Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,8,Mod(35,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.35");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.f (of order \(2\), degree \(1\), 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: | \(22.4917218349\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 35.22 | ||
Character | \(\chi\) | \(=\) | 72.35 |
Dual form | 72.8.f.a.35.21 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.14946 | + | 7.84769i | 0.720317 | + | 0.693645i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.82744 | + | 127.909i | 0.0377144 | + | 0.999289i | ||||
\(5\) | −294.266 | −1.05280 | −0.526398 | − | 0.850238i | \(-0.676458\pi\) | ||||
−0.526398 | + | 0.850238i | \(0.676458\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 328.633i | − | 0.362133i | −0.983471 | − | 0.181066i | \(-0.942045\pi\) | ||
0.983471 | − | 0.181066i | \(-0.0579549\pi\) | |||||||
\(8\) | −964.449 | + | 1080.27i | −0.665985 | + | 0.745965i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2398.11 | − | 2309.31i | −0.758348 | − | 0.730266i | ||||
\(11\) | − | 2680.12i | − | 0.607126i | −0.952811 | − | 0.303563i | \(-0.901824\pi\) | ||
0.952811 | − | 0.303563i | \(-0.0981763\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1486.01i | − | 0.187595i | −0.995591 | − | 0.0937973i | \(-0.970099\pi\) | ||
0.995591 | − | 0.0937973i | \(-0.0299005\pi\) | |||||||
\(14\) | 2579.01 | − | 2678.18i | 0.251192 | − | 0.260851i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16337.4 | + | 1234.95i | −0.997155 | + | 0.0753752i | ||||
\(17\) | − | 35589.5i | − | 1.75692i | −0.477819 | − | 0.878458i | \(-0.658573\pi\) | ||
0.477819 | − | 0.878458i | \(-0.341427\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16097.0 | 0.538402 | 0.269201 | − | 0.963084i | \(-0.413240\pi\) | ||||
0.269201 | + | 0.963084i | \(0.413240\pi\) | |||||||
\(20\) | −1420.55 | − | 37639.2i | −0.0397056 | − | 1.05205i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 21032.7 | − | 21841.5i | 0.421130 | − | 0.437324i | ||||
\(23\) | 11593.2 | 0.198680 | 0.0993401 | − | 0.995054i | \(-0.468327\pi\) | ||||
0.0993401 | + | 0.995054i | \(0.468327\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8467.20 | 0.108380 | ||||||||
\(26\) | 11661.8 | − | 12110.2i | 0.130124 | − | 0.135128i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 42035.1 | − | 1586.46i | 0.361875 | − | 0.0136576i | ||||
\(29\) | −204036. | −1.55351 | −0.776753 | − | 0.629806i | \(-0.783135\pi\) | ||||
−0.776753 | + | 0.629806i | \(0.783135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 149568.i | − | 0.901722i | −0.892594 | − | 0.450861i | \(-0.851117\pi\) | ||
0.892594 | − | 0.450861i | \(-0.148883\pi\) | |||||||
\(32\) | −142832. | − | 118147.i | −0.770552 | − | 0.637377i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 279296. | − | 290036.i | 1.21868 | − | 1.26554i | ||||
\(35\) | 96705.4i | 0.381252i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 61595.2i | 0.199913i | 0.994992 | + | 0.0999564i | \(0.0318703\pi\) | ||||
−0.994992 | + | 0.0999564i | \(0.968130\pi\) | |||||||
\(38\) | 131182. | + | 126324.i | 0.387820 | + | 0.373459i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 283804. | − | 317887.i | 0.701146 | − | 0.785350i | ||||
\(41\) | − | 232923.i | − | 0.527799i | −0.964550 | − | 0.263900i | \(-0.914991\pi\) | ||
0.964550 | − | 0.263900i | \(-0.0850088\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 619370. | 1.18798 | 0.593992 | − | 0.804471i | \(-0.297551\pi\) | ||||
0.593992 | + | 0.804471i | \(0.297551\pi\) | |||||||
\(44\) | 342811. | − | 12938.1i | 0.606694 | − | 0.0228974i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 94478.0 | + | 90979.6i | 0.143113 | + | 0.137813i | ||||
\(47\) | −1.07968e6 | −1.51689 | −0.758445 | − | 0.651738i | \(-0.774040\pi\) | ||||
−0.758445 | + | 0.651738i | \(0.774040\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 715543. | 0.868860 | ||||||||
\(50\) | 69003.1 | + | 66448.0i | 0.0780681 | + | 0.0751773i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 190074. | − | 7173.63i | 0.187461 | − | 0.00707502i | ||||
\(53\) | −713736. | −0.658524 | −0.329262 | − | 0.944239i | \(-0.606800\pi\) | ||||
−0.329262 | + | 0.944239i | \(0.606800\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 788666.i | 0.639180i | ||||||||
\(56\) | 355013. | + | 316950.i | 0.270139 | + | 0.241175i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.66278e6 | − | 1.60121e6i | −1.11902 | − | 1.07758i | ||||
\(59\) | − | 1.30458e6i | − | 0.826965i | −0.910512 | − | 0.413483i | \(-0.864312\pi\) | ||
0.910512 | − | 0.413483i | \(-0.135688\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.52680e6i | 0.861248i | 0.902531 | + | 0.430624i | \(0.141707\pi\) | ||||
−0.902531 | + | 0.430624i | \(0.858293\pi\) | |||||||
\(62\) | 1.17376e6 | − | 1.21890e6i | 0.625474 | − | 0.649526i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −236829. | − | 2.08374e6i | −0.112929 | − | 0.993603i | ||||
\(65\) | 437282.i | 0.197499i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.81113e6 | −1.95427 | −0.977137 | − | 0.212610i | \(-0.931804\pi\) | ||||
−0.977137 | + | 0.212610i | \(0.931804\pi\) | |||||||
\(68\) | 4.55222e6 | − | 171807.i | 1.75567 | − | 0.0662611i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −758914. | + | 788097.i | −0.264454 | + | 0.274623i | ||||
\(71\) | −4.36754e6 | −1.44821 | −0.724107 | − | 0.689688i | \(-0.757748\pi\) | ||||
−0.724107 | + | 0.689688i | \(0.757748\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.23348e6 | −0.371108 | −0.185554 | − | 0.982634i | \(-0.559408\pi\) | ||||
−0.185554 | + | 0.982634i | \(0.559408\pi\) | |||||||
\(74\) | −483380. | + | 501968.i | −0.138668 | + | 0.144001i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 77707.2 | + | 2.05895e6i | 0.0203055 | + | 0.538019i | ||||
\(77\) | −880774. | −0.219860 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.34474e6i | 1.21964i | 0.792540 | + | 0.609820i | \(0.208758\pi\) | ||||
−0.792540 | + | 0.609820i | \(0.791242\pi\) | |||||||
\(80\) | 4.80753e6 | − | 363402.i | 1.04980 | − | 0.0793547i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.82791e6 | − | 1.89820e6i | 0.366105 | − | 0.380183i | ||||
\(83\) | 6.96837e6i | 1.33770i | 0.743398 | + | 0.668849i | \(0.233213\pi\) | ||||
−0.743398 | + | 0.668849i | \(0.766787\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.04728e7i | 1.84968i | ||||||||
\(86\) | 5.04753e6 | + | 4.86063e6i | 0.855726 | + | 0.824039i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.89526e6 | + | 2.58483e6i | 0.452895 | + | 0.404337i | ||||
\(89\) | − | 166492.i | − | 0.0250338i | −0.999922 | − | 0.0125169i | \(-0.996016\pi\) | ||
0.999922 | − | 0.0125169i | \(-0.00398436\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −488352. | −0.0679341 | ||||||||
\(92\) | 55965.3 | + | 1.48287e6i | 0.00749310 | + | 0.198539i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.79884e6 | − | 8.47302e6i | −1.09264 | − | 1.05218i | ||||
\(95\) | −4.73678e6 | −0.566827 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.05299e6 | 0.784644 | 0.392322 | − | 0.919828i | \(-0.371672\pi\) | ||||
0.392322 | + | 0.919828i | \(0.371672\pi\) | |||||||
\(98\) | 5.83129e6 | + | 5.61536e6i | 0.625855 | + | 0.602680i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 40875.0 | + | 1.08303e6i | 0.00408750 | + | 0.108303i | ||||
\(101\) | −5.23205e6 | −0.505298 | −0.252649 | − | 0.967558i | \(-0.581302\pi\) | ||||
−0.252649 | + | 0.967558i | \(0.581302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.46478e7i | − | 1.32081i | −0.750909 | − | 0.660406i | \(-0.770384\pi\) | ||
0.750909 | − | 0.660406i | \(-0.229616\pi\) | |||||||
\(104\) | 1.60530e6 | + | 1.43318e6i | 0.139939 | + | 0.124935i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.81656e6 | − | 5.60118e6i | −0.474347 | − | 0.456782i | ||||
\(107\) | 7.81950e6i | 0.617072i | 0.951213 | + | 0.308536i | \(0.0998391\pi\) | ||||
−0.951213 | + | 0.308536i | \(0.900161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.32338e7i | 0.978794i | 0.872061 | + | 0.489397i | \(0.162783\pi\) | ||||
−0.872061 | + | 0.489397i | \(0.837217\pi\) | |||||||
\(110\) | −6.18920e6 | + | 6.42720e6i | −0.443364 | + | 0.460413i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 405844. | + | 5.36901e6i | 0.0272958 | + | 0.361103i | ||||
\(113\) | − | 2.35216e7i | − | 1.53353i | −0.641927 | − | 0.766765i | \(-0.721865\pi\) | ||
0.641927 | − | 0.766765i | \(-0.278135\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.41147e6 | −0.209170 | ||||||||
\(116\) | −984970. | − | 2.60980e7i | −0.0585896 | − | 1.55240i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.02379e7 | − | 1.06316e7i | 0.573620 | − | 0.595677i | ||||
\(119\) | −1.16959e7 | −0.636237 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.23042e7 | 0.631398 | ||||||||
\(122\) | −1.19819e7 | + | 1.24426e7i | −0.597400 | + | 0.620372i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.91311e7 | − | 722031.i | 0.901080 | − | 0.0340079i | ||||
\(125\) | 2.04979e7 | 0.938694 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.98987e7i | − | 1.29521i | −0.761978 | − | 0.647603i | \(-0.775772\pi\) | ||
0.761978 | − | 0.647603i | \(-0.224228\pi\) | |||||||
\(128\) | 1.44225e7 | − | 1.88399e7i | 0.607863 | − | 0.794042i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.43165e6 | + | 3.56361e6i | −0.136994 | + | 0.142262i | ||||
\(131\) | − | 9.48915e6i | − | 0.368789i | −0.982852 | − | 0.184394i | \(-0.940968\pi\) | ||
0.982852 | − | 0.184394i | \(-0.0590324\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.28999e6i | − | 0.194973i | ||||||
\(134\) | −3.92081e7 | − | 3.77563e7i | −1.40770 | − | 1.35557i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.84464e7 | + | 3.43243e7i | 1.31060 | + | 1.17008i | ||||
\(137\) | − | 1.01971e7i | − | 0.338809i | −0.985547 | − | 0.169404i | \(-0.945816\pi\) | ||
0.985547 | − | 0.169404i | \(-0.0541844\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.97951e7 | −1.57266 | −0.786330 | − | 0.617807i | \(-0.788021\pi\) | ||||
−0.786330 | + | 0.617807i | \(0.788021\pi\) | |||||||
\(140\) | −1.23695e7 | + | 466840.i | −0.380981 | + | 0.0143787i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.55931e7 | − | 3.42751e7i | −1.04317 | − | 1.00455i | ||||
\(143\) | −3.98268e6 | −0.113894 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00406e7 | 1.63553 | ||||||||
\(146\) | −1.00522e7 | − | 9.67994e6i | −0.267316 | − | 0.257417i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.87857e6 | + | 297347.i | −0.199771 | + | 0.00753960i | ||||
\(149\) | 6.45647e7 | 1.59898 | 0.799490 | − | 0.600680i | \(-0.205103\pi\) | ||||
0.799490 | + | 0.600680i | \(0.205103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.38149e7i | − | 1.50835i | −0.656672 | − | 0.754177i | \(-0.728036\pi\) | ||
0.656672 | − | 0.754177i | \(-0.271964\pi\) | |||||||
\(152\) | −1.55247e7 | + | 1.73891e7i | −0.358567 | + | 0.401629i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.17784e6 | − | 6.91205e6i | −0.158369 | − | 0.152505i | ||||
\(155\) | 4.40127e7i | 0.949329i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1.74778e7i | − | 0.360444i | −0.983626 | − | 0.180222i | \(-0.942318\pi\) | ||
0.983626 | − | 0.180222i | \(-0.0576816\pi\) | |||||||
\(158\) | −4.19438e7 | + | 4.35567e7i | −0.845996 | + | 0.878528i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.20307e7 | + | 3.47665e7i | 0.811234 | + | 0.671028i | ||||
\(161\) | − | 3.80989e6i | − | 0.0719486i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 52066.5 | 0.000941677 | 0.000470839 | − | 1.00000i | \(-0.499850\pi\) | ||||
0.000470839 | 1.00000i | \(0.499850\pi\) | ||||||||
\(164\) | 2.97929e7 | − | 1.12442e6i | 0.527424 | − | 0.0199056i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.46856e7 | + | 5.67885e7i | −0.927887 | + | 0.963567i | ||||
\(167\) | −1.62528e7 | −0.270036 | −0.135018 | − | 0.990843i | \(-0.543109\pi\) | ||||
−0.135018 | + | 0.990843i | \(0.543109\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.05403e7 | 0.964808 | ||||||||
\(170\) | −8.21871e7 | + | 8.53475e7i | −1.28302 | + | 1.33235i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.98998e6 | + | 7.92230e7i | 0.0448041 | + | 1.18714i | ||||
\(173\) | 1.18628e8 | 1.74191 | 0.870954 | − | 0.491364i | \(-0.163502\pi\) | ||||
0.870954 | + | 0.491364i | \(0.163502\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.78260e6i | − | 0.0392480i | ||||||
\(176\) | 3.30980e6 | + | 4.37861e7i | 0.0457622 | + | 0.605399i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.30657e6 | − | 1.35682e6i | 0.0173646 | − | 0.0180323i | ||||
\(179\) | 4.22356e7i | 0.550419i | 0.961384 | + | 0.275210i | \(0.0887472\pi\) | ||||
−0.961384 | + | 0.275210i | \(0.911253\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.16870e8i | 1.46497i | 0.680781 | + | 0.732487i | \(0.261640\pi\) | ||||
−0.680781 | + | 0.732487i | \(0.738360\pi\) | |||||||
\(182\) | −3.97981e6 | − | 3.83244e6i | −0.0489342 | − | 0.0471222i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.11810e7 | + | 1.25238e7i | −0.132318 | + | 0.148208i | ||||
\(185\) | − | 1.81253e7i | − | 0.210468i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.53841e7 | −1.06667 | ||||||||
\(188\) | −5.21211e6 | − | 1.38101e8i | −0.0572086 | − | 1.51581i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.86022e7 | − | 3.71728e7i | −0.408296 | − | 0.393177i | ||||
\(191\) | 1.46598e8 | 1.52234 | 0.761171 | − | 0.648551i | \(-0.224625\pi\) | ||||
0.761171 | + | 0.648551i | \(0.224625\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.92822e7 | −0.994079 | −0.497039 | − | 0.867728i | \(-0.665580\pi\) | ||||
−0.497039 | + | 0.867728i | \(0.665580\pi\) | |||||||
\(194\) | 5.74781e7 | + | 5.53497e7i | 0.565192 | + | 0.544264i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.45425e6 | + | 9.15244e7i | 0.0327685 | + | 0.868242i | ||||
\(197\) | −2.90394e7 | −0.270618 | −0.135309 | − | 0.990803i | \(-0.543203\pi\) | ||||
−0.135309 | + | 0.990803i | \(0.543203\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.90948e8i | − | 1.71763i | −0.512288 | − | 0.858814i | \(-0.671202\pi\) | ||
0.512288 | − | 0.858814i | \(-0.328798\pi\) | |||||||
\(200\) | −8.16618e6 | + | 9.14689e6i | −0.0721796 | + | 0.0808479i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.26384e7 | − | 4.10595e7i | −0.363975 | − | 0.350497i | ||||
\(203\) | 6.70528e7i | 0.562576i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.85412e7i | 0.555665i | ||||||||
\(206\) | 1.14951e8 | − | 1.19371e8i | 0.916174 | − | 0.951403i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.83514e6 | + | 2.42775e7i | 0.0141400 | + | 0.187061i | ||||
\(209\) | − | 4.31417e7i | − | 0.326878i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.21971e8 | −0.893854 | −0.446927 | − | 0.894570i | \(-0.647482\pi\) | ||||
−0.446927 | + | 0.894570i | \(0.647482\pi\) | |||||||
\(212\) | −3.44552e6 | − | 9.12932e7i | −0.0248359 | − | 0.658056i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.13651e7 | + | 6.37247e7i | −0.428029 | + | 0.444488i | ||||
\(215\) | −1.82259e8 | −1.25071 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.91530e7 | −0.326543 | ||||||||
\(218\) | −1.03855e8 | + | 1.07848e8i | −0.678935 | + | 0.705042i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00877e8 | + | 3.80724e6i | −0.638726 | + | 0.0241063i | ||||
\(221\) | −5.28864e7 | −0.329588 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.53524e8i | 1.53092i | 0.643483 | + | 0.765460i | \(0.277489\pi\) | ||||
−0.643483 | + | 0.765460i | \(0.722511\pi\) | |||||||
\(224\) | −3.88269e7 | + | 4.69394e7i | −0.230815 | + | 0.279042i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.84590e8 | − | 1.91688e8i | 1.06373 | − | 1.10463i | ||||
\(227\) | 7.31259e7i | 0.414936i | 0.978242 | + | 0.207468i | \(0.0665222\pi\) | ||||
−0.978242 | + | 0.207468i | \(0.933478\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.41665e7i | − | 0.243035i | −0.992589 | − | 0.121518i | \(-0.961224\pi\) | ||
0.992589 | − | 0.121518i | \(-0.0387761\pi\) | |||||||
\(230\) | −2.78016e7 | − | 2.67721e7i | −0.150669 | − | 0.145089i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.96782e8 | − | 2.20414e8i | 1.03461 | − | 1.15886i | ||||
\(233\) | − | 1.86368e8i | − | 0.965219i | −0.875836 | − | 0.482609i | \(-0.839689\pi\) | ||
0.875836 | − | 0.482609i | \(-0.160311\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.17714e8 | 1.59698 | ||||||||
\(236\) | 1.66867e8 | − | 6.29777e6i | 0.826377 | − | 0.0311885i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.53152e7 | − | 9.17858e7i | −0.458293 | − | 0.441323i | ||||
\(239\) | −6.04324e7 | −0.286337 | −0.143168 | − | 0.989698i | \(-0.545729\pi\) | ||||
−0.143168 | + | 0.989698i | \(0.545729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.53357e8 | 1.16593 | 0.582965 | − | 0.812497i | \(-0.301892\pi\) | ||||
0.582965 | + | 0.812497i | \(0.301892\pi\) | |||||||
\(242\) | 1.00272e8 | + | 9.65592e7i | 0.454807 | + | 0.437966i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.95292e8 | + | 7.37055e6i | −0.860636 | + | 0.0324815i | ||||
\(245\) | −2.10560e8 | −0.914732 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.39203e7i | − | 0.101001i | ||||||
\(248\) | 1.61574e8 | + | 1.44251e8i | 0.672653 | + | 0.600533i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.67047e8 | + | 1.60861e8i | 0.676158 | + | 0.651120i | ||||
\(251\) | − | 4.32231e8i | − | 1.72527i | −0.505825 | − | 0.862636i | \(-0.668812\pi\) | ||
0.505825 | − | 0.862636i | \(-0.331188\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.10710e7i | − | 0.120624i | ||||||
\(254\) | 2.34635e8 | − | 2.43658e8i | 0.898412 | − | 0.932959i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.65385e8 | − | 4.03516e7i | 0.988637 | − | 0.150321i | ||||
\(257\) | 3.53732e8i | 1.29990i | 0.759978 | + | 0.649948i | \(0.225210\pi\) | ||||
−0.759978 | + | 0.649948i | \(0.774790\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.02422e7 | 0.0723950 | ||||||||
\(260\) | −5.59322e7 | + | 2.11095e6i | −0.197358 | + | 0.00744855i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.44679e7 | − | 7.73315e7i | 0.255808 | − | 0.265645i | ||||
\(263\) | −3.41375e8 | −1.15714 | −0.578571 | − | 0.815632i | \(-0.696389\pi\) | ||||
−0.578571 | + | 0.815632i | \(0.696389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.10028e8 | 0.693292 | ||||||||
\(266\) | 4.15142e7 | − | 4.31106e7i | 0.135242 | − | 0.140442i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.32255e7 | − | 6.15387e8i | −0.0737043 | − | 1.95288i | ||||
\(269\) | −4.19128e8 | −1.31284 | −0.656422 | − | 0.754394i | \(-0.727931\pi\) | ||||
−0.656422 | + | 0.754394i | \(0.727931\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.31720e8i | 1.01246i | 0.862397 | + | 0.506232i | \(0.168962\pi\) | ||||
−0.862397 | + | 0.506232i | \(0.831038\pi\) | |||||||
\(272\) | 4.39512e7 | + | 5.81440e8i | 0.132428 | + | 1.75192i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.00237e7 | − | 8.31009e7i | 0.235013 | − | 0.244050i | ||||
\(275\) | − | 2.26931e7i | − | 0.0658005i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.71149e8i | − | 0.483834i | −0.970297 | − | 0.241917i | \(-0.922224\pi\) | ||
0.970297 | − | 0.241917i | \(-0.0777761\pi\) | |||||||
\(278\) | −4.05803e8 | − | 3.90776e8i | −1.13281 | − | 1.09087i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.04468e8 | − | 9.32674e7i | −0.284401 | − | 0.253908i | ||||
\(281\) | 3.60548e8i | 0.969374i | 0.874688 | + | 0.484687i | \(0.161066\pi\) | ||||
−0.874688 | + | 0.484687i | \(0.838934\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.88163e7 | 0.206711 | 0.103356 | − | 0.994644i | \(-0.467042\pi\) | ||||
0.103356 | + | 0.994644i | \(0.467042\pi\) | |||||||
\(284\) | −2.10841e7 | − | 5.58647e8i | −0.0546185 | − | 1.44718i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.24567e7 | − | 3.12548e7i | −0.0820395 | − | 0.0790017i | ||||
\(287\) | −7.65462e7 | −0.191134 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.56276e8 | −2.08675 | ||||||||
\(290\) | 4.89299e8 | + | 4.71180e8i | 1.17810 | + | 1.13447i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.95454e6 | − | 1.57773e8i | −0.0139961 | − | 0.370844i | ||||
\(293\) | −1.16444e7 | −0.0270447 | −0.0135223 | − | 0.999909i | \(-0.504304\pi\) | ||||
−0.0135223 | + | 0.999909i | \(0.504304\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.83892e8i | 0.870626i | ||||||||
\(296\) | −6.65396e7 | − | 5.94054e7i | −0.149128 | − | 0.133139i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.26167e8 | + | 5.06684e8i | 1.15177 | + | 1.10912i | ||||
\(299\) | − | 1.72276e7i | − | 0.0372713i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.03545e8i | − | 0.430208i | ||||||
\(302\) | 5.00800e8 | − | 5.20057e8i | 1.04626 | − | 1.08649i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.62982e8 | + | 1.98789e7i | −0.536870 | + | 0.0405821i | ||||
\(305\) | − | 4.49285e8i | − | 0.906719i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.71307e8 | 0.732401 | 0.366201 | − | 0.930536i | \(-0.380658\pi\) | ||||
0.366201 | + | 0.930536i | \(0.380658\pi\) | |||||||
\(308\) | −4.25189e6 | − | 1.12659e8i | −0.00829191 | − | 0.219704i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.45398e8 | + | 3.58680e8i | −0.658497 | + | 0.683819i | ||||
\(311\) | 5.55339e8 | 1.04688 | 0.523440 | − | 0.852063i | \(-0.324648\pi\) | ||||
0.523440 | + | 0.852063i | \(0.324648\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.90438e8 | −1.27268 | −0.636340 | − | 0.771408i | \(-0.719553\pi\) | ||||
−0.636340 | + | 0.771408i | \(0.719553\pi\) | |||||||
\(314\) | 1.37160e8 | − | 1.42435e8i | 0.250020 | − | 0.259634i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.83640e8 | + | 2.58014e7i | −1.21877 | + | 0.0459980i | ||||
\(317\) | −6.87240e7 | −0.121172 | −0.0605858 | − | 0.998163i | \(-0.519297\pi\) | ||||
−0.0605858 | + | 0.998163i | \(0.519297\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.46839e8i | 0.943174i | ||||||||
\(320\) | 6.96905e7 | + | 6.13172e8i | 0.118891 | + | 1.04606i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.98989e7 | − | 3.10486e7i | 0.0499068 | − | 0.0518258i | ||||
\(323\) | − | 5.72883e8i | − | 0.945927i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.25824e7i | − | 0.0203315i | ||||||
\(326\) | 424314. | + | 408602.i | 0.000678306 | + | 0.000653189i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.51620e8 | + | 2.24642e8i | 0.393720 | + | 0.351506i | ||||
\(329\) | 3.54820e8i | 0.549315i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.13679e8 | −0.172299 | −0.0861496 | − | 0.996282i | \(-0.527456\pi\) | ||||
−0.0861496 | + | 0.996282i | \(0.527456\pi\) | |||||||
\(332\) | −8.91317e8 | + | 3.36394e7i | −1.33675 | + | 0.0504505i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.32452e8 | − | 1.27547e8i | −0.194511 | − | 0.187309i | ||||
\(335\) | 1.41575e9 | 2.05745 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.16559e8 | 0.165898 | 0.0829492 | − | 0.996554i | \(-0.473566\pi\) | ||||
0.0829492 | + | 0.996554i | \(0.473566\pi\) | |||||||
\(338\) | 4.93371e8 | + | 4.75102e8i | 0.694968 | + | 0.669234i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.33956e9 | + | 5.05567e7i | −1.84836 | + | 0.0697594i | ||||
\(341\) | −4.00859e8 | −0.547459 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 5.05795e8i | − | 0.676776i | ||||||
\(344\) | −5.97351e8 | + | 6.69089e8i | −0.791179 | + | 0.886195i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.66753e8 | + | 9.30955e8i | 1.25473 | + | 1.20827i | ||||
\(347\) | 7.74986e8i | 0.995729i | 0.867255 | + | 0.497864i | \(0.165882\pi\) | ||||
−0.867255 | + | 0.497864i | \(0.834118\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.75593e8i | − | 0.347039i | −0.984830 | − | 0.173520i | \(-0.944486\pi\) | ||
0.984830 | − | 0.173520i | \(-0.0555140\pi\) | |||||||
\(350\) | 2.18370e7 | − | 2.26767e7i | 0.0272242 | − | 0.0282710i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.16647e8 | + | 3.82807e8i | −0.386969 | + | 0.467822i | ||||
\(353\) | 7.91797e8i | 0.958081i | 0.877793 | + | 0.479041i | \(0.159015\pi\) | ||||
−0.877793 | + | 0.479041i | \(0.840985\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.28522e9 | 1.52467 | ||||||||
\(356\) | 2.12958e7 | − | 803729.i | 0.0250160 | − | 0.000944136i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.31452e8 | + | 3.44198e8i | −0.381795 | + | 0.396477i | ||||
\(359\) | 4.47158e8 | 0.510071 | 0.255035 | − | 0.966932i | \(-0.417913\pi\) | ||||
0.255035 | + | 0.966932i | \(0.417913\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.34759e8 | −0.710124 | ||||||||
\(362\) | −9.17163e8 | + | 9.52431e8i | −1.01617 | + | 1.05525i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.35749e6 | − | 6.24646e7i | −0.00256210 | − | 0.0678858i | ||||
\(365\) | 3.62970e8 | 0.390702 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.59899e8i | 0.696861i | 0.937335 | + | 0.348431i | \(0.113285\pi\) | ||||
−0.937335 | + | 0.348431i | \(0.886715\pi\) | |||||||
\(368\) | −1.89402e8 | + | 1.43169e7i | −0.198115 | + | 0.0149755i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.42242e8 | − | 1.47712e8i | 0.145990 | − | 0.151603i | ||||
\(371\) | 2.34557e8i | 0.238473i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.64257e9i | − | 1.63886i | −0.573177 | − | 0.819432i | \(-0.694289\pi\) | ||
0.573177 | − | 0.819432i | \(-0.305711\pi\) | |||||||
\(374\) | −7.77329e8 | − | 7.48545e8i | −0.768341 | − | 0.739890i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.04130e9 | − | 1.16635e9i | 1.01022 | − | 1.13155i | ||||
\(377\) | 3.03199e8i | 0.291429i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.91034e8 | −0.463313 | −0.231656 | − | 0.972798i | \(-0.574414\pi\) | ||||
−0.231656 | + | 0.972798i | \(0.574414\pi\) | |||||||
\(380\) | −2.28666e7 | − | 6.05877e8i | −0.0213776 | − | 0.566424i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.19470e9 | + | 1.15046e9i | 1.09657 | + | 1.05596i | ||||
\(383\) | 2.15258e8 | 0.195778 | 0.0978889 | − | 0.995197i | \(-0.468791\pi\) | ||||
0.0978889 | + | 0.995197i | \(0.468791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.59182e8 | 0.231468 | ||||||||
\(386\) | −8.09097e8 | − | 7.79136e8i | −0.716052 | − | 0.689537i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.40479e7 | + | 9.02141e8i | 0.0295924 | + | 0.784085i | ||||
\(389\) | 1.68469e9 | 1.45109 | 0.725547 | − | 0.688172i | \(-0.241587\pi\) | ||||
0.725547 | + | 0.688172i | \(0.241587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.12595e8i | − | 0.349064i | ||||||
\(392\) | −6.90105e8 | + | 7.72982e8i | −0.578647 | + | 0.648139i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.36656e8 | − | 2.27892e8i | −0.194931 | − | 0.187712i | ||||
\(395\) | − | 1.57277e9i | − | 1.28403i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 8.46867e8i | − | 0.679280i | −0.940556 | − | 0.339640i | \(-0.889695\pi\) | ||
0.940556 | − | 0.339640i | \(-0.110305\pi\) | |||||||
\(398\) | 1.49850e9 | − | 1.55612e9i | 1.19142 | − | 1.23724i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.38332e8 | + | 1.04565e7i | −0.108072 | + | 0.00816917i | ||||
\(401\) | − | 3.67705e8i | − | 0.284770i | −0.989811 | − | 0.142385i | \(-0.954523\pi\) | ||
0.989811 | − | 0.142385i | \(-0.0454771\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.22260e8 | −0.169158 | ||||||||
\(404\) | −2.52574e7 | − | 6.69226e8i | −0.0190570 | − | 0.504938i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.26210e8 | + | 5.46444e8i | −0.390227 | + | 0.405233i | ||||
\(407\) | 1.65082e8 | 0.121372 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.91851e8 | 0.210925 | 0.105463 | − | 0.994423i | \(-0.466368\pi\) | ||||
0.105463 | + | 0.994423i | \(0.466368\pi\) | |||||||
\(410\) | −5.37890e8 | + | 5.58574e8i | −0.385434 | + | 0.400255i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.87358e9 | − | 7.07112e7i | 1.31987 | − | 0.0498136i | ||||
\(413\) | −4.28726e8 | −0.299471 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.05055e9i | − | 1.40832i | ||||||
\(416\) | −1.75567e8 | + | 2.12250e8i | −0.119568 | + | 0.144551i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.38563e8 | − | 3.51582e8i | 0.226737 | − | 0.235456i | ||||
\(419\) | − | 8.75874e8i | − | 0.581691i | −0.956770 | − | 0.290845i | \(-0.906063\pi\) | ||
0.956770 | − | 0.290845i | \(-0.0939366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.93556e8i | 0.257051i | 0.991706 | + | 0.128526i | \(0.0410244\pi\) | ||||
−0.991706 | + | 0.128526i | \(0.958976\pi\) | |||||||
\(422\) | −9.93995e8 | − | 9.57188e8i | −0.643859 | − | 0.620017i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.88362e8 | − | 7.71030e8i | 0.438567 | − | 0.491236i | ||||
\(425\) | − | 3.01344e8i | − | 0.190415i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.01758e8 | 0.311886 | ||||||||
\(428\) | −1.00018e9 | + | 3.77482e7i | −0.616633 | + | 0.0232725i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.48532e9 | − | 1.43032e9i | −0.900905 | − | 0.867545i | ||||
\(431\) | −2.03454e9 | −1.22404 | −0.612020 | − | 0.790842i | \(-0.709643\pi\) | ||||
−0.612020 | + | 0.790842i | \(0.709643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.34016e9 | 0.793318 | 0.396659 | − | 0.917966i | \(-0.370169\pi\) | ||||
0.396659 | + | 0.917966i | \(0.370169\pi\) | |||||||
\(434\) | −4.00570e8 | − | 3.85737e8i | −0.235215 | − | 0.226505i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.69272e9 | + | 6.38854e7i | −0.978098 | + | 0.0369146i | ||||
\(437\) | 1.86615e8 | 0.106970 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.78225e9i | 1.00541i | 0.864459 | + | 0.502704i | \(0.167661\pi\) | ||||
−0.864459 | + | 0.502704i | \(0.832339\pi\) | |||||||
\(440\) | −8.51974e8 | − | 7.60628e8i | −0.476806 | − | 0.425684i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.30996e8 | − | 4.15036e8i | −0.237408 | − | 0.228617i | ||||
\(443\) | − | 7.08329e8i | − | 0.387099i | −0.981090 | − | 0.193550i | \(-0.938000\pi\) | ||
0.981090 | − | 0.193550i | \(-0.0620000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.89927e7i | 0.0263555i | ||||||||
\(446\) | −1.98958e9 | + | 2.06609e9i | −1.06191 | + | 1.10275i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.84785e8 | + | 7.78297e7i | −0.359816 | + | 0.0408952i | ||||
\(449\) | − | 1.08114e9i | − | 0.563665i | −0.959464 | − | 0.281832i | \(-0.909058\pi\) | ||
0.959464 | − | 0.281832i | \(-0.0909422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.24260e8 | −0.320441 | ||||||||
\(452\) | 3.00862e9 | − | 1.13549e8i | 1.53244 | − | 0.0578362i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.73870e8 | + | 5.95937e8i | −0.287818 | + | 0.298885i | ||||
\(455\) | 1.43705e8 | 0.0715208 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.45370e8 | 0.365313 | 0.182657 | − | 0.983177i | \(-0.441530\pi\) | ||||
0.182657 | + | 0.983177i | \(0.441530\pi\) | |||||||
\(458\) | 3.46605e8 | − | 3.59933e8i | 0.168580 | − | 0.175062i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.64687e7 | − | 4.36357e8i | −0.00788871 | − | 0.209021i | ||||
\(461\) | −1.30861e8 | −0.0622097 | −0.0311048 | − | 0.999516i | \(-0.509903\pi\) | ||||
−0.0311048 | + | 0.999516i | \(0.509903\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.29457e9i | − | 1.54264i | −0.636447 | − | 0.771321i | \(-0.719597\pi\) | ||
0.636447 | − | 0.771321i | \(-0.280403\pi\) | |||||||
\(464\) | 3.33341e9 | − | 2.51973e8i | 1.54909 | − | 0.117096i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.46256e9 | − | 1.51880e9i | 0.669519 | − | 0.695264i | ||||
\(467\) | 3.84572e9i | 1.74731i | 0.486549 | + | 0.873653i | \(0.338255\pi\) | ||||
−0.486549 | + | 0.873653i | \(0.661745\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.58110e9i | 0.707707i | ||||||||
\(470\) | 2.58919e9 | + | 2.49332e9i | 1.15033 | + | 1.10773i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.40930e9 | + | 1.25820e9i | 0.616887 | + | 0.550746i | ||||
\(473\) | − | 1.65998e9i | − | 0.721257i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.36296e8 | 0.0583521 | ||||||||
\(476\) | −5.64613e7 | − | 1.49601e9i | −0.0239953 | − | 0.635785i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.92492e8 | − | 4.74255e8i | −0.206253 | − | 0.198616i | ||||
\(479\) | −1.27149e9 | −0.528616 | −0.264308 | − | 0.964438i | \(-0.585143\pi\) | ||||
−0.264308 | + | 0.964438i | \(0.585143\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.15311e7 | 0.0375026 | ||||||||
\(482\) | 2.06472e9 | + | 1.98827e9i | 0.839840 | + | 0.808741i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.93976e7 | + | 1.57381e9i | 0.0238128 | + | 0.630948i | ||||
\(485\) | −2.07545e9 | −0.826070 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.64160e9i | 1.03637i | 0.855268 | + | 0.518185i | \(0.173392\pi\) | ||||
−0.855268 | + | 0.518185i | \(0.826608\pi\) | |||||||
\(488\) | −1.64936e9 | − | 1.47252e9i | −0.642461 | − | 0.573578i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.71595e9 | − | 1.65241e9i | −0.658898 | − | 0.634499i | ||||
\(491\) | 1.97319e9i | 0.752285i | 0.926562 | + | 0.376143i | \(0.122750\pi\) | ||||
−0.926562 | + | 0.376143i | \(0.877250\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.26153e9i | 2.72938i | ||||||||
\(494\) | 1.87719e8 | − | 1.94937e8i | 0.0700589 | − | 0.0727529i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.84708e8 | + | 2.44355e9i | 0.0679674 | + | 0.899157i | ||||
\(497\) | 1.43532e9i | 0.524446i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.39385e9 | −1.58304 | −0.791522 | − | 0.611140i | \(-0.790711\pi\) | ||||
−0.791522 | + | 0.611140i | \(0.790711\pi\) | |||||||
\(500\) | 9.89524e7 | + | 2.62186e9i | 0.0354023 | + | 0.938026i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.39201e9 | − | 3.52245e9i | 1.19673 | − | 1.24274i | ||||
\(503\) | 1.42589e8 | 0.0499574 | 0.0249787 | − | 0.999688i | \(-0.492048\pi\) | ||||
0.0249787 | + | 0.999688i | \(0.492048\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.53961e9 | 0.531975 | ||||||||
\(506\) | 2.43836e8 | − | 2.53212e8i | 0.0836701 | − | 0.0868875i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.82430e9 | − | 1.44334e8i | 1.29428 | − | 0.0488479i | ||||
\(509\) | 3.09362e8 | 0.103981 | 0.0519906 | − | 0.998648i | \(-0.483443\pi\) | ||||
0.0519906 | + | 0.998648i | \(0.483443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.05361e8i | 0.134391i | ||||||||
\(512\) | 2.47941e9 | + | 1.75382e9i | 0.816402 | + | 0.577484i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.77598e9 | + | 2.88273e9i | −0.901666 | + | 0.936338i | ||||
\(515\) | 4.31033e9i | 1.39055i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.89368e9i | 0.920943i | ||||||||
\(518\) | 1.64963e8 | + | 1.58855e8i | 0.0521474 | + | 0.0502164i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.72384e8 | − | 4.21736e8i | −0.147327 | − | 0.131531i | ||||
\(521\) | − | 2.29488e8i | − | 0.0710932i | −0.999368 | − | 0.0355466i | \(-0.988683\pi\) | ||
0.999368 | − | 0.0355466i | \(-0.0113172\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.09139e9 | −0.944926 | −0.472463 | − | 0.881351i | \(-0.656635\pi\) | ||||
−0.472463 | + | 0.881351i | \(0.656635\pi\) | |||||||
\(524\) | 1.21375e9 | − | 4.58083e7i | 0.368526 | − | 0.0139087i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.78202e9 | − | 2.67901e9i | −0.833510 | − | 0.802645i | ||||
\(527\) | −5.32305e9 | −1.58425 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.27042e9 | −0.960526 | ||||||||
\(530\) | 1.71161e9 | + | 1.64823e9i | 0.499390 | + | 0.480898i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.76637e8 | − | 2.55372e7i | 0.194834 | − | 0.00735329i | ||||
\(533\) | −3.46126e8 | −0.0990123 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.30101e9i | − | 0.649651i | ||||||
\(536\) | 4.64009e9 | − | 5.19734e9i | 1.30152 | − | 1.45782i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.41566e9 | − | 3.28918e9i | −0.945665 | − | 0.910648i | ||||
\(539\) | − | 1.91774e9i | − | 0.527508i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 3.25383e9i | − | 0.883497i | −0.897139 | − | 0.441748i | \(-0.854358\pi\) | ||
0.897139 | − | 0.441748i | \(-0.145642\pi\) | |||||||
\(542\) | −2.60324e9 | + | 2.70334e9i | −0.702290 | + | 0.729296i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.20478e9 | + | 5.08334e9i | −1.11982 | + | 1.35380i | ||||
\(545\) | − | 3.89425e9i | − | 1.03047i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.49458e9 | 0.390449 | 0.195224 | − | 0.980759i | \(-0.437457\pi\) | ||||
0.195224 | + | 0.980759i | \(0.437457\pi\) | |||||||
\(548\) | 1.30430e9 | − | 4.92259e7i | 0.338568 | − | 0.0127780i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.78088e8 | − | 1.84936e8i | 0.0456421 | − | 0.0473972i | ||||
\(551\) | −3.28435e9 | −0.836410 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.75646e9 | 0.441672 | ||||||||
\(554\) | 1.34313e9 | − | 1.39478e9i | 0.335609 | − | 0.348514i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.40383e8 | − | 6.36923e9i | −0.0593119 | − | 1.57154i | ||||
\(557\) | 4.01514e9 | 0.984483 | 0.492241 | − | 0.870459i | \(-0.336178\pi\) | ||||
0.492241 | + | 0.870459i | \(0.336178\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.20391e8i | − | 0.222859i | ||||||
\(560\) | −1.19426e8 | − | 1.57991e9i | −0.0287369 | − | 0.380168i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.82947e9 | + | 2.93827e9i | −0.672401 | + | 0.698257i | ||||
\(563\) | − | 2.87925e9i | − | 0.679987i | −0.940428 | − | 0.339994i | \(-0.889575\pi\) | ||
0.940428 | − | 0.339994i | \(-0.110425\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.92160e9i | 1.61450i | ||||||||
\(566\) | 6.42311e8 | + | 6.18526e8i | 0.148898 | + | 0.143384i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.21227e9 | − | 4.71814e9i | 0.964488 | − | 1.08032i | ||||
\(569\) | − | 1.91695e9i | − | 0.436233i | −0.975923 | − | 0.218116i | \(-0.930009\pi\) | ||
0.975923 | − | 0.218116i | \(-0.0699912\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.99834e9 | −0.898779 | −0.449389 | − | 0.893336i | \(-0.648358\pi\) | ||||
−0.449389 | + | 0.893336i | \(0.648358\pi\) | |||||||
\(572\) | −1.92262e7 | − | 5.09420e8i | −0.00429543 | − | 0.113813i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.23810e8 | − | 6.00711e8i | −0.137677 | − | 0.132579i | ||||
\(575\) | 9.81616e7 | 0.0215330 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.39033e9 | 1.81829 | 0.909146 | − | 0.416477i | \(-0.136735\pi\) | ||||
0.909146 | + | 0.416477i | \(0.136735\pi\) | |||||||
\(578\) | −6.97819e9 | − | 6.71979e9i | −1.50313 | − | 1.44747i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.89843e8 | + | 7.67973e9i | 0.0616829 | + | 1.63436i | ||||
\(581\) | 2.29004e9 | 0.484424 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.91289e9i | 0.399808i | ||||||||
\(584\) | 1.18962e9 | − | 1.33249e9i | 0.247153 | − | 0.276834i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.48959e7 | − | 9.13820e7i | −0.0194808 | − | 0.0187594i | ||||
\(587\) | − | 4.84669e9i | − | 0.989036i | −0.869167 | − | 0.494518i | \(-0.835345\pi\) | ||
0.869167 | − | 0.494518i | \(-0.164655\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.40759e9i | − | 0.485489i | ||||||
\(590\) | −3.01266e9 | + | 3.12851e9i | −0.603905 | + | 0.627127i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.60668e7 | − | 1.00630e9i | −0.0150685 | − | 0.199344i | ||||
\(593\) | 3.59521e9i | 0.708000i | 0.935245 | + | 0.354000i | \(0.115179\pi\) | ||||
−0.935245 | + | 0.354000i | \(0.884821\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.44170e9 | 0.669828 | ||||||||
\(596\) | 3.11682e8 | + | 8.25840e9i | 0.0603046 | + | 1.59784i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.35197e8 | − | 1.40395e8i | 0.0258530 | − | 0.0268472i | ||||
\(599\) | 3.60041e8 | 0.0684476 | 0.0342238 | − | 0.999414i | \(-0.489104\pi\) | ||||
0.0342238 | + | 0.999414i | \(0.489104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.21055e9 | 0.979091 | 0.489545 | − | 0.871978i | \(-0.337163\pi\) | ||||
0.489545 | + | 0.871978i | \(0.337163\pi\) | |||||||
\(602\) | 1.59736e9 | − | 1.65879e9i | 0.298412 | − | 0.309887i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.16250e9 | − | 3.08063e8i | 1.50728 | − | 0.0568867i | ||||
\(605\) | −3.62069e9 | −0.664733 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.88101e9i | − | 1.43028i | −0.698980 | − | 0.715141i | \(-0.746363\pi\) | ||
0.698980 | − | 0.715141i | \(-0.253637\pi\) | |||||||
\(608\) | −2.29917e9 | − | 1.90180e9i | −0.414866 | − | 0.343165i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.52585e9 | − | 3.66143e9i | 0.628941 | − | 0.653126i | ||||
\(611\) | 1.60442e9i | 0.284560i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.47669e9i | − | 1.48633i | −0.669109 | − | 0.743164i | \(-0.733324\pi\) | ||
0.669109 | − | 0.743164i | \(-0.266676\pi\) | |||||||
\(614\) | 3.02595e9 | + | 2.91390e9i | 0.527561 | + | 0.508026i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.49462e8 | − | 9.51477e8i | 0.146424 | − | 0.164008i | ||||
\(617\) | 1.30414e9i | 0.223525i | 0.993735 | + | 0.111762i | \(0.0356495\pi\) | ||||
−0.993735 | + | 0.111762i | \(0.964350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.50616e9 | −0.594175 | −0.297087 | − | 0.954850i | \(-0.596015\pi\) | ||||
−0.297087 | + | 0.954850i | \(0.596015\pi\) | |||||||
\(620\) | −5.62962e9 | + | 2.12469e8i | −0.948654 | + | 0.0358034i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.52571e9 | + | 4.35813e9i | 0.754086 | + | 0.726163i | ||||
\(623\) | −5.47146e7 | −0.00906557 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.69332e9 | −1.09663 | ||||||||
\(626\) | −5.62670e9 | − | 5.41835e9i | −0.916734 | − | 0.882788i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.23556e9 | − | 8.43730e7i | 0.360187 | − | 0.0135939i | ||||
\(629\) | 2.19214e9 | 0.351230 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.18649e9i | − | 0.346453i | −0.984882 | − | 0.173226i | \(-0.944581\pi\) | ||
0.984882 | − | 0.173226i | \(-0.0554193\pi\) | |||||||
\(632\) | −5.77378e9 | − | 5.15473e9i | −0.909809 | − | 0.812261i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.60064e8 | − | 5.39325e8i | −0.0872821 | − | 0.0840501i | ||||
\(635\) | 8.79814e9i | 1.36359i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.06330e9i | − | 0.162993i | ||||||
\(638\) | −4.29142e9 | + | 4.45644e9i | −0.654228 | + | 0.679385i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.24404e9 | + | 5.54393e9i | −0.639956 | + | 0.835965i | ||||
\(641\) | − | 3.64284e9i | − | 0.546308i | −0.961970 | − | 0.273154i | \(-0.911933\pi\) | ||
0.961970 | − | 0.273154i | \(-0.0880668\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.02912e10 | 1.52661 | 0.763304 | − | 0.646040i | \(-0.223576\pi\) | ||||
0.763304 | + | 0.646040i | \(0.223576\pi\) | |||||||
\(644\) | 4.87320e8 | − | 1.83921e7i | 0.0718974 | − | 0.00271350i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.49581e9 | − | 4.66869e9i | 0.656137 | − | 0.681367i | ||||
\(647\) | 8.42123e9 | 1.22239 | 0.611196 | − | 0.791479i | \(-0.290689\pi\) | ||||
0.611196 | + | 0.791479i | \(0.290689\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.49641e9 | −0.502072 | ||||||||
\(650\) | 9.87424e7 | − | 1.02539e8i | 0.0141029 | − | 0.0146452i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 251348. | + | 6.65977e6i | 3.55148e−5 | + | 0.000941007i | ||||
\(653\) | 7.12964e9 | 1.00201 | 0.501004 | − | 0.865445i | \(-0.332964\pi\) | ||||
0.501004 | + | 0.865445i | \(0.332964\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.79233e9i | 0.388260i | ||||||||
\(656\) | 2.87647e8 | + | 3.80535e9i | 0.0397830 | + | 0.526298i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.78451e9 | + | 2.89159e9i | −0.381030 | + | 0.395682i | ||||
\(659\) | 2.28313e9i | 0.310765i | 0.987854 | + | 0.155383i | \(0.0496610\pi\) | ||||
−0.987854 | + | 0.155383i | \(0.950339\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.04167e10i | − | 1.40290i | −0.712719 | − | 0.701450i | \(-0.752536\pi\) | ||
0.712719 | − | 0.701450i | \(-0.247464\pi\) | |||||||
\(662\) | −9.26424e8 | − | 8.92119e8i | −0.124110 | − | 0.119514i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.52774e9 | − | 6.72064e9i | −0.997876 | − | 0.890886i | ||||
\(665\) | 1.55666e9i | 0.205267i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.36542e9 | −0.308651 | ||||||||
\(668\) | −7.84596e7 | − | 2.07888e9i | −0.0101842 | − | 0.269843i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.15376e10 | + | 1.11104e10i | 1.48202 | + | 1.42714i | ||||
\(671\) | 4.09201e9 | 0.522887 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.55647e8 | 0.0702661 | 0.0351331 | − | 0.999383i | \(-0.488814\pi\) | ||||
0.0351331 | + | 0.999383i | \(0.488814\pi\) | |||||||
\(674\) | 9.49895e8 | + | 9.14721e8i | 0.119500 | + | 0.115075i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.92255e8 | + | 7.74364e9i | 0.0363872 | + | 0.964122i | ||||
\(677\) | −3.52244e9 | −0.436298 | −0.218149 | − | 0.975916i | \(-0.570002\pi\) | ||||
−0.218149 | + | 0.975916i | \(0.570002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.31785e9i | − | 0.284145i | ||||||
\(680\) | −1.13135e10 | − | 1.01005e10i | −1.37979 | − | 1.23186i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.26679e9 | − | 3.14582e9i | −0.394344 | − | 0.379742i | ||||
\(683\) | − | 9.97428e9i | − | 1.19787i | −0.800798 | − | 0.598934i | \(-0.795591\pi\) | ||
0.800798 | − | 0.598934i | \(-0.204409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.00065e9i | 0.356697i | ||||||||
\(686\) | 3.96932e9 | − | 4.12195e9i | 0.469442 | − | 0.487493i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.01189e10 | + | 7.64889e8i | −1.18460 | + | 0.0895445i | ||||
\(689\) | 1.06062e9i | 0.123536i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.63799e9 | 0.880655 | 0.440328 | − | 0.897837i | \(-0.354862\pi\) | ||||
0.440328 | + | 0.897837i | \(0.354862\pi\) | |||||||
\(692\) | 5.72669e8 | + | 1.51736e10i | 0.0656951 | + | 1.74067i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.08186e9 | + | 6.31572e9i | −0.690682 | + | 0.717241i | ||||
\(695\) | 1.46530e10 | 1.65569 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.28962e9 | −0.927299 | ||||||||
\(698\) | 2.16277e9 | − | 2.24593e9i | 0.240722 | − | 0.249979i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.55920e8 | − | 1.34329e7i | 0.0392201 | − | 0.00148022i | ||||
\(701\) | −3.19869e9 | −0.350719 | −0.175359 | − | 0.984504i | \(-0.556109\pi\) | ||||
−0.175359 | + | 0.984504i | \(0.556109\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.91496e8i | 0.107633i | ||||||||
\(704\) | −5.58465e9 | + | 6.34728e8i | −0.603243 | + | 0.0685620i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.21378e9 | + | 6.45272e9i | −0.664568 | + | 0.690123i | ||||
\(707\) | 1.71942e9i | 0.182985i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.38637e10i | 1.46088i | 0.682975 | + | 0.730442i | \(0.260686\pi\) | ||||
−0.682975 | + | 0.730442i | \(0.739314\pi\) | |||||||
\(710\) | 1.04738e10 | + | 1.00860e10i | 1.09825 | + | 1.05758i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.79856e8 | + | 1.60573e8i | 0.0186744 | + | 0.0166721i | ||||
\(713\) | − | 1.73396e9i | − | 0.179154i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.17197e9 | 0.119907 | ||||||||
\(716\) | −5.40232e9 | + | 2.03890e8i | −0.550028 | + | 0.0207587i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.64410e9 | + | 3.50916e9i | 0.367413 | + | 0.353808i | ||||
\(719\) | 1.52490e10 | 1.53000 | 0.765000 | − | 0.644030i | \(-0.222739\pi\) | ||||
0.765000 | + | 0.644030i | \(0.222739\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.81374e9 | −0.478309 | ||||||||
\(722\) | −5.17295e9 | − | 4.98140e9i | −0.511514 | − | 0.492573i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.49488e10 | + | 5.64186e8i | −1.46393 | + | 0.0552506i | ||||
\(725\) | −1.72761e9 | −0.168369 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.06784e10i | 1.03071i | 0.856977 | + | 0.515355i | \(0.172340\pi\) | ||||
−0.856977 | + | 0.515355i | \(0.827660\pi\) | |||||||
\(728\) | 4.70991e8 | − | 5.27554e8i | 0.0452431 | − | 0.0506765i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.95801e9 | + | 2.84847e9i | 0.281429 | + | 0.271008i | ||||
\(731\) | − | 2.20431e10i | − | 2.08719i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 2.09160e10i | − | 1.96162i | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||
0.194974 | − | 0.980808i | \(-0.437538\pi\) | |||||||
\(734\) | −5.17868e9 | + | 5.37782e9i | −0.483374 | + | 0.501961i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.65588e9 | − | 1.36969e9i | −0.153093 | − | 0.126634i | ||||
\(737\) | 1.28944e10i | 1.18649i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.69063e9 | −0.609834 | −0.304917 | − | 0.952379i | \(-0.598629\pi\) | ||||
−0.304917 | + | 0.952379i | \(0.598629\pi\) | |||||||
\(740\) | 2.31839e9 | − | 8.74991e7i | 0.210318 | − | 0.00793766i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.84073e9 | + | 1.91151e9i | −0.165416 | + | 0.171777i | ||||
\(743\) | −1.80945e10 | −1.61840 | −0.809198 | − | 0.587536i | \(-0.800098\pi\) | ||||
−0.809198 | + | 0.587536i | \(0.800098\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.89992e10 | −1.68340 | ||||||||
\(746\) | 1.28904e10 | − | 1.33861e10i | 1.13679 | − | 1.18050i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.60461e8 | − | 1.22005e10i | −0.0402288 | − | 1.06591i | ||||
\(749\) | 2.56975e9 | 0.223462 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.39247e10i | 1.19963i | 0.800138 | + | 0.599815i | \(0.204759\pi\) | ||||
−0.800138 | + | 0.599815i | \(0.795241\pi\) | |||||||
\(752\) | 1.76392e10 | − | 1.33335e9i | 1.51257 | − | 0.114336i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.37941e9 | + | 2.47091e9i | −0.202148 | + | 0.209921i | ||||
\(755\) | 1.87785e10i | 1.58799i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.41833e10i | − | 1.18834i | −0.804338 | − | 0.594171i | \(-0.797480\pi\) | ||
0.804338 | − | 0.594171i | \(-0.202520\pi\) | |||||||
\(758\) | −4.00166e9 | − | 3.85348e9i | −0.333732 | − | 0.321374i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.56838e9 | − | 5.11702e9i | 0.377498 | − | 0.422834i | ||||
\(761\) | 7.86744e9i | 0.647123i | 0.946207 | + | 0.323562i | \(0.104880\pi\) | ||||
−0.946207 | + | 0.323562i | \(0.895120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.34906e9 | 0.354454 | ||||||||
\(764\) | 7.07695e8 | + | 1.87512e10i | 0.0574142 | + | 1.52126i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.75424e9 | + | 1.68928e9i | 0.141022 | + | 0.135800i | ||||
\(767\) | −1.93861e9 | −0.155134 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.63912e9 | 0.129978 | 0.0649890 | − | 0.997886i | \(-0.479299\pi\) | ||||
0.0649890 | + | 0.997886i | \(0.479299\pi\) | |||||||
\(770\) | 2.11219e9 | + | 2.03398e9i | 0.166731 | + | 0.160557i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.79279e8 | − | 1.26991e10i | −0.0374911 | − | 0.993372i | ||||
\(773\) | 2.71642e9 | 0.211529 | 0.105764 | − | 0.994391i | \(-0.466271\pi\) | ||||
0.105764 | + | 0.994391i | \(0.466271\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.26642e9i | − | 0.0977288i | ||||||
\(776\) | −6.80225e9 | + | 7.61916e9i | −0.522561 | + | 0.585317i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.37293e10 | + | 1.32209e10i | 1.04525 | + | 1.00654i | ||||
\(779\) | − | 3.74935e9i | − | 0.284168i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.17055e10i | 0.879249i | ||||||||
\(782\) | 3.23792e9 | − | 3.36243e9i | 0.242127 | − | 0.251437i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.16901e10 | + | 8.83658e8i | −0.866388 | + | 0.0654904i | ||||
\(785\) | 5.14311e9i | 0.379474i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.31174e9 | 0.607827 | 0.303914 | − | 0.952700i | \(-0.401707\pi\) | ||||
0.303914 | + | 0.952700i | \(0.401707\pi\) | |||||||
\(788\) | −1.40186e8 | − | 3.71440e9i | −0.0102062 | − | 0.270425i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.23426e10 | − | 1.28172e10i | 0.890662 | − | 0.924911i | ||||
\(791\) | −7.72998e9 | −0.555342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.26884e9 | 0.161565 | ||||||||
\(794\) | 6.64595e9 | − | 6.90151e9i | 0.471179 | − | 0.489297i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.44239e10 | − | 9.21790e8i | 1.71641 | − | 0.0647793i | ||||
\(797\) | −1.72803e10 | −1.20906 | −0.604530 | − | 0.796582i | \(-0.706639\pi\) | ||||
−0.604530 | + | 0.796582i | \(0.706639\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.84254e10i | 2.66505i | ||||||||
\(800\) | −1.20939e9 | − | 1.00037e9i | −0.0835126 | − | 0.0690791i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.88564e9 | − | 2.99660e9i | 0.197529 | − | 0.205125i | ||||
\(803\) | 3.30586e9i | 0.225310i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.12112e9i | 0.0757472i | ||||||||
\(806\) | −1.81130e9 | − | 1.74422e9i | −0.121847 | − | 0.117336i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.04605e9 | − | 5.65205e9i | 0.336520 | − | 0.376934i | ||||
\(809\) | 2.23227e10i | 1.48227i | 0.671356 | + | 0.741135i | \(0.265712\pi\) | ||||
−0.671356 | + | 0.741135i | \(0.734288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.69423e9 | 0.638176 | 0.319088 | − | 0.947725i | \(-0.396623\pi\) | ||||
0.319088 | + | 0.947725i | \(0.396623\pi\) | |||||||
\(812\) | −8.57665e9 | + | 3.23694e8i | −0.562175 | + | 0.0212172i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.34533e9 | + | 1.29551e9i | 0.0874266 | + | 0.0841893i | ||||
\(815\) | −1.53214e7 | −0.000991394 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.96998e9 | 0.639613 | ||||||||
\(818\) | 2.37843e9 | + | 2.29035e9i | 0.151933 | + | 0.146307i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.76703e9 | + | 3.30879e8i | −0.555270 | + | 0.0209566i | ||||
\(821\) | −2.46999e10 | −1.55773 | −0.778867 | − | 0.627189i | \(-0.784205\pi\) | ||||
−0.778867 | + | 0.627189i | \(0.784205\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.00407e10i | − | 1.25318i | −0.779348 | − | 0.626591i | \(-0.784450\pi\) | ||
0.779348 | − | 0.626591i | \(-0.215550\pi\) | |||||||
\(824\) | 1.58236e10 | + | 1.41270e10i | 0.985279 | + | 0.879640i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.49389e9 | − | 3.36451e9i | −0.215714 | − | 0.207727i | ||||
\(827\) | − | 3.11012e10i | − | 1.91209i | −0.293219 | − | 0.956045i | \(-0.594727\pi\) | ||
0.293219 | − | 0.956045i | \(-0.405273\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.01877e9i | − | 0.244992i | −0.992469 | − | 0.122496i | \(-0.960910\pi\) | ||
0.992469 | − | 0.122496i | \(-0.0390899\pi\) | |||||||
\(830\) | 1.60921e10 | − | 1.67109e10i | 0.976876 | − | 1.01444i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.09645e9 | + | 3.51930e8i | −0.186394 | + | 0.0211848i | ||||
\(833\) | − | 2.54659e10i | − | 1.52651i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.78264e9 | 0.284292 | ||||||||
\(836\) | 5.51821e9 | − | 2.08264e8i | 0.326645 | − | 0.0123280i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.87359e9 | − | 7.13790e9i | 0.403487 | − | 0.419002i | ||||
\(839\) | −1.51383e10 | −0.884932 | −0.442466 | − | 0.896785i | \(-0.645896\pi\) | ||||
−0.442466 | + | 0.896785i | \(0.645896\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.43806e10 | 1.41338 | ||||||||
\(842\) | −3.08851e9 | + | 3.20727e9i | −0.178302 | + | 0.185158i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.88806e8 | − | 1.56011e10i | −0.0337112 | − | 0.893218i | ||||
\(845\) | −1.78149e10 | −1.01575 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.04355e9i | − | 0.228650i | ||||||
\(848\) | 1.16606e10 | − | 8.81426e8i | 0.656651 | − | 0.0496364i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.36485e9 | − | 2.45579e9i | 0.132080 | − | 0.137159i | ||||
\(851\) | 7.14083e8i | 0.0397187i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.53579e10i | − | 0.847247i | −0.905838 | − | 0.423624i | \(-0.860758\pi\) | ||
0.905838 | − | 0.423624i | \(-0.139242\pi\) | |||||||
\(854\) | 4.08905e9 | + | 3.93764e9i | 0.224657 | + | 0.216338i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.44720e9 | − | 7.54151e9i | −0.460314 | − | 0.410961i | ||||
\(857\) | − | 1.44454e10i | − | 0.783968i | −0.919972 | − | 0.391984i | \(-0.871789\pi\) | ||
0.919972 | − | 0.391984i | \(-0.128211\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.57453e9 | −0.407736 | −0.203868 | − | 0.978998i | \(-0.565351\pi\) | ||||
−0.203868 | + | 0.978998i | \(0.565351\pi\) | |||||||
\(860\) | −8.79847e8 | − | 2.33126e10i | −0.0471696 | − | 1.24982i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.65804e10 | − | 1.59664e10i | −0.881697 | − | 0.849049i | ||||
\(863\) | 1.16885e10 | 0.619045 | 0.309522 | − | 0.950892i | \(-0.399831\pi\) | ||||
0.309522 | + | 0.950892i | \(0.399831\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.49081e10 | −1.83387 | ||||||||
\(866\) | 1.09215e10 | + | 1.05171e10i | 0.571441 | + | 0.550281i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.37283e8 | − | 6.28710e9i | −0.0123154 | − | 0.326311i | ||||
\(869\) | 1.43245e10 | 0.740475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.14939e9i | 0.366611i | ||||||||
\(872\) | −1.42961e10 | − | 1.27633e10i | −0.730146 | − | 0.651862i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.52081e9 | + | 1.46449e9i | 0.0770521 | + | 0.0741990i | ||||
\(875\) | − | 6.73628e9i | − | 0.339932i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.94208e10i | 0.972231i | 0.873894 | + | 0.486116i | \(0.161587\pi\) | ||||
−0.873894 | + | 0.486116i | \(0.838413\pi\) | |||||||
\(878\) | −1.39865e10 | + | 1.45244e10i | −0.697395 | + | 0.724212i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.73960e8 | − | 1.28847e10i | −0.0481783 | − | 0.637362i | ||||
\(881\) | − | 1.00292e10i | − | 0.494139i | −0.968998 | − | 0.247069i | \(-0.920532\pi\) | ||
0.968998 | − | 0.247069i | \(-0.0794675\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.58464e10 | 1.75220 | 0.876098 | − | 0.482133i | \(-0.160138\pi\) | ||||
0.876098 | + | 0.482133i | \(0.160138\pi\) | |||||||
\(884\) | −2.55306e8 | − | 6.76465e9i | −0.0124302 | − | 0.329353i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.55875e9 | − | 5.77250e9i | 0.268509 | − | 0.278834i | ||||
\(887\) | −1.96838e10 | −0.947059 | −0.473529 | − | 0.880778i | \(-0.657020\pi\) | ||||
−0.473529 | + | 0.880778i | \(0.657020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.82568e9 | −0.469036 | ||||||||
\(890\) | −3.84480e8 | + | 3.99264e8i | −0.0182814 | + | 0.0189843i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.24280e10 | + | 1.22387e9i | −1.52983 | + | 0.0577378i | ||||
\(893\) | −1.73796e10 | −0.816696 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.24285e10i | − | 0.579479i | ||||||
\(896\) | −6.19141e9 | − | 4.73971e9i | −0.287549 | − | 0.220127i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.48447e9 | − | 8.81073e9i | 0.390983 | − | 0.406017i | ||||
\(899\) | 3.05172e10i | 1.40083i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.54015e10i | 1.15697i | ||||||||
\(902\) | −5.08739e9 | − | 4.89900e9i | −0.230819 | − | 0.222272i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.54098e10 | + | 2.26854e10i | 1.14396 | + | 1.02131i | ||||
\(905\) | − | 3.43910e10i | − | 1.54232i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.16289e10 | −1.85255 | −0.926273 | − | 0.376853i | \(-0.877006\pi\) | ||||
−0.926273 | + | 0.376853i | \(0.877006\pi\) | |||||||
\(908\) | −9.35346e9 | + | 3.53011e8i | −0.414640 | + | 0.0156491i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.17112e9 | + | 1.12775e9i | 0.0515177 | + | 0.0496100i | ||||
\(911\) | −7.63565e9 | −0.334604 | −0.167302 | − | 0.985906i | \(-0.553506\pi\) | ||||
−0.167302 | + | 0.985906i | \(0.553506\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.86760e10 | 0.812151 | ||||||||
\(914\) | 6.07436e9 | + | 5.84943e9i | 0.263141 | + | 0.253397i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.64929e9 | − | 2.13211e8i | 0.242862 | − | 0.00916592i | ||||
\(917\) | −3.11845e9 | −0.133551 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.38559e10i | − | 0.588886i | −0.955669 | − | 0.294443i | \(-0.904866\pi\) | ||
0.955669 | − | 0.294443i | \(-0.0951341\pi\) | |||||||
\(920\) | 3.29019e9 | − | 3.68532e9i | 0.139304 | − | 0.156033i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.06645e9 | − | 1.02696e9i | −0.0448107 | − | 0.0431514i | ||||
\(923\) | 6.49021e9i | 0.271677i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.21539e8i | 0.0216666i | ||||||||
\(926\) | 2.58547e10 | − | 2.68489e10i | 1.07004 | − | 1.11119i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.91429e10 | + | 2.41061e10i | 1.19706 | + | 0.990169i | ||||
\(929\) | 4.81860e10i | 1.97181i | 0.167294 | + | 0.985907i | \(0.446497\pi\) | ||||
−0.167294 | + | 0.985907i | \(0.553503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.15181e10 | 0.467796 | ||||||||
\(932\) | 2.38381e10 | − | 8.99681e8i | 0.964532 | − | 0.0364026i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.01801e10 | + | 3.13406e10i | −1.21201 | + | 1.25862i | ||||
\(935\) | 2.80682e10 | 1.12299 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.58203e8 | −0.0221668 | −0.0110834 | − | 0.999939i | \(-0.503528\pi\) | ||||
−0.0110834 | + | 0.999939i | \(0.503528\pi\) | |||||||
\(938\) | −1.24080e10 | + | 1.28851e10i | −0.490897 | + | 0.509774i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.53374e9 | + | 4.06384e10i | 0.0602290 | + | 1.59584i | ||||
\(941\) | 4.60090e10 | 1.80003 | 0.900014 | − | 0.435862i | \(-0.143556\pi\) | ||||
0.900014 | + | 0.435862i | \(0.143556\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.70031e9i | − | 0.104863i | ||||||
\(944\) | 1.61108e9 | + | 2.13134e10i | 0.0623326 | + | 0.824612i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.30270e10 | − | 1.35280e10i | 0.500296 | − | 0.519534i | ||||
\(947\) | 1.84738e10i | 0.706856i | 0.935462 | + | 0.353428i | \(0.114984\pi\) | ||||
−0.935462 | + | 0.353428i | \(0.885016\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.83296e9i | 0.0696179i | ||||||||
\(950\) | 1.11074e9 | + | 1.06961e9i | 0.0420320 | + | 0.0404756i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.12801e10 | − | 1.26348e10i | 0.423724 | − | 0.474611i | ||||
\(953\) | 1.94712e10i | 0.728732i | 0.931256 | + | 0.364366i | \(0.118714\pi\) | ||||
−0.931256 | + | 0.364366i | \(0.881286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.31388e10 | −1.60272 | ||||||||
\(956\) | −2.91734e8 | − | 7.72984e9i | −0.0107990 | − | 0.286133i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.03620e10 | − | 9.97829e9i | −0.380771 | − | 0.366671i | ||||
\(959\) | −3.35110e9 | −0.122694 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.14205e9 | 0.186898 | ||||||||
\(962\) | 7.45929e8 | + | 7.18308e8i | 0.0270137 | + | 0.0260134i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.22307e9 | + | 3.24066e10i | 0.0439724 | + | 1.16510i | ||||
\(965\) | 2.92153e10 | 1.04656 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.72332e9i | − | 0.0612876i | −0.999530 | − | 0.0306438i | \(-0.990244\pi\) | ||
0.999530 | − | 0.0306438i | \(-0.00975574\pi\) | |||||||
\(968\) | −1.18667e10 | + | 1.32918e10i | −0.420501 | + | 0.471001i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.69138e10 | − | 1.62875e10i | −0.595033 | − | 0.572999i | ||||
\(971\) | − | 1.13358e10i | − | 0.397359i | −0.980064 | − | 0.198680i | \(-0.936335\pi\) | ||
0.980064 | − | 0.198680i | \(-0.0636653\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.63643e10i | 0.569512i | ||||||||
\(974\) | −2.07304e10 | + | 2.15276e10i | −0.718873 | + | 0.746516i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.88552e9 | − | 2.49440e10i | −0.0649167 | − | 0.858798i | ||||
\(977\) | − | 2.58110e10i | − | 0.885470i | −0.896652 | − | 0.442735i | \(-0.854008\pi\) | ||
0.896652 | − | 0.442735i | \(-0.145992\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.46217e8 | −0.0151987 | ||||||||
\(980\) | −1.01647e9 | − | 2.69325e10i | −0.0344986 | − | 0.914082i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.54850e10 | + | 1.60804e10i | −0.521819 | + | 0.541884i | ||||
\(983\) | 1.58165e10 | 0.531097 | 0.265549 | − | 0.964098i | \(-0.414447\pi\) | ||||
0.265549 | + | 0.964098i | \(0.414447\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.54530e9 | 0.284905 | ||||||||
\(986\) | −5.69863e10 | + | 5.91776e10i | −1.89322 | + | 1.96602i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.05961e9 | − | 1.15474e8i | 0.100929 | − | 0.00380920i | ||||
\(989\) | 7.18046e9 | 0.236029 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 2.16501e10i | − | 0.706646i | −0.935501 | − | 0.353323i | \(-0.885052\pi\) | ||
0.935501 | − | 0.353323i | \(-0.114948\pi\) | |||||||
\(992\) | −1.76710e10 | + | 2.13632e10i | −0.574737 | + | 0.694823i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.12639e10 | + | 1.16971e10i | −0.363779 | + | 0.377767i | ||||
\(995\) | 5.61894e10i | 1.80831i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.30355e9i | 0.137529i | 0.997633 | + | 0.0687644i | \(0.0219057\pi\) | ||||
−0.997633 | + | 0.0687644i | \(0.978094\pi\) | |||||||
\(998\) | −3.58075e10 | − | 3.44816e10i | −1.14029 | − | 1.09807i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 72.8.f.a.35.22 | yes | 28 | |
3.2 | odd | 2 | inner | 72.8.f.a.35.7 | ✓ | 28 | |
4.3 | odd | 2 | 288.8.f.a.143.6 | 28 | |||
8.3 | odd | 2 | inner | 72.8.f.a.35.8 | yes | 28 | |
8.5 | even | 2 | 288.8.f.a.143.23 | 28 | |||
12.11 | even | 2 | 288.8.f.a.143.24 | 28 | |||
24.5 | odd | 2 | 288.8.f.a.143.5 | 28 | |||
24.11 | even | 2 | inner | 72.8.f.a.35.21 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.8.f.a.35.7 | ✓ | 28 | 3.2 | odd | 2 | inner | |
72.8.f.a.35.8 | yes | 28 | 8.3 | odd | 2 | inner | |
72.8.f.a.35.21 | yes | 28 | 24.11 | even | 2 | inner | |
72.8.f.a.35.22 | yes | 28 | 1.1 | even | 1 | trivial | |
288.8.f.a.143.5 | 28 | 24.5 | odd | 2 | |||
288.8.f.a.143.6 | 28 | 4.3 | odd | 2 | |||
288.8.f.a.143.23 | 28 | 8.5 | even | 2 | |||
288.8.f.a.143.24 | 28 | 12.11 | even | 2 |