+	8.86635i	−0.219095	+	0.126494i	−0.605531	−	0.795822i	$-0.707039\pi$
$17$	−15.3570	+	8.86635i	−0.219095	+	0.126494i	0.386436	+	0.922316i	$0.373706\pi$
$18$	−11.0000			−0.144040
$19$		−	143.451i		−	1.73210i	−0.499962	−	0.866048i	$-0.666653\pi$
$19$		−	143.451i		−	1.73210i	0.499962	−	0.866048i	$-0.333347\pi$
$20$		−	104.933i		−	1.17319i
$21$	−125.785	+	72.6223i	−1.30708	+	0.754642i
$22$	−2.96424			−0.0287263
$23$	−93.9285	+	54.2296i	−0.851541	+	0.491637i	−0.861170	−	0.508316i	$-0.830268\pi$
$23$	−93.9285	+	54.2296i	−0.851541	+	0.491637i	0.00962953	+	0.999954i	$0.496935\pi$
$24$	−30.0000	+	51.9615i	−0.255155	+	0.441942i
$25$	49.8570	+	86.3548i	0.398856	+	0.690838i
$26$	19.9106	−	11.4954i	0.150184	−	0.0867089i
$27$	152.000			1.08342
$28$		−	254.178i		−	1.71554i
$29$	82.9642	+	47.8994i	0.531244	+	0.306714i	0.741523	−	0.670928i	$-0.234104\pi$
$29$	82.9642	+	47.8994i	0.531244	+	0.306714i	−0.210279	+	0.977641i	$0.567437\pi$
$30$		−	59.9618i		−	0.364916i
$31$	40.8927	−	70.8283i	0.236921	−	0.410359i	−0.722908	−	0.690944i	$-0.757195\pi$
$31$	40.8927	−	70.8283i	0.236921	−	0.410359i	0.959829	+	0.280585i	$0.0905284\pi$
$32$	−80.5000	−	139.430i	−0.444704	−	0.770250i
$33$	11.8570			0.0625464
$34$		−	17.7327i		−	0.0894450i
$35$	272.160	+	471.395i	1.31439	+	2.27658i
$36$	−38.5000	+	66.6840i	−0.178241	+	0.308722i
$37$	−266.125	−	153.647i	−1.18245	−	0.682689i	−0.225871	−	0.974157i	$-0.572523\pi$
$37$	−266.125	−	153.647i	−1.18245	−	0.682689i	−0.956580	+	0.291468i	$0.905856\pi$
$38$	124.232	+	71.7253i	0.530344	+	0.306194i
$39$	−79.6424	+	45.9816i	−0.327000	+	0.188793i
$40$	194.732	+	112.428i	0.769745	+	0.444412i
$41$	377.249	+	217.805i	1.43699	+	0.829644i	0.997639	−	0.0686739i	$-0.0218768\pi$
$41$	377.249	+	217.805i	1.43699	+	0.829644i	0.439346	+	0.898318i	$0.355210\pi$
$42$		−	145.245i		−	0.533612i
$43$	−47.6424	+	82.5191i	−0.168963	+	0.292652i	−0.938055	−	0.346485i	$-0.887375\pi$
$43$	−47.6424	+	82.5191i	−0.168963	+	0.292652i	0.769093	+	0.639137i	$0.220708\pi$
$44$	−10.3748	+	17.9698i	−0.0355470	+	0.0615691i
$45$		−	164.895i		−	0.546247i
$46$		−	108.459i		−	0.347640i
$47$	−133.250			−0.413544			−0.206772	−	0.978389i	$-0.566296\pi$
$47$	−133.250			−0.413544			−0.206772	+	0.978389i	$0.566296\pi$
$48$	82.0000	+	142.028i	0.246577	+	0.427083i
$49$	487.749	+	844.806i	1.42201	+	2.46299i
$50$	−99.7139			−0.282034
$51$			70.9308i			0.194751i
$52$		−	160.935i		−	0.429187i
$53$	−10.9106	+	18.8977i	−0.0282771	+	0.0489774i	−0.879818	−	0.475311i	$-0.842335\pi$
$53$	−10.9106	+	18.8977i	−0.0282771	+	0.0489774i	0.851541	+	0.524289i	$0.175669\pi$
$54$	−76.0000	+	131.636i	−0.191524	+	0.331729i
$55$		−	44.4353i		−	0.108939i
$56$	471.695	+	272.333i	1.12559	+	0.649859i
$57$	−496.927	−	286.901i	−1.15473	−	0.666684i
$58$	−82.9642	+	47.8994i	−0.187823	+	0.108440i
$59$	−332.893	−	192.196i	−0.734558	−	0.424097i	0.0855291	−	0.996336i	$-0.472742\pi$
$59$	−332.893	−	192.196i	−0.734558	−	0.424097i	−0.820087	+	0.572238i	$0.806075\pi$
$60$	−363.499	−	209.866i	−0.782126	−	0.451561i
$61$	313.696	−	543.337i	0.658437	−	1.14045i	−0.322583	−	0.946541i	$-0.604551\pi$
$61$	313.696	−	543.337i	0.658437	−	1.14045i	0.981020	−	0.193905i	$-0.0621155\pi$
$62$	40.8927	+	70.8283i	0.0837642	+	0.145084i
$63$		−	399.422i		−	0.798770i
$64$	−167.000			−0.326172
$65$	172.321	+	298.469i	0.328828	+	0.569547i
$66$	−5.92848	+	10.2684i	−0.0110567	+	0.0191509i
$67$		−	615.824i		−	1.12291i	−0.827508	−	0.561454i	$-0.810242\pi$
$67$		−	615.824i		−	1.12291i	0.827508	−	0.561454i	$-0.189758\pi$
$68$	−107.499	−	62.0644i	−0.191708	−	0.110683i
$69$			433.837i			0.756925i
$70$	−544.321			−0.929411
$71$	−251.160	+	145.007i	−0.419820	+	0.242383i	−0.695000	−	0.719009i	$-0.744596\pi$
$71$	−251.160	+	145.007i	−0.419820	+	0.242383i	0.275180	+	0.961393i	$0.411263\pi$
$72$	−82.5000	−	142.894i	−0.135038	−	0.233892i
$73$	66.3921	−	114.994i	0.106447	−	0.184371i	−0.807882	−	0.589345i	$-0.799386\pi$
$73$	66.3921	−	114.994i	0.106447	−	0.184371i	0.914328	+	0.404974i	$0.132719\pi$
$74$	266.125	−	153.647i	0.418060	−	0.241367i
$75$	398.856			0.614078
$76$	869.623	−	502.077i	1.31253	−	0.757792i
$77$		−	107.635i		−	0.159300i
$78$		−	91.9631i		−	0.133497i
$79$	295.571			0.420941			0.210470	−	0.977600i	$-0.432500\pi$
$79$	295.571			0.420941			0.210470	+	0.977600i	$0.432500\pi$
$80$	532.267	−	307.304i	0.743866	−	0.429471i
$81$	155.500	−	269.334i	0.213306	−	0.369457i
$82$	−377.249	+	217.805i	−0.508051	+	0.293323i
$83$	−1183.57	+	683.333i	−1.56522	+	0.903682i	−0.568509	+	0.822677i	$0.692480\pi$
$83$	−1183.57	+	683.333i	−1.56522	+	0.903682i	−0.996714	+	0.0810050i	$0.974187\pi$
$84$	−880.498	−	508.356i	−1.14369	−	0.660311i
$85$	265.821			0.339204
$86$	−47.6424	−	82.5191i	−0.0597374	−	0.103468i
$87$	331.857	−	191.598i	0.408952	−	0.236108i
$88$	−22.2318	−	38.5066i	−0.0269309	−	0.0466457i
$89$	−788.068			−0.938596			−0.469298	−	0.883040i	$-0.655493\pi$
$89$	−788.068			−0.938596			−0.469298	+	0.883040i	$0.655493\pi$
$90$	142.803	+	82.4475i	0.167253	+	0.0965637i
$91$	417.411	+	722.976i	0.480841	+	0.832841i
$92$	−657.499	−	379.607i	−0.745098	−	0.430183i
$93$	−163.571	−	283.313i	−0.182382	−	0.315895i
$94$	66.6252	−	115.398i	0.0731049	−	0.126621i
$95$	−1075.19	+	1862.29i	−1.16119	+	2.01123i
$96$	−644.000			−0.684666
$97$	−719.284	+	628.732i	−0.752909	+	0.658125i
$97$	−719.284	+	628.732i	−0.752909	+	0.658125i
$98$	−975.498			−1.00551
$99$	−16.3033	+	28.2382i	−0.0165510	+	0.0286671i
$100$	−348.999	+	604.484i	−0.348999	+	0.604484i
$101$	−573.232	−	992.868i	−0.564740	−	0.978159i	−0.997074	−	0.0764450i	$-0.975643\pi$
$101$	−573.232	−	992.868i	−0.564740	−	0.978159i	0.432334	−	0.901714i	$-0.357690\pi$
$102$	−61.4278	−	35.4654i	−0.0596300	−	0.0344274i
$103$	−476.392	−	825.135i	−0.455731	−	0.789349i	0.542999	−	0.839733i	$-0.317289\pi$
$103$	−476.392	−	825.135i	−0.455731	−	0.789349i	−0.998730	+	0.0503840i	$0.983955\pi$
$104$	298.659	+	172.431i	0.281595	+	0.162579i
$105$	2177.28			2.02363
$106$	−10.9106	−	18.8977i	−0.00999746	−	0.0173161i
$107$	1093.66	−	631.423i	0.988110	−	0.570486i	0.0834015	−	0.996516i	$-0.473422\pi$
$107$	1093.66	−	631.423i	0.988110	−	0.570486i	0.904709	+	0.426030i	$0.140088\pi$
$108$	532.000	+	921.451i	0.473997	+	0.820988i
$109$	−1175.46			−1.03293			−0.516463	−	0.856309i	$-0.672752\pi$
$109$	−1175.46			−1.03293			−0.516463	+	0.856309i	$0.672752\pi$
$110$	38.4821	+	22.2177i	0.0333557	+	0.0192579i
$111$	−1064.50	+	614.590i	−0.910252	+	0.525534i
$112$	1289.30	−	744.378i	1.08775	−	0.628010i
$113$	−157.820	+	273.352i	−0.131385	+	0.227565i	−0.924211	−	0.381883i	$-0.875276\pi$
$113$	−157.820	+	273.352i	−0.131385	+	0.227565i	0.792826	+	0.609448i	$0.208609\pi$
$114$	496.927	−	286.901i	0.408259	−	0.235708i
$115$	1625.85			1.31836
$116$			670.592i			0.536749i
$117$		−	252.899i		−	0.199833i
$118$	332.893	−	192.196i	0.259706	−	0.149941i
$119$	643.894			0.496014
$120$	778.927	−	449.714i	0.592550	−	0.342109i
$121$	661.107	−	1145.07i	0.496699	−	0.860308i
$122$	313.696	+	543.337i	0.232793	+	0.403209i
$123$	1509.00	−	871.219i	1.10619	−	0.638660i
$124$	572.498			0.414612
$125$			379.050i			0.271226i
$126$	345.910	+	199.711i	0.244572	+	0.141204i
$127$		−	271.537i		−	0.189724i	−0.995490	−	0.0948622i	$-0.969759\pi$
$127$		−	271.537i		−	0.189724i	0.995490	−	0.0948622i	$-0.0302410\pi$
$128$	727.500	−	1260.07i	0.502363	−	0.870119i
$129$	190.570	+	330.076i	0.130068	+	0.225284i
$130$	−344.642			−0.232516
$131$		−	1812.36i		−	1.20875i	−0.796699	−	0.604377i	$-0.793422\pi$
$131$		−	1812.36i		−	1.20875i	0.796699	−	0.604377i	$-0.206578\pi$
$132$	41.4994	+	71.8790i	0.0273641	+	0.0473959i
$133$	−2604.43	+	4511.00i	−1.69799	+	2.94100i
$134$	533.319	+	307.912i	0.343819	+	0.198504i
$135$	−1973.28	−	1139.28i	−1.25802	−	0.726320i
$136$	230.354	−	132.995i	0.145241	−	0.0838547i
$137$	733.500	+	423.486i	0.457424	+	0.264094i	0.710961	−	0.703232i	$-0.248260\pi$
$137$	733.500	+	423.486i	0.457424	+	0.264094i	−0.253536	+	0.967326i	$0.581594\pi$
$138$	−375.714	−	216.919i	−0.231760	−	0.133807i
$139$		−	842.456i		−	0.514073i	−0.966402	−	0.257037i	$-0.917254\pi$
$139$		−	842.456i		−	0.514073i	0.966402	−	0.257037i	$-0.0827461\pi$
$140$	−1905.12	+	3299.77i	−1.15009	+	1.99201i
$141$	−266.501	+	461.593i	−0.159173	+	0.275696i
$142$		−	290.015i		−	0.171391i
$143$		−	68.1502i		−	0.0398532i
$144$	−451.000			−0.260995
$145$	−718.034	−	1243.67i	−0.411238	−	0.712285i
$146$	66.3921	+	114.994i	0.0376346	+	0.0651850i
$147$	3901.99			2.18933
$148$		−	2151.06i		−	1.19471i
$149$			421.506i			0.231752i	0.993264	+	0.115876i	$0.0369676\pi$
$149$			421.506i			0.231752i	−0.993264	+	0.115876i	$0.963032\pi$
$150$	−199.428	+	345.419i	−0.108555	+	0.188022i
$151$	−204.445	+	354.109i	−0.110182	+	0.190841i	−0.915844	−	0.401535i	$-0.868477\pi$
$151$	−204.445	+	354.109i	−0.110182	+	0.190841i	0.805661	+	0.592376i	$0.201810\pi$
$152$			2151.76i			1.14823i
$153$	−168.927	−	97.5298i	−0.0892608	−	0.0515347i
$154$	93.2146	+	53.8175i	0.0487756	+	0.0281606i
$155$	−1061.75	+	613.001i	−0.550204	+	0.317661i
$156$	−557.497	−	321.871i	−0.286125	−	0.165194i
$157$	−1429.19	−	825.145i	−0.726510	−	0.419451i	0.0906343	−	0.995884i	$-0.471111\pi$
$157$	−1429.19	−	825.145i	−0.726510	−	0.419451i	−0.817144	+	0.576434i	$0.804444\pi$
$158$	−147.785	+	255.972i	−0.0744125	+	0.128886i
$159$	43.6424	+	75.5909i	0.0217677	+	0.0377028i
$160$			2413.46i			1.19251i
$161$	3938.28			1.92782
$162$	155.500	+	269.334i	0.0754150	+	0.130623i
$163$	299.837	−	519.333i	0.144080	−	0.249554i	−0.784949	−	0.619560i	$-0.787311\pi$
$163$	299.837	−	519.333i	0.144080	−	0.249554i	0.929029	+	0.370006i	$0.120644\pi$
$164$			3049.27i			1.45188i
$165$	−153.928	−	88.8706i	−0.0726262	−	0.0419307i
$166$		−	1366.67i		−	0.639000i
$167$	4230.88			1.96045			0.980226	−	0.197881i	$-0.0634059\pi$
$167$	4230.88			1.96045			0.980226	+	0.197881i	$0.0634059\pi$
$168$	1886.78	−	1089.33i	0.866478	−	0.500262i
$169$	−834.212	−	1444.90i	−0.379705	−	0.657668i
$170$	−132.911	+	230.208i	−0.0599634	+	0.103860i
$171$	1366.55	−	788.978i	0.611127	−	0.352834i
$172$	−666.994			−0.295685
$173$	−1583.17	+	914.046i	−0.695760	+	0.401698i	−0.805766	−	0.592233i	$-0.798246\pi$
$173$	−1583.17	+	914.046i	−0.695760	+	0.401698i	0.110006	+	0.993931i	$0.464913\pi$
$174$			383.195i			0.166954i
$175$		−	3620.73i		−	1.56401i
$176$	−121.534			−0.0520509
$177$	−1331.57	+	768.783i	−0.565463	+	0.326470i
$178$	394.034	−	682.487i	0.165922	−	0.287385i
$179$	−2541.78	+	1467.50i	−1.06135	+	0.612770i	−0.925805	−	0.378001i	$-0.876612\pi$
$179$	−2541.78	+	1467.50i	−1.06135	+	0.612770i	−0.135544	+	0.990771i	$0.543278\pi$
$180$	999.623	−	577.133i	0.413931	−	0.238983i
$181$	2272.11	+	1311.80i	0.933062	+	0.538704i	0.887779	−	0.460270i	$-0.152248\pi$
$181$	2272.11	+	1311.80i	0.933062	+	0.538704i	0.0452836	+	0.998974i	$0.485581\pi$
$182$	−834.821			−0.340006
$183$	−1254.78	−	2173.35i	−0.506865	−	0.877916i
$184$	1408.93	−	813.444i	0.564497	−	0.325913i
$185$	2303.25	+	3989.34i	0.915341	+	1.58542i
$186$	327.142			0.128963
$187$	−45.5217	−	26.2820i	−0.0178015	−	0.0102777i
$188$	−466.376	−	807.787i	−0.180925	−	0.313372i
$189$	−4779.85	−	2759.65i	−1.83959	−	1.06209i
$190$	−1075.19	−	1862.29i	−0.410541	−	0.711078i
$191$	1546.94	−	2679.38i	0.586035	−	1.01504i	−0.408710	−	0.912664i	$-0.634021\pi$
$191$	1546.94	−	2679.38i	0.586035	−	1.01504i	0.994746	−	0.102378i	$-0.0326452\pi$
$192$	−334.000	+	578.505i	−0.125544	+	0.217448i
$193$	−3014.35			−1.12424			−0.562118	−	0.827057i	$-0.690013\pi$
$193$	−3014.35			−1.12424			−0.562118	+	0.827057i	$0.690013\pi$
$194$	−184.856	−	937.284i	−0.0684119	−	0.346871i
$195$	1378.57			0.506264
$196$	−3414.24	+	5913.64i	−1.24426	+	2.15512i
$197$	−2355.52	+	4079.88i	−0.851897	+	1.47553i	0.0275976	+	0.999619i	$0.491214\pi$
$197$	−2355.52	+	4079.88i	−0.851897	+	1.47553i	−0.879494	+	0.475909i	$0.842119\pi$
$198$	−16.3033	−	28.2382i	−0.00585165	−	0.0101354i
$199$	−1798.44	−	1038.33i	−0.640644	−	0.369876i	0.144218	−	0.989546i	$-0.453933\pi$
$199$	−1798.44	−	1038.33i	−0.640644	−	0.369876i	−0.784863	+	0.619670i	$0.787267\pi$
$200$	−747.854	−	1295.32i	−0.264406	−	0.457965i
$201$	−2133.28	−	1231.65i	−0.748606	−	0.432208i
$202$	1146.46			0.399332
$203$	−1739.28	−	3012.53i	−0.601348	−	1.04157i
$204$	−429.995	+	248.258i	−0.147577	+	0.0852035i
$205$	−3264.99	−	5655.14i	−1.11238	−	1.92669i
$206$	952.784			0.322251
$207$	−1033.21	−	596.526i	−0.346924	−	0.200297i
$208$	816.335	−	471.311i	0.272128	−	0.157113i
$209$	368.253	−	212.611i	0.121878	−	0.0703665i
$210$	−1088.64	+	1885.58i	−0.357730	+	0.619607i
$211$	3653.30	−	2109.23i	1.19196	−	0.688178i	0.233208	−	0.972427i	$-0.425078\pi$
$211$	3653.30	−	2109.23i	1.19196	−	0.688178i	0.958751	+	0.284249i	$0.0917442\pi$
$212$	−152.748			−0.0494849
$213$			1160.06i			0.373174i
$214$			1262.85i			0.403394i
$215$	1237.00	−	714.182i	0.392384	−	0.226543i
$216$	−2280.00			−0.718215
$217$	−2571.85	+	1484.86i	−0.804557	+	0.464511i
$218$	587.732	−	1017.98i	0.182597	−	0.316268i
$219$	−265.568	−	459.978i	−0.0819427	−	0.141929i
$220$	269.375	−	155.524i	0.0825511	−	0.0476609i
$221$	407.688			0.124091
$222$		−	1229.18i		−	0.371609i
$223$	3730.09	+	2153.57i	1.12011	+	0.646697i	0.941430	−	0.337209i	$-0.109483\pi$
$223$	3730.09	+	2153.57i	1.12011	+	0.646697i	0.178683	+	0.983907i	$0.442816\pi$
$224$			5846.09i			1.74379i
$225$	−548.427	+	949.903i	−0.162497	+	0.281453i
$226$	−157.820	−	273.352i	−0.0464514	−	0.0804563i
$227$	6761.56			1.97701			0.988503	−	0.151201i	$-0.0483141\pi$
$227$	6761.56			1.97701			0.988503	+	0.151201i	$0.0483141\pi$
$228$		−	4016.61i		−	1.16670i
$229$	970.142	+	1680.33i	0.279951	+	0.484889i	0.971372	−	0.237562i	$-0.0763485\pi$
$229$	970.142	+	1680.33i	0.279951	+	0.484889i	−0.691421	+	0.722452i	$0.743015\pi$
$230$	−812.927	+	1408.03i	−0.233056	+	0.403664i
$231$	−372.858	−	215.270i	−0.106200	−	0.0613148i
$232$	−1244.46	−	718.491i	−0.352168	−	0.203324i
$233$	156.100	−	90.1242i	0.0438902	−	0.0253400i	−0.477894	−	0.878417i	$-0.658600\pi$
$233$	156.100	−	90.1242i	0.0438902	−	0.0253400i	0.521785	+	0.853077i	$0.325266\pi$
$234$	219.017	+	126.449i	0.0611862	+	0.0353259i
$235$	1729.87	+	998.742i	0.480189	+	0.277237i
$236$		−	2690.74i		−	0.742171i
$237$	591.142	−	1023.89i	0.162020	−	0.280627i
$238$	−321.947	+	557.629i	−0.0876837	+	0.151873i
$239$			3060.21i			0.828237i	0.910223	+	0.414118i	$0.135910\pi$
$239$			3060.21i			0.828237i	−0.910223	+	0.414118i	$0.864090\pi$
$240$		−	2458.44i		−	0.661214i
$241$	−5839.78			−1.56089			−0.780443	−	0.625227i	$-0.785006\pi$
$241$	−5839.78			−1.56089			−0.780443	+	0.625227i	$0.785006\pi$
$242$	661.107	+	1145.07i	0.175610	+	0.304165i
$243$	1430.00	+	2476.83i	0.377508	+	0.653864i
$244$	4391.74			1.15226
$245$		−	14623.2i		−	3.81322i
$246$			1742.44i			0.451601i
$247$	−1649.02	+	2856.19i	−0.424796	+	0.735768i
$248$	−613.391	+	1062.42i	−0.157058	+	0.272032i
$249$			5466.67i			1.39131i
$250$	−328.267	−	189.525i	−0.0830457	−	0.0479465i
$251$	−6493.00	−	3748.73i	−1.63281	−	0.942701i	−0.983222	−	0.182412i	$-0.941610\pi$
$251$	−6493.00	−	3748.73i	−1.63281	−	0.942701i	−0.649584	−	0.760290i	$-0.725057\pi$
$252$	2421.37	−	1397.98i	0.605286	−	0.349462i
$253$	−278.427	−	160.750i	−0.0691879	−	0.0399456i
$254$	235.158	+	135.768i	0.0580910	+	0.0335388i
$255$	531.642	−	920.832i	0.130560	−	0.226136i
$256$	59.5000	+	103.057i	0.0145264	+	0.0251604i
$257$		−	1562.35i		−	0.379210i	−0.981860	−	0.189605i	$-0.939279\pi$
$257$		−	1562.35i		−	0.379210i	0.981860	−	0.189605i	$-0.0607208\pi$
$258$	−381.139			−0.0919717
$259$	5579.11	+	9663.30i	1.33849	+	2.31833i
$260$	−1206.25	+	2089.28i	−0.287724	+	0.498353i
$261$			1053.79i			0.249915i
$262$	1569.55	+	906.181i	0.370104	+	0.213680i
$263$			2143.13i			0.502476i	0.967925	+	0.251238i	$0.0808376\pi$
$263$			2143.13i			0.502476i	−0.967925	+	0.251238i	$0.919162\pi$
$264$	−177.854			−0.0414628
$265$	283.285	−	163.555i	0.0656683	−	0.0379136i
$266$	−2604.43	−	4511.00i	−0.600329	−	1.03980i
$267$	−1576.14	+	2729.95i	−0.361266	+	0.625730i
$268$	3733.23	−	2155.38i	0.850909	−	0.491273i
$269$	2309.67			0.523506			0.261753	−	0.965135i	$-0.415699\pi$
$269$	2309.67			0.523506			0.261753	+	0.965135i	$0.415699\pi$
$270$	1973.28	−	1139.28i	0.444778	−	0.256793i
$271$			6242.12i			1.39919i	0.714537	+	0.699597i	$0.246637\pi$
$271$			6242.12i			1.39919i	−0.714537	+	0.699597i	$0.753363\pi$
$272$		−	727.040i		−	0.162071i
$273$	3339.28			0.740303
$274$	−733.500	+	423.486i	−0.161724	+	0.0933714i
$275$	−147.788	+	255.976i	−0.0324071	+	0.0561307i
$276$	−2630.00	+	1518.43i	−0.573577	+	0.331155i
$277$	4171.52	−	2408.43i	0.904847	−	0.522413i	0.0260771	−	0.999660i	$-0.491698\pi$
$277$	4171.52	−	2408.43i	0.904847	−	0.522413i	0.878769	+	0.477247i	$0.158365\pi$
$278$	729.588	+	421.228i	0.157402	+	0.0908762i
$279$	899.640			0.193047
$280$	−4082.40	−	7070.93i	−0.871323	−	1.50917i
$281$	1162.32	−	671.068i	0.246756	−	0.142465i	−0.371522	−	0.928424i	$-0.621164\pi$
$281$	1162.32	−	671.068i	0.246756	−	0.142465i	0.618278	+	0.785959i	$0.287831\pi$
$282$	−266.501	−	461.593i	−0.0562762	−	0.0974732i
$283$	5040.31			1.05871			0.529355	−	0.848400i	$-0.322434\pi$
$283$	5040.31			1.05871			0.529355	+	0.848400i	$0.322434\pi$
$284$	−1758.12	−	1015.05i	−0.367343	−	0.212085i
$285$	4300.78	+	7449.17i	0.893881	+	1.54825i
$286$	59.0198	+	34.0751i	0.0122025	+	0.00704511i
$287$	−7908.74	−	13698.3i	−1.62661	−	2.81738i
$288$	885.500	−	1533.73i	0.181176	−	0.313805i
$289$	−2299.28	+	3982.46i	−0.467998	+	0.810597i
$290$	1436.07			0.290789
$291$	739.425	+	3749.14i	0.148955	+	0.755252i
$292$	929.489			0.186282
$293$	133.833	−	231.805i	0.0266846	−	0.0462191i	−0.852375	−	0.522931i	$-0.824838\pi$
$293$	133.833	−	231.805i	0.0266846	−	0.0462191i	0.879059	+	0.476712i	$0.158172\pi$
$294$	−1951.00	+	3379.22i	−0.387022	+	0.670341i
$295$	2881.10	+	4990.22i	0.568625	+	0.984887i
$296$	3991.88	+	2304.71i	0.783862	+	0.452563i
$297$	225.282	+	390.200i	0.0440141	+	0.0762347i
$298$	−365.034	−	210.753i	−0.0709593	−	0.0409684i
$299$	2493.56			0.482296
$300$	1395.99	+	2417.93i	0.268659	+	0.465332i
$301$	2996.36	−	1729.95i	0.573778	−	0.331271i
$302$	−204.445	−	354.109i	−0.0389553	−	0.0674725i
$303$	−4585.86			−0.869474
$304$	5093.50	+	2940.74i	0.960962	+	0.554812i
$305$	−8144.88	+	4702.45i	−1.52910	+	0.882824i
$306$	168.927	−	97.5298i	0.0315585	−	0.0182203i
$307$	2195.82	−	3803.27i	0.408215	−	0.707049i	−0.586475	−	0.809968i	$-0.699485\pi$
$307$	2195.82	−	3803.27i	0.408215	−	0.707049i	0.994690	+	0.102918i	$0.0328180\pi$
$308$	652.502	−	376.722i	0.120713	−	0.0696940i
$309$	−3811.14			−0.701644
$310$		−	1226.00i		−	0.224620i
$311$			486.234i			0.0886554i	0.999017	+	0.0443277i	$0.0141146\pi$
$311$			486.234i			0.0886554i	−0.999017	+	0.0443277i	$0.985885\pi$
$312$	1194.64	−	689.723i	0.216772	−	0.125154i
$313$	−1839.50			−0.332187			−0.166094	−	0.986110i	$-0.553115\pi$
$313$	−1839.50			−0.332187			−0.166094	+	0.986110i	$0.553115\pi$
$314$	1429.19	−	825.145i	0.256860	−	0.148298i
$315$	−2993.76	+	5185.35i	−0.535490	+	0.927496i
$316$	1034.50	+	1791.80i	0.184162	+	0.318977i
$317$	8214.97	−	4742.92i	1.45552	−	0.840343i	0.456731	−	0.889605i	$-0.349020\pi$
$317$	8214.97	−	4742.92i	1.45552	−	0.840343i	0.998786	+	0.0492615i	$0.0156868\pi$
$318$	−87.2848			−0.0153921
$319$			283.971i			0.0498411i
$320$	2168.01	+	1251.70i	0.378736	+	0.218664i
$321$		−	5051.39i		−	0.878320i
$322$	−1969.14	+	3410.65i	−0.340795	+	0.590273i
$323$	1271.88	+	2202.96i	0.219100	+	0.379493i
$324$	2177.00			0.373285
$325$		−	2292.50i		−	0.391277i
$326$	299.837	+	519.333i	0.0509400	+	0.0882307i
$327$	−2350.93	+	4071.93i	−0.397574	+	0.688618i
$328$	−5658.74	−	3267.07i	−0.952596	−	0.549981i
$329$	4190.24	+	2419.23i	0.702174	+	0.405400i
$330$	153.928	−	88.8706i	0.0256772	−	0.0148248i
$331$	−2098.30	−	1211.45i	−0.348438	−	0.201171i	0.315559	−	0.948906i	$-0.397808\pi$
$331$	−2098.30	−	1211.45i	−0.348438	−	0.201171i	−0.663997	+	0.747735i	$0.731141\pi$
$332$	−8284.98	−	4783.33i	−1.36957	−	0.790722i
$333$		−	3380.24i		−	0.556265i
$334$	−2115.44	+	3664.05i	−0.346562	+	0.600263i
$335$	−4615.74	+	7994.70i	−0.752791	+	1.30387i
$336$		−	5955.03i		−	0.966885i
$337$			6785.50i			1.09682i	0.836208	+	0.548412i	$0.184768\pi$
$337$			6785.50i			1.09682i	−0.836208	+	0.548412i	$0.815232\pi$
$338$	1668.42			0.268492
$339$	631.280	+	1093.41i	0.101140	+	0.175179i
$340$	930.374	+	1611.46i	0.148402	+	0.257040i
$341$	242.432			0.0384997
$342$			1577.96i			0.249491i
$343$		−	22966.7i		−	3.61541i
$344$	714.636	−	1237.79i	0.112008	−	0.194003i
$345$	3251.71	−	5632.12i	0.507438	−	0.878908i
$346$		−	1828.09i		−	0.284043i
$347$	797.785	+	460.601i	0.123422	+	0.0712576i	0.560440	−	0.828195i	$-0.310632\pi$
$347$	797.785	+	460.601i	0.123422	+	0.0712576i	−0.437018	+	0.899453i	$0.643965\pi$
$348$	2323.00	+	1341.18i	0.357833	+	0.206595i
$349$	−7401.74	+	4273.40i	−1.13526	+	0.655443i	−0.945253	−	0.326339i	$-0.894185\pi$
$349$	−7401.74	+	4273.40i	−1.13526	+	0.655443i	−0.190009	+	0.981782i	$0.560852\pi$
$350$	3135.64	+	1810.36i	0.478877	+	0.276480i
$351$	−3026.41	−	1747.30i	−0.460222	−	0.265709i
$352$	238.621	−	413.304i	0.0361323	−	0.0625829i
$353$	3840.54	+	6652.01i	0.579069	+	1.00298i	0.995586	+	0.0938488i	$0.0299170\pi$
$353$	3840.54	+	6652.01i	0.579069	+	1.00298i	−0.416518	+	0.909128i	$0.636750\pi$
$354$		−	1537.57i		−	0.230849i
$355$	4347.46			0.649969
$356$	−2758.24	−	4777.41i	−0.410636	−	0.711242i
$357$	1287.79	−	2230.51i	0.190916	−	0.330676i
$358$		−	2935.00i		−	0.433294i
$359$	2603.73	+	1503.26i	0.382784	+	0.221000i	0.679029	−	0.734112i	$-0.262401\pi$
$359$	2603.73	+	1503.26i	0.382784	+	0.221000i	−0.296245	+	0.955112i	$0.595734\pi$
$360$			2473.43i			0.362114i
$361$	−13719.1			−2.00015
$362$	−2272.11	+	1311.80i	−0.329887	+	0.190461i
$363$	−2644.43	−	4580.28i	−0.382359	−	0.662266i
$364$	−2921.87	+	5060.83i	−0.420736	+	0.728736i
$365$	−1723.82	+	995.248i	−0.247202	+	0.142722i
$366$	2509.57			0.358408
$367$	−1922.23	+	1109.80i	−0.273405	+	0.157851i	−0.630434	−	0.776243i	$-0.717123\pi$
$367$	−1922.23	+	1109.80i	−0.273405	+	0.157851i	0.357029	+	0.934093i	$0.383790\pi$
$368$		−	4446.83i		−	0.629910i
$369$			4791.71i			0.676006i
$370$	−4606.49			−0.647244
$371$	686.197	−	396.176i	0.0960258	−	0.0554405i
$372$	1145.00	−	1983.19i	0.159584	−	0.276408i
$373$	5462.99	−	3154.06i	0.758346	−	0.437831i	−0.0703559	−	0.997522i	$-0.522413\pi$
$373$	5462.99	−	3154.06i	0.758346	−	0.437831i	0.828701	+	0.559691i	$0.189080\pi$
$374$	45.5217	−	26.2820i	0.00629378	−	0.00363371i
$375$	1313.07	+	758.100i	0.180817	+	0.104395i
$376$	1998.75			0.274143
$377$	−1101.25	−	1907.41i	−0.150443	−	0.260575i
$378$	4779.85	−	2759.65i	0.650394	−	0.375505i
$379$	2247.73	+	3893.18i	0.304639	+	0.527650i	0.977181	−	0.212409i	$-0.0681310\pi$
$379$	2247.73	+	3893.18i	0.304639	+	0.527650i	−0.672542	+	0.740059i	$0.734798\pi$
$380$	−15052.7			−2.03208
$381$	−940.631	−	543.073i	−0.126483	−	0.0730249i
$382$	1546.94	+	2679.38i	0.207195	+	0.358872i
$383$	−1495.25	−	863.283i	−0.199488	−	0.115174i	0.396929	−	0.917849i	$-0.370076\pi$
$383$	−1495.25	−	863.283i	−0.199488	−	0.115174i	−0.596416	+	0.802675i	$0.703409\pi$
$384$	−2910.00	−	5040.27i	−0.386720	−	0.669818i
$385$	−806.748	+	1397.33i	−0.106794	+	0.184973i
$386$	1507.17	−	2610.50i	0.198739	−	0.344225i
$387$	−1048.13			−0.137673
$388$	−6328.98	−	2159.86i	−0.828106	−	0.282604i
$389$	−7892.01			−1.02864			−0.514320	−	0.857598i	$-0.671956\pi$
$389$	−7892.01			−1.02864			−0.514320	+	0.857598i	$0.671956\pi$
$390$	−689.285	+	1193.88i	−0.0894956	+	0.155011i
$391$	961.637	−	1665.60i	0.124379	−	0.215430i
$392$	−7316.24	−	12672.1i	−0.942668	−	1.63275i
$393$	−6278.20	−	3624.72i	−0.805836	−	0.465250i
$394$	−2355.52	−	4079.88i	−0.301191	−	0.521678i
$395$	−3837.14	−	2215.37i	−0.488778	−	0.282196i
$396$	−228.246			−0.0289642
$397$	962.503	+	1667.10i	0.121679	+	0.210755i	0.920430	−	0.390907i	$-0.127839\pi$
$397$	962.503	+	1667.10i	0.121679	+	0.210755i	−0.798751	+	0.601662i	$0.794505\pi$
$398$	1798.44	−	1038.33i	0.226502	−	0.130771i
$399$	10417.7	+	18044.0i	1.30711	+	2.26398i
$400$	−4088.27			−0.511034
$401$	2461.24	+	1421.00i	0.306505	+	0.176961i	0.645362	−	0.763877i	$-0.276707\pi$
$401$	2461.24	+	1421.00i	0.306505	+	0.176961i	−0.338856	+	0.940838i	$0.610040\pi$
$402$	2133.28	−	1231.65i	0.264672	−	0.152809i
$403$	−1628.40	+	940.156i	−0.201281	+	0.116210i
$404$	4012.63	−	6950.07i	0.494148	−	0.855889i
$405$	−4037.44	+	2331.02i	−0.495363	+	0.285998i
$406$	3478.56			0.425217
$407$		−	910.896i		−	0.110937i
$408$		−	1063.96i		−	0.129103i
$409$	1386.37	−	800.420i	0.167608	−	0.0967683i	−0.413850	−	0.910345i	$-0.635816\pi$
$409$	1386.37	−	800.420i	0.167608	−	0.0967683i	0.581457	+	0.813577i	$0.302483\pi$
$410$	6529.99			0.786569
$411$	2934.00	−	1693.95i	0.352125	−	0.203300i
$412$	3334.74	−	5775.95i	0.398765	−	0.690681i
$413$	6978.84	+	12087.7i	0.831493	+	1.44019i
$414$	1033.21	−	596.526i	0.122656	−	0.0708156i
$415$	20487.0			2.42329
$416$			3701.52i			0.436254i
$417$	−2918.35	−	1684.91i	−0.342715	−	0.197867i
$418$			425.222i			0.0497566i
$419$	7105.04	−	12306.3i	0.828410	−	1.43485i	−0.0708745	−	0.997485i	$-0.522579\pi$
$419$	7105.04	−	12306.3i	0.828410	−	1.43485i	0.899285	−	0.437364i	$-0.144088\pi$
$420$	7620.49	+	13199.1i	0.885337	+	1.53345i
$421$	−5286.53			−0.611995			−0.305997	−	0.952032i	$-0.598990\pi$
$421$	−5286.53			−0.611995			−0.305997	+	0.952032i	$0.598990\pi$
$422$			4218.46i			0.486615i
$423$	−732.877	−	1269.38i	−0.0842404	−	0.145909i
$424$	163.659	−	283.466i	0.0187452	−	0.0324677i
$425$	−1531.30	−	884.098i	−0.174774	−	0.100906i
$426$	−1004.64	−	580.030i	−0.114261	−	0.0659684i
$427$	−19729.2	+	11390.7i	−2.23598	+	1.29094i
$428$	7655.60	+	4419.96i	0.864597	+	0.499175i
$429$	−236.079	−	136.300i	−0.0265688	−	0.0153395i
$430$			1428.36i			0.160190i
$431$	−820.919	+	1421.87i	−0.0917454	+	0.158908i	−0.908246	−	0.418437i	$-0.862578\pi$
$431$	−820.919	+	1421.87i	−0.0917454	+	0.158908i	0.816500	+	0.577345i	$0.195911\pi$
$432$	−3116.00	+	5397.07i	−0.347034	+	0.601080i
$433$		−	8683.96i		−	0.963798i	−0.876227	−	0.481899i	$-0.839947\pi$
$433$		−	8683.96i		−	0.963798i	0.876227	−	0.481899i	$-0.160053\pi$
$434$		−	2969.72i		−	0.328459i
$435$	−5744.28			−0.633142
$436$	−4114.12	−	7125.87i	−0.451905	−	0.782723i
$437$	7779.27	+	13474.1i	0.851563	+	1.47495i
$438$	531.137			0.0579422
$439$		−	12070.8i		−	1.31232i	−0.754622	−	0.656160i	$-0.772180\pi$
$439$		−	12070.8i		−	1.31232i	0.754622	−	0.656160i	$-0.227820\pi$
$440$			666.530i			0.0722172i
$441$	−5365.24	+	9292.87i	−0.579337	+	1.00344i
$442$	−203.844	+	353.069i	−0.0219364	+	0.0379949i
$443$		−	5333.66i		−	0.572031i	−0.958225	−	0.286015i	$-0.907669\pi$
$443$		−	5333.66i		−	0.572031i	0.958225	−	0.286015i	$-0.0923309\pi$
$444$	−7451.50	−	4302.13i	−0.796470	−	0.459842i
$445$	10230.8	+	5906.75i	1.08986	+	0.629229i
$446$	−3730.09	+	2153.57i	−0.396020	+	0.228642i
$447$	1460.14	+	843.011i	0.154501	+	0.0892015i
$448$	5251.54	+	3031.98i	0.553822	+	0.319749i
$449$	−1595.81	+	2764.02i	−0.167730	+	0.290517i	−0.937621	−	0.347658i	$-0.886977\pi$
$449$	−1595.81	+	2764.02i	−0.167730	+	0.290517i	0.769891	+	0.638175i	$0.220310\pi$
$450$	−548.427	−	949.903i	−0.0574513	−	0.0995085i
$451$			1291.25i			0.134817i
$452$	−2209.48			−0.229923
$453$	817.780	+	1416.44i	0.0848183	+	0.146910i
$454$	−3380.78	+	5855.68i	−0.349489	+	0.605332i
$455$		−	12514.4i		−	1.28941i
$456$	7453.91	+	4303.52i	0.765485	+	0.441953i
$457$			1674.27i			0.171377i	0.996322	+	0.0856883i	$0.0273089\pi$
$457$			1674.27i			0.171377i	−0.996322	+	0.0856883i	$0.972691\pi$
$458$	−1940.28			−0.197955
$459$	−2334.26	+	1347.68i	−0.237372	+	0.137047i
$460$	5690.49	+	9856.22i	0.576784	+	0.999019i
$461$	6128.92	−	10615.6i	0.619203	−	1.07249i	−0.370429	−	0.928861i	$-0.620789\pi$
$461$	6128.92	−	10615.6i	0.619203	−	1.07249i	0.989632	−	0.143630i	$-0.0458774\pi$
$462$	372.858	−	215.270i	0.0375475	−	0.0216780i
$463$	4734.21			0.475200			0.237600	−	0.971363i	$-0.423639\pi$
$463$	4734.21			0.475200			0.237600	+	0.971363i	$0.423639\pi$
$464$	−3401.53	+	1963.88i	−0.340328	+	0.196489i
$465$			4904.01i			0.489071i
$466$			180.248i			0.0179181i
$467$	2039.53			0.202094			0.101047	−	0.994882i	$-0.467781\pi$
$467$	2039.53			0.202094			0.101047	+	0.994882i	$0.467781\pi$
$468$	1533.12	−	885.145i	0.151428	−	0.0874270i
$469$	−11180.6	+	19365.4i	−1.10080	+	1.90664i
$470$	−1729.87	+	998.742i	−0.169772	+	0.0980181i
$471$	−5716.77	+	3300.58i	−0.559267	+	0.322893i
$472$	4993.39	+	2882.94i	0.486948	+	0.281140i
$473$	−282.447			−0.0274565
$474$	591.142	+	1023.89i	0.0572828	+	0.0992167i
$475$	12387.6	−	7152.01i	1.19660	−	0.690856i
$476$	2253.63	+	3903.40i	0.217006	+	0.375866i
$477$	−240.033			−0.0230406
$478$	−2650.22	−	1530.11i	−0.253595	−	0.146413i
$479$	−8882.75	−	15385.4i	−0.847314	−	1.46759i	−0.883597	−	0.468249i	$-0.844885\pi$
$479$	−8882.75	−	15385.4i	−0.847314	−	1.46759i	0.0362827	−	0.999342i	$-0.488448\pi$
$480$	8360.49	+	4826.93i	0.795005	+	0.458996i
$481$	3532.47	+	6118.43i	0.334859	+	0.579992i
$482$	2919.89	−	5057.40i	0.275928	−	0.477922i
$483$	7876.56	−	13642.6i	0.742020	−	1.28522i
$484$	9255.49			0.869224
$485$	14050.3	−	2771.08i	1.31545	−	0.259440i
$486$	−2860.00			−0.266939
$487$	−407.370	+	705.585i	−0.0379049	+	0.0656532i	−0.884355	−	0.466814i	$-0.845402\pi$
$487$	−407.370	+	705.585i	−0.0379049	+	0.0656532i	0.846451	+	0.532467i	$0.178735\pi$
$488$	−4705.44	+	8150.06i	−0.436486	+	0.756016i
$489$	−1199.35	−	2077.33i	−0.110913	−	0.192107i
$490$	12664.0	+	7311.58i	1.16756	+	0.674089i
$491$	−7105.78	−	12307.6i	−0.653115	−	1.13123i	−0.982363	−	0.186985i	$-0.940128\pi$
$491$	−7105.78	−	12307.6i	−0.653115	−	1.13123i	0.329248	−	0.944244i	$-0.393205\pi$
$492$	10563.0	+	6098.54i	0.967918	+	0.558828i
$493$	−1698.77			−0.155190
$494$	−1649.02	−	2856.19i	−0.150188	−	0.260133i
$495$	423.303	−	244.394i	0.0384365	−	0.0221913i
$496$	1676.60	+	2903.96i	0.151777	+	0.262886i
$497$	10530.8			0.950442
$498$	−4734.27	−	2733.33i	−0.426000	−	0.245951i
$499$	−2605.04	+	1504.02i	−0.233702	+	0.134928i	−0.612279	−	0.790642i	$-0.709747\pi$
$499$	−2605.04	+	1504.02i	−0.233702	+	0.134928i	0.378577	+	0.925570i	$0.376414\pi$
$500$	−2297.87	+	1326.67i	−0.205528	+	0.118661i
$501$	8461.76	−	14656.2i	0.754578	−	1.30697i
$502$	6493.00	−	3748.73i	0.577284	−	0.333295i
$503$	−21576.7			−1.91264			−0.956319	−	0.292325i	$-0.905571\pi$
$503$	−21576.7			−1.91264			−0.956319	+	0.292325i	$0.905571\pi$
$504$			5991.34i			0.529515i
$505$			17186.0i			1.51439i
$506$	278.427	−	160.750i	0.0244616	−	0.0141229i
$507$	−6673.70			−0.584594
$508$	1646.10	−	950.379i	0.143768	−	0.0830044i
$509$	2546.84	−	4411.25i	0.221781	−	0.384136i	−0.733568	−	0.679616i	$-0.762146\pi$
$509$	2546.84	−	4411.25i	0.221781	−	0.384136i	0.955349	+	0.295480i	$0.0954797\pi$
$510$	531.642	+	920.832i	0.0461598	+	0.0799512i
$511$	−4175.58	+	2410.77i	−0.361481	+	0.208701i
$512$	11521.0			0.994455
$513$		−	21804.5i		−	1.87659i
$514$	1353.04	+	781.177i	0.116109	+	0.0670355i
$515$			14282.7i			1.22208i
$516$	−1333.99	+	2310.53i	−0.113809	+	0.197123i
$517$	−197.493	−	342.068i	−0.0168003	−	0.0290989i
$518$	−11158.2			−0.946456
$519$			7312.37i			0.618454i
$520$	−2584.82	−	4477.04i	−0.217984	−	0.377560i
$521$	7947.63	−	13765.7i	0.668315	−	1.15756i	−0.310060	−	0.950717i	$-0.600349\pi$
$521$	7947.63	−	13765.7i	0.668315	−	1.15756i	0.978375	−	0.206839i	$-0.0663175\pi$
$522$	−912.607	−	526.894i	−0.0765205	−	0.0441791i
$523$	10657.0	+	6152.83i	0.891011	+	0.514426i	0.874273	−	0.485434i	$-0.161338\pi$
$523$	10657.0	+	6152.83i	0.891011	+	0.514426i	0.0167383	+	0.999860i	$0.494672\pi$
$524$	10986.9	−	6343.27i	0.915960	−	0.528830i
$525$	−12542.6	−	7241.45i	−1.04267	−	0.601986i
$526$	−1856.01	−	1071.57i	−0.153851	−	0.0888260i
$527$			1450.28i			0.119877i
$528$	−243.068	+	421.006i	−0.0200344	+	0.0347006i
$529$	−201.794	+	349.517i	−0.0165853	+	0.0287266i
$530$			327.110i			0.0268090i
$531$		−	4228.31i		−	0.345561i
$532$	−36462.0			−2.97148
$533$	−5007.50	−	8673.25i	−0.406940	−	0.704841i
$534$	−1576.14	−	2729.95i	−0.127727	−	0.221229i
$535$	−18930.7			−1.52980
$536$			9237.36i			0.744390i
$537$			11740.0i			0.943422i
$538$	−1154.84	+	2000.23i	−0.0925436	+	0.160290i
$539$	−1445.81	+	2504.21i	−0.115538	+	0.200119i
$540$		−	15949.9i		−	1.27106i
$541$	−10066.3	−	5811.77i	−0.799968	−	0.461862i	0.0434917	−	0.999054i	$-0.486152\pi$
$541$	−10066.3	−	5811.77i	−0.799968	−	0.461862i	−0.843460	+	0.537192i	$0.819485\pi$
$542$	−5405.83	−	3121.06i	−0.428414	−	0.247345i
$543$	9088.42	−	5247.20i	0.718272	−	0.414694i
$544$	2472.47	+	1427.48i	0.194865	+	0.112505i
$545$	15260.0	+	8810.37i	1.19939	+	0.692468i
$546$	−1669.64	+	2891.91i	−0.130868	+	0.226671i
$547$	−1530.34	−	2650.63i	−0.119621	−	0.207190i	0.799996	−	0.600005i	$-0.204835\pi$
$547$	−1530.34	−	2650.63i	−0.119621	−	0.207190i	−0.919618	+	0.392815i	$0.871501\pi$
$548$			5928.81i			0.462165i
$549$	6901.31			0.536504
$550$	−147.788	−	255.976i	−0.0114576	−	0.0198452i
$551$	6871.20	−	11901.3i	0.531257	−	0.920165i
$552$		−	6507.56i		−	0.501775i
$553$	−9294.63	−	5366.26i	−0.714734	−	0.412652i
$554$			4816.86i			0.369402i
$555$	18426.0			1.40926
$556$	5107.12	−	2948.60i	0.389550	−	0.224907i
$557$	2663.64	+	4613.55i	0.202625	+	0.350956i	0.949373	−	0.314150i	$-0.101720\pi$
$557$	2663.64	+	4613.55i	0.202625	+	0.350956i	−0.746749	+	0.665106i	$0.768386\pi$
$558$	−449.820	+	779.111i	−0.0341262	+	0.0591082i
$559$	1897.18	−	1095.34i	0.143546	−	0.0828762i
$560$	−22317.1			−1.68406
$561$	−182.087	+	105.128i	−0.0137036	+	0.00791177i
$562$			1342.14i			0.100738i
$563$			19790.0i			1.48144i	0.671816	+	0.740718i	$0.265515\pi$
$563$			19790.0i			1.48144i	−0.671816	+	0.740718i	$0.734485\pi$
$564$	−3731.01			−0.278553
$565$	4097.67	−	2365.79i	0.305116	−	0.176159i
$566$	−2520.15	+	4365.03i	−0.187155	+	0.324163i
$567$	−9779.82	+	5646.38i	−0.724363	+	0.418211i
$568$	3767.40	−	2175.11i	0.278304	−	0.160679i
$569$	−19678.8	−	11361.5i	−1.44987	−	0.837084i	−0.451398	−	0.892323i	$-0.649075\pi$
$569$	−19678.8	−	11361.5i	−1.44987	−	0.837084i	−0.998473	+	0.0552390i	$0.982408\pi$
$570$	−8601.56			−0.632070
$571$	8422.31	+	14587.9i	0.617272	+	1.06915i	0.989981	+	0.141199i	$0.0450957\pi$
$571$	8422.31	+	14587.9i	0.617272	+	1.06915i	−0.372709	+	0.927948i	$0.621571\pi$
$572$	413.139	−	238.526i	0.0301996	−	0.0174358i
$573$	−6187.76	−	10717.5i	−0.451130	−	0.781380i
$574$	15817.5			1.15019
$575$	−9365.98	−	5407.45i	−0.679284	−	0.392185i
$576$	−918.500	−	1590.89i	−0.0664424	−	0.115082i
$577$	13227.9	+	7637.13i	0.954393	+	0.551019i	0.894443	−	0.447182i	$-0.147573\pi$
$577$	13227.9	+	7637.13i	0.954393	+	0.551019i	0.0599501	+	0.998201i	$0.480906\pi$
$578$	−2299.28	−	3982.46i	−0.165462	−	0.286589i
$579$	−6028.69	+	10442.0i	−0.432718	+	0.749490i
$580$	5026.24	−	8705.71i	0.359833	−	0.623250i
$581$	49625.2			3.54355
$582$	−3616.56	−	1234.21i	−0.257579	−	0.0879029i
$583$	−64.6833			−0.00459504
$584$	−995.881	+	1724.92i	−0.0705648	+	0.122222i
$585$	−1895.53	+	3283.16i	−0.133967	+	0.232038i
$586$	133.833	+	231.805i	0.00943443	+	0.0163409i
$587$	−8976.08	−	5182.34i	−0.631146	−	0.364392i	0.150050	−	0.988678i	$-0.452057\pi$
$587$	−8976.08	−	5182.34i	−0.631146	−	0.364392i	−0.781196	+	0.624286i	$0.785390\pi$
$588$	13657.0	+	23654.6i	0.957830	+	1.65901i
$589$	−10160.4	−	5866.08i	−0.710781	−	0.410370i
$590$	−5762.20			−0.402078
$591$	9422.07	+	16319.5i	0.655790	+	1.13586i
$592$	10911.1	−	6299.54i	0.757508	−	0.437347i
$593$	−3826.17	−	6627.12i	−0.264961	−	0.458926i	0.702592	−	0.711593i	$-0.252026\pi$
$593$	−3826.17	−	6627.12i	−0.264961	−	0.458926i	−0.967553	+	0.252666i	$0.918692\pi$
$594$	−450.564			−0.0311227
$595$	−8359.11	−	4826.13i	−0.575950	−	0.332525i
$596$	−2555.24	+	1475.27i	−0.175615	+	0.101392i
$597$	−7193.77	+	4153.33i	−0.493168	+	0.284731i
$598$	−1246.78	+	2159.49i	−0.0852587	+	0.147672i
$599$	3759.28	−	2170.42i	0.256428	−	0.148049i	−0.366276	−	0.930506i	$-0.619367\pi$
$599$	3759.28	−	2170.42i	0.256428	−	0.148049i	0.622704	+	0.782458i	$0.286034\pi$
$600$	−5982.84			−0.407080
$601$			10706.8i			0.726687i	0.931655	+	0.363343i	$0.118365\pi$
$601$			10706.8i			0.726687i	−0.931655	+	0.363343i	$0.881635\pi$
$602$			3459.90i			0.234244i
$603$	5866.51	−	3387.03i	0.396190	−	0.228741i
$604$	−2862.23			−0.192819
$605$	−17165.1	+	9910.29i	−1.15349	+	0.665968i
$606$	2292.93	−	3971.47i	0.153703	−	0.266221i
$607$	−2133.11	−	3694.66i	−0.142636	−	0.247053i	0.785852	−	0.618414i	$-0.212225\pi$
$607$	−2133.11	−	3694.66i	−0.142636	−	0.247053i	−0.928489	+	0.371361i	$0.878891\pi$
$608$	−20001.3	+	11547.8i	−1.33415	+	0.770269i
$609$	−13914.3			−0.925836
$610$		−	9404.90i		−	0.624251i
$611$	2653.09	+	1531.76i	0.175667	+	0.101422i
$612$		−	1365.42i		−	0.0901858i
$613$	4688.65	−	8120.98i	0.308928	−	0.535079i	−0.669200	−	0.743082i	$-0.733363\pi$
$613$	4688.65	−	8120.98i	0.308928	−	0.535079i	0.978128	+	0.208003i	$0.0666965\pi$
$614$	2195.82	+	3803.27i	0.144326	+	0.249980i
$615$	−26120.0			−1.71262
$616$			1614.52i			0.105602i
$617$	−10090.5	−	17477.2i	−0.658391	−	1.14037i	−0.981032	−	0.193845i	$-0.937904\pi$
$617$	−10090.5	−	17477.2i	−0.658391	−	1.14037i	0.322641	−	0.946521i	$-0.395429\pi$
$618$	1905.57	−	3300.54i	0.124034	−	0.214834i
$619$	−16139.9	−	9318.37i	−1.04801	−	0.605068i	−0.125917	−	0.992041i	$-0.540187\pi$
$619$	−16139.9	−	9318.37i	−1.04801	−	0.605068i	−0.922091	+	0.386973i	$0.873521\pi$
$620$	−7432.24	−	4291.01i	−0.481429	−	0.277953i
$621$	−14277.1	+	8242.90i	−0.922579	+	0.532651i
$622$	−421.091	−	243.117i	−0.0271451	−	0.0156722i
$623$	24781.9	+	14307.8i	1.59368	+	0.920113i
$624$		−	3770.49i		−	0.241892i
$625$	9073.19	−	15715.2i	0.580684	−	1.00577i
$626$	919.749	−	1593.05i	0.0587229	−	0.101711i
$627$		−	1700.89i		−	0.108336i
$628$		−	11552.0i		−	0.734038i
$629$	5449.16			0.345425
$630$	−2993.76	−	5185.35i	−0.189324	−	0.327919i
$631$	−11681.1	−	20232.3i	−0.736956	−	1.27645i	−0.953860	−	0.300252i	$-0.902929\pi$
$631$	−11681.1	−	20232.3i	−0.736956	−	1.27645i	0.216904	−	0.976193i	$-0.430404\pi$
$632$	−4433.56			−0.279047
$633$		−	16873.9i		−	1.05952i
$634$			9485.84i			0.594212i
$635$	−2035.23	+	3525.12i	−0.127190	+	0.220300i
$636$	−305.497	+	529.136i	−0.0190468	+	0.0329899i
$637$		−	22427.5i		−	1.39499i
$638$	−245.926	−	141.985i	−0.0152607	−	0.00881075i
$639$	−2762.76	−	1595.08i	−0.171038	−	0.0987488i
$640$	−18889.0	+	10905.6i	−1.16664	+	0.673563i
$641$	9434.24	+	5446.86i	0.581326	+	0.335629i	0.761660	−	0.647977i	$-0.224385\pi$
$641$	9434.24	+	5446.86i	0.581326	+	0.335629i	−0.180334	+	0.983605i	$0.557718\pi$
$642$	4374.63	+	2525.69i	0.268930	+	0.155267i
$643$	3136.17	−	5432.00i	0.192346	−	0.333153i	−0.753681	−	0.657240i	$-0.771724\pi$
$643$	3136.17	−	5432.00i	0.192346	−	0.333153i	0.946027	+	0.324087i	$0.105057\pi$
$644$	13784.0	+	23874.5i	0.843423	+	1.46085i
$645$		−	5713.45i		−	0.348786i
$646$	−2543.76			−0.154927
$647$	−13402.1	−	23213.2i	−0.814362	−	1.41052i	−0.909785	−	0.415080i	$-0.863754\pi$
$647$	−13402.1	−	23213.2i	−0.814362	−	1.41052i	0.0954230	−	0.995437i	$-0.469580\pi$
$648$	−2332.50	+	4040.01i	−0.141403	+	0.244917i
$649$		−	1139.43i		−	0.0689160i
$650$	1985.36	+	1146.25i	0.119804	+	0.0691687i
$651$			11878.9i			0.715162i
$652$	4197.72			0.252140
$653$	9148.30	−	5281.77i	0.548240	−	0.316527i	−0.200172	−	0.979761i	$-0.564150\pi$
$653$	9148.30	−	5281.77i	0.548240	−	0.316527i	0.748412	+	0.663234i	$0.230817\pi$
$654$	−2350.93	−	4071.93i	−0.140563	−	0.243463i
$655$	−13584.1	+	23528.3i	−0.810341	+	1.40355i
$656$	−15467.2	+	8930.00i	−0.920569	+	0.531491i
$657$	1460.63			0.0867343
$658$	−4190.24	+	2419.23i	−0.248256	+	0.143331i
$659$			22173.0i			1.31068i	0.755334	+	0.655340i	$0.227475\pi$
$659$			22173.0i			1.31068i	−0.755334	+	0.655340i	$0.772525\pi$
$660$		−	1244.19i		−	0.0733788i
$661$	10412.3			0.612693			0.306347	−	0.951920i	$-0.400893\pi$
$661$	10412.3			0.612693			0.306347	+	0.951920i	$0.400893\pi$
$662$	2098.30	−	1211.45i	0.123191	−	0.0711246i
$663$	815.377	−	1412.27i	0.0477626	−	0.0827273i
$664$	17753.5	−	10250.0i	1.03761	−	0.599062i
$665$	67621.9	−	39041.5i	3.94326	−	2.27664i
$666$	2927.38	+	1690.12i	0.170321	+	0.0983347i
$667$	−10390.3			−0.603168
$668$	14808.1	+	25648.4i	0.857698	+	1.48558i
$669$	14920.3	−	8614.27i	0.862263	−	0.497828i
$670$	−4615.74	−	7994.70i	−0.266152	−	0.460988i
$671$	1859.74			0.106996
$672$	20251.5	+	11692.2i	1.16253	+	0.671184i
$673$	−7506.16	−	13001.0i	−0.429927	−	0.744656i	0.566939	−	0.823760i	$-0.308127\pi$
$673$	−7506.16	−	13001.0i	−0.429927	−	0.744656i	−0.996866	+	0.0791039i	$0.974794\pi$
$674$	−5876.42	−	3392.75i	−0.335833	−	0.193893i
$675$	7578.26	+	13125.9i	0.432129	+	0.748470i
$676$	5839.48	−	10114.3i	0.332242	−	0.575460i
$677$	−9056.62	+	15686.5i	−0.514142	+	0.890521i	0.485723	+	0.874113i	$0.338556\pi$
$677$	−9056.62	+	15686.5i	−0.514142	+	0.890521i	−0.999865	+	0.0164079i	$0.994777\pi$
$678$	−1262.56			−0.0715167
$679$	34033.8	−	6712.34i	1.92356	−	0.379376i
$680$	−3987.32			−0.224863
$681$	13523.1	−	23422.7i	0.760950	−	1.31800i
$682$	−121.216	+	209.952i	−0.00680586	+	0.0117881i
$683$	3688.52	+	6388.70i	0.206643	+	0.357916i	0.950655	−	0.310250i	$-0.100413\pi$
$683$	3688.52	+	6388.70i	0.206643	+	0.357916i	−0.744012	+	0.668166i	$0.767079\pi$
$684$	9565.85	+	5522.85i	0.534736	+	0.308730i
$685$	−6348.26	−	10995.5i	−0.354094	−	0.613309i
$686$	19889.8	+	11483.4i	1.10699	+	0.639121i
$687$	7761.13			0.431013
$688$	−1953.34	−	3383.28i	−0.108242	−	0.187480i
$689$	434.473	−	250.843i	0.0240234	−	0.0138699i
$690$	3251.71	+	5632.12i	0.179406	+	0.310741i
$691$	−22293.0			−1.22730			−0.613650	−	0.789578i	$-0.710299\pi$
$691$	−22293.0			−1.22730			−0.613650	+	0.789578i	$0.710299\pi$
$692$	−11082.2	−	6398.33i	−0.608790	−	0.351485i
$693$	1025.36	−	591.992i	0.0562052	−	0.0324501i
$694$	−797.785	+	460.601i	−0.0436362	+	0.0251933i
$695$	−6314.40	+	10936.9i	−0.344631	+	0.596919i
$696$	−4977.85	+	2873.97i	−0.271099	+	0.156519i
$697$	−7724.53			−0.419781
$698$		−	8546.80i		−	0.463469i
$699$		−	720.993i		−	0.0390135i
$700$	21949.5	−	12672.5i	1.18516	−	0.684253i
$701$	−1704.01			−0.0918108			−0.0459054	−	0.998946i	$-0.514617\pi$
$701$	−1704.01			−0.0918108			−0.0459054	+	0.998946i	$0.514617\pi$
$702$	3026.41	−	1747.30i	0.162713	−	0.0939424i
$703$	−22040.8	+	38175.8i	−1.18248	+	2.04812i
$704$	−247.514	−	428.707i	−0.0132508	−	0.0229510i
$705$	6919.49	−	3994.97i	0.369650	−	0.213417i
$706$	−7681.08			−0.409463
$707$			41629.4i			2.21448i
$708$	−9321.00	−	5381.48i	−0.494780	−	0.285662i
$709$			8316.92i			0.440548i	0.975438	+	0.220274i	$0.0706951\pi$
$709$			8316.92i			0.440548i	−0.975438	+	0.220274i	$0.929305\pi$
$710$	−2173.73	+	3765.01i	−0.114899	+	0.199012i
$711$	1625.64	+	2815.69i	0.0857472	+	0.148519i
$712$	11821.0			0.622207
$713$			8870.39i			0.465917i
$714$	1287.79	+	2230.51i	0.0674990	+	0.116912i
$715$	−510.801	+	884.734i	−0.0267173	+	0.0462758i
$716$	−17792.5	−	10272.5i	−0.928681	−	0.536174i
$717$	10600.9	+	6120.42i	0.552158	+	0.318788i
$718$	−2603.73	+	1503.26i	−0.135335	+	0.0781354i
$719$	−5881.37	−	3395.61i	−0.305060	−	0.176126i	0.339654	−	0.940551i	$-0.389690\pi$
$719$	−5881.37	−	3395.61i	−0.305060	−	0.176126i	−0.644714	+	0.764424i	$0.723023\pi$
$720$	5854.94	+	3380.35i	0.303056	+	0.174970i
$721$			34596.7i			1.78703i
$722$	6859.53	−	11881.0i	0.353581	−	0.612419i
$723$	−11679.6	+	20229.6i	−0.600785	+	1.04059i
$724$			18365.2i			0.942732i
$725$			9552.48i			0.489338i
$726$	5288.85			0.270369
$727$	−11917.7	−	20642.1i	−0.607984	−	1.05306i	−0.991572	−	0.129555i	$-0.958645\pi$
$727$	−11917.7	−	20642.1i	−0.607984	−	1.05306i	0.383588	−	0.923504i	$-0.374688\pi$
$728$	−6261.16	−	10844.6i	−0.318755	−	0.552101i
$729$	19837.0			1.00782
$730$		−	1990.50i		−	0.100920i
$731$		−	1689.66i		−	0.0854914i
$732$	8783.49	−	15213.4i	0.443507	−	0.768177i
$733$	13293.6	−	23025.1i	0.669862	−	1.16024i	−0.308080	−	0.951360i	$-0.599686\pi$
$733$	13293.6	−	23025.1i	0.669862	−	1.16024i	0.977942	−	0.208875i	$-0.0669802\pi$
$734$		−	2219.60i		−	0.111617i
$735$	−50656.1	−	29246.3i	−2.54215	−	1.46771i
$736$	15122.5	+	8730.97i	0.757367	+	0.437266i
$737$	1580.89	−	912.725i	0.0790132	−	0.0456183i
$738$	−4149.74	−	2395.85i	−0.206984	−	0.119502i
$739$	11442.7	+	6606.45i	0.569590	+	0.328853i	0.756985	−	0.653432i	$-0.226671\pi$
$739$	11442.7	+	6606.45i	0.569590	+	0.328853i	−0.187396	+	0.982285i	$0.560005\pi$
$740$	−16122.7	+	27925.4i	−0.800923	+	1.38724i
$741$	6596.08	+	11424.7i	0.327008	+	0.566395i
$742$			792.352i			0.0392024i
$743$	11323.6			0.559116			0.279558	−	0.960129i	$-0.409812\pi$
$743$	11323.6			0.559116			0.279558	+	0.960129i	$0.409812\pi$
$744$	2453.56	+	4249.70i	0.120903	+	0.209411i
$745$	3159.28	−	5472.04i	0.155365	−	0.269100i
$746$			6308.12i			0.309593i
$747$	−13019.3	−	7516.67i	−0.637683	−	0.368167i
$748$		−	367.948i		−	0.0179860i
$749$	−45855.4			−2.23701
$750$	−1313.07	+	758.100i	−0.0639286	+	0.0369092i
$751$	13146.8	+	22770.9i	0.638794	+	1.10642i	0.985698	+	0.168522i	$0.0538996\pi$
$751$	13146.8	+	22770.9i	0.638794	+	1.10642i	−0.346904	+	0.937901i	$0.612767\pi$
$752$	2731.63	−	4731.32i	0.132463	−	0.229433i
$753$	−25972.0	+	14994.9i	−1.25694	+	0.725692i
$754$	2202.49			0.106379
$755$	5308.26	−	3064.73i	0.255877	−	0.147731i
$756$		−	38635.0i		−	1.85865i
$757$			22466.3i			1.07867i	0.842092	+	0.539334i	$0.181324\pi$
$757$			22466.3i			1.07867i	−0.842092	+	0.539334i	$0.818676\pi$
$758$	−4495.46			−0.215412
$759$	−1113.71	+	642.999i	−0.0532608	+	0.0307502i
$760$	16127.9	−	27934.4i	0.769765	−	1.33327i
$761$	−27238.2	+	15726.0i	−1.29748	+	0.749102i	−0.979969	−	0.199151i	$-0.936181\pi$
$761$	−27238.2	+	15726.0i	−1.29748	+	0.749102i	−0.317514	+	0.948253i	$0.602848\pi$
$762$	940.631	−	543.073i	0.0447185	−	0.0258182i
$763$	36964.1	+	21341.2i	1.75385	+	1.01259i
$764$	21657.2			1.02556
$765$	1462.02	+	2532.29i	0.0690972	+	0.119680i
$766$	1495.25	−	863.283i	0.0705295	−	0.0407202i
$767$	4418.73	+	7653.46i	0.208020	+	0.360301i
$768$	476.000			0.0223648
$769$	18786.5	+	10846.4i	0.880962	+	0.508624i	0.870976	−	0.491326i	$-0.163488\pi$
$769$	18786.5	+	10846.4i	0.880962	+	0.508624i	0.00998683	+	0.999950i	$0.496821\pi$
$770$	−806.748	−	1397.33i	−0.0377574	−	0.0653977i
$771$	−5412.16	−	3124.71i	−0.252807	−	0.145958i
$772$	−10550.2	−	18273.5i	−0.491853	−	0.851915i
$773$	−13182.6	+	22833.0i	−0.613385	+	1.06241i	0.377280	+	0.926099i	$0.376859\pi$
$773$	−13182.6	+	22833.0i	−0.613385	+	1.06241i	−0.990665	+	0.136315i	$0.956474\pi$
$774$	524.066	−	907.710i	0.0243374	−	0.0421537i
$775$	8155.15			0.377989
$776$	10789.3	−	9430.98i	0.499113	−	0.436279i
$777$	44632.9			2.06074
$778$	3946.01	−	6834.68i	0.181840	−	0.314955i
$779$	31244.2	−	54116.6i	1.43702	−	2.48900i
$780$	4824.99	+	8357.13i	0.221490	+	0.383633i
$781$	−744.499	−	429.837i	−0.0341105	−	0.0196937i
$782$	961.637	+	1665.60i	0.0439745	+	0.0761661i
$783$	12610.6	+	7280.71i	0.575562	+	0.332301i
$784$	−39995.4			−1.82195
$785$	12369.3	+	21424.3i	0.562394	+	0.974095i
$786$	6278.20	−	3624.72i	0.284906	−	0.164491i
$787$	6889.49	+	11932.9i	0.312051	+	0.540488i	0.978806	−	0.204789i	$-0.0656508\pi$
$787$	6889.49	+	11932.9i	0.312051	+	0.540488i	−0.666756	+	0.745276i	$0.732317\pi$
$788$	−32977.2			−1.49082
$789$	7424.02	+	4286.26i	0.334984	+	0.193403i
$790$	3837.14	−	2215.37i	0.172809	−	0.0997714i
$791$	9925.72	−	5730.62i	0.446167	−	0.257595i
$792$	244.550	−	423.573i	0.0109718	−	0.0190038i
$793$	−12491.8	+	7212.12i	−0.559389	+	0.322963i
$794$	−1925.01			−0.0860402
$795$		−	1308.44i		−	0.0583718i
$796$		−	14536.6i		−	0.647283i
$797$	−3466.05	+	2001.13i	−0.154045	+	0.0889379i	−0.575041	−	0.818125i	$-0.695014\pi$
$797$	−3466.05	+	2001.13i	−0.154045	+	0.0889379i	0.420996	+	0.907062i	$0.361681\pi$
$798$	−20835.4			−0.924267
$799$	2046.32	−	1181.44i	0.0906052	−	0.0523110i
$800$	8026.97	−	13903.1i	0.354745	−	0.614437i
$801$	−4334.37	−	7507.35i	−0.191195	−	0.331160i
$802$	−2461.24	+	1421.00i	−0.108366	+	0.0625652i
$803$	393.604			0.0172976
$804$		−	17243.1i		−	0.756364i
$805$	−51127.2	−	29518.3i	−2.23851	−	1.29240i
$806$		−	1880.31i		−	0.0821726i
$807$	4619.34	−	8000.93i	0.201498	−	0.349004i
$808$	8598.49	+	14893.0i	0.374373	+	0.648434i
$809$	−27398.6			−1.19071			−0.595355	−	0.803463i	$-0.702988\pi$
$809$	−27398.6			−1.19071			−0.595355	+	0.803463i	$0.702988\pi$
$810$		−	4662.03i		−	0.202231i
$811$	−7910.15	−	13700.8i	−0.342495	−	0.593218i	0.642401	−	0.766369i	$-0.277938\pi$
$811$	−7910.15	−	13700.8i	−0.342495	−	0.593218i	−0.984895	+	0.173151i	$0.944605\pi$
$812$	12175.0	−	21087.7i	0.526180	−	0.911370i
$813$	21623.3	+	12484.2i	0.932796	+	0.538550i
$814$	788.859	+	455.448i	0.0339674	+	0.0196111i
$815$	−7785.04	+	4494.70i	−0.334599	+	0.193181i
$816$	−2518.54	−	1454.08i	−0.108047	−	0.0623811i
$817$	11837.4	+	6834.33i	0.506901	+	0.292660i
$818$			1600.84i			0.0684255i
$819$	−4591.52	+	7952.74i	−0.195898	+	0.339306i
$820$	22855.0	−	39586.0i	0.973329	−	1.68586i
$821$		−	22532.0i		−	0.957822i	−0.877863	−	0.478911i	$-0.841032\pi$
$821$		−	22532.0i		−	0.957822i	0.877863	−	0.478911i	$-0.158968\pi$
$822$			3387.89i			0.143755i
$823$	9804.48			0.415265			0.207632	−	0.978207i	$-0.433424\pi$
$823$	9804.48			0.415265			0.207632	+	0.978207i	$0.433424\pi$
$824$	7145.88	+	12377.0i	0.302110	+	0.523270i
$825$	591.152	+	1023.91i	0.0249470	+	0.0432095i
$826$	−13957.7			−0.587954
$827$			19599.7i			0.824121i	0.911156	+	0.412061i	$0.135191\pi$
$827$			19599.7i			0.824121i	−0.911156	+	0.412061i	$0.864809\pi$
$828$		−	8351.36i		−	0.350519i
$829$	−2341.04	+	4054.80i	−0.0980791	+	0.169878i	−0.910890	−	0.412650i	$-0.864603\pi$
$829$	−2341.04	+	4054.80i	−0.0980791	+	0.169878i	0.812810	+	0.582528i	$0.197936\pi$
$830$	−10243.5	+	17742.2i	−0.428381	+	0.741978i
$831$		−	19267.4i		−	0.804308i
$832$	3325.07	+	1919.73i	0.138553	+	0.0799936i
$833$	−14980.7	−	8649.10i	−0.623109	−	0.359752i
$834$	2918.35	−	1684.91i	0.121168	−	0.0699565i
$835$	−54925.8	−	31711.4i	−2.27639	−	1.31427i
$836$	2577.77	+	1488.28i	0.106644	+	0.0615707i
$837$	6215.69	−	10765.9i	0.256686	−	0.444592i
$838$	7105.04	+	12306.3i	0.292887	+	0.507296i
$839$			31908.8i			1.31301i	0.754322	+	0.656505i	$0.227966\pi$
$839$			31908.8i			1.31301i	−0.754322	+	0.656505i	$0.772034\pi$
$840$	−32659.2			−1.34149
$841$	−7605.79	−	13173.6i	−0.311853	−	0.540146i
$842$	2643.27	−	4578.27i	0.108186	−	0.187384i
$843$		−	5368.55i		−	0.219339i
$844$	25573.1	+	14764.6i	1.04296	+	0.602156i
$845$			25010.4i			1.01821i
$846$	1465.75			0.0595670
$847$	−41578.8	+	24005.5i	−1.68673	+	0.973837i
$848$	−447.335	−	774.806i	−0.0181150	−	0.0313761i
$849$	10080.6	−	17460.1i	0.407498	−	0.705807i
$850$	1531.30	−	884.098i	0.0617921	−	0.0356757i
$851$	33329.0			1.34254
$852$	−7032.49	+	4060.21i	−0.282781	+	0.163263i
$853$			14533.8i			0.583387i	0.956512	+	0.291693i	$0.0942187\pi$
$853$			14533.8i			0.583387i	−0.956512	+	0.291693i	$0.905781\pi$
$854$		−	22781.3i		−	0.912834i
$855$	−23654.3			−0.946151
$856$	−16404.9	+	9471.35i	−0.655031	+	0.378182i
$857$	7546.98	−	13071.8i	0.300817	−	0.521030i	−0.675504	−	0.737356i	$-0.736074\pi$
$857$	7546.98	−	13071.8i	0.300817	−	0.521030i	0.976321	+	0.216326i	$0.0694074\pi$
$858$	236.079	−	136.300i	0.00939349	−	0.00542333i
$859$	−19490.8	+	11253.0i	−0.774176	+	0.446971i	−0.834362	−	0.551216i	$-0.814164\pi$
$859$	−19490.8	+	11253.0i	−0.774176	+	0.446971i	0.0601862	+	0.998187i	$0.480831\pi$
$860$	8658.99	+	4999.27i	0.343336	+	0.198225i
$861$	−63269.9			−2.50434
$862$	−820.919	−	1421.87i	−0.0324369	−	0.0561824i
$863$	6014.35	−	3472.39i	0.237232	−	0.136966i	−0.376672	−	0.926347i	$-0.622932\pi$
$863$	6014.35	−	3472.39i	0.237232	−	0.136966i	0.613904	+	0.789381i	$0.289598\pi$
$864$	−12236.0	−	21193.4i	−0.481802	−	0.834506i
$865$	27404.0			1.07718
$866$	7520.53	+	4341.98i	0.295102	+	0.170377i
$867$	9197.10	+	15929.9i	0.360265	+	0.623998i
$868$	−18003.0	−	10394.0i	−0.703987	−	0.406447i
$869$	438.072	+	758.762i	0.0171008	+	0.0296194i
$870$	2872.14	−	4974.69i	0.111925	−	0.193859i
$871$	−7079.14	+	12261.4i	−0.275393	+	0.476995i
$872$	17632.0			0.684740
$873$	−9945.54	−	3394.07i	−0.385573	−	0.131583i
$874$	−15558.5			−0.602146
$875$	6881.87	−	11919.7i	0.265885	−	0.460527i
$876$	1858.98	−	3219.84i	0.0716998	−	0.124188i
$877$	−12406.2	−	21488.2i	−0.477682	−	0.827370i	0.521990	−	0.852951i	$-0.325190\pi$
$877$	−12406.2	−	21488.2i	−0.477682	−	0.827370i	−0.999673	+	0.0255812i	$0.991856\pi$
$878$	10453.6	+	6035.41i	0.401814	+	0.231988i
$879$	−535.331	−	927.220i	−0.0205418	−	0.0355795i
$880$	1577.77	+	910.924i	0.0604392	+	0.0348946i
$881$	−15504.3			−0.592910			−0.296455	−	0.955047i	$-0.595804\pi$
$881$	−15504.3			−0.592910			−0.296455	+	0.955047i	$0.595804\pi$
$882$	−5365.24	−	9292.87i	−0.204827	−	0.354770i
$883$	6823.43	−	3939.51i	0.260053	−	0.150142i	−0.364306	−	0.931279i	$-0.618694\pi$
$883$	6823.43	−	3939.51i	0.260053	−	0.150142i	0.624359	+	0.781138i	$0.285360\pi$
$884$	1426.91	+	2471.48i	0.0542898	+	0.0940326i
$885$	23048.8			0.875455
$886$	4619.08	+	2666.83i	0.175148	+	0.101122i
$887$	−9256.64	+	5344.33i	−0.350403	+	0.202305i	−0.664863	−	0.746965i	$-0.731510\pi$
$887$	−9256.64	+	5344.33i	−0.350403	+	0.202305i	0.314460	+	0.949271i	$0.398177\pi$
$888$	15967.5	−	9218.85i	0.603417	−	0.348383i
$889$	−4929.90	+	8538.84i	−0.185988	+	0.322141i
$890$	−10230.8	+	5906.75i	−0.385322	+	0.222466i
$891$	921.879			0.0346623
$892$			30149.9i			1.13172i
$893$			19114.8i			0.716297i
$894$	−1460.14	+	843.011i	−0.0546245	+	0.0315375i
$895$	43996.9			1.64319
$896$	−45754.5	+	26416.3i	−1.70597	+	0.984942i
$897$	4987.13	−	8637.96i	0.185636	−	0.321531i
$898$	−1595.81	−	2764.02i	−0.0593015	−	0.102713i
$899$	6785.27	−	3917.48i	0.251726	−	0.145334i
$900$	−7677.97			−0.284369
$901$		−	386.949i		−	0.0143076i
$902$	−1118.26	−	645.626i	−0.0412792	−	0.0238326i
$903$		−	13839.6i		−	0.510025i
$904$	2367.30	−	4100.28i	0.0870964	−	0.150855i
$905$	−19664.5	−	34059.9i	−0.722287	−	1.25104i
$906$	−1635.56			−0.0599756
$907$		−	1446.72i		−	0.0529632i	−0.999649	−	0.0264816i	$-0.991570\pi$
$907$		−	1446.72i		−	0.0529632i	0.999649	−	0.0264816i	$-0.00843033\pi$
$908$	23665.5	+	40989.8i	0.864940	+	1.49812i
$909$	6305.56	−	10921.5i	0.230079	−	0.398509i
$910$	10837.7	+	6257.18i	0.394800	+	0.227938i
$911$	−36216.8	−	20909.8i	−1.31714	−	0.760452i	−0.333873	−	0.942618i	$-0.608356\pi$
$911$	−36216.8	−	20909.8i	−1.31714	−	0.760452i	−0.983268	+	0.182166i	$0.941689\pi$
$912$	20374.0	−	11762.9i	0.739749	−	0.427094i
$913$	−3508.38	−	2025.56i	−0.127175	−	0.0734243i
$914$	−1449.96	−	837.136i	−0.0524732	−	0.0302954i
$915$			37619.6i			1.35920i
$916$	−6790.99	+	11762.3i	−0.244957	+	0.424278i
$917$	−32904.4	+	56992.2i	−1.18495	+	2.05240i
$918$		−	2695.37i		−	0.0969068i
$919$		−	39537.1i		−	1.41916i	−0.704625	−	0.709580i	$-0.748885\pi$
$919$		−	39537.1i		−	1.41916i	0.704625	−	0.709580i	$-0.251115\pi$
$920$	−24387.8			−0.873959
$921$	−8783.28	−	15213.1i	−0.314244	−	0.544287i
$922$	6128.92	+	10615.6i	0.218921	+	0.379183i
$923$	6667.67			0.237778
$924$		−	3013.78i		−	0.107301i
$925$		−	30641.6i		−	1.08918i
$926$	−2367.11	+	4099.95i	−0.0840043	+	0.145500i
$927$	5240.31	−	9076.49i	0.185668	−	0.321587i
$928$		−	15423.6i		−	0.545587i
$929$	21398.7	+	12354.5i	0.755723	+	0.436317i	0.827758	−	0.561085i	$-0.189616\pi$
$929$	21398.7	+	12354.5i	0.755723	+	0.436317i	−0.0720348	+	0.997402i	$0.522949\pi$
$930$	−4246.99	−	2452.00i	−0.149747	−	0.0864563i
$931$	121188.	−	69967.9i	4.26614	−	2.46305i
$932$	1092.70	+	630.869i	0.0384040	+	0.0221725i
$933$	1684.37	+	972.469i	0.0591036	+	0.0341235i
$934$	−1019.76	+	1766.28i	−0.0357256	+	0.0618785i
$935$	393.979	+	682.392i	0.0137802	+	0.0238680i
$936$			3793.48i			0.132472i
$937$	−12011.0			−0.418765			−0.209383	−	0.977834i	$-0.567145\pi$
$937$	−12011.0			−0.418765			−0.209383	+	0.977834i	$0.567145\pi$
$938$	−11180.6	−	19365.4i	−0.389190	−	0.674098i
$939$	−3679.00	+	6372.21i	−0.127859	+	0.221458i
$940$			13982.4i			0.485165i
$941$	38826.6	+	22416.5i	1.34507	+	0.776576i	0.987546	−	0.157328i	$-0.0502879\pi$
$941$	38826.6	+	22416.5i	1.34507	+	0.776576i	0.357523	+	0.933904i	$0.383621\pi$
$942$		−	6601.16i		−	0.228320i
$943$	−47245.9			−1.63154
$944$	13648.6	−	7880.02i	0.470576	−	0.271687i
$945$	41368.4	+	71652.1i	1.42403	+	2.46650i
$946$	141.224	−	244.606i	0.00485367	−	0.00840680i
$947$	9177.73	−	5298.76i	0.314927	−	0.181823i	−0.334202	−	0.942501i	$-0.608467\pi$
$947$	9177.73	−	5298.76i	0.314927	−	0.181823i	0.649129	+	0.760678i	$0.275133\pi$
$948$	8275.98			0.283535
$949$	−2643.81	+	1526.41i	−0.0904339	+	0.0522120i
$950$			14304.0i			0.488509i
$951$		−	37943.3i		−	1.29379i
$952$	−9658.41			−0.328814
$953$	−10252.8	+	5919.43i	−0.348499	+	0.201206i	−0.664024	−	0.747711i	$-0.731153\pi$
$953$	−10252.8	+	5919.43i	−0.348499	+	0.201206i	0.315525	+	0.948917i	$0.397819\pi$
$954$	120.017	−	207.875i	0.00407304	−	0.00705471i
$955$	−40165.1	+	23189.4i	−1.36096	+	0.785749i
$956$	−18551.5	+	10710.7i	−0.627615	+	0.362354i
$957$	983.704	+	567.942i	0.0332274	+	0.0191838i
$958$	17765.5			0.599141
$959$	−15377.3	−	26634.2i	−0.517787	−	0.896834i
$960$	8672.06	−	5006.81i	0.291551	−	0.168327i
$961$	11551.1	+	20007.0i	0.387737	+	0.671580i
$962$	−7064.95			−0.236781
$963$	12030.2	+	6945.66i	0.402564	+	0.232420i
$964$	−20439.2	−	35401.8i	−0.682887	−	1.18280i
$965$	39132.6	+	22593.2i	1.30541	+	0.753681i
$966$	7876.56	+	13642.6i	0.262344	+	0.454393i
$967$	26775.2	−	46376.1i	0.890417	−	1.54225i	0.0510413	−	0.998697i	$-0.483746\pi$
$967$	26775.2	−	46376.1i	0.890417	−	1.54225i	0.839376	−	0.543551i	$-0.182921\pi$
$968$	−9916.60	+	17176.1i	−0.329268	+	0.570309i
$969$	10175.1			0.337327
$970$	−4625.33	+	13553.5i	−0.153104	+	0.448635i
$971$	3061.09			0.101169			0.0505844	−	0.998720i	$-0.483892\pi$
$971$	3061.09			0.101169			0.0505844	+	0.998720i	$0.483892\pi$
$972$	−10010.0	+	17337.8i	−0.330320	+	0.572131i
$973$	−15295.3	+	26492.2i	−0.503950	+	0.872867i
$974$	−407.370	−	705.585i	−0.0134014	−	0.0232119i
$975$	−7941.46	−	4585.00i	−0.260851	−	0.150603i
$976$	12861.5	+	22276.8i	0.421811	+	0.730599i
$977$	−8775.21	−	5066.37i	−0.287353	−	0.165903i	0.349394	−	0.936976i	$-0.386387\pi$
$977$	−8775.21	−	5066.37i	−0.287353	−	0.165903i	−0.636748	+	0.771072i	$0.719721\pi$
$978$	2398.70			0.0784273
$979$	−1168.01	−	2023.05i	−0.0381305	−	0.0660440i
$980$	88648.2	−	51181.1i	2.88956	−	1.66829i
$981$	−6465.05	−	11197.8i	−0.210411	−	0.364442i
$982$	14211.6			0.461822
$983$	26488.3	+	15293.0i	0.859457	+	0.496208i	0.863831	−	0.503782i	$-0.168059\pi$
$983$	26488.3	+	15293.0i	0.859457	+	0.496208i	−0.00437315	+	0.999990i	$0.501392\pi$
$984$	−22634.9	+	13068.3i	−0.733309	+	0.423376i
$985$	61159.2	−	35310.3i	1.97837	−	1.14221i
$986$	849.386	−	1471.18i	0.0274340	−	0.0475171i
$987$	16761.0	−	9676.94i	0.540534	−	0.312077i
$988$	−23086.3			−0.743393
$989$		−	10334.5i		−	0.332274i
$990$			488.789i			0.0156916i
$991$	−50234.9	+	29003.1i	−1.61026	+	0.929682i	−0.620947	+	0.783853i	$0.713252\pi$
$991$	−50234.9	+	29003.1i	−1.61026	+	0.929682i	−0.989310	+	0.145829i	$0.953415\pi$
$992$	−13167.5			−0.421439
$993$	−8393.19	+	4845.81i	−0.268228	+	0.154861i
$994$	−5265.38	+	9119.91i	−0.168016	+	0.291012i
$995$	15565.1	+	26959.5i	0.495925	+	0.858968i
$996$	−33139.9	+	19133.3i	−1.05430	+	0.608698i
$997$	30384.3			0.965176			0.482588	−	0.875848i	$-0.339697\pi$
$997$	30384.3			0.965176			0.482588	+	0.875848i	$0.339697\pi$
$998$		−	3008.04i		−	0.0954086i
$999$	−40451.0	−	23354.4i	−1.28109	−	0.739640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.4.e.a.36.1	✓	4
97.62	even	6	inner	97.4.e.a.62.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.4.e.a.36.1	✓	4	1.1	even	1	trivial
97.4.e.a.62.1	yes	4	97.62	even	6	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:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	97.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(2.00000 - 3.46410i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-12.9821 - 7.49523i) q^{5} +(2.00000 + 3.46410i) q^{6} +(-31.4464 - 18.1556i) q^{7} -15.0000 q^{8} +(5.50000 + 9.52628i) q^{9} +(12.9821 - 7.49523i) q^{10} +(1.48212 + 2.56711i) q^{11} +28.0000 q^{12} +(-19.9106 - 11.4954i) q^{13} +(31.4464 - 18.1556i) q^{14} +(-51.9285 + 29.9809i) q^{15} +(-20.5000 + 35.5070i) q^{16} +(-15.3570 + 8.86635i) q^{17} -11.0000 q^{18} -143.451i q^{19} -104.933i q^{20} +(-125.785 + 72.6223i) q^{21} -2.96424 q^{22} +(-93.9285 + 54.2296i) q^{23} +(-30.0000 + 51.9615i) q^{24} +(49.8570 + 86.3548i) q^{25} +(19.9106 - 11.4954i) q^{26} +152.000 q^{27} -254.178i q^{28} +(82.9642 + 47.8994i) q^{29} -59.9618i q^{30} +(40.8927 - 70.8283i) q^{31} +(-80.5000 - 139.430i) q^{32} +11.8570 q^{33} -17.7327i q^{34} +(272.160 + 471.395i) q^{35} +(-38.5000 + 66.6840i) q^{36} +(-266.125 - 153.647i) q^{37} +(124.232 + 71.7253i) q^{38} +(-79.6424 + 45.9816i) q^{39} +(194.732 + 112.428i) q^{40} +(377.249 + 217.805i) q^{41} -145.245i q^{42} +(-47.6424 + 82.5191i) q^{43} +(-10.3748 + 17.9698i) q^{44} -164.895i q^{45} -108.459i q^{46} -133.250 q^{47} +(82.0000 + 142.028i) q^{48} +(487.749 + 844.806i) q^{49} -99.7139 q^{50} +70.9308i q^{51} -160.935i q^{52} +(-10.9106 + 18.8977i) q^{53} +(-76.0000 + 131.636i) q^{54} -44.4353i q^{55} +(471.695 + 272.333i) q^{56} +(-496.927 - 286.901i) q^{57} +(-82.9642 + 47.8994i) q^{58} +(-332.893 - 192.196i) q^{59} +(-363.499 - 209.866i) q^{60} +(313.696 - 543.337i) q^{61} +(40.8927 + 70.8283i) q^{62} -399.422i q^{63} -167.000 q^{64} +(172.321 + 298.469i) q^{65} +(-5.92848 + 10.2684i) q^{66} -615.824i q^{67} +(-107.499 - 62.0644i) q^{68} +433.837i q^{69} -544.321 q^{70} +(-251.160 + 145.007i) q^{71} +(-82.5000 - 142.894i) q^{72} +(66.3921 - 114.994i) q^{73} +(266.125 - 153.647i) q^{74} +398.856 q^{75} +(869.623 - 502.077i) q^{76} -107.635i q^{77} -91.9631i q^{78} +295.571 q^{79} +(532.267 - 307.304i) q^{80} +(155.500 - 269.334i) q^{81} +(-377.249 + 217.805i) q^{82} +(-1183.57 + 683.333i) q^{83} +(-880.498 - 508.356i) q^{84} +265.821 q^{85} +(-47.6424 - 82.5191i) q^{86} +(331.857 - 191.598i) q^{87} +(-22.2318 - 38.5066i) q^{88} -788.068 q^{89} +(142.803 + 82.4475i) q^{90} +(417.411 + 722.976i) q^{91} +(-657.499 - 379.607i) q^{92} +(-163.571 - 283.313i) q^{93} +(66.6252 - 115.398i) q^{94} +(-1075.19 + 1862.29i) q^{95} -644.000 q^{96} +(-719.284 + 628.732i) q^{97} -975.498 q^{98} +(-16.3033 + 28.2382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 8 q^{3} + 14 q^{4} - 24 q^{5} + 8 q^{6} - 42 q^{7} - 60 q^{8} + 22 q^{9} + 24 q^{10} - 22 q^{11} + 112 q^{12} + 60 q^{13} + 42 q^{14} - 96 q^{15} - 82 q^{16} + 162 q^{17} - 44 q^{18} - 168 q^{21}+ \cdots + 242 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 8 * q^3 + 14 * q^4 - 24 * q^5 + 8 * q^6 - 42 * q^7 - 60 * q^8 + 22 * q^9 + 24 * q^10 - 22 * q^11 + 112 * q^12 + 60 * q^13 + 42 * q^14 - 96 * q^15 - 82 * q^16 + 162 * q^17 - 44 * q^18 - 168 * q^21 + 44 * q^22 - 264 * q^23 - 120 * q^24 - 24 * q^25 - 60 * q^26 + 608 * q^27 + 276 * q^29 - 4 * q^31 - 322 * q^32 - 176 * q^33 + 558 * q^35 - 154 * q^36 - 1260 * q^37 + 78 * q^38 + 240 * q^39 + 360 * q^40 + 336 * q^41 + 368 * q^43 + 154 * q^44 - 924 * q^47 + 328 * q^48 + 778 * q^49 + 48 * q^50 + 96 * q^53 - 304 * q^54 + 630 * q^56 - 312 * q^57 - 276 * q^58 - 1164 * q^59 - 672 * q^60 + 780 * q^61 - 4 * q^62 - 668 * q^64 + 410 * q^65 + 88 * q^66 + 1134 * q^68 - 1116 * q^70 - 474 * q^71 - 330 * q^72 - 684 * q^73 + 1260 * q^74 - 192 * q^75 + 546 * q^76 + 512 * q^79 + 984 * q^80 + 622 * q^81 - 336 * q^82 - 936 * q^83 - 1176 * q^84 + 784 * q^85 + 368 * q^86 + 1104 * q^87 + 330 * q^88 + 1428 * q^89 + 264 * q^90 + 1530 * q^91 - 1848 * q^92 + 16 * q^93 + 462 * q^94 - 2262 * q^95 - 2576 * q^96 - 196 * q^97 - 1556 * q^98 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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