Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,7,Mod(114,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("115.114");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.c (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: | \(26.4562196163\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 114.13 | ||
Character | \(\chi\) | \(=\) | 115.114 |
Dual form | 115.7.c.c.114.14 |
$q$-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 \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.35786i | − | 0.544733i | −0.962194 | − | 0.272366i | \(-0.912194\pi\) | ||
0.962194 | − | 0.272366i | \(-0.0878063\pi\) | |||||||
\(3\) | 24.6249i | 0.912034i | 0.889971 | + | 0.456017i | \(0.150724\pi\) | ||||
−0.889971 | + | 0.456017i | \(0.849276\pi\) | |||||||
\(4\) | 45.0090 | 0.703266 | ||||||||
\(5\) | 108.536 | + | 62.0072i | 0.868290 | + | 0.496058i | ||||
\(6\) | 107.312 | 0.496815 | ||||||||
\(7\) | −356.743 | −1.04007 | −0.520034 | − | 0.854146i | \(-0.674081\pi\) | ||||
−0.520034 | + | 0.854146i | \(0.674081\pi\) | |||||||
\(8\) | − | 475.046i | − | 0.927825i | ||||||
\(9\) | 122.613 | 0.168194 | ||||||||
\(10\) | 270.219 | − | 472.986i | 0.270219 | − | 0.472986i | ||||
\(11\) | − | 2460.25i | − | 1.84843i | −0.381878 | − | 0.924213i | \(-0.624723\pi\) | ||
0.381878 | − | 0.924213i | \(-0.375277\pi\) | |||||||
\(12\) | 1108.34i | 0.641403i | ||||||||
\(13\) | − | 3886.94i | − | 1.76920i | −0.466348 | − | 0.884601i | \(-0.654431\pi\) | ||
0.466348 | − | 0.884601i | \(-0.345569\pi\) | |||||||
\(14\) | 1554.64i | 0.566559i | ||||||||
\(15\) | −1526.92 | + | 2672.70i | −0.452422 | + | 0.791910i | ||||
\(16\) | 810.390 | 0.197849 | ||||||||
\(17\) | 5678.93 | 1.15590 | 0.577949 | − | 0.816073i | \(-0.303853\pi\) | ||||
0.577949 | + | 0.816073i | \(0.303853\pi\) | |||||||
\(18\) | − | 534.332i | − | 0.0916208i | ||||||
\(19\) | 4274.93i | 0.623259i | 0.950204 | + | 0.311629i | \(0.100875\pi\) | ||||
−0.950204 | + | 0.311629i | \(0.899125\pi\) | |||||||
\(20\) | 4885.11 | + | 2790.88i | 0.610639 | + | 0.348861i | ||||
\(21\) | − | 8784.77i | − | 0.948577i | ||||||
\(22\) | −10721.5 | −1.00690 | ||||||||
\(23\) | −11955.6 | − | 2258.26i | −0.982624 | − | 0.185606i | ||||
\(24\) | 11698.0 | 0.846208 | ||||||||
\(25\) | 7935.21 | + | 13460.1i | 0.507854 | + | 0.861443i | ||||
\(26\) | −16938.7 | −0.963743 | ||||||||
\(27\) | 20970.9i | 1.06543i | ||||||||
\(28\) | −16056.7 | −0.731444 | ||||||||
\(29\) | 31948.2 | 1.30994 | 0.654972 | − | 0.755653i | \(-0.272680\pi\) | ||||
0.654972 | + | 0.755653i | \(0.272680\pi\) | |||||||
\(30\) | 11647.2 | + | 6654.12i | 0.431379 | + | 0.246449i | ||||
\(31\) | 27146.6 | 0.911236 | 0.455618 | − | 0.890175i | \(-0.349418\pi\) | ||||
0.455618 | + | 0.890175i | \(0.349418\pi\) | |||||||
\(32\) | − | 33934.5i | − | 1.03560i | ||||||
\(33\) | 60583.6 | 1.68583 | ||||||||
\(34\) | − | 24748.0i | − | 0.629656i | ||||||
\(35\) | −38719.5 | − | 22120.6i | −0.903080 | − | 0.515933i | ||||
\(36\) | 5518.71 | 0.118285 | ||||||||
\(37\) | −6032.87 | −0.119102 | −0.0595510 | − | 0.998225i | \(-0.518967\pi\) | ||||
−0.0595510 | + | 0.998225i | \(0.518967\pi\) | |||||||
\(38\) | 18629.6 | 0.339510 | ||||||||
\(39\) | 95715.5 | 1.61357 | ||||||||
\(40\) | 29456.3 | − | 51559.7i | 0.460255 | − | 0.805621i | ||||
\(41\) | 103770. | 1.50564 | 0.752819 | − | 0.658227i | \(-0.228693\pi\) | ||||
0.752819 | + | 0.658227i | \(0.228693\pi\) | |||||||
\(42\) | −38282.8 | −0.516721 | ||||||||
\(43\) | −105331. | −1.32481 | −0.662403 | − | 0.749148i | \(-0.730463\pi\) | ||||
−0.662403 | + | 0.749148i | \(0.730463\pi\) | |||||||
\(44\) | − | 110734.i | − | 1.29993i | ||||||
\(45\) | 13308.0 | + | 7602.91i | 0.146041 | + | 0.0834339i | ||||
\(46\) | −9841.21 | + | 52100.8i | −0.101106 | + | 0.535268i | ||||
\(47\) | − | 6782.07i | − | 0.0653234i | −0.999466 | − | 0.0326617i | \(-0.989602\pi\) | ||
0.999466 | − | 0.0326617i | \(-0.0103984\pi\) | |||||||
\(48\) | 19955.8i | 0.180445i | ||||||||
\(49\) | 9616.64 | 0.0817401 | ||||||||
\(50\) | 58657.1 | − | 34580.6i | 0.469257 | − | 0.276645i | ||||
\(51\) | 139843.i | 1.05422i | ||||||||
\(52\) | − | 174947.i | − | 1.24422i | ||||||
\(53\) | −47948.2 | −0.322066 | −0.161033 | − | 0.986949i | \(-0.551483\pi\) | ||||
−0.161033 | + | 0.986949i | \(0.551483\pi\) | |||||||
\(54\) | 91388.4 | 0.580376 | ||||||||
\(55\) | 152554. | − | 267027.i | 0.916926 | − | 1.60497i | ||||
\(56\) | 169470.i | 0.965001i | ||||||||
\(57\) | −105270. | −0.568433 | ||||||||
\(58\) | − | 139226.i | − | 0.713570i | ||||||
\(59\) | −275854. | −1.34315 | −0.671574 | − | 0.740938i | \(-0.734381\pi\) | ||||
−0.671574 | + | 0.740938i | \(0.734381\pi\) | |||||||
\(60\) | −68725.3 | + | 120295.i | −0.318173 | + | 0.556923i | ||||
\(61\) | 44668.5i | 0.196794i | 0.995147 | + | 0.0983971i | \(0.0313715\pi\) | ||||
−0.995147 | + | 0.0983971i | \(0.968628\pi\) | |||||||
\(62\) | − | 118301.i | − | 0.496380i | ||||||
\(63\) | −43741.5 | −0.174933 | ||||||||
\(64\) | −96017.2 | −0.366276 | ||||||||
\(65\) | 241018. | − | 421873.i | 0.877626 | − | 1.53618i | ||||
\(66\) | − | 264015.i | − | 0.918326i | ||||||
\(67\) | −120875. | −0.401895 | −0.200947 | − | 0.979602i | \(-0.564402\pi\) | ||||
−0.200947 | + | 0.979602i | \(0.564402\pi\) | |||||||
\(68\) | 255603. | 0.812904 | ||||||||
\(69\) | 55609.6 | − | 294405.i | 0.169279 | − | 0.896187i | ||||
\(70\) | −96398.8 | + | 168734.i | −0.281046 | + | 0.491937i | ||||
\(71\) | 493278. | 1.37821 | 0.689107 | − | 0.724660i | \(-0.258003\pi\) | ||||
0.689107 | + | 0.724660i | \(0.258003\pi\) | |||||||
\(72\) | − | 58247.0i | − | 0.156055i | ||||||
\(73\) | 37898.7i | 0.0974218i | 0.998813 | + | 0.0487109i | \(0.0155113\pi\) | ||||
−0.998813 | + | 0.0487109i | \(0.984489\pi\) | |||||||
\(74\) | 26290.4i | 0.0648787i | ||||||||
\(75\) | −331453. | + | 195404.i | −0.785666 | + | 0.463180i | ||||
\(76\) | 192411.i | 0.438317i | ||||||||
\(77\) | 877679.i | 1.92249i | ||||||||
\(78\) | − | 417115.i | − | 0.878966i | ||||||
\(79\) | 532286.i | 1.07960i | 0.841793 | + | 0.539801i | \(0.181500\pi\) | ||||
−0.841793 | + | 0.539801i | \(0.818500\pi\) | |||||||
\(80\) | 87956.6 | + | 50250.0i | 0.171790 | + | 0.0981445i | ||||
\(81\) | −427022. | −0.803517 | ||||||||
\(82\) | − | 452216.i | − | 0.820171i | ||||||
\(83\) | 610329. | 1.06741 | 0.533703 | − | 0.845672i | \(-0.320800\pi\) | ||||
0.533703 | + | 0.845672i | \(0.320800\pi\) | |||||||
\(84\) | − | 395394.i | − | 0.667102i | ||||||
\(85\) | 616369. | + | 352135.i | 1.00365 | + | 0.573392i | ||||
\(86\) | 459020.i | 0.721665i | ||||||||
\(87\) | 786722.i | 1.19471i | ||||||||
\(88\) | −1.16874e6 | −1.71502 | ||||||||
\(89\) | − | 1.02095e6i | − | 1.44822i | −0.689684 | − | 0.724111i | \(-0.742250\pi\) | ||
0.689684 | − | 0.724111i | \(-0.257750\pi\) | |||||||
\(90\) | 33132.5 | − | 57994.4i | 0.0454492 | − | 0.0795533i | ||||
\(91\) | 1.38664e6i | 1.84009i | ||||||||
\(92\) | −538109. | − | 101642.i | −0.691046 | − | 0.130530i | ||||
\(93\) | 668484.i | 0.831079i | ||||||||
\(94\) | −29555.3 | −0.0355838 | ||||||||
\(95\) | −265077. | + | 463985.i | −0.309172 | + | 0.541169i | ||||
\(96\) | 835635. | 0.944503 | ||||||||
\(97\) | 837437. | 0.917566 | 0.458783 | − | 0.888548i | \(-0.348286\pi\) | ||||
0.458783 | + | 0.888548i | \(0.348286\pi\) | |||||||
\(98\) | − | 41908.0i | − | 0.0445265i | ||||||
\(99\) | − | 301660.i | − | 0.310894i | ||||||
\(100\) | 357156. | + | 605824.i | 0.357156 | + | 0.605824i | ||||
\(101\) | −1.04596e6 | −1.01519 | −0.507597 | − | 0.861595i | \(-0.669466\pi\) | ||||
−0.507597 | + | 0.861595i | \(0.669466\pi\) | |||||||
\(102\) | 609417. | 0.574268 | ||||||||
\(103\) | 234877. | 0.214945 | 0.107473 | − | 0.994208i | \(-0.465724\pi\) | ||||
0.107473 | + | 0.994208i | \(0.465724\pi\) | |||||||
\(104\) | −1.84648e6 | −1.64151 | ||||||||
\(105\) | 544719. | − | 953466.i | 0.470549 | − | 0.823639i | ||||
\(106\) | 208952.i | 0.175440i | ||||||||
\(107\) | −86713.5 | −0.0707841 | −0.0353920 | − | 0.999374i | \(-0.511268\pi\) | ||||
−0.0353920 | + | 0.999374i | \(0.511268\pi\) | |||||||
\(108\) | 943880.i | 0.749283i | ||||||||
\(109\) | − | 363988.i | − | 0.281066i | −0.990076 | − | 0.140533i | \(-0.955118\pi\) | ||
0.990076 | − | 0.140533i | \(-0.0448816\pi\) | |||||||
\(110\) | −1.16367e6 | − | 664807.i | −0.874279 | − | 0.499480i | ||||
\(111\) | − | 148559.i | − | 0.108625i | ||||||
\(112\) | −289101. | −0.205776 | ||||||||
\(113\) | −454665. | −0.315106 | −0.157553 | − | 0.987511i | \(-0.550360\pi\) | ||||
−0.157553 | + | 0.987511i | \(0.550360\pi\) | |||||||
\(114\) | 458752.i | 0.309644i | ||||||||
\(115\) | −1.15759e6 | − | 986436.i | −0.761131 | − | 0.648598i | ||||
\(116\) | 1.43796e6 | 0.921239 | ||||||||
\(117\) | − | 476590.i | − | 0.297569i | ||||||
\(118\) | 1.20214e6i | 0.731657i | ||||||||
\(119\) | −2.02592e6 | −1.20221 | ||||||||
\(120\) | 1.26965e6 | + | 725359.i | 0.734754 | + | 0.419768i | ||||
\(121\) | −4.28129e6 | −2.41668 | ||||||||
\(122\) | 194659. | 0.107200 | ||||||||
\(123\) | 2.55533e6i | 1.37319i | ||||||||
\(124\) | 1.22184e6 | 0.640841 | ||||||||
\(125\) | 26637.2 | + | 1.95294e6i | 0.0136382 | + | 0.999907i | ||||
\(126\) | 190619.i | 0.0952918i | ||||||||
\(127\) | − | 961934.i | − | 0.469606i | −0.972043 | − | 0.234803i | \(-0.924555\pi\) | ||
0.972043 | − | 0.234803i | \(-0.0754446\pi\) | |||||||
\(128\) | − | 1.75338e6i | − | 0.836077i | ||||||
\(129\) | − | 2.59378e6i | − | 1.20827i | ||||||
\(130\) | −1.83847e6 | − | 1.05032e6i | −0.836808 | − | 0.478072i | ||||
\(131\) | −1.68559e6 | −0.749786 | −0.374893 | − | 0.927068i | \(-0.622321\pi\) | ||||
−0.374893 | + | 0.927068i | \(0.622321\pi\) | |||||||
\(132\) | 2.72681e6 | 1.18558 | ||||||||
\(133\) | − | 1.52505e6i | − | 0.648231i | ||||||
\(134\) | 526757.i | 0.218925i | ||||||||
\(135\) | −1.30035e6 | + | 2.27610e6i | −0.528516 | + | 0.925104i | ||||
\(136\) | − | 2.69775e6i | − | 1.07247i | ||||||
\(137\) | 773225. | 0.300708 | 0.150354 | − | 0.988632i | \(-0.451959\pi\) | ||||
0.150354 | + | 0.988632i | \(0.451959\pi\) | |||||||
\(138\) | −1.28298e6 | − | 242339.i | −0.488183 | − | 0.0922117i | ||||
\(139\) | 3.65378e6 | 1.36050 | 0.680249 | − | 0.732981i | \(-0.261871\pi\) | ||||
0.680249 | + | 0.732981i | \(0.261871\pi\) | |||||||
\(140\) | −1.74273e6 | − | 995629.i | −0.635105 | − | 0.362838i | ||||
\(141\) | 167008. | 0.0595771 | ||||||||
\(142\) | − | 2.14964e6i | − | 0.750758i | ||||||
\(143\) | −9.56285e6 | −3.27024 | ||||||||
\(144\) | 99364.6 | 0.0332770 | ||||||||
\(145\) | 3.46754e6 | + | 1.98102e6i | 1.13741 | + | 0.649808i | ||||
\(146\) | 165158. | 0.0530689 | ||||||||
\(147\) | 236809.i | 0.0745498i | ||||||||
\(148\) | −271534. | −0.0837603 | ||||||||
\(149\) | 1.76101e6i | 0.532358i | 0.963924 | + | 0.266179i | \(0.0857612\pi\) | ||||
−0.963924 | + | 0.266179i | \(0.914239\pi\) | |||||||
\(150\) | 851544. | + | 1.44443e6i | 0.252309 | + | 0.427978i | ||||
\(151\) | 467646. | 0.135827 | 0.0679135 | − | 0.997691i | \(-0.478366\pi\) | ||||
0.0679135 | + | 0.997691i | \(0.478366\pi\) | |||||||
\(152\) | 2.03079e6 | 0.578275 | ||||||||
\(153\) | 696312. | 0.194415 | ||||||||
\(154\) | 3.82480e6 | 1.04724 | ||||||||
\(155\) | 2.94639e6 | + | 1.68329e6i | 0.791217 | + | 0.452026i | ||||
\(156\) | 4.30806e6 | 1.13477 | ||||||||
\(157\) | 2.91729e6 | 0.753842 | 0.376921 | − | 0.926245i | \(-0.376983\pi\) | ||||
0.376921 | + | 0.926245i | \(0.376983\pi\) | |||||||
\(158\) | 2.31963e6 | 0.588095 | ||||||||
\(159\) | − | 1.18072e6i | − | 0.293735i | ||||||
\(160\) | 2.10419e6 | − | 3.68313e6i | 0.513717 | − | 0.899201i | ||||
\(161\) | 4.26507e6 | + | 805620.i | 1.02200 | + | 0.193042i | ||||
\(162\) | 1.86090e6i | 0.437702i | ||||||||
\(163\) | − | 4.35741e6i | − | 1.00616i | −0.864241 | − | 0.503079i | \(-0.832201\pi\) | ||
0.864241 | − | 0.503079i | \(-0.167799\pi\) | |||||||
\(164\) | 4.67059e6 | 1.05886 | ||||||||
\(165\) | 6.57551e6 | + | 3.75662e6i | 1.46379 | + | 0.836267i | ||||
\(166\) | − | 2.65973e6i | − | 0.581451i | ||||||
\(167\) | 8.54229e6i | 1.83411i | 0.398763 | + | 0.917054i | \(0.369439\pi\) | ||||
−0.398763 | + | 0.917054i | \(0.630561\pi\) | |||||||
\(168\) | −4.17317e6 | −0.880113 | ||||||||
\(169\) | −1.02815e7 | −2.13008 | ||||||||
\(170\) | 1.53455e6 | − | 2.68605e6i | 0.312346 | − | 0.546724i | ||||
\(171\) | 524164.i | 0.104828i | ||||||||
\(172\) | −4.74086e6 | −0.931691 | ||||||||
\(173\) | 2.83226e6i | 0.547010i | 0.961871 | + | 0.273505i | \(0.0881829\pi\) | ||||
−0.961871 | + | 0.273505i | \(0.911817\pi\) | |||||||
\(174\) | 3.42843e6 | 0.650800 | ||||||||
\(175\) | −2.83083e6 | − | 4.80178e6i | −0.528202 | − | 0.895959i | ||||
\(176\) | − | 1.99376e6i | − | 0.365709i | ||||||
\(177\) | − | 6.79289e6i | − | 1.22500i | ||||||
\(178\) | −4.44917e6 | −0.788894 | ||||||||
\(179\) | −4.47118e6 | −0.779585 | −0.389792 | − | 0.920903i | \(-0.627453\pi\) | ||||
−0.389792 | + | 0.920903i | \(0.627453\pi\) | |||||||
\(180\) | 598979. | + | 342200.i | 0.102706 | + | 0.0586762i | ||||
\(181\) | 1.11610e6i | 0.188220i | 0.995562 | + | 0.0941101i | \(0.0300006\pi\) | ||||
−0.995562 | + | 0.0941101i | \(0.969999\pi\) | |||||||
\(182\) | 6.04278e6 | 1.00236 | ||||||||
\(183\) | −1.09996e6 | −0.179483 | ||||||||
\(184\) | −1.07278e6 | + | 5.67946e6i | −0.172210 | + | 0.911704i | ||||
\(185\) | −654785. | − | 374081.i | −0.103415 | − | 0.0590814i | ||||
\(186\) | 2.91316e6 | 0.452716 | ||||||||
\(187\) | − | 1.39716e7i | − | 2.13659i | ||||||
\(188\) | − | 305254.i | − | 0.0459397i | ||||||
\(189\) | − | 7.48123e6i | − | 1.10812i | ||||||
\(190\) | 2.02198e6 | + | 1.15517e6i | 0.294793 | + | 0.168416i | ||||
\(191\) | 2.93034e6i | 0.420550i | 0.977642 | + | 0.210275i | \(0.0674359\pi\) | ||||
−0.977642 | + | 0.210275i | \(0.932564\pi\) | |||||||
\(192\) | − | 2.36442e6i | − | 0.334057i | ||||||
\(193\) | 2.11862e6i | 0.294701i | 0.989084 | + | 0.147351i | \(0.0470746\pi\) | ||||
−0.989084 | + | 0.147351i | \(0.952925\pi\) | |||||||
\(194\) | − | 3.64944e6i | − | 0.499828i | ||||||
\(195\) | 1.03886e7 | + | 5.93505e6i | 1.40105 | + | 0.800425i | ||||
\(196\) | 432836. | 0.0574850 | ||||||||
\(197\) | 7.08008e6i | 0.926061i | 0.886342 | + | 0.463031i | \(0.153238\pi\) | ||||
−0.886342 | + | 0.463031i | \(0.846762\pi\) | |||||||
\(198\) | −1.31459e6 | −0.169354 | ||||||||
\(199\) | − | 3.90889e6i | − | 0.496015i | −0.968758 | − | 0.248007i | \(-0.920224\pi\) | ||
0.968758 | − | 0.248007i | \(-0.0797757\pi\) | |||||||
\(200\) | 6.39415e6 | − | 3.76959e6i | 0.799269 | − | 0.471199i | ||||
\(201\) | − | 2.97654e6i | − | 0.366542i | ||||||
\(202\) | 4.55813e6i | 0.553010i | ||||||||
\(203\) | −1.13973e7 | −1.36243 | ||||||||
\(204\) | 6.29420e6i | 0.741396i | ||||||||
\(205\) | 1.12628e7 | + | 6.43450e6i | 1.30733 | + | 0.746884i | ||||
\(206\) | − | 1.02356e6i | − | 0.117088i | ||||||
\(207\) | −1.46591e6 | − | 276893.i | −0.165271 | − | 0.0312177i | ||||
\(208\) | − | 3.14993e6i | − | 0.350035i | ||||||
\(209\) | 1.05174e7 | 1.15205 | ||||||||
\(210\) | −4.15507e6 | − | 2.37381e6i | −0.448664 | − | 0.256323i | ||||
\(211\) | −2.29079e6 | −0.243858 | −0.121929 | − | 0.992539i | \(-0.538908\pi\) | ||||
−0.121929 | + | 0.992539i | \(0.538908\pi\) | |||||||
\(212\) | −2.15810e6 | −0.226498 | ||||||||
\(213\) | 1.21469e7i | 1.25698i | ||||||||
\(214\) | 377886.i | 0.0385584i | ||||||||
\(215\) | −1.14323e7 | − | 6.53130e6i | −1.15032 | − | 0.657180i | ||||
\(216\) | 9.96216e6 | 0.988535 | ||||||||
\(217\) | −9.68438e6 | −0.947747 | ||||||||
\(218\) | −1.58621e6 | −0.153106 | ||||||||
\(219\) | −933253. | −0.0888520 | ||||||||
\(220\) | 6.86628e6 | − | 1.20186e7i | 0.644843 | − | 1.12872i | ||||
\(221\) | − | 2.20736e7i | − | 2.04502i | ||||||
\(222\) | −647399. | −0.0591716 | ||||||||
\(223\) | − | 1.12421e7i | − | 1.01375i | −0.862019 | − | 0.506877i | \(-0.830800\pi\) | ||
0.862019 | − | 0.506877i | \(-0.169200\pi\) | |||||||
\(224\) | 1.21059e7i | 1.07709i | ||||||||
\(225\) | 972963. | + | 1.65038e6i | 0.0854179 | + | 0.144890i | ||||
\(226\) | 1.98137e6i | 0.171648i | ||||||||
\(227\) | 1.25244e7 | 1.07073 | 0.535366 | − | 0.844620i | \(-0.320174\pi\) | ||||
0.535366 | + | 0.844620i | \(0.320174\pi\) | |||||||
\(228\) | −4.73809e6 | −0.399760 | ||||||||
\(229\) | 1.34835e7i | 1.12278i | 0.827551 | + | 0.561391i | \(0.189734\pi\) | ||||
−0.827551 | + | 0.561391i | \(0.810266\pi\) | |||||||
\(230\) | −4.29875e6 | + | 5.04460e6i | −0.353313 | + | 0.414613i | ||||
\(231\) | −2.16128e7 | −1.75337 | ||||||||
\(232\) | − | 1.51769e7i | − | 1.21540i | ||||||
\(233\) | 1.98445e6i | 0.156882i | 0.996919 | + | 0.0784408i | \(0.0249942\pi\) | ||||
−0.996919 | + | 0.0784408i | \(0.975006\pi\) | |||||||
\(234\) | −2.07692e6 | −0.162096 | ||||||||
\(235\) | 420537. | − | 736100.i | 0.0324042 | − | 0.0567196i | ||||
\(236\) | −1.24159e7 | −0.944590 | ||||||||
\(237\) | −1.31075e7 | −0.984633 | ||||||||
\(238\) | 8.82868e6i | 0.654885i | ||||||||
\(239\) | 3.91064e6 | 0.286454 | 0.143227 | − | 0.989690i | \(-0.454252\pi\) | ||||
0.143227 | + | 0.989690i | \(0.454252\pi\) | |||||||
\(240\) | −1.23740e6 | + | 2.16592e6i | −0.0895112 | + | 0.156679i | ||||
\(241\) | − | 1.91337e7i | − | 1.36693i | −0.729982 | − | 0.683467i | \(-0.760471\pi\) | ||
0.729982 | − | 0.683467i | \(-0.239529\pi\) | |||||||
\(242\) | 1.86573e7i | 1.31644i | ||||||||
\(243\) | 4.77241e6i | 0.332598i | ||||||||
\(244\) | 2.01049e6i | 0.138399i | ||||||||
\(245\) | 1.04375e6 | + | 596301.i | 0.0709741 | + | 0.0405478i | ||||
\(246\) | 1.11358e7 | 0.748024 | ||||||||
\(247\) | 1.66164e7 | 1.10267 | ||||||||
\(248\) | − | 1.28959e7i | − | 0.845468i | ||||||
\(249\) | 1.50293e7i | 0.973510i | ||||||||
\(250\) | 8.51066e6 | − | 116081.i | 0.544682 | − | 0.00742920i | ||||
\(251\) | 2.21200e7i | 1.39882i | 0.714719 | + | 0.699412i | \(0.246555\pi\) | ||||
−0.714719 | + | 0.699412i | \(0.753445\pi\) | |||||||
\(252\) | −1.96876e6 | −0.123024 | ||||||||
\(253\) | −5.55591e6 | + | 2.94138e7i | −0.343078 | + | 1.81631i | ||||
\(254\) | −4.19198e6 | −0.255810 | ||||||||
\(255\) | −8.67128e6 | + | 1.51780e7i | −0.522953 | + | 0.915367i | ||||
\(256\) | −1.37861e7 | −0.821715 | ||||||||
\(257\) | 2.05607e6i | 0.121126i | 0.998164 | + | 0.0605631i | \(0.0192896\pi\) | ||||
−0.998164 | + | 0.0605631i | \(0.980710\pi\) | |||||||
\(258\) | −1.13033e7 | −0.658183 | ||||||||
\(259\) | 2.15218e6 | 0.123874 | ||||||||
\(260\) | 1.08480e7 | − | 1.89881e7i | 0.617205 | − | 1.08034i | ||||
\(261\) | 3.91728e6 | 0.220325 | ||||||||
\(262\) | 7.34556e6i | 0.408433i | ||||||||
\(263\) | 3.64508e6 | 0.200373 | 0.100187 | − | 0.994969i | \(-0.468056\pi\) | ||||
0.100187 | + | 0.994969i | \(0.468056\pi\) | |||||||
\(264\) | − | 2.87800e7i | − | 1.56415i | ||||||
\(265\) | −5.20411e6 | − | 2.97313e6i | −0.279646 | − | 0.159763i | ||||
\(266\) | −6.64597e6 | −0.353113 | ||||||||
\(267\) | 2.51408e7 | 1.32083 | ||||||||
\(268\) | −5.44047e6 | −0.282639 | ||||||||
\(269\) | −3.78860e7 | −1.94635 | −0.973176 | − | 0.230061i | \(-0.926107\pi\) | ||||
−0.973176 | + | 0.230061i | \(0.926107\pi\) | |||||||
\(270\) | 9.91895e6 | + | 5.66674e6i | 0.503935 | + | 0.287900i | ||||
\(271\) | −1.07476e7 | −0.540011 | −0.270006 | − | 0.962859i | \(-0.587026\pi\) | ||||
−0.270006 | + | 0.962859i | \(0.587026\pi\) | |||||||
\(272\) | 4.60214e6 | 0.228693 | ||||||||
\(273\) | −3.41459e7 | −1.67822 | ||||||||
\(274\) | − | 3.36961e6i | − | 0.163805i | ||||||
\(275\) | 3.31152e7 | − | 1.95226e7i | 1.59231 | − | 0.938729i | ||||
\(276\) | 2.50293e6 | − | 1.32509e7i | 0.119048 | − | 0.630258i | ||||
\(277\) | 5.12768e6i | 0.241258i | 0.992698 | + | 0.120629i | \(0.0384911\pi\) | ||||
−0.992698 | + | 0.120629i | \(0.961509\pi\) | |||||||
\(278\) | − | 1.59227e7i | − | 0.741109i | ||||||
\(279\) | 3.32854e6 | 0.153264 | ||||||||
\(280\) | −1.05083e7 | + | 1.83936e7i | −0.478696 | + | 0.837900i | ||||
\(281\) | 3.59117e7i | 1.61852i | 0.587452 | + | 0.809259i | \(0.300131\pi\) | ||||
−0.587452 | + | 0.809259i | \(0.699869\pi\) | |||||||
\(282\) | − | 727798.i | − | 0.0324536i | ||||||
\(283\) | −1.46282e7 | −0.645402 | −0.322701 | − | 0.946501i | \(-0.604591\pi\) | ||||
−0.322701 | + | 0.946501i | \(0.604591\pi\) | |||||||
\(284\) | 2.22020e7 | 0.969251 | ||||||||
\(285\) | −1.14256e7 | − | 6.52749e6i | −0.493565 | − | 0.281976i | ||||
\(286\) | 4.16736e7i | 1.78141i | ||||||||
\(287\) | −3.70193e7 | −1.56597 | ||||||||
\(288\) | − | 4.16083e6i | − | 0.174182i | ||||||
\(289\) | 8.11266e6 | 0.336101 | ||||||||
\(290\) | 8.63302e6 | − | 1.51111e7i | 0.353972 | − | 0.619585i | ||||
\(291\) | 2.06218e7i | 0.836851i | ||||||||
\(292\) | 1.70579e6i | 0.0685134i | ||||||||
\(293\) | −1.11366e7 | −0.442742 | −0.221371 | − | 0.975190i | \(-0.571053\pi\) | ||||
−0.221371 | + | 0.975190i | \(0.571053\pi\) | |||||||
\(294\) | 1.03198e6 | 0.0406097 | ||||||||
\(295\) | −2.99402e7 | − | 1.71050e7i | −1.16624 | − | 0.666279i | ||||
\(296\) | 2.86589e6i | 0.110506i | ||||||||
\(297\) | 5.15938e7 | 1.96937 | ||||||||
\(298\) | 7.67425e6 | 0.289993 | ||||||||
\(299\) | −8.77773e6 | + | 4.64706e7i | −0.328374 | + | 1.73846i | ||||
\(300\) | −1.49184e7 | + | 8.79494e6i | −0.552532 | + | 0.325739i | ||||
\(301\) | 3.75762e7 | 1.37789 | ||||||||
\(302\) | − | 2.03794e6i | − | 0.0739895i | ||||||
\(303\) | − | 2.57566e7i | − | 0.925892i | ||||||
\(304\) | 3.46436e6i | 0.123311i | ||||||||
\(305\) | −2.76977e6 | + | 4.84815e6i | −0.0976212 | + | 0.170874i | ||||
\(306\) | − | 3.03443e6i | − | 0.105904i | ||||||
\(307\) | 1.31452e7i | 0.454311i | 0.973859 | + | 0.227155i | \(0.0729425\pi\) | ||||
−0.973859 | + | 0.227155i | \(0.927057\pi\) | |||||||
\(308\) | 3.95035e7i | 1.35202i | ||||||||
\(309\) | 5.78382e6i | 0.196037i | ||||||||
\(310\) | 7.33554e6 | − | 1.28400e7i | 0.246233 | − | 0.431002i | ||||
\(311\) | 3.84386e6 | 0.127787 | 0.0638935 | − | 0.997957i | \(-0.479648\pi\) | ||||
0.0638935 | + | 0.997957i | \(0.479648\pi\) | |||||||
\(312\) | − | 4.54693e7i | − | 1.49711i | ||||||
\(313\) | −5.42766e7 | −1.77003 | −0.885013 | − | 0.465566i | \(-0.845851\pi\) | ||||
−0.885013 | + | 0.465566i | \(0.845851\pi\) | |||||||
\(314\) | − | 1.27131e7i | − | 0.410643i | ||||||
\(315\) | −4.74753e6 | − | 2.71229e6i | −0.151892 | − | 0.0867768i | ||||
\(316\) | 2.39577e7i | 0.759247i | ||||||||
\(317\) | 2.12458e7i | 0.666954i | 0.942758 | + | 0.333477i | \(0.108222\pi\) | ||||
−0.942758 | + | 0.333477i | \(0.891778\pi\) | |||||||
\(318\) | −5.14542e6 | −0.160007 | ||||||||
\(319\) | − | 7.86008e7i | − | 2.42133i | ||||||
\(320\) | −1.04213e7 | − | 5.95376e6i | −0.318034 | − | 0.181694i | ||||
\(321\) | − | 2.13531e6i | − | 0.0645575i | ||||||
\(322\) | 3.51078e6 | − | 1.85866e7i | 0.105157 | − | 0.556715i | ||||
\(323\) | 2.42770e7i | 0.720424i | ||||||||
\(324\) | −1.92198e7 | −0.565086 | ||||||||
\(325\) | 5.23184e7 | − | 3.08437e7i | 1.52407 | − | 0.898496i | ||||
\(326\) | −1.89890e7 | −0.548087 | ||||||||
\(327\) | 8.96319e6 | 0.256342 | ||||||||
\(328\) | − | 4.92956e7i | − | 1.39697i | ||||||
\(329\) | 2.41946e6i | 0.0679407i | ||||||||
\(330\) | 1.63708e7 | − | 2.86552e7i | 0.455542 | − | 0.797373i | ||||
\(331\) | −2.69439e7 | −0.742979 | −0.371490 | − | 0.928437i | \(-0.621153\pi\) | ||||
−0.371490 | + | 0.928437i | \(0.621153\pi\) | |||||||
\(332\) | 2.74703e7 | 0.750670 | ||||||||
\(333\) | −739710. | −0.0200322 | ||||||||
\(334\) | 3.72261e7 | 0.999099 | ||||||||
\(335\) | −1.31193e7 | − | 7.49512e6i | −0.348961 | − | 0.199363i | ||||
\(336\) | − | 7.11909e6i | − | 0.187675i | ||||||
\(337\) | 4.90414e7 | 1.28137 | 0.640683 | − | 0.767806i | \(-0.278651\pi\) | ||||
0.640683 | + | 0.767806i | \(0.278651\pi\) | |||||||
\(338\) | 4.48053e7i | 1.16032i | ||||||||
\(339\) | − | 1.11961e7i | − | 0.287387i | ||||||
\(340\) | 2.77422e7 | + | 1.58492e7i | 0.705836 | + | 0.403247i | ||||
\(341\) | − | 6.67876e7i | − | 1.68435i | ||||||
\(342\) | 2.28423e6 | 0.0571034 | ||||||||
\(343\) | 3.85398e7 | 0.955052 | ||||||||
\(344\) | 5.00373e7i | 1.22919i | ||||||||
\(345\) | 2.42909e7 | − | 2.85055e7i | 0.591543 | − | 0.694178i | ||||
\(346\) | 1.23426e7 | 0.297974 | ||||||||
\(347\) | 4.12918e7i | 0.988270i | 0.869385 | + | 0.494135i | \(0.164515\pi\) | ||||
−0.869385 | + | 0.494135i | \(0.835485\pi\) | |||||||
\(348\) | 3.54096e7i | 0.840201i | ||||||||
\(349\) | 1.20243e7 | 0.282867 | 0.141434 | − | 0.989948i | \(-0.454829\pi\) | ||||
0.141434 | + | 0.989948i | \(0.454829\pi\) | |||||||
\(350\) | −2.09255e7 | + | 1.23364e7i | −0.488059 | + | 0.287729i | ||||
\(351\) | 8.15126e7 | 1.88497 | ||||||||
\(352\) | −8.34876e7 | −1.91423 | ||||||||
\(353\) | 5.15907e7i | 1.17286i | 0.809999 | + | 0.586431i | \(0.199468\pi\) | ||||
−0.809999 | + | 0.586431i | \(0.800532\pi\) | |||||||
\(354\) | −2.96025e7 | −0.667296 | ||||||||
\(355\) | 5.35385e7 | + | 3.05868e7i | 1.19669 | + | 0.683674i | ||||
\(356\) | − | 4.59520e7i | − | 1.01848i | ||||||
\(357\) | − | 4.98881e7i | − | 1.09646i | ||||||
\(358\) | 1.94848e7i | 0.424666i | ||||||||
\(359\) | − | 1.62740e7i | − | 0.351732i | −0.984414 | − | 0.175866i | \(-0.943728\pi\) | ||
0.984414 | − | 0.175866i | \(-0.0562725\pi\) | |||||||
\(360\) | 3.61174e6 | − | 6.32191e6i | 0.0774120 | − | 0.135500i | ||||
\(361\) | 2.87708e7 | 0.611548 | ||||||||
\(362\) | 4.86380e6 | 0.102530 | ||||||||
\(363\) | − | 1.05426e8i | − | 2.20409i | ||||||
\(364\) | 6.24112e7i | 1.29407i | ||||||||
\(365\) | −2.35000e6 | + | 4.11339e6i | −0.0483268 | + | 0.0845903i | ||||
\(366\) | 4.79347e6i | 0.0977703i | ||||||||
\(367\) | −1.09260e7 | −0.221036 | −0.110518 | − | 0.993874i | \(-0.535251\pi\) | ||||
−0.110518 | + | 0.993874i | \(0.535251\pi\) | |||||||
\(368\) | −9.68869e6 | − | 1.83007e6i | −0.194411 | − | 0.0367219i | ||||
\(369\) | 1.27236e7 | 0.253239 | ||||||||
\(370\) | −1.63020e6 | + | 2.85346e6i | −0.0321836 | + | 0.0563335i | ||||
\(371\) | 1.71052e7 | 0.334970 | ||||||||
\(372\) | 3.00878e7i | 0.584469i | ||||||||
\(373\) | 4.32586e7 | 0.833578 | 0.416789 | − | 0.909003i | \(-0.363155\pi\) | ||||
0.416789 | + | 0.909003i | \(0.363155\pi\) | |||||||
\(374\) | −6.08864e7 | −1.16387 | ||||||||
\(375\) | −4.80911e7 | + | 655939.i | −0.911949 | + | 0.0124385i | ||||
\(376\) | −3.22180e6 | −0.0606087 | ||||||||
\(377\) | − | 1.24181e8i | − | 2.31756i | ||||||
\(378\) | −3.26022e7 | −0.603630 | ||||||||
\(379\) | − | 7.86169e7i | − | 1.44410i | −0.691839 | − | 0.722052i | \(-0.743199\pi\) | ||
0.691839 | − | 0.722052i | \(-0.256801\pi\) | |||||||
\(380\) | −1.19308e7 | + | 2.08835e7i | −0.217430 | + | 0.380586i | ||||
\(381\) | 2.36875e7 | 0.428297 | ||||||||
\(382\) | 1.27700e7 | 0.229087 | ||||||||
\(383\) | −8.68806e7 | −1.54642 | −0.773208 | − | 0.634152i | \(-0.781349\pi\) | ||||
−0.773208 | + | 0.634152i | \(0.781349\pi\) | |||||||
\(384\) | 4.31769e7 | 0.762531 | ||||||||
\(385\) | −5.44224e7 | + | 9.52599e7i | −0.953665 | + | 1.66928i | ||||
\(386\) | 9.23267e6 | 0.160533 | ||||||||
\(387\) | −1.29150e7 | −0.222824 | ||||||||
\(388\) | 3.76922e7 | 0.645293 | ||||||||
\(389\) | 1.11129e8i | 1.88790i | 0.330095 | + | 0.943948i | \(0.392919\pi\) | ||||
−0.330095 | + | 0.943948i | \(0.607081\pi\) | |||||||
\(390\) | 2.58642e7 | − | 4.52721e7i | 0.436018 | − | 0.763197i | ||||
\(391\) | −6.78949e7 | − | 1.28245e7i | −1.13581 | − | 0.214541i | ||||
\(392\) | − | 4.56835e6i | − | 0.0758405i | ||||||
\(393\) | − | 4.15075e7i | − | 0.683830i | ||||||
\(394\) | 3.08540e7 | 0.504456 | ||||||||
\(395\) | −3.30055e7 | + | 5.77723e7i | −0.535545 | + | 0.937407i | ||||
\(396\) | − | 1.35774e7i | − | 0.218641i | ||||||
\(397\) | 2.70597e7i | 0.432465i | 0.976342 | + | 0.216233i | \(0.0693770\pi\) | ||||
−0.976342 | + | 0.216233i | \(0.930623\pi\) | |||||||
\(398\) | −1.70344e7 | −0.270196 | ||||||||
\(399\) | 3.75543e7 | 0.591209 | ||||||||
\(400\) | 6.43061e6 | + | 1.09079e7i | 0.100478 | + | 0.170436i | ||||
\(401\) | − | 5.03622e7i | − | 0.781036i | −0.920595 | − | 0.390518i | \(-0.872296\pi\) | ||
0.920595 | − | 0.390518i | \(-0.127704\pi\) | |||||||
\(402\) | −1.29713e7 | −0.199667 | ||||||||
\(403\) | − | 1.05517e8i | − | 1.61216i | ||||||
\(404\) | −4.70774e7 | −0.713951 | ||||||||
\(405\) | −4.63473e7 | − | 2.64784e7i | −0.697685 | − | 0.398591i | ||||
\(406\) | 4.96679e7i | 0.742160i | ||||||||
\(407\) | 1.48424e7i | 0.220151i | ||||||||
\(408\) | 6.64320e7 | 0.978131 | ||||||||
\(409\) | 1.10084e8 | 1.60900 | 0.804500 | − | 0.593953i | \(-0.202434\pi\) | ||||
0.804500 | + | 0.593953i | \(0.202434\pi\) | |||||||
\(410\) | 2.80407e7 | − | 4.90818e7i | 0.406852 | − | 0.712146i | ||||
\(411\) | 1.90406e7i | 0.274256i | ||||||||
\(412\) | 1.05716e7 | 0.151164 | ||||||||
\(413\) | 9.84091e7 | 1.39696 | ||||||||
\(414\) | −1.20666e6 | + | 6.38826e6i | −0.0170053 | + | 0.0900288i | ||||
\(415\) | 6.62427e7 | + | 3.78448e7i | 0.926817 | + | 0.529495i | ||||
\(416\) | −1.31901e8 | −1.83219 | ||||||||
\(417\) | 8.99741e7i | 1.24082i | ||||||||
\(418\) | − | 4.58335e7i | − | 0.627558i | ||||||
\(419\) | − | 1.05835e8i | − | 1.43876i | −0.694617 | − | 0.719380i | \(-0.744426\pi\) | ||
0.694617 | − | 0.719380i | \(-0.255574\pi\) | |||||||
\(420\) | 2.45173e7 | − | 4.29146e7i | 0.330921 | − | 0.579238i | ||||
\(421\) | − | 1.42758e6i | − | 0.0191317i | −0.999954 | − | 0.00956587i | \(-0.996955\pi\) | ||
0.999954 | − | 0.00956587i | \(-0.00304496\pi\) | |||||||
\(422\) | 9.98295e6i | 0.132838i | ||||||||
\(423\) | − | 831572.i | − | 0.0109870i | ||||||
\(424\) | 2.27776e7i | 0.298821i | ||||||||
\(425\) | 4.50635e7 | + | 7.64387e7i | 0.587027 | + | 0.995741i | ||||
\(426\) | 5.29347e7 | 0.684717 | ||||||||
\(427\) | − | 1.59352e7i | − | 0.204679i | ||||||
\(428\) | −3.90289e6 | −0.0497800 | ||||||||
\(429\) | − | 2.35485e8i | − | 2.98257i | ||||||
\(430\) | −2.84625e7 | + | 4.98202e7i | −0.357988 | + | 0.626615i | ||||
\(431\) | 1.40897e8i | 1.75982i | 0.475138 | + | 0.879912i | \(0.342398\pi\) | ||||
−0.475138 | + | 0.879912i | \(0.657602\pi\) | |||||||
\(432\) | 1.69946e7i | 0.210795i | ||||||||
\(433\) | 6.90311e7 | 0.850318 | 0.425159 | − | 0.905119i | \(-0.360218\pi\) | ||||
0.425159 | + | 0.905119i | \(0.360218\pi\) | |||||||
\(434\) | 4.22032e7i | 0.516269i | ||||||||
\(435\) | −4.87825e7 | + | 8.53879e7i | −0.592647 | + | 1.03736i | ||||
\(436\) | − | 1.63828e7i | − | 0.197664i | ||||||
\(437\) | 9.65393e6 | − | 5.11093e7i | 0.115680 | − | 0.612429i | ||||
\(438\) | 4.06699e6i | 0.0484006i | ||||||||
\(439\) | −1.53760e7 | −0.181740 | −0.0908698 | − | 0.995863i | \(-0.528965\pi\) | ||||
−0.0908698 | + | 0.995863i | \(0.528965\pi\) | |||||||
\(440\) | −1.26850e8 | − | 7.24700e7i | −1.48913 | − | 0.850747i | ||||
\(441\) | 1.17913e6 | 0.0137482 | ||||||||
\(442\) | −9.61939e7 | −1.11399 | ||||||||
\(443\) | − | 3.41033e7i | − | 0.392270i | −0.980577 | − | 0.196135i | \(-0.937161\pi\) | ||
0.980577 | − | 0.196135i | \(-0.0628391\pi\) | |||||||
\(444\) | − | 6.68649e6i | − | 0.0763923i | ||||||
\(445\) | 6.33063e7 | − | 1.10810e8i | 0.718401 | − | 1.25748i | ||||
\(446\) | −4.89915e7 | −0.552225 | ||||||||
\(447\) | −4.33648e7 | −0.485529 | ||||||||
\(448\) | 3.42535e7 | 0.380952 | ||||||||
\(449\) | −1.16340e8 | −1.28526 | −0.642628 | − | 0.766178i | \(-0.722156\pi\) | ||||
−0.642628 | + | 0.766178i | \(0.722156\pi\) | |||||||
\(450\) | 7.19214e6 | − | 4.24004e6i | 0.0789261 | − | 0.0465299i | ||||
\(451\) | − | 2.55301e8i | − | 2.78306i | ||||||
\(452\) | −2.04640e7 | −0.221603 | ||||||||
\(453\) | 1.15157e7i | 0.123879i | ||||||||
\(454\) | − | 5.45798e7i | − | 0.583262i | ||||||
\(455\) | −8.59816e7 | + | 1.50500e8i | −0.912791 | + | 1.59773i | ||||
\(456\) | 5.00081e7i | 0.527407i | ||||||||
\(457\) | −9.39087e7 | −0.983914 | −0.491957 | − | 0.870619i | \(-0.663718\pi\) | ||||
−0.491957 | + | 0.870619i | \(0.663718\pi\) | |||||||
\(458\) | 5.87591e7 | 0.611616 | ||||||||
\(459\) | 1.19092e8i | 1.23153i | ||||||||
\(460\) | −5.21018e7 | − | 4.43985e7i | −0.535278 | − | 0.456137i | ||||
\(461\) | 8.25346e7 | 0.842429 | 0.421215 | − | 0.906961i | \(-0.361604\pi\) | ||||
0.421215 | + | 0.906961i | \(0.361604\pi\) | |||||||
\(462\) | 9.41855e7i | 0.955120i | ||||||||
\(463\) | 1.26626e8i | 1.27579i | 0.770124 | + | 0.637895i | \(0.220194\pi\) | ||||
−0.770124 | + | 0.637895i | \(0.779806\pi\) | |||||||
\(464\) | 2.58905e7 | 0.259171 | ||||||||
\(465\) | −4.14508e7 | + | 7.25547e7i | −0.412263 | + | 0.721617i | ||||
\(466\) | 8.64796e6 | 0.0854586 | ||||||||
\(467\) | 1.17457e8 | 1.15326 | 0.576631 | − | 0.817005i | \(-0.304367\pi\) | ||||
0.576631 | + | 0.817005i | \(0.304367\pi\) | |||||||
\(468\) | − | 2.14509e7i | − | 0.209270i | ||||||
\(469\) | 4.31213e7 | 0.417997 | ||||||||
\(470\) | −3.20782e6 | − | 1.83264e6i | −0.0308970 | − | 0.0176516i | ||||
\(471\) | 7.18380e7i | 0.687530i | ||||||||
\(472\) | 1.31044e8i | 1.24621i | ||||||||
\(473\) | 2.59142e8i | 2.44881i | ||||||||
\(474\) | 5.71207e7i | 0.536362i | ||||||||
\(475\) | −5.75408e7 | + | 3.39225e7i | −0.536902 | + | 0.316524i | ||||
\(476\) | −9.11846e7 | −0.845475 | ||||||||
\(477\) | −5.87909e6 | −0.0541695 | ||||||||
\(478\) | − | 1.70421e7i | − | 0.156041i | ||||||
\(479\) | 9.17861e7i | 0.835161i | 0.908640 | + | 0.417581i | \(0.137122\pi\) | ||||
−0.908640 | + | 0.417581i | \(0.862878\pi\) | |||||||
\(480\) | 9.06967e7 | + | 5.18154e7i | 0.820102 | + | 0.468528i | ||||
\(481\) | 2.34494e7i | 0.210715i | ||||||||
\(482\) | −8.33820e7 | −0.744614 | ||||||||
\(483\) | −1.98383e7 | + | 1.05027e8i | −0.176061 | + | 0.932095i | ||||
\(484\) | −1.92697e8 | −1.69957 | ||||||||
\(485\) | 9.08923e7 | + | 5.19272e7i | 0.796713 | + | 0.455166i | ||||
\(486\) | 2.07975e7 | 0.181177 | ||||||||
\(487\) | 3.44496e7i | 0.298262i | 0.988817 | + | 0.149131i | \(0.0476475\pi\) | ||||
−0.988817 | + | 0.149131i | \(0.952352\pi\) | |||||||
\(488\) | 2.12196e7 | 0.182591 | ||||||||
\(489\) | 1.07301e8 | 0.917650 | ||||||||
\(490\) | 2.59860e6 | − | 4.54854e6i | 0.0220877 | − | 0.0386619i | ||||
\(491\) | −9.71931e7 | −0.821090 | −0.410545 | − | 0.911840i | \(-0.634662\pi\) | ||||
−0.410545 | + | 0.911840i | \(0.634662\pi\) | |||||||
\(492\) | 1.15013e8i | 0.965720i | ||||||||
\(493\) | 1.81432e8 | 1.51416 | ||||||||
\(494\) | − | 7.24120e7i | − | 0.600661i | ||||||
\(495\) | 1.87051e7 | − | 3.27410e7i | 0.154221 | − | 0.269946i | ||||
\(496\) | 2.19994e7 | 0.180287 | ||||||||
\(497\) | −1.75973e8 | −1.43344 | ||||||||
\(498\) | 6.54956e7 | 0.530303 | ||||||||
\(499\) | −3.80414e6 | −0.0306164 | −0.0153082 | − | 0.999883i | \(-0.504873\pi\) | ||||
−0.0153082 | + | 0.999883i | \(0.504873\pi\) | |||||||
\(500\) | 1.19891e6 | + | 8.79001e7i | 0.00959132 | + | 0.703201i | ||||
\(501\) | −2.10353e8 | −1.67277 | ||||||||
\(502\) | 9.63957e7 | 0.761985 | ||||||||
\(503\) | 1.14172e8 | 0.897128 | 0.448564 | − | 0.893751i | \(-0.351936\pi\) | ||||
0.448564 | + | 0.893751i | \(0.351936\pi\) | |||||||
\(504\) | 2.07792e7i | 0.162307i | ||||||||
\(505\) | −1.13524e8 | − | 6.48568e7i | −0.881482 | − | 0.503595i | ||||
\(506\) | 1.28181e8 | + | 2.42119e7i | 0.989403 | + | 0.186886i | ||||
\(507\) | − | 2.53180e8i | − | 1.94270i | ||||||
\(508\) | − | 4.32957e7i | − | 0.330258i | ||||||
\(509\) | −2.24320e8 | −1.70104 | −0.850521 | − | 0.525941i | \(-0.823713\pi\) | ||||
−0.850521 | + | 0.525941i | \(0.823713\pi\) | |||||||
\(510\) | 6.61438e7 | + | 3.77883e7i | 0.498631 | + | 0.284870i | ||||
\(511\) | − | 1.35201e7i | − | 0.101325i | ||||||
\(512\) | − | 5.21385e7i | − | 0.388462i | ||||||
\(513\) | −8.96492e7 | −0.664040 | ||||||||
\(514\) | 8.96006e6 | 0.0659814 | ||||||||
\(515\) | 2.54926e7 | + | 1.45640e7i | 0.186635 | + | 0.106625i | ||||
\(516\) | − | 1.16743e8i | − | 0.849734i | ||||||
\(517\) | −1.66856e7 | −0.120745 | ||||||||
\(518\) | − | 9.37893e6i | − | 0.0674783i | ||||||
\(519\) | −6.97442e7 | −0.498891 | ||||||||
\(520\) | −2.00409e8 | − | 1.14495e8i | −1.42531 | − | 0.814284i | ||||
\(521\) | − | 1.06077e8i | − | 0.750080i | −0.927009 | − | 0.375040i | \(-0.877629\pi\) | ||
0.927009 | − | 0.375040i | \(-0.122371\pi\) | |||||||
\(522\) | − | 1.70710e7i | − | 0.120018i | ||||||
\(523\) | 5.79765e7 | 0.405272 | 0.202636 | − | 0.979254i | \(-0.435049\pi\) | ||||
0.202636 | + | 0.979254i | \(0.435049\pi\) | |||||||
\(524\) | −7.58666e7 | −0.527299 | ||||||||
\(525\) | 1.18243e8 | − | 6.97090e7i | 0.817145 | − | 0.481738i | ||||
\(526\) | − | 1.58847e7i | − | 0.109150i | ||||||
\(527\) | 1.54164e8 | 1.05330 | ||||||||
\(528\) | 4.90963e7 | 0.333539 | ||||||||
\(529\) | 1.37836e8 | + | 5.39978e7i | 0.931101 | + | 0.364761i | ||||
\(530\) | −1.29565e7 | + | 2.26788e7i | −0.0870283 | + | 0.152333i | ||||
\(531\) | −3.38234e7 | −0.225909 | ||||||||
\(532\) | − | 6.86411e7i | − | 0.455879i | ||||||
\(533\) | − | 4.03348e8i | − | 2.66378i | ||||||
\(534\) | − | 1.09560e8i | − | 0.719498i | ||||||
\(535\) | −9.41156e6 | − | 5.37686e6i | −0.0614611 | − | 0.0351130i | ||||
\(536\) | 5.74212e7i | 0.372888i | ||||||||
\(537\) | − | 1.10103e8i | − | 0.711008i | ||||||
\(538\) | 1.65102e8i | 1.06024i | ||||||||
\(539\) | − | 2.36594e7i | − | 0.151090i | ||||||
\(540\) | −5.85274e7 | + | 1.02445e8i | −0.371687 | + | 0.650594i | ||||
\(541\) | 1.09975e7 | 0.0694545 | 0.0347272 | − | 0.999397i | \(-0.488944\pi\) | ||||
0.0347272 | + | 0.999397i | \(0.488944\pi\) | |||||||
\(542\) | 4.68365e7i | 0.294162i | ||||||||
\(543\) | −2.74838e7 | −0.171663 | ||||||||
\(544\) | − | 1.92712e8i | − | 1.19705i | ||||||
\(545\) | 2.25699e7 | − | 3.95059e7i | 0.139425 | − | 0.244047i | ||||
\(546\) | 1.48803e8i | 0.914184i | ||||||||
\(547\) | 1.41932e8i | 0.867200i | 0.901105 | + | 0.433600i | \(0.142757\pi\) | ||||
−0.901105 | + | 0.433600i | \(0.857243\pi\) | |||||||
\(548\) | 3.48021e7 | 0.211477 | ||||||||
\(549\) | 5.47696e6i | 0.0330996i | ||||||||
\(550\) | −8.50770e7 | − | 1.44311e8i | −0.511357 | − | 0.867386i | ||||
\(551\) | 1.36576e8i | 0.816434i | ||||||||
\(552\) | −1.39856e8 | − | 2.64171e7i | −0.831505 | − | 0.157061i | ||||
\(553\) | − | 1.89889e8i | − | 1.12286i | ||||||
\(554\) | 2.23457e7 | 0.131421 | ||||||||
\(555\) | 9.21172e6 | − | 1.61240e7i | 0.0538843 | − | 0.0943179i | ||||
\(556\) | 1.64453e8 | 0.956792 | ||||||||
\(557\) | −1.27913e8 | −0.740201 | −0.370101 | − | 0.928992i | \(-0.620677\pi\) | ||||
−0.370101 | + | 0.928992i | \(0.620677\pi\) | |||||||
\(558\) | − | 1.45053e7i | − | 0.0834882i | ||||||
\(559\) | 4.09416e8i | 2.34385i | ||||||||
\(560\) | −3.13779e7 | − | 1.79263e7i | −0.178673 | − | 0.102077i | ||||
\(561\) | 3.44050e8 | 1.94864 | ||||||||
\(562\) | 1.56498e8 | 0.881660 | ||||||||
\(563\) | 1.30431e8 | 0.730898 | 0.365449 | − | 0.930831i | \(-0.380915\pi\) | ||||
0.365449 | + | 0.930831i | \(0.380915\pi\) | |||||||
\(564\) | 7.51686e6 | 0.0418986 | ||||||||
\(565\) | −4.93476e7 | − | 2.81925e7i | −0.273603 | − | 0.156311i | ||||
\(566\) | 6.37475e7i | 0.351572i | ||||||||
\(567\) | 1.52337e8 | 0.835712 | ||||||||
\(568\) | − | 2.34330e8i | − | 1.27874i | ||||||
\(569\) | − | 2.35725e8i | − | 1.27958i | −0.768548 | − | 0.639792i | \(-0.779021\pi\) | ||
0.768548 | − | 0.639792i | \(-0.220979\pi\) | |||||||
\(570\) | −2.84459e7 | + | 4.97912e7i | −0.153601 | + | 0.268861i | ||||
\(571\) | − | 2.64145e7i | − | 0.141884i | −0.997480 | − | 0.0709422i | \(-0.977399\pi\) | ||
0.997480 | − | 0.0709422i | \(-0.0226006\pi\) | |||||||
\(572\) | −4.30415e8 | −2.29985 | ||||||||
\(573\) | −7.21593e7 | −0.383556 | ||||||||
\(574\) | 1.61325e8i | 0.853033i | ||||||||
\(575\) | −6.44738e7 | − | 1.78843e8i | −0.339140 | − | 0.940736i | ||||
\(576\) | −1.17730e7 | −0.0616055 | ||||||||
\(577\) | − | 1.93402e8i | − | 1.00678i | −0.864060 | − | 0.503389i | \(-0.832086\pi\) | ||
0.864060 | − | 0.503389i | \(-0.167914\pi\) | |||||||
\(578\) | − | 3.53539e7i | − | 0.183085i | ||||||
\(579\) | −5.21709e7 | −0.268778 | ||||||||
\(580\) | 1.56071e8 | + | 8.91638e7i | 0.799902 | + | 0.456988i | ||||
\(581\) | −2.17731e8 | −1.11017 | ||||||||
\(582\) | 8.98671e7 | 0.455860 | ||||||||
\(583\) | 1.17965e8i | 0.595314i | ||||||||
\(584\) | 1.80037e7 | 0.0903904 | ||||||||
\(585\) | 2.95520e7 | − | 5.17273e7i | 0.147611 | − | 0.258376i | ||||
\(586\) | 4.85318e7i | 0.241176i | ||||||||
\(587\) | 3.42598e8i | 1.69383i | 0.531725 | + | 0.846917i | \(0.321544\pi\) | ||||
−0.531725 | + | 0.846917i | \(0.678456\pi\) | |||||||
\(588\) | 1.06585e7i | 0.0524283i | ||||||||
\(589\) | 1.16050e8i | 0.567936i | ||||||||
\(590\) | −7.45411e7 | + | 1.30475e8i | −0.362944 | + | 0.635290i | ||||
\(591\) | −1.74346e8 | −0.844599 | ||||||||
\(592\) | −4.88897e6 | −0.0235642 | ||||||||
\(593\) | − | 2.68518e8i | − | 1.28768i | −0.765159 | − | 0.643842i | \(-0.777339\pi\) | ||
0.765159 | − | 0.643842i | \(-0.222661\pi\) | |||||||
\(594\) | − | 2.24839e8i | − | 1.07278i | ||||||
\(595\) | −2.19885e8 | − | 1.25622e8i | −1.04387 | − | 0.596367i | ||||
\(596\) | 7.92615e7i | 0.374389i | ||||||||
\(597\) | 9.62562e7 | 0.452382 | ||||||||
\(598\) | 2.02513e8 | + | 3.82522e7i | 0.946997 | + | 0.178876i | ||||
\(599\) | 3.92104e8 | 1.82441 | 0.912203 | − | 0.409739i | \(-0.134380\pi\) | ||||
0.912203 | + | 0.409739i | \(0.134380\pi\) | |||||||
\(600\) | 9.28260e7 | + | 1.57455e8i | 0.429750 | + | 0.728960i | ||||
\(601\) | 1.70258e8 | 0.784302 | 0.392151 | − | 0.919901i | \(-0.371731\pi\) | ||||
0.392151 | + | 0.919901i | \(0.371731\pi\) | |||||||
\(602\) | − | 1.63752e8i | − | 0.750581i | ||||||
\(603\) | −1.48209e7 | −0.0675962 | ||||||||
\(604\) | 2.10483e7 | 0.0955225 | ||||||||
\(605\) | −4.64675e8 | − | 2.65471e8i | −2.09838 | − | 1.19881i | ||||
\(606\) | −1.12244e8 | −0.504364 | ||||||||
\(607\) | − | 7.37280e6i | − | 0.0329660i | −0.999864 | − | 0.0164830i | \(-0.994753\pi\) | ||
0.999864 | − | 0.0164830i | \(-0.00524694\pi\) | |||||||
\(608\) | 1.45068e8 | 0.645447 | ||||||||
\(609\) | − | 2.80658e8i | − | 1.24258i | ||||||
\(610\) | 2.11276e7 | + | 1.20703e7i | 0.0930808 | + | 0.0531775i | ||||
\(611\) | −2.63615e7 | −0.115570 | ||||||||
\(612\) | 3.13403e7 | 0.136725 | ||||||||
\(613\) | 2.46648e8 | 1.07077 | 0.535386 | − | 0.844608i | \(-0.320166\pi\) | ||||
0.535386 | + | 0.844608i | \(0.320166\pi\) | |||||||
\(614\) | 5.72851e7 | 0.247478 | ||||||||
\(615\) | −1.58449e8 | + | 2.77346e8i | −0.681183 | + | 1.19233i | ||||
\(616\) | 4.16938e8 | 1.78373 | ||||||||
\(617\) | 1.82302e8 | 0.776134 | 0.388067 | − | 0.921631i | \(-0.373143\pi\) | ||||
0.388067 | + | 0.921631i | \(0.373143\pi\) | |||||||
\(618\) | 2.52051e7 | 0.106788 | ||||||||
\(619\) | 1.52689e8i | 0.643780i | 0.946777 | + | 0.321890i | \(0.104318\pi\) | ||||
−0.946777 | + | 0.321890i | \(0.895682\pi\) | |||||||
\(620\) | 1.32614e8 | + | 7.57631e7i | 0.556436 | + | 0.317894i | ||||
\(621\) | 4.73579e7 | − | 2.50720e8i | 0.197750 | − | 1.04692i | ||||
\(622\) | − | 1.67510e7i | − | 0.0696098i | ||||||
\(623\) | 3.64217e8i | 1.50625i | ||||||||
\(624\) | 7.75669e7 | 0.319244 | ||||||||
\(625\) | −1.18205e8 | + | 2.13617e8i | −0.484170 | + | 0.874974i | ||||
\(626\) | 2.36530e8i | 0.964192i | ||||||||
\(627\) | 2.58991e8i | 1.05071i | ||||||||
\(628\) | 1.31304e8 | 0.530151 | ||||||||
\(629\) | −3.42602e7 | −0.137670 | ||||||||
\(630\) | −1.18198e7 | + | 2.06891e7i | −0.0472702 | + | 0.0827408i | ||||
\(631\) | − | 1.07826e8i | − | 0.429175i | −0.976705 | − | 0.214587i | \(-0.931159\pi\) | ||
0.976705 | − | 0.214587i | \(-0.0688407\pi\) | |||||||
\(632\) | 2.52860e8 | 1.00168 | ||||||||
\(633\) | − | 5.64105e7i | − | 0.222407i | ||||||
\(634\) | 9.25865e7 | 0.363312 | ||||||||
\(635\) | 5.96468e7 | − | 1.04405e8i | 0.232952 | − | 0.407754i | ||||
\(636\) | − | 5.31430e7i | − | 0.206574i | ||||||
\(637\) | − | 3.73793e7i | − | 0.144615i | ||||||
\(638\) | −3.42531e8 | −1.31898 | ||||||||
\(639\) | 6.04824e7 | 0.231807 | ||||||||
\(640\) | 1.08722e8 | − | 1.90305e8i | 0.414743 | − | 0.725957i | ||||
\(641\) | 2.29008e8i | 0.869513i | 0.900548 | + | 0.434757i | \(0.143166\pi\) | ||||
−0.900548 | + | 0.434757i | \(0.856834\pi\) | |||||||
\(642\) | −9.30541e6 | −0.0351666 | ||||||||
\(643\) | −1.48088e8 | −0.557041 | −0.278520 | − | 0.960430i | \(-0.589844\pi\) | ||||
−0.278520 | + | 0.960430i | \(0.589844\pi\) | |||||||
\(644\) | 1.91967e8 | + | 3.62602e7i | 0.718735 | + | 0.135760i | ||||
\(645\) | 1.60833e8 | − | 2.81519e8i | 0.599371 | − | 1.04913i | ||||
\(646\) | 1.05796e8 | 0.392439 | ||||||||
\(647\) | − | 1.48933e8i | − | 0.549893i | −0.961459 | − | 0.274947i | \(-0.911340\pi\) | ||
0.961459 | − | 0.274947i | \(-0.0886602\pi\) | |||||||
\(648\) | 2.02855e8i | 0.745523i | ||||||||
\(649\) | 6.78672e8i | 2.48271i | ||||||||
\(650\) | −1.34413e8 | − | 2.27996e8i | −0.489440 | − | 0.830210i | ||||
\(651\) | − | 2.38477e8i | − | 0.864378i | ||||||
\(652\) | − | 1.96123e8i | − | 0.707596i | ||||||
\(653\) | − | 4.40549e8i | − | 1.58218i | −0.611703 | − | 0.791088i | \(-0.709515\pi\) | ||
0.611703 | − | 0.791088i | \(-0.290485\pi\) | |||||||
\(654\) | − | 3.90603e7i | − | 0.139638i | ||||||
\(655\) | −1.82947e8 | − | 1.04519e8i | −0.651031 | − | 0.371937i | ||||
\(656\) | 8.40942e7 | 0.297889 | ||||||||
\(657\) | 4.64689e6i | 0.0163858i | ||||||||
\(658\) | 1.05437e7 | 0.0370095 | ||||||||
\(659\) | − | 3.25083e8i | − | 1.13589i | −0.823065 | − | 0.567947i | \(-0.807738\pi\) | ||
0.823065 | − | 0.567947i | \(-0.192262\pi\) | |||||||
\(660\) | 2.95957e8 | + | 1.69082e8i | 1.02943 | + | 0.588118i | ||||
\(661\) | − | 3.66487e7i | − | 0.126898i | −0.997985 | − | 0.0634489i | \(-0.979790\pi\) | ||
0.997985 | − | 0.0634489i | \(-0.0202100\pi\) | |||||||
\(662\) | 1.17418e8i | 0.404725i | ||||||||
\(663\) | 5.43562e8 | 1.86513 | ||||||||
\(664\) | − | 2.89934e8i | − | 0.990366i | ||||||
\(665\) | 9.45643e7 | − | 1.65523e8i | 0.321560 | − | 0.562852i | ||||
\(666\) | 3.22356e6i | 0.0109122i | ||||||||
\(667\) | −3.81960e8 | − | 7.21475e7i | −1.28718 | − | 0.243133i | ||||
\(668\) | 3.84480e8i | 1.28987i | ||||||||
\(669\) | 2.76836e8 | 0.924578 | ||||||||
\(670\) | −3.26627e7 | + | 5.71722e7i | −0.108600 | + | 0.190090i | ||||
\(671\) | 1.09896e8 | 0.363759 | ||||||||
\(672\) | −2.98107e8 | −0.982346 | ||||||||
\(673\) | 2.87968e8i | 0.944712i | 0.881408 | + | 0.472356i | \(0.156596\pi\) | ||||
−0.881408 | + | 0.472356i | \(0.843404\pi\) | |||||||
\(674\) | − | 2.13716e8i | − | 0.698002i | ||||||
\(675\) | −2.82270e8 | + | 1.66409e8i | −0.917810 | + | 0.541084i | ||||
\(676\) | −4.62759e8 | −1.49801 | ||||||||
\(677\) | 5.61644e7 | 0.181007 | 0.0905035 | − | 0.995896i | \(-0.471152\pi\) | ||||
0.0905035 | + | 0.995896i | \(0.471152\pi\) | |||||||
\(678\) | −4.87910e7 | −0.156549 | ||||||||
\(679\) | −2.98750e8 | −0.954330 | ||||||||
\(680\) | 1.67280e8 | − | 2.92804e8i | 0.532008 | − | 0.931216i | ||||
\(681\) | 3.08413e8i | 0.976543i | ||||||||
\(682\) | −2.91051e8 | −0.917522 | ||||||||
\(683\) | 1.77141e8i | 0.555976i | 0.960585 | + | 0.277988i | \(0.0896675\pi\) | ||||
−0.960585 | + | 0.277988i | \(0.910332\pi\) | |||||||
\(684\) | 2.35921e7i | 0.0737222i | ||||||||
\(685\) | 8.39229e7 | + | 4.79455e7i | 0.261101 | + | 0.149168i | ||||
\(686\) | − | 1.67951e8i | − | 0.520248i | ||||||
\(687\) | −3.32029e8 | −1.02402 | ||||||||
\(688\) | −8.53594e7 | −0.262112 | ||||||||
\(689\) | 1.86372e8i | 0.569799i | ||||||||
\(690\) | −1.24223e8 | − | 1.05856e8i | −0.378141 | − | 0.322233i | ||||
\(691\) | −2.95017e8 | −0.894155 | −0.447078 | − | 0.894495i | \(-0.647535\pi\) | ||||
−0.447078 | + | 0.894495i | \(0.647535\pi\) | |||||||
\(692\) | 1.27477e8i | 0.384693i | ||||||||
\(693\) | 1.07615e8i | 0.323351i | ||||||||
\(694\) | 1.79944e8 | 0.538343 | ||||||||
\(695\) | 3.96568e8 | + | 2.26561e8i | 1.18131 | + | 0.674886i | ||||
\(696\) | 3.73730e8 | 1.10849 | ||||||||
\(697\) | 5.89303e8 | 1.74037 | ||||||||
\(698\) | − | 5.24002e7i | − | 0.154087i | ||||||
\(699\) | −4.88669e7 | −0.143081 | ||||||||
\(700\) | −1.27413e8 | − | 2.16123e8i | −0.371466 | − | 0.630098i | ||||
\(701\) | 9.95401e7i | 0.288964i | 0.989507 | + | 0.144482i | \(0.0461516\pi\) | ||||
−0.989507 | + | 0.144482i | \(0.953848\pi\) | |||||||
\(702\) | − | 3.55221e8i | − | 1.02680i | ||||||
\(703\) | − | 2.57901e7i | − | 0.0742313i | ||||||
\(704\) | 2.36227e8i | 0.677035i | ||||||||
\(705\) | 1.81264e7 | + | 1.03557e7i | 0.0517302 | + | 0.0295537i | ||||
\(706\) | 2.24825e8 | 0.638897 | ||||||||
\(707\) | 3.73137e8 | 1.05587 | ||||||||
\(708\) | − | 3.05741e8i | − | 0.861498i | ||||||
\(709\) | 5.67813e8i | 1.59319i | 0.604517 | + | 0.796593i | \(0.293366\pi\) | ||||
−0.604517 | + | 0.796593i | \(0.706634\pi\) | |||||||
\(710\) | 1.33293e8 | − | 2.33313e8i | 0.372420 | − | 0.651876i | ||||
\(711\) | 6.52653e7i | 0.181582i | ||||||||
\(712\) | −4.84999e8 | −1.34370 | ||||||||
\(713\) | −3.24554e8 | − | 6.13043e7i | −0.895403 | − | 0.169131i | ||||
\(714\) | −2.17405e8 | −0.597277 | ||||||||
\(715\) | −1.03792e9 | − | 5.92966e8i | −2.83951 | − | 1.62223i | ||||
\(716\) | −2.01244e8 | −0.548255 | ||||||||
\(717\) | 9.62993e7i | 0.261256i | ||||||||
\(718\) | −7.09199e7 | −0.191600 | ||||||||
\(719\) | −5.08780e8 | −1.36881 | −0.684405 | − | 0.729102i | \(-0.739938\pi\) | ||||
−0.684405 | + | 0.729102i | \(0.739938\pi\) | |||||||
\(720\) | 1.07847e7 | + | 6.16132e6i | 0.0288941 | + | 0.0165073i | ||||
\(721\) | −8.37906e7 | −0.223558 | ||||||||
\(722\) | − | 1.25379e8i | − | 0.333131i | ||||||
\(723\) | 4.71165e8 | 1.24669 | ||||||||
\(724\) | 5.02344e7i | 0.132369i | ||||||||
\(725\) | 2.53516e8 | + | 4.30025e8i | 0.665260 | + | 1.12844i | ||||
\(726\) | −4.59434e8 | −1.20064 | ||||||||
\(727\) | 2.73772e8 | 0.712503 | 0.356251 | − | 0.934390i | \(-0.384055\pi\) | ||||
0.356251 | + | 0.934390i | \(0.384055\pi\) | |||||||
\(728\) | 6.58718e8 | 1.70728 | ||||||||
\(729\) | −4.28819e8 | −1.10686 | ||||||||
\(730\) | 1.79256e7 | + | 1.02410e7i | 0.0460791 | + | 0.0263252i | ||||
\(731\) | −5.98169e8 | −1.53134 | ||||||||
\(732\) | −4.95081e7 | −0.126224 | ||||||||
\(733\) | −6.84631e8 | −1.73838 | −0.869190 | − | 0.494479i | \(-0.835359\pi\) | ||||
−0.869190 | + | 0.494479i | \(0.835359\pi\) | |||||||
\(734\) | 4.76141e7i | 0.120406i | ||||||||
\(735\) | −1.46839e7 | + | 2.57023e7i | −0.0369810 | + | 0.0647308i | ||||
\(736\) | −7.66332e7 | + | 4.05707e8i | −0.192213 | + | 1.01761i | ||||
\(737\) | 2.97383e8i | 0.742872i | ||||||||
\(738\) | − | 5.54477e7i | − | 0.137948i | ||||||
\(739\) | 3.13451e8 | 0.776669 | 0.388335 | − | 0.921518i | \(-0.373050\pi\) | ||||
0.388335 | + | 0.921518i | \(0.373050\pi\) | |||||||
\(740\) | −2.94712e7 | − | 1.68370e7i | −0.0727282 | − | 0.0415499i | ||||
\(741\) | 4.09177e8i | 1.00567i | ||||||||
\(742\) | − | 7.45420e7i | − | 0.182469i | ||||||
\(743\) | −6.52445e8 | −1.59066 | −0.795330 | − | 0.606176i | \(-0.792703\pi\) | ||||
−0.795330 | + | 0.606176i | \(0.792703\pi\) | |||||||
\(744\) | 3.17561e8 | 0.771096 | ||||||||
\(745\) | −1.09196e8 | + | 1.91134e8i | −0.264080 | + | 0.462241i | ||||
\(746\) | − | 1.88515e8i | − | 0.454078i | ||||||
\(747\) | 7.48344e7 | 0.179531 | ||||||||
\(748\) | − | 6.28848e8i | − | 1.50259i | ||||||
\(749\) | 3.09345e7 | 0.0736202 | ||||||||
\(750\) | 2.85849e6 | + | 2.09574e8i | 0.00677569 | + | 0.496769i | ||||
\(751\) | − | 4.00386e8i | − | 0.945277i | −0.881256 | − | 0.472638i | \(-0.843302\pi\) | ||
0.881256 | − | 0.472638i | \(-0.156698\pi\) | |||||||
\(752\) | − | 5.49612e6i | − | 0.0129242i | ||||||
\(753\) | −5.44702e8 | −1.27577 | ||||||||
\(754\) | −5.41163e8 | −1.26245 | ||||||||
\(755\) | 5.07565e7 | + | 2.89974e7i | 0.117937 | + | 0.0673781i | ||||
\(756\) | − | 3.36723e8i | − | 0.779304i | ||||||
\(757\) | 2.95647e8 | 0.681532 | 0.340766 | − | 0.940148i | \(-0.389314\pi\) | ||||
0.340766 | + | 0.940148i | \(0.389314\pi\) | |||||||
\(758\) | −3.42602e8 | −0.786651 | ||||||||
\(759\) | −7.24312e8 | − | 1.36814e8i | −1.65653 | − | 0.312899i | ||||
\(760\) | 2.20414e8 | + | 1.25924e8i | 0.502110 | + | 0.286858i | ||||
\(761\) | 4.67608e8 | 1.06103 | 0.530516 | − | 0.847675i | \(-0.321998\pi\) | ||||
0.530516 | + | 0.847675i | \(0.321998\pi\) | |||||||
\(762\) | − | 1.03227e8i | − | 0.233308i | ||||||
\(763\) | 1.29850e8i | 0.292327i | ||||||||
\(764\) | 1.31892e8i | 0.295758i | ||||||||
\(765\) | 7.55751e7 | + | 4.31764e7i | 0.168809 | + | 0.0964411i | ||||
\(766\) | 3.78614e8i | 0.842384i | ||||||||
\(767\) | 1.07223e9i | 2.37630i | ||||||||
\(768\) | − | 3.39481e8i | − | 0.749432i | ||||||
\(769\) | − | 5.90805e8i | − | 1.29917i | −0.760290 | − | 0.649584i | \(-0.774943\pi\) | ||
0.760290 | − | 0.649584i | \(-0.225057\pi\) | |||||||
\(770\) | 4.15130e8 | + | 2.37165e8i | 0.909309 | + | 0.519493i | ||||
\(771\) | −5.06305e7 | −0.110471 | ||||||||
\(772\) | 9.53572e7i | 0.207253i | ||||||||
\(773\) | −2.37718e8 | −0.514664 | −0.257332 | − | 0.966323i | \(-0.582843\pi\) | ||||
−0.257332 | + | 0.966323i | \(0.582843\pi\) | |||||||
\(774\) | 5.62819e7i | 0.121380i | ||||||||
\(775\) | 2.15414e8 | + | 3.65395e8i | 0.462775 | + | 0.784979i | ||||
\(776\) | − | 3.97822e8i | − | 0.851340i | ||||||
\(777\) | 5.29974e7i | 0.112977i | ||||||||
\(778\) | 4.84284e8 | 1.02840 | ||||||||
\(779\) | 4.43610e8i | 0.938403i | ||||||||
\(780\) | 4.67581e8 | + | 2.67131e8i | 0.985310 | + | 0.562912i | ||||
\(781\) | − | 1.21359e9i | − | 2.54753i | ||||||
\(782\) | −5.58875e7 | + | 2.95877e8i | −0.116868 | + | 0.618715i | ||||
\(783\) | 6.69983e8i | 1.39566i | ||||||||
\(784\) | 7.79323e6 | 0.0161722 | ||||||||
\(785\) | 3.16631e8 | + | 1.80893e8i | 0.654553 | + | 0.373949i | ||||
\(786\) | −1.80884e8 | −0.372505 | ||||||||
\(787\) | −6.53890e8 | −1.34147 | −0.670734 | − | 0.741698i | \(-0.734021\pi\) | ||||
−0.670734 | + | 0.741698i | \(0.734021\pi\) | |||||||
\(788\) | 3.18668e8i | 0.651267i | ||||||||
\(789\) | 8.97597e7i | 0.182747i | ||||||||
\(790\) | 2.51764e8 | + | 1.43834e8i | 0.510636 | + | 0.291729i | ||||
\(791\) | 1.62199e8 | 0.327731 | ||||||||
\(792\) | −1.43303e8 | −0.288455 | ||||||||
\(793\) | 1.73624e8 | 0.348169 | ||||||||
\(794\) | 1.17922e8 | 0.235578 | ||||||||
\(795\) | 7.32131e7 | − | 1.28151e8i | 0.145709 | − | 0.255047i | ||||
\(796\) | − | 1.75936e8i | − | 0.348830i | ||||||
\(797\) | 8.07485e8 | 1.59500 | 0.797498 | − | 0.603322i | \(-0.206157\pi\) | ||||
0.797498 | + | 0.603322i | \(0.206157\pi\) | |||||||
\(798\) | − | 1.63657e8i | − | 0.322051i | ||||||
\(799\) | − | 3.85149e7i | − | 0.0755072i | ||||||
\(800\) | 4.56761e8 | − | 2.69278e8i | 0.892111 | − | 0.525933i | ||||
\(801\) | − | 1.25182e8i | − | 0.243582i | ||||||
\(802\) | −2.19471e8 | −0.425456 | ||||||||
\(803\) | 9.32405e7 | 0.180077 | ||||||||
\(804\) | − | 1.33971e8i | − | 0.257776i | ||||||
\(805\) | 4.12961e8 | + | 3.51904e8i | 0.791628 | + | 0.674585i | ||||
\(806\) | −4.59830e8 | −0.878197 | ||||||||
\(807\) | − | 9.32939e8i | − | 1.77514i | ||||||
\(808\) | 4.96877e8i | 0.941923i | ||||||||
\(809\) | −3.45032e8 | −0.651649 | −0.325825 | − | 0.945430i | \(-0.605642\pi\) | ||||
−0.325825 | + | 0.945430i | \(0.605642\pi\) | |||||||
\(810\) | −1.15389e8 | + | 2.01975e8i | −0.217126 | + | 0.380052i | ||||
\(811\) | −2.38949e8 | −0.447964 | −0.223982 | − | 0.974593i | \(-0.571906\pi\) | ||||
−0.223982 | + | 0.974593i | \(0.571906\pi\) | |||||||
\(812\) | −5.12982e8 | −0.958151 | ||||||||
\(813\) | − | 2.64658e8i | − | 0.492509i | ||||||
\(814\) | 6.46811e7 | 0.119924 | ||||||||
\(815\) | 2.70191e8 | − | 4.72937e8i | 0.499112 | − | 0.873636i | ||||
\(816\) | 1.13327e8i | 0.208576i | ||||||||
\(817\) | − | 4.50284e8i | − | 0.825697i | ||||||
\(818\) | − | 4.79733e8i | − | 0.876475i | ||||||
\(819\) | 1.70020e8i | 0.309492i | ||||||||
\(820\) | 5.06928e8 | + | 2.89610e8i | 0.919401 | + | 0.525258i | ||||
\(821\) | 6.24654e8 | 1.12878 | 0.564391 | − | 0.825507i | \(-0.309111\pi\) | ||||
0.564391 | + | 0.825507i | \(0.309111\pi\) | |||||||
\(822\) | 8.29764e7 | 0.149396 | ||||||||
\(823\) | 4.88424e8i | 0.876189i | 0.898929 | + | 0.438094i | \(0.144346\pi\) | ||||
−0.898929 | + | 0.438094i | \(0.855654\pi\) | |||||||
\(824\) | − | 1.11577e8i | − | 0.199432i | ||||||
\(825\) | 4.80743e8 | + | 8.15458e8i | 0.856153 | + | 1.45224i | ||||
\(826\) | − | 4.28853e8i | − | 0.760972i | ||||||
\(827\) | 2.40129e7 | 0.0424550 | 0.0212275 | − | 0.999775i | \(-0.493243\pi\) | ||||
0.0212275 | + | 0.999775i | \(0.493243\pi\) | |||||||
\(828\) | −6.59794e7 | − | 1.24627e7i | −0.116230 | − | 0.0219544i | ||||
\(829\) | −8.77054e7 | −0.153944 | −0.0769720 | − | 0.997033i | \(-0.524525\pi\) | ||||
−0.0769720 | + | 0.997033i | \(0.524525\pi\) | |||||||
\(830\) | 1.64922e8 | − | 2.88677e8i | 0.288433 | − | 0.504868i | ||||
\(831\) | −1.26269e8 | −0.220035 | ||||||||
\(832\) | 3.73213e8i | 0.648017i | ||||||||
\(833\) | 5.46122e7 | 0.0944832 | ||||||||
\(834\) | 3.92095e8 | 0.675916 | ||||||||
\(835\) | −5.29683e8 | + | 9.27147e8i | −0.909823 | + | 1.59254i | ||||
\(836\) | 4.73379e8 | 0.810196 | ||||||||
\(837\) | 5.69290e8i | 0.970861i | ||||||||
\(838\) | −4.61216e8 | −0.783740 | ||||||||
\(839\) | 4.89140e8i | 0.828222i | 0.910226 | + | 0.414111i | \(0.135908\pi\) | ||||
−0.910226 | + | 0.414111i | \(0.864092\pi\) | |||||||
\(840\) | −4.52940e8 | − | 2.58767e8i | −0.764193 | − | 0.436587i | ||||
\(841\) | 4.25866e8 | 0.715953 | ||||||||
\(842\) | −6.22120e6 | −0.0104217 | ||||||||
\(843\) | −8.84324e8 | −1.47614 | ||||||||
\(844\) | −1.03106e8 | −0.171497 | ||||||||
\(845\) | −1.11591e9 | − | 6.37525e8i | −1.84952 | − | 1.05664i | ||||
\(846\) | −3.62388e6 | −0.00598498 | ||||||||
\(847\) | 1.52732e9 | 2.51351 | ||||||||
\(848\) | −3.88567e7 | −0.0637204 | ||||||||
\(849\) | − | 3.60217e8i | − | 0.588629i | ||||||
\(850\) | 3.33109e8 | − | 1.96381e8i | 0.542413 | − | 0.319773i | ||||
\(851\) | 7.21265e7 | + | 1.36238e7i | 0.117032 | + | 0.0221060i | ||||
\(852\) | 5.46721e8i | 0.883990i | ||||||||
\(853\) | 6.50958e8i | 1.04883i | 0.851462 | + | 0.524416i | \(0.175716\pi\) | ||||
−0.851462 | + | 0.524416i | \(0.824284\pi\) | |||||||
\(854\) | −6.94434e7 | −0.111495 | ||||||||
\(855\) | −3.25019e7 | + | 5.68907e7i | −0.0520009 | + | 0.0910213i | ||||
\(856\) | 4.11930e7i | 0.0656752i | ||||||||
\(857\) | − | 9.76530e8i | − | 1.55147i | −0.631059 | − | 0.775735i | \(-0.717379\pi\) | ||
0.631059 | − | 0.775735i | \(-0.282621\pi\) | |||||||
\(858\) | −1.02621e9 | −1.62470 | ||||||||
\(859\) | 3.68168e8 | 0.580853 | 0.290427 | − | 0.956897i | \(-0.406203\pi\) | ||||
0.290427 | + | 0.956897i | \(0.406203\pi\) | |||||||
\(860\) | −5.14555e8 | − | 2.93968e8i | −0.808978 | − | 0.462172i | ||||
\(861\) | − | 9.11597e8i | − | 1.42821i | ||||||
\(862\) | 6.14009e8 | 0.958634 | ||||||||
\(863\) | 9.21893e8i | 1.43433i | 0.696905 | + | 0.717163i | \(0.254560\pi\) | ||||
−0.696905 | + | 0.717163i | \(0.745440\pi\) | |||||||
\(864\) | 7.11638e8 | 1.10336 | ||||||||
\(865\) | −1.75621e8 | + | 3.07403e8i | −0.271348 | + | 0.474963i | ||||
\(866\) | − | 3.00828e8i | − | 0.463196i | ||||||
\(867\) | 1.99774e8i | 0.306535i | ||||||||
\(868\) | −4.35884e8 | −0.666518 | ||||||||
\(869\) | 1.30956e9 | 1.99556 | ||||||||
\(870\) | 3.72109e8 | + | 2.12587e8i | 0.565083 | + | 0.322834i | ||||
\(871\) | 4.69834e8i | 0.711033i | ||||||||
\(872\) | −1.72911e8 | −0.260780 | ||||||||
\(873\) | 1.02681e8 | 0.154329 | ||||||||
\(874\) | −2.22728e8 | − | 4.20705e7i | −0.333610 | − | 0.0630149i | ||||
\(875\) | −9.50264e6 | − | 6.96699e8i | −0.0141847 | − | 1.03997i | ||||
\(876\) | −4.20048e7 | −0.0624866 | ||||||||
\(877\) | − | 1.07484e8i | − | 0.159347i | −0.996821 | − | 0.0796737i | \(-0.974612\pi\) | ||
0.996821 | − | 0.0796737i | \(-0.0253878\pi\) | |||||||
\(878\) | 6.70065e7i | 0.0989996i | ||||||||
\(879\) | − | 2.74238e8i | − | 0.403795i | ||||||
\(880\) | 1.23628e8 | − | 2.16396e8i | 0.181413 | − | 0.317541i | ||||
\(881\) | 8.94812e7i | 0.130859i | 0.997857 | + | 0.0654295i | \(0.0208418\pi\) | ||||
−0.997857 | + | 0.0654295i | \(0.979158\pi\) | |||||||
\(882\) | − | 5.13848e6i | − | 0.00748909i | ||||||
\(883\) | − | 2.15585e8i | − | 0.313139i | −0.987667 | − | 0.156570i | \(-0.949956\pi\) | ||
0.987667 | − | 0.156570i | \(-0.0500435\pi\) | |||||||
\(884\) | − | 9.93513e8i | − | 1.43819i | ||||||
\(885\) | 4.21208e8 | − | 7.37274e8i | 0.607669 | − | 1.06365i | ||||
\(886\) | −1.48617e8 | −0.213682 | ||||||||
\(887\) | − | 1.32026e9i | − | 1.89185i | −0.324380 | − | 0.945927i | \(-0.605156\pi\) | ||
0.324380 | − | 0.945927i | \(-0.394844\pi\) | |||||||
\(888\) | −7.05724e7 | −0.100785 | ||||||||
\(889\) | 3.43163e8i | 0.488422i | ||||||||
\(890\) | −4.82896e8 | − | 2.75880e8i | −0.684988 | − | 0.391337i | ||||
\(891\) | 1.05058e9i | 1.48524i | ||||||||
\(892\) | − | 5.05995e8i | − | 0.712938i | ||||||
\(893\) | 2.89929e7 | 0.0407134 | ||||||||
\(894\) | 1.88978e8i | 0.264483i | ||||||||
\(895\) | −4.85285e8 | − | 2.77246e8i | −0.676905 | − | 0.386719i | ||||
\(896\) | 6.25507e8i | 0.869577i | ||||||||
\(897\) | −1.14434e9 | − | 2.16151e8i | −1.58554 | − | 0.299488i | ||||
\(898\) | 5.06994e8i | 0.700122i | ||||||||
\(899\) | 8.67287e8 | 1.19367 | ||||||||
\(900\) | 4.37921e7 | + | 7.42821e7i | 0.0600715 | + | 0.101896i | ||||
\(901\) | −2.72294e8 | −0.372275 | ||||||||
\(902\) | −1.11257e9 | −1.51603 | ||||||||
\(903\) | 9.25312e8i | 1.25668i | ||||||||
\(904\) | 2.15987e8i | 0.292363i | ||||||||
\(905\) | −6.92061e7 | + | 1.21137e8i | −0.0933681 | + | 0.163430i | ||||
\(906\) | 5.01840e7 | 0.0674809 | ||||||||
\(907\) | 1.36986e9 | 1.83592 | 0.917960 | − | 0.396673i | \(-0.129835\pi\) | ||||
0.917960 | + | 0.396673i | \(0.129835\pi\) | |||||||
\(908\) | 5.63712e8 | 0.753009 | ||||||||
\(909\) | −1.28248e8 | −0.170749 | ||||||||
\(910\) | 6.55860e8 | + | 3.74696e8i | 0.870336 | + | 0.497227i | ||||
\(911\) | 9.16919e8i | 1.21276i | 0.795174 | + | 0.606381i | \(0.207379\pi\) | ||||
−0.795174 | + | 0.606381i | \(0.792621\pi\) | |||||||
\(912\) | −8.53096e7 | −0.112464 | ||||||||
\(913\) | − | 1.50156e9i | − | 1.97302i | ||||||
\(914\) | 4.09241e8i | 0.535971i | ||||||||
\(915\) | −1.19385e8 | − | 6.82054e7i | −0.155843 | − | 0.0890339i | ||||
\(916\) | 6.06878e8i | 0.789614i | ||||||||
\(917\) | 6.01322e8 | 0.779828 | ||||||||
\(918\) | 5.18988e8 | 0.670856 | ||||||||
\(919\) | − | 1.23505e9i | − | 1.59125i | −0.605790 | − | 0.795625i | \(-0.707143\pi\) | ||
0.605790 | − | 0.795625i | \(-0.292857\pi\) | |||||||
\(920\) | −4.68603e8 | + | 5.49907e8i | −0.601785 | + | 0.706197i | ||||
\(921\) | −3.23700e8 | −0.414347 | ||||||||
\(922\) | − | 3.59675e8i | − | 0.458899i | ||||||
\(923\) | − | 1.91734e9i | − | 2.43834i | ||||||
\(924\) | −9.72770e8 | −1.23309 | ||||||||
\(925\) | −4.78721e7 | − | 8.12027e7i | −0.0604863 | − | 0.102600i | ||||
\(926\) | 5.51818e8 | 0.694965 | ||||||||
\(927\) | 2.87990e7 | 0.0361525 | ||||||||
\(928\) | − | 1.08415e9i | − | 1.35658i | ||||||
\(929\) | 8.18771e8 | 1.02121 | 0.510605 | − | 0.859815i | \(-0.329421\pi\) | ||||
0.510605 | + | 0.859815i | \(0.329421\pi\) | |||||||
\(930\) | 3.16183e8 | + | 1.80637e8i | 0.393088 | + | 0.224573i | ||||
\(931\) | 4.11105e7i | 0.0509452i | ||||||||
\(932\) | 8.93181e7i | 0.110330i | ||||||||
\(933\) | 9.46548e7i | 0.116546i | ||||||||
\(934\) | − | 5.11861e8i | − | 0.628220i | ||||||
\(935\) | 8.66340e8 | − | 1.51643e9i | 1.05987 | − | 1.85518i | ||||
\(936\) | −2.26403e8 | −0.276092 | ||||||||
\(937\) | −3.58530e8 | −0.435819 | −0.217910 | − | 0.975969i | \(-0.569924\pi\) | ||||
−0.217910 | + | 0.975969i | \(0.569924\pi\) | |||||||
\(938\) | − | 1.87917e8i | − | 0.227697i | ||||||
\(939\) | − | 1.33656e9i | − | 1.61432i | ||||||
\(940\) | 1.89280e7 | − | 3.31311e7i | 0.0227887 | − | 0.0398890i | ||||
\(941\) | 1.69067e8i | 0.202903i | 0.994840 | + | 0.101452i | \(0.0323487\pi\) | ||||
−0.994840 | + | 0.101452i | \(0.967651\pi\) | |||||||
\(942\) | 3.13060e8 | 0.374520 | ||||||||
\(943\) | −1.24063e9 | − | 2.34340e8i | −1.47948 | − | 0.279455i | ||||
\(944\) | −2.23549e8 | −0.265740 | ||||||||
\(945\) | 4.63890e8 | − | 8.11984e8i | 0.549692 | − | 0.962170i | ||||
\(946\) | 1.12931e9 | 1.33394 | ||||||||
\(947\) | 3.49591e8i | 0.411633i | 0.978591 | + | 0.205816i | \(0.0659849\pi\) | ||||
−0.978591 | + | 0.205816i | \(0.934015\pi\) | |||||||
\(948\) | −5.89955e8 | −0.692459 | ||||||||
\(949\) | 1.47310e8 | 0.172359 | ||||||||
\(950\) | 1.47830e8 | + | 2.50755e8i | 0.172421 | + | 0.292468i | ||||
\(951\) | −5.23177e8 | −0.608285 | ||||||||
\(952\) | 9.62405e8i | 1.11544i | ||||||||
\(953\) | −7.46030e8 | −0.861941 | −0.430970 | − | 0.902366i | \(-0.641829\pi\) | ||||
−0.430970 | + | 0.902366i | \(0.641829\pi\) | |||||||
\(954\) | 2.56203e7i | 0.0295079i | ||||||||
\(955\) | −1.81702e8 | + | 3.18048e8i | −0.208617 | + | 0.365159i | ||||
\(956\) | 1.76014e8 | 0.201453 | ||||||||
\(957\) | 1.93554e9 | 2.20834 | ||||||||
\(958\) | 3.99991e8 | 0.454940 | ||||||||
\(959\) | −2.75843e8 | −0.312756 | ||||||||
\(960\) | 1.46611e8 | − | 2.56625e8i | 0.165711 | − | 0.290058i | ||||
\(961\) | −1.50564e8 | −0.169648 | ||||||||
\(962\) | 1.02189e8 | 0.114784 | ||||||||
\(963\) | −1.06322e7 | −0.0119054 | ||||||||
\(964\) | − | 8.61188e8i | − | 0.961318i | ||||||
\(965\) | −1.31370e8 | + | 2.29947e8i | −0.146189 | + | 0.255886i | ||||
\(966\) | 4.57694e8 | + | 8.64528e7i | 0.507743 | + | 0.0959064i | ||||
\(967\) | − | 5.12211e8i | − | 0.566460i | −0.959052 | − | 0.283230i | \(-0.908594\pi\) | ||
0.959052 | − | 0.283230i | \(-0.0914060\pi\) | |||||||
\(968\) | 2.03381e9i | 2.24225i | ||||||||
\(969\) | −5.97820e8 | −0.657051 | ||||||||
\(970\) | 2.26291e8 | − | 3.96096e8i | 0.247944 | − | 0.433996i | ||||
\(971\) | 9.05048e8i | 0.988585i | 0.869296 | + | 0.494293i | \(0.164573\pi\) | ||||
−0.869296 | + | 0.494293i | \(0.835427\pi\) | |||||||
\(972\) | 2.14802e8i | 0.233905i | ||||||||
\(973\) | −1.30346e9 | −1.41501 | ||||||||
\(974\) | 1.50127e8 | 0.162473 | ||||||||
\(975\) | 7.59523e8 | + | 1.28834e9i | 0.819459 | + | 1.39000i | ||||
\(976\) | 3.61989e7i | 0.0389355i | ||||||||
\(977\) | −1.98357e8 | −0.212698 | −0.106349 | − | 0.994329i | \(-0.533916\pi\) | ||||
−0.106349 | + | 0.994329i | \(0.533916\pi\) | |||||||
\(978\) | − | 4.67603e8i | − | 0.499874i | ||||||
\(979\) | −2.51180e9 | −2.67693 | ||||||||
\(980\) | 4.69783e7 | + | 2.68389e7i | 0.0499137 | + | 0.0285159i | ||||
\(981\) | − | 4.46298e7i | − | 0.0472736i | ||||||
\(982\) | 4.23554e8i | 0.447275i | ||||||||
\(983\) | −1.31713e9 | −1.38666 | −0.693330 | − | 0.720621i | \(-0.743857\pi\) | ||||
−0.693330 | + | 0.720621i | \(0.743857\pi\) | |||||||
\(984\) | 1.21390e9 | 1.27408 | ||||||||
\(985\) | −4.39016e8 | + | 7.68445e8i | −0.459380 | + | 0.804089i | ||||
\(986\) | − | 7.90654e8i | − | 0.824814i | ||||||
\(987\) | −5.95789e7 | −0.0619642 | ||||||||
\(988\) | 7.47888e8 | 0.775471 | ||||||||
\(989\) | 1.25930e9 | + | 2.37866e8i | 1.30179 | + | 0.245892i | ||||
\(990\) | −1.42681e8 | − | 8.15143e7i | −0.147048 | − | 0.0840094i | ||||
\(991\) | −2.78887e8 | −0.286555 | −0.143277 | − | 0.989683i | \(-0.545764\pi\) | ||||
−0.143277 | + | 0.989683i | \(0.545764\pi\) | |||||||
\(992\) | − | 9.21209e8i | − | 0.943676i | ||||||
\(993\) | − | 6.63492e8i | − | 0.677623i | ||||||
\(994\) | 7.66868e8i | 0.780839i | ||||||||
\(995\) | 2.42380e8 | − | 4.24257e8i | 0.246052 | − | 0.430685i | ||||
\(996\) | 6.76454e8i | 0.684637i | ||||||||
\(997\) | − | 4.83529e8i | − | 0.487907i | −0.969787 | − | 0.243953i | \(-0.921556\pi\) | ||
0.969787 | − | 0.243953i | \(-0.0784444\pi\) | |||||||
\(998\) | 1.65779e7i | 0.0166778i | ||||||||
\(999\) | − | 1.26515e8i | − | 0.126895i |
(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 | 115.7.c.c.114.13 | ✓ | 68 | |
5.4 | even | 2 | inner | 115.7.c.c.114.56 | yes | 68 | |
23.22 | odd | 2 | inner | 115.7.c.c.114.55 | yes | 68 | |
115.114 | odd | 2 | inner | 115.7.c.c.114.14 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.7.c.c.114.13 | ✓ | 68 | 1.1 | even | 1 | trivial | |
115.7.c.c.114.14 | yes | 68 | 115.114 | odd | 2 | inner | |
115.7.c.c.114.55 | yes | 68 | 23.22 | odd | 2 | inner | |
115.7.c.c.114.56 | yes | 68 | 5.4 | even | 2 | inner |