Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,2,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.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: | \(7.84929451869\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.930689 | −0.658097 | −0.329048 | − | 0.944313i | \(-0.606728\pi\) | ||||
−0.329048 | + | 0.944313i | \(0.606728\pi\) | |||||||
\(3\) | −1.12871 | −0.651663 | −0.325832 | − | 0.945428i | \(-0.605644\pi\) | ||||
−0.325832 | + | 0.945428i | \(0.605644\pi\) | |||||||
\(4\) | −1.13382 | −0.566909 | ||||||||
\(5\) | 3.65614 | 1.63507 | 0.817537 | − | 0.575876i | \(-0.195339\pi\) | ||||
0.817537 | + | 0.575876i | \(0.195339\pi\) | |||||||
\(6\) | 1.05048 | 0.428857 | ||||||||
\(7\) | −1.39504 | −0.527275 | −0.263638 | − | 0.964622i | \(-0.584922\pi\) | ||||
−0.263638 | + | 0.964622i | \(0.584922\pi\) | |||||||
\(8\) | 2.91661 | 1.03118 | ||||||||
\(9\) | −1.72601 | −0.575335 | ||||||||
\(10\) | −3.40273 | −1.07604 | ||||||||
\(11\) | 1.37964 | 0.415978 | 0.207989 | − | 0.978131i | \(-0.433308\pi\) | ||||
0.207989 | + | 0.978131i | \(0.433308\pi\) | |||||||
\(12\) | 1.27976 | 0.369434 | ||||||||
\(13\) | −4.81779 | −1.33621 | −0.668107 | − | 0.744065i | \(-0.732895\pi\) | ||||
−0.668107 | + | 0.744065i | \(0.732895\pi\) | |||||||
\(14\) | 1.29835 | 0.346998 | ||||||||
\(15\) | −4.12673 | −1.06552 | ||||||||
\(16\) | −0.446823 | −0.111706 | ||||||||
\(17\) | −2.61914 | −0.635236 | −0.317618 | − | 0.948219i | \(-0.602883\pi\) | ||||
−0.317618 | + | 0.948219i | \(0.602883\pi\) | |||||||
\(18\) | 1.60637 | 0.378626 | ||||||||
\(19\) | 3.96315 | 0.909208 | 0.454604 | − | 0.890694i | \(-0.349781\pi\) | ||||
0.454604 | + | 0.890694i | \(0.349781\pi\) | |||||||
\(20\) | −4.14539 | −0.926938 | ||||||||
\(21\) | 1.57460 | 0.343606 | ||||||||
\(22\) | −1.28402 | −0.273754 | ||||||||
\(23\) | −5.45635 | −1.13773 | −0.568864 | − | 0.822432i | \(-0.692617\pi\) | ||||
−0.568864 | + | 0.822432i | \(0.692617\pi\) | |||||||
\(24\) | −3.29202 | −0.671980 | ||||||||
\(25\) | 8.36734 | 1.67347 | ||||||||
\(26\) | 4.48386 | 0.879358 | ||||||||
\(27\) | 5.33431 | 1.02659 | ||||||||
\(28\) | 1.58172 | 0.298917 | ||||||||
\(29\) | −0.992196 | −0.184246 | −0.0921231 | − | 0.995748i | \(-0.529365\pi\) | ||||
−0.0921231 | + | 0.995748i | \(0.529365\pi\) | |||||||
\(30\) | 3.84071 | 0.701214 | ||||||||
\(31\) | 1.16483 | 0.209210 | 0.104605 | − | 0.994514i | \(-0.466642\pi\) | ||||
0.104605 | + | 0.994514i | \(0.466642\pi\) | |||||||
\(32\) | −5.41737 | −0.957664 | ||||||||
\(33\) | −1.55722 | −0.271078 | ||||||||
\(34\) | 2.43761 | 0.418046 | ||||||||
\(35\) | −5.10045 | −0.862134 | ||||||||
\(36\) | 1.95698 | 0.326163 | ||||||||
\(37\) | −0.503291 | −0.0827405 | −0.0413703 | − | 0.999144i | \(-0.513172\pi\) | ||||
−0.0413703 | + | 0.999144i | \(0.513172\pi\) | |||||||
\(38\) | −3.68846 | −0.598347 | ||||||||
\(39\) | 5.43790 | 0.870761 | ||||||||
\(40\) | 10.6635 | 1.68605 | ||||||||
\(41\) | −2.17818 | −0.340174 | −0.170087 | − | 0.985429i | \(-0.554405\pi\) | ||||
−0.170087 | + | 0.985429i | \(0.554405\pi\) | |||||||
\(42\) | −1.46546 | −0.226126 | ||||||||
\(43\) | 5.94923 | 0.907249 | 0.453624 | − | 0.891193i | \(-0.350131\pi\) | ||||
0.453624 | + | 0.891193i | \(0.350131\pi\) | |||||||
\(44\) | −1.56426 | −0.235822 | ||||||||
\(45\) | −6.31051 | −0.940716 | ||||||||
\(46\) | 5.07816 | 0.748735 | ||||||||
\(47\) | −5.66455 | −0.826259 | −0.413129 | − | 0.910672i | \(-0.635564\pi\) | ||||
−0.413129 | + | 0.910672i | \(0.635564\pi\) | |||||||
\(48\) | 0.504335 | 0.0727945 | ||||||||
\(49\) | −5.05387 | −0.721981 | ||||||||
\(50\) | −7.78739 | −1.10130 | ||||||||
\(51\) | 2.95626 | 0.413960 | ||||||||
\(52\) | 5.46249 | 0.757511 | ||||||||
\(53\) | −7.42014 | −1.01923 | −0.509617 | − | 0.860401i | \(-0.670213\pi\) | ||||
−0.509617 | + | 0.860401i | \(0.670213\pi\) | |||||||
\(54\) | −4.96458 | −0.675594 | ||||||||
\(55\) | 5.04417 | 0.680156 | ||||||||
\(56\) | −4.06878 | −0.543714 | ||||||||
\(57\) | −4.47326 | −0.592498 | ||||||||
\(58\) | 0.923426 | 0.121252 | ||||||||
\(59\) | −5.25668 | −0.684362 | −0.342181 | − | 0.939634i | \(-0.611166\pi\) | ||||
−0.342181 | + | 0.939634i | \(0.611166\pi\) | |||||||
\(60\) | 4.67896 | 0.604051 | ||||||||
\(61\) | −3.98149 | −0.509778 | −0.254889 | − | 0.966970i | \(-0.582039\pi\) | ||||
−0.254889 | + | 0.966970i | \(0.582039\pi\) | |||||||
\(62\) | −1.08410 | −0.137680 | ||||||||
\(63\) | 2.40784 | 0.303360 | ||||||||
\(64\) | 5.93553 | 0.741941 | ||||||||
\(65\) | −17.6145 | −2.18481 | ||||||||
\(66\) | 1.44929 | 0.178395 | ||||||||
\(67\) | −15.3775 | −1.87866 | −0.939331 | − | 0.343011i | \(-0.888553\pi\) | ||||
−0.939331 | + | 0.343011i | \(0.888553\pi\) | |||||||
\(68\) | 2.96963 | 0.360121 | ||||||||
\(69\) | 6.15866 | 0.741415 | ||||||||
\(70\) | 4.74694 | 0.567367 | ||||||||
\(71\) | 7.91443 | 0.939270 | 0.469635 | − | 0.882861i | \(-0.344386\pi\) | ||||
0.469635 | + | 0.882861i | \(0.344386\pi\) | |||||||
\(72\) | −5.03409 | −0.593273 | ||||||||
\(73\) | −3.17316 | −0.371390 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(74\) | 0.468408 | 0.0544513 | ||||||||
\(75\) | −9.44433 | −1.09054 | ||||||||
\(76\) | −4.49349 | −0.515438 | ||||||||
\(77\) | −1.92466 | −0.219335 | ||||||||
\(78\) | −5.06100 | −0.573045 | ||||||||
\(79\) | −7.26789 | −0.817701 | −0.408851 | − | 0.912601i | \(-0.634070\pi\) | ||||
−0.408851 | + | 0.912601i | \(0.634070\pi\) | |||||||
\(80\) | −1.63365 | −0.182647 | ||||||||
\(81\) | −0.842889 | −0.0936543 | ||||||||
\(82\) | 2.02721 | 0.223868 | ||||||||
\(83\) | −5.01668 | −0.550652 | −0.275326 | − | 0.961351i | \(-0.588786\pi\) | ||||
−0.275326 | + | 0.961351i | \(0.588786\pi\) | |||||||
\(84\) | −1.78531 | −0.194793 | ||||||||
\(85\) | −9.57595 | −1.03866 | ||||||||
\(86\) | −5.53688 | −0.597058 | ||||||||
\(87\) | 1.11991 | 0.120066 | ||||||||
\(88\) | 4.02388 | 0.428947 | ||||||||
\(89\) | 0.319037 | 0.0338179 | 0.0169089 | − | 0.999857i | \(-0.494617\pi\) | ||||
0.0169089 | + | 0.999857i | \(0.494617\pi\) | |||||||
\(90\) | 5.87313 | 0.619082 | ||||||||
\(91\) | 6.72100 | 0.704552 | ||||||||
\(92\) | 6.18650 | 0.644988 | ||||||||
\(93\) | −1.31476 | −0.136334 | ||||||||
\(94\) | 5.27193 | 0.543758 | ||||||||
\(95\) | 14.4898 | 1.48662 | ||||||||
\(96\) | 6.11466 | 0.624075 | ||||||||
\(97\) | −9.75934 | −0.990911 | −0.495455 | − | 0.868633i | \(-0.664999\pi\) | ||||
−0.495455 | + | 0.868633i | \(0.664999\pi\) | |||||||
\(98\) | 4.70358 | 0.475133 | ||||||||
\(99\) | −2.38127 | −0.239327 | ||||||||
\(100\) | −9.48704 | −0.948704 | ||||||||
\(101\) | −14.3030 | −1.42320 | −0.711599 | − | 0.702586i | \(-0.752029\pi\) | ||||
−0.711599 | + | 0.702586i | \(0.752029\pi\) | |||||||
\(102\) | −2.75136 | −0.272425 | ||||||||
\(103\) | −2.31041 | −0.227651 | −0.113826 | − | 0.993501i | \(-0.536311\pi\) | ||||
−0.113826 | + | 0.993501i | \(0.536311\pi\) | |||||||
\(104\) | −14.0516 | −1.37787 | ||||||||
\(105\) | 5.75695 | 0.561821 | ||||||||
\(106\) | 6.90584 | 0.670755 | ||||||||
\(107\) | −9.73060 | −0.940692 | −0.470346 | − | 0.882482i | \(-0.655871\pi\) | ||||
−0.470346 | + | 0.882482i | \(0.655871\pi\) | |||||||
\(108\) | −6.04813 | −0.581982 | ||||||||
\(109\) | −11.8004 | −1.13028 | −0.565139 | − | 0.824996i | \(-0.691177\pi\) | ||||
−0.565139 | + | 0.824996i | \(0.691177\pi\) | |||||||
\(110\) | −4.69455 | −0.447608 | ||||||||
\(111\) | 0.568071 | 0.0539190 | ||||||||
\(112\) | 0.623335 | 0.0588996 | ||||||||
\(113\) | 10.7265 | 1.00907 | 0.504534 | − | 0.863392i | \(-0.331664\pi\) | ||||
0.504534 | + | 0.863392i | \(0.331664\pi\) | |||||||
\(114\) | 4.16321 | 0.389921 | ||||||||
\(115\) | −19.9492 | −1.86027 | ||||||||
\(116\) | 1.12497 | 0.104451 | ||||||||
\(117\) | 8.31553 | 0.768771 | ||||||||
\(118\) | 4.89234 | 0.450376 | ||||||||
\(119\) | 3.65381 | 0.334944 | ||||||||
\(120\) | −12.0361 | −1.09874 | ||||||||
\(121\) | −9.09658 | −0.826962 | ||||||||
\(122\) | 3.70553 | 0.335483 | ||||||||
\(123\) | 2.45854 | 0.221679 | ||||||||
\(124\) | −1.32071 | −0.118603 | ||||||||
\(125\) | 12.3115 | 1.10117 | ||||||||
\(126\) | −2.24095 | −0.199640 | ||||||||
\(127\) | 10.6710 | 0.946902 | 0.473451 | − | 0.880820i | \(-0.343008\pi\) | ||||
0.473451 | + | 0.880820i | \(0.343008\pi\) | |||||||
\(128\) | 5.31060 | 0.469395 | ||||||||
\(129\) | −6.71498 | −0.591221 | ||||||||
\(130\) | 16.3936 | 1.43782 | ||||||||
\(131\) | 17.0389 | 1.48869 | 0.744347 | − | 0.667793i | \(-0.232761\pi\) | ||||
0.744347 | + | 0.667793i | \(0.232761\pi\) | |||||||
\(132\) | 1.76561 | 0.153676 | ||||||||
\(133\) | −5.52874 | −0.479403 | ||||||||
\(134\) | 14.3117 | 1.23634 | ||||||||
\(135\) | 19.5030 | 1.67855 | ||||||||
\(136\) | −7.63902 | −0.655041 | ||||||||
\(137\) | −9.19141 | −0.785275 | −0.392638 | − | 0.919693i | \(-0.628437\pi\) | ||||
−0.392638 | + | 0.919693i | \(0.628437\pi\) | |||||||
\(138\) | −5.73179 | −0.487923 | ||||||||
\(139\) | −5.05347 | −0.428630 | −0.214315 | − | 0.976765i | \(-0.568752\pi\) | ||||
−0.214315 | + | 0.976765i | \(0.568752\pi\) | |||||||
\(140\) | 5.78298 | 0.488751 | ||||||||
\(141\) | 6.39365 | 0.538443 | ||||||||
\(142\) | −7.36588 | −0.618131 | ||||||||
\(143\) | −6.64683 | −0.555836 | ||||||||
\(144\) | 0.771218 | 0.0642682 | ||||||||
\(145\) | −3.62761 | −0.301256 | ||||||||
\(146\) | 2.95323 | 0.244411 | ||||||||
\(147\) | 5.70437 | 0.470488 | ||||||||
\(148\) | 0.570640 | 0.0469063 | ||||||||
\(149\) | −0.701009 | −0.0574289 | −0.0287145 | − | 0.999588i | \(-0.509141\pi\) | ||||
−0.0287145 | + | 0.999588i | \(0.509141\pi\) | |||||||
\(150\) | 8.78974 | 0.717679 | ||||||||
\(151\) | 15.6362 | 1.27246 | 0.636229 | − | 0.771500i | \(-0.280493\pi\) | ||||
0.636229 | + | 0.771500i | \(0.280493\pi\) | |||||||
\(152\) | 11.5590 | 0.937555 | ||||||||
\(153\) | 4.52066 | 0.365473 | ||||||||
\(154\) | 1.79126 | 0.144344 | ||||||||
\(155\) | 4.25878 | 0.342074 | ||||||||
\(156\) | −6.16559 | −0.493642 | ||||||||
\(157\) | 13.1604 | 1.05031 | 0.525156 | − | 0.851006i | \(-0.324007\pi\) | ||||
0.525156 | + | 0.851006i | \(0.324007\pi\) | |||||||
\(158\) | 6.76415 | 0.538127 | ||||||||
\(159\) | 8.37521 | 0.664197 | ||||||||
\(160\) | −19.8066 | −1.56585 | ||||||||
\(161\) | 7.61182 | 0.599895 | ||||||||
\(162\) | 0.784468 | 0.0616336 | ||||||||
\(163\) | −10.2695 | −0.804372 | −0.402186 | − | 0.915558i | \(-0.631750\pi\) | ||||
−0.402186 | + | 0.915558i | \(0.631750\pi\) | |||||||
\(164\) | 2.46966 | 0.192848 | ||||||||
\(165\) | −5.69342 | −0.443232 | ||||||||
\(166\) | 4.66897 | 0.362383 | ||||||||
\(167\) | 16.5575 | 1.28126 | 0.640631 | − | 0.767849i | \(-0.278673\pi\) | ||||
0.640631 | + | 0.767849i | \(0.278673\pi\) | |||||||
\(168\) | 4.59249 | 0.354318 | ||||||||
\(169\) | 10.2111 | 0.785467 | ||||||||
\(170\) | 8.91223 | 0.683537 | ||||||||
\(171\) | −6.84041 | −0.523099 | ||||||||
\(172\) | −6.74534 | −0.514327 | ||||||||
\(173\) | −5.59583 | −0.425443 | −0.212722 | − | 0.977113i | \(-0.568233\pi\) | ||||
−0.212722 | + | 0.977113i | \(0.568233\pi\) | |||||||
\(174\) | −1.04228 | −0.0790153 | ||||||||
\(175\) | −11.6728 | −0.882378 | ||||||||
\(176\) | −0.616456 | −0.0464671 | ||||||||
\(177\) | 5.93329 | 0.445973 | ||||||||
\(178\) | −0.296925 | −0.0222554 | ||||||||
\(179\) | −5.23442 | −0.391239 | −0.195619 | − | 0.980680i | \(-0.562672\pi\) | ||||
−0.195619 | + | 0.980680i | \(0.562672\pi\) | |||||||
\(180\) | 7.15497 | 0.533300 | ||||||||
\(181\) | 24.4388 | 1.81652 | 0.908262 | − | 0.418402i | \(-0.137410\pi\) | ||||
0.908262 | + | 0.418402i | \(0.137410\pi\) | |||||||
\(182\) | −6.25516 | −0.463663 | ||||||||
\(183\) | 4.49396 | 0.332203 | ||||||||
\(184\) | −15.9140 | −1.17320 | ||||||||
\(185\) | −1.84010 | −0.135287 | ||||||||
\(186\) | 1.22363 | 0.0897212 | ||||||||
\(187\) | −3.61349 | −0.264244 | ||||||||
\(188\) | 6.42256 | 0.468413 | ||||||||
\(189\) | −7.44156 | −0.541294 | ||||||||
\(190\) | −13.4855 | −0.978342 | ||||||||
\(191\) | 1.25181 | 0.0905775 | 0.0452887 | − | 0.998974i | \(-0.485579\pi\) | ||||
0.0452887 | + | 0.998974i | \(0.485579\pi\) | |||||||
\(192\) | −6.69952 | −0.483496 | ||||||||
\(193\) | −1.06630 | −0.0767543 | −0.0383772 | − | 0.999263i | \(-0.512219\pi\) | ||||
−0.0383772 | + | 0.999263i | \(0.512219\pi\) | |||||||
\(194\) | 9.08291 | 0.652115 | ||||||||
\(195\) | 19.8817 | 1.42376 | ||||||||
\(196\) | 5.73016 | 0.409297 | ||||||||
\(197\) | −18.6784 | −1.33078 | −0.665389 | − | 0.746497i | \(-0.731734\pi\) | ||||
−0.665389 | + | 0.746497i | \(0.731734\pi\) | |||||||
\(198\) | 2.21623 | 0.157500 | ||||||||
\(199\) | −2.28506 | −0.161983 | −0.0809917 | − | 0.996715i | \(-0.525809\pi\) | ||||
−0.0809917 | + | 0.996715i | \(0.525809\pi\) | |||||||
\(200\) | 24.4043 | 1.72564 | ||||||||
\(201\) | 17.3568 | 1.22426 | ||||||||
\(202\) | 13.3116 | 0.936602 | ||||||||
\(203\) | 1.38415 | 0.0971484 | ||||||||
\(204\) | −3.35186 | −0.234677 | ||||||||
\(205\) | −7.96372 | −0.556210 | ||||||||
\(206\) | 2.15027 | 0.149817 | ||||||||
\(207\) | 9.41769 | 0.654575 | ||||||||
\(208\) | 2.15270 | 0.149263 | ||||||||
\(209\) | 5.46773 | 0.378211 | ||||||||
\(210\) | −5.35793 | −0.369732 | ||||||||
\(211\) | 9.74582 | 0.670930 | 0.335465 | − | 0.942053i | \(-0.391107\pi\) | ||||
0.335465 | + | 0.942053i | \(0.391107\pi\) | |||||||
\(212\) | 8.41308 | 0.577813 | ||||||||
\(213\) | −8.93313 | −0.612088 | ||||||||
\(214\) | 9.05616 | 0.619067 | ||||||||
\(215\) | 21.7512 | 1.48342 | ||||||||
\(216\) | 15.5581 | 1.05859 | ||||||||
\(217\) | −1.62498 | −0.110311 | ||||||||
\(218\) | 10.9826 | 0.743832 | ||||||||
\(219\) | 3.58159 | 0.242021 | ||||||||
\(220\) | −5.71917 | −0.385586 | ||||||||
\(221\) | 12.6185 | 0.848811 | ||||||||
\(222\) | −0.528698 | −0.0354839 | ||||||||
\(223\) | 7.54988 | 0.505578 | 0.252789 | − | 0.967521i | \(-0.418652\pi\) | ||||
0.252789 | + | 0.967521i | \(0.418652\pi\) | |||||||
\(224\) | 7.55744 | 0.504953 | ||||||||
\(225\) | −14.4421 | −0.962805 | ||||||||
\(226\) | −9.98308 | −0.664065 | ||||||||
\(227\) | 16.7706 | 1.11310 | 0.556552 | − | 0.830813i | \(-0.312124\pi\) | ||||
0.556552 | + | 0.830813i | \(0.312124\pi\) | |||||||
\(228\) | 5.07186 | 0.335892 | ||||||||
\(229\) | −0.128761 | −0.00850876 | −0.00425438 | − | 0.999991i | \(-0.501354\pi\) | ||||
−0.00425438 | + | 0.999991i | \(0.501354\pi\) | |||||||
\(230\) | 18.5665 | 1.22424 | ||||||||
\(231\) | 2.17239 | 0.142933 | ||||||||
\(232\) | −2.89385 | −0.189991 | ||||||||
\(233\) | −6.66070 | −0.436357 | −0.218179 | − | 0.975909i | \(-0.570012\pi\) | ||||
−0.218179 | + | 0.975909i | \(0.570012\pi\) | |||||||
\(234\) | −7.73917 | −0.505925 | ||||||||
\(235\) | −20.7104 | −1.35099 | ||||||||
\(236\) | 5.96012 | 0.387971 | ||||||||
\(237\) | 8.20337 | 0.532866 | ||||||||
\(238\) | −3.40056 | −0.220425 | ||||||||
\(239\) | −7.99029 | −0.516849 | −0.258424 | − | 0.966031i | \(-0.583203\pi\) | ||||
−0.258424 | + | 0.966031i | \(0.583203\pi\) | |||||||
\(240\) | 1.84392 | 0.119024 | ||||||||
\(241\) | −25.3094 | −1.63032 | −0.815162 | − | 0.579234i | \(-0.803352\pi\) | ||||
−0.815162 | + | 0.579234i | \(0.803352\pi\) | |||||||
\(242\) | 8.46609 | 0.544221 | ||||||||
\(243\) | −15.0515 | −0.965557 | ||||||||
\(244\) | 4.51429 | 0.288997 | ||||||||
\(245\) | −18.4776 | −1.18049 | ||||||||
\(246\) | −2.28814 | −0.145886 | ||||||||
\(247\) | −19.0936 | −1.21490 | ||||||||
\(248\) | 3.39736 | 0.215733 | ||||||||
\(249\) | 5.66240 | 0.358840 | ||||||||
\(250\) | −11.4581 | −0.724677 | ||||||||
\(251\) | 3.56449 | 0.224989 | 0.112494 | − | 0.993652i | \(-0.464116\pi\) | ||||
0.112494 | + | 0.993652i | \(0.464116\pi\) | |||||||
\(252\) | −2.73006 | −0.171977 | ||||||||
\(253\) | −7.52782 | −0.473270 | ||||||||
\(254\) | −9.93143 | −0.623153 | ||||||||
\(255\) | 10.8085 | 0.676855 | ||||||||
\(256\) | −16.8136 | −1.05085 | ||||||||
\(257\) | −14.9858 | −0.934791 | −0.467395 | − | 0.884048i | \(-0.654808\pi\) | ||||
−0.467395 | + | 0.884048i | \(0.654808\pi\) | |||||||
\(258\) | 6.24956 | 0.389080 | ||||||||
\(259\) | 0.702111 | 0.0436270 | ||||||||
\(260\) | 19.9716 | 1.23859 | ||||||||
\(261\) | 1.71254 | 0.106003 | ||||||||
\(262\) | −15.8579 | −0.979705 | ||||||||
\(263\) | 24.0181 | 1.48102 | 0.740509 | − | 0.672047i | \(-0.234585\pi\) | ||||
0.740509 | + | 0.672047i | \(0.234585\pi\) | |||||||
\(264\) | −4.54181 | −0.279529 | ||||||||
\(265\) | −27.1290 | −1.66652 | ||||||||
\(266\) | 5.14554 | 0.315493 | ||||||||
\(267\) | −0.360102 | −0.0220379 | ||||||||
\(268\) | 17.4353 | 1.06503 | ||||||||
\(269\) | −6.00483 | −0.366121 | −0.183060 | − | 0.983102i | \(-0.558600\pi\) | ||||
−0.183060 | + | 0.983102i | \(0.558600\pi\) | |||||||
\(270\) | −18.1512 | −1.10465 | ||||||||
\(271\) | 18.1166 | 1.10051 | 0.550253 | − | 0.834998i | \(-0.314531\pi\) | ||||
0.550253 | + | 0.834998i | \(0.314531\pi\) | |||||||
\(272\) | 1.17029 | 0.0709594 | ||||||||
\(273\) | −7.58608 | −0.459131 | ||||||||
\(274\) | 8.55435 | 0.516787 | ||||||||
\(275\) | 11.5440 | 0.696127 | ||||||||
\(276\) | −6.98279 | −0.420315 | ||||||||
\(277\) | 18.1936 | 1.09315 | 0.546574 | − | 0.837411i | \(-0.315932\pi\) | ||||
0.546574 | + | 0.837411i | \(0.315932\pi\) | |||||||
\(278\) | 4.70321 | 0.282080 | ||||||||
\(279\) | −2.01051 | −0.120366 | ||||||||
\(280\) | −14.8760 | −0.889013 | ||||||||
\(281\) | 2.28385 | 0.136243 | 0.0681216 | − | 0.997677i | \(-0.478299\pi\) | ||||
0.0681216 | + | 0.997677i | \(0.478299\pi\) | |||||||
\(282\) | −5.95050 | −0.354347 | ||||||||
\(283\) | −20.4761 | −1.21718 | −0.608590 | − | 0.793485i | \(-0.708265\pi\) | ||||
−0.608590 | + | 0.793485i | \(0.708265\pi\) | |||||||
\(284\) | −8.97352 | −0.532480 | ||||||||
\(285\) | −16.3548 | −0.968777 | ||||||||
\(286\) | 6.18613 | 0.365794 | ||||||||
\(287\) | 3.03864 | 0.179365 | ||||||||
\(288\) | 9.35041 | 0.550978 | ||||||||
\(289\) | −10.1401 | −0.596476 | ||||||||
\(290\) | 3.37617 | 0.198256 | ||||||||
\(291\) | 11.0155 | 0.645740 | ||||||||
\(292\) | 3.59779 | 0.210545 | ||||||||
\(293\) | −29.8294 | −1.74265 | −0.871327 | − | 0.490702i | \(-0.836740\pi\) | ||||
−0.871327 | + | 0.490702i | \(0.836740\pi\) | |||||||
\(294\) | −5.30899 | −0.309627 | ||||||||
\(295\) | −19.2192 | −1.11898 | ||||||||
\(296\) | −1.46790 | −0.0853202 | ||||||||
\(297\) | 7.35945 | 0.427038 | ||||||||
\(298\) | 0.652422 | 0.0377938 | ||||||||
\(299\) | 26.2875 | 1.52025 | ||||||||
\(300\) | 10.7081 | 0.618235 | ||||||||
\(301\) | −8.29941 | −0.478370 | ||||||||
\(302\) | −14.5525 | −0.837401 | ||||||||
\(303\) | 16.1439 | 0.927446 | ||||||||
\(304\) | −1.77082 | −0.101564 | ||||||||
\(305\) | −14.5569 | −0.833525 | ||||||||
\(306\) | −4.20733 | −0.240517 | ||||||||
\(307\) | 10.3495 | 0.590678 | 0.295339 | − | 0.955393i | \(-0.404567\pi\) | ||||
0.295339 | + | 0.955393i | \(0.404567\pi\) | |||||||
\(308\) | 2.18221 | 0.124343 | ||||||||
\(309\) | 2.60779 | 0.148352 | ||||||||
\(310\) | −3.96360 | −0.225118 | ||||||||
\(311\) | 25.1043 | 1.42353 | 0.711766 | − | 0.702416i | \(-0.247895\pi\) | ||||
0.711766 | + | 0.702416i | \(0.247895\pi\) | |||||||
\(312\) | 15.8602 | 0.897909 | ||||||||
\(313\) | 22.6769 | 1.28177 | 0.640887 | − | 0.767636i | \(-0.278567\pi\) | ||||
0.640887 | + | 0.767636i | \(0.278567\pi\) | |||||||
\(314\) | −12.2482 | −0.691207 | ||||||||
\(315\) | 8.80341 | 0.496016 | ||||||||
\(316\) | 8.24046 | 0.463562 | ||||||||
\(317\) | 34.1075 | 1.91567 | 0.957834 | − | 0.287322i | \(-0.0927649\pi\) | ||||
0.957834 | + | 0.287322i | \(0.0927649\pi\) | |||||||
\(318\) | −7.79472 | −0.437106 | ||||||||
\(319\) | −1.36888 | −0.0766424 | ||||||||
\(320\) | 21.7011 | 1.21313 | ||||||||
\(321\) | 10.9831 | 0.613015 | ||||||||
\(322\) | −7.08424 | −0.394789 | ||||||||
\(323\) | −10.3801 | −0.577561 | ||||||||
\(324\) | 0.955682 | 0.0530935 | ||||||||
\(325\) | −40.3121 | −2.23611 | ||||||||
\(326\) | 9.55775 | 0.529355 | ||||||||
\(327\) | 13.3193 | 0.736561 | ||||||||
\(328\) | −6.35290 | −0.350780 | ||||||||
\(329\) | 7.90226 | 0.435666 | ||||||||
\(330\) | 5.29881 | 0.291690 | ||||||||
\(331\) | 25.4658 | 1.39973 | 0.699864 | − | 0.714277i | \(-0.253244\pi\) | ||||
0.699864 | + | 0.714277i | \(0.253244\pi\) | |||||||
\(332\) | 5.68800 | 0.312170 | ||||||||
\(333\) | 0.868683 | 0.0476035 | ||||||||
\(334\) | −15.4099 | −0.843194 | ||||||||
\(335\) | −56.2223 | −3.07175 | ||||||||
\(336\) | −0.703567 | −0.0383827 | ||||||||
\(337\) | −19.8215 | −1.07975 | −0.539873 | − | 0.841747i | \(-0.681528\pi\) | ||||
−0.539873 | + | 0.841747i | \(0.681528\pi\) | |||||||
\(338\) | −9.50333 | −0.516913 | ||||||||
\(339\) | −12.1072 | −0.657573 | ||||||||
\(340\) | 10.8574 | 0.588824 | ||||||||
\(341\) | 1.60705 | 0.0870268 | ||||||||
\(342\) | 6.36630 | 0.344250 | ||||||||
\(343\) | 16.8156 | 0.907958 | ||||||||
\(344\) | 17.3516 | 0.935535 | ||||||||
\(345\) | 22.5169 | 1.21227 | ||||||||
\(346\) | 5.20798 | 0.279983 | ||||||||
\(347\) | −11.2446 | −0.603643 | −0.301822 | − | 0.953364i | \(-0.597595\pi\) | ||||
−0.301822 | + | 0.953364i | \(0.597595\pi\) | |||||||
\(348\) | −1.26977 | −0.0680667 | ||||||||
\(349\) | −32.7339 | −1.75221 | −0.876104 | − | 0.482122i | \(-0.839866\pi\) | ||||
−0.876104 | + | 0.482122i | \(0.839866\pi\) | |||||||
\(350\) | 10.8637 | 0.580690 | ||||||||
\(351\) | −25.6996 | −1.37174 | ||||||||
\(352\) | −7.47404 | −0.398368 | ||||||||
\(353\) | 2.29608 | 0.122208 | 0.0611041 | − | 0.998131i | \(-0.480538\pi\) | ||||
0.0611041 | + | 0.998131i | \(0.480538\pi\) | |||||||
\(354\) | −5.52205 | −0.293494 | ||||||||
\(355\) | 28.9362 | 1.53578 | ||||||||
\(356\) | −0.361730 | −0.0191717 | ||||||||
\(357\) | −4.12410 | −0.218271 | ||||||||
\(358\) | 4.87162 | 0.257473 | ||||||||
\(359\) | 17.1885 | 0.907175 | 0.453587 | − | 0.891212i | \(-0.350144\pi\) | ||||
0.453587 | + | 0.891212i | \(0.350144\pi\) | |||||||
\(360\) | −18.4053 | −0.970045 | ||||||||
\(361\) | −3.29347 | −0.173340 | ||||||||
\(362\) | −22.7450 | −1.19545 | ||||||||
\(363\) | 10.2674 | 0.538901 | ||||||||
\(364\) | −7.62039 | −0.399417 | ||||||||
\(365\) | −11.6015 | −0.607251 | ||||||||
\(366\) | −4.18248 | −0.218622 | ||||||||
\(367\) | 18.4902 | 0.965183 | 0.482591 | − | 0.875846i | \(-0.339696\pi\) | ||||
0.482591 | + | 0.875846i | \(0.339696\pi\) | |||||||
\(368\) | 2.43802 | 0.127091 | ||||||||
\(369\) | 3.75955 | 0.195714 | ||||||||
\(370\) | 1.71256 | 0.0890319 | ||||||||
\(371\) | 10.3514 | 0.537417 | ||||||||
\(372\) | 1.49070 | 0.0772891 | ||||||||
\(373\) | 9.72193 | 0.503382 | 0.251691 | − | 0.967808i | \(-0.419013\pi\) | ||||
0.251691 | + | 0.967808i | \(0.419013\pi\) | |||||||
\(374\) | 3.36303 | 0.173898 | ||||||||
\(375\) | −13.8961 | −0.717592 | ||||||||
\(376\) | −16.5213 | −0.852020 | ||||||||
\(377\) | 4.78019 | 0.246192 | ||||||||
\(378\) | 6.92578 | 0.356224 | ||||||||
\(379\) | 17.3861 | 0.893064 | 0.446532 | − | 0.894768i | \(-0.352659\pi\) | ||||
0.446532 | + | 0.894768i | \(0.352659\pi\) | |||||||
\(380\) | −16.4288 | −0.842780 | ||||||||
\(381\) | −12.0446 | −0.617061 | ||||||||
\(382\) | −1.16504 | −0.0596087 | ||||||||
\(383\) | −24.4993 | −1.25185 | −0.625927 | − | 0.779882i | \(-0.715279\pi\) | ||||
−0.625927 | + | 0.779882i | \(0.715279\pi\) | |||||||
\(384\) | −5.99415 | −0.305888 | ||||||||
\(385\) | −7.03681 | −0.358629 | ||||||||
\(386\) | 0.992399 | 0.0505118 | ||||||||
\(387\) | −10.2684 | −0.521972 | ||||||||
\(388\) | 11.0653 | 0.561756 | ||||||||
\(389\) | −7.29617 | −0.369930 | −0.184965 | − | 0.982745i | \(-0.559217\pi\) | ||||
−0.184965 | + | 0.982745i | \(0.559217\pi\) | |||||||
\(390\) | −18.5037 | −0.936971 | ||||||||
\(391\) | 14.2910 | 0.722725 | ||||||||
\(392\) | −14.7402 | −0.744491 | ||||||||
\(393\) | −19.2320 | −0.970127 | ||||||||
\(394\) | 17.3837 | 0.875781 | ||||||||
\(395\) | −26.5724 | −1.33700 | ||||||||
\(396\) | 2.69993 | 0.135677 | ||||||||
\(397\) | −5.32902 | −0.267456 | −0.133728 | − | 0.991018i | \(-0.542695\pi\) | ||||
−0.133728 | + | 0.991018i | \(0.542695\pi\) | |||||||
\(398\) | 2.12668 | 0.106601 | ||||||||
\(399\) | 6.24037 | 0.312409 | ||||||||
\(400\) | −3.73872 | −0.186936 | ||||||||
\(401\) | 18.5132 | 0.924503 | 0.462252 | − | 0.886749i | \(-0.347042\pi\) | ||||
0.462252 | + | 0.886749i | \(0.347042\pi\) | |||||||
\(402\) | −16.1538 | −0.805678 | ||||||||
\(403\) | −5.61191 | −0.279549 | ||||||||
\(404\) | 16.2169 | 0.806823 | ||||||||
\(405\) | −3.08172 | −0.153132 | ||||||||
\(406\) | −1.28822 | −0.0639331 | ||||||||
\(407\) | −0.694363 | −0.0344183 | ||||||||
\(408\) | 8.62227 | 0.426866 | ||||||||
\(409\) | −21.9890 | −1.08728 | −0.543642 | − | 0.839317i | \(-0.682955\pi\) | ||||
−0.543642 | + | 0.839317i | \(0.682955\pi\) | |||||||
\(410\) | 7.41175 | 0.366040 | ||||||||
\(411\) | 10.3745 | 0.511735 | ||||||||
\(412\) | 2.61958 | 0.129058 | ||||||||
\(413\) | 7.33328 | 0.360847 | ||||||||
\(414\) | −8.76494 | −0.430773 | ||||||||
\(415\) | −18.3417 | −0.900358 | ||||||||
\(416\) | 26.0997 | 1.27964 | ||||||||
\(417\) | 5.70393 | 0.279322 | ||||||||
\(418\) | −5.08876 | −0.248899 | ||||||||
\(419\) | 3.13878 | 0.153340 | 0.0766698 | − | 0.997057i | \(-0.475571\pi\) | ||||
0.0766698 | + | 0.997057i | \(0.475571\pi\) | |||||||
\(420\) | −6.52733 | −0.318501 | ||||||||
\(421\) | 25.6436 | 1.24979 | 0.624897 | − | 0.780707i | \(-0.285141\pi\) | ||||
0.624897 | + | 0.780707i | \(0.285141\pi\) | |||||||
\(422\) | −9.07033 | −0.441537 | ||||||||
\(423\) | 9.77704 | 0.475376 | ||||||||
\(424\) | −21.6417 | −1.05101 | ||||||||
\(425\) | −21.9153 | −1.06305 | ||||||||
\(426\) | 8.31396 | 0.402813 | ||||||||
\(427\) | 5.55434 | 0.268793 | ||||||||
\(428\) | 11.0327 | 0.533287 | ||||||||
\(429\) | 7.50237 | 0.362218 | ||||||||
\(430\) | −20.2436 | −0.976233 | ||||||||
\(431\) | 11.0459 | 0.532064 | 0.266032 | − | 0.963964i | \(-0.414287\pi\) | ||||
0.266032 | + | 0.963964i | \(0.414287\pi\) | |||||||
\(432\) | −2.38349 | −0.114676 | ||||||||
\(433\) | 16.5427 | 0.794992 | 0.397496 | − | 0.917604i | \(-0.369879\pi\) | ||||
0.397496 | + | 0.917604i | \(0.369879\pi\) | |||||||
\(434\) | 1.51236 | 0.0725954 | ||||||||
\(435\) | 4.09453 | 0.196318 | ||||||||
\(436\) | 13.3796 | 0.640765 | ||||||||
\(437\) | −21.6243 | −1.03443 | ||||||||
\(438\) | −3.33335 | −0.159274 | ||||||||
\(439\) | −4.20024 | −0.200467 | −0.100233 | − | 0.994964i | \(-0.531959\pi\) | ||||
−0.100233 | + | 0.994964i | \(0.531959\pi\) | |||||||
\(440\) | 14.7119 | 0.701361 | ||||||||
\(441\) | 8.72300 | 0.415381 | ||||||||
\(442\) | −11.7439 | −0.558599 | ||||||||
\(443\) | 3.63885 | 0.172887 | 0.0864436 | − | 0.996257i | \(-0.472450\pi\) | ||||
0.0864436 | + | 0.996257i | \(0.472450\pi\) | |||||||
\(444\) | −0.644089 | −0.0305671 | ||||||||
\(445\) | 1.16644 | 0.0552948 | ||||||||
\(446\) | −7.02660 | −0.332719 | ||||||||
\(447\) | 0.791239 | 0.0374243 | ||||||||
\(448\) | −8.28030 | −0.391207 | ||||||||
\(449\) | 27.1676 | 1.28212 | 0.641060 | − | 0.767491i | \(-0.278495\pi\) | ||||
0.641060 | + | 0.767491i | \(0.278495\pi\) | |||||||
\(450\) | 13.4411 | 0.633619 | ||||||||
\(451\) | −3.00511 | −0.141505 | ||||||||
\(452\) | −12.1619 | −0.572050 | ||||||||
\(453\) | −17.6488 | −0.829215 | ||||||||
\(454\) | −15.6082 | −0.732529 | ||||||||
\(455\) | 24.5729 | 1.15200 | ||||||||
\(456\) | −13.0468 | −0.610970 | ||||||||
\(457\) | 22.0173 | 1.02993 | 0.514963 | − | 0.857212i | \(-0.327806\pi\) | ||||
0.514963 | + | 0.857212i | \(0.327806\pi\) | |||||||
\(458\) | 0.119836 | 0.00559958 | ||||||||
\(459\) | −13.9713 | −0.652125 | ||||||||
\(460\) | 22.6187 | 1.05460 | ||||||||
\(461\) | −15.3966 | −0.717093 | −0.358546 | − | 0.933512i | \(-0.616727\pi\) | ||||
−0.358546 | + | 0.933512i | \(0.616727\pi\) | |||||||
\(462\) | −2.02182 | −0.0940634 | ||||||||
\(463\) | −37.8087 | −1.75712 | −0.878561 | − | 0.477631i | \(-0.841496\pi\) | ||||
−0.878561 | + | 0.477631i | \(0.841496\pi\) | |||||||
\(464\) | 0.443336 | 0.0205813 | ||||||||
\(465\) | −4.80695 | −0.222917 | ||||||||
\(466\) | 6.19904 | 0.287165 | ||||||||
\(467\) | 15.9218 | 0.736773 | 0.368386 | − | 0.929673i | \(-0.379910\pi\) | ||||
0.368386 | + | 0.929673i | \(0.379910\pi\) | |||||||
\(468\) | −9.42829 | −0.435823 | ||||||||
\(469\) | 21.4522 | 0.990572 | ||||||||
\(470\) | 19.2749 | 0.889085 | ||||||||
\(471\) | −14.8543 | −0.684450 | ||||||||
\(472\) | −15.3317 | −0.705699 | ||||||||
\(473\) | 8.20782 | 0.377396 | ||||||||
\(474\) | −7.63478 | −0.350677 | ||||||||
\(475\) | 33.1610 | 1.52153 | ||||||||
\(476\) | −4.14275 | −0.189883 | ||||||||
\(477\) | 12.8072 | 0.586401 | ||||||||
\(478\) | 7.43648 | 0.340137 | ||||||||
\(479\) | −10.5176 | −0.480562 | −0.240281 | − | 0.970703i | \(-0.577240\pi\) | ||||
−0.240281 | + | 0.970703i | \(0.577240\pi\) | |||||||
\(480\) | 22.3560 | 1.02041 | ||||||||
\(481\) | 2.42475 | 0.110559 | ||||||||
\(482\) | 23.5552 | 1.07291 | ||||||||
\(483\) | −8.59156 | −0.390930 | ||||||||
\(484\) | 10.3139 | 0.468812 | ||||||||
\(485\) | −35.6815 | −1.62021 | ||||||||
\(486\) | 14.0083 | 0.635430 | ||||||||
\(487\) | −26.2427 | −1.18917 | −0.594586 | − | 0.804032i | \(-0.702684\pi\) | ||||
−0.594586 | + | 0.804032i | \(0.702684\pi\) | |||||||
\(488\) | −11.6125 | −0.525671 | ||||||||
\(489\) | 11.5914 | 0.524180 | ||||||||
\(490\) | 17.1969 | 0.776878 | ||||||||
\(491\) | −18.5837 | −0.838671 | −0.419336 | − | 0.907831i | \(-0.637737\pi\) | ||||
−0.419336 | + | 0.907831i | \(0.637737\pi\) | |||||||
\(492\) | −2.78754 | −0.125672 | ||||||||
\(493\) | 2.59870 | 0.117040 | ||||||||
\(494\) | 17.7702 | 0.799519 | ||||||||
\(495\) | −8.70626 | −0.391317 | ||||||||
\(496\) | −0.520473 | −0.0233699 | ||||||||
\(497\) | −11.0409 | −0.495254 | ||||||||
\(498\) | −5.26993 | −0.236151 | ||||||||
\(499\) | 35.6758 | 1.59707 | 0.798533 | − | 0.601951i | \(-0.205610\pi\) | ||||
0.798533 | + | 0.601951i | \(0.205610\pi\) | |||||||
\(500\) | −13.9590 | −0.624263 | ||||||||
\(501\) | −18.6887 | −0.834951 | ||||||||
\(502\) | −3.31743 | −0.148064 | ||||||||
\(503\) | 7.96197 | 0.355007 | 0.177503 | − | 0.984120i | \(-0.443198\pi\) | ||||
0.177503 | + | 0.984120i | \(0.443198\pi\) | |||||||
\(504\) | 7.02274 | 0.312818 | ||||||||
\(505\) | −52.2936 | −2.32703 | ||||||||
\(506\) | 7.00606 | 0.311457 | ||||||||
\(507\) | −11.5254 | −0.511860 | ||||||||
\(508\) | −12.0990 | −0.536807 | ||||||||
\(509\) | 12.1070 | 0.536633 | 0.268317 | − | 0.963331i | \(-0.413533\pi\) | ||||
0.268317 | + | 0.963331i | \(0.413533\pi\) | |||||||
\(510\) | −10.0594 | −0.445436 | ||||||||
\(511\) | 4.42668 | 0.195825 | ||||||||
\(512\) | 5.02702 | 0.222165 | ||||||||
\(513\) | 21.1406 | 0.933382 | ||||||||
\(514\) | 13.9472 | 0.615183 | ||||||||
\(515\) | −8.44717 | −0.372227 | ||||||||
\(516\) | 7.61356 | 0.335168 | ||||||||
\(517\) | −7.81506 | −0.343706 | ||||||||
\(518\) | −0.653447 | −0.0287108 | ||||||||
\(519\) | 6.31609 | 0.277246 | ||||||||
\(520\) | −51.3746 | −2.25293 | ||||||||
\(521\) | 8.29086 | 0.363229 | 0.181615 | − | 0.983370i | \(-0.441868\pi\) | ||||
0.181615 | + | 0.983370i | \(0.441868\pi\) | |||||||
\(522\) | −1.59384 | −0.0697604 | ||||||||
\(523\) | −42.8812 | −1.87507 | −0.937533 | − | 0.347896i | \(-0.886896\pi\) | ||||
−0.937533 | + | 0.347896i | \(0.886896\pi\) | |||||||
\(524\) | −19.3190 | −0.843954 | ||||||||
\(525\) | 13.1752 | 0.575013 | ||||||||
\(526\) | −22.3534 | −0.974653 | ||||||||
\(527\) | −3.05086 | −0.132898 | ||||||||
\(528\) | 0.695803 | 0.0302809 | ||||||||
\(529\) | 6.77174 | 0.294423 | ||||||||
\(530\) | 25.2487 | 1.09673 | ||||||||
\(531\) | 9.07306 | 0.393737 | ||||||||
\(532\) | 6.26859 | 0.271778 | ||||||||
\(533\) | 10.4940 | 0.454546 | ||||||||
\(534\) | 0.335143 | 0.0145031 | ||||||||
\(535\) | −35.5764 | −1.53810 | ||||||||
\(536\) | −44.8502 | −1.93723 | ||||||||
\(537\) | 5.90816 | 0.254956 | ||||||||
\(538\) | 5.58863 | 0.240943 | ||||||||
\(539\) | −6.97254 | −0.300328 | ||||||||
\(540\) | −22.1128 | −0.951583 | ||||||||
\(541\) | 34.2565 | 1.47280 | 0.736401 | − | 0.676546i | \(-0.236524\pi\) | ||||
0.736401 | + | 0.676546i | \(0.236524\pi\) | |||||||
\(542\) | −16.8610 | −0.724240 | ||||||||
\(543\) | −27.5844 | −1.18376 | ||||||||
\(544\) | 14.1889 | 0.608343 | ||||||||
\(545\) | −43.1441 | −1.84809 | ||||||||
\(546\) | 7.06029 | 0.302152 | ||||||||
\(547\) | −40.2915 | −1.72274 | −0.861371 | − | 0.507977i | \(-0.830394\pi\) | ||||
−0.861371 | + | 0.507977i | \(0.830394\pi\) | |||||||
\(548\) | 10.4214 | 0.445179 | ||||||||
\(549\) | 6.87208 | 0.293293 | ||||||||
\(550\) | −10.7438 | −0.458119 | ||||||||
\(551\) | −3.93222 | −0.167518 | ||||||||
\(552\) | 17.9624 | 0.764530 | ||||||||
\(553\) | 10.1390 | 0.431154 | ||||||||
\(554\) | −16.9326 | −0.719397 | ||||||||
\(555\) | 2.07695 | 0.0881615 | ||||||||
\(556\) | 5.72972 | 0.242994 | ||||||||
\(557\) | −41.8987 | −1.77531 | −0.887653 | − | 0.460513i | \(-0.847665\pi\) | ||||
−0.887653 | + | 0.460513i | \(0.847665\pi\) | |||||||
\(558\) | 1.87116 | 0.0792123 | ||||||||
\(559\) | −28.6621 | −1.21228 | ||||||||
\(560\) | 2.27900 | 0.0963053 | ||||||||
\(561\) | 4.07859 | 0.172198 | ||||||||
\(562\) | −2.12556 | −0.0896612 | ||||||||
\(563\) | −14.9368 | −0.629509 | −0.314754 | − | 0.949173i | \(-0.601922\pi\) | ||||
−0.314754 | + | 0.949173i | \(0.601922\pi\) | |||||||
\(564\) | −7.24923 | −0.305248 | ||||||||
\(565\) | 39.2177 | 1.64990 | ||||||||
\(566\) | 19.0569 | 0.801022 | ||||||||
\(567\) | 1.17586 | 0.0493816 | ||||||||
\(568\) | 23.0833 | 0.968554 | ||||||||
\(569\) | −9.80169 | −0.410908 | −0.205454 | − | 0.978667i | \(-0.565867\pi\) | ||||
−0.205454 | + | 0.978667i | \(0.565867\pi\) | |||||||
\(570\) | 15.2213 | 0.637549 | ||||||||
\(571\) | −34.8837 | −1.45984 | −0.729920 | − | 0.683533i | \(-0.760443\pi\) | ||||
−0.729920 | + | 0.683533i | \(0.760443\pi\) | |||||||
\(572\) | 7.53629 | 0.315108 | ||||||||
\(573\) | −1.41293 | −0.0590260 | ||||||||
\(574\) | −2.82803 | −0.118040 | ||||||||
\(575\) | −45.6551 | −1.90395 | ||||||||
\(576\) | −10.2448 | −0.426865 | ||||||||
\(577\) | −30.6694 | −1.27678 | −0.638391 | − | 0.769712i | \(-0.720400\pi\) | ||||
−0.638391 | + | 0.769712i | \(0.720400\pi\) | |||||||
\(578\) | 9.43727 | 0.392539 | ||||||||
\(579\) | 1.20355 | 0.0500180 | ||||||||
\(580\) | 4.11304 | 0.170785 | ||||||||
\(581\) | 6.99847 | 0.290345 | ||||||||
\(582\) | −10.2520 | −0.424959 | ||||||||
\(583\) | −10.2371 | −0.423979 | ||||||||
\(584\) | −9.25488 | −0.382969 | ||||||||
\(585\) | 30.4027 | 1.25700 | ||||||||
\(586\) | 27.7619 | 1.14684 | ||||||||
\(587\) | 8.44245 | 0.348457 | 0.174229 | − | 0.984705i | \(-0.444257\pi\) | ||||
0.174229 | + | 0.984705i | \(0.444257\pi\) | |||||||
\(588\) | −6.46771 | −0.266724 | ||||||||
\(589\) | 4.61640 | 0.190215 | ||||||||
\(590\) | 17.8871 | 0.736399 | ||||||||
\(591\) | 21.0825 | 0.867219 | ||||||||
\(592\) | 0.224882 | 0.00924259 | ||||||||
\(593\) | 48.0421 | 1.97285 | 0.986426 | − | 0.164208i | \(-0.0525068\pi\) | ||||
0.986426 | + | 0.164208i | \(0.0525068\pi\) | |||||||
\(594\) | −6.84936 | −0.281032 | ||||||||
\(595\) | 13.3588 | 0.547658 | ||||||||
\(596\) | 0.794816 | 0.0325569 | ||||||||
\(597\) | 2.57918 | 0.105559 | ||||||||
\(598\) | −24.4655 | −1.00047 | ||||||||
\(599\) | 18.1382 | 0.741105 | 0.370553 | − | 0.928811i | \(-0.379168\pi\) | ||||
0.370553 | + | 0.928811i | \(0.379168\pi\) | |||||||
\(600\) | −27.5454 | −1.12454 | ||||||||
\(601\) | 28.5285 | 1.16370 | 0.581850 | − | 0.813296i | \(-0.302329\pi\) | ||||
0.581850 | + | 0.813296i | \(0.302329\pi\) | |||||||
\(602\) | 7.72417 | 0.314814 | ||||||||
\(603\) | 26.5417 | 1.08086 | ||||||||
\(604\) | −17.7286 | −0.721368 | ||||||||
\(605\) | −33.2584 | −1.35214 | ||||||||
\(606\) | −15.0250 | −0.610349 | ||||||||
\(607\) | −19.6002 | −0.795549 | −0.397774 | − | 0.917483i | \(-0.630217\pi\) | ||||
−0.397774 | + | 0.917483i | \(0.630217\pi\) | |||||||
\(608\) | −21.4698 | −0.870716 | ||||||||
\(609\) | −1.56231 | −0.0633081 | ||||||||
\(610\) | 13.5479 | 0.548540 | ||||||||
\(611\) | 27.2906 | 1.10406 | ||||||||
\(612\) | −5.12560 | −0.207190 | ||||||||
\(613\) | −41.6567 | −1.68250 | −0.841249 | − | 0.540648i | \(-0.818179\pi\) | ||||
−0.841249 | + | 0.540648i | \(0.818179\pi\) | |||||||
\(614\) | −9.63218 | −0.388723 | ||||||||
\(615\) | 8.98876 | 0.362462 | ||||||||
\(616\) | −5.61347 | −0.226173 | ||||||||
\(617\) | 21.0187 | 0.846182 | 0.423091 | − | 0.906087i | \(-0.360945\pi\) | ||||
0.423091 | + | 0.906087i | \(0.360945\pi\) | |||||||
\(618\) | −2.42704 | −0.0976300 | ||||||||
\(619\) | −15.8469 | −0.636941 | −0.318471 | − | 0.947933i | \(-0.603169\pi\) | ||||
−0.318471 | + | 0.947933i | \(0.603169\pi\) | |||||||
\(620\) | −4.82868 | −0.193925 | ||||||||
\(621\) | −29.1058 | −1.16798 | ||||||||
\(622\) | −23.3643 | −0.936822 | ||||||||
\(623\) | −0.445069 | −0.0178313 | ||||||||
\(624\) | −2.42978 | −0.0972690 | ||||||||
\(625\) | 3.17569 | 0.127028 | ||||||||
\(626\) | −21.1051 | −0.843531 | ||||||||
\(627\) | −6.17150 | −0.246466 | ||||||||
\(628\) | −14.9215 | −0.595431 | ||||||||
\(629\) | 1.31819 | 0.0525597 | ||||||||
\(630\) | −8.19324 | −0.326426 | ||||||||
\(631\) | 9.45459 | 0.376381 | 0.188191 | − | 0.982133i | \(-0.439738\pi\) | ||||
0.188191 | + | 0.982133i | \(0.439738\pi\) | |||||||
\(632\) | −21.1976 | −0.843195 | ||||||||
\(633\) | −11.0002 | −0.437220 | ||||||||
\(634\) | −31.7435 | −1.26069 | ||||||||
\(635\) | 39.0148 | 1.54826 | ||||||||
\(636\) | −9.49596 | −0.376539 | ||||||||
\(637\) | 24.3485 | 0.964721 | ||||||||
\(638\) | 1.27400 | 0.0504381 | ||||||||
\(639\) | −13.6603 | −0.540395 | ||||||||
\(640\) | 19.4163 | 0.767496 | ||||||||
\(641\) | 33.9176 | 1.33966 | 0.669832 | − | 0.742513i | \(-0.266366\pi\) | ||||
0.669832 | + | 0.742513i | \(0.266366\pi\) | |||||||
\(642\) | −10.2218 | −0.403423 | ||||||||
\(643\) | −29.7215 | −1.17210 | −0.586051 | − | 0.810274i | \(-0.699318\pi\) | ||||
−0.586051 | + | 0.810274i | \(0.699318\pi\) | |||||||
\(644\) | −8.63041 | −0.340086 | ||||||||
\(645\) | −24.5509 | −0.966690 | ||||||||
\(646\) | 9.66060 | 0.380091 | ||||||||
\(647\) | −12.6090 | −0.495711 | −0.247856 | − | 0.968797i | \(-0.579726\pi\) | ||||
−0.247856 | + | 0.968797i | \(0.579726\pi\) | |||||||
\(648\) | −2.45838 | −0.0965742 | ||||||||
\(649\) | −7.25235 | −0.284680 | ||||||||
\(650\) | 37.5180 | 1.47158 | ||||||||
\(651\) | 1.83414 | 0.0718857 | ||||||||
\(652\) | 11.6438 | 0.456006 | ||||||||
\(653\) | −17.2643 | −0.675606 | −0.337803 | − | 0.941217i | \(-0.609684\pi\) | ||||
−0.337803 | + | 0.941217i | \(0.609684\pi\) | |||||||
\(654\) | −12.3962 | −0.484728 | ||||||||
\(655\) | 62.2965 | 2.43413 | ||||||||
\(656\) | 0.973259 | 0.0379994 | ||||||||
\(657\) | 5.47689 | 0.213674 | ||||||||
\(658\) | −7.35455 | −0.286710 | ||||||||
\(659\) | 42.1769 | 1.64298 | 0.821488 | − | 0.570225i | \(-0.193144\pi\) | ||||
0.821488 | + | 0.570225i | \(0.193144\pi\) | |||||||
\(660\) | 6.45530 | 0.251272 | ||||||||
\(661\) | 5.32523 | 0.207127 | 0.103564 | − | 0.994623i | \(-0.466975\pi\) | ||||
0.103564 | + | 0.994623i | \(0.466975\pi\) | |||||||
\(662\) | −23.7007 | −0.921156 | ||||||||
\(663\) | −14.2426 | −0.553139 | ||||||||
\(664\) | −14.6317 | −0.567820 | ||||||||
\(665\) | −20.2138 | −0.783859 | ||||||||
\(666\) | −0.808474 | −0.0313277 | ||||||||
\(667\) | 5.41377 | 0.209622 | ||||||||
\(668\) | −18.7732 | −0.726358 | ||||||||
\(669\) | −8.52166 | −0.329466 | ||||||||
\(670\) | 52.3255 | 2.02151 | ||||||||
\(671\) | −5.49304 | −0.212057 | ||||||||
\(672\) | −8.53018 | −0.329059 | ||||||||
\(673\) | 2.73271 | 0.105338 | 0.0526692 | − | 0.998612i | \(-0.483227\pi\) | ||||
0.0526692 | + | 0.998612i | \(0.483227\pi\) | |||||||
\(674\) | 18.4477 | 0.710577 | ||||||||
\(675\) | 44.6340 | 1.71796 | ||||||||
\(676\) | −11.5775 | −0.445288 | ||||||||
\(677\) | −1.03727 | −0.0398656 | −0.0199328 | − | 0.999801i | \(-0.506345\pi\) | ||||
−0.0199328 | + | 0.999801i | \(0.506345\pi\) | |||||||
\(678\) | 11.2680 | 0.432747 | ||||||||
\(679\) | 13.6147 | 0.522483 | ||||||||
\(680\) | −27.9293 | −1.07104 | ||||||||
\(681\) | −18.9292 | −0.725368 | ||||||||
\(682\) | −1.49567 | −0.0572720 | ||||||||
\(683\) | 34.4325 | 1.31752 | 0.658761 | − | 0.752352i | \(-0.271081\pi\) | ||||
0.658761 | + | 0.752352i | \(0.271081\pi\) | |||||||
\(684\) | 7.75578 | 0.296550 | ||||||||
\(685\) | −33.6051 | −1.28398 | ||||||||
\(686\) | −15.6501 | −0.597524 | ||||||||
\(687\) | 0.145334 | 0.00554484 | ||||||||
\(688\) | −2.65825 | −0.101345 | ||||||||
\(689\) | 35.7486 | 1.36191 | ||||||||
\(690\) | −20.9562 | −0.797790 | ||||||||
\(691\) | −42.1965 | −1.60523 | −0.802615 | − | 0.596498i | \(-0.796558\pi\) | ||||
−0.802615 | + | 0.596498i | \(0.796558\pi\) | |||||||
\(692\) | 6.34465 | 0.241188 | ||||||||
\(693\) | 3.32197 | 0.126191 | ||||||||
\(694\) | 10.4653 | 0.397255 | ||||||||
\(695\) | −18.4762 | −0.700842 | ||||||||
\(696\) | 3.26633 | 0.123810 | ||||||||
\(697\) | 5.70496 | 0.216091 | ||||||||
\(698\) | 30.4651 | 1.15312 | ||||||||
\(699\) | 7.51803 | 0.284358 | ||||||||
\(700\) | 13.2348 | 0.500228 | ||||||||
\(701\) | 43.7951 | 1.65412 | 0.827059 | − | 0.562115i | \(-0.190012\pi\) | ||||
0.827059 | + | 0.562115i | \(0.190012\pi\) | |||||||
\(702\) | 23.9183 | 0.902738 | ||||||||
\(703\) | −1.99462 | −0.0752284 | ||||||||
\(704\) | 8.18892 | 0.308632 | ||||||||
\(705\) | 23.3761 | 0.880394 | ||||||||
\(706\) | −2.13694 | −0.0804248 | ||||||||
\(707\) | 19.9532 | 0.750417 | ||||||||
\(708\) | −6.72727 | −0.252826 | ||||||||
\(709\) | 0.0332206 | 0.00124763 | 0.000623813 | − | 1.00000i | \(-0.499801\pi\) | ||||
0.000623813 | 1.00000i | \(0.499801\pi\) | ||||||||
\(710\) | −26.9307 | −1.01069 | ||||||||
\(711\) | 12.5444 | 0.470452 | ||||||||
\(712\) | 0.930508 | 0.0348722 | ||||||||
\(713\) | −6.35573 | −0.238024 | ||||||||
\(714\) | 3.83826 | 0.143643 | ||||||||
\(715\) | −24.3017 | −0.908833 | ||||||||
\(716\) | 5.93488 | 0.221797 | ||||||||
\(717\) | 9.01875 | 0.336811 | ||||||||
\(718\) | −15.9972 | −0.597009 | ||||||||
\(719\) | −28.2468 | −1.05343 | −0.526713 | − | 0.850043i | \(-0.676576\pi\) | ||||
−0.526713 | + | 0.850043i | \(0.676576\pi\) | |||||||
\(720\) | 2.81968 | 0.105083 | ||||||||
\(721\) | 3.22311 | 0.120035 | ||||||||
\(722\) | 3.06519 | 0.114075 | ||||||||
\(723\) | 28.5671 | 1.06242 | ||||||||
\(724\) | −27.7092 | −1.02980 | ||||||||
\(725\) | −8.30204 | −0.308330 | ||||||||
\(726\) | −9.55579 | −0.354649 | ||||||||
\(727\) | 19.0989 | 0.708339 | 0.354169 | − | 0.935181i | \(-0.384764\pi\) | ||||
0.354169 | + | 0.935181i | \(0.384764\pi\) | |||||||
\(728\) | 19.6025 | 0.726518 | ||||||||
\(729\) | 19.5175 | 0.722872 | ||||||||
\(730\) | 10.7974 | 0.399630 | ||||||||
\(731\) | −15.5819 | −0.576317 | ||||||||
\(732\) | −5.09534 | −0.188329 | ||||||||
\(733\) | 27.2179 | 1.00532 | 0.502659 | − | 0.864485i | \(-0.332355\pi\) | ||||
0.502659 | + | 0.864485i | \(0.332355\pi\) | |||||||
\(734\) | −17.2087 | −0.635183 | ||||||||
\(735\) | 20.8560 | 0.769284 | ||||||||
\(736\) | 29.5590 | 1.08956 | ||||||||
\(737\) | −21.2155 | −0.781483 | ||||||||
\(738\) | −3.49897 | −0.128799 | ||||||||
\(739\) | 23.4362 | 0.862115 | 0.431057 | − | 0.902325i | \(-0.358141\pi\) | ||||
0.431057 | + | 0.902325i | \(0.358141\pi\) | |||||||
\(740\) | 2.08634 | 0.0766953 | ||||||||
\(741\) | 21.5512 | 0.791703 | ||||||||
\(742\) | −9.63392 | −0.353672 | ||||||||
\(743\) | −11.7677 | −0.431716 | −0.215858 | − | 0.976425i | \(-0.569255\pi\) | ||||
−0.215858 | + | 0.976425i | \(0.569255\pi\) | |||||||
\(744\) | −3.83465 | −0.140585 | ||||||||
\(745\) | −2.56299 | −0.0939005 | ||||||||
\(746\) | −9.04809 | −0.331274 | ||||||||
\(747\) | 8.65882 | 0.316810 | ||||||||
\(748\) | 4.09703 | 0.149802 | ||||||||
\(749\) | 13.5746 | 0.496004 | ||||||||
\(750\) | 12.9330 | 0.472245 | ||||||||
\(751\) | −10.1956 | −0.372043 | −0.186021 | − | 0.982546i | \(-0.559559\pi\) | ||||
−0.186021 | + | 0.982546i | \(0.559559\pi\) | |||||||
\(752\) | 2.53105 | 0.0922978 | ||||||||
\(753\) | −4.02329 | −0.146617 | ||||||||
\(754\) | −4.44887 | −0.162018 | ||||||||
\(755\) | 57.1682 | 2.08056 | ||||||||
\(756\) | 8.43738 | 0.306864 | ||||||||
\(757\) | −1.24101 | −0.0451052 | −0.0225526 | − | 0.999746i | \(-0.507179\pi\) | ||||
−0.0225526 | + | 0.999746i | \(0.507179\pi\) | |||||||
\(758\) | −16.1811 | −0.587723 | ||||||||
\(759\) | 8.49675 | 0.308413 | ||||||||
\(760\) | 42.2611 | 1.53297 | ||||||||
\(761\) | 27.0312 | 0.979881 | 0.489941 | − | 0.871756i | \(-0.337018\pi\) | ||||
0.489941 | + | 0.871756i | \(0.337018\pi\) | |||||||
\(762\) | 11.2097 | 0.406086 | ||||||||
\(763\) | 16.4621 | 0.595967 | ||||||||
\(764\) | −1.41932 | −0.0513492 | ||||||||
\(765\) | 16.5281 | 0.597576 | ||||||||
\(766\) | 22.8012 | 0.823841 | ||||||||
\(767\) | 25.3256 | 0.914454 | ||||||||
\(768\) | 18.9777 | 0.684799 | ||||||||
\(769\) | 35.8201 | 1.29171 | 0.645854 | − | 0.763461i | \(-0.276502\pi\) | ||||
0.645854 | + | 0.763461i | \(0.276502\pi\) | |||||||
\(770\) | 6.54908 | 0.236013 | ||||||||
\(771\) | 16.9147 | 0.609169 | ||||||||
\(772\) | 1.20900 | 0.0435127 | ||||||||
\(773\) | 52.9323 | 1.90384 | 0.951921 | − | 0.306343i | \(-0.0991054\pi\) | ||||
0.951921 | + | 0.306343i | \(0.0991054\pi\) | |||||||
\(774\) | 9.55669 | 0.343508 | ||||||||
\(775\) | 9.74654 | 0.350106 | ||||||||
\(776\) | −28.4642 | −1.02180 | ||||||||
\(777\) | −0.792482 | −0.0284301 | ||||||||
\(778\) | 6.79047 | 0.243450 | ||||||||
\(779\) | −8.63244 | −0.309289 | ||||||||
\(780\) | −22.5422 | −0.807142 | ||||||||
\(781\) | 10.9191 | 0.390716 | ||||||||
\(782\) | −13.3004 | −0.475623 | ||||||||
\(783\) | −5.29268 | −0.189145 | ||||||||
\(784\) | 2.25818 | 0.0806494 | ||||||||
\(785\) | 48.1162 | 1.71734 | ||||||||
\(786\) | 17.8990 | 0.638437 | ||||||||
\(787\) | −17.1660 | −0.611903 | −0.305951 | − | 0.952047i | \(-0.598974\pi\) | ||||
−0.305951 | + | 0.952047i | \(0.598974\pi\) | |||||||
\(788\) | 21.1779 | 0.754430 | ||||||||
\(789\) | −27.1095 | −0.965124 | ||||||||
\(790\) | 24.7306 | 0.879877 | ||||||||
\(791\) | −14.9640 | −0.532057 | ||||||||
\(792\) | −6.94525 | −0.246789 | ||||||||
\(793\) | 19.1820 | 0.681172 | ||||||||
\(794\) | 4.95966 | 0.176012 | ||||||||
\(795\) | 30.6209 | 1.08601 | ||||||||
\(796\) | 2.59084 | 0.0918299 | ||||||||
\(797\) | −14.6775 | −0.519902 | −0.259951 | − | 0.965622i | \(-0.583706\pi\) | ||||
−0.259951 | + | 0.965622i | \(0.583706\pi\) | |||||||
\(798\) | −5.80784 | −0.205595 | ||||||||
\(799\) | 14.8363 | 0.524869 | ||||||||
\(800\) | −45.3290 | −1.60262 | ||||||||
\(801\) | −0.550660 | −0.0194566 | ||||||||
\(802\) | −17.2300 | −0.608412 | ||||||||
\(803\) | −4.37783 | −0.154490 | ||||||||
\(804\) | −19.6795 | −0.694041 | ||||||||
\(805\) | 27.8299 | 0.980873 | ||||||||
\(806\) | 5.22294 | 0.183970 | ||||||||
\(807\) | 6.77773 | 0.238587 | ||||||||
\(808\) | −41.7162 | −1.46757 | ||||||||
\(809\) | 51.6201 | 1.81486 | 0.907432 | − | 0.420199i | \(-0.138040\pi\) | ||||
0.907432 | + | 0.420199i | \(0.138040\pi\) | |||||||
\(810\) | 2.86812 | 0.100776 | ||||||||
\(811\) | −20.0135 | −0.702769 | −0.351385 | − | 0.936231i | \(-0.614289\pi\) | ||||
−0.351385 | + | 0.936231i | \(0.614289\pi\) | |||||||
\(812\) | −1.56938 | −0.0550743 | ||||||||
\(813\) | −20.4485 | −0.717160 | ||||||||
\(814\) | 0.646236 | 0.0226506 | ||||||||
\(815\) | −37.5468 | −1.31521 | ||||||||
\(816\) | −1.32093 | −0.0462416 | ||||||||
\(817\) | 23.5777 | 0.824878 | ||||||||
\(818\) | 20.4649 | 0.715538 | ||||||||
\(819\) | −11.6005 | −0.405354 | ||||||||
\(820\) | 9.02940 | 0.315320 | ||||||||
\(821\) | 46.1263 | 1.60982 | 0.804909 | − | 0.593398i | \(-0.202214\pi\) | ||||
0.804909 | + | 0.593398i | \(0.202214\pi\) | |||||||
\(822\) | −9.65541 | −0.336771 | ||||||||
\(823\) | −47.5554 | −1.65768 | −0.828839 | − | 0.559487i | \(-0.810998\pi\) | ||||
−0.828839 | + | 0.559487i | \(0.810998\pi\) | |||||||
\(824\) | −6.73856 | −0.234749 | ||||||||
\(825\) | −13.0298 | −0.453640 | ||||||||
\(826\) | −6.82500 | −0.237472 | ||||||||
\(827\) | −55.6918 | −1.93660 | −0.968298 | − | 0.249799i | \(-0.919635\pi\) | ||||
−0.968298 | + | 0.249799i | \(0.919635\pi\) | |||||||
\(828\) | −10.6779 | −0.371084 | ||||||||
\(829\) | 23.8072 | 0.826859 | 0.413430 | − | 0.910536i | \(-0.364331\pi\) | ||||
0.413430 | + | 0.910536i | \(0.364331\pi\) | |||||||
\(830\) | 17.0704 | 0.592522 | ||||||||
\(831\) | −20.5354 | −0.712364 | ||||||||
\(832\) | −28.5961 | −0.991392 | ||||||||
\(833\) | 13.2368 | 0.458628 | ||||||||
\(834\) | −5.30858 | −0.183821 | ||||||||
\(835\) | 60.5367 | 2.09496 | ||||||||
\(836\) | −6.19941 | −0.214411 | ||||||||
\(837\) | 6.21357 | 0.214772 | ||||||||
\(838\) | −2.92123 | −0.100912 | ||||||||
\(839\) | 33.9473 | 1.17199 | 0.585996 | − | 0.810314i | \(-0.300703\pi\) | ||||
0.585996 | + | 0.810314i | \(0.300703\pi\) | |||||||
\(840\) | 16.7908 | 0.579337 | ||||||||
\(841\) | −28.0155 | −0.966053 | ||||||||
\(842\) | −23.8662 | −0.822485 | ||||||||
\(843\) | −2.57782 | −0.0887847 | ||||||||
\(844\) | −11.0500 | −0.380356 | ||||||||
\(845\) | 37.3331 | 1.28430 | ||||||||
\(846\) | −9.09938 | −0.312843 | ||||||||
\(847\) | 12.6901 | 0.436036 | ||||||||
\(848\) | 3.31549 | 0.113854 | ||||||||
\(849\) | 23.1117 | 0.793191 | ||||||||
\(850\) | 20.3963 | 0.699587 | ||||||||
\(851\) | 2.74613 | 0.0941362 | ||||||||
\(852\) | 10.1285 | 0.346998 | ||||||||
\(853\) | 4.94436 | 0.169292 | 0.0846458 | − | 0.996411i | \(-0.473024\pi\) | ||||
0.0846458 | + | 0.996411i | \(0.473024\pi\) | |||||||
\(854\) | −5.16936 | −0.176892 | ||||||||
\(855\) | −25.0095 | −0.855307 | ||||||||
\(856\) | −28.3804 | −0.970021 | ||||||||
\(857\) | −41.4317 | −1.41528 | −0.707641 | − | 0.706573i | \(-0.750240\pi\) | ||||
−0.707641 | + | 0.706573i | \(0.750240\pi\) | |||||||
\(858\) | −6.98237 | −0.238374 | ||||||||
\(859\) | 19.7989 | 0.675528 | 0.337764 | − | 0.941231i | \(-0.390329\pi\) | ||||
0.337764 | + | 0.941231i | \(0.390329\pi\) | |||||||
\(860\) | −24.6619 | −0.840964 | ||||||||
\(861\) | −3.42976 | −0.116886 | ||||||||
\(862\) | −10.2803 | −0.350150 | ||||||||
\(863\) | 7.69678 | 0.262001 | 0.131001 | − | 0.991382i | \(-0.458181\pi\) | ||||
0.131001 | + | 0.991382i | \(0.458181\pi\) | |||||||
\(864\) | −28.8979 | −0.983127 | ||||||||
\(865\) | −20.4591 | −0.695632 | ||||||||
\(866\) | −15.3961 | −0.523182 | ||||||||
\(867\) | 11.4453 | 0.388701 | ||||||||
\(868\) | 1.84244 | 0.0625364 | ||||||||
\(869\) | −10.0271 | −0.340146 | ||||||||
\(870\) | −3.81073 | −0.129196 | ||||||||
\(871\) | 74.0856 | 2.51029 | ||||||||
\(872\) | −34.4173 | −1.16552 | ||||||||
\(873\) | 16.8447 | 0.570106 | ||||||||
\(874\) | 20.1255 | 0.680756 | ||||||||
\(875\) | −17.1750 | −0.580620 | ||||||||
\(876\) | −4.06087 | −0.137204 | ||||||||
\(877\) | −0.324494 | −0.0109574 | −0.00547868 | − | 0.999985i | \(-0.501744\pi\) | ||||
−0.00547868 | + | 0.999985i | \(0.501744\pi\) | |||||||
\(878\) | 3.90912 | 0.131926 | ||||||||
\(879\) | 33.6689 | 1.13562 | ||||||||
\(880\) | −2.25385 | −0.0759772 | ||||||||
\(881\) | −10.8507 | −0.365571 | −0.182785 | − | 0.983153i | \(-0.558511\pi\) | ||||
−0.182785 | + | 0.983153i | \(0.558511\pi\) | |||||||
\(882\) | −8.11840 | −0.273361 | ||||||||
\(883\) | −20.5832 | −0.692679 | −0.346340 | − | 0.938109i | \(-0.612576\pi\) | ||||
−0.346340 | + | 0.938109i | \(0.612576\pi\) | |||||||
\(884\) | −14.3070 | −0.481198 | ||||||||
\(885\) | 21.6929 | 0.729200 | ||||||||
\(886\) | −3.38664 | −0.113776 | ||||||||
\(887\) | −20.0521 | −0.673284 | −0.336642 | − | 0.941633i | \(-0.609291\pi\) | ||||
−0.336642 | + | 0.941633i | \(0.609291\pi\) | |||||||
\(888\) | 1.65684 | 0.0556000 | ||||||||
\(889\) | −14.8865 | −0.499278 | ||||||||
\(890\) | −1.08560 | −0.0363893 | ||||||||
\(891\) | −1.16289 | −0.0389582 | ||||||||
\(892\) | −8.56019 | −0.286616 | ||||||||
\(893\) | −22.4494 | −0.751241 | ||||||||
\(894\) | −0.736397 | −0.0246288 | ||||||||
\(895\) | −19.1378 | −0.639705 | ||||||||
\(896\) | −7.40849 | −0.247500 | ||||||||
\(897\) | −29.6711 | −0.990689 | ||||||||
\(898\) | −25.2846 | −0.843759 | ||||||||
\(899\) | −1.15574 | −0.0385461 | ||||||||
\(900\) | 16.3747 | 0.545823 | ||||||||
\(901\) | 19.4344 | 0.647454 | ||||||||
\(902\) | 2.79682 | 0.0931241 | ||||||||
\(903\) | 9.36765 | 0.311736 | ||||||||
\(904\) | 31.2852 | 1.04053 | ||||||||
\(905\) | 89.3517 | 2.97015 | ||||||||
\(906\) | 16.4256 | 0.545703 | ||||||||
\(907\) | 32.5307 | 1.08016 | 0.540082 | − | 0.841612i | \(-0.318393\pi\) | ||||
0.540082 | + | 0.841612i | \(0.318393\pi\) | |||||||
\(908\) | −19.0148 | −0.631028 | ||||||||
\(909\) | 24.6870 | 0.818816 | ||||||||
\(910\) | −22.8697 | −0.758124 | ||||||||
\(911\) | −2.26910 | −0.0751786 | −0.0375893 | − | 0.999293i | \(-0.511968\pi\) | ||||
−0.0375893 | + | 0.999293i | \(0.511968\pi\) | |||||||
\(912\) | 1.99875 | 0.0661853 | ||||||||
\(913\) | −6.92124 | −0.229059 | ||||||||
\(914\) | −20.4913 | −0.677791 | ||||||||
\(915\) | 16.4306 | 0.543177 | ||||||||
\(916\) | 0.145991 | 0.00482369 | ||||||||
\(917\) | −23.7699 | −0.784951 | ||||||||
\(918\) | 13.0030 | 0.429161 | ||||||||
\(919\) | 8.15596 | 0.269040 | 0.134520 | − | 0.990911i | \(-0.457051\pi\) | ||||
0.134520 | + | 0.990911i | \(0.457051\pi\) | |||||||
\(920\) | −58.1839 | −1.91827 | ||||||||
\(921\) | −11.6816 | −0.384923 | ||||||||
\(922\) | 14.3295 | 0.471916 | ||||||||
\(923\) | −38.1300 | −1.25507 | ||||||||
\(924\) | −2.46309 | −0.0810297 | ||||||||
\(925\) | −4.21121 | −0.138464 | ||||||||
\(926\) | 35.1882 | 1.15636 | ||||||||
\(927\) | 3.98778 | 0.130976 | ||||||||
\(928\) | 5.37509 | 0.176446 | ||||||||
\(929\) | −41.7468 | −1.36967 | −0.684834 | − | 0.728699i | \(-0.740125\pi\) | ||||
−0.684834 | + | 0.728699i | \(0.740125\pi\) | |||||||
\(930\) | 4.47377 | 0.146701 | ||||||||
\(931\) | −20.0292 | −0.656431 | ||||||||
\(932\) | 7.55202 | 0.247375 | ||||||||
\(933\) | −28.3355 | −0.927664 | ||||||||
\(934\) | −14.8182 | −0.484868 | ||||||||
\(935\) | −13.2114 | −0.432059 | ||||||||
\(936\) | 24.2531 | 0.792739 | ||||||||
\(937\) | −11.5755 | −0.378156 | −0.189078 | − | 0.981962i | \(-0.560550\pi\) | ||||
−0.189078 | + | 0.981962i | \(0.560550\pi\) | |||||||
\(938\) | −19.9654 | −0.651892 | ||||||||
\(939\) | −25.5957 | −0.835284 | ||||||||
\(940\) | 23.4818 | 0.765891 | ||||||||
\(941\) | −13.7623 | −0.448639 | −0.224320 | − | 0.974516i | \(-0.572016\pi\) | ||||
−0.224320 | + | 0.974516i | \(0.572016\pi\) | |||||||
\(942\) | 13.8247 | 0.450434 | ||||||||
\(943\) | 11.8849 | 0.387026 | ||||||||
\(944\) | 2.34881 | 0.0764471 | ||||||||
\(945\) | −27.2074 | −0.885056 | ||||||||
\(946\) | −7.63893 | −0.248363 | ||||||||
\(947\) | 45.1759 | 1.46802 | 0.734010 | − | 0.679139i | \(-0.237647\pi\) | ||||
0.734010 | + | 0.679139i | \(0.237647\pi\) | |||||||
\(948\) | −9.30112 | −0.302086 | ||||||||
\(949\) | 15.2876 | 0.496257 | ||||||||
\(950\) | −30.8626 | −1.00131 | ||||||||
\(951\) | −38.4976 | −1.24837 | ||||||||
\(952\) | 10.6567 | 0.345387 | ||||||||
\(953\) | −25.3947 | −0.822616 | −0.411308 | − | 0.911497i | \(-0.634928\pi\) | ||||
−0.411308 | + | 0.911497i | \(0.634928\pi\) | |||||||
\(954\) | −11.9195 | −0.385909 | ||||||||
\(955\) | 4.57677 | 0.148101 | ||||||||
\(956\) | 9.05953 | 0.293006 | ||||||||
\(957\) | 1.54507 | 0.0499451 | ||||||||
\(958\) | 9.78863 | 0.316256 | ||||||||
\(959\) | 12.8224 | 0.414056 | ||||||||
\(960\) | −24.4943 | −0.790552 | ||||||||
\(961\) | −29.6432 | −0.956231 | ||||||||
\(962\) | −2.25669 | −0.0727585 | ||||||||
\(963\) | 16.7951 | 0.541213 | ||||||||
\(964\) | 28.6963 | 0.924244 | ||||||||
\(965\) | −3.89856 | −0.125499 | ||||||||
\(966\) | 7.99607 | 0.257269 | ||||||||
\(967\) | −15.3953 | −0.495078 | −0.247539 | − | 0.968878i | \(-0.579622\pi\) | ||||
−0.247539 | + | 0.968878i | \(0.579622\pi\) | |||||||
\(968\) | −26.5312 | −0.852745 | ||||||||
\(969\) | 11.7161 | 0.376376 | ||||||||
\(970\) | 33.2084 | 1.06626 | ||||||||
\(971\) | −37.9457 | −1.21773 | −0.608867 | − | 0.793272i | \(-0.708376\pi\) | ||||
−0.608867 | + | 0.793272i | \(0.708376\pi\) | |||||||
\(972\) | 17.0657 | 0.547383 | ||||||||
\(973\) | 7.04979 | 0.226006 | ||||||||
\(974\) | 24.4238 | 0.782590 | ||||||||
\(975\) | 45.5008 | 1.45719 | ||||||||
\(976\) | 1.77902 | 0.0569451 | ||||||||
\(977\) | −29.0856 | −0.930532 | −0.465266 | − | 0.885171i | \(-0.654041\pi\) | ||||
−0.465266 | + | 0.885171i | \(0.654041\pi\) | |||||||
\(978\) | −10.7880 | −0.344961 | ||||||||
\(979\) | 0.440158 | 0.0140675 | ||||||||
\(980\) | 20.9503 | 0.669232 | ||||||||
\(981\) | 20.3676 | 0.650289 | ||||||||
\(982\) | 17.2957 | 0.551927 | ||||||||
\(983\) | −1.00000 | −0.0318950 | ||||||||
\(984\) | 7.17060 | 0.228590 | ||||||||
\(985\) | −68.2907 | −2.17592 | ||||||||
\(986\) | −2.41859 | −0.0770235 | ||||||||
\(987\) | −8.91939 | −0.283907 | ||||||||
\(988\) | 21.6487 | 0.688735 | ||||||||
\(989\) | −32.4611 | −1.03220 | ||||||||
\(990\) | 8.10282 | 0.257525 | ||||||||
\(991\) | 29.2932 | 0.930529 | 0.465264 | − | 0.885172i | \(-0.345959\pi\) | ||||
0.465264 | + | 0.885172i | \(0.345959\pi\) | |||||||
\(992\) | −6.31032 | −0.200353 | ||||||||
\(993\) | −28.7436 | −0.912151 | ||||||||
\(994\) | 10.2757 | 0.325925 | ||||||||
\(995\) | −8.35449 | −0.264855 | ||||||||
\(996\) | −6.42013 | −0.203429 | ||||||||
\(997\) | 38.5516 | 1.22094 | 0.610471 | − | 0.792038i | \(-0.290980\pi\) | ||||
0.610471 | + | 0.792038i | \(0.290980\pi\) | |||||||
\(998\) | −33.2030 | −1.05102 | ||||||||
\(999\) | −2.68471 | −0.0849404 |
(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 | 983.2.a.a.1.11 | ✓ | 28 | |
3.2 | odd | 2 | 8847.2.a.b.1.18 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.2.a.a.1.11 | ✓ | 28 | 1.1 | even | 1 | trivial | |
8847.2.a.b.1.18 | 28 | 3.2 | odd | 2 |