Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.67");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.c (of order \(3\), degree \(2\), 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: | \(50.4735119441\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.67 |
Dual form | 98.10.c.e.79.1 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | + | 13.8564i | 0.353553 | + | 0.612372i | ||||
\(3\) | −3.00000 | + | 5.19615i | −0.0213833 | + | 0.0370370i | −0.876519 | − | 0.481367i | \(-0.840140\pi\) |
0.855136 | + | 0.518404i | \(0.173474\pi\) | |||||||
\(4\) | −128.000 | + | 221.703i | −0.250000 | + | 0.433013i | ||||
\(5\) | 280.000 | + | 484.974i | 0.200352 | + | 0.347019i | 0.948642 | − | 0.316352i | \(-0.102458\pi\) |
−0.748290 | + | 0.663372i | \(0.769125\pi\) | |||||||
\(6\) | −96.0000 | −0.0302406 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | 9823.50 | + | 17014.8i | 0.499086 | + | 0.864441i | ||||
\(10\) | −4480.00 | + | 7759.59i | −0.141670 | + | 0.245380i | ||||
\(11\) | 27076.0 | − | 46897.0i | 0.557593 | − | 0.965780i | −0.440104 | − | 0.897947i | \(-0.645058\pi\) |
0.997697 | − | 0.0678326i | \(-0.0216084\pi\) | |||||||
\(12\) | −768.000 | − | 1330.22i | −0.0106917 | − | 0.0185185i | ||||
\(13\) | 113172. | 1.09899 | 0.549495 | − | 0.835497i | \(-0.314820\pi\) | ||||
0.549495 | + | 0.835497i | \(0.314820\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3360.00 | −0.0171368 | ||||||||
\(16\) | −32768.0 | − | 56755.8i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3131.00 | − | 5423.05i | 0.00909207 | − | 0.0157479i | −0.861444 | − | 0.507853i | \(-0.830439\pi\) |
0.870536 | + | 0.492105i | \(0.163773\pi\) | |||||||
\(18\) | −157176. | + | 272237.i | −0.352907 | + | 0.611252i | ||||
\(19\) | 128539. | + | 222636.i | 0.226279 | + | 0.391926i | 0.956702 | − | 0.291068i | \(-0.0940107\pi\) |
−0.730424 | + | 0.682994i | \(0.760677\pi\) | |||||||
\(20\) | −143360. | −0.200352 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 866432. | 0.788556 | ||||||||
\(23\) | 133000. | + | 230363.i | 0.0991006 | + | 0.171647i | 0.911313 | − | 0.411715i | \(-0.135070\pi\) |
−0.812212 | + | 0.583362i | \(0.801737\pi\) | |||||||
\(24\) | 12288.0 | − | 21283.4i | 0.00756015 | − | 0.0130946i | ||||
\(25\) | 819762. | − | 1.41987e6i | 0.419718 | − | 0.726974i | ||||
\(26\) | 905376. | + | 1.56816e6i | 0.388552 | + | 0.672991i | ||||
\(27\) | −235980. | −0.0854552 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.57471e6 | 0.413438 | 0.206719 | − | 0.978400i | \(-0.433721\pi\) | ||||
0.206719 | + | 0.978400i | \(0.433721\pi\) | |||||||
\(30\) | −26880.0 | − | 46557.5i | −0.00605876 | − | 0.0104941i | ||||
\(31\) | −2.31874e6 | + | 4.01618e6i | −0.450946 | + | 0.781062i | −0.998445 | − | 0.0557446i | \(-0.982247\pi\) |
0.547499 | + | 0.836806i | \(0.315580\pi\) | |||||||
\(32\) | 524288. | − | 908093.i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 162456. | + | 281382.i | 0.0238464 | + | 0.0413032i | ||||
\(34\) | 100192. | 0.0128581 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.02963e6 | −0.499086 | ||||||||
\(37\) | 5.97312e6 | + | 1.03457e7i | 0.523954 | + | 0.907515i | 0.999611 | + | 0.0278845i | \(0.00887708\pi\) |
−0.475657 | + | 0.879631i | \(0.657790\pi\) | |||||||
\(38\) | −2.05662e6 | + | 3.56218e6i | −0.160003 | + | 0.277134i | ||||
\(39\) | −339516. | + | 588059.i | −0.0235001 | + | 0.0407033i | ||||
\(40\) | −1.14688e6 | − | 1.98645e6i | −0.0708350 | − | 0.122690i | ||||
\(41\) | −2.19091e7 | −1.21087 | −0.605435 | − | 0.795895i | \(-0.707001\pi\) | ||||
−0.605435 | + | 0.795895i | \(0.707001\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.75206e7 | 1.22758 | 0.613790 | − | 0.789469i | \(-0.289644\pi\) | ||||
0.613790 | + | 0.789469i | \(0.289644\pi\) | |||||||
\(44\) | 6.93146e6 | + | 1.20056e7i | 0.278797 | + | 0.482890i | ||||
\(45\) | −5.50116e6 | + | 9.52829e6i | −0.199985 | + | 0.346385i | ||||
\(46\) | −2.12800e6 | + | 3.68580e6i | −0.0700747 | + | 0.121373i | ||||
\(47\) | 2.64639e7 | + | 4.58369e7i | 0.791068 | + | 1.37017i | 0.925306 | + | 0.379221i | \(0.123808\pi\) |
−0.134238 | + | 0.990949i | \(0.542859\pi\) | |||||||
\(48\) | 393216. | 0.0106917 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.62324e7 | 0.593571 | ||||||||
\(51\) | 18786.0 | + | 32538.3i | 0.000388838 | + | 0.000673487i | ||||
\(52\) | −1.44860e7 | + | 2.50905e7i | −0.274748 | + | 0.475877i | ||||
\(53\) | −8.11061e6 | + | 1.40480e7i | −0.141193 | + | 0.244553i | −0.927946 | − | 0.372715i | \(-0.878427\pi\) |
0.786753 | + | 0.617268i | \(0.211760\pi\) | |||||||
\(54\) | −1.88784e6 | − | 3.26983e6i | −0.0302130 | − | 0.0523304i | ||||
\(55\) | 3.03251e7 | 0.446859 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.54247e6 | −0.0193544 | ||||||||
\(58\) | 1.25977e7 | + | 2.18199e7i | 0.146173 | + | 0.253178i | ||||
\(59\) | −7.02548e7 | + | 1.21685e8i | −0.754818 | + | 1.30738i | 0.190647 | + | 0.981659i | \(0.438941\pi\) |
−0.945465 | + | 0.325724i | \(0.894392\pi\) | |||||||
\(60\) | 430080. | − | 744920.i | 0.00428419 | − | 0.00742043i | ||||
\(61\) | −1.01482e8 | − | 1.75772e8i | −0.938434 | − | 1.62542i | −0.768393 | − | 0.639979i | \(-0.778943\pi\) |
−0.170042 | − | 0.985437i | \(-0.554390\pi\) | |||||||
\(62\) | −7.41997e7 | −0.637734 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | 3.16882e7 | + | 5.48855e7i | 0.220185 | + | 0.381371i | ||||
\(66\) | −2.59930e6 | + | 4.50211e6i | −0.0168620 | + | 0.0292058i | ||||
\(67\) | −7.68673e7 | + | 1.33138e8i | −0.466020 | + | 0.807171i | −0.999247 | − | 0.0388015i | \(-0.987646\pi\) |
0.533227 | + | 0.845972i | \(0.320979\pi\) | |||||||
\(68\) | 801536. | + | 1.38830e6i | 0.00454604 | + | 0.00787397i | ||||
\(69\) | −1.59600e6 | −0.00847641 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.79656e8 | 1.30606 | 0.653028 | − | 0.757334i | \(-0.273499\pi\) | ||||
0.653028 | + | 0.757334i | \(0.273499\pi\) | |||||||
\(72\) | −4.02371e7 | − | 6.96926e7i | −0.176453 | − | 0.305626i | ||||
\(73\) | −2.02011e8 | + | 3.49894e8i | −0.832574 | + | 1.44206i | 0.0634158 | + | 0.997987i | \(0.479801\pi\) |
−0.895990 | + | 0.444074i | \(0.853533\pi\) | |||||||
\(74\) | −9.55699e7 | + | 1.65532e8i | −0.370492 | + | 0.641710i | ||||
\(75\) | 4.91858e6 | + | 8.51922e6i | 0.0179500 | + | 0.0310903i | ||||
\(76\) | −6.58120e7 | −0.226279 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.08645e7 | −0.0332341 | ||||||||
\(79\) | 6.53449e7 | + | 1.13181e8i | 0.188751 | + | 0.326927i | 0.944834 | − | 0.327549i | \(-0.106223\pi\) |
−0.756083 | + | 0.654476i | \(0.772889\pi\) | |||||||
\(80\) | 1.83501e7 | − | 3.17833e7i | 0.0500879 | − | 0.0867548i | ||||
\(81\) | −1.92648e8 | + | 3.33676e8i | −0.497258 | + | 0.861276i | ||||
\(82\) | −1.75273e8 | − | 3.03582e8i | −0.428107 | − | 0.741504i | ||||
\(83\) | −4.20134e8 | −0.971709 | −0.485855 | − | 0.874040i | \(-0.661492\pi\) | ||||
−0.485855 | + | 0.874040i | \(0.661492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.50672e6 | 0.00728645 | ||||||||
\(86\) | 2.20165e8 | + | 3.81337e8i | 0.434015 | + | 0.751736i | ||||
\(87\) | −4.72414e6 | + | 8.18245e6i | −0.00884069 | + | 0.0153125i | ||||
\(88\) | −1.10903e8 | + | 1.92090e8i | −0.197139 | + | 0.341455i | ||||
\(89\) | −2.34771e8 | − | 4.06636e8i | −0.396634 | − | 0.686990i | 0.596674 | − | 0.802483i | \(-0.296488\pi\) |
−0.993308 | + | 0.115493i | \(0.963155\pi\) | |||||||
\(90\) | −1.76037e8 | −0.282822 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.80960e7 | −0.0991006 | ||||||||
\(93\) | −1.39125e7 | − | 2.40971e7i | −0.0192855 | − | 0.0334034i | ||||
\(94\) | −4.23423e8 | + | 7.33390e8i | −0.559370 | + | 0.968856i | ||||
\(95\) | −7.19818e7 | + | 1.24676e8i | −0.0906706 | + | 0.157046i | ||||
\(96\) | 3.14573e6 | + | 5.44856e6i | 0.00378008 | + | 0.00654729i | ||||
\(97\) | 8.72502e8 | 1.00068 | 0.500338 | − | 0.865830i | \(-0.333209\pi\) | ||||
0.500338 | + | 0.865830i | \(0.333209\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.06392e9 | 1.11315 | ||||||||
\(100\) | 2.09859e8 | + | 3.63487e8i | 0.209859 | + | 0.363487i | ||||
\(101\) | −6.04507e8 | + | 1.04704e9i | −0.578037 | + | 1.00119i | 0.417668 | + | 0.908600i | \(0.362848\pi\) |
−0.995704 | + | 0.0925891i | \(0.970486\pi\) | |||||||
\(102\) | −300576. | + | 520613.i | −0.000274950 | + | 0.000476227i | ||||
\(103\) | 3.45281e8 | + | 5.98045e8i | 0.302277 | + | 0.523560i | 0.976651 | − | 0.214830i | \(-0.0689198\pi\) |
−0.674374 | + | 0.738390i | \(0.735586\pi\) | |||||||
\(104\) | −4.63553e8 | −0.388552 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.59540e8 | −0.199677 | ||||||||
\(107\) | −8.97497e7 | − | 1.55451e8i | −0.0661921 | − | 0.114648i | 0.831030 | − | 0.556227i | \(-0.187752\pi\) |
−0.897222 | + | 0.441579i | \(0.854418\pi\) | |||||||
\(108\) | 3.02054e7 | − | 5.23174e7i | 0.0213638 | − | 0.0370032i | ||||
\(109\) | 8.01804e8 | − | 1.38877e9i | 0.544063 | − | 0.942345i | −0.454602 | − | 0.890695i | \(-0.650219\pi\) |
0.998665 | − | 0.0516501i | \(-0.0164480\pi\) | |||||||
\(110\) | 2.42601e8 | + | 4.20197e8i | 0.157988 | + | 0.273644i | ||||
\(111\) | −7.16774e7 | −0.0448156 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.42785e9 | 0.823815 | 0.411908 | − | 0.911226i | \(-0.364863\pi\) | ||||
0.411908 | + | 0.911226i | \(0.364863\pi\) | |||||||
\(114\) | −1.23397e7 | − | 2.13731e7i | −0.00684281 | − | 0.0118521i | ||||
\(115\) | −7.44800e7 | + | 1.29003e8i | −0.0397100 | + | 0.0687797i | ||||
\(116\) | −2.01563e8 | + | 3.49118e8i | −0.103360 | + | 0.179024i | ||||
\(117\) | 1.11175e9 | + | 1.92560e9i | 0.548490 | + | 0.950013i | ||||
\(118\) | −2.24815e9 | −1.06747 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.37626e7 | 0.00605876 | ||||||||
\(121\) | −2.87246e8 | − | 4.97524e8i | −0.121820 | − | 0.210999i | ||||
\(122\) | 1.62371e9 | − | 2.81235e9i | 0.663573 | − | 1.14934i | ||||
\(123\) | 6.57274e7 | − | 1.13843e8i | 0.0258925 | − | 0.0448471i | ||||
\(124\) | −5.93598e8 | − | 1.02814e9i | −0.225473 | − | 0.390531i | ||||
\(125\) | 2.01188e9 | 0.737069 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.35873e9 | −0.804565 | −0.402282 | − | 0.915516i | \(-0.631783\pi\) | ||||
−0.402282 | + | 0.915516i | \(0.631783\pi\) | |||||||
\(128\) | 1.34218e8 | + | 2.32472e8i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −8.25618e7 | + | 1.43001e8i | −0.0262498 | + | 0.0454659i | ||||
\(130\) | −5.07011e8 | + | 8.78168e8i | −0.155694 | + | 0.269670i | ||||
\(131\) | 3.00833e8 | + | 5.21057e8i | 0.0892492 | + | 0.154584i | 0.907194 | − | 0.420713i | \(-0.138220\pi\) |
−0.817945 | + | 0.575297i | \(0.804887\pi\) | |||||||
\(132\) | −8.31775e7 | −0.0238464 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.45975e9 | −0.659052 | ||||||||
\(135\) | −6.60744e7 | − | 1.14444e8i | −0.0171211 | − | 0.0296546i | ||||
\(136\) | −1.28246e7 | + | 2.22128e7i | −0.00321453 | + | 0.00556773i | ||||
\(137\) | 2.58004e9 | − | 4.46877e9i | 0.625726 | − | 1.08379i | −0.362673 | − | 0.931916i | \(-0.618136\pi\) |
0.988400 | − | 0.151874i | \(-0.0485307\pi\) | |||||||
\(138\) | −1.27680e7 | − | 2.21148e7i | −0.00299686 | − | 0.00519072i | ||||
\(139\) | 7.14356e9 | 1.62311 | 0.811556 | − | 0.584275i | \(-0.198621\pi\) | ||||
0.811556 | + | 0.584275i | \(0.198621\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.17567e8 | −0.0676627 | ||||||||
\(142\) | 2.23725e9 | + | 3.87503e9i | 0.461760 | + | 0.799792i | ||||
\(143\) | 3.06425e9 | − | 5.30743e9i | 0.612790 | − | 1.06138i | ||||
\(144\) | 6.43793e8 | − | 1.11508e9i | 0.124771 | − | 0.216110i | ||||
\(145\) | 4.40920e8 | + | 7.63696e8i | 0.0828331 | + | 0.143471i | ||||
\(146\) | −6.46437e9 | −1.17744 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.05824e9 | −0.523954 | ||||||||
\(149\) | −4.55212e9 | − | 7.88450e9i | −0.756616 | − | 1.31050i | −0.944567 | − | 0.328319i | \(-0.893518\pi\) |
0.187951 | − | 0.982178i | \(-0.439815\pi\) | |||||||
\(150\) | −7.86972e7 | + | 1.36308e8i | −0.0126925 | + | 0.0219841i | ||||
\(151\) | 1.44716e8 | − | 2.50655e8i | 0.0226527 | − | 0.0392357i | −0.854477 | − | 0.519490i | \(-0.826122\pi\) |
0.877130 | + | 0.480254i | \(0.159455\pi\) | |||||||
\(152\) | −5.26496e8 | − | 9.11917e8i | −0.0800016 | − | 0.138567i | ||||
\(153\) | 1.23030e8 | 0.0181509 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.59699e9 | −0.361391 | ||||||||
\(156\) | −8.69161e7 | − | 1.50543e8i | −0.0117500 | − | 0.0203517i | ||||
\(157\) | 6.95339e9 | − | 1.20436e10i | 0.913373 | − | 1.58201i | 0.104107 | − | 0.994566i | \(-0.466802\pi\) |
0.809266 | − | 0.587442i | \(-0.199865\pi\) | |||||||
\(158\) | −1.04552e9 | + | 1.81089e9i | −0.133467 | + | 0.231172i | ||||
\(159\) | −4.86637e7 | − | 8.42879e7i | −0.00603834 | − | 0.0104587i | ||||
\(160\) | 5.87203e8 | 0.0708350 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.16474e9 | −0.703229 | ||||||||
\(163\) | −8.31162e9 | − | 1.43962e10i | −0.922235 | − | 1.59736i | −0.795948 | − | 0.605364i | \(-0.793027\pi\) |
−0.126287 | − | 0.991994i | \(-0.540306\pi\) | |||||||
\(164\) | 2.80437e9 | − | 4.85731e9i | 0.302718 | − | 0.524322i | ||||
\(165\) | −9.09754e7 | + | 1.57574e8i | −0.00955534 | + | 0.0165503i | ||||
\(166\) | −3.36107e9 | − | 5.82155e9i | −0.343551 | − | 0.595048i | ||||
\(167\) | 1.58019e10 | 1.57212 | 0.786061 | − | 0.618149i | \(-0.212117\pi\) | ||||
0.786061 | + | 0.618149i | \(0.212117\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.20340e9 | 0.207780 | ||||||||
\(170\) | 2.80538e7 | + | 4.85905e7i | 0.00257615 | + | 0.00446202i | ||||
\(171\) | −2.52541e9 | + | 4.37413e9i | −0.225865 | + | 0.391209i | ||||
\(172\) | −3.52264e9 | + | 6.10138e9i | −0.306895 | + | 0.531558i | ||||
\(173\) | 1.61562e9 | + | 2.79834e9i | 0.137130 | + | 0.237516i | 0.926409 | − | 0.376518i | \(-0.122879\pi\) |
−0.789279 | + | 0.614035i | \(0.789545\pi\) | |||||||
\(174\) | −1.51173e8 | −0.0125026 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.54891e9 | −0.278797 | ||||||||
\(177\) | −4.21529e8 | − | 7.30109e8i | −0.0322810 | − | 0.0559124i | ||||
\(178\) | 3.75634e9 | − | 6.50617e9i | 0.280462 | − | 0.485775i | ||||
\(179\) | 1.20704e10 | − | 2.09065e10i | 0.878785 | − | 1.52210i | 0.0261099 | − | 0.999659i | \(-0.491688\pi\) |
0.852675 | − | 0.522441i | \(-0.174979\pi\) | |||||||
\(180\) | −1.40830e9 | − | 2.43924e9i | −0.0999926 | − | 0.173192i | ||||
\(181\) | 3.89332e9 | 0.269629 | 0.134814 | − | 0.990871i | \(-0.456956\pi\) | ||||
0.134814 | + | 0.990871i | \(0.456956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.21778e9 | 0.0802674 | ||||||||
\(184\) | −5.44768e8 | − | 9.43566e8i | −0.0350374 | − | 0.0606865i | ||||
\(185\) | −3.34495e9 | + | 5.79362e9i | −0.209950 | + | 0.363645i | ||||
\(186\) | 2.22599e8 | − | 3.85553e8i | 0.0136369 | − | 0.0236198i | ||||
\(187\) | −1.69550e8 | − | 2.93669e8i | −0.0101394 | − | 0.0175619i | ||||
\(188\) | −1.35495e10 | −0.791068 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.30342e9 | −0.128228 | ||||||||
\(191\) | 1.29494e10 | + | 2.24290e10i | 0.704043 | + | 1.21944i | 0.967036 | + | 0.254641i | \(0.0819571\pi\) |
−0.262993 | + | 0.964798i | \(0.584710\pi\) | |||||||
\(192\) | −5.03316e7 | + | 8.71770e7i | −0.00267292 | + | 0.00462963i | ||||
\(193\) | −7.96837e9 | + | 1.38016e10i | −0.413391 | + | 0.716015i | −0.995258 | − | 0.0972694i | \(-0.968989\pi\) |
0.581867 | + | 0.813284i | \(0.302323\pi\) | |||||||
\(194\) | 6.98001e9 | + | 1.20897e10i | 0.353792 | + | 0.612786i | ||||
\(195\) | −3.80258e8 | −0.0188331 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.34685e9 | −0.158321 | −0.0791604 | − | 0.996862i | \(-0.525224\pi\) | ||||
−0.0791604 | + | 0.996862i | \(0.525224\pi\) | |||||||
\(198\) | 8.51139e9 | + | 1.47422e10i | 0.393557 | + | 0.681660i | ||||
\(199\) | −6.71304e9 | + | 1.16273e10i | −0.303445 | + | 0.525583i | −0.976914 | − | 0.213633i | \(-0.931470\pi\) |
0.673469 | + | 0.739216i | \(0.264804\pi\) | |||||||
\(200\) | −3.35775e9 | + | 5.81579e9i | −0.148393 | + | 0.257024i | ||||
\(201\) | −4.61204e8 | − | 7.98828e8i | −0.0199301 | − | 0.0345200i | ||||
\(202\) | −1.93442e10 | −0.817467 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −9.61843e6 | −0.000388838 | ||||||||
\(205\) | −6.13456e9 | − | 1.06254e10i | −0.242600 | − | 0.420195i | ||||
\(206\) | −5.52450e9 | + | 9.56872e9i | −0.213742 | + | 0.370213i | ||||
\(207\) | −2.61305e9 | + | 4.52594e9i | −0.0989194 | + | 0.171333i | ||||
\(208\) | −3.70842e9 | − | 6.42317e9i | −0.137374 | − | 0.237938i | ||||
\(209\) | 1.39213e10 | 0.504686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.01702e10 | 1.04787 | 0.523935 | − | 0.851759i | \(-0.324464\pi\) | ||||
0.523935 | + | 0.851759i | \(0.324464\pi\) | |||||||
\(212\) | −2.07632e9 | − | 3.59629e9i | −0.0705963 | − | 0.122276i | ||||
\(213\) | −8.38968e8 | + | 1.45313e9i | −0.0279278 | + | 0.0483724i | ||||
\(214\) | 1.43599e9 | − | 2.48722e9i | 0.0468049 | − | 0.0810684i | ||||
\(215\) | 7.70577e9 | + | 1.33468e10i | 0.245948 | + | 0.425994i | ||||
\(216\) | 9.66574e8 | 0.0302130 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.56577e10 | 0.769421 | ||||||||
\(219\) | −1.21207e9 | − | 2.09936e9i | −0.0356064 | − | 0.0616722i | ||||
\(220\) | −3.88162e9 | + | 6.72316e9i | −0.111715 | + | 0.193496i | ||||
\(221\) | 3.54342e8 | − | 6.13738e8i | 0.00999210 | − | 0.0173068i | ||||
\(222\) | −5.73419e8 | − | 9.93192e8i | −0.0158447 | − | 0.0274438i | ||||
\(223\) | −5.35030e10 | −1.44879 | −0.724396 | − | 0.689384i | \(-0.757881\pi\) | ||||
−0.724396 | + | 0.689384i | \(0.757881\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.22117e10 | 0.837901 | ||||||||
\(226\) | 1.14228e10 | + | 1.97849e10i | 0.291263 | + | 0.504482i | ||||
\(227\) | −2.01352e10 | + | 3.48752e10i | −0.503315 | + | 0.871766i | 0.496678 | + | 0.867935i | \(0.334553\pi\) |
−0.999993 | + | 0.00383159i | \(0.998780\pi\) | |||||||
\(228\) | 1.97436e8 | − | 3.41969e8i | 0.00483860 | − | 0.00838069i | ||||
\(229\) | 9.51236e9 | + | 1.64759e10i | 0.228575 | + | 0.395903i | 0.957386 | − | 0.288812i | \(-0.0932601\pi\) |
−0.728811 | + | 0.684715i | \(0.759927\pi\) | |||||||
\(230\) | −2.38336e9 | −0.0561584 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.45003e9 | −0.146173 | ||||||||
\(233\) | 1.83874e10 | + | 3.18479e10i | 0.408713 | + | 0.707911i | 0.994746 | − | 0.102376i | \(-0.0326444\pi\) |
−0.586033 | + | 0.810287i | \(0.699311\pi\) | |||||||
\(234\) | −1.77879e10 | + | 3.08096e10i | −0.387841 | + | 0.671761i | ||||
\(235\) | −1.48198e10 | + | 2.56686e10i | −0.316984 | + | 0.549032i | ||||
\(236\) | −1.79852e10 | − | 3.11513e10i | −0.377409 | − | 0.653691i | ||||
\(237\) | −7.84139e8 | −0.0161445 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.56110e9 | 0.130073 | 0.0650363 | − | 0.997883i | \(-0.479284\pi\) | ||||
0.0650363 | + | 0.997883i | \(0.479284\pi\) | |||||||
\(240\) | 1.10100e8 | + | 1.90700e8i | 0.00214209 | + | 0.00371022i | ||||
\(241\) | −4.48409e10 | + | 7.76667e10i | −0.856244 | + | 1.48306i | 0.0192424 | + | 0.999815i | \(0.493875\pi\) |
−0.875486 | + | 0.483243i | \(0.839459\pi\) | |||||||
\(242\) | 4.59593e9 | − | 7.96039e9i | 0.0861399 | − | 0.149199i | ||||
\(243\) | −3.47829e9 | − | 6.02457e9i | −0.0639937 | − | 0.110840i | ||||
\(244\) | 5.19587e10 | 0.938434 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.10328e9 | 0.0366175 | ||||||||
\(247\) | 1.45470e10 | + | 2.51962e10i | 0.248678 | + | 0.430723i | ||||
\(248\) | 9.49757e9 | − | 1.64503e10i | 0.159434 | − | 0.276147i | ||||
\(249\) | 1.26040e9 | − | 2.18308e9i | 0.0207784 | − | 0.0359892i | ||||
\(250\) | 1.60951e10 | + | 2.78775e10i | 0.260593 | + | 0.451360i | ||||
\(251\) | −5.33703e9 | −0.0848727 | −0.0424363 | − | 0.999099i | \(-0.513512\pi\) | ||||
−0.0424363 | + | 0.999099i | \(0.513512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.44044e10 | 0.221031 | ||||||||
\(254\) | −1.88698e10 | − | 3.26835e10i | −0.284457 | − | 0.492693i | ||||
\(255\) | −1.05202e7 | + | 1.82215e7i | −0.000155809 | + | 0.000269868i | ||||
\(256\) | −2.14748e9 | + | 3.71955e9i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −4.17788e10 | − | 7.23630e10i | −0.597388 | − | 1.03471i | −0.993205 | − | 0.116377i | \(-0.962872\pi\) |
0.395817 | − | 0.918329i | \(-0.370461\pi\) | |||||||
\(258\) | −2.64198e9 | −0.0371228 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.62243e10 | −0.220185 | ||||||||
\(261\) | 1.54692e10 | + | 2.67934e10i | 0.206341 | + | 0.357393i | ||||
\(262\) | −4.81332e9 | + | 8.33692e9i | −0.0631087 | + | 0.109307i | ||||
\(263\) | −5.43174e10 | + | 9.40806e10i | −0.700065 | + | 1.21255i | 0.268378 | + | 0.963314i | \(0.413512\pi\) |
−0.968443 | + | 0.249235i | \(0.919821\pi\) | |||||||
\(264\) | −6.65420e8 | − | 1.15254e9i | −0.00843098 | − | 0.0146029i | ||||
\(265\) | −9.08388e9 | −0.113153 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.81725e9 | 0.0339254 | ||||||||
\(268\) | −1.96780e10 | − | 3.40833e10i | −0.233010 | − | 0.403586i | ||||
\(269\) | 7.07003e10 | − | 1.22456e11i | 0.823258 | − | 1.42592i | −0.0799860 | − | 0.996796i | \(-0.525488\pi\) |
0.903244 | − | 0.429128i | \(-0.141179\pi\) | |||||||
\(270\) | 1.05719e9 | − | 1.83111e9i | 0.0121064 | − | 0.0209690i | ||||
\(271\) | −4.54176e10 | − | 7.86657e10i | −0.511520 | − | 0.885979i | −0.999911 | − | 0.0133539i | \(-0.995749\pi\) |
0.488391 | − | 0.872625i | \(-0.337584\pi\) | |||||||
\(272\) | −4.10386e8 | −0.00454604 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.25614e10 | 0.884911 | ||||||||
\(275\) | −4.43918e10 | − | 7.68888e10i | −0.468064 | − | 0.810711i | ||||
\(276\) | 2.04288e8 | − | 3.53837e8i | 0.00211910 | − | 0.00367039i | ||||
\(277\) | 1.32538e10 | − | 2.29562e10i | 0.135263 | − | 0.234283i | −0.790435 | − | 0.612546i | \(-0.790145\pi\) |
0.925698 | + | 0.378263i | \(0.123479\pi\) | |||||||
\(278\) | 5.71485e10 | + | 9.89841e10i | 0.573857 | + | 0.993949i | ||||
\(279\) | −9.11126e10 | −0.900243 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.86968e11 | −1.78891 | −0.894455 | − | 0.447158i | \(-0.852436\pi\) | ||||
−0.894455 | + | 0.447158i | \(0.852436\pi\) | |||||||
\(282\) | −2.54054e9 | − | 4.40034e9i | −0.0239224 | − | 0.0414348i | ||||
\(283\) | −2.66706e9 | + | 4.61949e9i | −0.0247169 | + | 0.0428110i | −0.878119 | − | 0.478442i | \(-0.841202\pi\) |
0.853402 | + | 0.521253i | \(0.174535\pi\) | |||||||
\(284\) | −3.57960e10 | + | 6.20004e10i | −0.326514 | + | 0.565538i | ||||
\(285\) | −4.31891e8 | − | 7.48057e8i | −0.00387768 | − | 0.00671634i | ||||
\(286\) | 9.80558e10 | 0.866615 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.06014e10 | 0.176453 | ||||||||
\(289\) | 5.92743e10 | + | 1.02666e11i | 0.499835 | + | 0.865739i | ||||
\(290\) | −7.05472e9 | + | 1.22191e10i | −0.0585718 | + | 0.101449i | ||||
\(291\) | −2.61751e9 | + | 4.53365e9i | −0.0213978 | + | 0.0370621i | ||||
\(292\) | −5.17149e10 | − | 8.95729e10i | −0.416287 | − | 0.721031i | ||||
\(293\) | −7.65433e10 | −0.606741 | −0.303370 | − | 0.952873i | \(-0.598112\pi\) | ||||
−0.303370 | + | 0.952873i | \(0.598112\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.86854e10 | −0.604916 | ||||||||
\(296\) | −2.44659e10 | − | 4.23762e10i | −0.185246 | − | 0.320855i | ||||
\(297\) | −6.38939e9 | + | 1.10668e10i | −0.0476492 | + | 0.0825308i | ||||
\(298\) | 7.28339e10 | − | 1.26152e11i | 0.535008 | − | 0.926662i | ||||
\(299\) | 1.50519e10 | + | 2.60706e10i | 0.108911 | + | 0.188639i | ||||
\(300\) | −2.51831e9 | −0.0179500 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.63091e9 | 0.0320358 | ||||||||
\(303\) | −3.62704e9 | − | 6.28223e9i | −0.0247207 | − | 0.0428175i | ||||
\(304\) | 8.42393e9 | − | 1.45907e10i | 0.0565697 | − | 0.0979816i | ||||
\(305\) | 5.68298e10 | − | 9.84321e10i | 0.376034 | − | 0.651310i | ||||
\(306\) | 9.84236e8 | + | 1.70475e9i | 0.00641731 | + | 0.0111151i | ||||
\(307\) | 7.51944e10 | 0.483128 | 0.241564 | − | 0.970385i | \(-0.422340\pi\) | ||||
0.241564 | + | 0.970385i | \(0.422340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.14338e9 | −0.0258548 | ||||||||
\(310\) | −2.07759e10 | − | 3.59850e10i | −0.127771 | − | 0.221306i | ||||
\(311\) | 1.07567e11 | − | 1.86311e11i | 0.652014 | − | 1.12932i | −0.330619 | − | 0.943764i | \(-0.607257\pi\) |
0.982633 | − | 0.185558i | \(-0.0594092\pi\) | |||||||
\(312\) | 1.39066e9 | − | 2.40869e9i | 0.00830854 | − | 0.0143908i | ||||
\(313\) | 4.79537e10 | + | 8.30583e10i | 0.282405 | + | 0.489140i | 0.971977 | − | 0.235077i | \(-0.0755344\pi\) |
−0.689571 | + | 0.724218i | \(0.742201\pi\) | |||||||
\(314\) | 2.22508e11 | 1.29170 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.34566e10 | −0.188751 | ||||||||
\(317\) | −8.52932e10 | − | 1.47732e11i | −0.474403 | − | 0.821691i | 0.525167 | − | 0.850999i | \(-0.324003\pi\) |
−0.999570 | + | 0.0293083i | \(0.990670\pi\) | |||||||
\(318\) | 7.78619e8 | − | 1.34861e9i | 0.00426975 | − | 0.00739543i | ||||
\(319\) | 4.26370e10 | − | 7.38494e10i | 0.230530 | − | 0.399290i | ||||
\(320\) | 4.69762e9 | + | 8.13652e9i | 0.0250440 | + | 0.0433774i | ||||
\(321\) | 1.07700e9 | 0.00566163 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.60982e9 | 0.00822937 | ||||||||
\(324\) | −4.93179e10 | − | 8.54211e10i | −0.248629 | − | 0.430638i | ||||
\(325\) | 9.27742e10 | − | 1.60690e11i | 0.461266 | − | 0.798937i | ||||
\(326\) | 1.32986e11 | − | 2.30338e11i | 0.652119 | − | 1.12950i | ||||
\(327\) | 4.81083e9 | + | 8.33259e9i | 0.0232678 | + | 0.0403010i | ||||
\(328\) | 8.97398e10 | 0.428107 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.91121e9 | −0.0135133 | ||||||||
\(331\) | 6.19958e10 | + | 1.07380e11i | 0.283881 | + | 0.491697i | 0.972337 | − | 0.233581i | \(-0.0750445\pi\) |
−0.688456 | + | 0.725278i | \(0.741711\pi\) | |||||||
\(332\) | 5.37772e10 | − | 9.31448e10i | 0.242927 | − | 0.420763i | ||||
\(333\) | −1.17354e11 | + | 2.03263e11i | −0.522996 | + | 0.905856i | ||||
\(334\) | 1.26416e11 | + | 2.18958e11i | 0.555829 | + | 0.962724i | ||||
\(335\) | −8.60914e10 | −0.373472 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.29335e10 | −0.308030 | −0.154015 | − | 0.988069i | \(-0.549220\pi\) | ||||
−0.154015 | + | 0.988069i | \(0.549220\pi\) | |||||||
\(338\) | 1.76272e10 | + | 3.05312e10i | 0.0734613 | + | 0.127239i | ||||
\(339\) | −4.28355e9 | + | 7.41933e9i | −0.0176159 | + | 0.0305117i | ||||
\(340\) | −4.48860e8 | + | 7.77449e8i | −0.00182161 | + | 0.00315512i | ||||
\(341\) | 1.25565e11 | + | 2.17484e11i | 0.502889 | + | 0.871029i | ||||
\(342\) | −8.08130e10 | −0.319421 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.12724e11 | −0.434015 | ||||||||
\(345\) | −4.46880e8 | − | 7.74019e8i | −0.00169826 | − | 0.00294148i | ||||
\(346\) | −2.58500e10 | + | 4.47735e10i | −0.0969657 | + | 0.167949i | ||||
\(347\) | 7.78602e10 | − | 1.34858e11i | 0.288292 | − | 0.499337i | −0.685110 | − | 0.728440i | \(-0.740246\pi\) |
0.973402 | + | 0.229103i | \(0.0735792\pi\) | |||||||
\(348\) | −1.20938e9 | − | 2.09471e9i | −0.00442035 | − | 0.00765626i | ||||
\(349\) | −1.08728e11 | −0.392310 | −0.196155 | − | 0.980573i | \(-0.562846\pi\) | ||||
−0.196155 | + | 0.980573i | \(0.562846\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.67063e10 | −0.0939144 | ||||||||
\(352\) | −2.83912e10 | − | 4.91751e10i | −0.0985695 | − | 0.170727i | ||||
\(353\) | 1.62793e11 | − | 2.81965e11i | 0.558018 | − | 0.966516i | −0.439644 | − | 0.898172i | \(-0.644895\pi\) |
0.997662 | − | 0.0683436i | \(-0.0217714\pi\) | |||||||
\(354\) | 6.74446e9 | − | 1.16818e10i | 0.0228261 | − | 0.0395360i | ||||
\(355\) | 7.83037e10 | + | 1.35626e11i | 0.261670 | + | 0.453226i | ||||
\(356\) | 1.20203e11 | 0.396634 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.86252e11 | 1.24279 | ||||||||
\(359\) | 1.13775e11 | + | 1.97064e11i | 0.361511 | + | 0.626155i | 0.988210 | − | 0.153106i | \(-0.0489277\pi\) |
−0.626699 | + | 0.779261i | \(0.715594\pi\) | |||||||
\(360\) | 2.25328e10 | − | 3.90279e10i | 0.0707055 | − | 0.122465i | ||||
\(361\) | 1.28299e11 | − | 2.22221e11i | 0.397596 | − | 0.688656i | ||||
\(362\) | 3.11465e10 | + | 5.39474e10i | 0.0953282 | + | 0.165113i | ||||
\(363\) | 3.44695e9 | 0.0104197 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.26253e11 | −0.667231 | ||||||||
\(366\) | 9.74225e9 | + | 1.68741e10i | 0.0283788 | + | 0.0491536i | ||||
\(367\) | −2.10996e11 | + | 3.65457e11i | −0.607125 | + | 1.05157i | 0.384587 | + | 0.923089i | \(0.374344\pi\) |
−0.991712 | + | 0.128482i | \(0.958989\pi\) | |||||||
\(368\) | 8.71629e9 | − | 1.50971e10i | 0.0247752 | − | 0.0429118i | ||||
\(369\) | −2.15224e11 | − | 3.72779e11i | −0.604328 | − | 1.04673i | ||||
\(370\) | −1.07038e11 | −0.296915 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.12318e9 | 0.0192855 | ||||||||
\(373\) | −1.91642e11 | − | 3.31933e11i | −0.512625 | − | 0.887893i | −0.999893 | − | 0.0146401i | \(-0.995340\pi\) |
0.487268 | − | 0.873253i | \(-0.337994\pi\) | |||||||
\(374\) | 2.71280e9 | − | 4.69870e9i | 0.00716961 | − | 0.0124181i | ||||
\(375\) | −6.03565e9 | + | 1.04541e10i | −0.0157610 | + | 0.0272988i | ||||
\(376\) | −1.08396e11 | − | 1.87748e11i | −0.279685 | − | 0.484428i | ||||
\(377\) | 1.78214e11 | 0.454365 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.21462e11 | −0.302386 | −0.151193 | − | 0.988504i | \(-0.548312\pi\) | ||||
−0.151193 | + | 0.988504i | \(0.548312\pi\) | |||||||
\(380\) | −1.84274e10 | − | 3.19171e10i | −0.0453353 | − | 0.0785231i | ||||
\(381\) | 7.07618e9 | − | 1.22563e10i | 0.0172043 | − | 0.0297987i | ||||
\(382\) | −2.07190e11 | + | 3.58864e11i | −0.497834 | + | 0.862273i | ||||
\(383\) | −1.98860e11 | − | 3.44436e11i | −0.472230 | − | 0.817927i | 0.527265 | − | 0.849701i | \(-0.323218\pi\) |
−0.999495 | + | 0.0317740i | \(0.989884\pi\) | |||||||
\(384\) | −1.61061e9 | −0.00378008 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.54988e11 | −0.584624 | ||||||||
\(387\) | 2.70349e11 | + | 4.68257e11i | 0.612667 | + | 1.06117i | ||||
\(388\) | −1.11680e11 | + | 1.93436e11i | −0.250169 | + | 0.433305i | ||||
\(389\) | −3.37731e10 | + | 5.84968e10i | −0.0747821 | + | 0.129526i | −0.900992 | − | 0.433837i | \(-0.857159\pi\) |
0.826209 | + | 0.563363i | \(0.190493\pi\) | |||||||
\(390\) | −3.04206e9 | − | 5.26901e9i | −0.00665852 | − | 0.0115329i | ||||
\(391\) | 1.66569e9 | 0.00360412 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.60999e9 | −0.00763378 | ||||||||
\(394\) | −2.67748e10 | − | 4.63753e10i | −0.0559748 | − | 0.0969512i | ||||
\(395\) | −3.65931e10 | + | 6.33812e10i | −0.0756333 | + | 0.131001i | ||||
\(396\) | −1.36182e11 | + | 2.35875e11i | −0.278287 | + | 0.482007i | ||||
\(397\) | 6.23278e10 | + | 1.07955e11i | 0.125929 | + | 0.218115i | 0.922096 | − | 0.386962i | \(-0.126476\pi\) |
−0.796167 | + | 0.605077i | \(0.793142\pi\) | |||||||
\(398\) | −2.14817e11 | −0.429136 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.07448e11 | −0.209859 | ||||||||
\(401\) | −1.75598e11 | − | 3.04144e11i | −0.339133 | − | 0.587395i | 0.645137 | − | 0.764067i | \(-0.276800\pi\) |
−0.984270 | + | 0.176672i | \(0.943467\pi\) | |||||||
\(402\) | 7.37926e9 | − | 1.27813e10i | 0.0140927 | − | 0.0244093i | ||||
\(403\) | −2.62417e11 | + | 4.54519e11i | −0.495586 | + | 0.858380i | ||||
\(404\) | −1.54754e11 | − | 2.68042e11i | −0.289018 | − | 0.500594i | ||||
\(405\) | −2.15766e11 | −0.398506 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.46913e11 | 1.16861 | ||||||||
\(408\) | −7.69475e7 | − | 1.33277e8i | −0.000137475 | − | 0.000238114i | ||||
\(409\) | −1.90978e10 | + | 3.30784e10i | −0.0337465 | + | 0.0584506i | −0.882405 | − | 0.470490i | \(-0.844077\pi\) |
0.848659 | + | 0.528941i | \(0.177411\pi\) | |||||||
\(410\) | 9.81529e10 | − | 1.70006e11i | 0.171544 | − | 0.297123i | ||||
\(411\) | 1.54803e10 | + | 2.68126e10i | 0.0267602 | + | 0.0463501i | ||||
\(412\) | −1.76784e11 | −0.302277 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.36176e10 | −0.139893 | ||||||||
\(415\) | −1.17638e11 | − | 2.03754e11i | −0.194684 | − | 0.337202i | ||||
\(416\) | 5.93347e10 | − | 1.02771e11i | 0.0971379 | − | 0.168248i | ||||
\(417\) | −2.14307e10 | + | 3.71190e10i | −0.0347075 | + | 0.0601152i | ||||
\(418\) | 1.11370e11 | + | 1.92899e11i | 0.178433 | + | 0.309056i | ||||
\(419\) | −2.15268e11 | −0.341205 | −0.170603 | − | 0.985340i | \(-0.554571\pi\) | ||||
−0.170603 | + | 0.985340i | \(0.554571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.19933e12 | 1.86066 | 0.930332 | − | 0.366718i | \(-0.119519\pi\) | ||||
0.930332 | + | 0.366718i | \(0.119519\pi\) | |||||||
\(422\) | 2.41362e11 | + | 4.18050e11i | 0.370478 | + | 0.641686i | ||||
\(423\) | −5.19937e11 | + | 9.00557e11i | −0.789621 | + | 1.36766i | ||||
\(424\) | 3.32211e10 | − | 5.75406e10i | 0.0499191 | − | 0.0864625i | ||||
\(425\) | −5.13335e9 | − | 8.89123e9i | −0.00763222 | − | 0.0132194i | ||||
\(426\) | −2.68470e10 | −0.0394959 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.59518e10 | 0.0661921 | ||||||||
\(429\) | 1.83855e10 | + | 3.18446e10i | 0.0262070 | + | 0.0453918i | ||||
\(430\) | −1.23292e11 | + | 2.13548e11i | −0.173911 | + | 0.301223i | ||||
\(431\) | −3.95559e11 | + | 6.85128e11i | −0.552158 | + | 0.956365i | 0.445961 | + | 0.895052i | \(0.352862\pi\) |
−0.998119 | + | 0.0613129i | \(0.980471\pi\) | |||||||
\(432\) | 7.73259e9 | + | 1.33932e10i | 0.0106819 | + | 0.0185016i | ||||
\(433\) | 1.15451e12 | 1.57834 | 0.789170 | − | 0.614174i | \(-0.210511\pi\) | ||||
0.789170 | + | 0.614174i | \(0.210511\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.29104e9 | −0.00708499 | ||||||||
\(436\) | 2.05262e11 | + | 3.55524e11i | 0.272031 | + | 0.471172i | ||||
\(437\) | −3.41914e10 | + | 5.92212e10i | −0.0448487 | + | 0.0776803i | ||||
\(438\) | 1.93931e10 | − | 3.35898e10i | 0.0251776 | − | 0.0436088i | ||||
\(439\) | −1.06364e11 | − | 1.84228e11i | −0.136680 | − | 0.236737i | 0.789558 | − | 0.613676i | \(-0.210310\pi\) |
−0.926238 | + | 0.376939i | \(0.876977\pi\) | |||||||
\(440\) | −1.24212e11 | −0.157988 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.13389e10 | 0.0141310 | ||||||||
\(443\) | 3.24150e10 | + | 5.61444e10i | 0.0399880 | + | 0.0692612i | 0.885327 | − | 0.464969i | \(-0.153935\pi\) |
−0.845339 | + | 0.534231i | \(0.820601\pi\) | |||||||
\(444\) | 9.17471e9 | − | 1.58911e10i | 0.0112039 | − | 0.0194057i | ||||
\(445\) | 1.31472e11 | − | 2.27716e11i | 0.158933 | − | 0.275279i | ||||
\(446\) | −4.28024e11 | − | 7.41359e11i | −0.512225 | − | 0.887200i | ||||
\(447\) | 5.46255e10 | 0.0647159 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.08031e12 | −1.25441 | −0.627207 | − | 0.778853i | \(-0.715802\pi\) | ||||
−0.627207 | + | 0.778853i | \(0.715802\pi\) | |||||||
\(450\) | 2.57694e11 | + | 4.46339e11i | 0.296243 | + | 0.513108i | ||||
\(451\) | −5.93211e11 | + | 1.02747e12i | −0.675173 | + | 1.16943i | ||||
\(452\) | −1.82765e11 | + | 3.16558e11i | −0.205954 | + | 0.356722i | ||||
\(453\) | 8.68296e8 | + | 1.50393e9i | 0.000968782 | + | 0.00167798i | ||||
\(454\) | −6.44326e11 | −0.711794 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.31795e9 | 0.00684281 | ||||||||
\(457\) | 3.23363e10 | + | 5.60081e10i | 0.0346790 | + | 0.0600658i | 0.882844 | − | 0.469666i | \(-0.155626\pi\) |
−0.848165 | + | 0.529732i | \(0.822292\pi\) | |||||||
\(458\) | −1.52198e11 | + | 2.63614e11i | −0.161627 | + | 0.279946i | ||||
\(459\) | −7.38853e8 | + | 1.27973e9i | −0.000776965 | + | 0.00134574i | ||||
\(460\) | −1.90669e10 | − | 3.30248e10i | −0.0198550 | − | 0.0343898i | ||||
\(461\) | −4.29254e11 | −0.442649 | −0.221325 | − | 0.975200i | \(-0.571038\pi\) | ||||
−0.221325 | + | 0.975200i | \(0.571038\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.61883e12 | 1.63715 | 0.818574 | − | 0.574401i | \(-0.194765\pi\) | ||||
0.818574 | + | 0.574401i | \(0.194765\pi\) | |||||||
\(464\) | −5.16002e10 | − | 8.93742e10i | −0.0516798 | − | 0.0895120i | ||||
\(465\) | 7.79097e9 | − | 1.34944e10i | 0.00772776 | − | 0.0133849i | ||||
\(466\) | −2.94198e11 | + | 5.09566e11i | −0.289004 | + | 0.500569i | ||||
\(467\) | 1.63661e11 | + | 2.83468e11i | 0.159228 | + | 0.275790i | 0.934590 | − | 0.355726i | \(-0.115766\pi\) |
−0.775363 | + | 0.631516i | \(0.782433\pi\) | |||||||
\(468\) | −5.69214e11 | −0.548490 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.74233e11 | −0.448283 | ||||||||
\(471\) | 4.17203e10 | + | 7.22617e10i | 0.0390619 | + | 0.0676573i | ||||
\(472\) | 2.87764e11 | − | 4.98421e11i | 0.266868 | − | 0.462229i | ||||
\(473\) | 7.45148e11 | − | 1.29063e12i | 0.684490 | − | 1.18557i | ||||
\(474\) | −6.27311e9 | − | 1.08653e10i | −0.00570795 | − | 0.00988647i | ||||
\(475\) | 4.21486e11 | 0.379893 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.18698e11 | −0.281869 | ||||||||
\(478\) | 5.24888e10 | + | 9.09132e10i | 0.0459876 | + | 0.0796529i | ||||
\(479\) | 1.42406e11 | − | 2.46654e11i | 0.123600 | − | 0.214081i | −0.797585 | − | 0.603206i | \(-0.793889\pi\) |
0.921185 | + | 0.389126i | \(0.127223\pi\) | |||||||
\(480\) | −1.76161e9 | + | 3.05119e9i | −0.00151469 | + | 0.00262352i | ||||
\(481\) | 6.75990e11 | + | 1.17085e12i | 0.575821 | + | 0.997351i | ||||
\(482\) | −1.43491e12 | −1.21091 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.47070e11 | 0.121820 | ||||||||
\(485\) | 2.44300e11 | + | 4.23141e11i | 0.200487 | + | 0.347254i | ||||
\(486\) | 5.56526e10 | − | 9.63931e10i | 0.0452504 | − | 0.0783759i | ||||
\(487\) | 3.57388e11 | − | 6.19014e11i | 0.287912 | − | 0.498678i | −0.685399 | − | 0.728167i | \(-0.740372\pi\) |
0.973311 | + | 0.229490i | \(0.0737057\pi\) | |||||||
\(488\) | 4.15669e11 | + | 7.19960e11i | 0.331787 | + | 0.574671i | ||||
\(489\) | 9.97395e10 | 0.0788819 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.01506e12 | 0.788176 | 0.394088 | − | 0.919073i | \(-0.371061\pi\) | ||||
0.394088 | + | 0.919073i | \(0.371061\pi\) | |||||||
\(492\) | 1.68262e10 | + | 2.91438e10i | 0.0129462 | + | 0.0224235i | ||||
\(493\) | 4.93043e9 | − | 8.53975e9i | 0.00375901 | − | 0.00651080i | ||||
\(494\) | −2.32752e11 | + | 4.03139e11i | −0.175842 | + | 0.304567i | ||||
\(495\) | 2.97899e11 | + | 5.15976e11i | 0.223021 | + | 0.386283i | ||||
\(496\) | 3.03922e11 | 0.225473 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.03329e10 | 0.0293851 | ||||||||
\(499\) | −6.67062e11 | − | 1.15539e12i | −0.481630 | − | 0.834208i | 0.518148 | − | 0.855291i | \(-0.326622\pi\) |
−0.999778 | + | 0.0210833i | \(0.993288\pi\) | |||||||
\(500\) | −2.57521e11 | + | 4.46040e11i | −0.184267 | + | 0.319160i | ||||
\(501\) | −4.74058e10 | + | 8.21093e10i | −0.0336172 | + | 0.0582267i | ||||
\(502\) | −4.26962e10 | − | 7.39520e10i | −0.0300070 | − | 0.0519737i | ||||
\(503\) | 5.68445e11 | 0.395943 | 0.197971 | − | 0.980208i | \(-0.436565\pi\) | ||||
0.197971 | + | 0.980208i | \(0.436565\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.77048e11 | −0.463243 | ||||||||
\(506\) | 1.15235e11 | + | 1.99594e11i | 0.0781464 | + | 0.135353i | ||||
\(507\) | −6.61021e9 | + | 1.14492e10i | −0.00444303 | + | 0.00769555i | ||||
\(508\) | 3.01917e11 | − | 5.22936e11i | 0.201141 | − | 0.348387i | ||||
\(509\) | 1.78586e11 | + | 3.09321e11i | 0.117928 | + | 0.204258i | 0.918947 | − | 0.394382i | \(-0.129041\pi\) |
−0.801018 | + | 0.598640i | \(0.795708\pi\) | |||||||
\(510\) | −3.36645e8 | −0.000220347 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | −3.03326e10 | − | 5.25377e10i | −0.0193367 | − | 0.0334921i | ||||
\(514\) | 6.68460e11 | − | 1.15781e12i | 0.422417 | − | 0.731648i | ||||
\(515\) | −1.93358e11 | + | 3.34905e11i | −0.121124 | + | 0.209792i | ||||
\(516\) | −2.11358e10 | − | 3.66083e10i | −0.0131249 | − | 0.0227330i | ||||
\(517\) | 2.86615e12 | 1.76438 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.93875e10 | −0.0117292 | ||||||||
\(520\) | −1.29795e11 | − | 2.24811e11i | −0.0778470 | − | 0.134835i | ||||
\(521\) | 1.08986e12 | − | 1.88770e12i | 0.648040 | − | 1.12244i | −0.335550 | − | 0.942022i | \(-0.608922\pi\) |
0.983590 | − | 0.180416i | \(-0.0577444\pi\) | |||||||
\(522\) | −2.47507e11 | + | 4.28695e11i | −0.145905 | + | 0.252715i | ||||
\(523\) | −7.85404e11 | − | 1.36036e12i | −0.459024 | − | 0.795053i | 0.539885 | − | 0.841738i | \(-0.318468\pi\) |
−0.998910 | + | 0.0466853i | \(0.985134\pi\) | |||||||
\(524\) | −1.54026e11 | −0.0892492 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.73816e12 | −0.990042 | ||||||||
\(527\) | 1.45200e10 | + | 2.51493e10i | 0.00820007 | + | 0.0142029i | ||||
\(528\) | 1.06467e10 | − | 1.84407e10i | 0.00596160 | − | 0.0103258i | ||||
\(529\) | 8.65198e11 | − | 1.49857e12i | 0.480358 | − | 0.832005i | ||||
\(530\) | −7.26711e10 | − | 1.25870e11i | −0.0400055 | − | 0.0692916i | ||||
\(531\) | −2.76059e12 | −1.50687 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.47950e12 | −1.33074 | ||||||||
\(534\) | 2.25380e10 | + | 3.90370e10i | 0.0119945 | + | 0.0207750i | ||||
\(535\) | 5.02598e10 | − | 8.70526e10i | 0.0265234 | − | 0.0459399i | ||||
\(536\) | 3.14848e11 | − | 5.45333e11i | 0.164763 | − | 0.285378i | ||||
\(537\) | 7.24223e10 | + | 1.25439e11i | 0.0375827 | + | 0.0650952i | ||||
\(538\) | 2.26241e12 | 1.16426 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.38301e10 | 0.0171211 | ||||||||
\(541\) | −1.12272e12 | − | 1.94460e12i | −0.563486 | − | 0.975986i | −0.997189 | − | 0.0749302i | \(-0.976127\pi\) |
0.433703 | − | 0.901056i | \(-0.357207\pi\) | |||||||
\(542\) | 7.26682e11 | − | 1.25865e12i | 0.361699 | − | 0.626482i | ||||
\(543\) | −1.16800e10 | + | 2.02303e10i | −0.00576556 | + | 0.00998625i | ||||
\(544\) | −3.28309e9 | − | 5.68648e9i | −0.00160727 | − | 0.00278387i | ||||
\(545\) | 8.98021e11 | 0.436016 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.86062e11 | −0.184380 | −0.0921899 | − | 0.995741i | \(-0.529387\pi\) | ||||
−0.0921899 | + | 0.995741i | \(0.529387\pi\) | |||||||
\(548\) | 6.60491e11 | + | 1.14400e12i | 0.312863 | + | 0.541895i | ||||
\(549\) | 1.99381e12 | − | 3.45338e12i | 0.936718 | − | 1.62244i | ||||
\(550\) | 7.10268e11 | − | 1.23022e12i | 0.330971 | − | 0.573259i | ||||
\(551\) | 2.02412e11 | + | 3.50588e11i | 0.0935523 | + | 0.162037i | ||||
\(552\) | 6.53722e9 | 0.00299686 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.24120e11 | 0.191291 | ||||||||
\(555\) | −2.00697e10 | − | 3.47617e10i | −0.00897888 | − | 0.0155519i | ||||
\(556\) | −9.14376e11 | + | 1.58375e12i | −0.405778 | + | 0.702828i | ||||
\(557\) | 3.97551e11 | − | 6.88578e11i | 0.175003 | − | 0.303113i | −0.765160 | − | 0.643841i | \(-0.777340\pi\) |
0.940162 | + | 0.340727i | \(0.110673\pi\) | |||||||
\(558\) | −7.28901e11 | − | 1.26249e12i | −0.318284 | − | 0.551284i | ||||
\(559\) | 3.11456e12 | 1.34910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.03460e9 | 0.000867253 | ||||||||
\(562\) | −1.49574e12 | − | 2.59070e12i | −0.632475 | − | 1.09548i | ||||
\(563\) | −1.06834e12 | + | 1.85041e12i | −0.448146 | + | 0.776212i | −0.998265 | − | 0.0588741i | \(-0.981249\pi\) |
0.550119 | + | 0.835086i | \(0.314582\pi\) | |||||||
\(564\) | 4.06486e10 | − | 7.04054e10i | 0.0169157 | − | 0.0292988i | ||||
\(565\) | 3.99798e11 | + | 6.92471e11i | 0.165053 | + | 0.285880i | ||||
\(566\) | −8.53460e10 | −0.0349550 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.14547e12 | −0.461760 | ||||||||
\(569\) | −1.08731e12 | − | 1.88327e12i | −0.434857 | − | 0.753194i | 0.562427 | − | 0.826847i | \(-0.309868\pi\) |
−0.997284 | + | 0.0736527i | \(0.976534\pi\) | |||||||
\(570\) | 6.91026e9 | − | 1.19689e10i | 0.00274194 | − | 0.00474917i | ||||
\(571\) | −4.97538e11 | + | 8.61760e11i | −0.195868 | + | 0.339253i | −0.947185 | − | 0.320689i | \(-0.896086\pi\) |
0.751317 | + | 0.659942i | \(0.229419\pi\) | |||||||
\(572\) | 7.84447e11 | + | 1.35870e12i | 0.306395 | + | 0.530691i | ||||
\(573\) | −1.55393e11 | −0.0602192 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.36114e11 | 0.166377 | ||||||||
\(576\) | 1.64811e11 | + | 2.85461e11i | 0.0623857 | + | 0.108055i | ||||
\(577\) | 2.15294e12 | − | 3.72900e12i | 0.808614 | − | 1.40056i | −0.105211 | − | 0.994450i | \(-0.533552\pi\) |
0.913824 | − | 0.406110i | \(-0.133115\pi\) | |||||||
\(578\) | −9.48389e11 | + | 1.64266e12i | −0.353436 | + | 0.612170i | ||||
\(579\) | −4.78102e10 | − | 8.28097e10i | −0.0176794 | − | 0.0306216i | ||||
\(580\) | −2.25751e11 | −0.0828331 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.37602e10 | −0.0302611 | ||||||||
\(583\) | 4.39206e11 | + | 7.60727e11i | 0.157456 | + | 0.272722i | ||||
\(584\) | 8.27439e11 | − | 1.43317e12i | 0.294359 | − | 0.509846i | ||||
\(585\) | −6.22577e11 | + | 1.07834e12i | −0.219782 | + | 0.380673i | ||||
\(586\) | −6.12347e11 | − | 1.06062e12i | −0.214515 | − | 0.371551i | ||||
\(587\) | −5.05762e12 | −1.75822 | −0.879112 | − | 0.476615i | \(-0.841864\pi\) | ||||
−0.879112 | + | 0.476615i | \(0.841864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.19220e12 | −0.408158 | ||||||||
\(590\) | −6.29483e11 | − | 1.09030e12i | −0.213870 | − | 0.370434i | ||||
\(591\) | 1.00405e10 | − | 1.73907e10i | 0.00338543 | − | 0.00586373i | ||||
\(592\) | 3.91454e11 | − | 6.78019e11i | 0.130989 | − | 0.226879i | ||||
\(593\) | −1.40150e12 | − | 2.42747e12i | −0.465422 | − | 0.806135i | 0.533798 | − | 0.845612i | \(-0.320764\pi\) |
−0.999220 | + | 0.0394771i | \(0.987431\pi\) | |||||||
\(594\) | −2.04461e11 | −0.0673862 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.33069e12 | 0.756616 | ||||||||
\(597\) | −4.02782e10 | − | 6.97640e10i | −0.0129773 | − | 0.0224774i | ||||
\(598\) | −2.40830e11 | + | 4.17130e11i | −0.0770114 | + | 0.133388i | ||||
\(599\) | −1.60454e12 | + | 2.77914e12i | −0.509247 | + | 0.882042i | 0.490696 | + | 0.871331i | \(0.336743\pi\) |
−0.999943 | + | 0.0107108i | \(0.996591\pi\) | |||||||
\(600\) | −2.01465e10 | − | 3.48947e10i | −0.00634627 | − | 0.0109921i | ||||
\(601\) | −7.49502e11 | −0.234335 | −0.117168 | − | 0.993112i | \(-0.537381\pi\) | ||||
−0.117168 | + | 0.993112i | \(0.537381\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.02042e12 | −0.930336 | ||||||||
\(604\) | 3.70473e10 | + | 6.41678e10i | 0.0113264 | + | 0.0196178i | ||||
\(605\) | 1.60858e11 | − | 2.78614e11i | 0.0488138 | − | 0.0845479i | ||||
\(606\) | 5.80327e10 | − | 1.00516e11i | 0.0174802 | − | 0.0302766i | ||||
\(607\) | −8.70485e11 | − | 1.50772e12i | −0.260263 | − | 0.450789i | 0.706049 | − | 0.708163i | \(-0.250476\pi\) |
−0.966312 | + | 0.257375i | \(0.917143\pi\) | |||||||
\(608\) | 2.69566e11 | 0.0800016 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.81855e12 | 0.531792 | ||||||||
\(611\) | 2.99497e12 | + | 5.18745e12i | 0.869376 | + | 1.50580i | ||||
\(612\) | −1.57478e10 | + | 2.72760e10i | −0.00453772 | + | 0.00785956i | ||||
\(613\) | 2.01989e12 | − | 3.49854e12i | 0.577770 | − | 1.00073i | −0.417965 | − | 0.908463i | \(-0.637257\pi\) |
0.995735 | − | 0.0922632i | \(-0.0294101\pi\) | |||||||
\(614\) | 6.01555e11 | + | 1.04192e12i | 0.170812 | + | 0.295855i | ||||
\(615\) | 7.36147e10 | 0.0207504 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.93367e12 | −0.814945 | −0.407472 | − | 0.913218i | \(-0.633590\pi\) | ||||
−0.407472 | + | 0.913218i | \(0.633590\pi\) | |||||||
\(618\) | −3.31470e10 | − | 5.74123e10i | −0.00914105 | − | 0.0158328i | ||||
\(619\) | −2.88846e12 | + | 5.00295e12i | −0.790784 | + | 1.36968i | 0.134698 | + | 0.990887i | \(0.456994\pi\) |
−0.925482 | + | 0.378792i | \(0.876340\pi\) | |||||||
\(620\) | 3.32415e11 | − | 5.75759e11i | 0.0903478 | − | 0.156487i | ||||
\(621\) | −3.13853e10 | − | 5.43610e10i | −0.00846866 | − | 0.0146681i | ||||
\(622\) | 3.44214e12 | 0.922088 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.45010e10 | 0.0117500 | ||||||||
\(625\) | −1.03777e12 | − | 1.79747e12i | −0.272045 | − | 0.471197i | ||||
\(626\) | −7.67260e11 | + | 1.32893e12i | −0.199691 | + | 0.345874i | ||||
\(627\) | −4.17639e10 | + | 7.23371e10i | −0.0107919 | + | 0.0186921i | ||||
\(628\) | 1.78007e12 | + | 3.08317e12i | 0.456686 | + | 0.791004i | ||||
\(629\) | 7.48073e10 | 0.0190553 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.99985e12 | 1.00441 | 0.502206 | − | 0.864748i | \(-0.332522\pi\) | ||||
0.502206 | + | 0.864748i | \(0.332522\pi\) | |||||||
\(632\) | −2.67653e11 | − | 4.63588e11i | −0.0667336 | − | 0.115586i | ||||
\(633\) | −9.05106e10 | + | 1.56769e11i | −0.0224069 | + | 0.0388100i | ||||
\(634\) | 1.36469e12 | − | 2.36372e12i | 0.335454 | − | 0.581023i | ||||
\(635\) | −6.60444e11 | − | 1.14392e12i | −0.161196 | − | 0.279200i | ||||
\(636\) | 2.49158e10 | 0.00603834 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.36438e12 | 0.326019 | ||||||||
\(639\) | 2.74720e12 | + | 4.75829e12i | 0.651833 | + | 1.12901i | ||||
\(640\) | −7.51619e10 | + | 1.30184e11i | −0.0177088 | + | 0.0306725i | ||||
\(641\) | −2.34164e12 | + | 4.05584e12i | −0.547846 | + | 0.948898i | 0.450575 | + | 0.892738i | \(0.351219\pi\) |
−0.998422 | + | 0.0561595i | \(0.982114\pi\) | |||||||
\(642\) | 8.61597e9 | + | 1.49233e10i | 0.00200169 | + | 0.00346703i | ||||
\(643\) | 1.54877e12 | 0.357304 | 0.178652 | − | 0.983912i | \(-0.442826\pi\) | ||||
0.178652 | + | 0.983912i | \(0.442826\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.24692e10 | −0.0210367 | ||||||||
\(646\) | 1.28786e10 | + | 2.23064e10i | 0.00290952 | + | 0.00503944i | ||||
\(647\) | −4.07246e12 | + | 7.05372e12i | −0.913667 | + | 1.58252i | −0.104826 | + | 0.994491i | \(0.533429\pi\) |
−0.808841 | + | 0.588028i | \(0.799905\pi\) | |||||||
\(648\) | 7.89086e11 | − | 1.36674e12i | 0.175807 | − | 0.304507i | ||||
\(649\) | 3.80444e12 | + | 6.58948e12i | 0.841762 | + | 1.45797i | ||||
\(650\) | 2.96877e12 | 0.652329 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.25555e12 | 0.922235 | ||||||||
\(653\) | 1.44463e12 | + | 2.50216e12i | 0.310918 | + | 0.538526i | 0.978561 | − | 0.205955i | \(-0.0660302\pi\) |
−0.667643 | + | 0.744481i | \(0.732697\pi\) | |||||||
\(654\) | −7.69732e10 | + | 1.33322e11i | −0.0164528 | + | 0.0284971i | ||||
\(655\) | −1.68466e11 | + | 2.91792e11i | −0.0357624 | + | 0.0619424i | ||||
\(656\) | 7.17918e11 | + | 1.24347e12i | 0.151359 | + | 0.262161i | ||||
\(657\) | −7.93784e12 | −1.66210 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.20255e12 | 1.07456 | 0.537281 | − | 0.843403i | \(-0.319451\pi\) | ||||
0.537281 | + | 0.843403i | \(0.319451\pi\) | |||||||
\(660\) | −2.32897e10 | − | 4.03389e10i | −0.00477767 | − | 0.00827517i | ||||
\(661\) | 1.44486e12 | − | 2.50258e12i | 0.294388 | − | 0.509896i | −0.680454 | − | 0.732791i | \(-0.738217\pi\) |
0.974842 | + | 0.222895i | \(0.0715507\pi\) | |||||||
\(662\) | −9.91933e11 | + | 1.71808e12i | −0.200734 | + | 0.347682i | ||||
\(663\) | 2.12605e9 | + | 3.68243e9i | 0.000427329 | + | 0.000740156i | ||||
\(664\) | 1.72087e12 | 0.343551 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.75532e12 | −0.739628 | ||||||||
\(667\) | 2.09437e11 | + | 3.62755e11i | 0.0409720 | + | 0.0709656i | ||||
\(668\) | −2.02265e12 | + | 3.50333e12i | −0.393031 | + | 0.680749i | ||||
\(669\) | 1.60509e11 | − | 2.78009e11i | 0.0309800 | − | 0.0536589i | ||||
\(670\) | −6.88731e11 | − | 1.19292e12i | −0.132042 | − | 0.228704i | ||||
\(671\) | −1.09909e13 | −2.09306 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.46362e12 | 1.77824 | 0.889119 | − | 0.457677i | \(-0.151318\pi\) | ||||
0.889119 | + | 0.457677i | \(0.151318\pi\) | |||||||
\(674\) | −5.83468e11 | − | 1.01060e12i | −0.108905 | − | 0.188629i | ||||
\(675\) | −1.93448e11 | + | 3.35061e11i | −0.0358671 | + | 0.0621236i | ||||
\(676\) | −2.82035e11 | + | 4.88500e11i | −0.0519450 | + | 0.0899714i | ||||
\(677\) | −3.26134e12 | − | 5.64881e12i | −0.596688 | − | 1.03349i | −0.993306 | − | 0.115510i | \(-0.963150\pi\) |
0.396619 | − | 0.917983i | \(-0.370183\pi\) | |||||||
\(678\) | −1.37074e11 | −0.0249127 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.43635e10 | −0.00257615 | ||||||||
\(681\) | −1.20811e11 | − | 2.09251e11i | −0.0215251 | − | 0.0372826i | ||||
\(682\) | −2.00903e12 | + | 3.47975e12i | −0.355596 | + | 0.615911i | ||||
\(683\) | −2.68620e12 | + | 4.65264e12i | −0.472330 | + | 0.818099i | −0.999499 | − | 0.0316613i | \(-0.989920\pi\) |
0.527169 | + | 0.849761i | \(0.323254\pi\) | |||||||
\(684\) | −6.46504e11 | − | 1.11978e12i | −0.112932 | − | 0.195605i | ||||
\(685\) | 2.88965e12 | 0.501461 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.14148e11 | −0.0195508 | ||||||||
\(688\) | −9.01795e11 | − | 1.56195e12i | −0.153447 | − | 0.265779i | ||||
\(689\) | −9.17894e11 | + | 1.58984e12i | −0.155169 | + | 0.268761i | ||||
\(690\) | 7.15008e9 | − | 1.23843e10i | 0.00120085 | − | 0.00207994i | ||||
\(691\) | 1.00781e12 | + | 1.74559e12i | 0.168163 | + | 0.291266i | 0.937774 | − | 0.347246i | \(-0.112883\pi\) |
−0.769611 | + | 0.638513i | \(0.779550\pi\) | |||||||
\(692\) | −8.27200e11 | −0.137130 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.49153e12 | 0.407707 | ||||||||
\(695\) | 2.00020e12 | + | 3.46444e12i | 0.325193 | + | 0.563251i | ||||
\(696\) | 1.93501e10 | − | 3.35153e10i | 0.00312566 | − | 0.00541380i | ||||
\(697\) | −6.85975e10 | + | 1.18814e11i | −0.0110093 | + | 0.0190687i | ||||
\(698\) | −8.69828e11 | − | 1.50659e12i | −0.138702 | − | 0.240240i | ||||
\(699\) | −2.20649e11 | −0.0349586 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.06523e13 | −1.66614 | −0.833068 | − | 0.553171i | \(-0.813418\pi\) | ||||
−0.833068 | + | 0.553171i | \(0.813418\pi\) | |||||||
\(702\) | −2.13651e11 | − | 3.70054e11i | −0.0332038 | − | 0.0575106i | ||||
\(703\) | −1.53556e12 | + | 2.65966e12i | −0.237119 | + | 0.410703i | ||||
\(704\) | 4.54260e11 | − | 7.86801e11i | 0.0696991 | − | 0.120722i | ||||
\(705\) | −8.89188e10 | − | 1.54012e11i | −0.0135563 | − | 0.0234803i | ||||
\(706\) | 5.20936e12 | 0.789157 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.15823e11 | 0.0322810 | ||||||||
\(709\) | −1.73093e12 | − | 2.99807e12i | −0.257260 | − | 0.445588i | 0.708247 | − | 0.705965i | \(-0.249486\pi\) |
−0.965507 | + | 0.260377i | \(0.916153\pi\) | |||||||
\(710\) | −1.25286e12 | + | 2.17001e12i | −0.185029 | + | 0.320479i | ||||
\(711\) | −1.28383e12 | + | 2.22366e12i | −0.188406 | + | 0.326329i | ||||
\(712\) | 9.61623e11 | + | 1.66558e12i | 0.140231 | + | 0.242888i | ||||
\(713\) | −1.23357e12 | −0.178756 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.43195e12 | 0.491094 | ||||||||
\(716\) | 3.09002e12 | + | 5.35207e12i | 0.439393 | + | 0.761050i | ||||
\(717\) | −1.96833e10 | + | 3.40925e10i | −0.00278139 | + | 0.00481750i | ||||
\(718\) | −1.82040e12 | + | 3.15302e12i | −0.255627 | + | 0.442758i | ||||
\(719\) | −4.81013e12 | − | 8.33138e12i | −0.671238 | − | 1.16262i | −0.977553 | − | 0.210688i | \(-0.932430\pi\) |
0.306316 | − | 0.951930i | \(-0.400904\pi\) | |||||||
\(720\) | 7.21048e11 | 0.0999926 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.10558e12 | 0.562285 | ||||||||
\(723\) | −2.69045e11 | − | 4.66000e11i | −0.0366187 | − | 0.0634255i | ||||
\(724\) | −4.98345e11 | + | 8.63158e11i | −0.0674072 | + | 0.116753i | ||||
\(725\) | 1.29089e12 | − | 2.23589e12i | 0.173528 | − | 0.300559i | ||||
\(726\) | 2.75756e10 | + | 4.77623e10i | 0.00368392 | + | 0.00638073i | ||||
\(727\) | 3.13479e12 | 0.416202 | 0.208101 | − | 0.978107i | \(-0.433272\pi\) | ||||
0.208101 | + | 0.978107i | \(0.433272\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.54204e12 | −0.989043 | ||||||||
\(730\) | −1.81002e12 | − | 3.13505e12i | −0.235902 | − | 0.408594i | ||||
\(731\) | 8.61670e10 | − | 1.49246e11i | 0.0111612 | − | 0.0193318i | ||||
\(732\) | −1.55876e11 | + | 2.69985e11i | −0.0200669 | + | 0.0347568i | ||||
\(733\) | 3.23887e12 | + | 5.60989e12i | 0.414406 | + | 0.717772i | 0.995366 | − | 0.0961599i | \(-0.0306560\pi\) |
−0.580960 | + | 0.813932i | \(0.697323\pi\) | |||||||
\(734\) | −6.75189e12 | −0.858604 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.78921e11 | 0.0350374 | ||||||||
\(737\) | 4.16252e12 | + | 7.20969e12i | 0.519700 | + | 0.900146i | ||||
\(738\) | 3.44359e12 | − | 5.96447e12i | 0.427324 | − | 0.740148i | ||||
\(739\) | 5.62550e11 | − | 9.74365e11i | 0.0693843 | − | 0.120177i | −0.829246 | − | 0.558884i | \(-0.811230\pi\) |
0.898630 | + | 0.438706i | \(0.144563\pi\) | |||||||
\(740\) | −8.56306e11 | − | 1.48317e12i | −0.104975 | − | 0.181822i | ||||
\(741\) | −1.74564e11 | −0.0212703 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.65266e12 | 0.198945 | 0.0994725 | − | 0.995040i | \(-0.468284\pi\) | ||||
0.0994725 | + | 0.995040i | \(0.468284\pi\) | |||||||
\(744\) | 5.69854e10 | + | 9.87016e10i | 0.00681845 | + | 0.0118099i | ||||
\(745\) | 2.54919e12 | − | 4.41532e12i | 0.303179 | − | 0.525121i | ||||
\(746\) | 3.06626e12 | − | 5.31093e12i | 0.362481 | − | 0.627835i | ||||
\(747\) | −4.12719e12 | − | 7.14850e12i | −0.484966 | − | 0.839986i | ||||
\(748\) | 8.68096e10 | 0.0101394 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.93141e11 | −0.0222894 | ||||||||
\(751\) | −3.01649e12 | − | 5.22472e12i | −0.346037 | − | 0.599354i | 0.639505 | − | 0.768787i | \(-0.279140\pi\) |
−0.985542 | + | 0.169434i | \(0.945806\pi\) | |||||||
\(752\) | 1.73434e12 | − | 3.00396e12i | 0.197767 | − | 0.342542i | ||||
\(753\) | 1.60111e10 | − | 2.77320e10i | 0.00181486 | − | 0.00314343i | ||||
\(754\) | 1.42571e12 | + | 2.46940e12i | 0.160642 | + | 0.278240i | ||||
\(755\) | 1.62082e11 | 0.0181540 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.02798e12 | −0.888535 | −0.444268 | − | 0.895894i | \(-0.646536\pi\) | ||||
−0.444268 | + | 0.895894i | \(0.646536\pi\) | |||||||
\(758\) | −9.71692e11 | − | 1.68302e12i | −0.106910 | − | 0.185173i | ||||
\(759\) | −4.32133e10 | + | 7.48476e10i | −0.00472639 | + | 0.00818634i | ||||
\(760\) | 2.94838e11 | − | 5.10674e11i | 0.0320569 | − | 0.0555242i | ||||
\(761\) | −3.25961e12 | − | 5.64582e12i | −0.352318 | − | 0.610233i | 0.634337 | − | 0.773057i | \(-0.281273\pi\) |
−0.986655 | + | 0.162824i | \(0.947940\pi\) | |||||||
\(762\) | 2.26438e11 | 0.0243305 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.63009e12 | −0.704043 | ||||||||
\(765\) | 3.44483e10 | + | 5.96661e10i | 0.00363656 | + | 0.00629871i | ||||
\(766\) | 3.18177e12 | − | 5.51098e12i | 0.333917 | − | 0.578362i | ||||
\(767\) | −7.95088e12 | + | 1.37713e13i | −0.829537 | + | 1.43680i | ||||
\(768\) | −1.28849e10 | − | 2.23173e10i | −0.00133646 | − | 0.00231481i | ||||
\(769\) | 1.34250e13 | 1.38435 | 0.692175 | − | 0.721730i | \(-0.256653\pi\) | ||||
0.692175 | + | 0.721730i | \(0.256653\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.01345e11 | 0.0510966 | ||||||||
\(772\) | −2.03990e12 | − | 3.53321e12i | −0.206696 | − | 0.358007i | ||||
\(773\) | 3.92967e12 | − | 6.80639e12i | 0.395866 | − | 0.685660i | −0.597345 | − | 0.801984i | \(-0.703778\pi\) |
0.993211 | + | 0.116324i | \(0.0371110\pi\) | |||||||
\(774\) | −4.32558e12 | + | 7.49212e12i | −0.433221 | + | 0.750361i | ||||
\(775\) | 3.80164e12 | + | 6.58463e12i | 0.378541 | + | 0.655652i | ||||
\(776\) | −3.57377e12 | −0.353792 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.08074e12 | −0.105758 | ||||||||
\(779\) | −2.81618e12 | − | 4.87776e12i | −0.273994 | − | 0.474572i | ||||
\(780\) | 4.86730e10 | − | 8.43041e10i | 0.00470828 | − | 0.00815498i | ||||
\(781\) | 7.57196e12 | − | 1.31150e13i | 0.728247 | − | 1.26136i | ||||
\(782\) | 1.33255e10 | + | 2.30805e10i | 0.00127425 | + | 0.00220706i | ||||
\(783\) | −3.71601e11 | −0.0353304 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.78780e12 | 0.731983 | ||||||||
\(786\) | −2.88799e10 | − | 5.00215e10i | −0.00269895 | − | 0.00467472i | ||||
\(787\) | −7.38601e11 | + | 1.27930e12i | −0.0686316 | + | 0.118873i | −0.898299 | − | 0.439384i | \(-0.855197\pi\) |
0.829668 | + | 0.558258i | \(0.188530\pi\) | |||||||
\(788\) | 4.28396e11 | − | 7.42004e11i | 0.0395802 | − | 0.0685549i | ||||
\(789\) | −3.25905e11 | − | 5.64483e11i | −0.0299395 | − | 0.0518567i | ||||
\(790\) | −1.17098e12 | −0.106962 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.35783e12 | −0.393557 | ||||||||
\(793\) | −1.14849e13 | − | 1.98924e13i | −1.03133 | − | 1.78632i | ||||
\(794\) | −9.97245e11 | + | 1.72728e12i | −0.0890450 | + | 0.154231i | ||||
\(795\) | 2.72517e10 | − | 4.72012e10i | 0.00241958 | − | 0.00419084i | ||||
\(796\) | −1.71854e12 | − | 2.97660e12i | −0.151723 | − | 0.262791i | ||||
\(797\) | 6.47327e12 | 0.568278 | 0.284139 | − | 0.958783i | \(-0.408292\pi\) | ||||
0.284139 | + | 0.958783i | \(0.408292\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.31434e11 | 0.0287698 | ||||||||
\(800\) | −8.59583e11 | − | 1.48884e12i | −0.0741964 | − | 0.128512i | ||||
\(801\) | 4.61255e12 | − | 7.98917e12i | 0.395908 | − | 0.685733i | ||||
\(802\) | 2.80957e12 | − | 4.86631e12i | 0.239803 | − | 0.415351i | ||||
\(803\) | 1.09393e13 | + | 1.89475e13i | 0.928476 | + | 1.60817i | ||||
\(804\) | 2.36136e11 | 0.0199301 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.39733e12 | −0.700864 | ||||||||
\(807\) | 4.24202e11 | + | 7.34739e11i | 0.0352080 | + | 0.0609820i | ||||
\(808\) | 2.47606e12 | − | 4.28867e12i | 0.204367 | − | 0.353974i | ||||
\(809\) | 7.68155e12 | − | 1.33048e13i | 0.630493 | − | 1.09205i | −0.356958 | − | 0.934120i | \(-0.616186\pi\) |
0.987451 | − | 0.157925i | \(-0.0504806\pi\) | |||||||
\(810\) | −1.72613e12 | − | 2.98974e12i | −0.140893 | − | 0.244034i | ||||
\(811\) | 1.29056e13 | 1.04757 | 0.523787 | − | 0.851849i | \(-0.324519\pi\) | ||||
0.523787 | + | 0.851849i | \(0.324519\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.45012e11 | 0.0437520 | ||||||||
\(814\) | 5.17530e12 | + | 8.96389e12i | 0.413167 | + | 0.715627i | ||||
\(815\) | 4.65451e12 | − | 8.06185e12i | 0.369543 | − | 0.640067i | ||||
\(816\) | 1.23116e9 | − | 2.13243e9i | 9.72095e−5 | − | 0.000168372i | ||||
\(817\) | 3.53747e12 | + | 6.12708e12i | 0.277775 | + | 0.481121i | ||||
\(818\) | −6.11130e11 | −0.0477247 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.14089e12 | 0.242600 | ||||||||
\(821\) | −4.46886e11 | − | 7.74029e11i | −0.0343283 | − | 0.0594583i | 0.848351 | − | 0.529434i | \(-0.177596\pi\) |
−0.882679 | + | 0.469976i | \(0.844263\pi\) | |||||||
\(822\) | −2.47684e11 | + | 4.29002e11i | −0.0189224 | + | 0.0327745i | ||||
\(823\) | 1.14922e13 | − | 1.99051e13i | 0.873182 | − | 1.51240i | 0.0144950 | − | 0.999895i | \(-0.495386\pi\) |
0.858687 | − | 0.512501i | \(-0.171281\pi\) | |||||||
\(824\) | −1.41427e12 | − | 2.44959e12i | −0.106871 | − | 0.185106i | ||||
\(825\) | 5.32701e11 | 0.0400351 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.75618e12 | −0.204896 | −0.102448 | − | 0.994738i | \(-0.532667\pi\) | ||||
−0.102448 | + | 0.994738i | \(0.532667\pi\) | |||||||
\(828\) | −6.68941e11 | − | 1.15864e12i | −0.0494597 | − | 0.0856667i | ||||
\(829\) | −1.57962e12 | + | 2.73599e12i | −0.116160 | + | 0.201196i | −0.918243 | − | 0.396017i | \(-0.870392\pi\) |
0.802083 | + | 0.597213i | \(0.203725\pi\) | |||||||
\(830\) | 1.88220e12 | − | 3.26007e12i | 0.137662 | − | 0.238438i | ||||
\(831\) | 7.95225e10 | + | 1.37737e11i | 0.00578476 | + | 0.0100195i | ||||
\(832\) | 1.89871e12 | 0.137374 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.85782e11 | −0.0490839 | ||||||||
\(835\) | 4.42454e12 | + | 7.66353e12i | 0.314977 | + | 0.545557i | ||||
\(836\) | −1.78192e12 | + | 3.08638e12i | −0.126171 | + | 0.218535i | ||||
\(837\) | 5.47177e11 | − | 9.47738e11i | 0.0385357 | − | 0.0667458i | ||||
\(838\) | −1.72214e12 | − | 2.98284e12i | −0.120634 | − | 0.208945i | ||||
\(839\) | −1.92403e13 | −1.34055 | −0.670277 | − | 0.742111i | \(-0.733825\pi\) | ||||
−0.670277 | + | 0.742111i | \(0.733825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.20274e13 | −0.829069 | ||||||||
\(842\) | 9.59461e12 | + | 1.66184e13i | 0.657844 | + | 1.13942i | ||||
\(843\) | 5.60904e11 | − | 9.71514e11i | 0.0382529 | − | 0.0662559i | ||||
\(844\) | −3.86178e12 | + | 6.68881e12i | −0.261967 | + | 0.453741i | ||||
\(845\) | 6.16953e11 | + | 1.06859e12i | 0.0416291 | + | 0.0721036i | ||||
\(846\) | −1.66380e13 | −1.11669 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.06307e12 | 0.0705963 | ||||||||
\(849\) | −1.60024e10 | − | 2.77169e10i | −0.00105706 | − | 0.00183088i | ||||
\(850\) | 8.21336e10 | − | 1.42260e11i | 0.00539680 | − | 0.00934752i | ||||
\(851\) | −1.58885e12 | + | 2.75197e12i | −0.103848 | + | 0.179871i | ||||
\(852\) | −2.14776e11 | − | 3.72003e11i | −0.0139639 | − | 0.0241862i | ||||
\(853\) | 2.60804e13 | 1.68672 | 0.843362 | − | 0.537345i | \(-0.180573\pi\) | ||||
0.843362 | + | 0.537345i | \(0.180573\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.82845e12 | −0.181010 | ||||||||
\(856\) | 3.67615e11 | + | 6.36727e11i | 0.0234024 | + | 0.0405342i | ||||
\(857\) | 1.09588e13 | − | 1.89813e13i | 0.693986 | − | 1.20202i | −0.276535 | − | 0.961004i | \(-0.589186\pi\) |
0.970521 | − | 0.241015i | \(-0.0774804\pi\) | |||||||
\(858\) | −2.94168e11 | + | 5.09513e11i | −0.0185311 | + | 0.0320969i | ||||
\(859\) | −1.77794e12 | − | 3.07948e12i | −0.111416 | − | 0.192978i | 0.804925 | − | 0.593376i | \(-0.202205\pi\) |
−0.916341 | + | 0.400398i | \(0.868872\pi\) | |||||||
\(860\) | −3.94535e12 | −0.245948 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.26579e13 | −0.780869 | ||||||||
\(863\) | −1.11042e13 | − | 1.92330e13i | −0.681458 | − | 1.18032i | −0.974536 | − | 0.224231i | \(-0.928013\pi\) |
0.293079 | − | 0.956088i | \(-0.405320\pi\) | |||||||
\(864\) | −1.23721e11 | + | 2.14292e11i | −0.00755324 | + | 0.0130826i | ||||
\(865\) | −9.04750e11 | + | 1.56707e12i | −0.0549485 | + | 0.0951736i | ||||
\(866\) | 9.23605e12 | + | 1.59973e13i | 0.558028 | + | 0.966532i | ||||
\(867\) | −7.11292e11 | −0.0427525 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.07711e12 | 0.420986 | ||||||||
\(870\) | −4.23283e10 | − | 7.33148e10i | −0.00250492 | − | 0.00433865i | ||||
\(871\) | −8.69922e12 | + | 1.50675e13i | −0.512152 | + | 0.887073i | ||||
\(872\) | −3.28419e12 | + | 5.68838e12i | −0.192355 | + | 0.333169i | ||||
\(873\) | 8.57102e12 | + | 1.48454e13i | 0.499423 | + | 0.865026i | ||||
\(874\) | −1.09412e12 | −0.0634257 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.20579e11 | 0.0356064 | ||||||||
\(877\) | −1.69002e12 | − | 2.92720e12i | −0.0964703 | − | 0.167091i | 0.813751 | − | 0.581214i | \(-0.197422\pi\) |
−0.910221 | + | 0.414122i | \(0.864089\pi\) | |||||||
\(878\) | 1.70183e12 | − | 2.94765e12i | 0.0966473 | − | 0.167398i | ||||
\(879\) | 2.29630e11 | − | 3.97731e11i | 0.0129741 | − | 0.0224719i | ||||
\(880\) | −9.93694e11 | − | 1.72113e12i | −0.0558574 | − | 0.0967478i | ||||
\(881\) | −5.25103e11 | −0.0293665 | −0.0146833 | − | 0.999892i | \(-0.504674\pi\) | ||||
−0.0146833 | + | 0.999892i | \(0.504674\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.33972e13 | 1.84879 | 0.924393 | − | 0.381441i | \(-0.124572\pi\) | ||||
0.924393 | + | 0.381441i | \(0.124572\pi\) | |||||||
\(884\) | 9.07114e10 | + | 1.57117e11i | 0.00499605 | + | 0.00865341i | ||||
\(885\) | 2.36056e11 | − | 4.08861e11i | 0.0129351 | − | 0.0224043i | ||||
\(886\) | −5.18640e11 | + | 8.98311e11i | −0.0282758 | + | 0.0489750i | ||||
\(887\) | −4.80982e12 | − | 8.33086e12i | −0.260899 | − | 0.451891i | 0.705582 | − | 0.708628i | \(-0.250686\pi\) |
−0.966481 | + | 0.256738i | \(0.917352\pi\) | |||||||
\(888\) | 2.93591e11 | 0.0158447 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.20710e12 | 0.224765 | ||||||||
\(891\) | 1.04323e13 | + | 1.80692e13i | 0.554536 | + | 0.960484i | ||||
\(892\) | 6.84838e12 | − | 1.18617e13i | 0.362198 | − | 0.627345i | ||||
\(893\) | −6.80329e12 | + | 1.17836e13i | −0.358004 | + | 0.620081i | ||||
\(894\) | 4.37004e11 | + | 7.56912e11i | 0.0228805 | + | 0.0396303i | ||||
\(895\) | 1.35188e13 | 0.704264 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.80623e11 | −0.00931549 | ||||||||
\(898\) | −8.64250e12 | − | 1.49692e13i | −0.443502 | − | 0.768168i | ||||
\(899\) | −3.65136e12 | + | 6.32433e12i | −0.186438 | + | 0.322921i | ||||
\(900\) | −4.12310e12 | + | 7.14143e12i | −0.209475 | + | 0.362822i | ||||
\(901\) | 5.07886e10 | + | 8.79685e10i | 0.00256747 | + | 0.00444699i | ||||
\(902\) | −1.89828e13 | −0.954839 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.84848e12 | −0.291263 | ||||||||
\(905\) | 1.09013e12 | + | 1.88816e12i | 0.0540206 | + | 0.0935664i | ||||
\(906\) | −1.38927e10 | + | 2.40629e10i | −0.000685032 | + | 0.00118651i | ||||
\(907\) | 1.04170e13 | − | 1.80428e13i | 0.511107 | − | 0.885263i | −0.488811 | − | 0.872390i | \(-0.662569\pi\) |
0.999917 | − | 0.0128726i | \(-0.00409760\pi\) | |||||||
\(908\) | −5.15461e12 | − | 8.92805e12i | −0.251657 | − | 0.435883i | ||||
\(909\) | −2.37535e13 | −1.15396 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.33789e13 | −0.643560 | −0.321780 | − | 0.946814i | \(-0.604281\pi\) | ||||
−0.321780 | + | 0.946814i | \(0.604281\pi\) | |||||||
\(912\) | 5.05436e10 | + | 8.75441e10i | 0.00241930 | + | 0.00419035i | ||||
\(913\) | −1.13755e13 | + | 1.97030e13i | −0.541819 | + | 0.938457i | ||||
\(914\) | −5.17380e11 | + | 8.96129e11i | −0.0245218 | + | 0.0424730i | ||||
\(915\) | 3.40979e11 | + | 5.90593e11i | 0.0160817 | + | 0.0278544i | ||||
\(916\) | −4.87033e12 | −0.228575 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.36433e10 | −0.00109879 | ||||||||
\(919\) | 6.91758e12 | + | 1.19816e13i | 0.319915 | + | 0.554109i | 0.980470 | − | 0.196669i | \(-0.0630123\pi\) |
−0.660555 | + | 0.750778i | \(0.729679\pi\) | |||||||
\(920\) | 3.05070e11 | − | 5.28397e11i | 0.0140396 | − | 0.0243173i | ||||
\(921\) | −2.25583e11 | + | 3.90721e11i | −0.0103309 | + | 0.0178936i | ||||
\(922\) | −3.43403e12 | − | 5.94791e12i | −0.156500 | − | 0.271066i | ||||
\(923\) | 3.16492e13 | 1.43534 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.95862e13 | 0.879653 | ||||||||
\(926\) | 1.29507e13 | + | 2.24312e13i | 0.578819 | + | 1.00254i | ||||
\(927\) | −6.78374e12 | + | 1.17498e13i | −0.301724 | + | 0.522602i | ||||
\(928\) | 8.25604e11 | − | 1.42999e12i | 0.0365431 | − | 0.0632946i | ||||
\(929\) | −8.70364e12 | − | 1.50751e13i | −0.383380 | − | 0.664034i | 0.608163 | − | 0.793812i | \(-0.291907\pi\) |
−0.991543 | + | 0.129778i | \(0.958574\pi\) | |||||||
\(930\) | 2.49311e11 | 0.0109287 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.41434e12 | −0.408713 | ||||||||
\(933\) | 6.45402e11 | + | 1.11787e12i | 0.0278845 | + | 0.0482974i | ||||
\(934\) | −2.61857e12 | + | 4.53549e12i | −0.112591 | + | 0.195013i | ||||
\(935\) | 9.49480e10 | − | 1.64455e11i | 0.00406287 | − | 0.00703710i | ||||
\(936\) | −4.55371e12 | − | 7.88725e12i | −0.193921 | − | 0.335880i | ||||
\(937\) | −1.98361e12 | −0.0840676 | −0.0420338 | − | 0.999116i | \(-0.513384\pi\) | ||||
−0.0420338 | + | 0.999116i | \(0.513384\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.75445e11 | −0.0241551 | ||||||||
\(940\) | −3.79387e12 | − | 6.57117e12i | −0.158492 | − | 0.274516i | ||||
\(941\) | −1.16767e13 | + | 2.02246e13i | −0.485473 | + | 0.840864i | −0.999861 | − | 0.0166939i | \(-0.994686\pi\) |
0.514388 | + | 0.857558i | \(0.328019\pi\) | |||||||
\(942\) | −6.67525e11 | + | 1.15619e12i | −0.0276210 | + | 0.0478409i | ||||
\(943\) | −2.91391e12 | − | 5.04705e12i | −0.119998 | − | 0.207843i | ||||
\(944\) | 9.20844e12 | 0.377409 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.38447e13 | 0.968015 | ||||||||
\(947\) | −1.79941e13 | − | 3.11667e13i | −0.727035 | − | 1.25926i | −0.958131 | − | 0.286331i | \(-0.907564\pi\) |
0.231095 | − | 0.972931i | \(-0.425769\pi\) | |||||||
\(948\) | 1.00370e11 | − | 1.73846e11i | 0.00403613 | − | 0.00699079i | ||||
\(949\) | −2.28620e13 | + | 3.95982e13i | −0.914991 | + | 1.58481i | ||||
\(950\) | 3.37189e12 | + | 5.84028e12i | 0.134313 | + | 0.232636i | ||||
\(951\) | 1.02352e12 | 0.0405773 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.37662e13 | −0.540624 | −0.270312 | − | 0.962773i | \(-0.587127\pi\) | ||||
−0.270312 | + | 0.962773i | \(0.587127\pi\) | |||||||
\(954\) | −2.54959e12 | − | 4.41601e12i | −0.0996557 | − | 0.172609i | ||||
\(955\) | −7.25166e12 | + | 1.25602e13i | −0.282112 | + | 0.488633i | ||||
\(956\) | −8.39820e11 | + | 1.45461e12i | −0.0325181 | + | 0.0563231i | ||||
\(957\) | 2.55822e11 | + | 4.43096e11i | 0.00985902 | + | 0.0170763i | ||||
\(958\) | 4.55698e12 | 0.174796 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.63714e10 | −0.00214209 | ||||||||
\(961\) | 2.46668e12 | + | 4.27242e12i | 0.0932949 | + | 0.161592i | ||||
\(962\) | −1.08158e13 | + | 1.87336e13i | −0.407167 | + | 0.705234i | ||||
\(963\) | 1.76331e12 | − | 3.05415e12i | 0.0660710 | − | 0.114438i | ||||
\(964\) | −1.14793e13 | − | 1.98827e13i | −0.428122 | − | 0.741529i | ||||
\(965\) | −8.92457e12 | −0.331295 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.02718e12 | −0.111332 | −0.0556659 | − | 0.998449i | \(-0.517728\pi\) | ||||
−0.0556659 | + | 0.998449i | \(0.517728\pi\) | |||||||
\(968\) | 1.17656e12 | + | 2.03786e12i | 0.0430700 | + | 0.0745993i | ||||
\(969\) | −4.82947e9 | + | 8.36488e9i | −0.000175971 | + | 0.000304792i | ||||
\(970\) | −3.90881e12 | + | 6.77025e12i | −0.141766 | + | 0.245546i | ||||
\(971\) | −1.26591e13 | − | 2.19263e13i | −0.457002 | − | 0.791550i | 0.541799 | − | 0.840508i | \(-0.317743\pi\) |
−0.998801 | + | 0.0489579i | \(0.984410\pi\) | |||||||
\(972\) | 1.78088e12 | 0.0639937 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.14364e13 | 0.407169 | ||||||||
\(975\) | 5.56645e11 | + | 9.64137e11i | 0.0197268 | + | 0.0341679i | ||||
\(976\) | −6.65071e12 | + | 1.15194e13i | −0.234609 | + | 0.406354i | ||||
\(977\) | −4.95365e12 | + | 8.57997e12i | −0.173940 | + | 0.301273i | −0.939794 | − | 0.341742i | \(-0.888983\pi\) |
0.765854 | + | 0.643015i | \(0.222317\pi\) | |||||||
\(978\) | 7.97916e11 | + | 1.38203e12i | 0.0278890 | + | 0.0483051i | ||||
\(979\) | −2.54267e13 | −0.884641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.15061e13 | 1.08614 | ||||||||
\(982\) | 8.12045e12 | + | 1.40650e13i | 0.278662 | + | 0.482657i | ||||
\(983\) | 1.20262e13 | − | 2.08299e13i | 0.410805 | − | 0.711536i | −0.584173 | − | 0.811629i | \(-0.698581\pi\) |
0.994978 | + | 0.100094i | \(0.0319143\pi\) | |||||||
\(984\) | −2.69219e11 | + | 4.66302e11i | −0.00915437 | + | 0.0158558i | ||||
\(985\) | −9.37117e11 | − | 1.62313e12i | −0.0317198 | − | 0.0549403i | ||||
\(986\) | 1.57774e11 | 0.00531604 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.44807e12 | −0.248678 | ||||||||
\(989\) | 3.66024e12 | + | 6.33972e12i | 0.121654 | + | 0.210711i | ||||
\(990\) | −4.76638e12 | + | 8.25561e12i | −0.157700 | + | 0.273144i | ||||
\(991\) | −1.57891e13 | + | 2.73475e13i | −0.520027 | + | 0.900713i | 0.479702 | + | 0.877431i | \(0.340745\pi\) |
−0.999729 | + | 0.0232813i | \(0.992589\pi\) | |||||||
\(992\) | 2.43138e12 | + | 4.21127e12i | 0.0797168 | + | 0.138074i | ||||
\(993\) | −7.43950e11 | −0.0242813 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.51860e12 | −0.243183 | ||||||||
\(996\) | 3.22663e11 | + | 5.58869e11i | 0.0103892 | + | 0.0179946i | ||||
\(997\) | 4.66121e12 | − | 8.07345e12i | 0.149407 | − | 0.258780i | −0.781602 | − | 0.623778i | \(-0.785597\pi\) |
0.931008 | + | 0.364998i | \(0.118930\pi\) | |||||||
\(998\) | 1.06730e13 | − | 1.84862e13i | 0.340564 | − | 0.589874i | ||||
\(999\) | −1.40954e12 | − | 2.44139e12i | −0.0447746 | − | 0.0775519i |
(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 | 98.10.c.e.67.1 | 2 | ||
7.2 | even | 3 | inner | 98.10.c.e.79.1 | 2 | ||
7.3 | odd | 6 | 14.10.a.a.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 98.10.a.a.1.1 | 1 | |||
7.5 | odd | 6 | 98.10.c.f.79.1 | 2 | |||
7.6 | odd | 2 | 98.10.c.f.67.1 | 2 | |||
21.17 | even | 6 | 126.10.a.e.1.1 | 1 | |||
28.3 | even | 6 | 112.10.a.b.1.1 | 1 | |||
35.3 | even | 12 | 350.10.c.b.99.2 | 2 | |||
35.17 | even | 12 | 350.10.c.b.99.1 | 2 | |||
35.24 | odd | 6 | 350.10.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.10.a.a.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
98.10.a.a.1.1 | 1 | 7.4 | even | 3 | |||
98.10.c.e.67.1 | 2 | 1.1 | even | 1 | trivial | ||
98.10.c.e.79.1 | 2 | 7.2 | even | 3 | inner | ||
98.10.c.f.67.1 | 2 | 7.6 | odd | 2 | |||
98.10.c.f.79.1 | 2 | 7.5 | odd | 6 | |||
112.10.a.b.1.1 | 1 | 28.3 | even | 6 | |||
126.10.a.e.1.1 | 1 | 21.17 | even | 6 | |||
350.10.a.c.1.1 | 1 | 35.24 | odd | 6 | |||
350.10.c.b.99.1 | 2 | 35.17 | even | 12 | |||
350.10.c.b.99.2 | 2 | 35.3 | even | 12 |