LMFDB - Embedded newform 69.8.g.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,8,Mod(5,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	69.g (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$21.5545667584$
Analytic rank:	$0$
Dimension:	$540$
Relative dimension:	$54$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	69.5
Dual form			69.8.g.a.14.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.92412 + 16.7700i) q^{2} +(15.0326 + 44.2834i) q^{3} +(-149.305 - 95.9528i) q^{4} +(-35.8560 + 249.384i) q^{5} +(-816.655 + 34.0408i) q^{6} +(-759.793 + 346.986i) q^{7} +(653.576 - 566.327i) q^{8} +(-1735.04 + 1331.39i) q^{9} +O(q^{10})$	\(q+(-4.92412 + 16.7700i) q^{2} +(15.0326 + 44.2834i) q^{3} +(-149.305 - 95.9528i) q^{4} +(-35.8560 + 249.384i) q^{5} +(-816.655 + 34.0408i) q^{6} +(-759.793 + 346.986i) q^{7} +(653.576 - 566.327i) q^{8} +(-1735.04 + 1331.39i) q^{9} +(-4005.61 - 1829.30i) q^{10} +(6210.50 - 1823.57i) q^{11} +(2004.66 - 8054.18i) q^{12} +(-3706.33 + 8115.72i) q^{13} +(-2077.64 - 14450.3i) q^{14} +(-11582.6 + 2161.07i) q^{15} +(-3158.13 - 6915.35i) q^{16} +(-19799.4 + 12724.3i) q^{17} +(-13783.9 - 35652.5i) q^{18} +(14056.2 - 21871.8i) q^{19} +(29282.6 - 33793.9i) q^{20} +(-26787.4 - 28430.1i) q^{21} +113130. i q^{22} +(-22206.4 - 53960.2i) q^{23} +(34903.9 + 20429.2i) q^{24} +(14053.7 + 4126.53i) q^{25} +(-117850. - 102118. i) q^{26} +(-85040.9 - 56819.1i) q^{27} +(146736. + 21097.4i) q^{28} +(119913. + 186588. i) q^{29} +(20792.7 - 204881. i) q^{30} +(173874. + 200661. i) q^{31} +(241090. - 34663.5i) q^{32} +(174114. + 247609. i) q^{33} +(-115892. - 394691. i) q^{34} +(-59289.6 - 201922. i) q^{35} +(386802. - 32302.4i) q^{36} +(-78372.0 + 11268.2i) q^{37} +(297576. + 343422. i) q^{38} +(-415108. - 42127.9i) q^{39} +(117798. + 183298. i) q^{40} +(296977. + 42698.8i) q^{41} +(608677. - 309232. i) q^{42} +(65450.7 + 56713.3i) q^{43} +(-1.10224e6 - 323646. i) q^{44} +(-269817. - 480429. i) q^{45} +(1.01426e6 - 106695. i) q^{46} -1.07259e6i q^{47} +(258760. - 243809. i) q^{48} +(-82419.4 + 95117.1i) q^{49} +(-138404. + 215361. i) q^{50} +(-861112. - 685504. i) q^{51} +(1.33210e6 - 856089. i) q^{52} +(209591. + 458941. i) q^{53} +(1.37161e6 - 1.14635e6i) q^{54} +(232085. + 1.61419e6i) q^{55} +(-300075. + 657073. i) q^{56} +(1.17986e6 + 293664. i) q^{57} +(-3.71955e6 + 1.09216e6i) q^{58} +(-1.28204e6 - 585487. i) q^{59} +(1.93670e6 + 788720. i) q^{60} +(-1.83676e6 + 1.59156e6i) q^{61} +(-4.22127e6 + 1.92779e6i) q^{62} +(856296. - 1.61362e6i) q^{63} +(-467360. + 3.25056e6i) q^{64} +(-1.89104e6 - 1.21530e6i) q^{65} +(-5.00976e6 + 1.70064e6i) q^{66} +(-306647. + 1.04434e6i) q^{67} +4.17709e6 q^{68} +(2.05572e6 - 1.79454e6i) q^{69} +3.67818e6 q^{70} +(1.12695e6 - 3.83804e6i) q^{71} +(-379976. + 1.85277e6i) q^{72} +(-1.50341e6 - 966181. i) q^{73} +(196945. - 1.36978e6i) q^{74} +(28527.1 + 684378. i) q^{75} +(-4.19733e6 + 1.91686e6i) q^{76} +(-4.08594e6 + 3.54049e6i) q^{77} +(2.75052e6 - 6.75391e6i) q^{78} +(-2.64843e6 - 1.20950e6i) q^{79} +(1.83781e6 - 539631. i) q^{80} +(1.23775e6 - 4.62004e6i) q^{81} +(-2.17841e6 + 4.77005e6i) q^{82} +(-314690. - 2.18871e6i) q^{83} +(1.27156e6 + 6.81510e6i) q^{84} +(-2.46331e6 - 5.39389e6i) q^{85} +(-1.27337e6 + 818345. i) q^{86} +(-6.46015e6 + 8.11507e6i) q^{87} +(3.02630e6 - 4.70901e6i) q^{88} +(797191. - 920008. i) q^{89} +(9.38541e6 - 2.15913e6i) q^{90} -7.45231e6i q^{91} +(-1.86209e6 + 1.01873e7i) q^{92} +(-6.27218e6 + 1.07162e7i) q^{93} +(1.79873e7 + 5.28153e6i) q^{94} +(4.95049e6 + 4.28962e6i) q^{95} +(5.15923e6 + 1.01552e7i) q^{96} +(-6.45213e6 - 927676. i) q^{97} +(-1.18927e6 - 1.85054e6i) q^{98} +(-8.34758e6 + 1.14326e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9}+O(q^{10}) $ 540 * q - 35 * q^3 + 3362 * q^4 - 1280 * q^6 - 22 * q^7 - 659 * q^9	\( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9} - 22 q^{10} + 4756 q^{12} + 4970 q^{13} + 3828 q^{15} - 174622 q^{16} + 250050 q^{18} - 22 q^{19} - 221738 q^{21} + 94934 q^{24} - 788392 q^{25} + 1020934 q^{27} - 22 q^{28} - 1480875 q^{30} + 738458 q^{31} + 1215192 q^{33} + 1815924 q^{34} - 394502 q^{36} - 905234 q^{37} - 1635803 q^{39} + 10260228 q^{40} - 11 q^{42} - 1694330 q^{43} - 6978726 q^{46} + 134426 q^{48} + 7785740 q^{49} - 11 q^{51} + 16219654 q^{52} - 10697559 q^{54} - 1371960 q^{55} + 7508908 q^{57} - 21860696 q^{58} - 21971851 q^{60} - 11102850 q^{61} - 9022926 q^{63} + 2572060 q^{64} + 16582830 q^{66} + 6031564 q^{67} + 12019470 q^{69} - 2949828 q^{70} + 12828949 q^{72} - 1809596 q^{73} - 16620656 q^{75} - 42651158 q^{76} - 47106384 q^{78} - 1156914 q^{79} + 48837101 q^{81} + 47208588 q^{82} + 124183367 q^{84} + 5833252 q^{85} - 17916287 q^{87} + 360426 q^{88} - 142298860 q^{90} - 51670516 q^{93} - 18401348 q^{94} + 36462337 q^{96} - 63860500 q^{97} + 135683977 q^{99}+O(q^{100}) \) 540 * q - 35 * q^3 + 3362 * q^4 - 1280 * q^6 - 22 * q^7 - 659 * q^9 - 22 * q^10 + 4756 * q^12 + 4970 * q^13 + 3828 * q^15 - 174622 * q^16 + 250050 * q^18 - 22 * q^19 - 221738 * q^21 + 94934 * q^24 - 788392 * q^25 + 1020934 * q^27 - 22 * q^28 - 1480875 * q^30 + 738458 * q^31 + 1215192 * q^33 + 1815924 * q^34 - 394502 * q^36 - 905234 * q^37 - 1635803 * q^39 + 10260228 * q^40 - 11 * q^42 - 1694330 * q^43 - 6978726 * q^46 + 134426 * q^48 + 7785740 * q^49 - 11 * q^51 + 16219654 * q^52 - 10697559 * q^54 - 1371960 * q^55 + 7508908 * q^57 - 21860696 * q^58 - 21971851 * q^60 - 11102850 * q^61 - 9022926 * q^63 + 2572060 * q^64 + 16582830 * q^66 + 6031564 * q^67 + 12019470 * q^69 - 2949828 * q^70 + 12828949 * q^72 - 1809596 * q^73 - 16620656 * q^75 - 42651158 * q^76 - 47106384 * q^78 - 1156914 * q^79 + 48837101 * q^81 + 47208588 * q^82 + 124183367 * q^84 + 5833252 * q^85 - 17916287 * q^87 + 360426 * q^88 - 142298860 * q^90 - 51670516 * q^93 - 18401348 * q^94 + 36462337 * q^96 - 63860500 * q^97 + 135683977 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$

Coefficient data

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

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

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

$2$	−4.92412	+	16.7700i	−0.435234	+	1.48227i	0.391763	+	0.920066i	$0.371865\pi$
$2$	−4.92412	+	16.7700i	−0.435234	+	1.48227i	−0.826997	+	0.562206i	$0.809953\pi$
$3$	15.0326	+	44.2834i	0.321448	+	0.946927i
$3$	15.0326	+	44.2834i	0.321448	+	0.946927i
$4$	−149.305	−	95.9528i	−1.16645	−	0.749631i
$5$	−35.8560	+	249.384i	−0.128282	+	0.892223i	0.819449	+	0.573153i	$0.194280\pi$
$5$	−35.8560	+	249.384i	−0.128282	+	0.892223i	−0.947731	+	0.319071i	$0.896629\pi$
$6$	−816.655	+	34.0408i	−1.54351	+	0.0643385i
$7$	−759.793	+	346.986i	−0.837245	+	0.382357i	−0.787432	−	0.616402i	$-0.788590\pi$
$7$	−759.793	+	346.986i	−0.837245	+	0.382357i	−0.0498127	+	0.998759i	$0.515862\pi$
$8$	653.576	−	566.327i	0.451317	−	0.391068i
$9$	−1735.04	+	1331.39i	−0.793342	+	0.608776i
$10$	−4005.61	−	1829.30i	−1.26668	−	0.578476i
$11$	6210.50	−	1823.57i	1.40686	−	0.413093i	0.511829	−	0.859087i	$-0.328968\pi$
$11$	6210.50	−	1823.57i	1.40686	−	0.413093i	0.895036	+	0.445995i	$0.147150\pi$
$12$	2004.66	−	8054.18i	0.334893	−	1.34551i
$13$	−3706.33	+	8115.72i	−0.467888	+	1.02453i	0.517730	+	0.855544i	$0.326777\pi$
$13$	−3706.33	+	8115.72i	−0.467888	+	1.02453i	−0.985618	+	0.168988i	$0.945950\pi$
$14$	−2077.64	−	14450.3i	−0.202359	−	1.40744i
$15$	−11582.6	+	2161.07i	−0.886106	+	0.165330i
$16$	−3158.13	−	6915.35i	−0.192757	−	0.422079i
$17$	−19799.4	+	12724.3i	−0.977418	+	0.628148i	−0.928766	−	0.370667i	$-0.879129\pi$
$17$	−19799.4	+	12724.3i	−0.977418	+	0.628148i	−0.0486524	+	0.998816i	$0.515493\pi$
$18$	−13783.9	−	35652.5i	−0.557082	−	1.44091i
$19$	14056.2	−	21871.8i	0.470143	−	0.731556i	−0.522500	−	0.852640i	$-0.675000\pi$
$19$	14056.2	−	21871.8i	0.470143	−	0.731556i	0.992642	+	0.121083i	$0.0386368\pi$
$20$	29282.6	−	33793.9i	0.818473	−	0.944568i
$21$	−26787.4	−	28430.1i	−0.631195	−	0.669902i
$22$			113130.i			2.26515i
$23$	−22206.4	−	53960.2i	−0.380566	−	0.924754i
$23$	−22206.4	−	53960.2i	−0.380566	−	0.924754i
$24$	34903.9	+	20429.2i	0.515388	+	0.301656i
$25$	14053.7	+	4126.53i	0.179887	+	0.0528196i
$26$	−117850.	−	102118.i	−1.31499	−	1.13945i
$27$	−85040.9	−	56819.1i	−0.831485	−	0.555547i
$28$	146736.	+	21097.4i	1.26323	+	0.181625i
$29$	119913.	+	186588.i	0.913005	+	1.42066i	0.907209	+	0.420680i	$0.138208\pi$
$29$	119913.	+	186588.i	0.913005	+	1.42066i	0.00579575	+	0.999983i	$0.498155\pi$
$30$	20792.7	−	204881.i	0.140601	−	1.38541i
$31$	173874.	+	200661.i	1.04826	+	1.20976i	0.977208	+	0.212284i	$0.0680901\pi$
$31$	173874.	+	200661.i	1.04826	+	1.20976i	0.0710519	+	0.997473i	$0.477364\pi$
$32$	241090.	−	34663.5i	1.30063	−	0.187002i
$33$	174114.	+	247609.i	0.843403	+	1.19941i
$34$	−115892.	−	394691.i	−0.505681	−	1.72219i
$35$	−59289.6	−	201922.i	−0.233744	−	0.796059i
$36$	386802.	−	32302.4i	1.38175	−	0.115392i
$37$	−78372.0	+	11268.2i	−0.254364	+	0.0365720i	−0.268317	−	0.963331i	$-0.586467\pi$
$37$	−78372.0	+	11268.2i	−0.254364	+	0.0365720i	0.0139534	+	0.999903i	$0.495558\pi$
$38$	297576.	+	343422.i	0.879743	+	1.01528i
$39$	−415108.	−	42127.9i	−1.12056	−	0.113722i
$40$	117798.	+	183298.i	0.291024	+	0.452842i
$41$	296977.	+	42698.8i	0.672944	+	0.0967548i	0.470312	−	0.882500i	$-0.344141\pi$
$41$	296977.	+	42698.8i	0.672944	+	0.0967548i	0.202632	+	0.979255i	$0.435050\pi$
$42$	608677.	−	309232.i	1.26769	−	0.644038i
$43$	65450.7	+	56713.3i	0.125538	+	0.108779i	0.715367	−	0.698749i	$-0.246260\pi$
$43$	65450.7	+	56713.3i	0.125538	+	0.108779i	−0.589829	+	0.807528i	$0.700805\pi$
$44$	−1.10224e6	−	323646.i	−1.95070	−	0.572778i
$45$	−269817.	−	480429.i	−0.441392	−	0.785933i
$46$	1.01426e6	−	106695.i	1.53637	−	0.161619i
$47$		−	1.07259e6i		−	1.50692i	−0.657495	−	0.753459i	$-0.728384\pi$
$47$		−	1.07259e6i		−	1.50692i	0.657495	−	0.753459i	$-0.271616\pi$
$48$	258760.	−	243809.i	0.337717	−	0.318204i
$49$	−82419.4	+	95117.1i	−0.100079	+	0.115497i
$50$	−138404.	+	215361.i	−0.156586	+	0.243653i
$51$	−861112.	−	685504.i	−0.909000	−	0.723627i
$52$	1.33210e6	−	856089.i	1.31379	−	0.844320i
$53$	209591.	+	458941.i	0.193378	+	0.423439i	0.981339	−	0.192286i	$-0.0615903\pi$
$53$	209591.	+	458941.i	0.193378	+	0.423439i	−0.787961	+	0.615726i	$0.788863\pi$
$54$	1.37161e6	−	1.14635e6i	1.18536	−	0.990694i
$55$	232085.	+	1.61419e6i	0.188095	+	1.30823i
$56$	−300075.	+	657073.i	−0.228335	+	0.499983i
$57$	1.17986e6	+	293664.i	0.843857	+	0.210033i
$58$	−3.71955e6	+	1.09216e6i	−2.50318	+	0.735000i
$59$	−1.28204e6	−	585487.i	−0.812678	−	0.371138i	−0.0346756	−	0.999399i	$-0.511040\pi$
$59$	−1.28204e6	−	585487.i	−0.812678	−	0.371138i	−0.778003	+	0.628261i	$0.783767\pi$
$60$	1.93670e6	+	788720.i	1.15753	+	0.471405i
$61$	−1.83676e6	+	1.59156e6i	−1.03609	+	0.897777i	−0.994849	−	0.101372i	$-0.967677\pi$
$61$	−1.83676e6	+	1.59156e6i	−1.03609	+	0.897777i	−0.0412411	+	0.999149i	$0.513131\pi$
$62$	−4.22127e6	+	1.92779e6i	−2.24943	+	1.02728i
$63$	856296.	−	1.61362e6i	0.431452	−	0.813034i
$64$	−467360.	+	3.25056e6i	−0.222855	+	1.54999i
$65$	−1.89104e6	−	1.21530e6i	−0.854089	−	0.548890i
$66$	−5.00976e6	+	1.70064e6i	−2.14493	+	0.728128i
$67$	−306647.	+	1.04434e6i	−0.124559	+	0.424210i	−0.998035	−	0.0626575i	$-0.980042\pi$
$67$	−306647.	+	1.04434e6i	−0.124559	+	0.424210i	0.873476	+	0.486868i	$0.161861\pi$
$68$	4.17709e6			1.61099
$69$	2.05572e6	−	1.79454e6i	0.753342	−	0.657629i
$70$	3.67818e6			1.28171
$71$	1.12695e6	−	3.83804e6i	0.373680	−	1.27264i	−0.531300	−	0.847184i	$-0.678296\pi$
$71$	1.12695e6	−	3.83804e6i	0.373680	−	1.27264i	0.904980	−	0.425454i	$-0.139886\pi$
$72$	−379976.	+	1.85277e6i	−0.119976	+	0.585001i
$73$	−1.50341e6	−	966181.i	−0.452321	−	0.290689i	0.294577	−	0.955628i	$-0.404821\pi$
$73$	−1.50341e6	−	966181.i	−0.452321	−	0.290689i	−0.746898	+	0.664939i	$0.768458\pi$
$74$	196945.	−	1.36978e6i	0.0564982	−	0.392953i
$75$	28527.1	+	684378.i	0.00780806	+	0.187319i
$76$	−4.19733e6	+	1.91686e6i	−1.09679	+	0.500889i
$77$	−4.08594e6	+	3.54049e6i	−1.01994	+	0.883784i
$78$	2.75052e6	−	6.75391e6i	0.656273	−	1.61148i
$79$	−2.64843e6	−	1.20950e6i	−0.604357	−	0.276000i	0.0896451	−	0.995974i	$-0.471427\pi$
$79$	−2.64843e6	−	1.20950e6i	−0.604357	−	0.276000i	−0.694002	+	0.719973i	$0.744154\pi$
$80$	1.83781e6	−	539631.i	0.401316	−	0.117837i
$81$	1.23775e6	−	4.62004e6i	0.258783	−	0.965935i
$82$	−2.17841e6	+	4.77005e6i	−0.436306	+	0.955376i
$83$	−314690.	−	2.18871e6i	−0.0604100	−	0.420161i	−0.997476	−	0.0710079i	$-0.977378\pi$
$83$	−314690.	−	2.18871e6i	−0.0604100	−	0.420161i	0.937066	−	0.349153i	$-0.113531\pi$
$84$	1.27156e6	+	6.81510e6i	0.234077	+	1.25457i
$85$	−2.46331e6	−	5.39389e6i	−0.435063	−	0.952655i
$86$	−1.27337e6	+	818345.i	−0.215879	+	0.138737i
$87$	−6.46015e6	+	8.11507e6i	−1.05178	+	1.32122i
$88$	3.02630e6	−	4.70901e6i	0.473394	−	0.736615i
$89$	797191.	−	920008.i	0.119866	−	0.138333i	−0.692645	−	0.721279i	$-0.743555\pi$
$89$	797191.	−	920008.i	0.119866	−	0.138333i	0.812511	+	0.582946i	$0.198100\pi$
$90$	9.38541e6	−	2.15913e6i	1.35708	−	0.312198i
$91$		−	7.45231e6i		−	1.03668i
$92$	−1.86209e6	+	1.01873e7i	−0.249313	+	1.36396i
$93$	−6.27218e6	+	1.07162e7i	−0.808590	+	1.38150i
$94$	1.79873e7	+	5.28153e6i	2.23366	+	0.655862i
$95$	4.95049e6	+	4.28962e6i	0.592401	+	0.513318i
$96$	5.15923e6	+	1.01552e7i	0.595163	+	1.17149i
$97$	−6.45213e6	−	927676.i	−0.717797	−	0.103204i	−0.226269	−	0.974065i	$-0.572653\pi$
$97$	−6.45213e6	−	927676.i	−0.717797	−	0.103204i	−0.491529	+	0.870861i	$0.663562\pi$
$98$	−1.18927e6	−	1.85054e6i	−0.127641	−	0.198613i
$99$	−8.34758e6	+	1.14326e7i	−0.864644	+	1.18419i
$100$	−1.70234e6	−	1.96460e6i	−0.170234	−	0.196460i
$101$	8.34132e6	−	1.19930e6i	0.805583	−	0.115825i	0.272793	−	0.962073i	$-0.412053\pi$
$101$	8.34132e6	−	1.19930e6i	0.805583	−	0.115825i	0.532790	+	0.846247i	$0.321144\pi$
$102$	1.57361e7	−	1.10653e7i	1.46824	−	1.03244i
$103$	−1.96143e6	−	6.68003e6i	−0.176866	−	0.602349i	−0.999433	−	0.0336808i	$-0.989277\pi$
$103$	−1.96143e6	−	6.68003e6i	−0.176866	−	0.602349i	0.822567	−	0.568668i	$-0.192541\pi$
$104$	2.17379e6	+	7.40323e6i	0.189496	+	0.645364i
$105$	8.05050e6	−	5.66096e6i	0.678673	−	0.477230i
$106$	−8.72849e6	+	1.25497e6i	−0.711817	+	0.102344i
$107$	4.67767e6	+	5.39832e6i	0.369136	+	0.426006i	0.909680	−	0.415310i	$-0.136327\pi$
$107$	4.67767e6	+	5.39832e6i	0.369136	+	0.426006i	−0.540544	+	0.841316i	$0.681781\pi$
$108$	7.24511e6	+	1.66433e7i	0.553429	+	1.27132i
$109$	1.31288e6	+	2.04288e6i	0.0971028	+	0.151095i	0.886406	−	0.462909i	$-0.153194\pi$
$109$	1.31288e6	+	2.04288e6i	0.0971028	+	0.151095i	−0.789303	+	0.614004i	$0.789558\pi$
$110$	−2.82127e7	−	4.05637e6i	−2.02102	−	0.290578i
$111$	−1.67713e6	−	3.30119e6i	−0.116396	−	0.229108i
$112$	4.79906e6	+	4.15841e6i	0.322770	+	0.279682i
$113$	−2.16405e7	−	6.35422e6i	−1.41089	−	0.414274i	−0.514480	−	0.857502i	$-0.672015\pi$
$113$	−2.16405e7	−	6.35422e6i	−1.41089	−	0.414274i	−0.896409	+	0.443228i	$0.853833\pi$
$114$	−1.07345e7	+	1.83402e7i	−0.678602	+	1.15941i
$115$	1.42530e7	−	3.60312e6i	0.873907	−	0.220921i
$116$		−	3.93646e7i		−	2.34155i
$117$	−4.37460e6	−	1.90157e7i	−0.252515	−	1.09764i
$118$	1.61315e7	−	1.86168e7i	0.903833	−	1.04308i
$119$	1.06283e7	−	1.65379e7i	0.578161	−	0.899636i
$120$	−6.34622e6	+	7.97195e6i	−0.335259	+	0.421144i
$121$	1.88513e7	−	1.21150e7i	0.967368	−	0.621690i
$122$	−1.76460e7	−	3.86394e7i	−0.879808	−	1.92651i
$123$	2.57350e6	+	1.37930e7i	0.124697	+	0.668331i
$124$	−6.70633e6	−	4.66435e7i	−0.315870	−	2.19693i
$125$	−9.70981e6	+	2.12615e7i	−0.444658	+	0.973664i
$126$	2.28439e7	+	2.23057e7i	1.01736	+	0.993389i
$127$	−3.89604e7	+	1.14398e7i	−1.68776	+	0.495570i	−0.977953	−	0.208827i	$-0.933035\pi$
$127$	−3.89604e7	+	1.14398e7i	−1.68776	+	0.495570i	−0.709805	+	0.704398i	$0.751217\pi$
$128$	−2.38512e7	−	1.08925e7i	−1.00525	−	0.459083i
$129$	−1.52756e6	+	3.75093e6i	−0.0626520	+	0.153842i
$130$	2.96922e7	−	2.57284e7i	1.18533	−	1.02710i
$131$	1.60665e7	−	7.33733e6i	0.624413	−	0.285160i	−0.0779735	−	0.996955i	$-0.524845\pi$
$131$	1.60665e7	−	7.33733e6i	0.624413	−	0.285160i	0.702387	+	0.711795i	$0.252118\pi$
$132$	−2.23739e6	−	5.36761e7i	−0.0846708	−	2.03129i
$133$	−3.09057e6	+	2.14954e7i	−0.113909	+	0.792254i
$134$	−1.60037e7	−	1.02849e7i	−0.574582	−	0.369262i
$135$	1.72190e7	−	1.91705e7i	0.602337	−	0.670603i
$136$	−5.73429e6	+	1.95292e7i	−0.195476	+	0.665731i
$137$	−4.33244e7			−1.43950			−0.719749	−	0.694235i	$-0.755743\pi$
$137$	−4.33244e7			−1.43950			−0.719749	+	0.694235i	$0.755743\pi$
$138$	1.99718e7	+	4.33109e7i	0.646905	+	1.40288i
$139$	−1.72119e6			−0.0543596			−0.0271798	−	0.999631i	$-0.508653\pi$
$139$	−1.72119e6			−0.0543596			−0.0271798	+	0.999631i	$0.508653\pi$
$140$	−1.05227e7	+	3.58370e7i	−0.324100	+	1.10378i
$141$	4.74977e7	−	1.61238e7i	1.42694	−	0.484396i
$142$	5.88146e7	+	3.77979e7i	1.72376	+	1.10779i
$143$	−8.21857e6	+	5.71614e7i	−0.235028	+	1.63466i
$144$	1.46865e7	+	7.79368e6i	0.409874	+	0.217507i
$145$	−5.08317e7	+	2.32141e7i	−1.38467	+	0.632358i
$146$	2.36058e7	−	2.04545e7i	0.627746	−	0.543945i
$147$	−5.45109e6	−	2.21995e6i	−0.141538	−	0.0576412i
$148$	1.27826e7	+	5.83761e6i	0.324118	+	0.148020i
$149$	2.66462e7	−	7.82402e6i	0.659907	−	0.193766i	0.0654030	−	0.997859i	$-0.479167\pi$
$149$	2.66462e7	−	7.82402e6i	0.659907	−	0.193766i	0.594504	+	0.804093i	$0.297349\pi$
$150$	−1.16175e7	−	2.89156e6i	−0.281056	−	0.0699539i
$151$	1.19636e7	−	2.61967e7i	0.282777	−	0.619195i	−0.713936	−	0.700211i	$-0.753089\pi$
$151$	1.19636e7	−	2.61967e7i	0.282777	−	0.619195i	0.996713	+	0.0810163i	$0.0258166\pi$
$152$	−3.19983e6	−	2.22553e7i	−0.0739051	−	0.514021i
$153$	1.74117e7	−	4.84379e7i	0.393025	−	1.09337i
$154$	−3.92544e7	−	8.59551e7i	−0.866095	−	1.89648i
$155$	−5.62762e7	+	3.61665e7i	−1.21385	+	0.780091i
$156$	5.79355e7	+	4.61207e7i	1.22182	+	0.972656i
$157$	−2.73684e7	+	4.25860e7i	−0.564417	+	0.878250i	−0.999758	−	0.0220161i	$-0.992991\pi$
$157$	−2.73684e7	+	4.25860e7i	−0.564417	+	0.878250i	0.435341	+	0.900266i	$0.356628\pi$
$158$	3.33244e7	−	3.84584e7i	0.672145	−	0.775696i
$159$	−1.71727e7	+	1.61805e7i	−0.338805	+	0.319229i
$160$			6.13668e7i			1.18444i
$161$	3.55957e7	+	3.32933e7i	0.672213	+	0.628733i
$162$	7.13832e7	+	4.35067e7i	1.31915	+	0.803996i
$163$	1.56748e7	+	4.60254e6i	0.283495	+	0.0832418i	0.420389	−	0.907344i	$-0.361894\pi$
$163$	1.56748e7	+	4.60254e6i	0.283495	+	0.0832418i	−0.136894	+	0.990586i	$0.543712\pi$
$164$	−4.02432e7	−	3.48709e7i	−0.712425	−	0.617320i
$165$	−6.79928e7	+	3.45430e7i	−1.17834	+	0.598640i
$166$	3.82543e7	+	5.50014e6i	0.649085	+	0.0933244i
$167$	3.99919e7	+	6.22287e7i	0.664454	+	1.03391i	0.995902	+	0.0904368i	$0.0288263\pi$
$167$	3.99919e7	+	6.22287e7i	0.664454	+	1.03391i	−0.331449	+	0.943473i	$0.607537\pi$
$168$	−3.36084e7	−	3.41081e6i	−0.546846	−	0.0554976i
$169$	−1.10365e7	−	1.27368e7i	−0.175885	−	0.202982i
$170$	1.02585e8	−	1.47495e7i	1.60145	−	0.230254i
$171$	4.73200e6	+	5.66628e7i	0.0723700	+	0.866586i
$172$	−4.33034e6	−	1.47478e7i	−0.0648892	−	0.220992i
$173$	3.43164e7	+	1.16871e8i	0.503895	+	1.71611i	0.681330	+	0.731976i	$0.261402\pi$
$173$	3.43164e7	+	1.16871e8i	0.503895	+	1.71611i	−0.177436	+	0.984132i	$0.556780\pi$
$174$	−1.04279e8	−	1.48296e8i	−1.50063	−	2.13407i
$175$	−1.21097e7	+	1.74112e6i	−0.170805	+	0.0245581i
$176$	−3.22242e7	−	3.71887e7i	−0.445541	−	0.514182i
$177$	6.65494e6	−	6.55744e7i	0.0902064	−	0.888849i
$178$	1.15031e7	+	1.78991e7i	0.152878	+	0.237882i
$179$	−4.55933e6	−	655532.i	−0.0594176	−	0.00854296i	0.112542	−	0.993647i	$-0.464101\pi$
$179$	−4.55933e6	−	655532.i	−0.0594176	−	0.00854296i	−0.171960	+	0.985104i	$0.555010\pi$
$180$	−5.81345e6	+	9.76204e7i	−0.0742985	+	1.24763i
$181$	6.38831e7	+	5.53550e7i	0.800775	+	0.693876i	0.955794	−	0.294036i	$-0.0949985\pi$
$181$	6.38831e7	+	5.53550e7i	0.800775	+	0.693876i	−0.155019	+	0.987911i	$0.549544\pi$
$182$	1.24975e8	+	3.66961e7i	1.53665	+	0.451200i
$183$	−9.80910e7	−	5.74125e7i	−1.18318	−	0.692513i
$184$	−4.50727e7	−	2.26910e7i	−0.533398	−	0.268529i
$185$		−	1.99488e7i		−	0.231641i
$186$	−1.48826e8	−	1.57952e8i	−1.69583	−	1.79983i
$187$	−9.97605e7	+	1.15130e8i	−1.11561	+	1.28748i
$188$	−1.02918e8	+	1.60143e8i	−1.12963	+	1.75774i
$189$	8.43289e7	+	1.36628e7i	0.908573	+	0.147205i
$190$	−9.63137e7	+	6.18971e7i	−1.01871	+	0.654685i
$191$	−4.94079e7	−	1.08188e8i	−0.513073	−	1.12347i	−0.971996	−	0.234998i	$-0.924492\pi$
$191$	−4.94079e7	−	1.08188e8i	−0.513073	−	1.12347i	0.458923	−	0.888476i	$-0.348236\pi$
$192$	−1.50972e8	+	2.81683e7i	−1.53936	+	0.287214i
$193$	−1.31755e7	−	9.16373e7i	−0.131921	−	0.917533i	−0.943047	−	0.332661i	$-0.892054\pi$
$193$	−1.31755e7	−	9.16373e7i	−0.131921	−	0.917533i	0.811125	−	0.584873i	$-0.198855\pi$
$194$	4.73281e7	−	1.03634e8i	0.465386	−	1.01905i
$195$	2.53901e7	−	1.02011e8i	0.245213	−	0.985200i
$196$	2.14324e7	−	6.29312e6i	0.203318	−	0.0596994i
$197$	1.53395e8	+	7.00531e7i	1.42948	+	0.652823i	0.971695	−	0.236239i	$-0.0759148\pi$
$197$	1.53395e8	+	7.00531e7i	1.42948	+	0.652823i	0.457787	+	0.889062i	$0.348642\pi$
$198$	−1.50620e8	−	1.96284e8i	−1.37897	−	1.79704i
$199$	−1.24998e8	+	1.08311e8i	−1.12439	+	0.974288i	−0.999839	−	0.0179256i	$-0.994294\pi$
$199$	−1.24998e8	+	1.08311e8i	−1.12439	+	0.974288i	−0.124549	+	0.992213i	$0.539748\pi$
$200$	1.15221e7	−	5.26198e6i	0.101842	−	0.0465097i
$201$	−5.08567e7	+	2.11987e6i	−0.441735	+	0.0184130i
$202$	−2.09614e7	+	1.45789e8i	−0.178933	+	1.24450i
$203$	−1.55853e8	−	1.00160e8i	−1.30761	−	0.840349i
$204$	6.27926e7	+	1.84976e8i	0.517849	+	1.52549i
$205$	−2.12968e7	+	7.25303e7i	−0.172654	+	0.588005i
$206$	1.21682e8			0.969823
$207$	1.10371e8	+	6.40576e7i	0.864887	+	0.501966i
$208$	6.78281e7			0.522622
$209$	4.74111e7	−	1.61467e8i	0.359226	−	1.22341i
$210$	5.52927e7	+	1.62882e8i	0.412003	+	1.21369i
$211$	1.33695e7	+	8.59204e6i	0.0979774	+	0.0629662i	0.588712	−	0.808343i	$-0.299635\pi$
$211$	1.33695e7	+	8.59204e6i	0.0979774	+	0.0629662i	−0.490735	+	0.871309i	$0.663272\pi$
$212$	1.27435e7	−	8.86332e7i	0.0918574	−	0.638882i
$213$	1.86902e8	−	7.79070e6i	1.32521	−	0.0552392i
$214$	−1.13563e8	+	5.18626e7i	−0.792117	+	0.361748i
$215$	−1.64902e7	+	1.42888e7i	−0.113160	+	0.0980533i
$216$	−8.77588e7	+	1.10253e7i	−0.592520	+	0.0744396i
$217$	−2.01735e8	−	9.21293e7i	−1.34021	−	0.612053i
$218$	−4.07238e7	+	1.19576e7i	−0.266226	+	0.0781711i
$219$	2.01856e7	−	8.11002e7i	0.129863	−	0.521756i
$220$	1.20234e8	−	2.63276e8i	0.761286	−	1.66698i
$221$	−2.98838e7	−	2.07847e8i	−0.186236	−	1.29530i
$222$	6.36193e7	−	1.18701e7i	0.390260	−	0.0728145i
$223$	1.90856e7	+	4.17917e7i	0.115250	+	0.252362i	0.958463	−	0.285218i	$-0.0920660\pi$
$223$	1.90856e7	+	4.17917e7i	0.115250	+	0.252362i	−0.843213	+	0.537580i	$0.819339\pi$
$224$	−1.71151e8	+	1.09992e8i	−1.01744	+	0.653871i
$225$	−2.98777e7	+	1.15513e7i	−0.174867	+	0.0676070i
$226$	2.13121e8	−	3.31622e8i	1.22813	−	1.91101i
$227$	−1.43436e8	+	1.65534e8i	−0.813893	+	0.939283i	−0.999057	−	0.0434249i	$-0.986173\pi$
$227$	−1.43436e8	+	1.65534e8i	−0.813893	+	0.939283i	0.185164	+	0.982708i	$0.440719\pi$
$228$	−1.47982e8	−	1.57057e8i	−0.826868	−	0.877575i
$229$			8.35734e7i			0.459879i	0.973205	+	0.229940i	$0.0738529\pi$
$229$			8.35734e7i			0.459879i	−0.973205	+	0.229940i	$0.926147\pi$
$230$	−9.75927e6	+	2.56766e8i	−0.0528896	+	1.39152i
$231$	−2.18208e8	−	1.27717e8i	−1.16474	−	0.681719i
$232$	1.84042e8	+	5.40397e7i	0.967630	+	0.284122i
$233$	1.02607e8	+	8.89097e7i	0.531413	+	0.460472i	0.878760	−	0.477265i	$-0.158372\pi$
$233$	1.02607e8	+	8.89097e7i	0.531413	+	0.460472i	−0.347346	+	0.937737i	$0.612917\pi$
$234$	3.40434e8	+	2.02734e7i	1.73691	+	0.103436i
$235$	2.67486e8	+	3.84586e7i	1.34451	+	0.193311i
$236$	1.35236e8	+	2.10431e8i	0.669731	+	1.04212i
$237$	1.37477e7	−	1.35463e8i	0.0670829	−	0.661002i
$238$	2.25006e8	+	2.59671e8i	1.08187	+	1.24854i
$239$	2.01618e7	−	2.89883e6i	0.0955292	−	0.0137350i	−0.0943844	−	0.995536i	$-0.530088\pi$
$239$	2.01618e7	−	2.89883e6i	0.0955292	−	0.0137350i	0.189914	+	0.981801i	$0.439179\pi$
$240$	5.15239e7	+	7.32726e7i	0.240586	+	0.342139i
$241$	−5.96466e7	−	2.03138e8i	−0.274490	−	0.934826i	−0.975190	−	0.221370i	$-0.928947\pi$
$241$	−5.96466e7	−	2.03138e8i	−0.274490	−	0.934826i	0.700700	−	0.713456i	$-0.252871\pi$
$242$	1.10342e8	+	3.75791e8i	0.500482	+	1.70448i
$243$	2.23198e8	−	1.46395e7i	0.997856	−	0.0654492i
$244$	4.26952e8	−	6.13865e7i	1.88155	−	0.270526i
$245$	−2.07654e7	−	2.39646e7i	−0.0902111	−	0.104109i
$246$	−2.43981e8	−	2.47609e7i	−1.04492	−	0.106046i
$247$	1.25409e8	+	1.95140e8i	0.529529	+	0.823963i
$248$	2.27280e8	+	3.26779e7i	0.946194	+	0.136042i
$249$	9.21931e7	−	4.68377e7i	0.378443	−	0.192264i
$250$	−3.08743e8	−	2.67528e8i	−1.24971	−	1.08288i
$251$	3.04264e8	+	8.93400e7i	1.21449	+	0.356605i	0.825375	−	0.564585i	$-0.190964\pi$
$251$	3.04264e8	+	8.93400e7i	1.21449	+	0.356605i	0.389111	+	0.921191i	$0.372782\pi$
$252$	−2.82681e8	+	1.58758e8i	−1.11274	+	0.624933i
$253$	−2.36313e8	−	2.94625e8i	−0.917414	−	1.14379i
$254$		−	7.09696e8i		−	2.71741i
$255$	2.01830e8	−	1.90168e8i	0.762245	−	0.718202i
$256$	2.48414e7	−	2.86685e7i	0.0925414	−	0.106798i
$257$	2.24835e8	−	3.49850e8i	0.826224	−	1.28563i	−0.129564	−	0.991571i	$-0.541358\pi$
$257$	2.24835e8	−	3.49850e8i	0.826224	−	1.28563i	0.955788	−	0.294058i	$-0.0950060\pi$
$258$	−5.53812e7	−	4.40872e7i	−0.200767	−	0.159825i
$259$	5.56366e7	−	3.57555e7i	0.198981	−	0.127877i
$260$	1.65731e8	+	3.62900e8i	0.584786	+	1.28050i
$261$	−4.56476e8	−	1.64087e8i	−1.58919	−	0.571256i
$262$	4.39337e7	+	3.05565e8i	0.150919	+	1.04966i
$263$	1.42334e7	−	3.11669e7i	0.0482464	−	0.105645i	−0.883974	−	0.467536i	$-0.845142\pi$
$263$	1.42334e7	−	3.11669e7i	0.0482464	−	0.105645i	0.932220	+	0.361892i	$0.117869\pi$
$264$	2.54024e8	+	6.32259e7i	0.849693	+	0.211486i
$265$	−1.21968e8	+	3.58129e7i	−0.402609	+	0.118217i
$266$	−3.45259e8	−	1.57675e8i	−1.12476	−	0.513660i
$267$	5.27250e7	+	2.14722e7i	0.169522	+	0.0690378i
$268$	1.45992e8	−	1.26502e8i	0.463293	−	0.401446i
$269$	−2.95019e8	+	1.34731e8i	−0.924096	+	0.422021i	−0.819881	−	0.572534i	$-0.805960\pi$
$269$	−2.95019e8	+	1.34731e8i	−0.924096	+	0.422021i	−0.104215	+	0.994555i	$0.533233\pi$
$270$	2.36701e8	+	3.83160e8i	0.731859	+	1.18470i
$271$	−4.12722e7	+	2.87055e8i	−0.125970	+	0.876137i	0.824620	+	0.565687i	$0.191389\pi$
$271$	−4.12722e7	+	2.87055e8i	−0.125970	+	0.876137i	−0.950590	+	0.310450i	$0.899520\pi$
$272$	1.50522e8	+	9.67346e7i	0.453533	+	0.291468i
$273$	3.30014e8	−	1.12028e8i	0.981664	−	0.333240i
$274$	2.13334e8	−	7.26550e8i	0.626519	−	2.13373i
$275$	9.48054e7			0.274896
$276$	−4.79121e8	+	7.06824e7i	−1.37171	+	0.202362i
$277$	−1.03566e8			−0.292779			−0.146389	−	0.989227i	$-0.546765\pi$
$277$	−1.03566e8			−0.292779			−0.146389	+	0.989227i	$0.546765\pi$
$278$	8.47533e6	−	2.88643e7i	0.0236592	−	0.0805758i
$279$	−5.68838e8	−	1.16661e8i	−1.56810	−	0.321595i
$280$	−1.53104e8	−	9.83940e7i	−0.416806	−	0.267865i
$281$	1.09252e7	−	7.59861e7i	0.0293735	−	0.204297i	−0.969850	−	0.243704i	$-0.921638\pi$
$281$	1.09252e7	−	7.59861e7i	0.0293735	−	0.204297i	0.999223	+	0.0394064i	$0.0125467\pi$
$282$	3.65117e7	+	8.75932e8i	0.0969528	+	2.32594i
$283$	−1.29441e8	+	5.91135e7i	−0.339483	+	0.155037i	−0.577860	−	0.816136i	$-0.696112\pi$
$283$	−1.29441e8	+	5.91135e7i	−0.339483	+	0.155037i	0.238377	+	0.971173i	$0.423385\pi$
$284$	−5.36530e8	+	4.64906e8i	−1.38989	+	1.20434i
$285$	−1.15540e8	+	2.83709e8i	−0.295649	+	0.725965i
$286$	−9.18128e8	−	4.19295e8i	−2.32072	−	1.05984i
$287$	−2.40457e8	+	7.06045e7i	−0.600414	+	0.176297i
$288$	−3.72149e8	+	3.81128e8i	−0.918002	+	0.940149i
$289$	5.96471e7	−	1.30609e8i	0.145361	−	0.318295i
$290$	−1.38999e8	−	9.66756e8i	−0.334670	−	2.32768i
$291$	−5.59119e7	−	2.99668e8i	−0.133008	−	0.712877i
$292$	1.31759e8	+	2.88512e8i	0.309699	+	0.678147i
$293$	1.79505e8	−	1.15361e8i	0.416907	−	0.267930i	−0.315327	−	0.948983i	$-0.602114\pi$
$293$	1.79505e8	−	1.15361e8i	0.416907	−	0.267930i	0.732234	+	0.681053i	$0.238478\pi$
$294$	6.40704e7	−	8.04835e7i	0.147042	−	0.184710i
$295$	1.91980e8	−	2.98726e8i	0.435390	−	0.677480i
$296$	−4.48406e7	+	5.17488e7i	−0.100496	+	0.115979i
$297$	−6.31760e8	−	1.97797e8i	−1.39928	−	0.438099i
$298$			4.85382e8i			1.06250i
$299$	5.20230e8	+	1.97731e7i	1.12550	+	0.0427786i
$300$	6.14087e7	−	1.04919e8i	0.131312	−	0.224351i
$301$	−6.94077e7	−	2.03799e7i	−0.146698	−	0.0430745i
$302$	3.80408e8	+	3.29626e8i	0.794741	+	0.688647i
$303$	1.78501e8	+	3.51354e8i	0.368631	+	0.725596i
$304$	−1.95643e8	−	2.81292e7i	−0.399398	−	0.0574248i
$305$	−3.31051e8	−	5.15125e8i	−0.668105	−	1.03959i
$306$	7.26566e8	+	5.30507e8i	1.44961	+	1.05844i
$307$	−2.90286e8	−	3.35008e8i	−0.572588	−	0.660802i	0.393406	−	0.919365i	$-0.371297\pi$
$307$	−2.90286e8	−	3.35008e8i	−0.572588	−	0.660802i	−0.965994	+	0.258563i	$0.916751\pi$
$308$	9.49774e8	−	1.36557e8i	1.85222	−	0.266309i
$309$	2.66329e8	−	1.87277e8i	0.513527	−	0.361103i
$310$	−3.29402e8	−	1.12184e9i	−0.628000	−	2.13877i
$311$	1.87686e8	+	6.39200e8i	0.353810	+	1.20497i	0.923658	+	0.383217i	$0.125184\pi$
$311$	1.87686e8	+	6.39200e8i	0.353810	+	1.20497i	−0.569848	+	0.821750i	$0.692998\pi$
$312$	−2.95163e8	+	2.07553e8i	−0.550200	+	0.386890i
$313$	8.09581e8	−	1.16400e8i	1.49230	−	0.214560i	0.652636	−	0.757672i	$-0.273663\pi$
$313$	8.09581e8	−	1.16400e8i	1.49230	−	0.214560i	0.839660	+	0.543112i	$0.182754\pi$
$314$	−5.79402e8	−	6.68666e8i	−1.05615	−	1.21886i
$315$	3.71707e8	+	2.71404e8i	0.670060	+	0.489249i
$316$	2.79370e8	+	4.34708e8i	0.498053	+	0.774985i
$317$	−1.86511e8	−	2.68162e7i	−0.328849	−	0.0472814i	−0.0240871	−	0.999710i	$-0.507668\pi$
$317$	−1.86511e8	−	2.68162e7i	−0.328849	−	0.0472814i	−0.304762	+	0.952428i	$0.598577\pi$
$318$	−1.86786e8	−	3.67662e8i	−0.325724	−	0.641141i
$319$	1.08498e9	+	9.40137e8i	1.87134	+	1.62152i
$320$	−7.93881e8	−	2.33104e8i	−1.35435	−	0.397673i
$321$	−1.68738e8	+	2.88294e8i	−0.284738	+	0.486484i
$322$	−7.33606e8	+	4.33000e8i	−1.22452	+	0.722757i
$323$			6.11904e8i			1.01036i
$324$	−6.28109e8	+	5.71031e8i	−1.02595	+	0.932722i
$325$	−8.55773e7	+	9.87615e7i	−0.138282	+	0.159586i
$326$	−1.54369e8	+	2.40203e8i	−0.246774	+	0.383988i
$327$	−7.07295e7	+	8.88485e7i	−0.111862	+	0.140518i
$328$	2.18279e8	−	1.40279e8i	0.341549	−	0.219500i
$329$	3.72172e8	+	8.14943e8i	0.576180	+	1.26166i
$330$	−2.44481e8	−	1.31033e9i	−0.374496	−	2.00716i
$331$	1.14871e8	+	7.98946e8i	0.174106	+	1.21093i	0.870097	+	0.492881i	$0.164056\pi$
$331$	1.14871e8	+	7.98946e8i	0.174106	+	1.21093i	−0.695991	+	0.718050i	$0.745035\pi$
$332$	−1.63028e8	+	3.56982e8i	−0.244500	+	0.535381i
$333$	1.20976e8	−	1.23895e8i	0.179533	−	0.183865i
$334$	−1.24050e9	+	3.64243e8i	−1.82173	+	0.534908i
$335$	−2.49447e8	−	1.13919e8i	−0.362511	−	0.165553i
$336$	−1.12006e8	+	2.75030e8i	−0.161084	+	0.395543i
$337$	−7.30881e8	+	6.33312e8i	−1.04026	+	0.901391i	−0.995226	−	0.0975944i	$-0.968885\pi$
$337$	−7.30881e8	+	6.33312e8i	−1.04026	+	0.901391i	−0.0450344	+	0.998985i	$0.514340\pi$
$338$	2.67942e8	−	1.22365e8i	0.377427	−	0.172365i
$339$	−4.39273e7	−	1.05384e9i	−0.0612401	−	1.46918i
$340$	−1.49774e8	+	1.04170e9i	−0.206661	+	1.43736i
$341$	1.44576e9	+	9.29137e8i	1.97450	+	1.26893i
$342$	−9.73536e8	−	1.99659e8i	−1.31601	−	0.269896i
$343$	2.23417e8	−	7.60889e8i	0.298942	−	1.01810i
$344$	7.48953e7			0.0991973
$345$	3.73819e8	+	5.77009e8i	0.490111	+	0.756511i
$346$	−2.12890e9			−2.76305
$347$	9.37188e7	−	3.19177e8i	0.120413	−	0.410089i	−0.877121	−	0.480269i	$-0.840539\pi$
$347$	9.37188e7	−	3.19177e8i	0.120413	−	0.410089i	0.997534	+	0.0701797i	$0.0223573\pi$
$348$	1.74320e9	−	5.91754e8i	2.21727	−	0.752686i
$349$	9.20371e7	+	5.91486e7i	0.115897	+	0.0744828i	0.597305	−	0.802014i	$-0.296238\pi$
$349$	9.20371e7	+	5.91486e7i	0.115897	+	0.0744828i	−0.481408	+	0.876497i	$0.659874\pi$
$350$	3.04312e7	−	2.11654e8i	0.0379386	−	0.263869i
$351$	7.76317e8	−	4.79578e8i	0.958218	−	0.591949i
$352$	1.43408e9	−	6.54921e8i	1.75256	−	0.800368i
$353$	−9.26924e8	+	8.03184e8i	−1.12159	+	0.971860i	−0.999786	−	0.0206948i	$-0.993412\pi$
$353$	−9.26924e8	+	8.03184e8i	−1.12159	+	0.971860i	−0.121800	+	0.992555i	$0.538867\pi$
$354$	1.06691e9	+	4.34499e8i	1.27826	+	0.520568i
$355$	9.16737e8	+	4.18660e8i	1.08754	+	0.496663i
$356$	−2.07302e8	+	6.08695e7i	−0.243517	+	0.0715030i
$357$	8.92127e8	+	2.22048e8i	1.03774	+	0.258290i
$358$	3.34439e7	−	7.32320e7i	0.0385236	−	0.0843549i
$359$	−1.68341e8	−	1.17084e9i	−0.192026	−	1.33557i	−0.826635	−	0.562738i	$-0.809748\pi$
$359$	−1.68341e8	−	1.17084e9i	−0.192026	−	1.33557i	0.634609	−	0.772833i	$-0.281161\pi$
$360$	−4.48426e8	−	1.61193e8i	−0.506561	−	0.182090i
$361$	9.05264e7	+	1.98225e8i	0.101274	+	0.221760i
$362$	−1.24287e9	+	7.98744e8i	−1.37704	+	0.884968i
$363$	8.19877e8	+	6.52678e8i	0.899654	+	0.716186i
$364$	−7.15070e8	+	1.11267e9i	−0.777130	+	1.20924i
$365$	2.94856e8	−	3.40282e8i	0.317384	−	0.366281i
$366$	1.44582e9	−	1.36228e9i	1.54145	−	1.45239i
$367$		−	1.80717e9i		−	1.90840i	−0.299174	−	0.954198i	$-0.596711\pi$
$367$		−	1.80717e9i		−	1.90840i	0.299174	−	0.954198i	$-0.403289\pi$
$368$	−3.03023e8	+	3.23978e8i	−0.316962	+	0.338882i
$369$	−5.72116e8	+	3.21309e8i	−0.592777	+	0.332913i
$370$	3.34541e8	+	9.82300e7i	0.343354	+	0.100818i
$371$	−3.18492e8	−	2.75975e8i	−0.323810	−	0.280583i
$372$	1.96472e9	−	9.98155e8i	1.97879	−	1.00530i
$373$	1.90696e9	+	2.74180e8i	1.90266	+	0.273562i	0.990632	−	0.136560i	$-0.0436047\pi$
$373$	1.90696e9	+	2.74180e8i	1.90266	+	0.273562i	0.912031	+	0.410122i	$0.134514\pi$
$374$	−1.43949e9	−	2.23989e9i	−1.42285	−	2.21400i
$375$	−1.08750e9	−	1.10367e8i	−1.06492	−	0.108076i
$376$	−6.07434e8	−	7.01016e8i	−0.589307	−	0.680097i
$377$	−1.95873e9	+	2.81623e8i	−1.88270	+	0.270691i
$378$	−6.44370e8	+	1.34692e9i	−0.613640	+	1.28268i
$379$	1.11991e8	+	3.81406e8i	0.105669	+	0.359874i	0.995304	−	0.0967971i	$-0.0308598\pi$
$379$	1.11991e8	+	3.81406e8i	0.105669	+	0.359874i	−0.889636	+	0.456671i	$0.849042\pi$
$380$	−3.27534e8	−	1.11548e9i	−0.306206	−	1.04284i
$381$	−1.09227e9	−	1.55333e9i	−1.01180	−	1.43888i
$382$	2.05761e9	−	2.95839e8i	1.88860	−	0.271540i
$383$	6.71837e8	+	7.75342e8i	0.611038	+	0.705176i	0.973979	−	0.226636i	$-0.0727729\pi$
$383$	6.71837e8	+	7.75342e8i	0.611038	+	0.705176i	−0.362941	+	0.931812i	$0.618227\pi$
$384$	1.23809e8	−	1.21995e9i	0.111582	−	1.09947i
$385$	−7.36436e8	−	1.14592e9i	−0.657692	−	1.02339i
$386$	1.60164e9	+	2.30280e8i	1.41745	+	0.203799i
$387$	−1.89067e8	−	1.12593e7i	−0.165817	−	0.00987465i
$388$	8.74325e8	+	7.57607e8i	0.759909	+	0.658465i
$389$	−2.75399e8	−	8.08644e7i	−0.237213	−	0.0696521i	0.160965	−	0.986960i	$-0.448539\pi$
$389$	−2.75399e8	−	8.08644e7i	−0.237213	−	0.0696521i	−0.398178	+	0.917308i	$0.630357\pi$
$390$	1.58569e9	+	9.28105e8i	1.35361	+	0.792266i
$391$	1.12628e9	+	7.85818e8i	0.952855	+	0.664819i
$392$			1.08843e8i			0.0912636i
$393$	5.66444e8	+	6.01180e8i	0.470742	+	0.499610i
$394$	−1.93012e9	+	2.22748e9i	−1.58982	+	1.83475i
$395$	3.96591e8	−	6.17108e8i	0.323782	−	0.503815i
$396$	2.34333e9	−	9.05973e8i	1.89627	−	0.733132i
$397$	−1.65511e9	+	1.06367e9i	−1.32757	+	0.853181i	−0.995922	−	0.0902209i	$-0.971243\pi$
$397$	−1.65511e9	+	1.06367e9i	−1.32757	+	0.853181i	−0.331653	+	0.943401i	$0.607606\pi$
$398$	−1.20087e9	−	2.62955e9i	−0.954788	−	2.09069i
$399$	−9.98348e8	+	1.86271e8i	−0.786822	+	0.146805i
$400$	−1.58470e7	−	1.10218e8i	−0.0123805	−	0.0861080i
$401$	−4.18106e8	+	9.15524e8i	−0.323803	+	0.709030i	−0.999606	−	0.0280523i	$-0.991070\pi$
$401$	−4.18106e8	+	9.15524e8i	−0.323803	+	0.709030i	0.675803	+	0.737082i	$0.263797\pi$
$402$	2.14874e8	−	8.63306e8i	0.164965	−	0.662786i
$403$	−2.27295e9	+	6.67397e8i	−1.72990	+	0.507945i
$404$	−1.36048e9	−	6.21311e8i	−1.02650	−	0.468786i
$405$	1.10778e9	+	4.74332e8i	0.828633	+	0.354805i
$406$	2.44712e9	−	2.12045e9i	1.81474	−	1.57248i
$407$	−4.66181e8	+	2.12898e8i	−0.342747	+	0.156528i
$408$	−9.51022e8	+	3.96417e7i	−0.693234	+	0.0288963i
$409$	3.29046e8	−	2.28857e9i	0.237807	−	1.65399i	−0.424998	−	0.905194i	$-0.639725\pi$
$409$	3.29046e8	−	2.28857e9i	0.237807	−	1.65399i	0.662805	−	0.748792i	$-0.269366\pi$
$410$	−1.11146e9	−	7.14295e8i	−0.796438	−	0.511840i
$411$	−6.51281e8	−	1.91855e9i	−0.462724	−	1.36310i
$412$	−3.48115e8	+	1.18557e9i	−0.245235	+	0.835193i
$413$	1.17724e9			0.822318
$414$	−1.61773e9	+	1.53550e9i	−1.12048	+	1.06353i
$415$	5.57114e8			0.382627
$416$	−6.12238e8	+	2.08509e9i	−0.416959	+	1.42003i
$417$	−2.58740e7	−	7.62201e7i	−0.0174738	−	0.0514746i
$418$	2.47435e9	+	1.59017e9i	1.65708	+	1.06494i
$419$	5.90190e7	−	4.10486e8i	0.0391961	−	0.272615i	−0.960793	−	0.277266i	$-0.910572\pi$
$419$	5.90190e7	−	4.10486e8i	0.0391961	−	0.272615i	0.999989	+	0.00465149i	$0.00148062\pi$
$420$	−1.74517e9	+	7.27443e7i	−1.14938	+	0.0479101i
$421$	−2.59117e9	+	1.18335e9i	−1.69242	+	0.772904i	−0.693817	+	0.720152i	$0.744072\pi$
$421$	−2.59117e9	+	1.18335e9i	−1.69242	+	0.772904i	−0.998608	+	0.0527527i	$0.983200\pi$
$422$	−2.09921e8	+	1.81898e8i	−0.135976	+	0.117824i
$423$	1.42803e9	+	1.86098e9i	0.917375	+	1.19550i
$424$	3.96894e8	+	1.81256e8i	0.252868	+	0.115481i
$425$	−3.30761e8	+	9.71203e7i	−0.209004	+	0.0613690i
$426$	−7.89679e8	+	3.17271e9i	−0.494899	+	1.98837i
$427$	8.43307e8	−	1.84659e9i	0.524189	−	1.14781i
$428$	−1.80418e8	−	1.25483e9i	−0.111231	−	0.773630i
$429$	−2.65485e9	+	4.95341e8i	−1.62345	+	0.302903i
$430$	−1.58424e8	−	3.46900e8i	−0.0960908	−	0.210409i
$431$	2.55362e9	−	1.64111e9i	1.53633	−	0.987340i	0.547752	−	0.836641i	$-0.315484\pi$
$431$	2.55362e9	−	1.64111e9i	1.53633	−	0.987340i	0.988580	−	0.150700i	$-0.0481527\pi$
$432$	−1.24353e8	+	7.67529e8i	−0.0742103	+	0.458038i
$433$	2.18706e8	−	3.40313e8i	0.129465	−	0.201452i	−0.770469	−	0.637477i	$-0.779978\pi$
$433$	2.18706e8	−	3.40313e8i	0.129465	−	0.201452i	0.899934	+	0.436026i	$0.143614\pi$
$434$	2.53838e9	−	2.92944e9i	1.49053	−	1.72017i
$435$	−1.79213e9	−	1.90203e9i	−1.04390	−	1.10791i
$436$		−	4.30987e8i		−	0.249036i
$437$	−1.49235e9	−	2.72779e8i	−0.855430	−	0.156360i
$438$	1.26065e9	+	7.37859e8i	0.716864	+	0.419579i
$439$	−2.00784e9	−	5.89554e8i	−1.13267	−	0.332581i	−0.338912	−	0.940818i	$-0.610059\pi$
$439$	−2.00784e9	−	5.89554e8i	−1.13267	−	0.332581i	−0.793756	+	0.608237i	$0.791877\pi$
$440$	1.06584e9	+	9.23557e8i	0.596497	+	0.516868i
$441$	1.63627e7	−	2.74765e8i	0.00908488	−	0.152555i
$442$	3.63274e9	+	5.22309e8i	2.00104	+	0.287706i
$443$	1.11159e9	+	1.72967e9i	0.607482	+	0.945260i	0.999678	+	0.0253785i	$0.00807910\pi$
$443$	1.11159e9	+	1.72967e9i	0.607482	+	0.945260i	−0.392196	+	0.919882i	$0.628285\pi$
$444$	−6.63532e7	+	6.53811e8i	−0.0359767	+	0.354496i
$445$	2.00851e8	+	2.31795e8i	0.108047	+	0.124693i
$446$	−7.94827e8	+	1.14279e8i	−0.424229	+	0.0609950i
$447$	7.47036e8	+	1.06237e9i	0.395608	+	0.562598i
$448$	−7.72803e8	−	2.63192e9i	−0.406065	−	1.38293i
$449$	−1.96092e8	−	6.67829e8i	−0.102235	−	0.348180i	0.892450	−	0.451146i	$-0.148985\pi$
$449$	−1.96092e8	−	6.67829e8i	−0.102235	−	0.348180i	−0.994685	+	0.102967i	$0.967167\pi$
$450$	−4.65936e7	−	5.57929e8i	−0.0241036	−	0.288626i
$451$	1.92224e9	−	2.76376e8i	0.986710	−	0.141868i
$452$	2.62134e9	+	3.02519e9i	1.33518	+	1.54088i
$453$	1.33992e9	+	1.35985e8i	0.677230	+	0.0687299i
$454$	−2.06971e9	−	3.22053e9i	−1.03804	−	1.61522i
$455$	1.85849e9	+	2.67210e8i	0.924953	+	0.132988i
$456$	9.37439e8	−	4.76256e8i	0.462984	−	0.235214i
$457$	1.07152e9	+	9.28482e8i	0.525165	+	0.455058i	0.876645	−	0.481137i	$-0.159776\pi$
$457$	1.07152e9	+	9.28482e8i	0.525165	+	0.455058i	−0.351480	+	0.936195i	$0.614322\pi$
$458$	−1.40153e9	−	4.11525e8i	−0.681667	−	0.200155i
$459$	2.40674e9	+	4.28980e7i	1.16167	+	0.0207058i
$460$	−2.47379e9	−	8.29653e8i	−1.18498	−	0.397415i
$461$			2.76755e9i			1.31566i	0.753168	+	0.657828i	$0.228525\pi$
$461$			2.76755e9i			1.31566i	−0.753168	+	0.657828i	$0.771475\pi$
$462$	3.21629e9	−	3.03045e9i	1.51743	−	1.42975i
$463$	1.39162e9	−	1.60601e9i	0.651607	−	0.751995i	−0.329775	−	0.944060i	$-0.606973\pi$
$463$	1.39162e9	−	1.60601e9i	0.651607	−	0.751995i	0.981382	+	0.192065i	$0.0615183\pi$
$464$	9.11621e8	−	1.41851e9i	0.423644	−	0.659203i
$465$	−2.44756e9	−	1.94842e9i	−1.12888	−	0.898665i
$466$	−1.99627e9	+	1.28292e9i	−0.913835	+	0.587286i
$467$	3.06990e8	+	6.72215e8i	0.139481	+	0.305421i	0.966462	−	0.256809i	$-0.0826710\pi$
$467$	3.06990e8	+	6.72215e8i	0.139481	+	0.305421i	−0.826981	+	0.562230i	$0.809944\pi$
$468$	−1.17146e9	+	3.25890e9i	−0.528281	+	1.46964i
$469$	−1.29384e8	−	8.99886e8i	−0.0579130	−	0.402794i
$470$	−1.96208e9	+	4.29636e9i	−0.871715	+	1.90879i
$471$	−2.29727e9	−	5.71784e8i	−1.01307	−	0.252150i
$472$	−1.16949e9	+	3.43392e8i	−0.511915	+	0.150312i
$473$	5.09902e8	+	2.32864e8i	0.221551	+	0.101179i
$474$	2.20402e9	+	8.97587e8i	0.950588	+	0.387126i
$475$	2.87796e8	−	2.49377e8i	0.123213	−	0.106765i
$476$	−3.17372e9	+	1.44939e9i	−1.34879	+	0.615972i
$477$	−9.74679e8	−	5.17232e8i	−0.411195	−	0.218208i
$478$	−5.06656e7	+	3.52387e8i	−0.0212186	+	0.147578i
$479$	3.17992e8	+	2.04361e8i	0.132203	+	0.0849618i	0.605071	−	0.796172i	$-0.293145\pi$
$479$	3.17992e8	+	2.04361e8i	0.132203	+	0.0849618i	−0.472868	+	0.881133i	$0.656781\pi$
$480$	−2.71753e9	+	9.22505e8i	−1.12158	+	0.380737i
$481$	1.99023e8	−	6.77809e8i	0.0815445	−	0.277715i
$482$	3.70032e9			1.50513
$483$	−9.39242e8	+	2.07678e9i	−0.379282	+	0.838642i
$484$	−3.97706e9			−1.59442
$485$	4.62695e8	−	1.57579e9i	0.184161	−	0.627196i
$486$	−8.53547e8	+	3.81511e9i	−0.337288	+	1.50758i
$487$	1.80045e9	+	1.15708e9i	0.706368	+	0.453955i	0.843871	−	0.536546i	$-0.180271\pi$
$487$	1.80045e9	+	1.15708e9i	0.706368	+	0.453955i	−0.137503	+	0.990501i	$0.543908\pi$
$488$	−2.99118e8	+	2.08041e9i	−0.116513	+	0.810363i
$489$	3.18178e7	+	7.63323e8i	0.0123052	+	0.295207i
$490$	5.04138e8	−	2.30232e8i	0.193581	−	0.0884055i
$491$	1.40789e9	−	1.21994e9i	0.536763	−	0.465108i	−0.343796	−	0.939044i	$-0.611713\pi$
$491$	1.40789e9	−	1.21994e9i	0.536763	−	0.465108i	0.880559	+	0.473937i	$0.157167\pi$
$492$	9.39242e8	−	2.30631e9i	0.355549	−	0.873051i
$493$	−4.74840e9	−	2.16852e9i	−1.78477	−	0.815079i
$494$	−3.89003e9	+	1.14222e9i	−1.45181	+	0.426289i
$495$	−2.55179e9	−	2.49168e9i	−0.945642	−	0.923366i
$496$	8.38526e8	−	1.83612e9i	0.308554	−	0.675638i
$497$	4.75496e8	+	3.30715e9i	0.173740	+	1.20839i
$498$	3.31498e8	+	1.77671e9i	0.120276	+	0.644636i
$499$	7.23925e8	+	1.58517e9i	0.260820	+	0.571117i	0.994058	−	0.108856i	$-0.0347188\pi$
$499$	7.23925e8	+	1.58517e9i	0.260820	+	0.571117i	−0.733237	+	0.679973i	$0.761991\pi$
$500$	3.48983e9	−	2.24278e9i	1.24856	−	0.802400i
$501$	−2.15451e9	+	2.70644e9i	−0.765450	+	0.961538i
$502$	−2.99646e9	+	4.66259e9i	−1.05717	+	1.64499i
$503$	−1.57146e9	+	1.81356e9i	−0.550572	+	0.635394i	−0.961016	−	0.276492i	$-0.910828\pi$
$503$	−1.57146e9	+	1.81356e9i	−0.550572	+	0.635394i	0.410444	+	0.911886i	$0.365374\pi$
$504$	−3.54180e8	−	1.53957e9i	−0.123230	−	0.535663i
$505$			2.12319e9i			0.733618i
$506$	6.10449e9	−	2.51220e9i	2.09470	−	0.862039i
$507$	3.98123e8	−	6.80204e8i	0.135672	−	0.231799i
$508$	6.91468e9	+	2.03033e9i	2.34018	+	0.687138i
$509$	1.03605e9	+	8.97739e8i	0.348230	+	0.301743i	0.811360	−	0.584547i	$-0.198728\pi$
$509$	1.03605e9	+	8.97739e8i	0.348230	+	0.301743i	−0.463129	+	0.886291i	$0.653273\pi$
$510$	2.19528e9	+	4.32109e9i	0.732816	+	1.44244i
$511$	1.47753e9	+	2.12437e8i	0.489850	+	0.0704298i
$512$	−1.45608e9	−	2.26570e9i	−0.479445	−	0.746032i
$513$	−2.43809e9	+	1.06134e9i	−0.797331	+	0.347092i
$514$	4.75987e9	+	5.49318e9i	1.54605	+	1.78424i
$515$	1.73622e9	−	2.49631e8i	0.560118	−	0.0805329i
$516$	5.87986e8	−	4.13460e8i	0.188405	−	0.132483i
$517$	−1.95593e9	−	6.66129e9i	−0.622496	−	2.12003i
$518$	3.25658e8	+	1.10909e9i	0.102946	+	0.350601i
$519$	−4.65957e9	+	3.27652e9i	−1.46305	+	1.02879i
$520$	−1.92419e9	+	2.76657e8i	−0.600118	+	0.0862839i
$521$	−2.73312e9	−	3.15419e9i	−0.846696	−	0.977139i	0.153243	−	0.988188i	$-0.451028\pi$
$521$	−2.73312e9	−	3.15419e9i	−0.846696	−	0.977139i	−0.999939	+	0.0110496i	$0.996483\pi$
$522$	4.99947e9	−	6.84712e9i	1.53843	−	2.10698i
$523$	−1.82424e9	−	2.83857e9i	−0.557603	−	0.867647i	0.441965	−	0.897032i	$-0.354281\pi$
$523$	−1.82424e9	−	2.83857e9i	−0.557603	−	0.867647i	−0.999568	+	0.0293853i	$0.990645\pi$
$524$	−3.10286e9	−	4.46123e8i	−0.942111	−	0.135455i
$525$	−2.59144e8	−	5.10087e8i	−0.0781599	−	0.153846i
$526$	4.52581e8	+	3.92164e8i	0.135596	+	0.117495i
$527$	−5.99587e9	−	1.76055e9i	−1.78449	−	0.523975i
$528$	1.16243e9	−	1.98604e9i	0.343674	−	0.587178i
$529$	−2.41858e9	+	2.39652e9i	−0.710338	+	0.703860i
$530$		−	2.22174e9i		−	0.648229i
$531$	3.00390e9	−	6.91053e8i	0.870672	−	0.200300i
$532$	2.52398e9	−	2.91283e9i	0.726767	−	0.838734i
$533$	−1.44723e9	+	2.25193e9i	−0.413991	+	0.644182i
$534$	−6.19712e8	+	7.78466e8i	−0.176115	+	0.221231i
$535$	−1.51398e9	+	9.72974e8i	−0.427446	+	0.274703i
$536$	3.91022e8	+	8.56219e8i	0.109679	+	0.240164i
$537$	−3.95096e7	−	2.11757e8i	−0.0110101	−	0.0590103i
$538$	−8.06726e8	−	5.61090e9i	−0.223351	−	1.55344i
$539$	−3.38413e8	+	7.41022e8i	−0.0930865	+	0.203831i
$540$	−4.41035e9	+	1.21005e9i	−1.20530	+	0.330694i
$541$	−3.11925e9	+	9.15895e8i	−0.846954	+	0.248688i	−0.676285	−	0.736640i	$-0.736411\pi$
$541$	−3.11925e9	+	9.15895e8i	−0.846954	+	0.248688i	−0.170669	+	0.985328i	$0.554593\pi$
$542$	−4.61068e9	−	2.10563e9i	−1.24385	−	0.568046i
$543$	−1.49098e9	+	3.66109e9i	−0.399642	+	0.981321i
$544$	−4.33236e9	+	3.75401e9i	−1.15379	+	0.999768i
$545$	−5.56535e8	+	2.54161e8i	−0.147267	+	0.0672545i
$546$	2.53683e8	+	6.08597e9i	0.0666987	+	1.60013i
$547$	1.89857e6	−	1.32049e7i	0.000495989	−	0.00344968i	−0.989572	−	0.144039i	$-0.953991\pi$
$547$	1.89857e6	−	1.32049e7i	0.000495989	−	0.00344968i	0.990068	+	0.140590i	$0.0448999\pi$
$548$	6.46857e9	+	4.15710e9i	1.67910	+	1.07909i
$549$	1.06785e9	−	5.20686e9i	0.275429	−	1.34299i
$550$	−4.66833e8	+	1.58989e9i	−0.119644	+	0.407471i
$551$	5.76655e9			1.46854
$552$	3.27274e8	−	2.33708e9i	0.0828179	−	0.591407i
$553$	2.43194e9			0.611525
$554$	5.09972e8	−	1.73681e9i	0.127427	−	0.433978i
$555$	8.83399e8	−	2.99883e8i	0.219347	−	0.0744605i
$556$	2.56983e8	+	1.65153e8i	0.0634077	+	0.0407497i
$557$	1.00994e8	−	7.02426e8i	0.0247629	−	0.172229i	−0.973687	−	0.227890i	$-0.926817\pi$
$557$	1.00994e8	−	7.02426e8i	0.0247629	−	0.172229i	0.998450	+	0.0556605i	$0.0177265\pi$
$558$	4.75742e9	−	8.96496e9i	1.15918	−	2.18438i
$559$	−7.02851e8	+	3.20981e8i	−0.170185	+	0.0777210i
$560$	−1.20911e9	+	1.04770e9i	−0.290944	+	0.252104i
$561$	−6.59800e9	−	2.68703e9i	−1.57776	−	0.642543i
$562$	1.22049e9	+	5.57379e8i	0.290040	+	0.132457i
$563$	2.35265e8	−	6.90799e7i	0.0555619	−	0.0163145i	−0.253833	−	0.967248i	$-0.581692\pi$
$563$	2.35265e8	−	6.90799e7i	0.0555619	−	0.0163145i	0.309395	+	0.950933i	$0.399873\pi$
$564$	−8.63879e9	−	2.15017e9i	−2.02757	−	0.504656i
$565$	2.36058e9	−	5.16896e9i	0.550617	−	1.20568i
$566$	−3.53953e8	−	2.46180e9i	−0.0820519	−	0.570684i
$567$	6.62652e8	+	3.93976e9i	0.152667	+	0.907672i
$568$	−1.43704e9	−	3.14667e9i	−0.329040	−	0.720497i
$569$	−5.34680e9	+	3.43618e9i	−1.21675	+	0.781957i	−0.981775	−	0.190045i	$-0.939137\pi$
$569$	−5.34680e9	+	3.43618e9i	−1.21675	+	0.781957i	−0.234973	+	0.972002i	$0.575500\pi$
$570$	−4.18886e9	−	3.33462e9i	−0.947402	−	0.754197i
$571$	−6.32192e8	+	9.83709e8i	−0.142109	+	0.221126i	−0.905011	−	0.425388i	$-0.860138\pi$
$571$	−6.32192e8	+	9.83709e8i	−0.142109	+	0.221126i	0.762902	+	0.646514i	$0.223774\pi$
$572$	6.71187e9	−	7.74592e9i	1.49954	−	1.73056i
$573$	4.04821e9	−	3.81430e9i	0.898921	−	0.846982i
$574$		−	4.38013e9i		−	0.966708i
$575$	−8.94130e7	−	8.49975e8i	−0.0196139	−	0.186453i
$576$	−3.51689e9	−	6.26210e9i	−0.766796	−	1.36534i
$577$	−2.98251e9	−	8.75744e8i	−0.646348	−	0.189785i	−0.0579033	−	0.998322i	$-0.518441\pi$
$577$	−2.98251e9	−	8.75744e8i	−0.646348	−	0.189785i	−0.588445	+	0.808537i	$0.700260\pi$
$578$	1.89660e9	+	1.64341e9i	0.408534	+	0.353997i
$579$	3.85995e9	−	1.96101e9i	0.826431	−	0.419859i
$580$	9.81690e9	+	1.41146e9i	2.08918	+	0.300379i
$581$	9.98552e8	+	1.55378e9i	0.211229	+	0.328679i
$582$	5.30074e9	+	5.37955e8i	1.11457	+	0.113114i
$583$	2.13858e9	+	2.46805e9i	0.446976	+	0.515838i
$584$	−1.52977e9	+	2.19947e8i	−0.317819	+	0.0456955i
$585$	4.89906e9	−	4.09128e8i	1.01174	−	0.0844917i
$586$	1.05070e9	+	3.57834e9i	0.215693	+	0.734582i
$587$	2.67100e8	+	9.09660e8i	0.0545056	+	0.185629i	0.982246	−	0.187597i	$-0.0600698\pi$
$587$	2.67100e8	+	9.09660e8i	0.0545056	+	0.185629i	−0.927741	+	0.373226i	$0.878252\pi$
$588$	6.00867e8	+	8.54498e8i	0.121887	+	0.173337i
$589$	6.83284e9	−	9.82414e8i	1.37784	−	0.198103i
$590$	4.06431e9	+	4.69046e9i	0.814713	+	0.940229i
$591$	−7.96258e8	+	7.84593e9i	−0.158671	+	1.56346i
$592$	3.25433e8	+	5.06383e8i	0.0644667	+	0.100312i
$593$	2.72457e9	+	3.91734e8i	0.536545	+	0.0771435i	0.405261	−	0.914201i	$-0.367181\pi$
$593$	2.72457e9	+	3.91734e8i	0.536545	+	0.0771435i	0.131284	+	0.991345i	$0.458090\pi$
$594$	6.42791e9	−	9.62063e9i	1.25840	−	1.88344i
$595$	3.74321e9	+	3.24351e9i	0.728508	+	0.631256i
$596$	−4.72915e9	−	1.38860e9i	−0.915000	−	0.268668i
$597$	−6.67543e9	−	3.90712e9i	−1.28401	−	0.751531i
$598$	−2.89327e9	+	8.62689e9i	−0.553267	+	1.64968i
$599$		−	6.57117e8i		−	0.124925i	−0.998047	−	0.0624625i	$-0.980105\pi$
$599$		−	6.57117e8i		−	0.124925i	0.998047	−	0.0624625i	$-0.0198954\pi$
$600$	4.06226e8	+	4.31137e8i	0.0767783	+	0.0814866i
$601$	−2.19839e9	+	2.53708e9i	−0.413089	+	0.476730i	−0.923719	−	0.383070i	$-0.874867\pi$
$601$	−2.19839e9	+	2.53708e9i	−0.413089	+	0.476730i	0.510630	+	0.859801i	$0.329412\pi$
$602$	6.83543e8	−	1.06361e9i	0.127696	−	0.198699i
$603$	−8.58386e8	−	2.22024e9i	−0.159431	−	0.412372i
$604$	−4.29988e9	+	2.76337e9i	−0.794012	+	0.510281i
$605$	2.34535e9	+	5.13560e9i	0.430590	+	0.942860i
$606$	−6.77116e9	+	1.26336e9i	−1.23597	+	0.230607i
$607$	7.36593e8	+	5.12312e9i	0.133680	+	0.929767i	0.940699	+	0.339241i	$0.110170\pi$
$607$	7.36593e8	+	5.12312e9i	0.133680	+	0.929767i	−0.807019	+	0.590525i	$0.798921\pi$
$608$	2.63065e9	−	5.76031e9i	0.474679	−	1.03940i
$609$	2.09256e9	−	8.40735e9i	0.375421	−	1.50834i
$610$	1.02688e10	−	3.01518e9i	1.83174	−	0.537848i
$611$	8.70480e9	+	3.97535e9i	1.54388	+	0.705068i
$612$	−7.24741e9	+	5.56134e9i	−1.27806	+	0.980731i
$613$	7.64812e9	−	6.62713e9i	1.34104	−	1.16202i	0.368413	−	0.929662i	$-0.379901\pi$
$613$	7.64812e9	−	6.62713e9i	1.34104	−	1.16202i	0.972630	−	0.232358i	$-0.0746442\pi$
$614$	7.04749e9	−	3.21848e9i	1.22870	−	0.561128i
$615$	−3.53203e9	+	1.47227e8i	−0.612297	+	0.0255225i
$616$	−6.65400e8	+	4.62796e9i	−0.114697	+	0.797732i
$617$	1.14940e9	+	7.38676e8i	0.197004	+	0.126606i	0.635424	−	0.772164i	$-0.280825\pi$
$617$	1.14940e9	+	7.38676e8i	0.197004	+	0.126606i	−0.438420	+	0.898770i	$0.644462\pi$
$618$	1.82921e9	+	5.38851e9i	0.311748	+	0.918352i
$619$	−1.46071e9	+	4.97472e9i	−0.247540	+	0.843045i	0.738173	+	0.674612i	$0.235689\pi$
$619$	−1.46071e9	+	4.97472e9i	−0.247540	+	0.843045i	−0.985713	+	0.168434i	$0.946129\pi$
$620$	1.18726e10			2.00067
$621$	−1.17752e9	+	5.85057e9i	−0.197309	+	0.980341i
$622$	−1.16436e10			−1.94008
$623$	−2.86471e8	+	9.75630e8i	−0.0474649	+	0.161650i
$624$	1.01964e9	+	3.00366e9i	0.167996	+	0.494885i
$625$	−3.99148e9	−	2.56517e9i	−0.653965	−	0.420278i
$626$	−2.03444e9	+	1.41498e10i	−0.331463	+	2.30537i
$627$	7.86304e9	−	3.27757e8i	1.27396	−	0.0531026i
$628$	8.17249e9	−	3.73225e9i	1.31673	−	0.601329i
$629$	1.40834e9	−	1.22033e9i	0.225647	−	0.195524i
$630$	−6.38178e9	+	4.89710e9i	−1.01683	+	0.780274i
$631$	6.45391e9	+	2.94740e9i	1.02263	+	0.467021i	0.854890	−	0.518809i	$-0.173625\pi$
$631$	6.45391e9	+	2.94740e9i	1.02263	+	0.467021i	0.167744	+	0.985831i	$0.446352\pi$
$632$	−2.41592e9	+	7.09378e8i	−0.380691	+	0.111781i
$633$	−1.79506e8	+	7.21207e8i	−0.0281298	+	0.113018i
$634$	1.36811e9	−	2.99574e9i	0.213210	−	0.466866i
$635$	−1.45594e9	−	1.01263e10i	−0.225650	−	1.56943i
$636$	4.11655e9	−	7.68065e8i	0.634502	−	0.118385i
$637$	−4.66470e8	−	1.02143e9i	−0.0715050	−	0.156574i
$638$	−2.11086e10	+	1.35657e10i	−3.21801	+	2.06809i
$639$	3.15463e9	+	8.15955e9i	0.478295	+	1.23712i
$640$	3.57161e9	−	5.55754e9i	0.538561	−	0.838017i
$641$	1.49002e9	−	1.71958e9i	0.223455	−	0.257881i	−0.632942	−	0.774200i	$-0.718153\pi$
$641$	1.49002e9	−	1.71958e9i	0.223455	−	0.257881i	0.856396	+	0.516319i	$0.172698\pi$
$642$	−4.00381e9	−	4.24933e9i	−0.597173	−	0.633794i
$643$			1.04023e10i			1.54309i	0.636175	+	0.771545i	$0.280516\pi$
$643$			1.04023e10i			1.54309i	−0.636175	+	0.771545i	$0.719484\pi$
$644$	−2.12005e9	−	8.38637e9i	−0.312784	−	1.23730i
$645$	−8.80650e8	−	5.15443e8i	−0.129224	−	0.0756348i
$646$	−1.02616e10	−	3.01309e9i	−1.49762	−	0.439742i
$647$	5.21561e9	+	4.51935e9i	0.757077	+	0.656011i	0.945332	−	0.326109i	$-0.105738\pi$
$647$	5.21561e9	+	4.51935e9i	0.757077	+	0.656011i	−0.188255	+	0.982120i	$0.560283\pi$
$648$	−1.80749e9	−	3.72052e9i	−0.260953	−	0.537145i
$649$	−9.02977e9	−	1.29828e9i	−1.29664	−	0.186429i
$650$	−1.23484e9	−	1.92144e9i	−0.176365	−	0.274430i
$651$	1.04719e9	−	1.03185e10i	0.148762	−	1.46582i
$652$	−1.89871e9	−	2.19123e9i	−0.268282	−	0.309614i
$653$	6.19937e9	−	8.91335e8i	0.871267	−	0.125269i	0.307843	−	0.951437i	$-0.400393\pi$
$653$	6.19937e9	−	8.91335e8i	0.871267	−	0.125269i	0.563424	+	0.826168i	$0.309484\pi$
$654$	−1.14171e9	−	1.62363e9i	−0.159600	−	0.226969i
$655$	1.25373e9	+	4.26982e9i	0.174325	+	0.593697i
$656$	−6.42615e8	−	2.18855e9i	−0.0888766	−	0.302686i
$657$	3.89484e9	−	3.25264e8i	0.535809	−	0.0447463i
$658$	−1.54992e10	+	2.22845e9i	−2.12089	+	0.304939i
$659$	−7.76044e9	−	8.95602e9i	−1.05630	−	1.21903i	−0.974967	−	0.222348i	$-0.928628\pi$
$659$	−7.76044e9	−	8.95602e9i	−1.05630	−	1.21903i	−0.0813322	−	0.996687i	$-0.525917\pi$
$660$	1.34662e10	+	1.36664e9i	1.82323	+	0.185033i
$661$	2.40004e9	+	3.73454e9i	0.323232	+	0.502958i	0.964402	−	0.264440i	$-0.0851872\pi$
$661$	2.40004e9	+	3.73454e9i	0.323232	+	0.502958i	−0.641170	+	0.767399i	$0.721551\pi$
$662$	−1.39640e10	−	2.00771e9i	−1.87071	−	0.268967i
$663$	8.75492e9	−	4.44784e9i	1.16669	−	0.592723i
$664$	−1.44520e9	−	1.25227e9i	−0.191576	−	0.166001i
$665$	−5.24979e9	−	1.54148e9i	−0.692255	−	0.203264i
$666$	1.48201e9	+	2.63884e9i	0.194398	+	0.346141i
$667$	7.40550e9	−	1.06140e10i	0.966304	−	1.38496i
$668$		−	1.31284e10i		−	1.70410i
$669$	−1.56377e9	+	1.47342e9i	−0.201921	+	0.190254i
$670$	3.13872e9	−	3.62228e9i	0.403173	−	0.465286i
$671$	−8.50487e9	+	1.32338e10i	−1.08677	+	1.69105i
$672$	−7.44366e9	−	5.92566e9i	−0.946224	−	0.753259i
$673$	−4.89592e9	+	3.14641e9i	−0.619129	+	0.397890i	−0.812271	−	0.583281i	$-0.801769\pi$
$673$	−4.89592e9	+	3.14641e9i	−0.619129	+	0.397890i	0.193142	+	0.981171i	$0.438132\pi$
$674$	−7.02170e9	−	1.53754e10i	−0.883350	−	1.93427i
$675$	−9.60671e8	−	1.14944e9i	−0.120230	−	0.143855i
$676$	4.25680e8	+	2.96067e9i	0.0529992	+	0.368618i
$677$	−2.90805e9	+	6.36774e9i	−0.360198	+	0.788724i	0.639601	+	0.768707i	$0.279099\pi$
$677$	−2.90805e9	+	6.36774e9i	−0.360198	+	0.788724i	−0.999800	+	0.0200173i	$0.993628\pi$
$678$	1.78891e10	+	4.45255e9i	2.20437	+	0.548662i
$679$	5.22417e9	−	1.53396e9i	0.640433	−	0.188048i
$680$	−4.66466e9	−	2.13028e9i	−0.568904	−	0.259810i
$681$	−9.48662e9	−	3.86342e9i	−1.15106	−	0.468767i
$682$	−2.27007e10	+	1.96703e10i	−2.74028	+	2.37446i
$683$	−1.51689e9	+	6.92739e8i	−0.182172	+	0.0831950i	−0.504413	−	0.863463i	$-0.668291\pi$
$683$	−1.51689e9	+	6.92739e8i	−0.182172	+	0.0831950i	0.322241	+	0.946658i	$0.395564\pi$
$684$	4.73044e9	−	8.91411e9i	0.565204	−	1.06508i
$685$	1.55344e9	−	1.08044e10i	0.184662	−	1.28435i
$686$	1.16600e10	+	7.49341e9i	1.37900	+	0.886227i
$687$	−3.70092e9	+	1.25633e9i	−0.435472	+	0.147827i
$688$	1.85490e8	−	6.31722e8i	0.0217151	−	0.0739549i
$689$	−4.50145e9			−0.524306
$690$	−1.15172e10	+	3.42769e9i	−1.33467	+	0.397219i
$691$	−3.98349e9			−0.459294			−0.229647	−	0.973274i	$-0.573757\pi$
$691$	−3.98349e9			−0.459294			−0.229647	+	0.973274i	$0.573757\pi$
$692$	6.09046e9	−	2.07422e10i	0.698681	−	2.37949i
$693$	2.37549e9	−	1.15829e10i	0.271136	−	1.32206i
$694$	4.89111e9	+	3.14333e9i	0.555456	+	0.356970i
$695$	6.17149e7	−	4.29237e8i	0.00697338	−	0.0485009i
$696$	3.73581e8	+	8.96237e9i	0.0420003	+	1.00761i
$697$	−6.42327e9	+	2.93341e9i	−0.718524	+	0.328139i
$698$	−1.44512e9	+	1.25221e9i	−0.160846	+	0.139374i
$699$	−2.39477e9	+	5.88035e9i	−0.265212	+	0.651228i
$700$	1.97512e9	+	9.02005e8i	0.217645	+	0.0993953i
$701$	3.07931e9	−	9.04166e8i	0.337629	−	0.0991369i	−0.108523	−	0.994094i	$-0.534612\pi$
$701$	3.07931e9	−	9.04166e8i	0.337629	−	0.0991369i	0.446152	+	0.894957i	$0.352794\pi$
$702$	4.21985e9	+	1.53803e10i	0.460380	+	1.67798i
$703$	−8.55155e8	+	1.87253e9i	−0.0928327	+	0.203275i
$704$	3.02508e9	+	2.10399e10i	0.326763	+	2.27268i
$705$	2.31794e9	+	1.24233e10i	0.249138	+	1.33529i
$706$	−8.90512e9	−	1.94995e10i	−0.952408	−	2.08548i
$707$	−5.92154e9	+	3.80554e9i	−0.630183	+	0.404994i
$708$	−7.28566e9	+	9.15205e9i	−0.771530	+	0.969175i
$709$	5.10877e9	−	7.94939e9i	0.538337	−	0.837669i	−0.460410	−	0.887706i	$-0.652298\pi$
$709$	5.10877e9	−	7.94939e9i	0.538337	−	0.837669i	0.998747	+	0.0500376i	$0.0159341\pi$
$710$	−1.15350e10	+	1.33121e10i	−1.20952	+	1.39587i
$711$	6.20544e9	−	1.42758e9i	0.647484	−	0.148955i
$712$		−	1.05277e9i		−	0.109308i
$713$	6.96661e9	−	1.38382e10i	0.719794	−	1.42977i
$714$	−8.11668e9	+	1.38676e10i	−0.834516	+	1.42579i
$715$	−1.39605e10	−	4.09916e9i	−1.42833	−	0.419395i
$716$	6.17832e8	+	5.35355e8i	0.0629035	+	0.0545062i
$717$	4.31455e8	+	8.49255e8i	0.0437138	+	0.0860441i
$718$	2.04639e10	+	2.94227e9i	2.06326	+	0.296651i
$719$	−1.30363e9	−	2.02849e9i	−0.130798	−	0.203526i	0.769677	−	0.638434i	$-0.220417\pi$
$719$	−1.30363e9	−	2.02849e9i	−0.130798	−	0.203526i	−0.900475	+	0.434907i	$0.856781\pi$
$720$	−2.47022e9	+	3.38313e9i	−0.246645	+	0.337797i
$721$	3.80816e9	+	4.39485e9i	0.378392	+	0.436688i
$722$	−3.77000e9	+	5.42044e8i	−0.372787	+	0.0535987i
$723$	8.09898e9	−	5.69505e9i	0.796978	−	0.560420i
$724$	−4.22662e9	−	1.43946e10i	−0.413912	−	1.40966i
$725$	9.15256e8	+	3.11708e9i	0.0891989	+	0.303784i
$726$	−1.49826e10	+	1.05355e10i	−1.45314	+	1.02182i
$727$	−1.04167e10	+	1.49769e9i	−1.00545	+	0.144562i	−0.625317	−	0.780371i	$-0.715030\pi$
$727$	−1.04167e10	+	1.49769e9i	−1.00545	+	0.144562i	−0.380131	+	0.924933i	$0.624121\pi$
$728$	−4.22045e9	−	4.87065e9i	−0.405414	−	0.467872i
$729$	4.00354e9	+	9.66388e9i	0.382735	+	0.923858i
$730$	4.25462e9	+	6.62032e9i	0.404791	+	0.629868i
$731$	−2.01752e9	−	2.90076e8i	−0.191032	−	0.0274663i
$732$	9.13663e9	+	1.79841e10i	0.860988	+	1.69473i
$733$	1.17510e10	+	1.01823e10i	1.10208	+	0.954956i	0.999210	−	0.0397392i	$-0.0126527\pi$
$733$	1.17510e10	+	1.01823e10i	1.10208	+	0.954956i	0.102868	+	0.994695i	$0.467198\pi$
$734$	3.03063e10	+	8.89873e9i	2.82876	+	0.830600i
$735$	7.49074e8	−	1.27982e9i	0.0695856	−	0.118889i
$736$	−7.22418e9	−	1.22395e10i	−0.667907	−	1.13160i
$737$			7.04508e9i			0.648261i
$738$	−2.57119e9	−	1.11765e10i	−0.235470	−	1.02355i
$739$	−5.96673e9	+	6.88597e9i	−0.543852	+	0.627639i	−0.959439	−	0.281915i	$-0.909031\pi$
$739$	−5.96673e9	+	6.88597e9i	−0.543852	+	0.627639i	0.415588	+	0.909553i	$0.363576\pi$
$740$	−1.91414e9	+	2.97846e9i	−0.173645	+	0.270197i
$741$	−6.75624e9	+	8.48701e9i	−0.610016	+	0.766286i
$742$	6.19639e9	−	3.98218e9i	0.556833	−	0.357855i
$743$	−7.15000e9	−	1.56563e10i	−0.639507	−	1.40033i	−0.900445	−	0.434970i	$-0.856759\pi$
$743$	−7.15000e9	−	1.56563e10i	−0.639507	−	1.40033i	0.260938	−	0.965356i	$-0.415968\pi$
$744$	1.96953e9	+	1.05560e10i	0.175330	+	0.939707i
$745$	9.95760e8	+	6.92566e9i	0.0882282	+	0.613641i
$746$	−1.39881e10	+	3.06297e10i	−1.23360	+	2.70120i
$747$	3.46004e9	+	3.37853e9i	0.303710	+	0.296555i
$748$	2.59418e10	−	7.61720e9i	2.26644	−	0.665487i
$749$	−5.42720e9	−	2.47852e9i	−0.471943	−	0.215529i
$750$	7.20580e9	−	1.76939e10i	0.623689	−	1.53147i
$751$	1.42966e10	−	1.23881e10i	1.23167	−	1.06724i	0.236241	−	0.971694i	$-0.424085\pi$
$751$	1.42966e10	−	1.23881e10i	1.23167	−	1.06724i	0.995425	−	0.0955499i	$-0.0304609\pi$
$752$	−7.41730e9	+	3.38737e9i	−0.636038	+	0.290469i
$753$	6.17615e8	+	1.48169e10i	0.0527152	+	1.26466i
$754$	4.92221e9	−	3.42347e10i	0.418177	−	2.90849i
$755$	6.10407e9	+	3.92285e9i	0.516184	+	0.331732i
$756$	−1.12798e10	−	1.01315e10i	−0.949455	−	0.852802i
$757$	−3.61842e9	+	1.23232e10i	−0.303168	+	1.03250i	0.657190	+	0.753725i	$0.271745\pi$
$757$	−3.61842e9	+	1.23232e10i	−0.303168	+	1.03250i	−0.960358	+	0.278770i	$0.910073\pi$
$758$	−6.94764e9			−0.579422
$759$	9.49459e9	−	1.48937e10i	0.788188	−	1.23639i
$760$	5.66485e9			0.468102
$761$	5.87879e9	−	2.00213e10i	0.483551	−	1.64682i	−0.250791	−	0.968041i	$-0.580691\pi$
$761$	5.87879e9	−	2.00213e10i	0.483551	−	1.64682i	0.734341	−	0.678781i	$-0.237491\pi$
$762$	3.14278e10	−	1.06686e10i	2.57319	−	0.873505i
$763$	−1.70637e9	−	1.09661e9i	−0.139071	−	0.0893754i
$764$	−3.00409e9	+	2.08939e10i	−0.243717	+	1.69509i
$765$	1.14553e10	+	6.07898e9i	0.925108	+	0.490926i
$766$	−1.63107e10	+	7.44884e9i	−1.31121	+	0.598808i
$767$	9.50330e9	−	8.23465e9i	0.760485	−	0.658964i
$768$	1.64297e9	+	6.69098e8i	0.130878	+	0.0532998i
$769$	−5.33822e7	−	2.43789e7i	−0.00423306	−	0.00193317i	0.413297	−	0.910596i	$-0.364377\pi$
$769$	−5.33822e7	−	2.43789e7i	−0.00423306	−	0.00193317i	−0.417530	+	0.908663i	$0.637104\pi$
$770$	2.28433e10	−	6.70740e9i	1.80319	−	0.529465i
$771$	1.88724e10	+	4.69728e9i	1.48299	+	0.369111i
$772$	−6.82569e9	+	1.49462e10i	−0.533932	+	1.16915i
$773$	−3.70404e7	−	2.57622e8i	−0.00288435	−	0.0200611i	0.988328	−	0.152338i	$-0.0486803\pi$
$773$	−3.70404e7	−	2.57622e8i	−0.00288435	−	0.0200611i	−0.991213	+	0.132277i	$0.957771\pi$
$774$	1.11981e9	−	3.11522e9i	0.0868060	−	0.241488i
$775$	1.61554e9	+	3.53753e9i	0.124670	+	0.272988i
$776$	−4.74233e9	+	3.04771e9i	−0.364314	+	0.234130i
$777$	2.41974e9	+	1.92628e9i	0.185053	+	0.147315i
$778$	2.71219e9	−	4.22025e9i	0.206487	−	0.321299i
$779$	5.10826e9	−	5.89525e9i	0.387162	−	0.446808i
$780$	−1.35791e10	+	1.27945e10i	−1.02457	+	0.965366i
$781$		−	2.58912e10i		−	1.94479i
$782$	−1.87241e10	+	1.50182e10i	−1.40016	+	1.12304i
$783$	4.04268e8	−	2.26810e10i	0.0300956	−	1.68848i
$784$	9.18059e8	+	2.69566e8i	0.0680400	+	0.0199783i
$785$	−9.63894e9	−	8.35219e9i	−0.711190	−	0.616250i
$786$	−1.28710e10	+	6.53899e9i	−0.945441	+	0.480321i
$787$	3.03040e9	+	4.35706e8i	0.221610	+	0.0318627i	0.252225	−	0.967669i	$-0.418838\pi$
$787$	3.03040e9	+	4.35706e8i	0.221610	+	0.0318627i	−0.0306155	+	0.999531i	$0.509747\pi$
$788$	−1.61809e10	−	2.51780e10i	−1.17804	−	1.83307i
$789$	1.59414e9	+	1.61784e8i	0.115547	+	0.0117265i
$790$	8.39603e9	+	9.68954e9i	0.605870	+	0.699211i
$791$	1.86471e10	−	2.68105e9i	1.33966	−	0.192614i
$792$	1.01880e9	+	1.21995e10i	0.0728705	+	0.872579i
$793$	−6.10903e9	−	2.08054e10i	−0.435027	−	1.48157i
$794$	−9.68784e9	−	3.29938e10i	−0.686840	−	2.33916i
$795$	−3.41941e9	−	4.86278e9i	−0.241361	−	0.343241i
$796$	2.90556e10	−	4.17756e9i	2.04190	−	0.293581i
$797$	−2.67930e9	−	3.09207e9i	−0.187464	−	0.216344i	0.654236	−	0.756290i	$-0.272990\pi$
$797$	−2.67930e9	−	3.09207e9i	−0.187464	−	0.216344i	−0.841700	+	0.539946i	$0.818445\pi$
$798$	1.79221e9	−	1.76595e10i	0.124847	−	1.23018i
$799$	1.36479e10	+	2.12365e10i	0.946568	+	1.47289i
$800$	3.53124e9	+	5.07715e8i	0.243844	+	0.0350595i
$801$	−1.58266e8	+	2.65763e9i	−0.0108811	+	0.182717i
$802$	−1.32945e10	−	1.15198e10i	−0.910045	−	0.788558i
$803$	−1.10988e10	−	3.25890e9i	−0.756435	−	0.222109i
$804$	7.79659e9	+	4.56334e9i	0.529065	+	0.309661i
$805$	−9.57913e9	+	7.68323e9i	−0.647203	+	0.519109i
$806$		−	4.14036e10i		−	2.78526i
$807$	−1.04013e10	−	1.10391e10i	−0.696672	−	0.739394i
$808$	4.77249e9	−	5.50775e9i	0.318277	−	0.367312i
$809$	−7.96405e9	+	1.23923e10i	−0.528827	+	0.822872i	−0.998190	−	0.0601338i	$-0.980847\pi$
$809$	−7.96405e9	+	1.23923e10i	−0.528827	+	0.822872i	0.469363	+	0.883005i	$0.344484\pi$
$810$	−1.34094e10	+	1.62418e10i	−0.886567	+	1.07384i
$811$	−2.14255e10	+	1.37693e10i	−1.41045	+	0.906443i	−0.999985	−	0.00543299i	$-0.998271\pi$
$811$	−2.14255e10	+	1.37693e10i	−1.41045	+	0.906443i	−0.410467	+	0.911876i	$0.634634\pi$
$812$	1.36590e10	+	2.99090e10i	0.895307	+	1.96045i
$813$	−1.33322e10	+	2.48752e9i	−0.870131	+	0.162349i
$814$	−1.27477e9	−	8.86619e9i	−0.0828409	−	0.576171i
$815$	−1.70984e9	+	3.74402e9i	−0.110638	+	0.242263i
$816$	−2.02099e9	+	8.11980e9i	−0.130211	+	0.523154i
$817$	2.16041e9	−	6.34354e8i	0.138599	−	0.0406963i
$818$	3.67590e10	+	1.67873e10i	2.34816	+	1.07237i
$819$	9.92196e9	+	1.29301e10i	0.631108	+	0.822445i
$820$	1.01392e10	−	8.78568e9i	0.642178	−	0.556451i
$821$	7.88930e9	−	3.60292e9i	0.497551	−	0.227224i	−0.150802	−	0.988564i	$-0.548185\pi$
$821$	7.88930e9	−	3.60292e9i	0.497551	−	0.227224i	0.648353	+	0.761340i	$0.275458\pi$
$822$	3.53811e10	−	1.47480e9i	2.22188	−	0.0926151i
$823$	−8.18881e8	+	5.69544e9i	−0.0512061	+	0.356146i	0.948069	+	0.318066i	$0.103033\pi$
$823$	−8.18881e8	+	5.69544e9i	−0.0512061	+	0.356146i	−0.999275	+	0.0380802i	$0.987876\pi$
$824$	−5.06503e9	−	3.25510e9i	−0.315382	−	0.202684i
$825$	1.42518e9	+	4.19831e9i	0.0883649	+	0.260307i
$826$	−5.79686e9	+	1.97423e10i	−0.357901	+	1.21890i
$827$	−1.28111e10			−0.787621			−0.393811	−	0.919192i	$-0.628843\pi$
$827$	−1.28111e10			−0.787621			−0.393811	+	0.919192i	$0.628843\pi$
$828$	−1.03325e10	−	2.01546e10i	−0.632557	−	1.23386i
$829$	1.97584e10			1.20451			0.602255	−	0.798304i	$-0.294269\pi$
$829$	1.97584e10			1.20451			0.602255	+	0.798304i	$0.294269\pi$
$830$	−2.74329e9	+	9.34279e9i	−0.166532	+	0.567157i
$831$	−1.55688e9	−	4.58627e9i	−0.0941131	−	0.277240i
$832$	−2.46485e10	−	1.58406e10i	−1.48374	−	0.953543i
$833$	4.21556e8	−	2.93199e9i	0.0252696	−	0.175754i
$834$	1.40562e9	−	5.85907e7i	0.0839046	−	0.00349742i
$835$	−1.69528e10	+	7.74207e9i	−1.00772	+	0.460209i
$836$	−2.25720e10	+	1.95587e10i	−1.33613	+	1.15776i
$837$	−3.38501e9	−	2.69438e10i	−0.199536	−	1.58825i
$838$	6.59324e9	+	3.01103e9i	0.387030	+	0.176751i
$839$	4.83902e9	−	1.42087e9i	0.282873	−	0.0830589i	−0.137219	−	0.990541i	$-0.543816\pi$
$839$	4.83902e9	−	1.42087e9i	0.282873	−	0.0830589i	0.420091	+	0.907482i	$0.361998\pi$
$840$	2.05566e9	−	8.25909e9i	0.119667	−	0.480789i
$841$	−1.32702e10	+	2.90576e10i	−0.769291	+	1.68451i
$842$	−7.08553e9	−	4.92809e10i	−0.409053	−	2.84503i
$843$	3.52916e9	−	6.58470e8i	0.202897	−	0.0378564i
$844$	−1.17171e9	−	2.56568e9i	−0.0670841	−	0.146894i
$845$	3.57209e9	−	2.29564e9i	0.203669	−	0.130890i
$846$	−3.82404e10	+	1.47844e10i	−2.17133	+	0.839477i
$847$	−1.01193e10	+	1.57460e10i	−0.572216	+	0.890386i
$848$	2.51182e9	−	2.89879e9i	0.141450	−	0.163242i
$849$	−4.56358e9	−	4.84344e9i	−0.255935	−	0.271629i
$850$		−	6.02510e9i		−	0.336510i
$851$	2.34839e9	+	3.97874e9i	0.130622	+	0.221306i
$852$	−2.86531e10	−	1.67706e10i	−1.58720	−	0.928988i
$853$	1.78755e10	+	5.24873e9i	0.986137	+	0.289556i	0.734756	−	0.678332i	$-0.237297\pi$
$853$	1.78755e10	+	5.24873e9i	0.986137	+	0.289556i	0.251382	+	0.967888i	$0.419115\pi$
$854$	2.68147e10	+	2.32351e10i	1.47323	+	1.27656i
$855$	−1.43005e10	−	8.51616e8i	−0.782472	−	0.0465975i
$856$	6.11443e9	+	8.79122e8i	0.333194	+	0.0479061i
$857$	−9.25260e9	−	1.43973e10i	−0.502147	−	0.781356i	0.493962	−	0.869483i	$-0.335548\pi$
$857$	−9.25260e9	−	1.43973e10i	−0.502147	−	0.781356i	−0.996109	+	0.0881272i	$0.971912\pi$
$858$	4.76592e9	−	4.69609e10i	0.257597	−	2.53823i
$859$	1.11187e10	+	1.28317e10i	0.598519	+	0.690728i	0.971481	−	0.237119i	$-0.0762030\pi$
$859$	1.11187e10	+	1.28317e10i	0.598519	+	0.690728i	−0.372961	+	0.927847i	$0.621658\pi$
$860$	3.83313e9	−	5.51121e8i	0.205499	−	0.0295462i
$861$	−6.74131e9	−	9.58688e9i	−0.359943	−	0.511878i
$862$	1.49471e10	+	5.09051e10i	0.794843	+	2.70699i
$863$	−3.38735e9	−	1.15362e10i	−0.179400	−	0.610979i	−0.999262	−	0.0384183i	$-0.987768\pi$
$863$	−3.38735e9	−	1.15362e10i	−0.179400	−	0.610979i	0.819862	−	0.572561i	$-0.194050\pi$
$864$	−2.24720e10	−	1.07507e10i	−1.18534	−	0.567072i
$865$	−3.03762e10	+	4.36743e9i	−1.59579	+	0.229440i
$866$	4.63012e9	+	5.34344e9i	0.242259	+	0.279581i
$867$	6.68046e9	+	6.77978e8i	0.348128	+	0.0353304i
$868$	2.12801e10	+	3.31124e10i	1.10447	+	1.71859i
$869$	−1.86537e10	−	2.68199e9i	−0.964262	−	0.138640i
$870$	4.07217e10	−	2.06882e10i	2.09657	−	1.06514i
$871$	−7.33906e9	−	6.35933e9i	−0.376337	−	0.326098i
$872$	2.01500e9	+	5.91658e8i	0.102912	+	0.0302178i
$873$	1.24298e10	−	6.98077e9i	0.632287	−	0.355102i
$874$	1.19230e10	−	2.36834e10i	0.604081	−	1.19993i
$875$		−	1.95235e10i		−	0.985213i
$876$	−1.07956e10	+	1.01718e10i	−0.542604	+	0.511252i
$877$	4.84404e9	−	5.59032e9i	0.242498	−	0.279858i	−0.621433	−	0.783467i	$-0.713449\pi$
$877$	4.84404e9	−	5.59032e9i	0.242498	−	0.279858i	0.863932	+	0.503609i	$0.167995\pi$
$878$	1.97736e10	−	3.07684e10i	0.985952	−	1.53417i
$879$	7.80699e9	+	6.21490e9i	0.387724	+	0.308655i
$880$	1.04297e10	−	6.70276e9i	0.515920	−	0.331562i
$881$	1.51090e9	+	3.30841e9i	0.0744423	+	0.163006i	0.943194	−	0.332241i	$-0.107805\pi$
$881$	1.51090e9	+	3.30841e9i	0.0744423	+	0.163006i	−0.868752	+	0.495247i	$0.835078\pi$
$882$	4.52723e9	+	1.62737e9i	0.222174	+	0.0798633i
$883$	−7.27190e8	−	5.05771e9i	−0.0355455	−	0.247225i	0.964300	−	0.264813i	$-0.0853102\pi$
$883$	−7.27190e8	−	5.05771e9i	−0.0355455	−	0.247225i	−0.999845	+	0.0175884i	$0.994401\pi$
$884$	−1.54816e10	+	3.39001e10i	−0.753762	+	1.65051i
$885$	1.61146e10	+	4.01087e9i	0.781480	+	0.194508i
$886$	−3.44803e10	+	1.01243e10i	−1.66553	+	0.489044i
$887$	1.56582e10	+	7.15086e9i	0.753371	+	0.344053i	0.754808	−	0.655946i	$-0.227730\pi$
$887$	1.56582e10	+	7.15086e9i	0.753371	+	0.344053i	−0.00143662	+	0.999999i	$0.500457\pi$
$888$	−2.96569e9	−	1.20777e9i	−0.142128	−	0.0578815i
$889$	2.56324e10	−	2.22106e10i	1.22358	−	1.06024i
$890$	−4.87621e9	+	2.22689e9i	−0.231855	+	0.105885i
$891$	−7.37889e8	−	3.09499e10i	−0.0349477	−	1.46584i
$892$	1.16044e9	−	8.07105e9i	0.0547453	−	0.380762i
$893$	−2.34594e10	−	1.50765e10i	−1.10239	−	0.708466i
$894$	−2.14944e10	+	7.29658e9i	−1.00611	+	0.341537i
$895$	3.26959e8	−	1.11352e9i	0.0152445	−	0.0519179i
$896$	2.19015e10			1.01718
$897$	6.94481e9	+	2.33348e10i	0.321282	+	1.07952i
$898$	1.21651e10			0.560593
$899$	−1.65913e10	+	5.65048e10i	−0.761590	+	2.59374i
$900$	5.56928e9	+	1.14218e9i	0.254654	+	0.0522260i
$901$	−9.98947e9	−	6.41984e9i	−0.454994	−	0.292407i
$902$	−4.83050e9	+	3.35969e10i	−0.219164	+	1.52432i
$903$	−1.40888e8	−	3.37997e9i	−0.00636748	−	0.152759i
$904$	−1.77423e10	+	8.10263e9i	−0.798767	+	0.364785i
$905$	−1.60952e10	+	1.39466e10i	−0.721817	+	0.625458i
$906$	−8.87840e9	+	2.18009e10i	−0.396630	+	0.973926i
$907$	1.44466e9	+	6.59753e8i	0.0642894	+	0.0293600i	0.447300	−	0.894384i	$-0.352386\pi$
$907$	1.44466e9	+	6.59753e8i	0.0642894	+	0.0293600i	−0.383011	+	0.923744i	$0.625113\pi$
$908$	3.72992e10	−	1.09520e10i	1.65348	−	0.485506i
$909$	−1.28758e10	+	1.31864e10i	−0.568591	+	0.582309i
$910$	−1.36325e10	+	2.98511e10i	−0.599696	+	1.31315i
$911$	2.69509e9	+	1.87448e10i	0.118103	+	0.821421i	0.959642	+	0.281225i	$0.0907408\pi$
$911$	2.69509e9	+	1.87448e10i	0.118103	+	0.821421i	−0.841539	+	0.540196i	$0.818350\pi$
$912$	−1.69537e9	−	9.08658e9i	−0.0740087	−	0.396660i
$913$	−5.94565e9	−	1.30191e10i	−0.258554	−	0.566154i
$914$	−2.08469e10	+	1.33975e10i	−0.903089	+	0.580380i
$915$	1.78349e10	−	2.24037e10i	0.769657	−	0.966822i
$916$	8.01910e9	−	1.24780e10i	0.344740	−	0.536426i
$917$	−9.66128e9	+	1.11497e10i	−0.413754	+	0.477497i
$918$	−1.25705e10	+	4.01498e10i	−0.536292	+	1.71291i
$919$		−	3.80484e10i		−	1.61708i	−0.588441	−	0.808540i	$-0.700258\pi$
$919$		−	3.80484e10i		−	1.61708i	0.588441	−	0.808540i	$-0.299742\pi$
$920$	7.27490e9	−	1.04268e10i	0.308013	−	0.441462i
$921$	1.04715e10	−	1.78909e10i	0.441674	−	0.754613i
$922$	−4.64118e10	−	1.36277e10i	−1.95016	−	0.572619i
$923$	2.69716e10	+	2.33710e10i	1.12902	+	0.978299i
$924$	2.03248e10	+	4.00064e10i	0.847568	+	1.66831i
$925$	−1.14791e9	−	1.65045e8i	−0.0476885	−	0.00685656i
$926$	2.00803e10	+	3.12456e10i	0.831059	+	1.29315i
$927$	1.22969e10	+	8.97867e9i	0.507011	+	0.370197i
$928$	3.53776e10	+	4.08279e10i	1.45315	+	1.67702i
$929$	1.69523e10	−	2.43737e9i	0.693701	−	0.0997392i	0.213559	−	0.976930i	$-0.431494\pi$
$929$	1.69523e10	−	2.43737e9i	0.693701	−	0.0997392i	0.480142	+	0.877191i	$0.340585\pi$
$930$	4.47271e10	−	3.14512e10i	1.82339	−	1.28218i
$931$	9.21884e8	+	3.13965e9i	0.0374414	+	0.127514i
$932$	−6.78869e9	−	2.31202e10i	−0.274682	−	0.935481i
$933$	−2.54845e10	+	1.79202e10i	−1.02728	+	0.722367i
$934$	−1.27847e10	+	1.83816e9i	−0.513424	+	0.0738192i
$935$	−2.51345e10	−	2.90067e10i	−1.00561	−	1.16054i
$936$	−1.36282e10	−	9.95074e9i	−0.543217	−	0.396634i
$937$	−6.83159e9	−	1.06302e10i	−0.271290	−	0.422135i	0.678700	−	0.734415i	$-0.262543\pi$
$937$	−6.83159e9	−	1.06302e10i	−0.271290	−	0.422135i	−0.949990	+	0.312280i	$0.898907\pi$
$938$	1.57282e10	+	2.26137e9i	0.622256	+	0.0894669i
$939$	1.73247e10	+	3.41012e10i	0.682869	+	1.34413i
$940$	−3.62468e10	−	3.14081e10i	−1.42339	−	1.23337i
$941$	1.39787e10	+	4.10452e9i	0.546895	+	0.160583i	0.543496	−	0.839411i	$-0.317100\pi$
$941$	1.39787e10	+	4.10452e9i	0.546895	+	0.160583i	0.00339821	+	0.999994i	$0.498918\pi$
$942$	2.09008e10	−	3.57097e10i	0.814677	−	1.39190i
$943$	−4.29075e9	−	1.69731e10i	−0.166626	−	0.659129i
$944$			1.07148e10i			0.414554i
$945$	−6.43097e9	+	2.05404e10i	−0.247894	+	0.791767i
$946$	−6.41595e9	+	7.40441e9i	−0.246401	+	0.284362i
$947$	−2.46023e10	+	3.82820e10i	−0.941351	+	1.46477i	−0.0567685	+	0.998387i	$0.518080\pi$
$947$	−2.46023e10	+	3.82820e10i	−0.941351	+	1.46477i	−0.884583	+	0.466384i	$0.845557\pi$
$948$	−1.50507e10	+	1.89063e10i	−0.573756	+	0.720737i
$949$	1.34134e10	−	8.62025e9i	0.509455	−	0.327407i
$950$	2.76491e9	+	6.05430e9i	0.104628	+	0.229103i
$951$	−1.61624e9	−	8.66246e9i	−0.0609360	−	0.326595i
$952$	−2.41948e9	−	1.68279e10i	−0.0908853	−	0.632121i
$953$	−1.57045e9	+	3.43880e9i	−0.0587757	+	0.128701i	−0.936741	−	0.350024i	$-0.886173\pi$
$953$	−1.57045e9	+	3.43880e9i	−0.0587757	+	0.128701i	0.877965	+	0.478725i	$0.158901\pi$
$954$	1.34734e10	−	1.37985e10i	0.502410	−	0.514531i
$955$	2.87520e10	−	8.44234e9i	1.06821	−	0.313654i
$956$	−3.28841e9	−	1.50177e9i	−0.121726	−	0.0555905i
$957$	−2.53224e10	+	6.21791e10i	−0.933927	+	2.29326i
$958$	−4.99296e9	+	4.32643e9i	−0.183476	+	0.158983i
$959$	3.29176e10	−	1.50330e10i	1.20521	−	0.550401i
$960$	−1.61147e9	−	3.86599e10i	−0.0587859	−	1.41030i
$961$	−6.11735e9	+	4.25471e10i	−0.222347	+	1.54646i
$962$	1.03868e10	+	6.67522e9i	0.376158	+	0.241742i
$963$	−1.53032e10	−	3.13848e9i	−0.552193	−	0.113247i
$964$	−1.05861e10	+	3.60528e10i	−0.380596	+	1.29619i
$965$	2.33253e10			0.835568
$966$	−3.02027e10	−	2.59774e10i	−1.07802	−	0.927206i
$967$	6.41126e8			0.0228009			0.0114004	−	0.999935i	$-0.496371\pi$
$967$	6.41126e8			0.0228009			0.0114004	+	0.999935i	$0.496371\pi$
$968$	5.45970e9	−	1.85940e10i	0.193466	−	0.658886i
$969$	−2.70972e10	+	9.19853e9i	−0.956733	+	0.324777i
$970$	2.41477e10	+	1.55188e10i	0.849522	+	0.545955i
$971$	1.59056e9	−	1.10626e10i	0.0557547	−	0.387782i	−0.942768	−	0.333449i	$-0.891788\pi$
$971$	1.59056e9	−	1.10626e10i	0.0557547	−	0.387782i	0.998523	−	0.0543334i	$-0.0173034\pi$
$972$	−3.47293e10	−	1.92307e10i	−1.21301	−	0.671681i
$973$	1.30775e9	−	5.97228e8i	0.0455123	−	0.0207848i
$974$	−2.82699e10	+	2.44960e10i	−0.980320	+	0.849453i
$975$	−5.65995e9	−	2.30501e9i	−0.195567	−	0.0796446i
$976$	1.68069e10	+	7.67546e9i	0.578647	+	0.264259i
$977$	2.25840e10	−	6.63127e9i	0.774766	−	0.227492i	0.129633	−	0.991562i	$-0.458620\pi$
$977$	2.25840e10	−	6.63127e9i	0.774766	−	0.227492i	0.645133	+	0.764070i	$0.276802\pi$
$978$	−1.29576e10	−	3.22511e9i	−0.442933	−	0.110245i
$979$	3.27326e9	−	7.16744e9i	0.111491	−	0.244132i
$980$	8.00924e8	+	5.57055e9i	0.0271832	+	0.189063i
$981$	−4.99777e9	−	1.79652e9i	−0.169019	−	0.0607561i
$982$	1.35258e10	+	2.96174e10i	0.455798	+	0.998059i
$983$	2.01327e10	−	1.29385e10i	0.676028	−	0.434457i	−0.157066	−	0.987588i	$-0.550204\pi$
$983$	2.01327e10	−	1.29385e10i	0.676028	−	0.434457i	0.833094	+	0.553131i	$0.186567\pi$
$984$	9.49334e9	+	7.55735e9i	0.317641	+	0.252864i
$985$	−2.29702e10	+	3.57424e10i	−0.765841	+	1.19167i
$986$	5.97478e10	−	6.89527e10i	1.98496	−	2.29077i
$987$	−3.04937e10	+	2.87318e10i	−1.00949	+	0.951158i
$988$		−	4.11688e10i		−	1.35806i
$989$	1.60684e9	−	4.79113e9i	0.0528184	−	0.157489i
$990$	5.43507e10	−	3.05242e10i	1.78026	−	0.999819i
$991$	−4.23893e10	−	1.24466e10i	−1.38356	−	0.406250i	−0.496554	−	0.868006i	$-0.665402\pi$
$991$	−4.23893e10	−	1.24466e10i	−1.38356	−	0.406250i	−0.887007	+	0.461755i	$0.847220\pi$
$992$	4.88749e10	+	4.23503e10i	1.58963	+	1.37742i
$993$	−3.36532e10	+	1.70972e10i	−1.09070	+	0.554117i
$994$	−5.78023e10	−	8.31071e9i	−1.86678	−	0.268402i
$995$	−2.25291e10	−	3.50560e10i	−0.725043	−	1.12819i
$996$	−1.82591e10	−	1.85306e9i	−0.585561	−	0.0594268i
$997$	1.83564e10	+	2.11844e10i	0.586617	+	0.676992i	0.969014	−	0.247006i	$-0.0794467\pi$
$997$	1.83564e10	+	2.11844e10i	0.586617	+	0.676992i	−0.382397	+	0.923998i	$0.624901\pi$
$998$	−3.01481e10	+	4.33464e9i	−0.960069	+	0.138037i
$999$	7.30507e9	+	3.49477e9i	0.231817	+	0.110902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.8.g.a.5.8	✓	540
3.2	odd	2	inner	69.8.g.a.5.47	yes	540
23.14	odd	22	inner	69.8.g.a.14.47	yes	540
69.14	even	22	inner	69.8.g.a.14.8	yes	540

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.g.a.5.8	✓	540	1.1	even	1	trivial
69.8.g.a.5.47	yes	540	3.2	odd	2	inner
69.8.g.a.14.8	yes	540	69.14	even	22	inner
69.8.g.a.14.47	yes	540	23.14	odd	22	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	69.g (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.92412 + 16.7700i) q^{2} +(15.0326 + 44.2834i) q^{3} +(-149.305 - 95.9528i) q^{4} +(-35.8560 + 249.384i) q^{5} +(-816.655 + 34.0408i) q^{6} +(-759.793 + 346.986i) q^{7} +(653.576 - 566.327i) q^{8} +(-1735.04 + 1331.39i) q^{9} +O(q^{10})\)	\(q+(-4.92412 + 16.7700i) q^{2} +(15.0326 + 44.2834i) q^{3} +(-149.305 - 95.9528i) q^{4} +(-35.8560 + 249.384i) q^{5} +(-816.655 + 34.0408i) q^{6} +(-759.793 + 346.986i) q^{7} +(653.576 - 566.327i) q^{8} +(-1735.04 + 1331.39i) q^{9} +(-4005.61 - 1829.30i) q^{10} +(6210.50 - 1823.57i) q^{11} +(2004.66 - 8054.18i) q^{12} +(-3706.33 + 8115.72i) q^{13} +(-2077.64 - 14450.3i) q^{14} +(-11582.6 + 2161.07i) q^{15} +(-3158.13 - 6915.35i) q^{16} +(-19799.4 + 12724.3i) q^{17} +(-13783.9 - 35652.5i) q^{18} +(14056.2 - 21871.8i) q^{19} +(29282.6 - 33793.9i) q^{20} +(-26787.4 - 28430.1i) q^{21} +113130. i q^{22} +(-22206.4 - 53960.2i) q^{23} +(34903.9 + 20429.2i) q^{24} +(14053.7 + 4126.53i) q^{25} +(-117850. - 102118. i) q^{26} +(-85040.9 - 56819.1i) q^{27} +(146736. + 21097.4i) q^{28} +(119913. + 186588. i) q^{29} +(20792.7 - 204881. i) q^{30} +(173874. + 200661. i) q^{31} +(241090. - 34663.5i) q^{32} +(174114. + 247609. i) q^{33} +(-115892. - 394691. i) q^{34} +(-59289.6 - 201922. i) q^{35} +(386802. - 32302.4i) q^{36} +(-78372.0 + 11268.2i) q^{37} +(297576. + 343422. i) q^{38} +(-415108. - 42127.9i) q^{39} +(117798. + 183298. i) q^{40} +(296977. + 42698.8i) q^{41} +(608677. - 309232. i) q^{42} +(65450.7 + 56713.3i) q^{43} +(-1.10224e6 - 323646. i) q^{44} +(-269817. - 480429. i) q^{45} +(1.01426e6 - 106695. i) q^{46} -1.07259e6i q^{47} +(258760. - 243809. i) q^{48} +(-82419.4 + 95117.1i) q^{49} +(-138404. + 215361. i) q^{50} +(-861112. - 685504. i) q^{51} +(1.33210e6 - 856089. i) q^{52} +(209591. + 458941. i) q^{53} +(1.37161e6 - 1.14635e6i) q^{54} +(232085. + 1.61419e6i) q^{55} +(-300075. + 657073. i) q^{56} +(1.17986e6 + 293664. i) q^{57} +(-3.71955e6 + 1.09216e6i) q^{58} +(-1.28204e6 - 585487. i) q^{59} +(1.93670e6 + 788720. i) q^{60} +(-1.83676e6 + 1.59156e6i) q^{61} +(-4.22127e6 + 1.92779e6i) q^{62} +(856296. - 1.61362e6i) q^{63} +(-467360. + 3.25056e6i) q^{64} +(-1.89104e6 - 1.21530e6i) q^{65} +(-5.00976e6 + 1.70064e6i) q^{66} +(-306647. + 1.04434e6i) q^{67} +4.17709e6 q^{68} +(2.05572e6 - 1.79454e6i) q^{69} +3.67818e6 q^{70} +(1.12695e6 - 3.83804e6i) q^{71} +(-379976. + 1.85277e6i) q^{72} +(-1.50341e6 - 966181. i) q^{73} +(196945. - 1.36978e6i) q^{74} +(28527.1 + 684378. i) q^{75} +(-4.19733e6 + 1.91686e6i) q^{76} +(-4.08594e6 + 3.54049e6i) q^{77} +(2.75052e6 - 6.75391e6i) q^{78} +(-2.64843e6 - 1.20950e6i) q^{79} +(1.83781e6 - 539631. i) q^{80} +(1.23775e6 - 4.62004e6i) q^{81} +(-2.17841e6 + 4.77005e6i) q^{82} +(-314690. - 2.18871e6i) q^{83} +(1.27156e6 + 6.81510e6i) q^{84} +(-2.46331e6 - 5.39389e6i) q^{85} +(-1.27337e6 + 818345. i) q^{86} +(-6.46015e6 + 8.11507e6i) q^{87} +(3.02630e6 - 4.70901e6i) q^{88} +(797191. - 920008. i) q^{89} +(9.38541e6 - 2.15913e6i) q^{90} -7.45231e6i q^{91} +(-1.86209e6 + 1.01873e7i) q^{92} +(-6.27218e6 + 1.07162e7i) q^{93} +(1.79873e7 + 5.28153e6i) q^{94} +(4.95049e6 + 4.28962e6i) q^{95} +(5.15923e6 + 1.01552e7i) q^{96} +(-6.45213e6 - 927676. i) q^{97} +(-1.18927e6 - 1.85054e6i) q^{98} +(-8.34758e6 + 1.14326e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9}+O(q^{10}) \) 540 * q - 35 * q^3 + 3362 * q^4 - 1280 * q^6 - 22 * q^7 - 659 * q^9	\( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9} - 22 q^{10} + 4756 q^{12} + 4970 q^{13} + 3828 q^{15} - 174622 q^{16} + 250050 q^{18} - 22 q^{19} - 221738 q^{21} + 94934 q^{24} - 788392 q^{25} + 1020934 q^{27} - 22 q^{28} - 1480875 q^{30} + 738458 q^{31} + 1215192 q^{33} + 1815924 q^{34} - 394502 q^{36} - 905234 q^{37} - 1635803 q^{39} + 10260228 q^{40} - 11 q^{42} - 1694330 q^{43} - 6978726 q^{46} + 134426 q^{48} + 7785740 q^{49} - 11 q^{51} + 16219654 q^{52} - 10697559 q^{54} - 1371960 q^{55} + 7508908 q^{57} - 21860696 q^{58} - 21971851 q^{60} - 11102850 q^{61} - 9022926 q^{63} + 2572060 q^{64} + 16582830 q^{66} + 6031564 q^{67} + 12019470 q^{69} - 2949828 q^{70} + 12828949 q^{72} - 1809596 q^{73} - 16620656 q^{75} - 42651158 q^{76} - 47106384 q^{78} - 1156914 q^{79} + 48837101 q^{81} + 47208588 q^{82} + 124183367 q^{84} + 5833252 q^{85} - 17916287 q^{87} + 360426 q^{88} - 142298860 q^{90} - 51670516 q^{93} - 18401348 q^{94} + 36462337 q^{96} - 63860500 q^{97} + 135683977 q^{99}+O(q^{100}) \) 540 * q - 35 * q^3 + 3362 * q^4 - 1280 * q^6 - 22 * q^7 - 659 * q^9 - 22 * q^10 + 4756 * q^12 + 4970 * q^13 + 3828 * q^15 - 174622 * q^16 + 250050 * q^18 - 22 * q^19 - 221738 * q^21 + 94934 * q^24 - 788392 * q^25 + 1020934 * q^27 - 22 * q^28 - 1480875 * q^30 + 738458 * q^31 + 1215192 * q^33 + 1815924 * q^34 - 394502 * q^36 - 905234 * q^37 - 1635803 * q^39 + 10260228 * q^40 - 11 * q^42 - 1694330 * q^43 - 6978726 * q^46 + 134426 * q^48 + 7785740 * q^49 - 11 * q^51 + 16219654 * q^52 - 10697559 * q^54 - 1371960 * q^55 + 7508908 * q^57 - 21860696 * q^58 - 21971851 * q^60 - 11102850 * q^61 - 9022926 * q^63 + 2572060 * q^64 + 16582830 * q^66 + 6031564 * q^67 + 12019470 * q^69 - 2949828 * q^70 + 12828949 * q^72 - 1809596 * q^73 - 16620656 * q^75 - 42651158 * q^76 - 47106384 * q^78 - 1156914 * q^79 + 48837101 * q^81 + 47208588 * q^82 + 124183367 * q^84 + 5833252 * q^85 - 17916287 * q^87 + 360426 * q^88 - 142298860 * q^90 - 51670516 * q^93 - 18401348 * q^94 + 36462337 * q^96 - 63860500 * q^97 + 135683977 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more