Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.27855 | −1.61118 | −0.805590 | − | 0.592473i | \(-0.798152\pi\) | ||||
−0.805590 | + | 0.592473i | \(0.798152\pi\) | |||||||
\(3\) | −2.02568 | −1.16953 | −0.584765 | − | 0.811203i | \(-0.698813\pi\) | ||||
−0.584765 | + | 0.811203i | \(0.698813\pi\) | |||||||
\(4\) | 3.19181 | 1.59590 | ||||||||
\(5\) | −1.32967 | −0.594645 | −0.297323 | − | 0.954777i | \(-0.596094\pi\) | ||||
−0.297323 | + | 0.954777i | \(0.596094\pi\) | |||||||
\(6\) | 4.61563 | 1.88432 | ||||||||
\(7\) | 2.20899 | 0.834921 | 0.417461 | − | 0.908695i | \(-0.362920\pi\) | ||||
0.417461 | + | 0.908695i | \(0.362920\pi\) | |||||||
\(8\) | −2.71560 | −0.960109 | ||||||||
\(9\) | 1.10340 | 0.367800 | ||||||||
\(10\) | 3.02972 | 0.958081 | ||||||||
\(11\) | 3.01218 | 0.908206 | 0.454103 | − | 0.890949i | \(-0.349960\pi\) | ||||
0.454103 | + | 0.890949i | \(0.349960\pi\) | |||||||
\(12\) | −6.46560 | −1.86646 | ||||||||
\(13\) | 3.26538 | 0.905654 | 0.452827 | − | 0.891598i | \(-0.350416\pi\) | ||||
0.452827 | + | 0.891598i | \(0.350416\pi\) | |||||||
\(14\) | −5.03331 | −1.34521 | ||||||||
\(15\) | 2.69349 | 0.695455 | ||||||||
\(16\) | −0.195977 | −0.0489941 | ||||||||
\(17\) | −3.42969 | −0.831822 | −0.415911 | − | 0.909405i | \(-0.636537\pi\) | ||||
−0.415911 | + | 0.909405i | \(0.636537\pi\) | |||||||
\(18\) | −2.51415 | −0.592592 | ||||||||
\(19\) | 7.40650 | 1.69917 | 0.849583 | − | 0.527454i | \(-0.176853\pi\) | ||||
0.849583 | + | 0.527454i | \(0.176853\pi\) | |||||||
\(20\) | −4.24404 | −0.948997 | ||||||||
\(21\) | −4.47472 | −0.976465 | ||||||||
\(22\) | −6.86341 | −1.46328 | ||||||||
\(23\) | −3.27201 | −0.682261 | −0.341130 | − | 0.940016i | \(-0.610810\pi\) | ||||
−0.341130 | + | 0.940016i | \(0.610810\pi\) | |||||||
\(24\) | 5.50095 | 1.12288 | ||||||||
\(25\) | −3.23198 | −0.646397 | ||||||||
\(26\) | −7.44035 | −1.45917 | ||||||||
\(27\) | 3.84192 | 0.739377 | ||||||||
\(28\) | 7.05068 | 1.33245 | ||||||||
\(29\) | −6.08679 | −1.13029 | −0.565144 | − | 0.824992i | \(-0.691180\pi\) | ||||
−0.565144 | + | 0.824992i | \(0.691180\pi\) | |||||||
\(30\) | −6.13726 | −1.12050 | ||||||||
\(31\) | 9.24208 | 1.65993 | 0.829963 | − | 0.557819i | \(-0.188362\pi\) | ||||
0.829963 | + | 0.557819i | \(0.188362\pi\) | |||||||
\(32\) | 5.87774 | 1.03905 | ||||||||
\(33\) | −6.10172 | −1.06217 | ||||||||
\(34\) | 7.81473 | 1.34022 | ||||||||
\(35\) | −2.93723 | −0.496482 | ||||||||
\(36\) | 3.52184 | 0.586973 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | −16.8761 | −2.73767 | ||||||||
\(39\) | −6.61463 | −1.05919 | ||||||||
\(40\) | 3.61084 | 0.570925 | ||||||||
\(41\) | −5.52935 | −0.863539 | −0.431770 | − | 0.901984i | \(-0.642111\pi\) | ||||
−0.431770 | + | 0.901984i | \(0.642111\pi\) | |||||||
\(42\) | 10.1959 | 1.57326 | ||||||||
\(43\) | −8.51355 | −1.29830 | −0.649152 | − | 0.760658i | \(-0.724876\pi\) | ||||
−0.649152 | + | 0.760658i | \(0.724876\pi\) | |||||||
\(44\) | 9.61429 | 1.44941 | ||||||||
\(45\) | −1.46715 | −0.218710 | ||||||||
\(46\) | 7.45545 | 1.09925 | ||||||||
\(47\) | 0.687745 | 0.100318 | 0.0501590 | − | 0.998741i | \(-0.484027\pi\) | ||||
0.0501590 | + | 0.998741i | \(0.484027\pi\) | |||||||
\(48\) | 0.396987 | 0.0573001 | ||||||||
\(49\) | −2.12035 | −0.302907 | ||||||||
\(50\) | 7.36425 | 1.04146 | ||||||||
\(51\) | 6.94747 | 0.972840 | ||||||||
\(52\) | 10.4225 | 1.44534 | ||||||||
\(53\) | −11.3154 | −1.55430 | −0.777148 | − | 0.629318i | \(-0.783334\pi\) | ||||
−0.777148 | + | 0.629318i | \(0.783334\pi\) | |||||||
\(54\) | −8.75401 | −1.19127 | ||||||||
\(55\) | −4.00519 | −0.540060 | ||||||||
\(56\) | −5.99874 | −0.801616 | ||||||||
\(57\) | −15.0032 | −1.98723 | ||||||||
\(58\) | 13.8691 | 1.82110 | ||||||||
\(59\) | −2.57226 | −0.334880 | −0.167440 | − | 0.985882i | \(-0.553550\pi\) | ||||
−0.167440 | + | 0.985882i | \(0.553550\pi\) | |||||||
\(60\) | 8.59709 | 1.10988 | ||||||||
\(61\) | −3.70675 | −0.474601 | −0.237300 | − | 0.971436i | \(-0.576263\pi\) | ||||
−0.237300 | + | 0.971436i | \(0.576263\pi\) | |||||||
\(62\) | −21.0586 | −2.67444 | ||||||||
\(63\) | 2.43740 | 0.307084 | ||||||||
\(64\) | −13.0008 | −1.62510 | ||||||||
\(65\) | −4.34187 | −0.538543 | ||||||||
\(66\) | 13.9031 | 1.71135 | ||||||||
\(67\) | −10.1990 | −1.24601 | −0.623004 | − | 0.782219i | \(-0.714088\pi\) | ||||
−0.623004 | + | 0.782219i | \(0.714088\pi\) | |||||||
\(68\) | −10.9469 | −1.32751 | ||||||||
\(69\) | 6.62806 | 0.797924 | ||||||||
\(70\) | 6.69263 | 0.799922 | ||||||||
\(71\) | 14.6737 | 1.74144 | 0.870722 | − | 0.491776i | \(-0.163652\pi\) | ||||
0.870722 | + | 0.491776i | \(0.163652\pi\) | |||||||
\(72\) | −2.99639 | −0.353128 | ||||||||
\(73\) | 1.15575 | 0.135271 | 0.0676353 | − | 0.997710i | \(-0.478455\pi\) | ||||
0.0676353 | + | 0.997710i | \(0.478455\pi\) | |||||||
\(74\) | 2.27855 | 0.264877 | ||||||||
\(75\) | 6.54698 | 0.755980 | ||||||||
\(76\) | 23.6401 | 2.71171 | ||||||||
\(77\) | 6.65388 | 0.758280 | ||||||||
\(78\) | 15.0718 | 1.70655 | ||||||||
\(79\) | 7.31062 | 0.822509 | 0.411255 | − | 0.911520i | \(-0.365091\pi\) | ||||
0.411255 | + | 0.911520i | \(0.365091\pi\) | |||||||
\(80\) | 0.260584 | 0.0291341 | ||||||||
\(81\) | −11.0927 | −1.23252 | ||||||||
\(82\) | 12.5989 | 1.39132 | ||||||||
\(83\) | 7.03276 | 0.771945 | 0.385973 | − | 0.922510i | \(-0.373866\pi\) | ||||
0.385973 | + | 0.922510i | \(0.373866\pi\) | |||||||
\(84\) | −14.2825 | −1.55834 | ||||||||
\(85\) | 4.56034 | 0.494639 | ||||||||
\(86\) | 19.3986 | 2.09180 | ||||||||
\(87\) | 12.3299 | 1.32191 | ||||||||
\(88\) | −8.17987 | −0.871977 | ||||||||
\(89\) | −16.7495 | −1.77544 | −0.887720 | − | 0.460384i | \(-0.847712\pi\) | ||||
−0.887720 | + | 0.460384i | \(0.847712\pi\) | |||||||
\(90\) | 3.34299 | 0.352382 | ||||||||
\(91\) | 7.21321 | 0.756149 | ||||||||
\(92\) | −10.4436 | −1.08882 | ||||||||
\(93\) | −18.7215 | −1.94133 | ||||||||
\(94\) | −1.56706 | −0.161630 | ||||||||
\(95\) | −9.84818 | −1.01040 | ||||||||
\(96\) | −11.9065 | −1.21520 | ||||||||
\(97\) | −2.27322 | −0.230811 | −0.115405 | − | 0.993318i | \(-0.536817\pi\) | ||||
−0.115405 | + | 0.993318i | \(0.536817\pi\) | |||||||
\(98\) | 4.83133 | 0.488038 | ||||||||
\(99\) | 3.32363 | 0.334038 | ||||||||
\(100\) | −10.3159 | −1.03159 | ||||||||
\(101\) | 12.0462 | 1.19864 | 0.599322 | − | 0.800508i | \(-0.295437\pi\) | ||||
0.599322 | + | 0.800508i | \(0.295437\pi\) | |||||||
\(102\) | −15.8302 | −1.56742 | ||||||||
\(103\) | 9.62249 | 0.948132 | 0.474066 | − | 0.880489i | \(-0.342786\pi\) | ||||
0.474066 | + | 0.880489i | \(0.342786\pi\) | |||||||
\(104\) | −8.86747 | −0.869527 | ||||||||
\(105\) | 5.94990 | 0.580650 | ||||||||
\(106\) | 25.7829 | 2.50425 | ||||||||
\(107\) | −7.26039 | −0.701889 | −0.350944 | − | 0.936396i | \(-0.614139\pi\) | ||||
−0.350944 | + | 0.936396i | \(0.614139\pi\) | |||||||
\(108\) | 12.2627 | 1.17997 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | 9.12605 | 0.870135 | ||||||||
\(111\) | 2.02568 | 0.192269 | ||||||||
\(112\) | −0.432911 | −0.0409062 | ||||||||
\(113\) | −1.67006 | −0.157106 | −0.0785530 | − | 0.996910i | \(-0.525030\pi\) | ||||
−0.0785530 | + | 0.996910i | \(0.525030\pi\) | |||||||
\(114\) | 34.1857 | 3.20178 | ||||||||
\(115\) | 4.35068 | 0.405703 | ||||||||
\(116\) | −19.4279 | −1.80383 | ||||||||
\(117\) | 3.60302 | 0.333099 | ||||||||
\(118\) | 5.86104 | 0.539553 | ||||||||
\(119\) | −7.57616 | −0.694505 | ||||||||
\(120\) | −7.31443 | −0.667713 | ||||||||
\(121\) | −1.92679 | −0.175163 | ||||||||
\(122\) | 8.44603 | 0.764667 | ||||||||
\(123\) | 11.2007 | 1.00993 | ||||||||
\(124\) | 29.4989 | 2.64908 | ||||||||
\(125\) | 10.9458 | 0.979022 | ||||||||
\(126\) | −5.55375 | −0.494767 | ||||||||
\(127\) | 15.3448 | 1.36163 | 0.680813 | − | 0.732457i | \(-0.261626\pi\) | ||||
0.680813 | + | 0.732457i | \(0.261626\pi\) | |||||||
\(128\) | 17.8675 | 1.57928 | ||||||||
\(129\) | 17.2458 | 1.51841 | ||||||||
\(130\) | 9.89319 | 0.867690 | ||||||||
\(131\) | −0.952744 | −0.0832416 | −0.0416208 | − | 0.999133i | \(-0.513252\pi\) | ||||
−0.0416208 | + | 0.999133i | \(0.513252\pi\) | |||||||
\(132\) | −19.4755 | −1.69513 | ||||||||
\(133\) | 16.3609 | 1.41867 | ||||||||
\(134\) | 23.2390 | 2.00754 | ||||||||
\(135\) | −5.10847 | −0.439667 | ||||||||
\(136\) | 9.31366 | 0.798640 | ||||||||
\(137\) | −8.13948 | −0.695403 | −0.347701 | − | 0.937605i | \(-0.613038\pi\) | ||||
−0.347701 | + | 0.937605i | \(0.613038\pi\) | |||||||
\(138\) | −15.1024 | −1.28560 | ||||||||
\(139\) | −8.21718 | −0.696972 | −0.348486 | − | 0.937314i | \(-0.613304\pi\) | ||||
−0.348486 | + | 0.937314i | \(0.613304\pi\) | |||||||
\(140\) | −9.37506 | −0.792338 | ||||||||
\(141\) | −1.39315 | −0.117325 | ||||||||
\(142\) | −33.4347 | −2.80578 | ||||||||
\(143\) | 9.83591 | 0.822520 | ||||||||
\(144\) | −0.216240 | −0.0180200 | ||||||||
\(145\) | 8.09341 | 0.672121 | ||||||||
\(146\) | −2.63345 | −0.217946 | ||||||||
\(147\) | 4.29516 | 0.354258 | ||||||||
\(148\) | −3.19181 | −0.262365 | ||||||||
\(149\) | −5.03263 | −0.412289 | −0.206145 | − | 0.978522i | \(-0.566092\pi\) | ||||
−0.206145 | + | 0.978522i | \(0.566092\pi\) | |||||||
\(150\) | −14.9177 | −1.21802 | ||||||||
\(151\) | 3.95007 | 0.321452 | 0.160726 | − | 0.986999i | \(-0.448616\pi\) | ||||
0.160726 | + | 0.986999i | \(0.448616\pi\) | |||||||
\(152\) | −20.1131 | −1.63139 | ||||||||
\(153\) | −3.78431 | −0.305944 | ||||||||
\(154\) | −15.1612 | −1.22173 | ||||||||
\(155\) | −12.2889 | −0.987067 | ||||||||
\(156\) | −21.1126 | −1.69036 | ||||||||
\(157\) | −2.14937 | −0.171538 | −0.0857692 | − | 0.996315i | \(-0.527335\pi\) | ||||
−0.0857692 | + | 0.996315i | \(0.527335\pi\) | |||||||
\(158\) | −16.6576 | −1.32521 | ||||||||
\(159\) | 22.9215 | 1.81780 | ||||||||
\(160\) | −7.81544 | −0.617865 | ||||||||
\(161\) | −7.22784 | −0.569634 | ||||||||
\(162\) | 25.2753 | 1.98582 | ||||||||
\(163\) | −21.8714 | −1.71310 | −0.856550 | − | 0.516064i | \(-0.827397\pi\) | ||||
−0.856550 | + | 0.516064i | \(0.827397\pi\) | |||||||
\(164\) | −17.6486 | −1.37813 | ||||||||
\(165\) | 8.11326 | 0.631616 | ||||||||
\(166\) | −16.0245 | −1.24374 | ||||||||
\(167\) | −5.73252 | −0.443596 | −0.221798 | − | 0.975093i | \(-0.571193\pi\) | ||||
−0.221798 | + | 0.975093i | \(0.571193\pi\) | |||||||
\(168\) | 12.1516 | 0.937513 | ||||||||
\(169\) | −2.33729 | −0.179791 | ||||||||
\(170\) | −10.3910 | −0.796953 | ||||||||
\(171\) | 8.17232 | 0.624953 | ||||||||
\(172\) | −27.1736 | −2.07197 | ||||||||
\(173\) | 11.8926 | 0.904177 | 0.452089 | − | 0.891973i | \(-0.350679\pi\) | ||||
0.452089 | + | 0.891973i | \(0.350679\pi\) | |||||||
\(174\) | −28.0944 | −2.12983 | ||||||||
\(175\) | −7.13943 | −0.539690 | ||||||||
\(176\) | −0.590316 | −0.0444967 | ||||||||
\(177\) | 5.21060 | 0.391652 | ||||||||
\(178\) | 38.1646 | 2.86055 | ||||||||
\(179\) | 8.58866 | 0.641947 | 0.320973 | − | 0.947088i | \(-0.395990\pi\) | ||||
0.320973 | + | 0.947088i | \(0.395990\pi\) | |||||||
\(180\) | −4.68287 | −0.349041 | ||||||||
\(181\) | 2.86228 | 0.212752 | 0.106376 | − | 0.994326i | \(-0.466075\pi\) | ||||
0.106376 | + | 0.994326i | \(0.466075\pi\) | |||||||
\(182\) | −16.4357 | −1.21829 | ||||||||
\(183\) | 7.50870 | 0.555059 | ||||||||
\(184\) | 8.88546 | 0.655045 | ||||||||
\(185\) | 1.32967 | 0.0977591 | ||||||||
\(186\) | 42.6580 | 3.12784 | ||||||||
\(187\) | −10.3308 | −0.755465 | ||||||||
\(188\) | 2.19515 | 0.160098 | ||||||||
\(189\) | 8.48677 | 0.617322 | ||||||||
\(190\) | 22.4396 | 1.62794 | ||||||||
\(191\) | 10.6560 | 0.771045 | 0.385522 | − | 0.922699i | \(-0.374021\pi\) | ||||
0.385522 | + | 0.922699i | \(0.374021\pi\) | |||||||
\(192\) | 26.3355 | 1.90060 | ||||||||
\(193\) | 5.31819 | 0.382811 | 0.191406 | − | 0.981511i | \(-0.438695\pi\) | ||||
0.191406 | + | 0.981511i | \(0.438695\pi\) | |||||||
\(194\) | 5.17966 | 0.371878 | ||||||||
\(195\) | 8.79526 | 0.629842 | ||||||||
\(196\) | −6.76774 | −0.483410 | ||||||||
\(197\) | 13.3860 | 0.953712 | 0.476856 | − | 0.878981i | \(-0.341776\pi\) | ||||
0.476856 | + | 0.878981i | \(0.341776\pi\) | |||||||
\(198\) | −7.57308 | −0.538195 | ||||||||
\(199\) | 19.3494 | 1.37165 | 0.685823 | − | 0.727769i | \(-0.259443\pi\) | ||||
0.685823 | + | 0.727769i | \(0.259443\pi\) | |||||||
\(200\) | 8.77678 | 0.620612 | ||||||||
\(201\) | 20.6600 | 1.45724 | ||||||||
\(202\) | −27.4480 | −1.93123 | ||||||||
\(203\) | −13.4457 | −0.943702 | ||||||||
\(204\) | 22.1750 | 1.55256 | ||||||||
\(205\) | 7.35220 | 0.513500 | ||||||||
\(206\) | −21.9254 | −1.52761 | ||||||||
\(207\) | −3.61033 | −0.250935 | ||||||||
\(208\) | −0.639938 | −0.0443717 | ||||||||
\(209\) | 22.3097 | 1.54319 | ||||||||
\(210\) | −13.5572 | −0.935533 | ||||||||
\(211\) | −12.1549 | −0.836777 | −0.418388 | − | 0.908268i | \(-0.637405\pi\) | ||||
−0.418388 | + | 0.908268i | \(0.637405\pi\) | |||||||
\(212\) | −36.1167 | −2.48051 | ||||||||
\(213\) | −29.7242 | −2.03667 | ||||||||
\(214\) | 16.5432 | 1.13087 | ||||||||
\(215\) | 11.3202 | 0.772031 | ||||||||
\(216\) | −10.4331 | −0.709883 | ||||||||
\(217\) | 20.4157 | 1.38591 | ||||||||
\(218\) | 2.27855 | 0.154323 | ||||||||
\(219\) | −2.34119 | −0.158203 | ||||||||
\(220\) | −12.7838 | −0.861884 | ||||||||
\(221\) | −11.1992 | −0.753342 | ||||||||
\(222\) | −4.61563 | −0.309781 | ||||||||
\(223\) | 3.88466 | 0.260136 | 0.130068 | − | 0.991505i | \(-0.458480\pi\) | ||||
0.130068 | + | 0.991505i | \(0.458480\pi\) | |||||||
\(224\) | 12.9839 | 0.867523 | ||||||||
\(225\) | −3.56617 | −0.237745 | ||||||||
\(226\) | 3.80532 | 0.253126 | ||||||||
\(227\) | −16.7237 | −1.10999 | −0.554996 | − | 0.831853i | \(-0.687280\pi\) | ||||
−0.554996 | + | 0.831853i | \(0.687280\pi\) | |||||||
\(228\) | −47.8874 | −3.17142 | ||||||||
\(229\) | 13.5835 | 0.897624 | 0.448812 | − | 0.893626i | \(-0.351847\pi\) | ||||
0.448812 | + | 0.893626i | \(0.351847\pi\) | |||||||
\(230\) | −9.91326 | −0.653661 | ||||||||
\(231\) | −13.4787 | −0.886831 | ||||||||
\(232\) | 16.5293 | 1.08520 | ||||||||
\(233\) | 0.657731 | 0.0430894 | 0.0215447 | − | 0.999768i | \(-0.493142\pi\) | ||||
0.0215447 | + | 0.999768i | \(0.493142\pi\) | |||||||
\(234\) | −8.20967 | −0.536683 | ||||||||
\(235\) | −0.914472 | −0.0596536 | ||||||||
\(236\) | −8.21017 | −0.534437 | ||||||||
\(237\) | −14.8090 | −0.961949 | ||||||||
\(238\) | 17.2627 | 1.11897 | ||||||||
\(239\) | −9.00287 | −0.582347 | −0.291174 | − | 0.956670i | \(-0.594046\pi\) | ||||
−0.291174 | + | 0.956670i | \(0.594046\pi\) | |||||||
\(240\) | −0.527860 | −0.0340732 | ||||||||
\(241\) | 6.30220 | 0.405960 | 0.202980 | − | 0.979183i | \(-0.434937\pi\) | ||||
0.202980 | + | 0.979183i | \(0.434937\pi\) | |||||||
\(242\) | 4.39029 | 0.282219 | ||||||||
\(243\) | 10.9446 | 0.702095 | ||||||||
\(244\) | −11.8312 | −0.757417 | ||||||||
\(245\) | 2.81936 | 0.180122 | ||||||||
\(246\) | −25.5214 | −1.62719 | ||||||||
\(247\) | 24.1850 | 1.53886 | ||||||||
\(248\) | −25.0978 | −1.59371 | ||||||||
\(249\) | −14.2461 | −0.902813 | ||||||||
\(250\) | −24.9406 | −1.57738 | ||||||||
\(251\) | 12.4969 | 0.788796 | 0.394398 | − | 0.918940i | \(-0.370953\pi\) | ||||
0.394398 | + | 0.918940i | \(0.370953\pi\) | |||||||
\(252\) | 7.77972 | 0.490076 | ||||||||
\(253\) | −9.85587 | −0.619633 | ||||||||
\(254\) | −34.9638 | −2.19383 | ||||||||
\(255\) | −9.23782 | −0.578495 | ||||||||
\(256\) | −14.7106 | −0.919410 | ||||||||
\(257\) | −11.7281 | −0.731580 | −0.365790 | − | 0.930697i | \(-0.619201\pi\) | ||||
−0.365790 | + | 0.930697i | \(0.619201\pi\) | |||||||
\(258\) | −39.2954 | −2.44643 | ||||||||
\(259\) | −2.20899 | −0.137260 | ||||||||
\(260\) | −13.8584 | −0.859463 | ||||||||
\(261\) | −6.71616 | −0.415720 | ||||||||
\(262\) | 2.17088 | 0.134117 | ||||||||
\(263\) | −6.44448 | −0.397383 | −0.198692 | − | 0.980062i | \(-0.563669\pi\) | ||||
−0.198692 | + | 0.980062i | \(0.563669\pi\) | |||||||
\(264\) | 16.5698 | 1.01980 | ||||||||
\(265\) | 15.0458 | 0.924255 | ||||||||
\(266\) | −37.2792 | −2.28573 | ||||||||
\(267\) | 33.9291 | 2.07643 | ||||||||
\(268\) | −32.5533 | −1.98851 | ||||||||
\(269\) | 6.33179 | 0.386056 | 0.193028 | − | 0.981193i | \(-0.438169\pi\) | ||||
0.193028 | + | 0.981193i | \(0.438169\pi\) | |||||||
\(270\) | 11.6399 | 0.708383 | ||||||||
\(271\) | −1.28736 | −0.0782014 | −0.0391007 | − | 0.999235i | \(-0.512449\pi\) | ||||
−0.0391007 | + | 0.999235i | \(0.512449\pi\) | |||||||
\(272\) | 0.672138 | 0.0407544 | ||||||||
\(273\) | −14.6117 | −0.884339 | ||||||||
\(274\) | 18.5462 | 1.12042 | ||||||||
\(275\) | −9.73531 | −0.587061 | ||||||||
\(276\) | 21.1555 | 1.27341 | ||||||||
\(277\) | −23.2025 | −1.39410 | −0.697051 | − | 0.717021i | \(-0.745505\pi\) | ||||
−0.697051 | + | 0.717021i | \(0.745505\pi\) | |||||||
\(278\) | 18.7233 | 1.12295 | ||||||||
\(279\) | 10.1977 | 0.610520 | ||||||||
\(280\) | 7.97633 | 0.476677 | ||||||||
\(281\) | −11.5857 | −0.691144 | −0.345572 | − | 0.938392i | \(-0.612315\pi\) | ||||
−0.345572 | + | 0.938392i | \(0.612315\pi\) | |||||||
\(282\) | 3.17438 | 0.189031 | ||||||||
\(283\) | −11.5051 | −0.683907 | −0.341954 | − | 0.939717i | \(-0.611089\pi\) | ||||
−0.341954 | + | 0.939717i | \(0.611089\pi\) | |||||||
\(284\) | 46.8355 | 2.77918 | ||||||||
\(285\) | 19.9493 | 1.18169 | ||||||||
\(286\) | −22.4116 | −1.32523 | ||||||||
\(287\) | −12.2143 | −0.720987 | ||||||||
\(288\) | 6.48549 | 0.382161 | ||||||||
\(289\) | −5.23724 | −0.308073 | ||||||||
\(290\) | −18.4413 | −1.08291 | ||||||||
\(291\) | 4.60483 | 0.269940 | ||||||||
\(292\) | 3.68894 | 0.215879 | ||||||||
\(293\) | 29.6626 | 1.73291 | 0.866455 | − | 0.499255i | \(-0.166393\pi\) | ||||
0.866455 | + | 0.499255i | \(0.166393\pi\) | |||||||
\(294\) | −9.78674 | −0.570774 | ||||||||
\(295\) | 3.42026 | 0.199135 | ||||||||
\(296\) | 2.71560 | 0.157841 | ||||||||
\(297\) | 11.5725 | 0.671506 | ||||||||
\(298\) | 11.4671 | 0.664273 | ||||||||
\(299\) | −10.6844 | −0.617892 | ||||||||
\(300\) | 20.8967 | 1.20647 | ||||||||
\(301\) | −18.8064 | −1.08398 | ||||||||
\(302\) | −9.00045 | −0.517917 | ||||||||
\(303\) | −24.4019 | −1.40185 | ||||||||
\(304\) | −1.45150 | −0.0832492 | ||||||||
\(305\) | 4.92874 | 0.282219 | ||||||||
\(306\) | 8.62277 | 0.492931 | ||||||||
\(307\) | −7.26778 | −0.414794 | −0.207397 | − | 0.978257i | \(-0.566499\pi\) | ||||
−0.207397 | + | 0.978257i | \(0.566499\pi\) | |||||||
\(308\) | 21.2379 | 1.21014 | ||||||||
\(309\) | −19.4921 | −1.10887 | ||||||||
\(310\) | 28.0009 | 1.59034 | ||||||||
\(311\) | −25.9585 | −1.47197 | −0.735986 | − | 0.676997i | \(-0.763281\pi\) | ||||
−0.735986 | + | 0.676997i | \(0.763281\pi\) | |||||||
\(312\) | 17.9627 | 1.01694 | ||||||||
\(313\) | −15.3192 | −0.865892 | −0.432946 | − | 0.901420i | \(-0.642526\pi\) | ||||
−0.432946 | + | 0.901420i | \(0.642526\pi\) | |||||||
\(314\) | 4.89746 | 0.276379 | ||||||||
\(315\) | −3.24093 | −0.182606 | ||||||||
\(316\) | 23.3341 | 1.31265 | ||||||||
\(317\) | −18.1478 | −1.01928 | −0.509642 | − | 0.860386i | \(-0.670222\pi\) | ||||
−0.509642 | + | 0.860386i | \(0.670222\pi\) | |||||||
\(318\) | −52.2279 | −2.92880 | ||||||||
\(319\) | −18.3345 | −1.02653 | ||||||||
\(320\) | 17.2867 | 0.966358 | ||||||||
\(321\) | 14.7073 | 0.820880 | ||||||||
\(322\) | 16.4690 | 0.917783 | ||||||||
\(323\) | −25.4020 | −1.41340 | ||||||||
\(324\) | −35.4058 | −1.96699 | ||||||||
\(325\) | −10.5537 | −0.585412 | ||||||||
\(326\) | 49.8352 | 2.76011 | ||||||||
\(327\) | 2.02568 | 0.112021 | ||||||||
\(328\) | 15.0155 | 0.829092 | ||||||||
\(329\) | 1.51922 | 0.0837576 | ||||||||
\(330\) | −18.4865 | −1.01765 | ||||||||
\(331\) | 10.9990 | 0.604558 | 0.302279 | − | 0.953219i | \(-0.402253\pi\) | ||||
0.302279 | + | 0.953219i | \(0.402253\pi\) | |||||||
\(332\) | 22.4472 | 1.23195 | ||||||||
\(333\) | −1.10340 | −0.0604659 | ||||||||
\(334\) | 13.0619 | 0.714714 | ||||||||
\(335\) | 13.5613 | 0.740933 | ||||||||
\(336\) | 0.876941 | 0.0478411 | ||||||||
\(337\) | 16.0753 | 0.875680 | 0.437840 | − | 0.899053i | \(-0.355744\pi\) | ||||
0.437840 | + | 0.899053i | \(0.355744\pi\) | |||||||
\(338\) | 5.32563 | 0.289676 | ||||||||
\(339\) | 3.38301 | 0.183740 | ||||||||
\(340\) | 14.5557 | 0.789396 | ||||||||
\(341\) | 27.8388 | 1.50755 | ||||||||
\(342\) | −18.6211 | −1.00691 | ||||||||
\(343\) | −20.1468 | −1.08782 | ||||||||
\(344\) | 23.1194 | 1.24651 | ||||||||
\(345\) | −8.81311 | −0.474482 | ||||||||
\(346\) | −27.0979 | −1.45679 | ||||||||
\(347\) | −10.7209 | −0.575528 | −0.287764 | − | 0.957701i | \(-0.592912\pi\) | ||||
−0.287764 | + | 0.957701i | \(0.592912\pi\) | |||||||
\(348\) | 39.3547 | 2.10964 | ||||||||
\(349\) | −30.8818 | −1.65306 | −0.826531 | − | 0.562891i | \(-0.809689\pi\) | ||||
−0.826531 | + | 0.562891i | \(0.809689\pi\) | |||||||
\(350\) | 16.2676 | 0.869539 | ||||||||
\(351\) | 12.5453 | 0.669620 | ||||||||
\(352\) | 17.7048 | 0.943669 | ||||||||
\(353\) | −22.7095 | −1.20870 | −0.604352 | − | 0.796717i | \(-0.706568\pi\) | ||||
−0.604352 | + | 0.796717i | \(0.706568\pi\) | |||||||
\(354\) | −11.8726 | −0.631023 | ||||||||
\(355\) | −19.5111 | −1.03554 | ||||||||
\(356\) | −53.4611 | −2.83343 | ||||||||
\(357\) | 15.3469 | 0.812245 | ||||||||
\(358\) | −19.5697 | −1.03429 | ||||||||
\(359\) | 6.74457 | 0.355965 | 0.177982 | − | 0.984034i | \(-0.443043\pi\) | ||||
0.177982 | + | 0.984034i | \(0.443043\pi\) | |||||||
\(360\) | 3.98420 | 0.209986 | ||||||||
\(361\) | 35.8562 | 1.88717 | ||||||||
\(362\) | −6.52186 | −0.342781 | ||||||||
\(363\) | 3.90307 | 0.204858 | ||||||||
\(364\) | 23.0232 | 1.20674 | ||||||||
\(365\) | −1.53677 | −0.0804381 | ||||||||
\(366\) | −17.1090 | −0.894301 | ||||||||
\(367\) | 6.25311 | 0.326410 | 0.163205 | − | 0.986592i | \(-0.447817\pi\) | ||||
0.163205 | + | 0.986592i | \(0.447817\pi\) | |||||||
\(368\) | 0.641237 | 0.0334268 | ||||||||
\(369\) | −6.10108 | −0.317609 | ||||||||
\(370\) | −3.02972 | −0.157508 | ||||||||
\(371\) | −24.9957 | −1.29771 | ||||||||
\(372\) | −59.7555 | −3.09818 | ||||||||
\(373\) | −25.9620 | −1.34426 | −0.672130 | − | 0.740433i | \(-0.734620\pi\) | ||||
−0.672130 | + | 0.740433i | \(0.734620\pi\) | |||||||
\(374\) | 23.5394 | 1.21719 | ||||||||
\(375\) | −22.1727 | −1.14500 | ||||||||
\(376\) | −1.86764 | −0.0963162 | ||||||||
\(377\) | −19.8757 | −1.02365 | ||||||||
\(378\) | −19.3376 | −0.994617 | ||||||||
\(379\) | 26.2988 | 1.35088 | 0.675439 | − | 0.737416i | \(-0.263954\pi\) | ||||
0.675439 | + | 0.737416i | \(0.263954\pi\) | |||||||
\(380\) | −31.4335 | −1.61250 | ||||||||
\(381\) | −31.0836 | −1.59246 | ||||||||
\(382\) | −24.2804 | −1.24229 | ||||||||
\(383\) | −29.1346 | −1.48871 | −0.744353 | − | 0.667786i | \(-0.767242\pi\) | ||||
−0.744353 | + | 0.667786i | \(0.767242\pi\) | |||||||
\(384\) | −36.1940 | −1.84702 | ||||||||
\(385\) | −8.84745 | −0.450908 | ||||||||
\(386\) | −12.1178 | −0.616778 | ||||||||
\(387\) | −9.39385 | −0.477516 | ||||||||
\(388\) | −7.25569 | −0.368352 | ||||||||
\(389\) | 8.37378 | 0.424567 | 0.212284 | − | 0.977208i | \(-0.431910\pi\) | ||||
0.212284 | + | 0.977208i | \(0.431910\pi\) | |||||||
\(390\) | −20.0405 | −1.01479 | ||||||||
\(391\) | 11.2220 | 0.567519 | ||||||||
\(392\) | 5.75801 | 0.290824 | ||||||||
\(393\) | 1.92996 | 0.0973535 | ||||||||
\(394\) | −30.5007 | −1.53660 | ||||||||
\(395\) | −9.72070 | −0.489101 | ||||||||
\(396\) | 10.6084 | 0.533092 | ||||||||
\(397\) | −25.8696 | −1.29836 | −0.649178 | − | 0.760636i | \(-0.724887\pi\) | ||||
−0.649178 | + | 0.760636i | \(0.724887\pi\) | |||||||
\(398\) | −44.0887 | −2.20997 | ||||||||
\(399\) | −33.1420 | −1.65918 | ||||||||
\(400\) | 0.633393 | 0.0316697 | ||||||||
\(401\) | −27.3623 | −1.36641 | −0.683204 | − | 0.730228i | \(-0.739414\pi\) | ||||
−0.683204 | + | 0.730228i | \(0.739414\pi\) | |||||||
\(402\) | −47.0749 | −2.34788 | ||||||||
\(403\) | 30.1789 | 1.50332 | ||||||||
\(404\) | 38.4492 | 1.91292 | ||||||||
\(405\) | 14.7496 | 0.732914 | ||||||||
\(406\) | 30.6367 | 1.52047 | ||||||||
\(407\) | −3.01218 | −0.149308 | ||||||||
\(408\) | −18.8665 | −0.934033 | ||||||||
\(409\) | −1.60723 | −0.0794726 | −0.0397363 | − | 0.999210i | \(-0.512652\pi\) | ||||
−0.0397363 | + | 0.999210i | \(0.512652\pi\) | |||||||
\(410\) | −16.7524 | −0.827341 | ||||||||
\(411\) | 16.4880 | 0.813294 | ||||||||
\(412\) | 30.7132 | 1.51313 | ||||||||
\(413\) | −5.68211 | −0.279599 | ||||||||
\(414\) | 8.22633 | 0.404302 | ||||||||
\(415\) | −9.35123 | −0.459034 | ||||||||
\(416\) | 19.1931 | 0.941018 | ||||||||
\(417\) | 16.6454 | 0.815129 | ||||||||
\(418\) | −50.8338 | −2.48636 | ||||||||
\(419\) | 21.2476 | 1.03801 | 0.519007 | − | 0.854770i | \(-0.326302\pi\) | ||||
0.519007 | + | 0.854770i | \(0.326302\pi\) | |||||||
\(420\) | 18.9909 | 0.926662 | ||||||||
\(421\) | 21.2541 | 1.03586 | 0.517931 | − | 0.855423i | \(-0.326702\pi\) | ||||
0.517931 | + | 0.855423i | \(0.326702\pi\) | |||||||
\(422\) | 27.6956 | 1.34820 | ||||||||
\(423\) | 0.758857 | 0.0368969 | ||||||||
\(424\) | 30.7282 | 1.49229 | ||||||||
\(425\) | 11.0847 | 0.537687 | ||||||||
\(426\) | 67.7282 | 3.28144 | ||||||||
\(427\) | −8.18818 | −0.396254 | ||||||||
\(428\) | −23.1738 | −1.12015 | ||||||||
\(429\) | −19.9244 | −0.961961 | ||||||||
\(430\) | −25.7937 | −1.24388 | ||||||||
\(431\) | −34.9924 | −1.68553 | −0.842763 | − | 0.538285i | \(-0.819072\pi\) | ||||
−0.842763 | + | 0.538285i | \(0.819072\pi\) | |||||||
\(432\) | −0.752925 | −0.0362251 | ||||||||
\(433\) | −37.8076 | −1.81692 | −0.908458 | − | 0.417977i | \(-0.862739\pi\) | ||||
−0.908458 | + | 0.417977i | \(0.862739\pi\) | |||||||
\(434\) | −46.5182 | −2.23295 | ||||||||
\(435\) | −16.3947 | −0.786065 | ||||||||
\(436\) | −3.19181 | −0.152860 | ||||||||
\(437\) | −24.2341 | −1.15927 | ||||||||
\(438\) | 5.33453 | 0.254894 | ||||||||
\(439\) | 22.5208 | 1.07486 | 0.537430 | − | 0.843309i | \(-0.319395\pi\) | ||||
0.537430 | + | 0.843309i | \(0.319395\pi\) | |||||||
\(440\) | 10.8765 | 0.518517 | ||||||||
\(441\) | −2.33959 | −0.111409 | ||||||||
\(442\) | 25.5181 | 1.21377 | ||||||||
\(443\) | −8.81901 | −0.419004 | −0.209502 | − | 0.977808i | \(-0.567184\pi\) | ||||
−0.209502 | + | 0.977808i | \(0.567184\pi\) | |||||||
\(444\) | 6.46560 | 0.306844 | ||||||||
\(445\) | 22.2712 | 1.05576 | ||||||||
\(446\) | −8.85141 | −0.419126 | ||||||||
\(447\) | 10.1945 | 0.482185 | ||||||||
\(448\) | −28.7187 | −1.35683 | ||||||||
\(449\) | −24.1815 | −1.14120 | −0.570598 | − | 0.821229i | \(-0.693289\pi\) | ||||
−0.570598 | + | 0.821229i | \(0.693289\pi\) | |||||||
\(450\) | 8.12571 | 0.383050 | ||||||||
\(451\) | −16.6554 | −0.784271 | ||||||||
\(452\) | −5.33051 | −0.250726 | ||||||||
\(453\) | −8.00159 | −0.375948 | ||||||||
\(454\) | 38.1059 | 1.78840 | ||||||||
\(455\) | −9.59116 | −0.449641 | ||||||||
\(456\) | 40.7428 | 1.90795 | ||||||||
\(457\) | −21.8843 | −1.02370 | −0.511852 | − | 0.859074i | \(-0.671040\pi\) | ||||
−0.511852 | + | 0.859074i | \(0.671040\pi\) | |||||||
\(458\) | −30.9508 | −1.44623 | ||||||||
\(459\) | −13.1766 | −0.615030 | ||||||||
\(460\) | 13.8865 | 0.647463 | ||||||||
\(461\) | 0.0156943 | 0.000730956 0 | 0.000365478 | − | 1.00000i | \(-0.499884\pi\) | ||||
0.000365478 | 1.00000i | \(0.499884\pi\) | ||||||||
\(462\) | 30.7119 | 1.42885 | ||||||||
\(463\) | 42.2851 | 1.96515 | 0.982577 | − | 0.185857i | \(-0.0595060\pi\) | ||||
0.982577 | + | 0.185857i | \(0.0595060\pi\) | |||||||
\(464\) | 1.19287 | 0.0553775 | ||||||||
\(465\) | 24.8934 | 1.15440 | ||||||||
\(466\) | −1.49867 | −0.0694248 | ||||||||
\(467\) | 21.7149 | 1.00484 | 0.502422 | − | 0.864622i | \(-0.332442\pi\) | ||||
0.502422 | + | 0.864622i | \(0.332442\pi\) | |||||||
\(468\) | 11.5001 | 0.531594 | ||||||||
\(469\) | −22.5295 | −1.04032 | ||||||||
\(470\) | 2.08367 | 0.0961127 | ||||||||
\(471\) | 4.35395 | 0.200619 | ||||||||
\(472\) | 6.98524 | 0.321522 | ||||||||
\(473\) | −25.6443 | −1.17913 | ||||||||
\(474\) | 33.7431 | 1.54987 | ||||||||
\(475\) | −23.9377 | −1.09834 | ||||||||
\(476\) | −24.1817 | −1.10836 | ||||||||
\(477\) | −12.4854 | −0.571669 | ||||||||
\(478\) | 20.5135 | 0.938267 | ||||||||
\(479\) | 11.9819 | 0.547468 | 0.273734 | − | 0.961805i | \(-0.411741\pi\) | ||||
0.273734 | + | 0.961805i | \(0.411741\pi\) | |||||||
\(480\) | 15.8316 | 0.722611 | ||||||||
\(481\) | −3.26538 | −0.148889 | ||||||||
\(482\) | −14.3599 | −0.654075 | ||||||||
\(483\) | 14.6413 | 0.666204 | ||||||||
\(484\) | −6.14994 | −0.279543 | ||||||||
\(485\) | 3.02263 | 0.137250 | ||||||||
\(486\) | −24.9378 | −1.13120 | ||||||||
\(487\) | 5.92913 | 0.268674 | 0.134337 | − | 0.990936i | \(-0.457109\pi\) | ||||
0.134337 | + | 0.990936i | \(0.457109\pi\) | |||||||
\(488\) | 10.0660 | 0.455668 | ||||||||
\(489\) | 44.3046 | 2.00352 | ||||||||
\(490\) | −6.42406 | −0.290209 | ||||||||
\(491\) | −13.1771 | −0.594672 | −0.297336 | − | 0.954773i | \(-0.596098\pi\) | ||||
−0.297336 | + | 0.954773i | \(0.596098\pi\) | |||||||
\(492\) | 35.7506 | 1.61176 | ||||||||
\(493\) | 20.8758 | 0.940199 | ||||||||
\(494\) | −55.1069 | −2.47938 | ||||||||
\(495\) | −4.41933 | −0.198634 | ||||||||
\(496\) | −1.81123 | −0.0813266 | ||||||||
\(497\) | 32.4140 | 1.45397 | ||||||||
\(498\) | 32.4606 | 1.45459 | ||||||||
\(499\) | −26.6542 | −1.19321 | −0.596603 | − | 0.802537i | \(-0.703483\pi\) | ||||
−0.596603 | + | 0.802537i | \(0.703483\pi\) | |||||||
\(500\) | 34.9369 | 1.56243 | ||||||||
\(501\) | 11.6123 | 0.518799 | ||||||||
\(502\) | −28.4748 | −1.27089 | ||||||||
\(503\) | −22.0724 | −0.984159 | −0.492080 | − | 0.870550i | \(-0.663763\pi\) | ||||
−0.492080 | + | 0.870550i | \(0.663763\pi\) | |||||||
\(504\) | −6.61901 | −0.294834 | ||||||||
\(505\) | −16.0175 | −0.712768 | ||||||||
\(506\) | 22.4571 | 0.998341 | ||||||||
\(507\) | 4.73461 | 0.210271 | ||||||||
\(508\) | 48.9775 | 2.17303 | ||||||||
\(509\) | −16.8509 | −0.746905 | −0.373453 | − | 0.927649i | \(-0.621826\pi\) | ||||
−0.373453 | + | 0.927649i | \(0.621826\pi\) | |||||||
\(510\) | 21.0489 | 0.932060 | ||||||||
\(511\) | 2.55305 | 0.112940 | ||||||||
\(512\) | −2.21629 | −0.0979470 | ||||||||
\(513\) | 28.4551 | 1.25632 | ||||||||
\(514\) | 26.7232 | 1.17871 | ||||||||
\(515\) | −12.7947 | −0.563803 | ||||||||
\(516\) | 55.0452 | 2.42323 | ||||||||
\(517\) | 2.07161 | 0.0911093 | ||||||||
\(518\) | 5.03331 | 0.221151 | ||||||||
\(519\) | −24.0906 | −1.05746 | ||||||||
\(520\) | 11.7908 | 0.517060 | ||||||||
\(521\) | 20.1149 | 0.881249 | 0.440625 | − | 0.897691i | \(-0.354757\pi\) | ||||
0.440625 | + | 0.897691i | \(0.354757\pi\) | |||||||
\(522\) | 15.3031 | 0.669800 | ||||||||
\(523\) | −18.5804 | −0.812464 | −0.406232 | − | 0.913770i | \(-0.633158\pi\) | ||||
−0.406232 | + | 0.913770i | \(0.633158\pi\) | |||||||
\(524\) | −3.04098 | −0.132846 | ||||||||
\(525\) | 14.4622 | 0.631184 | ||||||||
\(526\) | 14.6841 | 0.640257 | ||||||||
\(527\) | −31.6974 | −1.38076 | ||||||||
\(528\) | 1.19579 | 0.0520403 | ||||||||
\(529\) | −12.2940 | −0.534520 | ||||||||
\(530\) | −34.2826 | −1.48914 | ||||||||
\(531\) | −2.83823 | −0.123169 | ||||||||
\(532\) | 52.2209 | 2.26406 | ||||||||
\(533\) | −18.0554 | −0.782068 | ||||||||
\(534\) | −77.3094 | −3.34550 | ||||||||
\(535\) | 9.65391 | 0.417375 | ||||||||
\(536\) | 27.6964 | 1.19630 | ||||||||
\(537\) | −17.3979 | −0.750776 | ||||||||
\(538\) | −14.4273 | −0.622006 | ||||||||
\(539\) | −6.38686 | −0.275102 | ||||||||
\(540\) | −16.3053 | −0.701667 | ||||||||
\(541\) | 26.7444 | 1.14983 | 0.574916 | − | 0.818213i | \(-0.305035\pi\) | ||||
0.574916 | + | 0.818213i | \(0.305035\pi\) | |||||||
\(542\) | 2.93332 | 0.125997 | ||||||||
\(543\) | −5.79808 | −0.248819 | ||||||||
\(544\) | −20.1588 | −0.864302 | ||||||||
\(545\) | 1.32967 | 0.0569567 | ||||||||
\(546\) | 33.2935 | 1.42483 | ||||||||
\(547\) | 4.33001 | 0.185138 | 0.0925688 | − | 0.995706i | \(-0.470492\pi\) | ||||
0.0925688 | + | 0.995706i | \(0.470492\pi\) | |||||||
\(548\) | −25.9797 | −1.10980 | ||||||||
\(549\) | −4.09002 | −0.174558 | ||||||||
\(550\) | 22.1824 | 0.945862 | ||||||||
\(551\) | −45.0818 | −1.92055 | ||||||||
\(552\) | −17.9991 | −0.766095 | ||||||||
\(553\) | 16.1491 | 0.686730 | ||||||||
\(554\) | 52.8681 | 2.24615 | ||||||||
\(555\) | −2.69349 | −0.114332 | ||||||||
\(556\) | −26.2277 | −1.11230 | ||||||||
\(557\) | −7.47786 | −0.316847 | −0.158424 | − | 0.987371i | \(-0.550641\pi\) | ||||
−0.158424 | + | 0.987371i | \(0.550641\pi\) | |||||||
\(558\) | −23.2360 | −0.983658 | ||||||||
\(559\) | −27.8000 | −1.17581 | ||||||||
\(560\) | 0.575627 | 0.0243247 | ||||||||
\(561\) | 20.9270 | 0.883539 | ||||||||
\(562\) | 26.3986 | 1.11356 | ||||||||
\(563\) | 32.1159 | 1.35353 | 0.676763 | − | 0.736201i | \(-0.263382\pi\) | ||||
0.676763 | + | 0.736201i | \(0.263382\pi\) | |||||||
\(564\) | −4.44668 | −0.187239 | ||||||||
\(565\) | 2.22062 | 0.0934224 | ||||||||
\(566\) | 26.2150 | 1.10190 | ||||||||
\(567\) | −24.5037 | −1.02906 | ||||||||
\(568\) | −39.8478 | −1.67198 | ||||||||
\(569\) | −27.2656 | −1.14303 | −0.571516 | − | 0.820591i | \(-0.693644\pi\) | ||||
−0.571516 | + | 0.820591i | \(0.693644\pi\) | |||||||
\(570\) | −45.4556 | −1.90392 | ||||||||
\(571\) | 22.7540 | 0.952227 | 0.476114 | − | 0.879384i | \(-0.342045\pi\) | ||||
0.476114 | + | 0.879384i | \(0.342045\pi\) | |||||||
\(572\) | 31.3943 | 1.31266 | ||||||||
\(573\) | −21.5858 | −0.901760 | ||||||||
\(574\) | 27.8309 | 1.16164 | ||||||||
\(575\) | 10.5751 | 0.441011 | ||||||||
\(576\) | −14.3451 | −0.597711 | ||||||||
\(577\) | −9.64440 | −0.401502 | −0.200751 | − | 0.979642i | \(-0.564338\pi\) | ||||
−0.200751 | + | 0.979642i | \(0.564338\pi\) | |||||||
\(578\) | 11.9333 | 0.496361 | ||||||||
\(579\) | −10.7730 | −0.447709 | ||||||||
\(580\) | 25.8326 | 1.07264 | ||||||||
\(581\) | 15.5353 | 0.644513 | ||||||||
\(582\) | −10.4924 | −0.434922 | ||||||||
\(583\) | −34.0841 | −1.41162 | ||||||||
\(584\) | −3.13856 | −0.129875 | ||||||||
\(585\) | −4.79082 | −0.198076 | ||||||||
\(586\) | −67.5879 | −2.79203 | ||||||||
\(587\) | 0.417407 | 0.0172282 | 0.00861411 | − | 0.999963i | \(-0.497258\pi\) | ||||
0.00861411 | + | 0.999963i | \(0.497258\pi\) | |||||||
\(588\) | 13.7093 | 0.565362 | ||||||||
\(589\) | 68.4514 | 2.82049 | ||||||||
\(590\) | −7.79324 | −0.320842 | ||||||||
\(591\) | −27.1158 | −1.11539 | ||||||||
\(592\) | 0.195977 | 0.00805459 | ||||||||
\(593\) | 10.2890 | 0.422520 | 0.211260 | − | 0.977430i | \(-0.432243\pi\) | ||||
0.211260 | + | 0.977430i | \(0.432243\pi\) | |||||||
\(594\) | −26.3686 | −1.08192 | ||||||||
\(595\) | 10.0738 | 0.412984 | ||||||||
\(596\) | −16.0632 | −0.657974 | ||||||||
\(597\) | −39.1959 | −1.60418 | ||||||||
\(598\) | 24.3449 | 0.995536 | ||||||||
\(599\) | 18.2932 | 0.747439 | 0.373719 | − | 0.927542i | \(-0.378082\pi\) | ||||
0.373719 | + | 0.927542i | \(0.378082\pi\) | |||||||
\(600\) | −17.7790 | −0.725824 | ||||||||
\(601\) | −16.7823 | −0.684564 | −0.342282 | − | 0.939597i | \(-0.611200\pi\) | ||||
−0.342282 | + | 0.939597i | \(0.611200\pi\) | |||||||
\(602\) | 42.8514 | 1.74649 | ||||||||
\(603\) | −11.2536 | −0.458281 | ||||||||
\(604\) | 12.6079 | 0.513007 | ||||||||
\(605\) | 2.56199 | 0.104160 | ||||||||
\(606\) | 55.6009 | 2.25863 | ||||||||
\(607\) | −27.4739 | −1.11513 | −0.557566 | − | 0.830132i | \(-0.688265\pi\) | ||||
−0.557566 | + | 0.830132i | \(0.688265\pi\) | |||||||
\(608\) | 43.5335 | 1.76552 | ||||||||
\(609\) | 27.2367 | 1.10369 | ||||||||
\(610\) | −11.2304 | −0.454706 | ||||||||
\(611\) | 2.24575 | 0.0908533 | ||||||||
\(612\) | −12.0788 | −0.488257 | ||||||||
\(613\) | 21.0839 | 0.851569 | 0.425785 | − | 0.904825i | \(-0.359998\pi\) | ||||
0.425785 | + | 0.904825i | \(0.359998\pi\) | |||||||
\(614\) | 16.5600 | 0.668308 | ||||||||
\(615\) | −14.8932 | −0.600553 | ||||||||
\(616\) | −18.0693 | −0.728032 | ||||||||
\(617\) | 7.26400 | 0.292437 | 0.146219 | − | 0.989252i | \(-0.453290\pi\) | ||||
0.146219 | + | 0.989252i | \(0.453290\pi\) | |||||||
\(618\) | 44.4139 | 1.78659 | ||||||||
\(619\) | 45.2965 | 1.82062 | 0.910310 | − | 0.413927i | \(-0.135843\pi\) | ||||
0.910310 | + | 0.413927i | \(0.135843\pi\) | |||||||
\(620\) | −39.2238 | −1.57526 | ||||||||
\(621\) | −12.5708 | −0.504448 | ||||||||
\(622\) | 59.1479 | 2.37161 | ||||||||
\(623\) | −36.9995 | −1.48235 | ||||||||
\(624\) | 1.29631 | 0.0518940 | ||||||||
\(625\) | 1.60565 | 0.0642260 | ||||||||
\(626\) | 34.9056 | 1.39511 | ||||||||
\(627\) | −45.1924 | −1.80481 | ||||||||
\(628\) | −6.86038 | −0.273759 | ||||||||
\(629\) | 3.42969 | 0.136751 | ||||||||
\(630\) | 7.38464 | 0.294211 | ||||||||
\(631\) | 10.3181 | 0.410757 | 0.205378 | − | 0.978683i | \(-0.434158\pi\) | ||||
0.205378 | + | 0.978683i | \(0.434158\pi\) | |||||||
\(632\) | −19.8527 | −0.789699 | ||||||||
\(633\) | 24.6220 | 0.978635 | ||||||||
\(634\) | 41.3508 | 1.64225 | ||||||||
\(635\) | −20.4034 | −0.809685 | ||||||||
\(636\) | 73.1611 | 2.90103 | ||||||||
\(637\) | −6.92374 | −0.274329 | ||||||||
\(638\) | 41.7761 | 1.65393 | ||||||||
\(639\) | 16.1909 | 0.640502 | ||||||||
\(640\) | −23.7579 | −0.939113 | ||||||||
\(641\) | 2.91433 | 0.115109 | 0.0575545 | − | 0.998342i | \(-0.481670\pi\) | ||||
0.0575545 | + | 0.998342i | \(0.481670\pi\) | |||||||
\(642\) | −33.5113 | −1.32259 | ||||||||
\(643\) | −24.5561 | −0.968399 | −0.484200 | − | 0.874958i | \(-0.660889\pi\) | ||||
−0.484200 | + | 0.874958i | \(0.660889\pi\) | |||||||
\(644\) | −23.0699 | −0.909081 | ||||||||
\(645\) | −22.9311 | −0.902913 | ||||||||
\(646\) | 57.8798 | 2.27725 | ||||||||
\(647\) | −27.2420 | −1.07099 | −0.535496 | − | 0.844538i | \(-0.679875\pi\) | ||||
−0.535496 | + | 0.844538i | \(0.679875\pi\) | |||||||
\(648\) | 30.1234 | 1.18336 | ||||||||
\(649\) | −7.74811 | −0.304140 | ||||||||
\(650\) | 24.0471 | 0.943204 | ||||||||
\(651\) | −41.3557 | −1.62086 | ||||||||
\(652\) | −69.8093 | −2.73394 | ||||||||
\(653\) | −28.1153 | −1.10024 | −0.550118 | − | 0.835087i | \(-0.685417\pi\) | ||||
−0.550118 | + | 0.835087i | \(0.685417\pi\) | |||||||
\(654\) | −4.61563 | −0.180486 | ||||||||
\(655\) | 1.26683 | 0.0494992 | ||||||||
\(656\) | 1.08362 | 0.0423084 | ||||||||
\(657\) | 1.27526 | 0.0497525 | ||||||||
\(658\) | −3.46164 | −0.134949 | ||||||||
\(659\) | 11.5646 | 0.450494 | 0.225247 | − | 0.974302i | \(-0.427681\pi\) | ||||
0.225247 | + | 0.974302i | \(0.427681\pi\) | |||||||
\(660\) | 25.8960 | 1.00800 | ||||||||
\(661\) | 28.3169 | 1.10140 | 0.550699 | − | 0.834704i | \(-0.314361\pi\) | ||||
0.550699 | + | 0.834704i | \(0.314361\pi\) | |||||||
\(662\) | −25.0618 | −0.974053 | ||||||||
\(663\) | 22.6861 | 0.881056 | ||||||||
\(664\) | −19.0981 | −0.741152 | ||||||||
\(665\) | −21.7546 | −0.843606 | ||||||||
\(666\) | 2.51415 | 0.0974215 | ||||||||
\(667\) | 19.9160 | 0.771152 | ||||||||
\(668\) | −18.2971 | −0.707937 | ||||||||
\(669\) | −7.86910 | −0.304237 | ||||||||
\(670\) | −30.9001 | −1.19378 | ||||||||
\(671\) | −11.1654 | −0.431035 | ||||||||
\(672\) | −26.3013 | −1.01459 | ||||||||
\(673\) | −0.149299 | −0.00575506 | −0.00287753 | − | 0.999996i | \(-0.500916\pi\) | ||||
−0.00287753 | + | 0.999996i | \(0.500916\pi\) | |||||||
\(674\) | −36.6285 | −1.41088 | ||||||||
\(675\) | −12.4170 | −0.477931 | ||||||||
\(676\) | −7.46017 | −0.286930 | ||||||||
\(677\) | −16.4402 | −0.631847 | −0.315923 | − | 0.948785i | \(-0.602314\pi\) | ||||
−0.315923 | + | 0.948785i | \(0.602314\pi\) | |||||||
\(678\) | −7.70838 | −0.296039 | ||||||||
\(679\) | −5.02153 | −0.192709 | ||||||||
\(680\) | −12.3841 | −0.474907 | ||||||||
\(681\) | 33.8770 | 1.29817 | ||||||||
\(682\) | −63.4321 | −2.42894 | ||||||||
\(683\) | −16.9704 | −0.649352 | −0.324676 | − | 0.945825i | \(-0.605255\pi\) | ||||
−0.324676 | + | 0.945825i | \(0.605255\pi\) | |||||||
\(684\) | 26.0845 | 0.997365 | ||||||||
\(685\) | 10.8228 | 0.413518 | ||||||||
\(686\) | 45.9055 | 1.75268 | ||||||||
\(687\) | −27.5159 | −1.04980 | ||||||||
\(688\) | 1.66846 | 0.0636093 | ||||||||
\(689\) | −36.9492 | −1.40765 | ||||||||
\(690\) | 20.0811 | 0.764476 | ||||||||
\(691\) | 11.1449 | 0.423973 | 0.211986 | − | 0.977273i | \(-0.432007\pi\) | ||||
0.211986 | + | 0.977273i | \(0.432007\pi\) | |||||||
\(692\) | 37.9589 | 1.44298 | ||||||||
\(693\) | 7.34188 | 0.278895 | ||||||||
\(694\) | 24.4281 | 0.927280 | ||||||||
\(695\) | 10.9261 | 0.414451 | ||||||||
\(696\) | −33.4831 | −1.26917 | ||||||||
\(697\) | 18.9639 | 0.718311 | ||||||||
\(698\) | 70.3658 | 2.66338 | ||||||||
\(699\) | −1.33235 | −0.0503943 | ||||||||
\(700\) | −22.7877 | −0.861294 | ||||||||
\(701\) | 36.8255 | 1.39088 | 0.695441 | − | 0.718583i | \(-0.255209\pi\) | ||||
0.695441 | + | 0.718583i | \(0.255209\pi\) | |||||||
\(702\) | −28.5852 | −1.07888 | ||||||||
\(703\) | −7.40650 | −0.279341 | ||||||||
\(704\) | −39.1607 | −1.47592 | ||||||||
\(705\) | 1.85243 | 0.0697666 | ||||||||
\(706\) | 51.7448 | 1.94744 | ||||||||
\(707\) | 26.6100 | 1.00077 | ||||||||
\(708\) | 16.6312 | 0.625040 | ||||||||
\(709\) | −29.4450 | −1.10583 | −0.552915 | − | 0.833237i | \(-0.686485\pi\) | ||||
−0.552915 | + | 0.833237i | \(0.686485\pi\) | |||||||
\(710\) | 44.4571 | 1.66844 | ||||||||
\(711\) | 8.06653 | 0.302519 | ||||||||
\(712\) | 45.4848 | 1.70462 | ||||||||
\(713\) | −30.2401 | −1.13250 | ||||||||
\(714\) | −34.9688 | −1.30867 | ||||||||
\(715\) | −13.0785 | −0.489108 | ||||||||
\(716\) | 27.4134 | 1.02449 | ||||||||
\(717\) | 18.2370 | 0.681073 | ||||||||
\(718\) | −15.3679 | −0.573523 | ||||||||
\(719\) | 0.395812 | 0.0147613 | 0.00738065 | − | 0.999973i | \(-0.497651\pi\) | ||||
0.00738065 | + | 0.999973i | \(0.497651\pi\) | |||||||
\(720\) | 0.287528 | 0.0107155 | ||||||||
\(721\) | 21.2560 | 0.791616 | ||||||||
\(722\) | −81.7002 | −3.04057 | ||||||||
\(723\) | −12.7663 | −0.474782 | ||||||||
\(724\) | 9.13585 | 0.339531 | ||||||||
\(725\) | 19.6724 | 0.730615 | ||||||||
\(726\) | −8.89335 | −0.330063 | ||||||||
\(727\) | 46.8317 | 1.73689 | 0.868446 | − | 0.495783i | \(-0.165119\pi\) | ||||
0.868446 | + | 0.495783i | \(0.165119\pi\) | |||||||
\(728\) | −19.5882 | −0.725986 | ||||||||
\(729\) | 11.1079 | 0.411402 | ||||||||
\(730\) | 3.50161 | 0.129600 | ||||||||
\(731\) | 29.1988 | 1.07996 | ||||||||
\(732\) | 23.9663 | 0.885822 | ||||||||
\(733\) | 14.4578 | 0.534011 | 0.267006 | − | 0.963695i | \(-0.413966\pi\) | ||||
0.267006 | + | 0.963695i | \(0.413966\pi\) | |||||||
\(734\) | −14.2481 | −0.525905 | ||||||||
\(735\) | −5.71113 | −0.210658 | ||||||||
\(736\) | −19.2320 | −0.708902 | ||||||||
\(737\) | −30.7212 | −1.13163 | ||||||||
\(738\) | 13.9016 | 0.511726 | ||||||||
\(739\) | −19.6171 | −0.721627 | −0.360813 | − | 0.932638i | \(-0.617501\pi\) | ||||
−0.360813 | + | 0.932638i | \(0.617501\pi\) | |||||||
\(740\) | 4.24404 | 0.156014 | ||||||||
\(741\) | −48.9913 | −1.79974 | ||||||||
\(742\) | 56.9542 | 2.09085 | ||||||||
\(743\) | −44.4388 | −1.63030 | −0.815151 | − | 0.579248i | \(-0.803346\pi\) | ||||
−0.815151 | + | 0.579248i | \(0.803346\pi\) | |||||||
\(744\) | 50.8402 | 1.86389 | ||||||||
\(745\) | 6.69173 | 0.245166 | ||||||||
\(746\) | 59.1557 | 2.16585 | ||||||||
\(747\) | 7.75994 | 0.283921 | ||||||||
\(748\) | −32.9740 | −1.20565 | ||||||||
\(749\) | −16.0382 | −0.586022 | ||||||||
\(750\) | 50.5218 | 1.84480 | ||||||||
\(751\) | −37.1409 | −1.35529 | −0.677646 | − | 0.735388i | \(-0.737000\pi\) | ||||
−0.677646 | + | 0.735388i | \(0.737000\pi\) | |||||||
\(752\) | −0.134782 | −0.00491499 | ||||||||
\(753\) | −25.3147 | −0.922521 | ||||||||
\(754\) | 45.2878 | 1.64929 | ||||||||
\(755\) | −5.25228 | −0.191150 | ||||||||
\(756\) | 27.0881 | 0.985186 | ||||||||
\(757\) | 10.8691 | 0.395042 | 0.197521 | − | 0.980299i | \(-0.436711\pi\) | ||||
0.197521 | + | 0.980299i | \(0.436711\pi\) | |||||||
\(758\) | −59.9232 | −2.17651 | ||||||||
\(759\) | 19.9649 | 0.724679 | ||||||||
\(760\) | 26.7437 | 0.970096 | ||||||||
\(761\) | 24.2576 | 0.879336 | 0.439668 | − | 0.898160i | \(-0.355096\pi\) | ||||
0.439668 | + | 0.898160i | \(0.355096\pi\) | |||||||
\(762\) | 70.8257 | 2.56575 | ||||||||
\(763\) | −2.20899 | −0.0799709 | ||||||||
\(764\) | 34.0121 | 1.23051 | ||||||||
\(765\) | 5.03188 | 0.181928 | ||||||||
\(766\) | 66.3847 | 2.39858 | ||||||||
\(767\) | −8.39942 | −0.303286 | ||||||||
\(768\) | 29.7989 | 1.07528 | ||||||||
\(769\) | −12.6106 | −0.454749 | −0.227375 | − | 0.973807i | \(-0.573014\pi\) | ||||
−0.227375 | + | 0.973807i | \(0.573014\pi\) | |||||||
\(770\) | 20.1594 | 0.726494 | ||||||||
\(771\) | 23.7575 | 0.855605 | ||||||||
\(772\) | 16.9746 | 0.610930 | ||||||||
\(773\) | 22.7759 | 0.819193 | 0.409597 | − | 0.912267i | \(-0.365669\pi\) | ||||
0.409597 | + | 0.912267i | \(0.365669\pi\) | |||||||
\(774\) | 21.4044 | 0.769365 | ||||||||
\(775\) | −29.8702 | −1.07297 | ||||||||
\(776\) | 6.17316 | 0.221603 | ||||||||
\(777\) | 4.47472 | 0.160530 | ||||||||
\(778\) | −19.0801 | −0.684055 | ||||||||
\(779\) | −40.9531 | −1.46730 | ||||||||
\(780\) | 28.0728 | 1.00517 | ||||||||
\(781\) | 44.1997 | 1.58159 | ||||||||
\(782\) | −25.5699 | −0.914376 | ||||||||
\(783\) | −23.3849 | −0.835710 | ||||||||
\(784\) | 0.415538 | 0.0148407 | ||||||||
\(785\) | 2.85795 | 0.102005 | ||||||||
\(786\) | −4.39751 | −0.156854 | ||||||||
\(787\) | 31.8726 | 1.13614 | 0.568068 | − | 0.822982i | \(-0.307691\pi\) | ||||
0.568068 | + | 0.822982i | \(0.307691\pi\) | |||||||
\(788\) | 42.7255 | 1.52203 | ||||||||
\(789\) | 13.0545 | 0.464752 | ||||||||
\(790\) | 22.1491 | 0.788031 | ||||||||
\(791\) | −3.68915 | −0.131171 | ||||||||
\(792\) | −9.02566 | −0.320713 | ||||||||
\(793\) | −12.1039 | −0.429824 | ||||||||
\(794\) | 58.9452 | 2.09189 | ||||||||
\(795\) | −30.4780 | −1.08094 | ||||||||
\(796\) | 61.7597 | 2.18901 | ||||||||
\(797\) | 25.3339 | 0.897372 | 0.448686 | − | 0.893690i | \(-0.351892\pi\) | ||||
0.448686 | + | 0.893690i | \(0.351892\pi\) | |||||||
\(798\) | 75.5159 | 2.67323 | ||||||||
\(799\) | −2.35875 | −0.0834466 | ||||||||
\(800\) | −18.9968 | −0.671637 | ||||||||
\(801\) | −18.4813 | −0.653006 | ||||||||
\(802\) | 62.3465 | 2.20153 | ||||||||
\(803\) | 3.48133 | 0.122854 | ||||||||
\(804\) | 65.9427 | 2.32562 | ||||||||
\(805\) | 9.61063 | 0.338730 | ||||||||
\(806\) | −68.7643 | −2.42212 | ||||||||
\(807\) | −12.8262 | −0.451504 | ||||||||
\(808\) | −32.7127 | −1.15083 | ||||||||
\(809\) | 6.61829 | 0.232687 | 0.116343 | − | 0.993209i | \(-0.462883\pi\) | ||||
0.116343 | + | 0.993209i | \(0.462883\pi\) | |||||||
\(810\) | −33.6078 | −1.18086 | ||||||||
\(811\) | 11.9125 | 0.418303 | 0.209151 | − | 0.977883i | \(-0.432930\pi\) | ||||
0.209151 | + | 0.977883i | \(0.432930\pi\) | |||||||
\(812\) | −42.9160 | −1.50606 | ||||||||
\(813\) | 2.60778 | 0.0914589 | ||||||||
\(814\) | 6.86341 | 0.240562 | ||||||||
\(815\) | 29.0817 | 1.01869 | ||||||||
\(816\) | −1.36154 | −0.0476635 | ||||||||
\(817\) | −63.0556 | −2.20604 | ||||||||
\(818\) | 3.66217 | 0.128045 | ||||||||
\(819\) | 7.95904 | 0.278111 | ||||||||
\(820\) | 23.4668 | 0.819496 | ||||||||
\(821\) | 3.71471 | 0.129644 | 0.0648221 | − | 0.997897i | \(-0.479352\pi\) | ||||
0.0648221 | + | 0.997897i | \(0.479352\pi\) | |||||||
\(822\) | −37.5689 | −1.31036 | ||||||||
\(823\) | −1.70002 | −0.0592589 | −0.0296295 | − | 0.999561i | \(-0.509433\pi\) | ||||
−0.0296295 | + | 0.999561i | \(0.509433\pi\) | |||||||
\(824\) | −26.1308 | −0.910311 | ||||||||
\(825\) | 19.7207 | 0.686586 | ||||||||
\(826\) | 12.9470 | 0.450484 | ||||||||
\(827\) | −11.7542 | −0.408733 | −0.204366 | − | 0.978894i | \(-0.565513\pi\) | ||||
−0.204366 | + | 0.978894i | \(0.565513\pi\) | |||||||
\(828\) | −11.5235 | −0.400469 | ||||||||
\(829\) | −12.5076 | −0.434406 | −0.217203 | − | 0.976127i | \(-0.569693\pi\) | ||||
−0.217203 | + | 0.976127i | \(0.569693\pi\) | |||||||
\(830\) | 21.3073 | 0.739586 | ||||||||
\(831\) | 47.0009 | 1.63044 | ||||||||
\(832\) | −42.4526 | −1.47178 | ||||||||
\(833\) | 7.27213 | 0.251964 | ||||||||
\(834\) | −37.9275 | −1.31332 | ||||||||
\(835\) | 7.62235 | 0.263782 | ||||||||
\(836\) | 71.2082 | 2.46279 | ||||||||
\(837\) | 35.5073 | 1.22731 | ||||||||
\(838\) | −48.4139 | −1.67243 | ||||||||
\(839\) | 24.0395 | 0.829936 | 0.414968 | − | 0.909836i | \(-0.363793\pi\) | ||||
0.414968 | + | 0.909836i | \(0.363793\pi\) | |||||||
\(840\) | −16.1575 | −0.557488 | ||||||||
\(841\) | 8.04902 | 0.277553 | ||||||||
\(842\) | −48.4286 | −1.66896 | ||||||||
\(843\) | 23.4690 | 0.808314 | ||||||||
\(844\) | −38.7961 | −1.33542 | ||||||||
\(845\) | 3.10781 | 0.106912 | ||||||||
\(846\) | −1.72910 | −0.0594476 | ||||||||
\(847\) | −4.25626 | −0.146247 | ||||||||
\(848\) | 2.21756 | 0.0761514 | ||||||||
\(849\) | 23.3057 | 0.799850 | ||||||||
\(850\) | −25.2571 | −0.866311 | ||||||||
\(851\) | 3.27201 | 0.112163 | ||||||||
\(852\) | −94.8740 | −3.25033 | ||||||||
\(853\) | −40.5273 | −1.38763 | −0.693814 | − | 0.720154i | \(-0.744071\pi\) | ||||
−0.693814 | + | 0.720154i | \(0.744071\pi\) | |||||||
\(854\) | 18.6572 | 0.638437 | ||||||||
\(855\) | −10.8665 | −0.371625 | ||||||||
\(856\) | 19.7163 | 0.673890 | ||||||||
\(857\) | −44.8884 | −1.53336 | −0.766679 | − | 0.642030i | \(-0.778092\pi\) | ||||
−0.766679 | + | 0.642030i | \(0.778092\pi\) | |||||||
\(858\) | 45.3989 | 1.54989 | ||||||||
\(859\) | 4.29568 | 0.146567 | 0.0732833 | − | 0.997311i | \(-0.476652\pi\) | ||||
0.0732833 | + | 0.997311i | \(0.476652\pi\) | |||||||
\(860\) | 36.1319 | 1.23209 | ||||||||
\(861\) | 24.7423 | 0.843216 | ||||||||
\(862\) | 79.7321 | 2.71569 | ||||||||
\(863\) | −23.8712 | −0.812585 | −0.406293 | − | 0.913743i | \(-0.633179\pi\) | ||||
−0.406293 | + | 0.913743i | \(0.633179\pi\) | |||||||
\(864\) | 22.5818 | 0.768248 | ||||||||
\(865\) | −15.8132 | −0.537665 | ||||||||
\(866\) | 86.1466 | 2.92738 | ||||||||
\(867\) | 10.6090 | 0.360300 | ||||||||
\(868\) | 65.1630 | 2.21177 | ||||||||
\(869\) | 22.0209 | 0.747008 | ||||||||
\(870\) | 37.3562 | 1.26649 | ||||||||
\(871\) | −33.3037 | −1.12845 | ||||||||
\(872\) | 2.71560 | 0.0919618 | ||||||||
\(873\) | −2.50827 | −0.0848921 | ||||||||
\(874\) | 55.2187 | 1.86780 | ||||||||
\(875\) | 24.1792 | 0.817406 | ||||||||
\(876\) | −7.47263 | −0.252477 | ||||||||
\(877\) | −19.9793 | −0.674653 | −0.337327 | − | 0.941388i | \(-0.609523\pi\) | ||||
−0.337327 | + | 0.941388i | \(0.609523\pi\) | |||||||
\(878\) | −51.3149 | −1.73179 | ||||||||
\(879\) | −60.0872 | −2.02669 | ||||||||
\(880\) | 0.784924 | 0.0264598 | ||||||||
\(881\) | 17.0452 | 0.574269 | 0.287134 | − | 0.957890i | \(-0.407297\pi\) | ||||
0.287134 | + | 0.957890i | \(0.407297\pi\) | |||||||
\(882\) | 5.33088 | 0.179500 | ||||||||
\(883\) | −38.7495 | −1.30402 | −0.652012 | − | 0.758208i | \(-0.726075\pi\) | ||||
−0.652012 | + | 0.758208i | \(0.726075\pi\) | |||||||
\(884\) | −35.7458 | −1.20226 | ||||||||
\(885\) | −6.92836 | −0.232894 | ||||||||
\(886\) | 20.0946 | 0.675091 | ||||||||
\(887\) | −26.1564 | −0.878247 | −0.439124 | − | 0.898427i | \(-0.644711\pi\) | ||||
−0.439124 | + | 0.898427i | \(0.644711\pi\) | |||||||
\(888\) | −5.50095 | −0.184600 | ||||||||
\(889\) | 33.8965 | 1.13685 | ||||||||
\(890\) | −50.7462 | −1.70102 | ||||||||
\(891\) | −33.4132 | −1.11938 | ||||||||
\(892\) | 12.3991 | 0.415152 | ||||||||
\(893\) | 5.09378 | 0.170457 | ||||||||
\(894\) | −23.2288 | −0.776887 | ||||||||
\(895\) | −11.4201 | −0.381731 | ||||||||
\(896\) | 39.4693 | 1.31858 | ||||||||
\(897\) | 21.6431 | 0.722643 | ||||||||
\(898\) | 55.0989 | 1.83867 | ||||||||
\(899\) | −56.2546 | −1.87620 | ||||||||
\(900\) | −11.3825 | −0.379418 | ||||||||
\(901\) | 38.8085 | 1.29290 | ||||||||
\(902\) | 37.9502 | 1.26360 | ||||||||
\(903\) | 38.0958 | 1.26775 | ||||||||
\(904\) | 4.53521 | 0.150839 | ||||||||
\(905\) | −3.80588 | −0.126512 | ||||||||
\(906\) | 18.2321 | 0.605720 | ||||||||
\(907\) | −17.3010 | −0.574469 | −0.287235 | − | 0.957860i | \(-0.592736\pi\) | ||||
−0.287235 | + | 0.957860i | \(0.592736\pi\) | |||||||
\(908\) | −53.3789 | −1.77144 | ||||||||
\(909\) | 13.2918 | 0.440861 | ||||||||
\(910\) | 21.8540 | 0.724453 | ||||||||
\(911\) | 1.31058 | 0.0434216 | 0.0217108 | − | 0.999764i | \(-0.493089\pi\) | ||||
0.0217108 | + | 0.999764i | \(0.493089\pi\) | |||||||
\(912\) | 2.94028 | 0.0973624 | ||||||||
\(913\) | 21.1839 | 0.701085 | ||||||||
\(914\) | 49.8645 | 1.64937 | ||||||||
\(915\) | −9.98408 | −0.330063 | ||||||||
\(916\) | 43.3560 | 1.43252 | ||||||||
\(917\) | −2.10460 | −0.0695002 | ||||||||
\(918\) | 30.0235 | 0.990924 | ||||||||
\(919\) | −54.6539 | −1.80287 | −0.901433 | − | 0.432919i | \(-0.857484\pi\) | ||||
−0.901433 | + | 0.432919i | \(0.857484\pi\) | |||||||
\(920\) | −11.8147 | −0.389519 | ||||||||
\(921\) | 14.7222 | 0.485114 | ||||||||
\(922\) | −0.0357603 | −0.00117770 | ||||||||
\(923\) | 47.9151 | 1.57715 | ||||||||
\(924\) | −43.0213 | −1.41530 | ||||||||
\(925\) | 3.23198 | 0.106267 | ||||||||
\(926\) | −96.3488 | −3.16622 | ||||||||
\(927\) | 10.6174 | 0.348723 | ||||||||
\(928\) | −35.7766 | −1.17442 | ||||||||
\(929\) | −10.0083 | −0.328360 | −0.164180 | − | 0.986430i | \(-0.552498\pi\) | ||||
−0.164180 | + | 0.986430i | \(0.552498\pi\) | |||||||
\(930\) | −56.7210 | −1.85995 | ||||||||
\(931\) | −15.7043 | −0.514689 | ||||||||
\(932\) | 2.09935 | 0.0687665 | ||||||||
\(933\) | 52.5838 | 1.72151 | ||||||||
\(934\) | −49.4785 | −1.61899 | ||||||||
\(935\) | 13.7366 | 0.449234 | ||||||||
\(936\) | −9.78435 | −0.319812 | ||||||||
\(937\) | 37.5868 | 1.22791 | 0.613954 | − | 0.789342i | \(-0.289578\pi\) | ||||
0.613954 | + | 0.789342i | \(0.289578\pi\) | |||||||
\(938\) | 51.3348 | 1.67614 | ||||||||
\(939\) | 31.0319 | 1.01269 | ||||||||
\(940\) | −2.91882 | −0.0952014 | ||||||||
\(941\) | −13.0015 | −0.423837 | −0.211918 | − | 0.977287i | \(-0.567971\pi\) | ||||
−0.211918 | + | 0.977287i | \(0.567971\pi\) | |||||||
\(942\) | −9.92070 | −0.323234 | ||||||||
\(943\) | 18.0921 | 0.589159 | ||||||||
\(944\) | 0.504103 | 0.0164072 | ||||||||
\(945\) | −11.2846 | −0.367087 | ||||||||
\(946\) | 58.4320 | 1.89979 | ||||||||
\(947\) | 13.9342 | 0.452800 | 0.226400 | − | 0.974034i | \(-0.427304\pi\) | ||||
0.226400 | + | 0.974034i | \(0.427304\pi\) | |||||||
\(948\) | −47.2675 | −1.53518 | ||||||||
\(949\) | 3.77397 | 0.122508 | ||||||||
\(950\) | 54.5433 | 1.76962 | ||||||||
\(951\) | 36.7618 | 1.19208 | ||||||||
\(952\) | 20.5738 | 0.666801 | ||||||||
\(953\) | 30.4093 | 0.985053 | 0.492526 | − | 0.870298i | \(-0.336074\pi\) | ||||
0.492526 | + | 0.870298i | \(0.336074\pi\) | |||||||
\(954\) | 28.4488 | 0.921063 | ||||||||
\(955\) | −14.1690 | −0.458498 | ||||||||
\(956\) | −28.7354 | −0.929371 | ||||||||
\(957\) | 37.1399 | 1.20056 | ||||||||
\(958\) | −27.3015 | −0.882071 | ||||||||
\(959\) | −17.9801 | −0.580606 | ||||||||
\(960\) | −35.0175 | −1.13018 | ||||||||
\(961\) | 54.4160 | 1.75535 | ||||||||
\(962\) | 7.44035 | 0.239886 | ||||||||
\(963\) | −8.01111 | −0.258154 | ||||||||
\(964\) | 20.1154 | 0.647874 | ||||||||
\(965\) | −7.07142 | −0.227637 | ||||||||
\(966\) | −33.3611 | −1.07337 | ||||||||
\(967\) | 51.4531 | 1.65462 | 0.827310 | − | 0.561745i | \(-0.189870\pi\) | ||||
0.827310 | + | 0.561745i | \(0.189870\pi\) | |||||||
\(968\) | 5.23238 | 0.168175 | ||||||||
\(969\) | 51.4564 | 1.65302 | ||||||||
\(970\) | −6.88722 | −0.221135 | ||||||||
\(971\) | 57.1482 | 1.83397 | 0.916986 | − | 0.398919i | \(-0.130614\pi\) | ||||
0.916986 | + | 0.398919i | \(0.130614\pi\) | |||||||
\(972\) | 34.9330 | 1.12048 | ||||||||
\(973\) | −18.1517 | −0.581917 | ||||||||
\(974\) | −13.5098 | −0.432883 | ||||||||
\(975\) | 21.3784 | 0.684657 | ||||||||
\(976\) | 0.726436 | 0.0232526 | ||||||||
\(977\) | −28.0599 | −0.897716 | −0.448858 | − | 0.893603i | \(-0.648169\pi\) | ||||
−0.448858 | + | 0.893603i | \(0.648169\pi\) | |||||||
\(978\) | −100.950 | −3.22804 | ||||||||
\(979\) | −50.4523 | −1.61246 | ||||||||
\(980\) | 8.99885 | 0.287458 | ||||||||
\(981\) | −1.10340 | −0.0352288 | ||||||||
\(982\) | 30.0246 | 0.958124 | ||||||||
\(983\) | 60.1511 | 1.91852 | 0.959261 | − | 0.282523i | \(-0.0911713\pi\) | ||||
0.959261 | + | 0.282523i | \(0.0911713\pi\) | |||||||
\(984\) | −30.4167 | −0.969648 | ||||||||
\(985\) | −17.7989 | −0.567121 | ||||||||
\(986\) | −47.5666 | −1.51483 | ||||||||
\(987\) | −3.07747 | −0.0979570 | ||||||||
\(988\) | 77.1940 | 2.45587 | ||||||||
\(989\) | 27.8564 | 0.885783 | ||||||||
\(990\) | 10.0697 | 0.320035 | ||||||||
\(991\) | −4.54431 | −0.144355 | −0.0721775 | − | 0.997392i | \(-0.522995\pi\) | ||||
−0.0721775 | + | 0.997392i | \(0.522995\pi\) | |||||||
\(992\) | 54.3225 | 1.72474 | ||||||||
\(993\) | −22.2805 | −0.707049 | ||||||||
\(994\) | −73.8571 | −2.34261 | ||||||||
\(995\) | −25.7283 | −0.815643 | ||||||||
\(996\) | −45.4710 | −1.44080 | ||||||||
\(997\) | −35.1439 | −1.11302 | −0.556510 | − | 0.830841i | \(-0.687860\pi\) | ||||
−0.556510 | + | 0.830841i | \(0.687860\pi\) | |||||||
\(998\) | 60.7330 | 1.92247 | ||||||||
\(999\) | −3.84192 | −0.121553 |
(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 | 4033.2.a.d.1.11 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.11 | ✓ | 79 | 1.1 | even | 1 | trivial |