Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, 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("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.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: | \(4.94273988512\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.45503 | 1.02886 | 0.514431 | − | 0.857532i | \(-0.328003\pi\) | ||||
0.514431 | + | 0.857532i | \(0.328003\pi\) | |||||||
\(3\) | −3.26388 | −1.88440 | −0.942202 | − | 0.335046i | \(-0.891248\pi\) | ||||
−0.942202 | + | 0.335046i | \(0.891248\pi\) | |||||||
\(4\) | 0.117111 | 0.0585557 | ||||||||
\(5\) | −2.69944 | −1.20723 | −0.603614 | − | 0.797277i | \(-0.706273\pi\) | ||||
−0.603614 | + | 0.797277i | \(0.706273\pi\) | |||||||
\(6\) | −4.74905 | −1.93879 | ||||||||
\(7\) | −1.44249 | −0.545209 | −0.272605 | − | 0.962126i | \(-0.587885\pi\) | ||||
−0.272605 | + | 0.962126i | \(0.587885\pi\) | |||||||
\(8\) | −2.73966 | −0.968616 | ||||||||
\(9\) | 7.65293 | 2.55098 | ||||||||
\(10\) | −3.92777 | −1.24207 | ||||||||
\(11\) | 4.50441 | 1.35813 | 0.679066 | − | 0.734077i | \(-0.262385\pi\) | ||||
0.679066 | + | 0.734077i | \(0.262385\pi\) | |||||||
\(12\) | −0.382238 | −0.110343 | ||||||||
\(13\) | 0.198137 | 0.0549534 | 0.0274767 | − | 0.999622i | \(-0.491253\pi\) | ||||
0.0274767 | + | 0.999622i | \(0.491253\pi\) | |||||||
\(14\) | −2.09886 | −0.560945 | ||||||||
\(15\) | 8.81067 | 2.27490 | ||||||||
\(16\) | −4.22051 | −1.05513 | ||||||||
\(17\) | −1.93683 | −0.469750 | −0.234875 | − | 0.972026i | \(-0.575468\pi\) | ||||
−0.234875 | + | 0.972026i | \(0.575468\pi\) | |||||||
\(18\) | 11.1352 | 2.62460 | ||||||||
\(19\) | 3.86501 | 0.886693 | 0.443347 | − | 0.896350i | \(-0.353791\pi\) | ||||
0.443347 | + | 0.896350i | \(0.353791\pi\) | |||||||
\(20\) | −0.316135 | −0.0706900 | ||||||||
\(21\) | 4.70811 | 1.02739 | ||||||||
\(22\) | 6.55406 | 1.39733 | ||||||||
\(23\) | 0.808761 | 0.168638 | 0.0843192 | − | 0.996439i | \(-0.473128\pi\) | ||||
0.0843192 | + | 0.996439i | \(0.473128\pi\) | |||||||
\(24\) | 8.94193 | 1.82526 | ||||||||
\(25\) | 2.28699 | 0.457398 | ||||||||
\(26\) | 0.288296 | 0.0565395 | ||||||||
\(27\) | −15.1866 | −2.92267 | ||||||||
\(28\) | −0.168932 | −0.0319251 | ||||||||
\(29\) | 6.96153 | 1.29272 | 0.646362 | − | 0.763031i | \(-0.276290\pi\) | ||||
0.646362 | + | 0.763031i | \(0.276290\pi\) | |||||||
\(30\) | 12.8198 | 2.34056 | ||||||||
\(31\) | 1.02658 | 0.184380 | 0.0921900 | − | 0.995741i | \(-0.470613\pi\) | ||||
0.0921900 | + | 0.995741i | \(0.470613\pi\) | |||||||
\(32\) | −0.661646 | −0.116964 | ||||||||
\(33\) | −14.7019 | −2.55927 | ||||||||
\(34\) | −2.81814 | −0.483307 | ||||||||
\(35\) | 3.89391 | 0.658192 | ||||||||
\(36\) | 0.896245 | 0.149374 | ||||||||
\(37\) | 6.22281 | 1.02302 | 0.511512 | − | 0.859276i | \(-0.329086\pi\) | ||||
0.511512 | + | 0.859276i | \(0.329086\pi\) | |||||||
\(38\) | 5.62370 | 0.912284 | ||||||||
\(39\) | −0.646697 | −0.103554 | ||||||||
\(40\) | 7.39555 | 1.16934 | ||||||||
\(41\) | 5.92980 | 0.926079 | 0.463039 | − | 0.886338i | \(-0.346759\pi\) | ||||
0.463039 | + | 0.886338i | \(0.346759\pi\) | |||||||
\(42\) | 6.85044 | 1.05705 | ||||||||
\(43\) | 1.11330 | 0.169776 | 0.0848882 | − | 0.996390i | \(-0.472947\pi\) | ||||
0.0848882 | + | 0.996390i | \(0.472947\pi\) | |||||||
\(44\) | 0.527518 | 0.0795263 | ||||||||
\(45\) | −20.6586 | −3.07961 | ||||||||
\(46\) | 1.17677 | 0.173506 | ||||||||
\(47\) | −7.77508 | −1.13411 | −0.567056 | − | 0.823679i | \(-0.691918\pi\) | ||||
−0.567056 | + | 0.823679i | \(0.691918\pi\) | |||||||
\(48\) | 13.7752 | 1.98828 | ||||||||
\(49\) | −4.91923 | −0.702747 | ||||||||
\(50\) | 3.32764 | 0.470599 | ||||||||
\(51\) | 6.32158 | 0.885198 | ||||||||
\(52\) | 0.0232041 | 0.00321784 | ||||||||
\(53\) | 5.75008 | 0.789834 | 0.394917 | − | 0.918717i | \(-0.370773\pi\) | ||||
0.394917 | + | 0.918717i | \(0.370773\pi\) | |||||||
\(54\) | −22.0970 | −3.00702 | ||||||||
\(55\) | −12.1594 | −1.63957 | ||||||||
\(56\) | 3.95193 | 0.528098 | ||||||||
\(57\) | −12.6149 | −1.67089 | ||||||||
\(58\) | 10.1292 | 1.33003 | ||||||||
\(59\) | −7.95759 | −1.03599 | −0.517995 | − | 0.855384i | \(-0.673321\pi\) | ||||
−0.517995 | + | 0.855384i | \(0.673321\pi\) | |||||||
\(60\) | 1.03183 | 0.133209 | ||||||||
\(61\) | 6.64190 | 0.850408 | 0.425204 | − | 0.905097i | \(-0.360202\pi\) | ||||
0.425204 | + | 0.905097i | \(0.360202\pi\) | |||||||
\(62\) | 1.49371 | 0.189702 | ||||||||
\(63\) | −11.0393 | −1.39082 | ||||||||
\(64\) | 7.47830 | 0.934788 | ||||||||
\(65\) | −0.534861 | −0.0663413 | ||||||||
\(66\) | −21.3917 | −2.63313 | ||||||||
\(67\) | −13.5542 | −1.65591 | −0.827956 | − | 0.560793i | \(-0.810496\pi\) | ||||
−0.827956 | + | 0.560793i | \(0.810496\pi\) | |||||||
\(68\) | −0.226825 | −0.0275065 | ||||||||
\(69\) | −2.63970 | −0.317783 | ||||||||
\(70\) | 5.66576 | 0.677188 | ||||||||
\(71\) | −7.35863 | −0.873309 | −0.436654 | − | 0.899629i | \(-0.643837\pi\) | ||||
−0.436654 | + | 0.899629i | \(0.643837\pi\) | |||||||
\(72\) | −20.9664 | −2.47092 | ||||||||
\(73\) | 8.20815 | 0.960691 | 0.480346 | − | 0.877079i | \(-0.340511\pi\) | ||||
0.480346 | + | 0.877079i | \(0.340511\pi\) | |||||||
\(74\) | 9.05438 | 1.05255 | ||||||||
\(75\) | −7.46447 | −0.861923 | ||||||||
\(76\) | 0.452636 | 0.0519209 | ||||||||
\(77\) | −6.49757 | −0.740466 | ||||||||
\(78\) | −0.940964 | −0.106543 | ||||||||
\(79\) | 7.47172 | 0.840635 | 0.420317 | − | 0.907377i | \(-0.361919\pi\) | ||||
0.420317 | + | 0.907377i | \(0.361919\pi\) | |||||||
\(80\) | 11.3930 | 1.27378 | ||||||||
\(81\) | 26.6086 | 2.95651 | ||||||||
\(82\) | 8.62803 | 0.952806 | ||||||||
\(83\) | 15.5874 | 1.71093 | 0.855467 | − | 0.517857i | \(-0.173270\pi\) | ||||
0.855467 | + | 0.517857i | \(0.173270\pi\) | |||||||
\(84\) | 0.551373 | 0.0601598 | ||||||||
\(85\) | 5.22836 | 0.567095 | ||||||||
\(86\) | 1.61988 | 0.174676 | ||||||||
\(87\) | −22.7216 | −2.43601 | ||||||||
\(88\) | −12.3406 | −1.31551 | ||||||||
\(89\) | 16.4390 | 1.74253 | 0.871266 | − | 0.490811i | \(-0.163299\pi\) | ||||
0.871266 | + | 0.490811i | \(0.163299\pi\) | |||||||
\(90\) | −30.0589 | −3.16849 | ||||||||
\(91\) | −0.285811 | −0.0299611 | ||||||||
\(92\) | 0.0947151 | 0.00987474 | ||||||||
\(93\) | −3.35065 | −0.347446 | ||||||||
\(94\) | −11.3130 | −1.16684 | ||||||||
\(95\) | −10.4334 | −1.07044 | ||||||||
\(96\) | 2.15954 | 0.220407 | ||||||||
\(97\) | −18.6262 | −1.89120 | −0.945600 | − | 0.325332i | \(-0.894524\pi\) | ||||
−0.945600 | + | 0.325332i | \(0.894524\pi\) | |||||||
\(98\) | −7.15762 | −0.723029 | ||||||||
\(99\) | 34.4720 | 3.46456 | ||||||||
\(100\) | 0.267833 | 0.0267833 | ||||||||
\(101\) | 7.22564 | 0.718978 | 0.359489 | − | 0.933149i | \(-0.382951\pi\) | ||||
0.359489 | + | 0.933149i | \(0.382951\pi\) | |||||||
\(102\) | 9.19809 | 0.910746 | ||||||||
\(103\) | 18.4839 | 1.82127 | 0.910636 | − | 0.413209i | \(-0.135592\pi\) | ||||
0.910636 | + | 0.413209i | \(0.135592\pi\) | |||||||
\(104\) | −0.542829 | −0.0532288 | ||||||||
\(105\) | −12.7093 | −1.24030 | ||||||||
\(106\) | 8.36653 | 0.812629 | ||||||||
\(107\) | 13.6163 | 1.31634 | 0.658171 | − | 0.752869i | \(-0.271331\pi\) | ||||
0.658171 | + | 0.752869i | \(0.271331\pi\) | |||||||
\(108\) | −1.77853 | −0.171139 | ||||||||
\(109\) | 10.9783 | 1.05153 | 0.525763 | − | 0.850631i | \(-0.323780\pi\) | ||||
0.525763 | + | 0.850631i | \(0.323780\pi\) | |||||||
\(110\) | −17.6923 | −1.68689 | ||||||||
\(111\) | −20.3105 | −1.92779 | ||||||||
\(112\) | 6.08803 | 0.575265 | ||||||||
\(113\) | 9.20959 | 0.866365 | 0.433183 | − | 0.901306i | \(-0.357391\pi\) | ||||
0.433183 | + | 0.901306i | \(0.357391\pi\) | |||||||
\(114\) | −18.3551 | −1.71911 | ||||||||
\(115\) | −2.18321 | −0.203585 | ||||||||
\(116\) | 0.815275 | 0.0756964 | ||||||||
\(117\) | 1.51633 | 0.140185 | ||||||||
\(118\) | −11.5785 | −1.06589 | ||||||||
\(119\) | 2.79385 | 0.256112 | ||||||||
\(120\) | −24.1382 | −2.20351 | ||||||||
\(121\) | 9.28975 | 0.844523 | ||||||||
\(122\) | 9.66416 | 0.874952 | ||||||||
\(123\) | −19.3542 | −1.74511 | ||||||||
\(124\) | 0.120225 | 0.0107965 | ||||||||
\(125\) | 7.32361 | 0.655044 | ||||||||
\(126\) | −16.0625 | −1.43096 | ||||||||
\(127\) | −8.31505 | −0.737842 | −0.368921 | − | 0.929461i | \(-0.620273\pi\) | ||||
−0.368921 | + | 0.929461i | \(0.620273\pi\) | |||||||
\(128\) | 12.2044 | 1.07873 | ||||||||
\(129\) | −3.63368 | −0.319927 | ||||||||
\(130\) | −0.778238 | −0.0682560 | ||||||||
\(131\) | −16.2234 | −1.41745 | −0.708723 | − | 0.705487i | \(-0.750728\pi\) | ||||
−0.708723 | + | 0.705487i | \(0.750728\pi\) | |||||||
\(132\) | −1.72176 | −0.149860 | ||||||||
\(133\) | −5.57523 | −0.483433 | ||||||||
\(134\) | −19.7218 | −1.70370 | ||||||||
\(135\) | 40.9954 | 3.52832 | ||||||||
\(136\) | 5.30625 | 0.455007 | ||||||||
\(137\) | 14.9392 | 1.27634 | 0.638170 | − | 0.769895i | \(-0.279692\pi\) | ||||
0.638170 | + | 0.769895i | \(0.279692\pi\) | |||||||
\(138\) | −3.84085 | −0.326954 | ||||||||
\(139\) | −11.9566 | −1.01415 | −0.507075 | − | 0.861902i | \(-0.669273\pi\) | ||||
−0.507075 | + | 0.861902i | \(0.669273\pi\) | |||||||
\(140\) | 0.456022 | 0.0385409 | ||||||||
\(141\) | 25.3769 | 2.13712 | ||||||||
\(142\) | −10.7070 | −0.898514 | ||||||||
\(143\) | 0.892493 | 0.0746340 | ||||||||
\(144\) | −32.2993 | −2.69160 | ||||||||
\(145\) | −18.7923 | −1.56061 | ||||||||
\(146\) | 11.9431 | 0.988418 | ||||||||
\(147\) | 16.0558 | 1.32426 | ||||||||
\(148\) | 0.728762 | 0.0599039 | ||||||||
\(149\) | 8.24104 | 0.675132 | 0.337566 | − | 0.941302i | \(-0.390396\pi\) | ||||
0.337566 | + | 0.941302i | \(0.390396\pi\) | |||||||
\(150\) | −10.8610 | −0.886799 | ||||||||
\(151\) | −13.8051 | −1.12344 | −0.561720 | − | 0.827327i | \(-0.689860\pi\) | ||||
−0.561720 | + | 0.827327i | \(0.689860\pi\) | |||||||
\(152\) | −10.5888 | −0.858865 | ||||||||
\(153\) | −14.8224 | −1.19832 | ||||||||
\(154\) | −9.45415 | −0.761837 | ||||||||
\(155\) | −2.77121 | −0.222589 | ||||||||
\(156\) | −0.0757356 | −0.00606370 | ||||||||
\(157\) | −14.6039 | −1.16552 | −0.582759 | − | 0.812645i | \(-0.698027\pi\) | ||||
−0.582759 | + | 0.812645i | \(0.698027\pi\) | |||||||
\(158\) | 10.8716 | 0.864896 | ||||||||
\(159\) | −18.7676 | −1.48837 | ||||||||
\(160\) | 1.78608 | 0.141202 | ||||||||
\(161\) | −1.16663 | −0.0919432 | ||||||||
\(162\) | 38.7162 | 3.04184 | ||||||||
\(163\) | 12.7376 | 0.997689 | 0.498844 | − | 0.866692i | \(-0.333758\pi\) | ||||
0.498844 | + | 0.866692i | \(0.333758\pi\) | |||||||
\(164\) | 0.694446 | 0.0542272 | ||||||||
\(165\) | 39.6869 | 3.08962 | ||||||||
\(166\) | 22.6801 | 1.76031 | ||||||||
\(167\) | −10.4856 | −0.811400 | −0.405700 | − | 0.914006i | \(-0.632972\pi\) | ||||
−0.405700 | + | 0.914006i | \(0.632972\pi\) | |||||||
\(168\) | −12.8986 | −0.995150 | ||||||||
\(169\) | −12.9607 | −0.996980 | ||||||||
\(170\) | 7.60741 | 0.583462 | ||||||||
\(171\) | 29.5786 | 2.26193 | ||||||||
\(172\) | 0.130380 | 0.00994137 | ||||||||
\(173\) | 0.373888 | 0.0284261 | 0.0142131 | − | 0.999899i | \(-0.495476\pi\) | ||||
0.0142131 | + | 0.999899i | \(0.495476\pi\) | |||||||
\(174\) | −33.0606 | −2.50632 | ||||||||
\(175\) | −3.29896 | −0.249378 | ||||||||
\(176\) | −19.0109 | −1.43300 | ||||||||
\(177\) | 25.9726 | 1.95222 | ||||||||
\(178\) | 23.9193 | 1.79282 | ||||||||
\(179\) | −2.36663 | −0.176890 | −0.0884449 | − | 0.996081i | \(-0.528190\pi\) | ||||
−0.0884449 | + | 0.996081i | \(0.528190\pi\) | |||||||
\(180\) | −2.41936 | −0.180329 | ||||||||
\(181\) | 21.0280 | 1.56300 | 0.781498 | − | 0.623908i | \(-0.214456\pi\) | ||||
0.781498 | + | 0.623908i | \(0.214456\pi\) | |||||||
\(182\) | −0.415863 | −0.0308258 | ||||||||
\(183\) | −21.6784 | −1.60251 | ||||||||
\(184\) | −2.21573 | −0.163346 | ||||||||
\(185\) | −16.7981 | −1.23502 | ||||||||
\(186\) | −4.87530 | −0.357474 | ||||||||
\(187\) | −8.72428 | −0.637982 | ||||||||
\(188\) | −0.910550 | −0.0664087 | ||||||||
\(189\) | 21.9065 | 1.59347 | ||||||||
\(190\) | −15.1809 | −1.10133 | ||||||||
\(191\) | −13.6361 | −0.986674 | −0.493337 | − | 0.869838i | \(-0.664223\pi\) | ||||
−0.493337 | + | 0.869838i | \(0.664223\pi\) | |||||||
\(192\) | −24.4083 | −1.76152 | ||||||||
\(193\) | 3.03369 | 0.218370 | 0.109185 | − | 0.994021i | \(-0.465176\pi\) | ||||
0.109185 | + | 0.994021i | \(0.465176\pi\) | |||||||
\(194\) | −27.1016 | −1.94578 | ||||||||
\(195\) | 1.74572 | 0.125014 | ||||||||
\(196\) | −0.576097 | −0.0411498 | ||||||||
\(197\) | 10.7235 | 0.764016 | 0.382008 | − | 0.924159i | \(-0.375233\pi\) | ||||
0.382008 | + | 0.924159i | \(0.375233\pi\) | |||||||
\(198\) | 50.1577 | 3.56456 | ||||||||
\(199\) | 23.2432 | 1.64766 | 0.823832 | − | 0.566834i | \(-0.191832\pi\) | ||||
0.823832 | + | 0.566834i | \(0.191832\pi\) | |||||||
\(200\) | −6.26558 | −0.443043 | ||||||||
\(201\) | 44.2394 | 3.12041 | ||||||||
\(202\) | 10.5135 | 0.739729 | ||||||||
\(203\) | −10.0419 | −0.704805 | ||||||||
\(204\) | 0.740329 | 0.0518334 | ||||||||
\(205\) | −16.0071 | −1.11799 | ||||||||
\(206\) | 26.8946 | 1.87384 | ||||||||
\(207\) | 6.18939 | 0.430193 | ||||||||
\(208\) | −0.836240 | −0.0579828 | ||||||||
\(209\) | 17.4096 | 1.20425 | ||||||||
\(210\) | −18.4924 | −1.27610 | ||||||||
\(211\) | −10.8969 | −0.750177 | −0.375088 | − | 0.926989i | \(-0.622388\pi\) | ||||
−0.375088 | + | 0.926989i | \(0.622388\pi\) | |||||||
\(212\) | 0.673399 | 0.0462492 | ||||||||
\(213\) | 24.0177 | 1.64567 | ||||||||
\(214\) | 19.8122 | 1.35433 | ||||||||
\(215\) | −3.00529 | −0.204959 | ||||||||
\(216\) | 41.6062 | 2.83094 | ||||||||
\(217\) | −1.48084 | −0.100526 | ||||||||
\(218\) | 15.9737 | 1.08187 | ||||||||
\(219\) | −26.7904 | −1.81033 | ||||||||
\(220\) | −1.42400 | −0.0960064 | ||||||||
\(221\) | −0.383758 | −0.0258144 | ||||||||
\(222\) | −29.5524 | −1.98343 | ||||||||
\(223\) | 7.05320 | 0.472317 | 0.236159 | − | 0.971715i | \(-0.424111\pi\) | ||||
0.236159 | + | 0.971715i | \(0.424111\pi\) | |||||||
\(224\) | 0.954417 | 0.0637697 | ||||||||
\(225\) | 17.5022 | 1.16681 | ||||||||
\(226\) | 13.4002 | 0.891370 | ||||||||
\(227\) | 15.6090 | 1.03601 | 0.518004 | − | 0.855378i | \(-0.326675\pi\) | ||||
0.518004 | + | 0.855378i | \(0.326675\pi\) | |||||||
\(228\) | −1.47735 | −0.0978400 | ||||||||
\(229\) | 22.1927 | 1.46654 | 0.733268 | − | 0.679940i | \(-0.237994\pi\) | ||||
0.733268 | + | 0.679940i | \(0.237994\pi\) | |||||||
\(230\) | −3.17663 | −0.209461 | ||||||||
\(231\) | 21.2073 | 1.39534 | ||||||||
\(232\) | −19.0722 | −1.25215 | ||||||||
\(233\) | −2.04681 | −0.134091 | −0.0670455 | − | 0.997750i | \(-0.521357\pi\) | ||||
−0.0670455 | + | 0.997750i | \(0.521357\pi\) | |||||||
\(234\) | 2.20631 | 0.144231 | ||||||||
\(235\) | 20.9884 | 1.36913 | ||||||||
\(236\) | −0.931924 | −0.0606631 | ||||||||
\(237\) | −24.3868 | −1.58409 | ||||||||
\(238\) | 4.06514 | 0.263504 | ||||||||
\(239\) | 4.19951 | 0.271644 | 0.135822 | − | 0.990733i | \(-0.456632\pi\) | ||||
0.135822 | + | 0.990733i | \(0.456632\pi\) | |||||||
\(240\) | −37.1855 | −2.40031 | ||||||||
\(241\) | −8.22325 | −0.529706 | −0.264853 | − | 0.964289i | \(-0.585323\pi\) | ||||
−0.264853 | + | 0.964289i | \(0.585323\pi\) | |||||||
\(242\) | 13.5169 | 0.868897 | ||||||||
\(243\) | −41.2874 | −2.64859 | ||||||||
\(244\) | 0.777842 | 0.0497962 | ||||||||
\(245\) | 13.2792 | 0.848375 | ||||||||
\(246\) | −28.1609 | −1.79547 | ||||||||
\(247\) | 0.765802 | 0.0487268 | ||||||||
\(248\) | −2.81249 | −0.178593 | ||||||||
\(249\) | −50.8753 | −3.22409 | ||||||||
\(250\) | 10.6561 | 0.673949 | ||||||||
\(251\) | 12.5908 | 0.794726 | 0.397363 | − | 0.917661i | \(-0.369925\pi\) | ||||
0.397363 | + | 0.917661i | \(0.369925\pi\) | |||||||
\(252\) | −1.29282 | −0.0814402 | ||||||||
\(253\) | 3.64300 | 0.229033 | ||||||||
\(254\) | −12.0986 | −0.759137 | ||||||||
\(255\) | −17.0647 | −1.06864 | ||||||||
\(256\) | 2.80122 | 0.175076 | ||||||||
\(257\) | −16.3841 | −1.02201 | −0.511005 | − | 0.859578i | \(-0.670727\pi\) | ||||
−0.511005 | + | 0.859578i | \(0.670727\pi\) | |||||||
\(258\) | −5.28711 | −0.329161 | ||||||||
\(259\) | −8.97634 | −0.557762 | ||||||||
\(260\) | −0.0626383 | −0.00388466 | ||||||||
\(261\) | 53.2761 | 3.29771 | ||||||||
\(262\) | −23.6055 | −1.45836 | ||||||||
\(263\) | −4.40532 | −0.271644 | −0.135822 | − | 0.990733i | \(-0.543367\pi\) | ||||
−0.135822 | + | 0.990733i | \(0.543367\pi\) | |||||||
\(264\) | 40.2781 | 2.47895 | ||||||||
\(265\) | −15.5220 | −0.953509 | ||||||||
\(266\) | −8.11212 | −0.497386 | ||||||||
\(267\) | −53.6550 | −3.28363 | ||||||||
\(268\) | −1.58735 | −0.0969631 | ||||||||
\(269\) | −12.1275 | −0.739424 | −0.369712 | − | 0.929146i | \(-0.620544\pi\) | ||||
−0.369712 | + | 0.929146i | \(0.620544\pi\) | |||||||
\(270\) | 59.6495 | 3.63016 | ||||||||
\(271\) | −15.1314 | −0.919167 | −0.459583 | − | 0.888135i | \(-0.652001\pi\) | ||||
−0.459583 | + | 0.888135i | \(0.652001\pi\) | |||||||
\(272\) | 8.17440 | 0.495646 | ||||||||
\(273\) | 0.932853 | 0.0564588 | ||||||||
\(274\) | 21.7369 | 1.31318 | ||||||||
\(275\) | 10.3016 | 0.621207 | ||||||||
\(276\) | −0.309139 | −0.0186080 | ||||||||
\(277\) | 24.2812 | 1.45892 | 0.729459 | − | 0.684025i | \(-0.239772\pi\) | ||||
0.729459 | + | 0.684025i | \(0.239772\pi\) | |||||||
\(278\) | −17.3973 | −1.04342 | ||||||||
\(279\) | 7.85638 | 0.470349 | ||||||||
\(280\) | −10.6680 | −0.637535 | ||||||||
\(281\) | −24.6461 | −1.47026 | −0.735130 | − | 0.677926i | \(-0.762879\pi\) | ||||
−0.735130 | + | 0.677926i | \(0.762879\pi\) | |||||||
\(282\) | 36.9242 | 2.19880 | ||||||||
\(283\) | 1.64814 | 0.0979715 | 0.0489858 | − | 0.998799i | \(-0.484401\pi\) | ||||
0.0489858 | + | 0.998799i | \(0.484401\pi\) | |||||||
\(284\) | −0.861779 | −0.0511372 | ||||||||
\(285\) | 34.0533 | 2.01714 | ||||||||
\(286\) | 1.29860 | 0.0767881 | ||||||||
\(287\) | −8.55366 | −0.504907 | ||||||||
\(288\) | −5.06353 | −0.298372 | ||||||||
\(289\) | −13.2487 | −0.779335 | ||||||||
\(290\) | −27.3433 | −1.60565 | ||||||||
\(291\) | 60.7936 | 3.56378 | ||||||||
\(292\) | 0.961267 | 0.0562539 | ||||||||
\(293\) | −1.23309 | −0.0720377 | −0.0360189 | − | 0.999351i | \(-0.511468\pi\) | ||||
−0.0360189 | + | 0.999351i | \(0.511468\pi\) | |||||||
\(294\) | 23.3616 | 1.36248 | ||||||||
\(295\) | 21.4811 | 1.25068 | ||||||||
\(296\) | −17.0484 | −0.990917 | ||||||||
\(297\) | −68.4068 | −3.96937 | ||||||||
\(298\) | 11.9910 | 0.694618 | ||||||||
\(299\) | 0.160246 | 0.00926726 | ||||||||
\(300\) | −0.874175 | −0.0504705 | ||||||||
\(301\) | −1.60592 | −0.0925637 | ||||||||
\(302\) | −20.0868 | −1.15586 | ||||||||
\(303\) | −23.5836 | −1.35484 | ||||||||
\(304\) | −16.3123 | −0.935574 | ||||||||
\(305\) | −17.9294 | −1.02664 | ||||||||
\(306\) | −21.5670 | −1.23291 | ||||||||
\(307\) | 2.61165 | 0.149055 | 0.0745274 | − | 0.997219i | \(-0.476255\pi\) | ||||
0.0745274 | + | 0.997219i | \(0.476255\pi\) | |||||||
\(308\) | −0.760939 | −0.0433585 | ||||||||
\(309\) | −60.3293 | −3.43201 | ||||||||
\(310\) | −4.03219 | −0.229013 | ||||||||
\(311\) | 21.4251 | 1.21491 | 0.607454 | − | 0.794355i | \(-0.292191\pi\) | ||||
0.607454 | + | 0.794355i | \(0.292191\pi\) | |||||||
\(312\) | 1.77173 | 0.100304 | ||||||||
\(313\) | −25.5877 | −1.44630 | −0.723152 | − | 0.690689i | \(-0.757308\pi\) | ||||
−0.723152 | + | 0.690689i | \(0.757308\pi\) | |||||||
\(314\) | −21.2491 | −1.19916 | ||||||||
\(315\) | 29.7999 | 1.67903 | ||||||||
\(316\) | 0.875024 | 0.0492239 | ||||||||
\(317\) | 23.4782 | 1.31866 | 0.659332 | − | 0.751852i | \(-0.270839\pi\) | ||||
0.659332 | + | 0.751852i | \(0.270839\pi\) | |||||||
\(318\) | −27.3074 | −1.53132 | ||||||||
\(319\) | 31.3576 | 1.75569 | ||||||||
\(320\) | −20.1872 | −1.12850 | ||||||||
\(321\) | −44.4421 | −2.48052 | ||||||||
\(322\) | −1.69748 | −0.0945968 | ||||||||
\(323\) | −7.48585 | −0.416524 | ||||||||
\(324\) | 3.11616 | 0.173120 | ||||||||
\(325\) | 0.453139 | 0.0251356 | ||||||||
\(326\) | 18.5336 | 1.02648 | ||||||||
\(327\) | −35.8317 | −1.98150 | ||||||||
\(328\) | −16.2456 | −0.897014 | ||||||||
\(329\) | 11.2155 | 0.618328 | ||||||||
\(330\) | 57.7456 | 3.17879 | ||||||||
\(331\) | −6.06252 | −0.333227 | −0.166613 | − | 0.986022i | \(-0.553283\pi\) | ||||
−0.166613 | + | 0.986022i | \(0.553283\pi\) | |||||||
\(332\) | 1.82546 | 0.100185 | ||||||||
\(333\) | 47.6228 | 2.60971 | ||||||||
\(334\) | −15.2569 | −0.834818 | ||||||||
\(335\) | 36.5889 | 1.99906 | ||||||||
\(336\) | −19.8706 | −1.08403 | ||||||||
\(337\) | −27.7433 | −1.51127 | −0.755637 | − | 0.654990i | \(-0.772673\pi\) | ||||
−0.755637 | + | 0.654990i | \(0.772673\pi\) | |||||||
\(338\) | −18.8583 | −1.02575 | ||||||||
\(339\) | −30.0590 | −1.63258 | ||||||||
\(340\) | 0.612300 | 0.0332066 | ||||||||
\(341\) | 4.62416 | 0.250412 | ||||||||
\(342\) | 43.0378 | 2.32722 | ||||||||
\(343\) | 17.1933 | 0.928353 | ||||||||
\(344\) | −3.05006 | −0.164448 | ||||||||
\(345\) | 7.12573 | 0.383636 | ||||||||
\(346\) | 0.544017 | 0.0292466 | ||||||||
\(347\) | 31.7210 | 1.70287 | 0.851436 | − | 0.524458i | \(-0.175732\pi\) | ||||
0.851436 | + | 0.524458i | \(0.175732\pi\) | |||||||
\(348\) | −2.66096 | −0.142642 | ||||||||
\(349\) | −2.75301 | −0.147365 | −0.0736827 | − | 0.997282i | \(-0.523475\pi\) | ||||
−0.0736827 | + | 0.997282i | \(0.523475\pi\) | |||||||
\(350\) | −4.80008 | −0.256575 | ||||||||
\(351\) | −3.00904 | −0.160611 | ||||||||
\(352\) | −2.98033 | −0.158852 | ||||||||
\(353\) | 6.68412 | 0.355760 | 0.177880 | − | 0.984052i | \(-0.443076\pi\) | ||||
0.177880 | + | 0.984052i | \(0.443076\pi\) | |||||||
\(354\) | 37.7910 | 2.00857 | ||||||||
\(355\) | 19.8642 | 1.05428 | ||||||||
\(356\) | 1.92520 | 0.102035 | ||||||||
\(357\) | −9.11881 | −0.482618 | ||||||||
\(358\) | −3.44351 | −0.181995 | ||||||||
\(359\) | −5.53478 | −0.292114 | −0.146057 | − | 0.989276i | \(-0.546658\pi\) | ||||
−0.146057 | + | 0.989276i | \(0.546658\pi\) | |||||||
\(360\) | 56.5977 | 2.98296 | ||||||||
\(361\) | −4.06173 | −0.213775 | ||||||||
\(362\) | 30.5963 | 1.60811 | ||||||||
\(363\) | −30.3207 | −1.59142 | ||||||||
\(364\) | −0.0334717 | −0.00175439 | ||||||||
\(365\) | −22.1574 | −1.15977 | ||||||||
\(366\) | −31.5427 | −1.64876 | ||||||||
\(367\) | 15.8704 | 0.828426 | 0.414213 | − | 0.910180i | \(-0.364057\pi\) | ||||
0.414213 | + | 0.910180i | \(0.364057\pi\) | |||||||
\(368\) | −3.41338 | −0.177935 | ||||||||
\(369\) | 45.3803 | 2.36240 | ||||||||
\(370\) | −24.4418 | −1.27067 | ||||||||
\(371\) | −8.29442 | −0.430625 | ||||||||
\(372\) | −0.392399 | −0.0203450 | ||||||||
\(373\) | −30.3655 | −1.57227 | −0.786134 | − | 0.618057i | \(-0.787920\pi\) | ||||
−0.786134 | + | 0.618057i | \(0.787920\pi\) | |||||||
\(374\) | −12.6941 | −0.656395 | ||||||||
\(375\) | −23.9034 | −1.23437 | ||||||||
\(376\) | 21.3011 | 1.09852 | ||||||||
\(377\) | 1.37934 | 0.0710396 | ||||||||
\(378\) | 31.8746 | 1.63945 | ||||||||
\(379\) | −27.3973 | −1.40731 | −0.703653 | − | 0.710544i | \(-0.748449\pi\) | ||||
−0.703653 | + | 0.710544i | \(0.748449\pi\) | |||||||
\(380\) | −1.22187 | −0.0626804 | ||||||||
\(381\) | 27.1394 | 1.39039 | ||||||||
\(382\) | −19.8409 | −1.01515 | ||||||||
\(383\) | 12.8193 | 0.655037 | 0.327518 | − | 0.944845i | \(-0.393788\pi\) | ||||
0.327518 | + | 0.944845i | \(0.393788\pi\) | |||||||
\(384\) | −39.8339 | −2.03276 | ||||||||
\(385\) | 17.5398 | 0.893911 | ||||||||
\(386\) | 4.41411 | 0.224672 | ||||||||
\(387\) | 8.52000 | 0.433096 | ||||||||
\(388\) | −2.18133 | −0.110740 | ||||||||
\(389\) | 31.8869 | 1.61673 | 0.808366 | − | 0.588680i | \(-0.200352\pi\) | ||||
0.808366 | + | 0.588680i | \(0.200352\pi\) | |||||||
\(390\) | 2.54008 | 0.128622 | ||||||||
\(391\) | −1.56643 | −0.0792179 | ||||||||
\(392\) | 13.4770 | 0.680692 | ||||||||
\(393\) | 52.9513 | 2.67104 | ||||||||
\(394\) | 15.6030 | 0.786066 | ||||||||
\(395\) | −20.1695 | −1.01484 | ||||||||
\(396\) | 4.03706 | 0.202870 | ||||||||
\(397\) | −5.27927 | −0.264959 | −0.132480 | − | 0.991186i | \(-0.542294\pi\) | ||||
−0.132480 | + | 0.991186i | \(0.542294\pi\) | |||||||
\(398\) | 33.8195 | 1.69522 | ||||||||
\(399\) | 18.1969 | 0.910984 | ||||||||
\(400\) | −9.65227 | −0.482613 | ||||||||
\(401\) | 16.6475 | 0.831337 | 0.415668 | − | 0.909516i | \(-0.363548\pi\) | ||||
0.415668 | + | 0.909516i | \(0.363548\pi\) | |||||||
\(402\) | 64.3696 | 3.21047 | ||||||||
\(403\) | 0.203405 | 0.0101323 | ||||||||
\(404\) | 0.846204 | 0.0421002 | ||||||||
\(405\) | −71.8283 | −3.56918 | ||||||||
\(406\) | −14.6113 | −0.725147 | ||||||||
\(407\) | 28.0301 | 1.38940 | ||||||||
\(408\) | −17.3190 | −0.857417 | ||||||||
\(409\) | −35.3883 | −1.74984 | −0.874920 | − | 0.484267i | \(-0.839086\pi\) | ||||
−0.874920 | + | 0.484267i | \(0.839086\pi\) | |||||||
\(410\) | −23.2909 | −1.15025 | ||||||||
\(411\) | −48.7597 | −2.40514 | ||||||||
\(412\) | 2.16467 | 0.106646 | ||||||||
\(413\) | 11.4787 | 0.564832 | ||||||||
\(414\) | 9.00575 | 0.442609 | ||||||||
\(415\) | −42.0772 | −2.06549 | ||||||||
\(416\) | −0.131097 | −0.00642755 | ||||||||
\(417\) | 39.0251 | 1.91107 | ||||||||
\(418\) | 25.3315 | 1.23900 | ||||||||
\(419\) | −2.99594 | −0.146361 | −0.0731805 | − | 0.997319i | \(-0.523315\pi\) | ||||
−0.0731805 | + | 0.997319i | \(0.523315\pi\) | |||||||
\(420\) | −1.48840 | −0.0726265 | ||||||||
\(421\) | −22.9087 | −1.11650 | −0.558252 | − | 0.829672i | \(-0.688528\pi\) | ||||
−0.558252 | + | 0.829672i | \(0.688528\pi\) | |||||||
\(422\) | −15.8554 | −0.771828 | ||||||||
\(423\) | −59.5021 | −2.89309 | ||||||||
\(424\) | −15.7532 | −0.765045 | ||||||||
\(425\) | −4.42951 | −0.214863 | ||||||||
\(426\) | 34.9465 | 1.69316 | ||||||||
\(427\) | −9.58087 | −0.463651 | ||||||||
\(428\) | 1.59463 | 0.0770792 | ||||||||
\(429\) | −2.91299 | −0.140641 | ||||||||
\(430\) | −4.37278 | −0.210874 | ||||||||
\(431\) | 34.0116 | 1.63828 | 0.819141 | − | 0.573592i | \(-0.194451\pi\) | ||||
0.819141 | + | 0.573592i | \(0.194451\pi\) | |||||||
\(432\) | 64.0953 | 3.08378 | ||||||||
\(433\) | 7.85344 | 0.377412 | 0.188706 | − | 0.982034i | \(-0.439571\pi\) | ||||
0.188706 | + | 0.982034i | \(0.439571\pi\) | |||||||
\(434\) | −2.15466 | −0.103427 | ||||||||
\(435\) | 61.3357 | 2.94082 | ||||||||
\(436\) | 1.28568 | 0.0615728 | ||||||||
\(437\) | 3.12587 | 0.149531 | ||||||||
\(438\) | −38.9809 | −1.86258 | ||||||||
\(439\) | −8.49965 | −0.405666 | −0.202833 | − | 0.979213i | \(-0.565015\pi\) | ||||
−0.202833 | + | 0.979213i | \(0.565015\pi\) | |||||||
\(440\) | 33.3126 | 1.58812 | ||||||||
\(441\) | −37.6465 | −1.79269 | ||||||||
\(442\) | −0.558379 | −0.0265594 | ||||||||
\(443\) | 0.532143 | 0.0252829 | 0.0126414 | − | 0.999920i | \(-0.495976\pi\) | ||||
0.0126414 | + | 0.999920i | \(0.495976\pi\) | |||||||
\(444\) | −2.37859 | −0.112883 | ||||||||
\(445\) | −44.3762 | −2.10363 | ||||||||
\(446\) | 10.2626 | 0.485949 | ||||||||
\(447\) | −26.8978 | −1.27222 | ||||||||
\(448\) | −10.7874 | −0.509655 | ||||||||
\(449\) | −11.0838 | −0.523077 | −0.261538 | − | 0.965193i | \(-0.584230\pi\) | ||||
−0.261538 | + | 0.965193i | \(0.584230\pi\) | |||||||
\(450\) | 25.4662 | 1.20049 | ||||||||
\(451\) | 26.7103 | 1.25774 | ||||||||
\(452\) | 1.07855 | 0.0507306 | ||||||||
\(453\) | 45.0581 | 2.11702 | ||||||||
\(454\) | 22.7116 | 1.06591 | ||||||||
\(455\) | 0.771530 | 0.0361699 | ||||||||
\(456\) | 34.5606 | 1.61845 | ||||||||
\(457\) | 32.6997 | 1.52963 | 0.764815 | − | 0.644250i | \(-0.222831\pi\) | ||||
0.764815 | + | 0.644250i | \(0.222831\pi\) | |||||||
\(458\) | 32.2911 | 1.50886 | ||||||||
\(459\) | 29.4139 | 1.37292 | ||||||||
\(460\) | −0.255678 | −0.0119211 | ||||||||
\(461\) | −10.3452 | −0.481824 | −0.240912 | − | 0.970547i | \(-0.577446\pi\) | ||||
−0.240912 | + | 0.970547i | \(0.577446\pi\) | |||||||
\(462\) | 30.8572 | 1.43561 | ||||||||
\(463\) | 5.60035 | 0.260271 | 0.130135 | − | 0.991496i | \(-0.458459\pi\) | ||||
0.130135 | + | 0.991496i | \(0.458459\pi\) | |||||||
\(464\) | −29.3812 | −1.36399 | ||||||||
\(465\) | 9.04489 | 0.419447 | ||||||||
\(466\) | −2.97817 | −0.137961 | ||||||||
\(467\) | 16.9894 | 0.786174 | 0.393087 | − | 0.919501i | \(-0.371407\pi\) | ||||
0.393087 | + | 0.919501i | \(0.371407\pi\) | |||||||
\(468\) | 0.177580 | 0.00820862 | ||||||||
\(469\) | 19.5518 | 0.902819 | ||||||||
\(470\) | 30.5387 | 1.40865 | ||||||||
\(471\) | 47.6654 | 2.19631 | ||||||||
\(472\) | 21.8011 | 1.00348 | ||||||||
\(473\) | 5.01476 | 0.230579 | ||||||||
\(474\) | −35.4836 | −1.62981 | ||||||||
\(475\) | 8.83924 | 0.405572 | ||||||||
\(476\) | 0.327192 | 0.0149968 | ||||||||
\(477\) | 44.0049 | 2.01485 | ||||||||
\(478\) | 6.11042 | 0.279484 | ||||||||
\(479\) | −16.0046 | −0.731269 | −0.365634 | − | 0.930759i | \(-0.619148\pi\) | ||||
−0.365634 | + | 0.930759i | \(0.619148\pi\) | |||||||
\(480\) | −5.82954 | −0.266081 | ||||||||
\(481\) | 1.23297 | 0.0562187 | ||||||||
\(482\) | −11.9651 | −0.544994 | ||||||||
\(483\) | 3.80774 | 0.173258 | ||||||||
\(484\) | 1.08794 | 0.0494516 | ||||||||
\(485\) | 50.2802 | 2.28311 | ||||||||
\(486\) | −60.0743 | −2.72503 | ||||||||
\(487\) | 9.76453 | 0.442473 | 0.221237 | − | 0.975220i | \(-0.428991\pi\) | ||||
0.221237 | + | 0.975220i | \(0.428991\pi\) | |||||||
\(488\) | −18.1965 | −0.823719 | ||||||||
\(489\) | −41.5742 | −1.88005 | ||||||||
\(490\) | 19.3216 | 0.872861 | ||||||||
\(491\) | −8.02281 | −0.362065 | −0.181032 | − | 0.983477i | \(-0.557944\pi\) | ||||
−0.181032 | + | 0.983477i | \(0.557944\pi\) | |||||||
\(492\) | −2.26659 | −0.102186 | ||||||||
\(493\) | −13.4833 | −0.607257 | ||||||||
\(494\) | 1.11427 | 0.0501332 | ||||||||
\(495\) | −93.0551 | −4.18252 | ||||||||
\(496\) | −4.33271 | −0.194544 | ||||||||
\(497\) | 10.6147 | 0.476136 | ||||||||
\(498\) | −74.0251 | −3.31714 | ||||||||
\(499\) | 11.1118 | 0.497432 | 0.248716 | − | 0.968577i | \(-0.419991\pi\) | ||||
0.248716 | + | 0.968577i | \(0.419991\pi\) | |||||||
\(500\) | 0.857678 | 0.0383565 | ||||||||
\(501\) | 34.2238 | 1.52900 | ||||||||
\(502\) | 18.3200 | 0.817663 | ||||||||
\(503\) | −13.3780 | −0.596495 | −0.298248 | − | 0.954489i | \(-0.596402\pi\) | ||||
−0.298248 | + | 0.954489i | \(0.596402\pi\) | |||||||
\(504\) | 30.2438 | 1.34717 | ||||||||
\(505\) | −19.5052 | −0.867970 | ||||||||
\(506\) | 5.30067 | 0.235643 | ||||||||
\(507\) | 42.3023 | 1.87871 | ||||||||
\(508\) | −0.973787 | −0.0432048 | ||||||||
\(509\) | 34.4226 | 1.52576 | 0.762878 | − | 0.646542i | \(-0.223786\pi\) | ||||
0.762878 | + | 0.646542i | \(0.223786\pi\) | |||||||
\(510\) | −24.8297 | −1.09948 | ||||||||
\(511\) | −11.8402 | −0.523778 | ||||||||
\(512\) | −20.3330 | −0.898601 | ||||||||
\(513\) | −58.6964 | −2.59151 | ||||||||
\(514\) | −23.8393 | −1.05151 | ||||||||
\(515\) | −49.8962 | −2.19869 | ||||||||
\(516\) | −0.425545 | −0.0187336 | ||||||||
\(517\) | −35.0222 | −1.54027 | ||||||||
\(518\) | −13.0608 | −0.573860 | ||||||||
\(519\) | −1.22033 | −0.0535663 | ||||||||
\(520\) | 1.46534 | 0.0642592 | ||||||||
\(521\) | 29.0308 | 1.27186 | 0.635932 | − | 0.771745i | \(-0.280616\pi\) | ||||
0.635932 | + | 0.771745i | \(0.280616\pi\) | |||||||
\(522\) | 77.5184 | 3.39289 | ||||||||
\(523\) | −12.0058 | −0.524977 | −0.262489 | − | 0.964935i | \(-0.584543\pi\) | ||||
−0.262489 | + | 0.964935i | \(0.584543\pi\) | |||||||
\(524\) | −1.89995 | −0.0829995 | ||||||||
\(525\) | 10.7674 | 0.469928 | ||||||||
\(526\) | −6.40987 | −0.279484 | ||||||||
\(527\) | −1.98832 | −0.0866125 | ||||||||
\(528\) | 62.0494 | 2.70035 | ||||||||
\(529\) | −22.3459 | −0.971561 | ||||||||
\(530\) | −22.5850 | −0.981028 | ||||||||
\(531\) | −60.8989 | −2.64279 | ||||||||
\(532\) | −0.652922 | −0.0283078 | ||||||||
\(533\) | 1.17491 | 0.0508912 | ||||||||
\(534\) | −78.0697 | −3.37841 | ||||||||
\(535\) | −36.7565 | −1.58912 | ||||||||
\(536\) | 37.1340 | 1.60394 | ||||||||
\(537\) | 7.72439 | 0.333332 | ||||||||
\(538\) | −17.6458 | −0.760765 | ||||||||
\(539\) | −22.1582 | −0.954423 | ||||||||
\(540\) | 4.80103 | 0.206603 | ||||||||
\(541\) | 6.60138 | 0.283816 | 0.141908 | − | 0.989880i | \(-0.454676\pi\) | ||||
0.141908 | + | 0.989880i | \(0.454676\pi\) | |||||||
\(542\) | −22.0166 | −0.945695 | ||||||||
\(543\) | −68.6328 | −2.94532 | ||||||||
\(544\) | 1.28149 | 0.0549436 | ||||||||
\(545\) | −29.6352 | −1.26943 | ||||||||
\(546\) | 1.35733 | 0.0580883 | ||||||||
\(547\) | 22.0708 | 0.943677 | 0.471839 | − | 0.881685i | \(-0.343591\pi\) | ||||
0.471839 | + | 0.881685i | \(0.343591\pi\) | |||||||
\(548\) | 1.74955 | 0.0747370 | ||||||||
\(549\) | 50.8300 | 2.16937 | ||||||||
\(550\) | 14.9891 | 0.639136 | ||||||||
\(551\) | 26.9064 | 1.14625 | ||||||||
\(552\) | 7.23188 | 0.307809 | ||||||||
\(553\) | −10.7779 | −0.458322 | ||||||||
\(554\) | 35.3299 | 1.50102 | ||||||||
\(555\) | 54.8271 | 2.32728 | ||||||||
\(556\) | −1.40026 | −0.0593842 | ||||||||
\(557\) | −10.6720 | −0.452189 | −0.226094 | − | 0.974105i | \(-0.572596\pi\) | ||||
−0.226094 | + | 0.974105i | \(0.572596\pi\) | |||||||
\(558\) | 11.4313 | 0.483924 | ||||||||
\(559\) | 0.220586 | 0.00932980 | ||||||||
\(560\) | −16.4343 | −0.694476 | ||||||||
\(561\) | 28.4750 | 1.20222 | ||||||||
\(562\) | −35.8608 | −1.51269 | ||||||||
\(563\) | −15.9951 | −0.674114 | −0.337057 | − | 0.941484i | \(-0.609432\pi\) | ||||
−0.337057 | + | 0.941484i | \(0.609432\pi\) | |||||||
\(564\) | 2.97193 | 0.125141 | ||||||||
\(565\) | −24.8608 | −1.04590 | ||||||||
\(566\) | 2.39809 | 0.100799 | ||||||||
\(567\) | −38.3825 | −1.61192 | ||||||||
\(568\) | 20.1601 | 0.845901 | ||||||||
\(569\) | 30.3674 | 1.27307 | 0.636535 | − | 0.771248i | \(-0.280367\pi\) | ||||
0.636535 | + | 0.771248i | \(0.280367\pi\) | |||||||
\(570\) | 49.5485 | 2.07536 | ||||||||
\(571\) | −25.1730 | −1.05346 | −0.526729 | − | 0.850033i | \(-0.676582\pi\) | ||||
−0.526729 | + | 0.850033i | \(0.676582\pi\) | |||||||
\(572\) | 0.104521 | 0.00437025 | ||||||||
\(573\) | 44.5067 | 1.85929 | ||||||||
\(574\) | −12.4458 | −0.519479 | ||||||||
\(575\) | 1.84963 | 0.0771349 | ||||||||
\(576\) | 57.2309 | 2.38462 | ||||||||
\(577\) | 16.9543 | 0.705817 | 0.352909 | − | 0.935658i | \(-0.385193\pi\) | ||||
0.352909 | + | 0.935658i | \(0.385193\pi\) | |||||||
\(578\) | −19.2772 | −0.801828 | ||||||||
\(579\) | −9.90161 | −0.411497 | ||||||||
\(580\) | −2.20079 | −0.0913827 | ||||||||
\(581\) | −22.4846 | −0.932818 | ||||||||
\(582\) | 88.4565 | 3.66664 | ||||||||
\(583\) | 25.9007 | 1.07270 | ||||||||
\(584\) | −22.4875 | −0.930540 | ||||||||
\(585\) | −4.09325 | −0.169235 | ||||||||
\(586\) | −1.79418 | −0.0741168 | ||||||||
\(587\) | 0.234134 | 0.00966375 | 0.00483187 | − | 0.999988i | \(-0.498462\pi\) | ||||
0.00483187 | + | 0.999988i | \(0.498462\pi\) | |||||||
\(588\) | 1.88031 | 0.0775429 | ||||||||
\(589\) | 3.96776 | 0.163489 | ||||||||
\(590\) | 31.2556 | 1.28677 | ||||||||
\(591\) | −35.0002 | −1.43971 | ||||||||
\(592\) | −26.2634 | −1.07942 | ||||||||
\(593\) | 25.8018 | 1.05955 | 0.529777 | − | 0.848137i | \(-0.322276\pi\) | ||||
0.529777 | + | 0.848137i | \(0.322276\pi\) | |||||||
\(594\) | −99.5340 | −4.08393 | ||||||||
\(595\) | −7.54184 | −0.309185 | ||||||||
\(596\) | 0.965119 | 0.0395328 | ||||||||
\(597\) | −75.8630 | −3.10486 | ||||||||
\(598\) | 0.233163 | 0.00953472 | ||||||||
\(599\) | −17.1524 | −0.700829 | −0.350415 | − | 0.936595i | \(-0.613959\pi\) | ||||
−0.350415 | + | 0.936595i | \(0.613959\pi\) | |||||||
\(600\) | 20.4501 | 0.834872 | ||||||||
\(601\) | −27.0121 | −1.10185 | −0.550923 | − | 0.834556i | \(-0.685724\pi\) | ||||
−0.550923 | + | 0.834556i | \(0.685724\pi\) | |||||||
\(602\) | −2.33666 | −0.0952352 | ||||||||
\(603\) | −103.730 | −4.22419 | ||||||||
\(604\) | −1.61673 | −0.0657838 | ||||||||
\(605\) | −25.0771 | −1.01953 | ||||||||
\(606\) | −34.3149 | −1.39395 | ||||||||
\(607\) | −18.1553 | −0.736901 | −0.368451 | − | 0.929647i | \(-0.620112\pi\) | ||||
−0.368451 | + | 0.929647i | \(0.620112\pi\) | |||||||
\(608\) | −2.55727 | −0.103711 | ||||||||
\(609\) | 32.7757 | 1.32814 | ||||||||
\(610\) | −26.0879 | −1.05627 | ||||||||
\(611\) | −1.54053 | −0.0623233 | ||||||||
\(612\) | −1.73587 | −0.0701685 | ||||||||
\(613\) | −16.5866 | −0.669926 | −0.334963 | − | 0.942231i | \(-0.608724\pi\) | ||||
−0.334963 | + | 0.942231i | \(0.608724\pi\) | |||||||
\(614\) | 3.80003 | 0.153357 | ||||||||
\(615\) | 52.2454 | 2.10674 | ||||||||
\(616\) | 17.8011 | 0.717227 | ||||||||
\(617\) | −37.5797 | −1.51290 | −0.756452 | − | 0.654049i | \(-0.773069\pi\) | ||||
−0.756452 | + | 0.654049i | \(0.773069\pi\) | |||||||
\(618\) | −87.7809 | −3.53107 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | −0.324540 | −0.0130338 | ||||||||
\(621\) | −12.2824 | −0.492874 | ||||||||
\(622\) | 31.1742 | 1.24997 | ||||||||
\(623\) | −23.7131 | −0.950045 | ||||||||
\(624\) | 2.72939 | 0.109263 | ||||||||
\(625\) | −31.2046 | −1.24819 | ||||||||
\(626\) | −37.2309 | −1.48805 | ||||||||
\(627\) | −56.8229 | −2.26929 | ||||||||
\(628\) | −1.71028 | −0.0682477 | ||||||||
\(629\) | −12.0525 | −0.480565 | ||||||||
\(630\) | 43.3597 | 1.72749 | ||||||||
\(631\) | −17.9210 | −0.713423 | −0.356711 | − | 0.934215i | \(-0.616102\pi\) | ||||
−0.356711 | + | 0.934215i | \(0.616102\pi\) | |||||||
\(632\) | −20.4700 | −0.814252 | ||||||||
\(633\) | 35.5664 | 1.41364 | ||||||||
\(634\) | 34.1614 | 1.35672 | ||||||||
\(635\) | 22.4460 | 0.890743 | ||||||||
\(636\) | −2.19790 | −0.0871522 | ||||||||
\(637\) | −0.974683 | −0.0386183 | ||||||||
\(638\) | 45.6263 | 1.80636 | ||||||||
\(639\) | −56.3151 | −2.22779 | ||||||||
\(640\) | −32.9452 | −1.30227 | ||||||||
\(641\) | 20.3082 | 0.802124 | 0.401062 | − | 0.916051i | \(-0.368641\pi\) | ||||
0.401062 | + | 0.916051i | \(0.368641\pi\) | |||||||
\(642\) | −64.6646 | −2.55211 | ||||||||
\(643\) | −9.94038 | −0.392010 | −0.196005 | − | 0.980603i | \(-0.562797\pi\) | ||||
−0.196005 | + | 0.980603i | \(0.562797\pi\) | |||||||
\(644\) | −0.136625 | −0.00538380 | ||||||||
\(645\) | 9.80890 | 0.386225 | ||||||||
\(646\) | −10.8921 | −0.428545 | ||||||||
\(647\) | −22.4111 | −0.881070 | −0.440535 | − | 0.897735i | \(-0.645211\pi\) | ||||
−0.440535 | + | 0.897735i | \(0.645211\pi\) | |||||||
\(648\) | −72.8984 | −2.86372 | ||||||||
\(649\) | −35.8443 | −1.40701 | ||||||||
\(650\) | 0.659330 | 0.0258611 | ||||||||
\(651\) | 4.83328 | 0.189431 | ||||||||
\(652\) | 1.49172 | 0.0584203 | ||||||||
\(653\) | 34.5540 | 1.35220 | 0.676102 | − | 0.736808i | \(-0.263668\pi\) | ||||
0.676102 | + | 0.736808i | \(0.263668\pi\) | |||||||
\(654\) | −52.1362 | −2.03869 | ||||||||
\(655\) | 43.7942 | 1.71118 | ||||||||
\(656\) | −25.0267 | −0.977130 | ||||||||
\(657\) | 62.8164 | 2.45070 | ||||||||
\(658\) | 16.3188 | 0.636174 | ||||||||
\(659\) | −20.8525 | −0.812297 | −0.406148 | − | 0.913807i | \(-0.633128\pi\) | ||||
−0.406148 | + | 0.913807i | \(0.633128\pi\) | |||||||
\(660\) | 4.64779 | 0.180915 | ||||||||
\(661\) | 30.6607 | 1.19256 | 0.596281 | − | 0.802776i | \(-0.296644\pi\) | ||||
0.596281 | + | 0.802776i | \(0.296644\pi\) | |||||||
\(662\) | −8.82115 | −0.342844 | ||||||||
\(663\) | 1.25254 | 0.0486447 | ||||||||
\(664\) | −42.7040 | −1.65724 | ||||||||
\(665\) | 15.0500 | 0.583614 | ||||||||
\(666\) | 69.2925 | 2.68503 | ||||||||
\(667\) | 5.63022 | 0.218003 | ||||||||
\(668\) | −1.22798 | −0.0475121 | ||||||||
\(669\) | −23.0208 | −0.890036 | ||||||||
\(670\) | 53.2379 | 2.05676 | ||||||||
\(671\) | 29.9179 | 1.15497 | ||||||||
\(672\) | −3.11510 | −0.120168 | ||||||||
\(673\) | 51.4652 | 1.98384 | 0.991918 | − | 0.126879i | \(-0.0404959\pi\) | ||||
0.991918 | + | 0.126879i | \(0.0404959\pi\) | |||||||
\(674\) | −40.3673 | −1.55489 | ||||||||
\(675\) | −34.7317 | −1.33682 | ||||||||
\(676\) | −1.51785 | −0.0583788 | ||||||||
\(677\) | 43.6169 | 1.67633 | 0.838166 | − | 0.545415i | \(-0.183628\pi\) | ||||
0.838166 | + | 0.545415i | \(0.183628\pi\) | |||||||
\(678\) | −43.7368 | −1.67970 | ||||||||
\(679\) | 26.8680 | 1.03110 | ||||||||
\(680\) | −14.3239 | −0.549297 | ||||||||
\(681\) | −50.9461 | −1.95226 | ||||||||
\(682\) | 6.72829 | 0.257640 | ||||||||
\(683\) | 29.0416 | 1.11125 | 0.555624 | − | 0.831434i | \(-0.312480\pi\) | ||||
0.555624 | + | 0.831434i | \(0.312480\pi\) | |||||||
\(684\) | 3.46399 | 0.132449 | ||||||||
\(685\) | −40.3275 | −1.54083 | ||||||||
\(686\) | 25.0168 | 0.955147 | ||||||||
\(687\) | −72.4344 | −2.76354 | ||||||||
\(688\) | −4.69868 | −0.179136 | ||||||||
\(689\) | 1.13931 | 0.0434041 | ||||||||
\(690\) | 10.3681 | 0.394708 | ||||||||
\(691\) | −31.5302 | −1.19947 | −0.599733 | − | 0.800200i | \(-0.704726\pi\) | ||||
−0.599733 | + | 0.800200i | \(0.704726\pi\) | |||||||
\(692\) | 0.0437865 | 0.00166451 | ||||||||
\(693\) | −49.7254 | −1.88891 | ||||||||
\(694\) | 46.1550 | 1.75202 | ||||||||
\(695\) | 32.2763 | 1.22431 | ||||||||
\(696\) | 62.2495 | 2.35956 | ||||||||
\(697\) | −11.4850 | −0.435025 | ||||||||
\(698\) | −4.00572 | −0.151619 | ||||||||
\(699\) | 6.68054 | 0.252681 | ||||||||
\(700\) | −0.386346 | −0.0146025 | ||||||||
\(701\) | 11.1053 | 0.419440 | 0.209720 | − | 0.977761i | \(-0.432745\pi\) | ||||
0.209720 | + | 0.977761i | \(0.432745\pi\) | |||||||
\(702\) | −4.37824 | −0.165246 | ||||||||
\(703\) | 24.0512 | 0.907109 | ||||||||
\(704\) | 33.6854 | 1.26956 | ||||||||
\(705\) | −68.5036 | −2.57999 | ||||||||
\(706\) | 9.72559 | 0.366028 | ||||||||
\(707\) | −10.4229 | −0.391994 | ||||||||
\(708\) | 3.04169 | 0.114314 | ||||||||
\(709\) | 29.2939 | 1.10016 | 0.550079 | − | 0.835113i | \(-0.314598\pi\) | ||||
0.550079 | + | 0.835113i | \(0.314598\pi\) | |||||||
\(710\) | 28.9030 | 1.08471 | ||||||||
\(711\) | 57.1806 | 2.14444 | ||||||||
\(712\) | −45.0373 | −1.68784 | ||||||||
\(713\) | 0.830262 | 0.0310936 | ||||||||
\(714\) | −13.2681 | −0.496547 | ||||||||
\(715\) | −2.40923 | −0.0901002 | ||||||||
\(716\) | −0.277159 | −0.0103579 | ||||||||
\(717\) | −13.7067 | −0.511887 | ||||||||
\(718\) | −8.05326 | −0.300545 | ||||||||
\(719\) | 20.8433 | 0.777324 | 0.388662 | − | 0.921380i | \(-0.372937\pi\) | ||||
0.388662 | + | 0.921380i | \(0.372937\pi\) | |||||||
\(720\) | 87.1900 | 3.24938 | ||||||||
\(721\) | −26.6628 | −0.992975 | ||||||||
\(722\) | −5.90994 | −0.219945 | ||||||||
\(723\) | 26.8397 | 0.998180 | ||||||||
\(724\) | 2.46261 | 0.0915223 | ||||||||
\(725\) | 15.9210 | 0.591290 | ||||||||
\(726\) | −44.1174 | −1.63735 | ||||||||
\(727\) | 46.8273 | 1.73673 | 0.868364 | − | 0.495927i | \(-0.165172\pi\) | ||||
0.868364 | + | 0.495927i | \(0.165172\pi\) | |||||||
\(728\) | 0.783024 | 0.0290208 | ||||||||
\(729\) | 54.9314 | 2.03450 | ||||||||
\(730\) | −32.2397 | −1.19325 | ||||||||
\(731\) | −2.15627 | −0.0797524 | ||||||||
\(732\) | −2.53879 | −0.0938362 | ||||||||
\(733\) | −21.0505 | −0.777518 | −0.388759 | − | 0.921339i | \(-0.627096\pi\) | ||||
−0.388759 | + | 0.921339i | \(0.627096\pi\) | |||||||
\(734\) | 23.0918 | 0.852335 | ||||||||
\(735\) | −43.3417 | −1.59868 | ||||||||
\(736\) | −0.535114 | −0.0197246 | ||||||||
\(737\) | −61.0538 | −2.24895 | ||||||||
\(738\) | 66.0297 | 2.43059 | ||||||||
\(739\) | 23.3449 | 0.858758 | 0.429379 | − | 0.903124i | \(-0.358733\pi\) | ||||
0.429379 | + | 0.903124i | \(0.358733\pi\) | |||||||
\(740\) | −1.96725 | −0.0723176 | ||||||||
\(741\) | −2.49949 | −0.0918210 | ||||||||
\(742\) | −12.0686 | −0.443053 | ||||||||
\(743\) | −26.2395 | −0.962633 | −0.481316 | − | 0.876547i | \(-0.659841\pi\) | ||||
−0.481316 | + | 0.876547i | \(0.659841\pi\) | |||||||
\(744\) | 9.17964 | 0.336542 | ||||||||
\(745\) | −22.2462 | −0.815038 | ||||||||
\(746\) | −44.1827 | −1.61765 | ||||||||
\(747\) | 119.289 | 4.36456 | ||||||||
\(748\) | −1.02171 | −0.0373575 | ||||||||
\(749\) | −19.6414 | −0.717681 | ||||||||
\(750\) | −34.7802 | −1.26999 | ||||||||
\(751\) | 24.3104 | 0.887100 | 0.443550 | − | 0.896250i | \(-0.353719\pi\) | ||||
0.443550 | + | 0.896250i | \(0.353719\pi\) | |||||||
\(752\) | 32.8148 | 1.19663 | ||||||||
\(753\) | −41.0950 | −1.49759 | ||||||||
\(754\) | 2.00698 | 0.0730899 | ||||||||
\(755\) | 37.2660 | 1.35625 | ||||||||
\(756\) | 2.56550 | 0.0933064 | ||||||||
\(757\) | −27.6139 | −1.00364 | −0.501821 | − | 0.864971i | \(-0.667337\pi\) | ||||
−0.501821 | + | 0.864971i | \(0.667337\pi\) | |||||||
\(758\) | −39.8639 | −1.44792 | ||||||||
\(759\) | −11.8903 | −0.431591 | ||||||||
\(760\) | 28.5839 | 1.03685 | ||||||||
\(761\) | 34.0614 | 1.23472 | 0.617362 | − | 0.786680i | \(-0.288202\pi\) | ||||
0.617362 | + | 0.786680i | \(0.288202\pi\) | |||||||
\(762\) | 39.4886 | 1.43052 | ||||||||
\(763\) | −15.8360 | −0.573302 | ||||||||
\(764\) | −1.59694 | −0.0577754 | ||||||||
\(765\) | 40.0123 | 1.44665 | ||||||||
\(766\) | 18.6525 | 0.673942 | ||||||||
\(767\) | −1.57670 | −0.0569312 | ||||||||
\(768\) | −9.14287 | −0.329915 | ||||||||
\(769\) | 34.9720 | 1.26112 | 0.630562 | − | 0.776139i | \(-0.282824\pi\) | ||||
0.630562 | + | 0.776139i | \(0.282824\pi\) | |||||||
\(770\) | 25.5209 | 0.919711 | ||||||||
\(771\) | 53.4757 | 1.92588 | ||||||||
\(772\) | 0.355280 | 0.0127868 | ||||||||
\(773\) | −28.9546 | −1.04142 | −0.520712 | − | 0.853732i | \(-0.674334\pi\) | ||||
−0.520712 | + | 0.853732i | \(0.674334\pi\) | |||||||
\(774\) | 12.3968 | 0.445595 | ||||||||
\(775\) | 2.34779 | 0.0843351 | ||||||||
\(776\) | 51.0293 | 1.83185 | ||||||||
\(777\) | 29.2977 | 1.05105 | ||||||||
\(778\) | 46.3964 | 1.66339 | ||||||||
\(779\) | 22.9187 | 0.821147 | ||||||||
\(780\) | 0.204444 | 0.00732027 | ||||||||
\(781\) | −33.1463 | −1.18607 | ||||||||
\(782\) | −2.27920 | −0.0815042 | ||||||||
\(783\) | −105.722 | −3.77820 | ||||||||
\(784\) | 20.7616 | 0.741487 | ||||||||
\(785\) | 39.4224 | 1.40705 | ||||||||
\(786\) | 77.0457 | 2.74813 | ||||||||
\(787\) | −10.9034 | −0.388663 | −0.194331 | − | 0.980936i | \(-0.562254\pi\) | ||||
−0.194331 | + | 0.980936i | \(0.562254\pi\) | |||||||
\(788\) | 1.25584 | 0.0447375 | ||||||||
\(789\) | 14.3784 | 0.511886 | ||||||||
\(790\) | −29.3472 | −1.04413 | ||||||||
\(791\) | −13.2847 | −0.472350 | ||||||||
\(792\) | −94.4414 | −3.35583 | ||||||||
\(793\) | 1.31601 | 0.0467329 | ||||||||
\(794\) | −7.68150 | −0.272606 | ||||||||
\(795\) | 50.6620 | 1.79680 | ||||||||
\(796\) | 2.72204 | 0.0964801 | ||||||||
\(797\) | −19.1652 | −0.678865 | −0.339433 | − | 0.940630i | \(-0.610235\pi\) | ||||
−0.339433 | + | 0.940630i | \(0.610235\pi\) | |||||||
\(798\) | 26.4770 | 0.937276 | ||||||||
\(799\) | 15.0590 | 0.532749 | ||||||||
\(800\) | −1.51318 | −0.0534990 | ||||||||
\(801\) | 125.807 | 4.44516 | ||||||||
\(802\) | 24.2226 | 0.855330 | ||||||||
\(803\) | 36.9729 | 1.30475 | ||||||||
\(804\) | 5.18094 | 0.182718 | ||||||||
\(805\) | 3.14925 | 0.110996 | ||||||||
\(806\) | 0.295960 | 0.0104247 | ||||||||
\(807\) | 39.5826 | 1.39337 | ||||||||
\(808\) | −19.7958 | −0.696413 | ||||||||
\(809\) | −5.88096 | −0.206764 | −0.103382 | − | 0.994642i | \(-0.532966\pi\) | ||||
−0.103382 | + | 0.994642i | \(0.532966\pi\) | |||||||
\(810\) | −104.512 | −3.67219 | ||||||||
\(811\) | 1.76023 | 0.0618101 | 0.0309051 | − | 0.999522i | \(-0.490161\pi\) | ||||
0.0309051 | + | 0.999522i | \(0.490161\pi\) | |||||||
\(812\) | −1.17602 | −0.0412704 | ||||||||
\(813\) | 49.3871 | 1.73208 | ||||||||
\(814\) | 40.7847 | 1.42950 | ||||||||
\(815\) | −34.3845 | −1.20444 | ||||||||
\(816\) | −26.6803 | −0.933997 | ||||||||
\(817\) | 4.30290 | 0.150540 | ||||||||
\(818\) | −51.4911 | −1.80034 | ||||||||
\(819\) | −2.18729 | −0.0764301 | ||||||||
\(820\) | −1.87462 | −0.0654645 | ||||||||
\(821\) | −33.0842 | −1.15465 | −0.577323 | − | 0.816516i | \(-0.695903\pi\) | ||||
−0.577323 | + | 0.816516i | \(0.695903\pi\) | |||||||
\(822\) | −70.9469 | −2.47456 | ||||||||
\(823\) | 6.54633 | 0.228191 | 0.114095 | − | 0.993470i | \(-0.463603\pi\) | ||||
0.114095 | + | 0.993470i | \(0.463603\pi\) | |||||||
\(824\) | −50.6396 | −1.76411 | ||||||||
\(825\) | −33.6231 | −1.17061 | ||||||||
\(826\) | 16.7019 | 0.581133 | ||||||||
\(827\) | −0.130403 | −0.00453456 | −0.00226728 | − | 0.999997i | \(-0.500722\pi\) | ||||
−0.00226728 | + | 0.999997i | \(0.500722\pi\) | |||||||
\(828\) | 0.724848 | 0.0251902 | ||||||||
\(829\) | 18.1137 | 0.629114 | 0.314557 | − | 0.949239i | \(-0.398144\pi\) | ||||
0.314557 | + | 0.949239i | \(0.398144\pi\) | |||||||
\(830\) | −61.2235 | −2.12510 | ||||||||
\(831\) | −79.2511 | −2.74919 | ||||||||
\(832\) | 1.48173 | 0.0513698 | ||||||||
\(833\) | 9.52770 | 0.330115 | ||||||||
\(834\) | 56.7827 | 1.96622 | ||||||||
\(835\) | 28.3053 | 0.979544 | ||||||||
\(836\) | 2.03886 | 0.0705155 | ||||||||
\(837\) | −15.5904 | −0.538881 | ||||||||
\(838\) | −4.35918 | −0.150585 | ||||||||
\(839\) | 27.5593 | 0.951452 | 0.475726 | − | 0.879594i | \(-0.342185\pi\) | ||||
0.475726 | + | 0.879594i | \(0.342185\pi\) | |||||||
\(840\) | 34.8191 | 1.20137 | ||||||||
\(841\) | 19.4630 | 0.671136 | ||||||||
\(842\) | −33.3329 | −1.14873 | ||||||||
\(843\) | 80.4419 | 2.77057 | ||||||||
\(844\) | −1.27616 | −0.0439271 | ||||||||
\(845\) | 34.9868 | 1.20358 | ||||||||
\(846\) | −86.5774 | −2.97659 | ||||||||
\(847\) | −13.4004 | −0.460442 | ||||||||
\(848\) | −24.2682 | −0.833375 | ||||||||
\(849\) | −5.37932 | −0.184618 | ||||||||
\(850\) | −6.44507 | −0.221064 | ||||||||
\(851\) | 5.03277 | 0.172521 | ||||||||
\(852\) | 2.81275 | 0.0963631 | ||||||||
\(853\) | −40.3891 | −1.38290 | −0.691448 | − | 0.722427i | \(-0.743027\pi\) | ||||
−0.691448 | + | 0.722427i | \(0.743027\pi\) | |||||||
\(854\) | −13.9404 | −0.477032 | ||||||||
\(855\) | −79.8458 | −2.73067 | ||||||||
\(856\) | −37.3041 | −1.27503 | ||||||||
\(857\) | 35.8393 | 1.22425 | 0.612124 | − | 0.790762i | \(-0.290316\pi\) | ||||
0.612124 | + | 0.790762i | \(0.290316\pi\) | |||||||
\(858\) | −4.23849 | −0.144700 | ||||||||
\(859\) | 32.2117 | 1.09905 | 0.549525 | − | 0.835477i | \(-0.314809\pi\) | ||||
0.549525 | + | 0.835477i | \(0.314809\pi\) | |||||||
\(860\) | −0.351953 | −0.0120015 | ||||||||
\(861\) | 27.9181 | 0.951448 | ||||||||
\(862\) | 49.4879 | 1.68557 | ||||||||
\(863\) | −21.6667 | −0.737544 | −0.368772 | − | 0.929520i | \(-0.620222\pi\) | ||||
−0.368772 | + | 0.929520i | \(0.620222\pi\) | |||||||
\(864\) | 10.0482 | 0.341846 | ||||||||
\(865\) | −1.00929 | −0.0343168 | ||||||||
\(866\) | 11.4270 | 0.388305 | ||||||||
\(867\) | 43.2422 | 1.46858 | ||||||||
\(868\) | −0.173423 | −0.00588635 | ||||||||
\(869\) | 33.6557 | 1.14169 | ||||||||
\(870\) | 89.2453 | 3.02570 | ||||||||
\(871\) | −2.68560 | −0.0909981 | ||||||||
\(872\) | −30.0767 | −1.01852 | ||||||||
\(873\) | −142.545 | −4.82441 | ||||||||
\(874\) | 4.54823 | 0.153846 | ||||||||
\(875\) | −10.5642 | −0.357136 | ||||||||
\(876\) | −3.13746 | −0.106005 | ||||||||
\(877\) | 33.9945 | 1.14791 | 0.573957 | − | 0.818886i | \(-0.305408\pi\) | ||||
0.573957 | + | 0.818886i | \(0.305408\pi\) | |||||||
\(878\) | −12.3672 | −0.417374 | ||||||||
\(879\) | 4.02465 | 0.135748 | ||||||||
\(880\) | 51.3189 | 1.72996 | ||||||||
\(881\) | 17.3024 | 0.582932 | 0.291466 | − | 0.956581i | \(-0.405857\pi\) | ||||
0.291466 | + | 0.956581i | \(0.405857\pi\) | |||||||
\(882\) | −54.7768 | −1.84443 | ||||||||
\(883\) | −41.4804 | −1.39593 | −0.697963 | − | 0.716134i | \(-0.745910\pi\) | ||||
−0.697963 | + | 0.716134i | \(0.745910\pi\) | |||||||
\(884\) | −0.0449424 | −0.00151158 | ||||||||
\(885\) | −70.1117 | −2.35678 | ||||||||
\(886\) | 0.774283 | 0.0260126 | ||||||||
\(887\) | 20.6409 | 0.693053 | 0.346526 | − | 0.938040i | \(-0.387361\pi\) | ||||
0.346526 | + | 0.938040i | \(0.387361\pi\) | |||||||
\(888\) | 55.6439 | 1.86729 | ||||||||
\(889\) | 11.9944 | 0.402278 | ||||||||
\(890\) | −64.5687 | −2.16435 | ||||||||
\(891\) | 119.856 | 4.01533 | ||||||||
\(892\) | 0.826010 | 0.0276569 | ||||||||
\(893\) | −30.0507 | −1.00561 | ||||||||
\(894\) | −39.1371 | −1.30894 | ||||||||
\(895\) | 6.38857 | 0.213546 | ||||||||
\(896\) | −17.6048 | −0.588134 | ||||||||
\(897\) | −0.523024 | −0.0174633 | ||||||||
\(898\) | −16.1272 | −0.538173 | ||||||||
\(899\) | 7.14660 | 0.238353 | ||||||||
\(900\) | 2.04971 | 0.0683235 | ||||||||
\(901\) | −11.1369 | −0.371024 | ||||||||
\(902\) | 38.8642 | 1.29404 | ||||||||
\(903\) | 5.24153 | 0.174427 | ||||||||
\(904\) | −25.2311 | −0.839175 | ||||||||
\(905\) | −56.7638 | −1.88689 | ||||||||
\(906\) | 65.5609 | 2.17812 | ||||||||
\(907\) | 12.8852 | 0.427846 | 0.213923 | − | 0.976851i | \(-0.431376\pi\) | ||||
0.213923 | + | 0.976851i | \(0.431376\pi\) | |||||||
\(908\) | 1.82800 | 0.0606642 | ||||||||
\(909\) | 55.2973 | 1.83410 | ||||||||
\(910\) | 1.12260 | 0.0372138 | ||||||||
\(911\) | 32.6028 | 1.08018 | 0.540089 | − | 0.841608i | \(-0.318391\pi\) | ||||
0.540089 | + | 0.841608i | \(0.318391\pi\) | |||||||
\(912\) | 53.2414 | 1.76300 | ||||||||
\(913\) | 70.2119 | 2.32368 | ||||||||
\(914\) | 47.5791 | 1.57378 | ||||||||
\(915\) | 58.5196 | 1.93460 | ||||||||
\(916\) | 2.59902 | 0.0858740 | ||||||||
\(917\) | 23.4021 | 0.772805 | ||||||||
\(918\) | 42.7981 | 1.41255 | ||||||||
\(919\) | −54.1757 | −1.78709 | −0.893545 | − | 0.448973i | \(-0.851790\pi\) | ||||
−0.893545 | + | 0.448973i | \(0.851790\pi\) | |||||||
\(920\) | 5.98124 | 0.197196 | ||||||||
\(921\) | −8.52412 | −0.280879 | ||||||||
\(922\) | −15.0526 | −0.495730 | ||||||||
\(923\) | −1.45802 | −0.0479913 | ||||||||
\(924\) | 2.48361 | 0.0817049 | ||||||||
\(925\) | 14.2315 | 0.467930 | ||||||||
\(926\) | 8.14868 | 0.267782 | ||||||||
\(927\) | 141.456 | 4.64602 | ||||||||
\(928\) | −4.60607 | −0.151202 | ||||||||
\(929\) | −9.40444 | −0.308550 | −0.154275 | − | 0.988028i | \(-0.549304\pi\) | ||||
−0.154275 | + | 0.988028i | \(0.549304\pi\) | |||||||
\(930\) | 13.1606 | 0.431553 | ||||||||
\(931\) | −19.0128 | −0.623121 | ||||||||
\(932\) | −0.239705 | −0.00785178 | ||||||||
\(933\) | −69.9291 | −2.28938 | ||||||||
\(934\) | 24.7200 | 0.808864 | ||||||||
\(935\) | 23.5507 | 0.770190 | ||||||||
\(936\) | −4.15423 | −0.135785 | ||||||||
\(937\) | −26.6094 | −0.869292 | −0.434646 | − | 0.900601i | \(-0.643126\pi\) | ||||
−0.434646 | + | 0.900601i | \(0.643126\pi\) | |||||||
\(938\) | 28.4485 | 0.928875 | ||||||||
\(939\) | 83.5154 | 2.72542 | ||||||||
\(940\) | 2.45798 | 0.0801704 | ||||||||
\(941\) | 46.7143 | 1.52284 | 0.761422 | − | 0.648257i | \(-0.224502\pi\) | ||||
0.761422 | + | 0.648257i | \(0.224502\pi\) | |||||||
\(942\) | 69.3546 | 2.25969 | ||||||||
\(943\) | 4.79579 | 0.156172 | ||||||||
\(944\) | 33.5851 | 1.09310 | ||||||||
\(945\) | −59.1354 | −1.92368 | ||||||||
\(946\) | 7.29662 | 0.237234 | ||||||||
\(947\) | −46.1737 | −1.50044 | −0.750221 | − | 0.661187i | \(-0.770053\pi\) | ||||
−0.750221 | + | 0.661187i | \(0.770053\pi\) | |||||||
\(948\) | −2.85597 | −0.0927577 | ||||||||
\(949\) | 1.62634 | 0.0527933 | ||||||||
\(950\) | 12.8614 | 0.417277 | ||||||||
\(951\) | −76.6299 | −2.48490 | ||||||||
\(952\) | −7.65420 | −0.248074 | ||||||||
\(953\) | 43.7291 | 1.41653 | 0.708263 | − | 0.705949i | \(-0.249479\pi\) | ||||
0.708263 | + | 0.705949i | \(0.249479\pi\) | |||||||
\(954\) | 64.0285 | 2.07300 | ||||||||
\(955\) | 36.8099 | 1.19114 | ||||||||
\(956\) | 0.491811 | 0.0159063 | ||||||||
\(957\) | −102.348 | −3.30843 | ||||||||
\(958\) | −23.2872 | −0.752374 | ||||||||
\(959\) | −21.5496 | −0.695873 | ||||||||
\(960\) | 65.8888 | 2.12655 | ||||||||
\(961\) | −29.9461 | −0.966004 | ||||||||
\(962\) | 1.79401 | 0.0578412 | ||||||||
\(963\) | 104.205 | 3.35796 | ||||||||
\(964\) | −0.963036 | −0.0310173 | ||||||||
\(965\) | −8.18927 | −0.263622 | ||||||||
\(966\) | 5.54037 | 0.178259 | ||||||||
\(967\) | −6.19072 | −0.199080 | −0.0995400 | − | 0.995034i | \(-0.531737\pi\) | ||||
−0.0995400 | + | 0.995034i | \(0.531737\pi\) | |||||||
\(968\) | −25.4507 | −0.818018 | ||||||||
\(969\) | 24.4329 | 0.784899 | ||||||||
\(970\) | 73.1592 | 2.34900 | ||||||||
\(971\) | −18.1743 | −0.583240 | −0.291620 | − | 0.956534i | \(-0.594194\pi\) | ||||
−0.291620 | + | 0.956534i | \(0.594194\pi\) | |||||||
\(972\) | −4.83522 | −0.155090 | ||||||||
\(973\) | 17.2473 | 0.552924 | ||||||||
\(974\) | 14.2077 | 0.455244 | ||||||||
\(975\) | −1.47899 | −0.0473656 | ||||||||
\(976\) | −28.0322 | −0.897289 | ||||||||
\(977\) | −33.3552 | −1.06713 | −0.533563 | − | 0.845760i | \(-0.679147\pi\) | ||||
−0.533563 | + | 0.845760i | \(0.679147\pi\) | |||||||
\(978\) | −60.4916 | −1.93431 | ||||||||
\(979\) | 74.0482 | 2.36659 | ||||||||
\(980\) | 1.55514 | 0.0496772 | ||||||||
\(981\) | 84.0158 | 2.68242 | ||||||||
\(982\) | −11.6734 | −0.372514 | ||||||||
\(983\) | 27.2974 | 0.870651 | 0.435325 | − | 0.900273i | \(-0.356633\pi\) | ||||
0.435325 | + | 0.900273i | \(0.356633\pi\) | |||||||
\(984\) | 53.0238 | 1.69034 | ||||||||
\(985\) | −28.9474 | −0.922341 | ||||||||
\(986\) | −19.6186 | −0.624783 | ||||||||
\(987\) | −36.6059 | −1.16518 | ||||||||
\(988\) | 0.0896841 | 0.00285323 | ||||||||
\(989\) | 0.900393 | 0.0286308 | ||||||||
\(990\) | −135.398 | −4.30323 | ||||||||
\(991\) | −10.0739 | −0.320007 | −0.160003 | − | 0.987116i | \(-0.551150\pi\) | ||||
−0.160003 | + | 0.987116i | \(0.551150\pi\) | |||||||
\(992\) | −0.679236 | −0.0215658 | ||||||||
\(993\) | 19.7874 | 0.627933 | ||||||||
\(994\) | 15.4448 | 0.489878 | ||||||||
\(995\) | −62.7436 | −1.98911 | ||||||||
\(996\) | −5.95808 | −0.188789 | ||||||||
\(997\) | −47.1640 | −1.49370 | −0.746850 | − | 0.664992i | \(-0.768435\pi\) | ||||
−0.746850 | + | 0.664992i | \(0.768435\pi\) | |||||||
\(998\) | 16.1680 | 0.511788 | ||||||||
\(999\) | −94.5035 | −2.98996 |
(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 | 619.2.a.b.1.20 | ✓ | 30 | |
3.2 | odd | 2 | 5571.2.a.g.1.11 | 30 | |||
4.3 | odd | 2 | 9904.2.a.n.1.30 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.b.1.20 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5571.2.a.g.1.11 | 30 | 3.2 | odd | 2 | |||
9904.2.a.n.1.30 | 30 | 4.3 | odd | 2 |