Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(74,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.74");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 943 x^{18} + 318815 x^{16} + 48938090 x^{14} + 3842259173 x^{12} + 159675554657 x^{10} + 3390679484573 x^{8} + 32981662033730 x^{6} + \cdots + 336685801 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{28}\cdot 3^{22}\cdot 5^{32} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 74.15 | ||
Root | \(7.34058i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.74 |
Dual form | 75.9.d.c.74.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.2357 | 0.639734 | 0.319867 | − | 0.947463i | \(-0.396362\pi\) | ||||
0.319867 | + | 0.947463i | \(0.396362\pi\) | |||||||
\(3\) | 56.7364 | − | 57.8099i | 0.700450 | − | 0.713702i | ||||
\(4\) | −151.230 | −0.590741 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 580.739 | − | 591.726i | 0.448101 | − | 0.456579i | ||||
\(7\) | − | 3448.05i | − | 1.43609i | −0.695996 | − | 0.718045i | \(-0.745037\pi\) | ||
0.695996 | − | 0.718045i | \(-0.254963\pi\) | |||||||
\(8\) | −4168.30 | −1.01765 | ||||||||
\(9\) | −122.959 | − | 6559.85i | −0.0187409 | − | 0.999824i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7123.65i | 0.486555i | 0.969957 | + | 0.243277i | \(0.0782225\pi\) | ||||
−0.969957 | + | 0.243277i | \(0.921777\pi\) | |||||||
\(12\) | −8580.23 | + | 8742.57i | −0.413784 | + | 0.421613i | ||||
\(13\) | 41361.3i | 1.44818i | 0.689708 | + | 0.724088i | \(0.257739\pi\) | ||||
−0.689708 | + | 0.724088i | \(0.742261\pi\) | |||||||
\(14\) | − | 35293.4i | − | 0.918715i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3950.77 | −0.0602840 | ||||||||
\(17\) | −119540. | −1.43126 | −0.715631 | − | 0.698479i | \(-0.753861\pi\) | ||||
−0.715631 | + | 0.698479i | \(0.753861\pi\) | |||||||
\(18\) | −1258.58 | − | 67144.9i | −0.0119892 | − | 0.639621i | ||||
\(19\) | 86288.8 | 0.662125 | 0.331063 | − | 0.943609i | \(-0.392593\pi\) | ||||
0.331063 | + | 0.943609i | \(0.392593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −199331. | − | 195630.i | −1.02494 | − | 1.00591i | ||||
\(22\) | 72915.8i | 0.311265i | ||||||||
\(23\) | −317353. | −1.13405 | −0.567024 | − | 0.823701i | \(-0.691905\pi\) | ||||
−0.567024 | + | 0.823701i | \(0.691905\pi\) | |||||||
\(24\) | −236494. | + | 240969.i | −0.712813 | + | 0.726299i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 423364.i | 0.926447i | ||||||||
\(27\) | −386200. | − | 365074.i | −0.726704 | − | 0.686951i | ||||
\(28\) | 521448.i | 0.848358i | ||||||||
\(29\) | 59853.0i | 0.0846240i | 0.999104 | + | 0.0423120i | \(0.0134724\pi\) | ||||
−0.999104 | + | 0.0423120i | \(0.986528\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.02106e6 | −1.10562 | −0.552809 | − | 0.833308i | \(-0.686444\pi\) | ||||
−0.552809 | + | 0.833308i | \(0.686444\pi\) | |||||||
\(32\) | 1.02664e6 | 0.979085 | ||||||||
\(33\) | 411817. | + | 404170.i | 0.347255 | + | 0.340807i | ||||
\(34\) | −1.22358e6 | −0.915626 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 18595.0 | + | 992044.i | 0.0110710 | + | 0.590637i | ||||
\(37\) | − | 877366.i | − | 0.468138i | −0.972220 | − | 0.234069i | \(-0.924796\pi\) | ||
0.972220 | − | 0.234069i | \(-0.0752042\pi\) | |||||||
\(38\) | 883230. | 0.423584 | ||||||||
\(39\) | 2.39109e6 | + | 2.34669e6i | 1.03357 | + | 1.01437i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.55753e6i | 0.551189i | 0.961274 | + | 0.275595i | \(0.0888747\pi\) | ||||
−0.961274 | + | 0.275595i | \(0.911125\pi\) | |||||||
\(42\) | −2.04030e6 | − | 2.00242e6i | −0.655689 | − | 0.643514i | ||||
\(43\) | − | 2.56966e6i | − | 0.751626i | −0.926696 | − | 0.375813i | \(-0.877364\pi\) | ||
0.926696 | − | 0.375813i | \(-0.122636\pi\) | |||||||
\(44\) | − | 1.07731e6i | − | 0.287428i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.24834e6 | −0.725489 | ||||||||
\(47\) | −8.98739e6 | −1.84180 | −0.920899 | − | 0.389800i | \(-0.872544\pi\) | ||||
−0.920899 | + | 0.389800i | \(0.872544\pi\) | |||||||
\(48\) | −224153. | + | 228394.i | −0.0422259 | + | 0.0430248i | ||||
\(49\) | −6.12427e6 | −1.06236 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.78229e6 | + | 6.91061e6i | −1.00253 | + | 1.02149i | ||||
\(52\) | − | 6.25506e6i | − | 0.855497i | ||||||
\(53\) | 6.22182e6 | 0.788522 | 0.394261 | − | 0.918999i | \(-0.371001\pi\) | ||||
0.394261 | + | 0.918999i | \(0.371001\pi\) | |||||||
\(54\) | −3.95304e6 | − | 3.73680e6i | −0.464897 | − | 0.439466i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.43725e7i | 1.46144i | ||||||||
\(57\) | 4.89572e6 | − | 4.98835e6i | 0.463785 | − | 0.472560i | ||||
\(58\) | 612639.i | 0.0541368i | ||||||||
\(59\) | 3.96940e6i | 0.327580i | 0.986495 | + | 0.163790i | \(0.0523719\pi\) | ||||
−0.986495 | + | 0.163790i | \(0.947628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −563629. | −0.0407074 | −0.0203537 | − | 0.999793i | \(-0.506479\pi\) | ||||
−0.0203537 | + | 0.999793i | \(0.506479\pi\) | |||||||
\(62\) | −1.04513e7 | −0.707300 | ||||||||
\(63\) | −2.26187e7 | + | 423969.i | −1.43584 | + | 0.0269136i | ||||
\(64\) | 1.15199e7 | 0.686637 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.21525e6 | + | 4.13698e6i | 0.222151 | + | 0.218026i | ||||
\(67\) | − | 1.34009e7i | − | 0.665021i | −0.943100 | − | 0.332510i | \(-0.892104\pi\) | ||
0.943100 | − | 0.332510i | \(-0.107896\pi\) | |||||||
\(68\) | 1.80781e7 | 0.845505 | ||||||||
\(69\) | −1.80055e7 | + | 1.83461e7i | −0.794343 | + | 0.809372i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.56270e7i | − | 1.40199i | −0.713165 | − | 0.700997i | \(-0.752739\pi\) | ||
0.713165 | − | 0.700997i | \(-0.247261\pi\) | |||||||
\(72\) | 512529. | + | 2.73434e7i | 0.0190717 | + | 1.01747i | ||||
\(73\) | 970897.i | 0.0341886i | 0.999854 | + | 0.0170943i | \(0.00544155\pi\) | ||||
−0.999854 | + | 0.0170943i | \(0.994558\pi\) | |||||||
\(74\) | − | 8.98049e6i | − | 0.299484i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.30494e7 | −0.391145 | ||||||||
\(77\) | 2.45627e7 | 0.698737 | ||||||||
\(78\) | 2.44746e7 | + | 2.40201e7i | 0.661207 | + | 0.648929i | ||||
\(79\) | 2.78755e7 | 0.715672 | 0.357836 | − | 0.933784i | \(-0.383515\pi\) | ||||
0.357836 | + | 0.933784i | \(0.383515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.30165e7 | + | 1.61318e6i | −0.999298 | + | 0.0374752i | ||||
\(82\) | 1.59425e7i | 0.352614i | ||||||||
\(83\) | −2.25794e7 | −0.475773 | −0.237886 | − | 0.971293i | \(-0.576455\pi\) | ||||
−0.237886 | + | 0.971293i | \(0.576455\pi\) | |||||||
\(84\) | 3.01448e7 | + | 2.95851e7i | 0.605474 | + | 0.594232i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 2.63024e7i | − | 0.480840i | ||||||
\(87\) | 3.46009e6 | + | 3.39584e6i | 0.0603963 | + | 0.0592749i | ||||
\(88\) | − | 2.96935e7i | − | 0.495143i | ||||||
\(89\) | − | 5.73209e7i | − | 0.913593i | −0.889571 | − | 0.456796i | \(-0.848997\pi\) | ||
0.889571 | − | 0.456796i | \(-0.151003\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.42616e8 | 2.07971 | ||||||||
\(92\) | 4.79932e7 | 0.669929 | ||||||||
\(93\) | −5.79313e7 | + | 5.90274e7i | −0.774429 | + | 0.789081i | ||||
\(94\) | −9.19926e7 | −1.17826 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.82481e7 | − | 5.93502e7i | 0.685799 | − | 0.698775i | ||||
\(97\) | 3.31851e7i | 0.374848i | 0.982279 | + | 0.187424i | \(0.0600139\pi\) | ||||
−0.982279 | + | 0.187424i | \(0.939986\pi\) | |||||||
\(98\) | −6.26864e7 | −0.679625 | ||||||||
\(99\) | 4.67301e7 | − | 875917.i | 0.486469 | − | 0.00911847i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 65955.2i | − | 0.000633816i | −1.00000 | 0.000316908i | \(-0.999899\pi\) | |||
1.00000 | 0.000316908i | \(-0.000100875\pi\) | ||||||||
\(102\) | −6.94218e7 | + | 7.07352e7i | −0.641350 | + | 0.653484i | ||||
\(103\) | − | 2.03592e8i | − | 1.80889i | −0.426593 | − | 0.904444i | \(-0.640286\pi\) | ||
0.426593 | − | 0.904444i | \(-0.359714\pi\) | |||||||
\(104\) | − | 1.72406e8i | − | 1.47374i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.36849e7 | 0.504444 | ||||||||
\(107\) | 3.26956e7 | 0.249433 | 0.124716 | − | 0.992192i | \(-0.460198\pi\) | ||||
0.124716 | + | 0.992192i | \(0.460198\pi\) | |||||||
\(108\) | 5.84049e7 | + | 5.52100e7i | 0.429294 | + | 0.405810i | ||||
\(109\) | 6.88723e7 | 0.487909 | 0.243954 | − | 0.969787i | \(-0.421555\pi\) | ||||
0.243954 | + | 0.969787i | \(0.421555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.07204e7 | − | 4.97786e7i | −0.334111 | − | 0.327907i | ||||
\(112\) | 1.36225e7i | 0.0865733i | ||||||||
\(113\) | 2.24841e8 | 1.37899 | 0.689497 | − | 0.724289i | \(-0.257832\pi\) | ||||
0.689497 | + | 0.724289i | \(0.257832\pi\) | |||||||
\(114\) | 5.01113e7 | − | 5.10594e7i | 0.296699 | − | 0.302313i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 9.05155e6i | − | 0.0499909i | ||||||
\(117\) | 2.71324e8 | − | 5.08575e6i | 1.44792 | − | 0.0271401i | ||||
\(118\) | 4.06297e7i | 0.209564i | ||||||||
\(119\) | 4.12182e8i | 2.05542i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.63612e8 | 0.763264 | ||||||||
\(122\) | −5.76915e6 | −0.0260419 | ||||||||
\(123\) | 9.00405e7 | + | 8.83686e7i | 0.393385 | + | 0.386080i | ||||
\(124\) | 1.54415e8 | 0.653133 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.31519e8 | + | 4.33964e6i | −0.918554 | + | 0.0172175i | ||||
\(127\) | 1.02495e7i | 0.0393993i | 0.999806 | + | 0.0196996i | \(0.00627099\pi\) | ||||
−0.999806 | + | 0.0196996i | \(0.993729\pi\) | |||||||
\(128\) | −1.44907e8 | −0.539820 | ||||||||
\(129\) | −1.48552e8 | − | 1.45793e8i | −0.536437 | − | 0.526476i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.55607e7i | − | 0.290529i | −0.989393 | − | 0.145264i | \(-0.953597\pi\) | ||
0.989393 | − | 0.145264i | \(-0.0464033\pi\) | |||||||
\(132\) | −6.22790e7 | − | 6.11226e7i | −0.205138 | − | 0.201329i | ||||
\(133\) | − | 2.97529e8i | − | 0.950872i | ||||||
\(134\) | − | 1.37168e8i | − | 0.425436i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.98280e8 | 1.45652 | ||||||||
\(137\) | −2.41199e7 | −0.0684688 | −0.0342344 | − | 0.999414i | \(-0.510899\pi\) | ||||
−0.0342344 | + | 0.999414i | \(0.510899\pi\) | |||||||
\(138\) | −1.84299e8 | + | 1.87786e8i | −0.508168 | + | 0.517783i | ||||
\(139\) | −4.84604e8 | −1.29816 | −0.649079 | − | 0.760721i | \(-0.724846\pi\) | ||||
−0.649079 | + | 0.760721i | \(0.724846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.09912e8 | + | 5.19560e8i | −1.29009 | + | 1.31450i | ||||
\(142\) | − | 3.64669e8i | − | 0.896902i | ||||||
\(143\) | −2.94644e8 | −0.704617 | ||||||||
\(144\) | 485783. | + | 2.59165e7i | 0.00112978 | + | 0.0602734i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.93784e6i | 0.0218716i | ||||||||
\(147\) | −3.47469e8 | + | 3.54043e8i | −0.744127 | + | 0.758206i | ||||
\(148\) | 1.32684e8i | 0.276548i | ||||||||
\(149\) | 6.26323e8i | 1.27073i | 0.772212 | + | 0.635365i | \(0.219150\pi\) | ||||
−0.772212 | + | 0.635365i | \(0.780850\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.61203e8 | −1.84887 | −0.924437 | − | 0.381334i | \(-0.875465\pi\) | ||||
−0.924437 | + | 0.381334i | \(0.875465\pi\) | |||||||
\(152\) | −3.59677e8 | −0.673812 | ||||||||
\(153\) | 1.46986e7 | + | 7.84167e8i | 0.0268231 | + | 1.43101i | ||||
\(154\) | 2.51418e8 | 0.447005 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.61604e8 | − | 3.54890e8i | −0.610570 | − | 0.599232i | ||||
\(157\) | − | 9.24294e8i | − | 1.52129i | −0.649169 | − | 0.760644i | \(-0.724883\pi\) | ||
0.649169 | − | 0.760644i | \(-0.275117\pi\) | |||||||
\(158\) | 2.85326e8 | 0.457839 | ||||||||
\(159\) | 3.53004e8 | − | 3.59682e8i | 0.552320 | − | 0.562770i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.09425e9i | 1.62860i | ||||||||
\(162\) | −4.40305e8 | + | 1.65121e7i | −0.639284 | + | 0.0239741i | ||||
\(163\) | − | 1.30110e9i | − | 1.84315i | −0.388200 | − | 0.921575i | \(-0.626903\pi\) | ||
0.388200 | − | 0.921575i | \(-0.373097\pi\) | |||||||
\(164\) | − | 2.35545e8i | − | 0.325610i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.31117e8 | −0.304368 | ||||||||
\(167\) | −1.12208e9 | −1.44263 | −0.721317 | − | 0.692605i | \(-0.756463\pi\) | ||||
−0.721317 | + | 0.692605i | \(0.756463\pi\) | |||||||
\(168\) | 8.30873e8 | + | 8.15444e8i | 1.04303 | + | 1.02366i | ||||
\(169\) | −8.95030e8 | −1.09721 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.06100e7 | − | 5.66042e8i | −0.0124088 | − | 0.662009i | ||||
\(172\) | 3.88609e8i | 0.444016i | ||||||||
\(173\) | −1.21708e9 | −1.35874 | −0.679369 | − | 0.733797i | \(-0.737746\pi\) | ||||
−0.679369 | + | 0.733797i | \(0.737746\pi\) | |||||||
\(174\) | 3.54166e7 | + | 3.47590e7i | 0.0386376 | + | 0.0379201i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.81439e7i | − | 0.0293315i | ||||||
\(177\) | 2.29471e8 | + | 2.25210e8i | 0.233794 | + | 0.229453i | ||||
\(178\) | − | 5.86721e8i | − | 0.584456i | ||||||
\(179\) | − | 3.40141e8i | − | 0.331320i | −0.986183 | − | 0.165660i | \(-0.947025\pi\) | ||
0.986183 | − | 0.165660i | \(-0.0529754\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.89427e9 | 1.76493 | 0.882466 | − | 0.470377i | \(-0.155882\pi\) | ||||
0.882466 | + | 0.470377i | \(0.155882\pi\) | |||||||
\(182\) | 1.45978e9 | 1.33046 | ||||||||
\(183\) | −3.19783e7 | + | 3.25833e7i | −0.0285135 | + | 0.0290530i | ||||
\(184\) | 1.32282e9 | 1.15406 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.92970e8 | + | 6.04189e8i | −0.495428 | + | 0.504802i | ||||
\(187\) | − | 8.51564e8i | − | 0.696387i | ||||||
\(188\) | 1.35916e9 | 1.08803 | ||||||||
\(189\) | −1.25879e9 | + | 1.33164e9i | −0.986524 | + | 1.04361i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.22208e9i | 0.918262i | 0.888369 | + | 0.459131i | \(0.151839\pi\) | ||||
−0.888369 | + | 0.459131i | \(0.848161\pi\) | |||||||
\(192\) | 6.53596e8 | − | 6.65962e8i | 0.480955 | − | 0.490054i | ||||
\(193\) | 3.63918e8i | 0.262286i | 0.991363 | + | 0.131143i | \(0.0418646\pi\) | ||||
−0.991363 | + | 0.131143i | \(0.958135\pi\) | |||||||
\(194\) | 3.39674e8i | 0.239803i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.26172e8 | 0.627577 | ||||||||
\(197\) | 1.98338e9 | 1.31687 | 0.658434 | − | 0.752639i | \(-0.271219\pi\) | ||||
0.658434 | + | 0.752639i | \(0.271219\pi\) | |||||||
\(198\) | 4.78317e8 | − | 8.96565e6i | 0.311211 | − | 0.00583339i | ||||
\(199\) | −6.06495e8 | −0.386736 | −0.193368 | − | 0.981126i | \(-0.561941\pi\) | ||||
−0.193368 | + | 0.981126i | \(0.561941\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.74705e8 | − | 7.60320e8i | −0.474627 | − | 0.465814i | ||||
\(202\) | − | 675100.i | − | 0.000405474i | ||||||
\(203\) | 2.06376e8 | 0.121528 | ||||||||
\(204\) | 1.02568e9 | − | 1.04509e9i | 0.592233 | − | 0.603438i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 2.08391e9i | − | 1.15721i | ||||||
\(207\) | 3.90214e7 | + | 2.08179e9i | 0.0212531 | + | 1.13385i | ||||
\(208\) | − | 1.63409e8i | − | 0.0873019i | ||||||
\(209\) | 6.14691e8i | 0.322160i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.10164e8 | −0.206932 | −0.103466 | − | 0.994633i | \(-0.532993\pi\) | ||||
−0.103466 | + | 0.994633i | \(0.532993\pi\) | |||||||
\(212\) | −9.40924e8 | −0.465812 | ||||||||
\(213\) | −2.05959e9 | − | 2.02135e9i | −1.00061 | − | 0.982026i | ||||
\(214\) | 3.34663e8 | 0.159571 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.60980e9 | + | 1.52174e9i | 0.739530 | + | 0.699076i | ||||
\(217\) | 3.52067e9i | 1.58777i | ||||||||
\(218\) | 7.04958e8 | 0.312131 | ||||||||
\(219\) | 5.61274e7 | + | 5.50852e7i | 0.0244005 | + | 0.0239474i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.94435e9i | − | 2.07272i | ||||||
\(222\) | −5.19161e8 | − | 5.09521e8i | −0.213742 | − | 0.209773i | ||||
\(223\) | − | 4.68112e8i | − | 0.189291i | −0.995511 | − | 0.0946455i | \(-0.969828\pi\) | ||
0.995511 | − | 0.0946455i | \(-0.0301718\pi\) | |||||||
\(224\) | − | 3.53993e9i | − | 1.40605i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.30142e9 | 0.882188 | ||||||||
\(227\) | −2.13615e9 | −0.804503 | −0.402251 | − | 0.915529i | \(-0.631772\pi\) | ||||
−0.402251 | + | 0.915529i | \(0.631772\pi\) | |||||||
\(228\) | −7.40378e8 | + | 7.54386e8i | −0.273977 | + | 0.279161i | ||||
\(229\) | 7.50976e8 | 0.273076 | 0.136538 | − | 0.990635i | \(-0.456402\pi\) | ||||
0.136538 | + | 0.990635i | \(0.456402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.39360e9 | − | 1.41997e9i | 0.489430 | − | 0.498690i | ||||
\(232\) | − | 2.49485e8i | − | 0.0861177i | ||||||
\(233\) | −2.03107e9 | −0.689129 | −0.344565 | − | 0.938763i | \(-0.611973\pi\) | ||||
−0.344565 | + | 0.938763i | \(0.611973\pi\) | |||||||
\(234\) | 2.77720e9 | − | 5.20564e7i | 0.926284 | − | 0.0173624i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 6.00291e8i | − | 0.193515i | ||||||
\(237\) | 1.58156e9 | − | 1.61148e9i | 0.501292 | − | 0.510777i | ||||
\(238\) | 4.21898e9i | 1.31492i | ||||||||
\(239\) | − | 1.54091e9i | − | 0.472265i | −0.971721 | − | 0.236133i | \(-0.924120\pi\) | ||
0.971721 | − | 0.236133i | \(-0.0758800\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.80028e8 | −0.290516 | −0.145258 | − | 0.989394i | \(-0.546401\pi\) | ||||
−0.145258 | + | 0.989394i | \(0.546401\pi\) | |||||||
\(242\) | 1.67469e9 | 0.488286 | ||||||||
\(243\) | −2.34734e9 | + | 2.57830e9i | −0.673211 | + | 0.739450i | ||||
\(244\) | 8.52374e7 | 0.0240475 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.21631e8 | + | 9.04518e8i | 0.251661 | + | 0.246988i | ||||
\(247\) | 3.56902e9i | 0.958874i | ||||||||
\(248\) | 4.25608e9 | 1.12513 | ||||||||
\(249\) | −1.28107e9 | + | 1.30531e9i | −0.333255 | + | 0.339560i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.36978e9i | 0.848997i | 0.905429 | + | 0.424499i | \(0.139550\pi\) | ||||
−0.905429 | + | 0.424499i | \(0.860450\pi\) | |||||||
\(252\) | 3.42062e9 | − | 6.41167e7i | 0.848209 | − | 0.0158990i | ||||
\(253\) | − | 2.26071e9i | − | 0.551777i | ||||||
\(254\) | 1.04911e8i | 0.0252050i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.43231e9 | −1.03198 | ||||||||
\(257\) | −6.58864e8 | −0.151030 | −0.0755150 | − | 0.997145i | \(-0.524060\pi\) | ||||
−0.0755150 | + | 0.997145i | \(0.524060\pi\) | |||||||
\(258\) | −1.52054e9 | − | 1.49230e9i | −0.343177 | − | 0.336804i | ||||
\(259\) | −3.02521e9 | −0.672289 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.92626e8 | − | 7.35946e6i | 0.0846092 | − | 0.00158593i | ||||
\(262\) | − | 8.75777e8i | − | 0.185861i | ||||||
\(263\) | −1.12759e9 | −0.235682 | −0.117841 | − | 0.993032i | \(-0.537597\pi\) | ||||
−0.117841 | + | 0.993032i | \(0.537597\pi\) | |||||||
\(264\) | −1.71658e9 | − | 1.68470e9i | −0.353384 | − | 0.346822i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 3.04542e9i | − | 0.608305i | ||||||
\(267\) | −3.31371e9 | − | 3.25218e9i | −0.652033 | − | 0.639926i | ||||
\(268\) | 2.02662e9i | 0.392855i | ||||||||
\(269\) | 5.06830e9i | 0.967950i | 0.875082 | + | 0.483975i | \(0.160807\pi\) | ||||
−0.875082 | + | 0.483975i | \(0.839193\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.89969e9 | −0.537618 | −0.268809 | − | 0.963194i | \(-0.586630\pi\) | ||||
−0.268809 | + | 0.963194i | \(0.586630\pi\) | |||||||
\(272\) | 4.72277e8 | 0.0862822 | ||||||||
\(273\) | 8.09153e9 | − | 8.24462e9i | 1.45673 | − | 1.48429i | ||||
\(274\) | −2.46885e8 | −0.0438018 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.72296e9 | − | 2.77448e9i | 0.469251 | − | 0.478129i | ||||
\(277\) | − | 6.70508e9i | − | 1.13890i | −0.822027 | − | 0.569449i | \(-0.807157\pi\) | ||
0.822027 | − | 0.569449i | \(-0.192843\pi\) | |||||||
\(278\) | −4.96028e9 | −0.830476 | ||||||||
\(279\) | 1.25549e8 | + | 6.69800e9i | 0.0207202 | + | 1.10542i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.08727e10i | 1.74387i | 0.489625 | + | 0.871933i | \(0.337134\pi\) | ||||
−0.489625 | + | 0.871933i | \(0.662866\pi\) | |||||||
\(282\) | −5.21933e9 | + | 5.31808e9i | −0.825312 | + | 0.840927i | ||||
\(283\) | 3.48119e9i | 0.542728i | 0.962477 | + | 0.271364i | \(0.0874747\pi\) | ||||
−0.962477 | + | 0.271364i | \(0.912525\pi\) | |||||||
\(284\) | 5.38786e9i | 0.828215i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.01590e9 | −0.450767 | ||||||||
\(287\) | 5.37044e9 | 0.791558 | ||||||||
\(288\) | −1.26235e8 | − | 6.73463e9i | −0.0183489 | − | 0.978913i | ||||
\(289\) | 7.31415e9 | 1.04851 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.91842e9 | + | 1.88280e9i | 0.267530 | + | 0.262562i | ||||
\(292\) | − | 1.46828e8i | − | 0.0201966i | ||||||
\(293\) | 9.46915e9 | 1.28481 | 0.642407 | − | 0.766364i | \(-0.277936\pi\) | ||||
0.642407 | + | 0.766364i | \(0.277936\pi\) | |||||||
\(294\) | −3.55660e9 | + | 3.62389e9i | −0.476043 | + | 0.485050i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.65712e9i | 0.476401i | ||||||||
\(297\) | 2.60066e9 | − | 2.75115e9i | 0.334239 | − | 0.353581i | ||||
\(298\) | 6.41088e9i | 0.812929i | ||||||||
\(299\) | − | 1.31262e10i | − | 1.64230i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.86032e9 | −1.07940 | ||||||||
\(302\) | −9.83862e9 | −1.18279 | ||||||||
\(303\) | −3.81286e6 | − | 3.74206e6i | −0.000452356 | − | 0.000443956i | ||||
\(304\) | −3.40908e8 | −0.0399156 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.50451e8 | + | 8.02652e9i | 0.0171596 | + | 0.915465i | ||||
\(307\) | − | 8.28984e9i | − | 0.933239i | −0.884458 | − | 0.466619i | \(-0.845472\pi\) | ||
0.884458 | − | 0.466619i | \(-0.154528\pi\) | |||||||
\(308\) | −3.71461e9 | −0.412773 | ||||||||
\(309\) | −1.17696e10 | − | 1.15511e10i | −1.29101 | − | 1.26703i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.23247e9i | 0.880012i | 0.897995 | + | 0.440006i | \(0.145024\pi\) | ||||
−0.897995 | + | 0.440006i | \(0.854976\pi\) | |||||||
\(312\) | −9.96679e9 | − | 9.78172e9i | −1.05181 | − | 1.03228i | ||||
\(313\) | 1.27222e10i | 1.32551i | 0.748835 | + | 0.662757i | \(0.230614\pi\) | ||||
−0.748835 | + | 0.662757i | \(0.769386\pi\) | |||||||
\(314\) | − | 9.46083e9i | − | 0.973219i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.21560e9 | −0.422777 | ||||||||
\(317\) | −6.36014e9 | −0.629839 | −0.314920 | − | 0.949118i | \(-0.601978\pi\) | ||||
−0.314920 | + | 0.949118i | \(0.601978\pi\) | |||||||
\(318\) | 3.61325e9 | − | 3.68161e9i | 0.353338 | − | 0.360023i | ||||
\(319\) | −4.26372e8 | −0.0411742 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.85503e9 | − | 1.89013e9i | 0.174715 | − | 0.178021i | ||||
\(322\) | 1.12005e10i | 1.04187i | ||||||||
\(323\) | −1.03150e10 | −0.947674 | ||||||||
\(324\) | 6.50537e9 | − | 2.43961e8i | 0.590326 | − | 0.0221381i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 1.33177e10i | − | 1.17913i | ||||||
\(327\) | 3.90757e9 | − | 3.98150e9i | 0.341755 | − | 0.348221i | ||||
\(328\) | − | 6.49224e9i | − | 0.560918i | ||||||
\(329\) | 3.09890e10i | 2.64499i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.25518e9 | 0.104567 | 0.0522836 | − | 0.998632i | \(-0.483350\pi\) | ||||
0.0522836 | + | 0.998632i | \(0.483350\pi\) | |||||||
\(332\) | 3.41467e9 | 0.281059 | ||||||||
\(333\) | −5.75539e9 | + | 1.07880e8i | −0.468056 | + | 0.00877332i | ||||
\(334\) | −1.14853e10 | −0.922902 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.87514e8 | + | 7.72891e8i | 0.0617875 | + | 0.0606402i | ||||
\(337\) | 8.02773e9i | 0.622405i | 0.950344 | + | 0.311203i | \(0.100732\pi\) | ||||
−0.950344 | + | 0.311203i | \(0.899268\pi\) | |||||||
\(338\) | −9.16129e9 | −0.701924 | ||||||||
\(339\) | 1.27567e10 | − | 1.29980e10i | 0.965915 | − | 0.984190i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 7.27368e9i | − | 0.537943i | ||||||
\(342\) | −1.08601e8 | − | 5.79385e9i | −0.00793834 | − | 0.423509i | ||||
\(343\) | 1.23948e9i | 0.0895491i | ||||||||
\(344\) | 1.07111e10i | 0.764892i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.24577e10 | −0.869230 | ||||||||
\(347\) | −6.89272e9 | −0.475415 | −0.237707 | − | 0.971337i | \(-0.576396\pi\) | ||||
−0.237707 | + | 0.971337i | \(0.576396\pi\) | |||||||
\(348\) | −5.23269e8 | − | 5.13552e8i | −0.0356786 | − | 0.0350161i | ||||
\(349\) | 1.26058e10 | 0.849703 | 0.424852 | − | 0.905263i | \(-0.360326\pi\) | ||||
0.424852 | + | 0.905263i | \(0.360326\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.51000e10 | − | 1.59738e10i | 0.994826 | − | 1.05239i | ||||
\(352\) | 7.31346e9i | 0.476378i | ||||||||
\(353\) | 1.83440e10 | 1.18139 | 0.590697 | − | 0.806894i | \(-0.298853\pi\) | ||||
0.590697 | + | 0.806894i | \(0.298853\pi\) | |||||||
\(354\) | 2.34880e9 | + | 2.30519e9i | 0.149566 | + | 0.146789i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.66862e9i | 0.539697i | ||||||||
\(357\) | 2.38282e10 | + | 2.33857e10i | 1.46696 | + | 1.43972i | ||||
\(358\) | − | 3.48160e9i | − | 0.211956i | ||||||
\(359\) | − | 1.55471e7i | − | 0.000935992i | −1.00000 | 0.000467996i | \(-0.999851\pi\) | |||
1.00000 | 0.000467996i | \(-0.000148968\pi\) | ||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.53780e9 | −0.561590 | ||||||||
\(362\) | 1.93893e10 | 1.12909 | ||||||||
\(363\) | 9.28279e9 | − | 9.45842e9i | 0.534628 | − | 0.544743i | ||||
\(364\) | −2.15678e10 | −1.22857 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.27321e8 | + | 3.33514e8i | −0.0182410 | + | 0.0185862i | ||||
\(367\) | 4.76932e9i | 0.262901i | 0.991323 | + | 0.131450i | \(0.0419634\pi\) | ||||
−0.991323 | + | 0.131450i | \(0.958037\pi\) | |||||||
\(368\) | 1.25379e9 | 0.0683650 | ||||||||
\(369\) | 1.02172e10 | − | 1.91512e8i | 0.551092 | − | 0.0103298i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.14532e10i | − | 1.13239i | ||||||
\(372\) | 8.76094e9 | − | 8.92669e9i | 0.457487 | − | 0.466143i | ||||
\(373\) | 2.29205e10i | 1.18410i | 0.805901 | + | 0.592051i | \(0.201681\pi\) | ||||
−0.805901 | + | 0.592051i | \(0.798319\pi\) | |||||||
\(374\) | − | 8.71638e9i | − | 0.445502i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.74621e10 | 1.87431 | ||||||||
\(377\) | −2.47560e9 | −0.122550 | ||||||||
\(378\) | −1.28847e10 | + | 1.36303e10i | −0.631112 | + | 0.667634i | ||||
\(379\) | 6.81528e9 | 0.330314 | 0.165157 | − | 0.986267i | \(-0.447187\pi\) | ||||
0.165157 | + | 0.986267i | \(0.447187\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.92522e8 | + | 5.81520e8i | 0.0281193 | + | 0.0275972i | ||||
\(382\) | 1.25089e10i | 0.587443i | ||||||||
\(383\) | −1.07682e10 | −0.500437 | −0.250219 | − | 0.968189i | \(-0.580503\pi\) | ||||
−0.250219 | + | 0.968189i | \(0.580503\pi\) | |||||||
\(384\) | −8.22149e9 | + | 8.37704e9i | −0.378116 | + | 0.385270i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.72497e9i | 0.167793i | ||||||||
\(387\) | −1.68566e10 | + | 3.15963e8i | −0.751494 | + | 0.0140861i | ||||
\(388\) | − | 5.01857e9i | − | 0.221438i | ||||||
\(389\) | − | 3.21668e10i | − | 1.40479i | −0.711790 | − | 0.702393i | \(-0.752115\pi\) | ||
0.711790 | − | 0.702393i | \(-0.247885\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.79365e10 | 1.62312 | ||||||||
\(392\) | 2.55278e10 | 1.08111 | ||||||||
\(393\) | −4.94625e9 | − | 4.85441e9i | −0.207351 | − | 0.203501i | ||||
\(394\) | 2.03014e10 | 0.842444 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.06697e9 | + | 1.32465e8i | −0.287377 | + | 0.00538665i | ||||
\(397\) | − | 3.26005e10i | − | 1.31239i | −0.754592 | − | 0.656194i | \(-0.772165\pi\) | ||
0.754592 | − | 0.656194i | \(-0.227835\pi\) | |||||||
\(398\) | −6.20792e9 | −0.247408 | ||||||||
\(399\) | −1.72001e10 | − | 1.68807e10i | −0.678639 | − | 0.666038i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.38085e10i | − | 0.920778i | −0.887717 | − | 0.460389i | \(-0.847710\pi\) | ||
0.887717 | − | 0.460389i | \(-0.152290\pi\) | |||||||
\(402\) | −7.92968e9 | − | 7.78244e9i | −0.303635 | − | 0.297997i | ||||
\(403\) | − | 4.22324e10i | − | 1.60113i | ||||||
\(404\) | 9.97438e6i | 0.000374421i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.11241e9 | 0.0777454 | ||||||||
\(407\) | 6.25005e9 | 0.227775 | ||||||||
\(408\) | 2.82706e10 | − | 2.88055e10i | 1.02022 | − | 1.03952i | ||||
\(409\) | 3.89304e10 | 1.39122 | 0.695609 | − | 0.718420i | \(-0.255134\pi\) | ||||
0.695609 | + | 0.718420i | \(0.255134\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.36847e9 | + | 1.39437e9i | −0.0479589 | + | 0.0488663i | ||||
\(412\) | 3.07891e10i | 1.06858i | ||||||||
\(413\) | 1.36867e10 | 0.470434 | ||||||||
\(414\) | 3.99413e8 | + | 2.13086e10i | 0.0135963 | + | 0.725361i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.24634e10i | 1.41789i | ||||||||
\(417\) | −2.74947e10 | + | 2.80149e10i | −0.909295 | + | 0.926498i | ||||
\(418\) | 6.29182e9i | 0.206097i | ||||||||
\(419\) | − | 3.25983e10i | − | 1.05764i | −0.848733 | − | 0.528821i | \(-0.822634\pi\) | ||
0.848733 | − | 0.528821i | \(-0.177366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.59023e9 | −0.146119 | −0.0730594 | − | 0.997328i | \(-0.523276\pi\) | ||||
−0.0730594 | + | 0.997328i | \(0.523276\pi\) | |||||||
\(422\) | −4.19833e9 | −0.132381 | ||||||||
\(423\) | 1.10508e9 | + | 5.89559e10i | 0.0345169 | + | 1.84148i | ||||
\(424\) | −2.59344e10 | −0.802440 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.10814e10 | − | 2.06900e10i | −0.640121 | − | 0.628235i | ||||
\(427\) | 1.94342e9i | 0.0584596i | ||||||||
\(428\) | −4.94454e9 | −0.147350 | ||||||||
\(429\) | −1.67170e10 | + | 1.70333e10i | −0.493549 | + | 0.502886i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.76624e10i | − | 0.511848i | −0.966697 | − | 0.255924i | \(-0.917620\pi\) | ||
0.966697 | − | 0.255924i | \(-0.0823797\pi\) | |||||||
\(432\) | 1.52579e9 | + | 1.44232e9i | 0.0438086 | + | 0.0414122i | ||||
\(433\) | − | 2.38480e10i | − | 0.678424i | −0.940710 | − | 0.339212i | \(-0.889840\pi\) | ||
0.940710 | − | 0.339212i | \(-0.110160\pi\) | |||||||
\(434\) | 3.60367e10i | 1.01575i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.04155e10 | −0.288228 | ||||||||
\(437\) | −2.73840e10 | −0.750882 | ||||||||
\(438\) | 5.74505e8 | + | 5.63838e8i | 0.0156098 | + | 0.0153200i | ||||
\(439\) | −1.28782e10 | −0.346734 | −0.173367 | − | 0.984857i | \(-0.555465\pi\) | ||||
−0.173367 | + | 0.984857i | \(0.555465\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.53034e8 | + | 4.01743e10i | 0.0199095 | + | 1.06217i | ||||
\(442\) | − | 5.06091e10i | − | 1.32599i | ||||||
\(443\) | 1.07169e10 | 0.278261 | 0.139131 | − | 0.990274i | \(-0.455569\pi\) | ||||
0.139131 | + | 0.990274i | \(0.455569\pi\) | |||||||
\(444\) | 7.67043e9 | + | 7.52800e9i | 0.197373 | + | 0.193708i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 4.79147e9i | − | 0.121096i | ||||||
\(447\) | 3.62076e10 | + | 3.55353e10i | 0.906923 | + | 0.890082i | ||||
\(448\) | − | 3.97211e10i | − | 0.986073i | ||||||
\(449\) | − | 1.78639e10i | − | 0.439532i | −0.975553 | − | 0.219766i | \(-0.929471\pi\) | ||
0.975553 | − | 0.219766i | \(-0.0705294\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.10953e10 | −0.268184 | ||||||||
\(452\) | −3.40027e10 | −0.814628 | ||||||||
\(453\) | −5.45352e10 | + | 5.55670e10i | −1.29504 | + | 1.31955i | ||||
\(454\) | −2.18650e10 | −0.514667 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.04068e10 | + | 2.07929e10i | −0.471971 | + | 0.480901i | ||||
\(457\) | − | 6.60639e10i | − | 1.51460i | −0.653064 | − | 0.757302i | \(-0.726517\pi\) | ||
0.653064 | − | 0.757302i | \(-0.273483\pi\) | |||||||
\(458\) | 7.68679e9 | 0.174696 | ||||||||
\(459\) | 4.61665e10 | + | 4.36411e10i | 1.04010 | + | 0.983207i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.51600e10i | 1.44270i | 0.692569 | + | 0.721352i | \(0.256479\pi\) | ||||
−0.692569 | + | 0.721352i | \(0.743521\pi\) | |||||||
\(462\) | 1.42645e10 | − | 1.45344e10i | 0.313105 | − | 0.319029i | ||||
\(463\) | 1.65087e10i | 0.359244i | 0.983736 | + | 0.179622i | \(0.0574874\pi\) | ||||
−0.983736 | + | 0.179622i | \(0.942513\pi\) | |||||||
\(464\) | − | 2.36466e8i | − | 0.00510148i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.07895e10 | −0.440859 | ||||||||
\(467\) | 3.64524e10 | 0.766404 | 0.383202 | − | 0.923664i | \(-0.374821\pi\) | ||||
0.383202 | + | 0.923664i | \(0.374821\pi\) | |||||||
\(468\) | −4.10323e10 | + | 7.69116e8i | −0.855347 | + | 0.0160328i | ||||
\(469\) | −4.62071e10 | −0.955030 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.34333e10 | − | 5.24411e10i | −1.08575 | − | 1.06559i | ||||
\(472\) | − | 1.65456e10i | − | 0.333362i | ||||||
\(473\) | 1.83054e10 | 0.365707 | ||||||||
\(474\) | 1.61884e10 | − | 1.64947e10i | 0.320693 | − | 0.326761i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 6.23341e10i | − | 1.21422i | ||||||
\(477\) | −7.65028e8 | − | 4.08142e10i | −0.0147776 | − | 0.788384i | ||||
\(478\) | − | 1.57724e10i | − | 0.302124i | ||||||
\(479\) | 5.54555e10i | 1.05342i | 0.850044 | + | 0.526711i | \(0.176575\pi\) | ||||
−0.850044 | + | 0.526711i | \(0.823425\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.62890e10 | 0.677946 | ||||||||
\(482\) | −1.00313e10 | −0.185853 | ||||||||
\(483\) | 6.32585e10 | + | 6.20839e10i | 1.16233 | + | 1.14075i | ||||
\(484\) | −2.47431e10 | −0.450892 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.40268e10 | + | 2.63908e10i | −0.430676 | + | 0.473051i | ||||
\(487\) | 4.92651e10i | 0.875837i | 0.899015 | + | 0.437919i | \(0.144284\pi\) | ||||
−0.899015 | + | 0.437919i | \(0.855716\pi\) | |||||||
\(488\) | 2.34937e9 | 0.0414259 | ||||||||
\(489\) | −7.52165e10 | − | 7.38198e10i | −1.31546 | − | 1.29103i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.73149e10i | 1.15820i | 0.815255 | + | 0.579102i | \(0.196597\pi\) | ||||
−0.815255 | + | 0.579102i | \(0.803403\pi\) | |||||||
\(492\) | −1.36168e10 | − | 1.33640e10i | −0.232389 | − | 0.228073i | ||||
\(493\) | − | 7.15485e9i | − | 0.121119i | ||||||
\(494\) | 3.65316e10i | 0.613424i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.03398e9 | 0.0666511 | ||||||||
\(497\) | −1.22844e11 | −2.01339 | ||||||||
\(498\) | −1.31127e10 | + | 1.33608e10i | −0.213194 | + | 0.217228i | ||||
\(499\) | 8.14015e10 | 1.31290 | 0.656448 | − | 0.754371i | \(-0.272058\pi\) | ||||
0.656448 | + | 0.754371i | \(0.272058\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.36626e10 | + | 6.48670e10i | −1.01049 | + | 1.02961i | ||||
\(502\) | 3.44922e10i | 0.543132i | ||||||||
\(503\) | 4.27491e10 | 0.667814 | 0.333907 | − | 0.942606i | \(-0.391633\pi\) | ||||
0.333907 | + | 0.942606i | \(0.391633\pi\) | |||||||
\(504\) | 9.42815e10 | − | 1.76723e9i | 1.46118 | − | 0.0273886i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 2.31401e10i | − | 0.352990i | ||||||
\(507\) | −5.07808e10 | + | 5.17416e10i | −0.768542 | + | 0.783083i | ||||
\(508\) | − | 1.55003e9i | − | 0.0232748i | ||||||
\(509\) | − | 6.30456e10i | − | 0.939255i | −0.882865 | − | 0.469628i | \(-0.844388\pi\) | ||
0.882865 | − | 0.469628i | \(-0.155612\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.34770e9 | 0.0490980 | ||||||||
\(512\) | −8.27185e9 | −0.120371 | ||||||||
\(513\) | −3.33248e10 | − | 3.15018e10i | −0.481169 | − | 0.454848i | ||||
\(514\) | −6.74396e9 | −0.0966189 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.24654e10 | + | 2.20483e10i | 0.316895 | + | 0.311011i | ||||
\(517\) | − | 6.40230e10i | − | 0.896136i | ||||||
\(518\) | −3.09652e10 | −0.430086 | ||||||||
\(519\) | −6.90529e10 | + | 7.03594e10i | −0.951727 | + | 0.969734i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.92618e10i | − | 1.07575i | −0.843023 | − | 0.537877i | \(-0.819226\pi\) | ||
0.843023 | − | 0.537877i | \(-0.180774\pi\) | |||||||
\(522\) | 4.01882e9 | − | 7.53295e7i | 0.0541273 | − | 0.00101457i | ||||
\(523\) | − | 8.10207e10i | − | 1.08290i | −0.840732 | − | 0.541451i | \(-0.817875\pi\) | ||
0.840732 | − | 0.541451i | \(-0.182125\pi\) | |||||||
\(524\) | 1.29393e10i | 0.171627i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.15417e10 | −0.150774 | ||||||||
\(527\) | 1.22058e11 | 1.58243 | ||||||||
\(528\) | −1.62700e9 | − | 1.59679e9i | −0.0209339 | − | 0.0205452i | ||||
\(529\) | 2.24020e10 | 0.286065 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.60387e10 | − | 4.88073e8i | 0.327522 | − | 0.00613913i | ||||
\(532\) | 4.49951e10i | 0.561719i | ||||||||
\(533\) | −6.44215e10 | −0.798219 | ||||||||
\(534\) | −3.39183e10 | − | 3.32885e10i | −0.417127 | − | 0.409382i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.58590e10i | 0.676759i | ||||||||
\(537\) | −1.96635e10 | − | 1.92984e10i | −0.236463 | − | 0.232073i | ||||
\(538\) | 5.18778e10i | 0.619230i | ||||||||
\(539\) | − | 4.36272e10i | − | 0.516895i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.57616e10 | 0.884423 | 0.442212 | − | 0.896911i | \(-0.354194\pi\) | ||||
0.442212 | + | 0.896911i | \(0.354194\pi\) | |||||||
\(542\) | −2.96804e10 | −0.343932 | ||||||||
\(543\) | 1.07474e11 | − | 1.09508e11i | 1.23625 | − | 1.25963i | ||||
\(544\) | −1.22726e11 | −1.40133 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.28227e10 | − | 8.43897e10i | 0.931921 | − | 0.949553i | ||||
\(547\) | − | 1.08131e11i | − | 1.20782i | −0.797053 | − | 0.603909i | \(-0.793609\pi\) | ||
0.797053 | − | 0.603909i | \(-0.206391\pi\) | |||||||
\(548\) | 3.64764e9 | 0.0404473 | ||||||||
\(549\) | 6.93032e7 | + | 3.69732e9i | 0.000762893 | + | 0.0407003i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.16464e9i | 0.0560317i | ||||||||
\(552\) | 7.50522e10 | − | 7.64721e10i | 0.808364 | − | 0.823658i | ||||
\(553\) | − | 9.61162e10i | − | 1.02777i | ||||||
\(554\) | − | 6.86314e10i | − | 0.728591i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.32865e10 | 0.766876 | ||||||||
\(557\) | 1.02611e11 | 1.06604 | 0.533019 | − | 0.846103i | \(-0.321057\pi\) | ||||
0.533019 | + | 0.846103i | \(0.321057\pi\) | |||||||
\(558\) | 1.28508e9 | + | 6.85590e10i | 0.0132554 | + | 0.707176i | ||||
\(559\) | 1.06285e11 | 1.08849 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.92288e10 | − | 4.83147e10i | −0.497013 | − | 0.487784i | ||||
\(562\) | 1.11290e11i | 1.11561i | ||||||||
\(563\) | −8.67308e10 | −0.863256 | −0.431628 | − | 0.902052i | \(-0.642061\pi\) | ||||
−0.431628 | + | 0.902052i | \(0.642061\pi\) | |||||||
\(564\) | 7.71139e10 | − | 7.85729e10i | 0.762107 | − | 0.776526i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.56326e10i | 0.347201i | ||||||||
\(567\) | 5.56235e9 | + | 1.48323e11i | 0.0538178 | + | 1.43508i | ||||
\(568\) | 1.48504e11i | 1.42674i | ||||||||
\(569\) | 1.42835e11i | 1.36265i | 0.731981 | + | 0.681325i | \(0.238596\pi\) | ||||
−0.731981 | + | 0.681325i | \(0.761404\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.15522e10 | 0.390886 | 0.195443 | − | 0.980715i | \(-0.437386\pi\) | ||||
0.195443 | + | 0.980715i | \(0.437386\pi\) | |||||||
\(572\) | 4.45589e10 | 0.416246 | ||||||||
\(573\) | 7.06483e10 | + | 6.93365e10i | 0.655365 | + | 0.643196i | ||||
\(574\) | 5.49704e10 | 0.506386 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.41647e9 | − | 7.55685e10i | −0.0128682 | − | 0.686517i | ||||
\(577\) | 1.37843e11i | 1.24360i | 0.783176 | + | 0.621800i | \(0.213598\pi\) | ||||
−0.783176 | + | 0.621800i | \(0.786402\pi\) | |||||||
\(578\) | 7.48657e10 | 0.670767 | ||||||||
\(579\) | 2.10381e10 | + | 2.06474e10i | 0.187194 | + | 0.183718i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.78549e10i | 0.683253i | ||||||||
\(582\) | 1.96365e10 | + | 1.92719e10i | 0.171148 | + | 0.167970i | ||||
\(583\) | 4.43221e10i | 0.383659i | ||||||||
\(584\) | − | 4.04699e9i | − | 0.0347921i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.69237e10 | 0.821939 | ||||||||
\(587\) | 2.08977e11 | 1.76014 | 0.880068 | − | 0.474848i | \(-0.157497\pi\) | ||||
0.880068 | + | 0.474848i | \(0.157497\pi\) | |||||||
\(588\) | 5.25477e10 | − | 5.35419e10i | 0.439586 | − | 0.447903i | ||||
\(589\) | −8.81061e10 | −0.732057 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.12530e11 | − | 1.14659e11i | 0.922399 | − | 0.939851i | ||||
\(592\) | 3.46627e9i | 0.0282212i | ||||||||
\(593\) | −4.25547e10 | −0.344135 | −0.172067 | − | 0.985085i | \(-0.555045\pi\) | ||||
−0.172067 | + | 0.985085i | \(0.555045\pi\) | |||||||
\(594\) | 2.66197e10 | − | 2.81601e10i | 0.213824 | − | 0.226198i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 9.47187e10i | − | 0.750672i | ||||||
\(597\) | −3.44104e10 | + | 3.50614e10i | −0.270889 | + | 0.276014i | ||||
\(598\) | − | 1.34356e11i | − | 1.05063i | ||||||
\(599\) | 6.86408e10i | 0.533182i | 0.963810 | + | 0.266591i | \(0.0858972\pi\) | ||||
−0.963810 | + | 0.266591i | \(0.914103\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.16080e11 | −1.65622 | −0.828109 | − | 0.560567i | \(-0.810583\pi\) | ||||
−0.828109 | + | 0.560567i | \(0.810583\pi\) | |||||||
\(602\) | −9.06919e10 | −0.690530 | ||||||||
\(603\) | −8.79080e10 | + | 1.64776e9i | −0.664904 | + | 0.0124631i | ||||
\(604\) | 1.45363e11 | 1.09221 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.90274e7 | − | 3.83027e7i | −0.000289387 | − | 0.000284014i | ||||
\(607\) | − | 2.36866e10i | − | 0.174481i | −0.996187 | − | 0.0872405i | \(-0.972195\pi\) | ||
0.996187 | − | 0.0872405i | \(-0.0278049\pi\) | |||||||
\(608\) | 8.85880e10 | 0.648277 | ||||||||
\(609\) | 1.17090e10 | − | 1.19306e10i | 0.0851241 | − | 0.0867346i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.71731e11i | − | 2.66725i | ||||||
\(612\) | −2.22286e9 | − | 1.18589e11i | −0.0158455 | − | 0.845356i | ||||
\(613\) | 1.04944e9i | 0.00743219i | 0.999993 | + | 0.00371609i | \(0.00118287\pi\) | ||||
−0.999993 | + | 0.00371609i | \(0.998817\pi\) | |||||||
\(614\) | − | 8.48526e10i | − | 0.597024i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.02385e11 | −0.711070 | ||||||||
\(617\) | −1.92658e11 | −1.32937 | −0.664684 | − | 0.747124i | \(-0.731434\pi\) | ||||
−0.664684 | + | 0.747124i | \(0.731434\pi\) | |||||||
\(618\) | −1.20471e11 | − | 1.18234e11i | −0.825900 | − | 0.810565i | ||||
\(619\) | −3.90898e10 | −0.266257 | −0.133129 | − | 0.991099i | \(-0.542502\pi\) | ||||
−0.133129 | + | 0.991099i | \(0.542502\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.22562e11 | + | 1.15857e11i | 0.824117 | + | 0.779036i | ||||
\(622\) | 8.42654e10i | 0.562973i | ||||||||
\(623\) | −1.97645e11 | −1.31200 | ||||||||
\(624\) | −9.44667e9 | − | 9.27126e9i | −0.0623075 | − | 0.0611506i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.30221e11i | 0.847976i | ||||||||
\(627\) | 3.55352e10 | + | 3.48754e10i | 0.229926 | + | 0.225657i | ||||
\(628\) | 1.39781e11i | 0.898687i | ||||||||
\(629\) | 1.04881e11i | 0.670028i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.46902e10 | −0.0926636 | −0.0463318 | − | 0.998926i | \(-0.514753\pi\) | ||||
−0.0463318 | + | 0.998926i | \(0.514753\pi\) | |||||||
\(632\) | −1.16193e11 | −0.728304 | ||||||||
\(633\) | −2.32712e10 | + | 2.37115e10i | −0.144945 | + | 0.147688i | ||||
\(634\) | −6.51007e10 | −0.402929 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.33846e10 | + | 5.43947e10i | −0.326278 | + | 0.332451i | ||||
\(637\) | − | 2.53308e11i | − | 1.53848i | ||||||
\(638\) | −4.36423e9 | −0.0263405 | ||||||||
\(639\) | −2.33708e11 | + | 4.38066e9i | −1.40175 | + | 0.0262746i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.98992e11i | 1.17870i | 0.807879 | + | 0.589349i | \(0.200616\pi\) | ||||
−0.807879 | + | 0.589349i | \(0.799384\pi\) | |||||||
\(642\) | 1.89876e10 | − | 1.93468e10i | 0.111771 | − | 0.113886i | ||||
\(643\) | 1.32563e11i | 0.775495i | 0.921766 | + | 0.387748i | \(0.126747\pi\) | ||||
−0.921766 | + | 0.387748i | \(0.873253\pi\) | |||||||
\(644\) | − | 1.65483e11i | − | 0.962078i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.05582e11 | −0.606259 | ||||||||
\(647\) | 1.66551e10 | 0.0950453 | 0.0475227 | − | 0.998870i | \(-0.484867\pi\) | ||||
0.0475227 | + | 0.998870i | \(0.484867\pi\) | |||||||
\(648\) | 1.79305e11 | − | 6.72423e9i | 1.01694 | − | 0.0381366i | ||||
\(649\) | −2.82766e10 | −0.159385 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.03530e11 | + | 1.99750e11i | 1.13319 | + | 1.11215i | ||||
\(652\) | 1.96765e11i | 1.08882i | ||||||||
\(653\) | −6.15244e10 | −0.338372 | −0.169186 | − | 0.985584i | \(-0.554114\pi\) | ||||
−0.169186 | + | 0.985584i | \(0.554114\pi\) | |||||||
\(654\) | 3.99968e10 | − | 4.07535e10i | 0.218632 | − | 0.222769i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 6.15344e9i | − | 0.0332279i | ||||||
\(657\) | 6.36894e9 | − | 1.19380e8i | 0.0341826 | − | 0.000640725i | ||||
\(658\) | 3.17195e11i | 1.69209i | ||||||||
\(659\) | − | 6.62231e10i | − | 0.351130i | −0.984468 | − | 0.175565i | \(-0.943825\pi\) | ||
0.984468 | − | 0.175565i | \(-0.0561752\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.16830e11 | −1.65966 | −0.829832 | − | 0.558014i | \(-0.811564\pi\) | ||||
−0.829832 | + | 0.558014i | \(0.811564\pi\) | |||||||
\(662\) | 1.28477e10 | 0.0668951 | ||||||||
\(663\) | −2.85832e11 | − | 2.80525e11i | −1.47930 | − | 1.45183i | ||||
\(664\) | 9.41176e10 | 0.484171 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.89106e10 | + | 1.10423e9i | −0.299431 | + | 0.00561259i | ||||
\(667\) | − | 1.89945e10i | − | 0.0959677i | ||||||
\(668\) | 1.69691e11 | 0.852223 | ||||||||
\(669\) | −2.70615e10 | − | 2.65590e10i | −0.135097 | − | 0.132589i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.01509e9i | − | 0.0198064i | ||||||
\(672\) | −2.04643e11 | − | 2.00843e11i | −1.00350 | − | 0.984870i | ||||
\(673\) | − | 2.15656e10i | − | 0.105124i | −0.998618 | − | 0.0525618i | \(-0.983261\pi\) | ||
0.998618 | − | 0.0525618i | \(-0.0167387\pi\) | |||||||
\(674\) | 8.21697e10i | 0.398173i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.35355e11 | 0.648169 | ||||||||
\(677\) | −2.05571e11 | −0.978605 | −0.489303 | − | 0.872114i | \(-0.662749\pi\) | ||||
−0.489303 | + | 0.872114i | \(0.662749\pi\) | |||||||
\(678\) | 1.30574e11 | − | 1.33045e11i | 0.617928 | − | 0.629620i | ||||
\(679\) | 1.14424e11 | 0.538316 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.21197e11 | + | 1.23490e11i | −0.563514 | + | 0.574175i | ||||
\(682\) | − | 7.44515e10i | − | 0.344140i | ||||||
\(683\) | 3.27181e11 | 1.50351 | 0.751753 | − | 0.659445i | \(-0.229209\pi\) | ||||
0.751753 | + | 0.659445i | \(0.229209\pi\) | |||||||
\(684\) | 1.60455e9 | + | 8.56023e10i | 0.00733040 | + | 0.391076i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.26869e10i | 0.0572876i | ||||||||
\(687\) | 4.26077e10 | − | 4.34138e10i | 0.191276 | − | 0.194895i | ||||
\(688\) | 1.01521e10i | 0.0453110i | ||||||||
\(689\) | 2.57343e11i | 1.14192i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.11252e10 | 0.224245 | 0.112122 | − | 0.993694i | \(-0.464235\pi\) | ||||
0.112122 | + | 0.993694i | \(0.464235\pi\) | |||||||
\(692\) | 1.84059e11 | 0.802662 | ||||||||
\(693\) | −3.02021e9 | − | 1.61128e11i | −0.0130949 | − | 0.698614i | ||||
\(694\) | −7.05521e10 | −0.304139 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.44227e10 | − | 1.41549e10i | −0.0614624 | − | 0.0603211i | ||||
\(697\) | − | 1.86188e11i | − | 0.788896i | ||||||
\(698\) | 1.29029e11 | 0.543584 | ||||||||
\(699\) | −1.15235e11 | + | 1.17416e11i | −0.482700 | + | 0.491833i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.49396e11i | 0.618681i | 0.950951 | + | 0.309341i | \(0.100108\pi\) | ||||
−0.950951 | + | 0.309341i | \(0.899892\pi\) | |||||||
\(702\) | 1.54559e11 | − | 1.63503e11i | 0.636424 | − | 0.673252i | ||||
\(703\) | − | 7.57069e10i | − | 0.309966i | ||||||
\(704\) | 8.20635e10i | 0.334087i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.87764e11 | 0.755777 | ||||||||
\(707\) | −2.27417e8 | −0.000910218 | ||||||||
\(708\) | −3.47028e10 | − | 3.40584e10i | −0.138112 | − | 0.135547i | ||||
\(709\) | −1.80177e10 | −0.0713041 | −0.0356520 | − | 0.999364i | \(-0.511351\pi\) | ||||
−0.0356520 | + | 0.999364i | \(0.511351\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.42754e9 | − | 1.82859e11i | −0.0134123 | − | 0.715546i | ||||
\(712\) | 2.38930e11i | 0.929718i | ||||||||
\(713\) | 3.24037e11 | 1.25382 | ||||||||
\(714\) | 2.43899e11 | + | 2.39370e11i | 0.938462 | + | 0.921036i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.14395e10i | 0.195724i | ||||||||
\(717\) | −8.90799e10 | − | 8.74258e10i | −0.337057 | − | 0.330798i | ||||
\(718\) | − | 1.59136e8i | − | 0.000598785i | ||||||
\(719\) | − | 4.58130e11i | − | 1.71425i | −0.515112 | − | 0.857123i | \(-0.672250\pi\) | ||
0.515112 | − | 0.857123i | \(-0.327750\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.01996e11 | −2.59773 | ||||||||
\(722\) | −9.76264e10 | −0.359268 | ||||||||
\(723\) | −5.56032e10 | + | 5.66552e10i | −0.203492 | + | 0.207342i | ||||
\(724\) | −2.86470e11 | −1.04262 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.50162e10 | − | 9.68138e10i | 0.342020 | − | 0.348491i | ||||
\(727\) | 1.27196e11i | 0.455342i | 0.973738 | + | 0.227671i | \(0.0731110\pi\) | ||||
−0.973738 | + | 0.227671i | \(0.926889\pi\) | |||||||
\(728\) | −5.94466e11 | −2.11642 | ||||||||
\(729\) | 1.58715e10 | + | 2.81983e11i | 0.0561963 | + | 0.998420i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.07178e11i | 1.07577i | ||||||||
\(732\) | 4.83606e9 | − | 4.92756e9i | 0.0168441 | − | 0.0171628i | ||||
\(733\) | 2.10630e11i | 0.729631i | 0.931080 | + | 0.364816i | \(0.118868\pi\) | ||||
−0.931080 | + | 0.364816i | \(0.881132\pi\) | |||||||
\(734\) | 4.88175e10i | 0.168186i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.25809e11 | −1.11033 | ||||||||
\(737\) | 9.54634e10 | 0.323569 | ||||||||
\(738\) | 1.04580e11 | − | 1.96027e9i | 0.352552 | − | 0.00660830i | ||||
\(739\) | −2.18560e11 | −0.732811 | −0.366405 | − | 0.930455i | \(-0.619412\pi\) | ||||
−0.366405 | + | 0.930455i | \(0.619412\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.06325e11 | + | 2.02494e11i | 0.684350 | + | 0.671643i | ||||
\(742\) | − | 2.19589e11i | − | 0.724427i | ||||||
\(743\) | −1.82763e11 | −0.599700 | −0.299850 | − | 0.953986i | \(-0.596937\pi\) | ||||
−0.299850 | + | 0.953986i | \(0.596937\pi\) | |||||||
\(744\) | 2.41475e11 | − | 2.46044e11i | 0.788098 | − | 0.803009i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.34608e11i | 0.757509i | ||||||||
\(747\) | 2.77634e9 | + | 1.48117e11i | 0.00891641 | + | 0.475689i | ||||
\(748\) | 1.28782e11i | 0.411384i | ||||||||
\(749\) | − | 1.12736e11i | − | 0.358208i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.51243e11 | 1.73294 | 0.866469 | − | 0.499230i | \(-0.166384\pi\) | ||||
0.866469 | + | 0.499230i | \(0.166384\pi\) | |||||||
\(752\) | 3.55071e10 | 0.111031 | ||||||||
\(753\) | 1.94806e11 | + | 1.91189e11i | 0.605931 | + | 0.594680i | ||||
\(754\) | −2.53396e10 | −0.0783996 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.90367e11 | − | 2.01383e11i | 0.582780 | − | 0.616505i | ||||
\(757\) | 4.36075e10i | 0.132794i | 0.997793 | + | 0.0663969i | \(0.0211504\pi\) | ||||
−0.997793 | + | 0.0663969i | \(0.978850\pi\) | |||||||
\(758\) | 6.97594e10 | 0.211313 | ||||||||
\(759\) | −1.30691e11 | − | 1.28265e11i | −0.393804 | − | 0.386492i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.60493e11i | − | 1.37304i | −0.727110 | − | 0.686521i | \(-0.759137\pi\) | ||
0.727110 | − | 0.686521i | \(-0.240863\pi\) | |||||||
\(762\) | 6.06490e9 | + | 5.95229e9i | 0.0179889 | + | 0.0176548i | ||||
\(763\) | − | 2.37475e11i | − | 0.700681i | ||||||
\(764\) | − | 1.84815e11i | − | 0.542455i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.10221e11 | −0.320147 | ||||||||
\(767\) | −1.64180e11 | −0.474393 | ||||||||
\(768\) | −2.51473e11 | + | 2.56231e11i | −0.722849 | + | 0.736525i | ||||
\(769\) | 1.46976e11 | 0.420281 | 0.210140 | − | 0.977671i | \(-0.432608\pi\) | ||||
0.210140 | + | 0.977671i | \(0.432608\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.73816e10 | + | 3.80888e10i | −0.105789 | + | 0.107790i | ||||
\(772\) | − | 5.50352e10i | − | 0.154943i | ||||||
\(773\) | −1.06663e11 | −0.298741 | −0.149371 | − | 0.988781i | \(-0.547725\pi\) | ||||
−0.149371 | + | 0.988781i | \(0.547725\pi\) | |||||||
\(774\) | −1.72539e11 | + | 3.23411e9i | −0.480756 | + | 0.00901137i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 1.38325e11i | − | 0.381465i | ||||||
\(777\) | −1.71639e11 | + | 1.74887e11i | −0.470904 | + | 0.479814i | ||||
\(778\) | − | 3.29251e11i | − | 0.898688i | ||||||
\(779\) | 1.34397e11i | 0.364956i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.53794e11 | 0.682147 | ||||||||
\(782\) | 3.88308e11 | 1.03836 | ||||||||
\(783\) | 2.18508e10 | − | 2.31152e10i | 0.0581326 | − | 0.0614966i | ||||
\(784\) | 2.41956e10 | 0.0640431 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.06285e10 | − | 4.96885e10i | −0.132649 | − | 0.130186i | ||||
\(787\) | 6.64587e11i | 1.73242i | 0.499682 | + | 0.866209i | \(0.333450\pi\) | ||||
−0.499682 | + | 0.866209i | \(0.666550\pi\) | |||||||
\(788\) | −2.99947e11 | −0.777928 | ||||||||
\(789\) | −6.39752e10 | + | 6.51856e10i | −0.165083 | + | 0.168207i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.75265e11i | − | 1.98036i | ||||||
\(792\) | −1.94785e11 | + | 3.65108e9i | −0.495056 | + | 0.00927941i | ||||
\(793\) | − | 2.33124e10i | − | 0.0589515i | ||||||
\(794\) | − | 3.33690e11i | − | 0.839578i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.17201e10 | 0.228461 | ||||||||
\(797\) | −2.85566e11 | −0.707738 | −0.353869 | − | 0.935295i | \(-0.615134\pi\) | ||||
−0.353869 | + | 0.935295i | \(0.615134\pi\) | |||||||
\(798\) | −1.76055e11 | − | 1.72786e11i | −0.434148 | − | 0.426087i | ||||
\(799\) | 1.07436e12 | 2.63610 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.76016e11 | + | 7.04811e9i | −0.913432 | + | 0.0171215i | ||||
\(802\) | − | 2.43698e11i | − | 0.589052i | ||||||
\(803\) | −6.91633e9 | −0.0166346 | ||||||||
\(804\) | 1.17158e11 | + | 1.14983e11i | 0.280381 | + | 0.275175i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 4.32280e11i | − | 1.02430i | ||||||
\(807\) | 2.92998e11 | + | 2.87557e11i | 0.690828 | + | 0.678000i | ||||
\(808\) | 2.74921e8i | 0.000645003i | ||||||||
\(809\) | − | 6.31328e10i | − | 0.147388i | −0.997281 | − | 0.0736938i | \(-0.976521\pi\) | ||
0.997281 | − | 0.0736938i | \(-0.0234788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.09177e11 | 1.40819 | 0.704093 | − | 0.710107i | \(-0.251354\pi\) | ||||
0.704093 | + | 0.710107i | \(0.251354\pi\) | |||||||
\(812\) | −3.12102e10 | −0.0717914 | ||||||||
\(813\) | −1.64518e11 | + | 1.67630e11i | −0.376574 | + | 0.383699i | ||||
\(814\) | 6.39738e10 | 0.145715 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.67953e10 | − | 2.73023e10i | 0.0604363 | − | 0.0615798i | ||||
\(817\) | − | 2.21733e11i | − | 0.497671i | ||||||
\(818\) | 3.98481e11 | 0.890009 | ||||||||
\(819\) | −1.75359e10 | − | 9.35540e11i | −0.0389756 | − | 2.07935i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.63422e11i | 1.02001i | 0.860172 | + | 0.510004i | \(0.170356\pi\) | ||||
−0.860172 | + | 0.510004i | \(0.829644\pi\) | |||||||
\(822\) | −1.40073e10 | + | 1.42724e10i | −0.0306809 | + | 0.0312614i | ||||
\(823\) | 6.84569e11i | 1.49217i | 0.665851 | + | 0.746085i | \(0.268069\pi\) | ||||
−0.665851 | + | 0.746085i | \(0.731931\pi\) | |||||||
\(824\) | 8.48631e11i | 1.84082i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.40094e11 | 0.300952 | ||||||||
\(827\) | 5.73805e11 | 1.22671 | 0.613355 | − | 0.789807i | \(-0.289819\pi\) | ||||
0.613355 | + | 0.789807i | \(0.289819\pi\) | |||||||
\(828\) | −5.90120e9 | − | 3.14828e11i | −0.0125551 | − | 0.669811i | ||||
\(829\) | −5.68680e11 | −1.20407 | −0.602033 | − | 0.798471i | \(-0.705642\pi\) | ||||
−0.602033 | + | 0.798471i | \(0.705642\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.87620e11 | − | 3.80422e11i | −0.812834 | − | 0.797741i | ||||
\(832\) | 4.76477e11i | 0.994371i | ||||||||
\(833\) | 7.32098e11 | 1.52051 | ||||||||
\(834\) | −2.81428e11 | + | 2.86753e11i | −0.581706 | + | 0.592712i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 9.29596e10i | − | 0.190313i | ||||||
\(837\) | 3.94334e11 | + | 3.72763e11i | 0.803456 | + | 0.759505i | ||||
\(838\) | − | 3.33668e11i | − | 0.676609i | ||||||
\(839\) | − | 2.49035e10i | − | 0.0502588i | −0.999684 | − | 0.0251294i | \(-0.992000\pi\) | ||
0.999684 | − | 0.0251294i | \(-0.00799977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.96664e11 | 0.992839 | ||||||||
\(842\) | −4.69844e10 | −0.0934772 | ||||||||
\(843\) | 6.28551e11 | + | 6.16880e11i | 1.24460 | + | 1.22149i | ||||
\(844\) | 6.20289e10 | 0.122243 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.13113e10 | + | 6.03457e11i | 0.0220816 | + | 1.17805i | ||||
\(847\) | − | 5.64145e11i | − | 1.09612i | ||||||
\(848\) | −2.45810e10 | −0.0475353 | ||||||||
\(849\) | 2.01247e11 | + | 1.97510e11i | 0.387346 | + | 0.380154i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.78435e11i | 0.530891i | ||||||||
\(852\) | 3.11471e11 | + | 3.05688e11i | 0.591099 | + | 0.580123i | ||||
\(853\) | − | 7.97637e11i | − | 1.50664i | −0.657655 | − | 0.753319i | \(-0.728451\pi\) | ||
0.657655 | − | 0.753319i | \(-0.271549\pi\) | |||||||
\(854\) | 1.98924e10i | 0.0373985i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.36285e11 | −0.253836 | ||||||||
\(857\) | 7.68355e11 | 1.42442 | 0.712211 | − | 0.701965i | \(-0.247694\pi\) | ||||
0.712211 | + | 0.701965i | \(0.247694\pi\) | |||||||
\(858\) | −1.71111e11 | + | 1.74348e11i | −0.315740 | + | 0.321713i | ||||
\(859\) | 5.30152e10 | 0.0973706 | 0.0486853 | − | 0.998814i | \(-0.484497\pi\) | ||||
0.0486853 | + | 0.998814i | \(0.484497\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.04700e11 | − | 3.10465e11i | 0.554446 | − | 0.564936i | ||||
\(862\) | − | 1.80788e11i | − | 0.327447i | ||||||
\(863\) | −8.01812e11 | −1.44554 | −0.722769 | − | 0.691090i | \(-0.757131\pi\) | ||||
−0.722769 | + | 0.691090i | \(0.757131\pi\) | |||||||
\(864\) | −3.96490e11 | − | 3.74801e11i | −0.711504 | − | 0.672583i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 2.44102e11i | − | 0.434010i | ||||||
\(867\) | 4.14978e11 | − | 4.22830e11i | 0.734428 | − | 0.748323i | ||||
\(868\) | − | 5.32430e11i | − | 0.937959i | ||||||
\(869\) | 1.98575e11i | 0.348214i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.54280e11 | 0.963067 | ||||||||
\(872\) | −2.87080e11 | −0.496520 | ||||||||
\(873\) | 2.17689e11 | − | 4.08040e9i | 0.374783 | − | 0.00702499i | ||||
\(874\) | −2.80296e11 | −0.480364 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.48813e9 | − | 8.33052e9i | −0.0144144 | − | 0.0141467i | ||||
\(877\) | − | 5.88957e11i | − | 0.995601i | −0.867292 | − | 0.497800i | \(-0.834141\pi\) | ||
0.867292 | − | 0.497800i | \(-0.165859\pi\) | |||||||
\(878\) | −1.31818e11 | −0.221817 | ||||||||
\(879\) | 5.37245e11 | − | 5.47410e11i | 0.899948 | − | 0.916974i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.89776e11i | 1.31099i | 0.755198 | + | 0.655497i | \(0.227541\pi\) | ||||
−0.755198 | + | 0.655497i | \(0.772459\pi\) | |||||||
\(882\) | 7.70786e9 | + | 4.11213e11i | 0.0127368 | + | 0.679506i | ||||
\(883\) | − | 4.30157e11i | − | 0.707594i | −0.935322 | − | 0.353797i | \(-0.884890\pi\) | ||
0.935322 | − | 0.353797i | \(-0.115110\pi\) | |||||||
\(884\) | 7.47733e11i | 1.22444i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.09695e11 | 0.178013 | ||||||||
\(887\) | −1.14158e12 | −1.84421 | −0.922107 | − | 0.386934i | \(-0.873534\pi\) | ||||
−0.922107 | + | 0.386934i | \(0.873534\pi\) | |||||||
\(888\) | 2.11418e11 | + | 2.07492e11i | 0.340008 | + | 0.333695i | ||||
\(889\) | 3.53408e10 | 0.0565809 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.14918e10 | − | 3.06434e11i | −0.0182337 | − | 0.486213i | ||||
\(892\) | 7.07924e10i | 0.111822i | ||||||||
\(893\) | −7.75511e11 | −1.21950 | ||||||||
\(894\) | 3.70612e11 | + | 3.63730e11i | 0.580189 | + | 0.569416i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.99646e11i | 0.775230i | ||||||||
\(897\) | −7.58821e11 | − | 7.44731e11i | −1.17211 | − | 1.15035i | ||||
\(898\) | − | 1.82850e11i | − | 0.281183i | ||||||
\(899\) | − | 6.11135e10i | − | 0.0935618i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.43759e11 | −1.12858 | ||||||||
\(902\) | −1.13568e11 | −0.171566 | ||||||||
\(903\) | −5.02703e11 | + | 5.12214e11i | −0.756067 | + | 0.770372i | ||||
\(904\) | −9.37205e11 | −1.40333 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.58208e11 | + | 5.68769e11i | −0.828483 | + | 0.844158i | ||||
\(907\) | 3.91779e11i | 0.578911i | 0.957191 | + | 0.289455i | \(0.0934742\pi\) | ||||
−0.957191 | + | 0.289455i | \(0.906526\pi\) | |||||||
\(908\) | 3.23049e11 | 0.475253 | ||||||||
\(909\) | −4.32656e8 | + | 8.10978e6i | −0.000633705 | + | 1.18783e-5i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.39414e11i | − | 0.347597i | −0.984781 | − | 0.173799i | \(-0.944396\pi\) | ||
0.984781 | − | 0.173799i | \(-0.0556042\pi\) | |||||||
\(912\) | −1.93419e10 | + | 1.97078e10i | −0.0279588 | + | 0.0284878i | ||||
\(913\) | − | 1.60848e11i | − | 0.231490i | ||||||
\(914\) | − | 6.76212e11i | − | 0.968943i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.13570e11 | −0.161317 | ||||||||
\(917\) | −2.95018e11 | −0.417226 | ||||||||
\(918\) | 4.72548e11 | + | 4.46699e11i | 0.665389 | + | 0.628990i | ||||
\(919\) | −2.64317e11 | −0.370563 | −0.185282 | − | 0.982685i | \(-0.559320\pi\) | ||||
−0.185282 | + | 0.982685i | \(0.559320\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.79235e11 | − | 4.70336e11i | −0.666054 | − | 0.653687i | ||||
\(922\) | 6.66960e11i | 0.922946i | ||||||||
\(923\) | 1.47358e12 | 2.03033 | ||||||||
\(924\) | −2.10754e11 | + | 2.14741e11i | −0.289126 | + | 0.294597i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.68979e11i | 0.229820i | ||||||||
\(927\) | −1.33553e12 | + | 2.50335e10i | −1.80857 | + | 0.0339002i | ||||
\(928\) | 6.14477e10i | 0.0828541i | ||||||||
\(929\) | − | 8.24093e11i | − | 1.10640i | −0.833047 | − | 0.553202i | \(-0.813406\pi\) | ||
0.833047 | − | 0.553202i | \(-0.186594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.28456e11 | −0.703413 | ||||||||
\(932\) | 3.07158e11 | 0.407097 | ||||||||
\(933\) | 4.75918e11 | + | 4.67081e11i | 0.628066 | + | 0.616404i | ||||
\(934\) | 3.73117e11 | 0.490295 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.13096e12 | + | 2.11989e10i | −1.47348 | + | 0.0276191i | ||||
\(937\) | − | 3.88885e11i | − | 0.504502i | −0.967662 | − | 0.252251i | \(-0.918829\pi\) | ||
0.967662 | − | 0.252251i | \(-0.0811709\pi\) | |||||||
\(938\) | −4.72964e11 | −0.610965 | ||||||||
\(939\) | 7.35467e11 | + | 7.21811e11i | 0.946022 | + | 0.928455i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.71451e11i | 0.728821i | 0.931239 | + | 0.364410i | \(0.118729\pi\) | ||||
−0.931239 | + | 0.364410i | \(0.881271\pi\) | |||||||
\(942\) | −5.46929e11 | − | 5.36774e11i | −0.694588 | − | 0.681691i | ||||
\(943\) | − | 4.94287e11i | − | 0.625075i | ||||||
\(944\) | − | 1.56822e10i | − | 0.0197478i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.87369e11 | 0.233955 | ||||||||
\(947\) | −7.99848e10 | −0.0994507 | −0.0497253 | − | 0.998763i | \(-0.515835\pi\) | ||||
−0.0497253 | + | 0.998763i | \(0.515835\pi\) | |||||||
\(948\) | −2.39178e11 | + | 2.43703e11i | −0.296134 | + | 0.301737i | ||||
\(949\) | −4.01576e10 | −0.0495111 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.60852e11 | + | 3.67679e11i | −0.441171 | + | 0.449517i | ||||
\(952\) | − | 1.71810e12i | − | 2.09170i | ||||||
\(953\) | −1.05398e12 | −1.27779 | −0.638894 | − | 0.769294i | \(-0.720608\pi\) | ||||
−0.638894 | + | 0.769294i | \(0.720608\pi\) | |||||||
\(954\) | −7.83063e9 | − | 4.17763e11i | −0.00945373 | − | 0.504355i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.33032e11i | 0.278987i | ||||||||
\(957\) | −2.41908e10 | + | 2.46485e10i | −0.0288405 | + | 0.0293861i | ||||
\(958\) | 5.67628e11i | 0.673910i | ||||||||
\(959\) | 8.31666e10i | 0.0983274i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.89674e11 | 0.222389 | ||||||||
\(962\) | 3.71445e11 | 0.433705 | ||||||||
\(963\) | −4.02021e9 | − | 2.14478e11i | −0.00467459 | − | 0.249389i | ||||
\(964\) | 1.48209e11 | 0.171620 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.47497e11 | + | 6.35474e11i | 0.743583 | + | 0.729775i | ||||
\(967\) | 4.82707e11i | 0.552049i | 0.961151 | + | 0.276025i | \(0.0890172\pi\) | ||||
−0.961151 | + | 0.276025i | \(0.910983\pi\) | |||||||
\(968\) | −6.81985e11 | −0.776736 | ||||||||
\(969\) | −5.85236e11 | + | 5.96309e11i | −0.663798 | + | 0.676357i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 9.01068e11i | − | 1.01363i | −0.862054 | − | 0.506817i | \(-0.830822\pi\) | ||
0.862054 | − | 0.506817i | \(-0.169178\pi\) | |||||||
\(972\) | 3.54988e11 | − | 3.89916e11i | 0.397694 | − | 0.436823i | ||||
\(973\) | 1.67094e12i | 1.86427i | ||||||||
\(974\) | 5.04264e11i | 0.560302i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.22677e9 | 0.00245401 | ||||||||
\(977\) | 2.30964e11 | 0.253493 | 0.126747 | − | 0.991935i | \(-0.459546\pi\) | ||||
0.126747 | + | 0.991935i | \(0.459546\pi\) | |||||||
\(978\) | −7.69896e11 | − | 7.55600e11i | −0.841544 | − | 0.825918i | ||||
\(979\) | 4.08334e11 | 0.444513 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.46846e9 | − | 4.51792e11i | −0.00914384 | − | 0.487823i | ||||
\(982\) | 6.89017e11i | 0.740942i | ||||||||
\(983\) | 1.09320e10 | 0.0117080 | 0.00585402 | − | 0.999983i | \(-0.498137\pi\) | ||||
0.00585402 | + | 0.999983i | \(0.498137\pi\) | |||||||
\(984\) | −3.75316e11 | − | 3.68346e11i | −0.400328 | − | 0.392895i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 7.32351e10i | − | 0.0774840i | ||||||
\(987\) | 1.79147e12 | + | 1.75820e12i | 1.88773 | + | 1.85268i | ||||
\(988\) | − | 5.39742e11i | − | 0.566446i | ||||||
\(989\) | 8.15489e11i | 0.852380i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.43139e10 | 0.0563140 | 0.0281570 | − | 0.999604i | \(-0.491036\pi\) | ||||
0.0281570 | + | 0.999604i | \(0.491036\pi\) | |||||||
\(992\) | −1.04827e12 | −1.08249 | ||||||||
\(993\) | 7.12146e10 | − | 7.25620e10i | 0.0732440 | − | 0.0746298i | ||||
\(994\) | −1.25740e12 | −1.28803 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.93736e11 | − | 1.97402e11i | 0.196867 | − | 0.200592i | ||||
\(997\) | − | 1.85628e12i | − | 1.87872i | −0.342929 | − | 0.939361i | \(-0.611419\pi\) | ||
0.342929 | − | 0.939361i | \(-0.388581\pi\) | |||||||
\(998\) | 8.33205e11 | 0.839904 | ||||||||
\(999\) | −3.20304e11 | + | 3.38839e11i | −0.321588 | + | 0.340198i |
(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 | 75.9.d.c.74.15 | 20 | ||
3.2 | odd | 2 | inner | 75.9.d.c.74.5 | 20 | ||
5.2 | odd | 4 | 15.9.c.a.11.8 | yes | 10 | ||
5.3 | odd | 4 | 75.9.c.g.26.3 | 10 | |||
5.4 | even | 2 | inner | 75.9.d.c.74.6 | 20 | ||
15.2 | even | 4 | 15.9.c.a.11.3 | ✓ | 10 | ||
15.8 | even | 4 | 75.9.c.g.26.8 | 10 | |||
15.14 | odd | 2 | inner | 75.9.d.c.74.16 | 20 | ||
20.7 | even | 4 | 240.9.l.b.161.8 | 10 | |||
60.47 | odd | 4 | 240.9.l.b.161.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.9.c.a.11.3 | ✓ | 10 | 15.2 | even | 4 | ||
15.9.c.a.11.8 | yes | 10 | 5.2 | odd | 4 | ||
75.9.c.g.26.3 | 10 | 5.3 | odd | 4 | |||
75.9.c.g.26.8 | 10 | 15.8 | even | 4 | |||
75.9.d.c.74.5 | 20 | 3.2 | odd | 2 | inner | ||
75.9.d.c.74.6 | 20 | 5.4 | even | 2 | inner | ||
75.9.d.c.74.15 | 20 | 1.1 | even | 1 | trivial | ||
75.9.d.c.74.16 | 20 | 15.14 | odd | 2 | inner | ||
240.9.l.b.161.7 | 10 | 60.47 | odd | 4 | |||
240.9.l.b.161.8 | 10 | 20.7 | even | 4 |