Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [11,13,Mod(10,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11.10");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 11 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 11.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: | \(10.0539319900\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 30654x^{8} + 318945120x^{6} + 1305642637440x^{4} + 2049564619929600x^{2} + 957721368231936000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{3}\cdot 11^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 10.4 | ||
Root | \(-45.2549i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 11.10 |
Dual form | 11.13.b.b.10.7 |
$q$-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 \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 45.2549i | − | 0.707107i | −0.935414 | − | 0.353554i | \(-0.884973\pi\) | ||
0.935414 | − | 0.353554i | \(-0.115027\pi\) | |||||||
\(3\) | −583.849 | −0.800891 | −0.400445 | − | 0.916321i | \(-0.631145\pi\) | ||||
−0.400445 | + | 0.916321i | \(0.631145\pi\) | |||||||
\(4\) | 2048.00 | 0.500000 | ||||||||
\(5\) | 15889.4 | 1.01692 | 0.508461 | − | 0.861085i | \(-0.330215\pi\) | ||||
0.508461 | + | 0.861085i | \(0.330215\pi\) | |||||||
\(6\) | 26422.0i | 0.566316i | ||||||||
\(7\) | − | 93839.3i | − | 0.797621i | −0.917033 | − | 0.398810i | \(-0.869423\pi\) | ||
0.917033 | − | 0.398810i | \(-0.130577\pi\) | |||||||
\(8\) | − | 278046.i | − | 1.06066i | ||||||
\(9\) | −190561. | −0.358574 | ||||||||
\(10\) | − | 719072.i | − | 0.719072i | ||||||
\(11\) | −1.18566e6 | + | 1.31629e6i | −0.669276 | + | 0.743014i | ||||
\(12\) | −1.19572e6 | −0.400445 | ||||||||
\(13\) | − | 5.35422e6i | − | 1.10927i | −0.832094 | − | 0.554634i | \(-0.812858\pi\) | ||
0.832094 | − | 0.554634i | \(-0.187142\pi\) | |||||||
\(14\) | −4.24668e6 | −0.564003 | ||||||||
\(15\) | −9.27701e6 | −0.814443 | ||||||||
\(16\) | −4.19432e6 | −0.250001 | ||||||||
\(17\) | − | 4.63980e7i | − | 1.92223i | −0.276143 | − | 0.961117i | \(-0.589056\pi\) | ||
0.276143 | − | 0.961117i | \(-0.410944\pi\) | |||||||
\(18\) | 8.62381e6i | 0.253550i | ||||||||
\(19\) | − | 4.52775e6i | − | 0.0962412i | −0.998842 | − | 0.0481206i | \(-0.984677\pi\) | ||
0.998842 | − | 0.0481206i | \(-0.0153232\pi\) | |||||||
\(20\) | 3.25414e7 | 0.508460 | ||||||||
\(21\) | 5.47880e7i | 0.638807i | ||||||||
\(22\) | 5.95687e7 | + | 5.36570e7i | 0.525390 | + | 0.473250i | ||||
\(23\) | 86765.3 | 0.000586110 | 0.000293055 | − | 1.00000i | \(-0.499907\pi\) | ||||
0.000293055 | 1.00000i | \(0.499907\pi\) | ||||||||
\(24\) | 1.62337e8i | 0.849473i | ||||||||
\(25\) | 8.33211e6 | 0.0341283 | ||||||||
\(26\) | −2.42305e8 | −0.784371 | ||||||||
\(27\) | 4.21540e8 | 1.08807 | ||||||||
\(28\) | − | 1.92183e8i | − | 0.398810i | ||||||
\(29\) | 5.83163e8i | 0.980397i | 0.871611 | + | 0.490199i | \(0.163076\pi\) | ||||
−0.871611 | + | 0.490199i | \(0.836924\pi\) | |||||||
\(30\) | 4.19830e8i | 0.575898i | ||||||||
\(31\) | 7.40408e8 | 0.834259 | 0.417129 | − | 0.908847i | \(-0.363036\pi\) | ||||
0.417129 | + | 0.908847i | \(0.363036\pi\) | |||||||
\(32\) | − | 9.49062e8i | − | 0.883883i | ||||||
\(33\) | 6.92249e8 | − | 7.68518e8i | 0.536017 | − | 0.595073i | ||||
\(34\) | −2.09974e9 | −1.35922 | ||||||||
\(35\) | − | 1.49105e9i | − | 0.811117i | ||||||
\(36\) | −3.90268e8 | −0.179287 | ||||||||
\(37\) | −3.08141e9 | −1.20099 | −0.600495 | − | 0.799628i | \(-0.705030\pi\) | ||||
−0.600495 | + | 0.799628i | \(0.705030\pi\) | |||||||
\(38\) | −2.04903e8 | −0.0680528 | ||||||||
\(39\) | 3.12606e9i | 0.888402i | ||||||||
\(40\) | − | 4.41798e9i | − | 1.07861i | ||||||
\(41\) | − | 1.18839e9i | − | 0.250181i | −0.992145 | − | 0.125090i | \(-0.960078\pi\) | ||
0.992145 | − | 0.125090i | \(-0.0399221\pi\) | |||||||
\(42\) | 2.47942e9 | 0.451705 | ||||||||
\(43\) | 3.38609e9i | 0.535658i | 0.963467 | + | 0.267829i | \(0.0863062\pi\) | ||||
−0.963467 | + | 0.267829i | \(0.913694\pi\) | |||||||
\(44\) | −2.42824e9 | + | 2.69577e9i | −0.334638 | + | 0.371507i | ||||
\(45\) | −3.02790e9 | −0.364641 | ||||||||
\(46\) | − | 3.92655e6i | − | 0.000414442i | ||||||
\(47\) | 1.92096e10 | 1.78210 | 0.891049 | − | 0.453907i | \(-0.149970\pi\) | ||||
0.891049 | + | 0.453907i | \(0.149970\pi\) | |||||||
\(48\) | 2.44885e9 | 0.200223 | ||||||||
\(49\) | 5.03547e9 | 0.363801 | ||||||||
\(50\) | − | 3.77068e8i | − | 0.0241324i | ||||||
\(51\) | 2.70895e10i | 1.53950i | ||||||||
\(52\) | − | 1.09654e10i | − | 0.554633i | ||||||
\(53\) | 9.28686e8 | 0.0419000 | 0.0209500 | − | 0.999781i | \(-0.493331\pi\) | ||||
0.0209500 | + | 0.999781i | \(0.493331\pi\) | |||||||
\(54\) | − | 1.90767e10i | − | 0.769382i | ||||||
\(55\) | −1.88395e10 | + | 2.09151e10i | −0.680601 | + | 0.755587i | ||||
\(56\) | −2.60916e10 | −0.846005 | ||||||||
\(57\) | 2.64352e9i | 0.0770787i | ||||||||
\(58\) | 2.63910e10 | 0.693246 | ||||||||
\(59\) | 1.61409e10 | 0.382663 | 0.191331 | − | 0.981525i | \(-0.438719\pi\) | ||||
0.191331 | + | 0.981525i | \(0.438719\pi\) | |||||||
\(60\) | −1.89993e10 | −0.407221 | ||||||||
\(61\) | − | 8.95382e9i | − | 0.173792i | −0.996217 | − | 0.0868959i | \(-0.972305\pi\) | ||
0.996217 | − | 0.0868959i | \(-0.0276948\pi\) | |||||||
\(62\) | − | 3.35070e10i | − | 0.589910i | ||||||
\(63\) | 1.78821e10i | 0.286006i | ||||||||
\(64\) | −6.01296e10 | −0.875001 | ||||||||
\(65\) | − | 8.50754e10i | − | 1.12804i | ||||||
\(66\) | −3.47792e10 | − | 3.13276e10i | −0.420780 | − | 0.379021i | ||||
\(67\) | 1.68840e10 | 0.186649 | 0.0933247 | − | 0.995636i | \(-0.470251\pi\) | ||||
0.0933247 | + | 0.995636i | \(0.470251\pi\) | |||||||
\(68\) | − | 9.50231e10i | − | 0.961116i | ||||||
\(69\) | −5.06579e7 | −0.000469410 | ||||||||
\(70\) | −6.74772e10 | −0.573547 | ||||||||
\(71\) | 1.56336e11 | 1.22042 | 0.610209 | − | 0.792240i | \(-0.291085\pi\) | ||||
0.610209 | + | 0.792240i | \(0.291085\pi\) | |||||||
\(72\) | 5.29847e10i | 0.380325i | ||||||||
\(73\) | 2.47953e11i | 1.63844i | 0.573477 | + | 0.819222i | \(0.305594\pi\) | ||||
−0.573477 | + | 0.819222i | \(0.694406\pi\) | |||||||
\(74\) | 1.39449e11i | 0.849229i | ||||||||
\(75\) | −4.86470e9 | −0.0273331 | ||||||||
\(76\) | − | 9.27282e9i | − | 0.0481205i | ||||||
\(77\) | 1.23520e11 | + | 1.11262e11i | 0.592643 | + | 0.533828i | ||||
\(78\) | 1.41469e11 | 0.628196 | ||||||||
\(79\) | − | 1.69948e11i | − | 0.699123i | −0.936913 | − | 0.349562i | \(-0.886330\pi\) | ||
0.936913 | − | 0.349562i | \(-0.113670\pi\) | |||||||
\(80\) | −6.66452e10 | −0.254231 | ||||||||
\(81\) | −1.44844e11 | −0.512851 | ||||||||
\(82\) | −5.37802e10 | −0.176905 | ||||||||
\(83\) | 4.27097e11i | 1.30635i | 0.757208 | + | 0.653173i | \(0.226563\pi\) | ||||
−0.757208 | + | 0.653173i | \(0.773437\pi\) | |||||||
\(84\) | 1.12206e11i | 0.319403i | ||||||||
\(85\) | − | 7.37237e11i | − | 1.95476i | ||||||
\(86\) | 1.53237e11 | 0.378767 | ||||||||
\(87\) | − | 3.40479e11i | − | 0.785191i | ||||||
\(88\) | 3.65990e11 | + | 3.29669e11i | 0.788085 | + | 0.709874i | ||||
\(89\) | 2.30558e11 | 0.463918 | 0.231959 | − | 0.972726i | \(-0.425487\pi\) | ||||
0.231959 | + | 0.972726i | \(0.425487\pi\) | |||||||
\(90\) | 1.37027e11i | 0.257841i | ||||||||
\(91\) | −5.02437e11 | −0.884775 | ||||||||
\(92\) | 1.77695e8 | 0.000293055 | ||||||||
\(93\) | −4.32287e11 | −0.668150 | ||||||||
\(94\) | − | 8.69328e11i | − | 1.26013i | ||||||
\(95\) | − | 7.19432e10i | − | 0.0978697i | ||||||
\(96\) | 5.54109e11i | 0.707894i | ||||||||
\(97\) | −1.43458e12 | −1.72224 | −0.861119 | − | 0.508403i | \(-0.830236\pi\) | ||||
−0.861119 | + | 0.508403i | \(0.830236\pi\) | |||||||
\(98\) | − | 2.27880e11i | − | 0.257246i | ||||||
\(99\) | 2.25941e11 | − | 2.50834e11i | 0.239985 | − | 0.266425i | ||||
\(100\) | 1.70641e10 | 0.0170641 | ||||||||
\(101\) | − | 4.36023e11i | − | 0.410754i | −0.978683 | − | 0.205377i | \(-0.934158\pi\) | ||
0.978683 | − | 0.205377i | \(-0.0658420\pi\) | |||||||
\(102\) | 1.22593e12 | 1.08859 | ||||||||
\(103\) | 4.90318e9 | 0.00410634 | 0.00205317 | − | 0.999998i | \(-0.499346\pi\) | ||||
0.00205317 | + | 0.999998i | \(0.499346\pi\) | |||||||
\(104\) | −1.48872e12 | −1.17656 | ||||||||
\(105\) | 8.70548e11i | 0.649616i | ||||||||
\(106\) | − | 4.20276e10i | − | 0.0296278i | ||||||
\(107\) | 1.09730e12i | 0.731176i | 0.930777 | + | 0.365588i | \(0.119132\pi\) | ||||
−0.930777 | + | 0.365588i | \(0.880868\pi\) | |||||||
\(108\) | 8.63314e11 | 0.544034 | ||||||||
\(109\) | − | 9.64140e11i | − | 0.574885i | −0.957798 | − | 0.287443i | \(-0.907195\pi\) | ||
0.957798 | − | 0.287443i | \(-0.0928050\pi\) | |||||||
\(110\) | 9.46511e11 | + | 8.52577e11i | 0.534281 | + | 0.481258i | ||||
\(111\) | 1.79908e12 | 0.961862 | ||||||||
\(112\) | 3.93592e11i | 0.199406i | ||||||||
\(113\) | 2.76940e12 | 1.33019 | 0.665097 | − | 0.746757i | \(-0.268390\pi\) | ||||
0.665097 | + | 0.746757i | \(0.268390\pi\) | |||||||
\(114\) | 1.19632e11 | 0.0545029 | ||||||||
\(115\) | 1.37865e9 | 0.000596027 | ||||||||
\(116\) | 1.19432e12i | 0.490198i | ||||||||
\(117\) | 1.02031e12i | 0.397755i | ||||||||
\(118\) | − | 7.30455e11i | − | 0.270584i | ||||||
\(119\) | −4.35396e12 | −1.53321 | ||||||||
\(120\) | 2.57943e12i | 0.863847i | ||||||||
\(121\) | −3.26834e11 | − | 3.12136e12i | −0.104140 | − | 0.994563i | ||||
\(122\) | −4.05204e11 | −0.122889 | ||||||||
\(123\) | 6.93838e11i | 0.200368i | ||||||||
\(124\) | 1.51635e12 | 0.417129 | ||||||||
\(125\) | −3.74685e12 | −0.982215 | ||||||||
\(126\) | 8.09252e11 | 0.202237 | ||||||||
\(127\) | − | 5.35860e12i | − | 1.27711i | −0.769575 | − | 0.638556i | \(-0.779532\pi\) | ||
0.769575 | − | 0.638556i | \(-0.220468\pi\) | |||||||
\(128\) | − | 1.16620e12i | − | 0.265164i | ||||||
\(129\) | − | 1.97696e12i | − | 0.429003i | ||||||
\(130\) | −3.85007e12 | −0.797644 | ||||||||
\(131\) | 7.33586e12i | 1.45152i | 0.687948 | + | 0.725760i | \(0.258512\pi\) | ||||
−0.687948 | + | 0.725760i | \(0.741488\pi\) | |||||||
\(132\) | 1.41772e12 | − | 1.57392e12i | 0.268008 | − | 0.297536i | ||||
\(133\) | −4.24881e11 | −0.0767639 | ||||||||
\(134\) | − | 7.64083e11i | − | 0.131981i | ||||||
\(135\) | 6.69802e12 | 1.10648 | ||||||||
\(136\) | −1.29008e13 | −2.03884 | ||||||||
\(137\) | 1.09495e13 | 1.65604 | 0.828020 | − | 0.560699i | \(-0.189467\pi\) | ||||
0.828020 | + | 0.560699i | \(0.189467\pi\) | |||||||
\(138\) | 2.29251e9i | 0.000331923i | ||||||||
\(139\) | − | 1.04640e13i | − | 1.45080i | −0.688326 | − | 0.725401i | \(-0.741654\pi\) | ||
0.688326 | − | 0.725401i | \(-0.258346\pi\) | |||||||
\(140\) | − | 3.05367e12i | − | 0.405558i | ||||||
\(141\) | −1.12155e13 | −1.42727 | ||||||||
\(142\) | − | 7.07496e12i | − | 0.862966i | ||||||
\(143\) | 7.04774e12 | + | 6.34831e12i | 0.824202 | + | 0.742406i | ||||
\(144\) | 7.99273e11 | 0.0896438 | ||||||||
\(145\) | 9.26610e12i | 0.996986i | ||||||||
\(146\) | 1.12211e13 | 1.15855 | ||||||||
\(147\) | −2.93996e12 | −0.291365 | ||||||||
\(148\) | −6.31073e12 | −0.600495 | ||||||||
\(149\) | 7.98543e12i | 0.729761i | 0.931054 | + | 0.364880i | \(0.118890\pi\) | ||||
−0.931054 | + | 0.364880i | \(0.881110\pi\) | |||||||
\(150\) | 2.20151e11i | 0.0193274i | ||||||||
\(151\) | 1.51955e13i | 1.28190i | 0.767585 | + | 0.640948i | \(0.221458\pi\) | ||||
−0.767585 | + | 0.640948i | \(0.778542\pi\) | |||||||
\(152\) | −1.25892e12 | −0.102079 | ||||||||
\(153\) | 8.84165e12i | 0.689263i | ||||||||
\(154\) | 5.03514e12 | − | 5.58989e12i | 0.377474 | − | 0.419062i | ||||
\(155\) | 1.17646e13 | 0.848375 | ||||||||
\(156\) | 6.40217e12i | 0.444201i | ||||||||
\(157\) | 1.21874e13 | 0.813793 | 0.406897 | − | 0.913474i | \(-0.366611\pi\) | ||||
0.406897 | + | 0.913474i | \(0.366611\pi\) | |||||||
\(158\) | −7.69098e12 | −0.494355 | ||||||||
\(159\) | −5.42213e11 | −0.0335573 | ||||||||
\(160\) | − | 1.50800e13i | − | 0.898839i | ||||||
\(161\) | − | 8.14199e9i | − | 0.000467493i | ||||||
\(162\) | 6.55490e12i | 0.362640i | ||||||||
\(163\) | −3.06577e13 | −1.63461 | −0.817304 | − | 0.576207i | \(-0.804532\pi\) | ||||
−0.817304 | + | 0.576207i | \(0.804532\pi\) | |||||||
\(164\) | − | 2.43381e12i | − | 0.125090i | ||||||
\(165\) | 1.09994e13 | − | 1.22113e13i | 0.545087 | − | 0.605142i | ||||
\(166\) | 1.93282e13 | 0.923727 | ||||||||
\(167\) | − | 9.57636e12i | − | 0.441471i | −0.975334 | − | 0.220735i | \(-0.929154\pi\) | ||
0.975334 | − | 0.220735i | \(-0.0708457\pi\) | |||||||
\(168\) | 1.52336e13 | 0.677557 | ||||||||
\(169\) | −5.36963e12 | −0.230475 | ||||||||
\(170\) | −3.33635e13 | −1.38222 | ||||||||
\(171\) | 8.62812e11i | 0.0345096i | ||||||||
\(172\) | 6.93470e12i | 0.267829i | ||||||||
\(173\) | − | 4.01016e13i | − | 1.49584i | −0.663789 | − | 0.747920i | \(-0.731053\pi\) | ||
0.663789 | − | 0.747920i | \(-0.268947\pi\) | |||||||
\(174\) | −1.54083e13 | −0.555214 | ||||||||
\(175\) | − | 7.81879e11i | − | 0.0272215i | ||||||
\(176\) | 4.97305e12 | − | 5.52096e12i | 0.167320 | − | 0.185754i | ||||
\(177\) | −9.42387e12 | −0.306471 | ||||||||
\(178\) | − | 1.04339e13i | − | 0.328040i | ||||||
\(179\) | 2.59046e13 | 0.787515 | 0.393757 | − | 0.919214i | \(-0.371175\pi\) | ||||
0.393757 | + | 0.919214i | \(0.371175\pi\) | |||||||
\(180\) | −6.20113e12 | −0.182321 | ||||||||
\(181\) | −4.82686e13 | −1.37276 | −0.686378 | − | 0.727245i | \(-0.740800\pi\) | ||||
−0.686378 | + | 0.727245i | \(0.740800\pi\) | |||||||
\(182\) | 2.27377e13i | 0.625631i | ||||||||
\(183\) | 5.22768e12i | 0.139188i | ||||||||
\(184\) | − | 2.41247e10i | − | 0.000621663i | ||||||
\(185\) | −4.89618e13 | −1.22131 | ||||||||
\(186\) | 1.95631e13i | 0.472454i | ||||||||
\(187\) | 6.10735e13 | + | 5.50124e13i | 1.42825 | + | 1.28650i | ||||
\(188\) | 3.93413e13 | 0.891048 | ||||||||
\(189\) | − | 3.95570e13i | − | 0.867867i | ||||||
\(190\) | −3.25578e12 | −0.0692043 | ||||||||
\(191\) | −5.63833e12 | −0.116132 | −0.0580658 | − | 0.998313i | \(-0.518493\pi\) | ||||
−0.0580658 | + | 0.998313i | \(0.518493\pi\) | |||||||
\(192\) | 3.51066e13 | 0.700780 | ||||||||
\(193\) | − | 2.63508e13i | − | 0.509859i | −0.966960 | − | 0.254929i | \(-0.917948\pi\) | ||
0.966960 | − | 0.254929i | \(-0.0820522\pi\) | |||||||
\(194\) | 6.49216e13i | 1.21781i | ||||||||
\(195\) | 4.96712e13i | 0.903435i | ||||||||
\(196\) | 1.03126e13 | 0.181900 | ||||||||
\(197\) | − | 9.38115e13i | − | 1.60494i | −0.596693 | − | 0.802470i | \(-0.703519\pi\) | ||
0.596693 | − | 0.802470i | \(-0.296481\pi\) | |||||||
\(198\) | −1.13515e13 | − | 1.02249e13i | −0.188391 | − | 0.169695i | ||||
\(199\) | 3.46444e13 | 0.557847 | 0.278923 | − | 0.960313i | \(-0.410022\pi\) | ||||
0.278923 | + | 0.960313i | \(0.410022\pi\) | |||||||
\(200\) | − | 2.31671e12i | − | 0.0361986i | ||||||
\(201\) | −9.85772e12 | −0.149486 | ||||||||
\(202\) | −1.97322e13 | −0.290447 | ||||||||
\(203\) | 5.47236e13 | 0.781985 | ||||||||
\(204\) | 5.54792e13i | 0.769749i | ||||||||
\(205\) | − | 1.88827e13i | − | 0.254414i | ||||||
\(206\) | − | 2.21893e11i | − | 0.00290362i | ||||||
\(207\) | −1.65341e10 | −0.000210164 | ||||||||
\(208\) | 2.24573e13i | 0.277318i | ||||||||
\(209\) | 5.95985e12 | + | 5.36839e12i | 0.0715085 | + | 0.0644119i | ||||
\(210\) | 3.93965e13 | 0.459348 | ||||||||
\(211\) | 1.13559e14i | 1.28685i | 0.765510 | + | 0.643423i | \(0.222487\pi\) | ||||
−0.765510 | + | 0.643423i | \(0.777513\pi\) | |||||||
\(212\) | 1.90195e12 | 0.0209500 | ||||||||
\(213\) | −9.12766e13 | −0.977422 | ||||||||
\(214\) | 4.96581e13 | 0.517020 | ||||||||
\(215\) | 5.38028e13i | 0.544721i | ||||||||
\(216\) | − | 1.17208e14i | − | 1.15407i | ||||||
\(217\) | − | 6.94793e13i | − | 0.665422i | ||||||
\(218\) | −4.36320e13 | −0.406505 | ||||||||
\(219\) | − | 1.44767e14i | − | 1.31221i | ||||||
\(220\) | −3.85832e13 | + | 4.28341e13i | −0.340300 | + | 0.377793i | ||||
\(221\) | −2.48426e14 | −2.13227 | ||||||||
\(222\) | − | 8.14172e13i | − | 0.680140i | ||||||
\(223\) | 7.27694e12 | 0.0591724 | 0.0295862 | − | 0.999562i | \(-0.490581\pi\) | ||||
0.0295862 | + | 0.999562i | \(0.490581\pi\) | |||||||
\(224\) | −8.90593e13 | −0.705003 | ||||||||
\(225\) | −1.58777e12 | −0.0122375 | ||||||||
\(226\) | − | 1.25329e14i | − | 0.940589i | ||||||
\(227\) | 1.58791e14i | 1.16057i | 0.814413 | + | 0.580285i | \(0.197059\pi\) | ||||
−0.814413 | + | 0.580285i | \(0.802941\pi\) | |||||||
\(228\) | 5.41393e12i | 0.0385393i | ||||||||
\(229\) | 6.63257e13 | 0.459906 | 0.229953 | − | 0.973202i | \(-0.426143\pi\) | ||||
0.229953 | + | 0.973202i | \(0.426143\pi\) | |||||||
\(230\) | − | 6.23905e10i | − | 0.000421455i | ||||||
\(231\) | −7.21172e13 | − | 6.49601e13i | −0.474643 | − | 0.427538i | ||||
\(232\) | 1.62146e14 | 1.03987 | ||||||||
\(233\) | − | 1.89857e14i | − | 1.18656i | −0.804995 | − | 0.593281i | \(-0.797832\pi\) | ||
0.804995 | − | 0.593281i | \(-0.202168\pi\) | |||||||
\(234\) | 4.61738e13 | 0.281255 | ||||||||
\(235\) | 3.05229e14 | 1.81225 | ||||||||
\(236\) | 3.30566e13 | 0.191331 | ||||||||
\(237\) | 9.92241e13i | 0.559922i | ||||||||
\(238\) | 1.97038e14i | 1.08415i | ||||||||
\(239\) | − | 3.28675e13i | − | 0.176351i | −0.996105 | − | 0.0881757i | \(-0.971896\pi\) | ||
0.996105 | − | 0.0881757i | \(-0.0281037\pi\) | |||||||
\(240\) | 3.89107e13 | 0.203611 | ||||||||
\(241\) | 3.63345e14i | 1.85446i | 0.374496 | + | 0.927228i | \(0.377816\pi\) | ||||
−0.374496 | + | 0.927228i | \(0.622184\pi\) | |||||||
\(242\) | −1.41257e14 | + | 1.47908e13i | −0.703262 | + | 0.0736378i | ||||
\(243\) | −1.39457e14 | −0.677332 | ||||||||
\(244\) | − | 1.83374e13i | − | 0.0868959i | ||||||
\(245\) | 8.00106e13 | 0.369957 | ||||||||
\(246\) | 3.13995e13 | 0.141681 | ||||||||
\(247\) | −2.42426e13 | −0.106757 | ||||||||
\(248\) | − | 2.05867e14i | − | 0.884865i | ||||||
\(249\) | − | 2.49361e14i | − | 1.04624i | ||||||
\(250\) | 1.69563e14i | 0.694531i | ||||||||
\(251\) | 2.63589e14 | 1.05411 | 0.527055 | − | 0.849831i | \(-0.323296\pi\) | ||||
0.527055 | + | 0.849831i | \(0.323296\pi\) | |||||||
\(252\) | 3.66225e13i | 0.143003i | ||||||||
\(253\) | −1.02874e11 | + | 1.14209e11i | −0.000392269 | + | 0.000435488i | ||||
\(254\) | −2.42503e14 | −0.903055 | ||||||||
\(255\) | 4.30435e14i | 1.56555i | ||||||||
\(256\) | −2.99067e14 | −1.06250 | ||||||||
\(257\) | 3.54050e14 | 1.22876 | 0.614379 | − | 0.789011i | \(-0.289407\pi\) | ||||
0.614379 | + | 0.789011i | \(0.289407\pi\) | |||||||
\(258\) | −8.94672e13 | −0.303351 | ||||||||
\(259\) | 2.89158e14i | 0.957935i | ||||||||
\(260\) | − | 1.74234e14i | − | 0.564018i | ||||||
\(261\) | − | 1.11128e14i | − | 0.351545i | ||||||
\(262\) | 3.31983e14 | 1.02638 | ||||||||
\(263\) | 1.07330e14i | 0.324331i | 0.986764 | + | 0.162166i | \(0.0518478\pi\) | ||||
−0.986764 | + | 0.162166i | \(0.948152\pi\) | |||||||
\(264\) | −2.13683e14 | − | 1.92477e14i | −0.631170 | − | 0.568532i | ||||
\(265\) | 1.47563e13 | 0.0426090 | ||||||||
\(266\) | 1.92279e13i | 0.0542803i | ||||||||
\(267\) | −1.34611e14 | −0.371547 | ||||||||
\(268\) | 3.45784e13 | 0.0933246 | ||||||||
\(269\) | −8.70810e13 | −0.229832 | −0.114916 | − | 0.993375i | \(-0.536660\pi\) | ||||
−0.114916 | + | 0.993375i | \(0.536660\pi\) | |||||||
\(270\) | − | 3.03118e14i | − | 0.782400i | ||||||
\(271\) | − | 5.05202e14i | − | 1.27541i | −0.770282 | − | 0.637704i | \(-0.779884\pi\) | ||
0.770282 | − | 0.637704i | \(-0.220116\pi\) | |||||||
\(272\) | 1.94608e14i | 0.480560i | ||||||||
\(273\) | 2.93347e14 | 0.708608 | ||||||||
\(274\) | − | 4.95518e14i | − | 1.17100i | ||||||
\(275\) | −9.87907e12 | + | 1.09675e13i | −0.0228413 | + | 0.0253578i | ||||
\(276\) | −1.03747e11 | −0.000234705 | ||||||||
\(277\) | 9.28827e13i | 0.205616i | 0.994701 | + | 0.102808i | \(0.0327827\pi\) | ||||
−0.994701 | + | 0.102808i | \(0.967217\pi\) | |||||||
\(278\) | −4.73546e14 | −1.02587 | ||||||||
\(279\) | −1.41093e14 | −0.299144 | ||||||||
\(280\) | −4.14580e14 | −0.860320 | ||||||||
\(281\) | − | 3.62924e14i | − | 0.737186i | −0.929591 | − | 0.368593i | \(-0.879840\pi\) | ||
0.929591 | − | 0.368593i | \(-0.120160\pi\) | |||||||
\(282\) | 5.07557e14i | 1.00923i | ||||||||
\(283\) | − | 2.03412e14i | − | 0.395966i | −0.980205 | − | 0.197983i | \(-0.936561\pi\) | ||
0.980205 | − | 0.197983i | \(-0.0634390\pi\) | |||||||
\(284\) | 3.20176e14 | 0.610208 | ||||||||
\(285\) | 4.20040e13i | 0.0783829i | ||||||||
\(286\) | 2.87292e14 | − | 3.18944e14i | 0.524961 | − | 0.582799i | ||||
\(287\) | −1.11517e14 | −0.199549 | ||||||||
\(288\) | 1.80854e14i | 0.316937i | ||||||||
\(289\) | −1.57016e15 | −2.69498 | ||||||||
\(290\) | 4.19336e14 | 0.704976 | ||||||||
\(291\) | 8.37577e14 | 1.37933 | ||||||||
\(292\) | 5.07806e14i | 0.819221i | ||||||||
\(293\) | − | 5.03086e14i | − | 0.795127i | −0.917575 | − | 0.397563i | \(-0.869856\pi\) | ||
0.917575 | − | 0.397563i | \(-0.130144\pi\) | |||||||
\(294\) | 1.33047e14i | 0.206026i | ||||||||
\(295\) | 2.56469e14 | 0.389138 | ||||||||
\(296\) | 8.56774e14i | 1.27384i | ||||||||
\(297\) | −4.99805e14 | + | 5.54871e14i | −0.728219 | + | 0.808451i | ||||
\(298\) | 3.61379e14 | 0.516019 | ||||||||
\(299\) | − | 4.64561e11i | − | 0.000650153i | ||||||
\(300\) | −9.96289e12 | −0.0136665 | ||||||||
\(301\) | 3.17748e14 | 0.427252 | ||||||||
\(302\) | 6.87669e14 | 0.906437 | ||||||||
\(303\) | 2.54572e14i | 0.328969i | ||||||||
\(304\) | 1.89908e13i | 0.0240604i | ||||||||
\(305\) | − | 1.42271e14i | − | 0.176733i | ||||||
\(306\) | 4.00128e14 | 0.487383 | ||||||||
\(307\) | 5.84980e14i | 0.698733i | 0.936986 | + | 0.349366i | \(0.113603\pi\) | ||||
−0.936986 | + | 0.349366i | \(0.886397\pi\) | |||||||
\(308\) | 2.52969e14 | + | 2.27864e14i | 0.296321 | + | 0.266914i | ||||
\(309\) | −2.86272e12 | −0.00328873 | ||||||||
\(310\) | − | 5.32407e14i | − | 0.599892i | ||||||
\(311\) | 1.16661e14 | 0.128933 | 0.0644665 | − | 0.997920i | \(-0.479465\pi\) | ||||
0.0644665 | + | 0.997920i | \(0.479465\pi\) | |||||||
\(312\) | 8.69188e14 | 0.942293 | ||||||||
\(313\) | −5.54943e14 | −0.590177 | −0.295088 | − | 0.955470i | \(-0.595349\pi\) | ||||
−0.295088 | + | 0.955470i | \(0.595349\pi\) | |||||||
\(314\) | − | 5.51540e14i | − | 0.575439i | ||||||
\(315\) | 2.84136e14i | 0.290846i | ||||||||
\(316\) | − | 3.48053e14i | − | 0.349561i | ||||||
\(317\) | 4.97730e14 | 0.490499 | 0.245250 | − | 0.969460i | \(-0.421130\pi\) | ||||
0.245250 | + | 0.969460i | \(0.421130\pi\) | |||||||
\(318\) | 2.45378e13i | 0.0237286i | ||||||||
\(319\) | −7.67614e14 | − | 6.91435e14i | −0.728449 | − | 0.656156i | ||||
\(320\) | −9.55423e14 | −0.889807 | ||||||||
\(321\) | − | 6.40657e14i | − | 0.585592i | ||||||
\(322\) | −3.68465e11 | −0.000330568 | ||||||||
\(323\) | −2.10079e14 | −0.184998 | ||||||||
\(324\) | −2.96641e14 | −0.256425 | ||||||||
\(325\) | − | 4.46120e13i | − | 0.0378575i | ||||||
\(326\) | 1.38741e15i | 1.15584i | ||||||||
\(327\) | 5.62913e14i | 0.460420i | ||||||||
\(328\) | −3.30425e14 | −0.265357 | ||||||||
\(329\) | − | 1.80262e15i | − | 1.42144i | ||||||
\(330\) | −5.52620e14 | − | 4.97777e14i | −0.427900 | − | 0.385435i | ||||
\(331\) | 3.12132e14 | 0.237340 | 0.118670 | − | 0.992934i | \(-0.462137\pi\) | ||||
0.118670 | + | 0.992934i | \(0.462137\pi\) | |||||||
\(332\) | 8.74695e14i | 0.653173i | ||||||||
\(333\) | 5.87197e14 | 0.430644 | ||||||||
\(334\) | −4.33377e14 | −0.312167 | ||||||||
\(335\) | 2.68277e14 | 0.189808 | ||||||||
\(336\) | − | 2.29798e14i | − | 0.159702i | ||||||
\(337\) | 5.21950e14i | 0.356328i | 0.984001 | + | 0.178164i | \(0.0570157\pi\) | ||||
−0.984001 | + | 0.178164i | \(0.942984\pi\) | |||||||
\(338\) | 2.43002e14i | 0.162971i | ||||||||
\(339\) | −1.61691e15 | −1.06534 | ||||||||
\(340\) | − | 1.50986e15i | − | 0.977379i | ||||||
\(341\) | −8.77874e14 | + | 9.74595e14i | −0.558349 | + | 0.619866i | ||||
\(342\) | 3.90464e13 | 0.0244020 | ||||||||
\(343\) | − | 1.77138e15i | − | 1.08780i | ||||||
\(344\) | 9.41487e14 | 0.568151 | ||||||||
\(345\) | −8.04923e11 | −0.000477353 | ||||||||
\(346\) | −1.81479e15 | −1.05772 | ||||||||
\(347\) | 2.41432e15i | 1.38299i | 0.722383 | + | 0.691493i | \(0.243047\pi\) | ||||
−0.722383 | + | 0.691493i | \(0.756953\pi\) | |||||||
\(348\) | − | 6.97301e14i | − | 0.392595i | ||||||
\(349\) | − | 9.52967e14i | − | 0.527382i | −0.964607 | − | 0.263691i | \(-0.915060\pi\) | ||
0.964607 | − | 0.263691i | \(-0.0849399\pi\) | |||||||
\(350\) | −3.53838e13 | −0.0192485 | ||||||||
\(351\) | − | 2.25702e15i | − | 1.20696i | ||||||
\(352\) | 1.24925e15 | + | 1.12527e15i | 0.656737 | + | 0.591562i | ||||
\(353\) | −9.47694e14 | −0.489801 | −0.244901 | − | 0.969548i | \(-0.578755\pi\) | ||||
−0.244901 | + | 0.969548i | \(0.578755\pi\) | |||||||
\(354\) | 4.26476e14i | 0.216708i | ||||||||
\(355\) | 2.48408e15 | 1.24107 | ||||||||
\(356\) | 4.72183e14 | 0.231959 | ||||||||
\(357\) | 2.54206e15 | 1.22794 | ||||||||
\(358\) | − | 1.17231e15i | − | 0.556857i | ||||||
\(359\) | − | 1.97930e15i | − | 0.924580i | −0.886729 | − | 0.462290i | \(-0.847028\pi\) | ||
0.886729 | − | 0.462290i | \(-0.152972\pi\) | |||||||
\(360\) | 8.41894e14i | 0.386761i | ||||||||
\(361\) | 2.19281e15 | 0.990738 | ||||||||
\(362\) | 2.18439e15i | 0.970685i | ||||||||
\(363\) | 1.90822e14 | + | 1.82241e15i | 0.0834044 | + | 0.796536i | ||||
\(364\) | −1.02899e15 | −0.442387 | ||||||||
\(365\) | 3.93982e15i | 1.66617i | ||||||||
\(366\) | 2.36578e14 | 0.0984210 | ||||||||
\(367\) | −2.92957e15 | −1.19897 | −0.599483 | − | 0.800387i | \(-0.704627\pi\) | ||||
−0.599483 | + | 0.800387i | \(0.704627\pi\) | |||||||
\(368\) | −3.63921e11 | −0.000146528 | ||||||||
\(369\) | 2.26460e14i | 0.0897083i | ||||||||
\(370\) | 2.21576e15i | 0.863599i | ||||||||
\(371\) | − | 8.71473e13i | − | 0.0334203i | ||||||
\(372\) | −8.85322e14 | −0.334075 | ||||||||
\(373\) | 2.49431e15i | 0.926185i | 0.886310 | + | 0.463093i | \(0.153260\pi\) | ||||
−0.886310 | + | 0.463093i | \(0.846740\pi\) | |||||||
\(374\) | 2.48958e15 | − | 2.76387e15i | 0.909696 | − | 1.00992i | ||||
\(375\) | 2.18760e15 | 0.786647 | ||||||||
\(376\) | − | 5.34115e15i | − | 1.89020i | ||||||
\(377\) | 3.12239e15 | 1.08752 | ||||||||
\(378\) | −1.79015e15 | −0.613675 | ||||||||
\(379\) | −1.69160e15 | −0.570773 | −0.285386 | − | 0.958413i | \(-0.592122\pi\) | ||||
−0.285386 | + | 0.958413i | \(0.592122\pi\) | |||||||
\(380\) | − | 1.47340e14i | − | 0.0489348i | ||||||
\(381\) | 3.12862e15i | 1.02283i | ||||||||
\(382\) | 2.55162e14i | 0.0821175i | ||||||||
\(383\) | −3.61809e15 | −1.14627 | −0.573135 | − | 0.819461i | \(-0.694273\pi\) | ||||
−0.573135 | + | 0.819461i | \(0.694273\pi\) | |||||||
\(384\) | 6.80886e14i | 0.212367i | ||||||||
\(385\) | 1.96266e15 | + | 1.76788e15i | 0.602672 | + | 0.542861i | ||||
\(386\) | −1.19250e15 | −0.360525 | ||||||||
\(387\) | − | 6.45256e14i | − | 0.192073i | ||||||
\(388\) | −2.93801e15 | −0.861119 | ||||||||
\(389\) | −2.41426e15 | −0.696765 | −0.348382 | − | 0.937352i | \(-0.613269\pi\) | ||||
−0.348382 | + | 0.937352i | \(0.613269\pi\) | |||||||
\(390\) | 2.24786e15 | 0.638825 | ||||||||
\(391\) | − | 4.02574e12i | − | 0.00112664i | ||||||
\(392\) | − | 1.40009e15i | − | 0.385869i | ||||||
\(393\) | − | 4.28303e15i | − | 1.16251i | ||||||
\(394\) | −4.24543e15 | −1.13486 | ||||||||
\(395\) | − | 2.70037e15i | − | 0.710953i | ||||||
\(396\) | 4.62727e14 | − | 5.13708e14i | 0.119992 | − | 0.133213i | ||||
\(397\) | 3.56388e15 | 0.910290 | 0.455145 | − | 0.890417i | \(-0.349587\pi\) | ||||
0.455145 | + | 0.890417i | \(0.349587\pi\) | |||||||
\(398\) | − | 1.56783e15i | − | 0.394457i | ||||||
\(399\) | 2.48066e14 | 0.0614795 | ||||||||
\(400\) | −3.49475e13 | −0.00853211 | ||||||||
\(401\) | −2.74552e15 | −0.660326 | −0.330163 | − | 0.943924i | \(-0.607104\pi\) | ||||
−0.330163 | + | 0.943924i | \(0.607104\pi\) | |||||||
\(402\) | 4.46110e14i | 0.105702i | ||||||||
\(403\) | − | 3.96431e15i | − | 0.925417i | ||||||
\(404\) | − | 8.92975e14i | − | 0.205377i | ||||||
\(405\) | −2.30149e15 | −0.521529 | ||||||||
\(406\) | − | 2.47651e15i | − | 0.552947i | ||||||
\(407\) | 3.65352e15 | − | 4.05605e15i | 0.803794 | − | 0.892353i | ||||
\(408\) | 7.53211e15 | 1.63289 | ||||||||
\(409\) | 6.34707e15i | 1.35592i | 0.735099 | + | 0.677959i | \(0.237135\pi\) | ||||
−0.735099 | + | 0.677959i | \(0.762865\pi\) | |||||||
\(410\) | −8.54535e14 | −0.179898 | ||||||||
\(411\) | −6.39286e15 | −1.32631 | ||||||||
\(412\) | 1.00417e13 | 0.00205317 | ||||||||
\(413\) | − | 1.51465e15i | − | 0.305220i | ||||||
\(414\) | 7.48247e11i | 0.000148608i | ||||||||
\(415\) | 6.78632e15i | 1.32845i | ||||||||
\(416\) | −5.08149e15 | −0.980463 | ||||||||
\(417\) | 6.10939e15i | 1.16193i | ||||||||
\(418\) | 2.42946e14 | − | 2.69712e14i | 0.0455461 | − | 0.0505642i | ||||
\(419\) | 1.52674e13 | 0.00282150 | 0.00141075 | − | 0.999999i | \(-0.499551\pi\) | ||||
0.00141075 | + | 0.999999i | \(0.499551\pi\) | |||||||
\(420\) | 1.78288e15i | 0.324808i | ||||||||
\(421\) | 8.78015e15 | 1.57692 | 0.788459 | − | 0.615087i | \(-0.210879\pi\) | ||||
0.788459 | + | 0.615087i | \(0.210879\pi\) | |||||||
\(422\) | 5.13910e15 | 0.909939 | ||||||||
\(423\) | −3.66060e15 | −0.639014 | ||||||||
\(424\) | − | 2.58217e14i | − | 0.0444417i | ||||||
\(425\) | − | 3.86594e14i | − | 0.0656026i | ||||||
\(426\) | 4.13071e15i | 0.691142i | ||||||||
\(427\) | −8.40220e14 | −0.138620 | ||||||||
\(428\) | 2.24726e15i | 0.365588i | ||||||||
\(429\) | −4.11482e15 | − | 3.70645e15i | −0.660095 | − | 0.594586i | ||||
\(430\) | 2.43484e15 | 0.385176 | ||||||||
\(431\) | − | 1.60776e15i | − | 0.250817i | −0.992105 | − | 0.125409i | \(-0.959976\pi\) | ||
0.992105 | − | 0.125409i | \(-0.0400242\pi\) | |||||||
\(432\) | −1.76808e15 | −0.272018 | ||||||||
\(433\) | 4.45744e15 | 0.676329 | 0.338165 | − | 0.941087i | \(-0.390194\pi\) | ||||
0.338165 | + | 0.941087i | \(0.390194\pi\) | |||||||
\(434\) | −3.14428e15 | −0.470525 | ||||||||
\(435\) | − | 5.41001e15i | − | 0.798477i | ||||||
\(436\) | − | 1.97456e15i | − | 0.287442i | ||||||
\(437\) | − | 3.92852e11i | − | 5.64079e-5i | ||||||
\(438\) | −6.55141e15 | −0.927876 | ||||||||
\(439\) | 2.62206e15i | 0.366315i | 0.983084 | + | 0.183158i | \(0.0586319\pi\) | ||||
−0.983084 | + | 0.183158i | \(0.941368\pi\) | |||||||
\(440\) | 5.81536e15 | + | 5.23823e15i | 0.801421 | + | 0.721886i | ||||
\(441\) | −9.59565e14 | −0.130450 | ||||||||
\(442\) | 1.12425e16i | 1.50774i | ||||||||
\(443\) | 4.90406e15 | 0.648833 | 0.324417 | − | 0.945914i | \(-0.394832\pi\) | ||||
0.324417 | + | 0.945914i | \(0.394832\pi\) | |||||||
\(444\) | 3.68452e15 | 0.480931 | ||||||||
\(445\) | 3.66343e15 | 0.471768 | ||||||||
\(446\) | − | 3.29317e14i | − | 0.0418412i | ||||||
\(447\) | − | 4.66229e15i | − | 0.584459i | ||||||
\(448\) | 5.64252e15i | 0.697919i | ||||||||
\(449\) | 2.07520e15 | 0.253268 | 0.126634 | − | 0.991949i | \(-0.459583\pi\) | ||||
0.126634 | + | 0.991949i | \(0.459583\pi\) | |||||||
\(450\) | 7.18545e13i | 0.00865324i | ||||||||
\(451\) | 1.56426e15 | + | 1.40902e15i | 0.185888 | + | 0.167440i | ||||
\(452\) | 5.67172e15 | 0.665096 | ||||||||
\(453\) | − | 8.87187e15i | − | 1.02666i | ||||||
\(454\) | 7.18608e15 | 0.820648 | ||||||||
\(455\) | −7.98341e15 | −0.899746 | ||||||||
\(456\) | 7.35021e14 | 0.0817543 | ||||||||
\(457\) | 4.28819e15i | 0.470736i | 0.971906 | + | 0.235368i | \(0.0756295\pi\) | ||||
−0.971906 | + | 0.235368i | \(0.924370\pi\) | |||||||
\(458\) | − | 3.00156e15i | − | 0.325203i | ||||||
\(459\) | − | 1.95586e16i | − | 2.09152i | ||||||
\(460\) | 2.82347e12 | 0.000298013 | ||||||||
\(461\) | 2.53696e15i | 0.264306i | 0.991229 | + | 0.132153i | \(0.0421891\pi\) | ||||
−0.991229 | + | 0.132153i | \(0.957811\pi\) | |||||||
\(462\) | −2.93976e15 | + | 3.26365e15i | −0.302315 | + | 0.335623i | ||||
\(463\) | −1.34919e16 | −1.36958 | −0.684791 | − | 0.728740i | \(-0.740106\pi\) | ||||
−0.684791 | + | 0.728740i | \(0.740106\pi\) | |||||||
\(464\) | − | 2.44597e15i | − | 0.245100i | ||||||
\(465\) | −6.86877e15 | −0.679456 | ||||||||
\(466\) | −8.59194e15 | −0.839027 | ||||||||
\(467\) | −2.42591e15 | −0.233869 | −0.116934 | − | 0.993140i | \(-0.537307\pi\) | ||||
−0.116934 | + | 0.993140i | \(0.537307\pi\) | |||||||
\(468\) | 2.08958e15i | 0.198877i | ||||||||
\(469\) | − | 1.58438e15i | − | 0.148875i | ||||||
\(470\) | − | 1.38131e16i | − | 1.28146i | ||||||
\(471\) | −7.11562e15 | −0.651759 | ||||||||
\(472\) | − | 4.48792e15i | − | 0.405875i | ||||||
\(473\) | −4.45709e15 | − | 4.01476e15i | −0.398001 | − | 0.358503i | ||||
\(474\) | 4.49037e15 | 0.395924 | ||||||||
\(475\) | − | 3.77257e13i | − | 0.00328455i | ||||||
\(476\) | −8.91690e15 | −0.766606 | ||||||||
\(477\) | −1.76971e14 | −0.0150242 | ||||||||
\(478\) | −1.48741e15 | −0.124699 | ||||||||
\(479\) | 4.83691e14i | 0.0400456i | 0.999800 | + | 0.0200228i | \(0.00637388\pi\) | ||||
−0.999800 | + | 0.0200228i | \(0.993626\pi\) | |||||||
\(480\) | 8.80446e15i | 0.719872i | ||||||||
\(481\) | 1.64986e16i | 1.33222i | ||||||||
\(482\) | 1.64431e16 | 1.31130 | ||||||||
\(483\) | 4.75370e12i | 0.000374411i | ||||||||
\(484\) | −6.69356e14 | − | 6.39255e15i | −0.0520697 | − | 0.497281i | ||||
\(485\) | −2.27946e16 | −1.75138 | ||||||||
\(486\) | 6.31109e15i | 0.478946i | ||||||||
\(487\) | 2.09252e16 | 1.56854 | 0.784270 | − | 0.620419i | \(-0.213038\pi\) | ||||
0.784270 | + | 0.620419i | \(0.213038\pi\) | |||||||
\(488\) | −2.48957e15 | −0.184334 | ||||||||
\(489\) | 1.78995e16 | 1.30914 | ||||||||
\(490\) | − | 3.62087e15i | − | 0.261599i | ||||||
\(491\) | 1.72260e16i | 1.22940i | 0.788759 | + | 0.614702i | \(0.210724\pi\) | ||||
−0.788759 | + | 0.614702i | \(0.789276\pi\) | |||||||
\(492\) | 1.42098e15i | 0.100184i | ||||||||
\(493\) | 2.70576e16 | 1.88455 | ||||||||
\(494\) | 1.09709e15i | 0.0754888i | ||||||||
\(495\) | 3.59007e15 | − | 3.98560e15i | 0.244046 | − | 0.270934i | ||||
\(496\) | −3.10551e15 | −0.208566 | ||||||||
\(497\) | − | 1.46705e16i | − | 0.973431i | ||||||
\(498\) | −1.12848e16 | −0.739804 | ||||||||
\(499\) | −7.15013e15 | −0.463138 | −0.231569 | − | 0.972818i | \(-0.574386\pi\) | ||||
−0.231569 | + | 0.972818i | \(0.574386\pi\) | |||||||
\(500\) | −7.67355e15 | −0.491107 | ||||||||
\(501\) | 5.59115e15i | 0.353570i | ||||||||
\(502\) | − | 1.19287e16i | − | 0.745368i | ||||||
\(503\) | 2.87430e16i | 1.77470i | 0.461100 | + | 0.887348i | \(0.347455\pi\) | ||||
−0.461100 | + | 0.887348i | \(0.652545\pi\) | |||||||
\(504\) | 4.97204e15 | 0.303355 | ||||||||
\(505\) | − | 6.92815e15i | − | 0.417704i | ||||||
\(506\) | 5.16850e12 | + | 4.65557e12i | 0.000307937 | + | 0.000277376i | ||||
\(507\) | 3.13506e15 | 0.184586 | ||||||||
\(508\) | − | 1.09744e16i | − | 0.638556i | ||||||
\(509\) | −9.99694e15 | −0.574858 | −0.287429 | − | 0.957802i | \(-0.592800\pi\) | ||||
−0.287429 | + | 0.957802i | \(0.592800\pi\) | |||||||
\(510\) | 1.94793e16 | 1.10701 | ||||||||
\(511\) | 2.32677e16 | 1.30686 | ||||||||
\(512\) | 8.75748e15i | 0.486138i | ||||||||
\(513\) | − | 1.90863e15i | − | 0.104717i | ||||||
\(514\) | − | 1.60225e16i | − | 0.868864i | ||||||
\(515\) | 7.79086e13 | 0.00417582 | ||||||||
\(516\) | − | 4.04882e15i | − | 0.214501i | ||||||
\(517\) | −2.27761e16 | + | 2.52855e16i | −1.19272 | + | 1.32412i | ||||
\(518\) | 1.30858e16 | 0.677363 | ||||||||
\(519\) | 2.34133e16i | 1.19800i | ||||||||
\(520\) | −2.36548e16 | −1.19647 | ||||||||
\(521\) | 2.47231e16 | 1.23617 | 0.618084 | − | 0.786112i | \(-0.287909\pi\) | ||||
0.618084 | + | 0.786112i | \(0.287909\pi\) | |||||||
\(522\) | −5.02908e15 | −0.248580 | ||||||||
\(523\) | − | 6.03331e15i | − | 0.294812i | −0.989076 | − | 0.147406i | \(-0.952908\pi\) | ||
0.989076 | − | 0.147406i | \(-0.0470924\pi\) | |||||||
\(524\) | 1.50238e16i | 0.725759i | ||||||||
\(525\) | 4.56500e14i | 0.0218014i | ||||||||
\(526\) | 4.85722e15 | 0.229337 | ||||||||
\(527\) | − | 3.43535e16i | − | 1.60364i | ||||||
\(528\) | −2.90351e15 | + | 3.22341e15i | −0.134005 | + | 0.148769i | ||||
\(529\) | −2.19146e16 | −1.00000 | ||||||||
\(530\) | − | 6.67793e14i | − | 0.0301291i | ||||||
\(531\) | −3.07583e15 | −0.137213 | ||||||||
\(532\) | −8.70155e14 | −0.0383819 | ||||||||
\(533\) | −6.36288e15 | −0.277518 | ||||||||
\(534\) | 6.09182e15i | 0.262724i | ||||||||
\(535\) | 1.74354e16i | 0.743548i | ||||||||
\(536\) | − | 4.69453e15i | − | 0.197972i | ||||||
\(537\) | −1.51244e16 | −0.630713 | ||||||||
\(538\) | 3.94084e15i | 0.162516i | ||||||||
\(539\) | −5.97038e15 | + | 6.62817e15i | −0.243483 | + | 0.270309i | ||||
\(540\) | 1.37175e16 | 0.553240 | ||||||||
\(541\) | − | 3.89009e16i | − | 1.55159i | −0.630986 | − | 0.775794i | \(-0.717350\pi\) | ||
0.630986 | − | 0.775794i | \(-0.282650\pi\) | |||||||
\(542\) | −2.28628e16 | −0.901850 | ||||||||
\(543\) | 2.81816e16 | 1.09943 | ||||||||
\(544\) | −4.40346e16 | −1.69903 | ||||||||
\(545\) | − | 1.53196e16i | − | 0.584613i | ||||||
\(546\) | − | 1.32754e16i | − | 0.501062i | ||||||
\(547\) | − | 2.77072e16i | − | 1.03435i | −0.855878 | − | 0.517177i | \(-0.826983\pi\) | ||
0.855878 | − | 0.517177i | \(-0.173017\pi\) | |||||||
\(548\) | 2.24245e16 | 0.828019 | ||||||||
\(549\) | 1.70625e15i | 0.0623172i | ||||||||
\(550\) | 4.96333e14 | + | 4.47076e14i | 0.0179307 | + | 0.0161512i | ||||
\(551\) | 2.64042e15 | 0.0943545 | ||||||||
\(552\) | 1.40852e13i | 0.000497885i | ||||||||
\(553\) | −1.59478e16 | −0.557635 | ||||||||
\(554\) | 4.20339e15 | 0.145392 | ||||||||
\(555\) | 2.85863e16 | 0.978138 | ||||||||
\(556\) | − | 2.14302e16i | − | 0.725401i | ||||||
\(557\) | 1.72578e16i | 0.577904i | 0.957344 | + | 0.288952i | \(0.0933067\pi\) | ||||
−0.957344 | + | 0.288952i | \(0.906693\pi\) | |||||||
\(558\) | 6.38513e15i | 0.211527i | ||||||||
\(559\) | 1.81299e16 | 0.594188 | ||||||||
\(560\) | 6.25394e15i | 0.202780i | ||||||||
\(561\) | −3.56577e16 | − | 3.21190e16i | −1.14387 | − | 1.03035i | ||||
\(562\) | −1.64241e16 | −0.521270 | ||||||||
\(563\) | 2.74432e16i | 0.861755i | 0.902410 | + | 0.430878i | \(0.141796\pi\) | ||||
−0.902410 | + | 0.430878i | \(0.858204\pi\) | |||||||
\(564\) | −2.29694e16 | −0.713632 | ||||||||
\(565\) | 4.40041e16 | 1.35270 | ||||||||
\(566\) | −9.20537e15 | −0.279990 | ||||||||
\(567\) | 1.35921e16i | 0.409060i | ||||||||
\(568\) | − | 4.34685e16i | − | 1.29445i | ||||||
\(569\) | − | 2.81521e16i | − | 0.829539i | −0.909927 | − | 0.414769i | \(-0.863862\pi\) | ||
0.909927 | − | 0.414769i | \(-0.136138\pi\) | |||||||
\(570\) | 1.90088e15 | 0.0554251 | ||||||||
\(571\) | 6.44451e16i | 1.85940i | 0.368315 | + | 0.929701i | \(0.379935\pi\) | ||||
−0.368315 | + | 0.929701i | \(0.620065\pi\) | |||||||
\(572\) | 1.44338e16 | + | 1.30013e16i | 0.412100 | + | 0.371203i | ||||
\(573\) | 3.29194e15 | 0.0930087 | ||||||||
\(574\) | 5.04670e15i | 0.141103i | ||||||||
\(575\) | 7.22938e11 | 2.00029e−5 | ||||||||
\(576\) | 1.14584e16 | 0.313753 | ||||||||
\(577\) | 7.11084e14 | 0.0192693 | 0.00963465 | − | 0.999954i | \(-0.496933\pi\) | ||||
0.00963465 | + | 0.999954i | \(0.496933\pi\) | |||||||
\(578\) | 7.10572e16i | 1.90564i | ||||||||
\(579\) | 1.53849e16i | 0.408341i | ||||||||
\(580\) | 1.89770e16i | 0.498493i | ||||||||
\(581\) | 4.00785e16 | 1.04197 | ||||||||
\(582\) | − | 3.79044e16i | − | 0.975331i | ||||||
\(583\) | −1.10111e15 | + | 1.22242e15i | −0.0280427 | + | 0.0311323i | ||||
\(584\) | 6.89422e16 | 1.73783 | ||||||||
\(585\) | 1.62120e16i | 0.404485i | ||||||||
\(586\) | −2.27671e16 | −0.562240 | ||||||||
\(587\) | −4.34217e16 | −1.06140 | −0.530698 | − | 0.847561i | \(-0.678070\pi\) | ||||
−0.530698 | + | 0.847561i | \(0.678070\pi\) | |||||||
\(588\) | −6.02103e15 | −0.145682 | ||||||||
\(589\) | − | 3.35238e15i | − | 0.0802900i | ||||||
\(590\) | − | 1.16065e16i | − | 0.275162i | ||||||
\(591\) | 5.47718e16i | 1.28538i | ||||||||
\(592\) | 1.29244e16 | 0.300249 | ||||||||
\(593\) | − | 2.06442e16i | − | 0.474755i | −0.971417 | − | 0.237378i | \(-0.923712\pi\) | ||
0.971417 | − | 0.237378i | \(-0.0762879\pi\) | |||||||
\(594\) | 2.51106e16 | + | 2.26186e16i | 0.571661 | + | 0.514929i | ||||
\(595\) | −6.91818e16 | −1.55916 | ||||||||
\(596\) | 1.63541e16i | 0.364880i | ||||||||
\(597\) | −2.02271e16 | −0.446774 | ||||||||
\(598\) | −2.10236e13 | −0.000459728 | ||||||||
\(599\) | 5.11034e16 | 1.10634 | 0.553170 | − | 0.833068i | \(-0.313418\pi\) | ||||
0.553170 | + | 0.833068i | \(0.313418\pi\) | |||||||
\(600\) | 1.35261e15i | 0.0289911i | ||||||||
\(601\) | − | 1.59698e16i | − | 0.338885i | −0.985540 | − | 0.169443i | \(-0.945803\pi\) | ||
0.985540 | − | 0.169443i | \(-0.0541967\pi\) | |||||||
\(602\) | − | 1.43796e16i | − | 0.302113i | ||||||
\(603\) | −3.21743e15 | −0.0669276 | ||||||||
\(604\) | 3.11203e16i | 0.640947i | ||||||||
\(605\) | −5.19320e15 | − | 4.95966e16i | −0.105902 | − | 1.01139i | ||||
\(606\) | 1.15206e16 | 0.232616 | ||||||||
\(607\) | − | 8.43021e16i | − | 1.68541i | −0.538374 | − | 0.842706i | \(-0.680961\pi\) | ||
0.538374 | − | 0.842706i | \(-0.319039\pi\) | |||||||
\(608\) | −4.29712e15 | −0.0850659 | ||||||||
\(609\) | −3.19503e16 | −0.626285 | ||||||||
\(610\) | −6.43844e15 | −0.124969 | ||||||||
\(611\) | − | 1.02853e17i | − | 1.97682i | ||||||
\(612\) | 1.81077e16i | 0.344631i | ||||||||
\(613\) | 5.83080e16i | 1.09892i | 0.835521 | + | 0.549459i | \(0.185166\pi\) | ||||
−0.835521 | + | 0.549459i | \(0.814834\pi\) | |||||||
\(614\) | 2.64732e16 | 0.494079 | ||||||||
\(615\) | 1.10247e16i | 0.203758i | ||||||||
\(616\) | 3.09359e16 | − | 3.43443e16i | 0.566211 | − | 0.628593i | ||||
\(617\) | −9.24355e16 | −1.67544 | −0.837718 | − | 0.546103i | \(-0.816111\pi\) | ||||
−0.837718 | + | 0.546103i | \(0.816111\pi\) | |||||||
\(618\) | 1.29552e14i | 0.00232548i | ||||||||
\(619\) | 7.32170e16 | 1.30157 | 0.650786 | − | 0.759262i | \(-0.274440\pi\) | ||||
0.650786 | + | 0.759262i | \(0.274440\pi\) | |||||||
\(620\) | 2.40939e16 | 0.424187 | ||||||||
\(621\) | 3.65751e13 | 0.000637728 | ||||||||
\(622\) | − | 5.27948e15i | − | 0.0911694i | ||||||
\(623\) | − | 2.16354e16i | − | 0.370030i | ||||||
\(624\) | − | 1.31117e16i | − | 0.222101i | ||||||
\(625\) | −6.15694e16 | −1.03296 | ||||||||
\(626\) | 2.51139e16i | 0.417318i | ||||||||
\(627\) | −3.47966e15 | − | 3.13433e15i | −0.0572705 | − | 0.0515869i | ||||
\(628\) | 2.49598e16 | 0.406896 | ||||||||
\(629\) | 1.42972e17i | 2.30858i | ||||||||
\(630\) | 1.28585e16 | 0.205659 | ||||||||
\(631\) | −8.52905e16 | −1.35121 | −0.675607 | − | 0.737262i | \(-0.736119\pi\) | ||||
−0.675607 | + | 0.737262i | \(0.736119\pi\) | |||||||
\(632\) | −4.72534e16 | −0.741533 | ||||||||
\(633\) | − | 6.63014e16i | − | 1.03062i | ||||||
\(634\) | − | 2.25247e16i | − | 0.346836i | ||||||
\(635\) | − | 8.51449e16i | − | 1.29872i | ||||||
\(636\) | −1.11045e15 | −0.0167786 | ||||||||
\(637\) | − | 2.69611e16i | − | 0.403553i | ||||||
\(638\) | −3.12908e16 | + | 3.47383e16i | −0.463973 | + | 0.515091i | ||||
\(639\) | −2.97915e16 | −0.437610 | ||||||||
\(640\) | − | 1.85302e16i | − | 0.269650i | ||||||
\(641\) | 9.80934e16 | 1.41414 | 0.707069 | − | 0.707145i | \(-0.250017\pi\) | ||||
0.707069 | + | 0.707145i | \(0.250017\pi\) | |||||||
\(642\) | −2.89928e16 | −0.414076 | ||||||||
\(643\) | 3.74612e16 | 0.530048 | 0.265024 | − | 0.964242i | \(-0.414620\pi\) | ||||
0.265024 | + | 0.964242i | \(0.414620\pi\) | |||||||
\(644\) | − | 1.66748e13i | − | 0.000233746i | ||||||
\(645\) | − | 3.14128e16i | − | 0.436262i | ||||||
\(646\) | 9.50708e15i | 0.130813i | ||||||||
\(647\) | −5.38286e15 | −0.0733816 | −0.0366908 | − | 0.999327i | \(-0.511682\pi\) | ||||
−0.0366908 | + | 0.999327i | \(0.511682\pi\) | |||||||
\(648\) | 4.02733e16i | 0.543960i | ||||||||
\(649\) | −1.91377e16 | + | 2.12462e16i | −0.256107 | + | 0.284324i | ||||
\(650\) | −2.01891e15 | −0.0267693 | ||||||||
\(651\) | 4.05655e16i | 0.532931i | ||||||||
\(652\) | −6.27869e16 | −0.817303 | ||||||||
\(653\) | −3.12894e16 | −0.403570 | −0.201785 | − | 0.979430i | \(-0.564674\pi\) | ||||
−0.201785 | + | 0.979430i | \(0.564674\pi\) | |||||||
\(654\) | 2.54745e16 | 0.325566 | ||||||||
\(655\) | 1.16562e17i | 1.47608i | ||||||||
\(656\) | 4.98447e15i | 0.0625454i | ||||||||
\(657\) | − | 4.72501e16i | − | 0.587503i | ||||||
\(658\) | −8.15772e16 | −1.00511 | ||||||||
\(659\) | 8.92827e16i | 1.09007i | 0.838413 | + | 0.545035i | \(0.183484\pi\) | ||||
−0.838413 | + | 0.545035i | \(0.816516\pi\) | |||||||
\(660\) | 2.25268e16 | − | 2.50087e16i | 0.272543 | − | 0.302571i | ||||
\(661\) | 1.06958e17 | 1.28234 | 0.641170 | − | 0.767399i | \(-0.278449\pi\) | ||||
0.641170 | + | 0.767399i | \(0.278449\pi\) | |||||||
\(662\) | − | 1.41255e16i | − | 0.167825i | ||||||
\(663\) | 1.45043e17 | 1.70772 | ||||||||
\(664\) | 1.18753e17 | 1.38559 | ||||||||
\(665\) | −6.75110e15 | −0.0780629 | ||||||||
\(666\) | − | 2.65735e16i | − | 0.304511i | ||||||
\(667\) | 5.05983e13i | 0.000574620i | ||||||||
\(668\) | − | 1.96124e16i | − | 0.220735i | ||||||
\(669\) | −4.24863e15 | −0.0473906 | ||||||||
\(670\) | − | 1.21408e16i | − | 0.134214i | ||||||
\(671\) | 1.17859e16 | + | 1.06162e16i | 0.129130 | + | 0.116315i | ||||
\(672\) | 5.19972e16 | 0.564631 | ||||||||
\(673\) | − | 7.50491e16i | − | 0.807709i | −0.914823 | − | 0.403855i | \(-0.867670\pi\) | ||
0.914823 | − | 0.403855i | \(-0.132330\pi\) | |||||||
\(674\) | 2.36208e16 | 0.251962 | ||||||||
\(675\) | 3.51232e15 | 0.0371340 | ||||||||
\(676\) | −1.09970e16 | −0.115238 | ||||||||
\(677\) | 8.14864e16i | 0.846357i | 0.906046 | + | 0.423178i | \(0.139086\pi\) | ||||
−0.906046 | + | 0.423178i | \(0.860914\pi\) | |||||||
\(678\) | 7.31731e16i | 0.753309i | ||||||||
\(679\) | 1.34620e17i | 1.37369i | ||||||||
\(680\) | −2.04985e17 | −2.07334 | ||||||||
\(681\) | − | 9.27102e16i | − | 0.929491i | ||||||
\(682\) | 4.41051e16 | + | 3.97281e16i | 0.438312 | + | 0.394813i | ||||
\(683\) | 5.33960e16 | 0.525998 | 0.262999 | − | 0.964796i | \(-0.415288\pi\) | ||||
0.262999 | + | 0.964796i | \(0.415288\pi\) | |||||||
\(684\) | 1.76704e15i | 0.0172548i | ||||||||
\(685\) | 1.73981e17 | 1.68406 | ||||||||
\(686\) | −8.01636e16 | −0.769188 | ||||||||
\(687\) | −3.87242e16 | −0.368335 | ||||||||
\(688\) | − | 1.42023e16i | − | 0.133915i | ||||||
\(689\) | − | 4.97240e15i | − | 0.0464783i | ||||||
\(690\) | 3.64267e13i | 0.000337540i | ||||||||
\(691\) | 1.48870e13 | 0.000136753 | 6.83767e−5 | − | 1.00000i | \(-0.499978\pi\) | ||||
6.83767e−5 | 1.00000i | \(0.499978\pi\) | ||||||||
\(692\) | − | 8.21280e16i | − | 0.747919i | ||||||
\(693\) | −2.35381e16 | − | 2.12021e16i | −0.212507 | − | 0.191417i | ||||
\(694\) | 1.09260e17 | 0.977919 | ||||||||
\(695\) | − | 1.66266e17i | − | 1.47535i | ||||||
\(696\) | −9.46688e16 | −0.832821 | ||||||||
\(697\) | −5.51387e16 | −0.480906 | ||||||||
\(698\) | −4.31264e16 | −0.372915 | ||||||||
\(699\) | 1.10848e17i | 0.950307i | ||||||||
\(700\) | − | 1.60129e15i | − | 0.0136107i | ||||||
\(701\) | 4.73316e16i | 0.398881i | 0.979910 | + | 0.199440i | \(0.0639124\pi\) | ||||
−0.979910 | + | 0.199440i | \(0.936088\pi\) | |||||||
\(702\) | −1.02141e17 | −0.853450 | ||||||||
\(703\) | 1.39519e16i | 0.115585i | ||||||||
\(704\) | 7.12934e16 | − | 7.91483e16i | 0.585617 | − | 0.650138i | ||||
\(705\) | −1.78208e17 | −1.45142 | ||||||||
\(706\) | 4.28877e16i | 0.346342i | ||||||||
\(707\) | −4.09161e16 | −0.327626 | ||||||||
\(708\) | −1.93001e16 | −0.153235 | ||||||||
\(709\) | −7.91916e16 | −0.623450 | −0.311725 | − | 0.950172i | \(-0.600907\pi\) | ||||
−0.311725 | + | 0.950172i | \(0.600907\pi\) | |||||||
\(710\) | − | 1.12417e17i | − | 0.877569i | ||||||
\(711\) | 3.23855e16i | 0.250687i | ||||||||
\(712\) | − | 6.41058e16i | − | 0.492059i | ||||||
\(713\) | 6.42417e13 | 0.000488967 | ||||||||
\(714\) | − | 1.15040e17i | − | 0.868283i | ||||||
\(715\) | 1.11984e17 | + | 1.00871e17i | 0.838148 | + | 0.754969i | ||||
\(716\) | 5.30526e16 | 0.393757 | ||||||||
\(717\) | 1.91897e16i | 0.141238i | ||||||||
\(718\) | −8.95728e16 | −0.653777 | ||||||||
\(719\) | −2.67561e17 | −1.93664 | −0.968320 | − | 0.249713i | \(-0.919664\pi\) | ||||
−0.968320 | + | 0.249713i | \(0.919664\pi\) | |||||||
\(720\) | 1.27000e16 | 0.0911607 | ||||||||
\(721\) | − | 4.60111e14i | − | 0.00327530i | ||||||
\(722\) | − | 9.92355e16i | − | 0.700558i | ||||||
\(723\) | − | 2.12139e17i | − | 1.48522i | ||||||
\(724\) | −9.88540e16 | −0.686377 | ||||||||
\(725\) | 4.85898e15i | 0.0334593i | ||||||||
\(726\) | 8.24727e16 | − | 8.63563e15i | 0.563236 | − | 0.0589758i | ||||
\(727\) | 1.63508e17 | 1.10747 | 0.553735 | − | 0.832693i | \(-0.313202\pi\) | ||||
0.553735 | + | 0.832693i | \(0.313202\pi\) | |||||||
\(728\) | 1.39700e17i | 0.938446i | ||||||||
\(729\) | 1.58398e17 | 1.05532 | ||||||||
\(730\) | 1.78296e17 | 1.17816 | ||||||||
\(731\) | 1.57108e17 | 1.02966 | ||||||||
\(732\) | 1.07063e16i | 0.0695941i | ||||||||
\(733\) | 1.00783e17i | 0.649775i | 0.945753 | + | 0.324888i | \(0.105326\pi\) | ||||
−0.945753 | + | 0.324888i | \(0.894674\pi\) | |||||||
\(734\) | 1.32577e17i | 0.847798i | ||||||||
\(735\) | −4.67142e16 | −0.296295 | ||||||||
\(736\) | − | 8.23456e13i | − | 0.000518052i | ||||||
\(737\) | −2.00187e16 | + | 2.22243e16i | −0.124920 | + | 0.138683i | ||||
\(738\) | 1.02484e16 | 0.0634334 | ||||||||
\(739\) | − | 5.78425e16i | − | 0.355124i | −0.984110 | − | 0.177562i | \(-0.943179\pi\) | ||
0.984110 | − | 0.177562i | \(-0.0568211\pi\) | |||||||
\(740\) | −1.00274e17 | −0.610656 | ||||||||
\(741\) | 1.41540e16 | 0.0855009 | ||||||||
\(742\) | −3.94384e15 | −0.0236317 | ||||||||
\(743\) | − | 1.39628e17i | − | 0.829927i | −0.909838 | − | 0.414964i | \(-0.863794\pi\) | ||
0.909838 | − | 0.414964i | \(-0.136206\pi\) | |||||||
\(744\) | 1.20195e17i | 0.708680i | ||||||||
\(745\) | 1.26884e17i | 0.742109i | ||||||||
\(746\) | 1.12880e17 | 0.654912 | ||||||||
\(747\) | − | 8.13881e16i | − | 0.468422i | ||||||
\(748\) | 1.25078e17 | + | 1.12665e17i | 0.714122 | + | 0.643252i | ||||
\(749\) | 1.02970e17 | 0.583201 | ||||||||
\(750\) | − | 9.89994e16i | − | 0.556244i | ||||||
\(751\) | −2.06894e17 | −1.15321 | −0.576604 | − | 0.817024i | \(-0.695623\pi\) | ||||
−0.576604 | + | 0.817024i | \(0.695623\pi\) | |||||||
\(752\) | −8.05713e16 | −0.445526 | ||||||||
\(753\) | −1.53896e17 | −0.844226 | ||||||||
\(754\) | − | 1.41303e17i | − | 0.768995i | ||||||
\(755\) | 2.41447e17i | 1.30359i | ||||||||
\(756\) | − | 8.10128e16i | − | 0.433933i | ||||||
\(757\) | 5.99623e16 | 0.318642 | 0.159321 | − | 0.987227i | \(-0.449070\pi\) | ||||
0.159321 | + | 0.987227i | \(0.449070\pi\) | |||||||
\(758\) | 7.65533e16i | 0.403598i | ||||||||
\(759\) | 6.00632e13 | − | 6.66807e13i | 0.000314165 | − | 0.000348778i | ||||
\(760\) | −2.00035e16 | −0.103806 | ||||||||
\(761\) | − | 6.17443e16i | − | 0.317899i | −0.987287 | − | 0.158949i | \(-0.949189\pi\) | ||
0.987287 | − | 0.158949i | \(-0.0508107\pi\) | |||||||
\(762\) | 1.41585e17 | 0.723249 | ||||||||
\(763\) | −9.04742e16 | −0.458540 | ||||||||
\(764\) | −1.15473e16 | −0.0580657 | ||||||||
\(765\) | 1.40488e17i | 0.700926i | ||||||||
\(766\) | 1.63736e17i | 0.810535i | ||||||||
\(767\) | − | 8.64221e16i | − | 0.424476i | ||||||
\(768\) | 1.74610e17 | 0.850946 | ||||||||
\(769\) | 4.02843e16i | 0.194795i | 0.995246 | + | 0.0973974i | \(0.0310518\pi\) | ||||
−0.995246 | + | 0.0973974i | \(0.968948\pi\) | |||||||
\(770\) | 8.00052e16 | − | 8.88199e16i | 0.383861 | − | 0.426153i | ||||
\(771\) | −2.06712e17 | −0.984101 | ||||||||
\(772\) | − | 5.39664e16i | − | 0.254929i | ||||||
\(773\) | 3.19844e17 | 1.49921 | 0.749603 | − | 0.661887i | \(-0.230244\pi\) | ||||
0.749603 | + | 0.661887i | \(0.230244\pi\) | |||||||
\(774\) | −2.92010e16 | −0.135816 | ||||||||
\(775\) | 6.16916e15 | 0.0284719 | ||||||||
\(776\) | 3.98878e17i | 1.82671i | ||||||||
\(777\) | − | 1.68825e17i | − | 0.767201i | ||||||
\(778\) | 1.09257e17i | 0.492687i | ||||||||
\(779\) | −5.38071e15 | −0.0240777 | ||||||||
\(780\) | 1.01727e17i | 0.451717i | ||||||||
\(781\) | −1.85362e17 | + | 2.05784e17i | −0.816796 | + | 0.906788i | ||||
\(782\) | −1.82184e14 | −0.000796655 | ||||||||
\(783\) | 2.45827e17i | 1.06674i | ||||||||
\(784\) | −2.11204e16 | −0.0909506 | ||||||||
\(785\) | 1.93651e17 | 0.827563 | ||||||||
\(786\) | −1.93828e17 | −0.822018 | ||||||||
\(787\) | − | 1.58026e17i | − | 0.665088i | −0.943088 | − | 0.332544i | \(-0.892093\pi\) | ||
0.943088 | − | 0.332544i | \(-0.107907\pi\) | |||||||
\(788\) | − | 1.92126e17i | − | 0.802469i | ||||||
\(789\) | − | 6.26648e16i | − | 0.259754i | ||||||
\(790\) | −1.22205e17 | −0.502720 | ||||||||
\(791\) | − | 2.59878e17i | − | 1.06099i | ||||||
\(792\) | −6.97434e16 | − | 6.28219e16i | −0.282587 | − | 0.254542i | ||||
\(793\) | −4.79408e16 | −0.192782 | ||||||||
\(794\) | − | 1.61283e17i | − | 0.643673i | ||||||
\(795\) | −8.61543e15 | −0.0341251 | ||||||||
\(796\) | 7.09517e16 | 0.278923 | ||||||||
\(797\) | 2.90707e17 | 1.13424 | 0.567121 | − | 0.823634i | \(-0.308057\pi\) | ||||
0.567121 | + | 0.823634i | \(0.308057\pi\) | |||||||
\(798\) | − | 1.12262e16i | − | 0.0434726i | ||||||
\(799\) | − | 8.91289e17i | − | 3.42561i | ||||||
\(800\) | − | 7.90769e15i | − | 0.0301654i | ||||||
\(801\) | −4.39354e16 | −0.166349 | ||||||||
\(802\) | 1.24248e17i | 0.466921i | ||||||||
\(803\) | −3.26379e17 | − | 2.93988e17i | −1.21739 | − | 1.09657i | ||||
\(804\) | −2.01886e16 | −0.0747428 | ||||||||
\(805\) | − | 1.29371e14i | − | 0.000475404i | ||||||
\(806\) | −1.79404e17 | −0.654369 | ||||||||
\(807\) | 5.08422e16 | 0.184070 | ||||||||
\(808\) | −1.21234e17 | −0.435670 | ||||||||
\(809\) | 6.90335e16i | 0.246246i | 0.992391 | + | 0.123123i | \(0.0392909\pi\) | ||||
−0.992391 | + | 0.123123i | \(0.960709\pi\) | |||||||
\(810\) | 1.04153e17i | 0.368777i | ||||||||
\(811\) | − | 9.40439e16i | − | 0.330526i | −0.986250 | − | 0.165263i | \(-0.947153\pi\) | ||
0.986250 | − | 0.165263i | \(-0.0528473\pi\) | |||||||
\(812\) | 1.12074e17 | 0.390992 | ||||||||
\(813\) | 2.94962e17i | 1.02146i | ||||||||
\(814\) | −1.83556e17 | − | 1.65339e17i | −0.630989 | − | 0.568369i | ||||
\(815\) | −4.87132e17 | −1.66227 | ||||||||
\(816\) | − | 1.13622e17i | − | 0.384876i | ||||||
\(817\) | 1.53314e16 | 0.0515523 | ||||||||
\(818\) | 2.87236e17 | 0.958780 | ||||||||
\(819\) | 9.57448e16 | 0.317257 | ||||||||
\(820\) | − | 3.86718e16i | − | 0.127207i | ||||||
\(821\) | 2.96469e17i | 0.968100i | 0.875040 | + | 0.484050i | \(0.160835\pi\) | ||||
−0.875040 | + | 0.484050i | \(0.839165\pi\) | |||||||
\(822\) | 2.89308e17i | 0.937841i | ||||||||
\(823\) | 1.43405e17 | 0.461494 | 0.230747 | − | 0.973014i | \(-0.425883\pi\) | ||||
0.230747 | + | 0.973014i | \(0.425883\pi\) | |||||||
\(824\) | − | 1.36331e15i | − | 0.00435543i | ||||||
\(825\) | 5.76789e15 | − | 6.40337e15i | 0.0182934 | − | 0.0203088i | ||||
\(826\) | −6.85454e16 | −0.215823 | ||||||||
\(827\) | 4.94576e17i | 1.54597i | 0.634426 | + | 0.772984i | \(0.281237\pi\) | ||||
−0.634426 | + | 0.772984i | \(0.718763\pi\) | |||||||
\(828\) | −3.38618e13 | −0.000105082 | ||||||||
\(829\) | 2.13899e16 | 0.0658996 | 0.0329498 | − | 0.999457i | \(-0.489510\pi\) | ||||
0.0329498 | + | 0.999457i | \(0.489510\pi\) | |||||||
\(830\) | 3.07114e17 | 0.939357 | ||||||||
\(831\) | − | 5.42295e16i | − | 0.164676i | ||||||
\(832\) | 3.21947e17i | 0.970610i | ||||||||
\(833\) | − | 2.33636e17i | − | 0.699310i | ||||||
\(834\) | 2.76480e17 | 0.821612 | ||||||||
\(835\) | − | 1.52163e17i | − | 0.448941i | ||||||
\(836\) | 1.22058e16 | + | 1.09944e16i | 0.0357542 | + | 0.0322059i | ||||
\(837\) | 3.12112e17 | 0.907732 | ||||||||
\(838\) | − | 6.90923e14i | − | 0.00199510i | ||||||
\(839\) | −4.67383e17 | −1.33999 | −0.669994 | − | 0.742367i | \(-0.733703\pi\) | ||||
−0.669994 | + | 0.742367i | \(0.733703\pi\) | |||||||
\(840\) | 2.42052e17 | 0.689022 | ||||||||
\(841\) | 1.37357e16 | 0.0388217 | ||||||||
\(842\) | − | 3.97344e17i | − | 1.11505i | ||||||
\(843\) | 2.11893e17i | 0.590406i | ||||||||
\(844\) | 2.32569e17i | 0.643423i | ||||||||
\(845\) | −8.53202e16 | −0.234375 | ||||||||
\(846\) | 1.65660e17i | 0.451851i | ||||||||
\(847\) | −2.92907e17 | + | 3.06699e16i | −0.793284 | + | 0.0830639i | ||||
\(848\) | −3.89521e15 | −0.0104750 | ||||||||
\(849\) | 1.18762e17i | 0.317125i | ||||||||
\(850\) | −1.74952e16 | −0.0463881 | ||||||||
\(851\) | −2.67360e14 | −0.000703913 | ||||||||
\(852\) | −1.86934e17 | −0.488710 | ||||||||
\(853\) | 4.39225e16i | 0.114023i | 0.998374 | + | 0.0570116i | \(0.0181572\pi\) | ||||
−0.998374 | + | 0.0570116i | \(0.981843\pi\) | |||||||
\(854\) | 3.80240e16i | 0.0980192i | ||||||||
\(855\) | 1.37096e16i | 0.0350935i | ||||||||
\(856\) | 3.05099e17 | 0.775529 | ||||||||
\(857\) | 3.73692e17i | 0.943255i | 0.881798 | + | 0.471627i | \(0.156333\pi\) | ||||
−0.881798 | + | 0.471627i | \(0.843667\pi\) | |||||||
\(858\) | −1.67735e17 | + | 1.86215e17i | −0.420436 | + | 0.466758i | ||||
\(859\) | −8.11917e16 | −0.202094 | −0.101047 | − | 0.994882i | \(-0.532219\pi\) | ||||
−0.101047 | + | 0.994882i | \(0.532219\pi\) | |||||||
\(860\) | 1.10188e17i | 0.272360i | ||||||||
\(861\) | 6.51093e16 | 0.159817 | ||||||||
\(862\) | −7.27589e16 | −0.177355 | ||||||||
\(863\) | 6.05756e17 | 1.46634 | 0.733168 | − | 0.680048i | \(-0.238041\pi\) | ||||
0.733168 | + | 0.680048i | \(0.238041\pi\) | |||||||
\(864\) | − | 4.00068e17i | − | 0.961726i | ||||||
\(865\) | − | 6.37190e17i | − | 1.52115i | ||||||
\(866\) | − | 2.01721e17i | − | 0.478237i | ||||||
\(867\) | 9.16734e17 | 2.15839 | ||||||||
\(868\) | − | 1.42294e17i | − | 0.332711i | ||||||
\(869\) | 2.23702e17 | + | 2.01501e17i | 0.519458 | + | 0.467906i | ||||
\(870\) | −2.44829e17 | −0.564609 | ||||||||
\(871\) | − | 9.04008e16i | − | 0.207044i | ||||||
\(872\) | −2.68075e17 | −0.609758 | ||||||||
\(873\) | 2.73374e17 | 0.617550 | ||||||||
\(874\) | −1.77784e13 | −3.98864e−5 | ||||||||
\(875\) | 3.51602e17i | 0.783435i | ||||||||
\(876\) | − | 2.96482e17i | − | 0.656106i | ||||||
\(877\) | 2.56337e17i | 0.563397i | 0.959503 | + | 0.281698i | \(0.0908978\pi\) | ||||
−0.959503 | + | 0.281698i | \(0.909102\pi\) | |||||||
\(878\) | 1.18661e17 | 0.259024 | ||||||||
\(879\) | 2.93726e17i | 0.636809i | ||||||||
\(880\) | 7.90187e16 | − | 8.77247e16i | 0.170151 | − | 0.188897i | ||||
\(881\) | 4.66763e16 | 0.0998255 | 0.0499127 | − | 0.998754i | \(-0.484106\pi\) | ||||
0.0499127 | + | 0.998754i | \(0.484106\pi\) | |||||||
\(882\) | 4.34250e16i | 0.0922418i | ||||||||
\(883\) | −7.55573e17 | −1.59409 | −0.797044 | − | 0.603922i | \(-0.793604\pi\) | ||||
−0.797044 | + | 0.603922i | \(0.793604\pi\) | |||||||
\(884\) | −5.08775e17 | −1.06613 | ||||||||
\(885\) | −1.49740e17 | −0.311657 | ||||||||
\(886\) | − | 2.21932e17i | − | 0.458795i | ||||||
\(887\) | 3.74340e17i | 0.768643i | 0.923199 | + | 0.384321i | \(0.125565\pi\) | ||||
−0.923199 | + | 0.384321i | \(0.874435\pi\) | |||||||
\(888\) | − | 5.00227e17i | − | 1.02021i | ||||||
\(889\) | −5.02847e17 | −1.01865 | ||||||||
\(890\) | − | 1.65788e17i | − | 0.333590i | ||||||
\(891\) | 1.71736e17 | − | 1.90658e17i | 0.343239 | − | 0.381055i | ||||
\(892\) | 1.49032e16 | 0.0295862 | ||||||||
\(893\) | − | 8.69763e16i | − | 0.171511i | ||||||
\(894\) | −2.10991e17 | −0.413275 | ||||||||
\(895\) | 4.11608e17 | 0.800840 | ||||||||
\(896\) | −1.09436e17 | −0.211500 | ||||||||
\(897\) | 2.71234e14i | 0.000520701i | ||||||||
\(898\) | − | 9.39127e16i | − | 0.179088i | ||||||
\(899\) | 4.31778e17i | 0.817905i | ||||||||
\(900\) | −3.25176e15 | −0.00611876 | ||||||||
\(901\) | − | 4.30892e16i | − | 0.0805416i | ||||||
\(902\) | 6.37652e16 | − | 7.07906e16i | 0.118398 | − | 0.131443i | ||||
\(903\) | −1.85517e17 | −0.342182 | ||||||||
\(904\) | − | 7.70020e17i | − | 1.41088i | ||||||
\(905\) | −7.66959e17 | −1.39598 | ||||||||
\(906\) | −4.01495e17 | −0.725957 | ||||||||
\(907\) | 1.34785e17 | 0.242102 | 0.121051 | − | 0.992646i | \(-0.461373\pi\) | ||||
0.121051 | + | 0.992646i | \(0.461373\pi\) | |||||||
\(908\) | 3.25204e17i | 0.580285i | ||||||||
\(909\) | 8.30890e16i | 0.147286i | ||||||||
\(910\) | 3.61288e17i | 0.636217i | ||||||||
\(911\) | 5.77555e17 | 1.01038 | 0.505188 | − | 0.863009i | \(-0.331423\pi\) | ||||
0.505188 | + | 0.863009i | \(0.331423\pi\) | |||||||
\(912\) | − | 1.10878e16i | − | 0.0192697i | ||||||
\(913\) | −5.62186e17 | − | 5.06394e17i | −0.970634 | − | 0.874306i | ||||
\(914\) | 1.94062e17 | 0.332861 | ||||||||
\(915\) | 8.30647e16i | 0.141544i | ||||||||
\(916\) | 1.35835e17 | 0.229953 | ||||||||
\(917\) | 6.88391e17 | 1.15776 | ||||||||
\(918\) | −8.85124e17 | −1.47893 | ||||||||
\(919\) | 2.03581e17i | 0.337943i | 0.985621 | + | 0.168972i | \(0.0540446\pi\) | ||||
−0.985621 | + | 0.168972i | \(0.945955\pi\) | |||||||
\(920\) | − | 3.83327e14i | − | 0.000632183i | ||||||
\(921\) | − | 3.41540e17i | − | 0.559609i | ||||||
\(922\) | 1.14810e17 | 0.186893 | ||||||||
\(923\) | − | 8.37058e17i | − | 1.35377i | ||||||
\(924\) | −1.47696e17 | − | 1.33038e17i | −0.237321 | − | 0.213769i | ||||
\(925\) | −2.56747e16 | −0.0409878 | ||||||||
\(926\) | 6.10575e17i | 0.968441i | ||||||||
\(927\) | −9.34355e14 | −0.00147243 | ||||||||
\(928\) | 5.53458e17 | 0.866556 | ||||||||
\(929\) | −7.33904e17 | −1.14168 | −0.570841 | − | 0.821061i | \(-0.693383\pi\) | ||||
−0.570841 | + | 0.821061i | \(0.693383\pi\) | |||||||
\(930\) | 3.10845e17i | 0.480448i | ||||||||
\(931\) | − | 2.27994e16i | − | 0.0350126i | ||||||
\(932\) | − | 3.88826e17i | − | 0.593281i | ||||||
\(933\) | −6.81125e16 | −0.103261 | ||||||||
\(934\) | 1.09784e17i | 0.165370i | ||||||||
\(935\) | 9.70420e17 | + | 8.74114e17i | 1.45241 | + | 1.30827i | ||||
\(936\) | 2.83692e17 | 0.421883 | ||||||||
\(937\) | − | 3.99860e17i | − | 0.590841i | −0.955367 | − | 0.295420i | \(-0.904540\pi\) | ||
0.955367 | − | 0.295420i | \(-0.0954597\pi\) | |||||||
\(938\) | −7.17010e16 | −0.105271 | ||||||||
\(939\) | 3.24003e17 | 0.472667 | ||||||||
\(940\) | 6.25109e17 | 0.906126 | ||||||||
\(941\) | 2.03014e17i | 0.292408i | 0.989254 | + | 0.146204i | \(0.0467055\pi\) | ||||
−0.989254 | + | 0.146204i | \(0.953294\pi\) | |||||||
\(942\) | 3.22016e17i | 0.460864i | ||||||||
\(943\) | − | 1.03111e14i | − | 0.000146633i | ||||||
\(944\) | −6.77002e16 | −0.0956661 | ||||||||
\(945\) | − | 6.28537e17i | − | 0.882552i | ||||||
\(946\) | −1.81687e17 | + | 2.01705e17i | −0.253500 | + | 0.281429i | ||||
\(947\) | −1.59725e17 | −0.221449 | −0.110725 | − | 0.993851i | \(-0.535317\pi\) | ||||
−0.110725 | + | 0.993851i | \(0.535317\pi\) | |||||||
\(948\) | 2.03211e17i | 0.279960i | ||||||||
\(949\) | 1.32759e18 | 1.81747 | ||||||||
\(950\) | −1.70727e15 | −0.00232253 | ||||||||
\(951\) | −2.90599e17 | −0.392836 | ||||||||
\(952\) | 1.21060e18i | 1.62622i | ||||||||
\(953\) | 3.94451e17i | 0.526545i | 0.964722 | + | 0.263272i | \(0.0848018\pi\) | ||||
−0.964722 | + | 0.263272i | \(0.915198\pi\) | |||||||
\(954\) | 8.00881e15i | 0.0106238i | ||||||||
\(955\) | −8.95897e16 | −0.118097 | ||||||||
\(956\) | − | 6.73125e16i | − | 0.0881756i | ||||||
\(957\) | 4.48171e17 | + | 4.03694e17i | 0.583408 | + | 0.525509i | ||||
\(958\) | 2.18893e16 | 0.0283165 | ||||||||
\(959\) | − | 1.02749e18i | − | 1.32089i | ||||||
\(960\) | 5.57823e17 | 0.712638 | ||||||||
\(961\) | −2.39459e17 | −0.304012 | ||||||||
\(962\) | 7.46641e17 | 0.942023 | ||||||||
\(963\) | − | 2.09102e17i | − | 0.262181i | ||||||
\(964\) | 7.44129e17i | 0.927227i | ||||||||
\(965\) | − | 4.18698e17i | − | 0.518486i | ||||||
\(966\) | 2.15128e14 | 0.000264749 | ||||||||
\(967\) | 8.27880e17i | 1.01253i | 0.862378 | + | 0.506266i | \(0.168974\pi\) | ||||
−0.862378 | + | 0.506266i | \(0.831026\pi\) | |||||||
\(968\) | −8.67882e17 | + | 9.08749e16i | −1.05489 | + | 0.110457i | ||||
\(969\) | 1.22654e17 | 0.148163 | ||||||||
\(970\) | 1.03156e18i | 1.23841i | ||||||||
\(971\) | −2.82655e17 | −0.337242 | −0.168621 | − | 0.985681i | \(-0.553931\pi\) | ||||
−0.168621 | + | 0.985681i | \(0.553931\pi\) | |||||||
\(972\) | −2.85607e17 | −0.338666 | ||||||||
\(973\) | −9.81933e17 | −1.15719 | ||||||||
\(974\) | − | 9.46967e17i | − | 1.10913i | ||||||
\(975\) | 2.60467e16i | 0.0303197i | ||||||||
\(976\) | 3.75552e16i | 0.0434481i | ||||||||
\(977\) | −1.27034e18 | −1.46068 | −0.730338 | − | 0.683086i | \(-0.760637\pi\) | ||||
−0.730338 | + | 0.683086i | \(0.760637\pi\) | |||||||
\(978\) | − | 8.10038e17i | − | 0.925704i | ||||||
\(979\) | −2.73365e17 | + | 3.03483e17i | −0.310489 | + | 0.344697i | ||||
\(980\) | 1.63862e17 | 0.184978 | ||||||||
\(981\) | 1.83727e17i | 0.206139i | ||||||||
\(982\) | 7.79559e17 | 0.869320 | ||||||||
\(983\) | −5.26692e17 | −0.583762 | −0.291881 | − | 0.956455i | \(-0.594281\pi\) | ||||
−0.291881 | + | 0.956455i | \(0.594281\pi\) | |||||||
\(984\) | 1.92919e17 | 0.212522 | ||||||||
\(985\) | − | 1.49061e18i | − | 1.63210i | ||||||
\(986\) | − | 1.22449e18i | − | 1.33258i | ||||||
\(987\) | 1.05246e18i | 1.13842i | ||||||||
\(988\) | −4.96488e16 | −0.0533786 | ||||||||
\(989\) | 2.93795e14i | 0.000313954i | ||||||||
\(990\) | −1.80368e17 | − | 1.62468e17i | −0.191579 | − | 0.172566i | ||||
\(991\) | 2.71502e17 | 0.286636 | 0.143318 | − | 0.989677i | \(-0.454223\pi\) | ||||
0.143318 | + | 0.989677i | \(0.454223\pi\) | |||||||
\(992\) | − | 7.02693e17i | − | 0.737387i | ||||||
\(993\) | −1.82238e17 | −0.190083 | ||||||||
\(994\) | −6.63909e17 | −0.688320 | ||||||||
\(995\) | 5.50479e17 | 0.567286 | ||||||||
\(996\) | − | 5.10690e17i | − | 0.523120i | ||||||
\(997\) | 1.50550e18i | 1.53289i | 0.642312 | + | 0.766443i | \(0.277975\pi\) | ||||
−0.642312 | + | 0.766443i | \(0.722025\pi\) | |||||||
\(998\) | 3.23578e17i | 0.327488i | ||||||||
\(999\) | −1.29894e18 | −1.30676 |
(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 | 11.13.b.b.10.4 | ✓ | 10 | |
3.2 | odd | 2 | 99.13.c.b.10.7 | 10 | |||
4.3 | odd | 2 | 176.13.h.c.65.8 | 10 | |||
11.10 | odd | 2 | inner | 11.13.b.b.10.7 | yes | 10 | |
33.32 | even | 2 | 99.13.c.b.10.4 | 10 | |||
44.43 | even | 2 | 176.13.h.c.65.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.13.b.b.10.4 | ✓ | 10 | 1.1 | even | 1 | trivial | |
11.13.b.b.10.7 | yes | 10 | 11.10 | odd | 2 | inner | |
99.13.c.b.10.4 | 10 | 33.32 | even | 2 | |||
99.13.c.b.10.7 | 10 | 3.2 | odd | 2 | |||
176.13.h.c.65.7 | 10 | 44.43 | even | 2 | |||
176.13.h.c.65.8 | 10 | 4.3 | odd | 2 |