Properties

Label 99.8.j.a.8.19
Level $99$
Weight $8$
Character 99.8
Analytic conductor $30.926$
Analytic rank $0$
Dimension $112$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,8,Mod(8,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.8");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 99.j (of order \(10\), degree \(4\), 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: \(30.9261175229\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(28\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 8.19
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(6.50881 - 4.72893i) q^{2} +(-19.5523 + 60.1758i) q^{4} +(-255.658 + 351.883i) q^{5} +(-495.513 - 161.002i) q^{7} +(475.531 + 1463.54i) q^{8} +O(q^{10})\) \(q+(6.50881 - 4.72893i) q^{2} +(-19.5523 + 60.1758i) q^{4} +(-255.658 + 351.883i) q^{5} +(-495.513 - 161.002i) q^{7} +(475.531 + 1463.54i) q^{8} +3499.33i q^{10} +(4407.95 + 239.048i) q^{11} +(-1893.40 - 2606.04i) q^{13} +(-3986.57 + 1295.31i) q^{14} +(3463.95 + 2516.71i) q^{16} +(-24695.9 - 17942.7i) q^{17} +(-3098.98 + 1006.92i) q^{19} +(-16176.2 - 22264.6i) q^{20} +(29821.0 - 19289.0i) q^{22} -21503.8i q^{23} +(-34318.8 - 105622. i) q^{25} +(-24647.5 - 8008.47i) q^{26} +(19376.9 - 26670.0i) q^{28} +(42595.2 - 131094. i) q^{29} +(-1639.21 + 1190.96i) q^{31} -162525. q^{32} -245591. q^{34} +(183336. - 133201. i) q^{35} +(-134323. + 413405. i) q^{37} +(-15409.0 + 21208.7i) q^{38} +(-636567. - 206833. i) q^{40} +(-33032.5 - 101664. i) q^{41} +109382. i q^{43} +(-100571. + 260578. i) q^{44} +(-101690. - 139964. i) q^{46} +(893228. - 290227. i) q^{47} +(-446649. - 324509. i) q^{49} +(-722855. - 525185. i) q^{50} +(193841. - 62982.7i) q^{52} +(-989381. - 1.36177e6i) q^{53} +(-1.21105e6 + 1.48997e6i) q^{55} -801762. i q^{56} +(-342692. - 1.05470e6i) q^{58} +(2.04315e6 + 663860. i) q^{59} +(-286690. + 394595. i) q^{61} +(-5037.37 + 15503.4i) q^{62} +(-1.50123e6 + 1.09071e6i) q^{64} +1.40108e6 q^{65} -3.77992e6 q^{67} +(1.56258e6 - 1.13528e6i) q^{68} +(563399. - 1.73396e6i) q^{70} +(-862546. + 1.18719e6i) q^{71} +(-1.90472e6 - 618882. i) q^{73} +(1.08068e6 + 3.32598e6i) q^{74} -206171. i q^{76} +(-2.14571e6 - 828140. i) q^{77} +(1.30874e6 + 1.80133e6i) q^{79} +(-1.77118e6 + 575490. i) q^{80} +(-695762. - 505501. i) q^{82} +(-5.87409e6 - 4.26777e6i) q^{83} +(1.26274e7 - 4.10290e6i) q^{85} +(517262. + 711950. i) q^{86} +(1.74626e6 + 6.56487e6i) q^{88} -7.30242e6i q^{89} +(518626. + 1.59617e6i) q^{91} +(1.29401e6 + 420449. i) q^{92} +(4.44139e6 - 6.11305e6i) q^{94} +(437962. - 1.34791e6i) q^{95} +(2.06576e6 - 1.50086e6i) q^{97} -4.44173e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 1792 q^{4} - 134096 q^{16} + 401484 q^{22} - 68552 q^{25} + 1493020 q^{28} - 398144 q^{31} - 729944 q^{34} + 685476 q^{37} - 399360 q^{40} - 1410880 q^{46} + 2923872 q^{49} + 6472520 q^{52} + 1445488 q^{55} + 13215936 q^{58} - 7843440 q^{61} - 12806712 q^{64} + 1864032 q^{67} - 1233728 q^{70} + 53841940 q^{73} - 53845440 q^{79} - 36360204 q^{82} + 41703500 q^{85} + 21474024 q^{88} + 27611736 q^{91} - 94707560 q^{94} - 27695460 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.50881 4.72893i 0.575303 0.417982i −0.261725 0.965143i \(-0.584291\pi\)
0.837028 + 0.547160i \(0.184291\pi\)
\(3\) 0 0
\(4\) −19.5523 + 60.1758i −0.152752 + 0.470124i
\(5\) −255.658 + 351.883i −0.914670 + 1.25894i 0.0508762 + 0.998705i \(0.483799\pi\)
−0.965546 + 0.260231i \(0.916201\pi\)
\(6\) 0 0
\(7\) −495.513 161.002i −0.546024 0.177414i 0.0229989 0.999735i \(-0.492679\pi\)
−0.569023 + 0.822321i \(0.692679\pi\)
\(8\) 475.531 + 1463.54i 0.328371 + 1.01062i
\(9\) 0 0
\(10\) 3499.33i 1.10659i
\(11\) 4407.95 + 239.048i 0.998533 + 0.0541515i
\(12\) 0 0
\(13\) −1893.40 2606.04i −0.239023 0.328987i 0.672606 0.740001i \(-0.265175\pi\)
−0.911629 + 0.411013i \(0.865175\pi\)
\(14\) −3986.57 + 1295.31i −0.388285 + 0.126162i
\(15\) 0 0
\(16\) 3463.95 + 2516.71i 0.211423 + 0.153608i
\(17\) −24695.9 17942.7i −1.21914 0.885759i −0.223114 0.974792i \(-0.571622\pi\)
−0.996029 + 0.0890338i \(0.971622\pi\)
\(18\) 0 0
\(19\) −3098.98 + 1006.92i −0.103653 + 0.0336789i −0.360384 0.932804i \(-0.617354\pi\)
0.256731 + 0.966483i \(0.417354\pi\)
\(20\) −16176.2 22264.6i −0.452137 0.622314i
\(21\) 0 0
\(22\) 29821.0 19289.0i 0.597093 0.386215i
\(23\) 21503.8i 0.368526i −0.982877 0.184263i \(-0.941010\pi\)
0.982877 0.184263i \(-0.0589898\pi\)
\(24\) 0 0
\(25\) −34318.8 105622.i −0.439280 1.35197i
\(26\) −24647.5 8008.47i −0.275022 0.0893600i
\(27\) 0 0
\(28\) 19376.9 26670.0i 0.166813 0.229599i
\(29\) 42595.2 131094.i 0.324315 0.998140i −0.647434 0.762122i \(-0.724158\pi\)
0.971749 0.236018i \(-0.0758423\pi\)
\(30\) 0 0
\(31\) −1639.21 + 1190.96i −0.00988256 + 0.00718010i −0.592716 0.805412i \(-0.701944\pi\)
0.582833 + 0.812592i \(0.301944\pi\)
\(32\) −162525. −0.876792
\(33\) 0 0
\(34\) −245591. −1.07161
\(35\) 183336. 133201.i 0.722785 0.525134i
\(36\) 0 0
\(37\) −134323. + 413405.i −0.435959 + 1.34174i 0.456142 + 0.889907i \(0.349231\pi\)
−0.892101 + 0.451836i \(0.850769\pi\)
\(38\) −15409.0 + 21208.7i −0.0455547 + 0.0627006i
\(39\) 0 0
\(40\) −636567. 206833.i −1.57266 0.510987i
\(41\) −33032.5 101664.i −0.0748511 0.230368i 0.906630 0.421926i \(-0.138646\pi\)
−0.981481 + 0.191558i \(0.938646\pi\)
\(42\) 0 0
\(43\) 109382.i 0.209801i 0.994483 + 0.104901i \(0.0334524\pi\)
−0.994483 + 0.104901i \(0.966548\pi\)
\(44\) −100571. + 260578.i −0.177986 + 0.461162i
\(45\) 0 0
\(46\) −101690. 139964.i −0.154037 0.212014i
\(47\) 893228. 290227.i 1.25493 0.407752i 0.395246 0.918575i \(-0.370659\pi\)
0.859686 + 0.510824i \(0.170659\pi\)
\(48\) 0 0
\(49\) −446649. 324509.i −0.542350 0.394040i
\(50\) −722855. 525185.i −0.817817 0.594179i
\(51\) 0 0
\(52\) 193841. 62982.7i 0.191176 0.0621169i
\(53\) −989381. 1.36177e6i −0.912847 1.25643i −0.966185 0.257850i \(-0.916986\pi\)
0.0533380 0.998577i \(-0.483014\pi\)
\(54\) 0 0
\(55\) −1.21105e6 + 1.48997e6i −0.981501 + 1.20756i
\(56\) 801762.i 0.610081i
\(57\) 0 0
\(58\) −342692. 1.05470e6i −0.230625 0.709791i
\(59\) 2.04315e6 + 663860.i 1.29514 + 0.420818i 0.873890 0.486124i \(-0.161590\pi\)
0.421255 + 0.906942i \(0.361590\pi\)
\(60\) 0 0
\(61\) −286690. + 394595.i −0.161718 + 0.222586i −0.882184 0.470904i \(-0.843928\pi\)
0.720466 + 0.693490i \(0.243928\pi\)
\(62\) −5037.37 + 15503.4i −0.00268431 + 0.00826147i
\(63\) 0 0
\(64\) −1.50123e6 + 1.09071e6i −0.715844 + 0.520091i
\(65\) 1.40108e6 0.632801
\(66\) 0 0
\(67\) −3.77992e6 −1.53540 −0.767698 0.640811i \(-0.778598\pi\)
−0.767698 + 0.640811i \(0.778598\pi\)
\(68\) 1.56258e6 1.13528e6i 0.602643 0.437846i
\(69\) 0 0
\(70\) 563399. 1.73396e6i 0.196324 0.604223i
\(71\) −862546. + 1.18719e6i −0.286008 + 0.393656i −0.927712 0.373296i \(-0.878228\pi\)
0.641704 + 0.766952i \(0.278228\pi\)
\(72\) 0 0
\(73\) −1.90472e6 618882.i −0.573062 0.186199i 0.00812809 0.999967i \(-0.497413\pi\)
−0.581190 + 0.813768i \(0.697413\pi\)
\(74\) 1.08068e6 + 3.32598e6i 0.310016 + 0.954132i
\(75\) 0 0
\(76\) 206171.i 0.0538742i
\(77\) −2.14571e6 828140.i −0.535616 0.206722i
\(78\) 0 0
\(79\) 1.30874e6 + 1.80133e6i 0.298648 + 0.411054i 0.931799 0.362975i \(-0.118239\pi\)
−0.633151 + 0.774028i \(0.718239\pi\)
\(80\) −1.77118e6 + 575490.i −0.386765 + 0.125667i
\(81\) 0 0
\(82\) −695762. 505501.i −0.139352 0.101245i
\(83\) −5.87409e6 4.26777e6i −1.12763 0.819272i −0.142283 0.989826i \(-0.545444\pi\)
−0.985348 + 0.170554i \(0.945444\pi\)
\(84\) 0 0
\(85\) 1.26274e7 4.10290e6i 2.23023 0.724644i
\(86\) 517262. + 711950.i 0.0876932 + 0.120699i
\(87\) 0 0
\(88\) 1.74626e6 + 6.56487e6i 0.273162 + 1.02692i
\(89\) 7.30242e6i 1.09800i −0.835823 0.548999i \(-0.815009\pi\)
0.835823 0.548999i \(-0.184991\pi\)
\(90\) 0 0
\(91\) 518626. + 1.59617e6i 0.0721456 + 0.222041i
\(92\) 1.29401e6 + 420449.i 0.173253 + 0.0562932i
\(93\) 0 0
\(94\) 4.44139e6 6.11305e6i 0.551533 0.759120i
\(95\) 437962. 1.34791e6i 0.0524087 0.161297i
\(96\) 0 0
\(97\) 2.06576e6 1.50086e6i 0.229815 0.166971i −0.466919 0.884300i \(-0.654636\pi\)
0.696734 + 0.717330i \(0.254636\pi\)
\(98\) −4.44173e6 −0.476718
\(99\) 0 0
\(100\) 7.02692e6 0.702692
\(101\) −1.25581e7 + 9.12396e6i −1.21282 + 0.881168i −0.995484 0.0949284i \(-0.969738\pi\)
−0.217339 + 0.976096i \(0.569738\pi\)
\(102\) 0 0
\(103\) 5.26372e6 1.62001e7i 0.474638 1.46079i −0.371807 0.928310i \(-0.621262\pi\)
0.846445 0.532476i \(-0.178738\pi\)
\(104\) 2.91366e6 4.01031e6i 0.253993 0.349592i
\(105\) 0 0
\(106\) −1.28794e7 4.18477e6i −1.05033 0.341272i
\(107\) 6.45648e6 + 1.98710e7i 0.509510 + 1.56811i 0.793055 + 0.609150i \(0.208489\pi\)
−0.283545 + 0.958959i \(0.591511\pi\)
\(108\) 0 0
\(109\) 2.64245e7i 1.95440i 0.212315 + 0.977201i \(0.431900\pi\)
−0.212315 + 0.977201i \(0.568100\pi\)
\(110\) −836507. + 1.54249e7i −0.0599232 + 1.10496i
\(111\) 0 0
\(112\) −1.31124e6 1.80477e6i −0.0881899 0.121383i
\(113\) 1.41768e7 4.60633e6i 0.924282 0.300317i 0.192060 0.981383i \(-0.438483\pi\)
0.732222 + 0.681066i \(0.238483\pi\)
\(114\) 0 0
\(115\) 7.56683e6 + 5.49762e6i 0.463950 + 0.337080i
\(116\) 7.05588e6 + 5.12640e6i 0.419709 + 0.304937i
\(117\) 0 0
\(118\) 1.64378e7 5.34097e6i 0.920995 0.299249i
\(119\) 9.34836e6 + 1.28669e7i 0.508535 + 0.699939i
\(120\) 0 0
\(121\) 1.93729e7 + 2.10742e6i 0.994135 + 0.108144i
\(122\) 3.92408e6i 0.195650i
\(123\) 0 0
\(124\) −39616.5 121927.i −0.00186595 0.00574280i
\(125\) 1.36231e7 + 4.42642e6i 0.623866 + 0.202706i
\(126\) 0 0
\(127\) −1.96790e7 + 2.70858e7i −0.852491 + 1.17335i 0.130818 + 0.991406i \(0.458240\pi\)
−0.983308 + 0.181947i \(0.941760\pi\)
\(128\) 1.81520e6 5.58663e6i 0.0765052 0.235459i
\(129\) 0 0
\(130\) 9.11939e6 6.62563e6i 0.364053 0.264500i
\(131\) −1.47194e7 −0.572059 −0.286030 0.958221i \(-0.592336\pi\)
−0.286030 + 0.958221i \(0.592336\pi\)
\(132\) 0 0
\(133\) 1.69770e6 0.0625721
\(134\) −2.46028e7 + 1.78750e7i −0.883318 + 0.641768i
\(135\) 0 0
\(136\) 1.45160e7 4.46757e7i 0.494836 1.52295i
\(137\) 2.37397e7 3.26749e7i 0.788776 1.08566i −0.205484 0.978661i \(-0.565877\pi\)
0.994259 0.106996i \(-0.0341232\pi\)
\(138\) 0 0
\(139\) −1.46000e7 4.74384e6i −0.461107 0.149823i 0.0692458 0.997600i \(-0.477941\pi\)
−0.530353 + 0.847777i \(0.677941\pi\)
\(140\) 4.43086e6 + 1.36368e7i 0.136471 + 0.420014i
\(141\) 0 0
\(142\) 1.18061e7i 0.346018i
\(143\) −7.72304e6 1.19399e7i −0.220857 0.341448i
\(144\) 0 0
\(145\) 3.52401e7 + 4.85039e7i 0.959952 + 1.32126i
\(146\) −1.53241e7 + 4.97911e6i −0.407512 + 0.132409i
\(147\) 0 0
\(148\) −2.22506e7 1.61660e7i −0.564192 0.409909i
\(149\) −2.91657e7 2.11901e7i −0.722305 0.524785i 0.164815 0.986325i \(-0.447297\pi\)
−0.887120 + 0.461539i \(0.847297\pi\)
\(150\) 0 0
\(151\) −4.83160e7 + 1.56988e7i −1.14202 + 0.371063i −0.818130 0.575033i \(-0.804989\pi\)
−0.323885 + 0.946096i \(0.604989\pi\)
\(152\) −2.94733e6 4.05665e6i −0.0680731 0.0936946i
\(153\) 0 0
\(154\) −1.78822e7 + 4.75670e6i −0.394548 + 0.104950i
\(155\) 881289.i 0.0190089i
\(156\) 0 0
\(157\) 3.42934e6 + 1.05544e7i 0.0707231 + 0.217663i 0.980171 0.198155i \(-0.0634951\pi\)
−0.909448 + 0.415819i \(0.863495\pi\)
\(158\) 1.70367e7 + 5.53557e6i 0.343626 + 0.111651i
\(159\) 0 0
\(160\) 4.15510e7 5.71900e7i 0.801976 1.10382i
\(161\) −3.46216e6 + 1.06554e7i −0.0653817 + 0.201224i
\(162\) 0 0
\(163\) −4.63209e7 + 3.36541e7i −0.837761 + 0.608669i −0.921744 0.387798i \(-0.873236\pi\)
0.0839833 + 0.996467i \(0.473236\pi\)
\(164\) 6.76355e6 0.119735
\(165\) 0 0
\(166\) −5.84153e7 −0.991170
\(167\) 1.95458e7 1.42009e7i 0.324748 0.235943i −0.413451 0.910526i \(-0.635677\pi\)
0.738199 + 0.674583i \(0.235677\pi\)
\(168\) 0 0
\(169\) 1.61839e7 4.98088e7i 0.257916 0.793785i
\(170\) 6.27873e7 8.64193e7i 0.980168 1.34908i
\(171\) 0 0
\(172\) −6.58218e6 2.13868e6i −0.0986325 0.0320476i
\(173\) −6.71698e6 2.06727e7i −0.0986308 0.303554i 0.889552 0.456834i \(-0.151017\pi\)
−0.988183 + 0.153279i \(0.951017\pi\)
\(174\) 0 0
\(175\) 5.78626e7i 0.816141i
\(176\) 1.46673e7 + 1.19216e7i 0.202795 + 0.164831i
\(177\) 0 0
\(178\) −3.45326e7 4.75301e7i −0.458944 0.631682i
\(179\) −3.79480e7 + 1.23301e7i −0.494543 + 0.160687i −0.545661 0.838006i \(-0.683721\pi\)
0.0511184 + 0.998693i \(0.483721\pi\)
\(180\) 0 0
\(181\) −6.30689e7 4.58222e7i −0.790569 0.574382i 0.117563 0.993065i \(-0.462492\pi\)
−0.908132 + 0.418683i \(0.862492\pi\)
\(182\) 1.09238e7 + 7.93661e6i 0.134315 + 0.0975854i
\(183\) 0 0
\(184\) 3.14716e7 1.02257e7i 0.372440 0.121013i
\(185\) −1.11129e8 1.52956e8i −1.29041 1.77610i
\(186\) 0 0
\(187\) −1.04569e8 8.49938e7i −1.16939 0.950477i
\(188\) 5.94254e7i 0.652258i
\(189\) 0 0
\(190\) −3.52355e6 1.08444e7i −0.0372685 0.114701i
\(191\) −7.13053e7 2.31685e7i −0.740465 0.240592i −0.0855919 0.996330i \(-0.527278\pi\)
−0.654874 + 0.755738i \(0.727278\pi\)
\(192\) 0 0
\(193\) −6.70714e7 + 9.23158e7i −0.671563 + 0.924327i −0.999795 0.0202702i \(-0.993547\pi\)
0.328232 + 0.944597i \(0.393547\pi\)
\(194\) 6.34817e6 1.95377e7i 0.0624227 0.192117i
\(195\) 0 0
\(196\) 2.82606e7 2.05325e7i 0.268093 0.194781i
\(197\) −6.90285e7 −0.643275 −0.321637 0.946863i \(-0.604233\pi\)
−0.321637 + 0.946863i \(0.604233\pi\)
\(198\) 0 0
\(199\) 6.29377e7 0.566141 0.283071 0.959099i \(-0.408647\pi\)
0.283071 + 0.959099i \(0.408647\pi\)
\(200\) 1.38262e8 1.00453e8i 1.22208 0.887891i
\(201\) 0 0
\(202\) −3.85915e7 + 1.18772e8i −0.329429 + 1.01388i
\(203\) −4.22129e7 + 5.81011e7i −0.354168 + 0.487470i
\(204\) 0 0
\(205\) 4.42187e7 + 1.43675e7i 0.358482 + 0.116478i
\(206\) −4.23484e7 1.30335e8i −0.337522 1.03878i
\(207\) 0 0
\(208\) 1.37923e7i 0.106271i
\(209\) −1.39009e7 + 3.69765e6i −0.105325 + 0.0280165i
\(210\) 0 0
\(211\) −8.40807e6 1.15727e7i −0.0616180 0.0848099i 0.777096 0.629382i \(-0.216692\pi\)
−0.838714 + 0.544572i \(0.816692\pi\)
\(212\) 1.01290e8 3.29111e7i 0.730115 0.237229i
\(213\) 0 0
\(214\) 1.35992e8 + 9.88043e7i 0.948564 + 0.689172i
\(215\) −3.84898e7 2.79645e7i −0.264126 0.191899i
\(216\) 0 0
\(217\) 1.00400e6 326219.i 0.00666997 0.00216720i
\(218\) 1.24960e8 + 1.71992e8i 0.816905 + 1.12437i
\(219\) 0 0
\(220\) −6.59814e7 1.02008e8i −0.417775 0.645884i
\(221\) 9.83312e7i 0.612799i
\(222\) 0 0
\(223\) −4.59088e7 1.41293e8i −0.277223 0.853204i −0.988623 0.150416i \(-0.951939\pi\)
0.711400 0.702787i \(-0.248061\pi\)
\(224\) 8.05335e7 + 2.61669e7i 0.478750 + 0.155555i
\(225\) 0 0
\(226\) 7.04913e7 9.70229e7i 0.406215 0.559107i
\(227\) −8.54557e7 + 2.63006e8i −0.484898 + 1.49236i 0.347231 + 0.937780i \(0.387122\pi\)
−0.832129 + 0.554583i \(0.812878\pi\)
\(228\) 0 0
\(229\) −2.02689e8 + 1.47262e8i −1.11534 + 0.810340i −0.983496 0.180930i \(-0.942089\pi\)
−0.131842 + 0.991271i \(0.542089\pi\)
\(230\) 7.52489e7 0.407805
\(231\) 0 0
\(232\) 2.12117e8 1.11524
\(233\) 4.03091e7 2.92863e7i 0.208765 0.151676i −0.478490 0.878093i \(-0.658816\pi\)
0.687255 + 0.726417i \(0.258816\pi\)
\(234\) 0 0
\(235\) −1.26235e8 + 3.88511e8i −0.634515 + 1.95284i
\(236\) −7.98966e7 + 1.09968e8i −0.395673 + 0.544597i
\(237\) 0 0
\(238\) 1.21693e8 + 3.95406e7i 0.585124 + 0.190118i
\(239\) 9.37104e7 + 2.88411e8i 0.444012 + 1.36653i 0.883563 + 0.468312i \(0.155138\pi\)
−0.439551 + 0.898218i \(0.644862\pi\)
\(240\) 0 0
\(241\) 9.17688e7i 0.422314i 0.977452 + 0.211157i \(0.0677231\pi\)
−0.977452 + 0.211157i \(0.932277\pi\)
\(242\) 1.36060e8 7.78962e7i 0.617131 0.353315i
\(243\) 0 0
\(244\) −1.81396e7 2.49671e7i −0.0799400 0.110028i
\(245\) 2.28379e8 7.42047e7i 0.992143 0.322367i
\(246\) 0 0
\(247\) 8.49168e6 + 6.16957e6i 0.0358554 + 0.0260505i
\(248\) −2.52251e6 1.83271e6i −0.0105015 0.00762978i
\(249\) 0 0
\(250\) 1.09603e8 3.56120e7i 0.443640 0.144147i
\(251\) 487266. + 670664.i 0.00194495 + 0.00267699i 0.809988 0.586446i \(-0.199473\pi\)
−0.808043 + 0.589123i \(0.799473\pi\)
\(252\) 0 0
\(253\) 5.14044e6 9.47877e7i 0.0199562 0.367985i
\(254\) 2.69357e8i 1.03136i
\(255\) 0 0
\(256\) −8.80017e7 2.70841e8i −0.327832 1.00896i
\(257\) −4.77866e8 1.55268e8i −1.75606 0.570580i −0.759284 0.650760i \(-0.774450\pi\)
−0.996780 + 0.0801800i \(0.974450\pi\)
\(258\) 0 0
\(259\) 1.33118e8 1.83221e8i 0.476088 0.655279i
\(260\) −2.73944e7 + 8.43114e7i −0.0966620 + 0.297495i
\(261\) 0 0
\(262\) −9.58059e7 + 6.96071e7i −0.329108 + 0.239111i
\(263\) −1.61207e8 −0.546437 −0.273218 0.961952i \(-0.588088\pi\)
−0.273218 + 0.961952i \(0.588088\pi\)
\(264\) 0 0
\(265\) 7.32126e8 2.41671
\(266\) 1.10500e7 8.02831e6i 0.0359979 0.0261540i
\(267\) 0 0
\(268\) 7.39061e7 2.27460e8i 0.234536 0.721826i
\(269\) 6.47544e7 8.91267e7i 0.202832 0.279174i −0.695468 0.718557i \(-0.744803\pi\)
0.898300 + 0.439383i \(0.144803\pi\)
\(270\) 0 0
\(271\) 5.20551e8 + 1.69137e8i 1.58881 + 0.516234i 0.964306 0.264791i \(-0.0853028\pi\)
0.624500 + 0.781025i \(0.285303\pi\)
\(272\) −4.03891e7 1.24305e8i −0.121695 0.374539i
\(273\) 0 0
\(274\) 3.24938e8i 0.954276i
\(275\) −1.26027e8 4.73782e8i −0.365425 1.37377i
\(276\) 0 0
\(277\) −8.76823e7 1.20684e8i −0.247875 0.341171i 0.666891 0.745156i \(-0.267625\pi\)
−0.914766 + 0.403985i \(0.867625\pi\)
\(278\) −1.17462e8 + 3.81658e7i −0.327900 + 0.106541i
\(279\) 0 0
\(280\) 2.82127e8 + 2.04977e8i 0.768053 + 0.558023i
\(281\) 1.49611e8 + 1.08699e8i 0.402246 + 0.292249i 0.770455 0.637494i \(-0.220029\pi\)
−0.368209 + 0.929743i \(0.620029\pi\)
\(282\) 0 0
\(283\) 2.39964e8 7.79689e7i 0.629351 0.204489i 0.0230635 0.999734i \(-0.492658\pi\)
0.606288 + 0.795245i \(0.292658\pi\)
\(284\) −5.45755e7 7.51168e7i −0.141379 0.194591i
\(285\) 0 0
\(286\) −1.06731e8 4.11929e7i −0.269779 0.104122i
\(287\) 5.56939e7i 0.139066i
\(288\) 0 0
\(289\) 1.61149e8 + 4.95966e8i 0.392722 + 1.20868i
\(290\) 4.58743e8 + 1.49055e8i 1.10453 + 0.358882i
\(291\) 0 0
\(292\) 7.44834e7 1.02518e8i 0.175073 0.240968i
\(293\) −1.95002e8 + 6.00155e8i −0.452900 + 1.39388i 0.420682 + 0.907208i \(0.361791\pi\)
−0.873583 + 0.486676i \(0.838209\pi\)
\(294\) 0 0
\(295\) −7.55949e8 + 5.49229e8i −1.71441 + 1.24559i
\(296\) −6.68907e8 −1.49915
\(297\) 0 0
\(298\) −2.90041e8 −0.634895
\(299\) −5.60398e7 + 4.07153e7i −0.121240 + 0.0880863i
\(300\) 0 0
\(301\) 1.76108e7 5.42004e7i 0.0372217 0.114557i
\(302\) −2.40241e8 + 3.30664e8i −0.501907 + 0.690816i
\(303\) 0 0
\(304\) −1.32689e7 4.31131e6i −0.0270879 0.00880140i
\(305\) −6.55568e7 2.01763e8i −0.132303 0.407185i
\(306\) 0 0
\(307\) 9.84115e7i 0.194116i 0.995279 + 0.0970580i \(0.0309432\pi\)
−0.995279 + 0.0970580i \(0.969057\pi\)
\(308\) 9.17876e7 1.12928e8i 0.179001 0.220229i
\(309\) 0 0
\(310\) −4.16755e6 5.73615e6i −0.00794539 0.0109359i
\(311\) 6.96049e8 2.26160e8i 1.31213 0.426338i 0.432348 0.901707i \(-0.357685\pi\)
0.879787 + 0.475369i \(0.157685\pi\)
\(312\) 0 0
\(313\) −7.66271e8 5.56729e8i −1.41246 1.02622i −0.992959 0.118462i \(-0.962203\pi\)
−0.419506 0.907753i \(-0.637797\pi\)
\(314\) 7.22320e7 + 5.24796e7i 0.131667 + 0.0956614i
\(315\) 0 0
\(316\) −1.33985e8 + 4.35345e7i −0.238865 + 0.0776120i
\(317\) 2.94325e8 + 4.05104e8i 0.518943 + 0.714264i 0.985395 0.170282i \(-0.0544679\pi\)
−0.466452 + 0.884547i \(0.654468\pi\)
\(318\) 0 0
\(319\) 2.19095e8 5.67676e8i 0.377890 0.979113i
\(320\) 8.07108e8i 1.37691i
\(321\) 0 0
\(322\) 2.78542e7 + 8.57264e7i 0.0464938 + 0.143093i
\(323\) 9.45991e7 + 3.07371e7i 0.156199 + 0.0507521i
\(324\) 0 0
\(325\) −2.10277e8 + 2.89421e8i −0.339781 + 0.467669i
\(326\) −1.42346e8 + 4.38096e8i −0.227554 + 0.700338i
\(327\) 0 0
\(328\) 1.33080e8 9.66884e7i 0.208236 0.151292i
\(329\) −4.89333e8 −0.757564
\(330\) 0 0
\(331\) −1.32695e8 −0.201120 −0.100560 0.994931i \(-0.532063\pi\)
−0.100560 + 0.994931i \(0.532063\pi\)
\(332\) 3.71669e8 2.70033e8i 0.557407 0.404980i
\(333\) 0 0
\(334\) 6.00651e7 1.84861e8i 0.0882083 0.271477i
\(335\) 9.66367e8 1.33009e9i 1.40438 1.93297i
\(336\) 0 0
\(337\) −1.03298e9 3.35635e8i −1.47024 0.477709i −0.539057 0.842269i \(-0.681219\pi\)
−0.931180 + 0.364561i \(0.881219\pi\)
\(338\) −1.30205e8 4.00729e8i −0.183408 0.564472i
\(339\) 0 0
\(340\) 8.40088e8i 1.15917i
\(341\) −7.51026e6 + 4.85783e6i −0.0102569 + 0.00663441i
\(342\) 0 0
\(343\) 4.21279e8 + 5.79840e8i 0.563690 + 0.775852i
\(344\) −1.60085e8 + 5.20148e7i −0.212029 + 0.0688925i
\(345\) 0 0
\(346\) −1.41479e8 1.02791e8i −0.183623 0.133410i
\(347\) −1.00403e9 7.29468e8i −1.29001 0.937245i −0.290201 0.956966i \(-0.593722\pi\)
−0.999806 + 0.0197206i \(0.993722\pi\)
\(348\) 0 0
\(349\) 5.77319e8 1.87582e8i 0.726987 0.236212i 0.0779371 0.996958i \(-0.475167\pi\)
0.649050 + 0.760746i \(0.275167\pi\)
\(350\) 2.73628e8 + 3.76617e8i 0.341132 + 0.469528i
\(351\) 0 0
\(352\) −7.16404e8 3.88513e7i −0.875505 0.0474796i
\(353\) 1.17353e9i 1.41998i 0.704212 + 0.709989i \(0.251300\pi\)
−0.704212 + 0.709989i \(0.748700\pi\)
\(354\) 0 0
\(355\) −1.97236e8 6.07031e8i −0.233985 0.720131i
\(356\) 4.39429e8 + 1.42779e8i 0.516195 + 0.167722i
\(357\) 0 0
\(358\) −1.88689e8 + 2.59708e8i −0.217348 + 0.299154i
\(359\) 4.18584e8 1.28827e9i 0.477477 1.46952i −0.365111 0.930964i \(-0.618969\pi\)
0.842588 0.538559i \(-0.181031\pi\)
\(360\) 0 0
\(361\) −7.14568e8 + 5.19164e8i −0.799407 + 0.580803i
\(362\) −6.27193e8 −0.694899
\(363\) 0 0
\(364\) −1.06191e8 −0.115407
\(365\) 7.04732e8 5.12018e8i 0.758575 0.551137i
\(366\) 0 0
\(367\) 1.82865e8 5.62802e8i 0.193108 0.594325i −0.806885 0.590708i \(-0.798849\pi\)
0.999993 0.00361747i \(-0.00115148\pi\)
\(368\) 5.41188e7 7.44882e7i 0.0566084 0.0779148i
\(369\) 0 0
\(370\) −1.44664e9 4.70042e8i −1.48475 0.482426i
\(371\) 2.71004e8 + 8.34065e8i 0.275529 + 0.847991i
\(372\) 0 0
\(373\) 6.19141e8i 0.617744i 0.951104 + 0.308872i \(0.0999515\pi\)
−0.951104 + 0.308872i \(0.900048\pi\)
\(374\) −1.08255e9 5.87079e7i −1.07004 0.0580291i
\(375\) 0 0
\(376\) 8.49516e8 + 1.16926e9i 0.824165 + 1.13437i
\(377\) −4.22287e8 + 1.37209e8i −0.405894 + 0.131883i
\(378\) 0 0
\(379\) −1.12795e9 8.19503e8i −1.06427 0.773238i −0.0893971 0.995996i \(-0.528494\pi\)
−0.974874 + 0.222758i \(0.928494\pi\)
\(380\) 7.25483e7 + 5.27094e7i 0.0678242 + 0.0492771i
\(381\) 0 0
\(382\) −5.73675e8 + 1.86398e8i −0.526555 + 0.171088i
\(383\) 1.37392e8 + 1.89104e8i 0.124959 + 0.171991i 0.866913 0.498460i \(-0.166101\pi\)
−0.741954 + 0.670451i \(0.766101\pi\)
\(384\) 0 0
\(385\) 8.39977e8 5.43319e8i 0.750161 0.485224i
\(386\) 9.18042e8i 0.812469i
\(387\) 0 0
\(388\) 4.99253e7 + 1.53654e8i 0.0433920 + 0.133547i
\(389\) 1.44499e9 + 4.69506e8i 1.24463 + 0.404406i 0.855995 0.516984i \(-0.172945\pi\)
0.388639 + 0.921390i \(0.372945\pi\)
\(390\) 0 0
\(391\) −3.85835e8 + 5.31057e8i −0.326425 + 0.449286i
\(392\) 2.62535e8 8.08000e8i 0.220134 0.677502i
\(393\) 0 0
\(394\) −4.49293e8 + 3.26431e8i −0.370078 + 0.268877i
\(395\) −9.68448e8 −0.790654
\(396\) 0 0
\(397\) −3.19951e8 −0.256635 −0.128318 0.991733i \(-0.540958\pi\)
−0.128318 + 0.991733i \(0.540958\pi\)
\(398\) 4.09649e8 2.97628e8i 0.325703 0.236637i
\(399\) 0 0
\(400\) 1.46942e8 4.52241e8i 0.114798 0.353313i
\(401\) 5.65594e8 7.78473e8i 0.438026 0.602890i −0.531746 0.846904i \(-0.678464\pi\)
0.969772 + 0.244013i \(0.0784640\pi\)
\(402\) 0 0
\(403\) 6.20736e6 + 2.01690e6i 0.00472432 + 0.00153503i
\(404\) −3.03503e8 9.34086e8i −0.228996 0.704778i
\(405\) 0 0
\(406\) 5.77791e8i 0.428479i
\(407\) −6.90914e8 + 1.79016e9i −0.507977 + 1.31617i
\(408\) 0 0
\(409\) 8.14543e8 + 1.12112e9i 0.588684 + 0.810254i 0.994614 0.103650i \(-0.0330522\pi\)
−0.405930 + 0.913904i \(0.633052\pi\)
\(410\) 3.55754e8 1.15592e8i 0.254922 0.0828291i
\(411\) 0 0
\(412\) 8.71934e8 + 6.33497e8i 0.614248 + 0.446277i
\(413\) −9.05525e8 6.57902e8i −0.632522 0.459554i
\(414\) 0 0
\(415\) 3.00352e9 9.75901e8i 2.06282 0.670251i
\(416\) 3.07725e8 + 4.23548e8i 0.209574 + 0.288453i
\(417\) 0 0
\(418\) −7.29922e7 + 8.98035e7i −0.0488832 + 0.0601418i
\(419\) 2.19843e9i 1.46003i −0.683429 0.730017i \(-0.739512\pi\)
0.683429 0.730017i \(-0.260488\pi\)
\(420\) 0 0
\(421\) 4746.78 + 14609.1i 3.10036e−6 + 9.54191e-6i 0.951058 0.309012i \(-0.0999984\pi\)
−0.951055 + 0.309022i \(0.899998\pi\)
\(422\) −1.09453e8 3.55635e7i −0.0708981 0.0230362i
\(423\) 0 0
\(424\) 1.52251e9 2.09556e9i 0.970018 1.33512i
\(425\) −1.04761e9 + 3.22421e9i −0.661970 + 2.03733i
\(426\) 0 0
\(427\) 2.05589e8 1.49369e8i 0.127792 0.0928462i
\(428\) −1.32199e9 −0.815034
\(429\) 0 0
\(430\) −3.82765e8 −0.232163
\(431\) 3.07914e8 2.23712e8i 0.185250 0.134592i −0.491295 0.870993i \(-0.663476\pi\)
0.676545 + 0.736401i \(0.263476\pi\)
\(432\) 0 0
\(433\) 8.55895e8 2.63417e9i 0.506655 1.55932i −0.291315 0.956627i \(-0.594093\pi\)
0.797970 0.602697i \(-0.205907\pi\)
\(434\) 4.99217e6 6.87113e6i 0.00293140 0.00403473i
\(435\) 0 0
\(436\) −1.59012e9 5.16660e8i −0.918811 0.298540i
\(437\) 2.16526e7 + 6.66399e7i 0.0124115 + 0.0381988i
\(438\) 0 0
\(439\) 3.18916e9i 1.79908i −0.436838 0.899540i \(-0.643902\pi\)
0.436838 0.899540i \(-0.356098\pi\)
\(440\) −2.75651e9 1.06388e9i −1.54268 0.595399i
\(441\) 0 0
\(442\) 4.65001e8 + 6.40019e8i 0.256139 + 0.352545i
\(443\) 1.84748e9 6.00284e8i 1.00964 0.328053i 0.242931 0.970044i \(-0.421891\pi\)
0.766712 + 0.641991i \(0.221891\pi\)
\(444\) 0 0
\(445\) 2.56960e9 + 1.86692e9i 1.38231 + 1.00431i
\(446\) −9.66975e8 7.02548e8i −0.516111 0.374977i
\(447\) 0 0
\(448\) 9.19488e8 2.98760e8i 0.483140 0.156982i
\(449\) 1.36366e9 + 1.87692e9i 0.710959 + 0.978551i 0.999776 + 0.0211663i \(0.00673795\pi\)
−0.288817 + 0.957384i \(0.593262\pi\)
\(450\) 0 0
\(451\) −1.21303e8 4.56024e8i −0.0622665 0.234083i
\(452\) 9.43167e8i 0.480401i
\(453\) 0 0
\(454\) 6.87519e8 + 2.11597e9i 0.344818 + 1.06124i
\(455\) −6.94256e8 2.25577e8i −0.345525 0.112268i
\(456\) 0 0
\(457\) −2.34981e8 + 3.23423e8i −0.115166 + 0.158513i −0.862709 0.505701i \(-0.831234\pi\)
0.747542 + 0.664214i \(0.231234\pi\)
\(458\) −6.22873e8 + 1.91701e9i −0.302949 + 0.932383i
\(459\) 0 0
\(460\) −4.78773e8 + 3.47849e8i −0.229339 + 0.166624i
\(461\) 1.03369e9 0.491402 0.245701 0.969346i \(-0.420982\pi\)
0.245701 + 0.969346i \(0.420982\pi\)
\(462\) 0 0
\(463\) −1.37166e9 −0.642263 −0.321131 0.947035i \(-0.604063\pi\)
−0.321131 + 0.947035i \(0.604063\pi\)
\(464\) 4.77474e8 3.46905e8i 0.221890 0.161212i
\(465\) 0 0
\(466\) 1.23872e8 3.81238e8i 0.0567050 0.174520i
\(467\) 2.24293e9 3.08712e9i 1.01907 1.40264i 0.106223 0.994342i \(-0.466124\pi\)
0.912851 0.408293i \(-0.133876\pi\)
\(468\) 0 0
\(469\) 1.87300e9 + 6.08574e8i 0.838364 + 0.272401i
\(470\) 1.01560e9 + 3.12570e9i 0.451212 + 1.38869i
\(471\) 0 0
\(472\) 3.30591e9i 1.44708i
\(473\) −2.61476e7 + 4.82152e8i −0.0113610 + 0.209493i
\(474\) 0 0
\(475\) 2.12706e8 + 2.92765e8i 0.0910653 + 0.125341i
\(476\) −9.57059e8 + 3.10967e8i −0.406738 + 0.132157i
\(477\) 0 0
\(478\) 1.97382e9 + 1.43406e9i 0.826626 + 0.600579i
\(479\) 1.96561e9 + 1.42810e9i 0.817188 + 0.593722i 0.915906 0.401393i \(-0.131474\pi\)
−0.0987173 + 0.995116i \(0.531474\pi\)
\(480\) 0 0
\(481\) 1.33168e9 4.32688e8i 0.545621 0.177283i
\(482\) 4.33968e8 + 5.97306e8i 0.176520 + 0.242958i
\(483\) 0 0
\(484\) −5.05600e8 + 1.12457e9i −0.202698 + 0.450847i
\(485\) 1.11061e9i 0.442045i
\(486\) 0 0
\(487\) −3.48895e8 1.07379e9i −0.136881 0.421276i 0.858997 0.511981i \(-0.171088\pi\)
−0.995878 + 0.0907045i \(0.971088\pi\)
\(488\) −7.13834e8 2.31939e8i −0.278053 0.0903450i
\(489\) 0 0
\(490\) 1.13556e9 1.56297e9i 0.436039 0.600157i
\(491\) −1.30879e9 + 4.02804e9i −0.498981 + 1.53571i 0.311678 + 0.950188i \(0.399109\pi\)
−0.810659 + 0.585518i \(0.800891\pi\)
\(492\) 0 0
\(493\) −3.40411e9 + 2.47323e9i −1.27950 + 0.929609i
\(494\) 8.44462e7 0.0315163
\(495\) 0 0
\(496\) −8.67545e6 −0.00319232
\(497\) 6.18543e8 4.49398e8i 0.226007 0.164204i
\(498\) 0 0
\(499\) −1.51352e9 + 4.65814e9i −0.545301 + 1.67826i 0.174972 + 0.984573i \(0.444017\pi\)
−0.720273 + 0.693691i \(0.755983\pi\)
\(500\) −5.32727e8 + 7.33236e8i −0.190594 + 0.262330i
\(501\) 0 0
\(502\) 6.34304e6 + 2.06098e6i 0.00223787 + 0.000727127i
\(503\) 5.89693e7 + 1.81489e8i 0.0206604 + 0.0635860i 0.960855 0.277051i \(-0.0893572\pi\)
−0.940195 + 0.340637i \(0.889357\pi\)
\(504\) 0 0
\(505\) 6.75158e9i 2.33284i
\(506\) −4.14786e8 6.41264e8i −0.142330 0.220044i
\(507\) 0 0
\(508\) −1.24514e9 1.71379e9i −0.421401 0.580009i
\(509\) 2.20279e9 7.15730e8i 0.740390 0.240567i 0.0855491 0.996334i \(-0.472736\pi\)
0.654841 + 0.755767i \(0.272736\pi\)
\(510\) 0 0
\(511\) 8.44174e8 + 6.13328e8i 0.279871 + 0.203339i
\(512\) −1.24529e9 9.04753e8i −0.410038 0.297910i
\(513\) 0 0
\(514\) −3.84459e9 + 1.24918e9i −1.24876 + 0.405747i
\(515\) 4.35482e9 + 5.99389e9i 1.40490 + 1.93368i
\(516\) 0 0
\(517\) 4.00668e9 1.06578e9i 1.27517 0.339197i
\(518\) 1.82206e9i 0.575981i
\(519\) 0 0
\(520\) 6.66259e8 + 2.05054e9i 0.207793 + 0.639522i
\(521\) −4.71705e9 1.53266e9i −1.46130 0.474805i −0.532832 0.846221i \(-0.678872\pi\)
−0.928466 + 0.371417i \(0.878872\pi\)
\(522\) 0 0
\(523\) 1.22878e9 1.69127e9i 0.375594 0.516960i −0.578817 0.815458i \(-0.696485\pi\)
0.954410 + 0.298497i \(0.0964854\pi\)
\(524\) 2.87799e8 8.85753e8i 0.0873835 0.268939i
\(525\) 0 0
\(526\) −1.04927e9 + 7.62338e8i −0.314367 + 0.228401i
\(527\) 6.18508e7 0.0184081
\(528\) 0 0
\(529\) 2.94241e9 0.864189
\(530\) 4.76527e9 3.46217e9i 1.39034 1.01014i
\(531\) 0 0
\(532\) −3.31940e7 + 1.02161e8i −0.00955804 + 0.0294166i
\(533\) −2.02396e8 + 2.78574e8i −0.0578970 + 0.0796883i
\(534\) 0 0
\(535\) −8.64292e9 2.80825e9i −2.44018 0.792863i
\(536\) −1.79747e9 5.53204e9i −0.504179 1.55170i
\(537\) 0 0
\(538\) 8.86328e8i 0.245390i
\(539\) −1.89123e9 1.53719e9i −0.520216 0.422831i
\(540\) 0 0
\(541\) −1.73698e8 2.39075e8i −0.0471633 0.0649148i 0.784784 0.619769i \(-0.212774\pi\)
−0.831947 + 0.554855i \(0.812774\pi\)
\(542\) 4.18801e9 1.36077e9i 1.12982 0.367101i
\(543\) 0 0
\(544\) 4.01372e9 + 2.91614e9i 1.06893 + 0.776626i
\(545\) −9.29834e9 6.75564e9i −2.46047 1.78763i
\(546\) 0 0
\(547\) −3.34395e9 + 1.08651e9i −0.873582 + 0.283844i −0.711290 0.702899i \(-0.751889\pi\)
−0.162292 + 0.986743i \(0.551889\pi\)
\(548\) 1.50207e9 + 2.06743e9i 0.389905 + 0.536659i
\(549\) 0 0
\(550\) −3.06076e9 2.48778e9i −0.784441 0.637593i
\(551\) 4.49149e8i 0.114383i
\(552\) 0 0
\(553\) −3.58482e8 1.10329e9i −0.0901423 0.277430i
\(554\) −1.14142e9 3.70868e8i −0.285207 0.0926692i
\(555\) 0 0
\(556\) 5.70929e8 7.85816e8i 0.140871 0.193892i
\(557\) −6.37197e8 + 1.96109e9i −0.156236 + 0.480845i −0.998284 0.0585578i \(-0.981350\pi\)
0.842048 + 0.539402i \(0.181350\pi\)
\(558\) 0 0
\(559\) 2.85055e8 2.07105e8i 0.0690219 0.0501474i
\(560\) 9.70296e8 0.233478
\(561\) 0 0
\(562\) 1.48782e9 0.353568
\(563\) 4.18404e8 3.03988e8i 0.0988136 0.0717923i −0.537281 0.843403i \(-0.680549\pi\)
0.636095 + 0.771611i \(0.280549\pi\)
\(564\) 0 0
\(565\) −2.00353e9 + 6.16623e9i −0.467333 + 1.43830i
\(566\) 1.19317e9 1.64226e9i 0.276595 0.380700i
\(567\) 0 0
\(568\) −2.14767e9 6.97819e8i −0.491754 0.159780i
\(569\) −2.36726e9 7.28569e9i −0.538709 1.65797i −0.735496 0.677529i \(-0.763051\pi\)
0.196788 0.980446i \(-0.436949\pi\)
\(570\) 0 0
\(571\) 7.09604e9i 1.59511i −0.603249 0.797553i \(-0.706127\pi\)
0.603249 0.797553i \(-0.293873\pi\)
\(572\) 8.69497e8 2.31288e8i 0.194259 0.0516733i
\(573\) 0 0
\(574\) 2.63373e8 + 3.62501e8i 0.0581272 + 0.0800052i
\(575\) −2.27128e9 + 7.37984e8i −0.498234 + 0.161886i
\(576\) 0 0
\(577\) 9.91453e8 + 7.20333e8i 0.214861 + 0.156105i 0.690010 0.723800i \(-0.257606\pi\)
−0.475150 + 0.879905i \(0.657606\pi\)
\(578\) 3.39428e9 + 2.46609e9i 0.731139 + 0.531204i
\(579\) 0 0
\(580\) −3.60779e9 + 1.17224e9i −0.767791 + 0.249470i
\(581\) 2.22357e9 + 3.06048e9i 0.470364 + 0.647400i
\(582\) 0 0
\(583\) −4.03562e9 6.23911e9i −0.843470 1.30401i
\(584\) 3.08193e9i 0.640291i
\(585\) 0 0
\(586\) 1.56886e9 + 4.82845e9i 0.322064 + 0.991210i
\(587\) −1.65761e9 5.38590e8i −0.338258 0.109907i 0.134962 0.990851i \(-0.456909\pi\)
−0.473221 + 0.880944i \(0.656909\pi\)
\(588\) 0 0
\(589\) 3.88069e6 5.34131e6i 0.000782538 0.00107707i
\(590\) −2.32306e9 + 7.14966e9i −0.465671 + 1.43319i
\(591\) 0 0
\(592\) −1.50571e9 + 1.09396e9i −0.298274 + 0.216709i
\(593\) 2.02896e9 0.399560 0.199780 0.979841i \(-0.435977\pi\)
0.199780 + 0.979841i \(0.435977\pi\)
\(594\) 0 0
\(595\) −6.91764e9 −1.34632
\(596\) 1.84539e9 1.34076e9i 0.357048 0.259410i
\(597\) 0 0
\(598\) −1.72213e8 + 5.30016e8i −0.0329315 + 0.101353i
\(599\) 2.64600e9 3.64190e9i 0.503032 0.692364i −0.479693 0.877436i \(-0.659252\pi\)
0.982725 + 0.185073i \(0.0592520\pi\)
\(600\) 0 0
\(601\) 1.47101e9 + 4.77961e8i 0.276411 + 0.0898114i 0.443942 0.896055i \(-0.353580\pi\)
−0.167531 + 0.985867i \(0.553580\pi\)
\(602\) −1.41685e8 4.36061e8i −0.0264689 0.0814628i
\(603\) 0 0
\(604\) 3.21441e9i 0.593570i
\(605\) −5.69440e9 + 6.27821e9i −1.04545 + 1.15264i
\(606\) 0 0
\(607\) 2.86458e9 + 3.94275e9i 0.519876 + 0.715548i 0.985546 0.169411i \(-0.0541864\pi\)
−0.465669 + 0.884959i \(0.654186\pi\)
\(608\) 5.03664e8 1.63650e8i 0.0908820 0.0295294i
\(609\) 0 0
\(610\) −1.38082e9 1.00322e9i −0.246310 0.178955i
\(611\) −2.44758e9 1.77827e9i −0.434103 0.315394i
\(612\) 0 0
\(613\) −3.71776e9 + 1.20797e9i −0.651883 + 0.211810i −0.616244 0.787555i \(-0.711347\pi\)
−0.0356387 + 0.999365i \(0.511347\pi\)
\(614\) 4.65381e8 + 6.40542e8i 0.0811370 + 0.111676i
\(615\) 0 0
\(616\) 1.91659e8 3.53413e9i 0.0330368 0.609186i
\(617\) 1.35400e9i 0.232071i −0.993245 0.116036i \(-0.962981\pi\)
0.993245 0.116036i \(-0.0370187\pi\)
\(618\) 0 0
\(619\) 1.98636e9 + 6.11339e9i 0.336621 + 1.03601i 0.965918 + 0.258848i \(0.0833429\pi\)
−0.629297 + 0.777165i \(0.716657\pi\)
\(620\) 5.30323e7 + 1.72312e7i 0.00893655 + 0.00290366i
\(621\) 0 0
\(622\) 3.46096e9 4.76360e9i 0.576673 0.793723i
\(623\) −1.17570e9 + 3.61844e9i −0.194800 + 0.599534i
\(624\) 0 0
\(625\) 1.97891e9 1.43776e9i 0.324224 0.235563i
\(626\) −7.62025e9 −1.24153
\(627\) 0 0
\(628\) −7.02172e8 −0.113132
\(629\) 1.07348e10 7.79930e9i 1.71996 1.24962i
\(630\) 0 0
\(631\) −2.07581e9 + 6.38870e9i −0.328916 + 1.01230i 0.640725 + 0.767770i \(0.278634\pi\)
−0.969642 + 0.244530i \(0.921366\pi\)
\(632\) −2.01396e9 + 2.77198e9i −0.317352 + 0.436798i
\(633\) 0 0
\(634\) 3.83141e9 + 1.24490e9i 0.597099 + 0.194009i
\(635\) −4.49995e9 1.38494e10i −0.697428 2.14646i
\(636\) 0 0
\(637\) 1.77841e9i 0.272611i
\(638\) −1.25845e9 4.73098e9i −0.191850 0.721238i
\(639\) 0 0
\(640\) 1.50177e9 + 2.06701e9i 0.226450 + 0.311682i
\(641\) −2.72345e9 + 8.84902e8i −0.408429 + 0.132707i −0.506023 0.862520i \(-0.668885\pi\)
0.0975948 + 0.995226i \(0.468885\pi\)
\(642\) 0 0
\(643\) −3.30844e9 2.40372e9i −0.490777 0.356570i 0.314706 0.949189i \(-0.398094\pi\)
−0.805483 + 0.592619i \(0.798094\pi\)
\(644\) −5.73506e8 4.16676e8i −0.0846130 0.0614750i
\(645\) 0 0
\(646\) 7.61081e8 2.47290e8i 0.111075 0.0360905i
\(647\) 3.17664e9 + 4.37228e9i 0.461109 + 0.634662i 0.974738 0.223350i \(-0.0716993\pi\)
−0.513629 + 0.858012i \(0.671699\pi\)
\(648\) 0 0
\(649\) 8.84741e9 + 3.41467e9i 1.27046 + 0.490335i
\(650\) 2.87817e9i 0.411074i
\(651\) 0 0
\(652\) −1.11948e9 3.44541e9i −0.158180 0.486827i
\(653\) 8.27669e9 + 2.68926e9i 1.16322 + 0.377952i 0.826107 0.563513i \(-0.190551\pi\)
0.337110 + 0.941465i \(0.390551\pi\)
\(654\) 0 0
\(655\) 3.76314e9 5.17952e9i 0.523246 0.720186i
\(656\) 1.41435e8 4.35291e8i 0.0195611 0.0602028i
\(657\) 0 0
\(658\) −3.18498e9 + 2.31402e9i −0.435829 + 0.316648i
\(659\) 3.78669e9 0.515420 0.257710 0.966222i \(-0.417032\pi\)
0.257710 + 0.966222i \(0.417032\pi\)
\(660\) 0 0
\(661\) 1.65486e9 0.222872 0.111436 0.993772i \(-0.464455\pi\)
0.111436 + 0.993772i \(0.464455\pi\)
\(662\) −8.63685e8 + 6.27504e8i −0.115705 + 0.0840647i
\(663\) 0 0
\(664\) 3.45272e9 1.06264e10i 0.457692 1.40863i
\(665\) −4.34031e8 + 5.97393e8i −0.0572329 + 0.0787743i
\(666\) 0 0
\(667\) −2.81903e9 9.15958e8i −0.367840 0.119519i
\(668\) 4.72383e8 + 1.45384e9i 0.0613164 + 0.188712i
\(669\) 0 0
\(670\) 1.32272e10i 1.69905i
\(671\) −1.35804e9 + 1.67082e9i −0.173534 + 0.213502i
\(672\) 0 0
\(673\) 5.07620e9 + 6.98679e9i 0.641927 + 0.883537i 0.998717 0.0506476i \(-0.0161285\pi\)
−0.356789 + 0.934185i \(0.616129\pi\)
\(674\) −8.31067e9 + 2.70030e9i −1.04551 + 0.339705i
\(675\) 0 0
\(676\) 2.68086e9 + 1.94776e9i 0.333780 + 0.242505i
\(677\) 4.17812e9 + 3.03558e9i 0.517512 + 0.375994i 0.815666 0.578523i \(-0.196371\pi\)
−0.298154 + 0.954518i \(0.596371\pi\)
\(678\) 0 0
\(679\) −1.26525e9 + 4.11106e8i −0.155108 + 0.0503975i
\(680\) 1.20095e10 + 1.65296e10i 1.46468 + 2.01596i
\(681\) 0 0
\(682\) −2.59105e7 + 6.71342e7i −0.00312774 + 0.00810398i
\(683\) 9.84573e9i 1.18243i 0.806514 + 0.591215i \(0.201352\pi\)
−0.806514 + 0.591215i \(0.798648\pi\)
\(684\) 0 0
\(685\) 5.42850e9 + 1.67072e10i 0.645302 + 1.98604i
\(686\) 5.48405e9 + 1.78187e9i 0.648585 + 0.210738i
\(687\) 0 0
\(688\) −2.75284e8 + 3.78896e8i −0.0322271 + 0.0443568i
\(689\) −1.67552e9 + 5.15673e9i −0.195157 + 0.600630i
\(690\) 0 0
\(691\) −2.26217e9 + 1.64356e9i −0.260827 + 0.189502i −0.710511 0.703686i \(-0.751536\pi\)
0.449685 + 0.893187i \(0.351536\pi\)
\(692\) 1.37533e9 0.157774
\(693\) 0 0
\(694\) −9.98462e9 −1.13390
\(695\) 5.40189e9 3.92471e9i 0.610379 0.443466i
\(696\) 0 0
\(697\) −1.00835e9 + 3.10337e9i −0.112796 + 0.347151i
\(698\) 2.87060e9 3.95104e9i 0.319505 0.439761i
\(699\) 0 0
\(700\) −3.48193e9 1.13135e9i −0.383687 0.124667i
\(701\) 5.38717e9 + 1.65800e10i 0.590674 + 1.81791i 0.575179 + 0.818028i \(0.304933\pi\)
0.0154954 + 0.999880i \(0.495067\pi\)
\(702\) 0 0
\(703\) 1.41639e9i 0.153758i
\(704\) −6.87810e9 + 4.44893e9i −0.742957 + 0.480564i
\(705\) 0 0
\(706\) 5.54953e9 + 7.63827e9i 0.593526 + 0.816918i
\(707\) 7.69166e9 2.49917e9i 0.818563 0.265967i
\(708\) 0 0
\(709\) 1.24352e10 + 9.03467e9i 1.31036 + 0.952029i 0.999999 + 0.00140939i \(0.000448622\pi\)
0.310357 + 0.950620i \(0.399551\pi\)
\(710\) −4.15438e9 3.01833e9i −0.435614 0.316492i
\(711\) 0 0
\(712\) 1.06873e10 3.47253e9i 1.10966 0.360550i
\(713\) 2.56101e7 + 3.52493e7i 0.00264605 + 0.00364198i
\(714\) 0 0
\(715\) 6.17591e9 + 3.34926e8i 0.631873 + 0.0342671i
\(716\) 2.52464e9i 0.257042i
\(717\) 0 0
\(718\) −3.36765e9 1.03646e10i −0.339540 1.04500i
\(719\) −1.01252e10 3.28988e9i −1.01590 0.330087i −0.246701 0.969092i \(-0.579347\pi\)
−0.769203 + 0.639004i \(0.779347\pi\)
\(720\) 0 0
\(721\) −5.21648e9 + 7.17988e9i −0.518328 + 0.713417i
\(722\) −2.19590e9 + 6.75828e9i −0.217136 + 0.668276i
\(723\) 0 0
\(724\) 3.99053e9 2.89929e9i 0.390792 0.283927i
\(725\) −1.53083e10 −1.49192
\(726\) 0 0
\(727\) 5.62481e8 0.0542922 0.0271461 0.999631i \(-0.491358\pi\)
0.0271461 + 0.999631i \(0.491358\pi\)
\(728\) −2.08942e9 + 1.51806e9i −0.200709 + 0.145824i
\(729\) 0 0
\(730\) 2.16567e9 6.66525e9i 0.206045 0.634142i
\(731\) 1.96261e9 2.70130e9i 0.185833 0.255778i
\(732\) 0 0
\(733\) −1.35246e10 4.39440e9i −1.26841 0.412131i −0.403926 0.914792i \(-0.632355\pi\)
−0.864484 + 0.502661i \(0.832355\pi\)
\(734\) −1.47121e9 4.52793e9i −0.137322 0.422633i
\(735\) 0 0
\(736\) 3.49492e9i 0.323121i
\(737\) −1.66617e10 9.03581e8i −1.53314 0.0831440i
\(738\) 0 0
\(739\) 4.02134e9 + 5.53490e9i 0.366535 + 0.504492i 0.951955 0.306238i \(-0.0990704\pi\)
−0.585420 + 0.810730i \(0.699070\pi\)
\(740\) 1.13771e10 3.69665e9i 1.03210 0.335349i
\(741\) 0 0
\(742\) 5.70815e9 + 4.14721e9i 0.512958 + 0.372686i
\(743\) 3.08647e9 + 2.24245e9i 0.276059 + 0.200568i 0.717197 0.696871i \(-0.245425\pi\)
−0.441138 + 0.897439i \(0.645425\pi\)
\(744\) 0 0
\(745\) 1.49129e10 4.84550e9i 1.32134 0.429330i
\(746\) 2.92787e9 + 4.02987e9i 0.258206 + 0.355390i
\(747\) 0 0
\(748\) 7.15915e9 4.63072e9i 0.625469 0.404569i
\(749\) 1.08858e10i 0.946620i
\(750\) 0 0
\(751\) −2.62241e9 8.07096e9i −0.225924 0.695321i −0.998197 0.0600305i \(-0.980880\pi\)
0.772273 0.635291i \(-0.219120\pi\)
\(752\) 3.82452e9 + 1.24266e9i 0.327955 + 0.106559i
\(753\) 0 0
\(754\) −2.09973e9 + 2.89003e9i −0.178387 + 0.245529i
\(755\) 6.82823e9 2.10151e10i 0.577423 1.77712i
\(756\) 0 0
\(757\) 8.36660e8 6.07869e8i 0.0700993 0.0509301i −0.552184 0.833722i \(-0.686205\pi\)
0.622283 + 0.782792i \(0.286205\pi\)
\(758\) −1.12170e10 −0.935478
\(759\) 0 0
\(760\) 2.18097e9 0.180220
\(761\) −1.05094e10 + 7.63554e9i −0.864435 + 0.628049i −0.929088 0.369859i \(-0.879406\pi\)
0.0646529 + 0.997908i \(0.479406\pi\)
\(762\) 0 0
\(763\) 4.25440e9 1.30937e10i 0.346739 1.06715i
\(764\) 2.78837e9 3.83786e9i 0.226216 0.311359i
\(765\) 0 0
\(766\) 1.78852e9 + 5.81125e8i 0.143778 + 0.0467163i
\(767\) −2.13845e9 6.58148e9i −0.171126 0.526672i
\(768\) 0 0
\(769\) 3.10564e9i 0.246269i 0.992390 + 0.123134i \(0.0392946\pi\)
−0.992390 + 0.123134i \(0.960705\pi\)
\(770\) 2.89794e9 7.50855e9i 0.228755 0.592705i
\(771\) 0 0
\(772\) −4.24378e9 5.84106e9i −0.331965 0.456911i
\(773\) 2.15004e9 6.98590e8i 0.167424 0.0543994i −0.224106 0.974565i \(-0.571946\pi\)