Properties

Label 54.9.f.a.5.5
Level $54$
Weight $9$
Character 54.5
Analytic conductor $21.998$
Analytic rank $0$
Dimension $144$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [54,9,Mod(5,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("54.5");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 54.f (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(21.9984449433\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.5
Character \(\chi\) \(=\) 54.5
Dual form 54.9.f.a.11.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.27231 - 8.66680i) q^{2} +(-21.3841 + 78.1263i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-192.252 - 528.207i) q^{5} +(832.617 - 382.827i) q^{6} +(240.528 + 1364.10i) q^{7} +(1254.14 - 724.077i) q^{8} +(-5646.44 - 3341.33i) q^{9} +O(q^{10})\) \(q+(-7.27231 - 8.66680i) q^{2} +(-21.3841 + 78.1263i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-192.252 - 528.207i) q^{5} +(832.617 - 382.827i) q^{6} +(240.528 + 1364.10i) q^{7} +(1254.14 - 724.077i) q^{8} +(-5646.44 - 3341.33i) q^{9} +(-3179.75 + 5507.49i) q^{10} +(-7826.12 + 21502.1i) q^{11} +(-9372.94 - 4432.10i) q^{12} +(-20250.9 - 16992.5i) q^{13} +(10073.2 - 12004.8i) q^{14} +(45378.0 - 3724.66i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(50687.2 + 29264.3i) q^{17} +(12104.0 + 73235.7i) q^{18} +(-59286.9 - 102688. i) q^{19} +(70856.5 - 12493.9i) q^{20} +(-111716. - 10378.6i) q^{21} +(243268. - 88542.5i) q^{22} +(519317. + 91569.6i) q^{23} +(29750.8 + 113465. i) q^{24} +(57194.3 - 47991.7i) q^{25} +299085. i q^{26} +(381790. - 369684. i) q^{27} -177298. q^{28} +(-862682. - 1.02810e6i) q^{29} +(-362284. - 366195. i) q^{30} +(155672. - 882860. i) q^{31} +(63398.2 + 174185. i) q^{32} +(-1.51252e6 - 1.07123e6i) q^{33} +(-114985. - 652115. i) q^{34} +(674285. - 389299. i) q^{35} +(546695. - 637496. i) q^{36} +(259538. - 449532. i) q^{37} +(-458823. + 1.26061e6i) q^{38} +(1.76061e6 - 1.21876e6i) q^{39} +(-623573. - 523240. i) q^{40} +(1.71355e6 - 2.04212e6i) q^{41} +(722481. + 1.04369e6i) q^{42} +(193524. + 70436.9i) q^{43} +(-2.53650e6 - 1.46445e6i) q^{44} +(-679375. + 3.62486e6i) q^{45} +(-2.98302e6 - 5.16674e6i) q^{46} +(2.74431e6 - 483895. i) q^{47} +(767021. - 1.08300e6i) q^{48} +(3.61423e6 - 1.31547e6i) q^{49} +(-831870. - 146681. i) q^{50} +(-3.37021e6 + 3.33421e6i) q^{51} +(2.59211e6 - 2.17504e6i) q^{52} +9.40230e6i q^{53} +(-5.98047e6 - 620438. i) q^{54} +1.28621e7 q^{55} +(1.28937e6 + 1.53661e6i) q^{56} +(9.29043e6 - 2.43597e6i) q^{57} +(-2.63669e6 + 1.49534e7i) q^{58} +(85357.7 + 234518. i) q^{59} +(-539101. + 5.80293e6i) q^{60} +(-3.66121e6 - 2.07638e7i) q^{61} +(-8.78367e6 + 5.07126e6i) q^{62} +(3.19978e6 - 8.50599e6i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(-5.08230e6 + 1.39635e7i) q^{65} +(1.71541e6 + 2.08991e7i) q^{66} +(-2.43959e6 - 2.04706e6i) q^{67} +(-4.81554e6 + 5.73894e6i) q^{68} +(-1.82591e7 + 3.86142e7i) q^{69} +(-8.27759e6 - 3.01279e6i) q^{70} +(3.38031e7 + 1.95162e7i) q^{71} +(-9.50080e6 - 102028. i) q^{72} +(-1.64136e7 - 2.84292e7i) q^{73} +(-5.78344e6 + 1.01978e6i) q^{74} +(2.52637e6 + 5.49464e6i) q^{75} +(1.42621e7 - 5.19099e6i) q^{76} +(-3.12134e7 - 5.50376e6i) q^{77} +(-2.33664e7 - 6.39568e6i) q^{78} +(-9.42934e6 + 7.91216e6i) q^{79} +9.20954e6i q^{80} +(2.07178e7 + 3.77332e7i) q^{81} -3.01601e7 q^{82} +(-3.79516e7 - 4.52290e7i) q^{83} +(3.79137e6 - 1.38517e7i) q^{84} +(5.71290e6 - 3.23994e7i) q^{85} +(-796902. - 2.18947e6i) q^{86} +(9.87697e7 - 4.54130e7i) q^{87} +(5.75414e6 + 3.26333e7i) q^{88} +(-5.40997e7 + 3.12345e7i) q^{89} +(3.63566e7 - 2.04731e7i) q^{90} +(1.83086e7 - 3.17114e7i) q^{91} +(-2.30857e7 + 6.34274e7i) q^{92} +(6.56457e7 + 3.10413e7i) q^{93} +(-2.41513e7 - 2.02653e7i) q^{94} +(-4.28425e7 + 5.10577e7i) q^{95} +(-1.49641e7 + 1.22827e6i) q^{96} +(5.25431e7 + 1.91241e7i) q^{97} +(-3.76847e7 - 2.17573e7i) q^{98} +(1.16035e8 - 9.52606e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).

\(n\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.27231 8.66680i −0.454519 0.541675i
\(3\) −21.3841 + 78.1263i −0.264002 + 0.964522i
\(4\) −22.2270 + 126.055i −0.0868241 + 0.492404i
\(5\) −192.252 528.207i −0.307603 0.845131i −0.993123 0.117077i \(-0.962647\pi\)
0.685520 0.728054i \(-0.259575\pi\)
\(6\) 832.617 382.827i 0.642452 0.295391i
\(7\) 240.528 + 1364.10i 0.100178 + 0.568138i 0.993037 + 0.117802i \(0.0375848\pi\)
−0.892859 + 0.450336i \(0.851304\pi\)
\(8\) 1254.14 724.077i 0.306186 0.176777i
\(9\) −5646.44 3341.33i −0.860606 0.509271i
\(10\) −3179.75 + 5507.49i −0.317975 + 0.550749i
\(11\) −7826.12 + 21502.1i −0.534535 + 1.46862i 0.319085 + 0.947726i \(0.396624\pi\)
−0.853620 + 0.520896i \(0.825598\pi\)
\(12\) −9372.94 4432.10i −0.452013 0.213739i
\(13\) −20250.9 16992.5i −0.709040 0.594955i 0.215290 0.976550i \(-0.430930\pi\)
−0.924330 + 0.381595i \(0.875375\pi\)
\(14\) 10073.2 12004.8i 0.262213 0.312494i
\(15\) 45378.0 3724.66i 0.896355 0.0735736i
\(16\) −15395.9 5603.66i −0.234923 0.0855050i
\(17\) 50687.2 + 29264.3i 0.606880 + 0.350382i 0.771743 0.635934i \(-0.219385\pi\)
−0.164863 + 0.986316i \(0.552718\pi\)
\(18\) 12104.0 + 73235.7i 0.115303 + 0.697643i
\(19\) −59286.9 102688.i −0.454930 0.787961i 0.543754 0.839244i \(-0.317002\pi\)
−0.998684 + 0.0512830i \(0.983669\pi\)
\(20\) 70856.5 12493.9i 0.442853 0.0780869i
\(21\) −111716. 10378.6i −0.574429 0.0533654i
\(22\) 243268. 88542.5i 1.03847 0.377973i
\(23\) 519317. + 91569.6i 1.85576 + 0.327220i 0.986063 0.166372i \(-0.0532053\pi\)
0.869693 + 0.493592i \(0.164316\pi\)
\(24\) 29750.8 + 113465.i 0.0896714 + 0.341993i
\(25\) 57194.3 47991.7i 0.146417 0.122859i
\(26\) 299085.i 0.654488i
\(27\) 381790. 369684.i 0.718404 0.695626i
\(28\) −177298. −0.288451
\(29\) −862682. 1.02810e6i −1.21972 1.45360i −0.851902 0.523702i \(-0.824551\pi\)
−0.367814 0.929899i \(-0.619894\pi\)
\(30\) −362284. 366195.i −0.447264 0.452093i
\(31\) 155672. 882860.i 0.168564 0.955972i −0.776750 0.629809i \(-0.783133\pi\)
0.945314 0.326163i \(-0.105756\pi\)
\(32\) 63398.2 + 174185.i 0.0604612 + 0.166116i
\(33\) −1.51252e6 1.07123e6i −1.27540 0.903289i
\(34\) −114985. 652115.i −0.0860454 0.487987i
\(35\) 674285. 389299.i 0.449336 0.259424i
\(36\) 546695. 637496.i 0.325488 0.379549i
\(37\) 259538. 449532.i 0.138482 0.239858i −0.788440 0.615111i \(-0.789111\pi\)
0.926922 + 0.375254i \(0.122444\pi\)
\(38\) −458823. + 1.26061e6i −0.220045 + 0.604568i
\(39\) 1.76061e6 1.21876e6i 0.761035 0.526816i
\(40\) −623573. 523240.i −0.243583 0.204390i
\(41\) 1.71355e6 2.04212e6i 0.606401 0.722681i −0.372267 0.928126i \(-0.621420\pi\)
0.978669 + 0.205445i \(0.0658640\pi\)
\(42\) 722481. + 1.04369e6i 0.232183 + 0.335410i
\(43\) 193524. + 70436.9i 0.0566057 + 0.0206028i 0.370168 0.928965i \(-0.379300\pi\)
−0.313562 + 0.949568i \(0.601522\pi\)
\(44\) −2.53650e6 1.46445e6i −0.676745 0.390719i
\(45\) −679375. + 3.62486e6i −0.165676 + 0.883978i
\(46\) −2.98302e6 5.16674e6i −0.666231 1.15395i
\(47\) 2.74431e6 483895.i 0.562395 0.0991653i 0.114778 0.993391i \(-0.463384\pi\)
0.447616 + 0.894226i \(0.352273\pi\)
\(48\) 767021. 1.08300e6i 0.144492 0.204015i
\(49\) 3.61423e6 1.31547e6i 0.626947 0.228190i
\(50\) −831870. 146681.i −0.133099 0.0234690i
\(51\) −3.37021e6 + 3.33421e6i −0.498169 + 0.492848i
\(52\) 2.59211e6 2.17504e6i 0.354520 0.297477i
\(53\) 9.40230e6i 1.19160i 0.803133 + 0.595800i \(0.203165\pi\)
−0.803133 + 0.595800i \(0.796835\pi\)
\(54\) −5.98047e6 620438.i −0.703332 0.0729665i
\(55\) 1.28621e7 1.40560
\(56\) 1.28937e6 + 1.53661e6i 0.131107 + 0.156247i
\(57\) 9.29043e6 2.43597e6i 0.880108 0.230767i
\(58\) −2.63669e6 + 1.49534e7i −0.232995 + 1.32138i
\(59\) 85357.7 + 234518.i 0.00704425 + 0.0193539i 0.943165 0.332325i \(-0.107833\pi\)
−0.936121 + 0.351679i \(0.885611\pi\)
\(60\) −539101. + 5.80293e6i −0.0415973 + 0.447757i
\(61\) −3.66121e6 2.07638e7i −0.264427 1.49964i −0.770662 0.637244i \(-0.780074\pi\)
0.506235 0.862396i \(-0.331037\pi\)
\(62\) −8.78367e6 + 5.07126e6i −0.594442 + 0.343201i
\(63\) 3.19978e6 8.50599e6i 0.203122 0.539961i
\(64\) 1.04858e6 1.81619e6i 0.0625000 0.108253i
\(65\) −5.08230e6 + 1.39635e7i −0.284712 + 0.782241i
\(66\) 1.71541e6 + 2.08991e7i 0.0904051 + 1.10142i
\(67\) −2.43959e6 2.04706e6i −0.121065 0.101585i 0.580245 0.814442i \(-0.302957\pi\)
−0.701310 + 0.712856i \(0.747401\pi\)
\(68\) −4.81554e6 + 5.73894e6i −0.225221 + 0.268408i
\(69\) −1.82591e7 + 3.86142e7i −0.805534 + 1.70353i
\(70\) −8.27759e6 3.01279e6i −0.344756 0.125481i
\(71\) 3.38031e7 + 1.95162e7i 1.33022 + 0.768002i 0.985333 0.170642i \(-0.0545842\pi\)
0.344886 + 0.938645i \(0.387918\pi\)
\(72\) −9.50080e6 102028.i −0.353533 0.00379656i
\(73\) −1.64136e7 2.84292e7i −0.577980 1.00109i −0.995711 0.0925202i \(-0.970508\pi\)
0.417731 0.908571i \(-0.362826\pi\)
\(74\) −5.78344e6 + 1.01978e6i −0.192868 + 0.0340078i
\(75\) 2.52637e6 + 5.49464e6i 0.0798456 + 0.173658i
\(76\) 1.42621e7 5.19099e6i 0.427494 0.155595i
\(77\) −3.12134e7 5.50376e6i −0.887929 0.156566i
\(78\) −2.33664e7 6.39568e6i −0.631268 0.172786i
\(79\) −9.42934e6 + 7.91216e6i −0.242088 + 0.203136i −0.755756 0.654853i \(-0.772731\pi\)
0.513668 + 0.857989i \(0.328286\pi\)
\(80\) 9.20954e6i 0.224842i
\(81\) 2.07178e7 + 3.77332e7i 0.481287 + 0.876563i
\(82\) −3.01601e7 −0.667080
\(83\) −3.79516e7 4.52290e7i −0.799683 0.953025i 0.199958 0.979804i \(-0.435919\pi\)
−0.999641 + 0.0267791i \(0.991475\pi\)
\(84\) 3.79137e6 1.38517e7i 0.0761516 0.278218i
\(85\) 5.71290e6 3.23994e7i 0.109441 0.620672i
\(86\) −796902. 2.18947e6i −0.0145684 0.0400263i
\(87\) 9.87697e7 4.54130e7i 1.72404 0.792690i
\(88\) 5.75414e6 + 3.26333e7i 0.0959510 + 0.544165i
\(89\) −5.40997e7 + 3.12345e7i −0.862253 + 0.497822i −0.864766 0.502175i \(-0.832533\pi\)
0.00251282 + 0.999997i \(0.499200\pi\)
\(90\) 3.63566e7 2.04731e7i 0.554132 0.312043i
\(91\) 1.83086e7 3.17114e7i 0.266986 0.462434i
\(92\) −2.30857e7 + 6.34274e7i −0.322249 + 0.885371i
\(93\) 6.56457e7 + 3.10413e7i 0.877555 + 0.414962i
\(94\) −2.41513e7 2.02653e7i −0.309335 0.259563i
\(95\) −4.28425e7 + 5.10577e7i −0.525993 + 0.626854i
\(96\) −1.49641e7 + 1.22827e6i −0.176184 + 0.0144613i
\(97\) 5.25431e7 + 1.91241e7i 0.593511 + 0.216020i 0.621273 0.783594i \(-0.286616\pi\)
−0.0277620 + 0.999615i \(0.508838\pi\)
\(98\) −3.76847e7 2.17573e7i −0.408565 0.235885i
\(99\) 1.16035e8 9.52606e7i 1.20795 0.991682i
\(100\) 4.77836e6 + 8.27636e6i 0.0477836 + 0.0827636i
\(101\) 2.52684e7 4.45550e6i 0.242825 0.0428165i −0.0509112 0.998703i \(-0.516213\pi\)
0.293736 + 0.955887i \(0.405101\pi\)
\(102\) 5.34062e7 + 4.96152e6i 0.493391 + 0.0458368i
\(103\) −7.97422e7 + 2.90238e7i −0.708499 + 0.257873i −0.671035 0.741425i \(-0.734150\pi\)
−0.0374637 + 0.999298i \(0.511928\pi\)
\(104\) −3.77013e7 6.64776e6i −0.322272 0.0568253i
\(105\) 1.59955e7 + 6.10042e7i 0.131595 + 0.501883i
\(106\) 8.14879e7 6.83764e7i 0.645460 0.541605i
\(107\) 5.75074e7i 0.438721i 0.975644 + 0.219361i \(0.0703972\pi\)
−0.975644 + 0.219361i \(0.929603\pi\)
\(108\) 3.81146e7 + 5.63436e7i 0.280154 + 0.414142i
\(109\) 8.98364e7 0.636423 0.318212 0.948020i \(-0.396918\pi\)
0.318212 + 0.948020i \(0.396918\pi\)
\(110\) −9.35375e7 1.11474e8i −0.638874 0.761380i
\(111\) 2.95703e7 + 2.98896e7i 0.194789 + 0.196892i
\(112\) 3.94080e6 2.23494e7i 0.0250445 0.142035i
\(113\) −9.50024e7 2.61017e8i −0.582667 1.60087i −0.783603 0.621261i \(-0.786621\pi\)
0.200936 0.979604i \(-0.435602\pi\)
\(114\) −8.86750e7 6.28031e7i −0.525027 0.371845i
\(115\) −5.14718e7 2.91911e8i −0.294292 1.66901i
\(116\) 1.48773e8 8.58941e7i 0.821659 0.474385i
\(117\) 5.75679e7 + 1.63612e8i 0.307211 + 0.873115i
\(118\) 1.41178e6 2.44527e6i 0.00728179 0.0126124i
\(119\) −2.77277e7 + 7.61813e7i −0.138270 + 0.379892i
\(120\) 5.42133e7 3.75284e7i 0.261446 0.180982i
\(121\) −2.36883e8 1.98769e8i −1.10508 0.927271i
\(122\) −1.53330e8 + 1.82732e8i −0.692131 + 0.824849i
\(123\) 1.22901e8 + 1.77542e8i 0.536951 + 0.775677i
\(124\) 1.07829e8 + 3.92466e7i 0.456089 + 0.166003i
\(125\) −2.26501e8 1.30770e8i −0.927747 0.535635i
\(126\) −9.69895e7 + 3.41263e7i −0.384807 + 0.135397i
\(127\) 5.20580e7 + 9.01671e7i 0.200112 + 0.346604i 0.948564 0.316585i \(-0.102536\pi\)
−0.748453 + 0.663188i \(0.769203\pi\)
\(128\) −2.33661e7 + 4.12008e6i −0.0870455 + 0.0153485i
\(129\) −9.64131e6 + 1.36131e7i −0.0348159 + 0.0491583i
\(130\) 1.57979e8 5.74996e7i 0.553128 0.201322i
\(131\) −3.09694e8 5.46075e7i −1.05159 0.185424i −0.378970 0.925409i \(-0.623722\pi\)
−0.672624 + 0.739985i \(0.734833\pi\)
\(132\) 1.68653e8 1.66852e8i 0.555519 0.549585i
\(133\) 1.25816e8 1.05573e8i 0.402097 0.337399i
\(134\) 3.60302e7i 0.111750i
\(135\) −2.68669e8 1.30592e8i −0.808878 0.393170i
\(136\) 8.47584e7 0.247758
\(137\) 3.60356e8 + 4.29456e8i 1.02294 + 1.21909i 0.975450 + 0.220219i \(0.0706772\pi\)
0.0474882 + 0.998872i \(0.484878\pi\)
\(138\) 4.67447e8 1.22566e8i 1.28889 0.337951i
\(139\) 6.16550e7 3.49663e8i 0.165162 0.936677i −0.783736 0.621094i \(-0.786689\pi\)
0.948898 0.315584i \(-0.102200\pi\)
\(140\) 3.40859e7 + 9.36502e7i 0.0887284 + 0.243779i
\(141\) −2.08797e7 + 2.24750e8i −0.0528259 + 0.568622i
\(142\) −7.66834e7 4.34893e8i −0.188603 1.06962i
\(143\) 5.23860e8 3.02451e8i 1.25277 0.723287i
\(144\) 6.82085e7 + 8.30835e7i 0.158631 + 0.193226i
\(145\) −3.77200e8 + 6.53329e8i −0.853295 + 1.47795i
\(146\) −1.27026e8 + 3.49000e8i −0.279563 + 0.768093i
\(147\) 2.54858e7 + 3.10496e8i 0.0545794 + 0.664947i
\(148\) 5.08972e7 + 4.27078e7i 0.106083 + 0.0890145i
\(149\) −4.98049e7 + 5.93552e7i −0.101048 + 0.120424i −0.814198 0.580587i \(-0.802823\pi\)
0.713150 + 0.701011i \(0.247268\pi\)
\(150\) 2.92485e7 6.18543e7i 0.0577747 0.122181i
\(151\) −4.00273e8 1.45688e8i −0.769926 0.280230i −0.0729606 0.997335i \(-0.523245\pi\)
−0.696965 + 0.717105i \(0.745467\pi\)
\(152\) −1.48708e8 8.58566e7i −0.278586 0.160842i
\(153\) −1.88421e8 3.34601e8i −0.343845 0.610607i
\(154\) 1.79294e8 + 3.10546e8i 0.318773 + 0.552131i
\(155\) −4.96261e8 + 8.75042e7i −0.859772 + 0.151601i
\(156\) 1.14498e8 + 2.49024e8i 0.193330 + 0.420477i
\(157\) −1.49239e8 + 5.43187e7i −0.245632 + 0.0894027i −0.461902 0.886931i \(-0.652833\pi\)
0.216270 + 0.976333i \(0.430611\pi\)
\(158\) 1.37146e8 + 2.41826e7i 0.220067 + 0.0388038i
\(159\) −7.34567e8 2.01060e8i −1.14932 0.314584i
\(160\) 7.98173e7 6.69747e7i 0.121792 0.102195i
\(161\) 7.30425e8i 1.08711i
\(162\) 1.76360e8 4.53965e8i 0.256059 0.659116i
\(163\) −2.92100e8 −0.413791 −0.206895 0.978363i \(-0.566336\pi\)
−0.206895 + 0.978363i \(0.566336\pi\)
\(164\) 2.19334e8 + 2.61392e8i 0.303201 + 0.361341i
\(165\) −2.75046e8 + 1.00487e9i −0.371081 + 1.35573i
\(166\) −1.15995e8 + 6.57839e8i −0.152759 + 0.866337i
\(167\) 4.46328e7 + 1.22628e8i 0.0573837 + 0.157660i 0.965072 0.261984i \(-0.0843769\pi\)
−0.907688 + 0.419645i \(0.862155\pi\)
\(168\) −1.47622e8 + 6.78746e7i −0.185316 + 0.0852059i
\(169\) −2.02972e7 1.15111e8i −0.0248823 0.141114i
\(170\) −3.22346e8 + 1.86106e8i −0.385946 + 0.222826i
\(171\) −8.35398e6 + 7.77918e8i −0.00977033 + 0.909807i
\(172\) −1.31804e7 + 2.28291e7i −0.0150596 + 0.0260841i
\(173\) 2.85410e8 7.84157e8i 0.318628 0.875424i −0.672209 0.740362i \(-0.734654\pi\)
0.990837 0.135063i \(-0.0431236\pi\)
\(174\) −1.11187e9 5.25760e8i −1.21299 0.573575i
\(175\) 7.92223e7 + 6.64754e7i 0.0844686 + 0.0708776i
\(176\) 2.40981e8 2.87190e8i 0.251149 0.299308i
\(177\) −2.01473e7 + 1.65371e6i −0.0205270 + 0.00168487i
\(178\) 6.64133e8 + 2.41725e8i 0.661569 + 0.240791i
\(179\) 1.17110e9 + 6.76137e8i 1.14073 + 0.658601i 0.946611 0.322377i \(-0.104482\pi\)
0.194119 + 0.980978i \(0.437815\pi\)
\(180\) −4.41833e8 1.66209e8i −0.420890 0.158330i
\(181\) 4.41747e8 + 7.65129e8i 0.411585 + 0.712886i 0.995063 0.0992426i \(-0.0316420\pi\)
−0.583478 + 0.812129i \(0.698309\pi\)
\(182\) −4.07982e8 + 7.19383e7i −0.371840 + 0.0655653i
\(183\) 1.70049e9 + 1.57978e8i 1.51625 + 0.140862i
\(184\) 7.17599e8 2.61185e8i 0.626052 0.227864i
\(185\) −2.87342e8 5.06662e7i −0.245309 0.0432545i
\(186\) −2.08367e8 7.94680e8i −0.174092 0.663958i
\(187\) −1.02593e9 + 8.60856e8i −0.838978 + 0.703986i
\(188\) 3.56690e8i 0.285535i
\(189\) 5.96117e8 + 4.31880e8i 0.467180 + 0.338467i
\(190\) 7.54070e8 0.578625
\(191\) −2.19721e8 2.61853e8i −0.165096 0.196754i 0.677153 0.735842i \(-0.263213\pi\)
−0.842249 + 0.539088i \(0.818769\pi\)
\(192\) 1.19469e8 + 1.20759e8i 0.0879125 + 0.0888617i
\(193\) 3.32192e8 1.88395e9i 0.239419 1.35782i −0.593684 0.804698i \(-0.702327\pi\)
0.833103 0.553117i \(-0.186562\pi\)
\(194\) −2.16365e8 5.94457e8i −0.152749 0.419676i
\(195\) −9.82236e8 6.95658e8i −0.679324 0.481124i
\(196\) 8.54889e7 + 4.84832e8i 0.0579276 + 0.328524i
\(197\) 2.42189e9 1.39828e9i 1.60801 0.928387i 0.618199 0.786022i \(-0.287863\pi\)
0.989814 0.142365i \(-0.0454707\pi\)
\(198\) −1.66945e9 3.12889e8i −1.08621 0.203578i
\(199\) 7.89202e7 1.36694e8i 0.0503241 0.0871639i −0.839766 0.542948i \(-0.817308\pi\)
0.890090 + 0.455785i \(0.150641\pi\)
\(200\) 3.69799e7 1.01601e8i 0.0231124 0.0635009i
\(201\) 2.12097e8 1.46821e8i 0.129942 0.0899508i
\(202\) −2.22375e8 1.86595e8i −0.133561 0.112071i
\(203\) 1.19494e9 1.42407e9i 0.703657 0.838586i
\(204\) −3.45386e8 4.98943e8i −0.199427 0.288091i
\(205\) −1.40810e9 5.12505e8i −0.797291 0.290190i
\(206\) 8.31453e8 + 4.80040e8i 0.461710 + 0.266568i
\(207\) −2.62633e9 2.25225e9i −1.43043 1.22669i
\(208\) 2.16561e8 + 3.75094e8i 0.115698 + 0.200395i
\(209\) 2.67199e9 4.71144e8i 1.40039 0.246927i
\(210\) 4.12387e8 5.82271e8i 0.212045 0.299397i
\(211\) −1.66152e9 + 6.04745e8i −0.838256 + 0.305100i −0.725243 0.688493i \(-0.758272\pi\)
−0.113013 + 0.993593i \(0.536050\pi\)
\(212\) −1.18521e9 2.08985e8i −0.586748 0.103460i
\(213\) −2.24758e9 + 2.22357e9i −1.09194 + 1.08027i
\(214\) 4.98406e8 4.18212e8i 0.237645 0.199407i
\(215\) 1.15762e8i 0.0541767i
\(216\) 2.11137e8 7.40080e8i 0.0969951 0.339988i
\(217\) 1.24175e9 0.560011
\(218\) −6.53318e8 7.78594e8i −0.289267 0.344735i
\(219\) 2.57206e9 6.74401e8i 1.11816 0.293185i
\(220\) −2.85886e8 + 1.62134e9i −0.122040 + 0.692124i
\(221\) −5.29187e8 1.45393e9i −0.221840 0.609501i
\(222\) 4.40025e7 4.73646e8i 0.0181161 0.195003i
\(223\) −3.92006e8 2.22317e9i −0.158516 0.898988i −0.955501 0.294989i \(-0.904684\pi\)
0.796985 0.603999i \(-0.206427\pi\)
\(224\) −2.22357e8 + 1.28378e8i −0.0883198 + 0.0509915i
\(225\) −4.83300e8 + 7.98775e7i −0.188576 + 0.0311669i
\(226\) −1.57130e9 + 2.72156e9i −0.602316 + 1.04324i
\(227\) 1.32868e9 3.65053e9i 0.500401 1.37484i −0.390483 0.920610i \(-0.627692\pi\)
0.890884 0.454231i \(-0.150086\pi\)
\(228\) 1.00570e8 + 1.22525e9i 0.0372158 + 0.453405i
\(229\) 4.18612e9 + 3.51257e9i 1.52219 + 1.27727i 0.834037 + 0.551708i \(0.186024\pi\)
0.688155 + 0.725563i \(0.258421\pi\)
\(230\) −2.15562e9 + 2.56896e9i −0.770301 + 0.918008i
\(231\) 1.09746e9 2.32089e9i 0.385426 0.815094i
\(232\) −1.82635e9 6.64737e8i −0.630423 0.229455i
\(233\) 8.64942e7 + 4.99375e7i 0.0293470 + 0.0169435i 0.514602 0.857429i \(-0.327940\pi\)
−0.485255 + 0.874373i \(0.661273\pi\)
\(234\) 9.99341e8 1.68877e9i 0.333312 0.563256i
\(235\) −7.83194e8 1.35653e9i −0.256802 0.444794i
\(236\) −3.14595e7 + 5.54717e6i −0.0101415 + 0.00178823i
\(237\) −4.16509e8 9.05874e8i −0.132017 0.287127i
\(238\) 8.61893e8 3.13703e8i 0.268624 0.0977713i
\(239\) −1.33878e9 2.36063e8i −0.410315 0.0723495i −0.0353189 0.999376i \(-0.511245\pi\)
−0.374996 + 0.927027i \(0.622356\pi\)
\(240\) −7.19508e8 1.96938e8i −0.216865 0.0593587i
\(241\) −4.21680e8 + 3.53832e8i −0.125001 + 0.104889i −0.703145 0.711046i \(-0.748222\pi\)
0.578144 + 0.815935i \(0.303777\pi\)
\(242\) 3.49853e9i 1.02006i
\(243\) −3.39099e9 + 8.11714e8i −0.972525 + 0.232797i
\(244\) 2.69876e9 0.761387
\(245\) −1.38968e9 1.65616e9i −0.385701 0.459661i
\(246\) 6.44948e8 2.35630e9i 0.176110 0.643413i
\(247\) −5.44313e8 + 3.08695e9i −0.146238 + 0.829359i
\(248\) −4.44025e8 1.21995e9i −0.117382 0.322504i
\(249\) 4.34514e9 1.99784e9i 1.13033 0.519712i
\(250\) 5.13824e8 + 2.91404e9i 0.131539 + 0.745994i
\(251\) 3.36664e9 1.94373e9i 0.848206 0.489712i −0.0118389 0.999930i \(-0.503769\pi\)
0.860045 + 0.510218i \(0.170435\pi\)
\(252\) 1.00110e9 + 5.92412e8i 0.248243 + 0.146900i
\(253\) −6.03317e9 + 1.04498e10i −1.47253 + 2.55049i
\(254\) 4.02878e8 1.10690e9i 0.0967919 0.265934i
\(255\) 2.40908e9 + 1.13916e9i 0.569759 + 0.269417i
\(256\) 2.05633e8 + 1.72547e8i 0.0478778 + 0.0401742i
\(257\) 6.95694e8 8.29096e8i 0.159473 0.190052i −0.680391 0.732849i \(-0.738190\pi\)
0.839864 + 0.542797i \(0.182635\pi\)
\(258\) 1.88096e8 1.54391e7i 0.0424523 0.00348452i
\(259\) 6.75633e8 + 2.45910e8i 0.150145 + 0.0546484i
\(260\) −1.64721e9 9.51017e8i −0.360459 0.208111i
\(261\) 1.43585e9 + 8.68763e9i 0.309419 + 1.87214i
\(262\) 1.77892e9 + 3.08118e9i 0.377530 + 0.653901i
\(263\) 6.74222e9 1.18884e9i 1.40922 0.248484i 0.583296 0.812260i \(-0.301763\pi\)
0.825928 + 0.563775i \(0.190652\pi\)
\(264\) −2.67257e9 2.48286e8i −0.550191 0.0511136i
\(265\) 4.96636e9 1.80761e9i 1.00706 0.366539i
\(266\) −1.82995e9 3.22670e8i −0.365522 0.0644514i
\(267\) −1.28336e9 4.89453e9i −0.252524 0.963088i
\(268\) 3.12267e8 2.62023e8i 0.0605323 0.0507926i
\(269\) 8.33901e9i 1.59260i 0.604905 + 0.796298i \(0.293211\pi\)
−0.604905 + 0.796298i \(0.706789\pi\)
\(270\) 8.22035e8 + 3.27821e9i 0.154680 + 0.616852i
\(271\) −5.83337e9 −1.08154 −0.540769 0.841171i \(-0.681867\pi\)
−0.540769 + 0.841171i \(0.681867\pi\)
\(272\) −6.16390e8 7.34585e8i −0.112611 0.134204i
\(273\) 2.08598e9 + 2.10850e9i 0.375543 + 0.379598i
\(274\) 1.10139e9 6.24627e9i 0.195406 1.10820i
\(275\) 5.84313e8 + 1.60539e9i 0.102168 + 0.280704i
\(276\) −4.46168e9 3.15994e9i −0.768886 0.544555i
\(277\) −1.41740e8 8.03849e8i −0.0240754 0.136539i 0.970401 0.241500i \(-0.0776393\pi\)
−0.994476 + 0.104961i \(0.966528\pi\)
\(278\) −3.47883e9 + 2.00850e9i −0.582444 + 0.336274i
\(279\) −3.82892e9 + 4.46487e9i −0.631916 + 0.736871i
\(280\) 5.63765e8 9.76469e8i 0.0917204 0.158864i
\(281\) −1.69758e9 + 4.66406e9i −0.272273 + 0.748064i 0.725909 + 0.687791i \(0.241419\pi\)
−0.998182 + 0.0602730i \(0.980803\pi\)
\(282\) 2.09971e9 1.45349e9i 0.332019 0.229835i
\(283\) −5.52673e9 4.63748e9i −0.861634 0.722996i 0.100686 0.994918i \(-0.467896\pi\)
−0.962319 + 0.271922i \(0.912341\pi\)
\(284\) −3.21147e9 + 3.82728e9i −0.493662 + 0.588324i
\(285\) −3.07280e9 4.43895e9i −0.465752 0.672822i
\(286\) −6.43096e9 2.34068e9i −0.961195 0.349846i
\(287\) 3.19782e9 + 1.84626e9i 0.471331 + 0.272123i
\(288\) 2.24035e8 1.19536e9i 0.0325646 0.173751i
\(289\) −1.77508e9 3.07453e9i −0.254464 0.440745i
\(290\) 8.40539e9 1.48210e9i 1.18841 0.209549i
\(291\) −2.61769e9 + 3.69604e9i −0.365044 + 0.515425i
\(292\) 3.94848e9 1.43713e9i 0.543124 0.197681i
\(293\) −6.31134e9 1.11286e9i −0.856349 0.150998i −0.271798 0.962354i \(-0.587618\pi\)
−0.584551 + 0.811357i \(0.698729\pi\)
\(294\) 2.50567e9 2.47891e9i 0.335378 0.331796i
\(295\) 1.07464e8 9.01730e7i 0.0141898 0.0119066i
\(296\) 7.51701e8i 0.0979215i
\(297\) 4.96105e9 + 1.11025e10i 0.637599 + 1.42690i
\(298\) 8.76617e8 0.111159
\(299\) −8.96063e9 1.06789e10i −1.12112 1.33610i
\(300\) −7.48783e8 + 1.96333e8i −0.0924423 + 0.0242386i
\(301\) −4.95351e7 + 2.80928e8i −0.00603459 + 0.0342238i
\(302\) 1.64827e9 + 4.52858e9i 0.198153 + 0.544420i
\(303\) −1.92251e8 + 2.06941e9i −0.0228086 + 0.245513i
\(304\) 3.37349e8 + 1.91320e9i 0.0394989 + 0.224009i
\(305\) −1.02637e10 + 5.92575e9i −1.18605 + 0.684768i
\(306\) −1.52967e9 + 4.06633e9i −0.174467 + 0.463785i
\(307\) 4.00271e9 6.93290e9i 0.450610 0.780480i −0.547814 0.836600i \(-0.684540\pi\)
0.998424 + 0.0561204i \(0.0178731\pi\)
\(308\) 1.38756e9 3.81229e9i 0.154187 0.423626i
\(309\) −5.62304e8 6.85061e9i −0.0616790 0.751442i
\(310\) 4.36735e9 + 3.66464e9i 0.472902 + 0.396812i
\(311\) −6.13269e9 + 7.30865e9i −0.655555 + 0.781260i −0.986741 0.162306i \(-0.948107\pi\)
0.331185 + 0.943566i \(0.392551\pi\)
\(312\) 1.32557e9 2.80331e9i 0.139890 0.295837i
\(313\) −1.17664e10 4.28261e9i −1.22593 0.446202i −0.353728 0.935348i \(-0.615086\pi\)
−0.872202 + 0.489147i \(0.837308\pi\)
\(314\) 1.55608e9 + 8.98405e8i 0.160072 + 0.0924174i
\(315\) −5.10808e9 5.48552e7i −0.518819 0.00557155i
\(316\) −7.87785e8 1.36448e9i −0.0790058 0.136842i
\(317\) 8.73428e9 1.54009e9i 0.864948 0.152514i 0.276466 0.961024i \(-0.410837\pi\)
0.588482 + 0.808510i \(0.299726\pi\)
\(318\) 3.59945e9 + 7.82851e9i 0.351988 + 0.765545i
\(319\) 2.88578e10 1.05034e10i 2.78677 1.01430i
\(320\) −1.16091e9 2.04700e8i −0.110713 0.0195217i
\(321\) −4.49284e9 1.22975e9i −0.423157 0.115823i
\(322\) 6.33045e9 5.31188e9i 0.588859 0.494111i
\(323\) 6.93995e9i 0.637597i
\(324\) −5.21696e9 + 1.77290e9i −0.473410 + 0.160881i
\(325\) −1.97374e9 −0.176911
\(326\) 2.12424e9 + 2.53157e9i 0.188076 + 0.224140i
\(327\) −1.92107e9 + 7.01858e9i −0.168017 + 0.613845i
\(328\) 6.70368e8 3.80185e9i 0.0579186 0.328473i
\(329\) 1.32016e9 + 3.62712e9i 0.112679 + 0.309584i
\(330\) 1.07092e10 4.92397e9i 0.903031 0.415202i
\(331\) −3.72282e9 2.11132e10i −0.310142 1.75890i −0.598254 0.801306i \(-0.704139\pi\)
0.288112 0.957597i \(-0.406972\pi\)
\(332\) 6.54491e9 3.77870e9i 0.538705 0.311022i
\(333\) −2.96750e9 + 1.67106e9i −0.241331 + 0.135898i
\(334\) 7.38206e8 1.27861e9i 0.0593188 0.102743i
\(335\) −6.12255e8 + 1.68216e9i −0.0486130 + 0.133563i
\(336\) 1.66181e9 + 7.85803e8i 0.130384 + 0.0616533i
\(337\) −3.06551e9 2.57227e9i −0.237675 0.199433i 0.516169 0.856487i \(-0.327358\pi\)
−0.753843 + 0.657054i \(0.771802\pi\)
\(338\) −8.50039e8 + 1.01304e9i −0.0651287 + 0.0776173i
\(339\) 2.24238e10 1.84057e9i 1.69790 0.139365i
\(340\) 3.95714e9 + 1.44028e9i 0.296119 + 0.107778i
\(341\) 1.77650e10 + 1.02566e10i 1.31386 + 0.758557i
\(342\) 6.80281e9 5.58486e9i 0.497261 0.408233i
\(343\) 6.65629e9 + 1.15290e10i 0.480901 + 0.832945i
\(344\) 2.93707e8 5.17885e7i 0.0209740 0.00369828i
\(345\) 2.39066e10 + 2.22096e9i 1.68749 + 0.156771i
\(346\) −8.87172e9 + 3.22904e9i −0.619019 + 0.225304i
\(347\) −1.87458e10 3.30539e9i −1.29296 0.227984i −0.515488 0.856897i \(-0.672389\pi\)
−0.777476 + 0.628912i \(0.783500\pi\)
\(348\) 3.52921e9 + 1.34598e10i 0.240636 + 0.917747i
\(349\) −1.64128e10 + 1.37720e10i −1.10632 + 0.928313i −0.997834 0.0657851i \(-0.979045\pi\)
−0.108486 + 0.994098i \(0.534600\pi\)
\(350\) 1.17003e9i 0.0779698i
\(351\) −1.40134e10 + 9.98865e8i −0.923243 + 0.0658079i
\(352\) −4.24150e9 −0.276280
\(353\) −9.29044e9 1.10719e10i −0.598326 0.713057i 0.378858 0.925455i \(-0.376317\pi\)
−0.977183 + 0.212398i \(0.931873\pi\)
\(354\) 1.60850e8 + 1.62587e8i 0.0102426 + 0.0103531i
\(355\) 3.80991e9 2.16071e10i 0.239884 1.36045i
\(356\) −2.73480e9 7.51381e9i −0.170265 0.467800i
\(357\) −5.35883e9 3.79534e9i −0.329911 0.233656i
\(358\) −2.65668e9 1.50668e10i −0.161736 0.917253i
\(359\) −1.58454e10 + 9.14836e9i −0.953951 + 0.550764i −0.894306 0.447455i \(-0.852330\pi\)
−0.0596453 + 0.998220i \(0.518997\pi\)
\(360\) 1.77265e9 + 5.03800e9i 0.105539 + 0.299950i
\(361\) 1.46191e9 2.53210e9i 0.0860780 0.149091i
\(362\) 3.41870e9 9.39279e9i 0.199079 0.546966i
\(363\) 2.05946e10 1.42563e10i 1.18612 0.821072i
\(364\) 3.59045e9 + 3.01274e9i 0.204523 + 0.171616i
\(365\) −1.18610e10 + 1.41354e10i −0.668265 + 0.796407i
\(366\) −1.09973e10 1.58867e10i −0.612862 0.885337i
\(367\) −2.03310e10 7.39989e9i −1.12072 0.407907i −0.285802 0.958289i \(-0.592260\pi\)
−0.834913 + 0.550382i \(0.814482\pi\)
\(368\) −7.48224e9 4.31987e9i −0.407981 0.235548i
\(369\) −1.64988e10 + 5.80521e9i −0.889913 + 0.313121i
\(370\) 1.65053e9 + 2.85880e9i 0.0880677 + 0.152538i
\(371\) −1.28257e10 + 2.26151e9i −0.676993 + 0.119372i
\(372\) −5.37203e9 + 7.58504e9i −0.280522 + 0.396083i
\(373\) 1.72101e10 6.26396e9i 0.889094 0.323604i 0.143220 0.989691i \(-0.454254\pi\)
0.745874 + 0.666087i \(0.232032\pi\)
\(374\) 1.49217e10 + 2.63110e9i 0.762663 + 0.134478i
\(375\) 1.50601e10 1.48993e10i 0.761559 0.753424i
\(376\) 3.09136e9 2.59396e9i 0.154667 0.129781i
\(377\) 3.54792e10i 1.75634i
\(378\) −5.92129e8 8.30719e9i −0.0290034 0.406899i
\(379\) 1.33117e10 0.645172 0.322586 0.946540i \(-0.395448\pi\)
0.322586 + 0.946540i \(0.395448\pi\)
\(380\) −5.48383e9 6.53538e9i −0.262997 0.313427i
\(381\) −8.15763e9 + 2.13895e9i −0.387137 + 0.101508i
\(382\) −6.71550e8 + 3.80855e9i −0.0315373 + 0.178857i
\(383\) −1.68146e9 4.61978e9i −0.0781434 0.214697i 0.894469 0.447130i \(-0.147554\pi\)
−0.972613 + 0.232432i \(0.925332\pi\)
\(384\) 1.77778e8 1.91361e9i 0.00817621 0.0880094i
\(385\) 3.09370e9 + 1.75452e10i 0.140811 + 0.798576i
\(386\) −1.87436e10 + 1.08217e10i −0.844316 + 0.487466i
\(387\) −8.57367e8 1.04434e9i −0.0382228 0.0465586i
\(388\) −3.57857e9 + 6.19827e9i −0.157900 + 0.273491i
\(389\) 1.18972e10 3.26874e10i 0.519574 1.42752i −0.351416 0.936219i \(-0.614300\pi\)
0.870991 0.491299i \(-0.163478\pi\)
\(390\) 1.11399e9 + 1.35719e10i 0.0481530 + 0.586654i
\(391\) 2.36430e10 + 1.98388e10i 1.01157 + 0.848807i
\(392\) 3.58024e9 4.26676e9i 0.151624 0.180698i
\(393\) 1.08888e10 2.30275e10i 0.456468 0.965333i
\(394\) −2.97314e10 1.08213e10i −1.23376 0.449051i
\(395\) 5.99206e9 + 3.45952e9i 0.246143 + 0.142111i
\(396\) 9.42900e9 + 1.67442e10i 0.383429 + 0.680901i
\(397\) −9.81230e9 1.69954e10i −0.395011 0.684179i 0.598092 0.801428i \(-0.295926\pi\)
−0.993103 + 0.117249i \(0.962592\pi\)
\(398\) −1.75863e9 + 3.10094e8i −0.0700878 + 0.0123584i
\(399\) 5.55752e9 + 1.20871e10i 0.219275 + 0.476905i
\(400\) −1.14949e9 + 4.18380e8i −0.0449019 + 0.0163430i
\(401\) 3.14372e9 + 5.54323e8i 0.121581 + 0.0214381i 0.234108 0.972211i \(-0.424783\pi\)
−0.112526 + 0.993649i \(0.535894\pi\)
\(402\) −2.81491e9 7.70475e8i −0.107785 0.0295022i
\(403\) −1.81545e10 + 1.52334e10i −0.688279 + 0.577534i
\(404\) 3.28425e9i 0.123285i
\(405\) 1.59479e10 1.81975e10i 0.592766 0.676383i
\(406\) −2.10321e10 −0.774067
\(407\) 7.63471e9 + 9.09869e9i 0.278237 + 0.331590i
\(408\) −1.81248e9 + 6.62186e9i −0.0654084 + 0.238968i
\(409\) −1.91660e9 + 1.08696e10i −0.0684918 + 0.388436i 0.931221 + 0.364456i \(0.118745\pi\)
−0.999712 + 0.0239802i \(0.992366\pi\)
\(410\) 5.79833e9 + 1.59308e10i 0.205195 + 0.563770i
\(411\) −4.12577e10 + 1.89698e10i −1.44590 + 0.664805i
\(412\) −1.88618e9 1.06970e10i −0.0654627 0.371257i
\(413\) −2.99375e8 + 1.72845e8i −0.0102900 + 0.00594094i
\(414\) −4.20330e8 + 3.91409e10i −0.0143083 + 1.33238i
\(415\) −1.65940e10 + 2.87416e10i −0.559447 + 0.968990i
\(416\) 1.67597e9 4.60469e9i 0.0559620 0.153754i
\(417\) 2.59994e10 + 1.22941e10i 0.859843 + 0.406586i
\(418\) −2.35149e10 1.97313e10i −0.770260 0.646325i
\(419\) 1.25360e10 1.49398e10i 0.406727 0.484718i −0.523332 0.852129i \(-0.675311\pi\)
0.930059 + 0.367411i \(0.119756\pi\)
\(420\) −8.04544e9 + 6.60376e8i −0.258555 + 0.0212224i
\(421\) 5.53351e10 + 2.01403e10i 1.76146 + 0.641118i 0.999975 0.00706623i \(-0.00224927\pi\)
0.761483 + 0.648185i \(0.224471\pi\)
\(422\) 1.73243e10 + 1.00022e10i 0.546269 + 0.315388i
\(423\) −1.71124e10 6.43734e9i −0.534502 0.201069i
\(424\) 6.80799e9 + 1.17918e10i 0.210647 + 0.364851i
\(425\) 4.30346e9 7.58817e8i 0.131905 0.0232585i
\(426\) 3.56164e10 + 3.30882e9i 1.08146 + 0.100470i
\(427\) 2.74432e10 9.98852e9i 0.825513 0.300462i
\(428\) −7.24912e9 1.27822e9i −0.216028 0.0380916i
\(429\) 1.24271e10 + 4.73949e10i 0.366893 + 1.39927i
\(430\) −1.00329e9 + 8.41859e8i −0.0293462 + 0.0246244i
\(431\) 1.41725e10i 0.410712i −0.978687 0.205356i \(-0.934165\pi\)
0.978687 0.205356i \(-0.0658352\pi\)
\(432\) −7.94959e9 + 3.55221e9i −0.228249 + 0.101991i
\(433\) −1.15687e10 −0.329103 −0.164552 0.986368i \(-0.552618\pi\)
−0.164552 + 0.986368i \(0.552618\pi\)
\(434\) −9.03042e9 1.07620e10i −0.254536 0.303344i
\(435\) −4.29761e10 4.34401e10i −1.20025 1.21320i
\(436\) −1.99679e9 + 1.13244e10i −0.0552569 + 0.313377i
\(437\) −2.13856e10 5.87564e10i −0.586402 1.61113i
\(438\) −2.45497e10 1.73871e10i −0.667038 0.472423i
\(439\) 2.27216e9 + 1.28861e10i 0.0611760 + 0.346946i 0.999997 + 0.00254016i \(0.000808560\pi\)
−0.938821 + 0.344406i \(0.888080\pi\)
\(440\) 1.61309e10 9.31318e9i 0.430376 0.248478i
\(441\) −2.48029e10 4.64858e9i −0.655765 0.122904i
\(442\) −8.75252e9 + 1.51598e10i −0.229321 + 0.397196i
\(443\) −2.41376e10 + 6.63175e10i −0.626728 + 1.72192i 0.0631568 + 0.998004i \(0.479883\pi\)
−0.689885 + 0.723919i \(0.742339\pi\)
\(444\) −4.42500e9 + 3.06314e9i −0.113863 + 0.0788198i
\(445\) 2.68990e10 + 2.25710e10i 0.685956 + 0.575586i
\(446\) −1.64170e10 + 1.95650e10i −0.414911 + 0.494472i
\(447\) −3.57217e9 5.16033e9i −0.0894750 0.129255i
\(448\) 2.72967e9 + 9.93519e8i 0.0677639 + 0.0246640i
\(449\) 2.60097e10 + 1.50167e10i 0.639955 + 0.369478i 0.784597 0.620006i \(-0.212870\pi\)
−0.144642 + 0.989484i \(0.546203\pi\)
\(450\) 4.20699e9 + 3.60777e9i 0.102594 + 0.0879811i
\(451\) 3.04995e10 + 5.28267e10i 0.737203 + 1.27687i
\(452\) 3.50142e10 6.17395e9i 0.838862 0.147914i
\(453\) 1.99415e10 2.81565e10i 0.473550 0.668630i
\(454\) −4.13010e10 + 1.50323e10i −0.972160 + 0.353837i
\(455\) −2.02700e10 3.57415e9i −0.472943 0.0833926i
\(456\) 9.88765e9 9.78204e9i 0.228683 0.226240i
\(457\) −5.48694e9 + 4.60409e9i −0.125796 + 0.105555i −0.703515 0.710680i \(-0.748387\pi\)
0.577719 + 0.816235i \(0.303943\pi\)
\(458\) 6.18248e10i 1.40508i
\(459\) 3.01704e10 7.56546e9i 0.679720 0.170445i
\(460\) 3.79410e10 0.847379
\(461\) −2.31457e10 2.75840e10i −0.512469 0.610737i 0.446314 0.894876i \(-0.352736\pi\)
−0.958783 + 0.284140i \(0.908292\pi\)
\(462\) −2.80958e10 + 7.36680e9i −0.616700 + 0.161700i
\(463\) −3.09508e9 + 1.75531e10i −0.0673517 + 0.381970i 0.932435 + 0.361337i \(0.117679\pi\)
−0.999787 + 0.0206337i \(0.993432\pi\)
\(464\) 7.52064e9 + 2.06628e10i 0.162249 + 0.445776i
\(465\) 3.77573e9 4.06422e10i 0.0807587 0.869292i
\(466\) −1.96215e8 1.11279e9i −0.00416091 0.0235977i
\(467\) 1.28838e10 7.43844e9i 0.270879 0.156392i −0.358408 0.933565i \(-0.616680\pi\)
0.629287 + 0.777173i \(0.283347\pi\)
\(468\) −2.19037e10 + 3.62014e9i −0.456599 + 0.0754644i
\(469\) 2.20560e9 3.82021e9i 0.0455864 0.0789580i
\(470\) −6.06116e9 + 1.66529e10i −0.124212 + 0.341270i
\(471\) −1.05236e9 1.28211e10i −0.0213837 0.260520i
\(472\) 2.76860e8 + 2.32313e8i 0.00557817 + 0.00468064i
\(473\) −3.02908e9 + 3.60992e9i −0.0605155 + 0.0721195i
\(474\) −4.82205e9 + 1.01976e10i −0.0955253 + 0.202016i
\(475\) −8.31904e9 3.02788e9i −0.163418 0.0594792i
\(476\) −8.98676e9 5.18851e9i −0.175055 0.101068i
\(477\) 3.14161e10 5.30895e10i 0.606847 1.02550i
\(478\) 7.69010e9 + 1.33196e10i 0.147306 + 0.255142i
\(479\) 8.09444e10 1.42727e10i 1.53760 0.271121i 0.660281 0.751019i \(-0.270437\pi\)
0.877324 + 0.479898i \(0.159326\pi\)
\(480\) 3.52566e9 + 7.66803e9i 0.0664164 + 0.144450i
\(481\) −1.28945e10 + 4.69323e9i −0.240894 + 0.0876782i
\(482\) 6.13318e9 + 1.08144e9i 0.113631 + 0.0200362i
\(483\) −5.70654e10 1.56195e10i −1.04854 0.286998i
\(484\) 3.03211e10 2.54424e10i 0.552539 0.463636i
\(485\) 3.14303e10i 0.568043i
\(486\) 3.16953e10 + 2.34860e10i 0.568132 + 0.420982i
\(487\) −4.74284e9 −0.0843184 −0.0421592 0.999111i \(-0.513424\pi\)
−0.0421592 + 0.999111i \(0.513424\pi\)
\(488\) −1.96262e10 2.33897e10i −0.346065 0.412425i
\(489\) 6.24630e9 2.28207e10i 0.109241 0.399110i
\(490\) −4.24740e9 + 2.40882e10i −0.0736781 + 0.417849i
\(491\) 2.82219e9 + 7.75391e9i 0.0485580 + 0.133412i 0.961601 0.274451i \(-0.0884962\pi\)
−0.913043 + 0.407863i \(0.866274\pi\)
\(492\) −2.51118e10 + 1.15461e10i −0.428566 + 0.197049i
\(493\) −1.36402e10 7.73575e10i −0.230905 1.30953i
\(494\) 3.07124e10 1.77318e10i 0.515711 0.297746i
\(495\) −7.26253e10 4.29766e10i −1.20967 0.715832i
\(496\) −7.34396e9 + 1.27201e10i −0.121340 + 0.210167i
\(497\) −1.84915e10 + 5.08050e10i −0.303073 + 0.832685i
\(498\) −4.89140e10 2.31295e10i −0.795273 0.376053i
\(499\) −8.69878e10 7.29914e10i −1.40299 1.17725i −0.959752 0.280850i \(-0.909384\pi\)
−0.443243 0.896402i \(-0.646172\pi\)
\(500\) 2.15187e10 2.56450e10i 0.344300 0.410320i
\(501\) −1.05349e10 + 8.64712e8i −0.167216 + 0.0137253i
\(502\) −4.13292e10 1.50426e10i −0.650791 0.236869i
\(503\) 7.41830e10 + 4.28295e10i 1.15886 + 0.669070i 0.951031 0.309095i \(-0.100026\pi\)
0.207832 + 0.978165i \(0.433359\pi\)
\(504\) −2.14603e9 1.29846e10i −0.0332593 0.201236i
\(505\) −7.21132e9 1.24904e10i −0.110879 0.192048i
\(506\) 1.34441e11 2.37056e10i 2.05083 0.361617i
\(507\) 9.42726e9 + 8.75807e8i 0.142677 + 0.0132549i
\(508\) −1.25231e10 + 4.55805e9i −0.188043 + 0.0684422i
\(509\) −3.32208e10 5.85773e9i −0.494925 0.0872686i −0.0793859 0.996844i \(-0.525296\pi\)
−0.415539 + 0.909575i \(0.636407\pi\)
\(510\) −7.64672e9 2.91634e10i −0.113030 0.431079i
\(511\) 3.48324e10 2.92278e10i 0.510857 0.428660i
\(512\) 3.03700e9i 0.0441942i
\(513\) −6.05972e10 1.72878e10i −0.874950 0.249614i
\(514\) −1.22449e10 −0.175430
\(515\) 3.06611e10 + 3.65405e10i 0.435872 + 0.519452i
\(516\) −1.50170e9 1.51792e9i −0.0211829 0.0214116i
\(517\) −1.10725e10 + 6.27954e10i −0.154983 + 0.878952i
\(518\) −2.78216e9 7.64391e9i −0.0386423 0.106169i
\(519\) 5.51601e10 + 3.90665e10i 0.760248 + 0.538438i
\(520\) 3.73674e9 + 2.11921e10i 0.0511070 + 0.289842i
\(521\) 9.03255e10 5.21494e10i 1.22591 0.707781i 0.259740 0.965679i \(-0.416363\pi\)
0.966172 + 0.257898i \(0.0830298\pi\)
\(522\) 6.48520e10 7.56234e10i 0.873457 1.01853i
\(523\) 3.82596e10 6.62675e10i 0.511368 0.885715i −0.488546 0.872538i \(-0.662472\pi\)
0.999913 0.0131762i \(-0.00419424\pi\)
\(524\) 1.37671e10 3.78249e10i 0.182607 0.501710i
\(525\) −6.88758e9 + 4.76783e9i −0.0906628 + 0.0627601i
\(526\) −5.93349e10 4.97879e10i −0.775118 0.650401i
\(527\) 3.37269e10 4.01941e10i 0.437254 0.521099i
\(528\) 1.72839e10 + 2.49682e10i 0.222385 + 0.321257i
\(529\) 1.87717e11 + 6.83233e10i 2.39707 + 0.872461i
\(530\) −5.17831e10 2.98970e10i −0.656273 0.378899i
\(531\) 3.01635e8 1.60940e9i 0.00379406 0.0202435i
\(532\) 1.05115e10 + 1.82064e10i 0.131225 + 0.227288i
\(533\) −6.94016e10 + 1.22374e10i −0.859925 + 0.151628i
\(534\) −3.30870e10 + 4.67172e10i −0.406904 + 0.574529i
\(535\) 3.03758e10 1.10559e10i 0.370777 0.134952i
\(536\) −4.54181e9 8.00843e8i −0.0550262 0.00970260i
\(537\) −7.78671e10 + 7.70354e10i −0.936390 + 0.926388i
\(538\) 7.22726e10 6.06439e10i 0.862670 0.723866i
\(539\) 8.80085e10i 1.04272i
\(540\) 2.24335e10 3.09646e10i 0.263828 0.364158i
\(541\) −1.26790e11 −1.48012 −0.740058 0.672543i \(-0.765202\pi\)
−0.740058 + 0.672543i \(0.765202\pi\)
\(542\) 4.24221e10 + 5.05566e10i 0.491581 + 0.585843i
\(543\) −6.92231e10 + 1.81505e10i −0.796254 + 0.208780i
\(544\) −1.88392e9 + 1.06843e10i −0.0215113 + 0.121997i
\(545\) −1.72712e10 4.74522e10i −0.195765 0.537861i
\(546\) 3.10407e9 3.34125e10i 0.0349270 0.375957i
\(547\) 3.03751e10 + 1.72266e11i 0.339288 + 1.92420i 0.379907 + 0.925025i \(0.375956\pi\)
−0.0406190 + 0.999175i \(0.512933\pi\)
\(548\) −6.21448e10 + 3.58793e10i −0.689101 + 0.397852i
\(549\) −4.87057e10 + 1.29475e11i −0.536155 + 1.42526i
\(550\) 9.66426e9 1.67390e10i 0.105613 0.182927i
\(551\) −5.44281e10 + 1.49540e11i −0.590496 + 1.62238i
\(552\) 5.06016e9 + 6.16485e10i 0.0545015 + 0.663998i
\(553\) −1.30610e10 1.09595e10i −0.139661 0.117190i
\(554\) −5.93602e9 + 7.07427e9i −0.0630168 + 0.0751005i
\(555\) 1.01029e10 2.13656e10i 0.106482 0.225186i
\(556\) 4.27065e10 + 1.55439e10i 0.446884 + 0.162652i
\(557\) −1.00295e11 5.79055e10i −1.04198 0.601588i −0.121587 0.992581i \(-0.538798\pi\)
−0.920394 + 0.390993i \(0.872132\pi\)
\(558\) 6.65412e10 + 7.14579e8i 0.686363 + 0.00737078i
\(559\) −2.72213e9 4.71486e9i −0.0278780 0.0482861i
\(560\) −1.25627e10 + 2.21515e9i −0.127742 + 0.0225243i
\(561\) −4.53169e10 9.85606e10i −0.457519 0.995066i
\(562\) 5.27678e10 1.92059e10i 0.528961 0.192526i
\(563\) 1.37951e11 + 2.43246e10i 1.37307 + 0.242109i 0.811032 0.585002i \(-0.198906\pi\)
0.562038 + 0.827111i \(0.310017\pi\)
\(564\) −2.78669e10 7.62751e9i −0.275405 0.0753817i
\(565\) −1.19607e11 + 1.00362e11i −1.17371 + 0.984861i
\(566\) 8.16243e10i 0.795341i
\(567\) −4.64886e10 + 3.73370e10i −0.449795 + 0.361250i
\(568\) 5.65250e10 0.543060
\(569\) −1.16489e11 1.38826e11i −1.11131 1.32441i −0.940766 0.339055i \(-0.889893\pi\)
−0.170542 0.985350i \(-0.554552\pi\)
\(570\) −1.61251e10 + 5.89127e10i −0.152758 + 0.558097i
\(571\) 2.82095e9 1.59984e10i 0.0265370 0.150499i −0.968660 0.248390i \(-0.920099\pi\)
0.995197 + 0.0978911i \(0.0312097\pi\)
\(572\) 2.64817e10 + 7.27580e10i 0.247379 + 0.679668i
\(573\) 2.51561e10 1.15665e10i 0.233359 0.107296i
\(574\) −7.25434e9 4.11414e10i −0.0668268 0.378993i
\(575\) 3.40965e10 1.96856e10i 0.311917 0.180085i
\(576\) −1.19892e10 + 6.75135e9i −0.108918 + 0.0613339i
\(577\) 3.86412e10 6.69285e10i 0.348616 0.603821i −0.637388 0.770543i \(-0.719985\pi\)
0.986004 + 0.166722i \(0.0533184\pi\)
\(578\) −1.37374e10 + 3.77433e10i −0.123082 + 0.338164i
\(579\) 1.40083e11 + 6.62396e10i 1.24644 + 0.589391i
\(580\) −7.39717e10 6.20696e10i −0.653662 0.548488i
\(581\) 5.25684e10 6.26486e10i 0.461339 0.549803i
\(582\) 5.10695e10 4.19183e9i 0.445113 0.0365352i
\(583\) −2.02169e11 7.35835e10i −1.75001 0.636951i
\(584\) −4.11699e10 2.37695e10i −0.353939 0.204347i
\(585\) 7.53534e10 6.18624e10i 0.643398 0.528206i
\(586\) 3.62531e10 + 6.27922e10i 0.307436 + 0.532495i
\(587\) −1.88005e11 + 3.31503e10i −1.58349 + 0.279213i −0.895012 0.446042i \(-0.852833\pi\)
−0.688481 + 0.725255i \(0.741722\pi\)
\(588\) −3.97062e10 3.68877e9i −0.332161 0.0308583i
\(589\) −9.98884e10 + 3.63564e10i −0.829954 + 0.302078i
\(590\) −1.56302e9 2.75603e8i −0.0128990 0.00227445i
\(591\) 5.74524e10 + 2.19114e11i 0.470932 + 1.79606i
\(592\) −6.51484e9 + 5.46660e9i −0.0530417 + 0.0445073i
\(593\) 3.99880e10i 0.323378i −0.986842 0.161689i \(-0.948306\pi\)
0.986842 0.161689i \(-0.0516942\pi\)
\(594\) 6.01446e10 1.23737e11i 0.483116 0.993926i
\(595\) 4.55702e10 0.363591
\(596\) −6.37503e9 7.59746e9i −0.0505239 0.0602121i
\(597\) 8.99174e9 + 9.08882e9i 0.0707859 + 0.0715501i
\(598\) −2.73871e10 + 1.55320e11i −0.214161 + 1.21457i
\(599\) 2.70603e10 + 7.43475e10i 0.210196 + 0.577509i 0.999326 0.0367176i \(-0.0116902\pi\)
−0.789130 + 0.614227i \(0.789468\pi\)
\(600\) 7.14696e9 + 5.06176e9i 0.0551463 + 0.0390568i
\(601\) 6.09335e8 + 3.45571e9i 0.00467044 + 0.0264874i 0.987054 0.160389i \(-0.0512748\pi\)
−0.982383 + 0.186876i \(0.940164\pi\)
\(602\) 2.79498e9 1.61368e9i 0.0212810 0.0122866i
\(603\) 6.93509e9 + 1.97100e10i 0.0524545 + 0.149080i
\(604\) 2.72616e10 4.72184e10i 0.204835 0.354784i
\(605\) −5.94498e10 + 1.63337e11i −0.443741 + 1.21917i
\(606\) 1.93332e10 1.33832e10i 0.143355 0.0992357i
\(607\) 7.79516e10 + 6.54092e10i 0.574210 + 0.481819i 0.883040 0.469298i \(-0.155493\pi\)
−0.308830 + 0.951117i \(0.599937\pi\)
\(608\) 1.41280e10 1.68371e10i 0.103387 0.123212i
\(609\) 8.57048e10 + 1.23809e11i 0.623068 + 0.900081i
\(610\) 1.25998e11 + 4.58595e10i 0.910007 + 0.331215i
\(611\) −6.37972e10 3.68333e10i −0.457759 0.264287i
\(612\) 4.63663e10 1.63143e10i 0.330520 0.116295i
\(613\) −6.80077e10 1.17793e11i −0.481633 0.834212i 0.518145 0.855293i \(-0.326623\pi\)
−0.999778 + 0.0210804i \(0.993289\pi\)
\(614\) −8.91951e10 + 1.57275e10i −0.627578 + 0.110659i
\(615\) 7.01510e10 9.90498e10i 0.490381 0.692394i
\(616\) −4.31311e10 + 1.56984e10i −0.299549 + 0.109027i
\(617\) −4.42979e10 7.81091e9i −0.305662 0.0538965i 0.0187132 0.999825i \(-0.494043\pi\)
−0.324376 + 0.945928i \(0.605154\pi\)
\(618\) −5.52836e10 + 5.46931e10i −0.379003 + 0.374955i
\(619\) 1.17003e11 9.81772e10i 0.796957 0.668726i −0.150500 0.988610i \(-0.548088\pi\)
0.947457 + 0.319884i \(0.103644\pi\)
\(620\) 6.45013e10i 0.436518i
\(621\) 2.32122e11 1.57023e11i 1.56081 1.05584i
\(622\) 1.07941e11 0.721152
\(623\) −5.56194e10 6.62847e10i −0.369211 0.440008i
\(624\) −3.39357e10 + 8.89803e9i −0.223830 + 0.0586889i
\(625\) −2.04642e10 + 1.16058e11i −0.134114 + 0.760600i
\(626\) 4.84522e10 + 1.33121e11i 0.315512 + 0.866863i
\(627\) −2.03295e10 + 2.18828e11i −0.131539 + 1.41590i
\(628\) −3.53002e9 2.00198e10i −0.0226955 0.128712i
\(629\) 2.63105e10 1.51904e10i 0.168084 0.0970433i
\(630\) 3.66721e10 + 4.46697e10i 0.232795 + 0.283564i
\(631\) 1.58464e10 2.74468e10i 0.0999571 0.173131i −0.811710 0.584061i \(-0.801463\pi\)
0.911667 + 0.410931i \(0.134796\pi\)
\(632\) −6.09669e9 + 1.67505e10i −0.0382143 + 0.104993i
\(633\) −1.17163e10 1.42741e11i −0.0729750 0.889063i
\(634\) −7.68660e10 6.44982e10i −0.475748 0.399200i
\(635\) 3.76186e10 4.48321e10i 0.231371 0.275737i
\(636\) 4.16719e10 8.81271e10i 0.254692 0.538618i
\(637\) −9.55444e10 3.47753e10i −0.580293 0.211210i
\(638\) −3.00894e11 1.73721e11i −1.81606 1.04850i
\(639\) −1.25657e11 2.23144e11i −0.753674 1.33839i
\(640\) 6.66842e9 + 1.15500e10i 0.0397469 + 0.0688436i
\(641\) 6.17877e10 1.08948e10i 0.365990 0.0645340i 0.0123713 0.999923i \(-0.496062\pi\)
0.353619 + 0.935389i \(0.384951\pi\)
\(642\) 2.20154e10 + 4.78817e10i 0.129594 + 0.281857i
\(643\) 2.34065e11 8.51928e10i 1.36928 0.498378i 0.450371 0.892842i \(-0.351292\pi\)
0.918912 + 0.394464i \(0.129070\pi\)
\(644\) −9.20740e10 1.62351e10i −0.535295 0.0943870i
\(645\) 9.04407e9 + 2.47547e9i 0.0522547 + 0.0143027i
\(646\) −6.01472e10 + 5.04695e10i −0.345371 + 0.289800i
\(647\) 1.97433e11i 1.12668i −0.826224 0.563342i \(-0.809515\pi\)
0.826224 0.563342i \(-0.190485\pi\)
\(648\) 5.33047e10 + 3.23213e10i 0.302319 + 0.183311i
\(649\) −5.71065e9 −0.0321890
\(650\) 1.43536e10 + 1.71060e10i 0.0804096 + 0.0958284i
\(651\) −2.65538e10 + 9.70136e10i −0.147844 + 0.540143i
\(652\) 6.49249e9 3.68207e10i 0.0359270 0.203752i
\(653\) −7.62838e10 2.09588e11i −0.419546 1.15269i −0.951963 0.306212i \(-0.900938\pi\)
0.532417 0.846482i \(-0.321284\pi\)
\(654\) 7.47993e10 3.43918e10i 0.408871 0.187994i
\(655\) 3.06952e10 + 1.74081e11i 0.166765 + 0.945771i
\(656\) −3.78250e10 + 2.18383e10i −0.204251 + 0.117924i
\(657\) −2.31281e9 + 2.15367e11i −0.0124130 + 1.15589i
\(658\) 2.18349e10 3.78191e10i 0.116479 0.201747i
\(659\) −9.35909e10 + 2.57139e11i −0.496240 + 1.36341i 0.398642 + 0.917106i \(0.369481\pi\)
−0.894882 + 0.446302i \(0.852741\pi\)
\(660\) −1.20556e11 5.70062e10i −0.635350 0.300432i
\(661\) −1.94158e11 1.62918e11i −1.01707 0.853421i −0.0278111 0.999613i \(-0.508854\pi\)
−0.989256 + 0.146192i \(0.953298\pi\)
\(662\) −1.55910e11 + 1.85807e11i −0.811788 + 0.967452i
\(663\) 1.24906e11 1.02524e10i 0.646444 0.0530606i
\(664\) −8.03459e10 2.92435e10i −0.413325 0.150438i
\(665\) −7.99525e10 4.61606e10i −0.408833 0.236040i
\(666\) 3.60633e10 + 1.35663e10i 0.183302 + 0.0689546i
\(667\) −3.53862e11 6.12907e11i −1.78785 3.09664i
\(668\) −1.64499e10 + 2.90057e9i −0.0826149 + 0.0145672i
\(669\) 1.82071e11 + 1.69147e10i 0.908942 + 0.0844422i
\(670\) 1.90314e10 6.92687e9i 0.0944435 0.0343746i
\(671\) 4.75118e11 + 8.37761e10i 2.34375 + 0.413266i
\(672\) −5.27477e9 2.01172e10i −0.0258658 0.0986483i
\(673\) 5.73025e10 4.80825e10i 0.279327 0.234383i −0.492351 0.870397i \(-0.663862\pi\)
0.771678 + 0.636014i \(0.219418\pi\)
\(674\) 4.52745e10i 0.219389i
\(675\) 4.09442e9 3.94666e10i 0.0197232 0.190114i
\(676\) 1.49615e10 0.0716456
\(677\) 2.12307e11 + 2.53018e11i 1.01067 + 1.20447i 0.978766 + 0.204981i \(0.0657131\pi\)
0.0319055 + 0.999491i \(0.489842\pi\)
\(678\) −1.79025e11 1.80958e11i −0.847217 0.856364i
\(679\) −1.34491e10 + 7.62739e10i −0.0632726 + 0.358837i
\(680\) −1.62949e10 4.47700e10i −0.0762109 0.209388i
\(681\) 2.56790e11 + 1.81869e11i 1.19396 + 0.845608i
\(682\) −4.03005e10 2.28556e11i −0.186283 1.05646i
\(683\) −1.58814e11 + 9.16916e10i −0.729806 + 0.421354i −0.818351 0.574719i \(-0.805112\pi\)
0.0885453 + 0.996072i \(0.471778\pi\)
\(684\) −9.78750e10 1.83438e10i −0.447144 0.0838041i
\(685\) 1.57562e11 2.72906e11i 0.715633 1.23951i
\(686\) 5.15133e10 1.41532e11i 0.232607 0.639082i
\(687\) −3.63941e11 + 2.51933e11i −1.63382 + 1.13099i
\(688\) −2.58477e9 2.16888e9i −0.0115364 0.00968015i
\(689\) 1.59769e11 1.90405e11i 0.708948 0.844892i
\(690\) −1.54608e11 2.23345e11i −0.682079 0.985328i
\(691\) 1.99994e11 + 7.27919e10i 0.877213 + 0.319279i 0.741085 0.671412i \(-0.234312\pi\)
0.136129 + 0.990691i \(0.456534\pi\)
\(692\) 9.25034e10 + 5.34069e10i 0.403398 + 0.232902i
\(693\) 1.57855e11 + 1.35371e11i 0.684423 + 0.586938i
\(694\) 1.07678e11 + 1.86504e11i 0.464184 + 0.803990i
\(695\) −1.96547e11 + 3.46566e10i −0.842419 + 0.148541i
\(696\) 9.09883e10 1.28471e11i 0.387747 0.547480i
\(697\) 1.46616e11 5.33639e10i 0.621227 0.226108i
\(698\) 2.38718e11 + 4.20924e10i 1.00569 + 0.177330i
\(699\) −5.75103e9 + 5.68960e9i −0.0240900 + 0.0238327i
\(700\) −1.01405e10 + 8.50885e9i −0.0422343 + 0.0354388i
\(701\) 2.36276e10i 0.0978470i −0.998803 0.0489235i \(-0.984421\pi\)
0.998803 0.0489235i \(-0.0155791\pi\)
\(702\) 1.10567e11 + 1.14188e11i 0.455279 + 0.470187i
\(703\) −6.15487e10 −0.251998
\(704\) 3.08455e10 + 3.67603e10i 0.125575 + 0.149654i
\(705\) 1.22729e11 3.21798e10i 0.496809 0.130265i
\(706\) −2.83951e10 + 1.61037e11i −0.114294 + 0.648196i
\(707\) 1.21555e10 + 3.33970e10i 0.0486514 + 0.133669i
\(708\) 2.39355e8 2.57644e9i 0.000952599 0.0102538i
\(709\) 6.41935e10 + 3.64059e11i 0.254042 + 1.44075i 0.798519 + 0.601970i \(0.205617\pi\)
−0.544477 + 0.838776i \(0.683272\pi\)
\(710\) −2.14971e11 + 1.24114e11i −0.845953 + 0.488411i
\(711\) 7.96793e10 1.31690e10i 0.311794 0.0515317i
\(712\) −4.52324e10 + 7.83448e10i −0.176007 + 0.304853i
\(713\) 1.61686e11 4.44229e11i 0.625626 1.71889i
\(714\) 6.07766e9 + 7.40448e10i 0.0233853 + 0.284906i
\(715\) −2.60470e11 2.18560e11i −0.996628 0.836270i
\(716\) −1.11261e11 + 1.32595e11i −0.423341 + 0.504518i
\(717\) 4.70713e10 9.95458e10i 0.178106 0.376657i
\(718\) 1.94520e11 + 7.07995e10i 0.731925 + 0.266399i
\(719\) 2.14515e11 + 1.23850e11i 0.802678 + 0.463427i 0.844407 0.535702i \(-0.179953\pi\)
−0.0417284 + 0.999129i \(0.513286\pi\)
\(720\) 3.07721e10 5.20011e10i 0.114506 0.193501i
\(721\) −5.87715e10 1.01795e11i −0.217483 0.376692i
\(722\) −3.25767e10 + 5.74415e9i −0.119883 + 0.0211386i
\(723\) −1.86263e10 4.05107e10i −0.0681668 0.148257i
\(724\) −1.06267e11 + 3.86781e10i −0.386763 + 0.140770i
\(725\) −9.86810e10 1.74001e10i −0.357175 0.0629796i
\(726\) −2.73327e11 7.48130e10i −0.983867 0.269297i
\(727\) 1.79324e10 1.50471e10i 0.0641950 0.0538660i −0.610126 0.792305i \(-0.708881\pi\)
0.674321 + 0.738439i \(0.264437\pi\)
\(728\) 5.30273e10i 0.188788i
\(729\) 9.09703e9 2.82283e11i 0.0322099 0.999481i
\(730\) 2.08765e11 0.735133
\(731\) 7.74790e9 + 9.23358e9i 0.0271340 + 0.0323371i
\(732\) −5.77107e10 + 2.10844e11i −0.201007 + 0.734375i
\(733\) −2.55676e9 + 1.45001e10i −0.00885674 + 0.0502290i −0.988916 0.148477i \(-0.952563\pi\)
0.980059 + 0.198706i \(0.0636740\pi\)
\(734\) 8.37202e10 + 2.30019e11i 0.288434 + 0.792465i
\(735\) 1.59107e11 7.31552e10i 0.545179 0.250666i
\(736\) 1.69737e10 + 9.62625e10i 0.0578449 + 0.328055i
\(737\) 6.31085e10 3.64357e10i 0.213903 0.123497i
\(738\) 1.70297e11 + 1.00775e11i 0.574093 + 0.339724i
\(739\) −3.66731e9 + 6.35196e9i −0.0122962 + 0.0212976i −0.872108 0.489313i \(-0.837247\pi\)
0.859812 + 0.510611i \(0.170581\pi\)
\(740\) 1.27735e10 3.50949e10i 0.0425974 0.117035i
\(741\) −2.29533e11 1.08537e11i −0.761328 0.360002i
\(742\) 1.12872e11 + 9.47111e10i 0.372368 + 0.312454i
\(743\) −3.11941e10 + 3.71757e10i −0.102357 + 0.121984i −0.814791 0.579755i \(-0.803148\pi\)
0.712434 + 0.701739i \(0.247593\pi\)
\(744\) 1.04805e11 8.60249e9i 0.342051 0.0280758i
\(745\) 4.09269e10 + 1.48962e10i 0.132857 + 0.0483559i
\(746\) −1.79446e11 1.03603e11i −0.579399 0.334516i
\(747\) 6.31667e10 + 3.82191e11i 0.202864 + 1.22743i
\(748\) −8.57122e10 1.48458e11i −0.273802 0.474239i
\(749\) −7.84459e10 + 1.38321e10i −0.249254 + 0.0439503i
\(750\) −2.38651e11 2.21710e10i −0.754254 0.0700714i
\(751\) 3.18222e11 1.15823e11i 1.00039 0.364114i 0.210657 0.977560i \(-0.432440\pi\)
0.789736 + 0.613446i \(0.210217\pi\)
\(752\) −4.49627e10 7.92814e9i −0.140599 0.0247913i
\(753\) 7.98638e10 + 3.04588e11i 0.248410 + 0.947399i
\(754\) 3.07491e11 2.58015e11i 0.951364 0.798289i
\(755\) 2.39436e11i 0.736888i