Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | 0.237080 | 0.136878 | 0.0684390 | − | 0.997655i | \(-0.478198\pi\) | ||||
0.0684390 | + | 0.997655i | \(0.478198\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.796437 | 0.356177 | 0.178089 | − | 0.984014i | \(-0.443009\pi\) | ||||
0.178089 | + | 0.984014i | \(0.443009\pi\) | |||||||
\(6\) | −0.237080 | −0.0967874 | ||||||||
\(7\) | 2.80350 | 1.05962 | 0.529811 | − | 0.848116i | \(-0.322263\pi\) | ||||
0.529811 | + | 0.848116i | \(0.322263\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.94379 | −0.981264 | ||||||||
\(10\) | −0.796437 | −0.251855 | ||||||||
\(11\) | 4.74002 | 1.42917 | 0.714584 | − | 0.699549i | \(-0.246616\pi\) | ||||
0.714584 | + | 0.699549i | \(0.246616\pi\) | |||||||
\(12\) | 0.237080 | 0.0684390 | ||||||||
\(13\) | −2.18494 | −0.605995 | −0.302997 | − | 0.952991i | \(-0.597987\pi\) | ||||
−0.302997 | + | 0.952991i | \(0.597987\pi\) | |||||||
\(14\) | −2.80350 | −0.749266 | ||||||||
\(15\) | 0.188819 | 0.0487529 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.02982 | 1.46245 | 0.731223 | − | 0.682138i | \(-0.238950\pi\) | ||||
0.731223 | + | 0.682138i | \(0.238950\pi\) | |||||||
\(18\) | 2.94379 | 0.693859 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.796437 | 0.178089 | ||||||||
\(21\) | 0.664653 | 0.145039 | ||||||||
\(22\) | −4.74002 | −1.01057 | ||||||||
\(23\) | −6.41578 | −1.33778 | −0.668891 | − | 0.743360i | \(-0.733231\pi\) | ||||
−0.668891 | + | 0.743360i | \(0.733231\pi\) | |||||||
\(24\) | −0.237080 | −0.0483937 | ||||||||
\(25\) | −4.36569 | −0.873138 | ||||||||
\(26\) | 2.18494 | 0.428503 | ||||||||
\(27\) | −1.40915 | −0.271192 | ||||||||
\(28\) | 2.80350 | 0.529811 | ||||||||
\(29\) | 3.23999 | 0.601650 | 0.300825 | − | 0.953679i | \(-0.402738\pi\) | ||||
0.300825 | + | 0.953679i | \(0.402738\pi\) | |||||||
\(30\) | −0.188819 | −0.0344735 | ||||||||
\(31\) | 0.792931 | 0.142415 | 0.0712073 | − | 0.997462i | \(-0.477315\pi\) | ||||
0.0712073 | + | 0.997462i | \(0.477315\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.12376 | 0.195622 | ||||||||
\(34\) | −6.02982 | −1.03411 | ||||||||
\(35\) | 2.23281 | 0.377413 | ||||||||
\(36\) | −2.94379 | −0.490632 | ||||||||
\(37\) | 11.7320 | 1.92872 | 0.964361 | − | 0.264589i | \(-0.0852362\pi\) | ||||
0.964361 | + | 0.264589i | \(0.0852362\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −0.518006 | −0.0829474 | ||||||||
\(40\) | −0.796437 | −0.125928 | ||||||||
\(41\) | −3.14607 | −0.491333 | −0.245667 | − | 0.969354i | \(-0.579007\pi\) | ||||
−0.245667 | + | 0.969354i | \(0.579007\pi\) | |||||||
\(42\) | −0.664653 | −0.102558 | ||||||||
\(43\) | 1.10829 | 0.169012 | 0.0845061 | − | 0.996423i | \(-0.473069\pi\) | ||||
0.0845061 | + | 0.996423i | \(0.473069\pi\) | |||||||
\(44\) | 4.74002 | 0.714584 | ||||||||
\(45\) | −2.34454 | −0.349504 | ||||||||
\(46\) | 6.41578 | 0.945955 | ||||||||
\(47\) | 4.60234 | 0.671321 | 0.335660 | − | 0.941983i | \(-0.391041\pi\) | ||||
0.335660 | + | 0.941983i | \(0.391041\pi\) | |||||||
\(48\) | 0.237080 | 0.0342195 | ||||||||
\(49\) | 0.859599 | 0.122800 | ||||||||
\(50\) | 4.36569 | 0.617402 | ||||||||
\(51\) | 1.42955 | 0.200177 | ||||||||
\(52\) | −2.18494 | −0.302997 | ||||||||
\(53\) | −4.63474 | −0.636630 | −0.318315 | − | 0.947985i | \(-0.603117\pi\) | ||||
−0.318315 | + | 0.947985i | \(0.603117\pi\) | |||||||
\(54\) | 1.40915 | 0.191761 | ||||||||
\(55\) | 3.77512 | 0.509037 | ||||||||
\(56\) | −2.80350 | −0.374633 | ||||||||
\(57\) | −0.237080 | −0.0314020 | ||||||||
\(58\) | −3.23999 | −0.425431 | ||||||||
\(59\) | 8.43747 | 1.09847 | 0.549233 | − | 0.835669i | \(-0.314920\pi\) | ||||
0.549233 | + | 0.835669i | \(0.314920\pi\) | |||||||
\(60\) | 0.188819 | 0.0243764 | ||||||||
\(61\) | −11.8128 | −1.51248 | −0.756240 | − | 0.654294i | \(-0.772966\pi\) | ||||
−0.756240 | + | 0.654294i | \(0.772966\pi\) | |||||||
\(62\) | −0.792931 | −0.100702 | ||||||||
\(63\) | −8.25292 | −1.03977 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.74017 | −0.215841 | ||||||||
\(66\) | −1.12376 | −0.138326 | ||||||||
\(67\) | 12.0282 | 1.46947 | 0.734737 | − | 0.678352i | \(-0.237305\pi\) | ||||
0.734737 | + | 0.678352i | \(0.237305\pi\) | |||||||
\(68\) | 6.02982 | 0.731223 | ||||||||
\(69\) | −1.52105 | −0.183113 | ||||||||
\(70\) | −2.23281 | −0.266872 | ||||||||
\(71\) | −1.83288 | −0.217523 | −0.108762 | − | 0.994068i | \(-0.534688\pi\) | ||||
−0.108762 | + | 0.994068i | \(0.534688\pi\) | |||||||
\(72\) | 2.94379 | 0.346929 | ||||||||
\(73\) | 0.274289 | 0.0321031 | 0.0160516 | − | 0.999871i | \(-0.494890\pi\) | ||||
0.0160516 | + | 0.999871i | \(0.494890\pi\) | |||||||
\(74\) | −11.7320 | −1.36381 | ||||||||
\(75\) | −1.03502 | −0.119513 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 13.2886 | 1.51438 | ||||||||
\(78\) | 0.518006 | 0.0586527 | ||||||||
\(79\) | 10.6669 | 1.20012 | 0.600058 | − | 0.799957i | \(-0.295144\pi\) | ||||
0.600058 | + | 0.799957i | \(0.295144\pi\) | |||||||
\(80\) | 0.796437 | 0.0890443 | ||||||||
\(81\) | 8.49730 | 0.944144 | ||||||||
\(82\) | 3.14607 | 0.347425 | ||||||||
\(83\) | −13.3575 | −1.46618 | −0.733090 | − | 0.680132i | \(-0.761923\pi\) | ||||
−0.733090 | + | 0.680132i | \(0.761923\pi\) | |||||||
\(84\) | 0.664653 | 0.0725195 | ||||||||
\(85\) | 4.80237 | 0.520890 | ||||||||
\(86\) | −1.10829 | −0.119510 | ||||||||
\(87\) | 0.768135 | 0.0823527 | ||||||||
\(88\) | −4.74002 | −0.505287 | ||||||||
\(89\) | 9.60551 | 1.01818 | 0.509091 | − | 0.860713i | \(-0.329982\pi\) | ||||
0.509091 | + | 0.860713i | \(0.329982\pi\) | |||||||
\(90\) | 2.34454 | 0.247137 | ||||||||
\(91\) | −6.12549 | −0.642126 | ||||||||
\(92\) | −6.41578 | −0.668891 | ||||||||
\(93\) | 0.187988 | 0.0194935 | ||||||||
\(94\) | −4.60234 | −0.474695 | ||||||||
\(95\) | −0.796437 | −0.0817127 | ||||||||
\(96\) | −0.237080 | −0.0241969 | ||||||||
\(97\) | −2.53730 | −0.257623 | −0.128812 | − | 0.991669i | \(-0.541116\pi\) | ||||
−0.128812 | + | 0.991669i | \(0.541116\pi\) | |||||||
\(98\) | −0.859599 | −0.0868326 | ||||||||
\(99\) | −13.9536 | −1.40239 | ||||||||
\(100\) | −4.36569 | −0.436569 | ||||||||
\(101\) | 15.5527 | 1.54755 | 0.773777 | − | 0.633458i | \(-0.218365\pi\) | ||||
0.773777 | + | 0.633458i | \(0.218365\pi\) | |||||||
\(102\) | −1.42955 | −0.141546 | ||||||||
\(103\) | 16.7261 | 1.64807 | 0.824037 | − | 0.566535i | \(-0.191717\pi\) | ||||
0.824037 | + | 0.566535i | \(0.191717\pi\) | |||||||
\(104\) | 2.18494 | 0.214251 | ||||||||
\(105\) | 0.529354 | 0.0516596 | ||||||||
\(106\) | 4.63474 | 0.450165 | ||||||||
\(107\) | 6.68154 | 0.645929 | 0.322964 | − | 0.946411i | \(-0.395321\pi\) | ||||
0.322964 | + | 0.946411i | \(0.395321\pi\) | |||||||
\(108\) | −1.40915 | −0.135596 | ||||||||
\(109\) | 3.41840 | 0.327424 | 0.163712 | − | 0.986508i | \(-0.447653\pi\) | ||||
0.163712 | + | 0.986508i | \(0.447653\pi\) | |||||||
\(110\) | −3.77512 | −0.359944 | ||||||||
\(111\) | 2.78141 | 0.264000 | ||||||||
\(112\) | 2.80350 | 0.264906 | ||||||||
\(113\) | 2.58372 | 0.243056 | 0.121528 | − | 0.992588i | \(-0.461221\pi\) | ||||
0.121528 | + | 0.992588i | \(0.461221\pi\) | |||||||
\(114\) | 0.237080 | 0.0222046 | ||||||||
\(115\) | −5.10976 | −0.476488 | ||||||||
\(116\) | 3.23999 | 0.300825 | ||||||||
\(117\) | 6.43203 | 0.594641 | ||||||||
\(118\) | −8.43747 | −0.776732 | ||||||||
\(119\) | 16.9046 | 1.54964 | ||||||||
\(120\) | −0.188819 | −0.0172367 | ||||||||
\(121\) | 11.4678 | 1.04252 | ||||||||
\(122\) | 11.8128 | 1.06948 | ||||||||
\(123\) | −0.745869 | −0.0672527 | ||||||||
\(124\) | 0.792931 | 0.0712073 | ||||||||
\(125\) | −7.45918 | −0.667169 | ||||||||
\(126\) | 8.25292 | 0.735228 | ||||||||
\(127\) | −17.6380 | −1.56512 | −0.782561 | − | 0.622574i | \(-0.786087\pi\) | ||||
−0.782561 | + | 0.622574i | \(0.786087\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.262753 | 0.0231341 | ||||||||
\(130\) | 1.74017 | 0.152623 | ||||||||
\(131\) | 4.98659 | 0.435681 | 0.217840 | − | 0.975984i | \(-0.430099\pi\) | ||||
0.217840 | + | 0.975984i | \(0.430099\pi\) | |||||||
\(132\) | 1.12376 | 0.0978109 | ||||||||
\(133\) | −2.80350 | −0.243094 | ||||||||
\(134\) | −12.0282 | −1.03908 | ||||||||
\(135\) | −1.12230 | −0.0965923 | ||||||||
\(136\) | −6.02982 | −0.517053 | ||||||||
\(137\) | −1.37086 | −0.117120 | −0.0585602 | − | 0.998284i | \(-0.518651\pi\) | ||||
−0.0585602 | + | 0.998284i | \(0.518651\pi\) | |||||||
\(138\) | 1.52105 | 0.129481 | ||||||||
\(139\) | 11.0267 | 0.935275 | 0.467638 | − | 0.883920i | \(-0.345105\pi\) | ||||
0.467638 | + | 0.883920i | \(0.345105\pi\) | |||||||
\(140\) | 2.23281 | 0.188707 | ||||||||
\(141\) | 1.09112 | 0.0918891 | ||||||||
\(142\) | 1.83288 | 0.153812 | ||||||||
\(143\) | −10.3567 | −0.866069 | ||||||||
\(144\) | −2.94379 | −0.245316 | ||||||||
\(145\) | 2.58044 | 0.214294 | ||||||||
\(146\) | −0.274289 | −0.0227003 | ||||||||
\(147\) | 0.203794 | 0.0168086 | ||||||||
\(148\) | 11.7320 | 0.964361 | ||||||||
\(149\) | 13.7411 | 1.12571 | 0.562857 | − | 0.826554i | \(-0.309702\pi\) | ||||
0.562857 | + | 0.826554i | \(0.309702\pi\) | |||||||
\(150\) | 1.03502 | 0.0845088 | ||||||||
\(151\) | −24.2927 | −1.97691 | −0.988456 | − | 0.151508i | \(-0.951587\pi\) | ||||
−0.988456 | + | 0.151508i | \(0.951587\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −17.7505 | −1.43505 | ||||||||
\(154\) | −13.2886 | −1.07083 | ||||||||
\(155\) | 0.631520 | 0.0507249 | ||||||||
\(156\) | −0.518006 | −0.0414737 | ||||||||
\(157\) | 12.5534 | 1.00187 | 0.500934 | − | 0.865486i | \(-0.332990\pi\) | ||||
0.500934 | + | 0.865486i | \(0.332990\pi\) | |||||||
\(158\) | −10.6669 | −0.848610 | ||||||||
\(159\) | −1.09880 | −0.0871407 | ||||||||
\(160\) | −0.796437 | −0.0629638 | ||||||||
\(161\) | −17.9866 | −1.41754 | ||||||||
\(162\) | −8.49730 | −0.667611 | ||||||||
\(163\) | −4.58633 | −0.359229 | −0.179615 | − | 0.983737i | \(-0.557485\pi\) | ||||
−0.179615 | + | 0.983737i | \(0.557485\pi\) | |||||||
\(164\) | −3.14607 | −0.245667 | ||||||||
\(165\) | 0.895005 | 0.0696761 | ||||||||
\(166\) | 13.3575 | 1.03675 | ||||||||
\(167\) | −12.2850 | −0.950645 | −0.475323 | − | 0.879812i | \(-0.657669\pi\) | ||||
−0.475323 | + | 0.879812i | \(0.657669\pi\) | |||||||
\(168\) | −0.664653 | −0.0512791 | ||||||||
\(169\) | −8.22602 | −0.632771 | ||||||||
\(170\) | −4.80237 | −0.368325 | ||||||||
\(171\) | 2.94379 | 0.225117 | ||||||||
\(172\) | 1.10829 | 0.0845061 | ||||||||
\(173\) | −5.04705 | −0.383720 | −0.191860 | − | 0.981422i | \(-0.561452\pi\) | ||||
−0.191860 | + | 0.981422i | \(0.561452\pi\) | |||||||
\(174\) | −0.768135 | −0.0582322 | ||||||||
\(175\) | −12.2392 | −0.925196 | ||||||||
\(176\) | 4.74002 | 0.357292 | ||||||||
\(177\) | 2.00035 | 0.150356 | ||||||||
\(178\) | −9.60551 | −0.719964 | ||||||||
\(179\) | −9.77614 | −0.730703 | −0.365352 | − | 0.930870i | \(-0.619051\pi\) | ||||
−0.365352 | + | 0.930870i | \(0.619051\pi\) | |||||||
\(180\) | −2.34454 | −0.174752 | ||||||||
\(181\) | 6.61384 | 0.491603 | 0.245802 | − | 0.969320i | \(-0.420949\pi\) | ||||
0.245802 | + | 0.969320i | \(0.420949\pi\) | |||||||
\(182\) | 6.12549 | 0.454051 | ||||||||
\(183\) | −2.80059 | −0.207025 | ||||||||
\(184\) | 6.41578 | 0.472978 | ||||||||
\(185\) | 9.34376 | 0.686967 | ||||||||
\(186\) | −0.187988 | −0.0137840 | ||||||||
\(187\) | 28.5814 | 2.09008 | ||||||||
\(188\) | 4.60234 | 0.335660 | ||||||||
\(189\) | −3.95056 | −0.287361 | ||||||||
\(190\) | 0.796437 | 0.0577796 | ||||||||
\(191\) | 20.0904 | 1.45369 | 0.726844 | − | 0.686802i | \(-0.240986\pi\) | ||||
0.726844 | + | 0.686802i | \(0.240986\pi\) | |||||||
\(192\) | 0.237080 | 0.0171098 | ||||||||
\(193\) | 17.4991 | 1.25961 | 0.629807 | − | 0.776752i | \(-0.283134\pi\) | ||||
0.629807 | + | 0.776752i | \(0.283134\pi\) | |||||||
\(194\) | 2.53730 | 0.182167 | ||||||||
\(195\) | −0.412559 | −0.0295440 | ||||||||
\(196\) | 0.859599 | 0.0613999 | ||||||||
\(197\) | 5.51988 | 0.393275 | 0.196638 | − | 0.980476i | \(-0.436998\pi\) | ||||
0.196638 | + | 0.980476i | \(0.436998\pi\) | |||||||
\(198\) | 13.9536 | 0.991641 | ||||||||
\(199\) | −2.23267 | −0.158270 | −0.0791350 | − | 0.996864i | \(-0.525216\pi\) | ||||
−0.0791350 | + | 0.996864i | \(0.525216\pi\) | |||||||
\(200\) | 4.36569 | 0.308701 | ||||||||
\(201\) | 2.85164 | 0.201139 | ||||||||
\(202\) | −15.5527 | −1.09429 | ||||||||
\(203\) | 9.08329 | 0.637522 | ||||||||
\(204\) | 1.42955 | 0.100088 | ||||||||
\(205\) | −2.50564 | −0.175002 | ||||||||
\(206\) | −16.7261 | −1.16536 | ||||||||
\(207\) | 18.8867 | 1.31272 | ||||||||
\(208\) | −2.18494 | −0.151499 | ||||||||
\(209\) | −4.74002 | −0.327874 | ||||||||
\(210\) | −0.529354 | −0.0365289 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −4.63474 | −0.318315 | ||||||||
\(213\) | −0.434539 | −0.0297741 | ||||||||
\(214\) | −6.68154 | −0.456741 | ||||||||
\(215\) | 0.882681 | 0.0601983 | ||||||||
\(216\) | 1.40915 | 0.0958807 | ||||||||
\(217\) | 2.22298 | 0.150906 | ||||||||
\(218\) | −3.41840 | −0.231523 | ||||||||
\(219\) | 0.0650284 | 0.00439421 | ||||||||
\(220\) | 3.77512 | 0.254519 | ||||||||
\(221\) | −13.1748 | −0.886235 | ||||||||
\(222\) | −2.78141 | −0.186676 | ||||||||
\(223\) | −1.65228 | −0.110645 | −0.0553223 | − | 0.998469i | \(-0.517619\pi\) | ||||
−0.0553223 | + | 0.998469i | \(0.517619\pi\) | |||||||
\(224\) | −2.80350 | −0.187317 | ||||||||
\(225\) | 12.8517 | 0.856779 | ||||||||
\(226\) | −2.58372 | −0.171867 | ||||||||
\(227\) | −3.88178 | −0.257643 | −0.128822 | − | 0.991668i | \(-0.541119\pi\) | ||||
−0.128822 | + | 0.991668i | \(0.541119\pi\) | |||||||
\(228\) | −0.237080 | −0.0157010 | ||||||||
\(229\) | −6.59438 | −0.435769 | −0.217884 | − | 0.975975i | \(-0.569916\pi\) | ||||
−0.217884 | + | 0.975975i | \(0.569916\pi\) | |||||||
\(230\) | 5.10976 | 0.336928 | ||||||||
\(231\) | 3.15046 | 0.207285 | ||||||||
\(232\) | −3.23999 | −0.212715 | ||||||||
\(233\) | 12.1671 | 0.797096 | 0.398548 | − | 0.917148i | \(-0.369514\pi\) | ||||
0.398548 | + | 0.917148i | \(0.369514\pi\) | |||||||
\(234\) | −6.43203 | −0.420475 | ||||||||
\(235\) | 3.66547 | 0.239109 | ||||||||
\(236\) | 8.43747 | 0.549233 | ||||||||
\(237\) | 2.52890 | 0.164270 | ||||||||
\(238\) | −16.9046 | −1.09576 | ||||||||
\(239\) | −0.200567 | −0.0129736 | −0.00648681 | − | 0.999979i | \(-0.502065\pi\) | ||||
−0.00648681 | + | 0.999979i | \(0.502065\pi\) | |||||||
\(240\) | 0.188819 | 0.0121882 | ||||||||
\(241\) | −3.87182 | −0.249406 | −0.124703 | − | 0.992194i | \(-0.539798\pi\) | ||||
−0.124703 | + | 0.992194i | \(0.539798\pi\) | |||||||
\(242\) | −11.4678 | −0.737175 | ||||||||
\(243\) | 6.24200 | 0.400424 | ||||||||
\(244\) | −11.8128 | −0.756240 | ||||||||
\(245\) | 0.684616 | 0.0437385 | ||||||||
\(246\) | 0.745869 | 0.0475549 | ||||||||
\(247\) | 2.18494 | 0.139025 | ||||||||
\(248\) | −0.792931 | −0.0503512 | ||||||||
\(249\) | −3.16680 | −0.200688 | ||||||||
\(250\) | 7.45918 | 0.471760 | ||||||||
\(251\) | −2.25610 | −0.142404 | −0.0712019 | − | 0.997462i | \(-0.522683\pi\) | ||||
−0.0712019 | + | 0.997462i | \(0.522683\pi\) | |||||||
\(252\) | −8.25292 | −0.519885 | ||||||||
\(253\) | −30.4109 | −1.91192 | ||||||||
\(254\) | 17.6380 | 1.10671 | ||||||||
\(255\) | 1.13854 | 0.0712984 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.51684 | 0.281752 | 0.140876 | − | 0.990027i | \(-0.455008\pi\) | ||||
0.140876 | + | 0.990027i | \(0.455008\pi\) | |||||||
\(258\) | −0.262753 | −0.0163583 | ||||||||
\(259\) | 32.8905 | 2.04372 | ||||||||
\(260\) | −1.74017 | −0.107921 | ||||||||
\(261\) | −9.53785 | −0.590378 | ||||||||
\(262\) | −4.98659 | −0.308073 | ||||||||
\(263\) | 8.32235 | 0.513178 | 0.256589 | − | 0.966521i | \(-0.417401\pi\) | ||||
0.256589 | + | 0.966521i | \(0.417401\pi\) | |||||||
\(264\) | −1.12376 | −0.0691628 | ||||||||
\(265\) | −3.69127 | −0.226753 | ||||||||
\(266\) | 2.80350 | 0.171893 | ||||||||
\(267\) | 2.27727 | 0.139367 | ||||||||
\(268\) | 12.0282 | 0.734737 | ||||||||
\(269\) | 13.3153 | 0.811850 | 0.405925 | − | 0.913906i | \(-0.366949\pi\) | ||||
0.405925 | + | 0.913906i | \(0.366949\pi\) | |||||||
\(270\) | 1.12230 | 0.0683011 | ||||||||
\(271\) | 8.31037 | 0.504819 | 0.252410 | − | 0.967620i | \(-0.418777\pi\) | ||||
0.252410 | + | 0.967620i | \(0.418777\pi\) | |||||||
\(272\) | 6.02982 | 0.365612 | ||||||||
\(273\) | −1.45223 | −0.0878929 | ||||||||
\(274\) | 1.37086 | 0.0828166 | ||||||||
\(275\) | −20.6934 | −1.24786 | ||||||||
\(276\) | −1.52105 | −0.0915565 | ||||||||
\(277\) | −7.78159 | −0.467550 | −0.233775 | − | 0.972291i | \(-0.575108\pi\) | ||||
−0.233775 | + | 0.972291i | \(0.575108\pi\) | |||||||
\(278\) | −11.0267 | −0.661339 | ||||||||
\(279\) | −2.33423 | −0.139746 | ||||||||
\(280\) | −2.23281 | −0.133436 | ||||||||
\(281\) | 8.97741 | 0.535547 | 0.267774 | − | 0.963482i | \(-0.413712\pi\) | ||||
0.267774 | + | 0.963482i | \(0.413712\pi\) | |||||||
\(282\) | −1.09112 | −0.0649754 | ||||||||
\(283\) | −10.5496 | −0.627110 | −0.313555 | − | 0.949570i | \(-0.601520\pi\) | ||||
−0.313555 | + | 0.949570i | \(0.601520\pi\) | |||||||
\(284\) | −1.83288 | −0.108762 | ||||||||
\(285\) | −0.188819 | −0.0111847 | ||||||||
\(286\) | 10.3567 | 0.612403 | ||||||||
\(287\) | −8.81999 | −0.520628 | ||||||||
\(288\) | 2.94379 | 0.173465 | ||||||||
\(289\) | 19.3587 | 1.13875 | ||||||||
\(290\) | −2.58044 | −0.151529 | ||||||||
\(291\) | −0.601542 | −0.0352630 | ||||||||
\(292\) | 0.274289 | 0.0160516 | ||||||||
\(293\) | 31.7950 | 1.85748 | 0.928741 | − | 0.370730i | \(-0.120893\pi\) | ||||
0.928741 | + | 0.370730i | \(0.120893\pi\) | |||||||
\(294\) | −0.203794 | −0.0118855 | ||||||||
\(295\) | 6.71991 | 0.391248 | ||||||||
\(296\) | −11.7320 | −0.681906 | ||||||||
\(297\) | −6.67941 | −0.387579 | ||||||||
\(298\) | −13.7411 | −0.796000 | ||||||||
\(299\) | 14.0181 | 0.810689 | ||||||||
\(300\) | −1.03502 | −0.0597567 | ||||||||
\(301\) | 3.10708 | 0.179089 | ||||||||
\(302\) | 24.2927 | 1.39789 | ||||||||
\(303\) | 3.68724 | 0.211826 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −9.40818 | −0.538711 | ||||||||
\(306\) | 17.7505 | 1.01473 | ||||||||
\(307\) | 16.2302 | 0.926309 | 0.463154 | − | 0.886278i | \(-0.346718\pi\) | ||||
0.463154 | + | 0.886278i | \(0.346718\pi\) | |||||||
\(308\) | 13.2886 | 0.757190 | ||||||||
\(309\) | 3.96543 | 0.225585 | ||||||||
\(310\) | −0.631520 | −0.0358679 | ||||||||
\(311\) | −19.9063 | −1.12878 | −0.564390 | − | 0.825508i | \(-0.690889\pi\) | ||||
−0.564390 | + | 0.825508i | \(0.690889\pi\) | |||||||
\(312\) | 0.518006 | 0.0293263 | ||||||||
\(313\) | −5.50408 | −0.311109 | −0.155555 | − | 0.987827i | \(-0.549716\pi\) | ||||
−0.155555 | + | 0.987827i | \(0.549716\pi\) | |||||||
\(314\) | −12.5534 | −0.708427 | ||||||||
\(315\) | −6.57292 | −0.370342 | ||||||||
\(316\) | 10.6669 | 0.600058 | ||||||||
\(317\) | 14.4269 | 0.810298 | 0.405149 | − | 0.914251i | \(-0.367220\pi\) | ||||
0.405149 | + | 0.914251i | \(0.367220\pi\) | |||||||
\(318\) | 1.09880 | 0.0616178 | ||||||||
\(319\) | 15.3576 | 0.859860 | ||||||||
\(320\) | 0.796437 | 0.0445222 | ||||||||
\(321\) | 1.58406 | 0.0884135 | ||||||||
\(322\) | 17.9866 | 1.00236 | ||||||||
\(323\) | −6.02982 | −0.335508 | ||||||||
\(324\) | 8.49730 | 0.472072 | ||||||||
\(325\) | 9.53879 | 0.529117 | ||||||||
\(326\) | 4.58633 | 0.254013 | ||||||||
\(327\) | 0.810434 | 0.0448171 | ||||||||
\(328\) | 3.14607 | 0.173713 | ||||||||
\(329\) | 12.9027 | 0.711347 | ||||||||
\(330\) | −0.895005 | −0.0492684 | ||||||||
\(331\) | 9.33740 | 0.513230 | 0.256615 | − | 0.966514i | \(-0.417393\pi\) | ||||
0.256615 | + | 0.966514i | \(0.417393\pi\) | |||||||
\(332\) | −13.3575 | −0.733090 | ||||||||
\(333\) | −34.5365 | −1.89259 | ||||||||
\(334\) | 12.2850 | 0.672208 | ||||||||
\(335\) | 9.57967 | 0.523393 | ||||||||
\(336\) | 0.664653 | 0.0362598 | ||||||||
\(337\) | 0.379590 | 0.0206776 | 0.0103388 | − | 0.999947i | \(-0.496709\pi\) | ||||
0.0103388 | + | 0.999947i | \(0.496709\pi\) | |||||||
\(338\) | 8.22602 | 0.447436 | ||||||||
\(339\) | 0.612549 | 0.0332691 | ||||||||
\(340\) | 4.80237 | 0.260445 | ||||||||
\(341\) | 3.75851 | 0.203535 | ||||||||
\(342\) | −2.94379 | −0.159182 | ||||||||
\(343\) | −17.2146 | −0.929501 | ||||||||
\(344\) | −1.10829 | −0.0597549 | ||||||||
\(345\) | −1.21142 | −0.0652207 | ||||||||
\(346\) | 5.04705 | 0.271331 | ||||||||
\(347\) | −7.90658 | −0.424448 | −0.212224 | − | 0.977221i | \(-0.568071\pi\) | ||||
−0.212224 | + | 0.977221i | \(0.568071\pi\) | |||||||
\(348\) | 0.768135 | 0.0411764 | ||||||||
\(349\) | 0.827802 | 0.0443112 | 0.0221556 | − | 0.999755i | \(-0.492947\pi\) | ||||
0.0221556 | + | 0.999755i | \(0.492947\pi\) | |||||||
\(350\) | 12.2392 | 0.654213 | ||||||||
\(351\) | 3.07892 | 0.164341 | ||||||||
\(352\) | −4.74002 | −0.252644 | ||||||||
\(353\) | −16.6005 | −0.883556 | −0.441778 | − | 0.897124i | \(-0.645652\pi\) | ||||
−0.441778 | + | 0.897124i | \(0.645652\pi\) | |||||||
\(354\) | −2.00035 | −0.106318 | ||||||||
\(355\) | −1.45977 | −0.0774768 | ||||||||
\(356\) | 9.60551 | 0.509091 | ||||||||
\(357\) | 4.00774 | 0.212112 | ||||||||
\(358\) | 9.77614 | 0.516685 | ||||||||
\(359\) | −36.9679 | −1.95109 | −0.975546 | − | 0.219796i | \(-0.929461\pi\) | ||||
−0.975546 | + | 0.219796i | \(0.929461\pi\) | |||||||
\(360\) | 2.34454 | 0.123568 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −6.61384 | −0.347616 | ||||||||
\(363\) | 2.71877 | 0.142699 | ||||||||
\(364\) | −6.12549 | −0.321063 | ||||||||
\(365\) | 0.218454 | 0.0114344 | ||||||||
\(366\) | 2.80059 | 0.146389 | ||||||||
\(367\) | 9.88440 | 0.515962 | 0.257981 | − | 0.966150i | \(-0.416943\pi\) | ||||
0.257981 | + | 0.966150i | \(0.416943\pi\) | |||||||
\(368\) | −6.41578 | −0.334446 | ||||||||
\(369\) | 9.26137 | 0.482128 | ||||||||
\(370\) | −9.34376 | −0.485759 | ||||||||
\(371\) | −12.9935 | −0.674587 | ||||||||
\(372\) | 0.187988 | 0.00974673 | ||||||||
\(373\) | 4.81776 | 0.249454 | 0.124727 | − | 0.992191i | \(-0.460194\pi\) | ||||
0.124727 | + | 0.992191i | \(0.460194\pi\) | |||||||
\(374\) | −28.5814 | −1.47791 | ||||||||
\(375\) | −1.76842 | −0.0913208 | ||||||||
\(376\) | −4.60234 | −0.237348 | ||||||||
\(377\) | −7.07919 | −0.364597 | ||||||||
\(378\) | 3.95056 | 0.203195 | ||||||||
\(379\) | 15.4554 | 0.793888 | 0.396944 | − | 0.917843i | \(-0.370071\pi\) | ||||
0.396944 | + | 0.917843i | \(0.370071\pi\) | |||||||
\(380\) | −0.796437 | −0.0408563 | ||||||||
\(381\) | −4.18162 | −0.214231 | ||||||||
\(382\) | −20.0904 | −1.02791 | ||||||||
\(383\) | −1.03318 | −0.0527933 | −0.0263966 | − | 0.999652i | \(-0.508403\pi\) | ||||
−0.0263966 | + | 0.999652i | \(0.508403\pi\) | |||||||
\(384\) | −0.237080 | −0.0120984 | ||||||||
\(385\) | 10.5835 | 0.539387 | ||||||||
\(386\) | −17.4991 | −0.890682 | ||||||||
\(387\) | −3.26257 | −0.165846 | ||||||||
\(388\) | −2.53730 | −0.128812 | ||||||||
\(389\) | −23.7639 | −1.20488 | −0.602439 | − | 0.798165i | \(-0.705804\pi\) | ||||
−0.602439 | + | 0.798165i | \(0.705804\pi\) | |||||||
\(390\) | 0.412559 | 0.0208907 | ||||||||
\(391\) | −38.6860 | −1.95644 | ||||||||
\(392\) | −0.859599 | −0.0434163 | ||||||||
\(393\) | 1.18222 | 0.0596351 | ||||||||
\(394\) | −5.51988 | −0.278088 | ||||||||
\(395\) | 8.49548 | 0.427454 | ||||||||
\(396\) | −13.9536 | −0.701196 | ||||||||
\(397\) | −12.1950 | −0.612049 | −0.306024 | − | 0.952024i | \(-0.598999\pi\) | ||||
−0.306024 | + | 0.952024i | \(0.598999\pi\) | |||||||
\(398\) | 2.23267 | 0.111914 | ||||||||
\(399\) | −0.664653 | −0.0332743 | ||||||||
\(400\) | −4.36569 | −0.218284 | ||||||||
\(401\) | −6.63757 | −0.331464 | −0.165732 | − | 0.986171i | \(-0.552999\pi\) | ||||
−0.165732 | + | 0.986171i | \(0.552999\pi\) | |||||||
\(402\) | −2.85164 | −0.142227 | ||||||||
\(403\) | −1.73251 | −0.0863025 | ||||||||
\(404\) | 15.5527 | 0.773777 | ||||||||
\(405\) | 6.76756 | 0.336283 | ||||||||
\(406\) | −9.08329 | −0.450796 | ||||||||
\(407\) | 55.6097 | 2.75647 | ||||||||
\(408\) | −1.42955 | −0.0707732 | ||||||||
\(409\) | 20.5774 | 1.01749 | 0.508744 | − | 0.860918i | \(-0.330110\pi\) | ||||
0.508744 | + | 0.860918i | \(0.330110\pi\) | |||||||
\(410\) | 2.50564 | 0.123745 | ||||||||
\(411\) | −0.325003 | −0.0160312 | ||||||||
\(412\) | 16.7261 | 0.824037 | ||||||||
\(413\) | 23.6544 | 1.16396 | ||||||||
\(414\) | −18.8867 | −0.928232 | ||||||||
\(415\) | −10.6384 | −0.522220 | ||||||||
\(416\) | 2.18494 | 0.107126 | ||||||||
\(417\) | 2.61422 | 0.128019 | ||||||||
\(418\) | 4.74002 | 0.231842 | ||||||||
\(419\) | 9.00900 | 0.440118 | 0.220059 | − | 0.975487i | \(-0.429375\pi\) | ||||
0.220059 | + | 0.975487i | \(0.429375\pi\) | |||||||
\(420\) | 0.529354 | 0.0258298 | ||||||||
\(421\) | −7.90629 | −0.385329 | −0.192665 | − | 0.981265i | \(-0.561713\pi\) | ||||
−0.192665 | + | 0.981265i | \(0.561713\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −13.5483 | −0.658743 | ||||||||
\(424\) | 4.63474 | 0.225083 | ||||||||
\(425\) | −26.3243 | −1.27692 | ||||||||
\(426\) | 0.434539 | 0.0210535 | ||||||||
\(427\) | −33.1173 | −1.60266 | ||||||||
\(428\) | 6.68154 | 0.322964 | ||||||||
\(429\) | −2.45536 | −0.118546 | ||||||||
\(430\) | −0.882681 | −0.0425666 | ||||||||
\(431\) | 22.1765 | 1.06820 | 0.534102 | − | 0.845420i | \(-0.320650\pi\) | ||||
0.534102 | + | 0.845420i | \(0.320650\pi\) | |||||||
\(432\) | −1.40915 | −0.0677979 | ||||||||
\(433\) | −12.1969 | −0.586144 | −0.293072 | − | 0.956090i | \(-0.594677\pi\) | ||||
−0.293072 | + | 0.956090i | \(0.594677\pi\) | |||||||
\(434\) | −2.22298 | −0.106707 | ||||||||
\(435\) | 0.611771 | 0.0293322 | ||||||||
\(436\) | 3.41840 | 0.163712 | ||||||||
\(437\) | 6.41578 | 0.306908 | ||||||||
\(438\) | −0.0650284 | −0.00310718 | ||||||||
\(439\) | −11.6481 | −0.555932 | −0.277966 | − | 0.960591i | \(-0.589660\pi\) | ||||
−0.277966 | + | 0.960591i | \(0.589660\pi\) | |||||||
\(440\) | −3.77512 | −0.179972 | ||||||||
\(441\) | −2.53048 | −0.120499 | ||||||||
\(442\) | 13.1748 | 0.626663 | ||||||||
\(443\) | −27.2039 | −1.29249 | −0.646247 | − | 0.763128i | \(-0.723662\pi\) | ||||
−0.646247 | + | 0.763128i | \(0.723662\pi\) | |||||||
\(444\) | 2.78141 | 0.132000 | ||||||||
\(445\) | 7.65018 | 0.362653 | ||||||||
\(446\) | 1.65228 | 0.0782375 | ||||||||
\(447\) | 3.25773 | 0.154086 | ||||||||
\(448\) | 2.80350 | 0.132453 | ||||||||
\(449\) | 19.5281 | 0.921586 | 0.460793 | − | 0.887508i | \(-0.347565\pi\) | ||||
0.460793 | + | 0.887508i | \(0.347565\pi\) | |||||||
\(450\) | −12.8517 | −0.605834 | ||||||||
\(451\) | −14.9124 | −0.702198 | ||||||||
\(452\) | 2.58372 | 0.121528 | ||||||||
\(453\) | −5.75931 | −0.270596 | ||||||||
\(454\) | 3.88178 | 0.182181 | ||||||||
\(455\) | −4.87856 | −0.228711 | ||||||||
\(456\) | 0.237080 | 0.0111023 | ||||||||
\(457\) | −2.20192 | −0.103001 | −0.0515007 | − | 0.998673i | \(-0.516400\pi\) | ||||
−0.0515007 | + | 0.998673i | \(0.516400\pi\) | |||||||
\(458\) | 6.59438 | 0.308135 | ||||||||
\(459\) | −8.49694 | −0.396603 | ||||||||
\(460\) | −5.10976 | −0.238244 | ||||||||
\(461\) | 36.5871 | 1.70403 | 0.852016 | − | 0.523516i | \(-0.175380\pi\) | ||||
0.852016 | + | 0.523516i | \(0.175380\pi\) | |||||||
\(462\) | −3.15046 | −0.146573 | ||||||||
\(463\) | 28.0188 | 1.30214 | 0.651072 | − | 0.759016i | \(-0.274319\pi\) | ||||
0.651072 | + | 0.759016i | \(0.274319\pi\) | |||||||
\(464\) | 3.23999 | 0.150413 | ||||||||
\(465\) | 0.149721 | 0.00694312 | ||||||||
\(466\) | −12.1671 | −0.563632 | ||||||||
\(467\) | −41.5663 | −1.92346 | −0.961729 | − | 0.274004i | \(-0.911652\pi\) | ||||
−0.961729 | + | 0.274004i | \(0.911652\pi\) | |||||||
\(468\) | 6.43203 | 0.297320 | ||||||||
\(469\) | 33.7209 | 1.55709 | ||||||||
\(470\) | −3.66547 | −0.169076 | ||||||||
\(471\) | 2.97615 | 0.137134 | ||||||||
\(472\) | −8.43747 | −0.388366 | ||||||||
\(473\) | 5.25330 | 0.241547 | ||||||||
\(474\) | −2.52890 | −0.116156 | ||||||||
\(475\) | 4.36569 | 0.200312 | ||||||||
\(476\) | 16.9046 | 0.774821 | ||||||||
\(477\) | 13.6437 | 0.624702 | ||||||||
\(478\) | 0.200567 | 0.00917373 | ||||||||
\(479\) | −15.9662 | −0.729513 | −0.364757 | − | 0.931103i | \(-0.618848\pi\) | ||||
−0.364757 | + | 0.931103i | \(0.618848\pi\) | |||||||
\(480\) | −0.188819 | −0.00861837 | ||||||||
\(481\) | −25.6337 | −1.16880 | ||||||||
\(482\) | 3.87182 | 0.176357 | ||||||||
\(483\) | −4.26426 | −0.194031 | ||||||||
\(484\) | 11.4678 | 0.521262 | ||||||||
\(485\) | −2.02080 | −0.0917596 | ||||||||
\(486\) | −6.24200 | −0.283143 | ||||||||
\(487\) | 27.7570 | 1.25779 | 0.628895 | − | 0.777490i | \(-0.283508\pi\) | ||||
0.628895 | + | 0.777490i | \(0.283508\pi\) | |||||||
\(488\) | 11.8128 | 0.534742 | ||||||||
\(489\) | −1.08733 | −0.0491706 | ||||||||
\(490\) | −0.684616 | −0.0309278 | ||||||||
\(491\) | −32.0305 | −1.44552 | −0.722759 | − | 0.691100i | \(-0.757126\pi\) | ||||
−0.722759 | + | 0.691100i | \(0.757126\pi\) | |||||||
\(492\) | −0.745869 | −0.0336264 | ||||||||
\(493\) | 19.5365 | 0.879881 | ||||||||
\(494\) | −2.18494 | −0.0983053 | ||||||||
\(495\) | −11.1132 | −0.499500 | ||||||||
\(496\) | 0.792931 | 0.0356037 | ||||||||
\(497\) | −5.13848 | −0.230492 | ||||||||
\(498\) | 3.16680 | 0.141908 | ||||||||
\(499\) | −15.2312 | −0.681843 | −0.340921 | − | 0.940092i | \(-0.610739\pi\) | ||||
−0.340921 | + | 0.940092i | \(0.610739\pi\) | |||||||
\(500\) | −7.45918 | −0.333585 | ||||||||
\(501\) | −2.91253 | −0.130122 | ||||||||
\(502\) | 2.25610 | 0.100695 | ||||||||
\(503\) | −23.1514 | −1.03227 | −0.516136 | − | 0.856507i | \(-0.672630\pi\) | ||||
−0.516136 | + | 0.856507i | \(0.672630\pi\) | |||||||
\(504\) | 8.25292 | 0.367614 | ||||||||
\(505\) | 12.3868 | 0.551203 | ||||||||
\(506\) | 30.4109 | 1.35193 | ||||||||
\(507\) | −1.95022 | −0.0866124 | ||||||||
\(508\) | −17.6380 | −0.782561 | ||||||||
\(509\) | −28.4776 | −1.26225 | −0.631123 | − | 0.775683i | \(-0.717406\pi\) | ||||
−0.631123 | + | 0.775683i | \(0.717406\pi\) | |||||||
\(510\) | −1.13854 | −0.0504156 | ||||||||
\(511\) | 0.768969 | 0.0340172 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.40915 | 0.0622156 | ||||||||
\(514\) | −4.51684 | −0.199229 | ||||||||
\(515\) | 13.3213 | 0.587007 | ||||||||
\(516\) | 0.262753 | 0.0115670 | ||||||||
\(517\) | 21.8152 | 0.959430 | ||||||||
\(518\) | −32.8905 | −1.44513 | ||||||||
\(519\) | −1.19655 | −0.0525229 | ||||||||
\(520\) | 1.74017 | 0.0763115 | ||||||||
\(521\) | −35.4119 | −1.55142 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(522\) | 9.53785 | 0.417460 | ||||||||
\(523\) | 17.5085 | 0.765593 | 0.382797 | − | 0.923833i | \(-0.374961\pi\) | ||||
0.382797 | + | 0.923833i | \(0.374961\pi\) | |||||||
\(524\) | 4.98659 | 0.217840 | ||||||||
\(525\) | −2.90167 | −0.126639 | ||||||||
\(526\) | −8.32235 | −0.362872 | ||||||||
\(527\) | 4.78123 | 0.208274 | ||||||||
\(528\) | 1.12376 | 0.0489055 | ||||||||
\(529\) | 18.1622 | 0.789662 | ||||||||
\(530\) | 3.69127 | 0.160339 | ||||||||
\(531\) | −24.8382 | −1.07788 | ||||||||
\(532\) | −2.80350 | −0.121547 | ||||||||
\(533\) | 6.87398 | 0.297745 | ||||||||
\(534\) | −2.27727 | −0.0985472 | ||||||||
\(535\) | 5.32142 | 0.230065 | ||||||||
\(536\) | −12.0282 | −0.519538 | ||||||||
\(537\) | −2.31773 | −0.100017 | ||||||||
\(538\) | −13.3153 | −0.574064 | ||||||||
\(539\) | 4.07451 | 0.175502 | ||||||||
\(540\) | −1.12230 | −0.0482961 | ||||||||
\(541\) | 38.0795 | 1.63717 | 0.818583 | − | 0.574389i | \(-0.194760\pi\) | ||||
0.818583 | + | 0.574389i | \(0.194760\pi\) | |||||||
\(542\) | −8.31037 | −0.356961 | ||||||||
\(543\) | 1.56801 | 0.0672897 | ||||||||
\(544\) | −6.02982 | −0.258526 | ||||||||
\(545\) | 2.72254 | 0.116621 | ||||||||
\(546\) | 1.45223 | 0.0621497 | ||||||||
\(547\) | 10.9403 | 0.467775 | 0.233887 | − | 0.972264i | \(-0.424855\pi\) | ||||
0.233887 | + | 0.972264i | \(0.424855\pi\) | |||||||
\(548\) | −1.37086 | −0.0585602 | ||||||||
\(549\) | 34.7746 | 1.48414 | ||||||||
\(550\) | 20.6934 | 0.882371 | ||||||||
\(551\) | −3.23999 | −0.138028 | ||||||||
\(552\) | 1.52105 | 0.0647403 | ||||||||
\(553\) | 29.9045 | 1.27167 | ||||||||
\(554\) | 7.78159 | 0.330608 | ||||||||
\(555\) | 2.21522 | 0.0940307 | ||||||||
\(556\) | 11.0267 | 0.467638 | ||||||||
\(557\) | 6.87702 | 0.291389 | 0.145694 | − | 0.989330i | \(-0.453458\pi\) | ||||
0.145694 | + | 0.989330i | \(0.453458\pi\) | |||||||
\(558\) | 2.33423 | 0.0988157 | ||||||||
\(559\) | −2.42155 | −0.102421 | ||||||||
\(560\) | 2.23281 | 0.0943534 | ||||||||
\(561\) | 6.77608 | 0.286086 | ||||||||
\(562\) | −8.97741 | −0.378689 | ||||||||
\(563\) | 25.0697 | 1.05656 | 0.528280 | − | 0.849070i | \(-0.322837\pi\) | ||||
0.528280 | + | 0.849070i | \(0.322837\pi\) | |||||||
\(564\) | 1.09112 | 0.0459445 | ||||||||
\(565\) | 2.05777 | 0.0865711 | ||||||||
\(566\) | 10.5496 | 0.443434 | ||||||||
\(567\) | 23.8222 | 1.00044 | ||||||||
\(568\) | 1.83288 | 0.0769060 | ||||||||
\(569\) | 38.8551 | 1.62889 | 0.814445 | − | 0.580241i | \(-0.197042\pi\) | ||||
0.814445 | + | 0.580241i | \(0.197042\pi\) | |||||||
\(570\) | 0.188819 | 0.00790876 | ||||||||
\(571\) | −8.71079 | −0.364535 | −0.182268 | − | 0.983249i | \(-0.558344\pi\) | ||||
−0.182268 | + | 0.983249i | \(0.558344\pi\) | |||||||
\(572\) | −10.3567 | −0.433034 | ||||||||
\(573\) | 4.76302 | 0.198978 | ||||||||
\(574\) | 8.81999 | 0.368139 | ||||||||
\(575\) | 28.0093 | 1.16807 | ||||||||
\(576\) | −2.94379 | −0.122658 | ||||||||
\(577\) | 18.1506 | 0.755620 | 0.377810 | − | 0.925883i | \(-0.376677\pi\) | ||||
0.377810 | + | 0.925883i | \(0.376677\pi\) | |||||||
\(578\) | −19.3587 | −0.805218 | ||||||||
\(579\) | 4.14869 | 0.172414 | ||||||||
\(580\) | 2.58044 | 0.107147 | ||||||||
\(581\) | −37.4478 | −1.55360 | ||||||||
\(582\) | 0.601542 | 0.0249347 | ||||||||
\(583\) | −21.9687 | −0.909852 | ||||||||
\(584\) | −0.274289 | −0.0113502 | ||||||||
\(585\) | 5.12270 | 0.211798 | ||||||||
\(586\) | −31.7950 | −1.31344 | ||||||||
\(587\) | 22.3523 | 0.922579 | 0.461289 | − | 0.887250i | \(-0.347387\pi\) | ||||
0.461289 | + | 0.887250i | \(0.347387\pi\) | |||||||
\(588\) | 0.203794 | 0.00840430 | ||||||||
\(589\) | −0.792931 | −0.0326722 | ||||||||
\(590\) | −6.71991 | −0.276654 | ||||||||
\(591\) | 1.30865 | 0.0538308 | ||||||||
\(592\) | 11.7320 | 0.482181 | ||||||||
\(593\) | −28.6467 | −1.17638 | −0.588189 | − | 0.808724i | \(-0.700159\pi\) | ||||
−0.588189 | + | 0.808724i | \(0.700159\pi\) | |||||||
\(594\) | 6.67941 | 0.274059 | ||||||||
\(595\) | 13.4634 | 0.551947 | ||||||||
\(596\) | 13.7411 | 0.562857 | ||||||||
\(597\) | −0.529322 | −0.0216637 | ||||||||
\(598\) | −14.0181 | −0.573244 | ||||||||
\(599\) | −6.15284 | −0.251398 | −0.125699 | − | 0.992068i | \(-0.540117\pi\) | ||||
−0.125699 | + | 0.992068i | \(0.540117\pi\) | |||||||
\(600\) | 1.03502 | 0.0422544 | ||||||||
\(601\) | −29.5567 | −1.20564 | −0.602821 | − | 0.797876i | \(-0.705957\pi\) | ||||
−0.602821 | + | 0.797876i | \(0.705957\pi\) | |||||||
\(602\) | −3.10708 | −0.126635 | ||||||||
\(603\) | −35.4084 | −1.44194 | ||||||||
\(604\) | −24.2927 | −0.988456 | ||||||||
\(605\) | 9.13334 | 0.371323 | ||||||||
\(606\) | −3.68724 | −0.149784 | ||||||||
\(607\) | −16.1759 | −0.656559 | −0.328279 | − | 0.944581i | \(-0.606469\pi\) | ||||
−0.328279 | + | 0.944581i | \(0.606469\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 2.15346 | 0.0872628 | ||||||||
\(610\) | 9.40818 | 0.380926 | ||||||||
\(611\) | −10.0559 | −0.406817 | ||||||||
\(612\) | −17.7505 | −0.717523 | ||||||||
\(613\) | 9.30887 | 0.375982 | 0.187991 | − | 0.982171i | \(-0.439802\pi\) | ||||
0.187991 | + | 0.982171i | \(0.439802\pi\) | |||||||
\(614\) | −16.2302 | −0.654999 | ||||||||
\(615\) | −0.594037 | −0.0239539 | ||||||||
\(616\) | −13.2886 | −0.535414 | ||||||||
\(617\) | −44.6222 | −1.79642 | −0.898211 | − | 0.439565i | \(-0.855133\pi\) | ||||
−0.898211 | + | 0.439565i | \(0.855133\pi\) | |||||||
\(618\) | −3.96543 | −0.159513 | ||||||||
\(619\) | 39.9917 | 1.60740 | 0.803701 | − | 0.595034i | \(-0.202861\pi\) | ||||
0.803701 | + | 0.595034i | \(0.202861\pi\) | |||||||
\(620\) | 0.631520 | 0.0253624 | ||||||||
\(621\) | 9.04082 | 0.362795 | ||||||||
\(622\) | 19.9063 | 0.798169 | ||||||||
\(623\) | 26.9290 | 1.07889 | ||||||||
\(624\) | −0.518006 | −0.0207368 | ||||||||
\(625\) | 15.8877 | 0.635507 | ||||||||
\(626\) | 5.50408 | 0.219987 | ||||||||
\(627\) | −1.12376 | −0.0448787 | ||||||||
\(628\) | 12.5534 | 0.500934 | ||||||||
\(629\) | 70.7416 | 2.82065 | ||||||||
\(630\) | 6.57292 | 0.261872 | ||||||||
\(631\) | 43.2124 | 1.72026 | 0.860130 | − | 0.510075i | \(-0.170382\pi\) | ||||
0.860130 | + | 0.510075i | \(0.170382\pi\) | |||||||
\(632\) | −10.6669 | −0.424305 | ||||||||
\(633\) | 0.237080 | 0.00942308 | ||||||||
\(634\) | −14.4269 | −0.572967 | ||||||||
\(635\) | −14.0476 | −0.557461 | ||||||||
\(636\) | −1.09880 | −0.0435703 | ||||||||
\(637\) | −1.87818 | −0.0744160 | ||||||||
\(638\) | −15.3576 | −0.608013 | ||||||||
\(639\) | 5.39563 | 0.213448 | ||||||||
\(640\) | −0.796437 | −0.0314819 | ||||||||
\(641\) | −29.0630 | −1.14792 | −0.573960 | − | 0.818884i | \(-0.694593\pi\) | ||||
−0.573960 | + | 0.818884i | \(0.694593\pi\) | |||||||
\(642\) | −1.58406 | −0.0625178 | ||||||||
\(643\) | 21.5250 | 0.848862 | 0.424431 | − | 0.905460i | \(-0.360474\pi\) | ||||
0.424431 | + | 0.905460i | \(0.360474\pi\) | |||||||
\(644\) | −17.9866 | −0.708772 | ||||||||
\(645\) | 0.209266 | 0.00823983 | ||||||||
\(646\) | 6.02982 | 0.237240 | ||||||||
\(647\) | −38.2295 | −1.50295 | −0.751477 | − | 0.659759i | \(-0.770658\pi\) | ||||
−0.751477 | + | 0.659759i | \(0.770658\pi\) | |||||||
\(648\) | −8.49730 | −0.333805 | ||||||||
\(649\) | 39.9938 | 1.56989 | ||||||||
\(650\) | −9.53879 | −0.374142 | ||||||||
\(651\) | 0.527024 | 0.0206557 | ||||||||
\(652\) | −4.58633 | −0.179615 | ||||||||
\(653\) | −8.77932 | −0.343561 | −0.171781 | − | 0.985135i | \(-0.554952\pi\) | ||||
−0.171781 | + | 0.985135i | \(0.554952\pi\) | |||||||
\(654\) | −0.810434 | −0.0316905 | ||||||||
\(655\) | 3.97151 | 0.155180 | ||||||||
\(656\) | −3.14607 | −0.122833 | ||||||||
\(657\) | −0.807450 | −0.0315016 | ||||||||
\(658\) | −12.9027 | −0.502998 | ||||||||
\(659\) | −24.3506 | −0.948565 | −0.474283 | − | 0.880373i | \(-0.657293\pi\) | ||||
−0.474283 | + | 0.880373i | \(0.657293\pi\) | |||||||
\(660\) | 0.895005 | 0.0348380 | ||||||||
\(661\) | 35.8758 | 1.39541 | 0.697704 | − | 0.716386i | \(-0.254205\pi\) | ||||
0.697704 | + | 0.716386i | \(0.254205\pi\) | |||||||
\(662\) | −9.33740 | −0.362908 | ||||||||
\(663\) | −3.12348 | −0.121306 | ||||||||
\(664\) | 13.3575 | 0.518373 | ||||||||
\(665\) | −2.23281 | −0.0865846 | ||||||||
\(666\) | 34.5365 | 1.33826 | ||||||||
\(667\) | −20.7870 | −0.804877 | ||||||||
\(668\) | −12.2850 | −0.475323 | ||||||||
\(669\) | −0.391721 | −0.0151448 | ||||||||
\(670\) | −9.57967 | −0.370095 | ||||||||
\(671\) | −55.9931 | −2.16159 | ||||||||
\(672\) | −0.664653 | −0.0256395 | ||||||||
\(673\) | 2.38936 | 0.0921031 | 0.0460516 | − | 0.998939i | \(-0.485336\pi\) | ||||
0.0460516 | + | 0.998939i | \(0.485336\pi\) | |||||||
\(674\) | −0.379590 | −0.0146212 | ||||||||
\(675\) | 6.15192 | 0.236788 | ||||||||
\(676\) | −8.22602 | −0.316385 | ||||||||
\(677\) | 44.2452 | 1.70048 | 0.850240 | − | 0.526396i | \(-0.176457\pi\) | ||||
0.850240 | + | 0.526396i | \(0.176457\pi\) | |||||||
\(678\) | −0.612549 | −0.0235248 | ||||||||
\(679\) | −7.11330 | −0.272984 | ||||||||
\(680\) | −4.80237 | −0.184162 | ||||||||
\(681\) | −0.920293 | −0.0352657 | ||||||||
\(682\) | −3.75851 | −0.143921 | ||||||||
\(683\) | 29.2560 | 1.11945 | 0.559726 | − | 0.828678i | \(-0.310907\pi\) | ||||
0.559726 | + | 0.828678i | \(0.310907\pi\) | |||||||
\(684\) | 2.94379 | 0.112559 | ||||||||
\(685\) | −1.09180 | −0.0417156 | ||||||||
\(686\) | 17.2146 | 0.657256 | ||||||||
\(687\) | −1.56339 | −0.0596472 | ||||||||
\(688\) | 1.10829 | 0.0422531 | ||||||||
\(689\) | 10.1266 | 0.385794 | ||||||||
\(690\) | 1.21142 | 0.0461180 | ||||||||
\(691\) | 33.7427 | 1.28363 | 0.641816 | − | 0.766859i | \(-0.278181\pi\) | ||||
0.641816 | + | 0.766859i | \(0.278181\pi\) | |||||||
\(692\) | −5.04705 | −0.191860 | ||||||||
\(693\) | −39.1190 | −1.48601 | ||||||||
\(694\) | 7.90658 | 0.300130 | ||||||||
\(695\) | 8.78209 | 0.333124 | ||||||||
\(696\) | −0.768135 | −0.0291161 | ||||||||
\(697\) | −18.9702 | −0.718548 | ||||||||
\(698\) | −0.827802 | −0.0313328 | ||||||||
\(699\) | 2.88458 | 0.109105 | ||||||||
\(700\) | −12.2392 | −0.462598 | ||||||||
\(701\) | −19.4305 | −0.733878 | −0.366939 | − | 0.930245i | \(-0.619594\pi\) | ||||
−0.366939 | + | 0.930245i | \(0.619594\pi\) | |||||||
\(702\) | −3.07892 | −0.116206 | ||||||||
\(703\) | −11.7320 | −0.442479 | ||||||||
\(704\) | 4.74002 | 0.178646 | ||||||||
\(705\) | 0.869010 | 0.0327288 | ||||||||
\(706\) | 16.6005 | 0.624768 | ||||||||
\(707\) | 43.6020 | 1.63982 | ||||||||
\(708\) | 2.00035 | 0.0751779 | ||||||||
\(709\) | 43.2623 | 1.62475 | 0.812375 | − | 0.583136i | \(-0.198174\pi\) | ||||
0.812375 | + | 0.583136i | \(0.198174\pi\) | |||||||
\(710\) | 1.45977 | 0.0547843 | ||||||||
\(711\) | −31.4010 | −1.17763 | ||||||||
\(712\) | −9.60551 | −0.359982 | ||||||||
\(713\) | −5.08727 | −0.190520 | ||||||||
\(714\) | −4.00774 | −0.149986 | ||||||||
\(715\) | −8.24843 | −0.308474 | ||||||||
\(716\) | −9.77614 | −0.365352 | ||||||||
\(717\) | −0.0475504 | −0.00177580 | ||||||||
\(718\) | 36.9679 | 1.37963 | ||||||||
\(719\) | 3.30694 | 0.123328 | 0.0616641 | − | 0.998097i | \(-0.480359\pi\) | ||||
0.0616641 | + | 0.998097i | \(0.480359\pi\) | |||||||
\(720\) | −2.34454 | −0.0873760 | ||||||||
\(721\) | 46.8917 | 1.74634 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −0.917931 | −0.0341382 | ||||||||
\(724\) | 6.61384 | 0.245802 | ||||||||
\(725\) | −14.1448 | −0.525323 | ||||||||
\(726\) | −2.71877 | −0.100903 | ||||||||
\(727\) | 26.6851 | 0.989695 | 0.494847 | − | 0.868980i | \(-0.335224\pi\) | ||||
0.494847 | + | 0.868980i | \(0.335224\pi\) | |||||||
\(728\) | 6.12549 | 0.227026 | ||||||||
\(729\) | −24.0120 | −0.889335 | ||||||||
\(730\) | −0.218454 | −0.00808534 | ||||||||
\(731\) | 6.68278 | 0.247171 | ||||||||
\(732\) | −2.80059 | −0.103513 | ||||||||
\(733\) | 0.985023 | 0.0363827 | 0.0181913 | − | 0.999835i | \(-0.494209\pi\) | ||||
0.0181913 | + | 0.999835i | \(0.494209\pi\) | |||||||
\(734\) | −9.88440 | −0.364840 | ||||||||
\(735\) | 0.162309 | 0.00598684 | ||||||||
\(736\) | 6.41578 | 0.236489 | ||||||||
\(737\) | 57.0137 | 2.10013 | ||||||||
\(738\) | −9.26137 | −0.340916 | ||||||||
\(739\) | 18.7916 | 0.691259 | 0.345630 | − | 0.938371i | \(-0.387665\pi\) | ||||
0.345630 | + | 0.938371i | \(0.387665\pi\) | |||||||
\(740\) | 9.34376 | 0.343484 | ||||||||
\(741\) | 0.518006 | 0.0190294 | ||||||||
\(742\) | 12.9935 | 0.477005 | ||||||||
\(743\) | 7.95243 | 0.291746 | 0.145873 | − | 0.989303i | \(-0.453401\pi\) | ||||
0.145873 | + | 0.989303i | \(0.453401\pi\) | |||||||
\(744\) | −0.187988 | −0.00689198 | ||||||||
\(745\) | 10.9439 | 0.400954 | ||||||||
\(746\) | −4.81776 | −0.176391 | ||||||||
\(747\) | 39.3218 | 1.43871 | ||||||||
\(748\) | 28.5814 | 1.04504 | ||||||||
\(749\) | 18.7317 | 0.684441 | ||||||||
\(750\) | 1.76842 | 0.0645736 | ||||||||
\(751\) | 53.3930 | 1.94834 | 0.974170 | − | 0.225817i | \(-0.0725051\pi\) | ||||
0.974170 | + | 0.225817i | \(0.0725051\pi\) | |||||||
\(752\) | 4.60234 | 0.167830 | ||||||||
\(753\) | −0.534875 | −0.0194919 | ||||||||
\(754\) | 7.07919 | 0.257809 | ||||||||
\(755\) | −19.3476 | −0.704131 | ||||||||
\(756\) | −3.95056 | −0.143680 | ||||||||
\(757\) | 20.9481 | 0.761370 | 0.380685 | − | 0.924705i | \(-0.375688\pi\) | ||||
0.380685 | + | 0.924705i | \(0.375688\pi\) | |||||||
\(758\) | −15.4554 | −0.561364 | ||||||||
\(759\) | −7.20981 | −0.261699 | ||||||||
\(760\) | 0.796437 | 0.0288898 | ||||||||
\(761\) | 21.0222 | 0.762054 | 0.381027 | − | 0.924564i | \(-0.375570\pi\) | ||||
0.381027 | + | 0.924564i | \(0.375570\pi\) | |||||||
\(762\) | 4.18162 | 0.151484 | ||||||||
\(763\) | 9.58348 | 0.346945 | ||||||||
\(764\) | 20.0904 | 0.726844 | ||||||||
\(765\) | −14.1372 | −0.511131 | ||||||||
\(766\) | 1.03318 | 0.0373305 | ||||||||
\(767\) | −18.4354 | −0.665664 | ||||||||
\(768\) | 0.237080 | 0.00855488 | ||||||||
\(769\) | −1.27262 | −0.0458917 | −0.0229459 | − | 0.999737i | \(-0.507305\pi\) | ||||
−0.0229459 | + | 0.999737i | \(0.507305\pi\) | |||||||
\(770\) | −10.5835 | −0.381405 | ||||||||
\(771\) | 1.07085 | 0.0385657 | ||||||||
\(772\) | 17.4991 | 0.629807 | ||||||||
\(773\) | 24.8387 | 0.893385 | 0.446693 | − | 0.894687i | \(-0.352602\pi\) | ||||
0.446693 | + | 0.894687i | \(0.352602\pi\) | |||||||
\(774\) | 3.26257 | 0.117271 | ||||||||
\(775\) | −3.46169 | −0.124348 | ||||||||
\(776\) | 2.53730 | 0.0910836 | ||||||||
\(777\) | 7.79768 | 0.279740 | ||||||||
\(778\) | 23.7639 | 0.851977 | ||||||||
\(779\) | 3.14607 | 0.112720 | ||||||||
\(780\) | −0.412559 | −0.0147720 | ||||||||
\(781\) | −8.68789 | −0.310877 | ||||||||
\(782\) | 38.6860 | 1.38341 | ||||||||
\(783\) | −4.56564 | −0.163163 | ||||||||
\(784\) | 0.859599 | 0.0307000 | ||||||||
\(785\) | 9.99796 | 0.356842 | ||||||||
\(786\) | −1.18222 | −0.0421684 | ||||||||
\(787\) | 51.3821 | 1.83157 | 0.915787 | − | 0.401664i | \(-0.131568\pi\) | ||||
0.915787 | + | 0.401664i | \(0.131568\pi\) | |||||||
\(788\) | 5.51988 | 0.196638 | ||||||||
\(789\) | 1.97306 | 0.0702429 | ||||||||
\(790\) | −8.49548 | −0.302256 | ||||||||
\(791\) | 7.24346 | 0.257548 | ||||||||
\(792\) | 13.9536 | 0.495821 | ||||||||
\(793\) | 25.8104 | 0.916555 | ||||||||
\(794\) | 12.1950 | 0.432784 | ||||||||
\(795\) | −0.875126 | −0.0310375 | ||||||||
\(796\) | −2.23267 | −0.0791350 | ||||||||
\(797\) | −46.1364 | −1.63424 | −0.817118 | − | 0.576470i | \(-0.804430\pi\) | ||||
−0.817118 | + | 0.576470i | \(0.804430\pi\) | |||||||
\(798\) | 0.664653 | 0.0235284 | ||||||||
\(799\) | 27.7513 | 0.981771 | ||||||||
\(800\) | 4.36569 | 0.154350 | ||||||||
\(801\) | −28.2766 | −0.999106 | ||||||||
\(802\) | 6.63757 | 0.234381 | ||||||||
\(803\) | 1.30013 | 0.0458808 | ||||||||
\(804\) | 2.85164 | 0.100569 | ||||||||
\(805\) | −14.3252 | −0.504897 | ||||||||
\(806\) | 1.73251 | 0.0610251 | ||||||||
\(807\) | 3.15679 | 0.111124 | ||||||||
\(808\) | −15.5527 | −0.547143 | ||||||||
\(809\) | 16.2206 | 0.570285 | 0.285142 | − | 0.958485i | \(-0.407959\pi\) | ||||
0.285142 | + | 0.958485i | \(0.407959\pi\) | |||||||
\(810\) | −6.76756 | −0.237788 | ||||||||
\(811\) | −46.7936 | −1.64314 | −0.821572 | − | 0.570104i | \(-0.806903\pi\) | ||||
−0.821572 | + | 0.570104i | \(0.806903\pi\) | |||||||
\(812\) | 9.08329 | 0.318761 | ||||||||
\(813\) | 1.97022 | 0.0690987 | ||||||||
\(814\) | −55.6097 | −1.94912 | ||||||||
\(815\) | −3.65272 | −0.127949 | ||||||||
\(816\) | 1.42955 | 0.0500442 | ||||||||
\(817\) | −1.10829 | −0.0387741 | ||||||||
\(818\) | −20.5774 | −0.719473 | ||||||||
\(819\) | 18.0322 | 0.630095 | ||||||||
\(820\) | −2.50564 | −0.0875008 | ||||||||
\(821\) | 8.86584 | 0.309420 | 0.154710 | − | 0.987960i | \(-0.450556\pi\) | ||||
0.154710 | + | 0.987960i | \(0.450556\pi\) | |||||||
\(822\) | 0.325003 | 0.0113358 | ||||||||
\(823\) | −33.3108 | −1.16114 | −0.580571 | − | 0.814209i | \(-0.697171\pi\) | ||||
−0.580571 | + | 0.814209i | \(0.697171\pi\) | |||||||
\(824\) | −16.7261 | −0.582682 | ||||||||
\(825\) | −4.90600 | −0.170805 | ||||||||
\(826\) | −23.6544 | −0.823043 | ||||||||
\(827\) | −15.4961 | −0.538853 | −0.269426 | − | 0.963021i | \(-0.586834\pi\) | ||||
−0.269426 | + | 0.963021i | \(0.586834\pi\) | |||||||
\(828\) | 18.8867 | 0.656359 | ||||||||
\(829\) | 13.5489 | 0.470574 | 0.235287 | − | 0.971926i | \(-0.424397\pi\) | ||||
0.235287 | + | 0.971926i | \(0.424397\pi\) | |||||||
\(830\) | 10.6384 | 0.369265 | ||||||||
\(831\) | −1.84486 | −0.0639974 | ||||||||
\(832\) | −2.18494 | −0.0757493 | ||||||||
\(833\) | 5.18323 | 0.179588 | ||||||||
\(834\) | −2.61422 | −0.0905229 | ||||||||
\(835\) | −9.78426 | −0.338598 | ||||||||
\(836\) | −4.74002 | −0.163937 | ||||||||
\(837\) | −1.11736 | −0.0386217 | ||||||||
\(838\) | −9.00900 | −0.311211 | ||||||||
\(839\) | 21.4194 | 0.739481 | 0.369740 | − | 0.929135i | \(-0.379447\pi\) | ||||
0.369740 | + | 0.929135i | \(0.379447\pi\) | |||||||
\(840\) | −0.529354 | −0.0182644 | ||||||||
\(841\) | −18.5025 | −0.638017 | ||||||||
\(842\) | 7.90629 | 0.272469 | ||||||||
\(843\) | 2.12836 | 0.0733047 | ||||||||
\(844\) | 1.00000 | 0.0344214 | ||||||||
\(845\) | −6.55150 | −0.225378 | ||||||||
\(846\) | 13.5483 | 0.465802 | ||||||||
\(847\) | 32.1498 | 1.10468 | ||||||||
\(848\) | −4.63474 | −0.159157 | ||||||||
\(849\) | −2.50110 | −0.0858377 | ||||||||
\(850\) | 26.3243 | 0.902917 | ||||||||
\(851\) | −75.2697 | −2.58021 | ||||||||
\(852\) | −0.434539 | −0.0148871 | ||||||||
\(853\) | 27.6082 | 0.945287 | 0.472643 | − | 0.881254i | \(-0.343300\pi\) | ||||
0.472643 | + | 0.881254i | \(0.343300\pi\) | |||||||
\(854\) | 33.1173 | 1.13325 | ||||||||
\(855\) | 2.34454 | 0.0801817 | ||||||||
\(856\) | −6.68154 | −0.228370 | ||||||||
\(857\) | 26.0097 | 0.888473 | 0.444237 | − | 0.895909i | \(-0.353475\pi\) | ||||
0.444237 | + | 0.895909i | \(0.353475\pi\) | |||||||
\(858\) | 2.45536 | 0.0838245 | ||||||||
\(859\) | −11.2328 | −0.383258 | −0.191629 | − | 0.981467i | \(-0.561377\pi\) | ||||
−0.191629 | + | 0.981467i | \(0.561377\pi\) | |||||||
\(860\) | 0.882681 | 0.0300992 | ||||||||
\(861\) | −2.09104 | −0.0712625 | ||||||||
\(862\) | −22.1765 | −0.755335 | ||||||||
\(863\) | 14.9063 | 0.507416 | 0.253708 | − | 0.967281i | \(-0.418350\pi\) | ||||
0.253708 | + | 0.967281i | \(0.418350\pi\) | |||||||
\(864\) | 1.40915 | 0.0479404 | ||||||||
\(865\) | −4.01965 | −0.136672 | ||||||||
\(866\) | 12.1969 | 0.414466 | ||||||||
\(867\) | 4.58957 | 0.155870 | ||||||||
\(868\) | 2.22298 | 0.0754529 | ||||||||
\(869\) | 50.5611 | 1.71517 | ||||||||
\(870\) | −0.611771 | −0.0207410 | ||||||||
\(871\) | −26.2809 | −0.890494 | ||||||||
\(872\) | −3.41840 | −0.115762 | ||||||||
\(873\) | 7.46927 | 0.252797 | ||||||||
\(874\) | −6.41578 | −0.217017 | ||||||||
\(875\) | −20.9118 | −0.706947 | ||||||||
\(876\) | 0.0650284 | 0.00219711 | ||||||||
\(877\) | 3.27326 | 0.110530 | 0.0552651 | − | 0.998472i | \(-0.482400\pi\) | ||||
0.0552651 | + | 0.998472i | \(0.482400\pi\) | |||||||
\(878\) | 11.6481 | 0.393103 | ||||||||
\(879\) | 7.53794 | 0.254248 | ||||||||
\(880\) | 3.77512 | 0.127259 | ||||||||
\(881\) | −13.1729 | −0.443806 | −0.221903 | − | 0.975069i | \(-0.571227\pi\) | ||||
−0.221903 | + | 0.975069i | \(0.571227\pi\) | |||||||
\(882\) | 2.53048 | 0.0852057 | ||||||||
\(883\) | −1.16511 | −0.0392092 | −0.0196046 | − | 0.999808i | \(-0.506241\pi\) | ||||
−0.0196046 | + | 0.999808i | \(0.506241\pi\) | |||||||
\(884\) | −13.1748 | −0.443117 | ||||||||
\(885\) | 1.59316 | 0.0535533 | ||||||||
\(886\) | 27.2039 | 0.913931 | ||||||||
\(887\) | −8.52239 | −0.286154 | −0.143077 | − | 0.989712i | \(-0.545700\pi\) | ||||
−0.143077 | + | 0.989712i | \(0.545700\pi\) | |||||||
\(888\) | −2.78141 | −0.0933380 | ||||||||
\(889\) | −49.4482 | −1.65844 | ||||||||
\(890\) | −7.65018 | −0.256435 | ||||||||
\(891\) | 40.2773 | 1.34934 | ||||||||
\(892\) | −1.65228 | −0.0553223 | ||||||||
\(893\) | −4.60234 | −0.154012 | ||||||||
\(894\) | −3.25773 | −0.108955 | ||||||||
\(895\) | −7.78608 | −0.260260 | ||||||||
\(896\) | −2.80350 | −0.0936583 | ||||||||
\(897\) | 3.32341 | 0.110966 | ||||||||
\(898\) | −19.5281 | −0.651660 | ||||||||
\(899\) | 2.56909 | 0.0856838 | ||||||||
\(900\) | 12.8517 | 0.428390 | ||||||||
\(901\) | −27.9466 | −0.931037 | ||||||||
\(902\) | 14.9124 | 0.496529 | ||||||||
\(903\) | 0.736626 | 0.0245134 | ||||||||
\(904\) | −2.58372 | −0.0859334 | ||||||||
\(905\) | 5.26751 | 0.175098 | ||||||||
\(906\) | 5.75931 | 0.191340 | ||||||||
\(907\) | 50.1763 | 1.66608 | 0.833038 | − | 0.553215i | \(-0.186599\pi\) | ||||
0.833038 | + | 0.553215i | \(0.186599\pi\) | |||||||
\(908\) | −3.88178 | −0.128822 | ||||||||
\(909\) | −45.7840 | −1.51856 | ||||||||
\(910\) | 4.87856 | 0.161723 | ||||||||
\(911\) | −10.5112 | −0.348252 | −0.174126 | − | 0.984723i | \(-0.555710\pi\) | ||||
−0.174126 | + | 0.984723i | \(0.555710\pi\) | |||||||
\(912\) | −0.237080 | −0.00785050 | ||||||||
\(913\) | −63.3149 | −2.09542 | ||||||||
\(914\) | 2.20192 | 0.0728330 | ||||||||
\(915\) | −2.23049 | −0.0737377 | ||||||||
\(916\) | −6.59438 | −0.217884 | ||||||||
\(917\) | 13.9799 | 0.461657 | ||||||||
\(918\) | 8.49694 | 0.280441 | ||||||||
\(919\) | −20.9716 | −0.691789 | −0.345895 | − | 0.938273i | \(-0.612425\pi\) | ||||
−0.345895 | + | 0.938273i | \(0.612425\pi\) | |||||||
\(920\) | 5.10976 | 0.168464 | ||||||||
\(921\) | 3.84786 | 0.126791 | ||||||||
\(922\) | −36.5871 | −1.20493 | ||||||||
\(923\) | 4.00475 | 0.131818 | ||||||||
\(924\) | 3.15046 | 0.103643 | ||||||||
\(925\) | −51.2181 | −1.68404 | ||||||||
\(926\) | −28.0188 | −0.920755 | ||||||||
\(927\) | −49.2383 | −1.61720 | ||||||||
\(928\) | −3.23999 | −0.106358 | ||||||||
\(929\) | 8.57591 | 0.281367 | 0.140683 | − | 0.990055i | \(-0.455070\pi\) | ||||
0.140683 | + | 0.990055i | \(0.455070\pi\) | |||||||
\(930\) | −0.149721 | −0.00490953 | ||||||||
\(931\) | −0.859599 | −0.0281722 | ||||||||
\(932\) | 12.1671 | 0.398548 | ||||||||
\(933\) | −4.71937 | −0.154505 | ||||||||
\(934\) | 41.5663 | 1.36009 | ||||||||
\(935\) | 22.7633 | 0.744440 | ||||||||
\(936\) | −6.43203 | −0.210237 | ||||||||
\(937\) | 31.3884 | 1.02542 | 0.512708 | − | 0.858563i | \(-0.328643\pi\) | ||||
0.512708 | + | 0.858563i | \(0.328643\pi\) | |||||||
\(938\) | −33.7209 | −1.10103 | ||||||||
\(939\) | −1.30491 | −0.0425840 | ||||||||
\(940\) | 3.66547 | 0.119555 | ||||||||
\(941\) | −41.1008 | −1.33985 | −0.669924 | − | 0.742430i | \(-0.733673\pi\) | ||||
−0.669924 | + | 0.742430i | \(0.733673\pi\) | |||||||
\(942\) | −2.97615 | −0.0969682 | ||||||||
\(943\) | 20.1845 | 0.657297 | ||||||||
\(944\) | 8.43747 | 0.274616 | ||||||||
\(945\) | −3.14637 | −0.102351 | ||||||||
\(946\) | −5.25330 | −0.170800 | ||||||||
\(947\) | 56.8589 | 1.84767 | 0.923833 | − | 0.382795i | \(-0.125039\pi\) | ||||
0.923833 | + | 0.382795i | \(0.125039\pi\) | |||||||
\(948\) | 2.52890 | 0.0821348 | ||||||||
\(949\) | −0.599307 | −0.0194543 | ||||||||
\(950\) | −4.36569 | −0.141642 | ||||||||
\(951\) | 3.42034 | 0.110912 | ||||||||
\(952\) | −16.9046 | −0.547881 | ||||||||
\(953\) | 14.7202 | 0.476833 | 0.238417 | − | 0.971163i | \(-0.423372\pi\) | ||||
0.238417 | + | 0.971163i | \(0.423372\pi\) | |||||||
\(954\) | −13.6437 | −0.441731 | ||||||||
\(955\) | 16.0007 | 0.517771 | ||||||||
\(956\) | −0.200567 | −0.00648681 | ||||||||
\(957\) | 3.64097 | 0.117696 | ||||||||
\(958\) | 15.9662 | 0.515844 | ||||||||
\(959\) | −3.84320 | −0.124103 | ||||||||
\(960\) | 0.188819 | 0.00609411 | ||||||||
\(961\) | −30.3713 | −0.979718 | ||||||||
\(962\) | 25.6337 | 0.826463 | ||||||||
\(963\) | −19.6691 | −0.633827 | ||||||||
\(964\) | −3.87182 | −0.124703 | ||||||||
\(965\) | 13.9369 | 0.448646 | ||||||||
\(966\) | 4.26426 | 0.137200 | ||||||||
\(967\) | 40.6887 | 1.30846 | 0.654230 | − | 0.756295i | \(-0.272993\pi\) | ||||
0.654230 | + | 0.756295i | \(0.272993\pi\) | |||||||
\(968\) | −11.4678 | −0.368588 | ||||||||
\(969\) | −1.42955 | −0.0459237 | ||||||||
\(970\) | 2.02080 | 0.0648838 | ||||||||
\(971\) | −25.3784 | −0.814432 | −0.407216 | − | 0.913332i | \(-0.633500\pi\) | ||||
−0.407216 | + | 0.913332i | \(0.633500\pi\) | |||||||
\(972\) | 6.24200 | 0.200212 | ||||||||
\(973\) | 30.9134 | 0.991039 | ||||||||
\(974\) | −27.7570 | −0.889392 | ||||||||
\(975\) | 2.26145 | 0.0724245 | ||||||||
\(976\) | −11.8128 | −0.378120 | ||||||||
\(977\) | −39.0591 | −1.24961 | −0.624806 | − | 0.780780i | \(-0.714822\pi\) | ||||
−0.624806 | + | 0.780780i | \(0.714822\pi\) | |||||||
\(978\) | 1.08733 | 0.0347689 | ||||||||
\(979\) | 45.5303 | 1.45515 | ||||||||
\(980\) | 0.684616 | 0.0218693 | ||||||||
\(981\) | −10.0631 | −0.321289 | ||||||||
\(982\) | 32.0305 | 1.02214 | ||||||||
\(983\) | 14.4996 | 0.462464 | 0.231232 | − | 0.972899i | \(-0.425724\pi\) | ||||
0.231232 | + | 0.972899i | \(0.425724\pi\) | |||||||
\(984\) | 0.745869 | 0.0237774 | ||||||||
\(985\) | 4.39624 | 0.140076 | ||||||||
\(986\) | −19.5365 | −0.622170 | ||||||||
\(987\) | 3.05896 | 0.0973677 | ||||||||
\(988\) | 2.18494 | 0.0695124 | ||||||||
\(989\) | −7.11053 | −0.226102 | ||||||||
\(990\) | 11.1132 | 0.353200 | ||||||||
\(991\) | 57.5515 | 1.82818 | 0.914092 | − | 0.405507i | \(-0.132905\pi\) | ||||
0.914092 | + | 0.405507i | \(0.132905\pi\) | |||||||
\(992\) | −0.792931 | −0.0251756 | ||||||||
\(993\) | 2.21371 | 0.0702499 | ||||||||
\(994\) | 5.13848 | 0.162983 | ||||||||
\(995\) | −1.77818 | −0.0563722 | ||||||||
\(996\) | −3.16680 | −0.100344 | ||||||||
\(997\) | −32.0248 | −1.01424 | −0.507118 | − | 0.861877i | \(-0.669289\pi\) | ||||
−0.507118 | + | 0.861877i | \(0.669289\pi\) | |||||||
\(998\) | 15.2312 | 0.482135 | ||||||||
\(999\) | −16.5321 | −0.523054 |
(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 | 8018.2.a.h.1.20 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.h.1.20 | ✓ | 41 | 1.1 | even | 1 | trivial |