Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,9,Mod(19,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.19");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.n (of order \(6\), degree \(2\), 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: | \(51.3297048677\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 1771 x^{10} + 26038 x^{9} + 2442597 x^{8} + 26522276 x^{7} + 1175865280 x^{6} + 6901058684 x^{5} + 370996492174 x^{4} + \cdots + 36\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{10}\cdot 7^{3} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(20.6104 - 35.6982i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.19 |
Dual form | 126.9.n.b.73.1 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.65685 | + | 9.79796i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −64.0000 | − | 110.851i | −0.250000 | − | 0.433013i | ||||
\(5\) | −928.109 | − | 535.844i | −1.48497 | − | 0.857350i | −0.485120 | − | 0.874448i | \(-0.661224\pi\) |
−0.999854 | + | 0.0170975i | \(0.994557\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2212.86 | + | 931.703i | 0.921639 | + | 0.388048i | ||||
\(8\) | 1448.15 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10500.4 | − | 6062.38i | 1.05004 | − | 0.606238i | ||||
\(11\) | −312.559 | − | 541.368i | −0.0213482 | − | 0.0369762i | 0.855154 | − | 0.518374i | \(-0.173463\pi\) |
−0.876502 | + | 0.481398i | \(0.840129\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 43334.3i | 1.51725i | 0.651526 | + | 0.758626i | \(0.274129\pi\) | ||||
−0.651526 | + | 0.758626i | \(0.725871\pi\) | |||||||
\(14\) | −21646.6 | + | 16411.0i | −0.563478 | + | 0.427191i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8192.00 | + | 14189.0i | −0.125000 | + | 0.216506i | ||||
\(17\) | −91086.4 | + | 52588.8i | −1.09058 | + | 0.629647i | −0.933731 | − | 0.357975i | \(-0.883467\pi\) |
−0.156850 | + | 0.987622i | \(0.550134\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −138800. | − | 80136.4i | −1.06506 | − | 0.614915i | −0.138236 | − | 0.990399i | \(-0.544143\pi\) |
−0.926829 | + | 0.375484i | \(0.877476\pi\) | |||||||
\(20\) | 137176.i | 0.857350i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7072.40 | 0.0301909 | ||||||||
\(23\) | 12272.7 | − | 21256.9i | 0.0438559 | − | 0.0759606i | −0.843264 | − | 0.537499i | \(-0.819369\pi\) |
0.887120 | + | 0.461539i | \(0.152702\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 378945. | + | 656351.i | 0.970098 | + | 1.68026i | ||||
\(26\) | −424587. | − | 245136.i | −0.929124 | − | 0.536430i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −38342.4 | − | 304927.i | −0.0623802 | − | 0.496093i | ||||
\(29\) | 201272. | 0.284572 | 0.142286 | − | 0.989826i | \(-0.454555\pi\) | ||||
0.142286 | + | 0.989826i | \(0.454555\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 757712. | − | 437465.i | 0.820459 | − | 0.473692i | −0.0301154 | − | 0.999546i | \(-0.509587\pi\) |
0.850575 | + | 0.525854i | \(0.176254\pi\) | |||||||
\(32\) | −92681.9 | − | 160530.i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.18995e6i | − | 0.890456i | ||||||
\(35\) | −1.55452e6 | − | 2.05047e6i | −1.03592 | − | 1.36641i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 830325. | − | 1.43817e6i | 0.443038 | − | 0.767365i | −0.554875 | − | 0.831934i | \(-0.687234\pi\) |
0.997913 | + | 0.0645689i | \(0.0205672\pi\) | |||||||
\(38\) | 1.57035e6 | − | 906640.i | 0.753114 | − | 0.434811i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.34404e6 | − | 775985.i | −0.525018 | − | 0.303119i | ||||
\(41\) | − | 464024.i | − | 0.164212i | −0.996624 | − | 0.0821060i | \(-0.973835\pi\) | ||
0.996624 | − | 0.0821060i | \(-0.0261646\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.94357e6 | −0.860994 | −0.430497 | − | 0.902592i | \(-0.641662\pi\) | ||||
−0.430497 | + | 0.902592i | \(0.641662\pi\) | |||||||
\(44\) | −40007.5 | + | 69295.1i | −0.0106741 | + | 0.0184881i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 138849. | + | 240494.i | 0.0310108 | + | 0.0537123i | ||||
\(47\) | 2.19794e6 | + | 1.26898e6i | 0.450427 | + | 0.260054i | 0.708011 | − | 0.706202i | \(-0.249593\pi\) |
−0.257583 | + | 0.966256i | \(0.582926\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.02866e6 | + | 4.12345e6i | 0.698838 | + | 0.715280i | ||||
\(50\) | −8.57454e6 | −1.37193 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.80366e6 | − | 2.77339e6i | 0.656990 | − | 0.379313i | ||||
\(53\) | 1.79237e6 | + | 3.10447e6i | 0.227156 | + | 0.393445i | 0.956964 | − | 0.290207i | \(-0.0937240\pi\) |
−0.729808 | + | 0.683652i | \(0.760391\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 669931.i | 0.0732115i | ||||||||
\(56\) | 3.20456e6 | + | 1.34925e6i | 0.325849 | + | 0.137196i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.13857e6 | + | 1.97206e6i | −0.100611 | + | 0.174264i | ||||
\(59\) | −5.42785e6 | + | 3.13377e6i | −0.447940 | + | 0.258618i | −0.706960 | − | 0.707254i | \(-0.749934\pi\) |
0.259020 | + | 0.965872i | \(0.416600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.03573e7 | − | 5.97980e6i | −0.748045 | − | 0.431884i | 0.0769420 | − | 0.997036i | \(-0.475484\pi\) |
−0.824987 | + | 0.565152i | \(0.808818\pi\) | |||||||
\(62\) | 9.89870e6i | 0.669902i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.09715e6 | 0.125000 | ||||||||
\(65\) | 2.32204e7 | − | 4.02189e7i | 1.30082 | − | 2.25308i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.34103e6 | − | 9.25093e6i | −0.265049 | − | 0.459078i | 0.702528 | − | 0.711656i | \(-0.252055\pi\) |
−0.967576 | + | 0.252579i | \(0.918721\pi\) | |||||||
\(68\) | 1.16591e7 | + | 6.73136e6i | 0.545291 | + | 0.314824i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.88841e7 | − | 3.63197e6i | 1.20300 | − | 0.151269i | ||||
\(71\) | 2.25839e7 | 0.888721 | 0.444361 | − | 0.895848i | \(-0.353431\pi\) | ||||
0.444361 | + | 0.895848i | \(0.353431\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.20899e7 | − | 2.43006e7i | 1.48213 | − | 0.855709i | 0.482337 | − | 0.875986i | \(-0.339788\pi\) |
0.999794 | + | 0.0202769i | \(0.00645479\pi\) | |||||||
\(74\) | 9.39406e6 | + | 1.62710e7i | 0.313275 | + | 0.542609i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.05149e7i | 0.614915i | ||||||||
\(77\) | −187254. | − | 1.48918e6i | −0.00532682 | − | 0.0423628i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.70859e7 | − | 4.69142e7i | 0.695401 | − | 1.20447i | −0.274645 | − | 0.961546i | \(-0.588560\pi\) |
0.970045 | − | 0.242924i | \(-0.0781064\pi\) | |||||||
\(80\) | 1.52061e7 | − | 8.77926e6i | 0.371243 | − | 0.214338i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.54649e6 | + | 2.62492e6i | 0.100559 | + | 0.0580577i | ||||
\(83\) | − | 2.28950e7i | − | 0.482424i | −0.970472 | − | 0.241212i | \(-0.922455\pi\) | ||
0.970472 | − | 0.241212i | \(-0.0775449\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.12717e8 | 2.15931 | ||||||||
\(86\) | 1.66513e7 | − | 2.88409e7i | 0.304407 | − | 0.527249i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −452634. | − | 783985.i | −0.00754773 | − | 0.0130730i | ||||
\(89\) | −7.46258e7 | − | 4.30852e7i | −1.18940 | − | 0.686702i | −0.231232 | − | 0.972899i | \(-0.574276\pi\) |
−0.958171 | + | 0.286197i | \(0.907609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.03747e7 | + | 9.58925e7i | −0.588767 | + | 1.39836i | ||||
\(92\) | −3.14181e6 | −0.0438559 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.48669e7 | + | 1.43569e7i | −0.318500 | + | 0.183886i | ||||
\(95\) | 8.58812e7 | + | 1.48751e8i | 1.05440 | + | 1.82627i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.34358e8i | − | 1.51766i | −0.651287 | − | 0.758831i | \(-0.725771\pi\) | ||
0.651287 | − | 0.758831i | \(-0.274229\pi\) | |||||||
\(98\) | −6.31909e7 | + | 1.61469e7i | −0.685094 | + | 0.175059i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.85049e7 | − | 8.40130e7i | 0.485049 | − | 0.840130i | ||||
\(101\) | 3.28253e7 | − | 1.89517e7i | 0.315445 | − | 0.182122i | −0.333915 | − | 0.942603i | \(-0.608370\pi\) |
0.649360 | + | 0.760481i | \(0.275037\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.02126e8 | + | 5.89624e7i | 0.907375 | + | 0.523873i | 0.879586 | − | 0.475741i | \(-0.157820\pi\) |
0.0277893 | + | 0.999614i | \(0.491153\pi\) | |||||||
\(104\) | 6.27547e7i | 0.536430i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.05567e7 | −0.321247 | ||||||||
\(107\) | 2.25483e7 | − | 3.90548e7i | 0.172020 | − | 0.297947i | −0.767106 | − | 0.641520i | \(-0.778304\pi\) |
0.939126 | + | 0.343573i | \(0.111637\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 722053. | + | 1.25063e6i | 0.00511520 | + | 0.00885979i | 0.868572 | − | 0.495564i | \(-0.165038\pi\) |
−0.863456 | + | 0.504423i | \(0.831705\pi\) | |||||||
\(110\) | −6.56396e6 | − | 3.78970e6i | −0.0448327 | − | 0.0258842i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.13476e7 | + | 2.37656e7i | −0.199220 | + | 0.151035i | ||||
\(113\) | 2.56178e8 | 1.57119 | 0.785594 | − | 0.618742i | \(-0.212357\pi\) | ||||
0.785594 | + | 0.618742i | \(0.212357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.27808e7 | + | 1.31525e7i | −0.130250 | + | 0.0751997i | ||||
\(116\) | −1.28814e7 | − | 2.23113e7i | −0.0711430 | − | 0.123223i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 7.09091e7i | − | 0.365741i | ||||||
\(119\) | −2.50558e8 | + | 3.15059e7i | −1.24946 | + | 0.157110i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.06984e8 | − | 1.85302e8i | 0.499089 | − | 0.864447i | ||||
\(122\) | 1.17180e8 | − | 6.76537e7i | 0.528948 | − | 0.305388i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.69871e7 | − | 5.59955e7i | −0.410230 | − | 0.236846i | ||||
\(125\) | − | 3.93593e8i | − | 1.61215i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.98954e8 | −0.764783 | −0.382391 | − | 0.924000i | \(-0.624899\pi\) | ||||
−0.382391 | + | 0.924000i | \(0.624899\pi\) | |||||||
\(128\) | −1.18633e7 | + | 2.05478e7i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.62709e8 | + | 4.55025e8i | 0.919816 | + | 1.59317i | ||||
\(131\) | −3.13374e8 | − | 1.80926e8i | −1.06409 | − | 0.614351i | −0.137527 | − | 0.990498i | \(-0.543915\pi\) |
−0.926560 | + | 0.376147i | \(0.877249\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.32482e8 | − | 3.06651e8i | −0.742989 | − | 0.980026i | ||||
\(134\) | 1.20854e8 | 0.374836 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.31907e8 | + | 7.61567e7i | −0.385579 | + | 0.222614i | ||||
\(137\) | −8.75137e6 | − | 1.51578e7i | −0.0248424 | − | 0.0430283i | 0.853337 | − | 0.521360i | \(-0.174575\pi\) |
−0.878179 | + | 0.478332i | \(0.841242\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.04614e8i | 1.35176i | 0.737011 | + | 0.675881i | \(0.236237\pi\) | ||||
−0.737011 | + | 0.675881i | \(0.763763\pi\) | |||||||
\(140\) | −1.27807e8 | + | 3.03551e8i | −0.332693 | + | 0.790167i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.27754e8 | + | 2.21276e8i | −0.314210 | + | 0.544229i | ||||
\(143\) | 2.34598e7 | − | 1.35445e7i | 0.0561022 | − | 0.0323906i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.86803e8 | − | 1.07850e8i | −0.422582 | − | 0.243978i | ||||
\(146\) | 5.49860e8i | 1.21016i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.12563e8 | −0.443038 | ||||||||
\(149\) | 1.33029e8 | − | 2.30412e8i | 0.269898 | − | 0.467477i | −0.698937 | − | 0.715183i | \(-0.746343\pi\) |
0.968835 | + | 0.247706i | \(0.0796767\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.14108e8 | − | 5.44051e8i | −0.604187 | − | 1.04648i | −0.992179 | − | 0.124820i | \(-0.960165\pi\) |
0.387992 | − | 0.921663i | \(-0.373169\pi\) | |||||||
\(152\) | −2.01004e8 | − | 1.16050e8i | −0.376557 | − | 0.217405i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.56502e7 | + | 6.58938e6i | 0.0278251 | + | 0.0117155i | ||||
\(155\) | −9.37652e8 | −1.62448 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.35298e8 | + | 7.81141e7i | −0.222685 | + | 0.128567i | −0.607193 | − | 0.794554i | \(-0.707705\pi\) |
0.384508 | + | 0.923122i | \(0.374371\pi\) | |||||||
\(158\) | 3.06442e8 | + | 5.30773e8i | 0.491723 | + | 0.851688i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.98652e8i | 0.303119i | ||||||||
\(161\) | 4.69628e7 | − | 3.56040e7i | 0.0698957 | − | 0.0529901i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.22381e8 | − | 5.58380e8i | 0.456687 | − | 0.791005i | −0.542096 | − | 0.840316i | \(-0.682369\pi\) |
0.998783 | + | 0.0493110i | \(0.0157025\pi\) | |||||||
\(164\) | −5.14376e7 | + | 2.96975e7i | −0.0711059 | + | 0.0410530i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.24325e8 | + | 1.29514e8i | 0.295423 | + | 0.170563i | ||||
\(167\) | − | 4.01008e8i | − | 0.515569i | −0.966202 | − | 0.257785i | \(-0.917007\pi\) | ||
0.966202 | − | 0.257785i | \(-0.0829925\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.06213e9 | −1.30206 | ||||||||
\(170\) | −6.37626e8 | + | 1.10440e9i | −0.763432 | + | 1.32230i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.88388e8 | + | 3.26298e8i | 0.215248 | + | 0.372821i | ||||
\(173\) | 6.72494e8 | + | 3.88265e8i | 0.750765 | + | 0.433454i | 0.825970 | − | 0.563714i | \(-0.190628\pi\) |
−0.0752052 | + | 0.997168i | \(0.523961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.27025e8 | + | 1.80547e9i | 0.242060 | + | 1.92504i | ||||
\(176\) | 1.02419e7 | 0.0106741 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.44295e8 | − | 4.87454e8i | 0.841035 | − | 0.485572i | ||||
\(179\) | −1.31349e8 | − | 2.27504e8i | −0.127943 | − | 0.221604i | 0.794937 | − | 0.606693i | \(-0.207504\pi\) |
−0.922879 | + | 0.385089i | \(0.874171\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.26304e8i | 0.583540i | 0.956488 | + | 0.291770i | \(0.0942442\pi\) | ||||
−0.956488 | + | 0.291770i | \(0.905756\pi\) | |||||||
\(182\) | −7.11157e8 | − | 9.38039e8i | −0.648157 | − | 0.854939i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.77727e7 | − | 3.07833e7i | 0.0155054 | − | 0.0268561i | ||||
\(185\) | −1.54126e9 | + | 8.89849e8i | −1.31580 | + | 0.759678i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.69398e7 | + | 3.28742e7i | 0.0465639 | + | 0.0268837i | ||||
\(188\) | − | 3.24859e8i | − | 0.260054i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.94327e9 | −1.49114 | ||||||||
\(191\) | 1.19335e9 | − | 2.06694e9i | 0.896673 | − | 1.55308i | 0.0649528 | − | 0.997888i | \(-0.479310\pi\) |
0.831720 | − | 0.555195i | \(-0.187356\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.37008e8 | − | 4.10510e8i | −0.170818 | − | 0.295865i | 0.767888 | − | 0.640584i | \(-0.221308\pi\) |
−0.938706 | + | 0.344719i | \(0.887974\pi\) | |||||||
\(194\) | 1.31643e9 | + | 7.60041e8i | 0.929375 | + | 0.536575i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.99255e8 | − | 7.10483e8i | 0.135016 | − | 0.481426i | ||||
\(197\) | 2.00834e9 | 1.33343 | 0.666717 | − | 0.745311i | \(-0.267699\pi\) | ||||
0.666717 | + | 0.745311i | \(0.267699\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.10273e8 | + | 4.67811e8i | −0.516677 | + | 0.298303i | −0.735574 | − | 0.677444i | \(-0.763087\pi\) |
0.218897 | + | 0.975748i | \(0.429754\pi\) | |||||||
\(200\) | 5.48770e8 | + | 9.50498e8i | 0.342982 | + | 0.594061i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.28828e8i | 0.257560i | ||||||||
\(203\) | 4.45386e8 | + | 1.87526e8i | 0.262273 | + | 0.110427i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.48644e8 | + | 4.30665e8i | −0.140787 | + | 0.243851i | ||||
\(206\) | −1.15542e9 | + | 6.67083e8i | −0.641611 | + | 0.370434i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.14868e8 | − | 3.54994e8i | −0.328495 | − | 0.189657i | ||||
\(209\) | 1.00189e8i | 0.0525093i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.34825e9 | 0.680205 | 0.340103 | − | 0.940388i | \(-0.389538\pi\) | ||||
0.340103 | + | 0.940388i | \(0.389538\pi\) | |||||||
\(212\) | 2.29423e8 | − | 3.97373e8i | 0.113578 | − | 0.196723i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.55105e8 | + | 4.41854e8i | 0.121636 | + | 0.210680i | ||||
\(215\) | 2.73195e9 | + | 1.57729e9i | 1.27855 | + | 0.738173i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.08429e9 | − | 2.62085e8i | 0.939983 | − | 0.118196i | ||||
\(218\) | −1.63382e7 | −0.00723399 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.42627e7 | − | 4.28756e7i | 0.0317015 | − | 0.0183029i | ||||
\(221\) | −2.27890e9 | − | 3.94716e9i | −0.955334 | − | 1.65469i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.27893e9i | − | 0.921533i | −0.887521 | − | 0.460767i | \(-0.847575\pi\) | ||
0.887521 | − | 0.460767i | \(-0.152425\pi\) | |||||||
\(224\) | −5.55257e7 | − | 4.41581e8i | −0.0220547 | − | 0.175396i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.44916e9 | + | 2.51002e9i | −0.555499 | + | 0.962153i | ||||
\(227\) | −2.55953e9 | + | 1.47774e9i | −0.963954 | + | 0.556539i | −0.897388 | − | 0.441243i | \(-0.854538\pi\) |
−0.0665664 | + | 0.997782i | \(0.521204\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.42462e8 | + | 8.22504e7i | 0.0518032 | + | 0.0299086i | 0.525678 | − | 0.850684i | \(-0.323812\pi\) |
−0.473875 | + | 0.880592i | \(0.657145\pi\) | |||||||
\(230\) | − | 2.97607e8i | − | 0.106348i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.91473e8 | 0.100611 | ||||||||
\(233\) | −2.52459e9 | + | 4.37272e9i | −0.856579 | + | 1.48364i | 0.0185942 | + | 0.999827i | \(0.494081\pi\) |
−0.875173 | + | 0.483811i | \(0.839252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.35995e9 | − | 2.35551e9i | −0.445915 | − | 0.772347i | ||||
\(236\) | 6.94765e8 | + | 4.01123e8i | 0.223970 | + | 0.129309i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.10868e9 | − | 2.63318e9i | 0.345539 | − | 0.820679i | ||||
\(239\) | −5.80584e8 | −0.177940 | −0.0889699 | − | 0.996034i | \(-0.528358\pi\) | ||||
−0.0889699 | + | 0.996034i | \(0.528358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.79705e9 | + | 2.19223e9i | −1.12559 | + | 0.649857i | −0.942821 | − | 0.333300i | \(-0.891838\pi\) |
−0.182765 | + | 0.983157i | \(0.558505\pi\) | |||||||
\(242\) | 1.21039e9 | + | 2.09645e9i | 0.352909 | + | 0.611256i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.53083e9i | 0.431884i | ||||||||
\(245\) | −1.52951e9 | − | 5.98574e9i | −0.424510 | − | 1.66132i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.47265e9 | − | 6.01481e9i | 0.932982 | − | 1.61597i | ||||
\(248\) | 1.09728e9 | − | 6.33517e8i | 0.290076 | − | 0.167476i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.85640e9 | + | 2.22650e9i | 0.987239 | + | 0.569983i | ||||
\(251\) | − | 4.01412e9i | − | 1.01134i | −0.862728 | − | 0.505668i | \(-0.831246\pi\) | ||
0.862728 | − | 0.505668i | \(-0.168754\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.53437e7 | −0.00374498 | ||||||||
\(254\) | 1.12545e9 | − | 1.94935e9i | 0.270392 | − | 0.468332i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.34218e8 | − | 2.32472e8i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.04886e9 | + | 2.91496e9i | 1.15734 | + | 0.668190i | 0.950665 | − | 0.310220i | \(-0.100403\pi\) |
0.206674 | + | 0.978410i | \(0.433736\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.17733e9 | − | 2.40884e9i | 0.706096 | − | 0.535314i | ||||
\(260\) | −5.94442e9 | −1.30082 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.54542e9 | − | 2.04695e9i | 0.752423 | − | 0.434412i | ||||
\(263\) | −4.65172e6 | − | 8.05701e6i | −0.000972278 | − | 0.00168403i | 0.865539 | − | 0.500842i | \(-0.166976\pi\) |
−0.866511 | + | 0.499158i | \(0.833643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.84172e9i | − | 0.779008i | ||||||
\(266\) | 4.31967e9 | − | 5.43167e8i | 0.862827 | − | 0.108494i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.83652e8 | + | 1.18412e9i | −0.132524 | + | 0.229539i | ||||
\(269\) | 2.50581e9 | − | 1.44673e9i | 0.478563 | − | 0.276298i | −0.241255 | − | 0.970462i | \(-0.577559\pi\) |
0.719817 | + | 0.694164i | \(0.244226\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.08901e9 | + | 1.78344e9i | 0.572719 | + | 0.330660i | 0.758235 | − | 0.651982i | \(-0.226062\pi\) |
−0.185515 | + | 0.982641i | \(0.559395\pi\) | |||||||
\(272\) | − | 1.72323e9i | − | 0.314824i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.98021e8 | 0.0351325 | ||||||||
\(275\) | 2.36885e8 | − | 4.10297e8i | 0.0414197 | − | 0.0717410i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.37953e9 | + | 7.58557e9i | 0.743890 | + | 1.28846i | 0.950712 | + | 0.310076i | \(0.100355\pi\) |
−0.206822 | + | 0.978379i | \(0.566312\pi\) | |||||||
\(278\) | −4.94419e9 | − | 2.85453e9i | −0.827782 | − | 0.477920i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.25119e9 | − | 2.96939e9i | −0.366252 | − | 0.483098i | ||||
\(281\) | −1.01410e9 | −0.162650 | −0.0813251 | − | 0.996688i | \(-0.525915\pi\) | ||||
−0.0813251 | + | 0.996688i | \(0.525915\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.88672e9 | − | 1.08930e9i | 0.294145 | − | 0.169825i | −0.345665 | − | 0.938358i | \(-0.612347\pi\) |
0.639810 | + | 0.768534i | \(0.279013\pi\) | |||||||
\(284\) | −1.44537e9 | − | 2.50345e9i | −0.222180 | − | 0.384828i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.06477e8i | 0.0458072i | ||||||||
\(287\) | 4.32332e8 | − | 1.02682e9i | 0.0637221 | − | 0.151344i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.04328e9 | − | 3.53906e9i | 0.292912 | − | 0.507338i | ||||
\(290\) | 2.11343e9 | − | 1.22019e9i | 0.298810 | − | 0.172518i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.38751e9 | − | 3.11048e9i | −0.741066 | − | 0.427854i | ||||
\(293\) | 5.77278e9i | 0.783275i | 0.920120 | + | 0.391637i | \(0.128091\pi\) | ||||
−0.920120 | + | 0.391637i | \(0.871909\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.71684e9 | 0.886905 | ||||||||
\(296\) | 1.20244e9 | − | 2.08269e9i | 0.156638 | − | 0.271304i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.50505e9 | + | 2.60682e9i | 0.190847 | + | 0.330556i | ||||
\(299\) | 9.21152e8 | + | 5.31827e8i | 0.115251 | + | 0.0665405i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.51369e9 | − | 2.74253e9i | −0.793525 | − | 0.334107i | ||||
\(302\) | 7.10746e9 | 0.854449 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.27410e9 | − | 1.31295e9i | 0.266266 | − | 0.153729i | ||||
\(305\) | 6.40847e9 | + | 1.10998e10i | 0.740552 | + | 1.28267i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.41085e9i | 0.946862i | 0.880831 | + | 0.473431i | \(0.156985\pi\) | ||||
−0.880831 | + | 0.473431i | \(0.843015\pi\) | |||||||
\(308\) | −1.53093e8 | + | 1.16065e8i | −0.0170119 | + | 0.0128973i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.30416e9 | − | 9.18707e9i | 0.574341 | − | 0.994787i | ||||
\(311\) | −1.22281e10 | + | 7.05989e9i | −1.30713 | + | 0.754669i | −0.981615 | − | 0.190869i | \(-0.938869\pi\) |
−0.325510 | + | 0.945539i | \(0.605536\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.89621e9 | + | 2.82683e9i | 0.510132 | + | 0.294525i | 0.732888 | − | 0.680349i | \(-0.238172\pi\) |
−0.222756 | + | 0.974874i | \(0.571505\pi\) | |||||||
\(314\) | − | 1.76752e9i | − | 0.181822i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.93399e9 | −0.695401 | ||||||||
\(317\) | −1.02907e9 | + | 1.78241e9i | −0.101908 | + | 0.176510i | −0.912471 | − | 0.409142i | \(-0.865828\pi\) |
0.810563 | + | 0.585652i | \(0.199161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.29094e7 | − | 1.08962e8i | −0.00607509 | − | 0.0105224i | ||||
\(320\) | −1.94638e9 | − | 1.12375e9i | −0.185622 | − | 0.107169i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.31846e7 | + | 6.61546e8i | 0.00773784 | + | 0.0615370i | ||||
\(323\) | 1.68571e10 | 1.54872 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.84425e10 | + | 1.64213e10i | −2.54938 | + | 1.47188i | ||||
\(326\) | 3.64732e9 | + | 6.31735e9i | 0.322927 | + | 0.559325i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6.71978e8i | − | 0.0580577i | ||||||
\(329\) | 3.68141e9 | + | 4.85590e9i | 0.314218 | + | 0.414463i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.84939e9 | + | 3.20323e9i | −0.154069 | + | 0.266856i | −0.932720 | − | 0.360602i | \(-0.882571\pi\) |
0.778650 | + | 0.627458i | \(0.215905\pi\) | |||||||
\(332\) | −2.53794e9 | + | 1.46528e9i | −0.208896 | + | 0.120606i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.92906e9 | + | 2.26844e9i | 0.315720 | + | 0.182281i | ||||
\(335\) | 1.14478e10i | 0.908958i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.14169e10 | 0.885171 | 0.442586 | − | 0.896726i | \(-0.354061\pi\) | ||||
0.442586 | + | 0.896726i | \(0.354061\pi\) | |||||||
\(338\) | 6.00830e9 | − | 1.04067e10i | 0.460346 | − | 0.797343i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.21392e9 | − | 1.24949e10i | −0.539828 | − | 0.935010i | ||||
\(341\) | −4.73659e8 | − | 2.73467e8i | −0.0350307 | − | 0.0202250i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.07302e9 | + | 1.28781e10i | 0.366513 | + | 0.930413i | ||||
\(344\) | −4.26274e9 | −0.304407 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.60840e9 | + | 4.39271e9i | −0.530871 | + | 0.306499i | ||||
\(347\) | −5.05429e9 | − | 8.75429e9i | −0.348612 | − | 0.603814i | 0.637391 | − | 0.770540i | \(-0.280014\pi\) |
−0.986003 | + | 0.166727i | \(0.946680\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.23530e9i | − | 0.150672i | −0.997158 | − | 0.0753362i | \(-0.975997\pi\) | ||
0.997158 | − | 0.0753362i | \(-0.0240030\pi\) | |||||||
\(350\) | −1.89742e10 | − | 7.98892e9i | −1.26442 | − | 0.532373i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.79371e7 | + | 1.00350e8i | −0.00377386 | + | 0.00653652i | ||||
\(353\) | 1.12278e10 | − | 6.48240e9i | 0.723098 | − | 0.417481i | −0.0927937 | − | 0.995685i | \(-0.529580\pi\) |
0.815892 | + | 0.578204i | \(0.196246\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.09603e10 | − | 1.21014e10i | −1.31973 | − | 0.761945i | ||||
\(356\) | 1.10298e10i | 0.686702i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.97210e9 | 0.180939 | ||||||||
\(359\) | 1.51567e10 | − | 2.62522e10i | 0.912488 | − | 1.58048i | 0.101950 | − | 0.994790i | \(-0.467492\pi\) |
0.810538 | − | 0.585686i | \(-0.199175\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.35190e9 | + | 7.53770e9i | 0.256242 | + | 0.443823i | ||||
\(362\) | −6.13650e9 | − | 3.54291e9i | −0.357344 | − | 0.206313i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.32138e10 | − | 1.66154e9i | 0.752699 | − | 0.0946465i | ||||
\(365\) | −5.20854e10 | −2.93457 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.69235e9 | + | 2.70913e9i | −0.258658 | + | 0.149336i | −0.623722 | − | 0.781646i | \(-0.714380\pi\) |
0.365064 | + | 0.930982i | \(0.381047\pi\) | |||||||
\(368\) | 2.01076e8 | + | 3.48273e8i | 0.0109640 | + | 0.0189902i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 2.01350e10i | − | 1.07435i | ||||||
\(371\) | 1.07381e9 | + | 8.53971e9i | 0.0566801 | + | 0.450762i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.95213e9 | − | 6.84529e9i | 0.204172 | − | 0.353636i | −0.745697 | − | 0.666286i | \(-0.767883\pi\) |
0.949869 | + | 0.312649i | \(0.101217\pi\) | |||||||
\(374\) | −6.44200e8 | + | 3.71929e8i | −0.0329256 | + | 0.0190096i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.18296e9 | + | 1.83768e9i | 0.159250 | + | 0.0919431i | ||||
\(377\) | 8.72198e9i | 0.431767i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.84501e10 | −0.894216 | −0.447108 | − | 0.894480i | \(-0.647546\pi\) | ||||
−0.447108 | + | 0.894480i | \(0.647546\pi\) | |||||||
\(380\) | 1.09928e10 | − | 1.90401e10i | 0.527198 | − | 0.913133i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.35012e10 | + | 2.33848e10i | 0.634044 | + | 1.09820i | ||||
\(383\) | 8.39027e9 | + | 4.84413e9i | 0.389925 | + | 0.225123i | 0.682128 | − | 0.731233i | \(-0.261055\pi\) |
−0.292203 | + | 0.956356i | \(0.594388\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.24177e8 | + | 1.48246e9i | −0.0284096 | + | 0.0674746i | ||||
\(386\) | 5.36287e9 | 0.241573 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.48937e10 | + | 8.59888e9i | −0.657167 | + | 0.379416i | ||||
\(389\) | 1.29668e10 | + | 2.24592e10i | 0.566285 | + | 0.980834i | 0.996929 | + | 0.0783124i | \(0.0249532\pi\) |
−0.430644 | + | 0.902522i | \(0.641714\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58162e9i | 0.110455i | ||||||||
\(392\) | 5.83412e9 | + | 5.97139e9i | 0.247076 | + | 0.252890i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.13609e10 | + | 1.96776e10i | −0.471440 | + | 0.816558i | ||||
\(395\) | −5.02773e10 | + | 2.90276e10i | −2.06530 | + | 1.19240i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.43145e10 | − | 1.98115e10i | −1.38139 | − | 0.797545i | −0.389065 | − | 0.921210i | \(-0.627202\pi\) |
−0.992324 | + | 0.123665i | \(0.960535\pi\) | |||||||
\(398\) | − | 1.05854e10i | − | 0.421865i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.24173e10 | −0.485049 | ||||||||
\(401\) | 1.82067e9 | − | 3.15349e9i | 0.0704131 | − | 0.121959i | −0.828669 | − | 0.559738i | \(-0.810902\pi\) |
0.899082 | + | 0.437779i | \(0.144235\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.89572e10 | + | 3.28349e10i | 0.718711 | + | 1.24484i | ||||
\(404\) | −4.20164e9 | − | 2.42582e9i | −0.157723 | − | 0.0910611i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.35686e9 | + | 3.30307e9i | −0.160350 | + | 0.121566i | ||||
\(407\) | −1.03810e9 | −0.0378323 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.30558e10 | − | 1.90847e10i | 1.18128 | − | 0.682014i | 0.224972 | − | 0.974365i | \(-0.427771\pi\) |
0.956311 | + | 0.292352i | \(0.0944377\pi\) | |||||||
\(410\) | −2.81309e9 | − | 4.87241e9i | −0.0995516 | − | 0.172428i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 1.50944e10i | − | 0.523873i | ||||||
\(413\) | −1.49308e10 | + | 1.87744e9i | −0.513195 | + | 0.0645306i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.22682e10 | + | 2.12491e10i | −0.413606 | + | 0.716387i | ||||
\(416\) | 6.95644e9 | − | 4.01630e9i | 0.232281 | − | 0.134107i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.81651e8 | − | 5.66757e8i | −0.0321553 | − | 0.0185649i | ||||
\(419\) | 1.70754e10i | 0.554007i | 0.960869 | + | 0.277004i | \(0.0893414\pi\) | ||||
−0.960869 | + | 0.277004i | \(0.910659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.86510e10 | −0.912033 | −0.456017 | − | 0.889971i | \(-0.650724\pi\) | ||||
−0.456017 | + | 0.889971i | \(0.650724\pi\) | |||||||
\(422\) | −7.62684e9 | + | 1.32101e10i | −0.240489 | + | 0.416539i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.59563e9 | + | 4.49576e9i | 0.0803117 | + | 0.139104i | ||||
\(425\) | −6.90334e10 | − | 3.98565e10i | −2.11594 | − | 1.22164i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.73478e10 | − | 2.28824e10i | −0.521836 | − | 0.688319i | ||||
\(428\) | −5.77236e9 | −0.172020 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.09085e10 | + | 1.78450e10i | −0.904073 | + | 0.521967i | ||||
\(431\) | 2.28785e10 | + | 3.96268e10i | 0.663009 | + | 1.14836i | 0.979821 | + | 0.199876i | \(0.0640541\pi\) |
−0.316813 | + | 0.948488i | \(0.602613\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.41731e10i | − | 0.403193i | −0.979469 | − | 0.201597i | \(-0.935387\pi\) | ||
0.979469 | − | 0.201597i | \(-0.0646130\pi\) | |||||||
\(434\) | −9.22265e9 | + | 2.19044e10i | −0.259954 | + | 0.617408i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.24228e7 | − | 1.60081e8i | 0.00255760 | − | 0.00442990i | ||||
\(437\) | −3.40690e9 | + | 1.96698e9i | −0.0934187 | + | 0.0539353i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.46361e9 | − | 4.88647e9i | −0.227875 | − | 0.131564i | 0.381716 | − | 0.924280i | \(-0.375333\pi\) |
−0.609592 | + | 0.792716i | \(0.708667\pi\) | |||||||
\(440\) | 9.70164e8i | 0.0258842i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.15655e10 | 1.35105 | ||||||||
\(443\) | 2.55450e10 | − | 4.42452e10i | 0.663270 | − | 1.14882i | −0.316481 | − | 0.948599i | \(-0.602501\pi\) |
0.979751 | − | 0.200219i | \(-0.0641653\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.61739e10 | + | 7.99755e10i | 1.17749 | + | 2.03947i | ||||
\(446\) | 2.23288e10 | + | 1.28916e10i | 0.564321 | + | 0.325811i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.64070e9 | + | 1.95392e9i | 0.115205 | + | 0.0485060i | ||||
\(449\) | 2.61180e10 | 0.642620 | 0.321310 | − | 0.946974i | \(-0.395877\pi\) | ||||
0.321310 | + | 0.946974i | \(0.395877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.51208e8 | + | 1.45035e8i | −0.00607193 | + | 0.00350563i | ||||
\(452\) | −1.63954e10 | − | 2.83977e10i | −0.392797 | − | 0.680345i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 3.34375e10i | − | 0.787065i | ||||||
\(455\) | 8.88554e10 | − | 6.73641e10i | 2.07319 | − | 1.57175i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.19803e10 | − | 5.53914e10i | 0.733191 | − | 1.26992i | −0.222322 | − | 0.974973i | \(-0.571363\pi\) |
0.955513 | − | 0.294951i | \(-0.0953032\pi\) | |||||||
\(458\) | −1.61177e9 | + | 9.30557e8i | −0.0366304 | + | 0.0211486i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.91594e9 | + | 1.68352e9i | 0.0651248 | + | 0.0375998i | ||||
\(461\) | − | 6.21950e10i | − | 1.37706i | −0.725210 | − | 0.688528i | \(-0.758257\pi\) | ||
0.725210 | − | 0.688528i | \(-0.241743\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.25332e10 | 0.707951 | 0.353976 | − | 0.935255i | \(-0.384830\pi\) | ||||
0.353976 | + | 0.935255i | \(0.384830\pi\) | |||||||
\(464\) | −1.64882e9 | + | 2.85584e9i | −0.0355715 | + | 0.0616116i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.85625e10 | − | 4.94717e10i | −0.605693 | − | 1.04909i | ||||
\(467\) | 7.58397e10 | + | 4.37861e10i | 1.59452 | + | 0.920594i | 0.992518 | + | 0.122097i | \(0.0389619\pi\) |
0.601998 | + | 0.798497i | \(0.294371\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.19981e9 | − | 2.54472e10i | −0.0661352 | − | 0.525956i | ||||
\(470\) | 3.07722e10 | 0.630619 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.86036e9 | + | 4.53818e9i | −0.158371 | + | 0.0914353i | ||||
\(473\) | 9.20038e8 | + | 1.59355e9i | 0.0183807 | + | 0.0318362i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.21469e11i | − | 2.38611i | ||||||
\(476\) | 1.95282e10 | + | 2.57583e10i | 0.380395 | + | 0.501753i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.28428e9 | − | 5.68854e9i | 0.0629112 | − | 0.108965i | ||||
\(479\) | 5.86256e10 | − | 3.38475e10i | 1.11364 | − | 0.642960i | 0.173870 | − | 0.984769i | \(-0.444373\pi\) |
0.939770 | + | 0.341808i | \(0.111039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.23218e10 | + | 3.59815e10i | 1.16429 | + | 0.672201i | ||||
\(482\) | − | 4.96045e10i | − | 0.919037i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.73879e10 | −0.499089 | ||||||||
\(485\) | −7.19947e10 | + | 1.24698e11i | −1.30117 | + | 2.25369i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.77087e8 | − | 3.06724e8i | −0.00314826 | − | 0.00545295i | 0.864447 | − | 0.502724i | \(-0.167669\pi\) |
−0.867595 | + | 0.497271i | \(0.834335\pi\) | |||||||
\(488\) | −1.49990e10 | − | 8.65967e9i | −0.264474 | − | 0.152694i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.73003e10 | + | 1.88744e10i | 1.16743 | + | 0.327407i | ||||
\(491\) | −3.00967e10 | −0.517837 | −0.258918 | − | 0.965899i | \(-0.583366\pi\) | ||||
−0.258918 | + | 0.965899i | \(0.583366\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.83332e10 | + | 1.05847e10i | −0.310349 | + | 0.179180i | ||||
\(494\) | 3.92886e10 | + | 6.80498e10i | 0.659718 | + | 1.14266i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.43349e10i | 0.236846i | ||||||||
\(497\) | 4.99749e10 | + | 2.10415e10i | 0.819081 | + | 0.344866i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.64618e10 | + | 4.58332e10i | −0.426793 | + | 0.739228i | −0.996586 | − | 0.0825607i | \(-0.973690\pi\) |
0.569793 | + | 0.821788i | \(0.307023\pi\) | |||||||
\(500\) | −4.36302e10 | + | 2.51899e10i | −0.698084 | + | 0.403039i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.93301e10 | + | 2.27073e10i | 0.619314 | + | 0.357561i | ||||
\(503\) | − | 9.78079e10i | − | 1.52793i | −0.645261 | − | 0.763963i | \(-0.723251\pi\) | ||
0.645261 | − | 0.763963i | \(-0.276749\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.06206e10 | −0.624570 | ||||||||
\(506\) | 8.67973e7 | − | 1.50337e8i | 0.00132405 | − | 0.00229332i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.27331e10 | + | 2.20543e10i | 0.191196 | + | 0.331161i | ||||
\(509\) | −1.25561e10 | − | 7.24925e9i | −0.187061 | − | 0.108000i | 0.403545 | − | 0.914960i | \(-0.367778\pi\) |
−0.590606 | + | 0.806960i | \(0.701111\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.15780e11 | − | 1.45585e10i | 1.69805 | − | 0.213517i | ||||
\(512\) | 3.03700e9 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.71213e10 | + | 3.29790e10i | −0.818362 | + | 0.472482i | ||||
\(515\) | −6.31893e10 | − | 1.09447e11i | −0.898285 | − | 1.55588i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.58653e9i | − | 0.0222068i | ||||||
\(518\) | 5.62797e9 | + | 4.47578e10i | 0.0781687 | + | 0.621656i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.36267e10 | − | 5.82432e10i | 0.459908 | − | 0.796584i | ||||
\(521\) | −2.40889e10 | + | 1.39077e10i | −0.326938 | + | 0.188758i | −0.654481 | − | 0.756079i | \(-0.727113\pi\) |
0.327543 | + | 0.944836i | \(0.393779\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.13262e10 | + | 2.38597e10i | 0.552355 | + | 0.318902i | 0.750071 | − | 0.661357i | \(-0.230019\pi\) |
−0.197716 | + | 0.980259i | \(0.563352\pi\) | |||||||
\(524\) | 4.63171e10i | 0.614351i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.05256e8 | 0.00137501 | ||||||||
\(527\) | −4.60115e10 | + | 7.96942e10i | −0.596518 | + | 1.03320i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.88543e10 | + | 6.72975e10i | 0.496153 | + | 0.859363i | ||||
\(530\) | 3.76410e10 | + | 2.17320e10i | 0.477043 | + | 0.275421i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.91138e10 | + | 4.53965e10i | −0.238617 | + | 0.566730i | ||||
\(533\) | 2.01081e10 | 0.249151 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.18545e10 | + | 2.41647e10i | −0.510890 | + | 0.294962i | ||||
\(536\) | −7.73464e9 | − | 1.33968e10i | −0.0937089 | − | 0.162309i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.27358e10i | 0.390745i | ||||||||
\(539\) | 9.73109e8 | − | 3.46981e9i | 0.0115294 | − | 0.0411103i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.34084e10 | − | 7.51855e10i | 0.506739 | − | 0.877697i | −0.493231 | − | 0.869899i | \(-0.664184\pi\) |
0.999970 | − | 0.00779894i | \(-0.00248250\pi\) | |||||||
\(542\) | −3.49481e10 | + | 2.01773e10i | −0.404974 | + | 0.233812i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.68841e10 | + | 9.74806e9i | 0.192789 | + | 0.111307i | ||||
\(545\) | − | 1.54763e9i | − | 0.0175421i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.29408e8 | −0.00926443 | −0.00463222 | − | 0.999989i | \(-0.501474\pi\) | ||||
−0.00463222 | + | 0.999989i | \(0.501474\pi\) | |||||||
\(548\) | −1.12018e9 | + | 1.94020e9i | −0.0124212 | + | 0.0215142i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.68005e9 | + | 4.64198e9i | 0.0292881 | + | 0.0507286i | ||||
\(551\) | −2.79366e10 | − | 1.61292e10i | −0.303087 | − | 0.174988i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.03647e11 | − | 7.85783e10i | 1.10830 | − | 0.840238i | ||||
\(554\) | −9.90975e10 | −1.05202 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.59371e10 | − | 3.22953e10i | 0.585330 | − | 0.337941i | ||||
\(557\) | −3.13936e10 | − | 5.43753e10i | −0.326152 | − | 0.564913i | 0.655593 | − | 0.755115i | \(-0.272419\pi\) |
−0.981745 | + | 0.190202i | \(0.939086\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.27557e11i | − | 1.30634i | ||||||
\(560\) | 4.18286e10 | − | 5.25965e9i | 0.425326 | − | 0.0534817i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.73660e9 | − | 9.93609e9i | 0.0575055 | − | 0.0996025i | ||||
\(563\) | 1.44357e11 | − | 8.33443e10i | 1.43682 | − | 0.829550i | 0.439195 | − | 0.898392i | \(-0.355264\pi\) |
0.997628 | + | 0.0688418i | \(0.0219304\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.37761e11 | − | 1.37271e11i | −2.33317 | − | 1.34706i | ||||
\(566\) | 2.46480e10i | 0.240168i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.27050e10 | 0.314210 | ||||||||
\(569\) | 5.98889e10 | − | 1.03731e11i | 0.571344 | − | 0.989596i | −0.425085 | − | 0.905154i | \(-0.639756\pi\) |
0.996428 | − | 0.0844427i | \(-0.0269110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.41052e10 | − | 5.90720e10i | −0.320831 | − | 0.555696i | 0.659829 | − | 0.751416i | \(-0.270629\pi\) |
−0.980660 | + | 0.195720i | \(0.937296\pi\) | |||||||
\(572\) | −3.00285e9 | − | 1.73370e9i | −0.0280511 | − | 0.0161953i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.61508e9 | + | 1.00445e10i | 0.0701499 | + | 0.0925299i | ||||
\(575\) | 1.86027e10 | 0.170178 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.44054e11 | + | 8.31694e10i | −1.29963 | + | 0.750344i | −0.980341 | − | 0.197312i | \(-0.936779\pi\) |
−0.319293 | + | 0.947656i | \(0.603445\pi\) | |||||||
\(578\) | 2.31171e10 | + | 4.00399e10i | 0.207120 | + | 0.358742i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.76097e10i | 0.243978i | ||||||||
\(581\) | 2.13314e10 | − | 5.06634e10i | 0.187204 | − | 0.444621i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.12044e9 | − | 1.94066e9i | 0.00969873 | − | 0.0167987i | ||||
\(584\) | 6.09527e10 | − | 3.51911e10i | 0.524013 | − | 0.302539i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.65614e10 | − | 3.26558e10i | −0.479656 | − | 0.276930i | ||||
\(587\) | − | 1.46339e11i | − | 1.23256i | −0.787526 | − | 0.616281i | \(-0.788639\pi\) | ||
0.787526 | − | 0.616281i | \(-0.211361\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.40227e11 | −1.16512 | ||||||||
\(590\) | −3.79962e10 | + | 6.58114e10i | −0.313568 | + | 0.543116i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.36040e10 | + | 2.35629e10i | 0.110760 | + | 0.191841i | ||||
\(593\) | −1.94527e11 | − | 1.12310e11i | −1.57312 | − | 0.908242i | −0.995783 | − | 0.0917357i | \(-0.970759\pi\) |
−0.577337 | − | 0.816506i | \(-0.695908\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.49428e11 | + | 1.05019e11i | 1.99011 | + | 0.837917i | ||||
\(596\) | −3.40553e10 | −0.269898 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.04216e10 | + | 6.01694e9i | −0.0814951 | + | 0.0470512i | ||||
\(599\) | 8.39482e10 | + | 1.45403e11i | 0.652085 | + | 1.12944i | 0.982616 | + | 0.185649i | \(0.0594387\pi\) |
−0.330531 | + | 0.943795i | \(0.607228\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.01982e11i | 1.54816i | 0.633088 | + | 0.774080i | \(0.281787\pi\) | ||||
−0.633088 | + | 0.774080i | \(0.718213\pi\) | |||||||
\(602\) | 6.37182e10 | − | 4.83067e10i | 0.485151 | − | 0.367809i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.02058e10 | + | 6.96386e10i | −0.302094 | + | 0.523241i | ||||
\(605\) | −1.98586e11 | + | 1.14653e11i | −1.48227 | + | 0.855787i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.69808e11 | − | 9.80385e10i | −1.25084 | − | 0.722174i | −0.279565 | − | 0.960127i | \(-0.590190\pi\) |
−0.971277 | + | 0.237953i | \(0.923524\pi\) | |||||||
\(608\) | 2.97088e10i | 0.217405i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.45007e11 | −1.04730 | ||||||||
\(611\) | −5.49904e10 | + | 9.52461e10i | −0.394568 | + | 0.683412i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.21921e10 | + | 2.11174e10i | 0.0863451 | + | 0.149554i | 0.905964 | − | 0.423356i | \(-0.139148\pi\) |
−0.819619 | + | 0.572910i | \(0.805815\pi\) | |||||||
\(614\) | −8.24092e10 | − | 4.75790e10i | −0.579832 | − | 0.334766i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.71173e8 | − | 2.15656e9i | −0.00188331 | − | 0.0149775i | ||||
\(617\) | 6.93902e10 | 0.478804 | 0.239402 | − | 0.970921i | \(-0.423049\pi\) | ||||
0.239402 | + | 0.970921i | \(0.423049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.63983e10 | − | 1.52411e10i | 0.179810 | − | 0.103813i | −0.407394 | − | 0.913253i | \(-0.633562\pi\) |
0.587203 | + | 0.809439i | \(0.300229\pi\) | |||||||
\(620\) | 6.00097e10 | + | 1.03940e11i | 0.406120 | + | 0.703421i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 1.59747e11i | − | 1.06726i | ||||||
\(623\) | −1.24994e11 | − | 1.64870e11i | −0.829727 | − | 1.09444i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.28789e10 | + | 1.08909e11i | −0.412083 | + | 0.713749i | ||||
\(626\) | −5.53943e10 | + | 3.19819e10i | −0.360718 | + | 0.208261i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.73181e10 | + | 9.99860e9i | 0.111343 | + | 0.0642837i | ||||
\(629\) | 1.74663e11i | 1.11583i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.98314e10 | 0.503566 | 0.251783 | − | 0.967784i | \(-0.418983\pi\) | ||||
0.251783 | + | 0.967784i | \(0.418983\pi\) | |||||||
\(632\) | 3.92246e10 | − | 6.79390e10i | 0.245861 | − | 0.425844i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.16426e10 | − | 2.01656e10i | −0.0720600 | − | 0.124812i | ||||
\(635\) | 1.84651e11 | + | 1.06608e11i | 1.13568 | + | 0.655687i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.78687e11 | + | 1.74579e11i | −1.08526 | + | 1.06031i | ||||
\(638\) | 1.42348e9 | 0.00859148 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.20208e10 | − | 1.27137e10i | 0.131254 | − | 0.0757798i | ||||
\(641\) | 8.08656e10 | + | 1.40063e11i | 0.478996 | + | 0.829645i | 0.999710 | − | 0.0240860i | \(-0.00766754\pi\) |
−0.520714 | + | 0.853731i | \(0.674334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.63061e11i | − | 0.953906i | −0.878929 | − | 0.476953i | \(-0.841741\pi\) | ||
0.878929 | − | 0.476953i | \(-0.158259\pi\) | |||||||
\(644\) | −6.95236e9 | − | 2.92723e9i | −0.0404193 | − | 0.0170182i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.53581e10 | + | 1.65165e11i | −0.547555 | + | 0.948393i | ||||
\(647\) | −1.56164e11 | + | 9.01611e10i | −0.891174 | + | 0.514520i | −0.874326 | − | 0.485338i | \(-0.838696\pi\) |
−0.0168480 | + | 0.999858i | \(0.505363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.39305e9 | + | 1.95898e9i | 0.0191254 | + | 0.0110421i | ||||
\(650\) | − | 3.71571e11i | − | 2.08156i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.25295e10 | −0.456687 | ||||||||
\(653\) | −9.24573e10 | + | 1.60141e11i | −0.508497 | + | 0.880743i | 0.491454 | + | 0.870903i | \(0.336465\pi\) |
−0.999952 | + | 0.00983959i | \(0.996868\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.93897e11 | + | 3.35839e11i | 1.05343 | + | 1.82459i | ||||
\(656\) | 6.58402e9 | + | 3.80128e9i | 0.0355529 | + | 0.0205265i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.84031e10 | + | 8.60120e9i | −0.364899 | + | 0.0458834i | ||||
\(659\) | 1.54086e11 | 0.816997 | 0.408498 | − | 0.912759i | \(-0.366053\pi\) | ||||
0.408498 | + | 0.912759i | \(0.366053\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.25654e11 | + | 1.30282e11i | −1.18206 | + | 0.682460i | −0.956489 | − | 0.291768i | \(-0.905756\pi\) |
−0.225566 | + | 0.974228i | \(0.572423\pi\) | |||||||
\(662\) | −2.09234e10 | − | 3.62405e10i | −0.108943 | − | 0.188696i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 3.31555e10i | − | 0.170563i | ||||||
\(665\) | 5.14513e10 | + | 4.09179e11i | 0.263094 | + | 2.09231i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.47015e9 | − | 4.27842e9i | 0.0124802 | − | 0.0216163i | ||||
\(668\) | −4.44522e10 | + | 2.56645e10i | −0.223248 | + | 0.128892i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.12165e11 | − | 6.47587e10i | −0.556621 | − | 0.321365i | ||||
\(671\) | 7.47616e9i | 0.0368798i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.66660e11 | 0.812401 | 0.406201 | − | 0.913784i | \(-0.366853\pi\) | ||||
0.406201 | + | 0.913784i | \(0.366853\pi\) | |||||||
\(674\) | −6.45836e10 | + | 1.11862e11i | −0.312955 | + | 0.542055i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.79762e10 | + | 1.17738e11i | 0.325514 | + | 0.563807i | ||||
\(677\) | −2.97264e11 | − | 1.71626e11i | −1.41510 | − | 0.817010i | −0.419239 | − | 0.907876i | \(-0.637703\pi\) |
−0.995863 | + | 0.0908659i | \(0.971037\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.25181e11 | − | 2.97314e11i | 0.588926 | − | 1.39874i | ||||
\(680\) | 1.63232e11 | 0.763432 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.35884e9 | − | 3.09393e9i | 0.0247704 | − | 0.0143012i | ||||
\(683\) | 7.86838e10 | + | 1.36284e11i | 0.361578 | + | 0.626272i | 0.988221 | − | 0.153035i | \(-0.0489046\pi\) |
−0.626642 | + | 0.779307i | \(0.715571\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.87575e10i | 0.0851946i | ||||||||
\(686\) | −1.54877e11 | − | 2.31444e10i | −0.699341 | − | 0.104508i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.41137e10 | − | 4.17661e10i | 0.107624 | − | 0.186411i | ||||
\(689\) | −1.34530e11 | + | 7.76710e10i | −0.596956 | + | 0.344653i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.95389e10 | + | 1.70543e10i | 0.129564 | + | 0.0748035i | 0.563381 | − | 0.826197i | \(-0.309500\pi\) |
−0.433817 | + | 0.901001i | \(0.642834\pi\) | |||||||
\(692\) | − | 9.93958e10i | − | 0.433454i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.14366e11 | 0.493012 | ||||||||
\(695\) | 2.70394e11 | − | 4.68337e11i | 1.15893 | − | 2.00733i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.44024e10 | + | 4.22663e10i | 0.103396 | + | 0.179086i | ||||
\(698\) | 2.19014e10 | + | 1.26448e10i | 0.0922676 | + | 0.0532707i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.85609e11 | − | 1.40716e11i | 0.773051 | − | 0.586074i | ||||
\(701\) | 4.82108e10 | 0.199651 | 0.0998256 | − | 0.995005i | \(-0.468172\pi\) | ||||
0.0998256 | + | 0.995005i | \(0.468172\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.30499e11 | + | 1.33078e11i | −0.943729 | + | 0.544862i | ||||
\(704\) | −6.55484e8 | − | 1.13533e9i | −0.00266852 | − | 0.00462202i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.46680e11i | 0.590407i | ||||||||
\(707\) | 9.02951e10 | − | 1.13540e10i | 0.361399 | − | 0.0454433i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.77293e11 | − | 3.07080e11i | 0.701627 | − | 1.21525i | −0.266269 | − | 0.963899i | \(-0.585791\pi\) |
0.967895 | − | 0.251354i | \(-0.0808759\pi\) | |||||||
\(710\) | 2.37139e11 | − | 1.36912e11i | 0.933189 | − | 0.538777i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.08070e11 | − | 6.23941e10i | −0.420517 | − | 0.242786i | ||||
\(713\) | − | 2.14755e10i | − | 0.0830968i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.90310e10 | −0.111080 | ||||||||
\(716\) | −1.68127e10 | + | 2.91205e10i | −0.0639714 | + | 0.110802i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.71479e11 | + | 2.97010e11i | 0.645226 | + | 1.11756i | ||||
\(719\) | −3.74314e11 | − | 2.16110e11i | −1.40062 | − | 0.808649i | −0.406165 | − | 0.913800i | \(-0.633134\pi\) |
−0.994456 | + | 0.105151i | \(0.966467\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.71054e11 | + | 2.25626e11i | 0.632985 | + | 0.834927i | ||||
\(722\) | −9.84722e10 | −0.362380 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.94266e10 | − | 4.00835e10i | 0.252680 | − | 0.145885i | ||||
\(725\) | 7.62710e10 | + | 1.32105e11i | 0.276063 | + | 0.478154i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.64649e10i | − | 0.0947397i | −0.998877 | − | 0.0473698i | \(-0.984916\pi\) | ||
0.998877 | − | 0.0473698i | \(-0.0150839\pi\) | |||||||
\(728\) | −5.84687e10 | + | 1.38867e11i | −0.208160 | + | 0.494395i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.94639e11 | − | 5.10330e11i | 1.03753 | − | 1.79705i | ||||
\(731\) | 2.68119e11 | − | 1.54799e11i | 0.938983 | − | 0.542122i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.25895e11 | − | 1.88156e11i | −1.12892 | − | 0.651780i | −0.185254 | − | 0.982691i | \(-0.559311\pi\) |
−0.943662 | + | 0.330910i | \(0.892644\pi\) | |||||||
\(734\) | − | 6.13006e10i | − | 0.211193i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.54982e9 | −0.0155054 | ||||||||
\(737\) | −3.33877e9 | + | 5.78292e9i | −0.0113166 | + | 0.0196010i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.33306e11 | − | 4.04098e11i | −0.782255 | − | 1.35491i | −0.930625 | − | 0.365974i | \(-0.880736\pi\) |
0.148370 | − | 0.988932i | \(-0.452598\pi\) | |||||||
\(740\) | 1.97282e11 | + | 1.13901e11i | 0.657900 | + | 0.379839i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.97461e10 | − | 3.77868e10i | −0.296074 | − | 0.124659i | ||||
\(743\) | 2.39593e11 | 0.786175 | 0.393088 | − | 0.919501i | \(-0.371407\pi\) | ||||
0.393088 | + | 0.919501i | \(0.371407\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.46930e11 | + | 1.42565e11i | −0.801583 | + | 0.462794i | ||||
\(746\) | 4.47133e10 | + | 7.74456e10i | 0.144371 | + | 0.250058i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 8.41579e9i | − | 0.0268837i | ||||||
\(749\) | 8.62835e10 | − | 6.54143e10i | 0.274158 | − | 0.207848i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.07451e11 | + | 1.86111e11i | −0.337793 | + | 0.585075i | −0.984017 | − | 0.178072i | \(-0.943014\pi\) |
0.646224 | + | 0.763148i | \(0.276347\pi\) | |||||||
\(752\) | −3.60111e10 | + | 2.07910e10i | −0.112607 | + | 0.0650136i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.54576e10 | − | 4.93390e10i | −0.264402 | − | 0.152653i | ||||
\(755\) | 6.73252e11i | 2.07200i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.69943e11 | 1.12655 | 0.563276 | − | 0.826269i | \(-0.309541\pi\) | ||||
0.563276 | + | 0.826269i | \(0.309541\pi\) | |||||||
\(758\) | 1.04370e11 | − | 1.80774e11i | 0.316153 | − | 0.547593i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.24369e11 | + | 2.15414e11i | 0.372785 | + | 0.645683i | ||||
\(761\) | −2.53298e11 | − | 1.46242e11i | −0.755255 | − | 0.436047i | 0.0723346 | − | 0.997380i | \(-0.476955\pi\) |
−0.827589 | + | 0.561334i | \(0.810288\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.32581e8 | + | 3.44021e9i | 0.00127635 | + | 0.0101505i | ||||
\(764\) | −3.05497e11 | −0.896673 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.49251e10 | + | 5.48050e10i | −0.275719 | + | 0.159186i | ||||
\(767\) | −1.35800e11 | − | 2.35212e11i | −0.392389 | − | 0.679638i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4.88004e10i | − | 0.139546i | −0.997563 | − | 0.0697732i | \(-0.977772\pi\) | ||
0.997563 | − | 0.0697732i | \(-0.0222275\pi\) | |||||||
\(770\) | −1.09942e10 | − | 1.45017e10i | −0.0312753 | − | 0.0412531i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.03370e10 | + | 5.25452e10i | −0.0854090 | + | 0.147933i | ||||
\(773\) | −2.18055e11 | + | 1.25894e11i | −0.610729 | + | 0.352604i | −0.773251 | − | 0.634101i | \(-0.781371\pi\) |
0.162522 | + | 0.986705i | \(0.448037\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.74261e11 | + | 3.31550e11i | 1.59185 | + | 0.919057i | ||||
\(776\) | − | 1.94571e11i | − | 0.536575i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.93406e11 | −0.800848 | ||||||||
\(779\) | −3.71852e10 | + | 6.44066e10i | −0.100976 | + | 0.174896i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.05880e9 | − | 1.22262e10i | −0.0189726 | − | 0.0328615i | ||||
\(782\) | −2.52946e10 | − | 1.46038e10i | −0.0676396 | − | 0.0390517i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.15102e10 | + | 2.33832e10i | −0.242217 | + | 0.0618928i | ||||
\(785\) | 1.67428e11 | 0.440909 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.64633e11 | − | 9.50509e10i | 0.429159 | − | 0.247775i | −0.269830 | − | 0.962908i | \(-0.586967\pi\) |
0.698988 | + | 0.715133i | \(0.253634\pi\) | |||||||
\(788\) | −1.28533e11 | − | 2.22626e11i | −0.333358 | − | 0.577394i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 6.56820e11i | − | 1.68631i | ||||||
\(791\) | 5.66885e11 | + | 2.38682e11i | 1.44807 | + | 0.609696i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.59130e11 | − | 4.48827e11i | 0.655277 | − | 1.13497i | ||||
\(794\) | 3.88225e11 | − | 2.24142e11i | 0.976790 | − | 0.563950i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.03715e11 | + | 5.98798e10i | 0.258338 | + | 0.149152i | ||||
\(797\) | − | 4.35825e11i | − | 1.08014i | −0.841621 | − | 0.540069i | \(-0.818398\pi\) | ||
0.841621 | − | 0.540069i | \(-0.181602\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.66937e11 | −0.654970 | ||||||||
\(800\) | 7.02426e10 | − | 1.21664e11i | 0.171491 | − | 0.297031i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.05985e10 | + | 3.56777e10i | 0.0497896 | + | 0.0862381i | ||||
\(803\) | −2.63112e10 | − | 1.51908e10i | −0.0632817 | − | 0.0365357i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.26647e10 | + | 7.87964e9i | −0.149224 | + | 0.0187639i | ||||
\(806\) | −4.28953e11 | −1.01641 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.75362e10 | − | 2.74450e10i | 0.111527 | − | 0.0643900i | ||||
\(809\) | 1.12279e11 | + | 1.94473e11i | 0.262123 | + | 0.454011i | 0.966806 | − | 0.255512i | \(-0.0822440\pi\) |
−0.704683 | + | 0.709523i | \(0.748911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.24327e10i | 0.121204i | 0.998162 | + | 0.0606022i | \(0.0193021\pi\) | ||||
−0.998162 | + | 0.0606022i | \(0.980698\pi\) | |||||||
\(812\) | −7.71725e9 | − | 6.13733e10i | −0.0177516 | − | 0.141174i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.87239e9 | − | 1.01713e10i | 0.0133757 | − | 0.0231674i | ||||
\(815\) | −5.98409e11 | + | 3.45492e11i | −1.35634 | + | 0.783082i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.08568e11 | + | 2.35887e11i | 0.917014 | + | 0.529438i | ||||
\(818\) | 4.31839e11i | 0.964513i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.36529e10 | 0.140787 | ||||||||
\(821\) | 1.49561e10 | − | 2.59046e10i | 0.0329188 | − | 0.0570171i | −0.849097 | − | 0.528238i | \(-0.822853\pi\) |
0.882015 | + | 0.471220i | \(0.156186\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.11555e11 | + | 5.39629e11i | 0.679102 | + | 1.17624i | 0.975252 | + | 0.221098i | \(0.0709641\pi\) |
−0.296149 | + | 0.955142i | \(0.595703\pi\) | |||||||
\(824\) | 1.47894e11 | + | 8.53867e10i | 0.320805 | + | 0.185217i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.60662e10 | − | 1.56912e11i | 0.141925 | − | 0.337082i | ||||
\(827\) | 2.57252e11 | 0.549968 | 0.274984 | − | 0.961449i | \(-0.411328\pi\) | ||||
0.274984 | + | 0.961449i | \(0.411328\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.81907e10 | − | 3.35964e10i | 0.123207 | − | 0.0711336i | −0.437130 | − | 0.899398i | \(-0.644005\pi\) |
0.560337 | + | 0.828265i | \(0.310672\pi\) | |||||||
\(830\) | −1.38798e11 | − | 2.40406e11i | −0.292464 | − | 0.506562i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.08785e10i | 0.189657i | ||||||||
\(833\) | −5.83803e11 | − | 1.63728e11i | −1.21251 | − | 0.340050i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.14878e11 | + | 3.72179e11i | −0.442023 | + | 0.765607i | ||||
\(836\) | 1.11061e10 | − | 6.41212e9i | 0.0227372 | − | 0.0131273i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.67304e11 | − | 9.65932e10i | −0.339259 | − | 0.195871i | ||||
\(839\) | − | 4.03627e11i | − | 0.814577i | −0.913300 | − | 0.407289i | \(-0.866474\pi\) | ||
0.913300 | − | 0.407289i | \(-0.133526\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.59736e11 | −0.919019 | ||||||||
\(842\) | 1.62074e11 | − | 2.80721e11i | 0.322452 | − | 0.558504i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.62879e10 | − | 1.49455e11i | −0.170051 | − | 0.294537i | ||||
\(845\) | 9.85770e11 | + | 5.69134e11i | 1.93352 | + | 1.11632i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.09387e11 | − | 3.10369e11i | 0.795426 | − | 0.603038i | ||||
\(848\) | −5.87323e10 | −0.113578 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.81024e11 | − | 4.50924e11i | 1.49620 | − | 0.863830i | ||||
\(851\) | −2.03806e10 | − | 3.53003e10i | −0.0388597 | − | 0.0673069i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.87913e11i | − | 0.354945i | −0.984126 | − | 0.177472i | \(-0.943208\pi\) | ||
0.984126 | − | 0.177472i | \(-0.0567921\pi\) | |||||||
\(854\) | 3.22335e11 | − | 4.05313e10i | 0.606004 | − | 0.0762007i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.26534e10 | − | 5.65573e10i | 0.0608181 | − | 0.105340i | ||||
\(857\) | −5.48475e10 | + | 3.16662e10i | −0.101680 | + | 0.0587047i | −0.549977 | − | 0.835179i | \(-0.685364\pi\) |
0.448298 | + | 0.893884i | \(0.352030\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.97843e11 | + | 1.71960e11i | 0.547034 | + | 0.315830i | 0.747925 | − | 0.663783i | \(-0.231050\pi\) |
−0.200891 | + | 0.979614i | \(0.564384\pi\) | |||||||
\(860\) | − | 4.03787e11i | − | 0.738173i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.17682e11 | −0.937636 | ||||||||
\(863\) | 2.48122e10 | − | 4.29760e10i | 0.0447324 | − | 0.0774789i | −0.842792 | − | 0.538239i | \(-0.819090\pi\) |
0.887525 | + | 0.460760i | \(0.152423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.16098e11 | − | 7.20704e11i | −0.743244 | − | 1.28734i | ||||
\(866\) | 1.38867e11 | + | 8.01752e10i | 0.246904 | + | 0.142550i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.62447e11 | − | 2.14273e11i | −0.286176 | − | 0.377476i | ||||
\(869\) | −3.38638e10 | −0.0593822 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00882e11 | − | 2.31450e11i | 0.696537 | − | 0.402146i | ||||
\(872\) | 1.04564e9 | + | 1.81111e9i | 0.00180850 | + | 0.00313241i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 4.45076e10i | − | 0.0762761i | ||||||
\(875\) | 3.66711e11 | − | 8.70963e11i | 0.625593 | − | 1.48583i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.26476e11 | + | 5.65473e11i | −0.551890 | + | 0.955902i | 0.446248 | + | 0.894909i | \(0.352760\pi\) |
−0.998138 | + | 0.0609924i | \(0.980573\pi\) | |||||||
\(878\) | 9.57548e10 | − | 5.52841e10i | 0.161132 | − | 0.0930298i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.50562e9 | − | 5.48807e9i | −0.0158508 | − | 0.00915144i | ||||
\(881\) | 8.21158e11i | 1.36309i | 0.731778 | + | 0.681543i | \(0.238691\pi\) | ||||
−0.731778 | + | 0.681543i | \(0.761309\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.78470e11 | 1.60955 | 0.804775 | − | 0.593580i | \(-0.202286\pi\) | ||||
0.804775 | + | 0.593580i | \(0.202286\pi\) | |||||||
\(884\) | −2.91699e11 | + | 5.05237e11i | −0.477667 | + | 0.827344i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.89008e11 | + | 5.00577e11i | 0.469003 | + | 0.812337i | ||||
\(887\) | 3.32455e11 | + | 1.91943e11i | 0.537080 | + | 0.310083i | 0.743895 | − | 0.668297i | \(-0.232976\pi\) |
−0.206815 | + | 0.978380i | \(0.566310\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.40257e11 | − | 1.85366e11i | −0.704854 | − | 0.296772i | ||||
\(890\) | −1.04480e12 | −1.66522 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.52622e11 | + | 1.45851e11i | −0.399036 | + | 0.230383i | ||||
\(893\) | −2.03383e11 | − | 3.52270e11i | −0.319823 | − | 0.553949i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.81531e11i | 0.438767i | ||||||||
\(896\) | −4.53962e10 | + | 3.44163e10i | −0.0704348 | + | 0.0533989i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.47746e11 | + | 2.55903e11i | −0.227200 | + | 0.393523i | ||||
\(899\) | 1.52506e11 | − | 8.80496e10i | 0.233480 | − | 0.134800i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.26521e11 | − | 1.88517e11i | −0.495464 | − | 0.286056i | ||||
\(902\) | − | 3.28176e9i | − | 0.00495771i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.70986e11 | 0.555499 | ||||||||
\(905\) | 3.35601e11 | − | 5.81278e11i | 0.500298 | − | 0.866542i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.87195e11 | − | 1.01705e12i | −0.867667 | − | 1.50284i | −0.864375 | − | 0.502848i | \(-0.832285\pi\) |
−0.00329220 | − | 0.999995i | \(-0.501048\pi\) | |||||||
\(908\) | 3.27620e11 | + | 1.89151e11i | 0.481977 | + | 0.278270i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.57389e11 | + | 1.25167e12i | 0.229513 | + | 1.82526i | ||||
\(911\) | −1.28724e12 | −1.86890 | −0.934449 | − | 0.356096i | \(-0.884107\pi\) | ||||
−0.934449 | + | 0.356096i | \(0.884107\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.23946e10 | + | 7.15605e9i | −0.0178382 | + | 0.0102989i | ||||
\(914\) | 3.61815e11 | + | 6.26682e11i | 0.518444 | + | 0.897972i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 2.10561e10i | − | 0.0299086i | ||||||
\(917\) | −5.24881e11 | − | 6.92335e11i | −0.742307 | − | 0.979127i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.53931e11 | + | 4.39821e11i | −0.356002 | + | 0.616614i | −0.987289 | − | 0.158935i | \(-0.949194\pi\) |
0.631287 | + | 0.775550i | \(0.282527\pi\) | |||||||
\(920\) | −3.29901e10 | + | 1.90468e10i | −0.0460502 | + | 0.0265871i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.09384e11 | + | 3.51828e11i | 0.843271 | + | 0.486863i | ||||
\(923\) | 9.78657e11i | 1.34842i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.25859e12 | 1.71916 | ||||||||
\(926\) | −1.84036e11 | + | 3.18759e11i | −0.250298 | + | 0.433530i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.86543e10 | − | 3.23102e10i | −0.0251528 | − | 0.0435660i | ||||
\(929\) | 1.48512e11 | + | 8.57434e10i | 0.199388 | + | 0.115117i | 0.596370 | − | 0.802710i | \(-0.296609\pi\) |
−0.396982 | + | 0.917826i | \(0.629943\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.28741e11 | − | 8.95178e11i | −0.304471 | − | 1.19155i | ||||
\(932\) | 6.46295e11 | 0.856579 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.58028e11 | + | 4.95383e11i | −1.12749 | + | 0.650959i | ||||
\(935\) | −3.52309e10 | − | 6.10216e10i | −0.0460974 | − | 0.0798431i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 9.69345e11i | − | 1.25754i | −0.777593 | − | 0.628768i | \(-0.783560\pi\) | ||
0.777593 | − | 0.628768i | \(-0.216440\pi\) | |||||||
\(938\) | 2.67432e11 | + | 1.12600e11i | 0.345463 | + | 0.145454i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.74074e11 | + | 3.01505e11i | −0.222957 | + | 0.386174i | ||||
\(941\) | −5.54229e11 | + | 3.19984e11i | −0.706856 | + | 0.408103i | −0.809896 | − | 0.586574i | \(-0.800476\pi\) |
0.103040 | + | 0.994677i | \(0.467143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.86371e9 | − | 5.69481e9i | −0.0124736 | − | 0.00720166i | ||||
\(944\) | − | 1.02687e11i | − | 0.129309i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.08181e10 | −0.0259942 | ||||||||
\(947\) | −2.62353e11 | + | 4.54409e11i | −0.326202 | + | 0.564998i | −0.981755 | − | 0.190151i | \(-0.939102\pi\) |
0.655553 | + | 0.755149i | \(0.272436\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.05305e12 | + | 1.82394e12i | 1.29833 | + | 2.24877i | ||||
\(950\) | 1.19015e12 | + | 6.87132e11i | 1.46119 | + | 0.843618i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.62847e11 | + | 4.56254e10i | −0.441749 | + | 0.0555468i | ||||
\(953\) | −3.48057e11 | −0.421967 | −0.210983 | − | 0.977490i | \(-0.567667\pi\) | ||||
−0.210983 | + | 0.977490i | \(0.567667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.21512e12 | + | 1.27890e12i | −2.66307 | + | 1.53753i | ||||
\(956\) | 3.71574e10 | + | 6.43584e10i | 0.0444850 | + | 0.0770502i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.65881e11i | 0.909283i | ||||||||
\(959\) | −5.24294e9 | − | 4.16957e10i | −0.00619870 | − | 0.0492966i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.36943e10 | + | 7.56808e10i | −0.0512308 | + | 0.0887344i | ||||
\(962\) | −7.05091e11 | + | 4.07084e11i | −0.823275 | + | 0.475318i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.86023e11 | + | 2.80605e11i | 0.562793 | + | 0.324929i | ||||
\(965\) | 5.07997e11i | 0.585803i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.63339e12 | −1.86803 | −0.934013 | − | 0.357240i | \(-0.883718\pi\) | ||||
−0.934013 | + | 0.357240i | \(0.883718\pi\) | |||||||
\(968\) | 1.54929e11 | − | 2.68346e11i | 0.176454 | − | 0.305628i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.14527e11 | − | 1.41080e12i | −0.920065 | − | 1.59360i | ||||
\(971\) | 3.36844e11 | + | 1.94477e11i | 0.378924 | + | 0.218772i | 0.677350 | − | 0.735661i | \(-0.263128\pi\) |
−0.298426 | + | 0.954433i | \(0.596462\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.70151e11 | + | 1.11664e12i | −0.524548 | + | 1.24584i | ||||
\(974\) | 4.00702e9 | 0.00445231 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.69694e11 | − | 9.79730e10i | 0.187011 | − | 0.107971i | ||||
\(977\) | −3.10825e11 | − | 5.38365e11i | −0.341144 | − | 0.590879i | 0.643501 | − | 0.765445i | \(-0.277481\pi\) |
−0.984645 | + | 0.174566i | \(0.944148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.38667e10i | 0.0586394i | ||||||||
\(980\) | −5.65638e11 | + | 5.52636e11i | −0.613245 | + | 0.599149i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.70253e11 | − | 2.94886e11i | 0.183083 | − | 0.317109i | ||||
\(983\) | 1.22811e12 | − | 7.09049e11i | 1.31529 | − | 0.759385i | 0.332326 | − | 0.943165i | \(-0.392167\pi\) |
0.982967 | + | 0.183780i | \(0.0588333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.86395e12 | − | 1.07615e12i | −1.98011 | − | 1.14322i | ||||
\(986\) | − | 2.39504e11i | − | 0.253399i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.88999e11 | −0.932982 | ||||||||
\(989\) | −3.61254e10 | + | 6.25711e10i | −0.0377596 | + | 0.0654016i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.91519e11 | − | 1.37095e12i | −0.820666 | − | 1.42144i | −0.905187 | − | 0.425014i | \(-0.860269\pi\) |
0.0845208 | − | 0.996422i | \(-0.473064\pi\) | |||||||
\(992\) | −1.40452e11 | − | 8.10902e10i | −0.145038 | − | 0.0837378i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.88865e11 | + | 3.70624e11i | −0.500775 | + | 0.379654i | ||||
\(995\) | 1.00269e12 | 1.02300 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.14818e12 | − | 6.62901e11i | 1.16206 | − | 0.670916i | 0.210263 | − | 0.977645i | \(-0.432568\pi\) |
0.951797 | + | 0.306729i | \(0.0992345\pi\) | |||||||
\(998\) | −2.99381e11 | − | 5.18544e11i | −0.301788 | − | 0.522713i | ||||
\(999\) | 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 | 126.9.n.b.19.1 | 12 | ||
3.2 | odd | 2 | 14.9.d.a.5.4 | yes | 12 | ||
7.3 | odd | 6 | inner | 126.9.n.b.73.1 | 12 | ||
12.11 | even | 2 | 112.9.s.c.33.5 | 12 | |||
21.2 | odd | 6 | 98.9.b.c.97.2 | 12 | |||
21.5 | even | 6 | 98.9.b.c.97.5 | 12 | |||
21.11 | odd | 6 | 98.9.d.b.31.6 | 12 | |||
21.17 | even | 6 | 14.9.d.a.3.4 | ✓ | 12 | ||
21.20 | even | 2 | 98.9.d.b.19.6 | 12 | |||
84.59 | odd | 6 | 112.9.s.c.17.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.9.d.a.3.4 | ✓ | 12 | 21.17 | even | 6 | ||
14.9.d.a.5.4 | yes | 12 | 3.2 | odd | 2 | ||
98.9.b.c.97.2 | 12 | 21.2 | odd | 6 | |||
98.9.b.c.97.5 | 12 | 21.5 | even | 6 | |||
98.9.d.b.19.6 | 12 | 21.20 | even | 2 | |||
98.9.d.b.31.6 | 12 | 21.11 | odd | 6 | |||
112.9.s.c.17.5 | 12 | 84.59 | odd | 6 | |||
112.9.s.c.33.5 | 12 | 12.11 | even | 2 | |||
126.9.n.b.19.1 | 12 | 1.1 | even | 1 | trivial | ||
126.9.n.b.73.1 | 12 | 7.3 | odd | 6 | inner |