Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + \cdots - 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.302778\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.302778 | −0.214097 | −0.107048 | − | 0.994254i | \(-0.534140\pi\) | ||||
−0.107048 | + | 0.994254i | \(0.534140\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.90833 | −0.954163 | ||||||||
\(5\) | 3.34986 | 1.49810 | 0.749051 | − | 0.662512i | \(-0.230510\pi\) | ||||
0.749051 | + | 0.662512i | \(0.230510\pi\) | |||||||
\(6\) | −0.302778 | −0.123609 | ||||||||
\(7\) | 0.428154 | 0.161827 | 0.0809134 | − | 0.996721i | \(-0.474216\pi\) | ||||
0.0809134 | + | 0.996721i | \(0.474216\pi\) | |||||||
\(8\) | 1.18336 | 0.418379 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.01426 | −0.320739 | ||||||||
\(11\) | 4.01497 | 1.21056 | 0.605279 | − | 0.796013i | \(-0.293061\pi\) | ||||
0.605279 | + | 0.796013i | \(0.293061\pi\) | |||||||
\(12\) | −1.90833 | −0.550886 | ||||||||
\(13\) | 5.31187 | 1.47325 | 0.736624 | − | 0.676302i | \(-0.236419\pi\) | ||||
0.736624 | + | 0.676302i | \(0.236419\pi\) | |||||||
\(14\) | −0.129636 | −0.0346466 | ||||||||
\(15\) | 3.34986 | 0.864930 | ||||||||
\(16\) | 3.45836 | 0.864589 | ||||||||
\(17\) | 1.05018 | 0.254707 | 0.127354 | − | 0.991857i | \(-0.459352\pi\) | ||||
0.127354 | + | 0.991857i | \(0.459352\pi\) | |||||||
\(18\) | −0.302778 | −0.0713655 | ||||||||
\(19\) | −3.12533 | −0.717000 | −0.358500 | − | 0.933530i | \(-0.616712\pi\) | ||||
−0.358500 | + | 0.933530i | \(0.616712\pi\) | |||||||
\(20\) | −6.39262 | −1.42943 | ||||||||
\(21\) | 0.428154 | 0.0934308 | ||||||||
\(22\) | −1.21565 | −0.259176 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.18336 | 0.241552 | ||||||||
\(25\) | 6.22156 | 1.24431 | ||||||||
\(26\) | −1.60832 | −0.315418 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.817056 | −0.154409 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −1.01426 | −0.185179 | ||||||||
\(31\) | −10.3617 | −1.86102 | −0.930508 | − | 0.366271i | \(-0.880634\pi\) | ||||
−0.930508 | + | 0.366271i | \(0.880634\pi\) | |||||||
\(32\) | −3.41383 | −0.603485 | ||||||||
\(33\) | 4.01497 | 0.698916 | ||||||||
\(34\) | −0.317973 | −0.0545319 | ||||||||
\(35\) | 1.43425 | 0.242433 | ||||||||
\(36\) | −1.90833 | −0.318054 | ||||||||
\(37\) | −10.3543 | −1.70224 | −0.851119 | − | 0.524972i | \(-0.824076\pi\) | ||||
−0.851119 | + | 0.524972i | \(0.824076\pi\) | |||||||
\(38\) | 0.946281 | 0.153507 | ||||||||
\(39\) | 5.31187 | 0.850581 | ||||||||
\(40\) | 3.96408 | 0.626775 | ||||||||
\(41\) | 7.14375 | 1.11567 | 0.557833 | − | 0.829953i | \(-0.311633\pi\) | ||||
0.557833 | + | 0.829953i | \(0.311633\pi\) | |||||||
\(42\) | −0.129636 | −0.0200032 | ||||||||
\(43\) | 3.22443 | 0.491721 | 0.245861 | − | 0.969305i | \(-0.420929\pi\) | ||||
0.245861 | + | 0.969305i | \(0.420929\pi\) | |||||||
\(44\) | −7.66187 | −1.15507 | ||||||||
\(45\) | 3.34986 | 0.499368 | ||||||||
\(46\) | −0.302778 | −0.0446422 | ||||||||
\(47\) | 10.8487 | 1.58244 | 0.791222 | − | 0.611529i | \(-0.209445\pi\) | ||||
0.791222 | + | 0.611529i | \(0.209445\pi\) | |||||||
\(48\) | 3.45836 | 0.499171 | ||||||||
\(49\) | −6.81668 | −0.973812 | ||||||||
\(50\) | −1.88375 | −0.266403 | ||||||||
\(51\) | 1.05018 | 0.147055 | ||||||||
\(52\) | −10.1368 | −1.40572 | ||||||||
\(53\) | −9.70877 | −1.33360 | −0.666801 | − | 0.745236i | \(-0.732337\pi\) | ||||
−0.666801 | + | 0.745236i | \(0.732337\pi\) | |||||||
\(54\) | −0.302778 | −0.0412029 | ||||||||
\(55\) | 13.4496 | 1.81354 | ||||||||
\(56\) | 0.506658 | 0.0677050 | ||||||||
\(57\) | −3.12533 | −0.413960 | ||||||||
\(58\) | −0.302778 | −0.0397567 | ||||||||
\(59\) | −4.68976 | −0.610555 | −0.305277 | − | 0.952263i | \(-0.598749\pi\) | ||||
−0.305277 | + | 0.952263i | \(0.598749\pi\) | |||||||
\(60\) | −6.39262 | −0.825284 | ||||||||
\(61\) | −4.20131 | −0.537923 | −0.268962 | − | 0.963151i | \(-0.586680\pi\) | ||||
−0.268962 | + | 0.963151i | \(0.586680\pi\) | |||||||
\(62\) | 3.13730 | 0.398437 | ||||||||
\(63\) | 0.428154 | 0.0539423 | ||||||||
\(64\) | −5.88308 | −0.735385 | ||||||||
\(65\) | 17.7940 | 2.20708 | ||||||||
\(66\) | −1.21565 | −0.149636 | ||||||||
\(67\) | −3.89854 | −0.476283 | −0.238141 | − | 0.971231i | \(-0.576538\pi\) | ||||
−0.238141 | + | 0.971231i | \(0.576538\pi\) | |||||||
\(68\) | −2.00409 | −0.243032 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −0.434261 | −0.0519041 | ||||||||
\(71\) | 13.7035 | 1.62630 | 0.813152 | − | 0.582052i | \(-0.197750\pi\) | ||||
0.813152 | + | 0.582052i | \(0.197750\pi\) | |||||||
\(72\) | 1.18336 | 0.139460 | ||||||||
\(73\) | 8.38069 | 0.980886 | 0.490443 | − | 0.871473i | \(-0.336835\pi\) | ||||
0.490443 | + | 0.871473i | \(0.336835\pi\) | |||||||
\(74\) | 3.13506 | 0.364443 | ||||||||
\(75\) | 6.22156 | 0.718403 | ||||||||
\(76\) | 5.96414 | 0.684134 | ||||||||
\(77\) | 1.71902 | 0.195901 | ||||||||
\(78\) | −1.60832 | −0.182106 | ||||||||
\(79\) | 8.80707 | 0.990873 | 0.495437 | − | 0.868644i | \(-0.335008\pi\) | ||||
0.495437 | + | 0.868644i | \(0.335008\pi\) | |||||||
\(80\) | 11.5850 | 1.29524 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.16297 | −0.238860 | ||||||||
\(83\) | 7.18985 | 0.789189 | 0.394594 | − | 0.918855i | \(-0.370885\pi\) | ||||
0.394594 | + | 0.918855i | \(0.370885\pi\) | |||||||
\(84\) | −0.817056 | −0.0891482 | ||||||||
\(85\) | 3.51797 | 0.381577 | ||||||||
\(86\) | −0.976287 | −0.105276 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 4.75114 | 0.506473 | ||||||||
\(89\) | −10.2900 | −1.09074 | −0.545368 | − | 0.838197i | \(-0.683610\pi\) | ||||
−0.545368 | + | 0.838197i | \(0.683610\pi\) | |||||||
\(90\) | −1.01426 | −0.106913 | ||||||||
\(91\) | 2.27430 | 0.238411 | ||||||||
\(92\) | −1.90833 | −0.198957 | ||||||||
\(93\) | −10.3617 | −1.07446 | ||||||||
\(94\) | −3.28475 | −0.338796 | ||||||||
\(95\) | −10.4694 | −1.07414 | ||||||||
\(96\) | −3.41383 | −0.348422 | ||||||||
\(97\) | −3.31072 | −0.336153 | −0.168076 | − | 0.985774i | \(-0.553756\pi\) | ||||
−0.168076 | + | 0.985774i | \(0.553756\pi\) | |||||||
\(98\) | 2.06394 | 0.208490 | ||||||||
\(99\) | 4.01497 | 0.403520 | ||||||||
\(100\) | −11.8728 | −1.18728 | ||||||||
\(101\) | −4.08415 | −0.406388 | −0.203194 | − | 0.979138i | \(-0.565132\pi\) | ||||
−0.203194 | + | 0.979138i | \(0.565132\pi\) | |||||||
\(102\) | −0.317973 | −0.0314840 | ||||||||
\(103\) | 14.4370 | 1.42252 | 0.711260 | − | 0.702929i | \(-0.248125\pi\) | ||||
0.711260 | + | 0.702929i | \(0.248125\pi\) | |||||||
\(104\) | 6.28584 | 0.616377 | ||||||||
\(105\) | 1.43425 | 0.139969 | ||||||||
\(106\) | 2.93960 | 0.285520 | ||||||||
\(107\) | 6.88495 | 0.665593 | 0.332796 | − | 0.942999i | \(-0.392008\pi\) | ||||
0.332796 | + | 0.942999i | \(0.392008\pi\) | |||||||
\(108\) | −1.90833 | −0.183629 | ||||||||
\(109\) | −15.2270 | −1.45848 | −0.729240 | − | 0.684257i | \(-0.760126\pi\) | ||||
−0.729240 | + | 0.684257i | \(0.760126\pi\) | |||||||
\(110\) | −4.07224 | −0.388273 | ||||||||
\(111\) | −10.3543 | −0.982788 | ||||||||
\(112\) | 1.48071 | 0.139914 | ||||||||
\(113\) | −5.66251 | −0.532684 | −0.266342 | − | 0.963879i | \(-0.585815\pi\) | ||||
−0.266342 | + | 0.963879i | \(0.585815\pi\) | |||||||
\(114\) | 0.946281 | 0.0886274 | ||||||||
\(115\) | 3.34986 | 0.312376 | ||||||||
\(116\) | −1.90833 | −0.177184 | ||||||||
\(117\) | 5.31187 | 0.491083 | ||||||||
\(118\) | 1.41996 | 0.130718 | ||||||||
\(119\) | 0.449640 | 0.0412184 | ||||||||
\(120\) | 3.96408 | 0.361869 | ||||||||
\(121\) | 5.11998 | 0.465453 | ||||||||
\(122\) | 1.27207 | 0.115168 | ||||||||
\(123\) | 7.14375 | 0.644130 | ||||||||
\(124\) | 19.7735 | 1.77571 | ||||||||
\(125\) | 4.09204 | 0.366003 | ||||||||
\(126\) | −0.129636 | −0.0115489 | ||||||||
\(127\) | 6.52259 | 0.578786 | 0.289393 | − | 0.957210i | \(-0.406546\pi\) | ||||
0.289393 | + | 0.957210i | \(0.406546\pi\) | |||||||
\(128\) | 8.60892 | 0.760928 | ||||||||
\(129\) | 3.22443 | 0.283895 | ||||||||
\(130\) | −5.38765 | −0.472528 | ||||||||
\(131\) | −5.30306 | −0.463331 | −0.231665 | − | 0.972796i | \(-0.574417\pi\) | ||||
−0.231665 | + | 0.972796i | \(0.574417\pi\) | |||||||
\(132\) | −7.66187 | −0.666880 | ||||||||
\(133\) | −1.33812 | −0.116030 | ||||||||
\(134\) | 1.18039 | 0.101970 | ||||||||
\(135\) | 3.34986 | 0.288310 | ||||||||
\(136\) | 1.24274 | 0.106564 | ||||||||
\(137\) | −13.1674 | −1.12496 | −0.562482 | − | 0.826810i | \(-0.690153\pi\) | ||||
−0.562482 | + | 0.826810i | \(0.690153\pi\) | |||||||
\(138\) | −0.302778 | −0.0257742 | ||||||||
\(139\) | −2.28705 | −0.193985 | −0.0969925 | − | 0.995285i | \(-0.530922\pi\) | ||||
−0.0969925 | + | 0.995285i | \(0.530922\pi\) | |||||||
\(140\) | −2.73702 | −0.231321 | ||||||||
\(141\) | 10.8487 | 0.913624 | ||||||||
\(142\) | −4.14911 | −0.348186 | ||||||||
\(143\) | 21.3270 | 1.78345 | ||||||||
\(144\) | 3.45836 | 0.288196 | ||||||||
\(145\) | 3.34986 | 0.278191 | ||||||||
\(146\) | −2.53749 | −0.210004 | ||||||||
\(147\) | −6.81668 | −0.562231 | ||||||||
\(148\) | 19.7594 | 1.62421 | ||||||||
\(149\) | −11.9584 | −0.979672 | −0.489836 | − | 0.871815i | \(-0.662943\pi\) | ||||
−0.489836 | + | 0.871815i | \(0.662943\pi\) | |||||||
\(150\) | −1.88375 | −0.153808 | ||||||||
\(151\) | 24.0005 | 1.95313 | 0.976567 | − | 0.215213i | \(-0.0690446\pi\) | ||||
0.976567 | + | 0.215213i | \(0.0690446\pi\) | |||||||
\(152\) | −3.69838 | −0.299978 | ||||||||
\(153\) | 1.05018 | 0.0849024 | ||||||||
\(154\) | −0.520483 | −0.0419417 | ||||||||
\(155\) | −34.7102 | −2.78799 | ||||||||
\(156\) | −10.1368 | −0.811592 | ||||||||
\(157\) | 2.54328 | 0.202976 | 0.101488 | − | 0.994837i | \(-0.467640\pi\) | ||||
0.101488 | + | 0.994837i | \(0.467640\pi\) | |||||||
\(158\) | −2.66659 | −0.212143 | ||||||||
\(159\) | −9.70877 | −0.769955 | ||||||||
\(160\) | −11.4358 | −0.904082 | ||||||||
\(161\) | 0.428154 | 0.0337432 | ||||||||
\(162\) | −0.302778 | −0.0237885 | ||||||||
\(163\) | −20.4369 | −1.60074 | −0.800372 | − | 0.599504i | \(-0.795365\pi\) | ||||
−0.800372 | + | 0.599504i | \(0.795365\pi\) | |||||||
\(164\) | −13.6326 | −1.06453 | ||||||||
\(165\) | 13.4496 | 1.04705 | ||||||||
\(166\) | −2.17693 | −0.168963 | ||||||||
\(167\) | 12.3398 | 0.954885 | 0.477443 | − | 0.878663i | \(-0.341564\pi\) | ||||
0.477443 | + | 0.878663i | \(0.341564\pi\) | |||||||
\(168\) | 0.506658 | 0.0390895 | ||||||||
\(169\) | 15.2160 | 1.17046 | ||||||||
\(170\) | −1.06516 | −0.0816944 | ||||||||
\(171\) | −3.12533 | −0.239000 | ||||||||
\(172\) | −6.15326 | −0.469182 | ||||||||
\(173\) | −11.3271 | −0.861186 | −0.430593 | − | 0.902546i | \(-0.641696\pi\) | ||||
−0.430593 | + | 0.902546i | \(0.641696\pi\) | |||||||
\(174\) | −0.302778 | −0.0229536 | ||||||||
\(175\) | 2.66378 | 0.201363 | ||||||||
\(176\) | 13.8852 | 1.04664 | ||||||||
\(177\) | −4.68976 | −0.352504 | ||||||||
\(178\) | 3.11558 | 0.233523 | ||||||||
\(179\) | 12.6720 | 0.947153 | 0.473577 | − | 0.880753i | \(-0.342963\pi\) | ||||
0.473577 | + | 0.880753i | \(0.342963\pi\) | |||||||
\(180\) | −6.39262 | −0.476478 | ||||||||
\(181\) | 21.2565 | 1.57998 | 0.789992 | − | 0.613117i | \(-0.210084\pi\) | ||||
0.789992 | + | 0.613117i | \(0.210084\pi\) | |||||||
\(182\) | −0.688608 | −0.0510430 | ||||||||
\(183\) | −4.20131 | −0.310570 | ||||||||
\(184\) | 1.18336 | 0.0872382 | ||||||||
\(185\) | −34.6855 | −2.55013 | ||||||||
\(186\) | 3.13730 | 0.230038 | ||||||||
\(187\) | 4.21646 | 0.308338 | ||||||||
\(188\) | −20.7028 | −1.50991 | ||||||||
\(189\) | 0.428154 | 0.0311436 | ||||||||
\(190\) | 3.16991 | 0.229969 | ||||||||
\(191\) | −11.9418 | −0.864078 | −0.432039 | − | 0.901855i | \(-0.642206\pi\) | ||||
−0.432039 | + | 0.901855i | \(0.642206\pi\) | |||||||
\(192\) | −5.88308 | −0.424575 | ||||||||
\(193\) | 9.05494 | 0.651789 | 0.325894 | − | 0.945406i | \(-0.394335\pi\) | ||||
0.325894 | + | 0.945406i | \(0.394335\pi\) | |||||||
\(194\) | 1.00241 | 0.0719692 | ||||||||
\(195\) | 17.7940 | 1.27426 | ||||||||
\(196\) | 13.0085 | 0.929175 | ||||||||
\(197\) | 6.84424 | 0.487632 | 0.243816 | − | 0.969822i | \(-0.421601\pi\) | ||||
0.243816 | + | 0.969822i | \(0.421601\pi\) | |||||||
\(198\) | −1.21565 | −0.0863922 | ||||||||
\(199\) | 12.4741 | 0.884269 | 0.442134 | − | 0.896949i | \(-0.354221\pi\) | ||||
0.442134 | + | 0.896949i | \(0.354221\pi\) | |||||||
\(200\) | 7.36232 | 0.520594 | ||||||||
\(201\) | −3.89854 | −0.274982 | ||||||||
\(202\) | 1.23659 | 0.0870063 | ||||||||
\(203\) | 0.428154 | 0.0300505 | ||||||||
\(204\) | −2.00409 | −0.140315 | ||||||||
\(205\) | 23.9305 | 1.67138 | ||||||||
\(206\) | −4.37121 | −0.304556 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 18.3704 | 1.27375 | ||||||||
\(209\) | −12.5481 | −0.867970 | ||||||||
\(210\) | −0.434261 | −0.0299669 | ||||||||
\(211\) | −16.1997 | −1.11524 | −0.557618 | − | 0.830098i | \(-0.688285\pi\) | ||||
−0.557618 | + | 0.830098i | \(0.688285\pi\) | |||||||
\(212\) | 18.5275 | 1.27247 | ||||||||
\(213\) | 13.7035 | 0.938947 | ||||||||
\(214\) | −2.08461 | −0.142501 | ||||||||
\(215\) | 10.8014 | 0.736649 | ||||||||
\(216\) | 1.18336 | 0.0805172 | ||||||||
\(217\) | −4.43640 | −0.301162 | ||||||||
\(218\) | 4.61040 | 0.312256 | ||||||||
\(219\) | 8.38069 | 0.566315 | ||||||||
\(220\) | −25.6662 | −1.73041 | ||||||||
\(221\) | 5.57845 | 0.375247 | ||||||||
\(222\) | 3.13506 | 0.210412 | ||||||||
\(223\) | −4.70284 | −0.314926 | −0.157463 | − | 0.987525i | \(-0.550331\pi\) | ||||
−0.157463 | + | 0.987525i | \(0.550331\pi\) | |||||||
\(224\) | −1.46164 | −0.0976601 | ||||||||
\(225\) | 6.22156 | 0.414770 | ||||||||
\(226\) | 1.71448 | 0.114046 | ||||||||
\(227\) | −27.4304 | −1.82062 | −0.910309 | − | 0.413928i | \(-0.864156\pi\) | ||||
−0.910309 | + | 0.413928i | \(0.864156\pi\) | |||||||
\(228\) | 5.96414 | 0.394985 | ||||||||
\(229\) | 0.510879 | 0.0337598 | 0.0168799 | − | 0.999858i | \(-0.494627\pi\) | ||||
0.0168799 | + | 0.999858i | \(0.494627\pi\) | |||||||
\(230\) | −1.01426 | −0.0668786 | ||||||||
\(231\) | 1.71902 | 0.113103 | ||||||||
\(232\) | 1.18336 | 0.0776911 | ||||||||
\(233\) | 11.3044 | 0.740577 | 0.370289 | − | 0.928917i | \(-0.379259\pi\) | ||||
0.370289 | + | 0.928917i | \(0.379259\pi\) | |||||||
\(234\) | −1.60832 | −0.105139 | ||||||||
\(235\) | 36.3416 | 2.37066 | ||||||||
\(236\) | 8.94959 | 0.582569 | ||||||||
\(237\) | 8.80707 | 0.572081 | ||||||||
\(238\) | −0.136141 | −0.00882473 | ||||||||
\(239\) | −10.3539 | −0.669737 | −0.334868 | − | 0.942265i | \(-0.608692\pi\) | ||||
−0.334868 | + | 0.942265i | \(0.608692\pi\) | |||||||
\(240\) | 11.5850 | 0.747809 | ||||||||
\(241\) | −3.01550 | −0.194246 | −0.0971228 | − | 0.995272i | \(-0.530964\pi\) | ||||
−0.0971228 | + | 0.995272i | \(0.530964\pi\) | |||||||
\(242\) | −1.55022 | −0.0996518 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 8.01748 | 0.513266 | ||||||||
\(245\) | −22.8349 | −1.45887 | ||||||||
\(246\) | −2.16297 | −0.137906 | ||||||||
\(247\) | −16.6014 | −1.05632 | ||||||||
\(248\) | −12.2616 | −0.778611 | ||||||||
\(249\) | 7.18985 | 0.455638 | ||||||||
\(250\) | −1.23898 | −0.0783601 | ||||||||
\(251\) | 16.0714 | 1.01442 | 0.507208 | − | 0.861823i | \(-0.330677\pi\) | ||||
0.507208 | + | 0.861823i | \(0.330677\pi\) | |||||||
\(252\) | −0.817056 | −0.0514697 | ||||||||
\(253\) | 4.01497 | 0.252419 | ||||||||
\(254\) | −1.97490 | −0.123916 | ||||||||
\(255\) | 3.51797 | 0.220304 | ||||||||
\(256\) | 9.15957 | 0.572473 | ||||||||
\(257\) | 19.4598 | 1.21387 | 0.606935 | − | 0.794752i | \(-0.292399\pi\) | ||||
0.606935 | + | 0.794752i | \(0.292399\pi\) | |||||||
\(258\) | −0.976287 | −0.0607810 | ||||||||
\(259\) | −4.43324 | −0.275468 | ||||||||
\(260\) | −33.9568 | −2.10591 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 1.60565 | 0.0991975 | ||||||||
\(263\) | 28.1751 | 1.73735 | 0.868675 | − | 0.495382i | \(-0.164972\pi\) | ||||
0.868675 | + | 0.495382i | \(0.164972\pi\) | |||||||
\(264\) | 4.75114 | 0.292412 | ||||||||
\(265\) | −32.5230 | −1.99787 | ||||||||
\(266\) | 0.405154 | 0.0248416 | ||||||||
\(267\) | −10.2900 | −0.629737 | ||||||||
\(268\) | 7.43969 | 0.454451 | ||||||||
\(269\) | −12.0815 | −0.736623 | −0.368312 | − | 0.929702i | \(-0.620064\pi\) | ||||
−0.368312 | + | 0.929702i | \(0.620064\pi\) | |||||||
\(270\) | −1.01426 | −0.0617262 | ||||||||
\(271\) | −29.4534 | −1.78917 | −0.894583 | − | 0.446903i | \(-0.852527\pi\) | ||||
−0.894583 | + | 0.446903i | \(0.852527\pi\) | |||||||
\(272\) | 3.63191 | 0.220217 | ||||||||
\(273\) | 2.27430 | 0.137647 | ||||||||
\(274\) | 3.98679 | 0.240851 | ||||||||
\(275\) | 24.9794 | 1.50631 | ||||||||
\(276\) | −1.90833 | −0.114868 | ||||||||
\(277\) | 10.2385 | 0.615172 | 0.307586 | − | 0.951520i | \(-0.400479\pi\) | ||||
0.307586 | + | 0.951520i | \(0.400479\pi\) | |||||||
\(278\) | 0.692469 | 0.0415315 | ||||||||
\(279\) | −10.3617 | −0.620339 | ||||||||
\(280\) | 1.69723 | 0.101429 | ||||||||
\(281\) | −16.2447 | −0.969077 | −0.484538 | − | 0.874770i | \(-0.661012\pi\) | ||||
−0.484538 | + | 0.874770i | \(0.661012\pi\) | |||||||
\(282\) | −3.28475 | −0.195604 | ||||||||
\(283\) | 18.9453 | 1.12618 | 0.563091 | − | 0.826395i | \(-0.309612\pi\) | ||||
0.563091 | + | 0.826395i | \(0.309612\pi\) | |||||||
\(284\) | −26.1507 | −1.55176 | ||||||||
\(285\) | −10.4694 | −0.620154 | ||||||||
\(286\) | −6.45736 | −0.381831 | ||||||||
\(287\) | 3.05862 | 0.180545 | ||||||||
\(288\) | −3.41383 | −0.201162 | ||||||||
\(289\) | −15.8971 | −0.935124 | ||||||||
\(290\) | −1.01426 | −0.0595597 | ||||||||
\(291\) | −3.31072 | −0.194078 | ||||||||
\(292\) | −15.9931 | −0.935924 | ||||||||
\(293\) | −12.8758 | −0.752213 | −0.376106 | − | 0.926577i | \(-0.622737\pi\) | ||||
−0.376106 | + | 0.926577i | \(0.622737\pi\) | |||||||
\(294\) | 2.06394 | 0.120372 | ||||||||
\(295\) | −15.7100 | −0.914674 | ||||||||
\(296\) | −12.2528 | −0.712182 | ||||||||
\(297\) | 4.01497 | 0.232972 | ||||||||
\(298\) | 3.62075 | 0.209744 | ||||||||
\(299\) | 5.31187 | 0.307194 | ||||||||
\(300\) | −11.8728 | −0.685474 | ||||||||
\(301\) | 1.38055 | 0.0795737 | ||||||||
\(302\) | −7.26683 | −0.418159 | ||||||||
\(303\) | −4.08415 | −0.234628 | ||||||||
\(304\) | −10.8085 | −0.619910 | ||||||||
\(305\) | −14.0738 | −0.805864 | ||||||||
\(306\) | −0.317973 | −0.0181773 | ||||||||
\(307\) | −19.1819 | −1.09477 | −0.547385 | − | 0.836881i | \(-0.684377\pi\) | ||||
−0.547385 | + | 0.836881i | \(0.684377\pi\) | |||||||
\(308\) | −3.28046 | −0.186921 | ||||||||
\(309\) | 14.4370 | 0.821292 | ||||||||
\(310\) | 10.5095 | 0.596900 | ||||||||
\(311\) | −25.1290 | −1.42493 | −0.712466 | − | 0.701707i | \(-0.752422\pi\) | ||||
−0.712466 | + | 0.701707i | \(0.752422\pi\) | |||||||
\(312\) | 6.28584 | 0.355866 | ||||||||
\(313\) | −1.00877 | −0.0570190 | −0.0285095 | − | 0.999594i | \(-0.509076\pi\) | ||||
−0.0285095 | + | 0.999594i | \(0.509076\pi\) | |||||||
\(314\) | −0.770051 | −0.0434565 | ||||||||
\(315\) | 1.43425 | 0.0808111 | ||||||||
\(316\) | −16.8068 | −0.945454 | ||||||||
\(317\) | −3.08943 | −0.173520 | −0.0867599 | − | 0.996229i | \(-0.527651\pi\) | ||||
−0.0867599 | + | 0.996229i | \(0.527651\pi\) | |||||||
\(318\) | 2.93960 | 0.164845 | ||||||||
\(319\) | 4.01497 | 0.224795 | ||||||||
\(320\) | −19.7075 | −1.10168 | ||||||||
\(321\) | 6.88495 | 0.384280 | ||||||||
\(322\) | −0.129636 | −0.00722431 | ||||||||
\(323\) | −3.28217 | −0.182625 | ||||||||
\(324\) | −1.90833 | −0.106018 | ||||||||
\(325\) | 33.0481 | 1.83318 | ||||||||
\(326\) | 6.18786 | 0.342714 | ||||||||
\(327\) | −15.2270 | −0.842054 | ||||||||
\(328\) | 8.45359 | 0.466772 | ||||||||
\(329\) | 4.64490 | 0.256082 | ||||||||
\(330\) | −4.07224 | −0.224169 | ||||||||
\(331\) | 14.8847 | 0.818139 | 0.409069 | − | 0.912503i | \(-0.365853\pi\) | ||||
0.409069 | + | 0.912503i | \(0.365853\pi\) | |||||||
\(332\) | −13.7206 | −0.753015 | ||||||||
\(333\) | −10.3543 | −0.567413 | ||||||||
\(334\) | −3.73623 | −0.204438 | ||||||||
\(335\) | −13.0596 | −0.713520 | ||||||||
\(336\) | 1.48071 | 0.0807792 | ||||||||
\(337\) | 23.9721 | 1.30584 | 0.652921 | − | 0.757426i | \(-0.273543\pi\) | ||||
0.652921 | + | 0.757426i | \(0.273543\pi\) | |||||||
\(338\) | −4.60708 | −0.250592 | ||||||||
\(339\) | −5.66251 | −0.307545 | ||||||||
\(340\) | −6.71343 | −0.364087 | ||||||||
\(341\) | −41.6019 | −2.25287 | ||||||||
\(342\) | 0.946281 | 0.0511690 | ||||||||
\(343\) | −5.91566 | −0.319416 | ||||||||
\(344\) | 3.81565 | 0.205726 | ||||||||
\(345\) | 3.34986 | 0.180350 | ||||||||
\(346\) | 3.42961 | 0.184377 | ||||||||
\(347\) | −29.4423 | −1.58055 | −0.790273 | − | 0.612755i | \(-0.790061\pi\) | ||||
−0.790273 | + | 0.612755i | \(0.790061\pi\) | |||||||
\(348\) | −1.90833 | −0.102297 | ||||||||
\(349\) | −4.84185 | −0.259178 | −0.129589 | − | 0.991568i | \(-0.541366\pi\) | ||||
−0.129589 | + | 0.991568i | \(0.541366\pi\) | |||||||
\(350\) | −0.806535 | −0.0431111 | ||||||||
\(351\) | 5.31187 | 0.283527 | ||||||||
\(352\) | −13.7064 | −0.730554 | ||||||||
\(353\) | 11.1009 | 0.590839 | 0.295420 | − | 0.955368i | \(-0.404541\pi\) | ||||
0.295420 | + | 0.955368i | \(0.404541\pi\) | |||||||
\(354\) | 1.41996 | 0.0754699 | ||||||||
\(355\) | 45.9047 | 2.43637 | ||||||||
\(356\) | 19.6366 | 1.04074 | ||||||||
\(357\) | 0.449640 | 0.0237975 | ||||||||
\(358\) | −3.83682 | −0.202782 | ||||||||
\(359\) | 21.0718 | 1.11213 | 0.556063 | − | 0.831140i | \(-0.312311\pi\) | ||||
0.556063 | + | 0.831140i | \(0.312311\pi\) | |||||||
\(360\) | 3.96408 | 0.208925 | ||||||||
\(361\) | −9.23232 | −0.485912 | ||||||||
\(362\) | −6.43601 | −0.338269 | ||||||||
\(363\) | 5.11998 | 0.268729 | ||||||||
\(364\) | −4.34010 | −0.227483 | ||||||||
\(365\) | 28.0741 | 1.46947 | ||||||||
\(366\) | 1.27207 | 0.0664920 | ||||||||
\(367\) | −31.5820 | −1.64857 | −0.824283 | − | 0.566178i | \(-0.808421\pi\) | ||||
−0.824283 | + | 0.566178i | \(0.808421\pi\) | |||||||
\(368\) | 3.45836 | 0.180279 | ||||||||
\(369\) | 7.14375 | 0.371889 | ||||||||
\(370\) | 10.5020 | 0.545974 | ||||||||
\(371\) | −4.15684 | −0.215813 | ||||||||
\(372\) | 19.7735 | 1.02521 | ||||||||
\(373\) | −6.16681 | −0.319305 | −0.159653 | − | 0.987173i | \(-0.551037\pi\) | ||||
−0.159653 | + | 0.987173i | \(0.551037\pi\) | |||||||
\(374\) | −1.27665 | −0.0660141 | ||||||||
\(375\) | 4.09204 | 0.211312 | ||||||||
\(376\) | 12.8379 | 0.662062 | ||||||||
\(377\) | 5.31187 | 0.273575 | ||||||||
\(378\) | −0.129636 | −0.00666774 | ||||||||
\(379\) | 12.6195 | 0.648219 | 0.324109 | − | 0.946020i | \(-0.394935\pi\) | ||||
0.324109 | + | 0.946020i | \(0.394935\pi\) | |||||||
\(380\) | 19.9790 | 1.02490 | ||||||||
\(381\) | 6.52259 | 0.334163 | ||||||||
\(382\) | 3.61572 | 0.184996 | ||||||||
\(383\) | −5.45898 | −0.278941 | −0.139470 | − | 0.990226i | \(-0.544540\pi\) | ||||
−0.139470 | + | 0.990226i | \(0.544540\pi\) | |||||||
\(384\) | 8.60892 | 0.439322 | ||||||||
\(385\) | 5.75849 | 0.293480 | ||||||||
\(386\) | −2.74164 | −0.139546 | ||||||||
\(387\) | 3.22443 | 0.163907 | ||||||||
\(388\) | 6.31794 | 0.320745 | ||||||||
\(389\) | −17.4154 | −0.882996 | −0.441498 | − | 0.897262i | \(-0.645553\pi\) | ||||
−0.441498 | + | 0.897262i | \(0.645553\pi\) | |||||||
\(390\) | −5.38765 | −0.272814 | ||||||||
\(391\) | 1.05018 | 0.0531101 | ||||||||
\(392\) | −8.06656 | −0.407423 | ||||||||
\(393\) | −5.30306 | −0.267504 | ||||||||
\(394\) | −2.07229 | −0.104400 | ||||||||
\(395\) | 29.5025 | 1.48443 | ||||||||
\(396\) | −7.66187 | −0.385023 | ||||||||
\(397\) | −29.5353 | −1.48234 | −0.741168 | − | 0.671320i | \(-0.765728\pi\) | ||||
−0.741168 | + | 0.671320i | \(0.765728\pi\) | |||||||
\(398\) | −3.77690 | −0.189319 | ||||||||
\(399\) | −1.33812 | −0.0669898 | ||||||||
\(400\) | 21.5164 | 1.07582 | ||||||||
\(401\) | −19.0745 | −0.952537 | −0.476268 | − | 0.879300i | \(-0.658011\pi\) | ||||
−0.476268 | + | 0.879300i | \(0.658011\pi\) | |||||||
\(402\) | 1.18039 | 0.0588727 | ||||||||
\(403\) | −55.0401 | −2.74174 | ||||||||
\(404\) | 7.79389 | 0.387760 | ||||||||
\(405\) | 3.34986 | 0.166456 | ||||||||
\(406\) | −0.129636 | −0.00643371 | ||||||||
\(407\) | −41.5723 | −2.06066 | ||||||||
\(408\) | 1.24274 | 0.0615249 | ||||||||
\(409\) | 33.1090 | 1.63714 | 0.818568 | − | 0.574410i | \(-0.194768\pi\) | ||||
0.818568 | + | 0.574410i | \(0.194768\pi\) | |||||||
\(410\) | −7.24565 | −0.357837 | ||||||||
\(411\) | −13.1674 | −0.649498 | ||||||||
\(412\) | −27.5505 | −1.35731 | ||||||||
\(413\) | −2.00794 | −0.0988042 | ||||||||
\(414\) | −0.302778 | −0.0148807 | ||||||||
\(415\) | 24.0850 | 1.18229 | ||||||||
\(416\) | −18.1338 | −0.889084 | ||||||||
\(417\) | −2.28705 | −0.111997 | ||||||||
\(418\) | 3.79929 | 0.185829 | ||||||||
\(419\) | 17.5578 | 0.857754 | 0.428877 | − | 0.903363i | \(-0.358909\pi\) | ||||
0.428877 | + | 0.903363i | \(0.358909\pi\) | |||||||
\(420\) | −2.73702 | −0.133553 | ||||||||
\(421\) | −4.35212 | −0.212109 | −0.106055 | − | 0.994360i | \(-0.533822\pi\) | ||||
−0.106055 | + | 0.994360i | \(0.533822\pi\) | |||||||
\(422\) | 4.90493 | 0.238768 | ||||||||
\(423\) | 10.8487 | 0.527481 | ||||||||
\(424\) | −11.4889 | −0.557952 | ||||||||
\(425\) | 6.53378 | 0.316935 | ||||||||
\(426\) | −4.14911 | −0.201025 | ||||||||
\(427\) | −1.79881 | −0.0870504 | ||||||||
\(428\) | −13.1387 | −0.635084 | ||||||||
\(429\) | 21.3270 | 1.02968 | ||||||||
\(430\) | −3.27043 | −0.157714 | ||||||||
\(431\) | 0.733390 | 0.0353261 | 0.0176631 | − | 0.999844i | \(-0.494377\pi\) | ||||
0.0176631 | + | 0.999844i | \(0.494377\pi\) | |||||||
\(432\) | 3.45836 | 0.166390 | ||||||||
\(433\) | 21.2117 | 1.01937 | 0.509686 | − | 0.860361i | \(-0.329762\pi\) | ||||
0.509686 | + | 0.860361i | \(0.329762\pi\) | |||||||
\(434\) | 1.34325 | 0.0644778 | ||||||||
\(435\) | 3.34986 | 0.160613 | ||||||||
\(436\) | 29.0580 | 1.39163 | ||||||||
\(437\) | −3.12533 | −0.149505 | ||||||||
\(438\) | −2.53749 | −0.121246 | ||||||||
\(439\) | −25.0957 | −1.19775 | −0.598877 | − | 0.800841i | \(-0.704386\pi\) | ||||
−0.598877 | + | 0.800841i | \(0.704386\pi\) | |||||||
\(440\) | 15.9156 | 0.758748 | ||||||||
\(441\) | −6.81668 | −0.324604 | ||||||||
\(442\) | −1.68903 | −0.0803391 | ||||||||
\(443\) | 35.2387 | 1.67424 | 0.837121 | − | 0.547017i | \(-0.184237\pi\) | ||||
0.837121 | + | 0.547017i | \(0.184237\pi\) | |||||||
\(444\) | 19.7594 | 0.937740 | ||||||||
\(445\) | −34.4700 | −1.63403 | ||||||||
\(446\) | 1.42392 | 0.0674245 | ||||||||
\(447\) | −11.9584 | −0.565614 | ||||||||
\(448\) | −2.51886 | −0.119005 | ||||||||
\(449\) | −11.4866 | −0.542086 | −0.271043 | − | 0.962567i | \(-0.587369\pi\) | ||||
−0.271043 | + | 0.962567i | \(0.587369\pi\) | |||||||
\(450\) | −1.88375 | −0.0888009 | ||||||||
\(451\) | 28.6819 | 1.35058 | ||||||||
\(452\) | 10.8059 | 0.508267 | ||||||||
\(453\) | 24.0005 | 1.12764 | ||||||||
\(454\) | 8.30532 | 0.389788 | ||||||||
\(455\) | 7.61858 | 0.357164 | ||||||||
\(456\) | −3.69838 | −0.173192 | ||||||||
\(457\) | 10.2250 | 0.478307 | 0.239154 | − | 0.970982i | \(-0.423130\pi\) | ||||
0.239154 | + | 0.970982i | \(0.423130\pi\) | |||||||
\(458\) | −0.154683 | −0.00722786 | ||||||||
\(459\) | 1.05018 | 0.0490184 | ||||||||
\(460\) | −6.39262 | −0.298057 | ||||||||
\(461\) | 8.68719 | 0.404603 | 0.202301 | − | 0.979323i | \(-0.435158\pi\) | ||||
0.202301 | + | 0.979323i | \(0.435158\pi\) | |||||||
\(462\) | −0.520483 | −0.0242151 | ||||||||
\(463\) | −11.5538 | −0.536950 | −0.268475 | − | 0.963287i | \(-0.586520\pi\) | ||||
−0.268475 | + | 0.963287i | \(0.586520\pi\) | |||||||
\(464\) | 3.45836 | 0.160550 | ||||||||
\(465\) | −34.7102 | −1.60965 | ||||||||
\(466\) | −3.42273 | −0.158555 | ||||||||
\(467\) | −33.0201 | −1.52799 | −0.763994 | − | 0.645223i | \(-0.776764\pi\) | ||||
−0.763994 | + | 0.645223i | \(0.776764\pi\) | |||||||
\(468\) | −10.1368 | −0.468573 | ||||||||
\(469\) | −1.66917 | −0.0770753 | ||||||||
\(470\) | −11.0034 | −0.507551 | ||||||||
\(471\) | 2.54328 | 0.117188 | ||||||||
\(472\) | −5.54966 | −0.255444 | ||||||||
\(473\) | 12.9460 | 0.595257 | ||||||||
\(474\) | −2.66659 | −0.122481 | ||||||||
\(475\) | −19.4444 | −0.892171 | ||||||||
\(476\) | −0.858060 | −0.0393291 | ||||||||
\(477\) | −9.70877 | −0.444534 | ||||||||
\(478\) | 3.13493 | 0.143388 | ||||||||
\(479\) | −18.5401 | −0.847118 | −0.423559 | − | 0.905869i | \(-0.639219\pi\) | ||||
−0.423559 | + | 0.905869i | \(0.639219\pi\) | |||||||
\(480\) | −11.4358 | −0.521972 | ||||||||
\(481\) | −55.0008 | −2.50782 | ||||||||
\(482\) | 0.913029 | 0.0415873 | ||||||||
\(483\) | 0.428154 | 0.0194817 | ||||||||
\(484\) | −9.77059 | −0.444118 | ||||||||
\(485\) | −11.0905 | −0.503592 | ||||||||
\(486\) | −0.302778 | −0.0137343 | ||||||||
\(487\) | 7.53967 | 0.341655 | 0.170828 | − | 0.985301i | \(-0.445356\pi\) | ||||
0.170828 | + | 0.985301i | \(0.445356\pi\) | |||||||
\(488\) | −4.97165 | −0.225056 | ||||||||
\(489\) | −20.4369 | −0.924190 | ||||||||
\(490\) | 6.91392 | 0.312339 | ||||||||
\(491\) | 1.90597 | 0.0860154 | 0.0430077 | − | 0.999075i | \(-0.486306\pi\) | ||||
0.0430077 | + | 0.999075i | \(0.486306\pi\) | |||||||
\(492\) | −13.6326 | −0.614605 | ||||||||
\(493\) | 1.05018 | 0.0472979 | ||||||||
\(494\) | 5.02653 | 0.226154 | ||||||||
\(495\) | 13.4496 | 0.604514 | ||||||||
\(496\) | −35.8345 | −1.60901 | ||||||||
\(497\) | 5.86719 | 0.263180 | ||||||||
\(498\) | −2.17693 | −0.0975506 | ||||||||
\(499\) | 9.26667 | 0.414833 | 0.207417 | − | 0.978253i | \(-0.433494\pi\) | ||||
0.207417 | + | 0.978253i | \(0.433494\pi\) | |||||||
\(500\) | −7.80895 | −0.349227 | ||||||||
\(501\) | 12.3398 | 0.551303 | ||||||||
\(502\) | −4.86606 | −0.217183 | ||||||||
\(503\) | −16.4993 | −0.735667 | −0.367833 | − | 0.929892i | \(-0.619900\pi\) | ||||
−0.367833 | + | 0.929892i | \(0.619900\pi\) | |||||||
\(504\) | 0.506658 | 0.0225683 | ||||||||
\(505\) | −13.6813 | −0.608811 | ||||||||
\(506\) | −1.21565 | −0.0540420 | ||||||||
\(507\) | 15.2160 | 0.675767 | ||||||||
\(508\) | −12.4472 | −0.552256 | ||||||||
\(509\) | −19.3897 | −0.859434 | −0.429717 | − | 0.902964i | \(-0.641387\pi\) | ||||
−0.429717 | + | 0.902964i | \(0.641387\pi\) | |||||||
\(510\) | −1.06516 | −0.0471663 | ||||||||
\(511\) | 3.58822 | 0.158734 | ||||||||
\(512\) | −19.9912 | −0.883493 | ||||||||
\(513\) | −3.12533 | −0.137987 | ||||||||
\(514\) | −5.89201 | −0.259885 | ||||||||
\(515\) | 48.3619 | 2.13108 | ||||||||
\(516\) | −6.15326 | −0.270882 | ||||||||
\(517\) | 43.5571 | 1.91564 | ||||||||
\(518\) | 1.34229 | 0.0589767 | ||||||||
\(519\) | −11.3271 | −0.497206 | ||||||||
\(520\) | 21.0567 | 0.923396 | ||||||||
\(521\) | 19.8726 | 0.870633 | 0.435316 | − | 0.900277i | \(-0.356636\pi\) | ||||
0.435316 | + | 0.900277i | \(0.356636\pi\) | |||||||
\(522\) | −0.302778 | −0.0132522 | ||||||||
\(523\) | 5.32708 | 0.232937 | 0.116468 | − | 0.993194i | \(-0.462843\pi\) | ||||
0.116468 | + | 0.993194i | \(0.462843\pi\) | |||||||
\(524\) | 10.1200 | 0.442093 | ||||||||
\(525\) | 2.66378 | 0.116257 | ||||||||
\(526\) | −8.53080 | −0.371961 | ||||||||
\(527\) | −10.8817 | −0.474014 | ||||||||
\(528\) | 13.8852 | 0.604276 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 9.84726 | 0.427738 | ||||||||
\(531\) | −4.68976 | −0.203518 | ||||||||
\(532\) | 2.55357 | 0.110711 | ||||||||
\(533\) | 37.9467 | 1.64365 | ||||||||
\(534\) | 3.11558 | 0.134824 | ||||||||
\(535\) | 23.0636 | 0.997127 | ||||||||
\(536\) | −4.61336 | −0.199267 | ||||||||
\(537\) | 12.6720 | 0.546839 | ||||||||
\(538\) | 3.65802 | 0.157709 | ||||||||
\(539\) | −27.3688 | −1.17886 | ||||||||
\(540\) | −6.39262 | −0.275095 | ||||||||
\(541\) | −39.5108 | −1.69870 | −0.849351 | − | 0.527828i | \(-0.823007\pi\) | ||||
−0.849351 | + | 0.527828i | \(0.823007\pi\) | |||||||
\(542\) | 8.91784 | 0.383054 | ||||||||
\(543\) | 21.2565 | 0.912205 | ||||||||
\(544\) | −3.58515 | −0.153712 | ||||||||
\(545\) | −51.0083 | −2.18495 | ||||||||
\(546\) | −0.688608 | −0.0294697 | ||||||||
\(547\) | 25.8008 | 1.10316 | 0.551581 | − | 0.834121i | \(-0.314025\pi\) | ||||
0.551581 | + | 0.834121i | \(0.314025\pi\) | |||||||
\(548\) | 25.1276 | 1.07340 | ||||||||
\(549\) | −4.20131 | −0.179308 | ||||||||
\(550\) | −7.56321 | −0.322496 | ||||||||
\(551\) | −3.12533 | −0.133143 | ||||||||
\(552\) | 1.18336 | 0.0503670 | ||||||||
\(553\) | 3.77078 | 0.160350 | ||||||||
\(554\) | −3.09999 | −0.131706 | ||||||||
\(555\) | −34.6855 | −1.47232 | ||||||||
\(556\) | 4.36443 | 0.185093 | ||||||||
\(557\) | −22.5345 | −0.954818 | −0.477409 | − | 0.878681i | \(-0.658424\pi\) | ||||
−0.477409 | + | 0.878681i | \(0.658424\pi\) | |||||||
\(558\) | 3.13730 | 0.132812 | ||||||||
\(559\) | 17.1278 | 0.724428 | ||||||||
\(560\) | 4.96016 | 0.209605 | ||||||||
\(561\) | 4.21646 | 0.178019 | ||||||||
\(562\) | 4.91854 | 0.207476 | ||||||||
\(563\) | −4.25638 | −0.179385 | −0.0896926 | − | 0.995969i | \(-0.528588\pi\) | ||||
−0.0896926 | + | 0.995969i | \(0.528588\pi\) | |||||||
\(564\) | −20.7028 | −0.871746 | ||||||||
\(565\) | −18.9686 | −0.798015 | ||||||||
\(566\) | −5.73623 | −0.241112 | ||||||||
\(567\) | 0.428154 | 0.0179808 | ||||||||
\(568\) | 16.2161 | 0.680412 | ||||||||
\(569\) | −41.4992 | −1.73974 | −0.869868 | − | 0.493284i | \(-0.835796\pi\) | ||||
−0.869868 | + | 0.493284i | \(0.835796\pi\) | |||||||
\(570\) | 3.16991 | 0.132773 | ||||||||
\(571\) | 20.8965 | 0.874490 | 0.437245 | − | 0.899343i | \(-0.355954\pi\) | ||||
0.437245 | + | 0.899343i | \(0.355954\pi\) | |||||||
\(572\) | −40.6989 | −1.70171 | ||||||||
\(573\) | −11.9418 | −0.498876 | ||||||||
\(574\) | −0.926084 | −0.0386540 | ||||||||
\(575\) | 6.22156 | 0.259457 | ||||||||
\(576\) | −5.88308 | −0.245128 | ||||||||
\(577\) | 10.2811 | 0.428007 | 0.214004 | − | 0.976833i | \(-0.431350\pi\) | ||||
0.214004 | + | 0.976833i | \(0.431350\pi\) | |||||||
\(578\) | 4.81330 | 0.200207 | ||||||||
\(579\) | 9.05494 | 0.376310 | ||||||||
\(580\) | −6.39262 | −0.265439 | ||||||||
\(581\) | 3.07836 | 0.127712 | ||||||||
\(582\) | 1.00241 | 0.0415514 | ||||||||
\(583\) | −38.9804 | −1.61440 | ||||||||
\(584\) | 9.91734 | 0.410382 | ||||||||
\(585\) | 17.7940 | 0.735693 | ||||||||
\(586\) | 3.89851 | 0.161046 | ||||||||
\(587\) | −11.8524 | −0.489201 | −0.244601 | − | 0.969624i | \(-0.578657\pi\) | ||||
−0.244601 | + | 0.969624i | \(0.578657\pi\) | |||||||
\(588\) | 13.0085 | 0.536460 | ||||||||
\(589\) | 32.3837 | 1.33435 | ||||||||
\(590\) | 4.75666 | 0.195829 | ||||||||
\(591\) | 6.84424 | 0.281534 | ||||||||
\(592\) | −35.8089 | −1.47174 | ||||||||
\(593\) | 6.17813 | 0.253705 | 0.126853 | − | 0.991922i | \(-0.459512\pi\) | ||||
0.126853 | + | 0.991922i | \(0.459512\pi\) | |||||||
\(594\) | −1.21565 | −0.0498785 | ||||||||
\(595\) | 1.50623 | 0.0617495 | ||||||||
\(596\) | 22.8205 | 0.934766 | ||||||||
\(597\) | 12.4741 | 0.510533 | ||||||||
\(598\) | −1.60832 | −0.0657691 | ||||||||
\(599\) | 18.0981 | 0.739467 | 0.369734 | − | 0.929138i | \(-0.379449\pi\) | ||||
0.369734 | + | 0.929138i | \(0.379449\pi\) | |||||||
\(600\) | 7.36232 | 0.300565 | ||||||||
\(601\) | −6.20128 | −0.252956 | −0.126478 | − | 0.991969i | \(-0.540367\pi\) | ||||
−0.126478 | + | 0.991969i | \(0.540367\pi\) | |||||||
\(602\) | −0.418001 | −0.0170364 | ||||||||
\(603\) | −3.89854 | −0.158761 | ||||||||
\(604\) | −45.8008 | −1.86361 | ||||||||
\(605\) | 17.1512 | 0.697296 | ||||||||
\(606\) | 1.23659 | 0.0502331 | ||||||||
\(607\) | 13.0037 | 0.527804 | 0.263902 | − | 0.964550i | \(-0.414990\pi\) | ||||
0.263902 | + | 0.964550i | \(0.414990\pi\) | |||||||
\(608\) | 10.6693 | 0.432698 | ||||||||
\(609\) | 0.428154 | 0.0173497 | ||||||||
\(610\) | 4.26124 | 0.172533 | ||||||||
\(611\) | 57.6269 | 2.33133 | ||||||||
\(612\) | −2.00409 | −0.0810107 | ||||||||
\(613\) | −26.0974 | −1.05406 | −0.527031 | − | 0.849846i | \(-0.676695\pi\) | ||||
−0.527031 | + | 0.849846i | \(0.676695\pi\) | |||||||
\(614\) | 5.80787 | 0.234386 | ||||||||
\(615\) | 23.9305 | 0.964973 | ||||||||
\(616\) | 2.03422 | 0.0819609 | ||||||||
\(617\) | −4.77204 | −0.192115 | −0.0960576 | − | 0.995376i | \(-0.530623\pi\) | ||||
−0.0960576 | + | 0.995376i | \(0.530623\pi\) | |||||||
\(618\) | −4.37121 | −0.175836 | ||||||||
\(619\) | 7.79517 | 0.313314 | 0.156657 | − | 0.987653i | \(-0.449928\pi\) | ||||
0.156657 | + | 0.987653i | \(0.449928\pi\) | |||||||
\(620\) | 66.2384 | 2.66020 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 7.60850 | 0.305073 | ||||||||
\(623\) | −4.40569 | −0.176510 | ||||||||
\(624\) | 18.3704 | 0.735403 | ||||||||
\(625\) | −17.4000 | −0.696001 | ||||||||
\(626\) | 0.305434 | 0.0122076 | ||||||||
\(627\) | −12.5481 | −0.501123 | ||||||||
\(628\) | −4.85341 | −0.193672 | ||||||||
\(629\) | −10.8739 | −0.433572 | ||||||||
\(630\) | −0.434261 | −0.0173014 | ||||||||
\(631\) | 13.9161 | 0.553990 | 0.276995 | − | 0.960871i | \(-0.410661\pi\) | ||||
0.276995 | + | 0.960871i | \(0.410661\pi\) | |||||||
\(632\) | 10.4219 | 0.414561 | ||||||||
\(633\) | −16.1997 | −0.643882 | ||||||||
\(634\) | 0.935413 | 0.0371500 | ||||||||
\(635\) | 21.8498 | 0.867082 | ||||||||
\(636\) | 18.5275 | 0.734663 | ||||||||
\(637\) | −36.2094 | −1.43467 | ||||||||
\(638\) | −1.21565 | −0.0481279 | ||||||||
\(639\) | 13.7035 | 0.542101 | ||||||||
\(640\) | 28.8387 | 1.13995 | ||||||||
\(641\) | −7.91467 | −0.312611 | −0.156305 | − | 0.987709i | \(-0.549958\pi\) | ||||
−0.156305 | + | 0.987709i | \(0.549958\pi\) | |||||||
\(642\) | −2.08461 | −0.0822731 | ||||||||
\(643\) | −13.3238 | −0.525439 | −0.262720 | − | 0.964872i | \(-0.584619\pi\) | ||||
−0.262720 | + | 0.964872i | \(0.584619\pi\) | |||||||
\(644\) | −0.817056 | −0.0321965 | ||||||||
\(645\) | 10.8014 | 0.425304 | ||||||||
\(646\) | 0.993770 | 0.0390994 | ||||||||
\(647\) | 1.47922 | 0.0581543 | 0.0290771 | − | 0.999577i | \(-0.490743\pi\) | ||||
0.0290771 | + | 0.999577i | \(0.490743\pi\) | |||||||
\(648\) | 1.18336 | 0.0464866 | ||||||||
\(649\) | −18.8292 | −0.739113 | ||||||||
\(650\) | −10.0063 | −0.392478 | ||||||||
\(651\) | −4.43640 | −0.173876 | ||||||||
\(652\) | 39.0003 | 1.52737 | ||||||||
\(653\) | 28.7736 | 1.12600 | 0.562998 | − | 0.826458i | \(-0.309648\pi\) | ||||
0.562998 | + | 0.826458i | \(0.309648\pi\) | |||||||
\(654\) | 4.61040 | 0.180281 | ||||||||
\(655\) | −17.7645 | −0.694117 | ||||||||
\(656\) | 24.7056 | 0.964592 | ||||||||
\(657\) | 8.38069 | 0.326962 | ||||||||
\(658\) | −1.40638 | −0.0548262 | ||||||||
\(659\) | −18.2082 | −0.709293 | −0.354646 | − | 0.935001i | \(-0.615399\pi\) | ||||
−0.354646 | + | 0.935001i | \(0.615399\pi\) | |||||||
\(660\) | −25.6662 | −0.999055 | ||||||||
\(661\) | 13.9217 | 0.541493 | 0.270746 | − | 0.962651i | \(-0.412729\pi\) | ||||
0.270746 | + | 0.962651i | \(0.412729\pi\) | |||||||
\(662\) | −4.50677 | −0.175161 | ||||||||
\(663\) | 5.57845 | 0.216649 | ||||||||
\(664\) | 8.50816 | 0.330180 | ||||||||
\(665\) | −4.48252 | −0.173824 | ||||||||
\(666\) | 3.13506 | 0.121481 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −23.5484 | −0.911116 | ||||||||
\(669\) | −4.70284 | −0.181822 | ||||||||
\(670\) | 3.95415 | 0.152762 | ||||||||
\(671\) | −16.8682 | −0.651188 | ||||||||
\(672\) | −1.46164 | −0.0563841 | ||||||||
\(673\) | −29.7330 | −1.14612 | −0.573062 | − | 0.819512i | \(-0.694245\pi\) | ||||
−0.573062 | + | 0.819512i | \(0.694245\pi\) | |||||||
\(674\) | −7.25822 | −0.279576 | ||||||||
\(675\) | 6.22156 | 0.239468 | ||||||||
\(676\) | −29.0371 | −1.11681 | ||||||||
\(677\) | 0.854675 | 0.0328478 | 0.0164239 | − | 0.999865i | \(-0.494772\pi\) | ||||
0.0164239 | + | 0.999865i | \(0.494772\pi\) | |||||||
\(678\) | 1.71448 | 0.0658443 | ||||||||
\(679\) | −1.41750 | −0.0543986 | ||||||||
\(680\) | 4.16301 | 0.159644 | ||||||||
\(681\) | −27.4304 | −1.05113 | ||||||||
\(682\) | 12.5962 | 0.482332 | ||||||||
\(683\) | −17.6454 | −0.675183 | −0.337591 | − | 0.941293i | \(-0.609612\pi\) | ||||
−0.337591 | + | 0.941293i | \(0.609612\pi\) | |||||||
\(684\) | 5.96414 | 0.228045 | ||||||||
\(685\) | −44.1088 | −1.68531 | ||||||||
\(686\) | 1.79113 | 0.0683858 | ||||||||
\(687\) | 0.510879 | 0.0194912 | ||||||||
\(688\) | 11.1512 | 0.425137 | ||||||||
\(689\) | −51.5718 | −1.96473 | ||||||||
\(690\) | −1.01426 | −0.0386124 | ||||||||
\(691\) | −27.0772 | −1.03007 | −0.515033 | − | 0.857170i | \(-0.672220\pi\) | ||||
−0.515033 | + | 0.857170i | \(0.672220\pi\) | |||||||
\(692\) | 21.6159 | 0.821712 | ||||||||
\(693\) | 1.71902 | 0.0653003 | ||||||||
\(694\) | 8.91449 | 0.338389 | ||||||||
\(695\) | −7.66129 | −0.290609 | ||||||||
\(696\) | 1.18336 | 0.0448550 | ||||||||
\(697\) | 7.50225 | 0.284168 | ||||||||
\(698\) | 1.46601 | 0.0554891 | ||||||||
\(699\) | 11.3044 | 0.427573 | ||||||||
\(700\) | −5.08336 | −0.192133 | ||||||||
\(701\) | −41.8074 | −1.57904 | −0.789522 | − | 0.613722i | \(-0.789672\pi\) | ||||
−0.789522 | + | 0.613722i | \(0.789672\pi\) | |||||||
\(702\) | −1.60832 | −0.0607021 | ||||||||
\(703\) | 32.3606 | 1.22050 | ||||||||
\(704\) | −23.6204 | −0.890227 | ||||||||
\(705\) | 36.3416 | 1.36870 | ||||||||
\(706\) | −3.36110 | −0.126497 | ||||||||
\(707\) | −1.74864 | −0.0657645 | ||||||||
\(708\) | 8.94959 | 0.336346 | ||||||||
\(709\) | 28.6271 | 1.07511 | 0.537557 | − | 0.843228i | \(-0.319347\pi\) | ||||
0.537557 | + | 0.843228i | \(0.319347\pi\) | |||||||
\(710\) | −13.8989 | −0.521618 | ||||||||
\(711\) | 8.80707 | 0.330291 | ||||||||
\(712\) | −12.1767 | −0.456342 | ||||||||
\(713\) | −10.3617 | −0.388049 | ||||||||
\(714\) | −0.136141 | −0.00509496 | ||||||||
\(715\) | 71.4425 | 2.67180 | ||||||||
\(716\) | −24.1824 | −0.903738 | ||||||||
\(717\) | −10.3539 | −0.386673 | ||||||||
\(718\) | −6.38008 | −0.238102 | ||||||||
\(719\) | −32.5891 | −1.21537 | −0.607685 | − | 0.794178i | \(-0.707902\pi\) | ||||
−0.607685 | + | 0.794178i | \(0.707902\pi\) | |||||||
\(720\) | 11.5850 | 0.431748 | ||||||||
\(721\) | 6.18125 | 0.230202 | ||||||||
\(722\) | 2.79535 | 0.104032 | ||||||||
\(723\) | −3.01550 | −0.112148 | ||||||||
\(724\) | −40.5644 | −1.50756 | ||||||||
\(725\) | 6.22156 | 0.231063 | ||||||||
\(726\) | −1.55022 | −0.0575340 | ||||||||
\(727\) | 46.4493 | 1.72271 | 0.861354 | − | 0.508005i | \(-0.169617\pi\) | ||||
0.861354 | + | 0.508005i | \(0.169617\pi\) | |||||||
\(728\) | 2.69130 | 0.0997464 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.50024 | −0.314608 | ||||||||
\(731\) | 3.38625 | 0.125245 | ||||||||
\(732\) | 8.01748 | 0.296334 | ||||||||
\(733\) | −49.8584 | −1.84156 | −0.920781 | − | 0.390079i | \(-0.872448\pi\) | ||||
−0.920781 | + | 0.390079i | \(0.872448\pi\) | |||||||
\(734\) | 9.56233 | 0.352952 | ||||||||
\(735\) | −22.8349 | −0.842279 | ||||||||
\(736\) | −3.41383 | −0.125835 | ||||||||
\(737\) | −15.6525 | −0.576568 | ||||||||
\(738\) | −2.16297 | −0.0796201 | ||||||||
\(739\) | −42.1893 | −1.55196 | −0.775979 | − | 0.630759i | \(-0.782744\pi\) | ||||
−0.775979 | + | 0.630759i | \(0.782744\pi\) | |||||||
\(740\) | 66.1912 | 2.43324 | ||||||||
\(741\) | −16.6014 | −0.609866 | ||||||||
\(742\) | 1.25860 | 0.0462047 | ||||||||
\(743\) | 9.91569 | 0.363771 | 0.181886 | − | 0.983320i | \(-0.441780\pi\) | ||||
0.181886 | + | 0.983320i | \(0.441780\pi\) | |||||||
\(744\) | −12.2616 | −0.449531 | ||||||||
\(745\) | −40.0590 | −1.46765 | ||||||||
\(746\) | 1.86718 | 0.0683622 | ||||||||
\(747\) | 7.18985 | 0.263063 | ||||||||
\(748\) | −8.04637 | −0.294205 | ||||||||
\(749\) | 2.94781 | 0.107711 | ||||||||
\(750\) | −1.23898 | −0.0452412 | ||||||||
\(751\) | −18.1042 | −0.660632 | −0.330316 | − | 0.943870i | \(-0.607155\pi\) | ||||
−0.330316 | + | 0.943870i | \(0.607155\pi\) | |||||||
\(752\) | 37.5186 | 1.36816 | ||||||||
\(753\) | 16.0714 | 0.585674 | ||||||||
\(754\) | −1.60832 | −0.0585716 | ||||||||
\(755\) | 80.3983 | 2.92600 | ||||||||
\(756\) | −0.817056 | −0.0297161 | ||||||||
\(757\) | −9.06824 | −0.329591 | −0.164795 | − | 0.986328i | \(-0.552696\pi\) | ||||
−0.164795 | + | 0.986328i | \(0.552696\pi\) | |||||||
\(758\) | −3.82090 | −0.138781 | ||||||||
\(759\) | 4.01497 | 0.145734 | ||||||||
\(760\) | −12.3890 | −0.449398 | ||||||||
\(761\) | −53.3930 | −1.93549 | −0.967747 | − | 0.251924i | \(-0.918937\pi\) | ||||
−0.967747 | + | 0.251924i | \(0.918937\pi\) | |||||||
\(762\) | −1.97490 | −0.0715430 | ||||||||
\(763\) | −6.51949 | −0.236021 | ||||||||
\(764\) | 22.7888 | 0.824471 | ||||||||
\(765\) | 3.51797 | 0.127192 | ||||||||
\(766\) | 1.65286 | 0.0597203 | ||||||||
\(767\) | −24.9114 | −0.899499 | ||||||||
\(768\) | 9.15957 | 0.330517 | ||||||||
\(769\) | 21.6662 | 0.781305 | 0.390652 | − | 0.920538i | \(-0.372249\pi\) | ||||
0.390652 | + | 0.920538i | \(0.372249\pi\) | |||||||
\(770\) | −1.74354 | −0.0628330 | ||||||||
\(771\) | 19.4598 | 0.700828 | ||||||||
\(772\) | −17.2798 | −0.621912 | ||||||||
\(773\) | 26.9885 | 0.970710 | 0.485355 | − | 0.874317i | \(-0.338690\pi\) | ||||
0.485355 | + | 0.874317i | \(0.338690\pi\) | |||||||
\(774\) | −0.976287 | −0.0350919 | ||||||||
\(775\) | −64.4659 | −2.31568 | ||||||||
\(776\) | −3.91776 | −0.140639 | ||||||||
\(777\) | −4.43324 | −0.159041 | ||||||||
\(778\) | 5.27301 | 0.189046 | ||||||||
\(779\) | −22.3266 | −0.799932 | ||||||||
\(780\) | −33.9568 | −1.21585 | ||||||||
\(781\) | 55.0190 | 1.96874 | ||||||||
\(782\) | −0.317973 | −0.0113707 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | −23.5745 | −0.841947 | ||||||||
\(785\) | 8.51964 | 0.304079 | ||||||||
\(786\) | 1.60565 | 0.0572717 | ||||||||
\(787\) | 40.2357 | 1.43425 | 0.717125 | − | 0.696945i | \(-0.245458\pi\) | ||||
0.717125 | + | 0.696945i | \(0.245458\pi\) | |||||||
\(788\) | −13.0610 | −0.465280 | ||||||||
\(789\) | 28.1751 | 1.00306 | ||||||||
\(790\) | −8.93270 | −0.317811 | ||||||||
\(791\) | −2.42442 | −0.0862025 | ||||||||
\(792\) | 4.75114 | 0.168824 | ||||||||
\(793\) | −22.3169 | −0.792495 | ||||||||
\(794\) | 8.94265 | 0.317363 | ||||||||
\(795\) | −32.5230 | −1.15347 | ||||||||
\(796\) | −23.8047 | −0.843736 | ||||||||
\(797\) | 25.7410 | 0.911792 | 0.455896 | − | 0.890033i | \(-0.349319\pi\) | ||||
0.455896 | + | 0.890033i | \(0.349319\pi\) | |||||||
\(798\) | 0.405154 | 0.0143423 | ||||||||
\(799\) | 11.3931 | 0.403060 | ||||||||
\(800\) | −21.2393 | −0.750923 | ||||||||
\(801\) | −10.2900 | −0.363579 | ||||||||
\(802\) | 5.77535 | 0.203935 | ||||||||
\(803\) | 33.6482 | 1.18742 | ||||||||
\(804\) | 7.43969 | 0.262377 | ||||||||
\(805\) | 1.43425 | 0.0505508 | ||||||||
\(806\) | 16.6649 | 0.586997 | ||||||||
\(807\) | −12.0815 | −0.425290 | ||||||||
\(808\) | −4.83300 | −0.170024 | ||||||||
\(809\) | −37.9813 | −1.33535 | −0.667675 | − | 0.744453i | \(-0.732711\pi\) | ||||
−0.667675 | + | 0.744453i | \(0.732711\pi\) | |||||||
\(810\) | −1.01426 | −0.0356376 | ||||||||
\(811\) | 41.0679 | 1.44209 | 0.721045 | − | 0.692888i | \(-0.243662\pi\) | ||||
0.721045 | + | 0.692888i | \(0.243662\pi\) | |||||||
\(812\) | −0.817056 | −0.0286731 | ||||||||
\(813\) | −29.4534 | −1.03297 | ||||||||
\(814\) | 12.5872 | 0.441180 | ||||||||
\(815\) | −68.4608 | −2.39808 | ||||||||
\(816\) | 3.63191 | 0.127142 | ||||||||
\(817\) | −10.0774 | −0.352564 | ||||||||
\(818\) | −10.0247 | −0.350505 | ||||||||
\(819\) | 2.27430 | 0.0794704 | ||||||||
\(820\) | −45.6673 | −1.59477 | ||||||||
\(821\) | 43.9349 | 1.53334 | 0.766670 | − | 0.642042i | \(-0.221912\pi\) | ||||
0.766670 | + | 0.642042i | \(0.221912\pi\) | |||||||
\(822\) | 3.98679 | 0.139055 | ||||||||
\(823\) | −7.58709 | −0.264469 | −0.132235 | − | 0.991218i | \(-0.542215\pi\) | ||||
−0.132235 | + | 0.991218i | \(0.542215\pi\) | |||||||
\(824\) | 17.0841 | 0.595153 | ||||||||
\(825\) | 24.9794 | 0.869670 | ||||||||
\(826\) | 0.607960 | 0.0211536 | ||||||||
\(827\) | 32.5844 | 1.13307 | 0.566536 | − | 0.824037i | \(-0.308283\pi\) | ||||
0.566536 | + | 0.824037i | \(0.308283\pi\) | |||||||
\(828\) | −1.90833 | −0.0663189 | ||||||||
\(829\) | 52.0958 | 1.80936 | 0.904681 | − | 0.426089i | \(-0.140109\pi\) | ||||
0.904681 | + | 0.426089i | \(0.140109\pi\) | |||||||
\(830\) | −7.29241 | −0.253123 | ||||||||
\(831\) | 10.2385 | 0.355169 | ||||||||
\(832\) | −31.2502 | −1.08341 | ||||||||
\(833\) | −7.15877 | −0.248037 | ||||||||
\(834\) | 0.692469 | 0.0239782 | ||||||||
\(835\) | 41.3367 | 1.43052 | ||||||||
\(836\) | 23.9459 | 0.828185 | ||||||||
\(837\) | −10.3617 | −0.358153 | ||||||||
\(838\) | −5.31611 | −0.183642 | ||||||||
\(839\) | 37.5788 | 1.29736 | 0.648682 | − | 0.761059i | \(-0.275320\pi\) | ||||
0.648682 | + | 0.761059i | \(0.275320\pi\) | |||||||
\(840\) | 1.69723 | 0.0585601 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 1.31773 | 0.0454119 | ||||||||
\(843\) | −16.2447 | −0.559497 | ||||||||
\(844\) | 30.9144 | 1.06412 | ||||||||
\(845\) | 50.9715 | 1.75347 | ||||||||
\(846\) | −3.28475 | −0.112932 | ||||||||
\(847\) | 2.19214 | 0.0753227 | ||||||||
\(848\) | −33.5764 | −1.15302 | ||||||||
\(849\) | 18.9453 | 0.650201 | ||||||||
\(850\) | −1.97829 | −0.0678547 | ||||||||
\(851\) | −10.3543 | −0.354941 | ||||||||
\(852\) | −26.1507 | −0.895908 | ||||||||
\(853\) | −1.37770 | −0.0471717 | −0.0235858 | − | 0.999722i | \(-0.507508\pi\) | ||||
−0.0235858 | + | 0.999722i | \(0.507508\pi\) | |||||||
\(854\) | 0.544640 | 0.0186372 | ||||||||
\(855\) | −10.4694 | −0.358046 | ||||||||
\(856\) | 8.14734 | 0.278470 | ||||||||
\(857\) | 10.7773 | 0.368145 | 0.184072 | − | 0.982913i | \(-0.441072\pi\) | ||||
0.184072 | + | 0.982913i | \(0.441072\pi\) | |||||||
\(858\) | −6.45736 | −0.220451 | ||||||||
\(859\) | −43.8307 | −1.49549 | −0.747743 | − | 0.663988i | \(-0.768862\pi\) | ||||
−0.747743 | + | 0.663988i | \(0.768862\pi\) | |||||||
\(860\) | −20.6126 | −0.702883 | ||||||||
\(861\) | 3.05862 | 0.104238 | ||||||||
\(862\) | −0.222054 | −0.00756320 | ||||||||
\(863\) | 31.7238 | 1.07989 | 0.539946 | − | 0.841700i | \(-0.318445\pi\) | ||||
0.539946 | + | 0.841700i | \(0.318445\pi\) | |||||||
\(864\) | −3.41383 | −0.116141 | ||||||||
\(865\) | −37.9443 | −1.29015 | ||||||||
\(866\) | −6.42245 | −0.218244 | ||||||||
\(867\) | −15.8971 | −0.539894 | ||||||||
\(868\) | 8.46609 | 0.287358 | ||||||||
\(869\) | 35.3601 | 1.19951 | ||||||||
\(870\) | −1.01426 | −0.0343868 | ||||||||
\(871\) | −20.7086 | −0.701683 | ||||||||
\(872\) | −18.0189 | −0.610199 | ||||||||
\(873\) | −3.31072 | −0.112051 | ||||||||
\(874\) | 0.946281 | 0.0320084 | ||||||||
\(875\) | 1.75202 | 0.0592292 | ||||||||
\(876\) | −15.9931 | −0.540356 | ||||||||
\(877\) | 58.0758 | 1.96108 | 0.980540 | − | 0.196319i | \(-0.0628988\pi\) | ||||
0.980540 | + | 0.196319i | \(0.0628988\pi\) | |||||||
\(878\) | 7.59844 | 0.256435 | ||||||||
\(879\) | −12.8758 | −0.434290 | ||||||||
\(880\) | 46.5134 | 1.56797 | ||||||||
\(881\) | 50.1319 | 1.68899 | 0.844493 | − | 0.535567i | \(-0.179902\pi\) | ||||
0.844493 | + | 0.535567i | \(0.179902\pi\) | |||||||
\(882\) | 2.06394 | 0.0694966 | ||||||||
\(883\) | 10.4412 | 0.351375 | 0.175687 | − | 0.984446i | \(-0.443785\pi\) | ||||
0.175687 | + | 0.984446i | \(0.443785\pi\) | |||||||
\(884\) | −10.6455 | −0.358047 | ||||||||
\(885\) | −15.7100 | −0.528087 | ||||||||
\(886\) | −10.6695 | −0.358450 | ||||||||
\(887\) | 33.4645 | 1.12363 | 0.561815 | − | 0.827263i | \(-0.310103\pi\) | ||||
0.561815 | + | 0.827263i | \(0.310103\pi\) | |||||||
\(888\) | −12.2528 | −0.411178 | ||||||||
\(889\) | 2.79267 | 0.0936632 | ||||||||
\(890\) | 10.4368 | 0.349841 | ||||||||
\(891\) | 4.01497 | 0.134507 | ||||||||
\(892\) | 8.97456 | 0.300490 | ||||||||
\(893\) | −33.9057 | −1.13461 | ||||||||
\(894\) | 3.62075 | 0.121096 | ||||||||
\(895\) | 42.4496 | 1.41893 | ||||||||
\(896\) | 3.68594 | 0.123139 | ||||||||
\(897\) | 5.31187 | 0.177358 | ||||||||
\(898\) | 3.47789 | 0.116059 | ||||||||
\(899\) | −10.3617 | −0.345582 | ||||||||
\(900\) | −11.8728 | −0.395758 | ||||||||
\(901\) | −10.1960 | −0.339678 | ||||||||
\(902\) | −8.68426 | −0.289154 | ||||||||
\(903\) | 1.38055 | 0.0459419 | ||||||||
\(904\) | −6.70076 | −0.222864 | ||||||||
\(905\) | 71.2064 | 2.36698 | ||||||||
\(906\) | −7.26683 | −0.241424 | ||||||||
\(907\) | −38.3696 | −1.27404 | −0.637021 | − | 0.770846i | \(-0.719834\pi\) | ||||
−0.637021 | + | 0.770846i | \(0.719834\pi\) | |||||||
\(908\) | 52.3461 | 1.73717 | ||||||||
\(909\) | −4.08415 | −0.135463 | ||||||||
\(910\) | −2.30674 | −0.0764677 | ||||||||
\(911\) | −30.9361 | −1.02496 | −0.512480 | − | 0.858699i | \(-0.671273\pi\) | ||||
−0.512480 | + | 0.858699i | \(0.671273\pi\) | |||||||
\(912\) | −10.8085 | −0.357905 | ||||||||
\(913\) | 28.8670 | 0.955360 | ||||||||
\(914\) | −3.09592 | −0.102404 | ||||||||
\(915\) | −14.0738 | −0.465266 | ||||||||
\(916\) | −0.974923 | −0.0322124 | ||||||||
\(917\) | −2.27052 | −0.0749793 | ||||||||
\(918\) | −0.317973 | −0.0104947 | ||||||||
\(919\) | −15.7028 | −0.517986 | −0.258993 | − | 0.965879i | \(-0.583391\pi\) | ||||
−0.258993 | + | 0.965879i | \(0.583391\pi\) | |||||||
\(920\) | 3.96408 | 0.130692 | ||||||||
\(921\) | −19.1819 | −0.632066 | ||||||||
\(922\) | −2.63029 | −0.0866241 | ||||||||
\(923\) | 72.7911 | 2.39595 | ||||||||
\(924\) | −3.28046 | −0.107919 | ||||||||
\(925\) | −64.4200 | −2.11811 | ||||||||
\(926\) | 3.49824 | 0.114959 | ||||||||
\(927\) | 14.4370 | 0.474173 | ||||||||
\(928\) | −3.41383 | −0.112064 | ||||||||
\(929\) | 40.9864 | 1.34472 | 0.672360 | − | 0.740224i | \(-0.265281\pi\) | ||||
0.672360 | + | 0.740224i | \(0.265281\pi\) | |||||||
\(930\) | 10.5095 | 0.344620 | ||||||||
\(931\) | 21.3044 | 0.698223 | ||||||||
\(932\) | −21.5725 | −0.706631 | ||||||||
\(933\) | −25.1290 | −0.822685 | ||||||||
\(934\) | 9.99777 | 0.327137 | ||||||||
\(935\) | 14.1245 | 0.461922 | ||||||||
\(936\) | 6.28584 | 0.205459 | ||||||||
\(937\) | −28.1083 | −0.918260 | −0.459130 | − | 0.888369i | \(-0.651839\pi\) | ||||
−0.459130 | + | 0.888369i | \(0.651839\pi\) | |||||||
\(938\) | 0.505390 | 0.0165016 | ||||||||
\(939\) | −1.00877 | −0.0329200 | ||||||||
\(940\) | −69.3515 | −2.26200 | ||||||||
\(941\) | −3.64388 | −0.118787 | −0.0593935 | − | 0.998235i | \(-0.518917\pi\) | ||||
−0.0593935 | + | 0.998235i | \(0.518917\pi\) | |||||||
\(942\) | −0.770051 | −0.0250896 | ||||||||
\(943\) | 7.14375 | 0.232632 | ||||||||
\(944\) | −16.2189 | −0.527879 | ||||||||
\(945\) | 1.43425 | 0.0466563 | ||||||||
\(946\) | −3.91976 | −0.127443 | ||||||||
\(947\) | −19.1649 | −0.622775 | −0.311388 | − | 0.950283i | \(-0.600794\pi\) | ||||
−0.311388 | + | 0.950283i | \(0.600794\pi\) | |||||||
\(948\) | −16.8068 | −0.545858 | ||||||||
\(949\) | 44.5172 | 1.44509 | ||||||||
\(950\) | 5.88734 | 0.191011 | ||||||||
\(951\) | −3.08943 | −0.100182 | ||||||||
\(952\) | 0.532084 | 0.0172450 | ||||||||
\(953\) | 31.6253 | 1.02445 | 0.512223 | − | 0.858853i | \(-0.328822\pi\) | ||||
0.512223 | + | 0.858853i | \(0.328822\pi\) | |||||||
\(954\) | 2.93960 | 0.0951732 | ||||||||
\(955\) | −40.0033 | −1.29448 | ||||||||
\(956\) | 19.7586 | 0.639038 | ||||||||
\(957\) | 4.01497 | 0.129786 | ||||||||
\(958\) | 5.61353 | 0.181365 | ||||||||
\(959\) | −5.63765 | −0.182049 | ||||||||
\(960\) | −19.7075 | −0.636056 | ||||||||
\(961\) | 76.3649 | 2.46338 | ||||||||
\(962\) | 16.6531 | 0.536916 | ||||||||
\(963\) | 6.88495 | 0.221864 | ||||||||
\(964\) | 5.75456 | 0.185342 | ||||||||
\(965\) | 30.3328 | 0.976446 | ||||||||
\(966\) | −0.129636 | −0.00417096 | ||||||||
\(967\) | −27.6891 | −0.890421 | −0.445211 | − | 0.895426i | \(-0.646871\pi\) | ||||
−0.445211 | + | 0.895426i | \(0.646871\pi\) | |||||||
\(968\) | 6.05876 | 0.194736 | ||||||||
\(969\) | −3.28217 | −0.105439 | ||||||||
\(970\) | 3.35795 | 0.107817 | ||||||||
\(971\) | −35.9385 | −1.15332 | −0.576661 | − | 0.816984i | \(-0.695644\pi\) | ||||
−0.576661 | + | 0.816984i | \(0.695644\pi\) | |||||||
\(972\) | −1.90833 | −0.0612096 | ||||||||
\(973\) | −0.979208 | −0.0313920 | ||||||||
\(974\) | −2.28285 | −0.0731472 | ||||||||
\(975\) | 33.0481 | 1.05839 | ||||||||
\(976\) | −14.5296 | −0.465083 | ||||||||
\(977\) | 38.4441 | 1.22993 | 0.614967 | − | 0.788553i | \(-0.289169\pi\) | ||||
0.614967 | + | 0.788553i | \(0.289169\pi\) | |||||||
\(978\) | 6.18786 | 0.197866 | ||||||||
\(979\) | −41.3140 | −1.32040 | ||||||||
\(980\) | 43.5765 | 1.39200 | ||||||||
\(981\) | −15.2270 | −0.486160 | ||||||||
\(982\) | −0.577088 | −0.0184156 | ||||||||
\(983\) | −17.4592 | −0.556863 | −0.278431 | − | 0.960456i | \(-0.589814\pi\) | ||||
−0.278431 | + | 0.960456i | \(0.589814\pi\) | |||||||
\(984\) | 8.45359 | 0.269491 | ||||||||
\(985\) | 22.9272 | 0.730522 | ||||||||
\(986\) | −0.317973 | −0.0101263 | ||||||||
\(987\) | 4.64490 | 0.147849 | ||||||||
\(988\) | 31.6808 | 1.00790 | ||||||||
\(989\) | 3.22443 | 0.102531 | ||||||||
\(990\) | −4.07224 | −0.129424 | ||||||||
\(991\) | 42.9628 | 1.36476 | 0.682380 | − | 0.730998i | \(-0.260945\pi\) | ||||
0.682380 | + | 0.730998i | \(0.260945\pi\) | |||||||
\(992\) | 35.3731 | 1.12310 | ||||||||
\(993\) | 14.8847 | 0.472353 | ||||||||
\(994\) | −1.77646 | −0.0563458 | ||||||||
\(995\) | 41.7866 | 1.32473 | ||||||||
\(996\) | −13.7206 | −0.434753 | ||||||||
\(997\) | −16.7387 | −0.530121 | −0.265061 | − | 0.964232i | \(-0.585392\pi\) | ||||
−0.265061 | + | 0.964232i | \(0.585392\pi\) | |||||||
\(998\) | −2.80575 | −0.0888144 | ||||||||
\(999\) | −10.3543 | −0.327596 |
(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 | 2001.2.a.o.1.9 | ✓ | 20 | |
3.2 | odd | 2 | 6003.2.a.s.1.12 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.o.1.9 | ✓ | 20 | 1.1 | even | 1 | trivial | |
6003.2.a.s.1.12 | 20 | 3.2 | odd | 2 |