Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, 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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(169\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.35439 | −1.66481 | −0.832404 | − | 0.554169i | \(-0.813036\pi\) | ||||
−0.832404 | + | 0.554169i | \(0.813036\pi\) | |||||||
\(3\) | −0.664496 | −0.383647 | −0.191824 | − | 0.981429i | \(-0.561440\pi\) | ||||
−0.191824 | + | 0.981429i | \(0.561440\pi\) | |||||||
\(4\) | 3.54317 | 1.77159 | ||||||||
\(5\) | −2.57609 | −1.15206 | −0.576032 | − | 0.817427i | \(-0.695400\pi\) | ||||
−0.576032 | + | 0.817427i | \(0.695400\pi\) | |||||||
\(6\) | 1.56449 | 0.638699 | ||||||||
\(7\) | 5.27951 | 1.99547 | 0.997734 | − | 0.0672890i | \(-0.0214350\pi\) | ||||
0.997734 | + | 0.0672890i | \(0.0214350\pi\) | |||||||
\(8\) | −3.63324 | −1.28454 | ||||||||
\(9\) | −2.55844 | −0.852815 | ||||||||
\(10\) | 6.06514 | 1.91796 | ||||||||
\(11\) | 2.79332 | 0.842219 | 0.421109 | − | 0.907010i | \(-0.361641\pi\) | ||||
0.421109 | + | 0.907010i | \(0.361641\pi\) | |||||||
\(12\) | −2.35442 | −0.679664 | ||||||||
\(13\) | 5.32795 | 1.47771 | 0.738854 | − | 0.673865i | \(-0.235367\pi\) | ||||
0.738854 | + | 0.673865i | \(0.235367\pi\) | |||||||
\(14\) | −12.4300 | −3.32207 | ||||||||
\(15\) | 1.71180 | 0.441986 | ||||||||
\(16\) | 1.46772 | 0.366931 | ||||||||
\(17\) | −1.92061 | −0.465817 | −0.232909 | − | 0.972499i | \(-0.574824\pi\) | ||||
−0.232909 | + | 0.972499i | \(0.574824\pi\) | |||||||
\(18\) | 6.02359 | 1.41977 | ||||||||
\(19\) | 5.13540 | 1.17814 | 0.589071 | − | 0.808081i | \(-0.299494\pi\) | ||||
0.589071 | + | 0.808081i | \(0.299494\pi\) | |||||||
\(20\) | −9.12754 | −2.04098 | ||||||||
\(21\) | −3.50821 | −0.765555 | ||||||||
\(22\) | −6.57659 | −1.40213 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.41427 | 0.492811 | ||||||||
\(25\) | 1.63625 | 0.327251 | ||||||||
\(26\) | −12.5441 | −2.46010 | ||||||||
\(27\) | 3.69357 | 0.710827 | ||||||||
\(28\) | 18.7062 | 3.53514 | ||||||||
\(29\) | 1.16397 | 0.216143 | 0.108072 | − | 0.994143i | \(-0.465532\pi\) | ||||
0.108072 | + | 0.994143i | \(0.465532\pi\) | |||||||
\(30\) | −4.03026 | −0.735821 | ||||||||
\(31\) | 2.64100 | 0.474338 | 0.237169 | − | 0.971468i | \(-0.423780\pi\) | ||||
0.237169 | + | 0.971468i | \(0.423780\pi\) | |||||||
\(32\) | 3.81087 | 0.673673 | ||||||||
\(33\) | −1.85615 | −0.323115 | ||||||||
\(34\) | 4.52188 | 0.775496 | ||||||||
\(35\) | −13.6005 | −2.29890 | ||||||||
\(36\) | −9.06501 | −1.51084 | ||||||||
\(37\) | 4.37306 | 0.718927 | 0.359463 | − | 0.933159i | \(-0.382960\pi\) | ||||
0.359463 | + | 0.933159i | \(0.382960\pi\) | |||||||
\(38\) | −12.0908 | −1.96138 | ||||||||
\(39\) | −3.54040 | −0.566918 | ||||||||
\(40\) | 9.35955 | 1.47987 | ||||||||
\(41\) | 3.73840 | 0.583840 | 0.291920 | − | 0.956443i | \(-0.405706\pi\) | ||||
0.291920 | + | 0.956443i | \(0.405706\pi\) | |||||||
\(42\) | 8.25972 | 1.27450 | ||||||||
\(43\) | −0.476886 | −0.0727245 | −0.0363622 | − | 0.999339i | \(-0.511577\pi\) | ||||
−0.0363622 | + | 0.999339i | \(0.511577\pi\) | |||||||
\(44\) | 9.89723 | 1.49206 | ||||||||
\(45\) | 6.59079 | 0.982497 | ||||||||
\(46\) | 2.35439 | 0.347136 | ||||||||
\(47\) | 4.70831 | 0.686778 | 0.343389 | − | 0.939193i | \(-0.388425\pi\) | ||||
0.343389 | + | 0.939193i | \(0.388425\pi\) | |||||||
\(48\) | −0.975297 | −0.140772 | ||||||||
\(49\) | 20.8732 | 2.98189 | ||||||||
\(50\) | −3.85238 | −0.544809 | ||||||||
\(51\) | 1.27624 | 0.178709 | ||||||||
\(52\) | 18.8779 | 2.61789 | ||||||||
\(53\) | −13.4409 | −1.84625 | −0.923127 | − | 0.384496i | \(-0.874375\pi\) | ||||
−0.923127 | + | 0.384496i | \(0.874375\pi\) | |||||||
\(54\) | −8.69611 | −1.18339 | ||||||||
\(55\) | −7.19586 | −0.970290 | ||||||||
\(56\) | −19.1817 | −2.56326 | ||||||||
\(57\) | −3.41246 | −0.451991 | ||||||||
\(58\) | −2.74044 | −0.359837 | ||||||||
\(59\) | −10.9624 | −1.42718 | −0.713591 | − | 0.700562i | \(-0.752933\pi\) | ||||
−0.713591 | + | 0.700562i | \(0.752933\pi\) | |||||||
\(60\) | 6.06521 | 0.783016 | ||||||||
\(61\) | 4.95692 | 0.634668 | 0.317334 | − | 0.948314i | \(-0.397212\pi\) | ||||
0.317334 | + | 0.948314i | \(0.397212\pi\) | |||||||
\(62\) | −6.21796 | −0.789682 | ||||||||
\(63\) | −13.5073 | −1.70176 | ||||||||
\(64\) | −11.9077 | −1.48847 | ||||||||
\(65\) | −13.7253 | −1.70241 | ||||||||
\(66\) | 4.37012 | 0.537924 | ||||||||
\(67\) | 13.2442 | 1.61804 | 0.809020 | − | 0.587781i | \(-0.199998\pi\) | ||||
0.809020 | + | 0.587781i | \(0.199998\pi\) | |||||||
\(68\) | −6.80507 | −0.825235 | ||||||||
\(69\) | 0.664496 | 0.0799959 | ||||||||
\(70\) | 32.0210 | 3.82724 | ||||||||
\(71\) | 9.98798 | 1.18536 | 0.592678 | − | 0.805440i | \(-0.298071\pi\) | ||||
0.592678 | + | 0.805440i | \(0.298071\pi\) | |||||||
\(72\) | 9.29543 | 1.09548 | ||||||||
\(73\) | 8.89751 | 1.04137 | 0.520687 | − | 0.853748i | \(-0.325676\pi\) | ||||
0.520687 | + | 0.853748i | \(0.325676\pi\) | |||||||
\(74\) | −10.2959 | −1.19688 | ||||||||
\(75\) | −1.08728 | −0.125549 | ||||||||
\(76\) | 18.1956 | 2.08718 | ||||||||
\(77\) | 14.7474 | 1.68062 | ||||||||
\(78\) | 8.33551 | 0.943810 | ||||||||
\(79\) | −9.04039 | −1.01712 | −0.508561 | − | 0.861026i | \(-0.669823\pi\) | ||||
−0.508561 | + | 0.861026i | \(0.669823\pi\) | |||||||
\(80\) | −3.78099 | −0.422728 | ||||||||
\(81\) | 5.22098 | 0.580108 | ||||||||
\(82\) | −8.80167 | −0.971982 | ||||||||
\(83\) | 9.12073 | 1.00113 | 0.500565 | − | 0.865699i | \(-0.333126\pi\) | ||||
0.500565 | + | 0.865699i | \(0.333126\pi\) | |||||||
\(84\) | −12.4302 | −1.35625 | ||||||||
\(85\) | 4.94768 | 0.536651 | ||||||||
\(86\) | 1.12278 | 0.121072 | ||||||||
\(87\) | −0.773452 | −0.0829227 | ||||||||
\(88\) | −10.1488 | −1.08187 | ||||||||
\(89\) | 15.0901 | 1.59954 | 0.799771 | − | 0.600305i | \(-0.204954\pi\) | ||||
0.799771 | + | 0.600305i | \(0.204954\pi\) | |||||||
\(90\) | −15.5173 | −1.63567 | ||||||||
\(91\) | 28.1290 | 2.94872 | ||||||||
\(92\) | −3.54317 | −0.369401 | ||||||||
\(93\) | −1.75494 | −0.181978 | ||||||||
\(94\) | −11.0852 | −1.14335 | ||||||||
\(95\) | −13.2293 | −1.35729 | ||||||||
\(96\) | −2.53231 | −0.258453 | ||||||||
\(97\) | −8.07812 | −0.820209 | −0.410104 | − | 0.912039i | \(-0.634508\pi\) | ||||
−0.410104 | + | 0.912039i | \(0.634508\pi\) | |||||||
\(98\) | −49.1438 | −4.96427 | ||||||||
\(99\) | −7.14657 | −0.718257 | ||||||||
\(100\) | 5.79753 | 0.579753 | ||||||||
\(101\) | 10.9538 | 1.08995 | 0.544973 | − | 0.838453i | \(-0.316540\pi\) | ||||
0.544973 | + | 0.838453i | \(0.316540\pi\) | |||||||
\(102\) | −3.00477 | −0.297517 | ||||||||
\(103\) | 6.12042 | 0.603063 | 0.301531 | − | 0.953456i | \(-0.402502\pi\) | ||||
0.301531 | + | 0.953456i | \(0.402502\pi\) | |||||||
\(104\) | −19.3577 | −1.89818 | ||||||||
\(105\) | 9.03748 | 0.881968 | ||||||||
\(106\) | 31.6452 | 3.07366 | ||||||||
\(107\) | −10.8595 | −1.04983 | −0.524913 | − | 0.851156i | \(-0.675902\pi\) | ||||
−0.524913 | + | 0.851156i | \(0.675902\pi\) | |||||||
\(108\) | 13.0869 | 1.25929 | ||||||||
\(109\) | −3.34788 | −0.320669 | −0.160334 | − | 0.987063i | \(-0.551257\pi\) | ||||
−0.160334 | + | 0.987063i | \(0.551257\pi\) | |||||||
\(110\) | 16.9419 | 1.61535 | ||||||||
\(111\) | −2.90588 | −0.275814 | ||||||||
\(112\) | 7.74886 | 0.732199 | ||||||||
\(113\) | 4.18428 | 0.393624 | 0.196812 | − | 0.980441i | \(-0.436941\pi\) | ||||
0.196812 | + | 0.980441i | \(0.436941\pi\) | |||||||
\(114\) | 8.03427 | 0.752478 | ||||||||
\(115\) | 2.57609 | 0.240222 | ||||||||
\(116\) | 4.12414 | 0.382916 | ||||||||
\(117\) | −13.6313 | −1.26021 | ||||||||
\(118\) | 25.8098 | 2.37598 | ||||||||
\(119\) | −10.1399 | −0.929523 | ||||||||
\(120\) | −6.21939 | −0.567750 | ||||||||
\(121\) | −3.19734 | −0.290667 | ||||||||
\(122\) | −11.6705 | −1.05660 | ||||||||
\(123\) | −2.48415 | −0.223989 | ||||||||
\(124\) | 9.35753 | 0.840331 | ||||||||
\(125\) | 8.66532 | 0.775050 | ||||||||
\(126\) | 31.8016 | 2.83311 | ||||||||
\(127\) | 14.4500 | 1.28223 | 0.641113 | − | 0.767446i | \(-0.278473\pi\) | ||||
0.641113 | + | 0.767446i | \(0.278473\pi\) | |||||||
\(128\) | 20.4138 | 1.80434 | ||||||||
\(129\) | 0.316889 | 0.0279005 | ||||||||
\(130\) | 32.3148 | 2.83419 | ||||||||
\(131\) | 21.7044 | 1.89633 | 0.948163 | − | 0.317786i | \(-0.102939\pi\) | ||||
0.948163 | + | 0.317786i | \(0.102939\pi\) | |||||||
\(132\) | −6.57667 | −0.572426 | ||||||||
\(133\) | 27.1124 | 2.35094 | ||||||||
\(134\) | −31.1821 | −2.69373 | ||||||||
\(135\) | −9.51497 | −0.818918 | ||||||||
\(136\) | 6.97804 | 0.598362 | ||||||||
\(137\) | −15.7186 | −1.34293 | −0.671466 | − | 0.741035i | \(-0.734335\pi\) | ||||
−0.671466 | + | 0.741035i | \(0.734335\pi\) | |||||||
\(138\) | −1.56449 | −0.133178 | ||||||||
\(139\) | −22.8942 | −1.94186 | −0.970930 | − | 0.239363i | \(-0.923061\pi\) | ||||
−0.970930 | + | 0.239363i | \(0.923061\pi\) | |||||||
\(140\) | −48.1889 | −4.07271 | ||||||||
\(141\) | −3.12865 | −0.263480 | ||||||||
\(142\) | −23.5157 | −1.97339 | ||||||||
\(143\) | 14.8827 | 1.24455 | ||||||||
\(144\) | −3.75509 | −0.312924 | ||||||||
\(145\) | −2.99849 | −0.249011 | ||||||||
\(146\) | −20.9482 | −1.73369 | ||||||||
\(147\) | −13.8702 | −1.14399 | ||||||||
\(148\) | 15.4945 | 1.27364 | ||||||||
\(149\) | 4.23477 | 0.346926 | 0.173463 | − | 0.984840i | \(-0.444504\pi\) | ||||
0.173463 | + | 0.984840i | \(0.444504\pi\) | |||||||
\(150\) | 2.55989 | 0.209014 | ||||||||
\(151\) | −15.6609 | −1.27446 | −0.637232 | − | 0.770672i | \(-0.719921\pi\) | ||||
−0.637232 | + | 0.770672i | \(0.719921\pi\) | |||||||
\(152\) | −18.6581 | −1.51337 | ||||||||
\(153\) | 4.91379 | 0.397256 | ||||||||
\(154\) | −34.7211 | −2.79791 | ||||||||
\(155\) | −6.80347 | −0.546468 | ||||||||
\(156\) | −12.5443 | −1.00434 | ||||||||
\(157\) | −0.565708 | −0.0451484 | −0.0225742 | − | 0.999745i | \(-0.507186\pi\) | ||||
−0.0225742 | + | 0.999745i | \(0.507186\pi\) | |||||||
\(158\) | 21.2846 | 1.69331 | ||||||||
\(159\) | 8.93144 | 0.708309 | ||||||||
\(160\) | −9.81715 | −0.776114 | ||||||||
\(161\) | −5.27951 | −0.416084 | ||||||||
\(162\) | −12.2922 | −0.965769 | ||||||||
\(163\) | −14.6626 | −1.14847 | −0.574234 | − | 0.818692i | \(-0.694700\pi\) | ||||
−0.574234 | + | 0.818692i | \(0.694700\pi\) | |||||||
\(164\) | 13.2458 | 1.03432 | ||||||||
\(165\) | 4.78162 | 0.372249 | ||||||||
\(166\) | −21.4738 | −1.66669 | ||||||||
\(167\) | 16.0896 | 1.24505 | 0.622526 | − | 0.782599i | \(-0.286107\pi\) | ||||
0.622526 | + | 0.782599i | \(0.286107\pi\) | |||||||
\(168\) | 12.7462 | 0.983388 | ||||||||
\(169\) | 15.3871 | 1.18362 | ||||||||
\(170\) | −11.6488 | −0.893421 | ||||||||
\(171\) | −13.1386 | −1.00474 | ||||||||
\(172\) | −1.68969 | −0.128838 | ||||||||
\(173\) | −3.44496 | −0.261916 | −0.130958 | − | 0.991388i | \(-0.541805\pi\) | ||||
−0.130958 | + | 0.991388i | \(0.541805\pi\) | |||||||
\(174\) | 1.82101 | 0.138050 | ||||||||
\(175\) | 8.63861 | 0.653018 | ||||||||
\(176\) | 4.09983 | 0.309036 | ||||||||
\(177\) | 7.28447 | 0.547534 | ||||||||
\(178\) | −35.5279 | −2.66293 | ||||||||
\(179\) | 12.7332 | 0.951721 | 0.475860 | − | 0.879521i | \(-0.342137\pi\) | ||||
0.475860 | + | 0.879521i | \(0.342137\pi\) | |||||||
\(180\) | 23.3523 | 1.74058 | ||||||||
\(181\) | −0.976934 | −0.0726149 | −0.0363075 | − | 0.999341i | \(-0.511560\pi\) | ||||
−0.0363075 | + | 0.999341i | \(0.511560\pi\) | |||||||
\(182\) | −66.2267 | −4.90905 | ||||||||
\(183\) | −3.29385 | −0.243488 | ||||||||
\(184\) | 3.63324 | 0.267846 | ||||||||
\(185\) | −11.2654 | −0.828249 | ||||||||
\(186\) | 4.13181 | 0.302959 | ||||||||
\(187\) | −5.36490 | −0.392320 | ||||||||
\(188\) | 16.6824 | 1.21669 | ||||||||
\(189\) | 19.5002 | 1.41843 | ||||||||
\(190\) | 31.1469 | 2.25964 | ||||||||
\(191\) | 22.0741 | 1.59723 | 0.798613 | − | 0.601845i | \(-0.205567\pi\) | ||||
0.798613 | + | 0.601845i | \(0.205567\pi\) | |||||||
\(192\) | 7.91264 | 0.571046 | ||||||||
\(193\) | −21.4358 | −1.54298 | −0.771491 | − | 0.636240i | \(-0.780489\pi\) | ||||
−0.771491 | + | 0.636240i | \(0.780489\pi\) | |||||||
\(194\) | 19.0191 | 1.36549 | ||||||||
\(195\) | 9.12041 | 0.653126 | ||||||||
\(196\) | 73.9574 | 5.28267 | ||||||||
\(197\) | −19.4469 | −1.38553 | −0.692766 | − | 0.721163i | \(-0.743608\pi\) | ||||
−0.692766 | + | 0.721163i | \(0.743608\pi\) | |||||||
\(198\) | 16.8258 | 1.19576 | ||||||||
\(199\) | −4.56548 | −0.323638 | −0.161819 | − | 0.986820i | \(-0.551736\pi\) | ||||
−0.161819 | + | 0.986820i | \(0.551736\pi\) | |||||||
\(200\) | −5.94489 | −0.420367 | ||||||||
\(201\) | −8.80074 | −0.620756 | ||||||||
\(202\) | −25.7896 | −1.81455 | ||||||||
\(203\) | 6.14518 | 0.431307 | ||||||||
\(204\) | 4.52194 | 0.316599 | ||||||||
\(205\) | −9.63047 | −0.672621 | ||||||||
\(206\) | −14.4099 | −1.00398 | ||||||||
\(207\) | 2.55844 | 0.177824 | ||||||||
\(208\) | 7.81997 | 0.542217 | ||||||||
\(209\) | 14.3448 | 0.992254 | ||||||||
\(210\) | −21.2778 | −1.46831 | ||||||||
\(211\) | 17.9262 | 1.23409 | 0.617046 | − | 0.786927i | \(-0.288329\pi\) | ||||
0.617046 | + | 0.786927i | \(0.288329\pi\) | |||||||
\(212\) | −47.6235 | −3.27080 | ||||||||
\(213\) | −6.63698 | −0.454758 | ||||||||
\(214\) | 25.5675 | 1.74776 | ||||||||
\(215\) | 1.22850 | 0.0837832 | ||||||||
\(216\) | −13.4196 | −0.913088 | ||||||||
\(217\) | 13.9432 | 0.946526 | ||||||||
\(218\) | 7.88224 | 0.533852 | ||||||||
\(219\) | −5.91236 | −0.399520 | ||||||||
\(220\) | −25.4962 | −1.71895 | ||||||||
\(221\) | −10.2329 | −0.688342 | ||||||||
\(222\) | 6.84159 | 0.459178 | ||||||||
\(223\) | −4.49245 | −0.300837 | −0.150418 | − | 0.988622i | \(-0.548062\pi\) | ||||
−0.150418 | + | 0.988622i | \(0.548062\pi\) | |||||||
\(224\) | 20.1195 | 1.34429 | ||||||||
\(225\) | −4.18626 | −0.279084 | ||||||||
\(226\) | −9.85145 | −0.655309 | ||||||||
\(227\) | 12.2062 | 0.810155 | 0.405078 | − | 0.914282i | \(-0.367244\pi\) | ||||
0.405078 | + | 0.914282i | \(0.367244\pi\) | |||||||
\(228\) | −12.0909 | −0.800741 | ||||||||
\(229\) | −26.1308 | −1.72677 | −0.863386 | − | 0.504543i | \(-0.831661\pi\) | ||||
−0.863386 | + | 0.504543i | \(0.831661\pi\) | |||||||
\(230\) | −6.06514 | −0.399923 | ||||||||
\(231\) | −9.79958 | −0.644765 | ||||||||
\(232\) | −4.22897 | −0.277645 | ||||||||
\(233\) | −19.8797 | −1.30236 | −0.651180 | − | 0.758923i | \(-0.725726\pi\) | ||||
−0.651180 | + | 0.758923i | \(0.725726\pi\) | |||||||
\(234\) | 32.0934 | 2.09801 | ||||||||
\(235\) | −12.1290 | −0.791211 | ||||||||
\(236\) | −38.8416 | −2.52838 | ||||||||
\(237\) | 6.00730 | 0.390216 | ||||||||
\(238\) | 23.8733 | 1.54748 | ||||||||
\(239\) | 5.22114 | 0.337727 | 0.168864 | − | 0.985639i | \(-0.445990\pi\) | ||||
0.168864 | + | 0.985639i | \(0.445990\pi\) | |||||||
\(240\) | 2.51246 | 0.162178 | ||||||||
\(241\) | −1.65231 | −0.106435 | −0.0532173 | − | 0.998583i | \(-0.516948\pi\) | ||||
−0.0532173 | + | 0.998583i | \(0.516948\pi\) | |||||||
\(242\) | 7.52780 | 0.483905 | ||||||||
\(243\) | −14.5500 | −0.933384 | ||||||||
\(244\) | 17.5632 | 1.12437 | ||||||||
\(245\) | −53.7713 | −3.43533 | ||||||||
\(246\) | 5.84868 | 0.372898 | ||||||||
\(247\) | 27.3612 | 1.74095 | ||||||||
\(248\) | −9.59539 | −0.609308 | ||||||||
\(249\) | −6.06069 | −0.384081 | ||||||||
\(250\) | −20.4016 | −1.29031 | ||||||||
\(251\) | 25.3961 | 1.60299 | 0.801495 | − | 0.598002i | \(-0.204038\pi\) | ||||
0.801495 | + | 0.598002i | \(0.204038\pi\) | |||||||
\(252\) | −47.8588 | −3.01482 | ||||||||
\(253\) | −2.79332 | −0.175615 | ||||||||
\(254\) | −34.0209 | −2.13466 | ||||||||
\(255\) | −3.28771 | −0.205885 | ||||||||
\(256\) | −24.2466 | −1.51541 | ||||||||
\(257\) | −11.7728 | −0.734365 | −0.367182 | − | 0.930149i | \(-0.619678\pi\) | ||||
−0.367182 | + | 0.930149i | \(0.619678\pi\) | |||||||
\(258\) | −0.746082 | −0.0464490 | ||||||||
\(259\) | 23.0876 | 1.43459 | ||||||||
\(260\) | −48.6311 | −3.01597 | ||||||||
\(261\) | −2.97795 | −0.184330 | ||||||||
\(262\) | −51.1008 | −3.15702 | ||||||||
\(263\) | −5.95698 | −0.367323 | −0.183662 | − | 0.982990i | \(-0.558795\pi\) | ||||
−0.183662 | + | 0.982990i | \(0.558795\pi\) | |||||||
\(264\) | 6.74384 | 0.415055 | ||||||||
\(265\) | 34.6251 | 2.12700 | ||||||||
\(266\) | −63.8333 | −3.91387 | ||||||||
\(267\) | −10.0273 | −0.613660 | ||||||||
\(268\) | 46.9266 | 2.86650 | ||||||||
\(269\) | −5.79447 | −0.353295 | −0.176648 | − | 0.984274i | \(-0.556525\pi\) | ||||
−0.176648 | + | 0.984274i | \(0.556525\pi\) | |||||||
\(270\) | 22.4020 | 1.36334 | ||||||||
\(271\) | −18.0197 | −1.09462 | −0.547311 | − | 0.836930i | \(-0.684348\pi\) | ||||
−0.547311 | + | 0.836930i | \(0.684348\pi\) | |||||||
\(272\) | −2.81893 | −0.170923 | ||||||||
\(273\) | −18.6916 | −1.13127 | ||||||||
\(274\) | 37.0078 | 2.23572 | ||||||||
\(275\) | 4.57058 | 0.275617 | ||||||||
\(276\) | 2.35442 | 0.141720 | ||||||||
\(277\) | −5.91958 | −0.355673 | −0.177836 | − | 0.984060i | \(-0.556910\pi\) | ||||
−0.177836 | + | 0.984060i | \(0.556910\pi\) | |||||||
\(278\) | 53.9020 | 3.23282 | ||||||||
\(279\) | −6.75686 | −0.404523 | ||||||||
\(280\) | 49.4138 | 2.95304 | ||||||||
\(281\) | −23.6554 | −1.41116 | −0.705582 | − | 0.708629i | \(-0.749314\pi\) | ||||
−0.705582 | + | 0.708629i | \(0.749314\pi\) | |||||||
\(282\) | 7.36608 | 0.438644 | ||||||||
\(283\) | 27.6601 | 1.64422 | 0.822111 | − | 0.569327i | \(-0.192796\pi\) | ||||
0.822111 | + | 0.569327i | \(0.192796\pi\) | |||||||
\(284\) | 35.3891 | 2.09996 | ||||||||
\(285\) | 8.79080 | 0.520722 | ||||||||
\(286\) | −35.0397 | −2.07194 | ||||||||
\(287\) | 19.7369 | 1.16503 | ||||||||
\(288\) | −9.74990 | −0.574518 | ||||||||
\(289\) | −13.3112 | −0.783014 | ||||||||
\(290\) | 7.05962 | 0.414555 | ||||||||
\(291\) | 5.36788 | 0.314671 | ||||||||
\(292\) | 31.5254 | 1.84488 | ||||||||
\(293\) | 19.8953 | 1.16230 | 0.581148 | − | 0.813798i | \(-0.302604\pi\) | ||||
0.581148 | + | 0.813798i | \(0.302604\pi\) | |||||||
\(294\) | 32.6559 | 1.90453 | ||||||||
\(295\) | 28.2401 | 1.64420 | ||||||||
\(296\) | −15.8884 | −0.923492 | ||||||||
\(297\) | 10.3173 | 0.598672 | ||||||||
\(298\) | −9.97033 | −0.577566 | ||||||||
\(299\) | −5.32795 | −0.308123 | ||||||||
\(300\) | −3.85243 | −0.222420 | ||||||||
\(301\) | −2.51773 | −0.145119 | ||||||||
\(302\) | 36.8719 | 2.12174 | ||||||||
\(303\) | −7.27877 | −0.418155 | ||||||||
\(304\) | 7.53736 | 0.432297 | ||||||||
\(305\) | −12.7695 | −0.731178 | ||||||||
\(306\) | −11.5690 | −0.661355 | ||||||||
\(307\) | −21.1808 | −1.20885 | −0.604427 | − | 0.796661i | \(-0.706598\pi\) | ||||
−0.604427 | + | 0.796661i | \(0.706598\pi\) | |||||||
\(308\) | 52.2525 | 2.97736 | ||||||||
\(309\) | −4.06699 | −0.231363 | ||||||||
\(310\) | 16.0180 | 0.909764 | ||||||||
\(311\) | 17.7846 | 1.00847 | 0.504237 | − | 0.863565i | \(-0.331774\pi\) | ||||
0.504237 | + | 0.863565i | \(0.331774\pi\) | |||||||
\(312\) | 12.8631 | 0.728231 | ||||||||
\(313\) | −30.7473 | −1.73794 | −0.868971 | − | 0.494863i | \(-0.835218\pi\) | ||||
−0.868971 | + | 0.494863i | \(0.835218\pi\) | |||||||
\(314\) | 1.33190 | 0.0751634 | ||||||||
\(315\) | 34.7961 | 1.96054 | ||||||||
\(316\) | −32.0316 | −1.80192 | ||||||||
\(317\) | 17.1704 | 0.964386 | 0.482193 | − | 0.876065i | \(-0.339840\pi\) | ||||
0.482193 | + | 0.876065i | \(0.339840\pi\) | |||||||
\(318\) | −21.0281 | −1.17920 | ||||||||
\(319\) | 3.25134 | 0.182040 | ||||||||
\(320\) | 30.6754 | 1.71481 | ||||||||
\(321\) | 7.21609 | 0.402763 | ||||||||
\(322\) | 12.4300 | 0.692699 | ||||||||
\(323\) | −9.86313 | −0.548799 | ||||||||
\(324\) | 18.4988 | 1.02771 | ||||||||
\(325\) | 8.71788 | 0.483581 | ||||||||
\(326\) | 34.5217 | 1.91198 | ||||||||
\(327\) | 2.22465 | 0.123024 | ||||||||
\(328\) | −13.5825 | −0.749968 | ||||||||
\(329\) | 24.8576 | 1.37044 | ||||||||
\(330\) | −11.2578 | −0.619723 | ||||||||
\(331\) | −26.5576 | −1.45974 | −0.729869 | − | 0.683587i | \(-0.760419\pi\) | ||||
−0.729869 | + | 0.683587i | \(0.760419\pi\) | |||||||
\(332\) | 32.3163 | 1.77359 | ||||||||
\(333\) | −11.1882 | −0.613112 | ||||||||
\(334\) | −37.8813 | −2.07277 | ||||||||
\(335\) | −34.1184 | −1.86409 | ||||||||
\(336\) | −5.14909 | −0.280906 | ||||||||
\(337\) | −2.70884 | −0.147560 | −0.0737800 | − | 0.997275i | \(-0.523506\pi\) | ||||
−0.0737800 | + | 0.997275i | \(0.523506\pi\) | |||||||
\(338\) | −36.2273 | −1.97050 | ||||||||
\(339\) | −2.78044 | −0.151013 | ||||||||
\(340\) | 17.5305 | 0.950724 | ||||||||
\(341\) | 7.37718 | 0.399497 | ||||||||
\(342\) | 30.9336 | 1.67270 | ||||||||
\(343\) | 73.2438 | 3.95479 | ||||||||
\(344\) | 1.73264 | 0.0934177 | ||||||||
\(345\) | −1.71180 | −0.0921604 | ||||||||
\(346\) | 8.11080 | 0.436039 | ||||||||
\(347\) | −27.5750 | −1.48030 | −0.740152 | − | 0.672440i | \(-0.765246\pi\) | ||||
−0.740152 | + | 0.672440i | \(0.765246\pi\) | |||||||
\(348\) | −2.74047 | −0.146905 | ||||||||
\(349\) | 1.00000 | 0.0535288 | ||||||||
\(350\) | −20.3387 | −1.08715 | ||||||||
\(351\) | 19.6791 | 1.05039 | ||||||||
\(352\) | 10.6450 | 0.567380 | ||||||||
\(353\) | −7.86169 | −0.418435 | −0.209218 | − | 0.977869i | \(-0.567092\pi\) | ||||
−0.209218 | + | 0.977869i | \(0.567092\pi\) | |||||||
\(354\) | −17.1505 | −0.911539 | ||||||||
\(355\) | −25.7300 | −1.36561 | ||||||||
\(356\) | 53.4667 | 2.83373 | ||||||||
\(357\) | 6.73792 | 0.356609 | ||||||||
\(358\) | −29.9789 | −1.58443 | ||||||||
\(359\) | 12.5854 | 0.664233 | 0.332117 | − | 0.943238i | \(-0.392237\pi\) | ||||
0.332117 | + | 0.943238i | \(0.392237\pi\) | |||||||
\(360\) | −23.9459 | −1.26206 | ||||||||
\(361\) | 7.37237 | 0.388019 | ||||||||
\(362\) | 2.30009 | 0.120890 | ||||||||
\(363\) | 2.12462 | 0.111514 | ||||||||
\(364\) | 99.6658 | 5.22391 | ||||||||
\(365\) | −22.9208 | −1.19973 | ||||||||
\(366\) | 7.75502 | 0.405362 | ||||||||
\(367\) | 8.89587 | 0.464361 | 0.232180 | − | 0.972673i | \(-0.425414\pi\) | ||||
0.232180 | + | 0.972673i | \(0.425414\pi\) | |||||||
\(368\) | −1.46772 | −0.0765104 | ||||||||
\(369\) | −9.56449 | −0.497908 | ||||||||
\(370\) | 26.5232 | 1.37888 | ||||||||
\(371\) | −70.9615 | −3.68414 | ||||||||
\(372\) | −6.21804 | −0.322390 | ||||||||
\(373\) | −4.96659 | −0.257160 | −0.128580 | − | 0.991699i | \(-0.541042\pi\) | ||||
−0.128580 | + | 0.991699i | \(0.541042\pi\) | |||||||
\(374\) | 12.6311 | 0.653138 | ||||||||
\(375\) | −5.75807 | −0.297346 | ||||||||
\(376\) | −17.1064 | −0.882195 | ||||||||
\(377\) | 6.20156 | 0.319397 | ||||||||
\(378\) | −45.9112 | −2.36142 | ||||||||
\(379\) | 24.8108 | 1.27445 | 0.637223 | − | 0.770680i | \(-0.280083\pi\) | ||||
0.637223 | + | 0.770680i | \(0.280083\pi\) | |||||||
\(380\) | −46.8736 | −2.40456 | ||||||||
\(381\) | −9.60194 | −0.491922 | ||||||||
\(382\) | −51.9711 | −2.65907 | ||||||||
\(383\) | −31.7458 | −1.62213 | −0.811067 | − | 0.584954i | \(-0.801113\pi\) | ||||
−0.811067 | + | 0.584954i | \(0.801113\pi\) | |||||||
\(384\) | −13.5649 | −0.692229 | ||||||||
\(385\) | −37.9906 | −1.93618 | ||||||||
\(386\) | 50.4683 | 2.56877 | ||||||||
\(387\) | 1.22009 | 0.0620205 | ||||||||
\(388\) | −28.6222 | −1.45307 | ||||||||
\(389\) | −29.5882 | −1.50018 | −0.750092 | − | 0.661334i | \(-0.769991\pi\) | ||||
−0.750092 | + | 0.661334i | \(0.769991\pi\) | |||||||
\(390\) | −21.4730 | −1.08733 | ||||||||
\(391\) | 1.92061 | 0.0971296 | ||||||||
\(392\) | −75.8373 | −3.83036 | ||||||||
\(393\) | −14.4225 | −0.727519 | ||||||||
\(394\) | 45.7856 | 2.30664 | ||||||||
\(395\) | 23.2889 | 1.17179 | ||||||||
\(396\) | −25.3215 | −1.27245 | ||||||||
\(397\) | −18.7251 | −0.939786 | −0.469893 | − | 0.882723i | \(-0.655708\pi\) | ||||
−0.469893 | + | 0.882723i | \(0.655708\pi\) | |||||||
\(398\) | 10.7489 | 0.538796 | ||||||||
\(399\) | −18.0161 | −0.901933 | ||||||||
\(400\) | 2.40157 | 0.120078 | ||||||||
\(401\) | −16.4592 | −0.821932 | −0.410966 | − | 0.911651i | \(-0.634809\pi\) | ||||
−0.410966 | + | 0.911651i | \(0.634809\pi\) | |||||||
\(402\) | 20.7204 | 1.03344 | ||||||||
\(403\) | 14.0711 | 0.700934 | ||||||||
\(404\) | 38.8113 | 1.93093 | ||||||||
\(405\) | −13.4497 | −0.668322 | ||||||||
\(406\) | −14.4682 | −0.718043 | ||||||||
\(407\) | 12.2154 | 0.605494 | ||||||||
\(408\) | −4.63688 | −0.229560 | ||||||||
\(409\) | 28.6441 | 1.41636 | 0.708180 | − | 0.706032i | \(-0.249517\pi\) | ||||
0.708180 | + | 0.706032i | \(0.249517\pi\) | |||||||
\(410\) | 22.6739 | 1.11978 | ||||||||
\(411\) | 10.4450 | 0.515212 | ||||||||
\(412\) | 21.6857 | 1.06838 | ||||||||
\(413\) | −57.8761 | −2.84790 | ||||||||
\(414\) | −6.02359 | −0.296043 | ||||||||
\(415\) | −23.4959 | −1.15337 | ||||||||
\(416\) | 20.3041 | 0.995492 | ||||||||
\(417\) | 15.2131 | 0.744989 | ||||||||
\(418\) | −33.7734 | −1.65191 | ||||||||
\(419\) | −24.2444 | −1.18442 | −0.592209 | − | 0.805784i | \(-0.701744\pi\) | ||||
−0.592209 | + | 0.805784i | \(0.701744\pi\) | |||||||
\(420\) | 32.0214 | 1.56248 | ||||||||
\(421\) | −24.1595 | −1.17746 | −0.588731 | − | 0.808329i | \(-0.700372\pi\) | ||||
−0.588731 | + | 0.808329i | \(0.700372\pi\) | |||||||
\(422\) | −42.2054 | −2.05453 | ||||||||
\(423\) | −12.0460 | −0.585694 | ||||||||
\(424\) | 48.8340 | 2.37159 | ||||||||
\(425\) | −3.14261 | −0.152439 | ||||||||
\(426\) | 15.6261 | 0.757085 | ||||||||
\(427\) | 26.1701 | 1.26646 | ||||||||
\(428\) | −38.4770 | −1.85986 | ||||||||
\(429\) | −9.88950 | −0.477469 | ||||||||
\(430\) | −2.89238 | −0.139483 | ||||||||
\(431\) | −20.5292 | −0.988856 | −0.494428 | − | 0.869219i | \(-0.664622\pi\) | ||||
−0.494428 | + | 0.869219i | \(0.664622\pi\) | |||||||
\(432\) | 5.42114 | 0.260824 | ||||||||
\(433\) | 30.8535 | 1.48272 | 0.741361 | − | 0.671106i | \(-0.234181\pi\) | ||||
0.741361 | + | 0.671106i | \(0.234181\pi\) | |||||||
\(434\) | −32.8278 | −1.57578 | ||||||||
\(435\) | 1.99248 | 0.0955323 | ||||||||
\(436\) | −11.8621 | −0.568093 | ||||||||
\(437\) | −5.13540 | −0.245660 | ||||||||
\(438\) | 13.9200 | 0.665124 | ||||||||
\(439\) | 27.3357 | 1.30466 | 0.652332 | − | 0.757933i | \(-0.273791\pi\) | ||||
0.652332 | + | 0.757933i | \(0.273791\pi\) | |||||||
\(440\) | 26.1443 | 1.24638 | ||||||||
\(441\) | −53.4030 | −2.54300 | ||||||||
\(442\) | 24.0924 | 1.14596 | ||||||||
\(443\) | 24.8170 | 1.17909 | 0.589547 | − | 0.807734i | \(-0.299306\pi\) | ||||
0.589547 | + | 0.807734i | \(0.299306\pi\) | |||||||
\(444\) | −10.2960 | −0.488628 | ||||||||
\(445\) | −38.8734 | −1.84278 | ||||||||
\(446\) | 10.5770 | 0.500835 | ||||||||
\(447\) | −2.81399 | −0.133097 | ||||||||
\(448\) | −62.8670 | −2.97019 | ||||||||
\(449\) | −12.6673 | −0.597809 | −0.298904 | − | 0.954283i | \(-0.596621\pi\) | ||||
−0.298904 | + | 0.954283i | \(0.596621\pi\) | |||||||
\(450\) | 9.85611 | 0.464622 | ||||||||
\(451\) | 10.4426 | 0.491721 | ||||||||
\(452\) | 14.8256 | 0.697339 | ||||||||
\(453\) | 10.4066 | 0.488944 | ||||||||
\(454\) | −28.7383 | −1.34875 | ||||||||
\(455\) | −72.4629 | −3.39711 | ||||||||
\(456\) | 12.3983 | 0.580601 | ||||||||
\(457\) | 41.3665 | 1.93504 | 0.967521 | − | 0.252792i | \(-0.0813488\pi\) | ||||
0.967521 | + | 0.252792i | \(0.0813488\pi\) | |||||||
\(458\) | 61.5222 | 2.87475 | ||||||||
\(459\) | −7.09391 | −0.331115 | ||||||||
\(460\) | 9.12754 | 0.425574 | ||||||||
\(461\) | −0.440990 | −0.0205389 | −0.0102695 | − | 0.999947i | \(-0.503269\pi\) | ||||
−0.0102695 | + | 0.999947i | \(0.503269\pi\) | |||||||
\(462\) | 23.0721 | 1.07341 | ||||||||
\(463\) | 2.61481 | 0.121521 | 0.0607603 | − | 0.998152i | \(-0.480647\pi\) | ||||
0.0607603 | + | 0.998152i | \(0.480647\pi\) | |||||||
\(464\) | 1.70838 | 0.0793097 | ||||||||
\(465\) | 4.52088 | 0.209651 | ||||||||
\(466\) | 46.8046 | 2.16818 | ||||||||
\(467\) | 1.89119 | 0.0875140 | 0.0437570 | − | 0.999042i | \(-0.486067\pi\) | ||||
0.0437570 | + | 0.999042i | \(0.486067\pi\) | |||||||
\(468\) | −48.2980 | −2.23257 | ||||||||
\(469\) | 69.9230 | 3.22875 | ||||||||
\(470\) | 28.5565 | 1.31722 | ||||||||
\(471\) | 0.375910 | 0.0173210 | ||||||||
\(472\) | 39.8290 | 1.83328 | ||||||||
\(473\) | −1.33210 | −0.0612499 | ||||||||
\(474\) | −14.1436 | −0.649635 | ||||||||
\(475\) | 8.40282 | 0.385548 | ||||||||
\(476\) | −35.9274 | −1.64673 | ||||||||
\(477\) | 34.3879 | 1.57451 | ||||||||
\(478\) | −12.2926 | −0.562251 | ||||||||
\(479\) | 0.667933 | 0.0305186 | 0.0152593 | − | 0.999884i | \(-0.495143\pi\) | ||||
0.0152593 | + | 0.999884i | \(0.495143\pi\) | |||||||
\(480\) | 6.52346 | 0.297754 | ||||||||
\(481\) | 23.2995 | 1.06236 | ||||||||
\(482\) | 3.89019 | 0.177193 | ||||||||
\(483\) | 3.50821 | 0.159629 | ||||||||
\(484\) | −11.3287 | −0.514942 | ||||||||
\(485\) | 20.8100 | 0.944933 | ||||||||
\(486\) | 34.2565 | 1.55390 | ||||||||
\(487\) | 13.2822 | 0.601875 | 0.300938 | − | 0.953644i | \(-0.402700\pi\) | ||||
0.300938 | + | 0.953644i | \(0.402700\pi\) | |||||||
\(488\) | −18.0096 | −0.815258 | ||||||||
\(489\) | 9.74327 | 0.440606 | ||||||||
\(490\) | 126.599 | 5.71916 | ||||||||
\(491\) | 11.1947 | 0.505210 | 0.252605 | − | 0.967570i | \(-0.418713\pi\) | ||||
0.252605 | + | 0.967570i | \(0.418713\pi\) | |||||||
\(492\) | −8.80178 | −0.396815 | ||||||||
\(493\) | −2.23553 | −0.100683 | ||||||||
\(494\) | −64.4190 | −2.89835 | ||||||||
\(495\) | 18.4102 | 0.827478 | ||||||||
\(496\) | 3.87627 | 0.174049 | ||||||||
\(497\) | 52.7317 | 2.36534 | ||||||||
\(498\) | 14.2693 | 0.639421 | ||||||||
\(499\) | 8.73848 | 0.391188 | 0.195594 | − | 0.980685i | \(-0.437336\pi\) | ||||
0.195594 | + | 0.980685i | \(0.437336\pi\) | |||||||
\(500\) | 30.7027 | 1.37307 | ||||||||
\(501\) | −10.6915 | −0.477660 | ||||||||
\(502\) | −59.7925 | −2.66867 | ||||||||
\(503\) | 30.5405 | 1.36173 | 0.680866 | − | 0.732408i | \(-0.261604\pi\) | ||||
0.680866 | + | 0.732408i | \(0.261604\pi\) | |||||||
\(504\) | 49.0753 | 2.18599 | ||||||||
\(505\) | −28.2181 | −1.25569 | ||||||||
\(506\) | 6.57659 | 0.292365 | ||||||||
\(507\) | −10.2247 | −0.454093 | ||||||||
\(508\) | 51.1987 | 2.27157 | ||||||||
\(509\) | −15.0212 | −0.665804 | −0.332902 | − | 0.942961i | \(-0.608028\pi\) | ||||
−0.332902 | + | 0.942961i | \(0.608028\pi\) | |||||||
\(510\) | 7.74057 | 0.342758 | ||||||||
\(511\) | 46.9745 | 2.07803 | ||||||||
\(512\) | 16.2585 | 0.718530 | ||||||||
\(513\) | 18.9679 | 0.837455 | ||||||||
\(514\) | 27.7177 | 1.22258 | ||||||||
\(515\) | −15.7668 | −0.694766 | ||||||||
\(516\) | 1.12279 | 0.0494282 | ||||||||
\(517\) | 13.1518 | 0.578417 | ||||||||
\(518\) | −54.3574 | −2.38833 | ||||||||
\(519\) | 2.28916 | 0.100483 | ||||||||
\(520\) | 49.8672 | 2.18682 | ||||||||
\(521\) | 35.3551 | 1.54893 | 0.774467 | − | 0.632614i | \(-0.218018\pi\) | ||||
0.774467 | + | 0.632614i | \(0.218018\pi\) | |||||||
\(522\) | 7.01126 | 0.306874 | ||||||||
\(523\) | −10.0585 | −0.439829 | −0.219914 | − | 0.975519i | \(-0.570578\pi\) | ||||
−0.219914 | + | 0.975519i | \(0.570578\pi\) | |||||||
\(524\) | 76.9025 | 3.35950 | ||||||||
\(525\) | −5.74032 | −0.250528 | ||||||||
\(526\) | 14.0251 | 0.611523 | ||||||||
\(527\) | −5.07235 | −0.220955 | ||||||||
\(528\) | −2.72432 | −0.118561 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −81.5211 | −3.54105 | ||||||||
\(531\) | 28.0467 | 1.21712 | ||||||||
\(532\) | 96.0639 | 4.16490 | ||||||||
\(533\) | 19.9180 | 0.862745 | ||||||||
\(534\) | 23.6082 | 1.02163 | ||||||||
\(535\) | 27.9750 | 1.20947 | ||||||||
\(536\) | −48.1194 | −2.07844 | ||||||||
\(537\) | −8.46113 | −0.365125 | ||||||||
\(538\) | 13.6425 | 0.588169 | ||||||||
\(539\) | 58.3057 | 2.51140 | ||||||||
\(540\) | −33.7132 | −1.45078 | ||||||||
\(541\) | −17.3320 | −0.745162 | −0.372581 | − | 0.928000i | \(-0.621527\pi\) | ||||
−0.372581 | + | 0.928000i | \(0.621527\pi\) | |||||||
\(542\) | 42.4256 | 1.82233 | ||||||||
\(543\) | 0.649169 | 0.0278585 | ||||||||
\(544\) | −7.31921 | −0.313808 | ||||||||
\(545\) | 8.62446 | 0.369431 | ||||||||
\(546\) | 44.0074 | 1.88334 | ||||||||
\(547\) | −28.1777 | −1.20479 | −0.602396 | − | 0.798197i | \(-0.705787\pi\) | ||||
−0.602396 | + | 0.798197i | \(0.705787\pi\) | |||||||
\(548\) | −55.6938 | −2.37912 | ||||||||
\(549\) | −12.6820 | −0.541254 | ||||||||
\(550\) | −10.7610 | −0.458849 | ||||||||
\(551\) | 5.97744 | 0.254648 | ||||||||
\(552\) | −2.41427 | −0.102758 | ||||||||
\(553\) | −47.7288 | −2.02964 | ||||||||
\(554\) | 13.9370 | 0.592127 | ||||||||
\(555\) | 7.48582 | 0.317755 | ||||||||
\(556\) | −81.1181 | −3.44017 | ||||||||
\(557\) | −25.6868 | −1.08838 | −0.544192 | − | 0.838960i | \(-0.683164\pi\) | ||||
−0.544192 | + | 0.838960i | \(0.683164\pi\) | |||||||
\(558\) | 15.9083 | 0.673453 | ||||||||
\(559\) | −2.54083 | −0.107466 | ||||||||
\(560\) | −19.9618 | −0.843540 | ||||||||
\(561\) | 3.56495 | 0.150512 | ||||||||
\(562\) | 55.6942 | 2.34932 | ||||||||
\(563\) | −7.37845 | −0.310965 | −0.155482 | − | 0.987839i | \(-0.549693\pi\) | ||||
−0.155482 | + | 0.987839i | \(0.549693\pi\) | |||||||
\(564\) | −11.0854 | −0.466778 | ||||||||
\(565\) | −10.7791 | −0.453480 | ||||||||
\(566\) | −65.1228 | −2.73732 | ||||||||
\(567\) | 27.5642 | 1.15759 | ||||||||
\(568\) | −36.2887 | −1.52264 | ||||||||
\(569\) | −34.5638 | −1.44899 | −0.724495 | − | 0.689280i | \(-0.757927\pi\) | ||||
−0.724495 | + | 0.689280i | \(0.757927\pi\) | |||||||
\(570\) | −20.6970 | −0.866902 | ||||||||
\(571\) | 21.4148 | 0.896179 | 0.448090 | − | 0.893989i | \(-0.352105\pi\) | ||||
0.448090 | + | 0.893989i | \(0.352105\pi\) | |||||||
\(572\) | 52.7320 | 2.20483 | ||||||||
\(573\) | −14.6682 | −0.612771 | ||||||||
\(574\) | −46.4685 | −1.93956 | ||||||||
\(575\) | −1.63625 | −0.0682365 | ||||||||
\(576\) | 30.4653 | 1.26939 | ||||||||
\(577\) | 3.75037 | 0.156130 | 0.0780649 | − | 0.996948i | \(-0.475126\pi\) | ||||
0.0780649 | + | 0.996948i | \(0.475126\pi\) | |||||||
\(578\) | 31.3399 | 1.30357 | ||||||||
\(579\) | 14.2440 | 0.591961 | ||||||||
\(580\) | −10.6242 | −0.441144 | ||||||||
\(581\) | 48.1530 | 1.99772 | ||||||||
\(582\) | −12.6381 | −0.523866 | ||||||||
\(583\) | −37.5449 | −1.55495 | ||||||||
\(584\) | −32.3267 | −1.33769 | ||||||||
\(585\) | 35.1154 | 1.45184 | ||||||||
\(586\) | −46.8414 | −1.93500 | ||||||||
\(587\) | 16.5557 | 0.683328 | 0.341664 | − | 0.939822i | \(-0.389009\pi\) | ||||
0.341664 | + | 0.939822i | \(0.389009\pi\) | |||||||
\(588\) | −49.1444 | −2.02668 | ||||||||
\(589\) | 13.5626 | 0.558838 | ||||||||
\(590\) | −66.4884 | −2.73729 | ||||||||
\(591\) | 12.9224 | 0.531555 | ||||||||
\(592\) | 6.41845 | 0.263797 | ||||||||
\(593\) | 11.3051 | 0.464246 | 0.232123 | − | 0.972686i | \(-0.425433\pi\) | ||||
0.232123 | + | 0.972686i | \(0.425433\pi\) | |||||||
\(594\) | −24.2910 | −0.996674 | ||||||||
\(595\) | 26.1213 | 1.07087 | ||||||||
\(596\) | 15.0045 | 0.614610 | ||||||||
\(597\) | 3.03375 | 0.124163 | ||||||||
\(598\) | 12.5441 | 0.512966 | ||||||||
\(599\) | 29.4591 | 1.20366 | 0.601832 | − | 0.798622i | \(-0.294438\pi\) | ||||
0.601832 | + | 0.798622i | \(0.294438\pi\) | |||||||
\(600\) | 3.95036 | 0.161273 | ||||||||
\(601\) | −39.5561 | −1.61353 | −0.806763 | − | 0.590875i | \(-0.798783\pi\) | ||||
−0.806763 | + | 0.590875i | \(0.798783\pi\) | |||||||
\(602\) | 5.92772 | 0.241596 | ||||||||
\(603\) | −33.8846 | −1.37989 | ||||||||
\(604\) | −55.4892 | −2.25782 | ||||||||
\(605\) | 8.23665 | 0.334867 | ||||||||
\(606\) | 17.1371 | 0.696147 | ||||||||
\(607\) | −5.25178 | −0.213163 | −0.106582 | − | 0.994304i | \(-0.533991\pi\) | ||||
−0.106582 | + | 0.994304i | \(0.533991\pi\) | |||||||
\(608\) | 19.5704 | 0.793683 | ||||||||
\(609\) | −4.08345 | −0.165470 | ||||||||
\(610\) | 30.0644 | 1.21727 | ||||||||
\(611\) | 25.0857 | 1.01486 | ||||||||
\(612\) | 17.4104 | 0.703773 | ||||||||
\(613\) | 21.1096 | 0.852610 | 0.426305 | − | 0.904580i | \(-0.359815\pi\) | ||||
0.426305 | + | 0.904580i | \(0.359815\pi\) | |||||||
\(614\) | 49.8680 | 2.01251 | ||||||||
\(615\) | 6.39941 | 0.258049 | ||||||||
\(616\) | −53.5807 | −2.15883 | ||||||||
\(617\) | 9.37767 | 0.377531 | 0.188765 | − | 0.982022i | \(-0.439551\pi\) | ||||
0.188765 | + | 0.982022i | \(0.439551\pi\) | |||||||
\(618\) | 9.57531 | 0.385175 | ||||||||
\(619\) | 19.2082 | 0.772044 | 0.386022 | − | 0.922489i | \(-0.373849\pi\) | ||||
0.386022 | + | 0.922489i | \(0.373849\pi\) | |||||||
\(620\) | −24.1059 | −0.968115 | ||||||||
\(621\) | −3.69357 | −0.148218 | ||||||||
\(622\) | −41.8720 | −1.67892 | ||||||||
\(623\) | 79.6681 | 3.19184 | ||||||||
\(624\) | −5.19634 | −0.208020 | ||||||||
\(625\) | −30.5039 | −1.22016 | ||||||||
\(626\) | 72.3914 | 2.89334 | ||||||||
\(627\) | −9.53209 | −0.380675 | ||||||||
\(628\) | −2.00440 | −0.0799842 | ||||||||
\(629\) | −8.39896 | −0.334889 | ||||||||
\(630\) | −81.9238 | −3.26392 | ||||||||
\(631\) | −18.4714 | −0.735335 | −0.367668 | − | 0.929957i | \(-0.619844\pi\) | ||||
−0.367668 | + | 0.929957i | \(0.619844\pi\) | |||||||
\(632\) | 32.8459 | 1.30654 | ||||||||
\(633\) | −11.9119 | −0.473456 | ||||||||
\(634\) | −40.4259 | −1.60552 | ||||||||
\(635\) | −37.2244 | −1.47721 | ||||||||
\(636\) | 31.6456 | 1.25483 | ||||||||
\(637\) | 111.212 | 4.40636 | ||||||||
\(638\) | −7.65493 | −0.303062 | ||||||||
\(639\) | −25.5537 | −1.01089 | ||||||||
\(640\) | −52.5878 | −2.07871 | ||||||||
\(641\) | −14.1575 | −0.559188 | −0.279594 | − | 0.960118i | \(-0.590200\pi\) | ||||
−0.279594 | + | 0.960118i | \(0.590200\pi\) | |||||||
\(642\) | −16.9895 | −0.670522 | ||||||||
\(643\) | −33.8500 | −1.33491 | −0.667456 | − | 0.744649i | \(-0.732617\pi\) | ||||
−0.667456 | + | 0.744649i | \(0.732617\pi\) | |||||||
\(644\) | −18.7062 | −0.737128 | ||||||||
\(645\) | −0.816335 | −0.0321432 | ||||||||
\(646\) | 23.2217 | 0.913645 | ||||||||
\(647\) | −17.8895 | −0.703310 | −0.351655 | − | 0.936130i | \(-0.614381\pi\) | ||||
−0.351655 | + | 0.936130i | \(0.614381\pi\) | |||||||
\(648\) | −18.9690 | −0.745174 | ||||||||
\(649\) | −30.6215 | −1.20200 | ||||||||
\(650\) | −20.5253 | −0.805069 | ||||||||
\(651\) | −9.26520 | −0.363132 | ||||||||
\(652\) | −51.9523 | −2.03461 | ||||||||
\(653\) | 40.8799 | 1.59975 | 0.799877 | − | 0.600164i | \(-0.204898\pi\) | ||||
0.799877 | + | 0.600164i | \(0.204898\pi\) | |||||||
\(654\) | −5.23771 | −0.204811 | ||||||||
\(655\) | −55.9126 | −2.18469 | ||||||||
\(656\) | 5.48694 | 0.214229 | ||||||||
\(657\) | −22.7638 | −0.888100 | ||||||||
\(658\) | −58.5245 | −2.28152 | ||||||||
\(659\) | −30.1956 | −1.17625 | −0.588126 | − | 0.808769i | \(-0.700134\pi\) | ||||
−0.588126 | + | 0.808769i | \(0.700134\pi\) | |||||||
\(660\) | 16.9421 | 0.659471 | ||||||||
\(661\) | −0.769647 | −0.0299358 | −0.0149679 | − | 0.999888i | \(-0.504765\pi\) | ||||
−0.0149679 | + | 0.999888i | \(0.504765\pi\) | |||||||
\(662\) | 62.5271 | 2.43018 | ||||||||
\(663\) | 6.79975 | 0.264080 | ||||||||
\(664\) | −33.1378 | −1.28599 | ||||||||
\(665\) | −69.8441 | −2.70844 | ||||||||
\(666\) | 26.3415 | 1.02071 | ||||||||
\(667\) | −1.16397 | −0.0450690 | ||||||||
\(668\) | 57.0083 | 2.20572 | ||||||||
\(669\) | 2.98521 | 0.115415 | ||||||||
\(670\) | 80.3281 | 3.10334 | ||||||||
\(671\) | 13.8463 | 0.534529 | ||||||||
\(672\) | −13.3693 | −0.515734 | ||||||||
\(673\) | 47.5846 | 1.83425 | 0.917125 | − | 0.398599i | \(-0.130503\pi\) | ||||
0.917125 | + | 0.398599i | \(0.130503\pi\) | |||||||
\(674\) | 6.37768 | 0.245659 | ||||||||
\(675\) | 6.04361 | 0.232619 | ||||||||
\(676\) | 54.5191 | 2.09689 | ||||||||
\(677\) | −26.1501 | −1.00503 | −0.502516 | − | 0.864568i | \(-0.667592\pi\) | ||||
−0.502516 | + | 0.864568i | \(0.667592\pi\) | |||||||
\(678\) | 6.54625 | 0.251407 | ||||||||
\(679\) | −42.6485 | −1.63670 | ||||||||
\(680\) | −17.9761 | −0.689351 | ||||||||
\(681\) | −8.11099 | −0.310814 | ||||||||
\(682\) | −17.3688 | −0.665085 | ||||||||
\(683\) | −16.6038 | −0.635327 | −0.317663 | − | 0.948204i | \(-0.602898\pi\) | ||||
−0.317663 | + | 0.948204i | \(0.602898\pi\) | |||||||
\(684\) | −46.5525 | −1.77998 | ||||||||
\(685\) | 40.4926 | 1.54714 | ||||||||
\(686\) | −172.445 | −6.58397 | ||||||||
\(687\) | 17.3638 | 0.662471 | ||||||||
\(688\) | −0.699938 | −0.0266849 | ||||||||
\(689\) | −71.6126 | −2.72822 | ||||||||
\(690\) | 4.03026 | 0.153429 | ||||||||
\(691\) | 12.2928 | 0.467641 | 0.233820 | − | 0.972280i | \(-0.424877\pi\) | ||||
0.233820 | + | 0.972280i | \(0.424877\pi\) | |||||||
\(692\) | −12.2061 | −0.464006 | ||||||||
\(693\) | −37.7304 | −1.43326 | ||||||||
\(694\) | 64.9224 | 2.46442 | ||||||||
\(695\) | 58.9776 | 2.23715 | ||||||||
\(696\) | 2.81013 | 0.106518 | ||||||||
\(697\) | −7.18003 | −0.271963 | ||||||||
\(698\) | −2.35439 | −0.0891151 | ||||||||
\(699\) | 13.2100 | 0.499647 | ||||||||
\(700\) | 30.6081 | 1.15688 | ||||||||
\(701\) | −17.0118 | −0.642526 | −0.321263 | − | 0.946990i | \(-0.604107\pi\) | ||||
−0.321263 | + | 0.946990i | \(0.604107\pi\) | |||||||
\(702\) | −46.3325 | −1.74871 | ||||||||
\(703\) | 22.4574 | 0.846998 | ||||||||
\(704\) | −33.2622 | −1.25362 | ||||||||
\(705\) | 8.05970 | 0.303546 | ||||||||
\(706\) | 18.5095 | 0.696614 | ||||||||
\(707\) | 57.8308 | 2.17495 | ||||||||
\(708\) | 25.8101 | 0.970004 | ||||||||
\(709\) | −51.7564 | −1.94375 | −0.971876 | − | 0.235491i | \(-0.924330\pi\) | ||||
−0.971876 | + | 0.235491i | \(0.924330\pi\) | |||||||
\(710\) | 60.5785 | 2.27347 | ||||||||
\(711\) | 23.1293 | 0.867418 | ||||||||
\(712\) | −54.8257 | −2.05468 | ||||||||
\(713\) | −2.64100 | −0.0989064 | ||||||||
\(714\) | −15.8637 | −0.593685 | ||||||||
\(715\) | −38.3392 | −1.43381 | ||||||||
\(716\) | 45.1158 | 1.68606 | ||||||||
\(717\) | −3.46943 | −0.129568 | ||||||||
\(718\) | −29.6311 | −1.10582 | ||||||||
\(719\) | −26.0533 | −0.971625 | −0.485813 | − | 0.874063i | \(-0.661476\pi\) | ||||
−0.485813 | + | 0.874063i | \(0.661476\pi\) | |||||||
\(720\) | 9.67346 | 0.360509 | ||||||||
\(721\) | 32.3128 | 1.20339 | ||||||||
\(722\) | −17.3575 | −0.645978 | ||||||||
\(723\) | 1.09795 | 0.0408333 | ||||||||
\(724\) | −3.46144 | −0.128644 | ||||||||
\(725\) | 1.90454 | 0.0707330 | ||||||||
\(726\) | −5.00220 | −0.185649 | ||||||||
\(727\) | 48.0771 | 1.78308 | 0.891540 | − | 0.452942i | \(-0.149626\pi\) | ||||
0.891540 | + | 0.452942i | \(0.149626\pi\) | |||||||
\(728\) | −102.199 | −3.78775 | ||||||||
\(729\) | −5.99450 | −0.222018 | ||||||||
\(730\) | 53.9646 | 1.99732 | ||||||||
\(731\) | 0.915914 | 0.0338763 | ||||||||
\(732\) | −11.6707 | −0.431361 | ||||||||
\(733\) | 29.0280 | 1.07218 | 0.536088 | − | 0.844162i | \(-0.319902\pi\) | ||||
0.536088 | + | 0.844162i | \(0.319902\pi\) | |||||||
\(734\) | −20.9444 | −0.773071 | ||||||||
\(735\) | 35.7309 | 1.31795 | ||||||||
\(736\) | −3.81087 | −0.140471 | ||||||||
\(737\) | 36.9954 | 1.36274 | ||||||||
\(738\) | 22.5186 | 0.828921 | ||||||||
\(739\) | 23.6526 | 0.870077 | 0.435038 | − | 0.900412i | \(-0.356735\pi\) | ||||
0.435038 | + | 0.900412i | \(0.356735\pi\) | |||||||
\(740\) | −39.9153 | −1.46732 | ||||||||
\(741\) | −18.1814 | −0.667911 | ||||||||
\(742\) | 167.071 | 6.13338 | ||||||||
\(743\) | 7.90002 | 0.289824 | 0.144912 | − | 0.989445i | \(-0.453710\pi\) | ||||
0.144912 | + | 0.989445i | \(0.453710\pi\) | |||||||
\(744\) | 6.37610 | 0.233759 | ||||||||
\(745\) | −10.9092 | −0.399681 | ||||||||
\(746\) | 11.6933 | 0.428122 | ||||||||
\(747\) | −23.3349 | −0.853779 | ||||||||
\(748\) | −19.0088 | −0.695029 | ||||||||
\(749\) | −57.3328 | −2.09489 | ||||||||
\(750\) | 13.5568 | 0.495023 | ||||||||
\(751\) | −11.9975 | −0.437794 | −0.218897 | − | 0.975748i | \(-0.570246\pi\) | ||||
−0.218897 | + | 0.975748i | \(0.570246\pi\) | |||||||
\(752\) | 6.91050 | 0.252000 | ||||||||
\(753\) | −16.8756 | −0.614982 | ||||||||
\(754\) | −14.6009 | −0.531734 | ||||||||
\(755\) | 40.3439 | 1.46826 | ||||||||
\(756\) | 69.0926 | 2.51287 | ||||||||
\(757\) | −10.8266 | −0.393500 | −0.196750 | − | 0.980454i | \(-0.563039\pi\) | ||||
−0.196750 | + | 0.980454i | \(0.563039\pi\) | |||||||
\(758\) | −58.4144 | −2.12171 | ||||||||
\(759\) | 1.85615 | 0.0673741 | ||||||||
\(760\) | 48.0651 | 1.74350 | ||||||||
\(761\) | −11.9901 | −0.434639 | −0.217320 | − | 0.976101i | \(-0.569731\pi\) | ||||
−0.217320 | + | 0.976101i | \(0.569731\pi\) | |||||||
\(762\) | 22.6068 | 0.818956 | ||||||||
\(763\) | −17.6752 | −0.639884 | ||||||||
\(764\) | 78.2123 | 2.82962 | ||||||||
\(765\) | −12.6584 | −0.457664 | ||||||||
\(766\) | 74.7421 | 2.70054 | ||||||||
\(767\) | −58.4071 | −2.10896 | ||||||||
\(768\) | 16.1118 | 0.581383 | ||||||||
\(769\) | 21.8900 | 0.789373 | 0.394686 | − | 0.918816i | \(-0.370853\pi\) | ||||
0.394686 | + | 0.918816i | \(0.370853\pi\) | |||||||
\(770\) | 89.4449 | 3.22337 | ||||||||
\(771\) | 7.82296 | 0.281737 | ||||||||
\(772\) | −75.9507 | −2.73353 | ||||||||
\(773\) | 15.3916 | 0.553597 | 0.276798 | − | 0.960928i | \(-0.410727\pi\) | ||||
0.276798 | + | 0.960928i | \(0.410727\pi\) | |||||||
\(774\) | −2.87257 | −0.103252 | ||||||||
\(775\) | 4.32135 | 0.155227 | ||||||||
\(776\) | 29.3497 | 1.05359 | ||||||||
\(777\) | −15.3416 | −0.550378 | ||||||||
\(778\) | 69.6624 | 2.49752 | ||||||||
\(779\) | 19.1982 | 0.687847 | ||||||||
\(780\) | 32.3152 | 1.15707 | ||||||||
\(781\) | 27.8997 | 0.998329 | ||||||||
\(782\) | −4.52188 | −0.161702 | ||||||||
\(783\) | 4.29919 | 0.153640 | ||||||||
\(784\) | 30.6361 | 1.09415 | ||||||||
\(785\) | 1.45731 | 0.0520138 | ||||||||
\(786\) | 33.9563 | 1.21118 | ||||||||
\(787\) | 23.5168 | 0.838285 | 0.419143 | − | 0.907920i | \(-0.362331\pi\) | ||||
0.419143 | + | 0.907920i | \(0.362331\pi\) | |||||||
\(788\) | −68.9036 | −2.45459 | ||||||||
\(789\) | 3.95839 | 0.140922 | ||||||||
\(790\) | −54.8312 | −1.95081 | ||||||||
\(791\) | 22.0910 | 0.785464 | ||||||||
\(792\) | 25.9652 | 0.922632 | ||||||||
\(793\) | 26.4102 | 0.937854 | ||||||||
\(794\) | 44.0863 | 1.56456 | ||||||||
\(795\) | −23.0082 | −0.816018 | ||||||||
\(796\) | −16.1763 | −0.573353 | ||||||||
\(797\) | −36.6206 | −1.29717 | −0.648584 | − | 0.761143i | \(-0.724639\pi\) | ||||
−0.648584 | + | 0.761143i | \(0.724639\pi\) | |||||||
\(798\) | 42.4170 | 1.50154 | ||||||||
\(799\) | −9.04285 | −0.319913 | ||||||||
\(800\) | 6.23555 | 0.220460 | ||||||||
\(801\) | −38.6071 | −1.36411 | ||||||||
\(802\) | 38.7514 | 1.36836 | ||||||||
\(803\) | 24.8536 | 0.877065 | ||||||||
\(804\) | −31.1825 | −1.09972 | ||||||||
\(805\) | 13.6005 | 0.479355 | ||||||||
\(806\) | −33.1290 | −1.16692 | ||||||||
\(807\) | 3.85040 | 0.135541 | ||||||||
\(808\) | −39.7978 | −1.40008 | ||||||||
\(809\) | 2.63889 | 0.0927784 | 0.0463892 | − | 0.998923i | \(-0.485229\pi\) | ||||
0.0463892 | + | 0.998923i | \(0.485229\pi\) | |||||||
\(810\) | 31.6659 | 1.11263 | ||||||||
\(811\) | 39.0416 | 1.37093 | 0.685467 | − | 0.728103i | \(-0.259598\pi\) | ||||
0.685467 | + | 0.728103i | \(0.259598\pi\) | |||||||
\(812\) | 21.7734 | 0.764097 | ||||||||
\(813\) | 11.9740 | 0.419948 | ||||||||
\(814\) | −28.7598 | −1.00803 | ||||||||
\(815\) | 37.7723 | 1.32311 | ||||||||
\(816\) | 1.87317 | 0.0655740 | ||||||||
\(817\) | −2.44900 | −0.0856798 | ||||||||
\(818\) | −67.4395 | −2.35797 | ||||||||
\(819\) | −71.9664 | −2.51471 | ||||||||
\(820\) | −34.1224 | −1.19161 | ||||||||
\(821\) | 54.1788 | 1.89085 | 0.945426 | − | 0.325836i | \(-0.105646\pi\) | ||||
0.945426 | + | 0.325836i | \(0.105646\pi\) | |||||||
\(822\) | −24.5915 | −0.857729 | ||||||||
\(823\) | −15.2423 | −0.531312 | −0.265656 | − | 0.964068i | \(-0.585589\pi\) | ||||
−0.265656 | + | 0.964068i | \(0.585589\pi\) | |||||||
\(824\) | −22.2369 | −0.774660 | ||||||||
\(825\) | −3.03714 | −0.105739 | ||||||||
\(826\) | 136.263 | 4.74120 | ||||||||
\(827\) | 36.5122 | 1.26965 | 0.634827 | − | 0.772654i | \(-0.281071\pi\) | ||||
0.634827 | + | 0.772654i | \(0.281071\pi\) | |||||||
\(828\) | 9.06501 | 0.315031 | ||||||||
\(829\) | 5.61321 | 0.194955 | 0.0974775 | − | 0.995238i | \(-0.468923\pi\) | ||||
0.0974775 | + | 0.995238i | \(0.468923\pi\) | |||||||
\(830\) | 55.3185 | 1.92013 | ||||||||
\(831\) | 3.93354 | 0.136453 | ||||||||
\(832\) | −63.4439 | −2.19952 | ||||||||
\(833\) | −40.0894 | −1.38902 | ||||||||
\(834\) | −35.8176 | −1.24026 | ||||||||
\(835\) | −41.4483 | −1.43438 | ||||||||
\(836\) | 50.8263 | 1.75786 | ||||||||
\(837\) | 9.75472 | 0.337172 | ||||||||
\(838\) | 57.0810 | 1.97183 | ||||||||
\(839\) | 22.5889 | 0.779856 | 0.389928 | − | 0.920845i | \(-0.372500\pi\) | ||||
0.389928 | + | 0.920845i | \(0.372500\pi\) | |||||||
\(840\) | −32.8353 | −1.13293 | ||||||||
\(841\) | −27.6452 | −0.953282 | ||||||||
\(842\) | 56.8810 | 1.96025 | ||||||||
\(843\) | 15.7189 | 0.541389 | ||||||||
\(844\) | 63.5157 | 2.18630 | ||||||||
\(845\) | −39.6386 | −1.36361 | ||||||||
\(846\) | 28.3609 | 0.975068 | ||||||||
\(847\) | −16.8804 | −0.580017 | ||||||||
\(848\) | −19.7276 | −0.677448 | ||||||||
\(849\) | −18.3800 | −0.630801 | ||||||||
\(850\) | 7.39894 | 0.253782 | ||||||||
\(851\) | −4.37306 | −0.149907 | ||||||||
\(852\) | −23.5160 | −0.805643 | ||||||||
\(853\) | 25.3916 | 0.869390 | 0.434695 | − | 0.900578i | \(-0.356856\pi\) | ||||
0.434695 | + | 0.900578i | \(0.356856\pi\) | |||||||
\(854\) | −61.6147 | −2.10841 | ||||||||
\(855\) | 33.8464 | 1.15752 | ||||||||
\(856\) | 39.4551 | 1.34855 | ||||||||
\(857\) | 29.8582 | 1.01994 | 0.509969 | − | 0.860193i | \(-0.329657\pi\) | ||||
0.509969 | + | 0.860193i | \(0.329657\pi\) | |||||||
\(858\) | 23.2838 | 0.794895 | ||||||||
\(859\) | 6.04647 | 0.206303 | 0.103152 | − | 0.994666i | \(-0.467107\pi\) | ||||
0.103152 | + | 0.994666i | \(0.467107\pi\) | |||||||
\(860\) | 4.35280 | 0.148429 | ||||||||
\(861\) | −13.1151 | −0.446962 | ||||||||
\(862\) | 48.3338 | 1.64626 | ||||||||
\(863\) | 46.7367 | 1.59094 | 0.795468 | − | 0.605996i | \(-0.207225\pi\) | ||||
0.795468 | + | 0.605996i | \(0.207225\pi\) | |||||||
\(864\) | 14.0757 | 0.478865 | ||||||||
\(865\) | 8.87454 | 0.301743 | ||||||||
\(866\) | −72.6412 | −2.46845 | ||||||||
\(867\) | 8.84527 | 0.300401 | ||||||||
\(868\) | 49.4032 | 1.67685 | ||||||||
\(869\) | −25.2527 | −0.856640 | ||||||||
\(870\) | −4.69109 | −0.159043 | ||||||||
\(871\) | 70.5646 | 2.39099 | ||||||||
\(872\) | 12.1636 | 0.411913 | ||||||||
\(873\) | 20.6674 | 0.699486 | ||||||||
\(874\) | 12.0908 | 0.408976 | ||||||||
\(875\) | 45.7487 | 1.54659 | ||||||||
\(876\) | −20.9485 | −0.707784 | ||||||||
\(877\) | −41.0299 | −1.38548 | −0.692740 | − | 0.721187i | \(-0.743597\pi\) | ||||
−0.692740 | + | 0.721187i | \(0.743597\pi\) | |||||||
\(878\) | −64.3591 | −2.17201 | ||||||||
\(879\) | −13.2204 | −0.445911 | ||||||||
\(880\) | −10.5615 | −0.356029 | ||||||||
\(881\) | −5.68596 | −0.191565 | −0.0957824 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957824 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(882\) | 125.732 | 4.23361 | ||||||||
\(883\) | 13.1482 | 0.442471 | 0.221236 | − | 0.975220i | \(-0.428991\pi\) | ||||
0.221236 | + | 0.975220i | \(0.428991\pi\) | |||||||
\(884\) | −36.2571 | −1.21946 | ||||||||
\(885\) | −18.7655 | −0.630794 | ||||||||
\(886\) | −58.4291 | −1.96296 | ||||||||
\(887\) | 9.89477 | 0.332234 | 0.166117 | − | 0.986106i | \(-0.446877\pi\) | ||||
0.166117 | + | 0.986106i | \(0.446877\pi\) | |||||||
\(888\) | 10.5578 | 0.354295 | ||||||||
\(889\) | 76.2887 | 2.55864 | ||||||||
\(890\) | 91.5233 | 3.06787 | ||||||||
\(891\) | 14.5839 | 0.488578 | ||||||||
\(892\) | −15.9175 | −0.532958 | ||||||||
\(893\) | 24.1791 | 0.809122 | ||||||||
\(894\) | 6.62524 | 0.221581 | ||||||||
\(895\) | −32.8018 | −1.09644 | ||||||||
\(896\) | 107.775 | 3.60050 | ||||||||
\(897\) | 3.54040 | 0.118211 | ||||||||
\(898\) | 29.8239 | 0.995237 | ||||||||
\(899\) | 3.07404 | 0.102525 | ||||||||
\(900\) | −14.8326 | −0.494422 | ||||||||
\(901\) | 25.8148 | 0.860017 | ||||||||
\(902\) | −24.5859 | −0.818621 | ||||||||
\(903\) | 1.67302 | 0.0556746 | ||||||||
\(904\) | −15.2025 | −0.505627 | ||||||||
\(905\) | 2.51667 | 0.0836570 | ||||||||
\(906\) | −24.5012 | −0.813998 | ||||||||
\(907\) | 13.1332 | 0.436079 | 0.218040 | − | 0.975940i | \(-0.430034\pi\) | ||||
0.218040 | + | 0.975940i | \(0.430034\pi\) | |||||||
\(908\) | 43.2487 | 1.43526 | ||||||||
\(909\) | −28.0248 | −0.929523 | ||||||||
\(910\) | 170.606 | 5.65554 | ||||||||
\(911\) | 11.6950 | 0.387473 | 0.193736 | − | 0.981054i | \(-0.437939\pi\) | ||||
0.193736 | + | 0.981054i | \(0.437939\pi\) | |||||||
\(912\) | −5.00854 | −0.165849 | ||||||||
\(913\) | 25.4772 | 0.843171 | ||||||||
\(914\) | −97.3930 | −3.22147 | ||||||||
\(915\) | 8.48527 | 0.280514 | ||||||||
\(916\) | −92.5860 | −3.05913 | ||||||||
\(917\) | 114.589 | 3.78405 | ||||||||
\(918\) | 16.7019 | 0.551244 | ||||||||
\(919\) | 2.64499 | 0.0872502 | 0.0436251 | − | 0.999048i | \(-0.486109\pi\) | ||||
0.0436251 | + | 0.999048i | \(0.486109\pi\) | |||||||
\(920\) | −9.35955 | −0.308575 | ||||||||
\(921\) | 14.0746 | 0.463773 | ||||||||
\(922\) | 1.03826 | 0.0341934 | ||||||||
\(923\) | 53.2155 | 1.75161 | ||||||||
\(924\) | −34.7216 | −1.14226 | ||||||||
\(925\) | 7.15543 | 0.235269 | ||||||||
\(926\) | −6.15630 | −0.202309 | ||||||||
\(927\) | −15.6588 | −0.514301 | ||||||||
\(928\) | 4.43573 | 0.145610 | ||||||||
\(929\) | −34.8081 | −1.14202 | −0.571008 | − | 0.820944i | \(-0.693447\pi\) | ||||
−0.571008 | + | 0.820944i | \(0.693447\pi\) | |||||||
\(930\) | −10.6439 | −0.349028 | ||||||||
\(931\) | 107.192 | 3.51309 | ||||||||
\(932\) | −70.4371 | −2.30724 | ||||||||
\(933\) | −11.8178 | −0.386898 | ||||||||
\(934\) | −4.45261 | −0.145694 | ||||||||
\(935\) | 13.8205 | 0.451978 | ||||||||
\(936\) | 49.5256 | 1.61880 | ||||||||
\(937\) | 34.0629 | 1.11279 | 0.556393 | − | 0.830919i | \(-0.312185\pi\) | ||||
0.556393 | + | 0.830919i | \(0.312185\pi\) | |||||||
\(938\) | −164.626 | −5.37524 | ||||||||
\(939\) | 20.4315 | 0.666756 | ||||||||
\(940\) | −42.9753 | −1.40170 | ||||||||
\(941\) | −21.3703 | −0.696652 | −0.348326 | − | 0.937373i | \(-0.613250\pi\) | ||||
−0.348326 | + | 0.937373i | \(0.613250\pi\) | |||||||
\(942\) | −0.885041 | −0.0288362 | ||||||||
\(943\) | −3.73840 | −0.121739 | ||||||||
\(944\) | −16.0898 | −0.523678 | ||||||||
\(945\) | −50.2344 | −1.63412 | ||||||||
\(946\) | 3.13628 | 0.101969 | ||||||||
\(947\) | 29.4520 | 0.957061 | 0.478531 | − | 0.878071i | \(-0.341170\pi\) | ||||
0.478531 | + | 0.878071i | \(0.341170\pi\) | |||||||
\(948\) | 21.2849 | 0.691302 | ||||||||
\(949\) | 47.4055 | 1.53885 | ||||||||
\(950\) | −19.7835 | −0.641863 | ||||||||
\(951\) | −11.4097 | −0.369984 | ||||||||
\(952\) | 36.8406 | 1.19401 | ||||||||
\(953\) | 19.4500 | 0.630048 | 0.315024 | − | 0.949084i | \(-0.397987\pi\) | ||||
0.315024 | + | 0.949084i | \(0.397987\pi\) | |||||||
\(954\) | −80.9626 | −2.62126 | ||||||||
\(955\) | −56.8649 | −1.84011 | ||||||||
\(956\) | 18.4994 | 0.598313 | ||||||||
\(957\) | −2.16050 | −0.0698391 | ||||||||
\(958\) | −1.57258 | −0.0508077 | ||||||||
\(959\) | −82.9866 | −2.67978 | ||||||||
\(960\) | −20.3837 | −0.657881 | ||||||||
\(961\) | −24.0251 | −0.775003 | ||||||||
\(962\) | −54.8561 | −1.76863 | ||||||||
\(963\) | 27.7834 | 0.895307 | ||||||||
\(964\) | −5.85442 | −0.188558 | ||||||||
\(965\) | 55.2206 | 1.77761 | ||||||||
\(966\) | −8.25972 | −0.265752 | ||||||||
\(967\) | −9.95382 | −0.320093 | −0.160047 | − | 0.987109i | \(-0.551164\pi\) | ||||
−0.160047 | + | 0.987109i | \(0.551164\pi\) | |||||||
\(968\) | 11.6167 | 0.373375 | ||||||||
\(969\) | 6.55401 | 0.210545 | ||||||||
\(970\) | −48.9949 | −1.57313 | ||||||||
\(971\) | 26.9705 | 0.865523 | 0.432762 | − | 0.901508i | \(-0.357539\pi\) | ||||
0.432762 | + | 0.901508i | \(0.357539\pi\) | |||||||
\(972\) | −51.5532 | −1.65357 | ||||||||
\(973\) | −120.870 | −3.87492 | ||||||||
\(974\) | −31.2716 | −1.00201 | ||||||||
\(975\) | −5.79300 | −0.185524 | ||||||||
\(976\) | 7.27539 | 0.232879 | ||||||||
\(977\) | −12.4933 | −0.399696 | −0.199848 | − | 0.979827i | \(-0.564045\pi\) | ||||
−0.199848 | + | 0.979827i | \(0.564045\pi\) | |||||||
\(978\) | −22.9395 | −0.733524 | ||||||||
\(979\) | 42.1514 | 1.34717 | ||||||||
\(980\) | −190.521 | −6.08597 | ||||||||
\(981\) | 8.56537 | 0.273471 | ||||||||
\(982\) | −26.3567 | −0.841077 | ||||||||
\(983\) | 34.4942 | 1.10019 | 0.550097 | − | 0.835101i | \(-0.314591\pi\) | ||||
0.550097 | + | 0.835101i | \(0.314591\pi\) | |||||||
\(984\) | 9.02551 | 0.287723 | ||||||||
\(985\) | 50.0969 | 1.59622 | ||||||||
\(986\) | 5.26332 | 0.167618 | ||||||||
\(987\) | −16.5178 | −0.525766 | ||||||||
\(988\) | 96.9454 | 3.08424 | ||||||||
\(989\) | 0.476886 | 0.0151641 | ||||||||
\(990\) | −43.3449 | −1.37759 | ||||||||
\(991\) | −39.1610 | −1.24399 | −0.621995 | − | 0.783022i | \(-0.713677\pi\) | ||||
−0.621995 | + | 0.783022i | \(0.713677\pi\) | |||||||
\(992\) | 10.0645 | 0.319549 | ||||||||
\(993\) | 17.6474 | 0.560024 | ||||||||
\(994\) | −124.151 | −3.93783 | ||||||||
\(995\) | 11.7611 | 0.372852 | ||||||||
\(996\) | −21.4741 | −0.680432 | ||||||||
\(997\) | 60.3891 | 1.91254 | 0.956271 | − | 0.292482i | \(-0.0944813\pi\) | ||||
0.956271 | + | 0.292482i | \(0.0944813\pi\) | |||||||
\(998\) | −20.5738 | −0.651253 | ||||||||
\(999\) | 16.1522 | 0.511033 |
(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 | 8027.2.a.e.1.18 | ✓ | 169 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.e.1.18 | ✓ | 169 | 1.1 | even | 1 | trivial |