Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [28,4,Mod(27,28)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("28.27");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 28 = 2^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 28.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(1.65205348016\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 30x^{6} + 84x^{5} + 493x^{4} - 464x^{3} - 3172x^{2} + 1072x + 8978 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 27.3 | ||
Root | \(-2.60656 + 0.736813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 28.27 |
Dual form | 28.4.d.b.27.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | + | 1.47363i | −0.853553 | + | 0.521005i | ||||
\(3\) | −4.79890 | −0.923549 | −0.461774 | − | 0.886997i | \(-0.652787\pi\) | ||||
−0.461774 | + | 0.886997i | \(0.652787\pi\) | |||||||
\(4\) | 3.65685 | − | 7.11529i | 0.457107 | − | 0.889412i | ||||
\(5\) | − | 17.0728i | − | 1.52704i | −0.645786 | − | 0.763518i | \(-0.723470\pi\) | ||
0.645786 | − | 0.763518i | \(-0.276530\pi\) | |||||||
\(6\) | 11.5856 | − | 7.07178i | 0.788298 | − | 0.481174i | ||||
\(7\) | −18.3722 | + | 2.33686i | −0.992008 | + | 0.126178i | ||||
\(8\) | 1.65685 | + | 22.5667i | 0.0732233 | + | 0.997316i | ||||
\(9\) | −3.97056 | −0.147058 | ||||||||
\(10\) | 25.1589 | + | 41.2174i | 0.795594 | + | 1.30341i | ||||
\(11\) | − | 41.4710i | − | 1.13672i | −0.822778 | − | 0.568362i | \(-0.807577\pi\) | ||
0.822778 | − | 0.568362i | \(-0.192423\pi\) | |||||||
\(12\) | −17.5489 | + | 34.1456i | −0.422160 | + | 0.821415i | ||||
\(13\) | 45.3599i | 0.967737i | 0.875141 | + | 0.483868i | \(0.160769\pi\) | ||||
−0.875141 | + | 0.483868i | \(0.839231\pi\) | |||||||
\(14\) | 40.9109 | − | 32.7155i | 0.780992 | − | 0.624541i | ||||
\(15\) | 81.9306i | 1.41029i | ||||||||
\(16\) | −37.2548 | − | 52.0392i | −0.582107 | − | 0.813112i | ||||
\(17\) | − | 28.2871i | − | 0.403567i | −0.979430 | − | 0.201783i | \(-0.935326\pi\) | ||
0.979430 | − | 0.201783i | \(-0.0646737\pi\) | |||||||
\(18\) | 9.58579 | − | 5.85112i | 0.125522 | − | 0.0766179i | ||||
\(19\) | 41.5434 | 0.501616 | 0.250808 | − | 0.968037i | \(-0.419304\pi\) | ||||
0.250808 | + | 0.968037i | \(0.419304\pi\) | |||||||
\(20\) | −121.478 | − | 62.4327i | −1.35816 | − | 0.698019i | ||||
\(21\) | 88.1665 | − | 11.2143i | 0.916167 | − | 0.116532i | ||||
\(22\) | 61.1127 | + | 100.120i | 0.592240 | + | 0.970255i | ||||
\(23\) | − | 93.9291i | − | 0.851546i | −0.904830 | − | 0.425773i | \(-0.860002\pi\) | ||
0.904830 | − | 0.425773i | \(-0.139998\pi\) | |||||||
\(24\) | −7.95108 | − | 108.295i | −0.0676253 | − | 0.921069i | ||||
\(25\) | −166.480 | −1.33184 | ||||||||
\(26\) | −66.8435 | − | 109.509i | −0.504196 | − | 0.826015i | ||||
\(27\) | 148.625 | 1.05936 | ||||||||
\(28\) | −50.5572 | + | 139.269i | −0.341229 | + | 0.939980i | ||||
\(29\) | 27.8234 | 0.178161 | 0.0890805 | − | 0.996024i | \(-0.471607\pi\) | ||||
0.0890805 | + | 0.996024i | \(0.471607\pi\) | |||||||
\(30\) | −120.735 | − | 197.798i | −0.734770 | − | 1.20376i | ||||
\(31\) | −81.4400 | −0.471841 | −0.235920 | − | 0.971772i | \(-0.575810\pi\) | ||||
−0.235920 | + | 0.971772i | \(0.575810\pi\) | |||||||
\(32\) | 166.627 | + | 70.7340i | 0.920495 | + | 0.390754i | ||||
\(33\) | 199.015i | 1.04982i | ||||||||
\(34\) | 41.6846 | + | 68.2912i | 0.210260 | + | 0.344466i | ||||
\(35\) | 39.8967 | + | 313.665i | 0.192679 | + | 1.51483i | ||||
\(36\) | −14.5198 | + | 28.2517i | −0.0672212 | + | 0.130795i | ||||
\(37\) | 94.8040 | 0.421235 | 0.210617 | − | 0.977569i | \(-0.432453\pi\) | ||||
0.210617 | + | 0.977569i | \(0.432453\pi\) | |||||||
\(38\) | −100.295 | + | 61.2194i | −0.428156 | + | 0.261345i | ||||
\(39\) | − | 217.678i | − | 0.893752i | ||||||
\(40\) | 385.276 | − | 28.2871i | 1.52294 | − | 0.111815i | ||||
\(41\) | − | 227.302i | − | 0.865820i | −0.901437 | − | 0.432910i | \(-0.857487\pi\) | ||
0.901437 | − | 0.432910i | \(-0.142513\pi\) | |||||||
\(42\) | −196.327 | + | 156.998i | −0.721284 | + | 0.576794i | ||||
\(43\) | − | 171.988i | − | 0.609951i | −0.952360 | − | 0.304976i | \(-0.901352\pi\) | ||
0.952360 | − | 0.304976i | \(-0.0986483\pi\) | |||||||
\(44\) | −295.078 | − | 151.653i | −1.01102 | − | 0.519604i | ||||
\(45\) | 67.7886i | 0.224563i | ||||||||
\(46\) | 138.416 | + | 226.765i | 0.443660 | + | 0.726840i | ||||
\(47\) | −286.005 | −0.887619 | −0.443809 | − | 0.896121i | \(-0.646373\pi\) | ||||
−0.443809 | + | 0.896121i | \(0.646373\pi\) | |||||||
\(48\) | 178.782 | + | 249.731i | 0.537604 | + | 0.750949i | ||||
\(49\) | 332.078 | − | 85.8665i | 0.968158 | − | 0.250340i | ||||
\(50\) | 401.919 | − | 245.330i | 1.13680 | − | 0.693897i | ||||
\(51\) | 135.747i | 0.372714i | ||||||||
\(52\) | 322.749 | + | 165.875i | 0.860717 | + | 0.442359i | ||||
\(53\) | −575.921 | −1.49262 | −0.746310 | − | 0.665599i | \(-0.768176\pi\) | ||||
−0.746310 | + | 0.665599i | \(0.768176\pi\) | |||||||
\(54\) | −358.812 | + | 219.017i | −0.904224 | + | 0.551934i | ||||
\(55\) | −708.025 | −1.73582 | ||||||||
\(56\) | −83.1752 | − | 410.728i | −0.198478 | − | 0.980105i | ||||
\(57\) | −199.362 | −0.463267 | ||||||||
\(58\) | −67.1716 | + | 41.0012i | −0.152070 | + | 0.0928229i | ||||
\(59\) | 411.999 | 0.909114 | 0.454557 | − | 0.890718i | \(-0.349798\pi\) | ||||
0.454557 | + | 0.890718i | \(0.349798\pi\) | |||||||
\(60\) | 582.960 | + | 299.608i | 1.25433 | + | 0.644654i | ||||
\(61\) | − | 778.987i | − | 1.63507i | −0.575881 | − | 0.817534i | \(-0.695341\pi\) | ||
0.575881 | − | 0.817534i | \(-0.304659\pi\) | |||||||
\(62\) | 196.614 | − | 120.012i | 0.402741 | − | 0.245832i | ||||
\(63\) | 72.9481 | − | 9.27863i | 0.145883 | − | 0.0185555i | ||||
\(64\) | −506.510 | + | 74.7794i | −0.989277 | + | 0.146053i | ||||
\(65\) | 774.420 | 1.47777 | ||||||||
\(66\) | −293.274 | − | 480.465i | −0.546962 | − | 0.896078i | ||||
\(67\) | − | 198.773i | − | 0.362448i | −0.983442 | − | 0.181224i | \(-0.941994\pi\) | ||
0.983442 | − | 0.181224i | \(-0.0580060\pi\) | |||||||
\(68\) | −201.271 | − | 103.442i | −0.358937 | − | 0.184473i | ||||
\(69\) | 450.756i | 0.786444i | ||||||||
\(70\) | −558.544 | − | 698.463i | −0.953698 | − | 1.19260i | ||||
\(71\) | − | 197.762i | − | 0.330564i | −0.986246 | − | 0.165282i | \(-0.947147\pi\) | ||
0.986246 | − | 0.165282i | \(-0.0528534\pi\) | |||||||
\(72\) | −6.57864 | − | 89.6024i | −0.0107681 | − | 0.146663i | ||||
\(73\) | 255.589i | 0.409787i | 0.978784 | + | 0.204894i | \(0.0656848\pi\) | ||||
−0.978784 | + | 0.204894i | \(0.934315\pi\) | |||||||
\(74\) | −228.877 | + | 139.706i | −0.359546 | + | 0.219466i | ||||
\(75\) | 798.922 | 1.23002 | ||||||||
\(76\) | 151.918 | − | 295.593i | 0.229292 | − | 0.446143i | ||||
\(77\) | 96.9117 | + | 761.915i | 0.143430 | + | 1.12764i | ||||
\(78\) | 320.775 | + | 525.520i | 0.465650 | + | 0.762865i | ||||
\(79\) | 1178.49i | 1.67836i | 0.543856 | + | 0.839179i | \(0.316964\pi\) | ||||
−0.543856 | + | 0.839179i | \(0.683036\pi\) | |||||||
\(80\) | −888.454 | + | 636.044i | −1.24165 | + | 0.888899i | ||||
\(81\) | −606.029 | −0.831316 | ||||||||
\(82\) | 334.958 | + | 548.756i | 0.451097 | + | 0.739024i | ||||
\(83\) | 938.514 | 1.24115 | 0.620574 | − | 0.784148i | \(-0.286900\pi\) | ||||
0.620574 | + | 0.784148i | \(0.286900\pi\) | |||||||
\(84\) | 242.619 | − | 668.340i | 0.315141 | − | 0.868117i | ||||
\(85\) | −482.940 | −0.616261 | ||||||||
\(86\) | 253.446 | + | 415.215i | 0.317788 | + | 0.520626i | ||||
\(87\) | −133.522 | −0.164540 | ||||||||
\(88\) | 935.862 | − | 68.7114i | 1.13367 | − | 0.0832347i | ||||
\(89\) | 1166.81i | 1.38968i | 0.719165 | + | 0.694840i | \(0.244525\pi\) | ||||
−0.719165 | + | 0.694840i | \(0.755475\pi\) | |||||||
\(90\) | −99.8950 | − | 163.656i | −0.116998 | − | 0.191676i | ||||
\(91\) | −106.000 | − | 833.363i | −0.122107 | − | 0.960002i | ||||
\(92\) | −668.333 | − | 343.485i | −0.757375 | − | 0.389248i | ||||
\(93\) | 390.823 | 0.435768 | ||||||||
\(94\) | 690.476 | − | 421.464i | 0.757630 | − | 0.462454i | ||||
\(95\) | − | 709.261i | − | 0.765986i | ||||||
\(96\) | −799.628 | − | 339.446i | −0.850122 | − | 0.360880i | ||||
\(97\) | − | 656.635i | − | 0.687332i | −0.939092 | − | 0.343666i | \(-0.888331\pi\) | ||
0.939092 | − | 0.343666i | \(-0.111669\pi\) | |||||||
\(98\) | −675.173 | + | 696.659i | −0.695946 | + | 0.718094i | ||||
\(99\) | 164.663i | 0.167164i | ||||||||
\(100\) | −608.794 | + | 1184.56i | −0.608794 | + | 1.18456i | ||||
\(101\) | − | 999.426i | − | 0.984620i | −0.870420 | − | 0.492310i | \(-0.836153\pi\) | ||
0.870420 | − | 0.492310i | \(-0.163847\pi\) | |||||||
\(102\) | −200.040 | − | 327.722i | −0.194186 | − | 0.318131i | ||||
\(103\) | −958.932 | −0.917344 | −0.458672 | − | 0.888606i | \(-0.651675\pi\) | ||||
−0.458672 | + | 0.888606i | \(0.651675\pi\) | |||||||
\(104\) | −1023.62 | + | 75.1548i | −0.965139 | + | 0.0708609i | ||||
\(105\) | −191.460 | − | 1505.25i | −0.177948 | − | 1.39902i | ||||
\(106\) | 1390.40 | − | 848.692i | 1.27403 | − | 0.777663i | ||||
\(107\) | 685.893i | 0.619699i | 0.950786 | + | 0.309849i | \(0.100279\pi\) | ||||
−0.950786 | + | 0.309849i | \(0.899721\pi\) | |||||||
\(108\) | 543.499 | − | 1057.51i | 0.484242 | − | 0.942211i | ||||
\(109\) | 1127.80 | 0.991045 | 0.495523 | − | 0.868595i | \(-0.334977\pi\) | ||||
0.495523 | + | 0.868595i | \(0.334977\pi\) | |||||||
\(110\) | 1709.32 | − | 1043.36i | 1.48162 | − | 0.904372i | ||||
\(111\) | −454.955 | −0.389031 | ||||||||
\(112\) | 806.063 | + | 869.017i | 0.680052 | + | 0.733164i | ||||
\(113\) | −10.0488 | −0.00836557 | −0.00418278 | − | 0.999991i | \(-0.501331\pi\) | ||||
−0.00418278 | + | 0.999991i | \(0.501331\pi\) | |||||||
\(114\) | 481.304 | − | 293.786i | 0.395423 | − | 0.241364i | ||||
\(115\) | −1603.63 | −1.30034 | ||||||||
\(116\) | 101.746 | − | 197.972i | 0.0814386 | − | 0.158459i | ||||
\(117\) | − | 180.104i | − | 0.142313i | ||||||
\(118\) | −994.654 | + | 607.132i | −0.775977 | + | 0.473653i | ||||
\(119\) | 66.1029 | + | 519.698i | 0.0509214 | + | 0.400341i | ||||
\(120\) | −1848.90 | + | 135.747i | −1.40651 | + | 0.103266i | ||||
\(121\) | −388.842 | −0.292143 | ||||||||
\(122\) | 1147.94 | + | 1880.64i | 0.851879 | + | 1.39562i | ||||
\(123\) | 1090.80i | 0.799627i | ||||||||
\(124\) | −297.814 | + | 579.470i | −0.215682 | + | 0.419661i | ||||
\(125\) | 708.183i | 0.506735i | ||||||||
\(126\) | −162.439 | + | 129.899i | −0.114851 | + | 0.0918437i | ||||
\(127\) | − | 1347.06i | − | 0.941198i | −0.882347 | − | 0.470599i | \(-0.844038\pi\) | ||
0.882347 | − | 0.470599i | \(-0.155962\pi\) | |||||||
\(128\) | 1112.63 | − | 926.939i | 0.768306 | − | 0.640083i | ||||
\(129\) | 825.352i | 0.563320i | ||||||||
\(130\) | −1869.62 | + | 1141.21i | −1.26136 | + | 0.769926i | ||||
\(131\) | −480.265 | −0.320313 | −0.160156 | − | 0.987092i | \(-0.551200\pi\) | ||||
−0.160156 | + | 0.987092i | \(0.551200\pi\) | |||||||
\(132\) | 1416.05 | + | 727.769i | 0.933723 | + | 0.479880i | ||||
\(133\) | −763.245 | + | 97.0809i | −0.497607 | + | 0.0632931i | ||||
\(134\) | 292.918 | + | 479.881i | 0.188838 | + | 0.309369i | ||||
\(135\) | − | 2537.44i | − | 1.61769i | ||||||
\(136\) | 638.346 | − | 46.8676i | 0.402483 | − | 0.0295505i | ||||
\(137\) | −247.803 | −0.154535 | −0.0772674 | − | 0.997010i | \(-0.524620\pi\) | ||||
−0.0772674 | + | 0.997010i | \(0.524620\pi\) | |||||||
\(138\) | −664.246 | − | 1088.22i | −0.409742 | − | 0.671272i | ||||
\(139\) | 1842.35 | 1.12422 | 0.562109 | − | 0.827063i | \(-0.309990\pi\) | ||||
0.562109 | + | 0.827063i | \(0.309990\pi\) | |||||||
\(140\) | 2377.72 | + | 863.152i | 1.43538 | + | 0.521069i | ||||
\(141\) | 1372.51 | 0.819759 | ||||||||
\(142\) | 291.427 | + | 477.440i | 0.172226 | + | 0.282154i | ||||
\(143\) | 1881.12 | 1.10005 | ||||||||
\(144\) | 147.923 | + | 206.625i | 0.0856034 | + | 0.119575i | ||||
\(145\) | − | 475.023i | − | 0.272059i | ||||||
\(146\) | −376.643 | − | 617.047i | −0.213501 | − | 0.349775i | ||||
\(147\) | −1593.61 | + | 412.065i | −0.894141 | + | 0.231201i | ||||
\(148\) | 346.685 | − | 674.559i | 0.192549 | − | 0.374651i | ||||
\(149\) | −2200.82 | −1.21006 | −0.605028 | − | 0.796204i | \(-0.706838\pi\) | ||||
−0.605028 | + | 0.796204i | \(0.706838\pi\) | |||||||
\(150\) | −1928.77 | + | 1177.31i | −1.04989 | + | 0.640847i | ||||
\(151\) | 3208.96i | 1.72941i | 0.502279 | + | 0.864706i | \(0.332495\pi\) | ||||
−0.502279 | + | 0.864706i | \(0.667505\pi\) | |||||||
\(152\) | 68.8313 | + | 937.496i | 0.0367300 | + | 0.500269i | ||||
\(153\) | 112.316i | 0.0593477i | ||||||||
\(154\) | −1356.74 | − | 1696.61i | −0.709931 | − | 0.887773i | ||||
\(155\) | 1390.41i | 0.720518i | ||||||||
\(156\) | −1548.84 | − | 796.016i | −0.794914 | − | 0.408540i | ||||
\(157\) | 636.547i | 0.323579i | 0.986825 | + | 0.161790i | \(0.0517266\pi\) | ||||
−0.986825 | + | 0.161790i | \(0.948273\pi\) | |||||||
\(158\) | −1736.65 | − | 2845.12i | −0.874433 | − | 1.43257i | ||||
\(159\) | 2763.79 | 1.37851 | ||||||||
\(160\) | 1207.63 | − | 2844.80i | 0.596696 | − | 1.40563i | ||||
\(161\) | 219.499 | + | 1725.69i | 0.107447 | + | 0.844740i | ||||
\(162\) | 1463.08 | − | 893.061i | 0.709573 | − | 0.433120i | ||||
\(163\) | − | 2460.38i | − | 1.18228i | −0.806568 | − | 0.591141i | \(-0.798677\pi\) | ||
0.806568 | − | 0.591141i | \(-0.201323\pi\) | |||||||
\(164\) | −1617.32 | − | 831.211i | −0.770071 | − | 0.395772i | ||||
\(165\) | 3397.74 | 1.60311 | ||||||||
\(166\) | −2265.77 | + | 1383.02i | −1.05939 | + | 0.646645i | ||||
\(167\) | −2133.16 | −0.988435 | −0.494218 | − | 0.869338i | \(-0.664545\pi\) | ||||
−0.494218 | + | 0.869338i | \(0.664545\pi\) | |||||||
\(168\) | 399.149 | + | 1971.04i | 0.183304 | + | 0.905175i | ||||
\(169\) | 139.478 | 0.0634855 | ||||||||
\(170\) | 1165.92 | − | 711.673i | 0.526012 | − | 0.321076i | ||||
\(171\) | −164.951 | −0.0737666 | ||||||||
\(172\) | −1223.74 | − | 628.935i | −0.542498 | − | 0.278813i | ||||
\(173\) | − | 1462.73i | − | 0.642829i | −0.946939 | − | 0.321415i | \(-0.895842\pi\) | ||
0.946939 | − | 0.321415i | \(-0.104158\pi\) | |||||||
\(174\) | 322.350 | − | 196.761i | 0.140444 | − | 0.0857264i | ||||
\(175\) | 3058.61 | − | 389.040i | 1.32120 | − | 0.168050i | ||||
\(176\) | −2158.12 | + | 1544.99i | −0.924285 | + | 0.661695i | ||||
\(177\) | −1977.14 | −0.839611 | ||||||||
\(178\) | −1719.44 | − | 2816.92i | −0.724030 | − | 1.18617i | ||||
\(179\) | − | 3038.97i | − | 1.26896i | −0.772941 | − | 0.634478i | \(-0.781215\pi\) | ||
0.772941 | − | 0.634478i | \(-0.218785\pi\) | |||||||
\(180\) | 482.336 | + | 247.893i | 0.199729 | + | 0.102649i | ||||
\(181\) | 384.978i | 0.158095i | 0.996871 | + | 0.0790475i | \(0.0251879\pi\) | ||||
−0.996871 | + | 0.0790475i | \(0.974812\pi\) | |||||||
\(182\) | 1483.97 | + | 1855.71i | 0.604392 | + | 0.755795i | ||||
\(183\) | 3738.28i | 1.51006i | ||||||||
\(184\) | 2119.67 | − | 155.627i | 0.849260 | − | 0.0623530i | ||||
\(185\) | − | 1618.57i | − | 0.643241i | ||||||
\(186\) | −943.529 | + | 575.926i | −0.371951 | + | 0.227037i | ||||
\(187\) | −1173.09 | −0.458744 | ||||||||
\(188\) | −1045.88 | + | 2035.01i | −0.405736 | + | 0.789459i | ||||
\(189\) | −2730.57 | + | 347.314i | −1.05090 | + | 0.133669i | ||||
\(190\) | 1045.19 | + | 1712.31i | 0.399083 | + | 0.653810i | ||||
\(191\) | − | 505.605i | − | 0.191541i | −0.995403 | − | 0.0957704i | \(-0.969469\pi\) | ||
0.995403 | − | 0.0957704i | \(-0.0305314\pi\) | |||||||
\(192\) | 2430.69 | − | 358.859i | 0.913645 | − | 0.134887i | ||||
\(193\) | 1921.91 | 0.716798 | 0.358399 | − | 0.933569i | \(-0.383323\pi\) | ||||
0.358399 | + | 0.933569i | \(0.383323\pi\) | |||||||
\(194\) | 967.634 | + | 1585.26i | 0.358103 | + | 0.586674i | ||||
\(195\) | −3716.37 | −1.36479 | ||||||||
\(196\) | 603.396 | − | 2676.84i | 0.219896 | − | 0.975523i | ||||
\(197\) | 1603.63 | 0.579968 | 0.289984 | − | 0.957031i | \(-0.406350\pi\) | ||||
0.289984 | + | 0.957031i | \(0.406350\pi\) | |||||||
\(198\) | −242.652 | − | 397.532i | −0.0870935 | − | 0.142684i | ||||
\(199\) | 2558.75 | 0.911484 | 0.455742 | − | 0.890112i | \(-0.349374\pi\) | ||||
0.455742 | + | 0.890112i | \(0.349374\pi\) | |||||||
\(200\) | −275.833 | − | 3756.91i | −0.0975219 | − | 1.32827i | ||||
\(201\) | 953.894i | 0.334739i | ||||||||
\(202\) | 1472.78 | + | 2412.83i | 0.512992 | + | 0.840426i | ||||
\(203\) | −511.178 | + | 65.0192i | −0.176737 | + | 0.0224801i | ||||
\(204\) | 965.881 | + | 496.407i | 0.331496 | + | 0.170370i | ||||
\(205\) | −3880.68 | −1.32214 | ||||||||
\(206\) | 2315.07 | − | 1413.11i | 0.783002 | − | 0.477941i | ||||
\(207\) | 372.951i | 0.125227i | ||||||||
\(208\) | 2360.49 | − | 1689.88i | 0.786879 | − | 0.563326i | ||||
\(209\) | − | 1722.84i | − | 0.570199i | ||||||
\(210\) | 2680.40 | + | 3351.85i | 0.880786 | + | 1.10143i | ||||
\(211\) | − | 381.389i | − | 0.124436i | −0.998063 | − | 0.0622178i | \(-0.980183\pi\) | ||
0.998063 | − | 0.0622178i | \(-0.0198173\pi\) | |||||||
\(212\) | −2106.06 | + | 4097.85i | −0.682286 | + | 1.32755i | ||||
\(213\) | 949.040i | 0.305292i | ||||||||
\(214\) | −1010.75 | − | 1655.89i | −0.322866 | − | 0.528946i | ||||
\(215\) | −2936.31 | −0.931418 | ||||||||
\(216\) | 246.249 | + | 3353.96i | 0.0775701 | + | 1.05652i | ||||
\(217\) | 1496.24 | − | 190.314i | 0.468070 | − | 0.0595361i | ||||
\(218\) | −2722.76 | + | 1661.96i | −0.845910 | + | 0.516340i | ||||
\(219\) | − | 1226.55i | − | 0.378458i | ||||||
\(220\) | −2589.15 | + | 5037.81i | −0.793455 | + | 1.54386i | ||||
\(221\) | 1283.10 | 0.390546 | ||||||||
\(222\) | 1098.36 | − | 670.434i | 0.332059 | − | 0.202687i | ||||
\(223\) | 2943.88 | 0.884023 | 0.442011 | − | 0.897009i | \(-0.354265\pi\) | ||||
0.442011 | + | 0.897009i | \(0.354265\pi\) | |||||||
\(224\) | −3226.61 | − | 910.158i | −0.962443 | − | 0.271484i | ||||
\(225\) | 661.020 | 0.195858 | ||||||||
\(226\) | 24.2599 | − | 14.8081i | 0.00714046 | − | 0.00435851i | ||||
\(227\) | −5786.10 | −1.69179 | −0.845897 | − | 0.533346i | \(-0.820934\pi\) | ||||
−0.845897 | + | 0.533346i | \(0.820934\pi\) | |||||||
\(228\) | −729.040 | + | 1418.52i | −0.211762 | + | 0.412035i | ||||
\(229\) | 4303.85i | 1.24195i | 0.783830 | + | 0.620975i | \(0.213263\pi\) | ||||
−0.783830 | + | 0.620975i | \(0.786737\pi\) | |||||||
\(230\) | 3871.51 | − | 2363.15i | 1.10991 | − | 0.677486i | ||||
\(231\) | −465.069 | − | 3656.35i | −0.132465 | − | 1.04143i | ||||
\(232\) | 46.0993 | + | 627.881i | 0.0130455 | + | 0.177683i | ||||
\(233\) | 5133.92 | 1.44349 | 0.721747 | − | 0.692157i | \(-0.243340\pi\) | ||||
0.721747 | + | 0.692157i | \(0.243340\pi\) | |||||||
\(234\) | 265.406 | + | 434.811i | 0.0741460 | + | 0.121472i | ||||
\(235\) | 4882.90i | 1.35543i | ||||||||
\(236\) | 1506.62 | − | 2931.49i | 0.415562 | − | 0.808576i | ||||
\(237\) | − | 5655.44i | − | 1.55004i | ||||||
\(238\) | −925.427 | − | 1157.25i | −0.252044 | − | 0.315182i | ||||
\(239\) | 468.448i | 0.126784i | 0.997989 | + | 0.0633920i | \(0.0201919\pi\) | ||||
−0.997989 | + | 0.0633920i | \(0.979808\pi\) | |||||||
\(240\) | 4263.60 | − | 3052.31i | 1.14673 | − | 0.820941i | ||||
\(241\) | 389.501i | 0.104108i | 0.998644 | + | 0.0520539i | \(0.0165768\pi\) | ||||
−0.998644 | + | 0.0520539i | \(0.983423\pi\) | |||||||
\(242\) | 938.747 | − | 573.007i | 0.249359 | − | 0.152208i | ||||
\(243\) | −1104.59 | −0.291603 | ||||||||
\(244\) | −5542.72 | − | 2848.64i | −1.45425 | − | 0.747400i | ||||
\(245\) | −1465.98 | − | 5669.50i | −0.382278 | − | 1.47841i | ||||
\(246\) | −1607.43 | − | 2633.42i | −0.416610 | − | 0.682525i | ||||
\(247\) | 1884.40i | 0.485432i | ||||||||
\(248\) | −134.934 | − | 1837.83i | −0.0345497 | − | 0.470574i | ||||
\(249\) | −4503.83 | −1.14626 | ||||||||
\(250\) | −1043.60 | − | 1709.71i | −0.264012 | − | 0.432525i | ||||
\(251\) | 4690.59 | 1.17955 | 0.589776 | − | 0.807567i | \(-0.299216\pi\) | ||||
0.589776 | + | 0.807567i | \(0.299216\pi\) | |||||||
\(252\) | 200.740 | − | 552.978i | 0.0501804 | − | 0.138232i | ||||
\(253\) | −3895.33 | −0.967974 | ||||||||
\(254\) | 1985.06 | + | 3252.09i | 0.490369 | + | 0.803363i | ||||
\(255\) | 2317.58 | 0.569147 | ||||||||
\(256\) | −1320.15 | + | 3877.42i | −0.322303 | + | 0.946636i | ||||
\(257\) | − | 5223.27i | − | 1.26778i | −0.773425 | − | 0.633888i | \(-0.781458\pi\) | ||
0.773425 | − | 0.633888i | \(-0.218542\pi\) | |||||||
\(258\) | −1216.26 | − | 1992.58i | −0.293493 | − | 0.480823i | ||||
\(259\) | −1741.76 | + | 221.543i | −0.417868 | + | 0.0531507i | ||||
\(260\) | 2831.94 | − | 5510.23i | 0.675499 | − | 1.31435i | ||||
\(261\) | −110.474 | −0.0262000 | ||||||||
\(262\) | 1159.46 | − | 707.731i | 0.273404 | − | 0.166885i | ||||
\(263\) | − | 4704.80i | − | 1.10308i | −0.834148 | − | 0.551541i | \(-0.814040\pi\) | ||
0.834148 | − | 0.551541i | \(-0.185960\pi\) | |||||||
\(264\) | −4491.11 | + | 329.739i | −1.04700 | + | 0.0768713i | ||||
\(265\) | 9832.58i | 2.27928i | ||||||||
\(266\) | 1699.57 | − | 1359.11i | 0.391758 | − | 0.313280i | ||||
\(267\) | − | 5599.40i | − | 1.28344i | ||||||
\(268\) | −1414.33 | − | 726.885i | −0.322366 | − | 0.165678i | ||||
\(269\) | 3444.53i | 0.780730i | 0.920660 | + | 0.390365i | \(0.127651\pi\) | ||||
−0.920660 | + | 0.390365i | \(0.872349\pi\) | |||||||
\(270\) | 3739.23 | + | 6125.92i | 0.842824 | + | 1.38078i | ||||
\(271\) | 5251.78 | 1.17721 | 0.588603 | − | 0.808422i | \(-0.299678\pi\) | ||||
0.588603 | + | 0.808422i | \(0.299678\pi\) | |||||||
\(272\) | −1472.04 | + | 1053.83i | −0.328145 | + | 0.234919i | ||||
\(273\) | 508.681 | + | 3999.23i | 0.112772 | + | 0.886609i | ||||
\(274\) | 598.250 | − | 365.169i | 0.131904 | − | 0.0805134i | ||||
\(275\) | 6904.10i | 1.51394i | ||||||||
\(276\) | 3207.26 | + | 1648.35i | 0.699473 | + | 0.359489i | ||||
\(277\) | 6003.19 | 1.30215 | 0.651077 | − | 0.759012i | \(-0.274317\pi\) | ||||
0.651077 | + | 0.759012i | \(0.274317\pi\) | |||||||
\(278\) | −4447.84 | + | 2714.94i | −0.959581 | + | 0.585724i | ||||
\(279\) | 323.363 | 0.0693879 | ||||||||
\(280\) | −7012.28 | + | 1420.03i | −1.49666 | + | 0.303083i | ||||
\(281\) | −1870.63 | −0.397125 | −0.198563 | − | 0.980088i | \(-0.563627\pi\) | ||||
−0.198563 | + | 0.980088i | \(0.563627\pi\) | |||||||
\(282\) | −3313.53 | + | 2022.56i | −0.699708 | + | 0.427099i | ||||
\(283\) | 3963.42 | 0.832512 | 0.416256 | − | 0.909248i | \(-0.363342\pi\) | ||||
0.416256 | + | 0.909248i | \(0.363342\pi\) | |||||||
\(284\) | −1407.14 | − | 723.187i | −0.294007 | − | 0.151103i | ||||
\(285\) | 3403.67i | 0.707425i | ||||||||
\(286\) | −4541.43 | + | 2772.07i | −0.938952 | + | 0.573132i | ||||
\(287\) | 531.172 | + | 4176.05i | 0.109248 | + | 0.858900i | ||||
\(288\) | −661.605 | − | 280.854i | −0.135366 | − | 0.0574635i | ||||
\(289\) | 4112.84 | 0.837134 | ||||||||
\(290\) | 700.006 | + | 1146.81i | 0.141744 | + | 0.232216i | ||||
\(291\) | 3151.12i | 0.634784i | ||||||||
\(292\) | 1818.59 | + | 934.653i | 0.364470 | + | 0.187317i | ||||
\(293\) | 4654.67i | 0.928084i | 0.885813 | + | 0.464042i | \(0.153601\pi\) | ||||
−0.885813 | + | 0.464042i | \(0.846399\pi\) | |||||||
\(294\) | 3240.09 | − | 3343.20i | 0.642740 | − | 0.663195i | ||||
\(295\) | − | 7033.97i | − | 1.38825i | ||||||
\(296\) | 157.076 | + | 2139.41i | 0.0308442 | + | 0.420104i | ||||
\(297\) | − | 6163.61i | − | 1.20420i | ||||||
\(298\) | 5313.26 | − | 3243.19i | 1.03285 | − | 0.630446i | ||||
\(299\) | 4260.62 | 0.824073 | ||||||||
\(300\) | 2921.54 | − | 5684.56i | 0.562251 | − | 1.09399i | ||||
\(301\) | 401.911 | + | 3159.80i | 0.0769626 | + | 0.605076i | ||||
\(302\) | −4728.80 | − | 7747.10i | −0.901033 | − | 1.47614i | ||||
\(303\) | 4796.14i | 0.909344i | ||||||||
\(304\) | −1547.69 | − | 2161.88i | −0.291994 | − | 0.407870i | ||||
\(305\) | −13299.5 | −2.49681 | ||||||||
\(306\) | −165.511 | − | 271.154i | −0.0309205 | − | 0.0506564i | ||||
\(307\) | −2828.15 | −0.525769 | −0.262884 | − | 0.964827i | \(-0.584674\pi\) | ||||
−0.262884 | + | 0.964827i | \(0.584674\pi\) | |||||||
\(308\) | 5775.64 | + | 2096.66i | 1.06850 | + | 0.387883i | ||||
\(309\) | 4601.82 | 0.847212 | ||||||||
\(310\) | −2048.94 | − | 3356.74i | −0.375394 | − | 0.615001i | ||||
\(311\) | −6559.10 | −1.19592 | −0.597962 | − | 0.801524i | \(-0.704023\pi\) | ||||
−0.597962 | + | 0.801524i | \(0.704023\pi\) | |||||||
\(312\) | 4912.26 | − | 360.660i | 0.891353 | − | 0.0654435i | ||||
\(313\) | − | 6217.17i | − | 1.12273i | −0.827568 | − | 0.561366i | \(-0.810276\pi\) | ||
0.827568 | − | 0.561366i | \(-0.189724\pi\) | |||||||
\(314\) | −938.031 | − | 1536.76i | −0.168587 | − | 0.276192i | ||||
\(315\) | −158.412 | − | 1245.43i | −0.0283350 | − | 0.222768i | ||||
\(316\) | 8385.29 | + | 4309.56i | 1.49275 | + | 0.767189i | ||||
\(317\) | 3254.84 | 0.576687 | 0.288344 | − | 0.957527i | \(-0.406895\pi\) | ||||
0.288344 | + | 0.957527i | \(0.406895\pi\) | |||||||
\(318\) | −6672.37 | + | 4072.79i | −1.17663 | + | 0.718209i | ||||
\(319\) | − | 1153.86i | − | 0.202520i | ||||||
\(320\) | 1276.69 | + | 8647.53i | 0.223029 | + | 1.51066i | ||||
\(321\) | − | 3291.53i | − | 0.572322i | ||||||
\(322\) | −3072.93 | − | 3842.72i | −0.531826 | − | 0.665051i | ||||
\(323\) | − | 1175.14i | − | 0.202436i | ||||||
\(324\) | −2216.16 | + | 4312.08i | −0.380000 | + | 0.739382i | ||||
\(325\) | − | 7551.53i | − | 1.28887i | ||||||
\(326\) | 3625.68 | + | 5939.89i | 0.615976 | + | 1.00914i | ||||
\(327\) | −5412.21 | −0.915279 | ||||||||
\(328\) | 5129.45 | − | 376.607i | 0.863496 | − | 0.0633982i | ||||
\(329\) | 5254.55 | − | 668.352i | 0.880524 | − | 0.111998i | ||||
\(330\) | −8202.88 | + | 5007.00i | −1.36834 | + | 0.835231i | ||||
\(331\) | − | 4385.31i | − | 0.728212i | −0.931357 | − | 0.364106i | \(-0.881375\pi\) | ||
0.931357 | − | 0.364106i | \(-0.118625\pi\) | |||||||
\(332\) | 3432.01 | − | 6677.80i | 0.567337 | − | 1.10389i | ||||
\(333\) | −376.425 | −0.0619459 | ||||||||
\(334\) | 5149.90 | − | 3143.48i | 0.843682 | − | 0.514980i | ||||
\(335\) | −3393.62 | −0.553472 | ||||||||
\(336\) | −3868.21 | − | 4170.33i | −0.628061 | − | 0.677113i | ||||
\(337\) | −9569.41 | −1.54682 | −0.773411 | − | 0.633905i | \(-0.781451\pi\) | ||||
−0.773411 | + | 0.633905i | \(0.781451\pi\) | |||||||
\(338\) | −336.729 | + | 205.538i | −0.0541883 | + | 0.0330763i | ||||
\(339\) | 48.2231 | 0.00772601 | ||||||||
\(340\) | −1766.04 | + | 3436.26i | −0.281697 | + | 0.548110i | ||||
\(341\) | 3377.40i | 0.536353i | ||||||||
\(342\) | 398.226 | − | 243.075i | 0.0629637 | − | 0.0384328i | ||||
\(343\) | −5900.36 | + | 2353.58i | −0.928833 | + | 0.370500i | ||||
\(344\) | 3881.19 | − | 284.959i | 0.608314 | − | 0.0446626i | ||||
\(345\) | 7695.67 | 1.20093 | ||||||||
\(346\) | 2155.52 | + | 3531.35i | 0.334917 | + | 0.548689i | ||||
\(347\) | − | 10409.6i | − | 1.61043i | −0.592985 | − | 0.805214i | \(-0.702050\pi\) | ||
0.592985 | − | 0.805214i | \(-0.297950\pi\) | |||||||
\(348\) | −488.269 | + | 950.045i | −0.0752125 | + | 0.146344i | ||||
\(349\) | − | 12612.4i | − | 1.93446i | −0.253895 | − | 0.967232i | \(-0.581712\pi\) | ||
0.253895 | − | 0.967232i | \(-0.418288\pi\) | |||||||
\(350\) | −6810.85 | + | 5446.48i | −1.04016 | + | 0.831790i | ||||
\(351\) | 6741.60i | 1.02519i | ||||||||
\(352\) | 2933.41 | − | 6910.20i | 0.444180 | − | 1.04635i | ||||
\(353\) | 10352.1i | 1.56087i | 0.625236 | + | 0.780435i | \(0.285003\pi\) | ||||
−0.625236 | + | 0.780435i | \(0.714997\pi\) | |||||||
\(354\) | 4773.24 | − | 2913.57i | 0.716653 | − | 0.437442i | ||||
\(355\) | −3376.35 | −0.504783 | ||||||||
\(356\) | 8302.18 | + | 4266.85i | 1.23600 | + | 0.635232i | ||||
\(357\) | −317.221 | − | 2493.98i | −0.0470284 | − | 0.369735i | ||||
\(358\) | 4478.30 | + | 7336.72i | 0.661133 | + | 1.08312i | ||||
\(359\) | 3721.83i | 0.547161i | 0.961849 | + | 0.273580i | \(0.0882080\pi\) | ||||
−0.961849 | + | 0.273580i | \(0.911792\pi\) | |||||||
\(360\) | −1529.76 | + | 112.316i | −0.223960 | + | 0.0164432i | ||||
\(361\) | −5133.15 | −0.748381 | ||||||||
\(362\) | −567.313 | − | 929.419i | −0.0823683 | − | 0.134942i | ||||
\(363\) | 1866.01 | 0.269808 | ||||||||
\(364\) | −6317.25 | − | 2293.27i | −0.909653 | − | 0.330220i | ||||
\(365\) | 4363.62 | 0.625760 | ||||||||
\(366\) | −5508.83 | − | 9025.01i | −0.786752 | − | 1.28892i | ||||
\(367\) | −4676.11 | −0.665097 | −0.332549 | − | 0.943086i | \(-0.607909\pi\) | ||||
−0.332549 | + | 0.943086i | \(0.607909\pi\) | |||||||
\(368\) | −4887.99 | + | 3499.31i | −0.692403 | + | 0.495691i | ||||
\(369\) | 902.518i | 0.127326i | ||||||||
\(370\) | 2385.17 | + | 3907.57i | 0.335132 | + | 0.549041i | ||||
\(371\) | 10581.0 | − | 1345.84i | 1.48069 | − | 0.188336i | ||||
\(372\) | 1429.18 | − | 2780.82i | 0.199192 | − | 0.387577i | ||||
\(373\) | −6601.94 | −0.916448 | −0.458224 | − | 0.888837i | \(-0.651514\pi\) | ||||
−0.458224 | + | 0.888837i | \(0.651514\pi\) | |||||||
\(374\) | 2832.10 | − | 1728.70i | 0.391563 | − | 0.239008i | ||||
\(375\) | − | 3398.50i | − | 0.467994i | ||||||
\(376\) | −473.868 | − | 6454.18i | −0.0649944 | − | 0.885236i | ||||
\(377\) | 1262.07i | 0.172413i | ||||||||
\(378\) | 6080.36 | − | 4862.32i | 0.827354 | − | 0.661616i | ||||
\(379\) | 12756.2i | 1.72887i | 0.502747 | + | 0.864434i | \(0.332323\pi\) | ||||
−0.502747 | + | 0.864434i | \(0.667677\pi\) | |||||||
\(380\) | −5046.60 | − | 2593.67i | −0.681277 | − | 0.350137i | ||||
\(381\) | 6464.40i | 0.869242i | ||||||||
\(382\) | 745.072 | + | 1220.64i | 0.0997938 | + | 0.163490i | ||||
\(383\) | −1573.51 | −0.209929 | −0.104965 | − | 0.994476i | \(-0.533473\pi\) | ||||
−0.104965 | + | 0.994476i | \(0.533473\pi\) | |||||||
\(384\) | −5339.38 | + | 4448.29i | −0.709568 | + | 0.591148i | ||||
\(385\) | 13008.0 | − | 1654.55i | 1.72195 | − | 0.219023i | ||||
\(386\) | −4639.89 | + | 2832.17i | −0.611825 | + | 0.373455i | ||||
\(387\) | 682.889i | 0.0896981i | ||||||||
\(388\) | −4672.15 | − | 2401.22i | −0.611321 | − | 0.314184i | ||||
\(389\) | −4022.95 | −0.524349 | −0.262174 | − | 0.965021i | \(-0.584440\pi\) | ||||
−0.262174 | + | 0.965021i | \(0.584440\pi\) | |||||||
\(390\) | 8972.10 | − | 5476.53i | 1.16492 | − | 0.711064i | ||||
\(391\) | −2656.98 | −0.343656 | ||||||||
\(392\) | 2487.93 | + | 7351.63i | 0.320559 | + | 0.947228i | ||||
\(393\) | 2304.74 | 0.295824 | ||||||||
\(394\) | −3871.50 | + | 2363.15i | −0.495034 | + | 0.302167i | ||||
\(395\) | 20120.1 | 2.56291 | ||||||||
\(396\) | 1171.63 | + | 602.149i | 0.148678 | + | 0.0764119i | ||||
\(397\) | 3987.32i | 0.504075i | 0.967717 | + | 0.252038i | \(0.0811007\pi\) | ||||
−0.967717 | + | 0.252038i | \(0.918899\pi\) | |||||||
\(398\) | −6177.38 | + | 3770.65i | −0.778000 | + | 0.474888i | ||||
\(399\) | 3662.73 | − | 465.881i | 0.459564 | − | 0.0584542i | ||||
\(400\) | 6202.19 | + | 8663.50i | 0.775274 | + | 1.08294i | ||||
\(401\) | 4624.46 | 0.575897 | 0.287948 | − | 0.957646i | \(-0.407027\pi\) | ||||
0.287948 | + | 0.957646i | \(0.407027\pi\) | |||||||
\(402\) | −1405.68 | − | 2302.90i | −0.174401 | − | 0.285717i | ||||
\(403\) | − | 3694.11i | − | 0.456618i | ||||||
\(404\) | −7111.21 | − | 3654.76i | −0.875733 | − | 0.450076i | ||||
\(405\) | 10346.6i | 1.26945i | ||||||||
\(406\) | 1138.28 | − | 910.255i | 0.139142 | − | 0.111269i | ||||
\(407\) | − | 3931.62i | − | 0.478828i | ||||||
\(408\) | −3063.36 | + | 224.913i | −0.371713 | + | 0.0272913i | ||||
\(409\) | 633.029i | 0.0765312i | 0.999268 | + | 0.0382656i | \(0.0121833\pi\) | ||||
−0.999268 | + | 0.0382656i | \(0.987817\pi\) | |||||||
\(410\) | 9368.80 | − | 5718.67i | 1.12852 | − | 0.688842i | ||||
\(411\) | 1189.18 | 0.142720 | ||||||||
\(412\) | −3506.68 | + | 6823.09i | −0.419324 | + | 0.815896i | ||||
\(413\) | −7569.34 | + | 962.782i | −0.901848 | + | 0.114710i | ||||
\(414\) | −549.591 | − | 900.384i | −0.0652437 | − | 0.106888i | ||||
\(415\) | − | 16023.1i | − | 1.89528i | ||||||
\(416\) | −3208.49 | + | 7558.21i | −0.378147 | + | 0.890797i | ||||
\(417\) | −8841.27 | −1.03827 | ||||||||
\(418\) | 2538.83 | + | 4159.31i | 0.297077 | + | 0.486695i | ||||
\(419\) | −3197.39 | −0.372799 | −0.186399 | − | 0.982474i | \(-0.559682\pi\) | ||||
−0.186399 | + | 0.982474i | \(0.559682\pi\) | |||||||
\(420\) | −11410.4 | − | 4142.18i | −1.32565 | − | 0.481233i | ||||
\(421\) | −5489.09 | −0.635444 | −0.317722 | − | 0.948184i | \(-0.602918\pi\) | ||||
−0.317722 | + | 0.948184i | \(0.602918\pi\) | |||||||
\(422\) | 562.025 | + | 920.755i | 0.0648316 | + | 0.106212i | ||||
\(423\) | 1135.60 | 0.130531 | ||||||||
\(424\) | −954.217 | − | 12996.6i | −0.109295 | − | 1.48861i | ||||
\(425\) | 4709.25i | 0.537487i | ||||||||
\(426\) | −1398.53 | − | 2291.19i | −0.159059 | − | 0.260583i | ||||
\(427\) | 1820.38 | + | 14311.7i | 0.206310 | + | 1.62200i | ||||
\(428\) | 4880.33 | + | 2508.21i | 0.551167 | + | 0.283268i | ||||
\(429\) | −9027.31 | −1.01595 | ||||||||
\(430\) | 7088.89 | − | 4327.03i | 0.795015 | − | 0.485274i | ||||
\(431\) | 4178.34i | 0.466968i | 0.972361 | + | 0.233484i | \(0.0750127\pi\) | ||||
−0.972361 | + | 0.233484i | \(0.924987\pi\) | |||||||
\(432\) | −5536.99 | − | 7734.30i | −0.616663 | − | 0.861382i | ||||
\(433\) | − | 9306.18i | − | 1.03286i | −0.856331 | − | 0.516428i | \(-0.827261\pi\) | ||
0.856331 | − | 0.516428i | \(-0.172739\pi\) | |||||||
\(434\) | −3331.78 | + | 2664.35i | −0.368504 | + | 0.294684i | ||||
\(435\) | 2279.59i | 0.251259i | ||||||||
\(436\) | 4124.21 | − | 8024.65i | 0.453014 | − | 0.881448i | ||||
\(437\) | − | 3902.13i | − | 0.427149i | ||||||
\(438\) | 1807.47 | + | 2961.15i | 0.197179 | + | 0.323034i | ||||
\(439\) | −2931.42 | −0.318700 | −0.159350 | − | 0.987222i | \(-0.550940\pi\) | ||||
−0.159350 | + | 0.987222i | \(0.550940\pi\) | |||||||
\(440\) | −1173.09 | − | 15977.8i | −0.127103 | − | 1.73116i | ||||
\(441\) | −1318.54 | + | 340.938i | −0.142375 | + | 0.0368144i | ||||
\(442\) | −3097.68 | + | 1890.81i | −0.333352 | + | 0.203477i | ||||
\(443\) | 5884.29i | 0.631086i | 0.948911 | + | 0.315543i | \(0.102187\pi\) | ||||
−0.948911 | + | 0.315543i | \(0.897813\pi\) | |||||||
\(444\) | −1663.70 | + | 3237.14i | −0.177829 | + | 0.346009i | ||||
\(445\) | 19920.7 | 2.12209 | ||||||||
\(446\) | −7107.17 | + | 4338.18i | −0.754561 | + | 0.460581i | ||||
\(447\) | 10561.5 | 1.11755 | ||||||||
\(448\) | 9130.97 | − | 2557.50i | 0.962941 | − | 0.269711i | ||||
\(449\) | 12856.4 | 1.35129 | 0.675646 | − | 0.737227i | \(-0.263865\pi\) | ||||
0.675646 | + | 0.737227i | \(0.263865\pi\) | |||||||
\(450\) | −1595.84 | + | 974.096i | −0.167175 | + | 0.102043i | ||||
\(451\) | −9426.44 | −0.984199 | ||||||||
\(452\) | −36.7469 | + | 71.5000i | −0.00382396 | + | 0.00744043i | ||||
\(453\) | − | 15399.5i | − | 1.59720i | ||||||
\(454\) | 13968.9 | − | 8526.55i | 1.44404 | − | 0.881434i | ||||
\(455\) | −14227.8 | + | 1809.71i | −1.46596 | + | 0.186463i | ||||
\(456\) | −330.315 | − | 4498.95i | −0.0339219 | − | 0.462023i | ||||
\(457\) | 1831.12 | 0.187431 | 0.0937157 | − | 0.995599i | \(-0.470126\pi\) | ||||
0.0937157 | + | 0.995599i | \(0.470126\pi\) | |||||||
\(458\) | −6342.27 | − | 10390.4i | −0.647063 | − | 1.06007i | ||||
\(459\) | − | 4204.16i | − | 0.427524i | ||||||
\(460\) | −5864.25 | + | 11410.3i | −0.594395 | + | 1.15654i | ||||
\(461\) | 609.925i | 0.0616205i | 0.999525 | + | 0.0308102i | \(0.00980875\pi\) | ||||
−0.999525 | + | 0.0308102i | \(0.990191\pi\) | |||||||
\(462\) | 6510.87 | + | 8141.88i | 0.655656 | + | 0.819901i | ||||
\(463\) | − | 7896.96i | − | 0.792663i | −0.918107 | − | 0.396332i | \(-0.870283\pi\) | ||
0.918107 | − | 0.396332i | \(-0.129717\pi\) | |||||||
\(464\) | −1036.56 | − | 1447.91i | −0.103709 | − | 0.144865i | ||||
\(465\) | − | 6672.43i | − | 0.665434i | ||||||
\(466\) | −12394.4 | + | 7565.47i | −1.23210 | + | 0.752068i | ||||
\(467\) | 14588.0 | 1.44551 | 0.722755 | − | 0.691104i | \(-0.242875\pi\) | ||||
0.722755 | + | 0.691104i | \(0.242875\pi\) | |||||||
\(468\) | −1281.50 | − | 658.616i | −0.126575 | − | 0.0650524i | ||||
\(469\) | 464.505 | + | 3651.91i | 0.0457331 | + | 0.359551i | ||||
\(470\) | −7195.57 | − | 11788.4i | −0.706184 | − | 1.15693i | ||||
\(471\) | − | 3054.72i | − | 0.298841i | ||||||
\(472\) | 682.622 | + | 9297.45i | 0.0665683 | + | 0.906673i | ||||
\(473\) | −7132.50 | −0.693347 | ||||||||
\(474\) | 8334.01 | + | 13653.5i | 0.807582 | + | 1.32305i | ||||
\(475\) | −6916.15 | −0.668073 | ||||||||
\(476\) | 3939.53 | + | 1430.12i | 0.379345 | + | 0.137709i | ||||
\(477\) | 2286.73 | 0.219501 | ||||||||
\(478\) | −690.317 | − | 1130.93i | −0.0660552 | − | 0.108217i | ||||
\(479\) | −18352.1 | −1.75058 | −0.875289 | − | 0.483599i | \(-0.839329\pi\) | ||||
−0.875289 | + | 0.483599i | \(0.839329\pi\) | |||||||
\(480\) | −5795.28 | + | 13651.9i | −0.551078 | + | 1.29817i | ||||
\(481\) | 4300.30i | 0.407644i | ||||||||
\(482\) | −573.979 | − | 940.339i | −0.0542407 | − | 0.0888615i | ||||
\(483\) | −1053.35 | − | 8281.40i | −0.0992323 | − | 0.780159i | ||||
\(484\) | −1421.94 | + | 2766.72i | −0.133540 | + | 0.259835i | ||||
\(485\) | −11210.6 | −1.04958 | ||||||||
\(486\) | 2666.72 | − | 1627.75i | 0.248899 | − | 0.151927i | ||||
\(487\) | 14673.5i | 1.36534i | 0.730729 | + | 0.682668i | \(0.239180\pi\) | ||||
−0.730729 | + | 0.682668i | \(0.760820\pi\) | |||||||
\(488\) | 17579.2 | − | 1290.67i | 1.63068 | − | 0.119725i | ||||
\(489\) | 11807.1i | 1.09190i | ||||||||
\(490\) | 11893.9 | + | 11527.1i | 1.09656 | + | 1.06274i | ||||
\(491\) | − | 3216.95i | − | 0.295680i | −0.989011 | − | 0.147840i | \(-0.952768\pi\) | ||
0.989011 | − | 0.147840i | \(-0.0472321\pi\) | |||||||
\(492\) | 7761.37 | + | 3988.90i | 0.711198 | + | 0.365515i | ||||
\(493\) | − | 787.043i | − | 0.0718999i | ||||||
\(494\) | −2776.91 | − | 4549.35i | −0.252913 | − | 0.414342i | ||||
\(495\) | 2811.26 | 0.255266 | ||||||||
\(496\) | 3034.03 | + | 4238.07i | 0.274662 | + | 0.383659i | ||||
\(497\) | 462.141 | + | 3633.33i | 0.0417100 | + | 0.327922i | ||||
\(498\) | 10873.2 | − | 6636.97i | 0.978394 | − | 0.597208i | ||||
\(499\) | − | 8857.13i | − | 0.794589i | −0.917691 | − | 0.397294i | \(-0.869949\pi\) | ||
0.917691 | − | 0.397294i | \(-0.130051\pi\) | |||||||
\(500\) | 5038.93 | + | 2589.72i | 0.450696 | + | 0.231632i | ||||
\(501\) | 10236.8 | 0.912868 | ||||||||
\(502\) | −11324.1 | + | 6912.18i | −1.00681 | + | 0.614553i | ||||
\(503\) | 5037.58 | 0.446550 | 0.223275 | − | 0.974756i | \(-0.428325\pi\) | ||||
0.223275 | + | 0.974756i | \(0.428325\pi\) | |||||||
\(504\) | 330.252 | + | 1630.82i | 0.0291877 | + | 0.144132i | ||||
\(505\) | −17063.0 | −1.50355 | ||||||||
\(506\) | 9404.16 | − | 5740.26i | 0.826217 | − | 0.504319i | ||||
\(507\) | −669.339 | −0.0586319 | ||||||||
\(508\) | −9584.72 | − | 4926.00i | −0.837113 | − | 0.430228i | ||||
\(509\) | − | 10689.6i | − | 0.930860i | −0.885085 | − | 0.465430i | \(-0.845900\pi\) | ||
0.885085 | − | 0.465430i | \(-0.154100\pi\) | |||||||
\(510\) | −5595.14 | + | 3415.25i | −0.485798 | + | 0.296529i | ||||
\(511\) | −597.275 | − | 4695.75i | −0.0517063 | − | 0.406512i | ||||
\(512\) | −2526.73 | − | 11306.3i | −0.218100 | − | 0.975927i | ||||
\(513\) | 6174.37 | 0.531394 | ||||||||
\(514\) | 7697.14 | + | 12610.1i | 0.660518 | + | 1.08212i | ||||
\(515\) | 16371.7i | 1.40082i | ||||||||
\(516\) | 5872.63 | + | 3018.19i | 0.501023 | + | 0.257497i | ||||
\(517\) | 11860.9i | 1.00898i | ||||||||
\(518\) | 3878.51 | − | 3101.56i | 0.328981 | − | 0.263079i | ||||
\(519\) | 7019.50i | 0.593684i | ||||||||
\(520\) | 1283.10 | + | 17476.1i | 0.108207 | + | 1.47380i | ||||
\(521\) | − | 13501.9i | − | 1.13537i | −0.823246 | − | 0.567685i | \(-0.807839\pi\) | ||
0.823246 | − | 0.567685i | \(-0.192161\pi\) | |||||||
\(522\) | 266.709 | − | 162.798i | 0.0223631 | − | 0.0136503i | ||||
\(523\) | −13819.9 | −1.15546 | −0.577728 | − | 0.816229i | \(-0.696061\pi\) | ||||
−0.577728 | + | 0.816229i | \(0.696061\pi\) | |||||||
\(524\) | −1756.26 | + | 3417.23i | −0.146417 | + | 0.284890i | ||||
\(525\) | −14678.0 | + | 1866.97i | −1.22019 | + | 0.155202i | ||||
\(526\) | 6933.12 | + | 11358.4i | 0.574711 | + | 0.941539i | ||||
\(527\) | 2303.70i | 0.190419i | ||||||||
\(528\) | 10356.6 | − | 7414.27i | 0.853622 | − | 0.611108i | ||||
\(529\) | 3344.33 | 0.274869 | ||||||||
\(530\) | −14489.5 | − | 23737.9i | −1.18752 | − | 1.94549i | ||||
\(531\) | −1635.87 | −0.133692 | ||||||||
\(532\) | −2100.32 | + | 5785.72i | −0.171166 | + | 0.471509i | ||||
\(533\) | 10310.4 | 0.837886 | ||||||||
\(534\) | 8251.41 | + | 13518.1i | 0.668677 | + | 1.09548i | ||||
\(535\) | 11710.1 | 0.946303 | ||||||||
\(536\) | 4485.65 | − | 329.339i | 0.361475 | − | 0.0265397i | ||||
\(537\) | 14583.7i | 1.17194i | ||||||||
\(538\) | −5075.94 | − | 8315.82i | −0.406765 | − | 0.666395i | ||||
\(539\) | −3560.97 | − | 13771.6i | −0.284567 | − | 1.10053i | ||||
\(540\) | −18054.6 | − | 9279.04i | −1.43879 | − | 0.739456i | ||||
\(541\) | −1383.46 | −0.109944 | −0.0549720 | − | 0.998488i | \(-0.517507\pi\) | ||||
−0.0549720 | + | 0.998488i | \(0.517507\pi\) | |||||||
\(542\) | −12678.9 | + | 7739.16i | −1.00481 | + | 0.613331i | ||||
\(543\) | − | 1847.47i | − | 0.146008i | ||||||
\(544\) | 2000.86 | − | 4713.41i | 0.157695 | − | 0.371481i | ||||
\(545\) | − | 19254.7i | − | 1.51336i | ||||||
\(546\) | −7121.43 | − | 8905.38i | −0.558185 | − | 0.698013i | ||||
\(547\) | − | 19306.3i | − | 1.50910i | −0.656243 | − | 0.754550i | \(-0.727855\pi\) | ||
0.656243 | − | 0.754550i | \(-0.272145\pi\) | |||||||
\(548\) | −906.180 | + | 1763.19i | −0.0706389 | + | 0.137445i | ||||
\(549\) | 3093.02i | 0.240450i | ||||||||
\(550\) | −10174.1 | − | 16668.0i | −0.788769 | − | 1.29223i | ||||
\(551\) | 1155.88 | 0.0893684 | ||||||||
\(552\) | −10172.1 | + | 746.837i | −0.784333 | + | 0.0575861i | ||||
\(553\) | −2753.96 | − | 21651.5i | −0.211772 | − | 1.66494i | ||||
\(554\) | −14493.0 | + | 8846.46i | −1.11146 | + | 0.678429i | ||||
\(555\) | 7767.35i | 0.594064i | ||||||||
\(556\) | 6737.22 | − | 13108.9i | 0.513888 | − | 0.999893i | ||||
\(557\) | 25149.0 | 1.91310 | 0.956551 | − | 0.291564i | \(-0.0941755\pi\) | ||||
0.956551 | + | 0.291564i | \(0.0941755\pi\) | |||||||
\(558\) | −780.667 | + | 476.516i | −0.0592263 | + | 0.0361515i | ||||
\(559\) | 7801.36 | 0.590272 | ||||||||
\(560\) | 14836.5 | − | 13761.7i | 1.11957 | − | 1.03846i | ||||
\(561\) | 5629.56 | 0.423673 | ||||||||
\(562\) | 4516.09 | − | 2756.60i | 0.338968 | − | 0.206904i | ||||
\(563\) | 11127.2 | 0.832956 | 0.416478 | − | 0.909146i | \(-0.363264\pi\) | ||||
0.416478 | + | 0.909146i | \(0.363264\pi\) | |||||||
\(564\) | 5019.06 | − | 9765.80i | 0.374717 | − | 0.729103i | ||||
\(565\) | 171.561i | 0.0127745i | ||||||||
\(566\) | −9568.54 | + | 5840.60i | −0.710593 | + | 0.433743i | ||||
\(567\) | 11134.1 | − | 1416.20i | 0.824672 | − | 0.104894i | ||||
\(568\) | 4462.83 | − | 327.663i | 0.329677 | − | 0.0242050i | ||||
\(569\) | −2444.10 | −0.180074 | −0.0900368 | − | 0.995938i | \(-0.528698\pi\) | ||||
−0.0900368 | + | 0.995938i | \(0.528698\pi\) | |||||||
\(570\) | −5015.74 | − | 8217.20i | −0.368572 | − | 0.603825i | ||||
\(571\) | 7744.79i | 0.567617i | 0.958881 | + | 0.283809i | \(0.0915980\pi\) | ||||
−0.958881 | + | 0.283809i | \(0.908402\pi\) | |||||||
\(572\) | 6878.98 | − | 13384.7i | 0.502840 | − | 0.978398i | ||||
\(573\) | 2426.35i | 0.176897i | ||||||||
\(574\) | −7436.30 | − | 9299.13i | −0.540741 | − | 0.676199i | ||||
\(575\) | 15637.3i | 1.13413i | ||||||||
\(576\) | 2011.13 | − | 296.916i | 0.145481 | − | 0.0214783i | ||||
\(577\) | 27283.3i | 1.96849i | 0.176805 | + | 0.984246i | \(0.443424\pi\) | ||||
−0.176805 | + | 0.984246i | \(0.556576\pi\) | |||||||
\(578\) | −9929.27 | + | 6060.78i | −0.714538 | + | 0.436151i | ||||
\(579\) | −9223.04 | −0.661997 | ||||||||
\(580\) | −3379.93 | − | 1737.09i | −0.241972 | − | 0.124360i | ||||
\(581\) | −17242.6 | + | 2193.17i | −1.23123 | + | 0.156606i | ||||
\(582\) | −4643.58 | − | 7607.49i | −0.330726 | − | 0.541822i | ||||
\(583\) | 23884.0i | 1.69670i | ||||||||
\(584\) | −5767.80 | + | 423.474i | −0.408687 | + | 0.0300060i | ||||
\(585\) | −3074.89 | −0.217318 | ||||||||
\(586\) | −6859.24 | − | 11237.4i | −0.483537 | − | 0.792169i | ||||
\(587\) | −3068.80 | −0.215780 | −0.107890 | − | 0.994163i | \(-0.534409\pi\) | ||||
−0.107890 | + | 0.994163i | \(0.534409\pi\) | |||||||
\(588\) | −2895.64 | + | 12845.9i | −0.203085 | + | 0.900943i | ||||
\(589\) | −3383.29 | −0.236683 | ||||||||
\(590\) | 10365.4 | + | 16981.5i | 0.723286 | + | 1.18495i | ||||
\(591\) | −7695.65 | −0.535629 | ||||||||
\(592\) | −3531.91 | − | 4933.53i | −0.245204 | − | 0.342511i | ||||
\(593\) | 21823.7i | 1.51129i | 0.654984 | + | 0.755643i | \(0.272675\pi\) | ||||
−0.654984 | + | 0.755643i | \(0.727325\pi\) | |||||||
\(594\) | 9082.85 | + | 14880.3i | 0.627397 | + | 1.02785i | ||||
\(595\) | 8872.69 | − | 1128.56i | 0.611336 | − | 0.0777589i | ||||
\(596\) | −8048.09 | + | 15659.5i | −0.553125 | + | 1.07624i | ||||
\(597\) | −12279.2 | −0.841800 | ||||||||
\(598\) | −10286.0 | + | 6278.55i | −0.703390 | + | 0.429346i | ||||
\(599\) | − | 19352.6i | − | 1.32007i | −0.751233 | − | 0.660037i | \(-0.770541\pi\) | ||
0.751233 | − | 0.660037i | \(-0.229459\pi\) | |||||||
\(600\) | 1323.70 | + | 18029.0i | 0.0900662 | + | 1.22672i | ||||
\(601\) | − | 8218.83i | − | 0.557826i | −0.960316 | − | 0.278913i | \(-0.910026\pi\) | ||
0.960316 | − | 0.278913i | \(-0.0899740\pi\) | |||||||
\(602\) | −5626.66 | − | 7036.17i | −0.380940 | − | 0.476367i | ||||
\(603\) | 789.242i | 0.0533009i | ||||||||
\(604\) | 22832.7 | + | 11734.7i | 1.53816 | + | 0.790526i | ||||
\(605\) | 6638.62i | 0.446113i | ||||||||
\(606\) | −7067.72 | − | 11578.9i | −0.473773 | − | 0.776174i | ||||
\(607\) | 23793.3 | 1.59101 | 0.795503 | − | 0.605950i | \(-0.207207\pi\) | ||||
0.795503 | + | 0.605950i | \(0.207207\pi\) | |||||||
\(608\) | 6922.27 | + | 2938.53i | 0.461735 | + | 0.196008i | ||||
\(609\) | 2453.09 | − | 312.021i | 0.163225 | − | 0.0207614i | ||||
\(610\) | 32107.8 | − | 19598.5i | 2.13116 | − | 1.30085i | ||||
\(611\) | − | 12973.2i | − | 0.858981i | ||||||
\(612\) | 799.160 | + | 410.723i | 0.0527845 | + | 0.0271282i | ||||
\(613\) | 19490.1 | 1.28417 | 0.642087 | − | 0.766632i | \(-0.278069\pi\) | ||||
0.642087 | + | 0.766632i | \(0.278069\pi\) | |||||||
\(614\) | 6827.76 | − | 4167.63i | 0.448772 | − | 0.273928i | ||||
\(615\) | 18623.0 | 1.22106 | ||||||||
\(616\) | −17033.3 | + | 3449.36i | −1.11411 | + | 0.225614i | ||||
\(617\) | −12532.4 | −0.817724 | −0.408862 | − | 0.912596i | \(-0.634074\pi\) | ||||
−0.408862 | + | 0.912596i | \(0.634074\pi\) | |||||||
\(618\) | −11109.8 | + | 6781.36i | −0.723140 | + | 0.441402i | ||||
\(619\) | −3577.14 | −0.232274 | −0.116137 | − | 0.993233i | \(-0.537051\pi\) | ||||
−0.116137 | + | 0.993233i | \(0.537051\pi\) | |||||||
\(620\) | 9893.17 | + | 5084.52i | 0.640837 | + | 0.329354i | ||||
\(621\) | − | 13960.2i | − | 0.902097i | ||||||
\(622\) | 15835.1 | − | 9665.66i | 1.02078 | − | 0.623083i | ||||
\(623\) | −2726.66 | − | 21436.9i | −0.175347 | − | 1.37857i | ||||
\(624\) | −11327.8 | + | 8109.55i | −0.726721 | + | 0.520259i | ||||
\(625\) | −8719.36 | −0.558039 | ||||||||
\(626\) | 9161.78 | + | 15009.6i | 0.584949 | + | 0.958312i | ||||
\(627\) | 8267.76i | 0.526607i | ||||||||
\(628\) | 4529.22 | + | 2327.76i | 0.287795 | + | 0.147910i | ||||
\(629\) | − | 2681.73i | − | 0.169996i | ||||||
\(630\) | 2217.74 | + | 2773.29i | 0.140249 | + | 0.175382i | ||||
\(631\) | − | 2950.67i | − | 0.186156i | −0.995659 | − | 0.0930779i | \(-0.970329\pi\) | ||
0.995659 | − | 0.0930779i | \(-0.0296706\pi\) | |||||||
\(632\) | −26594.6 | + | 1952.58i | −1.67385 | + | 0.122895i | ||||
\(633\) | 1830.25i | 0.114922i | ||||||||
\(634\) | −7857.87 | + | 4796.41i | −0.492233 | + | 0.300457i | ||||
\(635\) | −22998.1 | −1.43724 | ||||||||
\(636\) | 10106.8 | − | 19665.2i | 0.630125 | − | 1.22606i | ||||
\(637\) | 3894.90 | + | 15063.0i | 0.242263 | + | 0.936922i | ||||
\(638\) | 1700.36 | + | 2785.67i | 0.105514 | + | 0.172862i | ||||
\(639\) | 785.227i | 0.0486120i | ||||||||
\(640\) | −15825.4 | − | 18995.6i | −0.977430 | − | 1.17323i | ||||
\(641\) | −2474.02 | −0.152446 | −0.0762229 | − | 0.997091i | \(-0.524286\pi\) | ||||
−0.0762229 | + | 0.997091i | \(0.524286\pi\) | |||||||
\(642\) | 4850.48 | + | 7946.46i | 0.298183 | + | 0.488507i | ||||
\(643\) | −20855.1 | −1.27907 | −0.639537 | − | 0.768760i | \(-0.720874\pi\) | ||||
−0.639537 | + | 0.768760i | \(0.720874\pi\) | |||||||
\(644\) | 13081.4 | + | 4748.79i | 0.800437 | + | 0.290572i | ||||
\(645\) | 14091.1 | 0.860210 | ||||||||
\(646\) | 1731.72 | + | 2837.05i | 0.105470 | + | 0.172790i | ||||
\(647\) | 24529.0 | 1.49047 | 0.745237 | − | 0.666800i | \(-0.232337\pi\) | ||||
0.745237 | + | 0.666800i | \(0.232337\pi\) | |||||||
\(648\) | −1004.10 | − | 13676.1i | −0.0608717 | − | 0.829084i | ||||
\(649\) | − | 17086.0i | − | 1.03341i | ||||||
\(650\) | 11128.1 | + | 18231.0i | 0.671509 | + | 1.10012i | ||||
\(651\) | −7180.28 | + | 913.296i | −0.432285 | + | 0.0549845i | ||||
\(652\) | −17506.4 | − | 8997.26i | −1.05154 | − | 0.540430i | ||||
\(653\) | 8840.01 | 0.529765 | 0.264882 | − | 0.964281i | \(-0.414667\pi\) | ||||
0.264882 | + | 0.964281i | \(0.414667\pi\) | |||||||
\(654\) | 13066.2 | − | 7975.58i | 0.781239 | − | 0.476865i | ||||
\(655\) | 8199.47i | 0.489129i | ||||||||
\(656\) | −11828.6 | + | 8468.10i | −0.704009 | + | 0.504000i | ||||
\(657\) | − | 1014.83i | − | 0.0602624i | ||||||
\(658\) | −11700.7 | + | 9356.78i | −0.693223 | + | 0.554354i | ||||
\(659\) | 26347.9i | 1.55746i | 0.627356 | + | 0.778732i | \(0.284137\pi\) | ||||
−0.627356 | + | 0.778732i | \(0.715863\pi\) | |||||||
\(660\) | 12425.0 | − | 24175.9i | 0.732795 | − | 1.42583i | ||||
\(661\) | − | 22699.6i | − | 1.33572i | −0.744286 | − | 0.667861i | \(-0.767210\pi\) | ||
0.744286 | − | 0.667861i | \(-0.232790\pi\) | |||||||
\(662\) | 6462.30 | + | 10587.1i | 0.379403 | + | 0.621568i | ||||
\(663\) | −6157.48 | −0.360689 | ||||||||
\(664\) | 1554.98 | + | 21179.1i | 0.0908809 | + | 1.23782i | ||||
\(665\) | 1657.44 | + | 13030.7i | 0.0966509 | + | 0.759864i | ||||
\(666\) | 908.771 | − | 554.710i | 0.0528741 | − | 0.0322741i | ||||
\(667\) | − | 2613.42i | − | 0.151712i | ||||||
\(668\) | −7800.65 | + | 15178.0i | −0.451820 | + | 0.879126i | ||||
\(669\) | −14127.4 | −0.816438 | ||||||||
\(670\) | 8192.92 | − | 5000.92i | 0.472418 | − | 0.288362i | ||||
\(671\) | −32305.4 | −1.85862 | ||||||||
\(672\) | 15484.2 | + | 4367.76i | 0.888863 | + | 0.250729i | ||||
\(673\) | −5208.40 | −0.298319 | −0.149160 | − | 0.988813i | \(-0.547657\pi\) | ||||
−0.149160 | + | 0.988813i | \(0.547657\pi\) | |||||||
\(674\) | 23102.6 | − | 14101.7i | 1.32029 | − | 0.805902i | ||||
\(675\) | −24743.1 | −1.41090 | ||||||||
\(676\) | 510.049 | − | 992.424i | 0.0290196 | − | 0.0564647i | ||||
\(677\) | 3144.71i | 0.178524i | 0.996008 | + | 0.0892622i | \(0.0284509\pi\) | ||||
−0.996008 | + | 0.0892622i | \(0.971549\pi\) | |||||||
\(678\) | −116.421 | + | 71.0627i | −0.00659456 | + | 0.00402529i | ||||
\(679\) | 1534.46 | + | 12063.9i | 0.0867264 | + | 0.681838i | ||||
\(680\) | −800.162 | − | 10898.4i | −0.0451247 | − | 0.614607i | ||||
\(681\) | 27766.9 | 1.56245 | ||||||||
\(682\) | −4977.02 | − | 8153.76i | −0.279443 | − | 0.457806i | ||||
\(683\) | 11895.3i | 0.666415i | 0.942854 | + | 0.333208i | \(0.108131\pi\) | ||||
−0.942854 | + | 0.333208i | \(0.891869\pi\) | |||||||
\(684\) | −603.200 | + | 1173.67i | −0.0337192 | + | 0.0656089i | ||||
\(685\) | 4230.69i | 0.235980i | ||||||||
\(686\) | 10776.4 | − | 14377.0i | 0.599776 | − | 0.800168i | ||||
\(687\) | − | 20653.8i | − | 1.14700i | ||||||
\(688\) | −8950.11 | + | 6407.38i | −0.495959 | + | 0.355057i | ||||
\(689\) | − | 26123.7i | − | 1.44446i | ||||||
\(690\) | −18579.0 | + | 11340.5i | −1.02506 | + | 0.625691i | ||||
\(691\) | 24606.5 | 1.35467 | 0.677333 | − | 0.735676i | \(-0.263136\pi\) | ||||
0.677333 | + | 0.735676i | \(0.263136\pi\) | |||||||
\(692\) | −10407.8 | − | 5349.00i | −0.571740 | − | 0.293842i | ||||
\(693\) | −384.794 | − | 3025.23i | −0.0210925 | − | 0.165828i | ||||
\(694\) | 15339.9 | + | 25131.1i | 0.839042 | + | 1.37459i | ||||
\(695\) | − | 31454.1i | − | 1.71672i | ||||||
\(696\) | −221.226 | − | 3013.14i | −0.0120482 | − | 0.164099i | ||||
\(697\) | −6429.73 | −0.349416 | ||||||||
\(698\) | 18586.0 | + | 30449.1i | 1.00787 | + | 1.65117i | ||||
\(699\) | −24637.1 | −1.33314 | ||||||||
\(700\) | 8416.77 | − | 23185.6i | 0.454463 | − | 1.25191i | ||||
\(701\) | −1627.77 | −0.0877033 | −0.0438516 | − | 0.999038i | \(-0.513963\pi\) | ||||
−0.0438516 | + | 0.999038i | \(0.513963\pi\) | |||||||
\(702\) | −9934.60 | − | 16275.7i | −0.534127 | − | 0.875050i | ||||
\(703\) | 3938.48 | 0.211298 | ||||||||
\(704\) | 3101.17 | + | 21005.5i | 0.166023 | + | 1.12454i | ||||
\(705\) | − | 23432.5i | − | 1.25180i | ||||||
\(706\) | −15255.1 | − | 24992.2i | −0.813222 | − | 1.33229i | ||||
\(707\) | 2335.51 | + | 18361.7i | 0.124238 | + | 0.976750i | ||||
\(708\) | −7230.12 | + | 14067.9i | −0.383792 | + | 0.746760i | ||||
\(709\) | −27634.3 | −1.46379 | −0.731896 | − | 0.681416i | \(-0.761364\pi\) | ||||
−0.731896 | + | 0.681416i | \(0.761364\pi\) | |||||||
\(710\) | 8151.23 | − | 4975.48i | 0.430860 | − | 0.262995i | ||||
\(711\) | − | 4679.26i | − | 0.246816i | ||||||
\(712\) | −26331.0 | + | 1933.23i | −1.38595 | + | 0.101757i | ||||
\(713\) | 7649.59i | 0.401794i | ||||||||
\(714\) | 4441.03 | + | 5553.53i | 0.232775 | + | 0.291086i | ||||
\(715\) | − | 32116.0i | − | 1.67982i | ||||||
\(716\) | −21623.1 | − | 11113.1i | −1.12862 | − | 0.580048i | ||||
\(717\) | − | 2248.04i | − | 0.117091i | ||||||
\(718\) | −5484.59 | − | 8985.30i | −0.285074 | − | 0.467031i | ||||
\(719\) | −5943.23 | −0.308269 | −0.154134 | − | 0.988050i | \(-0.549259\pi\) | ||||
−0.154134 | + | 0.988050i | \(0.549259\pi\) | |||||||
\(720\) | 3527.66 | − | 2525.45i | 0.182595 | − | 0.130720i | ||||
\(721\) | 17617.7 | − | 2240.89i | 0.910012 | − | 0.115749i | ||||
\(722\) | 12392.5 | − | 7564.34i | 0.638783 | − | 0.389911i | ||||
\(723\) | − | 1869.18i | − | 0.0961486i | ||||||
\(724\) | 2739.23 | + | 1407.81i | 0.140612 | + | 0.0722663i | ||||
\(725\) | −4632.04 | −0.237282 | ||||||||
\(726\) | −4504.95 | + | 2749.80i | −0.230295 | + | 0.140571i | ||||
\(727\) | 20574.9 | 1.04963 | 0.524816 | − | 0.851216i | \(-0.324134\pi\) | ||||
0.524816 | + | 0.851216i | \(0.324134\pi\) | |||||||
\(728\) | 18630.6 | − | 3772.82i | 0.948484 | − | 0.192074i | ||||
\(729\) | 21663.6 | 1.10063 | ||||||||
\(730\) | −10534.7 | + | 6430.35i | −0.534120 | + | 0.326024i | ||||
\(731\) | −4865.04 | −0.246156 | ||||||||
\(732\) | 26599.0 | + | 13670.4i | 1.34307 | + | 0.690261i | ||||
\(733\) | 16226.5i | 0.817655i | 0.912612 | + | 0.408828i | \(0.134062\pi\) | ||||
−0.912612 | + | 0.408828i | \(0.865938\pi\) | |||||||
\(734\) | 11289.1 | − | 6890.83i | 0.567696 | − | 0.346519i | ||||
\(735\) | 7035.10 | + | 27207.4i | 0.353052 | + | 1.36539i | ||||
\(736\) | 6643.98 | − | 15651.2i | 0.332745 | − | 0.783844i | ||||
\(737\) | −8243.33 | −0.412004 | ||||||||
\(738\) | −1329.97 | − | 2178.87i | −0.0663374 | − | 0.108679i | ||||
\(739\) | − | 27285.1i | − | 1.35818i | −0.734054 | − | 0.679092i | \(-0.762374\pi\) | ||
0.734054 | − | 0.679092i | \(-0.237626\pi\) | |||||||
\(740\) | −11516.6 | − | 5918.87i | −0.572106 | − | 0.294030i | ||||
\(741\) | − | 9043.07i | − | 0.448320i | ||||||
\(742\) | −23561.4 | + | 18841.5i | −1.16572 | + | 0.932202i | ||||
\(743\) | 15043.5i | 0.742791i | 0.928475 | + | 0.371396i | \(0.121121\pi\) | ||||
−0.928475 | + | 0.371396i | \(0.878879\pi\) | |||||||
\(744\) | 647.536 | + | 8819.56i | 0.0319084 | + | 0.434598i | ||||
\(745\) | 37574.2i | 1.84780i | ||||||||
\(746\) | 15938.5 | − | 9728.78i | 0.782238 | − | 0.477475i | ||||
\(747\) | −3726.43 | −0.182521 | ||||||||
\(748\) | −4289.84 | + | 8346.92i | −0.209695 | + | 0.408013i | ||||
\(749\) | −1602.83 | − | 12601.4i | −0.0781926 | − | 0.614746i | ||||
\(750\) | 5008.12 | + | 8204.71i | 0.243828 | + | 0.399458i | ||||
\(751\) | 17941.4i | 0.871757i | 0.900006 | + | 0.435879i | \(0.143562\pi\) | ||||
−0.900006 | + | 0.435879i | \(0.856438\pi\) | |||||||
\(752\) | 10655.1 | + | 14883.5i | 0.516689 | + | 0.721734i | ||||
\(753\) | −22509.7 | −1.08937 | ||||||||
\(754\) | −1859.81 | − | 3046.90i | −0.0898281 | − | 0.147164i | ||||
\(755\) | 54785.8 | 2.64088 | ||||||||
\(756\) | −7514.04 | + | 20698.9i | −0.361486 | + | 0.995781i | ||||
\(757\) | −12961.3 | −0.622305 | −0.311152 | − | 0.950360i | \(-0.600715\pi\) | ||||
−0.311152 | + | 0.950360i | \(0.600715\pi\) | |||||||
\(758\) | −18797.8 | − | 30796.1i | −0.900749 | − | 1.47568i | ||||
\(759\) | 18693.3 | 0.893971 | ||||||||
\(760\) | 16005.7 | − | 1175.14i | 0.763930 | − | 0.0560880i | ||||
\(761\) | 8866.11i | 0.422334i | 0.977450 | + | 0.211167i | \(0.0677264\pi\) | ||||
−0.977450 | + | 0.211167i | \(0.932274\pi\) | |||||||
\(762\) | −9526.11 | − | 15606.4i | −0.452880 | − | 0.741945i | ||||
\(763\) | −20720.3 | + | 2635.51i | −0.983125 | + | 0.125048i | ||||
\(764\) | −3597.53 | − | 1848.92i | −0.170359 | − | 0.0875546i | ||||
\(765\) | 1917.54 | 0.0906261 | ||||||||
\(766\) | 3798.80 | − | 2318.77i | 0.179186 | − | 0.109374i | ||||
\(767\) | 18688.2i | 0.879783i | ||||||||
\(768\) | 6335.29 | − | 18607.4i | 0.297663 | − | 0.874265i | ||||
\(769\) | 31664.2i | 1.48484i | 0.669937 | + | 0.742418i | \(0.266321\pi\) | ||||
−0.669937 | + | 0.742418i | \(0.733679\pi\) | |||||||
\(770\) | −28965.9 | + | 23163.4i | −1.35566 | + | 1.08409i | ||||
\(771\) | 25065.9i | 1.17085i | ||||||||
\(772\) | 7028.14 | − | 13674.9i | 0.327653 | − | 0.637528i | ||||
\(773\) | 19253.1i | 0.895842i | 0.894073 | + | 0.447921i | \(0.147835\pi\) | ||||
−0.894073 | + | 0.447921i | \(0.852165\pi\) | |||||||
\(774\) | −1006.32 | − | 1648.64i | −0.0467332 | − | 0.0765621i | ||||
\(775\) | 13558.2 | 0.628417 | ||||||||
\(776\) | 14818.1 | − | 1087.95i | 0.685487 | − | 0.0503287i | ||||
\(777\) | 8358.54 | − | 1063.16i | 0.385922 | − | 0.0490873i | ||||
\(778\) | 9712.26 | − | 5928.32i | 0.447559 | − | 0.273188i | ||||
\(779\) | − | 9442.90i | − | 0.434309i | ||||||
\(780\) | −13590.2 | + | 26443.0i | −0.623856 | + | 1.21386i | ||||
\(781\) | −8201.39 | −0.375760 | ||||||||
\(782\) | 6414.53 | − | 3915.40i | 0.293329 | − | 0.179047i | ||||
\(783\) | 4135.24 | 0.188737 | ||||||||
\(784\) | −16839.9 | − | 14082.1i | −0.767126 | − | 0.641497i | ||||
\(785\) | 10867.6 | 0.494118 | ||||||||
\(786\) | −5564.15 | + | 3396.33i | −0.252502 | + | 0.154126i | ||||
\(787\) | 1284.72 | 0.0581897 | 0.0290949 | − | 0.999577i | \(-0.490738\pi\) | ||||
0.0290949 | + | 0.999577i | \(0.490738\pi\) | |||||||
\(788\) | 5864.23 | − | 11410.3i | 0.265108 | − | 0.515831i | ||||
\(789\) | 22577.9i | 1.01875i | ||||||||
\(790\) | −48574.2 | + | 29649.5i | −2.18758 | + | 1.33529i | ||||
\(791\) | 184.618 | − | 23.4825i | 0.00829871 | − | 0.00105555i | ||||
\(792\) | −3715.90 | + | 272.823i | −0.166716 | + | 0.0122403i | ||||
\(793\) | 35334.8 | 1.58231 | ||||||||
\(794\) | −5875.82 | − | 9626.25i | −0.262626 | − | 0.430255i | ||||
\(795\) | − | 47185.6i | − | 2.10503i | ||||||
\(796\) | 9356.99 | − | 18206.3i | 0.416645 | − | 0.810684i | ||||
\(797\) | 2593.21i | 0.115253i | 0.998338 | + | 0.0576263i | \(0.0183532\pi\) | ||||
−0.998338 | + | 0.0576263i | \(0.981647\pi\) | |||||||
\(798\) | −8156.09 | + | 6522.24i | −0.361808 | + | 0.289329i | ||||
\(799\) | 8090.25i | 0.358213i | ||||||||
\(800\) | −27740.2 | − | 11775.8i | −1.22595 | − | 0.520423i | ||||
\(801\) | − | 4632.89i | − | 0.204363i | ||||||
\(802\) | −11164.4 | + | 6814.72i | −0.491559 | + | 0.300045i | ||||
\(803\) | 10599.5 | 0.465815 | ||||||||
\(804\) | 6787.23 | + | 3488.25i | 0.297721 | + | 0.153011i | ||||
\(805\) | 29462.3 | − | 3747.46i | 1.28995 | − | 0.164075i | ||||
\(806\) | 5443.74 | + | 8918.38i | 0.237900 | + | 0.389747i | ||||
\(807\) | − | 16529.9i | − | 0.721042i | ||||||
\(808\) | 22553.7 | − | 1655.90i | 0.981977 | − | 0.0720971i | ||||
\(809\) | −11424.8 | −0.496508 | −0.248254 | − | 0.968695i | \(-0.579857\pi\) | ||||
−0.248254 | + | 0.968695i | \(0.579857\pi\) | |||||||
\(810\) | −15247.0 | − | 24978.9i | −0.661390 | − | 1.08354i | ||||
\(811\) | 32094.4 | 1.38962 | 0.694812 | − | 0.719191i | \(-0.255487\pi\) | ||||
0.694812 | + | 0.719191i | \(0.255487\pi\) | |||||||
\(812\) | −1406.67 | + | 3874.95i | −0.0607937 | + | 0.167468i | ||||
\(813\) | −25202.8 | −1.08721 | ||||||||
\(814\) | 5793.73 | + | 9491.76i | 0.249472 | + | 0.408705i | ||||
\(815\) | −42005.6 | −1.80539 | ||||||||
\(816\) | 7064.17 | − | 5057.24i | 0.303058 | − | 0.216959i | ||||
\(817\) | − | 7144.96i | − | 0.305961i | ||||||
\(818\) | −932.847 | − | 1528.27i | −0.0398732 | − | 0.0653234i | ||||
\(819\) | 420.878 | + | 3308.92i | 0.0179569 | + | 0.141176i | ||||
\(820\) | −14191.1 | + | 27612.2i | −0.604359 | + | 1.17593i | ||||
\(821\) | 3861.07 | 0.164132 | 0.0820660 | − | 0.996627i | \(-0.473848\pi\) | ||||
0.0820660 | + | 0.996627i | \(0.473848\pi\) | |||||||
\(822\) | −2870.94 | + | 1752.41i | −0.121819 | + | 0.0743581i | ||||
\(823\) | − | 4840.43i | − | 0.205014i | −0.994732 | − | 0.102507i | \(-0.967314\pi\) | ||
0.994732 | − | 0.102507i | \(-0.0326865\pi\) | |||||||
\(824\) | −1588.81 | − | 21639.9i | −0.0671709 | − | 0.914881i | ||||
\(825\) | − | 33132.1i | − | 1.39819i | ||||||
\(826\) | 16855.2 | − | 13478.7i | 0.710010 | − | 0.567779i | ||||
\(827\) | 831.897i | 0.0349793i | 0.999847 | + | 0.0174897i | \(0.00556741\pi\) | ||||
−0.999847 | + | 0.0174897i | \(0.994433\pi\) | |||||||
\(828\) | 2653.66 | + | 1363.83i | 0.111378 | + | 0.0572419i | ||||
\(829\) | − | 24696.3i | − | 1.03467i | −0.855784 | − | 0.517333i | \(-0.826925\pi\) | ||
0.855784 | − | 0.517333i | \(-0.173075\pi\) | |||||||
\(830\) | 23612.0 | + | 38683.1i | 0.987450 | + | 1.61772i | ||||
\(831\) | −28808.7 | −1.20260 | ||||||||
\(832\) | −3391.99 | − | 22975.2i | −0.141341 | − | 0.957359i | ||||
\(833\) | −2428.92 | − | 9393.54i | −0.101029 | − | 0.390716i | ||||
\(834\) | 21344.7 | − | 13028.7i | 0.886219 | − | 0.540945i | ||||
\(835\) | 36419.0i | 1.50938i | ||||||||
\(836\) | −12258.5 | − | 6300.19i | −0.507142 | − | 0.260642i | ||||
\(837\) | −12104.0 | −0.499851 | ||||||||
\(838\) | 7719.18 | − | 4711.75i | 0.318203 | − | 0.194230i | ||||
\(839\) | −20023.0 | −0.823922 | −0.411961 | − | 0.911202i | \(-0.635156\pi\) | ||||
−0.411961 | + | 0.911202i | \(0.635156\pi\) | |||||||
\(840\) | 33651.2 | − | 6814.59i | 1.38224 | − | 0.279912i | ||||
\(841\) | −23614.9 | −0.968259 | ||||||||
\(842\) | 13251.8 | − | 8088.87i | 0.542385 | − | 0.331070i | ||||
\(843\) | 8976.94 | 0.366764 | ||||||||
\(844\) | −2713.70 | − | 1394.68i | −0.110674 | − | 0.0568803i | ||||
\(845\) | − | 2381.27i | − | 0.0969447i | ||||||
\(846\) | −2741.58 | + | 1673.45i | −0.111415 | + | 0.0680075i | ||||
\(847\) | 7143.89 | − | 908.667i | 0.289808 | − | 0.0368621i | ||||
\(848\) | 21455.8 | + | 29970.5i | 0.868864 | + | 1.21367i | ||||
\(849\) | −19020.0 | −0.768865 | ||||||||
\(850\) | −6939.67 | − | 11369.1i | −0.280034 | − | 0.458774i | ||||
\(851\) | − | 8904.86i | − | 0.358701i | ||||||
\(852\) | 6752.70 | + | 3470.50i | 0.271530 | + | 0.139551i | ||||
\(853\) | − | 25542.4i | − | 1.02527i | −0.858606 | − | 0.512636i | \(-0.828669\pi\) | ||
0.858606 | − | 0.512636i | \(-0.171331\pi\) | |||||||
\(854\) | −25484.9 | − | 31869.0i | −1.02117 | − | 1.27697i | ||||
\(855\) | 2816.17i | 0.112644i | ||||||||
\(856\) | −15478.3 | + | 1136.42i | −0.618035 | + | 0.0453764i | ||||
\(857\) | − | 25923.2i | − | 1.03328i | −0.856204 | − | 0.516638i | \(-0.827183\pi\) | ||
0.856204 | − | 0.516638i | \(-0.172817\pi\) | |||||||
\(858\) | 21793.8 | − | 13302.9i | 0.867167 | − | 0.529315i | ||||
\(859\) | −25807.8 | −1.02509 | −0.512544 | − | 0.858661i | \(-0.671297\pi\) | ||||
−0.512544 | + | 0.858661i | \(0.671297\pi\) | |||||||
\(860\) | −10737.7 | + | 20892.7i | −0.425758 | + | 0.828414i | ||||
\(861\) | −2549.04 | − | 20040.4i | −0.100896 | − | 0.793236i | ||||
\(862\) | −6157.30 | − | 10087.4i | −0.243293 | − | 0.398582i | ||||
\(863\) | 1101.05i | 0.0434302i | 0.999764 | + | 0.0217151i | \(0.00691267\pi\) | ||||
−0.999764 | + | 0.0217151i | \(0.993087\pi\) | |||||||
\(864\) | 24764.9 | + | 10512.8i | 0.975139 | + | 0.413951i | ||||
\(865\) | −24972.9 | −0.981624 | ||||||||
\(866\) | 13713.8 | + | 22467.1i | 0.538123 | + | 0.881597i | ||||
\(867\) | −19737.1 | −0.773134 | ||||||||
\(868\) | 4117.38 | − | 11342.1i | 0.161006 | − | 0.443521i | ||||
\(869\) | 48873.0 | 1.90783 | ||||||||
\(870\) | −3359.26 | − | 5503.41i | −0.130907 | − | 0.214463i | ||||
\(871\) | 9016.35 | 0.350755 | ||||||||
\(872\) | 1868.61 | + | 25450.8i | 0.0725676 | + | 0.988385i | ||||
\(873\) | 2607.21i | 0.101078i | ||||||||
\(874\) | 5750.28 | + | 9420.58i | 0.222547 | + | 0.364595i | ||||
\(875\) | −1654.92 | − | 13010.9i | −0.0639390 | − | 0.502685i | ||||
\(876\) | −8727.25 | − | 4485.31i | −0.336605 | − | 0.172996i | ||||
\(877\) | 43509.3 | 1.67526 | 0.837631 | − | 0.546237i | \(-0.183940\pi\) | ||||
0.837631 | + | 0.546237i | \(0.183940\pi\) | |||||||
\(878\) | 7077.08 | − | 4319.82i | 0.272027 | − | 0.166044i | ||||
\(879\) | − | 22337.3i | − | 0.857131i | ||||||
\(880\) | 26377.4 | + | 36845.1i | 1.01043 | + | 1.41142i | ||||
\(881\) | 39281.4i | 1.50219i | 0.660197 | + | 0.751093i | \(0.270473\pi\) | ||||
−0.660197 | + | 0.751093i | \(0.729527\pi\) | |||||||
\(882\) | 2680.82 | − | 2766.13i | 0.102344 | − | 0.105601i | ||||
\(883\) | − | 4217.95i | − | 0.160754i | −0.996765 | − | 0.0803768i | \(-0.974388\pi\) | ||
0.996765 | − | 0.0803768i | \(-0.0256123\pi\) | |||||||
\(884\) | 4692.12 | − | 9129.65i | 0.178521 | − | 0.347357i | ||||
\(885\) | 33755.3i | 1.28212i | ||||||||
\(886\) | −8671.25 | − | 14205.9i | −0.328799 | − | 0.538666i | ||||
\(887\) | −7206.54 | −0.272798 | −0.136399 | − | 0.990654i | \(-0.543553\pi\) | ||||
−0.136399 | + | 0.990654i | \(0.543553\pi\) | |||||||
\(888\) | −753.794 | − | 10266.8i | −0.0284861 | − | 0.387987i | ||||
\(889\) | 3147.88 | + | 24748.5i | 0.118759 | + | 0.933675i | ||||
\(890\) | −48092.8 | + | 29355.6i | −1.81132 | + | 1.10562i | ||||
\(891\) | 25132.6i | 0.944977i | ||||||||
\(892\) | 10765.4 | − | 20946.6i | 0.404093 | − | 0.786260i | ||||
\(893\) | −11881.6 | −0.445244 | ||||||||
\(894\) | −25497.8 | + | 15563.7i | −0.953885 | + | 0.582247i | ||||
\(895\) | −51883.7 | −1.93774 | ||||||||
\(896\) | −18275.3 | + | 19630.0i | −0.681401 | + | 0.731911i | ||||
\(897\) | −20446.3 | −0.761071 | ||||||||
\(898\) | −31038.0 | + | 18945.5i | −1.15340 | + | 0.704030i | ||||
\(899\) | −2265.94 | −0.0840636 | ||||||||
\(900\) | 2417.25 | − | 4703.35i | 0.0895279 | − | 0.174198i | ||||
\(901\) | 16291.1i | 0.602372i | ||||||||
\(902\) | 22757.4 | − | 13891.0i | 0.840067 | − | 0.512773i | ||||
\(903\) | −1928.73 | − | 15163.6i | −0.0710787 | − | 0.558817i | ||||
\(904\) | −16.6494 | − | 226.767i | −0.000612554 | − | 0.00834311i | ||||
\(905\) | 6572.65 | 0.241417 | ||||||||
\(906\) | 22693.0 | + | 37177.6i | 0.832147 | + | 1.36329i | ||||
\(907\) | 28116.4i | 1.02932i | 0.857395 | + | 0.514659i | \(0.172081\pi\) | ||||
−0.857395 | + | 0.514659i | \(0.827919\pi\) | |||||||
\(908\) | −21158.9 | + | 41169.8i | −0.773331 | + | 1.50470i | ||||
\(909\) | 3968.28i | 0.144796i | ||||||||
\(910\) | 31682.2 | − | 25335.5i | 1.15413 | − | 0.922928i | ||||
\(911\) | − | 36758.1i | − | 1.33683i | −0.743790 | − | 0.668414i | \(-0.766974\pi\) | ||
0.743790 | − | 0.668414i | \(-0.233026\pi\) | |||||||
\(912\) | 7427.22 | + | 10374.7i | 0.269671 | + | 0.376688i | ||||
\(913\) | − | 38921.1i | − | 1.41084i | ||||||
\(914\) | −4420.71 | + | 2698.38i | −0.159983 | + | 0.0976527i | ||||
\(915\) | 63822.9 | 2.30592 | ||||||||
\(916\) | 30623.2 | + | 15738.6i | 1.10460 | + | 0.567704i | ||||
\(917\) | 8823.55 | − | 1122.31i | 0.317753 | − | 0.0404165i | ||||
\(918\) | 6195.36 | + | 10149.7i | 0.222742 | + | 0.364915i | ||||
\(919\) | 4560.64i | 0.163702i | 0.996645 | + | 0.0818508i | \(0.0260831\pi\) | ||||
−0.996645 | + | 0.0818508i | \(0.973917\pi\) | |||||||
\(920\) | −2656.98 | − | 36188.6i | −0.0952154 | − | 1.29685i | ||||
\(921\) | 13572.0 | 0.485573 | ||||||||
\(922\) | −898.801 | − | 1472.49i | −0.0321046 | − | 0.0525964i | ||||
\(923\) | 8970.47 | 0.319899 | ||||||||
\(924\) | −27716.7 | − | 10061.6i | −0.986810 | − | 0.358229i | ||||
\(925\) | −15783.0 | −0.561018 | ||||||||
\(926\) | 11637.2 | + | 19065.0i | 0.412982 | + | 0.676580i | ||||
\(927\) | 3807.50 | 0.134903 | ||||||||
\(928\) | 4636.14 | + | 1968.06i | 0.163996 | + | 0.0696172i | ||||
\(929\) | − | 47031.3i | − | 1.66098i | −0.557037 | − | 0.830488i | \(-0.688062\pi\) | ||
0.557037 | − | 0.830488i | \(-0.311938\pi\) | |||||||
\(930\) | 9832.67 | + | 16108.7i | 0.346694 | + | 0.567983i | ||||
\(931\) | 13795.6 | − | 3567.19i | 0.485644 | − | 0.125574i | ||||
\(932\) | 18774.0 | − | 36529.3i | 0.659831 | − | 1.28386i | ||||
\(933\) | 31476.5 | 1.10449 | ||||||||
\(934\) | −35218.6 | + | 21497.3i | −1.23382 | + | 0.753119i | ||||
\(935\) | 20028.0i | 0.700520i | ||||||||
\(936\) | 4064.36 | − | 298.407i | 0.141931 | − | 0.0104207i | ||||
\(937\) | − | 958.545i | − | 0.0334197i | −0.999860 | − | 0.0167099i | \(-0.994681\pi\) | ||
0.999860 | − | 0.0167099i | \(-0.00531916\pi\) | |||||||
\(938\) | −6502.97 | − | 8131.99i | −0.226364 | − | 0.283069i | ||||
\(939\) | 29835.6i | 1.03690i | ||||||||
\(940\) | 34743.3 | + | 17856.1i | 1.20553 | + | 0.619575i | ||||
\(941\) | 26664.8i | 0.923748i | 0.886945 | + | 0.461874i | \(0.152823\pi\) | ||||
−0.886945 | + | 0.461874i | \(0.847177\pi\) | |||||||
\(942\) | 4501.52 | + | 7374.75i | 0.155698 | + | 0.255077i | ||||
\(943\) | −21350.3 | −0.737286 | ||||||||
\(944\) | −15349.0 | − | 21440.1i | −0.529201 | − | 0.739212i | ||||
\(945\) | 5929.62 | + | 46618.4i | 0.204117 | + | 1.60476i | ||||
\(946\) | 17219.4 | − | 10510.6i | 0.591808 | − | 0.361237i | ||||
\(947\) | 3408.56i | 0.116962i | 0.998289 | + | 0.0584812i | \(0.0186258\pi\) | ||||
−0.998289 | + | 0.0584812i | \(0.981374\pi\) | |||||||
\(948\) | −40240.2 | − | 20681.1i | −1.37863 | − | 0.708536i | ||||
\(949\) | −11593.5 | −0.396566 | ||||||||
\(950\) | 16697.1 | − | 10191.8i | 0.570236 | − | 0.348070i | ||||
\(951\) | −15619.6 | −0.532599 | ||||||||
\(952\) | −11618.3 | + | 2352.79i | −0.395538 | + | 0.0800990i | ||||
\(953\) | −30025.2 | −1.02058 | −0.510290 | − | 0.860002i | \(-0.670462\pi\) | ||||
−0.510290 | + | 0.860002i | \(0.670462\pi\) | |||||||
\(954\) | −5520.65 | + | 3369.78i | −0.187356 | + | 0.114361i | ||||
\(955\) | −8632.09 | −0.292490 | ||||||||
\(956\) | 3333.15 | + | 1713.05i | 0.112763 | + | 0.0579539i | ||||
\(957\) | 5537.27i | 0.187037i | ||||||||
\(958\) | 44305.8 | − | 27044.1i | 1.49421 | − | 0.912061i | ||||
\(959\) | 4552.70 | − | 579.080i | 0.153300 | − | 0.0194989i | ||||
\(960\) | −6126.72 | − | 41498.6i | −0.205978 | − | 1.39517i | ||||
\(961\) | −23158.5 | −0.777366 | ||||||||
\(962\) | −6337.04 | − | 10381.9i | −0.212385 | − | 0.347946i | ||||
\(963\) | − | 2723.38i | − | 0.0911316i | ||||||
\(964\) | 2771.42 | + | 1424.35i | 0.0925947 | + | 0.0475884i | ||||
\(965\) | − | 32812.3i | − | 1.09458i | ||||||
\(966\) | 14746.7 | + | 18440.8i | 0.491167 | + | 0.614207i | ||||
\(967\) | − | 21764.9i | − | 0.723798i | −0.932217 | − | 0.361899i | \(-0.882128\pi\) | ||
0.932217 | − | 0.361899i | \(-0.117872\pi\) | |||||||
\(968\) | −644.254 | − | 8774.87i | −0.0213916 | − | 0.291358i | ||||
\(969\) | 5639.39i | 0.186959i | ||||||||
\(970\) | 27064.8 | − | 16520.2i | 0.895873 | − | 0.546837i | ||||
\(971\) | 21876.6 | 0.723021 | 0.361511 | − | 0.932368i | \(-0.382261\pi\) | ||||
0.361511 | + | 0.932368i | \(0.382261\pi\) | |||||||
\(972\) | −4039.33 | + | 7859.49i | −0.133294 | + | 0.259355i | ||||
\(973\) | −33848.2 | + | 4305.31i | −1.11523 | + | 0.141852i | ||||
\(974\) | −21623.2 | − | 35424.9i | −0.711347 | − | 1.16539i | ||||
\(975\) | 36239.0i | 1.19034i | ||||||||
\(976\) | −40537.9 | + | 29021.0i | −1.32949 | + | 0.951784i | ||||
\(977\) | 33945.5 | 1.11158 | 0.555789 | − | 0.831323i | \(-0.312416\pi\) | ||||
0.555789 | + | 0.831323i | \(0.312416\pi\) | |||||||
\(978\) | −17399.3 | − | 28504.9i | −0.568884 | − | 0.931991i | ||||
\(979\) | 48388.7 | 1.57968 | ||||||||
\(980\) | −45701.1 | − | 10301.7i | −1.48966 | − | 0.335790i | ||||
\(981\) | −4478.01 | −0.145741 | ||||||||
\(982\) | 4740.58 | + | 7766.41i | 0.154051 | + | 0.252379i | ||||
\(983\) | 23428.5 | 0.760176 | 0.380088 | − | 0.924950i | \(-0.375894\pi\) | ||||
0.380088 | + | 0.924950i | \(0.375894\pi\) | |||||||
\(984\) | −24615.7 | + | 1807.30i | −0.797481 | + | 0.0585514i | ||||
\(985\) | − | 27378.4i | − | 0.885633i | ||||||
\(986\) | 1159.81 | + | 1900.09i | 0.0374602 | + | 0.0613704i | ||||
\(987\) | −25216.0 | + | 3207.35i | −0.813207 | + | 0.103436i | ||||
\(988\) | 13408.1 | + | 6890.99i | 0.431749 | + | 0.221894i | ||||
\(989\) | −16154.7 | −0.519402 | ||||||||
\(990\) | −6786.98 | + | 4142.74i | −0.217883 | + | 0.132995i | ||||
\(991\) | − | 54992.8i | − | 1.76277i | −0.472399 | − | 0.881385i | \(-0.656612\pi\) | ||
0.472399 | − | 0.881385i | \(-0.343388\pi\) | |||||||
\(992\) | −13570.1 | − | 5760.58i | −0.434327 | − | 0.184374i | ||||
\(993\) | 21044.7i | 0.672540i | ||||||||
\(994\) | −6469.88 | − | 8090.61i | −0.206451 | − | 0.258168i | ||||
\(995\) | − | 43685.1i | − | 1.39187i | ||||||
\(996\) | −16469.9 | + | 32046.1i | −0.523963 | + | 1.01950i | ||||
\(997\) | 1381.20i | 0.0438747i | 0.999759 | + | 0.0219374i | \(0.00698344\pi\) | ||||
−0.999759 | + | 0.0219374i | \(0.993017\pi\) | |||||||
\(998\) | 13052.1 | + | 21383.0i | 0.413985 | + | 0.678224i | ||||
\(999\) | 14090.2 | 0.446241 |
(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 | 28.4.d.b.27.3 | yes | 8 | |
3.2 | odd | 2 | 252.4.b.d.55.6 | 8 | |||
4.3 | odd | 2 | inner | 28.4.d.b.27.2 | yes | 8 | |
7.2 | even | 3 | 196.4.f.c.31.8 | 16 | |||
7.3 | odd | 6 | 196.4.f.c.19.3 | 16 | |||
7.4 | even | 3 | 196.4.f.c.19.4 | 16 | |||
7.5 | odd | 6 | 196.4.f.c.31.7 | 16 | |||
7.6 | odd | 2 | inner | 28.4.d.b.27.4 | yes | 8 | |
8.3 | odd | 2 | 448.4.f.d.447.4 | 8 | |||
8.5 | even | 2 | 448.4.f.d.447.6 | 8 | |||
12.11 | even | 2 | 252.4.b.d.55.8 | 8 | |||
21.20 | even | 2 | 252.4.b.d.55.5 | 8 | |||
28.3 | even | 6 | 196.4.f.c.19.8 | 16 | |||
28.11 | odd | 6 | 196.4.f.c.19.7 | 16 | |||
28.19 | even | 6 | 196.4.f.c.31.4 | 16 | |||
28.23 | odd | 6 | 196.4.f.c.31.3 | 16 | |||
28.27 | even | 2 | inner | 28.4.d.b.27.1 | ✓ | 8 | |
56.13 | odd | 2 | 448.4.f.d.447.3 | 8 | |||
56.27 | even | 2 | 448.4.f.d.447.5 | 8 | |||
84.83 | odd | 2 | 252.4.b.d.55.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.d.b.27.1 | ✓ | 8 | 28.27 | even | 2 | inner | |
28.4.d.b.27.2 | yes | 8 | 4.3 | odd | 2 | inner | |
28.4.d.b.27.3 | yes | 8 | 1.1 | even | 1 | trivial | |
28.4.d.b.27.4 | yes | 8 | 7.6 | odd | 2 | inner | |
196.4.f.c.19.3 | 16 | 7.3 | odd | 6 | |||
196.4.f.c.19.4 | 16 | 7.4 | even | 3 | |||
196.4.f.c.19.7 | 16 | 28.11 | odd | 6 | |||
196.4.f.c.19.8 | 16 | 28.3 | even | 6 | |||
196.4.f.c.31.3 | 16 | 28.23 | odd | 6 | |||
196.4.f.c.31.4 | 16 | 28.19 | even | 6 | |||
196.4.f.c.31.7 | 16 | 7.5 | odd | 6 | |||
196.4.f.c.31.8 | 16 | 7.2 | even | 3 | |||
252.4.b.d.55.5 | 8 | 21.20 | even | 2 | |||
252.4.b.d.55.6 | 8 | 3.2 | odd | 2 | |||
252.4.b.d.55.7 | 8 | 84.83 | odd | 2 | |||
252.4.b.d.55.8 | 8 | 12.11 | even | 2 | |||
448.4.f.d.447.3 | 8 | 56.13 | odd | 2 | |||
448.4.f.d.447.4 | 8 | 8.3 | odd | 2 | |||
448.4.f.d.447.5 | 8 | 56.27 | even | 2 | |||
448.4.f.d.447.6 | 8 | 8.5 | even | 2 |