Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,9,Mod(6,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7.6");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.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: | \(2.85165027043\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1016x^{2} + 51570 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 3\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 6.1 | ||
Root | \(-31.0228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.6 |
Dual form | 7.9.b.b.6.2 |
$q$-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 \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.56466 | −0.347791 | −0.173896 | − | 0.984764i | \(-0.555636\pi\) | ||||
−0.173896 | + | 0.984764i | \(0.555636\pi\) | |||||||
\(3\) | − | 53.0420i | − | 0.654840i | −0.944879 | − | 0.327420i | \(-0.893821\pi\) | ||
0.944879 | − | 0.327420i | \(-0.106179\pi\) | |||||||
\(4\) | −225.035 | −0.879041 | ||||||||
\(5\) | − | 1090.79i | − | 1.74527i | −0.488377 | − | 0.872633i | \(-0.662411\pi\) | ||
0.488377 | − | 0.872633i | \(-0.337589\pi\) | |||||||
\(6\) | 295.161i | 0.227747i | ||||||||
\(7\) | −1257.19 | + | 2045.55i | −0.523613 | + | 0.851956i | ||||
\(8\) | 2676.79 | 0.653514 | ||||||||
\(9\) | 3747.55 | 0.571185 | ||||||||
\(10\) | 6069.88i | 0.606988i | ||||||||
\(11\) | −4619.60 | −0.315525 | −0.157763 | − | 0.987477i | \(-0.550428\pi\) | ||||
−0.157763 | + | 0.987477i | \(0.550428\pi\) | |||||||
\(12\) | 11936.3i | 0.575631i | ||||||||
\(13\) | − | 34774.3i | − | 1.21754i | −0.793345 | − | 0.608772i | \(-0.791662\pi\) | ||
0.793345 | − | 0.608772i | \(-0.208338\pi\) | |||||||
\(14\) | 6995.86 | − | 11382.8i | 0.182108 | − | 0.296303i | ||||
\(15\) | −57857.7 | −1.14287 | ||||||||
\(16\) | 42713.4 | 0.651755 | ||||||||
\(17\) | − | 11872.7i | − | 0.142152i | −0.997471 | − | 0.0710762i | \(-0.977357\pi\) | ||
0.997471 | − | 0.0710762i | \(-0.0226434\pi\) | |||||||
\(18\) | −20853.8 | −0.198653 | ||||||||
\(19\) | − | 70683.5i | − | 0.542380i | −0.962526 | − | 0.271190i | \(-0.912583\pi\) | ||
0.962526 | − | 0.271190i | \(-0.0874172\pi\) | |||||||
\(20\) | 245466.i | 1.53416i | ||||||||
\(21\) | 108500. | + | 66684.1i | 0.557895 | + | 0.342882i | ||||
\(22\) | 25706.5 | 0.109737 | ||||||||
\(23\) | 308189. | 1.10130 | 0.550650 | − | 0.834736i | \(-0.314380\pi\) | ||||
0.550650 | + | 0.834736i | \(0.314380\pi\) | |||||||
\(24\) | − | 141983.i | − | 0.427947i | ||||||
\(25\) | −799200. | −2.04595 | ||||||||
\(26\) | 193507.i | 0.423451i | ||||||||
\(27\) | − | 546786.i | − | 1.02887i | ||||||
\(28\) | 282912. | − | 460319.i | 0.460277 | − | 0.748905i | ||||
\(29\) | −51871.9 | −0.0733398 | −0.0366699 | − | 0.999327i | \(-0.511675\pi\) | ||||
−0.0366699 | + | 0.999327i | \(0.511675\pi\) | |||||||
\(30\) | 321959. | 0.397480 | ||||||||
\(31\) | 492602.i | 0.533395i | 0.963780 | + | 0.266698i | \(0.0859325\pi\) | ||||
−0.963780 | + | 0.266698i | \(0.914067\pi\) | |||||||
\(32\) | −922945. | −0.880189 | ||||||||
\(33\) | 245033.i | 0.206618i | ||||||||
\(34\) | 66067.6i | 0.0494394i | ||||||||
\(35\) | 2.23126e6 | + | 1.37134e6i | 1.48689 | + | 0.913843i | ||||
\(36\) | −843327. | −0.502095 | ||||||||
\(37\) | 1.27573e6 | 0.680694 | 0.340347 | − | 0.940300i | \(-0.389455\pi\) | ||||
0.340347 | + | 0.940300i | \(0.389455\pi\) | |||||||
\(38\) | 393330.i | 0.188635i | ||||||||
\(39\) | −1.84450e6 | −0.797297 | ||||||||
\(40\) | − | 2.91982e6i | − | 1.14056i | ||||||
\(41\) | 1.22535e6i | 0.433637i | 0.976212 | + | 0.216818i | \(0.0695679\pi\) | ||||
−0.976212 | + | 0.216818i | \(0.930432\pi\) | |||||||
\(42\) | −603765. | − | 371074.i | −0.194031 | − | 0.119252i | ||||
\(43\) | −918567. | −0.268681 | −0.134340 | − | 0.990935i | \(-0.542892\pi\) | ||||
−0.134340 | + | 0.990935i | \(0.542892\pi\) | |||||||
\(44\) | 1.03957e6 | 0.277360 | ||||||||
\(45\) | − | 4.08779e6i | − | 0.996870i | ||||||
\(46\) | −1.71497e6 | −0.383023 | ||||||||
\(47\) | 5.57969e6i | 1.14345i | 0.820444 | + | 0.571727i | \(0.193726\pi\) | ||||
−0.820444 | + | 0.571727i | \(0.806274\pi\) | |||||||
\(48\) | − | 2.26560e6i | − | 0.426795i | ||||||
\(49\) | −2.60372e6 | − | 5.14330e6i | −0.451659 | − | 0.892191i | ||||
\(50\) | 4.44728e6 | 0.711564 | ||||||||
\(51\) | −629753. | −0.0930871 | ||||||||
\(52\) | 7.82542e6i | 1.07027i | ||||||||
\(53\) | 6.83969e6 | 0.866828 | 0.433414 | − | 0.901195i | \(-0.357309\pi\) | ||||
0.433414 | + | 0.901195i | \(0.357309\pi\) | |||||||
\(54\) | 3.04268e6i | 0.357833i | ||||||||
\(55\) | 5.03902e6i | 0.550675i | ||||||||
\(56\) | −3.36525e6 | + | 5.47551e6i | −0.342188 | + | 0.556765i | ||||
\(57\) | −3.74920e6 | −0.355172 | ||||||||
\(58\) | 288649. | 0.0255070 | ||||||||
\(59\) | − | 8.16175e6i | − | 0.673559i | −0.941584 | − | 0.336779i | \(-0.890662\pi\) | ||
0.941584 | − | 0.336779i | \(-0.109338\pi\) | |||||||
\(60\) | 1.30200e7 | 1.00463 | ||||||||
\(61\) | − | 1.94292e7i | − | 1.40325i | −0.712547 | − | 0.701625i | \(-0.752458\pi\) | ||
0.712547 | − | 0.701625i | \(-0.247542\pi\) | |||||||
\(62\) | − | 2.74116e6i | − | 0.185510i | ||||||
\(63\) | −4.71139e6 | + | 7.66578e6i | −0.299080 | + | 0.486625i | ||||
\(64\) | −5.79876e6 | −0.345633 | ||||||||
\(65\) | −3.79315e7 | −2.12494 | ||||||||
\(66\) | − | 1.36353e6i | − | 0.0718601i | ||||||
\(67\) | 2.53838e7 | 1.25967 | 0.629837 | − | 0.776728i | \(-0.283122\pi\) | ||||
0.629837 | + | 0.776728i | \(0.283122\pi\) | |||||||
\(68\) | 2.67177e6i | 0.124958i | ||||||||
\(69\) | − | 1.63470e7i | − | 0.721175i | ||||||
\(70\) | −1.24162e7 | − | 7.63102e6i | −0.517127 | − | 0.317827i | ||||
\(71\) | 2.99440e7 | 1.17836 | 0.589178 | − | 0.808003i | \(-0.299452\pi\) | ||||
0.589178 | + | 0.808003i | \(0.299452\pi\) | |||||||
\(72\) | 1.00314e7 | 0.373277 | ||||||||
\(73\) | 3.30065e7i | 1.16227i | 0.813806 | + | 0.581137i | \(0.197392\pi\) | ||||
−0.813806 | + | 0.581137i | \(0.802608\pi\) | |||||||
\(74\) | −7.09901e6 | −0.236739 | ||||||||
\(75\) | 4.23912e7i | 1.33977i | ||||||||
\(76\) | 1.59062e7i | 0.476775i | ||||||||
\(77\) | 5.80774e6 | − | 9.44962e6i | 0.165213 | − | 0.268814i | ||||
\(78\) | 1.02640e7 | 0.277293 | ||||||||
\(79\) | −6.23959e6 | −0.160195 | −0.0800973 | − | 0.996787i | \(-0.525523\pi\) | ||||
−0.0800973 | + | 0.996787i | \(0.525523\pi\) | |||||||
\(80\) | − | 4.65914e7i | − | 1.13749i | ||||||
\(81\) | −4.41498e6 | −0.102563 | ||||||||
\(82\) | − | 6.81868e6i | − | 0.150815i | ||||||
\(83\) | 9.62572e6i | 0.202825i | 0.994844 | + | 0.101412i | \(0.0323361\pi\) | ||||
−0.994844 | + | 0.101412i | \(0.967664\pi\) | |||||||
\(84\) | −2.44162e7 | − | 1.50062e7i | −0.490413 | − | 0.301408i | ||||
\(85\) | −1.29507e7 | −0.248094 | ||||||||
\(86\) | 5.11151e6 | 0.0934449 | ||||||||
\(87\) | 2.75139e6i | 0.0480258i | ||||||||
\(88\) | −1.23657e7 | −0.206200 | ||||||||
\(89\) | − | 9.84326e7i | − | 1.56884i | −0.620229 | − | 0.784421i | \(-0.712960\pi\) | ||
0.620229 | − | 0.784421i | \(-0.287040\pi\) | |||||||
\(90\) | 2.27472e7i | 0.346703i | ||||||||
\(91\) | 7.11325e7 | + | 4.37181e7i | 1.03730 | + | 0.637522i | ||||
\(92\) | −6.93532e7 | −0.968088 | ||||||||
\(93\) | 2.61286e7 | 0.349288 | ||||||||
\(94\) | − | 3.10491e7i | − | 0.397683i | ||||||
\(95\) | −7.71010e7 | −0.946597 | ||||||||
\(96\) | 4.89548e7i | 0.576382i | ||||||||
\(97\) | − | 4.75670e6i | − | 0.0537302i | −0.999639 | − | 0.0268651i | \(-0.991448\pi\) | ||
0.999639 | − | 0.0268651i | \(-0.00855246\pi\) | |||||||
\(98\) | 1.44888e7 | + | 2.86207e7i | 0.157083 | + | 0.310296i | ||||
\(99\) | −1.73122e7 | −0.180223 | ||||||||
\(100\) | 1.79848e8 | 1.79848 | ||||||||
\(101\) | 9.65936e7i | 0.928246i | 0.885771 | + | 0.464123i | \(0.153630\pi\) | ||||
−0.885771 | + | 0.464123i | \(0.846370\pi\) | |||||||
\(102\) | 3.50436e6 | 0.0323749 | ||||||||
\(103\) | 1.13982e8i | 1.01272i | 0.862323 | + | 0.506358i | \(0.169008\pi\) | ||||
−0.862323 | + | 0.506358i | \(0.830992\pi\) | |||||||
\(104\) | − | 9.30836e7i | − | 0.795683i | ||||||
\(105\) | 7.27384e7 | − | 1.18351e8i | 0.598421 | − | 0.973674i | ||||
\(106\) | −3.80605e7 | −0.301475 | ||||||||
\(107\) | −1.90137e7 | −0.145054 | −0.0725272 | − | 0.997366i | \(-0.523106\pi\) | ||||
−0.0725272 | + | 0.997366i | \(0.523106\pi\) | |||||||
\(108\) | 1.23046e8i | 0.904423i | ||||||||
\(109\) | −2.50660e8 | −1.77574 | −0.887869 | − | 0.460096i | \(-0.847815\pi\) | ||||
−0.887869 | + | 0.460096i | \(0.847815\pi\) | |||||||
\(110\) | − | 2.80404e7i | − | 0.191520i | ||||||
\(111\) | − | 6.76673e7i | − | 0.445746i | ||||||
\(112\) | −5.36991e7 | + | 8.73723e7i | −0.341267 | + | 0.555267i | ||||
\(113\) | 1.89409e8 | 1.16168 | 0.580839 | − | 0.814018i | \(-0.302724\pi\) | ||||
0.580839 | + | 0.814018i | \(0.302724\pi\) | |||||||
\(114\) | 2.08630e7 | 0.123526 | ||||||||
\(115\) | − | 3.36170e8i | − | 1.92206i | ||||||
\(116\) | 1.16730e7 | 0.0644687 | ||||||||
\(117\) | − | 1.30318e8i | − | 0.695443i | ||||||
\(118\) | 4.54174e7i | 0.234258i | ||||||||
\(119\) | 2.42862e7 | + | 1.49263e7i | 0.121108 | + | 0.0744329i | ||||
\(120\) | −1.54873e8 | −0.746881 | ||||||||
\(121\) | −1.93018e8 | −0.900444 | ||||||||
\(122\) | 1.08117e8i | 0.488038i | ||||||||
\(123\) | 6.49952e7 | 0.283962 | ||||||||
\(124\) | − | 1.10852e8i | − | 0.468876i | ||||||
\(125\) | 4.45670e8i | 1.82546i | ||||||||
\(126\) | 2.62173e7 | − | 4.26575e7i | 0.104017 | − | 0.169244i | ||||
\(127\) | 1.14559e8 | 0.440368 | 0.220184 | − | 0.975458i | \(-0.429334\pi\) | ||||
0.220184 | + | 0.975458i | \(0.429334\pi\) | |||||||
\(128\) | 2.68542e8 | 1.00040 | ||||||||
\(129\) | 4.87226e7i | 0.175943i | ||||||||
\(130\) | 2.11076e8 | 0.739035 | ||||||||
\(131\) | 2.36265e8i | 0.802257i | 0.916022 | + | 0.401128i | \(0.131382\pi\) | ||||
−0.916022 | + | 0.401128i | \(0.868618\pi\) | |||||||
\(132\) | − | 5.51409e7i | − | 0.181626i | ||||||
\(133\) | 1.44586e8 | + | 8.88630e7i | 0.462084 | + | 0.283997i | ||||
\(134\) | −1.41252e8 | −0.438103 | ||||||||
\(135\) | −5.96429e8 | −1.79566 | ||||||||
\(136\) | − | 3.17808e7i | − | 0.0928987i | ||||||
\(137\) | 4.33194e8 | 1.22970 | 0.614851 | − | 0.788643i | \(-0.289216\pi\) | ||||
0.614851 | + | 0.788643i | \(0.289216\pi\) | |||||||
\(138\) | 9.09653e7i | 0.250818i | ||||||||
\(139\) | − | 5.35069e8i | − | 1.43334i | −0.697410 | − | 0.716672i | \(-0.745664\pi\) | ||
0.697410 | − | 0.716672i | \(-0.254336\pi\) | |||||||
\(140\) | −5.02112e8 | − | 3.08598e8i | −1.30704 | − | 0.803306i | ||||
\(141\) | 2.95958e8 | 0.748779 | ||||||||
\(142\) | −1.66628e8 | −0.409822 | ||||||||
\(143\) | 1.60643e8i | 0.384166i | ||||||||
\(144\) | 1.60070e8 | 0.372273 | ||||||||
\(145\) | 5.65814e7i | 0.127997i | ||||||||
\(146\) | − | 1.83670e8i | − | 0.404229i | ||||||
\(147\) | −2.72811e8 | + | 1.38107e8i | −0.584242 | + | 0.295764i | ||||
\(148\) | −2.87083e8 | −0.598358 | ||||||||
\(149\) | −4.22768e7 | −0.0857743 | −0.0428871 | − | 0.999080i | \(-0.513656\pi\) | ||||
−0.0428871 | + | 0.999080i | \(0.513656\pi\) | |||||||
\(150\) | − | 2.35892e8i | − | 0.465960i | ||||||
\(151\) | 1.14410e8 | 0.220068 | 0.110034 | − | 0.993928i | \(-0.464904\pi\) | ||||
0.110034 | + | 0.993928i | \(0.464904\pi\) | |||||||
\(152\) | − | 1.89205e8i | − | 0.354453i | ||||||
\(153\) | − | 4.44935e7i | − | 0.0811954i | ||||||
\(154\) | −3.23181e7 | + | 5.25839e7i | −0.0574596 | + | 0.0934910i | ||||
\(155\) | 5.37325e8 | 0.930916 | ||||||||
\(156\) | 4.15076e8 | 0.700857 | ||||||||
\(157\) | 4.34094e8i | 0.714472i | 0.934014 | + | 0.357236i | \(0.116281\pi\) | ||||
−0.934014 | + | 0.357236i | \(0.883719\pi\) | |||||||
\(158\) | 3.47212e7 | 0.0557142 | ||||||||
\(159\) | − | 3.62791e8i | − | 0.567633i | ||||||
\(160\) | 1.00674e9i | 1.53616i | ||||||||
\(161\) | −3.87453e8 | + | 6.30415e8i | −0.576655 | + | 0.938260i | ||||
\(162\) | 2.45679e7 | 0.0356704 | ||||||||
\(163\) | −2.23602e8 | −0.316756 | −0.158378 | − | 0.987379i | \(-0.550626\pi\) | ||||
−0.158378 | + | 0.987379i | \(0.550626\pi\) | |||||||
\(164\) | − | 2.75747e8i | − | 0.381184i | ||||||
\(165\) | 2.67280e8 | 0.360604 | ||||||||
\(166\) | − | 5.35638e7i | − | 0.0705406i | ||||||
\(167\) | − | 2.88063e8i | − | 0.370358i | −0.982705 | − | 0.185179i | \(-0.940714\pi\) | ||
0.982705 | − | 0.185179i | \(-0.0592865\pi\) | |||||||
\(168\) | 2.90432e8 | + | 1.78500e8i | 0.364592 | + | 0.224079i | ||||
\(169\) | −3.93521e8 | −0.482416 | ||||||||
\(170\) | 7.20660e7 | 0.0862849 | ||||||||
\(171\) | − | 2.64890e8i | − | 0.309799i | ||||||
\(172\) | 2.06709e8 | 0.236182 | ||||||||
\(173\) | 1.75344e8i | 0.195752i | 0.995199 | + | 0.0978762i | \(0.0312049\pi\) | ||||
−0.995199 | + | 0.0978762i | \(0.968795\pi\) | |||||||
\(174\) | − | 1.53105e7i | − | 0.0167030i | ||||||
\(175\) | 1.00475e9 | − | 1.63480e9i | 1.07129 | − | 1.74306i | ||||
\(176\) | −1.97319e8 | −0.205645 | ||||||||
\(177\) | −4.32916e8 | −0.441073 | ||||||||
\(178\) | 5.47744e8i | 0.545629i | ||||||||
\(179\) | −1.46595e9 | −1.42793 | −0.713964 | − | 0.700182i | \(-0.753102\pi\) | ||||
−0.713964 | + | 0.700182i | \(0.753102\pi\) | |||||||
\(180\) | 9.19894e8i | 0.876289i | ||||||||
\(181\) | − | 1.47207e8i | − | 0.137156i | −0.997646 | − | 0.0685778i | \(-0.978154\pi\) | ||
0.997646 | − | 0.0685778i | \(-0.0218462\pi\) | |||||||
\(182\) | −3.95828e8 | − | 2.43276e8i | −0.360762 | − | 0.221725i | ||||
\(183\) | −1.03056e9 | −0.918903 | ||||||||
\(184\) | 8.24958e8 | 0.719715 | ||||||||
\(185\) | − | 1.39156e9i | − | 1.18799i | ||||||
\(186\) | −1.45397e8 | −0.121479 | ||||||||
\(187\) | 5.48472e7i | 0.0448527i | ||||||||
\(188\) | − | 1.25562e9i | − | 1.00514i | ||||||
\(189\) | 1.11848e9 | + | 6.87416e8i | 0.876556 | + | 0.538732i | ||||
\(190\) | 4.29041e8 | 0.329218 | ||||||||
\(191\) | 9.48564e8 | 0.712743 | 0.356372 | − | 0.934344i | \(-0.384014\pi\) | ||||
0.356372 | + | 0.934344i | \(0.384014\pi\) | |||||||
\(192\) | 3.07578e8i | 0.226334i | ||||||||
\(193\) | −1.41990e9 | −1.02336 | −0.511681 | − | 0.859175i | \(-0.670977\pi\) | ||||
−0.511681 | + | 0.859175i | \(0.670977\pi\) | |||||||
\(194\) | 2.64694e7i | 0.0186869i | ||||||||
\(195\) | 2.01196e9i | 1.39149i | ||||||||
\(196\) | 5.85928e8 | + | 1.15742e9i | 0.397027 | + | 0.784272i | ||||
\(197\) | 1.85323e9 | 1.23045 | 0.615226 | − | 0.788351i | \(-0.289065\pi\) | ||||
0.615226 | + | 0.788351i | \(0.289065\pi\) | |||||||
\(198\) | 9.63363e7 | 0.0626801 | ||||||||
\(199\) | 2.41054e9i | 1.53710i | 0.639789 | + | 0.768551i | \(0.279022\pi\) | ||||
−0.639789 | + | 0.768551i | \(0.720978\pi\) | |||||||
\(200\) | −2.13929e9 | −1.33706 | ||||||||
\(201\) | − | 1.34641e9i | − | 0.824884i | ||||||
\(202\) | − | 5.37511e8i | − | 0.322836i | ||||||
\(203\) | 6.52130e7 | − | 1.06106e8i | 0.0384017 | − | 0.0624823i | ||||
\(204\) | 1.41716e8 | 0.0818274 | ||||||||
\(205\) | 1.33660e9 | 0.756811 | ||||||||
\(206\) | − | 6.34271e8i | − | 0.352214i | ||||||
\(207\) | 1.15495e9 | 0.629046 | ||||||||
\(208\) | − | 1.48533e9i | − | 0.793541i | ||||||
\(209\) | 3.26530e8i | 0.171135i | ||||||||
\(210\) | −4.04765e8 | + | 6.58582e8i | −0.208126 | + | 0.338635i | ||||
\(211\) | −2.68024e9 | −1.35221 | −0.676105 | − | 0.736806i | \(-0.736333\pi\) | ||||
−0.676105 | + | 0.736806i | \(0.736333\pi\) | |||||||
\(212\) | −1.53917e9 | −0.761977 | ||||||||
\(213\) | − | 1.58829e9i | − | 0.771634i | ||||||
\(214\) | 1.05805e8 | 0.0504486 | ||||||||
\(215\) | 1.00196e9i | 0.468920i | ||||||||
\(216\) | − | 1.46363e9i | − | 0.672384i | ||||||
\(217\) | −1.00764e9 | − | 6.19296e8i | −0.454429 | − | 0.279293i | ||||
\(218\) | 1.39484e9 | 0.617586 | ||||||||
\(219\) | 1.75073e9 | 0.761103 | ||||||||
\(220\) | − | 1.13395e9i | − | 0.484066i | ||||||
\(221\) | −4.12865e8 | −0.173077 | ||||||||
\(222\) | 3.76546e8i | 0.155026i | ||||||||
\(223\) | − | 1.59059e9i | − | 0.643191i | −0.946877 | − | 0.321595i | \(-0.895781\pi\) | ||
0.946877 | − | 0.321595i | \(-0.104219\pi\) | |||||||
\(224\) | 1.16032e9 | − | 1.88793e9i | 0.460878 | − | 0.749882i | ||||
\(225\) | −2.99504e9 | −1.16862 | ||||||||
\(226\) | −1.05399e9 | −0.404022 | ||||||||
\(227\) | 3.14403e9i | 1.18408i | 0.805907 | + | 0.592042i | \(0.201678\pi\) | ||||
−0.805907 | + | 0.592042i | \(0.798322\pi\) | |||||||
\(228\) | 8.43699e8 | 0.312211 | ||||||||
\(229\) | 3.13926e9i | 1.14152i | 0.821115 | + | 0.570762i | \(0.193352\pi\) | ||||
−0.821115 | + | 0.570762i | \(0.806648\pi\) | |||||||
\(230\) | 1.87067e9i | 0.668476i | ||||||||
\(231\) | −5.01227e8 | − | 3.08054e8i | −0.176030 | − | 0.108188i | ||||
\(232\) | −1.38850e8 | −0.0479286 | ||||||||
\(233\) | −2.14656e8 | −0.0728316 | −0.0364158 | − | 0.999337i | \(-0.511594\pi\) | ||||
−0.0364158 | + | 0.999337i | \(0.511594\pi\) | |||||||
\(234\) | 7.25177e8i | 0.241869i | ||||||||
\(235\) | 6.08628e9 | 1.99563 | ||||||||
\(236\) | 1.83668e9i | 0.592086i | ||||||||
\(237\) | 3.30960e8i | 0.104902i | ||||||||
\(238\) | −1.35144e8 | − | 8.30599e7i | −0.0421202 | − | 0.0258871i | ||||
\(239\) | 4.65634e9 | 1.42709 | 0.713547 | − | 0.700607i | \(-0.247087\pi\) | ||||
0.713547 | + | 0.700607i | \(0.247087\pi\) | |||||||
\(240\) | −2.47130e9 | −0.744870 | ||||||||
\(241\) | − | 4.83663e9i | − | 1.43375i | −0.697200 | − | 0.716877i | \(-0.745571\pi\) | ||
0.697200 | − | 0.716877i | \(-0.254429\pi\) | |||||||
\(242\) | 1.07408e9 | 0.313167 | ||||||||
\(243\) | − | 3.35328e9i | − | 0.961712i | ||||||
\(244\) | 4.37223e9i | 1.23351i | ||||||||
\(245\) | −5.61027e9 | + | 2.84012e9i | −1.55711 | + | 0.788265i | ||||
\(246\) | −3.61676e8 | −0.0987596 | ||||||||
\(247\) | −2.45797e9 | −0.660372 | ||||||||
\(248\) | 1.31859e9i | 0.348581i | ||||||||
\(249\) | 5.10567e8 | 0.132818 | ||||||||
\(250\) | − | 2.48000e9i | − | 0.634880i | ||||||
\(251\) | − | 9.65082e8i | − | 0.243147i | −0.992582 | − | 0.121574i | \(-0.961206\pi\) | ||
0.992582 | − | 0.121574i | \(-0.0387941\pi\) | |||||||
\(252\) | 1.06023e9 | − | 1.72507e9i | 0.262904 | − | 0.427763i | ||||
\(253\) | −1.42371e9 | −0.347488 | ||||||||
\(254\) | −6.37484e8 | −0.153156 | ||||||||
\(255\) | 6.86929e8i | 0.162462i | ||||||||
\(256\) | −9.86300e6 | −0.00229641 | ||||||||
\(257\) | − | 4.81547e9i | − | 1.10384i | −0.833897 | − | 0.551920i | \(-0.813895\pi\) | ||
0.833897 | − | 0.551920i | \(-0.186105\pi\) | |||||||
\(258\) | − | 2.71125e8i | − | 0.0611914i | ||||||
\(259\) | −1.60384e9 | + | 2.60957e9i | −0.356420 | + | 0.579922i | ||||
\(260\) | 8.53590e9 | 1.86791 | ||||||||
\(261\) | −1.94392e8 | −0.0418906 | ||||||||
\(262\) | − | 1.31473e9i | − | 0.279018i | ||||||
\(263\) | −2.09659e9 | −0.438218 | −0.219109 | − | 0.975700i | \(-0.570315\pi\) | ||||
−0.219109 | + | 0.975700i | \(0.570315\pi\) | |||||||
\(264\) | 6.55903e8i | 0.135028i | ||||||||
\(265\) | − | 7.46067e9i | − | 1.51284i | ||||||
\(266\) | −8.04575e8 | − | 4.94492e8i | −0.160709 | − | 0.0987718i | ||||
\(267\) | −5.22107e9 | −1.02734 | ||||||||
\(268\) | −5.71224e9 | −1.10730 | ||||||||
\(269\) | 3.85590e9i | 0.736404i | 0.929746 | + | 0.368202i | \(0.120027\pi\) | ||||
−0.929746 | + | 0.368202i | \(0.879973\pi\) | |||||||
\(270\) | 3.31893e9 | 0.624514 | ||||||||
\(271\) | 8.41141e9i | 1.55952i | 0.626077 | + | 0.779761i | \(0.284659\pi\) | ||||
−0.626077 | + | 0.779761i | \(0.715341\pi\) | |||||||
\(272\) | − | 5.07124e8i | − | 0.0926486i | ||||||
\(273\) | 2.31889e9 | − | 3.77301e9i | 0.417475 | − | 0.679262i | ||||
\(274\) | −2.41058e9 | −0.427680 | ||||||||
\(275\) | 3.69199e9 | 0.645549 | ||||||||
\(276\) | 3.67863e9i | 0.633943i | ||||||||
\(277\) | 4.95554e9 | 0.841728 | 0.420864 | − | 0.907124i | \(-0.361727\pi\) | ||||
0.420864 | + | 0.907124i | \(0.361727\pi\) | |||||||
\(278\) | 2.97748e9i | 0.498505i | ||||||||
\(279\) | 1.84605e9i | 0.304667i | ||||||||
\(280\) | 5.97263e9 | + | 3.67078e9i | 0.971704 | + | 0.597210i | ||||
\(281\) | 4.41060e9 | 0.707412 | 0.353706 | − | 0.935357i | \(-0.384921\pi\) | ||||
0.353706 | + | 0.935357i | \(0.384921\pi\) | |||||||
\(282\) | −1.64691e9 | −0.260419 | ||||||||
\(283\) | − | 4.90528e9i | − | 0.764747i | −0.924008 | − | 0.382374i | \(-0.875107\pi\) | ||
0.924008 | − | 0.382374i | \(-0.124893\pi\) | |||||||
\(284\) | −6.73843e9 | −1.03582 | ||||||||
\(285\) | 4.08959e9i | 0.619870i | ||||||||
\(286\) | − | 8.93926e8i | − | 0.133610i | ||||||
\(287\) | −2.50652e9 | − | 1.54051e9i | −0.369439 | − | 0.227058i | ||||
\(288\) | −3.45878e9 | −0.502751 | ||||||||
\(289\) | 6.83480e9 | 0.979793 | ||||||||
\(290\) | − | 3.14856e8i | − | 0.0445164i | ||||||
\(291\) | −2.52305e8 | −0.0351847 | ||||||||
\(292\) | − | 7.42761e9i | − | 1.02169i | ||||||
\(293\) | 9.91738e9i | 1.34563i | 0.739810 | + | 0.672816i | \(0.234915\pi\) | ||||
−0.739810 | + | 0.672816i | \(0.765085\pi\) | |||||||
\(294\) | 1.51810e9 | − | 7.68517e8i | 0.203194 | − | 0.102864i | ||||
\(295\) | −8.90276e9 | −1.17554 | ||||||||
\(296\) | 3.41487e9 | 0.444843 | ||||||||
\(297\) | 2.52593e9i | 0.324636i | ||||||||
\(298\) | 2.35256e8 | 0.0298315 | ||||||||
\(299\) | − | 1.07171e10i | − | 1.34088i | ||||||
\(300\) | − | 9.53948e9i | − | 1.17771i | ||||||
\(301\) | 1.15482e9 | − | 1.87897e9i | 0.140685 | − | 0.228904i | ||||
\(302\) | −6.36654e8 | −0.0765377 | ||||||||
\(303\) | 5.12352e9 | 0.607852 | ||||||||
\(304\) | − | 3.01913e9i | − | 0.353499i | ||||||
\(305\) | −2.11932e10 | −2.44904 | ||||||||
\(306\) | 2.47591e8i | 0.0282390i | ||||||||
\(307\) | 1.23430e10i | 1.38953i | 0.719237 | + | 0.694765i | \(0.244492\pi\) | ||||
−0.719237 | + | 0.694765i | \(0.755508\pi\) | |||||||
\(308\) | −1.30694e9 | + | 2.12649e9i | −0.145229 | + | 0.236298i | ||||
\(309\) | 6.04584e9 | 0.663166 | ||||||||
\(310\) | −2.99003e9 | −0.323765 | ||||||||
\(311\) | − | 1.55097e10i | − | 1.65791i | −0.559315 | − | 0.828955i | \(-0.688936\pi\) | ||
0.559315 | − | 0.828955i | \(-0.311064\pi\) | |||||||
\(312\) | −4.93734e9 | −0.521045 | ||||||||
\(313\) | − | 3.48632e8i | − | 0.0363237i | −0.999835 | − | 0.0181619i | \(-0.994219\pi\) | ||
0.999835 | − | 0.0181619i | \(-0.00578141\pi\) | |||||||
\(314\) | − | 2.41558e9i | − | 0.248487i | ||||||
\(315\) | 8.36176e9 | + | 5.13914e9i | 0.849289 | + | 0.521974i | ||||
\(316\) | 1.40412e9 | 0.140818 | ||||||||
\(317\) | 1.67563e10 | 1.65936 | 0.829682 | − | 0.558237i | \(-0.188522\pi\) | ||||
0.829682 | + | 0.558237i | \(0.188522\pi\) | |||||||
\(318\) | 2.01881e9i | 0.197418i | ||||||||
\(319\) | 2.39627e8 | 0.0231406 | ||||||||
\(320\) | 6.32523e9i | 0.603221i | ||||||||
\(321\) | 1.00852e9i | 0.0949873i | ||||||||
\(322\) | 2.15605e9 | − | 3.50804e9i | 0.200556 | − | 0.326318i | ||||
\(323\) | −8.39206e8 | −0.0771007 | ||||||||
\(324\) | 9.93524e8 | 0.0901567 | ||||||||
\(325\) | 2.77916e10i | 2.49104i | ||||||||
\(326\) | 1.24427e9 | 0.110165 | ||||||||
\(327\) | 1.32955e10i | 1.16282i | ||||||||
\(328\) | 3.28002e9i | 0.283388i | ||||||||
\(329\) | −1.14135e10 | − | 7.01476e9i | −0.974173 | − | 0.598727i | ||||
\(330\) | −1.48732e9 | −0.125415 | ||||||||
\(331\) | −5.54002e9 | −0.461530 | −0.230765 | − | 0.973010i | \(-0.574123\pi\) | ||||
−0.230765 | + | 0.973010i | \(0.574123\pi\) | |||||||
\(332\) | − | 2.16612e9i | − | 0.178291i | ||||||
\(333\) | 4.78086e9 | 0.388802 | ||||||||
\(334\) | 1.60297e9i | 0.128807i | ||||||||
\(335\) | − | 2.76885e10i | − | 2.19846i | ||||||
\(336\) | 4.63440e9 | + | 2.84831e9i | 0.363611 | + | 0.223475i | ||||
\(337\) | 1.42537e9 | 0.110512 | 0.0552560 | − | 0.998472i | \(-0.482403\pi\) | ||||
0.0552560 | + | 0.998472i | \(0.482403\pi\) | |||||||
\(338\) | 2.18981e9 | 0.167780 | ||||||||
\(339\) | − | 1.00466e10i | − | 0.760713i | ||||||
\(340\) | 2.91434e9 | 0.218085 | ||||||||
\(341\) | − | 2.27562e9i | − | 0.168300i | ||||||
\(342\) | 1.47402e9i | 0.107746i | ||||||||
\(343\) | 1.37943e10 | + | 1.14009e9i | 0.996602 | + | 0.0823687i | ||||
\(344\) | −2.45881e9 | −0.175587 | ||||||||
\(345\) | −1.78311e10 | −1.25864 | ||||||||
\(346\) | − | 9.75731e8i | − | 0.0680809i | ||||||
\(347\) | −1.75840e9 | −0.121283 | −0.0606415 | − | 0.998160i | \(-0.519315\pi\) | ||||
−0.0606415 | + | 0.998160i | \(0.519315\pi\) | |||||||
\(348\) | − | 6.19157e8i | − | 0.0422167i | ||||||
\(349\) | − | 6.24983e9i | − | 0.421276i | −0.977564 | − | 0.210638i | \(-0.932446\pi\) | ||
0.977564 | − | 0.210638i | \(-0.0675541\pi\) | |||||||
\(350\) | −5.59109e9 | + | 9.09711e9i | −0.372584 | + | 0.606221i | ||||
\(351\) | −1.90141e10 | −1.25270 | ||||||||
\(352\) | 4.26364e9 | 0.277722 | ||||||||
\(353\) | 3.49131e9i | 0.224848i | 0.993660 | + | 0.112424i | \(0.0358616\pi\) | ||||
−0.993660 | + | 0.112424i | \(0.964138\pi\) | |||||||
\(354\) | 2.40903e9 | 0.153401 | ||||||||
\(355\) | − | 3.26626e10i | − | 2.05654i | ||||||
\(356\) | 2.21507e10i | 1.37908i | ||||||||
\(357\) | 7.91722e8 | − | 1.28819e9i | 0.0487416 | − | 0.0793061i | ||||
\(358\) | 8.15750e9 | 0.496621 | ||||||||
\(359\) | −2.24032e10 | −1.34875 | −0.674376 | − | 0.738388i | \(-0.735587\pi\) | ||||
−0.674376 | + | 0.738388i | \(0.735587\pi\) | |||||||
\(360\) | − | 1.09422e10i | − | 0.651468i | ||||||
\(361\) | 1.19874e10 | 0.705824 | ||||||||
\(362\) | 8.19156e8i | 0.0477015i | ||||||||
\(363\) | 1.02381e10i | 0.589646i | ||||||||
\(364\) | −1.60073e10 | − | 9.83807e9i | −0.911825 | − | 0.560408i | ||||
\(365\) | 3.60032e10 | 2.02848 | ||||||||
\(366\) | 5.73473e9 | 0.319587 | ||||||||
\(367\) | 6.13435e9i | 0.338146i | 0.985604 | + | 0.169073i | \(0.0540774\pi\) | ||||
−0.985604 | + | 0.169073i | \(0.945923\pi\) | |||||||
\(368\) | 1.31638e10 | 0.717778 | ||||||||
\(369\) | 4.59207e9i | 0.247687i | ||||||||
\(370\) | 7.74353e9i | 0.413173i | ||||||||
\(371\) | −8.59882e9 | + | 1.39909e10i | −0.453882 | + | 0.738499i | ||||
\(372\) | −5.87983e9 | −0.307039 | ||||||||
\(373\) | −1.89260e10 | −0.977738 | −0.488869 | − | 0.872357i | \(-0.662590\pi\) | ||||
−0.488869 | + | 0.872357i | \(0.662590\pi\) | |||||||
\(374\) | − | 3.05206e8i | − | 0.0155994i | ||||||
\(375\) | 2.36392e10 | 1.19539 | ||||||||
\(376\) | 1.49357e10i | 0.747263i | ||||||||
\(377\) | 1.80381e9i | 0.0892945i | ||||||||
\(378\) | −6.22394e9 | − | 3.82524e9i | −0.304858 | − | 0.187366i | ||||
\(379\) | −1.23203e9 | −0.0597126 | −0.0298563 | − | 0.999554i | \(-0.509505\pi\) | ||||
−0.0298563 | + | 0.999554i | \(0.509505\pi\) | |||||||
\(380\) | 1.73504e10 | 0.832098 | ||||||||
\(381\) | − | 6.07646e9i | − | 0.288370i | ||||||
\(382\) | −5.27844e9 | −0.247886 | ||||||||
\(383\) | 2.90499e10i | 1.35005i | 0.737795 | + | 0.675025i | \(0.235867\pi\) | ||||
−0.737795 | + | 0.675025i | \(0.764133\pi\) | |||||||
\(384\) | − | 1.42440e10i | − | 0.655099i | ||||||
\(385\) | −1.03076e10 | − | 6.33503e9i | −0.469151 | − | 0.288341i | ||||
\(386\) | 7.90128e9 | 0.355917 | ||||||||
\(387\) | −3.44237e9 | −0.153467 | ||||||||
\(388\) | 1.07042e9i | 0.0472311i | ||||||||
\(389\) | −1.24931e9 | −0.0545598 | −0.0272799 | − | 0.999628i | \(-0.508685\pi\) | ||||
−0.0272799 | + | 0.999628i | \(0.508685\pi\) | |||||||
\(390\) | − | 1.11959e10i | − | 0.483950i | ||||||
\(391\) | − | 3.65904e9i | − | 0.156553i | ||||||
\(392\) | −6.96963e9 | − | 1.37676e10i | −0.295166 | − | 0.583059i | ||||
\(393\) | 1.25319e10 | 0.525350 | ||||||||
\(394\) | −1.03126e10 | −0.427940 | ||||||||
\(395\) | 6.80609e9i | 0.279582i | ||||||||
\(396\) | 3.89584e9 | 0.158424 | ||||||||
\(397\) | 1.31642e10i | 0.529946i | 0.964256 | + | 0.264973i | \(0.0853631\pi\) | ||||
−0.964256 | + | 0.264973i | \(0.914637\pi\) | |||||||
\(398\) | − | 1.34138e10i | − | 0.534590i | ||||||
\(399\) | 4.71347e9 | − | 7.66916e9i | 0.185973 | − | 0.302591i | ||||
\(400\) | −3.41365e10 | −1.33346 | ||||||||
\(401\) | −3.42284e9 | −0.132376 | −0.0661879 | − | 0.997807i | \(-0.521084\pi\) | ||||
−0.0661879 | + | 0.997807i | \(0.521084\pi\) | |||||||
\(402\) | 7.49231e9i | 0.286887i | ||||||||
\(403\) | 1.71299e10 | 0.649433 | ||||||||
\(404\) | − | 2.17369e10i | − | 0.815966i | ||||||
\(405\) | 4.81582e9i | 0.178999i | ||||||||
\(406\) | −3.62888e8 | + | 5.90446e8i | −0.0133558 | + | 0.0217308i | ||||
\(407\) | −5.89337e9 | −0.214776 | ||||||||
\(408\) | −1.68572e9 | −0.0608337 | ||||||||
\(409\) | − | 3.67295e10i | − | 1.31257i | −0.754514 | − | 0.656284i | \(-0.772127\pi\) | ||
0.754514 | − | 0.656284i | \(-0.227873\pi\) | |||||||
\(410\) | −7.43775e9 | −0.263212 | ||||||||
\(411\) | − | 2.29775e10i | − | 0.805258i | ||||||
\(412\) | − | 2.56499e10i | − | 0.890219i | ||||||
\(413\) | 1.66952e10 | + | 1.02609e10i | 0.573842 | + | 0.352684i | ||||
\(414\) | −6.42691e9 | −0.218777 | ||||||||
\(415\) | 1.04996e10 | 0.353983 | ||||||||
\(416\) | 3.20948e10i | 1.07167i | ||||||||
\(417\) | −2.83811e10 | −0.938611 | ||||||||
\(418\) | − | 1.81703e9i | − | 0.0595191i | ||||||
\(419\) | 3.44354e10i | 1.11725i | 0.829421 | + | 0.558623i | \(0.188670\pi\) | ||||
−0.829421 | + | 0.558623i | \(0.811330\pi\) | |||||||
\(420\) | −1.63687e10 | + | 2.66330e10i | −0.526037 | + | 0.855900i | ||||
\(421\) | −8.91543e9 | −0.283801 | −0.141900 | − | 0.989881i | \(-0.545321\pi\) | ||||
−0.141900 | + | 0.989881i | \(0.545321\pi\) | |||||||
\(422\) | 1.49146e10 | 0.470286 | ||||||||
\(423\) | 2.09101e10i | 0.653124i | ||||||||
\(424\) | 1.83084e10 | 0.566484 | ||||||||
\(425\) | 9.48867e9i | 0.290837i | ||||||||
\(426\) | 8.83829e9i | 0.268367i | ||||||||
\(427\) | 3.97433e10 | + | 2.44262e10i | 1.19551 | + | 0.734760i | ||||
\(428\) | 4.27873e9 | 0.127509 | ||||||||
\(429\) | 8.52085e9 | 0.251567 | ||||||||
\(430\) | − | 5.57559e9i | − | 0.163086i | ||||||
\(431\) | 8.63513e9 | 0.250242 | 0.125121 | − | 0.992141i | \(-0.460068\pi\) | ||||
0.125121 | + | 0.992141i | \(0.460068\pi\) | |||||||
\(432\) | − | 2.33551e10i | − | 0.670574i | ||||||
\(433\) | − | 1.00230e10i | − | 0.285133i | −0.989785 | − | 0.142566i | \(-0.954465\pi\) | ||
0.989785 | − | 0.142566i | \(-0.0455354\pi\) | |||||||
\(434\) | 5.60717e9 | + | 3.44617e9i | 0.158047 | + | 0.0971355i | ||||
\(435\) | 3.00119e9 | 0.0838178 | ||||||||
\(436\) | 5.64072e10 | 1.56095 | ||||||||
\(437\) | − | 2.17839e10i | − | 0.597323i | ||||||
\(438\) | −9.74224e9 | −0.264705 | ||||||||
\(439\) | 1.95383e10i | 0.526052i | 0.964789 | + | 0.263026i | \(0.0847205\pi\) | ||||
−0.964789 | + | 0.263026i | \(0.915280\pi\) | |||||||
\(440\) | 1.34884e10i | 0.359874i | ||||||||
\(441\) | −9.75758e9 | − | 1.92748e10i | −0.257981 | − | 0.509606i | ||||
\(442\) | 2.29746e9 | 0.0601947 | ||||||||
\(443\) | −6.16372e10 | −1.60040 | −0.800198 | − | 0.599735i | \(-0.795272\pi\) | ||||
−0.800198 | + | 0.599735i | \(0.795272\pi\) | |||||||
\(444\) | 1.52275e10i | 0.391829i | ||||||||
\(445\) | −1.07369e11 | −2.73805 | ||||||||
\(446\) | 8.85111e9i | 0.223696i | ||||||||
\(447\) | 2.24245e9i | 0.0561684i | ||||||||
\(448\) | 7.29017e9 | − | 1.18616e10i | 0.180978 | − | 0.294464i | ||||
\(449\) | 4.20875e10 | 1.03554 | 0.517772 | − | 0.855519i | \(-0.326762\pi\) | ||||
0.517772 | + | 0.855519i | \(0.326762\pi\) | |||||||
\(450\) | 1.66664e10 | 0.406435 | ||||||||
\(451\) | − | 5.66065e9i | − | 0.136823i | ||||||
\(452\) | −4.26235e10 | −1.02116 | ||||||||
\(453\) | − | 6.06855e9i | − | 0.144109i | ||||||
\(454\) | − | 1.74954e10i | − | 0.411814i | ||||||
\(455\) | 4.76873e10 | − | 7.75907e10i | 1.11265 | − | 1.81036i | ||||
\(456\) | −1.00358e10 | −0.232110 | ||||||||
\(457\) | 3.52520e10 | 0.808201 | 0.404101 | − | 0.914715i | \(-0.367585\pi\) | ||||
0.404101 | + | 0.914715i | \(0.367585\pi\) | |||||||
\(458\) | − | 1.74689e10i | − | 0.397012i | ||||||
\(459\) | −6.49184e9 | −0.146257 | ||||||||
\(460\) | 7.56498e10i | 1.68957i | ||||||||
\(461\) | − | 6.35329e10i | − | 1.40668i | −0.710854 | − | 0.703340i | \(-0.751691\pi\) | ||
0.710854 | − | 0.703340i | \(-0.248309\pi\) | |||||||
\(462\) | 2.78916e9 | + | 1.71422e9i | 0.0612216 | + | 0.0376268i | ||||
\(463\) | −1.97409e10 | −0.429580 | −0.214790 | − | 0.976660i | \(-0.568907\pi\) | ||||
−0.214790 | + | 0.976660i | \(0.568907\pi\) | |||||||
\(464\) | −2.21562e9 | −0.0477996 | ||||||||
\(465\) | − | 2.85008e10i | − | 0.609601i | ||||||
\(466\) | 1.19449e9 | 0.0253302 | ||||||||
\(467\) | − | 2.52130e10i | − | 0.530098i | −0.964235 | − | 0.265049i | \(-0.914612\pi\) | ||
0.964235 | − | 0.265049i | \(-0.0853882\pi\) | |||||||
\(468\) | 2.93261e10i | 0.611323i | ||||||||
\(469\) | −3.19124e10 | + | 5.19238e10i | −0.659581 | + | 1.07319i | ||||
\(470\) | −3.38681e10 | −0.694063 | ||||||||
\(471\) | 2.30252e10 | 0.467864 | ||||||||
\(472\) | − | 2.18473e10i | − | 0.440180i | ||||||
\(473\) | 4.24341e9 | 0.0847756 | ||||||||
\(474\) | − | 1.84168e9i | − | 0.0364839i | ||||||
\(475\) | 5.64903e10i | 1.10968i | ||||||||
\(476\) | −5.46524e9 | − | 3.35894e9i | −0.106459 | − | 0.0654296i | ||||
\(477\) | 2.56320e10 | 0.495119 | ||||||||
\(478\) | −2.59109e10 | −0.496331 | ||||||||
\(479\) | 8.60005e10i | 1.63365i | 0.576886 | + | 0.816825i | \(0.304268\pi\) | ||||
−0.576886 | + | 0.816825i | \(0.695732\pi\) | |||||||
\(480\) | 5.33995e10 | 1.00594 | ||||||||
\(481\) | − | 4.43626e10i | − | 0.828776i | ||||||
\(482\) | 2.69142e10i | 0.498647i | ||||||||
\(483\) | 3.34385e10 | + | 2.05513e10i | 0.614410 | + | 0.377617i | ||||
\(484\) | 4.34358e10 | 0.791527 | ||||||||
\(485\) | −5.18856e9 | −0.0937735 | ||||||||
\(486\) | 1.86599e10i | 0.334475i | ||||||||
\(487\) | 3.49822e10 | 0.621915 | 0.310957 | − | 0.950424i | \(-0.399350\pi\) | ||||
0.310957 | + | 0.950424i | \(0.399350\pi\) | |||||||
\(488\) | − | 5.20079e10i | − | 0.917043i | ||||||
\(489\) | 1.18603e10i | 0.207424i | ||||||||
\(490\) | 3.12192e10 | − | 1.58043e10i | 0.541549 | − | 0.274152i | ||||
\(491\) | −1.12326e11 | −1.93265 | −0.966324 | − | 0.257327i | \(-0.917158\pi\) | ||||
−0.966324 | + | 0.257327i | \(0.917158\pi\) | |||||||
\(492\) | −1.46262e10 | −0.249615 | ||||||||
\(493\) | 6.15860e8i | 0.0104254i | ||||||||
\(494\) | 1.36778e10 | 0.229672 | ||||||||
\(495\) | 1.88840e10i | 0.314537i | ||||||||
\(496\) | 2.10407e10i | 0.347643i | ||||||||
\(497\) | −3.76454e10 | + | 6.12518e10i | −0.617002 | + | 1.00391i | ||||
\(498\) | −2.84113e9 | −0.0461928 | ||||||||
\(499\) | 2.70319e10 | 0.435988 | 0.217994 | − | 0.975950i | \(-0.430049\pi\) | ||||
0.217994 | + | 0.975950i | \(0.430049\pi\) | |||||||
\(500\) | − | 1.00291e11i | − | 1.60466i | ||||||
\(501\) | −1.52794e10 | −0.242525 | ||||||||
\(502\) | 5.37035e9i | 0.0845645i | ||||||||
\(503\) | − | 9.55454e10i | − | 1.49258i | −0.665621 | − | 0.746290i | \(-0.731833\pi\) | ||
0.665621 | − | 0.746290i | \(-0.268167\pi\) | |||||||
\(504\) | −1.26114e10 | + | 2.05197e10i | −0.195453 | + | 0.318016i | ||||
\(505\) | 1.05363e11 | 1.62004 | ||||||||
\(506\) | 7.92246e9 | 0.120853 | ||||||||
\(507\) | 2.08732e10i | 0.315905i | ||||||||
\(508\) | −2.57798e10 | −0.387101 | ||||||||
\(509\) | 3.53308e10i | 0.526359i | 0.964747 | + | 0.263180i | \(0.0847712\pi\) | ||||
−0.964747 | + | 0.263180i | \(0.915229\pi\) | |||||||
\(510\) | − | 3.82252e9i | − | 0.0565027i | ||||||
\(511\) | −6.75165e10 | − | 4.14957e10i | −0.990207 | − | 0.608582i | ||||
\(512\) | −6.86919e10 | −0.999598 | ||||||||
\(513\) | −3.86488e10 | −0.558041 | ||||||||
\(514\) | 2.67965e10i | 0.383906i | ||||||||
\(515\) | 1.24331e11 | 1.76746 | ||||||||
\(516\) | − | 1.09643e10i | − | 0.154661i | ||||||
\(517\) | − | 2.57760e10i | − | 0.360789i | ||||||
\(518\) | 8.92483e9 | − | 1.45214e10i | 0.123960 | − | 0.201692i | ||||
\(519\) | 9.30061e9 | 0.128186 | ||||||||
\(520\) | −1.01535e11 | −1.38868 | ||||||||
\(521\) | 4.31721e10i | 0.585938i | 0.956122 | + | 0.292969i | \(0.0946433\pi\) | ||||
−0.956122 | + | 0.292969i | \(0.905357\pi\) | |||||||
\(522\) | 1.08173e9 | 0.0145692 | ||||||||
\(523\) | − | 3.35907e10i | − | 0.448965i | −0.974478 | − | 0.224482i | \(-0.927931\pi\) | ||
0.974478 | − | 0.224482i | \(-0.0720691\pi\) | |||||||
\(524\) | − | 5.31677e10i | − | 0.705217i | ||||||
\(525\) | −8.67131e10 | − | 5.32939e10i | −1.14143 | − | 0.701521i | ||||
\(526\) | 1.16668e10 | 0.152408 | ||||||||
\(527\) | 5.84852e9 | 0.0758235 | ||||||||
\(528\) | 1.04662e10i | 0.134664i | ||||||||
\(529\) | 1.66694e10 | 0.212862 | ||||||||
\(530\) | 4.15161e10i | 0.526154i | ||||||||
\(531\) | − | 3.05865e10i | − | 0.384727i | ||||||
\(532\) | −3.25370e10 | − | 1.99972e10i | −0.406191 | − | 0.249645i | ||||
\(533\) | 4.26108e10 | 0.527972 | ||||||||
\(534\) | 2.90535e10 | 0.357300 | ||||||||
\(535\) | 2.07399e10i | 0.253158i | ||||||||
\(536\) | 6.79473e10 | 0.823214 | ||||||||
\(537\) | 7.77568e10i | 0.935064i | ||||||||
\(538\) | − | 2.14568e10i | − | 0.256115i | ||||||
\(539\) | 1.20282e10 | + | 2.37600e10i | 0.142510 | + | 0.281509i | ||||
\(540\) | 1.34217e11 | 1.57846 | ||||||||
\(541\) | 4.61851e10 | 0.539154 | 0.269577 | − | 0.962979i | \(-0.413116\pi\) | ||||
0.269577 | + | 0.962979i | \(0.413116\pi\) | |||||||
\(542\) | − | 4.68066e10i | − | 0.542388i | ||||||
\(543\) | −7.80815e9 | −0.0898150 | ||||||||
\(544\) | 1.09579e10i | 0.125121i | ||||||||
\(545\) | 2.73418e11i | 3.09914i | ||||||||
\(546\) | −1.29039e10 | + | 2.09955e10i | −0.145194 | + | 0.236241i | ||||
\(547\) | −6.37938e10 | −0.712572 | −0.356286 | − | 0.934377i | \(-0.615957\pi\) | ||||
−0.356286 | + | 0.934377i | \(0.615957\pi\) | |||||||
\(548\) | −9.74836e10 | −1.08096 | ||||||||
\(549\) | − | 7.28117e10i | − | 0.801515i | ||||||
\(550\) | −2.05446e10 | −0.224516 | ||||||||
\(551\) | 3.66649e9i | 0.0397781i | ||||||||
\(552\) | − | 4.37574e10i | − | 0.471298i | ||||||
\(553\) | 7.84438e9 | − | 1.27634e10i | 0.0838799 | − | 0.136479i | ||||
\(554\) | −2.75759e10 | −0.292746 | ||||||||
\(555\) | −7.38109e10 | −0.777944 | ||||||||
\(556\) | 1.20409e11i | 1.25997i | ||||||||
\(557\) | 1.37758e11 | 1.43118 | 0.715591 | − | 0.698519i | \(-0.246157\pi\) | ||||
0.715591 | + | 0.698519i | \(0.246157\pi\) | |||||||
\(558\) | − | 1.02726e10i | − | 0.105961i | ||||||
\(559\) | 3.19425e10i | 0.327131i | ||||||||
\(560\) | 9.53049e10 | + | 5.85744e10i | 0.969088 | + | 0.595602i | ||||
\(561\) | 2.90921e9 | 0.0293713 | ||||||||
\(562\) | −2.45435e10 | −0.246032 | ||||||||
\(563\) | − | 1.49790e11i | − | 1.49090i | −0.666561 | − | 0.745450i | \(-0.732235\pi\) | ||
0.666561 | − | 0.745450i | \(-0.267765\pi\) | |||||||
\(564\) | −6.66008e10 | −0.658208 | ||||||||
\(565\) | − | 2.06605e11i | − | 2.02744i | ||||||
\(566\) | 2.72962e10i | 0.265972i | ||||||||
\(567\) | 5.55049e9 | − | 9.03105e9i | 0.0537031 | − | 0.0873788i | ||||
\(568\) | 8.01539e10 | 0.770072 | ||||||||
\(569\) | 8.86831e10 | 0.846042 | 0.423021 | − | 0.906120i | \(-0.360970\pi\) | ||||
0.423021 | + | 0.906120i | \(0.360970\pi\) | |||||||
\(570\) | − | 2.27572e10i | − | 0.215585i | ||||||
\(571\) | −3.26006e10 | −0.306677 | −0.153338 | − | 0.988174i | \(-0.549002\pi\) | ||||
−0.153338 | + | 0.988174i | \(0.549002\pi\) | |||||||
\(572\) | − | 3.61503e10i | − | 0.337698i | ||||||
\(573\) | − | 5.03137e10i | − | 0.466733i | ||||||
\(574\) | 1.39479e10 | + | 8.57240e9i | 0.128488 | + | 0.0789687i | ||||
\(575\) | −2.46305e11 | −2.25321 | ||||||||
\(576\) | −2.17311e10 | −0.197420 | ||||||||
\(577\) | 2.58510e10i | 0.233225i | 0.993177 | + | 0.116612i | \(0.0372035\pi\) | ||||
−0.993177 | + | 0.116612i | \(0.962796\pi\) | |||||||
\(578\) | −3.80333e10 | −0.340763 | ||||||||
\(579\) | 7.53145e10i | 0.670138i | ||||||||
\(580\) | − | 1.27328e10i | − | 0.112515i | ||||||
\(581\) | −1.96899e10 | − | 1.21014e10i | −0.172798 | − | 0.106202i | ||||
\(582\) | 1.40399e9 | 0.0122369 | ||||||||
\(583\) | −3.15966e10 | −0.273506 | ||||||||
\(584\) | 8.83517e10i | 0.759563i | ||||||||
\(585\) | −1.42150e11 | −1.21373 | ||||||||
\(586\) | − | 5.51868e10i | − | 0.467999i | ||||||
\(587\) | − | 1.55628e11i | − | 1.31079i | −0.755285 | − | 0.655396i | \(-0.772502\pi\) | ||
0.755285 | − | 0.655396i | \(-0.227498\pi\) | |||||||
\(588\) | 6.13919e10 | − | 3.10788e10i | 0.513573 | − | 0.259989i | ||||
\(589\) | 3.48188e10 | 0.289303 | ||||||||
\(590\) | 4.95409e10 | 0.408842 | ||||||||
\(591\) | − | 9.82991e10i | − | 0.805748i | ||||||
\(592\) | 5.44908e10 | 0.443646 | ||||||||
\(593\) | 1.26533e11i | 1.02325i | 0.859208 | + | 0.511627i | \(0.170957\pi\) | ||||
−0.859208 | + | 0.511627i | \(0.829043\pi\) | |||||||
\(594\) | − | 1.40560e10i | − | 0.112905i | ||||||
\(595\) | 1.62815e10 | − | 2.64912e10i | 0.129905 | − | 0.211365i | ||||
\(596\) | 9.51374e9 | 0.0753991 | ||||||||
\(597\) | 1.27860e11 | 1.00655 | ||||||||
\(598\) | 5.96368e10i | 0.466347i | ||||||||
\(599\) | −1.90322e10 | −0.147836 | −0.0739182 | − | 0.997264i | \(-0.523550\pi\) | ||||
−0.0739182 | + | 0.997264i | \(0.523550\pi\) | |||||||
\(600\) | 1.13472e11i | 0.875559i | ||||||||
\(601\) | − | 3.70216e10i | − | 0.283764i | −0.989884 | − | 0.141882i | \(-0.954685\pi\) | ||
0.989884 | − | 0.141882i | \(-0.0453154\pi\) | |||||||
\(602\) | −6.42616e9 | + | 1.04558e10i | −0.0489289 | + | 0.0796109i | ||||
\(603\) | 9.51271e10 | 0.719507 | ||||||||
\(604\) | −2.57462e10 | −0.193449 | ||||||||
\(605\) | 2.10542e11i | 1.57151i | ||||||||
\(606\) | −2.85106e10 | −0.211406 | ||||||||
\(607\) | 1.82542e11i | 1.34464i | 0.740259 | + | 0.672322i | \(0.234703\pi\) | ||||
−0.740259 | + | 0.672322i | \(0.765297\pi\) | |||||||
\(608\) | 6.52370e10i | 0.477397i | ||||||||
\(609\) | −5.62809e9 | − | 3.45903e9i | −0.0409159 | − | 0.0251469i | ||||
\(610\) | 1.17933e11 | 0.851756 | ||||||||
\(611\) | 1.94030e11 | 1.39221 | ||||||||
\(612\) | 1.00126e10i | 0.0713741i | ||||||||
\(613\) | −2.40596e11 | −1.70391 | −0.851954 | − | 0.523616i | \(-0.824583\pi\) | ||||
−0.851954 | + | 0.523616i | \(0.824583\pi\) | |||||||
\(614\) | − | 6.86847e10i | − | 0.483266i | ||||||
\(615\) | − | 7.08962e10i | − | 0.495590i | ||||||
\(616\) | 1.55461e10 | − | 2.52947e10i | 0.107969 | − | 0.175673i | ||||
\(617\) | −6.10078e10 | −0.420964 | −0.210482 | − | 0.977598i | \(-0.567503\pi\) | ||||
−0.210482 | + | 0.977598i | \(0.567503\pi\) | |||||||
\(618\) | −3.36430e10 | −0.230643 | ||||||||
\(619\) | − | 1.29814e11i | − | 0.884215i | −0.896962 | − | 0.442108i | \(-0.854231\pi\) | ||
0.896962 | − | 0.442108i | \(-0.145769\pi\) | |||||||
\(620\) | −1.20917e11 | −0.818314 | ||||||||
\(621\) | − | 1.68513e11i | − | 1.13310i | ||||||
\(622\) | 8.63060e10i | 0.576607i | ||||||||
\(623\) | 2.01349e11 | + | 1.23749e11i | 1.33658 | + | 0.821466i | ||||
\(624\) | −7.87848e10 | −0.519642 | ||||||||
\(625\) | 1.73945e11 | 1.13997 | ||||||||
\(626\) | 1.94002e9i | 0.0126331i | ||||||||
\(627\) | 1.73198e10 | 0.112066 | ||||||||
\(628\) | − | 9.76861e10i | − | 0.628050i | ||||||
\(629\) | − | 1.51464e10i | − | 0.0967624i | ||||||
\(630\) | −4.65304e10 | − | 2.85976e10i | −0.295375 | − | 0.181538i | ||||
\(631\) | −1.95506e11 | −1.23323 | −0.616614 | − | 0.787266i | \(-0.711496\pi\) | ||||
−0.616614 | + | 0.787266i | \(0.711496\pi\) | |||||||
\(632\) | −1.67021e10 | −0.104689 | ||||||||
\(633\) | 1.42165e11i | 0.885480i | ||||||||
\(634\) | −9.32432e10 | −0.577112 | ||||||||
\(635\) | − | 1.24960e11i | − | 0.768559i | ||||||
\(636\) | 8.16404e10i | 0.498973i | ||||||||
\(637\) | −1.78855e11 | + | 9.05427e10i | −1.08628 | + | 0.549915i | ||||
\(638\) | −1.33345e9 | −0.00804808 | ||||||||
\(639\) | 1.12216e11 | 0.673059 | ||||||||
\(640\) | − | 2.92923e11i | − | 1.74596i | ||||||
\(641\) | 7.18991e10 | 0.425884 | 0.212942 | − | 0.977065i | \(-0.431695\pi\) | ||||
0.212942 | + | 0.977065i | \(0.431695\pi\) | |||||||
\(642\) | − | 5.61209e9i | − | 0.0330358i | ||||||
\(643\) | 1.33296e11i | 0.779784i | 0.920861 | + | 0.389892i | \(0.127488\pi\) | ||||
−0.920861 | + | 0.389892i | \(0.872512\pi\) | |||||||
\(644\) | 8.71904e10 | − | 1.41865e11i | 0.506903 | − | 0.824769i | ||||
\(645\) | 5.31462e10 | 0.307067 | ||||||||
\(646\) | 4.66989e9 | 0.0268149 | ||||||||
\(647\) | − | 1.36807e11i | − | 0.780715i | −0.920663 | − | 0.390358i | \(-0.872351\pi\) | ||
0.920663 | − | 0.390358i | \(-0.127649\pi\) | |||||||
\(648\) | −1.18180e10 | −0.0670261 | ||||||||
\(649\) | 3.77041e10i | 0.212525i | ||||||||
\(650\) | − | 1.54651e11i | − | 0.866361i | ||||||
\(651\) | −3.28487e10 | + | 5.34473e10i | −0.182892 | + | 0.297578i | ||||
\(652\) | 5.03181e10 | 0.278442 | ||||||||
\(653\) | −2.96176e11 | −1.62891 | −0.814454 | − | 0.580228i | \(-0.802963\pi\) | ||||
−0.814454 | + | 0.580228i | \(0.802963\pi\) | |||||||
\(654\) | − | 7.39850e10i | − | 0.404420i | ||||||
\(655\) | 2.57715e11 | 1.40015 | ||||||||
\(656\) | 5.23390e10i | 0.282625i | ||||||||
\(657\) | 1.23694e11i | 0.663874i | ||||||||
\(658\) | 6.35124e10 | + | 3.90347e10i | 0.338809 | + | 0.208232i | ||||
\(659\) | −2.23698e11 | −1.18610 | −0.593050 | − | 0.805166i | \(-0.702076\pi\) | ||||
−0.593050 | + | 0.805166i | \(0.702076\pi\) | |||||||
\(660\) | −6.01472e10 | −0.316986 | ||||||||
\(661\) | 6.94168e10i | 0.363629i | 0.983333 | + | 0.181815i | \(0.0581971\pi\) | ||||
−0.983333 | + | 0.181815i | \(0.941803\pi\) | |||||||
\(662\) | 3.08283e10 | 0.160516 | ||||||||
\(663\) | 2.18992e10i | 0.113338i | ||||||||
\(664\) | 2.57661e10i | 0.132549i | ||||||||
\(665\) | 9.69309e10 | − | 1.57714e11i | 0.495651 | − | 0.806460i | ||||
\(666\) | −2.66038e10 | −0.135222 | ||||||||
\(667\) | −1.59863e10 | −0.0807692 | ||||||||
\(668\) | 6.48241e10i | 0.325560i | ||||||||
\(669\) | −8.43683e10 | −0.421187 | ||||||||
\(670\) | 1.54077e11i | 0.764607i | ||||||||
\(671\) | 8.97551e10i | 0.442760i | ||||||||
\(672\) | −1.00139e11 | − | 6.15458e10i | −0.491053 | − | 0.301801i | ||||
\(673\) | 2.96996e11 | 1.44774 | 0.723868 | − | 0.689938i | \(-0.242362\pi\) | ||||
0.723868 | + | 0.689938i | \(0.242362\pi\) | |||||||
\(674\) | −7.93172e9 | −0.0384351 | ||||||||
\(675\) | 4.36991e11i | 2.10503i | ||||||||
\(676\) | 8.85559e10 | 0.424063 | ||||||||
\(677\) | − | 6.21127e10i | − | 0.295683i | −0.989011 | − | 0.147841i | \(-0.952768\pi\) | ||
0.989011 | − | 0.147841i | \(-0.0472325\pi\) | |||||||
\(678\) | 5.59060e10i | 0.264569i | ||||||||
\(679\) | 9.73005e9 | + | 5.98010e9i | 0.0457758 | + | 0.0281338i | ||||
\(680\) | −3.46662e10 | −0.162133 | ||||||||
\(681\) | 1.66765e11 | 0.775385 | ||||||||
\(682\) | 1.26631e10i | 0.0585331i | ||||||||
\(683\) | 1.74236e11 | 0.800675 | 0.400337 | − | 0.916368i | \(-0.368893\pi\) | ||||
0.400337 | + | 0.916368i | \(0.368893\pi\) | |||||||
\(684\) | 5.96093e10i | 0.272327i | ||||||||
\(685\) | − | 4.72524e11i | − | 2.14616i | ||||||
\(686\) | −7.67603e10 | − | 6.34421e9i | −0.346609 | − | 0.0286471i | ||||
\(687\) | 1.66513e11 | 0.747515 | ||||||||
\(688\) | −3.92351e10 | −0.175114 | ||||||||
\(689\) | − | 2.37845e11i | − | 1.05540i | ||||||
\(690\) | 9.92241e10 | 0.437745 | ||||||||
\(691\) | 3.76057e11i | 1.64946i | 0.565529 | + | 0.824729i | \(0.308672\pi\) | ||||
−0.565529 | + | 0.824729i | \(0.691328\pi\) | |||||||
\(692\) | − | 3.94585e10i | − | 0.172074i | ||||||
\(693\) | 2.17648e10 | − | 3.54129e10i | 0.0943672 | − | 0.153542i | ||||
\(694\) | 9.78491e9 | 0.0421812 | ||||||||
\(695\) | −5.83648e11 | −2.50157 | ||||||||
\(696\) | 7.36490e9i | 0.0313856i | ||||||||
\(697\) | 1.45483e10 | 0.0616425 | ||||||||
\(698\) | 3.47782e10i | 0.146516i | ||||||||
\(699\) | 1.13858e10i | 0.0476930i | ||||||||
\(700\) | −2.26103e11 | + | 3.67887e11i | −0.941705 | + | 1.53222i | ||||
\(701\) | 5.52623e10 | 0.228853 | 0.114426 | − | 0.993432i | \(-0.463497\pi\) | ||||
0.114426 | + | 0.993432i | \(0.463497\pi\) | |||||||
\(702\) | 1.05807e11 | 0.435678 | ||||||||
\(703\) | − | 9.01731e10i | − | 0.369195i | ||||||
\(704\) | 2.67880e10 | 0.109056 | ||||||||
\(705\) | − | 3.22828e11i | − | 1.30682i | ||||||
\(706\) | − | 1.94280e10i | − | 0.0782003i | ||||||
\(707\) | −1.97587e11 | − | 1.21437e11i | −0.790825 | − | 0.486041i | ||||
\(708\) | 9.74210e10 | 0.387721 | ||||||||
\(709\) | −1.95876e11 | −0.775168 | −0.387584 | − | 0.921834i | \(-0.626690\pi\) | ||||
−0.387584 | + | 0.921834i | \(0.626690\pi\) | |||||||
\(710\) | 1.81756e11i | 0.715248i | ||||||||
\(711\) | −2.33831e10 | −0.0915007 | ||||||||
\(712\) | − | 2.63484e11i | − | 1.02526i | ||||||
\(713\) | 1.51814e11i | 0.587428i | ||||||||
\(714\) | −4.40566e9 | + | 7.16833e9i | −0.0169519 | + | 0.0275820i | ||||
\(715\) | 1.75228e11 | 0.670472 | ||||||||
\(716\) | 3.29889e11 | 1.25521 | ||||||||
\(717\) | − | 2.46982e11i | − | 0.934518i | ||||||
\(718\) | 1.24666e11 | 0.469084 | ||||||||
\(719\) | − | 5.03402e11i | − | 1.88365i | −0.336107 | − | 0.941824i | \(-0.609110\pi\) | ||
0.336107 | − | 0.941824i | \(-0.390890\pi\) | |||||||
\(720\) | − | 1.74603e11i | − | 0.649714i | ||||||
\(721\) | −2.33156e11 | − | 1.43298e11i | −0.862789 | − | 0.530271i | ||||
\(722\) | −6.67058e10 | −0.245479 | ||||||||
\(723\) | −2.56545e11 | −0.938879 | ||||||||
\(724\) | 3.31266e10i | 0.120566i | ||||||||
\(725\) | 4.14560e10 | 0.150050 | ||||||||
\(726\) | − | 5.69714e10i | − | 0.205074i | ||||||
\(727\) | 3.52126e11i | 1.26055i | 0.776371 | + | 0.630276i | \(0.217058\pi\) | ||||
−0.776371 | + | 0.630276i | \(0.782942\pi\) | |||||||
\(728\) | 1.90407e11 | + | 1.17024e11i | 0.677887 | + | 0.416630i | ||||
\(729\) | −2.06832e11 | −0.732330 | ||||||||
\(730\) | −2.00346e11 | −0.705487 | ||||||||
\(731\) | 1.09059e10i | 0.0381937i | ||||||||
\(732\) | 2.31912e11 | 0.807754 | ||||||||
\(733\) | 3.13444e11i | 1.08579i | 0.839802 | + | 0.542893i | \(0.182671\pi\) | ||||
−0.839802 | + | 0.542893i | \(0.817329\pi\) | |||||||
\(734\) | − | 3.41356e10i | − | 0.117604i | ||||||
\(735\) | 1.50646e11 | + | 2.97580e11i | 0.516187 | + | 1.01966i | ||||
\(736\) | −2.84441e11 | −0.969352 | ||||||||
\(737\) | −1.17263e11 | −0.397459 | ||||||||
\(738\) | − | 2.55533e10i | − | 0.0861433i | ||||||
\(739\) | 1.23610e11 | 0.414453 | 0.207227 | − | 0.978293i | \(-0.433556\pi\) | ||||
0.207227 | + | 0.978293i | \(0.433556\pi\) | |||||||
\(740\) | 3.13148e11i | 1.04429i | ||||||||
\(741\) | 1.30376e11i | 0.432438i | ||||||||
\(742\) | 4.78495e10 | − | 7.78546e10i | 0.157856 | − | 0.256844i | ||||
\(743\) | 4.82588e11 | 1.58351 | 0.791756 | − | 0.610837i | \(-0.209167\pi\) | ||||
0.791756 | + | 0.610837i | \(0.209167\pi\) | |||||||
\(744\) | 6.99408e10 | 0.228265 | ||||||||
\(745\) | 4.61151e10i | 0.149699i | ||||||||
\(746\) | 1.05317e11 | 0.340049 | ||||||||
\(747\) | 3.60728e10i | 0.115850i | ||||||||
\(748\) | − | 1.23425e10i | − | 0.0394274i | ||||||
\(749\) | 2.39039e10 | − | 3.88933e10i | 0.0759523 | − | 0.123580i | ||||
\(750\) | −1.31544e11 | −0.415745 | ||||||||
\(751\) | 6.28682e11 | 1.97638 | 0.988192 | − | 0.153223i | \(-0.0489653\pi\) | ||||
0.988192 | + | 0.153223i | \(0.0489653\pi\) | |||||||
\(752\) | 2.38328e11i | 0.745252i | ||||||||
\(753\) | −5.11899e10 | −0.159222 | ||||||||
\(754\) | − | 1.00376e10i | − | 0.0310559i | ||||||
\(755\) | − | 1.24798e11i | − | 0.384077i | ||||||
\(756\) | −2.51696e11 | − | 1.54692e11i | −0.770529 | − | 0.473567i | ||||
\(757\) | −2.63545e11 | −0.802548 | −0.401274 | − | 0.915958i | \(-0.631432\pi\) | ||||
−0.401274 | + | 0.915958i | \(0.631432\pi\) | |||||||
\(758\) | 6.85585e9 | 0.0207675 | ||||||||
\(759\) | 7.55165e10i | 0.227549i | ||||||||
\(760\) | −2.06383e11 | −0.618615 | ||||||||
\(761\) | 5.81694e11i | 1.73443i | 0.497937 | + | 0.867213i | \(0.334091\pi\) | ||||
−0.497937 | + | 0.867213i | \(0.665909\pi\) | |||||||
\(762\) | 3.38134e10i | 0.100293i | ||||||||
\(763\) | 3.15128e11 | − | 5.12737e11i | 0.929800 | − | 1.51285i | ||||
\(764\) | −2.13460e11 | −0.626531 | ||||||||
\(765\) | −4.85332e10 | −0.141707 | ||||||||
\(766\) | − | 1.61653e11i | − | 0.469536i | ||||||
\(767\) | −2.83819e11 | −0.820088 | ||||||||
\(768\) | 5.23153e8i | 0.00150378i | ||||||||
\(769\) | − | 1.04399e11i | − | 0.298533i | −0.988797 | − | 0.149267i | \(-0.952309\pi\) | ||
0.988797 | − | 0.149267i | \(-0.0476912\pi\) | |||||||
\(770\) | 5.73580e10 | + | 3.52523e10i | 0.163167 | + | 0.100282i | ||||
\(771\) | −2.55422e11 | −0.722838 | ||||||||
\(772\) | 3.19527e11 | 0.899578 | ||||||||
\(773\) | − | 1.57883e11i | − | 0.442199i | −0.975251 | − | 0.221100i | \(-0.929035\pi\) | ||
0.975251 | − | 0.221100i | \(-0.0709646\pi\) | |||||||
\(774\) | 1.91556e10 | 0.0533743 | ||||||||
\(775\) | − | 3.93687e11i | − | 1.09130i | ||||||
\(776\) | − | 1.27327e10i | − | 0.0351135i | ||||||
\(777\) | 1.38417e11 | + | 8.50710e10i | 0.379756 | + | 0.233398i | ||||
\(778\) | 6.95200e9 | 0.0189754 | ||||||||
\(779\) | 8.66123e10 | 0.235196 | ||||||||
\(780\) | − | 4.52761e11i | − | 1.22318i | ||||||
\(781\) | −1.38329e11 | −0.371801 | ||||||||
\(782\) | 2.03613e10i | 0.0544476i | ||||||||
\(783\) | 2.83628e10i | 0.0754575i | ||||||||
\(784\) | −1.11214e11 | − | 2.19688e11i | −0.294371 | − | 0.581489i | ||||
\(785\) | 4.73506e11 | 1.24694 | ||||||||
\(786\) | −6.97360e10 | −0.182712 | ||||||||
\(787\) | 4.73305e11i | 1.23379i | 0.787045 | + | 0.616896i | \(0.211610\pi\) | ||||
−0.787045 | + | 0.616896i | \(0.788390\pi\) | |||||||
\(788\) | −4.17041e11 | −1.08162 | ||||||||
\(789\) | 1.11207e11i | 0.286963i | ||||||||
\(790\) | − | 3.78736e10i | − | 0.0972362i | ||||||
\(791\) | −2.38124e11 | + | 3.87444e11i | −0.608270 | + | 0.989700i | ||||
\(792\) | −4.63411e10 | −0.117778 | ||||||||
\(793\) | −6.75636e11 | −1.70852 | ||||||||
\(794\) | − | 7.32542e10i | − | 0.184311i | ||||||
\(795\) | −3.95729e11 | −0.990670 | ||||||||
\(796\) | − | 5.42455e11i | − | 1.35118i | ||||||
\(797\) | − | 1.42604e11i | − | 0.353427i | −0.984262 | − | 0.176714i | \(-0.943453\pi\) | ||
0.984262 | − | 0.176714i | \(-0.0565466\pi\) | |||||||
\(798\) | −2.62289e10 | + | 4.26763e10i | −0.0646797 | + | 0.105239i | ||||
\(799\) | 6.62461e10 | 0.162545 | ||||||||
\(800\) | 7.37617e11 | 1.80082 | ||||||||
\(801\) | − | 3.68881e11i | − | 0.896099i | ||||||
\(802\) | 1.90469e10 | 0.0460392 | ||||||||
\(803\) | − | 1.52477e11i | − | 0.366727i | ||||||
\(804\) | 3.02989e11i | 0.725107i | ||||||||
\(805\) | 6.87651e11 | + | 4.22631e11i | 1.63751 | + | 1.00642i | ||||
\(806\) | −9.53220e10 | −0.225867 | ||||||||
\(807\) | 2.04525e11 | 0.482227 | ||||||||
\(808\) | 2.58561e11i | 0.606622i | ||||||||
\(809\) | −8.94669e10 | −0.208866 | −0.104433 | − | 0.994532i | \(-0.533303\pi\) | ||||
−0.104433 | + | 0.994532i | \(0.533303\pi\) | |||||||
\(810\) | − | 2.67984e10i | − | 0.0622543i | ||||||
\(811\) | − | 1.52760e11i | − | 0.353123i | −0.984290 | − | 0.176562i | \(-0.943502\pi\) | ||
0.984290 | − | 0.176562i | \(-0.0564975\pi\) | |||||||
\(812\) | −1.46752e10 | + | 2.38776e10i | −0.0337567 | + | 0.0549245i | ||||
\(813\) | 4.46158e11 | 1.02124 | ||||||||
\(814\) | 3.27946e10 | 0.0746973 | ||||||||
\(815\) | 2.43903e11i | 0.552823i | ||||||||
\(816\) | −2.68989e10 | −0.0606699 | ||||||||
\(817\) | 6.49275e10i | 0.145727i | ||||||||
\(818\) | 2.04387e11i | 0.456500i | ||||||||
\(819\) | 2.66572e11 | + | 1.63835e11i | 0.592487 | + | 0.364143i | ||||
\(820\) | −3.00782e11 | −0.665268 | ||||||||
\(821\) | 6.73481e11 | 1.48236 | 0.741178 | − | 0.671309i | \(-0.234268\pi\) | ||||
0.741178 | + | 0.671309i | \(0.234268\pi\) | |||||||
\(822\) | 1.27862e11i | 0.280062i | ||||||||
\(823\) | −8.00004e11 | −1.74379 | −0.871893 | − | 0.489697i | \(-0.837107\pi\) | ||||
−0.871893 | + | 0.489697i | \(0.837107\pi\) | |||||||
\(824\) | 3.05106e11i | 0.661824i | ||||||||
\(825\) | − | 1.95830e11i | − | 0.422731i | ||||||
\(826\) | −9.29034e10 | − | 5.70985e10i | −0.199577 | − | 0.122660i | ||||
\(827\) | −1.04890e11 | −0.224239 | −0.112119 | − | 0.993695i | \(-0.535764\pi\) | ||||
−0.112119 | + | 0.993695i | \(0.535764\pi\) | |||||||
\(828\) | −2.59904e11 | −0.552958 | ||||||||
\(829\) | 4.44519e11i | 0.941179i | 0.882352 | + | 0.470589i | \(0.155959\pi\) | ||||
−0.882352 | + | 0.470589i | \(0.844041\pi\) | |||||||
\(830\) | −5.84269e10 | −0.123112 | ||||||||
\(831\) | − | 2.62852e11i | − | 0.551197i | ||||||
\(832\) | 2.01648e11i | 0.420824i | ||||||||
\(833\) | −6.10650e10 | + | 3.09133e10i | −0.126827 | + | 0.0642045i | ||||
\(834\) | 1.57931e11 | 0.326441 | ||||||||
\(835\) | −3.14216e11 | −0.646373 | ||||||||
\(836\) | − | 7.34805e10i | − | 0.150434i | ||||||
\(837\) | 2.69348e11 | 0.548797 | ||||||||
\(838\) | − | 1.91621e11i | − | 0.388569i | ||||||
\(839\) | − | 3.50412e10i | − | 0.0707181i | −0.999375 | − | 0.0353591i | \(-0.988743\pi\) | ||
0.999375 | − | 0.0353591i | \(-0.0112575\pi\) | |||||||
\(840\) | 1.94706e11 | − | 3.16801e11i | 0.391077 | − | 0.636310i | ||||
\(841\) | −4.97556e11 | −0.994621 | ||||||||
\(842\) | 4.96113e10 | 0.0987035 | ||||||||
\(843\) | − | 2.33947e11i | − | 0.463241i | ||||||
\(844\) | 6.03147e11 | 1.18865 | ||||||||
\(845\) | 4.29249e11i | 0.841943i | ||||||||
\(846\) | − | 1.16358e11i | − | 0.227151i | ||||||
\(847\) | 2.42661e11 | − | 3.94828e11i | 0.471484 | − | 0.767139i | ||||
\(848\) | 2.92146e11 | 0.564959 | ||||||||
\(849\) | −2.60186e11 | −0.500787 | ||||||||
\(850\) | − | 5.28012e10i | − | 0.101151i | ||||||
\(851\) | 3.93166e11 | 0.749649 | ||||||||
\(852\) | 3.57420e11i | 0.678298i | ||||||||
\(853\) | − | 3.49404e11i | − | 0.659982i | −0.943984 | − | 0.329991i | \(-0.892954\pi\) | ||
0.943984 | − | 0.329991i | \(-0.107046\pi\) | |||||||
\(854\) | −2.21158e11 | − | 1.35924e11i | −0.415787 | − | 0.255543i | ||||
\(855\) | −2.88939e11 | −0.540682 | ||||||||
\(856\) | −5.08957e10 | −0.0947950 | ||||||||
\(857\) | − | 4.87905e11i | − | 0.904507i | −0.891889 | − | 0.452254i | \(-0.850620\pi\) | ||
0.891889 | − | 0.452254i | \(-0.149380\pi\) | |||||||
\(858\) | −4.74156e10 | −0.0874928 | ||||||||
\(859\) | 2.43546e11i | 0.447309i | 0.974668 | + | 0.223655i | \(0.0717988\pi\) | ||||
−0.974668 | + | 0.223655i | \(0.928201\pi\) | |||||||
\(860\) | − | 2.25477e11i | − | 0.412200i | ||||||
\(861\) | −8.17116e10 | + | 1.32951e11i | −0.148686 | + | 0.241924i | ||||
\(862\) | −4.80516e10 | −0.0870319 | ||||||||
\(863\) | −9.85522e11 | −1.77674 | −0.888369 | − | 0.459130i | \(-0.848161\pi\) | ||||
−0.888369 | + | 0.459130i | \(0.848161\pi\) | |||||||
\(864\) | 5.04653e11i | 0.905603i | ||||||||
\(865\) | 1.91264e11 | 0.341640 | ||||||||
\(866\) | 5.57747e10i | 0.0991667i | ||||||||
\(867\) | − | 3.62531e11i | − | 0.641607i | ||||||
\(868\) | 2.26754e11 | + | 1.39363e11i | 0.399462 | + | 0.245510i | ||||
\(869\) | 2.88244e10 | 0.0505454 | ||||||||
\(870\) | −1.67006e10 | −0.0291511 | ||||||||
\(871\) | − | 8.82705e11i | − | 1.53371i | ||||||
\(872\) | −6.70965e11 | −1.16047 | ||||||||
\(873\) | − | 1.78259e10i | − | 0.0306899i | ||||||
\(874\) | 1.21220e11i | 0.207744i | ||||||||
\(875\) | −9.11638e11 | − | 5.60293e11i | −1.55521 | − | 0.955836i | ||||
\(876\) | −3.93976e11 | −0.669041 | ||||||||
\(877\) | 6.65633e11 | 1.12522 | 0.562609 | − | 0.826723i | \(-0.309798\pi\) | ||||
0.562609 | + | 0.826723i | \(0.309798\pi\) | |||||||
\(878\) | − | 1.08724e11i | − | 0.182956i | ||||||
\(879\) | 5.26038e11 | 0.881173 | ||||||||
\(880\) | 2.15234e11i | 0.358905i | ||||||||
\(881\) | 6.98615e11i | 1.15967i | 0.814734 | + | 0.579835i | \(0.196883\pi\) | ||||
−0.814734 | + | 0.579835i | \(0.803117\pi\) | |||||||
\(882\) | 5.42976e10 | + | 1.07257e11i | 0.0897235 | + | 0.177236i | ||||
\(883\) | 7.15472e11 | 1.17693 | 0.588464 | − | 0.808523i | \(-0.299733\pi\) | ||||
0.588464 | + | 0.808523i | \(0.299733\pi\) | |||||||
\(884\) | 9.29090e10 | 0.152142 | ||||||||
\(885\) | 4.72221e11i | 0.769789i | ||||||||
\(886\) | 3.42990e11 | 0.556604 | ||||||||
\(887\) | − | 1.12134e12i | − | 1.81152i | −0.423787 | − | 0.905762i | \(-0.639299\pi\) | ||
0.423787 | − | 0.905762i | \(-0.360701\pi\) | |||||||
\(888\) | − | 1.81131e11i | − | 0.291301i | ||||||
\(889\) | −1.44023e11 | + | 2.34336e11i | −0.230582 | + | 0.375174i | ||||
\(890\) | 5.97474e11 | 0.952268 | ||||||||
\(891\) | 2.03955e10 | 0.0323611 | ||||||||
\(892\) | 3.57939e11i | 0.565391i | ||||||||
\(893\) | 3.94392e11 | 0.620187 | ||||||||
\(894\) | − | 1.24785e10i | − | 0.0195349i | ||||||
\(895\) | 1.59904e12i | 2.49211i | ||||||||
\(896\) | −3.37609e11 | + | 5.49315e11i | −0.523821 | + | 0.852294i | ||||
\(897\) | −5.68454e11 | −0.878063 | ||||||||
\(898\) | −2.34203e11 | −0.360153 | ||||||||
\(899\) | − | 2.55522e10i | − | 0.0391191i | ||||||
\(900\) | 6.73987e11 | 1.02726 | ||||||||
\(901\) | − | 8.12057e10i | − | 0.123222i | ||||||
\(902\) | 3.14996e10i | 0.0475859i | ||||||||
\(903\) | −9.96644e10 | − | 6.12538e10i | −0.149896 | − | 0.0921260i | ||||
\(904\) | 5.07008e11 | 0.759173 | ||||||||
\(905\) | −1.60572e11 | −0.239373 | ||||||||
\(906\) | 3.37694e10i | 0.0501199i | ||||||||
\(907\) | −5.76730e10 | −0.0852203 | −0.0426102 | − | 0.999092i | \(-0.513567\pi\) | ||||
−0.0426102 | + | 0.999092i | \(0.513567\pi\) | |||||||
\(908\) | − | 7.07514e11i | − | 1.04086i | ||||||
\(909\) | 3.61989e11i | 0.530200i | ||||||||
\(910\) | −2.65363e11 | + | 4.31766e11i | −0.386968 | + | 0.629626i | ||||
\(911\) | 6.14760e11 | 0.892548 | 0.446274 | − | 0.894896i | \(-0.352751\pi\) | ||||
0.446274 | + | 0.894896i | \(0.352751\pi\) | |||||||
\(912\) | −1.60141e11 | −0.231485 | ||||||||
\(913\) | − | 4.44670e10i | − | 0.0639963i | ||||||
\(914\) | −1.96166e11 | −0.281085 | ||||||||
\(915\) | 1.12413e12i | 1.60373i | ||||||||
\(916\) | − | 7.06442e11i | − | 1.00345i | ||||||
\(917\) | −4.83290e11 | − | 2.97030e11i | −0.683488 | − | 0.420072i | ||||
\(918\) | 3.61249e10 | 0.0508669 | ||||||||
\(919\) | 3.09399e11 | 0.433768 | 0.216884 | − | 0.976197i | \(-0.430411\pi\) | ||||
0.216884 | + | 0.976197i | \(0.430411\pi\) | |||||||
\(920\) | − | 8.99857e11i | − | 1.25609i | ||||||
\(921\) | 6.54698e11 | 0.909919 | ||||||||
\(922\) | 3.53539e11i | 0.489231i | ||||||||
\(923\) | − | 1.04128e12i | − | 1.43470i | ||||||
\(924\) | 1.12793e11 | + | 6.93228e10i | 0.154737 | + | 0.0951017i | ||||
\(925\) | −1.01956e12 | −1.39267 | ||||||||
\(926\) | 1.09852e11 | 0.149404 | ||||||||
\(927\) | 4.27153e11i | 0.578448i | ||||||||
\(928\) | 4.78749e10 | 0.0645529 | ||||||||
\(929\) | − | 4.52187e11i | − | 0.607093i | −0.952817 | − | 0.303547i | \(-0.901829\pi\) | ||
0.952817 | − | 0.303547i | \(-0.0981709\pi\) | |||||||
\(930\) | 1.58597e11i | 0.212014i | ||||||||
\(931\) | −3.63547e11 | + | 1.84040e11i | −0.483907 | + | 0.244971i | ||||
\(932\) | 4.83051e10 | 0.0640220 | ||||||||
\(933\) | −8.22664e11 | −1.08567 | ||||||||
\(934\) | 1.40302e11i | 0.184364i | ||||||||
\(935\) | 5.98269e10 | 0.0782798 | ||||||||
\(936\) | − | 3.48835e11i | − | 0.454482i | ||||||
\(937\) | − | 8.14555e11i | − | 1.05672i | −0.849019 | − | 0.528362i | \(-0.822806\pi\) | ||
0.849019 | − | 0.528362i | \(-0.177194\pi\) | |||||||
\(938\) | 1.77582e11 | − | 2.88938e11i | 0.229397 | − | 0.373245i | ||||
\(939\) | −1.84922e10 | −0.0237862 | ||||||||
\(940\) | −1.36962e12 | −1.75424 | ||||||||
\(941\) | 1.39547e12i | 1.77977i | 0.456188 | + | 0.889883i | \(0.349214\pi\) | ||||
−0.456188 | + | 0.889883i | \(0.650786\pi\) | |||||||
\(942\) | −1.28127e11 | −0.162719 | ||||||||
\(943\) | 3.77640e11i | 0.477564i | ||||||||
\(944\) | − | 3.48616e11i | − | 0.438995i | ||||||
\(945\) | 7.49827e11 | − | 1.22002e12i | 0.940230 | − | 1.52982i | ||||
\(946\) | −2.36132e10 | −0.0294842 | ||||||||
\(947\) | 5.69289e11 | 0.707837 | 0.353918 | − | 0.935276i | \(-0.384849\pi\) | ||||
0.353918 | + | 0.935276i | \(0.384849\pi\) | |||||||
\(948\) | − | 7.44775e10i | − | 0.0922129i | ||||||
\(949\) | 1.14778e12 | 1.41512 | ||||||||
\(950\) | − | 3.14349e11i | − | 0.385938i | ||||||
\(951\) | − | 8.88789e11i | − | 1.08662i | ||||||
\(952\) | 6.50092e10 | + | 3.99547e10i | 0.0791456 | + | 0.0486429i | ||||
\(953\) | 1.65586e11 | 0.200748 | 0.100374 | − | 0.994950i | \(-0.467996\pi\) | ||||
0.100374 | + | 0.994950i | \(0.467996\pi\) | |||||||
\(954\) | −1.42634e11 | −0.172198 | ||||||||
\(955\) | − | 1.03468e12i | − | 1.24393i | ||||||
\(956\) | −1.04784e12 | −1.25448 | ||||||||
\(957\) | − | 1.27103e10i | − | 0.0151534i | ||||||
\(958\) | − | 4.78564e11i | − | 0.568169i | ||||||
\(959\) | −5.44609e11 | + | 8.86119e11i | −0.643888 | + | 1.04765i | ||||
\(960\) | 3.35503e11 | 0.395013 | ||||||||
\(961\) | 6.10235e11 | 0.715489 | ||||||||
\(962\) | 2.46863e11i | 0.288241i | ||||||||
\(963\) | −7.12546e10 | −0.0828529 | ||||||||
\(964\) | 1.08841e12i | 1.26033i | ||||||||
\(965\) | 1.54882e12i | 1.78604i | ||||||||
\(966\) | −1.86074e11 | − | 1.14361e11i | −0.213686 | − | 0.131332i | ||||
\(967\) | −8.88485e11 | −1.01612 | −0.508059 | − | 0.861322i | \(-0.669637\pi\) | ||||
−0.508059 | + | 0.861322i | \(0.669637\pi\) | |||||||
\(968\) | −5.16670e11 | −0.588453 | ||||||||
\(969\) | 4.45132e10i | 0.0504886i | ||||||||
\(970\) | 2.88726e10 | 0.0326136 | ||||||||
\(971\) | 1.28823e12i | 1.44916i | 0.689191 | + | 0.724580i | \(0.257966\pi\) | ||||
−0.689191 | + | 0.724580i | \(0.742034\pi\) | |||||||
\(972\) | 7.54605e11i | 0.845385i | ||||||||
\(973\) | 1.09451e12 | + | 6.72686e11i | 1.22115 | + | 0.750517i | ||||
\(974\) | −1.94664e11 | −0.216297 | ||||||||
\(975\) | 1.47412e12 | 1.63123 | ||||||||
\(976\) | − | 8.29886e11i | − | 0.914575i | ||||||
\(977\) | −4.18373e11 | −0.459183 | −0.229592 | − | 0.973287i | \(-0.573739\pi\) | ||||
−0.229592 | + | 0.973287i | \(0.573739\pi\) | |||||||
\(978\) | − | 6.59985e10i | − | 0.0721404i | ||||||
\(979\) | 4.54720e11i | 0.495009i | ||||||||
\(980\) | 1.26250e12 | − | 6.39125e11i | 1.36876 | − | 0.692917i | ||||
\(981\) | −9.39360e11 | −1.01428 | ||||||||
\(982\) | 6.25054e11 | 0.672158 | ||||||||
\(983\) | 7.99049e11i | 0.855774i | 0.903832 | + | 0.427887i | \(0.140742\pi\) | ||||
−0.903832 | + | 0.427887i | \(0.859258\pi\) | |||||||
\(984\) | 1.73979e11 | 0.185573 | ||||||||
\(985\) | − | 2.02149e12i | − | 2.14746i | ||||||
\(986\) | − | 3.42705e9i | − | 0.00362588i | ||||||
\(987\) | −3.72077e11 | + | 6.05396e11i | −0.392070 | + | 0.637927i | ||||
\(988\) | 5.53128e11 | 0.580494 | ||||||||
\(989\) | −2.83092e11 | −0.295898 | ||||||||
\(990\) | − | 1.05083e11i | − | 0.109393i | ||||||
\(991\) | −1.46398e12 | −1.51789 | −0.758944 | − | 0.651155i | \(-0.774285\pi\) | ||||
−0.758944 | + | 0.651155i | \(0.774285\pi\) | |||||||
\(992\) | − | 4.54644e11i | − | 0.469488i | ||||||
\(993\) | 2.93854e11i | 0.302228i | ||||||||
\(994\) | 2.09484e11 | − | 3.40846e11i | 0.214588 | − | 0.349150i | ||||
\(995\) | 2.62940e12 | 2.68265 | ||||||||
\(996\) | −1.14895e11 | −0.116752 | ||||||||
\(997\) | − | 3.58073e11i | − | 0.362402i | −0.983446 | − | 0.181201i | \(-0.942001\pi\) | ||
0.983446 | − | 0.181201i | \(-0.0579985\pi\) | |||||||
\(998\) | −1.50423e11 | −0.151633 | ||||||||
\(999\) | − | 6.97552e11i | − | 0.700349i |
(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 | 7.9.b.b.6.1 | ✓ | 4 | |
3.2 | odd | 2 | 63.9.d.c.55.4 | 4 | |||
4.3 | odd | 2 | 112.9.c.b.97.3 | 4 | |||
5.2 | odd | 4 | 175.9.c.c.174.3 | 8 | |||
5.3 | odd | 4 | 175.9.c.c.174.6 | 8 | |||
5.4 | even | 2 | 175.9.d.e.76.4 | 4 | |||
7.2 | even | 3 | 49.9.d.b.31.4 | 8 | |||
7.3 | odd | 6 | 49.9.d.b.19.4 | 8 | |||
7.4 | even | 3 | 49.9.d.b.19.3 | 8 | |||
7.5 | odd | 6 | 49.9.d.b.31.3 | 8 | |||
7.6 | odd | 2 | inner | 7.9.b.b.6.2 | yes | 4 | |
21.20 | even | 2 | 63.9.d.c.55.3 | 4 | |||
28.27 | even | 2 | 112.9.c.b.97.2 | 4 | |||
35.13 | even | 4 | 175.9.c.c.174.5 | 8 | |||
35.27 | even | 4 | 175.9.c.c.174.4 | 8 | |||
35.34 | odd | 2 | 175.9.d.e.76.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.9.b.b.6.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7.9.b.b.6.2 | yes | 4 | 7.6 | odd | 2 | inner | |
49.9.d.b.19.3 | 8 | 7.4 | even | 3 | |||
49.9.d.b.19.4 | 8 | 7.3 | odd | 6 | |||
49.9.d.b.31.3 | 8 | 7.5 | odd | 6 | |||
49.9.d.b.31.4 | 8 | 7.2 | even | 3 | |||
63.9.d.c.55.3 | 4 | 21.20 | even | 2 | |||
63.9.d.c.55.4 | 4 | 3.2 | odd | 2 | |||
112.9.c.b.97.2 | 4 | 28.27 | even | 2 | |||
112.9.c.b.97.3 | 4 | 4.3 | odd | 2 | |||
175.9.c.c.174.3 | 8 | 5.2 | odd | 4 | |||
175.9.c.c.174.4 | 8 | 35.27 | even | 4 | |||
175.9.c.c.174.5 | 8 | 35.13 | even | 4 | |||
175.9.c.c.174.6 | 8 | 5.3 | odd | 4 | |||
175.9.d.e.76.3 | 4 | 35.34 | odd | 2 | |||
175.9.d.e.76.4 | 4 | 5.4 | even | 2 |