Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8017,2,Mod(1,8017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8017, 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("8017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8017.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: | \(64.0160673005\) |
Analytic rank: | \(0\) |
Dimension: | \(340\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64379 | −1.86944 | −0.934722 | − | 0.355380i | \(-0.884351\pi\) | ||||
−0.934722 | + | 0.355380i | \(0.884351\pi\) | |||||||
\(3\) | 0.908830 | 0.524713 | 0.262357 | − | 0.964971i | \(-0.415500\pi\) | ||||
0.262357 | + | 0.964971i | \(0.415500\pi\) | |||||||
\(4\) | 4.98964 | 2.49482 | ||||||||
\(5\) | −0.356677 | −0.159511 | −0.0797554 | − | 0.996814i | \(-0.525414\pi\) | ||||
−0.0797554 | + | 0.996814i | \(0.525414\pi\) | |||||||
\(6\) | −2.40276 | −0.980921 | ||||||||
\(7\) | −1.07237 | −0.405316 | −0.202658 | − | 0.979250i | \(-0.564958\pi\) | ||||
−0.202658 | + | 0.979250i | \(0.564958\pi\) | |||||||
\(8\) | −7.90399 | −2.79448 | ||||||||
\(9\) | −2.17403 | −0.724676 | ||||||||
\(10\) | 0.942979 | 0.298196 | ||||||||
\(11\) | −0.652772 | −0.196818 | −0.0984091 | − | 0.995146i | \(-0.531375\pi\) | ||||
−0.0984091 | + | 0.995146i | \(0.531375\pi\) | |||||||
\(12\) | 4.53473 | 1.30906 | ||||||||
\(13\) | −3.79655 | −1.05297 | −0.526486 | − | 0.850184i | \(-0.676491\pi\) | ||||
−0.526486 | + | 0.850184i | \(0.676491\pi\) | |||||||
\(14\) | 2.83511 | 0.757716 | ||||||||
\(15\) | −0.324158 | −0.0836973 | ||||||||
\(16\) | 10.9172 | 2.72930 | ||||||||
\(17\) | −0.227594 | −0.0551997 | −0.0275999 | − | 0.999619i | \(-0.508786\pi\) | ||||
−0.0275999 | + | 0.999619i | \(0.508786\pi\) | |||||||
\(18\) | 5.74768 | 1.35474 | ||||||||
\(19\) | −1.90322 | −0.436628 | −0.218314 | − | 0.975879i | \(-0.570056\pi\) | ||||
−0.218314 | + | 0.975879i | \(0.570056\pi\) | |||||||
\(20\) | −1.77969 | −0.397950 | ||||||||
\(21\) | −0.974599 | −0.212675 | ||||||||
\(22\) | 1.72579 | 0.367940 | ||||||||
\(23\) | −3.74691 | −0.781285 | −0.390642 | − | 0.920543i | \(-0.627747\pi\) | ||||
−0.390642 | + | 0.920543i | \(0.627747\pi\) | |||||||
\(24\) | −7.18338 | −1.46630 | ||||||||
\(25\) | −4.87278 | −0.974556 | ||||||||
\(26\) | 10.0373 | 1.96847 | ||||||||
\(27\) | −4.70231 | −0.904960 | ||||||||
\(28\) | −5.35072 | −1.01119 | ||||||||
\(29\) | −9.34950 | −1.73616 | −0.868079 | − | 0.496426i | \(-0.834645\pi\) | ||||
−0.868079 | + | 0.496426i | \(0.834645\pi\) | |||||||
\(30\) | 0.857008 | 0.156467 | ||||||||
\(31\) | −10.6116 | −1.90590 | −0.952951 | − | 0.303123i | \(-0.901971\pi\) | ||||
−0.952951 | + | 0.303123i | \(0.901971\pi\) | |||||||
\(32\) | −13.0549 | −2.30780 | ||||||||
\(33\) | −0.593258 | −0.103273 | ||||||||
\(34\) | 0.601712 | 0.103193 | ||||||||
\(35\) | 0.382488 | 0.0646523 | ||||||||
\(36\) | −10.8476 | −1.80794 | ||||||||
\(37\) | −0.200630 | −0.0329834 | −0.0164917 | − | 0.999864i | \(-0.505250\pi\) | ||||
−0.0164917 | + | 0.999864i | \(0.505250\pi\) | |||||||
\(38\) | 5.03171 | 0.816252 | ||||||||
\(39\) | −3.45041 | −0.552508 | ||||||||
\(40\) | 2.81917 | 0.445750 | ||||||||
\(41\) | −2.97114 | −0.464014 | −0.232007 | − | 0.972714i | \(-0.574529\pi\) | ||||
−0.232007 | + | 0.972714i | \(0.574529\pi\) | |||||||
\(42\) | 2.57664 | 0.397584 | ||||||||
\(43\) | −5.29616 | −0.807657 | −0.403828 | − | 0.914835i | \(-0.632321\pi\) | ||||
−0.403828 | + | 0.914835i | \(0.632321\pi\) | |||||||
\(44\) | −3.25710 | −0.491026 | ||||||||
\(45\) | 0.775426 | 0.115594 | ||||||||
\(46\) | 9.90605 | 1.46057 | ||||||||
\(47\) | 9.33521 | 1.36168 | 0.680840 | − | 0.732432i | \(-0.261615\pi\) | ||||
0.680840 | + | 0.732432i | \(0.261615\pi\) | |||||||
\(48\) | 9.92189 | 1.43210 | ||||||||
\(49\) | −5.85003 | −0.835719 | ||||||||
\(50\) | 12.8826 | 1.82188 | ||||||||
\(51\) | −0.206845 | −0.0289640 | ||||||||
\(52\) | −18.9434 | −2.62698 | ||||||||
\(53\) | −2.52609 | −0.346985 | −0.173493 | − | 0.984835i | \(-0.555505\pi\) | ||||
−0.173493 | + | 0.984835i | \(0.555505\pi\) | |||||||
\(54\) | 12.4319 | 1.69177 | ||||||||
\(55\) | 0.232829 | 0.0313946 | ||||||||
\(56\) | 8.47597 | 1.13265 | ||||||||
\(57\) | −1.72970 | −0.229104 | ||||||||
\(58\) | 24.7181 | 3.24565 | ||||||||
\(59\) | −1.40468 | −0.182874 | −0.0914368 | − | 0.995811i | \(-0.529146\pi\) | ||||
−0.0914368 | + | 0.995811i | \(0.529146\pi\) | |||||||
\(60\) | −1.61743 | −0.208810 | ||||||||
\(61\) | 9.22310 | 1.18090 | 0.590448 | − | 0.807075i | \(-0.298951\pi\) | ||||
0.590448 | + | 0.807075i | \(0.298951\pi\) | |||||||
\(62\) | 28.0549 | 3.56298 | ||||||||
\(63\) | 2.33136 | 0.293723 | ||||||||
\(64\) | 12.6800 | 1.58500 | ||||||||
\(65\) | 1.35414 | 0.167960 | ||||||||
\(66\) | 1.56845 | 0.193063 | ||||||||
\(67\) | 13.6519 | 1.66784 | 0.833921 | − | 0.551884i | \(-0.186091\pi\) | ||||
0.833921 | + | 0.551884i | \(0.186091\pi\) | |||||||
\(68\) | −1.13561 | −0.137713 | ||||||||
\(69\) | −3.40530 | −0.409950 | ||||||||
\(70\) | −1.01122 | −0.120864 | ||||||||
\(71\) | −0.588825 | −0.0698806 | −0.0349403 | − | 0.999389i | \(-0.511124\pi\) | ||||
−0.0349403 | + | 0.999389i | \(0.511124\pi\) | |||||||
\(72\) | 17.1835 | 2.02509 | ||||||||
\(73\) | −3.20753 | −0.375413 | −0.187706 | − | 0.982225i | \(-0.560105\pi\) | ||||
−0.187706 | + | 0.982225i | \(0.560105\pi\) | |||||||
\(74\) | 0.530425 | 0.0616607 | ||||||||
\(75\) | −4.42853 | −0.511362 | ||||||||
\(76\) | −9.49637 | −1.08931 | ||||||||
\(77\) | 0.700011 | 0.0797736 | ||||||||
\(78\) | 9.12218 | 1.03288 | ||||||||
\(79\) | −4.36678 | −0.491302 | −0.245651 | − | 0.969358i | \(-0.579002\pi\) | ||||
−0.245651 | + | 0.969358i | \(0.579002\pi\) | |||||||
\(80\) | −3.89392 | −0.435353 | ||||||||
\(81\) | 2.24849 | 0.249832 | ||||||||
\(82\) | 7.85508 | 0.867449 | ||||||||
\(83\) | −11.1794 | −1.22709 | −0.613547 | − | 0.789658i | \(-0.710258\pi\) | ||||
−0.613547 | + | 0.789658i | \(0.710258\pi\) | |||||||
\(84\) | −4.86289 | −0.530585 | ||||||||
\(85\) | 0.0811776 | 0.00880495 | ||||||||
\(86\) | 14.0020 | 1.50987 | ||||||||
\(87\) | −8.49710 | −0.910985 | ||||||||
\(88\) | 5.15950 | 0.550004 | ||||||||
\(89\) | 3.34007 | 0.354047 | 0.177023 | − | 0.984207i | \(-0.443353\pi\) | ||||
0.177023 | + | 0.984207i | \(0.443353\pi\) | |||||||
\(90\) | −2.05006 | −0.216096 | ||||||||
\(91\) | 4.07129 | 0.426787 | ||||||||
\(92\) | −18.6957 | −1.94916 | ||||||||
\(93\) | −9.64415 | −1.00005 | ||||||||
\(94\) | −24.6803 | −2.54558 | ||||||||
\(95\) | 0.678834 | 0.0696469 | ||||||||
\(96\) | −11.8647 | −1.21093 | ||||||||
\(97\) | −11.5196 | −1.16964 | −0.584819 | − | 0.811164i | \(-0.698835\pi\) | ||||
−0.584819 | + | 0.811164i | \(0.698835\pi\) | |||||||
\(98\) | 15.4663 | 1.56233 | ||||||||
\(99\) | 1.41914 | 0.142629 | ||||||||
\(100\) | −24.3134 | −2.43134 | ||||||||
\(101\) | 8.25202 | 0.821106 | 0.410553 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410553 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(102\) | 0.546854 | 0.0541466 | ||||||||
\(103\) | −9.12163 | −0.898781 | −0.449390 | − | 0.893336i | \(-0.648359\pi\) | ||||
−0.449390 | + | 0.893336i | \(0.648359\pi\) | |||||||
\(104\) | 30.0079 | 2.94251 | ||||||||
\(105\) | 0.347617 | 0.0339239 | ||||||||
\(106\) | 6.67846 | 0.648670 | ||||||||
\(107\) | 4.46472 | 0.431621 | 0.215810 | − | 0.976435i | \(-0.430761\pi\) | ||||
0.215810 | + | 0.976435i | \(0.430761\pi\) | |||||||
\(108\) | −23.4628 | −2.25771 | ||||||||
\(109\) | 12.6304 | 1.20977 | 0.604885 | − | 0.796313i | \(-0.293219\pi\) | ||||
0.604885 | + | 0.796313i | \(0.293219\pi\) | |||||||
\(110\) | −0.615550 | −0.0586904 | ||||||||
\(111\) | −0.182339 | −0.0173068 | ||||||||
\(112\) | −11.7073 | −1.10623 | ||||||||
\(113\) | −11.8602 | −1.11571 | −0.557855 | − | 0.829938i | \(-0.688376\pi\) | ||||
−0.557855 | + | 0.829938i | \(0.688376\pi\) | |||||||
\(114\) | 4.57297 | 0.428298 | ||||||||
\(115\) | 1.33644 | 0.124623 | ||||||||
\(116\) | −46.6506 | −4.33140 | ||||||||
\(117\) | 8.25380 | 0.763064 | ||||||||
\(118\) | 3.71368 | 0.341872 | ||||||||
\(119\) | 0.244065 | 0.0223734 | ||||||||
\(120\) | 2.56214 | 0.233891 | ||||||||
\(121\) | −10.5739 | −0.961263 | ||||||||
\(122\) | −24.3840 | −2.20762 | ||||||||
\(123\) | −2.70026 | −0.243474 | ||||||||
\(124\) | −52.9481 | −4.75488 | ||||||||
\(125\) | 3.52139 | 0.314963 | ||||||||
\(126\) | −6.16362 | −0.549099 | ||||||||
\(127\) | −10.5950 | −0.940150 | −0.470075 | − | 0.882627i | \(-0.655773\pi\) | ||||
−0.470075 | + | 0.882627i | \(0.655773\pi\) | |||||||
\(128\) | −7.41347 | −0.655265 | ||||||||
\(129\) | −4.81331 | −0.423788 | ||||||||
\(130\) | −3.58007 | −0.313993 | ||||||||
\(131\) | 19.9734 | 1.74508 | 0.872542 | − | 0.488540i | \(-0.162470\pi\) | ||||
0.872542 | + | 0.488540i | \(0.162470\pi\) | |||||||
\(132\) | −2.96015 | −0.257648 | ||||||||
\(133\) | 2.04095 | 0.176973 | ||||||||
\(134\) | −36.0927 | −3.11794 | ||||||||
\(135\) | 1.67721 | 0.144351 | ||||||||
\(136\) | 1.79890 | 0.154255 | ||||||||
\(137\) | 16.9407 | 1.44734 | 0.723671 | − | 0.690145i | \(-0.242453\pi\) | ||||
0.723671 | + | 0.690145i | \(0.242453\pi\) | |||||||
\(138\) | 9.00292 | 0.766379 | ||||||||
\(139\) | 22.7870 | 1.93277 | 0.966386 | − | 0.257096i | \(-0.0827656\pi\) | ||||
0.966386 | + | 0.257096i | \(0.0827656\pi\) | |||||||
\(140\) | 1.90848 | 0.161296 | ||||||||
\(141\) | 8.48411 | 0.714491 | ||||||||
\(142\) | 1.55673 | 0.130638 | ||||||||
\(143\) | 2.47828 | 0.207244 | ||||||||
\(144\) | −23.7343 | −1.97786 | ||||||||
\(145\) | 3.33475 | 0.276936 | ||||||||
\(146\) | 8.48004 | 0.701813 | ||||||||
\(147\) | −5.31668 | −0.438512 | ||||||||
\(148\) | −1.00107 | −0.0822878 | ||||||||
\(149\) | 10.5857 | 0.867213 | 0.433607 | − | 0.901102i | \(-0.357241\pi\) | ||||
0.433607 | + | 0.901102i | \(0.357241\pi\) | |||||||
\(150\) | 11.7081 | 0.955963 | ||||||||
\(151\) | −5.45502 | −0.443924 | −0.221962 | − | 0.975055i | \(-0.571246\pi\) | ||||
−0.221962 | + | 0.975055i | \(0.571246\pi\) | |||||||
\(152\) | 15.0430 | 1.22015 | ||||||||
\(153\) | 0.494797 | 0.0400019 | ||||||||
\(154\) | −1.85068 | −0.149132 | ||||||||
\(155\) | 3.78492 | 0.304012 | ||||||||
\(156\) | −17.2163 | −1.37841 | ||||||||
\(157\) | 7.40151 | 0.590705 | 0.295352 | − | 0.955388i | \(-0.404563\pi\) | ||||
0.295352 | + | 0.955388i | \(0.404563\pi\) | |||||||
\(158\) | 11.5449 | 0.918461 | ||||||||
\(159\) | −2.29579 | −0.182068 | ||||||||
\(160\) | 4.65638 | 0.368119 | ||||||||
\(161\) | 4.01806 | 0.316668 | ||||||||
\(162\) | −5.94453 | −0.467047 | ||||||||
\(163\) | 0.540141 | 0.0423071 | 0.0211536 | − | 0.999776i | \(-0.493266\pi\) | ||||
0.0211536 | + | 0.999776i | \(0.493266\pi\) | |||||||
\(164\) | −14.8249 | −1.15763 | ||||||||
\(165\) | 0.211601 | 0.0164732 | ||||||||
\(166\) | 29.5559 | 2.29398 | ||||||||
\(167\) | −24.1159 | −1.86614 | −0.933072 | − | 0.359690i | \(-0.882882\pi\) | ||||
−0.933072 | + | 0.359690i | \(0.882882\pi\) | |||||||
\(168\) | 7.70321 | 0.594316 | ||||||||
\(169\) | 1.41377 | 0.108751 | ||||||||
\(170\) | −0.214617 | −0.0164604 | ||||||||
\(171\) | 4.13765 | 0.316414 | ||||||||
\(172\) | −26.4259 | −2.01496 | ||||||||
\(173\) | 17.5529 | 1.33452 | 0.667261 | − | 0.744824i | \(-0.267467\pi\) | ||||
0.667261 | + | 0.744824i | \(0.267467\pi\) | |||||||
\(174\) | 22.4646 | 1.70303 | ||||||||
\(175\) | 5.22541 | 0.395004 | ||||||||
\(176\) | −7.12645 | −0.537177 | ||||||||
\(177\) | −1.27661 | −0.0959562 | ||||||||
\(178\) | −8.83045 | −0.661870 | ||||||||
\(179\) | 5.44975 | 0.407333 | 0.203667 | − | 0.979040i | \(-0.434714\pi\) | ||||
0.203667 | + | 0.979040i | \(0.434714\pi\) | |||||||
\(180\) | 3.86909 | 0.288385 | ||||||||
\(181\) | −16.5309 | −1.22873 | −0.614365 | − | 0.789022i | \(-0.710588\pi\) | ||||
−0.614365 | + | 0.789022i | \(0.710588\pi\) | |||||||
\(182\) | −10.7636 | −0.797855 | ||||||||
\(183\) | 8.38223 | 0.619632 | ||||||||
\(184\) | 29.6155 | 2.18329 | ||||||||
\(185\) | 0.0715602 | 0.00526121 | ||||||||
\(186\) | 25.4971 | 1.86954 | ||||||||
\(187\) | 0.148567 | 0.0108643 | ||||||||
\(188\) | 46.5793 | 3.39714 | ||||||||
\(189\) | 5.04260 | 0.366795 | ||||||||
\(190\) | −1.79470 | −0.130201 | ||||||||
\(191\) | −7.86741 | −0.569265 | −0.284633 | − | 0.958637i | \(-0.591872\pi\) | ||||
−0.284633 | + | 0.958637i | \(0.591872\pi\) | |||||||
\(192\) | 11.5239 | 0.831669 | ||||||||
\(193\) | −14.3749 | −1.03473 | −0.517364 | − | 0.855766i | \(-0.673087\pi\) | ||||
−0.517364 | + | 0.855766i | \(0.673087\pi\) | |||||||
\(194\) | 30.4554 | 2.18657 | ||||||||
\(195\) | 1.23068 | 0.0881310 | ||||||||
\(196\) | −29.1895 | −2.08497 | ||||||||
\(197\) | 24.6343 | 1.75512 | 0.877560 | − | 0.479466i | \(-0.159170\pi\) | ||||
0.877560 | + | 0.479466i | \(0.159170\pi\) | |||||||
\(198\) | −3.75192 | −0.266638 | ||||||||
\(199\) | 0.571632 | 0.0405219 | 0.0202609 | − | 0.999795i | \(-0.493550\pi\) | ||||
0.0202609 | + | 0.999795i | \(0.493550\pi\) | |||||||
\(200\) | 38.5144 | 2.72338 | ||||||||
\(201\) | 12.4072 | 0.875138 | ||||||||
\(202\) | −21.8166 | −1.53501 | ||||||||
\(203\) | 10.0261 | 0.703694 | ||||||||
\(204\) | −1.03208 | −0.0722600 | ||||||||
\(205\) | 1.05974 | 0.0740153 | ||||||||
\(206\) | 24.1157 | 1.68022 | ||||||||
\(207\) | 8.14589 | 0.566179 | ||||||||
\(208\) | −41.4477 | −2.87388 | ||||||||
\(209\) | 1.24237 | 0.0859363 | ||||||||
\(210\) | −0.919026 | −0.0634188 | ||||||||
\(211\) | 11.1453 | 0.767274 | 0.383637 | − | 0.923484i | \(-0.374671\pi\) | ||||
0.383637 | + | 0.923484i | \(0.374671\pi\) | |||||||
\(212\) | −12.6043 | −0.865666 | ||||||||
\(213\) | −0.535141 | −0.0366673 | ||||||||
\(214\) | −11.8038 | −0.806891 | ||||||||
\(215\) | 1.88902 | 0.128830 | ||||||||
\(216\) | 37.1670 | 2.52889 | ||||||||
\(217\) | 11.3795 | 0.772494 | ||||||||
\(218\) | −33.3921 | −2.26160 | ||||||||
\(219\) | −2.91510 | −0.196984 | ||||||||
\(220\) | 1.16173 | 0.0783238 | ||||||||
\(221\) | 0.864073 | 0.0581238 | ||||||||
\(222\) | 0.482066 | 0.0323542 | ||||||||
\(223\) | −10.6803 | −0.715204 | −0.357602 | − | 0.933874i | \(-0.616406\pi\) | ||||
−0.357602 | + | 0.933874i | \(0.616406\pi\) | |||||||
\(224\) | 13.9996 | 0.935390 | ||||||||
\(225\) | 10.5936 | 0.706238 | ||||||||
\(226\) | 31.3558 | 2.08576 | ||||||||
\(227\) | −10.5338 | −0.699154 | −0.349577 | − | 0.936908i | \(-0.613675\pi\) | ||||
−0.349577 | + | 0.936908i | \(0.613675\pi\) | |||||||
\(228\) | −8.63058 | −0.571574 | ||||||||
\(229\) | 4.78513 | 0.316210 | 0.158105 | − | 0.987422i | \(-0.449462\pi\) | ||||
0.158105 | + | 0.987422i | \(0.449462\pi\) | |||||||
\(230\) | −3.53326 | −0.232976 | ||||||||
\(231\) | 0.636190 | 0.0418583 | ||||||||
\(232\) | 73.8983 | 4.85166 | ||||||||
\(233\) | 15.1962 | 0.995537 | 0.497769 | − | 0.867310i | \(-0.334153\pi\) | ||||
0.497769 | + | 0.867310i | \(0.334153\pi\) | |||||||
\(234\) | −21.8213 | −1.42651 | ||||||||
\(235\) | −3.32965 | −0.217202 | ||||||||
\(236\) | −7.00884 | −0.456237 | ||||||||
\(237\) | −3.96866 | −0.257792 | ||||||||
\(238\) | −0.645256 | −0.0418257 | ||||||||
\(239\) | −21.9089 | −1.41717 | −0.708584 | − | 0.705626i | \(-0.750666\pi\) | ||||
−0.708584 | + | 0.705626i | \(0.750666\pi\) | |||||||
\(240\) | −3.53891 | −0.228436 | ||||||||
\(241\) | −6.99140 | −0.450356 | −0.225178 | − | 0.974318i | \(-0.572296\pi\) | ||||
−0.225178 | + | 0.974318i | \(0.572296\pi\) | |||||||
\(242\) | 27.9552 | 1.79703 | ||||||||
\(243\) | 16.1504 | 1.03605 | ||||||||
\(244\) | 46.0199 | 2.94612 | ||||||||
\(245\) | 2.08657 | 0.133306 | ||||||||
\(246\) | 7.13893 | 0.455162 | ||||||||
\(247\) | 7.22566 | 0.459757 | ||||||||
\(248\) | 83.8741 | 5.32601 | ||||||||
\(249\) | −10.1601 | −0.643872 | ||||||||
\(250\) | −9.30983 | −0.588805 | ||||||||
\(251\) | 11.4771 | 0.724431 | 0.362215 | − | 0.932094i | \(-0.382020\pi\) | ||||
0.362215 | + | 0.932094i | \(0.382020\pi\) | |||||||
\(252\) | 11.6326 | 0.732786 | ||||||||
\(253\) | 2.44588 | 0.153771 | ||||||||
\(254\) | 28.0109 | 1.75756 | ||||||||
\(255\) | 0.0737766 | 0.00462007 | ||||||||
\(256\) | −5.76029 | −0.360018 | ||||||||
\(257\) | −13.9209 | −0.868360 | −0.434180 | − | 0.900826i | \(-0.642962\pi\) | ||||
−0.434180 | + | 0.900826i | \(0.642962\pi\) | |||||||
\(258\) | 12.7254 | 0.792248 | ||||||||
\(259\) | 0.215149 | 0.0133687 | ||||||||
\(260\) | 6.75667 | 0.419031 | ||||||||
\(261\) | 20.3261 | 1.25815 | ||||||||
\(262\) | −52.8055 | −3.26233 | ||||||||
\(263\) | 8.40769 | 0.518440 | 0.259220 | − | 0.965818i | \(-0.416534\pi\) | ||||
0.259220 | + | 0.965818i | \(0.416534\pi\) | |||||||
\(264\) | 4.68911 | 0.288594 | ||||||||
\(265\) | 0.900999 | 0.0553479 | ||||||||
\(266\) | −5.39584 | −0.330840 | ||||||||
\(267\) | 3.03555 | 0.185773 | ||||||||
\(268\) | 68.1179 | 4.16096 | ||||||||
\(269\) | −11.6712 | −0.711604 | −0.355802 | − | 0.934561i | \(-0.615792\pi\) | ||||
−0.355802 | + | 0.934561i | \(0.615792\pi\) | |||||||
\(270\) | −4.43418 | −0.269856 | ||||||||
\(271\) | −1.43636 | −0.0872528 | −0.0436264 | − | 0.999048i | \(-0.513891\pi\) | ||||
−0.0436264 | + | 0.999048i | \(0.513891\pi\) | |||||||
\(272\) | −2.48470 | −0.150657 | ||||||||
\(273\) | 3.70011 | 0.223941 | ||||||||
\(274\) | −44.7877 | −2.70572 | ||||||||
\(275\) | 3.18081 | 0.191810 | ||||||||
\(276\) | −16.9912 | −1.02275 | ||||||||
\(277\) | 9.97030 | 0.599057 | 0.299529 | − | 0.954087i | \(-0.403171\pi\) | ||||
0.299529 | + | 0.954087i | \(0.403171\pi\) | |||||||
\(278\) | −60.2442 | −3.61321 | ||||||||
\(279\) | 23.0700 | 1.38116 | ||||||||
\(280\) | −3.02318 | −0.180670 | ||||||||
\(281\) | −12.2578 | −0.731239 | −0.365620 | − | 0.930764i | \(-0.619143\pi\) | ||||
−0.365620 | + | 0.930764i | \(0.619143\pi\) | |||||||
\(282\) | −22.4302 | −1.33570 | ||||||||
\(283\) | −1.27881 | −0.0760172 | −0.0380086 | − | 0.999277i | \(-0.512101\pi\) | ||||
−0.0380086 | + | 0.999277i | \(0.512101\pi\) | |||||||
\(284\) | −2.93802 | −0.174340 | ||||||||
\(285\) | 0.616944 | 0.0365446 | ||||||||
\(286\) | −6.55205 | −0.387431 | ||||||||
\(287\) | 3.18615 | 0.188073 | ||||||||
\(288\) | 28.3817 | 1.67241 | ||||||||
\(289\) | −16.9482 | −0.996953 | ||||||||
\(290\) | −8.81638 | −0.517716 | ||||||||
\(291\) | −10.4694 | −0.613725 | ||||||||
\(292\) | −16.0044 | −0.936587 | ||||||||
\(293\) | 18.2664 | 1.06714 | 0.533568 | − | 0.845757i | \(-0.320851\pi\) | ||||
0.533568 | + | 0.845757i | \(0.320851\pi\) | |||||||
\(294\) | 14.0562 | 0.819774 | ||||||||
\(295\) | 0.501017 | 0.0291703 | ||||||||
\(296\) | 1.58578 | 0.0921716 | ||||||||
\(297\) | 3.06954 | 0.178113 | ||||||||
\(298\) | −27.9864 | −1.62121 | ||||||||
\(299\) | 14.2253 | 0.822672 | ||||||||
\(300\) | −22.0968 | −1.27576 | ||||||||
\(301\) | 5.67943 | 0.327357 | ||||||||
\(302\) | 14.4220 | 0.829890 | ||||||||
\(303\) | 7.49968 | 0.430845 | ||||||||
\(304\) | −20.7778 | −1.19169 | ||||||||
\(305\) | −3.28967 | −0.188366 | ||||||||
\(306\) | −1.30814 | −0.0747814 | ||||||||
\(307\) | −23.0818 | −1.31735 | −0.658674 | − | 0.752428i | \(-0.728882\pi\) | ||||
−0.658674 | + | 0.752428i | \(0.728882\pi\) | |||||||
\(308\) | 3.49280 | 0.199021 | ||||||||
\(309\) | −8.29001 | −0.471602 | ||||||||
\(310\) | −10.0065 | −0.568333 | ||||||||
\(311\) | 6.94828 | 0.394001 | 0.197000 | − | 0.980403i | \(-0.436880\pi\) | ||||
0.197000 | + | 0.980403i | \(0.436880\pi\) | |||||||
\(312\) | 27.2720 | 1.54397 | ||||||||
\(313\) | −5.31450 | −0.300393 | −0.150197 | − | 0.988656i | \(-0.547991\pi\) | ||||
−0.150197 | + | 0.988656i | \(0.547991\pi\) | |||||||
\(314\) | −19.5681 | −1.10429 | ||||||||
\(315\) | −0.831540 | −0.0468520 | ||||||||
\(316\) | −21.7887 | −1.22571 | ||||||||
\(317\) | 18.3966 | 1.03326 | 0.516628 | − | 0.856210i | \(-0.327187\pi\) | ||||
0.516628 | + | 0.856210i | \(0.327187\pi\) | |||||||
\(318\) | 6.06959 | 0.340366 | ||||||||
\(319\) | 6.10309 | 0.341707 | ||||||||
\(320\) | −4.52266 | −0.252824 | ||||||||
\(321\) | 4.05767 | 0.226477 | ||||||||
\(322\) | −10.6229 | −0.591992 | ||||||||
\(323\) | 0.433162 | 0.0241018 | ||||||||
\(324\) | 11.2191 | 0.623285 | ||||||||
\(325\) | 18.4997 | 1.02618 | ||||||||
\(326\) | −1.42802 | −0.0790908 | ||||||||
\(327\) | 11.4789 | 0.634782 | ||||||||
\(328\) | 23.4839 | 1.29668 | ||||||||
\(329\) | −10.0108 | −0.551911 | ||||||||
\(330\) | −0.559430 | −0.0307956 | ||||||||
\(331\) | −4.22492 | −0.232222 | −0.116111 | − | 0.993236i | \(-0.537043\pi\) | ||||
−0.116111 | + | 0.993236i | \(0.537043\pi\) | |||||||
\(332\) | −55.7810 | −3.06138 | ||||||||
\(333\) | 0.436176 | 0.0239023 | ||||||||
\(334\) | 63.7574 | 3.48865 | ||||||||
\(335\) | −4.86931 | −0.266039 | ||||||||
\(336\) | −10.6399 | −0.580454 | ||||||||
\(337\) | 20.7196 | 1.12867 | 0.564335 | − | 0.825546i | \(-0.309133\pi\) | ||||
0.564335 | + | 0.825546i | \(0.309133\pi\) | |||||||
\(338\) | −3.73771 | −0.203305 | ||||||||
\(339\) | −10.7789 | −0.585428 | ||||||||
\(340\) | 0.405047 | 0.0219668 | ||||||||
\(341\) | 6.92697 | 0.375116 | ||||||||
\(342\) | −10.9391 | −0.591518 | ||||||||
\(343\) | 13.7799 | 0.744047 | ||||||||
\(344\) | 41.8608 | 2.25698 | ||||||||
\(345\) | 1.21459 | 0.0653915 | ||||||||
\(346\) | −46.4062 | −2.49481 | ||||||||
\(347\) | 23.9713 | 1.28685 | 0.643424 | − | 0.765510i | \(-0.277513\pi\) | ||||
0.643424 | + | 0.765510i | \(0.277513\pi\) | |||||||
\(348\) | −42.3975 | −2.27274 | ||||||||
\(349\) | −17.0362 | −0.911928 | −0.455964 | − | 0.889998i | \(-0.650705\pi\) | ||||
−0.455964 | + | 0.889998i | \(0.650705\pi\) | |||||||
\(350\) | −13.8149 | −0.738437 | ||||||||
\(351\) | 17.8525 | 0.952898 | ||||||||
\(352\) | 8.52187 | 0.454217 | ||||||||
\(353\) | −1.32391 | −0.0704645 | −0.0352323 | − | 0.999379i | \(-0.511217\pi\) | ||||
−0.0352323 | + | 0.999379i | \(0.511217\pi\) | |||||||
\(354\) | 3.37510 | 0.179385 | ||||||||
\(355\) | 0.210020 | 0.0111467 | ||||||||
\(356\) | 16.6657 | 0.883283 | ||||||||
\(357\) | 0.221813 | 0.0117396 | ||||||||
\(358\) | −14.4080 | −0.761487 | ||||||||
\(359\) | −7.47054 | −0.394280 | −0.197140 | − | 0.980375i | \(-0.563165\pi\) | ||||
−0.197140 | + | 0.980375i | \(0.563165\pi\) | |||||||
\(360\) | −6.12895 | −0.323024 | ||||||||
\(361\) | −15.3778 | −0.809356 | ||||||||
\(362\) | 43.7042 | 2.29704 | ||||||||
\(363\) | −9.60986 | −0.504387 | ||||||||
\(364\) | 20.3143 | 1.06476 | ||||||||
\(365\) | 1.14405 | 0.0598824 | ||||||||
\(366\) | −22.1609 | −1.15837 | ||||||||
\(367\) | 9.20668 | 0.480585 | 0.240292 | − | 0.970701i | \(-0.422757\pi\) | ||||
0.240292 | + | 0.970701i | \(0.422757\pi\) | |||||||
\(368\) | −40.9058 | −2.13236 | ||||||||
\(369\) | 6.45935 | 0.336260 | ||||||||
\(370\) | −0.189190 | −0.00983554 | ||||||||
\(371\) | 2.70890 | 0.140639 | ||||||||
\(372\) | −48.1208 | −2.49495 | ||||||||
\(373\) | −24.4075 | −1.26377 | −0.631887 | − | 0.775060i | \(-0.717719\pi\) | ||||
−0.631887 | + | 0.775060i | \(0.717719\pi\) | |||||||
\(374\) | −0.392781 | −0.0203102 | ||||||||
\(375\) | 3.20035 | 0.165265 | ||||||||
\(376\) | −73.7853 | −3.80519 | ||||||||
\(377\) | 35.4958 | 1.82813 | ||||||||
\(378\) | −13.3316 | −0.685703 | ||||||||
\(379\) | −35.1655 | −1.80633 | −0.903164 | − | 0.429295i | \(-0.858762\pi\) | ||||
−0.903164 | + | 0.429295i | \(0.858762\pi\) | |||||||
\(380\) | 3.38713 | 0.173756 | ||||||||
\(381\) | −9.62901 | −0.493309 | ||||||||
\(382\) | 20.7998 | 1.06421 | ||||||||
\(383\) | 31.9516 | 1.63265 | 0.816326 | − | 0.577591i | \(-0.196007\pi\) | ||||
0.816326 | + | 0.577591i | \(0.196007\pi\) | |||||||
\(384\) | −6.73758 | −0.343826 | ||||||||
\(385\) | −0.249678 | −0.0127247 | ||||||||
\(386\) | 38.0042 | 1.93436 | ||||||||
\(387\) | 11.5140 | 0.585290 | ||||||||
\(388\) | −57.4787 | −2.91804 | ||||||||
\(389\) | −22.6466 | −1.14823 | −0.574114 | − | 0.818776i | \(-0.694653\pi\) | ||||
−0.574114 | + | 0.818776i | \(0.694653\pi\) | |||||||
\(390\) | −3.25367 | −0.164756 | ||||||||
\(391\) | 0.852776 | 0.0431267 | ||||||||
\(392\) | 46.2386 | 2.33540 | ||||||||
\(393\) | 18.1524 | 0.915668 | ||||||||
\(394\) | −65.1280 | −3.28110 | ||||||||
\(395\) | 1.55753 | 0.0783679 | ||||||||
\(396\) | 7.08102 | 0.355835 | ||||||||
\(397\) | 13.4830 | 0.676693 | 0.338346 | − | 0.941022i | \(-0.390132\pi\) | ||||
0.338346 | + | 0.941022i | \(0.390132\pi\) | |||||||
\(398\) | −1.51128 | −0.0757534 | ||||||||
\(399\) | 1.85487 | 0.0928598 | ||||||||
\(400\) | −53.1972 | −2.65986 | ||||||||
\(401\) | 13.5522 | 0.676763 | 0.338381 | − | 0.941009i | \(-0.390121\pi\) | ||||
0.338381 | + | 0.941009i | \(0.390121\pi\) | |||||||
\(402\) | −32.8021 | −1.63602 | ||||||||
\(403\) | 40.2875 | 2.00686 | ||||||||
\(404\) | 41.1746 | 2.04851 | ||||||||
\(405\) | −0.801983 | −0.0398509 | ||||||||
\(406\) | −26.5069 | −1.31552 | ||||||||
\(407\) | 0.130966 | 0.00649174 | ||||||||
\(408\) | 1.63490 | 0.0809394 | ||||||||
\(409\) | −12.3883 | −0.612563 | −0.306281 | − | 0.951941i | \(-0.599085\pi\) | ||||
−0.306281 | + | 0.951941i | \(0.599085\pi\) | |||||||
\(410\) | −2.80173 | −0.138367 | ||||||||
\(411\) | 15.3962 | 0.759439 | ||||||||
\(412\) | −45.5136 | −2.24230 | ||||||||
\(413\) | 1.50633 | 0.0741217 | ||||||||
\(414\) | −21.5360 | −1.05844 | ||||||||
\(415\) | 3.98742 | 0.195735 | ||||||||
\(416\) | 49.5635 | 2.43005 | ||||||||
\(417\) | 20.7095 | 1.01415 | ||||||||
\(418\) | −3.28456 | −0.160653 | ||||||||
\(419\) | 0.755266 | 0.0368972 | 0.0184486 | − | 0.999830i | \(-0.494127\pi\) | ||||
0.0184486 | + | 0.999830i | \(0.494127\pi\) | |||||||
\(420\) | 1.73448 | 0.0846340 | ||||||||
\(421\) | 20.8623 | 1.01677 | 0.508383 | − | 0.861131i | \(-0.330244\pi\) | ||||
0.508383 | + | 0.861131i | \(0.330244\pi\) | |||||||
\(422\) | −29.4659 | −1.43438 | ||||||||
\(423\) | −20.2950 | −0.986777 | ||||||||
\(424\) | 19.9662 | 0.969644 | ||||||||
\(425\) | 1.10902 | 0.0537953 | ||||||||
\(426\) | 1.41480 | 0.0685474 | ||||||||
\(427\) | −9.89054 | −0.478637 | ||||||||
\(428\) | 22.2773 | 1.07682 | ||||||||
\(429\) | 2.25233 | 0.108744 | ||||||||
\(430\) | −4.99417 | −0.240840 | ||||||||
\(431\) | −22.5143 | −1.08448 | −0.542238 | − | 0.840225i | \(-0.682423\pi\) | ||||
−0.542238 | + | 0.840225i | \(0.682423\pi\) | |||||||
\(432\) | −51.3362 | −2.46991 | ||||||||
\(433\) | −3.15249 | −0.151499 | −0.0757494 | − | 0.997127i | \(-0.524135\pi\) | ||||
−0.0757494 | + | 0.997127i | \(0.524135\pi\) | |||||||
\(434\) | −30.0852 | −1.44413 | ||||||||
\(435\) | 3.03072 | 0.145312 | ||||||||
\(436\) | 63.0210 | 3.01816 | ||||||||
\(437\) | 7.13119 | 0.341131 | ||||||||
\(438\) | 7.70691 | 0.368251 | ||||||||
\(439\) | −5.86133 | −0.279746 | −0.139873 | − | 0.990169i | \(-0.544669\pi\) | ||||
−0.139873 | + | 0.990169i | \(0.544669\pi\) | |||||||
\(440\) | −1.84027 | −0.0877316 | ||||||||
\(441\) | 12.7181 | 0.605625 | ||||||||
\(442\) | −2.28443 | −0.108659 | ||||||||
\(443\) | 10.0904 | 0.479410 | 0.239705 | − | 0.970846i | \(-0.422949\pi\) | ||||
0.239705 | + | 0.970846i | \(0.422949\pi\) | |||||||
\(444\) | −0.909805 | −0.0431775 | ||||||||
\(445\) | −1.19133 | −0.0564742 | ||||||||
\(446\) | 28.2364 | 1.33703 | ||||||||
\(447\) | 9.62059 | 0.455038 | ||||||||
\(448\) | −13.5976 | −0.642426 | ||||||||
\(449\) | −40.4369 | −1.90834 | −0.954168 | − | 0.299272i | \(-0.903256\pi\) | ||||
−0.954168 | + | 0.299272i | \(0.903256\pi\) | |||||||
\(450\) | −28.0072 | −1.32027 | ||||||||
\(451\) | 1.93948 | 0.0913265 | ||||||||
\(452\) | −59.1779 | −2.78350 | ||||||||
\(453\) | −4.95769 | −0.232932 | ||||||||
\(454\) | 27.8492 | 1.30703 | ||||||||
\(455\) | −1.45213 | −0.0680771 | ||||||||
\(456\) | 13.6715 | 0.640228 | ||||||||
\(457\) | −13.1113 | −0.613320 | −0.306660 | − | 0.951819i | \(-0.599212\pi\) | ||||
−0.306660 | + | 0.951819i | \(0.599212\pi\) | |||||||
\(458\) | −12.6509 | −0.591137 | ||||||||
\(459\) | 1.07022 | 0.0499536 | ||||||||
\(460\) | 6.66833 | 0.310913 | ||||||||
\(461\) | −7.09043 | −0.330234 | −0.165117 | − | 0.986274i | \(-0.552800\pi\) | ||||
−0.165117 | + | 0.986274i | \(0.552800\pi\) | |||||||
\(462\) | −1.68196 | −0.0782517 | ||||||||
\(463\) | −21.8302 | −1.01454 | −0.507269 | − | 0.861788i | \(-0.669345\pi\) | ||||
−0.507269 | + | 0.861788i | \(0.669345\pi\) | |||||||
\(464\) | −102.071 | −4.73851 | ||||||||
\(465\) | 3.43985 | 0.159519 | ||||||||
\(466\) | −40.1757 | −1.86110 | ||||||||
\(467\) | −20.2586 | −0.937455 | −0.468728 | − | 0.883343i | \(-0.655287\pi\) | ||||
−0.468728 | + | 0.883343i | \(0.655287\pi\) | |||||||
\(468\) | 41.1835 | 1.90371 | ||||||||
\(469\) | −14.6398 | −0.676004 | ||||||||
\(470\) | 8.80291 | 0.406048 | ||||||||
\(471\) | 6.72671 | 0.309950 | ||||||||
\(472\) | 11.1026 | 0.511037 | ||||||||
\(473\) | 3.45718 | 0.158962 | ||||||||
\(474\) | 10.4923 | 0.481928 | ||||||||
\(475\) | 9.27397 | 0.425519 | ||||||||
\(476\) | 1.21779 | 0.0558175 | ||||||||
\(477\) | 5.49180 | 0.251452 | ||||||||
\(478\) | 57.9226 | 2.64932 | ||||||||
\(479\) | −30.9697 | −1.41504 | −0.707522 | − | 0.706692i | \(-0.750187\pi\) | ||||
−0.707522 | + | 0.706692i | \(0.750187\pi\) | |||||||
\(480\) | 4.23185 | 0.193157 | ||||||||
\(481\) | 0.761703 | 0.0347307 | ||||||||
\(482\) | 18.4838 | 0.841915 | ||||||||
\(483\) | 3.65173 | 0.166160 | ||||||||
\(484\) | −52.7599 | −2.39818 | ||||||||
\(485\) | 4.10878 | 0.186570 | ||||||||
\(486\) | −42.6984 | −1.93684 | ||||||||
\(487\) | −2.25031 | −0.101971 | −0.0509855 | − | 0.998699i | \(-0.516236\pi\) | ||||
−0.0509855 | + | 0.998699i | \(0.516236\pi\) | |||||||
\(488\) | −72.8992 | −3.29999 | ||||||||
\(489\) | 0.490897 | 0.0221991 | ||||||||
\(490\) | −5.51646 | −0.249208 | ||||||||
\(491\) | −15.2552 | −0.688459 | −0.344229 | − | 0.938886i | \(-0.611860\pi\) | ||||
−0.344229 | + | 0.938886i | \(0.611860\pi\) | |||||||
\(492\) | −13.4733 | −0.607425 | ||||||||
\(493\) | 2.12789 | 0.0958355 | ||||||||
\(494\) | −19.1031 | −0.859491 | ||||||||
\(495\) | −0.506176 | −0.0227509 | ||||||||
\(496\) | −115.849 | −5.20179 | ||||||||
\(497\) | 0.631436 | 0.0283238 | ||||||||
\(498\) | 26.8613 | 1.20368 | ||||||||
\(499\) | −9.45334 | −0.423190 | −0.211595 | − | 0.977357i | \(-0.567866\pi\) | ||||
−0.211595 | + | 0.977357i | \(0.567866\pi\) | |||||||
\(500\) | 17.5705 | 0.785776 | ||||||||
\(501\) | −21.9172 | −0.979190 | ||||||||
\(502\) | −30.3432 | −1.35428 | ||||||||
\(503\) | 13.3344 | 0.594551 | 0.297276 | − | 0.954792i | \(-0.403922\pi\) | ||||
0.297276 | + | 0.954792i | \(0.403922\pi\) | |||||||
\(504\) | −18.4270 | −0.820804 | ||||||||
\(505\) | −2.94330 | −0.130975 | ||||||||
\(506\) | −6.46639 | −0.287466 | ||||||||
\(507\) | 1.28487 | 0.0570633 | ||||||||
\(508\) | −52.8650 | −2.34550 | ||||||||
\(509\) | −19.0744 | −0.845460 | −0.422730 | − | 0.906256i | \(-0.638928\pi\) | ||||
−0.422730 | + | 0.906256i | \(0.638928\pi\) | |||||||
\(510\) | −0.195050 | −0.00863696 | ||||||||
\(511\) | 3.43965 | 0.152161 | ||||||||
\(512\) | 30.0560 | 1.32830 | ||||||||
\(513\) | 8.94952 | 0.395131 | ||||||||
\(514\) | 36.8039 | 1.62335 | ||||||||
\(515\) | 3.25347 | 0.143365 | ||||||||
\(516\) | −24.0167 | −1.05727 | ||||||||
\(517\) | −6.09376 | −0.268003 | ||||||||
\(518\) | −0.568810 | −0.0249921 | ||||||||
\(519\) | 15.9526 | 0.700241 | ||||||||
\(520\) | −10.7031 | −0.469362 | ||||||||
\(521\) | 7.77550 | 0.340651 | 0.170325 | − | 0.985388i | \(-0.445518\pi\) | ||||
0.170325 | + | 0.985388i | \(0.445518\pi\) | |||||||
\(522\) | −53.7379 | −2.35205 | ||||||||
\(523\) | −25.1515 | −1.09980 | −0.549898 | − | 0.835232i | \(-0.685334\pi\) | ||||
−0.549898 | + | 0.835232i | \(0.685334\pi\) | |||||||
\(524\) | 99.6600 | 4.35367 | ||||||||
\(525\) | 4.74901 | 0.207264 | ||||||||
\(526\) | −22.2282 | −0.969195 | ||||||||
\(527\) | 2.41514 | 0.105205 | ||||||||
\(528\) | −6.47673 | −0.281864 | ||||||||
\(529\) | −8.96066 | −0.389594 | ||||||||
\(530\) | −2.38205 | −0.103470 | ||||||||
\(531\) | 3.05381 | 0.132524 | ||||||||
\(532\) | 10.1836 | 0.441515 | ||||||||
\(533\) | 11.2801 | 0.488595 | ||||||||
\(534\) | −8.02538 | −0.347292 | ||||||||
\(535\) | −1.59246 | −0.0688481 | ||||||||
\(536\) | −107.904 | −4.66075 | ||||||||
\(537\) | 4.95289 | 0.213733 | ||||||||
\(538\) | 30.8562 | 1.33030 | ||||||||
\(539\) | 3.81873 | 0.164485 | ||||||||
\(540\) | 8.36865 | 0.360129 | ||||||||
\(541\) | −13.2217 | −0.568446 | −0.284223 | − | 0.958758i | \(-0.591736\pi\) | ||||
−0.284223 | + | 0.958758i | \(0.591736\pi\) | |||||||
\(542\) | 3.79745 | 0.163114 | ||||||||
\(543\) | −15.0237 | −0.644730 | ||||||||
\(544\) | 2.97122 | 0.127390 | ||||||||
\(545\) | −4.50496 | −0.192971 | ||||||||
\(546\) | −9.78232 | −0.418645 | ||||||||
\(547\) | −11.0248 | −0.471387 | −0.235694 | − | 0.971827i | \(-0.575736\pi\) | ||||
−0.235694 | + | 0.971827i | \(0.575736\pi\) | |||||||
\(548\) | 84.5280 | 3.61086 | ||||||||
\(549\) | −20.0513 | −0.855768 | ||||||||
\(550\) | −8.40941 | −0.358579 | ||||||||
\(551\) | 17.7941 | 0.758056 | ||||||||
\(552\) | 26.9155 | 1.14560 | ||||||||
\(553\) | 4.68279 | 0.199133 | ||||||||
\(554\) | −26.3594 | −1.11990 | ||||||||
\(555\) | 0.0650361 | 0.00276063 | ||||||||
\(556\) | 113.699 | 4.82192 | ||||||||
\(557\) | 5.53247 | 0.234418 | 0.117209 | − | 0.993107i | \(-0.462605\pi\) | ||||
0.117209 | + | 0.993107i | \(0.462605\pi\) | |||||||
\(558\) | −60.9922 | −2.58201 | ||||||||
\(559\) | 20.1071 | 0.850441 | ||||||||
\(560\) | 4.17571 | 0.176456 | ||||||||
\(561\) | 0.135022 | 0.00570064 | ||||||||
\(562\) | 32.4071 | 1.36701 | ||||||||
\(563\) | 35.3766 | 1.49095 | 0.745474 | − | 0.666535i | \(-0.232223\pi\) | ||||
0.745474 | + | 0.666535i | \(0.232223\pi\) | |||||||
\(564\) | 42.3327 | 1.78253 | ||||||||
\(565\) | 4.23024 | 0.177968 | ||||||||
\(566\) | 3.38090 | 0.142110 | ||||||||
\(567\) | −2.41120 | −0.101261 | ||||||||
\(568\) | 4.65406 | 0.195280 | ||||||||
\(569\) | 21.9689 | 0.920985 | 0.460492 | − | 0.887664i | \(-0.347673\pi\) | ||||
0.460492 | + | 0.887664i | \(0.347673\pi\) | |||||||
\(570\) | −1.63107 | −0.0683181 | ||||||||
\(571\) | 23.5846 | 0.986984 | 0.493492 | − | 0.869750i | \(-0.335720\pi\) | ||||
0.493492 | + | 0.869750i | \(0.335720\pi\) | |||||||
\(572\) | 12.3657 | 0.517037 | ||||||||
\(573\) | −7.15013 | −0.298701 | ||||||||
\(574\) | −8.42353 | −0.351591 | ||||||||
\(575\) | 18.2579 | 0.761406 | ||||||||
\(576\) | −27.5667 | −1.14861 | ||||||||
\(577\) | 2.64797 | 0.110236 | 0.0551182 | − | 0.998480i | \(-0.482446\pi\) | ||||
0.0551182 | + | 0.998480i | \(0.482446\pi\) | |||||||
\(578\) | 44.8075 | 1.86375 | ||||||||
\(579\) | −13.0643 | −0.542935 | ||||||||
\(580\) | 16.6392 | 0.690905 | ||||||||
\(581\) | 11.9884 | 0.497361 | ||||||||
\(582\) | 27.6788 | 1.14732 | ||||||||
\(583\) | 1.64896 | 0.0682930 | ||||||||
\(584\) | 25.3523 | 1.04908 | ||||||||
\(585\) | −2.94394 | −0.121717 | ||||||||
\(586\) | −48.2927 | −1.99495 | ||||||||
\(587\) | 10.8798 | 0.449059 | 0.224530 | − | 0.974467i | \(-0.427915\pi\) | ||||
0.224530 | + | 0.974467i | \(0.427915\pi\) | |||||||
\(588\) | −26.5283 | −1.09401 | ||||||||
\(589\) | 20.1962 | 0.832171 | ||||||||
\(590\) | −1.32458 | −0.0545322 | ||||||||
\(591\) | 22.3884 | 0.920935 | ||||||||
\(592\) | −2.19033 | −0.0900219 | ||||||||
\(593\) | 14.1932 | 0.582844 | 0.291422 | − | 0.956595i | \(-0.405872\pi\) | ||||
0.291422 | + | 0.956595i | \(0.405872\pi\) | |||||||
\(594\) | −8.11522 | −0.332971 | ||||||||
\(595\) | −0.0870522 | −0.00356879 | ||||||||
\(596\) | 52.8188 | 2.16354 | ||||||||
\(597\) | 0.519516 | 0.0212624 | ||||||||
\(598\) | −37.6088 | −1.53794 | ||||||||
\(599\) | −27.8602 | −1.13834 | −0.569168 | − | 0.822221i | \(-0.692735\pi\) | ||||
−0.569168 | + | 0.822221i | \(0.692735\pi\) | |||||||
\(600\) | 35.0030 | 1.42899 | ||||||||
\(601\) | −30.7049 | −1.25248 | −0.626239 | − | 0.779631i | \(-0.715407\pi\) | ||||
−0.626239 | + | 0.779631i | \(0.715407\pi\) | |||||||
\(602\) | −15.0152 | −0.611975 | ||||||||
\(603\) | −29.6796 | −1.20864 | ||||||||
\(604\) | −27.2186 | −1.10751 | ||||||||
\(605\) | 3.77146 | 0.153332 | ||||||||
\(606\) | −19.8276 | −0.805441 | ||||||||
\(607\) | −0.580860 | −0.0235764 | −0.0117882 | − | 0.999931i | \(-0.503752\pi\) | ||||
−0.0117882 | + | 0.999931i | \(0.503752\pi\) | |||||||
\(608\) | 24.8463 | 1.00765 | ||||||||
\(609\) | 9.11201 | 0.369237 | ||||||||
\(610\) | 8.69719 | 0.352139 | ||||||||
\(611\) | −35.4415 | −1.43381 | ||||||||
\(612\) | 2.46886 | 0.0997976 | ||||||||
\(613\) | 30.5031 | 1.23201 | 0.616005 | − | 0.787742i | \(-0.288750\pi\) | ||||
0.616005 | + | 0.787742i | \(0.288750\pi\) | |||||||
\(614\) | 61.0235 | 2.46271 | ||||||||
\(615\) | 0.963121 | 0.0388368 | ||||||||
\(616\) | −5.53287 | −0.222926 | ||||||||
\(617\) | 20.8984 | 0.841339 | 0.420670 | − | 0.907214i | \(-0.361795\pi\) | ||||
0.420670 | + | 0.907214i | \(0.361795\pi\) | |||||||
\(618\) | 21.9171 | 0.881633 | ||||||||
\(619\) | −39.8652 | −1.60232 | −0.801158 | − | 0.598453i | \(-0.795782\pi\) | ||||
−0.801158 | + | 0.598453i | \(0.795782\pi\) | |||||||
\(620\) | 18.8854 | 0.758455 | ||||||||
\(621\) | 17.6191 | 0.707032 | ||||||||
\(622\) | −18.3698 | −0.736562 | ||||||||
\(623\) | −3.58178 | −0.143501 | ||||||||
\(624\) | −37.6689 | −1.50796 | ||||||||
\(625\) | 23.1079 | 0.924316 | ||||||||
\(626\) | 14.0504 | 0.561568 | ||||||||
\(627\) | 1.12910 | 0.0450919 | ||||||||
\(628\) | 36.9309 | 1.47370 | ||||||||
\(629\) | 0.0456624 | 0.00182068 | ||||||||
\(630\) | 2.19842 | 0.0875872 | ||||||||
\(631\) | 8.13020 | 0.323658 | 0.161829 | − | 0.986819i | \(-0.448261\pi\) | ||||
0.161829 | + | 0.986819i | \(0.448261\pi\) | |||||||
\(632\) | 34.5150 | 1.37293 | ||||||||
\(633\) | 10.1292 | 0.402599 | ||||||||
\(634\) | −48.6368 | −1.93162 | ||||||||
\(635\) | 3.77897 | 0.149964 | ||||||||
\(636\) | −11.4552 | −0.454226 | ||||||||
\(637\) | 22.2099 | 0.879989 | ||||||||
\(638\) | −16.1353 | −0.638803 | ||||||||
\(639\) | 1.28012 | 0.0506408 | ||||||||
\(640\) | 2.64421 | 0.104522 | ||||||||
\(641\) | −42.7840 | −1.68987 | −0.844934 | − | 0.534871i | \(-0.820360\pi\) | ||||
−0.844934 | + | 0.534871i | \(0.820360\pi\) | |||||||
\(642\) | −10.7276 | −0.423386 | ||||||||
\(643\) | −9.47879 | −0.373807 | −0.186903 | − | 0.982378i | \(-0.559845\pi\) | ||||
−0.186903 | + | 0.982378i | \(0.559845\pi\) | |||||||
\(644\) | 20.0487 | 0.790028 | ||||||||
\(645\) | 1.71680 | 0.0675987 | ||||||||
\(646\) | −1.14519 | −0.0450569 | ||||||||
\(647\) | 11.1859 | 0.439763 | 0.219882 | − | 0.975527i | \(-0.429433\pi\) | ||||
0.219882 | + | 0.975527i | \(0.429433\pi\) | |||||||
\(648\) | −17.7720 | −0.698150 | ||||||||
\(649\) | 0.916935 | 0.0359928 | ||||||||
\(650\) | −48.9095 | −1.91839 | ||||||||
\(651\) | 10.3421 | 0.405338 | ||||||||
\(652\) | 2.69511 | 0.105549 | ||||||||
\(653\) | −47.9946 | −1.87818 | −0.939088 | − | 0.343677i | \(-0.888327\pi\) | ||||
−0.939088 | + | 0.343677i | \(0.888327\pi\) | |||||||
\(654\) | −30.3477 | −1.18669 | ||||||||
\(655\) | −7.12404 | −0.278359 | ||||||||
\(656\) | −32.4366 | −1.26644 | ||||||||
\(657\) | 6.97326 | 0.272053 | ||||||||
\(658\) | 26.4664 | 1.03177 | ||||||||
\(659\) | 3.64355 | 0.141932 | 0.0709662 | − | 0.997479i | \(-0.477392\pi\) | ||||
0.0709662 | + | 0.997479i | \(0.477392\pi\) | |||||||
\(660\) | 1.05582 | 0.0410975 | ||||||||
\(661\) | −27.8058 | −1.08152 | −0.540759 | − | 0.841177i | \(-0.681863\pi\) | ||||
−0.540759 | + | 0.841177i | \(0.681863\pi\) | |||||||
\(662\) | 11.1698 | 0.434127 | ||||||||
\(663\) | 0.785295 | 0.0304983 | ||||||||
\(664\) | 88.3615 | 3.42909 | ||||||||
\(665\) | −0.727959 | −0.0282290 | ||||||||
\(666\) | −1.15316 | −0.0446840 | ||||||||
\(667\) | 35.0317 | 1.35643 | ||||||||
\(668\) | −120.330 | −4.65569 | ||||||||
\(669\) | −9.70655 | −0.375277 | ||||||||
\(670\) | 12.8734 | 0.497344 | ||||||||
\(671\) | −6.02058 | −0.232422 | ||||||||
\(672\) | 12.7233 | 0.490811 | ||||||||
\(673\) | 25.7178 | 0.991348 | 0.495674 | − | 0.868509i | \(-0.334921\pi\) | ||||
0.495674 | + | 0.868509i | \(0.334921\pi\) | |||||||
\(674\) | −54.7784 | −2.10999 | ||||||||
\(675\) | 22.9133 | 0.881935 | ||||||||
\(676\) | 7.05419 | 0.271315 | ||||||||
\(677\) | −11.9187 | −0.458074 | −0.229037 | − | 0.973418i | \(-0.573558\pi\) | ||||
−0.229037 | + | 0.973418i | \(0.573558\pi\) | |||||||
\(678\) | 28.4971 | 1.09442 | ||||||||
\(679\) | 12.3532 | 0.474074 | ||||||||
\(680\) | −0.641627 | −0.0246053 | ||||||||
\(681\) | −9.57344 | −0.366855 | ||||||||
\(682\) | −18.3135 | −0.701259 | ||||||||
\(683\) | −1.63351 | −0.0625046 | −0.0312523 | − | 0.999512i | \(-0.509950\pi\) | ||||
−0.0312523 | + | 0.999512i | \(0.509950\pi\) | |||||||
\(684\) | 20.6454 | 0.789396 | ||||||||
\(685\) | −6.04235 | −0.230866 | ||||||||
\(686\) | −36.4313 | −1.39095 | ||||||||
\(687\) | 4.34887 | 0.165920 | ||||||||
\(688\) | −57.8193 | −2.20434 | ||||||||
\(689\) | 9.59043 | 0.365366 | ||||||||
\(690\) | −3.21113 | −0.122246 | ||||||||
\(691\) | −36.6133 | −1.39283 | −0.696417 | − | 0.717637i | \(-0.745224\pi\) | ||||
−0.696417 | + | 0.717637i | \(0.745224\pi\) | |||||||
\(692\) | 87.5826 | 3.32939 | ||||||||
\(693\) | −1.52184 | −0.0578100 | ||||||||
\(694\) | −63.3752 | −2.40569 | ||||||||
\(695\) | −8.12761 | −0.308298 | ||||||||
\(696\) | 67.1610 | 2.54573 | ||||||||
\(697\) | 0.676215 | 0.0256135 | ||||||||
\(698\) | 45.0402 | 1.70480 | ||||||||
\(699\) | 13.8108 | 0.522371 | ||||||||
\(700\) | 26.0729 | 0.985463 | ||||||||
\(701\) | 13.2305 | 0.499709 | 0.249854 | − | 0.968283i | \(-0.419617\pi\) | ||||
0.249854 | + | 0.968283i | \(0.419617\pi\) | |||||||
\(702\) | −47.1984 | −1.78139 | ||||||||
\(703\) | 0.381844 | 0.0144015 | ||||||||
\(704\) | −8.27714 | −0.311956 | ||||||||
\(705\) | −3.02609 | −0.113969 | ||||||||
\(706\) | 3.50014 | 0.131729 | ||||||||
\(707\) | −8.84918 | −0.332808 | ||||||||
\(708\) | −6.36984 | −0.239393 | ||||||||
\(709\) | −36.5704 | −1.37343 | −0.686715 | − | 0.726927i | \(-0.740948\pi\) | ||||
−0.686715 | + | 0.726927i | \(0.740948\pi\) | |||||||
\(710\) | −0.555250 | −0.0208381 | ||||||||
\(711\) | 9.49351 | 0.356035 | ||||||||
\(712\) | −26.3999 | −0.989377 | ||||||||
\(713\) | 39.7608 | 1.48905 | ||||||||
\(714\) | −0.586428 | −0.0219465 | ||||||||
\(715\) | −0.883944 | −0.0330576 | ||||||||
\(716\) | 27.1923 | 1.01622 | ||||||||
\(717\) | −19.9114 | −0.743607 | ||||||||
\(718\) | 19.7505 | 0.737084 | ||||||||
\(719\) | 6.99009 | 0.260686 | 0.130343 | − | 0.991469i | \(-0.458392\pi\) | ||||
0.130343 | + | 0.991469i | \(0.458392\pi\) | |||||||
\(720\) | 8.46549 | 0.315490 | ||||||||
\(721\) | 9.78173 | 0.364291 | ||||||||
\(722\) | 40.6556 | 1.51305 | ||||||||
\(723\) | −6.35399 | −0.236307 | ||||||||
\(724\) | −82.4830 | −3.06546 | ||||||||
\(725\) | 45.5581 | 1.69198 | ||||||||
\(726\) | 25.4065 | 0.942923 | ||||||||
\(727\) | −17.5545 | −0.651061 | −0.325530 | − | 0.945532i | \(-0.605543\pi\) | ||||
−0.325530 | + | 0.945532i | \(0.605543\pi\) | |||||||
\(728\) | −32.1794 | −1.19265 | ||||||||
\(729\) | 7.93252 | 0.293797 | ||||||||
\(730\) | −3.02463 | −0.111947 | ||||||||
\(731\) | 1.20538 | 0.0445825 | ||||||||
\(732\) | 41.8243 | 1.54587 | ||||||||
\(733\) | 32.9913 | 1.21856 | 0.609281 | − | 0.792955i | \(-0.291458\pi\) | ||||
0.609281 | + | 0.792955i | \(0.291458\pi\) | |||||||
\(734\) | −24.3406 | −0.898426 | ||||||||
\(735\) | 1.89634 | 0.0699474 | ||||||||
\(736\) | 48.9155 | 1.80305 | ||||||||
\(737\) | −8.91156 | −0.328261 | ||||||||
\(738\) | −17.0772 | −0.628620 | ||||||||
\(739\) | −25.9519 | −0.954655 | −0.477327 | − | 0.878726i | \(-0.658394\pi\) | ||||
−0.477327 | + | 0.878726i | \(0.658394\pi\) | |||||||
\(740\) | 0.357060 | 0.0131258 | ||||||||
\(741\) | 6.56689 | 0.241241 | ||||||||
\(742\) | −7.16176 | −0.262917 | ||||||||
\(743\) | 2.73628 | 0.100384 | 0.0501922 | − | 0.998740i | \(-0.484017\pi\) | ||||
0.0501922 | + | 0.998740i | \(0.484017\pi\) | |||||||
\(744\) | 76.2272 | 2.79463 | ||||||||
\(745\) | −3.77567 | −0.138330 | ||||||||
\(746\) | 64.5285 | 2.36256 | ||||||||
\(747\) | 24.3042 | 0.889246 | ||||||||
\(748\) | 0.741297 | 0.0271045 | ||||||||
\(749\) | −4.78782 | −0.174943 | ||||||||
\(750\) | −8.46105 | −0.308954 | ||||||||
\(751\) | 34.6993 | 1.26620 | 0.633098 | − | 0.774072i | \(-0.281783\pi\) | ||||
0.633098 | + | 0.774072i | \(0.281783\pi\) | |||||||
\(752\) | 101.914 | 3.71644 | ||||||||
\(753\) | 10.4308 | 0.380118 | ||||||||
\(754\) | −93.8436 | −3.41758 | ||||||||
\(755\) | 1.94568 | 0.0708106 | ||||||||
\(756\) | 25.1608 | 0.915088 | ||||||||
\(757\) | 41.2209 | 1.49820 | 0.749100 | − | 0.662457i | \(-0.230486\pi\) | ||||
0.749100 | + | 0.662457i | \(0.230486\pi\) | |||||||
\(758\) | 92.9702 | 3.37683 | ||||||||
\(759\) | 2.22289 | 0.0806856 | ||||||||
\(760\) | −5.36549 | −0.194627 | ||||||||
\(761\) | −26.6743 | −0.966944 | −0.483472 | − | 0.875360i | \(-0.660624\pi\) | ||||
−0.483472 | + | 0.875360i | \(0.660624\pi\) | |||||||
\(762\) | 25.4571 | 0.922213 | ||||||||
\(763\) | −13.5444 | −0.490340 | ||||||||
\(764\) | −39.2555 | −1.42021 | ||||||||
\(765\) | −0.176483 | −0.00638074 | ||||||||
\(766\) | −84.4735 | −3.05215 | ||||||||
\(767\) | 5.33293 | 0.192561 | ||||||||
\(768\) | −5.23512 | −0.188906 | ||||||||
\(769\) | 22.4663 | 0.810156 | 0.405078 | − | 0.914282i | \(-0.367244\pi\) | ||||
0.405078 | + | 0.914282i | \(0.367244\pi\) | |||||||
\(770\) | 0.660096 | 0.0237882 | ||||||||
\(771\) | −12.6517 | −0.455640 | ||||||||
\(772\) | −71.7255 | −2.58146 | ||||||||
\(773\) | 45.1633 | 1.62441 | 0.812205 | − | 0.583372i | \(-0.198267\pi\) | ||||
0.812205 | + | 0.583372i | \(0.198267\pi\) | |||||||
\(774\) | −30.4406 | −1.09417 | ||||||||
\(775\) | 51.7081 | 1.85741 | ||||||||
\(776\) | 91.0508 | 3.26853 | ||||||||
\(777\) | 0.195534 | 0.00701475 | ||||||||
\(778\) | 59.8729 | 2.14655 | ||||||||
\(779\) | 5.65473 | 0.202602 | ||||||||
\(780\) | 6.14066 | 0.219871 | ||||||||
\(781\) | 0.384368 | 0.0137538 | ||||||||
\(782\) | −2.25456 | −0.0806230 | ||||||||
\(783\) | 43.9642 | 1.57115 | ||||||||
\(784\) | −63.8661 | −2.28093 | ||||||||
\(785\) | −2.63995 | −0.0942237 | ||||||||
\(786\) | −47.9912 | −1.71179 | ||||||||
\(787\) | 12.7979 | 0.456195 | 0.228097 | − | 0.973638i | \(-0.426750\pi\) | ||||
0.228097 | + | 0.973638i | \(0.426750\pi\) | |||||||
\(788\) | 122.916 | 4.37871 | ||||||||
\(789\) | 7.64116 | 0.272032 | ||||||||
\(790\) | −4.11779 | −0.146504 | ||||||||
\(791\) | 12.7184 | 0.452216 | ||||||||
\(792\) | −11.2169 | −0.398575 | ||||||||
\(793\) | −35.0159 | −1.24345 | ||||||||
\(794\) | −35.6463 | −1.26504 | ||||||||
\(795\) | 0.818854 | 0.0290418 | ||||||||
\(796\) | 2.85223 | 0.101095 | ||||||||
\(797\) | −5.15377 | −0.182556 | −0.0912780 | − | 0.995825i | \(-0.529095\pi\) | ||||
−0.0912780 | + | 0.995825i | \(0.529095\pi\) | |||||||
\(798\) | −4.90390 | −0.173596 | ||||||||
\(799\) | −2.12464 | −0.0751644 | ||||||||
\(800\) | 63.6136 | 2.24908 | ||||||||
\(801\) | −7.26141 | −0.256569 | ||||||||
\(802\) | −35.8291 | −1.26517 | ||||||||
\(803\) | 2.09378 | 0.0738880 | ||||||||
\(804\) | 61.9076 | 2.18331 | ||||||||
\(805\) | −1.43315 | −0.0505119 | ||||||||
\(806\) | −106.512 | −3.75172 | ||||||||
\(807\) | −10.6071 | −0.373388 | ||||||||
\(808\) | −65.2238 | −2.29457 | ||||||||
\(809\) | 27.0151 | 0.949802 | 0.474901 | − | 0.880039i | \(-0.342484\pi\) | ||||
0.474901 | + | 0.880039i | \(0.342484\pi\) | |||||||
\(810\) | 2.12028 | 0.0744989 | ||||||||
\(811\) | 5.03656 | 0.176858 | 0.0884288 | − | 0.996082i | \(-0.471815\pi\) | ||||
0.0884288 | + | 0.996082i | \(0.471815\pi\) | |||||||
\(812\) | 50.0266 | 1.75559 | ||||||||
\(813\) | −1.30541 | −0.0457827 | ||||||||
\(814\) | −0.346247 | −0.0121359 | ||||||||
\(815\) | −0.192656 | −0.00674844 | ||||||||
\(816\) | −2.25817 | −0.0790517 | ||||||||
\(817\) | 10.0797 | 0.352646 | ||||||||
\(818\) | 32.7521 | 1.14515 | ||||||||
\(819\) | −8.85110 | −0.309282 | ||||||||
\(820\) | 5.28771 | 0.184655 | ||||||||
\(821\) | −15.4479 | −0.539136 | −0.269568 | − | 0.962981i | \(-0.586881\pi\) | ||||
−0.269568 | + | 0.962981i | \(0.586881\pi\) | |||||||
\(822\) | −40.7044 | −1.41973 | ||||||||
\(823\) | −16.7527 | −0.583962 | −0.291981 | − | 0.956424i | \(-0.594314\pi\) | ||||
−0.291981 | + | 0.956424i | \(0.594314\pi\) | |||||||
\(824\) | 72.0972 | 2.51163 | ||||||||
\(825\) | 2.89082 | 0.100645 | ||||||||
\(826\) | −3.98243 | −0.138566 | ||||||||
\(827\) | −26.3078 | −0.914810 | −0.457405 | − | 0.889258i | \(-0.651221\pi\) | ||||
−0.457405 | + | 0.889258i | \(0.651221\pi\) | |||||||
\(828\) | 40.6451 | 1.41251 | ||||||||
\(829\) | −4.59660 | −0.159647 | −0.0798233 | − | 0.996809i | \(-0.525436\pi\) | ||||
−0.0798233 | + | 0.996809i | \(0.525436\pi\) | |||||||
\(830\) | −10.5419 | −0.365915 | ||||||||
\(831\) | 9.06130 | 0.314333 | ||||||||
\(832\) | −48.1402 | −1.66896 | ||||||||
\(833\) | 1.33143 | 0.0461315 | ||||||||
\(834\) | −54.7517 | −1.89590 | ||||||||
\(835\) | 8.60158 | 0.297670 | ||||||||
\(836\) | 6.19896 | 0.214396 | ||||||||
\(837\) | 49.8991 | 1.72477 | ||||||||
\(838\) | −1.99677 | −0.0689772 | ||||||||
\(839\) | 28.1790 | 0.972848 | 0.486424 | − | 0.873723i | \(-0.338301\pi\) | ||||
0.486424 | + | 0.873723i | \(0.338301\pi\) | |||||||
\(840\) | −2.74756 | −0.0947997 | ||||||||
\(841\) | 58.4131 | 2.01425 | ||||||||
\(842\) | −55.1555 | −1.90079 | ||||||||
\(843\) | −11.1403 | −0.383691 | ||||||||
\(844\) | 55.6110 | 1.91421 | ||||||||
\(845\) | −0.504258 | −0.0173470 | ||||||||
\(846\) | 53.6558 | 1.84472 | ||||||||
\(847\) | 11.3391 | 0.389616 | ||||||||
\(848\) | −27.5779 | −0.947029 | ||||||||
\(849\) | −1.16222 | −0.0398872 | ||||||||
\(850\) | −2.93201 | −0.100567 | ||||||||
\(851\) | 0.751744 | 0.0257695 | ||||||||
\(852\) | −2.67016 | −0.0914783 | ||||||||
\(853\) | −40.4047 | −1.38343 | −0.691716 | − | 0.722170i | \(-0.743145\pi\) | ||||
−0.691716 | + | 0.722170i | \(0.743145\pi\) | |||||||
\(854\) | 26.1485 | 0.894785 | ||||||||
\(855\) | −1.47580 | −0.0504714 | ||||||||
\(856\) | −35.2891 | −1.20616 | ||||||||
\(857\) | 40.5405 | 1.38484 | 0.692419 | − | 0.721495i | \(-0.256545\pi\) | ||||
0.692419 | + | 0.721495i | \(0.256545\pi\) | |||||||
\(858\) | −5.95470 | −0.203290 | ||||||||
\(859\) | 22.2655 | 0.759690 | 0.379845 | − | 0.925050i | \(-0.375977\pi\) | ||||
0.379845 | + | 0.925050i | \(0.375977\pi\) | |||||||
\(860\) | 9.42552 | 0.321407 | ||||||||
\(861\) | 2.89567 | 0.0986842 | ||||||||
\(862\) | 59.5232 | 2.02737 | ||||||||
\(863\) | 44.9559 | 1.53032 | 0.765159 | − | 0.643842i | \(-0.222660\pi\) | ||||
0.765159 | + | 0.643842i | \(0.222660\pi\) | |||||||
\(864\) | 61.3882 | 2.08847 | ||||||||
\(865\) | −6.26071 | −0.212871 | ||||||||
\(866\) | 8.33452 | 0.283218 | ||||||||
\(867\) | −15.4030 | −0.523114 | ||||||||
\(868\) | 56.7798 | 1.92723 | ||||||||
\(869\) | 2.85051 | 0.0966970 | ||||||||
\(870\) | −8.01259 | −0.271652 | ||||||||
\(871\) | −51.8300 | −1.75619 | ||||||||
\(872\) | −99.8302 | −3.38068 | ||||||||
\(873\) | 25.0440 | 0.847609 | ||||||||
\(874\) | −18.8534 | −0.637725 | ||||||||
\(875\) | −3.77622 | −0.127660 | ||||||||
\(876\) | −14.5453 | −0.491440 | ||||||||
\(877\) | −9.74140 | −0.328944 | −0.164472 | − | 0.986382i | \(-0.552592\pi\) | ||||
−0.164472 | + | 0.986382i | \(0.552592\pi\) | |||||||
\(878\) | 15.4961 | 0.522970 | ||||||||
\(879\) | 16.6011 | 0.559941 | ||||||||
\(880\) | 2.54184 | 0.0856854 | ||||||||
\(881\) | −53.2661 | −1.79458 | −0.897290 | − | 0.441442i | \(-0.854467\pi\) | ||||
−0.897290 | + | 0.441442i | \(0.854467\pi\) | |||||||
\(882\) | −33.6241 | −1.13218 | ||||||||
\(883\) | −14.2258 | −0.478735 | −0.239368 | − | 0.970929i | \(-0.576940\pi\) | ||||
−0.239368 | + | 0.970929i | \(0.576940\pi\) | |||||||
\(884\) | 4.31141 | 0.145008 | ||||||||
\(885\) | 0.455339 | 0.0153060 | ||||||||
\(886\) | −26.6770 | −0.896230 | ||||||||
\(887\) | −26.0159 | −0.873530 | −0.436765 | − | 0.899576i | \(-0.643876\pi\) | ||||
−0.436765 | + | 0.899576i | \(0.643876\pi\) | |||||||
\(888\) | 1.44120 | 0.0483636 | ||||||||
\(889\) | 11.3617 | 0.381058 | ||||||||
\(890\) | 3.14962 | 0.105575 | ||||||||
\(891\) | −1.46775 | −0.0491714 | ||||||||
\(892\) | −53.2907 | −1.78430 | ||||||||
\(893\) | −17.7669 | −0.594548 | ||||||||
\(894\) | −25.4348 | −0.850668 | ||||||||
\(895\) | −1.94380 | −0.0649740 | ||||||||
\(896\) | 7.94996 | 0.265590 | ||||||||
\(897\) | 12.9284 | 0.431666 | ||||||||
\(898\) | 106.907 | 3.56753 | ||||||||
\(899\) | 99.2133 | 3.30895 | ||||||||
\(900\) | 52.8581 | 1.76194 | ||||||||
\(901\) | 0.574924 | 0.0191535 | ||||||||
\(902\) | −5.12758 | −0.170730 | ||||||||
\(903\) | 5.16163 | 0.171768 | ||||||||
\(904\) | 93.7425 | 3.11783 | ||||||||
\(905\) | 5.89618 | 0.195996 | ||||||||
\(906\) | 13.1071 | 0.435454 | ||||||||
\(907\) | 10.9410 | 0.363290 | 0.181645 | − | 0.983364i | \(-0.441858\pi\) | ||||
0.181645 | + | 0.983364i | \(0.441858\pi\) | |||||||
\(908\) | −52.5599 | −1.74426 | ||||||||
\(909\) | −17.9401 | −0.595036 | ||||||||
\(910\) | 3.83914 | 0.127266 | ||||||||
\(911\) | 5.70259 | 0.188935 | 0.0944676 | − | 0.995528i | \(-0.469885\pi\) | ||||
0.0944676 | + | 0.995528i | \(0.469885\pi\) | |||||||
\(912\) | −18.8835 | −0.625296 | ||||||||
\(913\) | 7.29757 | 0.241514 | ||||||||
\(914\) | 34.6635 | 1.14657 | ||||||||
\(915\) | −2.98975 | −0.0988379 | ||||||||
\(916\) | 23.8761 | 0.788888 | ||||||||
\(917\) | −21.4188 | −0.707311 | ||||||||
\(918\) | −2.82944 | −0.0933854 | ||||||||
\(919\) | −22.8882 | −0.755013 | −0.377506 | − | 0.926007i | \(-0.623218\pi\) | ||||
−0.377506 | + | 0.926007i | \(0.623218\pi\) | |||||||
\(920\) | −10.5632 | −0.348257 | ||||||||
\(921\) | −20.9774 | −0.691230 | ||||||||
\(922\) | 18.7456 | 0.617355 | ||||||||
\(923\) | 2.23550 | 0.0735824 | ||||||||
\(924\) | 3.17436 | 0.104429 | ||||||||
\(925\) | 0.977629 | 0.0321442 | ||||||||
\(926\) | 57.7146 | 1.89662 | ||||||||
\(927\) | 19.8307 | 0.651325 | ||||||||
\(928\) | 122.057 | 4.00671 | ||||||||
\(929\) | 42.3049 | 1.38798 | 0.693989 | − | 0.719985i | \(-0.255852\pi\) | ||||
0.693989 | + | 0.719985i | \(0.255852\pi\) | |||||||
\(930\) | −9.09424 | −0.298212 | ||||||||
\(931\) | 11.1339 | 0.364898 | ||||||||
\(932\) | 75.8236 | 2.48369 | ||||||||
\(933\) | 6.31480 | 0.206737 | ||||||||
\(934\) | 53.5595 | 1.75252 | ||||||||
\(935\) | −0.0529905 | −0.00173297 | ||||||||
\(936\) | −65.2379 | −2.13237 | ||||||||
\(937\) | −11.3496 | −0.370775 | −0.185387 | − | 0.982666i | \(-0.559354\pi\) | ||||
−0.185387 | + | 0.982666i | \(0.559354\pi\) | |||||||
\(938\) | 38.7046 | 1.26375 | ||||||||
\(939\) | −4.82998 | −0.157620 | ||||||||
\(940\) | −16.6138 | −0.541881 | ||||||||
\(941\) | −55.3391 | −1.80400 | −0.902001 | − | 0.431733i | \(-0.857902\pi\) | ||||
−0.902001 | + | 0.431733i | \(0.857902\pi\) | |||||||
\(942\) | −17.7840 | −0.579435 | ||||||||
\(943\) | 11.1326 | 0.362527 | ||||||||
\(944\) | −15.3352 | −0.499118 | ||||||||
\(945\) | −1.79858 | −0.0585078 | ||||||||
\(946\) | −9.14008 | −0.297170 | ||||||||
\(947\) | −44.2160 | −1.43683 | −0.718413 | − | 0.695617i | \(-0.755131\pi\) | ||||
−0.718413 | + | 0.695617i | \(0.755131\pi\) | |||||||
\(948\) | −19.8022 | −0.643145 | ||||||||
\(949\) | 12.1775 | 0.395299 | ||||||||
\(950\) | −24.5184 | −0.795483 | ||||||||
\(951\) | 16.7194 | 0.542163 | ||||||||
\(952\) | −1.92908 | −0.0625219 | ||||||||
\(953\) | −21.3144 | −0.690442 | −0.345221 | − | 0.938521i | \(-0.612196\pi\) | ||||
−0.345221 | + | 0.938521i | \(0.612196\pi\) | |||||||
\(954\) | −14.5192 | −0.470076 | ||||||||
\(955\) | 2.80612 | 0.0908039 | ||||||||
\(956\) | −109.317 | −3.53558 | ||||||||
\(957\) | 5.54667 | 0.179298 | ||||||||
\(958\) | 81.8775 | 2.64534 | ||||||||
\(959\) | −18.1666 | −0.586631 | ||||||||
\(960\) | −4.11033 | −0.132660 | ||||||||
\(961\) | 81.6064 | 2.63247 | ||||||||
\(962\) | −2.01378 | −0.0649270 | ||||||||
\(963\) | −9.70643 | −0.312785 | ||||||||
\(964\) | −34.8846 | −1.12356 | ||||||||
\(965\) | 5.12719 | 0.165050 | ||||||||
\(966\) | −9.65443 | −0.310626 | ||||||||
\(967\) | 12.3781 | 0.398053 | 0.199026 | − | 0.979994i | \(-0.436222\pi\) | ||||
0.199026 | + | 0.979994i | \(0.436222\pi\) | |||||||
\(968\) | 83.5759 | 2.68623 | ||||||||
\(969\) | 0.393670 | 0.0126465 | ||||||||
\(970\) | −10.8628 | −0.348782 | ||||||||
\(971\) | −52.8904 | −1.69733 | −0.848666 | − | 0.528929i | \(-0.822594\pi\) | ||||
−0.848666 | + | 0.528929i | \(0.822594\pi\) | |||||||
\(972\) | 80.5848 | 2.58476 | ||||||||
\(973\) | −24.4361 | −0.783384 | ||||||||
\(974\) | 5.94934 | 0.190629 | ||||||||
\(975\) | 16.8131 | 0.538451 | ||||||||
\(976\) | 100.691 | 3.22303 | ||||||||
\(977\) | −51.5584 | −1.64950 | −0.824750 | − | 0.565497i | \(-0.808684\pi\) | ||||
−0.824750 | + | 0.565497i | \(0.808684\pi\) | |||||||
\(978\) | −1.29783 | −0.0415000 | ||||||||
\(979\) | −2.18030 | −0.0696828 | ||||||||
\(980\) | 10.4112 | 0.332575 | ||||||||
\(981\) | −27.4588 | −0.876691 | ||||||||
\(982\) | 40.3317 | 1.28704 | ||||||||
\(983\) | −27.5402 | −0.878395 | −0.439198 | − | 0.898390i | \(-0.644737\pi\) | ||||
−0.439198 | + | 0.898390i | \(0.644737\pi\) | |||||||
\(984\) | 21.3428 | 0.680385 | ||||||||
\(985\) | −8.78648 | −0.279961 | ||||||||
\(986\) | −5.62571 | −0.179159 | ||||||||
\(987\) | −9.09808 | −0.289595 | ||||||||
\(988\) | 36.0534 | 1.14701 | ||||||||
\(989\) | 19.8442 | 0.631010 | ||||||||
\(990\) | 1.33822 | 0.0425316 | ||||||||
\(991\) | 37.8505 | 1.20236 | 0.601180 | − | 0.799113i | \(-0.294697\pi\) | ||||
0.601180 | + | 0.799113i | \(0.294697\pi\) | |||||||
\(992\) | 138.534 | 4.39844 | ||||||||
\(993\) | −3.83973 | −0.121850 | ||||||||
\(994\) | −1.66939 | −0.0529497 | ||||||||
\(995\) | −0.203888 | −0.00646367 | ||||||||
\(996\) | −50.6954 | −1.60635 | ||||||||
\(997\) | 44.3745 | 1.40535 | 0.702677 | − | 0.711509i | \(-0.251988\pi\) | ||||
0.702677 | + | 0.711509i | \(0.251988\pi\) | |||||||
\(998\) | 24.9927 | 0.791130 | ||||||||
\(999\) | 0.943427 | 0.0298487 |
(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 | 8017.2.a.b.1.11 | ✓ | 340 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8017.2.a.b.1.11 | ✓ | 340 | 1.1 | even | 1 | trivial |