LMFDB - Embedded newform 62.8.g.b.7.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,144] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	62.7
Dual form			62.8.g.b.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.47214 - 7.60845i) q^{2} +(-85.5242 + 18.1787i) q^{3} +(-51.7771 + 37.6183i) q^{4} +(85.4938 - 148.080i) q^{5} +(349.740 + 605.767i) q^{6} +(403.909 + 179.832i) q^{7} +(414.217 + 300.946i) q^{8} +(4986.00 - 2219.91i) q^{9} +(-1338.01 - 284.403i) q^{10} +(-560.166 - 5329.63i) q^{11} +(3744.34 - 4158.51i) q^{12} +(3853.68 + 4279.94i) q^{13} +(369.724 - 3517.69i) q^{14} +(-4619.89 + 14218.6i) q^{15} +(1265.73 - 3895.53i) q^{16} +(-1625.08 + 15461.6i) q^{17} +(-29216.2 - 32447.9i) q^{18} +(5330.68 - 5920.31i) q^{19} +(1143.88 + 10883.3i) q^{20} +(-37813.1 - 8037.43i) q^{21} +(-39165.4 + 17437.6i) q^{22} +(-69437.0 - 50449.0i) q^{23} +(-40896.4 - 18208.2i) q^{24} +(24444.1 + 42338.5i) q^{25} +(23036.9 - 39901.1i) q^{26} +(-231369. + 168099. i) q^{27} +(-27678.2 + 5883.18i) q^{28} +(-12672.3 - 39001.5i) q^{29} +119602. q^{30} +(-9391.56 - 165603. i) q^{31} -32768.0 q^{32} +(144794. + 445629. i) q^{33} +(121656. - 25858.9i) q^{34} +(61161.1 - 44436.2i) q^{35} +(-174652. + 302505. i) q^{36} +(170741. + 295731. i) q^{37} +(-58222.6 - 25922.4i) q^{38} +(-407387. - 295984. i) q^{39} +(79976.9 - 35608.0i) q^{40} +(-758477. - 161219. i) q^{41} +(32326.8 + 307569. i) q^{42} +(235145. - 261155. i) q^{43} +(229495. + 254880. i) q^{44} +(97548.7 - 928114. i) q^{45} +(-212181. + 653025. i) q^{46} +(16396.0 - 50461.6i) q^{47} +(-37435.1 + 356171. i) q^{48} +(-420255. - 466740. i) q^{49} +(261701. - 290648. i) q^{50} +(-142089. - 1.35188e6i) q^{51} +(-360536. - 76634.3i) q^{52} +(-43915.3 + 19552.4i) q^{53} +(1.85095e6 + 1.34479e6i) q^{54} +(-837100. - 372701. i) q^{55} +(113186. + 196044. i) q^{56} +(-348278. + 603235. i) q^{57} +(-265413. + 192834. i) q^{58} +(-1.91506e6 + 407059. i) q^{59} +(-295673. - 909988. i) q^{60} -424643. q^{61} +(-1.23677e6 + 480849. i) q^{62} +2.41310e6 q^{63} +(81007.0 + 249314. i) q^{64} +(963238. - 204743. i) q^{65} +(3.03260e6 - 2.20331e6i) q^{66} +(2.28524e6 - 3.95815e6i) q^{67} +(-497497. - 861690. i) q^{68} +(6.85565e6 + 3.05233e6i) q^{69} +(-489289. - 355489. i) q^{70} +(-849762. + 378338. i) q^{71} +(2.73336e6 + 580994. i) q^{72} +(223521. + 2.12666e6i) q^{73} +(1.82796e6 - 2.03016e6i) q^{74} +(-2.86022e6 - 3.17660e6i) q^{75} +(-53294.9 + 507067. i) q^{76} +(732180. - 2.25342e6i) q^{77} +(-1.24486e6 + 3.83130e6i) q^{78} +(-851780. + 8.10414e6i) q^{79} +(-468636. - 520473. i) q^{80} +(8.74483e6 - 9.71211e6i) q^{81} +(648429. + 6.16939e6i) q^{82} +(-8.50322e6 - 1.80742e6i) q^{83} +(2.26021e6 - 1.00631e6i) q^{84} +(2.15061e6 + 1.56251e6i) q^{85} +(-2.56830e6 - 1.14348e6i) q^{86} +(1.79279e6 + 3.10520e6i) q^{87} +(1.37190e6 - 2.37620e6i) q^{88} +(-6.59609e6 + 4.79234e6i) q^{89} +(-7.30267e6 + 1.55223e6i) q^{90} +(786865. + 2.42172e6i) q^{91} +5.49305e6 q^{92} +(3.81366e6 + 1.39924e7i) q^{93} -424467. q^{94} +(-420938. - 1.29551e6i) q^{95} +(2.80246e6 - 595681. i) q^{96} +(1.23841e6 - 899756. i) q^{97} +(-2.51224e6 + 4.35134e6i) q^{98} +(-1.46243e7 - 2.53300e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 144 q^{2} + 53 q^{3} - 1152 q^{4} + 97 q^{5} + 656 q^{6} - 3516 q^{7} + 9216 q^{8} + 4100 q^{9} - 3616 q^{10} - 6385 q^{11} + 3392 q^{12} - 7108 q^{13} - 25872 q^{14} - 37456 q^{15} - 73728 q^{16}+ \cdots + 20676441 q^{99}+O(q^{100}) $ 72 * q + 144 * q^2 + 53 * q^3 - 1152 * q^4 + 97 * q^5 + 656 * q^6 - 3516 * q^7 + 9216 * q^8 + 4100 * q^9 - 3616 * q^10 - 6385 * q^11 + 3392 * q^12 - 7108 * q^13 - 25872 * q^14 - 37456 * q^15 - 73728 * q^16 - 8376 * q^17 - 70280 * q^18 - 49913 * q^19 + 2048 * q^20 + 323383 * q^21 - 67960 * q^22 - 345829 * q^23 + 6144 * q^24 - 372591 * q^25 + 227584 * q^26 - 71038 * q^27 - 142784 * q^28 - 324657 * q^29 - 926672 * q^30 - 1450215 * q^31 - 2359296 * q^32 + 83140 * q^33 + 542768 * q^34 + 220312 * q^35 - 1649280 * q^36 - 1077276 * q^37 + 242544 * q^38 - 2082538 * q^39 - 16384 * q^40 - 561831 * q^41 + 2046856 * q^42 + 541504 * q^43 + 69440 * q^44 - 3560198 * q^45 - 1210168 * q^46 + 701593 * q^47 - 49152 * q^48 + 2939863 * q^49 - 2047672 * q^50 + 2343644 * q^51 - 454912 * q^52 + 5870237 * q^53 + 568304 * q^54 + 4095901 * q^55 + 358912 * q^56 - 2524936 * q^57 - 4505944 * q^58 + 3564614 * q^59 - 2397184 * q^60 + 6621588 * q^61 - 6588440 * q^62 + 37503466 * q^63 - 4718592 * q^64 + 2623034 * q^65 - 1265000 * q^66 + 6997086 * q^67 + 1117376 * q^68 + 18122809 * q^69 - 1762496 * q^70 + 17340555 * q^71 - 4497920 * q^72 + 893895 * q^73 - 7099272 * q^74 - 4691620 * q^75 + 11121408 * q^76 - 12966527 * q^77 - 31068816 * q^78 + 16057037 * q^79 - 2510848 * q^80 + 17531660 * q^81 + 31965608 * q^82 + 35981510 * q^83 + 13155712 * q^84 + 8693293 * q^85 - 8631272 * q^86 - 7183623 * q^87 + 263680 * q^88 - 23416374 * q^89 - 76756056 * q^90 + 13467668 * q^91 + 24903424 * q^92 - 88528776 * q^93 - 19578704 * q^94 - 9538258 * q^95 - 1736704 * q^96 - 11254011 * q^97 + 30592696 * q^98 + 20676441 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

Coefficient data

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

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

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

$2$	−2.47214	−	7.60845i	−0.218508	−	0.672499i
$2$	−2.47214	−	7.60845i	−0.218508	−	0.672499i
$3$	−85.5242	+	18.1787i	−1.82879	+	0.388722i	−0.988228	−	0.152987i	$-0.951111\pi$
$3$	−85.5242	+	18.1787i	−1.82879	+	0.388722i	−0.840566	+	0.541709i	$0.817777\pi$
$4$	−51.7771	+	37.6183i	−0.404508	+	0.293893i
$5$	85.4938	−	148.080i	0.305872	−	0.529786i	−0.671583	−	0.740929i	$-0.734385\pi$
$5$	85.4938	−	148.080i	0.305872	−	0.529786i	0.977455	+	0.211144i	$0.0677187\pi$
$6$	349.740	+	605.767i	0.661021	+	1.14492i
$7$	403.909	+	179.832i	0.445082	+	0.198163i	0.617025	−	0.786944i	$-0.288338\pi$
$7$	403.909	+	179.832i	0.445082	+	0.198163i	−0.171943	+	0.985107i	$0.555004\pi$
$8$	414.217	+	300.946i	0.286031	+	0.207813i
$9$	4986.00	−	2219.91i	2.27984	−	1.01505i
$10$	−1338.01	−	284.403i	−0.423116	−	0.0899360i
$11$	−560.166	−	5329.63i	−0.126894	−	1.20732i	−0.853807	−	0.520590i	$-0.825712\pi$
$11$	−560.166	−	5329.63i	−0.126894	−	1.20732i	0.726913	−	0.686730i	$-0.240955\pi$
$12$	3744.34	−	4158.51i	0.625520	−	0.694711i
$13$	3853.68	+	4279.94i	0.486490	+	0.540302i	0.935547	−	0.353201i	$-0.114907\pi$
$13$	3853.68	+	4279.94i	0.486490	+	0.540302i	−0.449058	+	0.893503i	$0.648240\pi$
$14$	369.724	−	3517.69i	0.0360105	−	0.342617i
$15$	−4619.89	+	14218.6i	−0.353437	+	1.08777i
$16$	1265.73	−	3895.53i	0.0772542	−	0.237764i
$17$	−1625.08	+	15461.6i	−0.0802239	+	0.763279i	0.878270	+	0.478165i	$0.158698\pi$
$17$	−1625.08	+	15461.6i	−0.0802239	+	0.763279i	−0.958494	+	0.285114i	$0.907969\pi$
$18$	−29216.2	−	32447.9i	−1.18078	−	1.31139i
$19$	5330.68	−	5920.31i	0.178297	−	0.198019i	−0.647371	−	0.762175i	$-0.724132\pi$
$19$	5330.68	−	5920.31i	0.178297	−	0.198019i	0.825668	+	0.564156i	$0.190798\pi$
$20$	1143.88	+	10883.3i	0.0319723	+	0.304196i
$21$	−37813.1	−	8037.43i	−0.890994	−	0.189387i
$22$	−39165.4	+	17437.6i	−0.784193	+	0.349145i
$23$	−69437.0	−	50449.0i	−1.18999	−	0.864579i	−0.196728	−	0.980458i	$-0.563032\pi$
$23$	−69437.0	−	50449.0i	−1.18999	−	0.864579i	−0.993263	+	0.115879i	$0.963032\pi$
$24$	−40896.4	−	18208.2i	−0.603873	−	0.268862i
$25$	24444.1	+	42338.5i	0.312885	+	0.541932i
$26$	23036.9	−	39901.1i	0.257050	−	0.445224i
$27$	−231369.	+	168099.i	−2.26220	+	1.64359i
$28$	−27678.2	+	5883.18i	−0.238278	+	0.0506476i
$29$	−12672.3	−	39001.5i	−0.0964860	−	0.296953i	0.891152	−	0.453705i	$-0.149898\pi$
$29$	−12672.3	−	39001.5i	−0.0964860	−	0.296953i	−0.987638	+	0.156751i	$0.949898\pi$
$30$	119602.			0.808751
$31$	−9391.56	−	165603.i	−0.0566202	−	0.998396i
$31$	−9391.56	−	165603.i	−0.0566202	−	0.998396i
$32$	−32768.0			−0.176777
$33$	144794.	+	445629.i	0.701376	+	2.15861i
$34$	121656.	−	25858.9i	0.530834	−	0.112832i
$35$	61161.1	−	44436.2i	0.241122	−	0.175186i
$36$	−174652.	+	302505.i	−0.623898	+	1.08062i
$37$	170741.	+	295731.i	0.554154	+	0.959823i	0.997969	+	0.0637046i	$0.0202915\pi$
$37$	170741.	+	295731.i	0.554154	+	0.959823i	−0.443815	+	0.896119i	$0.646375\pi$
$38$	−58222.6	−	25922.4i	−0.172127	−	0.0766359i
$39$	−407387.	−	295984.i	−1.09972	−	0.798991i
$40$	79976.9	−	35608.0i	0.197585	−	0.0879707i
$41$	−758477.	−	161219.i	−1.71869	−	0.365320i	−0.760037	−	0.649880i	$-0.774819\pi$
$41$	−758477.	−	161219.i	−1.71869	−	0.365320i	−0.958658	+	0.284560i	$0.908152\pi$
$42$	32326.8	+	307569.i	0.0673271	+	0.640575i
$43$	235145.	−	261155.i	0.451021	−	0.500909i	−0.474159	−	0.880439i	$-0.657248\pi$
$43$	235145.	−	261155.i	0.451021	−	0.500909i	0.925179	+	0.379530i	$0.123914\pi$
$44$	229495.	+	254880.i	0.406152	+	0.451078i
$45$	97548.7	−	928114.i	0.159580	−	1.51830i
$46$	−212181.	+	653025.i	−0.321406	+	0.989185i
$47$	16396.0	−	50461.6i	0.0230353	−	0.0708954i	−0.938878	−	0.344250i	$-0.888133\pi$
$47$	16396.0	−	50461.6i	0.0230353	−	0.0708954i	0.961913	+	0.273355i	$0.0881332\pi$
$48$	−37435.1	+	356171.i	−0.0488579	+	0.464852i
$49$	−420255.	−	466740.i	−0.510301	−	0.566747i
$50$	261701.	−	290648.i	0.296081	−	0.328831i
$51$	−142089.	−	1.35188e6i	−0.149991	−	1.42707i
$52$	−360536.	−	76634.3i	−0.355580	−	0.0755808i
$53$	−43915.3	+	19552.4i	−0.0405183	+	0.0180399i	−0.426896	−	0.904301i	$-0.640393\pi$
$53$	−43915.3	+	19552.4i	−0.0405183	+	0.0180399i	0.386377	+	0.922341i	$0.373726\pi$
$54$	1.85095e6	+	1.34479e6i	1.59962	+	1.16219i
$55$	−837100.	−	372701.i	−0.678434	−	0.302058i
$56$	113186.	+	196044.i	0.0861262	+	0.149175i
$57$	−348278.	+	603235.i	−0.249095	+	0.431444i
$58$	−265413.	+	192834.i	−0.178618	+	0.129773i
$59$	−1.91506e6	+	407059.i	−1.21395	+	0.258033i	−0.770015	−	0.638025i	$-0.779752\pi$
$59$	−1.91506e6	+	407059.i	−1.21395	+	0.258033i	−0.443936	+	0.896059i	$0.646418\pi$
$60$	−295673.	−	909988.i	−0.176719	−	0.543884i
$61$	−424643.			−0.239535			−0.119768	−	0.992802i	$-0.538215\pi$
$61$	−424643.			−0.239535			−0.119768	+	0.992802i	$0.538215\pi$
$62$	−1.23677e6	+	480849.i	−0.659048	+	0.256235i
$63$	2.41310e6			1.21586
$64$	81007.0	+	249314.i	0.0386271	+	0.118882i
$65$	963238.	−	204743.i	0.435048	−	0.0924722i
$66$	3.03260e6	−	2.20331e6i	1.29841	−	0.943348i
$67$	2.28524e6	−	3.95815e6i	0.928260	−	1.60779i	0.142028	−	0.989863i	$-0.454638\pi$
$67$	2.28524e6	−	3.95815e6i	0.928260	−	1.60779i	0.786232	−	0.617931i	$-0.212029\pi$
$68$	−497497.	−	861690.i	−0.191871	−	0.332330i
$69$	6.85565e6	+	3.05233e6i	2.51233	+	1.11856i
$70$	−489289.	−	355489.i	−0.170499	−	0.123875i
$71$	−849762.	+	378338.i	−0.281769	+	0.125452i	−0.542755	−	0.839891i	$-0.682619\pi$
$71$	−849762.	+	378338.i	−0.281769	+	0.125452i	0.260986	+	0.965342i	$0.415952\pi$
$72$	2.73336e6	+	580994.i	0.863044	+	0.183446i
$73$	223521.	+	2.12666e6i	0.0672493	+	0.639834i	0.975286	+	0.220944i	$0.0709139\pi$
$73$	223521.	+	2.12666e6i	0.0672493	+	0.639834i	−0.908037	+	0.418890i	$0.862419\pi$
$74$	1.82796e6	−	2.03016e6i	0.524393	−	0.582397i
$75$	−2.86022e6	−	3.17660e6i	−0.782863	−	0.869457i
$76$	−53294.9	+	507067.i	−0.0139264	+	0.132501i
$77$	732180.	−	2.25342e6i	0.182768	−	0.562502i
$78$	−1.24486e6	+	3.83130e6i	−0.297023	+	0.914144i
$79$	−851780.	+	8.10414e6i	−0.194371	+	1.84932i	0.268980	+	0.963146i	$0.413313\pi$
$79$	−851780.	+	8.10414e6i	−0.194371	+	1.84932i	−0.463351	+	0.886175i	$0.653353\pi$
$80$	−468636.	−	520473.i	−0.102334	−	0.113654i
$81$	8.74483e6	−	9.71211e6i	1.82833	−	2.03056i
$82$	648429.	+	6.16939e6i	0.129872	+	1.23564i
$83$	−8.50322e6	−	1.80742e6i	−1.63234	−	0.346964i	−0.701578	−	0.712593i	$-0.747521\pi$
$83$	−8.50322e6	−	1.80742e6i	−1.63234	−	0.346964i	−0.930761	+	0.365629i	$0.880854\pi$
$84$	2.26021e6	−	1.00631e6i	0.416074	−	0.185248i
$85$	2.15061e6	+	1.56251e6i	0.379836	+	0.275967i
$86$	−2.56830e6	−	1.14348e6i	−0.435412	−	0.193858i
$87$	1.79279e6	+	3.10520e6i	0.291885	+	0.505560i
$88$	1.37190e6	−	2.37620e6i	0.214602	−	0.371701i
$89$	−6.59609e6	+	4.79234e6i	−0.991794	+	0.720580i	−0.960313	−	0.278924i	$-0.910022\pi$
$89$	−6.59609e6	+	4.79234e6i	−0.991794	+	0.720580i	−0.0314805	+	0.999504i	$0.510022\pi$
$90$	−7.30267e6	+	1.55223e6i	−1.05592	+	0.224444i
$91$	786865.	+	2.42172e6i	0.109460	+	0.336883i
$92$	5.49305e6			0.735455
$93$	3.81366e6	+	1.39924e7i	0.491645	+	1.80385i
$94$	−424467.			−0.0527105
$95$	−420938.	−	1.29551e6i	−0.0503716	−	0.155028i
$96$	2.80246e6	−	595681.i	0.323288	−	0.0687170i
$97$	1.23841e6	−	899756.i	0.137773	−	0.100098i	−0.516764	−	0.856128i	$-0.672864\pi$
$97$	1.23841e6	−	899756.i	0.137773	−	0.100098i	0.654537	+	0.756030i	$0.272864\pi$
$98$	−2.51224e6	+	4.35134e6i	−0.269632	+	0.467015i
$99$	−1.46243e7	−	2.53300e7i	−1.51479	−	2.62369i
$100$	−2.85834e6	−	1.27262e6i	−0.285834	−	0.127262i
$101$	−3.64615e6	−	2.64908e6i	−0.352135	−	0.255841i	0.397629	−	0.917546i	$-0.369833\pi$
$101$	−3.64615e6	−	2.64908e6i	−0.352135	−	0.255841i	−0.749764	+	0.661705i	$0.769833\pi$
$102$	−9.93448e6	+	4.42312e6i	−0.926925	+	0.412694i
$103$	−1.49861e7	−	3.18539e6i	−1.35132	−	0.287232i	−0.525321	−	0.850904i	$-0.676055\pi$
$103$	−1.49861e7	−	3.18539e6i	−1.35132	−	0.287232i	−0.825999	+	0.563672i	$0.809388\pi$
$104$	308226.	+	2.93257e6i	0.0268691	+	0.255642i
$105$	−4.42297e6	+	4.91220e6i	−0.372864	+	0.414108i
$106$	257328.	+	285792.i	0.0209854	+	0.0233066i
$107$	23489.2	−	223485.i	0.00185364	−	0.0176362i	−0.993556	−	0.113342i	$-0.963844\pi$
$107$	23489.2	−	223485.i	0.00185364	−	0.0176362i	0.995410	+	0.0957062i	$0.0305109\pi$
$108$	5.65600e6	−	1.74074e7i	0.432042	−	1.32969i
$109$	2.24200e6	−	6.90015e6i	0.165822	−	0.510348i	−0.833274	−	0.552860i	$-0.813536\pi$
$109$	2.24200e6	−	6.90015e6i	0.165822	−	0.510348i	0.999096	+	0.0425127i	$0.0135363\pi$
$110$	−766252.	+	7.29040e6i	−0.0548905	+	0.522248i
$111$	−1.99785e7	−	2.21883e7i	−1.38654	−	1.53991i
$112$	1.21178e6	−	1.34582e6i	0.0815006	−	0.0905156i
$113$	269793.	+	2.56691e6i	0.0175896	+	0.167354i	0.999790	−	0.0204807i	$-0.00651967\pi$
$113$	269793.	+	2.56691e6i	0.0175896	+	0.167354i	−0.982201	+	0.187835i	$0.939853\pi$
$114$	5.45068e6	+	1.15858e6i	0.344575	+	0.0732416i
$115$	−1.34069e7	+	5.96913e6i	−0.822026	+	0.365990i
$116$	2.12330e6	+	1.54267e6i	0.126302	+	0.0917636i
$117$	2.87156e7	+	1.27850e7i	1.65755	+	0.737989i
$118$	7.83139e6	+	1.35644e7i	0.438785	+	0.759998i
$119$	−3.43687e6	+	5.95284e6i	−0.186960	+	0.323825i
$120$	−6.19266e6	+	4.49923e6i	−0.327147	+	0.237686i
$121$	−9.02980e6	+	1.91934e6i	−0.463371	+	0.0984926i
$122$	1.04978e6	+	3.23088e6i	0.0523404	+	0.161087i
$123$	6.77989e7			3.28515
$124$	6.71597e6	+	8.22116e6i	0.316325	+	0.387219i
$125$	2.17177e7			0.994554
$126$	−5.96552e6	−	1.83600e7i	−0.265675	−	0.817665i
$127$	−2.73149e7	+	5.80596e6i	−1.18328	+	0.251513i	−0.757206	−	0.653177i	$-0.773436\pi$
$127$	−2.73149e7	+	5.80596e6i	−1.18328	+	0.251513i	−0.426071	+	0.904690i	$0.640103\pi$
$128$	1.69663e6	−	1.23268e6i	0.0715077	−	0.0519534i
$129$	−1.53631e7	+	2.66097e7i	−0.630109	+	1.09138i
$130$	−3.93903e6	−	6.82260e6i	−0.157249	−	0.272363i
$131$	9.69783e6	+	4.31775e6i	0.376899	+	0.167806i	0.586438	−	0.809994i	$-0.300530\pi$
$131$	9.69783e6	+	4.31775e6i	0.376899	+	0.167806i	−0.209539	+	0.977800i	$0.567196\pi$
$132$	−2.42608e7	−	1.76265e7i	−0.918113	−	0.667048i
$133$	3.21777e6	−	1.43264e6i	0.118597	−	0.0528028i
$134$	−3.57648e7	−	7.60204e6i	−1.28407	−	0.272938i
$135$	5.11147e6	+	4.86324e7i	0.178804	+	1.70121i
$136$	−5.32625e6	+	5.91540e6i	−0.181566	+	0.201650i
$137$	−3.57067e7	−	3.96563e7i	−1.18639	−	1.31762i	−0.937047	−	0.349203i	$-0.886452\pi$
$137$	−3.57067e7	−	3.96563e7i	−1.18639	−	1.31762i	−0.249342	−	0.968415i	$-0.580214\pi$
$138$	6.27542e6	−	5.97066e7i	0.203267	−	1.93395i
$139$	−1.29848e7	+	3.99632e7i	−0.410095	+	1.26214i	0.506470	+	0.862257i	$0.330950\pi$
$139$	−1.29848e7	+	3.99632e7i	−0.410095	+	1.26214i	−0.916565	+	0.399885i	$0.869050\pi$
$140$	−1.49513e6	+	4.60155e6i	−0.0460503	+	0.141728i
$141$	−484924.	+	4.61375e6i	−0.0145682	+	0.138607i
$142$	4.97930e6	+	5.53007e6i	0.145935	+	0.162077i
$143$	2.06518e7	−	2.29361e7i	0.590584	−	0.655910i
$144$	−2.33678e6	−	2.22329e7i	−0.0652151	−	0.620480i
$145$	−6.85873e6	−	1.45787e6i	−0.186834	−	0.0397128i
$146$	1.56280e7	−	6.95803e6i	0.415593	−	0.185034i
$147$	4.44267e7	+	3.22779e7i	1.15354	+	0.838098i
$148$	−1.99653e7	−	8.88914e6i	−0.506245	−	0.225395i
$149$	4.09744e6	+	7.09698e6i	0.101475	+	0.175761i	0.912293	−	0.409539i	$-0.134310\pi$
$149$	4.09744e6	+	7.09698e6i	0.101475	+	0.175761i	−0.810817	+	0.585299i	$0.800977\pi$
$150$	−1.70982e7	+	2.96149e7i	−0.413647	+	0.716458i
$151$	−1.59909e7	+	1.16181e7i	−0.377968	+	0.274610i	−0.760507	−	0.649330i	$-0.775050\pi$
$151$	−1.59909e7	+	1.16181e7i	−0.377968	+	0.274610i	0.382539	+	0.923939i	$0.375050\pi$
$152$	3.98975e6	−	848048.i	0.0921495	−	0.0195870i
$153$	2.62208e7	+	8.06992e7i	0.591869	+	1.82158i
$154$	−1.89551e7			−0.418218
$155$	−2.53254e7	−	1.27673e7i	−0.546254	−	0.275385i
$156$	3.22277e7			0.679662
$157$	−2.11273e7	−	6.50230e7i	−0.435707	−	1.34097i	−0.892360	−	0.451324i	$-0.850952\pi$
$157$	−2.11273e7	−	6.50230e7i	−0.435707	−	1.34097i	0.456653	−	0.889645i	$-0.349048\pi$
$158$	6.37657e7	−	1.35538e7i	1.28614	−	0.273377i
$159$	3.40039e6	−	2.47053e6i	0.0670870	−	0.0487416i
$160$	−2.80146e6	+	4.85227e6i	−0.0540710	+	0.0936538i
$161$	−1.89739e7	−	3.28638e7i	−0.358316	−	0.620622i
$162$	−9.55125e7	−	4.25249e7i	−1.76505	−	0.785852i
$163$	6.17493e7	+	4.48635e7i	1.11680	+	0.811403i	0.983721	−	0.179702i	$-0.0575135\pi$
$163$	6.17493e7	+	4.48635e7i	1.11680	+	0.811403i	0.133079	+	0.991105i	$0.457513\pi$
$164$	4.53365e7	−	2.01851e7i	0.802591	−	0.357337i
$165$	7.83675e7	+	1.66575e7i	1.35813	+	0.288680i
$166$	7.26949e6	+	6.91645e7i	0.123346	+	1.17356i
$167$	1.84675e7	−	2.05102e7i	0.306831	−	0.340771i	−0.569933	−	0.821691i	$-0.693031\pi$
$167$	1.84675e7	−	2.05102e7i	0.306831	−	0.340771i	0.876764	+	0.480920i	$0.159697\pi$
$168$	−1.32440e7	−	1.47089e7i	−0.215495	−	0.239331i
$169$	3.09193e6	−	2.94177e7i	0.0492749	−	0.468819i
$170$	6.57169e6	−	2.02256e7i	0.102590	−	0.315740i
$171$	1.34362e7	−	4.13523e7i	0.205490	−	0.632432i
$172$	−2.35093e6	+	2.23676e7i	−0.0352282	+	0.335174i
$173$	2.42660e7	+	2.69501e7i	0.356317	+	0.395730i	0.894478	−	0.447112i	$-0.147548\pi$
$173$	2.42660e7	+	2.69501e7i	0.356317	+	0.395730i	−0.538161	+	0.842842i	$0.680881\pi$
$174$	1.91938e7	−	2.13168e7i	0.276209	−	0.306761i
$175$	2.25940e6	+	2.14967e7i	0.0318683	+	0.303207i
$176$	−2.14707e7	−	4.56374e6i	−0.296860	−	0.0630996i
$177$	1.56385e8	−	6.96269e7i	2.11976	−	0.943780i
$178$	5.27687e7	+	3.83387e7i	0.701304	+	0.509527i
$179$	−8.45853e7	−	3.76598e7i	−1.10232	−	0.490786i	−0.226790	−	0.973944i	$-0.572823\pi$
$179$	−8.45853e7	−	3.76598e7i	−1.10232	−	0.490786i	−0.875533	+	0.483158i	$0.839490\pi$
$180$	2.98632e7	+	5.17247e7i	0.381666	+	0.661065i
$181$	1.19726e7	−	2.07372e7i	0.150077	−	0.259941i	−0.781179	−	0.624307i	$-0.785381\pi$
$181$	1.19726e7	−	2.07372e7i	0.150077	−	0.259941i	0.931255	+	0.364367i	$0.118715\pi$
$182$	1.64803e7	−	1.19736e7i	0.202636	−	0.147223i
$183$	3.63173e7	−	7.71948e6i	0.438061	−	0.0931127i
$184$	−1.35796e7	−	4.17936e7i	−0.160703	−	0.494592i
$185$	5.83890e7			0.678001
$186$	9.70323e7	−	6.36071e7i	1.10566	−	0.724787i
$187$	8.33149e7			0.931702
$188$	1.04934e6	+	3.22954e6i	0.0115177	+	0.0354477i
$189$	−1.23681e8	+	2.62893e7i	−1.33256	+	0.283245i
$190$	−8.81624e6	+	6.40538e6i	−0.0932494	+	0.0677496i
$191$	5.87705e7	−	1.01794e8i	0.610299	−	1.05707i	−0.380891	−	0.924620i	$-0.624383\pi$
$191$	5.87705e7	−	1.01794e8i	0.610299	−	1.05707i	0.991190	−	0.132449i	$-0.0422841\pi$
$192$	−1.14603e7	−	1.98498e7i	−0.116853	−	0.202396i
$193$	−8.54524e7	−	3.80459e7i	−0.855606	−	0.380940i	−0.0684202	−	0.997657i	$-0.521796\pi$
$193$	−8.54524e7	−	3.80459e7i	−0.855606	−	0.380940i	−0.787185	+	0.616716i	$0.788463\pi$
$194$	−9.90726e6	−	7.19805e6i	−0.0974199	−	0.0707797i
$195$	−7.86582e7	+	3.50209e7i	−0.759666	+	0.338225i
$196$	3.93175e7	+	8.35720e6i	0.372984	+	0.0792802i
$197$	−1.72897e7	−	1.64500e8i	−0.161122	−	1.53297i	−0.714258	−	0.699883i	$-0.753235\pi$
$197$	−1.72897e7	−	1.64500e8i	−0.161122	−	1.53297i	0.553135	−	0.833091i	$-0.313431\pi$
$198$	−1.56569e8	+	1.73887e8i	−1.43343	+	1.59199i
$199$	−8.77119e7	−	9.74139e7i	−0.788992	−	0.876265i	0.205757	−	0.978603i	$-0.434034\pi$
$199$	−8.77119e7	−	9.74139e7i	−0.788992	−	0.876265i	−0.994750	+	0.102338i	$0.967368\pi$
$200$	−2.61643e6	+	2.48937e7i	−0.0231262	+	0.220031i
$201$	−1.23489e8	+	3.80060e8i	−1.07261	+	3.30116i
$202$	−1.11416e7	+	3.42904e7i	−0.0951084	+	0.292714i
$203$	1.89523e6	−	1.80319e7i	0.0159011	−	0.151289i
$204$	5.82125e7	+	6.46515e7i	0.480077	+	0.533179i
$205$	−8.87183e7	+	9.85317e7i	−0.719242	+	0.798799i
$206$	1.28118e7	+	1.21896e8i	0.102111	+	0.971523i
$207$	−4.58206e8	−	9.73946e7i	−3.59058	−	0.763201i
$208$	2.15504e7	−	9.59484e6i	0.166048	−	0.0739292i
$209$	−3.45391e7	−	2.50941e7i	−0.261697	−	0.190134i
$210$	4.83084e7	+	2.15083e7i	0.359961	+	0.160265i
$211$	−6.94202e7	−	1.20239e8i	−0.508741	−	0.881166i	−0.999949	−	0.0101232i	$-0.996778\pi$
$211$	−6.94202e7	−	1.20239e8i	−0.508741	−	0.881166i	0.491207	−	0.871043i	$-0.336556\pi$
$212$	1.53828e6	−	2.66438e6i	0.0110882	−	0.0192053i
$213$	6.57975e7	−	4.78047e7i	0.466531	−	0.338955i
$214$	−1.75844e6	+	373769.i	−0.0122654	+	0.00260708i
$215$	−1.85683e7	−	5.71473e7i	−0.127420	−	0.392158i
$216$	−1.46426e8			−0.988619
$217$	2.59874e7	−	6.85775e7i	0.172645	−	0.455588i
$218$	−5.80420e7			−0.379441
$219$	−5.77764e7	−	1.77817e8i	−0.371703	−	1.14398i
$220$	5.73629e7	−	1.21929e7i	0.363205	−	0.0772016i
$221$	−7.24374e7	+	5.26288e7i	−0.451429	+	0.327983i
$222$	−1.19429e8	+	2.06858e8i	−0.732615	+	1.26893i
$223$	1.60248e8	+	2.77558e8i	0.967667	+	1.67605i	0.702273	+	0.711907i	$0.252168\pi$
$223$	1.60248e8	+	2.77558e8i	0.967667	+	1.67605i	0.265393	+	0.964140i	$0.414498\pi$
$224$	−1.32353e7	−	5.89273e6i	−0.0786802	−	0.0350307i
$225$	2.15866e8	+	1.56836e8i	1.26341	+	0.917924i
$226$	1.88633e7	−	8.39847e6i	0.108702	−	0.0483972i
$227$	3.17567e8	+	6.75009e7i	1.80196	+	0.383018i	0.981920	−	0.189294i	$-0.0606200\pi$
$227$	3.17567e8	+	6.75009e7i	1.80196	+	0.383018i	0.820036	+	0.572312i	$0.193953\pi$
$228$	−4.65984e6	−	4.43354e7i	−0.0260375	−	0.247730i
$229$	−1.13899e8	+	1.26497e8i	−0.626750	+	0.696077i	−0.969983	−	0.243174i	$-0.921811\pi$
$229$	−1.13899e8	+	1.26497e8i	−0.626750	+	0.696077i	0.343233	+	0.939250i	$0.388478\pi$
$230$	7.85595e7	+	8.72492e7i	0.425747	+	0.472840i
$231$	−2.16548e7	+	2.06032e8i	−0.115588	+	1.09975i
$232$	6.48824e6	−	1.99688e7i	0.0341129	−	0.104989i
$233$	2.87456e7	−	8.84698e7i	0.148876	−	0.458194i	−0.848613	−	0.529014i	$-0.822562\pi$
$233$	2.87456e7	−	8.84698e7i	0.148876	−	0.458194i	0.997489	+	0.0708206i	$0.0225618\pi$
$234$	2.62852e7	−	2.50087e8i	0.134108	−	1.27596i
$235$	−6.07058e6	−	6.74206e6i	−0.0305135	−	0.0338887i
$236$	8.38436e7	−	9.31177e7i	0.415220	−	0.461148i
$237$	−7.44753e7	−	7.08585e8i	−0.363407	−	3.45758i
$238$	5.37883e7	+	1.14331e7i	0.258624	+	0.0549722i
$239$	−3.14543e8	+	1.40043e8i	−1.49035	+	0.663545i	−0.980464	−	0.196699i	$-0.936978\pi$
$239$	−3.14543e8	+	1.40043e8i	−1.49035	+	0.663545i	−0.509882	+	0.860244i	$0.670311\pi$
$240$	4.95412e7	+	3.59938e7i	0.231328	+	0.168069i
$241$	4.74834e7	+	2.11410e7i	0.218515	+	0.0972893i	0.513075	−	0.858344i	$-0.328506\pi$
$241$	4.74834e7	+	2.11410e7i	0.218515	+	0.0972893i	−0.294560	+	0.955633i	$0.595173\pi$
$242$	3.69261e7	+	6.39579e7i	0.167487	+	0.290095i
$243$	−2.58613e8	+	4.47931e8i	−1.15619	+	2.00258i
$244$	2.19868e7	−	1.59743e7i	0.0968941	−	0.0703977i
$245$	−1.05044e8	+	2.23278e7i	−0.456341	+	0.0969983i
$246$	−1.67608e8	−	5.15845e8i	−0.717831	−	2.20926i
$247$	4.58813e7			0.193730
$248$	4.59475e7	−	7.14220e7i	0.191285	−	0.297338i
$249$	7.60088e8			3.12008
$250$	−5.36891e7	−	1.65238e8i	−0.217318	−	0.668836i
$251$	2.75859e8	−	5.86357e7i	1.10111	−	0.234047i	0.378702	−	0.925519i	$-0.376370\pi$
$251$	2.75859e8	−	5.86357e7i	1.10111	−	0.234047i	0.722404	+	0.691471i	$0.243037\pi$
$252$	−1.24943e8	+	9.07767e7i	−0.491826	+	0.357332i
$253$	−2.29978e8	+	3.98333e8i	−0.892820	+	1.54641i
$254$	1.11700e8	+	1.93471e8i	0.427698	+	0.740794i
$255$	−2.12334e8	−	9.45373e7i	−0.801917	−	0.357036i
$256$	−1.35731e7	−	9.86140e6i	−0.0505636	−	0.0367366i
$257$	1.76226e8	−	7.84610e7i	0.647597	−	0.288329i	−0.0565323	−	0.998401i	$-0.518004\pi$
$257$	1.76226e8	−	7.84610e7i	0.647597	−	0.288329i	0.704129	+	0.710072i	$0.251338\pi$
$258$	2.40439e8	+	5.11068e7i	0.871636	+	0.185272i
$259$	1.57817e7	+	1.50153e8i	0.0564424	+	0.537013i
$260$	−4.21716e7	+	4.68363e7i	−0.148804	+	0.165263i
$261$	−1.49764e8	−	1.66330e8i	−0.521394	−	0.579067i
$262$	8.87705e6	−	8.44595e7i	0.0304940	−	0.290131i
$263$	−4.26264e7	+	1.31191e8i	−0.144489	+	0.444691i	−0.996945	−	0.0781081i	$-0.975112\pi$
$263$	−4.26264e7	+	1.31191e8i	−0.144489	+	0.444691i	0.852456	+	0.522799i	$0.175112\pi$
$264$	−7.41344e7	+	2.28162e8i	−0.247974	+	0.763185i
$265$	−859182.	+	8.17457e6i	−0.00283612	+	0.0269839i
$266$	−1.88550e7	−	2.09405e7i	−0.0614242	−	0.0682185i
$267$	4.77007e8	−	5.29770e8i	1.53368	−	1.70333i
$268$	3.05757e7	+	2.90908e8i	0.0970296	+	0.923175i
$269$	2.88734e8	+	6.13722e7i	0.904408	+	0.192238i	0.636564	−	0.771224i	$-0.280355\pi$
$269$	2.88734e8	+	6.13722e7i	0.904408	+	0.192238i	0.267845	+	0.963462i	$0.413689\pi$
$270$	3.57381e8	−	1.59116e8i	1.10499	−	0.491973i
$271$	−4.67563e8	−	3.39704e8i	−1.42708	−	1.03683i	−0.990552	−	0.137141i	$-0.956209\pi$
$271$	−4.67563e8	−	3.39704e8i	−1.42708	−	1.03683i	−0.436526	−	0.899692i	$-0.643791\pi$
$272$	5.81742e7	+	2.59008e7i	0.175283	+	0.0780409i
$273$	−1.11320e8	−	1.92812e8i	−0.331134	−	0.573540i
$274$	−2.13451e8	+	3.69708e8i	−0.626861	+	1.08576i
$275$	2.11955e8	−	1.53995e8i	0.614582	−	0.446520i
$276$	−4.69789e8	+	9.98567e7i	−1.34500	+	0.285888i
$277$	9.76965e6	+	3.00679e7i	0.0276185	+	0.0850010i	0.963916	−	0.266208i	$-0.0857707\pi$
$277$	9.76965e6	+	3.00679e7i	0.0276185	+	0.0850010i	−0.936297	+	0.351209i	$0.885771\pi$
$278$	3.36158e8			0.938398
$279$	−4.14451e8	−	8.04850e8i	−1.14251	−	2.21871i
$280$	3.87068e7			0.105374
$281$	−1.49223e8	−	4.59260e8i	−0.401202	−	1.23477i	−0.924026	−	0.382331i	$-0.875121\pi$
$281$	−1.49223e8	−	4.59260e8i	−0.401202	−	1.23477i	0.522824	−	0.852441i	$-0.324879\pi$
$282$	3.63023e7	−	7.71628e6i	0.0963966	−	0.0204897i
$283$	−1.00915e8	+	7.33190e7i	−0.264669	+	0.192293i	−0.712203	−	0.701974i	$-0.752302\pi$
$283$	−1.00915e8	+	7.33190e7i	−0.264669	+	0.192293i	0.447534	+	0.894267i	$0.352302\pi$
$284$	2.97658e7	−	5.15558e7i	0.0771086	−	0.133556i
$285$	5.95512e7	+	1.03146e8i	0.152382	+	0.263933i
$286$	−2.25563e8	−	1.00427e8i	−0.570146	−	0.253845i
$287$	−2.77363e8	−	2.01516e8i	−0.692567	−	0.503180i
$288$	−1.63381e8	+	7.27421e7i	−0.403022	+	0.179437i
$289$	1.64951e8	+	3.50615e7i	0.401988	+	0.0854452i
$290$	5.86359e6	+	5.57884e7i	0.0141179	+	0.134323i
$291$	−8.95575e7	+	9.94637e7i	−0.213047	+	0.236613i
$292$	−9.15743e7	−	1.01704e8i	−0.215245	−	0.239054i
$293$	−7.56629e7	+	7.19885e8i	−0.175730	+	1.67196i	0.450846	+	0.892602i	$0.351122\pi$
$293$	−7.56629e7	+	7.19885e8i	−0.175730	+	1.67196i	−0.626576	+	0.779360i	$0.715544\pi$
$294$	1.35756e8	−	4.17814e8i	0.311561	−	0.958887i
$295$	−1.03449e8	+	3.18383e8i	−0.234611	+	0.722059i
$296$	−1.82756e7	+	1.73881e8i	−0.0409591	+	0.389700i
$297$	1.02551e9	+	1.13895e9i	2.27139	+	2.52264i
$298$	4.38676e7	−	4.87199e7i	0.0960256	−	0.106647i
$299$	−5.16693e7	−	4.91601e8i	−0.111785	−	1.06356i
$300$	2.67592e8	+	5.68785e7i	0.572202	+	0.121625i
$301$	1.41941e8	−	6.31963e7i	0.300003	−	0.133570i
$302$	1.27928e8	+	9.29448e7i	0.267264	+	0.194178i
$303$	3.59991e8	+	1.60278e8i	0.743434	+	0.330998i
$304$	−1.63155e7	−	2.82593e7i	−0.0333076	−	0.0576905i
$305$	−3.63043e7	+	6.28810e7i	−0.0732671	+	0.126902i
$306$	5.49175e8	−	3.98999e8i	1.09568	−	0.796061i
$307$	−7.18344e8	+	1.52689e8i	−1.41693	+	0.301177i	−0.851818	−	0.523838i	$-0.824500\pi$
$307$	−7.18344e8	+	1.52689e8i	−1.41693	+	0.301177i	−0.565111	+	0.825015i	$0.691166\pi$
$308$	4.68595e7	+	1.44219e8i	0.0913841	+	0.281251i
$309$	1.33958e9			2.58294
$310$	−3.45320e7	+	2.24249e8i	−0.0658348	+	0.427529i
$311$	−2.08476e8			−0.393001			−0.196501	−	0.980504i	$-0.562958\pi$
$311$	−2.08476e8			−0.393001			−0.196501	+	0.980504i	$0.562958\pi$
$312$	−7.96713e7	−	2.45203e8i	−0.148512	−	0.457072i
$313$	5.53741e8	−	1.17701e8i	1.02071	−	0.216958i	0.332986	−	0.942932i	$-0.391944\pi$
$313$	5.53741e8	−	1.17701e8i	1.02071	−	0.216958i	0.687722	+	0.725974i	$0.258611\pi$
$314$	−4.42495e8	+	3.21492e8i	−0.806594	+	0.586025i
$315$	2.06305e8	−	3.57331e8i	0.371898	−	0.644146i
$316$	−2.60761e8	−	4.51651e8i	−0.464877	−	0.805190i
$317$	3.74660e8	+	1.66809e8i	0.660586	+	0.294112i	0.709515	−	0.704690i	$-0.248914\pi$
$317$	3.74660e8	+	1.66809e8i	0.660586	+	0.294112i	−0.0489287	+	0.998802i	$0.515581\pi$
$318$	−2.72031e7	−	1.97642e7i	−0.0474377	−	0.0344655i
$319$	−2.00765e8	+	8.93862e7i	−0.346274	+	0.154171i
$320$	4.38439e7	+	9.31930e6i	0.0747970	+	0.0158986i
$321$	2.05378e6	+	1.95404e7i	0.00346566	+	0.0329735i
$322$	−2.03136e8	+	2.25606e8i	−0.339072	+	0.376578i
$323$	8.28748e7	+	9.20418e7i	0.136840	+	0.151976i
$324$	−8.74289e7	+	8.31830e8i	−0.142806	+	1.35871i
$325$	−8.70064e7	+	2.67778e8i	−0.140592	+	0.432697i
$326$	1.88689e8	−	5.80725e8i	0.301637	−	0.928345i
$327$	−6.63089e7	+	6.30887e8i	−0.104871	+	0.997779i
$328$	−2.65655e8	−	2.95040e8i	−0.415681	−	0.461661i
$329$	1.56971e7	−	1.74334e7i	0.0243015	−	0.0269895i
$330$	−6.69971e7	−	6.37435e8i	−0.102626	−	0.976421i
$331$	−8.65525e8	−	1.83973e8i	−1.31184	−	0.278841i	−0.501683	−	0.865051i	$-0.667286\pi$
$331$	−8.65525e8	−	1.83973e8i	−1.31184	−	0.278841i	−0.810159	+	0.586211i	$0.800619\pi$
$332$	5.08264e8	−	2.26294e8i	0.762265	−	0.339382i
$333$	1.50781e9	+	1.09549e9i	2.23765	+	1.62575i
$334$	−2.01705e8	−	8.98049e7i	−0.296213	−	0.131883i
$335$	−3.90747e8	−	6.76794e8i	−0.567857	−	0.983558i
$336$	−7.91713e7	+	1.37129e8i	−0.113862	+	0.197216i
$337$	−6.66355e8	+	4.84135e8i	−0.948421	+	0.689068i	−0.950433	−	0.310930i	$-0.899360\pi$
$337$	−6.66355e8	+	4.84135e8i	−0.948421	+	0.689068i	0.00201206	+	0.999998i	$0.499360\pi$
$338$	−2.31467e8	+	4.91998e7i	−0.326047	+	0.0693035i
$339$	−6.97371e7	−	2.14629e8i	−0.0972221	−	0.299219i
$340$	−1.70132e8			−0.234752
$341$	−8.77342e8	+	1.42819e8i	−1.19820	+	0.195050i
$342$	−3.47843e8			−0.470211
$343$	−1.98328e8	−	6.10391e8i	−0.265372	−	0.816730i
$344$	1.75995e8	−	3.74088e7i	0.233101	−	0.0495472i
$345$	1.03810e9	−	7.54226e8i	1.36105	−	0.988860i
$346$	1.45060e8	−	2.51251e8i	0.188270	−	0.326092i
$347$	3.51084e8	+	6.08096e8i	0.451085	+	0.781302i	0.998454	−	0.0555897i	$-0.0177039\pi$
$347$	3.51084e8	+	6.08096e8i	0.451085	+	0.781302i	−0.547369	+	0.836891i	$0.684371\pi$
$348$	−2.09638e8	−	9.33368e7i	−0.266650	−	0.118720i
$349$	−5.04499e8	−	3.66540e8i	−0.635289	−	0.461564i	0.222940	−	0.974832i	$-0.428435\pi$
$349$	−5.04499e8	−	3.66540e8i	−0.635289	−	0.461564i	−0.858228	+	0.513268i	$0.828435\pi$
$350$	1.57971e8	−	7.03333e7i	0.196943	−	0.0876845i
$351$	−1.61108e9	−	3.42445e8i	−1.98857	−	0.422684i
$352$	1.83555e7	+	1.74641e8i	0.0224320	+	0.213426i
$353$	−6.64492e8	+	7.37993e8i	−0.804041	+	0.892978i	−0.996084	−	0.0884085i	$-0.971822\pi$
$353$	−6.64492e8	+	7.37993e8i	−0.804041	+	0.892978i	0.192043	+	0.981386i	$0.438489\pi$
$354$	−9.16357e8	−	1.01772e9i	−1.09788	−	1.21931i
$355$	−1.66252e7	+	1.58178e8i	−0.0197227	+	0.187649i
$356$	1.61247e8	−	4.96267e8i	0.189416	−	0.582962i
$357$	1.85721e8	−	5.71590e8i	0.216034	−	0.664884i
$358$	−7.74264e7	+	7.36663e8i	−0.0891864	+	0.848552i
$359$	7.59940e8	+	8.43999e8i	0.866860	+	0.962746i	0.999596	−	0.0284058i	$-0.00904307\pi$
$359$	7.59940e8	+	8.43999e8i	0.866860	+	0.962746i	−0.132737	+	0.991151i	$0.542376\pi$
$360$	3.19719e8	−	3.55083e8i	0.361168	−	0.401118i
$361$	8.68010e7	+	8.25856e8i	0.0971068	+	0.923909i
$362$	−1.87376e8	−	3.98279e7i	−0.207603	−	0.0441273i
$363$	7.37375e8	−	3.28301e8i	0.809125	−	0.360245i
$364$	−1.31843e8	−	9.57892e7i	−0.143285	−	0.104103i
$365$	3.34024e8	+	1.48717e8i	0.359545	+	0.160080i
$366$	−1.48515e8	−	2.57235e8i	−0.158338	−	0.274249i
$367$	−6.81396e8	+	1.18021e9i	−0.719562	+	1.24632i	0.241611	+	0.970373i	$0.422324\pi$
$367$	−6.81396e8	+	1.18021e9i	−0.719562	+	1.24632i	−0.961173	+	0.275945i	$0.911009\pi$
$368$	−2.84414e8	+	2.06639e8i	−0.297498	+	0.216145i
$369$	−4.13966e9	+	8.79912e8i	−4.28916	+	0.911690i
$370$	−1.44346e8	−	4.44250e8i	−0.148149	−	0.455954i
$371$	−2.12539e7			−0.0216088
$372$	−7.23828e8	−	5.81020e8i	−0.729013	−	0.585182i
$373$	−2.64620e8			−0.264023			−0.132012	−	0.991248i	$-0.542144\pi$
$373$	−2.64620e8			−0.264023			−0.132012	+	0.991248i	$0.542144\pi$
$374$	−2.05966e8	−	6.33898e8i	−0.203584	−	0.626568i
$375$	−1.85739e9	+	3.94800e8i	−1.81884	+	0.386605i
$376$	2.19777e7	−	1.59677e7i	0.0213218	−	0.0154912i
$377$	1.18089e8	−	2.04536e8i	0.113505	−	0.196596i
$378$	5.05778e8	+	8.76034e8i	0.481658	+	0.834256i
$379$	1.39804e9	+	6.22448e8i	1.31911	+	0.587308i	0.940986	−	0.338446i	$-0.109901\pi$
$379$	1.39804e9	+	6.22448e8i	1.31911	+	0.587308i	0.378128	+	0.925753i	$0.376568\pi$
$380$	7.05299e7	+	5.12430e7i	0.0659373	+	0.0479062i
$381$	2.23054e9	−	9.93100e8i	2.06620	−	0.919931i
$382$	−9.19780e8	−	1.95505e8i	−0.844233	−	0.179447i
$383$	3.80395e7	+	3.61922e8i	0.0345970	+	0.329169i	0.998107	+	0.0614973i	$0.0195875\pi$
$383$	3.80395e7	+	3.61922e8i	0.0345970	+	0.329169i	−0.963510	+	0.267672i	$0.913746\pi$
$384$	−1.22695e8	+	1.36266e8i	−0.110577	+	0.122809i
$385$	−2.71089e8	−	3.01074e8i	−0.242102	−	0.268882i
$386$	−7.82201e7	+	7.44215e8i	−0.0692250	+	0.658632i
$387$	5.92693e8	−	1.82412e9i	0.519806	−	1.59980i
$388$	−3.02739e7	+	9.31735e7i	−0.0263122	+	0.0809807i
$389$	1.04452e8	−	9.93793e8i	0.0899689	−	0.855997i	−0.852730	−	0.522352i	$-0.825055\pi$
$389$	1.04452e8	−	9.93793e8i	0.0899689	−	0.855997i	0.942699	−	0.333645i	$-0.108279\pi$
$390$	4.60909e8	+	5.11891e8i	0.393449	+	0.436970i
$391$	8.92863e8	−	9.91625e8i	0.755381	−	0.838936i
$392$	−3.36129e7	−	3.19806e8i	−0.0281842	−	0.268154i
$393$	−9.07891e8	−	1.92978e8i	−0.754501	−	0.160374i
$394$	−1.20885e9	+	5.38215e8i	−0.995716	+	0.443322i
$395$	1.12724e9	+	8.18985e8i	0.920291	+	0.668630i
$396$	1.71007e9	+	7.61374e8i	1.38383	+	0.616120i
$397$	2.48134e8	+	4.29780e8i	0.199030	+	0.344731i	0.948214	−	0.317631i	$-0.102887\pi$
$397$	2.48134e8	+	4.29780e8i	0.199030	+	0.344731i	−0.749184	+	0.662362i	$0.769554\pi$
$398$	−5.24334e8	+	9.08172e8i	−0.416886	+	0.722067i
$399$	−2.49154e8	+	1.81021e8i	−0.196364	+	0.142667i
$400$	1.95870e8	−	4.16335e7i	0.153024	−	0.0325262i
$401$	−3.11360e8	−	9.58269e8i	−0.241134	−	0.742133i	−0.996248	−	0.0865405i	$-0.972419\pi$
$401$	−3.11360e8	−	9.58269e8i	−0.241134	−	0.742133i	0.755115	−	0.655593i	$-0.227581\pi$
$402$	3.19695e9			2.45440
$403$	6.72580e8	−	6.78377e8i	0.511890	−	0.516301i
$404$	2.88441e8			0.217631
$405$	−6.90537e8	−	2.12526e9i	−0.516529	−	1.58971i
$406$	−1.41880e8	+	3.01576e7i	−0.105216	+	0.0223643i
$407$	1.48049e9	−	1.07564e9i	1.08849	−	0.790838i
$408$	3.47989e8	−	6.02734e8i	0.253662	−	0.439355i
$409$	−3.96053e7	−	6.85984e7i	−0.0286234	−	0.0495773i	0.851359	−	0.524584i	$-0.175779\pi$
$409$	−3.96053e7	−	6.85984e7i	−0.0286234	−	0.0495773i	−0.879982	+	0.475007i	$0.842446\pi$
$410$	9.68997e8	+	4.31425e8i	0.694351	+	0.309145i
$411$	3.77468e9	+	2.74247e9i	2.68185	+	1.94848i
$412$	8.95765e8	−	3.98820e8i	0.631036	−	0.280955i
$413$	−8.46714e8	−	1.79975e8i	−0.591441	−	0.125715i
$414$	3.91724e8	+	3.72701e9i	0.271318	+	2.58142i
$415$	−9.94614e8	+	1.10463e9i	−0.683103	+	0.758663i
$416$	−1.26277e8	−	1.40245e8i	−0.0860001	−	0.0955127i
$417$	3.84037e8	−	3.65387e9i	0.259356	−	2.46761i
$418$	−1.05542e8	+	3.24825e8i	−0.0706820	+	0.217537i
$419$	3.18756e7	−	9.81030e7i	0.0211694	−	0.0651528i	−0.939914	−	0.341412i	$-0.889095\pi$
$419$	3.18756e7	−	9.81030e7i	0.0211694	−	0.0651528i	0.961083	+	0.276259i	$0.0890948\pi$
$420$	4.42198e7	−	4.20724e8i	0.0291236	−	0.277092i
$421$	4.31004e8	+	4.78679e8i	0.281510	+	0.312649i	0.867272	−	0.497834i	$-0.165871\pi$
$421$	4.31004e8	+	4.78679e8i	0.281510	+	0.312649i	−0.585762	+	0.810483i	$0.699205\pi$
$422$	−7.43218e8	+	8.25428e8i	−0.481419	+	0.534670i
$423$	−3.02699e7	−	2.87999e8i	−0.0194455	−	0.185012i
$424$	−2.40747e7	−	5.11723e6i	−0.0153384	−	0.00326028i
$425$	−6.94345e8	+	3.09142e8i	−0.438747	+	0.195343i
$426$	−5.26380e8	−	3.82438e8i	−0.329888	−	0.239677i
$427$	−1.71517e8	−	7.63643e7i	−0.106613	−	0.0474671i
$428$	7.19091e6	+	1.24550e7i	0.00443334	+	0.00767877i
$429$	−1.34928e9	+	2.33702e9i	−0.825090	+	1.42910i
$430$	−3.88899e8	+	2.82552e8i	−0.235884	+	0.171379i
$431$	−2.82981e9	+	6.01496e8i	−1.70250	+	0.361878i	−0.953663	−	0.300875i	$-0.902721\pi$
$431$	−2.82981e9	+	6.01496e8i	−1.70250	+	0.361878i	−0.748838	+	0.662753i	$0.769388\pi$
$432$	3.61984e8	+	1.11407e9i	0.216021	+	0.664844i
$433$	6.56851e8			0.388830			0.194415	−	0.980919i	$-0.437719\pi$
$433$	6.56851e8			0.388830			0.194415	+	0.980919i	$0.437719\pi$
$434$	−5.86013e8	−	2.81909e7i	−0.344107	−	0.0165537i
$435$	6.13090e8			0.357118
$436$	1.43488e8	+	4.41610e8i	0.0829110	+	0.255174i
$437$	−6.68820e8	+	1.42162e8i	−0.383375	+	0.0814890i
$438$	−1.21008e9	+	8.79177e8i	−0.688107	+	0.499939i
$439$	1.08592e9	−	1.88087e9i	0.612594	−	1.06104i	−0.378207	−	0.925721i	$-0.623459\pi$
$439$	1.08592e9	−	1.88087e9i	0.612594	−	1.06104i	0.990802	−	0.135323i	$-0.0432073\pi$
$440$	−2.34578e8	−	4.06301e8i	−0.131281	−	0.227386i
$441$	−3.13152e9	−	1.39424e9i	−1.73868	−	0.774110i
$442$	5.79499e8	+	4.21031e8i	0.319209	+	0.231919i
$443$	1.33731e9	−	5.95410e8i	0.730837	−	0.325389i	−0.00736199	−	0.999973i	$-0.502343\pi$
$443$	1.33731e9	−	5.95410e8i	0.730837	−	0.325389i	0.738199	+	0.674583i	$0.235677\pi$
$444$	1.86911e9	+	3.97292e8i	1.01343	+	0.215412i
$445$	1.45723e8	+	1.38646e9i	0.0783913	+	0.745843i
$446$	1.71563e9	−	1.90540e9i	0.915697	−	1.01698i
$447$	−4.79445e8	−	5.32478e8i	−0.253900	−	0.281984i
$448$	−1.21151e7	+	1.15268e8i	−0.00636583	+	0.0605668i
$449$	7.97057e7	−	2.45309e8i	0.0415554	−	0.127894i	−0.928127	−	0.372265i	$-0.878581\pi$
$449$	7.97057e7	−	2.45309e8i	0.0415554	−	0.127894i	0.969682	+	0.244371i	$0.0785813\pi$
$450$	6.59628e8	−	2.03013e9i	0.341237	−	1.05022i
$451$	−4.34365e8	+	4.13271e9i	−0.222965	+	2.12137i
$452$	−1.10532e8	−	1.22758e8i	−0.0562993	−	0.0625267i
$453$	1.15641e9	−	1.28432e9i	0.584478	−	0.649129i
$454$	−2.71491e8	−	2.58306e9i	−0.136163	−	1.29551i
$455$	4.25880e8	+	9.05235e7i	0.211957	+	0.0450528i
$456$	−3.25804e8	+	1.45057e8i	−0.160909	+	0.0716411i
$457$	−1.26897e8	−	9.21960e7i	−0.0621934	−	0.0451862i	0.556254	−	0.831012i	$-0.312238\pi$
$457$	−1.26897e8	−	9.21960e7i	−0.0621934	−	0.0451862i	−0.618448	+	0.785826i	$0.712238\pi$
$458$	1.24402e9	+	5.53874e8i	0.605060	+	0.269390i
$459$	−2.22309e9	−	3.85051e9i	−1.07303	−	1.85855i
$460$	4.69622e8	−	8.13408e8i	0.224955	−	0.389633i
$461$	1.23520e9	−	8.97425e8i	0.587197	−	0.426624i	−0.254115	−	0.967174i	$-0.581784\pi$
$461$	1.23520e9	−	8.97425e8i	0.587197	−	0.426624i	0.841312	+	0.540551i	$0.181784\pi$
$462$	1.62112e9	−	3.44579e8i	0.764835	−	0.162571i
$463$	−4.27912e8	−	1.31698e9i	−0.200365	−	0.616659i	−0.999872	−	0.0160026i	$-0.994906\pi$
$463$	−4.27912e8	−	1.31698e9i	−0.200365	−	0.616659i	0.799507	−	0.600656i	$-0.205094\pi$
$464$	−1.67971e8			−0.0780588
$465$	2.39803e9	+	6.31534e8i	1.10603	+	0.291281i
$466$	−7.44181e8			−0.340665
$467$	−6.08134e8	−	1.87164e9i	−0.276306	−	0.850382i	−0.988871	−	0.148776i	$-0.952467\pi$
$467$	−6.08134e8	−	1.87164e9i	−0.276306	−	0.850382i	0.712565	−	0.701606i	$-0.247533\pi$
$468$	−1.96776e9	+	4.18260e8i	−0.887383	+	0.188619i
$469$	1.63483e9	−	1.18777e9i	0.731758	−	0.531653i
$470$	−3.62893e7	+	6.28550e7i	−0.0161227	+	0.0279253i
$471$	2.98893e9	+	5.17698e9i	1.31808	+	2.28299i
$472$	−9.15755e8	−	4.07720e8i	−0.400850	−	0.178470i
$473$	−1.52358e9	−	1.10695e9i	−0.661990	−	0.480964i
$474$	−5.20712e9	+	2.31836e9i	−2.24581	+	0.999900i
$475$	3.80961e8	+	8.09757e7i	0.163099	+	0.0346679i
$476$	−4.59842e7	−	4.37510e8i	−0.0195427	−	0.185936i
$477$	−1.75558e8	+	1.94976e8i	−0.0740637	+	0.0822560i
$478$	1.84311e9	+	2.04698e9i	0.771885	+	0.857266i
$479$	−6.92168e7	+	6.58554e8i	−0.0287765	+	0.273790i	0.970667	+	0.240428i	$0.0772879\pi$
$479$	−6.92168e7	+	6.58554e8i	−0.0287765	+	0.273790i	−0.999443	+	0.0333614i	$0.989379\pi$
$480$	1.51385e8	−	4.65914e8i	0.0624795	−	0.192292i
$481$	−6.07734e8	+	1.87041e9i	−0.249004	+	0.766355i
$482$	4.34646e7	−	4.13539e8i	0.0176796	−	0.168210i
$483$	2.22015e9	+	2.46573e9i	0.896536	+	0.995704i
$484$	3.95334e8	−	4.39063e8i	0.158491	−	0.176023i
$485$	−2.73593e7	−	2.60307e8i	−0.0108895	−	0.103607i
$486$	4.04739e9	+	8.60300e8i	1.59937	+	0.339956i
$487$	3.85283e9	−	1.71539e9i	1.51157	−	0.672994i	0.527302	−	0.849678i	$-0.323204\pi$
$487$	3.85283e9	−	1.71539e9i	1.51157	−	0.672994i	0.984268	+	0.176684i	$0.0565371\pi$
$488$	−1.75894e8	−	1.27795e8i	−0.0685145	−	0.0497787i
$489$	−6.09662e9	−	2.71439e9i	−2.35781	−	1.04976i
$490$	4.29563e8	+	7.44024e8i	0.164945	+	0.285694i
$491$	1.96094e9	−	3.39645e9i	0.747617	−	1.29491i	−0.201344	−	0.979521i	$-0.564531\pi$
$491$	1.96094e9	−	3.39645e9i	0.747617	−	1.29491i	0.948962	−	0.315391i	$-0.102136\pi$
$492$	−3.51043e9	+	2.55048e9i	−1.32887	+	0.965480i
$493$	6.23619e8	−	1.32554e8i	0.234399	−	0.0498230i
$494$	−1.13425e8	−	3.49086e8i	−0.0423315	−	0.130283i
$495$	−5.00114e9			−1.85332
$496$	−6.56999e8	−	1.73024e8i	−0.241757	−	0.0636681i
$497$	−4.11264e8			−0.150270
$498$	−1.87904e9	−	5.78309e9i	−0.681763	−	2.09825i
$499$	2.58872e9	−	5.50250e8i	0.932681	−	0.198248i	0.283579	−	0.958949i	$-0.408478\pi$
$499$	2.58872e9	−	5.50250e8i	0.932681	−	0.198248i	0.649102	+	0.760701i	$0.275145\pi$
$500$	−1.12448e9	+	8.16982e8i	−0.402306	+	0.292292i
$501$	−1.20657e9	+	2.08984e9i	−0.428666	+	0.742472i
$502$	−1.12809e9	−	1.95391e9i	−0.397997	−	0.689351i
$503$	6.16079e8	+	2.74296e8i	0.215848	+	0.0961019i	0.511813	−	0.859097i	$-0.328974\pi$
$503$	6.16079e8	+	2.74296e8i	0.215848	+	0.0961019i	−0.295964	+	0.955199i	$0.595641\pi$
$504$	9.99547e8	+	7.26214e8i	0.347773	+	0.252672i
$505$	−7.03998e8	+	3.13440e8i	−0.243249	+	0.108302i
$506$	3.59924e9	+	7.65041e8i	1.23505	+	0.262517i
$507$	2.70342e8	+	2.57214e9i	0.0921269	+	0.876528i
$508$	1.19587e9	−	1.32815e9i	0.404727	−	0.449495i
$509$	8.26843e8	+	9.18302e8i	0.277914	+	0.308655i	0.865901	−	0.500216i	$-0.166746\pi$
$509$	8.26843e8	+	9.18302e8i	0.277914	+	0.308655i	−0.587987	+	0.808871i	$0.700079\pi$
$510$	−1.94363e8	+	1.84924e9i	−0.0648812	+	0.617303i
$511$	−2.92159e8	+	8.99172e8i	−0.0968602	+	0.298105i
$512$	−4.14756e7	+	1.27649e8i	−0.0136568	+	0.0420312i
$513$	−2.38151e8	+	2.26586e9i	−0.0778829	+	0.741006i
$514$	−1.03262e9	−	1.14684e9i	−0.335406	−	0.372506i
$515$	−1.75291e9	+	1.94680e9i	−0.565502	+	0.628054i
$516$	−2.05553e8	−	1.95571e9i	−0.0658644	−	0.626658i
$517$	−2.78126e8	−	5.91175e7i	−0.0885165	−	0.0188148i
$518$	1.10342e9	−	4.91273e8i	0.348808	−	0.155299i
$519$	−2.56525e9	−	1.86376e9i	−0.805458	−	0.585200i
$520$	4.60606e8	+	2.05075e8i	0.143654	+	0.0639589i
$521$	8.84282e8	+	1.53162e9i	0.273942	+	0.474482i	0.969868	−	0.243632i	$-0.0783390\pi$
$521$	8.84282e8	+	1.53162e9i	0.273942	+	0.474482i	−0.695926	+	0.718114i	$0.745006\pi$
$522$	−8.95277e8	+	1.55066e9i	−0.275493	+	0.477168i
$523$	4.71581e9	−	3.42624e9i	1.44145	−	1.04728i	0.453717	−	0.891146i	$-0.350098\pi$
$523$	4.71581e9	−	3.42624e9i	1.44145	−	1.04728i	0.987736	−	0.156132i	$-0.0499025\pi$
$524$	−6.64552e8	+	1.41255e8i	−0.201776	+	0.0428888i
$525$	−5.84016e8	−	1.79742e9i	−0.176144	−	0.542115i
$526$	1.10354e9			0.330626
$527$	2.57575e9	+	1.23910e8i	0.766597	+	0.0368781i
$528$	1.91923e9			0.567425
$529$	1.22426e9	+	3.76787e9i	0.359565	+	1.10663i
$530$	6.43198e7	−	1.36716e7i	0.0187663	−	0.00398891i
$531$	−8.64488e9	+	6.28087e9i	−2.50570	+	1.82049i
$532$	−1.12713e8	+	1.95225e8i	−0.0324552	+	0.0562140i
$533$	−2.23292e9	−	3.86752e9i	−0.638744	−	1.10634i
$534$	−5.20995e9	−	2.31962e9i	−1.48061	−	0.659208i
$535$	−3.10854e7	−	2.25849e7i	−0.00877643	−	0.00637645i
$536$	2.13777e9	−	9.51798e8i	0.599632	−	0.266973i
$537$	7.91870e9	+	1.68317e9i	2.20670	+	0.469049i
$538$	−2.46841e8	−	2.34854e9i	−0.0683407	−	0.650219i
$539$	−2.25214e9	+	2.50125e9i	−0.619490	+	0.688014i
$540$	−2.09412e9	−	2.32576e9i	−0.572301	−	0.635604i
$541$	2.99038e8	−	2.84516e9i	0.0811963	−	0.772531i	−0.875847	−	0.482588i	$-0.839697\pi$
$541$	2.99038e8	−	2.84516e9i	0.0811963	−	0.772531i	0.957044	−	0.289943i	$-0.0936365\pi$
$542$	−1.42875e9	+	4.39723e9i	−0.385440	+	1.18626i
$543$	−6.46972e8	+	1.99118e9i	−0.173415	+	0.533716i
$544$	5.32506e7	−	5.06646e8i	0.0141817	−	0.134930i
$545$	−8.30095e8	−	9.21914e8i	−0.219655	−	0.243951i
$546$	−1.19180e9	+	1.32363e9i	−0.313350	+	0.348010i
$547$	−2.27711e8	−	2.16653e9i	−0.0594879	−	0.565989i	−0.983152	−	0.182787i	$-0.941488\pi$
$547$	−2.27711e8	−	2.16653e9i	−0.0594879	−	0.565989i	0.923665	−	0.383202i	$-0.125179\pi$
$548$	3.34059e9	+	7.10063e8i	0.867143	+	0.184317i
$549$	−2.11727e9	+	9.42670e8i	−0.546102	+	0.243140i
$550$	−1.69564e9	−	1.23196e9i	−0.434575	−	0.315737i
$551$	−2.98453e8	−	1.32880e8i	−0.0760056	−	0.0338399i
$552$	1.92114e9	+	3.32751e9i	0.486151	+	0.842039i
$553$	−1.80142e9	+	3.12016e9i	−0.452979	+	0.784582i
$554$	2.04618e8	−	1.48664e8i	0.0511282	−	0.0371468i
$555$	−4.99368e9	+	1.06144e9i	−1.23992	+	0.263554i
$556$	−8.31029e8	−	2.55764e9i	−0.205047	−	0.631071i
$557$	−6.89948e9			−1.69170			−0.845850	−	0.533421i	$-0.820906\pi$
$557$	−6.89948e9			−1.69170			−0.845850	+	0.533421i	$0.820906\pi$
$558$	−5.09908e9	+	5.14303e9i	−1.24243	+	1.25314i
$559$	2.02390e9			0.490059
$560$	−9.56886e7	−	2.94499e8i	−0.0230251	−	0.0708641i
$561$	−7.12544e9	+	1.51456e9i	−1.70389	+	0.362173i
$562$	−3.12536e9	+	2.27071e9i	−0.742716	+	0.539615i
$563$	−3.62350e8	+	6.27609e8i	−0.0855754	+	0.148221i	−0.905636	−	0.424055i	$-0.860606\pi$
$563$	−3.62350e8	+	6.27609e8i	−0.0855754	+	0.148221i	0.820061	+	0.572276i	$0.193940\pi$
$564$	−1.48453e8	−	2.57128e8i	−0.0348427	−	0.0603494i
$565$	4.03173e8	+	1.79504e8i	0.0940420	+	0.0418702i
$566$	8.07319e8	+	5.86552e8i	0.187149	+	0.135972i
$567$	5.27866e9	−	2.35021e9i	1.21614	−	0.541460i
$568$	−4.65845e8	−	9.90184e7i	−0.106665	−	0.0226724i
$569$	−8.46815e8	−	8.05691e9i	−0.192706	−	1.83348i	−0.481923	−	0.876213i	$-0.660062\pi$
$569$	−8.46815e8	−	8.05691e9i	−0.192706	−	1.83348i	0.289217	−	0.957264i	$-0.406605\pi$
$570$	6.37561e8	−	7.08083e8i	0.144198	−	0.160148i
$571$	−4.99020e8	−	5.54218e8i	−0.112174	−	0.124582i	0.684443	−	0.729067i	$-0.260046\pi$
$571$	−4.99020e8	−	5.54218e8i	−0.112174	−	0.124582i	−0.796617	+	0.604485i	$0.793379\pi$
$572$	−2.06472e8	+	1.96445e9i	−0.0461291	+	0.438889i
$573$	−3.17583e9	+	9.77419e9i	−0.705205	+	2.17040i
$574$	−8.47546e8	+	2.60848e9i	−0.187056	+	0.575699i
$575$	4.38604e8	−	4.17304e9i	0.0962133	−	0.915408i
$576$	9.57356e8	+	1.06325e9i	0.208735	+	0.231823i
$577$	5.34984e9	−	5.94160e9i	1.15938	−	1.28762i	0.208513	−	0.978020i	$-0.433138\pi$
$577$	5.34984e9	−	5.94160e9i	1.15938	−	1.28762i	0.950866	−	0.309602i	$-0.100196\pi$
$578$	−1.41018e8	−	1.34170e9i	−0.0303758	−	0.289007i
$579$	7.99987e9	+	1.70043e9i	1.71281	+	0.364068i
$580$	4.09967e8	−	1.82529e8i	0.0872472	−	0.0388450i
$581$	−3.10950e9	−	2.25918e9i	−0.657769	−	0.477897i
$582$	9.78163e8	+	4.35506e8i	0.205675	+	0.0915722i
$583$	1.28807e8	+	2.23100e8i	0.0269215	+	0.0466293i
$584$	−5.47423e8	+	9.48164e8i	−0.113731	+	0.196987i
$585$	4.34820e9	−	3.15915e9i	0.897974	−	0.652416i
$586$	5.66426e9	−	1.20398e9i	1.16279	−	0.247159i
$587$	1.41580e9	+	4.35739e9i	0.288914	+	0.889187i	0.985198	+	0.171420i	$0.0548355\pi$
$587$	1.41580e9	+	4.35739e9i	0.288914	+	0.889187i	−0.696284	+	0.717767i	$0.745164\pi$
$588$	−3.51453e9			−0.712929
$589$	−1.03049e9	−	8.27176e8i	−0.207797	−	0.166799i
$590$	2.67814e9			0.536848
$591$	4.46909e9	+	1.37545e10i	0.890560	+	2.74086i
$592$	1.36814e9	−	2.90807e8i	0.271022	−	0.0576076i
$593$	7.42107e7	−	5.39172e7i	0.0146142	−	0.0106178i	−0.580454	−	0.814293i	$-0.697125\pi$
$593$	7.42107e7	−	5.39172e7i	0.0146142	−	0.0106178i	0.595068	+	0.803675i	$0.297125\pi$
$594$	6.13041e9	−	1.06182e10i	1.20015	−	2.07873i
$595$	5.87663e8	+	1.01786e9i	0.114372	+	0.198098i
$596$	−4.79130e8	−	2.13322e8i	−0.0927025	−	0.0412738i
$597$	9.27236e9	+	6.73676e9i	1.78353	+	1.29581i
$598$	−3.61259e9	+	1.60843e9i	−0.690819	+	0.307572i
$599$	−8.31672e9	−	1.76777e9i	−1.58110	−	0.336072i	−0.668110	−	0.744062i	$-0.732897\pi$
$599$	−8.31672e9	−	1.76777e9i	−1.58110	−	0.336072i	−0.912987	+	0.407990i	$0.866230\pi$
$600$	−2.28767e8	−	2.17657e9i	−0.0432379	−	0.411381i
$601$	1.24419e9	−	1.38182e9i	0.233790	−	0.259651i	−0.614822	−	0.788666i	$-0.710772\pi$
$601$	1.24419e9	−	1.38182e9i	0.233790	−	0.259651i	0.848612	+	0.529016i	$0.177439\pi$
$602$	−8.31724e8	−	9.23723e8i	−0.155379	−	0.172566i
$603$	2.60747e9	−	2.48084e10i	0.484293	−	4.60774i
$604$	3.90912e8	−	1.20310e9i	0.0721854	−	0.222164i
$605$	−4.87776e8	+	1.50122e9i	−0.0895523	+	0.275614i
$606$	3.29523e8	−	3.13520e9i	0.0601495	−	0.572284i
$607$	3.17045e9	+	3.52114e9i	0.575388	+	0.639033i	0.958644	−	0.284609i	$-0.0918638\pi$
$607$	3.17045e9	+	3.52114e9i	0.575388	+	0.639033i	−0.383256	+	0.923642i	$0.625197\pi$
$608$	−1.74676e8	+	1.93997e8i	−0.0315188	+	0.0350052i
$609$	1.65709e8	+	1.57662e9i	0.0297294	+	0.282857i
$610$	5.68176e8	+	1.20770e8i	0.101351	+	0.0215428i
$611$	2.79157e8	−	1.24289e8i	0.0495114	−	0.0220439i
$612$	−4.39340e9	−	3.19199e9i	−0.774766	−	0.562900i
$613$	−5.21583e9	−	2.32224e9i	−0.914559	−	0.407188i	−0.105166	−	0.994455i	$-0.533537\pi$
$613$	−5.21583e9	−	2.32224e9i	−0.914559	−	0.407188i	−0.809394	+	0.587267i	$0.800204\pi$
$614$	2.93757e9	+	5.08802e9i	0.512152	+	0.887073i
$615$	5.79638e9	−	1.00396e10i	1.00483	−	1.74042i
$616$	9.81439e8	−	7.13057e8i	0.169173	−	0.122911i
$617$	−4.45926e9	+	9.47846e8i	−0.764302	+	0.162457i	−0.573539	−	0.819179i	$-0.694430\pi$
$617$	−4.45926e9	+	9.47846e8i	−0.764302	+	0.162457i	−0.190764	+	0.981636i	$0.561096\pi$
$618$	−3.31162e9	−	1.01921e10i	−0.564393	−	1.73702i
$619$	3.81790e9			0.647004			0.323502	−	0.946227i	$-0.395140\pi$
$619$	3.81790e9			0.647004			0.323502	+	0.946227i	$0.395140\pi$
$620$	1.79156e9	−	2.91640e8i	0.301898	−	0.0491447i
$621$	2.45460e10			4.11301
$622$	5.15380e8	+	1.58618e9i	0.0858739	+	0.264293i
$623$	−3.52603e9	+	7.49481e8i	−0.584222	+	0.124180i
$624$	−1.66866e9	+	1.21235e9i	−0.274929	+	0.199748i
$625$	−5.29697e7	+	9.17463e7i	−0.00867856	+	0.0150317i
$626$	−2.26445e9	−	3.92214e9i	−0.368937	−	0.639018i
$627$	3.41011e9	+	1.51828e9i	0.552500	+	0.245989i
$628$	3.53996e9	+	2.57193e9i	0.570348	+	0.414382i
$629$	−4.84995e9	+	2.15934e9i	−0.777070	+	0.345974i
$630$	−3.22875e9	−	6.86292e8i	−0.514450	−	0.109350i
$631$	−5.26028e8	−	5.00482e9i	−0.0833501	−	0.793023i	−0.953734	−	0.300650i	$-0.902796\pi$
$631$	−5.26028e8	−	5.00482e9i	−0.0833501	−	0.793023i	0.870384	−	0.492373i	$-0.163870\pi$
$632$	−2.79173e9	+	3.10053e9i	−0.439910	+	0.488569i
$633$	8.12290e9	+	9.02140e9i	1.27291	+	1.41371i
$634$	3.42950e8	−	3.26296e9i	0.0534465	−	0.508509i
$635$	−1.47551e9	+	4.54115e9i	−0.228683	+	0.703814i
$636$	−8.31253e7	+	2.55833e8i	−0.0128125	+	0.0394328i
$637$	3.78095e8	−	3.59733e9i	0.0579579	−	0.551433i
$638$	1.17641e9	+	1.30653e9i	0.179343	+	0.199181i
$639$	−3.39704e9	+	3.77279e9i	−0.515048	+	0.572018i
$640$	−3.74825e7	−	3.56623e8i	−0.00565196	−	0.0537748i
$641$	4.35608e9	+	9.25914e8i	0.653270	+	0.138857i	0.522612	−	0.852571i	$-0.324958\pi$
$641$	4.35608e9	+	9.25914e8i	0.653270	+	0.138857i	0.130658	+	0.991427i	$0.458291\pi$
$642$	1.43595e8	−	6.39326e7i	0.0214174	−	0.00953563i
$643$	−1.36055e9	−	9.88500e8i	−0.201826	−	0.146635i	0.482282	−	0.876016i	$-0.339808\pi$
$643$	−1.36055e9	−	9.88500e8i	−0.201826	−	0.146635i	−0.684108	+	0.729381i	$0.739808\pi$
$644$	2.21869e9	+	9.87825e8i	0.327338	+	0.145740i
$645$	2.62691e9	+	4.54993e9i	0.385465	+	0.667646i
$646$	4.95418e8	−	8.58089e8i	0.0723033	−	0.125233i
$647$	−1.93818e9	+	1.40817e9i	−0.281338	+	0.204404i	−0.719501	−	0.694492i	$-0.755629\pi$
$647$	−1.93818e9	+	1.40817e9i	−0.281338	+	0.204404i	0.438163	+	0.898896i	$0.355629\pi$
$648$	6.54508e9	−	1.39120e9i	0.944935	−	0.200852i
$649$	3.24223e9	+	9.97856e9i	0.465572	+	1.43288i
$650$	2.25247e9			0.321708
$651$	−9.75899e8	+	6.33746e9i	−0.138635	+	0.900288i
$652$	−4.88489e9			−0.690221
$653$	8.82512e8	+	2.71609e9i	0.124029	+	0.381723i	0.993723	−	0.111869i	$-0.0356836\pi$
$653$	8.82512e8	+	2.71609e9i	0.124029	+	0.381723i	−0.869694	+	0.493592i	$0.835684\pi$
$654$	4.96400e9	−	1.05513e9i	0.693920	−	0.147497i
$655$	1.46847e9	−	1.06691e9i	0.204184	−	0.148348i
$656$	−1.58806e9	+	2.75061e9i	−0.219636	+	0.380421i
$657$	5.83546e9	+	1.01073e10i	0.802780	+	1.39046i
$658$	−1.71446e8	−	7.63328e7i	−0.0234605	−	0.0104453i
$659$	−4.31025e9	−	3.13158e9i	−0.586683	−	0.426250i	0.254444	−	0.967087i	$-0.418107\pi$
$659$	−4.31025e9	−	3.13158e9i	−0.586683	−	0.426250i	−0.841127	+	0.540838i	$0.818107\pi$
$660$	−4.68427e9	+	2.08557e9i	−0.634217	+	0.282372i
$661$	1.19700e9	+	2.54430e8i	0.161208	+	0.0342659i	0.287809	−	0.957688i	$-0.407073\pi$
$661$	1.19700e9	+	2.54430e8i	0.161208	+	0.0342659i	−0.126600	+	0.991954i	$0.540407\pi$
$662$	7.39945e8	+	7.04011e9i	0.0991281	+	0.943141i
$663$	5.23842e9	−	5.81786e9i	0.698077	−	0.775293i
$664$	−2.97824e9	−	3.30767e9i	−0.394795	−	0.438464i
$665$	6.29541e7	−	5.98968e8i	0.00830134	−	0.0789819i
$666$	4.60746e9	−	1.41803e10i	0.604368	−	1.86005i
$667$	−1.08765e9	+	3.34745e9i	−0.141922	+	0.436791i
$668$	−1.84634e8	+	1.75667e9i	−0.0239659	+	0.228020i
$669$	−1.87507e10	−	2.08248e10i	−2.42118	−	2.68899i
$670$	−4.18338e9	+	4.64611e9i	−0.537360	+	0.596798i
$671$	2.37871e8	+	2.26319e9i	0.0303957	+	0.289196i
$672$	1.23906e9	+	2.63370e8i	0.157507	+	0.0334792i
$673$	−6.05904e9	+	2.69766e9i	−0.766216	+	0.341141i	−0.752351	−	0.658762i	$-0.771080\pi$
$673$	−6.05904e9	+	2.69766e9i	−0.766216	+	0.341141i	−0.0138652	+	0.999904i	$0.504414\pi$
$674$	5.33084e9	+	3.87308e9i	0.670635	+	0.487245i
$675$	−1.27727e10	−	5.68676e9i	−1.59852	−	0.711707i
$676$	9.46553e8	+	1.63948e9i	0.117850	+	0.204123i
$677$	−6.39291e8	+	1.10728e9i	−0.0791841	+	0.137151i	−0.902898	−	0.429855i	$-0.858565\pi$
$677$	−6.39291e8	+	1.10728e9i	−0.0791841	+	0.137151i	0.823714	+	0.567005i	$0.191898\pi$
$678$	−1.46059e9	+	1.06118e9i	−0.179980	+	0.130763i
$679$	6.62009e8	−	1.40714e8i	0.0811558	−	0.0172502i
$680$	4.20588e8	+	1.29444e9i	0.0512951	+	0.157870i
$681$	−2.83867e10			−3.44429
$682$	3.25554e9	+	6.32215e9i	0.392986	+	0.763167i
$683$	−7.39079e9			−0.887602			−0.443801	−	0.896125i	$-0.646370\pi$
$683$	−7.39079e9			−0.887602			−0.443801	+	0.896125i	$0.646370\pi$
$684$	8.59916e8	+	2.64655e9i	0.102745	+	0.316216i
$685$	−8.92498e9	+	1.89706e9i	−1.06094	+	0.225509i
$686$	−4.15383e9	+	3.01794e9i	−0.491264	+	0.356924i
$687$	7.44154e9	−	1.28891e10i	0.875617	−	1.51661i
$688$	−7.19706e8	−	1.24657e9i	−0.0842550	−	0.145934i
$689$	−2.52919e8	−	1.12607e8i	−0.0294587	−	0.0131159i
$690$	−8.30483e9	−	6.03381e9i	−0.962407	−	0.699229i
$691$	−3.31627e9	+	1.47650e9i	−0.382363	+	0.170239i	−0.588912	−	0.808197i	$-0.700444\pi$
$691$	−3.31627e9	+	1.47650e9i	−0.382363	+	0.170239i	0.206549	+	0.978436i	$0.433777\pi$
$692$	−2.27023e9	−	4.82553e8i	−0.260435	−	0.0553572i
$693$	−1.35174e9	−	1.28609e10i	−0.154286	−	1.46793i
$694$	3.75874e9	−	4.17450e9i	0.426859	−	0.474074i
$695$	4.80761e9	+	5.33939e9i	0.543228	+	0.603316i
$696$	−1.91895e8	+	1.82576e9i	−0.0215741	+	0.205263i
$697$	3.72529e9	−	1.14653e10i	0.416721	−	1.28254i
$698$	−1.54161e9	+	4.74459e9i	−0.171586	+	0.528086i
$699$	−8.50174e8	+	8.08887e9i	−0.0941538	+	0.895813i
$700$	−9.25654e8	−	1.02804e9i	−0.102001	−	0.113284i
$701$	4.09519e9	−	4.54817e9i	0.449015	−	0.498682i	−0.475559	−	0.879684i	$-0.657754\pi$
$701$	4.09519e9	−	4.54817e9i	0.449015	−	0.498682i	0.924574	+	0.381002i	$0.124421\pi$
$702$	1.37732e9	+	1.31044e10i	0.150264	+	1.42967i
$703$	2.66098e9	+	5.65610e8i	0.288868	+	0.0614007i
$704$	1.28337e9	−	5.71394e8i	0.138627	−	0.0617208i
$705$	6.41743e8	+	4.66254e8i	0.0689762	+	0.0501142i
$706$	7.25770e9	+	3.23134e9i	0.776216	+	0.345594i
$707$	−9.96322e8	−	1.72568e9i	−0.106031	−	0.183651i
$708$	−5.47790e9	+	9.48799e9i	−0.580093	+	1.00475i
$709$	−6.21715e8	+	4.51703e8i	−0.0655133	+	0.0475982i	−0.620060	−	0.784554i	$-0.712892\pi$
$709$	−6.21715e8	+	4.51703e8i	−0.0655133	+	0.0475982i	0.554547	+	0.832153i	$0.312892\pi$
$710$	1.24459e9	−	2.64546e8i	0.130503	−	0.0277393i
$711$	1.37435e10	+	4.22982e10i	1.43402	+	4.41345i
$712$	−4.17444e9			−0.433430
$713$	−7.70239e9	+	1.19728e10i	−0.795815	+	1.23703i
$714$	−4.80804e9			−0.494339
$715$	−1.63077e9	−	5.01901e9i	−0.166849	−	0.513507i
$716$	5.79627e9	−	1.23204e9i	0.590138	−	0.125438i
$717$	2.43552e10	−	1.76951e10i	2.46760	−	1.79282i
$718$	4.54285e9	−	7.86845e9i	0.458029	−	0.793330i
$719$	−4.87781e9	−	8.44861e9i	−0.489411	−	0.847685i	0.510515	−	0.859869i	$-0.329455\pi$
$719$	−4.87781e9	−	8.44861e9i	−0.489411	−	0.847685i	−0.999926	+	0.0121843i	$0.996122\pi$
$720$	−3.49202e9	−	1.55475e9i	−0.348669	−	0.155237i
$721$	−5.48018e9	−	3.98158e9i	−0.544530	−	0.395624i
$722$	6.06891e9	−	2.70205e9i	0.600109	−	0.267186i
$723$	−4.44530e9	−	9.44877e8i	−0.437438	−	0.0929804i
$724$	1.60189e8	+	1.52410e9i	0.0156873	+	0.149255i
$725$	1.34150e9	−	1.48988e9i	0.130740	−	0.145201i
$726$	−4.32075e9	−	4.79868e9i	−0.419065	−	0.465419i
$727$	−6.27801e8	+	5.97313e9i	−0.0605970	+	0.576542i	0.921528	+	0.388312i	$0.126942\pi$
$727$	−6.27801e8	+	5.97313e9i	−0.0605970	+	0.576542i	−0.982125	+	0.188230i	$0.939725\pi$
$728$	−4.02875e8	+	1.23992e9i	−0.0386999	+	0.119106i
$729$	5.14263e9	−	1.58274e10i	0.491631	−	1.51308i
$730$	3.05754e8	−	2.90905e9i	0.0290899	−	0.276772i
$731$	3.65575e9	+	4.06012e9i	0.346151	+	0.384440i
$732$	−1.59001e9	+	1.76588e9i	−0.149834	+	0.166408i
$733$	−1.52769e9	−	1.45350e10i	−0.143275	−	1.36317i	−0.795872	−	0.605465i	$-0.792987\pi$
$733$	−1.52769e9	−	1.45350e10i	−0.143275	−	1.36317i	0.652597	−	0.757705i	$-0.273679\pi$
$734$	1.06641e10	+	2.26672e9i	0.995378	+	0.211574i
$735$	8.57791e9	−	3.81913e9i	0.796848	−	0.354780i
$736$	2.27531e9	+	1.65311e9i	0.210363	+	0.152837i
$737$	−2.23756e10	−	9.96224e9i	−2.05891	−	0.916687i
$738$	1.69286e10	+	2.93211e10i	1.55033	+	2.68524i
$739$	1.11165e9	−	1.92544e9i	0.101324	−	0.175499i	−0.810906	−	0.585176i	$-0.801025\pi$
$739$	1.11165e9	−	1.92544e9i	0.101324	−	0.175499i	0.912231	+	0.409677i	$0.134359\pi$
$740$	−3.02321e9	+	2.19649e9i	−0.274257	+	0.199259i
$741$	−3.92396e9	+	8.34064e8i	−0.354292	+	0.0753071i
$742$	5.25426e7	+	1.61710e8i	0.00472170	+	0.0145319i
$743$	1.83220e10			1.63874			0.819372	−	0.573263i	$-0.194323\pi$
$743$	1.83220e10			1.63874			0.819372	+	0.573263i	$0.194323\pi$
$744$	−2.63126e9	+	6.94358e9i	−0.234239	+	0.618127i
$745$	1.40122e9			0.124154
$746$	6.54177e8	+	2.01335e9i	0.0576912	+	0.177555i
$747$	−4.64094e10	+	9.86463e9i	−4.07365	+	0.865882i
$748$	−4.31380e9	+	3.13416e9i	−0.376881	+	0.273820i
$749$	4.96772e7	−	8.60435e7i	0.00431987	−	0.00748224i
$750$	7.59554e9	+	1.31559e10i	0.657422	+	1.13869i
$751$	1.37507e10	+	6.12222e9i	1.18464	+	0.527435i	0.901977	−	0.431784i	$-0.142116\pi$
$751$	1.37507e10	+	6.12222e9i	1.18464	+	0.527435i	0.282662	+	0.959220i	$0.408782\pi$
$752$	−1.75822e8	−	1.27742e8i	−0.0150768	−	0.0109539i
$753$	−2.25267e10	+	1.00295e10i	−1.92272	+	0.856049i
$754$	−1.84813e9	−	3.92833e8i	−0.157012	−	0.0333740i
$755$	3.53277e8	+	3.36121e9i	0.0298745	+	0.284237i
$756$	5.41491e9	−	6.01386e9i	0.455790	−	0.506206i
$757$	−8.29245e8	−	9.20970e8i	−0.0694780	−	0.0771631i	0.707404	−	0.706810i	$-0.249866\pi$
$757$	−8.29245e8	−	9.20970e8i	−0.0694780	−	0.0771631i	−0.776882	+	0.629647i	$0.783200\pi$
$758$	1.27972e9	−	1.21757e10i	0.106726	−	1.01543i
$759$	1.24275e10	−	3.82479e10i	1.03166	−	3.17512i
$760$	2.15520e8	−	6.63303e8i	0.0178090	−	0.0548106i
$761$	9.58852e8	−	9.12287e9i	0.0788688	−	0.750387i	−0.881600	−	0.471998i	$-0.843533\pi$
$761$	9.58852e8	−	9.12287e9i	0.0788688	−	0.750387i	0.960468	−	0.278389i	$-0.0898004\pi$
$762$	−1.30701e10	−	1.45159e10i	−1.07013	−	1.18850i
$763$	2.14643e9	−	2.38385e9i	0.174937	−	0.194287i
$764$	7.86329e8	+	7.48142e9i	0.0637936	+	0.606956i
$765$	1.41916e10	+	3.01652e9i	1.14608	+	0.243608i
$766$	2.65962e9	−	1.18414e9i	0.213806	−	0.0951925i
$767$	−9.12223e9	−	6.62769e9i	−0.729991	−	0.530369i
$768$	1.34009e9	+	5.96648e8i	0.106751	+	0.0475285i
$769$	−3.12804e8	−	5.41793e8i	−0.0248045	−	0.0429627i	0.853357	−	0.521327i	$-0.174563\pi$
$769$	−3.12804e8	−	5.41793e8i	−0.0248045	−	0.0429627i	−0.878161	+	0.478365i	$0.841230\pi$
$770$	−1.62054e9	+	2.80686e9i	−0.127921	+	0.221566i
$771$	−1.36453e10	+	9.91388e9i	−1.07224	+	0.779029i
$772$	5.85569e9	−	1.24467e9i	0.458055	−	0.0973626i
$773$	5.75231e9	+	1.77038e10i	0.447934	+	1.37860i	0.879234	+	0.476390i	$0.158055\pi$
$773$	5.75231e9	+	1.77038e10i	0.447934	+	1.37860i	−0.431300	+	0.902208i	$0.641945\pi$
$774$	−1.53440e10			−1.18944
$775$	6.78182e9	−	4.44565e9i	0.523347	−	0.343067i
$776$	7.83747e8			0.0602088
$777$	−4.07931e9	−	1.25548e10i	−0.311970	−	0.960146i
$778$	−7.81944e9	+	1.66207e9i	−0.595315	+	0.126538i
$779$	−4.99766e9	+	3.63101e9i	−0.378779	+	0.275199i
$780$	2.75527e9	−	4.77226e9i	0.207890	−	0.360075i
$781$	2.49241e9	+	4.31698e9i	0.187215	+	0.324266i
$782$	−9.75201e9	−	4.34187e9i	−0.729240	−	0.324679i
$783$	9.48810e9	+	6.89351e9i	0.706339	+	0.513185i
$784$	−2.35013e9	+	1.04635e9i	−0.174175	+	0.0775477i
$785$	−1.14348e10	−	2.43055e9i	−0.843696	−	0.179333i
$786$	7.76164e8	+	7.38471e9i	0.0570131	+	0.542444i
$787$	8.30871e9	−	9.22775e9i	0.607606	−	0.674814i	−0.358331	−	0.933595i	$-0.616654\pi$
$787$	8.30871e9	−	9.22775e9i	0.607606	−	0.674814i	0.965936	+	0.258780i	$0.0833206\pi$
$788$	7.08342e9	+	7.86694e9i	0.515705	+	0.572749i
$789$	1.26071e9	−	1.19949e10i	0.0913790	−	0.869413i
$790$	3.44453e9	−	1.06012e10i	0.248562	−	0.764995i
$791$	−3.52641e8	+	1.08532e9i	−0.0253346	+	0.0779720i
$792$	1.56534e9	−	1.48932e10i	0.111962	−	1.06525i
$793$	−1.63644e9	−	1.81745e9i	−0.116532	−	0.129421i
$794$	2.65654e9	−	2.95039e9i	0.188341	−	0.209174i
$795$	−7.51225e7	−	7.14743e8i	−0.00530255	−	0.0504504i
$796$	8.20601e9	+	1.74424e9i	0.576682	+	0.122578i
$797$	−9.28161e9	+	4.13244e9i	−0.649410	+	0.289136i	−0.704882	−	0.709324i	$-0.749000\pi$
$797$	−9.28161e9	+	4.13244e9i	−0.649410	+	0.289136i	0.0554721	+	0.998460i	$0.482334\pi$
$798$	1.99323e9	+	1.44817e9i	0.138850	+	0.100881i
$799$	7.53572e8	+	3.35512e8i	0.0522650	+	0.0232699i
$800$	−8.00985e8	−	1.38735e9i	−0.0553107	−	0.0958010i
$801$	−2.22495e10	+	3.85373e10i	−1.52970	+	2.64953i
$802$	−6.52122e9	+	4.73794e9i	−0.446394	+	0.324324i
$803$	1.12091e10	−	2.38256e9i	0.763951	−	0.162383i
$804$	−7.90330e9	−	2.43239e10i	−0.536306	−	1.65058i
$805$	−6.48861e9			−0.438395
$806$	−6.82411e9	−	3.44025e9i	−0.459064	−	0.231429i
$807$	−2.58094e10			−1.72870
$808$	−7.13065e8	−	2.19459e9i	−0.0475542	−	0.146357i
$809$	1.12191e10	−	2.38469e9i	0.744968	−	0.158348i	0.180237	−	0.983623i	$-0.442313\pi$
$809$	1.12191e10	−	2.38469e9i	0.744968	−	0.158348i	0.564730	+	0.825275i	$0.308980\pi$
$810$	−1.44628e10	+	1.05078e10i	−0.956214	+	0.694730i
$811$	3.41331e9	−	5.91203e9i	0.224700	−	0.389192i	−0.731529	−	0.681810i	$-0.761193\pi$
$811$	3.41331e9	−	5.91203e9i	0.224700	−	0.389192i	0.956229	+	0.292618i	$0.0945264\pi$
$812$	5.80200e8	+	1.00494e9i	0.0380305	+	0.0658707i
$813$	4.61634e10	+	2.05533e10i	3.01287	+	1.34142i
$814$	−1.18440e10	−	8.60514e9i	−0.769682	−	0.559207i
$815$	1.19226e10	−	5.30826e9i	0.771467	−	0.343479i
$816$	−5.44615e9	−	1.15761e9i	−0.350892	−	0.0745845i
$817$	−2.92638e8	−	2.78427e9i	−0.0187739	−	0.178621i
$818$	−4.24018e8	+	4.70920e8i	−0.0270862	+	0.0300823i
$819$	9.29932e9	+	1.03279e10i	0.591504	+	0.656932i
$820$	8.86986e8	−	8.43911e9i	0.0561783	−	0.534501i
$821$	−4.43944e9	+	1.36632e10i	−0.279980	+	0.861691i	0.707878	+	0.706335i	$0.249653\pi$
$821$	−4.43944e9	+	1.36632e10i	−0.279980	+	0.861691i	−0.987858	+	0.155356i	$0.950347\pi$
$822$	1.15344e10	−	3.54993e10i	0.724343	−	2.22930i
$823$	−1.69906e9	+	1.61655e10i	−0.106245	+	1.01086i	0.803392	+	0.595451i	$0.203027\pi$
$823$	−1.69906e9	+	1.61655e10i	−0.106245	+	1.01086i	−0.909637	+	0.415404i	$0.863640\pi$
$824$	−5.24886e9	−	5.82945e9i	−0.326828	−	0.362980i
$825$	−1.53279e10	+	1.70234e10i	−0.950372	+	1.05550i
$826$	7.23864e8	+	6.88710e9i	0.0446917	+	0.425213i
$827$	5.63752e9	+	1.19829e9i	0.346592	+	0.0736705i	0.377919	−	0.925839i	$-0.376640\pi$
$827$	5.63752e9	+	1.19829e9i	0.346592	+	0.0736705i	−0.0313265	+	0.999509i	$0.509973\pi$
$828$	2.73884e10	−	1.21941e10i	1.67672	−	0.746523i
$829$	−4.02483e9	−	2.92421e9i	−0.245362	−	0.178266i	0.458307	−	0.888794i	$-0.348456\pi$
$829$	−4.02483e9	−	2.92421e9i	−0.245362	−	0.178266i	−0.703669	+	0.710528i	$0.748456\pi$
$830$	1.08634e10	+	4.83668e9i	0.659463	+	0.293612i
$831$	−1.38214e9	−	2.39393e9i	−0.0835503	−	0.144713i
$832$	−7.54874e8	+	1.30748e9i	−0.0454405	+	0.0787052i
$833$	7.89951e9	−	5.73933e9i	0.473524	−	0.344036i
$834$	−2.87497e10	+	6.11093e9i	−1.71614	+	0.364776i
$835$	−1.45829e9	−	4.48815e9i	−0.0866844	−	0.266787i
$836$	2.73233e9			0.161738
$837$	3.00107e10	+	3.67367e10i	1.76904	+	2.16551i
$838$	−8.25213e8			−0.0484409
$839$	3.97245e9	+	1.22259e10i	0.232216	+	0.714686i	0.997479	+	0.0709682i	$0.0226089\pi$
$839$	3.97245e9	+	1.22259e10i	0.232216	+	0.714686i	−0.765263	+	0.643718i	$0.777391\pi$
$840$	−3.31037e9	+	7.03642e8i	−0.192708	+	0.0409613i
$841$	1.25949e10	−	9.15074e9i	0.730145	−	0.530482i
$842$	2.57650e9	−	4.46263e9i	0.148744	−	0.257631i
$843$	2.11109e10	+	3.65652e10i	1.21370	+	2.10219i
$844$	8.11756e9	+	3.61417e9i	0.464758	+	0.206924i
$845$	−4.09182e9	−	2.97288e9i	−0.233302	−	0.169504i
$846$	−2.11640e9	+	9.42281e8i	−0.120171	+	0.0535037i
$847$	−3.99237e9	−	8.48605e8i	−0.225756	−	0.0479859i
$848$	2.05817e7	+	1.95822e8i	0.00115903	+	0.0110274i
$849$	7.29783e9	−	8.10506e9i	0.409276	−	0.454547i
$850$	4.06861e9	+	4.51865e9i	0.227237	+	0.252373i
$851$	3.06362e9	−	2.91484e10i	0.170405	−	1.62129i
$852$	−1.60847e9	+	4.95038e9i	−0.0890996	+	0.274220i
$853$	9.89326e8	−	3.04483e9i	0.0545780	−	0.167974i	−0.920052	−	0.391797i	$-0.871854\pi$
$853$	9.89326e8	−	3.04483e9i	0.0545780	−	0.167974i	0.974630	+	0.223823i	$0.0718537\pi$
$854$	−1.57001e8	+	1.49376e9i	−0.00862580	+	0.0820690i
$855$	−4.97473e9	−	5.52499e9i	−0.272200	−	0.302309i
$856$	7.69866e7	−	8.55022e7i	0.00419524	−	0.00465929i
$857$	4.56861e8	+	4.34674e9i	0.0247942	+	0.235901i	0.999900	+	0.0141600i	$0.00450743\pi$
$857$	4.56861e8	+	4.34674e9i	0.0247942	+	0.235901i	−0.975105	+	0.221741i	$0.928826\pi$
$858$	2.11167e10	+	4.48849e9i	1.14135	+	0.242602i
$859$	−1.47848e10	+	6.58261e9i	−0.795864	+	0.354341i	−0.764054	−	0.645153i	$-0.776794\pi$
$859$	−1.47848e10	+	6.58261e9i	−0.795864	+	0.354341i	−0.0318099	+	0.999494i	$0.510127\pi$
$860$	3.11120e9	+	2.26042e9i	0.166795	+	0.121184i
$861$	2.73846e10	+	1.21924e10i	1.46216	+	0.650996i
$862$	1.15721e10	+	2.00435e10i	0.615373	+	1.06586i
$863$	1.13488e10	−	1.96567e10i	0.601051	−	1.04105i	−0.391611	−	0.920131i	$-0.628082\pi$
$863$	1.13488e10	−	1.96567e10i	0.601051	−	1.04105i	0.992662	−	0.120920i	$-0.0385845\pi$
$864$	7.58149e9	−	5.50827e9i	0.399905	−	0.290548i
$865$	6.06534e9	−	1.28923e9i	0.318639	−	0.0677288i
$866$	−1.62383e9	−	4.99762e9i	−0.0849624	−	0.261487i
$867$	−1.47447e10			−0.768368
$868$	1.23421e9	+	4.52834e9i	0.0640577	+	0.235028i
$869$	4.36692e10			2.25739
$870$	−1.51564e9	−	4.66466e9i	−0.0780331	−	0.240161i
$871$	2.57472e10	−	5.47274e9i	1.32028	−	0.280635i
$872$	3.00525e9	−	2.18344e9i	0.153487	−	0.111515i
$873$	4.17733e9	−	7.23535e9i	0.212495	−	0.368052i
$874$	2.73505e9	+	4.73724e9i	0.138572	+	0.240013i
$875$	8.77197e9	+	3.90553e9i	0.442659	+	0.197084i
$876$	9.68067e9	+	7.03342e9i	0.486565	+	0.353510i
$877$	2.55490e10	−	1.13751e10i	1.27901	−	0.569453i	0.349049	−	0.937104i	$-0.386505\pi$
$877$	2.55490e10	−	1.13751e10i	1.27901	−	0.569453i	0.929964	+	0.367651i	$0.119838\pi$
$878$	−1.69951e10	−	3.61241e9i	−0.847407	−	0.180122i
$879$	−6.61558e9	−	6.29431e10i	−0.328554	−	3.12598i
$880$	−2.51141e9	+	2.78920e9i	−0.124231	+	0.137972i
$881$	−4.03968e9	−	4.48651e9i	−0.199036	−	0.221051i	0.635362	−	0.772214i	$-0.280851\pi$
$881$	−4.03968e9	−	4.48651e9i	−0.199036	−	0.221051i	−0.834398	+	0.551163i	$0.814184\pi$
$882$	−2.86648e9	+	2.72727e10i	−0.140672	+	1.33841i
$883$	1.63303e9	−	5.02594e9i	0.0798235	−	0.245672i	−0.903179	−	0.429265i	$-0.858773\pi$
$883$	1.63303e9	−	5.02594e9i	0.0798235	−	0.245672i	0.983002	+	0.183593i	$0.0587728\pi$
$884$	1.77079e9	−	5.44993e9i	0.0862153	−	0.265343i
$885$	3.05959e9	−	2.91100e10i	0.148375	−	1.41170i
$886$	−7.83617e9	−	8.70295e9i	−0.378518	−	0.420386i
$887$	−2.40743e10	+	2.67373e10i	−1.15830	+	1.28642i	−0.206938	+	0.978354i	$0.566350\pi$
$887$	−2.40743e10	+	2.67373e10i	−1.15830	+	1.28642i	−0.951364	+	0.308070i	$0.900317\pi$
$888$	−1.59792e9	−	1.52032e10i	−0.0765792	−	0.728602i
$889$	−1.20768e10	−	2.56701e9i	−0.576496	−	0.122538i
$890$	1.01886e10	−	4.53625e9i	0.484449	−	0.215691i
$891$	−5.66605e10	−	4.11663e10i	−2.68354	−	1.94971i
$892$	−1.87384e10	−	8.34288e9i	−0.884007	−	0.393585i
$893$	−2.11347e8	−	3.66063e8i	−0.00993152	−	0.0172019i
$894$	−2.86608e9	+	4.96419e9i	−0.134155	+	0.232363i
$895$	−1.28082e10	+	9.30567e9i	−0.597181	+	0.433878i
$896$	9.06959e8	−	1.92780e8i	0.0421221	−	0.00895332i
$897$	1.33557e10	+	4.11045e10i	0.617862	+	1.90158i
$898$	−2.06346e9			−0.0950889
$899$	−6.33976e9	+	2.46487e9i	−0.291014	+	0.113145i
$900$	−1.70768e10			−0.780833
$901$	−2.30945e8	−	7.10776e8i	−0.0105189	−	0.0323740i
$902$	3.25173e10	−	6.91177e9i	1.47534	−	0.313593i
$903$	−1.09906e10	+	7.98513e9i	−0.496722	+	0.360890i
$904$	−6.60749e8	+	1.14445e9i	−0.0297473	+	0.0515238i
$905$	−2.04717e9	−	3.54580e9i	−0.0918085	−	0.159017i
$906$	−1.26305e10	−	5.62347e9i	−0.564251	−	0.251221i
$907$	1.07877e10	+	7.83774e9i	0.480070	+	0.348791i	0.801353	−	0.598192i	$-0.204114\pi$
$907$	1.07877e10	+	7.83774e9i	0.480070	+	0.348791i	−0.321283	+	0.946983i	$0.604114\pi$
$908$	−1.89819e10	+	8.45130e9i	−0.841473	+	0.374648i
$909$	−2.40604e10	−	5.11420e9i	−1.06250	−	0.225842i
$910$	−3.64088e8	−	3.46407e9i	−0.0160163	−	0.152385i
$911$	−1.20601e10	+	1.33941e10i	−0.528490	+	0.586948i	−0.946988	−	0.321270i	$-0.895890\pi$
$911$	−1.20601e10	+	1.33941e10i	−0.528490	+	0.586948i	0.418497	+	0.908218i	$0.362557\pi$
$912$	1.90909e9	+	2.12026e9i	0.0833384	+	0.0925566i
$913$	−4.86963e9	+	4.63315e10i	−0.211762	+	2.01478i
$914$	−3.87763e8	+	1.19341e9i	−0.0167979	+	0.0516985i
$915$	1.96180e9	−	6.03781e9i	0.0846607	−	0.260559i
$916$	1.13873e9	−	1.08343e10i	0.0489540	−	0.465766i
$917$	3.14057e9	+	3.48796e9i	0.134498	+	0.149375i
$918$	−2.38006e10	+	2.64333e10i	−1.01540	+	1.12772i
$919$	−1.58966e9	−	1.51246e10i	−0.0675615	−	0.642805i	−0.974937	−	0.222483i	$-0.928584\pi$
$919$	−1.58966e9	−	1.51246e10i	−0.0675615	−	0.642805i	0.907375	−	0.420322i	$-0.138083\pi$
$920$	−7.34975e9	−	1.56224e9i	−0.311182	−	0.0661439i
$921$	5.86601e10	−	2.61172e10i	2.47420	−	1.10158i
$922$	−9.88159e9	−	7.17940e9i	−0.415211	−	0.301668i
$923$	−4.89397e9	−	2.17894e9i	−0.204859	−	0.0912093i
$924$	−6.62934e9	−	1.14824e10i	−0.276451	−	0.478828i
$925$	−8.34721e9	+	1.44578e10i	−0.346773	+	0.600628i
$926$	−8.96231e9	+	6.51150e9i	−0.370921	+	0.269490i
$927$	−8.17920e10	+	1.73854e10i	−3.37234	+	0.716814i
$928$	4.15247e8	+	1.27800e9i	0.0170565	+	0.0524944i
$929$	−1.03949e10			−0.425369			−0.212684	−	0.977121i	$-0.568221\pi$
$929$	−1.03949e10			−0.425369			−0.212684	+	0.977121i	$0.568221\pi$
$930$	−1.12325e9	−	1.98065e10i	−0.0457917	−	0.807454i
$931$	−5.00349e9			−0.203212
$932$	1.83972e9	+	5.66206e9i	0.0744381	+	0.229097i
$933$	1.78297e10	−	3.78982e9i	0.718719	−	0.152768i
$934$	−1.27369e10	+	9.25391e9i	−0.511505	+	0.371630i
$935$	7.12291e9	−	1.23372e10i	0.284982	−	0.493602i
$936$	8.04687e9	+	1.39376e10i	0.320746	+	0.555549i
$937$	−3.12590e10	−	1.39174e10i	−1.24133	−	0.552676i	−0.322215	−	0.946666i	$-0.604427\pi$
$937$	−3.12590e10	−	1.39174e10i	−1.24133	−	0.552676i	−0.919114	+	0.393991i	$0.871094\pi$
$938$	−1.30786e10	−	9.50218e9i	−0.517431	−	0.375936i
$939$	−4.52186e10	+	2.01326e10i	−1.78233	+	0.793544i
$940$	5.67941e8	+	1.20720e8i	0.0223026	+	0.00474057i
$941$	−4.89790e9	−	4.66004e10i	−0.191622	−	1.82316i	−0.493419	−	0.869792i	$-0.664253\pi$
$941$	−4.89790e9	−	4.66004e10i	−0.191622	−	1.82316i	0.301797	−	0.953372i	$-0.402414\pi$
$942$	3.19998e10	−	3.55393e10i	1.24729	−	1.38526i
$943$	4.45330e10	+	4.94589e10i	1.72938	+	1.92068i
$944$	−8.38250e8	+	7.97541e9i	−0.0324318	+	0.308568i
$945$	−6.68109e9	+	2.05623e10i	−0.257535	+	0.792610i
$946$	−4.65565e9	+	1.43286e10i	−0.178797	+	0.550281i
$947$	8.23718e8	−	7.83716e9i	0.0315177	−	0.299870i	−0.967396	−	0.253269i	$-0.918494\pi$
$947$	8.23718e8	−	7.83716e9i	0.0315177	−	0.299870i	0.998914	−	0.0466015i	$-0.0148391\pi$
$948$	3.05118e10	+	3.38868e10i	1.16316	+	1.29182i
$949$	−8.24059e9	+	9.15210e9i	−0.312987	+	0.347608i
$950$	−3.25687e8	−	3.09870e9i	−0.0123245	−	0.117259i
$951$	−3.50749e10	−	7.45539e9i	−1.32240	−	0.281086i
$952$	−3.21509e9	+	1.43145e9i	−0.120772	+	0.0537709i
$953$	2.18303e10	+	1.58606e10i	0.817024	+	0.593603i	0.915858	−	0.401501i	$-0.131511\pi$
$953$	2.18303e10	+	1.58606e10i	0.817024	+	0.593603i	−0.0988346	+	0.995104i	$0.531511\pi$
$954$	1.91747e9	+	8.53713e8i	0.0715006	+	0.0318341i
$955$	−1.00490e10	−	1.74054e10i	−0.373347	−	0.646655i
$956$	1.10179e10	−	1.90836e10i	0.407847	−	0.706411i
$957$	1.55453e10	−	1.12943e10i	0.573334	−	0.416552i
$958$	5.18169e9	−	1.10140e9i	0.190411	−	0.0404731i
$959$	−7.29078e9	−	2.24387e10i	−0.266937	−	0.821548i
$960$	−3.91913e9			−0.142968
$961$	−2.73362e10	+	3.11054e9i	−0.993588	+	0.113059i
$962$	1.57333e10			0.569782
$963$	−3.79000e8	−	1.16644e9i	−0.0136756	−	0.0420892i
$964$	−3.25384e9	+	6.91625e8i	−0.116984	+	0.0248657i
$965$	−1.29395e10	+	9.40107e9i	−0.463522	+	0.336769i
$966$	1.32719e10	−	2.29875e10i	0.473709	−	0.820488i
$967$	1.88497e10	+	3.26487e10i	0.670367	+	1.16111i	0.977800	+	0.209540i	$0.0671966\pi$
$967$	1.88497e10	+	3.26487e10i	0.670367	+	1.16111i	−0.307433	+	0.951570i	$0.599470\pi$
$968$	−4.31791e9	−	1.92246e9i	−0.153007	−	0.0681229i
$969$	−8.76101e9	−	6.36525e9i	−0.309329	−	0.224741i
$970$	−1.91289e9	+	8.51675e8i	−0.0672961	+	0.0299621i
$971$	4.05898e10	+	8.62762e9i	1.42282	+	0.302429i	0.854102	−	0.520105i	$-0.174107\pi$
$971$	4.05898e10	+	8.62762e9i	1.42282	+	0.302429i	0.568716	+	0.822534i	$0.307440\pi$
$972$	−3.46015e9	−	3.29212e10i	−0.120855	−	1.14986i
$973$	−1.24313e10	+	1.38064e10i	−0.432636	+	0.480491i
$974$	−2.25762e10	−	2.50734e10i	−0.782878	−	0.869474i
$975$	2.57329e9	−	2.44832e10i	0.0889144	−	0.845964i
$976$	−5.37485e8	+	1.65421e9i	−0.0185051	+	0.0569529i
$977$	−3.28284e9	+	1.01035e10i	−0.112621	+	0.346611i	−0.991443	−	0.130537i	$-0.958330\pi$
$977$	−3.28284e9	+	1.01035e10i	−0.112621	+	0.346611i	0.878823	+	0.477149i	$0.158330\pi$
$978$	−5.58064e9	+	5.30962e10i	−0.190765	+	1.81500i
$979$	2.92363e10	+	3.24702e10i	0.995824	+	1.10597i
$980$	4.59894e9	−	5.10764e9i	0.156087	−	0.173352i
$981$	−4.13913e9	−	3.93812e10i	−0.139981	−	1.33183i
$982$	−3.06894e10	−	6.52324e9i	−1.03419	−	0.219823i
$983$	3.25229e10	−	1.44801e10i	1.09208	−	0.486223i	0.219953	−	0.975511i	$-0.429410\pi$
$983$	3.25229e10	−	1.44801e10i	1.09208	−	0.486223i	0.872123	+	0.489287i	$0.162743\pi$
$984$	2.80834e10	+	2.04038e10i	0.939653	+	0.682698i
$985$	−2.58373e10	−	1.15035e10i	−0.861430	−	0.383534i
$986$	−2.55021e9	−	4.41708e9i	−0.0847239	−	0.146746i
$987$	−1.02556e9	+	1.77633e9i	−0.0339510	+	0.0588048i
$988$	−2.37560e9	+	1.72598e9i	−0.0783654	+	0.0569358i
$989$	−2.95028e10	+	6.27101e9i	−0.969786	+	0.206134i
$990$	1.23635e10	+	3.80510e10i	0.404966	+	1.24636i
$991$	−3.27375e9			−0.106853			−0.0534266	−	0.998572i	$-0.517014\pi$
$991$	−3.27375e9			−0.106853			−0.0534266	+	0.998572i	$0.517014\pi$
$992$	3.07743e8	+	5.42648e9i	0.0100091	+	0.176493i
$993$	7.73677e10			2.50748
$994$	1.01670e9	+	3.12908e9i	0.0328352	+	0.101057i
$995$	−2.19238e10	+	4.66006e9i	−0.705563	+	0.149972i
$996$	−3.93552e10	+	2.85932e10i	−1.26210	+	0.916970i
$997$	−2.54824e10	+	4.41368e10i	−0.814342	+	1.41048i	0.0954573	+	0.995434i	$0.469569\pi$
$997$	−2.54824e10	+	4.41368e10i	−0.814342	+	1.41048i	−0.909799	+	0.415048i	$0.863765\pi$
$998$	−1.05862e10	−	1.83359e10i	−0.337119	−	0.583908i
$999$	−8.92162e10	−	3.97216e10i	−2.83116	−	1.26051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.g.b.7.1	✓	72
31.9	even	15	inner	62.8.g.b.9.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.g.b.7.1	✓	72	1.1	even	1	trivial
62.8.g.b.9.1	yes	72	31.9	even	15	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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.47214 - 7.60845i) q^{2} +(-85.5242 + 18.1787i) q^{3} +(-51.7771 + 37.6183i) q^{4} +(85.4938 - 148.080i) q^{5} +(349.740 + 605.767i) q^{6} +(403.909 + 179.832i) q^{7} +(414.217 + 300.946i) q^{8} +(4986.00 - 2219.91i) q^{9} +(-1338.01 - 284.403i) q^{10} +(-560.166 - 5329.63i) q^{11} +(3744.34 - 4158.51i) q^{12} +(3853.68 + 4279.94i) q^{13} +(369.724 - 3517.69i) q^{14} +(-4619.89 + 14218.6i) q^{15} +(1265.73 - 3895.53i) q^{16} +(-1625.08 + 15461.6i) q^{17} +(-29216.2 - 32447.9i) q^{18} +(5330.68 - 5920.31i) q^{19} +(1143.88 + 10883.3i) q^{20} +(-37813.1 - 8037.43i) q^{21} +(-39165.4 + 17437.6i) q^{22} +(-69437.0 - 50449.0i) q^{23} +(-40896.4 - 18208.2i) q^{24} +(24444.1 + 42338.5i) q^{25} +(23036.9 - 39901.1i) q^{26} +(-231369. + 168099. i) q^{27} +(-27678.2 + 5883.18i) q^{28} +(-12672.3 - 39001.5i) q^{29} +119602. q^{30} +(-9391.56 - 165603. i) q^{31} -32768.0 q^{32} +(144794. + 445629. i) q^{33} +(121656. - 25858.9i) q^{34} +(61161.1 - 44436.2i) q^{35} +(-174652. + 302505. i) q^{36} +(170741. + 295731. i) q^{37} +(-58222.6 - 25922.4i) q^{38} +(-407387. - 295984. i) q^{39} +(79976.9 - 35608.0i) q^{40} +(-758477. - 161219. i) q^{41} +(32326.8 + 307569. i) q^{42} +(235145. - 261155. i) q^{43} +(229495. + 254880. i) q^{44} +(97548.7 - 928114. i) q^{45} +(-212181. + 653025. i) q^{46} +(16396.0 - 50461.6i) q^{47} +(-37435.1 + 356171. i) q^{48} +(-420255. - 466740. i) q^{49} +(261701. - 290648. i) q^{50} +(-142089. - 1.35188e6i) q^{51} +(-360536. - 76634.3i) q^{52} +(-43915.3 + 19552.4i) q^{53} +(1.85095e6 + 1.34479e6i) q^{54} +(-837100. - 372701. i) q^{55} +(113186. + 196044. i) q^{56} +(-348278. + 603235. i) q^{57} +(-265413. + 192834. i) q^{58} +(-1.91506e6 + 407059. i) q^{59} +(-295673. - 909988. i) q^{60} -424643. q^{61} +(-1.23677e6 + 480849. i) q^{62} +2.41310e6 q^{63} +(81007.0 + 249314. i) q^{64} +(963238. - 204743. i) q^{65} +(3.03260e6 - 2.20331e6i) q^{66} +(2.28524e6 - 3.95815e6i) q^{67} +(-497497. - 861690. i) q^{68} +(6.85565e6 + 3.05233e6i) q^{69} +(-489289. - 355489. i) q^{70} +(-849762. + 378338. i) q^{71} +(2.73336e6 + 580994. i) q^{72} +(223521. + 2.12666e6i) q^{73} +(1.82796e6 - 2.03016e6i) q^{74} +(-2.86022e6 - 3.17660e6i) q^{75} +(-53294.9 + 507067. i) q^{76} +(732180. - 2.25342e6i) q^{77} +(-1.24486e6 + 3.83130e6i) q^{78} +(-851780. + 8.10414e6i) q^{79} +(-468636. - 520473. i) q^{80} +(8.74483e6 - 9.71211e6i) q^{81} +(648429. + 6.16939e6i) q^{82} +(-8.50322e6 - 1.80742e6i) q^{83} +(2.26021e6 - 1.00631e6i) q^{84} +(2.15061e6 + 1.56251e6i) q^{85} +(-2.56830e6 - 1.14348e6i) q^{86} +(1.79279e6 + 3.10520e6i) q^{87} +(1.37190e6 - 2.37620e6i) q^{88} +(-6.59609e6 + 4.79234e6i) q^{89} +(-7.30267e6 + 1.55223e6i) q^{90} +(786865. + 2.42172e6i) q^{91} +5.49305e6 q^{92} +(3.81366e6 + 1.39924e7i) q^{93} -424467. q^{94} +(-420938. - 1.29551e6i) q^{95} +(2.80246e6 - 595681. i) q^{96} +(1.23841e6 - 899756. i) q^{97} +(-2.51224e6 + 4.35134e6i) q^{98} +(-1.46243e7 - 2.53300e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 144 q^{2} + 53 q^{3} - 1152 q^{4} + 97 q^{5} + 656 q^{6} - 3516 q^{7} + 9216 q^{8} + 4100 q^{9} - 3616 q^{10} - 6385 q^{11} + 3392 q^{12} - 7108 q^{13} - 25872 q^{14} - 37456 q^{15} - 73728 q^{16}+ \cdots + 20676441 q^{99}+O(q^{100}) \) 72 * q + 144 * q^2 + 53 * q^3 - 1152 * q^4 + 97 * q^5 + 656 * q^6 - 3516 * q^7 + 9216 * q^8 + 4100 * q^9 - 3616 * q^10 - 6385 * q^11 + 3392 * q^12 - 7108 * q^13 - 25872 * q^14 - 37456 * q^15 - 73728 * q^16 - 8376 * q^17 - 70280 * q^18 - 49913 * q^19 + 2048 * q^20 + 323383 * q^21 - 67960 * q^22 - 345829 * q^23 + 6144 * q^24 - 372591 * q^25 + 227584 * q^26 - 71038 * q^27 - 142784 * q^28 - 324657 * q^29 - 926672 * q^30 - 1450215 * q^31 - 2359296 * q^32 + 83140 * q^33 + 542768 * q^34 + 220312 * q^35 - 1649280 * q^36 - 1077276 * q^37 + 242544 * q^38 - 2082538 * q^39 - 16384 * q^40 - 561831 * q^41 + 2046856 * q^42 + 541504 * q^43 + 69440 * q^44 - 3560198 * q^45 - 1210168 * q^46 + 701593 * q^47 - 49152 * q^48 + 2939863 * q^49 - 2047672 * q^50 + 2343644 * q^51 - 454912 * q^52 + 5870237 * q^53 + 568304 * q^54 + 4095901 * q^55 + 358912 * q^56 - 2524936 * q^57 - 4505944 * q^58 + 3564614 * q^59 - 2397184 * q^60 + 6621588 * q^61 - 6588440 * q^62 + 37503466 * q^63 - 4718592 * q^64 + 2623034 * q^65 - 1265000 * q^66 + 6997086 * q^67 + 1117376 * q^68 + 18122809 * q^69 - 1762496 * q^70 + 17340555 * q^71 - 4497920 * q^72 + 893895 * q^73 - 7099272 * q^74 - 4691620 * q^75 + 11121408 * q^76 - 12966527 * q^77 - 31068816 * q^78 + 16057037 * q^79 - 2510848 * q^80 + 17531660 * q^81 + 31965608 * q^82 + 35981510 * q^83 + 13155712 * q^84 + 8693293 * q^85 - 8631272 * q^86 - 7183623 * q^87 + 263680 * q^88 - 23416374 * q^89 - 76756056 * q^90 + 13467668 * q^91 + 24903424 * q^92 - 88528776 * q^93 - 19578704 * q^94 - 9538258 * q^95 - 1736704 * q^96 - 11254011 * q^97 + 30592696 * q^98 + 20676441 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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