Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,15,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.b (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: | \(7.45973808911\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-35})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} + 23x^{2} - 22x + 51 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.3 | ||
Root | \(0.500000 + 1.54383i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.15.b.a.5.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 90.5097i | 0.707107i | ||||||||
\(3\) | −2023.79 | + | 829.000i | −0.925373 | + | 0.379058i | ||||
\(4\) | −8192.00 | −0.500000 | ||||||||
\(5\) | − | 40425.0i | − | 0.517440i | −0.965952 | − | 0.258720i | \(-0.916699\pi\) | ||
0.965952 | − | 0.258720i | \(-0.0833007\pi\) | |||||||
\(6\) | −75032.5 | − | 183173.i | −0.268035 | − | 0.654337i | ||||
\(7\) | 388872. | 0.472194 | 0.236097 | − | 0.971729i | \(-0.424132\pi\) | ||||
0.236097 | + | 0.971729i | \(0.424132\pi\) | |||||||
\(8\) | − | 741455.i | − | 0.353553i | ||||||
\(9\) | 3.40849e6 | − | 3.35545e6i | 0.712630 | − | 0.701540i | ||||
\(10\) | 3.65885e6 | 0.365885 | ||||||||
\(11\) | − | 3.20747e7i | − | 1.64594i | −0.568086 | − | 0.822969i | \(-0.692316\pi\) | ||
0.568086 | − | 0.822969i | \(-0.307684\pi\) | |||||||
\(12\) | 1.65789e7 | − | 6.79117e6i | 0.462686 | − | 0.189529i | ||||
\(13\) | −5.64146e7 | −0.899059 | −0.449529 | − | 0.893266i | \(-0.648408\pi\) | ||||
−0.449529 | + | 0.893266i | \(0.648408\pi\) | |||||||
\(14\) | 3.51967e7i | 0.333892i | ||||||||
\(15\) | 3.35123e7 | + | 8.18117e7i | 0.196140 | + | 0.478825i | ||||
\(16\) | 6.71089e7 | 0.250000 | ||||||||
\(17\) | 2.36470e8i | 0.576280i | 0.957588 | + | 0.288140i | \(0.0930369\pi\) | ||||
−0.957588 | + | 0.288140i | \(0.906963\pi\) | |||||||
\(18\) | 3.03700e8 | + | 3.08501e8i | 0.496064 | + | 0.503905i | ||||
\(19\) | −1.43439e9 | −1.60469 | −0.802347 | − | 0.596858i | \(-0.796415\pi\) | ||||
−0.802347 | + | 0.596858i | \(0.796415\pi\) | |||||||
\(20\) | 3.31162e8i | 0.258720i | ||||||||
\(21\) | −7.86996e8 | + | 3.22375e8i | −0.436956 | + | 0.178989i | ||||
\(22\) | 2.90307e9 | 1.16385 | ||||||||
\(23\) | − | 6.74668e9i | − | 1.98150i | −0.135684 | − | 0.990752i | \(-0.543323\pi\) | ||
0.135684 | − | 0.990752i | \(-0.456677\pi\) | |||||||
\(24\) | 6.14666e8 | + | 1.50055e9i | 0.134017 | + | 0.327169i | ||||
\(25\) | 4.46934e9 | 0.732256 | ||||||||
\(26\) | − | 5.10607e9i | − | 0.635731i | ||||||
\(27\) | −4.11640e9 | + | 9.61635e9i | −0.393524 | + | 0.919314i | ||||
\(28\) | −3.18564e9 | −0.236097 | ||||||||
\(29\) | − | 8.00214e9i | − | 0.463896i | −0.972728 | − | 0.231948i | \(-0.925490\pi\) | ||
0.972728 | − | 0.231948i | \(-0.0745099\pi\) | |||||||
\(30\) | −7.40475e9 | + | 3.03319e9i | −0.338580 | + | 0.138692i | ||||
\(31\) | −7.26470e9 | −0.264050 | −0.132025 | − | 0.991246i | \(-0.542148\pi\) | ||||
−0.132025 | + | 0.991246i | \(0.542148\pi\) | |||||||
\(32\) | 6.07400e9i | 0.176777i | ||||||||
\(33\) | 2.65899e10 | + | 6.49124e10i | 0.623906 | + | 1.52311i | ||||
\(34\) | −2.14028e10 | −0.407492 | ||||||||
\(35\) | − | 1.57202e10i | − | 0.244332i | ||||||
\(36\) | −2.79223e10 | + | 2.74878e10i | −0.356315 | + | 0.350770i | ||||
\(37\) | 2.67765e10 | 0.282060 | 0.141030 | − | 0.990005i | \(-0.454959\pi\) | ||||
0.141030 | + | 0.990005i | \(0.454959\pi\) | |||||||
\(38\) | − | 1.29826e11i | − | 1.13469i | ||||||
\(39\) | 1.14171e11 | − | 4.67677e10i | 0.831965 | − | 0.340796i | ||||
\(40\) | −2.99733e10 | −0.182943 | ||||||||
\(41\) | − | 1.45007e11i | − | 0.744564i | −0.928120 | − | 0.372282i | \(-0.878575\pi\) | ||
0.928120 | − | 0.372282i | \(-0.121425\pi\) | |||||||
\(42\) | −2.91781e10 | − | 7.12308e10i | −0.126564 | − | 0.308974i | ||||
\(43\) | −1.21747e11 | −0.447896 | −0.223948 | − | 0.974601i | \(-0.571895\pi\) | ||||
−0.223948 | + | 0.974601i | \(0.571895\pi\) | |||||||
\(44\) | 2.62756e11i | 0.822969i | ||||||||
\(45\) | −1.35644e11 | − | 1.37788e11i | −0.363005 | − | 0.368743i | ||||
\(46\) | 6.10639e11 | 1.40114 | ||||||||
\(47\) | 5.48796e11i | 1.08324i | 0.840623 | + | 0.541621i | \(0.182189\pi\) | ||||
−0.840623 | + | 0.541621i | \(0.817811\pi\) | |||||||
\(48\) | −1.35814e11 | + | 5.56333e10i | −0.231343 | + | 0.0947645i | ||||
\(49\) | −5.27001e11 | −0.777032 | ||||||||
\(50\) | 4.04518e11i | 0.517783i | ||||||||
\(51\) | −1.96034e11 | − | 4.78566e11i | −0.218444 | − | 0.533274i | ||||
\(52\) | 4.62148e11 | 0.449529 | ||||||||
\(53\) | 8.99111e11i | 0.765389i | 0.923875 | + | 0.382695i | \(0.125004\pi\) | ||||
−0.923875 | + | 0.382695i | \(0.874996\pi\) | |||||||
\(54\) | −8.70373e11 | − | 3.72574e11i | −0.650053 | − | 0.278263i | ||||
\(55\) | −1.29662e12 | −0.851674 | ||||||||
\(56\) | − | 2.88331e11i | − | 0.166946i | ||||||
\(57\) | 2.90290e12 | − | 1.18911e12i | 1.48494 | − | 0.608272i | ||||
\(58\) | 7.24271e11 | 0.328024 | ||||||||
\(59\) | − | 1.29697e12i | − | 0.521152i | −0.965453 | − | 0.260576i | \(-0.916087\pi\) | ||
0.965453 | − | 0.260576i | \(-0.0839125\pi\) | |||||||
\(60\) | −2.74533e11 | − | 6.70202e11i | −0.0980699 | − | 0.239412i | ||||
\(61\) | 1.73638e12 | 0.552504 | 0.276252 | − | 0.961085i | \(-0.410908\pi\) | ||||
0.276252 | + | 0.961085i | \(0.410908\pi\) | |||||||
\(62\) | − | 6.57526e11i | − | 0.186711i | ||||||
\(63\) | 1.32547e12 | − | 1.30484e12i | 0.336500 | − | 0.331263i | ||||
\(64\) | −5.49756e11 | −0.125000 | ||||||||
\(65\) | 2.28056e12i | 0.465209i | ||||||||
\(66\) | −5.87520e12 | + | 2.40664e12i | −1.07700 | + | 0.441168i | ||||
\(67\) | −7.50142e12 | −1.23771 | −0.618856 | − | 0.785504i | \(-0.712404\pi\) | ||||
−0.618856 | + | 0.785504i | \(0.712404\pi\) | |||||||
\(68\) | − | 1.93716e12i | − | 0.288140i | ||||||
\(69\) | 5.59300e12 | + | 1.36539e13i | 0.751105 | + | 1.83363i | ||||
\(70\) | 1.42283e12 | 0.172769 | ||||||||
\(71\) | − | 4.94522e12i | − | 0.543722i | −0.962336 | − | 0.271861i | \(-0.912361\pi\) | ||
0.962336 | − | 0.271861i | \(-0.0876391\pi\) | |||||||
\(72\) | −2.48791e12 | − | 2.52724e12i | −0.248032 | − | 0.251953i | ||||
\(73\) | 9.76842e12 | 0.884228 | 0.442114 | − | 0.896959i | \(-0.354229\pi\) | ||||
0.442114 | + | 0.896959i | \(0.354229\pi\) | |||||||
\(74\) | 2.42353e12i | 0.199447i | ||||||||
\(75\) | −9.04500e12 | + | 3.70508e12i | −0.677610 | + | 0.277568i | ||||
\(76\) | 1.17505e13 | 0.802347 | ||||||||
\(77\) | − | 1.24730e13i | − | 0.777203i | ||||||
\(78\) | 4.23293e12 | + | 1.03336e13i | 0.240979 | + | 0.588288i | ||||
\(79\) | −2.22658e13 | −1.15944 | −0.579721 | − | 0.814815i | \(-0.696838\pi\) | ||||
−0.579721 | + | 0.814815i | \(0.696838\pi\) | |||||||
\(80\) | − | 2.71288e12i | − | 0.129360i | ||||||
\(81\) | 3.58768e11 | − | 2.28740e13i | 0.0156826 | − | 0.999877i | ||||
\(82\) | 1.31245e13 | 0.526486 | ||||||||
\(83\) | − | 2.67183e13i | − | 0.984606i | −0.870424 | − | 0.492303i | \(-0.836155\pi\) | ||
0.870424 | − | 0.492303i | \(-0.163845\pi\) | |||||||
\(84\) | 6.44707e12 | − | 2.64090e12i | 0.218478 | − | 0.0894946i | ||||
\(85\) | 9.55930e12 | 0.298190 | ||||||||
\(86\) | − | 1.10192e13i | − | 0.316710i | ||||||
\(87\) | 6.63378e12 | + | 1.61947e13i | 0.175843 | + | 0.429276i | ||||
\(88\) | −2.37819e13 | −0.581927 | ||||||||
\(89\) | 7.12613e13i | 1.61110i | 0.592525 | + | 0.805552i | \(0.298131\pi\) | ||||
−0.592525 | + | 0.805552i | \(0.701869\pi\) | |||||||
\(90\) | 1.24712e13 | − | 1.22771e13i | 0.260741 | − | 0.256683i | ||||
\(91\) | −2.19381e13 | −0.424531 | ||||||||
\(92\) | 5.52688e13i | 0.990752i | ||||||||
\(93\) | 1.47022e13 | − | 6.02244e12i | 0.244345 | − | 0.100090i | ||||
\(94\) | −4.96713e13 | −0.765968 | ||||||||
\(95\) | 5.79852e13i | 0.830333i | ||||||||
\(96\) | −5.03535e12 | − | 1.22925e13i | −0.0670086 | − | 0.163584i | ||||
\(97\) | 8.75400e13 | 1.08344 | 0.541719 | − | 0.840560i | \(-0.317774\pi\) | ||||
0.541719 | + | 0.840560i | \(0.317774\pi\) | |||||||
\(98\) | − | 4.76987e13i | − | 0.549445i | ||||||
\(99\) | −1.07625e14 | − | 1.09326e14i | −1.15469 | − | 1.17294i | ||||
\(100\) | −3.66128e13 | −0.366128 | ||||||||
\(101\) | 7.53448e12i | 0.0702754i | 0.999382 | + | 0.0351377i | \(0.0111870\pi\) | ||||
−0.999382 | + | 0.0351377i | \(0.988813\pi\) | |||||||
\(102\) | 4.33148e13 | − | 1.77429e13i | 0.377082 | − | 0.154463i | ||||
\(103\) | 1.12865e14 | 0.917694 | 0.458847 | − | 0.888515i | \(-0.348263\pi\) | ||||
0.458847 | + | 0.888515i | \(0.348263\pi\) | |||||||
\(104\) | 4.18289e13i | 0.317865i | ||||||||
\(105\) | 1.30320e13 | + | 3.18143e13i | 0.0926161 | + | 0.226098i | ||||
\(106\) | −8.13782e13 | −0.541212 | ||||||||
\(107\) | − | 8.18220e13i | − | 0.509546i | −0.967001 | − | 0.254773i | \(-0.917999\pi\) | ||
0.967001 | − | 0.254773i | \(-0.0820007\pi\) | |||||||
\(108\) | 3.37215e13 | − | 7.87772e13i | 0.196762 | − | 0.459657i | ||||
\(109\) | 1.73006e14 | 0.946400 | 0.473200 | − | 0.880955i | \(-0.343099\pi\) | ||||
0.473200 | + | 0.880955i | \(0.343099\pi\) | |||||||
\(110\) | − | 1.17357e14i | − | 0.602225i | ||||||
\(111\) | −5.41901e13 | + | 2.21977e13i | −0.261011 | + | 0.106917i | ||||
\(112\) | 2.60968e13 | 0.118049 | ||||||||
\(113\) | − | 9.87778e13i | − | 0.419866i | −0.977716 | − | 0.209933i | \(-0.932675\pi\) | ||
0.977716 | − | 0.209933i | \(-0.0673245\pi\) | |||||||
\(114\) | 1.07626e14 | + | 2.62741e14i | 0.430113 | + | 1.05001i | ||||
\(115\) | −2.72734e14 | −1.02531 | ||||||||
\(116\) | 6.55535e13i | 0.231948i | ||||||||
\(117\) | −1.92288e14 | + | 1.89296e14i | −0.640696 | + | 0.630726i | ||||
\(118\) | 1.17388e14 | 0.368510 | ||||||||
\(119\) | 9.19567e13i | 0.272116i | ||||||||
\(120\) | 6.06597e13 | − | 2.48479e13i | 0.169290 | − | 0.0693459i | ||||
\(121\) | −6.49036e14 | −1.70911 | ||||||||
\(122\) | 1.57159e14i | 0.390679i | ||||||||
\(123\) | 1.20211e14 | + | 2.93464e14i | 0.282233 | + | 0.688999i | ||||
\(124\) | 5.95125e13 | 0.132025 | ||||||||
\(125\) | − | 4.27407e14i | − | 0.896338i | ||||||
\(126\) | 1.18101e14 | + | 1.19968e14i | 0.234239 | + | 0.237941i | ||||
\(127\) | 9.57895e14 | 1.79759 | 0.898797 | − | 0.438364i | \(-0.144442\pi\) | ||||
0.898797 | + | 0.438364i | \(0.144442\pi\) | |||||||
\(128\) | − | 4.97582e13i | − | 0.0883883i | ||||||
\(129\) | 2.46389e14 | − | 1.00928e14i | 0.414471 | − | 0.169779i | ||||
\(130\) | −2.06413e14 | −0.328952 | ||||||||
\(131\) | − | 3.06170e14i | − | 0.462448i | −0.972900 | − | 0.231224i | \(-0.925727\pi\) | ||
0.972900 | − | 0.231224i | \(-0.0742731\pi\) | |||||||
\(132\) | −2.17825e14 | − | 5.31763e14i | −0.311953 | − | 0.761553i | ||||
\(133\) | −5.57795e14 | −0.757727 | ||||||||
\(134\) | − | 6.78951e14i | − | 0.875195i | ||||||
\(135\) | 3.88741e14 | + | 1.66405e14i | 0.475690 | + | 0.203625i | ||||
\(136\) | 1.75332e14 | 0.203746 | ||||||||
\(137\) | 1.50579e13i | 0.0166235i | 0.999965 | + | 0.00831173i | \(0.00264574\pi\) | ||||
−0.999965 | + | 0.00831173i | \(0.997354\pi\) | |||||||
\(138\) | −1.23581e15 | + | 5.06220e14i | −1.29657 | + | 0.531112i | ||||
\(139\) | 7.56720e14 | 0.754800 | 0.377400 | − | 0.926050i | \(-0.376818\pi\) | ||||
0.377400 | + | 0.926050i | \(0.376818\pi\) | |||||||
\(140\) | 1.28780e14i | 0.122166i | ||||||||
\(141\) | −4.54952e14 | − | 1.11065e15i | −0.410612 | − | 1.00240i | ||||
\(142\) | 4.47590e14 | 0.384470 | ||||||||
\(143\) | 1.80948e15i | 1.47980i | ||||||||
\(144\) | 2.28740e14 | − | 2.25180e14i | 0.178157 | − | 0.175385i | ||||
\(145\) | −3.23487e14 | −0.240038 | ||||||||
\(146\) | 8.84137e14i | 0.625244i | ||||||||
\(147\) | 1.06654e15 | − | 4.36884e14i | 0.719045 | − | 0.294540i | ||||
\(148\) | −2.19353e14 | −0.141030 | ||||||||
\(149\) | 1.43757e15i | 0.881711i | 0.897578 | + | 0.440855i | \(0.145325\pi\) | ||||
−0.897578 | + | 0.440855i | \(0.854675\pi\) | |||||||
\(150\) | −3.35346e14 | − | 8.18660e14i | −0.196270 | − | 0.479142i | ||||
\(151\) | −1.35748e15 | −0.758393 | −0.379197 | − | 0.925316i | \(-0.623800\pi\) | ||||
−0.379197 | + | 0.925316i | \(0.623800\pi\) | |||||||
\(152\) | 1.06354e15i | 0.567345i | ||||||||
\(153\) | 7.93462e14 | + | 8.06005e14i | 0.404284 | + | 0.410674i | ||||
\(154\) | 1.12892e15 | 0.549566 | ||||||||
\(155\) | 2.93676e14i | 0.136630i | ||||||||
\(156\) | −9.35292e14 | + | 3.83121e14i | −0.415982 | + | 0.170398i | ||||
\(157\) | −2.68723e15 | −1.14290 | −0.571449 | − | 0.820638i | \(-0.693618\pi\) | ||||
−0.571449 | + | 0.820638i | \(0.693618\pi\) | |||||||
\(158\) | − | 2.01527e15i | − | 0.819849i | ||||||
\(159\) | −7.45363e14 | − | 1.81961e15i | −0.290127 | − | 0.708270i | ||||
\(160\) | 2.45541e14 | 0.0914713 | ||||||||
\(161\) | − | 2.62360e15i | − | 0.935655i | ||||||
\(162\) | 2.07032e15 | + | 3.24719e13i | 0.707020 | + | 0.0110893i | ||||
\(163\) | 1.31621e15 | 0.430540 | 0.215270 | − | 0.976555i | \(-0.430937\pi\) | ||||
0.215270 | + | 0.976555i | \(0.430937\pi\) | |||||||
\(164\) | 1.18790e15i | 0.372282i | ||||||||
\(165\) | 2.62409e15 | − | 1.07490e15i | 0.788116 | − | 0.322834i | ||||
\(166\) | 2.41827e15 | 0.696222 | ||||||||
\(167\) | − | 5.56602e15i | − | 1.53649i | −0.640157 | − | 0.768244i | \(-0.721131\pi\) | ||
0.640157 | − | 0.768244i | \(-0.278869\pi\) | |||||||
\(168\) | 2.39027e14 | + | 5.83523e14i | 0.0632822 | + | 0.154487i | ||||
\(169\) | −7.54768e14 | −0.191693 | ||||||||
\(170\) | 8.65209e14i | 0.210852i | ||||||||
\(171\) | −4.88910e15 | + | 4.81302e15i | −1.14355 | + | 1.12576i | ||||
\(172\) | 9.97348e14 | 0.223948 | ||||||||
\(173\) | 3.55586e15i | 0.766694i | 0.923604 | + | 0.383347i | \(0.125229\pi\) | ||||
−0.923604 | + | 0.383347i | \(0.874771\pi\) | |||||||
\(174\) | −1.46577e15 | + | 6.00421e14i | −0.303544 | + | 0.124340i | ||||
\(175\) | 1.73800e15 | 0.345767 | ||||||||
\(176\) | − | 2.15250e15i | − | 0.411485i | ||||||
\(177\) | 1.07519e15 | + | 2.62479e15i | 0.197547 | + | 0.482260i | ||||
\(178\) | −6.44984e15 | −1.13922 | ||||||||
\(179\) | 1.48854e15i | 0.252807i | 0.991979 | + | 0.126404i | \(0.0403435\pi\) | ||||
−0.991979 | + | 0.126404i | \(0.959657\pi\) | |||||||
\(180\) | 1.11119e15 | + | 1.12876e15i | 0.181502 | + | 0.184372i | ||||
\(181\) | 3.47684e15 | 0.546304 | 0.273152 | − | 0.961971i | \(-0.411934\pi\) | ||||
0.273152 | + | 0.961971i | \(0.411934\pi\) | |||||||
\(182\) | − | 1.98561e15i | − | 0.300188i | ||||||
\(183\) | −3.51406e15 | + | 1.43946e15i | −0.511272 | + | 0.209431i | ||||
\(184\) | −5.00236e15 | −0.700568 | ||||||||
\(185\) | − | 1.08244e15i | − | 0.145949i | ||||||
\(186\) | 5.45089e14 | + | 1.33069e15i | 0.0707745 | + | 0.172778i | ||||
\(187\) | 7.58470e15 | 0.948522 | ||||||||
\(188\) | − | 4.49573e15i | − | 0.541621i | ||||||
\(189\) | −1.60075e15 | + | 3.73953e15i | −0.185820 | + | 0.434095i | ||||
\(190\) | −5.24822e15 | −0.587134 | ||||||||
\(191\) | 4.10002e15i | 0.442133i | 0.975259 | + | 0.221066i | \(0.0709537\pi\) | ||||
−0.975259 | + | 0.221066i | \(0.929046\pi\) | |||||||
\(192\) | 1.11259e15 | − | 4.55748e14i | 0.115672 | − | 0.0473823i | ||||
\(193\) | 7.91819e15 | 0.793825 | 0.396913 | − | 0.917856i | \(-0.370082\pi\) | ||||
0.396913 | + | 0.917856i | \(0.370082\pi\) | |||||||
\(194\) | 7.92321e15i | 0.766107i | ||||||||
\(195\) | −1.89059e15 | − | 4.61538e15i | −0.176341 | − | 0.430492i | ||||
\(196\) | 4.31719e15 | 0.388516 | ||||||||
\(197\) | − | 1.65493e16i | − | 1.43720i | −0.695425 | − | 0.718599i | \(-0.744784\pi\) | ||
0.695425 | − | 0.718599i | \(-0.255216\pi\) | |||||||
\(198\) | 9.89507e15 | − | 9.74109e15i | 0.829397 | − | 0.816491i | ||||
\(199\) | −1.14009e16 | −0.922500 | −0.461250 | − | 0.887270i | \(-0.652599\pi\) | ||||
−0.461250 | + | 0.887270i | \(0.652599\pi\) | |||||||
\(200\) | − | 3.31381e15i | − | 0.258892i | ||||||
\(201\) | 1.51813e16 | − | 6.21868e15i | 1.14535 | − | 0.469165i | ||||
\(202\) | −6.81943e14 | −0.0496922 | ||||||||
\(203\) | − | 3.11181e15i | − | 0.219049i | ||||||
\(204\) | 1.60591e15 | + | 3.92041e15i | 0.109222 | + | 0.266637i | ||||
\(205\) | −5.86191e15 | −0.385267 | ||||||||
\(206\) | 1.02153e16i | 0.648907i | ||||||||
\(207\) | −2.26381e16 | − | 2.29960e16i | −1.39011 | − | 1.41208i | ||||
\(208\) | −3.78592e15 | −0.224765 | ||||||||
\(209\) | 4.60076e16i | 2.64123i | ||||||||
\(210\) | −2.87950e15 | + | 1.17952e15i | −0.159876 | + | 0.0654895i | ||||
\(211\) | −9.58039e14 | −0.0514524 | −0.0257262 | − | 0.999669i | \(-0.508190\pi\) | ||||
−0.0257262 | + | 0.999669i | \(0.508190\pi\) | |||||||
\(212\) | − | 7.36552e15i | − | 0.382695i | ||||||
\(213\) | 4.09959e15 | + | 1.00081e16i | 0.206102 | + | 0.503146i | ||||
\(214\) | 7.40568e15 | 0.360303 | ||||||||
\(215\) | 4.92160e15i | 0.231759i | ||||||||
\(216\) | 7.13010e15 | + | 3.05212e15i | 0.325027 | + | 0.139132i | ||||
\(217\) | −2.82504e15 | −0.124683 | ||||||||
\(218\) | 1.56587e16i | 0.669206i | ||||||||
\(219\) | −1.97692e16 | + | 8.09802e15i | −0.818241 | + | 0.335174i | ||||
\(220\) | 1.06219e16 | 0.425837 | ||||||||
\(221\) | − | 1.33404e16i | − | 0.518110i | ||||||
\(222\) | −2.00911e15 | − | 4.90473e15i | −0.0756019 | − | 0.184563i | ||||
\(223\) | 2.35994e16 | 0.860532 | 0.430266 | − | 0.902702i | \(-0.358420\pi\) | ||||
0.430266 | + | 0.902702i | \(0.358420\pi\) | |||||||
\(224\) | 2.36201e15i | 0.0834730i | ||||||||
\(225\) | 1.52337e16 | − | 1.49966e16i | 0.521827 | − | 0.513707i | ||||
\(226\) | 8.94035e15 | 0.296890 | ||||||||
\(227\) | − | 1.56244e16i | − | 0.503063i | −0.967849 | − | 0.251531i | \(-0.919066\pi\) | ||
0.967849 | − | 0.251531i | \(-0.0809342\pi\) | |||||||
\(228\) | −2.37806e16 | + | 9.74119e15i | −0.742470 | + | 0.304136i | ||||
\(229\) | −3.99912e16 | −1.21092 | −0.605461 | − | 0.795875i | \(-0.707011\pi\) | ||||
−0.605461 | + | 0.795875i | \(0.707011\pi\) | |||||||
\(230\) | − | 2.46851e16i | − | 0.725003i | ||||||
\(231\) | 1.03401e16 | + | 2.52427e16i | 0.294605 | + | 0.719203i | ||||
\(232\) | −5.93323e15 | −0.164012 | ||||||||
\(233\) | − | 2.76210e16i | − | 0.740881i | −0.928856 | − | 0.370441i | \(-0.879207\pi\) | ||
0.928856 | − | 0.370441i | \(-0.120793\pi\) | |||||||
\(234\) | −1.71331e16 | − | 1.74040e16i | −0.445991 | − | 0.453041i | ||||
\(235\) | 2.21851e16 | 0.560513 | ||||||||
\(236\) | 1.06248e16i | 0.260576i | ||||||||
\(237\) | 4.50614e16 | − | 1.84584e16i | 1.07292 | − | 0.439496i | ||||
\(238\) | −8.32297e15 | −0.192415 | ||||||||
\(239\) | − | 1.77539e16i | − | 0.398574i | −0.979941 | − | 0.199287i | \(-0.936137\pi\) | ||
0.979941 | − | 0.199287i | \(-0.0638626\pi\) | |||||||
\(240\) | 2.24897e15 | + | 5.49029e15i | 0.0490350 | + | 0.119706i | ||||
\(241\) | −7.98776e15 | −0.169163 | −0.0845816 | − | 0.996417i | \(-0.526955\pi\) | ||||
−0.0845816 | + | 0.996417i | \(0.526955\pi\) | |||||||
\(242\) | − | 5.87440e16i | − | 1.20853i | ||||||
\(243\) | 1.82365e16 | + | 4.65896e16i | 0.364499 | + | 0.931204i | ||||
\(244\) | −1.42244e16 | −0.276252 | ||||||||
\(245\) | 2.13040e16i | 0.402068i | ||||||||
\(246\) | −2.65613e16 | + | 1.08802e16i | −0.487196 | + | 0.199569i | ||||
\(247\) | 8.09206e16 | 1.44271 | ||||||||
\(248\) | 5.38645e15i | 0.0933557i | ||||||||
\(249\) | 2.21495e16 | + | 5.40723e16i | 0.373223 | + | 0.911128i | ||||
\(250\) | 3.86845e16 | 0.633807 | ||||||||
\(251\) | 1.42116e16i | 0.226426i | 0.993571 | + | 0.113213i | \(0.0361142\pi\) | ||||
−0.993571 | + | 0.113213i | \(0.963886\pi\) | |||||||
\(252\) | −1.08582e16 | + | 1.06893e16i | −0.168250 | + | 0.165632i | ||||
\(253\) | −2.16398e17 | −3.26143 | ||||||||
\(254\) | 8.66987e16i | 1.27109i | ||||||||
\(255\) | −1.93460e16 | + | 7.92466e15i | −0.275937 | + | 0.113031i | ||||
\(256\) | 4.50360e15 | 0.0625000 | ||||||||
\(257\) | − | 9.79504e16i | − | 1.32274i | −0.750060 | − | 0.661369i | \(-0.769976\pi\) | ||
0.750060 | − | 0.661369i | \(-0.230024\pi\) | |||||||
\(258\) | 9.13495e15 | + | 2.23006e16i | 0.120052 | + | 0.293075i | ||||
\(259\) | 1.04127e16 | 0.133187 | ||||||||
\(260\) | − | 1.86824e16i | − | 0.232605i | ||||||
\(261\) | −2.68507e16 | − | 2.72752e16i | −0.325441 | − | 0.330586i | ||||
\(262\) | 2.77113e16 | 0.327000 | ||||||||
\(263\) | 1.56067e17i | 1.79316i | 0.442880 | + | 0.896581i | \(0.353957\pi\) | ||||
−0.442880 | + | 0.896581i | \(0.646043\pi\) | |||||||
\(264\) | 4.81297e16 | − | 1.97152e16i | 0.538500 | − | 0.220584i | ||||
\(265\) | 3.63466e16 | 0.396043 | ||||||||
\(266\) | − | 5.04858e16i | − | 0.535794i | ||||||
\(267\) | −5.90756e16 | − | 1.44218e17i | −0.610702 | − | 1.49087i | ||||
\(268\) | 6.14516e16 | 0.618856 | ||||||||
\(269\) | − | 2.69565e16i | − | 0.264483i | −0.991218 | − | 0.132241i | \(-0.957783\pi\) | ||
0.991218 | − | 0.132241i | \(-0.0422174\pi\) | |||||||
\(270\) | −1.50613e16 | + | 3.51848e16i | −0.143985 | + | 0.336364i | ||||
\(271\) | 1.23902e17 | 1.15423 | 0.577117 | − | 0.816662i | \(-0.304178\pi\) | ||||
0.577117 | + | 0.816662i | \(0.304178\pi\) | |||||||
\(272\) | 1.58692e16i | 0.144070i | ||||||||
\(273\) | 4.43981e16 | − | 1.81867e16i | 0.392849 | − | 0.160922i | ||||
\(274\) | −1.36289e15 | −0.0117546 | ||||||||
\(275\) | − | 1.43353e17i | − | 1.20525i | ||||||
\(276\) | −4.58178e16 | − | 1.11852e17i | −0.375553 | − | 0.916815i | ||||
\(277\) | −3.99146e16 | −0.318987 | −0.159494 | − | 0.987199i | \(-0.550986\pi\) | ||||
−0.159494 | + | 0.987199i | \(0.550986\pi\) | |||||||
\(278\) | 6.84905e16i | 0.533724i | ||||||||
\(279\) | −2.47616e16 | + | 2.43763e16i | −0.188170 | + | 0.185242i | ||||
\(280\) | −1.16558e16 | −0.0863845 | ||||||||
\(281\) | 2.39181e17i | 1.72895i | 0.502677 | + | 0.864474i | \(0.332349\pi\) | ||||
−0.502677 | + | 0.864474i | \(0.667651\pi\) | |||||||
\(282\) | 1.00524e17 | − | 4.11775e16i | 0.708806 | − | 0.290346i | ||||
\(283\) | 8.74437e15 | 0.0601483 | 0.0300741 | − | 0.999548i | \(-0.490426\pi\) | ||||
0.0300741 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(284\) | 4.05112e16i | 0.271861i | ||||||||
\(285\) | −4.80698e16 | − | 1.17350e17i | −0.314744 | − | 0.768367i | ||||
\(286\) | −1.63776e17 | −1.04637 | ||||||||
\(287\) | − | 5.63892e16i | − | 0.351579i | ||||||
\(288\) | 2.03810e16 | + | 2.07032e16i | 0.124016 | + | 0.125976i | ||||
\(289\) | 1.12460e17 | 0.667901 | ||||||||
\(290\) | − | 2.92787e16i | − | 0.169733i | ||||||
\(291\) | −1.77163e17 | + | 7.25706e16i | −1.00258 | + | 0.410686i | ||||
\(292\) | −8.00229e16 | −0.442114 | ||||||||
\(293\) | − | 2.23167e16i | − | 0.120381i | −0.998187 | − | 0.0601904i | \(-0.980829\pi\) | ||
0.998187 | − | 0.0601904i | \(-0.0191708\pi\) | |||||||
\(294\) | 3.95422e16 | + | 9.65322e16i | 0.208272 | + | 0.508441i | ||||
\(295\) | −5.24299e16 | −0.269665 | ||||||||
\(296\) | − | 1.98536e16i | − | 0.0997234i | ||||||
\(297\) | 3.08442e17 | + | 1.32032e17i | 1.51314 | + | 0.647716i | ||||
\(298\) | −1.30114e17 | −0.623464 | ||||||||
\(299\) | 3.80611e17i | 1.78149i | ||||||||
\(300\) | 7.40966e16 | − | 3.03520e16i | 0.338805 | − | 0.138784i | ||||
\(301\) | −4.73439e16 | −0.211494 | ||||||||
\(302\) | − | 1.22865e17i | − | 0.536265i | ||||||
\(303\) | −6.24608e15 | − | 1.52482e16i | −0.0266385 | − | 0.0650310i | ||||
\(304\) | −9.62603e16 | −0.401173 | ||||||||
\(305\) | − | 7.01930e16i | − | 0.285887i | ||||||
\(306\) | −7.29512e16 | + | 7.18160e16i | −0.290391 | + | 0.285872i | ||||
\(307\) | 2.99304e17 | 1.16451 | 0.582255 | − | 0.813006i | \(-0.302171\pi\) | ||||
0.582255 | + | 0.813006i | \(0.302171\pi\) | |||||||
\(308\) | 1.02178e17i | 0.388602i | ||||||||
\(309\) | −2.28415e17 | + | 9.35649e16i | −0.849209 | + | 0.347859i | ||||
\(310\) | −2.65805e16 | −0.0966120 | ||||||||
\(311\) | − | 4.57198e17i | − | 1.62473i | −0.583149 | − | 0.812365i | \(-0.698180\pi\) | ||
0.583149 | − | 0.812365i | \(-0.301820\pi\) | |||||||
\(312\) | −3.46762e16 | − | 8.46529e16i | −0.120489 | − | 0.294144i | ||||
\(313\) | 2.39273e17 | 0.812986 | 0.406493 | − | 0.913654i | \(-0.366751\pi\) | ||||
0.406493 | + | 0.913654i | \(0.366751\pi\) | |||||||
\(314\) | − | 2.43220e17i | − | 0.808151i | ||||||
\(315\) | −5.27482e16 | − | 5.35820e16i | −0.171409 | − | 0.174118i | ||||
\(316\) | 1.82402e17 | 0.579721 | ||||||||
\(317\) | − | 3.46468e17i | − | 1.07708i | −0.842599 | − | 0.538541i | \(-0.818976\pi\) | ||
0.842599 | − | 0.538541i | \(-0.181024\pi\) | |||||||
\(318\) | 1.64693e17 | − | 6.74626e16i | 0.500823 | − | 0.205151i | ||||
\(319\) | −2.56666e17 | −0.763544 | ||||||||
\(320\) | 2.22239e16i | 0.0646800i | ||||||||
\(321\) | 6.78304e16 | + | 1.65590e17i | 0.193148 | + | 0.471520i | ||||
\(322\) | 2.37461e17 | 0.661608 | ||||||||
\(323\) | − | 3.39190e17i | − | 0.924753i | ||||||
\(324\) | −2.93902e15 | + | 1.87384e17i | −0.00784130 | + | 0.499939i | ||||
\(325\) | −2.52136e17 | −0.658341 | ||||||||
\(326\) | 1.19130e17i | 0.304437i | ||||||||
\(327\) | −3.50127e17 | + | 1.43422e17i | −0.875773 | + | 0.358741i | ||||
\(328\) | −1.07516e17 | −0.263243 | ||||||||
\(329\) | 2.13411e17i | 0.511501i | ||||||||
\(330\) | 9.72886e16 | + | 2.37505e17i | 0.228278 | + | 0.557282i | ||||
\(331\) | −2.72422e17 | −0.625816 | −0.312908 | − | 0.949783i | \(-0.601303\pi\) | ||||
−0.312908 | + | 0.949783i | \(0.601303\pi\) | |||||||
\(332\) | 2.18877e17i | 0.492303i | ||||||||
\(333\) | 9.12674e16 | − | 8.98472e16i | 0.201005 | − | 0.197877i | ||||
\(334\) | 5.03778e17 | 1.08646 | ||||||||
\(335\) | 3.03245e17i | 0.640442i | ||||||||
\(336\) | −5.28144e16 | + | 2.16342e16i | −0.109239 | + | 0.0447473i | ||||
\(337\) | 4.80474e17 | 0.973330 | 0.486665 | − | 0.873589i | \(-0.338213\pi\) | ||||
0.486665 | + | 0.873589i | \(0.338213\pi\) | |||||||
\(338\) | − | 6.83138e16i | − | 0.135548i | ||||||
\(339\) | 8.18868e16 | + | 1.99906e17i | 0.159154 | + | 0.388532i | ||||
\(340\) | −7.83098e16 | −0.149095 | ||||||||
\(341\) | 2.33013e17i | 0.434610i | ||||||||
\(342\) | −4.35625e17 | − | 4.42511e17i | −0.796030 | − | 0.808614i | ||||
\(343\) | −4.68679e17 | −0.839105 | ||||||||
\(344\) | 9.02696e16i | 0.158355i | ||||||||
\(345\) | 5.51957e17 | − | 2.26097e17i | 0.948794 | − | 0.388652i | ||||
\(346\) | −3.21840e17 | −0.542134 | ||||||||
\(347\) | 3.71323e17i | 0.612979i | 0.951874 | + | 0.306490i | \(0.0991545\pi\) | ||||
−0.951874 | + | 0.306490i | \(0.900846\pi\) | |||||||
\(348\) | −5.43439e16 | − | 1.32667e17i | −0.0879217 | − | 0.214638i | ||||
\(349\) | −6.63718e17 | −1.05246 | −0.526230 | − | 0.850342i | \(-0.676395\pi\) | ||||
−0.526230 | + | 0.850342i | \(0.676395\pi\) | |||||||
\(350\) | 1.57306e17i | 0.244494i | ||||||||
\(351\) | 2.32225e17 | − | 5.42503e17i | 0.353801 | − | 0.826518i | ||||
\(352\) | 1.94822e17 | 0.290964 | ||||||||
\(353\) | 8.30669e17i | 1.21620i | 0.793861 | + | 0.608100i | \(0.208068\pi\) | ||||
−0.793861 | + | 0.608100i | \(0.791932\pi\) | |||||||
\(354\) | −2.37569e17 | + | 9.73147e16i | −0.341010 | + | 0.139687i | ||||
\(355\) | −1.99910e17 | −0.281344 | ||||||||
\(356\) | − | 5.83773e17i | − | 0.805552i | ||||||
\(357\) | −7.62321e16 | − | 1.86101e17i | −0.103148 | − | 0.251809i | ||||
\(358\) | −1.34727e17 | −0.178762 | ||||||||
\(359\) | − | 7.84251e17i | − | 1.02045i | −0.860040 | − | 0.510227i | \(-0.829561\pi\) | ||
0.860040 | − | 0.510227i | \(-0.170439\pi\) | |||||||
\(360\) | −1.02164e17 | + | 1.00574e17i | −0.130370 | + | 0.128342i | ||||
\(361\) | 1.25847e18 | 1.57504 | ||||||||
\(362\) | 3.14687e17i | 0.386295i | ||||||||
\(363\) | 1.31351e18 | − | 5.38051e17i | 1.58157 | − | 0.647853i | ||||
\(364\) | 1.79717e17 | 0.212265 | ||||||||
\(365\) | − | 3.94888e17i | − | 0.457535i | ||||||
\(366\) | −1.30285e17 | − | 3.18057e17i | −0.148090 | − | 0.361524i | ||||
\(367\) | −1.84129e17 | −0.205333 | −0.102667 | − | 0.994716i | \(-0.532738\pi\) | ||||
−0.102667 | + | 0.994716i | \(0.532738\pi\) | |||||||
\(368\) | − | 4.52762e17i | − | 0.495376i | ||||||
\(369\) | −4.86563e17 | − | 4.94254e17i | −0.522341 | − | 0.530598i | ||||
\(370\) | 9.79714e16 | 0.103202 | ||||||||
\(371\) | 3.49640e17i | 0.361412i | ||||||||
\(372\) | −1.20441e17 | + | 4.93358e16i | −0.122172 | + | 0.0500451i | ||||
\(373\) | 3.45886e16 | 0.0344327 | 0.0172164 | − | 0.999852i | \(-0.494520\pi\) | ||||
0.0172164 | + | 0.999852i | \(0.494520\pi\) | |||||||
\(374\) | 6.86489e17i | 0.670706i | ||||||||
\(375\) | 3.54321e17 | + | 8.64983e17i | 0.339764 | + | 0.829447i | ||||
\(376\) | 4.06907e17 | 0.382984 | ||||||||
\(377\) | 4.51438e17i | 0.417069i | ||||||||
\(378\) | −3.38464e17 | − | 1.44884e17i | −0.306952 | − | 0.131394i | ||||
\(379\) | −3.21511e17 | −0.286234 | −0.143117 | − | 0.989706i | \(-0.545713\pi\) | ||||
−0.143117 | + | 0.989706i | \(0.545713\pi\) | |||||||
\(380\) | − | 4.75015e17i | − | 0.415166i | ||||||
\(381\) | −1.93858e18 | + | 7.94095e17i | −1.66345 | + | 0.681393i | ||||
\(382\) | −3.71092e17 | −0.312635 | ||||||||
\(383\) | 8.54161e17i | 0.706559i | 0.935518 | + | 0.353279i | \(0.114933\pi\) | ||||
−0.935518 | + | 0.353279i | \(0.885067\pi\) | |||||||
\(384\) | 4.12496e16 | + | 1.00700e17i | 0.0335043 | + | 0.0817922i | ||||
\(385\) | −5.04219e17 | −0.402156 | ||||||||
\(386\) | 7.16673e17i | 0.561319i | ||||||||
\(387\) | −4.14971e17 | + | 4.08514e17i | −0.319184 | + | 0.314217i | ||||
\(388\) | −7.17127e17 | −0.541719 | ||||||||
\(389\) | − | 1.95449e18i | − | 1.45006i | −0.688716 | − | 0.725031i | \(-0.741825\pi\) | ||
0.688716 | − | 0.725031i | \(-0.258175\pi\) | |||||||
\(390\) | 4.17736e17 | − | 1.71116e17i | 0.304404 | − | 0.124692i | ||||
\(391\) | 1.59539e18 | 1.14190 | ||||||||
\(392\) | 3.90748e17i | 0.274722i | ||||||||
\(393\) | 2.53815e17 | + | 6.19624e17i | 0.175295 | + | 0.427937i | ||||
\(394\) | 1.49787e18 | 1.01625 | ||||||||
\(395\) | 9.00096e17i | 0.599942i | ||||||||
\(396\) | 8.81663e17 | + | 8.95600e17i | 0.577346 | + | 0.586472i | ||||
\(397\) | −2.77977e18 | −1.78844 | −0.894221 | − | 0.447625i | \(-0.852270\pi\) | ||||
−0.894221 | + | 0.447625i | \(0.852270\pi\) | |||||||
\(398\) | − | 1.03189e18i | − | 0.652306i | ||||||
\(399\) | 1.12886e18 | − | 4.62412e17i | 0.701180 | − | 0.287223i | ||||
\(400\) | 2.99932e17 | 0.183064 | ||||||||
\(401\) | − | 2.16906e18i | − | 1.30095i | −0.759526 | − | 0.650477i | \(-0.774569\pi\) | ||
0.759526 | − | 0.650477i | \(-0.225431\pi\) | |||||||
\(402\) | 5.62850e17 | + | 1.37405e18i | 0.331750 | + | 0.809882i | ||||
\(403\) | 4.09835e17 | 0.237396 | ||||||||
\(404\) | − | 6.17224e16i | − | 0.0351377i | ||||||
\(405\) | −9.24681e17 | − | 1.45032e16i | −0.517376 | − | 0.00811481i | ||||
\(406\) | 2.81649e17 | 0.154891 | ||||||||
\(407\) | − | 8.58849e17i | − | 0.464254i | ||||||
\(408\) | −3.54835e17 | + | 1.45350e17i | −0.188541 | + | 0.0772315i | ||||
\(409\) | 1.41898e18 | 0.741163 | 0.370581 | − | 0.928800i | \(-0.379158\pi\) | ||||
0.370581 | + | 0.928800i | \(0.379158\pi\) | |||||||
\(410\) | − | 5.30559e17i | − | 0.272425i | ||||||
\(411\) | −1.24830e16 | − | 3.04741e16i | −0.00630126 | − | 0.0153829i | ||||
\(412\) | −9.24588e17 | −0.458847 | ||||||||
\(413\) | − | 5.04355e17i | − | 0.246085i | ||||||
\(414\) | 2.08136e18 | − | 2.04897e18i | 0.998491 | − | 0.982953i | ||||
\(415\) | −1.08009e18 | −0.509475 | ||||||||
\(416\) | − | 3.42662e17i | − | 0.158933i | ||||||
\(417\) | −1.53144e18 | + | 6.27321e17i | −0.698471 | + | 0.286113i | ||||
\(418\) | −4.16413e18 | −1.86763 | ||||||||
\(419\) | − | 1.61537e18i | − | 0.712481i | −0.934394 | − | 0.356241i | \(-0.884058\pi\) | ||
0.934394 | − | 0.356241i | \(-0.115942\pi\) | |||||||
\(420\) | −1.06758e17 | − | 2.60623e17i | −0.0463081 | − | 0.113049i | ||||
\(421\) | 3.64786e18 | 1.55619 | 0.778097 | − | 0.628144i | \(-0.216185\pi\) | ||||
0.778097 | + | 0.628144i | \(0.216185\pi\) | |||||||
\(422\) | − | 8.67117e16i | − | 0.0363824i | ||||||
\(423\) | 1.84145e18 | + | 1.87056e18i | 0.759938 | + | 0.771951i | ||||
\(424\) | 6.66651e17 | 0.270606 | ||||||||
\(425\) | 1.05686e18i | 0.421984i | ||||||||
\(426\) | −9.05829e17 | + | 3.71052e17i | −0.355778 | + | 0.145736i | ||||
\(427\) | 6.75229e17 | 0.260889 | ||||||||
\(428\) | 6.70285e17i | 0.254773i | ||||||||
\(429\) | −1.50006e18 | − | 3.66201e18i | −0.560929 | − | 1.36936i | ||||
\(430\) | −4.45453e17 | −0.163879 | ||||||||
\(431\) | 3.81936e18i | 1.38245i | 0.722640 | + | 0.691225i | \(0.242929\pi\) | ||||
−0.722640 | + | 0.691225i | \(0.757071\pi\) | |||||||
\(432\) | −2.76247e17 | + | 6.45343e17i | −0.0983809 | + | 0.229829i | ||||
\(433\) | 1.76262e18 | 0.617653 | 0.308827 | − | 0.951118i | \(-0.400064\pi\) | ||||
0.308827 | + | 0.951118i | \(0.400064\pi\) | |||||||
\(434\) | − | 2.55694e17i | − | 0.0881641i | ||||||
\(435\) | 6.54669e17 | − | 2.68170e17i | 0.222125 | − | 0.0909884i | ||||
\(436\) | −1.41726e18 | −0.473200 | ||||||||
\(437\) | 9.67737e18i | 3.17971i | ||||||||
\(438\) | −7.32949e17 | − | 1.78931e18i | −0.237004 | − | 0.578584i | ||||
\(439\) | −2.33405e18 | −0.742778 | −0.371389 | − | 0.928477i | \(-0.621118\pi\) | ||||
−0.371389 | + | 0.928477i | \(0.621118\pi\) | |||||||
\(440\) | 9.61385e17i | 0.301112i | ||||||||
\(441\) | −1.79628e18 | + | 1.76832e18i | −0.553736 | + | 0.545119i | ||||
\(442\) | 1.20743e18 | 0.366359 | ||||||||
\(443\) | − | 5.51352e18i | − | 1.64665i | −0.567567 | − | 0.823327i | \(-0.692115\pi\) | ||
0.567567 | − | 0.823327i | \(-0.307885\pi\) | |||||||
\(444\) | 4.43925e17 | − | 1.81844e17i | 0.130506 | − | 0.0534587i | ||||
\(445\) | 2.88074e18 | 0.833650 | ||||||||
\(446\) | 2.13597e18i | 0.608488i | ||||||||
\(447\) | −1.19175e18 | − | 2.90935e18i | −0.334220 | − | 0.815911i | ||||
\(448\) | −2.13785e17 | −0.0590243 | ||||||||
\(449\) | − | 1.61107e18i | − | 0.437916i | −0.975734 | − | 0.218958i | \(-0.929734\pi\) | ||
0.975734 | − | 0.218958i | \(-0.0702657\pi\) | |||||||
\(450\) | 1.35734e18 | + | 1.37879e18i | 0.363246 | + | 0.368988i | ||||
\(451\) | −4.65105e18 | −1.22551 | ||||||||
\(452\) | 8.09188e17i | 0.209933i | ||||||||
\(453\) | 2.74725e18 | − | 1.12535e18i | 0.701796 | − | 0.287475i | ||||
\(454\) | 1.41416e18 | 0.355719 | ||||||||
\(455\) | 8.86847e17i | 0.219669i | ||||||||
\(456\) | −8.81671e17 | − | 2.15237e18i | −0.215057 | − | 0.525005i | ||||
\(457\) | 2.15795e18 | 0.518357 | 0.259178 | − | 0.965829i | \(-0.416548\pi\) | ||||
0.259178 | + | 0.965829i | \(0.416548\pi\) | |||||||
\(458\) | − | 3.61959e18i | − | 0.856252i | ||||||
\(459\) | −2.27398e18 | − | 9.73405e17i | −0.529783 | − | 0.226780i | ||||
\(460\) | 2.23424e18 | 0.512655 | ||||||||
\(461\) | − | 7.87564e18i | − | 1.77983i | −0.456122 | − | 0.889917i | \(-0.650762\pi\) | ||
0.456122 | − | 0.889917i | \(-0.349238\pi\) | |||||||
\(462\) | −2.28470e18 | + | 9.35878e17i | −0.508553 | + | 0.208317i | ||||
\(463\) | 6.63457e17 | 0.145461 | 0.0727304 | − | 0.997352i | \(-0.476829\pi\) | ||||
0.0727304 | + | 0.997352i | \(0.476829\pi\) | |||||||
\(464\) | − | 5.37015e17i | − | 0.115974i | ||||||
\(465\) | −2.43457e17 | − | 5.94338e17i | −0.0517907 | − | 0.126434i | ||||
\(466\) | 2.49997e18 | 0.523882 | ||||||||
\(467\) | 4.86419e18i | 1.00414i | 0.864828 | + | 0.502068i | \(0.167427\pi\) | ||||
−0.864828 | + | 0.502068i | \(0.832573\pi\) | |||||||
\(468\) | 1.57523e18 | − | 1.55071e18i | 0.320348 | − | 0.315363i | ||||
\(469\) | −2.91710e18 | −0.584441 | ||||||||
\(470\) | 2.00796e18i | 0.396342i | ||||||||
\(471\) | 5.43839e18 | − | 2.22771e18i | 1.05761 | − | 0.433225i | ||||
\(472\) | −9.61643e17 | −0.184255 | ||||||||
\(473\) | 3.90498e18i | 0.737210i | ||||||||
\(474\) | 1.67066e18 | + | 4.07849e18i | 0.310771 | + | 0.758666i | ||||
\(475\) | −6.41077e18 | −1.17505 | ||||||||
\(476\) | − | 7.53309e17i | − | 0.136058i | ||||||
\(477\) | 3.01692e18 | + | 3.06461e18i | 0.536951 | + | 0.545439i | ||||
\(478\) | 1.60690e18 | 0.281834 | ||||||||
\(479\) | − | 4.20027e18i | − | 0.725987i | −0.931792 | − | 0.362994i | \(-0.881755\pi\) | ||
0.931792 | − | 0.362994i | \(-0.118245\pi\) | |||||||
\(480\) | −4.96925e17 | + | 2.03554e17i | −0.0846451 | + | 0.0346730i | ||||
\(481\) | −1.51059e18 | −0.253589 | ||||||||
\(482\) | − | 7.22970e17i | − | 0.119616i | ||||||
\(483\) | 2.17496e18 | + | 5.30961e18i | 0.354668 | + | 0.865830i | ||||
\(484\) | 5.31690e18 | 0.854557 | ||||||||
\(485\) | − | 3.53880e18i | − | 0.560614i | ||||||
\(486\) | −4.21681e18 | + | 1.65058e18i | −0.658460 | + | 0.257740i | ||||
\(487\) | −7.32539e18 | −1.12753 | −0.563765 | − | 0.825935i | \(-0.690648\pi\) | ||||
−0.563765 | + | 0.825935i | \(0.690648\pi\) | |||||||
\(488\) | − | 1.28745e18i | − | 0.195340i | ||||||
\(489\) | −2.66374e18 | + | 1.09114e18i | −0.398410 | + | 0.163200i | ||||
\(490\) | −1.92822e18 | −0.284305 | ||||||||
\(491\) | − | 1.51721e18i | − | 0.220533i | −0.993902 | − | 0.110267i | \(-0.964830\pi\) | ||
0.993902 | − | 0.110267i | \(-0.0351705\pi\) | |||||||
\(492\) | −9.84767e17 | − | 2.40405e18i | −0.141116 | − | 0.344499i | ||||
\(493\) | 1.89227e18 | 0.267334 | ||||||||
\(494\) | 7.32409e18i | 1.02015i | ||||||||
\(495\) | −4.41951e18 | + | 4.35073e18i | −0.606929 | + | 0.597484i | ||||
\(496\) | −4.87526e17 | −0.0660125 | ||||||||
\(497\) | − | 1.92306e18i | − | 0.256743i | ||||||
\(498\) | −4.89407e18 | + | 2.00474e18i | −0.644265 | + | 0.263909i | ||||
\(499\) | 7.25157e18 | 0.941300 | 0.470650 | − | 0.882320i | \(-0.344019\pi\) | ||||
0.470650 | + | 0.882320i | \(0.344019\pi\) | |||||||
\(500\) | 3.50132e18i | 0.448169i | ||||||||
\(501\) | 4.61423e18 | + | 1.12645e19i | 0.582418 | + | 1.42182i | ||||
\(502\) | −1.28628e18 | −0.160107 | ||||||||
\(503\) | − | 8.22025e17i | − | 0.100904i | −0.998726 | − | 0.0504521i | \(-0.983934\pi\) | ||
0.998726 | − | 0.0504521i | \(-0.0160662\pi\) | |||||||
\(504\) | −9.67480e17 | − | 9.82774e17i | −0.117119 | − | 0.118971i | ||||
\(505\) | 3.04581e17 | 0.0363633 | ||||||||
\(506\) | − | 1.95861e19i | − | 2.30618i | ||||||
\(507\) | 1.52749e18 | − | 6.25703e17i | 0.177388 | − | 0.0726628i | ||||
\(508\) | −7.84707e18 | −0.898797 | ||||||||
\(509\) | 6.28539e18i | 0.710081i | 0.934851 | + | 0.355040i | \(0.115533\pi\) | ||||
−0.934851 | + | 0.355040i | \(0.884467\pi\) | |||||||
\(510\) | −7.17258e17 | − | 1.75100e18i | −0.0799253 | − | 0.195117i | ||||
\(511\) | 3.79867e18 | 0.417528 | ||||||||
\(512\) | 4.07619e17i | 0.0441942i | ||||||||
\(513\) | 5.90452e18 | − | 1.37936e19i | 0.631485 | − | 1.47522i | ||||
\(514\) | 8.86545e18 | 0.935318 | ||||||||
\(515\) | − | 4.56256e18i | − | 0.474851i | ||||||
\(516\) | −2.01842e18 | + | 8.26801e17i | −0.207235 | + | 0.0848894i | ||||
\(517\) | 1.76024e19 | 1.78295 | ||||||||
\(518\) | 9.42446e17i | 0.0941777i | ||||||||
\(519\) | −2.94781e18 | − | 7.19631e18i | −0.290621 | − | 0.709477i | ||||
\(520\) | 1.69093e18 | 0.164476 | ||||||||
\(521\) | − | 1.31562e18i | − | 0.126260i | −0.998005 | − | 0.0631299i | \(-0.979892\pi\) | ||
0.998005 | − | 0.0631299i | \(-0.0201083\pi\) | |||||||
\(522\) | 2.46867e18 | − | 2.43025e18i | 0.233759 | − | 0.230122i | ||||
\(523\) | 8.43843e18 | 0.788406 | 0.394203 | − | 0.919023i | \(-0.371021\pi\) | ||||
0.394203 | + | 0.919023i | \(0.371021\pi\) | |||||||
\(524\) | 2.50814e18i | 0.231224i | ||||||||
\(525\) | −3.51735e18 | + | 1.44080e18i | −0.319964 | + | 0.131066i | ||||
\(526\) | −1.41255e19 | −1.26796 | ||||||||
\(527\) | − | 1.71788e18i | − | 0.152167i | ||||||
\(528\) | 1.78442e18 | + | 4.35620e18i | 0.155977 | + | 0.380777i | ||||
\(529\) | −3.39248e19 | −2.92636 | ||||||||
\(530\) | 3.28972e18i | 0.280045i | ||||||||
\(531\) | −4.35190e18 | − | 4.42069e18i | −0.365609 | − | 0.371389i | ||||
\(532\) | 4.56945e18 | 0.378864 | ||||||||
\(533\) | 8.18051e18i | 0.669407i | ||||||||
\(534\) | 1.30531e19 | − | 5.34692e18i | 1.05421 | − | 0.431832i | ||||
\(535\) | −3.30765e18 | −0.263659 | ||||||||
\(536\) | 5.56197e18i | 0.437598i | ||||||||
\(537\) | −1.23400e18 | − | 3.01250e18i | −0.0958287 | − | 0.233941i | ||||
\(538\) | 2.43982e18 | 0.187017 | ||||||||
\(539\) | 1.69034e19i | 1.27895i | ||||||||
\(540\) | −3.18457e18 | − | 1.36319e18i | −0.237845 | − | 0.101812i | ||||
\(541\) | 4.60856e17 | 0.0339769 | 0.0169885 | − | 0.999856i | \(-0.494592\pi\) | ||||
0.0169885 | + | 0.999856i | \(0.494592\pi\) | |||||||
\(542\) | 1.12143e19i | 0.816166i | ||||||||
\(543\) | −7.03639e18 | + | 2.88230e18i | −0.505535 | + | 0.207081i | ||||
\(544\) | −1.43632e18 | −0.101873 | ||||||||
\(545\) | − | 6.99375e18i | − | 0.489705i | ||||||
\(546\) | 1.64607e18 | + | 4.01846e18i | 0.113789 | + | 0.277786i | ||||
\(547\) | 1.04234e19 | 0.711376 | 0.355688 | − | 0.934605i | \(-0.384247\pi\) | ||||
0.355688 | + | 0.934605i | \(0.384247\pi\) | |||||||
\(548\) | − | 1.23355e17i | − | 0.00831173i | ||||||
\(549\) | 5.91842e18 | − | 5.82632e18i | 0.393731 | − | 0.387603i | ||||
\(550\) | 1.29748e19 | 0.852239 | ||||||||
\(551\) | 1.14782e19i | 0.744410i | ||||||||
\(552\) | 1.01237e19 | − | 4.14696e18i | 0.648286 | − | 0.265556i | ||||
\(553\) | −8.65856e18 | −0.547482 | ||||||||
\(554\) | − | 3.61266e18i | − | 0.225558i | ||||||
\(555\) | 8.97344e17 | + | 2.19063e18i | 0.0553233 | + | 0.135058i | ||||
\(556\) | −6.19905e18 | −0.377400 | ||||||||
\(557\) | 5.90126e16i | 0.00354779i | 0.999998 | + | 0.00177390i | \(0.000564649\pi\) | ||||
−0.999998 | + | 0.00177390i | \(0.999435\pi\) | |||||||
\(558\) | −2.20629e18 | − | 2.24117e18i | −0.130986 | − | 0.133056i | ||||
\(559\) | 6.86828e18 | 0.402685 | ||||||||
\(560\) | − | 1.05496e18i | − | 0.0610831i | ||||||
\(561\) | −1.53498e19 | + | 6.28772e18i | −0.877736 | + | 0.359545i | ||||
\(562\) | −2.16482e19 | −1.22255 | ||||||||
\(563\) | 7.69233e18i | 0.429041i | 0.976719 | + | 0.214521i | \(0.0688189\pi\) | ||||
−0.976719 | + | 0.214521i | \(0.931181\pi\) | |||||||
\(564\) | 3.72696e18 | + | 9.09842e18i | 0.205306 | + | 0.501202i | ||||
\(565\) | −3.99309e18 | −0.217255 | ||||||||
\(566\) | 7.91450e17i | 0.0425313i | ||||||||
\(567\) | 1.39515e17 | − | 8.89506e18i | 0.00740524 | − | 0.472136i | ||||
\(568\) | −3.66666e18 | −0.192235 | ||||||||
\(569\) | − | 1.74875e19i | − | 0.905612i | −0.891609 | − | 0.452806i | \(-0.850423\pi\) | ||
0.891609 | − | 0.452806i | \(-0.149577\pi\) | |||||||
\(570\) | 1.06213e19 | − | 4.35078e18i | 0.543318 | − | 0.222558i | ||||
\(571\) | 3.30803e19 | 1.67154 | 0.835769 | − | 0.549081i | \(-0.185022\pi\) | ||||
0.835769 | + | 0.549081i | \(0.185022\pi\) | |||||||
\(572\) | − | 1.48233e19i | − | 0.739898i | ||||||
\(573\) | −3.39892e18 | − | 8.29758e18i | −0.167594 | − | 0.409137i | ||||
\(574\) | 5.10377e18 | 0.248604 | ||||||||
\(575\) | − | 3.01532e19i | − | 1.45097i | ||||||
\(576\) | −1.87384e18 | + | 1.84468e18i | −0.0890787 | + | 0.0876925i | ||||
\(577\) | −1.68751e19 | −0.792530 | −0.396265 | − | 0.918136i | \(-0.629694\pi\) | ||||
−0.396265 | + | 0.918136i | \(0.629694\pi\) | |||||||
\(578\) | 1.01787e19i | 0.472278i | ||||||||
\(579\) | −1.60248e19 | + | 6.56418e18i | −0.734584 | + | 0.300906i | ||||
\(580\) | 2.65000e18 | 0.120019 | ||||||||
\(581\) | − | 1.03900e19i | − | 0.464926i | ||||||
\(582\) | −6.56834e18 | − | 1.60349e19i | −0.290399 | − | 0.708934i | ||||
\(583\) | 2.88387e19 | 1.25978 | ||||||||
\(584\) | − | 7.24285e18i | − | 0.312622i | ||||||
\(585\) | 7.65230e18 | + | 7.77326e18i | 0.326363 | + | 0.331522i | ||||
\(586\) | 2.01988e18 | 0.0851221 | ||||||||
\(587\) | − | 2.61913e18i | − | 0.109066i | −0.998512 | − | 0.0545331i | \(-0.982633\pi\) | ||
0.998512 | − | 0.0545331i | \(-0.0173670\pi\) | |||||||
\(588\) | −8.73710e18 | + | 3.57896e18i | −0.359522 | + | 0.147270i | ||||
\(589\) | 1.04204e19 | 0.423719 | ||||||||
\(590\) | − | 4.74541e18i | − | 0.190682i | ||||||
\(591\) | 1.37194e19 | + | 3.34923e19i | 0.544781 | + | 1.32994i | ||||
\(592\) | 1.79694e18 | 0.0705151 | ||||||||
\(593\) | 1.72412e19i | 0.668628i | 0.942462 | + | 0.334314i | \(0.108505\pi\) | ||||
−0.942462 | + | 0.334314i | \(0.891495\pi\) | |||||||
\(594\) | −1.19502e19 | + | 2.79169e19i | −0.458004 | + | 1.06995i | ||||
\(595\) | 3.71735e18 | 0.140804 | ||||||||
\(596\) | − | 1.17766e19i | − | 0.440855i | ||||||
\(597\) | 2.30730e19 | − | 9.45132e18i | 0.853656 | − | 0.349681i | ||||
\(598\) | −3.44490e19 | −1.25970 | ||||||||
\(599\) | 1.31700e19i | 0.475992i | 0.971266 | + | 0.237996i | \(0.0764905\pi\) | ||||
−0.971266 | + | 0.237996i | \(0.923510\pi\) | |||||||
\(600\) | 2.74715e18 | + | 6.70646e18i | 0.0981349 | + | 0.239571i | ||||
\(601\) | −2.22713e19 | −0.786366 | −0.393183 | − | 0.919460i | \(-0.628626\pi\) | ||||
−0.393183 | + | 0.919460i | \(0.628626\pi\) | |||||||
\(602\) | − | 4.28508e18i | − | 0.149549i | ||||||
\(603\) | −2.55685e19 | + | 2.51706e19i | −0.882031 | + | 0.868305i | ||||
\(604\) | 1.11205e19 | 0.379197 | ||||||||
\(605\) | 2.62373e19i | 0.884364i | ||||||||
\(606\) | 1.38011e18 | − | 5.65331e17i | 0.0459838 | − | 0.0188362i | ||||
\(607\) | −9.19398e18 | −0.302819 | −0.151409 | − | 0.988471i | \(-0.548381\pi\) | ||||
−0.151409 | + | 0.988471i | \(0.548381\pi\) | |||||||
\(608\) | − | 8.71249e18i | − | 0.283672i | ||||||
\(609\) | 2.57969e18 | + | 6.29766e18i | 0.0830323 | + | 0.202702i | ||||
\(610\) | 6.35315e18 | 0.202153 | ||||||||
\(611\) | − | 3.09601e19i | − | 0.973899i | ||||||
\(612\) | −6.50004e18 | − | 6.60279e18i | −0.202142 | − | 0.205337i | ||||
\(613\) | −1.27074e19 | −0.390691 | −0.195346 | − | 0.980734i | \(-0.562583\pi\) | ||||
−0.195346 | + | 0.980734i | \(0.562583\pi\) | |||||||
\(614\) | 2.70899e19i | 0.823433i | ||||||||
\(615\) | 1.18633e19 | − | 4.85952e18i | 0.356516 | − | 0.146039i | ||||
\(616\) | −9.24814e18 | −0.274783 | ||||||||
\(617\) | − | 3.04798e19i | − | 0.895399i | −0.894184 | − | 0.447699i | \(-0.852243\pi\) | ||
0.894184 | − | 0.447699i | \(-0.147757\pi\) | |||||||
\(618\) | −8.46853e18 | − | 2.06737e19i | −0.245974 | − | 0.600481i | ||||
\(619\) | −5.37193e19 | −1.54275 | −0.771375 | − | 0.636380i | \(-0.780431\pi\) | ||||
−0.771375 | + | 0.636380i | \(0.780431\pi\) | |||||||
\(620\) | − | 2.40579e18i | − | 0.0683150i | ||||||
\(621\) | 6.48784e19 | + | 2.77720e19i | 1.82163 | + | 0.779769i | ||||
\(622\) | 4.13808e19 | 1.14886 | ||||||||
\(623\) | 2.77116e19i | 0.760755i | ||||||||
\(624\) | 7.66191e18 | − | 3.13853e18i | 0.207991 | − | 0.0851989i | ||||
\(625\) | 1.00007e19 | 0.268454 | ||||||||
\(626\) | 2.16565e19i | 0.574868i | ||||||||
\(627\) | −3.81403e19 | − | 9.31098e19i | −1.00118 | − | 2.44412i | ||||
\(628\) | 2.20138e19 | 0.571449 | ||||||||
\(629\) | 6.33185e18i | 0.162546i | ||||||||
\(630\) | 4.84969e18 | − | 4.77422e18i | 0.123120 | − | 0.121204i | ||||
\(631\) | −4.49810e19 | −1.12934 | −0.564669 | − | 0.825318i | \(-0.690996\pi\) | ||||
−0.564669 | + | 0.825318i | \(0.690996\pi\) | |||||||
\(632\) | 1.65091e19i | 0.409925i | ||||||||
\(633\) | 1.93887e18 | − | 7.94214e17i | 0.0476127 | − | 0.0195035i | ||||
\(634\) | 3.13587e19 | 0.761612 | ||||||||
\(635\) | − | 3.87229e19i | − | 0.930147i | ||||||
\(636\) | 6.10602e18 | + | 1.49063e19i | 0.145063 | + | 0.354135i | ||||
\(637\) | 2.97306e19 | 0.698598 | ||||||||
\(638\) | − | 2.32308e19i | − | 0.539907i | ||||||
\(639\) | −1.65934e19 | − | 1.68557e19i | −0.381443 | − | 0.387473i | ||||
\(640\) | −2.01148e18 | −0.0457357 | ||||||||
\(641\) | 1.10795e19i | 0.249180i | 0.992208 | + | 0.124590i | \(0.0397615\pi\) | ||||
−0.992208 | + | 0.124590i | \(0.960238\pi\) | |||||||
\(642\) | −1.49875e19 | + | 6.13931e18i | −0.333415 | + | 0.136576i | ||||
\(643\) | 5.52622e19 | 1.21605 | 0.608025 | − | 0.793918i | \(-0.291962\pi\) | ||||
0.608025 | + | 0.793918i | \(0.291962\pi\) | |||||||
\(644\) | 2.14925e19i | 0.467828i | ||||||||
\(645\) | −4.08001e18 | − | 9.96029e18i | −0.0878503 | − | 0.214464i | ||||
\(646\) | 3.07000e19 | 0.653899 | ||||||||
\(647\) | 1.49668e19i | 0.315355i | 0.987491 | + | 0.157678i | \(0.0504007\pi\) | ||||
−0.987491 | + | 0.157678i | \(0.949599\pi\) | |||||||
\(648\) | −1.69600e19 | − | 2.66010e17i | −0.353510 | − | 0.00554464i | ||||
\(649\) | −4.15998e19 | −0.857785 | ||||||||
\(650\) | − | 2.28207e19i | − | 0.465517i | ||||||
\(651\) | 5.71729e18 | − | 2.34196e18i | 0.115378 | − | 0.0472621i | ||||
\(652\) | −1.07824e19 | −0.215270 | ||||||||
\(653\) | 1.04550e19i | 0.206506i | 0.994655 | + | 0.103253i | \(0.0329251\pi\) | ||||
−0.994655 | + | 0.103253i | \(0.967075\pi\) | |||||||
\(654\) | −1.29811e19 | − | 3.16899e19i | −0.253668 | − | 0.619265i | ||||
\(655\) | −1.23769e19 | −0.239289 | ||||||||
\(656\) | − | 9.73125e18i | − | 0.186141i | ||||||
\(657\) | 3.32955e19 | − | 3.27774e19i | 0.630127 | − | 0.620322i | ||||
\(658\) | −1.93158e19 | −0.361686 | ||||||||
\(659\) | 1.04417e20i | 1.93452i | 0.253789 | + | 0.967260i | \(0.418323\pi\) | ||||
−0.253789 | + | 0.967260i | \(0.581677\pi\) | |||||||
\(660\) | −2.14965e19 | + | 8.80556e18i | −0.394058 | + | 0.161417i | ||||
\(661\) | 1.08289e18 | 0.0196415 | 0.00982073 | − | 0.999952i | \(-0.496874\pi\) | ||||
0.00982073 | + | 0.999952i | \(0.496874\pi\) | |||||||
\(662\) | − | 2.46568e19i | − | 0.442519i | ||||||
\(663\) | 1.10592e19 | + | 2.69981e19i | 0.196394 | + | 0.479445i | ||||
\(664\) | −1.98104e19 | −0.348111 | ||||||||
\(665\) | 2.25489e19i | 0.392078i | ||||||||
\(666\) | 8.13204e18 | + | 8.26058e18i | 0.139920 | + | 0.142132i | ||||
\(667\) | −5.39879e19 | −0.919211 | ||||||||
\(668\) | 4.55968e19i | 0.768244i | ||||||||
\(669\) | −4.77602e19 | + | 1.95639e19i | −0.796313 | + | 0.326192i | ||||
\(670\) | −2.74466e19 | −0.452861 | ||||||||
\(671\) | − | 5.56937e19i | − | 0.909387i | ||||||
\(672\) | −1.95811e18 | − | 4.78022e18i | −0.0316411 | − | 0.0772436i | ||||
\(673\) | 9.20725e19 | 1.47239 | 0.736197 | − | 0.676767i | \(-0.236620\pi\) | ||||
0.736197 | + | 0.676767i | \(0.236620\pi\) | |||||||
\(674\) | 4.34875e19i | 0.688248i | ||||||||
\(675\) | −1.83976e19 | + | 4.29787e19i | −0.288160 | + | 0.673173i | ||||
\(676\) | 6.18306e18 | 0.0958466 | ||||||||
\(677\) | 5.38915e19i | 0.826799i | 0.910550 | + | 0.413399i | \(0.135659\pi\) | ||||
−0.910550 | + | 0.413399i | \(0.864341\pi\) | |||||||
\(678\) | −1.80934e19 | + | 7.41155e18i | −0.274734 | + | 0.112539i | ||||
\(679\) | 3.40419e19 | 0.511594 | ||||||||
\(680\) | − | 7.08779e18i | − | 0.105426i | ||||||
\(681\) | 1.29526e19 | + | 3.16205e19i | 0.190690 | + | 0.465521i | ||||
\(682\) | −2.10899e19 | −0.307316 | ||||||||
\(683\) | − | 5.26049e19i | − | 0.758719i | −0.925249 | − | 0.379360i | \(-0.876144\pi\) | ||
0.925249 | − | 0.379360i | \(-0.123856\pi\) | |||||||
\(684\) | 4.00515e19 | − | 3.94282e19i | 0.571776 | − | 0.562878i | ||||
\(685\) | 6.08717e17 | 0.00860164 | ||||||||
\(686\) | − | 4.24199e19i | − | 0.593337i | ||||||
\(687\) | 8.09339e19 | − | 3.31527e19i | 1.12055 | − | 0.459010i | ||||
\(688\) | −8.17027e18 | −0.111974 | ||||||||
\(689\) | − | 5.07230e19i | − | 0.688130i | ||||||
\(690\) | 2.04640e19 | + | 4.99575e19i | 0.274818 | + | 0.670898i | ||||
\(691\) | 1.69293e19 | 0.225057 | 0.112529 | − | 0.993648i | \(-0.464105\pi\) | ||||
0.112529 | + | 0.993648i | \(0.464105\pi\) | |||||||
\(692\) | − | 2.91296e19i | − | 0.383347i | ||||||
\(693\) | −4.18523e19 | − | 4.25139e19i | −0.545239 | − | 0.553858i | ||||
\(694\) | −3.36083e19 | −0.433442 | ||||||||
\(695\) | − | 3.05904e19i | − | 0.390564i | ||||||
\(696\) | 1.20076e19 | − | 4.91865e18i | 0.151772 | − | 0.0621700i | ||||
\(697\) | 3.42898e19 | 0.429077 | ||||||||
\(698\) | − | 6.00729e19i | − | 0.744202i | ||||||
\(699\) | 2.28978e19 | + | 5.58992e19i | 0.280837 | + | 0.685591i | ||||
\(700\) | −1.42377e19 | −0.172884 | ||||||||
\(701\) | − | 1.46538e20i | − | 1.76166i | −0.473430 | − | 0.880831i | \(-0.656984\pi\) | ||
0.473430 | − | 0.880831i | \(-0.343016\pi\) | |||||||
\(702\) | 4.91018e19 | + | 2.10186e19i | 0.584436 | + | 0.250175i | ||||
\(703\) | −3.84080e19 | −0.452621 | ||||||||
\(704\) | 1.76332e19i | 0.205742i | ||||||||
\(705\) | −4.48979e19 | + | 1.83914e19i | −0.518683 | + | 0.212467i | ||||
\(706\) | −7.51835e19 | −0.859983 | ||||||||
\(707\) | 2.92995e18i | 0.0331837i | ||||||||
\(708\) | −8.80792e18 | − | 2.15023e19i | −0.0987735 | − | 0.241130i | ||||
\(709\) | −6.40379e19 | −0.711072 | −0.355536 | − | 0.934663i | \(-0.615702\pi\) | ||||
−0.355536 | + | 0.934663i | \(0.615702\pi\) | |||||||
\(710\) | − | 1.80938e19i | − | 0.198940i | ||||||
\(711\) | −7.58928e19 | + | 7.47117e19i | −0.826253 | + | 0.813395i | ||||
\(712\) | 5.28371e19 | 0.569611 | ||||||||
\(713\) | 4.90126e19i | 0.523216i | ||||||||
\(714\) | 1.68439e19 | − | 6.89974e18i | 0.178056 | − | 0.0729366i | ||||
\(715\) | 7.31483e19 | 0.765705 | ||||||||
\(716\) | − | 1.21941e19i | − | 0.126404i | ||||||
\(717\) | 1.47180e19 | + | 3.59302e19i | 0.151083 | + | 0.368830i | ||||
\(718\) | 7.09823e19 | 0.721570 | ||||||||
\(719\) | − | 7.12152e18i | − | 0.0716920i | −0.999357 | − | 0.0358460i | \(-0.988587\pi\) | ||
0.999357 | − | 0.0358460i | \(-0.0114126\pi\) | |||||||
\(720\) | −9.10291e18 | − | 9.24680e18i | −0.0907512 | − | 0.0921858i | ||||
\(721\) | 4.38900e19 | 0.433330 | ||||||||
\(722\) | 1.13904e20i | 1.11372i | ||||||||
\(723\) | 1.61656e19 | − | 6.62186e18i | 0.156539 | − | 0.0641227i | ||||
\(724\) | −2.84822e19 | −0.273152 | ||||||||
\(725\) | − | 3.57643e19i | − | 0.339690i | ||||||
\(726\) | 4.86988e19 | + | 1.18886e20i | 0.458102 | + | 1.11834i | ||||
\(727\) | −6.63685e19 | −0.618331 | −0.309165 | − | 0.951008i | \(-0.600050\pi\) | ||||
−0.309165 | + | 0.951008i | \(0.600050\pi\) | |||||||
\(728\) | 1.62661e19i | 0.150094i | ||||||||
\(729\) | −7.55295e19 | − | 7.91695e19i | −0.690278 | − | 0.723544i | ||||
\(730\) | 3.57412e19 | 0.323526 | ||||||||
\(731\) | − | 2.87894e19i | − | 0.258114i | ||||||
\(732\) | 2.87872e19 | − | 1.17920e19i | 0.255636 | − | 0.104715i | ||||
\(733\) | −8.99402e19 | −0.791090 | −0.395545 | − | 0.918447i | \(-0.629444\pi\) | ||||
−0.395545 | + | 0.918447i | \(0.629444\pi\) | |||||||
\(734\) | − | 1.66655e19i | − | 0.145193i | ||||||
\(735\) | −1.76610e19 | − | 4.31149e19i | −0.152407 | − | 0.372062i | ||||
\(736\) | 4.09793e19 | 0.350284 | ||||||||
\(737\) | 2.40606e20i | 2.03720i | ||||||||
\(738\) | 4.47348e19 | − | 4.40386e19i | 0.375190 | − | 0.369351i | ||||
\(739\) | 1.79121e20 | 1.48811 | 0.744056 | − | 0.668118i | \(-0.232900\pi\) | ||||
0.744056 | + | 0.668118i | \(0.232900\pi\) | |||||||
\(740\) | 8.86736e18i | 0.0729747i | ||||||||
\(741\) | −1.63766e20 | + | 6.70832e19i | −1.33505 | + | 0.546872i | ||||
\(742\) | −3.16458e19 | −0.255557 | ||||||||
\(743\) | 8.18780e19i | 0.655007i | 0.944850 | + | 0.327503i | \(0.106207\pi\) | ||||
−0.944850 | + | 0.327503i | \(0.893793\pi\) | |||||||
\(744\) | −4.46537e18 | − | 1.09011e19i | −0.0353873 | − | 0.0863889i | ||||
\(745\) | 5.81139e19 | 0.456232 | ||||||||
\(746\) | 3.13060e18i | 0.0243476i | ||||||||
\(747\) | −8.96519e19 | − | 9.10691e19i | −0.690741 | − | 0.701660i | ||||
\(748\) | −6.21339e19 | −0.474261 | ||||||||
\(749\) | − | 3.18183e19i | − | 0.240605i | ||||||
\(750\) | −7.82893e19 | + | 3.20695e19i | −0.586508 | + | 0.240250i | ||||
\(751\) | −1.87139e20 | −1.38895 | −0.694474 | − | 0.719518i | \(-0.744363\pi\) | ||||
−0.694474 | + | 0.719518i | \(0.744363\pi\) | |||||||
\(752\) | 3.68291e19i | 0.270811i | ||||||||
\(753\) | −1.17814e19 | − | 2.87612e19i | −0.0858284 | − | 0.209528i | ||||
\(754\) | −4.08595e19 | −0.294913 | ||||||||
\(755\) | 5.48761e19i | 0.392423i | ||||||||
\(756\) | 1.31134e19 | − | 3.06343e19i | 0.0929099 | − | 0.217048i | ||||
\(757\) | 3.06234e18 | 0.0214972 | 0.0107486 | − | 0.999942i | \(-0.496579\pi\) | ||||
0.0107486 | + | 0.999942i | \(0.496579\pi\) | |||||||
\(758\) | − | 2.90999e19i | − | 0.202398i | ||||||
\(759\) | 4.37943e20 | − | 1.79394e20i | 3.01804 | − | 1.23627i | ||||
\(760\) | 4.29934e19 | 0.293567 | ||||||||
\(761\) | − | 1.96596e20i | − | 1.33009i | −0.746801 | − | 0.665047i | \(-0.768411\pi\) | ||
0.746801 | − | 0.665047i | \(-0.231589\pi\) | |||||||
\(762\) | −7.18733e19 | − | 1.75460e20i | −0.481818 | − | 1.17623i | ||||
\(763\) | 6.72771e19 | 0.446885 | ||||||||
\(764\) | − | 3.35874e19i | − | 0.221066i | ||||||
\(765\) | 3.25827e19 | − | 3.20757e19i | 0.212499 | − | 0.209193i | ||||
\(766\) | −7.73098e19 | −0.499612 | ||||||||
\(767\) | 7.31679e19i | 0.468547i | ||||||||
\(768\) | −9.11434e18 | + | 3.73348e18i | −0.0578358 | + | 0.0236911i | ||||
\(769\) | 2.28748e20 | 1.43838 | 0.719190 | − | 0.694813i | \(-0.244513\pi\) | ||||
0.719190 | + | 0.694813i | \(0.244513\pi\) | |||||||
\(770\) | − | 4.56367e19i | − | 0.284367i | ||||||
\(771\) | 8.12009e19 | + | 1.98231e20i | 0.501395 | + | 1.22403i | ||||
\(772\) | −6.48658e19 | −0.396913 | ||||||||
\(773\) | − | 1.59306e20i | − | 0.965997i | −0.875621 | − | 0.482999i | \(-0.839548\pi\) | ||
0.875621 | − | 0.482999i | \(-0.160452\pi\) | |||||||
\(774\) | −3.69744e19 | − | 3.75589e19i | −0.222185 | − | 0.225697i | ||||
\(775\) | −3.24684e19 | −0.193352 | ||||||||
\(776\) | − | 6.49070e19i | − | 0.383053i | ||||||
\(777\) | −2.10730e19 | + | 8.63209e18i | −0.123248 | + | 0.0504858i | ||||
\(778\) | 1.76900e20 | 1.02535 | ||||||||
\(779\) | 2.07997e20i | 1.19480i | ||||||||
\(780\) | 1.54877e19 | + | 3.78092e19i | 0.0881706 | + | 0.215246i | ||||
\(781\) | −1.58616e20 | −0.894933 | ||||||||
\(782\) | 1.44398e20i | 0.807446i | ||||||||
\(783\) | 7.69514e19 | + | 3.29400e19i | 0.426466 | + | 0.182554i | ||||
\(784\) | −3.53665e19 | −0.194258 | ||||||||
\(785\) | 1.08631e20i | 0.591381i | ||||||||
\(786\) | −5.60819e19 | + | 2.29727e19i | −0.302597 | + | 0.123952i | ||||
\(787\) | −1.03633e20 | −0.554212 | −0.277106 | − | 0.960839i | \(-0.589375\pi\) | ||||
−0.277106 | + | 0.960839i | \(0.589375\pi\) | |||||||
\(788\) | 1.35572e20i | 0.718599i | ||||||||
\(789\) | −1.29379e20 | − | 3.15846e20i | −0.679713 | − | 1.65934i | ||||
\(790\) | −8.14674e19 | −0.424223 | ||||||||
\(791\) | − | 3.84120e19i | − | 0.198258i | ||||||
\(792\) | −8.10604e19 | + | 7.97990e19i | −0.414699 | + | 0.408245i | ||||
\(793\) | −9.79570e19 | −0.496733 | ||||||||
\(794\) | − | 2.51596e20i | − | 1.26462i | ||||||
\(795\) | −7.35578e19 | + | 3.01313e19i | −0.366487 | + | 0.150123i | ||||
\(796\) | 9.33959e19 | 0.461250 | ||||||||
\(797\) | 3.68547e20i | 1.80420i | 0.431527 | + | 0.902100i | \(0.357975\pi\) | ||||
−0.431527 | + | 0.902100i | \(0.642025\pi\) | |||||||
\(798\) | 4.18528e19 | + | 1.02173e20i | 0.203097 | + | 0.495809i | ||||
\(799\) | −1.29774e20 | −0.624251 | ||||||||
\(800\) | 2.71467e19i | 0.129446i | ||||||||
\(801\) | 2.39113e20 | + | 2.42893e20i | 1.13025 | + | 1.14812i | ||||
\(802\) | 1.96321e20 | 0.919913 | ||||||||
\(803\) | − | 3.13319e20i | − | 1.45539i | ||||||
\(804\) | −1.24365e20 | + | 5.09434e19i | −0.572673 | + | 0.234583i | ||||
\(805\) | −1.06059e20 | −0.484146 | ||||||||
\(806\) | 3.70941e19i | 0.167865i | ||||||||
\(807\) | 2.23469e19 | + | 5.45543e19i | 0.100254 | + | 0.244745i | ||||
\(808\) | 5.58648e18 | 0.0248461 | ||||||||
\(809\) | − | 1.33306e20i | − | 0.587772i | −0.955840 | − | 0.293886i | \(-0.905051\pi\) | ||
0.955840 | − | 0.293886i | \(-0.0949486\pi\) | |||||||
\(810\) | 1.31268e18 | − | 8.36925e19i | 0.00573803 | − | 0.365840i | ||||
\(811\) | 1.22205e20 | 0.529593 | 0.264797 | − | 0.964304i | \(-0.414695\pi\) | ||||
0.264797 | + | 0.964304i | \(0.414695\pi\) | |||||||
\(812\) | 2.54920e19i | 0.109524i | ||||||||
\(813\) | −2.50752e20 | + | 1.02715e20i | −1.06810 | + | 0.437521i | ||||
\(814\) | 7.77341e19 | 0.328277 | ||||||||
\(815\) | − | 5.32079e19i | − | 0.222778i | ||||||
\(816\) | −1.31556e19 | − | 3.21160e19i | −0.0546109 | − | 0.133318i | ||||
\(817\) | 1.74632e20 | 0.718736 | ||||||||
\(818\) | 1.28432e20i | 0.524081i | ||||||||
\(819\) | −7.47757e19 | + | 7.36120e19i | −0.302533 | + | 0.297825i | ||||
\(820\) | 4.80207e19 | 0.192634 | ||||||||
\(821\) | − | 2.89339e20i | − | 1.15082i | −0.817867 | − | 0.575408i | \(-0.804843\pi\) | ||
0.817867 | − | 0.575408i | \(-0.195157\pi\) | |||||||
\(822\) | 2.75820e18 | − | 1.12983e18i | 0.0108773 | − | 0.00445566i | ||||
\(823\) | −4.11108e20 | −1.60752 | −0.803761 | − | 0.594952i | \(-0.797171\pi\) | ||||
−0.803761 | + | 0.594952i | \(0.797171\pi\) | |||||||
\(824\) | − | 8.36841e19i | − | 0.324454i | ||||||
\(825\) | 1.18839e20 | + | 2.90115e20i | 0.456859 | + | 1.11530i | ||||
\(826\) | 4.56490e19 | 0.174009 | ||||||||
\(827\) | 2.05905e19i | 0.0778267i | 0.999243 | + | 0.0389133i | \(0.0123896\pi\) | ||||
−0.999243 | + | 0.0389133i | \(0.987610\pi\) | |||||||
\(828\) | 1.85451e20 | + | 1.88383e20i | 0.695053 | + | 0.706040i | ||||
\(829\) | 4.12783e20 | 1.53405 | 0.767025 | − | 0.641617i | \(-0.221736\pi\) | ||||
0.767025 | + | 0.641617i | \(0.221736\pi\) | |||||||
\(830\) | − | 9.77585e19i | − | 0.360253i | ||||||
\(831\) | 8.07788e19 | − | 3.30892e19i | 0.295182 | − | 0.120915i | ||||
\(832\) | 3.10143e19 | 0.112382 | ||||||||
\(833\) | − | 1.24620e20i | − | 0.447788i | ||||||
\(834\) | −5.67786e19 | − | 1.38610e20i | −0.202312 | − | 0.493894i | ||||
\(835\) | −2.25006e20 | −0.795040 | ||||||||
\(836\) | − | 3.76894e20i | − | 1.32061i | ||||||
\(837\) | 2.99044e19 | − | 6.98600e19i | 0.103910 | − | 0.242745i | ||||
\(838\) | 1.46207e20 | 0.503800 | ||||||||
\(839\) | − | 3.20024e20i | − | 1.09358i | −0.837271 | − | 0.546789i | \(-0.815850\pi\) | ||
0.837271 | − | 0.546789i | \(-0.184150\pi\) | |||||||
\(840\) | 2.35889e19 | − | 9.66266e18i | 0.0799379 | − | 0.0327448i | ||||
\(841\) | 2.33524e20 | 0.784801 | ||||||||
\(842\) | 3.30167e20i | 1.10039i | ||||||||
\(843\) | −1.98281e20 | − | 4.84052e20i | −0.655372 | − | 1.59992i | ||||
\(844\) | 7.84825e18 | 0.0257262 | ||||||||
\(845\) | 3.05115e19i | 0.0991897i | ||||||||
\(846\) | −1.69304e20 | + | 1.66669e20i | −0.545852 | + | 0.537357i | ||||
\(847\) | −2.52392e20 | −0.807034 | ||||||||
\(848\) | 6.03383e19i | 0.191347i | ||||||||
\(849\) | −1.76968e19 | + | 7.24908e18i | −0.0556596 | + | 0.0227997i | ||||
\(850\) | −9.56564e19 | −0.298388 | ||||||||
\(851\) | − | 1.80653e20i | − | 0.558904i | ||||||
\(852\) | −3.35838e19 | − | 8.19863e19i | −0.103051 | − | 0.251573i | ||||
\(853\) | −1.37167e18 | −0.00417453 | −0.00208726 | − | 0.999998i | \(-0.500664\pi\) | ||||
−0.00208726 | + | 0.999998i | \(0.500664\pi\) | |||||||
\(854\) | 6.11148e19i | 0.184476i | ||||||||
\(855\) | 1.94566e20 | + | 1.97642e20i | 0.582512 | + | 0.591720i | ||||
\(856\) | −6.06673e19 | −0.180152 | ||||||||
\(857\) | 1.79112e20i | 0.527544i | 0.964585 | + | 0.263772i | \(0.0849667\pi\) | ||||
−0.964585 | + | 0.263772i | \(0.915033\pi\) | |||||||
\(858\) | 3.31447e20 | − | 1.35770e20i | 0.968286 | − | 0.396636i | ||||
\(859\) | −1.12363e20 | −0.325590 | −0.162795 | − | 0.986660i | \(-0.552051\pi\) | ||||
−0.162795 | + | 0.986660i | \(0.552051\pi\) | |||||||
\(860\) | − | 4.03178e19i | − | 0.115880i | ||||||
\(861\) | 4.67467e19 | + | 1.14120e20i | 0.133269 | + | 0.325342i | ||||
\(862\) | −3.45689e20 | −0.977540 | ||||||||
\(863\) | 5.93686e20i | 1.66526i | 0.553832 | + | 0.832628i | \(0.313165\pi\) | ||||
−0.553832 | + | 0.832628i | \(0.686835\pi\) | |||||||
\(864\) | −5.84097e19 | − | 2.50030e19i | −0.162513 | − | 0.0695658i | ||||
\(865\) | 1.43746e20 | 0.396718 | ||||||||
\(866\) | 1.59535e20i | 0.436747i | ||||||||
\(867\) | −2.27595e20 | + | 9.32292e19i | −0.618058 | + | 0.253173i | ||||
\(868\) | 2.31428e19 | 0.0623415 | ||||||||
\(869\) | 7.14169e20i | 1.90837i | ||||||||
\(870\) | 2.42720e19 | + | 5.92539e19i | 0.0643385 | + | 0.157066i | ||||
\(871\) | 4.23190e20 | 1.11278 | ||||||||
\(872\) | − | 1.28276e20i | − | 0.334603i | ||||||
\(873\) | 2.98379e20 | − | 2.93736e20i | 0.772090 | − | 0.760076i | ||||
\(874\) | −8.75895e20 | −2.24839 | ||||||||
\(875\) | − | 1.66207e20i | − | 0.423246i | ||||||
\(876\) | 1.61950e20 | − | 6.63390e19i | 0.409120 | − | 0.167587i | ||||
\(877\) | −2.81536e20 | −0.705565 | −0.352783 | − | 0.935705i | \(-0.614764\pi\) | ||||
−0.352783 | + | 0.935705i | \(0.614764\pi\) | |||||||
\(878\) | − | 2.11254e20i | − | 0.525223i | ||||||
\(879\) | 1.85006e19 | + | 4.51644e19i | 0.0456313 | + | 0.111397i | ||||
\(880\) | −8.70146e19 | −0.212919 | ||||||||
\(881\) | 4.59687e20i | 1.11592i | 0.829869 | + | 0.557958i | \(0.188415\pi\) | ||||
−0.829869 | + | 0.557958i | \(0.811585\pi\) | |||||||
\(882\) | −1.60050e20 | − | 1.62580e20i | −0.385458 | − | 0.391551i | ||||
\(883\) | 5.05033e20 | 1.20669 | 0.603343 | − | 0.797482i | \(-0.293835\pi\) | ||||
0.603343 | + | 0.797482i | \(0.293835\pi\) | |||||||
\(884\) | 1.09284e20i | 0.259055i | ||||||||
\(885\) | 1.06107e20 | − | 4.34644e19i | 0.249541 | − | 0.102219i | ||||
\(886\) | 4.99027e20 | 1.16436 | ||||||||
\(887\) | 2.84488e20i | 0.658564i | 0.944232 | + | 0.329282i | \(0.106807\pi\) | ||||
−0.944232 | + | 0.329282i | \(0.893193\pi\) | |||||||
\(888\) | 1.64586e19 | + | 4.01795e19i | 0.0378010 | + | 0.0922813i | ||||
\(889\) | 3.72499e20 | 0.848814 | ||||||||
\(890\) | 2.60735e20i | 0.589480i | ||||||||
\(891\) | −7.33676e20 | − | 1.15074e19i | −1.64574 | − | 0.0258126i | ||||
\(892\) | −1.93326e20 | −0.430266 | ||||||||
\(893\) | − | 7.87187e20i | − | 1.73827i | ||||||
\(894\) | 2.63324e20 | − | 1.07865e20i | 0.576936 | − | 0.236329i | ||||
\(895\) | 6.01743e19 | 0.130813 | ||||||||
\(896\) | − | 1.93496e19i | − | 0.0417365i | ||||||
\(897\) | −3.15527e20 | − | 7.70277e20i | −0.675288 | − | 1.64854i | ||||
\(898\) | 1.45818e20 | 0.309653 | ||||||||
\(899\) | 5.81332e19i | 0.122492i | ||||||||
\(900\) | −1.24794e20 | + | 1.22852e20i | −0.260914 | + | 0.256853i | ||||
\(901\) | −2.12613e20 | −0.441078 | ||||||||
\(902\) | − | 4.20965e20i | − | 0.866564i | ||||||
\(903\) | 9.58141e19 | − | 3.92481e19i | 0.195711 | − | 0.0801686i | ||||
\(904\) | −7.32393e19 | −0.148445 | ||||||||
\(905\) | − | 1.40551e20i | − | 0.282679i | ||||||
\(906\) | 1.01855e20 | + | 2.48653e20i | 0.203276 | + | 0.496245i | ||||
\(907\) | 3.38318e20 | 0.669999 | 0.335000 | − | 0.942218i | \(-0.391264\pi\) | ||||
0.335000 | + | 0.942218i | \(0.391264\pi\) | |||||||
\(908\) | 1.27995e20i | 0.251531i | ||||||||
\(909\) | 2.52815e19 | + | 2.56812e19i | 0.0493010 | + | 0.0500804i | ||||
\(910\) | −8.02682e19 | −0.155330 | ||||||||
\(911\) | − | 4.84530e20i | − | 0.930449i | −0.885193 | − | 0.465224i | \(-0.845974\pi\) | ||
0.885193 | − | 0.465224i | \(-0.154026\pi\) | |||||||
\(912\) | 1.94811e20 | − | 7.97998e19i | 0.371235 | − | 0.152068i | ||||
\(913\) | −8.56982e20 | −1.62060 | ||||||||
\(914\) | 1.95316e20i | 0.366534i | ||||||||
\(915\) | 5.81900e19 | + | 1.42056e20i | 0.108368 | + | 0.264552i | ||||
\(916\) | 3.27608e20 | 0.605461 | ||||||||
\(917\) | − | 1.19061e20i | − | 0.218366i | ||||||
\(918\) | 8.81025e19 | − | 2.05817e20i | 0.160358 | − | 0.374613i | ||||
\(919\) | 2.01048e20 | 0.363155 | 0.181577 | − | 0.983377i | \(-0.441880\pi\) | ||||
0.181577 | + | 0.983377i | \(0.441880\pi\) | |||||||
\(920\) | 2.02220e20i | 0.362502i | ||||||||
\(921\) | −6.05728e20 | + | 2.48123e20i | −1.07761 | + | 0.441417i | ||||
\(922\) | 7.12822e20 | 1.25853 | ||||||||
\(923\) | 2.78983e20i | 0.488838i | ||||||||
\(924\) | −8.47060e19 | − | 2.06788e20i | −0.147303 | − | 0.359601i | ||||
\(925\) | 1.19673e20 | 0.206540 | ||||||||
\(926\) | 6.00492e19i | 0.102856i | ||||||||
\(927\) | 3.84698e20 | − | 3.78711e20i | 0.653976 | − | 0.643799i | ||||
\(928\) | 4.86050e19 | 0.0820059 | ||||||||
\(929\) | − | 1.15283e20i | − | 0.193044i | −0.995331 | − | 0.0965220i | \(-0.969228\pi\) | ||
0.995331 | − | 0.0965220i | \(-0.0307718\pi\) | |||||||
\(930\) | 5.37933e19 | − | 2.20352e19i | 0.0894021 | − | 0.0366216i | ||||
\(931\) | 7.55925e20 | 1.24690 | ||||||||
\(932\) | 2.26272e20i | 0.370441i | ||||||||
\(933\) | 3.79017e20 | + | 9.25272e20i | 0.615867 | + | 1.50348i | ||||
\(934\) | −4.40256e20 | −0.710031 | ||||||||
\(935\) | − | 3.06612e20i | − | 0.490803i | ||||||
\(936\) | 1.40355e20 | + | 1.42573e20i | 0.222995 | + | 0.226520i | ||||
\(937\) | −4.45216e20 | −0.702091 | −0.351046 | − | 0.936358i | \(-0.614174\pi\) | ||||
−0.351046 | + | 0.936358i | \(0.614174\pi\) | |||||||
\(938\) | − | 2.64025e20i | − | 0.413262i | ||||||
\(939\) | −4.84238e20 | + | 1.98357e20i | −0.752316 | + | 0.308169i | ||||
\(940\) | −1.81740e20 | −0.280256 | ||||||||
\(941\) | − | 3.84694e20i | − | 0.588828i | −0.955678 | − | 0.294414i | \(-0.904876\pi\) | ||
0.955678 | − | 0.294414i | \(-0.0951244\pi\) | |||||||
\(942\) | 2.01630e20 | + | 4.92227e20i | 0.306336 | + | 0.747841i | ||||
\(943\) | −9.78315e20 | −1.47536 | ||||||||
\(944\) | − | 8.70380e19i | − | 0.130288i | ||||||
\(945\) | 1.51171e20 | + | 6.47105e19i | 0.224618 | + | 0.0961506i | ||||
\(946\) | −3.53439e20 | −0.521286 | ||||||||
\(947\) | 8.36588e20i | 1.22479i | 0.790552 | + | 0.612395i | \(0.209794\pi\) | ||||
−0.790552 | + | 0.612395i | \(0.790206\pi\) | |||||||
\(948\) | −3.69143e20 | + | 1.51211e20i | −0.536458 | + | 0.219748i | ||||
\(949\) | −5.51082e20 | −0.794973 | ||||||||
\(950\) | − | 5.80237e20i | − | 0.830883i | ||||||
\(951\) | 2.87222e20 | + | 7.01179e20i | 0.408277 | + | 0.996702i | ||||
\(952\) | 6.81817e19 | 0.0962076 | ||||||||
\(953\) | 1.09883e20i | 0.153915i | 0.997034 | + | 0.0769575i | \(0.0245206\pi\) | ||||
−0.997034 | + | 0.0769575i | \(0.975479\pi\) | |||||||
\(954\) | −2.77377e20 | + | 2.73060e20i | −0.385684 | + | 0.379682i | ||||
\(955\) | 1.65743e20 | 0.228777 | ||||||||
\(956\) | 1.45440e20i | 0.199287i | ||||||||
\(957\) | 5.19439e20 | − | 2.12776e20i | 0.706563 | − | 0.289427i | ||||
\(958\) | 3.80165e20 | 0.513350 | ||||||||
\(959\) | 5.85561e18i | 0.00784950i | ||||||||
\(960\) | −1.84236e19 | − | 4.49765e19i | −0.0245175 | − | 0.0598531i | ||||
\(961\) | −7.04168e20 | −0.930278 | ||||||||
\(962\) | − | 1.36723e20i | − | 0.179314i | ||||||
\(963\) | −2.74549e20 | − | 2.78889e20i | −0.357467 | − | 0.363118i | ||||
\(964\) | 6.54357e19 | 0.0845816 | ||||||||
\(965\) | − | 3.20093e20i | − | 0.410757i | ||||||
\(966\) | −4.80571e20 | + | 1.96855e20i | −0.612234 | + | 0.250788i | ||||
\(967\) | 2.27258e20 | 0.287431 | 0.143715 | − | 0.989619i | \(-0.454095\pi\) | ||||
0.143715 | + | 0.989619i | \(0.454095\pi\) | |||||||
\(968\) | 4.81231e20i | 0.604263i | ||||||||
\(969\) | 2.81189e20 | + | 6.86450e20i | 0.350535 | + | 0.855741i | ||||
\(970\) | 3.20296e20 | 0.396414 | ||||||||
\(971\) | − | 7.80153e20i | − | 0.958618i | −0.877646 | − | 0.479309i | \(-0.840887\pi\) | ||
0.877646 | − | 0.479309i | \(-0.159113\pi\) | |||||||
\(972\) | −1.49393e20 | − | 3.81662e20i | −0.182250 | − | 0.465602i | ||||
\(973\) | 2.94268e20 | 0.356412 | ||||||||
\(974\) | − | 6.63019e20i | − | 0.797284i | ||||||
\(975\) | 5.10270e20 | − | 2.09021e20i | 0.609211 | − | 0.249550i | ||||
\(976\) | 1.16526e20 | 0.138126 | ||||||||
\(977\) | − | 1.06441e21i | − | 1.25270i | −0.779541 | − | 0.626352i | \(-0.784547\pi\) | ||
0.779541 | − | 0.626352i | \(-0.215453\pi\) | |||||||
\(978\) | −9.87588e19 | − | 2.41094e20i | −0.115399 | − | 0.281718i | ||||
\(979\) | 2.28568e21 | 2.65178 | ||||||||
\(980\) | − | 1.74523e20i | − | 0.201034i | ||||||
\(981\) | 5.89687e20 | − | 5.80511e20i | 0.674433 | − | 0.663938i | ||||
\(982\) | 1.37322e20 | 0.155941 | ||||||||
\(983\) | 4.92533e20i | 0.555343i | 0.960676 | + | 0.277671i | \(0.0895626\pi\) | ||||
−0.960676 | + | 0.277671i | \(0.910437\pi\) | |||||||
\(984\) | 2.17590e20 | − | 8.91309e19i | 0.243598 | − | 0.0997844i | ||||
\(985\) | −6.69006e20 | −0.743663 | ||||||||
\(986\) | 1.71268e20i | 0.189034i | ||||||||
\(987\) | −1.76918e20 | − | 4.31900e20i | −0.193889 | − | 0.473329i | ||||
\(988\) | −6.62901e20 | −0.721357 | ||||||||
\(989\) | 8.21384e20i | 0.887508i | ||||||||
\(990\) | −3.93784e20 | − | 4.00008e20i | −0.422485 | − | 0.429163i | ||||
\(991\) | −1.28336e21 | −1.36720 | −0.683601 | − | 0.729856i | \(-0.739587\pi\) | ||||
−0.683601 | + | 0.729856i | \(0.739587\pi\) | |||||||
\(992\) | − | 4.41258e19i | − | 0.0466779i | ||||||
\(993\) | 5.51325e20 | − | 2.25838e20i | 0.579113 | − | 0.237221i | ||||
\(994\) | 1.74055e20 | 0.181544 | ||||||||
\(995\) | 4.60880e20i | 0.477338i | ||||||||
\(996\) | −1.81449e20 | − | 4.42960e20i | −0.186612 | − | 0.455564i | ||||
\(997\) | 6.77562e20 | 0.691963 | 0.345982 | − | 0.938241i | \(-0.387546\pi\) | ||||
0.345982 | + | 0.938241i | \(0.387546\pi\) | |||||||
\(998\) | 6.56337e20i | 0.665600i | ||||||||
\(999\) | −1.10223e20 | + | 2.57493e20i | −0.110997 | + | 0.259302i |
(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 | 6.15.b.a.5.3 | yes | 4 | |
3.2 | odd | 2 | inner | 6.15.b.a.5.1 | ✓ | 4 | |
4.3 | odd | 2 | 48.15.e.d.17.3 | 4 | |||
5.2 | odd | 4 | 150.15.b.a.149.4 | 8 | |||
5.3 | odd | 4 | 150.15.b.a.149.5 | 8 | |||
5.4 | even | 2 | 150.15.d.a.101.2 | 4 | |||
12.11 | even | 2 | 48.15.e.d.17.4 | 4 | |||
15.2 | even | 4 | 150.15.b.a.149.6 | 8 | |||
15.8 | even | 4 | 150.15.b.a.149.3 | 8 | |||
15.14 | odd | 2 | 150.15.d.a.101.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.15.b.a.5.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
6.15.b.a.5.3 | yes | 4 | 1.1 | even | 1 | trivial | |
48.15.e.d.17.3 | 4 | 4.3 | odd | 2 | |||
48.15.e.d.17.4 | 4 | 12.11 | even | 2 | |||
150.15.b.a.149.3 | 8 | 15.8 | even | 4 | |||
150.15.b.a.149.4 | 8 | 5.2 | odd | 4 | |||
150.15.b.a.149.5 | 8 | 5.3 | odd | 4 | |||
150.15.b.a.149.6 | 8 | 15.2 | even | 4 | |||
150.15.d.a.101.2 | 4 | 5.4 | even | 2 | |||
150.15.d.a.101.4 | 4 | 15.14 | odd | 2 |