Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), not 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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.95327307.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 85x^{2} - 68x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 136.3 | ||
Root | \(0.500000 + 2.36807i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.136 |
Dual form | 405.4.e.r.271.3 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.22969 | − | 3.86194i | 0.788315 | − | 1.36540i | −0.138684 | − | 0.990337i | \(-0.544287\pi\) |
0.926999 | − | 0.375065i | \(-0.122380\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.94305 | − | 10.2937i | −0.742881 | − | 1.28671i | ||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.54062 | + | 4.40048i | −0.137180 | + | 0.237603i | −0.926428 | − | 0.376471i | \(-0.877137\pi\) |
0.789248 | + | 0.614075i | \(0.210471\pi\) | |||||||
\(8\) | −17.3296 | −0.765867 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 22.2969 | 0.705090 | ||||||||
\(11\) | 29.1503 | − | 50.4899i | 0.799014 | − | 1.38393i | −0.121244 | − | 0.992623i | \(-0.538688\pi\) |
0.920259 | − | 0.391311i | \(-0.127978\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.6060 | − | 18.3701i | −0.226274 | − | 0.391918i | 0.730427 | − | 0.682991i | \(-0.239321\pi\) |
−0.956701 | + | 0.291073i | \(0.905988\pi\) | |||||||
\(14\) | 11.3296 | + | 19.6234i | 0.216283 | + | 0.374613i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.90475 | − | 15.4235i | 0.139137 | − | 0.240992i | ||||
\(17\) | 68.8451 | 0.982199 | 0.491099 | − | 0.871104i | \(-0.336595\pi\) | ||||
0.491099 | + | 0.871104i | \(0.336595\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −40.8133 | −0.492800 | −0.246400 | − | 0.969168i | \(-0.579248\pi\) | ||||
−0.246400 | + | 0.969168i | \(0.579248\pi\) | |||||||
\(20\) | 29.7152 | − | 51.4683i | 0.332226 | − | 0.575433i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −129.993 | − | 225.154i | −1.25975 | − | 2.18195i | ||||
\(23\) | −72.1592 | − | 124.983i | −0.654184 | − | 1.13308i | −0.982098 | − | 0.188372i | \(-0.939679\pi\) |
0.327914 | − | 0.944708i | \(-0.393654\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | −94.5921 | −0.713501 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 60.3960 | 0.407635 | ||||||||
\(29\) | −110.029 | + | 190.576i | −0.704547 | + | 1.22031i | 0.262308 | + | 0.964984i | \(0.415516\pi\) |
−0.966855 | + | 0.255327i | \(0.917817\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −145.773 | − | 252.486i | −0.844566 | − | 1.46283i | −0.885998 | − | 0.463690i | \(-0.846525\pi\) |
0.0414319 | − | 0.999141i | \(-0.486808\pi\) | |||||||
\(32\) | −109.028 | − | 188.842i | −0.602301 | − | 1.04322i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 153.503 | − | 265.875i | 0.774282 | − | 1.34110i | ||||
\(35\) | −25.4062 | −0.122698 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 260.637 | 1.15807 | 0.579033 | − | 0.815304i | \(-0.303430\pi\) | ||||
0.579033 | + | 0.815304i | \(0.303430\pi\) | |||||||
\(38\) | −91.0010 | + | 157.618i | −0.388482 | + | 0.672870i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −43.3240 | − | 75.0393i | −0.171253 | − | 0.296619i | ||||
\(41\) | −84.8832 | − | 147.022i | −0.323330 | − | 0.560024i | 0.657843 | − | 0.753155i | \(-0.271469\pi\) |
−0.981173 | + | 0.193131i | \(0.938136\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 219.298 | − | 379.835i | 0.777735 | − | 1.34708i | −0.155509 | − | 0.987834i | \(-0.549702\pi\) |
0.933244 | − | 0.359242i | \(-0.116965\pi\) | |||||||
\(44\) | −692.967 | −2.37429 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −643.571 | −2.06281 | ||||||||
\(47\) | −127.740 | + | 221.253i | −0.396444 | + | 0.686661i | −0.993284 | − | 0.115699i | \(-0.963089\pi\) |
0.596841 | + | 0.802360i | \(0.296422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 158.591 | + | 274.687i | 0.462363 | + | 0.800836i | ||||
\(50\) | 55.7423 | + | 96.5485i | 0.157663 | + | 0.273080i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −126.063 | + | 218.348i | −0.336189 | + | 0.582297i | ||||
\(53\) | −214.714 | −0.556477 | −0.278239 | − | 0.960512i | \(-0.589751\pi\) | ||||
−0.278239 | + | 0.960512i | \(0.589751\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 291.503 | 0.714660 | ||||||||
\(56\) | 44.0278 | − | 76.2585i | 0.105062 | − | 0.181973i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 490.661 | + | 849.850i | 1.11081 | + | 1.92398i | ||||
\(59\) | 165.762 | + | 287.108i | 0.365769 | + | 0.633530i | 0.988899 | − | 0.148588i | \(-0.0474728\pi\) |
−0.623131 | + | 0.782118i | \(0.714139\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −27.4823 | + | 47.6008i | −0.0576845 | + | 0.0999124i | −0.893426 | − | 0.449211i | \(-0.851705\pi\) |
0.835741 | + | 0.549124i | \(0.185038\pi\) | |||||||
\(62\) | −1300.11 | −2.66314 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −829.920 | −1.62094 | ||||||||
\(65\) | 53.0298 | − | 91.8503i | 0.101193 | − | 0.175271i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −379.090 | − | 656.603i | −0.691241 | − | 1.19727i | −0.971431 | − | 0.237321i | \(-0.923731\pi\) |
0.280190 | − | 0.959945i | \(-0.409603\pi\) | |||||||
\(68\) | −409.149 | − | 708.668i | −0.729657 | − | 1.26380i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −56.6479 | + | 98.1171i | −0.0967246 | + | 0.167532i | ||||
\(71\) | 904.348 | 1.51164 | 0.755819 | − | 0.654780i | \(-0.227239\pi\) | ||||
0.755819 | + | 0.654780i | \(0.227239\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 866.622 | 1.38946 | 0.694729 | − | 0.719271i | \(-0.255524\pi\) | ||||
0.694729 | + | 0.719271i | \(0.255524\pi\) | |||||||
\(74\) | 581.139 | − | 1006.56i | 0.912920 | − | 1.58122i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 242.555 | + | 420.118i | 0.366092 | + | 0.634090i | ||||
\(77\) | 148.120 | + | 256.551i | 0.219218 | + | 0.379697i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −103.480 | + | 179.233i | −0.147373 | + | 0.255257i | −0.930256 | − | 0.366912i | \(-0.880415\pi\) |
0.782883 | + | 0.622169i | \(0.213748\pi\) | |||||||
\(80\) | 89.0475 | 0.124448 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −757.054 | −1.01954 | ||||||||
\(83\) | −231.699 | + | 401.314i | −0.306412 | + | 0.530722i | −0.977575 | − | 0.210589i | \(-0.932462\pi\) |
0.671162 | + | 0.741310i | \(0.265795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 172.113 | + | 298.108i | 0.219626 | + | 0.380404i | ||||
\(86\) | −977.933 | − | 1693.83i | −1.22620 | − | 2.12384i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −505.163 | + | 874.968i | −0.611938 | + | 1.05991i | ||||
\(89\) | −601.736 | −0.716673 | −0.358337 | − | 0.933592i | \(-0.616656\pi\) | ||||
−0.358337 | + | 0.933592i | \(0.616656\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 107.783 | 0.124162 | ||||||||
\(92\) | −857.691 | + | 1485.56i | −0.971961 | + | 1.68349i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 569.643 | + | 986.651i | 0.625045 | + | 1.08261i | ||||
\(95\) | −102.033 | − | 176.727i | −0.110194 | − | 0.190861i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −114.682 | + | 198.634i | −0.120043 | + | 0.207920i | −0.919784 | − | 0.392424i | \(-0.871637\pi\) |
0.799741 | + | 0.600345i | \(0.204970\pi\) | |||||||
\(98\) | 1414.43 | 1.45795 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 297.152 | 0.297152 | ||||||||
\(101\) | 672.831 | − | 1165.38i | 0.662863 | − | 1.14811i | −0.316997 | − | 0.948427i | \(-0.602674\pi\) |
0.979860 | − | 0.199686i | \(-0.0639923\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 798.149 | + | 1382.44i | 0.763534 | + | 1.32248i | 0.941018 | + | 0.338356i | \(0.109871\pi\) |
−0.177484 | + | 0.984124i | \(0.556796\pi\) | |||||||
\(104\) | 183.797 | + | 318.345i | 0.173296 | + | 0.300157i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −478.747 | + | 829.214i | −0.438679 | + | 0.759815i | ||||
\(107\) | −958.786 | −0.866256 | −0.433128 | − | 0.901333i | \(-0.642590\pi\) | ||||
−0.433128 | + | 0.901333i | \(0.642590\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1690.23 | 1.48527 | 0.742635 | − | 0.669696i | \(-0.233576\pi\) | ||||
0.742635 | + | 0.669696i | \(0.233576\pi\) | |||||||
\(110\) | 649.963 | − | 1125.77i | 0.563377 | − | 0.975798i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 45.2471 | + | 78.3703i | 0.0381737 | + | 0.0661188i | ||||
\(113\) | −5.81057 | − | 10.0642i | −0.00483728 | − | 0.00837842i | 0.863597 | − | 0.504183i | \(-0.168206\pi\) |
−0.868434 | + | 0.495805i | \(0.834873\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 360.796 | − | 624.917i | 0.292560 | − | 0.506729i | ||||
\(116\) | 2615.63 | 2.09358 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1478.39 | 1.15336 | ||||||||
\(119\) | −174.909 | + | 302.951i | −0.134738 | + | 0.233374i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1033.98 | − | 1790.91i | −0.776848 | − | 1.34554i | ||||
\(122\) | 122.554 | + | 212.270i | 0.0909471 | + | 0.157525i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1732.67 | + | 3001.07i | −1.25482 | + | 2.17342i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 309.141 | 0.215999 | 0.107999 | − | 0.994151i | \(-0.465556\pi\) | ||||
0.107999 | + | 0.994151i | \(0.465556\pi\) | |||||||
\(128\) | −978.240 | + | 1694.36i | −0.675508 | + | 1.17001i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −236.480 | − | 409.596i | −0.159544 | − | 0.276338i | ||||
\(131\) | 1392.51 | + | 2411.90i | 0.928736 | + | 1.60862i | 0.785440 | + | 0.618938i | \(0.212437\pi\) |
0.143296 | + | 0.989680i | \(0.454230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 103.691 | − | 179.598i | 0.0676026 | − | 0.117091i | ||||
\(134\) | −3381.01 | −2.17966 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1193.06 | −0.752233 | ||||||||
\(137\) | −1244.71 | + | 2155.89i | −0.776222 | + | 1.34446i | 0.157884 | + | 0.987458i | \(0.449533\pi\) |
−0.934105 | + | 0.356998i | \(0.883800\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −893.026 | − | 1546.77i | −0.544931 | − | 0.943849i | −0.998611 | − | 0.0526839i | \(-0.983222\pi\) |
0.453680 | − | 0.891165i | \(-0.350111\pi\) | |||||||
\(140\) | 150.990 | + | 261.523i | 0.0911499 | + | 0.157876i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2016.42 | − | 3492.54i | 1.19165 | − | 2.06399i | ||||
\(143\) | −1236.67 | −0.723185 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1100.29 | −0.630166 | ||||||||
\(146\) | 1932.30 | − | 3346.84i | 1.09533 | − | 1.89717i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1548.98 | − | 2682.91i | −0.860304 | − | 1.49009i | ||||
\(149\) | 784.416 | + | 1358.65i | 0.431288 | + | 0.747012i | 0.996984 | − | 0.0776011i | \(-0.0247261\pi\) |
−0.565697 | + | 0.824613i | \(0.691393\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 219.163 | − | 379.602i | 0.118114 | − | 0.204580i | −0.800906 | − | 0.598790i | \(-0.795648\pi\) |
0.919020 | + | 0.394210i | \(0.128982\pi\) | |||||||
\(152\) | 707.277 | 0.377419 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1321.04 | 0.691252 | ||||||||
\(155\) | 728.863 | − | 1262.43i | 0.377701 | − | 0.654198i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.3739 | + | 38.7528i | 0.0113735 | + | 0.0196994i | 0.871656 | − | 0.490118i | \(-0.163046\pi\) |
−0.860283 | + | 0.509817i | \(0.829713\pi\) | |||||||
\(158\) | 461.458 | + | 799.270i | 0.232352 | + | 0.402446i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 545.140 | − | 944.211i | 0.269357 | − | 0.466540i | ||||
\(161\) | 733.315 | 0.358965 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2611.84 | −1.25506 | −0.627531 | − | 0.778591i | \(-0.715935\pi\) | ||||
−0.627531 | + | 0.778591i | \(0.715935\pi\) | |||||||
\(164\) | −1008.93 | + | 1747.52i | −0.480391 | + | 0.832062i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1033.23 | + | 1789.61i | 0.483099 | + | 0.836752i | ||||
\(167\) | −94.4733 | − | 163.633i | −0.0437758 | − | 0.0758220i | 0.843307 | − | 0.537432i | \(-0.180605\pi\) |
−0.887083 | + | 0.461610i | \(0.847272\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 873.527 | − | 1512.99i | 0.397600 | − | 0.688663i | ||||
\(170\) | 1535.03 | 0.692539 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5213.19 | −2.31106 | ||||||||
\(173\) | −752.510 | + | 1303.38i | −0.330707 | + | 0.572801i | −0.982651 | − | 0.185466i | \(-0.940620\pi\) |
0.651944 | + | 0.758267i | \(0.273954\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −63.5154 | − | 110.012i | −0.0274361 | − | 0.0475207i | ||||
\(176\) | −519.153 | − | 899.200i | −0.222345 | − | 0.385112i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1341.69 | + | 2323.87i | −0.564964 | + | 0.978547i | ||||
\(179\) | 3136.62 | 1.30973 | 0.654865 | − | 0.755746i | \(-0.272725\pi\) | ||||
0.654865 | + | 0.755746i | \(0.272725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4512.67 | 1.85317 | 0.926586 | − | 0.376084i | \(-0.122730\pi\) | ||||
0.926586 | + | 0.376084i | \(0.122730\pi\) | |||||||
\(182\) | 240.322 | − | 416.250i | 0.0978784 | − | 0.169530i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1250.49 | + | 2165.91i | 0.501018 | + | 0.867788i | ||||
\(185\) | 651.592 | + | 1128.59i | 0.258951 | + | 0.448517i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2006.86 | − | 3475.98i | 0.784791 | − | 1.35930i | ||||
\(188\) | 3036.67 | 1.17804 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −910.010 | −0.347469 | ||||||||
\(191\) | 603.717 | − | 1045.67i | 0.228709 | − | 0.396136i | −0.728717 | − | 0.684815i | \(-0.759883\pi\) |
0.957426 | + | 0.288680i | \(0.0932162\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −461.582 | − | 799.483i | −0.172152 | − | 0.298177i | 0.767020 | − | 0.641623i | \(-0.221739\pi\) |
−0.939172 | + | 0.343447i | \(0.888405\pi\) | |||||||
\(194\) | 511.409 | + | 885.787i | 0.189263 | + | 0.327813i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1885.02 | − | 3264.95i | 0.686961 | − | 1.18985i | ||||
\(197\) | 1180.87 | 0.427075 | 0.213537 | − | 0.976935i | \(-0.431501\pi\) | ||||
0.213537 | + | 0.976935i | \(0.431501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −839.805 | −0.299157 | −0.149578 | − | 0.988750i | \(-0.547792\pi\) | ||||
−0.149578 | + | 0.988750i | \(0.547792\pi\) | |||||||
\(200\) | 216.620 | − | 375.197i | 0.0765867 | − | 0.132652i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3000.41 | − | 5196.87i | −1.04509 | − | 1.81015i | ||||
\(203\) | −559.083 | − | 968.360i | −0.193300 | − | 0.334806i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 424.416 | − | 735.110i | 0.144598 | − | 0.250450i | ||||
\(206\) | 7118.51 | 2.40762 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −377.774 | −0.125932 | ||||||||
\(209\) | −1189.72 | + | 2060.66i | −0.393755 | + | 0.682003i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1294.82 | + | 2242.70i | 0.422461 | + | 0.731725i | 0.996180 | − | 0.0873280i | \(-0.0278328\pi\) |
−0.573718 | + | 0.819053i | \(0.694499\pi\) | |||||||
\(212\) | 1276.06 | + | 2210.20i | 0.413396 | + | 0.716023i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2137.80 | + | 3702.77i | −0.682882 | + | 1.18279i | ||||
\(215\) | 2192.98 | 0.695627 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1481.41 | 0.463432 | ||||||||
\(218\) | 3768.69 | − | 6527.56i | 1.17086 | − | 2.02799i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1732.42 | − | 3000.64i | −0.530907 | − | 0.919559i | ||||
\(221\) | −730.168 | − | 1264.69i | −0.222246 | − | 0.384942i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2090.38 | − | 3620.64i | 0.627722 | − | 1.08725i | −0.360285 | − | 0.932842i | \(-0.617321\pi\) |
0.988008 | − | 0.154405i | \(-0.0493459\pi\) | |||||||
\(224\) | 1107.99 | 0.330495 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −51.8232 | −0.0152532 | ||||||||
\(227\) | −1301.34 | + | 2253.98i | −0.380497 | + | 0.659039i | −0.991133 | − | 0.132872i | \(-0.957580\pi\) |
0.610637 | + | 0.791911i | \(0.290914\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 922.676 | + | 1598.12i | 0.266254 | + | 0.461165i | 0.967891 | − | 0.251369i | \(-0.0808807\pi\) |
−0.701638 | + | 0.712534i | \(0.747547\pi\) | |||||||
\(230\) | −1608.93 | − | 2786.74i | −0.461259 | − | 0.798923i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1906.76 | − | 3302.60i | 0.539589 | − | 0.934596i | ||||
\(233\) | −240.637 | −0.0676594 | −0.0338297 | − | 0.999428i | \(-0.510770\pi\) | ||||
−0.0338297 | + | 0.999428i | \(0.510770\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1277.40 | −0.354590 | ||||||||
\(236\) | 1970.26 | − | 3412.59i | 0.543445 | − | 0.941275i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 779.986 | + | 1350.98i | 0.212433 | + | 0.367944i | ||||
\(239\) | 1283.82 | + | 2223.64i | 0.347462 | + | 0.601822i | 0.985798 | − | 0.167936i | \(-0.0537102\pi\) |
−0.638336 | + | 0.769758i | \(0.720377\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1994.00 | + | 3453.70i | −0.532965 | + | 0.923122i | 0.466294 | + | 0.884630i | \(0.345589\pi\) |
−0.999259 | + | 0.0384925i | \(0.987744\pi\) | |||||||
\(242\) | −9221.86 | −2.44960 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 653.315 | 0.171411 | ||||||||
\(245\) | −792.953 | + | 1373.43i | −0.206775 | + | 0.358145i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 432.864 | + | 749.742i | 0.111508 | + | 0.193137i | ||||
\(248\) | 2526.18 | + | 4375.47i | 0.646825 | + | 1.12033i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −278.711 | + | 482.742i | −0.0705090 | + | 0.122125i | ||||
\(251\) | −967.393 | −0.243272 | −0.121636 | − | 0.992575i | \(-0.538814\pi\) | ||||
−0.121636 | + | 0.992575i | \(0.538814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8413.86 | −2.09081 | ||||||||
\(254\) | 689.289 | − | 1193.88i | 0.170275 | − | 0.294925i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1042.67 | + | 1805.96i | 0.254558 | + | 0.440907i | ||||
\(257\) | 1871.52 | + | 3241.56i | 0.454249 | + | 0.786783i | 0.998645 | − | 0.0520460i | \(-0.0165742\pi\) |
−0.544396 | + | 0.838829i | \(0.683241\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −662.178 | + | 1146.93i | −0.158864 | + | 0.275160i | ||||
\(260\) | −1260.63 | −0.300697 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12419.5 | 2.92855 | ||||||||
\(263\) | −1248.74 | + | 2162.88i | −0.292777 | + | 0.507105i | −0.974465 | − | 0.224538i | \(-0.927913\pi\) |
0.681688 | + | 0.731643i | \(0.261246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −536.786 | − | 929.741i | −0.124432 | − | 0.215523i | ||||
\(266\) | −462.397 | − | 800.896i | −0.106584 | − | 0.184609i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4505.90 | + | 7804.44i | −1.02702 | + | 1.77885i | ||||
\(269\) | 2142.91 | 0.485709 | 0.242855 | − | 0.970063i | \(-0.421916\pi\) | ||||
0.242855 | + | 0.970063i | \(0.421916\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1540.64 | 0.345341 | 0.172671 | − | 0.984980i | \(-0.444760\pi\) | ||||
0.172671 | + | 0.984980i | \(0.444760\pi\) | |||||||
\(272\) | 613.048 | − | 1061.83i | 0.136660 | − | 0.236702i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5550.62 | + | 9613.95i | 1.22381 | + | 2.11971i | ||||
\(275\) | 728.758 | + | 1262.25i | 0.159803 | + | 0.276787i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3388.90 | + | 5869.75i | −0.735088 | + | 1.27321i | 0.219597 | + | 0.975591i | \(0.429526\pi\) |
−0.954685 | + | 0.297619i | \(0.903808\pi\) | |||||||
\(278\) | −7964.69 | −1.71831 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 440.278 | 0.0939702 | ||||||||
\(281\) | 413.827 | − | 716.769i | 0.0878535 | − | 0.152167i | −0.818750 | − | 0.574150i | \(-0.805333\pi\) |
0.906604 | + | 0.421983i | \(0.138666\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1585.99 | + | 2747.01i | 0.333135 | + | 0.577007i | 0.983125 | − | 0.182936i | \(-0.0585602\pi\) |
−0.649990 | + | 0.759943i | \(0.725227\pi\) | |||||||
\(284\) | −5374.58 | − | 9309.05i | −1.12297 | − | 1.94504i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2757.39 | + | 4775.94i | −0.570098 | + | 0.987438i | ||||
\(287\) | 862.623 | 0.177418 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −173.358 | −0.0352856 | ||||||||
\(290\) | −2453.31 | + | 4249.25i | −0.496769 | + | 0.860430i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5150.38 | − | 8920.71i | −1.03220 | − | 1.78783i | ||||
\(293\) | 688.012 | + | 1191.67i | 0.137181 | + | 0.237605i | 0.926429 | − | 0.376471i | \(-0.122862\pi\) |
−0.789247 | + | 0.614075i | \(0.789529\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −828.809 | + | 1435.54i | −0.163577 | + | 0.283323i | ||||
\(296\) | −4516.73 | −0.886923 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6996.02 | 1.35996 | ||||||||
\(299\) | −1530.63 | + | 2651.14i | −0.296050 | + | 0.512773i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1114.30 | + | 1930.03i | 0.213380 | + | 0.369585i | ||||
\(302\) | −977.333 | − | 1692.79i | −0.186223 | − | 0.322547i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −363.432 | + | 629.483i | −0.0685666 | + | 0.118761i | ||||
\(305\) | −274.823 | −0.0515946 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −119.504 | −0.0222165 | −0.0111083 | − | 0.999938i | \(-0.503536\pi\) | ||||
−0.0111083 | + | 0.999938i | \(0.503536\pi\) | |||||||
\(308\) | 1760.56 | − | 3049.39i | 0.325706 | − | 0.564140i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3250.28 | − | 5629.65i | −0.595495 | − | 1.03143i | ||||
\(311\) | 1069.68 | + | 1852.73i | 0.195035 | + | 0.337810i | 0.946912 | − | 0.321493i | \(-0.104185\pi\) |
−0.751877 | + | 0.659303i | \(0.770851\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2581.75 | + | 4471.72i | −0.466227 | + | 0.807529i | −0.999256 | − | 0.0385677i | \(-0.987720\pi\) |
0.533029 | + | 0.846097i | \(0.321054\pi\) | |||||||
\(314\) | 199.548 | 0.0358635 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2459.95 | 0.437922 | ||||||||
\(317\) | −4315.85 | + | 7475.26i | −0.764675 | + | 1.32446i | 0.175743 | + | 0.984436i | \(0.443767\pi\) |
−0.940418 | + | 0.340020i | \(0.889566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6414.76 | + | 11110.7i | 1.12589 | + | 1.95009i | ||||
\(320\) | −2074.80 | − | 3593.66i | −0.362452 | − | 0.627786i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1635.07 | − | 2832.02i | 0.282977 | − | 0.490131i | ||||
\(323\) | −2809.79 | −0.484028 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 530.298 | 0.0905097 | ||||||||
\(326\) | −5823.60 | + | 10086.8i | −0.989385 | + | 1.71366i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1470.99 | + | 2547.83i | 0.247628 | + | 0.428904i | ||||
\(329\) | −649.079 | − | 1124.24i | −0.108769 | − | 0.188393i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1471.17 | − | 2548.14i | 0.244298 | − | 0.423137i | −0.717636 | − | 0.696419i | \(-0.754776\pi\) |
0.961934 | + | 0.273281i | \(0.0881090\pi\) | |||||||
\(332\) | 5507.98 | 0.910512 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −842.585 | −0.138037 | ||||||||
\(335\) | 1895.45 | − | 3283.01i | 0.309133 | − | 0.535433i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4948.73 | − | 8571.45i | −0.799924 | − | 1.38551i | −0.919665 | − | 0.392704i | \(-0.871540\pi\) |
0.119740 | − | 0.992805i | \(-0.461794\pi\) | |||||||
\(338\) | −3895.39 | − | 6747.02i | −0.626868 | − | 1.08577i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2045.75 | − | 3543.34i | 0.326312 | − | 0.565190i | ||||
\(341\) | −16997.3 | −2.69928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3354.53 | −0.528070 | ||||||||
\(344\) | −3800.34 | + | 6582.38i | −0.595641 | + | 1.03168i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3355.73 | + | 5812.29i | 0.521402 | + | 0.903095i | ||||
\(347\) | −6007.87 | − | 10405.9i | −0.929451 | − | 1.60986i | −0.784242 | − | 0.620454i | \(-0.786948\pi\) |
−0.145208 | − | 0.989401i | \(-0.546385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3947.31 | + | 6836.94i | −0.605428 | + | 1.04863i | 0.386555 | + | 0.922266i | \(0.373665\pi\) |
−0.991984 | + | 0.126367i | \(0.959668\pi\) | |||||||
\(350\) | −566.479 | −0.0865131 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12712.8 | −1.92499 | ||||||||
\(353\) | 370.577 | − | 641.858i | 0.0558748 | − | 0.0967781i | −0.836735 | − | 0.547608i | \(-0.815539\pi\) |
0.892610 | + | 0.450830i | \(0.148872\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2260.87 | + | 3915.94i | 0.338013 | + | 0.585455i | ||||
\(356\) | 3576.15 | + | 6194.07i | 0.532403 | + | 0.922149i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6993.68 | − | 12113.4i | 1.03248 | − | 1.78831i | ||||
\(359\) | 11564.4 | 1.70012 | 0.850060 | − | 0.526685i | \(-0.176565\pi\) | ||||
0.850060 | + | 0.526685i | \(0.176565\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5193.28 | −0.757148 | ||||||||
\(362\) | 10061.9 | − | 17427.6i | 1.46088 | − | 2.53032i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −640.558 | − | 1109.48i | −0.0922372 | − | 0.159760i | ||||
\(365\) | 2166.56 | + | 3752.58i | 0.310692 | + | 0.538135i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 574.284 | − | 994.690i | 0.0816823 | − | 0.141478i | −0.822290 | − | 0.569068i | \(-0.807304\pi\) |
0.903973 | + | 0.427590i | \(0.140637\pi\) | |||||||
\(368\) | −2570.24 | −0.364084 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5811.39 | 0.816540 | ||||||||
\(371\) | 545.507 | − | 944.846i | 0.0763378 | − | 0.132221i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2301.49 | + | 3986.29i | 0.319481 | + | 0.553358i | 0.980380 | − | 0.197117i | \(-0.0631580\pi\) |
−0.660899 | + | 0.750475i | \(0.729825\pi\) | |||||||
\(374\) | −8949.34 | − | 15500.7i | −1.23732 | − | 2.14311i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2213.69 | − | 3834.22i | 0.303623 | − | 0.525890i | ||||
\(377\) | 4667.85 | 0.637683 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3988.46 | −0.540563 | −0.270282 | − | 0.962781i | \(-0.587117\pi\) | ||||
−0.270282 | + | 0.962781i | \(0.587117\pi\) | |||||||
\(380\) | −1212.78 | + | 2100.59i | −0.163721 | + | 0.283574i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2692.21 | − | 4663.04i | −0.360590 | − | 0.624559i | ||||
\(383\) | 3894.10 | + | 6744.78i | 0.519528 | + | 0.899849i | 0.999742 | + | 0.0226975i | \(0.00722546\pi\) |
−0.480215 | + | 0.877151i | \(0.659441\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −740.599 | + | 1282.75i | −0.0980374 | + | 0.169806i | ||||
\(386\) | −4116.74 | −0.542841 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2726.23 | 0.356710 | ||||||||
\(389\) | 4262.43 | − | 7382.75i | 0.555563 | − | 0.962263i | −0.442297 | − | 0.896869i | \(-0.645836\pi\) |
0.997859 | − | 0.0653944i | \(-0.0208305\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4967.80 | − | 8604.49i | −0.642538 | − | 1.11291i | ||||
\(392\) | −2748.31 | − | 4760.21i | −0.354108 | − | 0.613334i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2632.98 | − | 4560.46i | 0.336669 | − | 0.583129i | ||||
\(395\) | −1034.80 | −0.131814 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −155.729 | −0.0196872 | −0.00984361 | − | 0.999952i | \(-0.503133\pi\) | ||||
−0.00984361 | + | 0.999952i | \(0.503133\pi\) | |||||||
\(398\) | −1872.51 | + | 3243.27i | −0.235830 | + | 0.408469i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 222.619 | + | 385.587i | 0.0278274 | + | 0.0481984i | ||||
\(401\) | 2966.98 | + | 5138.96i | 0.369486 | + | 0.639968i | 0.989485 | − | 0.144634i | \(-0.0462005\pi\) |
−0.619999 | + | 0.784602i | \(0.712867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3092.12 | + | 5355.70i | −0.382207 | + | 0.662002i | ||||
\(404\) | −15994.7 | −1.96971 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4986.33 | −0.609526 | ||||||||
\(407\) | 7597.65 | − | 13159.5i | 0.925311 | − | 1.60268i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7080.71 | − | 12264.1i | −0.856035 | − | 1.48270i | −0.875681 | − | 0.482890i | \(-0.839587\pi\) |
0.0196459 | − | 0.999807i | \(-0.493746\pi\) | |||||||
\(410\) | −1892.63 | − | 3278.14i | −0.227977 | − | 0.394868i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9486.88 | − | 16431.8i | 1.13443 | − | 1.96489i | ||||
\(413\) | −1684.55 | −0.200705 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2316.99 | −0.274064 | ||||||||
\(416\) | −2312.69 | + | 4005.70i | −0.272570 | + | 0.472105i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5305.42 | + | 9189.26i | 0.620805 | + | 1.07527i | ||||
\(419\) | 4812.12 | + | 8334.84i | 0.561068 | + | 0.971798i | 0.997404 | + | 0.0720142i | \(0.0229427\pi\) |
−0.436336 | + | 0.899784i | \(0.643724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 768.128 | − | 1330.44i | 0.0889223 | − | 0.154018i | −0.818134 | − | 0.575028i | \(-0.804991\pi\) |
0.907056 | + | 0.421010i | \(0.138324\pi\) | |||||||
\(422\) | 11548.2 | 1.33213 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3720.91 | 0.426187 | ||||||||
\(425\) | −860.563 | + | 1490.54i | −0.0982199 | + | 0.170122i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −139.644 | − | 241.871i | −0.0158264 | − | 0.0274121i | ||||
\(428\) | 5698.11 | + | 9869.42i | 0.643525 | + | 1.11462i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4889.67 | − | 8469.15i | 0.548373 | − | 0.949811i | ||||
\(431\) | −11582.2 | −1.29441 | −0.647207 | − | 0.762314i | \(-0.724063\pi\) | ||||
−0.647207 | + | 0.762314i | \(0.724063\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14892.6 | 1.65287 | 0.826437 | − | 0.563029i | \(-0.190364\pi\) | ||||
0.826437 | + | 0.563029i | \(0.190364\pi\) | |||||||
\(434\) | 3303.09 | − | 5721.11i | 0.365330 | − | 0.632770i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10045.1 | − | 17398.6i | −1.10338 | − | 1.91111i | ||||
\(437\) | 2945.05 | + | 5100.98i | 0.322382 | + | 0.558382i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 821.253 | − | 1422.45i | 0.0892853 | − | 0.154647i | −0.817924 | − | 0.575326i | \(-0.804875\pi\) |
0.907209 | + | 0.420680i | \(0.138208\pi\) | |||||||
\(440\) | −5051.63 | −0.547334 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6512.20 | −0.700800 | ||||||||
\(443\) | 1958.15 | − | 3391.62i | 0.210011 | − | 0.363749i | −0.741707 | − | 0.670724i | \(-0.765983\pi\) |
0.951718 | + | 0.306975i | \(0.0993168\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1504.34 | − | 2605.59i | −0.160253 | − | 0.277566i | ||||
\(446\) | −9321.79 | − | 16145.8i | −0.989686 | − | 1.71419i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2108.51 | − | 3652.04i | 0.222361 | − | 0.385140i | ||||
\(449\) | 3985.25 | 0.418876 | 0.209438 | − | 0.977822i | \(-0.432837\pi\) | ||||
0.209438 | + | 0.977822i | \(0.432837\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9897.50 | −1.03338 | ||||||||
\(452\) | −69.0650 | + | 119.624i | −0.00718705 | + | 0.0124483i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5803.16 | + | 10051.4i | 0.599902 | + | 1.03906i | ||||
\(455\) | 269.457 | + | 466.713i | 0.0277634 | + | 0.0480876i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7088.89 | − | 12278.3i | 0.725611 | − | 1.25680i | −0.233111 | − | 0.972450i | \(-0.574890\pi\) |
0.958722 | − | 0.284345i | \(-0.0917763\pi\) | |||||||
\(458\) | 8229.13 | 0.839567 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8576.91 | −0.869349 | ||||||||
\(461\) | −8197.14 | + | 14197.9i | −0.828154 | + | 1.43441i | 0.0713305 | + | 0.997453i | \(0.477275\pi\) |
−0.899485 | + | 0.436952i | \(0.856058\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1659.80 | − | 2874.86i | −0.166603 | − | 0.288566i | 0.770620 | − | 0.637295i | \(-0.219947\pi\) |
−0.937224 | + | 0.348729i | \(0.886613\pi\) | |||||||
\(464\) | 1959.56 | + | 3394.06i | 0.196057 | + | 0.339580i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −536.546 | + | 929.324i | −0.0533369 | + | 0.0923822i | ||||
\(467\) | 2529.79 | 0.250674 | 0.125337 | − | 0.992114i | \(-0.459999\pi\) | ||||
0.125337 | + | 0.992114i | \(0.459999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3852.49 | 0.379299 | ||||||||
\(470\) | −2848.22 | + | 4933.26i | −0.279529 | + | 0.484158i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2872.58 | − | 4975.46i | −0.280130 | − | 0.485199i | ||||
\(473\) | −12785.2 | − | 22144.6i | −1.24284 | − | 2.15267i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 510.166 | − | 883.633i | 0.0492800 | − | 0.0853555i | ||||
\(476\) | 4157.97 | 0.400379 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11450.1 | 1.09564 | ||||||||
\(479\) | −4323.38 | + | 7488.31i | −0.412401 | + | 0.714300i | −0.995152 | − | 0.0983514i | \(-0.968643\pi\) |
0.582751 | + | 0.812651i | \(0.301976\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2764.30 | − | 4787.91i | −0.262040 | − | 0.453867i | ||||
\(482\) | 8891.99 | + | 15401.4i | 0.840288 | + | 1.45542i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12290.0 | + | 21287.0i | −1.15421 | + | 1.99915i | ||||
\(485\) | −1146.82 | −0.107370 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15251.7 | −1.41914 | −0.709569 | − | 0.704636i | \(-0.751110\pi\) | ||||
−0.709569 | + | 0.704636i | \(0.751110\pi\) | |||||||
\(488\) | 476.257 | − | 824.902i | 0.0441786 | − | 0.0765196i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3536.08 | + | 6124.67i | 0.326008 | + | 0.564662i | ||||
\(491\) | −883.434 | − | 1530.15i | −0.0811992 | − | 0.140641i | 0.822566 | − | 0.568670i | \(-0.192542\pi\) |
−0.903765 | + | 0.428028i | \(0.859208\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7574.95 | + | 13120.2i | −0.692005 | + | 1.19859i | ||||
\(494\) | 3860.61 | 0.351614 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5192.28 | −0.470041 | ||||||||
\(497\) | −2297.60 | + | 3979.56i | −0.207367 | + | 0.359171i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5866.92 | − | 10161.8i | −0.526332 | − | 0.911633i | −0.999529 | − | 0.0306768i | \(-0.990234\pi\) |
0.473198 | − | 0.880956i | \(-0.343100\pi\) | |||||||
\(500\) | 742.881 | + | 1286.71i | 0.0664453 | + | 0.115087i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2156.99 | + | 3736.01i | −0.191775 | + | 0.332164i | ||||
\(503\) | 977.608 | 0.0866589 | 0.0433294 | − | 0.999061i | \(-0.486203\pi\) | ||||
0.0433294 | + | 0.999061i | \(0.486203\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6728.31 | 0.592883 | ||||||||
\(506\) | −18760.3 | + | 32493.8i | −1.64822 | + | 2.85479i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1837.24 | − | 3182.19i | −0.160461 | − | 0.277927i | ||||
\(509\) | 4837.36 | + | 8378.55i | 0.421242 | + | 0.729613i | 0.996061 | − | 0.0886678i | \(-0.0282609\pi\) |
−0.574819 | + | 0.818280i | \(0.694928\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2201.76 | + | 3813.55i | −0.190607 | + | 0.330140i | ||||
\(512\) | −6352.52 | −0.548329 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16691.6 | 1.43237 | ||||||||
\(515\) | −3990.75 | + | 6912.18i | −0.341463 | + | 0.591431i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7447.35 | + | 12899.2i | 0.633528 | + | 1.09730i | ||||
\(518\) | 2952.91 | + | 5114.58i | 0.250470 | + | 0.433826i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −918.984 | + | 1591.73i | −0.0775002 | + | 0.134234i | ||||
\(521\) | −5178.95 | −0.435497 | −0.217748 | − | 0.976005i | \(-0.569871\pi\) | ||||
−0.217748 | + | 0.976005i | \(0.569871\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14280.7 | 1.19398 | 0.596992 | − | 0.802248i | \(-0.296363\pi\) | ||||
0.596992 | + | 0.802248i | \(0.296363\pi\) | |||||||
\(524\) | 16551.5 | − | 28668.1i | 1.37988 | − | 2.39002i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5568.60 | + | 9645.09i | 0.461601 | + | 0.799517i | ||||
\(527\) | −10035.7 | − | 17382.4i | −0.829532 | − | 1.43679i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4330.39 | + | 7500.46i | −0.355913 | + | 0.616459i | ||||
\(530\) | −4787.47 | −0.392367 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2464.96 | −0.200883 | ||||||||
\(533\) | −1800.54 | + | 3118.62i | −0.146322 | + | 0.253438i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2396.97 | − | 4151.67i | −0.193701 | − | 0.335499i | ||||
\(536\) | 6569.47 | + | 11378.7i | 0.529399 | + | 0.916946i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4778.04 | − | 8275.80i | 0.382892 | − | 0.663188i | ||||
\(539\) | 18491.9 | 1.47774 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12923.8 | 1.02706 | 0.513529 | − | 0.858072i | \(-0.328338\pi\) | ||||
0.513529 | + | 0.858072i | \(0.328338\pi\) | |||||||
\(542\) | 3435.16 | − | 5949.87i | 0.272238 | − | 0.471529i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7506.04 | − | 13000.8i | −0.591579 | − | 1.02464i | ||||
\(545\) | 4225.57 | + | 7318.90i | 0.332117 | + | 0.575243i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6826.66 | + | 11824.1i | −0.533614 | + | 0.924246i | 0.465615 | + | 0.884987i | \(0.345833\pi\) |
−0.999229 | + | 0.0392591i | \(0.987500\pi\) | |||||||
\(548\) | 29589.4 | 2.30656 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6499.63 | 0.503900 | ||||||||
\(551\) | 4490.64 | − | 7778.02i | 0.347201 | − | 0.601370i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −525.808 | − | 910.726i | −0.0404333 | − | 0.0700326i | ||||
\(554\) | 15112.4 | + | 26175.5i | 1.15896 | + | 2.00738i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10614.6 | + | 18385.0i | −0.809638 | + | 1.40233i | ||||
\(557\) | 9313.63 | 0.708494 | 0.354247 | − | 0.935152i | \(-0.384737\pi\) | ||||
0.354247 | + | 0.935152i | \(0.384737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9303.46 | −0.703925 | ||||||||
\(560\) | −226.236 | + | 391.852i | −0.0170718 | + | 0.0295692i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1845.41 | − | 3196.35i | −0.138512 | − | 0.239911i | ||||
\(563\) | −5312.70 | − | 9201.86i | −0.397697 | − | 0.688831i | 0.595744 | − | 0.803174i | \(-0.296857\pi\) |
−0.993441 | + | 0.114343i | \(0.963524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.0529 | − | 50.3211i | 0.00216330 | − | 0.00374694i | ||||
\(566\) | 14145.1 | 1.05046 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15672.0 | −1.15771 | ||||||||
\(569\) | 4530.25 | − | 7846.62i | 0.333775 | − | 0.578115i | −0.649474 | − | 0.760384i | \(-0.725011\pi\) |
0.983249 | + | 0.182269i | \(0.0583441\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10689.6 | + | 18514.9i | 0.783440 | + | 1.35696i | 0.929926 | + | 0.367746i | \(0.119870\pi\) |
−0.146486 | + | 0.989213i | \(0.546796\pi\) | |||||||
\(572\) | 7349.58 | + | 12729.9i | 0.537240 | + | 0.930528i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1923.38 | − | 3331.40i | 0.139861 | − | 0.242247i | ||||
\(575\) | 3607.96 | 0.261674 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6347.76 | 0.457991 | 0.228996 | − | 0.973427i | \(-0.426456\pi\) | ||||
0.228996 | + | 0.973427i | \(0.426456\pi\) | |||||||
\(578\) | −386.535 | + | 669.499i | −0.0278162 | + | 0.0481791i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6539.07 | + | 11326.0i | 0.468138 | + | 0.810839i | ||||
\(581\) | −1177.32 | − | 2039.17i | −0.0840676 | − | 0.145609i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6259.00 | + | 10840.9i | −0.444633 | + | 0.770127i | ||||
\(584\) | −15018.2 | −1.06414 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6136.22 | 0.432568 | ||||||||
\(587\) | 7386.86 | − | 12794.4i | 0.519401 | − | 0.899628i | −0.480345 | − | 0.877080i | \(-0.659489\pi\) |
0.999746 | − | 0.0225488i | \(-0.00717811\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5949.46 | + | 10304.8i | 0.416202 | + | 0.720884i | ||||
\(590\) | 3695.98 | + | 6401.62i | 0.257900 | + | 0.446696i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2320.91 | − | 4019.93i | 0.161129 | − | 0.279084i | ||||
\(593\) | −26868.1 | −1.86061 | −0.930304 | − | 0.366790i | \(-0.880457\pi\) | ||||
−0.930304 | + | 0.366790i | \(0.880457\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1749.09 | −0.120514 | ||||||||
\(596\) | 9323.64 | − | 16149.0i | 0.640791 | − | 1.10988i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6825.68 | + | 11822.4i | 0.466761 | + | 0.808454i | ||||
\(599\) | −874.913 | − | 1515.39i | −0.0596794 | − | 0.103368i | 0.834642 | − | 0.550793i | \(-0.185675\pi\) |
−0.894322 | + | 0.447425i | \(0.852341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8981.99 | − | 15557.3i | 0.609622 | − | 1.05590i | −0.381680 | − | 0.924294i | \(-0.624654\pi\) |
0.991303 | − | 0.131602i | \(-0.0420122\pi\) | |||||||
\(602\) | 9938.21 | 0.672843 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5209.99 | −0.350979 | ||||||||
\(605\) | 5169.92 | − | 8954.57i | 0.347417 | − | 0.601744i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2209.11 | + | 3826.29i | 0.147718 | + | 0.255856i | 0.930384 | − | 0.366587i | \(-0.119474\pi\) |
−0.782666 | + | 0.622443i | \(0.786140\pi\) | |||||||
\(608\) | 4449.79 | + | 7707.26i | 0.296814 | + | 0.514097i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −612.771 | + | 1061.35i | −0.0406728 | + | 0.0704473i | ||||
\(611\) | 5419.24 | 0.358820 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20179.7 | −1.32961 | −0.664804 | − | 0.747018i | \(-0.731485\pi\) | ||||
−0.664804 | + | 0.747018i | \(0.731485\pi\) | |||||||
\(614\) | −266.458 | + | 461.518i | −0.0175136 | + | 0.0303345i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2566.85 | − | 4445.92i | −0.167892 | − | 0.290797i | ||||
\(617\) | −2336.51 | − | 4046.95i | −0.152454 | − | 0.264058i | 0.779675 | − | 0.626184i | \(-0.215384\pi\) |
−0.932129 | + | 0.362126i | \(0.882051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9988.40 | − | 17300.4i | 0.648574 | − | 1.12336i | −0.334889 | − | 0.942258i | \(-0.608699\pi\) |
0.983464 | − | 0.181106i | \(-0.0579678\pi\) | |||||||
\(620\) | −17326.7 | −1.12235 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9540.19 | 0.614994 | ||||||||
\(623\) | 1528.78 | − | 2647.93i | 0.0983136 | − | 0.170284i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 11513.0 | + | 19941.1i | 0.735068 | + | 1.27318i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 265.939 | − | 460.619i | 0.0168983 | − | 0.0292686i | ||||
\(629\) | 17943.5 | 1.13745 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10457.5 | 0.659757 | 0.329879 | − | 0.944023i | \(-0.392992\pi\) | ||||
0.329879 | + | 0.944023i | \(0.392992\pi\) | |||||||
\(632\) | 1793.27 | − | 3106.04i | 0.112868 | − | 0.195493i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19246.0 | + | 33335.1i | 1.20561 | + | 2.08818i | ||||
\(635\) | 772.852 | + | 1338.62i | 0.0482988 | + | 0.0836559i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3364.01 | − | 5826.63i | 0.209242 | − | 0.362417i | ||||
\(638\) | 57211.8 | 3.55021 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9782.40 | −0.604193 | ||||||||
\(641\) | 2197.93 | − | 3806.92i | 0.135434 | − | 0.234578i | −0.790329 | − | 0.612682i | \(-0.790091\pi\) |
0.925763 | + | 0.378104i | \(0.123424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2893.18 | − | 5011.13i | −0.177443 | − | 0.307340i | 0.763561 | − | 0.645736i | \(-0.223449\pi\) |
−0.941004 | + | 0.338395i | \(0.890116\pi\) | |||||||
\(644\) | −4358.13 | − | 7548.50i | −0.266668 | − | 0.461883i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6264.97 | + | 10851.2i | −0.381566 | + | 0.660892i | ||||
\(647\) | 25367.7 | 1.54143 | 0.770717 | − | 0.637178i | \(-0.219898\pi\) | ||||
0.770717 | + | 0.637178i | \(0.219898\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19328.1 | 1.16902 | ||||||||
\(650\) | 1182.40 | − | 2047.98i | 0.0713501 | − | 0.123582i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15522.3 | + | 26885.4i | 0.932362 | + | 1.61490i | ||||
\(653\) | −10816.6 | − | 18734.9i | −0.648218 | − | 1.12275i | −0.983548 | − | 0.180646i | \(-0.942181\pi\) |
0.335330 | − | 0.942101i | \(-0.391152\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6962.56 | + | 12059.5i | −0.415343 | + | 0.719396i | ||||
\(656\) | −3023.46 | −0.179948 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5788.98 | −0.342976 | ||||||||
\(659\) | 9156.22 | − | 15859.0i | 0.541238 | − | 0.937451i | −0.457596 | − | 0.889160i | \(-0.651289\pi\) |
0.998833 | − | 0.0482907i | \(-0.0153774\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2763.04 | + | 4785.73i | 0.162587 | + | 0.281609i | 0.935796 | − | 0.352543i | \(-0.114683\pi\) |
−0.773209 | + | 0.634151i | \(0.781350\pi\) | |||||||
\(662\) | −6560.51 | − | 11363.1i | −0.385168 | − | 0.667131i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4015.24 | − | 6954.60i | 0.234671 | − | 0.406462i | ||||
\(665\) | 1036.91 | 0.0604656 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31758.4 | 1.84361 | ||||||||
\(668\) | −1122.92 | + | 1944.95i | −0.0650404 | + | 0.112653i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8452.53 | − | 14640.2i | −0.487388 | − | 0.844180i | ||||
\(671\) | 1602.24 | + | 2775.16i | 0.0921814 | + | 0.159663i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −718.621 | + | 1244.69i | −0.0411602 | + | 0.0712916i | −0.885872 | − | 0.463931i | \(-0.846439\pi\) |
0.844711 | + | 0.535222i | \(0.179772\pi\) | |||||||
\(674\) | −44136.6 | −2.52237 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20765.7 | −1.18148 | ||||||||
\(677\) | −11702.9 | + | 20270.1i | −0.664373 | + | 1.15073i | 0.315082 | + | 0.949064i | \(0.397968\pi\) |
−0.979455 | + | 0.201663i | \(0.935365\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −582.724 | − | 1009.31i | −0.0329351 | − | 0.0570452i | ||||
\(680\) | −2982.64 | − | 5166.08i | −0.168204 | − | 0.291339i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −37898.7 | + | 65642.5i | −2.12788 | + | 3.68560i | ||||
\(683\) | −19227.4 | −1.07719 | −0.538593 | − | 0.842566i | \(-0.681044\pi\) | ||||
−0.538593 | + | 0.842566i | \(0.681044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12447.1 | −0.694274 | ||||||||
\(686\) | −7479.58 | + | 12955.0i | −0.416285 | + | 0.721027i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3905.59 | − | 6764.67i | −0.216423 | − | 0.374856i | ||||
\(689\) | 2277.25 | + | 3944.32i | 0.125916 | + | 0.218094i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17642.4 | − | 30557.5i | 0.971271 | − | 1.68229i | 0.279544 | − | 0.960133i | \(-0.409817\pi\) |
0.691728 | − | 0.722158i | \(-0.256850\pi\) | |||||||
\(692\) | 17888.8 | 0.982703 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −53582.8 | −2.93080 | ||||||||
\(695\) | 4465.13 | − | 7733.83i | 0.243701 | − | 0.422102i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5843.79 | − | 10121.7i | −0.317574 | − | 0.550055i | ||||
\(698\) | 17602.6 | + | 30488.5i | 0.954537 | + | 1.65331i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −754.950 | + | 1307.61i | −0.0407635 | + | 0.0706044i | ||||
\(701\) | −9173.00 | −0.494236 | −0.247118 | − | 0.968985i | \(-0.579484\pi\) | ||||
−0.247118 | + | 0.968985i | \(0.579484\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10637.4 | −0.570695 | ||||||||
\(704\) | −24192.4 | + | 41902.5i | −1.29515 | + | 2.24327i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1652.54 | − | 2862.29i | −0.0880940 | − | 0.152583i | ||||
\(707\) | 3418.81 | + | 5921.56i | 0.181864 | + | 0.314997i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16975.8 | − | 29403.0i | 0.899210 | − | 1.55748i | 0.0707045 | − | 0.997497i | \(-0.477475\pi\) |
0.828506 | − | 0.559981i | \(-0.189191\pi\) | |||||||
\(710\) | 20164.2 | 1.06584 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10427.8 | 0.548876 | ||||||||
\(713\) | −21037.7 | + | 36438.3i | −1.10500 | + | 1.91392i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3091.67 | − | 5354.93i | −0.161709 | − | 0.280088i | ||||
\(716\) | −18641.1 | − | 32287.3i | −0.972973 | − | 1.68524i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 25784.9 | − | 44660.8i | 1.34023 | − | 2.32135i | ||||
\(719\) | 6727.90 | 0.348968 | 0.174484 | − | 0.984660i | \(-0.444174\pi\) | ||||
0.174484 | + | 0.984660i | \(0.444174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8111.17 | −0.418968 | ||||||||
\(722\) | −11579.4 | + | 20056.1i | −0.596871 | + | 1.03381i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −26819.0 | − | 46451.9i | −1.37669 | − | 2.38449i | ||||
\(725\) | −2750.72 | − | 4764.39i | −0.140909 | − | 0.244062i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18363.1 | − | 31805.8i | 0.936793 | − | 1.62257i | 0.165387 | − | 0.986229i | \(-0.447113\pi\) |
0.771406 | − | 0.636344i | \(-0.219554\pi\) | |||||||
\(728\) | −1867.83 | −0.0950912 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19323.0 | 0.979694 | ||||||||
\(731\) | 15097.6 | − | 26149.8i | 0.763890 | − | 1.32310i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13345.7 | − | 23115.4i | −0.672489 | − | 1.16478i | −0.977196 | − | 0.212338i | \(-0.931892\pi\) |
0.304708 | − | 0.952446i | \(-0.401441\pi\) | |||||||
\(734\) | −2560.95 | − | 4435.70i | −0.128783 | − | 0.223058i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15734.7 | + | 27253.4i | −0.788030 | + | 1.36491i | ||||
\(737\) | −44202.4 | −2.20925 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12207.0 | 0.607634 | 0.303817 | − | 0.952730i | \(-0.401739\pi\) | ||||
0.303817 | + | 0.952730i | \(0.401739\pi\) | |||||||
\(740\) | 7744.88 | − | 13414.5i | 0.384740 | − | 0.666389i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2432.62 | − | 4213.43i | −0.120356 | − | 0.208463i | ||||
\(743\) | −6236.64 | − | 10802.2i | −0.307941 | − | 0.533370i | 0.669971 | − | 0.742388i | \(-0.266307\pi\) |
−0.977912 | + | 0.209018i | \(0.932973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3922.08 | + | 6793.24i | −0.192878 | + | 0.334074i | ||||
\(746\) | 20526.4 | 1.00741 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −47707.4 | −2.33202 | ||||||||
\(749\) | 2435.91 | − | 4219.12i | 0.118833 | − | 0.205825i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7551.32 | + | 13079.3i | 0.366913 | + | 0.635511i | 0.989081 | − | 0.147372i | \(-0.0470814\pi\) |
−0.622168 | + | 0.782883i | \(0.713748\pi\) | |||||||
\(752\) | 2274.99 | + | 3940.40i | 0.110320 | + | 0.191079i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10407.9 | − | 18027.0i | 0.502695 | − | 0.870693i | ||||
\(755\) | 2191.63 | 0.105645 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3418.34 | −0.164124 | −0.0820618 | − | 0.996627i | \(-0.526150\pi\) | ||||
−0.0820618 | + | 0.996627i | \(0.526150\pi\) | |||||||
\(758\) | −8893.04 | + | 15403.2i | −0.426134 | + | 0.738086i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1768.19 | + | 3062.60i | 0.0843935 | + | 0.146174i | ||||
\(761\) | −6342.27 | − | 10985.1i | −0.302112 | − | 0.523273i | 0.674502 | − | 0.738273i | \(-0.264358\pi\) |
−0.976614 | + | 0.215000i | \(0.931025\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4294.22 | + | 7437.81i | −0.203750 | + | 0.352906i | ||||
\(764\) | −14351.7 | −0.679614 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34730.6 | 1.63821 | ||||||||
\(767\) | 3516.13 | − | 6090.11i | 0.165528 | − | 0.286703i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13790.1 | + | 23885.2i | 0.646663 | + | 1.12005i | 0.983915 | + | 0.178639i | \(0.0571693\pi\) |
−0.337252 | + | 0.941415i | \(0.609497\pi\) | |||||||
\(770\) | 3302.61 | + | 5720.29i | 0.154569 | + | 0.267721i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5486.41 | + | 9502.74i | −0.255777 | + | 0.443019i | ||||
\(773\) | −17386.0 | −0.808966 | −0.404483 | − | 0.914546i | \(-0.632548\pi\) | ||||
−0.404483 | + | 0.914546i | \(0.632548\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7288.63 | 0.337826 | ||||||||
\(776\) | 1987.39 | − | 3442.25i | 0.0919368 | − | 0.159239i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19007.8 | − | 32922.5i | −0.875917 | − | 1.51713i | ||||
\(779\) | 3464.36 | + | 6000.45i | 0.159337 | + | 0.275980i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26362.0 | − | 45660.4i | 1.20782 | − | 2.09201i | ||||
\(782\) | −44306.7 | −2.02609 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5648.84 | 0.257327 | ||||||||
\(785\) | −111.870 | + | 193.764i | −0.00508637 | + | 0.00880985i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2340.15 | − | 4053.25i | −0.105994 | − | 0.183587i | 0.808150 | − | 0.588977i | \(-0.200469\pi\) |
−0.914144 | + | 0.405390i | \(0.867136\pi\) | |||||||
\(788\) | −7017.99 | − | 12155.5i | −0.317266 | − | 0.549520i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2307.29 | + | 3996.35i | −0.103911 | + | 0.179979i | ||||
\(791\) | 59.0498 | 0.00265432 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1165.91 | 0.0522100 | ||||||||
\(794\) | −347.228 | + | 601.417i | −0.0155197 | + | 0.0268810i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4991.00 | + | 8644.66i | 0.222238 | + | 0.384927i | ||||
\(797\) | 3639.31 | + | 6303.47i | 0.161745 | + | 0.280151i | 0.935495 | − | 0.353341i | \(-0.114954\pi\) |
−0.773749 | + | 0.633492i | \(0.781621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8794.30 | + | 15232.2i | −0.389386 | + | 0.674437i | ||||
\(800\) | 5451.40 | 0.240920 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26461.8 | 1.16508 | ||||||||
\(803\) | 25262.3 | − | 43755.6i | 1.11020 | − | 1.92292i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1833.29 | + | 3175.35i | 0.0802670 | + | 0.139026i | ||||
\(806\) | 13788.9 | + | 23883.1i | 0.602599 | + | 1.04373i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11659.9 | + | 20195.5i | −0.507665 | + | 0.879301i | ||||
\(809\) | −29212.5 | −1.26954 | −0.634770 | − | 0.772701i | \(-0.718905\pi\) | ||||
−0.634770 | + | 0.772701i | \(0.718905\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41992.4 | 1.81819 | 0.909094 | − | 0.416590i | \(-0.136775\pi\) | ||||
0.909094 | + | 0.416590i | \(0.136775\pi\) | |||||||
\(812\) | −6645.31 | + | 11510.0i | −0.287198 | + | 0.497441i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −33880.8 | − | 58683.3i | −1.45887 | − | 2.52684i | ||||
\(815\) | −6529.61 | − | 11309.6i | −0.280641 | − | 0.486084i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8950.26 | + | 15502.3i | −0.383268 | + | 0.663840i | ||||
\(818\) | −63151.2 | −2.69930 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10089.3 | −0.429675 | ||||||||
\(821\) | −4361.49 | + | 7554.33i | −0.185405 | + | 0.321130i | −0.943713 | − | 0.330766i | \(-0.892693\pi\) |
0.758308 | + | 0.651896i | \(0.226026\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6792.41 | − | 11764.8i | −0.287690 | − | 0.498293i | 0.685568 | − | 0.728008i | \(-0.259554\pi\) |
−0.973258 | + | 0.229715i | \(0.926220\pi\) | |||||||
\(824\) | −13831.6 | − | 23957.0i | −0.584765 | − | 1.01284i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3756.03 | + | 6505.63i | −0.158219 | + | 0.274043i | ||||
\(827\) | −26573.6 | −1.11736 | −0.558679 | − | 0.829384i | \(-0.688692\pi\) | ||||
−0.558679 | + | 0.829384i | \(0.688692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43238.4 | −1.81150 | −0.905748 | − | 0.423816i | \(-0.860690\pi\) | ||||
−0.905748 | + | 0.423816i | \(0.860690\pi\) | |||||||
\(830\) | −5166.16 | + | 8948.06i | −0.216048 | + | 0.374207i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8802.09 | + | 15245.7i | 0.366776 | + | 0.635275i | ||||
\(833\) | 10918.2 | + | 18910.8i | 0.454132 | + | 0.786580i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 472.366 | − | 818.163i | 0.0195771 | − | 0.0339086i | ||||
\(836\) | 28282.3 | 1.17005 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 42918.2 | 1.76919 | ||||||||
\(839\) | −2046.61 | + | 3544.83i | −0.0842154 | + | 0.145865i | −0.905057 | − | 0.425291i | \(-0.860172\pi\) |
0.820841 | + | 0.571156i | \(0.193505\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12018.2 | − | 20816.2i | −0.492773 | − | 0.853508i | ||||
\(842\) | −3425.38 | − | 5932.93i | −0.140197 | − | 0.242829i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15390.4 | − | 26657.0i | 0.627677 | − | 1.08717i | ||||
\(845\) | 8735.27 | 0.355624 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10507.8 | 0.426273 | ||||||||
\(848\) | −1911.98 | + | 3311.64i | −0.0774264 | + | 0.134107i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3837.58 | + | 6646.88i | 0.154856 | + | 0.268219i | ||||
\(851\) | −18807.3 | − | 32575.2i | −0.757587 | − | 1.31218i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10100.7 | − | 17495.0i | 0.405443 | − | 0.702248i | −0.588930 | − | 0.808184i | \(-0.700451\pi\) |
0.994373 | + | 0.105936i | \(0.0337839\pi\) | |||||||
\(854\) | −1245.45 | −0.0499046 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16615.4 | 0.663436 | ||||||||
\(857\) | 2275.83 | − | 3941.85i | 0.0907126 | − | 0.157119i | −0.817099 | − | 0.576498i | \(-0.804419\pi\) |
0.907811 | + | 0.419379i | \(0.137752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5981.28 | − | 10359.9i | −0.237577 | − | 0.411496i | 0.722441 | − | 0.691432i | \(-0.243020\pi\) |
−0.960019 | + | 0.279937i | \(0.909687\pi\) | |||||||
\(860\) | −13033.0 | − | 22573.8i | −0.516768 | − | 0.895069i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25824.6 | + | 44729.6i | −1.02041 | + | 1.76740i | ||||
\(863\) | 7164.61 | 0.282603 | 0.141301 | − | 0.989967i | \(-0.454871\pi\) | ||||
0.141301 | + | 0.989967i | \(0.454871\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7525.10 | −0.295793 | ||||||||
\(866\) | 33206.0 | − | 57514.5i | 1.30299 | − | 2.25684i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8804.09 | − | 15249.1i | −0.344275 | − | 0.596301i | ||||
\(869\) | 6032.97 | + | 10449.4i | 0.235506 | + | 0.407908i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8041.22 | + | 13927.8i | −0.312820 | + | 0.541820i | ||||
\(872\) | −29291.0 | −1.13752 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 26266.2 | 1.01655 | ||||||||
\(875\) | 317.577 | − | 550.060i | 0.0122698 | − | 0.0212519i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9609.34 | + | 16643.9i | 0.369994 | + | 0.640848i | 0.989564 | − | 0.144093i | \(-0.0460265\pi\) |
−0.619570 | + | 0.784941i | \(0.712693\pi\) | |||||||
\(878\) | −3662.28 | − | 6343.26i | −0.140770 | − | 0.243821i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2595.77 | − | 4496.00i | 0.0994355 | − | 0.172227i | ||||
\(881\) | 45914.5 | 1.75585 | 0.877923 | − | 0.478802i | \(-0.158929\pi\) | ||||
0.877923 | + | 0.478802i | \(0.158929\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44656.7 | −1.70194 | −0.850972 | − | 0.525211i | \(-0.823986\pi\) | ||||
−0.850972 | + | 0.525211i | \(0.823986\pi\) | |||||||
\(884\) | −8678.84 | + | 15032.2i | −0.330205 | + | 0.571932i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8732.16 | − | 15124.5i | −0.331109 | − | 0.573498i | ||||
\(887\) | 7487.58 | + | 12968.9i | 0.283437 | + | 0.490926i | 0.972229 | − | 0.234032i | \(-0.0751921\pi\) |
−0.688792 | + | 0.724959i | \(0.741859\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −785.409 | + | 1360.37i | −0.0296308 | + | 0.0513220i | ||||
\(890\) | −13416.9 | −0.505319 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −49692.9 | −1.86529 | ||||||||
\(893\) | 5213.50 | − | 9030.05i | 0.195368 | − | 0.338387i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7841.54 | + | 13581.9i | 0.292865 | + | 0.507256i | ||||
\(896\) | −4970.67 | − | 8609.45i | −0.185333 | − | 0.321006i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8885.87 | − | 15390.8i | 0.330206 | − | 0.571934i | ||||
\(899\) | 64156.8 | 2.38015 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14782.0 | −0.546571 | ||||||||
\(902\) | −22068.4 | + | 38223.5i | −0.814630 | + | 1.41098i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 100.695 | + | 174.409i | 0.00370471 | + | 0.00641675i | ||||
\(905\) | 11281.7 | + | 19540.4i | 0.414382 | + | 0.717730i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7409.07 | − | 12832.9i | 0.271240 | − | 0.469801i | −0.697940 | − | 0.716156i | \(-0.745900\pi\) |
0.969180 | + | 0.246356i | \(0.0792331\pi\) | |||||||
\(908\) | 30935.6 | 1.13065 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2403.22 | 0.0875451 | ||||||||
\(911\) | 10923.2 | − | 18919.6i | 0.397259 | − | 0.688073i | −0.596128 | − | 0.802890i | \(-0.703295\pi\) |
0.993387 | + | 0.114817i | \(0.0366282\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13508.2 | + | 23396.9i | 0.489656 | + | 0.848109i | ||||
\(914\) | −31612.1 | − | 54753.7i | −1.14402 | − | 1.98150i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10967.0 | − | 18995.4i | 0.395590 | − | 0.685182i | ||||
\(917\) | −14151.4 | −0.509618 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28878.9 | 1.03659 | 0.518296 | − | 0.855201i | \(-0.326566\pi\) | ||||
0.518296 | + | 0.855201i | \(0.326566\pi\) | |||||||
\(920\) | −6252.44 | + | 10829.5i | −0.224062 | + | 0.388087i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36554.2 | + | 63313.7i | 1.30569 | + | 2.26153i | ||||
\(923\) | −9591.47 | − | 16612.9i | −0.342045 | − | 0.592439i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3257.96 | + | 5642.95i | −0.115807 | + | 0.200583i | ||||
\(926\) | −14803.4 | −0.525344 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 47985.0 | 1.69740 | ||||||||
\(929\) | 2304.39 | − | 3991.33i | 0.0813829 | − | 0.140959i | −0.822461 | − | 0.568821i | \(-0.807400\pi\) |
0.903844 | + | 0.427862i | \(0.140733\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6472.60 | − | 11210.9i | −0.227853 | − | 0.394652i | ||||
\(932\) | 1430.12 | + | 2477.03i | 0.0502629 | + | 0.0870578i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5640.65 | − | 9769.89i | 0.197610 | − | 0.342270i | ||||
\(935\) | 20068.6 | 0.701938 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21063.8 | −0.734391 | −0.367195 | − | 0.930144i | \(-0.619682\pi\) | ||||
−0.367195 | + | 0.930144i | \(0.619682\pi\) | |||||||
\(938\) | 8589.86 | − | 14878.1i | 0.299007 | − | 0.517896i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7591.67 | + | 13149.2i | 0.263418 | + | 0.456254i | ||||
\(941\) | −10122.4 | − | 17532.5i | −0.350670 | − | 0.607378i | 0.635697 | − | 0.771938i | \(-0.280713\pi\) |
−0.986367 | + | 0.164561i | \(0.947379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12250.2 | + | 21218.0i | −0.423035 | + | 0.732717i | ||||
\(944\) | 5904.27 | 0.203567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −114028. | −3.91901 | ||||||||
\(947\) | −14989.2 | + | 25962.0i | −0.514342 | + | 0.890867i | 0.485519 | + | 0.874226i | \(0.338631\pi\) |
−0.999862 | + | 0.0166412i | \(0.994703\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9191.36 | − | 15919.9i | −0.314398 | − | 0.544554i | ||||
\(950\) | −2275.02 | − | 3940.46i | −0.0776964 | − | 0.134574i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3031.10 | − | 5250.02i | 0.103192 | − | 0.178733i | ||||
\(953\) | −5782.65 | −0.196556 | −0.0982782 | − | 0.995159i | \(-0.531334\pi\) | ||||
−0.0982782 | + | 0.995159i | \(0.531334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6037.17 | 0.204564 | ||||||||
\(956\) | 15259.6 | − | 26430.4i | 0.516246 | − | 0.894164i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19279.6 | + | 33393.2i | 0.650204 | + | 1.12619i | ||||
\(959\) | −6324.64 | − | 10954.6i | −0.212965 | − | 0.368866i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27603.8 | + | 47811.2i | −0.926583 | + | 1.60489i | ||||
\(962\) | −24654.2 | −0.826281 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 47401.6 | 1.58372 | ||||||||
\(965\) | 2307.91 | − | 3997.42i | 0.0769889 | − | 0.133349i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13059.6 | + | 22619.9i | 0.434300 | + | 0.752229i | 0.997238 | − | 0.0742695i | \(-0.0236625\pi\) |
−0.562938 | + | 0.826499i | \(0.690329\pi\) | |||||||
\(968\) | 17918.5 | + | 31035.8i | 0.594962 | + | 1.03050i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2557.05 | + | 4428.94i | −0.0846411 | + | 0.146603i | ||||
\(971\) | −5101.93 | −0.168619 | −0.0843093 | − | 0.996440i | \(-0.526868\pi\) | ||||
−0.0843093 | + | 0.996440i | \(0.526868\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9075.34 | 0.299016 | ||||||||
\(974\) | −34006.6 | + | 58901.1i | −1.11873 | + | 1.93769i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 489.447 | + | 847.747i | 0.0160521 | + | 0.0278030i | ||||
\(977\) | −22951.2 | − | 39752.6i | −0.751559 | − | 1.30174i | −0.947067 | − | 0.321037i | \(-0.895969\pi\) |
0.195508 | − | 0.980702i | \(-0.437365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17540.8 | + | 30381.6i | −0.572632 | + | 0.991828i | ||||
\(980\) | 18850.2 | 0.614437 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7879.14 | −0.256042 | ||||||||
\(983\) | 6708.27 | − | 11619.1i | 0.217661 | − | 0.376999i | −0.736432 | − | 0.676512i | \(-0.763491\pi\) |
0.954092 | + | 0.299513i | \(0.0968241\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2952.18 | + | 5113.33i | 0.0954968 | + | 0.165405i | ||||
\(986\) | 33779.6 | + | 58508.0i | 1.09104 | + | 1.88973i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5145.06 | − | 8911.51i | 0.165674 | − | 0.286956i | ||||
\(989\) | −63297.4 | −2.03513 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3806.66 | 0.122021 | 0.0610104 | − | 0.998137i | \(-0.480568\pi\) | ||||
0.0610104 | + | 0.998137i | \(0.480568\pi\) | |||||||
\(992\) | −31786.6 | + | 55056.0i | −1.01736 | + | 1.76213i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10245.9 | + | 17746.4i | 0.326941 | + | 0.566279i | ||||
\(995\) | −2099.51 | − | 3636.46i | −0.0668935 | − | 0.115863i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11261.9 | − | 19506.2i | 0.357742 | − | 0.619627i | −0.629841 | − | 0.776724i | \(-0.716880\pi\) |
0.987583 | + | 0.157097i | \(0.0502135\pi\) | |||||||
\(998\) | −52325.7 | −1.65966 | ||||||||
\(999\) | 0 | 0 |
(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 | 405.4.e.r.136.3 | 6 | ||
3.2 | odd | 2 | 405.4.e.t.136.1 | 6 | |||
9.2 | odd | 6 | 135.4.a.f.1.3 | ✓ | 3 | ||
9.4 | even | 3 | inner | 405.4.e.r.271.3 | 6 | ||
9.5 | odd | 6 | 405.4.e.t.271.1 | 6 | |||
9.7 | even | 3 | 135.4.a.g.1.1 | yes | 3 | ||
36.7 | odd | 6 | 2160.4.a.be.1.3 | 3 | |||
36.11 | even | 6 | 2160.4.a.bm.1.3 | 3 | |||
45.2 | even | 12 | 675.4.b.l.649.5 | 6 | |||
45.7 | odd | 12 | 675.4.b.k.649.2 | 6 | |||
45.29 | odd | 6 | 675.4.a.r.1.1 | 3 | |||
45.34 | even | 6 | 675.4.a.q.1.3 | 3 | |||
45.38 | even | 12 | 675.4.b.l.649.2 | 6 | |||
45.43 | odd | 12 | 675.4.b.k.649.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.f.1.3 | ✓ | 3 | 9.2 | odd | 6 | ||
135.4.a.g.1.1 | yes | 3 | 9.7 | even | 3 | ||
405.4.e.r.136.3 | 6 | 1.1 | even | 1 | trivial | ||
405.4.e.r.271.3 | 6 | 9.4 | even | 3 | inner | ||
405.4.e.t.136.1 | 6 | 3.2 | odd | 2 | |||
405.4.e.t.271.1 | 6 | 9.5 | odd | 6 | |||
675.4.a.q.1.3 | 3 | 45.34 | even | 6 | |||
675.4.a.r.1.1 | 3 | 45.29 | odd | 6 | |||
675.4.b.k.649.2 | 6 | 45.7 | odd | 12 | |||
675.4.b.k.649.5 | 6 | 45.43 | odd | 12 | |||
675.4.b.l.649.2 | 6 | 45.38 | even | 12 | |||
675.4.b.l.649.5 | 6 | 45.2 | even | 12 | |||
2160.4.a.be.1.3 | 3 | 36.7 | odd | 6 | |||
2160.4.a.bm.1.3 | 3 | 36.11 | even | 6 |