Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,6,Mod(32,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.32");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.29266605383\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 195 x^{14} - 642 x^{13} + 89670 x^{12} + 53946 x^{11} + 91115757 x^{10} + \cdots + 92\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 32.1 | ||
Root | \(-2.15316 + 11.0840i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.32 |
Dual form | 33.6.d.b.32.2 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.1143 | −1.78797 | −0.893983 | − | 0.448102i | \(-0.852100\pi\) | ||||
−0.893983 | + | 0.448102i | \(0.852100\pi\) | |||||||
\(3\) | −10.9611 | − | 11.0840i | −0.703155 | − | 0.711037i | ||||
\(4\) | 70.2982 | 2.19682 | ||||||||
\(5\) | − | 88.5196i | − | 1.58349i | −0.610854 | − | 0.791744i | \(-0.709174\pi\) | ||
0.610854 | − | 0.791744i | \(-0.290826\pi\) | |||||||
\(6\) | 110.863 | + | 112.106i | 1.25722 | + | 1.27131i | ||||
\(7\) | − | 126.220i | − | 0.973605i | −0.873512 | − | 0.486803i | \(-0.838163\pi\) | ||
0.873512 | − | 0.486803i | \(-0.161837\pi\) | |||||||
\(8\) | −387.358 | −2.13987 | ||||||||
\(9\) | −2.70883 | + | 242.985i | −0.0111475 | + | 0.999938i | ||||
\(10\) | 895.310i | 2.83122i | ||||||||
\(11\) | −398.959 | + | 43.3939i | −0.994137 | + | 0.108130i | ||||
\(12\) | −770.545 | − | 779.183i | −1.54470 | − | 1.56202i | ||||
\(13\) | − | 523.100i | − | 0.858473i | −0.903192 | − | 0.429236i | \(-0.858783\pi\) | ||
0.903192 | − | 0.429236i | \(-0.141217\pi\) | |||||||
\(14\) | 1276.62i | 1.74077i | ||||||||
\(15\) | −981.149 | + | 970.272i | −1.12592 | + | 1.11344i | ||||
\(16\) | 1668.30 | 1.62920 | ||||||||
\(17\) | 1039.45 | 0.872332 | 0.436166 | − | 0.899866i | \(-0.356336\pi\) | ||||
0.436166 | + | 0.899866i | \(0.356336\pi\) | |||||||
\(18\) | 27.3978 | − | 2457.61i | 0.0199313 | − | 1.78785i | ||||
\(19\) | 842.227i | 0.535236i | 0.963525 | + | 0.267618i | \(0.0862365\pi\) | ||||
−0.963525 | + | 0.267618i | \(0.913764\pi\) | |||||||
\(20\) | − | 6222.77i | − | 3.47864i | ||||||
\(21\) | −1399.02 | + | 1383.51i | −0.692269 | + | 0.684595i | ||||
\(22\) | 4035.17 | − | 438.897i | 1.77748 | − | 0.193333i | ||||
\(23\) | 2472.99i | 0.974770i | 0.873187 | + | 0.487385i | \(0.162049\pi\) | ||||
−0.873187 | + | 0.487385i | \(0.837951\pi\) | |||||||
\(24\) | 4245.87 | + | 4293.47i | 1.50466 | + | 1.52153i | ||||
\(25\) | −4710.72 | −1.50743 | ||||||||
\(26\) | 5290.77i | 1.53492i | ||||||||
\(27\) | 2722.93 | − | 2633.36i | 0.718831 | − | 0.695185i | ||||
\(28\) | − | 8873.04i | − | 2.13883i | ||||||
\(29\) | −3569.99 | −0.788265 | −0.394133 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394133 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(30\) | 9923.59 | − | 9813.58i | 2.01310 | − | 1.99078i | ||||
\(31\) | −215.057 | −0.0401929 | −0.0200964 | − | 0.999798i | \(-0.506397\pi\) | ||||
−0.0200964 | + | 0.999798i | \(0.506397\pi\) | |||||||
\(32\) | −4478.13 | −0.773074 | ||||||||
\(33\) | 4854.00 | + | 3946.40i | 0.775916 | + | 0.630836i | ||||
\(34\) | −10513.3 | −1.55970 | ||||||||
\(35\) | −11172.9 | −1.54169 | ||||||||
\(36\) | −190.426 | + | 17081.4i | −0.0244889 | + | 2.19668i | ||||
\(37\) | −3626.51 | −0.435496 | −0.217748 | − | 0.976005i | \(-0.569871\pi\) | ||||
−0.217748 | + | 0.976005i | \(0.569871\pi\) | |||||||
\(38\) | − | 8518.50i | − | 0.956983i | ||||||
\(39\) | −5798.03 | + | 5733.75i | −0.610406 | + | 0.603639i | ||||
\(40\) | 34288.8i | 3.38846i | ||||||||
\(41\) | 8845.46 | 0.821790 | 0.410895 | − | 0.911683i | \(-0.365216\pi\) | ||||
0.410895 | + | 0.911683i | \(0.365216\pi\) | |||||||
\(42\) | 14150.0 | − | 13993.2i | 1.23775 | − | 1.22403i | ||||
\(43\) | 5262.04i | 0.433993i | 0.976172 | + | 0.216996i | \(0.0696260\pi\) | ||||
−0.976172 | + | 0.216996i | \(0.930374\pi\) | |||||||
\(44\) | −28046.1 | + | 3050.51i | −2.18394 | + | 0.237543i | ||||
\(45\) | 21508.9 | + | 239.785i | 1.58339 | + | 0.0176518i | ||||
\(46\) | − | 25012.4i | − | 1.74285i | ||||||
\(47\) | − | 9059.89i | − | 0.598244i | −0.954215 | − | 0.299122i | \(-0.903306\pi\) | ||
0.954215 | − | 0.299122i | \(-0.0966938\pi\) | |||||||
\(48\) | −18286.4 | − | 18491.4i | −1.14558 | − | 1.15842i | ||||
\(49\) | 875.528 | 0.0520931 | ||||||||
\(50\) | 47645.5 | 2.69523 | ||||||||
\(51\) | −11393.5 | − | 11521.2i | −0.613384 | − | 0.620260i | ||||
\(52\) | − | 36773.0i | − | 1.88591i | ||||||
\(53\) | − | 897.191i | − | 0.0438728i | −0.999759 | − | 0.0219364i | \(-0.993017\pi\) | ||
0.999759 | − | 0.0219364i | \(-0.00698313\pi\) | |||||||
\(54\) | −27540.4 | + | 26634.4i | −1.28525 | + | 1.24297i | ||||
\(55\) | 3841.21 | + | 35315.7i | 0.171223 | + | 1.57420i | ||||
\(56\) | 48892.3i | 2.08339i | ||||||||
\(57\) | 9335.22 | − | 9231.73i | 0.380572 | − | 0.376353i | ||||
\(58\) | 36107.8 | 1.40939 | ||||||||
\(59\) | − | 36226.0i | − | 1.35485i | −0.735593 | − | 0.677424i | \(-0.763096\pi\) | ||
0.735593 | − | 0.677424i | \(-0.236904\pi\) | |||||||
\(60\) | −68973.0 | + | 68208.4i | −2.47344 | + | 2.44602i | ||||
\(61\) | − | 15319.3i | − | 0.527125i | −0.964642 | − | 0.263563i | \(-0.915102\pi\) | ||
0.964642 | − | 0.263563i | \(-0.0848976\pi\) | |||||||
\(62\) | 2175.14 | 0.0718634 | ||||||||
\(63\) | 30669.5 | + | 341.908i | 0.973545 | + | 0.0108532i | ||||
\(64\) | −8092.58 | −0.246966 | ||||||||
\(65\) | −46304.6 | −1.35938 | ||||||||
\(66\) | −49094.6 | − | 39914.9i | −1.38731 | − | 1.12791i | ||||
\(67\) | −53380.7 | −1.45277 | −0.726385 | − | 0.687288i | \(-0.758801\pi\) | ||||
−0.726385 | + | 0.687288i | \(0.758801\pi\) | |||||||
\(68\) | 73071.6 | 1.91636 | ||||||||
\(69\) | 27410.5 | − | 27106.6i | 0.693098 | − | 0.685414i | ||||
\(70\) | 113006. | 2.75649 | ||||||||
\(71\) | 33693.5i | 0.793233i | 0.917984 | + | 0.396616i | \(0.129816\pi\) | ||||
−0.917984 | + | 0.396616i | \(0.870184\pi\) | |||||||
\(72\) | 1049.29 | − | 94122.2i | 0.0238541 | − | 2.13974i | ||||
\(73\) | − | 76140.5i | − | 1.67228i | −0.548518 | − | 0.836139i | \(-0.684808\pi\) | ||
0.548518 | − | 0.836139i | \(-0.315192\pi\) | |||||||
\(74\) | 36679.4 | 0.778652 | ||||||||
\(75\) | 51634.7 | + | 52213.5i | 1.05996 | + | 1.07184i | ||||
\(76\) | 59207.1i | 1.17582i | ||||||||
\(77\) | 5477.18 | + | 50356.5i | 0.105276 | + | 0.967897i | ||||
\(78\) | 58642.7 | − | 57992.6i | 1.09138 | − | 1.07929i | ||||
\(79\) | 106783.i | 1.92502i | 0.271251 | + | 0.962509i | \(0.412563\pi\) | ||||
−0.271251 | + | 0.962509i | \(0.587437\pi\) | |||||||
\(80\) | − | 147677.i | − | 2.57981i | ||||||
\(81\) | −59034.3 | − | 1316.41i | −0.999751 | − | 0.0222935i | ||||
\(82\) | −89465.2 | −1.46933 | ||||||||
\(83\) | −20385.5 | −0.324808 | −0.162404 | − | 0.986724i | \(-0.551925\pi\) | ||||
−0.162404 | + | 0.986724i | \(0.551925\pi\) | |||||||
\(84\) | −98348.5 | + | 97258.2i | −1.52079 | + | 1.50393i | ||||
\(85\) | − | 92011.8i | − | 1.38133i | ||||||
\(86\) | − | 53221.6i | − | 0.775964i | ||||||
\(87\) | 39131.0 | + | 39569.7i | 0.554272 | + | 0.560486i | ||||
\(88\) | 154540. | − | 16809.0i | 2.12732 | − | 0.231385i | ||||
\(89\) | 11850.9i | 0.158591i | 0.996851 | + | 0.0792953i | \(0.0252670\pi\) | ||||
−0.996851 | + | 0.0792953i | \(0.974733\pi\) | |||||||
\(90\) | −217547. | − | 2425.24i | −2.83104 | − | 0.0315609i | ||||
\(91\) | −66025.7 | −0.835813 | ||||||||
\(92\) | 173847.i | 2.14139i | ||||||||
\(93\) | 2357.26 | + | 2383.68i | 0.0282618 | + | 0.0285786i | ||||
\(94\) | 91634.1i | 1.06964i | ||||||||
\(95\) | 74553.6 | 0.847539 | ||||||||
\(96\) | 49085.2 | + | 49635.4i | 0.543591 | + | 0.549685i | ||||
\(97\) | −67716.0 | −0.730738 | −0.365369 | − | 0.930863i | \(-0.619057\pi\) | ||||
−0.365369 | + | 0.930863i | \(0.619057\pi\) | |||||||
\(98\) | −8855.32 | −0.0931406 | ||||||||
\(99\) | −9463.35 | − | 97058.5i | −0.0970414 | − | 0.995280i | ||||
\(100\) | −331155. | −3.31155 | ||||||||
\(101\) | 90346.0 | 0.881263 | 0.440631 | − | 0.897688i | \(-0.354755\pi\) | ||||
0.440631 | + | 0.897688i | \(0.354755\pi\) | |||||||
\(102\) | 115237. | + | 116529.i | 1.09671 | + | 1.10900i | ||||
\(103\) | −11291.0 | −0.104867 | −0.0524335 | − | 0.998624i | \(-0.516698\pi\) | ||||
−0.0524335 | + | 0.998624i | \(0.516698\pi\) | |||||||
\(104\) | 202627.i | 1.83702i | ||||||||
\(105\) | 122468. | + | 123841.i | 1.08405 | + | 1.09620i | ||||
\(106\) | 9074.42i | 0.0784430i | ||||||||
\(107\) | −187842. | −1.58611 | −0.793054 | − | 0.609151i | \(-0.791510\pi\) | ||||
−0.793054 | + | 0.609151i | \(0.791510\pi\) | |||||||
\(108\) | 191417. | − | 185120.i | 1.57914 | − | 1.52719i | ||||
\(109\) | − | 85380.2i | − | 0.688321i | −0.938911 | − | 0.344161i | \(-0.888164\pi\) | ||
0.938911 | − | 0.344161i | \(-0.111836\pi\) | |||||||
\(110\) | −38851.0 | − | 357192.i | −0.306140 | − | 2.81462i | ||||
\(111\) | 39750.5 | + | 40196.1i | 0.306221 | + | 0.309654i | ||||
\(112\) | − | 210572.i | − | 1.58619i | ||||||
\(113\) | − | 72617.4i | − | 0.534989i | −0.963559 | − | 0.267494i | \(-0.913804\pi\) | ||
0.963559 | − | 0.267494i | \(-0.0861957\pi\) | |||||||
\(114\) | −94418.8 | + | 93372.1i | −0.680450 | + | 0.672907i | ||||
\(115\) | 218908. | 1.54354 | ||||||||
\(116\) | −250964. | −1.73168 | ||||||||
\(117\) | 127105. | + | 1416.99i | 0.858419 | + | 0.00956978i | ||||
\(118\) | 366399.i | 2.42242i | ||||||||
\(119\) | − | 131199.i | − | 0.849307i | ||||||
\(120\) | 380056. | − | 375843.i | 2.40932 | − | 2.38261i | ||||
\(121\) | 157285. | − | 34624.8i | 0.976616 | − | 0.214992i | ||||
\(122\) | 154943.i | 0.942482i | ||||||||
\(123\) | −96955.9 | − | 98042.8i | −0.577845 | − | 0.584323i | ||||
\(124\) | −15118.1 | −0.0882965 | ||||||||
\(125\) | 140368.i | 0.803511i | ||||||||
\(126\) | −310200. | − | 3458.15i | −1.74066 | − | 0.0194052i | ||||
\(127\) | − | 151435.i | − | 0.833139i | −0.909104 | − | 0.416569i | \(-0.863232\pi\) | ||
0.909104 | − | 0.416569i | \(-0.136768\pi\) | |||||||
\(128\) | 225150. | 1.21464 | ||||||||
\(129\) | 58324.3 | − | 57677.7i | 0.308585 | − | 0.305164i | ||||
\(130\) | 468337. | 2.43052 | ||||||||
\(131\) | −206332. | −1.05048 | −0.525242 | − | 0.850953i | \(-0.676025\pi\) | ||||
−0.525242 | + | 0.850953i | \(0.676025\pi\) | |||||||
\(132\) | 341228. | + | 277425.i | 1.70455 | + | 1.38583i | ||||
\(133\) | 106306. | 0.521108 | ||||||||
\(134\) | 539906. | 2.59750 | ||||||||
\(135\) | −233104. | − | 241033.i | −1.10082 | − | 1.13826i | ||||
\(136\) | −402640. | −1.86668 | ||||||||
\(137\) | − | 275648.i | − | 1.25474i | −0.778721 | − | 0.627371i | \(-0.784131\pi\) | ||
0.778721 | − | 0.627371i | \(-0.215869\pi\) | |||||||
\(138\) | −277237. | + | 274164.i | −1.23923 | + | 1.22550i | ||||
\(139\) | − | 81387.0i | − | 0.357288i | −0.983914 | − | 0.178644i | \(-0.942829\pi\) | ||
0.983914 | − | 0.178644i | \(-0.0571710\pi\) | |||||||
\(140\) | −785438. | −3.38682 | ||||||||
\(141\) | −100420. | + | 99306.4i | −0.425374 | + | 0.420658i | ||||
\(142\) | − | 340785.i | − | 1.41827i | ||||||
\(143\) | 22699.4 | + | 208695.i | 0.0928268 | + | 0.853439i | ||||
\(144\) | −4519.13 | + | 405371.i | −0.0181614 | + | 1.62909i | ||||
\(145\) | 316014.i | 1.24821i | ||||||||
\(146\) | 770104.i | 2.98997i | ||||||||
\(147\) | −9596.74 | − | 9704.33i | −0.0366295 | − | 0.0370401i | ||||
\(148\) | −254937. | −0.956706 | ||||||||
\(149\) | 60929.5 | 0.224834 | 0.112417 | − | 0.993661i | \(-0.464141\pi\) | ||||
0.112417 | + | 0.993661i | \(0.464141\pi\) | |||||||
\(150\) | −522246. | − | 528101.i | −1.89517 | − | 1.91641i | ||||
\(151\) | 438115.i | 1.56367i | 0.623483 | + | 0.781837i | \(0.285717\pi\) | ||||
−0.623483 | + | 0.781837i | \(0.714283\pi\) | |||||||
\(152\) | − | 326243.i | − | 1.14534i | ||||||
\(153\) | −2815.70 | + | 252571.i | −0.00972428 | + | 0.872278i | ||||
\(154\) | −55397.6 | − | 509319.i | −0.188230 | − | 1.73057i | ||||
\(155\) | 19036.7i | 0.0636449i | ||||||||
\(156\) | −407591. | + | 403072.i | −1.34095 | + | 1.32609i | ||||
\(157\) | 345267. | 1.11791 | 0.558954 | − | 0.829198i | \(-0.311203\pi\) | ||||
0.558954 | + | 0.829198i | \(0.311203\pi\) | |||||||
\(158\) | − | 1.08003e6i | − | 3.44186i | ||||||
\(159\) | −9944.43 | + | 9834.19i | −0.0311952 | + | 0.0308493i | ||||
\(160\) | 396402.i | 1.22415i | ||||||||
\(161\) | 312140. | 0.949041 | ||||||||
\(162\) | 597088. | + | 13314.5i | 1.78752 | + | 0.0398600i | ||||
\(163\) | 65897.0 | 0.194266 | 0.0971330 | − | 0.995271i | \(-0.469033\pi\) | ||||
0.0971330 | + | 0.995271i | \(0.469033\pi\) | |||||||
\(164\) | 621820. | 1.80532 | ||||||||
\(165\) | 349334. | − | 429674.i | 0.998920 | − | 1.22865i | ||||
\(166\) | 206185. | 0.580746 | ||||||||
\(167\) | −685804. | −1.90287 | −0.951434 | − | 0.307852i | \(-0.900390\pi\) | ||||
−0.951434 | + | 0.307852i | \(0.900390\pi\) | |||||||
\(168\) | 541921. | − | 535913.i | 1.48137 | − | 1.46494i | ||||
\(169\) | 97659.3 | 0.263025 | ||||||||
\(170\) | 930631.i | 2.46976i | ||||||||
\(171\) | −204648. | − | 2281.45i | −0.535203 | − | 0.00596652i | ||||
\(172\) | 369912.i | 0.953404i | ||||||||
\(173\) | −331628. | −0.842434 | −0.421217 | − | 0.906960i | \(-0.638397\pi\) | ||||
−0.421217 | + | 0.906960i | \(0.638397\pi\) | |||||||
\(174\) | −395781. | − | 400218.i | −0.991019 | − | 1.00213i | ||||
\(175\) | 594587.i | 1.46764i | ||||||||
\(176\) | −665581. | + | 72393.9i | −1.61964 | + | 0.176165i | ||||
\(177\) | −401528. | + | 397077.i | −0.963347 | + | 0.952668i | ||||
\(178\) | − | 119863.i | − | 0.283554i | ||||||
\(179\) | − | 502450.i | − | 1.17209i | −0.810279 | − | 0.586044i | \(-0.800685\pi\) | ||
0.810279 | − | 0.586044i | \(-0.199315\pi\) | |||||||
\(180\) | 1.51204e6 | + | 16856.4i | 3.47842 | + | 0.0387779i | ||||
\(181\) | −815453. | −1.85013 | −0.925066 | − | 0.379808i | \(-0.875990\pi\) | ||||
−0.925066 | + | 0.379808i | \(0.875990\pi\) | |||||||
\(182\) | 667801. | 1.49440 | ||||||||
\(183\) | −169799. | + | 167916.i | −0.374806 | + | 0.370651i | ||||
\(184\) | − | 957931.i | − | 2.08588i | ||||||
\(185\) | 321017.i | 0.689602i | ||||||||
\(186\) | −23841.9 | − | 24109.2i | −0.0505311 | − | 0.0510976i | ||||
\(187\) | −414698. | + | 45105.9i | −0.867217 | + | 0.0943255i | ||||
\(188\) | − | 636894.i | − | 1.31423i | ||||||
\(189\) | −332382. | − | 343688.i | −0.676835 | − | 0.699858i | ||||
\(190\) | −754054. | −1.51537 | ||||||||
\(191\) | 527471.i | 1.04620i | 0.852271 | + | 0.523100i | \(0.175225\pi\) | ||||
−0.852271 | + | 0.523100i | \(0.824775\pi\) | |||||||
\(192\) | 88703.6 | + | 89697.9i | 0.173655 | + | 0.175602i | ||||
\(193\) | − | 572950.i | − | 1.10719i | −0.832785 | − | 0.553597i | \(-0.813255\pi\) | ||
0.832785 | − | 0.553597i | \(-0.186745\pi\) | |||||||
\(194\) | 684897. | 1.30653 | ||||||||
\(195\) | 507549. | + | 513239.i | 0.955854 | + | 0.966570i | ||||
\(196\) | 61548.1 | 0.114439 | ||||||||
\(197\) | −284594. | −0.522468 | −0.261234 | − | 0.965276i | \(-0.584129\pi\) | ||||
−0.261234 | + | 0.965276i | \(0.584129\pi\) | |||||||
\(198\) | 95714.8 | + | 981674.i | 0.173507 | + | 1.77953i | ||||
\(199\) | 425383. | 0.761461 | 0.380730 | − | 0.924686i | \(-0.375673\pi\) | ||||
0.380730 | + | 0.924686i | \(0.375673\pi\) | |||||||
\(200\) | 1.82474e6 | 3.22571 | ||||||||
\(201\) | 585110. | + | 591670.i | 1.02152 | + | 1.03297i | ||||
\(202\) | −913783. | −1.57567 | ||||||||
\(203\) | 450604.i | 0.767459i | ||||||||
\(204\) | −800944. | − | 809923.i | −1.34749 | − | 1.36260i | ||||
\(205\) | − | 782997.i | − | 1.30129i | ||||||
\(206\) | 114200. | 0.187499 | ||||||||
\(207\) | −600898. | − | 6698.90i | −0.974709 | − | 0.0108662i | ||||
\(208\) | − | 872686.i | − | 1.39862i | ||||||
\(209\) | −36547.5 | − | 336014.i | −0.0578752 | − | 0.532098i | ||||
\(210\) | −1.23867e6 | − | 1.25256e6i | −1.93824 | − | 1.95997i | ||||
\(211\) | − | 120728.i | − | 0.186682i | −0.995634 | − | 0.0933410i | \(-0.970245\pi\) | ||
0.995634 | − | 0.0933410i | \(-0.0297547\pi\) | |||||||
\(212\) | − | 63070.9i | − | 0.0963805i | ||||||
\(213\) | 373458. | − | 369318.i | 0.564018 | − | 0.557765i | ||||
\(214\) | 1.89988e6 | 2.83591 | ||||||||
\(215\) | 465793. | 0.687222 | ||||||||
\(216\) | −1.05475e6 | + | 1.02005e6i | −1.53821 | + | 1.48761i | ||||
\(217\) | 27144.5i | 0.0391320i | ||||||||
\(218\) | 863558.i | 1.23069i | ||||||||
\(219\) | −843939. | + | 834583.i | −1.18905 | + | 1.17587i | ||||
\(220\) | 270030. | + | 2.48263e6i | 0.376146 | + | 3.45824i | ||||
\(221\) | − | 543737.i | − | 0.748873i | ||||||
\(222\) | −402047. | − | 406554.i | −0.547512 | − | 0.553650i | ||||
\(223\) | 307332. | 0.413853 | 0.206926 | − | 0.978357i | \(-0.433654\pi\) | ||||
0.206926 | + | 0.978357i | \(0.433654\pi\) | |||||||
\(224\) | 565229.i | 0.752669i | ||||||||
\(225\) | 12760.6 | − | 1.14463e6i | 0.0168040 | − | 1.50734i | ||||
\(226\) | 734471.i | 0.956542i | ||||||||
\(227\) | 458186. | 0.590170 | 0.295085 | − | 0.955471i | \(-0.404652\pi\) | ||||
0.295085 | + | 0.955471i | \(0.404652\pi\) | |||||||
\(228\) | 656249. | − | 648974.i | 0.836049 | − | 0.826781i | ||||
\(229\) | 246534. | 0.310662 | 0.155331 | − | 0.987862i | \(-0.450356\pi\) | ||||
0.155331 | + | 0.987862i | \(0.450356\pi\) | |||||||
\(230\) | −2.21409e6 | −2.75979 | ||||||||
\(231\) | 498114. | − | 612672.i | 0.614185 | − | 0.755436i | ||||
\(232\) | 1.38287e6 | 1.68679 | ||||||||
\(233\) | 599273. | 0.723161 | 0.361580 | − | 0.932341i | \(-0.382237\pi\) | ||||
0.361580 | + | 0.932341i | \(0.382237\pi\) | |||||||
\(234\) | −1.28558e6 | − | 14331.8i | −1.53482 | − | 0.0171104i | ||||
\(235\) | −801978. | −0.947312 | ||||||||
\(236\) | − | 2.54663e6i | − | 2.97636i | ||||||
\(237\) | 1.18358e6 | − | 1.17046e6i | 1.36876 | − | 1.35358i | ||||
\(238\) | 1.32699e6i | 1.51853i | ||||||||
\(239\) | 357849. | 0.405234 | 0.202617 | − | 0.979258i | \(-0.435055\pi\) | ||||
0.202617 | + | 0.979258i | \(0.435055\pi\) | |||||||
\(240\) | −1.63685e6 | + | 1.61870e6i | −1.83434 | + | 1.81401i | ||||
\(241\) | 570630.i | 0.632867i | 0.948615 | + | 0.316433i | \(0.102485\pi\) | ||||
−0.948615 | + | 0.316433i | \(0.897515\pi\) | |||||||
\(242\) | −1.59082e6 | + | 350204.i | −1.74615 | + | 0.384399i | ||||
\(243\) | 632490. | + | 668764.i | 0.687128 | + | 0.726536i | ||||
\(244\) | − | 1.07692e6i | − | 1.15800i | ||||||
\(245\) | − | 77501.4i | − | 0.0824887i | ||||||
\(246\) | 980637. | + | 991630.i | 1.03317 | + | 1.04475i | ||||
\(247\) | 440569. | 0.459485 | ||||||||
\(248\) | 83304.0 | 0.0860076 | ||||||||
\(249\) | 223448. | + | 225953.i | 0.228390 | + | 0.230951i | ||||
\(250\) | − | 1.41971e6i | − | 1.43665i | ||||||
\(251\) | − | 823625.i | − | 0.825173i | −0.910918 | − | 0.412587i | \(-0.864625\pi\) | ||
0.910918 | − | 0.412587i | \(-0.135375\pi\) | |||||||
\(252\) | 2.15601e6 | + | 24035.6i | 2.13870 | + | 0.0238426i | ||||
\(253\) | −107313. | − | 986619.i | −0.105402 | − | 0.969055i | ||||
\(254\) | 1.53165e6i | 1.48962i | ||||||||
\(255\) | −1.01986e6 | + | 1.00855e6i | −0.982174 | + | 0.971286i | ||||
\(256\) | −2.01827e6 | −1.92477 | ||||||||
\(257\) | 1.66449e6i | 1.57198i | 0.618238 | + | 0.785991i | \(0.287847\pi\) | ||||
−0.618238 | + | 0.785991i | \(0.712153\pi\) | |||||||
\(258\) | −589907. | + | 583367.i | −0.551739 | + | 0.545623i | ||||
\(259\) | 457737.i | 0.424001i | ||||||||
\(260\) | −3.25513e6 | −2.98631 | ||||||||
\(261\) | 9670.51 | − | 867454.i | 0.00878715 | − | 0.788216i | ||||
\(262\) | 2.08690e6 | 1.87823 | ||||||||
\(263\) | −612387. | −0.545929 | −0.272965 | − | 0.962024i | \(-0.588004\pi\) | ||||
−0.272965 | + | 0.962024i | \(0.588004\pi\) | |||||||
\(264\) | −1.88024e6 | − | 1.52867e6i | −1.66036 | − | 1.34991i | ||||
\(265\) | −79419.0 | −0.0694720 | ||||||||
\(266\) | −1.07520e6 | −0.931723 | ||||||||
\(267\) | 131355. | − | 129899.i | 0.112764 | − | 0.111514i | ||||
\(268\) | −3.75257e6 | −3.19147 | ||||||||
\(269\) | − | 662606.i | − | 0.558309i | −0.960246 | − | 0.279155i | \(-0.909946\pi\) | ||
0.960246 | − | 0.279155i | \(-0.0900542\pi\) | |||||||
\(270\) | 2.35767e6 | + | 2.43787e6i | 1.96822 | + | 2.03517i | ||||
\(271\) | − | 1.01210e6i | − | 0.837144i | −0.908184 | − | 0.418572i | \(-0.862531\pi\) | ||
0.908184 | − | 0.418572i | \(-0.137469\pi\) | |||||||
\(272\) | 1.73411e6 | 1.42120 | ||||||||
\(273\) | 723713. | + | 731826.i | 0.587706 | + | 0.594294i | ||||
\(274\) | 2.78798e6i | 2.24343i | ||||||||
\(275\) | 1.87938e6 | − | 204417.i | 1.49859 | − | 0.162999i | ||||
\(276\) | 1.92691e6 | − | 1.90555e6i | 1.52261 | − | 1.50573i | ||||
\(277\) | 2.02312e6i | 1.58425i | 0.610360 | + | 0.792124i | \(0.291025\pi\) | ||||
−0.610360 | + | 0.792124i | \(0.708975\pi\) | |||||||
\(278\) | 823169.i | 0.638818i | ||||||||
\(279\) | 582.553 | − | 52255.6i | 0.000448048 | − | 0.0401904i | ||||
\(280\) | 4.32793e6 | 3.29902 | ||||||||
\(281\) | −818601. | −0.618453 | −0.309226 | − | 0.950988i | \(-0.600070\pi\) | ||||
−0.309226 | + | 0.950988i | \(0.600070\pi\) | |||||||
\(282\) | 1.01567e6 | − | 1.00441e6i | 0.760554 | − | 0.752122i | ||||
\(283\) | − | 1.73555e6i | − | 1.28816i | −0.764957 | − | 0.644081i | \(-0.777240\pi\) | ||
0.764957 | − | 0.644081i | \(-0.222760\pi\) | |||||||
\(284\) | 2.36860e6i | 1.74259i | ||||||||
\(285\) | −817189. | − | 826350.i | −0.595951 | − | 0.602632i | ||||
\(286\) | −229587. | − | 2.11080e6i | −0.165971 | − | 1.52592i | ||||
\(287\) | − | 1.11647e6i | − | 0.800099i | ||||||
\(288\) | 12130.5 | − | 1.08812e6i | 0.00861781 | − | 0.773026i | ||||
\(289\) | −339398. | −0.239037 | ||||||||
\(290\) | − | 3.19625e6i | − | 2.23175i | ||||||
\(291\) | 742241. | + | 750562.i | 0.513822 | + | 0.519582i | ||||
\(292\) | − | 5.35254e6i | − | 3.67369i | ||||||
\(293\) | 2.61963e6 | 1.78267 | 0.891336 | − | 0.453344i | \(-0.149769\pi\) | ||||
0.891336 | + | 0.453344i | \(0.149769\pi\) | |||||||
\(294\) | 97063.9 | + | 98152.1i | 0.0654922 | + | 0.0662264i | ||||
\(295\) | −3.20671e6 | −2.14538 | ||||||||
\(296\) | 1.40476e6 | 0.931905 | ||||||||
\(297\) | −972064. | + | 1.16876e6i | −0.639446 | + | 0.768836i | ||||
\(298\) | −616257. | −0.401995 | ||||||||
\(299\) | 1.29362e6 | 0.836813 | ||||||||
\(300\) | 3.62983e6 | + | 3.67052e6i | 2.32853 | + | 2.35464i | ||||
\(301\) | 664174. | 0.422538 | ||||||||
\(302\) | − | 4.43121e6i | − | 2.79579i | ||||||
\(303\) | −990291. | − | 1.00139e6i | −0.619664 | − | 0.626610i | ||||
\(304\) | 1.40508e6i | 0.872004i | ||||||||
\(305\) | −1.35606e6 | −0.834696 | ||||||||
\(306\) | 28478.7 | − | 2.55457e6i | 0.0173867 | − | 1.55960i | ||||
\(307\) | 103438.i | 0.0626377i | 0.999509 | + | 0.0313188i | \(0.00997072\pi\) | ||||
−0.999509 | + | 0.0313188i | \(0.990029\pi\) | |||||||
\(308\) | 385036. | + | 3.53997e6i | 0.231273 | + | 2.12629i | ||||
\(309\) | 123762. | + | 125149.i | 0.0737377 | + | 0.0745643i | ||||
\(310\) | − | 192543.i | − | 0.113795i | ||||||
\(311\) | − | 1.12357e6i | − | 0.658716i | −0.944205 | − | 0.329358i | \(-0.893168\pi\) | ||
0.944205 | − | 0.329358i | \(-0.106832\pi\) | |||||||
\(312\) | 2.24591e6 | − | 2.22101e6i | 1.30619 | − | 1.29171i | ||||
\(313\) | −1.99753e6 | −1.15248 | −0.576239 | − | 0.817281i | \(-0.695480\pi\) | ||||
−0.576239 | + | 0.817281i | \(0.695480\pi\) | |||||||
\(314\) | −3.49212e6 | −1.99878 | ||||||||
\(315\) | 30265.6 | − | 2.71486e6i | 0.0171859 | − | 1.54160i | ||||
\(316\) | 7.50666e6i | 4.22892i | ||||||||
\(317\) | 2.55991e6i | 1.43079i | 0.698720 | + | 0.715395i | \(0.253753\pi\) | ||||
−0.698720 | + | 0.715395i | \(0.746247\pi\) | |||||||
\(318\) | 100581. | − | 99465.5i | 0.0557759 | − | 0.0551575i | ||||
\(319\) | 1.42428e6 | − | 154916.i | 0.783643 | − | 0.0852353i | ||||
\(320\) | 716352.i | 0.391067i | ||||||||
\(321\) | 2.05895e6 | + | 2.08203e6i | 1.11528 | + | 1.12778i | ||||
\(322\) | −3.15707e6 | −1.69685 | ||||||||
\(323\) | 875454.i | 0.466903i | ||||||||
\(324\) | −4.15001e6 | − | 92541.3i | −2.19627 | − | 0.0489748i | ||||
\(325\) | 2.46418e6i | 1.29409i | ||||||||
\(326\) | −666499. | −0.347341 | ||||||||
\(327\) | −946352. | + | 935861.i | −0.489422 | + | 0.483996i | ||||
\(328\) | −3.42636e6 | −1.75852 | ||||||||
\(329\) | −1.14354e6 | −0.582454 | ||||||||
\(330\) | −3.53325e6 | + | 4.34584e6i | −1.78603 | + | 2.19679i | ||||
\(331\) | −537352. | −0.269581 | −0.134790 | − | 0.990874i | \(-0.543036\pi\) | ||||
−0.134790 | + | 0.990874i | \(0.543036\pi\) | |||||||
\(332\) | −1.43307e6 | −0.713545 | ||||||||
\(333\) | 9823.59 | − | 881186.i | 0.00485467 | − | 0.435469i | ||||
\(334\) | 6.93640e6 | 3.40226 | ||||||||
\(335\) | 4.72524e6i | 2.30044i | ||||||||
\(336\) | −2.33398e6 | + | 2.30810e6i | −1.12784 | + | 1.11534i | ||||
\(337\) | − | 156793.i | − | 0.0752058i | −0.999293 | − | 0.0376029i | \(-0.988028\pi\) | ||
0.999293 | − | 0.0376029i | \(-0.0119722\pi\) | |||||||
\(338\) | −987752. | −0.470279 | ||||||||
\(339\) | −804889. | + | 795966.i | −0.380397 | + | 0.376180i | ||||
\(340\) | − | 6.46827e6i | − | 3.03453i | ||||||
\(341\) | 85798.8 | − | 9332.16i | 0.0399572 | − | 0.00434606i | ||||
\(342\) | 2.06987e6 | + | 23075.2i | 0.956923 | + | 0.0106679i | ||||
\(343\) | − | 2.23189e6i | − | 1.02432i | ||||||
\(344\) | − | 2.03829e6i | − | 0.928689i | ||||||
\(345\) | −2.39947e6 | − | 2.42637e6i | −1.08534 | − | 1.09751i | ||||
\(346\) | 3.35417e6 | 1.50624 | ||||||||
\(347\) | 1.90705e6 | 0.850235 | 0.425117 | − | 0.905138i | \(-0.360233\pi\) | ||||
0.425117 | + | 0.905138i | \(0.360233\pi\) | |||||||
\(348\) | 2.75084e6 | + | 2.78168e6i | 1.21764 | + | 1.23129i | ||||
\(349\) | 444271.i | 0.195247i | 0.995223 | + | 0.0976236i | \(0.0311241\pi\) | ||||
−0.995223 | + | 0.0976236i | \(0.968876\pi\) | |||||||
\(350\) | − | 6.01381e6i | − | 2.62409i | ||||||
\(351\) | −1.37751e6 | − | 1.42436e6i | −0.596797 | − | 0.617097i | ||||
\(352\) | 1.78659e6 | − | 194323.i | 0.768542 | − | 0.0835927i | ||||
\(353\) | − | 3.40494e6i | − | 1.45436i | −0.686444 | − | 0.727182i | \(-0.740829\pi\) | ||
0.686444 | − | 0.727182i | \(-0.259171\pi\) | |||||||
\(354\) | 4.06116e6 | − | 4.01614e6i | 1.72243 | − | 1.70334i | ||||
\(355\) | 2.98254e6 | 1.25607 | ||||||||
\(356\) | 833099.i | 0.348395i | ||||||||
\(357\) | −1.45421e6 | + | 1.43809e6i | −0.603889 | + | 0.597194i | ||||
\(358\) | 5.08191e6i | 2.09565i | ||||||||
\(359\) | −585269. | −0.239673 | −0.119837 | − | 0.992794i | \(-0.538237\pi\) | ||||
−0.119837 | + | 0.992794i | \(0.538237\pi\) | |||||||
\(360\) | −8.33166e6 | − | 92882.5i | −3.38825 | − | 0.0377727i | ||||
\(361\) | 1.76675e6 | 0.713523 | ||||||||
\(362\) | 8.24770e6 | 3.30797 | ||||||||
\(363\) | −2.10779e6 | − | 1.36382e6i | −0.839579 | − | 0.543237i | ||||
\(364\) | −4.64149e6 | −1.83613 | ||||||||
\(365\) | −6.73993e6 | −2.64803 | ||||||||
\(366\) | 1.71739e6 | − | 1.69835e6i | 0.670140 | − | 0.662710i | ||||
\(367\) | −314950. | −0.122061 | −0.0610304 | − | 0.998136i | \(-0.519439\pi\) | ||||
−0.0610304 | + | 0.998136i | \(0.519439\pi\) | |||||||
\(368\) | 4.12568e6i | 1.58809i | ||||||||
\(369\) | −23960.9 | + | 2.14931e6i | −0.00916086 | + | 0.821739i | ||||
\(370\) | − | 3.24685e6i | − | 1.23298i | ||||||
\(371\) | −113243. | −0.0427148 | ||||||||
\(372\) | 165711. | + | 167569.i | 0.0620861 | + | 0.0627821i | ||||
\(373\) | 2.27086e6i | 0.845121i | 0.906335 | + | 0.422561i | \(0.138869\pi\) | ||||
−0.906335 | + | 0.422561i | \(0.861131\pi\) | |||||||
\(374\) | 4.19436e6 | − | 456212.i | 1.55055 | − | 0.168651i | ||||
\(375\) | 1.55583e6 | − | 1.53858e6i | 0.571326 | − | 0.564992i | ||||
\(376\) | 3.50942e6i | 1.28017i | ||||||||
\(377\) | 1.86746e6i | 0.676704i | ||||||||
\(378\) | 3.36180e6 | + | 3.47615e6i | 1.21016 | + | 1.25132i | ||||
\(379\) | 3.88525e6 | 1.38938 | 0.694691 | − | 0.719309i | \(-0.255541\pi\) | ||||
0.694691 | + | 0.719309i | \(0.255541\pi\) | |||||||
\(380\) | 5.24099e6 | 1.86189 | ||||||||
\(381\) | −1.67850e6 | + | 1.65989e6i | −0.592392 | + | 0.585825i | ||||
\(382\) | − | 5.33498e6i | − | 1.87057i | ||||||
\(383\) | − | 2.31613e6i | − | 0.806801i | −0.915023 | − | 0.403401i | \(-0.867828\pi\) | ||
0.915023 | − | 0.403401i | \(-0.132172\pi\) | |||||||
\(384\) | −2.46790e6 | − | 2.49556e6i | −0.854080 | − | 0.863655i | ||||
\(385\) | 4.45754e6 | − | 484838.i | 1.53265 | − | 0.166703i | ||||
\(386\) | 5.79497e6i | 1.97962i | ||||||||
\(387\) | −1.27860e6 | − | 14254.0i | −0.433966 | − | 0.00483792i | ||||
\(388\) | −4.76031e6 | −1.60530 | ||||||||
\(389\) | − | 3.97451e6i | − | 1.33171i | −0.746081 | − | 0.665855i | \(-0.768067\pi\) | ||
0.746081 | − | 0.665855i | \(-0.231933\pi\) | |||||||
\(390\) | −5.13348e6 | − | 5.19103e6i | −1.70903 | − | 1.72819i | ||||
\(391\) | 2.57055e6i | 0.850323i | ||||||||
\(392\) | −339143. | −0.111472 | ||||||||
\(393\) | 2.26163e6 | + | 2.28698e6i | 0.738652 | + | 0.746933i | ||||
\(394\) | 2.87845e6 | 0.934154 | ||||||||
\(395\) | 9.45240e6 | 3.04824 | ||||||||
\(396\) | −665257. | − | 6.82304e6i | −0.213182 | − | 2.18645i | ||||
\(397\) | −2.41352e6 | −0.768554 | −0.384277 | − | 0.923218i | \(-0.625549\pi\) | ||||
−0.384277 | + | 0.923218i | \(0.625549\pi\) | |||||||
\(398\) | −4.30243e6 | −1.36146 | ||||||||
\(399\) | −1.16523e6 | − | 1.17829e6i | −0.366420 | − | 0.370527i | ||||
\(400\) | −7.85888e6 | −2.45590 | ||||||||
\(401\) | − | 2.99915e6i | − | 0.931402i | −0.884942 | − | 0.465701i | \(-0.845802\pi\) | ||
0.884942 | − | 0.465701i | \(-0.154198\pi\) | |||||||
\(402\) | −5.91796e6 | − | 5.98430e6i | −1.82645 | − | 1.84692i | ||||
\(403\) | 112496.i | 0.0345045i | ||||||||
\(404\) | 6.35116e6 | 1.93598 | ||||||||
\(405\) | −116528. | + | 5.22570e6i | −0.0353015 | + | 1.58309i | ||||
\(406\) | − | 4.55753e6i | − | 1.37219i | ||||||
\(407\) | 1.44683e6 | − | 157368.i | 0.432943 | − | 0.0470903i | ||||
\(408\) | 4.41337e6 | + | 4.46285e6i | 1.31256 | + | 1.32728i | ||||
\(409\) | − | 3.05264e6i | − | 0.902335i | −0.892439 | − | 0.451167i | \(-0.851008\pi\) | ||
0.892439 | − | 0.451167i | \(-0.148992\pi\) | |||||||
\(410\) | 7.91943e6i | 2.32667i | ||||||||
\(411\) | −3.05528e6 | + | 3.02141e6i | −0.892168 | + | 0.882277i | ||||
\(412\) | −793736. | −0.230374 | ||||||||
\(413\) | −4.57245e6 | −1.31909 | ||||||||
\(414\) | 6.07764e6 | + | 67754.4i | 1.74275 | + | 0.0194284i | ||||
\(415\) | 1.80452e6i | 0.514330i | ||||||||
\(416\) | 2.34251e6i | 0.663663i | ||||||||
\(417\) | −902091. | + | 892090.i | −0.254045 | + | 0.251228i | ||||
\(418\) | 369651. | + | 3.39853e6i | 0.103479 | + | 0.951372i | ||||
\(419\) | − | 1.96679e6i | − | 0.547296i | −0.961830 | − | 0.273648i | \(-0.911770\pi\) | ||
0.961830 | − | 0.273648i | \(-0.0882304\pi\) | |||||||
\(420\) | 8.60926e6 | + | 8.70577e6i | 2.38146 | + | 2.40815i | ||||
\(421\) | 3.03122e6 | 0.833514 | 0.416757 | − | 0.909018i | \(-0.363167\pi\) | ||||
0.416757 | + | 0.909018i | \(0.363167\pi\) | |||||||
\(422\) | 1.22108e6i | 0.333781i | ||||||||
\(423\) | 2.20142e6 | + | 24541.7i | 0.598207 | + | 0.00666890i | ||||
\(424\) | 347534.i | 0.0938821i | ||||||||
\(425\) | −4.89657e6 | −1.31498 | ||||||||
\(426\) | −3.77725e6 | + | 3.73538e6i | −1.00844 | + | 0.997265i | ||||
\(427\) | −1.93360e6 | −0.513212 | ||||||||
\(428\) | −1.32049e7 | −3.48439 | ||||||||
\(429\) | 2.06436e6 | − | 2.53913e6i | 0.541555 | − | 0.666103i | ||||
\(430\) | −4.71116e6 | −1.22873 | ||||||||
\(431\) | 1.36368e6 | 0.353605 | 0.176802 | − | 0.984246i | \(-0.443425\pi\) | ||||
0.176802 | + | 0.984246i | \(0.443425\pi\) | |||||||
\(432\) | 4.54265e6 | − | 4.39322e6i | 1.17112 | − | 1.13259i | ||||
\(433\) | −5.36351e6 | −1.37477 | −0.687384 | − | 0.726295i | \(-0.741241\pi\) | ||||
−0.687384 | + | 0.726295i | \(0.741241\pi\) | |||||||
\(434\) | − | 274546.i | − | 0.0699666i | ||||||
\(435\) | 3.50269e6 | − | 3.46386e6i | 0.887522 | − | 0.877683i | ||||
\(436\) | − | 6.00208e6i | − | 1.51212i | ||||||
\(437\) | −2.08282e6 | −0.521732 | ||||||||
\(438\) | 8.53581e6 | − | 8.44119e6i | 2.12598 | − | 2.10241i | ||||
\(439\) | 406895.i | 0.100768i | 0.998730 | + | 0.0503839i | \(0.0160445\pi\) | ||||
−0.998730 | + | 0.0503839i | \(0.983956\pi\) | |||||||
\(440\) | −1.48792e6 | − | 1.36798e7i | −0.366395 | − | 3.36859i | ||||
\(441\) | −2371.66 | + | 212740.i | −0.000580705 | + | 0.0520898i | ||||
\(442\) | 5.49950e6i | 1.33896i | ||||||||
\(443\) | − | 2.29937e6i | − | 0.556673i | −0.960484 | − | 0.278337i | \(-0.910217\pi\) | ||
0.960484 | − | 0.278337i | \(-0.0897831\pi\) | |||||||
\(444\) | 2.79439e6 | + | 2.82571e6i | 0.672712 | + | 0.680253i | ||||
\(445\) | 1.04904e6 | 0.251126 | ||||||||
\(446\) | −3.10844e6 | −0.739954 | ||||||||
\(447\) | −667854. | − | 675341.i | −0.158093 | − | 0.159865i | ||||
\(448\) | 1.02145e6i | 0.240447i | ||||||||
\(449\) | 6.52698e6i | 1.52791i | 0.645272 | + | 0.763953i | \(0.276744\pi\) | ||||
−0.645272 | + | 0.763953i | \(0.723256\pi\) | |||||||
\(450\) | −129064. | + | 1.15771e7i | −0.0300450 | + | 2.69507i | ||||
\(451\) | −3.52897e6 | + | 383839.i | −0.816971 | + | 0.0888603i | ||||
\(452\) | − | 5.10488e6i | − | 1.17527i | ||||||
\(453\) | 4.85606e6 | − | 4.80222e6i | 1.11183 | − | 1.09950i | ||||
\(454\) | −4.63421e6 | −1.05520 | ||||||||
\(455\) | 5.84457e6i | 1.32350i | ||||||||
\(456\) | −3.61607e6 | + | 3.57598e6i | −0.814376 | + | 0.805348i | ||||
\(457\) | − | 7.61992e6i | − | 1.70671i | −0.521330 | − | 0.853355i | \(-0.674564\pi\) | ||
0.521330 | − | 0.853355i | \(-0.325436\pi\) | |||||||
\(458\) | −2.49351e6 | −0.555453 | ||||||||
\(459\) | 2.83035e6 | − | 2.73725e6i | 0.627060 | − | 0.606432i | ||||
\(460\) | 1.53888e7 | 3.39087 | ||||||||
\(461\) | 1.84657e6 | 0.404682 | 0.202341 | − | 0.979315i | \(-0.435145\pi\) | ||||
0.202341 | + | 0.979315i | \(0.435145\pi\) | |||||||
\(462\) | −5.03806e6 | + | 6.19672e6i | −1.09814 | + | 1.35069i | ||||
\(463\) | 8.90164e6 | 1.92982 | 0.964912 | − | 0.262573i | \(-0.0845711\pi\) | ||||
0.964912 | + | 0.262573i | \(0.0845711\pi\) | |||||||
\(464\) | −5.95581e6 | −1.28424 | ||||||||
\(465\) | 211003. | − | 208664.i | 0.0452539 | − | 0.0447522i | ||||
\(466\) | −6.06120e6 | −1.29299 | ||||||||
\(467\) | 3.83609e6i | 0.813947i | 0.913440 | + | 0.406974i | \(0.133416\pi\) | ||||
−0.913440 | + | 0.406974i | \(0.866584\pi\) | |||||||
\(468\) | 8.93528e6 | + | 99611.9i | 1.88579 | + | 0.0210231i | ||||
\(469\) | 6.73770e6i | 1.41442i | ||||||||
\(470\) | 8.11142e6 | 1.69376 | ||||||||
\(471\) | −3.78451e6 | − | 3.82693e6i | −0.786063 | − | 0.794875i | ||||
\(472\) | 1.40324e7i | 2.89920i | ||||||||
\(473\) | −228340. | − | 2.09933e6i | −0.0469278 | − | 0.431448i | ||||
\(474\) | −1.19710e7 | + | 1.18383e7i | −2.44729 | + | 2.42016i | ||||
\(475\) | − | 3.96750e6i | − | 0.806831i | ||||||
\(476\) | − | 9.22309e6i | − | 1.86577i | ||||||
\(477\) | 218004. | + | 2430.34i | 0.0438700 | + | 0.000489070i | ||||
\(478\) | −3.61938e6 | −0.724544 | ||||||||
\(479\) | −4.28323e6 | −0.852968 | −0.426484 | − | 0.904495i | \(-0.640248\pi\) | ||||
−0.426484 | + | 0.904495i | \(0.640248\pi\) | |||||||
\(480\) | 4.39371e6 | − | 4.34500e6i | 0.870418 | − | 0.860769i | ||||
\(481\) | 1.89703e6i | 0.373861i | ||||||||
\(482\) | − | 5.77150e6i | − | 1.13154i | ||||||
\(483\) | −3.42140e6 | − | 3.45975e6i | −0.667323 | − | 0.674803i | ||||
\(484\) | 1.10569e7 | − | 2.43406e6i | 2.14545 | − | 0.472300i | ||||
\(485\) | 5.99419e6i | 1.15711i | ||||||||
\(486\) | −6.39716e6 | − | 6.76405e6i | −1.22856 | − | 1.29902i | ||||
\(487\) | −7.16028e6 | −1.36807 | −0.684034 | − | 0.729450i | \(-0.739776\pi\) | ||||
−0.684034 | + | 0.729450i | \(0.739776\pi\) | |||||||
\(488\) | 5.93405e6i | 1.12798i | ||||||||
\(489\) | −722303. | − | 730400.i | −0.136599 | − | 0.138130i | ||||
\(490\) | 783869.i | 0.147487i | ||||||||
\(491\) | 2.57405e6 | 0.481851 | 0.240925 | − | 0.970544i | \(-0.422549\pi\) | ||||
0.240925 | + | 0.970544i | \(0.422549\pi\) | |||||||
\(492\) | −6.81583e6 | − | 6.89223e6i | −1.26942 | − | 1.28365i | ||||
\(493\) | −3.71083e6 | −0.687629 | ||||||||
\(494\) | −4.45603e6 | −0.821544 | ||||||||
\(495\) | −8.59158e6 | + | 837693.i | −1.57601 | + | 0.153664i | ||||
\(496\) | −358779. | −0.0654821 | ||||||||
\(497\) | 4.25280e6 | 0.772296 | ||||||||
\(498\) | −2.26001e6 | − | 2.28534e6i | −0.408354 | − | 0.412932i | ||||
\(499\) | 3.30406e6 | 0.594014 | 0.297007 | − | 0.954875i | \(-0.404012\pi\) | ||||
0.297007 | + | 0.954875i | \(0.404012\pi\) | |||||||
\(500\) | 9.86759e6i | 1.76517i | ||||||||
\(501\) | 7.51716e6 | + | 7.60143e6i | 1.33801 | + | 1.35301i | ||||
\(502\) | 8.33035e6i | 1.47538i | ||||||||
\(503\) | 934368. | 0.164664 | 0.0823318 | − | 0.996605i | \(-0.473763\pi\) | ||||
0.0823318 | + | 0.996605i | \(0.473763\pi\) | |||||||
\(504\) | −1.18801e7 | − | 132441.i | −2.08326 | − | 0.0232245i | ||||
\(505\) | − | 7.99739e6i | − | 1.39547i | ||||||
\(506\) | 1.08539e6 | + | 9.97892e6i | 0.188455 | + | 1.73264i | ||||
\(507\) | −1.07045e6 | − | 1.08245e6i | −0.184947 | − | 0.187020i | ||||
\(508\) | − | 1.06456e7i | − | 1.83026i | ||||||
\(509\) | − | 2.42079e6i | − | 0.414155i | −0.978325 | − | 0.207077i | \(-0.933605\pi\) | ||
0.978325 | − | 0.207077i | \(-0.0663952\pi\) | |||||||
\(510\) | 1.03151e7 | − | 1.02007e7i | 1.75609 | − | 1.73663i | ||||
\(511\) | −9.61045e6 | −1.62814 | ||||||||
\(512\) | 1.32085e7 | 2.22678 | ||||||||
\(513\) | 2.21788e6 | + | 2.29332e6i | 0.372088 | + | 0.384744i | ||||
\(514\) | − | 1.68350e7i | − | 2.81065i | ||||||
\(515\) | 999474.i | 0.166056i | ||||||||
\(516\) | 4.10009e6 | − | 4.05464e6i | 0.677906 | − | 0.670390i | ||||
\(517\) | 393144. | + | 3.61452e6i | 0.0646883 | + | 0.594737i | ||||
\(518\) | − | 4.62967e6i | − | 0.758099i | ||||||
\(519\) | 3.63500e6 | + | 3.67575e6i | 0.592361 | + | 0.599002i | ||||
\(520\) | 1.79365e7 | 2.90890 | ||||||||
\(521\) | − | 5.66823e6i | − | 0.914858i | −0.889246 | − | 0.457429i | \(-0.848770\pi\) | ||
0.889246 | − | 0.457429i | \(-0.151230\pi\) | |||||||
\(522\) | −97810.0 | + | 8.77366e6i | −0.0157111 | + | 1.40930i | ||||
\(523\) | − | 7.10021e6i | − | 1.13506i | −0.823354 | − | 0.567528i | \(-0.807900\pi\) | ||
0.823354 | − | 0.567528i | \(-0.192100\pi\) | |||||||
\(524\) | −1.45048e7 | −2.30772 | ||||||||
\(525\) | 6.59039e6 | − | 6.51733e6i | 1.04355 | − | 1.03198i | ||||
\(526\) | 6.19384e6 | 0.976102 | ||||||||
\(527\) | −223541. | −0.0350615 | ||||||||
\(528\) | 8.09791e6 | + | 6.58377e6i | 1.26412 | + | 1.02776i | ||||
\(529\) | 320681. | 0.0498234 | ||||||||
\(530\) | 803264. | 0.124213 | ||||||||
\(531\) | 8.80238e6 | + | 98130.2i | 1.35476 | + | 0.0151031i | ||||
\(532\) | 7.47311e6 | 1.14478 | ||||||||
\(533\) | − | 4.62706e6i | − | 0.705484i | ||||||
\(534\) | −1.32856e6 | + | 1.31383e6i | −0.201618 | + | 0.199383i | ||||
\(535\) | 1.66277e7i | 2.51158i | ||||||||
\(536\) | 2.06774e7 | 3.10874 | ||||||||
\(537\) | −5.56914e6 | + | 5.50740e6i | −0.833398 | + | 0.824159i | ||||
\(538\) | 6.70177e6i | 0.998237i | ||||||||
\(539\) | −349299. | + | 37992.6i | −0.0517876 | + | 0.00563283i | ||||
\(540\) | −1.63868e7 | − | 1.69442e7i | −2.41829 | − | 2.50055i | ||||
\(541\) | 4.83518e6i | 0.710263i | 0.934816 | + | 0.355132i | \(0.115564\pi\) | ||||
−0.934816 | + | 0.355132i | \(0.884436\pi\) | |||||||
\(542\) | 1.02366e7i | 1.49678i | ||||||||
\(543\) | 8.93826e6 | + | 9.03846e6i | 1.30093 | + | 1.31551i | ||||
\(544\) | −4.65479e6 | −0.674378 | ||||||||
\(545\) | −7.55783e6 | −1.08995 | ||||||||
\(546\) | −7.31982e6 | − | 7.40188e6i | −1.05080 | − | 1.06258i | ||||
\(547\) | − | 5.54075e6i | − | 0.791773i | −0.918300 | − | 0.395886i | \(-0.870437\pi\) | ||
0.918300 | − | 0.395886i | \(-0.129563\pi\) | |||||||
\(548\) | − | 1.93776e7i | − | 2.75644i | ||||||
\(549\) | 3.72236e6 | + | 41497.4i | 0.527093 | + | 0.00587611i | ||||
\(550\) | −1.90086e7 | + | 2.06752e6i | −2.67943 | + | 0.291436i | ||||
\(551\) | − | 3.00674e6i | − | 0.421908i | ||||||
\(552\) | −1.06177e7 | + | 1.05000e7i | −1.48314 | + | 1.46670i | ||||
\(553\) | 1.34782e7 | 1.87421 | ||||||||
\(554\) | − | 2.04624e7i | − | 2.83258i | ||||||
\(555\) | 3.55814e6 | − | 3.51870e6i | 0.490333 | − | 0.484897i | ||||
\(556\) | − | 5.72136e6i | − | 0.784896i | ||||||
\(557\) | −7.00403e6 | −0.956555 | −0.478278 | − | 0.878209i | \(-0.658739\pi\) | ||||
−0.478278 | + | 0.878209i | \(0.658739\pi\) | |||||||
\(558\) | −5892.09 | + | 528526.i | −0.000801094 | + | 0.0718590i | ||||
\(559\) | 2.75257e6 | 0.372571 | ||||||||
\(560\) | −1.86398e7 | −2.51172 | ||||||||
\(561\) | 5.04550e6 | + | 4.10209e6i | 0.676857 | + | 0.550298i | ||||
\(562\) | 8.27954e6 | 1.10577 | ||||||||
\(563\) | 7.81431e6 | 1.03901 | 0.519505 | − | 0.854468i | \(-0.326117\pi\) | ||||
0.519505 | + | 0.854468i | \(0.326117\pi\) | |||||||
\(564\) | −7.05932e6 | + | 6.98106e6i | −0.934469 | + | 0.924110i | ||||
\(565\) | −6.42807e6 | −0.847148 | ||||||||
\(566\) | 1.75538e7i | 2.30319i | ||||||||
\(567\) | −166157. | + | 7.45131e6i | −0.0217051 | + | 0.973363i | ||||
\(568\) | − | 1.30515e7i | − | 1.69742i | ||||||
\(569\) | −1.22848e7 | −1.59069 | −0.795347 | − | 0.606154i | \(-0.792712\pi\) | ||||
−0.795347 | + | 0.606154i | \(0.792712\pi\) | |||||||
\(570\) | 8.26526e6 | + | 8.35792e6i | 1.06554 | + | 1.07748i | ||||
\(571\) | − | 1.28754e7i | − | 1.65262i | −0.563218 | − | 0.826308i | \(-0.690437\pi\) | ||
0.563218 | − | 0.826308i | \(-0.309563\pi\) | |||||||
\(572\) | 1.59572e6 | + | 1.46709e7i | 0.203924 | + | 1.87485i | ||||
\(573\) | 5.84647e6 | − | 5.78166e6i | 0.743887 | − | 0.735641i | ||||
\(574\) | 1.12923e7i | 1.43055i | ||||||||
\(575\) | − | 1.16496e7i | − | 1.46940i | ||||||
\(576\) | 21921.4 | − | 1.96638e6i | 0.00275304 | − | 0.246951i | ||||
\(577\) | −9.45884e6 | −1.18276 | −0.591382 | − | 0.806391i | \(-0.701418\pi\) | ||||
−0.591382 | + | 0.806391i | \(0.701418\pi\) | |||||||
\(578\) | 3.43276e6 | 0.427389 | ||||||||
\(579\) | −6.35056e6 | + | 6.28016e6i | −0.787256 | + | 0.778528i | ||||
\(580\) | 2.22153e7i | 2.74209i | ||||||||
\(581\) | 2.57306e6i | 0.316235i | ||||||||
\(582\) | −7.50722e6 | − | 7.59138e6i | −0.918696 | − | 0.928994i | ||||
\(583\) | 38932.6 | + | 357942.i | 0.00474397 | + | 0.0436155i | ||||
\(584\) | 2.94936e7i | 3.57846i | ||||||||
\(585\) | 125431. | − | 1.12513e7i | 0.0151536 | − | 1.35930i | ||||
\(586\) | −2.64956e7 | −3.18735 | ||||||||
\(587\) | 1.02802e7i | 1.23142i | 0.787972 | + | 0.615711i | \(0.211131\pi\) | ||||
−0.787972 | + | 0.615711i | \(0.788869\pi\) | |||||||
\(588\) | −674634. | − | 682197.i | −0.0804683 | − | 0.0813704i | ||||
\(589\) | − | 181127.i | − | 0.0215127i | ||||||
\(590\) | 3.24335e7 | 3.83587 | ||||||||
\(591\) | 3.11946e6 | + | 3.15443e6i | 0.367376 | + | 0.371494i | ||||
\(592\) | −6.05009e6 | −0.709508 | ||||||||
\(593\) | 1.25800e7 | 1.46907 | 0.734536 | − | 0.678569i | \(-0.237400\pi\) | ||||
0.734536 | + | 0.678569i | \(0.237400\pi\) | |||||||
\(594\) | 9.83171e6 | − | 1.18211e7i | 1.14331 | − | 1.37465i | ||||
\(595\) | −1.16137e7 | −1.34487 | ||||||||
\(596\) | 4.28324e6 | 0.493920 | ||||||||
\(597\) | −4.66266e6 | − | 4.71493e6i | −0.535424 | − | 0.541427i | ||||
\(598\) | −1.30840e7 | −1.49619 | ||||||||
\(599\) | − | 6.21604e6i | − | 0.707858i | −0.935272 | − | 0.353929i | \(-0.884845\pi\) | ||
0.935272 | − | 0.353929i | \(-0.115155\pi\) | |||||||
\(600\) | −2.00011e7 | − | 2.02253e7i | −2.26817 | − | 2.29360i | ||||
\(601\) | − | 1.28321e7i | − | 1.44914i | −0.689199 | − | 0.724572i | \(-0.742038\pi\) | ||
0.689199 | − | 0.724572i | \(-0.257962\pi\) | |||||||
\(602\) | −6.71763e6 | −0.755483 | ||||||||
\(603\) | 144599. | − | 1.29707e7i | 0.0161947 | − | 1.45268i | ||||
\(604\) | 3.07987e7i | 3.43511i | ||||||||
\(605\) | −3.06497e6 | − | 1.39228e7i | −0.340438 | − | 1.54646i | ||||
\(606\) | 1.00161e7 | + | 1.01283e7i | 1.10794 | + | 1.12036i | ||||
\(607\) | 3.31925e6i | 0.365652i | 0.983145 | + | 0.182826i | \(0.0585245\pi\) | ||||
−0.983145 | + | 0.182826i | \(0.941476\pi\) | |||||||
\(608\) | − | 3.77160e6i | − | 0.413777i | ||||||
\(609\) | 4.99448e6 | − | 4.93912e6i | 0.545692 | − | 0.539642i | ||||
\(610\) | 1.37155e7 | 1.49241 | ||||||||
\(611\) | −4.73923e6 | −0.513576 | ||||||||
\(612\) | −197939. | + | 1.77553e7i | −0.0213625 | + | 1.91624i | ||||
\(613\) | 5.25789e6i | 0.565145i | 0.959246 | + | 0.282573i | \(0.0911878\pi\) | ||||
−0.959246 | + | 0.282573i | \(0.908812\pi\) | |||||||
\(614\) | − | 1.04620e6i | − | 0.111994i | ||||||
\(615\) | −8.67871e6 | + | 8.58250e6i | −0.925268 | + | 0.915010i | ||||
\(616\) | −2.12163e6 | − | 1.95060e7i | −0.225277 | − | 2.07117i | ||||
\(617\) | 8.52105e6i | 0.901115i | 0.892748 | + | 0.450557i | \(0.148775\pi\) | ||||
−0.892748 | + | 0.450557i | \(0.851225\pi\) | |||||||
\(618\) | −1.25176e6 | − | 1.26579e6i | −0.131840 | − | 0.133318i | ||||
\(619\) | 1.37799e7 | 1.44550 | 0.722751 | − | 0.691108i | \(-0.242877\pi\) | ||||
0.722751 | + | 0.691108i | \(0.242877\pi\) | |||||||
\(620\) | 1.33825e6i | 0.139816i | ||||||||
\(621\) | 6.51225e6 | + | 6.73377e6i | 0.677645 | + | 0.700695i | ||||
\(622\) | 1.13641e7i | 1.17776i | ||||||||
\(623\) | 1.49582e6 | 0.154405 | ||||||||
\(624\) | −9.67283e6 | + | 9.56559e6i | −0.994471 | + | 0.983446i | ||||
\(625\) | −2.29572e6 | −0.235082 | ||||||||
\(626\) | 2.02036e7 | 2.06059 | ||||||||
\(627\) | −3.32377e6 | + | 4.08817e6i | −0.337646 | + | 0.415298i | ||||
\(628\) | 2.42717e7 | 2.45584 | ||||||||
\(629\) | −3.76958e6 | −0.379897 | ||||||||
\(630\) | −306114. | + | 2.74588e7i | −0.0307278 | + | 2.75632i | ||||
\(631\) | −2.97282e6 | −0.297231 | −0.148616 | − | 0.988895i | \(-0.547482\pi\) | ||||
−0.148616 | + | 0.988895i | \(0.547482\pi\) | |||||||
\(632\) | − | 4.13633e7i | − | 4.11929i | ||||||
\(633\) | −1.33815e6 | + | 1.32331e6i | −0.132738 | + | 0.131266i | ||||
\(634\) | − | 2.58916e7i | − | 2.55820i | ||||||
\(635\) | −1.34050e7 | −1.31926 | ||||||||
\(636\) | −699076. | + | 691326.i | −0.0685301 | + | 0.0677704i | ||||
\(637\) | − | 457989.i | − | 0.0447205i | ||||||
\(638\) | −1.44055e7 | + | 1.56686e6i | −1.40113 | + | 0.152398i | ||||
\(639\) | −8.18702e6 | − | 91270.1i | −0.793184 | − | 0.00884253i | ||||
\(640\) | − | 1.99302e7i | − | 1.92337i | ||||||
\(641\) | 1.03887e7i | 0.998658i | 0.866413 | + | 0.499329i | \(0.166420\pi\) | ||||
−0.866413 | + | 0.499329i | \(0.833580\pi\) | |||||||
\(642\) | −2.08248e7 | − | 2.10582e7i | −1.99408 | − | 2.01644i | ||||
\(643\) | 2.23793e6 | 0.213462 | 0.106731 | − | 0.994288i | \(-0.465962\pi\) | ||||
0.106731 | + | 0.994288i | \(0.465962\pi\) | |||||||
\(644\) | 2.19429e7 | 2.08487 | ||||||||
\(645\) | −5.10561e6 | − | 5.16284e6i | −0.483223 | − | 0.488641i | ||||
\(646\) | − | 8.85457e6i | − | 0.834807i | ||||||
\(647\) | 9.54481e6i | 0.896409i | 0.893931 | + | 0.448205i | \(0.147936\pi\) | ||||
−0.893931 | + | 0.448205i | \(0.852064\pi\) | |||||||
\(648\) | 2.28674e7 | + | 509922.i | 2.13934 | + | 0.0477053i | ||||
\(649\) | 1.57199e6 | + | 1.44527e7i | 0.146500 | + | 1.34690i | ||||
\(650\) | − | 2.49233e7i | − | 2.31378i | ||||||
\(651\) | 300868. | − | 297533.i | 0.0278243 | − | 0.0275158i | ||||
\(652\) | 4.63244e6 | 0.426767 | ||||||||
\(653\) | 1.60519e7i | 1.47314i | 0.676360 | + | 0.736571i | \(0.263556\pi\) | ||||
−0.676360 | + | 0.736571i | \(0.736444\pi\) | |||||||
\(654\) | 9.57165e6 | − | 9.46554e6i | 0.875069 | − | 0.865368i | ||||
\(655\) | 1.82645e7i | 1.66343i | ||||||||
\(656\) | 1.47568e7 | 1.33886 | ||||||||
\(657\) | 1.85010e7 | + | 206252.i | 1.67217 | + | 0.0186416i | ||||
\(658\) | 1.15661e7 | 1.04141 | ||||||||
\(659\) | 1.21513e7 | 1.08996 | 0.544979 | − | 0.838450i | \(-0.316538\pi\) | ||||
0.544979 | + | 0.838450i | \(0.316538\pi\) | |||||||
\(660\) | 2.45576e7 | − | 3.02053e7i | 2.19445 | − | 2.69913i | ||||
\(661\) | 8.00011e6 | 0.712184 | 0.356092 | − | 0.934451i | \(-0.384109\pi\) | ||||
0.356092 | + | 0.934451i | \(0.384109\pi\) | |||||||
\(662\) | 5.43492e6 | 0.482001 | ||||||||
\(663\) | −6.02677e6 | + | 5.95995e6i | −0.532477 | + | 0.526574i | ||||
\(664\) | 7.89651e6 | 0.695048 | ||||||||
\(665\) | − | 9.41015e6i | − | 0.825168i | ||||||
\(666\) | −99358.3 | + | 8.91255e6i | −0.00867998 | + | 0.778603i | ||||
\(667\) | − | 8.82854e6i | − | 0.768377i | ||||||
\(668\) | −4.82108e7 | −4.18026 | ||||||||
\(669\) | −3.36870e6 | − | 3.40646e6i | −0.291002 | − | 0.294265i | ||||
\(670\) | − | 4.77923e7i | − | 4.11311i | ||||||
\(671\) | 664764. | + | 6.11176e6i | 0.0569982 | + | 0.524035i | ||||
\(672\) | 6.26498e6 | − | 6.19552e6i | 0.535176 | − | 0.529243i | ||||
\(673\) | 7.19089e6i | 0.611991i | 0.952033 | + | 0.305995i | \(0.0989892\pi\) | ||||
−0.952033 | + | 0.305995i | \(0.901011\pi\) | |||||||
\(674\) | 1.58584e6i | 0.134465i | ||||||||
\(675\) | −1.28270e7 | + | 1.24050e7i | −1.08359 | + | 1.04794i | ||||
\(676\) | 6.86528e6 | 0.577818 | ||||||||
\(677\) | −2.50078e6 | −0.209703 | −0.104851 | − | 0.994488i | \(-0.533437\pi\) | ||||
−0.104851 | + | 0.994488i | \(0.533437\pi\) | |||||||
\(678\) | 8.14086e6 | − | 8.05061e6i | 0.680136 | − | 0.672596i | ||||
\(679\) | 8.54711e6i | 0.711450i | ||||||||
\(680\) | 3.56415e7i | 2.95586i | ||||||||
\(681\) | −5.02222e6 | − | 5.07852e6i | −0.414981 | − | 0.419633i | ||||
\(682\) | −867791. | + | 94387.8i | −0.0714421 | + | 0.00777061i | ||||
\(683\) | − | 1.69294e6i | − | 0.138864i | −0.997587 | − | 0.0694319i | \(-0.977881\pi\) | ||
0.997587 | − | 0.0694319i | \(-0.0221187\pi\) | |||||||
\(684\) | −1.43864e7 | − | 160382.i | −1.17574 | − | 0.0131074i | ||||
\(685\) | −2.44003e7 | −1.98687 | ||||||||
\(686\) | 2.25739e7i | 1.83145i | ||||||||
\(687\) | −2.70228e6 | − | 2.73258e6i | −0.218443 | − | 0.220892i | ||||
\(688\) | 8.77864e6i | 0.707060i | ||||||||
\(689\) | −469320. | −0.0376636 | ||||||||
\(690\) | 2.42689e7 | + | 2.45409e7i | 1.94056 | + | 1.96231i | ||||
\(691\) | −8.84676e6 | −0.704838 | −0.352419 | − | 0.935842i | \(-0.614641\pi\) | ||||
−0.352419 | + | 0.935842i | \(0.614641\pi\) | |||||||
\(692\) | −2.33128e7 | −1.85067 | ||||||||
\(693\) | −1.22507e7 | + | 1.19446e6i | −0.969010 | + | 0.0944800i | ||||
\(694\) | −1.92884e7 | −1.52019 | ||||||||
\(695\) | −7.20434e6 | −0.565760 | ||||||||
\(696\) | −1.51577e7 | − | 1.53276e7i | −1.18607 | − | 1.19937i | ||||
\(697\) | 9.19442e6 | 0.716874 | ||||||||
\(698\) | − | 4.49348e6i | − | 0.349095i | ||||||
\(699\) | −6.56869e6 | − | 6.64232e6i | −0.508494 | − | 0.514194i | ||||
\(700\) | 4.17984e7i | 3.22415i | ||||||||
\(701\) | 1.16656e6 | 0.0896631 | 0.0448315 | − | 0.998995i | \(-0.485725\pi\) | ||||
0.0448315 | + | 0.998995i | \(0.485725\pi\) | |||||||
\(702\) | 1.39325e7 | + | 1.44064e7i | 1.06705 | + | 1.10335i | ||||
\(703\) | − | 3.05434e6i | − | 0.233093i | ||||||
\(704\) | 3.22861e6 | − | 351169.i | 0.245518 | − | 0.0267045i | ||||
\(705\) | 8.79056e6 | + | 8.88911e6i | 0.666107 | + | 0.673574i | ||||
\(706\) | 3.44385e7i | 2.60035i | ||||||||
\(707\) | − | 1.14035e7i | − | 0.858002i | ||||||
\(708\) | −2.82267e7 | + | 2.79138e7i | −2.11630 | + | 2.09284i | ||||
\(709\) | 9.21961e6 | 0.688806 | 0.344403 | − | 0.938822i | \(-0.388081\pi\) | ||||
0.344403 | + | 0.938822i | \(0.388081\pi\) | |||||||
\(710\) | −3.01662e7 | −2.24582 | ||||||||
\(711\) | −2.59467e7 | − | 289257.i | −1.92490 | − | 0.0214590i | ||||
\(712\) | − | 4.59055e6i | − | 0.339363i | ||||||
\(713\) | − | 531833.i | − | 0.0391788i | ||||||
\(714\) | 1.47083e7 | − | 1.45452e7i | 1.07973 | − | 1.06776i | ||||
\(715\) | 1.84736e7 | − | 2.00934e6i | 1.35141 | − | 0.146990i | ||||
\(716\) | − | 3.53213e7i | − | 2.57486i | ||||||
\(717\) | −3.92242e6 | − | 3.96639e6i | −0.284942 | − | 0.288136i | ||||
\(718\) | 5.91956e6 | 0.428527 | ||||||||
\(719\) | − | 2.18224e7i | − | 1.57427i | −0.616779 | − | 0.787136i | \(-0.711563\pi\) | ||
0.616779 | − | 0.787136i | \(-0.288437\pi\) | |||||||
\(720\) | 3.58833e7 | + | 400032.i | 2.57965 | + | 0.0287583i | ||||
\(721\) | 1.42515e6i | 0.102099i | ||||||||
\(722\) | −1.78694e7 | −1.27575 | ||||||||
\(723\) | 6.32485e6 | − | 6.25473e6i | 0.449992 | − | 0.445003i | ||||
\(724\) | −5.73249e7 | −4.06440 | ||||||||
\(725\) | 1.68172e7 | 1.18826 | ||||||||
\(726\) | 2.13188e7 | + | 1.37940e7i | 1.50114 | + | 0.971289i | ||||
\(727\) | −741663. | −0.0520440 | −0.0260220 | − | 0.999661i | \(-0.508284\pi\) | ||||
−0.0260220 | + | 0.999661i | \(0.508284\pi\) | |||||||
\(728\) | 2.55756e7 | 1.78853 | ||||||||
\(729\) | 479782. | − | 1.43409e7i | 0.0334368 | − | 0.999441i | ||||
\(730\) | 6.81693e7 | 4.73459 | ||||||||
\(731\) | 5.46963e6i | 0.378586i | ||||||||
\(732\) | −1.19365e7 | + | 1.18042e7i | −0.823380 | + | 0.814252i | ||||
\(733\) | − | 6.80074e6i | − | 0.467516i | −0.972295 | − | 0.233758i | \(-0.924898\pi\) | ||
0.972295 | − | 0.233758i | \(-0.0751023\pi\) | |||||||
\(734\) | 3.18548e6 | 0.218240 | ||||||||
\(735\) | −859023. | + | 849500.i | −0.0586525 | + | 0.0580023i | ||||
\(736\) | − | 1.10743e7i | − | 0.753570i | ||||||
\(737\) | 2.12967e7 | − | 2.31640e6i | 1.44425 | − | 0.157088i | ||||
\(738\) | 242346. | − | 2.17387e7i | 0.0163793 | − | 1.46924i | ||||
\(739\) | − | 9.15287e6i | − | 0.616519i | −0.951302 | − | 0.308259i | \(-0.900254\pi\) | ||
0.951302 | − | 0.308259i | \(-0.0997465\pi\) | |||||||
\(740\) | 2.25669e7i | 1.51493i | ||||||||
\(741\) | −4.82912e6 | − | 4.88325e6i | −0.323089 | − | 0.326711i | ||||
\(742\) | 1.14537e6 | 0.0763725 | ||||||||
\(743\) | −1.25723e7 | −0.835490 | −0.417745 | − | 0.908564i | \(-0.637180\pi\) | ||||
−0.417745 | + | 0.908564i | \(0.637180\pi\) | |||||||
\(744\) | −913103. | − | 923339.i | −0.0604766 | − | 0.0611546i | ||||
\(745\) | − | 5.39346e6i | − | 0.356022i | ||||||
\(746\) | − | 2.29681e7i | − | 1.51105i | ||||||
\(747\) | 55221.0 | − | 4.95338e6i | 0.00362078 | − | 0.324788i | ||||
\(748\) | −2.91525e7 | + | 3.17086e6i | −1.90512 | + | 0.207216i | ||||
\(749\) | 2.37094e7i | 1.54424i | ||||||||
\(750\) | −1.57361e7 | + | 1.55616e7i | −1.02151 | + | 1.01019i | ||||
\(751\) | 1.79363e7 | 1.16047 | 0.580235 | − | 0.814449i | \(-0.302961\pi\) | ||||
0.580235 | + | 0.814449i | \(0.302961\pi\) | |||||||
\(752\) | − | 1.51146e7i | − | 0.974657i | ||||||
\(753\) | −9.12903e6 | + | 9.02783e6i | −0.586729 | + | 0.580224i | ||||
\(754\) | − | 1.88880e7i | − | 1.20992i | ||||||
\(755\) | 3.87818e7 | 2.47606 | ||||||||
\(756\) | −2.33659e7 | − | 2.41607e7i | −1.48688 | − | 1.53746i | ||||
\(757\) | 1.91439e7 | 1.21420 | 0.607099 | − | 0.794626i | \(-0.292333\pi\) | ||||
0.607099 | + | 0.794626i | \(0.292333\pi\) | |||||||
\(758\) | −3.92965e7 | −2.48417 | ||||||||
\(759\) | −9.75940e6 | + | 1.20039e7i | −0.614920 | + | 0.756340i | ||||
\(760\) | −2.88789e7 | −1.81362 | ||||||||
\(761\) | 5.64221e6 | 0.353173 | 0.176586 | − | 0.984285i | \(-0.443494\pi\) | ||||
0.176586 | + | 0.984285i | \(0.443494\pi\) | |||||||
\(762\) | 1.69768e7 | − | 1.67886e7i | 1.05918 | − | 1.04744i | ||||
\(763\) | −1.07767e7 | −0.670153 | ||||||||
\(764\) | 3.70803e7i | 2.29831i | ||||||||
\(765\) | 2.23575e7 | + | 249245.i | 1.38124 | + | 0.0153983i | ||||
\(766\) | 2.34260e7i | 1.44253i | ||||||||
\(767\) | −1.89498e7 | −1.16310 | ||||||||
\(768\) | 2.21224e7 | + | 2.23704e7i | 1.35341 | + | 1.36858i | ||||
\(769\) | − | 5.21462e6i | − | 0.317985i | −0.987280 | − | 0.158992i | \(-0.949175\pi\) | ||
0.987280 | − | 0.158992i | \(-0.0508246\pi\) | |||||||
\(770\) | −4.50847e7 | + | 4.90377e6i | −2.74033 | + | 0.298060i | ||||
\(771\) | 1.84491e7 | − | 1.82446e7i | 1.11774 | − | 1.10535i | ||||
\(772\) | − | 4.02774e7i | − | 2.43230i | ||||||
\(773\) | − | 6.01544e6i | − | 0.362092i | −0.983475 | − | 0.181046i | \(-0.942052\pi\) | ||
0.983475 | − | 0.181046i | \(-0.0579483\pi\) | |||||||
\(774\) | 1.29320e7 | + | 144168.i | 0.775916 | + | 0.00865003i | ||||
\(775\) | 1.01307e6 | 0.0605880 | ||||||||
\(776\) | 2.62303e7 | 1.56369 | ||||||||
\(777\) | 5.07355e6 | − | 5.01730e6i | 0.301480 | − | 0.298138i | ||||
\(778\) | 4.01992e7i | 2.38105i | ||||||||
\(779\) | 7.44988e6i | 0.439851i | ||||||||
\(780\) | 3.56798e7 | + | 3.60798e7i | 2.09984 | + | 2.12338i | ||||
\(781\) | −1.46209e6 | − | 1.34423e7i | −0.0857725 | − | 0.788582i | ||||
\(782\) | − | 2.59992e7i | − | 1.52035i | ||||||
\(783\) | −9.72084e6 | + | 9.40106e6i | −0.566630 | + | 0.547990i | ||||
\(784\) | 1.46064e6 | 0.0848698 | ||||||||
\(785\) | − | 3.05629e7i | − | 1.77019i | ||||||
\(786\) | −2.28747e7 | − | 2.31311e7i | −1.32068 | − | 1.33549i | ||||
\(787\) | 2.03633e7i | 1.17196i | 0.810327 | + | 0.585978i | \(0.199289\pi\) | ||||
−0.810327 | + | 0.585978i | \(0.800711\pi\) | |||||||
\(788\) | −2.00064e7 | −1.14777 | ||||||||
\(789\) | 6.71243e6 | + | 6.78767e6i | 0.383873 | + | 0.388176i | ||||
\(790\) | −9.56040e7 | −5.45015 | ||||||||
\(791\) | −9.16577e6 | −0.520868 | ||||||||
\(792\) | 3.66571e6 | + | 3.75964e7i | 0.207656 | + | 2.12977i | ||||
\(793\) | −8.01352e6 | −0.452523 | ||||||||
\(794\) | 2.44109e7 | 1.37415 | ||||||||
\(795\) | 870519. | + | 880278.i | 0.0488495 | + | 0.0493971i | ||||
\(796\) | 2.99037e7 | 1.67279 | ||||||||
\(797\) | 2.95689e6i | 0.164888i | 0.996596 | + | 0.0824441i | \(0.0262726\pi\) | ||||
−0.996596 | + | 0.0824441i | \(0.973727\pi\) | |||||||
\(798\) | 1.17854e7 | + | 1.19175e7i | 0.655146 | + | 0.662490i | ||||
\(799\) | − | 9.41732e6i | − | 0.521868i | ||||||
\(800\) | 2.10952e7 | 1.16536 | ||||||||
\(801\) | −2.87960e6 | − | 32102.2i | −0.158581 | − | 0.00176788i | ||||
\(802\) | 3.03342e7i | 1.66531i | ||||||||
\(803\) | 3.30403e6 | + | 3.03769e7i | 0.180824 | + | 1.66247i | ||||
\(804\) | 4.11322e7 | + | 4.15933e7i | 2.24410 | + | 2.26926i | ||||
\(805\) | − | 2.76305e7i | − | 1.50279i | ||||||
\(806\) | − | 1.13782e6i | − | 0.0616928i | ||||||
\(807\) | −7.34431e6 | + | 7.26289e6i | −0.396978 | + | 0.392578i | ||||
\(808\) | −3.49962e7 | −1.88579 | ||||||||
\(809\) | 1.71808e7 | 0.922938 | 0.461469 | − | 0.887156i | \(-0.347322\pi\) | ||||
0.461469 | + | 0.887156i | \(0.347322\pi\) | |||||||
\(810\) | 1.17860e6 | − | 5.28540e7i | 0.0631179 | − | 2.83052i | ||||
\(811\) | − | 2.36051e7i | − | 1.26024i | −0.776496 | − | 0.630122i | \(-0.783005\pi\) | ||
0.776496 | − | 0.630122i | \(-0.216995\pi\) | |||||||
\(812\) | 3.16767e7i | 1.68597i | ||||||||
\(813\) | −1.12181e7 | + | 1.10937e7i | −0.595241 | + | 0.588642i | ||||
\(814\) | −1.46336e7 | + | 1.59166e6i | −0.774086 | + | 0.0841958i | ||||
\(815\) | − | 5.83318e6i | − | 0.307618i | ||||||
\(816\) | −1.90078e7 | − | 1.92209e7i | −0.999323 | − | 1.01053i | ||||
\(817\) | −4.43183e6 | −0.232289 | ||||||||
\(818\) | 3.08752e7i | 1.61334i | ||||||||
\(819\) | 178852. | − | 1.60432e7i | 0.00931719 | − | 0.835761i | ||||
\(820\) | − | 5.50433e7i | − | 2.85871i | ||||||
\(821\) | 1.40053e7 | 0.725160 | 0.362580 | − | 0.931953i | \(-0.381896\pi\) | ||||
0.362580 | + | 0.931953i | \(0.381896\pi\) | |||||||
\(822\) | 3.09019e7 | − | 3.05593e7i | 1.59516 | − | 1.57748i | ||||
\(823\) | 3.05211e7 | 1.57073 | 0.785365 | − | 0.619034i | \(-0.212476\pi\) | ||||
0.785365 | + | 0.619034i | \(0.212476\pi\) | |||||||
\(824\) | 4.37365e6 | 0.224402 | ||||||||
\(825\) | −2.28658e7 | − | 1.85904e7i | −1.16964 | − | 0.950942i | ||||
\(826\) | 4.62469e7 | 2.35848 | ||||||||
\(827\) | 1.02977e7 | 0.523573 | 0.261786 | − | 0.965126i | \(-0.415688\pi\) | ||||
0.261786 | + | 0.965126i | \(0.415688\pi\) | |||||||
\(828\) | −4.22421e7 | − | 470921.i | −2.14126 | − | 0.0238711i | ||||
\(829\) | 3.54953e7 | 1.79385 | 0.896923 | − | 0.442187i | \(-0.145797\pi\) | ||||
0.896923 | + | 0.442187i | \(0.145797\pi\) | |||||||
\(830\) | − | 1.82514e7i | − | 0.919604i | ||||||
\(831\) | 2.24243e7 | − | 2.21757e7i | 1.12646 | − | 1.11397i | ||||
\(832\) | 4.23323e6i | 0.212014i | ||||||||
\(833\) | 910069. | 0.0454424 | ||||||||
\(834\) | 9.12398e6 | − | 9.02283e6i | 0.454223 | − | 0.449188i | ||||
\(835\) | 6.07071e7i | 3.01317i | ||||||||
\(836\) | −2.56923e6 | − | 2.36212e7i | −0.127141 | − | 1.16892i | ||||
\(837\) | −585585. | + | 566321.i | −0.0288919 | + | 0.0279415i | ||||
\(838\) | 1.98926e7i | 0.978547i | ||||||||
\(839\) | − | 9.16702e6i | − | 0.449597i | −0.974405 | − | 0.224799i | \(-0.927828\pi\) | ||
0.974405 | − | 0.224799i | \(-0.0721724\pi\) | |||||||
\(840\) | −4.74388e7 | − | 4.79706e7i | −2.31972 | − | 2.34573i | ||||
\(841\) | −7.76630e6 | −0.378638 | ||||||||
\(842\) | −3.06586e7 | −1.49029 | ||||||||
\(843\) | 8.97277e6 | + | 9.07335e6i | 0.434868 | + | 0.439743i | ||||
\(844\) | − | 8.48697e6i | − | 0.410106i | ||||||
\(845\) | − | 8.64477e6i | − | 0.416497i | ||||||
\(846\) | −2.22657e7 | − | 248221.i | −1.06957 | − | 0.0119238i | ||||
\(847\) | −4.37033e6 | − | 1.98525e7i | −0.209318 | − | 0.950838i | ||||
\(848\) | − | 1.49678e6i | − | 0.0714773i | ||||||
\(849\) | −1.92368e7 | + | 1.90235e7i | −0.915931 | + | 0.905777i | ||||
\(850\) | 4.95251e7 | 2.35114 | ||||||||
\(851\) | − | 8.96830e6i | − | 0.424508i | ||||||
\(852\) | 2.62534e7 | − | 2.59624e7i | 1.23905 | − | 1.22531i | ||||
\(853\) | − | 3.24615e7i | − | 1.52755i | −0.645481 | − | 0.763777i | \(-0.723343\pi\) | ||
0.645481 | − | 0.763777i | \(-0.276657\pi\) | |||||||
\(854\) | 1.95569e7 | 0.917605 | ||||||||
\(855\) | −201953. | + | 1.81154e7i | −0.00944790 | + | 0.847486i | ||||
\(856\) | 7.27621e7 | 3.39407 | ||||||||
\(857\) | −2.58007e7 | −1.19999 | −0.599997 | − | 0.800002i | \(-0.704832\pi\) | ||||
−0.599997 | + | 0.800002i | \(0.704832\pi\) | |||||||
\(858\) | −2.08795e7 | + | 2.56814e7i | −0.968282 | + | 1.19097i | ||||
\(859\) | −3.96275e7 | −1.83237 | −0.916186 | − | 0.400753i | \(-0.868749\pi\) | ||||
−0.916186 | + | 0.400753i | \(0.868749\pi\) | |||||||
\(860\) | 3.27445e7 | 1.50970 | ||||||||
\(861\) | −1.23750e7 | + | 1.22378e7i | −0.568900 | + | 0.562593i | ||||
\(862\) | −1.37926e7 | −0.632233 | ||||||||
\(863\) | 2.53981e7i | 1.16085i | 0.814315 | + | 0.580423i | \(0.197113\pi\) | ||||
−0.814315 | + | 0.580423i | \(0.802887\pi\) | |||||||
\(864\) | −1.21936e7 | + | 1.17925e7i | −0.555710 | + | 0.537429i | ||||
\(865\) | 2.93556e7i | 1.33398i | ||||||||
\(866\) | 5.42479e7 | 2.45804 | ||||||||
\(867\) | 3.72017e6 | + | 3.76188e6i | 0.168080 | + | 0.169964i | ||||
\(868\) | 1.90821e6i | 0.0859659i | ||||||||
\(869\) | −4.63373e6 | − | 4.26020e7i | −0.208153 | − | 1.91373i | ||||
\(870\) | −3.54272e7 | + | 3.50344e7i | −1.58686 | + | 1.56927i | ||||
\(871\) | 2.79234e7i | 1.24716i | ||||||||
\(872\) | 3.30727e7i | 1.47292i | ||||||||
\(873\) | 183431. | − | 1.64540e7i | 0.00814587 | − | 0.730693i | ||||
\(874\) | 2.10661e7 | 0.932838 | ||||||||
\(875\) | 1.77172e7 | 0.782302 | ||||||||
\(876\) | −5.93274e7 | + | 5.86697e7i | −2.61213 | + | 2.58317i | ||||
\(877\) | − | 1.68679e7i | − | 0.740562i | −0.928920 | − | 0.370281i | \(-0.879261\pi\) | ||
0.928920 | − | 0.370281i | \(-0.120739\pi\) | |||||||
\(878\) | − | 4.11545e6i | − | 0.180169i | ||||||
\(879\) | −2.87140e7 | − | 2.90359e7i | −1.25349 | − | 1.26755i | ||||
\(880\) | 6.40828e6 | + | 5.89170e7i | 0.278956 | + | 2.56468i | ||||
\(881\) | − | 5.24399e6i | − | 0.227626i | −0.993502 | − | 0.113813i | \(-0.963693\pi\) | ||
0.993502 | − | 0.113813i | \(-0.0363065\pi\) | |||||||
\(882\) | 23987.6 | − | 2.15171e6i | 0.00103828 | − | 0.0931348i | ||||
\(883\) | −1.16775e7 | −0.504022 | −0.252011 | − | 0.967724i | \(-0.581092\pi\) | ||||
−0.252011 | + | 0.967724i | \(0.581092\pi\) | |||||||
\(884\) | − | 3.82237e7i | − | 1.64514i | ||||||
\(885\) | 3.51491e7 | + | 3.55431e7i | 1.50854 | + | 1.52545i | ||||
\(886\) | 2.32565e7i | 0.995312i | ||||||||
\(887\) | −2.36878e7 | −1.01092 | −0.505459 | − | 0.862850i | \(-0.668677\pi\) | ||||
−0.505459 | + | 0.862850i | \(0.668677\pi\) | |||||||
\(888\) | −1.53977e7 | − | 1.55703e7i | −0.655273 | − | 0.662619i | ||||
\(889\) | −1.91141e7 | −0.811148 | ||||||||
\(890\) | −1.06103e7 | −0.449005 | ||||||||
\(891\) | 2.36094e7 | − | 2.03654e6i | 0.996300 | − | 0.0859405i | ||||
\(892\) | 2.16049e7 | 0.909160 | ||||||||
\(893\) | 7.63049e6 | 0.320202 | ||||||||
\(894\) | 6.75485e6 | + | 6.83057e6i | 0.282665 | + | 0.285834i | ||||
\(895\) | −4.44767e7 | −1.85599 | ||||||||
\(896\) | − | 2.84185e7i | − | 1.18258i | ||||||
\(897\) | −1.41795e7 | − | 1.43384e7i | −0.588409 | − | 0.595005i | ||||
\(898\) | − | 6.60156e7i | − | 2.73184i | ||||||
\(899\) | 767751. | 0.0316826 | ||||||||
\(900\) | 897044. | − | 8.04658e7i | 0.0369154 | − | 3.31135i | ||||
\(901\) | − | 932586.i | − | 0.0382716i | ||||||
\(902\) | 3.56929e7 | − | 3.88225e6i | 1.46072 | − | 0.158879i | ||||
\(903\) | −7.28007e6 | − | 7.36168e6i | −0.297109 | − | 0.300440i | ||||
\(904\) | 2.81289e7i | 1.14481i | ||||||||
\(905\) | 7.21836e7i | 2.92966i | ||||||||
\(906\) | −4.91154e7 | + | 4.85709e7i | −1.98791 | + | 1.96588i | ||||
\(907\) | −1.16913e7 | −0.471893 | −0.235947 | − | 0.971766i | \(-0.575819\pi\) | ||||
−0.235947 | + | 0.971766i | \(0.575819\pi\) | |||||||
\(908\) | 3.22097e7 | 1.29650 | ||||||||
\(909\) | −244732. | + | 2.19527e7i | −0.00982383 | + | 0.881208i | ||||
\(910\) | − | 5.91134e7i | − | 2.36637i | ||||||
\(911\) | − | 1.28663e7i | − | 0.513639i | −0.966459 | − | 0.256820i | \(-0.917325\pi\) | ||
0.966459 | − | 0.256820i | \(-0.0826747\pi\) | |||||||
\(912\) | 1.55739e7 | − | 1.54013e7i | 0.620027 | − | 0.613154i | ||||
\(913\) | 8.13299e6 | − | 884609.i | 0.322904 | − | 0.0351216i | ||||
\(914\) | 7.70698e7i | 3.05154i | ||||||||
\(915\) | 1.48639e7 | + | 1.50305e7i | 0.586920 | + | 0.593500i | ||||
\(916\) | 1.73309e7 | 0.682468 | ||||||||
\(917\) | 2.60433e7i | 1.02276i | ||||||||
\(918\) | −2.86269e7 | + | 2.76852e7i | −1.12116 | + | 1.08428i | ||||
\(919\) | 275353.i | 0.0107548i | 0.999986 | + | 0.00537738i | \(0.00171168\pi\) | ||||
−0.999986 | + | 0.00537738i | \(0.998288\pi\) | |||||||
\(920\) | −8.47957e7 | −3.30297 | ||||||||
\(921\) | 1.14651e6 | − | 1.13380e6i | 0.0445377 | − | 0.0440440i | ||||
\(922\) | −1.86767e7 | −0.723558 | ||||||||
\(923\) | 1.76251e7 | 0.680969 | ||||||||
\(924\) | 3.50166e7 | − | 4.30697e7i | 1.34925 | − | 1.65956i | ||||
\(925\) | 1.70835e7 | 0.656480 | ||||||||
\(926\) | −9.00335e7 | −3.45046 | ||||||||
\(927\) | 30585.4 | − | 2.74354e6i | 0.00116900 | − | 0.104860i | ||||
\(928\) | 1.59869e7 | 0.609388 | ||||||||
\(929\) | 2.62372e6i | 0.0997419i | 0.998756 | + | 0.0498710i | \(0.0158810\pi\) | ||||
−0.998756 | + | 0.0498710i | \(0.984119\pi\) | |||||||
\(930\) | −2.13414e6 | + | 2.11048e6i | −0.0809123 | + | 0.0800154i | ||||
\(931\) | 737393.i | 0.0278821i | ||||||||
\(932\) | 4.21278e7 | 1.58865 | ||||||||
\(933\) | −1.24536e7 | + | 1.23155e7i | −0.468372 | + | 0.463179i | ||||
\(934\) | − | 3.87992e7i | − | 1.45531i | ||||||
\(935\) | 3.99275e6 | + | 3.67089e7i | 0.149363 | + | 1.37323i | ||||
\(936\) | −4.92353e7 | − | 548882.i | −1.83691 | − | 0.0204781i | ||||
\(937\) | 2.07014e7i | 0.770282i | 0.922858 | + | 0.385141i | \(0.125847\pi\) | ||||
−0.922858 | + | 0.385141i | \(0.874153\pi\) | |||||||
\(938\) | − | 6.81469e7i | − | 2.52894i | ||||||
\(939\) | 2.18951e7 | + | 2.21406e7i | 0.810371 | + | 0.819455i | ||||
\(940\) | −5.63777e7 | −2.08107 | ||||||||
\(941\) | −3.59089e7 | −1.32199 | −0.660995 | − | 0.750390i | \(-0.729866\pi\) | ||||
−0.660995 | + | 0.750390i | \(0.729866\pi\) | |||||||
\(942\) | 3.82775e7 | + | 3.87066e7i | 1.40545 | + | 1.42121i | ||||
\(943\) | 2.18747e7i | 0.801056i | ||||||||
\(944\) | − | 6.04358e7i | − | 2.20731i | ||||||
\(945\) | −3.04231e7 | + | 2.94223e7i | −1.10822 | + | 1.07176i | ||||
\(946\) | 2.30949e6 | + | 2.12332e7i | 0.0839052 | + | 0.771415i | ||||
\(947\) | − | 1.48621e7i | − | 0.538525i | −0.963067 | − | 0.269262i | \(-0.913220\pi\) | ||
0.963067 | − | 0.269262i | \(-0.0867799\pi\) | |||||||
\(948\) | 8.32036e7 | − | 8.22812e7i | 3.00692 | − | 2.97358i | ||||
\(949\) | −3.98291e7 | −1.43560 | ||||||||
\(950\) | 4.01283e7i | 1.44259i | ||||||||
\(951\) | 2.83739e7 | − | 2.80594e7i | 1.01735 | − | 1.00607i | ||||
\(952\) | 5.08212e7i | 1.81741i | ||||||||
\(953\) | 4.21166e7 | 1.50218 | 0.751089 | − | 0.660201i | \(-0.229529\pi\) | ||||
0.751089 | + | 0.660201i | \(0.229529\pi\) | |||||||
\(954\) | −2.20495e6 | − | 24581.1i | −0.0784381 | − | 0.000874439i | ||||
\(955\) | 4.66915e7 | 1.65665 | ||||||||
\(956\) | 2.51562e7 | 0.890225 | ||||||||
\(957\) | −1.73287e7 | − | 1.40886e7i | −0.611628 | − | 0.497266i | ||||
\(958\) | 4.33217e7 | 1.52508 | ||||||||
\(959\) | −3.47923e7 | −1.22162 | ||||||||
\(960\) | 7.94003e6 | − | 7.85200e6i | 0.278063 | − | 0.274981i | ||||
\(961\) | −2.85829e7 | −0.998385 | ||||||||
\(962\) | − | 1.91870e7i | − | 0.668451i | ||||||
\(963\) | 508832. | − | 4.56427e7i | 0.0176811 | − | 1.58601i | ||||
\(964\) | 4.01143e7i | 1.39029i | ||||||||
\(965\) | −5.07173e7 | −1.75323 | ||||||||
\(966\) | 3.46049e7 | + | 3.49928e7i | 1.19315 | + | 1.20652i | ||||
\(967\) | 8.56810e6i | 0.294658i | 0.989088 | + | 0.147329i | \(0.0470676\pi\) | ||||
−0.989088 | + | 0.147329i | \(0.952932\pi\) | |||||||
\(968\) | −6.09256e7 | + | 1.34122e7i | −2.08983 | + | 0.460056i | ||||
\(969\) | 9.70351e6 | − | 9.59593e6i | 0.331986 | − | 0.328305i | ||||
\(970\) | − | 6.06268e7i | − | 2.06888i | ||||||
\(971\) | 2.19573e7i | 0.747361i | 0.927558 | + | 0.373680i | \(0.121904\pi\) | ||||
−0.927558 | + | 0.373680i | \(0.878096\pi\) | |||||||
\(972\) | 4.44629e7 | + | 4.70129e7i | 1.50950 | + | 1.59607i | ||||
\(973\) | −1.02727e7 | −0.347857 | ||||||||
\(974\) | 7.24210e7 | 2.44606 | ||||||||
\(975\) | 2.73129e7 | − | 2.70101e7i | 0.920145 | − | 0.909944i | ||||
\(976\) | − | 2.55571e7i | − | 0.858791i | ||||||
\(977\) | − | 5.22389e7i | − | 1.75088i | −0.483324 | − | 0.875442i | \(-0.660571\pi\) | ||
0.483324 | − | 0.875442i | \(-0.339429\pi\) | |||||||
\(978\) | 7.30556e6 | + | 7.38746e6i | 0.244234 | + | 0.246972i | ||||
\(979\) | −514258. | − | 4.72803e6i | −0.0171484 | − | 0.157661i | ||||
\(980\) | − | 5.44821e6i | − | 0.181213i | ||||||
\(981\) | 2.07461e7 | + | 231281.i | 0.688278 | + | 0.00767303i | ||||
\(982\) | −2.60346e7 | −0.861532 | ||||||||
\(983\) | − | 2.73562e7i | − | 0.902967i | −0.892279 | − | 0.451484i | \(-0.850895\pi\) | ||
0.892279 | − | 0.451484i | \(-0.149105\pi\) | |||||||
\(984\) | 3.75567e7 | + | 3.79777e7i | 1.23651 | + | 1.25038i | ||||
\(985\) | 2.51921e7i | 0.827321i | ||||||||
\(986\) | 3.75323e7 | 1.22946 | ||||||||
\(987\) | 1.25344e7 | + | 1.26750e7i | 0.409555 | + | 0.414146i | ||||
\(988\) | 3.09712e7 | 1.00941 | ||||||||
\(989\) | −1.30129e7 | −0.423043 | ||||||||
\(990\) | 8.68974e7 | − | 8.47264e6i | 2.81786 | − | 0.274746i | ||||
\(991\) | −3.70174e7 | −1.19735 | −0.598676 | − | 0.800991i | \(-0.704306\pi\) | ||||
−0.598676 | + | 0.800991i | \(0.704306\pi\) | |||||||
\(992\) | 963051. | 0.0310721 | ||||||||
\(993\) | 5.88996e6 | + | 5.95599e6i | 0.189557 | + | 0.191682i | ||||
\(994\) | −4.30139e7 | −1.38084 | ||||||||
\(995\) | − | 3.76547e7i | − | 1.20576i | ||||||
\(996\) | 1.57080e7 | + | 1.58841e7i | 0.501732 | + | 0.507357i | ||||
\(997\) | − | 4.63374e7i | − | 1.47636i | −0.674601 | − | 0.738182i | \(-0.735684\pi\) | ||
0.674601 | − | 0.738182i | \(-0.264316\pi\) | |||||||
\(998\) | −3.34181e7 | −1.06208 | ||||||||
\(999\) | −9.87472e6 | + | 9.54988e6i | −0.313048 | + | 0.302750i |
(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 | 33.6.d.b.32.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 33.6.d.b.32.16 | yes | 16 | |
11.10 | odd | 2 | inner | 33.6.d.b.32.15 | yes | 16 | |
33.32 | even | 2 | inner | 33.6.d.b.32.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.d.b.32.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
33.6.d.b.32.2 | yes | 16 | 33.32 | even | 2 | inner | |
33.6.d.b.32.15 | yes | 16 | 11.10 | odd | 2 | inner | |
33.6.d.b.32.16 | yes | 16 | 3.2 | odd | 2 | inner |