Properties

Label 99.8.j.a.8.6
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 8.6
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-11.6523 + 8.46591i) q^{2} +(24.5509 - 75.5599i) q^{4} +(-325.140 + 447.517i) q^{5} +(1250.84 + 406.423i) q^{7} +(-216.093 - 665.067i) q^{8} +O(q^{10})\) \(q+(-11.6523 + 8.46591i) q^{2} +(24.5509 - 75.5599i) q^{4} +(-325.140 + 447.517i) q^{5} +(1250.84 + 406.423i) q^{7} +(-216.093 - 665.067i) q^{8} -7967.22i q^{10} +(-3390.20 - 2827.32i) q^{11} +(-376.885 - 518.737i) q^{13} +(-18015.9 + 5853.73i) q^{14} +(16375.6 + 11897.6i) q^{16} +(-13489.3 - 9800.59i) q^{17} +(-36233.6 + 11773.0i) q^{19} +(25831.9 + 35554.5i) q^{20} +(63439.5 + 4243.72i) q^{22} +16956.4i q^{23} +(-70413.5 - 216710. i) q^{25} +(8783.17 + 2853.82i) q^{26} +(61418.5 - 84535.3i) q^{28} +(26392.1 - 81226.4i) q^{29} +(-46216.9 + 33578.6i) q^{31} -202028. q^{32} +240153. q^{34} +(-588580. + 427628. i) q^{35} +(137209. - 422285. i) q^{37} +(322536. - 443933. i) q^{38} +(367889. + 119535. i) q^{40} +(88318.9 + 271818. i) q^{41} -120737. i q^{43} +(-296864. + 186750. i) q^{44} +(-143552. - 197582. i) q^{46} +(1.17108e6 - 380508. i) q^{47} +(733163. + 532674. i) q^{49} +(2.65513e6 + 1.92907e6i) q^{50} +(-48448.6 + 15741.9i) q^{52} +(1.07598e6 + 1.48096e6i) q^{53} +(2.36756e6 - 597897. i) q^{55} -919718. i q^{56} +(380127. + 1.16991e6i) q^{58} +(-956400. - 310753. i) q^{59} +(-1.23092e6 + 1.69422e6i) q^{61} +(254262. - 782537. i) q^{62} +(258020. - 187463. i) q^{64} +354684. q^{65} -2.00100e6 q^{67} +(-1.07171e6 + 778640. i) q^{68} +(3.23806e6 - 9.96573e6i) q^{70} +(2.59916e6 - 3.57744e6i) q^{71} +(-1.15433e6 - 375064. i) q^{73} +(1.97622e6 + 6.08219e6i) q^{74} +3.02684e6i q^{76} +(-3.09151e6 - 4.91438e6i) q^{77} +(1.99565e6 + 2.74677e6i) q^{79} +(-1.06487e7 + 3.45998e6i) q^{80} +(-3.33030e6 - 2.41961e6i) q^{82} +(-54736.3 - 39768.3i) q^{83} +(8.77186e6 - 2.85015e6i) q^{85} +(1.02215e6 + 1.40686e6i) q^{86} +(-1.14776e6 + 2.86567e6i) q^{88} +7.70323e6i q^{89} +(-260596. - 802032. i) q^{91} +(1.28123e6 + 416296. i) q^{92} +(-1.04245e7 + 1.43481e7i) q^{94} +(6.51237e6 - 2.00430e7i) q^{95} +(6.15921e6 - 4.47493e6i) q^{97} -1.30526e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.6523 + 8.46591i −1.02993 + 0.748288i −0.968295 0.249811i \(-0.919632\pi\)
−0.0616352 + 0.998099i \(0.519632\pi\)
\(3\) 0 0
\(4\) 24.5509 75.5599i 0.191804 0.590311i
\(5\) −325.140 + 447.517i −1.16326 + 1.60109i −0.464840 + 0.885395i \(0.653888\pi\)
−0.698417 + 0.715691i \(0.746112\pi\)
\(6\) 0 0
\(7\) 1250.84 + 406.423i 1.37835 + 0.447852i 0.902126 0.431473i \(-0.142006\pi\)
0.476222 + 0.879325i \(0.342006\pi\)
\(8\) −216.093 665.067i −0.149220 0.459251i
\(9\) 0 0
\(10\) 7967.22i 2.51946i
\(11\) −3390.20 2827.32i −0.767981 0.640472i
\(12\) 0 0
\(13\) −376.885 518.737i −0.0475781 0.0654856i 0.784565 0.620046i \(-0.212886\pi\)
−0.832143 + 0.554561i \(0.812886\pi\)
\(14\) −18015.9 + 5853.73i −1.75472 + 0.570144i
\(15\) 0 0
\(16\) 16375.6 + 11897.6i 0.999487 + 0.726170i
\(17\) −13489.3 9800.59i −0.665917 0.483817i 0.202739 0.979233i \(-0.435016\pi\)
−0.868656 + 0.495416i \(0.835016\pi\)
\(18\) 0 0
\(19\) −36233.6 + 11773.0i −1.21192 + 0.393776i −0.844133 0.536134i \(-0.819884\pi\)
−0.367786 + 0.929910i \(0.619884\pi\)
\(20\) 25831.9 + 35554.5i 0.722022 + 0.993778i
\(21\) 0 0
\(22\) 63439.5 + 4243.72i 1.27022 + 0.0849704i
\(23\) 16956.4i 0.290594i 0.989388 + 0.145297i \(0.0464138\pi\)
−0.989388 + 0.145297i \(0.953586\pi\)
\(24\) 0 0
\(25\) −70413.5 216710.i −0.901292 2.77389i
\(26\) 8783.17 + 2853.82i 0.0980041 + 0.0318435i
\(27\) 0 0
\(28\) 61418.5 84535.3i 0.528745 0.727755i
\(29\) 26392.1 81226.4i 0.200946 0.618450i −0.798909 0.601452i \(-0.794589\pi\)
0.999856 0.0169978i \(-0.00541083\pi\)
\(30\) 0 0
\(31\) −46216.9 + 33578.6i −0.278635 + 0.202440i −0.718322 0.695711i \(-0.755089\pi\)
0.439687 + 0.898151i \(0.355089\pi\)
\(32\) −202028. −1.08990
\(33\) 0 0
\(34\) 240153. 1.04788
\(35\) −588580. + 427628.i −2.32042 + 1.68589i
\(36\) 0 0
\(37\) 137209. 422285.i 0.445323 1.37056i −0.436806 0.899556i \(-0.643890\pi\)
0.882129 0.471008i \(-0.156110\pi\)
\(38\) 322536. 443933.i 0.953534 1.31243i
\(39\) 0 0
\(40\) 367889. + 119535.i 0.908882 + 0.295314i
\(41\) 88318.9 + 271818.i 0.200129 + 0.615934i 0.999878 + 0.0155997i \(0.00496574\pi\)
−0.799749 + 0.600334i \(0.795034\pi\)
\(42\) 0 0
\(43\) 120737.i 0.231580i −0.993274 0.115790i \(-0.963060\pi\)
0.993274 0.115790i \(-0.0369399\pi\)
\(44\) −296864. + 186750.i −0.525380 + 0.330503i
\(45\) 0 0
\(46\) −143552. 197582.i −0.217448 0.299292i
\(47\) 1.17108e6 380508.i 1.64530 0.534591i 0.667587 0.744532i \(-0.267327\pi\)
0.977714 + 0.209941i \(0.0673273\pi\)
\(48\) 0 0
\(49\) 733163. + 532674.i 0.890254 + 0.646808i
\(50\) 2.65513e6 + 1.92907e6i 3.00394 + 2.18249i
\(51\) 0 0
\(52\) −48448.6 + 15741.9i −0.0477825 + 0.0155255i
\(53\) 1.07598e6 + 1.48096e6i 0.992748 + 1.36640i 0.929670 + 0.368392i \(0.120092\pi\)
0.0630779 + 0.998009i \(0.479908\pi\)
\(54\) 0 0
\(55\) 2.36756e6 597897.i 1.91881 0.484570i
\(56\) 919718.i 0.699837i
\(57\) 0 0
\(58\) 380127. + 1.16991e6i 0.255818 + 0.787326i
\(59\) −956400. 310753.i −0.606258 0.196985i −0.0102286 0.999948i \(-0.503256\pi\)
−0.596030 + 0.802962i \(0.703256\pi\)
\(60\) 0 0
\(61\) −1.23092e6 + 1.69422e6i −0.694348 + 0.955688i 0.305646 + 0.952145i \(0.401128\pi\)
−0.999994 + 0.00354258i \(0.998872\pi\)
\(62\) 254262. 782537.i 0.135491 0.416998i
\(63\) 0 0
\(64\) 258020. 187463.i 0.123034 0.0893892i
\(65\) 354684. 0.160194
\(66\) 0 0
\(67\) −2.00100e6 −0.812802 −0.406401 0.913695i \(-0.633216\pi\)
−0.406401 + 0.913695i \(0.633216\pi\)
\(68\) −1.07171e6 + 778640.i −0.413328 + 0.300300i
\(69\) 0 0
\(70\) 3.23806e6 9.96573e6i 1.12834 3.47269i
\(71\) 2.59916e6 3.57744e6i 0.861846 1.18623i −0.119281 0.992861i \(-0.538059\pi\)
0.981126 0.193368i \(-0.0619411\pi\)
\(72\) 0 0
\(73\) −1.15433e6 375064.i −0.347296 0.112843i 0.130175 0.991491i \(-0.458446\pi\)
−0.477470 + 0.878648i \(0.658446\pi\)
\(74\) 1.97622e6 + 6.08219e6i 0.566925 + 1.74481i
\(75\) 0 0
\(76\) 3.02684e6i 0.790938i
\(77\) −3.09151e6 4.91438e6i −0.771708 1.22674i
\(78\) 0 0
\(79\) 1.99565e6 + 2.74677e6i 0.455396 + 0.626798i 0.973546 0.228491i \(-0.0733792\pi\)
−0.518150 + 0.855290i \(0.673379\pi\)
\(80\) −1.06487e7 + 3.45998e6i −2.32532 + 0.755542i
\(81\) 0 0
\(82\) −3.33030e6 2.41961e6i −0.667015 0.484615i
\(83\) −54736.3 39768.3i −0.0105076 0.00763420i 0.582519 0.812817i \(-0.302067\pi\)
−0.593027 + 0.805183i \(0.702067\pi\)
\(84\) 0 0
\(85\) 8.77186e6 2.85015e6i 1.54926 0.503386i
\(86\) 1.02215e6 + 1.40686e6i 0.173288 + 0.238511i
\(87\) 0 0
\(88\) −1.14776e6 + 2.86567e6i −0.179540 + 0.448268i
\(89\) 7.70323e6i 1.15826i 0.815234 + 0.579132i \(0.196609\pi\)
−0.815234 + 0.579132i \(0.803391\pi\)
\(90\) 0 0
\(91\) −260596. 802032.i −0.0362513 0.111570i
\(92\) 1.28123e6 + 416296.i 0.171541 + 0.0557371i
\(93\) 0 0
\(94\) −1.04245e7 + 1.43481e7i −1.29452 + 1.78175i
\(95\) 6.51237e6 2.00430e7i 0.779304 2.39845i
\(96\) 0 0
\(97\) 6.15921e6 4.47493e6i 0.685211 0.497835i −0.189871 0.981809i \(-0.560807\pi\)
0.875082 + 0.483974i \(0.160807\pi\)
\(98\) −1.30526e7 −1.40090
\(99\) 0 0
\(100\) −1.81033e7 −1.81033
\(101\) 1.52020e6 1.10449e6i 0.146817 0.106669i −0.511952 0.859014i \(-0.671077\pi\)
0.658769 + 0.752345i \(0.271077\pi\)
\(102\) 0 0
\(103\) −483273. + 1.48736e6i −0.0435775 + 0.134118i −0.970478 0.241189i \(-0.922463\pi\)
0.926901 + 0.375307i \(0.122463\pi\)
\(104\) −263553. + 362749.i −0.0229748 + 0.0316220i
\(105\) 0 0
\(106\) −2.50754e7 8.14748e6i −2.04492 0.664436i
\(107\) −6.89514e6 2.12211e7i −0.544127 1.67465i −0.723057 0.690788i \(-0.757264\pi\)
0.178931 0.983862i \(-0.442736\pi\)
\(108\) 0 0
\(109\) 7.79718e6i 0.576693i −0.957526 0.288346i \(-0.906895\pi\)
0.957526 0.288346i \(-0.0931055\pi\)
\(110\) −2.25259e7 + 2.70105e7i −1.61364 + 1.93490i
\(111\) 0 0
\(112\) 1.56478e7 + 2.15374e7i 1.05242 + 1.44854i
\(113\) 3.13809e6 1.01963e6i 0.204593 0.0664763i −0.204928 0.978777i \(-0.565696\pi\)
0.409521 + 0.912301i \(0.365696\pi\)
\(114\) 0 0
\(115\) −7.58830e6 5.51322e6i −0.465267 0.338036i
\(116\) −5.48951e6 3.98836e6i −0.326536 0.237242i
\(117\) 0 0
\(118\) 1.37751e7 4.47580e6i 0.771805 0.250775i
\(119\) −1.28898e7 1.77414e7i −0.701186 0.965100i
\(120\) 0 0
\(121\) 3.49971e6 + 1.91703e7i 0.179591 + 0.983741i
\(122\) 3.01625e7i 1.50386i
\(123\) 0 0
\(124\) 1.40253e6 + 4.31653e6i 0.0660594 + 0.203310i
\(125\) 7.87752e7 + 2.55956e7i 3.60748 + 1.17214i
\(126\) 0 0
\(127\) −3.65733e6 + 5.03389e6i −0.158435 + 0.218067i −0.880854 0.473389i \(-0.843031\pi\)
0.722418 + 0.691456i \(0.243031\pi\)
\(128\) 6.57156e6 2.02252e7i 0.276970 0.852427i
\(129\) 0 0
\(130\) −4.13290e6 + 3.00272e6i −0.164988 + 0.119871i
\(131\) −1.47555e7 −0.573462 −0.286731 0.958011i \(-0.592569\pi\)
−0.286731 + 0.958011i \(0.592569\pi\)
\(132\) 0 0
\(133\) −5.01073e7 −1.84680
\(134\) 2.33163e7 1.69403e7i 0.837129 0.608210i
\(135\) 0 0
\(136\) −3.60309e6 + 1.10892e7i −0.122826 + 0.378018i
\(137\) −1.64119e7 + 2.25890e7i −0.545301 + 0.750543i −0.989365 0.145452i \(-0.953536\pi\)
0.444064 + 0.895995i \(0.353536\pi\)
\(138\) 0 0
\(139\) −927100. 301233.i −0.0292803 0.00951373i 0.294340 0.955701i \(-0.404900\pi\)
−0.323621 + 0.946187i \(0.604900\pi\)
\(140\) 1.78614e7 + 5.49717e7i 0.550132 + 1.69313i
\(141\) 0 0
\(142\) 6.36898e7i 1.86664i
\(143\) −188922. + 2.82420e6i −0.00540264 + 0.0807641i
\(144\) 0 0
\(145\) 2.77691e7 + 3.82209e7i 0.756439 + 1.04115i
\(146\) 1.66259e7 5.40207e6i 0.442130 0.143657i
\(147\) 0 0
\(148\) −2.85392e7 2.07349e7i −0.723645 0.525759i
\(149\) −9.82502e6 7.13830e6i −0.243322 0.176784i 0.459440 0.888209i \(-0.348050\pi\)
−0.702762 + 0.711425i \(0.748050\pi\)
\(150\) 0 0
\(151\) 1.32203e7 4.29555e6i 0.312481 0.101531i −0.148578 0.988901i \(-0.547470\pi\)
0.461059 + 0.887370i \(0.347470\pi\)
\(152\) 1.56597e7 + 2.15537e7i 0.361685 + 0.497816i
\(153\) 0 0
\(154\) 7.76280e7 + 3.10915e7i 1.71276 + 0.685992i
\(155\) 3.16006e7i 0.681608i
\(156\) 0 0
\(157\) −1.69859e7 5.22772e7i −0.350299 1.07811i −0.958685 0.284469i \(-0.908183\pi\)
0.608386 0.793641i \(-0.291817\pi\)
\(158\) −4.65079e7 1.51113e7i −0.938051 0.304791i
\(159\) 0 0
\(160\) 6.56874e7 9.04110e7i 1.26783 1.74502i
\(161\) −6.89148e6 + 2.12098e7i −0.130143 + 0.400540i
\(162\) 0 0
\(163\) 1.65126e7 1.19971e7i 0.298647 0.216980i −0.428363 0.903607i \(-0.640909\pi\)
0.727010 + 0.686627i \(0.240909\pi\)
\(164\) 2.27068e7 0.401978
\(165\) 0 0
\(166\) 974481. 0.0165346
\(167\) −3.44736e7 + 2.50466e7i −0.572769 + 0.416141i −0.836110 0.548562i \(-0.815176\pi\)
0.263341 + 0.964703i \(0.415176\pi\)
\(168\) 0 0
\(169\) 1.92633e7 5.92864e7i 0.306992 0.944825i
\(170\) −7.80835e7 + 1.07473e8i −1.21896 + 1.67775i
\(171\) 0 0
\(172\) −9.12286e6 2.96420e6i −0.136704 0.0444178i
\(173\) −2.96087e7 9.11263e7i −0.434769 1.33808i −0.893323 0.449415i \(-0.851632\pi\)
0.458554 0.888666i \(-0.348368\pi\)
\(174\) 0 0
\(175\) 2.99688e8i 4.22703i
\(176\) −2.18783e7 8.66341e7i −0.302496 1.19783i
\(177\) 0 0
\(178\) −6.52149e7 8.97605e7i −0.866715 1.19293i
\(179\) −2.90347e7 + 9.43394e6i −0.378383 + 0.122944i −0.492032 0.870577i \(-0.663746\pi\)
0.113650 + 0.993521i \(0.463746\pi\)
\(180\) 0 0
\(181\) 2.04656e7 + 1.48691e7i 0.256537 + 0.186385i 0.708619 0.705591i \(-0.249319\pi\)
−0.452082 + 0.891976i \(0.649319\pi\)
\(182\) 9.82648e6 + 7.13936e6i 0.120823 + 0.0877828i
\(183\) 0 0
\(184\) 1.12772e7 3.66417e6i 0.133456 0.0433624i
\(185\) 1.44368e8 + 1.98705e8i 1.67637 + 2.30732i
\(186\) 0 0
\(187\) 1.80222e7 + 7.13646e7i 0.201540 + 0.798063i
\(188\) 9.78287e7i 1.07378i
\(189\) 0 0
\(190\) 9.37981e7 + 2.88681e8i 0.992103 + 3.05338i
\(191\) −2.50673e7 8.14486e6i −0.260310 0.0845799i 0.175955 0.984398i \(-0.443699\pi\)
−0.436265 + 0.899818i \(0.643699\pi\)
\(192\) 0 0
\(193\) −7.71476e7 + 1.06185e8i −0.772453 + 1.06319i 0.223622 + 0.974676i \(0.428212\pi\)
−0.996075 + 0.0885144i \(0.971788\pi\)
\(194\) −3.38848e7 + 1.04287e8i −0.333195 + 1.02547i
\(195\) 0 0
\(196\) 5.82486e7 4.23201e7i 0.552572 0.401467i
\(197\) 9.85940e7 0.918796 0.459398 0.888231i \(-0.348065\pi\)
0.459398 + 0.888231i \(0.348065\pi\)
\(198\) 0 0
\(199\) 1.79937e8 1.61858 0.809290 0.587409i \(-0.199852\pi\)
0.809290 + 0.587409i \(0.199852\pi\)
\(200\) −1.28911e8 + 9.36593e7i −1.13942 + 0.827839i
\(201\) 0 0
\(202\) −8.36337e6 + 2.57398e7i −0.0713923 + 0.219723i
\(203\) 6.60245e7 9.08750e7i 0.553948 0.762444i
\(204\) 0 0
\(205\) −1.50359e8 4.88546e7i −1.21896 0.396066i
\(206\) −6.96062e6 2.14226e7i −0.0554769 0.170740i
\(207\) 0 0
\(208\) 1.29786e7i 0.100002i
\(209\) 1.56125e8 + 6.25310e7i 1.18293 + 0.473788i
\(210\) 0 0
\(211\) −1.14640e8 1.57789e8i −0.840133 1.15634i −0.985951 0.167033i \(-0.946581\pi\)
0.145818 0.989311i \(-0.453419\pi\)
\(212\) 1.38318e8 4.49421e7i 0.997015 0.323950i
\(213\) 0 0
\(214\) 2.60000e8 + 1.88901e8i 1.81353 + 1.31761i
\(215\) 5.40318e7 + 3.92564e7i 0.370779 + 0.269386i
\(216\) 0 0
\(217\) −7.14571e7 + 2.32178e7i −0.474719 + 0.154246i
\(218\) 6.60102e7 + 9.08552e7i 0.431532 + 0.593953i
\(219\) 0 0
\(220\) 1.29488e7 1.93572e8i 0.0819878 1.22564i
\(221\) 1.06911e7i 0.0666270i
\(222\) 0 0
\(223\) −3.87658e7 1.19309e8i −0.234090 0.720454i −0.997241 0.0742337i \(-0.976349\pi\)
0.763151 0.646220i \(-0.223651\pi\)
\(224\) −2.52705e8 8.21088e7i −1.50226 0.488114i
\(225\) 0 0
\(226\) −2.79340e7 + 3.84478e7i −0.160973 + 0.221560i
\(227\) 3.34258e7 1.02874e8i 0.189667 0.583734i −0.810331 0.585972i \(-0.800713\pi\)
0.999997 + 0.00223893i \(0.000712674\pi\)
\(228\) 0 0
\(229\) 1.20306e7 8.74076e6i 0.0662009 0.0480978i −0.554193 0.832388i \(-0.686973\pi\)
0.620394 + 0.784291i \(0.286973\pi\)
\(230\) 1.35096e8 0.732140
\(231\) 0 0
\(232\) −5.97242e7 −0.314009
\(233\) 1.81504e8 1.31870e8i 0.940028 0.682970i −0.00839961 0.999965i \(-0.502674\pi\)
0.948427 + 0.316995i \(0.102674\pi\)
\(234\) 0 0
\(235\) −2.10482e8 + 6.47798e8i −1.05798 + 3.25613i
\(236\) −4.69609e7 + 6.46362e7i −0.232565 + 0.320099i
\(237\) 0 0
\(238\) 3.00393e8 + 9.76037e7i 1.44435 + 0.469296i
\(239\) −7.76499e7 2.38982e8i −0.367916 1.13233i −0.948135 0.317868i \(-0.897033\pi\)
0.580219 0.814460i \(-0.302967\pi\)
\(240\) 0 0
\(241\) 3.26887e8i 1.50431i −0.658984 0.752157i \(-0.729014\pi\)
0.658984 0.752157i \(-0.270986\pi\)
\(242\) −2.03074e8 1.93751e8i −0.921088 0.878799i
\(243\) 0 0
\(244\) 9.77949e7 + 1.34603e8i 0.430975 + 0.593186i
\(245\) −4.76761e8 + 1.54909e8i −2.07119 + 0.672970i
\(246\) 0 0
\(247\) 1.97630e7 + 1.43586e7i 0.0834474 + 0.0606281i
\(248\) 3.23192e7 + 2.34813e7i 0.134549 + 0.0977553i
\(249\) 0 0
\(250\) −1.13460e9 + 3.68655e8i −4.59256 + 1.49221i
\(251\) 7.16071e7 + 9.85587e7i 0.285823 + 0.393402i 0.927652 0.373446i \(-0.121824\pi\)
−0.641828 + 0.766848i \(0.721824\pi\)
\(252\) 0 0
\(253\) 4.79413e7 5.74857e7i 0.186118 0.223171i
\(254\) 8.96192e7i 0.343149i
\(255\) 0 0
\(256\) 1.07266e8 + 3.30130e8i 0.399596 + 1.22983i
\(257\) −1.06527e8 3.46126e7i −0.391465 0.127195i 0.106670 0.994295i \(-0.465981\pi\)
−0.498134 + 0.867100i \(0.665981\pi\)
\(258\) 0 0
\(259\) 3.43252e8 4.72446e8i 1.22762 1.68967i
\(260\) 8.70781e6 2.67999e7i 0.0307257 0.0945641i
\(261\) 0 0
\(262\) 1.71936e8 1.24919e8i 0.590625 0.429114i
\(263\) 4.46775e8 1.51441 0.757206 0.653176i \(-0.226564\pi\)
0.757206 + 0.653176i \(0.226564\pi\)
\(264\) 0 0
\(265\) −1.01260e9 −3.34255
\(266\) 5.83866e8 4.24204e8i 1.90207 1.38194i
\(267\) 0 0
\(268\) −4.91263e7 + 1.51195e8i −0.155899 + 0.479806i
\(269\) 3.43377e7 4.72618e7i 0.107557 0.148039i −0.751845 0.659340i \(-0.770836\pi\)
0.859402 + 0.511300i \(0.170836\pi\)
\(270\) 0 0
\(271\) 3.02925e7 + 9.84265e6i 0.0924577 + 0.0300413i 0.354881 0.934912i \(-0.384522\pi\)
−0.262423 + 0.964953i \(0.584522\pi\)
\(272\) −1.04293e8 3.20981e8i −0.314242 0.967137i
\(273\) 0 0
\(274\) 4.02156e8i 1.18105i
\(275\) −3.73994e8 + 9.33772e8i −1.08443 + 2.70755i
\(276\) 0 0
\(277\) 1.60153e8 + 2.20432e8i 0.452748 + 0.623154i 0.972985 0.230868i \(-0.0741564\pi\)
−0.520237 + 0.854022i \(0.674156\pi\)
\(278\) 1.33531e7 4.33868e6i 0.0372756 0.0121116i
\(279\) 0 0
\(280\) 4.11590e8 + 2.99037e8i 1.12050 + 0.814090i
\(281\) −4.10221e8 2.98043e8i −1.10293 0.801322i −0.121390 0.992605i \(-0.538735\pi\)
−0.981535 + 0.191283i \(0.938735\pi\)
\(282\) 0 0
\(283\) 4.12897e7 1.34158e7i 0.108290 0.0351856i −0.254371 0.967107i \(-0.581868\pi\)
0.362661 + 0.931921i \(0.381868\pi\)
\(284\) −2.06499e8 2.84222e8i −0.534939 0.736280i
\(285\) 0 0
\(286\) −2.17080e7 3.45078e7i −0.0548705 0.0872241i
\(287\) 3.75895e8i 0.938599i
\(288\) 0 0
\(289\) −4.08906e7 1.25848e8i −0.0996508 0.306693i
\(290\) −6.47149e8 2.10271e8i −1.55816 0.506276i
\(291\) 0 0
\(292\) −5.66796e7 + 7.80128e7i −0.133225 + 0.183369i
\(293\) −1.82780e8 + 5.62539e8i −0.424514 + 1.30652i 0.478945 + 0.877845i \(0.341019\pi\)
−0.903459 + 0.428675i \(0.858981\pi\)
\(294\) 0 0
\(295\) 4.50032e8 3.26967e8i 1.02062 0.741527i
\(296\) −3.10497e8 −0.695884
\(297\) 0 0
\(298\) 1.74917e8 0.382890
\(299\) 8.79594e6 6.39062e6i 0.0190297 0.0138259i
\(300\) 0 0
\(301\) 4.90702e7 1.51023e8i 0.103713 0.319197i
\(302\) −1.17682e8 + 1.61975e8i −0.245859 + 0.338395i
\(303\) 0 0
\(304\) −7.33417e8 2.38301e8i −1.49725 0.486485i
\(305\) −3.57970e8 1.10172e9i −0.722433 2.22342i
\(306\) 0 0
\(307\) 5.23476e8i 1.03255i −0.856422 0.516277i \(-0.827317\pi\)
0.856422 0.516277i \(-0.172683\pi\)
\(308\) −4.47229e8 + 1.12942e8i −0.872173 + 0.220256i
\(309\) 0 0
\(310\) 2.67528e8 + 3.68221e8i 0.510039 + 0.702008i
\(311\) −4.20066e7 + 1.36488e7i −0.0791875 + 0.0257296i −0.348343 0.937367i \(-0.613255\pi\)
0.269155 + 0.963097i \(0.413255\pi\)
\(312\) 0 0
\(313\) 2.57831e8 + 1.87326e8i 0.475259 + 0.345296i 0.799487 0.600683i \(-0.205105\pi\)
−0.324228 + 0.945979i \(0.605105\pi\)
\(314\) 6.40499e8 + 4.65350e8i 1.16752 + 0.848254i
\(315\) 0 0
\(316\) 2.56541e8 8.33551e7i 0.457353 0.148603i
\(317\) −3.27856e8 4.51255e8i −0.578064 0.795637i 0.415417 0.909631i \(-0.363636\pi\)
−0.993481 + 0.113994i \(0.963636\pi\)
\(318\) 0 0
\(319\) −3.19127e8 + 2.00755e8i −0.550423 + 0.346257i
\(320\) 1.76420e8i 0.300970i
\(321\) 0 0
\(322\) −9.92585e7 3.05486e8i −0.165681 0.509913i
\(323\) 6.04150e8 + 1.96300e8i 0.997553 + 0.324124i
\(324\) 0 0
\(325\) −8.58780e7 + 1.18201e8i −0.138768 + 0.190998i
\(326\) −9.08437e7 + 2.79588e8i −0.145222 + 0.446948i
\(327\) 0 0
\(328\) 1.61692e8 1.17476e8i 0.253005 0.183819i
\(329\) 1.61949e9 2.50721
\(330\) 0 0
\(331\) −8.12025e8 −1.23076 −0.615378 0.788233i \(-0.710996\pi\)
−0.615378 + 0.788233i \(0.710996\pi\)
\(332\) −4.34871e6 + 3.15952e6i −0.00652195 + 0.00473847i
\(333\) 0 0
\(334\) 1.89656e8 5.83701e8i 0.278519 0.857192i
\(335\) 6.50605e8 8.95481e8i 0.945498 1.30137i
\(336\) 0 0
\(337\) 2.59580e8 + 8.43425e7i 0.369459 + 0.120044i 0.487861 0.872921i \(-0.337777\pi\)
−0.118402 + 0.992966i \(0.537777\pi\)
\(338\) 2.77451e8 + 8.53906e8i 0.390821 + 1.20282i
\(339\) 0 0
\(340\) 7.32774e8i 1.01110i
\(341\) 2.51622e8 + 1.68320e7i 0.343644 + 0.0229877i
\(342\) 0 0
\(343\) 6.39291e7 + 8.79908e7i 0.0855399 + 0.117736i
\(344\) −8.02981e7 + 2.60904e7i −0.106353 + 0.0345562i
\(345\) 0 0
\(346\) 1.11648e9 + 8.11169e8i 1.44905 + 1.05280i
\(347\) −5.74010e8 4.17043e8i −0.737507 0.535830i 0.154422 0.988005i \(-0.450648\pi\)
−0.891930 + 0.452174i \(0.850648\pi\)
\(348\) 0 0
\(349\) 1.02337e9 3.32513e8i 1.28868 0.418716i 0.417048 0.908884i \(-0.363065\pi\)
0.871628 + 0.490168i \(0.163065\pi\)
\(350\) 2.53713e9 + 3.49206e9i 3.16304 + 4.35355i
\(351\) 0 0
\(352\) 6.84915e8 + 5.71198e8i 0.837023 + 0.698051i
\(353\) 1.03279e9i 1.24968i −0.780752 0.624841i \(-0.785164\pi\)
0.780752 0.624841i \(-0.214836\pi\)
\(354\) 0 0
\(355\) 7.55874e8 + 2.32634e9i 0.896706 + 2.75978i
\(356\) 5.82055e8 + 1.89121e8i 0.683737 + 0.222160i
\(357\) 0 0
\(358\) 2.58455e8 3.55732e8i 0.297710 0.409763i
\(359\) 2.81543e8 8.66500e8i 0.321155 0.988412i −0.651992 0.758226i \(-0.726066\pi\)
0.973147 0.230186i \(-0.0739336\pi\)
\(360\) 0 0
\(361\) 4.51111e8 3.27751e8i 0.504671 0.366665i
\(362\) −3.64353e8 −0.403685
\(363\) 0 0
\(364\) −6.69993e7 −0.0728141
\(365\) 5.43166e8 3.94633e8i 0.584666 0.424785i
\(366\) 0 0
\(367\) −2.74633e8 + 8.45232e8i −0.290015 + 0.892575i 0.694835 + 0.719169i \(0.255477\pi\)
−0.984850 + 0.173406i \(0.944523\pi\)
\(368\) −2.01740e8 + 2.77672e8i −0.211021 + 0.290445i
\(369\) 0 0
\(370\) −3.36444e9 1.09317e9i −3.45308 1.12197i
\(371\) 7.43985e8 + 2.28975e9i 0.756407 + 2.32798i
\(372\) 0 0
\(373\) 5.86987e8i 0.585663i −0.956164 0.292831i \(-0.905403\pi\)
0.956164 0.292831i \(-0.0945975\pi\)
\(374\) −8.14167e8 6.78989e8i −0.804753 0.671139i
\(375\) 0 0
\(376\) −5.06127e8 6.96624e8i −0.491023 0.675835i
\(377\) −5.20819e7 + 1.69224e7i −0.0500602 + 0.0162655i
\(378\) 0 0
\(379\) −1.81025e8 1.31523e8i −0.170806 0.124097i 0.499098 0.866545i \(-0.333665\pi\)
−0.669904 + 0.742448i \(0.733665\pi\)
\(380\) −1.35456e9 9.84148e8i −1.26636 0.920064i
\(381\) 0 0
\(382\) 3.61046e8 1.17311e8i 0.331391 0.107676i
\(383\) 7.82084e8 + 1.07645e9i 0.711308 + 0.979031i 0.999768 + 0.0215395i \(0.00685677\pi\)
−0.288460 + 0.957492i \(0.593143\pi\)
\(384\) 0 0
\(385\) 3.20444e9 + 2.14358e8i 2.86180 + 0.191438i
\(386\) 1.89042e9i 1.67303i
\(387\) 0 0
\(388\) −1.86911e8 5.75253e8i −0.162452 0.499974i
\(389\) −1.54400e9 5.01677e8i −1.32992 0.432116i −0.444028 0.896013i \(-0.646451\pi\)
−0.885890 + 0.463896i \(0.846451\pi\)
\(390\) 0 0
\(391\) 1.66183e8 2.28731e8i 0.140594 0.193512i
\(392\) 1.95832e8 6.02710e8i 0.164204 0.505367i
\(393\) 0 0
\(394\) −1.14885e9 + 8.34688e8i −0.946295 + 0.687524i
\(395\) −1.87809e9 −1.53330
\(396\) 0 0
\(397\) 3.29446e8 0.264251 0.132126 0.991233i \(-0.457820\pi\)
0.132126 + 0.991233i \(0.457820\pi\)
\(398\) −2.09668e9 + 1.52333e9i −1.66702 + 1.21116i
\(399\) 0 0
\(400\) 1.42526e9 4.38651e9i 1.11349 3.42696i
\(401\) 3.40446e8 4.68583e8i 0.263659 0.362896i −0.656577 0.754259i \(-0.727996\pi\)
0.920236 + 0.391363i \(0.127996\pi\)
\(402\) 0 0
\(403\) 3.48369e7 + 1.13192e7i 0.0265138 + 0.00861486i
\(404\) −4.61329e7 1.41983e8i −0.0348078 0.107127i
\(405\) 0 0
\(406\) 1.61786e9i 1.19978i
\(407\) −1.65910e9 + 1.04370e9i −1.21981 + 0.767350i
\(408\) 0 0
\(409\) 6.44635e8 + 8.87264e8i 0.465889 + 0.641241i 0.975717 0.219035i \(-0.0702910\pi\)
−0.509828 + 0.860276i \(0.670291\pi\)
\(410\) 2.16563e9 7.03656e8i 1.55182 0.504217i
\(411\) 0 0
\(412\) 1.00520e8 + 7.30321e7i 0.0708129 + 0.0514486i
\(413\) −1.07001e9 7.77406e8i −0.747414 0.543028i
\(414\) 0 0
\(415\) 3.55940e7 1.15652e7i 0.0244460 0.00794299i
\(416\) 7.61413e7 + 1.04799e8i 0.0518553 + 0.0713728i
\(417\) 0 0
\(418\) −2.34860e9 + 5.93108e8i −1.57287 + 0.397207i
\(419\) 2.22173e9i 1.47551i −0.675068 0.737756i \(-0.735886\pi\)
0.675068 0.737756i \(-0.264114\pi\)
\(420\) 0 0
\(421\) 1.76744e8 + 5.43961e8i 0.115440 + 0.355288i 0.992039 0.125935i \(-0.0401930\pi\)
−0.876599 + 0.481222i \(0.840193\pi\)
\(422\) 2.67165e9 + 8.68071e8i 1.73056 + 0.562292i
\(423\) 0 0
\(424\) 7.52426e8 1.03563e9i 0.479384 0.659815i
\(425\) −1.17406e9 + 3.61337e9i −0.741870 + 2.28324i
\(426\) 0 0
\(427\) −2.22826e9 + 1.61893e9i −1.38506 + 1.00631i
\(428\) −1.77274e9 −1.09293
\(429\) 0 0
\(430\) −9.61937e8 −0.583455
\(431\) 4.16579e8 3.02662e8i 0.250626 0.182091i −0.455378 0.890298i \(-0.650496\pi\)
0.706004 + 0.708207i \(0.250496\pi\)
\(432\) 0 0
\(433\) −4.37765e8 + 1.34730e9i −0.259139 + 0.797549i 0.733847 + 0.679315i \(0.237723\pi\)
−0.992986 + 0.118233i \(0.962277\pi\)
\(434\) 6.36082e8 8.75491e8i 0.373507 0.514088i
\(435\) 0 0
\(436\) −5.89154e8 1.91428e8i −0.340428 0.110612i
\(437\) −1.99628e8 6.14393e8i −0.114429 0.352177i
\(438\) 0 0
\(439\) 2.14595e9i 1.21058i −0.796005 0.605290i \(-0.793057\pi\)
0.796005 0.605290i \(-0.206943\pi\)
\(440\) −9.09256e8 1.44539e9i −0.508864 0.808909i
\(441\) 0 0
\(442\) −9.05101e7 1.24576e8i −0.0498562 0.0686211i
\(443\) 1.72276e9 5.59759e8i 0.941482 0.305906i 0.202232 0.979338i \(-0.435180\pi\)
0.739249 + 0.673432i \(0.235180\pi\)
\(444\) 0 0
\(445\) −3.44733e9 2.50463e9i −1.85448 1.34736i
\(446\) 1.46177e9 + 1.06204e9i 0.780202 + 0.566850i
\(447\) 0 0
\(448\) 3.98931e8 1.29621e8i 0.209616 0.0681085i
\(449\) −1.04798e9 1.44242e9i −0.546376 0.752022i 0.443139 0.896453i \(-0.353865\pi\)
−0.989515 + 0.144431i \(0.953865\pi\)
\(450\) 0 0
\(451\) 4.69096e8 1.17122e9i 0.240793 0.601203i
\(452\) 2.62146e8i 0.133524i
\(453\) 0 0
\(454\) 4.81433e8 + 1.48170e9i 0.241457 + 0.743130i
\(455\) 4.43653e8 + 1.44152e8i 0.220802 + 0.0717431i
\(456\) 0 0
\(457\) −2.20740e9 + 3.03823e9i −1.08187 + 1.48907i −0.224424 + 0.974492i \(0.572050\pi\)
−0.857446 + 0.514574i \(0.827950\pi\)
\(458\) −6.61863e7 + 2.03700e8i −0.0321913 + 0.0990747i
\(459\) 0 0
\(460\) −6.02878e8 + 4.38016e8i −0.288786 + 0.209816i
\(461\) −2.07464e9 −0.986255 −0.493127 0.869957i \(-0.664146\pi\)
−0.493127 + 0.869957i \(0.664146\pi\)
\(462\) 0 0
\(463\) −9.87231e8 −0.462259 −0.231129 0.972923i \(-0.574242\pi\)
−0.231129 + 0.972923i \(0.574242\pi\)
\(464\) 1.39858e9 1.01613e9i 0.649943 0.472211i
\(465\) 0 0
\(466\) −9.98541e8 + 3.07319e9i −0.457104 + 1.40682i
\(467\) −1.92924e9 + 2.65537e9i −0.876552 + 1.20647i 0.100812 + 0.994906i \(0.467856\pi\)
−0.977364 + 0.211565i \(0.932144\pi\)
\(468\) 0 0
\(469\) −2.50293e9 8.13251e8i −1.12032 0.364015i
\(470\) −3.03159e9 9.33028e9i −1.34688 4.14527i
\(471\) 0 0
\(472\) 7.03222e8i 0.307819i
\(473\) −3.41361e8 + 4.09322e8i −0.148320 + 0.177849i
\(474\) 0 0
\(475\) 5.10266e9 + 7.02321e9i 2.18459 + 3.00683i
\(476\) −1.65699e9 + 5.38389e8i −0.704200 + 0.228808i
\(477\) 0 0
\(478\) 2.92800e9 + 2.12732e9i 1.22623 + 0.890912i
\(479\) −2.78114e9 2.02061e9i −1.15624 0.840058i −0.166942 0.985967i \(-0.553389\pi\)
−0.989298 + 0.145909i \(0.953389\pi\)
\(480\) 0 0
\(481\) −2.70767e8 + 8.79774e7i −0.110940 + 0.0360465i
\(482\) 2.76740e9 + 3.80900e9i 1.12566 + 1.54934i
\(483\) 0 0
\(484\) 1.53443e9 + 2.06211e8i 0.615160 + 0.0826709i
\(485\) 4.21133e9i 1.67619i
\(486\) 0 0
\(487\) −1.10486e9 3.40042e9i −0.433469 1.33408i −0.894648 0.446772i \(-0.852573\pi\)
0.461179 0.887307i \(-0.347427\pi\)
\(488\) 1.39277e9 + 4.52537e8i 0.542511 + 0.176273i
\(489\) 0 0
\(490\) 4.24393e9 5.84127e9i 1.62960 2.24296i
\(491\) −4.91901e8 + 1.51392e9i −0.187540 + 0.577187i −0.999983 0.00585281i \(-0.998137\pi\)
0.812443 + 0.583040i \(0.198137\pi\)
\(492\) 0 0
\(493\) −1.15208e9 + 8.37034e8i −0.433030 + 0.314615i
\(494\) −3.51844e8 −0.131312
\(495\) 0 0
\(496\) −1.15633e9 −0.425498
\(497\) 4.70509e9 3.41845e9i 1.71918 1.24906i
\(498\) 0 0
\(499\) 4.08060e8 1.25588e9i 0.147018 0.452476i −0.850247 0.526385i \(-0.823547\pi\)
0.997265 + 0.0739084i \(0.0235472\pi\)
\(500\) 3.86800e9 5.32385e9i 1.38386 1.90472i
\(501\) 0 0
\(502\) −1.66878e9 5.42219e8i −0.588756 0.191298i
\(503\) 1.38564e9 + 4.26457e9i 0.485471 + 1.49413i 0.831297 + 0.555828i \(0.187599\pi\)
−0.345826 + 0.938299i \(0.612401\pi\)
\(504\) 0 0
\(505\) 1.03943e9i 0.359150i
\(506\) −7.19584e7 + 1.07571e9i −0.0246919 + 0.369120i
\(507\) 0 0
\(508\) 2.90569e8 + 3.99934e8i 0.0983391 + 0.135352i
\(509\) −7.87747e8 + 2.55955e8i −0.264774 + 0.0860302i −0.438395 0.898782i \(-0.644453\pi\)
0.173622 + 0.984812i \(0.444453\pi\)
\(510\) 0 0
\(511\) −1.29145e9 9.38291e8i −0.428157 0.311074i
\(512\) −1.84256e9 1.33870e9i −0.606703 0.440796i
\(513\) 0 0
\(514\) 1.53431e9 4.98528e8i 0.498359 0.161927i
\(515\) −5.08488e8 6.99874e8i −0.164042 0.225785i
\(516\) 0 0
\(517\) −5.04602e9 2.02103e9i −1.60595 0.643214i
\(518\) 8.41104e9i 2.65886i
\(519\) 0 0
\(520\) −7.66449e7 2.35889e8i −0.0239041 0.0735691i
\(521\) 1.16545e9 + 3.78676e8i 0.361044 + 0.117310i 0.483921 0.875112i \(-0.339212\pi\)
−0.122877 + 0.992422i \(0.539212\pi\)
\(522\) 0 0
\(523\) −2.12670e9 + 2.92715e9i −0.650054 + 0.894723i −0.999101 0.0423823i \(-0.986505\pi\)
0.349047 + 0.937105i \(0.386505\pi\)
\(524\) −3.62261e8 + 1.11492e9i −0.109992 + 0.338521i
\(525\) 0 0
\(526\) −5.20597e9 + 3.78236e9i −1.55974 + 1.13322i
\(527\) 9.52526e8 0.283491
\(528\) 0 0
\(529\) 3.11730e9 0.915555
\(530\) 1.17991e10 8.57258e9i 3.44259 2.50119i
\(531\) 0 0
\(532\) −1.23018e9 + 3.78610e9i −0.354223 + 1.09019i
\(533\) 1.07716e8 1.48258e8i 0.0308130 0.0424105i
\(534\) 0 0
\(535\) 1.17387e10 + 3.81413e9i 3.31422 + 1.07685i
\(536\) 4.32402e8 + 1.33080e9i 0.121286 + 0.373280i
\(537\) 0 0
\(538\) 8.41410e8i 0.232954i
\(539\) −9.79528e8 3.87875e9i −0.269436 1.06692i
\(540\) 0 0
\(541\) −1.57991e9 2.17456e9i −0.428986 0.590448i 0.538734 0.842476i \(-0.318903\pi\)
−0.967720 + 0.252028i \(0.918903\pi\)
\(542\) −4.36306e8 + 1.41764e8i −0.117705 + 0.0382445i
\(543\) 0 0
\(544\) 2.72523e9 + 1.97999e9i 0.725783 + 0.527312i
\(545\) 3.48937e9 + 2.53518e9i 0.923335 + 0.670842i
\(546\) 0 0
\(547\) 2.35993e9 7.66788e8i 0.616515 0.200318i 0.0159224 0.999873i \(-0.494932\pi\)
0.600592 + 0.799555i \(0.294932\pi\)
\(548\) 1.30390e9 + 1.79466e9i 0.338463 + 0.465854i
\(549\) 0 0
\(550\) −3.54734e9 1.40468e10i −0.909145 3.60005i
\(551\) 3.25384e9i 0.828639i
\(552\) 0 0
\(553\) 1.37989e9 + 4.24685e9i 0.346981 + 1.06790i
\(554\) −3.73232e9 1.21270e9i −0.932597 0.303019i
\(555\) 0 0
\(556\) −4.55223e7 + 6.26560e7i −0.0112321 + 0.0154597i
\(557\) −1.03874e9 + 3.19690e9i −0.254690 + 0.783855i 0.739201 + 0.673485i \(0.235204\pi\)
−0.993891 + 0.110370i \(0.964796\pi\)
\(558\) 0 0
\(559\) −6.26307e7 + 4.55039e7i −0.0151651 + 0.0110181i
\(560\) −1.47261e10 −3.54347
\(561\) 0 0
\(562\) 7.30324e9 1.73556
\(563\) −3.50516e9 + 2.54665e9i −0.827806 + 0.601436i −0.918938 0.394403i \(-0.870951\pi\)
0.0911319 + 0.995839i \(0.470951\pi\)
\(564\) 0 0
\(565\) −5.64019e8 + 1.73587e9i −0.131560 + 0.404900i
\(566\) −3.67544e8 + 5.05881e8i −0.0852024 + 0.117271i
\(567\) 0 0
\(568\) −2.94090e9 9.55556e8i −0.673381 0.218795i
\(569\) −3.18313e8 9.79666e8i −0.0724371 0.222939i 0.908283 0.418356i \(-0.137394\pi\)
−0.980720 + 0.195418i \(0.937394\pi\)
\(570\) 0 0
\(571\) 5.34370e9i 1.20120i −0.799549 0.600600i \(-0.794928\pi\)
0.799549 0.600600i \(-0.205072\pi\)
\(572\) 2.08758e8 + 8.36114e7i 0.0466398 + 0.0186801i
\(573\) 0 0
\(574\) −3.18230e9 4.38005e9i −0.702343 0.966692i
\(575\) 3.67464e9 1.19396e9i 0.806078 0.261911i
\(576\) 0 0
\(577\) −3.20168e9 2.32616e9i −0.693846 0.504108i 0.184076 0.982912i \(-0.441071\pi\)
−0.877922 + 0.478804i \(0.841071\pi\)
\(578\) 1.54189e9 + 1.12025e9i 0.332128 + 0.241305i
\(579\) 0 0
\(580\) 3.56972e9 1.15987e9i 0.759690 0.246838i
\(581\) −5.23037e7 7.19899e7i −0.0110641 0.0152284i
\(582\) 0 0
\(583\) 5.39359e8 8.06289e9i 0.112730 1.68520i
\(584\) 8.48755e8i 0.176334i
\(585\) 0 0
\(586\) −2.63259e9 8.10229e9i −0.540433 1.66328i
\(587\) −7.64902e9 2.48532e9i −1.56089 0.507164i −0.603846 0.797101i \(-0.706366\pi\)
−0.957046 + 0.289937i \(0.906366\pi\)
\(588\) 0 0
\(589\) 1.27928e9 1.76078e9i 0.257967 0.355061i
\(590\) −2.47584e9 + 7.61985e9i −0.496296 + 1.52744i
\(591\) 0 0
\(592\) 7.27103e9 5.28271e9i 1.44036 1.04648i
\(593\) 5.24738e9 1.03336 0.516679 0.856179i \(-0.327168\pi\)
0.516679 + 0.856179i \(0.327168\pi\)
\(594\) 0 0
\(595\) 1.21306e10 2.36087
\(596\) −7.80582e8 + 5.67126e8i −0.151028 + 0.109728i
\(597\) 0 0
\(598\) −4.83907e7 + 1.48931e8i −0.00925354 + 0.0284795i
\(599\) 4.00225e9 5.50862e9i 0.760869 1.04725i −0.236272 0.971687i \(-0.575926\pi\)
0.997141 0.0755594i \(-0.0240742\pi\)
\(600\) 0 0
\(601\) −2.96451e9 9.63227e8i −0.557047 0.180996i 0.0169449 0.999856i \(-0.494606\pi\)
−0.573992 + 0.818861i \(0.694606\pi\)
\(602\) 7.06761e8 + 2.17519e9i 0.132034 + 0.406358i
\(603\) 0 0
\(604\) 1.10439e9i 0.203935i
\(605\) −9.71695e9 4.66687e9i −1.78396 0.856804i
\(606\) 0 0
\(607\) −7.82771e8 1.07739e9i −0.142061 0.195530i 0.732058 0.681243i \(-0.238560\pi\)
−0.874119 + 0.485713i \(0.838560\pi\)
\(608\) 7.32020e9 2.37848e9i 1.32087 0.429177i
\(609\) 0 0
\(610\) 1.34982e10 + 9.80705e9i 2.40781 + 1.74938i
\(611\) −6.38747e8 4.64077e8i −0.113288 0.0823087i
\(612\) 0 0
\(613\) −9.95999e8 + 3.23620e8i −0.174641 + 0.0567444i −0.395032 0.918667i \(-0.629267\pi\)
0.220391 + 0.975412i \(0.429267\pi\)
\(614\) 4.43170e9 + 6.09972e9i 0.772648 + 1.06346i
\(615\) 0 0
\(616\) −2.60034e9 + 3.11803e9i −0.448226 + 0.537461i
\(617\) 5.93196e8i 0.101672i −0.998707 0.0508358i \(-0.983811\pi\)
0.998707 0.0508358i \(-0.0161885\pi\)
\(618\) 0 0
\(619\) 1.50987e9 + 4.64691e9i 0.255872 + 0.787493i 0.993657 + 0.112457i \(0.0358721\pi\)
−0.737784 + 0.675036i \(0.764128\pi\)
\(620\) −2.38774e9 7.75823e8i −0.402361 0.130735i
\(621\) 0 0
\(622\) 3.73926e8 5.14664e8i 0.0623044 0.0857547i
\(623\) −3.13077e9 + 9.63551e9i −0.518732 + 1.59649i
\(624\) 0 0
\(625\) −2.26655e10 + 1.64675e10i −3.71352 + 2.69803i
\(626\) −4.59022e9 −0.747865
\(627\) 0 0
\(628\) −4.36707e9 −0.703610
\(629\) −5.98949e9 + 4.35162e9i −0.959650 + 0.697226i
\(630\) 0 0
\(631\) 2.84355e9 8.75154e9i 0.450565 1.38670i −0.425699 0.904865i \(-0.639972\pi\)
0.876264 0.481832i \(-0.160028\pi\)
\(632\) 1.39554e9 1.92080e9i 0.219904 0.302672i
\(633\) 0 0
\(634\) 7.64058e9 + 2.48257e9i 1.19073 + 0.386892i
\(635\) −1.06360e9 3.27344e9i −0.164844 0.507337i
\(636\) 0 0
\(637\) 5.81075e8i 0.0890727i
\(638\) 2.01900e9 5.04096e9i 0.307797 0.768495i
\(639\) 0 0
\(640\) 6.91443e9 + 9.51690e9i 1.04262 + 1.43505i
\(641\) 1.02195e10 3.32053e9i 1.53260 0.497971i 0.583274 0.812275i \(-0.301771\pi\)
0.949322 + 0.314305i \(0.101771\pi\)
\(642\) 0 0
\(643\) −3.89977e9 2.83335e9i −0.578496 0.420302i 0.259685 0.965693i \(-0.416381\pi\)
−0.838182 + 0.545391i \(0.816381\pi\)
\(644\) 1.43342e9 + 1.04144e9i 0.211481 + 0.153650i
\(645\) 0 0
\(646\) −8.70161e9 + 2.82732e9i −1.26995 + 0.412631i
\(647\) 5.09161e9 + 7.00800e9i 0.739078 + 1.01725i 0.998671 + 0.0515358i \(0.0164116\pi\)
−0.259593 + 0.965718i \(0.583588\pi\)
\(648\) 0 0
\(649\) 2.36379e9 + 3.75756e9i 0.339431 + 0.539572i
\(650\) 2.10435e9i 0.300553i
\(651\) 0 0
\(652\) −5.01100e8 1.54223e9i −0.0708040 0.217912i
\(653\) 4.89829e9 + 1.59155e9i 0.688412 + 0.223679i 0.632274 0.774745i \(-0.282122\pi\)
0.0561373 + 0.998423i \(0.482122\pi\)
\(654\) 0 0
\(655\) 4.79761e9 6.60334e9i 0.667083 0.918161i
\(656\) −1.78769e9 + 5.50195e9i −0.247246 + 0.760946i
\(657\) 0 0
\(658\) −1.88708e10 + 1.37104e10i −2.58226 + 1.87612i
\(659\) 1.05603e9 0.143741 0.0718703 0.997414i \(-0.477103\pi\)
0.0718703 + 0.997414i \(0.477103\pi\)
\(660\) 0 0
\(661\) −1.59865e8 −0.0215303 −0.0107651 0.999942i \(-0.503427\pi\)
−0.0107651 + 0.999942i \(0.503427\pi\)
\(662\) 9.46198e9 6.87453e9i 1.26759 0.920959i
\(663\) 0 0
\(664\) −1.46204e7 + 4.49970e7i −0.00193808 + 0.00596479i
\(665\) 1.62919e10 2.24239e10i 2.14830 2.95689i
\(666\) 0 0
\(667\) 1.37731e9 + 4.47516e8i 0.179718 + 0.0583939i
\(668\) 1.04616e9 + 3.21974e9i 0.135794 + 0.417929i
\(669\) 0 0
\(670\) 1.59424e10i 2.04782i
\(671\) 8.96319e9 2.26353e9i 1.14534 0.289240i
\(672\) 0 0
\(673\) −6.92839e9 9.53612e9i −0.876153 1.20592i −0.977472 0.211067i \(-0.932306\pi\)
0.101319 0.994854i \(-0.467694\pi\)
\(674\) −3.73874e9 + 1.21479e9i −0.470344 + 0.152824i
\(675\) 0 0
\(676\) −4.00674e9 2.91107e9i −0.498859 0.362442i
\(677\) −4.63099e9 3.36461e9i −0.573606 0.416749i 0.262807 0.964848i \(-0.415352\pi\)
−0.836413 + 0.548099i \(0.815352\pi\)
\(678\) 0 0
\(679\) 9.52291e9 3.09418e9i 1.16742 0.379316i
\(680\) −3.79108e9 5.21798e9i −0.462362 0.636386i
\(681\) 0 0
\(682\) −3.07448e9 + 1.93408e9i −0.371130 + 0.233469i
\(683\) 5.04965e9i 0.606442i 0.952920 + 0.303221i \(0.0980620\pi\)
−0.952920 + 0.303221i \(0.901938\pi\)
\(684\) 0 0
\(685\) −4.77281e9 1.46892e10i −0.567358 1.74615i
\(686\) −1.48984e9 4.84080e8i −0.176200 0.0572509i
\(687\) 0 0
\(688\) 1.43647e9 1.97714e9i 0.168166 0.231461i
\(689\) 3.62709e8 1.11630e9i 0.0422465 0.130021i
\(690\) 0 0
\(691\) −1.56805e9 + 1.13926e9i −0.180796 + 0.131356i −0.674502 0.738273i \(-0.735642\pi\)
0.493707 + 0.869629i \(0.335642\pi\)
\(692\) −7.61241e9 −0.873275
\(693\) 0 0
\(694\) 1.02192e10 1.16054
\(695\) 4.36244e8 3.16950e8i 0.0492928 0.0358133i
\(696\) 0 0
\(697\) 1.47261e9 4.53222e9i 0.164730 0.506986i
\(698\) −9.10962e9 + 1.25383e10i −1.01393 + 1.39555i
\(699\) 0 0
\(700\) −2.26444e10 7.35760e9i −2.49527 0.810761i
\(701\) 1.12219e9 + 3.45375e9i 0.123042 + 0.378684i 0.993539 0.113489i \(-0.0362026\pi\)
−0.870497 + 0.492173i \(0.836203\pi\)
\(702\) 0 0
\(703\) 1.69162e10i 1.83637i
\(704\) −1.40476e9 9.39698e7i −0.151739 0.0101504i
\(705\) 0 0
\(706\) 8.74349e9 + 1.20344e10i 0.935122 + 1.28709i
\(707\) 2.35042e9 7.63698e8i 0.250137 0.0812744i
\(708\) 0 0
\(709\) 6.30642e9 + 4.58188e9i 0.664540 + 0.482816i 0.868193 0.496227i \(-0.165281\pi\)
−0.203653 + 0.979043i \(0.565281\pi\)
\(710\) −2.85023e10 2.07081e10i −2.98865 2.17138i
\(711\) 0 0
\(712\) 5.12316e9 1.66462e9i 0.531935 0.172836i
\(713\) −5.69373e8 7.83675e8i −0.0588279 0.0809697i
\(714\) 0 0
\(715\) −1.20245e9 1.00281e9i −0.123026 0.102600i
\(716\) 2.42547e9i 0.246945i
\(717\) 0 0
\(718\) 4.05508e9 + 1.24803e10i 0.408850 + 1.25831i
\(719\) −3.56651e9 1.15883e9i −0.357843 0.116270i 0.124578 0.992210i \(-0.460242\pi\)
−0.482421 + 0.875940i \(0.660242\pi\)
\(720\) 0 0
\(721\) −1.20900e9 + 1.66404e9i −0.120130 + 0.165345i
\(722\) −2.48178e9 + 7.63813e9i −0.245405 + 0.755278i
\(723\) 0 0
\(724\) 1.62596e9 1.18133e9i 0.159230 0.115687i
\(725\) −1.94610e10 −1.89662
\(726\) 0 0
\(727\) −1.34608e10 −1.29928 −0.649638 0.760244i \(-0.725080\pi\)
−0.649638 + 0.760244i \(0.725080\pi\)
\(728\) −4.77092e8 + 3.46628e8i −0.0458292 + 0.0332969i
\(729\) 0 0
\(730\) −2.98822e9 + 9.19680e9i −0.284304 + 0.874997i
\(731\) −1.18329e9 + 1.62866e9i −0.112042 + 0.154213i
\(732\) 0 0
\(733\) −5.99605e9 1.94823e9i −0.562343 0.182716i 0.0140322 0.999902i \(-0.495533\pi\)
−0.576375 + 0.817185i \(0.695533\pi\)
\(734\) −3.95555e9 1.21739e10i −0.369208 1.13630i
\(735\) 0 0
\(736\) 3.42568e9i 0.316719i
\(737\) 6.78378e9 + 5.65746e9i 0.624217 + 0.520577i
\(738\) 0 0
\(739\) 5.57739e9 + 7.67661e9i 0.508365 + 0.699704i 0.983642 0.180132i \(-0.0576525\pi\)
−0.475278 + 0.879836i \(0.657652\pi\)
\(740\) 1.85585e10 6.03001e9i 1.68357 0.547025i
\(741\) 0 0
\(742\) −2.80540e10 2.03824e10i −2.52105 1.83165i
\(743\) 7.41652e8 + 5.38842e8i 0.0663345 + 0.0481948i 0.620458 0.784239i \(-0.286947\pi\)
−0.554124 + 0.832434i \(0.686947\pi\)
\(744\) 0 0
\(745\) 6.38902e9 2.07592e9i 0.566092 0.183935i
\(746\) 4.96938e9 + 6.83976e9i 0.438244 + 0.603192i
\(747\) 0 0
\(748\) 5.83476e9 + 3.90310e8i 0.509762 + 0.0341000i
\(749\) 2.93465e10i 2.55194i
\(750\) 0 0
\(751\) 2.88398e9 + 8.87598e9i 0.248458 + 0.764674i 0.995049 + 0.0993906i \(0.0316893\pi\)
−0.746591 + 0.665283i \(0.768311\pi\)
\(752\) 2.37043e10 + 7.70200e9i 2.03266 + 0.660451i
\(753\) 0 0
\(754\) 4.63612e8 6.38107e8i 0.0393872 0.0542118i
\(755\) −2.37613e9 + 7.31298e9i −0.200935 + 0.618415i
\(756\) 0 0
\(757\) 1.32597e10 9.63376e9i 1.11096 0.807161i 0.128147 0.991755i \(-0.459097\pi\)
0.982815 + 0.184594i \(0.0590971\pi\)
\(758\) 3.22282e9 0.268778
\(759\) 0 0
\(760\) −1.47372e10 −1.21778
\(761\) 6.60238e9 4.79691e9i 0.543068 0.394562i −0.282155 0.959369i \(-0.591049\pi\)
0.825223 + 0.564807i \(0.191049\pi\)
\(762\) 0 0
\(763\) 3.16895e9 9.75303e9i 0.258273 0.794883i
\(764\) −1.23085e9 + 1.69412e9i −0.0998569 + 0.137441i
\(765\) 0 0
\(766\) −1.82262e10 5.92205e9i −1.46519 0.476071i
\(767\) 1.99253e8 + 6.13239e8i 0.0159449 + 0.0490733i
\(768\) 0 0
\(769\) 5.33884e9i 0.423355i −0.977340 0.211678i \(-0.932107\pi\)
0.977340 0.211678i \(-0.0678927\pi\)
\(770\) −3.91539e10 + 2.46308e10i −3.09071 + 1.94429i
\(771\) 0 0
\(772\) 6.12925e9 + 8.43619e9i 0.479454 + 0.659912i
\(773\) −2.28640e10 + 7.42897e9i −1.78043 + 0.578496i −0.998966 0.0454580i \(-0.985525\pi\)
&