LMFDB - Embedded newform 100.9.j.b.11.33

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(11,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.11"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [464] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			11.33
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9.51677 + 12.8620i) q^{2} +(-66.9566 - 21.7555i) q^{3} +(-74.8622 - 244.809i) q^{4} +(-7.73474 + 624.952i) q^{5} +(917.030 - 654.154i) q^{6} +539.637i q^{7} +(3861.19 + 1366.92i) q^{8} +(-1298.07 - 943.105i) q^{9} +(-7964.53 - 6047.01i) q^{10} +(3618.94 + 4981.05i) q^{11} +(-313.436 + 18020.3i) q^{12} +(2340.29 + 1700.32i) q^{13} +(-6940.82 - 5135.60i) q^{14} +(14114.1 - 41676.4i) q^{15} +(-54327.3 + 36654.0i) q^{16} +(-39654.3 - 122043. i) q^{17} +(24483.7 - 7720.51i) q^{18} +(-218786. + 71087.9i) q^{19} +(153573. - 44891.8i) q^{20} +(11740.1 - 36132.3i) q^{21} +(-98506.9 - 856.627i) q^{22} +(-135470. - 186458. i) q^{23} +(-228794. - 175526. i) q^{24} +(-390505. - 9667.69i) q^{25} +(-44141.4 + 13919.2i) q^{26} +(337901. + 465080. i) q^{27} +(132108. - 40398.4i) q^{28} +(227566. - 700375. i) q^{29} +(401722. + 578160. i) q^{30} +(1.05782e6 - 343705. i) q^{31} +(45577.1 - 1.04759e6i) q^{32} +(-133947. - 412246. i) q^{33} +(1.94710e6 + 651425. i) q^{34} +(-337247. - 4173.96i) q^{35} +(-133704. + 388384. i) q^{36} +(-1.73367e6 - 1.25958e6i) q^{37} +(1.16780e6 - 3.49055e6i) q^{38} +(-119706. - 164762. i) q^{39} +(-884123. + 2.40248e6i) q^{40} +(2.70407e6 + 1.96462e6i) q^{41} +(353006. + 494864. i) q^{42} +3.01287e6i q^{43} +(948486. - 1.25884e6i) q^{44} +(599436. - 803939. i) q^{45} +(3.68745e6 + 32066.5i) q^{46} +(-2.28936e6 - 743857. i) q^{47} +(4.43500e6 - 1.27231e6i) q^{48} +5.47359e6 q^{49} +(3.84069e6 - 4.93068e6i) q^{50} +9.03432e6i q^{51} +(241055. - 700214. i) q^{52} +(-3.42085e6 + 1.05283e7i) q^{53} +(-9.19759e6 - 79983.2i) q^{54} +(-3.14091e6 + 2.22314e6i) q^{55} +(-737639. + 2.08364e6i) q^{56} +1.61957e7 q^{57} +(6.84253e6 + 9.59225e6i) q^{58} +(-7.70792e6 + 1.06090e7i) q^{59} +(-1.12594e7 - 335265. i) q^{60} +(1.03807e7 - 7.54199e6i) q^{61} +(-5.64625e6 + 1.68766e7i) q^{62} +(508935. - 700489. i) q^{63} +(1.30403e7 + 1.05558e7i) q^{64} +(-1.08072e6 + 1.44942e6i) q^{65} +(6.57706e6 + 2.20043e6i) q^{66} +(-2.51604e7 + 8.17511e6i) q^{67} +(-2.69088e7 + 1.88442e7i) q^{68} +(5.01410e6 + 1.54318e7i) q^{69} +(3.26319e6 - 4.29796e6i) q^{70} +(-6.65726e6 - 2.16308e6i) q^{71} +(-3.72296e6 - 5.41586e6i) q^{72} +(4.14409e7 - 3.01085e7i) q^{73} +(3.26997e7 - 1.03113e7i) q^{74} +(2.59366e7 + 9.14297e6i) q^{75} +(3.37818e7 + 4.82391e7i) q^{76} +(-2.68796e6 + 1.95292e6i) q^{77} +(3.25838e6 + 28335.2i) q^{78} +(5.38806e7 + 1.75069e7i) q^{79} +(-2.24868e7 - 3.42355e7i) q^{80} +(-9.25355e6 - 2.84795e7i) q^{81} +(-5.10029e7 + 1.60829e7i) q^{82} +(5.49796e7 - 1.78640e7i) q^{83} +(-9.72442e6 - 169142. i) q^{84} +(7.65780e7 - 2.38381e7i) q^{85} +(-3.87516e7 - 2.86728e7i) q^{86} +(-3.04740e7 + 4.19439e7i) q^{87} +(7.16474e6 + 2.41796e7i) q^{88} +(2.82158e7 - 2.05000e7i) q^{89} +(4.63557e6 + 1.53609e7i) q^{90} +(-917555. + 1.26291e6i) q^{91} +(-3.55051e7 + 4.71229e7i) q^{92} -7.83052e7 q^{93} +(3.13548e7 - 2.23666e7i) q^{94} +(-4.27343e7 - 1.37281e8i) q^{95} +(-2.58425e7 + 6.91512e7i) q^{96} +(-9.23936e6 + 2.84358e7i) q^{97} +(-5.20909e7 + 7.04014e7i) q^{98} -9.87881e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) $ 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−9.51677	+	12.8620i	−0.594798	+	0.803875i
$2$	−9.51677	+	12.8620i	−0.594798	+	0.803875i
$3$	−66.9566	−	21.7555i	−0.826625	−	0.268587i	−0.135002	−	0.990845i	$-0.543104\pi$
$3$	−66.9566	−	21.7555i	−0.826625	−	0.268587i	−0.691623	+	0.722259i	$0.743104\pi$
$4$	−74.8622	−	244.809i	−0.292431	−	0.956287i
$5$	−7.73474	+	624.952i	−0.0123756	+	0.999923i
$5$	−7.73474	+	624.952i	−0.0123756	+	0.999923i
$6$	917.030	−	654.154i	0.707585	−	0.504748i
$7$			539.637i			0.224755i	0.993666	+	0.112378i	$0.0358466\pi$
$7$			539.637i			0.224755i	−0.993666	+	0.112378i	$0.964153\pi$
$8$	3861.19	+	1366.92i	0.942672	+	0.333720i
$9$	−1298.07	−	943.105i	−0.197847	−	0.143744i
$10$	−7964.53	−	6047.01i	−0.796453	−	0.604701i
$11$	3618.94	+	4981.05i	0.247179	+	0.340212i	0.914521	−	0.404539i	$-0.132568\pi$
$11$	3618.94	+	4981.05i	0.247179	+	0.340212i	−0.667342	+	0.744751i	$0.732568\pi$
$12$	−313.436	+	18020.3i	−0.0151156	+	0.869034i
$13$	2340.29	+	1700.32i	0.0819399	+	0.0595328i	0.628001	−	0.778213i	$-0.283873\pi$
$13$	2340.29	+	1700.32i	0.0819399	+	0.0595328i	−0.546061	+	0.837745i	$0.683873\pi$
$14$	−6940.82	−	5135.60i	−0.180675	−	0.133684i
$15$	14114.1	−	41676.4i	0.278796	−	0.823238i
$16$	−54327.3	+	36654.0i	−0.828969	+	0.559295i
$17$	−39654.3	−	122043.i	−0.474783	−	1.46123i	−0.846251	−	0.532785i	$-0.821146\pi$
$17$	−39654.3	−	122043.i	−0.474783	−	1.46123i	0.371468	−	0.928446i	$-0.378854\pi$
$18$	24483.7	−	7720.51i	0.233231	−	0.0735454i
$19$	−218786.	+	71087.9i	−1.67882	+	0.545483i	−0.984683	−	0.174355i	$-0.944216\pi$
$19$	−218786.	+	71087.9i	−1.67882	+	0.545483i	−0.694142	+	0.719839i	$0.744216\pi$
$20$	153573.	−	44891.8i	0.959833	−	0.280574i
$21$	11740.1	−	36132.3i	0.0603663	−	0.185788i
$22$	−98506.9	−	856.627i	−0.420510	−	0.00365680i
$23$	−135470.	−	186458.i	−0.484095	−	0.666299i	0.495191	−	0.868784i	$-0.335098\pi$
$23$	−135470.	−	186458.i	−0.484095	−	0.666299i	−0.979285	+	0.202485i	$0.935098\pi$
$24$	−228794.	−	175526.i	−0.689604	−	0.529050i
$25$	−390505.	−	9667.69i	−0.999694	−	0.0247493i
$26$	−44141.4	+	13919.2i	−0.0965947	+	0.0304594i
$27$	337901.	+	465080.i	0.635820	+	0.875131i
$28$	132108.	−	40398.4i	0.214930	−	0.0657253i
$29$	227566.	−	700375.i	0.321747	−	0.990235i	−0.651141	−	0.758957i	$-0.725709\pi$
$29$	227566.	−	700375.i	0.321747	−	0.990235i	0.972888	−	0.231278i	$-0.0742908\pi$
$30$	401722.	+	578160.i	0.495953	+	0.713778i
$31$	1.05782e6	−	343705.i	1.14542	−	0.372168i	0.326001	−	0.945369i	$-0.394299\pi$
$31$	1.05782e6	−	343705.i	1.14542	−	0.372168i	0.819414	+	0.573201i	$0.194299\pi$
$32$	45577.1	−	1.04759e6i	0.0434657	−	0.999055i
$33$	−133947.	−	412246.i	−0.112948	−	0.347617i
$34$	1.94710e6	+	651425.i	1.45705	+	0.487471i
$35$	−337247.	−	4173.96i	−0.224738	−	0.00278148i
$36$	−133704.	+	388384.i	−0.0796042	+	0.231234i
$37$	−1.73367e6	−	1.25958e6i	−0.925037	−	0.672079i	0.0197357	−	0.999805i	$-0.493718\pi$
$37$	−1.73367e6	−	1.25958e6i	−0.925037	−	0.672079i	−0.944773	+	0.327727i	$0.893718\pi$
$38$	1.16780e6	−	3.49055e6i	0.560061	−	1.67402i
$39$	−119706.	−	164762.i	−0.0517439	−	0.0712193i
$40$	−884123.	+	2.40248e6i	−0.345360	+	0.938470i
$41$	2.70407e6	+	1.96462e6i	0.956933	+	0.695253i	0.952437	−	0.304737i	$-0.0985686\pi$
$41$	2.70407e6	+	1.96462e6i	0.956933	+	0.695253i	0.00449687	+	0.999990i	$0.498569\pi$
$42$	353006.	+	494864.i	0.113445	+	0.159033i
$43$			3.01287e6i			0.881266i	0.897687	+	0.440633i	$0.145246\pi$
$43$			3.01287e6i			0.881266i	−0.897687	+	0.440633i	$0.854754\pi$
$44$	948486.	−	1.25884e6i	0.253058	−	0.335862i
$45$	599436.	−	803939.i	0.146182	−	0.196053i
$46$	3.68745e6	+	32066.5i	0.823560	+	0.00716177i
$47$	−2.28936e6	−	743857.i	−0.469161	−	0.152440i	0.0648891	−	0.997892i	$-0.479331\pi$
$47$	−2.28936e6	−	743857.i	−0.469161	−	0.152440i	−0.534050	+	0.845453i	$0.679331\pi$
$48$	4.43500e6	−	1.27231e6i	0.835466	−	0.239677i
$49$	5.47359e6			0.949485
$50$	3.84069e6	−	4.93068e6i	0.614511	−	0.788908i
$51$			9.03432e6i			1.33541i
$52$	241055.	−	700214.i	0.0329687	−	0.0957673i
$53$	−3.42085e6	+	1.05283e7i	−0.433542	+	1.33430i	0.461032	+	0.887384i	$0.347479\pi$
$53$	−3.42085e6	+	1.05283e7i	−0.433542	+	1.33430i	−0.894574	+	0.446921i	$0.852521\pi$
$54$	−9.19759e6	−	79983.2i	−1.08168	−	0.00940641i
$55$	−3.14091e6	+	2.22314e6i	−0.343245	+	0.242950i
$56$	−737639.	+	2.08364e6i	−0.0750053	+	0.211871i
$57$	1.61957e7			1.53427
$58$	6.84253e6	+	9.59225e6i	0.604651	+	0.847634i
$59$	−7.70792e6	+	1.06090e7i	−0.636106	+	0.875524i	−0.998400	−	0.0565392i	$-0.981993\pi$
$59$	−7.70792e6	+	1.06090e7i	−0.636106	+	0.875524i	0.362295	+	0.932064i	$0.381993\pi$
$60$	−1.12594e7	−	335265.i	−0.868780	−	0.0258692i
$61$	1.03807e7	−	7.54199e6i	0.749731	−	0.544711i	−0.146013	−	0.989283i	$-0.546644\pi$
$61$	1.03807e7	−	7.54199e6i	0.749731	−	0.544711i	0.895743	+	0.444571i	$0.146644\pi$
$62$	−5.64625e6	+	1.68766e7i	−0.382114	+	1.14214i
$63$	508935.	−	700489.i	0.0323073	−	0.0444671i
$64$	1.30403e7	+	1.05558e7i	0.777262	+	0.629177i
$65$	−1.08072e6	+	1.44942e6i	−0.0605423	+	0.0811969i
$66$	6.57706e6	+	2.20043e6i	0.346622	+	0.115966i
$67$	−2.51604e7	+	8.17511e6i	−1.24859	+	0.405690i	−0.857414	−	0.514627i	$-0.827930\pi$
$67$	−2.51604e7	+	8.17511e6i	−1.24859	+	0.405690i	−0.391172	+	0.920317i	$0.627930\pi$
$68$	−2.69088e7	+	1.88442e7i	−1.25851	+	0.881337i
$69$	5.01410e6	+	1.54318e7i	0.221206	+	0.680801i
$70$	3.26319e6	−	4.29796e6i	0.135910	−	0.179007i
$71$	−6.65726e6	−	2.16308e6i	−0.261976	−	0.0851213i	0.175084	−	0.984554i	$-0.443980\pi$
$71$	−6.65726e6	−	2.16308e6i	−0.261976	−	0.0851213i	−0.437060	+	0.899432i	$0.643980\pi$
$72$	−3.72296e6	−	5.41586e6i	−0.138534	−	0.201529i
$73$	4.14409e7	−	3.01085e7i	1.45928	−	1.06023i	0.475725	−	0.879594i	$-0.342186\pi$
$73$	4.14409e7	−	3.01085e7i	1.45928	−	1.06023i	0.983551	−	0.180632i	$-0.0578142\pi$
$74$	3.26997e7	−	1.03113e7i	1.09048	−	0.343863i
$75$	2.59366e7	+	9.14297e6i	0.819725	+	0.288963i
$76$	3.37818e7	+	4.82391e7i	1.01258	+	1.44592i
$77$	−2.68796e6	+	1.95292e6i	−0.0764645	+	0.0555547i
$78$	3.25838e6	+	28335.2i	0.0880286	+	0.000765506i
$79$	5.38806e7	+	1.75069e7i	1.38333	+	0.449470i	0.903761	−	0.428037i	$-0.140795\pi$
$79$	5.38806e7	+	1.75069e7i	1.38333	+	0.449470i	0.479564	+	0.877507i	$0.340795\pi$
$80$	−2.24868e7	−	3.42355e7i	−0.548993	−	0.835827i
$81$	−9.25355e6	−	2.84795e7i	−0.214965	−	0.661595i
$82$	−5.10029e7	+	1.60829e7i	−1.12808	+	0.355720i
$83$	5.49796e7	−	1.78640e7i	1.15848	−	0.376414i	0.334150	−	0.942520i	$-0.391551\pi$
$83$	5.49796e7	−	1.78640e7i	1.15848	−	0.376414i	0.824332	+	0.566106i	$0.191551\pi$
$84$	−9.72442e6	−	169142.i	−0.195320	−	0.00339730i
$85$	7.65780e7	−	2.38381e7i	1.46699	−	0.456663i
$86$	−3.87516e7	−	2.86728e7i	−0.708428	−	0.524175i
$87$	−3.04740e7	+	4.19439e7i	−0.531928	+	0.732136i
$88$	7.16474e6	+	2.41796e7i	0.119473	+	0.403197i
$89$	2.82158e7	−	2.05000e7i	0.449710	−	0.326734i	−0.339771	−	0.940508i	$-0.610350\pi$
$89$	2.82158e7	−	2.05000e7i	0.449710	−	0.326734i	0.789481	+	0.613774i	$0.210350\pi$
$90$	4.63557e6	+	1.53609e7i	0.0706534	+	0.234124i
$91$	−917555.	+	1.26291e6i	−0.0133803	+	0.0184164i
$92$	−3.55051e7	+	4.71229e7i	−0.495609	+	0.657780i
$93$	−7.83052e7			−1.04679
$94$	3.13548e7	−	2.23666e7i	0.401598	−	0.286476i
$95$	−4.27343e7	−	1.37281e8i	−0.524665	−	1.68545i
$96$	−2.58425e7	+	6.91512e7i	−0.304263	+	0.814169i
$97$	−9.23936e6	+	2.84358e7i	−0.104365	+	0.321202i	−0.989581	−	0.143978i	$-0.954011\pi$
$97$	−9.23936e6	+	2.84358e7i	−0.104365	+	0.321202i	0.885216	+	0.465180i	$0.154011\pi$
$98$	−5.20909e7	+	7.04014e7i	−0.564752	+	0.763267i
$99$		−	9.87881e6i		−	0.102840i
$100$	2.68674e7	+	9.63231e7i	0.268674	+	0.963231i
$101$	1.29415e8			1.24365			0.621826	−	0.783155i	$-0.286391\pi$
$101$	1.29415e8			1.24365			0.621826	+	0.783155i	$0.286391\pi$
$102$	−1.16199e8	−	8.59775e7i	−1.07350	−	0.794299i
$103$	6.38086e7	+	2.07327e7i	0.566931	+	0.184207i	0.578437	−	0.815727i	$-0.303663\pi$
$103$	6.38086e7	+	2.07327e7i	0.566931	+	0.184207i	−0.0115064	+	0.999934i	$0.503663\pi$
$104$	6.71209e6	+	9.76422e6i	0.0573752	+	0.0834649i
$105$	2.24901e7	+	7.61647e6i	0.185027	+	0.0626609i
$106$	−1.02860e8	−	1.44194e8i	−0.814744	−	1.14216i
$107$			3.63646e6i			0.0277424i	0.999904	+	0.0138712i	$0.00441548\pi$
$107$			3.63646e6i			0.0277424i	−0.999904	+	0.0138712i	$0.995585\pi$
$108$	8.85601e7	−	1.17538e8i	0.650943	−	0.863941i
$109$	−3.37170e7	−	2.44968e7i	−0.238859	−	0.173542i	0.461916	−	0.886924i	$-0.347162\pi$
$109$	−3.37170e7	−	2.44968e7i	−0.238859	−	0.173542i	−0.700775	+	0.713382i	$0.747162\pi$
$110$	1.29728e6	−	6.15555e7i	0.00886057	−	0.420432i
$111$	8.86777e7	+	1.22054e8i	0.584147	+	0.804010i
$112$	−1.97798e7	−	2.93170e7i	−0.125704	−	0.186315i
$113$	1.04031e8	+	7.55829e7i	0.638041	+	0.463564i	0.859177	−	0.511679i	$-0.170976\pi$
$113$	1.04031e8	+	7.55829e7i	0.638041	+	0.463564i	−0.221136	+	0.975243i	$0.570976\pi$
$114$	−1.54131e8	+	2.08310e8i	−0.912579	+	1.23336i
$115$	1.17575e8	−	8.32198e7i	0.672239	−	0.475812i
$116$	−1.88494e8	−	3.27858e6i	−1.04104	−	0.0181073i
$117$	−1.43428e6	−	4.41427e6i	−0.00765406	−	0.0235568i
$118$	−6.30991e7	−	2.00103e8i	−0.325458	−	1.03211i
$119$	6.58592e7	−	2.13989e7i	0.328419	−	0.106710i
$120$	1.11465e8	−	1.41628e8i	0.537544	−	0.683004i
$121$	5.45264e7	−	1.67815e8i	0.254370	−	0.782870i
$122$	−1.78524e6	+	2.05291e8i	−0.00805854	+	0.926683i
$123$	−1.38314e8	−	1.90373e8i	−0.604289	−	0.831733i
$124$	−1.63333e8	−	2.33233e8i	−0.690854	−	0.986512i
$125$	9.06230e6	−	2.43972e8i	0.0371192	−	0.999311i
$126$	4.16627e6	+	1.32123e7i	0.0165297	+	0.0524200i
$127$	8.07030e7	+	1.11078e8i	0.310223	+	0.426986i	0.935451	−	0.353457i	$-0.114994\pi$
$127$	8.07030e7	+	1.11078e8i	0.310223	+	0.426986i	−0.625227	+	0.780443i	$0.714994\pi$
$128$	−2.59871e8	+	6.72668e7i	−0.968094	+	0.250588i
$129$	6.55467e7	−	2.01732e8i	0.236696	−	0.728477i
$130$	−8.35743e6	−	2.76940e7i	−0.0292617	−	0.0969642i
$131$	−2.87458e8	+	9.34006e7i	−0.976087	+	0.317150i	−0.753271	−	0.657711i	$-0.771525\pi$
$131$	−2.87458e8	+	9.34006e7i	−0.976087	+	0.317150i	−0.222816	+	0.974860i	$0.571525\pi$
$132$	−9.08942e7	+	6.36532e7i	−0.299392	+	0.209664i
$133$	−3.83617e7	−	1.18065e8i	−0.122600	−	0.377325i
$134$	1.34298e8	−	4.01414e8i	0.416532	−	1.24501i
$135$	−2.93267e8	+	2.07574e8i	−0.882932	+	0.624941i
$136$	1.37105e7	−	5.25436e8i	0.0400773	−	1.53591i
$137$	−1.87550e8	−	1.36263e8i	−0.532396	−	0.386808i	0.288857	−	0.957372i	$-0.406725\pi$
$137$	−1.87550e8	−	1.36263e8i	−0.532396	−	0.386808i	−0.821253	+	0.570564i	$0.806725\pi$
$138$	−2.46202e8	−	8.23696e7i	−0.678852	−	0.227117i
$139$	1.29325e8	+	1.78001e8i	0.346437	+	0.476830i	0.946308	−	0.323267i	$-0.104781\pi$
$139$	1.29325e8	+	1.78001e8i	0.346437	+	0.476830i	−0.599871	+	0.800097i	$0.704781\pi$
$140$	2.42253e7	+	8.28738e7i	0.0630604	+	0.215727i
$141$	1.37105e8	+	9.96123e7i	0.346877	+	0.252021i
$142$	9.11771e7	−	6.50402e7i	0.224250	−	0.159966i
$143$			1.78104e7i			0.0425922i
$144$	1.05089e8	+	3.65686e6i	0.244404	+	0.00850468i
$145$	4.35940e8	+	1.47635e8i	0.986178	+	0.333977i
$146$	−7.12688e6	+	8.19549e8i	−0.0156851	+	1.80370i
$147$	−3.66493e8	−	1.19081e8i	−0.784868	−	0.255019i
$148$	−1.78572e8	+	5.18713e8i	−0.372191	+	1.08114i
$149$	−3.01581e7			−0.0611869			−0.0305935	−	0.999532i	$-0.509740\pi$
$149$	−3.01581e7			−0.0611869			−0.0305935	+	0.999532i	$0.509740\pi$
$150$	−3.64429e8	+	2.46585e8i	−0.719861	+	0.487082i
$151$			3.98894e8i			0.767272i	0.923484	+	0.383636i	$0.125328\pi$
$151$			3.98894e8i			0.767272i	−0.923484	+	0.383636i	$0.874672\pi$
$152$	−9.41945e8	−	2.45787e7i	−1.76462	−	0.0460452i
$153$	−6.36256e7	+	1.95820e8i	−0.116109	+	0.357347i
$154$	462268.	−	5.31580e7i	0.000821884	−	0.0945118i
$155$	2.06617e8	+	6.63742e8i	0.357964	+	1.14993i
$156$	−3.13737e7	+	4.16397e7i	−0.0529746	+	0.0703087i
$157$	−1.05338e8			−0.173376			−0.0866879	−	0.996236i	$-0.527628\pi$
$157$	−1.05338e8			−0.173376			−0.0866879	+	0.996236i	$0.527628\pi$
$158$	−7.37943e8	+	5.26404e8i	−1.18412	+	0.844677i
$159$	4.58098e8	−	6.30517e8i	0.716753	−	0.986526i
$160$	6.54338e8	+	3.65863e7i	0.998440	+	0.0558263i
$161$	1.00620e8	−	7.31044e7i	0.149754	−	0.108803i
$162$	4.54367e8	+	1.52014e8i	0.659701	+	0.220710i
$163$	4.60251e8	−	6.33482e8i	0.651996	−	0.897395i	−0.347188	−	0.937796i	$-0.612863\pi$
$163$	4.60251e8	−	6.33482e8i	0.651996	−	0.897395i	0.999184	+	0.0404007i	$0.0128634\pi$
$164$	2.78525e8	−	8.09056e8i	0.385025	−	1.11842i
$165$	2.58670e8	−	8.05218e7i	0.348988	−	0.108637i
$166$	−2.93462e8	+	8.77155e8i	−0.386473	+	1.15516i
$167$	−1.28104e9	+	4.16236e8i	−1.64702	+	0.535148i	−0.978091	−	0.208180i	$-0.933246\pi$
$167$	−1.28104e9	+	4.16236e8i	−1.64702	+	0.535148i	−0.668927	+	0.743328i	$0.733246\pi$
$168$	9.47205e7	−	1.23466e8i	0.118907	−	0.154992i
$169$	−2.49489e8	−	7.67848e8i	−0.305847	−	0.941300i
$170$	−4.22170e8	+	1.21181e9i	−0.505466	+	1.45090i
$171$	3.51044e8	+	1.14061e8i	0.410560	+	0.133399i
$172$	7.37580e8	−	2.25550e8i	0.842743	−	0.257709i
$173$	1.65812e8	−	1.20470e8i	0.185111	−	0.134491i	−0.491370	−	0.870951i	$-0.663504\pi$
$173$	1.65812e8	−	1.20470e8i	0.185111	−	0.134491i	0.676482	+	0.736460i	$0.263504\pi$
$174$	−2.49468e8	−	7.91128e8i	−0.272156	−	0.863077i
$175$	5.21704e6	−	2.10731e8i	0.00556253	−	0.224686i
$176$	−3.79183e8	−	1.37958e8i	−0.395183	−	0.143780i
$177$	7.46902e8	−	5.42656e8i	0.760975	−	0.552881i
$178$	−4.85248e6	+	5.58006e8i	−0.00483374	+	0.555852i
$179$	1.47939e9	+	4.80683e8i	1.44102	+	0.468216i	0.922216	−	0.386676i	$-0.126377\pi$
$179$	1.47939e9	+	4.80683e8i	1.44102	+	0.468216i	0.518806	+	0.854892i	$0.326377\pi$
$180$	−2.41687e8	−	8.65629e7i	−0.230231	−	0.0824597i
$181$	2.40647e8	+	7.40634e8i	0.224215	+	0.690064i	0.998370	+	0.0570677i	$0.0181751\pi$
$181$	2.40647e8	+	7.40634e8i	0.224215	+	0.690064i	−0.774155	+	0.632996i	$0.781825\pi$
$182$	−7.51134e6	−	2.38204e7i	−0.00684592	−	0.0217102i
$183$	−8.59134e8	+	2.79149e8i	−0.766049	+	0.248904i
$184$	−2.68201e8	−	9.05124e8i	−0.233985	−	0.789654i
$185$	8.00589e8	−	1.07372e9i	0.683475	−	0.916649i
$186$	7.45213e8	−	1.00716e9i	0.622628	−	0.841487i
$187$	4.64398e8	−	6.39189e8i	0.379773	−	0.522712i
$188$	−1.07169e7	+	6.16143e8i	−0.00857902	+	0.493230i
$189$	−2.50975e8	+	1.82344e8i	−0.196690	+	0.142904i
$190$	2.17240e9	+	7.56820e8i	1.66696	+	0.580735i
$191$	1.18237e9	−	1.62739e9i	0.888422	−	1.22281i	−0.0855942	−	0.996330i	$-0.527279\pi$
$191$	1.18237e9	−	1.62739e9i	0.888422	−	1.22281i	0.974016	−	0.226478i	$-0.0727211\pi$
$192$	−6.43486e8	−	9.90482e8i	−0.473516	−	0.728856i
$193$	5.96776e8			0.430112			0.215056	−	0.976602i	$-0.431007\pi$
$193$	5.96776e8			0.430112			0.215056	+	0.976602i	$0.431007\pi$
$194$	−2.77813e8	−	3.89454e8i	−0.196131	−	0.274947i
$195$	1.03894e8	−	7.35364e7i	0.0718542	−	0.0508585i
$196$	−4.09765e8	−	1.33999e9i	−0.277658	−	0.907980i
$197$	−5.04184e8	+	1.55172e9i	−0.334753	+	1.03026i	0.632091	+	0.774894i	$0.282197\pi$
$197$	−5.04184e8	+	1.55172e9i	−0.334753	+	1.03026i	−0.966844	+	0.255369i	$0.917803\pi$
$198$	1.27061e8	+	9.40144e7i	0.0826709	+	0.0611693i
$199$		−	3.43759e8i		−	0.219200i	−0.993976	−	0.109600i	$-0.965043\pi$
$199$		−	3.43759e8i		−	0.219200i	0.993976	−	0.109600i	$-0.0349571\pi$
$200$	−1.49460e9	−	5.71117e8i	−0.934124	−	0.356948i
$201$	1.86251e9			1.14108
$202$	−1.23161e9	+	1.66454e9i	−0.739722	+	0.999741i
$203$	3.77948e8	+	1.22803e8i	0.222561	+	0.0723143i
$204$	2.21169e9	−	6.76329e8i	1.27703	−	0.390515i
$205$	−1.24871e9	+	1.67472e9i	−0.707042	+	0.948256i
$206$	−8.73915e8	+	6.23398e8i	−0.485289	+	0.346176i
$207$			3.69798e8i			0.201411i
$208$	−1.89465e8	−	6.59291e6i	−0.101222	−	0.00352228i
$209$	−1.14587e9	−	8.32521e8i	−0.600550	−	0.436325i
$210$	−3.11997e8	+	2.16784e8i	−0.160425	+	0.111468i
$211$	2.22947e9	+	3.06860e9i	1.12479	+	1.54814i	0.797603	+	0.603182i	$0.206101\pi$
$211$	2.22947e9	+	3.06860e9i	1.12479	+	1.54814i	0.327187	+	0.944959i	$0.393899\pi$
$212$	2.83352e9	+	4.92849e7i	1.40276	+	0.0243989i
$213$	3.98689e8	+	2.89664e8i	0.193694	+	0.140727i
$214$	−4.67722e7	−	3.46074e7i	−0.0223014	−	0.0165011i
$215$	−1.88290e9	−	2.33038e7i	−0.881199	−	0.0109062i
$216$	6.68971e8	+	2.25764e9i	0.307321	+	1.03715i
$217$	1.85476e8	+	5.70837e8i	0.0836467	+	0.257438i
$218$	6.35955e8	−	2.00537e8i	0.281579	−	0.0887910i
$219$	−3.42977e9	+	1.11440e9i	−1.49104	+	0.484467i
$220$	7.79381e8	+	6.02495e8i	0.332705	+	0.257195i
$221$	1.14710e8	−	3.53041e8i	0.0480875	−	0.147998i
$222$	−2.41379e9	−	2.09906e7i	−0.993773	−	0.00864196i
$223$	−1.04648e9	−	1.44036e9i	−0.423167	−	0.582439i	0.543201	−	0.839603i	$-0.317212\pi$
$223$	−1.04648e9	−	1.44036e9i	−0.423167	−	0.582439i	−0.966368	+	0.257164i	$0.917212\pi$
$224$	5.65316e8	+	2.45951e7i	0.224543	+	0.00976915i
$225$	4.97787e8	+	3.80837e8i	0.194229	+	0.148597i
$226$	−1.96218e9	+	6.18741e8i	−0.752153	+	0.237178i
$227$	−1.64338e9	−	2.26192e9i	−0.618919	−	0.851870i	0.378354	−	0.925661i	$-0.376490\pi$
$227$	−1.64338e9	−	2.26192e9i	−0.618919	−	0.851870i	−0.997274	+	0.0737913i	$0.976490\pi$
$228$	−1.21245e9	−	3.96487e9i	−0.448667	−	1.46720i
$229$	2.98197e8	−	9.17755e8i	0.108433	−	0.333722i	−0.882088	−	0.471085i	$-0.843863\pi$
$229$	2.98197e8	−	9.17755e8i	0.108433	−	0.333722i	0.990521	+	0.137363i	$0.0438626\pi$
$230$	−4.85615e7	+	2.30423e9i	−0.0173533	+	0.823408i
$231$	2.22464e8	−	7.22828e7i	0.0781287	−	0.0253856i
$232$	1.83603e9	−	2.39321e9i	0.633763	−	0.826094i
$233$	8.46546e8	+	2.60540e9i	0.287228	+	0.883997i	0.985722	+	0.168381i	$0.0538539\pi$
$233$	8.46546e8	+	2.60540e9i	0.287228	+	0.883997i	−0.698494	+	0.715616i	$0.746146\pi$
$234$	7.04261e7	+	2.35618e7i	0.0234893	+	0.00785861i
$235$	4.82582e8	−	1.42498e9i	0.158234	−	0.467238i
$236$	3.17423e9	+	1.09276e9i	1.02327	+	0.352269i
$237$	−3.22679e9	−	2.34440e9i	−1.02277	−	0.743086i
$238$	−3.51533e8	+	1.05073e9i	−0.109562	+	0.327479i
$239$	2.97325e9	+	4.09233e9i	0.911254	+	1.25423i	0.966737	+	0.255774i	$0.0823304\pi$
$239$	2.97325e9	+	4.09233e9i	0.911254	+	1.25423i	−0.0554821	+	0.998460i	$0.517670\pi$
$240$	7.60827e8	+	2.78150e9i	0.229319	+	0.838368i
$241$	8.91706e8	+	6.47863e8i	0.264334	+	0.192050i	0.712056	−	0.702123i	$-0.247764\pi$
$241$	8.91706e8	+	6.47863e8i	0.264334	+	0.192050i	−0.447721	+	0.894173i	$0.647764\pi$
$242$	1.63952e9	+	2.29838e9i	0.478031	+	0.670131i
$243$		−	1.66352e9i		−	0.477093i
$244$	−2.62347e9	−	1.97667e9i	−0.740144	−	0.557667i
$245$	−4.23368e7	+	3.42073e9i	−0.0117504	+	0.949412i
$246$	3.76487e9	+	3.27397e7i	1.02804	+	0.00893994i
$247$	−6.32894e8	−	2.05640e8i	−0.170037	−	0.0552483i
$248$	4.55424e9	+	1.18836e8i	1.20395	+	0.0314154i
$249$	−4.06989e9			−1.05873
$250$	3.05173e9	+	2.43839e9i	0.781243	+	0.624227i
$251$			4.01460e9i			1.01146i	0.862692	+	0.505729i	$0.168776\pi$
$251$			4.01460e9i			1.01146i	−0.862692	+	0.505729i	$0.831224\pi$
$252$	−2.09586e8	−	7.21519e7i	−0.0519709	−	0.0178915i
$253$	4.38499e8	−	1.34956e9i	0.107025	−	0.329390i
$254$	−2.19672e9	−	1.91029e7i	−0.527764	−	0.00458949i
$255$	−5.64602e9	−	6.98781e7i	−1.33531	−	0.0165265i
$256$	1.60794e9	−	3.98262e9i	0.374378	−	0.927276i
$257$	−5.60682e8			−0.128524			−0.0642619	−	0.997933i	$-0.520469\pi$
$257$	−5.60682e8			−0.128524			−0.0642619	+	0.997933i	$0.520469\pi$
$258$	1.97088e9	+	2.76290e9i	0.444818	+	0.623571i
$259$	6.79718e8	−	9.35552e8i	0.151053	−	0.207907i
$260$	4.35735e8	+	1.56064e8i	0.0953519	+	0.0341514i
$261$	−9.55924e8	+	6.94519e8i	−0.205997	+	0.149666i
$262$	1.53435e9	−	4.58615e9i	0.325626	−	0.973292i
$263$	2.03531e9	−	2.80136e9i	0.425409	−	0.585525i	−0.541483	−	0.840712i	$-0.682137\pi$
$263$	2.03531e9	−	2.80136e9i	0.425409	−	0.585525i	0.966892	+	0.255186i	$0.0821369\pi$
$264$	4.63123e7	−	1.77485e9i	0.00953412	−	0.365382i
$265$	−6.55323e9	−	2.21930e9i	−1.32884	−	0.450021i
$266$	1.88363e9	+	6.30190e8i	0.376244	+	0.125877i
$267$	−2.33523e9	+	7.58761e8i	−0.459498	+	0.149300i
$268$	3.88491e9	+	5.54750e9i	0.753081	+	1.07537i
$269$	−1.55613e8	−	4.78926e8i	−0.0297191	−	0.0914660i	0.935097	−	0.354392i	$-0.115312\pi$
$269$	−1.55613e8	−	4.78926e8i	−0.0297191	−	0.0914660i	−0.964816	+	0.262927i	$0.915312\pi$
$270$	1.21127e8	−	5.74743e9i	0.0227921	−	1.08148i
$271$	6.81481e9	+	2.21427e9i	1.26350	+	0.410538i	0.862742	−	0.505644i	$-0.168745\pi$
$271$	6.81481e9	+	2.21427e9i	1.26350	+	0.410538i	0.400763	+	0.916182i	$0.368745\pi$
$272$	6.62769e9	+	5.17680e9i	1.21084	+	0.945771i
$273$	8.89115e7	−	6.45980e7i	0.0160069	−	0.0116297i
$274$	3.53749e9	−	1.11548e9i	0.627614	−	0.197907i
$275$	−1.36506e9	−	1.98011e9i	−0.238683	−	0.346226i
$276$	3.40248e9	−	2.38276e9i	0.586354	−	0.410623i
$277$	−6.94768e9	+	5.04778e9i	−1.18011	+	0.857397i	−0.992183	−	0.124787i	$-0.960175\pi$
$277$	−6.94768e9	+	5.04778e9i	−1.18011	+	0.857397i	−0.187922	+	0.982184i	$0.560175\pi$
$278$	−3.52021e9	−	3.06121e7i	−0.589372	−	0.00512524i
$279$	−1.69727e9	−	5.51477e8i	−0.280114	−	0.0910145i
$280$	−1.29647e9	−	4.77106e8i	−0.210926	−	0.0776216i
$281$	−2.71712e9	−	8.36245e9i	−0.435797	−	1.34125i	−0.892268	−	0.451507i	$-0.850887\pi$
$281$	−2.71712e9	−	8.36245e9i	−0.435797	−	1.34125i	0.456471	−	0.889738i	$-0.349113\pi$
$282$	−2.58601e9	+	8.15452e8i	−0.408915	+	0.128944i
$283$	1.26089e9	−	4.09687e8i	0.196576	−	0.0638714i	−0.209074	−	0.977900i	$-0.567045\pi$
$283$	1.26089e9	−	4.09687e8i	0.196576	−	0.0638714i	0.405650	+	0.914028i	$0.367045\pi$
$284$	−3.11639e7	+	1.79169e9i	−0.00479047	+	0.275417i
$285$	−1.25270e8	+	1.01216e10i	−0.0189875	+	1.53415i
$286$	−2.29078e8	−	1.69498e8i	−0.0342388	−	0.0253338i
$287$	−1.06018e9	+	1.45921e9i	−0.156262	+	0.215076i
$288$	−1.04715e9	+	1.31686e9i	−0.152208	+	0.191412i
$289$	−7.67863e9	+	5.57885e9i	−1.10076	+	0.799748i
$290$	−6.04762e9	+	4.20206e9i	−0.855052	+	0.594115i
$291$	1.23727e9	−	1.70296e9i	0.172541	−	0.237483i
$292$	−1.04732e10	−	7.89112e9i	−1.44062	−	1.08544i
$293$	9.51666e8			0.129126			0.0645630	−	0.997914i	$-0.479435\pi$
$293$	9.51666e8			0.129126			0.0645630	+	0.997914i	$0.479435\pi$
$294$	5.01945e9	−	3.58057e9i	0.671842	−	0.479251i
$295$	−6.57053e9	−	4.89914e9i	−0.867585	−	0.646892i
$296$	−4.97227e9	−	7.23327e9i	−0.647721	−	0.942253i
$297$	−1.09374e9	+	3.36620e9i	−0.140569	+	0.432628i
$298$	2.87007e8	−	3.87893e8i	0.0363939	−	0.0491866i
$299$		−	6.66706e8i		−	0.0834161i
$300$	2.96613e8	−	7.03399e9i	0.0366189	−	0.868393i
$301$	−1.62586e9			−0.198069
$302$	−5.13057e9	−	3.79618e9i	−0.616791	−	0.456372i
$303$	−8.66519e9	−	2.81549e9i	−1.02803	−	0.334028i
$304$	9.28040e9	−	1.18814e10i	1.08661	−	1.39115i
$305$	4.63309e9	+	6.54575e9i	0.535391	+	0.756415i
$306$	−1.91312e9	−	2.68192e9i	−0.218201	−	0.305887i
$307$		−	1.03098e10i		−	1.16064i	−0.814389	−	0.580319i	$-0.802928\pi$
$307$		−	1.03098e10i		−	1.16064i	0.814389	−	0.580319i	$-0.197072\pi$
$308$	6.79319e8	+	5.11838e8i	0.0754868	+	0.0568761i
$309$	−3.82136e9	−	2.77638e9i	−0.419164	−	0.304540i
$310$	−1.05034e10	−	3.65917e9i	−1.13732	−	0.396220i
$311$	−7.85698e9	−	1.08142e10i	−0.839874	−	1.15599i	−0.986004	−	0.166722i	$-0.946682\pi$
$311$	−7.85698e9	−	1.08142e10i	−0.839874	−	1.15599i	0.146130	−	0.989265i	$-0.453318\pi$
$312$	−2.36993e8	−	7.99804e8i	−0.0250102	−	0.0844044i
$313$	4.85076e7	+	3.52429e7i	0.00505397	+	0.00367193i	0.590309	−	0.807177i	$-0.299006\pi$
$313$	4.85076e7	+	3.52429e7i	0.00505397	+	0.00367193i	−0.585255	+	0.810849i	$0.699006\pi$
$314$	1.00248e9	−	1.35486e9i	0.103124	−	0.139372i
$315$	4.33836e8	+	3.23478e8i	0.0440639	+	0.0328551i
$316$	2.52225e8	−	1.45011e10i	0.0252953	−	1.45429i
$317$	−6.03850e9	−	1.85846e10i	−0.597987	−	1.84042i	−0.539257	−	0.842141i	$-0.681295\pi$
$317$	−6.03850e9	−	1.85846e10i	−0.597987	−	1.84042i	−0.0587304	−	0.998274i	$-0.518705\pi$
$318$	3.75011e9	+	1.18925e10i	0.366720	+	1.16296i
$319$	4.31215e9	−	1.40110e9i	0.416419	−	0.135303i
$320$	−6.69776e9	+	8.06791e9i	−0.638748	+	0.769416i
$321$	7.91132e7	−	2.43485e8i	0.00745124	−	0.0229326i
$322$	−1.73043e7	+	1.98989e9i	−0.00160964	+	0.185099i
$323$	1.73516e10	+	2.38825e10i	1.59415	+	2.19416i
$324$	−6.27931e9	+	4.39739e9i	−0.569812	+	0.399039i
$325$	−8.97456e8	−	6.86608e8i	−0.0804414	−	0.0615426i
$326$	3.76774e9	+	1.19485e10i	0.333588	+	1.05789i
$327$	1.72463e9	+	2.37375e9i	0.150836	+	0.207608i
$328$	7.75543e9	+	1.12820e10i	0.670055	+	0.974743i
$329$	4.01413e8	−	1.23542e9i	0.0342616	−	0.105446i
$330$	−1.42603e9	+	4.09333e9i	−0.120247	+	0.345160i
$331$	1.23005e10	−	3.99669e9i	1.02474	−	0.332957i	0.252029	−	0.967720i	$-0.418902\pi$
$331$	1.23005e10	−	3.99669e9i	1.02474	−	0.332957i	0.772707	+	0.634762i	$0.218902\pi$
$332$	−8.48916e9	−	1.21222e10i	−0.698735	−	0.997766i
$333$	1.06251e9	+	3.27006e9i	0.0864083	+	0.265937i
$334$	6.83777e9	−	2.04380e10i	0.549450	−	1.64230i
$335$	−4.91445e9	−	1.57873e10i	−0.390207	−	1.25351i
$336$	6.86584e8	+	2.39329e9i	0.0538687	+	0.187775i
$337$	−4.92192e9	−	3.57599e9i	−0.381606	−	0.277253i	0.380401	−	0.924822i	$-0.375786\pi$
$337$	−4.92192e9	−	3.57599e9i	−0.381606	−	0.277253i	−0.762007	+	0.647569i	$0.775786\pi$
$338$	1.22504e10	+	4.09850e9i	0.938605	+	0.314021i
$339$	−5.32121e9	−	7.32402e9i	−0.402913	−	0.554563i
$340$	−1.15686e10	−	1.69624e10i	−0.865694	−	1.26933i
$341$	5.54019e9	+	4.02518e9i	0.409739	+	0.297692i
$342$	−4.80786e9	+	3.42963e9i	−0.351437	+	0.250694i
$343$			6.06466e9i			0.438157i
$344$	−4.11835e9	+	1.16333e10i	−0.294096	+	0.830745i
$345$	−9.68292e9	+	3.01421e9i	−0.683487	+	0.212763i
$346$	−2.85160e7	+	3.27916e9i	−0.00198968	+	0.228801i
$347$	1.59869e10	+	5.19445e9i	1.10267	+	0.358279i	0.803129	−	0.595805i	$-0.203167\pi$
$347$	1.59869e10	+	5.19445e9i	1.10267	+	0.358279i	0.299540	+	0.954084i	$0.403167\pi$
$348$	1.25496e10	+	4.32032e9i	0.855684	+	0.294577i
$349$	9.90906e9			0.667930			0.333965	−	0.942586i	$-0.391613\pi$
$349$	9.90906e9			0.667930			0.333965	+	0.942586i	$0.391613\pi$
$350$	2.66078e9	+	2.07258e9i	0.177311	+	0.138115i
$351$			1.66296e9i			0.109560i
$352$	5.38301e9	−	3.56413e9i	0.350635	−	0.232158i
$353$	−4.23838e9	+	1.30444e10i	−0.272961	+	0.840088i	0.716790	+	0.697289i	$0.245610\pi$
$353$	−4.23838e9	+	1.30444e10i	−0.272961	+	0.840088i	−0.989752	+	0.142800i	$0.954390\pi$
$354$	−1.28450e8	+	1.47710e10i	−0.00817940	+	0.940582i
$355$	1.40331e9	−	4.14374e9i	0.0883569	−	0.260903i
$356$	−7.13089e9	−	5.37283e9i	−0.443960	−	0.334505i
$357$	−4.87525e9			−0.300140
$358$	−2.02616e10	+	1.44534e10i	−1.23350	+	0.879907i
$359$	1.13620e10	−	1.56384e10i	0.684031	−	0.941488i	−0.315943	−	0.948778i	$-0.602321\pi$
$359$	1.13620e10	−	1.56384e10i	0.684031	−	0.941488i	0.999973	+	0.00729062i	$0.00232070\pi$
$360$	3.41345e9	−	2.28478e9i	0.203228	−	0.136030i
$361$	2.90739e10	−	2.11234e10i	1.71188	−	1.24376i
$362$	−1.18162e10	−	3.95324e9i	−0.688088	−	0.230207i
$363$	−7.30181e9	+	1.00501e10i	−0.420537	+	0.578820i
$364$	3.77861e8	+	1.30082e8i	0.0215242	+	0.00740989i
$365$	1.84959e10	+	2.61314e10i	1.04209	+	1.47228i
$366$	4.58576e9	−	1.37068e10i	0.255556	−	0.763855i
$367$	1.22415e10	−	3.97750e9i	0.674792	−	0.219253i	0.0484780	−	0.998824i	$-0.484563\pi$
$367$	1.22415e10	−	3.97750e9i	0.674792	−	0.219253i	0.626314	+	0.779571i	$0.284563\pi$
$368$	1.41941e10	+	5.16426e9i	0.773957	+	0.281590i
$369$	−1.65723e9	−	5.10044e9i	−0.0893877	−	0.275107i
$370$	6.19113e9	+	2.05155e10i	0.330341	+	1.09465i
$371$	−5.68146e9	−	1.84602e9i	−0.299892	−	0.0974408i
$372$	5.86210e9	+	1.91699e10i	0.306113	+	1.00103i
$373$	1.38694e10	−	1.00767e10i	0.716512	−	0.520576i	−0.168756	−	0.985658i	$-0.553975\pi$
$373$	1.38694e10	−	1.00767e10i	0.716512	−	0.520576i	0.885268	+	0.465082i	$0.153975\pi$
$374$	3.80168e9	+	1.20561e10i	0.194307	+	0.616198i
$375$	−5.91453e9	+	1.61384e10i	−0.299085	+	0.816086i
$376$	−7.82284e9	−	6.00153e9i	−0.391393	−	0.300269i
$377$	1.72343e9	−	1.25214e9i	0.0853154	−	0.0619853i
$378$	4.31619e7	−	4.96336e9i	0.00211414	−	0.243113i
$379$	6.33685e9	+	2.05897e9i	0.307126	+	0.0997914i	0.458525	−	0.888681i	$-0.348378\pi$
$379$	6.33685e9	+	2.05897e9i	0.307126	+	0.0997914i	−0.151399	+	0.988473i	$0.548378\pi$
$380$	−3.04084e10	+	2.07389e10i	−1.45834	+	0.994606i
$381$	−2.98704e9	−	9.19315e9i	−0.141756	−	0.436279i
$382$	9.67917e9	+	3.06951e10i	0.454553	+	1.44150i
$383$	−2.75702e10	+	8.95811e9i	−1.28128	+	0.416314i	−0.869032	−	0.494756i	$-0.835257\pi$
$383$	−2.75702e10	+	8.95811e9i	−1.28128	+	0.416314i	−0.412251	+	0.911070i	$0.635257\pi$
$384$	1.88635e10	+	1.14966e9i	0.867555	+	0.0528745i
$385$	−1.19969e9	−	1.69495e9i	−0.0546042	−	0.0771462i
$386$	−5.67938e9	+	7.67573e9i	−0.255830	+	0.345757i
$387$	2.84146e9	−	3.91093e9i	0.126677	−	0.174356i
$388$	7.65303e9	+	1.33113e8i	0.337681	+	0.00587346i
$389$	−2.30268e9	+	1.67299e9i	−0.100562	+	0.0730627i	−0.636930	−	0.770922i	$-0.719796\pi$
$389$	−2.30268e9	+	1.67299e9i	−0.100562	+	0.0730627i	0.536368	+	0.843984i	$0.319796\pi$
$390$	−4.29109e7	+	2.03611e9i	−0.00185485	+	0.0880124i
$391$	−1.73840e10	+	2.39270e10i	−0.743777	+	1.02372i
$392$	2.11346e10	+	7.48194e9i	0.895053	+	0.316862i
$393$	2.12792e10			0.892040
$394$	−1.51600e10	−	2.12522e10i	−0.629093	−	0.881898i
$395$	−1.13577e10	+	3.35374e10i	−0.466555	+	1.37766i
$396$	−2.41843e9	+	7.39550e8i	−0.0983450	+	0.0300737i
$397$	9.54450e9	−	2.93750e10i	0.384230	−	1.18254i	−0.552807	−	0.833309i	$-0.686443\pi$
$397$	9.54450e9	−	2.93750e10i	0.384230	−	1.18254i	0.937037	−	0.349229i	$-0.113557\pi$
$398$	4.42143e9	+	3.27147e9i	0.176210	+	0.130380i
$399$			8.73982e9i			0.344835i
$400$	2.15695e10	−	1.37883e10i	0.842557	−	0.538607i
$401$	3.30843e10			1.27951			0.639757	−	0.768577i	$-0.279035\pi$
$401$	3.30843e10			1.27951			0.639757	+	0.768577i	$0.279035\pi$
$402$	−1.77251e10	+	2.39556e10i	−0.678710	+	0.917283i
$403$	3.06000e9	+	9.94253e8i	0.116011	+	0.0376944i
$404$	−9.68829e9	−	3.16820e10i	−0.363682	−	1.18929i
$405$	1.78699e10	−	5.56274e9i	0.664205	−	0.206761i
$406$	−5.17634e9	+	3.69249e9i	−0.190510	+	0.135898i
$407$		−	1.31939e10i		−	0.480833i
$408$	−1.23492e10	+	3.48832e10i	−0.445653	+	1.25885i
$409$	8.68831e9	+	6.31243e9i	0.310486	+	0.225581i	0.732105	−	0.681192i	$-0.238538\pi$
$409$	8.68831e9	+	6.31243e9i	0.310486	+	0.225581i	−0.421619	+	0.906773i	$0.638538\pi$
$410$	−9.65653e9	−	3.19988e10i	−0.341732	−	1.13239i
$411$	9.59324e9	+	1.32040e10i	0.336200	+	0.462740i
$412$	2.98700e8	−	1.71730e10i	0.0103668	−	0.596016i
$413$	−5.72504e9	−	4.15948e9i	−0.196779	−	0.142968i
$414$	−4.75634e9	−	3.51928e9i	−0.161909	−	0.119799i
$415$	1.07389e10	+	3.44978e10i	0.362048	+	1.16305i
$416$	1.88789e9	−	2.37415e9i	0.0630381	−	0.0792748i
$417$	−4.78668e9	−	1.47319e10i	−0.158303	−	0.487208i
$418$	2.16128e10	−	6.81523e9i	0.707957	−	0.223242i
$419$	−1.66981e10	+	5.42556e9i	−0.541767	+	0.176031i	−0.567101	−	0.823648i	$-0.691935\pi$
$419$	−1.66981e10	+	5.42556e9i	−0.541767	+	0.176031i	0.0253342	+	0.999679i	$0.491935\pi$
$420$	1.80921e8	−	6.07599e9i	0.00581424	−	0.195263i
$421$	7.26131e9	−	2.23480e10i	0.231146	−	0.711394i	−0.766463	−	0.642288i	$-0.777985\pi$
$421$	7.26131e9	−	2.23480e10i	0.231146	−	0.711394i	0.997609	−	0.0691063i	$-0.0220147\pi$
$422$	−6.06857e10	−	5.27729e8i	−1.91354	−	0.0166403i
$423$	2.27022e9	+	3.12468e9i	0.0709097	+	0.0975988i
$424$	−2.75999e10	+	3.59757e10i	−0.853972	+	1.11313i
$425$	1.43053e10	+	4.80420e10i	0.438473	+	1.47253i
$426$	−7.51990e9	+	2.37127e9i	−0.228335	+	0.0720016i
$427$	4.06994e9	+	5.60179e9i	0.122427	+	0.168506i
$428$	8.90240e8	−	2.72234e8i	0.0265297	−	0.00811273i
$429$	3.87475e8	−	1.19253e9i	0.0114397	−	0.0352078i
$430$	1.82189e10	−	2.39961e10i	0.532903	−	0.701887i
$431$	−1.60330e10	+	5.20943e9i	−0.464628	+	0.150967i	−0.531970	−	0.846763i	$-0.678548\pi$
$431$	−1.60330e10	+	5.20943e9i	−0.464628	+	0.150967i	0.0673420	+	0.997730i	$0.478548\pi$
$432$	−3.54043e10	−	1.28812e10i	−1.01653	−	0.369845i
$433$	−6.84251e9	−	2.10591e10i	−0.194654	−	0.599084i	−0.999980	−	0.00625206i	$-0.998010\pi$
$433$	−6.84251e9	−	2.10591e10i	−0.194654	−	0.599084i	0.805326	−	0.592832i	$-0.201990\pi$
$434$	−9.10723e9	−	3.04693e9i	−0.256701	−	0.0858822i
$435$	−2.59772e10	−	1.93692e10i	−0.725497	−	0.540948i
$436$	−3.47292e9	+	1.00881e10i	−0.0961057	+	0.279167i
$437$	4.28938e10	+	3.11641e10i	1.17617	+	0.854534i
$438$	1.83069e10	−	5.47192e10i	0.497414	−	1.48677i
$439$	−6.77965e9	−	9.33139e9i	−0.182536	−	0.251240i	0.707937	−	0.706276i	$-0.249626\pi$
$439$	−6.77965e9	−	9.33139e9i	−0.182536	−	0.251240i	−0.890473	+	0.455036i	$0.849626\pi$
$440$	−1.51665e10	+	4.29060e9i	−0.404645	+	0.114474i
$441$	−7.10512e9	−	5.16218e9i	−0.187853	−	0.136483i
$442$	3.44915e9	+	4.83522e9i	0.0903697	+	0.126685i
$443$			2.58965e10i			0.672399i	0.941791	+	0.336199i	$0.109142\pi$
$443$			2.58965e10i			0.672399i	−0.941791	+	0.336199i	$0.890858\pi$
$444$	2.32414e10	−	3.08464e10i	0.598041	−	0.793729i
$445$	1.25933e10	+	1.77921e10i	0.321143	+	0.453719i
$446$	2.84850e10	+	2.47708e8i	0.719907	+	0.00626039i
$447$	2.01928e9	+	6.56105e8i	0.0505786	+	0.0164340i
$448$	−5.69632e9	+	7.03703e9i	−0.141411	+	0.174694i
$449$	−3.90008e10			−0.959595			−0.479797	−	0.877379i	$-0.659290\pi$
$449$	−3.90008e10			−0.959595			−0.479797	+	0.877379i	$0.659290\pi$
$450$	−9.63565e9	+	2.77820e9i	−0.234980	+	0.0677506i
$451$			2.05789e10i			0.497412i
$452$	1.07154e10	−	3.11260e10i	0.256717	−	0.745710i
$453$	8.67815e9	−	2.67086e10i	0.206079	−	0.634247i
$454$	4.47324e10	+	3.88998e8i	1.05293	+	0.00915638i
$455$	−7.82159e8	−	5.83196e8i	−0.0182494	−	0.0136072i
$456$	6.25347e10	+	2.21382e10i	1.44631	+	0.512016i
$457$	−1.74974e10			−0.401152			−0.200576	−	0.979678i	$-0.564281\pi$
$457$	−1.74974e10			−0.401152			−0.200576	+	0.979678i	$0.564281\pi$
$458$	8.96630e9	+	1.25695e10i	0.203775	+	0.285664i
$459$	4.33608e10	−	5.96810e10i	0.976892	−	1.34458i
$460$	−2.91749e10	−	2.25535e10i	−0.651596	−	0.503712i
$461$	3.03914e10	−	2.20807e10i	0.672896	−	0.488887i	−0.198098	−	0.980182i	$-0.563476\pi$
$461$	3.03914e10	−	2.20807e10i	0.672896	−	0.488887i	0.870993	+	0.491295i	$0.163476\pi$
$462$	−1.18743e9	+	3.54922e9i	−0.0260640	+	0.0779050i
$463$	2.48603e10	−	3.42172e10i	0.540981	−	0.744597i	−0.447773	−	0.894147i	$-0.647783\pi$
$463$	2.48603e10	−	3.42172e10i	0.540981	−	0.744597i	0.988754	+	0.149551i	$0.0477827\pi$
$464$	1.33085e10	+	4.63906e10i	0.287115	+	1.00083i
$465$	6.05671e8	−	4.89370e10i	0.0129546	−	1.04671i
$466$	−4.15671e10	−	1.39067e10i	−0.881466	−	0.294904i
$467$	1.40212e10	−	4.55578e9i	0.294794	−	0.0957845i	−0.157886	−	0.987457i	$-0.550468\pi$
$467$	1.40212e10	−	4.55578e9i	0.294794	−	0.0957845i	0.452680	+	0.891673i	$0.350468\pi$
$468$	−9.73282e8	+	6.81589e8i	−0.0202887	+	0.0142082i
$469$	−4.41160e9	−	1.35775e10i	−0.0911810	−	0.280626i
$470$	1.37355e10	+	1.97682e10i	0.281484	+	0.405113i
$471$	7.05311e9	+	2.29169e9i	0.143317	+	0.0465664i
$472$	−4.42634e10	+	3.04274e10i	−0.891819	+	0.613052i
$473$	−1.50073e10	+	1.09034e10i	−0.299818	+	0.217830i
$474$	6.08624e10	−	1.91919e10i	1.20569	−	0.380193i
$475$	8.61244e10	−	2.56451e10i	1.69181	−	0.503766i
$476$	−1.01690e10	−	1.45210e10i	−0.198085	−	0.282858i
$477$	1.43698e10	−	1.04403e10i	0.277573	−	0.201669i
$478$	−8.09312e10	−	7.03786e8i	−1.55026	−	0.0134812i
$479$	−5.86324e10	−	1.90508e10i	−1.11377	−	0.361886i	−0.306383	−	0.951908i	$-0.599119\pi$
$479$	−5.86324e10	−	1.90508e10i	−1.11377	−	0.361886i	−0.807387	+	0.590022i	$0.799119\pi$
$480$	−4.30163e10	−	1.66852e10i	−0.810342	−	0.314315i
$481$	−1.91559e9	−	5.89557e9i	−0.0357867	−	0.110140i
$482$	−1.68190e10	+	5.30357e9i	−0.311610	+	0.0982608i
$483$	−8.32758e9	+	2.70579e9i	−0.153014	+	0.0497171i
$484$	−4.51647e10	−	7.85573e8i	−0.823034	−	0.0143155i
$485$	−1.76996e10	−	5.99410e9i	−0.319886	−	0.108332i
$486$	2.13962e10	+	1.58314e10i	0.383524	+	0.283774i
$487$	3.24022e10	−	4.45978e10i	0.576048	−	0.792863i	−0.417207	−	0.908812i	$-0.636991\pi$
$487$	3.24022e10	−	4.45978e10i	0.576048	−	0.792863i	0.993255	+	0.115949i	$0.0369909\pi$
$488$	5.03909e10	−	1.49315e10i	0.888532	−	0.263284i
$489$	−4.45986e10	+	3.24028e10i	−0.779984	+	0.566692i
$490$	−4.35946e10	−	3.30989e10i	−0.756220	−	0.574155i
$491$	1.98955e10	−	2.73839e10i	0.342318	−	0.471160i	−0.602799	−	0.797893i	$-0.705948\pi$
$491$	1.98955e10	−	2.73839e10i	0.342318	−	0.471160i	0.945117	+	0.326733i	$0.105948\pi$
$492$	−3.62505e10	+	4.81122e10i	−0.618663	+	0.821098i
$493$	−9.45001e10			−1.59972
$494$	8.66804e9	−	6.18326e9i	0.145550	−	0.103827i
$495$	6.17379e9	+	7.64101e7i	0.102833	+	0.00127271i
$496$	−4.48701e10	+	5.74457e10i	−0.741362	+	0.949141i
$497$	1.16728e9	−	3.59251e9i	0.0191315	−	0.0588806i
$498$	3.87322e10	−	5.23469e10i	0.629730	−	0.851087i
$499$		−	5.90692e9i		−	0.0952706i	−0.998865	−	0.0476353i	$-0.984831\pi$
$499$		−	5.90692e9i		−	0.0952706i	0.998865	−	0.0476353i	$-0.0151685\pi$
$500$	−6.04052e10	+	1.60458e10i	−0.966483	+	0.256732i
$501$	9.48298e10			1.50520
$502$	−5.16358e10	−	3.82061e10i	−0.813086	−	0.601613i
$503$	1.69479e10	+	5.50671e9i	0.264755	+	0.0860241i	0.438386	−	0.898787i	$-0.355550\pi$
$503$	1.69479e10	+	5.50671e9i	0.264755	+	0.0860241i	−0.173631	+	0.984811i	$0.555550\pi$
$504$	2.92260e9	−	2.00905e9i	0.0452947	−	0.0311363i
$505$	−1.00099e9	+	8.08781e10i	−0.0153909	+	1.24356i
$506$	1.31850e10	+	1.84834e10i	0.201130	+	0.281956i
$507$			5.68402e10i			0.860249i
$508$	2.11514e10	−	2.80724e10i	0.317602	−	0.421526i
$509$	5.45699e9	+	3.96473e9i	0.0812984	+	0.0590667i	0.627692	−	0.778462i	$-0.284000\pi$
$509$	5.45699e9	+	3.96473e9i	0.0812984	+	0.0590667i	−0.546394	+	0.837529i	$0.684000\pi$
$510$	5.46306e10	−	7.19541e10i	0.807524	−	1.06359i
$511$	1.62477e10	+	2.23630e10i	0.238291	+	0.327980i
$512$	3.59220e10	+	5.85830e10i	0.522735	+	0.852495i
$513$	−1.06990e11	−	7.77325e10i	−1.54480	−	1.12236i
$514$	5.33588e9	−	7.21149e9i	0.0764458	−	0.103317i
$515$	−1.34505e10	+	3.97170e10i	−0.191209	+	0.564608i
$516$	−5.42928e10	−	9.44344e8i	−0.765850	−	0.0133208i
$517$	−4.57986e9	−	1.40954e10i	−0.0641048	−	0.197294i
$518$	5.56435e9	+	1.76460e10i	0.0772850	+	0.245091i
$519$	−1.37231e10	+	4.45891e9i	−0.189140	+	0.0614554i
$520$	−6.15408e9	+	4.11921e9i	−0.0841686	+	0.0563379i
$521$	−2.09956e10	+	6.46179e10i	−0.284956	+	0.877005i	0.701456	+	0.712713i	$0.252534\pi$
$521$	−2.09956e10	+	6.46179e10i	−0.284956	+	0.877005i	−0.986412	+	0.164292i	$0.947466\pi$
$522$	1.64397e8	−	1.89047e10i	0.00221418	−	0.254617i
$523$	−6.20610e10	−	8.54196e10i	−0.829491	−	1.14170i	−0.988018	−	0.154342i	$-0.950674\pi$
$523$	−6.20610e10	−	8.54196e10i	−0.829491	−	1.14170i	0.158526	−	0.987355i	$-0.449326\pi$
$524$	4.43851e10	+	6.33801e10i	0.588724	+	0.840675i
$525$	−4.93389e9	+	1.39964e10i	−0.0649459	+	0.184237i
$526$	1.66615e10	+	5.28380e10i	0.217657	+	0.690245i
$527$	−8.38939e10	−	1.15470e11i	−1.08765	−	1.49702i
$528$	2.23874e10	+	1.74865e10i	0.288050	+	0.224993i
$529$	7.78489e9	−	2.39594e10i	0.0994099	−	0.305952i
$530$	9.09102e10	−	6.31670e10i	1.15215	−	0.800547i
$531$	2.00109e10	−	6.50194e9i	0.251703	−	0.0817833i
$532$	−2.60316e10	+	1.82299e10i	−0.324978	+	0.227582i
$533$	2.98781e9	+	9.19554e9i	0.0370207	+	0.113938i
$534$	1.24646e10	−	3.72566e10i	0.153290	−	0.458183i
$535$	−2.27262e9	−	2.81271e7i	−0.0277403	−	0.000343328i
$536$	−1.08324e11	−	2.82655e9i	−1.31239	−	0.0342451i
$537$	−8.85974e10	−	6.43698e10i	−1.06543	−	0.774079i
$538$	7.64088e9	+	2.55634e9i	0.0912041	+	0.0305133i
$539$	1.98086e10	+	2.72642e10i	0.234693	+	0.323027i
$540$	7.27708e10	+	5.62549e10i	0.855819	+	0.661585i
$541$	7.18788e10	+	5.22230e10i	0.839096	+	0.609639i	0.922118	−	0.386909i	$-0.126457\pi$
$541$	7.18788e10	+	5.22230e10i	0.839096	+	0.609639i	−0.0830219	+	0.996548i	$0.526457\pi$
$542$	−9.33349e10	+	6.65795e10i	−1.08155	+	0.771513i
$543$		−	5.48257e10i		−	0.630645i
$544$	−1.29658e11	+	3.59789e10i	−1.48049	+	0.410820i
$545$	1.55701e10	−	2.08820e10i	0.176484	−	0.236693i
$546$	−1.52908e7	+	1.75834e9i	−0.000172051	+	0.0197849i
$547$	2.02094e10	+	6.56643e9i	0.225738	+	0.0733466i	0.419702	−	0.907662i	$-0.362135\pi$
$547$	2.02094e10	+	6.56643e9i	0.225738	+	0.0733466i	−0.193964	+	0.981009i	$0.562135\pi$
$548$	−1.93181e10	+	5.61150e10i	−0.214211	+	0.622238i
$549$	−2.05877e10			−0.226631
$550$	3.84592e10	+	1.28685e9i	0.420290	+	0.0140630i
$551$			1.69409e11i			1.83794i
$552$	−1.73363e9	+	6.64389e10i	−0.0186724	+	0.715593i
$553$	−9.44737e9	+	2.90760e10i	−0.101021	+	0.310910i
$554$	1.19484e9	−	1.37400e11i	0.0126844	−	1.45864i
$555$	−7.69640e10	+	5.44752e10i	−0.811177	+	0.574152i
$556$	3.38948e10	−	4.49856e10i	0.354677	−	0.470733i
$557$	1.04832e10			0.108911			0.0544557	−	0.998516i	$-0.482658\pi$
$557$	1.04832e10			0.108911			0.0544557	+	0.998516i	$0.482658\pi$
$558$	2.32456e10	−	1.65820e10i	0.239775	−	0.171041i
$559$	−5.12284e9	+	7.05099e9i	−0.0524643	+	0.0722109i
$560$	1.84747e10	−	1.21347e10i	0.187856	−	0.123389i
$561$	−4.50004e10	+	3.26947e10i	−0.454323	+	0.330085i
$562$	1.33416e11	+	4.46358e10i	1.33740	+	0.447444i
$563$	9.61648e10	−	1.32360e11i	0.957156	−	1.31741i	0.00888128	−	0.999961i	$-0.497173\pi$
$563$	9.61648e10	−	1.32360e11i	0.957156	−	1.31741i	0.948275	−	0.317451i	$-0.102827\pi$
$564$	1.41221e10	−	4.10217e10i	0.139567	−	0.405412i
$565$	−4.80403e10	+	6.44297e10i	−0.471424	+	0.632255i
$566$	−6.73018e9	+	2.01164e10i	−0.0655784	+	0.196013i
$567$	1.53686e10	−	4.99356e9i	0.148697	−	0.0483146i
$568$	−2.27482e10	−	1.74520e10i	−0.218551	−	0.167668i
$569$	3.56889e10	+	1.09839e11i	0.340474	+	1.04787i	0.963962	+	0.266039i	$0.0857150\pi$
$569$	3.56889e10	+	1.09839e11i	0.340474	+	1.04787i	−0.623488	+	0.781833i	$0.714285\pi$
$570$	−1.28991e11	−	9.79357e10i	−1.22197	−	0.927773i
$571$	−1.95923e11	−	6.36593e10i	−1.84307	−	0.598849i	−0.997931	−	0.0642996i	$-0.979519\pi$
$571$	−1.95923e11	−	6.36593e10i	−1.84307	−	0.598849i	−0.845137	−	0.534549i	$-0.820481\pi$
$572$	4.36016e9	−	1.33333e9i	0.0407304	−	0.0124553i
$573$	−1.14572e11	+	8.32415e10i	−1.06282	+	0.772185i
$574$	−8.67892e9	−	2.75231e10i	−0.0799499	−	0.253542i
$575$	5.10990e10	+	7.41225e10i	0.467456	+	0.678076i
$576$	−6.97199e9	−	2.60006e10i	−0.0633384	−	0.236208i
$577$	1.59202e11	−	1.15667e11i	1.43630	−	1.04353i	0.447503	−	0.894282i	$-0.352313\pi$
$577$	1.59202e11	−	1.15667e11i	1.43630	−	1.04353i	0.988799	−	0.149252i	$-0.0476866\pi$
$578$	1.32055e9	−	1.51855e11i	0.0118316	−	1.36056i
$579$	−3.99581e10	−	1.29832e10i	−0.355542	−	0.115522i
$580$	3.50691e9	−	1.17775e11i	0.0309894	−	1.04073i
$581$	9.64006e9	+	2.96690e10i	0.0846009	+	0.260375i
$582$	1.01286e10	+	3.21205e10i	0.0882793	+	0.279956i
$583$	−6.48219e10	+	2.10619e10i	−0.561109	+	0.182315i
$584$	2.01167e11	−	5.96085e10i	1.72944	−	0.512456i
$585$	2.76980e9	−	8.62216e8i	0.0236497	−	0.00736194i
$586$	−9.05678e9	+	1.22403e10i	−0.0768039	+	0.103801i
$587$	−2.90213e10	+	3.99444e10i	−0.244436	+	0.336437i	−0.913553	−	0.406720i	$-0.866672\pi$
$587$	−2.90213e10	+	3.99444e10i	−0.244436	+	0.336437i	0.669117	+	0.743157i	$0.266672\pi$
$588$	−1.71562e9	+	9.86357e10i	−0.0143520	+	0.825134i
$589$	−2.07002e11	+	1.50396e11i	−1.71994	+	1.24961i
$590$	1.25543e11	−	3.78861e10i	1.03606	−	0.312660i
$591$	6.75169e10	−	9.29291e10i	0.553430	−	0.761731i
$592$	1.40354e11	+	4.88399e9i	1.14272	+	0.0397638i
$593$	−8.77555e10			−0.709669			−0.354834	−	0.934929i	$-0.615463\pi$
$593$	−8.77555e10			−0.709669			−0.354834	+	0.934929i	$0.615463\pi$
$594$	−3.28872e10	−	4.61031e10i	−0.264168	−	0.370326i
$595$	1.28639e10	+	4.13244e10i	0.102637	+	0.329715i
$596$	2.25770e9	+	7.38298e9i	0.0178929	+	0.0585122i
$597$	−7.47865e9	+	2.30169e10i	−0.0588743	+	0.181197i
$598$	8.57517e9	+	6.34489e9i	0.0670561	+	0.0496157i
$599$		−	4.10745e10i		−	0.319055i	−0.987194	−	0.159527i	$-0.949003\pi$
$599$		−	4.10745e10i		−	0.319055i	0.987194	−	0.159527i	$-0.0509970\pi$
$600$	8.76483e10	+	7.07559e10i	0.676299	+	0.545956i
$601$	1.11309e11			0.853165			0.426582	−	0.904449i	$-0.359717\pi$
$601$	1.11309e11			0.853165			0.426582	+	0.904449i	$0.359717\pi$
$602$	1.54729e10	−	2.09118e10i	0.117811	−	0.159223i
$603$	4.03701e10	+	1.31170e10i	0.305345	+	0.0992125i
$604$	9.76530e10	−	2.98621e10i	0.733732	−	0.224374i
$605$	1.04455e11	+	3.53744e10i	0.779662	+	0.264039i
$606$	1.18677e11	−	8.46573e10i	0.879990	−	0.627731i
$607$			1.62599e11i			1.19774i	0.800847	+	0.598869i	$0.204383\pi$
$607$			1.62599e11i			1.19774i	−0.800847	+	0.598869i	$0.795617\pi$
$608$	6.44990e10	+	2.32437e11i	0.471996	+	1.70095i
$609$	−2.26345e10	−	1.64449e10i	−0.164551	−	0.119554i
$610$	−1.28283e11	−	2.70356e9i	−0.926513	−	0.0195262i
$611$	−4.09295e9	−	5.63347e9i	−0.0293678	−	0.0404214i
$612$	5.27016e10	+	9.16667e8i	0.375680	+	0.00653440i
$613$	−1.16342e11	−	8.45273e10i	−0.823937	−	0.598625i	0.0939006	−	0.995582i	$-0.470066\pi$
$613$	−1.16342e11	−	8.45273e10i	−0.823937	−	0.598625i	−0.917837	+	0.396956i	$0.870066\pi$
$614$	1.32605e11	+	9.81160e10i	0.933008	+	0.690345i
$615$	1.20044e11	−	8.49670e10i	0.839148	−	0.593950i
$616$	−1.30482e10	+	3.86636e9i	−0.0906207	+	0.0268522i
$617$	−1.97506e10	−	6.07860e10i	−0.136282	−	0.419434i	0.859505	−	0.511127i	$-0.170772\pi$
$617$	−1.97506e10	−	6.07860e10i	−0.136282	−	0.419434i	−0.995787	+	0.0916937i	$0.970772\pi$
$618$	7.20768e10	−	2.27282e10i	0.494130	−	0.155815i
$619$	−3.76130e10	+	1.22212e10i	−0.256198	+	0.0832437i	−0.434300	−	0.900768i	$-0.643004\pi$
$619$	−3.76130e10	+	1.22212e10i	−0.256198	+	0.0832437i	0.178102	+	0.984012i	$0.443004\pi$
$620$	1.47023e11	−	1.00271e11i	0.994986	−	0.678592i
$621$	4.09426e10	−	1.26008e11i	0.275302	−	0.847293i
$622$	2.13865e11	+	1.85980e9i	1.42882	+	0.0124252i
$623$	1.10626e10	+	1.52263e10i	0.0734351	+	0.101075i
$624$	1.25425e10	+	4.56334e9i	0.0827266	+	0.0300985i
$625$	1.52401e11	+	7.55057e9i	0.998775	+	0.0494834i
$626$	−9.14930e8	+	2.88507e8i	−0.00595786	+	0.00187871i
$627$	5.86115e10	+	8.06717e10i	0.379238	+	0.521977i
$628$	7.88587e9	+	2.57878e10i	0.0507003	+	0.165797i
$629$	−8.49765e10	+	2.61531e11i	−0.542870	+	1.67078i
$630$	−8.28929e9	+	2.50153e9i	−0.0526205	+	0.0158797i
$631$	−9.45954e10	+	3.07359e10i	−0.596695	+	0.193878i	−0.591766	−	0.806110i	$-0.701569\pi$
$631$	−9.45954e10	+	3.07359e10i	−0.596695	+	0.193878i	−0.00492939	+	0.999988i	$0.501569\pi$
$632$	1.84113e11	+	1.41248e11i	1.15403	+	0.885346i
$633$	−8.25187e10	−	2.53967e11i	−0.513970	−	1.58184i
$634$	2.96502e11	+	9.91980e10i	1.83515	+	0.613968i
$635$	−7.00427e10	+	4.95763e10i	−0.430793	+	0.304916i
$636$	−1.88651e11	−	6.49447e10i	−1.15300	−	0.396931i
$637$	1.28098e10	+	9.30684e9i	0.0778007	+	0.0565255i
$638$	−2.30167e10	+	6.87968e10i	−0.138919	+	0.415227i
$639$	6.60161e9	+	9.08633e9i	0.0395955	+	0.0544986i
$640$	−4.00285e10	−	1.62927e11i	−0.238589	−	0.971121i
$641$	−1.15873e11	−	8.41865e10i	−0.686356	−	0.498667i	0.189104	−	0.981957i	$-0.439442\pi$
$641$	−1.15873e11	−	8.41865e10i	−0.686356	−	0.498667i	−0.875460	+	0.483290i	$0.839442\pi$
$642$	2.37881e9	+	3.33475e9i	0.0140029	+	0.0196301i
$643$		−	1.23307e11i		−	0.721347i	−0.932692	−	0.360674i	$-0.882547\pi$
$643$		−	1.23307e11i		−	0.721347i	0.932692	−	0.360674i	$-0.117453\pi$
$644$	−2.54293e10	−	1.91599e10i	−0.147839	−	0.111391i
$645$	1.25566e11	+	4.25239e10i	0.725492	+	0.245694i
$646$	−4.72308e11	−	4.10724e9i	−2.71203	−	0.0235841i
$647$	2.57289e11	+	8.35982e10i	1.46826	+	0.477067i	0.930583	−	0.366082i	$-0.119301\pi$
$647$	2.57289e11	+	8.35982e10i	1.46826	+	0.477067i	0.537680	+	0.843149i	$0.319301\pi$
$648$	3.19942e9	−	1.22613e11i	0.0181456	−	0.695405i
$649$	−8.07387e10			−0.455096
$650$	1.73720e10	−	5.00879e9i	0.0973189	−	0.0280595i
$651$		−	4.22564e10i		−	0.235271i
$652$	−1.89538e11	−	6.52500e10i	−1.04883	−	0.361069i
$653$	4.66801e9	−	1.43666e10i	0.0256731	−	0.0790138i	−0.937399	−	0.348257i	$-0.886774\pi$
$653$	4.66801e9	−	1.43666e10i	0.0256731	−	0.0790138i	0.963072	+	0.269243i	$0.0867736\pi$
$654$	−4.69442e10	−	4.08231e8i	−0.256608	−	0.00223149i
$655$	−5.61475e10	−	1.80370e11i	−0.305046	−	0.979937i
$656$	−2.18916e11	−	7.61773e9i	−1.18212	−	0.0411349i
$657$	−8.21888e10			−0.441114
$658$	1.20698e10	+	1.69202e10i	0.0643870	+	0.0902614i
$659$	−1.08184e11	+	1.48903e11i	−0.573618	+	0.789518i	−0.992978	−	0.118302i	$-0.962255\pi$
$659$	−1.08184e11	+	1.48903e11i	−0.573618	+	0.789518i	0.419359	+	0.907820i	$0.362255\pi$
$660$	−3.90771e10	−	5.72969e10i	−0.205943	−	0.301964i
$661$	−1.57084e11	+	1.14128e11i	−0.822859	+	0.597842i	−0.917530	−	0.397667i	$-0.869820\pi$
$661$	−1.57084e11	+	1.14128e11i	−0.822859	+	0.597842i	0.0946712	+	0.995509i	$0.469820\pi$
$662$	−6.56560e10	+	1.96245e11i	−0.341855	+	1.02180i
$663$	−1.53612e10	+	2.11429e10i	−0.0795007	+	0.109423i
$664$	2.36705e11	+	6.17648e9i	1.21769	+	0.0317738i
$665$	7.40818e10	−	2.30610e10i	0.378813	−	0.117921i
$666$	−5.21712e10	−	1.74545e10i	−0.265176	−	0.0887175i
$667$	−1.61419e11	+	5.24481e10i	−0.815549	+	0.264988i
$668$	1.97800e11	+	2.82451e11i	0.993393	+	1.41853i
$669$	3.87331e10	+	1.19208e11i	0.193365	+	0.595116i
$670$	2.49826e11	+	8.70344e10i	1.23976	+	0.431908i
$671$	7.51340e10	+	2.44125e10i	0.370635	+	0.120427i
$672$	−3.73166e10	−	1.39456e10i	−0.182989	−	0.0683847i
$673$	−1.32891e11	+	9.65509e10i	−0.647791	+	0.470648i	−0.862518	−	0.506026i	$-0.831114\pi$
$673$	−1.32891e11	+	9.65509e10i	−0.647791	+	0.470648i	0.214727	+	0.976674i	$0.431114\pi$
$674$	9.28352e10	−	2.92740e10i	0.449855	−	0.141854i
$675$	−1.27456e11	−	1.84883e11i	−0.613966	−	0.890599i
$676$	−1.69299e11	+	1.18560e11i	−0.810714	+	0.567742i
$677$	2.13372e11	−	1.55024e11i	1.01574	−	0.737979i	0.0503360	−	0.998732i	$-0.483971\pi$
$677$	2.13372e11	−	1.55024e11i	1.01574	−	0.737979i	0.965406	+	0.260753i	$0.0839708\pi$
$678$	1.44842e11	+	1.25956e9i	0.685451	+	0.00596076i
$679$	−1.53450e10	−	4.98590e9i	−0.0721919	−	0.0234566i
$680$	3.28267e11	+	1.26325e10i	1.53529	+	0.0590819i
$681$	6.08259e10	+	1.87203e11i	0.282813	+	0.870410i
$682$	−1.04497e11	+	3.29512e10i	−0.483019	+	0.152312i
$683$	−6.03128e10	+	1.95968e10i	−0.277157	+	0.0900539i	−0.444298	−	0.895879i	$-0.646547\pi$
$683$	−6.03128e10	+	1.95968e10i	−0.277157	+	0.0900539i	0.167140	+	0.985933i	$0.446547\pi$
$684$	1.64330e9	−	9.44777e10i	0.00750745	−	0.431623i
$685$	8.66085e10	−	1.16156e11i	0.393367	−	0.527568i
$686$	−7.80036e10	−	5.77159e10i	−0.352224	−	0.260615i
$687$	−3.99325e10	+	5.49624e10i	−0.179267	+	0.246739i
$688$	−1.10434e11	−	1.63681e11i	−0.492888	−	0.730542i
$689$	−2.59072e10	+	1.88227e10i	−0.114959	+	0.0835228i
$690$	5.33814e10	−	1.53227e11i	0.235501	−	0.675989i
$691$	1.18650e10	−	1.63307e10i	0.0520420	−	0.0716297i	−0.782203	−	0.623024i	$-0.785904\pi$
$691$	1.18650e10	−	1.63307e10i	0.0520420	−	0.0716297i	0.834245	+	0.551394i	$0.185904\pi$
$692$	−4.19052e10	−	3.15738e10i	−0.182744	−	0.137690i
$693$	5.33098e9			0.0231139
$694$	−2.18954e11	+	1.56189e11i	−0.943877	+	0.673305i
$695$	−1.12242e11	+	7.94454e10i	−0.481081	+	0.340510i
$696$	−1.75000e11	+	1.20298e11i	−0.745762	+	0.512650i
$697$	1.32541e11	−	4.07919e11i	0.561589	−	1.72839i
$698$	−9.43022e10	+	1.27450e11i	−0.397283	+	0.536932i
$699$		−	1.92866e11i		−	0.807880i
$700$	−5.19796e10	+	1.44986e10i	−0.216491	+	0.0603858i
$701$	2.53912e11			1.05151			0.525753	−	0.850637i	$-0.323784\pi$
$701$	2.53912e11			1.05151			0.525753	+	0.850637i	$0.323784\pi$
$702$	−2.13890e10	−	1.58260e10i	−0.0880728	−	0.0651663i
$703$	4.68844e11	+	1.52337e11i	1.91958	+	0.623710i
$704$	−5.38705e9	+	1.03155e11i	−0.0219311	+	0.419953i
$705$	−6.33134e10	+	8.49133e10i	−0.256294	+	0.343731i
$706$	−1.27441e11	−	1.78654e11i	−0.512969	−	0.719110i
$707$			6.98371e10i			0.279517i
$708$	−1.88762e11	−	1.42224e11i	−0.751245	−	0.566031i
$709$	3.01136e11	+	2.18788e11i	1.19173	+	0.865841i	0.993446	−	0.114304i	$-0.0364636\pi$
$709$	3.01136e11	+	2.18788e11i	1.19173	+	0.865841i	0.198283	+	0.980145i	$0.436464\pi$
$710$	3.99418e10	+	5.74844e10i	0.157179	+	0.226212i
$711$	−5.34302e10	−	7.35403e10i	−0.209078	−	0.287771i
$712$	1.36968e11	−	4.05856e10i	0.532967	−	0.157926i
$713$	−2.07388e11	−	1.50676e11i	−0.802465	−	0.583025i
$714$	4.63967e10	−	6.27055e10i	0.178523	−	0.241275i
$715$	−1.11307e10	−	1.37759e8i	−0.0425890	−	0.000527104i
$716$	6.92529e9	−	3.98154e11i	0.0263503	−	1.51495i
$717$	−1.10048e11	−	3.38693e11i	−0.416395	−	1.28153i
$718$	9.30120e10	+	2.94965e11i	0.349978	+	1.10987i
$719$	−1.24036e11	+	4.03018e10i	−0.464122	+	0.150802i	−0.531738	−	0.846909i	$-0.678461\pi$
$719$	−1.24036e11	+	4.03018e10i	−0.464122	+	0.150802i	0.0676156	+	0.997711i	$0.478461\pi$
$720$	−3.09820e9	+	6.56475e10i	−0.0115287	+	0.244280i
$721$	−1.11881e10	+	3.44335e10i	−0.0414015	+	0.127421i
$722$	−5.00004e9	+	5.74975e11i	−0.0184003	+	2.11592i
$723$	−4.56111e10	−	6.27782e10i	−0.166923	−	0.229750i
$724$	1.63299e11	−	1.14358e11i	0.594331	−	0.416210i
$725$	−9.56365e10	+	2.71300e11i	−0.346156	+	0.981969i
$726$	−5.97745e10	−	1.89560e11i	−0.215164	−	0.682340i
$727$	1.20806e11	+	1.66275e11i	0.432464	+	0.595235i	0.968517	−	0.248949i	$-0.0800852\pi$
$727$	1.20806e11	+	1.66275e11i	0.432464	+	0.595235i	−0.536053	+	0.844184i	$0.680085\pi$
$728$	−5.26914e9	+	3.62209e9i	−0.0187592	+	0.0128954i
$729$	−9.69033e10	+	2.98238e11i	−0.343106	+	1.05597i
$730$	−5.12123e11	−	1.07930e10i	−1.80336	−	0.0380057i
$731$	3.67701e11	−	1.19473e11i	1.28773	−	0.418410i
$732$	1.32655e11	+	1.89426e11i	0.462040	+	0.659775i
$733$	8.67121e10	+	2.66872e11i	0.300375	+	0.924459i	0.981363	+	0.192164i	$0.0615506\pi$
$733$	8.67121e10	+	2.66872e11i	0.300375	+	0.924459i	−0.680988	+	0.732295i	$0.738449\pi$
$734$	−6.53408e10	+	1.95303e11i	−0.225113	+	0.672860i
$735$	7.72546e10	−	2.28120e11i	0.264713	−	0.781652i
$736$	−2.01505e11	+	1.33418e11i	−0.686711	+	0.454676i
$737$	−1.31775e11	−	9.57400e10i	−0.446645	−	0.324507i
$738$	8.13733e10	+	2.72244e10i	0.274319	+	0.0917766i
$739$	2.71817e11	+	3.74123e11i	0.911377	+	1.25440i	0.966694	+	0.255934i	$0.0823830\pi$
$739$	2.71817e11	+	3.74123e11i	0.911377	+	1.25440i	−0.0553171	+	0.998469i	$0.517617\pi$
$740$	−3.22790e11	−	1.15611e11i	−1.07645	−	0.385542i
$741$	3.79026e10	+	2.75379e10i	0.125718	+	0.0913393i
$742$	7.78127e10	−	5.55069e10i	0.256705	−	0.183118i
$743$		−	5.12783e11i		−	1.68259i	−0.540576	−	0.841295i	$-0.681794\pi$
$743$		−	5.12783e11i		−	1.68259i	0.540576	−	0.841295i	$-0.318206\pi$
$744$	−3.02351e11	−	1.07037e11i	−0.986778	−	0.349334i
$745$	2.33265e8	−	1.88474e10i	0.000757224	−	0.0611822i
$746$	−2.38523e9	+	2.74287e11i	−0.00770148	+	0.885624i
$747$	−8.82151e10	−	2.86628e10i	−0.283309	−	0.0920528i
$748$	−1.91245e11	−	6.58378e10i	−0.610920	−	0.210314i
$749$	−1.96237e9			−0.00623525
$750$	−1.51285e11	−	2.29658e11i	−0.478136	−	0.725833i
$751$			1.05588e11i			0.331935i	0.986131	+	0.165967i	$0.0530747\pi$
$751$			1.05588e11i			0.331935i	−0.986131	+	0.165967i	$0.946925\pi$
$752$	1.51640e11	−	4.35022e10i	0.474178	−	0.136032i
$753$	8.73398e10	−	2.68804e11i	0.271664	−	0.836097i
$754$	−2.96390e8	+	3.40831e10i	−0.000917019	+	0.105452i
$755$	−2.49290e11	−	3.08534e9i	−0.767214	−	0.00949545i
$756$	6.34280e10	+	4.77903e10i	0.194175	+	0.146303i
$757$	5.62221e11			1.71208			0.856038	−	0.516912i	$-0.172919\pi$
$757$	5.62221e11			1.71208			0.856038	+	0.516912i	$0.172919\pi$
$758$	−8.67888e10	+	6.19099e10i	−0.262898	+	0.187535i
$759$	−5.87208e10	+	8.08223e10i	−0.176940	+	0.243537i
$760$	2.26462e10	−	5.88480e11i	0.0678799	−	1.76391i
$761$	5.19399e11	−	3.77365e11i	1.54868	−	1.12518i	0.604099	−	0.796909i	$-0.293533\pi$
$761$	5.19399e11	−	3.77365e11i	1.54868	−	1.12518i	0.944583	−	0.328274i	$-0.106467\pi$
$762$	1.46669e11	+	4.90698e10i	0.435030	+	0.145544i
$763$	1.32194e10	−	1.81949e10i	0.0390044	−	0.0536849i
$764$	−4.86915e11	−	1.67625e11i	−1.42916	−	0.492000i
$765$	−1.21886e11	−	4.12776e10i	−0.355883	−	0.120523i
$766$	1.47160e11	−	4.39860e11i	0.427440	−	1.27761i
$767$	−3.60775e10	+	1.17223e10i	−0.104245	+	0.0338712i
$768$	−1.94306e11	+	2.31681e11i	−0.558525	+	0.665956i
$769$	5.09267e10	+	1.56736e11i	0.145626	+	0.448192i	0.997091	−	0.0762200i	$-0.0242851\pi$
$769$	5.09267e10	+	1.56736e11i	0.145626	+	0.448192i	−0.851465	+	0.524412i	$0.824285\pi$
$770$	3.32176e10	+	7.00059e8i	0.0944944	+	0.00199146i
$771$	3.75414e10	+	1.21979e10i	0.106241	+	0.0345198i
$772$	−4.46759e10	−	1.46096e11i	−0.125778	−	0.411311i
$773$	−1.88201e11	+	1.36736e11i	−0.527114	+	0.382971i	−0.819277	−	0.573398i	$-0.805625\pi$
$773$	−1.88201e11	+	1.36736e11i	−0.527114	+	0.382971i	0.292163	+	0.956368i	$0.405625\pi$
$774$	2.32609e10	+	7.37663e10i	0.0648131	+	0.205539i
$775$	−4.16405e11	+	1.23992e11i	−1.15428	+	0.343706i
$776$	−7.45443e10	+	9.71665e10i	−0.205574	+	0.267960i
$777$	−6.58651e10	+	4.78538e10i	−0.180705	+	0.131290i
$778$	3.96008e8	−	4.55385e10i	0.00108090	−	0.124297i
$779$	−7.31272e11	−	2.37605e11i	−1.98577	−	0.645216i
$780$	−2.57801e10	−	1.99291e10i	−0.0696477	−	0.0538407i
$781$	−1.33179e10	−	4.09882e10i	−0.0357957	−	0.110168i
$782$	−1.42310e11	−	4.51301e11i	−0.380547	−	1.20681i
$783$	4.02625e11	−	1.30821e11i	1.07116	−	0.348040i
$784$	−2.97365e11	+	2.00629e11i	−0.787093	+	0.531042i
$785$	8.14766e8	−	6.58315e10i	0.00214563	−	0.173362i
$786$	−2.02509e11	+	2.73693e11i	−0.530584	+	0.717089i
$787$	2.32649e11	−	3.20213e11i	0.606459	−	0.834719i	−0.389821	−	0.920890i	$-0.627463\pi$
$787$	2.32649e11	−	3.20213e11i	0.606459	−	0.834719i	0.996280	+	0.0861713i	$0.0274633\pi$
$788$	4.17620e11	+	7.26388e9i	1.08312	+	0.0188393i
$789$	−1.97222e11	+	1.43290e11i	−0.508918	+	0.369751i
$790$	−3.23269e11	−	4.65251e11i	−0.829958	−	1.19448i
$791$	−4.07873e10	+	5.61389e10i	−0.104188	+	0.143403i
$792$	1.35035e10	−	3.81439e10i	0.0343199	−	0.0969449i
$793$	3.71175e10			0.0938611
$794$	2.86988e11	+	4.02316e11i	0.722074	+	1.01224i
$795$	3.90500e11	+	2.91166e11i	0.977580	+	0.728907i
$796$	−8.41554e10	+	2.57345e10i	−0.209618	+	0.0641009i
$797$	7.39191e10	−	2.27500e11i	0.183199	−	0.563829i	−0.816714	−	0.577043i	$-0.804206\pi$
$797$	7.39191e10	−	2.27500e11i	0.183199	−	0.563829i	0.999913	+	0.0132143i	$0.00420636\pi$
$798$	−1.12412e11	−	8.31749e10i	−0.277204	−	0.205107i
$799$			3.08898e11i			0.757928i
$800$	−2.79258e10	+	4.08647e11i	−0.0681783	+	0.997673i
$801$	−5.59599e10			−0.135940
$802$	−3.14856e11	+	4.25531e11i	−0.761052	+	1.02857i
$803$	2.99944e11	+	9.74578e10i	0.721404	+	0.234398i
$804$	−1.39432e11	−	4.55960e11i	−0.333685	−	1.09120i
$805$	4.49085e10	+	6.34479e10i	0.106941	+	0.151089i
$806$	−4.19094e10	+	2.98956e10i	−0.0993050	+	0.0708382i
$807$			3.54527e10i			0.0835902i
$808$	4.99695e11	+	1.76899e11i	1.17236	+	0.415031i
$809$	−2.47358e11	−	1.79716e11i	−0.577473	−	0.419559i	0.260339	−	0.965517i	$-0.416166\pi$
$809$	−2.47358e11	−	1.79716e11i	−0.577473	−	0.419559i	−0.837812	+	0.545958i	$0.816166\pi$
$810$	−9.85156e10	+	2.82782e11i	−0.228857	+	0.656919i
$811$	8.33416e10	+	1.14710e11i	0.192654	+	0.265166i	0.894406	−	0.447256i	$-0.147599\pi$
$811$	8.33416e10	+	1.14710e11i	0.192654	+	0.265166i	−0.701752	+	0.712421i	$0.747599\pi$
$812$	1.76924e9	−	1.01719e11i	0.00406971	−	0.233979i
$813$	−4.08124e11	−	2.96520e11i	−0.934180	−	0.678721i
$814$	1.69699e11	+	1.25563e11i	0.386529	+	0.285998i
$815$	3.92336e11	+	2.92535e11i	0.889257	+	0.663051i
$816$	−3.31143e11	−	4.90810e11i	−0.746888	−	1.10701i
$817$	−2.14179e11	−	6.59175e11i	−0.480716	−	1.47949i
$818$	−1.63875e11	+	5.16752e10i	−0.366016	+	0.115417i
$819$	2.38211e9	−	7.73993e8i	0.00529451	−	0.00172029i
$820$	5.03467e11	+	1.80322e11i	1.11357	+	0.398836i
$821$	−1.36136e11	+	4.18984e11i	−0.299641	+	0.922200i	0.681982	+	0.731369i	$0.261118\pi$
$821$	−1.36136e11	+	4.18984e11i	−0.299641	+	0.922200i	−0.981623	+	0.190831i	$0.938882\pi$
$822$	−2.61126e11	−	2.27078e9i	−0.571957	−	0.00497379i
$823$	−4.55133e11	−	6.26437e11i	−0.992062	−	1.36546i	−0.930071	−	0.367380i	$-0.880255\pi$
$823$	−4.55133e11	−	6.26437e11i	−0.992062	−	1.36546i	−0.0619911	−	0.998077i	$-0.519745\pi$
$824$	2.18037e11	+	1.67274e11i	0.472957	+	0.362843i
$825$	4.83215e10	+	1.62279e11i	0.104310	+	0.350306i
$826$	1.07983e11	−	3.40506e10i	0.231972	−	0.0731484i
$827$	−1.38911e11	−	1.91195e11i	−0.296971	−	0.408746i	0.634292	−	0.773094i	$-0.281292\pi$
$827$	−1.38911e11	−	1.91195e11i	−0.296971	−	0.408746i	−0.931263	+	0.364348i	$0.881292\pi$
$828$	9.05301e10	−	2.76839e10i	0.192607	−	0.0588987i
$829$	1.68272e11	−	5.17889e11i	0.356283	−	1.09653i	−0.598979	−	0.800765i	$-0.704427\pi$
$829$	1.68272e11	−	5.17889e11i	0.356283	−	1.09653i	0.955262	−	0.295761i	$-0.0955733\pi$
$830$	−5.45910e11	−	1.90184e11i	−1.15029	−	0.400739i
$831$	5.75010e11	−	1.86832e11i	1.20579	−	0.391785i
$832$	1.25697e10	+	4.68763e10i	0.0262321	+	0.0978273i
$833$	−2.17052e11	−	6.68016e11i	−0.450799	−	1.38742i
$834$	2.35035e11	+	7.86337e10i	0.485813	+	0.162534i
$835$	−2.50219e11	−	8.03811e11i	−0.514725	−	1.65351i
$836$	−1.18027e11	+	3.42843e11i	−0.241633	+	0.701893i
$837$	5.17287e11	+	3.75831e11i	1.05397	+	0.765757i
$838$	8.91289e10	−	2.66405e11i	0.180735	−	0.540215i
$839$	2.14818e10	+	2.95672e10i	0.0433534	+	0.0596708i	0.830143	−	0.557550i	$-0.188259\pi$
$839$	2.14818e10	+	2.95672e10i	0.0433534	+	0.0596708i	−0.786790	+	0.617221i	$0.788259\pi$
$840$	7.64276e10	+	6.01508e10i	0.153509	+	0.120816i
$841$	−3.40307e10	−	2.47247e10i	−0.0680278	−	0.0494251i
$842$	2.18336e11	+	3.06076e11i	0.434387	+	0.608949i
$843$			6.19034e11i			1.22576i
$844$	5.84320e11	−	7.75517e11i	1.15154	−	1.52835i
$845$	4.81798e11	−	1.49979e11i	0.945013	−	0.294174i
$846$	−6.17948e10	−	5.37374e8i	−0.120634	−	0.00104905i
$847$	9.05593e10	+	2.94245e10i	0.175954	+	0.0571710i
$848$	−2.00058e11	−	6.97362e11i	−0.386877	−	1.34857i
$849$	−9.33377e10			−0.179650
$850$	−7.54057e11	−	2.73209e11i	−1.44454	−	0.523383i
$851$			4.93891e11i			0.941701i
$852$	4.10659e10	−	1.19288e11i	0.0779332	−	0.226380i
$853$	1.74054e11	−	5.35685e11i	0.328768	−	1.01184i	−0.640944	−	0.767588i	$-0.721457\pi$
$853$	1.74054e11	−	5.35685e11i	0.328768	−	1.01184i	0.969711	−	0.244255i	$-0.0785433\pi$
$854$	−1.10783e11	−	9.63380e8i	−0.208277	−	0.00181120i
$855$	−7.39979e10	+	2.18503e11i	−0.138470	+	0.408878i
$856$	−4.97074e9	+	1.40411e10i	−0.00925819	+	0.0261520i
$857$	4.99444e10			0.0925898			0.0462949	−	0.998928i	$-0.485259\pi$
$857$	4.99444e10			0.0925898			0.0462949	+	0.998928i	$0.485259\pi$
$858$	1.16508e10	+	1.63327e10i	0.0214984	+	0.0301376i
$859$	−3.09106e11	+	4.25448e11i	−0.567721	+	0.781401i	−0.992282	−	0.123998i	$-0.960428\pi$
$859$	−3.09106e11	+	4.25448e11i	−0.567721	+	0.781401i	0.424562	+	0.905399i	$0.360428\pi$
$860$	1.35253e11	+	4.62697e11i	0.247260	+	0.845868i
$861$	1.02732e11	−	7.46393e10i	0.186936	−	0.135817i
$862$	8.55785e10	−	2.55793e11i	0.155001	−	0.463298i
$863$	−4.15097e11	+	5.71332e11i	−0.748353	+	1.03002i	0.249741	+	0.968313i	$0.419655\pi$
$863$	−4.15097e11	+	5.71332e11i	−0.748353	+	1.03002i	−0.998094	+	0.0617073i	$0.980345\pi$
$864$	5.02612e11	−	3.32783e11i	0.901940	−	0.597181i
$865$	7.40053e10	+	1.04557e11i	0.132190	+	0.186761i
$866$	3.35980e11	+	1.12406e11i	0.597369	+	0.199856i
$867$	6.35506e11	−	2.06488e11i	1.12472	−	0.365443i
$868$	1.25861e11	−	8.81404e10i	0.221724	−	0.155273i
$869$	1.07788e11	+	3.31739e11i	0.189014	+	0.581724i
$870$	4.96347e11	−	1.49787e11i	0.866379	−	0.261454i
$871$	−7.27829e10	−	2.36486e10i	−0.126461	−	0.0410897i
$872$	−9.67024e10	−	1.40675e11i	−0.167252	−	0.243305i
$873$	3.88113e10	−	2.81981e10i	0.0668192	−	0.0485470i
$874$	−8.09043e11	+	2.55118e11i	−1.38652	+	0.437215i
$875$	1.31657e11	+	4.89035e9i	0.224600	+	0.00834273i
$876$	5.29575e11	+	7.56213e11i	0.899314	+	1.28419i
$877$	−4.92463e11	+	3.57795e11i	−0.832482	+	0.604834i	−0.920261	−	0.391306i	$-0.872023\pi$
$877$	−4.92463e11	+	3.57795e11i	−0.832482	+	0.604834i	0.0877781	+	0.996140i	$0.472023\pi$
$878$	1.84541e11	+	1.60479e9i	0.310538	+	0.00270047i
$879$	−6.37203e10	−	2.07040e10i	−0.106739	−	0.0346815i
$880$	8.91502e10	−	2.35904e11i	0.148659	−	0.393373i
$881$	−2.85302e11	−	8.78070e11i	−0.473589	−	1.45756i	−0.847851	−	0.530234i	$-0.822104\pi$
$881$	−2.85302e11	−	8.78070e11i	−0.473589	−	1.45756i	0.374262	−	0.927323i	$-0.377896\pi$
$882$	1.34014e11	−	4.22589e10i	0.221450	−	0.0698303i
$883$	−5.55241e11	+	1.80409e11i	−0.913354	+	0.296767i	−0.727738	−	0.685856i	$-0.759428\pi$
$883$	−5.55241e11	+	1.80409e11i	−0.913354	+	0.296767i	−0.185616	+	0.982622i	$0.559428\pi$
$884$	−9.50153e10	−	1.65265e9i	−0.155591	−	0.00270628i
$885$	3.33357e11	+	4.70975e11i	0.543421	+	0.767759i
$886$	−3.33081e11	−	2.46451e11i	−0.540525	−	0.399941i
$887$	−3.93732e11	+	5.41926e11i	−0.636073	+	0.875479i	−0.998398	−	0.0565727i	$-0.981983\pi$
$887$	−3.93732e11	+	5.41926e11i	−0.636073	+	0.875479i	0.362326	+	0.932051i	$0.381983\pi$
$888$	1.75563e11	+	5.92489e11i	0.282345	+	0.952859i
$889$	−5.99419e10	+	4.35503e10i	−0.0959673	+	0.0697244i
$890$	−3.48690e11	−	7.34860e9i	−0.555749	−	0.0117124i
$891$	1.08370e11	−	1.49158e11i	0.171948	−	0.236666i
$892$	−2.74271e11	+	3.64016e11i	−0.433232	+	0.574992i
$893$	5.53758e11			0.870792
$894$	−2.76559e10	+	1.97280e10i	−0.0432950	+	0.0308840i
$895$	−3.11846e11	+	9.20830e11i	−0.486014	+	1.43512i
$896$	−3.62997e10	−	1.40236e11i	−0.0563211	−	0.217584i
$897$	−1.45045e10	+	4.46404e10i	−0.0224044	+	0.0689538i
$898$	3.71161e11	−	5.01628e11i	0.570765	−	0.771394i
$899$		−	8.19082e11i		−	1.25397i
$900$	5.59671e10	−	1.50373e11i	0.0853027	−	0.229193i
$901$	1.42056e12			2.15556
$902$	−2.64686e11	−	1.95845e11i	−0.399857	−	0.295860i
$903$	1.08862e11	+	3.53714e10i	0.163729	+	0.0531988i
$904$	2.98367e11	+	4.34041e11i	0.446763	+	0.649916i
$905$	−4.64722e11	+	1.44664e11i	−0.692786	+	0.215658i
$906$	2.60938e11	+	3.65798e11i	0.387280	+	0.542911i
$907$			1.27954e11i			0.189071i	0.995521	+	0.0945357i	$0.0301367\pi$
$907$			1.27954e11i			0.189071i	−0.995521	+	0.0945357i	$0.969863\pi$
$908$	−4.30711e11	+	5.71647e11i	−0.633641	+	0.840977i
$909$	−1.67990e11	−	1.22052e11i	−0.246053	−	0.178768i
$910$	1.49447e10	−	4.50998e9i	0.0217932	−	0.00657672i
$911$	−3.64912e11	−	5.02258e11i	−0.529803	−	0.729211i	0.457297	−	0.889314i	$-0.348817\pi$
$911$	−3.64912e11	−	5.02258e11i	−0.529803	−	0.729211i	−0.987100	+	0.160103i	$0.948817\pi$
$912$	−8.79870e11	+	5.93638e11i	−1.27186	+	0.858108i
$913$	2.87949e11	+	2.09207e11i	0.414413	+	0.301088i
$914$	1.66519e11	−	2.25051e11i	0.238604	−	0.322476i
$915$	−1.67810e11	−	5.39076e11i	−0.239405	−	0.769070i
$916$	−2.46999e11	−	4.29618e9i	−0.350843	−	0.00610240i
$917$	−5.04025e10	−	1.55123e11i	−0.0712811	−	0.219381i
$918$	3.54963e11	+	1.12568e12i	0.499818	+	1.58505i
$919$	1.16838e12	−	3.79628e11i	1.63802	−	0.532227i	0.661929	−	0.749567i	$-0.269738\pi$
$919$	1.16838e12	−	3.79628e11i	1.63802	−	0.532227i	0.976096	+	0.217340i	$0.0697380\pi$
$920$	5.67734e11	−	1.60612e11i	0.792489	−	0.224195i
$921$	−2.24295e11	+	6.90310e11i	−0.311732	+	0.959413i
$922$	−5.22663e9	+	6.01032e11i	−0.00723267	+	0.831713i
$923$	−1.19020e10	−	1.63817e10i	−0.0163988	−	0.0225710i
$924$	−3.43496e10	−	4.90499e10i	−0.0471231	−	0.0672900i
$925$	6.64829e11	+	5.08635e11i	0.908120	+	0.694767i
$926$	2.03513e11	+	6.45391e11i	0.276788	+	0.877766i
$927$	−6.32751e10	−	8.70907e10i	−0.0856868	−	0.117938i
$928$	−7.23330e11	−	2.70315e11i	−0.975314	−	0.364484i
$929$	−2.84655e11	+	8.76078e11i	−0.382170	+	1.17620i	0.556343	+	0.830953i	$0.312204\pi$
$929$	−2.84655e11	+	8.76078e11i	−0.382170	+	1.17620i	−0.938513	+	0.345244i	$0.887796\pi$
$930$	6.23664e11	+	4.73512e11i	0.833717	+	0.632994i
$931$	−1.19755e12	+	3.89106e11i	−1.59402	+	0.517928i
$932$	5.74452e11	−	4.02289e11i	0.761361	−	0.533180i
$933$	2.90808e11	+	8.95015e11i	0.383778	+	1.18115i
$934$	−7.48405e10	+	2.23698e11i	−0.0983443	+	0.293950i
$935$	3.95870e11	+	2.95170e11i	0.517972	+	0.386212i
$936$	4.95905e8	−	1.90049e10i	0.000646093	−	0.0247606i
$937$	5.69339e11	+	4.13649e11i	0.738606	+	0.536629i	0.892274	−	0.451494i	$-0.149109\pi$
$937$	5.69339e11	+	4.13649e11i	0.738606	+	0.536629i	−0.153668	+	0.988123i	$0.549109\pi$
$938$	2.16618e11	+	7.24720e10i	0.279823	+	0.0936178i
$939$	−2.48118e9	−	3.41505e9i	−0.00319151	−	0.00439274i
$940$	−3.84977e11	−	1.14632e10i	−0.493086	−	0.0146824i
$941$	2.53092e11	+	1.83882e11i	0.322790	+	0.234520i	0.737365	−	0.675495i	$-0.236070\pi$
$941$	2.53092e11	+	1.83882e11i	0.322790	+	0.234520i	−0.414575	+	0.910015i	$0.636070\pi$
$942$	−9.65985e10	+	6.89076e10i	−0.122678	+	0.0875111i
$943$		−	7.70340e11i		−	0.974172i
$944$	2.98872e10	−	8.58887e11i	0.0376354	−	1.08155i
$945$	−1.12015e11	−	1.58258e11i	−0.140459	−	0.198444i
$946$	2.58091e9	−	2.96789e11i	0.00322261	−	0.370581i
$947$	−2.90253e11	−	9.43088e10i	−0.360891	−	0.117261i	0.122958	−	0.992412i	$-0.460762\pi$
$947$	−2.90253e11	−	9.43088e10i	−0.360891	−	0.117261i	−0.483850	+	0.875151i	$0.660762\pi$
$948$	−3.32367e11	+	9.65457e11i	−0.411514	+	1.19536i
$949$	1.48178e11			0.182691
$950$	−4.89779e11	+	1.35179e12i	−0.601320	+	1.65964i
$951$			1.37573e12i			1.68194i
$952$	2.83545e11	+	7.39871e9i	0.345203	+	0.00900758i
$953$	−4.20496e11	+	1.29415e12i	−0.509789	+	1.56897i	0.282779	+	0.959185i	$0.408744\pi$
$953$	−4.20496e11	+	1.29415e12i	−0.509789	+	1.56897i	−0.792568	+	0.609784i	$0.791256\pi$
$954$	−2.47128e9	+	2.84182e11i	−0.00298352	+	0.343087i
$955$	1.00790e12	+	7.51511e11i	1.21172	+	0.903487i
$956$	7.79256e11	−	1.03424e12i	0.932929	−	1.23820i
$957$	−3.19209e11			−0.380563
$958$	8.03023e11	−	5.72828e11i	0.953380	−	0.680083i
$959$	7.35326e10	−	1.01209e11i	0.0869372	−	0.119659i
$960$	6.23981e11	−	3.94487e11i	0.734660	−	0.464459i
$961$	3.10836e11	−	2.25836e11i	0.364450	−	0.264789i
$962$	9.40591e10	+	3.14685e10i	0.109825	+	0.0367431i
$963$	3.42957e9	−	4.72040e9i	0.00398781	−	0.00548875i
$964$	9.18478e10	−	2.66799e11i	0.106356	−	0.308941i
$965$	−4.61591e9	+	3.72956e11i	−0.00532289	+	0.430079i
$966$	4.44497e10	−	1.32860e11i	0.0510458	−	0.152576i
$967$	1.11243e12	−	3.61450e11i	1.27223	−	0.413373i	0.406394	−	0.913698i	$-0.366786\pi$
$967$	1.11243e12	−	3.61450e11i	1.27223	−	0.413373i	0.865838	+	0.500325i	$0.166786\pi$
$968$	4.39926e11	−	5.73432e11i	0.501047	−	0.653102i
$969$	−6.42231e11	−	1.97658e12i	−0.728444	−	2.24192i
$970$	2.45539e11	−	1.70607e11i	0.277353	−	0.192713i
$971$	−1.11450e12	−	3.62123e11i	−1.25373	−	0.407361i	−0.394473	−	0.918908i	$-0.629073\pi$
$971$	−1.11450e12	−	3.62123e11i	−1.25373	−	0.407361i	−0.859256	+	0.511547i	$0.829073\pi$
$972$	−4.07246e11	+	1.24535e11i	−0.456238	+	0.139517i
$973$	−9.60560e10	+	6.97888e10i	−0.107170	+	0.0778636i
$974$	2.65253e11	+	8.41185e11i	0.294730	+	0.934664i
$975$	4.51531e10	+	6.54976e10i	0.0499654	+	0.0724781i
$976$	−2.87509e11	+	7.90228e11i	−0.316849	+	0.870869i
$977$	−1.03882e12	+	7.54746e11i	−1.14015	+	0.828367i	−0.987140	−	0.159858i	$-0.948896\pi$
$977$	−1.03882e12	+	7.54746e11i	−1.14015	+	0.828367i	−0.153009	+	0.988225i	$0.548896\pi$
$978$	7.66994e9	−	8.81997e11i	0.00838372	−	0.964077i
$979$	2.04223e11	+	6.63561e10i	0.222318	+	0.0722354i
$980$	8.40597e11	−	2.45719e11i	0.911347	−	0.266400i
$981$	2.06640e10	+	6.35973e10i	0.0223120	+	0.0686693i
$982$	1.62870e11	+	5.16502e11i	0.175144	+	0.555426i
$983$	−1.18434e12	+	3.84814e11i	−1.26841	+	0.412133i	−0.864486	−	0.502657i	$-0.832356\pi$
$983$	−1.18434e12	+	3.84814e11i	−1.26841	+	0.412133i	−0.403929	+	0.914790i	$0.632356\pi$
$984$	−2.73832e11	−	9.24127e11i	−0.292081	−	0.985715i
$985$	−9.65850e11	−	3.27093e11i	−1.02604	−	0.347477i
$986$	8.99335e11	−	1.21546e12i	0.951511	−	1.28598i
$987$	−5.37545e10	+	7.39867e10i	−0.0566430	+	0.0779624i
$988$	−2.96269e9	+	1.70333e11i	−0.00310927	+	0.178760i
$989$	5.61774e11	−	4.08153e11i	0.587187	−	0.426616i
$990$	−5.97373e10	+	7.86801e10i	−0.0621877	+	0.0819076i
$991$	3.23321e11	−	4.45014e11i	0.335228	−	0.461401i	−0.607812	−	0.794081i	$-0.707953\pi$
$991$	3.23321e11	−	4.45014e11i	0.335228	−	0.461401i	0.943040	+	0.332680i	$0.107953\pi$
$992$	−3.11848e11	−	1.12382e12i	−0.322030	−	1.16051i
$993$	−9.10553e11			−0.936501
$994$	3.50981e10	+	4.92026e10i	0.0359533	+	0.0504014i
$995$	2.14833e11	+	2.65888e9i	0.219184	+	0.00271273i
$996$	3.04681e11	+	9.96347e11i	0.309605	+	1.01245i
$997$	−7.85296e10	+	2.41689e11i	−0.0794790	+	0.244611i	−0.982899	−	0.184145i	$-0.941048\pi$
$997$	−7.85296e10	+	2.41689e11i	−0.0794790	+	0.244611i	0.903420	+	0.428757i	$0.141048\pi$
$998$	7.59748e10	+	5.62148e10i	0.0765857	+	0.0566668i
$999$		−	1.23191e12i		−	1.23685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.33	yes	464
4.3	odd	2	inner	100.9.j.b.11.13	✓	464
25.16	even	5	inner	100.9.j.b.91.13	yes	464
100.91	odd	10	inner	100.9.j.b.91.33	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.13	✓	464	4.3	odd	2	inner
100.9.j.b.11.33	yes	464	1.1	even	1	trivial
100.9.j.b.91.13	yes	464	25.16	even	5	inner
100.9.j.b.91.33	yes	464	100.91	odd	10	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.51677 + 12.8620i) q^{2} +(-66.9566 - 21.7555i) q^{3} +(-74.8622 - 244.809i) q^{4} +(-7.73474 + 624.952i) q^{5} +(917.030 - 654.154i) q^{6} +539.637i q^{7} +(3861.19 + 1366.92i) q^{8} +(-1298.07 - 943.105i) q^{9} +(-7964.53 - 6047.01i) q^{10} +(3618.94 + 4981.05i) q^{11} +(-313.436 + 18020.3i) q^{12} +(2340.29 + 1700.32i) q^{13} +(-6940.82 - 5135.60i) q^{14} +(14114.1 - 41676.4i) q^{15} +(-54327.3 + 36654.0i) q^{16} +(-39654.3 - 122043. i) q^{17} +(24483.7 - 7720.51i) q^{18} +(-218786. + 71087.9i) q^{19} +(153573. - 44891.8i) q^{20} +(11740.1 - 36132.3i) q^{21} +(-98506.9 - 856.627i) q^{22} +(-135470. - 186458. i) q^{23} +(-228794. - 175526. i) q^{24} +(-390505. - 9667.69i) q^{25} +(-44141.4 + 13919.2i) q^{26} +(337901. + 465080. i) q^{27} +(132108. - 40398.4i) q^{28} +(227566. - 700375. i) q^{29} +(401722. + 578160. i) q^{30} +(1.05782e6 - 343705. i) q^{31} +(45577.1 - 1.04759e6i) q^{32} +(-133947. - 412246. i) q^{33} +(1.94710e6 + 651425. i) q^{34} +(-337247. - 4173.96i) q^{35} +(-133704. + 388384. i) q^{36} +(-1.73367e6 - 1.25958e6i) q^{37} +(1.16780e6 - 3.49055e6i) q^{38} +(-119706. - 164762. i) q^{39} +(-884123. + 2.40248e6i) q^{40} +(2.70407e6 + 1.96462e6i) q^{41} +(353006. + 494864. i) q^{42} +3.01287e6i q^{43} +(948486. - 1.25884e6i) q^{44} +(599436. - 803939. i) q^{45} +(3.68745e6 + 32066.5i) q^{46} +(-2.28936e6 - 743857. i) q^{47} +(4.43500e6 - 1.27231e6i) q^{48} +5.47359e6 q^{49} +(3.84069e6 - 4.93068e6i) q^{50} +9.03432e6i q^{51} +(241055. - 700214. i) q^{52} +(-3.42085e6 + 1.05283e7i) q^{53} +(-9.19759e6 - 79983.2i) q^{54} +(-3.14091e6 + 2.22314e6i) q^{55} +(-737639. + 2.08364e6i) q^{56} +1.61957e7 q^{57} +(6.84253e6 + 9.59225e6i) q^{58} +(-7.70792e6 + 1.06090e7i) q^{59} +(-1.12594e7 - 335265. i) q^{60} +(1.03807e7 - 7.54199e6i) q^{61} +(-5.64625e6 + 1.68766e7i) q^{62} +(508935. - 700489. i) q^{63} +(1.30403e7 + 1.05558e7i) q^{64} +(-1.08072e6 + 1.44942e6i) q^{65} +(6.57706e6 + 2.20043e6i) q^{66} +(-2.51604e7 + 8.17511e6i) q^{67} +(-2.69088e7 + 1.88442e7i) q^{68} +(5.01410e6 + 1.54318e7i) q^{69} +(3.26319e6 - 4.29796e6i) q^{70} +(-6.65726e6 - 2.16308e6i) q^{71} +(-3.72296e6 - 5.41586e6i) q^{72} +(4.14409e7 - 3.01085e7i) q^{73} +(3.26997e7 - 1.03113e7i) q^{74} +(2.59366e7 + 9.14297e6i) q^{75} +(3.37818e7 + 4.82391e7i) q^{76} +(-2.68796e6 + 1.95292e6i) q^{77} +(3.25838e6 + 28335.2i) q^{78} +(5.38806e7 + 1.75069e7i) q^{79} +(-2.24868e7 - 3.42355e7i) q^{80} +(-9.25355e6 - 2.84795e7i) q^{81} +(-5.10029e7 + 1.60829e7i) q^{82} +(5.49796e7 - 1.78640e7i) q^{83} +(-9.72442e6 - 169142. i) q^{84} +(7.65780e7 - 2.38381e7i) q^{85} +(-3.87516e7 - 2.86728e7i) q^{86} +(-3.04740e7 + 4.19439e7i) q^{87} +(7.16474e6 + 2.41796e7i) q^{88} +(2.82158e7 - 2.05000e7i) q^{89} +(4.63557e6 + 1.53609e7i) q^{90} +(-917555. + 1.26291e6i) q^{91} +(-3.55051e7 + 4.71229e7i) q^{92} -7.83052e7 q^{93} +(3.13548e7 - 2.23666e7i) q^{94} +(-4.27343e7 - 1.37281e8i) q^{95} +(-2.58425e7 + 6.91512e7i) q^{96} +(-9.23936e6 + 2.84358e7i) q^{97} +(-5.20909e7 + 7.04014e7i) q^{98} -9.87881e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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