Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,9,Mod(8,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.8");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.f (of order \(18\), degree \(6\), 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: | \(32.9976674150\) |
Analytic rank: | \(0\) |
Dimension: | \(138\) |
Relative dimension: | \(23\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 8.12 | ||
Character | \(\chi\) | \(=\) | 81.8 |
Dual form | 81.9.f.a.71.12 |
$q$-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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.46646 | + | 0.434904i | 0.154154 | + | 0.0271815i | 0.250193 | − | 0.968196i | \(-0.419506\pi\) |
−0.0960385 | + | 0.995378i | \(0.530617\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −234.667 | − | 85.4118i | −0.916668 | − | 0.333640i | ||||
\(5\) | 411.949 | + | 490.942i | 0.659119 | + | 0.785508i | 0.987259 | − | 0.159122i | \(-0.0508662\pi\) |
−0.328140 | + | 0.944629i | \(0.606422\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 243.334 | − | 88.5664i | 0.101347 | − | 0.0368873i | −0.290849 | − | 0.956769i | \(-0.593938\pi\) |
0.392196 | + | 0.919882i | \(0.371715\pi\) | |||||||
\(8\) | −1096.91 | − | 633.301i | −0.267800 | − | 0.154614i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 802.546 | + | 1390.05i | 0.0802546 | + | 0.139005i | ||||
\(11\) | −4355.96 | + | 5191.23i | −0.297518 | + | 0.354568i | −0.894007 | − | 0.448053i | \(-0.852118\pi\) |
0.596489 | + | 0.802621i | \(0.296562\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −733.507 | − | 4159.93i | −0.0256821 | − | 0.145651i | 0.969270 | − | 0.245998i | \(-0.0791157\pi\) |
−0.994952 | + | 0.100347i | \(0.968005\pi\) | |||||||
\(14\) | 638.693 | − | 112.619i | 0.0166257 | − | 0.00293156i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 46543.3 | + | 39054.5i | 0.710195 | + | 0.595924i | ||||
\(17\) | 27580.9 | − | 15923.8i | 0.330227 | − | 0.190656i | −0.325715 | − | 0.945468i | \(-0.605605\pi\) |
0.655942 | + | 0.754812i | \(0.272272\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −31761.5 | + | 55012.5i | −0.243717 | + | 0.422131i | −0.961770 | − | 0.273858i | \(-0.911700\pi\) |
0.718053 | + | 0.695989i | \(0.245034\pi\) | |||||||
\(20\) | −54738.7 | − | 150393.i | −0.342117 | − | 0.939958i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −13001.5 | + | 10909.6i | −0.0555013 | + | 0.0465711i | ||||
\(23\) | 67576.8 | − | 185666.i | 0.241483 | − | 0.663469i | −0.758448 | − | 0.651733i | \(-0.774042\pi\) |
0.999931 | − | 0.0117355i | \(-0.00373562\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3490.62 | + | 19796.3i | −0.00893599 | + | 0.0506785i | ||||
\(26\) | − | 10579.3i | − | 0.0231507i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −64667.1 | −0.105209 | ||||||||
\(29\) | −1.01674e6 | − | 179279.i | −1.43753 | − | 0.253476i | −0.600061 | − | 0.799954i | \(-0.704857\pi\) |
−0.837474 | + | 0.546478i | \(0.815968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.67239e6 | − | 608702.i | −1.81089 | − | 0.659110i | −0.996940 | − | 0.0781752i | \(-0.975091\pi\) |
−0.813950 | − | 0.580935i | \(-0.802687\pi\) | |||||||
\(32\) | 306236. | + | 364958.i | 0.292050 | + | 0.348051i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 74952.5 | − | 27280.5i | 0.0560881 | − | 0.0204144i | ||||
\(35\) | 143722. | + | 82978.2i | 0.0957750 | + | 0.0552957i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −711454. | − | 1.23227e6i | −0.379612 | − | 0.657507i | 0.611394 | − | 0.791327i | \(-0.290609\pi\) |
−0.991006 | + | 0.133819i | \(0.957276\pi\) | |||||||
\(38\) | −102264. | + | 121873.i | −0.0490442 | + | 0.0584486i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −140957. | − | 799407.i | −0.0550613 | − | 0.312268i | ||||
\(41\) | −47826.5 | + | 8433.11i | −0.0169252 | + | 0.00298437i | −0.182104 | − | 0.983279i | \(-0.558291\pi\) |
0.165179 | + | 0.986264i | \(0.447180\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 670492. | + | 562610.i | 0.196119 | + | 0.164564i | 0.735559 | − | 0.677461i | \(-0.236920\pi\) |
−0.539440 | + | 0.842024i | \(0.681364\pi\) | |||||||
\(44\) | 1.46559e6 | − | 846160.i | 0.391023 | − | 0.225757i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 247423. | − | 428549.i | 0.0552597 | − | 0.0957125i | ||||
\(47\) | −2.11724e6 | − | 5.81707e6i | −0.433889 | − | 1.19210i | −0.943406 | − | 0.331639i | \(-0.892398\pi\) |
0.509517 | − | 0.860460i | \(-0.329824\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.36473e6 | + | 3.66244e6i | −0.757134 | + | 0.635311i | ||||
\(50\) | −17219.0 | + | 47308.8i | −0.00275504 | + | 0.00756941i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −183177. | + | 1.03885e6i | −0.0250529 | + | 0.142082i | ||||
\(53\) | − | 9.95902e6i | − | 1.26216i | −0.775719 | − | 0.631078i | \(-0.782613\pi\) | ||
0.775719 | − | 0.631078i | \(-0.217387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.34303e6 | −0.474616 | ||||||||
\(56\) | −323005. | − | 56954.4i | −0.0328440 | − | 0.00579129i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.42979e6 | − | 884370.i | −0.214712 | − | 0.0781487i | ||||
\(59\) | −9.92151e6 | − | 1.18240e7i | −0.818785 | − | 0.975790i | 0.181186 | − | 0.983449i | \(-0.442006\pi\) |
−0.999971 | + | 0.00765928i | \(0.997562\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00776e7 | + | 7.30764e6i | −1.45008 | + | 0.527786i | −0.942613 | − | 0.333886i | \(-0.891640\pi\) |
−0.507466 | + | 0.861672i | \(0.669418\pi\) | |||||||
\(62\) | −3.86018e6 | − | 2.22867e6i | −0.261240 | − | 0.150827i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.18042e6 | − | 1.24369e7i | −0.427987 | − | 0.741295i | ||||
\(65\) | 1.74012e6 | − | 2.07379e6i | 0.0974821 | − | 0.116175i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.15182e6 | + | 1.22036e7i | 0.106784 | + | 0.605602i | 0.990493 | + | 0.137565i | \(0.0439276\pi\) |
−0.883709 | + | 0.468037i | \(0.844961\pi\) | |||||||
\(68\) | −7.83240e6 | + | 1.38106e6i | −0.366319 | + | 0.0645919i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 318399. | + | 267168.i | 0.0132611 | + | 0.0111274i | ||||
\(71\) | 2.36946e6 | − | 1.36801e6i | 0.0932429 | − | 0.0538338i | −0.452654 | − | 0.891686i | \(-0.649523\pi\) |
0.545896 | + | 0.837853i | \(0.316189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 874977. | − | 1.51550e6i | 0.0308109 | − | 0.0533661i | −0.850209 | − | 0.526446i | \(-0.823524\pi\) |
0.881020 | + | 0.473080i | \(0.156858\pi\) | |||||||
\(74\) | −1.21886e6 | − | 3.34878e6i | −0.0406467 | − | 0.111676i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.21521e7 | − | 1.01968e7i | 0.364248 | − | 0.305640i | ||||
\(77\) | −600185. | + | 1.64900e6i | −0.0170735 | + | 0.0469091i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.53737e6 | − | 4.27466e7i | 0.193514 | − | 1.09747i | −0.721006 | − | 0.692929i | \(-0.756320\pi\) |
0.914520 | − | 0.404542i | \(-0.132569\pi\) | |||||||
\(80\) | 3.89386e7i | 0.950648i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −121630. | −0.00269020 | ||||||||
\(83\) | 5.86063e7 | + | 1.03339e7i | 1.23490 | + | 0.217746i | 0.752729 | − | 0.658330i | \(-0.228737\pi\) |
0.482172 | + | 0.876077i | \(0.339848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.91796e7 | + | 6.98080e6i | 0.367421 | + | 0.133730i | ||||
\(86\) | 1.40906e6 | + | 1.67926e6i | 0.0257595 | + | 0.0306990i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.06570e6 | − | 2.93568e6i | 0.134497 | − | 0.0489528i | ||||
\(89\) | 3.32007e7 | + | 1.91684e7i | 0.529161 | + | 0.305511i | 0.740675 | − | 0.671864i | \(-0.234506\pi\) |
−0.211514 | + | 0.977375i | \(0.567839\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −546917. | − | 947288.i | −0.00797547 | − | 0.0138139i | ||||
\(92\) | −3.17161e7 | + | 3.77978e7i | −0.442719 | + | 0.527612i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.69223e6 | − | 1.52684e7i | −0.0344826 | − | 0.195561i | ||||
\(95\) | −4.00921e7 | + | 7.06932e6i | −0.492226 | + | 0.0867927i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.06250e8 | + | 8.91546e7i | 1.20017 | + | 1.00706i | 0.999625 | + | 0.0273787i | \(0.00871601\pi\) |
0.200546 | + | 0.979684i | \(0.435728\pi\) | |||||||
\(98\) | −1.23583e7 | + | 7.13504e6i | −0.133984 | + | 0.0773557i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.50997e6 | − | 4.34740e6i | 0.0250997 | − | 0.0434740i | ||||
\(101\) | −4.55685e7 | − | 1.25198e8i | −0.437904 | − | 1.20313i | −0.940853 | − | 0.338816i | \(-0.889974\pi\) |
0.502949 | − | 0.864316i | \(-0.332249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.13908e7 | + | 7.66860e7i | −0.811995 | + | 0.681345i | −0.951083 | − | 0.308935i | \(-0.900027\pi\) |
0.139088 | + | 0.990280i | \(0.455583\pi\) | |||||||
\(104\) | −1.82989e6 | + | 5.02759e6i | −0.0156420 | + | 0.0429761i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.33122e6 | − | 2.45636e7i | 0.0343073 | − | 0.194567i | ||||
\(107\) | 1.15116e8i | 0.878216i | 0.898434 | + | 0.439108i | \(0.144705\pi\) | ||||
−0.898434 | + | 0.439108i | \(0.855295\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.18734e7 | 0.225799 | 0.112900 | − | 0.993606i | \(-0.463986\pi\) | ||||
0.112900 | + | 0.993606i | \(0.463986\pi\) | |||||||
\(110\) | −1.07119e7 | − | 1.88880e6i | −0.0731639 | − | 0.0129008i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.47845e7 | + | 5.38112e6i | 0.0939582 | + | 0.0341980i | ||||
\(113\) | 4.45785e7 | + | 5.31266e7i | 0.273408 | + | 0.325835i | 0.885224 | − | 0.465165i | \(-0.154005\pi\) |
−0.611816 | + | 0.791000i | \(0.709561\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.18989e8 | − | 4.33086e7i | 0.680326 | − | 0.247618i | ||||
\(116\) | 2.23283e8 | + | 1.28913e8i | 1.23317 | + | 0.711972i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.93287e7 | − | 3.34784e7i | −0.0996955 | − | 0.172678i | ||||
\(119\) | 5.30105e6 | − | 6.31755e6i | 0.0264347 | − | 0.0315036i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.92485e7 | + | 1.65877e8i | 0.136447 | + | 0.773827i | ||||
\(122\) | −5.26987e7 | + | 9.29221e6i | −0.237882 | + | 0.0419449i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.40466e8 | + | 2.85685e8i | 1.44008 | + | 1.20837i | ||||
\(125\) | 2.05647e8 | − | 1.18730e8i | 0.842331 | − | 0.486320i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.33645e8 | − | 4.04684e8i | 0.898133 | − | 1.55561i | 0.0682548 | − | 0.997668i | \(-0.478257\pi\) |
0.829878 | − | 0.557944i | \(-0.188410\pi\) | |||||||
\(128\) | −5.40153e7 | − | 1.48406e8i | −0.201223 | − | 0.552855i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.19383e6 | − | 4.35814e6i | 0.0181851 | − | 0.0152591i | ||||
\(131\) | −1.80234e8 | + | 4.95187e8i | −0.611998 | + | 1.68145i | 0.113765 | + | 0.993508i | \(0.463709\pi\) |
−0.725763 | + | 0.687944i | \(0.758513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.85640e6 | + | 1.61994e7i | −0.00912876 | + | 0.0517718i | ||||
\(134\) | 3.10355e7i | 0.0962586i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.03382e7 | −0.117913 | ||||||||
\(137\) | 3.13130e8 | + | 5.52133e7i | 0.888879 | + | 0.156733i | 0.599399 | − | 0.800451i | \(-0.295406\pi\) |
0.289480 | + | 0.957184i | \(0.406518\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.17739e8 | − | 1.88442e8i | −1.38692 | − | 0.504798i | −0.462652 | − | 0.886540i | \(-0.653102\pi\) |
−0.924269 | + | 0.381742i | \(0.875324\pi\) | |||||||
\(140\) | −2.66396e7 | − | 3.17478e7i | −0.0693450 | − | 0.0826422i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.43914e6 | − | 2.34365e6i | 0.0158370 | − | 0.00576421i | ||||
\(143\) | 2.47903e7 | + | 1.43127e7i | 0.0592839 | + | 0.0342276i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.30830e8 | − | 5.73015e8i | −0.748399 | − | 1.29627i | ||||
\(146\) | 2.81720e6 | − | 3.35741e6i | 0.00620020 | − | 0.00738912i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.17040e7 | + | 3.49941e8i | 0.128608 | + | 0.729370i | ||||
\(149\) | −6.98309e8 | + | 1.23131e8i | −1.41678 | + | 0.249817i | −0.829021 | − | 0.559218i | \(-0.811101\pi\) |
−0.587761 | + | 0.809035i | \(0.699990\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.61562e8 | − | 2.19476e8i | −0.503114 | − | 0.422163i | 0.355584 | − | 0.934644i | \(-0.384282\pi\) |
−0.858698 | + | 0.512481i | \(0.828726\pi\) | |||||||
\(152\) | 6.96789e7 | − | 4.02291e7i | 0.130535 | − | 0.0753644i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.19749e6 | + | 3.80617e6i | −0.00390701 | + | 0.00676714i | ||||
\(155\) | −3.90105e8 | − | 1.07180e9i | −0.675856 | − | 1.85690i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.89517e8 | + | 5.78573e8i | −1.13487 | + | 0.952269i | −0.999259 | − | 0.0384927i | \(-0.987744\pi\) |
−0.135612 | + | 0.990762i | \(0.543300\pi\) | |||||||
\(158\) | 3.71813e7 | − | 1.02155e8i | 0.0596618 | − | 0.163920i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.30195e7 | + | 3.00689e8i | −0.0809014 | + | 0.458815i | ||||
\(161\) | − | 5.11639e7i | − | 0.0761483i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.07912e8 | −0.719512 | −0.359756 | − | 0.933046i | \(-0.617140\pi\) | ||||
−0.359756 | + | 0.933046i | \(0.617140\pi\) | |||||||
\(164\) | 1.19436e7 | + | 2.10598e6i | 0.0165105 | + | 0.00291124i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.40056e8 | + | 5.09763e7i | 0.184446 | + | 0.0671330i | ||||
\(167\) | −5.64103e8 | − | 6.72272e8i | −0.725258 | − | 0.864329i | 0.269872 | − | 0.962896i | \(-0.413019\pi\) |
−0.995130 | + | 0.0985671i | \(0.968574\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.49769e8 | − | 2.72894e8i | 0.919138 | − | 0.334539i | ||||
\(170\) | 4.42698e7 | + | 2.55592e7i | 0.0530044 | + | 0.0306021i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.09289e8 | − | 1.89294e8i | −0.124871 | − | 0.216283i | ||||
\(173\) | 9.08559e8 | − | 1.08278e9i | 1.01430 | − | 1.20880i | 0.0364893 | − | 0.999334i | \(-0.488383\pi\) |
0.977816 | − | 0.209467i | \(-0.0671730\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 903900. | + | 5.12627e6i | 0.000963758 | + | 0.00546574i | ||||
\(176\) | −4.05482e8 | + | 7.14974e7i | −0.422591 | + | 0.0745143i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.35520e7 | + | 6.17174e7i | 0.0732680 | + | 0.0614792i | ||||
\(179\) | 1.09594e8 | − | 6.32741e7i | 0.106752 | − | 0.0616330i | −0.445674 | − | 0.895196i | \(-0.647036\pi\) |
0.552425 | + | 0.833562i | \(0.313702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.30450e8 | + | 3.99152e8i | −0.214715 | + | 0.371898i | −0.953185 | − | 0.302389i | \(-0.902216\pi\) |
0.738469 | + | 0.674287i | \(0.235549\pi\) | |||||||
\(182\) | −936972. | − | 2.57431e6i | −0.000853967 | − | 0.00234626i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.91708e8 | + | 1.60862e8i | −0.167251 | + | 0.140340i | ||||
\(185\) | 3.11893e8 | − | 8.56918e8i | 0.266268 | − | 0.731564i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.74769e7 | + | 2.12542e8i | −0.0306477 | + | 0.173811i | ||||
\(188\) | 1.54591e9i | 1.23752i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.01960e8 | −0.0782378 | ||||||||
\(191\) | −7.37923e8 | − | 1.30116e8i | −0.554469 | − | 0.0977679i | −0.110609 | − | 0.993864i | \(-0.535280\pi\) |
−0.443860 | + | 0.896096i | \(0.646391\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.25557e9 | − | 4.56992e8i | −0.904927 | − | 0.329366i | −0.152701 | − | 0.988272i | \(-0.548797\pi\) |
−0.752225 | + | 0.658906i | \(0.771019\pi\) | |||||||
\(194\) | 2.23289e8 | + | 2.66105e8i | 0.157638 | + | 0.187865i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.33707e9 | − | 4.86655e8i | 0.906005 | − | 0.329759i | ||||
\(197\) | 8.27317e8 | + | 4.77652e8i | 0.549297 | + | 0.317137i | 0.748838 | − | 0.662753i | \(-0.230612\pi\) |
−0.199541 | + | 0.979889i | \(0.563945\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.23487e8 | − | 7.33501e8i | −0.270040 | − | 0.467723i | 0.698832 | − | 0.715286i | \(-0.253704\pi\) |
−0.968872 | + | 0.247563i | \(0.920370\pi\) | |||||||
\(200\) | 1.63659e7 | − | 1.95041e7i | 0.0102287 | − | 0.0121901i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.79438e7 | − | 3.28615e8i | −0.0348018 | − | 0.197371i | ||||
\(203\) | −2.63286e8 | + | 4.64244e7i | −0.155040 | + | 0.0273377i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.38423e7 | − | 2.00060e7i | −0.0135000 | − | 0.0113278i | ||||
\(206\) | −2.58763e8 | + | 1.49397e8i | −0.143692 | + | 0.0829608i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.28324e8 | − | 2.22264e8i | 0.0685574 | − | 0.118745i | ||||
\(209\) | −1.47231e8 | − | 4.04514e8i | −0.0771638 | − | 0.212006i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.74069e8 | + | 1.46061e8i | −0.0878195 | + | 0.0736893i | −0.685641 | − | 0.727940i | \(-0.740478\pi\) |
0.597821 | + | 0.801630i | \(0.296033\pi\) | |||||||
\(212\) | −8.50618e8 | + | 2.33705e9i | −0.421106 | + | 1.15698i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.00645e7 | + | 2.83930e8i | −0.0238712 | + | 0.135381i | ||||
\(215\) | 5.60940e8i | 0.262520i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.60861e8 | −0.207841 | ||||||||
\(218\) | 7.86146e7 | + | 1.38619e7i | 0.0348079 | + | 0.00613757i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.01917e9 | + | 3.70946e8i | 0.435065 | + | 0.158351i | ||||
\(221\) | −8.64727e7 | − | 1.03054e8i | −0.0362501 | − | 0.0432012i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.09381e8 | − | 2.21796e8i | 0.246416 | − | 0.0896882i | −0.215859 | − | 0.976424i | \(-0.569255\pi\) |
0.462276 | + | 0.886736i | \(0.347033\pi\) | |||||||
\(224\) | 1.06841e8 | + | 6.16846e7i | 0.0424371 | + | 0.0245010i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.68463e7 | + | 1.50422e8i | 0.0332903 | + | 0.0576605i | ||||
\(227\) | 6.84046e8 | − | 8.15215e8i | 0.257622 | − | 0.307021i | −0.621695 | − | 0.783260i | \(-0.713556\pi\) |
0.879316 | + | 0.476238i | \(0.158000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.42445e8 | + | 1.94210e9i | 0.124523 | + | 0.706205i | 0.981590 | + | 0.191000i | \(0.0611731\pi\) |
−0.857067 | + | 0.515205i | \(0.827716\pi\) | |||||||
\(230\) | 3.12318e8 | − | 5.50701e7i | 0.111606 | − | 0.0196791i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00173e9 | + | 8.40555e8i | 0.345781 | + | 0.290145i | ||||
\(233\) | 3.99283e9 | − | 2.30526e9i | 1.35474 | − | 0.782161i | 0.365833 | − | 0.930680i | \(-0.380784\pi\) |
0.988910 | + | 0.148519i | \(0.0474507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.98365e9 | − | 3.43578e9i | 0.650419 | − | 1.12656i | ||||
\(236\) | 1.31834e9 | + | 3.62212e9i | 0.424991 | + | 1.16765i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.58224e7 | − | 1.32766e7i | 0.00493133 | − | 0.00413788i | ||||
\(239\) | −4.79266e8 | + | 1.31677e9i | −0.146888 | + | 0.403570i | −0.991216 | − | 0.132256i | \(-0.957778\pi\) |
0.844328 | + | 0.535827i | \(0.180000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.55644e8 | + | 3.15122e9i | −0.164713 | + | 0.934136i | 0.784646 | + | 0.619944i | \(0.212845\pi\) |
−0.949359 | + | 0.314192i | \(0.898266\pi\) | |||||||
\(242\) | 4.21849e8i | 0.122997i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.33570e9 | 1.50533 | ||||||||
\(245\) | −3.59609e9 | − | 6.34088e8i | −0.998083 | − | 0.175989i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.52145e8 | + | 9.17734e7i | 0.0677428 | + | 0.0246564i | ||||
\(248\) | 1.44897e9 | + | 1.72682e9i | 0.383048 | + | 0.456499i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.58858e8 | − | 2.03408e8i | 0.143068 | − | 0.0520723i | ||||
\(251\) | −2.82883e9 | − | 1.63323e9i | −0.712709 | − | 0.411483i | 0.0993540 | − | 0.995052i | \(-0.468322\pi\) |
−0.812063 | + | 0.583569i | \(0.801656\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.69472e8 | + | 1.15956e9i | 0.163399 | + | 0.283016i | ||||
\(254\) | 7.52275e8 | − | 8.96526e8i | 0.180735 | − | 0.215391i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.69712e8 | + | 3.23100e9i | 0.132646 | + | 0.752275i | ||||
\(257\) | 1.01335e9 | − | 1.78680e8i | 0.232287 | − | 0.0409585i | −0.0562927 | − | 0.998414i | \(-0.517928\pi\) |
0.288580 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.82259e8 | − | 2.36844e8i | −0.0627262 | − | 0.0526336i | ||||
\(260\) | −5.85474e8 | + | 3.38023e8i | −0.128119 | + | 0.0739696i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.59899e8 | + | 1.14298e9i | −0.140046 | + | 0.242568i | ||||
\(263\) | 1.69620e9 | + | 4.66027e9i | 0.354531 | + | 0.974066i | 0.980895 | + | 0.194536i | \(0.0623200\pi\) |
−0.626364 | + | 0.779530i | \(0.715458\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.88931e9 | − | 4.10261e9i | 0.991434 | − | 0.831912i | ||||
\(266\) | −1.40904e7 | + | 3.87131e7i | −0.00281447 | + | 0.00773270i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.37368e8 | − | 3.04756e9i | 0.104168 | − | 0.590764i | ||||
\(269\) | 1.08134e9i | 0.206516i | 0.994655 | + | 0.103258i | \(0.0329267\pi\) | ||||
−0.994655 | + | 0.103258i | \(0.967073\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.66467e9 | −0.864855 | −0.432428 | − | 0.901669i | \(-0.642343\pi\) | ||||
−0.432428 | + | 0.901669i | \(0.642343\pi\) | |||||||
\(272\) | 1.90560e9 | + | 3.36009e8i | 0.348142 | + | 0.0613868i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.48312e8 | + | 2.72363e8i | 0.132764 | + | 0.0483221i | ||||
\(275\) | −8.75622e7 | − | 1.04353e8i | −0.0153104 | − | 0.0182462i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.24991e9 | + | 3.00272e9i | −1.40130 | + | 0.510030i | −0.928563 | − | 0.371175i | \(-0.878955\pi\) |
−0.472734 | + | 0.881205i | \(0.656733\pi\) | |||||||
\(278\) | −1.19503e9 | − | 6.89951e8i | −0.200078 | − | 0.115515i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.05100e8 | − | 1.82039e8i | −0.0170990 | − | 0.0296164i | ||||
\(281\) | −3.27244e9 | + | 3.89994e9i | −0.524864 | + | 0.625508i | −0.961724 | − | 0.274021i | \(-0.911646\pi\) |
0.436860 | + | 0.899530i | \(0.356091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.36212e9 | − | 7.72497e9i | −0.212359 | − | 1.20435i | −0.885432 | − | 0.464770i | \(-0.846137\pi\) |
0.673073 | − | 0.739576i | \(-0.264974\pi\) | |||||||
\(284\) | −6.72878e8 | + | 1.18646e8i | −0.103434 | + | 0.0182382i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.49197e7 | + | 4.60831e7i | 0.00820850 | + | 0.00688775i | ||||
\(287\) | −1.08909e7 | + | 6.28789e6i | −0.00160523 | + | 0.000926781i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.98074e9 | + | 5.16280e9i | −0.427300 | + | 0.740106i | ||||
\(290\) | −5.66775e8 | − | 1.55720e9i | −0.0801343 | − | 0.220167i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.34770e8 | + | 2.80905e8i | −0.0460485 | + | 0.0386393i | ||||
\(293\) | 4.13715e9 | − | 1.13667e10i | 0.561347 | − | 1.54229i | −0.256318 | − | 0.966592i | \(-0.582510\pi\) |
0.817665 | − | 0.575695i | \(-0.195268\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.71774e9 | − | 9.74178e9i | 0.226813 | − | 1.28632i | ||||
\(296\) | 1.80226e9i | 0.234774i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.77591e9 | −0.225193 | ||||||||
\(299\) | −8.21924e8 | − | 1.44927e8i | −0.102836 | − | 0.0181328i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.12982e8 | + | 7.75192e7i | 0.0259464 | + | 0.00944372i | ||||
\(302\) | −5.49682e8 | − | 6.55085e8i | −0.0660820 | − | 0.0787535i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.62677e9 | + | 1.32004e9i | −0.424645 | + | 0.154558i | ||||
\(305\) | −1.18586e10 | − | 6.84655e9i | −1.37035 | − | 0.791175i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.47222e9 | + | 1.12102e10i | 0.728618 | + | 1.26200i | 0.957467 | + | 0.288542i | \(0.0931705\pi\) |
−0.228849 | + | 0.973462i | \(0.573496\pi\) | |||||||
\(308\) | 2.81687e8 | − | 3.35702e8i | 0.0313015 | − | 0.0373036i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.96047e8 | − | 2.81322e9i | −0.0537126 | − | 0.304619i | ||||
\(311\) | 1.24197e10 | − | 2.18993e9i | 1.32761 | − | 0.234093i | 0.535531 | − | 0.844516i | \(-0.320112\pi\) |
0.792076 | + | 0.610423i | \(0.209000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.91530e9 | − | 5.80262e9i | −0.720499 | − | 0.604571i | 0.207024 | − | 0.978336i | \(-0.433622\pi\) |
−0.927523 | + | 0.373765i | \(0.878067\pi\) | |||||||
\(314\) | −1.95229e9 | + | 1.12716e9i | −0.200829 | + | 0.115949i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.41983e9 | + | 9.38743e9i | −0.543548 | + | 0.941452i | ||||
\(317\) | 8.52565e8 | + | 2.34240e9i | 0.0844287 | + | 0.231966i | 0.974722 | − | 0.223422i | \(-0.0717228\pi\) |
−0.890293 | + | 0.455388i | \(0.849501\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.35956e9 | − | 4.49721e9i | 0.517567 | − | 0.434290i | ||||
\(320\) | 3.14781e9 | − | 8.64853e9i | 0.300198 | − | 0.824788i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.22514e7 | − | 1.26194e8i | 0.00206983 | − | 0.0117386i | ||||
\(323\) | 2.02306e9i | 0.185865i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.49116e7 | 0.00761085 | ||||||||
\(326\) | −1.25275e9 | − | 2.20893e8i | −0.110916 | − | 0.0195574i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.78020e7 | + | 2.10382e7i | 0.00499399 | + | 0.00181766i | ||||
\(329\) | −1.03039e9 | − | 1.22798e9i | −0.0879467 | − | 0.104811i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.23169e10 | + | 4.48300e9i | −1.02610 | + | 0.373471i | −0.799596 | − | 0.600539i | \(-0.794953\pi\) |
−0.226507 | + | 0.974010i | \(0.572731\pi\) | |||||||
\(332\) | −1.28703e10 | − | 7.43069e9i | −1.05935 | − | 0.611614i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.09897e9 | − | 1.90347e9i | −0.0883077 | − | 0.152953i | ||||
\(335\) | −5.10481e9 | + | 6.08367e9i | −0.405322 | + | 0.483044i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.91787e8 | − | 1.65481e9i | −0.0226228 | − | 0.128300i | 0.971405 | − | 0.237430i | \(-0.0763049\pi\) |
−0.994028 | + | 0.109129i | \(0.965194\pi\) | |||||||
\(338\) | 1.96796e9 | − | 3.47005e8i | 0.150782 | − | 0.0265870i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.90457e9 | − | 3.27633e9i | −0.292185 | − | 0.245172i | ||||
\(341\) | 1.04448e10 | − | 6.03031e9i | 0.772472 | − | 0.445987i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.48412e9 | + | 2.57057e9i | −0.107224 | + | 0.185717i | ||||
\(344\) | −3.79168e8 | − | 1.04176e9i | −0.0270768 | − | 0.0743930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.71183e9 | − | 2.27550e9i | 0.189216 | − | 0.158771i | ||||
\(347\) | −2.77675e9 | + | 7.62907e9i | −0.191522 | + | 0.526203i | −0.997870 | − | 0.0652390i | \(-0.979219\pi\) |
0.806347 | + | 0.591442i | \(0.201441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.80498e7 | − | 1.02366e8i | 0.00121667 | − | 0.00690006i | −0.984193 | − | 0.177097i | \(-0.943329\pi\) |
0.985410 | + | 0.170197i | \(0.0544404\pi\) | |||||||
\(350\) | 1.30369e7i | 0.000868763i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.22854e9 | −0.210298 | ||||||||
\(353\) | 9.42955e9 | + | 1.66268e9i | 0.607285 | + | 0.107081i | 0.468830 | − | 0.883288i | \(-0.344676\pi\) |
0.138454 | + | 0.990369i | \(0.455787\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.64771e9 | + | 5.99717e8i | 0.103745 | + | 0.0377601i | ||||
\(356\) | −6.15390e9 | − | 7.33394e9i | −0.383134 | − | 0.456601i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.97828e8 | − | 1.08400e8i | 0.0181315 | − | 0.00659931i | ||||
\(359\) | −2.20697e10 | − | 1.27419e10i | −1.32867 | − | 0.767109i | −0.343578 | − | 0.939124i | \(-0.611639\pi\) |
−0.985094 | + | 0.172015i | \(0.944972\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.47420e9 | + | 1.12136e10i | 0.381204 | + | 0.660264i | ||||
\(362\) | −7.41991e8 | + | 8.84270e8i | −0.0432080 | + | 0.0514933i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.74338e7 | + | 2.69011e8i | 0.00270198 | + | 0.0153237i | ||||
\(365\) | 1.10447e9 | − | 1.94748e8i | 0.0622276 | − | 0.0109724i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.98172e8 | − | 4.18016e8i | −0.0274609 | − | 0.0230424i | 0.628954 | − | 0.777443i | \(-0.283483\pi\) |
−0.656415 | + | 0.754400i | \(0.727928\pi\) | |||||||
\(368\) | 1.03963e10 | − | 6.00232e9i | 0.566877 | − | 0.327287i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.14195e9 | − | 1.97791e9i | 0.0609312 | − | 0.105536i | ||||
\(371\) | −8.82035e8 | − | 2.42337e9i | −0.0465576 | − | 0.127916i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.77422e8 | − | 8.20154e8i | 0.0504948 | − | 0.0423702i | −0.617191 | − | 0.786813i | \(-0.711729\pi\) |
0.667686 | + | 0.744443i | \(0.267285\pi\) | |||||||
\(374\) | −1.84871e8 | + | 5.07929e8i | −0.00944892 | + | 0.0259607i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.36153e9 | + | 7.72164e9i | −0.0681204 | + | 0.386330i | ||||
\(377\) | 4.36107e9i | 0.215888i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.22343e10 | 1.07762 | 0.538811 | − | 0.842427i | \(-0.318874\pi\) | ||||
0.538811 | + | 0.842427i | \(0.318874\pi\) | |||||||
\(380\) | 1.00121e10 | + | 1.76540e9i | 0.480165 | + | 0.0846661i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.76347e9 | − | 6.41851e8i | −0.0828162 | − | 0.0301426i | ||||
\(383\) | 2.13080e10 | + | 2.53939e10i | 0.990258 | + | 1.18014i | 0.983636 | + | 0.180166i | \(0.0576634\pi\) |
0.00662182 | + | 0.999978i | \(0.497892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.05681e9 | + | 3.84647e8i | −0.0481009 | + | 0.0175073i | ||||
\(386\) | −2.89808e9 | − | 1.67321e9i | −0.130545 | − | 0.0753704i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.73186e10 | − | 2.99967e10i | −0.764162 | − | 1.32357i | ||||
\(389\) | −2.54213e10 | + | 3.02959e10i | −1.11019 | + | 1.32308i | −0.168845 | + | 0.985643i | \(0.554004\pi\) |
−0.941349 | + | 0.337435i | \(0.890441\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.09268e9 | − | 6.19690e9i | −0.0467505 | − | 0.265135i | ||||
\(392\) | 7.10713e9 | − | 1.25318e9i | 0.300989 | − | 0.0530724i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.83282e9 | + | 1.53792e9i | 0.0760561 | + | 0.0638186i | ||||
\(395\) | 2.40911e10 | − | 1.39090e10i | 0.989620 | − | 0.571357i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.01278e10 | − | 1.75419e10i | 0.407712 | − | 0.706179i | −0.586921 | − | 0.809645i | \(-0.699660\pi\) |
0.994633 | + | 0.103466i | \(0.0329932\pi\) | |||||||
\(398\) | −7.25513e8 | − | 1.99333e9i | −0.0289143 | − | 0.0794414i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.35600e8 | + | 7.85061e8i | −0.0365469 | + | 0.0306665i | ||||
\(401\) | −9.60582e9 | + | 2.63918e10i | −0.371498 | + | 1.02068i | 0.603284 | + | 0.797526i | \(0.293858\pi\) |
−0.974783 | + | 0.223157i | \(0.928364\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.30544e9 | + | 7.40353e9i | −0.0494923 | + | 0.280685i | ||||
\(404\) | 3.32720e10i | 1.24897i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.69576e8 | −0.0246431 | ||||||||
\(407\) | 9.49609e9 | + | 1.67442e9i | 0.346073 | + | 0.0610219i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.22849e10 | + | 8.11103e9i | 0.796374 | + | 0.289856i | 0.707983 | − | 0.706229i | \(-0.249605\pi\) |
0.0883910 | + | 0.996086i | \(0.471828\pi\) | |||||||
\(410\) | −5.01054e7 | − | 5.97133e7i | −0.00177317 | − | 0.00211318i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.79963e10 | − | 1.01898e10i | 0.971654 | − | 0.353653i | ||||
\(413\) | −3.46145e9 | − | 1.99847e9i | −0.118976 | − | 0.0686906i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.90695e10 | + | 3.30294e10i | 0.642906 | + | 1.11355i | ||||
\(416\) | 1.29357e9 | − | 1.54162e9i | 0.0431934 | − | 0.0514759i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.87215e8 | − | 1.06175e9i | −0.00613248 | − | 0.0347790i | ||||
\(419\) | −1.55067e10 | + | 2.73425e9i | −0.503111 | + | 0.0887120i | −0.419443 | − | 0.907782i | \(-0.637775\pi\) |
−0.0836677 | + | 0.996494i | \(0.526663\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.24333e9 | + | 2.72148e9i | 0.103244 | + | 0.0866316i | 0.692948 | − | 0.720987i | \(-0.256311\pi\) |
−0.589705 | + | 0.807619i | \(0.700756\pi\) | |||||||
\(422\) | −4.92857e8 | + | 2.84551e8i | −0.0155407 | + | 0.00897244i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.30706e9 | + | 1.09241e10i | −0.195148 | + | 0.338006i | ||||
\(425\) | 2.18958e8 | + | 6.01583e8i | 0.00671128 | + | 0.0184391i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.23835e9 | + | 3.55640e9i | −0.127493 | + | 0.106979i | ||||
\(428\) | 9.83228e9 | − | 2.70140e10i | 0.293008 | − | 0.805033i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.43955e8 | + | 1.38354e9i | −0.00713569 | + | 0.0404685i | ||||
\(431\) | 5.43801e10i | 1.57591i | 0.615734 | + | 0.787954i | \(0.288860\pi\) | ||||
−0.615734 | + | 0.787954i | \(0.711140\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.01330e10 | 0.288261 | 0.144130 | − | 0.989559i | \(-0.453962\pi\) | ||||
0.144130 | + | 0.989559i | \(0.453962\pi\) | |||||||
\(434\) | −1.13670e9 | − | 2.00431e8i | −0.0320395 | − | 0.00564944i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.47964e9 | − | 2.72237e9i | −0.206983 | − | 0.0753356i | ||||
\(437\) | 8.06760e9 | + | 9.61459e9i | 0.221217 | + | 0.263636i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.09720e10 | − | 1.49126e10i | 1.10314 | − | 0.401509i | 0.274665 | − | 0.961540i | \(-0.411433\pi\) |
0.828471 | + | 0.560031i | \(0.189211\pi\) | |||||||
\(440\) | 4.76391e9 | + | 2.75044e9i | 0.127102 | + | 0.0733824i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.68463e8 | − | 2.91787e8i | −0.00441383 | − | 0.00764498i | ||||
\(443\) | 2.87742e10 | − | 3.42918e10i | 0.747117 | − | 0.890379i | −0.249844 | − | 0.968286i | \(-0.580379\pi\) |
0.996961 | + | 0.0779071i | \(0.0248238\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.26642e9 | + | 2.41961e10i | 0.108799 | + | 0.617028i | ||||
\(446\) | 1.59948e9 | − | 2.82031e8i | 0.0404239 | − | 0.00712783i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.84873e9 | − | 2.39037e9i | −0.0707195 | − | 0.0593407i | ||||
\(449\) | 3.94571e10 | − | 2.27806e10i | 0.970823 | − | 0.560505i | 0.0713360 | − | 0.997452i | \(-0.477274\pi\) |
0.899487 | + | 0.436947i | \(0.143940\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.64552e8 | − | 2.85013e8i | 0.00397738 | − | 0.00688903i | ||||
\(452\) | −5.92346e9 | − | 1.62746e10i | −0.141913 | − | 0.389903i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.04172e9 | − | 1.71320e9i | 0.0480587 | − | 0.0403260i | ||||
\(455\) | 2.39762e8 | − | 6.58740e8i | 0.00559415 | − | 0.0153698i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.31714e9 | + | 4.14976e10i | −0.167755 | + | 0.951388i | 0.778422 | + | 0.627741i | \(0.216020\pi\) |
−0.946178 | + | 0.323647i | \(0.895091\pi\) | |||||||
\(458\) | 4.93906e9i | 0.112249i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.16220e10 | −0.706248 | ||||||||
\(461\) | −1.81731e10 | − | 3.20440e9i | −0.402369 | − | 0.0709484i | −0.0311982 | − | 0.999513i | \(-0.509932\pi\) |
−0.371170 | + | 0.928565i | \(0.621043\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.73595e10 | − | 9.95805e9i | −0.595367 | − | 0.216696i | 0.0267215 | − | 0.999643i | \(-0.491493\pi\) |
−0.622088 | + | 0.782947i | \(0.713715\pi\) | |||||||
\(464\) | −4.03209e10 | − | 4.80525e10i | −0.869877 | − | 1.03668i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.08507e10 | − | 3.94934e9i | 0.230099 | − | 0.0837493i | ||||
\(467\) | −4.63413e10 | − | 2.67552e10i | −0.974319 | − | 0.562523i | −0.0737688 | − | 0.997275i | \(-0.523503\pi\) |
−0.900550 | + | 0.434752i | \(0.856836\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.60444e9 | + | 2.77897e9i | 0.0331613 | + | 0.0574370i | ||||
\(470\) | 6.38683e9 | − | 7.61153e9i | 0.130886 | − | 0.155984i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.39485e9 | + | 1.92531e10i | 0.0683994 | + | 0.387912i | ||||
\(473\) | −5.84128e9 | + | 1.02997e9i | −0.116698 | + | 0.0205770i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.78177e8 | − | 8.20788e8i | −0.0192151 | − | 0.0161234i | ||||
\(476\) | −1.78357e9 | + | 1.02975e9i | −0.0347427 | + | 0.0200587i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.75476e9 | + | 3.03934e9i | −0.0336130 | + | 0.0582194i | ||||
\(479\) | −9.54151e9 | − | 2.62151e10i | −0.181249 | − | 0.497977i | 0.815481 | − | 0.578784i | \(-0.196473\pi\) |
−0.996730 | + | 0.0808069i | \(0.974250\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.60432e9 | + | 3.86348e9i | −0.0860171 | + | 0.0721769i | ||||
\(482\) | −2.74095e9 | + | 7.53071e9i | −0.0507825 | + | 0.139524i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.30416e9 | − | 4.14240e10i | 0.133103 | − | 0.754867i | ||||
\(485\) | 8.88899e10i | 1.60652i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.43062e10 | −0.965458 | −0.482729 | − | 0.875770i | \(-0.660354\pi\) | ||||
−0.482729 | + | 0.875770i | \(0.660354\pi\) | |||||||
\(488\) | 2.66512e10 | + | 4.69932e9i | 0.469934 | + | 0.0828621i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.59387e9 | − | 3.12791e9i | −0.149075 | − | 0.0542588i | ||||
\(491\) | −2.12598e10 | − | 2.53364e10i | −0.365791 | − | 0.435933i | 0.551485 | − | 0.834185i | \(-0.314061\pi\) |
−0.917276 | + | 0.398252i | \(0.869617\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.08974e10 | + | 1.12457e10i | −0.523039 | + | 0.190371i | ||||
\(494\) | 5.81995e8 | + | 3.36015e8i | 0.00977263 | + | 0.00564223i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.40663e10 | − | 9.36455e10i | −0.893305 | − | 1.54725i | ||||
\(497\) | 4.55411e8 | − | 5.42737e8i | 0.00746410 | − | 0.00889537i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.01014e9 | − | 3.97565e10i | −0.113064 | − | 0.641218i | −0.987691 | − | 0.156421i | \(-0.950004\pi\) |
0.874626 | − | 0.484798i | \(-0.161107\pi\) | |||||||
\(500\) | −5.83996e10 | + | 1.02974e10i | −0.934393 | + | 0.164759i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.26692e9 | − | 5.25857e9i | −0.0986823 | − | 0.0828043i | ||||
\(503\) | 1.03883e11 | − | 5.99768e10i | 1.62283 | − | 0.936940i | 0.636668 | − | 0.771138i | \(-0.280312\pi\) |
0.986159 | − | 0.165801i | \(-0.0530211\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.26933e10 | − | 7.39469e10i | 0.656438 | − | 1.13698i | ||||
\(506\) | 1.14693e9 | + | 3.15117e9i | 0.0174959 | + | 0.0480695i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.93935e10 | + | 7.50100e10i | −1.34230 | + | 1.12633i | ||||
\(509\) | −1.99802e10 | + | 5.48952e10i | −0.297666 | + | 0.817830i | 0.697223 | + | 0.716854i | \(0.254419\pi\) |
−0.994889 | + | 0.100976i | \(0.967803\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.86890e7 | − | 4.46268e8i | 0.00115407 | − | 0.00654503i | ||||
\(512\) | 4.86471e10i | 0.707908i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.57709e9 | 0.0369213 | ||||||||
\(515\) | −7.52968e10 | − | 1.32768e10i | −1.07040 | − | 0.188741i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.94203e10 | + | 1.43478e10i | 0.551770 | + | 0.200828i | ||||
\(518\) | −5.93178e8 | − | 7.06922e8i | −0.00823884 | − | 0.00981867i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.22208e9 | + | 1.17274e9i | −0.0440680 | + | 0.0160394i | ||||
\(521\) | −6.93877e9 | − | 4.00610e9i | −0.0941741 | − | 0.0543715i | 0.452173 | − | 0.891930i | \(-0.350649\pi\) |
−0.546347 | + | 0.837559i | \(0.683982\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.54192e10 | − | 4.40273e10i | −0.339746 | − | 0.588457i | 0.644639 | − | 0.764487i | \(-0.277008\pi\) |
−0.984385 | + | 0.176030i | \(0.943674\pi\) | |||||||
\(524\) | 8.45897e10 | − | 1.00810e11i | 1.12200 | − | 1.33715i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.15685e9 | + | 1.22321e10i | 0.0281758 | + | 0.159793i | ||||
\(527\) | −5.58189e10 | + | 9.84238e9i | −0.723667 | + | 0.127602i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.00845e10 | + | 2.52439e10i | 0.384168 | + | 0.322355i | ||||
\(530\) | 1.38435e10 | − | 7.99257e9i | 0.175446 | − | 0.101294i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.05392e9 | − | 3.55750e9i | 0.0256412 | − | 0.0444118i | ||||
\(533\) | 7.01622e7 | + | 1.92769e8i | 0.000869349 | + | 0.00238852i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.65154e10 | + | 4.74221e10i | −0.689845 | + | 0.578849i | ||||
\(536\) | 5.36818e9 | − | 1.47489e10i | 0.0650381 | − | 0.178691i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.70280e8 | + | 2.66709e9i | −0.00561342 | + | 0.0318353i | ||||
\(539\) | − | 3.86117e10i | − | 0.457472i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.99438e10 | 0.583032 | 0.291516 | − | 0.956566i | \(-0.405840\pi\) | ||||
0.291516 | + | 0.956566i | \(0.405840\pi\) | |||||||
\(542\) | −1.15052e10 | − | 2.02868e9i | −0.133321 | − | 0.0235081i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.42578e10 | + | 5.18941e9i | 0.162801 | + | 0.0592546i | ||||
\(545\) | 1.31302e10 | + | 1.56480e10i | 0.148829 | + | 0.177367i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.21042e10 | + | 8.04528e9i | −0.246903 | + | 0.0898653i | −0.462507 | − | 0.886616i | \(-0.653050\pi\) |
0.215604 | + | 0.976481i | \(0.430828\pi\) | |||||||
\(548\) | −6.87654e10 | − | 3.97017e10i | −0.762514 | − | 0.440238i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.70586e8 | − | 2.95463e8i | −0.00186420 | − | 0.00322888i | ||||
\(551\) | 4.21558e10 | − | 5.02393e10i | 0.457352 | − | 0.545051i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.95181e9 | − | 1.10693e10i | −0.0208707 | − | 0.118364i | ||||
\(554\) | −2.16540e10 | + | 3.81819e9i | −0.229879 | + | 0.0405339i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.05401e11 | + | 8.84420e10i | 1.10293 | + | 0.925464i | ||||
\(557\) | 1.24286e11 | − | 7.17563e10i | 1.29122 | − | 0.745486i | 0.312349 | − | 0.949968i | \(-0.398884\pi\) |
0.978870 | + | 0.204482i | \(0.0655509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.84861e9 | − | 3.20188e9i | 0.0189320 | − | 0.0327912i | ||||
\(560\) | 3.44865e9 | + | 9.47509e9i | 0.0350669 | + | 0.0963454i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.76746e9 | + | 8.19588e9i | −0.0979121 | + | 0.0821580i | ||||
\(563\) | −1.27931e10 | + | 3.51488e10i | −0.127334 | + | 0.349846i | −0.986935 | − | 0.161119i | \(-0.948490\pi\) |
0.859601 | + | 0.510965i | \(0.170712\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.71799e9 | + | 4.37709e10i | −0.0757375 | + | 0.429528i | ||||
\(566\) | − | 1.96458e10i | − | 0.191427i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.46544e9 | −0.0332939 | ||||||||
\(569\) | −1.61367e11 | − | 2.84534e10i | −1.53945 | − | 0.271447i | −0.661407 | − | 0.750028i | \(-0.730040\pi\) |
−0.878043 | + | 0.478581i | \(0.841151\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.72062e11 | − | 6.26253e10i | −1.61860 | − | 0.589122i | −0.635486 | − | 0.772112i | \(-0.719200\pi\) |
−0.983115 | + | 0.182990i | \(0.941422\pi\) | |||||||
\(572\) | −4.59499e9 | − | 5.47609e9i | −0.0429240 | − | 0.0511548i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.95967e7 | + | 1.07723e7i | −0.000272644 | + | 9.92344e-5i | ||||
\(575\) | 3.43961e9 | + | 1.98586e9i | 0.0314657 | + | 0.0181668i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.38743e10 | − | 2.40309e10i | −0.125172 | − | 0.216804i | 0.796628 | − | 0.604470i | \(-0.206615\pi\) |
−0.921800 | + | 0.387665i | \(0.873282\pi\) | |||||||
\(578\) | −9.59722e9 | + | 1.14375e10i | −0.0859873 | + | 0.102476i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.86927e10 | + | 1.62725e11i | 0.253548 | + | 1.43794i | ||||
\(581\) | 1.51762e10 | − | 2.67597e9i | 0.133186 | − | 0.0234842i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.16996e10 | + | 4.33811e10i | 0.447520 | + | 0.375514i | ||||
\(584\) | −1.91954e9 | + | 1.10825e9i | −0.0165023 | + | 0.00952763i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.51476e10 | − | 2.62364e10i | 0.128456 | − | 0.222492i | ||||
\(587\) | −1.84410e10 | − | 5.06662e10i | −0.155322 | − | 0.426743i | 0.837487 | − | 0.546458i | \(-0.184024\pi\) |
−0.992808 | + | 0.119715i | \(0.961802\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.66040e10 | − | 7.26694e10i | 0.719576 | − | 0.603796i | ||||
\(590\) | 8.47348e9 | − | 2.32807e10i | 0.0699284 | − | 0.192127i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.50124e10 | − | 8.51396e10i | 0.122226 | − | 0.693178i | ||||
\(593\) | 1.98579e11i | 1.60589i | 0.596054 | + | 0.802945i | \(0.296735\pi\) | ||||
−0.596054 | + | 0.802945i | \(0.703265\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.28532e9 | 0.0421700 | ||||||||
\(596\) | 1.74387e11 | + | 3.07491e10i | 1.38207 | + | 0.243696i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.96422e9 | − | 7.14917e8i | −0.0153598 | − | 0.00559050i | ||||
\(599\) | 1.00906e11 | + | 1.20255e11i | 0.783808 | + | 0.934105i | 0.999099 | − | 0.0424444i | \(-0.0135145\pi\) |
−0.215291 | + | 0.976550i | \(0.569070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.23406e10 | − | 4.49162e9i | 0.0945887 | − | 0.0344275i | −0.294292 | − | 0.955715i | \(-0.595084\pi\) |
0.388881 | + | 0.921288i | \(0.372862\pi\) | |||||||
\(602\) | 4.91599e8 | + | 2.83825e8i | 0.00374305 | + | 0.00216105i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.26340e10 | + | 7.38443e10i | 0.320338 | + | 0.554842i | ||||
\(605\) | −6.93870e10 | + | 8.26922e10i | −0.517912 | + | 0.617224i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.69000e10 | − | 1.52558e11i | −0.198152 | − | 1.12377i | −0.907858 | − | 0.419277i | \(-0.862284\pi\) |
0.709706 | − | 0.704497i | \(-0.248828\pi\) | |||||||
\(608\) | −2.98038e10 | + | 5.25521e9i | −0.218101 | + | 0.0384571i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.62711e10 | − | 2.20441e10i | −0.189740 | − | 0.159211i | ||||
\(611\) | −2.26456e10 | + | 1.30744e10i | −0.162487 | + | 0.0938118i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.82522e10 | + | 1.18216e11i | −0.483364 | + | 0.837212i | −0.999818 | − | 0.0191038i | \(-0.993919\pi\) |
0.516453 | + | 0.856315i | \(0.327252\pi\) | |||||||
\(614\) | 1.10881e10 | + | 3.04644e10i | 0.0780163 | + | 0.214348i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.70266e9 | − | 1.42870e9i | 0.0118251 | − | 0.00992244i | ||||
\(617\) | −1.05167e10 | + | 2.88945e10i | −0.0725672 | + | 0.199377i | −0.970673 | − | 0.240402i | \(-0.922721\pi\) |
0.898106 | + | 0.439778i | \(0.144943\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.29396e10 | − | 1.30097e11i | 0.156251 | − | 0.886143i | −0.801382 | − | 0.598152i | \(-0.795902\pi\) |
0.957633 | − | 0.287991i | \(-0.0929872\pi\) | |||||||
\(620\) | 2.84837e11i | 1.92765i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.15852e10 | 0.211019 | ||||||||
\(623\) | 9.77655e9 | + | 1.72387e9i | 0.0648983 | + | 0.0114433i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.50385e11 | + | 5.47355e10i | 0.985561 | + | 0.358715i | ||||
\(626\) | −1.45327e10 | − | 1.73195e10i | −0.0946347 | − | 0.112781i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.11224e11 | − | 7.68792e10i | 1.35801 | − | 0.494277i | ||||
\(629\) | −3.92450e10 | − | 2.26581e10i | −0.250716 | − | 0.144751i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.47545e10 | + | 1.12158e11i | 0.408463 | + | 0.707478i | 0.994718 | − | 0.102648i | \(-0.0327316\pi\) |
−0.586255 | + | 0.810127i | \(0.699398\pi\) | |||||||
\(632\) | −3.53392e10 | + | 4.21157e10i | −0.221508 | + | 0.263983i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.08410e9 | + | 6.14824e9i | 0.00670984 | + | 0.0380534i | ||||
\(635\) | 2.94926e11 | − | 5.20035e10i | 1.81392 | − | 0.319843i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.84370e10 | + | 1.54705e10i | 0.111978 | + | 0.0939609i | ||||
\(638\) | 1.51750e10 | − | 8.76130e9i | 0.0915897 | − | 0.0528793i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.06071e10 | − | 8.76541e10i | 0.301642 | − | 0.522459i | ||||
\(641\) | 5.46839e10 | + | 1.50243e11i | 0.323912 | + | 0.889941i | 0.989617 | + | 0.143726i | \(0.0459085\pi\) |
−0.665706 | + | 0.746215i | \(0.731869\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.61080e11 | − | 1.35162e11i | 0.942318 | − | 0.790699i | −0.0356691 | − | 0.999364i | \(-0.511356\pi\) |
0.977987 | + | 0.208665i | \(0.0669118\pi\) | |||||||
\(644\) | −4.37000e9 | + | 1.20065e10i | −0.0254061 | + | 0.0698027i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.79836e8 | + | 4.98980e9i | −0.00505210 | + | 0.0286519i | ||||
\(647\) | − | 1.78264e11i | − | 1.01730i | −0.860974 | − | 0.508648i | \(-0.830145\pi\) | ||
0.860974 | − | 0.508648i | \(-0.169855\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.04599e11 | 0.589587 | ||||||||
\(650\) | 2.09431e8 | + | 3.69284e7i | 0.00117324 | + | 0.000206875i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.19190e11 | + | 4.33817e10i | 0.659554 | + | 0.240058i | ||||
\(653\) | −6.49968e10 | − | 7.74602e10i | −0.357470 | − | 0.426016i | 0.557099 | − | 0.830446i | \(-0.311914\pi\) |
−0.914569 | + | 0.404430i | \(0.867470\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.17356e11 | + | 1.15508e11i | −1.72417 | + | 0.627548i | ||||
\(656\) | −2.55536e9 | − | 1.47534e9i | −0.0137986 | − | 0.00796664i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.00738e9 | − | 3.47688e9i | −0.0107084 | − | 0.0185475i | ||||
\(659\) | 1.04978e9 | − | 1.25108e9i | 0.00556616 | − | 0.00663349i | −0.763254 | − | 0.646098i | \(-0.776400\pi\) |
0.768820 | + | 0.639465i | \(0.220844\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.54225e10 | − | 8.74653e10i | −0.0807884 | − | 0.458174i | −0.998186 | − | 0.0602023i | \(-0.980825\pi\) |
0.917398 | − | 0.397971i | \(-0.130286\pi\) | |||||||
\(662\) | −3.23290e10 | + | 5.70047e9i | −0.168329 | + | 0.0296810i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.77414e10 | − | 4.84508e10i | −0.297040 | − | 0.249246i | ||||
\(665\) | −9.12968e9 | + | 5.27102e9i | −0.0466841 | + | 0.0269531i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.01994e11 | + | 1.76659e11i | −0.515314 | + | 0.892549i | ||||
\(668\) | 7.49564e10 | + | 2.05941e11i | 0.376446 | + | 1.03428i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.52366e10 | + | 1.27851e10i | −0.0756119 | + | 0.0634459i | ||||
\(671\) | 4.95214e10 | − | 1.36059e11i | 0.244289 | − | 0.671177i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.34793e10 | + | 7.64450e10i | −0.0657064 | + | 0.372640i | 0.934169 | + | 0.356832i | \(0.116143\pi\) |
−0.999875 | + | 0.0158078i | \(0.994968\pi\) | |||||||
\(674\) | − | 4.20842e9i | − | 0.0203929i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.99254e11 | −0.954160 | ||||||||
\(677\) | 1.68693e11 | + | 2.97451e10i | 0.803050 | + | 0.141599i | 0.560084 | − | 0.828436i | \(-0.310769\pi\) |
0.242965 | + | 0.970035i | \(0.421880\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.37504e10 | + | 1.22842e10i | 0.158782 | + | 0.0577918i | ||||
\(680\) | −1.66173e10 | − | 1.98037e10i | −0.0777187 | − | 0.0926215i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.83843e10 | − | 1.03311e10i | 0.131202 | − | 0.0477537i | ||||
\(683\) | −3.58504e11 | − | 2.06982e11i | −1.64744 | − | 0.951153i | −0.978083 | − | 0.208216i | \(-0.933234\pi\) |
−0.669362 | − | 0.742937i | \(-0.733432\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.01887e11 | + | 1.76474e11i | 0.462762 | + | 0.801527i | ||||
\(686\) | −4.77848e9 | + | 5.69477e9i | −0.0215771 | + | 0.0257146i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.23450e9 | + | 5.23715e10i | 0.0412154 | + | 0.233744i | ||||
\(689\) | −4.14288e10 | + | 7.30502e9i | −0.183834 | + | 0.0324149i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.19102e11 | − | 2.67758e11i | −1.39964 | − | 1.17444i | −0.961258 | − | 0.275650i | \(-0.911107\pi\) |
−0.438383 | − | 0.898788i | \(-0.644449\pi\) | |||||||
\(692\) | −3.05691e11 | + | 1.76491e11i | −1.33309 | + | 0.769657i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.01667e10 | + | 1.76092e10i | −0.0438269 | + | 0.0759105i | ||||
\(695\) | −1.20768e11 | − | 3.31808e11i | −0.517623 | − | 1.42216i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.18481e9 | + | 9.94173e8i | −0.00502016 | + | 0.00421241i | ||||
\(698\) | 8.90386e7 | − | 2.44632e8i | 0.000375108 | − | 0.00103060i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.25729e8 | − | 1.28017e9i | 0.000940144 | − | 0.00533182i | ||||
\(701\) | − | 4.23591e11i | − | 1.75418i | −0.480326 | − | 0.877090i | \(-0.659482\pi\) | ||
0.480326 | − | 0.877090i | \(-0.340518\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.03874e10 | 0.370072 | ||||||||
\(704\) | 9.58403e10 | + | 1.68992e10i | 0.390173 | + | 0.0687980i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.25345e10 | + | 8.20191e9i | 0.0907048 | + | 0.0330138i | ||||
\(707\) | −2.21767e10 | − | 2.64292e10i | −0.0887606 | − | 0.105781i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.98886e11 | + | 7.23886e10i | −0.787081 | + | 0.286474i | −0.704122 | − | 0.710079i | \(-0.748659\pi\) |
−0.0829588 | + | 0.996553i | \(0.526437\pi\) | |||||||
\(710\) | 3.80320e9 | + | 2.19578e9i | 0.0149663 | + | 0.00864082i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.42788e10 | − | 4.20521e10i | −0.0944728 | − | 0.163632i | ||||
\(713\) | −2.26030e11 | + | 2.69372e11i | −0.874598 | + | 1.04231i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.18564e9 | + | 1.80667e10i | 0.0121891 | + | 0.0691281i | ||||
\(716\) | −3.11224e10 | + | 5.48772e9i | −0.118419 | + | 0.0208805i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.88925e10 | − | 4.10257e10i | −0.183969 | − | 0.154368i | ||||
\(719\) | 3.55351e11 | − | 2.05162e11i | 1.32966 | − | 0.767681i | 0.344415 | − | 0.938817i | \(-0.388077\pi\) |
0.985247 | + | 0.171137i | \(0.0547439\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.54467e10 | + | 2.67545e10i | −0.0571603 | + | 0.0990046i | ||||
\(722\) | 1.10915e10 | + | 3.04737e10i | 0.0408171 | + | 0.112144i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.81714e10 | − | 7.39846e10i | 0.320903 | − | 0.269269i | ||||
\(725\) | 7.09812e9 | − | 1.95019e10i | 0.0256916 | − | 0.0705871i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.40742e10 | + | 3.06670e11i | −0.193576 | + | 1.09783i | 0.720855 | + | 0.693086i | \(0.243749\pi\) |
−0.914432 | + | 0.404741i | \(0.867362\pi\) | |||||||
\(728\) | 1.38545e9i | 0.00493249i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.80884e9 | 0.00989088 | ||||||||
\(731\) | 2.74517e10 | + | 4.84047e9i | 0.0961389 | + | 0.0169519i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.43090e11 | − | 5.20803e10i | −0.495669 | − | 0.180409i | 0.0820759 | − | 0.996626i | \(-0.473845\pi\) |
−0.577745 | + | 0.816217i | \(0.696067\pi\) | |||||||
\(734\) | −1.04693e9 | − | 1.24768e9i | −0.00360688 | − | 0.00429851i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.84547e10 | − | 3.21949e10i | 0.301446 | − | 0.109717i | ||||
\(737\) | −7.27248e10 | − | 4.19877e10i | −0.246497 | − | 0.142315i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.62658e10 | − | 6.28143e10i | −0.121596 | − | 0.210611i | 0.798801 | − | 0.601595i | \(-0.205468\pi\) |
−0.920397 | + | 0.390984i | \(0.872135\pi\) | |||||||
\(740\) | −1.46382e11 | + | 1.74451e11i | −0.488158 | + | 0.581764i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.12157e9 | − | 6.36076e9i | −0.00370009 | − | 0.0209842i | ||||
\(743\) | 2.97391e11 | − | 5.24380e10i | 0.975826 | − | 0.172064i | 0.337075 | − | 0.941478i | \(-0.390562\pi\) |
0.638751 | + | 0.769413i | \(0.279451\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.48118e11 | − | 2.92106e11i | −1.13006 | − | 0.948234i | ||||
\(746\) | 2.76746e9 | − | 1.59780e9i | 0.00893566 | − | 0.00515901i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.69482e10 | − | 4.66756e10i | 0.0860842 | − | 0.149102i | ||||
\(749\) | 1.01954e10 | + | 2.80117e10i | 0.0323950 | + | 0.0890046i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.35125e11 | − | 1.13384e11i | 0.424793 | − | 0.356443i | −0.405190 | − | 0.914232i | \(-0.632795\pi\) |
0.829983 | + | 0.557789i | \(0.188350\pi\) | |||||||
\(752\) | 1.28639e11 | − | 3.53433e11i | 0.402255 | − | 1.10519i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.89665e9 | + | 1.07564e10i | −0.00586815 | + | 0.0332799i | ||||
\(755\) | − | 2.18825e11i | − | 0.673455i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.08704e11 | 0.331025 | 0.165513 | − | 0.986208i | \(-0.447072\pi\) | ||||
0.165513 | + | 0.986208i | \(0.447072\pi\) | |||||||
\(758\) | 5.48401e10 | + | 9.66979e9i | 0.166120 | + | 0.0292914i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.84544e10 | + | 1.76360e10i | 0.145237 | + | 0.0528621i | ||||
\(761\) | 3.21895e11 | + | 3.83619e11i | 0.959788 | + | 1.14383i | 0.989538 | + | 0.144273i | \(0.0460845\pi\) |
−0.0297499 | + | 0.999557i | \(0.509471\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.75589e9 | − | 2.82291e9i | 0.0228841 | − | 0.00832913i | ||||
\(764\) | 1.62053e11 | + | 9.35612e10i | 0.475645 | + | 0.274614i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.15116e10 | + | 7.19002e10i | 0.120574 | + | 0.208841i | ||||
\(767\) | −4.19094e10 | + | 4.99457e10i | −0.121096 | + | 0.144317i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.36249e10 | − | 4.17547e11i | −0.210533 | − | 1.19399i | −0.888493 | − | 0.458891i | \(-0.848247\pi\) |
0.677960 | − | 0.735099i | \(-0.262864\pi\) | |||||||
\(770\) | −2.77386e9 | + | 4.89107e8i | −0.00789082 | + | 0.00139136i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.55609e11 | + | 2.14482e11i | 0.719627 | + | 0.603839i | ||||
\(773\) | −2.87823e11 | + | 1.66175e11i | −0.806134 | + | 0.465422i | −0.845612 | − | 0.533799i | \(-0.820764\pi\) |
0.0394773 | + | 0.999220i | \(0.487431\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.78877e10 | − | 3.09825e10i | 0.0495848 | − | 0.0858834i | ||||
\(776\) | −6.00852e10 | − | 1.65083e11i | −0.165699 | − | 0.455255i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.58765e10 | + | 6.36679e10i | −0.207104 | + | 0.173781i | ||||
\(779\) | 1.05512e9 | − | 2.89891e9i | 0.00286517 | − | 0.00787198i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.21962e9 | + | 1.82594e10i | −0.00865368 | + | 0.0490775i | ||||
\(782\) | − | 1.57596e10i | − | 0.0421424i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.46184e11 | −0.916310 | ||||||||
\(785\) | −5.68092e11 | − | 1.00170e11i | −1.49603 | − | 0.263790i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.41598e11 | − | 1.60728e11i | −1.15114 | − | 0.418980i | −0.305215 | − | 0.952283i | \(-0.598728\pi\) |
−0.845924 | + | 0.533303i | \(0.820951\pi\) | |||||||
\(788\) | −1.53347e11 | − | 1.82752e11i | −0.397714 | − | 0.473977i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.54690e10 | − | 2.38288e10i | 0.168084 | − | 0.0611777i | ||||
\(791\) | 1.55527e10 | + | 8.97936e9i | 0.0397283 | + | 0.0229371i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.51263e10 | + | 7.81610e10i | 0.114113 | + | 0.197650i | ||||
\(794\) | 3.26090e10 | − | 3.88618e10i | 0.0820455 | − | 0.0977781i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.67288e10 | + | 2.08299e11i | 0.0914859 | + | 0.518842i | ||||
\(797\) | 4.55285e10 | − | 8.02790e9i | 0.112837 | − | 0.0198961i | −0.116945 | − | 0.993138i | \(-0.537310\pi\) |
0.229781 | + | 0.973242i | \(0.426199\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.51025e11 | − | 1.26725e11i | −0.370563 | − | 0.310939i | ||||
\(800\) | −8.29378e9 | + | 4.78842e9i | −0.0202485 | + | 0.0116905i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.51703e10 | + | 6.09168e10i | −0.0850117 | + | 0.147245i | ||||
\(803\) | 4.05597e9 | + | 1.11437e10i | 0.00975512 | + | 0.0268020i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.51185e10 | − | 2.10769e10i | 0.0598150 | − | 0.0501908i | ||||
\(806\) | −6.43965e9 | + | 1.76928e10i | −0.0152589 | + | 0.0419234i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.93037e10 | + | 1.66190e11i | −0.0687508 | + | 0.389905i | ||||
\(809\) | − | 1.18357e11i | − | 0.276312i | −0.990410 | − | 0.138156i | \(-0.955882\pi\) | ||
0.990410 | − | 0.138156i | \(-0.0441175\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.39449e10 | 0.217165 | 0.108582 | − | 0.994087i | \(-0.465369\pi\) | ||||
0.108582 | + | 0.994087i | \(0.465369\pi\) | |||||||
\(812\) | 6.57497e10 | + | 1.15935e10i | 0.151241 | + | 0.0266679i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.26936e10 | + | 8.25978e9i | 0.0516898 | + | 0.0188136i | ||||
\(815\) | −2.09234e11 | − | 2.49355e11i | −0.474244 | − | 0.565182i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.22464e10 | + | 1.90161e10i | −0.117265 | + | 0.0426810i | ||||
\(818\) | 5.14373e10 | + | 2.96974e10i | 0.114886 | + | 0.0663292i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.88624e9 | + | 6.73117e9i | 0.00859557 | + | 0.0148880i | ||||
\(821\) | −1.46122e11 | + | 1.74141e11i | −0.321619 | + | 0.383291i | −0.902494 | − | 0.430702i | \(-0.858266\pi\) |
0.580875 | + | 0.813993i | \(0.302710\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.39160e9 | + | 3.62485e10i | 0.0139319 | + | 0.0790117i | 0.990981 | − | 0.134003i | \(-0.0427830\pi\) |
−0.977049 | + | 0.213014i | \(0.931672\pi\) | |||||||
\(824\) | 1.48813e11 | − | 2.62397e10i | 0.322798 | − | 0.0569180i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.66841e9 | − | 6.43456e9i | −0.0164735 | − | 0.0138229i | ||||
\(827\) | −3.00935e11 | + | 1.73745e11i | −0.643354 | + | 0.371441i | −0.785906 | − | 0.618347i | \(-0.787803\pi\) |
0.142551 | + | 0.989787i | \(0.454469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.97922e11 | + | 5.16016e11i | −0.630790 | + | 1.09256i | 0.356601 | + | 0.934257i | \(0.383936\pi\) |
−0.987391 | + | 0.158303i | \(0.949398\pi\) | |||||||
\(830\) | 3.26697e10 | + | 8.97592e10i | 0.0688387 | + | 0.189133i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.64695e10 | + | 3.89926e10i | −0.0969784 | + | 0.0813745i | ||||
\(833\) | −6.20629e10 | + | 1.70516e11i | −0.128900 | + | 0.354149i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.76647e10 | − | 5.53884e11i | 0.200905 | − | 1.13939i | ||||
\(836\) | 1.07501e11i | 0.220084i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.94359e10 | −0.0799678 | ||||||||
\(839\) | 3.77521e11 | + | 6.65672e10i | 0.761892 | + | 0.134342i | 0.541077 | − | 0.840973i | \(-0.318017\pi\) |
0.220816 | + | 0.975316i | \(0.429128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.31543e11 | + | 1.93466e11i | 1.06256 | + | 0.386741i | ||||
\(842\) | 6.81598e9 | + | 8.12297e9i | 0.0135606 | + | 0.0161609i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.33235e10 | − | 1.94082e10i | 0.105087 | − | 0.0382486i | ||||
\(845\) | 4.42842e11 | + | 2.55675e11i | 0.868604 | + | 0.501489i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.18083e10 | + | 3.77730e10i | 0.0423729 | + | 0.0733919i | ||||
\(848\) | 3.88945e11 | − | 4.63526e11i | 0.752150 | − | 0.896377i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.78422e8 | + | 1.57901e9i | 0.000533369 | + | 0.00302489i | ||||
\(851\) | −2.76869e11 | + | 4.88195e10i | −0.527906 | + | 0.0930840i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.58027e11 | + | 5.52150e11i | 1.24293 | + | 1.04294i | 0.997289 | + | 0.0735846i | \(0.0234439\pi\) |
0.245644 | + | 0.969360i | \(0.421001\pi\) | |||||||
\(854\) | −1.20004e10 | + | 6.92845e9i | −0.0225614 | + | 0.0130258i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.29032e10 | − | 1.26272e11i | 0.135785 | − | 0.235186i | ||||
\(857\) | 1.21489e11 | + | 3.33788e11i | 0.225223 | + | 0.618795i | 0.999908 | − | 0.0135519i | \(-0.00431385\pi\) |
−0.774685 | + | 0.632347i | \(0.782092\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.20921e11 | − | 2.69285e11i | 0.589421 | − | 0.494583i | −0.298605 | − | 0.954377i | \(-0.596521\pi\) |
0.888026 | + | 0.459794i | \(0.152077\pi\) | |||||||
\(860\) | 4.79109e10 | − | 1.31634e11i | 0.0875872 | − | 0.240644i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.36501e10 | + | 1.34127e11i | −0.0428356 | + | 0.242933i | ||||
\(863\) | − | 3.69630e11i | − | 0.666383i | −0.942859 | − | 0.333191i | \(-0.891875\pi\) | ||
0.942859 | − | 0.333191i | \(-0.108125\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.05862e11 | 1.61807 | ||||||||
\(866\) | 2.49926e10 | + | 4.40687e9i | 0.0444365 | + | 0.00783536i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.08149e11 | + | 3.93630e10i | 0.190521 | + | 0.0693441i | ||||
\(869\) | 1.89075e11 | + | 2.25331e11i | 0.331554 | + | 0.395131i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.91876e10 | − | 1.79028e10i | 0.0854639 | − | 0.0311063i | ||||
\(872\) | −3.49622e10 | − | 2.01855e10i | −0.0604691 | − | 0.0349118i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.57170e10 | + | 2.72227e10i | 0.0269355 | + | 0.0466536i | ||||
\(875\) | 3.95255e10 | − | 4.71046e10i | 0.0674287 | − | 0.0803584i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.45845e11 | + | 8.27127e11i | 0.246543 | + | 1.39821i | 0.816882 | + | 0.576805i | \(0.195701\pi\) |
−0.570339 | + | 0.821409i | \(0.693188\pi\) | |||||||
\(878\) | 1.07542e11 | − | 1.89625e10i | 0.180967 | − | 0.0319093i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.02139e11 | − | 1.69615e11i | −0.337070 | − | 0.282835i | ||||
\(881\) | −6.57619e11 | + | 3.79677e11i | −1.09162 | + | 0.630246i | −0.934007 | − | 0.357255i | \(-0.883713\pi\) |
−0.157612 | + | 0.987501i | \(0.550379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.00897e11 | − | 8.67579e11i | 0.823959 | − | 1.42714i | −0.0787530 | − | 0.996894i | \(-0.525094\pi\) |
0.902712 | − | 0.430245i | \(-0.141573\pi\) | |||||||
\(884\) | 1.14902e10 | + | 3.15692e10i | 0.0188157 | + | 0.0516957i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.58842e10 | − | 7.20654e10i | 0.139373 | − | 0.116948i | ||||
\(887\) | −2.56509e11 | + | 7.04753e11i | −0.414389 | + | 1.13853i | 0.540443 | + | 0.841380i | \(0.318257\pi\) |
−0.954832 | + | 0.297145i | \(0.903966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.10123e10 | − | 1.19167e11i | 0.0336408 | − | 0.190786i | ||||
\(890\) | 6.15342e10i | 0.0980747i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.61946e11 | −0.255805 | ||||||||
\(893\) | 3.87258e11 | + | 6.82841e10i | 0.608968 | + | 0.107378i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.62111e10 | + | 2.77386e10i | 0.118775 | + | 0.0432306i | ||||
\(896\) | −2.62876e10 | − | 3.13283e10i | −0.0407867 | − | 0.0486077i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.07227e11 | − | 3.90274e10i | 0.164892 | − | 0.0600157i | ||||
\(899\) | 1.59126e12 | + | 9.18717e11i | 2.43615 | + | 1.40651i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.58586e11 | − | 2.74678e11i | −0.240638 | − | 0.416798i | ||||
\(902\) | 5.29815e8 | − | 6.31409e8i | 0.000800384 | − | 0.000953861i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.52534e10 | − | 8.65066e10i | −0.0228399 | − | 0.129532i | ||||
\(905\) | −2.90895e11 | + | 5.12925e10i | −0.433652 | + | 0.0764645i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.50108e11 | + | 1.25956e11i | 0.221807 | + | 0.186118i | 0.746919 | − | 0.664915i | \(-0.231532\pi\) |
−0.525112 | + | 0.851033i | \(0.675977\pi\) | |||||||
\(908\) | −2.30152e11 | + | 1.32878e11i | −0.338588 | + | 0.195484i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.77852e8 | − | 1.52049e9i | 0.00128014 | − | 0.00221726i | ||||
\(911\) | 2.20777e11 | + | 6.06578e11i | 0.320538 | + | 0.880671i | 0.990406 | + | 0.138190i | \(0.0441285\pi\) |
−0.669868 | + | 0.742480i | \(0.733649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.08932e11 | + | 2.59225e11i | −0.444611 | + | 0.373073i | ||||
\(914\) | −3.60949e10 | + | 9.91700e10i | −0.0517204 | + | 0.142101i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.55180e10 | − | 4.84997e11i | 0.121472 | − | 0.688901i | ||||
\(917\) | 1.36459e11i | 0.192985i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.41781e11 | −0.899756 | −0.449878 | − | 0.893090i | \(-0.648532\pi\) | ||||
−0.449878 | + | 0.893090i | \(0.648532\pi\) | |||||||
\(920\) | −1.57948e11 | − | 2.78505e10i | −0.220477 | − | 0.0388760i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.34296e10 | − | 1.58071e10i | −0.0600983 | − | 0.0218740i | ||||
\(923\) | −7.42882e9 | − | 8.85333e9i | −0.0102356 | − | 0.0121983i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.68779e10 | − | 9.78276e9i | 0.0367137 | − | 0.0133627i | ||||
\(926\) | −6.31505e10 | − | 3.64600e10i | −0.0858881 | − | 0.0495875i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.45934e11 | − | 4.25970e11i | −0.331609 | − | 0.574363i | ||||
\(929\) | 8.58049e11 | − | 1.02258e12i | 1.15199 | − | 1.37289i | 0.235970 | − | 0.971760i | \(-0.424173\pi\) |
0.916021 | − | 0.401129i | \(-0.131382\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.28498e10 | − | 3.56439e11i | −0.0836576 | − | 0.474446i | ||||
\(932\) | −1.13388e12 | + | 1.99934e11i | −1.50281 | + | 0.264986i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.02663e11 | − | 8.61448e10i | −0.134905 | − | 0.113199i | ||||
\(935\) | −1.19784e11 | + | 6.91576e10i | −0.156731 | + | 0.0904885i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.84345e11 | + | 4.92500e11i | −0.368882 | + | 0.638922i | −0.989391 | − | 0.145277i | \(-0.953593\pi\) |
0.620509 | + | 0.784199i | \(0.286926\pi\) | |||||||
\(938\) | 2.74870e9 | + | 7.55200e9i | 0.00355072 | + | 0.00975552i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.58953e11 | + | 6.36837e11i | −0.972083 | + | 0.815675i | ||||
\(941\) | −1.33808e11 | + | 3.67635e11i | −0.170657 | + | 0.468876i | −0.995307 | − | 0.0967671i | \(-0.969150\pi\) |
0.824650 | + | 0.565643i | \(0.191372\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.66622e9 | + | 9.44963e9i | −0.00210711 | + | 0.0119500i | ||||
\(944\) | − | 9.37807e11i | − | 1.18093i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.48552e10 | −0.0185488 | ||||||||
\(947\) | −1.36936e12 | − | 2.41455e11i | −1.70262 | − | 0.300218i | −0.764011 | − | 0.645203i | \(-0.776773\pi\) |
−0.938608 | + | 0.344986i | \(0.887884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.94619e9 | − | 2.52821e9i | −0.00856410 | − | 0.00311708i | ||||
\(950\) | −2.05568e9 | − | 2.44986e9i | −0.00252383 | − | 0.00300778i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.81568e9 | + | 3.57261e9i | −0.0119501 | + | 0.00434949i | ||||
\(953\) | 2.09625e11 | + | 1.21027e11i | 0.254139 | + | 0.146727i | 0.621658 | − | 0.783289i | \(-0.286459\pi\) |
−0.367519 | + | 0.930016i | \(0.619793\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.40108e11 | − | 4.15879e11i | −0.288664 | − | 0.499980i | ||||
\(956\) | 2.24936e11 | − | 2.68068e11i | 0.269294 | − | 0.320932i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.21327e10 | − | 6.88082e10i | −0.0144045 | − | 0.0816918i | ||||
\(959\) | 8.10853e10 | − | 1.42975e10i | 0.0958667 | − | 0.0169039i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.77303e12 | + | 1.48775e12i | 2.07885 | + | 1.74436i | ||||
\(962\) | −1.30366e10 | + | 7.52670e9i | −0.0152218 | + | 0.00878829i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.99542e11 | − | 6.92028e11i | 0.462652 | − | 0.801337i | ||||
\(965\) | −2.92877e11 | − | 8.04672e11i | −0.337735 | − | 0.927918i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.96716e11 | + | 2.48974e11i | −0.339340 | + | 0.284740i | −0.796492 | − | 0.604648i | \(-0.793314\pi\) |
0.457153 | + | 0.889388i | \(0.348869\pi\) | |||||||
\(968\) | 7.29668e10 | − | 2.00475e11i | 0.0831044 | − | 0.228328i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.86586e10 | + | 2.19244e11i | −0.0436676 | + | 0.247651i | ||||
\(971\) | − | 4.12689e11i | − | 0.464243i | −0.972687 | − | 0.232122i | \(-0.925433\pi\) | ||
0.972687 | − | 0.232122i | \(-0.0745668\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.42673e11 | −0.159181 | ||||||||
\(974\) | −1.33944e11 | − | 2.36180e10i | −0.148829 | − | 0.0262426i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.21987e12 | − | 4.43997e11i | −1.34436 | − | 0.489307i | ||||
\(977\) | −2.63596e11 | − | 3.14142e11i | −0.289308 | − | 0.344784i | 0.601741 | − | 0.798692i | \(-0.294474\pi\) |
−0.891049 | + | 0.453907i | \(0.850030\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.44129e11 | + | 8.88556e10i | −0.265759 | + | 0.0967285i | ||||
\(980\) | 7.89726e11 | + | 4.55948e11i | 0.856194 | + | 0.494324i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.14176e10 | − | 7.17374e10i | −0.0445389 | − | 0.0771436i | ||||
\(983\) | 1.47538e11 | − | 1.75829e11i | 0.158012 | − | 0.188311i | −0.681230 | − | 0.732069i | \(-0.738555\pi\) |
0.839242 | + | 0.543758i | \(0.182999\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.06313e11 | + | 6.02934e11i | 0.112939 | + | 0.640508i | ||||
\(986\) | −8.10981e10 | + | 1.42998e10i | −0.0858031 | + | 0.0151294i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.13317e10 | − | 4.30724e10i | −0.0538713 | − | 0.0452034i | ||||
\(989\) | 1.49767e11 | − | 8.64681e10i | 0.156542 | − | 0.0903797i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.92488e11 | − | 5.06604e11i | 0.303259 | − | 0.525260i | −0.673613 | − | 0.739084i | \(-0.735259\pi\) |
0.976872 | + | 0.213824i | \(0.0685920\pi\) | |||||||
\(992\) | −2.89997e11 | − | 7.96761e11i | −0.299466 | − | 0.822775i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.35929e9 | − | 1.14058e9i | 0.00139241 | − | 0.00116837i | ||||
\(995\) | 1.85651e11 | − | 5.10073e11i | 0.189411 | − | 0.520403i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.61372e10 | + | 3.18370e11i | −0.0568160 | + | 0.322219i | −0.999948 | − | 0.0101990i | \(-0.996753\pi\) |
0.943132 | + | 0.332418i | \(0.107865\pi\) | |||||||
\(998\) | − | 1.01107e11i | − | 0.101920i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 81.9.f.a.8.12 | 138 | ||
3.2 | odd | 2 | 27.9.f.a.2.12 | ✓ | 138 | ||
27.13 | even | 9 | 27.9.f.a.14.12 | yes | 138 | ||
27.14 | odd | 18 | inner | 81.9.f.a.71.12 | 138 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.9.f.a.2.12 | ✓ | 138 | 3.2 | odd | 2 | ||
27.9.f.a.14.12 | yes | 138 | 27.13 | even | 9 | ||
81.9.f.a.8.12 | 138 | 1.1 | even | 1 | trivial | ||
81.9.f.a.71.12 | 138 | 27.14 | odd | 18 | inner |