Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,11,Mod(14,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.14");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.d (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: | \(9.53035879011\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 17880 x^{14} + 140656106 x^{12} + 568287997200 x^{10} + \cdots + 16\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{32}\cdot 5^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 14.8 | ||
Root | \(61.4341 - 30.7435i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.14 |
Dual form | 15.11.d.c.14.7 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.37421 | −0.105444 | −0.0527221 | − | 0.998609i | \(-0.516790\pi\) | ||||
−0.0527221 | + | 0.998609i | \(0.516790\pi\) | |||||||
\(3\) | −224.817 | + | 92.2305i | −0.925172 | + | 0.379549i | ||||
\(4\) | −1012.61 | −0.988882 | ||||||||
\(5\) | 862.380 | + | 3003.65i | 0.275962 | + | 0.961169i | ||||
\(6\) | 758.580 | − | 311.205i | 0.0975540 | − | 0.0400213i | ||||
\(7\) | − | 16006.0i | − | 0.952341i | −0.879353 | − | 0.476170i | \(-0.842025\pi\) | ||
0.879353 | − | 0.476170i | \(-0.157975\pi\) | |||||||
\(8\) | 6871.97 | 0.209716 | ||||||||
\(9\) | 42036.1 | − | 41469.9i | 0.711885 | − | 0.702296i | ||||
\(10\) | −2909.86 | − | 10135.0i | −0.0290986 | − | 0.101350i | ||||
\(11\) | 109087.i | 0.677346i | 0.940904 | + | 0.338673i | \(0.109978\pi\) | ||||
−0.940904 | + | 0.338673i | \(0.890022\pi\) | |||||||
\(12\) | 227653. | − | 93393.9i | 0.914885 | − | 0.375329i | ||||
\(13\) | − | 572716.i | − | 1.54249i | −0.636538 | − | 0.771245i | \(-0.719634\pi\) | ||
0.636538 | − | 0.771245i | \(-0.280366\pi\) | |||||||
\(14\) | 54007.6i | 0.100419i | ||||||||
\(15\) | −470906. | − | 595733.i | −0.620123 | − | 0.784505i | ||||
\(16\) | 1.01373e6 | 0.966768 | ||||||||
\(17\) | 1.54275e6 | 1.08656 | 0.543278 | − | 0.839553i | \(-0.317183\pi\) | ||||
0.543278 | + | 0.839553i | \(0.317183\pi\) | |||||||
\(18\) | −141839. | + | 139928.i | −0.0750641 | + | 0.0740531i | ||||
\(19\) | −720399. | −0.290941 | −0.145471 | − | 0.989363i | \(-0.546470\pi\) | ||||
−0.145471 | + | 0.989363i | \(0.546470\pi\) | |||||||
\(20\) | −873259. | − | 3.04154e6i | −0.272893 | − | 0.950482i | ||||
\(21\) | 1.47624e6 | + | 3.59841e6i | 0.361460 | + | 0.881079i | ||||
\(22\) | − | 368084.i | − | 0.0714222i | ||||||
\(23\) | −2.49708e6 | −0.387965 | −0.193983 | − | 0.981005i | \(-0.562141\pi\) | ||||
−0.193983 | + | 0.981005i | \(0.562141\pi\) | |||||||
\(24\) | −1.54493e6 | + | 633805.i | −0.194023 | + | 0.0795976i | ||||
\(25\) | −8.27823e6 | + | 5.18058e6i | −0.847690 | + | 0.530491i | ||||
\(26\) | 1.93247e6i | 0.162647i | ||||||||
\(27\) | −5.62563e6 | + | 1.32001e7i | −0.392060 | + | 0.919940i | ||||
\(28\) | 1.62079e7i | 0.941752i | ||||||||
\(29\) | − | 1.79908e7i | − | 0.877121i | −0.898702 | − | 0.438561i | \(-0.855488\pi\) | ||
0.898702 | − | 0.438561i | \(-0.144512\pi\) | |||||||
\(30\) | 1.58894e6 | + | 2.01013e6i | 0.0653883 | + | 0.0827215i | ||||
\(31\) | 1.83900e7 | 0.642352 | 0.321176 | − | 0.947020i | \(-0.395922\pi\) | ||||
0.321176 | + | 0.947020i | \(0.395922\pi\) | |||||||
\(32\) | −1.04574e7 | −0.311656 | ||||||||
\(33\) | −1.00612e7 | − | 2.45246e7i | −0.257086 | − | 0.626661i | ||||
\(34\) | −5.20558e6 | −0.114571 | ||||||||
\(35\) | 4.80764e7 | − | 1.38032e7i | 0.915360 | − | 0.262809i | ||||
\(36\) | −4.25664e7 | + | 4.19930e7i | −0.703970 | + | 0.694488i | ||||
\(37\) | − | 6.73581e7i | − | 0.971362i | −0.874136 | − | 0.485681i | \(-0.838572\pi\) | ||
0.874136 | − | 0.485681i | \(-0.161428\pi\) | |||||||
\(38\) | 2.43078e6 | 0.0306781 | ||||||||
\(39\) | 5.28219e7 | + | 1.28756e8i | 0.585451 | + | 1.42707i | ||||
\(40\) | 5.92625e6 | + | 2.06410e7i | 0.0578736 | + | 0.201572i | ||||
\(41\) | − | 1.78223e8i | − | 1.53832i | −0.639058 | − | 0.769158i | \(-0.720676\pi\) | ||
0.639058 | − | 0.769158i | \(-0.279324\pi\) | |||||||
\(42\) | −4.98115e6 | − | 1.21418e7i | −0.0381139 | − | 0.0929046i | ||||
\(43\) | − | 1.66496e8i | − | 1.13256i | −0.824212 | − | 0.566281i | \(-0.808382\pi\) | ||
0.824212 | − | 0.566281i | \(-0.191618\pi\) | |||||||
\(44\) | − | 1.10463e8i | − | 0.669815i | ||||||
\(45\) | 1.60812e8 | + | 9.04990e7i | 0.871478 | + | 0.490435i | ||||
\(46\) | 8.42568e6 | 0.0409087 | ||||||||
\(47\) | 2.99761e8 | 1.30703 | 0.653514 | − | 0.756914i | \(-0.273294\pi\) | ||||
0.653514 | + | 0.756914i | \(0.273294\pi\) | |||||||
\(48\) | −2.27903e8 | + | 9.34968e7i | −0.894426 | + | 0.366936i | ||||
\(49\) | 2.62835e7 | 0.0930472 | ||||||||
\(50\) | 2.79325e7 | − | 1.74804e7i | 0.0893840 | − | 0.0559372i | ||||
\(51\) | −3.46837e8 | + | 1.42289e8i | −1.00525 | + | 0.412402i | ||||
\(52\) | 5.79941e8i | 1.52534i | ||||||||
\(53\) | −6.37040e8 | −1.52331 | −0.761653 | − | 0.647985i | \(-0.775612\pi\) | ||||
−0.761653 | + | 0.647985i | \(0.775612\pi\) | |||||||
\(54\) | 1.89821e7 | − | 4.45401e7i | 0.0413404 | − | 0.0970023i | ||||
\(55\) | −3.27660e8 | + | 9.40747e7i | −0.651044 | + | 0.186922i | ||||
\(56\) | − | 1.09993e8i | − | 0.199721i | ||||||
\(57\) | 1.61958e8 | − | 6.64428e7i | 0.269171 | − | 0.110427i | ||||
\(58\) | 6.07047e7i | 0.0924873i | ||||||||
\(59\) | 3.05843e7i | 0.0427798i | 0.999771 | + | 0.0213899i | \(0.00680914\pi\) | ||||
−0.999771 | + | 0.0213899i | \(0.993191\pi\) | |||||||
\(60\) | 4.76846e8 | + | 6.03248e8i | 0.613228 | + | 0.775782i | ||||
\(61\) | 9.80370e8 | 1.16076 | 0.580378 | − | 0.814347i | \(-0.302905\pi\) | ||||
0.580378 | + | 0.814347i | \(0.302905\pi\) | |||||||
\(62\) | −6.20518e7 | −0.0677323 | ||||||||
\(63\) | −6.63767e8 | − | 6.72829e8i | −0.668825 | − | 0.677957i | ||||
\(64\) | −1.00277e9 | −0.933906 | ||||||||
\(65\) | 1.72024e9 | − | 4.93899e8i | 1.48259 | − | 0.425668i | ||||
\(66\) | 3.39485e7 | + | 8.27514e7i | 0.0271083 | + | 0.0660778i | ||||
\(67\) | − | 6.91391e8i | − | 0.512094i | −0.966664 | − | 0.256047i | \(-0.917580\pi\) | ||
0.966664 | − | 0.256047i | \(-0.0824203\pi\) | |||||||
\(68\) | −1.56222e9 | −1.07448 | ||||||||
\(69\) | 5.61385e8 | − | 2.30307e8i | 0.358935 | − | 0.147252i | ||||
\(70\) | −1.62220e8 | + | 4.65751e7i | −0.0965194 | + | 0.0277117i | ||||
\(71\) | 2.10199e9i | 1.16503i | 0.812819 | + | 0.582516i | \(0.197932\pi\) | ||||
−0.812819 | + | 0.582516i | \(0.802068\pi\) | |||||||
\(72\) | 2.88871e8 | − | 2.84980e8i | 0.149294 | − | 0.147283i | ||||
\(73\) | − | 2.47490e9i | − | 1.19383i | −0.802304 | − | 0.596916i | \(-0.796393\pi\) | ||
0.802304 | − | 0.596916i | \(-0.203607\pi\) | |||||||
\(74\) | 2.27281e8i | 0.102424i | ||||||||
\(75\) | 1.38328e9 | − | 1.92819e9i | 0.582911 | − | 0.812536i | ||||
\(76\) | 7.29487e8 | 0.287706 | ||||||||
\(77\) | 1.74605e9 | 0.645064 | ||||||||
\(78\) | −1.78232e8 | − | 4.34451e8i | −0.0617324 | − | 0.150476i | ||||
\(79\) | 1.45740e9 | 0.473635 | 0.236818 | − | 0.971554i | \(-0.423896\pi\) | ||||
0.236818 | + | 0.971554i | \(0.423896\pi\) | |||||||
\(80\) | 8.74220e8 | + | 3.04489e9i | 0.266791 | + | 0.929227i | ||||
\(81\) | 4.72803e7 | − | 3.48646e9i | 0.0135599 | − | 0.999908i | ||||
\(82\) | 6.01364e8i | 0.162207i | ||||||||
\(83\) | −6.85447e9 | −1.74014 | −0.870068 | − | 0.492931i | \(-0.835925\pi\) | ||||
−0.870068 | + | 0.492931i | \(0.835925\pi\) | |||||||
\(84\) | −1.49486e9 | − | 3.64381e9i | −0.357441 | − | 0.871282i | ||||
\(85\) | 1.33044e9 | + | 4.63390e9i | 0.299848 | + | 1.04436i | ||||
\(86\) | 5.61794e8i | 0.119422i | ||||||||
\(87\) | 1.65930e9 | + | 4.04462e9i | 0.332911 | + | 0.811487i | ||||
\(88\) | 7.49645e8i | 0.142050i | ||||||||
\(89\) | 5.45554e9i | 0.976985i | 0.872568 | + | 0.488493i | \(0.162453\pi\) | ||||
−0.872568 | + | 0.488493i | \(0.837547\pi\) | |||||||
\(90\) | −5.42615e8 | − | 3.05363e8i | −0.0918923 | − | 0.0517135i | ||||
\(91\) | −9.16689e9 | −1.46898 | ||||||||
\(92\) | 2.52858e9 | 0.383652 | ||||||||
\(93\) | −4.13438e9 | + | 1.69612e9i | −0.594286 | + | 0.243804i | ||||
\(94\) | −1.01146e9 | −0.137819 | ||||||||
\(95\) | −6.21258e8 | − | 2.16383e9i | −0.0802886 | − | 0.279644i | ||||
\(96\) | 2.35101e9 | − | 9.64495e8i | 0.288335 | − | 0.118289i | ||||
\(97\) | 3.04168e9i | 0.354205i | 0.984192 | + | 0.177103i | \(0.0566725\pi\) | ||||
−0.984192 | + | 0.177103i | \(0.943328\pi\) | |||||||
\(98\) | −8.86862e7 | −0.00981129 | ||||||||
\(99\) | 4.52384e9 | + | 4.58560e9i | 0.475698 | + | 0.482192i | ||||
\(100\) | 8.38265e9 | − | 5.24593e9i | 0.838265 | − | 0.524593i | ||||
\(101\) | − | 1.00889e10i | − | 0.959920i | −0.877290 | − | 0.479960i | \(-0.840651\pi\) | ||
0.877290 | − | 0.479960i | \(-0.159349\pi\) | |||||||
\(102\) | 1.17030e9 | − | 4.80113e8i | 0.105998 | − | 0.0434854i | ||||
\(103\) | 2.12524e9i | 0.183325i | 0.995790 | + | 0.0916626i | \(0.0292181\pi\) | ||||
−0.995790 | + | 0.0916626i | \(0.970782\pi\) | |||||||
\(104\) | − | 3.93569e9i | − | 0.323485i | ||||||
\(105\) | −9.53530e9 | + | 7.53731e9i | −0.747116 | + | 0.590568i | ||||
\(106\) | 2.14951e9 | 0.160624 | ||||||||
\(107\) | −4.65164e9 | −0.331656 | −0.165828 | − | 0.986155i | \(-0.553030\pi\) | ||||
−0.165828 | + | 0.986155i | \(0.553030\pi\) | |||||||
\(108\) | 5.69659e9 | − | 1.33666e10i | 0.387700 | − | 0.909712i | ||||
\(109\) | 1.40621e9 | 0.0913940 | 0.0456970 | − | 0.998955i | \(-0.485449\pi\) | ||||
0.0456970 | + | 0.998955i | \(0.485449\pi\) | |||||||
\(110\) | 1.10560e9 | − | 3.17428e8i | 0.0686488 | − | 0.0197098i | ||||
\(111\) | 6.21246e9 | + | 1.51432e10i | 0.368680 | + | 0.898676i | ||||
\(112\) | − | 1.62258e10i | − | 0.920693i | ||||||
\(113\) | 2.64325e10 | 1.43465 | 0.717324 | − | 0.696739i | \(-0.245367\pi\) | ||||
0.717324 | + | 0.696739i | \(0.245367\pi\) | |||||||
\(114\) | −5.46480e8 | + | 2.24192e8i | −0.0283825 | + | 0.0116438i | ||||
\(115\) | −2.15343e9 | − | 7.50036e9i | −0.107064 | − | 0.372900i | ||||
\(116\) | 1.82177e10i | 0.867369i | ||||||||
\(117\) | −2.37505e10 | − | 2.40747e10i | −1.08329 | − | 1.09808i | ||||
\(118\) | − | 1.03198e8i | − | 0.00451089i | ||||||
\(119\) | − | 2.46933e10i | − | 1.03477i | ||||||
\(120\) | −3.23605e9 | − | 4.09386e9i | −0.130050 | − | 0.164523i | ||||
\(121\) | 1.40374e10 | 0.541202 | ||||||||
\(122\) | −3.30798e9 | −0.122395 | ||||||||
\(123\) | 1.64376e10 | + | 4.00676e10i | 0.583867 | + | 1.42321i | ||||
\(124\) | −1.86220e10 | −0.635210 | ||||||||
\(125\) | −2.26996e10 | − | 2.03973e10i | −0.743822 | − | 0.668378i | ||||
\(126\) | 2.23969e9 | + | 2.27027e9i | 0.0705238 | + | 0.0714866i | ||||
\(127\) | 3.50550e10i | 1.06104i | 0.847673 | + | 0.530519i | \(0.178003\pi\) | ||||
−0.847673 | + | 0.530519i | \(0.821997\pi\) | |||||||
\(128\) | 1.40920e10 | 0.410131 | ||||||||
\(129\) | 1.53560e10 | + | 3.74311e10i | 0.429863 | + | 1.04781i | ||||
\(130\) | −5.80446e9 | + | 1.66652e9i | −0.156331 | + | 0.0448842i | ||||
\(131\) | − | 3.84731e10i | − | 0.997243i | −0.866820 | − | 0.498621i | \(-0.833840\pi\) | ||
0.866820 | − | 0.498621i | \(-0.166160\pi\) | |||||||
\(132\) | 1.01881e10 | + | 2.48340e10i | 0.254228 | + | 0.619694i | ||||
\(133\) | 1.15307e10i | 0.277075i | ||||||||
\(134\) | 2.33290e9i | 0.0539974i | ||||||||
\(135\) | −4.45000e10 | − | 5.51389e9i | −0.992411 | − | 0.122967i | ||||
\(136\) | 1.06018e10 | 0.227868 | ||||||||
\(137\) | −7.23598e9 | −0.149932 | −0.0749660 | − | 0.997186i | \(-0.523885\pi\) | ||||
−0.0749660 | + | 0.997186i | \(0.523885\pi\) | |||||||
\(138\) | −1.89423e9 | + | 7.77104e8i | −0.0378476 | + | 0.0155269i | ||||
\(139\) | −5.23987e10 | −1.00983 | −0.504913 | − | 0.863170i | \(-0.668475\pi\) | ||||
−0.504913 | + | 0.863170i | \(0.668475\pi\) | |||||||
\(140\) | −4.86829e10 | + | 1.39774e10i | −0.905183 | + | 0.259887i | ||||
\(141\) | −6.73912e10 | + | 2.76471e10i | −1.20923 | + | 0.496082i | ||||
\(142\) | − | 7.09255e9i | − | 0.122846i | ||||||
\(143\) | 6.24760e10 | 1.04480 | ||||||||
\(144\) | 4.26132e10 | − | 4.20393e10i | 0.688228 | − | 0.678958i | ||||
\(145\) | 5.40380e10 | − | 1.55149e10i | 0.843061 | − | 0.242052i | ||||
\(146\) | 8.35084e9i | 0.125883i | ||||||||
\(147\) | −5.90897e9 | + | 2.42414e9i | −0.0860846 | + | 0.0353160i | ||||
\(148\) | 6.82078e10i | 0.960562i | ||||||||
\(149\) | 1.02267e10i | 0.139253i | 0.997573 | + | 0.0696265i | \(0.0221808\pi\) | ||||
−0.997573 | + | 0.0696265i | \(0.977819\pi\) | |||||||
\(150\) | −4.66747e9 | + | 6.50611e9i | −0.0614646 | + | 0.0856772i | ||||
\(151\) | 4.69180e10 | 0.597661 | 0.298831 | − | 0.954306i | \(-0.403403\pi\) | ||||
0.298831 | + | 0.954306i | \(0.403403\pi\) | |||||||
\(152\) | −4.95057e9 | −0.0610150 | ||||||||
\(153\) | 6.48514e10 | − | 6.39779e10i | 0.773503 | − | 0.763084i | ||||
\(154\) | −5.89155e9 | −0.0680183 | ||||||||
\(155\) | 1.58592e10 | + | 5.52371e10i | 0.177265 | + | 0.617409i | ||||
\(156\) | −5.34882e10 | − | 1.30380e11i | −0.578942 | − | 1.41120i | ||||
\(157\) | − | 1.72513e11i | − | 1.80853i | −0.426976 | − | 0.904263i | \(-0.640421\pi\) | ||
0.426976 | − | 0.904263i | \(-0.359579\pi\) | |||||||
\(158\) | −4.91759e9 | −0.0499421 | ||||||||
\(159\) | 1.43217e11 | − | 5.87545e10i | 1.40932 | − | 0.578169i | ||||
\(160\) | −9.01829e9 | − | 3.14105e10i | −0.0860051 | − | 0.299554i | ||||
\(161\) | 3.99682e10i | 0.369475i | ||||||||
\(162\) | −1.59534e8 | + | 1.17641e10i | −0.00142981 | + | 0.105435i | ||||
\(163\) | − | 6.40750e10i | − | 0.556866i | −0.960456 | − | 0.278433i | \(-0.910185\pi\) | ||
0.960456 | − | 0.278433i | \(-0.0898151\pi\) | |||||||
\(164\) | 1.80472e11i | 1.52121i | ||||||||
\(165\) | 6.49869e10 | − | 5.13698e10i | 0.531381 | − | 0.420038i | ||||
\(166\) | 2.31284e10 | 0.183487 | ||||||||
\(167\) | −7.67116e10 | −0.590580 | −0.295290 | − | 0.955408i | \(-0.595416\pi\) | ||||
−0.295290 | + | 0.955408i | \(0.595416\pi\) | |||||||
\(168\) | 1.01447e10 | + | 2.47282e10i | 0.0758040 | + | 0.184776i | ||||
\(169\) | −1.90145e11 | −1.37928 | ||||||||
\(170\) | −4.48919e9 | − | 1.56358e10i | −0.0316172 | − | 0.110122i | ||||
\(171\) | −3.02828e10 | + | 2.98749e10i | −0.207117 | + | 0.204327i | ||||
\(172\) | 1.68596e11i | 1.11997i | ||||||||
\(173\) | −2.57821e10 | −0.166375 | −0.0831874 | − | 0.996534i | \(-0.526510\pi\) | ||||
−0.0831874 | + | 0.996534i | \(0.526510\pi\) | |||||||
\(174\) | −5.59882e9 | − | 1.36474e10i | −0.0351035 | − | 0.0855666i | ||||
\(175\) | 8.29203e10 | + | 1.32501e11i | 0.505208 | + | 0.807290i | ||||
\(176\) | 1.10585e11i | 0.654837i | ||||||||
\(177\) | −2.82081e9 | − | 6.87587e9i | −0.0162371 | − | 0.0395787i | ||||
\(178\) | − | 1.84082e10i | − | 0.103017i | ||||||
\(179\) | − | 1.90863e11i | − | 1.03862i | −0.854586 | − | 0.519309i | \(-0.826189\pi\) | ||
0.854586 | − | 0.519309i | \(-0.173811\pi\) | |||||||
\(180\) | −1.62841e11 | − | 9.16406e10i | −0.861789 | − | 0.484982i | ||||
\(181\) | 1.39429e11 | 0.717729 | 0.358864 | − | 0.933390i | \(-0.383164\pi\) | ||||
0.358864 | + | 0.933390i | \(0.383164\pi\) | |||||||
\(182\) | 3.09310e10 | 0.154895 | ||||||||
\(183\) | −2.20403e11 | + | 9.04200e10i | −1.07390 | + | 0.440564i | ||||
\(184\) | −1.71599e10 | −0.0813626 | ||||||||
\(185\) | 2.02320e11 | − | 5.80882e10i | 0.933642 | − | 0.268059i | ||||
\(186\) | 1.39503e10 | − | 5.72306e9i | 0.0626640 | − | 0.0257077i | ||||
\(187\) | 1.68295e11i | 0.735975i | ||||||||
\(188\) | −3.03542e11 | −1.29250 | ||||||||
\(189\) | 2.11281e11 | + | 9.00437e10i | 0.876096 | + | 0.373374i | ||||
\(190\) | 2.09626e9 | + | 7.30122e9i | 0.00846597 | + | 0.0294868i | ||||
\(191\) | − | 1.29311e10i | − | 0.0508709i | −0.999676 | − | 0.0254354i | \(-0.991903\pi\) | ||
0.999676 | − | 0.0254354i | \(-0.00809722\pi\) | |||||||
\(192\) | 2.25440e11 | − | 9.24863e10i | 0.864023 | − | 0.354463i | ||||
\(193\) | − | 2.61082e10i | − | 0.0974969i | −0.998811 | − | 0.0487484i | \(-0.984477\pi\) | ||
0.998811 | − | 0.0487484i | \(-0.0155233\pi\) | |||||||
\(194\) | − | 1.02633e10i | − | 0.0373489i | ||||||
\(195\) | −3.41186e11 | + | 2.69695e11i | −1.21009 | + | 0.956533i | ||||
\(196\) | −2.66151e10 | −0.0920126 | ||||||||
\(197\) | 1.49535e11 | 0.503977 | 0.251989 | − | 0.967730i | \(-0.418915\pi\) | ||||
0.251989 | + | 0.967730i | \(0.418915\pi\) | |||||||
\(198\) | −1.52644e10 | − | 1.54728e10i | −0.0501596 | − | 0.0508444i | ||||
\(199\) | −4.65959e11 | −1.49308 | −0.746539 | − | 0.665341i | \(-0.768286\pi\) | ||||
−0.746539 | + | 0.665341i | \(0.768286\pi\) | |||||||
\(200\) | −5.68878e10 | + | 3.56008e10i | −0.177774 | + | 0.111253i | ||||
\(201\) | 6.37674e10 | + | 1.55436e11i | 0.194365 | + | 0.473775i | ||||
\(202\) | 3.40419e10i | 0.101218i | ||||||||
\(203\) | −2.87960e11 | −0.835318 | ||||||||
\(204\) | 3.51212e11 | − | 1.44084e11i | 0.994074 | − | 0.407816i | ||||
\(205\) | 5.35321e11 | − | 1.53696e11i | 1.47858 | − | 0.424516i | ||||
\(206\) | − | 7.17102e9i | − | 0.0193306i | ||||||
\(207\) | −1.04967e11 | + | 1.03554e11i | −0.276187 | + | 0.272467i | ||||
\(208\) | − | 5.80579e11i | − | 1.49123i | ||||||
\(209\) | − | 7.85864e10i | − | 0.197068i | ||||||
\(210\) | 3.21742e10 | − | 2.54325e10i | 0.0787790 | − | 0.0622720i | ||||
\(211\) | −1.29382e11 | −0.309359 | −0.154679 | − | 0.987965i | \(-0.549434\pi\) | ||||
−0.154679 | + | 0.987965i | \(0.549434\pi\) | |||||||
\(212\) | 6.45076e11 | 1.50637 | ||||||||
\(213\) | −1.93867e11 | − | 4.72561e11i | −0.442187 | − | 1.07785i | ||||
\(214\) | 1.56956e10 | 0.0349712 | ||||||||
\(215\) | 5.00097e11 | − | 1.43583e11i | 1.08858 | − | 0.312544i | ||||
\(216\) | −3.86592e10 | + | 9.07110e10i | −0.0822212 | + | 0.192926i | ||||
\(217\) | − | 2.94350e11i | − | 0.611738i | ||||||
\(218\) | −4.74485e9 | −0.00963697 | ||||||||
\(219\) | 2.28261e11 | + | 5.56399e11i | 0.453118 | + | 1.10450i | ||||
\(220\) | 3.31794e11 | − | 9.52614e10i | 0.643805 | − | 0.184843i | ||||
\(221\) | − | 8.83560e11i | − | 1.67600i | ||||||
\(222\) | −2.09622e10 | − | 5.10965e10i | −0.0388751 | − | 0.0947602i | ||||
\(223\) | 6.06435e11i | 1.09966i | 0.835275 | + | 0.549832i | \(0.185308\pi\) | ||||
−0.835275 | + | 0.549832i | \(0.814692\pi\) | |||||||
\(224\) | 1.67382e11i | 0.296803i | ||||||||
\(225\) | −1.33146e11 | + | 5.61068e11i | −0.230896 | + | 0.972978i | ||||
\(226\) | −8.91888e10 | −0.151275 | ||||||||
\(227\) | −8.79312e11 | −1.45886 | −0.729431 | − | 0.684055i | \(-0.760215\pi\) | ||||
−0.729431 | + | 0.684055i | \(0.760215\pi\) | |||||||
\(228\) | −1.64001e11 | + | 6.72809e10i | −0.266178 | + | 0.109199i | ||||
\(229\) | −2.98404e11 | −0.473835 | −0.236918 | − | 0.971530i | \(-0.576137\pi\) | ||||
−0.236918 | + | 0.971530i | \(0.576137\pi\) | |||||||
\(230\) | 7.26614e9 | + | 2.53078e10i | 0.0112892 | + | 0.0393202i | ||||
\(231\) | −3.92541e11 | + | 1.61039e11i | −0.596795 | + | 0.244834i | ||||
\(232\) | − | 1.23632e11i | − | 0.183946i | ||||||
\(233\) | 1.62068e11 | 0.236003 | 0.118001 | − | 0.993013i | \(-0.462351\pi\) | ||||
0.118001 | + | 0.993013i | \(0.462351\pi\) | |||||||
\(234\) | 8.01392e10 | + | 8.12333e10i | 0.114226 | + | 0.115786i | ||||
\(235\) | 2.58507e11 | + | 9.00376e11i | 0.360690 | + | 1.25628i | ||||
\(236\) | − | 3.09702e10i | − | 0.0423042i | ||||||
\(237\) | −3.27648e11 | + | 1.34417e11i | −0.438194 | + | 0.179768i | ||||
\(238\) | 8.33205e10i | 0.109111i | ||||||||
\(239\) | − | 6.75549e11i | − | 0.866298i | −0.901322 | − | 0.433149i | \(-0.857402\pi\) | ||
0.901322 | − | 0.433149i | \(-0.142598\pi\) | |||||||
\(240\) | −4.77371e11 | − | 6.03913e11i | −0.599515 | − | 0.758434i | ||||
\(241\) | 2.09769e11 | 0.258022 | 0.129011 | − | 0.991643i | \(-0.458820\pi\) | ||||
0.129011 | + | 0.991643i | \(0.458820\pi\) | |||||||
\(242\) | −4.73652e10 | −0.0570666 | ||||||||
\(243\) | 3.10929e11 | + | 7.88176e11i | 0.366969 | + | 0.930233i | ||||
\(244\) | −9.92737e11 | −1.14785 | ||||||||
\(245\) | 2.26664e10 | + | 7.89466e10i | 0.0256774 | + | 0.0894340i | ||||
\(246\) | −5.54641e10 | − | 1.35197e11i | −0.0615654 | − | 0.150069i | ||||
\(247\) | 4.12584e11i | 0.448774i | ||||||||
\(248\) | 1.26376e11 | 0.134712 | ||||||||
\(249\) | 1.54100e12 | − | 6.32191e11i | 1.60992 | − | 0.660467i | ||||
\(250\) | 7.65934e10 | + | 6.88248e10i | 0.0784317 | + | 0.0704766i | ||||
\(251\) | 1.53797e12i | 1.54376i | 0.635769 | + | 0.771880i | \(0.280683\pi\) | ||||
−0.635769 | + | 0.771880i | \(0.719317\pi\) | |||||||
\(252\) | 6.72140e11 | + | 6.81317e11i | 0.661389 | + | 0.670419i | ||||
\(253\) | − | 2.72400e11i | − | 0.262787i | ||||||
\(254\) | − | 1.18283e11i | − | 0.111880i | ||||||
\(255\) | −7.26492e11 | − | 9.19070e11i | −0.673798 | − | 0.852409i | ||||
\(256\) | 9.79291e11 | 0.890660 | ||||||||
\(257\) | −3.09044e11 | −0.275648 | −0.137824 | − | 0.990457i | \(-0.544011\pi\) | ||||
−0.137824 | + | 0.990457i | \(0.544011\pi\) | |||||||
\(258\) | −5.18145e10 | − | 1.26301e11i | −0.0453266 | − | 0.110486i | ||||
\(259\) | −1.07813e12 | −0.925067 | ||||||||
\(260\) | −1.74194e12 | + | 5.00129e11i | −1.46611 | + | 0.420935i | ||||
\(261\) | −7.46075e11 | − | 7.56261e11i | −0.615999 | − | 0.624409i | ||||
\(262\) | 1.29817e11i | 0.105153i | ||||||||
\(263\) | 1.27422e12 | 1.01267 | 0.506333 | − | 0.862338i | \(-0.331001\pi\) | ||||
0.506333 | + | 0.862338i | \(0.331001\pi\) | |||||||
\(264\) | −6.91401e10 | − | 1.68533e11i | −0.0539151 | − | 0.131421i | ||||
\(265\) | −5.49370e11 | − | 1.91345e12i | −0.420374 | − | 1.46415i | ||||
\(266\) | − | 3.89071e10i | − | 0.0292160i | ||||||
\(267\) | −5.03167e11 | − | 1.22650e12i | −0.370814 | − | 0.903879i | ||||
\(268\) | 7.00113e11i | 0.506401i | ||||||||
\(269\) | 2.76933e12i | 1.96613i | 0.183253 | + | 0.983066i | \(0.441337\pi\) | ||||
−0.183253 | + | 0.983066i | \(0.558663\pi\) | |||||||
\(270\) | 1.50153e11 | + | 1.86051e10i | 0.104644 | + | 0.0129662i | ||||
\(271\) | 1.98616e12 | 1.35884 | 0.679421 | − | 0.733749i | \(-0.262231\pi\) | ||||
0.679421 | + | 0.733749i | \(0.262231\pi\) | |||||||
\(272\) | 1.56394e12 | 1.05045 | ||||||||
\(273\) | 2.06087e12 | − | 8.45466e11i | 1.35906 | − | 0.557549i | ||||
\(274\) | 2.44157e10 | 0.0158095 | ||||||||
\(275\) | −5.65135e11 | − | 9.03049e11i | −0.359326 | − | 0.574180i | ||||
\(276\) | −5.68467e11 | + | 2.33212e11i | −0.354944 | + | 0.145615i | ||||
\(277\) | − | 2.22799e12i | − | 1.36620i | −0.730324 | − | 0.683101i | \(-0.760631\pi\) | ||
0.730324 | − | 0.683101i | \(-0.239369\pi\) | |||||||
\(278\) | 1.76804e11 | 0.106480 | ||||||||
\(279\) | 7.73043e11 | − | 7.62631e11i | 0.457281 | − | 0.451121i | ||||
\(280\) | 3.30380e11 | − | 9.48556e10i | 0.191966 | − | 0.0551154i | ||||
\(281\) | 9.00059e11i | 0.513735i | 0.966447 | + | 0.256868i | \(0.0826905\pi\) | ||||
−0.966447 | + | 0.256868i | \(0.917310\pi\) | |||||||
\(282\) | 2.27392e11 | − | 9.32871e10i | 0.127506 | − | 0.0523089i | ||||
\(283\) | 4.14490e11i | 0.228340i | 0.993461 | + | 0.114170i | \(0.0364208\pi\) | ||||
−0.993461 | + | 0.114170i | \(0.963579\pi\) | |||||||
\(284\) | − | 2.12850e12i | − | 1.15208i | ||||||
\(285\) | 3.39240e11 | + | 4.29166e11i | 0.180419 | + | 0.228245i | ||||
\(286\) | −2.10807e11 | −0.110168 | ||||||||
\(287\) | −2.85264e12 | −1.46500 | ||||||||
\(288\) | −4.39590e11 | + | 4.33669e11i | −0.221863 | + | 0.218875i | ||||
\(289\) | 3.64097e11 | 0.180604 | ||||||||
\(290\) | −1.82336e11 | + | 5.23505e10i | −0.0888959 | + | 0.0255230i | ||||
\(291\) | −2.80536e11 | − | 6.83821e11i | −0.134438 | − | 0.327701i | ||||
\(292\) | 2.50612e12i | 1.18056i | ||||||||
\(293\) | 2.76959e12 | 1.28256 | 0.641280 | − | 0.767307i | \(-0.278404\pi\) | ||||
0.641280 | + | 0.767307i | \(0.278404\pi\) | |||||||
\(294\) | 1.99381e10 | − | 8.17957e9i | 0.00907712 | − | 0.00372387i | ||||
\(295\) | −9.18647e10 | + | 2.63753e10i | −0.0411186 | + | 0.0118056i | ||||
\(296\) | − | 4.62883e11i | − | 0.203710i | ||||||
\(297\) | −1.43997e12 | − | 6.13684e11i | −0.623118 | − | 0.265560i | ||||
\(298\) | − | 3.45071e10i | − | 0.0146834i | ||||||
\(299\) | 1.43012e12i | 0.598433i | ||||||||
\(300\) | −1.40073e12 | + | 1.95251e12i | −0.576430 | + | 0.803502i | ||||
\(301\) | −2.66494e12 | −1.07858 | ||||||||
\(302\) | −1.58312e11 | −0.0630199 | ||||||||
\(303\) | 9.30499e11 | + | 2.26814e12i | 0.364337 | + | 0.888090i | ||||
\(304\) | −7.30290e11 | −0.281273 | ||||||||
\(305\) | 8.45451e11 | + | 2.94469e12i | 0.320324 | + | 1.11568i | ||||
\(306\) | −2.18822e11 | + | 2.15875e11i | −0.0815614 | + | 0.0804628i | ||||
\(307\) | 4.47551e11i | 0.164116i | 0.996628 | + | 0.0820579i | \(0.0261492\pi\) | ||||
−0.996628 | + | 0.0820579i | \(0.973851\pi\) | |||||||
\(308\) | −1.76808e12 | −0.637892 | ||||||||
\(309\) | −1.96012e11 | − | 4.77790e11i | −0.0695810 | − | 0.169607i | ||||
\(310\) | −5.35122e10 | − | 1.86382e11i | −0.0186915 | − | 0.0651022i | ||||
\(311\) | − | 3.35727e12i | − | 1.15394i | −0.816765 | − | 0.576971i | \(-0.804235\pi\) | ||
0.816765 | − | 0.576971i | \(-0.195765\pi\) | |||||||
\(312\) | 3.62990e11 | + | 8.84809e11i | 0.122778 | + | 0.299279i | ||||
\(313\) | 1.38448e12i | 0.460857i | 0.973089 | + | 0.230428i | \(0.0740127\pi\) | ||||
−0.973089 | + | 0.230428i | \(0.925987\pi\) | |||||||
\(314\) | 5.82097e11i | 0.190699i | ||||||||
\(315\) | 1.44853e12 | − | 2.57396e12i | 0.467061 | − | 0.829944i | ||||
\(316\) | −1.47579e12 | −0.468369 | ||||||||
\(317\) | −1.97509e12 | −0.617008 | −0.308504 | − | 0.951223i | \(-0.599828\pi\) | ||||
−0.308504 | + | 0.951223i | \(0.599828\pi\) | |||||||
\(318\) | −4.83245e11 | + | 1.98250e11i | −0.148605 | + | 0.0609646i | ||||
\(319\) | 1.96256e12 | 0.594115 | ||||||||
\(320\) | −8.64772e11 | − | 3.01198e12i | −0.257722 | − | 0.897641i | ||||
\(321\) | 1.04577e12 | − | 4.29023e11i | 0.306838 | − | 0.125880i | ||||
\(322\) | − | 1.34861e11i | − | 0.0389590i | ||||||
\(323\) | −1.11140e12 | −0.316124 | ||||||||
\(324\) | −4.78767e10 | + | 3.53044e12i | −0.0134091 | + | 0.988791i | ||||
\(325\) | 2.96700e12 | + | 4.74107e12i | 0.818278 | + | 1.30755i | ||||
\(326\) | 2.16203e11i | 0.0587183i | ||||||||
\(327\) | −3.16139e11 | + | 1.29695e11i | −0.0845551 | + | 0.0346885i | ||||
\(328\) | − | 1.22475e12i | − | 0.322610i | ||||||
\(329\) | − | 4.79796e12i | − | 1.24474i | ||||||
\(330\) | −2.19280e11 | + | 1.73333e11i | −0.0560311 | + | 0.0442905i | ||||
\(331\) | 9.94662e11 | 0.250343 | 0.125171 | − | 0.992135i | \(-0.460052\pi\) | ||||
0.125171 | + | 0.992135i | \(0.460052\pi\) | |||||||
\(332\) | 6.94093e12 | 1.72079 | ||||||||
\(333\) | −2.79333e12 | − | 2.83147e12i | −0.682184 | − | 0.691498i | ||||
\(334\) | 2.58841e11 | 0.0622732 | ||||||||
\(335\) | 2.07670e12 | − | 5.96242e11i | 0.492209 | − | 0.141318i | ||||
\(336\) | 1.49651e12 | + | 3.64782e12i | 0.349448 | + | 0.851799i | ||||
\(337\) | − | 3.33420e12i | − | 0.767083i | −0.923524 | − | 0.383541i | \(-0.874704\pi\) | ||
0.923524 | − | 0.383541i | \(-0.125296\pi\) | |||||||
\(338\) | 6.41590e11 | 0.145437 | ||||||||
\(339\) | −5.94246e12 | + | 2.43788e12i | −1.32730 | + | 0.544520i | ||||
\(340\) | −1.34722e12 | − | 4.69235e12i | −0.296514 | − | 1.03275i | ||||
\(341\) | 2.00611e12i | 0.435095i | ||||||||
\(342\) | 1.02181e11 | − | 1.00804e11i | 0.0218392 | − | 0.0215451i | ||||
\(343\) | − | 4.94199e12i | − | 1.04095i | ||||||
\(344\) | − | 1.14416e12i | − | 0.237516i | ||||||
\(345\) | 1.17589e12 | + | 1.48759e12i | 0.240586 | + | 0.304361i | ||||
\(346\) | 8.69942e10 | 0.0175433 | ||||||||
\(347\) | 4.36427e12 | 0.867489 | 0.433745 | − | 0.901036i | \(-0.357192\pi\) | ||||
0.433745 | + | 0.901036i | \(0.357192\pi\) | |||||||
\(348\) | −1.68023e12 | − | 4.09564e12i | −0.329209 | − | 0.802465i | ||||
\(349\) | 2.40524e12 | 0.464548 | 0.232274 | − | 0.972650i | \(-0.425383\pi\) | ||||
0.232274 | + | 0.972650i | \(0.425383\pi\) | |||||||
\(350\) | −2.79791e11 | − | 4.47087e11i | −0.0532713 | − | 0.0851241i | ||||
\(351\) | 7.55993e12 | + | 3.22189e12i | 1.41900 | + | 0.604748i | ||||
\(352\) | − | 1.14077e12i | − | 0.211099i | ||||||
\(353\) | −7.89736e12 | −1.44081 | −0.720407 | − | 0.693551i | \(-0.756045\pi\) | ||||
−0.720407 | + | 0.693551i | \(0.756045\pi\) | |||||||
\(354\) | 9.51801e9 | + | 2.32007e10i | 0.00171210 | + | 0.00417334i | ||||
\(355\) | −6.31363e12 | + | 1.81271e12i | −1.11979 | + | 0.321504i | ||||
\(356\) | − | 5.52436e12i | − | 0.966123i | ||||||
\(357\) | 2.27748e12 | + | 5.55147e12i | 0.392747 | + | 0.957341i | ||||
\(358\) | 6.44012e11i | 0.109516i | ||||||||
\(359\) | − | 2.29923e10i | − | 0.00385576i | −0.999998 | − | 0.00192788i | \(-0.999386\pi\) | ||
0.999998 | − | 0.00192788i | \(-0.000613664\pi\) | |||||||
\(360\) | 1.10510e12 | + | 6.21907e11i | 0.182763 | + | 0.102852i | ||||
\(361\) | −5.61209e12 | −0.915353 | ||||||||
\(362\) | −4.70463e11 | −0.0756803 | ||||||||
\(363\) | −3.15584e12 | + | 1.29468e12i | −0.500705 | + | 0.205413i | ||||
\(364\) | 9.28252e12 | 1.45264 | ||||||||
\(365\) | 7.43374e12 | − | 2.13430e12i | 1.14747 | − | 0.329452i | ||||
\(366\) | 7.43689e11 | − | 3.05096e11i | 0.113236 | − | 0.0464549i | ||||
\(367\) | 5.32967e12i | 0.800516i | 0.916403 | + | 0.400258i | \(0.131079\pi\) | ||||
−0.916403 | + | 0.400258i | \(0.868921\pi\) | |||||||
\(368\) | −2.53136e12 | −0.375073 | ||||||||
\(369\) | −7.39091e12 | − | 7.49182e12i | −1.08035 | − | 1.09510i | ||||
\(370\) | −6.82672e11 | + | 1.96002e11i | −0.0984472 | + | 0.0282652i | ||||
\(371\) | 1.01964e13i | 1.45071i | ||||||||
\(372\) | 4.18653e12 | − | 1.71751e12i | 0.587678 | − | 0.241093i | ||||
\(373\) | 4.76124e12i | 0.659441i | 0.944079 | + | 0.329720i | \(0.106954\pi\) | ||||
−0.944079 | + | 0.329720i | \(0.893046\pi\) | |||||||
\(374\) | − | 5.67863e11i | − | 0.0776043i | ||||||
\(375\) | 6.98451e12 | + | 2.49205e12i | 0.941845 | + | 0.336048i | ||||
\(376\) | 2.05995e12 | 0.274105 | ||||||||
\(377\) | −1.03036e13 | −1.35295 | ||||||||
\(378\) | −7.12908e11 | − | 3.03827e11i | −0.0923793 | − | 0.0393701i | ||||
\(379\) | −1.90196e12 | −0.243224 | −0.121612 | − | 0.992578i | \(-0.538806\pi\) | ||||
−0.121612 | + | 0.992578i | \(0.538806\pi\) | |||||||
\(380\) | 6.29095e11 | + | 2.19112e12i | 0.0793959 | + | 0.276534i | ||||
\(381\) | −3.23314e12 | − | 7.88095e12i | −0.402716 | − | 0.981643i | ||||
\(382\) | 4.36323e10i | 0.00536404i | ||||||||
\(383\) | −3.90047e12 | −0.473285 | −0.236643 | − | 0.971597i | \(-0.576047\pi\) | ||||
−0.236643 | + | 0.971597i | \(0.576047\pi\) | |||||||
\(384\) | −3.16812e12 | + | 1.29971e12i | −0.379442 | + | 0.155665i | ||||
\(385\) | 1.50576e12 | + | 5.24453e12i | 0.178013 | + | 0.620016i | ||||
\(386\) | 8.80947e10i | 0.0102805i | ||||||||
\(387\) | −6.90458e12 | − | 6.99885e12i | −0.795394 | − | 0.806254i | ||||
\(388\) | − | 3.08005e12i | − | 0.350267i | ||||||
\(389\) | 1.17374e13i | 1.31772i | 0.752265 | + | 0.658860i | \(0.228961\pi\) | ||||
−0.752265 | + | 0.658860i | \(0.771039\pi\) | |||||||
\(390\) | 1.15123e12 | − | 9.10009e11i | 0.127597 | − | 0.100861i | ||||
\(391\) | −3.85238e12 | −0.421546 | ||||||||
\(392\) | 1.80620e11 | 0.0195135 | ||||||||
\(393\) | 3.54839e12 | + | 8.64940e12i | 0.378503 | + | 0.922621i | ||||
\(394\) | −5.04562e11 | −0.0531415 | ||||||||
\(395\) | 1.25683e12 | + | 4.37753e12i | 0.130705 | + | 0.455243i | ||||
\(396\) | −4.58090e12 | − | 4.64345e12i | −0.470409 | − | 0.476831i | ||||
\(397\) | 8.00409e12i | 0.811632i | 0.913955 | + | 0.405816i | \(0.133013\pi\) | ||||
−0.913955 | + | 0.405816i | \(0.866987\pi\) | |||||||
\(398\) | 1.57225e12 | 0.157437 | ||||||||
\(399\) | −1.06348e12 | − | 2.59229e12i | −0.105164 | − | 0.256342i | ||||
\(400\) | −8.39189e12 | + | 5.25171e12i | −0.819520 | + | 0.512862i | ||||
\(401\) | − | 1.05898e13i | − | 1.02133i | −0.859779 | − | 0.510667i | \(-0.829399\pi\) | ||
0.859779 | − | 0.510667i | \(-0.170601\pi\) | |||||||
\(402\) | −2.15165e11 | − | 5.24476e11i | −0.0204947 | − | 0.0499568i | ||||
\(403\) | − | 1.05322e13i | − | 0.990822i | ||||||
\(404\) | 1.02161e13i | 0.949247i | ||||||||
\(405\) | 1.05129e13 | − | 2.86464e12i | 0.964822 | − | 0.262903i | ||||
\(406\) | 9.71639e11 | 0.0880794 | ||||||||
\(407\) | 7.34791e12 | 0.657948 | ||||||||
\(408\) | −2.38345e12 | + | 9.77806e11i | −0.210817 | + | 0.0864872i | ||||
\(409\) | 2.15103e13 | 1.87945 | 0.939723 | − | 0.341937i | \(-0.111083\pi\) | ||||
0.939723 | + | 0.341937i | \(0.111083\pi\) | |||||||
\(410\) | −1.80629e12 | + | 5.18605e11i | −0.155908 | + | 0.0447628i | ||||
\(411\) | 1.62677e12 | − | 6.67377e11i | 0.138713 | − | 0.0569066i | ||||
\(412\) | − | 2.15205e12i | − | 0.181287i | ||||||
\(413\) | 4.89533e11 | 0.0407410 | ||||||||
\(414\) | 3.54183e11 | − | 3.49412e11i | 0.0291223 | − | 0.0287300i | ||||
\(415\) | −5.91116e12 | − | 2.05884e13i | −0.480211 | − | 1.67256i | ||||
\(416\) | 5.98914e12i | 0.480727i | ||||||||
\(417\) | 1.17801e13 | − | 4.83275e12i | 0.934262 | − | 0.383279i | ||||
\(418\) | 2.65167e11i | 0.0207797i | ||||||||
\(419\) | − | 2.02804e13i | − | 1.57039i | −0.619249 | − | 0.785194i | \(-0.712563\pi\) | ||
0.619249 | − | 0.785194i | \(-0.287437\pi\) | |||||||
\(420\) | 9.65559e12 | − | 7.63239e12i | 0.738809 | − | 0.584002i | ||||
\(421\) | −2.48486e12 | −0.187885 | −0.0939425 | − | 0.995578i | \(-0.529947\pi\) | ||||
−0.0939425 | + | 0.995578i | \(0.529947\pi\) | |||||||
\(422\) | 4.36563e11 | 0.0326201 | ||||||||
\(423\) | 1.26008e13 | − | 1.24310e13i | 0.930454 | − | 0.917921i | ||||
\(424\) | −4.37772e12 | −0.319462 | ||||||||
\(425\) | −1.27713e13 | + | 7.99236e12i | −0.921063 | + | 0.576409i | ||||
\(426\) | 6.54149e11 | + | 1.59452e12i | 0.0466261 | + | 0.113654i | ||||
\(427\) | − | 1.56918e13i | − | 1.10543i | ||||||
\(428\) | 4.71032e12 | 0.327968 | ||||||||
\(429\) | −1.40457e13 | + | 5.76219e12i | −0.966619 | + | 0.396553i | ||||
\(430\) | −1.68743e12 | + | 4.84480e11i | −0.114785 | + | 0.0329559i | ||||
\(431\) | 1.32401e13i | 0.890234i | 0.895472 | + | 0.445117i | \(0.146838\pi\) | ||||
−0.895472 | + | 0.445117i | \(0.853162\pi\) | |||||||
\(432\) | −5.70286e12 | + | 1.33814e13i | −0.379031 | + | 0.889369i | ||||
\(433\) | 1.35236e13i | 0.888490i | 0.895905 | + | 0.444245i | \(0.146528\pi\) | ||||
−0.895905 | + | 0.444245i | \(0.853472\pi\) | |||||||
\(434\) | 9.93200e11i | 0.0645042i | ||||||||
\(435\) | −1.07177e13 | + | 8.47195e12i | −0.688106 | + | 0.543923i | ||||
\(436\) | −1.42395e12 | −0.0903778 | ||||||||
\(437\) | 1.79889e12 | 0.112875 | ||||||||
\(438\) | −7.70202e11 | − | 1.87741e12i | −0.0477787 | − | 0.116463i | ||||
\(439\) | 8.77457e12 | 0.538150 | 0.269075 | − | 0.963119i | \(-0.413282\pi\) | ||||
0.269075 | + | 0.963119i | \(0.413282\pi\) | |||||||
\(440\) | −2.25167e12 | + | 6.46479e11i | −0.136534 | + | 0.0392004i | ||||
\(441\) | 1.10486e12 | − | 1.08997e12i | 0.0662389 | − | 0.0653467i | ||||
\(442\) | 2.98132e12i | 0.176725i | ||||||||
\(443\) | 2.84909e13 | 1.66989 | 0.834946 | − | 0.550333i | \(-0.185499\pi\) | ||||
0.834946 | + | 0.550333i | \(0.185499\pi\) | |||||||
\(444\) | −6.29083e12 | − | 1.53342e13i | −0.364580 | − | 0.888684i | ||||
\(445\) | −1.63866e13 | + | 4.70475e12i | −0.939048 | + | 0.269610i | ||||
\(446\) | − | 2.04624e12i | − | 0.115953i | ||||||
\(447\) | −9.43214e11 | − | 2.29914e12i | −0.0528534 | − | 0.128833i | ||||
\(448\) | 1.60504e13i | 0.889397i | ||||||||
\(449\) | 1.57522e13i | 0.863194i | 0.902066 | + | 0.431597i | \(0.142050\pi\) | ||||
−0.902066 | + | 0.431597i | \(0.857950\pi\) | |||||||
\(450\) | 4.49264e11 | − | 1.89317e12i | 0.0243466 | − | 0.102595i | ||||
\(451\) | 1.94419e13 | 1.04197 | ||||||||
\(452\) | −2.67659e13 | −1.41870 | ||||||||
\(453\) | −1.05480e13 | + | 4.32727e12i | −0.552939 | + | 0.226842i | ||||
\(454\) | 2.96699e12 | 0.153828 | ||||||||
\(455\) | −7.90534e12 | − | 2.75341e13i | −0.405381 | − | 1.41193i | ||||
\(456\) | 1.11297e12 | − | 4.56593e11i | 0.0564494 | − | 0.0231582i | ||||
\(457\) | 8.92089e9i | 0.000447535i | 1.00000 | 0.000223768i | \(7.12274e-5\pi\) | |||||
−1.00000 | 0.000223768i | \(0.999929\pi\) | ||||||||
\(458\) | 1.00688e12 | 0.0499632 | ||||||||
\(459\) | −8.67896e12 | + | 2.03646e13i | −0.425995 | + | 0.999566i | ||||
\(460\) | 2.18060e12 | + | 7.59497e12i | 0.105873 | + | 0.368754i | ||||
\(461\) | − | 2.32159e13i | − | 1.11502i | −0.830172 | − | 0.557508i | \(-0.811758\pi\) | ||
0.830172 | − | 0.557508i | \(-0.188242\pi\) | |||||||
\(462\) | 1.32452e12 | − | 5.43380e11i | 0.0629286 | − | 0.0258163i | ||||
\(463\) | 8.54316e12i | 0.401526i | 0.979640 | + | 0.200763i | \(0.0643421\pi\) | ||||
−0.979640 | + | 0.200763i | \(0.935658\pi\) | |||||||
\(464\) | − | 1.82378e13i | − | 0.847973i | ||||||
\(465\) | −8.65995e12 | − | 1.09555e13i | −0.398337 | − | 0.503928i | ||||
\(466\) | −5.46852e11 | −0.0248851 | ||||||||
\(467\) | −3.80094e12 | −0.171122 | −0.0855611 | − | 0.996333i | \(-0.527268\pi\) | ||||
−0.0855611 | + | 0.996333i | \(0.527268\pi\) | |||||||
\(468\) | 2.40501e13 | + | 2.43784e13i | 1.07124 | + | 1.08587i | ||||
\(469\) | −1.10664e13 | −0.487688 | ||||||||
\(470\) | −8.72260e11 | − | 3.03806e12i | −0.0380326 | − | 0.132467i | ||||
\(471\) | 1.59110e13 | + | 3.87839e13i | 0.686425 | + | 1.67320i | ||||
\(472\) | 2.10175e11i | 0.00897162i | ||||||||
\(473\) | 1.81626e13 | 0.767136 | ||||||||
\(474\) | 1.10556e12 | − | 4.53551e11i | 0.0462050 | − | 0.0189555i | ||||
\(475\) | 5.96363e12 | − | 3.73209e12i | 0.246628 | − | 0.154342i | ||||
\(476\) | 2.50048e13i | 1.02327i | ||||||||
\(477\) | −2.67786e13 | + | 2.64180e13i | −1.08442 | + | 1.06981i | ||||
\(478\) | 2.27945e12i | 0.0913461i | ||||||||
\(479\) | − | 2.00941e13i | − | 0.796878i | −0.917195 | − | 0.398439i | \(-0.869552\pi\) | ||
0.917195 | − | 0.398439i | \(-0.130448\pi\) | |||||||
\(480\) | 4.92447e12 | + | 6.22985e12i | 0.193265 | + | 0.244496i | ||||
\(481\) | −3.85770e13 | −1.49832 | ||||||||
\(482\) | −7.07807e11 | −0.0272069 | ||||||||
\(483\) | −3.68629e12 | − | 8.98552e12i | −0.140234 | − | 0.341828i | ||||
\(484\) | −1.42145e13 | −0.535185 | ||||||||
\(485\) | −9.13616e12 | + | 2.62309e12i | −0.340451 | + | 0.0977471i | ||||
\(486\) | −1.04914e12 | − | 2.65947e12i | −0.0386948 | − | 0.0980877i | ||||
\(487\) | − | 1.06632e13i | − | 0.389262i | −0.980876 | − | 0.194631i | \(-0.937649\pi\) | ||
0.980876 | − | 0.194631i | \(-0.0623510\pi\) | |||||||
\(488\) | 6.73708e12 | 0.243429 | ||||||||
\(489\) | 5.90967e12 | + | 1.44051e13i | 0.211358 | + | 0.515197i | ||||
\(490\) | −7.64813e10 | − | 2.66383e11i | −0.00270754 | − | 0.00943030i | ||||
\(491\) | − | 4.81742e13i | − | 1.68813i | −0.536238 | − | 0.844067i | \(-0.680155\pi\) | ||
0.536238 | − | 0.844067i | \(-0.319845\pi\) | |||||||
\(492\) | −1.66450e13 | − | 4.05731e13i | −0.577375 | − | 1.40738i | ||||
\(493\) | − | 2.77553e13i | − | 0.953041i | ||||||
\(494\) | − | 1.39215e12i | − | 0.0473206i | ||||||
\(495\) | −9.87228e12 | + | 1.75426e13i | −0.332194 | + | 0.590292i | ||||
\(496\) | 1.86425e13 | 0.621006 | ||||||||
\(497\) | 3.36444e13 | 1.10951 | ||||||||
\(498\) | −5.19966e12 | + | 2.13315e12i | −0.169757 | + | 0.0696425i | ||||
\(499\) | 5.42436e13 | 1.75326 | 0.876629 | − | 0.481167i | \(-0.159787\pi\) | ||||
0.876629 | + | 0.481167i | \(0.159787\pi\) | |||||||
\(500\) | 2.29860e13 | + | 2.06546e13i | 0.735551 | + | 0.660947i | ||||
\(501\) | 1.72460e13 | − | 7.07514e12i | 0.546388 | − | 0.224154i | ||||
\(502\) | − | 5.18945e12i | − | 0.162780i | ||||||
\(503\) | −1.00719e13 | −0.312804 | −0.156402 | − | 0.987694i | \(-0.549989\pi\) | ||||
−0.156402 | + | 0.987694i | \(0.549989\pi\) | |||||||
\(504\) | −4.56139e12 | − | 4.62366e12i | −0.140263 | − | 0.142178i | ||||
\(505\) | 3.03034e13 | − | 8.70042e12i | 0.922645 | − | 0.264901i | ||||
\(506\) | 9.19134e11i | 0.0277094i | ||||||||
\(507\) | 4.27478e13 | − | 1.75372e13i | 1.27607 | − | 0.523504i | ||||
\(508\) | − | 3.54972e13i | − | 1.04924i | ||||||
\(509\) | 4.99580e12i | 0.146223i | 0.997324 | + | 0.0731116i | \(0.0232929\pi\) | ||||
−0.997324 | + | 0.0731116i | \(0.976707\pi\) | |||||||
\(510\) | 2.45134e12 | + | 3.10114e12i | 0.0710481 | + | 0.0898815i | ||||
\(511\) | −3.96132e13 | −1.13694 | ||||||||
\(512\) | −1.77345e13 | −0.504046 | ||||||||
\(513\) | 4.05270e12 | − | 9.50936e12i | 0.114066 | − | 0.267648i | ||||
\(514\) | 1.04278e12 | 0.0290655 | ||||||||
\(515\) | −6.38349e12 | + | 1.83277e12i | −0.176207 | + | 0.0505907i | ||||
\(516\) | −1.55497e13 | − | 3.79033e13i | −0.425084 | − | 1.03616i | ||||
\(517\) | 3.27001e13i | 0.885311i | ||||||||
\(518\) | 3.63785e12 | 0.0975430 | ||||||||
\(519\) | 5.79624e12 | − | 2.37789e12i | 0.153925 | − | 0.0631474i | ||||
\(520\) | 1.18214e13 | − | 3.39406e12i | 0.310924 | − | 0.0892694i | ||||
\(521\) | 3.61057e13i | 0.940562i | 0.882517 | + | 0.470281i | \(0.155847\pi\) | ||||
−0.882517 | + | 0.470281i | \(0.844153\pi\) | |||||||
\(522\) | 2.51742e12 | + | 2.55179e12i | 0.0649535 | + | 0.0658403i | ||||
\(523\) | 5.28013e13i | 1.34939i | 0.738098 | + | 0.674693i | \(0.235724\pi\) | ||||
−0.738098 | + | 0.674693i | \(0.764276\pi\) | |||||||
\(524\) | 3.89585e13i | 0.986155i | ||||||||
\(525\) | −3.08625e13 | − | 2.21407e13i | −0.773811 | − | 0.555130i | ||||
\(526\) | −4.29950e12 | −0.106780 | ||||||||
\(527\) | 2.83712e13 | 0.697952 | ||||||||
\(528\) | −1.01993e13 | − | 2.48614e13i | −0.248543 | − | 0.605836i | ||||
\(529\) | −3.51911e13 | −0.849483 | ||||||||
\(530\) | 1.85369e12 | + | 6.45637e12i | 0.0443260 | + | 0.154387i | ||||
\(531\) | 1.26833e12 | + | 1.28565e12i | 0.0300441 | + | 0.0304543i | ||||
\(532\) | − | 1.16762e13i | − | 0.273994i | ||||||
\(533\) | −1.02071e14 | −2.37284 | ||||||||
\(534\) | 1.69779e12 | + | 4.13847e12i | 0.0391002 | + | 0.0953088i | ||||
\(535\) | −4.01148e12 | − | 1.39719e13i | −0.0915243 | − | 0.318777i | ||||
\(536\) | − | 4.75122e12i | − | 0.107394i | ||||||
\(537\) | 1.76034e13 | + | 4.29091e13i | 0.394207 | + | 0.960900i | ||||
\(538\) | − | 9.34430e12i | − | 0.207317i | ||||||
\(539\) | 2.86720e12i | 0.0630251i | ||||||||
\(540\) | 4.50614e13 | + | 5.58345e12i | 0.981377 | + | 0.121600i | ||||
\(541\) | 6.31636e12 | 0.136295 | 0.0681476 | − | 0.997675i | \(-0.478291\pi\) | ||||
0.0681476 | + | 0.997675i | \(0.478291\pi\) | |||||||
\(542\) | −6.70174e12 | −0.143282 | ||||||||
\(543\) | −3.13460e13 | + | 1.28596e13i | −0.664022 | + | 0.272413i | ||||
\(544\) | −1.61333e13 | −0.338632 | ||||||||
\(545\) | 1.21269e12 | + | 4.22376e12i | 0.0252212 | + | 0.0878450i | ||||
\(546\) | −6.95381e12 | + | 2.85278e12i | −0.143305 | + | 0.0587903i | ||||
\(547\) | 6.04095e13i | 1.23358i | 0.787126 | + | 0.616792i | \(0.211568\pi\) | ||||
−0.787126 | + | 0.616792i | \(0.788432\pi\) | |||||||
\(548\) | 7.32726e12 | 0.148265 | ||||||||
\(549\) | 4.12109e13 | − | 4.06558e13i | 0.826324 | − | 0.815194i | ||||
\(550\) | 1.90689e12 | + | 3.04708e12i | 0.0378889 | + | 0.0605439i | ||||
\(551\) | 1.29605e13i | 0.255191i | ||||||||
\(552\) | 3.85782e12 | − | 1.58266e12i | 0.0752743 | − | 0.0308811i | ||||
\(553\) | − | 2.33272e13i | − | 0.451062i | ||||||
\(554\) | 7.51772e12i | 0.144058i | ||||||||
\(555\) | −4.01274e13 | + | 3.17193e13i | −0.762038 | + | 0.602363i | ||||
\(556\) | 5.30597e13 | 0.998598 | ||||||||
\(557\) | 3.98198e13 | 0.742716 | 0.371358 | − | 0.928490i | \(-0.378892\pi\) | ||||
0.371358 | + | 0.928490i | \(0.378892\pi\) | |||||||
\(558\) | −2.60841e12 | + | 2.57328e12i | −0.0482176 | + | 0.0475681i | ||||
\(559\) | −9.53550e13 | −1.74697 | ||||||||
\(560\) | 4.87365e13 | − | 1.39928e13i | 0.884941 | − | 0.254076i | ||||
\(561\) | −1.55219e13 | − | 3.78355e13i | −0.279339 | − | 0.680903i | ||||
\(562\) | − | 3.03699e12i | − | 0.0541704i | ||||||
\(563\) | −4.77136e13 | −0.843530 | −0.421765 | − | 0.906705i | \(-0.638589\pi\) | ||||
−0.421765 | + | 0.906705i | \(0.638589\pi\) | |||||||
\(564\) | 6.82413e13 | − | 2.79958e13i | 1.19578 | − | 0.490566i | ||||
\(565\) | 2.27948e13 | + | 7.93940e13i | 0.395908 | + | 1.37894i | ||||
\(566\) | − | 1.39858e12i | − | 0.0240771i | ||||||
\(567\) | −5.58043e13 | − | 7.56768e11i | −0.952253 | − | 0.0129136i | ||||
\(568\) | 1.44448e13i | 0.244326i | ||||||||
\(569\) | − | 7.89252e12i | − | 0.132329i | −0.997809 | − | 0.0661644i | \(-0.978924\pi\) | ||
0.997809 | − | 0.0661644i | \(-0.0210762\pi\) | |||||||
\(570\) | −1.14467e12 | − | 1.44810e12i | −0.0190242 | − | 0.0240671i | ||||
\(571\) | 6.59396e13 | 1.08634 | 0.543170 | − | 0.839623i | \(-0.317224\pi\) | ||||
0.543170 | + | 0.839623i | \(0.317224\pi\) | |||||||
\(572\) | −6.32641e13 | −1.03318 | ||||||||
\(573\) | 1.19264e12 | + | 2.90713e12i | 0.0193080 | + | 0.0470643i | ||||
\(574\) | 9.62543e12 | 0.154476 | ||||||||
\(575\) | 2.06714e13 | − | 1.29363e13i | 0.328875 | − | 0.205812i | ||||
\(576\) | −4.21527e13 | + | 4.15849e13i | −0.664833 | + | 0.655879i | ||||
\(577\) | − | 7.94344e13i | − | 1.24202i | −0.783802 | − | 0.621011i | \(-0.786722\pi\) | ||
0.783802 | − | 0.621011i | \(-0.213278\pi\) | |||||||
\(578\) | −1.22854e12 | −0.0190437 | ||||||||
\(579\) | 2.40797e12 | + | 5.86956e12i | 0.0370049 | + | 0.0902014i | ||||
\(580\) | −5.47197e13 | + | 1.57106e13i | −0.833688 | + | 0.239361i | ||||
\(581\) | 1.09713e14i | 1.65720i | ||||||||
\(582\) | 9.46588e11 | + | 2.30736e12i | 0.0141758 | + | 0.0345541i | ||||
\(583\) | − | 6.94929e13i | − | 1.03181i | ||||||
\(584\) | − | 1.70074e13i | − | 0.250366i | ||||||
\(585\) | 5.18302e13 | − | 9.20997e13i | 0.756491 | − | 1.34425i | ||||
\(586\) | −9.34519e12 | −0.135238 | ||||||||
\(587\) | 2.48653e13 | 0.356783 | 0.178391 | − | 0.983960i | \(-0.442911\pi\) | ||||
0.178391 | + | 0.983960i | \(0.442911\pi\) | |||||||
\(588\) | 5.98351e12 | − | 2.45472e12i | 0.0851275 | − | 0.0349233i | ||||
\(589\) | −1.32481e13 | −0.186887 | ||||||||
\(590\) | 3.09971e11 | − | 8.89960e10i | 0.00433572 | − | 0.00124483i | ||||
\(591\) | −3.36179e13 | + | 1.37917e13i | −0.466266 | + | 0.191284i | ||||
\(592\) | − | 6.82829e13i | − | 0.939081i | ||||||
\(593\) | −8.66034e11 | −0.0118103 | −0.00590516 | − | 0.999983i | \(-0.501880\pi\) | ||||
−0.00590516 | + | 0.999983i | \(0.501880\pi\) | |||||||
\(594\) | 4.85876e12 | + | 2.07070e12i | 0.0657042 | + | 0.0280018i | ||||
\(595\) | 7.41701e13 | − | 2.12950e13i | 0.994590 | − | 0.285557i | ||||
\(596\) | − | 1.03557e13i | − | 0.137705i | ||||||
\(597\) | 1.04755e14 | − | 4.29757e13i | 1.38135 | − | 0.566697i | ||||
\(598\) | − | 4.82552e12i | − | 0.0631013i | ||||||
\(599\) | 4.91176e13i | 0.636946i | 0.947932 | + | 0.318473i | \(0.103170\pi\) | ||||
−0.947932 | + | 0.318473i | \(0.896830\pi\) | |||||||
\(600\) | 9.50584e12 | − | 1.32504e13i | 0.122246 | − | 0.170402i | ||||
\(601\) | 9.45088e13 | 1.20531 | 0.602656 | − | 0.798001i | \(-0.294109\pi\) | ||||
0.602656 | + | 0.798001i | \(0.294109\pi\) | |||||||
\(602\) | 8.99207e12 | 0.113731 | ||||||||
\(603\) | −2.86719e13 | − | 2.90634e13i | −0.359642 | − | 0.364552i | ||||
\(604\) | −4.75099e13 | −0.591016 | ||||||||
\(605\) | 1.21056e13 | + | 4.21634e13i | 0.149351 | + | 0.520187i | ||||
\(606\) | −3.13970e12 | − | 7.65320e12i | −0.0384172 | − | 0.0936440i | ||||
\(607\) | 8.45768e13i | 1.02638i | 0.858275 | + | 0.513190i | \(0.171536\pi\) | ||||
−0.858275 | + | 0.513190i | \(0.828464\pi\) | |||||||
\(608\) | 7.53353e12 | 0.0906736 | ||||||||
\(609\) | 6.47382e13 | − | 2.65587e13i | 0.772813 | − | 0.317044i | ||||
\(610\) | −2.85273e12 | − | 9.93602e12i | −0.0337763 | − | 0.117642i | ||||
\(611\) | − | 1.71678e14i | − | 2.01608i | ||||||
\(612\) | −6.56694e13 | + | 6.47849e13i | −0.764903 | + | 0.754600i | ||||
\(613\) | − | 5.40212e13i | − | 0.624111i | −0.950064 | − | 0.312056i | \(-0.898982\pi\) | ||
0.950064 | − | 0.312056i | \(-0.101018\pi\) | |||||||
\(614\) | − | 1.51013e12i | − | 0.0173051i | ||||||
\(615\) | −1.06174e14 | + | 8.39264e13i | −1.20682 | + | 0.953945i | ||||
\(616\) | 1.19988e13 | 0.135280 | ||||||||
\(617\) | 3.34524e13 | 0.374112 | 0.187056 | − | 0.982349i | \(-0.440105\pi\) | ||||
0.187056 | + | 0.982349i | \(0.440105\pi\) | |||||||
\(618\) | 6.61387e11 | + | 1.61217e12i | 0.00733691 | + | 0.0178841i | ||||
\(619\) | −1.09079e14 | −1.20030 | −0.600148 | − | 0.799889i | \(-0.704892\pi\) | ||||
−0.600148 | + | 0.799889i | \(0.704892\pi\) | |||||||
\(620\) | −1.60592e13 | − | 5.59339e13i | −0.175294 | − | 0.610544i | ||||
\(621\) | 1.40476e13 | − | 3.29618e13i | 0.152106 | − | 0.356905i | ||||
\(622\) | 1.13281e13i | 0.121676i | ||||||||
\(623\) | 8.73214e13 | 0.930423 | ||||||||
\(624\) | 5.35471e13 | + | 1.30524e14i | 0.565995 | + | 1.37964i | ||||
\(625\) | 4.16906e13 | − | 8.57720e13i | 0.437158 | − | 0.899385i | ||||
\(626\) | − | 4.67154e12i | − | 0.0485947i | ||||||
\(627\) | 7.24806e12 | + | 1.76675e13i | 0.0747970 | + | 0.182322i | ||||
\(628\) | 1.74690e14i | 1.78842i | ||||||||
\(629\) | − | 1.03917e14i | − | 1.05544i | ||||||
\(630\) | −4.88764e12 | + | 8.68509e12i | −0.0492488 | + | 0.0875128i | ||||
\(631\) | −1.15153e14 | −1.15114 | −0.575570 | − | 0.817752i | \(-0.695220\pi\) | ||||
−0.575570 | + | 0.817752i | \(0.695220\pi\) | |||||||
\(632\) | 1.00152e13 | 0.0993289 | ||||||||
\(633\) | 2.90873e13 | − | 1.19330e13i | 0.286210 | − | 0.117417i | ||||
\(634\) | 6.66438e12 | 0.0650599 | ||||||||
\(635\) | −1.05293e14 | + | 3.02307e13i | −1.01984 | + | 0.292806i | ||||
\(636\) | −1.45024e14 | + | 5.94956e13i | −1.39365 | + | 0.571741i | ||||
\(637\) | − | 1.50530e13i | − | 0.143524i | ||||||
\(638\) | −6.62211e12 | −0.0626459 | ||||||||
\(639\) | 8.71691e13 | + | 8.83592e13i | 0.818198 | + | 0.829369i | ||||
\(640\) | 1.21527e13 | + | 4.23275e13i | 0.113180 | + | 0.394205i | ||||
\(641\) | 4.03480e13i | 0.372848i | 0.982469 | + | 0.186424i | \(0.0596898\pi\) | ||||
−0.982469 | + | 0.186424i | \(0.940310\pi\) | |||||||
\(642\) | −3.52864e12 | + | 1.44762e12i | −0.0323543 | + | 0.0132733i | ||||
\(643\) | 7.11482e13i | 0.647305i | 0.946176 | + | 0.323652i | \(0.104911\pi\) | ||||
−0.946176 | + | 0.323652i | \(0.895089\pi\) | |||||||
\(644\) | − | 4.04724e13i | − | 0.365367i | ||||||
\(645\) | −9.91873e13 | + | 7.84040e13i | −0.888500 | + | 0.702327i | ||||
\(646\) | 3.75010e12 | 0.0333334 | ||||||||
\(647\) | −4.65327e13 | −0.410428 | −0.205214 | − | 0.978717i | \(-0.565789\pi\) | ||||
−0.205214 | + | 0.978717i | \(0.565789\pi\) | |||||||
\(648\) | 3.24909e11 | − | 2.39589e13i | 0.00284372 | − | 0.209697i | ||||
\(649\) | −3.33636e12 | −0.0289768 | ||||||||
\(650\) | −1.00113e13 | − | 1.59974e13i | −0.0862827 | − | 0.137874i | ||||
\(651\) | 2.71480e13 | + | 6.61748e13i | 0.232185 | + | 0.565963i | ||||
\(652\) | 6.48833e13i | 0.550675i | ||||||||
\(653\) | 3.78141e13 | 0.318484 | 0.159242 | − | 0.987240i | \(-0.449095\pi\) | ||||
0.159242 | + | 0.987240i | \(0.449095\pi\) | |||||||
\(654\) | 1.06672e12 | − | 4.37620e11i | 0.00891585 | − | 0.00365770i | ||||
\(655\) | 1.15560e14 | − | 3.31785e13i | 0.958519 | − | 0.275201i | ||||
\(656\) | − | 1.80670e14i | − | 1.48720i | ||||||
\(657\) | −1.02634e14 | − | 1.04035e14i | −0.838424 | − | 0.849871i | ||||
\(658\) | 1.61894e13i | 0.131250i | ||||||||
\(659\) | − | 7.78536e13i | − | 0.626400i | −0.949687 | − | 0.313200i | \(-0.898599\pi\) | ||
0.949687 | − | 0.313200i | \(-0.101401\pi\) | |||||||
\(660\) | −6.58067e13 | + | 5.20178e13i | −0.525473 | + | 0.415368i | ||||
\(661\) | −5.57101e13 | −0.441496 | −0.220748 | − | 0.975331i | \(-0.570850\pi\) | ||||
−0.220748 | + | 0.975331i | \(0.570850\pi\) | |||||||
\(662\) | −3.35620e12 | −0.0263972 | ||||||||
\(663\) | 8.14911e13 | + | 1.98639e14i | 0.636125 | + | 1.55059i | ||||
\(664\) | −4.71037e13 | −0.364934 | ||||||||
\(665\) | −3.46342e13 | + | 9.94385e12i | −0.266316 | + | 0.0764621i | ||||
\(666\) | 9.42530e12 | + | 9.55398e12i | 0.0719323 | + | 0.0729144i | ||||
\(667\) | 4.49243e13i | 0.340293i | ||||||||
\(668\) | 7.76793e13 | 0.584013 | ||||||||
\(669\) | −5.59318e13 | − | 1.36337e14i | −0.417377 | − | 1.01738i | ||||
\(670\) | −7.00723e12 | + | 2.01185e12i | −0.0519006 | + | 0.0149012i | ||||
\(671\) | 1.06946e14i | 0.786233i | ||||||||
\(672\) | −1.54377e13 | − | 3.76302e13i | −0.112651 | − | 0.274594i | ||||
\(673\) | − | 5.51238e13i | − | 0.399267i | −0.979871 | − | 0.199634i | \(-0.936025\pi\) | ||
0.979871 | − | 0.199634i | \(-0.0639752\pi\) | |||||||
\(674\) | 1.12503e13i | 0.0808844i | ||||||||
\(675\) | −2.18141e13 | − | 1.38418e14i | −0.155675 | − | 0.987808i | ||||
\(676\) | 1.92544e14 | 1.36394 | ||||||||
\(677\) | −1.36412e14 | −0.959202 | −0.479601 | − | 0.877487i | \(-0.659219\pi\) | ||||
−0.479601 | + | 0.877487i | \(0.659219\pi\) | |||||||
\(678\) | 2.00511e13 | − | 8.22593e12i | 0.139956 | − | 0.0574165i | ||||
\(679\) | 4.86851e13 | 0.337324 | ||||||||
\(680\) | 9.14275e12 | + | 3.18440e13i | 0.0628829 | + | 0.219020i | ||||
\(681\) | 1.97684e14 | − | 8.10994e13i | 1.34970 | − | 0.553710i | ||||
\(682\) | − | 6.76906e12i | − | 0.0458782i | ||||||
\(683\) | 2.62727e14 | 1.76767 | 0.883836 | − | 0.467797i | \(-0.154952\pi\) | ||||
0.883836 | + | 0.467797i | \(0.154952\pi\) | |||||||
\(684\) | 3.06648e13 | − | 3.02517e13i | 0.204814 | − | 0.202055i | ||||
\(685\) | −6.24016e12 | − | 2.17344e13i | −0.0413755 | − | 0.144110i | ||||
\(686\) | 1.66753e13i | 0.109762i | ||||||||
\(687\) | 6.70863e13 | − | 2.75220e13i | 0.438379 | − | 0.179844i | ||||
\(688\) | − | 1.68782e14i | − | 1.09492i | ||||||
\(689\) | 3.64843e14i | 2.34968i | ||||||||
\(690\) | −3.96770e12 | − | 5.01946e12i | −0.0253684 | − | 0.0320931i | ||||
\(691\) | −1.92807e14 | −1.22386 | −0.611931 | − | 0.790911i | \(-0.709607\pi\) | ||||
−0.611931 | + | 0.790911i | \(0.709607\pi\) | |||||||
\(692\) | 2.61073e13 | 0.164525 | ||||||||
\(693\) | 7.33971e13 | − | 7.24085e13i | 0.459211 | − | 0.453026i | ||||
\(694\) | −1.47260e13 | −0.0914717 | ||||||||
\(695\) | −4.51876e13 | − | 1.57387e14i | −0.278673 | − | 0.970613i | ||||
\(696\) | 1.14026e13 | + | 2.77945e13i | 0.0698167 | + | 0.170182i | ||||
\(697\) | − | 2.74955e14i | − | 1.67147i | ||||||
\(698\) | −8.11579e12 | −0.0489839 | ||||||||
\(699\) | −3.64356e13 | + | 1.49476e13i | −0.218343 | + | 0.0895747i | ||||
\(700\) | −8.39663e13 | − | 1.34173e14i | −0.499591 | − | 0.798314i | ||||
\(701\) | 2.04011e14i | 1.20521i | 0.798038 | + | 0.602607i | \(0.205871\pi\) | ||||
−0.798038 | + | 0.602607i | \(0.794129\pi\) | |||||||
\(702\) | −2.55088e13 | − | 1.08713e13i | −0.149625 | − | 0.0637672i | ||||
\(703\) | 4.85247e13i | 0.282609i | ||||||||
\(704\) | − | 1.09390e14i | − | 0.632578i | ||||||
\(705\) | −1.41159e14 | − | 1.78577e14i | −0.810518 | − | 1.02537i | ||||
\(706\) | 2.66474e13 | 0.151926 | ||||||||
\(707\) | −1.61482e14 | −0.914171 | ||||||||
\(708\) | 2.85639e12 | + | 6.96261e12i | 0.0160565 | + | 0.0391386i | ||||
\(709\) | 1.13809e14 | 0.635250 | 0.317625 | − | 0.948216i | \(-0.397115\pi\) | ||||
0.317625 | + | 0.948216i | \(0.397115\pi\) | |||||||
\(710\) | 2.13036e13 | − | 6.11647e12i | 0.118076 | − | 0.0339008i | ||||
\(711\) | 6.12635e13 | − | 6.04383e13i | 0.337174 | − | 0.332632i | ||||
\(712\) | 3.74904e13i | 0.204890i | ||||||||
\(713\) | −4.59213e13 | −0.249210 | ||||||||
\(714\) | −7.68469e12 | − | 1.87318e13i | −0.0414129 | − | 0.100946i | ||||
\(715\) | 5.38781e13 | + | 1.87656e14i | 0.288325 | + | 1.00423i | ||||
\(716\) | 1.93270e14i | 1.02707i | ||||||||
\(717\) | 6.23062e13 | + | 1.51875e14i | 0.328803 | + | 0.801474i | ||||
\(718\) | 7.75810e10i | 0.000406568i | ||||||||
\(719\) | − | 7.96589e13i | − | 0.414562i | −0.978281 | − | 0.207281i | \(-0.933539\pi\) | ||
0.978281 | − | 0.207281i | \(-0.0664615\pi\) | |||||||
\(720\) | 1.63020e14 | + | 9.17415e13i | 0.842517 | + | 0.474136i | ||||
\(721\) | 3.40166e13 | 0.174588 | ||||||||
\(722\) | 1.89364e13 | 0.0965187 | ||||||||
\(723\) | −4.71596e13 | + | 1.93471e13i | −0.238715 | + | 0.0979320i | ||||
\(724\) | −1.41188e14 | −0.709748 | ||||||||
\(725\) | 9.32026e13 | + | 1.48932e14i | 0.465305 | + | 0.743527i | ||||
\(726\) | 1.06485e13 | − | 4.36851e12i | 0.0527964 | − | 0.0216596i | ||||
\(727\) | 2.03214e13i | 0.100065i | 0.998748 | + | 0.0500323i | \(0.0159324\pi\) | ||||
−0.998748 | + | 0.0500323i | \(0.984068\pi\) | |||||||
\(728\) | −6.29946e13 | −0.308068 | ||||||||
\(729\) | −1.42596e14 | − | 1.48518e14i | −0.692579 | − | 0.721342i | ||||
\(730\) | −2.50830e13 | + | 7.20160e12i | −0.120994 | + | 0.0347388i | ||||
\(731\) | − | 2.56863e14i | − | 1.23059i | ||||||
\(732\) | 2.23184e14 | − | 9.15606e13i | 1.06196 | − | 0.435665i | ||||
\(733\) | 3.95830e14i | 1.87063i | 0.353810 | + | 0.935317i | \(0.384886\pi\) | ||||
−0.353810 | + | 0.935317i | \(0.615114\pi\) | |||||||
\(734\) | − | 1.79834e13i | − | 0.0844098i | ||||||
\(735\) | −1.23771e13 | − | 1.56580e13i | −0.0577007 | − | 0.0729960i | ||||
\(736\) | 2.61131e13 | 0.120912 | ||||||||
\(737\) | 7.54220e13 | 0.346865 | ||||||||
\(738\) | 2.49385e13 | + | 2.52790e13i | 0.113917 | + | 0.115472i | ||||
\(739\) | 2.22171e14 | 1.00801 | 0.504006 | − | 0.863700i | \(-0.331859\pi\) | ||||
0.504006 | + | 0.863700i | \(0.331859\pi\) | |||||||
\(740\) | −2.04872e14 | + | 5.88210e13i | −0.923262 | + | 0.265078i | ||||
\(741\) | −3.80528e13 | − | 9.27558e13i | −0.170332 | − | 0.415193i | ||||
\(742\) | − | 3.44050e13i | − | 0.152969i | ||||||
\(743\) | −2.64190e14 | −1.16673 | −0.583367 | − | 0.812209i | \(-0.698265\pi\) | ||||
−0.583367 | + | 0.812209i | \(0.698265\pi\) | |||||||
\(744\) | −2.84113e13 | + | 1.16557e13i | −0.124631 | + | 0.0511297i | ||||
\(745\) | −3.07175e13 | + | 8.81931e12i | −0.133846 | + | 0.0384285i | ||||
\(746\) | − | 1.60654e13i | − | 0.0695342i | ||||||
\(747\) | −2.88135e14 | + | 2.84254e14i | −1.23878 | + | 1.22209i | ||||
\(748\) | − | 1.70418e14i | − | 0.727792i | ||||||
\(749\) | 7.44542e13i | 0.315849i | ||||||||
\(750\) | −2.35672e13 | − | 8.40872e12i | −0.0993121 | − | 0.0354343i | ||||
\(751\) | −2.00121e14 | −0.837708 | −0.418854 | − | 0.908054i | \(-0.637568\pi\) | ||||
−0.418854 | + | 0.908054i | \(0.637568\pi\) | |||||||
\(752\) | 3.03876e14 | 1.26359 | ||||||||
\(753\) | −1.41848e14 | − | 3.45762e14i | −0.585933 | − | 1.42824i | ||||
\(754\) | 3.47665e13 | 0.142661 | ||||||||
\(755\) | 4.04612e13 | + | 1.40925e14i | 0.164932 | + | 0.574453i | ||||
\(756\) | −2.13946e14 | − | 9.11796e13i | −0.866355 | − | 0.369223i | ||||
\(757\) | 3.98484e14i | 1.60299i | 0.598001 | + | 0.801496i | \(0.295962\pi\) | ||||
−0.598001 | + | 0.801496i | \(0.704038\pi\) | |||||||
\(758\) | 6.41763e12 | 0.0256465 | ||||||||
\(759\) | 2.51235e13 | + | 6.12400e13i | 0.0997406 | + | 0.243123i | ||||
\(760\) | −4.26927e12 | − | 1.48698e13i | −0.0168378 | − | 0.0586457i | ||||
\(761\) | 1.37475e14i | 0.538642i | 0.963050 | + | 0.269321i | \(0.0867993\pi\) | ||||
−0.963050 | + | 0.269321i | \(0.913201\pi\) | |||||||
\(762\) | 1.09093e13 | + | 2.65920e13i | 0.0424641 | + | 0.103509i | ||||
\(763\) | − | 2.25078e13i | − | 0.0870382i | ||||||
\(764\) | 1.30942e13i | 0.0503053i | ||||||||
\(765\) | 2.48094e14 | + | 1.39618e14i | 0.946910 | + | 0.532885i | ||||
\(766\) | 1.31610e13 | 0.0499052 | ||||||||
\(767\) | 1.75161e13 | 0.0659875 | ||||||||
\(768\) | −2.20161e14 | + | 9.03205e13i | −0.824013 | + | 0.338049i | ||||
\(769\) | −4.46994e13 | −0.166215 | −0.0831074 | − | 0.996541i | \(-0.526484\pi\) | ||||
−0.0831074 | + | 0.996541i | \(0.526484\pi\) | |||||||
\(770\) | −5.08075e12 | − | 1.76962e13i | −0.0187704 | − | 0.0653771i | ||||
\(771\) | 6.94782e13 | − | 2.85033e13i | 0.255022 | − | 0.104622i | ||||
\(772\) | 2.64376e13i | 0.0964129i | ||||||||
\(773\) | −3.88269e14 | −1.40681 | −0.703405 | − | 0.710790i | \(-0.748338\pi\) | ||||
−0.703405 | + | 0.710790i | \(0.748338\pi\) | |||||||
\(774\) | 2.32975e13 | + | 2.36156e13i | 0.0838697 | + | 0.0850148i | ||||
\(775\) | −1.52237e14 | + | 9.52708e13i | −0.544516 | + | 0.340762i | ||||
\(776\) | 2.09024e13i | 0.0742826i | ||||||||
\(777\) | 2.42382e14 | − | 9.94366e13i | 0.855846 | − | 0.351109i | ||||
\(778\) | − | 3.96044e13i | − | 0.138946i | ||||||
\(779\) | 1.28392e14i | 0.447560i | ||||||||
\(780\) | 3.45490e14 | − | 2.73097e14i | 1.19664 | − | 0.945898i | ||||
\(781\) | −2.29300e14 | −0.789130 | ||||||||
\(782\) | 1.29988e13 | 0.0444496 | ||||||||
\(783\) | 2.37480e14 | + | 1.01209e14i | 0.806899 | + | 0.343884i | ||||
\(784\) | 2.66444e13 | 0.0899550 | ||||||||
\(785\) | 5.18170e14 | − | 1.48772e14i | 1.73830 | − | 0.499084i | ||||
\(786\) | −1.19730e13 | − | 2.91849e13i | −0.0399109 | − | 0.0972850i | ||||
\(787\) | − | 4.86473e14i | − | 1.61133i | −0.592371 | − | 0.805665i | \(-0.701808\pi\) | ||
0.592371 | − | 0.805665i | \(-0.298192\pi\) | |||||||
\(788\) | −1.51421e14 | −0.498374 | ||||||||
\(789\) | −2.86466e14 | + | 1.17522e14i | −0.936890 | + | 0.384357i | ||||
\(790\) | −4.24083e12 | − | 1.47707e13i | −0.0137821 | − | 0.0480028i | ||||
\(791\) | − | 4.23078e14i | − | 1.36627i | ||||||
\(792\) | 3.10877e13 | + | 3.15121e13i | 0.0997614 | + | 0.101123i | ||||
\(793\) | − | 5.61473e14i | − | 1.79045i | ||||||
\(794\) | − | 2.70075e13i | − | 0.0855819i | ||||||
\(795\) | 2.99986e14 | + | 3.79506e14i | 0.944636 | + | 1.19504i | ||||
\(796\) | 4.71837e14 | 1.47648 | ||||||||
\(797\) | −3.00706e14 | −0.935084 | −0.467542 | − | 0.883971i | \(-0.654860\pi\) | ||||
−0.467542 | + | 0.883971i | \(0.654860\pi\) | |||||||
\(798\) | 3.58842e12 | + | 8.74696e12i | 0.0110889 | + | 0.0270298i | ||||
\(799\) | 4.62457e14 | 1.42016 | ||||||||
\(800\) | 8.65691e13 | − | 5.41756e13i | 0.264188 | − | 0.165331i | ||||
\(801\) | 2.26241e14 | + | 2.29330e14i | 0.686133 | + | 0.695501i | ||||
\(802\) | 3.57324e13i | 0.107694i | ||||||||
\(803\) | 2.69980e14 | 0.808638 | ||||||||
\(804\) | −6.45718e13 | − | 1.57397e14i | −0.192204 | − | 0.468507i | ||||
\(805\) | −1.20051e14 | + | 3.44678e13i | −0.355128 | + | 0.101961i | ||||
\(806\) | 3.55380e13i | 0.104476i | ||||||||
\(807\) | −2.55416e14 | − | 6.22590e14i | −0.746244 | − | 1.81901i | ||||
\(808\) | − | 6.93303e13i | − | 0.201311i | ||||||
\(809\) | − | 2.06102e14i | − | 0.594756i | −0.954760 | − | 0.297378i | \(-0.903888\pi\) | ||
0.954760 | − | 0.297378i | \(-0.0961121\pi\) | |||||||
\(810\) | −3.54728e13 | + | 9.66592e12i | −0.101735 | + | 0.0277216i | ||||
\(811\) | −6.94199e13 | −0.197870 | −0.0989349 | − | 0.995094i | \(-0.531544\pi\) | ||||
−0.0989349 | + | 0.995094i | \(0.531544\pi\) | |||||||
\(812\) | 2.91592e14 | 0.826031 | ||||||||
\(813\) | −4.46523e14 | + | 1.83185e14i | −1.25716 | + | 0.515747i | ||||
\(814\) | −2.47934e13 | −0.0693768 | ||||||||
\(815\) | 1.92459e14 | − | 5.52570e13i | 0.535242 | − | 0.153674i | ||||
\(816\) | −3.51599e14 | + | 1.44243e14i | −0.971845 | + | 0.398697i | ||||
\(817\) | 1.19944e14i | 0.329509i | ||||||||
\(818\) | −7.25803e13 | −0.198177 | ||||||||
\(819\) | −3.85340e14 | + | 3.80150e14i | −1.04574 | + | 1.03166i | ||||
\(820\) | −5.42074e14 | + | 1.55635e14i | −1.46214 | + | 0.419796i | ||||
\(821\) | − | 9.32564e13i | − | 0.250013i | −0.992156 | − | 0.125007i | \(-0.960105\pi\) | ||
0.992156 | − | 0.125007i | \(-0.0398952\pi\) | |||||||
\(822\) | −5.48907e12 | + | 2.25187e12i | −0.0146265 | + | 0.00600047i | ||||
\(823\) | − | 6.30725e13i | − | 0.167048i | −0.996506 | − | 0.0835239i | \(-0.973382\pi\) | ||
0.996506 | − | 0.0835239i | \(-0.0266175\pi\) | |||||||
\(824\) | 1.46046e13i | 0.0384462i | ||||||||
\(825\) | 2.10340e14 | + | 1.50898e14i | 0.550368 | + | 0.394833i | ||||
\(826\) | −1.65179e12 | −0.00429590 | ||||||||
\(827\) | 9.76525e13 | 0.252439 | 0.126219 | − | 0.992002i | \(-0.459716\pi\) | ||||
0.126219 | + | 0.992002i | \(0.459716\pi\) | |||||||
\(828\) | 1.06292e14 | − | 1.04860e14i | 0.273116 | − | 0.269437i | ||||
\(829\) | 3.08315e14 | 0.787448 | 0.393724 | − | 0.919229i | \(-0.371187\pi\) | ||||
0.393724 | + | 0.919229i | \(0.371187\pi\) | |||||||
\(830\) | 1.99455e13 | + | 6.94698e13i | 0.0506355 | + | 0.176362i | ||||
\(831\) | 2.05489e14 | + | 5.00890e14i | 0.518541 | + | 1.26397i | ||||
\(832\) | 5.74305e14i | 1.44054i | ||||||||
\(833\) | 4.05490e13 | 0.101101 | ||||||||
\(834\) | −3.97486e13 | + | 1.63068e13i | −0.0985125 | + | 0.0404145i | ||||
\(835\) | −6.61545e13 | − | 2.30415e14i | −0.162977 | − | 0.567647i | ||||
\(836\) | 7.95777e13i | 0.194877i | ||||||||
\(837\) | −1.03455e14 | + | 2.42750e14i | −0.251840 | + | 0.590925i | ||||
\(838\) | 6.84305e13i | 0.165588i | ||||||||
\(839\) | − | 6.70121e14i | − | 1.61192i | −0.591971 | − | 0.805960i | \(-0.701650\pi\) | ||
0.591971 | − | 0.805960i | \(-0.298350\pi\) | |||||||
\(840\) | −6.55264e13 | + | 5.17962e13i | −0.156682 | + | 0.123852i | ||||
\(841\) | 9.70398e13 | 0.230659 | ||||||||
\(842\) | 8.38446e12 | 0.0198114 | ||||||||
\(843\) | −8.30129e13 | − | 2.02348e14i | −0.194988 | − | 0.475293i | ||||
\(844\) | 1.31014e14 | 0.305919 | ||||||||
\(845\) | −1.63977e14 | − | 5.71130e14i | −0.380628 | − | 1.32572i | ||||
\(846\) | −4.25177e13 | + | 4.19450e13i | −0.0981110 | + | 0.0967895i | ||||
\(847\) | − | 2.24682e14i | − | 0.515409i | ||||||
\(848\) | −6.45786e14 | −1.47268 | ||||||||
\(849\) | −3.82286e13 | − | 9.31842e13i | −0.0866662 | − | 0.211254i | ||||
\(850\) | 4.30930e13 | − | 2.69679e13i | 0.0971208 | − | 0.0607789i | ||||
\(851\) | 1.68198e14i | 0.376855i | ||||||||
\(852\) | 1.96313e14 | + | 4.78523e14i | 0.437271 | + | 1.06587i | ||||
\(853\) | 4.95600e14i | 1.09745i | 0.836002 | + | 0.548727i | \(0.184887\pi\) | ||||
−0.836002 | + | 0.548727i | \(0.815113\pi\) | |||||||
\(854\) | 5.29475e13i | 0.116562i | ||||||||
\(855\) | −1.15849e14 | − | 6.51954e13i | −0.253549 | − | 0.142688i | ||||
\(856\) | −3.19660e13 | −0.0695535 | ||||||||
\(857\) | 1.74867e14 | 0.378272 | 0.189136 | − | 0.981951i | \(-0.439431\pi\) | ||||
0.189136 | + | 0.981951i | \(0.439431\pi\) | |||||||
\(858\) | 4.73930e13 | − | 1.94429e13i | 0.101924 | − | 0.0418142i | ||||
\(859\) | −2.27200e14 | −0.485784 | −0.242892 | − | 0.970053i | \(-0.578096\pi\) | ||||
−0.242892 | + | 0.970053i | \(0.578096\pi\) | |||||||
\(860\) | −5.06405e14 | + | 1.45394e14i | −1.07648 | + | 0.309069i | ||||
\(861\) | 6.41322e14 | − | 2.63101e14i | 1.35538 | − | 0.556040i | ||||
\(862\) | − | 4.46749e13i | − | 0.0938700i | ||||||
\(863\) | 7.42681e14 | 1.55149 | 0.775744 | − | 0.631047i | \(-0.217375\pi\) | ||||
0.775744 | + | 0.631047i | \(0.217375\pi\) | |||||||
\(864\) | 5.88297e13 | − | 1.38040e14i | 0.122188 | − | 0.286705i | ||||
\(865\) | −2.22339e13 | − | 7.74404e13i | −0.0459130 | − | 0.159914i | ||||
\(866\) | − | 4.56315e13i | − | 0.0936861i | ||||||
\(867\) | −8.18551e13 | + | 3.35808e13i | −0.167090 | + | 0.0685482i | ||||
\(868\) | 2.98063e14i | 0.604936i | ||||||||
\(869\) | 1.58984e14i | 0.320815i | ||||||||
\(870\) | 3.61638e13 | − | 2.85862e13i | 0.0725568 | − | 0.0573535i | ||||
\(871\) | −3.95971e14 | −0.789901 | ||||||||
\(872\) | 9.66344e12 | 0.0191668 | ||||||||
\(873\) | 1.26138e14 | + | 1.27860e14i | 0.248757 | + | 0.252153i | ||||
\(874\) | −6.06985e12 | −0.0119020 | ||||||||
\(875\) | −3.26479e14 | + | 3.63330e14i | −0.636524 | + | 0.708372i | ||||
\(876\) | −2.31141e14 | − | 5.63418e14i | −0.448080 | − | 1.09222i | ||||
\(877\) | 2.63334e14i | 0.507585i | 0.967259 | + | 0.253793i | \(0.0816781\pi\) | ||||
−0.967259 | + | 0.253793i | \(0.918322\pi\) | |||||||
\(878\) | −2.96073e13 | −0.0567448 | ||||||||
\(879\) | −6.22650e14 | + | 2.55441e14i | −1.18659 | + | 0.486794i | ||||
\(880\) | −3.32159e14 | + | 9.53663e13i | −0.629409 | + | 0.180710i | ||||
\(881\) | 2.49117e14i | 0.469380i | 0.972070 | + | 0.234690i | \(0.0754074\pi\) | ||||
−0.972070 | + | 0.234690i | \(0.924593\pi\) | |||||||
\(882\) | −3.72802e12 | + | 3.67781e12i | −0.00698450 | + | 0.00689043i | ||||
\(883\) | 1.84295e14i | 0.343328i | 0.985156 | + | 0.171664i | \(0.0549144\pi\) | ||||
−0.985156 | + | 0.171664i | \(0.945086\pi\) | |||||||
\(884\) | 8.94706e14i | 1.65737i | ||||||||
\(885\) | 1.82201e13 | − | 1.44023e13i | 0.0335610 | − | 0.0265287i | ||||
\(886\) | −9.61345e13 | −0.176080 | ||||||||
\(887\) | −1.97737e14 | −0.360139 | −0.180070 | − | 0.983654i | \(-0.557632\pi\) | ||||
−0.180070 | + | 0.983654i | \(0.557632\pi\) | |||||||
\(888\) | 4.26919e13 | + | 1.04064e14i | 0.0773180 | + | 0.188467i | ||||
\(889\) | 5.61090e14 | 1.01047 | ||||||||
\(890\) | 5.52918e13 | − | 1.58748e13i | 0.0990171 | − | 0.0284289i | ||||
\(891\) | 3.80329e14 | + | 5.15768e12i | 0.677284 | + | 0.00918471i | ||||
\(892\) | − | 6.14085e14i | − | 1.08744i | ||||||
\(893\) | −2.15947e14 | −0.380269 | ||||||||
\(894\) | 3.18261e12 | + | 7.75778e12i | 0.00557308 | + | 0.0135847i | ||||
\(895\) | 5.73285e14 | − | 1.64596e14i | 0.998287 | − | 0.286619i | ||||
\(896\) | − | 2.25556e14i | − | 0.390585i | ||||||
\(897\) | −1.31900e14 | − | 3.21514e14i | −0.227135 | − | 0.553653i | ||||
\(898\) | − | 5.31512e13i | − | 0.0910188i | ||||||
\(899\) | − | 3.30850e14i | − | 0.563420i | ||||||
\(900\) | 1.34826e14 | − | 5.68146e14i | 0.228329 | − | 0.962160i | ||||
\(901\) | −9.82796e14 | −1.65516 | ||||||||
\(902\) | −6.56012e13 | −0.109870 | ||||||||
\(903\) | 5.99122e14 | − | 2.45788e14i | 0.997876 | − | 0.409376i | ||||
\(904\) | 1.81643e14 | 0.300869 | ||||||||
\(905\) | 1.20241e14 | + | 4.18796e14i | 0.198066 | + | 0.689858i | ||||
\(906\) | 3.55911e13 | − | 1.46011e13i | 0.0583042 | − | 0.0239192i | ||||
\(907\) | − | 6.26076e14i | − | 1.01998i | −0.860181 | − | 0.509989i | \(-0.829650\pi\) | ||
0.860181 | − | 0.509989i | \(-0.170350\pi\) | |||||||
\(908\) | 8.90405e14 | 1.44264 | ||||||||
\(909\) | −4.18384e14 | − | 4.24096e14i | −0.674148 | − | 0.683352i | ||||
\(910\) | 2.66743e13 | + | 9.29061e13i | 0.0427451 | + | 0.148880i | ||||
\(911\) | 1.45847e14i | 0.232437i | 0.993224 | + | 0.116219i | \(0.0370774\pi\) | ||||
−0.993224 | + | 0.116219i | \(0.962923\pi\) | |||||||
\(912\) | 1.64181e14 | − | 6.73550e13i | 0.260225 | − | 0.106757i | ||||
\(913\) | − | 7.47735e14i | − | 1.17867i | ||||||
\(914\) | − | 3.01010e10i | − | 4.71900e-5i | ||||||
\(915\) | −4.61662e14 | − | 5.84039e14i | −0.719811 | − | 0.910618i | ||||
\(916\) | 3.02169e14 | 0.468567 | ||||||||
\(917\) | −6.15800e14 | −0.949715 | ||||||||
\(918\) | 2.92847e13 | − | 6.87144e13i | 0.0449187 | − | 0.105398i | ||||
\(919\) | 1.05040e15 | 1.60242 | 0.801210 | − | 0.598383i | \(-0.204190\pi\) | ||||
0.801210 | + | 0.598383i | \(0.204190\pi\) | |||||||
\(920\) | −1.47983e13 | − | 5.15423e13i | −0.0224529 | − | 0.0782032i | ||||
\(921\) | −4.12778e13 | − | 1.00617e14i | −0.0622900 | − | 0.151835i | ||||
\(922\) | 7.83355e13i | 0.117572i | ||||||||
\(923\) | 1.20384e15 | 1.79705 | ||||||||
\(924\) | 3.97493e14 | − | 1.63070e14i | 0.590160 | − | 0.242111i | ||||
\(925\) | 3.48954e14 | + | 5.57605e14i | 0.515299 | + | 0.823414i | ||||
\(926\) | − | 2.88265e13i | − | 0.0423386i | ||||||
\(927\) | 8.81336e13 | + | 8.93369e13i | 0.128749 | + | 0.130506i | ||||
\(928\) | 1.88137e14i | 0.273360i | ||||||||
\(929\) | 3.64767e14i | 0.527154i | 0.964638 | + | 0.263577i | \(0.0849022\pi\) | ||||
−0.964638 | + | 0.263577i | \(0.915098\pi\) | |||||||
\(930\) | 2.92205e13 | + | 3.69663e13i | 0.0420023 | + | 0.0531363i | ||||
\(931\) | −1.89346e13 | −0.0270713 | ||||||||
\(932\) | −1.64112e14 | −0.233379 | ||||||||
\(933\) | 3.09642e14 | + | 7.54770e14i | 0.437978 | + | 1.06759i | ||||
\(934\) | 1.28252e13 | 0.0180438 | ||||||||
\(935\) | −5.05499e14 | + | 1.45134e14i | −0.707396 | + | 0.203101i | ||||
\(936\) | −1.63213e14 | − | 1.65441e14i | −0.227182 | − | 0.230284i | ||||
\(937\) | 2.49525e14i | 0.345474i | 0.984968 | + | 0.172737i | \(0.0552611\pi\) | ||||
−0.984968 | + | 0.172737i | \(0.944739\pi\) | |||||||
\(938\) | 3.73404e13 | 0.0514239 | ||||||||
\(939\) | −1.27691e14 | − | 3.11255e14i | −0.174918 | − | 0.426372i | ||||
\(940\) | −2.61768e14 | − | 9.11734e14i | −0.356679 | − | 1.24231i | ||||
\(941\) | − | 3.92974e14i | − | 0.532618i | −0.963888 | − | 0.266309i | \(-0.914196\pi\) | ||
0.963888 | − | 0.266309i | \(-0.0858041\pi\) | |||||||
\(942\) | −5.36871e13 | − | 1.30865e14i | −0.0723795 | − | 0.176429i | ||||
\(943\) | 4.45038e14i | 0.596814i | ||||||||
\(944\) | 3.10043e13i | 0.0413582i | ||||||||
\(945\) | −8.82553e13 | + | 7.12267e14i | −0.117107 | + | 0.945113i | ||||
\(946\) | −6.12846e13 | −0.0808901 | ||||||||
\(947\) | −7.14752e14 | −0.938438 | −0.469219 | − | 0.883082i | \(-0.655465\pi\) | ||||
−0.469219 | + | 0.883082i | \(0.655465\pi\) | |||||||
\(948\) | 3.31781e14 | − | 1.36112e14i | 0.433322 | − | 0.177769i | ||||
\(949\) | −1.41741e15 | −1.84147 | ||||||||
\(950\) | −2.01226e13 | + | 1.25929e13i | −0.0260055 | + | 0.0162744i | ||||
\(951\) | 4.44033e14 | − | 1.82164e14i | 0.570838 | − | 0.234185i | ||||
\(952\) | − | 1.69692e14i | − | 0.217008i | ||||||
\(953\) | −9.88465e14 | −1.25747 | −0.628734 | − | 0.777621i | \(-0.716426\pi\) | ||||
−0.628734 | + | 0.777621i | \(0.716426\pi\) | |||||||
\(954\) | 9.03569e13 | − | 8.91399e13i | 0.114346 | − | 0.112805i | ||||
\(955\) | 3.88406e13 | − | 1.11515e13i | 0.0488955 | − | 0.0140384i | ||||
\(956\) | 6.84071e14i | 0.856666i | ||||||||
\(957\) | −4.41217e14 | + | 1.81008e14i | −0.549658 | + | 0.225496i | ||||
\(958\) | 6.78019e13i | 0.0840261i | ||||||||
\(959\) | 1.15819e14i | 0.142786i | ||||||||
\(960\) | 4.72212e14 | + | 5.97386e14i | 0.579136 | + | 0.732654i | ||||
\(961\) | −4.81436e14 | −0.587384 | ||||||||
\(962\) | 1.30167e14 | 0.157989 | ||||||||
\(963\) | −1.95537e14 | + | 1.92903e14i | −0.236101 | + | 0.232921i | ||||
\(964\) | −2.12415e14 | −0.255153 | ||||||||
\(965\) | 7.84200e13 | − | 2.25152e13i | 0.0937110 | − | 0.0269054i | ||||
\(966\) | 1.24383e13 | + | 3.03191e13i | 0.0147869 | + | 0.0360438i | ||||
\(967\) | 3.84406e14i | 0.454629i | 0.973821 | + | 0.227315i | \(0.0729946\pi\) | ||||
−0.973821 | + | 0.227315i | \(0.927005\pi\) | |||||||
\(968\) | 9.64646e13 | 0.113499 | ||||||||
\(969\) | 2.49861e14 | − | 1.02505e14i | 0.292469 | − | 0.119985i | ||||
\(970\) | 3.08274e13 | − | 8.85086e12i | 0.0358986 | − | 0.0103069i | ||||
\(971\) | 5.38955e14i | 0.624391i | 0.950018 | + | 0.312195i | \(0.101064\pi\) | ||||
−0.950018 | + | 0.312195i | \(0.898936\pi\) | |||||||
\(972\) | −3.14851e14 | − | 7.98119e14i | −0.362889 | − | 0.919890i | ||||
\(973\) | 8.38693e14i | 0.961698i | ||||||||
\(974\) | 3.59799e13i | 0.0410455i | ||||||||
\(975\) | −1.10430e15 | − | 7.92224e14i | −1.25333 | − | 0.899135i | ||||
\(976\) | 9.93830e14 | 1.12218 | ||||||||
\(977\) | 9.01098e14 | 1.01228 | 0.506138 | − | 0.862452i | \(-0.331073\pi\) | ||||
0.506138 | + | 0.862452i | \(0.331073\pi\) | |||||||
\(978\) | −1.99405e13 | − | 4.86060e13i | −0.0222865 | − | 0.0543245i | ||||
\(979\) | −5.95131e14 | −0.661757 | ||||||||
\(980\) | −2.29523e13 | − | 7.99424e13i | −0.0253920 | − | 0.0884397i | ||||
\(981\) | 5.91115e13 | − | 5.83154e13i | 0.0650620 | − | 0.0641857i | ||||
\(982\) | 1.62550e14i | 0.178004i | ||||||||
\(983\) | 4.97465e14 | 0.541995 | 0.270997 | − | 0.962580i | \(-0.412647\pi\) | ||||
0.270997 | + | 0.962580i | \(0.412647\pi\) | |||||||
\(984\) | 1.12959e14 | + | 2.75344e14i | 0.122446 | + | 0.298469i | ||||
\(985\) | 1.28956e14 | + | 4.49150e14i | 0.139078 | + | 0.484407i | ||||
\(986\) | 9.36524e13i | 0.100493i | ||||||||
\(987\) | 4.42518e14 | + | 1.07866e15i | 0.472439 | + | 1.15159i | ||||
\(988\) | − | 4.17789e14i | − | 0.443784i | ||||||
\(989\) | 4.15754e14i | 0.439395i | ||||||||
\(990\) | 3.33112e13 | − | 5.91924e13i | 0.0350279 | − | 0.0622429i | ||||
\(991\) | 1.04277e15 | 1.09099 | 0.545497 | − | 0.838113i | \(-0.316341\pi\) | ||||
0.545497 | + | 0.838113i | \(0.316341\pi\) | |||||||
\(992\) | −1.92312e14 | −0.200193 | ||||||||
\(993\) | −2.23617e14 | + | 9.17381e13i | −0.231610 | + | 0.0950175i | ||||
\(994\) | −1.13523e14 | −0.116991 | ||||||||
\(995\) | −4.01834e14 | − | 1.39958e15i | −0.412032 | − | 1.43510i | ||||
\(996\) | −1.56044e15 | + | 6.40166e14i | −1.59202 | + | 0.653124i | ||||
\(997\) | 9.01890e14i | 0.915541i | 0.889070 | + | 0.457770i | \(0.151352\pi\) | ||||
−0.889070 | + | 0.457770i | \(0.848648\pi\) | |||||||
\(998\) | −1.83030e14 | −0.184871 | ||||||||
\(999\) | 8.89135e14 | + | 3.78931e14i | 0.893594 | + | 0.380832i |
(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 | 15.11.d.c.14.8 | yes | 16 | |
3.2 | odd | 2 | inner | 15.11.d.c.14.10 | yes | 16 | |
5.2 | odd | 4 | 75.11.c.h.26.8 | 16 | |||
5.3 | odd | 4 | 75.11.c.h.26.9 | 16 | |||
5.4 | even | 2 | inner | 15.11.d.c.14.9 | yes | 16 | |
15.2 | even | 4 | 75.11.c.h.26.10 | 16 | |||
15.8 | even | 4 | 75.11.c.h.26.7 | 16 | |||
15.14 | odd | 2 | inner | 15.11.d.c.14.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.11.d.c.14.7 | ✓ | 16 | 15.14 | odd | 2 | inner | |
15.11.d.c.14.8 | yes | 16 | 1.1 | even | 1 | trivial | |
15.11.d.c.14.9 | yes | 16 | 5.4 | even | 2 | inner | |
15.11.d.c.14.10 | yes | 16 | 3.2 | odd | 2 | inner | |
75.11.c.h.26.7 | 16 | 15.8 | even | 4 | |||
75.11.c.h.26.8 | 16 | 5.2 | odd | 4 | |||
75.11.c.h.26.9 | 16 | 5.3 | odd | 4 | |||
75.11.c.h.26.10 | 16 | 15.2 | even | 4 |