Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, 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("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57089 | −1.81789 | −0.908945 | − | 0.416916i | \(-0.863111\pi\) | ||||
−0.908945 | + | 0.416916i | \(0.863111\pi\) | |||||||
\(3\) | 0.190612 | 0.110050 | 0.0550250 | − | 0.998485i | \(-0.482476\pi\) | ||||
0.0550250 | + | 0.998485i | \(0.482476\pi\) | |||||||
\(4\) | 4.60945 | 2.30472 | ||||||||
\(5\) | −1.40475 | −0.628221 | −0.314111 | − | 0.949386i | \(-0.601706\pi\) | ||||
−0.314111 | + | 0.949386i | \(0.601706\pi\) | |||||||
\(6\) | −0.490042 | −0.200059 | ||||||||
\(7\) | 1.52623 | 0.576862 | 0.288431 | − | 0.957501i | \(-0.406866\pi\) | ||||
0.288431 | + | 0.957501i | \(0.406866\pi\) | |||||||
\(8\) | −6.70860 | −2.37185 | ||||||||
\(9\) | −2.96367 | −0.987889 | ||||||||
\(10\) | 3.61144 | 1.14204 | ||||||||
\(11\) | 4.90607 | 1.47924 | 0.739619 | − | 0.673026i | \(-0.235006\pi\) | ||||
0.739619 | + | 0.673026i | \(0.235006\pi\) | |||||||
\(12\) | 0.878618 | 0.253635 | ||||||||
\(13\) | −2.99179 | −0.829773 | −0.414886 | − | 0.909873i | \(-0.636179\pi\) | ||||
−0.414886 | + | 0.909873i | \(0.636179\pi\) | |||||||
\(14\) | −3.92377 | −1.04867 | ||||||||
\(15\) | −0.267762 | −0.0691358 | ||||||||
\(16\) | 8.02813 | 2.00703 | ||||||||
\(17\) | −0.189545 | −0.0459715 | −0.0229857 | − | 0.999736i | \(-0.507317\pi\) | ||||
−0.0229857 | + | 0.999736i | \(0.507317\pi\) | |||||||
\(18\) | 7.61925 | 1.79587 | ||||||||
\(19\) | −0.111372 | −0.0255505 | −0.0127752 | − | 0.999918i | \(-0.504067\pi\) | ||||
−0.0127752 | + | 0.999918i | \(0.504067\pi\) | |||||||
\(20\) | −6.47510 | −1.44788 | ||||||||
\(21\) | 0.290919 | 0.0634837 | ||||||||
\(22\) | −12.6130 | −2.68909 | ||||||||
\(23\) | 5.98917 | 1.24883 | 0.624414 | − | 0.781094i | \(-0.285338\pi\) | ||||
0.624414 | + | 0.781094i | \(0.285338\pi\) | |||||||
\(24\) | −1.27874 | −0.261022 | ||||||||
\(25\) | −3.02669 | −0.605338 | ||||||||
\(26\) | 7.69154 | 1.50844 | ||||||||
\(27\) | −1.13675 | −0.218767 | ||||||||
\(28\) | 7.03509 | 1.32951 | ||||||||
\(29\) | −8.54348 | −1.58648 | −0.793242 | − | 0.608906i | \(-0.791609\pi\) | ||||
−0.793242 | + | 0.608906i | \(0.791609\pi\) | |||||||
\(30\) | 0.688385 | 0.125681 | ||||||||
\(31\) | 4.85608 | 0.872178 | 0.436089 | − | 0.899904i | \(-0.356363\pi\) | ||||
0.436089 | + | 0.899904i | \(0.356363\pi\) | |||||||
\(32\) | −7.22221 | −1.27672 | ||||||||
\(33\) | 0.935158 | 0.162790 | ||||||||
\(34\) | 0.487299 | 0.0835711 | ||||||||
\(35\) | −2.14397 | −0.362397 | ||||||||
\(36\) | −13.6609 | −2.27681 | ||||||||
\(37\) | 2.51340 | 0.413200 | 0.206600 | − | 0.978425i | \(-0.433760\pi\) | ||||
0.206600 | + | 0.978425i | \(0.433760\pi\) | |||||||
\(38\) | 0.286325 | 0.0464480 | ||||||||
\(39\) | −0.570272 | −0.0913166 | ||||||||
\(40\) | 9.42387 | 1.49004 | ||||||||
\(41\) | 3.73074 | 0.582643 | 0.291322 | − | 0.956625i | \(-0.405905\pi\) | ||||
0.291322 | + | 0.956625i | \(0.405905\pi\) | |||||||
\(42\) | −0.747919 | −0.115406 | ||||||||
\(43\) | −12.4308 | −1.89568 | −0.947841 | − | 0.318743i | \(-0.896739\pi\) | ||||
−0.947841 | + | 0.318743i | \(0.896739\pi\) | |||||||
\(44\) | 22.6143 | 3.40923 | ||||||||
\(45\) | 4.16320 | 0.620613 | ||||||||
\(46\) | −15.3975 | −2.27023 | ||||||||
\(47\) | 7.35043 | 1.07217 | 0.536085 | − | 0.844164i | \(-0.319902\pi\) | ||||
0.536085 | + | 0.844164i | \(0.319902\pi\) | |||||||
\(48\) | 1.53026 | 0.220874 | ||||||||
\(49\) | −4.67061 | −0.667231 | ||||||||
\(50\) | 7.78127 | 1.10044 | ||||||||
\(51\) | −0.0361297 | −0.00505916 | ||||||||
\(52\) | −13.7905 | −1.91240 | ||||||||
\(53\) | 3.20655 | 0.440453 | 0.220227 | − | 0.975449i | \(-0.429320\pi\) | ||||
0.220227 | + | 0.975449i | \(0.429320\pi\) | |||||||
\(54\) | 2.92245 | 0.397695 | ||||||||
\(55\) | −6.89178 | −0.929288 | ||||||||
\(56\) | −10.2389 | −1.36823 | ||||||||
\(57\) | −0.0212289 | −0.00281183 | ||||||||
\(58\) | 21.9643 | 2.88406 | ||||||||
\(59\) | 3.87343 | 0.504277 | 0.252139 | − | 0.967691i | \(-0.418866\pi\) | ||||
0.252139 | + | 0.967691i | \(0.418866\pi\) | |||||||
\(60\) | −1.23423 | −0.159339 | ||||||||
\(61\) | −6.93168 | −0.887511 | −0.443755 | − | 0.896148i | \(-0.646354\pi\) | ||||
−0.443755 | + | 0.896148i | \(0.646354\pi\) | |||||||
\(62\) | −12.4844 | −1.58552 | ||||||||
\(63\) | −4.52325 | −0.569875 | ||||||||
\(64\) | 2.51120 | 0.313900 | ||||||||
\(65\) | 4.20270 | 0.521281 | ||||||||
\(66\) | −2.40418 | −0.295935 | ||||||||
\(67\) | 2.31949 | 0.283371 | 0.141685 | − | 0.989912i | \(-0.454748\pi\) | ||||
0.141685 | + | 0.989912i | \(0.454748\pi\) | |||||||
\(68\) | −0.873699 | −0.105952 | ||||||||
\(69\) | 1.14161 | 0.137434 | ||||||||
\(70\) | 5.51190 | 0.658798 | ||||||||
\(71\) | 4.63385 | 0.549937 | 0.274968 | − | 0.961453i | \(-0.411333\pi\) | ||||
0.274968 | + | 0.961453i | \(0.411333\pi\) | |||||||
\(72\) | 19.8820 | 2.34312 | ||||||||
\(73\) | 13.4275 | 1.57157 | 0.785784 | − | 0.618501i | \(-0.212260\pi\) | ||||
0.785784 | + | 0.618501i | \(0.212260\pi\) | |||||||
\(74\) | −6.46166 | −0.751153 | ||||||||
\(75\) | −0.576925 | −0.0666175 | ||||||||
\(76\) | −0.513363 | −0.0588868 | ||||||||
\(77\) | 7.48781 | 0.853315 | ||||||||
\(78\) | 1.46610 | 0.166004 | ||||||||
\(79\) | −14.6063 | −1.64334 | −0.821669 | − | 0.569965i | \(-0.806957\pi\) | ||||
−0.821669 | + | 0.569965i | \(0.806957\pi\) | |||||||
\(80\) | −11.2775 | −1.26086 | ||||||||
\(81\) | 8.67432 | 0.963814 | ||||||||
\(82\) | −9.59130 | −1.05918 | ||||||||
\(83\) | −12.6361 | −1.38699 | −0.693496 | − | 0.720461i | \(-0.743930\pi\) | ||||
−0.693496 | + | 0.720461i | \(0.743930\pi\) | |||||||
\(84\) | 1.34098 | 0.146312 | ||||||||
\(85\) | 0.266263 | 0.0288802 | ||||||||
\(86\) | 31.9582 | 3.44614 | ||||||||
\(87\) | −1.62849 | −0.174593 | ||||||||
\(88\) | −32.9129 | −3.50852 | ||||||||
\(89\) | 10.0468 | 1.06496 | 0.532480 | − | 0.846442i | \(-0.321260\pi\) | ||||
0.532480 | + | 0.846442i | \(0.321260\pi\) | |||||||
\(90\) | −10.7031 | −1.12821 | ||||||||
\(91\) | −4.56617 | −0.478664 | ||||||||
\(92\) | 27.6068 | 2.87820 | ||||||||
\(93\) | 0.925629 | 0.0959832 | ||||||||
\(94\) | −18.8971 | −1.94909 | ||||||||
\(95\) | 0.156449 | 0.0160514 | ||||||||
\(96\) | −1.37664 | −0.140503 | ||||||||
\(97\) | −7.10378 | −0.721280 | −0.360640 | − | 0.932705i | \(-0.617442\pi\) | ||||
−0.360640 | + | 0.932705i | \(0.617442\pi\) | |||||||
\(98\) | 12.0076 | 1.21295 | ||||||||
\(99\) | −14.5400 | −1.46132 | ||||||||
\(100\) | −13.9514 | −1.39514 | ||||||||
\(101\) | −7.37625 | −0.733964 | −0.366982 | − | 0.930228i | \(-0.619609\pi\) | ||||
−0.366982 | + | 0.930228i | \(0.619609\pi\) | |||||||
\(102\) | 0.0928852 | 0.00919700 | ||||||||
\(103\) | −10.1641 | −1.00150 | −0.500749 | − | 0.865593i | \(-0.666942\pi\) | ||||
−0.500749 | + | 0.865593i | \(0.666942\pi\) | |||||||
\(104\) | 20.0707 | 1.96809 | ||||||||
\(105\) | −0.408667 | −0.0398818 | ||||||||
\(106\) | −8.24366 | −0.800695 | ||||||||
\(107\) | −3.77084 | −0.364540 | −0.182270 | − | 0.983248i | \(-0.558345\pi\) | ||||
−0.182270 | + | 0.983248i | \(0.558345\pi\) | |||||||
\(108\) | −5.23979 | −0.504199 | ||||||||
\(109\) | −16.7082 | −1.60036 | −0.800179 | − | 0.599761i | \(-0.795262\pi\) | ||||
−0.800179 | + | 0.599761i | \(0.795262\pi\) | |||||||
\(110\) | 17.7180 | 1.68934 | ||||||||
\(111\) | 0.479085 | 0.0454727 | ||||||||
\(112\) | 12.2528 | 1.15778 | ||||||||
\(113\) | 10.7160 | 1.00807 | 0.504037 | − | 0.863682i | \(-0.331848\pi\) | ||||
0.504037 | + | 0.863682i | \(0.331848\pi\) | |||||||
\(114\) | 0.0545770 | 0.00511160 | ||||||||
\(115\) | −8.41325 | −0.784540 | ||||||||
\(116\) | −39.3808 | −3.65641 | ||||||||
\(117\) | 8.86666 | 0.819723 | ||||||||
\(118\) | −9.95814 | −0.916721 | ||||||||
\(119\) | −0.289290 | −0.0265192 | ||||||||
\(120\) | 1.79631 | 0.163980 | ||||||||
\(121\) | 13.0696 | 1.18814 | ||||||||
\(122\) | 17.8206 | 1.61340 | ||||||||
\(123\) | 0.711125 | 0.0641200 | ||||||||
\(124\) | 22.3839 | 2.01013 | ||||||||
\(125\) | 11.2755 | 1.00851 | ||||||||
\(126\) | 11.6287 | 1.03597 | ||||||||
\(127\) | 20.1958 | 1.79209 | 0.896044 | − | 0.443965i | \(-0.146429\pi\) | ||||
0.896044 | + | 0.443965i | \(0.146429\pi\) | |||||||
\(128\) | 7.98840 | 0.706081 | ||||||||
\(129\) | −2.36947 | −0.208620 | ||||||||
\(130\) | −10.8047 | −0.947631 | ||||||||
\(131\) | 4.07458 | 0.355998 | 0.177999 | − | 0.984031i | \(-0.443038\pi\) | ||||
0.177999 | + | 0.984031i | \(0.443038\pi\) | |||||||
\(132\) | 4.31057 | 0.375187 | ||||||||
\(133\) | −0.169980 | −0.0147391 | ||||||||
\(134\) | −5.96314 | −0.515137 | ||||||||
\(135\) | 1.59684 | 0.137434 | ||||||||
\(136\) | 1.27158 | 0.109037 | ||||||||
\(137\) | −4.66449 | −0.398514 | −0.199257 | − | 0.979947i | \(-0.563853\pi\) | ||||
−0.199257 | + | 0.979947i | \(0.563853\pi\) | |||||||
\(138\) | −2.93495 | −0.249839 | ||||||||
\(139\) | −4.14287 | −0.351394 | −0.175697 | − | 0.984444i | \(-0.556218\pi\) | ||||
−0.175697 | + | 0.984444i | \(0.556218\pi\) | |||||||
\(140\) | −9.88251 | −0.835225 | ||||||||
\(141\) | 1.40108 | 0.117992 | ||||||||
\(142\) | −11.9131 | −0.999725 | ||||||||
\(143\) | −14.6779 | −1.22743 | ||||||||
\(144\) | −23.7927 | −1.98273 | ||||||||
\(145\) | 12.0014 | 0.996663 | ||||||||
\(146\) | −34.5205 | −2.85694 | ||||||||
\(147\) | −0.890277 | −0.0734288 | ||||||||
\(148\) | 11.5854 | 0.952313 | ||||||||
\(149\) | −12.9993 | −1.06495 | −0.532474 | − | 0.846446i | \(-0.678738\pi\) | ||||
−0.532474 | + | 0.846446i | \(0.678738\pi\) | |||||||
\(150\) | 1.48321 | 0.121103 | ||||||||
\(151\) | −18.4497 | −1.50142 | −0.750710 | − | 0.660632i | \(-0.770288\pi\) | ||||
−0.750710 | + | 0.660632i | \(0.770288\pi\) | |||||||
\(152\) | 0.747149 | 0.0606018 | ||||||||
\(153\) | 0.561749 | 0.0454147 | ||||||||
\(154\) | −19.2503 | −1.55123 | ||||||||
\(155\) | −6.82155 | −0.547920 | ||||||||
\(156\) | −2.62864 | −0.210460 | ||||||||
\(157\) | 1.30139 | 0.103862 | 0.0519310 | − | 0.998651i | \(-0.483462\pi\) | ||||
0.0519310 | + | 0.998651i | \(0.483462\pi\) | |||||||
\(158\) | 37.5511 | 2.98741 | ||||||||
\(159\) | 0.611207 | 0.0484719 | ||||||||
\(160\) | 10.1454 | 0.802061 | ||||||||
\(161\) | 9.14086 | 0.720401 | ||||||||
\(162\) | −22.3007 | −1.75211 | ||||||||
\(163\) | 7.81357 | 0.612006 | 0.306003 | − | 0.952031i | \(-0.401008\pi\) | ||||
0.306003 | + | 0.952031i | \(0.401008\pi\) | |||||||
\(164\) | 17.1967 | 1.34283 | ||||||||
\(165\) | −1.31366 | −0.102268 | ||||||||
\(166\) | 32.4859 | 2.52140 | ||||||||
\(167\) | −22.4883 | −1.74020 | −0.870098 | − | 0.492880i | \(-0.835944\pi\) | ||||
−0.870098 | + | 0.492880i | \(0.835944\pi\) | |||||||
\(168\) | −1.95166 | −0.150574 | ||||||||
\(169\) | −4.04920 | −0.311477 | ||||||||
\(170\) | −0.684531 | −0.0525011 | ||||||||
\(171\) | 0.330069 | 0.0252410 | ||||||||
\(172\) | −57.2992 | −4.36903 | ||||||||
\(173\) | 6.72968 | 0.511648 | 0.255824 | − | 0.966723i | \(-0.417653\pi\) | ||||
0.255824 | + | 0.966723i | \(0.417653\pi\) | |||||||
\(174\) | 4.18667 | 0.317391 | ||||||||
\(175\) | −4.61943 | −0.349196 | ||||||||
\(176\) | 39.3866 | 2.96888 | ||||||||
\(177\) | 0.738323 | 0.0554958 | ||||||||
\(178\) | −25.8292 | −1.93598 | ||||||||
\(179\) | −3.14792 | −0.235286 | −0.117643 | − | 0.993056i | \(-0.537534\pi\) | ||||
−0.117643 | + | 0.993056i | \(0.537534\pi\) | |||||||
\(180\) | 19.1900 | 1.43034 | ||||||||
\(181\) | 1.44134 | 0.107134 | 0.0535669 | − | 0.998564i | \(-0.482941\pi\) | ||||
0.0535669 | + | 0.998564i | \(0.482941\pi\) | |||||||
\(182\) | 11.7391 | 0.870159 | ||||||||
\(183\) | −1.32126 | −0.0976706 | ||||||||
\(184\) | −40.1789 | −2.96203 | ||||||||
\(185\) | −3.53069 | −0.259581 | ||||||||
\(186\) | −2.37969 | −0.174487 | ||||||||
\(187\) | −0.929923 | −0.0680027 | ||||||||
\(188\) | 33.8815 | 2.47106 | ||||||||
\(189\) | −1.73494 | −0.126199 | ||||||||
\(190\) | −0.402213 | −0.0291796 | ||||||||
\(191\) | −1.27701 | −0.0924013 | −0.0462006 | − | 0.998932i | \(-0.514711\pi\) | ||||
−0.0462006 | + | 0.998932i | \(0.514711\pi\) | |||||||
\(192\) | 0.478666 | 0.0345447 | ||||||||
\(193\) | 25.6342 | 1.84519 | 0.922594 | − | 0.385772i | \(-0.126065\pi\) | ||||
0.922594 | + | 0.385772i | \(0.126065\pi\) | |||||||
\(194\) | 18.2630 | 1.31121 | ||||||||
\(195\) | 0.801087 | 0.0573670 | ||||||||
\(196\) | −21.5290 | −1.53778 | ||||||||
\(197\) | −2.69630 | −0.192103 | −0.0960517 | − | 0.995376i | \(-0.530621\pi\) | ||||
−0.0960517 | + | 0.995376i | \(0.530621\pi\) | |||||||
\(198\) | 37.3806 | 2.65652 | ||||||||
\(199\) | −15.3839 | −1.09054 | −0.545270 | − | 0.838261i | \(-0.683573\pi\) | ||||
−0.545270 | + | 0.838261i | \(0.683573\pi\) | |||||||
\(200\) | 20.3048 | 1.43577 | ||||||||
\(201\) | 0.442123 | 0.0311850 | ||||||||
\(202\) | 18.9635 | 1.33427 | ||||||||
\(203\) | −13.0393 | −0.915182 | ||||||||
\(204\) | −0.166538 | −0.0116600 | ||||||||
\(205\) | −5.24074 | −0.366029 | ||||||||
\(206\) | 26.1307 | 1.82061 | ||||||||
\(207\) | −17.7499 | −1.23370 | ||||||||
\(208\) | −24.0185 | −1.66538 | ||||||||
\(209\) | −0.546399 | −0.0377952 | ||||||||
\(210\) | 1.05064 | 0.0725007 | ||||||||
\(211\) | −0.836067 | −0.0575572 | −0.0287786 | − | 0.999586i | \(-0.509162\pi\) | ||||
−0.0287786 | + | 0.999586i | \(0.509162\pi\) | |||||||
\(212\) | 14.7804 | 1.01512 | ||||||||
\(213\) | 0.883269 | 0.0605206 | ||||||||
\(214\) | 9.69439 | 0.662695 | ||||||||
\(215\) | 17.4621 | 1.19091 | ||||||||
\(216\) | 7.62599 | 0.518883 | ||||||||
\(217\) | 7.41151 | 0.503126 | ||||||||
\(218\) | 42.9549 | 2.90927 | ||||||||
\(219\) | 2.55944 | 0.172951 | ||||||||
\(220\) | −31.7673 | −2.14175 | ||||||||
\(221\) | 0.567079 | 0.0381459 | ||||||||
\(222\) | −1.23167 | −0.0826645 | ||||||||
\(223\) | 19.8521 | 1.32939 | 0.664697 | − | 0.747113i | \(-0.268561\pi\) | ||||
0.664697 | + | 0.747113i | \(0.268561\pi\) | |||||||
\(224\) | −11.0228 | −0.736490 | ||||||||
\(225\) | 8.97010 | 0.598007 | ||||||||
\(226\) | −27.5495 | −1.83257 | ||||||||
\(227\) | −21.7789 | −1.44552 | −0.722758 | − | 0.691101i | \(-0.757126\pi\) | ||||
−0.722758 | + | 0.691101i | \(0.757126\pi\) | |||||||
\(228\) | −0.0978534 | −0.00648050 | ||||||||
\(229\) | 17.1392 | 1.13259 | 0.566297 | − | 0.824201i | \(-0.308376\pi\) | ||||
0.566297 | + | 0.824201i | \(0.308376\pi\) | |||||||
\(230\) | 21.6295 | 1.42621 | ||||||||
\(231\) | 1.42727 | 0.0939074 | ||||||||
\(232\) | 57.3148 | 3.76290 | ||||||||
\(233\) | −5.53066 | −0.362326 | −0.181163 | − | 0.983453i | \(-0.557986\pi\) | ||||
−0.181163 | + | 0.983453i | \(0.557986\pi\) | |||||||
\(234\) | −22.7952 | −1.49017 | ||||||||
\(235\) | −10.3255 | −0.673560 | ||||||||
\(236\) | 17.8544 | 1.16222 | ||||||||
\(237\) | −2.78414 | −0.180849 | ||||||||
\(238\) | 0.743732 | 0.0482090 | ||||||||
\(239\) | 23.6992 | 1.53297 | 0.766487 | − | 0.642260i | \(-0.222003\pi\) | ||||
0.766487 | + | 0.642260i | \(0.222003\pi\) | |||||||
\(240\) | −2.14963 | −0.138758 | ||||||||
\(241\) | 20.3636 | 1.31174 | 0.655869 | − | 0.754875i | \(-0.272302\pi\) | ||||
0.655869 | + | 0.754875i | \(0.272302\pi\) | |||||||
\(242\) | −33.6004 | −2.15991 | ||||||||
\(243\) | 5.06368 | 0.324835 | ||||||||
\(244\) | −31.9512 | −2.04547 | ||||||||
\(245\) | 6.56102 | 0.419168 | ||||||||
\(246\) | −1.82822 | −0.116563 | ||||||||
\(247\) | 0.333201 | 0.0212011 | ||||||||
\(248\) | −32.5775 | −2.06867 | ||||||||
\(249\) | −2.40860 | −0.152639 | ||||||||
\(250\) | −28.9879 | −1.83336 | ||||||||
\(251\) | −30.6631 | −1.93544 | −0.967718 | − | 0.252035i | \(-0.918900\pi\) | ||||
−0.967718 | + | 0.252035i | \(0.918900\pi\) | |||||||
\(252\) | −20.8497 | −1.31341 | ||||||||
\(253\) | 29.3833 | 1.84731 | ||||||||
\(254\) | −51.9211 | −3.25782 | ||||||||
\(255\) | 0.0507530 | 0.00317827 | ||||||||
\(256\) | −25.5597 | −1.59748 | ||||||||
\(257\) | −9.07953 | −0.566365 | −0.283183 | − | 0.959066i | \(-0.591390\pi\) | ||||
−0.283183 | + | 0.959066i | \(0.591390\pi\) | |||||||
\(258\) | 6.09163 | 0.379248 | ||||||||
\(259\) | 3.83603 | 0.238360 | ||||||||
\(260\) | 19.3721 | 1.20141 | ||||||||
\(261\) | 25.3200 | 1.56727 | ||||||||
\(262\) | −10.4753 | −0.647165 | ||||||||
\(263\) | 27.7582 | 1.71165 | 0.855823 | − | 0.517270i | \(-0.173052\pi\) | ||||
0.855823 | + | 0.517270i | \(0.173052\pi\) | |||||||
\(264\) | −6.27360 | −0.386113 | ||||||||
\(265\) | −4.50438 | −0.276702 | ||||||||
\(266\) | 0.436998 | 0.0267941 | ||||||||
\(267\) | 1.91505 | 0.117199 | ||||||||
\(268\) | 10.6916 | 0.653092 | ||||||||
\(269\) | 1.59950 | 0.0975232 | 0.0487616 | − | 0.998810i | \(-0.484473\pi\) | ||||
0.0487616 | + | 0.998810i | \(0.484473\pi\) | |||||||
\(270\) | −4.10530 | −0.249840 | ||||||||
\(271\) | 25.9659 | 1.57732 | 0.788658 | − | 0.614833i | \(-0.210776\pi\) | ||||
0.788658 | + | 0.614833i | \(0.210776\pi\) | |||||||
\(272\) | −1.52169 | −0.0922662 | ||||||||
\(273\) | −0.870368 | −0.0526770 | ||||||||
\(274\) | 11.9919 | 0.724455 | ||||||||
\(275\) | −14.8492 | −0.895439 | ||||||||
\(276\) | 5.26219 | 0.316747 | ||||||||
\(277\) | −24.3092 | −1.46060 | −0.730299 | − | 0.683127i | \(-0.760619\pi\) | ||||
−0.730299 | + | 0.683127i | \(0.760619\pi\) | |||||||
\(278\) | 10.6509 | 0.638796 | ||||||||
\(279\) | −14.3918 | −0.861615 | ||||||||
\(280\) | 14.3830 | 0.859550 | ||||||||
\(281\) | 6.63221 | 0.395644 | 0.197822 | − | 0.980238i | \(-0.436613\pi\) | ||||
0.197822 | + | 0.980238i | \(0.436613\pi\) | |||||||
\(282\) | −3.60202 | −0.214497 | ||||||||
\(283\) | 10.4707 | 0.622417 | 0.311208 | − | 0.950342i | \(-0.399266\pi\) | ||||
0.311208 | + | 0.950342i | \(0.399266\pi\) | |||||||
\(284\) | 21.3595 | 1.26745 | ||||||||
\(285\) | 0.0298212 | 0.00176645 | ||||||||
\(286\) | 37.7353 | 2.23133 | ||||||||
\(287\) | 5.69398 | 0.336105 | ||||||||
\(288\) | 21.4042 | 1.26126 | ||||||||
\(289\) | −16.9641 | −0.997887 | ||||||||
\(290\) | −30.8543 | −1.81182 | ||||||||
\(291\) | −1.35407 | −0.0793769 | ||||||||
\(292\) | 61.8933 | 3.62203 | ||||||||
\(293\) | −1.48028 | −0.0864787 | −0.0432394 | − | 0.999065i | \(-0.513768\pi\) | ||||
−0.0432394 | + | 0.999065i | \(0.513768\pi\) | |||||||
\(294\) | 2.28880 | 0.133485 | ||||||||
\(295\) | −5.44118 | −0.316798 | ||||||||
\(296\) | −16.8614 | −0.980048 | ||||||||
\(297\) | −5.57697 | −0.323609 | ||||||||
\(298\) | 33.4198 | 1.93596 | ||||||||
\(299\) | −17.9183 | −1.03624 | ||||||||
\(300\) | −2.65931 | −0.153535 | ||||||||
\(301\) | −18.9723 | −1.09355 | ||||||||
\(302\) | 47.4322 | 2.72942 | ||||||||
\(303\) | −1.40600 | −0.0807728 | ||||||||
\(304\) | −0.894108 | −0.0512806 | ||||||||
\(305\) | 9.73725 | 0.557553 | ||||||||
\(306\) | −1.44419 | −0.0825589 | ||||||||
\(307\) | −27.4938 | −1.56915 | −0.784576 | − | 0.620033i | \(-0.787119\pi\) | ||||
−0.784576 | + | 0.620033i | \(0.787119\pi\) | |||||||
\(308\) | 34.5147 | 1.96666 | ||||||||
\(309\) | −1.93740 | −0.110215 | ||||||||
\(310\) | 17.5374 | 0.996059 | ||||||||
\(311\) | −33.3387 | −1.89046 | −0.945232 | − | 0.326399i | \(-0.894165\pi\) | ||||
−0.945232 | + | 0.326399i | \(0.894165\pi\) | |||||||
\(312\) | 3.82572 | 0.216589 | ||||||||
\(313\) | −26.3939 | −1.49187 | −0.745934 | − | 0.666019i | \(-0.767997\pi\) | ||||
−0.745934 | + | 0.666019i | \(0.767997\pi\) | |||||||
\(314\) | −3.34572 | −0.188810 | ||||||||
\(315\) | 6.35401 | 0.358008 | ||||||||
\(316\) | −67.3270 | −3.78744 | ||||||||
\(317\) | 6.96008 | 0.390917 | 0.195458 | − | 0.980712i | \(-0.437381\pi\) | ||||
0.195458 | + | 0.980712i | \(0.437381\pi\) | |||||||
\(318\) | −1.57134 | −0.0881166 | ||||||||
\(319\) | −41.9150 | −2.34679 | ||||||||
\(320\) | −3.52760 | −0.197199 | ||||||||
\(321\) | −0.718768 | −0.0401177 | ||||||||
\(322\) | −23.5001 | −1.30961 | ||||||||
\(323\) | 0.0211100 | 0.00117459 | ||||||||
\(324\) | 39.9839 | 2.22133 | ||||||||
\(325\) | 9.05522 | 0.502293 | ||||||||
\(326\) | −20.0878 | −1.11256 | ||||||||
\(327\) | −3.18479 | −0.176120 | ||||||||
\(328\) | −25.0280 | −1.38194 | ||||||||
\(329\) | 11.2185 | 0.618494 | ||||||||
\(330\) | 3.37727 | 0.185912 | ||||||||
\(331\) | 12.6989 | 0.697994 | 0.348997 | − | 0.937124i | \(-0.386522\pi\) | ||||
0.348997 | + | 0.937124i | \(0.386522\pi\) | |||||||
\(332\) | −58.2454 | −3.19663 | ||||||||
\(333\) | −7.44888 | −0.408196 | ||||||||
\(334\) | 57.8148 | 3.16348 | ||||||||
\(335\) | −3.25829 | −0.178020 | ||||||||
\(336\) | 2.33553 | 0.127414 | ||||||||
\(337\) | −21.2437 | −1.15722 | −0.578608 | − | 0.815606i | \(-0.696404\pi\) | ||||
−0.578608 | + | 0.815606i | \(0.696404\pi\) | |||||||
\(338\) | 10.4100 | 0.566231 | ||||||||
\(339\) | 2.04260 | 0.110939 | ||||||||
\(340\) | 1.22732 | 0.0665610 | ||||||||
\(341\) | 23.8243 | 1.29016 | ||||||||
\(342\) | −0.848570 | −0.0458854 | ||||||||
\(343\) | −17.8121 | −0.961762 | ||||||||
\(344\) | 83.3934 | 4.49627 | ||||||||
\(345\) | −1.60367 | −0.0863387 | ||||||||
\(346\) | −17.3012 | −0.930120 | ||||||||
\(347\) | −4.94845 | −0.265646 | −0.132823 | − | 0.991140i | \(-0.542404\pi\) | ||||
−0.132823 | + | 0.991140i | \(0.542404\pi\) | |||||||
\(348\) | −7.50646 | −0.402388 | ||||||||
\(349\) | −19.4692 | −1.04216 | −0.521082 | − | 0.853506i | \(-0.674472\pi\) | ||||
−0.521082 | + | 0.853506i | \(0.674472\pi\) | |||||||
\(350\) | 11.8760 | 0.634801 | ||||||||
\(351\) | 3.40091 | 0.181527 | ||||||||
\(352\) | −35.4327 | −1.88857 | ||||||||
\(353\) | 20.2324 | 1.07686 | 0.538430 | − | 0.842670i | \(-0.319018\pi\) | ||||
0.538430 | + | 0.842670i | \(0.319018\pi\) | |||||||
\(354\) | −1.89814 | −0.100885 | ||||||||
\(355\) | −6.50938 | −0.345482 | ||||||||
\(356\) | 46.3103 | 2.45444 | ||||||||
\(357\) | −0.0551423 | −0.00291844 | ||||||||
\(358\) | 8.09294 | 0.427725 | ||||||||
\(359\) | −4.31362 | −0.227664 | −0.113832 | − | 0.993500i | \(-0.536313\pi\) | ||||
−0.113832 | + | 0.993500i | \(0.536313\pi\) | |||||||
\(360\) | −27.9292 | −1.47200 | ||||||||
\(361\) | −18.9876 | −0.999347 | ||||||||
\(362\) | −3.70551 | −0.194757 | ||||||||
\(363\) | 2.49122 | 0.130755 | ||||||||
\(364\) | −21.0475 | −1.10319 | ||||||||
\(365\) | −18.8622 | −0.987292 | ||||||||
\(366\) | 3.39682 | 0.177555 | ||||||||
\(367\) | 8.61722 | 0.449815 | 0.224908 | − | 0.974380i | \(-0.427792\pi\) | ||||
0.224908 | + | 0.974380i | \(0.427792\pi\) | |||||||
\(368\) | 48.0818 | 2.50644 | ||||||||
\(369\) | −11.0567 | −0.575587 | ||||||||
\(370\) | 9.07699 | 0.471890 | ||||||||
\(371\) | 4.89394 | 0.254081 | ||||||||
\(372\) | 4.26664 | 0.221215 | ||||||||
\(373\) | −7.65555 | −0.396389 | −0.198195 | − | 0.980163i | \(-0.563508\pi\) | ||||
−0.198195 | + | 0.980163i | \(0.563508\pi\) | |||||||
\(374\) | 2.39072 | 0.123621 | ||||||||
\(375\) | 2.14924 | 0.110986 | ||||||||
\(376\) | −49.3111 | −2.54302 | ||||||||
\(377\) | 25.5603 | 1.31642 | ||||||||
\(378\) | 4.46034 | 0.229415 | ||||||||
\(379\) | −3.24251 | −0.166557 | −0.0832783 | − | 0.996526i | \(-0.526539\pi\) | ||||
−0.0832783 | + | 0.996526i | \(0.526539\pi\) | |||||||
\(380\) | 0.721145 | 0.0369940 | ||||||||
\(381\) | 3.84957 | 0.197219 | ||||||||
\(382\) | 3.28305 | 0.167975 | ||||||||
\(383\) | 4.60080 | 0.235090 | 0.117545 | − | 0.993068i | \(-0.462498\pi\) | ||||
0.117545 | + | 0.993068i | \(0.462498\pi\) | |||||||
\(384\) | 1.52269 | 0.0777043 | ||||||||
\(385\) | −10.5185 | −0.536071 | ||||||||
\(386\) | −65.9025 | −3.35435 | ||||||||
\(387\) | 36.8408 | 1.87272 | ||||||||
\(388\) | −32.7445 | −1.66235 | ||||||||
\(389\) | −4.43350 | −0.224787 | −0.112394 | − | 0.993664i | \(-0.535852\pi\) | ||||
−0.112394 | + | 0.993664i | \(0.535852\pi\) | |||||||
\(390\) | −2.05950 | −0.104287 | ||||||||
\(391\) | −1.13522 | −0.0574104 | ||||||||
\(392\) | 31.3333 | 1.58257 | ||||||||
\(393\) | 0.776665 | 0.0391776 | ||||||||
\(394\) | 6.93188 | 0.349223 | ||||||||
\(395\) | 20.5181 | 1.03238 | ||||||||
\(396\) | −67.0213 | −3.36795 | ||||||||
\(397\) | −26.7763 | −1.34386 | −0.671932 | − | 0.740613i | \(-0.734535\pi\) | ||||
−0.671932 | + | 0.740613i | \(0.734535\pi\) | |||||||
\(398\) | 39.5504 | 1.98248 | ||||||||
\(399\) | −0.0324002 | −0.00162204 | ||||||||
\(400\) | −24.2987 | −1.21493 | ||||||||
\(401\) | 26.1492 | 1.30583 | 0.652913 | − | 0.757432i | \(-0.273547\pi\) | ||||
0.652913 | + | 0.757432i | \(0.273547\pi\) | |||||||
\(402\) | −1.13665 | −0.0566909 | ||||||||
\(403\) | −14.5284 | −0.723709 | ||||||||
\(404\) | −34.0004 | −1.69159 | ||||||||
\(405\) | −12.1852 | −0.605488 | ||||||||
\(406\) | 33.5226 | 1.66370 | ||||||||
\(407\) | 12.3309 | 0.611221 | ||||||||
\(408\) | 0.242379 | 0.0119996 | ||||||||
\(409\) | −29.8787 | −1.47741 | −0.738704 | − | 0.674030i | \(-0.764562\pi\) | ||||
−0.738704 | + | 0.674030i | \(0.764562\pi\) | |||||||
\(410\) | 13.4733 | 0.665400 | ||||||||
\(411\) | −0.889109 | −0.0438565 | ||||||||
\(412\) | −46.8509 | −2.30818 | ||||||||
\(413\) | 5.91175 | 0.290898 | ||||||||
\(414\) | 45.6329 | 2.24274 | ||||||||
\(415\) | 17.7505 | 0.871337 | ||||||||
\(416\) | 21.6073 | 1.05939 | ||||||||
\(417\) | −0.789683 | −0.0386709 | ||||||||
\(418\) | 1.40473 | 0.0687076 | ||||||||
\(419\) | −17.2139 | −0.840955 | −0.420478 | − | 0.907303i | \(-0.638138\pi\) | ||||
−0.420478 | + | 0.907303i | \(0.638138\pi\) | |||||||
\(420\) | −1.88373 | −0.0919166 | ||||||||
\(421\) | −11.9735 | −0.583553 | −0.291776 | − | 0.956487i | \(-0.594246\pi\) | ||||
−0.291776 | + | 0.956487i | \(0.594246\pi\) | |||||||
\(422\) | 2.14943 | 0.104633 | ||||||||
\(423\) | −21.7842 | −1.05919 | ||||||||
\(424\) | −21.5114 | −1.04469 | ||||||||
\(425\) | 0.573695 | 0.0278283 | ||||||||
\(426\) | −2.27078 | −0.110020 | ||||||||
\(427\) | −10.5794 | −0.511971 | ||||||||
\(428\) | −17.3815 | −0.840166 | ||||||||
\(429\) | −2.79780 | −0.135079 | ||||||||
\(430\) | −44.8931 | −2.16494 | ||||||||
\(431\) | −34.2594 | −1.65022 | −0.825109 | − | 0.564973i | \(-0.808886\pi\) | ||||
−0.825109 | + | 0.564973i | \(0.808886\pi\) | |||||||
\(432\) | −9.12596 | −0.439073 | ||||||||
\(433\) | −17.4810 | −0.840083 | −0.420041 | − | 0.907505i | \(-0.637984\pi\) | ||||
−0.420041 | + | 0.907505i | \(0.637984\pi\) | |||||||
\(434\) | −19.0541 | −0.914628 | ||||||||
\(435\) | 2.28762 | 0.109683 | ||||||||
\(436\) | −77.0157 | −3.68838 | ||||||||
\(437\) | −0.667025 | −0.0319081 | ||||||||
\(438\) | −6.58003 | −0.314406 | ||||||||
\(439\) | −7.02501 | −0.335285 | −0.167643 | − | 0.985848i | \(-0.553615\pi\) | ||||
−0.167643 | + | 0.985848i | \(0.553615\pi\) | |||||||
\(440\) | 46.2342 | 2.20413 | ||||||||
\(441\) | 13.8421 | 0.659150 | ||||||||
\(442\) | −1.45790 | −0.0693450 | ||||||||
\(443\) | −24.7040 | −1.17372 | −0.586860 | − | 0.809688i | \(-0.699636\pi\) | ||||
−0.586860 | + | 0.809688i | \(0.699636\pi\) | |||||||
\(444\) | 2.20832 | 0.104802 | ||||||||
\(445\) | −14.1132 | −0.669031 | ||||||||
\(446\) | −51.0374 | −2.41669 | ||||||||
\(447\) | −2.47784 | −0.117198 | ||||||||
\(448\) | 3.83268 | 0.181077 | ||||||||
\(449\) | −38.0305 | −1.79477 | −0.897384 | − | 0.441250i | \(-0.854535\pi\) | ||||
−0.897384 | + | 0.441250i | \(0.854535\pi\) | |||||||
\(450\) | −23.0611 | −1.08711 | ||||||||
\(451\) | 18.3033 | 0.861868 | ||||||||
\(452\) | 49.3947 | 2.32333 | ||||||||
\(453\) | −3.51675 | −0.165231 | ||||||||
\(454\) | 55.9911 | 2.62779 | ||||||||
\(455\) | 6.41430 | 0.300707 | ||||||||
\(456\) | 0.142416 | 0.00666924 | ||||||||
\(457\) | 1.66697 | 0.0779774 | 0.0389887 | − | 0.999240i | \(-0.487586\pi\) | ||||
0.0389887 | + | 0.999240i | \(0.487586\pi\) | |||||||
\(458\) | −44.0630 | −2.05893 | ||||||||
\(459\) | 0.215465 | 0.0100571 | ||||||||
\(460\) | −38.7805 | −1.80815 | ||||||||
\(461\) | −2.97689 | −0.138648 | −0.0693238 | − | 0.997594i | \(-0.522084\pi\) | ||||
−0.0693238 | + | 0.997594i | \(0.522084\pi\) | |||||||
\(462\) | −3.66935 | −0.170713 | ||||||||
\(463\) | −22.9068 | −1.06457 | −0.532284 | − | 0.846566i | \(-0.678666\pi\) | ||||
−0.532284 | + | 0.846566i | \(0.678666\pi\) | |||||||
\(464\) | −68.5882 | −3.18413 | ||||||||
\(465\) | −1.30027 | −0.0602987 | ||||||||
\(466\) | 14.2187 | 0.658668 | ||||||||
\(467\) | 19.4041 | 0.897914 | 0.448957 | − | 0.893553i | \(-0.351796\pi\) | ||||
0.448957 | + | 0.893553i | \(0.351796\pi\) | |||||||
\(468\) | 40.8704 | 1.88924 | ||||||||
\(469\) | 3.54008 | 0.163466 | ||||||||
\(470\) | 26.5456 | 1.22446 | ||||||||
\(471\) | 0.248061 | 0.0114300 | ||||||||
\(472\) | −25.9853 | −1.19607 | ||||||||
\(473\) | −60.9865 | −2.80416 | ||||||||
\(474\) | 7.15771 | 0.328765 | ||||||||
\(475\) | 0.337088 | 0.0154667 | ||||||||
\(476\) | −1.33347 | −0.0611194 | ||||||||
\(477\) | −9.50314 | −0.435119 | ||||||||
\(478\) | −60.9279 | −2.78678 | ||||||||
\(479\) | −33.5116 | −1.53118 | −0.765591 | − | 0.643328i | \(-0.777553\pi\) | ||||
−0.765591 | + | 0.643328i | \(0.777553\pi\) | |||||||
\(480\) | 1.93383 | 0.0882669 | ||||||||
\(481\) | −7.51956 | −0.342863 | ||||||||
\(482\) | −52.3526 | −2.38460 | ||||||||
\(483\) | 1.74236 | 0.0792802 | ||||||||
\(484\) | 60.2435 | 2.73834 | ||||||||
\(485\) | 9.97900 | 0.453123 | ||||||||
\(486\) | −13.0181 | −0.590515 | ||||||||
\(487\) | 17.7440 | 0.804059 | 0.402030 | − | 0.915627i | \(-0.368305\pi\) | ||||
0.402030 | + | 0.915627i | \(0.368305\pi\) | |||||||
\(488\) | 46.5019 | 2.10504 | ||||||||
\(489\) | 1.48936 | 0.0673513 | ||||||||
\(490\) | −16.8676 | −0.762002 | ||||||||
\(491\) | −38.8993 | −1.75550 | −0.877751 | − | 0.479117i | \(-0.840957\pi\) | ||||
−0.877751 | + | 0.479117i | \(0.840957\pi\) | |||||||
\(492\) | 3.27789 | 0.147779 | ||||||||
\(493\) | 1.61938 | 0.0729330 | ||||||||
\(494\) | −0.856622 | −0.0385413 | ||||||||
\(495\) | 20.4250 | 0.918033 | ||||||||
\(496\) | 38.9852 | 1.75049 | ||||||||
\(497\) | 7.07233 | 0.317238 | ||||||||
\(498\) | 6.19222 | 0.277480 | ||||||||
\(499\) | −26.9134 | −1.20481 | −0.602405 | − | 0.798191i | \(-0.705791\pi\) | ||||
−0.602405 | + | 0.798191i | \(0.705791\pi\) | |||||||
\(500\) | 51.9736 | 2.32433 | ||||||||
\(501\) | −4.28654 | −0.191509 | ||||||||
\(502\) | 78.8312 | 3.51841 | ||||||||
\(503\) | 16.9061 | 0.753806 | 0.376903 | − | 0.926253i | \(-0.376989\pi\) | ||||
0.376903 | + | 0.926253i | \(0.376989\pi\) | |||||||
\(504\) | 30.3446 | 1.35166 | ||||||||
\(505\) | 10.3617 | 0.461092 | ||||||||
\(506\) | −75.5411 | −3.35821 | ||||||||
\(507\) | −0.771828 | −0.0342781 | ||||||||
\(508\) | 93.0916 | 4.13027 | ||||||||
\(509\) | 13.9693 | 0.619180 | 0.309590 | − | 0.950870i | \(-0.399808\pi\) | ||||
0.309590 | + | 0.950870i | \(0.399808\pi\) | |||||||
\(510\) | −0.130480 | −0.00577775 | ||||||||
\(511\) | 20.4935 | 0.906577 | ||||||||
\(512\) | 49.7342 | 2.19796 | ||||||||
\(513\) | 0.126602 | 0.00558961 | ||||||||
\(514\) | 23.3424 | 1.02959 | ||||||||
\(515\) | 14.2780 | 0.629162 | ||||||||
\(516\) | −10.9219 | −0.480812 | ||||||||
\(517\) | 36.0618 | 1.58599 | ||||||||
\(518\) | −9.86200 | −0.433311 | ||||||||
\(519\) | 1.28276 | 0.0563069 | ||||||||
\(520\) | −28.1942 | −1.23640 | ||||||||
\(521\) | −16.1597 | −0.707969 | −0.353985 | − | 0.935251i | \(-0.615173\pi\) | ||||
−0.353985 | + | 0.935251i | \(0.615173\pi\) | |||||||
\(522\) | −65.0949 | −2.84913 | ||||||||
\(523\) | −34.5524 | −1.51087 | −0.755436 | − | 0.655222i | \(-0.772575\pi\) | ||||
−0.755436 | + | 0.655222i | \(0.772575\pi\) | |||||||
\(524\) | 18.7816 | 0.820477 | ||||||||
\(525\) | −0.880521 | −0.0384291 | ||||||||
\(526\) | −71.3632 | −3.11158 | ||||||||
\(527\) | −0.920447 | −0.0400953 | ||||||||
\(528\) | 7.50757 | 0.326725 | ||||||||
\(529\) | 12.8701 | 0.559571 | ||||||||
\(530\) | 11.5802 | 0.503014 | ||||||||
\(531\) | −11.4796 | −0.498170 | ||||||||
\(532\) | −0.783512 | −0.0339696 | ||||||||
\(533\) | −11.1616 | −0.483462 | ||||||||
\(534\) | −4.92337 | −0.213055 | ||||||||
\(535\) | 5.29706 | 0.229012 | ||||||||
\(536\) | −15.5605 | −0.672112 | ||||||||
\(537\) | −0.600032 | −0.0258933 | ||||||||
\(538\) | −4.11213 | −0.177286 | ||||||||
\(539\) | −22.9144 | −0.986992 | ||||||||
\(540\) | 7.36056 | 0.316748 | ||||||||
\(541\) | 3.32026 | 0.142749 | 0.0713747 | − | 0.997450i | \(-0.477261\pi\) | ||||
0.0713747 | + | 0.997450i | \(0.477261\pi\) | |||||||
\(542\) | −66.7553 | −2.86739 | ||||||||
\(543\) | 0.274737 | 0.0117901 | ||||||||
\(544\) | 1.36893 | 0.0586926 | ||||||||
\(545\) | 23.4708 | 1.00538 | ||||||||
\(546\) | 2.23761 | 0.0957611 | ||||||||
\(547\) | −16.0509 | −0.686285 | −0.343142 | − | 0.939283i | \(-0.611491\pi\) | ||||
−0.343142 | + | 0.939283i | \(0.611491\pi\) | |||||||
\(548\) | −21.5007 | −0.918466 | ||||||||
\(549\) | 20.5432 | 0.876762 | ||||||||
\(550\) | 38.1755 | 1.62781 | ||||||||
\(551\) | 0.951504 | 0.0405354 | ||||||||
\(552\) | −7.65860 | −0.325971 | ||||||||
\(553\) | −22.2926 | −0.947979 | ||||||||
\(554\) | 62.4962 | 2.65521 | ||||||||
\(555\) | −0.672993 | −0.0285669 | ||||||||
\(556\) | −19.0964 | −0.809867 | ||||||||
\(557\) | −4.99475 | −0.211634 | −0.105817 | − | 0.994386i | \(-0.533746\pi\) | ||||
−0.105817 | + | 0.994386i | \(0.533746\pi\) | |||||||
\(558\) | 36.9997 | 1.56632 | ||||||||
\(559\) | 37.1904 | 1.57299 | ||||||||
\(560\) | −17.2121 | −0.727342 | ||||||||
\(561\) | −0.177255 | −0.00748370 | ||||||||
\(562\) | −17.0506 | −0.719238 | ||||||||
\(563\) | −18.6702 | −0.786854 | −0.393427 | − | 0.919356i | \(-0.628711\pi\) | ||||
−0.393427 | + | 0.919356i | \(0.628711\pi\) | |||||||
\(564\) | 6.45822 | 0.271940 | ||||||||
\(565\) | −15.0532 | −0.633293 | ||||||||
\(566\) | −26.9189 | −1.13149 | ||||||||
\(567\) | 13.2390 | 0.555987 | ||||||||
\(568\) | −31.0866 | −1.30437 | ||||||||
\(569\) | −13.8393 | −0.580175 | −0.290088 | − | 0.957000i | \(-0.593684\pi\) | ||||
−0.290088 | + | 0.957000i | \(0.593684\pi\) | |||||||
\(570\) | −0.0766668 | −0.00321122 | ||||||||
\(571\) | 46.4575 | 1.94419 | 0.972094 | − | 0.234594i | \(-0.0753759\pi\) | ||||
0.972094 | + | 0.234594i | \(0.0753759\pi\) | |||||||
\(572\) | −67.6572 | −2.82889 | ||||||||
\(573\) | −0.243414 | −0.0101688 | ||||||||
\(574\) | −14.6386 | −0.611002 | ||||||||
\(575\) | −18.1274 | −0.755963 | ||||||||
\(576\) | −7.44237 | −0.310099 | ||||||||
\(577\) | −40.3325 | −1.67906 | −0.839531 | − | 0.543311i | \(-0.817170\pi\) | ||||
−0.839531 | + | 0.543311i | \(0.817170\pi\) | |||||||
\(578\) | 43.6127 | 1.81405 | ||||||||
\(579\) | 4.88619 | 0.203063 | ||||||||
\(580\) | 55.3199 | 2.29703 | ||||||||
\(581\) | −19.2856 | −0.800102 | ||||||||
\(582\) | 3.48115 | 0.144298 | ||||||||
\(583\) | 15.7316 | 0.651535 | ||||||||
\(584\) | −90.0795 | −3.72752 | ||||||||
\(585\) | −12.4554 | −0.514968 | ||||||||
\(586\) | 3.80562 | 0.157209 | ||||||||
\(587\) | 23.8280 | 0.983485 | 0.491743 | − | 0.870741i | \(-0.336360\pi\) | ||||
0.491743 | + | 0.870741i | \(0.336360\pi\) | |||||||
\(588\) | −4.10369 | −0.169233 | ||||||||
\(589\) | −0.540831 | −0.0222846 | ||||||||
\(590\) | 13.9886 | 0.575904 | ||||||||
\(591\) | −0.513948 | −0.0211410 | ||||||||
\(592\) | 20.1779 | 0.829307 | ||||||||
\(593\) | 4.01028 | 0.164682 | 0.0823412 | − | 0.996604i | \(-0.473760\pi\) | ||||
0.0823412 | + | 0.996604i | \(0.473760\pi\) | |||||||
\(594\) | 14.3378 | 0.588285 | ||||||||
\(595\) | 0.406379 | 0.0166599 | ||||||||
\(596\) | −59.9198 | −2.45441 | ||||||||
\(597\) | −2.93237 | −0.120014 | ||||||||
\(598\) | 46.0659 | 1.88378 | ||||||||
\(599\) | 19.4172 | 0.793366 | 0.396683 | − | 0.917956i | \(-0.370161\pi\) | ||||
0.396683 | + | 0.917956i | \(0.370161\pi\) | |||||||
\(600\) | 3.87035 | 0.158007 | ||||||||
\(601\) | 29.2910 | 1.19480 | 0.597402 | − | 0.801942i | \(-0.296200\pi\) | ||||
0.597402 | + | 0.801942i | \(0.296200\pi\) | |||||||
\(602\) | 48.7757 | 1.98795 | ||||||||
\(603\) | −6.87420 | −0.279939 | ||||||||
\(604\) | −85.0432 | −3.46036 | ||||||||
\(605\) | −18.3594 | −0.746416 | ||||||||
\(606\) | 3.61467 | 0.146836 | ||||||||
\(607\) | −18.5559 | −0.753161 | −0.376581 | − | 0.926384i | \(-0.622900\pi\) | ||||
−0.376581 | + | 0.926384i | \(0.622900\pi\) | |||||||
\(608\) | 0.804351 | 0.0326207 | ||||||||
\(609\) | −2.48546 | −0.100716 | ||||||||
\(610\) | −25.0333 | −1.01357 | ||||||||
\(611\) | −21.9909 | −0.889658 | ||||||||
\(612\) | 2.58935 | 0.104668 | ||||||||
\(613\) | −8.72673 | −0.352469 | −0.176235 | − | 0.984348i | \(-0.556392\pi\) | ||||
−0.176235 | + | 0.984348i | \(0.556392\pi\) | |||||||
\(614\) | 70.6833 | 2.85254 | ||||||||
\(615\) | −0.998949 | −0.0402815 | ||||||||
\(616\) | −50.2327 | −2.02393 | ||||||||
\(617\) | −25.5120 | −1.02707 | −0.513536 | − | 0.858068i | \(-0.671665\pi\) | ||||
−0.513536 | + | 0.858068i | \(0.671665\pi\) | |||||||
\(618\) | 4.98083 | 0.200359 | ||||||||
\(619\) | 37.7293 | 1.51647 | 0.758234 | − | 0.651982i | \(-0.226062\pi\) | ||||
0.758234 | + | 0.651982i | \(0.226062\pi\) | |||||||
\(620\) | −31.4436 | −1.26281 | ||||||||
\(621\) | −6.80818 | −0.273203 | ||||||||
\(622\) | 85.7100 | 3.43666 | ||||||||
\(623\) | 15.3338 | 0.614335 | ||||||||
\(624\) | −4.57822 | −0.183275 | ||||||||
\(625\) | −0.705688 | −0.0282275 | ||||||||
\(626\) | 67.8556 | 2.71205 | ||||||||
\(627\) | −0.104150 | −0.00415937 | ||||||||
\(628\) | 5.99868 | 0.239373 | ||||||||
\(629\) | −0.476403 | −0.0189954 | ||||||||
\(630\) | −16.3354 | −0.650819 | ||||||||
\(631\) | −25.1965 | −1.00305 | −0.501527 | − | 0.865142i | \(-0.667228\pi\) | ||||
−0.501527 | + | 0.865142i | \(0.667228\pi\) | |||||||
\(632\) | 97.9878 | 3.89775 | ||||||||
\(633\) | −0.159365 | −0.00633418 | ||||||||
\(634\) | −17.8936 | −0.710644 | ||||||||
\(635\) | −28.3700 | −1.12583 | ||||||||
\(636\) | 2.81733 | 0.111714 | ||||||||
\(637\) | 13.9735 | 0.553650 | ||||||||
\(638\) | 107.759 | 4.26620 | ||||||||
\(639\) | −13.7332 | −0.543277 | ||||||||
\(640\) | −11.2217 | −0.443575 | ||||||||
\(641\) | −2.24788 | −0.0887860 | −0.0443930 | − | 0.999014i | \(-0.514135\pi\) | ||||
−0.0443930 | + | 0.999014i | \(0.514135\pi\) | |||||||
\(642\) | 1.84787 | 0.0729296 | ||||||||
\(643\) | 14.7236 | 0.580644 | 0.290322 | − | 0.956929i | \(-0.406238\pi\) | ||||
0.290322 | + | 0.956929i | \(0.406238\pi\) | |||||||
\(644\) | 42.1344 | 1.66033 | ||||||||
\(645\) | 3.32850 | 0.131060 | ||||||||
\(646\) | −0.0542714 | −0.00213528 | ||||||||
\(647\) | 37.9498 | 1.49196 | 0.745981 | − | 0.665968i | \(-0.231981\pi\) | ||||
0.745981 | + | 0.665968i | \(0.231981\pi\) | |||||||
\(648\) | −58.1925 | −2.28602 | ||||||||
\(649\) | 19.0033 | 0.745946 | ||||||||
\(650\) | −23.2799 | −0.913114 | ||||||||
\(651\) | 1.41272 | 0.0553691 | ||||||||
\(652\) | 36.0163 | 1.41051 | ||||||||
\(653\) | −31.0108 | −1.21355 | −0.606773 | − | 0.794875i | \(-0.707536\pi\) | ||||
−0.606773 | + | 0.794875i | \(0.707536\pi\) | |||||||
\(654\) | 8.18774 | 0.320166 | ||||||||
\(655\) | −5.72375 | −0.223645 | ||||||||
\(656\) | 29.9509 | 1.16938 | ||||||||
\(657\) | −39.7946 | −1.55253 | ||||||||
\(658\) | −28.8414 | −1.12435 | ||||||||
\(659\) | −31.6736 | −1.23383 | −0.616913 | − | 0.787031i | \(-0.711617\pi\) | ||||
−0.616913 | + | 0.787031i | \(0.711617\pi\) | |||||||
\(660\) | −6.05525 | −0.235700 | ||||||||
\(661\) | −35.0311 | −1.36255 | −0.681276 | − | 0.732026i | \(-0.738575\pi\) | ||||
−0.681276 | + | 0.732026i | \(0.738575\pi\) | |||||||
\(662\) | −32.6474 | −1.26888 | ||||||||
\(663\) | 0.108092 | 0.00419796 | ||||||||
\(664\) | 84.7704 | 3.28973 | ||||||||
\(665\) | 0.238778 | 0.00925941 | ||||||||
\(666\) | 19.1502 | 0.742056 | ||||||||
\(667\) | −51.1683 | −1.98125 | ||||||||
\(668\) | −103.659 | −4.01067 | ||||||||
\(669\) | 3.78405 | 0.146300 | ||||||||
\(670\) | 8.37670 | 0.323620 | ||||||||
\(671\) | −34.0073 | −1.31284 | ||||||||
\(672\) | −2.10108 | −0.0810507 | ||||||||
\(673\) | 27.8738 | 1.07446 | 0.537229 | − | 0.843437i | \(-0.319471\pi\) | ||||
0.537229 | + | 0.843437i | \(0.319471\pi\) | |||||||
\(674\) | 54.6150 | 2.10369 | ||||||||
\(675\) | 3.44059 | 0.132428 | ||||||||
\(676\) | −18.6646 | −0.717869 | ||||||||
\(677\) | −12.2263 | −0.469895 | −0.234947 | − | 0.972008i | \(-0.575492\pi\) | ||||
−0.234947 | + | 0.972008i | \(0.575492\pi\) | |||||||
\(678\) | −5.25128 | −0.201674 | ||||||||
\(679\) | −10.8420 | −0.416079 | ||||||||
\(680\) | −1.78625 | −0.0684995 | ||||||||
\(681\) | −4.15133 | −0.159079 | ||||||||
\(682\) | −61.2495 | −2.34536 | ||||||||
\(683\) | −14.0620 | −0.538069 | −0.269034 | − | 0.963131i | \(-0.586705\pi\) | ||||
−0.269034 | + | 0.963131i | \(0.586705\pi\) | |||||||
\(684\) | 1.52144 | 0.0581736 | ||||||||
\(685\) | 6.55242 | 0.250355 | ||||||||
\(686\) | 45.7928 | 1.74838 | ||||||||
\(687\) | 3.26695 | 0.124642 | ||||||||
\(688\) | −99.7962 | −3.80470 | ||||||||
\(689\) | −9.59331 | −0.365476 | ||||||||
\(690\) | 4.12285 | 0.156954 | ||||||||
\(691\) | −44.7071 | −1.70074 | −0.850369 | − | 0.526186i | \(-0.823621\pi\) | ||||
−0.850369 | + | 0.526186i | \(0.823621\pi\) | |||||||
\(692\) | 31.0201 | 1.17921 | ||||||||
\(693\) | −22.1914 | −0.842981 | ||||||||
\(694\) | 12.7219 | 0.482916 | ||||||||
\(695\) | 5.81968 | 0.220753 | ||||||||
\(696\) | 10.9249 | 0.414107 | ||||||||
\(697\) | −0.707144 | −0.0267850 | ||||||||
\(698\) | 50.0532 | 1.89454 | ||||||||
\(699\) | −1.05421 | −0.0398740 | ||||||||
\(700\) | −21.2931 | −0.804802 | ||||||||
\(701\) | 18.8742 | 0.712870 | 0.356435 | − | 0.934320i | \(-0.383992\pi\) | ||||
0.356435 | + | 0.934320i | \(0.383992\pi\) | |||||||
\(702\) | −8.74335 | −0.329997 | ||||||||
\(703\) | −0.279922 | −0.0105575 | ||||||||
\(704\) | 12.3201 | 0.464333 | ||||||||
\(705\) | −1.96816 | −0.0741254 | ||||||||
\(706\) | −52.0151 | −1.95761 | ||||||||
\(707\) | −11.2579 | −0.423396 | ||||||||
\(708\) | 3.40326 | 0.127903 | ||||||||
\(709\) | −45.3761 | −1.70414 | −0.852068 | − | 0.523431i | \(-0.824652\pi\) | ||||
−0.852068 | + | 0.523431i | \(0.824652\pi\) | |||||||
\(710\) | 16.7349 | 0.628048 | ||||||||
\(711\) | 43.2882 | 1.62344 | ||||||||
\(712\) | −67.4001 | −2.52592 | ||||||||
\(713\) | 29.0839 | 1.08920 | ||||||||
\(714\) | 0.141764 | 0.00530540 | ||||||||
\(715\) | 20.6188 | 0.771098 | ||||||||
\(716\) | −14.5102 | −0.542271 | ||||||||
\(717\) | 4.51736 | 0.168704 | ||||||||
\(718\) | 11.0898 | 0.413868 | ||||||||
\(719\) | 7.72346 | 0.288036 | 0.144018 | − | 0.989575i | \(-0.453998\pi\) | ||||
0.144018 | + | 0.989575i | \(0.453998\pi\) | |||||||
\(720\) | 33.4227 | 1.24559 | ||||||||
\(721\) | −15.5128 | −0.577726 | ||||||||
\(722\) | 48.8149 | 1.81670 | ||||||||
\(723\) | 3.88156 | 0.144357 | ||||||||
\(724\) | 6.64377 | 0.246914 | ||||||||
\(725\) | 25.8585 | 0.960360 | ||||||||
\(726\) | −6.40464 | −0.237699 | ||||||||
\(727\) | 3.75970 | 0.139439 | 0.0697197 | − | 0.997567i | \(-0.477790\pi\) | ||||
0.0697197 | + | 0.997567i | \(0.477790\pi\) | |||||||
\(728\) | 30.6326 | 1.13532 | ||||||||
\(729\) | −25.0578 | −0.928065 | ||||||||
\(730\) | 48.4925 | 1.79479 | ||||||||
\(731\) | 2.35620 | 0.0871473 | ||||||||
\(732\) | −6.09030 | −0.225104 | ||||||||
\(733\) | 45.6238 | 1.68516 | 0.842578 | − | 0.538575i | \(-0.181037\pi\) | ||||
0.842578 | + | 0.538575i | \(0.181037\pi\) | |||||||
\(734\) | −22.1539 | −0.817715 | ||||||||
\(735\) | 1.25061 | 0.0461295 | ||||||||
\(736\) | −43.2550 | −1.59440 | ||||||||
\(737\) | 11.3796 | 0.419173 | ||||||||
\(738\) | 28.4254 | 1.04635 | ||||||||
\(739\) | 9.77553 | 0.359599 | 0.179799 | − | 0.983703i | \(-0.442455\pi\) | ||||
0.179799 | + | 0.983703i | \(0.442455\pi\) | |||||||
\(740\) | −16.2745 | −0.598263 | ||||||||
\(741\) | 0.0635123 | 0.00233318 | ||||||||
\(742\) | −12.5817 | −0.461890 | ||||||||
\(743\) | −8.13920 | −0.298598 | −0.149299 | − | 0.988792i | \(-0.547702\pi\) | ||||
−0.149299 | + | 0.988792i | \(0.547702\pi\) | |||||||
\(744\) | −6.20967 | −0.227658 | ||||||||
\(745\) | 18.2608 | 0.669023 | ||||||||
\(746\) | 19.6815 | 0.720593 | ||||||||
\(747\) | 37.4492 | 1.37019 | ||||||||
\(748\) | −4.28643 | −0.156728 | ||||||||
\(749\) | −5.75517 | −0.210289 | ||||||||
\(750\) | −5.52545 | −0.201761 | ||||||||
\(751\) | −37.9081 | −1.38329 | −0.691643 | − | 0.722240i | \(-0.743113\pi\) | ||||
−0.691643 | + | 0.722240i | \(0.743113\pi\) | |||||||
\(752\) | 59.0102 | 2.15188 | ||||||||
\(753\) | −5.84476 | −0.212995 | ||||||||
\(754\) | −65.7126 | −2.39311 | ||||||||
\(755\) | 25.9172 | 0.943223 | ||||||||
\(756\) | −7.99713 | −0.290853 | ||||||||
\(757\) | 10.5117 | 0.382054 | 0.191027 | − | 0.981585i | \(-0.438818\pi\) | ||||
0.191027 | + | 0.981585i | \(0.438818\pi\) | |||||||
\(758\) | 8.33612 | 0.302782 | ||||||||
\(759\) | 5.60082 | 0.203297 | ||||||||
\(760\) | −1.04955 | −0.0380713 | ||||||||
\(761\) | −9.89394 | −0.358655 | −0.179328 | − | 0.983789i | \(-0.557392\pi\) | ||||
−0.179328 | + | 0.983789i | \(0.557392\pi\) | |||||||
\(762\) | −9.89680 | −0.358523 | ||||||||
\(763\) | −25.5006 | −0.923185 | ||||||||
\(764\) | −5.88632 | −0.212960 | ||||||||
\(765\) | −0.789114 | −0.0285305 | ||||||||
\(766\) | −11.8281 | −0.427367 | ||||||||
\(767\) | −11.5885 | −0.418436 | ||||||||
\(768\) | −4.87199 | −0.175803 | ||||||||
\(769\) | 42.5087 | 1.53290 | 0.766452 | − | 0.642302i | \(-0.222020\pi\) | ||||
0.766452 | + | 0.642302i | \(0.222020\pi\) | |||||||
\(770\) | 27.0418 | 0.974518 | ||||||||
\(771\) | −1.73067 | −0.0623286 | ||||||||
\(772\) | 118.159 | 4.25265 | ||||||||
\(773\) | 26.8577 | 0.966005 | 0.483003 | − | 0.875619i | \(-0.339546\pi\) | ||||
0.483003 | + | 0.875619i | \(0.339546\pi\) | |||||||
\(774\) | −94.7135 | −3.40441 | ||||||||
\(775\) | −14.6979 | −0.527962 | ||||||||
\(776\) | 47.6564 | 1.71077 | ||||||||
\(777\) | 0.731195 | 0.0262315 | ||||||||
\(778\) | 11.3980 | 0.408639 | ||||||||
\(779\) | −0.415500 | −0.0148868 | ||||||||
\(780\) | 3.69257 | 0.132215 | ||||||||
\(781\) | 22.7340 | 0.813487 | ||||||||
\(782\) | 2.91851 | 0.104366 | ||||||||
\(783\) | 9.71179 | 0.347071 | ||||||||
\(784\) | −37.4963 | −1.33915 | ||||||||
\(785\) | −1.82812 | −0.0652483 | ||||||||
\(786\) | −1.99672 | −0.0712205 | ||||||||
\(787\) | 31.6039 | 1.12656 | 0.563279 | − | 0.826267i | \(-0.309539\pi\) | ||||
0.563279 | + | 0.826267i | \(0.309539\pi\) | |||||||
\(788\) | −12.4285 | −0.442746 | ||||||||
\(789\) | 5.29106 | 0.188367 | ||||||||
\(790\) | −52.7498 | −1.87675 | ||||||||
\(791\) | 16.3551 | 0.581519 | ||||||||
\(792\) | 97.5428 | 3.46603 | ||||||||
\(793\) | 20.7381 | 0.736432 | ||||||||
\(794\) | 68.8388 | 2.44300 | ||||||||
\(795\) | −0.858591 | −0.0304511 | ||||||||
\(796\) | −70.9115 | −2.51339 | ||||||||
\(797\) | 24.1072 | 0.853921 | 0.426960 | − | 0.904270i | \(-0.359584\pi\) | ||||
0.426960 | + | 0.904270i | \(0.359584\pi\) | |||||||
\(798\) | 0.0832972 | 0.00294869 | ||||||||
\(799\) | −1.39324 | −0.0492893 | ||||||||
\(800\) | 21.8594 | 0.772846 | ||||||||
\(801\) | −29.7754 | −1.05206 | ||||||||
\(802\) | −67.2265 | −2.37385 | ||||||||
\(803\) | 65.8762 | 2.32472 | ||||||||
\(804\) | 2.03795 | 0.0718728 | ||||||||
\(805\) | −12.8406 | −0.452571 | ||||||||
\(806\) | 37.3508 | 1.31562 | ||||||||
\(807\) | 0.304884 | 0.0107324 | ||||||||
\(808\) | 49.4843 | 1.74085 | ||||||||
\(809\) | −1.16627 | −0.0410038 | −0.0205019 | − | 0.999790i | \(-0.506526\pi\) | ||||
−0.0205019 | + | 0.999790i | \(0.506526\pi\) | |||||||
\(810\) | 31.3268 | 1.10071 | ||||||||
\(811\) | −30.9429 | −1.08655 | −0.543275 | − | 0.839555i | \(-0.682816\pi\) | ||||
−0.543275 | + | 0.839555i | \(0.682816\pi\) | |||||||
\(812\) | −60.1042 | −2.10924 | ||||||||
\(813\) | 4.94942 | 0.173584 | ||||||||
\(814\) | −31.7014 | −1.11113 | ||||||||
\(815\) | −10.9761 | −0.384475 | ||||||||
\(816\) | −0.290054 | −0.0101539 | ||||||||
\(817\) | 1.38444 | 0.0484356 | ||||||||
\(818\) | 76.8148 | 2.68577 | ||||||||
\(819\) | 13.5326 | 0.472867 | ||||||||
\(820\) | −24.1569 | −0.843596 | ||||||||
\(821\) | 20.8631 | 0.728127 | 0.364063 | − | 0.931374i | \(-0.381389\pi\) | ||||
0.364063 | + | 0.931374i | \(0.381389\pi\) | |||||||
\(822\) | 2.28580 | 0.0797263 | ||||||||
\(823\) | −5.86740 | −0.204525 | −0.102262 | − | 0.994757i | \(-0.532608\pi\) | ||||
−0.102262 | + | 0.994757i | \(0.532608\pi\) | |||||||
\(824\) | 68.1868 | 2.37540 | ||||||||
\(825\) | −2.83044 | −0.0985431 | ||||||||
\(826\) | −15.1984 | −0.528821 | ||||||||
\(827\) | 28.5448 | 0.992600 | 0.496300 | − | 0.868151i | \(-0.334692\pi\) | ||||
0.496300 | + | 0.868151i | \(0.334692\pi\) | |||||||
\(828\) | −81.8173 | −2.84335 | ||||||||
\(829\) | 14.2365 | 0.494454 | 0.247227 | − | 0.968958i | \(-0.420481\pi\) | ||||
0.247227 | + | 0.968958i | \(0.420481\pi\) | |||||||
\(830\) | −45.6345 | −1.58400 | ||||||||
\(831\) | −4.63364 | −0.160739 | ||||||||
\(832\) | −7.51298 | −0.260466 | ||||||||
\(833\) | 0.885292 | 0.0306736 | ||||||||
\(834\) | 2.03018 | 0.0702995 | ||||||||
\(835\) | 31.5903 | 1.09323 | ||||||||
\(836\) | −2.51860 | −0.0871076 | ||||||||
\(837\) | −5.52014 | −0.190804 | ||||||||
\(838\) | 44.2550 | 1.52876 | ||||||||
\(839\) | −48.8842 | −1.68767 | −0.843835 | − | 0.536603i | \(-0.819707\pi\) | ||||
−0.843835 | + | 0.536603i | \(0.819707\pi\) | |||||||
\(840\) | 2.74158 | 0.0945935 | ||||||||
\(841\) | 43.9911 | 1.51693 | ||||||||
\(842\) | 30.7825 | 1.06083 | ||||||||
\(843\) | 1.26418 | 0.0435407 | ||||||||
\(844\) | −3.85381 | −0.132654 | ||||||||
\(845\) | 5.68810 | 0.195676 | ||||||||
\(846\) | 56.0048 | 1.92548 | ||||||||
\(847\) | 19.9472 | 0.685394 | ||||||||
\(848\) | 25.7426 | 0.884004 | ||||||||
\(849\) | 1.99584 | 0.0684970 | ||||||||
\(850\) | −1.47490 | −0.0505888 | ||||||||
\(851\) | 15.0532 | 0.516016 | ||||||||
\(852\) | 4.07139 | 0.139483 | ||||||||
\(853\) | −31.6266 | −1.08287 | −0.541437 | − | 0.840741i | \(-0.682120\pi\) | ||||
−0.541437 | + | 0.840741i | \(0.682120\pi\) | |||||||
\(854\) | 27.1983 | 0.930707 | ||||||||
\(855\) | −0.463663 | −0.0158570 | ||||||||
\(856\) | 25.2970 | 0.864634 | ||||||||
\(857\) | −4.11144 | −0.140444 | −0.0702221 | − | 0.997531i | \(-0.522371\pi\) | ||||
−0.0702221 | + | 0.997531i | \(0.522371\pi\) | |||||||
\(858\) | 7.19281 | 0.245559 | ||||||||
\(859\) | 31.5693 | 1.07713 | 0.538565 | − | 0.842584i | \(-0.318967\pi\) | ||||
0.538565 | + | 0.842584i | \(0.318967\pi\) | |||||||
\(860\) | 80.4908 | 2.74472 | ||||||||
\(861\) | 1.08534 | 0.0369884 | ||||||||
\(862\) | 88.0770 | 2.99992 | ||||||||
\(863\) | 28.6341 | 0.974716 | 0.487358 | − | 0.873202i | \(-0.337961\pi\) | ||||
0.487358 | + | 0.873202i | \(0.337961\pi\) | |||||||
\(864\) | 8.20983 | 0.279304 | ||||||||
\(865\) | −9.45348 | −0.321428 | ||||||||
\(866\) | 44.9416 | 1.52718 | ||||||||
\(867\) | −3.23356 | −0.109818 | ||||||||
\(868\) | 34.1630 | 1.15957 | ||||||||
\(869\) | −71.6596 | −2.43089 | ||||||||
\(870\) | −5.88120 | −0.199391 | ||||||||
\(871\) | −6.93942 | −0.235133 | ||||||||
\(872\) | 112.089 | 3.79580 | ||||||||
\(873\) | 21.0532 | 0.712544 | ||||||||
\(874\) | 1.71485 | 0.0580055 | ||||||||
\(875\) | 17.2090 | 0.581769 | ||||||||
\(876\) | 11.7976 | 0.398605 | ||||||||
\(877\) | 32.0631 | 1.08269 | 0.541346 | − | 0.840800i | \(-0.317915\pi\) | ||||
0.541346 | + | 0.840800i | \(0.317915\pi\) | |||||||
\(878\) | 18.0605 | 0.609512 | ||||||||
\(879\) | −0.282159 | −0.00951699 | ||||||||
\(880\) | −55.3281 | −1.86511 | ||||||||
\(881\) | 49.3179 | 1.66156 | 0.830781 | − | 0.556599i | \(-0.187894\pi\) | ||||
0.830781 | + | 0.556599i | \(0.187894\pi\) | |||||||
\(882\) | −35.5866 | −1.19826 | ||||||||
\(883\) | −33.0512 | −1.11226 | −0.556131 | − | 0.831095i | \(-0.687715\pi\) | ||||
−0.556131 | + | 0.831095i | \(0.687715\pi\) | |||||||
\(884\) | 2.61392 | 0.0879157 | ||||||||
\(885\) | −1.03716 | −0.0348636 | ||||||||
\(886\) | 63.5110 | 2.13369 | ||||||||
\(887\) | −21.6937 | −0.728405 | −0.364202 | − | 0.931320i | \(-0.618658\pi\) | ||||
−0.364202 | + | 0.931320i | \(0.618658\pi\) | |||||||
\(888\) | −3.21399 | −0.107854 | ||||||||
\(889\) | 30.8235 | 1.03379 | ||||||||
\(890\) | 36.2835 | 1.21622 | ||||||||
\(891\) | 42.5569 | 1.42571 | ||||||||
\(892\) | 91.5072 | 3.06389 | ||||||||
\(893\) | −0.818632 | −0.0273945 | ||||||||
\(894\) | 6.37023 | 0.213052 | ||||||||
\(895\) | 4.42202 | 0.147812 | ||||||||
\(896\) | 12.1922 | 0.407311 | ||||||||
\(897\) | −3.41545 | −0.114039 | ||||||||
\(898\) | 97.7719 | 3.26269 | ||||||||
\(899\) | −41.4878 | −1.38370 | ||||||||
\(900\) | 41.3472 | 1.37824 | ||||||||
\(901\) | −0.607785 | −0.0202483 | ||||||||
\(902\) | −47.0556 | −1.56678 | ||||||||
\(903\) | −3.61636 | −0.120345 | ||||||||
\(904\) | −71.8891 | −2.39100 | ||||||||
\(905\) | −2.02471 | −0.0673037 | ||||||||
\(906\) | 9.04116 | 0.300372 | ||||||||
\(907\) | 40.7646 | 1.35357 | 0.676783 | − | 0.736182i | \(-0.263373\pi\) | ||||
0.676783 | + | 0.736182i | \(0.263373\pi\) | |||||||
\(908\) | −100.389 | −3.33152 | ||||||||
\(909\) | 21.8607 | 0.725075 | ||||||||
\(910\) | −16.4904 | −0.546652 | ||||||||
\(911\) | 46.5196 | 1.54126 | 0.770632 | − | 0.637281i | \(-0.219941\pi\) | ||||
0.770632 | + | 0.637281i | \(0.219941\pi\) | |||||||
\(912\) | −0.170428 | −0.00564344 | ||||||||
\(913\) | −61.9936 | −2.05169 | ||||||||
\(914\) | −4.28558 | −0.141754 | ||||||||
\(915\) | 1.85604 | 0.0613588 | ||||||||
\(916\) | 79.0025 | 2.61032 | ||||||||
\(917\) | 6.21876 | 0.205361 | ||||||||
\(918\) | −0.553936 | −0.0182826 | ||||||||
\(919\) | −41.9645 | −1.38428 | −0.692141 | − | 0.721762i | \(-0.743333\pi\) | ||||
−0.692141 | + | 0.721762i | \(0.743333\pi\) | |||||||
\(920\) | 56.4411 | 1.86081 | ||||||||
\(921\) | −5.24065 | −0.172685 | ||||||||
\(922\) | 7.65325 | 0.252046 | ||||||||
\(923\) | −13.8635 | −0.456323 | ||||||||
\(924\) | 6.57893 | 0.216431 | ||||||||
\(925\) | −7.60729 | −0.250126 | ||||||||
\(926\) | 58.8906 | 1.93527 | ||||||||
\(927\) | 30.1230 | 0.989368 | ||||||||
\(928\) | 61.7028 | 2.02549 | ||||||||
\(929\) | 26.2573 | 0.861474 | 0.430737 | − | 0.902477i | \(-0.358254\pi\) | ||||
0.430737 | + | 0.902477i | \(0.358254\pi\) | |||||||
\(930\) | 3.34285 | 0.109616 | ||||||||
\(931\) | 0.520175 | 0.0170481 | ||||||||
\(932\) | −25.4933 | −0.835061 | ||||||||
\(933\) | −6.35477 | −0.208046 | ||||||||
\(934\) | −49.8857 | −1.63231 | ||||||||
\(935\) | 1.30630 | 0.0427207 | ||||||||
\(936\) | −59.4829 | −1.94426 | ||||||||
\(937\) | −23.8821 | −0.780193 | −0.390097 | − | 0.920774i | \(-0.627558\pi\) | ||||
−0.390097 | + | 0.920774i | \(0.627558\pi\) | |||||||
\(938\) | −9.10114 | −0.297163 | ||||||||
\(939\) | −5.03099 | −0.164180 | ||||||||
\(940\) | −47.5948 | −1.55237 | ||||||||
\(941\) | −6.69890 | −0.218378 | −0.109189 | − | 0.994021i | \(-0.534825\pi\) | ||||
−0.109189 | + | 0.994021i | \(0.534825\pi\) | |||||||
\(942\) | −0.637735 | −0.0207785 | ||||||||
\(943\) | 22.3440 | 0.727621 | ||||||||
\(944\) | 31.0964 | 1.01210 | ||||||||
\(945\) | 2.43715 | 0.0792806 | ||||||||
\(946\) | 156.789 | 5.09766 | ||||||||
\(947\) | 43.3746 | 1.40949 | 0.704743 | − | 0.709463i | \(-0.251062\pi\) | ||||
0.704743 | + | 0.709463i | \(0.251062\pi\) | |||||||
\(948\) | −12.8334 | −0.416808 | ||||||||
\(949\) | −40.1722 | −1.30404 | ||||||||
\(950\) | −0.866616 | −0.0281167 | ||||||||
\(951\) | 1.32668 | 0.0430204 | ||||||||
\(952\) | 1.94073 | 0.0628994 | ||||||||
\(953\) | −26.1479 | −0.847015 | −0.423507 | − | 0.905893i | \(-0.639201\pi\) | ||||
−0.423507 | + | 0.905893i | \(0.639201\pi\) | |||||||
\(954\) | 24.4315 | 0.790998 | ||||||||
\(955\) | 1.79388 | 0.0580484 | ||||||||
\(956\) | 109.240 | 3.53308 | ||||||||
\(957\) | −7.98951 | −0.258264 | ||||||||
\(958\) | 86.1543 | 2.78352 | ||||||||
\(959\) | −7.11910 | −0.229888 | ||||||||
\(960\) | −0.672404 | −0.0217017 | ||||||||
\(961\) | −7.41849 | −0.239306 | ||||||||
\(962\) | 19.3319 | 0.623286 | ||||||||
\(963\) | 11.1755 | 0.360126 | ||||||||
\(964\) | 93.8652 | 3.02319 | ||||||||
\(965\) | −36.0095 | −1.15919 | ||||||||
\(966\) | −4.47941 | −0.144123 | ||||||||
\(967\) | 33.0871 | 1.06401 | 0.532005 | − | 0.846741i | \(-0.321439\pi\) | ||||
0.532005 | + | 0.846741i | \(0.321439\pi\) | |||||||
\(968\) | −87.6785 | −2.81809 | ||||||||
\(969\) | 0.00402383 | 0.000129264 0 | ||||||||
\(970\) | −25.6549 | −0.823728 | ||||||||
\(971\) | −22.0121 | −0.706403 | −0.353202 | − | 0.935547i | \(-0.614907\pi\) | ||||
−0.353202 | + | 0.935547i | \(0.614907\pi\) | |||||||
\(972\) | 23.3408 | 0.748656 | ||||||||
\(973\) | −6.32299 | −0.202706 | ||||||||
\(974\) | −45.6179 | −1.46169 | ||||||||
\(975\) | 1.72604 | 0.0552774 | ||||||||
\(976\) | −55.6484 | −1.78126 | ||||||||
\(977\) | 40.8260 | 1.30614 | 0.653070 | − | 0.757297i | \(-0.273481\pi\) | ||||
0.653070 | + | 0.757297i | \(0.273481\pi\) | |||||||
\(978\) | −3.82898 | −0.122437 | ||||||||
\(979\) | 49.2905 | 1.57533 | ||||||||
\(980\) | 30.2427 | 0.966068 | ||||||||
\(981\) | 49.5176 | 1.58098 | ||||||||
\(982\) | 100.006 | 3.19131 | ||||||||
\(983\) | −18.4293 | −0.587805 | −0.293902 | − | 0.955835i | \(-0.594954\pi\) | ||||
−0.293902 | + | 0.955835i | \(0.594954\pi\) | |||||||
\(984\) | −4.77065 | −0.152083 | ||||||||
\(985\) | 3.78761 | 0.120683 | ||||||||
\(986\) | −4.16323 | −0.132584 | ||||||||
\(987\) | 2.13838 | 0.0680654 | ||||||||
\(988\) | 1.53587 | 0.0488627 | ||||||||
\(989\) | −74.4503 | −2.36738 | ||||||||
\(990\) | −52.5102 | −1.66888 | ||||||||
\(991\) | −9.16979 | −0.291288 | −0.145644 | − | 0.989337i | \(-0.546525\pi\) | ||||
−0.145644 | + | 0.989337i | \(0.546525\pi\) | |||||||
\(992\) | −35.0716 | −1.11352 | ||||||||
\(993\) | 2.42057 | 0.0768143 | ||||||||
\(994\) | −18.1822 | −0.576703 | ||||||||
\(995\) | 21.6105 | 0.685100 | ||||||||
\(996\) | −11.1023 | −0.351790 | ||||||||
\(997\) | −19.3502 | −0.612826 | −0.306413 | − | 0.951899i | \(-0.599129\pi\) | ||||
−0.306413 | + | 0.951899i | \(0.599129\pi\) | |||||||
\(998\) | 69.1913 | 2.19021 | ||||||||
\(999\) | −2.85710 | −0.0903948 |
(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 | 4019.2.a.a.1.8 | ✓ | 149 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.a.1.8 | ✓ | 149 | 1.1 | even | 1 | trivial |