Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, 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("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.24 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.28149 | −0.739867 | −0.369933 | − | 0.929058i | \(-0.620619\pi\) | ||||
−0.369933 | + | 0.929058i | \(0.620619\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.444196 | −0.198651 | −0.0993253 | − | 0.995055i | \(-0.531668\pi\) | ||||
−0.0993253 | + | 0.995055i | \(0.531668\pi\) | |||||||
\(6\) | 1.28149 | 0.523165 | ||||||||
\(7\) | 1.92855 | 0.728923 | 0.364461 | − | 0.931218i | \(-0.381253\pi\) | ||||
0.364461 | + | 0.931218i | \(0.381253\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.35779 | −0.452597 | ||||||||
\(10\) | 0.444196 | 0.140467 | ||||||||
\(11\) | 2.61160 | 0.787428 | 0.393714 | − | 0.919233i | \(-0.371190\pi\) | ||||
0.393714 | + | 0.919233i | \(0.371190\pi\) | |||||||
\(12\) | −1.28149 | −0.369933 | ||||||||
\(13\) | −2.34755 | −0.651092 | −0.325546 | − | 0.945526i | \(-0.605548\pi\) | ||||
−0.325546 | + | 0.945526i | \(0.605548\pi\) | |||||||
\(14\) | −1.92855 | −0.515426 | ||||||||
\(15\) | 0.569232 | 0.146975 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.89602 | −1.18746 | −0.593730 | − | 0.804665i | \(-0.702345\pi\) | ||||
−0.593730 | + | 0.804665i | \(0.702345\pi\) | |||||||
\(18\) | 1.35779 | 0.320035 | ||||||||
\(19\) | 3.17903 | 0.729319 | 0.364659 | − | 0.931141i | \(-0.381185\pi\) | ||||
0.364659 | + | 0.931141i | \(0.381185\pi\) | |||||||
\(20\) | −0.444196 | −0.0993253 | ||||||||
\(21\) | −2.47141 | −0.539306 | ||||||||
\(22\) | −2.61160 | −0.556796 | ||||||||
\(23\) | −5.99830 | −1.25073 | −0.625366 | − | 0.780332i | \(-0.715050\pi\) | ||||
−0.625366 | + | 0.780332i | \(0.715050\pi\) | |||||||
\(24\) | 1.28149 | 0.261582 | ||||||||
\(25\) | −4.80269 | −0.960538 | ||||||||
\(26\) | 2.34755 | 0.460391 | ||||||||
\(27\) | 5.58445 | 1.07473 | ||||||||
\(28\) | 1.92855 | 0.364461 | ||||||||
\(29\) | −4.96047 | −0.921136 | −0.460568 | − | 0.887624i | \(-0.652354\pi\) | ||||
−0.460568 | + | 0.887624i | \(0.652354\pi\) | |||||||
\(30\) | −0.569232 | −0.103927 | ||||||||
\(31\) | −6.67509 | −1.19888 | −0.599441 | − | 0.800419i | \(-0.704610\pi\) | ||||
−0.599441 | + | 0.800419i | \(0.704610\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.34674 | −0.582592 | ||||||||
\(34\) | 4.89602 | 0.839660 | ||||||||
\(35\) | −0.856654 | −0.144801 | ||||||||
\(36\) | −1.35779 | −0.226299 | ||||||||
\(37\) | 8.13959 | 1.33814 | 0.669070 | − | 0.743199i | \(-0.266693\pi\) | ||||
0.669070 | + | 0.743199i | \(0.266693\pi\) | |||||||
\(38\) | −3.17903 | −0.515706 | ||||||||
\(39\) | 3.00835 | 0.481721 | ||||||||
\(40\) | 0.444196 | 0.0702336 | ||||||||
\(41\) | 1.24289 | 0.194107 | 0.0970536 | − | 0.995279i | \(-0.469058\pi\) | ||||
0.0970536 | + | 0.995279i | \(0.469058\pi\) | |||||||
\(42\) | 2.47141 | 0.381347 | ||||||||
\(43\) | −6.72451 | −1.02548 | −0.512739 | − | 0.858545i | \(-0.671369\pi\) | ||||
−0.512739 | + | 0.858545i | \(0.671369\pi\) | |||||||
\(44\) | 2.61160 | 0.393714 | ||||||||
\(45\) | 0.603126 | 0.0899088 | ||||||||
\(46\) | 5.99830 | 0.884401 | ||||||||
\(47\) | −8.23219 | −1.20079 | −0.600394 | − | 0.799704i | \(-0.704990\pi\) | ||||
−0.600394 | + | 0.799704i | \(0.704990\pi\) | |||||||
\(48\) | −1.28149 | −0.184967 | ||||||||
\(49\) | −3.28070 | −0.468671 | ||||||||
\(50\) | 4.80269 | 0.679203 | ||||||||
\(51\) | 6.27418 | 0.878561 | ||||||||
\(52\) | −2.34755 | −0.325546 | ||||||||
\(53\) | 12.6320 | 1.73514 | 0.867568 | − | 0.497318i | \(-0.165682\pi\) | ||||
0.867568 | + | 0.497318i | \(0.165682\pi\) | |||||||
\(54\) | −5.58445 | −0.759948 | ||||||||
\(55\) | −1.16007 | −0.156423 | ||||||||
\(56\) | −1.92855 | −0.257713 | ||||||||
\(57\) | −4.07388 | −0.539599 | ||||||||
\(58\) | 4.96047 | 0.651342 | ||||||||
\(59\) | 11.3965 | 1.48370 | 0.741851 | − | 0.670565i | \(-0.233948\pi\) | ||||
0.741851 | + | 0.670565i | \(0.233948\pi\) | |||||||
\(60\) | 0.569232 | 0.0734875 | ||||||||
\(61\) | 3.01624 | 0.386190 | 0.193095 | − | 0.981180i | \(-0.438147\pi\) | ||||
0.193095 | + | 0.981180i | \(0.438147\pi\) | |||||||
\(62\) | 6.67509 | 0.847737 | ||||||||
\(63\) | −2.61857 | −0.329909 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.04277 | 0.129340 | ||||||||
\(66\) | 3.34674 | 0.411955 | ||||||||
\(67\) | −4.38366 | −0.535550 | −0.267775 | − | 0.963482i | \(-0.586288\pi\) | ||||
−0.267775 | + | 0.963482i | \(0.586288\pi\) | |||||||
\(68\) | −4.89602 | −0.593730 | ||||||||
\(69\) | 7.68674 | 0.925375 | ||||||||
\(70\) | 0.856654 | 0.102390 | ||||||||
\(71\) | 2.29127 | 0.271923 | 0.135962 | − | 0.990714i | \(-0.456588\pi\) | ||||
0.135962 | + | 0.990714i | \(0.456588\pi\) | |||||||
\(72\) | 1.35779 | 0.160017 | ||||||||
\(73\) | −4.14794 | −0.485480 | −0.242740 | − | 0.970091i | \(-0.578046\pi\) | ||||
−0.242740 | + | 0.970091i | \(0.578046\pi\) | |||||||
\(74\) | −8.13959 | −0.946208 | ||||||||
\(75\) | 6.15458 | 0.710670 | ||||||||
\(76\) | 3.17903 | 0.364659 | ||||||||
\(77\) | 5.03661 | 0.573974 | ||||||||
\(78\) | −3.00835 | −0.340628 | ||||||||
\(79\) | −13.7362 | −1.54544 | −0.772719 | − | 0.634748i | \(-0.781104\pi\) | ||||
−0.772719 | + | 0.634748i | \(0.781104\pi\) | |||||||
\(80\) | −0.444196 | −0.0496627 | ||||||||
\(81\) | −3.08302 | −0.342558 | ||||||||
\(82\) | −1.24289 | −0.137255 | ||||||||
\(83\) | 6.48484 | 0.711804 | 0.355902 | − | 0.934523i | \(-0.384174\pi\) | ||||
0.355902 | + | 0.934523i | \(0.384174\pi\) | |||||||
\(84\) | −2.47141 | −0.269653 | ||||||||
\(85\) | 2.17479 | 0.235890 | ||||||||
\(86\) | 6.72451 | 0.725122 | ||||||||
\(87\) | 6.35678 | 0.681518 | ||||||||
\(88\) | −2.61160 | −0.278398 | ||||||||
\(89\) | 2.80274 | 0.297090 | 0.148545 | − | 0.988906i | \(-0.452541\pi\) | ||||
0.148545 | + | 0.988906i | \(0.452541\pi\) | |||||||
\(90\) | −0.603126 | −0.0635751 | ||||||||
\(91\) | −4.52735 | −0.474596 | ||||||||
\(92\) | −5.99830 | −0.625366 | ||||||||
\(93\) | 8.55404 | 0.887013 | ||||||||
\(94\) | 8.23219 | 0.849085 | ||||||||
\(95\) | −1.41211 | −0.144880 | ||||||||
\(96\) | 1.28149 | 0.130791 | ||||||||
\(97\) | 11.1750 | 1.13465 | 0.567325 | − | 0.823494i | \(-0.307978\pi\) | ||||
0.567325 | + | 0.823494i | \(0.307978\pi\) | |||||||
\(98\) | 3.28070 | 0.331401 | ||||||||
\(99\) | −3.54602 | −0.356388 | ||||||||
\(100\) | −4.80269 | −0.480269 | ||||||||
\(101\) | 0.0783921 | 0.00780030 | 0.00390015 | − | 0.999992i | \(-0.498759\pi\) | ||||
0.00390015 | + | 0.999992i | \(0.498759\pi\) | |||||||
\(102\) | −6.27418 | −0.621237 | ||||||||
\(103\) | 5.32059 | 0.524254 | 0.262127 | − | 0.965033i | \(-0.415576\pi\) | ||||
0.262127 | + | 0.965033i | \(0.415576\pi\) | |||||||
\(104\) | 2.34755 | 0.230196 | ||||||||
\(105\) | 1.09779 | 0.107133 | ||||||||
\(106\) | −12.6320 | −1.22693 | ||||||||
\(107\) | 16.0609 | 1.55266 | 0.776331 | − | 0.630325i | \(-0.217078\pi\) | ||||
0.776331 | + | 0.630325i | \(0.217078\pi\) | |||||||
\(108\) | 5.58445 | 0.537364 | ||||||||
\(109\) | −0.313546 | −0.0300323 | −0.0150161 | − | 0.999887i | \(-0.504780\pi\) | ||||
−0.0150161 | + | 0.999887i | \(0.504780\pi\) | |||||||
\(110\) | 1.16007 | 0.110608 | ||||||||
\(111\) | −10.4308 | −0.990045 | ||||||||
\(112\) | 1.92855 | 0.182231 | ||||||||
\(113\) | 13.8659 | 1.30440 | 0.652199 | − | 0.758048i | \(-0.273847\pi\) | ||||
0.652199 | + | 0.758048i | \(0.273847\pi\) | |||||||
\(114\) | 4.07388 | 0.381554 | ||||||||
\(115\) | 2.66442 | 0.248459 | ||||||||
\(116\) | −4.96047 | −0.460568 | ||||||||
\(117\) | 3.18748 | 0.294682 | ||||||||
\(118\) | −11.3965 | −1.04914 | ||||||||
\(119\) | −9.44221 | −0.865566 | ||||||||
\(120\) | −0.569232 | −0.0519635 | ||||||||
\(121\) | −4.17952 | −0.379957 | ||||||||
\(122\) | −3.01624 | −0.273078 | ||||||||
\(123\) | −1.59275 | −0.143613 | ||||||||
\(124\) | −6.67509 | −0.599441 | ||||||||
\(125\) | 4.35432 | 0.389462 | ||||||||
\(126\) | 2.61857 | 0.233281 | ||||||||
\(127\) | −18.3525 | −1.62852 | −0.814261 | − | 0.580499i | \(-0.802858\pi\) | ||||
−0.814261 | + | 0.580499i | \(0.802858\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.61737 | 0.758717 | ||||||||
\(130\) | −1.04277 | −0.0914571 | ||||||||
\(131\) | −9.86495 | −0.861905 | −0.430952 | − | 0.902375i | \(-0.641822\pi\) | ||||
−0.430952 | + | 0.902375i | \(0.641822\pi\) | |||||||
\(132\) | −3.34674 | −0.291296 | ||||||||
\(133\) | 6.13091 | 0.531617 | ||||||||
\(134\) | 4.38366 | 0.378691 | ||||||||
\(135\) | −2.48059 | −0.213496 | ||||||||
\(136\) | 4.89602 | 0.419830 | ||||||||
\(137\) | 4.15166 | 0.354700 | 0.177350 | − | 0.984148i | \(-0.443247\pi\) | ||||
0.177350 | + | 0.984148i | \(0.443247\pi\) | |||||||
\(138\) | −7.68674 | −0.654339 | ||||||||
\(139\) | −17.0535 | −1.44646 | −0.723229 | − | 0.690608i | \(-0.757343\pi\) | ||||
−0.723229 | + | 0.690608i | \(0.757343\pi\) | |||||||
\(140\) | −0.856654 | −0.0724005 | ||||||||
\(141\) | 10.5494 | 0.888423 | ||||||||
\(142\) | −2.29127 | −0.192279 | ||||||||
\(143\) | −6.13086 | −0.512688 | ||||||||
\(144\) | −1.35779 | −0.113149 | ||||||||
\(145\) | 2.20342 | 0.182984 | ||||||||
\(146\) | 4.14794 | 0.343286 | ||||||||
\(147\) | 4.20417 | 0.346754 | ||||||||
\(148\) | 8.13959 | 0.669070 | ||||||||
\(149\) | 8.75424 | 0.717175 | 0.358588 | − | 0.933496i | \(-0.383258\pi\) | ||||
0.358588 | + | 0.933496i | \(0.383258\pi\) | |||||||
\(150\) | −6.15458 | −0.502520 | ||||||||
\(151\) | 14.7565 | 1.20086 | 0.600432 | − | 0.799675i | \(-0.294995\pi\) | ||||
0.600432 | + | 0.799675i | \(0.294995\pi\) | |||||||
\(152\) | −3.17903 | −0.257853 | ||||||||
\(153\) | 6.64778 | 0.537441 | ||||||||
\(154\) | −5.03661 | −0.405861 | ||||||||
\(155\) | 2.96505 | 0.238159 | ||||||||
\(156\) | 3.00835 | 0.240861 | ||||||||
\(157\) | −11.1030 | −0.886118 | −0.443059 | − | 0.896492i | \(-0.646107\pi\) | ||||
−0.443059 | + | 0.896492i | \(0.646107\pi\) | |||||||
\(158\) | 13.7362 | 1.09279 | ||||||||
\(159\) | −16.1877 | −1.28377 | ||||||||
\(160\) | 0.444196 | 0.0351168 | ||||||||
\(161\) | −11.5680 | −0.911687 | ||||||||
\(162\) | 3.08302 | 0.242225 | ||||||||
\(163\) | 10.1334 | 0.793709 | 0.396855 | − | 0.917881i | \(-0.370102\pi\) | ||||
0.396855 | + | 0.917881i | \(0.370102\pi\) | |||||||
\(164\) | 1.24289 | 0.0970536 | ||||||||
\(165\) | 1.48661 | 0.115732 | ||||||||
\(166\) | −6.48484 | −0.503321 | ||||||||
\(167\) | 6.99047 | 0.540939 | 0.270469 | − | 0.962729i | \(-0.412821\pi\) | ||||
0.270469 | + | 0.962729i | \(0.412821\pi\) | |||||||
\(168\) | 2.47141 | 0.190673 | ||||||||
\(169\) | −7.48903 | −0.576079 | ||||||||
\(170\) | −2.17479 | −0.166799 | ||||||||
\(171\) | −4.31646 | −0.330088 | ||||||||
\(172\) | −6.72451 | −0.512739 | ||||||||
\(173\) | 22.5518 | 1.71458 | 0.857290 | − | 0.514833i | \(-0.172146\pi\) | ||||
0.857290 | + | 0.514833i | \(0.172146\pi\) | |||||||
\(174\) | −6.35678 | −0.481906 | ||||||||
\(175\) | −9.26222 | −0.700158 | ||||||||
\(176\) | 2.61160 | 0.196857 | ||||||||
\(177\) | −14.6045 | −1.09774 | ||||||||
\(178\) | −2.80274 | −0.210074 | ||||||||
\(179\) | −14.8361 | −1.10890 | −0.554451 | − | 0.832216i | \(-0.687072\pi\) | ||||
−0.554451 | + | 0.832216i | \(0.687072\pi\) | |||||||
\(180\) | 0.603126 | 0.0449544 | ||||||||
\(181\) | −5.05705 | −0.375888 | −0.187944 | − | 0.982180i | \(-0.560182\pi\) | ||||
−0.187944 | + | 0.982180i | \(0.560182\pi\) | |||||||
\(182\) | 4.52735 | 0.335590 | ||||||||
\(183\) | −3.86527 | −0.285729 | ||||||||
\(184\) | 5.99830 | 0.442200 | ||||||||
\(185\) | −3.61558 | −0.265822 | ||||||||
\(186\) | −8.55404 | −0.627213 | ||||||||
\(187\) | −12.7865 | −0.935039 | ||||||||
\(188\) | −8.23219 | −0.600394 | ||||||||
\(189\) | 10.7699 | 0.783394 | ||||||||
\(190\) | 1.41211 | 0.102445 | ||||||||
\(191\) | 4.15023 | 0.300300 | 0.150150 | − | 0.988663i | \(-0.452024\pi\) | ||||
0.150150 | + | 0.988663i | \(0.452024\pi\) | |||||||
\(192\) | −1.28149 | −0.0924833 | ||||||||
\(193\) | 13.2285 | 0.952205 | 0.476103 | − | 0.879390i | \(-0.342049\pi\) | ||||
0.476103 | + | 0.879390i | \(0.342049\pi\) | |||||||
\(194\) | −11.1750 | −0.802319 | ||||||||
\(195\) | −1.33630 | −0.0956942 | ||||||||
\(196\) | −3.28070 | −0.234336 | ||||||||
\(197\) | −5.25500 | −0.374403 | −0.187202 | − | 0.982322i | \(-0.559942\pi\) | ||||
−0.187202 | + | 0.982322i | \(0.559942\pi\) | |||||||
\(198\) | 3.54602 | 0.252004 | ||||||||
\(199\) | 0.250345 | 0.0177465 | 0.00887323 | − | 0.999961i | \(-0.497176\pi\) | ||||
0.00887323 | + | 0.999961i | \(0.497176\pi\) | |||||||
\(200\) | 4.80269 | 0.339601 | ||||||||
\(201\) | 5.61761 | 0.396235 | ||||||||
\(202\) | −0.0783921 | −0.00551565 | ||||||||
\(203\) | −9.56651 | −0.671437 | ||||||||
\(204\) | 6.27418 | 0.439281 | ||||||||
\(205\) | −0.552088 | −0.0385595 | ||||||||
\(206\) | −5.32059 | −0.370703 | ||||||||
\(207\) | 8.14444 | 0.566078 | ||||||||
\(208\) | −2.34755 | −0.162773 | ||||||||
\(209\) | 8.30236 | 0.574286 | ||||||||
\(210\) | −1.09779 | −0.0757548 | ||||||||
\(211\) | 8.95055 | 0.616181 | 0.308091 | − | 0.951357i | \(-0.400310\pi\) | ||||
0.308091 | + | 0.951357i | \(0.400310\pi\) | |||||||
\(212\) | 12.6320 | 0.867568 | ||||||||
\(213\) | −2.93623 | −0.201187 | ||||||||
\(214\) | −16.0609 | −1.09790 | ||||||||
\(215\) | 2.98700 | 0.203712 | ||||||||
\(216\) | −5.58445 | −0.379974 | ||||||||
\(217\) | −12.8732 | −0.873892 | ||||||||
\(218\) | 0.313546 | 0.0212360 | ||||||||
\(219\) | 5.31553 | 0.359190 | ||||||||
\(220\) | −1.16007 | −0.0782116 | ||||||||
\(221\) | 11.4936 | 0.773145 | ||||||||
\(222\) | 10.4308 | 0.700068 | ||||||||
\(223\) | 13.5470 | 0.907176 | 0.453588 | − | 0.891212i | \(-0.350144\pi\) | ||||
0.453588 | + | 0.891212i | \(0.350144\pi\) | |||||||
\(224\) | −1.92855 | −0.128857 | ||||||||
\(225\) | 6.52105 | 0.434737 | ||||||||
\(226\) | −13.8659 | −0.922349 | ||||||||
\(227\) | 11.5920 | 0.769388 | 0.384694 | − | 0.923044i | \(-0.374307\pi\) | ||||
0.384694 | + | 0.923044i | \(0.374307\pi\) | |||||||
\(228\) | −4.07388 | −0.269799 | ||||||||
\(229\) | −4.42095 | −0.292144 | −0.146072 | − | 0.989274i | \(-0.546663\pi\) | ||||
−0.146072 | + | 0.989274i | \(0.546663\pi\) | |||||||
\(230\) | −2.66442 | −0.175687 | ||||||||
\(231\) | −6.45434 | −0.424665 | ||||||||
\(232\) | 4.96047 | 0.325671 | ||||||||
\(233\) | −2.05348 | −0.134528 | −0.0672641 | − | 0.997735i | \(-0.521427\pi\) | ||||
−0.0672641 | + | 0.997735i | \(0.521427\pi\) | |||||||
\(234\) | −3.18748 | −0.208372 | ||||||||
\(235\) | 3.65671 | 0.238537 | ||||||||
\(236\) | 11.3965 | 0.741851 | ||||||||
\(237\) | 17.6027 | 1.14342 | ||||||||
\(238\) | 9.44221 | 0.612048 | ||||||||
\(239\) | −8.04445 | −0.520352 | −0.260176 | − | 0.965561i | \(-0.583781\pi\) | ||||
−0.260176 | + | 0.965561i | \(0.583781\pi\) | |||||||
\(240\) | 0.569232 | 0.0367438 | ||||||||
\(241\) | −23.3128 | −1.50171 | −0.750853 | − | 0.660469i | \(-0.770358\pi\) | ||||
−0.750853 | + | 0.660469i | \(0.770358\pi\) | |||||||
\(242\) | 4.17952 | 0.268670 | ||||||||
\(243\) | −12.8025 | −0.821281 | ||||||||
\(244\) | 3.01624 | 0.193095 | ||||||||
\(245\) | 1.45728 | 0.0931019 | ||||||||
\(246\) | 1.59275 | 0.101550 | ||||||||
\(247\) | −7.46291 | −0.474854 | ||||||||
\(248\) | 6.67509 | 0.423869 | ||||||||
\(249\) | −8.31024 | −0.526640 | ||||||||
\(250\) | −4.35432 | −0.275391 | ||||||||
\(251\) | 8.67424 | 0.547513 | 0.273757 | − | 0.961799i | \(-0.411734\pi\) | ||||
0.273757 | + | 0.961799i | \(0.411734\pi\) | |||||||
\(252\) | −2.61857 | −0.164954 | ||||||||
\(253\) | −15.6652 | −0.984861 | ||||||||
\(254\) | 18.3525 | 1.15154 | ||||||||
\(255\) | −2.78697 | −0.174527 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −30.9625 | −1.93138 | −0.965692 | − | 0.259688i | \(-0.916380\pi\) | ||||
−0.965692 | + | 0.259688i | \(0.916380\pi\) | |||||||
\(258\) | −8.61737 | −0.536494 | ||||||||
\(259\) | 15.6976 | 0.975401 | ||||||||
\(260\) | 1.04277 | 0.0646699 | ||||||||
\(261\) | 6.73529 | 0.416904 | ||||||||
\(262\) | 9.86495 | 0.609459 | ||||||||
\(263\) | 15.4625 | 0.953461 | 0.476730 | − | 0.879050i | \(-0.341822\pi\) | ||||
0.476730 | + | 0.879050i | \(0.341822\pi\) | |||||||
\(264\) | 3.34674 | 0.205977 | ||||||||
\(265\) | −5.61108 | −0.344686 | ||||||||
\(266\) | −6.13091 | −0.375910 | ||||||||
\(267\) | −3.59167 | −0.219807 | ||||||||
\(268\) | −4.38366 | −0.267775 | ||||||||
\(269\) | 14.6441 | 0.892865 | 0.446432 | − | 0.894817i | \(-0.352694\pi\) | ||||
0.446432 | + | 0.894817i | \(0.352694\pi\) | |||||||
\(270\) | 2.48059 | 0.150964 | ||||||||
\(271\) | 19.9045 | 1.20911 | 0.604555 | − | 0.796564i | \(-0.293351\pi\) | ||||
0.604555 | + | 0.796564i | \(0.293351\pi\) | |||||||
\(272\) | −4.89602 | −0.296865 | ||||||||
\(273\) | 5.80174 | 0.351138 | ||||||||
\(274\) | −4.15166 | −0.250811 | ||||||||
\(275\) | −12.5427 | −0.756355 | ||||||||
\(276\) | 7.68674 | 0.462687 | ||||||||
\(277\) | 4.25582 | 0.255708 | 0.127854 | − | 0.991793i | \(-0.459191\pi\) | ||||
0.127854 | + | 0.991793i | \(0.459191\pi\) | |||||||
\(278\) | 17.0535 | 1.02280 | ||||||||
\(279\) | 9.06339 | 0.542611 | ||||||||
\(280\) | 0.856654 | 0.0511949 | ||||||||
\(281\) | −6.91566 | −0.412554 | −0.206277 | − | 0.978494i | \(-0.566135\pi\) | ||||
−0.206277 | + | 0.978494i | \(0.566135\pi\) | |||||||
\(282\) | −10.5494 | −0.628210 | ||||||||
\(283\) | −3.17045 | −0.188464 | −0.0942320 | − | 0.995550i | \(-0.530040\pi\) | ||||
−0.0942320 | + | 0.995550i | \(0.530040\pi\) | |||||||
\(284\) | 2.29127 | 0.135962 | ||||||||
\(285\) | 1.80960 | 0.107192 | ||||||||
\(286\) | 6.13086 | 0.362525 | ||||||||
\(287\) | 2.39698 | 0.141489 | ||||||||
\(288\) | 1.35779 | 0.0800087 | ||||||||
\(289\) | 6.97100 | 0.410059 | ||||||||
\(290\) | −2.20342 | −0.129389 | ||||||||
\(291\) | −14.3206 | −0.839490 | ||||||||
\(292\) | −4.14794 | −0.242740 | ||||||||
\(293\) | 18.8052 | 1.09861 | 0.549304 | − | 0.835622i | \(-0.314893\pi\) | ||||
0.549304 | + | 0.835622i | \(0.314893\pi\) | |||||||
\(294\) | −4.20417 | −0.245192 | ||||||||
\(295\) | −5.06230 | −0.294738 | ||||||||
\(296\) | −8.13959 | −0.473104 | ||||||||
\(297\) | 14.5844 | 0.846271 | ||||||||
\(298\) | −8.75424 | −0.507120 | ||||||||
\(299\) | 14.0813 | 0.814341 | ||||||||
\(300\) | 6.15458 | 0.355335 | ||||||||
\(301\) | −12.9685 | −0.747494 | ||||||||
\(302\) | −14.7565 | −0.849140 | ||||||||
\(303\) | −0.100458 | −0.00577118 | ||||||||
\(304\) | 3.17903 | 0.182330 | ||||||||
\(305\) | −1.33980 | −0.0767169 | ||||||||
\(306\) | −6.64778 | −0.380028 | ||||||||
\(307\) | −10.6421 | −0.607379 | −0.303690 | − | 0.952771i | \(-0.598219\pi\) | ||||
−0.303690 | + | 0.952771i | \(0.598219\pi\) | |||||||
\(308\) | 5.03661 | 0.286987 | ||||||||
\(309\) | −6.81827 | −0.387878 | ||||||||
\(310\) | −2.96505 | −0.168404 | ||||||||
\(311\) | −13.1201 | −0.743974 | −0.371987 | − | 0.928238i | \(-0.621323\pi\) | ||||
−0.371987 | + | 0.928238i | \(0.621323\pi\) | |||||||
\(312\) | −3.00835 | −0.170314 | ||||||||
\(313\) | −1.47324 | −0.0832725 | −0.0416363 | − | 0.999133i | \(-0.513257\pi\) | ||||
−0.0416363 | + | 0.999133i | \(0.513257\pi\) | |||||||
\(314\) | 11.1030 | 0.626580 | ||||||||
\(315\) | 1.16316 | 0.0655366 | ||||||||
\(316\) | −13.7362 | −0.772719 | ||||||||
\(317\) | 4.44230 | 0.249505 | 0.124752 | − | 0.992188i | \(-0.460186\pi\) | ||||
0.124752 | + | 0.992188i | \(0.460186\pi\) | |||||||
\(318\) | 16.1877 | 0.907762 | ||||||||
\(319\) | −12.9548 | −0.725329 | ||||||||
\(320\) | −0.444196 | −0.0248313 | ||||||||
\(321\) | −20.5818 | −1.14876 | ||||||||
\(322\) | 11.5680 | 0.644660 | ||||||||
\(323\) | −15.5646 | −0.866036 | ||||||||
\(324\) | −3.08302 | −0.171279 | ||||||||
\(325\) | 11.2745 | 0.625398 | ||||||||
\(326\) | −10.1334 | −0.561237 | ||||||||
\(327\) | 0.401805 | 0.0222199 | ||||||||
\(328\) | −1.24289 | −0.0686273 | ||||||||
\(329\) | −15.8762 | −0.875282 | ||||||||
\(330\) | −1.48661 | −0.0818351 | ||||||||
\(331\) | 13.2676 | 0.729251 | 0.364625 | − | 0.931154i | \(-0.381197\pi\) | ||||
0.364625 | + | 0.931154i | \(0.381197\pi\) | |||||||
\(332\) | 6.48484 | 0.355902 | ||||||||
\(333\) | −11.0519 | −0.605639 | ||||||||
\(334\) | −6.99047 | −0.382501 | ||||||||
\(335\) | 1.94721 | 0.106387 | ||||||||
\(336\) | −2.47141 | −0.134826 | ||||||||
\(337\) | 2.94659 | 0.160511 | 0.0802554 | − | 0.996774i | \(-0.474426\pi\) | ||||
0.0802554 | + | 0.996774i | \(0.474426\pi\) | |||||||
\(338\) | 7.48903 | 0.407350 | ||||||||
\(339\) | −17.7690 | −0.965081 | ||||||||
\(340\) | 2.17479 | 0.117945 | ||||||||
\(341\) | −17.4327 | −0.944033 | ||||||||
\(342\) | 4.31646 | 0.233407 | ||||||||
\(343\) | −19.8268 | −1.07055 | ||||||||
\(344\) | 6.72451 | 0.362561 | ||||||||
\(345\) | −3.41442 | −0.183826 | ||||||||
\(346\) | −22.5518 | −1.21239 | ||||||||
\(347\) | 35.3434 | 1.89733 | 0.948666 | − | 0.316281i | \(-0.102434\pi\) | ||||
0.948666 | + | 0.316281i | \(0.102434\pi\) | |||||||
\(348\) | 6.35678 | 0.340759 | ||||||||
\(349\) | 26.4974 | 1.41837 | 0.709187 | − | 0.705020i | \(-0.249062\pi\) | ||||
0.709187 | + | 0.705020i | \(0.249062\pi\) | |||||||
\(350\) | 9.26222 | 0.495086 | ||||||||
\(351\) | −13.1098 | −0.699747 | ||||||||
\(352\) | −2.61160 | −0.139199 | ||||||||
\(353\) | 14.2395 | 0.757893 | 0.378947 | − | 0.925419i | \(-0.376286\pi\) | ||||
0.378947 | + | 0.925419i | \(0.376286\pi\) | |||||||
\(354\) | 14.6045 | 0.776220 | ||||||||
\(355\) | −1.01777 | −0.0540177 | ||||||||
\(356\) | 2.80274 | 0.148545 | ||||||||
\(357\) | 12.1001 | 0.640403 | ||||||||
\(358\) | 14.8361 | 0.784112 | ||||||||
\(359\) | −29.0838 | −1.53498 | −0.767491 | − | 0.641059i | \(-0.778495\pi\) | ||||
−0.767491 | + | 0.641059i | \(0.778495\pi\) | |||||||
\(360\) | −0.603126 | −0.0317876 | ||||||||
\(361\) | −8.89379 | −0.468094 | ||||||||
\(362\) | 5.05705 | 0.265793 | ||||||||
\(363\) | 5.35600 | 0.281117 | ||||||||
\(364\) | −4.52735 | −0.237298 | ||||||||
\(365\) | 1.84250 | 0.0964409 | ||||||||
\(366\) | 3.86527 | 0.202041 | ||||||||
\(367\) | −17.1077 | −0.893013 | −0.446506 | − | 0.894780i | \(-0.647332\pi\) | ||||
−0.446506 | + | 0.894780i | \(0.647332\pi\) | |||||||
\(368\) | −5.99830 | −0.312683 | ||||||||
\(369\) | −1.68759 | −0.0878524 | ||||||||
\(370\) | 3.61558 | 0.187965 | ||||||||
\(371\) | 24.3614 | 1.26478 | ||||||||
\(372\) | 8.55404 | 0.443506 | ||||||||
\(373\) | 28.5179 | 1.47660 | 0.738300 | − | 0.674473i | \(-0.235629\pi\) | ||||
0.738300 | + | 0.674473i | \(0.235629\pi\) | |||||||
\(374\) | 12.7865 | 0.661172 | ||||||||
\(375\) | −5.58000 | −0.288150 | ||||||||
\(376\) | 8.23219 | 0.424543 | ||||||||
\(377\) | 11.6449 | 0.599744 | ||||||||
\(378\) | −10.7699 | −0.553943 | ||||||||
\(379\) | −2.11558 | −0.108670 | −0.0543351 | − | 0.998523i | \(-0.517304\pi\) | ||||
−0.0543351 | + | 0.998523i | \(0.517304\pi\) | |||||||
\(380\) | −1.41211 | −0.0724398 | ||||||||
\(381\) | 23.5185 | 1.20489 | ||||||||
\(382\) | −4.15023 | −0.212344 | ||||||||
\(383\) | −3.74914 | −0.191572 | −0.0957860 | − | 0.995402i | \(-0.530536\pi\) | ||||
−0.0957860 | + | 0.995402i | \(0.530536\pi\) | |||||||
\(384\) | 1.28149 | 0.0653956 | ||||||||
\(385\) | −2.23724 | −0.114020 | ||||||||
\(386\) | −13.2285 | −0.673311 | ||||||||
\(387\) | 9.13048 | 0.464129 | ||||||||
\(388\) | 11.1750 | 0.567325 | ||||||||
\(389\) | 1.59074 | 0.0806539 | 0.0403269 | − | 0.999187i | \(-0.487160\pi\) | ||||
0.0403269 | + | 0.999187i | \(0.487160\pi\) | |||||||
\(390\) | 1.33630 | 0.0676660 | ||||||||
\(391\) | 29.3678 | 1.48519 | ||||||||
\(392\) | 3.28070 | 0.165700 | ||||||||
\(393\) | 12.6418 | 0.637694 | ||||||||
\(394\) | 5.25500 | 0.264743 | ||||||||
\(395\) | 6.10155 | 0.307002 | ||||||||
\(396\) | −3.54602 | −0.178194 | ||||||||
\(397\) | −13.1087 | −0.657906 | −0.328953 | − | 0.944346i | \(-0.606696\pi\) | ||||
−0.328953 | + | 0.944346i | \(0.606696\pi\) | |||||||
\(398\) | −0.250345 | −0.0125486 | ||||||||
\(399\) | −7.85668 | −0.393326 | ||||||||
\(400\) | −4.80269 | −0.240134 | ||||||||
\(401\) | −34.2894 | −1.71233 | −0.856165 | − | 0.516703i | \(-0.827159\pi\) | ||||
−0.856165 | + | 0.516703i | \(0.827159\pi\) | |||||||
\(402\) | −5.61761 | −0.280181 | ||||||||
\(403\) | 15.6701 | 0.780582 | ||||||||
\(404\) | 0.0783921 | 0.00390015 | ||||||||
\(405\) | 1.36947 | 0.0680494 | ||||||||
\(406\) | 9.56651 | 0.474778 | ||||||||
\(407\) | 21.2574 | 1.05369 | ||||||||
\(408\) | −6.27418 | −0.310618 | ||||||||
\(409\) | 30.1685 | 1.49174 | 0.745868 | − | 0.666094i | \(-0.232035\pi\) | ||||
0.745868 | + | 0.666094i | \(0.232035\pi\) | |||||||
\(410\) | 0.552088 | 0.0272657 | ||||||||
\(411\) | −5.32030 | −0.262431 | ||||||||
\(412\) | 5.32059 | 0.262127 | ||||||||
\(413\) | 21.9788 | 1.08150 | ||||||||
\(414\) | −8.14444 | −0.400277 | ||||||||
\(415\) | −2.88054 | −0.141400 | ||||||||
\(416\) | 2.34755 | 0.115098 | ||||||||
\(417\) | 21.8538 | 1.07019 | ||||||||
\(418\) | −8.30236 | −0.406082 | ||||||||
\(419\) | −11.5348 | −0.563513 | −0.281757 | − | 0.959486i | \(-0.590917\pi\) | ||||
−0.281757 | + | 0.959486i | \(0.590917\pi\) | |||||||
\(420\) | 1.09779 | 0.0535667 | ||||||||
\(421\) | 9.40504 | 0.458374 | 0.229187 | − | 0.973382i | \(-0.426393\pi\) | ||||
0.229187 | + | 0.973382i | \(0.426393\pi\) | |||||||
\(422\) | −8.95055 | −0.435706 | ||||||||
\(423\) | 11.1776 | 0.543473 | ||||||||
\(424\) | −12.6320 | −0.613464 | ||||||||
\(425\) | 23.5141 | 1.14060 | ||||||||
\(426\) | 2.93623 | 0.142261 | ||||||||
\(427\) | 5.81697 | 0.281503 | ||||||||
\(428\) | 16.0609 | 0.776331 | ||||||||
\(429\) | 7.85661 | 0.379321 | ||||||||
\(430\) | −2.98700 | −0.144046 | ||||||||
\(431\) | −19.1709 | −0.923431 | −0.461716 | − | 0.887028i | \(-0.652766\pi\) | ||||
−0.461716 | + | 0.887028i | \(0.652766\pi\) | |||||||
\(432\) | 5.58445 | 0.268682 | ||||||||
\(433\) | 11.5169 | 0.553465 | 0.276732 | − | 0.960947i | \(-0.410748\pi\) | ||||
0.276732 | + | 0.960947i | \(0.410748\pi\) | |||||||
\(434\) | 12.8732 | 0.617935 | ||||||||
\(435\) | −2.82366 | −0.135384 | ||||||||
\(436\) | −0.313546 | −0.0150161 | ||||||||
\(437\) | −19.0688 | −0.912182 | ||||||||
\(438\) | −5.31553 | −0.253986 | ||||||||
\(439\) | −8.05954 | −0.384661 | −0.192330 | − | 0.981330i | \(-0.561605\pi\) | ||||
−0.192330 | + | 0.981330i | \(0.561605\pi\) | |||||||
\(440\) | 1.16007 | 0.0553039 | ||||||||
\(441\) | 4.45451 | 0.212119 | ||||||||
\(442\) | −11.4936 | −0.546696 | ||||||||
\(443\) | 40.5401 | 1.92612 | 0.963060 | − | 0.269286i | \(-0.0867878\pi\) | ||||
0.963060 | + | 0.269286i | \(0.0867878\pi\) | |||||||
\(444\) | −10.4308 | −0.495023 | ||||||||
\(445\) | −1.24497 | −0.0590171 | ||||||||
\(446\) | −13.5470 | −0.641470 | ||||||||
\(447\) | −11.2184 | −0.530614 | ||||||||
\(448\) | 1.92855 | 0.0911154 | ||||||||
\(449\) | 1.90466 | 0.0898865 | 0.0449433 | − | 0.998990i | \(-0.485689\pi\) | ||||
0.0449433 | + | 0.998990i | \(0.485689\pi\) | |||||||
\(450\) | −6.52105 | −0.307405 | ||||||||
\(451\) | 3.24594 | 0.152845 | ||||||||
\(452\) | 13.8659 | 0.652199 | ||||||||
\(453\) | −18.9102 | −0.888480 | ||||||||
\(454\) | −11.5920 | −0.544039 | ||||||||
\(455\) | 2.01103 | 0.0942788 | ||||||||
\(456\) | 4.07388 | 0.190777 | ||||||||
\(457\) | −2.20960 | −0.103361 | −0.0516803 | − | 0.998664i | \(-0.516458\pi\) | ||||
−0.0516803 | + | 0.998664i | \(0.516458\pi\) | |||||||
\(458\) | 4.42095 | 0.206577 | ||||||||
\(459\) | −27.3416 | −1.27620 | ||||||||
\(460\) | 2.66442 | 0.124229 | ||||||||
\(461\) | −16.2813 | −0.758298 | −0.379149 | − | 0.925336i | \(-0.623783\pi\) | ||||
−0.379149 | + | 0.925336i | \(0.623783\pi\) | |||||||
\(462\) | 6.45434 | 0.300283 | ||||||||
\(463\) | 11.0963 | 0.515690 | 0.257845 | − | 0.966186i | \(-0.416988\pi\) | ||||
0.257845 | + | 0.966186i | \(0.416988\pi\) | |||||||
\(464\) | −4.96047 | −0.230284 | ||||||||
\(465\) | −3.79967 | −0.176206 | ||||||||
\(466\) | 2.05348 | 0.0951258 | ||||||||
\(467\) | −41.3828 | −1.91497 | −0.957484 | − | 0.288485i | \(-0.906849\pi\) | ||||
−0.957484 | + | 0.288485i | \(0.906849\pi\) | |||||||
\(468\) | 3.18748 | 0.147341 | ||||||||
\(469\) | −8.45411 | −0.390374 | ||||||||
\(470\) | −3.65671 | −0.168671 | ||||||||
\(471\) | 14.2284 | 0.655609 | ||||||||
\(472\) | −11.3965 | −0.524568 | ||||||||
\(473\) | −17.5618 | −0.807490 | ||||||||
\(474\) | −17.6027 | −0.808519 | ||||||||
\(475\) | −15.2679 | −0.700538 | ||||||||
\(476\) | −9.44221 | −0.432783 | ||||||||
\(477\) | −17.1516 | −0.785318 | ||||||||
\(478\) | 8.04445 | 0.367945 | ||||||||
\(479\) | −21.5887 | −0.986413 | −0.493206 | − | 0.869912i | \(-0.664175\pi\) | ||||
−0.493206 | + | 0.869912i | \(0.664175\pi\) | |||||||
\(480\) | −0.569232 | −0.0259818 | ||||||||
\(481\) | −19.1081 | −0.871252 | ||||||||
\(482\) | 23.3128 | 1.06187 | ||||||||
\(483\) | 14.8242 | 0.674527 | ||||||||
\(484\) | −4.17952 | −0.189978 | ||||||||
\(485\) | −4.96390 | −0.225399 | ||||||||
\(486\) | 12.8025 | 0.580733 | ||||||||
\(487\) | 20.3941 | 0.924145 | 0.462072 | − | 0.886842i | \(-0.347106\pi\) | ||||
0.462072 | + | 0.886842i | \(0.347106\pi\) | |||||||
\(488\) | −3.01624 | −0.136539 | ||||||||
\(489\) | −12.9858 | −0.587239 | ||||||||
\(490\) | −1.45728 | −0.0658330 | ||||||||
\(491\) | 35.7075 | 1.61146 | 0.805728 | − | 0.592286i | \(-0.201774\pi\) | ||||
0.805728 | + | 0.592286i | \(0.201774\pi\) | |||||||
\(492\) | −1.59275 | −0.0718067 | ||||||||
\(493\) | 24.2866 | 1.09381 | ||||||||
\(494\) | 7.46291 | 0.335772 | ||||||||
\(495\) | 1.57513 | 0.0707967 | ||||||||
\(496\) | −6.67509 | −0.299720 | ||||||||
\(497\) | 4.41882 | 0.198211 | ||||||||
\(498\) | 8.31024 | 0.372391 | ||||||||
\(499\) | 5.46065 | 0.244452 | 0.122226 | − | 0.992502i | \(-0.460997\pi\) | ||||
0.122226 | + | 0.992502i | \(0.460997\pi\) | |||||||
\(500\) | 4.35432 | 0.194731 | ||||||||
\(501\) | −8.95819 | −0.400222 | ||||||||
\(502\) | −8.67424 | −0.387150 | ||||||||
\(503\) | 34.3443 | 1.53134 | 0.765668 | − | 0.643236i | \(-0.222409\pi\) | ||||
0.765668 | + | 0.643236i | \(0.222409\pi\) | |||||||
\(504\) | 2.61857 | 0.116640 | ||||||||
\(505\) | −0.0348215 | −0.00154954 | ||||||||
\(506\) | 15.6652 | 0.696402 | ||||||||
\(507\) | 9.59709 | 0.426222 | ||||||||
\(508\) | −18.3525 | −0.814261 | ||||||||
\(509\) | 31.3862 | 1.39117 | 0.695584 | − | 0.718445i | \(-0.255146\pi\) | ||||
0.695584 | + | 0.718445i | \(0.255146\pi\) | |||||||
\(510\) | 2.78697 | 0.123409 | ||||||||
\(511\) | −7.99950 | −0.353877 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 17.7531 | 0.783820 | ||||||||
\(514\) | 30.9625 | 1.36570 | ||||||||
\(515\) | −2.36339 | −0.104143 | ||||||||
\(516\) | 8.61737 | 0.379358 | ||||||||
\(517\) | −21.4992 | −0.945534 | ||||||||
\(518\) | −15.6976 | −0.689713 | ||||||||
\(519\) | −28.8998 | −1.26856 | ||||||||
\(520\) | −1.04277 | −0.0457285 | ||||||||
\(521\) | −1.21298 | −0.0531416 | −0.0265708 | − | 0.999647i | \(-0.508459\pi\) | ||||
−0.0265708 | + | 0.999647i | \(0.508459\pi\) | |||||||
\(522\) | −6.73529 | −0.294795 | ||||||||
\(523\) | 37.2660 | 1.62953 | 0.814764 | − | 0.579793i | \(-0.196867\pi\) | ||||
0.814764 | + | 0.579793i | \(0.196867\pi\) | |||||||
\(524\) | −9.86495 | −0.430952 | ||||||||
\(525\) | 11.8694 | 0.518024 | ||||||||
\(526\) | −15.4625 | −0.674199 | ||||||||
\(527\) | 32.6814 | 1.42362 | ||||||||
\(528\) | −3.34674 | −0.145648 | ||||||||
\(529\) | 12.9796 | 0.564330 | ||||||||
\(530\) | 5.61108 | 0.243730 | ||||||||
\(531\) | −15.4741 | −0.671519 | ||||||||
\(532\) | 6.13091 | 0.265809 | ||||||||
\(533\) | −2.91775 | −0.126382 | ||||||||
\(534\) | 3.59167 | 0.155427 | ||||||||
\(535\) | −7.13418 | −0.308437 | ||||||||
\(536\) | 4.38366 | 0.189345 | ||||||||
\(537\) | 19.0123 | 0.820440 | ||||||||
\(538\) | −14.6441 | −0.631351 | ||||||||
\(539\) | −8.56789 | −0.369045 | ||||||||
\(540\) | −2.48059 | −0.106748 | ||||||||
\(541\) | 36.4018 | 1.56504 | 0.782518 | − | 0.622628i | \(-0.213935\pi\) | ||||
0.782518 | + | 0.622628i | \(0.213935\pi\) | |||||||
\(542\) | −19.9045 | −0.854970 | ||||||||
\(543\) | 6.48054 | 0.278107 | ||||||||
\(544\) | 4.89602 | 0.209915 | ||||||||
\(545\) | 0.139276 | 0.00596594 | ||||||||
\(546\) | −5.80174 | −0.248292 | ||||||||
\(547\) | 19.9794 | 0.854259 | 0.427130 | − | 0.904190i | \(-0.359525\pi\) | ||||
0.427130 | + | 0.904190i | \(0.359525\pi\) | |||||||
\(548\) | 4.15166 | 0.177350 | ||||||||
\(549\) | −4.09543 | −0.174789 | ||||||||
\(550\) | 12.5427 | 0.534824 | ||||||||
\(551\) | −15.7695 | −0.671802 | ||||||||
\(552\) | −7.68674 | −0.327169 | ||||||||
\(553\) | −26.4908 | −1.12651 | ||||||||
\(554\) | −4.25582 | −0.180813 | ||||||||
\(555\) | 4.63331 | 0.196673 | ||||||||
\(556\) | −17.0535 | −0.723229 | ||||||||
\(557\) | −5.23383 | −0.221764 | −0.110882 | − | 0.993834i | \(-0.535368\pi\) | ||||
−0.110882 | + | 0.993834i | \(0.535368\pi\) | |||||||
\(558\) | −9.06339 | −0.383684 | ||||||||
\(559\) | 15.7861 | 0.667680 | ||||||||
\(560\) | −0.856654 | −0.0362003 | ||||||||
\(561\) | 16.3857 | 0.691804 | ||||||||
\(562\) | 6.91566 | 0.291720 | ||||||||
\(563\) | 12.6524 | 0.533236 | 0.266618 | − | 0.963802i | \(-0.414094\pi\) | ||||
0.266618 | + | 0.963802i | \(0.414094\pi\) | |||||||
\(564\) | 10.5494 | 0.444211 | ||||||||
\(565\) | −6.15920 | −0.259120 | ||||||||
\(566\) | 3.17045 | 0.133264 | ||||||||
\(567\) | −5.94576 | −0.249699 | ||||||||
\(568\) | −2.29127 | −0.0961394 | ||||||||
\(569\) | −2.61190 | −0.109496 | −0.0547482 | − | 0.998500i | \(-0.517436\pi\) | ||||
−0.0547482 | + | 0.998500i | \(0.517436\pi\) | |||||||
\(570\) | −1.80960 | −0.0757959 | ||||||||
\(571\) | 5.87976 | 0.246060 | 0.123030 | − | 0.992403i | \(-0.460739\pi\) | ||||
0.123030 | + | 0.992403i | \(0.460739\pi\) | |||||||
\(572\) | −6.13086 | −0.256344 | ||||||||
\(573\) | −5.31846 | −0.222182 | ||||||||
\(574\) | −2.39698 | −0.100048 | ||||||||
\(575\) | 28.8080 | 1.20138 | ||||||||
\(576\) | −1.35779 | −0.0565747 | ||||||||
\(577\) | −15.2383 | −0.634381 | −0.317190 | − | 0.948362i | \(-0.602739\pi\) | ||||
−0.317190 | + | 0.948362i | \(0.602739\pi\) | |||||||
\(578\) | −6.97100 | −0.289955 | ||||||||
\(579\) | −16.9521 | −0.704505 | ||||||||
\(580\) | 2.20342 | 0.0914922 | ||||||||
\(581\) | 12.5063 | 0.518850 | ||||||||
\(582\) | 14.3206 | 0.593609 | ||||||||
\(583\) | 32.9897 | 1.36630 | ||||||||
\(584\) | 4.14794 | 0.171643 | ||||||||
\(585\) | −1.41587 | −0.0585389 | ||||||||
\(586\) | −18.8052 | −0.776834 | ||||||||
\(587\) | 9.77351 | 0.403396 | 0.201698 | − | 0.979448i | \(-0.435354\pi\) | ||||
0.201698 | + | 0.979448i | \(0.435354\pi\) | |||||||
\(588\) | 4.20417 | 0.173377 | ||||||||
\(589\) | −21.2203 | −0.874367 | ||||||||
\(590\) | 5.06230 | 0.208411 | ||||||||
\(591\) | 6.73421 | 0.277009 | ||||||||
\(592\) | 8.13959 | 0.334535 | ||||||||
\(593\) | 11.4282 | 0.469298 | 0.234649 | − | 0.972080i | \(-0.424606\pi\) | ||||
0.234649 | + | 0.972080i | \(0.424606\pi\) | |||||||
\(594\) | −14.5844 | −0.598404 | ||||||||
\(595\) | 4.19420 | 0.171945 | ||||||||
\(596\) | 8.75424 | 0.358588 | ||||||||
\(597\) | −0.320813 | −0.0131300 | ||||||||
\(598\) | −14.0813 | −0.575826 | ||||||||
\(599\) | 28.5897 | 1.16814 | 0.584072 | − | 0.811702i | \(-0.301459\pi\) | ||||
0.584072 | + | 0.811702i | \(0.301459\pi\) | |||||||
\(600\) | −6.15458 | −0.251260 | ||||||||
\(601\) | 19.3689 | 0.790076 | 0.395038 | − | 0.918665i | \(-0.370731\pi\) | ||||
0.395038 | + | 0.918665i | \(0.370731\pi\) | |||||||
\(602\) | 12.9685 | 0.528558 | ||||||||
\(603\) | 5.95210 | 0.242388 | ||||||||
\(604\) | 14.7565 | 0.600432 | ||||||||
\(605\) | 1.85653 | 0.0754787 | ||||||||
\(606\) | 0.100458 | 0.00408084 | ||||||||
\(607\) | 1.49904 | 0.0608441 | 0.0304221 | − | 0.999537i | \(-0.490315\pi\) | ||||
0.0304221 | + | 0.999537i | \(0.490315\pi\) | |||||||
\(608\) | −3.17903 | −0.128927 | ||||||||
\(609\) | 12.2594 | 0.496774 | ||||||||
\(610\) | 1.33980 | 0.0542471 | ||||||||
\(611\) | 19.3254 | 0.781823 | ||||||||
\(612\) | 6.64778 | 0.268720 | ||||||||
\(613\) | −25.0088 | −1.01010 | −0.505048 | − | 0.863091i | \(-0.668525\pi\) | ||||
−0.505048 | + | 0.863091i | \(0.668525\pi\) | |||||||
\(614\) | 10.6421 | 0.429482 | ||||||||
\(615\) | 0.707494 | 0.0285289 | ||||||||
\(616\) | −5.03661 | −0.202931 | ||||||||
\(617\) | −0.274941 | −0.0110687 | −0.00553436 | − | 0.999985i | \(-0.501762\pi\) | ||||
−0.00553436 | + | 0.999985i | \(0.501762\pi\) | |||||||
\(618\) | 6.81827 | 0.274271 | ||||||||
\(619\) | 42.6333 | 1.71358 | 0.856789 | − | 0.515668i | \(-0.172456\pi\) | ||||
0.856789 | + | 0.515668i | \(0.172456\pi\) | |||||||
\(620\) | 2.96505 | 0.119079 | ||||||||
\(621\) | −33.4972 | −1.34420 | ||||||||
\(622\) | 13.1201 | 0.526069 | ||||||||
\(623\) | 5.40522 | 0.216556 | ||||||||
\(624\) | 3.00835 | 0.120430 | ||||||||
\(625\) | 22.0793 | 0.883171 | ||||||||
\(626\) | 1.47324 | 0.0588826 | ||||||||
\(627\) | −10.6394 | −0.424895 | ||||||||
\(628\) | −11.1030 | −0.443059 | ||||||||
\(629\) | −39.8516 | −1.58899 | ||||||||
\(630\) | −1.16316 | −0.0463413 | ||||||||
\(631\) | 9.11841 | 0.362998 | 0.181499 | − | 0.983391i | \(-0.441905\pi\) | ||||
0.181499 | + | 0.983391i | \(0.441905\pi\) | |||||||
\(632\) | 13.7362 | 0.546395 | ||||||||
\(633\) | −11.4700 | −0.455892 | ||||||||
\(634\) | −4.44230 | −0.176426 | ||||||||
\(635\) | 8.15212 | 0.323507 | ||||||||
\(636\) | −16.1877 | −0.641885 | ||||||||
\(637\) | 7.70159 | 0.305148 | ||||||||
\(638\) | 12.9548 | 0.512885 | ||||||||
\(639\) | −3.11106 | −0.123072 | ||||||||
\(640\) | 0.444196 | 0.0175584 | ||||||||
\(641\) | 33.9575 | 1.34124 | 0.670620 | − | 0.741801i | \(-0.266028\pi\) | ||||
0.670620 | + | 0.741801i | \(0.266028\pi\) | |||||||
\(642\) | 20.5818 | 0.812298 | ||||||||
\(643\) | −18.7186 | −0.738190 | −0.369095 | − | 0.929392i | \(-0.620332\pi\) | ||||
−0.369095 | + | 0.929392i | \(0.620332\pi\) | |||||||
\(644\) | −11.5680 | −0.455843 | ||||||||
\(645\) | −3.82780 | −0.150720 | ||||||||
\(646\) | 15.5646 | 0.612380 | ||||||||
\(647\) | −29.4523 | −1.15789 | −0.578945 | − | 0.815366i | \(-0.696536\pi\) | ||||
−0.578945 | + | 0.815366i | \(0.696536\pi\) | |||||||
\(648\) | 3.08302 | 0.121113 | ||||||||
\(649\) | 29.7632 | 1.16831 | ||||||||
\(650\) | −11.2745 | −0.442223 | ||||||||
\(651\) | 16.4969 | 0.646564 | ||||||||
\(652\) | 10.1334 | 0.396855 | ||||||||
\(653\) | 9.54567 | 0.373551 | 0.186775 | − | 0.982403i | \(-0.440196\pi\) | ||||
0.186775 | + | 0.982403i | \(0.440196\pi\) | |||||||
\(654\) | −0.401805 | −0.0157118 | ||||||||
\(655\) | 4.38198 | 0.171218 | ||||||||
\(656\) | 1.24289 | 0.0485268 | ||||||||
\(657\) | 5.63204 | 0.219727 | ||||||||
\(658\) | 15.8762 | 0.618918 | ||||||||
\(659\) | 10.0451 | 0.391301 | 0.195650 | − | 0.980674i | \(-0.437318\pi\) | ||||
0.195650 | + | 0.980674i | \(0.437318\pi\) | |||||||
\(660\) | 1.48661 | 0.0578661 | ||||||||
\(661\) | 0.515682 | 0.0200577 | 0.0100289 | − | 0.999950i | \(-0.496808\pi\) | ||||
0.0100289 | + | 0.999950i | \(0.496808\pi\) | |||||||
\(662\) | −13.2676 | −0.515658 | ||||||||
\(663\) | −14.7289 | −0.572024 | ||||||||
\(664\) | −6.48484 | −0.251661 | ||||||||
\(665\) | −2.72333 | −0.105606 | ||||||||
\(666\) | 11.0519 | 0.428251 | ||||||||
\(667\) | 29.7544 | 1.15209 | ||||||||
\(668\) | 6.99047 | 0.270469 | ||||||||
\(669\) | −17.3603 | −0.671189 | ||||||||
\(670\) | −1.94721 | −0.0752272 | ||||||||
\(671\) | 7.87723 | 0.304097 | ||||||||
\(672\) | 2.47141 | 0.0953367 | ||||||||
\(673\) | −50.0967 | −1.93109 | −0.965544 | − | 0.260240i | \(-0.916198\pi\) | ||||
−0.965544 | + | 0.260240i | \(0.916198\pi\) | |||||||
\(674\) | −2.94659 | −0.113498 | ||||||||
\(675\) | −26.8204 | −1.03232 | ||||||||
\(676\) | −7.48903 | −0.288040 | ||||||||
\(677\) | 43.0916 | 1.65614 | 0.828072 | − | 0.560622i | \(-0.189438\pi\) | ||||
0.828072 | + | 0.560622i | \(0.189438\pi\) | |||||||
\(678\) | 17.7690 | 0.682415 | ||||||||
\(679\) | 21.5515 | 0.827073 | ||||||||
\(680\) | −2.17479 | −0.0833996 | ||||||||
\(681\) | −14.8550 | −0.569244 | ||||||||
\(682\) | 17.4327 | 0.667532 | ||||||||
\(683\) | −37.9121 | −1.45067 | −0.725334 | − | 0.688398i | \(-0.758314\pi\) | ||||
−0.725334 | + | 0.688398i | \(0.758314\pi\) | |||||||
\(684\) | −4.31646 | −0.165044 | ||||||||
\(685\) | −1.84415 | −0.0704615 | ||||||||
\(686\) | 19.8268 | 0.756992 | ||||||||
\(687\) | 5.66538 | 0.216148 | ||||||||
\(688\) | −6.72451 | −0.256369 | ||||||||
\(689\) | −29.6542 | −1.12973 | ||||||||
\(690\) | 3.41442 | 0.129985 | ||||||||
\(691\) | 50.5948 | 1.92472 | 0.962359 | − | 0.271781i | \(-0.0876125\pi\) | ||||
0.962359 | + | 0.271781i | \(0.0876125\pi\) | |||||||
\(692\) | 22.5518 | 0.857290 | ||||||||
\(693\) | −6.83866 | −0.259779 | ||||||||
\(694\) | −35.3434 | −1.34162 | ||||||||
\(695\) | 7.57510 | 0.287340 | ||||||||
\(696\) | −6.35678 | −0.240953 | ||||||||
\(697\) | −6.08522 | −0.230494 | ||||||||
\(698\) | −26.4974 | −1.00294 | ||||||||
\(699\) | 2.63151 | 0.0995329 | ||||||||
\(700\) | −9.26222 | −0.350079 | ||||||||
\(701\) | 13.0332 | 0.492256 | 0.246128 | − | 0.969237i | \(-0.420842\pi\) | ||||
0.246128 | + | 0.969237i | \(0.420842\pi\) | |||||||
\(702\) | 13.1098 | 0.494796 | ||||||||
\(703\) | 25.8760 | 0.975931 | ||||||||
\(704\) | 2.61160 | 0.0984285 | ||||||||
\(705\) | −4.68602 | −0.176486 | ||||||||
\(706\) | −14.2395 | −0.535912 | ||||||||
\(707\) | 0.151183 | 0.00568582 | ||||||||
\(708\) | −14.6045 | −0.548871 | ||||||||
\(709\) | −33.3029 | −1.25072 | −0.625358 | − | 0.780338i | \(-0.715047\pi\) | ||||
−0.625358 | + | 0.780338i | \(0.715047\pi\) | |||||||
\(710\) | 1.01777 | 0.0381963 | ||||||||
\(711\) | 18.6508 | 0.699461 | ||||||||
\(712\) | −2.80274 | −0.105037 | ||||||||
\(713\) | 40.0392 | 1.49948 | ||||||||
\(714\) | −12.1001 | −0.452834 | ||||||||
\(715\) | 2.72331 | 0.101846 | ||||||||
\(716\) | −14.8361 | −0.554451 | ||||||||
\(717\) | 10.3089 | 0.384991 | ||||||||
\(718\) | 29.0838 | 1.08540 | ||||||||
\(719\) | 18.3802 | 0.685464 | 0.342732 | − | 0.939433i | \(-0.388648\pi\) | ||||
0.342732 | + | 0.939433i | \(0.388648\pi\) | |||||||
\(720\) | 0.603126 | 0.0224772 | ||||||||
\(721\) | 10.2610 | 0.382140 | ||||||||
\(722\) | 8.89379 | 0.330993 | ||||||||
\(723\) | 29.8750 | 1.11106 | ||||||||
\(724\) | −5.05705 | −0.187944 | ||||||||
\(725\) | 23.8236 | 0.884786 | ||||||||
\(726\) | −5.35600 | −0.198780 | ||||||||
\(727\) | 29.5150 | 1.09465 | 0.547325 | − | 0.836920i | \(-0.315646\pi\) | ||||
0.547325 | + | 0.836920i | \(0.315646\pi\) | |||||||
\(728\) | 4.52735 | 0.167795 | ||||||||
\(729\) | 25.6553 | 0.950197 | ||||||||
\(730\) | −1.84250 | −0.0681940 | ||||||||
\(731\) | 32.9233 | 1.21771 | ||||||||
\(732\) | −3.86527 | −0.142865 | ||||||||
\(733\) | −20.5853 | −0.760335 | −0.380167 | − | 0.924918i | \(-0.624134\pi\) | ||||
−0.380167 | + | 0.924918i | \(0.624134\pi\) | |||||||
\(734\) | 17.1077 | 0.631455 | ||||||||
\(735\) | −1.86748 | −0.0688830 | ||||||||
\(736\) | 5.99830 | 0.221100 | ||||||||
\(737\) | −11.4484 | −0.421707 | ||||||||
\(738\) | 1.68759 | 0.0621210 | ||||||||
\(739\) | −45.7499 | −1.68294 | −0.841468 | − | 0.540307i | \(-0.818308\pi\) | ||||
−0.841468 | + | 0.540307i | \(0.818308\pi\) | |||||||
\(740\) | −3.61558 | −0.132911 | ||||||||
\(741\) | 9.56362 | 0.351328 | ||||||||
\(742\) | −24.3614 | −0.894335 | ||||||||
\(743\) | 4.75347 | 0.174388 | 0.0871940 | − | 0.996191i | \(-0.472210\pi\) | ||||
0.0871940 | + | 0.996191i | \(0.472210\pi\) | |||||||
\(744\) | −8.55404 | −0.313606 | ||||||||
\(745\) | −3.88860 | −0.142467 | ||||||||
\(746\) | −28.5179 | −1.04411 | ||||||||
\(747\) | −8.80507 | −0.322161 | ||||||||
\(748\) | −12.7865 | −0.467519 | ||||||||
\(749\) | 30.9742 | 1.13177 | ||||||||
\(750\) | 5.58000 | 0.203753 | ||||||||
\(751\) | 3.65764 | 0.133469 | 0.0667346 | − | 0.997771i | \(-0.478742\pi\) | ||||
0.0667346 | + | 0.997771i | \(0.478742\pi\) | |||||||
\(752\) | −8.23219 | −0.300197 | ||||||||
\(753\) | −11.1159 | −0.405087 | ||||||||
\(754\) | −11.6449 | −0.424083 | ||||||||
\(755\) | −6.55477 | −0.238553 | ||||||||
\(756\) | 10.7699 | 0.391697 | ||||||||
\(757\) | −1.61821 | −0.0588149 | −0.0294075 | − | 0.999568i | \(-0.509362\pi\) | ||||
−0.0294075 | + | 0.999568i | \(0.509362\pi\) | |||||||
\(758\) | 2.11558 | 0.0768414 | ||||||||
\(759\) | 20.0747 | 0.728666 | ||||||||
\(760\) | 1.41211 | 0.0512227 | ||||||||
\(761\) | 26.9525 | 0.977027 | 0.488514 | − | 0.872556i | \(-0.337539\pi\) | ||||
0.488514 | + | 0.872556i | \(0.337539\pi\) | |||||||
\(762\) | −23.5185 | −0.851985 | ||||||||
\(763\) | −0.604689 | −0.0218912 | ||||||||
\(764\) | 4.15023 | 0.150150 | ||||||||
\(765\) | −2.95292 | −0.106763 | ||||||||
\(766\) | 3.74914 | 0.135462 | ||||||||
\(767\) | −26.7539 | −0.966026 | ||||||||
\(768\) | −1.28149 | −0.0462417 | ||||||||
\(769\) | −12.2465 | −0.441621 | −0.220810 | − | 0.975317i | \(-0.570870\pi\) | ||||
−0.220810 | + | 0.975317i | \(0.570870\pi\) | |||||||
\(770\) | 2.23724 | 0.0806246 | ||||||||
\(771\) | 39.6780 | 1.42897 | ||||||||
\(772\) | 13.2285 | 0.476103 | ||||||||
\(773\) | −19.6075 | −0.705235 | −0.352617 | − | 0.935768i | \(-0.614708\pi\) | ||||
−0.352617 | + | 0.935768i | \(0.614708\pi\) | |||||||
\(774\) | −9.13048 | −0.328188 | ||||||||
\(775\) | 32.0584 | 1.15157 | ||||||||
\(776\) | −11.1750 | −0.401159 | ||||||||
\(777\) | −20.1163 | −0.721667 | ||||||||
\(778\) | −1.59074 | −0.0570309 | ||||||||
\(779\) | 3.95119 | 0.141566 | ||||||||
\(780\) | −1.33630 | −0.0478471 | ||||||||
\(781\) | 5.98388 | 0.214120 | ||||||||
\(782\) | −29.3678 | −1.05019 | ||||||||
\(783\) | −27.7015 | −0.989971 | ||||||||
\(784\) | −3.28070 | −0.117168 | ||||||||
\(785\) | 4.93193 | 0.176028 | ||||||||
\(786\) | −12.6418 | −0.450918 | ||||||||
\(787\) | −0.501678 | −0.0178829 | −0.00894145 | − | 0.999960i | \(-0.502846\pi\) | ||||
−0.00894145 | + | 0.999960i | \(0.502846\pi\) | |||||||
\(788\) | −5.25500 | −0.187202 | ||||||||
\(789\) | −19.8150 | −0.705434 | ||||||||
\(790\) | −6.10155 | −0.217083 | ||||||||
\(791\) | 26.7411 | 0.950805 | ||||||||
\(792\) | 3.54602 | 0.126002 | ||||||||
\(793\) | −7.08076 | −0.251445 | ||||||||
\(794\) | 13.1087 | 0.465210 | ||||||||
\(795\) | 7.19053 | 0.255022 | ||||||||
\(796\) | 0.250345 | 0.00887323 | ||||||||
\(797\) | −13.6881 | −0.484859 | −0.242430 | − | 0.970169i | \(-0.577944\pi\) | ||||
−0.242430 | + | 0.970169i | \(0.577944\pi\) | |||||||
\(798\) | 7.85668 | 0.278123 | ||||||||
\(799\) | 40.3049 | 1.42589 | ||||||||
\(800\) | 4.80269 | 0.169801 | ||||||||
\(801\) | −3.80554 | −0.134462 | ||||||||
\(802\) | 34.2894 | 1.21080 | ||||||||
\(803\) | −10.8328 | −0.382280 | ||||||||
\(804\) | 5.61761 | 0.198118 | ||||||||
\(805\) | 5.13847 | 0.181107 | ||||||||
\(806\) | −15.6701 | −0.551955 | ||||||||
\(807\) | −18.7662 | −0.660601 | ||||||||
\(808\) | −0.0783921 | −0.00275782 | ||||||||
\(809\) | −13.8045 | −0.485340 | −0.242670 | − | 0.970109i | \(-0.578023\pi\) | ||||
−0.242670 | + | 0.970109i | \(0.578023\pi\) | |||||||
\(810\) | −1.36947 | −0.0481182 | ||||||||
\(811\) | 24.0332 | 0.843921 | 0.421960 | − | 0.906614i | \(-0.361342\pi\) | ||||
0.421960 | + | 0.906614i | \(0.361342\pi\) | |||||||
\(812\) | −9.56651 | −0.335719 | ||||||||
\(813\) | −25.5073 | −0.894580 | ||||||||
\(814\) | −21.2574 | −0.745071 | ||||||||
\(815\) | −4.50122 | −0.157671 | ||||||||
\(816\) | 6.27418 | 0.219640 | ||||||||
\(817\) | −21.3774 | −0.747900 | ||||||||
\(818\) | −30.1685 | −1.05482 | ||||||||
\(819\) | 6.14721 | 0.214801 | ||||||||
\(820\) | −0.552088 | −0.0192798 | ||||||||
\(821\) | 47.2729 | 1.64983 | 0.824917 | − | 0.565253i | \(-0.191222\pi\) | ||||
0.824917 | + | 0.565253i | \(0.191222\pi\) | |||||||
\(822\) | 5.32030 | 0.185567 | ||||||||
\(823\) | 42.7677 | 1.49079 | 0.745395 | − | 0.666623i | \(-0.232261\pi\) | ||||
0.745395 | + | 0.666623i | \(0.232261\pi\) | |||||||
\(824\) | −5.32059 | −0.185352 | ||||||||
\(825\) | 16.0733 | 0.559602 | ||||||||
\(826\) | −21.9788 | −0.764739 | ||||||||
\(827\) | −7.16581 | −0.249180 | −0.124590 | − | 0.992208i | \(-0.539762\pi\) | ||||
−0.124590 | + | 0.992208i | \(0.539762\pi\) | |||||||
\(828\) | 8.14444 | 0.283039 | ||||||||
\(829\) | 6.01419 | 0.208881 | 0.104441 | − | 0.994531i | \(-0.466695\pi\) | ||||
0.104441 | + | 0.994531i | \(0.466695\pi\) | |||||||
\(830\) | 2.88054 | 0.0999852 | ||||||||
\(831\) | −5.45378 | −0.189189 | ||||||||
\(832\) | −2.34755 | −0.0813865 | ||||||||
\(833\) | 16.0624 | 0.556528 | ||||||||
\(834\) | −21.8538 | −0.756736 | ||||||||
\(835\) | −3.10514 | −0.107458 | ||||||||
\(836\) | 8.30236 | 0.287143 | ||||||||
\(837\) | −37.2767 | −1.28847 | ||||||||
\(838\) | 11.5348 | 0.398464 | ||||||||
\(839\) | 53.1519 | 1.83501 | 0.917503 | − | 0.397728i | \(-0.130201\pi\) | ||||
0.917503 | + | 0.397728i | \(0.130201\pi\) | |||||||
\(840\) | −1.09779 | −0.0378774 | ||||||||
\(841\) | −4.39374 | −0.151508 | ||||||||
\(842\) | −9.40504 | −0.324119 | ||||||||
\(843\) | 8.86233 | 0.305235 | ||||||||
\(844\) | 8.95055 | 0.308091 | ||||||||
\(845\) | 3.32660 | 0.114439 | ||||||||
\(846\) | −11.1776 | −0.384294 | ||||||||
\(847\) | −8.06042 | −0.276959 | ||||||||
\(848\) | 12.6320 | 0.433784 | ||||||||
\(849\) | 4.06290 | 0.139438 | ||||||||
\(850\) | −23.5141 | −0.806526 | ||||||||
\(851\) | −48.8237 | −1.67365 | ||||||||
\(852\) | −2.93623 | −0.100593 | ||||||||
\(853\) | 22.4049 | 0.767130 | 0.383565 | − | 0.923514i | \(-0.374696\pi\) | ||||
0.383565 | + | 0.923514i | \(0.374696\pi\) | |||||||
\(854\) | −5.81697 | −0.199053 | ||||||||
\(855\) | 1.91736 | 0.0655722 | ||||||||
\(856\) | −16.0609 | −0.548949 | ||||||||
\(857\) | 53.7524 | 1.83615 | 0.918073 | − | 0.396412i | \(-0.129745\pi\) | ||||
0.918073 | + | 0.396412i | \(0.129745\pi\) | |||||||
\(858\) | −7.85661 | −0.268220 | ||||||||
\(859\) | −41.4151 | −1.41306 | −0.706532 | − | 0.707681i | \(-0.749741\pi\) | ||||
−0.706532 | + | 0.707681i | \(0.749741\pi\) | |||||||
\(860\) | 2.98700 | 0.101856 | ||||||||
\(861\) | −3.07170 | −0.104683 | ||||||||
\(862\) | 19.1709 | 0.652964 | ||||||||
\(863\) | 47.6234 | 1.62112 | 0.810560 | − | 0.585656i | \(-0.199163\pi\) | ||||
0.810560 | + | 0.585656i | \(0.199163\pi\) | |||||||
\(864\) | −5.58445 | −0.189987 | ||||||||
\(865\) | −10.0174 | −0.340603 | ||||||||
\(866\) | −11.5169 | −0.391359 | ||||||||
\(867\) | −8.93325 | −0.303389 | ||||||||
\(868\) | −12.8732 | −0.436946 | ||||||||
\(869\) | −35.8734 | −1.21692 | ||||||||
\(870\) | 2.82366 | 0.0957309 | ||||||||
\(871\) | 10.2908 | 0.348692 | ||||||||
\(872\) | 0.313546 | 0.0106180 | ||||||||
\(873\) | −15.1733 | −0.513540 | ||||||||
\(874\) | 19.0688 | 0.645010 | ||||||||
\(875\) | 8.39752 | 0.283888 | ||||||||
\(876\) | 5.31553 | 0.179595 | ||||||||
\(877\) | −8.03858 | −0.271444 | −0.135722 | − | 0.990747i | \(-0.543335\pi\) | ||||
−0.135722 | + | 0.990747i | \(0.543335\pi\) | |||||||
\(878\) | 8.05954 | 0.271996 | ||||||||
\(879\) | −24.0986 | −0.812824 | ||||||||
\(880\) | −1.16007 | −0.0391058 | ||||||||
\(881\) | −15.3881 | −0.518439 | −0.259220 | − | 0.965818i | \(-0.583465\pi\) | ||||
−0.259220 | + | 0.965818i | \(0.583465\pi\) | |||||||
\(882\) | −4.45451 | −0.149991 | ||||||||
\(883\) | 56.4447 | 1.89952 | 0.949758 | − | 0.312985i | \(-0.101329\pi\) | ||||
0.949758 | + | 0.312985i | \(0.101329\pi\) | |||||||
\(884\) | 11.4936 | 0.386572 | ||||||||
\(885\) | 6.48727 | 0.218067 | ||||||||
\(886\) | −40.5401 | −1.36197 | ||||||||
\(887\) | 3.80241 | 0.127672 | 0.0638362 | − | 0.997960i | \(-0.479666\pi\) | ||||
0.0638362 | + | 0.997960i | \(0.479666\pi\) | |||||||
\(888\) | 10.4308 | 0.350034 | ||||||||
\(889\) | −35.3937 | −1.18707 | ||||||||
\(890\) | 1.24497 | 0.0417314 | ||||||||
\(891\) | −8.05164 | −0.269740 | ||||||||
\(892\) | 13.5470 | 0.453588 | ||||||||
\(893\) | −26.1703 | −0.875757 | ||||||||
\(894\) | 11.2184 | 0.375201 | ||||||||
\(895\) | 6.59014 | 0.220284 | ||||||||
\(896\) | −1.92855 | −0.0644283 | ||||||||
\(897\) | −18.0450 | −0.602504 | ||||||||
\(898\) | −1.90466 | −0.0635594 | ||||||||
\(899\) | 33.1116 | 1.10433 | ||||||||
\(900\) | 6.52105 | 0.217368 | ||||||||
\(901\) | −61.8464 | −2.06040 | ||||||||
\(902\) | −3.24594 | −0.108078 | ||||||||
\(903\) | 16.6190 | 0.553046 | ||||||||
\(904\) | −13.8659 | −0.461174 | ||||||||
\(905\) | 2.24632 | 0.0746703 | ||||||||
\(906\) | 18.9102 | 0.628250 | ||||||||
\(907\) | −22.5071 | −0.747337 | −0.373669 | − | 0.927562i | \(-0.621900\pi\) | ||||
−0.373669 | + | 0.927562i | \(0.621900\pi\) | |||||||
\(908\) | 11.5920 | 0.384694 | ||||||||
\(909\) | −0.106440 | −0.00353040 | ||||||||
\(910\) | −2.01103 | −0.0666652 | ||||||||
\(911\) | 13.0053 | 0.430884 | 0.215442 | − | 0.976517i | \(-0.430881\pi\) | ||||
0.215442 | + | 0.976517i | \(0.430881\pi\) | |||||||
\(912\) | −4.07388 | −0.134900 | ||||||||
\(913\) | 16.9358 | 0.560495 | ||||||||
\(914\) | 2.20960 | 0.0730870 | ||||||||
\(915\) | 1.71694 | 0.0567603 | ||||||||
\(916\) | −4.42095 | −0.146072 | ||||||||
\(917\) | −19.0250 | −0.628262 | ||||||||
\(918\) | 27.3416 | 0.902407 | ||||||||
\(919\) | −8.14130 | −0.268557 | −0.134278 | − | 0.990944i | \(-0.542872\pi\) | ||||
−0.134278 | + | 0.990944i | \(0.542872\pi\) | |||||||
\(920\) | −2.66442 | −0.0878434 | ||||||||
\(921\) | 13.6378 | 0.449379 | ||||||||
\(922\) | 16.2813 | 0.536197 | ||||||||
\(923\) | −5.37885 | −0.177047 | ||||||||
\(924\) | −6.45434 | −0.212332 | ||||||||
\(925\) | −39.0919 | −1.28533 | ||||||||
\(926\) | −11.0963 | −0.364648 | ||||||||
\(927\) | −7.22426 | −0.237276 | ||||||||
\(928\) | 4.96047 | 0.162835 | ||||||||
\(929\) | −4.08394 | −0.133990 | −0.0669948 | − | 0.997753i | \(-0.521341\pi\) | ||||
−0.0669948 | + | 0.997753i | \(0.521341\pi\) | |||||||
\(930\) | 3.79967 | 0.124596 | ||||||||
\(931\) | −10.4294 | −0.341811 | ||||||||
\(932\) | −2.05348 | −0.0672641 | ||||||||
\(933\) | 16.8133 | 0.550441 | ||||||||
\(934\) | 41.3828 | 1.35409 | ||||||||
\(935\) | 5.67970 | 0.185746 | ||||||||
\(936\) | −3.18748 | −0.104186 | ||||||||
\(937\) | −2.04053 | −0.0666612 | −0.0333306 | − | 0.999444i | \(-0.510611\pi\) | ||||
−0.0333306 | + | 0.999444i | \(0.510611\pi\) | |||||||
\(938\) | 8.45411 | 0.276036 | ||||||||
\(939\) | 1.88794 | 0.0616105 | ||||||||
\(940\) | 3.65671 | 0.119269 | ||||||||
\(941\) | 38.3103 | 1.24888 | 0.624439 | − | 0.781073i | \(-0.285327\pi\) | ||||
0.624439 | + | 0.781073i | \(0.285327\pi\) | |||||||
\(942\) | −14.2284 | −0.463586 | ||||||||
\(943\) | −7.45524 | −0.242776 | ||||||||
\(944\) | 11.3965 | 0.370925 | ||||||||
\(945\) | −4.78395 | −0.155622 | ||||||||
\(946\) | 17.5618 | 0.570982 | ||||||||
\(947\) | −3.35828 | −0.109129 | −0.0545647 | − | 0.998510i | \(-0.517377\pi\) | ||||
−0.0545647 | + | 0.998510i | \(0.517377\pi\) | |||||||
\(948\) | 17.6027 | 0.571709 | ||||||||
\(949\) | 9.73748 | 0.316092 | ||||||||
\(950\) | 15.2679 | 0.495355 | ||||||||
\(951\) | −5.69275 | −0.184600 | ||||||||
\(952\) | 9.44221 | 0.306024 | ||||||||
\(953\) | 3.07212 | 0.0995158 | 0.0497579 | − | 0.998761i | \(-0.484155\pi\) | ||||
0.0497579 | + | 0.998761i | \(0.484155\pi\) | |||||||
\(954\) | 17.1516 | 0.555304 | ||||||||
\(955\) | −1.84352 | −0.0596548 | ||||||||
\(956\) | −8.04445 | −0.260176 | ||||||||
\(957\) | 16.6014 | 0.536646 | ||||||||
\(958\) | 21.5887 | 0.697499 | ||||||||
\(959\) | 8.00668 | 0.258549 | ||||||||
\(960\) | 0.569232 | 0.0183719 | ||||||||
\(961\) | 13.5568 | 0.437318 | ||||||||
\(962\) | 19.1081 | 0.616068 | ||||||||
\(963\) | −21.8073 | −0.702731 | ||||||||
\(964\) | −23.3128 | −0.750853 | ||||||||
\(965\) | −5.87603 | −0.189156 | ||||||||
\(966\) | −14.8242 | −0.476962 | ||||||||
\(967\) | 43.4270 | 1.39652 | 0.698259 | − | 0.715846i | \(-0.253959\pi\) | ||||
0.698259 | + | 0.715846i | \(0.253959\pi\) | |||||||
\(968\) | 4.17952 | 0.134335 | ||||||||
\(969\) | 19.9458 | 0.640751 | ||||||||
\(970\) | 4.96390 | 0.159381 | ||||||||
\(971\) | 12.8866 | 0.413552 | 0.206776 | − | 0.978388i | \(-0.433703\pi\) | ||||
0.206776 | + | 0.978388i | \(0.433703\pi\) | |||||||
\(972\) | −12.8025 | −0.410640 | ||||||||
\(973\) | −32.8885 | −1.05436 | ||||||||
\(974\) | −20.3941 | −0.653469 | ||||||||
\(975\) | −14.4482 | −0.462711 | ||||||||
\(976\) | 3.01624 | 0.0965475 | ||||||||
\(977\) | −24.3447 | −0.778855 | −0.389427 | − | 0.921057i | \(-0.627327\pi\) | ||||
−0.389427 | + | 0.921057i | \(0.627327\pi\) | |||||||
\(978\) | 12.9858 | 0.415241 | ||||||||
\(979\) | 7.31965 | 0.233937 | ||||||||
\(980\) | 1.45728 | 0.0465510 | ||||||||
\(981\) | 0.425731 | 0.0135925 | ||||||||
\(982\) | −35.7075 | −1.13947 | ||||||||
\(983\) | 26.7994 | 0.854769 | 0.427385 | − | 0.904070i | \(-0.359435\pi\) | ||||
0.427385 | + | 0.904070i | \(0.359435\pi\) | |||||||
\(984\) | 1.59275 | 0.0507750 | ||||||||
\(985\) | 2.33425 | 0.0743755 | ||||||||
\(986\) | −24.2866 | −0.773441 | ||||||||
\(987\) | 20.3451 | 0.647592 | ||||||||
\(988\) | −7.46291 | −0.237427 | ||||||||
\(989\) | 40.3356 | 1.28260 | ||||||||
\(990\) | −1.57513 | −0.0500608 | ||||||||
\(991\) | −21.1945 | −0.673264 | −0.336632 | − | 0.941636i | \(-0.609288\pi\) | ||||
−0.336632 | + | 0.941636i | \(0.609288\pi\) | |||||||
\(992\) | 6.67509 | 0.211934 | ||||||||
\(993\) | −17.0022 | −0.539548 | ||||||||
\(994\) | −4.41882 | −0.140156 | ||||||||
\(995\) | −0.111202 | −0.00352535 | ||||||||
\(996\) | −8.31024 | −0.263320 | ||||||||
\(997\) | −3.80139 | −0.120391 | −0.0601956 | − | 0.998187i | \(-0.519172\pi\) | ||||
−0.0601956 | + | 0.998187i | \(0.519172\pi\) | |||||||
\(998\) | −5.46065 | −0.172854 | ||||||||
\(999\) | 45.4551 | 1.43814 |
(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 | 8002.2.a.e.1.24 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.24 | ✓ | 77 | 1.1 | even | 1 | trivial |