Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9042767376\) |
Analytic rank: | \(0\) |
Dimension: | \(172\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.79279 | −1.97480 | −0.987401 | − | 0.158236i | \(-0.949419\pi\) | ||||
−0.987401 | + | 0.158236i | \(0.949419\pi\) | |||||||
\(3\) | 3.40925 | 1.96833 | 0.984164 | − | 0.177259i | \(-0.0567229\pi\) | ||||
0.984164 | + | 0.177259i | \(0.0567229\pi\) | |||||||
\(4\) | 5.79969 | 2.89985 | ||||||||
\(5\) | 2.64273 | 1.18187 | 0.590933 | − | 0.806721i | \(-0.298760\pi\) | ||||
0.590933 | + | 0.806721i | \(0.298760\pi\) | |||||||
\(6\) | −9.52131 | −3.88706 | ||||||||
\(7\) | 3.16263 | 1.19536 | 0.597680 | − | 0.801735i | \(-0.296089\pi\) | ||||
0.597680 | + | 0.801735i | \(0.296089\pi\) | |||||||
\(8\) | −10.6117 | −3.75182 | ||||||||
\(9\) | 8.62295 | 2.87432 | ||||||||
\(10\) | −7.38060 | −2.33395 | ||||||||
\(11\) | 1.52129 | 0.458685 | 0.229342 | − | 0.973346i | \(-0.426342\pi\) | ||||
0.229342 | + | 0.973346i | \(0.426342\pi\) | |||||||
\(12\) | 19.7726 | 5.70785 | ||||||||
\(13\) | −3.08710 | −0.856208 | −0.428104 | − | 0.903729i | \(-0.640818\pi\) | ||||
−0.428104 | + | 0.903729i | \(0.640818\pi\) | |||||||
\(14\) | −8.83256 | −2.36060 | ||||||||
\(15\) | 9.00972 | 2.32630 | ||||||||
\(16\) | 18.0370 | 4.50926 | ||||||||
\(17\) | −0.165772 | −0.0402056 | −0.0201028 | − | 0.999798i | \(-0.506399\pi\) | ||||
−0.0201028 | + | 0.999798i | \(0.506399\pi\) | |||||||
\(18\) | −24.0821 | −5.67621 | ||||||||
\(19\) | −3.02173 | −0.693232 | −0.346616 | − | 0.938007i | \(-0.612669\pi\) | ||||
−0.346616 | + | 0.938007i | \(0.612669\pi\) | |||||||
\(20\) | 15.3270 | 3.42723 | ||||||||
\(21\) | 10.7822 | 2.35286 | ||||||||
\(22\) | −4.24863 | −0.905812 | ||||||||
\(23\) | −3.71651 | −0.774946 | −0.387473 | − | 0.921881i | \(-0.626652\pi\) | ||||
−0.387473 | + | 0.921881i | \(0.626652\pi\) | |||||||
\(24\) | −36.1780 | −7.38481 | ||||||||
\(25\) | 1.98403 | 0.396806 | ||||||||
\(26\) | 8.62164 | 1.69084 | ||||||||
\(27\) | 19.1700 | 3.68927 | ||||||||
\(28\) | 18.3423 | 3.46636 | ||||||||
\(29\) | 4.48131 | 0.832159 | 0.416079 | − | 0.909328i | \(-0.363404\pi\) | ||||
0.416079 | + | 0.909328i | \(0.363404\pi\) | |||||||
\(30\) | −25.1623 | −4.59398 | ||||||||
\(31\) | −2.77064 | −0.497622 | −0.248811 | − | 0.968552i | \(-0.580040\pi\) | ||||
−0.248811 | + | 0.968552i | \(0.580040\pi\) | |||||||
\(32\) | −29.1502 | −5.15307 | ||||||||
\(33\) | 5.18643 | 0.902842 | ||||||||
\(34\) | 0.462967 | 0.0793981 | ||||||||
\(35\) | 8.35797 | 1.41275 | ||||||||
\(36\) | 50.0105 | 8.33508 | ||||||||
\(37\) | 1.05579 | 0.173572 | 0.0867858 | − | 0.996227i | \(-0.472340\pi\) | ||||
0.0867858 | + | 0.996227i | \(0.472340\pi\) | |||||||
\(38\) | 8.43906 | 1.36900 | ||||||||
\(39\) | −10.5247 | −1.68530 | ||||||||
\(40\) | −28.0440 | −4.43414 | ||||||||
\(41\) | 7.11352 | 1.11095 | 0.555473 | − | 0.831535i | \(-0.312537\pi\) | ||||
0.555473 | + | 0.831535i | \(0.312537\pi\) | |||||||
\(42\) | −30.1124 | −4.64644 | ||||||||
\(43\) | −7.56573 | −1.15376 | −0.576881 | − | 0.816828i | \(-0.695730\pi\) | ||||
−0.576881 | + | 0.816828i | \(0.695730\pi\) | |||||||
\(44\) | 8.82298 | 1.33011 | ||||||||
\(45\) | 22.7881 | 3.39706 | ||||||||
\(46\) | 10.3794 | 1.53037 | ||||||||
\(47\) | 2.34704 | 0.342351 | 0.171176 | − | 0.985241i | \(-0.445243\pi\) | ||||
0.171176 | + | 0.985241i | \(0.445243\pi\) | |||||||
\(48\) | 61.4927 | 8.87570 | ||||||||
\(49\) | 3.00221 | 0.428886 | ||||||||
\(50\) | −5.54098 | −0.783613 | ||||||||
\(51\) | −0.565157 | −0.0791378 | ||||||||
\(52\) | −17.9042 | −2.48287 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | −53.5379 | −7.28559 | ||||||||
\(55\) | 4.02035 | 0.542104 | ||||||||
\(56\) | −33.5610 | −4.48478 | ||||||||
\(57\) | −10.3018 | −1.36451 | ||||||||
\(58\) | −12.5154 | −1.64335 | ||||||||
\(59\) | −9.08942 | −1.18334 | −0.591671 | − | 0.806180i | \(-0.701531\pi\) | ||||
−0.591671 | + | 0.806180i | \(0.701531\pi\) | |||||||
\(60\) | 52.2536 | 6.74591 | ||||||||
\(61\) | 6.11238 | 0.782610 | 0.391305 | − | 0.920261i | \(-0.372024\pi\) | ||||
0.391305 | + | 0.920261i | \(0.372024\pi\) | |||||||
\(62\) | 7.73783 | 0.982706 | ||||||||
\(63\) | 27.2712 | 3.43585 | ||||||||
\(64\) | 45.3364 | 5.66705 | ||||||||
\(65\) | −8.15838 | −1.01192 | ||||||||
\(66\) | −14.4846 | −1.78294 | ||||||||
\(67\) | 5.99829 | 0.732807 | 0.366404 | − | 0.930456i | \(-0.380589\pi\) | ||||
0.366404 | + | 0.930456i | \(0.380589\pi\) | |||||||
\(68\) | −0.961426 | −0.116590 | ||||||||
\(69\) | −12.6705 | −1.52535 | ||||||||
\(70\) | −23.3421 | −2.78991 | ||||||||
\(71\) | 12.3581 | 1.46663 | 0.733317 | − | 0.679887i | \(-0.237971\pi\) | ||||
0.733317 | + | 0.679887i | \(0.237971\pi\) | |||||||
\(72\) | −91.5046 | −10.7839 | ||||||||
\(73\) | 10.5006 | 1.22901 | 0.614503 | − | 0.788914i | \(-0.289356\pi\) | ||||
0.614503 | + | 0.788914i | \(0.289356\pi\) | |||||||
\(74\) | −2.94862 | −0.342770 | ||||||||
\(75\) | 6.76404 | 0.781044 | ||||||||
\(76\) | −17.5251 | −2.01026 | ||||||||
\(77\) | 4.81126 | 0.548294 | ||||||||
\(78\) | 29.3933 | 3.32813 | ||||||||
\(79\) | 8.53624 | 0.960402 | 0.480201 | − | 0.877158i | \(-0.340564\pi\) | ||||
0.480201 | + | 0.877158i | \(0.340564\pi\) | |||||||
\(80\) | 47.6670 | 5.32933 | ||||||||
\(81\) | 39.4865 | 4.38738 | ||||||||
\(82\) | −19.8666 | −2.19390 | ||||||||
\(83\) | −5.34613 | −0.586814 | −0.293407 | − | 0.955988i | \(-0.594789\pi\) | ||||
−0.293407 | + | 0.955988i | \(0.594789\pi\) | |||||||
\(84\) | 62.5332 | 6.82294 | ||||||||
\(85\) | −0.438091 | −0.0475176 | ||||||||
\(86\) | 21.1295 | 2.27845 | ||||||||
\(87\) | 15.2779 | 1.63796 | ||||||||
\(88\) | −16.1435 | −1.72090 | ||||||||
\(89\) | −15.1104 | −1.60169 | −0.800847 | − | 0.598869i | \(-0.795617\pi\) | ||||
−0.800847 | + | 0.598869i | \(0.795617\pi\) | |||||||
\(90\) | −63.6426 | −6.70852 | ||||||||
\(91\) | −9.76335 | −1.02348 | ||||||||
\(92\) | −21.5546 | −2.24722 | ||||||||
\(93\) | −9.44580 | −0.979484 | ||||||||
\(94\) | −6.55480 | −0.676076 | ||||||||
\(95\) | −7.98561 | −0.819307 | ||||||||
\(96\) | −99.3801 | −10.1429 | ||||||||
\(97\) | 17.3610 | 1.76274 | 0.881370 | − | 0.472427i | \(-0.156622\pi\) | ||||
0.881370 | + | 0.472427i | \(0.156622\pi\) | |||||||
\(98\) | −8.38454 | −0.846966 | ||||||||
\(99\) | 13.1180 | 1.31841 | ||||||||
\(100\) | 11.5067 | 1.15067 | ||||||||
\(101\) | −15.7977 | −1.57193 | −0.785965 | − | 0.618271i | \(-0.787833\pi\) | ||||
−0.785965 | + | 0.618271i | \(0.787833\pi\) | |||||||
\(102\) | 1.57837 | 0.156282 | ||||||||
\(103\) | 11.1528 | 1.09891 | 0.549457 | − | 0.835522i | \(-0.314835\pi\) | ||||
0.549457 | + | 0.835522i | \(0.314835\pi\) | |||||||
\(104\) | 32.7595 | 3.21234 | ||||||||
\(105\) | 28.4944 | 2.78077 | ||||||||
\(106\) | 2.79279 | 0.271260 | ||||||||
\(107\) | −6.56524 | −0.634686 | −0.317343 | − | 0.948311i | \(-0.602791\pi\) | ||||
−0.317343 | + | 0.948311i | \(0.602791\pi\) | |||||||
\(108\) | 111.180 | 10.6983 | ||||||||
\(109\) | 0.943928 | 0.0904120 | 0.0452060 | − | 0.998978i | \(-0.485606\pi\) | ||||
0.0452060 | + | 0.998978i | \(0.485606\pi\) | |||||||
\(110\) | −11.2280 | −1.07055 | ||||||||
\(111\) | 3.59946 | 0.341646 | ||||||||
\(112\) | 57.0444 | 5.39019 | ||||||||
\(113\) | 19.0630 | 1.79330 | 0.896648 | − | 0.442745i | \(-0.145995\pi\) | ||||
0.896648 | + | 0.442745i | \(0.145995\pi\) | |||||||
\(114\) | 28.7708 | 2.69463 | ||||||||
\(115\) | −9.82174 | −0.915882 | ||||||||
\(116\) | 25.9902 | 2.41313 | ||||||||
\(117\) | −26.6199 | −2.46101 | ||||||||
\(118\) | 25.3849 | 2.33686 | ||||||||
\(119\) | −0.524275 | −0.0480602 | ||||||||
\(120\) | −95.6089 | −8.72785 | ||||||||
\(121\) | −8.68569 | −0.789608 | ||||||||
\(122\) | −17.0706 | −1.54550 | ||||||||
\(123\) | 24.2517 | 2.18671 | ||||||||
\(124\) | −16.0689 | −1.44303 | ||||||||
\(125\) | −7.97040 | −0.712895 | ||||||||
\(126\) | −76.1627 | −6.78512 | ||||||||
\(127\) | −8.89800 | −0.789569 | −0.394785 | − | 0.918774i | \(-0.629181\pi\) | ||||
−0.394785 | + | 0.918774i | \(0.629181\pi\) | |||||||
\(128\) | −68.3147 | −6.03822 | ||||||||
\(129\) | −25.7934 | −2.27098 | ||||||||
\(130\) | 22.7847 | 1.99835 | ||||||||
\(131\) | −18.9361 | −1.65446 | −0.827228 | − | 0.561866i | \(-0.810084\pi\) | ||||
−0.827228 | + | 0.561866i | \(0.810084\pi\) | |||||||
\(132\) | 30.0797 | 2.61810 | ||||||||
\(133\) | −9.55659 | −0.828662 | ||||||||
\(134\) | −16.7520 | −1.44715 | ||||||||
\(135\) | 50.6612 | 4.36022 | ||||||||
\(136\) | 1.75913 | 0.150844 | ||||||||
\(137\) | 8.91004 | 0.761236 | 0.380618 | − | 0.924732i | \(-0.375711\pi\) | ||||
0.380618 | + | 0.924732i | \(0.375711\pi\) | |||||||
\(138\) | 35.3861 | 3.01226 | ||||||||
\(139\) | 7.03516 | 0.596715 | 0.298357 | − | 0.954454i | \(-0.403561\pi\) | ||||
0.298357 | + | 0.954454i | \(0.403561\pi\) | |||||||
\(140\) | 48.4736 | 4.09677 | ||||||||
\(141\) | 8.00164 | 0.673860 | ||||||||
\(142\) | −34.5135 | −2.89631 | ||||||||
\(143\) | −4.69636 | −0.392730 | ||||||||
\(144\) | 155.532 | 12.9610 | ||||||||
\(145\) | 11.8429 | 0.983500 | ||||||||
\(146\) | −29.3261 | −2.42705 | ||||||||
\(147\) | 10.2353 | 0.844190 | ||||||||
\(148\) | 6.12328 | 0.503331 | ||||||||
\(149\) | −5.43878 | −0.445562 | −0.222781 | − | 0.974868i | \(-0.571514\pi\) | ||||
−0.222781 | + | 0.974868i | \(0.571514\pi\) | |||||||
\(150\) | −18.8906 | −1.54241 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 32.0658 | 2.60088 | ||||||||
\(153\) | −1.42944 | −0.115564 | ||||||||
\(154\) | −13.4368 | −1.08277 | ||||||||
\(155\) | −7.32206 | −0.588122 | ||||||||
\(156\) | −61.0399 | −4.88711 | ||||||||
\(157\) | 4.11878 | 0.328715 | 0.164357 | − | 0.986401i | \(-0.447445\pi\) | ||||
0.164357 | + | 0.986401i | \(0.447445\pi\) | |||||||
\(158\) | −23.8400 | −1.89660 | ||||||||
\(159\) | −3.40925 | −0.270371 | ||||||||
\(160\) | −77.0361 | −6.09024 | ||||||||
\(161\) | −11.7539 | −0.926340 | ||||||||
\(162\) | −110.277 | −8.66422 | ||||||||
\(163\) | 18.3424 | 1.43669 | 0.718344 | − | 0.695688i | \(-0.244900\pi\) | ||||
0.718344 | + | 0.695688i | \(0.244900\pi\) | |||||||
\(164\) | 41.2562 | 3.22157 | ||||||||
\(165\) | 13.7064 | 1.06704 | ||||||||
\(166\) | 14.9306 | 1.15884 | ||||||||
\(167\) | −17.2435 | −1.33434 | −0.667170 | − | 0.744906i | \(-0.732494\pi\) | ||||
−0.667170 | + | 0.744906i | \(0.732494\pi\) | |||||||
\(168\) | −114.418 | −8.82751 | ||||||||
\(169\) | −3.46980 | −0.266908 | ||||||||
\(170\) | 1.22350 | 0.0938379 | ||||||||
\(171\) | −26.0562 | −1.99257 | ||||||||
\(172\) | −43.8789 | −3.34573 | ||||||||
\(173\) | 7.72314 | 0.587179 | 0.293590 | − | 0.955932i | \(-0.405150\pi\) | ||||
0.293590 | + | 0.955932i | \(0.405150\pi\) | |||||||
\(174\) | −42.6680 | −3.23465 | ||||||||
\(175\) | 6.27474 | 0.474326 | ||||||||
\(176\) | 27.4395 | 2.06833 | ||||||||
\(177\) | −30.9880 | −2.32920 | ||||||||
\(178\) | 42.2001 | 3.16303 | ||||||||
\(179\) | 1.89969 | 0.141990 | 0.0709948 | − | 0.997477i | \(-0.477383\pi\) | ||||
0.0709948 | + | 0.997477i | \(0.477383\pi\) | |||||||
\(180\) | 132.164 | 9.85094 | ||||||||
\(181\) | −11.1133 | −0.826042 | −0.413021 | − | 0.910722i | \(-0.635526\pi\) | ||||
−0.413021 | + | 0.910722i | \(0.635526\pi\) | |||||||
\(182\) | 27.2670 | 2.02117 | ||||||||
\(183\) | 20.8386 | 1.54043 | ||||||||
\(184\) | 39.4387 | 2.90746 | ||||||||
\(185\) | 2.79018 | 0.205138 | ||||||||
\(186\) | 26.3802 | 1.93429 | ||||||||
\(187\) | −0.252186 | −0.0184417 | ||||||||
\(188\) | 13.6121 | 0.992765 | ||||||||
\(189\) | 60.6276 | 4.41001 | ||||||||
\(190\) | 22.3022 | 1.61797 | ||||||||
\(191\) | −26.6640 | −1.92934 | −0.964669 | − | 0.263465i | \(-0.915135\pi\) | ||||
−0.964669 | + | 0.263465i | \(0.915135\pi\) | |||||||
\(192\) | 154.563 | 11.1546 | ||||||||
\(193\) | 20.2688 | 1.45898 | 0.729491 | − | 0.683990i | \(-0.239757\pi\) | ||||
0.729491 | + | 0.683990i | \(0.239757\pi\) | |||||||
\(194\) | −48.4856 | −3.48106 | ||||||||
\(195\) | −27.8139 | −1.99180 | ||||||||
\(196\) | 17.4119 | 1.24370 | ||||||||
\(197\) | 26.6551 | 1.89910 | 0.949548 | − | 0.313623i | \(-0.101543\pi\) | ||||
0.949548 | + | 0.313623i | \(0.101543\pi\) | |||||||
\(198\) | −36.6358 | −2.60359 | ||||||||
\(199\) | −0.956757 | −0.0678227 | −0.0339114 | − | 0.999425i | \(-0.510796\pi\) | ||||
−0.0339114 | + | 0.999425i | \(0.510796\pi\) | |||||||
\(200\) | −21.0540 | −1.48874 | ||||||||
\(201\) | 20.4496 | 1.44241 | ||||||||
\(202\) | 44.1197 | 3.10425 | ||||||||
\(203\) | 14.1727 | 0.994730 | ||||||||
\(204\) | −3.27774 | −0.229487 | ||||||||
\(205\) | 18.7991 | 1.31299 | ||||||||
\(206\) | −31.1473 | −2.17014 | ||||||||
\(207\) | −32.0473 | −2.22744 | ||||||||
\(208\) | −55.6821 | −3.86086 | ||||||||
\(209\) | −4.59691 | −0.317975 | ||||||||
\(210\) | −79.5789 | −5.49146 | ||||||||
\(211\) | 7.98963 | 0.550029 | 0.275015 | − | 0.961440i | \(-0.411317\pi\) | ||||
0.275015 | + | 0.961440i | \(0.411317\pi\) | |||||||
\(212\) | −5.79969 | −0.398324 | ||||||||
\(213\) | 42.1317 | 2.88682 | ||||||||
\(214\) | 18.3354 | 1.25338 | ||||||||
\(215\) | −19.9942 | −1.36359 | ||||||||
\(216\) | −203.427 | −13.8415 | ||||||||
\(217\) | −8.76251 | −0.594838 | ||||||||
\(218\) | −2.63620 | −0.178546 | ||||||||
\(219\) | 35.7992 | 2.41909 | ||||||||
\(220\) | 23.3168 | 1.57202 | ||||||||
\(221\) | 0.511755 | 0.0344244 | ||||||||
\(222\) | −10.0526 | −0.674683 | ||||||||
\(223\) | 28.3393 | 1.89774 | 0.948871 | − | 0.315664i | \(-0.102227\pi\) | ||||
0.948871 | + | 0.315664i | \(0.102227\pi\) | |||||||
\(224\) | −92.1911 | −6.15978 | ||||||||
\(225\) | 17.1082 | 1.14055 | ||||||||
\(226\) | −53.2390 | −3.54140 | ||||||||
\(227\) | −25.1412 | −1.66868 | −0.834340 | − | 0.551250i | \(-0.814151\pi\) | ||||
−0.834340 | + | 0.551250i | \(0.814151\pi\) | |||||||
\(228\) | −59.7473 | −3.95686 | ||||||||
\(229\) | 8.54268 | 0.564516 | 0.282258 | − | 0.959338i | \(-0.408917\pi\) | ||||
0.282258 | + | 0.959338i | \(0.408917\pi\) | |||||||
\(230\) | 27.4301 | 1.80869 | ||||||||
\(231\) | 16.4028 | 1.07922 | ||||||||
\(232\) | −47.5546 | −3.12211 | ||||||||
\(233\) | −9.52413 | −0.623947 | −0.311973 | − | 0.950091i | \(-0.600990\pi\) | ||||
−0.311973 | + | 0.950091i | \(0.600990\pi\) | |||||||
\(234\) | 74.3440 | 4.86002 | ||||||||
\(235\) | 6.20260 | 0.404613 | ||||||||
\(236\) | −52.7158 | −3.43151 | ||||||||
\(237\) | 29.1021 | 1.89039 | ||||||||
\(238\) | 1.46419 | 0.0949093 | ||||||||
\(239\) | 8.73804 | 0.565217 | 0.282608 | − | 0.959235i | \(-0.408800\pi\) | ||||
0.282608 | + | 0.959235i | \(0.408800\pi\) | |||||||
\(240\) | 162.509 | 10.4899 | ||||||||
\(241\) | 24.3057 | 1.56567 | 0.782834 | − | 0.622230i | \(-0.213773\pi\) | ||||
0.782834 | + | 0.622230i | \(0.213773\pi\) | |||||||
\(242\) | 24.2573 | 1.55932 | ||||||||
\(243\) | 77.1089 | 4.94654 | ||||||||
\(244\) | 35.4499 | 2.26945 | ||||||||
\(245\) | 7.93402 | 0.506886 | ||||||||
\(246\) | −67.7301 | −4.31831 | ||||||||
\(247\) | 9.32838 | 0.593551 | ||||||||
\(248\) | 29.4014 | 1.86699 | ||||||||
\(249\) | −18.2263 | −1.15504 | ||||||||
\(250\) | 22.2597 | 1.40783 | ||||||||
\(251\) | −13.9737 | −0.882013 | −0.441006 | − | 0.897504i | \(-0.645378\pi\) | ||||
−0.441006 | + | 0.897504i | \(0.645378\pi\) | |||||||
\(252\) | 158.164 | 9.96342 | ||||||||
\(253\) | −5.65388 | −0.355456 | ||||||||
\(254\) | 24.8503 | 1.55924 | ||||||||
\(255\) | −1.49356 | −0.0935302 | ||||||||
\(256\) | 100.116 | 6.25725 | ||||||||
\(257\) | 6.25915 | 0.390435 | 0.195217 | − | 0.980760i | \(-0.437459\pi\) | ||||
0.195217 | + | 0.980760i | \(0.437459\pi\) | |||||||
\(258\) | 72.0357 | 4.48475 | ||||||||
\(259\) | 3.33908 | 0.207481 | ||||||||
\(260\) | −47.3161 | −2.93442 | ||||||||
\(261\) | 38.6422 | 2.39189 | ||||||||
\(262\) | 52.8846 | 3.26722 | ||||||||
\(263\) | −24.2409 | −1.49476 | −0.747378 | − | 0.664399i | \(-0.768687\pi\) | ||||
−0.747378 | + | 0.664399i | \(0.768687\pi\) | |||||||
\(264\) | −55.0371 | −3.38730 | ||||||||
\(265\) | −2.64273 | −0.162342 | ||||||||
\(266\) | 26.6896 | 1.63644 | ||||||||
\(267\) | −51.5149 | −3.15266 | ||||||||
\(268\) | 34.7882 | 2.12503 | ||||||||
\(269\) | 11.6427 | 0.709867 | 0.354933 | − | 0.934892i | \(-0.384504\pi\) | ||||
0.354933 | + | 0.934892i | \(0.384504\pi\) | |||||||
\(270\) | −141.486 | −8.61058 | ||||||||
\(271\) | −5.06948 | −0.307949 | −0.153975 | − | 0.988075i | \(-0.549207\pi\) | ||||
−0.153975 | + | 0.988075i | \(0.549207\pi\) | |||||||
\(272\) | −2.99003 | −0.181297 | ||||||||
\(273\) | −33.2857 | −2.01454 | ||||||||
\(274\) | −24.8839 | −1.50329 | ||||||||
\(275\) | 3.01827 | 0.182009 | ||||||||
\(276\) | −73.4850 | −4.42328 | ||||||||
\(277\) | 20.3679 | 1.22379 | 0.611895 | − | 0.790939i | \(-0.290408\pi\) | ||||
0.611895 | + | 0.790939i | \(0.290408\pi\) | |||||||
\(278\) | −19.6477 | −1.17839 | ||||||||
\(279\) | −23.8911 | −1.43032 | ||||||||
\(280\) | −88.6927 | −5.30040 | ||||||||
\(281\) | −3.12641 | −0.186506 | −0.0932530 | − | 0.995642i | \(-0.529727\pi\) | ||||
−0.0932530 | + | 0.995642i | \(0.529727\pi\) | |||||||
\(282\) | −22.3469 | −1.33074 | ||||||||
\(283\) | −2.96933 | −0.176508 | −0.0882541 | − | 0.996098i | \(-0.528129\pi\) | ||||
−0.0882541 | + | 0.996098i | \(0.528129\pi\) | |||||||
\(284\) | 71.6730 | 4.25301 | ||||||||
\(285\) | −27.2249 | −1.61266 | ||||||||
\(286\) | 13.1160 | 0.775563 | ||||||||
\(287\) | 22.4974 | 1.32798 | ||||||||
\(288\) | −251.361 | −14.8116 | ||||||||
\(289\) | −16.9725 | −0.998384 | ||||||||
\(290\) | −33.0748 | −1.94222 | ||||||||
\(291\) | 59.1878 | 3.46965 | ||||||||
\(292\) | 60.9004 | 3.56393 | ||||||||
\(293\) | −0.910323 | −0.0531816 | −0.0265908 | − | 0.999646i | \(-0.508465\pi\) | ||||
−0.0265908 | + | 0.999646i | \(0.508465\pi\) | |||||||
\(294\) | −28.5849 | −1.66711 | ||||||||
\(295\) | −24.0209 | −1.39855 | ||||||||
\(296\) | −11.2038 | −0.651209 | ||||||||
\(297\) | 29.1631 | 1.69221 | ||||||||
\(298\) | 15.1894 | 0.879897 | ||||||||
\(299\) | 11.4733 | 0.663515 | ||||||||
\(300\) | 39.2293 | 2.26491 | ||||||||
\(301\) | −23.9276 | −1.37916 | ||||||||
\(302\) | −2.79279 | −0.160707 | ||||||||
\(303\) | −53.8582 | −3.09407 | ||||||||
\(304\) | −54.5030 | −3.12596 | ||||||||
\(305\) | 16.1534 | 0.924940 | ||||||||
\(306\) | 3.99214 | 0.228215 | ||||||||
\(307\) | 5.71222 | 0.326013 | 0.163007 | − | 0.986625i | \(-0.447881\pi\) | ||||
0.163007 | + | 0.986625i | \(0.447881\pi\) | |||||||
\(308\) | 27.9038 | 1.58997 | ||||||||
\(309\) | 38.0225 | 2.16302 | ||||||||
\(310\) | 20.4490 | 1.16143 | ||||||||
\(311\) | 5.42274 | 0.307495 | 0.153748 | − | 0.988110i | \(-0.450866\pi\) | ||||
0.153748 | + | 0.988110i | \(0.450866\pi\) | |||||||
\(312\) | 111.685 | 6.32294 | ||||||||
\(313\) | −2.82638 | −0.159756 | −0.0798782 | − | 0.996805i | \(-0.525453\pi\) | ||||
−0.0798782 | + | 0.996805i | \(0.525453\pi\) | |||||||
\(314\) | −11.5029 | −0.649147 | ||||||||
\(315\) | 72.0704 | 4.06071 | ||||||||
\(316\) | 49.5076 | 2.78502 | ||||||||
\(317\) | 2.52393 | 0.141758 | 0.0708791 | − | 0.997485i | \(-0.477420\pi\) | ||||
0.0708791 | + | 0.997485i | \(0.477420\pi\) | |||||||
\(318\) | 9.52131 | 0.533929 | ||||||||
\(319\) | 6.81735 | 0.381699 | ||||||||
\(320\) | 119.812 | 6.69768 | ||||||||
\(321\) | −22.3825 | −1.24927 | ||||||||
\(322\) | 32.8263 | 1.82934 | ||||||||
\(323\) | 0.500917 | 0.0278718 | ||||||||
\(324\) | 229.009 | 12.7227 | ||||||||
\(325\) | −6.12490 | −0.339748 | ||||||||
\(326\) | −51.2266 | −2.83718 | ||||||||
\(327\) | 3.21808 | 0.177960 | ||||||||
\(328\) | −75.4869 | −4.16807 | ||||||||
\(329\) | 7.42282 | 0.409233 | ||||||||
\(330\) | −38.2790 | −2.10719 | ||||||||
\(331\) | 14.9839 | 0.823587 | 0.411794 | − | 0.911277i | \(-0.364902\pi\) | ||||
0.411794 | + | 0.911277i | \(0.364902\pi\) | |||||||
\(332\) | −31.0059 | −1.70167 | ||||||||
\(333\) | 9.10407 | 0.498900 | ||||||||
\(334\) | 48.1574 | 2.63506 | ||||||||
\(335\) | 15.8519 | 0.866079 | ||||||||
\(336\) | 194.478 | 10.6097 | ||||||||
\(337\) | 13.7625 | 0.749693 | 0.374846 | − | 0.927087i | \(-0.377695\pi\) | ||||
0.374846 | + | 0.927087i | \(0.377695\pi\) | |||||||
\(338\) | 9.69043 | 0.527090 | ||||||||
\(339\) | 64.9904 | 3.52979 | ||||||||
\(340\) | −2.54079 | −0.137794 | ||||||||
\(341\) | −4.21494 | −0.228252 | ||||||||
\(342\) | 72.7696 | 3.93493 | ||||||||
\(343\) | −12.6435 | −0.682686 | ||||||||
\(344\) | 80.2856 | 4.32871 | ||||||||
\(345\) | −33.4847 | −1.80276 | ||||||||
\(346\) | −21.5691 | −1.15956 | ||||||||
\(347\) | −4.05674 | −0.217777 | −0.108889 | − | 0.994054i | \(-0.534729\pi\) | ||||
−0.108889 | + | 0.994054i | \(0.534729\pi\) | |||||||
\(348\) | 88.6071 | 4.74984 | ||||||||
\(349\) | −2.03062 | −0.108697 | −0.0543484 | − | 0.998522i | \(-0.517308\pi\) | ||||
−0.0543484 | + | 0.998522i | \(0.517308\pi\) | |||||||
\(350\) | −17.5240 | −0.936700 | ||||||||
\(351\) | −59.1798 | −3.15879 | ||||||||
\(352\) | −44.3457 | −2.36364 | ||||||||
\(353\) | 30.4506 | 1.62072 | 0.810362 | − | 0.585930i | \(-0.199271\pi\) | ||||
0.810362 | + | 0.585930i | \(0.199271\pi\) | |||||||
\(354\) | 86.5432 | 4.59972 | ||||||||
\(355\) | 32.6591 | 1.73336 | ||||||||
\(356\) | −87.6354 | −4.64467 | ||||||||
\(357\) | −1.78738 | −0.0945982 | ||||||||
\(358\) | −5.30544 | −0.280401 | ||||||||
\(359\) | −4.58939 | −0.242219 | −0.121109 | − | 0.992639i | \(-0.538645\pi\) | ||||
−0.121109 | + | 0.992639i | \(0.538645\pi\) | |||||||
\(360\) | −241.822 | −12.7451 | ||||||||
\(361\) | −9.86916 | −0.519430 | ||||||||
\(362\) | 31.0370 | 1.63127 | ||||||||
\(363\) | −29.6117 | −1.55421 | ||||||||
\(364\) | −56.6244 | −2.96793 | ||||||||
\(365\) | 27.7504 | 1.45252 | ||||||||
\(366\) | −58.1979 | −3.04205 | ||||||||
\(367\) | −18.9786 | −0.990674 | −0.495337 | − | 0.868701i | \(-0.664955\pi\) | ||||
−0.495337 | + | 0.868701i | \(0.664955\pi\) | |||||||
\(368\) | −67.0348 | −3.49443 | ||||||||
\(369\) | 61.3396 | 3.19321 | ||||||||
\(370\) | −7.79240 | −0.405108 | ||||||||
\(371\) | −3.16263 | −0.164195 | ||||||||
\(372\) | −54.7827 | −2.84035 | ||||||||
\(373\) | 9.81235 | 0.508064 | 0.254032 | − | 0.967196i | \(-0.418243\pi\) | ||||
0.254032 | + | 0.967196i | \(0.418243\pi\) | |||||||
\(374\) | 0.704304 | 0.0364187 | ||||||||
\(375\) | −27.1731 | −1.40321 | ||||||||
\(376\) | −24.9062 | −1.28444 | ||||||||
\(377\) | −13.8343 | −0.712501 | ||||||||
\(378\) | −169.320 | −8.70890 | ||||||||
\(379\) | −33.1417 | −1.70237 | −0.851186 | − | 0.524864i | \(-0.824116\pi\) | ||||
−0.851186 | + | 0.524864i | \(0.824116\pi\) | |||||||
\(380\) | −46.3141 | −2.37586 | ||||||||
\(381\) | −30.3354 | −1.55413 | ||||||||
\(382\) | 74.4670 | 3.81006 | ||||||||
\(383\) | 2.76840 | 0.141459 | 0.0707293 | − | 0.997496i | \(-0.477467\pi\) | ||||
0.0707293 | + | 0.997496i | \(0.477467\pi\) | |||||||
\(384\) | −232.902 | −11.8852 | ||||||||
\(385\) | 12.7149 | 0.648009 | ||||||||
\(386\) | −56.6067 | −2.88120 | ||||||||
\(387\) | −65.2389 | −3.31628 | ||||||||
\(388\) | 100.688 | 5.11167 | ||||||||
\(389\) | −26.7282 | −1.35517 | −0.677587 | − | 0.735442i | \(-0.736974\pi\) | ||||
−0.677587 | + | 0.735442i | \(0.736974\pi\) | |||||||
\(390\) | 77.6785 | 3.93340 | ||||||||
\(391\) | 0.616093 | 0.0311572 | ||||||||
\(392\) | −31.8586 | −1.60910 | ||||||||
\(393\) | −64.5579 | −3.25651 | ||||||||
\(394\) | −74.4421 | −3.75034 | ||||||||
\(395\) | 22.5590 | 1.13507 | ||||||||
\(396\) | 76.0802 | 3.82317 | ||||||||
\(397\) | 8.72177 | 0.437733 | 0.218866 | − | 0.975755i | \(-0.429764\pi\) | ||||
0.218866 | + | 0.975755i | \(0.429764\pi\) | |||||||
\(398\) | 2.67202 | 0.133936 | ||||||||
\(399\) | −32.5808 | −1.63108 | ||||||||
\(400\) | 35.7860 | 1.78930 | ||||||||
\(401\) | 14.7502 | 0.736588 | 0.368294 | − | 0.929709i | \(-0.379942\pi\) | ||||
0.368294 | + | 0.929709i | \(0.379942\pi\) | |||||||
\(402\) | −57.1116 | −2.84847 | ||||||||
\(403\) | 8.55326 | 0.426068 | ||||||||
\(404\) | −91.6218 | −4.55835 | ||||||||
\(405\) | 104.352 | 5.18530 | ||||||||
\(406\) | −39.5815 | −1.96439 | ||||||||
\(407\) | 1.60617 | 0.0796146 | ||||||||
\(408\) | 5.99730 | 0.296911 | ||||||||
\(409\) | −38.6742 | −1.91232 | −0.956158 | − | 0.292850i | \(-0.905396\pi\) | ||||
−0.956158 | + | 0.292850i | \(0.905396\pi\) | |||||||
\(410\) | −52.5021 | −2.59289 | ||||||||
\(411\) | 30.3765 | 1.49836 | ||||||||
\(412\) | 64.6825 | 3.18668 | ||||||||
\(413\) | −28.7464 | −1.41452 | ||||||||
\(414\) | 89.5015 | 4.39876 | ||||||||
\(415\) | −14.1284 | −0.693535 | ||||||||
\(416\) | 89.9896 | 4.41210 | ||||||||
\(417\) | 23.9846 | 1.17453 | ||||||||
\(418\) | 12.8382 | 0.627938 | ||||||||
\(419\) | 0.373425 | 0.0182430 | 0.00912151 | − | 0.999958i | \(-0.497096\pi\) | ||||
0.00912151 | + | 0.999958i | \(0.497096\pi\) | |||||||
\(420\) | 165.259 | 8.06379 | ||||||||
\(421\) | −11.0816 | −0.540085 | −0.270042 | − | 0.962848i | \(-0.587038\pi\) | ||||
−0.270042 | + | 0.962848i | \(0.587038\pi\) | |||||||
\(422\) | −22.3134 | −1.08620 | ||||||||
\(423\) | 20.2384 | 0.984026 | ||||||||
\(424\) | 10.6117 | 0.515352 | ||||||||
\(425\) | −0.328896 | −0.0159538 | ||||||||
\(426\) | −117.665 | −5.70089 | ||||||||
\(427\) | 19.3312 | 0.935501 | ||||||||
\(428\) | −38.0764 | −1.84049 | ||||||||
\(429\) | −16.0111 | −0.773021 | ||||||||
\(430\) | 55.8396 | 2.69283 | ||||||||
\(431\) | −24.7324 | −1.19132 | −0.595658 | − | 0.803238i | \(-0.703109\pi\) | ||||
−0.595658 | + | 0.803238i | \(0.703109\pi\) | |||||||
\(432\) | 345.770 | 16.6359 | ||||||||
\(433\) | −38.9077 | −1.86978 | −0.934892 | − | 0.354933i | \(-0.884504\pi\) | ||||
−0.934892 | + | 0.354933i | \(0.884504\pi\) | |||||||
\(434\) | 24.4719 | 1.17469 | ||||||||
\(435\) | 40.3754 | 1.93585 | ||||||||
\(436\) | 5.47449 | 0.262181 | ||||||||
\(437\) | 11.2303 | 0.537218 | ||||||||
\(438\) | −99.9799 | −4.77722 | ||||||||
\(439\) | −19.1826 | −0.915534 | −0.457767 | − | 0.889072i | \(-0.651351\pi\) | ||||
−0.457767 | + | 0.889072i | \(0.651351\pi\) | |||||||
\(440\) | −42.6629 | −2.03387 | ||||||||
\(441\) | 25.8879 | 1.23276 | ||||||||
\(442\) | −1.42922 | −0.0679813 | ||||||||
\(443\) | 3.51378 | 0.166945 | 0.0834723 | − | 0.996510i | \(-0.473399\pi\) | ||||
0.0834723 | + | 0.996510i | \(0.473399\pi\) | |||||||
\(444\) | 20.8758 | 0.990720 | ||||||||
\(445\) | −39.9326 | −1.89299 | ||||||||
\(446\) | −79.1459 | −3.74767 | ||||||||
\(447\) | −18.5421 | −0.877013 | ||||||||
\(448\) | 143.382 | 6.77416 | ||||||||
\(449\) | −31.5482 | −1.48885 | −0.744425 | − | 0.667706i | \(-0.767277\pi\) | ||||
−0.744425 | + | 0.667706i | \(0.767277\pi\) | |||||||
\(450\) | −47.7796 | −2.25235 | ||||||||
\(451\) | 10.8217 | 0.509574 | ||||||||
\(452\) | 110.559 | 5.20028 | ||||||||
\(453\) | 3.40925 | 0.160180 | ||||||||
\(454\) | 70.2142 | 3.29531 | ||||||||
\(455\) | −25.8019 | −1.20961 | ||||||||
\(456\) | 109.320 | 5.11939 | ||||||||
\(457\) | −11.3458 | −0.530736 | −0.265368 | − | 0.964147i | \(-0.585493\pi\) | ||||
−0.265368 | + | 0.964147i | \(0.585493\pi\) | |||||||
\(458\) | −23.8579 | −1.11481 | ||||||||
\(459\) | −3.17785 | −0.148329 | ||||||||
\(460\) | −56.9631 | −2.65592 | ||||||||
\(461\) | −11.7202 | −0.545865 | −0.272932 | − | 0.962033i | \(-0.587994\pi\) | ||||
−0.272932 | + | 0.962033i | \(0.587994\pi\) | |||||||
\(462\) | −45.8095 | −2.13125 | ||||||||
\(463\) | 6.64387 | 0.308767 | 0.154383 | − | 0.988011i | \(-0.450661\pi\) | ||||
0.154383 | + | 0.988011i | \(0.450661\pi\) | |||||||
\(464\) | 80.8296 | 3.75242 | ||||||||
\(465\) | −24.9627 | −1.15762 | ||||||||
\(466\) | 26.5989 | 1.23217 | ||||||||
\(467\) | −18.6131 | −0.861310 | −0.430655 | − | 0.902517i | \(-0.641717\pi\) | ||||
−0.430655 | + | 0.902517i | \(0.641717\pi\) | |||||||
\(468\) | −154.387 | −7.13656 | ||||||||
\(469\) | 18.9703 | 0.875969 | ||||||||
\(470\) | −17.3226 | −0.799031 | ||||||||
\(471\) | 14.0419 | 0.647019 | ||||||||
\(472\) | 96.4546 | 4.43968 | ||||||||
\(473\) | −11.5096 | −0.529213 | ||||||||
\(474\) | −81.2762 | −3.73314 | ||||||||
\(475\) | −5.99519 | −0.275078 | ||||||||
\(476\) | −3.04063 | −0.139367 | ||||||||
\(477\) | −8.62295 | −0.394818 | ||||||||
\(478\) | −24.4035 | −1.11619 | ||||||||
\(479\) | 6.64345 | 0.303547 | 0.151773 | − | 0.988415i | \(-0.451502\pi\) | ||||
0.151773 | + | 0.988415i | \(0.451502\pi\) | |||||||
\(480\) | −262.635 | −11.9876 | ||||||||
\(481\) | −3.25935 | −0.148613 | ||||||||
\(482\) | −67.8808 | −3.09189 | ||||||||
\(483\) | −40.0721 | −1.82334 | ||||||||
\(484\) | −50.3743 | −2.28974 | ||||||||
\(485\) | 45.8804 | 2.08332 | ||||||||
\(486\) | −215.349 | −9.76844 | ||||||||
\(487\) | −31.8382 | −1.44273 | −0.721364 | − | 0.692556i | \(-0.756485\pi\) | ||||
−0.721364 | + | 0.692556i | \(0.756485\pi\) | |||||||
\(488\) | −64.8631 | −2.93621 | ||||||||
\(489\) | 62.5338 | 2.82788 | ||||||||
\(490\) | −22.1581 | −1.00100 | ||||||||
\(491\) | −7.05164 | −0.318236 | −0.159118 | − | 0.987260i | \(-0.550865\pi\) | ||||
−0.159118 | + | 0.987260i | \(0.550865\pi\) | |||||||
\(492\) | 140.653 | 6.34111 | ||||||||
\(493\) | −0.742876 | −0.0334574 | ||||||||
\(494\) | −26.0522 | −1.17215 | ||||||||
\(495\) | 34.6673 | 1.55818 | ||||||||
\(496\) | −49.9742 | −2.24391 | ||||||||
\(497\) | 39.0840 | 1.75316 | ||||||||
\(498\) | 50.9022 | 2.28098 | ||||||||
\(499\) | 28.8664 | 1.29224 | 0.646119 | − | 0.763236i | \(-0.276391\pi\) | ||||
0.646119 | + | 0.763236i | \(0.276391\pi\) | |||||||
\(500\) | −46.2259 | −2.06728 | ||||||||
\(501\) | −58.7872 | −2.62642 | ||||||||
\(502\) | 39.0257 | 1.74180 | ||||||||
\(503\) | 6.00702 | 0.267840 | 0.133920 | − | 0.990992i | \(-0.457244\pi\) | ||||
0.133920 | + | 0.990992i | \(0.457244\pi\) | |||||||
\(504\) | −289.395 | −12.8907 | ||||||||
\(505\) | −41.7491 | −1.85781 | ||||||||
\(506\) | 15.7901 | 0.701956 | ||||||||
\(507\) | −11.8294 | −0.525362 | ||||||||
\(508\) | −51.6056 | −2.28963 | ||||||||
\(509\) | −5.41661 | −0.240087 | −0.120043 | − | 0.992769i | \(-0.538303\pi\) | ||||
−0.120043 | + | 0.992769i | \(0.538303\pi\) | |||||||
\(510\) | 4.17120 | 0.184704 | ||||||||
\(511\) | 33.2096 | 1.46911 | ||||||||
\(512\) | −142.974 | −6.31861 | ||||||||
\(513\) | −57.9266 | −2.55752 | ||||||||
\(514\) | −17.4805 | −0.771032 | ||||||||
\(515\) | 29.4737 | 1.29877 | ||||||||
\(516\) | −149.594 | −6.58550 | ||||||||
\(517\) | 3.57052 | 0.157031 | ||||||||
\(518\) | −9.32537 | −0.409733 | ||||||||
\(519\) | 26.3301 | 1.15576 | ||||||||
\(520\) | 86.5747 | 3.79655 | ||||||||
\(521\) | −5.00854 | −0.219428 | −0.109714 | − | 0.993963i | \(-0.534994\pi\) | ||||
−0.109714 | + | 0.993963i | \(0.534994\pi\) | |||||||
\(522\) | −107.920 | −4.72351 | ||||||||
\(523\) | 0.0363510 | 0.00158952 | 0.000794759 | − | 1.00000i | \(-0.499747\pi\) | ||||
0.000794759 | 1.00000i | \(0.499747\pi\) | ||||||||
\(524\) | −109.824 | −4.79767 | ||||||||
\(525\) | 21.3921 | 0.933629 | ||||||||
\(526\) | 67.6997 | 2.95185 | ||||||||
\(527\) | 0.459295 | 0.0200072 | ||||||||
\(528\) | 93.5479 | 4.07115 | ||||||||
\(529\) | −9.18753 | −0.399458 | ||||||||
\(530\) | 7.38060 | 0.320593 | ||||||||
\(531\) | −78.3776 | −3.40130 | ||||||||
\(532\) | −55.4253 | −2.40299 | ||||||||
\(533\) | −21.9602 | −0.951201 | ||||||||
\(534\) | 143.870 | 6.22588 | ||||||||
\(535\) | −17.3502 | −0.750113 | ||||||||
\(536\) | −63.6523 | −2.74936 | ||||||||
\(537\) | 6.47651 | 0.279482 | ||||||||
\(538\) | −32.5156 | −1.40185 | ||||||||
\(539\) | 4.56721 | 0.196724 | ||||||||
\(540\) | 293.819 | 12.6440 | ||||||||
\(541\) | 20.7724 | 0.893074 | 0.446537 | − | 0.894765i | \(-0.352657\pi\) | ||||
0.446537 | + | 0.894765i | \(0.352657\pi\) | |||||||
\(542\) | 14.1580 | 0.608139 | ||||||||
\(543\) | −37.8878 | −1.62592 | ||||||||
\(544\) | 4.83228 | 0.207182 | ||||||||
\(545\) | 2.49455 | 0.106855 | ||||||||
\(546\) | 92.9599 | 3.97832 | ||||||||
\(547\) | −41.2983 | −1.76579 | −0.882895 | − | 0.469571i | \(-0.844409\pi\) | ||||
−0.882895 | + | 0.469571i | \(0.844409\pi\) | |||||||
\(548\) | 51.6755 | 2.20747 | ||||||||
\(549\) | 52.7068 | 2.24947 | ||||||||
\(550\) | −8.42941 | −0.359431 | ||||||||
\(551\) | −13.5413 | −0.576879 | ||||||||
\(552\) | 134.456 | 5.72283 | ||||||||
\(553\) | 26.9969 | 1.14803 | ||||||||
\(554\) | −56.8833 | −2.41674 | ||||||||
\(555\) | 9.51241 | 0.403780 | ||||||||
\(556\) | 40.8018 | 1.73038 | ||||||||
\(557\) | −14.6650 | −0.621374 | −0.310687 | − | 0.950512i | \(-0.600559\pi\) | ||||
−0.310687 | + | 0.950512i | \(0.600559\pi\) | |||||||
\(558\) | 66.7230 | 2.82461 | ||||||||
\(559\) | 23.3562 | 0.987861 | ||||||||
\(560\) | 150.753 | 6.37048 | ||||||||
\(561\) | −0.859765 | −0.0362993 | ||||||||
\(562\) | 8.73141 | 0.368312 | ||||||||
\(563\) | 28.0238 | 1.18106 | 0.590532 | − | 0.807014i | \(-0.298918\pi\) | ||||
0.590532 | + | 0.807014i | \(0.298918\pi\) | |||||||
\(564\) | 46.4070 | 1.95409 | ||||||||
\(565\) | 50.3784 | 2.11943 | ||||||||
\(566\) | 8.29272 | 0.348569 | ||||||||
\(567\) | 124.881 | 5.24451 | ||||||||
\(568\) | −131.141 | −5.50255 | ||||||||
\(569\) | −18.7602 | −0.786467 | −0.393234 | − | 0.919439i | \(-0.628644\pi\) | ||||
−0.393234 | + | 0.919439i | \(0.628644\pi\) | |||||||
\(570\) | 76.0335 | 3.18469 | ||||||||
\(571\) | −39.0729 | −1.63515 | −0.817575 | − | 0.575822i | \(-0.804682\pi\) | ||||
−0.817575 | + | 0.575822i | \(0.804682\pi\) | |||||||
\(572\) | −27.2375 | −1.13886 | ||||||||
\(573\) | −90.9040 | −3.79757 | ||||||||
\(574\) | −62.8306 | −2.62250 | ||||||||
\(575\) | −7.37367 | −0.307503 | ||||||||
\(576\) | 390.933 | 16.2889 | ||||||||
\(577\) | −42.0695 | −1.75138 | −0.875689 | − | 0.482876i | \(-0.839592\pi\) | ||||
−0.875689 | + | 0.482876i | \(0.839592\pi\) | |||||||
\(578\) | 47.4007 | 1.97161 | ||||||||
\(579\) | 69.1014 | 2.87176 | ||||||||
\(580\) | 68.6852 | 2.85200 | ||||||||
\(581\) | −16.9078 | −0.701454 | ||||||||
\(582\) | −165.299 | −6.85188 | ||||||||
\(583\) | −1.52129 | −0.0630052 | ||||||||
\(584\) | −111.430 | −4.61101 | ||||||||
\(585\) | −70.3493 | −2.90859 | ||||||||
\(586\) | 2.54234 | 0.105023 | ||||||||
\(587\) | 23.2407 | 0.959247 | 0.479624 | − | 0.877474i | \(-0.340773\pi\) | ||||
0.479624 | + | 0.877474i | \(0.340773\pi\) | |||||||
\(588\) | 59.3613 | 2.44802 | ||||||||
\(589\) | 8.37213 | 0.344968 | ||||||||
\(590\) | 67.0853 | 2.76186 | ||||||||
\(591\) | 90.8737 | 3.73804 | ||||||||
\(592\) | 19.0434 | 0.782679 | ||||||||
\(593\) | −12.4341 | −0.510607 | −0.255304 | − | 0.966861i | \(-0.582175\pi\) | ||||
−0.255304 | + | 0.966861i | \(0.582175\pi\) | |||||||
\(594\) | −81.4464 | −3.34179 | ||||||||
\(595\) | −1.38552 | −0.0568006 | ||||||||
\(596\) | −31.5432 | −1.29206 | ||||||||
\(597\) | −3.26182 | −0.133497 | ||||||||
\(598\) | −32.0424 | −1.31031 | ||||||||
\(599\) | −14.4548 | −0.590606 | −0.295303 | − | 0.955404i | \(-0.595421\pi\) | ||||
−0.295303 | + | 0.955404i | \(0.595421\pi\) | |||||||
\(600\) | −71.7783 | −2.93034 | ||||||||
\(601\) | 29.8521 | 1.21769 | 0.608846 | − | 0.793288i | \(-0.291633\pi\) | ||||
0.608846 | + | 0.793288i | \(0.291633\pi\) | |||||||
\(602\) | 66.8247 | 2.72357 | ||||||||
\(603\) | 51.7229 | 2.10632 | ||||||||
\(604\) | 5.79969 | 0.235986 | ||||||||
\(605\) | −22.9539 | −0.933211 | ||||||||
\(606\) | 150.415 | 6.11019 | ||||||||
\(607\) | −11.2942 | −0.458416 | −0.229208 | − | 0.973377i | \(-0.573614\pi\) | ||||
−0.229208 | + | 0.973377i | \(0.573614\pi\) | |||||||
\(608\) | 88.0839 | 3.57227 | ||||||||
\(609\) | 48.3183 | 1.95796 | ||||||||
\(610\) | −45.1130 | −1.82657 | ||||||||
\(611\) | −7.24556 | −0.293124 | ||||||||
\(612\) | −8.29033 | −0.335117 | ||||||||
\(613\) | −5.16448 | −0.208592 | −0.104296 | − | 0.994546i | \(-0.533259\pi\) | ||||
−0.104296 | + | 0.994546i | \(0.533259\pi\) | |||||||
\(614\) | −15.9530 | −0.643812 | ||||||||
\(615\) | 64.0908 | 2.58439 | ||||||||
\(616\) | −51.0558 | −2.05710 | ||||||||
\(617\) | −34.9324 | −1.40632 | −0.703162 | − | 0.711029i | \(-0.748229\pi\) | ||||
−0.703162 | + | 0.711029i | \(0.748229\pi\) | |||||||
\(618\) | −106.189 | −4.27154 | ||||||||
\(619\) | −13.6582 | −0.548971 | −0.274485 | − | 0.961591i | \(-0.588507\pi\) | ||||
−0.274485 | + | 0.961591i | \(0.588507\pi\) | |||||||
\(620\) | −42.4657 | −1.70546 | ||||||||
\(621\) | −71.2456 | −2.85899 | ||||||||
\(622\) | −15.1446 | −0.607243 | ||||||||
\(623\) | −47.7884 | −1.91460 | ||||||||
\(624\) | −189.834 | −7.59945 | ||||||||
\(625\) | −30.9838 | −1.23935 | ||||||||
\(626\) | 7.89349 | 0.315487 | ||||||||
\(627\) | −15.6720 | −0.625879 | ||||||||
\(628\) | 23.8877 | 0.953222 | ||||||||
\(629\) | −0.175021 | −0.00697855 | ||||||||
\(630\) | −201.278 | −8.01909 | ||||||||
\(631\) | −28.4436 | −1.13232 | −0.566161 | − | 0.824294i | \(-0.691572\pi\) | ||||
−0.566161 | + | 0.824294i | \(0.691572\pi\) | |||||||
\(632\) | −90.5844 | −3.60326 | ||||||||
\(633\) | 27.2386 | 1.08264 | ||||||||
\(634\) | −7.04882 | −0.279944 | ||||||||
\(635\) | −23.5150 | −0.933165 | ||||||||
\(636\) | −19.7726 | −0.784033 | ||||||||
\(637\) | −9.26811 | −0.367216 | ||||||||
\(638\) | −19.0395 | −0.753779 | ||||||||
\(639\) | 106.563 | 4.21557 | ||||||||
\(640\) | −180.537 | −7.13637 | ||||||||
\(641\) | −3.66442 | −0.144736 | −0.0723680 | − | 0.997378i | \(-0.523056\pi\) | ||||
−0.0723680 | + | 0.997378i | \(0.523056\pi\) | |||||||
\(642\) | 62.5097 | 2.46706 | ||||||||
\(643\) | −0.0230049 | −0.000907224 0 | −0.000453612 | − | 1.00000i | \(-0.500144\pi\) | ||||
−0.000453612 | 1.00000i | \(0.500144\pi\) | ||||||||
\(644\) | −68.1692 | −2.68624 | ||||||||
\(645\) | −68.1651 | −2.68400 | ||||||||
\(646\) | −1.39896 | −0.0550413 | ||||||||
\(647\) | −1.71975 | −0.0676105 | −0.0338052 | − | 0.999428i | \(-0.510763\pi\) | ||||
−0.0338052 | + | 0.999428i | \(0.510763\pi\) | |||||||
\(648\) | −419.020 | −16.4607 | ||||||||
\(649\) | −13.8276 | −0.542780 | ||||||||
\(650\) | 17.1056 | 0.670936 | ||||||||
\(651\) | −29.8735 | −1.17084 | ||||||||
\(652\) | 106.380 | 4.16618 | ||||||||
\(653\) | 8.44514 | 0.330484 | 0.165242 | − | 0.986253i | \(-0.447160\pi\) | ||||
0.165242 | + | 0.986253i | \(0.447160\pi\) | |||||||
\(654\) | −8.98744 | −0.351437 | ||||||||
\(655\) | −50.0431 | −1.95534 | ||||||||
\(656\) | 128.307 | 5.00954 | ||||||||
\(657\) | 90.5465 | 3.53256 | ||||||||
\(658\) | −20.7304 | −0.808154 | ||||||||
\(659\) | 8.85856 | 0.345080 | 0.172540 | − | 0.985002i | \(-0.444803\pi\) | ||||
0.172540 | + | 0.985002i | \(0.444803\pi\) | |||||||
\(660\) | 79.4926 | 3.09425 | ||||||||
\(661\) | −39.5463 | −1.53817 | −0.769087 | − | 0.639144i | \(-0.779289\pi\) | ||||
−0.769087 | + | 0.639144i | \(0.779289\pi\) | |||||||
\(662\) | −41.8468 | −1.62642 | ||||||||
\(663\) | 1.74470 | 0.0677584 | ||||||||
\(664\) | 56.7318 | 2.20162 | ||||||||
\(665\) | −25.2555 | −0.979367 | ||||||||
\(666\) | −25.4258 | −0.985229 | ||||||||
\(667\) | −16.6549 | −0.644879 | ||||||||
\(668\) | −100.007 | −3.86938 | ||||||||
\(669\) | 96.6157 | 3.73538 | ||||||||
\(670\) | −44.2709 | −1.71034 | ||||||||
\(671\) | 9.29868 | 0.358971 | ||||||||
\(672\) | −314.302 | −12.1245 | ||||||||
\(673\) | 10.7219 | 0.413298 | 0.206649 | − | 0.978415i | \(-0.433744\pi\) | ||||
0.206649 | + | 0.978415i | \(0.433744\pi\) | |||||||
\(674\) | −38.4359 | −1.48050 | ||||||||
\(675\) | 38.0339 | 1.46392 | ||||||||
\(676\) | −20.1238 | −0.773991 | ||||||||
\(677\) | −48.9632 | −1.88181 | −0.940903 | − | 0.338675i | \(-0.890021\pi\) | ||||
−0.940903 | + | 0.338675i | \(0.890021\pi\) | |||||||
\(678\) | −181.505 | −6.97065 | ||||||||
\(679\) | 54.9063 | 2.10711 | ||||||||
\(680\) | 4.64891 | 0.178277 | ||||||||
\(681\) | −85.7125 | −3.28451 | ||||||||
\(682\) | 11.7714 | 0.450752 | ||||||||
\(683\) | 21.0604 | 0.805852 | 0.402926 | − | 0.915233i | \(-0.367993\pi\) | ||||
0.402926 | + | 0.915233i | \(0.367993\pi\) | |||||||
\(684\) | −151.118 | −5.77814 | ||||||||
\(685\) | 23.5469 | 0.899679 | ||||||||
\(686\) | 35.3108 | 1.34817 | ||||||||
\(687\) | 29.1241 | 1.11115 | ||||||||
\(688\) | −136.463 | −5.20261 | ||||||||
\(689\) | 3.08710 | 0.117609 | ||||||||
\(690\) | 93.5159 | 3.56009 | ||||||||
\(691\) | −36.9792 | −1.40676 | −0.703378 | − | 0.710816i | \(-0.748326\pi\) | ||||
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(692\) | 44.7918 | 1.70273 | ||||||||
\(693\) | 41.4872 | 1.57597 | ||||||||
\(694\) | 11.3296 | 0.430067 | ||||||||
\(695\) | 18.5920 | 0.705236 | ||||||||
\(696\) | −162.125 | −6.14534 | ||||||||
\(697\) | −1.17922 | −0.0446662 | ||||||||
\(698\) | 5.67111 | 0.214655 | ||||||||
\(699\) | −32.4701 | −1.22813 | ||||||||
\(700\) | 36.3915 | 1.37547 | ||||||||
\(701\) | 42.3310 | 1.59882 | 0.799410 | − | 0.600785i | \(-0.205145\pi\) | ||||
0.799410 | + | 0.600785i | \(0.205145\pi\) | |||||||
\(702\) | 165.277 | 6.23798 | ||||||||
\(703\) | −3.19032 | −0.120325 | ||||||||
\(704\) | 68.9695 | 2.59939 | ||||||||
\(705\) | 21.1462 | 0.796411 | ||||||||
\(706\) | −85.0423 | −3.20061 | ||||||||
\(707\) | −49.9622 | −1.87902 | ||||||||
\(708\) | −179.721 | −6.75433 | ||||||||
\(709\) | −45.2746 | −1.70032 | −0.850161 | − | 0.526523i | \(-0.823495\pi\) | ||||
−0.850161 | + | 0.526523i | \(0.823495\pi\) | |||||||
\(710\) | −91.2100 | −3.42305 | ||||||||
\(711\) | 73.6076 | 2.76050 | ||||||||
\(712\) | 160.347 | 6.00927 | ||||||||
\(713\) | 10.2971 | 0.385631 | ||||||||
\(714\) | 4.99178 | 0.186813 | ||||||||
\(715\) | −12.4112 | −0.464153 | ||||||||
\(716\) | 11.0176 | 0.411748 | ||||||||
\(717\) | 29.7901 | 1.11253 | ||||||||
\(718\) | 12.8172 | 0.478334 | ||||||||
\(719\) | −3.29101 | −0.122734 | −0.0613669 | − | 0.998115i | \(-0.519546\pi\) | ||||
−0.0613669 | + | 0.998115i | \(0.519546\pi\) | |||||||
\(720\) | 411.030 | 15.3182 | ||||||||
\(721\) | 35.2720 | 1.31360 | ||||||||
\(722\) | 27.5625 | 1.02577 | ||||||||
\(723\) | 82.8641 | 3.08175 | ||||||||
\(724\) | −64.4534 | −2.39539 | ||||||||
\(725\) | 8.89105 | 0.330205 | ||||||||
\(726\) | 82.6992 | 3.06926 | ||||||||
\(727\) | 0.291756 | 0.0108206 | 0.00541031 | − | 0.999985i | \(-0.498278\pi\) | ||||
0.00541031 | + | 0.999985i | \(0.498278\pi\) | |||||||
\(728\) | 103.606 | 3.83990 | ||||||||
\(729\) | 144.424 | 5.34903 | ||||||||
\(730\) | −77.5010 | −2.86844 | ||||||||
\(731\) | 1.25419 | 0.0463877 | ||||||||
\(732\) | 120.857 | 4.46702 | ||||||||
\(733\) | 32.0074 | 1.18222 | 0.591109 | − | 0.806591i | \(-0.298690\pi\) | ||||
0.591109 | + | 0.806591i | \(0.298690\pi\) | |||||||
\(734\) | 53.0033 | 1.95639 | ||||||||
\(735\) | 27.0490 | 0.997718 | ||||||||
\(736\) | 108.337 | 3.99336 | ||||||||
\(737\) | 9.12510 | 0.336128 | ||||||||
\(738\) | −171.309 | −6.30596 | ||||||||
\(739\) | −13.9514 | −0.513211 | −0.256606 | − | 0.966516i | \(-0.582604\pi\) | ||||
−0.256606 | + | 0.966516i | \(0.582604\pi\) | |||||||
\(740\) | 16.1822 | 0.594869 | ||||||||
\(741\) | 31.8027 | 1.16830 | ||||||||
\(742\) | 8.83256 | 0.324253 | ||||||||
\(743\) | −21.3794 | −0.784333 | −0.392166 | − | 0.919894i | \(-0.628274\pi\) | ||||
−0.392166 | + | 0.919894i | \(0.628274\pi\) | |||||||
\(744\) | 100.236 | 3.67485 | ||||||||
\(745\) | −14.3732 | −0.526595 | ||||||||
\(746\) | −27.4039 | −1.00333 | ||||||||
\(747\) | −46.0994 | −1.68669 | ||||||||
\(748\) | −1.46260 | −0.0534781 | ||||||||
\(749\) | −20.7634 | −0.758678 | ||||||||
\(750\) | 75.8887 | 2.77106 | ||||||||
\(751\) | −34.7134 | −1.26671 | −0.633354 | − | 0.773862i | \(-0.718322\pi\) | ||||
−0.633354 | + | 0.773862i | \(0.718322\pi\) | |||||||
\(752\) | 42.3337 | 1.54375 | ||||||||
\(753\) | −47.6398 | −1.73609 | ||||||||
\(754\) | 38.6362 | 1.40705 | ||||||||
\(755\) | 2.64273 | 0.0961788 | ||||||||
\(756\) | 351.621 | 12.7883 | ||||||||
\(757\) | 35.9194 | 1.30551 | 0.652756 | − | 0.757568i | \(-0.273613\pi\) | ||||
0.652756 | + | 0.757568i | \(0.273613\pi\) | |||||||
\(758\) | 92.5578 | 3.36185 | ||||||||
\(759\) | −19.2754 | −0.699654 | ||||||||
\(760\) | 84.7413 | 3.07389 | ||||||||
\(761\) | −21.1632 | −0.767165 | −0.383582 | − | 0.923507i | \(-0.625310\pi\) | ||||
−0.383582 | + | 0.923507i | \(0.625310\pi\) | |||||||
\(762\) | 84.7206 | 3.06910 | ||||||||
\(763\) | 2.98529 | 0.108075 | ||||||||
\(764\) | −154.643 | −5.59478 | ||||||||
\(765\) | −3.77763 | −0.136581 | ||||||||
\(766\) | −7.73157 | −0.279353 | ||||||||
\(767\) | 28.0600 | 1.01319 | ||||||||
\(768\) | 341.320 | 12.3163 | ||||||||
\(769\) | −24.0963 | −0.868934 | −0.434467 | − | 0.900688i | \(-0.643063\pi\) | ||||
−0.434467 | + | 0.900688i | \(0.643063\pi\) | |||||||
\(770\) | −35.5100 | −1.27969 | ||||||||
\(771\) | 21.3390 | 0.768504 | ||||||||
\(772\) | 117.553 | 4.23082 | ||||||||
\(773\) | −30.0257 | −1.07995 | −0.539974 | − | 0.841682i | \(-0.681566\pi\) | ||||
−0.539974 | + | 0.841682i | \(0.681566\pi\) | |||||||
\(774\) | 182.199 | 6.54900 | ||||||||
\(775\) | −5.49703 | −0.197459 | ||||||||
\(776\) | −184.230 | −6.61348 | ||||||||
\(777\) | 11.3838 | 0.408390 | ||||||||
\(778\) | 74.6464 | 2.67620 | ||||||||
\(779\) | −21.4951 | −0.770143 | ||||||||
\(780\) | −161.312 | −5.77590 | ||||||||
\(781\) | 18.8002 | 0.672723 | ||||||||
\(782\) | −1.72062 | −0.0615293 | ||||||||
\(783\) | 85.9069 | 3.07006 | ||||||||
\(784\) | 54.1509 | 1.93396 | ||||||||
\(785\) | 10.8848 | 0.388497 | ||||||||
\(786\) | 180.297 | 6.43097 | ||||||||
\(787\) | −19.9602 | −0.711504 | −0.355752 | − | 0.934580i | \(-0.615775\pi\) | ||||
−0.355752 | + | 0.934580i | \(0.615775\pi\) | |||||||
\(788\) | 154.591 | 5.50708 | ||||||||
\(789\) | −82.6431 | −2.94217 | ||||||||
\(790\) | −63.0026 | −2.24153 | ||||||||
\(791\) | 60.2891 | 2.14363 | ||||||||
\(792\) | −139.205 | −4.94642 | ||||||||
\(793\) | −18.8695 | −0.670077 | ||||||||
\(794\) | −24.3581 | −0.864436 | ||||||||
\(795\) | −9.00972 | −0.319542 | ||||||||
\(796\) | −5.54889 | −0.196675 | ||||||||
\(797\) | 40.1578 | 1.42246 | 0.711231 | − | 0.702959i | \(-0.248138\pi\) | ||||
0.711231 | + | 0.702959i | \(0.248138\pi\) | |||||||
\(798\) | 90.9913 | 3.22106 | ||||||||
\(799\) | −0.389074 | −0.0137644 | ||||||||
\(800\) | −57.8348 | −2.04477 | ||||||||
\(801\) | −130.296 | −4.60378 | ||||||||
\(802\) | −41.1941 | −1.45462 | ||||||||
\(803\) | 15.9745 | 0.563727 | ||||||||
\(804\) | 118.602 | 4.18275 | ||||||||
\(805\) | −31.0625 | −1.09481 | ||||||||
\(806\) | −23.8875 | −0.841400 | ||||||||
\(807\) | 39.6928 | 1.39725 | ||||||||
\(808\) | 167.641 | 5.89760 | ||||||||
\(809\) | −4.83199 | −0.169884 | −0.0849419 | − | 0.996386i | \(-0.527070\pi\) | ||||
−0.0849419 | + | 0.996386i | \(0.527070\pi\) | |||||||
\(810\) | −291.434 | −10.2399 | ||||||||
\(811\) | 41.0673 | 1.44207 | 0.721034 | − | 0.692900i | \(-0.243667\pi\) | ||||
0.721034 | + | 0.692900i | \(0.243667\pi\) | |||||||
\(812\) | 82.1974 | 2.88456 | ||||||||
\(813\) | −17.2831 | −0.606145 | ||||||||
\(814\) | −4.48569 | −0.157223 | ||||||||
\(815\) | 48.4741 | 1.69797 | ||||||||
\(816\) | −10.1938 | −0.356853 | ||||||||
\(817\) | 22.8616 | 0.799825 | ||||||||
\(818\) | 108.009 | 3.77645 | ||||||||
\(819\) | −84.1889 | −2.94180 | ||||||||
\(820\) | 109.029 | 3.80746 | ||||||||
\(821\) | 13.2896 | 0.463809 | 0.231905 | − | 0.972739i | \(-0.425504\pi\) | ||||
0.231905 | + | 0.972739i | \(0.425504\pi\) | |||||||
\(822\) | −84.8353 | −2.95897 | ||||||||
\(823\) | −46.0569 | −1.60544 | −0.802721 | − | 0.596355i | \(-0.796615\pi\) | ||||
−0.802721 | + | 0.596355i | \(0.796615\pi\) | |||||||
\(824\) | −118.350 | −4.12292 | ||||||||
\(825\) | 10.2900 | 0.358253 | ||||||||
\(826\) | 80.2828 | 2.79340 | ||||||||
\(827\) | −51.4982 | −1.79077 | −0.895385 | − | 0.445294i | \(-0.853099\pi\) | ||||
−0.895385 | + | 0.445294i | \(0.853099\pi\) | |||||||
\(828\) | −185.865 | −6.45924 | ||||||||
\(829\) | 13.1520 | 0.456787 | 0.228393 | − | 0.973569i | \(-0.426653\pi\) | ||||
0.228393 | + | 0.973569i | \(0.426653\pi\) | |||||||
\(830\) | 39.4576 | 1.36959 | ||||||||
\(831\) | 69.4392 | 2.40882 | ||||||||
\(832\) | −139.958 | −4.85217 | ||||||||
\(833\) | −0.497681 | −0.0172436 | ||||||||
\(834\) | −66.9840 | −2.31947 | ||||||||
\(835\) | −45.5698 | −1.57701 | ||||||||
\(836\) | −26.6606 | −0.922078 | ||||||||
\(837\) | −53.1133 | −1.83586 | ||||||||
\(838\) | −1.04290 | −0.0360263 | ||||||||
\(839\) | −3.44491 | −0.118931 | −0.0594657 | − | 0.998230i | \(-0.518940\pi\) | ||||
−0.0594657 | + | 0.998230i | \(0.518940\pi\) | |||||||
\(840\) | −302.375 | −10.4329 | ||||||||
\(841\) | −8.91783 | −0.307512 | ||||||||
\(842\) | 30.9487 | 1.06656 | ||||||||
\(843\) | −10.6587 | −0.367105 | ||||||||
\(844\) | 46.3374 | 1.59500 | ||||||||
\(845\) | −9.16975 | −0.315449 | ||||||||
\(846\) | −56.5217 | −1.94326 | ||||||||
\(847\) | −27.4696 | −0.943866 | ||||||||
\(848\) | −18.0370 | −0.619394 | ||||||||
\(849\) | −10.1232 | −0.347426 | ||||||||
\(850\) | 0.918539 | 0.0315056 | ||||||||
\(851\) | −3.92388 | −0.134509 | ||||||||
\(852\) | 244.351 | 8.37132 | ||||||||
\(853\) | 39.1765 | 1.34138 | 0.670688 | − | 0.741739i | \(-0.265999\pi\) | ||||
0.670688 | + | 0.741739i | \(0.265999\pi\) | |||||||
\(854\) | −53.9880 | −1.84743 | ||||||||
\(855\) | −68.8596 | −2.35495 | ||||||||
\(856\) | 69.6687 | 2.38123 | ||||||||
\(857\) | −2.13667 | −0.0729873 | −0.0364936 | − | 0.999334i | \(-0.511619\pi\) | ||||
−0.0364936 | + | 0.999334i | \(0.511619\pi\) | |||||||
\(858\) | 44.7155 | 1.52656 | ||||||||
\(859\) | −19.1467 | −0.653276 | −0.326638 | − | 0.945149i | \(-0.605916\pi\) | ||||
−0.326638 | + | 0.945149i | \(0.605916\pi\) | |||||||
\(860\) | −115.960 | −3.95421 | ||||||||
\(861\) | 76.6992 | 2.61390 | ||||||||
\(862\) | 69.0723 | 2.35261 | ||||||||
\(863\) | 31.1734 | 1.06116 | 0.530578 | − | 0.847636i | \(-0.321975\pi\) | ||||
0.530578 | + | 0.847636i | \(0.321975\pi\) | |||||||
\(864\) | −558.810 | −19.0111 | ||||||||
\(865\) | 20.4102 | 0.693967 | ||||||||
\(866\) | 108.661 | 3.69245 | ||||||||
\(867\) | −57.8635 | −1.96515 | ||||||||
\(868\) | −50.8198 | −1.72494 | ||||||||
\(869\) | 12.9861 | 0.440522 | ||||||||
\(870\) | −112.760 | −3.82292 | ||||||||
\(871\) | −18.5173 | −0.627436 | ||||||||
\(872\) | −10.0167 | −0.339209 | ||||||||
\(873\) | 149.703 | 5.06667 | ||||||||
\(874\) | −31.3639 | −1.06090 | ||||||||
\(875\) | −25.2074 | −0.852166 | ||||||||
\(876\) | 207.625 | 7.01498 | ||||||||
\(877\) | 36.5162 | 1.23306 | 0.616532 | − | 0.787330i | \(-0.288537\pi\) | ||||
0.616532 | + | 0.787330i | \(0.288537\pi\) | |||||||
\(878\) | 53.5729 | 1.80800 | ||||||||
\(879\) | −3.10351 | −0.104679 | ||||||||
\(880\) | 72.5151 | 2.44448 | ||||||||
\(881\) | −45.7898 | −1.54270 | −0.771348 | − | 0.636414i | \(-0.780417\pi\) | ||||
−0.771348 | + | 0.636414i | \(0.780417\pi\) | |||||||
\(882\) | −72.2995 | −2.43445 | ||||||||
\(883\) | 19.7147 | 0.663454 | 0.331727 | − | 0.943375i | \(-0.392369\pi\) | ||||
0.331727 | + | 0.943375i | \(0.392369\pi\) | |||||||
\(884\) | 2.96802 | 0.0998253 | ||||||||
\(885\) | −81.8931 | −2.75281 | ||||||||
\(886\) | −9.81325 | −0.329683 | ||||||||
\(887\) | −13.6433 | −0.458096 | −0.229048 | − | 0.973415i | \(-0.573561\pi\) | ||||
−0.229048 | + | 0.973415i | \(0.573561\pi\) | |||||||
\(888\) | −38.1966 | −1.28179 | ||||||||
\(889\) | −28.1410 | −0.943820 | ||||||||
\(890\) | 111.523 | 3.73828 | ||||||||
\(891\) | 60.0702 | 2.01243 | ||||||||
\(892\) | 164.359 | 5.50316 | ||||||||
\(893\) | −7.09212 | −0.237329 | ||||||||
\(894\) | 51.7843 | 1.73193 | ||||||||
\(895\) | 5.02037 | 0.167813 | ||||||||
\(896\) | −216.054 | −7.21785 | ||||||||
\(897\) | 39.1151 | 1.30602 | ||||||||
\(898\) | 88.1075 | 2.94019 | ||||||||
\(899\) | −12.4161 | −0.414101 | ||||||||
\(900\) | 99.2222 | 3.30741 | ||||||||
\(901\) | 0.165772 | 0.00552266 | ||||||||
\(902\) | −30.2228 | −1.00631 | ||||||||
\(903\) | −81.5750 | −2.71464 | ||||||||
\(904\) | −202.292 | −6.72812 | ||||||||
\(905\) | −29.3693 | −0.976270 | ||||||||
\(906\) | −9.52131 | −0.316324 | ||||||||
\(907\) | 8.33806 | 0.276861 | 0.138430 | − | 0.990372i | \(-0.455794\pi\) | ||||
0.138430 | + | 0.990372i | \(0.455794\pi\) | |||||||
\(908\) | −145.811 | −4.83892 | ||||||||
\(909\) | −136.223 | −4.51823 | ||||||||
\(910\) | 72.0594 | 2.38875 | ||||||||
\(911\) | 40.2144 | 1.33236 | 0.666182 | − | 0.745789i | \(-0.267927\pi\) | ||||
0.666182 | + | 0.745789i | \(0.267927\pi\) | |||||||
\(912\) | −185.814 | −6.15292 | ||||||||
\(913\) | −8.13298 | −0.269163 | ||||||||
\(914\) | 31.6866 | 1.04810 | ||||||||
\(915\) | 55.0708 | 1.82059 | ||||||||
\(916\) | 49.5449 | 1.63701 | ||||||||
\(917\) | −59.8879 | −1.97767 | ||||||||
\(918\) | 8.87508 | 0.292921 | ||||||||
\(919\) | 29.2563 | 0.965077 | 0.482539 | − | 0.875875i | \(-0.339715\pi\) | ||||
0.482539 | + | 0.875875i | \(0.339715\pi\) | |||||||
\(920\) | 104.226 | 3.43623 | ||||||||
\(921\) | 19.4744 | 0.641702 | ||||||||
\(922\) | 32.7321 | 1.07797 | ||||||||
\(923\) | −38.1506 | −1.25574 | ||||||||
\(924\) | 95.1309 | 3.12958 | ||||||||
\(925\) | 2.09473 | 0.0688742 | ||||||||
\(926\) | −18.5549 | −0.609753 | ||||||||
\(927\) | 96.1696 | 3.15863 | ||||||||
\(928\) | −130.631 | −4.28818 | ||||||||
\(929\) | −38.7575 | −1.27159 | −0.635796 | − | 0.771857i | \(-0.719328\pi\) | ||||
−0.635796 | + | 0.771857i | \(0.719328\pi\) | |||||||
\(930\) | 69.7157 | 2.28607 | ||||||||
\(931\) | −9.07185 | −0.297318 | ||||||||
\(932\) | −55.2370 | −1.80935 | ||||||||
\(933\) | 18.4875 | 0.605252 | ||||||||
\(934\) | 51.9825 | 1.70092 | ||||||||
\(935\) | −0.666461 | −0.0217956 | ||||||||
\(936\) | 282.484 | 9.23328 | ||||||||
\(937\) | 15.8952 | 0.519272 | 0.259636 | − | 0.965707i | \(-0.416397\pi\) | ||||
0.259636 | + | 0.965707i | \(0.416397\pi\) | |||||||
\(938\) | −52.9802 | −1.72987 | ||||||||
\(939\) | −9.63582 | −0.314453 | ||||||||
\(940\) | 35.9732 | 1.17332 | ||||||||
\(941\) | 40.8553 | 1.33184 | 0.665922 | − | 0.746021i | \(-0.268038\pi\) | ||||
0.665922 | + | 0.746021i | \(0.268038\pi\) | |||||||
\(942\) | −39.2162 | −1.27773 | ||||||||
\(943\) | −26.4375 | −0.860923 | ||||||||
\(944\) | −163.946 | −5.33599 | ||||||||
\(945\) | 160.223 | 5.21204 | ||||||||
\(946\) | 32.1440 | 1.04509 | ||||||||
\(947\) | −27.1367 | −0.881824 | −0.440912 | − | 0.897550i | \(-0.645345\pi\) | ||||
−0.440912 | + | 0.897550i | \(0.645345\pi\) | |||||||
\(948\) | 168.783 | 5.48183 | ||||||||
\(949\) | −32.4165 | −1.05229 | ||||||||
\(950\) | 16.7433 | 0.543225 | ||||||||
\(951\) | 8.60470 | 0.279027 | ||||||||
\(952\) | 5.56347 | 0.180313 | ||||||||
\(953\) | −32.7334 | −1.06034 | −0.530169 | − | 0.847892i | \(-0.677871\pi\) | ||||
−0.530169 | + | 0.847892i | \(0.677871\pi\) | |||||||
\(954\) | 24.0821 | 0.779687 | ||||||||
\(955\) | −70.4657 | −2.28022 | ||||||||
\(956\) | 50.6779 | 1.63904 | ||||||||
\(957\) | 23.2420 | 0.751308 | ||||||||
\(958\) | −18.5538 | −0.599445 | ||||||||
\(959\) | 28.1791 | 0.909952 | ||||||||
\(960\) | 408.468 | 13.1832 | ||||||||
\(961\) | −23.3235 | −0.752372 | ||||||||
\(962\) | 9.10268 | 0.293482 | ||||||||
\(963\) | −56.6118 | −1.82429 | ||||||||
\(964\) | 140.966 | 4.54020 | ||||||||
\(965\) | 53.5651 | 1.72432 | ||||||||
\(966\) | 111.913 | 3.60074 | ||||||||
\(967\) | −12.3713 | −0.397834 | −0.198917 | − | 0.980016i | \(-0.563742\pi\) | ||||
−0.198917 | + | 0.980016i | \(0.563742\pi\) | |||||||
\(968\) | 92.1704 | 2.96247 | ||||||||
\(969\) | 1.70775 | 0.0548609 | ||||||||
\(970\) | −128.134 | −4.11415 | ||||||||
\(971\) | −30.1248 | −0.966752 | −0.483376 | − | 0.875413i | \(-0.660590\pi\) | ||||
−0.483376 | + | 0.875413i | \(0.660590\pi\) | |||||||
\(972\) | 447.208 | 14.3442 | ||||||||
\(973\) | 22.2496 | 0.713289 | ||||||||
\(974\) | 88.9176 | 2.84910 | ||||||||
\(975\) | −20.8813 | −0.668736 | ||||||||
\(976\) | 110.249 | 3.52899 | ||||||||
\(977\) | 48.6443 | 1.55627 | 0.778134 | − | 0.628098i | \(-0.216166\pi\) | ||||
0.778134 | + | 0.628098i | \(0.216166\pi\) | |||||||
\(978\) | −174.644 | −5.58450 | ||||||||
\(979\) | −22.9872 | −0.734673 | ||||||||
\(980\) | 46.0149 | 1.46989 | ||||||||
\(981\) | 8.13945 | 0.259873 | ||||||||
\(982\) | 19.6938 | 0.628454 | ||||||||
\(983\) | −53.2984 | −1.69996 | −0.849978 | − | 0.526819i | \(-0.823385\pi\) | ||||
−0.849978 | + | 0.526819i | \(0.823385\pi\) | |||||||
\(984\) | −257.353 | −8.20413 | ||||||||
\(985\) | 70.4422 | 2.24447 | ||||||||
\(986\) | 2.07470 | 0.0660718 | ||||||||
\(987\) | 25.3062 | 0.805505 | ||||||||
\(988\) | 54.1017 | 1.72121 | ||||||||
\(989\) | 28.1181 | 0.894104 | ||||||||
\(990\) | −96.8185 | −3.07709 | ||||||||
\(991\) | 21.7853 | 0.692033 | 0.346017 | − | 0.938228i | \(-0.387534\pi\) | ||||
0.346017 | + | 0.938228i | \(0.387534\pi\) | |||||||
\(992\) | 80.7648 | 2.56428 | ||||||||
\(993\) | 51.0836 | 1.62109 | ||||||||
\(994\) | −109.153 | −3.46214 | ||||||||
\(995\) | −2.52845 | −0.0801573 | ||||||||
\(996\) | −105.707 | −3.34944 | ||||||||
\(997\) | −43.3661 | −1.37342 | −0.686709 | − | 0.726932i | \(-0.740945\pi\) | ||||
−0.686709 | + | 0.726932i | \(0.740945\pi\) | |||||||
\(998\) | −80.6179 | −2.55192 | ||||||||
\(999\) | 20.2396 | 0.640353 |
(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 | 8003.2.a.c.1.1 | ✓ | 172 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.c.1.1 | ✓ | 172 | 1.1 | even | 1 | trivial |