Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(74,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.74");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.d (of order \(2\), degree \(1\), not 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: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{14})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 49 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 3) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 74.1 | ||
Root | \(-1.87083 - 1.87083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.74 |
Dual form | 75.9.d.b.74.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −22.4499 | −1.40312 | −0.701561 | − | 0.712610i | \(-0.747513\pi\) | ||||
−0.701561 | + | 0.712610i | \(0.747513\pi\) | |||||||
\(3\) | −67.3498 | − | 45.0000i | −0.831479 | − | 0.555556i | ||||
\(4\) | 248.000 | 0.968750 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1512.00 | + | 1010.25i | 1.16667 | + | 0.779512i | ||||
\(7\) | − | 1750.00i | − | 0.728863i | −0.931230 | − | 0.364431i | \(-0.881263\pi\) | ||
0.931230 | − | 0.364431i | \(-0.118737\pi\) | |||||||
\(8\) | 179.600 | 0.0438475 | ||||||||
\(9\) | 2511.00 | + | 6061.48i | 0.382716 | + | 0.923866i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6959.48i | 0.475342i | 0.971346 | + | 0.237671i | \(0.0763840\pi\) | ||||
−0.971346 | + | 0.237671i | \(0.923616\pi\) | |||||||
\(12\) | −16702.8 | − | 11160.0i | −0.805496 | − | 0.538194i | ||||
\(13\) | − | 25730.0i | − | 0.900879i | −0.892807 | − | 0.450439i | \(-0.851267\pi\) | ||
0.892807 | − | 0.450439i | \(-0.148733\pi\) | |||||||
\(14\) | 39287.4i | 1.02268i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −67520.0 | −1.03027 | ||||||||
\(17\) | −74893.0 | −0.896697 | −0.448348 | − | 0.893859i | \(-0.647988\pi\) | ||||
−0.448348 | + | 0.893859i | \(0.647988\pi\) | |||||||
\(18\) | −56371.8 | − | 136080.i | −0.536997 | − | 1.29630i | ||||
\(19\) | −18938.0 | −0.145318 | −0.0726590 | − | 0.997357i | \(-0.523148\pi\) | ||||
−0.0726590 | + | 0.997357i | \(0.523148\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −78750.0 | + | 117862.i | −0.404924 | + | 0.606035i | ||||
\(22\) | − | 156240.i | − | 0.666963i | ||||||
\(23\) | −470461. | −1.68117 | −0.840586 | − | 0.541678i | \(-0.817789\pi\) | ||||
−0.840586 | + | 0.541678i | \(0.817789\pi\) | |||||||
\(24\) | −12096.0 | − | 8081.98i | −0.0364583 | − | 0.0243597i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 577637.i | 1.26404i | ||||||||
\(27\) | 103651. | − | 521235.i | 0.195038 | − | 0.980796i | ||||
\(28\) | − | 434000.i | − | 0.706086i | ||||||
\(29\) | − | 460897.i | − | 0.651647i | −0.945431 | − | 0.325823i | \(-0.894359\pi\) | ||
0.945431 | − | 0.325823i | \(-0.105641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −351478. | −0.380585 | −0.190292 | − | 0.981727i | \(-0.560944\pi\) | ||||
−0.190292 | + | 0.981727i | \(0.560944\pi\) | |||||||
\(32\) | 1.46984e6 | 1.40175 | ||||||||
\(33\) | 313177. | − | 468720.i | 0.264079 | − | 0.395237i | ||||
\(34\) | 1.68134e6 | 1.25817 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 622728. | + | 1.50325e6i | 0.370756 | + | 0.894995i | ||||
\(37\) | 1.33517e6i | 0.712409i | 0.934408 | + | 0.356205i | \(0.115929\pi\) | ||||
−0.934408 | + | 0.356205i | \(0.884071\pi\) | |||||||
\(38\) | 425157. | 0.203899 | ||||||||
\(39\) | −1.15785e6 | + | 1.73291e6i | −0.500488 | + | 0.749062i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.87547e6i | 0.663704i | 0.943331 | + | 0.331852i | \(0.107673\pi\) | ||||
−0.943331 | + | 0.331852i | \(0.892327\pi\) | |||||||
\(42\) | 1.76793e6 | − | 2.64600e6i | 0.568157 | − | 0.850340i | ||||
\(43\) | 3.52615e6i | 1.03140i | 0.856769 | + | 0.515700i | \(0.172468\pi\) | ||||
−0.856769 | + | 0.515700i | \(0.827532\pi\) | |||||||
\(44\) | 1.72595e6i | 0.460488i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.05618e7 | 2.35889 | ||||||||
\(47\) | 4.08104e6 | 0.836333 | 0.418167 | − | 0.908370i | \(-0.362673\pi\) | ||||
0.418167 | + | 0.908370i | \(0.362673\pi\) | |||||||
\(48\) | 4.54746e6 | + | 3.03840e6i | 0.856651 | + | 0.572374i | ||||
\(49\) | 2.70230e6 | 0.468759 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.04403e6 | + | 3.37019e6i | 0.745585 | + | 0.498165i | ||||
\(52\) | − | 6.38104e6i | − | 0.872726i | ||||||
\(53\) | −6.60177e6 | −0.836675 | −0.418337 | − | 0.908292i | \(-0.637387\pi\) | ||||
−0.418337 | + | 0.908292i | \(0.637387\pi\) | |||||||
\(54\) | −2.32697e6 | + | 1.17017e7i | −0.273663 | + | 1.37618i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 314299.i | − | 0.0319589i | ||||||
\(57\) | 1.27547e6 | + | 852210.i | 0.120829 | + | 0.0807323i | ||||
\(58\) | 1.03471e7i | 0.914340i | ||||||||
\(59\) | − | 1.37149e7i | − | 1.13184i | −0.824461 | − | 0.565919i | \(-0.808521\pi\) | ||
0.824461 | − | 0.565919i | \(-0.191479\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 753602. | 0.0544280 | 0.0272140 | − | 0.999630i | \(-0.491336\pi\) | ||||
0.0272140 | + | 0.999630i | \(0.491336\pi\) | |||||||
\(62\) | 7.89066e6 | 0.534007 | ||||||||
\(63\) | 1.06076e7 | − | 4.39425e6i | 0.673372 | − | 0.278948i | ||||
\(64\) | −1.57128e7 | −0.936554 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.03080e6 | + | 1.05227e7i | −0.370535 | + | 0.554566i | ||||
\(67\) | 2.26889e6i | 0.112594i | 0.998414 | + | 0.0562969i | \(0.0179293\pi\) | ||||
−0.998414 | + | 0.0562969i | \(0.982071\pi\) | |||||||
\(68\) | −1.85735e7 | −0.868675 | ||||||||
\(69\) | 3.16855e7 | + | 2.11707e7i | 1.39786 | + | 0.933985i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.70220e7i | 0.669849i | 0.942245 | + | 0.334925i | \(0.108711\pi\) | ||||
−0.942245 | + | 0.334925i | \(0.891289\pi\) | |||||||
\(72\) | 450974. | + | 1.08864e6i | 0.0167812 | + | 0.0405093i | ||||
\(73\) | − | 2.76728e7i | − | 0.974454i | −0.873275 | − | 0.487227i | \(-0.838008\pi\) | ||
0.873275 | − | 0.487227i | \(-0.161992\pi\) | |||||||
\(74\) | − | 2.99745e7i | − | 0.999597i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.69662e6 | −0.140777 | ||||||||
\(77\) | 1.21791e7 | 0.346459 | ||||||||
\(78\) | 2.59937e7 | − | 3.89038e7i | 0.702246 | − | 1.05103i | ||||
\(79\) | 2.29810e7 | 0.590011 | 0.295006 | − | 0.955496i | \(-0.404678\pi\) | ||||
0.295006 | + | 0.955496i | \(0.404678\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.04365e7 | + | 3.04408e7i | −0.707057 | + | 0.707157i | ||||
\(82\) | − | 4.21042e7i | − | 0.931257i | ||||||
\(83\) | −4.63952e7 | −0.977599 | −0.488799 | − | 0.872396i | \(-0.662565\pi\) | ||||
−0.488799 | + | 0.872396i | \(0.662565\pi\) | |||||||
\(84\) | −1.95300e7 | + | 2.92298e7i | −0.392270 | + | 0.587096i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 7.91619e7i | − | 1.44718i | ||||||
\(87\) | −2.07404e7 | + | 3.10414e7i | −0.362026 | + | 0.541831i | ||||
\(88\) | 1.24992e6i | 0.0208426i | ||||||||
\(89\) | − | 7.26152e7i | − | 1.15736i | −0.815555 | − | 0.578679i | \(-0.803568\pi\) | ||
0.815555 | − | 0.578679i | \(-0.196432\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.50275e7 | −0.656617 | ||||||||
\(92\) | −1.16674e8 | −1.62864 | ||||||||
\(93\) | 2.36720e7 | + | 1.58165e7i | 0.316448 | + | 0.211436i | ||||
\(94\) | −9.16191e7 | −1.17348 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.89937e7 | − | 6.61429e7i | −1.16553 | − | 0.778751i | ||||
\(97\) | 1.47271e8i | 1.66353i | 0.555129 | + | 0.831764i | \(0.312669\pi\) | ||||
−0.555129 | + | 0.831764i | \(0.687331\pi\) | |||||||
\(98\) | −6.06665e7 | −0.657726 | ||||||||
\(99\) | −4.21848e7 | + | 1.74753e7i | −0.439152 | + | 0.181921i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.03545e8i | − | 0.995045i | −0.867451 | − | 0.497522i | \(-0.834243\pi\) | ||
0.867451 | − | 0.497522i | \(-0.165757\pi\) | |||||||
\(102\) | −1.13238e8 | − | 7.56605e7i | −1.04615 | − | 0.698986i | ||||
\(103\) | 1.66064e8i | 1.47545i | 0.675100 | + | 0.737726i | \(0.264101\pi\) | ||||
−0.675100 | + | 0.737726i | \(0.735899\pi\) | |||||||
\(104\) | − | 4.62110e6i | − | 0.0395013i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.48209e8 | 1.17396 | ||||||||
\(107\) | 2.25540e7 | 0.172063 | 0.0860316 | − | 0.996292i | \(-0.472581\pi\) | ||||
0.0860316 | + | 0.996292i | \(0.472581\pi\) | |||||||
\(108\) | 2.57055e7 | − | 1.29266e8i | 0.188943 | − | 0.950146i | ||||
\(109\) | 1.09975e8 | 0.779091 | 0.389546 | − | 0.921007i | \(-0.372632\pi\) | ||||
0.389546 | + | 0.921007i | \(0.372632\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00826e7 | − | 8.99235e7i | 0.395783 | − | 0.592354i | ||||
\(112\) | 1.18160e8i | 0.750928i | ||||||||
\(113\) | 2.87748e8 | 1.76481 | 0.882405 | − | 0.470490i | \(-0.155923\pi\) | ||||
0.882405 | + | 0.470490i | \(0.155923\pi\) | |||||||
\(114\) | −2.86343e7 | − | 1.91321e7i | −0.169538 | − | 0.113277i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 1.14303e8i | − | 0.631283i | ||||||
\(117\) | 1.55962e8 | − | 6.46080e7i | 0.832291 | − | 0.344781i | ||||
\(118\) | 3.07899e8i | 1.58811i | ||||||||
\(119\) | 1.31063e8i | 0.653569i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.65924e8 | 0.774050 | ||||||||
\(122\) | −1.69183e7 | −0.0763692 | ||||||||
\(123\) | 8.43961e7 | − | 1.26312e8i | 0.368724 | − | 0.551856i | ||||
\(124\) | −8.71665e7 | −0.368691 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.38140e8 | + | 9.86507e7i | −0.944822 | + | 0.391397i | ||||
\(127\) | 2.75994e8i | 1.06092i | 0.847708 | + | 0.530462i | \(0.177982\pi\) | ||||
−0.847708 | + | 0.530462i | \(0.822018\pi\) | |||||||
\(128\) | −2.35290e7 | −0.0876523 | ||||||||
\(129\) | 1.58677e8 | − | 2.37486e8i | 0.573000 | − | 0.857588i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.89118e8i | 0.981725i | 0.871237 | + | 0.490862i | \(0.163318\pi\) | ||||
−0.871237 | + | 0.490862i | \(0.836682\pi\) | |||||||
\(132\) | 7.76678e7 | − | 1.16243e8i | 0.255826 | − | 0.382886i | ||||
\(133\) | 3.31415e7i | 0.105917i | ||||||||
\(134\) | − | 5.09365e7i | − | 0.157983i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.34508e7 | −0.0393180 | ||||||||
\(137\) | 2.07562e8 | 0.589205 | 0.294602 | − | 0.955620i | \(-0.404813\pi\) | ||||
0.294602 | + | 0.955620i | \(0.404813\pi\) | |||||||
\(138\) | −7.11337e8 | − | 4.75282e8i | −1.96137 | − | 1.31049i | ||||
\(139\) | 1.42668e8 | 0.382180 | 0.191090 | − | 0.981573i | \(-0.438798\pi\) | ||||
0.191090 | + | 0.981573i | \(0.438798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.74857e8 | − | 1.83647e8i | −0.695394 | − | 0.464630i | ||||
\(142\) | − | 3.82143e8i | − | 0.939880i | ||||||
\(143\) | 1.79067e8 | 0.428226 | ||||||||
\(144\) | −1.69543e8 | − | 4.09271e8i | −0.394302 | − | 0.951835i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.21252e8i | 1.36728i | ||||||||
\(147\) | −1.82000e8 | − | 1.21604e8i | −0.389763 | − | 0.260422i | ||||
\(148\) | 3.31122e8i | 0.690147i | ||||||||
\(149\) | 8.19236e8i | 1.66213i | 0.556179 | + | 0.831063i | \(0.312267\pi\) | ||||
−0.556179 | + | 0.831063i | \(0.687733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.23861e8 | 0.815296 | 0.407648 | − | 0.913139i | \(-0.366349\pi\) | ||||
0.407648 | + | 0.913139i | \(0.366349\pi\) | |||||||
\(152\) | −3.40126e6 | −0.00637184 | ||||||||
\(153\) | −1.88056e8 | − | 4.53963e8i | −0.343180 | − | 0.828428i | ||||
\(154\) | −2.73420e8 | −0.486124 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.87147e8 | + | 4.29762e8i | −0.484848 | + | 0.725654i | ||||
\(157\) | − | 7.59851e8i | − | 1.25063i | −0.780371 | − | 0.625316i | \(-0.784970\pi\) | ||
0.780371 | − | 0.625316i | \(-0.215030\pi\) | |||||||
\(158\) | −5.15922e8 | −0.827857 | ||||||||
\(159\) | 4.44628e8 | + | 2.97079e8i | 0.695678 | + | 0.464819i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.23307e8i | 1.22534i | ||||||||
\(162\) | 6.83297e8 | − | 6.83394e8i | 0.992087 | − | 0.992227i | ||||
\(163\) | − | 6.68160e8i | − | 0.946520i | −0.880923 | − | 0.473260i | \(-0.843077\pi\) | ||
0.880923 | − | 0.473260i | \(-0.156923\pi\) | |||||||
\(164\) | 4.65116e8i | 0.642963i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.04157e9 | 1.37169 | ||||||||
\(167\) | −1.96306e8 | −0.252387 | −0.126194 | − | 0.992006i | \(-0.540276\pi\) | ||||
−0.126194 | + | 0.992006i | \(0.540276\pi\) | |||||||
\(168\) | −1.41435e7 | + | 2.11680e7i | −0.0177549 | + | 0.0265731i | ||||
\(169\) | 1.53698e8 | 0.188417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.75533e7 | − | 1.14792e8i | −0.0556156 | − | 0.134254i | ||||
\(172\) | 8.74485e8i | 0.999168i | ||||||||
\(173\) | 1.02319e9 | 1.14228 | 0.571141 | − | 0.820852i | \(-0.306501\pi\) | ||||
0.571141 | + | 0.820852i | \(0.306501\pi\) | |||||||
\(174\) | 4.65620e8 | − | 6.96877e8i | 0.507966 | − | 0.760255i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.69904e8i | − | 0.489732i | ||||||
\(177\) | −6.17170e8 | + | 9.23696e8i | −0.628799 | + | 0.941100i | ||||
\(178\) | 1.63021e9i | 1.62391i | ||||||||
\(179\) | 1.28895e9i | 1.25552i | 0.778408 | + | 0.627759i | \(0.216028\pi\) | ||||
−0.778408 | + | 0.627759i | \(0.783972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.71707e8 | 0.439499 | 0.219749 | − | 0.975556i | \(-0.429476\pi\) | ||||
0.219749 | + | 0.975556i | \(0.429476\pi\) | |||||||
\(182\) | 1.01086e9 | 0.921314 | ||||||||
\(183\) | −5.07550e7 | − | 3.39121e7i | −0.0452558 | − | 0.0302378i | ||||
\(184\) | −8.44946e7 | −0.0737153 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.31435e8 | − | 3.55080e8i | −0.444016 | − | 0.296670i | ||||
\(187\) | − | 5.21217e8i | − | 0.426238i | ||||||
\(188\) | 1.01210e9 | 0.810198 | ||||||||
\(189\) | −9.12161e8 | − | 1.81390e8i | −0.714866 | − | 0.142156i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.61787e8i | − | 0.121565i | −0.998151 | − | 0.0607827i | \(-0.980640\pi\) | ||
0.998151 | − | 0.0607827i | \(-0.0193597\pi\) | |||||||
\(192\) | 1.05825e9 | + | 7.07075e8i | 0.778725 | + | 0.520308i | ||||
\(193\) | 1.58840e9i | 1.14480i | 0.819974 | + | 0.572401i | \(0.193988\pi\) | ||||
−0.819974 | + | 0.572401i | \(0.806012\pi\) | |||||||
\(194\) | − | 3.30623e9i | − | 2.33413i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.70171e8 | 0.454110 | ||||||||
\(197\) | 5.37769e8 | 0.357052 | 0.178526 | − | 0.983935i | \(-0.442867\pi\) | ||||
0.178526 | + | 0.983935i | \(0.442867\pi\) | |||||||
\(198\) | 9.47046e8 | − | 3.92319e8i | 0.616184 | − | 0.255257i | ||||
\(199\) | −6.47586e8 | −0.412938 | −0.206469 | − | 0.978453i | \(-0.566197\pi\) | ||||
−0.206469 | + | 0.978453i | \(0.566197\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.02100e8 | − | 1.52809e8i | 0.0625521 | − | 0.0936194i | ||||
\(202\) | 2.32457e9i | 1.39617i | ||||||||
\(203\) | −8.06570e8 | −0.474961 | ||||||||
\(204\) | 1.25092e9 | + | 8.35806e8i | 0.722285 | + | 0.482597i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 3.72812e9i | − | 2.07024i | ||||||
\(207\) | −1.18133e9 | − | 2.85169e9i | −0.643412 | − | 1.55318i | ||||
\(208\) | 1.73729e9i | 0.928152i | ||||||||
\(209\) | − | 1.31799e8i | − | 0.0690758i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.81104e7 | 0.0293173 | 0.0146586 | − | 0.999893i | \(-0.495334\pi\) | ||||
0.0146586 | + | 0.999893i | \(0.495334\pi\) | |||||||
\(212\) | −1.63724e9 | −0.810529 | ||||||||
\(213\) | 7.65990e8 | − | 1.14643e9i | 0.372139 | − | 0.556966i | ||||
\(214\) | −5.06336e8 | −0.241426 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.86157e7 | − | 9.36136e7i | 0.00855195 | − | 0.0430055i | ||||
\(217\) | 6.15086e8i | 0.277394i | ||||||||
\(218\) | −2.46893e9 | −1.09316 | ||||||||
\(219\) | −1.24527e9 | + | 1.86376e9i | −0.541363 | + | 0.810238i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.92700e9i | 0.807815i | ||||||||
\(222\) | −1.34885e9 | + | 2.01878e9i | −0.555332 | + | 0.831144i | ||||
\(223\) | − | 4.40200e9i | − | 1.78004i | −0.455920 | − | 0.890021i | \(-0.650690\pi\) | ||
0.455920 | − | 0.890021i | \(-0.349310\pi\) | |||||||
\(224\) | − | 2.57222e9i | − | 1.02168i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.45992e9 | −2.47624 | ||||||||
\(227\) | −3.53592e9 | −1.33168 | −0.665839 | − | 0.746095i | \(-0.731926\pi\) | ||||
−0.665839 | + | 0.746095i | \(0.731926\pi\) | |||||||
\(228\) | 3.16317e8 | + | 2.11348e8i | 0.117053 | + | 0.0782094i | ||||
\(229\) | 1.86569e9 | 0.678420 | 0.339210 | − | 0.940711i | \(-0.389840\pi\) | ||||
0.339210 | + | 0.940711i | \(0.389840\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.20260e8 | − | 5.48059e8i | −0.288074 | − | 0.192477i | ||||
\(232\) | − | 8.27770e7i | − | 0.0285731i | ||||||
\(233\) | −2.72132e9 | −0.923328 | −0.461664 | − | 0.887055i | \(-0.652747\pi\) | ||||
−0.461664 | + | 0.887055i | \(0.652747\pi\) | |||||||
\(234\) | −3.50134e9 | + | 1.45045e9i | −1.16781 | + | 0.483769i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 3.40129e9i | − | 1.09647i | ||||||
\(237\) | −1.54777e9 | − | 1.03414e9i | −0.490582 | − | 0.327784i | ||||
\(238\) | − | 2.94235e9i | − | 0.917037i | ||||||
\(239\) | 2.27461e9i | 0.697132i | 0.937284 | + | 0.348566i | \(0.113331\pi\) | ||||
−0.937284 | + | 0.348566i | \(0.886669\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.74667e9 | −0.517778 | −0.258889 | − | 0.965907i | \(-0.583356\pi\) | ||||
−0.258889 | + | 0.965907i | \(0.583356\pi\) | |||||||
\(242\) | −3.72500e9 | −1.08609 | ||||||||
\(243\) | 3.41973e9 | − | 6.80540e8i | 0.980768 | − | 0.195177i | ||||
\(244\) | 1.86893e8 | 0.0527272 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.89469e9 | + | 2.83571e9i | −0.517365 | + | 0.774321i | ||||
\(247\) | 4.87275e8i | 0.130914i | ||||||||
\(248\) | −6.31253e7 | −0.0166877 | ||||||||
\(249\) | 3.12471e9 | + | 2.08778e9i | 0.812853 | + | 0.543110i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.37549e9i | 0.346547i | 0.984874 | + | 0.173274i | \(0.0554345\pi\) | ||||
−0.984874 | + | 0.173274i | \(0.944566\pi\) | |||||||
\(252\) | 2.63068e9 | − | 1.08977e9i | 0.652329 | − | 0.270230i | ||||
\(253\) | − | 3.27417e9i | − | 0.799132i | ||||||
\(254\) | − | 6.19605e9i | − | 1.48861i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.55069e9 | 1.05954 | ||||||||
\(257\) | 7.93672e9 | 1.81932 | 0.909659 | − | 0.415356i | \(-0.136343\pi\) | ||||
0.909659 | + | 0.415356i | \(0.136343\pi\) | |||||||
\(258\) | −3.56228e9 | + | 5.33154e9i | −0.803988 | + | 1.20330i | ||||
\(259\) | 2.33655e9 | 0.519249 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.79372e9 | − | 1.15731e9i | 0.602034 | − | 0.249396i | ||||
\(262\) | − | 6.49068e9i | − | 1.37748i | ||||||
\(263\) | 3.22555e8 | 0.0674187 | 0.0337093 | − | 0.999432i | \(-0.489268\pi\) | ||||
0.0337093 | + | 0.999432i | \(0.489268\pi\) | |||||||
\(264\) | 5.62464e7 | − | 8.41819e7i | 0.0115792 | − | 0.0173302i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 7.44025e8i | − | 0.148614i | ||||||
\(267\) | −3.26769e9 | + | 4.89062e9i | −0.642977 | + | 0.962319i | ||||
\(268\) | 5.62685e8i | 0.109075i | ||||||||
\(269\) | − | 3.47314e9i | − | 0.663304i | −0.943402 | − | 0.331652i | \(-0.892394\pi\) | ||
0.943402 | − | 0.331652i | \(-0.107606\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.44216e9 | −0.267385 | −0.133693 | − | 0.991023i | \(-0.542683\pi\) | ||||
−0.133693 | + | 0.991023i | \(0.542683\pi\) | |||||||
\(272\) | 5.05678e9 | 0.923843 | ||||||||
\(273\) | 3.03259e9 | + | 2.02624e9i | 0.545964 | + | 0.364787i | ||||
\(274\) | −4.65976e9 | −0.826726 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.85800e9 | + | 5.25035e9i | 1.35418 | + | 0.904798i | ||||
\(277\) | 3.38046e9i | 0.574192i | 0.957902 | + | 0.287096i | \(0.0926899\pi\) | ||||
−0.957902 | + | 0.287096i | \(0.907310\pi\) | |||||||
\(278\) | −3.20289e9 | −0.536245 | ||||||||
\(279\) | −8.82561e8 | − | 2.13048e9i | −0.145656 | − | 0.351609i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.02262e9i | 0.645184i | 0.946538 | + | 0.322592i | \(0.104554\pi\) | ||||
−0.946538 | + | 0.322592i | \(0.895446\pi\) | |||||||
\(282\) | 6.17053e9 | + | 4.12286e9i | 0.975722 | + | 0.651932i | ||||
\(283\) | 1.04253e10i | 1.62533i | 0.582730 | + | 0.812666i | \(0.301984\pi\) | ||||
−0.582730 | + | 0.812666i | \(0.698016\pi\) | |||||||
\(284\) | 4.22146e9i | 0.648917i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.02006e9 | −0.600853 | ||||||||
\(287\) | 3.28207e9 | 0.483749 | ||||||||
\(288\) | 3.69078e9 | + | 8.90943e9i | 0.536473 | + | 1.29503i | ||||
\(289\) | −1.36679e9 | −0.195935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.62720e9 | − | 9.91868e9i | 0.924183 | − | 1.38319i | ||||
\(292\) | − | 6.86285e9i | − | 0.944002i | ||||||
\(293\) | 1.03927e10 | 1.41012 | 0.705061 | − | 0.709146i | \(-0.250919\pi\) | ||||
0.705061 | + | 0.709146i | \(0.250919\pi\) | |||||||
\(294\) | 4.08588e9 | + | 2.72999e9i | 0.546885 | + | 0.365403i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.39796e8i | 0.0312374i | ||||||||
\(297\) | 3.62753e9 | + | 7.21360e8i | 0.466213 | + | 0.0927099i | ||||
\(298\) | − | 1.83918e10i | − | 2.33216i | ||||||
\(299\) | 1.21050e10i | 1.51453i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.17076e9 | 0.751749 | ||||||||
\(302\) | −9.51565e9 | −1.14396 | ||||||||
\(303\) | −4.65951e9 | + | 6.97372e9i | −0.552803 | + | 0.827359i | ||||
\(304\) | 1.27869e9 | 0.149717 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.22185e9 | + | 1.01914e10i | 0.481524 | + | 1.16238i | ||||
\(307\) | − | 2.99309e9i | − | 0.336951i | −0.985706 | − | 0.168476i | \(-0.946116\pi\) | ||
0.985706 | − | 0.168476i | \(-0.0538844\pi\) | |||||||
\(308\) | 3.02042e9 | 0.335632 | ||||||||
\(309\) | 7.47286e9 | − | 1.11843e10i | 0.819696 | − | 1.22681i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.44832e9i | 0.689295i | 0.938732 | + | 0.344647i | \(0.112002\pi\) | ||||
−0.938732 | + | 0.344647i | \(0.887998\pi\) | |||||||
\(312\) | −2.07949e8 | + | 3.11230e8i | −0.0219452 | + | 0.0328445i | ||||
\(313\) | − | 3.27737e7i | − | 0.00341467i | −0.999999 | − | 0.00170733i | \(-0.999457\pi\) | ||
0.999999 | − | 0.00170733i | \(-0.000543462\pi\) | |||||||
\(314\) | 1.70586e10i | 1.75479i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.69928e9 | 0.571573 | ||||||||
\(317\) | 1.17797e10 | 1.16653 | 0.583264 | − | 0.812282i | \(-0.301775\pi\) | ||||
0.583264 | + | 0.812282i | \(0.301775\pi\) | |||||||
\(318\) | −9.98187e9 | − | 6.66942e9i | −0.976120 | − | 0.652198i | ||||
\(319\) | 3.20761e9 | 0.309755 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.51901e9 | − | 1.01493e9i | −0.143067 | − | 0.0955907i | ||||
\(322\) | − | 1.84832e10i | − | 1.71931i | ||||||
\(323\) | 1.41832e9 | 0.130306 | ||||||||
\(324\) | −7.54825e9 | + | 7.54931e9i | −0.684961 | + | 0.685058i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.50002e10i | 1.32808i | ||||||||
\(327\) | −7.40680e9 | − | 4.94888e9i | −0.647798 | − | 0.432829i | ||||
\(328\) | 3.36833e8i | 0.0291018i | ||||||||
\(329\) | − | 7.14182e9i | − | 0.609573i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.20100e10 | −1.00053 | −0.500265 | − | 0.865872i | \(-0.666764\pi\) | ||||
−0.500265 | + | 0.865872i | \(0.666764\pi\) | |||||||
\(332\) | −1.15060e10 | −0.947049 | ||||||||
\(333\) | −8.09311e9 | + | 3.35261e9i | −0.658171 | + | 0.272651i | ||||
\(334\) | 4.40705e9 | 0.354130 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.31720e9 | − | 7.95806e9i | 0.417182 | − | 0.624381i | ||||
\(337\) | 1.59214e10i | 1.23441i | 0.786801 | + | 0.617207i | \(0.211736\pi\) | ||||
−0.786801 | + | 0.617207i | \(0.788264\pi\) | |||||||
\(338\) | −3.45051e9 | −0.264372 | ||||||||
\(339\) | −1.93798e10 | − | 1.29486e10i | −1.46740 | − | 0.980451i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.44611e9i | − | 0.180908i | ||||||
\(342\) | 1.06757e9 | + | 2.57708e9i | 0.0780354 | + | 0.188375i | ||||
\(343\) | − | 1.48174e10i | − | 1.07052i | ||||||
\(344\) | 6.33295e8i | 0.0452243i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.29706e10 | −1.60276 | ||||||||
\(347\) | 4.94792e9 | 0.341275 | 0.170638 | − | 0.985334i | \(-0.445417\pi\) | ||||
0.170638 | + | 0.985334i | \(0.445417\pi\) | |||||||
\(348\) | −5.14361e9 | + | 7.69826e9i | −0.350713 | + | 0.524899i | ||||
\(349\) | 7.29567e9 | 0.491772 | 0.245886 | − | 0.969299i | \(-0.420921\pi\) | ||||
0.245886 | + | 0.969299i | \(0.420921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.34114e10 | − | 2.66695e9i | −0.883578 | − | 0.175706i | ||||
\(352\) | 1.02293e10i | 0.666311i | ||||||||
\(353\) | −6.93875e9 | −0.446871 | −0.223436 | − | 0.974719i | \(-0.571727\pi\) | ||||
−0.223436 | + | 0.974719i | \(0.571727\pi\) | |||||||
\(354\) | 1.38554e10 | − | 2.07369e10i | 0.882282 | − | 1.32048i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 1.80086e10i | − | 1.12119i | ||||||
\(357\) | 5.89782e9 | − | 8.82706e9i | 0.363094 | − | 0.543429i | ||||
\(358\) | − | 2.89368e10i | − | 1.76164i | ||||||
\(359\) | − | 1.60096e10i | − | 0.963838i | −0.876216 | − | 0.481919i | \(-0.839940\pi\) | ||
0.876216 | − | 0.481919i | \(-0.160060\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.66249e10 | −0.978883 | ||||||||
\(362\) | −1.05898e10 | −0.616670 | ||||||||
\(363\) | −1.11750e10 | − | 7.46660e9i | −0.643607 | − | 0.430028i | ||||
\(364\) | −1.11668e10 | −0.636098 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.13945e9 | + | 7.61325e8i | 0.0634994 | + | 0.0424273i | ||||
\(367\) | 1.36364e10i | 0.751686i | 0.926683 | + | 0.375843i | \(0.122647\pi\) | ||||
−0.926683 | + | 0.375843i | \(0.877353\pi\) | |||||||
\(368\) | 3.17655e10 | 1.73207 | ||||||||
\(369\) | −1.13681e10 | + | 4.70930e9i | −0.613173 | + | 0.254010i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.15531e10i | 0.609821i | ||||||||
\(372\) | 5.87065e9 | + | 3.92249e9i | 0.306559 | + | 0.204829i | ||||
\(373\) | 2.44062e10i | 1.26085i | 0.776248 | + | 0.630427i | \(0.217120\pi\) | ||||
−0.776248 | + | 0.630427i | \(0.782880\pi\) | |||||||
\(374\) | 1.17013e10i | 0.598063i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.32953e8 | 0.0366712 | ||||||||
\(377\) | −1.18589e10 | −0.587055 | ||||||||
\(378\) | 2.04780e10 | + | 4.07219e9i | 1.00304 | + | 0.199463i | ||||
\(379\) | 1.98392e10 | 0.961542 | 0.480771 | − | 0.876846i | \(-0.340357\pi\) | ||||
0.480771 | + | 0.876846i | \(0.340357\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.24197e10 | − | 1.85881e10i | 0.589403 | − | 0.882137i | ||||
\(382\) | 3.63211e9i | 0.170571i | ||||||||
\(383\) | −1.51133e10 | −0.702366 | −0.351183 | − | 0.936307i | \(-0.614220\pi\) | ||||
−0.351183 | + | 0.936307i | \(0.614220\pi\) | |||||||
\(384\) | 1.58467e9 | + | 1.05880e9i | 0.0728811 | + | 0.0486957i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 3.56594e10i | − | 1.60630i | ||||||
\(387\) | −2.13737e10 | + | 8.85416e9i | −0.952875 | + | 0.394733i | ||||
\(388\) | 3.65232e10i | 1.61154i | ||||||||
\(389\) | 1.79991e10i | 0.786056i | 0.919527 | + | 0.393028i | \(0.128572\pi\) | ||||
−0.919527 | + | 0.393028i | \(0.871428\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.52342e10 | 1.50750 | ||||||||
\(392\) | 4.85332e8 | 0.0205539 | ||||||||
\(393\) | 1.30103e10 | − | 1.94720e10i | 0.545403 | − | 0.816284i | ||||
\(394\) | −1.20729e10 | −0.500987 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.04618e10 | + | 4.33386e9i | −0.425429 | + | 0.176236i | ||||
\(397\) | − | 2.35673e10i | − | 0.948739i | −0.880326 | − | 0.474370i | \(-0.842676\pi\) | ||
0.880326 | − | 0.474370i | \(-0.157324\pi\) | |||||||
\(398\) | 1.45383e10 | 0.579403 | ||||||||
\(399\) | 1.49137e9 | − | 2.23207e9i | 0.0588428 | − | 0.0880678i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.37692e10i | 0.532515i | 0.963902 | + | 0.266257i | \(0.0857871\pi\) | ||||
−0.963902 | + | 0.266257i | \(0.914213\pi\) | |||||||
\(402\) | −2.29214e9 | + | 3.43056e9i | −0.0877682 | + | 0.131359i | ||||
\(403\) | 9.04353e9i | 0.342861i | ||||||||
\(404\) | − | 2.56791e10i | − | 0.963950i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.81075e10 | 0.666428 | ||||||||
\(407\) | −9.29209e9 | −0.338638 | ||||||||
\(408\) | 9.05906e8 | + | 6.05284e8i | 0.0326921 | + | 0.0218433i | ||||
\(409\) | −3.58480e10 | −1.28107 | −0.640533 | − | 0.767931i | \(-0.721286\pi\) | ||||
−0.640533 | + | 0.767931i | \(0.721286\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.39793e10 | − | 9.34031e9i | −0.489912 | − | 0.327336i | ||||
\(412\) | 4.11838e10i | 1.42934i | ||||||||
\(413\) | −2.40011e10 | −0.824955 | ||||||||
\(414\) | 2.65207e10 | + | 6.40203e10i | 0.902785 | + | 2.17930i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 3.78191e10i | − | 1.26281i | ||||||
\(417\) | −9.60868e9 | − | 6.42007e9i | −0.317775 | − | 0.212322i | ||||
\(418\) | 2.95887e9i | 0.0969217i | ||||||||
\(419\) | − | 2.23996e10i | − | 0.726750i | −0.931643 | − | 0.363375i | \(-0.881624\pi\) | ||
0.931643 | − | 0.363375i | \(-0.118376\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.49535e10 | −0.476008 | −0.238004 | − | 0.971264i | \(-0.576493\pi\) | ||||
−0.238004 | + | 0.971264i | \(0.576493\pi\) | |||||||
\(422\) | −1.30457e9 | −0.0411357 | ||||||||
\(423\) | 1.02475e10 | + | 2.47372e10i | 0.320078 | + | 0.772660i | ||||
\(424\) | −1.18567e9 | −0.0366861 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.71964e10 | + | 2.57373e10i | −0.522156 | + | 0.781491i | ||||
\(427\) | − | 1.31880e9i | − | 0.0396706i | ||||||
\(428\) | 5.59339e9 | 0.166686 | ||||||||
\(429\) | −1.20602e10 | − | 8.05804e9i | −0.356061 | − | 0.237903i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 6.40436e10i | − | 1.85595i | −0.372640 | − | 0.927976i | \(-0.621547\pi\) | ||
0.372640 | − | 0.927976i | \(-0.378453\pi\) | |||||||
\(432\) | −6.99854e9 | + | 3.51938e10i | −0.200943 | + | 1.01049i | ||||
\(433\) | 5.22954e9i | 0.148769i | 0.997230 | + | 0.0743843i | \(0.0236992\pi\) | ||||
−0.997230 | + | 0.0743843i | \(0.976301\pi\) | |||||||
\(434\) | − | 1.38087e10i | − | 0.389218i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.72738e10 | 0.754745 | ||||||||
\(437\) | 8.90959e9 | 0.244305 | ||||||||
\(438\) | 2.79563e10 | − | 4.18412e10i | 0.759598 | − | 1.13686i | ||||
\(439\) | −4.34801e10 | −1.17066 | −0.585332 | − | 0.810793i | \(-0.699036\pi\) | ||||
−0.585332 | + | 0.810793i | \(0.699036\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.78548e9 | + | 1.63800e10i | 0.179402 | + | 0.433070i | ||||
\(442\) | − | 4.32610e10i | − | 1.13346i | ||||||
\(443\) | −3.78737e10 | −0.983383 | −0.491691 | − | 0.870770i | \(-0.663621\pi\) | ||||
−0.491691 | + | 0.870770i | \(0.663621\pi\) | |||||||
\(444\) | 1.49005e10 | − | 2.23010e10i | 0.383415 | − | 0.573843i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.88246e10i | 2.49761i | ||||||||
\(447\) | 3.68656e10 | − | 5.51754e10i | 0.923403 | − | 1.38202i | ||||
\(448\) | 2.74973e10i | 0.682620i | ||||||||
\(449\) | − | 2.95505e10i | − | 0.727076i | −0.931579 | − | 0.363538i | \(-0.881569\pi\) | ||
0.931579 | − | 0.363538i | \(-0.118431\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.30523e10 | −0.315486 | ||||||||
\(452\) | 7.13614e10 | 1.70966 | ||||||||
\(453\) | −2.85469e10 | − | 1.90737e10i | −0.677902 | − | 0.452942i | ||||
\(454\) | 7.93813e10 | 1.86851 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.29074e8 | + | 1.53057e8i | 0.00529806 | + | 0.00353991i | ||||
\(457\) | − | 2.02181e10i | − | 0.463529i | −0.972772 | − | 0.231764i | \(-0.925550\pi\) | ||
0.972772 | − | 0.231764i | \(-0.0744498\pi\) | |||||||
\(458\) | −4.18847e10 | −0.951905 | ||||||||
\(459\) | −7.76277e9 | + | 3.90369e10i | −0.174890 | + | 0.879476i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.01826e10i | 1.55391i | 0.629556 | + | 0.776955i | \(0.283237\pi\) | ||||
−0.629556 | + | 0.776955i | \(0.716763\pi\) | |||||||
\(462\) | 1.84148e10 | + | 1.23039e10i | 0.404202 | + | 0.270069i | ||||
\(463\) | − | 4.16009e9i | − | 0.0905271i | −0.998975 | − | 0.0452635i | \(-0.985587\pi\) | ||
0.998975 | − | 0.0452635i | \(-0.0144128\pi\) | |||||||
\(464\) | 3.11198e10i | 0.671374i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.10935e10 | 1.29554 | ||||||||
\(467\) | −2.88138e10 | −0.605806 | −0.302903 | − | 0.953021i | \(-0.597956\pi\) | ||||
−0.302903 | + | 0.953021i | \(0.597956\pi\) | |||||||
\(468\) | 3.86786e10 | − | 1.60228e10i | 0.806282 | − | 0.334006i | ||||
\(469\) | 3.97056e9 | 0.0820654 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.41933e10 | + | 5.11758e10i | −0.694796 | + | 1.03988i | ||||
\(472\) | − | 2.46319e9i | − | 0.0496283i | ||||||
\(473\) | −2.45402e10 | −0.490268 | ||||||||
\(474\) | 3.47472e10 | + | 2.32165e10i | 0.688346 | + | 0.459921i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.25036e10i | 0.633145i | ||||||||
\(477\) | −1.65770e10 | − | 4.00165e10i | −0.320209 | − | 0.772975i | ||||
\(478\) | − | 5.10649e10i | − | 0.978161i | ||||||
\(479\) | − | 4.47149e10i | − | 0.849395i | −0.905335 | − | 0.424698i | \(-0.860380\pi\) | ||
0.905335 | − | 0.424698i | \(-0.139620\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.43539e10 | 0.641795 | ||||||||
\(482\) | 3.92127e10 | 0.726505 | ||||||||
\(483\) | 3.70488e10 | − | 5.54496e10i | 0.680747 | − | 1.01885i | ||||
\(484\) | 4.11493e10 | 0.749861 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.67727e10 | + | 1.52781e10i | −1.37614 | + | 0.273857i | ||||
\(487\) | 5.72836e10i | 1.01839i | 0.860651 | + | 0.509195i | \(0.170057\pi\) | ||||
−0.860651 | + | 0.509195i | \(0.829943\pi\) | |||||||
\(488\) | 1.35347e8 | 0.00238654 | ||||||||
\(489\) | −3.00672e10 | + | 4.50005e10i | −0.525845 | + | 0.787012i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.25262e10i | − | 1.24787i | −0.781477 | − | 0.623934i | \(-0.785533\pi\) | ||
0.781477 | − | 0.623934i | \(-0.214467\pi\) | |||||||
\(492\) | 2.09302e10 | − | 3.13255e10i | 0.357202 | − | 0.534611i | ||||
\(493\) | 3.45180e10i | 0.584330i | ||||||||
\(494\) | − | 1.09393e10i | − | 0.183688i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.37318e10 | 0.392106 | ||||||||
\(497\) | 2.97885e10 | 0.488228 | ||||||||
\(498\) | −7.01495e10 | − | 4.68706e10i | −1.14053 | − | 0.762050i | ||||
\(499\) | 2.64368e10 | 0.426389 | 0.213195 | − | 0.977010i | \(-0.431613\pi\) | ||||
0.213195 | + | 0.977010i | \(0.431613\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.32212e10 | + | 8.83376e9i | 0.209855 | + | 0.140215i | ||||
\(502\) | − | 3.08797e10i | − | 0.486248i | ||||||
\(503\) | 7.52828e10 | 1.17604 | 0.588022 | − | 0.808845i | \(-0.299907\pi\) | ||||
0.588022 | + | 0.808845i | \(0.299907\pi\) | |||||||
\(504\) | 1.90512e9 | − | 7.89205e8i | 0.0295257 | − | 0.0122312i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.35048e10i | 1.12128i | ||||||||
\(507\) | −1.03515e10 | − | 6.91640e9i | −0.156665 | − | 0.104676i | ||||
\(508\) | 6.84465e10i | 1.02777i | ||||||||
\(509\) | 6.45184e10i | 0.961197i | 0.876941 | + | 0.480599i | \(0.159581\pi\) | ||||
−0.876941 | + | 0.480599i | \(0.840419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.84273e10 | −0.710243 | ||||||||
\(512\) | −9.61394e10 | −1.39901 | ||||||||
\(513\) | −1.96295e9 | + | 9.87115e9i | −0.0283426 | + | 0.142527i | ||||
\(514\) | −1.78179e11 | −2.55272 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.93518e10 | − | 5.88964e10i | 0.555094 | − | 0.830788i | ||||
\(517\) | 2.84019e10i | 0.397544i | ||||||||
\(518\) | −5.24554e10 | −0.728569 | ||||||||
\(519\) | −6.89119e10 | − | 4.60437e10i | −0.949783 | − | 0.634601i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.65146e10i | − | 1.03847i | −0.854632 | − | 0.519235i | \(-0.826217\pi\) | ||
0.854632 | − | 0.519235i | \(-0.173783\pi\) | |||||||
\(522\) | −6.27189e10 | + | 2.59816e10i | −0.844727 | + | 0.349932i | ||||
\(523\) | 8.46771e10i | 1.13177i | 0.824483 | + | 0.565886i | \(0.191466\pi\) | ||||
−0.824483 | + | 0.565886i | \(0.808534\pi\) | |||||||
\(524\) | 7.17012e10i | 0.951046i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.24133e9 | −0.0945966 | ||||||||
\(527\) | 2.63232e10 | 0.341269 | ||||||||
\(528\) | −2.11457e10 | + | 3.16480e10i | −0.272073 | + | 0.407202i | ||||
\(529\) | 1.43023e11 | 1.82634 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.31326e10 | − | 3.44381e10i | 1.04567 | − | 0.433173i | ||||
\(532\) | 8.21909e9i | 0.102607i | ||||||||
\(533\) | 4.82558e10 | 0.597917 | ||||||||
\(534\) | 7.33594e10 | − | 1.09794e11i | 0.902175 | − | 1.35025i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.07492e8i | 0.00493696i | ||||||||
\(537\) | 5.80026e10 | − | 8.68104e10i | 0.697510 | − | 1.04394i | ||||
\(538\) | 7.79717e10i | 0.930696i | ||||||||
\(539\) | 1.88066e10i | 0.222821i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.43470e11 | 1.67483 | 0.837415 | − | 0.546568i | \(-0.184066\pi\) | ||||
0.837415 | + | 0.546568i | \(0.184066\pi\) | |||||||
\(542\) | 3.23765e10 | 0.375174 | ||||||||
\(543\) | −3.17694e10 | − | 2.12268e10i | −0.365434 | − | 0.244166i | ||||
\(544\) | −1.10081e11 | −1.25695 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.80816e10 | − | 4.54889e10i | −0.766053 | − | 0.511841i | ||||
\(547\) | 1.64171e11i | 1.83378i | 0.399134 | + | 0.916892i | \(0.369311\pi\) | ||||
−0.399134 | + | 0.916892i | \(0.630689\pi\) | |||||||
\(548\) | 5.14755e10 | 0.570792 | ||||||||
\(549\) | 1.89229e9 | + | 4.56795e9i | 0.0208305 | + | 0.0502842i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.72847e9i | 0.0946961i | ||||||||
\(552\) | 5.69070e9 | + | 3.80226e9i | 0.0612928 | + | 0.0409529i | ||||
\(553\) | − | 4.02167e10i | − | 0.430037i | ||||||
\(554\) | − | 7.58912e10i | − | 0.805661i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.53817e10 | 0.370237 | ||||||||
\(557\) | −1.54420e11 | −1.60429 | −0.802145 | − | 0.597130i | \(-0.796308\pi\) | ||||
−0.802145 | + | 0.597130i | \(0.796308\pi\) | |||||||
\(558\) | 1.98135e10 | + | 4.78291e10i | 0.204373 | + | 0.493351i | ||||
\(559\) | 9.07278e10 | 0.929166 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.34547e10 | + | 3.51039e10i | −0.236799 | + | 0.354408i | ||||
\(562\) | − | 9.03075e10i | − | 0.905271i | ||||||
\(563\) | 1.54622e11 | 1.53900 | 0.769500 | − | 0.638646i | \(-0.220505\pi\) | ||||
0.769500 | + | 0.638646i | \(0.220505\pi\) | |||||||
\(564\) | −6.81646e10 | − | 4.55444e10i | −0.673663 | − | 0.450110i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 2.34047e11i | − | 2.28054i | ||||||
\(567\) | 5.32714e10 | + | 5.32638e10i | 0.515420 | + | 0.515348i | ||||
\(568\) | 3.05714e9i | 0.0293712i | ||||||||
\(569\) | 1.15380e11i | 1.10073i | 0.834925 | + | 0.550364i | \(0.185511\pi\) | ||||
−0.834925 | + | 0.550364i | \(0.814489\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.63410e11 | −1.53722 | −0.768608 | − | 0.639720i | \(-0.779050\pi\) | ||||
−0.768608 | + | 0.639720i | \(0.779050\pi\) | |||||||
\(572\) | 4.44087e10 | 0.414844 | ||||||||
\(573\) | −7.28041e9 | + | 1.08963e10i | −0.0675363 | + | 0.101079i | ||||
\(574\) | −7.36823e10 | −0.678759 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.94548e10 | − | 9.52427e10i | −0.358434 | − | 0.865250i | ||||
\(577\) | 7.42282e10i | 0.669678i | 0.942275 | + | 0.334839i | \(0.108682\pi\) | ||||
−0.942275 | + | 0.334839i | \(0.891318\pi\) | |||||||
\(578\) | 3.06844e10 | 0.274920 | ||||||||
\(579\) | 7.14779e10 | − | 1.06978e11i | 0.636001 | − | 0.951879i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.11916e10i | 0.712535i | ||||||||
\(582\) | −1.48780e11 | + | 2.22674e11i | −1.29674 | + | 1.94078i | ||||
\(583\) | − | 4.59449e10i | − | 0.397707i | ||||||
\(584\) | − | 4.97002e9i | − | 0.0427274i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.33315e11 | −1.97857 | ||||||||
\(587\) | 6.72877e10 | 0.566739 | 0.283369 | − | 0.959011i | \(-0.408548\pi\) | ||||
0.283369 | + | 0.959011i | \(0.408548\pi\) | |||||||
\(588\) | −4.51359e10 | − | 3.01577e10i | −0.377583 | − | 0.252283i | ||||
\(589\) | 6.65629e9 | 0.0553059 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.62187e10 | − | 2.41996e10i | −0.296881 | − | 0.198362i | ||||
\(592\) | − | 9.01507e10i | − | 0.733977i | ||||||
\(593\) | −2.36444e10 | −0.191210 | −0.0956048 | − | 0.995419i | \(-0.530479\pi\) | ||||
−0.0956048 | + | 0.995419i | \(0.530479\pi\) | |||||||
\(594\) | −8.14378e10 | − | 1.61945e10i | −0.654154 | − | 0.130083i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.03170e11i | 1.61018i | ||||||||
\(597\) | 4.36148e10 | + | 2.91414e10i | 0.343350 | + | 0.229410i | ||||
\(598\) | − | 2.71756e11i | − | 2.12507i | ||||||
\(599\) | − | 3.03370e10i | − | 0.235649i | −0.993034 | − | 0.117825i | \(-0.962408\pi\) | ||
0.993034 | − | 0.117825i | \(-0.0375921\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.37911e10 | 0.259003 | 0.129501 | − | 0.991579i | \(-0.458662\pi\) | ||||
0.129501 | + | 0.991579i | \(0.458662\pi\) | |||||||
\(602\) | −1.38533e11 | −1.05480 | ||||||||
\(603\) | −1.37528e10 | + | 5.69718e9i | −0.104022 | + | 0.0430914i | ||||
\(604\) | 1.05117e11 | 0.789818 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.04606e11 | − | 1.56560e11i | 0.775649 | − | 1.16089i | ||||
\(607\) | − | 3.82366e10i | − | 0.281660i | −0.990034 | − | 0.140830i | \(-0.955023\pi\) | ||
0.990034 | − | 0.140830i | \(-0.0449771\pi\) | |||||||
\(608\) | −2.78359e10 | −0.203700 | ||||||||
\(609\) | 5.43224e10 | + | 3.62957e10i | 0.394920 | + | 0.263867i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.05005e11i | − | 0.753435i | ||||||
\(612\) | −4.66380e10 | − | 1.12583e11i | −0.332456 | − | 0.802539i | ||||
\(613\) | − | 1.08066e11i | − | 0.765330i | −0.923887 | − | 0.382665i | \(-0.875006\pi\) | ||
0.923887 | − | 0.382665i | \(-0.124994\pi\) | |||||||
\(614\) | 6.71948e10i | 0.472783i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.18736e9 | 0.0151914 | ||||||||
\(617\) | 4.72538e9 | 0.0326059 | 0.0163029 | − | 0.999867i | \(-0.494810\pi\) | ||||
0.0163029 | + | 0.999867i | \(0.494810\pi\) | |||||||
\(618\) | −1.67765e11 | + | 2.51088e11i | −1.15013 | + | 1.72136i | ||||
\(619\) | −2.29845e10 | −0.156557 | −0.0782786 | − | 0.996932i | \(-0.524942\pi\) | ||||
−0.0782786 | + | 0.996932i | \(0.524942\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.87639e10 | + | 2.45221e11i | −0.327893 | + | 1.64889i | ||||
\(622\) | − | 1.44764e11i | − | 0.967165i | ||||||
\(623\) | −1.27077e11 | −0.843555 | ||||||||
\(624\) | 7.81780e10 | − | 1.17006e11i | 0.515640 | − | 0.771739i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.35768e8i | 0.00479119i | ||||||||
\(627\) | −5.93094e9 | + | 8.87662e9i | −0.0383754 | + | 0.0574351i | ||||
\(628\) | − | 1.88443e11i | − | 1.21155i | ||||||
\(629\) | − | 9.99949e10i | − | 0.638815i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.01892e11 | −0.642722 | −0.321361 | − | 0.946957i | \(-0.604140\pi\) | ||||
−0.321361 | + | 0.946957i | \(0.604140\pi\) | |||||||
\(632\) | 4.12737e9 | 0.0258705 | ||||||||
\(633\) | −3.91372e9 | − | 2.61497e9i | −0.0243767 | − | 0.0162874i | ||||
\(634\) | −2.64453e11 | −1.63678 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.10268e11 | + | 7.36757e10i | 0.673938 | + | 0.450294i | ||||
\(637\) | − | 6.95302e10i | − | 0.422295i | ||||||
\(638\) | −7.20106e10 | −0.434624 | ||||||||
\(639\) | −1.03179e11 | + | 4.27422e10i | −0.618851 | + | 0.256362i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.17803e11i | 0.697791i | 0.937162 | + | 0.348896i | \(0.113443\pi\) | ||||
−0.937162 | + | 0.348896i | \(0.886557\pi\) | |||||||
\(642\) | 3.41016e10 | + | 2.27851e10i | 0.200740 | + | 0.134125i | ||||
\(643\) | 2.62680e10i | 0.153668i | 0.997044 | + | 0.0768339i | \(0.0244811\pi\) | ||||
−0.997044 | + | 0.0768339i | \(0.975519\pi\) | |||||||
\(644\) | 2.04180e11i | 1.18705i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.18413e10 | −0.182836 | ||||||||
\(647\) | −3.10527e11 | −1.77208 | −0.886038 | − | 0.463612i | \(-0.846553\pi\) | ||||
−0.886038 | + | 0.463612i | \(0.846553\pi\) | |||||||
\(648\) | −5.46638e9 | + | 5.46715e9i | −0.0310027 | + | 0.0310071i | ||||
\(649\) | 9.54486e10 | 0.538010 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.76789e10 | − | 4.14260e10i | 0.154108 | − | 0.230648i | ||||
\(652\) | − | 1.65704e11i | − | 0.916942i | ||||||
\(653\) | 3.48345e10 | 0.191583 | 0.0957914 | − | 0.995401i | \(-0.469462\pi\) | ||||
0.0957914 | + | 0.995401i | \(0.469462\pi\) | |||||||
\(654\) | 1.66282e11 | + | 1.11102e11i | 0.908940 | + | 0.607311i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.26632e11i | − | 0.683796i | ||||||
\(657\) | 1.67738e11 | − | 6.94863e10i | 0.900265 | − | 0.372939i | ||||
\(658\) | 1.60333e11i | 0.855304i | ||||||||
\(659\) | − | 3.77120e10i | − | 0.199957i | −0.994990 | − | 0.0999787i | \(-0.968123\pi\) | ||
0.994990 | − | 0.0999787i | \(-0.0318775\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.39619e11 | −0.731372 | −0.365686 | − | 0.930738i | \(-0.619166\pi\) | ||||
−0.365686 | + | 0.930738i | \(0.619166\pi\) | |||||||
\(662\) | 2.69623e11 | 1.40386 | ||||||||
\(663\) | 8.67149e10 | − | 1.29783e11i | 0.448786 | − | 0.671682i | ||||
\(664\) | −8.33256e9 | −0.0428653 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.81690e11 | − | 7.52659e10i | 0.923494 | − | 0.382562i | ||||
\(667\) | 2.16834e11i | 1.09553i | ||||||||
\(668\) | −4.86838e10 | −0.244500 | ||||||||
\(669\) | −1.98090e11 | + | 2.96474e11i | −0.988912 | + | 1.48007i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.24468e9i | 0.0258719i | ||||||||
\(672\) | −1.15750e11 | + | 1.73239e11i | −0.567603 | + | 0.849510i | ||||
\(673\) | 1.29783e11i | 0.632642i | 0.948652 | + | 0.316321i | \(0.102448\pi\) | ||||
−0.948652 | + | 0.316321i | \(0.897552\pi\) | |||||||
\(674\) | − | 3.57434e11i | − | 1.73203i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.81171e10 | 0.182529 | ||||||||
\(677\) | 3.40648e11 | 1.62163 | 0.810813 | − | 0.585306i | \(-0.199025\pi\) | ||||
0.810813 | + | 0.585306i | \(0.199025\pi\) | |||||||
\(678\) | 4.35075e11 | + | 2.90696e11i | 2.05895 | + | 1.37569i | ||||
\(679\) | 2.57724e11 | 1.21248 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.38144e11 | + | 1.59117e11i | 1.10726 | + | 0.739821i | ||||
\(682\) | 5.49149e10i | 0.253836i | ||||||||
\(683\) | 1.02876e11 | 0.472750 | 0.236375 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236375 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(684\) | −1.17932e10 | − | 2.84685e10i | −0.0538776 | − | 0.130059i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.32650e11i | 1.50208i | ||||||||
\(687\) | −1.25654e11 | − | 8.39562e10i | −0.564092 | − | 0.376900i | ||||
\(688\) | − | 2.38086e11i | − | 1.06262i | ||||||
\(689\) | 1.69863e11i | 0.753742i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.58259e11 | 1.57140 | 0.785698 | − | 0.618611i | \(-0.212304\pi\) | ||||
0.785698 | + | 0.618611i | \(0.212304\pi\) | |||||||
\(692\) | 2.53752e11 | 1.10659 | ||||||||
\(693\) | 3.05817e10 | + | 7.38234e10i | 0.132595 | + | 0.320082i | ||||
\(694\) | −1.11081e11 | −0.478851 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.72496e9 | + | 5.57501e9i | −0.0158740 | + | 0.0237580i | ||||
\(697\) | − | 1.40459e11i | − | 0.595141i | ||||||
\(698\) | −1.63787e11 | −0.690016 | ||||||||
\(699\) | 1.83280e11 | + | 1.22459e11i | 0.767728 | + | 0.512960i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.49323e11i | − | 1.03250i | −0.856438 | − | 0.516250i | \(-0.827327\pi\) | ||
0.856438 | − | 0.516250i | \(-0.172673\pi\) | |||||||
\(702\) | 3.01085e11 | + | 5.98729e10i | 1.23977 | + | 0.246537i | ||||
\(703\) | − | 2.52854e10i | − | 0.103526i | ||||||
\(704\) | − | 1.09353e11i | − | 0.445183i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.55775e11 | 0.627015 | ||||||||
\(707\) | −1.81203e11 | −0.725251 | ||||||||
\(708\) | −1.53058e11 | + | 2.29077e11i | −0.609149 | + | 0.911691i | ||||
\(709\) | 3.88874e11 | 1.53895 | 0.769474 | − | 0.638678i | \(-0.220518\pi\) | ||||
0.769474 | + | 0.638678i | \(0.220518\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.77052e10 | + | 1.39299e11i | 0.225807 | + | 0.545091i | ||||
\(712\) | − | 1.30417e10i | − | 0.0507473i | ||||||
\(713\) | 1.65357e11 | 0.639829 | ||||||||
\(714\) | −1.32406e11 | + | 1.98167e11i | −0.509465 | + | 0.762497i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.19659e11i | 1.21628i | ||||||||
\(717\) | 1.02357e11 | − | 1.53195e11i | 0.387296 | − | 0.579651i | ||||
\(718\) | 3.59416e11i | 1.35238i | ||||||||
\(719\) | − | 3.35735e10i | − | 0.125626i | −0.998025 | − | 0.0628132i | \(-0.979993\pi\) | ||
0.998025 | − | 0.0628132i | \(-0.0200072\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.90611e11 | 1.07540 | ||||||||
\(722\) | 3.73228e11 | 1.37349 | ||||||||
\(723\) | 1.17638e11 | + | 7.86002e10i | 0.430521 | + | 0.287654i | ||||
\(724\) | 1.16983e11 | 0.425764 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.50878e11 | + | 1.67625e11i | 0.903058 | + | 0.603381i | ||||
\(727\) | 2.53113e11i | 0.906102i | 0.891485 | + | 0.453051i | \(0.149664\pi\) | ||||
−0.891485 | + | 0.453051i | \(0.850336\pi\) | |||||||
\(728\) | −8.08692e9 | −0.0287911 | ||||||||
\(729\) | −2.60942e11 | − | 1.08053e11i | −0.923920 | − | 0.382586i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.64084e11i | − | 0.924853i | ||||||
\(732\) | −1.25872e10 | − | 8.41020e9i | −0.0438416 | − | 0.0292929i | ||||
\(733\) | − | 2.07602e11i | − | 0.719144i | −0.933117 | − | 0.359572i | \(-0.882923\pi\) | ||
0.933117 | − | 0.359572i | \(-0.117077\pi\) | |||||||
\(734\) | − | 3.06137e11i | − | 1.05471i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.91504e11 | −2.35659 | ||||||||
\(737\) | −1.57903e10 | −0.0535205 | ||||||||
\(738\) | 2.55214e11 | − | 1.05724e11i | 0.860357 | − | 0.356407i | ||||
\(739\) | −4.15014e11 | −1.39151 | −0.695753 | − | 0.718281i | \(-0.744929\pi\) | ||||
−0.695753 | + | 0.718281i | \(0.744929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.19274e10 | − | 3.28179e10i | 0.0727300 | − | 0.108852i | ||||
\(742\) | − | 2.59366e11i | − | 0.855653i | ||||||
\(743\) | −3.30690e11 | −1.08509 | −0.542545 | − | 0.840027i | \(-0.682539\pi\) | ||||
−0.542545 | + | 0.840027i | \(0.682539\pi\) | |||||||
\(744\) | 4.25148e9 | + | 2.84064e9i | 0.0138755 | + | 0.00927095i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 5.47918e11i | − | 1.76913i | ||||||
\(747\) | −1.16498e11 | − | 2.81224e11i | −0.374143 | − | 0.903170i | ||||
\(748\) | − | 1.29262e11i | − | 0.412918i | ||||||
\(749\) | − | 3.94695e10i | − | 0.125411i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.77978e11 | −1.50262 | −0.751308 | − | 0.659952i | \(-0.770577\pi\) | ||||
−0.751308 | + | 0.659952i | \(0.770577\pi\) | |||||||
\(752\) | −2.75552e11 | −0.861652 | ||||||||
\(753\) | 6.18970e10 | − | 9.26390e10i | 0.192526 | − | 0.288147i | ||||
\(754\) | 2.66231e11 | 0.823709 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.26216e11 | − | 4.49847e10i | −0.692526 | − | 0.137714i | ||||
\(757\) | − | 8.95066e10i | − | 0.272566i | −0.990670 | − | 0.136283i | \(-0.956484\pi\) | ||
0.990670 | − | 0.136283i | \(-0.0435156\pi\) | |||||||
\(758\) | −4.45390e11 | −1.34916 | ||||||||
\(759\) | −1.47337e11 | + | 2.20514e11i | −0.443962 | + | 0.664462i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.71473e11i | 1.70395i | 0.523581 | + | 0.851976i | \(0.324596\pi\) | ||||
−0.523581 | + | 0.851976i | \(0.675404\pi\) | |||||||
\(762\) | −2.78822e11 | + | 4.17303e11i | −0.827004 | + | 1.23775i | ||||
\(763\) | − | 1.92456e11i | − | 0.567851i | ||||||
\(764\) | − | 4.01231e10i | − | 0.117766i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.39292e11 | 0.985504 | ||||||||
\(767\) | −3.52884e11 | −1.01965 | ||||||||
\(768\) | −3.06488e11 | − | 2.04781e11i | −0.880986 | − | 0.588634i | ||||
\(769\) | −2.56194e11 | −0.732596 | −0.366298 | − | 0.930498i | \(-0.619375\pi\) | ||||
−0.366298 | + | 0.930498i | \(0.619375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.34537e11 | − | 3.57152e11i | −1.51273 | − | 1.01073i | ||||
\(772\) | 3.93923e11i | 1.10903i | ||||||||
\(773\) | −1.00523e11 | −0.281543 | −0.140772 | − | 0.990042i | \(-0.544958\pi\) |