Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,8,Mod(1,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.a (trivial) |
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: | yes |
Analytic conductor: | \(144.321881774\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 462.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.707107 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 182.000 | 0.651143 | 0.325571 | − | 0.945517i | \(-0.394443\pi\) | ||||
0.325571 | + | 0.945517i | \(0.394443\pi\) | |||||||
\(6\) | 216.000 | 0.408248 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −1456.00 | −0.460428 | ||||||||
\(11\) | 1331.00 | 0.301511 | ||||||||
\(12\) | −1728.00 | −0.288675 | ||||||||
\(13\) | 13758.0 | 1.73682 | 0.868408 | − | 0.495851i | \(-0.165144\pi\) | ||||
0.868408 | + | 0.495851i | \(0.165144\pi\) | |||||||
\(14\) | −2744.00 | −0.267261 | ||||||||
\(15\) | −4914.00 | −0.375938 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 14738.0 | 0.727558 | 0.363779 | − | 0.931485i | \(-0.381486\pi\) | ||||
0.363779 | + | 0.931485i | \(0.381486\pi\) | |||||||
\(18\) | −5832.00 | −0.235702 | ||||||||
\(19\) | 34516.0 | 1.15447 | 0.577235 | − | 0.816578i | \(-0.304132\pi\) | ||||
0.577235 | + | 0.816578i | \(0.304132\pi\) | |||||||
\(20\) | 11648.0 | 0.325571 | ||||||||
\(21\) | −9261.00 | −0.218218 | ||||||||
\(22\) | −10648.0 | −0.213201 | ||||||||
\(23\) | 49816.0 | 0.853732 | 0.426866 | − | 0.904315i | \(-0.359618\pi\) | ||||
0.426866 | + | 0.904315i | \(0.359618\pi\) | |||||||
\(24\) | 13824.0 | 0.204124 | ||||||||
\(25\) | −45001.0 | −0.576013 | ||||||||
\(26\) | −110064. | −1.22811 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | 141174. | 1.07488 | 0.537442 | − | 0.843301i | \(-0.319391\pi\) | ||||
0.537442 | + | 0.843301i | \(0.319391\pi\) | |||||||
\(30\) | 39312.0 | 0.265828 | ||||||||
\(31\) | −86112.0 | −0.519156 | −0.259578 | − | 0.965722i | \(-0.583583\pi\) | ||||
−0.259578 | + | 0.965722i | \(0.583583\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | −35937.0 | −0.174078 | ||||||||
\(34\) | −117904. | −0.514461 | ||||||||
\(35\) | 62426.0 | 0.246109 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 535038. | 1.73652 | 0.868258 | − | 0.496114i | \(-0.165240\pi\) | ||||
0.868258 | + | 0.496114i | \(0.165240\pi\) | |||||||
\(38\) | −276128. | −0.816334 | ||||||||
\(39\) | −371466. | −1.00275 | ||||||||
\(40\) | −93184.0 | −0.230214 | ||||||||
\(41\) | 708282. | 1.60495 | 0.802477 | − | 0.596683i | \(-0.203515\pi\) | ||||
0.802477 | + | 0.596683i | \(0.203515\pi\) | |||||||
\(42\) | 74088.0 | 0.154303 | ||||||||
\(43\) | 162292. | 0.311285 | 0.155642 | − | 0.987813i | \(-0.450255\pi\) | ||||
0.155642 | + | 0.987813i | \(0.450255\pi\) | |||||||
\(44\) | 85184.0 | 0.150756 | ||||||||
\(45\) | 132678. | 0.217048 | ||||||||
\(46\) | −398528. | −0.603680 | ||||||||
\(47\) | 397296. | 0.558177 | 0.279088 | − | 0.960265i | \(-0.409968\pi\) | ||||
0.279088 | + | 0.960265i | \(0.409968\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 360008. | 0.407303 | ||||||||
\(51\) | −397926. | −0.420056 | ||||||||
\(52\) | 880512. | 0.868408 | ||||||||
\(53\) | 224798. | 0.207409 | 0.103704 | − | 0.994608i | \(-0.466930\pi\) | ||||
0.103704 | + | 0.994608i | \(0.466930\pi\) | |||||||
\(54\) | 157464. | 0.136083 | ||||||||
\(55\) | 242242. | 0.196327 | ||||||||
\(56\) | −175616. | −0.133631 | ||||||||
\(57\) | −931932. | −0.666534 | ||||||||
\(58\) | −1.12939e6 | −0.760058 | ||||||||
\(59\) | 694668. | 0.440347 | 0.220174 | − | 0.975461i | \(-0.429338\pi\) | ||||
0.220174 | + | 0.975461i | \(0.429338\pi\) | |||||||
\(60\) | −314496. | −0.187969 | ||||||||
\(61\) | 50110.0 | 0.0282664 | 0.0141332 | − | 0.999900i | \(-0.495501\pi\) | ||||
0.0141332 | + | 0.999900i | \(0.495501\pi\) | |||||||
\(62\) | 688896. | 0.367099 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 2.50396e6 | 1.13091 | ||||||||
\(66\) | 287496. | 0.123091 | ||||||||
\(67\) | −3.22840e6 | −1.31137 | −0.655686 | − | 0.755033i | \(-0.727621\pi\) | ||||
−0.655686 | + | 0.755033i | \(0.727621\pi\) | |||||||
\(68\) | 943232. | 0.363779 | ||||||||
\(69\) | −1.34503e6 | −0.492902 | ||||||||
\(70\) | −499408. | −0.174025 | ||||||||
\(71\) | −1.87150e6 | −0.620561 | −0.310281 | − | 0.950645i | \(-0.600423\pi\) | ||||
−0.310281 | + | 0.950645i | \(0.600423\pi\) | |||||||
\(72\) | −373248. | −0.117851 | ||||||||
\(73\) | −937542. | −0.282072 | −0.141036 | − | 0.990004i | \(-0.545043\pi\) | ||||
−0.141036 | + | 0.990004i | \(0.545043\pi\) | |||||||
\(74\) | −4.28030e6 | −1.22790 | ||||||||
\(75\) | 1.21503e6 | 0.332561 | ||||||||
\(76\) | 2.20902e6 | 0.577235 | ||||||||
\(77\) | 456533. | 0.113961 | ||||||||
\(78\) | 2.97173e6 | 0.709052 | ||||||||
\(79\) | 1.26603e6 | 0.288902 | 0.144451 | − | 0.989512i | \(-0.453858\pi\) | ||||
0.144451 | + | 0.989512i | \(0.453858\pi\) | |||||||
\(80\) | 745472. | 0.162786 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −5.66626e6 | −1.13487 | ||||||||
\(83\) | −2.54500e6 | −0.488557 | −0.244278 | − | 0.969705i | \(-0.578551\pi\) | ||||
−0.244278 | + | 0.969705i | \(0.578551\pi\) | |||||||
\(84\) | −592704. | −0.109109 | ||||||||
\(85\) | 2.68232e6 | 0.473744 | ||||||||
\(86\) | −1.29834e6 | −0.220111 | ||||||||
\(87\) | −3.81170e6 | −0.620585 | ||||||||
\(88\) | −681472. | −0.106600 | ||||||||
\(89\) | −9.90983e6 | −1.49005 | −0.745026 | − | 0.667036i | \(-0.767563\pi\) | ||||
−0.745026 | + | 0.667036i | \(0.767563\pi\) | |||||||
\(90\) | −1.06142e6 | −0.153476 | ||||||||
\(91\) | 4.71899e6 | 0.656454 | ||||||||
\(92\) | 3.18822e6 | 0.426866 | ||||||||
\(93\) | 2.32502e6 | 0.299735 | ||||||||
\(94\) | −3.17837e6 | −0.394691 | ||||||||
\(95\) | 6.28191e6 | 0.751725 | ||||||||
\(96\) | 884736. | 0.102062 | ||||||||
\(97\) | −1.40108e7 | −1.55870 | −0.779350 | − | 0.626588i | \(-0.784451\pi\) | ||||
−0.779350 | + | 0.626588i | \(0.784451\pi\) | |||||||
\(98\) | −941192. | −0.101015 | ||||||||
\(99\) | 970299. | 0.100504 | ||||||||
\(100\) | −2.88006e6 | −0.288006 | ||||||||
\(101\) | −7.34281e6 | −0.709149 | −0.354574 | − | 0.935028i | \(-0.615374\pi\) | ||||
−0.354574 | + | 0.935028i | \(0.615374\pi\) | |||||||
\(102\) | 3.18341e6 | 0.297024 | ||||||||
\(103\) | −8.86030e6 | −0.798947 | −0.399473 | − | 0.916745i | \(-0.630807\pi\) | ||||
−0.399473 | + | 0.916745i | \(0.630807\pi\) | |||||||
\(104\) | −7.04410e6 | −0.614057 | ||||||||
\(105\) | −1.68550e6 | −0.142091 | ||||||||
\(106\) | −1.79838e6 | −0.146660 | ||||||||
\(107\) | −1.50185e7 | −1.18518 | −0.592588 | − | 0.805506i | \(-0.701894\pi\) | ||||
−0.592588 | + | 0.805506i | \(0.701894\pi\) | |||||||
\(108\) | −1.25971e6 | −0.0962250 | ||||||||
\(109\) | 1.06251e7 | 0.785851 | 0.392925 | − | 0.919570i | \(-0.371463\pi\) | ||||
0.392925 | + | 0.919570i | \(0.371463\pi\) | |||||||
\(110\) | −1.93794e6 | −0.138824 | ||||||||
\(111\) | −1.44460e7 | −1.00258 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | −7.09310e6 | −0.462447 | −0.231223 | − | 0.972901i | \(-0.574273\pi\) | ||||
−0.231223 | + | 0.972901i | \(0.574273\pi\) | |||||||
\(114\) | 7.45546e6 | 0.471311 | ||||||||
\(115\) | 9.06651e6 | 0.555901 | ||||||||
\(116\) | 9.03514e6 | 0.537442 | ||||||||
\(117\) | 1.00296e7 | 0.578938 | ||||||||
\(118\) | −5.55734e6 | −0.311373 | ||||||||
\(119\) | 5.05513e6 | 0.274991 | ||||||||
\(120\) | 2.51597e6 | 0.132914 | ||||||||
\(121\) | 1.77156e6 | 0.0909091 | ||||||||
\(122\) | −400880. | −0.0199873 | ||||||||
\(123\) | −1.91236e7 | −0.926621 | ||||||||
\(124\) | −5.51117e6 | −0.259578 | ||||||||
\(125\) | −2.24089e7 | −1.02621 | ||||||||
\(126\) | −2.00038e6 | −0.0890871 | ||||||||
\(127\) | 3.60394e7 | 1.56122 | 0.780611 | − | 0.625017i | \(-0.214908\pi\) | ||||
0.780611 | + | 0.625017i | \(0.214908\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | −4.38188e6 | −0.179720 | ||||||||
\(130\) | −2.00316e7 | −0.799678 | ||||||||
\(131\) | 2.25637e7 | 0.876923 | 0.438462 | − | 0.898750i | \(-0.355523\pi\) | ||||
0.438462 | + | 0.898750i | \(0.355523\pi\) | |||||||
\(132\) | −2.29997e6 | −0.0870388 | ||||||||
\(133\) | 1.18390e7 | 0.436349 | ||||||||
\(134\) | 2.58272e7 | 0.927280 | ||||||||
\(135\) | −3.58231e6 | −0.125313 | ||||||||
\(136\) | −7.54586e6 | −0.257230 | ||||||||
\(137\) | 1.24461e7 | 0.413535 | 0.206768 | − | 0.978390i | \(-0.433706\pi\) | ||||
0.206768 | + | 0.978390i | \(0.433706\pi\) | |||||||
\(138\) | 1.07603e7 | 0.348535 | ||||||||
\(139\) | 1.63300e6 | 0.0515746 | 0.0257873 | − | 0.999667i | \(-0.491791\pi\) | ||||
0.0257873 | + | 0.999667i | \(0.491791\pi\) | |||||||
\(140\) | 3.99526e6 | 0.123054 | ||||||||
\(141\) | −1.07270e7 | −0.322263 | ||||||||
\(142\) | 1.49720e7 | 0.438803 | ||||||||
\(143\) | 1.83119e7 | 0.523669 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | 2.56937e7 | 0.699903 | ||||||||
\(146\) | 7.50034e6 | 0.199455 | ||||||||
\(147\) | −3.17652e6 | −0.0824786 | ||||||||
\(148\) | 3.42424e7 | 0.868258 | ||||||||
\(149\) | 6.75131e7 | 1.67200 | 0.835999 | − | 0.548730i | \(-0.184889\pi\) | ||||
0.835999 | + | 0.548730i | \(0.184889\pi\) | |||||||
\(150\) | −9.72022e6 | −0.235156 | ||||||||
\(151\) | −6.23218e7 | −1.47306 | −0.736530 | − | 0.676405i | \(-0.763537\pi\) | ||||
−0.736530 | + | 0.676405i | \(0.763537\pi\) | |||||||
\(152\) | −1.76722e7 | −0.408167 | ||||||||
\(153\) | 1.07440e7 | 0.242519 | ||||||||
\(154\) | −3.65226e6 | −0.0805823 | ||||||||
\(155\) | −1.56724e7 | −0.338045 | ||||||||
\(156\) | −2.37738e7 | −0.501375 | ||||||||
\(157\) | −8.02772e7 | −1.65555 | −0.827777 | − | 0.561058i | \(-0.810395\pi\) | ||||
−0.827777 | + | 0.561058i | \(0.810395\pi\) | |||||||
\(158\) | −1.01283e7 | −0.204284 | ||||||||
\(159\) | −6.06955e6 | −0.119747 | ||||||||
\(160\) | −5.96378e6 | −0.115107 | ||||||||
\(161\) | 1.70869e7 | 0.322680 | ||||||||
\(162\) | −4.25153e6 | −0.0785674 | ||||||||
\(163\) | −1.17849e7 | −0.213143 | −0.106571 | − | 0.994305i | \(-0.533987\pi\) | ||||
−0.106571 | + | 0.994305i | \(0.533987\pi\) | |||||||
\(164\) | 4.53300e7 | 0.802477 | ||||||||
\(165\) | −6.54053e6 | −0.113349 | ||||||||
\(166\) | 2.03600e7 | 0.345462 | ||||||||
\(167\) | −5.51803e7 | −0.916805 | −0.458402 | − | 0.888745i | \(-0.651578\pi\) | ||||
−0.458402 | + | 0.888745i | \(0.651578\pi\) | |||||||
\(168\) | 4.74163e6 | 0.0771517 | ||||||||
\(169\) | 1.26534e8 | 2.01653 | ||||||||
\(170\) | −2.14585e7 | −0.334988 | ||||||||
\(171\) | 2.51622e7 | 0.384824 | ||||||||
\(172\) | 1.03867e7 | 0.155642 | ||||||||
\(173\) | 5.63952e7 | 0.828096 | 0.414048 | − | 0.910255i | \(-0.364114\pi\) | ||||
0.414048 | + | 0.910255i | \(0.364114\pi\) | |||||||
\(174\) | 3.04936e7 | 0.438820 | ||||||||
\(175\) | −1.54353e7 | −0.217712 | ||||||||
\(176\) | 5.45178e6 | 0.0753778 | ||||||||
\(177\) | −1.87560e7 | −0.254235 | ||||||||
\(178\) | 7.92786e7 | 1.05363 | ||||||||
\(179\) | 1.03312e7 | 0.134637 | 0.0673185 | − | 0.997732i | \(-0.478556\pi\) | ||||
0.0673185 | + | 0.997732i | \(0.478556\pi\) | |||||||
\(180\) | 8.49139e6 | 0.108524 | ||||||||
\(181\) | 6.67241e7 | 0.836388 | 0.418194 | − | 0.908358i | \(-0.362663\pi\) | ||||
0.418194 | + | 0.908358i | \(0.362663\pi\) | |||||||
\(182\) | −3.77520e7 | −0.464183 | ||||||||
\(183\) | −1.35297e6 | −0.0163196 | ||||||||
\(184\) | −2.55058e7 | −0.301840 | ||||||||
\(185\) | 9.73769e7 | 1.13072 | ||||||||
\(186\) | −1.86002e7 | −0.211944 | ||||||||
\(187\) | 1.96163e7 | 0.219367 | ||||||||
\(188\) | 2.54269e7 | 0.279088 | ||||||||
\(189\) | −6.75127e6 | −0.0727393 | ||||||||
\(190\) | −5.02553e7 | −0.531550 | ||||||||
\(191\) | −4.53862e7 | −0.471310 | −0.235655 | − | 0.971837i | \(-0.575724\pi\) | ||||
−0.235655 | + | 0.971837i | \(0.575724\pi\) | |||||||
\(192\) | −7.07789e6 | −0.0721688 | ||||||||
\(193\) | −2.92030e7 | −0.292399 | −0.146200 | − | 0.989255i | \(-0.546704\pi\) | ||||
−0.146200 | + | 0.989255i | \(0.546704\pi\) | |||||||
\(194\) | 1.12087e8 | 1.10217 | ||||||||
\(195\) | −6.76068e7 | −0.652934 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | 1.17638e8 | 1.09626 | 0.548131 | − | 0.836393i | \(-0.315340\pi\) | ||||
0.548131 | + | 0.836393i | \(0.315340\pi\) | |||||||
\(198\) | −7.76239e6 | −0.0710669 | ||||||||
\(199\) | −6.21347e7 | −0.558918 | −0.279459 | − | 0.960158i | \(-0.590155\pi\) | ||||
−0.279459 | + | 0.960158i | \(0.590155\pi\) | |||||||
\(200\) | 2.30405e7 | 0.203651 | ||||||||
\(201\) | 8.71669e7 | 0.757121 | ||||||||
\(202\) | 5.87425e7 | 0.501444 | ||||||||
\(203\) | 4.84227e7 | 0.406268 | ||||||||
\(204\) | −2.54673e7 | −0.210028 | ||||||||
\(205\) | 1.28907e8 | 1.04505 | ||||||||
\(206\) | 7.08824e7 | 0.564941 | ||||||||
\(207\) | 3.63159e7 | 0.284577 | ||||||||
\(208\) | 5.63528e7 | 0.434204 | ||||||||
\(209\) | 4.59408e7 | 0.348086 | ||||||||
\(210\) | 1.34840e7 | 0.100474 | ||||||||
\(211\) | −1.84022e8 | −1.34860 | −0.674299 | − | 0.738459i | \(-0.735554\pi\) | ||||
−0.674299 | + | 0.738459i | \(0.735554\pi\) | |||||||
\(212\) | 1.43871e7 | 0.103704 | ||||||||
\(213\) | 5.05304e7 | 0.358281 | ||||||||
\(214\) | 1.20148e8 | 0.838046 | ||||||||
\(215\) | 2.95371e7 | 0.202691 | ||||||||
\(216\) | 1.00777e7 | 0.0680414 | ||||||||
\(217\) | −2.95364e7 | −0.196222 | ||||||||
\(218\) | −8.50008e7 | −0.555680 | ||||||||
\(219\) | 2.53136e7 | 0.162855 | ||||||||
\(220\) | 1.55035e7 | 0.0981635 | ||||||||
\(221\) | 2.02765e8 | 1.26363 | ||||||||
\(222\) | 1.15568e8 | 0.708929 | ||||||||
\(223\) | 8.81072e7 | 0.532040 | 0.266020 | − | 0.963967i | \(-0.414291\pi\) | ||||
0.266020 | + | 0.963967i | \(0.414291\pi\) | |||||||
\(224\) | −1.12394e7 | −0.0668153 | ||||||||
\(225\) | −3.28057e7 | −0.192004 | ||||||||
\(226\) | 5.67448e7 | 0.326999 | ||||||||
\(227\) | 2.75878e8 | 1.56541 | 0.782703 | − | 0.622395i | \(-0.213840\pi\) | ||||
0.782703 | + | 0.622395i | \(0.213840\pi\) | |||||||
\(228\) | −5.96436e7 | −0.333267 | ||||||||
\(229\) | −8.28916e7 | −0.456128 | −0.228064 | − | 0.973646i | \(-0.573239\pi\) | ||||
−0.228064 | + | 0.973646i | \(0.573239\pi\) | |||||||
\(230\) | −7.25321e7 | −0.393082 | ||||||||
\(231\) | −1.23264e7 | −0.0657952 | ||||||||
\(232\) | −7.22811e7 | −0.380029 | ||||||||
\(233\) | −2.36402e8 | −1.22435 | −0.612175 | − | 0.790722i | \(-0.709705\pi\) | ||||
−0.612175 | + | 0.790722i | \(0.709705\pi\) | |||||||
\(234\) | −8.02367e7 | −0.409371 | ||||||||
\(235\) | 7.23079e7 | 0.363453 | ||||||||
\(236\) | 4.44588e7 | 0.220174 | ||||||||
\(237\) | −3.41829e7 | −0.166797 | ||||||||
\(238\) | −4.04411e7 | −0.194448 | ||||||||
\(239\) | 2.78052e8 | 1.31745 | 0.658725 | − | 0.752384i | \(-0.271096\pi\) | ||||
0.658725 | + | 0.752384i | \(0.271096\pi\) | |||||||
\(240\) | −2.01277e7 | −0.0939844 | ||||||||
\(241\) | −1.48269e8 | −0.682324 | −0.341162 | − | 0.940004i | \(-0.610821\pi\) | ||||
−0.341162 | + | 0.940004i | \(0.610821\pi\) | |||||||
\(242\) | −1.41725e7 | −0.0642824 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 3.20704e6 | 0.0141332 | ||||||||
\(245\) | 2.14121e7 | 0.0930204 | ||||||||
\(246\) | 1.52989e8 | 0.655220 | ||||||||
\(247\) | 4.74871e8 | 2.00510 | ||||||||
\(248\) | 4.40893e7 | 0.183549 | ||||||||
\(249\) | 6.87151e7 | 0.282068 | ||||||||
\(250\) | 1.79271e8 | 0.725640 | ||||||||
\(251\) | 2.89064e8 | 1.15381 | 0.576906 | − | 0.816810i | \(-0.304260\pi\) | ||||
0.576906 | + | 0.816810i | \(0.304260\pi\) | |||||||
\(252\) | 1.60030e7 | 0.0629941 | ||||||||
\(253\) | 6.63051e7 | 0.257410 | ||||||||
\(254\) | −2.88315e8 | −1.10395 | ||||||||
\(255\) | −7.24225e7 | −0.273516 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −1.99415e8 | −0.732813 | −0.366406 | − | 0.930455i | \(-0.619412\pi\) | ||||
−0.366406 | + | 0.930455i | \(0.619412\pi\) | |||||||
\(258\) | 3.50551e7 | 0.127081 | ||||||||
\(259\) | 1.83518e8 | 0.656341 | ||||||||
\(260\) | 1.60253e8 | 0.565457 | ||||||||
\(261\) | 1.02916e8 | 0.358295 | ||||||||
\(262\) | −1.80510e8 | −0.620079 | ||||||||
\(263\) | −4.04763e8 | −1.37200 | −0.686002 | − | 0.727600i | \(-0.740636\pi\) | ||||
−0.686002 | + | 0.727600i | \(0.740636\pi\) | |||||||
\(264\) | 1.83997e7 | 0.0615457 | ||||||||
\(265\) | 4.09132e7 | 0.135053 | ||||||||
\(266\) | −9.47119e7 | −0.308545 | ||||||||
\(267\) | 2.67565e8 | 0.860281 | ||||||||
\(268\) | −2.06618e8 | −0.655686 | ||||||||
\(269\) | 4.35356e7 | 0.136368 | 0.0681838 | − | 0.997673i | \(-0.478280\pi\) | ||||
0.0681838 | + | 0.997673i | \(0.478280\pi\) | |||||||
\(270\) | 2.86584e7 | 0.0886093 | ||||||||
\(271\) | −2.64981e8 | −0.808765 | −0.404382 | − | 0.914590i | \(-0.632514\pi\) | ||||
−0.404382 | + | 0.914590i | \(0.632514\pi\) | |||||||
\(272\) | 6.03668e7 | 0.181889 | ||||||||
\(273\) | −1.27413e8 | −0.379004 | ||||||||
\(274\) | −9.95691e7 | −0.292414 | ||||||||
\(275\) | −5.98963e7 | −0.173674 | ||||||||
\(276\) | −8.60820e7 | −0.246451 | ||||||||
\(277\) | 6.49499e8 | 1.83611 | 0.918057 | − | 0.396449i | \(-0.129758\pi\) | ||||
0.918057 | + | 0.396449i | \(0.129758\pi\) | |||||||
\(278\) | −1.30640e7 | −0.0364687 | ||||||||
\(279\) | −6.27756e7 | −0.173052 | ||||||||
\(280\) | −3.19621e7 | −0.0870126 | ||||||||
\(281\) | 1.75806e8 | 0.472674 | 0.236337 | − | 0.971671i | \(-0.424053\pi\) | ||||
0.236337 | + | 0.971671i | \(0.424053\pi\) | |||||||
\(282\) | 8.58159e7 | 0.227875 | ||||||||
\(283\) | −1.21587e8 | −0.318885 | −0.159443 | − | 0.987207i | \(-0.550970\pi\) | ||||
−0.159443 | + | 0.987207i | \(0.550970\pi\) | |||||||
\(284\) | −1.19776e8 | −0.310281 | ||||||||
\(285\) | −1.69612e8 | −0.434009 | ||||||||
\(286\) | −1.46495e8 | −0.370290 | ||||||||
\(287\) | 2.42941e8 | 0.606616 | ||||||||
\(288\) | −2.38879e7 | −0.0589256 | ||||||||
\(289\) | −1.93130e8 | −0.470660 | ||||||||
\(290\) | −2.05549e8 | −0.494906 | ||||||||
\(291\) | 3.78292e8 | 0.899916 | ||||||||
\(292\) | −6.00027e7 | −0.141036 | ||||||||
\(293\) | 5.27431e8 | 1.22498 | 0.612490 | − | 0.790478i | \(-0.290168\pi\) | ||||
0.612490 | + | 0.790478i | \(0.290168\pi\) | |||||||
\(294\) | 2.54122e7 | 0.0583212 | ||||||||
\(295\) | 1.26430e8 | 0.286729 | ||||||||
\(296\) | −2.73939e8 | −0.613951 | ||||||||
\(297\) | −2.61981e7 | −0.0580259 | ||||||||
\(298\) | −5.40105e8 | −1.18228 | ||||||||
\(299\) | 6.85369e8 | 1.48277 | ||||||||
\(300\) | 7.77617e7 | 0.166281 | ||||||||
\(301\) | 5.56662e7 | 0.117654 | ||||||||
\(302\) | 4.98574e8 | 1.04161 | ||||||||
\(303\) | 1.98256e8 | 0.409427 | ||||||||
\(304\) | 1.41378e8 | 0.288618 | ||||||||
\(305\) | 9.12002e6 | 0.0184054 | ||||||||
\(306\) | −8.59520e7 | −0.171487 | ||||||||
\(307\) | 1.23804e8 | 0.244203 | 0.122101 | − | 0.992518i | \(-0.461037\pi\) | ||||
0.122101 | + | 0.992518i | \(0.461037\pi\) | |||||||
\(308\) | 2.92181e7 | 0.0569803 | ||||||||
\(309\) | 2.39228e8 | 0.461272 | ||||||||
\(310\) | 1.25379e8 | 0.239034 | ||||||||
\(311\) | 5.17448e8 | 0.975451 | 0.487726 | − | 0.872997i | \(-0.337827\pi\) | ||||
0.487726 | + | 0.872997i | \(0.337827\pi\) | |||||||
\(312\) | 1.90191e8 | 0.354526 | ||||||||
\(313\) | −9.84678e7 | −0.181505 | −0.0907526 | − | 0.995873i | \(-0.528927\pi\) | ||||
−0.0907526 | + | 0.995873i | \(0.528927\pi\) | |||||||
\(314\) | 6.42217e8 | 1.17065 | ||||||||
\(315\) | 4.55086e7 | 0.0820363 | ||||||||
\(316\) | 8.10260e7 | 0.144451 | ||||||||
\(317\) | 3.52106e8 | 0.620820 | 0.310410 | − | 0.950603i | \(-0.399534\pi\) | ||||
0.310410 | + | 0.950603i | \(0.399534\pi\) | |||||||
\(318\) | 4.85564e7 | 0.0846742 | ||||||||
\(319\) | 1.87903e8 | 0.324090 | ||||||||
\(320\) | 4.77102e7 | 0.0813929 | ||||||||
\(321\) | 4.05499e8 | 0.684261 | ||||||||
\(322\) | −1.36695e8 | −0.228169 | ||||||||
\(323\) | 5.08697e8 | 0.839944 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −6.19124e8 | −1.00043 | ||||||||
\(326\) | 9.42795e7 | 0.150715 | ||||||||
\(327\) | −2.86878e8 | −0.453711 | ||||||||
\(328\) | −3.62640e8 | −0.567437 | ||||||||
\(329\) | 1.36273e8 | 0.210971 | ||||||||
\(330\) | 5.23243e7 | 0.0801502 | ||||||||
\(331\) | −5.36200e8 | −0.812697 | −0.406349 | − | 0.913718i | \(-0.633198\pi\) | ||||
−0.406349 | + | 0.913718i | \(0.633198\pi\) | |||||||
\(332\) | −1.62880e8 | −0.244278 | ||||||||
\(333\) | 3.90043e8 | 0.578838 | ||||||||
\(334\) | 4.41443e8 | 0.648279 | ||||||||
\(335\) | −5.87570e8 | −0.853891 | ||||||||
\(336\) | −3.79331e7 | −0.0545545 | ||||||||
\(337\) | −7.28923e8 | −1.03747 | −0.518737 | − | 0.854934i | \(-0.673598\pi\) | ||||
−0.518737 | + | 0.854934i | \(0.673598\pi\) | |||||||
\(338\) | −1.01227e9 | −1.42590 | ||||||||
\(339\) | 1.91514e8 | 0.266994 | ||||||||
\(340\) | 1.71668e8 | 0.236872 | ||||||||
\(341\) | −1.14615e8 | −0.156531 | ||||||||
\(342\) | −2.01297e8 | −0.272111 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | −8.30935e7 | −0.110056 | ||||||||
\(345\) | −2.44796e8 | −0.320950 | ||||||||
\(346\) | −4.51162e8 | −0.585553 | ||||||||
\(347\) | 8.08560e8 | 1.03887 | 0.519433 | − | 0.854511i | \(-0.326143\pi\) | ||||
0.519433 | + | 0.854511i | \(0.326143\pi\) | |||||||
\(348\) | −2.43949e8 | −0.310292 | ||||||||
\(349\) | −6.65358e8 | −0.837850 | −0.418925 | − | 0.908021i | \(-0.637593\pi\) | ||||
−0.418925 | + | 0.908021i | \(0.637593\pi\) | |||||||
\(350\) | 1.23483e8 | 0.153946 | ||||||||
\(351\) | −2.70799e8 | −0.334250 | ||||||||
\(352\) | −4.36142e7 | −0.0533002 | ||||||||
\(353\) | −6.66617e7 | −0.0806613 | −0.0403306 | − | 0.999186i | \(-0.512841\pi\) | ||||
−0.0403306 | + | 0.999186i | \(0.512841\pi\) | |||||||
\(354\) | 1.50048e8 | 0.179771 | ||||||||
\(355\) | −3.40612e8 | −0.404074 | ||||||||
\(356\) | −6.34229e8 | −0.745026 | ||||||||
\(357\) | −1.36489e8 | −0.158766 | ||||||||
\(358\) | −8.26494e7 | −0.0952027 | ||||||||
\(359\) | −4.00001e8 | −0.456279 | −0.228140 | − | 0.973628i | \(-0.573264\pi\) | ||||
−0.228140 | + | 0.973628i | \(0.573264\pi\) | |||||||
\(360\) | −6.79311e7 | −0.0767379 | ||||||||
\(361\) | 2.97483e8 | 0.332802 | ||||||||
\(362\) | −5.33793e8 | −0.591416 | ||||||||
\(363\) | −4.78321e7 | −0.0524864 | ||||||||
\(364\) | 3.02016e8 | 0.328227 | ||||||||
\(365\) | −1.70633e8 | −0.183670 | ||||||||
\(366\) | 1.08238e7 | 0.0115397 | ||||||||
\(367\) | −3.49648e8 | −0.369232 | −0.184616 | − | 0.982811i | \(-0.559104\pi\) | ||||
−0.184616 | + | 0.982811i | \(0.559104\pi\) | |||||||
\(368\) | 2.04046e8 | 0.213433 | ||||||||
\(369\) | 5.16338e8 | 0.534985 | ||||||||
\(370\) | −7.79015e8 | −0.799540 | ||||||||
\(371\) | 7.71057e7 | 0.0783931 | ||||||||
\(372\) | 1.48802e8 | 0.149867 | ||||||||
\(373\) | 3.23621e8 | 0.322891 | 0.161445 | − | 0.986882i | \(-0.448384\pi\) | ||||
0.161445 | + | 0.986882i | \(0.448384\pi\) | |||||||
\(374\) | −1.56930e8 | −0.155116 | ||||||||
\(375\) | 6.05041e8 | 0.592482 | ||||||||
\(376\) | −2.03416e8 | −0.197345 | ||||||||
\(377\) | 1.94227e9 | 1.86688 | ||||||||
\(378\) | 5.40102e7 | 0.0514344 | ||||||||
\(379\) | −6.49660e8 | −0.612984 | −0.306492 | − | 0.951873i | \(-0.599155\pi\) | ||||
−0.306492 | + | 0.951873i | \(0.599155\pi\) | |||||||
\(380\) | 4.02042e8 | 0.375863 | ||||||||
\(381\) | −9.73064e8 | −0.901372 | ||||||||
\(382\) | 3.63090e8 | 0.333267 | ||||||||
\(383\) | 1.11697e9 | 1.01589 | 0.507946 | − | 0.861389i | \(-0.330405\pi\) | ||||
0.507946 | + | 0.861389i | \(0.330405\pi\) | |||||||
\(384\) | 5.66231e7 | 0.0510310 | ||||||||
\(385\) | 8.30890e7 | 0.0742046 | ||||||||
\(386\) | 2.33624e8 | 0.206758 | ||||||||
\(387\) | 1.18311e8 | 0.103762 | ||||||||
\(388\) | −8.96693e8 | −0.779350 | ||||||||
\(389\) | 1.18772e9 | 1.02303 | 0.511517 | − | 0.859273i | \(-0.329084\pi\) | ||||
0.511517 | + | 0.859273i | \(0.329084\pi\) | |||||||
\(390\) | 5.40854e8 | 0.461694 | ||||||||
\(391\) | 7.34188e8 | 0.621139 | ||||||||
\(392\) | −6.02363e7 | −0.0505076 | ||||||||
\(393\) | −6.09221e8 | −0.506292 | ||||||||
\(394\) | −9.41100e8 | −0.775174 | ||||||||
\(395\) | 2.30418e8 | 0.188116 | ||||||||
\(396\) | 6.20991e7 | 0.0502519 | ||||||||
\(397\) | 2.20243e9 | 1.76659 | 0.883293 | − | 0.468822i | \(-0.155321\pi\) | ||||
0.883293 | + | 0.468822i | \(0.155321\pi\) | |||||||
\(398\) | 4.97078e8 | 0.395215 | ||||||||
\(399\) | −3.19653e8 | −0.251926 | ||||||||
\(400\) | −1.84324e8 | −0.144003 | ||||||||
\(401\) | 8.22757e8 | 0.637186 | 0.318593 | − | 0.947892i | \(-0.396790\pi\) | ||||
0.318593 | + | 0.947892i | \(0.396790\pi\) | |||||||
\(402\) | −6.97335e8 | −0.535366 | ||||||||
\(403\) | −1.18473e9 | −0.901678 | ||||||||
\(404\) | −4.69940e8 | −0.354574 | ||||||||
\(405\) | 9.67223e7 | 0.0723492 | ||||||||
\(406\) | −3.87381e8 | −0.287275 | ||||||||
\(407\) | 7.12136e8 | 0.523579 | ||||||||
\(408\) | 2.03738e8 | 0.148512 | ||||||||
\(409\) | 9.01095e8 | 0.651237 | 0.325618 | − | 0.945501i | \(-0.394428\pi\) | ||||
0.325618 | + | 0.945501i | \(0.394428\pi\) | |||||||
\(410\) | −1.03126e9 | −0.738965 | ||||||||
\(411\) | −3.36046e8 | −0.238755 | ||||||||
\(412\) | −5.67059e8 | −0.399473 | ||||||||
\(413\) | 2.38271e8 | 0.166436 | ||||||||
\(414\) | −2.90527e8 | −0.201227 | ||||||||
\(415\) | −4.63191e8 | −0.318120 | ||||||||
\(416\) | −4.50822e8 | −0.307028 | ||||||||
\(417\) | −4.40911e7 | −0.0297766 | ||||||||
\(418\) | −3.67526e8 | −0.246134 | ||||||||
\(419\) | −1.76829e9 | −1.17437 | −0.587184 | − | 0.809453i | \(-0.699764\pi\) | ||||
−0.587184 | + | 0.809453i | \(0.699764\pi\) | |||||||
\(420\) | −1.07872e8 | −0.0710455 | ||||||||
\(421\) | 4.56926e8 | 0.298441 | 0.149220 | − | 0.988804i | \(-0.452324\pi\) | ||||
0.149220 | + | 0.988804i | \(0.452324\pi\) | |||||||
\(422\) | 1.47218e9 | 0.953602 | ||||||||
\(423\) | 2.89629e8 | 0.186059 | ||||||||
\(424\) | −1.15097e8 | −0.0733300 | ||||||||
\(425\) | −6.63225e8 | −0.419082 | ||||||||
\(426\) | −4.04243e8 | −0.253343 | ||||||||
\(427\) | 1.71877e7 | 0.0106837 | ||||||||
\(428\) | −9.61182e8 | −0.592588 | ||||||||
\(429\) | −4.94421e8 | −0.302341 | ||||||||
\(430\) | −2.36297e8 | −0.143324 | ||||||||
\(431\) | −1.56635e9 | −0.942366 | −0.471183 | − | 0.882036i | \(-0.656173\pi\) | ||||
−0.471183 | + | 0.882036i | \(0.656173\pi\) | |||||||
\(432\) | −8.06216e7 | −0.0481125 | ||||||||
\(433\) | −1.70307e9 | −1.00815 | −0.504075 | − | 0.863660i | \(-0.668166\pi\) | ||||
−0.504075 | + | 0.863660i | \(0.668166\pi\) | |||||||
\(434\) | 2.36291e8 | 0.138750 | ||||||||
\(435\) | −6.93729e8 | −0.404089 | ||||||||
\(436\) | 6.80006e8 | 0.392925 | ||||||||
\(437\) | 1.71945e9 | 0.985608 | ||||||||
\(438\) | −2.02509e8 | −0.115156 | ||||||||
\(439\) | 1.64535e9 | 0.928179 | 0.464090 | − | 0.885788i | \(-0.346382\pi\) | ||||
0.464090 | + | 0.885788i | \(0.346382\pi\) | |||||||
\(440\) | −1.24028e8 | −0.0694121 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | −1.62212e9 | −0.893523 | ||||||||
\(443\) | 1.37306e9 | 0.750372 | 0.375186 | − | 0.926950i | \(-0.377579\pi\) | ||||
0.375186 | + | 0.926950i | \(0.377579\pi\) | |||||||
\(444\) | −9.24546e8 | −0.501289 | ||||||||
\(445\) | −1.80359e9 | −0.970236 | ||||||||
\(446\) | −7.04858e8 | −0.376209 | ||||||||
\(447\) | −1.82285e9 | −0.965329 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | 2.61157e9 | 1.36157 | 0.680785 | − | 0.732483i | \(-0.261639\pi\) | ||||
0.680785 | + | 0.732483i | \(0.261639\pi\) | |||||||
\(450\) | 2.62446e8 | 0.135768 | ||||||||
\(451\) | 9.42723e8 | 0.483912 | ||||||||
\(452\) | −4.53959e8 | −0.231223 | ||||||||
\(453\) | 1.68269e9 | 0.850472 | ||||||||
\(454\) | −2.20703e9 | −1.10691 | ||||||||
\(455\) | 8.58857e8 | 0.427446 | ||||||||
\(456\) | 4.77149e8 | 0.235655 | ||||||||
\(457\) | −3.13057e9 | −1.53432 | −0.767162 | − | 0.641453i | \(-0.778332\pi\) | ||||
−0.767162 | + | 0.641453i | \(0.778332\pi\) | |||||||
\(458\) | 6.63133e8 | 0.322531 | ||||||||
\(459\) | −2.90088e8 | −0.140019 | ||||||||
\(460\) | 5.80257e8 | 0.277951 | ||||||||
\(461\) | −1.69540e9 | −0.805968 | −0.402984 | − | 0.915207i | \(-0.632027\pi\) | ||||
−0.402984 | + | 0.915207i | \(0.632027\pi\) | |||||||
\(462\) | 9.86111e7 | 0.0465242 | ||||||||
\(463\) | −8.34761e8 | −0.390867 | −0.195433 | − | 0.980717i | \(-0.562611\pi\) | ||||
−0.195433 | + | 0.980717i | \(0.562611\pi\) | |||||||
\(464\) | 5.78249e8 | 0.268721 | ||||||||
\(465\) | 4.23154e8 | 0.195170 | ||||||||
\(466\) | 1.89122e9 | 0.865746 | ||||||||
\(467\) | −1.12459e9 | −0.510960 | −0.255480 | − | 0.966814i | \(-0.582233\pi\) | ||||
−0.255480 | + | 0.966814i | \(0.582233\pi\) | |||||||
\(468\) | 6.41893e8 | 0.289469 | ||||||||
\(469\) | −1.10734e9 | −0.495652 | ||||||||
\(470\) | −5.78463e8 | −0.257000 | ||||||||
\(471\) | 2.16748e9 | 0.955834 | ||||||||
\(472\) | −3.55670e8 | −0.155686 | ||||||||
\(473\) | 2.16011e8 | 0.0938558 | ||||||||
\(474\) | 2.73463e8 | 0.117944 | ||||||||
\(475\) | −1.55325e9 | −0.664990 | ||||||||
\(476\) | 3.23529e8 | 0.137495 | ||||||||
\(477\) | 1.63878e8 | 0.0691362 | ||||||||
\(478\) | −2.22442e9 | −0.931578 | ||||||||
\(479\) | −3.77226e9 | −1.56830 | −0.784148 | − | 0.620574i | \(-0.786899\pi\) | ||||
−0.784148 | + | 0.620574i | \(0.786899\pi\) | |||||||
\(480\) | 1.61022e8 | 0.0664570 | ||||||||
\(481\) | 7.36105e9 | 3.01601 | ||||||||
\(482\) | 1.18615e9 | 0.482476 | ||||||||
\(483\) | −4.61346e8 | −0.186300 | ||||||||
\(484\) | 1.13380e8 | 0.0454545 | ||||||||
\(485\) | −2.54997e9 | −1.01494 | ||||||||
\(486\) | 1.14791e8 | 0.0453609 | ||||||||
\(487\) | −4.40349e9 | −1.72761 | −0.863805 | − | 0.503827i | \(-0.831925\pi\) | ||||
−0.863805 | + | 0.503827i | \(0.831925\pi\) | |||||||
\(488\) | −2.56563e7 | −0.00999367 | ||||||||
\(489\) | 3.18193e8 | 0.123058 | ||||||||
\(490\) | −1.71297e8 | −0.0657754 | ||||||||
\(491\) | −2.61532e9 | −0.997102 | −0.498551 | − | 0.866860i | \(-0.666134\pi\) | ||||
−0.498551 | + | 0.866860i | \(0.666134\pi\) | |||||||
\(492\) | −1.22391e9 | −0.463310 | ||||||||
\(493\) | 2.08062e9 | 0.782040 | ||||||||
\(494\) | −3.79897e9 | −1.41782 | ||||||||
\(495\) | 1.76594e8 | 0.0654423 | ||||||||
\(496\) | −3.52715e8 | −0.129789 | ||||||||
\(497\) | −6.41923e8 | −0.234550 | ||||||||
\(498\) | −5.49721e8 | −0.199453 | ||||||||
\(499\) | 2.15541e9 | 0.776566 | 0.388283 | − | 0.921540i | \(-0.373068\pi\) | ||||
0.388283 | + | 0.921540i | \(0.373068\pi\) | |||||||
\(500\) | −1.43417e9 | −0.513105 | ||||||||
\(501\) | 1.48987e9 | 0.529317 | ||||||||
\(502\) | −2.31251e9 | −0.815869 | ||||||||
\(503\) | −4.75527e9 | −1.66605 | −0.833023 | − | 0.553238i | \(-0.813392\pi\) | ||||
−0.833023 | + | 0.553238i | \(0.813392\pi\) | |||||||
\(504\) | −1.28024e8 | −0.0445435 | ||||||||
\(505\) | −1.33639e9 | −0.461757 | ||||||||
\(506\) | −5.30441e8 | −0.182016 | ||||||||
\(507\) | −3.41642e9 | −1.16424 | ||||||||
\(508\) | 2.30652e9 | 0.780611 | ||||||||
\(509\) | −3.04257e9 | −1.02265 | −0.511326 | − | 0.859387i | \(-0.670845\pi\) | ||||
−0.511326 | + | 0.859387i | \(0.670845\pi\) | |||||||
\(510\) | 5.79380e8 | 0.193405 | ||||||||
\(511\) | −3.21577e8 | −0.106613 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | −6.79378e8 | −0.222178 | ||||||||
\(514\) | 1.59532e9 | 0.518177 | ||||||||
\(515\) | −1.61257e9 | −0.520229 | ||||||||
\(516\) | −2.80441e8 | −0.0898601 | ||||||||
\(517\) | 5.28801e8 | 0.168297 | ||||||||
\(518\) | −1.46814e9 | −0.464103 | ||||||||
\(519\) | −1.52267e9 | −0.478102 | ||||||||
\(520\) | −1.28203e9 | −0.399839 | ||||||||
\(521\) | −1.81380e9 | −0.561897 | −0.280949 | − | 0.959723i | \(-0.590649\pi\) | ||||
−0.280949 | + | 0.959723i | \(0.590649\pi\) | |||||||
\(522\) | −8.23327e8 | −0.253353 | ||||||||
\(523\) | 4.85164e8 | 0.148297 | 0.0741485 | − | 0.997247i | \(-0.476376\pi\) | ||||
0.0741485 | + | 0.997247i | \(0.476376\pi\) | |||||||
\(524\) | 1.44408e9 | 0.438462 | ||||||||
\(525\) | 4.16754e8 | 0.125696 | ||||||||
\(526\) | 3.23810e9 | 0.970153 | ||||||||
\(527\) | −1.26912e9 | −0.377716 | ||||||||
\(528\) | −1.47198e8 | −0.0435194 | ||||||||
\(529\) | −9.23192e8 | −0.271142 | ||||||||
\(530\) | −3.27306e8 | −0.0954967 | ||||||||
\(531\) | 5.06413e8 | 0.146782 | ||||||||
\(532\) | 7.57695e8 | 0.218174 | ||||||||
\(533\) | 9.74454e9 | 2.78751 | ||||||||
\(534\) | −2.14052e9 | −0.608311 | ||||||||
\(535\) | −2.73336e9 | −0.771719 | ||||||||
\(536\) | 1.65294e9 | 0.463640 | ||||||||
\(537\) | −2.78942e8 | −0.0777327 | ||||||||
\(538\) | −3.48285e8 | −0.0964265 | ||||||||
\(539\) | 1.56591e8 | 0.0430730 | ||||||||
\(540\) | −2.29268e8 | −0.0626563 | ||||||||
\(541\) | −4.45922e9 | −1.21079 | −0.605394 | − | 0.795926i | \(-0.706985\pi\) | ||||
−0.605394 | + | 0.795926i | \(0.706985\pi\) | |||||||
\(542\) | 2.11985e9 | 0.571883 | ||||||||
\(543\) | −1.80155e9 | −0.482889 | ||||||||
\(544\) | −4.82935e8 | −0.128615 | ||||||||
\(545\) | 1.93377e9 | 0.511701 | ||||||||
\(546\) | 1.01930e9 | 0.267996 | ||||||||
\(547\) | −3.95780e9 | −1.03395 | −0.516973 | − | 0.856002i | \(-0.672941\pi\) | ||||
−0.516973 | + | 0.856002i | \(0.672941\pi\) | |||||||
\(548\) | 7.96553e8 | 0.206768 | ||||||||
\(549\) | 3.65302e7 | 0.00942212 | ||||||||
\(550\) | 4.79171e8 | 0.122806 | ||||||||
\(551\) | 4.87276e9 | 1.24092 | ||||||||
\(552\) | 6.88656e8 | 0.174267 | ||||||||
\(553\) | 4.34249e8 | 0.109195 | ||||||||
\(554\) | −5.19599e9 | −1.29833 | ||||||||
\(555\) | −2.62918e9 | −0.652821 | ||||||||
\(556\) | 1.04512e8 | 0.0257873 | ||||||||
\(557\) | 2.30018e9 | 0.563987 | 0.281994 | − | 0.959416i | \(-0.409004\pi\) | ||||
0.281994 | + | 0.959416i | \(0.409004\pi\) | |||||||
\(558\) | 5.02205e8 | 0.122366 | ||||||||
\(559\) | 2.23281e9 | 0.540644 | ||||||||
\(560\) | 2.55697e8 | 0.0615272 | ||||||||
\(561\) | −5.29640e8 | −0.126652 | ||||||||
\(562\) | −1.40645e9 | −0.334231 | ||||||||
\(563\) | 3.77133e9 | 0.890667 | 0.445333 | − | 0.895365i | \(-0.353085\pi\) | ||||
0.445333 | + | 0.895365i | \(0.353085\pi\) | |||||||
\(564\) | −6.86527e8 | −0.161132 | ||||||||
\(565\) | −1.29094e9 | −0.301119 | ||||||||
\(566\) | 9.72695e8 | 0.225486 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | 9.58206e8 | 0.219402 | ||||||||
\(569\) | −3.86882e9 | −0.880412 | −0.440206 | − | 0.897897i | \(-0.645095\pi\) | ||||
−0.440206 | + | 0.897897i | \(0.645095\pi\) | |||||||
\(570\) | 1.35689e9 | 0.306891 | ||||||||
\(571\) | 2.65511e9 | 0.596837 | 0.298418 | − | 0.954435i | \(-0.403541\pi\) | ||||
0.298418 | + | 0.954435i | \(0.403541\pi\) | |||||||
\(572\) | 1.17196e9 | 0.261835 | ||||||||
\(573\) | 1.22543e9 | 0.272111 | ||||||||
\(574\) | −1.94353e9 | −0.428942 | ||||||||
\(575\) | −2.24177e9 | −0.491760 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | −6.50529e9 | −1.40978 | −0.704890 | − | 0.709317i | \(-0.749004\pi\) | ||||
−0.704890 | + | 0.709317i | \(0.749004\pi\) | |||||||
\(578\) | 1.54504e9 | 0.332807 | ||||||||
\(579\) | 7.88480e8 | 0.168817 | ||||||||
\(580\) | 1.64439e9 | 0.349952 | ||||||||
\(581\) | −8.72936e8 | −0.184657 | ||||||||
\(582\) | −3.02634e9 | −0.636337 | ||||||||
\(583\) | 2.99206e8 | 0.0625361 | ||||||||
\(584\) | 4.80022e8 | 0.0997277 | ||||||||
\(585\) | 1.82538e9 | 0.376972 | ||||||||
\(586\) | −4.21945e9 | −0.866192 | ||||||||
\(587\) | 5.82831e9 | 1.18935 | 0.594675 | − | 0.803966i | \(-0.297281\pi\) | ||||
0.594675 | + | 0.803966i | \(0.297281\pi\) | |||||||
\(588\) | −2.03297e8 | −0.0412393 | ||||||||
\(589\) | −2.97224e9 | −0.599350 | ||||||||
\(590\) | −1.01144e9 | −0.202748 | ||||||||
\(591\) | −3.17621e9 | −0.632927 | ||||||||
\(592\) | 2.19152e9 | 0.434129 | ||||||||
\(593\) | 9.21565e9 | 1.81482 | 0.907412 | − | 0.420243i | \(-0.138055\pi\) | ||||
0.907412 | + | 0.420243i | \(0.138055\pi\) | |||||||
\(594\) | 2.09585e8 | 0.0410305 | ||||||||
\(595\) | 9.20034e8 | 0.179058 | ||||||||
\(596\) | 4.32084e9 | 0.835999 | ||||||||
\(597\) | 1.67764e9 | 0.322692 | ||||||||
\(598\) | −5.48295e9 | −1.04848 | ||||||||
\(599\) | 8.32457e9 | 1.58259 | 0.791294 | − | 0.611436i | \(-0.209408\pi\) | ||||
0.791294 | + | 0.611436i | \(0.209408\pi\) | |||||||
\(600\) | −6.22094e8 | −0.117578 | ||||||||
\(601\) | −1.80533e9 | −0.339230 | −0.169615 | − | 0.985510i | \(-0.554252\pi\) | ||||
−0.169615 | + | 0.985510i | \(0.554252\pi\) | |||||||
\(602\) | −4.45329e8 | −0.0831943 | ||||||||
\(603\) | −2.35351e9 | −0.437124 | ||||||||
\(604\) | −3.98859e9 | −0.736530 | ||||||||
\(605\) | 3.22424e8 | 0.0591948 | ||||||||
\(606\) | −1.58605e9 | −0.289509 | ||||||||
\(607\) | 9.91327e9 | 1.79911 | 0.899553 | − | 0.436812i | \(-0.143892\pi\) | ||||
0.899553 | + | 0.436812i | \(0.143892\pi\) | |||||||
\(608\) | −1.13102e9 | −0.204083 | ||||||||
\(609\) | −1.30741e9 | −0.234559 | ||||||||
\(610\) | −7.29602e7 | −0.0130146 | ||||||||
\(611\) | 5.46600e9 | 0.969450 | ||||||||
\(612\) | 6.87616e8 | 0.121260 | ||||||||
\(613\) | −1.21157e9 | −0.212440 | −0.106220 | − | 0.994343i | \(-0.533875\pi\) | ||||
−0.106220 | + | 0.994343i | \(0.533875\pi\) | |||||||
\(614\) | −9.90432e8 | −0.172677 | ||||||||
\(615\) | −3.48050e9 | −0.603363 | ||||||||
\(616\) | −2.33745e8 | −0.0402911 | ||||||||
\(617\) | −9.57641e8 | −0.164136 | −0.0820681 | − | 0.996627i | \(-0.526153\pi\) | ||||
−0.0820681 | + | 0.996627i | \(0.526153\pi\) | |||||||
\(618\) | −1.91382e9 | −0.326169 | ||||||||
\(619\) | −4.81235e9 | −0.815531 | −0.407765 | − | 0.913087i | \(-0.633692\pi\) | ||||
−0.407765 | + | 0.913087i | \(0.633692\pi\) | |||||||
\(620\) | −1.00303e9 | −0.169022 | ||||||||
\(621\) | −9.80528e8 | −0.164301 | ||||||||
\(622\) | −4.13959e9 | −0.689748 | ||||||||
\(623\) | −3.39907e9 | −0.563186 | ||||||||
\(624\) | −1.52152e9 | −0.250688 | ||||||||
\(625\) | −5.62722e8 | −0.0921965 | ||||||||
\(626\) | 7.87743e8 | 0.128344 | ||||||||
\(627\) | −1.24040e9 | −0.200968 | ||||||||
\(628\) | −5.13774e9 | −0.827777 | ||||||||
\(629\) | 7.88539e9 | 1.26341 | ||||||||
\(630\) | −3.64068e8 | −0.0580084 | ||||||||
\(631\) | −5.18280e9 | −0.821224 | −0.410612 | − | 0.911810i | \(-0.634685\pi\) | ||||
−0.410612 | + | 0.911810i | \(0.634685\pi\) | |||||||
\(632\) | −6.48208e8 | −0.102142 | ||||||||
\(633\) | 4.96861e9 | 0.778613 | ||||||||
\(634\) | −2.81685e9 | −0.438986 | ||||||||
\(635\) | 6.55917e9 | 1.01658 | ||||||||
\(636\) | −3.88451e8 | −0.0598737 | ||||||||
\(637\) | 1.61861e9 | 0.248116 | ||||||||
\(638\) | −1.50322e9 | −0.229166 | ||||||||
\(639\) | −1.36432e9 | −0.206854 | ||||||||
\(640\) | −3.81682e8 | −0.0575535 | ||||||||
\(641\) | −2.63106e9 | −0.394574 | −0.197287 | − | 0.980346i | \(-0.563213\pi\) | ||||
−0.197287 | + | 0.980346i | \(0.563213\pi\) | |||||||
\(642\) | −3.24399e9 | −0.483846 | ||||||||
\(643\) | −4.32469e9 | −0.641530 | −0.320765 | − | 0.947159i | \(-0.603940\pi\) | ||||
−0.320765 | + | 0.947159i | \(0.603940\pi\) | |||||||
\(644\) | 1.09356e9 | 0.161340 | ||||||||
\(645\) | −7.97503e8 | −0.117024 | ||||||||
\(646\) | −4.06957e9 | −0.593930 | ||||||||
\(647\) | −4.34323e9 | −0.630446 | −0.315223 | − | 0.949018i | \(-0.602079\pi\) | ||||
−0.315223 | + | 0.949018i | \(0.602079\pi\) | |||||||
\(648\) | −2.72098e8 | −0.0392837 | ||||||||
\(649\) | 9.24603e8 | 0.132770 | ||||||||
\(650\) | 4.95299e9 | 0.707409 | ||||||||
\(651\) | 7.97483e8 | 0.113289 | ||||||||
\(652\) | −7.54236e8 | −0.106571 | ||||||||
\(653\) | 4.59143e9 | 0.645285 | 0.322643 | − | 0.946521i | \(-0.395429\pi\) | ||||
0.322643 | + | 0.946521i | \(0.395429\pi\) | |||||||
\(654\) | 2.29502e9 | 0.320822 | ||||||||
\(655\) | 4.10660e9 | 0.571003 | ||||||||
\(656\) | 2.90112e9 | 0.401239 | ||||||||
\(657\) | −6.83468e8 | −0.0940242 | ||||||||
\(658\) | −1.09018e9 | −0.149179 | ||||||||
\(659\) | 3.99244e9 | 0.543424 | 0.271712 | − | 0.962379i | \(-0.412410\pi\) | ||||
0.271712 | + | 0.962379i | \(0.412410\pi\) | |||||||
\(660\) | −4.18594e8 | −0.0566747 | ||||||||
\(661\) | −4.95805e9 | −0.667737 | −0.333869 | − | 0.942620i | \(-0.608354\pi\) | ||||
−0.333869 | + | 0.942620i | \(0.608354\pi\) | |||||||
\(662\) | 4.28960e9 | 0.574664 | ||||||||
\(663\) | −5.47467e9 | −0.729559 | ||||||||
\(664\) | 1.30304e9 | 0.172731 | ||||||||
\(665\) | 2.15470e9 | 0.284125 | ||||||||
\(666\) | −3.12034e9 | −0.409301 | ||||||||
\(667\) | 7.03272e9 | 0.917663 | ||||||||
\(668\) | −3.53154e9 | −0.458402 | ||||||||
\(669\) | −2.37889e9 | −0.307174 | ||||||||
\(670\) | 4.70056e9 | 0.603792 | ||||||||
\(671\) | 6.66964e7 | 0.00852263 | ||||||||
\(672\) | 3.03464e8 | 0.0385758 | ||||||||
\(673\) | 2.86855e8 | 0.0362751 | 0.0181376 | − | 0.999836i | \(-0.494226\pi\) | ||||
0.0181376 | + | 0.999836i | \(0.494226\pi\) | |||||||
\(674\) | 5.83138e9 | 0.733605 | ||||||||
\(675\) | 8.85755e8 | 0.110854 | ||||||||
\(676\) | 8.09818e9 | 1.00826 | ||||||||
\(677\) | 7.36156e8 | 0.0911821 | 0.0455911 | − | 0.998960i | \(-0.485483\pi\) | ||||
0.0455911 | + | 0.998960i | \(0.485483\pi\) | |||||||
\(678\) | −1.53211e9 | −0.188793 | ||||||||
\(679\) | −4.80571e9 | −0.589134 | ||||||||
\(680\) | −1.37335e9 | −0.167494 | ||||||||
\(681\) | −7.44872e9 | −0.903788 | ||||||||
\(682\) | 9.16921e8 | 0.110684 | ||||||||
\(683\) | 2.38050e8 | 0.0285888 | 0.0142944 | − | 0.999898i | \(-0.495450\pi\) | ||||
0.0142944 | + | 0.999898i | \(0.495450\pi\) | |||||||
\(684\) | 1.61038e9 | 0.192412 | ||||||||
\(685\) | 2.26520e9 | 0.269271 | ||||||||
\(686\) | −3.22829e8 | −0.0381802 | ||||||||
\(687\) | 2.23807e9 | 0.263345 | ||||||||
\(688\) | 6.64748e8 | 0.0778211 | ||||||||
\(689\) | 3.09277e9 | 0.360230 | ||||||||
\(690\) | 1.95837e9 | 0.226946 | ||||||||
\(691\) | 2.18434e9 | 0.251852 | 0.125926 | − | 0.992040i | \(-0.459810\pi\) | ||||
0.125926 | + | 0.992040i | \(0.459810\pi\) | |||||||
\(692\) | 3.60929e9 | 0.414048 | ||||||||
\(693\) | 3.32813e8 | 0.0379869 | ||||||||
\(694\) | −6.46848e9 | −0.734589 | ||||||||
\(695\) | 2.97207e8 | 0.0335824 | ||||||||
\(696\) | 1.95159e9 | 0.219410 | ||||||||
\(697\) | 1.04387e10 | 1.16770 | ||||||||
\(698\) | 5.32286e9 | 0.592449 | ||||||||
\(699\) | 6.38286e9 | 0.706879 | ||||||||
\(700\) | −9.87862e8 | −0.108856 | ||||||||
\(701\) | 1.33891e10 | 1.46804 | 0.734019 | − | 0.679129i | \(-0.237643\pi\) | ||||
0.734019 | + | 0.679129i | \(0.237643\pi\) | |||||||
\(702\) | 2.16639e9 | 0.236351 | ||||||||
\(703\) | 1.84674e10 | 2.00476 | ||||||||
\(704\) | 3.48914e8 | 0.0376889 | ||||||||
\(705\) | −1.95231e9 | −0.209840 | ||||||||
\(706\) | 5.33294e8 | 0.0570361 | ||||||||
\(707\) | −2.51858e9 | −0.268033 | ||||||||
\(708\) | −1.20039e9 | −0.127117 | ||||||||
\(709\) | 1.20468e10 | 1.26944 | 0.634718 | − | 0.772744i | \(-0.281116\pi\) | ||||
0.634718 | + | 0.772744i | \(0.281116\pi\) | |||||||
\(710\) | 2.72490e9 | 0.285724 | ||||||||
\(711\) | 9.22937e8 | 0.0963005 | ||||||||
\(712\) | 5.07383e9 | 0.526813 | ||||||||
\(713\) | −4.28976e9 | −0.443220 | ||||||||
\(714\) | 1.09191e9 | 0.112265 | ||||||||
\(715\) | 3.33277e9 | 0.340984 | ||||||||
\(716\) | 6.61196e8 | 0.0673185 | ||||||||
\(717\) | −7.50742e9 | −0.760630 | ||||||||
\(718\) | 3.20001e9 | 0.322638 | ||||||||
\(719\) | −1.40604e9 | −0.141074 | −0.0705368 | − | 0.997509i | \(-0.522471\pi\) | ||||
−0.0705368 | + | 0.997509i | \(0.522471\pi\) | |||||||
\(720\) | 5.43449e8 | 0.0542619 | ||||||||
\(721\) | −3.03908e9 | −0.301974 | ||||||||
\(722\) | −2.37986e9 | −0.235327 | ||||||||
\(723\) | 4.00327e9 | 0.393940 | ||||||||
\(724\) | 4.27034e9 | 0.418194 | ||||||||
\(725\) | −6.35297e9 | −0.619147 | ||||||||
\(726\) | 3.82657e8 | 0.0371135 | ||||||||
\(727\) | 2.21138e9 | 0.213448 | 0.106724 | − | 0.994289i | \(-0.465964\pi\) | ||||
0.106724 | + | 0.994289i | \(0.465964\pi\) | |||||||
\(728\) | −2.41612e9 | −0.232092 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 1.36506e9 | 0.129874 | ||||||||
\(731\) | 2.39186e9 | 0.226477 | ||||||||
\(732\) | −8.65901e7 | −0.00815980 | ||||||||
\(733\) | −6.28279e9 | −0.589235 | −0.294618 | − | 0.955615i | \(-0.595192\pi\) | ||||
−0.294618 | + | 0.955615i | \(0.595192\pi\) | |||||||
\(734\) | 2.79718e9 | 0.261087 | ||||||||
\(735\) | −5.78127e8 | −0.0537054 | ||||||||
\(736\) | −1.63237e9 | −0.150920 | ||||||||
\(737\) | −4.29701e9 | −0.395394 | ||||||||
\(738\) | −4.13070e9 | −0.378291 | ||||||||
\(739\) | −2.04236e10 | −1.86156 | −0.930779 | − | 0.365582i | \(-0.880870\pi\) | ||||
−0.930779 | + | 0.365582i | \(0.880870\pi\) | |||||||
\(740\) | 6.23212e9 | 0.565360 | ||||||||
\(741\) | −1.28215e10 | −1.15765 | ||||||||
\(742\) | −6.16846e8 | −0.0554323 | ||||||||
\(743\) | −1.04573e10 | −0.935314 | −0.467657 | − | 0.883910i | \(-0.654902\pi\) | ||||
−0.467657 | + | 0.883910i | \(0.654902\pi\) | |||||||
\(744\) | −1.19041e9 | −0.105972 | ||||||||
\(745\) | 1.22874e10 | 1.08871 | ||||||||
\(746\) | −2.58897e9 | −0.228318 | ||||||||
\(747\) | −1.85531e9 | −0.162852 | ||||||||
\(748\) | 1.25544e9 | 0.109683 | ||||||||
\(749\) | −5.15134e9 | −0.447954 | ||||||||
\(750\) | −4.84033e9 | −0.418948 | ||||||||
\(751\) | −3.96979e9 | −0.342001 | −0.171001 | − | 0.985271i | \(-0.554700\pi\) | ||||
−0.171001 | + | 0.985271i | \(0.554700\pi\) | |||||||
\(752\) | 1.62732e9 | 0.139544 | ||||||||
\(753\) | −7.80472e9 | −0.666154 | ||||||||
\(754\) | −1.55382e10 | −1.32008 | ||||||||
\(755\) | −1.13426e10 | −0.959173 | ||||||||
\(756\) | −4.32081e8 | −0.0363696 | ||||||||
\(757\) | −2.09521e9 | −0.175546 | −0.0877731 | − | 0.996140i | \(-0.527975\pi\) | ||||
−0.0877731 | + | 0.996140i | \(0.527975\pi\) | |||||||
\(758\) | 5.19728e9 | 0.433445 | ||||||||
\(759\) | −1.79024e9 | −0.148616 | ||||||||
\(760\) | −3.21634e9 | −0.265775 | ||||||||
\(761\) | 2.98963e9 | 0.245907 | 0.122954 | − | 0.992412i | \(-0.460763\pi\) | ||||
0.122954 | + | 0.992412i | \(0.460763\pi\) | |||||||
\(762\) | 7.78451e9 | 0.637366 | ||||||||
\(763\) | 3.64441e9 | 0.297024 | ||||||||
\(764\) | −2.90472e9 | −0.235655 | ||||||||
\(765\) | 1.95541e9 | 0.157915 | ||||||||
\(766\) | −8.93580e9 | −0.718344 | ||||||||
\(767\) | 9.55724e9 | 0.764802 | ||||||||
\(768\) | −4.52985e8 | −0.0360844 | ||||||||
\(769\) | 2.28863e10 | 1.81482 | 0.907411 | − | 0.420245i | \(-0.138056\pi\) | ||||
0.907411 | + | 0.420245i | \(0.138056\pi\) | |||||||
\(770\) | −6.64712e8 | −0.0524706 | ||||||||
\(771\) | 5.38422e9 | 0.423090 | ||||||||
\(772\) | −1.86899e9 | −0.146200 | ||||||||
\(773\) | 1.50121e10 | 1.16900 | 0.584499 | − | 0.811394i | \(-0.301291\pi\) | ||||
0.584499 | + | 0.811394i | \(0.301291\pi\) | |||||||
\(774\) | −9.46487e8 | −0.0733705 | ||||||||
\(775\) | 3.87513e9 | 0.299040 | ||||||||
\(776\) | 7.17354e9 | 0.551084 | ||||||||
\(777\) | −4.95499e9 | −0.378939 | ||||||||
\(778\) | −9.50175e9 | −0.723394 | ||||||||
\(779\) | 2.44471e10 | 1.85287 | ||||||||
\(780\) | −4.32684e9 | −0.326467 | ||||||||
\(781\) | −2.49096e9 | −0.187106 | ||||||||
\(782\) | −5.87351e9 | −0.439212 | ||||||||
\(783\) | −2.77873e9 | −0.206862 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | −1.46104e10 | −1.07800 | ||||||||
\(786\) | 4.87377e9 | 0.358003 | ||||||||
\(787\) | 1.23722e10 | 0.904762 | 0.452381 | − | 0.891825i | \(-0.350575\pi\) | ||||
0.452381 | + | 0.891825i | \(0.350575\pi\) | |||||||
\(788\) | 7.52880e9 | 0.548131 | ||||||||
\(789\) | 1.09286e10 | 0.792127 | ||||||||
\(790\) | −1.84334e9 | −0.133018 | ||||||||
\(791\) | −2.43293e9 | −0.174788 | ||||||||
\(792\) | −4.96793e8 | −0.0355335 | ||||||||
\(793\) | 6.89413e8 | 0.0490934 | ||||||||
\(794\) | −1.76194e10 | −1.24916 | ||||||||
\(795\) | −1.10466e9 | −0.0779727 | ||||||||
\(796\) | −3.97662e9 | −0.279459 | ||||||||
\(797\) | 1.59988e10 | 1.11939 | 0.559696 | − | 0.828698i | \(-0.310918\pi\) | ||||
0.559696 | + | 0.828698i | \(0.310918\pi\) | |||||||
\(798\) | 2.55722e9 | 0.178139 | ||||||||
\(799\) | 5.85535e9 | 0.406106 | ||||||||
\(800\) | 1.47459e9 | 0.101826 | ||||||||
\(801\) | −7.22427e9 | −0.496684 | ||||||||
\(802\) | −6.58206e9 | −0.450559 | ||||||||
\(803\) | −1.24787e9 | −0.0850481 | ||||||||
\(804\) | 5.57868e9 | 0.378561 | ||||||||
\(805\) | 3.10981e9 | 0.210111 | ||||||||
\(806\) | 9.47783e9 | 0.637582 | ||||||||
\(807\) | −1.17546e9 | −0.0787319 | ||||||||
\(808\) | 3.75952e9 | 0.250722 | ||||||||
\(809\) | 1.19166e10 | 0.791281 | 0.395641 | − | 0.918405i | \(-0.370523\pi\) | ||||
0.395641 | + | 0.918405i | \(0.370523\pi\) | |||||||
\(810\) | −7.73778e8 | −0.0511586 | ||||||||
\(811\) | −2.03252e10 | −1.33802 | −0.669010 | − | 0.743254i | \(-0.733282\pi\) | ||||
−0.669010 | + | 0.743254i | \(0.733282\pi\) | |||||||
\(812\) | 3.09905e9 | 0.203134 | ||||||||
\(813\) | 7.15449e9 | 0.466941 | ||||||||
\(814\) | −5.69708e9 | −0.370226 | ||||||||
\(815\) | −2.14486e9 | −0.138786 | ||||||||
\(816\) | −1.62990e9 | −0.105014 | ||||||||
\(817\) | 5.60167e9 | 0.359369 | ||||||||
\(818\) | −7.20876e9 | −0.460494 | ||||||||
\(819\) | 3.44015e9 | 0.218818 | ||||||||
\(820\) | 8.25007e9 | 0.522527 | ||||||||
\(821\) | −8.13232e9 | −0.512877 | −0.256439 | − | 0.966561i | \(-0.582549\pi\) | ||||
−0.256439 | + | 0.966561i | \(0.582549\pi\) | |||||||
\(822\) | 2.68837e9 | 0.168825 | ||||||||
\(823\) | 1.27514e10 | 0.797366 | 0.398683 | − | 0.917089i | \(-0.369467\pi\) | ||||
0.398683 | + | 0.917089i | \(0.369467\pi\) | |||||||
\(824\) | 4.53647e9 | 0.282470 | ||||||||
\(825\) | 1.61720e9 | 0.100271 | ||||||||
\(826\) | −1.90617e9 | −0.117688 | ||||||||
\(827\) | −3.43433e9 | −0.211141 | −0.105570 | − | 0.994412i | \(-0.533667\pi\) | ||||
−0.105570 | + | 0.994412i | \(0.533667\pi\) | |||||||
\(828\) | 2.32422e9 | 0.142289 | ||||||||
\(829\) | 3.10696e10 | 1.89407 | 0.947033 | − | 0.321136i | \(-0.104065\pi\) | ||||
0.947033 | + | 0.321136i | \(0.104065\pi\) | |||||||
\(830\) | 3.70553e9 | 0.224945 | ||||||||
\(831\) | −1.75365e10 | −1.06008 | ||||||||
\(832\) | 3.60658e9 | 0.217102 | ||||||||
\(833\) | 1.73391e9 | 0.103937 | ||||||||
\(834\) | 3.52729e8 | 0.0210552 | ||||||||
\(835\) | −1.00428e10 | −0.596971 | ||||||||
\(836\) | 2.94021e9 | 0.174043 | ||||||||
\(837\) | 1.69494e9 | 0.0999116 | ||||||||
\(838\) | 1.41463e10 | 0.830404 | ||||||||
\(839\) | −2.69261e10 | −1.57401 | −0.787003 | − | 0.616949i | \(-0.788368\pi\) | ||||
−0.787003 | + | 0.616949i | \(0.788368\pi\) | |||||||
\(840\) | 8.62977e8 | 0.0502368 | ||||||||
\(841\) | 2.68022e9 | 0.155376 | ||||||||
\(842\) | −3.65541e9 | −0.211030 | ||||||||
\(843\) | −4.74676e9 | −0.272898 | ||||||||
\(844\) | −1.17774e10 | −0.674299 | ||||||||
\(845\) | 2.30292e10 | 1.31305 | ||||||||
\(846\) | −2.31703e9 | −0.131564 | ||||||||
\(847\) | 6.07645e8 | 0.0343604 | ||||||||
\(848\) | 9.20773e8 | 0.0518522 | ||||||||
\(849\) | 3.28285e9 | 0.184108 | ||||||||
\(850\) | 5.30580e9 | 0.296336 | ||||||||
\(851\) | 2.66535e10 | 1.48252 | ||||||||
\(852\) | 3.23395e9 | 0.179141 | ||||||||
\(853\) | −2.28862e10 | −1.26256 | −0.631281 | − | 0.775554i | \(-0.717470\pi\) | ||||
−0.631281 | + | 0.775554i | \(0.717470\pi\) | |||||||
\(854\) | −1.37502e8 | −0.00755450 | ||||||||
\(855\) | 4.57951e9 | 0.250575 | ||||||||
\(856\) | 7.68946e9 | 0.419023 | ||||||||
\(857\) | −2.94221e10 | −1.59676 | −0.798382 | − | 0.602151i | \(-0.794311\pi\) | ||||
−0.798382 | + | 0.602151i | \(0.794311\pi\) | |||||||
\(858\) | 3.95537e9 | 0.213787 | ||||||||
\(859\) | −1.03932e10 | −0.559465 | −0.279733 | − | 0.960078i | \(-0.590246\pi\) | ||||
−0.279733 | + | 0.960078i | \(0.590246\pi\) | |||||||
\(860\) | 1.89038e9 | 0.101345 | ||||||||
\(861\) | −6.55940e9 | −0.350230 | ||||||||
\(862\) | 1.25308e10 | 0.666353 | ||||||||
\(863\) | 2.21900e10 | 1.17522 | 0.587610 | − | 0.809144i | \(-0.300069\pi\) | ||||
0.587610 | + | 0.809144i | \(0.300069\pi\) | |||||||
\(864\) | 6.44973e8 | 0.0340207 | ||||||||
\(865\) | 1.02639e10 | 0.539209 | ||||||||
\(866\) | 1.36246e10 | 0.712870 | ||||||||
\(867\) | 5.21451e9 | 0.271736 | ||||||||
\(868\) | −1.89033e9 | −0.0981112 | ||||||||
\(869\) | 1.68509e9 | 0.0871071 | ||||||||
\(870\) | 5.54983e9 | 0.285734 | ||||||||
\(871\) | −4.44164e10 | −2.27761 | ||||||||
\(872\) | −5.44005e9 | −0.277840 | ||||||||
\(873\) | −1.02139e10 | −0.519567 | ||||||||
\(874\) | −1.37556e10 | −0.696930 | ||||||||
\(875\) | −7.68626e9 | −0.387871 | ||||||||
\(876\) | 1.62007e9 | 0.0814273 | ||||||||
\(877\) | 3.59473e10 | 1.79957 | 0.899783 | − | 0.436337i | \(-0.143724\pi\) | ||||
0.899783 | + | 0.436337i | \(0.143724\pi\) | |||||||
\(878\) | −1.31628e10 | −0.656322 | ||||||||
\(879\) | −1.42406e10 | −0.707243 | ||||||||
\(880\) | 9.92223e8 | 0.0490817 | ||||||||
\(881\) | −2.76295e10 | −1.36131 | −0.680655 | − | 0.732605i | \(-0.738305\pi\) | ||||
−0.680655 | + | 0.732605i | \(0.738305\pi\) | |||||||
\(882\) | −6.86129e8 | −0.0336718 | ||||||||
\(883\) | −2.32225e10 | −1.13513 | −0.567567 | − | 0.823328i | \(-0.692115\pi\) | ||||
−0.567567 | + | 0.823328i | \(0.692115\pi\) | |||||||
\(884\) | 1.29770e10 | 0.631816 | ||||||||
\(885\) | −3.41360e9 | −0.165543 | ||||||||
\(886\) | −1.09845e10 | −0.530593 | ||||||||
\(887\) | 2.93323e10 | 1.41128 | 0.705641 | − | 0.708569i | \(-0.250659\pi\) | ||||
0.705641 | + | 0.708569i | \(0.250659\pi\) | |||||||
\(888\) | 7.39637e9 | 0.354465 | ||||||||
\(889\) | 1.23615e10 | 0.590086 | ||||||||
\(890\) | 1.44287e10 | 0.686061 | ||||||||
\(891\) | 7.07348e8 | 0.0335013 | ||||||||
\(892\) | 5.63886e9 | 0.266020 | ||||||||
\(893\) | 1.37131e10 | 0.644399 | ||||||||
\(894\) | 1.45828e10 | 0.682591 | ||||||||
\(895\) | 1.88027e9 | 0.0876679 | ||||||||
\(896\) | −7.19323e8 | −0.0334077 | ||||||||
\(897\) | −1.85050e10 | −0.856080 | ||||||||
\(898\) | −2.08926e10 | −0.962775 | ||||||||
\(899\) | −1.21568e10 | −0.558032 | ||||||||
\(900\) | −2.09957e9 | −0.0960021 | ||||||||
\(901\) | 3.31307e9 | 0.150902 | ||||||||
\(902\) | −7.54179e9 | −0.342177 | ||||||||
\(903\) | −1.50299e9 | −0.0679279 | ||||||||
\(904\) | 3.63167e9 | 0.163500 | ||||||||
\(905\) | 1.21438e10 | 0.544608 | ||||||||
\(906\) | −1.34615e10 | −0.601374 | ||||||||
\(907\) | −1.38883e10 | −0.618050 | −0.309025 | − | 0.951054i | \(-0.600003\pi\) | ||||
−0.309025 | + | 0.951054i | \(0.600003\pi\) | |||||||
\(908\) | 1.76562e10 | 0.782703 | ||||||||
\(909\) | −5.35291e9 | −0.236383 | ||||||||
\(910\) | −6.87086e9 | −0.302250 | ||||||||
\(911\) | 4.83193e9 | 0.211742 | 0.105871 | − | 0.994380i | \(-0.466237\pi\) | ||||
0.105871 | + | 0.994380i | \(0.466237\pi\) | |||||||
\(912\) | −3.81719e9 | −0.166633 | ||||||||
\(913\) | −3.38740e9 | −0.147305 | ||||||||
\(914\) | 2.50446e10 | 1.08493 | ||||||||
\(915\) | −2.46241e8 | −0.0106264 | ||||||||
\(916\) | −5.30506e9 | −0.228064 | ||||||||
\(917\) | 7.73937e9 | 0.331446 | ||||||||
\(918\) | 2.32070e9 | 0.0990080 | ||||||||
\(919\) | 1.95192e10 | 0.829578 | 0.414789 | − | 0.909918i | \(-0.363855\pi\) | ||||
0.414789 | + | 0.909918i | \(0.363855\pi\) | |||||||
\(920\) | −4.64205e9 | −0.196541 | ||||||||
\(921\) | −3.34271e9 | −0.140990 | ||||||||
\(922\) | 1.35632e10 | 0.569906 | ||||||||
\(923\) | −2.57480e10 | −1.07780 | ||||||||
\(924\) | −7.88889e8 | −0.0328976 | ||||||||
\(925\) | −2.40772e10 | −1.00025 | ||||||||
\(926\) | 6.67809e9 | 0.276385 | ||||||||
\(927\) | −6.45916e9 | −0.266316 | ||||||||
\(928\) | −4.62599e9 | −0.190014 | ||||||||
\(929\) | −3.96997e10 | −1.62455 | −0.812274 | − | 0.583277i | \(-0.801770\pi\) | ||||
−0.812274 | + | 0.583277i | \(0.801770\pi\) | |||||||
\(930\) | −3.38523e9 | −0.138006 | ||||||||
\(931\) | 4.06077e9 | 0.164924 | ||||||||
\(932\) | −1.51297e10 | −0.612175 | ||||||||
\(933\) | −1.39711e10 | −0.563177 | ||||||||
\(934\) | 8.99675e9 | 0.361303 | ||||||||
\(935\) | 3.57016e9 | 0.142839 | ||||||||
\(936\) | −5.13515e9 | −0.204686 | ||||||||
\(937\) | 3.04155e9 | 0.120783 | 0.0603916 | − | 0.998175i | \(-0.480765\pi\) | ||||
0.0603916 | + | 0.998175i | \(0.480765\pi\) | |||||||
\(938\) | 8.85874e9 | 0.350479 | ||||||||
\(939\) | 2.65863e9 | 0.104792 | ||||||||
\(940\) | 4.62770e9 | 0.181726 | ||||||||
\(941\) | −7.60593e9 | −0.297570 | −0.148785 | − | 0.988870i | \(-0.547536\pi\) | ||||
−0.148785 | + | 0.988870i | \(0.547536\pi\) | |||||||
\(942\) | −1.73399e10 | −0.675877 | ||||||||
\(943\) | 3.52838e10 | 1.37020 | ||||||||
\(944\) | 2.84536e9 | 0.110087 | ||||||||
\(945\) | −1.22873e9 | −0.0473637 | ||||||||
\(946\) | −1.72809e9 | −0.0663661 | ||||||||
\(947\) | 2.22782e10 | 0.852424 | 0.426212 | − | 0.904623i | \(-0.359848\pi\) | ||||
0.426212 | + | 0.904623i | \(0.359848\pi\) | |||||||
\(948\) | −2.18770e9 | −0.0833987 | ||||||||
\(949\) | −1.28987e10 | −0.489908 | ||||||||
\(950\) | 1.24260e10 | 0.470219 | ||||||||
\(951\) | −9.50685e9 | −0.358431 | ||||||||
\(952\) | −2.58823e9 | −0.0972240 | ||||||||
\(953\) | −4.93836e10 | −1.84824 | −0.924119 | − | 0.382106i | \(-0.875199\pi\) | ||||
−0.924119 | + | 0.382106i | \(0.875199\pi\) | |||||||
\(954\) | −1.31102e9 | −0.0488867 | ||||||||
\(955\) | −8.26029e9 | −0.306891 | ||||||||
\(956\) | 1.77954e10 | 0.658725 | ||||||||
\(957\) | −5.07337e9 | −0.187113 | ||||||||
\(958\) | 3.01781e10 | 1.10895 | ||||||||
\(959\) | 4.26903e9 | 0.156302 | ||||||||
\(960\) | −1.28818e9 | −0.0469922 | ||||||||
\(961\) | −2.00973e10 | −0.730477 | ||||||||
\(962\) | −5.88884e10 | −2.13264 | ||||||||
\(963\) | −1.09485e10 | −0.395058 | ||||||||
\(964\) | −9.48922e9 | −0.341162 | ||||||||
\(965\) | −5.31494e9 | −0.190394 | ||||||||
\(966\) | 3.69077e9 | 0.131734 | ||||||||
\(967\) | −4.59604e8 | −0.0163452 | −0.00817261 | − | 0.999967i | \(-0.502601\pi\) | ||||
−0.00817261 | + | 0.999967i | \(0.502601\pi\) | |||||||
\(968\) | −9.07039e8 | −0.0321412 | ||||||||
\(969\) | −1.37348e10 | −0.484942 | ||||||||
\(970\) | 2.03998e10 | 0.717669 | ||||||||
\(971\) | 2.51853e9 | 0.0882836 | 0.0441418 | − | 0.999025i | \(-0.485945\pi\) | ||||
0.0441418 | + | 0.999025i | \(0.485945\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | 5.60120e8 | 0.0194933 | ||||||||
\(974\) | 3.52279e10 | 1.22160 | ||||||||
\(975\) | 1.67163e10 | 0.577597 | ||||||||
\(976\) | 2.05251e8 | 0.00706659 | ||||||||
\(977\) | 2.47811e10 | 0.850137 | 0.425069 | − | 0.905161i | \(-0.360250\pi\) | ||||
0.425069 | + | 0.905161i | \(0.360250\pi\) | |||||||
\(978\) | −2.54555e9 | −0.0870151 | ||||||||
\(979\) | −1.31900e10 | −0.449267 | ||||||||
\(980\) | 1.37038e9 | 0.0465102 | ||||||||
\(981\) | 7.74569e9 | 0.261950 | ||||||||
\(982\) | 2.09226e10 | 0.705058 | ||||||||
\(983\) | 4.99754e10 | 1.67810 | 0.839052 | − | 0.544052i | \(-0.183110\pi\) | ||||
0.839052 | + | 0.544052i | \(0.183110\pi\) | |||||||
\(984\) | 9.79129e9 | 0.327610 | ||||||||
\(985\) | 2.14100e10 | 0.713823 | ||||||||
\(986\) | −1.66450e10 | −0.552986 | ||||||||
\(987\) | −3.67936e9 | −0.121804 | ||||||||
\(988\) | 3.03918e10 | 1.00255 | ||||||||
\(989\) | 8.08474e9 | 0.265753 | ||||||||
\(990\) | −1.41276e9 | −0.0462747 | ||||||||
\(991\) | 2.07635e9 | 0.0677708 | 0.0338854 | − | 0.999426i | \(-0.489212\pi\) | ||||
0.0338854 | + | 0.999426i | \(0.489212\pi\) | |||||||
\(992\) | 2.82172e9 | 0.0917747 | ||||||||
\(993\) | 1.44774e10 | 0.469211 | ||||||||
\(994\) | 5.13539e9 | 0.165852 | ||||||||
\(995\) | −1.13085e10 | −0.363936 | ||||||||
\(996\) | 4.39777e9 | 0.141034 | ||||||||
\(997\) | −1.92580e10 | −0.615428 | −0.307714 | − | 0.951479i | \(-0.599564\pi\) | ||||
−0.307714 | + | 0.951479i | \(0.599564\pi\) | |||||||
\(998\) | −1.72433e10 | −0.549115 | ||||||||
\(999\) | −1.05312e10 | −0.334193 |
(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 | 462.8.a.a.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.8.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial |