Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, 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("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(1\) |
Dimension: | \(142\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43267 | −1.72015 | −0.860077 | − | 0.510164i | \(-0.829585\pi\) | ||||
−0.860077 | + | 0.510164i | \(0.829585\pi\) | |||||||
\(3\) | −0.839960 | −0.484951 | −0.242476 | − | 0.970158i | \(-0.577959\pi\) | ||||
−0.242476 | + | 0.970158i | \(0.577959\pi\) | |||||||
\(4\) | 3.91786 | 1.95893 | ||||||||
\(5\) | −3.64522 | −1.63019 | −0.815097 | − | 0.579325i | \(-0.803316\pi\) | ||||
−0.815097 | + | 0.579325i | \(0.803316\pi\) | |||||||
\(6\) | 2.04334 | 0.834191 | ||||||||
\(7\) | −2.93716 | −1.11014 | −0.555071 | − | 0.831803i | \(-0.687309\pi\) | ||||
−0.555071 | + | 0.831803i | \(0.687309\pi\) | |||||||
\(8\) | −4.66552 | −1.64951 | ||||||||
\(9\) | −2.29447 | −0.764822 | ||||||||
\(10\) | 8.86761 | 2.80418 | ||||||||
\(11\) | −1.95237 | −0.588663 | −0.294331 | − | 0.955703i | \(-0.595097\pi\) | ||||
−0.294331 | + | 0.955703i | \(0.595097\pi\) | |||||||
\(12\) | −3.29085 | −0.949986 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 7.14513 | 1.90962 | ||||||||
\(15\) | 3.06184 | 0.790564 | ||||||||
\(16\) | 3.51393 | 0.878483 | ||||||||
\(17\) | −6.09230 | −1.47760 | −0.738800 | − | 0.673925i | \(-0.764607\pi\) | ||||
−0.738800 | + | 0.673925i | \(0.764607\pi\) | |||||||
\(18\) | 5.58167 | 1.31561 | ||||||||
\(19\) | 6.19342 | 1.42087 | 0.710434 | − | 0.703763i | \(-0.248498\pi\) | ||||
0.710434 | + | 0.703763i | \(0.248498\pi\) | |||||||
\(20\) | −14.2815 | −3.19344 | ||||||||
\(21\) | 2.46710 | 0.538365 | ||||||||
\(22\) | 4.74947 | 1.01259 | ||||||||
\(23\) | −5.35888 | −1.11740 | −0.558702 | − | 0.829369i | \(-0.688700\pi\) | ||||
−0.558702 | + | 0.829369i | \(0.688700\pi\) | |||||||
\(24\) | 3.91885 | 0.799933 | ||||||||
\(25\) | 8.28765 | 1.65753 | ||||||||
\(26\) | −2.43267 | −0.477085 | ||||||||
\(27\) | 4.44714 | 0.855853 | ||||||||
\(28\) | −11.5074 | −2.17469 | ||||||||
\(29\) | −3.08816 | −0.573456 | −0.286728 | − | 0.958012i | \(-0.592568\pi\) | ||||
−0.286728 | + | 0.958012i | \(0.592568\pi\) | |||||||
\(30\) | −7.44844 | −1.35989 | ||||||||
\(31\) | −2.60935 | −0.468652 | −0.234326 | − | 0.972158i | \(-0.575288\pi\) | ||||
−0.234326 | + | 0.972158i | \(0.575288\pi\) | |||||||
\(32\) | 0.782822 | 0.138385 | ||||||||
\(33\) | 1.63992 | 0.285473 | ||||||||
\(34\) | 14.8205 | 2.54170 | ||||||||
\(35\) | 10.7066 | 1.80975 | ||||||||
\(36\) | −8.98941 | −1.49824 | ||||||||
\(37\) | 0.220676 | 0.0362789 | 0.0181395 | − | 0.999835i | \(-0.494226\pi\) | ||||
0.0181395 | + | 0.999835i | \(0.494226\pi\) | |||||||
\(38\) | −15.0665 | −2.44411 | ||||||||
\(39\) | −0.839960 | −0.134501 | ||||||||
\(40\) | 17.0069 | 2.68902 | ||||||||
\(41\) | −9.64711 | −1.50663 | −0.753313 | − | 0.657663i | \(-0.771545\pi\) | ||||
−0.753313 | + | 0.657663i | \(0.771545\pi\) | |||||||
\(42\) | −6.00162 | −0.926071 | ||||||||
\(43\) | −11.3459 | −1.73023 | −0.865117 | − | 0.501570i | \(-0.832756\pi\) | ||||
−0.865117 | + | 0.501570i | \(0.832756\pi\) | |||||||
\(44\) | −7.64914 | −1.15315 | ||||||||
\(45\) | 8.36384 | 1.24681 | ||||||||
\(46\) | 13.0364 | 1.92211 | ||||||||
\(47\) | −0.488560 | −0.0712638 | −0.0356319 | − | 0.999365i | \(-0.511344\pi\) | ||||
−0.0356319 | + | 0.999365i | \(0.511344\pi\) | |||||||
\(48\) | −2.95156 | −0.426022 | ||||||||
\(49\) | 1.62691 | 0.232416 | ||||||||
\(50\) | −20.1611 | −2.85121 | ||||||||
\(51\) | 5.11729 | 0.716564 | ||||||||
\(52\) | 3.91786 | 0.543310 | ||||||||
\(53\) | −2.57418 | −0.353591 | −0.176795 | − | 0.984248i | \(-0.556573\pi\) | ||||
−0.176795 | + | 0.984248i | \(0.556573\pi\) | |||||||
\(54\) | −10.8184 | −1.47220 | ||||||||
\(55\) | 7.11684 | 0.959634 | ||||||||
\(56\) | 13.7034 | 1.83119 | ||||||||
\(57\) | −5.20223 | −0.689052 | ||||||||
\(58\) | 7.51246 | 0.986434 | ||||||||
\(59\) | 0.288421 | 0.0375493 | 0.0187746 | − | 0.999824i | \(-0.494023\pi\) | ||||
0.0187746 | + | 0.999824i | \(0.494023\pi\) | |||||||
\(60\) | 11.9959 | 1.54866 | ||||||||
\(61\) | 11.8875 | 1.52204 | 0.761021 | − | 0.648728i | \(-0.224699\pi\) | ||||
0.761021 | + | 0.648728i | \(0.224699\pi\) | |||||||
\(62\) | 6.34767 | 0.806154 | ||||||||
\(63\) | 6.73922 | 0.849062 | ||||||||
\(64\) | −8.93221 | −1.11653 | ||||||||
\(65\) | −3.64522 | −0.452134 | ||||||||
\(66\) | −3.98937 | −0.491057 | ||||||||
\(67\) | −4.74662 | −0.579892 | −0.289946 | − | 0.957043i | \(-0.593637\pi\) | ||||
−0.289946 | + | 0.957043i | \(0.593637\pi\) | |||||||
\(68\) | −23.8688 | −2.89452 | ||||||||
\(69\) | 4.50124 | 0.541886 | ||||||||
\(70\) | −26.0456 | −3.11304 | ||||||||
\(71\) | 4.41906 | 0.524446 | 0.262223 | − | 0.965007i | \(-0.415544\pi\) | ||||
0.262223 | + | 0.965007i | \(0.415544\pi\) | |||||||
\(72\) | 10.7049 | 1.26158 | ||||||||
\(73\) | −10.0232 | −1.17313 | −0.586564 | − | 0.809903i | \(-0.699520\pi\) | ||||
−0.586564 | + | 0.809903i | \(0.699520\pi\) | |||||||
\(74\) | −0.536831 | −0.0624053 | ||||||||
\(75\) | −6.96129 | −0.803821 | ||||||||
\(76\) | 24.2650 | 2.78339 | ||||||||
\(77\) | 5.73444 | 0.653500 | ||||||||
\(78\) | 2.04334 | 0.231363 | ||||||||
\(79\) | 4.45139 | 0.500821 | 0.250410 | − | 0.968140i | \(-0.419434\pi\) | ||||
0.250410 | + | 0.968140i | \(0.419434\pi\) | |||||||
\(80\) | −12.8091 | −1.43210 | ||||||||
\(81\) | 3.14798 | 0.349776 | ||||||||
\(82\) | 23.4682 | 2.59163 | ||||||||
\(83\) | 7.46556 | 0.819452 | 0.409726 | − | 0.912209i | \(-0.365624\pi\) | ||||
0.409726 | + | 0.912209i | \(0.365624\pi\) | |||||||
\(84\) | 9.66575 | 1.05462 | ||||||||
\(85\) | 22.2078 | 2.40877 | ||||||||
\(86\) | 27.6008 | 2.97627 | ||||||||
\(87\) | 2.59393 | 0.278098 | ||||||||
\(88\) | 9.10885 | 0.971006 | ||||||||
\(89\) | 7.26752 | 0.770356 | 0.385178 | − | 0.922842i | \(-0.374140\pi\) | ||||
0.385178 | + | 0.922842i | \(0.374140\pi\) | |||||||
\(90\) | −20.3464 | −2.14470 | ||||||||
\(91\) | −2.93716 | −0.307898 | ||||||||
\(92\) | −20.9954 | −2.18892 | ||||||||
\(93\) | 2.19175 | 0.227273 | ||||||||
\(94\) | 1.18850 | 0.122585 | ||||||||
\(95\) | −22.5764 | −2.31629 | ||||||||
\(96\) | −0.657539 | −0.0671098 | ||||||||
\(97\) | 12.9408 | 1.31393 | 0.656967 | − | 0.753919i | \(-0.271839\pi\) | ||||
0.656967 | + | 0.753919i | \(0.271839\pi\) | |||||||
\(98\) | −3.95773 | −0.399791 | ||||||||
\(99\) | 4.47966 | 0.450223 | ||||||||
\(100\) | 32.4699 | 3.24699 | ||||||||
\(101\) | −9.44266 | −0.939580 | −0.469790 | − | 0.882778i | \(-0.655670\pi\) | ||||
−0.469790 | + | 0.882778i | \(0.655670\pi\) | |||||||
\(102\) | −12.4487 | −1.23260 | ||||||||
\(103\) | 5.51149 | 0.543063 | 0.271532 | − | 0.962429i | \(-0.412470\pi\) | ||||
0.271532 | + | 0.962429i | \(0.412470\pi\) | |||||||
\(104\) | −4.66552 | −0.457492 | ||||||||
\(105\) | −8.99312 | −0.877639 | ||||||||
\(106\) | 6.26212 | 0.608230 | ||||||||
\(107\) | −13.8940 | −1.34318 | −0.671591 | − | 0.740922i | \(-0.734389\pi\) | ||||
−0.671591 | + | 0.740922i | \(0.734389\pi\) | |||||||
\(108\) | 17.4233 | 1.67656 | ||||||||
\(109\) | 10.8139 | 1.03578 | 0.517892 | − | 0.855446i | \(-0.326717\pi\) | ||||
0.517892 | + | 0.855446i | \(0.326717\pi\) | |||||||
\(110\) | −17.3129 | −1.65072 | ||||||||
\(111\) | −0.185359 | −0.0175935 | ||||||||
\(112\) | −10.3210 | −0.975241 | ||||||||
\(113\) | 9.00074 | 0.846719 | 0.423359 | − | 0.905962i | \(-0.360851\pi\) | ||||
0.423359 | + | 0.905962i | \(0.360851\pi\) | |||||||
\(114\) | 12.6553 | 1.18528 | ||||||||
\(115\) | 19.5343 | 1.82158 | ||||||||
\(116\) | −12.0990 | −1.12336 | ||||||||
\(117\) | −2.29447 | −0.212124 | ||||||||
\(118\) | −0.701633 | −0.0645905 | ||||||||
\(119\) | 17.8941 | 1.64035 | ||||||||
\(120\) | −14.2851 | −1.30404 | ||||||||
\(121\) | −7.18824 | −0.653476 | ||||||||
\(122\) | −28.9184 | −2.61815 | ||||||||
\(123\) | 8.10319 | 0.730640 | ||||||||
\(124\) | −10.2231 | −0.918058 | ||||||||
\(125\) | −11.9842 | −1.07190 | ||||||||
\(126\) | −16.3943 | −1.46052 | ||||||||
\(127\) | −0.678367 | −0.0601954 | −0.0300977 | − | 0.999547i | \(-0.509582\pi\) | ||||
−0.0300977 | + | 0.999547i | \(0.509582\pi\) | |||||||
\(128\) | 20.1634 | 1.78221 | ||||||||
\(129\) | 9.53011 | 0.839079 | ||||||||
\(130\) | 8.86761 | 0.777741 | ||||||||
\(131\) | 11.6202 | 1.01526 | 0.507629 | − | 0.861576i | \(-0.330522\pi\) | ||||
0.507629 | + | 0.861576i | \(0.330522\pi\) | |||||||
\(132\) | 6.42497 | 0.559222 | ||||||||
\(133\) | −18.1911 | −1.57737 | ||||||||
\(134\) | 11.5469 | 0.997504 | ||||||||
\(135\) | −16.2108 | −1.39521 | ||||||||
\(136\) | 28.4238 | 2.43732 | ||||||||
\(137\) | 12.8243 | 1.09566 | 0.547828 | − | 0.836591i | \(-0.315455\pi\) | ||||
0.547828 | + | 0.836591i | \(0.315455\pi\) | |||||||
\(138\) | −10.9500 | −0.932128 | ||||||||
\(139\) | 3.89399 | 0.330284 | 0.165142 | − | 0.986270i | \(-0.447192\pi\) | ||||
0.165142 | + | 0.986270i | \(0.447192\pi\) | |||||||
\(140\) | 41.9470 | 3.54517 | ||||||||
\(141\) | 0.410371 | 0.0345595 | ||||||||
\(142\) | −10.7501 | −0.902128 | ||||||||
\(143\) | −1.95237 | −0.163266 | ||||||||
\(144\) | −8.06260 | −0.671884 | ||||||||
\(145\) | 11.2570 | 0.934845 | ||||||||
\(146\) | 24.3831 | 2.01796 | ||||||||
\(147\) | −1.36654 | −0.112710 | ||||||||
\(148\) | 0.864578 | 0.0710679 | ||||||||
\(149\) | 9.41585 | 0.771376 | 0.385688 | − | 0.922629i | \(-0.373964\pi\) | ||||
0.385688 | + | 0.922629i | \(0.373964\pi\) | |||||||
\(150\) | 16.9345 | 1.38270 | ||||||||
\(151\) | 22.2475 | 1.81048 | 0.905238 | − | 0.424906i | \(-0.139693\pi\) | ||||
0.905238 | + | 0.424906i | \(0.139693\pi\) | |||||||
\(152\) | −28.8956 | −2.34374 | ||||||||
\(153\) | 13.9786 | 1.13010 | ||||||||
\(154\) | −13.9500 | −1.12412 | ||||||||
\(155\) | 9.51165 | 0.763994 | ||||||||
\(156\) | −3.29085 | −0.263479 | ||||||||
\(157\) | 7.35290 | 0.586826 | 0.293413 | − | 0.955986i | \(-0.405209\pi\) | ||||
0.293413 | + | 0.955986i | \(0.405209\pi\) | |||||||
\(158\) | −10.8287 | −0.861489 | ||||||||
\(159\) | 2.16221 | 0.171474 | ||||||||
\(160\) | −2.85356 | −0.225594 | ||||||||
\(161\) | 15.7399 | 1.24048 | ||||||||
\(162\) | −7.65799 | −0.601668 | ||||||||
\(163\) | −14.3471 | −1.12375 | −0.561877 | − | 0.827221i | \(-0.689921\pi\) | ||||
−0.561877 | + | 0.827221i | \(0.689921\pi\) | |||||||
\(164\) | −37.7961 | −2.95138 | ||||||||
\(165\) | −5.97786 | −0.465376 | ||||||||
\(166\) | −18.1612 | −1.40958 | ||||||||
\(167\) | 23.6284 | 1.82842 | 0.914210 | − | 0.405242i | \(-0.132813\pi\) | ||||
0.914210 | + | 0.405242i | \(0.132813\pi\) | |||||||
\(168\) | −11.5103 | −0.888039 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −54.0241 | −4.14346 | ||||||||
\(171\) | −14.2106 | −1.08671 | ||||||||
\(172\) | −44.4517 | −3.38941 | ||||||||
\(173\) | −10.0254 | −0.762219 | −0.381109 | − | 0.924530i | \(-0.624458\pi\) | ||||
−0.381109 | + | 0.924530i | \(0.624458\pi\) | |||||||
\(174\) | −6.31016 | −0.478372 | ||||||||
\(175\) | −24.3422 | −1.84009 | ||||||||
\(176\) | −6.86051 | −0.517131 | ||||||||
\(177\) | −0.242262 | −0.0182096 | ||||||||
\(178\) | −17.6795 | −1.32513 | ||||||||
\(179\) | 19.1672 | 1.43262 | 0.716310 | − | 0.697782i | \(-0.245830\pi\) | ||||
0.716310 | + | 0.697782i | \(0.245830\pi\) | |||||||
\(180\) | 32.7684 | 2.44241 | ||||||||
\(181\) | 4.06058 | 0.301820 | 0.150910 | − | 0.988547i | \(-0.451780\pi\) | ||||
0.150910 | + | 0.988547i | \(0.451780\pi\) | |||||||
\(182\) | 7.14513 | 0.529632 | ||||||||
\(183\) | −9.98504 | −0.738116 | ||||||||
\(184\) | 25.0020 | 1.84317 | ||||||||
\(185\) | −0.804413 | −0.0591416 | ||||||||
\(186\) | −5.33179 | −0.390946 | ||||||||
\(187\) | 11.8944 | 0.869808 | ||||||||
\(188\) | −1.91411 | −0.139601 | ||||||||
\(189\) | −13.0620 | −0.950118 | ||||||||
\(190\) | 54.9209 | 3.98438 | ||||||||
\(191\) | −14.5472 | −1.05260 | −0.526300 | − | 0.850299i | \(-0.676421\pi\) | ||||
−0.526300 | + | 0.850299i | \(0.676421\pi\) | |||||||
\(192\) | 7.50270 | 0.541461 | ||||||||
\(193\) | 15.2869 | 1.10038 | 0.550189 | − | 0.835040i | \(-0.314556\pi\) | ||||
0.550189 | + | 0.835040i | \(0.314556\pi\) | |||||||
\(194\) | −31.4805 | −2.26017 | ||||||||
\(195\) | 3.06184 | 0.219263 | ||||||||
\(196\) | 6.37402 | 0.455287 | ||||||||
\(197\) | −2.35092 | −0.167496 | −0.0837482 | − | 0.996487i | \(-0.526689\pi\) | ||||
−0.0837482 | + | 0.996487i | \(0.526689\pi\) | |||||||
\(198\) | −10.8975 | −0.774452 | ||||||||
\(199\) | −4.48196 | −0.317718 | −0.158859 | − | 0.987301i | \(-0.550782\pi\) | ||||
−0.158859 | + | 0.987301i | \(0.550782\pi\) | |||||||
\(200\) | −38.6662 | −2.73411 | ||||||||
\(201\) | 3.98697 | 0.281219 | ||||||||
\(202\) | 22.9708 | 1.61622 | ||||||||
\(203\) | 9.07041 | 0.636618 | ||||||||
\(204\) | 20.0488 | 1.40370 | ||||||||
\(205\) | 35.1659 | 2.45609 | ||||||||
\(206\) | −13.4076 | −0.934153 | ||||||||
\(207\) | 12.2958 | 0.854615 | ||||||||
\(208\) | 3.51393 | 0.243647 | ||||||||
\(209\) | −12.0919 | −0.836413 | ||||||||
\(210\) | 21.8773 | 1.50967 | ||||||||
\(211\) | 0.549258 | 0.0378125 | 0.0189062 | − | 0.999821i | \(-0.493982\pi\) | ||||
0.0189062 | + | 0.999821i | \(0.493982\pi\) | |||||||
\(212\) | −10.0853 | −0.692660 | ||||||||
\(213\) | −3.71183 | −0.254331 | ||||||||
\(214\) | 33.7994 | 2.31048 | ||||||||
\(215\) | 41.3584 | 2.82062 | ||||||||
\(216\) | −20.7482 | −1.41174 | ||||||||
\(217\) | 7.66407 | 0.520271 | ||||||||
\(218\) | −26.3066 | −1.78171 | ||||||||
\(219\) | 8.41910 | 0.568910 | ||||||||
\(220\) | 27.8828 | 1.87986 | ||||||||
\(221\) | −6.09230 | −0.409812 | ||||||||
\(222\) | 0.450917 | 0.0302635 | ||||||||
\(223\) | 0.0405410 | 0.00271482 | 0.00135741 | − | 0.999999i | \(-0.499568\pi\) | ||||
0.00135741 | + | 0.999999i | \(0.499568\pi\) | |||||||
\(224\) | −2.29927 | −0.153627 | ||||||||
\(225\) | −19.0157 | −1.26772 | ||||||||
\(226\) | −21.8958 | −1.45649 | ||||||||
\(227\) | −4.64935 | −0.308588 | −0.154294 | − | 0.988025i | \(-0.549310\pi\) | ||||
−0.154294 | + | 0.988025i | \(0.549310\pi\) | |||||||
\(228\) | −20.3816 | −1.34981 | ||||||||
\(229\) | −18.9317 | −1.25104 | −0.625520 | − | 0.780209i | \(-0.715113\pi\) | ||||
−0.625520 | + | 0.780209i | \(0.715113\pi\) | |||||||
\(230\) | −47.5204 | −3.13341 | ||||||||
\(231\) | −4.81670 | −0.316915 | ||||||||
\(232\) | 14.4079 | 0.945923 | ||||||||
\(233\) | 16.0613 | 1.05221 | 0.526104 | − | 0.850420i | \(-0.323652\pi\) | ||||
0.526104 | + | 0.850420i | \(0.323652\pi\) | |||||||
\(234\) | 5.58167 | 0.364885 | ||||||||
\(235\) | 1.78091 | 0.116174 | ||||||||
\(236\) | 1.13000 | 0.0735565 | ||||||||
\(237\) | −3.73899 | −0.242874 | ||||||||
\(238\) | −43.5303 | −2.82165 | ||||||||
\(239\) | −21.3159 | −1.37881 | −0.689405 | − | 0.724376i | \(-0.742128\pi\) | ||||
−0.689405 | + | 0.724376i | \(0.742128\pi\) | |||||||
\(240\) | 10.7591 | 0.694497 | ||||||||
\(241\) | 20.4739 | 1.31884 | 0.659419 | − | 0.751776i | \(-0.270803\pi\) | ||||
0.659419 | + | 0.751776i | \(0.270803\pi\) | |||||||
\(242\) | 17.4866 | 1.12408 | ||||||||
\(243\) | −15.9856 | −1.02548 | ||||||||
\(244\) | 46.5737 | 2.98158 | ||||||||
\(245\) | −5.93045 | −0.378883 | ||||||||
\(246\) | −19.7123 | −1.25681 | ||||||||
\(247\) | 6.19342 | 0.394078 | ||||||||
\(248\) | 12.1740 | 0.773047 | ||||||||
\(249\) | −6.27077 | −0.397394 | ||||||||
\(250\) | 29.1536 | 1.84383 | ||||||||
\(251\) | −9.23733 | −0.583055 | −0.291527 | − | 0.956562i | \(-0.594163\pi\) | ||||
−0.291527 | + | 0.956562i | \(0.594163\pi\) | |||||||
\(252\) | 26.4033 | 1.66325 | ||||||||
\(253\) | 10.4625 | 0.657774 | ||||||||
\(254\) | 1.65024 | 0.103545 | ||||||||
\(255\) | −18.6537 | −1.16814 | ||||||||
\(256\) | −31.1865 | −1.94916 | ||||||||
\(257\) | −6.66713 | −0.415884 | −0.207942 | − | 0.978141i | \(-0.566677\pi\) | ||||
−0.207942 | + | 0.978141i | \(0.566677\pi\) | |||||||
\(258\) | −23.1836 | −1.44335 | ||||||||
\(259\) | −0.648161 | −0.0402747 | ||||||||
\(260\) | −14.2815 | −0.885700 | ||||||||
\(261\) | 7.08567 | 0.438592 | ||||||||
\(262\) | −28.2680 | −1.74640 | ||||||||
\(263\) | 0.311831 | 0.0192283 | 0.00961417 | − | 0.999954i | \(-0.496940\pi\) | ||||
0.00961417 | + | 0.999954i | \(0.496940\pi\) | |||||||
\(264\) | −7.65107 | −0.470891 | ||||||||
\(265\) | 9.38345 | 0.576421 | ||||||||
\(266\) | 44.2528 | 2.71331 | ||||||||
\(267\) | −6.10443 | −0.373585 | ||||||||
\(268\) | −18.5966 | −1.13597 | ||||||||
\(269\) | 8.93944 | 0.545047 | 0.272524 | − | 0.962149i | \(-0.412142\pi\) | ||||
0.272524 | + | 0.962149i | \(0.412142\pi\) | |||||||
\(270\) | 39.4355 | 2.39997 | ||||||||
\(271\) | 1.73849 | 0.105606 | 0.0528029 | − | 0.998605i | \(-0.483184\pi\) | ||||
0.0528029 | + | 0.998605i | \(0.483184\pi\) | |||||||
\(272\) | −21.4079 | −1.29805 | ||||||||
\(273\) | 2.46710 | 0.149316 | ||||||||
\(274\) | −31.1973 | −1.88470 | ||||||||
\(275\) | −16.1806 | −0.975726 | ||||||||
\(276\) | 17.6353 | 1.06152 | ||||||||
\(277\) | −17.5446 | −1.05415 | −0.527077 | − | 0.849818i | \(-0.676712\pi\) | ||||
−0.527077 | + | 0.849818i | \(0.676712\pi\) | |||||||
\(278\) | −9.47277 | −0.568139 | ||||||||
\(279\) | 5.98706 | 0.358436 | ||||||||
\(280\) | −49.9519 | −2.98520 | ||||||||
\(281\) | 14.6425 | 0.873496 | 0.436748 | − | 0.899584i | \(-0.356130\pi\) | ||||
0.436748 | + | 0.899584i | \(0.356130\pi\) | |||||||
\(282\) | −0.998295 | −0.0594476 | ||||||||
\(283\) | −19.9903 | −1.18830 | −0.594150 | − | 0.804355i | \(-0.702511\pi\) | ||||
−0.594150 | + | 0.804355i | \(0.702511\pi\) | |||||||
\(284\) | 17.3133 | 1.02735 | ||||||||
\(285\) | 18.9633 | 1.12329 | ||||||||
\(286\) | 4.74947 | 0.280842 | ||||||||
\(287\) | 28.3351 | 1.67257 | ||||||||
\(288\) | −1.79616 | −0.105840 | ||||||||
\(289\) | 20.1161 | 1.18330 | ||||||||
\(290\) | −27.3846 | −1.60808 | ||||||||
\(291\) | −10.8697 | −0.637194 | ||||||||
\(292\) | −39.2696 | −2.29808 | ||||||||
\(293\) | −30.9640 | −1.80894 | −0.904469 | − | 0.426540i | \(-0.859732\pi\) | ||||
−0.904469 | + | 0.426540i | \(0.859732\pi\) | |||||||
\(294\) | 3.32434 | 0.193879 | ||||||||
\(295\) | −1.05136 | −0.0612125 | ||||||||
\(296\) | −1.02957 | −0.0598425 | ||||||||
\(297\) | −8.68248 | −0.503809 | ||||||||
\(298\) | −22.9056 | −1.32689 | ||||||||
\(299\) | −5.35888 | −0.309912 | ||||||||
\(300\) | −27.2734 | −1.57463 | ||||||||
\(301\) | 33.3247 | 1.92081 | ||||||||
\(302\) | −54.1207 | −3.11430 | ||||||||
\(303\) | 7.93146 | 0.455650 | ||||||||
\(304\) | 21.7633 | 1.24821 | ||||||||
\(305\) | −43.3327 | −2.48122 | ||||||||
\(306\) | −34.0052 | −1.94395 | ||||||||
\(307\) | 21.9702 | 1.25390 | 0.626952 | − | 0.779058i | \(-0.284302\pi\) | ||||
0.626952 | + | 0.779058i | \(0.284302\pi\) | |||||||
\(308\) | 22.4667 | 1.28016 | ||||||||
\(309\) | −4.62943 | −0.263359 | ||||||||
\(310\) | −23.1387 | −1.31419 | ||||||||
\(311\) | 5.77549 | 0.327498 | 0.163749 | − | 0.986502i | \(-0.447641\pi\) | ||||
0.163749 | + | 0.986502i | \(0.447641\pi\) | |||||||
\(312\) | 3.91885 | 0.221861 | ||||||||
\(313\) | −21.5018 | −1.21535 | −0.607675 | − | 0.794185i | \(-0.707898\pi\) | ||||
−0.607675 | + | 0.794185i | \(0.707898\pi\) | |||||||
\(314\) | −17.8872 | −1.00943 | ||||||||
\(315\) | −24.5659 | −1.38413 | ||||||||
\(316\) | 17.4399 | 0.981074 | ||||||||
\(317\) | −22.8103 | −1.28116 | −0.640578 | − | 0.767893i | \(-0.721305\pi\) | ||||
−0.640578 | + | 0.767893i | \(0.721305\pi\) | |||||||
\(318\) | −5.25993 | −0.294962 | ||||||||
\(319\) | 6.02924 | 0.337573 | ||||||||
\(320\) | 32.5599 | 1.82015 | ||||||||
\(321\) | 11.6704 | 0.651378 | ||||||||
\(322\) | −38.2899 | −2.13381 | ||||||||
\(323\) | −37.7322 | −2.09947 | ||||||||
\(324\) | 12.3334 | 0.685187 | ||||||||
\(325\) | 8.28765 | 0.459716 | ||||||||
\(326\) | 34.9018 | 1.93303 | ||||||||
\(327\) | −9.08324 | −0.502304 | ||||||||
\(328\) | 45.0088 | 2.48520 | ||||||||
\(329\) | 1.43498 | 0.0791130 | ||||||||
\(330\) | 14.5421 | 0.800518 | ||||||||
\(331\) | −20.9138 | −1.14952 | −0.574762 | − | 0.818320i | \(-0.694906\pi\) | ||||
−0.574762 | + | 0.818320i | \(0.694906\pi\) | |||||||
\(332\) | 29.2491 | 1.60525 | ||||||||
\(333\) | −0.506334 | −0.0277469 | ||||||||
\(334\) | −57.4800 | −3.14516 | ||||||||
\(335\) | 17.3025 | 0.945336 | ||||||||
\(336\) | 8.66922 | 0.472944 | ||||||||
\(337\) | −3.13546 | −0.170799 | −0.0853996 | − | 0.996347i | \(-0.527217\pi\) | ||||
−0.0853996 | + | 0.996347i | \(0.527217\pi\) | |||||||
\(338\) | −2.43267 | −0.132320 | ||||||||
\(339\) | −7.56026 | −0.410617 | ||||||||
\(340\) | 87.0071 | 4.71862 | ||||||||
\(341\) | 5.09442 | 0.275878 | ||||||||
\(342\) | 34.5697 | 1.86931 | ||||||||
\(343\) | 15.7816 | 0.852128 | ||||||||
\(344\) | 52.9346 | 2.85404 | ||||||||
\(345\) | −16.4080 | −0.883379 | ||||||||
\(346\) | 24.3885 | 1.31113 | ||||||||
\(347\) | 28.6562 | 1.53835 | 0.769173 | − | 0.639041i | \(-0.220668\pi\) | ||||
0.769173 | + | 0.639041i | \(0.220668\pi\) | |||||||
\(348\) | 10.1627 | 0.544776 | ||||||||
\(349\) | −16.8790 | −0.903514 | −0.451757 | − | 0.892141i | \(-0.649203\pi\) | ||||
−0.451757 | + | 0.892141i | \(0.649203\pi\) | |||||||
\(350\) | 59.2163 | 3.16525 | ||||||||
\(351\) | 4.44714 | 0.237371 | ||||||||
\(352\) | −1.52836 | −0.0814619 | ||||||||
\(353\) | 28.1451 | 1.49801 | 0.749006 | − | 0.662563i | \(-0.230531\pi\) | ||||
0.749006 | + | 0.662563i | \(0.230531\pi\) | |||||||
\(354\) | 0.589344 | 0.0313233 | ||||||||
\(355\) | −16.1085 | −0.854948 | ||||||||
\(356\) | 28.4732 | 1.50907 | ||||||||
\(357\) | −15.0303 | −0.795487 | ||||||||
\(358\) | −46.6273 | −2.46433 | ||||||||
\(359\) | −18.7833 | −0.991344 | −0.495672 | − | 0.868510i | \(-0.665078\pi\) | ||||
−0.495672 | + | 0.868510i | \(0.665078\pi\) | |||||||
\(360\) | −39.0217 | −2.05662 | ||||||||
\(361\) | 19.3585 | 1.01887 | ||||||||
\(362\) | −9.87803 | −0.519178 | ||||||||
\(363\) | 6.03783 | 0.316904 | ||||||||
\(364\) | −11.5074 | −0.603151 | ||||||||
\(365\) | 36.5368 | 1.91243 | ||||||||
\(366\) | 24.2903 | 1.26967 | ||||||||
\(367\) | −9.81686 | −0.512436 | −0.256218 | − | 0.966619i | \(-0.582476\pi\) | ||||
−0.256218 | + | 0.966619i | \(0.582476\pi\) | |||||||
\(368\) | −18.8307 | −0.981620 | ||||||||
\(369\) | 22.1350 | 1.15230 | ||||||||
\(370\) | 1.95687 | 0.101733 | ||||||||
\(371\) | 7.56077 | 0.392536 | ||||||||
\(372\) | 8.58696 | 0.445213 | ||||||||
\(373\) | 17.6484 | 0.913799 | 0.456899 | − | 0.889518i | \(-0.348960\pi\) | ||||
0.456899 | + | 0.889518i | \(0.348960\pi\) | |||||||
\(374\) | −28.9352 | −1.49620 | ||||||||
\(375\) | 10.0663 | 0.519819 | ||||||||
\(376\) | 2.27939 | 0.117550 | ||||||||
\(377\) | −3.08816 | −0.159048 | ||||||||
\(378\) | 31.7754 | 1.63435 | ||||||||
\(379\) | −15.6693 | −0.804879 | −0.402439 | − | 0.915447i | \(-0.631838\pi\) | ||||
−0.402439 | + | 0.915447i | \(0.631838\pi\) | |||||||
\(380\) | −88.4513 | −4.53746 | ||||||||
\(381\) | 0.569802 | 0.0291918 | ||||||||
\(382\) | 35.3885 | 1.81064 | ||||||||
\(383\) | 0.0432659 | 0.00221078 | 0.00110539 | − | 0.999999i | \(-0.499648\pi\) | ||||
0.00110539 | + | 0.999999i | \(0.499648\pi\) | |||||||
\(384\) | −16.9365 | −0.864286 | ||||||||
\(385\) | −20.9033 | −1.06533 | ||||||||
\(386\) | −37.1880 | −1.89282 | ||||||||
\(387\) | 26.0328 | 1.32332 | ||||||||
\(388\) | 50.7001 | 2.57391 | ||||||||
\(389\) | 39.1737 | 1.98619 | 0.993094 | − | 0.117325i | \(-0.0374318\pi\) | ||||
0.993094 | + | 0.117325i | \(0.0374318\pi\) | |||||||
\(390\) | −7.44844 | −0.377166 | ||||||||
\(391\) | 32.6479 | 1.65107 | ||||||||
\(392\) | −7.59039 | −0.383373 | ||||||||
\(393\) | −9.76047 | −0.492351 | ||||||||
\(394\) | 5.71901 | 0.288120 | ||||||||
\(395\) | −16.2263 | −0.816434 | ||||||||
\(396\) | 17.5507 | 0.881956 | ||||||||
\(397\) | −25.7581 | −1.29276 | −0.646381 | − | 0.763015i | \(-0.723718\pi\) | ||||
−0.646381 | + | 0.763015i | \(0.723718\pi\) | |||||||
\(398\) | 10.9031 | 0.546524 | ||||||||
\(399\) | 15.2798 | 0.764946 | ||||||||
\(400\) | 29.1222 | 1.45611 | ||||||||
\(401\) | 2.56358 | 0.128019 | 0.0640095 | − | 0.997949i | \(-0.479611\pi\) | ||||
0.0640095 | + | 0.997949i | \(0.479611\pi\) | |||||||
\(402\) | −9.69897 | −0.483741 | ||||||||
\(403\) | −2.60935 | −0.129981 | ||||||||
\(404\) | −36.9951 | −1.84057 | ||||||||
\(405\) | −11.4751 | −0.570202 | ||||||||
\(406\) | −22.0653 | −1.09508 | ||||||||
\(407\) | −0.430842 | −0.0213560 | ||||||||
\(408\) | −23.8748 | −1.18198 | ||||||||
\(409\) | 26.2935 | 1.30013 | 0.650066 | − | 0.759878i | \(-0.274741\pi\) | ||||
0.650066 | + | 0.759878i | \(0.274741\pi\) | |||||||
\(410\) | −85.5468 | −4.22486 | ||||||||
\(411\) | −10.7719 | −0.531340 | ||||||||
\(412\) | 21.5933 | 1.06382 | ||||||||
\(413\) | −0.847140 | −0.0416850 | ||||||||
\(414\) | −29.9115 | −1.47007 | ||||||||
\(415\) | −27.2136 | −1.33586 | ||||||||
\(416\) | 0.782822 | 0.0383810 | ||||||||
\(417\) | −3.27079 | −0.160171 | ||||||||
\(418\) | 29.4155 | 1.43876 | ||||||||
\(419\) | 12.1058 | 0.591406 | 0.295703 | − | 0.955280i | \(-0.404446\pi\) | ||||
0.295703 | + | 0.955280i | \(0.404446\pi\) | |||||||
\(420\) | −35.2338 | −1.71923 | ||||||||
\(421\) | 14.5550 | 0.709366 | 0.354683 | − | 0.934987i | \(-0.384589\pi\) | ||||
0.354683 | + | 0.934987i | \(0.384589\pi\) | |||||||
\(422\) | −1.33616 | −0.0650433 | ||||||||
\(423\) | 1.12098 | 0.0545041 | ||||||||
\(424\) | 12.0099 | 0.583252 | ||||||||
\(425\) | −50.4908 | −2.44916 | ||||||||
\(426\) | 9.02965 | 0.437488 | ||||||||
\(427\) | −34.9156 | −1.68968 | ||||||||
\(428\) | −54.4347 | −2.63120 | ||||||||
\(429\) | 1.63992 | 0.0791759 | ||||||||
\(430\) | −100.611 | −4.85190 | ||||||||
\(431\) | 20.9584 | 1.00953 | 0.504764 | − | 0.863257i | \(-0.331579\pi\) | ||||
0.504764 | + | 0.863257i | \(0.331579\pi\) | |||||||
\(432\) | 15.6270 | 0.751852 | ||||||||
\(433\) | 4.52672 | 0.217540 | 0.108770 | − | 0.994067i | \(-0.465309\pi\) | ||||
0.108770 | + | 0.994067i | \(0.465309\pi\) | |||||||
\(434\) | −18.6441 | −0.894946 | ||||||||
\(435\) | −9.45545 | −0.453354 | ||||||||
\(436\) | 42.3674 | 2.02903 | ||||||||
\(437\) | −33.1898 | −1.58768 | ||||||||
\(438\) | −20.4809 | −0.978613 | ||||||||
\(439\) | −36.8148 | −1.75707 | −0.878537 | − | 0.477675i | \(-0.841480\pi\) | ||||
−0.878537 | + | 0.477675i | \(0.841480\pi\) | |||||||
\(440\) | −33.2038 | −1.58293 | ||||||||
\(441\) | −3.73289 | −0.177757 | ||||||||
\(442\) | 14.8205 | 0.704941 | ||||||||
\(443\) | −28.7694 | −1.36688 | −0.683438 | − | 0.730008i | \(-0.739516\pi\) | ||||
−0.683438 | + | 0.730008i | \(0.739516\pi\) | |||||||
\(444\) | −0.726211 | −0.0344645 | ||||||||
\(445\) | −26.4917 | −1.25583 | ||||||||
\(446\) | −0.0986226 | −0.00466992 | ||||||||
\(447\) | −7.90893 | −0.374080 | ||||||||
\(448\) | 26.2353 | 1.23950 | ||||||||
\(449\) | 2.50012 | 0.117988 | 0.0589940 | − | 0.998258i | \(-0.481211\pi\) | ||||
0.0589940 | + | 0.998258i | \(0.481211\pi\) | |||||||
\(450\) | 46.2589 | 2.18067 | ||||||||
\(451\) | 18.8348 | 0.886894 | ||||||||
\(452\) | 35.2637 | 1.65866 | ||||||||
\(453\) | −18.6870 | −0.877992 | ||||||||
\(454\) | 11.3103 | 0.530819 | ||||||||
\(455\) | 10.7066 | 0.501933 | ||||||||
\(456\) | 24.2711 | 1.13660 | ||||||||
\(457\) | 35.5183 | 1.66148 | 0.830739 | − | 0.556663i | \(-0.187918\pi\) | ||||
0.830739 | + | 0.556663i | \(0.187918\pi\) | |||||||
\(458\) | 46.0544 | 2.15198 | ||||||||
\(459\) | −27.0933 | −1.26461 | ||||||||
\(460\) | 76.5328 | 3.56836 | ||||||||
\(461\) | 21.5051 | 1.00159 | 0.500795 | − | 0.865566i | \(-0.333041\pi\) | ||||
0.500795 | + | 0.865566i | \(0.333041\pi\) | |||||||
\(462\) | 11.7174 | 0.545143 | ||||||||
\(463\) | −31.1781 | −1.44897 | −0.724485 | − | 0.689290i | \(-0.757923\pi\) | ||||
−0.724485 | + | 0.689290i | \(0.757923\pi\) | |||||||
\(464\) | −10.8516 | −0.503772 | ||||||||
\(465\) | −7.98940 | −0.370500 | ||||||||
\(466\) | −39.0717 | −1.80996 | ||||||||
\(467\) | 13.4678 | 0.623215 | 0.311608 | − | 0.950211i | \(-0.399133\pi\) | ||||
0.311608 | + | 0.950211i | \(0.399133\pi\) | |||||||
\(468\) | −8.98941 | −0.415536 | ||||||||
\(469\) | 13.9416 | 0.643763 | ||||||||
\(470\) | −4.33236 | −0.199837 | ||||||||
\(471\) | −6.17615 | −0.284582 | ||||||||
\(472\) | −1.34564 | −0.0619379 | ||||||||
\(473\) | 22.1515 | 1.01852 | ||||||||
\(474\) | 9.09572 | 0.417780 | ||||||||
\(475\) | 51.3289 | 2.35513 | ||||||||
\(476\) | 70.1065 | 3.21333 | ||||||||
\(477\) | 5.90637 | 0.270434 | ||||||||
\(478\) | 51.8544 | 2.37177 | ||||||||
\(479\) | 3.89369 | 0.177907 | 0.0889536 | − | 0.996036i | \(-0.471648\pi\) | ||||
0.0889536 | + | 0.996036i | \(0.471648\pi\) | |||||||
\(480\) | 2.39688 | 0.109402 | ||||||||
\(481\) | 0.220676 | 0.0100620 | ||||||||
\(482\) | −49.8061 | −2.26860 | ||||||||
\(483\) | −13.2209 | −0.601571 | ||||||||
\(484\) | −28.1625 | −1.28012 | ||||||||
\(485\) | −47.1719 | −2.14197 | ||||||||
\(486\) | 38.8876 | 1.76398 | ||||||||
\(487\) | 36.8745 | 1.67094 | 0.835472 | − | 0.549534i | \(-0.185195\pi\) | ||||
0.835472 | + | 0.549534i | \(0.185195\pi\) | |||||||
\(488\) | −55.4615 | −2.51063 | ||||||||
\(489\) | 12.0510 | 0.544966 | ||||||||
\(490\) | 14.4268 | 0.651737 | ||||||||
\(491\) | −18.3643 | −0.828769 | −0.414384 | − | 0.910102i | \(-0.636003\pi\) | ||||
−0.414384 | + | 0.910102i | \(0.636003\pi\) | |||||||
\(492\) | 31.7472 | 1.43127 | ||||||||
\(493\) | 18.8140 | 0.847339 | ||||||||
\(494\) | −15.0665 | −0.677875 | ||||||||
\(495\) | −16.3294 | −0.733950 | ||||||||
\(496\) | −9.16907 | −0.411703 | ||||||||
\(497\) | −12.9795 | −0.582210 | ||||||||
\(498\) | 15.2547 | 0.683579 | ||||||||
\(499\) | −9.08841 | −0.406853 | −0.203427 | − | 0.979090i | \(-0.565208\pi\) | ||||
−0.203427 | + | 0.979090i | \(0.565208\pi\) | |||||||
\(500\) | −46.9525 | −2.09978 | ||||||||
\(501\) | −19.8469 | −0.886694 | ||||||||
\(502\) | 22.4713 | 1.00294 | ||||||||
\(503\) | −1.07688 | −0.0480157 | −0.0240078 | − | 0.999712i | \(-0.507643\pi\) | ||||
−0.0240078 | + | 0.999712i | \(0.507643\pi\) | |||||||
\(504\) | −31.4420 | −1.40054 | ||||||||
\(505\) | 34.4206 | 1.53170 | ||||||||
\(506\) | −25.4519 | −1.13147 | ||||||||
\(507\) | −0.839960 | −0.0373039 | ||||||||
\(508\) | −2.65775 | −0.117919 | ||||||||
\(509\) | 40.4809 | 1.79429 | 0.897143 | − | 0.441740i | \(-0.145639\pi\) | ||||
0.897143 | + | 0.441740i | \(0.145639\pi\) | |||||||
\(510\) | 45.3781 | 2.00938 | ||||||||
\(511\) | 29.4398 | 1.30234 | ||||||||
\(512\) | 35.5395 | 1.57064 | ||||||||
\(513\) | 27.5430 | 1.21605 | ||||||||
\(514\) | 16.2189 | 0.715385 | ||||||||
\(515\) | −20.0906 | −0.885298 | ||||||||
\(516\) | 37.3377 | 1.64370 | ||||||||
\(517\) | 0.953852 | 0.0419504 | ||||||||
\(518\) | 1.57676 | 0.0692788 | ||||||||
\(519\) | 8.42096 | 0.369639 | ||||||||
\(520\) | 17.0069 | 0.745801 | ||||||||
\(521\) | −7.01078 | −0.307148 | −0.153574 | − | 0.988137i | \(-0.549078\pi\) | ||||
−0.153574 | + | 0.988137i | \(0.549078\pi\) | |||||||
\(522\) | −17.2371 | −0.754447 | ||||||||
\(523\) | 29.3279 | 1.28242 | 0.641210 | − | 0.767365i | \(-0.278433\pi\) | ||||
0.641210 | + | 0.767365i | \(0.278433\pi\) | |||||||
\(524\) | 45.5262 | 1.98882 | ||||||||
\(525\) | 20.4464 | 0.892356 | ||||||||
\(526\) | −0.758582 | −0.0330757 | ||||||||
\(527\) | 15.8969 | 0.692480 | ||||||||
\(528\) | 5.76256 | 0.250783 | ||||||||
\(529\) | 5.71759 | 0.248591 | ||||||||
\(530\) | −22.8268 | −0.991533 | ||||||||
\(531\) | −0.661773 | −0.0287185 | ||||||||
\(532\) | −71.2702 | −3.08995 | ||||||||
\(533\) | −9.64711 | −0.417863 | ||||||||
\(534\) | 14.8500 | 0.642624 | ||||||||
\(535\) | 50.6467 | 2.18965 | ||||||||
\(536\) | 22.1455 | 0.956539 | ||||||||
\(537\) | −16.0996 | −0.694751 | ||||||||
\(538\) | −21.7467 | −0.937566 | ||||||||
\(539\) | −3.17634 | −0.136815 | ||||||||
\(540\) | −63.5118 | −2.73311 | ||||||||
\(541\) | 33.6492 | 1.44669 | 0.723346 | − | 0.690485i | \(-0.242603\pi\) | ||||
0.723346 | + | 0.690485i | \(0.242603\pi\) | |||||||
\(542\) | −4.22917 | −0.181658 | ||||||||
\(543\) | −3.41072 | −0.146368 | ||||||||
\(544\) | −4.76918 | −0.204477 | ||||||||
\(545\) | −39.4191 | −1.68853 | ||||||||
\(546\) | −6.00162 | −0.256846 | ||||||||
\(547\) | −23.9739 | −1.02505 | −0.512525 | − | 0.858672i | \(-0.671290\pi\) | ||||
−0.512525 | + | 0.858672i | \(0.671290\pi\) | |||||||
\(548\) | 50.2440 | 2.14632 | ||||||||
\(549\) | −27.2755 | −1.16409 | ||||||||
\(550\) | 39.3620 | 1.67840 | ||||||||
\(551\) | −19.1263 | −0.814806 | ||||||||
\(552\) | −21.0007 | −0.893848 | ||||||||
\(553\) | −13.0745 | −0.555982 | ||||||||
\(554\) | 42.6802 | 1.81331 | ||||||||
\(555\) | 0.675675 | 0.0286808 | ||||||||
\(556\) | 15.2561 | 0.647003 | ||||||||
\(557\) | −12.7715 | −0.541145 | −0.270572 | − | 0.962700i | \(-0.587213\pi\) | ||||
−0.270572 | + | 0.962700i | \(0.587213\pi\) | |||||||
\(558\) | −14.5645 | −0.616565 | ||||||||
\(559\) | −11.3459 | −0.479881 | ||||||||
\(560\) | 37.6223 | 1.58983 | ||||||||
\(561\) | −9.99086 | −0.421814 | ||||||||
\(562\) | −35.6202 | −1.50255 | ||||||||
\(563\) | 23.8832 | 1.00656 | 0.503278 | − | 0.864125i | \(-0.332127\pi\) | ||||
0.503278 | + | 0.864125i | \(0.332127\pi\) | |||||||
\(564\) | 1.60778 | 0.0676996 | ||||||||
\(565\) | −32.8097 | −1.38031 | ||||||||
\(566\) | 48.6297 | 2.04406 | ||||||||
\(567\) | −9.24612 | −0.388301 | ||||||||
\(568\) | −20.6172 | −0.865080 | ||||||||
\(569\) | −30.4046 | −1.27463 | −0.637314 | − | 0.770605i | \(-0.719954\pi\) | ||||
−0.637314 | + | 0.770605i | \(0.719954\pi\) | |||||||
\(570\) | −46.1313 | −1.93223 | ||||||||
\(571\) | 12.0930 | 0.506075 | 0.253037 | − | 0.967457i | \(-0.418570\pi\) | ||||
0.253037 | + | 0.967457i | \(0.418570\pi\) | |||||||
\(572\) | −7.64914 | −0.319826 | ||||||||
\(573\) | 12.2191 | 0.510460 | ||||||||
\(574\) | −68.9298 | −2.87708 | ||||||||
\(575\) | −44.4125 | −1.85213 | ||||||||
\(576\) | 20.4947 | 0.853944 | ||||||||
\(577\) | 33.6188 | 1.39957 | 0.699785 | − | 0.714354i | \(-0.253279\pi\) | ||||
0.699785 | + | 0.714354i | \(0.253279\pi\) | |||||||
\(578\) | −48.9358 | −2.03546 | ||||||||
\(579\) | −12.8404 | −0.533630 | ||||||||
\(580\) | 44.1035 | 1.83130 | ||||||||
\(581\) | −21.9275 | −0.909708 | ||||||||
\(582\) | 26.4424 | 1.09607 | ||||||||
\(583\) | 5.02576 | 0.208146 | ||||||||
\(584\) | 46.7635 | 1.93509 | ||||||||
\(585\) | 8.36384 | 0.345802 | ||||||||
\(586\) | 75.3251 | 3.11165 | ||||||||
\(587\) | −0.476412 | −0.0196636 | −0.00983181 | − | 0.999952i | \(-0.503130\pi\) | ||||
−0.00983181 | + | 0.999952i | \(0.503130\pi\) | |||||||
\(588\) | −5.35392 | −0.220792 | ||||||||
\(589\) | −16.1608 | −0.665893 | ||||||||
\(590\) | 2.55761 | 0.105295 | ||||||||
\(591\) | 1.97468 | 0.0812275 | ||||||||
\(592\) | 0.775441 | 0.0318704 | ||||||||
\(593\) | 10.3245 | 0.423978 | 0.211989 | − | 0.977272i | \(-0.432006\pi\) | ||||
0.211989 | + | 0.977272i | \(0.432006\pi\) | |||||||
\(594\) | 21.1216 | 0.866629 | ||||||||
\(595\) | −65.2278 | −2.67408 | ||||||||
\(596\) | 36.8900 | 1.51107 | ||||||||
\(597\) | 3.76467 | 0.154078 | ||||||||
\(598\) | 13.0364 | 0.533097 | ||||||||
\(599\) | 21.0777 | 0.861212 | 0.430606 | − | 0.902540i | \(-0.358300\pi\) | ||||
0.430606 | + | 0.902540i | \(0.358300\pi\) | |||||||
\(600\) | 32.4781 | 1.32591 | ||||||||
\(601\) | −14.2327 | −0.580564 | −0.290282 | − | 0.956941i | \(-0.593749\pi\) | ||||
−0.290282 | + | 0.956941i | \(0.593749\pi\) | |||||||
\(602\) | −81.0680 | −3.30408 | ||||||||
\(603\) | 10.8910 | 0.443514 | ||||||||
\(604\) | 87.1627 | 3.54660 | ||||||||
\(605\) | 26.2027 | 1.06529 | ||||||||
\(606\) | −19.2946 | −0.783789 | ||||||||
\(607\) | −33.3191 | −1.35238 | −0.676190 | − | 0.736727i | \(-0.736370\pi\) | ||||
−0.676190 | + | 0.736727i | \(0.736370\pi\) | |||||||
\(608\) | 4.84835 | 0.196626 | ||||||||
\(609\) | −7.61878 | −0.308729 | ||||||||
\(610\) | 105.414 | 4.26808 | ||||||||
\(611\) | −0.488560 | −0.0197650 | ||||||||
\(612\) | 54.7662 | 2.21379 | ||||||||
\(613\) | −47.3358 | −1.91187 | −0.955937 | − | 0.293570i | \(-0.905156\pi\) | ||||
−0.955937 | + | 0.293570i | \(0.905156\pi\) | |||||||
\(614\) | −53.4461 | −2.15691 | ||||||||
\(615\) | −29.5379 | −1.19108 | ||||||||
\(616\) | −26.7541 | −1.07796 | ||||||||
\(617\) | −0.451673 | −0.0181837 | −0.00909184 | − | 0.999959i | \(-0.502894\pi\) | ||||
−0.00909184 | + | 0.999959i | \(0.502894\pi\) | |||||||
\(618\) | 11.2619 | 0.453019 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 37.2653 | 1.49661 | ||||||||
\(621\) | −23.8317 | −0.956333 | ||||||||
\(622\) | −14.0498 | −0.563348 | ||||||||
\(623\) | −21.3459 | −0.855205 | ||||||||
\(624\) | −2.95156 | −0.118157 | ||||||||
\(625\) | 2.24688 | 0.0898750 | ||||||||
\(626\) | 52.3066 | 2.09059 | ||||||||
\(627\) | 10.1567 | 0.405619 | ||||||||
\(628\) | 28.8077 | 1.14955 | ||||||||
\(629\) | −1.34442 | −0.0536057 | ||||||||
\(630\) | 59.7608 | 2.38093 | ||||||||
\(631\) | 16.4564 | 0.655118 | 0.327559 | − | 0.944831i | \(-0.393774\pi\) | ||||
0.327559 | + | 0.944831i | \(0.393774\pi\) | |||||||
\(632\) | −20.7681 | −0.826110 | ||||||||
\(633\) | −0.461355 | −0.0183372 | ||||||||
\(634\) | 55.4899 | 2.20379 | ||||||||
\(635\) | 2.47280 | 0.0981301 | ||||||||
\(636\) | 8.47123 | 0.335906 | ||||||||
\(637\) | 1.62691 | 0.0644605 | ||||||||
\(638\) | −14.6671 | −0.580677 | ||||||||
\(639\) | −10.1394 | −0.401108 | ||||||||
\(640\) | −73.5002 | −2.90535 | ||||||||
\(641\) | −40.9811 | −1.61866 | −0.809328 | − | 0.587358i | \(-0.800168\pi\) | ||||
−0.809328 | + | 0.587358i | \(0.800168\pi\) | |||||||
\(642\) | −28.3902 | −1.12047 | ||||||||
\(643\) | 35.0821 | 1.38350 | 0.691752 | − | 0.722135i | \(-0.256839\pi\) | ||||
0.691752 | + | 0.722135i | \(0.256839\pi\) | |||||||
\(644\) | 61.6667 | 2.43001 | ||||||||
\(645\) | −34.7394 | −1.36786 | ||||||||
\(646\) | 91.7898 | 3.61142 | ||||||||
\(647\) | −9.70406 | −0.381506 | −0.190753 | − | 0.981638i | \(-0.561093\pi\) | ||||
−0.190753 | + | 0.981638i | \(0.561093\pi\) | |||||||
\(648\) | −14.6870 | −0.576959 | ||||||||
\(649\) | −0.563106 | −0.0221039 | ||||||||
\(650\) | −20.1611 | −0.790783 | ||||||||
\(651\) | −6.43751 | −0.252306 | ||||||||
\(652\) | −56.2102 | −2.20136 | ||||||||
\(653\) | −28.0300 | −1.09690 | −0.548450 | − | 0.836184i | \(-0.684782\pi\) | ||||
−0.548450 | + | 0.836184i | \(0.684782\pi\) | |||||||
\(654\) | 22.0965 | 0.864041 | ||||||||
\(655\) | −42.3581 | −1.65507 | ||||||||
\(656\) | −33.8993 | −1.32355 | ||||||||
\(657\) | 22.9979 | 0.897235 | ||||||||
\(658\) | −3.49082 | −0.136087 | ||||||||
\(659\) | −4.00968 | −0.156195 | −0.0780975 | − | 0.996946i | \(-0.524885\pi\) | ||||
−0.0780975 | + | 0.996946i | \(0.524885\pi\) | |||||||
\(660\) | −23.4204 | −0.911640 | ||||||||
\(661\) | −15.9496 | −0.620367 | −0.310183 | − | 0.950677i | \(-0.600390\pi\) | ||||
−0.310183 | + | 0.950677i | \(0.600390\pi\) | |||||||
\(662\) | 50.8762 | 1.97736 | ||||||||
\(663\) | 5.11729 | 0.198739 | ||||||||
\(664\) | −34.8307 | −1.35170 | ||||||||
\(665\) | 66.3105 | 2.57141 | ||||||||
\(666\) | 1.23174 | 0.0477290 | ||||||||
\(667\) | 16.5491 | 0.640782 | ||||||||
\(668\) | 92.5728 | 3.58175 | ||||||||
\(669\) | −0.0340528 | −0.00131656 | ||||||||
\(670\) | −42.0912 | −1.62612 | ||||||||
\(671\) | −23.2089 | −0.895969 | ||||||||
\(672\) | 1.93130 | 0.0745014 | ||||||||
\(673\) | 8.33607 | 0.321332 | 0.160666 | − | 0.987009i | \(-0.448636\pi\) | ||||
0.160666 | + | 0.987009i | \(0.448636\pi\) | |||||||
\(674\) | 7.62752 | 0.293801 | ||||||||
\(675\) | 36.8563 | 1.41860 | ||||||||
\(676\) | 3.91786 | 0.150687 | ||||||||
\(677\) | −40.8130 | −1.56857 | −0.784286 | − | 0.620399i | \(-0.786971\pi\) | ||||
−0.784286 | + | 0.620399i | \(0.786971\pi\) | |||||||
\(678\) | 18.3916 | 0.706325 | ||||||||
\(679\) | −38.0091 | −1.45865 | ||||||||
\(680\) | −103.611 | −3.97330 | ||||||||
\(681\) | 3.90526 | 0.149650 | ||||||||
\(682\) | −12.3930 | −0.474553 | ||||||||
\(683\) | 35.1141 | 1.34361 | 0.671803 | − | 0.740730i | \(-0.265520\pi\) | ||||
0.671803 | + | 0.740730i | \(0.265520\pi\) | |||||||
\(684\) | −55.6752 | −2.12880 | ||||||||
\(685\) | −46.7476 | −1.78613 | ||||||||
\(686\) | −38.3914 | −1.46579 | ||||||||
\(687\) | 15.9018 | 0.606693 | ||||||||
\(688\) | −39.8688 | −1.51998 | ||||||||
\(689\) | −2.57418 | −0.0980684 | ||||||||
\(690\) | 39.9153 | 1.51955 | ||||||||
\(691\) | 3.16458 | 0.120386 | 0.0601932 | − | 0.998187i | \(-0.480828\pi\) | ||||
0.0601932 | + | 0.998187i | \(0.480828\pi\) | |||||||
\(692\) | −39.2783 | −1.49314 | ||||||||
\(693\) | −13.1575 | −0.499811 | ||||||||
\(694\) | −69.7110 | −2.64619 | ||||||||
\(695\) | −14.1944 | −0.538426 | ||||||||
\(696\) | −12.1020 | −0.458726 | ||||||||
\(697\) | 58.7731 | 2.22619 | ||||||||
\(698\) | 41.0610 | 1.55418 | ||||||||
\(699\) | −13.4908 | −0.510269 | ||||||||
\(700\) | −95.3693 | −3.60462 | ||||||||
\(701\) | −17.4612 | −0.659500 | −0.329750 | − | 0.944068i | \(-0.606965\pi\) | ||||
−0.329750 | + | 0.944068i | \(0.606965\pi\) | |||||||
\(702\) | −10.8184 | −0.408315 | ||||||||
\(703\) | 1.36674 | 0.0515476 | ||||||||
\(704\) | 17.4390 | 0.657258 | ||||||||
\(705\) | −1.49589 | −0.0563386 | ||||||||
\(706\) | −68.4676 | −2.57681 | ||||||||
\(707\) | 27.7346 | 1.04307 | ||||||||
\(708\) | −0.949151 | −0.0356713 | ||||||||
\(709\) | −29.7660 | −1.11789 | −0.558943 | − | 0.829206i | \(-0.688793\pi\) | ||||
−0.558943 | + | 0.829206i | \(0.688793\pi\) | |||||||
\(710\) | 39.1865 | 1.47064 | ||||||||
\(711\) | −10.2136 | −0.383039 | ||||||||
\(712\) | −33.9068 | −1.27071 | ||||||||
\(713\) | 13.9832 | 0.523674 | ||||||||
\(714\) | 36.5637 | 1.36836 | ||||||||
\(715\) | 7.11684 | 0.266155 | ||||||||
\(716\) | 75.0943 | 2.80641 | ||||||||
\(717\) | 17.9045 | 0.668656 | ||||||||
\(718\) | 45.6934 | 1.70526 | ||||||||
\(719\) | 40.4446 | 1.50833 | 0.754164 | − | 0.656686i | \(-0.228042\pi\) | ||||
0.754164 | + | 0.656686i | \(0.228042\pi\) | |||||||
\(720\) | 29.3900 | 1.09530 | ||||||||
\(721\) | −16.1881 | −0.602878 | ||||||||
\(722\) | −47.0928 | −1.75261 | ||||||||
\(723\) | −17.1972 | −0.639572 | ||||||||
\(724\) | 15.9088 | 0.591246 | ||||||||
\(725\) | −25.5936 | −0.950521 | ||||||||
\(726\) | −14.6880 | −0.545124 | ||||||||
\(727\) | −47.9207 | −1.77728 | −0.888641 | − | 0.458603i | \(-0.848350\pi\) | ||||
−0.888641 | + | 0.458603i | \(0.848350\pi\) | |||||||
\(728\) | 13.7034 | 0.507881 | ||||||||
\(729\) | 3.98332 | 0.147531 | ||||||||
\(730\) | −88.8820 | −3.28967 | ||||||||
\(731\) | 69.1227 | 2.55659 | ||||||||
\(732\) | −39.1201 | −1.44592 | ||||||||
\(733\) | 0.795034 | 0.0293652 | 0.0146826 | − | 0.999892i | \(-0.495326\pi\) | ||||
0.0146826 | + | 0.999892i | \(0.495326\pi\) | |||||||
\(734\) | 23.8811 | 0.881469 | ||||||||
\(735\) | 4.98134 | 0.183740 | ||||||||
\(736\) | −4.19505 | −0.154631 | ||||||||
\(737\) | 9.26718 | 0.341361 | ||||||||
\(738\) | −53.8470 | −1.98214 | ||||||||
\(739\) | −33.3608 | −1.22720 | −0.613599 | − | 0.789618i | \(-0.710279\pi\) | ||||
−0.613599 | + | 0.789618i | \(0.710279\pi\) | |||||||
\(740\) | −3.15158 | −0.115854 | ||||||||
\(741\) | −5.20223 | −0.191109 | ||||||||
\(742\) | −18.3928 | −0.675222 | ||||||||
\(743\) | −5.17500 | −0.189852 | −0.0949262 | − | 0.995484i | \(-0.530262\pi\) | ||||
−0.0949262 | + | 0.995484i | \(0.530262\pi\) | |||||||
\(744\) | −10.2256 | −0.374890 | ||||||||
\(745\) | −34.3229 | −1.25749 | ||||||||
\(746\) | −42.9326 | −1.57188 | ||||||||
\(747\) | −17.1295 | −0.626735 | ||||||||
\(748\) | 46.6008 | 1.70389 | ||||||||
\(749\) | 40.8089 | 1.49112 | ||||||||
\(750\) | −24.4878 | −0.894170 | ||||||||
\(751\) | −34.1669 | −1.24677 | −0.623383 | − | 0.781916i | \(-0.714242\pi\) | ||||
−0.623383 | + | 0.781916i | \(0.714242\pi\) | |||||||
\(752\) | −1.71677 | −0.0626041 | ||||||||
\(753\) | 7.75899 | 0.282753 | ||||||||
\(754\) | 7.51246 | 0.273587 | ||||||||
\(755\) | −81.0971 | −2.95142 | ||||||||
\(756\) | −51.1750 | −1.86122 | ||||||||
\(757\) | 33.8610 | 1.23070 | 0.615350 | − | 0.788254i | \(-0.289015\pi\) | ||||
0.615350 | + | 0.788254i | \(0.289015\pi\) | |||||||
\(758\) | 38.1182 | 1.38452 | ||||||||
\(759\) | −8.78811 | −0.318988 | ||||||||
\(760\) | 105.331 | 3.82075 | ||||||||
\(761\) | 14.4804 | 0.524914 | 0.262457 | − | 0.964944i | \(-0.415467\pi\) | ||||
0.262457 | + | 0.964944i | \(0.415467\pi\) | |||||||
\(762\) | −1.38614 | −0.0502144 | ||||||||
\(763\) | −31.7622 | −1.14987 | ||||||||
\(764\) | −56.9941 | −2.06197 | ||||||||
\(765\) | −50.9550 | −1.84228 | ||||||||
\(766\) | −0.105251 | −0.00380289 | ||||||||
\(767\) | 0.288421 | 0.0104143 | ||||||||
\(768\) | 26.1954 | 0.945246 | ||||||||
\(769\) | −34.3195 | −1.23759 | −0.618797 | − | 0.785551i | \(-0.712380\pi\) | ||||
−0.618797 | + | 0.785551i | \(0.712380\pi\) | |||||||
\(770\) | 50.8507 | 1.83253 | ||||||||
\(771\) | 5.60012 | 0.201683 | ||||||||
\(772\) | 59.8922 | 2.15557 | ||||||||
\(773\) | 6.88095 | 0.247490 | 0.123745 | − | 0.992314i | \(-0.460509\pi\) | ||||
0.123745 | + | 0.992314i | \(0.460509\pi\) | |||||||
\(774\) | −63.3291 | −2.27632 | ||||||||
\(775\) | −21.6253 | −0.776805 | ||||||||
\(776\) | −60.3754 | −2.16735 | ||||||||
\(777\) | 0.544429 | 0.0195313 | ||||||||
\(778\) | −95.2966 | −3.41655 | ||||||||
\(779\) | −59.7486 | −2.14072 | ||||||||
\(780\) | 11.9959 | 0.429521 | ||||||||
\(781\) | −8.62766 | −0.308722 | ||||||||
\(782\) | −79.4214 | −2.84010 | ||||||||
\(783\) | −13.7335 | −0.490794 | ||||||||
\(784\) | 5.71686 | 0.204173 | ||||||||
\(785\) | −26.8030 | −0.956639 | ||||||||
\(786\) | 23.7440 | 0.846919 | ||||||||
\(787\) | −17.4441 | −0.621814 | −0.310907 | − | 0.950440i | \(-0.600633\pi\) | ||||
−0.310907 | + | 0.950440i | \(0.600633\pi\) | |||||||
\(788\) | −9.21060 | −0.328114 | ||||||||
\(789\) | −0.261926 | −0.00932481 | ||||||||
\(790\) | 39.4732 | 1.40439 | ||||||||
\(791\) | −26.4366 | −0.939978 | ||||||||
\(792\) | −20.9000 | −0.742647 | ||||||||
\(793\) | 11.8875 | 0.422138 | ||||||||
\(794\) | 62.6609 | 2.22375 | ||||||||
\(795\) | −7.88173 | −0.279536 | ||||||||
\(796\) | −17.5597 | −0.622388 | ||||||||
\(797\) | −36.1084 | −1.27903 | −0.639513 | − | 0.768780i | \(-0.720864\pi\) | ||||
−0.639513 | + | 0.768780i | \(0.720864\pi\) | |||||||
\(798\) | −37.1706 | −1.31583 | ||||||||
\(799\) | 2.97645 | 0.105299 | ||||||||
\(800\) | 6.48775 | 0.229377 | ||||||||
\(801\) | −16.6751 | −0.589185 | ||||||||
\(802\) | −6.23633 | −0.220212 | ||||||||
\(803\) | 19.5691 | 0.690577 | ||||||||
\(804\) | 15.6204 | 0.550890 | ||||||||
\(805\) | −57.3754 | −2.02222 | ||||||||
\(806\) | 6.34767 | 0.223587 | ||||||||
\(807\) | −7.50877 | −0.264321 | ||||||||
\(808\) | 44.0550 | 1.54985 | ||||||||
\(809\) | 45.2575 | 1.59117 | 0.795585 | − | 0.605842i | \(-0.207164\pi\) | ||||
0.795585 | + | 0.605842i | \(0.207164\pi\) | |||||||
\(810\) | 27.9151 | 0.980835 | ||||||||
\(811\) | 50.4390 | 1.77115 | 0.885576 | − | 0.464494i | \(-0.153764\pi\) | ||||
0.885576 | + | 0.464494i | \(0.153764\pi\) | |||||||
\(812\) | 35.5366 | 1.24709 | ||||||||
\(813\) | −1.46026 | −0.0512137 | ||||||||
\(814\) | 1.04809 | 0.0367357 | ||||||||
\(815\) | 52.2985 | 1.83194 | ||||||||
\(816\) | 17.9818 | 0.629489 | ||||||||
\(817\) | −70.2700 | −2.45844 | ||||||||
\(818\) | −63.9634 | −2.23643 | ||||||||
\(819\) | 6.73922 | 0.235487 | ||||||||
\(820\) | 137.775 | 4.81131 | ||||||||
\(821\) | −19.5226 | −0.681343 | −0.340671 | − | 0.940182i | \(-0.610654\pi\) | ||||
−0.340671 | + | 0.940182i | \(0.610654\pi\) | |||||||
\(822\) | 26.2045 | 0.913987 | ||||||||
\(823\) | 46.8485 | 1.63304 | 0.816518 | − | 0.577321i | \(-0.195902\pi\) | ||||
0.816518 | + | 0.577321i | \(0.195902\pi\) | |||||||
\(824\) | −25.7140 | −0.895790 | ||||||||
\(825\) | 13.5910 | 0.473180 | ||||||||
\(826\) | 2.06081 | 0.0717047 | ||||||||
\(827\) | −52.0032 | −1.80833 | −0.904164 | − | 0.427185i | \(-0.859505\pi\) | ||||
−0.904164 | + | 0.427185i | \(0.859505\pi\) | |||||||
\(828\) | 48.1732 | 1.67413 | ||||||||
\(829\) | 41.9539 | 1.45712 | 0.728560 | − | 0.684982i | \(-0.240190\pi\) | ||||
0.728560 | + | 0.684982i | \(0.240190\pi\) | |||||||
\(830\) | 66.2017 | 2.29789 | ||||||||
\(831\) | 14.7368 | 0.511213 | ||||||||
\(832\) | −8.93221 | −0.309669 | ||||||||
\(833\) | −9.91162 | −0.343417 | ||||||||
\(834\) | 7.95674 | 0.275520 | ||||||||
\(835\) | −86.1307 | −2.98068 | ||||||||
\(836\) | −47.3743 | −1.63848 | ||||||||
\(837\) | −11.6041 | −0.401097 | ||||||||
\(838\) | −29.4493 | −1.01731 | ||||||||
\(839\) | 43.9044 | 1.51575 | 0.757875 | − | 0.652400i | \(-0.226238\pi\) | ||||
0.757875 | + | 0.652400i | \(0.226238\pi\) | |||||||
\(840\) | 41.9576 | 1.44768 | ||||||||
\(841\) | −19.4633 | −0.671148 | ||||||||
\(842\) | −35.4074 | −1.22022 | ||||||||
\(843\) | −12.2991 | −0.423603 | ||||||||
\(844\) | 2.15192 | 0.0740721 | ||||||||
\(845\) | −3.64522 | −0.125399 | ||||||||
\(846\) | −2.72698 | −0.0937556 | ||||||||
\(847\) | 21.1130 | 0.725451 | ||||||||
\(848\) | −9.04549 | −0.310623 | ||||||||
\(849\) | 16.7910 | 0.576267 | ||||||||
\(850\) | 122.827 | 4.21294 | ||||||||
\(851\) | −1.18258 | −0.0405382 | ||||||||
\(852\) | −14.5425 | −0.498217 | ||||||||
\(853\) | 2.05638 | 0.0704091 | 0.0352046 | − | 0.999380i | \(-0.488792\pi\) | ||||
0.0352046 | + | 0.999380i | \(0.488792\pi\) | |||||||
\(854\) | 84.9379 | 2.90652 | ||||||||
\(855\) | 51.8008 | 1.77155 | ||||||||
\(856\) | 64.8227 | 2.21559 | ||||||||
\(857\) | −40.5263 | −1.38435 | −0.692176 | − | 0.721729i | \(-0.743348\pi\) | ||||
−0.692176 | + | 0.721729i | \(0.743348\pi\) | |||||||
\(858\) | −3.98937 | −0.136195 | ||||||||
\(859\) | 43.4286 | 1.48177 | 0.740883 | − | 0.671635i | \(-0.234408\pi\) | ||||
0.740883 | + | 0.671635i | \(0.234408\pi\) | |||||||
\(860\) | 162.036 | 5.52540 | ||||||||
\(861\) | −23.8004 | −0.811114 | ||||||||
\(862\) | −50.9847 | −1.73654 | ||||||||
\(863\) | −45.4429 | −1.54690 | −0.773448 | − | 0.633860i | \(-0.781469\pi\) | ||||
−0.773448 | + | 0.633860i | \(0.781469\pi\) | |||||||
\(864\) | 3.48132 | 0.118437 | ||||||||
\(865\) | 36.5449 | 1.24256 | ||||||||
\(866\) | −11.0120 | −0.374203 | ||||||||
\(867\) | −16.8967 | −0.573843 | ||||||||
\(868\) | 30.0268 | 1.01918 | ||||||||
\(869\) | −8.69078 | −0.294815 | ||||||||
\(870\) | 23.0019 | 0.779839 | ||||||||
\(871\) | −4.74662 | −0.160833 | ||||||||
\(872\) | −50.4525 | −1.70854 | ||||||||
\(873\) | −29.6921 | −1.00493 | ||||||||
\(874\) | 80.7397 | 2.73106 | ||||||||
\(875\) | 35.1995 | 1.18996 | ||||||||
\(876\) | 32.9849 | 1.11446 | ||||||||
\(877\) | −48.2621 | −1.62970 | −0.814848 | − | 0.579675i | \(-0.803180\pi\) | ||||
−0.814848 | + | 0.579675i | \(0.803180\pi\) | |||||||
\(878\) | 89.5581 | 3.02244 | ||||||||
\(879\) | 26.0085 | 0.877246 | ||||||||
\(880\) | 25.0081 | 0.843023 | ||||||||
\(881\) | −32.7464 | −1.10326 | −0.551628 | − | 0.834090i | \(-0.685993\pi\) | ||||
−0.551628 | + | 0.834090i | \(0.685993\pi\) | |||||||
\(882\) | 9.08088 | 0.305769 | ||||||||
\(883\) | −1.19651 | −0.0402658 | −0.0201329 | − | 0.999797i | \(-0.506409\pi\) | ||||
−0.0201329 | + | 0.999797i | \(0.506409\pi\) | |||||||
\(884\) | −23.8688 | −0.802795 | ||||||||
\(885\) | 0.883100 | 0.0296851 | ||||||||
\(886\) | 69.9864 | 2.35124 | ||||||||
\(887\) | −25.5300 | −0.857214 | −0.428607 | − | 0.903491i | \(-0.640995\pi\) | ||||
−0.428607 | + | 0.903491i | \(0.640995\pi\) | |||||||
\(888\) | 0.864797 | 0.0290207 | ||||||||
\(889\) | 1.99247 | 0.0668254 | ||||||||
\(890\) | 64.4456 | 2.16022 | ||||||||
\(891\) | −6.14604 | −0.205900 | ||||||||
\(892\) | 0.158834 | 0.00531816 | ||||||||
\(893\) | −3.02586 | −0.101257 | ||||||||
\(894\) | 19.2398 | 0.643475 | ||||||||
\(895\) | −69.8685 | −2.33545 | ||||||||
\(896\) | −59.2233 | −1.97851 | ||||||||
\(897\) | 4.50124 | 0.150292 | ||||||||
\(898\) | −6.08196 | −0.202958 | ||||||||
\(899\) | 8.05807 | 0.268752 | ||||||||
\(900\) | −74.5011 | −2.48337 | ||||||||
\(901\) | 15.6827 | 0.522465 | ||||||||
\(902\) | −45.8187 | −1.52560 | ||||||||
\(903\) | −27.9915 | −0.931497 | ||||||||
\(904\) | −41.9932 | −1.39667 | ||||||||
\(905\) | −14.8017 | −0.492025 | ||||||||
\(906\) | 45.4592 | 1.51028 | ||||||||
\(907\) | −7.60563 | −0.252541 | −0.126270 | − | 0.991996i | \(-0.540301\pi\) | ||||
−0.126270 | + | 0.991996i | \(0.540301\pi\) | |||||||
\(908\) | −18.2155 | −0.604503 | ||||||||
\(909\) | 21.6659 | 0.718612 | ||||||||
\(910\) | −26.0456 | −0.863403 | ||||||||
\(911\) | 39.0561 | 1.29399 | 0.646993 | − | 0.762496i | \(-0.276026\pi\) | ||||
0.646993 | + | 0.762496i | \(0.276026\pi\) | |||||||
\(912\) | −18.2803 | −0.605321 | ||||||||
\(913\) | −14.5756 | −0.482381 | ||||||||
\(914\) | −86.4042 | −2.85800 | ||||||||
\(915\) | 36.3977 | 1.20327 | ||||||||
\(916\) | −74.1717 | −2.45070 | ||||||||
\(917\) | −34.1303 | −1.12708 | ||||||||
\(918\) | 65.9090 | 2.17532 | ||||||||
\(919\) | −15.9975 | −0.527710 | −0.263855 | − | 0.964562i | \(-0.584994\pi\) | ||||
−0.263855 | + | 0.964562i | \(0.584994\pi\) | |||||||
\(920\) | −91.1378 | −3.00472 | ||||||||
\(921\) | −18.4541 | −0.608082 | ||||||||
\(922\) | −52.3146 | −1.72289 | ||||||||
\(923\) | 4.41906 | 0.145455 | ||||||||
\(924\) | −18.8712 | −0.620816 | ||||||||
\(925\) | 1.82888 | 0.0601334 | ||||||||
\(926\) | 75.8460 | 2.49245 | ||||||||
\(927\) | −12.6459 | −0.415347 | ||||||||
\(928\) | −2.41748 | −0.0793575 | ||||||||
\(929\) | 36.3506 | 1.19263 | 0.596313 | − | 0.802752i | \(-0.296632\pi\) | ||||
0.596313 | + | 0.802752i | \(0.296632\pi\) | |||||||
\(930\) | 19.4355 | 0.637317 | ||||||||
\(931\) | 10.0761 | 0.330232 | ||||||||
\(932\) | 62.9258 | 2.06120 | ||||||||
\(933\) | −4.85118 | −0.158821 | ||||||||
\(934\) | −32.7626 | −1.07203 | ||||||||
\(935\) | −43.3579 | −1.41796 | ||||||||
\(936\) | 10.7049 | 0.349900 | ||||||||
\(937\) | −43.0018 | −1.40481 | −0.702404 | − | 0.711779i | \(-0.747890\pi\) | ||||
−0.702404 | + | 0.711779i | \(0.747890\pi\) | |||||||
\(938\) | −33.9152 | −1.10737 | ||||||||
\(939\) | 18.0606 | 0.589386 | ||||||||
\(940\) | 6.97736 | 0.227577 | ||||||||
\(941\) | −7.30276 | −0.238063 | −0.119032 | − | 0.992890i | \(-0.537979\pi\) | ||||
−0.119032 | + | 0.992890i | \(0.537979\pi\) | |||||||
\(942\) | 15.0245 | 0.489525 | ||||||||
\(943\) | 51.6977 | 1.68351 | ||||||||
\(944\) | 1.01349 | 0.0329864 | ||||||||
\(945\) | 47.6138 | 1.54888 | ||||||||
\(946\) | −53.8871 | −1.75202 | ||||||||
\(947\) | −52.9038 | −1.71914 | −0.859571 | − | 0.511016i | \(-0.829269\pi\) | ||||
−0.859571 | + | 0.511016i | \(0.829269\pi\) | |||||||
\(948\) | −14.6489 | −0.475773 | ||||||||
\(949\) | −10.0232 | −0.325367 | ||||||||
\(950\) | −124.866 | −4.05119 | ||||||||
\(951\) | 19.1598 | 0.621298 | ||||||||
\(952\) | −83.4852 | −2.70577 | ||||||||
\(953\) | −7.50053 | −0.242966 | −0.121483 | − | 0.992594i | \(-0.538765\pi\) | ||||
−0.121483 | + | 0.992594i | \(0.538765\pi\) | |||||||
\(954\) | −14.3682 | −0.465188 | ||||||||
\(955\) | 53.0279 | 1.71594 | ||||||||
\(956\) | −83.5128 | −2.70100 | ||||||||
\(957\) | −5.06432 | −0.163706 | ||||||||
\(958\) | −9.47204 | −0.306028 | ||||||||
\(959\) | −37.6671 | −1.21633 | ||||||||
\(960\) | −27.3490 | −0.882686 | ||||||||
\(961\) | −24.1913 | −0.780365 | ||||||||
\(962\) | −0.536831 | −0.0173081 | ||||||||
\(963\) | 31.8793 | 1.02730 | ||||||||
\(964\) | 80.2138 | 2.58351 | ||||||||
\(965\) | −55.7243 | −1.79383 | ||||||||
\(966\) | 32.1620 | 1.03479 | ||||||||
\(967\) | −13.8994 | −0.446973 | −0.223487 | − | 0.974707i | \(-0.571744\pi\) | ||||
−0.223487 | + | 0.974707i | \(0.571744\pi\) | |||||||
\(968\) | 33.5369 | 1.07792 | ||||||||
\(969\) | 31.6935 | 1.01814 | ||||||||
\(970\) | 114.754 | 3.68451 | ||||||||
\(971\) | 15.3058 | 0.491187 | 0.245593 | − | 0.969373i | \(-0.421017\pi\) | ||||
0.245593 | + | 0.969373i | \(0.421017\pi\) | |||||||
\(972\) | −62.6294 | −2.00884 | ||||||||
\(973\) | −11.4373 | −0.366662 | ||||||||
\(974\) | −89.7033 | −2.87428 | ||||||||
\(975\) | −6.96129 | −0.222940 | ||||||||
\(976\) | 41.7720 | 1.33709 | ||||||||
\(977\) | −7.75540 | −0.248117 | −0.124059 | − | 0.992275i | \(-0.539591\pi\) | ||||
−0.124059 | + | 0.992275i | \(0.539591\pi\) | |||||||
\(978\) | −29.3161 | −0.937426 | ||||||||
\(979\) | −14.1889 | −0.453480 | ||||||||
\(980\) | −23.2347 | −0.742205 | ||||||||
\(981\) | −24.8121 | −0.792190 | ||||||||
\(982\) | 44.6742 | 1.42561 | ||||||||
\(983\) | −13.0950 | −0.417666 | −0.208833 | − | 0.977951i | \(-0.566966\pi\) | ||||
−0.208833 | + | 0.977951i | \(0.566966\pi\) | |||||||
\(984\) | −37.8056 | −1.20520 | ||||||||
\(985\) | 8.56964 | 0.273051 | ||||||||
\(986\) | −45.7681 | −1.45755 | ||||||||
\(987\) | −1.20533 | −0.0383659 | ||||||||
\(988\) | 24.2650 | 0.771972 | ||||||||
\(989\) | 60.8013 | 1.93337 | ||||||||
\(990\) | 39.7239 | 1.26251 | ||||||||
\(991\) | −29.3422 | −0.932087 | −0.466043 | − | 0.884762i | \(-0.654321\pi\) | ||||
−0.466043 | + | 0.884762i | \(0.654321\pi\) | |||||||
\(992\) | −2.04265 | −0.0648543 | ||||||||
\(993\) | 17.5667 | 0.557463 | ||||||||
\(994\) | 31.5748 | 1.00149 | ||||||||
\(995\) | 16.3378 | 0.517942 | ||||||||
\(996\) | −24.5680 | −0.778468 | ||||||||
\(997\) | 35.6671 | 1.12959 | 0.564794 | − | 0.825232i | \(-0.308956\pi\) | ||||
0.564794 | + | 0.825232i | \(0.308956\pi\) | |||||||
\(998\) | 22.1091 | 0.699850 | ||||||||
\(999\) | 0.981377 | 0.0310494 |
(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 | 8047.2.a.b.1.15 | ✓ | 142 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.b.1.15 | ✓ | 142 | 1.1 | even | 1 | trivial |