Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,4,Mod(123,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, 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("124.123");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.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: | \(7.31623684071\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 123.2 | ||
Character | \(\chi\) | \(=\) | 124.123 |
Dual form | 124.4.d.c.123.4 |
$q$-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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73824 | − | 0.708563i | −0.968113 | − | 0.250515i | ||||
\(3\) | 3.81956 | 0.735075 | 0.367537 | − | 0.930009i | \(-0.380201\pi\) | ||||
0.367537 | + | 0.930009i | \(0.380201\pi\) | |||||||
\(4\) | 6.99588 | + | 3.88043i | 0.874485 | + | 0.485053i | ||||
\(5\) | −9.46257 | −0.846358 | −0.423179 | − | 0.906046i | \(-0.639086\pi\) | ||||
−0.423179 | + | 0.906046i | \(0.639086\pi\) | |||||||
\(6\) | −10.4589 | − | 2.70640i | −0.711635 | − | 0.184147i | ||||
\(7\) | 9.26693i | 0.500367i | 0.968198 | + | 0.250184i | \(0.0804910\pi\) | ||||
−0.968198 | + | 0.250184i | \(0.919509\pi\) | |||||||
\(8\) | −16.4068 | − | 15.5825i | −0.725087 | − | 0.688658i | ||||
\(9\) | −12.4110 | −0.459665 | ||||||||
\(10\) | 25.9108 | + | 6.70483i | 0.819370 | + | 0.212025i | ||||
\(11\) | −30.4376 | −0.834299 | −0.417149 | − | 0.908838i | \(-0.636971\pi\) | ||||
−0.417149 | + | 0.908838i | \(0.636971\pi\) | |||||||
\(12\) | 26.7212 | + | 14.8215i | 0.642812 | + | 0.356550i | ||||
\(13\) | − | 64.5589i | − | 1.37734i | −0.725075 | − | 0.688670i | \(-0.758195\pi\) | ||
0.725075 | − | 0.688670i | \(-0.241805\pi\) | |||||||
\(14\) | 6.56620 | − | 25.3750i | 0.125349 | − | 0.484412i | ||||
\(15\) | −36.1429 | −0.622137 | ||||||||
\(16\) | 33.8846 | + | 54.2940i | 0.529447 | + | 0.848343i | ||||
\(17\) | 109.086i | 1.55631i | 0.628071 | + | 0.778156i | \(0.283845\pi\) | ||||
−0.628071 | + | 0.778156i | \(0.716155\pi\) | |||||||
\(18\) | 33.9841 | + | 8.79395i | 0.445008 | + | 0.115153i | ||||
\(19\) | − | 151.848i | − | 1.83349i | −0.399468 | − | 0.916747i | \(-0.630805\pi\) | ||
0.399468 | − | 0.916747i | \(-0.369195\pi\) | |||||||
\(20\) | −66.1990 | − | 36.7188i | −0.740127 | − | 0.410529i | ||||
\(21\) | 35.3956i | 0.367807i | ||||||||
\(22\) | 83.3454 | + | 21.5670i | 0.807695 | + | 0.209004i | ||||
\(23\) | −188.023 | −1.70458 | −0.852292 | − | 0.523067i | \(-0.824788\pi\) | ||||
−0.852292 | + | 0.523067i | \(0.824788\pi\) | |||||||
\(24\) | −62.6669 | − | 59.5185i | −0.532993 | − | 0.506215i | ||||
\(25\) | −35.4597 | −0.283678 | ||||||||
\(26\) | −45.7440 | + | 176.777i | −0.345044 | + | 1.33342i | ||||
\(27\) | −150.533 | −1.07296 | ||||||||
\(28\) | −35.9596 | + | 64.8303i | −0.242705 | + | 0.437563i | ||||
\(29\) | 186.328i | 1.19311i | 0.802570 | + | 0.596557i | \(0.203465\pi\) | ||||
−0.802570 | + | 0.596557i | \(0.796535\pi\) | |||||||
\(30\) | 98.9677 | + | 25.6095i | 0.602298 | + | 0.155854i | ||||
\(31\) | −157.033 | + | 71.6352i | −0.909806 | + | 0.415034i | ||||
\(32\) | −54.3133 | − | 172.679i | −0.300041 | − | 0.953926i | ||||
\(33\) | −116.258 | −0.613272 | ||||||||
\(34\) | 77.2945 | − | 298.704i | 0.389880 | − | 1.50669i | ||||
\(35\) | − | 87.6890i | − | 0.423490i | ||||||
\(36\) | −86.8255 | − | 48.1598i | −0.401970 | − | 0.222962i | ||||
\(37\) | − | 17.4257i | − | 0.0774262i | −0.999250 | − | 0.0387131i | \(-0.987674\pi\) | ||
0.999250 | − | 0.0387131i | \(-0.0123258\pi\) | |||||||
\(38\) | −107.594 | + | 415.797i | −0.459318 | + | 1.77503i | ||||
\(39\) | − | 246.587i | − | 1.01245i | ||||||
\(40\) | 155.251 | + | 147.451i | 0.613683 | + | 0.582851i | ||||
\(41\) | 130.136 | 0.495703 | 0.247851 | − | 0.968798i | \(-0.420276\pi\) | ||||
0.247851 | + | 0.968798i | \(0.420276\pi\) | |||||||
\(42\) | 25.0800 | − | 96.9215i | 0.0921412 | − | 0.356079i | ||||
\(43\) | 227.289 | 0.806077 | 0.403038 | − | 0.915183i | \(-0.367954\pi\) | ||||
0.403038 | + | 0.915183i | \(0.367954\pi\) | |||||||
\(44\) | −212.938 | − | 118.111i | −0.729581 | − | 0.404679i | ||||
\(45\) | 117.440 | 0.389041 | ||||||||
\(46\) | 514.850 | + | 133.226i | 1.65023 | + | 0.427024i | ||||
\(47\) | 4.18830i | 0.0129984i | 0.999979 | + | 0.00649922i | \(0.00206878\pi\) | ||||
−0.999979 | + | 0.00649922i | \(0.997931\pi\) | |||||||
\(48\) | 129.424 | + | 207.379i | 0.389183 | + | 0.623596i | ||||
\(49\) | 257.124 | 0.749633 | ||||||||
\(50\) | 97.0970 | + | 25.1254i | 0.274632 | + | 0.0710655i | ||||
\(51\) | 416.662i | 1.14401i | ||||||||
\(52\) | 250.516 | − | 451.646i | 0.668083 | − | 1.20446i | ||||
\(53\) | − | 575.583i | − | 1.49174i | −0.666089 | − | 0.745872i | \(-0.732033\pi\) | ||
0.666089 | − | 0.745872i | \(-0.267967\pi\) | |||||||
\(54\) | 412.194 | + | 106.662i | 1.03875 | + | 0.268793i | ||||
\(55\) | 288.018 | 0.706116 | ||||||||
\(56\) | 144.402 | − | 152.041i | 0.344582 | − | 0.362810i | ||||
\(57\) | − | 579.994i | − | 1.34776i | ||||||
\(58\) | 132.025 | − | 510.211i | 0.298893 | − | 1.15507i | ||||
\(59\) | 130.150i | 0.287189i | 0.989637 | + | 0.143595i | \(0.0458661\pi\) | ||||
−0.989637 | + | 0.143595i | \(0.954134\pi\) | |||||||
\(60\) | −252.851 | − | 140.250i | −0.544049 | − | 0.301769i | ||||
\(61\) | 479.687i | 1.00685i | 0.864040 | + | 0.503424i | \(0.167926\pi\) | ||||
−0.864040 | + | 0.503424i | \(0.832074\pi\) | |||||||
\(62\) | 480.752 | − | 84.8863i | 0.984767 | − | 0.173880i | ||||
\(63\) | − | 115.011i | − | 0.230001i | ||||||
\(64\) | 26.3686 | + | 511.321i | 0.0515012 | + | 0.998673i | ||||
\(65\) | 610.893i | 1.16572i | ||||||||
\(66\) | 318.343 | + | 82.3763i | 0.593716 | + | 0.153634i | ||||
\(67\) | 508.558i | 0.927316i | 0.886014 | + | 0.463658i | \(0.153463\pi\) | ||||
−0.886014 | + | 0.463658i | \(0.846537\pi\) | |||||||
\(68\) | −423.301 | + | 763.154i | −0.754895 | + | 1.36097i | ||||
\(69\) | −718.164 | −1.25300 | ||||||||
\(70\) | −62.1332 | + | 240.113i | −0.106091 | + | 0.409986i | ||||
\(71\) | − | 1125.13i | − | 1.88068i | −0.340236 | − | 0.940340i | \(-0.610507\pi\) | ||
0.340236 | − | 0.940340i | \(-0.389493\pi\) | |||||||
\(72\) | 203.625 | + | 193.394i | 0.333297 | + | 0.316552i | ||||
\(73\) | 155.093i | 0.248661i | 0.992241 | + | 0.124330i | \(0.0396782\pi\) | ||||
−0.992241 | + | 0.124330i | \(0.960322\pi\) | |||||||
\(74\) | −12.3472 | + | 47.7157i | −0.0193964 | + | 0.0749573i | ||||
\(75\) | −135.440 | −0.208524 | ||||||||
\(76\) | 589.236 | − | 1062.31i | 0.889342 | − | 1.60336i | ||||
\(77\) | − | 282.063i | − | 0.417456i | ||||||
\(78\) | −174.722 | + | 675.212i | −0.253633 | + | 0.980163i | ||||
\(79\) | −936.657 | −1.33395 | −0.666975 | − | 0.745080i | \(-0.732411\pi\) | ||||
−0.666975 | + | 0.745080i | \(0.732411\pi\) | |||||||
\(80\) | −320.635 | − | 513.761i | −0.448102 | − | 0.718002i | ||||
\(81\) | −239.872 | −0.329043 | ||||||||
\(82\) | −356.343 | − | 92.2095i | −0.479896 | − | 0.124181i | ||||
\(83\) | 635.990 | 0.841072 | 0.420536 | − | 0.907276i | \(-0.361842\pi\) | ||||
0.420536 | + | 0.907276i | \(0.361842\pi\) | |||||||
\(84\) | −137.350 | + | 247.623i | −0.178406 | + | 0.321642i | ||||
\(85\) | − | 1032.24i | − | 1.31720i | ||||||
\(86\) | −622.372 | − | 161.049i | −0.780373 | − | 0.201934i | ||||
\(87\) | 711.693i | 0.877029i | ||||||||
\(88\) | 499.385 | + | 474.295i | 0.604939 | + | 0.574546i | ||||
\(89\) | 757.874i | 0.902635i | 0.892363 | + | 0.451317i | \(0.149046\pi\) | ||||
−0.892363 | + | 0.451317i | \(0.850954\pi\) | |||||||
\(90\) | −321.577 | − | 83.2134i | −0.376636 | − | 0.0974607i | ||||
\(91\) | 598.263 | 0.689175 | ||||||||
\(92\) | −1315.38 | − | 729.608i | −1.49063 | − | 0.826814i | ||||
\(93\) | −599.797 | + | 273.615i | −0.668775 | + | 0.305081i | ||||
\(94\) | 2.96768 | − | 11.4686i | 0.00325630 | − | 0.0125840i | ||||
\(95\) | 1436.88i | 1.55179i | ||||||||
\(96\) | −207.453 | − | 659.558i | −0.220553 | − | 0.701207i | ||||
\(97\) | 1784.88 | 1.86832 | 0.934158 | − | 0.356860i | \(-0.116153\pi\) | ||||
0.934158 | + | 0.356860i | \(0.116153\pi\) | |||||||
\(98\) | −704.066 | − | 182.189i | −0.725729 | − | 0.187794i | ||||
\(99\) | 377.760 | 0.383498 | ||||||||
\(100\) | −248.072 | − | 137.599i | −0.248072 | − | 0.137599i | ||||
\(101\) | −169.443 | −0.166933 | −0.0834663 | − | 0.996511i | \(-0.526599\pi\) | ||||
−0.0834663 | + | 0.996511i | \(0.526599\pi\) | |||||||
\(102\) | 295.231 | − | 1140.92i | 0.286591 | − | 1.10753i | ||||
\(103\) | − | 936.624i | − | 0.896003i | −0.894033 | − | 0.448001i | \(-0.852136\pi\) | ||
0.894033 | − | 0.448001i | \(-0.147864\pi\) | |||||||
\(104\) | −1005.99 | + | 1059.21i | −0.948515 | + | 0.998690i | ||||
\(105\) | − | 334.933i | − | 0.311297i | ||||||
\(106\) | −407.837 | + | 1576.08i | −0.373704 | + | 1.44418i | ||||
\(107\) | − | 640.208i | − | 0.578423i | −0.957265 | − | 0.289212i | \(-0.906607\pi\) | ||
0.957265 | − | 0.289212i | \(-0.0933931\pi\) | |||||||
\(108\) | −1053.11 | − | 584.130i | −0.938290 | − | 0.520444i | ||||
\(109\) | −794.543 | −0.698197 | −0.349098 | − | 0.937086i | \(-0.613512\pi\) | ||||
−0.349098 | + | 0.937086i | \(0.613512\pi\) | |||||||
\(110\) | −788.662 | − | 204.079i | −0.683600 | − | 0.176892i | ||||
\(111\) | − | 66.5586i | − | 0.0569141i | ||||||
\(112\) | −503.138 | + | 314.006i | −0.424483 | + | 0.264918i | ||||
\(113\) | −80.4600 | −0.0669826 | −0.0334913 | − | 0.999439i | \(-0.510663\pi\) | ||||
−0.0334913 | + | 0.999439i | \(0.510663\pi\) | |||||||
\(114\) | −410.962 | + | 1588.16i | −0.337633 | + | 1.30478i | ||||
\(115\) | 1779.18 | 1.44269 | ||||||||
\(116\) | −723.034 | + | 1303.53i | −0.578724 | + | 1.04336i | ||||
\(117\) | 801.238i | 0.633115i | ||||||||
\(118\) | 92.2198 | − | 356.383i | 0.0719451 | − | 0.278031i | ||||
\(119\) | −1010.90 | −0.778728 | ||||||||
\(120\) | 592.990 | + | 563.198i | 0.451103 | + | 0.428439i | ||||
\(121\) | −404.552 | −0.303946 | ||||||||
\(122\) | 339.889 | − | 1313.50i | 0.252230 | − | 0.974742i | ||||
\(123\) | 497.062 | 0.364379 | ||||||||
\(124\) | −1376.56 | − | 108.204i | −0.996925 | − | 0.0783631i | ||||
\(125\) | 1518.36 | 1.08645 | ||||||||
\(126\) | −81.4929 | + | 314.929i | −0.0576187 | + | 0.222667i | ||||
\(127\) | −42.8766 | −0.0299581 | −0.0149791 | − | 0.999888i | \(-0.504768\pi\) | ||||
−0.0149791 | + | 0.999888i | \(0.504768\pi\) | |||||||
\(128\) | 290.099 | − | 1418.80i | 0.200323 | − | 0.979730i | ||||
\(129\) | 868.145 | 0.592527 | ||||||||
\(130\) | 432.856 | − | 1672.77i | 0.292031 | − | 1.12855i | ||||
\(131\) | 293.978i | 0.196068i | 0.995183 | + | 0.0980342i | \(0.0312555\pi\) | ||||
−0.995183 | + | 0.0980342i | \(0.968745\pi\) | |||||||
\(132\) | −813.329 | − | 451.132i | −0.536297 | − | 0.297470i | ||||
\(133\) | 1407.17 | 0.917420 | ||||||||
\(134\) | 360.345 | − | 1392.55i | 0.232307 | − | 0.897747i | ||||
\(135\) | 1424.43 | 0.908111 | ||||||||
\(136\) | 1699.84 | − | 1789.76i | 1.07177 | − | 1.12846i | ||||
\(137\) | 1051.10i | 0.655484i | 0.944767 | + | 0.327742i | \(0.106288\pi\) | ||||
−0.944767 | + | 0.327742i | \(0.893712\pi\) | |||||||
\(138\) | 1966.50 | + | 508.864i | 1.21304 | + | 0.313894i | ||||
\(139\) | −1797.90 | −1.09709 | −0.548547 | − | 0.836120i | \(-0.684819\pi\) | ||||
−0.548547 | + | 0.836120i | \(0.684819\pi\) | |||||||
\(140\) | 340.271 | − | 613.461i | 0.205415 | − | 0.370335i | ||||
\(141\) | 15.9975i | 0.00955482i | ||||||||
\(142\) | −797.225 | + | 3080.87i | −0.471138 | + | 1.82071i | ||||
\(143\) | 1965.02i | 1.14911i | ||||||||
\(144\) | −420.540 | − | 673.840i | −0.243368 | − | 0.389954i | ||||
\(145\) | − | 1763.15i | − | 1.00980i | ||||||
\(146\) | 109.893 | − | 424.680i | 0.0622932 | − | 0.240731i | ||||
\(147\) | 982.101 | 0.551036 | ||||||||
\(148\) | 67.6192 | − | 121.908i | 0.0375558 | − | 0.0677080i | ||||
\(149\) | −2424.79 | −1.33320 | −0.666598 | − | 0.745418i | \(-0.732250\pi\) | ||||
−0.666598 | + | 0.745418i | \(0.732250\pi\) | |||||||
\(150\) | 370.868 | + | 95.9681i | 0.201875 | + | 0.0522384i | ||||
\(151\) | 467.016 | 0.251690 | 0.125845 | − | 0.992050i | \(-0.459836\pi\) | ||||
0.125845 | + | 0.992050i | \(0.459836\pi\) | |||||||
\(152\) | −2366.18 | + | 2491.35i | −1.26265 | + | 1.32944i | ||||
\(153\) | − | 1353.87i | − | 0.715383i | ||||||
\(154\) | −199.860 | + | 772.356i | −0.104579 | + | 0.404144i | ||||
\(155\) | 1485.94 | − | 677.854i | 0.770022 | − | 0.351268i | ||||
\(156\) | 956.861 | − | 1725.09i | 0.491091 | − | 0.885370i | ||||
\(157\) | −1373.35 | −0.698125 | −0.349063 | − | 0.937099i | \(-0.613500\pi\) | ||||
−0.349063 | + | 0.937099i | \(0.613500\pi\) | |||||||
\(158\) | 2564.79 | + | 663.680i | 1.29141 | + | 0.334174i | ||||
\(159\) | − | 2198.47i | − | 1.09654i | ||||||
\(160\) | 513.944 | + | 1633.99i | 0.253943 | + | 0.807363i | ||||
\(161\) | − | 1742.39i | − | 0.852918i | ||||||
\(162\) | 656.827 | + | 169.965i | 0.318551 | + | 0.0824301i | ||||
\(163\) | 2019.82i | 0.970580i | 0.874353 | + | 0.485290i | \(0.161286\pi\) | ||||
−0.874353 | + | 0.485290i | \(0.838714\pi\) | |||||||
\(164\) | 910.415 | + | 504.983i | 0.433484 | + | 0.240442i | ||||
\(165\) | 1100.10 | 0.519048 | ||||||||
\(166\) | −1741.49 | − | 450.639i | −0.814252 | − | 0.210701i | ||||
\(167\) | −1328.55 | −0.615606 | −0.307803 | − | 0.951450i | \(-0.599594\pi\) | ||||
−0.307803 | + | 0.951450i | \(0.599594\pi\) | |||||||
\(168\) | 551.553 | − | 580.730i | 0.253293 | − | 0.266692i | ||||
\(169\) | −1970.85 | −0.897064 | ||||||||
\(170\) | −731.405 | + | 2826.51i | −0.329978 | + | 1.27520i | ||||
\(171\) | 1884.58i | 0.842793i | ||||||||
\(172\) | 1590.09 | + | 881.979i | 0.704902 | + | 0.390990i | ||||
\(173\) | 142.896 | 0.0627985 | 0.0313993 | − | 0.999507i | \(-0.490004\pi\) | ||||
0.0313993 | + | 0.999507i | \(0.490004\pi\) | |||||||
\(174\) | 504.279 | − | 1948.78i | 0.219709 | − | 0.849062i | ||||
\(175\) | − | 328.603i | − | 0.141943i | ||||||
\(176\) | −1031.37 | − | 1652.58i | −0.441717 | − | 0.707772i | ||||
\(177\) | 497.118i | 0.211105i | ||||||||
\(178\) | 537.002 | − | 2075.24i | 0.226123 | − | 0.873852i | ||||
\(179\) | −1070.32 | −0.446924 | −0.223462 | − | 0.974713i | \(-0.571736\pi\) | ||||
−0.223462 | + | 0.974713i | \(0.571736\pi\) | |||||||
\(180\) | 821.593 | + | 455.716i | 0.340211 | + | 0.188706i | ||||
\(181\) | 2749.35i | 1.12905i | 0.825417 | + | 0.564523i | \(0.190940\pi\) | ||||
−0.825417 | + | 0.564523i | \(0.809060\pi\) | |||||||
\(182\) | −1638.18 | − | 423.907i | −0.667199 | − | 0.172649i | ||||
\(183\) | 1832.20i | 0.740108i | ||||||||
\(184\) | 3084.86 | + | 2929.87i | 1.23597 | + | 1.17387i | ||||
\(185\) | 164.892i | 0.0655303i | ||||||||
\(186\) | 1836.26 | − | 324.228i | 0.723877 | − | 0.127815i | ||||
\(187\) | − | 3320.33i | − | 1.29843i | ||||||
\(188\) | −16.2524 | + | 29.3008i | −0.00630493 | + | 0.0113669i | ||||
\(189\) | − | 1394.97i | − | 0.536875i | ||||||
\(190\) | 1018.12 | − | 3934.51i | 0.388747 | − | 1.50231i | ||||
\(191\) | − | 4316.68i | − | 1.63531i | −0.575708 | − | 0.817655i | \(-0.695274\pi\) | ||
0.575708 | − | 0.817655i | \(-0.304726\pi\) | |||||||
\(192\) | 100.717 | + | 1953.02i | 0.0378572 | + | 0.734099i | ||||
\(193\) | 1237.75 | 0.461634 | 0.230817 | − | 0.972997i | \(-0.425860\pi\) | ||||
0.230817 | + | 0.972997i | \(0.425860\pi\) | |||||||
\(194\) | −4887.41 | − | 1264.70i | −1.80874 | − | 0.468041i | ||||
\(195\) | 2333.34i | 0.856893i | ||||||||
\(196\) | 1798.81 | + | 997.751i | 0.655542 | + | 0.363612i | ||||
\(197\) | − | 332.728i | − | 0.120335i | −0.998188 | − | 0.0601673i | \(-0.980837\pi\) | ||
0.998188 | − | 0.0601673i | \(-0.0191634\pi\) | |||||||
\(198\) | −1034.40 | − | 267.667i | −0.371269 | − | 0.0960720i | ||||
\(199\) | −2698.95 | −0.961423 | −0.480711 | − | 0.876879i | \(-0.659622\pi\) | ||||
−0.480711 | + | 0.876879i | \(0.659622\pi\) | |||||||
\(200\) | 581.781 | + | 552.552i | 0.205691 | + | 0.195357i | ||||
\(201\) | 1942.47i | 0.681647i | ||||||||
\(202\) | 463.975 | + | 120.061i | 0.161610 | + | 0.0418191i | ||||
\(203\) | −1726.69 | −0.596995 | ||||||||
\(204\) | −1616.83 | + | 2914.91i | −0.554904 | + | 1.00042i | ||||
\(205\) | −1231.42 | −0.419542 | ||||||||
\(206\) | −663.657 | + | 2564.70i | −0.224462 | + | 0.867432i | ||||
\(207\) | 2333.54 | 0.783538 | ||||||||
\(208\) | 3505.16 | − | 2187.55i | 1.16846 | − | 0.729228i | ||||
\(209\) | 4621.90i | 1.52968i | ||||||||
\(210\) | −237.321 | + | 917.127i | −0.0779845 | + | 0.301370i | ||||
\(211\) | 1290.39i | 0.421015i | 0.977592 | + | 0.210507i | \(0.0675116\pi\) | ||||
−0.977592 | + | 0.210507i | \(0.932488\pi\) | |||||||
\(212\) | 2233.51 | − | 4026.71i | 0.723575 | − | 1.30451i | ||||
\(213\) | − | 4297.50i | − | 1.38244i | ||||||
\(214\) | −453.628 | + | 1753.04i | −0.144904 | + | 0.559979i | ||||
\(215\) | −2150.74 | −0.682230 | ||||||||
\(216\) | 2469.76 | + | 2345.68i | 0.777991 | + | 0.738904i | ||||
\(217\) | −663.839 | − | 1455.21i | −0.207670 | − | 0.455237i | ||||
\(218\) | 2175.65 | + | 562.984i | 0.675933 | + | 0.174909i | ||||
\(219\) | 592.386i | 0.182784i | ||||||||
\(220\) | 2014.94 | + | 1117.63i | 0.617487 | + | 0.342504i | ||||
\(221\) | 7042.49 | 2.14357 | ||||||||
\(222\) | −47.1609 | + | 182.253i | −0.0142578 | + | 0.0550992i | ||||
\(223\) | 906.580 | 0.272238 | 0.136119 | − | 0.990692i | \(-0.456537\pi\) | ||||
0.136119 | + | 0.990692i | \(0.456537\pi\) | |||||||
\(224\) | 1600.20 | − | 503.317i | 0.477313 | − | 0.150131i | ||||
\(225\) | 440.089 | 0.130397 | ||||||||
\(226\) | 220.318 | + | 57.0110i | 0.0648468 | + | 0.0167802i | ||||
\(227\) | − | 3703.09i | − | 1.08274i | −0.840784 | − | 0.541371i | \(-0.817905\pi\) | ||
0.840784 | − | 0.541371i | \(-0.182095\pi\) | |||||||
\(228\) | 2250.62 | − | 4057.57i | 0.653733 | − | 1.17859i | ||||
\(229\) | 2450.12i | 0.707024i | 0.935430 | + | 0.353512i | \(0.115013\pi\) | ||||
−0.935430 | + | 0.353512i | \(0.884987\pi\) | |||||||
\(230\) | −4871.81 | − | 1260.66i | −1.39669 | − | 0.361415i | ||||
\(231\) | − | 1077.36i | − | 0.306861i | ||||||
\(232\) | 2903.47 | − | 3057.06i | 0.821648 | − | 0.865112i | ||||
\(233\) | −4653.13 | −1.30831 | −0.654156 | − | 0.756359i | \(-0.726976\pi\) | ||||
−0.654156 | + | 0.756359i | \(0.726976\pi\) | |||||||
\(234\) | 567.727 | − | 2193.98i | 0.158605 | − | 0.612927i | ||||
\(235\) | − | 39.6321i | − | 0.0110013i | ||||||
\(236\) | −505.039 | + | 910.517i | −0.139302 | + | 0.251142i | ||||
\(237\) | −3577.62 | −0.980553 | ||||||||
\(238\) | 2768.07 | + | 716.283i | 0.753896 | + | 0.195083i | ||||
\(239\) | −2406.38 | −0.651280 | −0.325640 | − | 0.945494i | \(-0.605580\pi\) | ||||
−0.325640 | + | 0.945494i | \(0.605580\pi\) | |||||||
\(240\) | −1224.69 | − | 1962.34i | −0.329388 | − | 0.527785i | ||||
\(241\) | − | 1415.16i | − | 0.378251i | −0.981953 | − | 0.189126i | \(-0.939435\pi\) | ||
0.981953 | − | 0.189126i | \(-0.0605653\pi\) | |||||||
\(242\) | 1107.76 | + | 286.650i | 0.294254 | + | 0.0761429i | ||||
\(243\) | 3148.17 | 0.831092 | ||||||||
\(244\) | −1861.39 | + | 3355.83i | −0.488375 | + | 0.880472i | ||||
\(245\) | −2433.06 | −0.634458 | ||||||||
\(246\) | −1361.07 | − | 352.200i | −0.352760 | − | 0.0912822i | ||||
\(247\) | −9803.16 | −2.52534 | ||||||||
\(248\) | 3692.68 | + | 1271.67i | 0.945505 | + | 0.325609i | ||||
\(249\) | 2429.20 | 0.618251 | ||||||||
\(250\) | −4157.63 | − | 1075.86i | −1.05181 | − | 0.272172i | ||||
\(251\) | −2537.00 | −0.637985 | −0.318993 | − | 0.947757i | \(-0.603345\pi\) | ||||
−0.318993 | + | 0.947757i | \(0.603345\pi\) | |||||||
\(252\) | 446.294 | − | 804.606i | 0.111563 | − | 0.201133i | ||||
\(253\) | 5722.96 | 1.42213 | ||||||||
\(254\) | 117.406 | + | 30.3807i | 0.0290028 | + | 0.00750495i | ||||
\(255\) | − | 3942.69i | − | 0.968239i | ||||||
\(256\) | −1799.67 | + | 3679.46i | −0.439373 | + | 0.898305i | ||||
\(257\) | 178.609 | 0.0433515 | 0.0216758 | − | 0.999765i | \(-0.493100\pi\) | ||||
0.0216758 | + | 0.999765i | \(0.493100\pi\) | |||||||
\(258\) | −2377.19 | − | 615.136i | −0.573633 | − | 0.148437i | ||||
\(259\) | 161.483 | 0.0387415 | ||||||||
\(260\) | −2370.53 | + | 4273.73i | −0.565438 | + | 1.01941i | ||||
\(261\) | − | 2312.51i | − | 0.548433i | ||||||
\(262\) | 208.302 | − | 804.981i | 0.0491181 | − | 0.189816i | ||||
\(263\) | 327.884 | 0.0768753 | 0.0384376 | − | 0.999261i | \(-0.487762\pi\) | ||||
0.0384376 | + | 0.999261i | \(0.487762\pi\) | |||||||
\(264\) | 1907.43 | + | 1811.60i | 0.444675 | + | 0.422334i | ||||
\(265\) | 5446.50i | 1.26255i | ||||||||
\(266\) | −3853.16 | − | 997.067i | −0.888166 | − | 0.229827i | ||||
\(267\) | 2894.75i | 0.663504i | ||||||||
\(268\) | −1973.42 | + | 3557.81i | −0.449798 | + | 0.810924i | ||||
\(269\) | 1387.76i | 0.314548i | 0.987555 | + | 0.157274i | \(0.0502706\pi\) | ||||
−0.987555 | + | 0.157274i | \(0.949729\pi\) | |||||||
\(270\) | −3900.41 | − | 1009.30i | −0.879154 | − | 0.227495i | ||||
\(271\) | −7466.85 | −1.67372 | −0.836861 | − | 0.547415i | \(-0.815612\pi\) | ||||
−0.836861 | + | 0.547415i | \(0.815612\pi\) | |||||||
\(272\) | −5922.73 | + | 3696.34i | −1.32029 | + | 0.823984i | ||||
\(273\) | 2285.10 | 0.506595 | ||||||||
\(274\) | 744.769 | − | 2878.15i | 0.164208 | − | 0.634582i | ||||
\(275\) | 1079.31 | 0.236672 | ||||||||
\(276\) | −5024.19 | − | 2786.78i | −1.09573 | − | 0.607770i | ||||
\(277\) | 1078.25i | 0.233884i | 0.993139 | + | 0.116942i | \(0.0373092\pi\) | ||||
−0.993139 | + | 0.116942i | \(0.962691\pi\) | |||||||
\(278\) | 4923.08 | + | 1273.93i | 1.06211 | + | 0.274838i | ||||
\(279\) | 1948.93 | − | 889.062i | 0.418206 | − | 0.190777i | ||||
\(280\) | −1366.42 | + | 1438.70i | −0.291640 | + | 0.307067i | ||||
\(281\) | −3150.77 | −0.668894 | −0.334447 | − | 0.942415i | \(-0.608550\pi\) | ||||
−0.334447 | + | 0.942415i | \(0.608550\pi\) | |||||||
\(282\) | 11.3352 | − | 43.8049i | 0.00239363 | − | 0.00925015i | ||||
\(283\) | − | 6582.92i | − | 1.38274i | −0.722503 | − | 0.691368i | \(-0.757009\pi\) | ||
0.722503 | − | 0.691368i | \(-0.242991\pi\) | |||||||
\(284\) | 4365.98 | − | 7871.27i | 0.912230 | − | 1.64463i | ||||
\(285\) | 5488.23i | 1.14068i | ||||||||
\(286\) | 1392.34 | − | 5380.68i | 0.287870 | − | 1.11247i | ||||
\(287\) | 1205.96i | 0.248033i | ||||||||
\(288\) | 674.080 | + | 2143.11i | 0.137919 | + | 0.438487i | ||||
\(289\) | −6986.82 | −1.42211 | ||||||||
\(290\) | −1249.30 | + | 4827.91i | −0.252971 | + | 0.977603i | ||||
\(291\) | 6817.44 | 1.37335 | ||||||||
\(292\) | −601.825 | + | 1085.01i | −0.120614 | + | 0.217450i | ||||
\(293\) | −5147.06 | −1.02626 | −0.513131 | − | 0.858310i | \(-0.671514\pi\) | ||||
−0.513131 | + | 0.858310i | \(0.671514\pi\) | |||||||
\(294\) | −2689.22 | − | 695.880i | −0.533465 | − | 0.138043i | ||||
\(295\) | − | 1231.56i | − | 0.243065i | ||||||
\(296\) | −271.537 | + | 285.901i | −0.0533202 | + | 0.0561407i | ||||
\(297\) | 4581.85 | 0.895172 | ||||||||
\(298\) | 6639.64 | + | 1718.11i | 1.29068 | + | 0.333985i | ||||
\(299\) | 12138.5i | 2.34779i | ||||||||
\(300\) | −947.525 | − | 525.567i | −0.182351 | − | 0.101145i | ||||
\(301\) | 2106.27i | 0.403334i | ||||||||
\(302\) | −1278.80 | − | 330.911i | −0.243665 | − | 0.0630522i | ||||
\(303\) | −647.197 | −0.122708 | ||||||||
\(304\) | 8244.45 | − | 5145.32i | 1.55543 | − | 0.970737i | ||||
\(305\) | − | 4539.08i | − | 0.852154i | ||||||
\(306\) | −959.299 | + | 3707.20i | −0.179214 | + | 0.692571i | ||||
\(307\) | − | 2143.54i | − | 0.398496i | −0.979949 | − | 0.199248i | \(-0.936150\pi\) | ||
0.979949 | − | 0.199248i | \(-0.0638500\pi\) | |||||||
\(308\) | 1094.53 | − | 1973.28i | 0.202488 | − | 0.365059i | ||||
\(309\) | − | 3577.49i | − | 0.658629i | ||||||
\(310\) | −4549.15 | + | 803.243i | −0.833466 | + | 0.147165i | ||||
\(311\) | 3855.76i | 0.703023i | 0.936184 | + | 0.351511i | \(0.114332\pi\) | ||||
−0.936184 | + | 0.351511i | \(0.885668\pi\) | |||||||
\(312\) | −3842.45 | + | 4045.71i | −0.697230 | + | 0.734112i | ||||
\(313\) | − | 8238.66i | − | 1.48779i | −0.668299 | − | 0.743893i | \(-0.732977\pi\) | ||
0.668299 | − | 0.743893i | \(-0.267023\pi\) | |||||||
\(314\) | 3760.57 | + | 973.109i | 0.675864 | + | 0.174891i | ||||
\(315\) | 1088.30i | 0.194664i | ||||||||
\(316\) | −6552.73 | − | 3634.63i | −1.16652 | − | 0.647037i | ||||
\(317\) | 2461.44 | 0.436114 | 0.218057 | − | 0.975936i | \(-0.430028\pi\) | ||||
0.218057 | + | 0.975936i | \(0.430028\pi\) | |||||||
\(318\) | −1557.76 | + | 6019.94i | −0.274700 | + | 1.06158i | ||||
\(319\) | − | 5671.39i | − | 0.995414i | ||||||
\(320\) | −249.515 | − | 4838.41i | −0.0435885 | − | 0.845235i | ||||
\(321\) | − | 2445.31i | − | 0.425184i | ||||||
\(322\) | −1234.59 | + | 4771.08i | −0.213669 | + | 0.825720i | ||||
\(323\) | 16564.6 | 2.85349 | ||||||||
\(324\) | −1678.12 | − | 930.807i | −0.287743 | − | 0.159603i | ||||
\(325\) | 2289.24i | 0.390720i | ||||||||
\(326\) | 1431.17 | − | 5530.74i | 0.243145 | − | 0.939631i | ||||
\(327\) | −3034.81 | −0.513227 | ||||||||
\(328\) | −2135.12 | − | 2027.85i | −0.359427 | − | 0.341369i | ||||
\(329\) | −38.8127 | −0.00650399 | ||||||||
\(330\) | −3012.34 | − | 779.492i | −0.502497 | − | 0.130029i | ||||
\(331\) | 4230.78 | 0.702553 | 0.351276 | − | 0.936272i | \(-0.385748\pi\) | ||||
0.351276 | + | 0.936272i | \(0.385748\pi\) | |||||||
\(332\) | 4449.31 | + | 2467.91i | 0.735504 | + | 0.407965i | ||||
\(333\) | 216.270i | 0.0355901i | ||||||||
\(334\) | 3637.88 | + | 941.361i | 0.595976 | + | 0.154219i | ||||
\(335\) | − | 4812.26i | − | 0.784842i | ||||||
\(336\) | −1921.77 | + | 1199.37i | −0.312027 | + | 0.194734i | ||||
\(337\) | 7430.42i | 1.20107i | 0.799598 | + | 0.600535i | \(0.205046\pi\) | ||||
−0.799598 | + | 0.600535i | \(0.794954\pi\) | |||||||
\(338\) | 5396.65 | + | 1396.47i | 0.868459 | + | 0.224728i | ||||
\(339\) | −307.322 | −0.0492373 | ||||||||
\(340\) | 4005.52 | − | 7221.40i | 0.638911 | − | 1.15187i | ||||
\(341\) | 4779.71 | − | 2180.41i | 0.759050 | − | 0.346263i | ||||
\(342\) | 1335.35 | − | 5160.43i | 0.211132 | − | 0.815919i | ||||
\(343\) | 5561.31i | 0.875459i | ||||||||
\(344\) | −3729.10 | − | 3541.75i | −0.584475 | − | 0.555111i | ||||
\(345\) | 6795.68 | 1.06048 | ||||||||
\(346\) | −391.282 | − | 101.251i | −0.0607961 | − | 0.0157320i | ||||
\(347\) | 8501.37 | 1.31521 | 0.657604 | − | 0.753363i | \(-0.271570\pi\) | ||||
0.657604 | + | 0.753363i | \(0.271570\pi\) | |||||||
\(348\) | −2761.67 | + | 4978.92i | −0.425406 | + | 0.766948i | ||||
\(349\) | −2706.83 | −0.415168 | −0.207584 | − | 0.978217i | \(-0.566560\pi\) | ||||
−0.207584 | + | 0.978217i | \(0.566560\pi\) | |||||||
\(350\) | −232.836 | + | 899.791i | −0.0355588 | + | 0.137417i | ||||
\(351\) | 9718.21i | 1.47783i | ||||||||
\(352\) | 1653.17 | + | 5255.94i | 0.250324 | + | 0.795859i | ||||
\(353\) | − | 9655.40i | − | 1.45582i | −0.685672 | − | 0.727911i | \(-0.740492\pi\) | ||
0.685672 | − | 0.727911i | \(-0.259508\pi\) | |||||||
\(354\) | 352.239 | − | 1361.23i | 0.0528850 | − | 0.204374i | ||||
\(355\) | 10646.6i | 1.59173i | ||||||||
\(356\) | −2940.87 | + | 5301.99i | −0.437826 | + | 0.789340i | ||||
\(357\) | −3861.18 | −0.572423 | ||||||||
\(358\) | 2930.78 | + | 758.388i | 0.432673 | + | 0.111961i | ||||
\(359\) | 476.929i | 0.0701151i | 0.999385 | + | 0.0350576i | \(0.0111615\pi\) | ||||
−0.999385 | + | 0.0350576i | \(0.988839\pi\) | |||||||
\(360\) | −1926.81 | − | 1830.01i | −0.282089 | − | 0.267916i | ||||
\(361\) | −16198.9 | −2.36170 | ||||||||
\(362\) | 1948.08 | − | 7528.36i | 0.282843 | − | 1.09304i | ||||
\(363\) | −1545.21 | −0.223423 | ||||||||
\(364\) | 4185.37 | + | 2321.51i | 0.602673 | + | 0.334287i | ||||
\(365\) | − | 1467.58i | − | 0.210456i | ||||||
\(366\) | 1298.23 | − | 5016.98i | 0.185408 | − | 0.716508i | ||||
\(367\) | −8768.34 | −1.24715 | −0.623575 | − | 0.781764i | \(-0.714320\pi\) | ||||
−0.623575 | + | 0.781764i | \(0.714320\pi\) | |||||||
\(368\) | −6371.07 | − | 10208.5i | −0.902486 | − | 1.44607i | ||||
\(369\) | −1615.11 | −0.227857 | ||||||||
\(370\) | 116.836 | − | 451.514i | 0.0164163 | − | 0.0634407i | ||||
\(371\) | 5333.89 | 0.746420 | ||||||||
\(372\) | −5257.85 | − | 413.293i | −0.732814 | − | 0.0576027i | ||||
\(373\) | 7522.64 | 1.04426 | 0.522128 | − | 0.852867i | \(-0.325138\pi\) | ||||
0.522128 | + | 0.852867i | \(0.325138\pi\) | |||||||
\(374\) | −2352.66 | + | 9091.84i | −0.325276 | + | 1.25703i | ||||
\(375\) | 5799.47 | 0.798623 | ||||||||
\(376\) | 65.2644 | − | 68.7168i | 0.00895147 | − | 0.00942499i | ||||
\(377\) | 12029.2 | 1.64332 | ||||||||
\(378\) | −988.427 | + | 3819.77i | −0.134495 | + | 0.519756i | ||||
\(379\) | − | 1738.11i | − | 0.235569i | −0.993039 | − | 0.117785i | \(-0.962421\pi\) | ||
0.993039 | − | 0.117785i | \(-0.0375792\pi\) | |||||||
\(380\) | −5575.69 | + | 10052.2i | −0.752702 | + | 1.35702i | ||||
\(381\) | −163.770 | −0.0220214 | ||||||||
\(382\) | −3058.64 | + | 11820.1i | −0.409670 | + | 1.58316i | ||||
\(383\) | 9366.09 | 1.24957 | 0.624784 | − | 0.780798i | \(-0.285187\pi\) | ||||
0.624784 | + | 0.780798i | \(0.285187\pi\) | |||||||
\(384\) | 1108.05 | − | 5419.19i | 0.147253 | − | 0.720175i | ||||
\(385\) | 2669.04i | 0.353317i | ||||||||
\(386\) | −3389.26 | − | 877.026i | −0.446914 | − | 0.115646i | ||||
\(387\) | −2820.88 | −0.370525 | ||||||||
\(388\) | 12486.8 | + | 6926.08i | 1.63381 | + | 0.906233i | ||||
\(389\) | − | 15028.2i | − | 1.95877i | −0.202004 | − | 0.979385i | \(-0.564745\pi\) | ||
0.202004 | − | 0.979385i | \(-0.435255\pi\) | |||||||
\(390\) | 1653.32 | − | 6389.25i | 0.214665 | − | 0.829569i | ||||
\(391\) | − | 20510.7i | − | 2.65287i | ||||||
\(392\) | −4218.59 | − | 4006.65i | −0.543549 | − | 0.516240i | ||||
\(393\) | 1122.87i | 0.144125i | ||||||||
\(394\) | −235.759 | + | 911.089i | −0.0301456 | + | 0.116497i | ||||
\(395\) | 8863.18 | 1.12900 | ||||||||
\(396\) | 2642.76 | + | 1465.87i | 0.335363 | + | 0.186017i | ||||
\(397\) | 9159.27 | 1.15791 | 0.578955 | − | 0.815359i | \(-0.303461\pi\) | ||||
0.578955 | + | 0.815359i | \(0.303461\pi\) | |||||||
\(398\) | 7390.35 | + | 1912.37i | 0.930766 | + | 0.240851i | ||||
\(399\) | 5374.76 | 0.674373 | ||||||||
\(400\) | −1201.54 | − | 1925.25i | −0.150192 | − | 0.240656i | ||||
\(401\) | 5548.22i | 0.690935i | 0.938431 | + | 0.345467i | \(0.112280\pi\) | ||||
−0.938431 | + | 0.345467i | \(0.887720\pi\) | |||||||
\(402\) | 1376.36 | − | 5318.93i | 0.170763 | − | 0.659911i | ||||
\(403\) | 4624.69 | + | 10137.9i | 0.571643 | + | 1.25311i | ||||
\(404\) | −1185.40 | − | 657.511i | −0.145980 | − | 0.0809712i | ||||
\(405\) | 2269.81 | 0.278488 | ||||||||
\(406\) | 4728.09 | + | 1223.47i | 0.577959 | + | 0.149556i | ||||
\(407\) | 530.397i | 0.0645966i | ||||||||
\(408\) | 6492.65 | − | 6836.10i | 0.787829 | − | 0.829504i | ||||
\(409\) | − | 5925.82i | − | 0.716413i | −0.933642 | − | 0.358207i | \(-0.883388\pi\) | ||
0.933642 | − | 0.358207i | \(-0.116612\pi\) | |||||||
\(410\) | 3371.92 | + | 872.539i | 0.406164 | + | 0.105102i | ||||
\(411\) | 4014.73i | 0.481830i | ||||||||
\(412\) | 3634.50 | − | 6552.50i | 0.434609 | − | 0.783540i | ||||
\(413\) | −1206.10 | −0.143700 | ||||||||
\(414\) | −6389.79 | − | 1653.46i | −0.758553 | − | 0.196288i | ||||
\(415\) | −6018.10 | −0.711848 | ||||||||
\(416\) | −11148.0 | + | 3506.41i | −1.31388 | + | 0.413259i | ||||
\(417\) | −6867.19 | −0.806446 | ||||||||
\(418\) | 3274.91 | − | 12655.9i | 0.383208 | − | 1.48090i | ||||
\(419\) | 5094.04i | 0.593938i | 0.954887 | + | 0.296969i | \(0.0959758\pi\) | ||||
−0.954887 | + | 0.296969i | \(0.904024\pi\) | |||||||
\(420\) | 1299.68 | − | 2343.15i | 0.150996 | − | 0.272224i | ||||
\(421\) | 6347.20 | 0.734782 | 0.367391 | − | 0.930066i | \(-0.380251\pi\) | ||||
0.367391 | + | 0.930066i | \(0.380251\pi\) | |||||||
\(422\) | 914.323 | − | 3533.39i | 0.105470 | − | 0.407590i | ||||
\(423\) | − | 51.9808i | − | 0.00597493i | ||||||
\(424\) | −8969.05 | + | 9443.50i | −1.02730 | + | 1.08164i | ||||
\(425\) | − | 3868.17i | − | 0.441491i | ||||||
\(426\) | −3045.05 | + | 11767.6i | −0.346322 | + | 1.33836i | ||||
\(427\) | −4445.23 | −0.503793 | ||||||||
\(428\) | 2484.28 | − | 4478.82i | 0.280566 | − | 0.505822i | ||||
\(429\) | 7505.51i | 0.844684i | ||||||||
\(430\) | 5889.24 | + | 1523.94i | 0.660475 | + | 0.170909i | ||||
\(431\) | 12542.6i | 1.40175i | 0.713284 | + | 0.700875i | \(0.247207\pi\) | ||||
−0.713284 | + | 0.700875i | \(0.752793\pi\) | |||||||
\(432\) | −5100.73 | − | 8173.01i | −0.568077 | − | 0.910241i | ||||
\(433\) | 13001.1i | 1.44293i | 0.692448 | + | 0.721467i | \(0.256532\pi\) | ||||
−0.692448 | + | 0.721467i | \(0.743468\pi\) | |||||||
\(434\) | 786.635 | + | 4455.09i | 0.0870039 | + | 0.492745i | ||||
\(435\) | − | 6734.45i | − | 0.742280i | ||||||
\(436\) | −5558.53 | − | 3083.17i | −0.610562 | − | 0.338663i | ||||
\(437\) | 28550.9i | 3.12534i | ||||||||
\(438\) | 419.743 | − | 1622.09i | 0.0457901 | − | 0.176956i | ||||
\(439\) | − | 10070.5i | − | 1.09485i | −0.836855 | − | 0.547424i | \(-0.815609\pi\) | ||
0.836855 | − | 0.547424i | \(-0.184391\pi\) | |||||||
\(440\) | −4725.47 | − | 4488.06i | −0.511995 | − | 0.486272i | ||||
\(441\) | −3191.16 | −0.344580 | ||||||||
\(442\) | −19284.0 | − | 4990.05i | −2.07522 | − | 0.536996i | ||||
\(443\) | 2712.26i | 0.290888i | 0.989366 | + | 0.145444i | \(0.0464611\pi\) | ||||
−0.989366 | + | 0.145444i | \(0.953539\pi\) | |||||||
\(444\) | 258.276 | − | 465.636i | 0.0276064 | − | 0.0497705i | ||||
\(445\) | − | 7171.44i | − | 0.763952i | ||||||
\(446\) | −2482.43 | − | 642.369i | −0.263557 | − | 0.0681997i | ||||
\(447\) | −9261.61 | −0.979998 | ||||||||
\(448\) | −4738.37 | + | 244.356i | −0.499703 | + | 0.0257695i | ||||
\(449\) | − | 2188.99i | − | 0.230077i | −0.993361 | − | 0.115039i | \(-0.963301\pi\) | ||
0.993361 | − | 0.115039i | \(-0.0366992\pi\) | |||||||
\(450\) | −1205.07 | − | 311.831i | −0.126239 | − | 0.0326663i | ||||
\(451\) | −3961.03 | −0.413564 | ||||||||
\(452\) | −562.888 | − | 312.219i | −0.0585753 | − | 0.0324902i | ||||
\(453\) | 1783.80 | 0.185011 | ||||||||
\(454\) | −2623.87 | + | 10139.9i | −0.271243 | + | 1.04822i | ||||
\(455\) | −5661.10 | −0.583289 | ||||||||
\(456\) | −9037.78 | + | 9515.86i | −0.928142 | + | 0.977239i | ||||
\(457\) | − | 12887.0i | − | 1.31910i | −0.751662 | − | 0.659549i | \(-0.770747\pi\) | ||
0.751662 | − | 0.659549i | \(-0.229253\pi\) | |||||||
\(458\) | 1736.06 | − | 6709.00i | 0.177120 | − | 0.684479i | ||||
\(459\) | − | 16421.0i | − | 1.66987i | ||||||
\(460\) | 12446.9 | + | 6903.97i | 1.26161 | + | 0.699781i | ||||
\(461\) | − | 3884.09i | − | 0.392408i | −0.980563 | − | 0.196204i | \(-0.937139\pi\) | ||
0.980563 | − | 0.196204i | \(-0.0628614\pi\) | |||||||
\(462\) | −763.376 | + | 2950.06i | −0.0768733 | + | 0.297076i | ||||
\(463\) | −10637.9 | −1.06778 | −0.533892 | − | 0.845553i | \(-0.679271\pi\) | ||||
−0.533892 | + | 0.845553i | \(0.679271\pi\) | |||||||
\(464\) | −10116.5 | + | 6313.66i | −1.01217 | + | 0.631691i | ||||
\(465\) | 5675.63 | − | 2589.10i | 0.566023 | − | 0.258208i | ||||
\(466\) | 12741.4 | + | 3297.04i | 1.26659 | + | 0.327752i | ||||
\(467\) | − | 12794.4i | − | 1.26778i | −0.773421 | − | 0.633892i | \(-0.781456\pi\) | ||
0.773421 | − | 0.633892i | \(-0.218544\pi\) | |||||||
\(468\) | −3109.14 | + | 5605.36i | −0.307094 | + | 0.553649i | ||||
\(469\) | −4712.77 | −0.463999 | ||||||||
\(470\) | −28.0818 | + | 108.522i | −0.00275600 | + | 0.0106505i | ||||
\(471\) | −5245.61 | −0.513174 | ||||||||
\(472\) | 2028.08 | − | 2135.36i | 0.197775 | − | 0.208237i | ||||
\(473\) | −6918.15 | −0.672509 | ||||||||
\(474\) | 9796.36 | + | 2534.97i | 0.949286 | + | 0.245643i | ||||
\(475\) | 5384.50i | 0.520121i | ||||||||
\(476\) | −7072.10 | − | 3922.70i | −0.680985 | − | 0.377724i | ||||
\(477\) | 7143.54i | 0.685703i | ||||||||
\(478\) | 6589.24 | + | 1705.07i | 0.630512 | + | 0.163155i | ||||
\(479\) | − | 81.3581i | − | 0.00776064i | −0.999992 | − | 0.00388032i | \(-0.998765\pi\) | ||
0.999992 | − | 0.00388032i | \(-0.00123515\pi\) | |||||||
\(480\) | 1963.04 | + | 6241.12i | 0.186667 | + | 0.593472i | ||||
\(481\) | −1124.98 | −0.106642 | ||||||||
\(482\) | −1002.73 | + | 3875.04i | −0.0947575 | + | 0.366190i | ||||
\(483\) | − | 6655.17i | − | 0.626958i | ||||||
\(484\) | −2830.19 | − | 1569.83i | −0.265796 | − | 0.147430i | ||||
\(485\) | −16889.5 | −1.58126 | ||||||||
\(486\) | −8620.44 | − | 2230.68i | −0.804591 | − | 0.208201i | ||||
\(487\) | 2758.76 | 0.256696 | 0.128348 | − | 0.991729i | \(-0.459032\pi\) | ||||
0.128348 | + | 0.991729i | \(0.459032\pi\) | |||||||
\(488\) | 7474.75 | − | 7870.15i | 0.693373 | − | 0.730051i | ||||
\(489\) | 7714.82i | 0.713449i | ||||||||
\(490\) | 6662.28 | + | 1723.97i | 0.614227 | + | 0.158941i | ||||
\(491\) | −16607.5 | −1.52645 | −0.763224 | − | 0.646134i | \(-0.776385\pi\) | ||||
−0.763224 | + | 0.646134i | \(0.776385\pi\) | |||||||
\(492\) | 3477.38 | + | 1928.81i | 0.318643 | + | 0.176743i | ||||
\(493\) | −20325.9 | −1.85686 | ||||||||
\(494\) | 26843.4 | + | 6946.16i | 2.44482 | + | 0.632636i | ||||
\(495\) | −3574.58 | −0.324577 | ||||||||
\(496\) | −9210.36 | − | 6098.62i | −0.833785 | − | 0.552089i | ||||
\(497\) | 10426.5 | 0.941031 | ||||||||
\(498\) | −6651.73 | − | 1721.24i | −0.598536 | − | 0.154881i | ||||
\(499\) | −18736.1 | −1.68084 | −0.840422 | − | 0.541932i | \(-0.817693\pi\) | ||||
−0.840422 | + | 0.541932i | \(0.817693\pi\) | |||||||
\(500\) | 10622.3 | + | 5891.89i | 0.950085 | + | 0.526987i | ||||
\(501\) | −5074.48 | −0.452517 | ||||||||
\(502\) | 6946.92 | + | 1797.63i | 0.617642 | + | 0.159825i | ||||
\(503\) | 3947.37i | 0.349910i | 0.984576 | + | 0.174955i | \(0.0559780\pi\) | ||||
−0.984576 | + | 0.174955i | \(0.944022\pi\) | |||||||
\(504\) | −1792.17 | + | 1886.97i | −0.158392 | + | 0.166771i | ||||
\(505\) | 1603.37 | 0.141285 | ||||||||
\(506\) | −15670.8 | − | 4055.08i | −1.37678 | − | 0.356265i | ||||
\(507\) | −7527.78 | −0.659409 | ||||||||
\(508\) | −299.959 | − | 166.379i | −0.0261979 | − | 0.0145313i | ||||
\(509\) | − | 10379.7i | − | 0.903873i | −0.892050 | − | 0.451937i | \(-0.850733\pi\) | ||
0.892050 | − | 0.451937i | \(-0.149267\pi\) | |||||||
\(510\) | −2793.65 | + | 10796.0i | −0.242558 | + | 0.937365i | ||||
\(511\) | −1437.23 | −0.124422 | ||||||||
\(512\) | 7535.05 | − | 8800.04i | 0.650401 | − | 0.759591i | ||||
\(513\) | 22858.1i | 1.96727i | ||||||||
\(514\) | −489.074 | − | 126.556i | −0.0419692 | − | 0.0108602i | ||||
\(515\) | 8862.87i | 0.758339i | ||||||||
\(516\) | 6073.44 | + | 3368.77i | 0.518155 | + | 0.287407i | ||||
\(517\) | − | 127.482i | − | 0.0108446i | ||||||
\(518\) | −442.178 | − | 114.421i | −0.0375062 | − | 0.00970533i | ||||
\(519\) | 545.798 | 0.0461616 | ||||||||
\(520\) | 9519.27 | − | 10022.8i | 0.802784 | − | 0.845250i | ||||
\(521\) | −3140.11 | −0.264051 | −0.132025 | − | 0.991246i | \(-0.542148\pi\) | ||||
−0.132025 | + | 0.991246i | \(0.542148\pi\) | |||||||
\(522\) | −1638.56 | + | 6332.21i | −0.137391 | + | 0.530945i | ||||
\(523\) | 3358.50 | 0.280797 | 0.140398 | − | 0.990095i | \(-0.455162\pi\) | ||||
0.140398 | + | 0.990095i | \(0.455162\pi\) | |||||||
\(524\) | −1140.76 | + | 2056.63i | −0.0951036 | + | 0.171459i | ||||
\(525\) | − | 1255.12i | − | 0.104339i | ||||||
\(526\) | −897.824 | − | 232.327i | −0.0744240 | − | 0.0192584i | ||||
\(527\) | −7814.42 | − | 17130.2i | −0.645923 | − | 1.41594i | ||||
\(528\) | −3939.36 | − | 6312.13i | −0.324695 | − | 0.520265i | ||||
\(529\) | 23185.5 | 1.90561 | ||||||||
\(530\) | 3859.19 | − | 14913.8i | 0.316288 | − | 1.22229i | ||||
\(531\) | − | 1615.29i | − | 0.132011i | ||||||
\(532\) | 9844.37 | + | 5460.41i | 0.802270 | + | 0.444998i | ||||
\(533\) | − | 8401.43i | − | 0.682751i | ||||||
\(534\) | 2051.11 | − | 7926.50i | 0.166218 | − | 0.642347i | ||||
\(535\) | 6058.02i | 0.489553i | ||||||||
\(536\) | 7924.62 | − | 8343.82i | 0.638603 | − | 0.672385i | ||||
\(537\) | −4088.15 | −0.328522 | ||||||||
\(538\) | 983.318 | − | 3800.02i | 0.0787989 | − | 0.304518i | ||||
\(539\) | −7826.24 | −0.625418 | ||||||||
\(540\) | 9965.10 | + | 5527.38i | 0.794129 | + | 0.440482i | ||||
\(541\) | −10801.4 | −0.858387 | −0.429193 | − | 0.903213i | \(-0.641202\pi\) | ||||
−0.429193 | + | 0.903213i | \(0.641202\pi\) | |||||||
\(542\) | 20446.0 | + | 5290.73i | 1.62035 | + | 0.419292i | ||||
\(543\) | 10501.3i | 0.829933i | ||||||||
\(544\) | 18836.9 | − | 5924.84i | 1.48461 | − | 0.466958i | ||||
\(545\) | 7518.42 | 0.590925 | ||||||||
\(546\) | −6257.14 | − | 1619.14i | −0.490441 | − | 0.126910i | ||||
\(547\) | 1639.49i | 0.128152i | 0.997945 | + | 0.0640762i | \(0.0204101\pi\) | ||||
−0.997945 | + | 0.0640762i | \(0.979590\pi\) | |||||||
\(548\) | −4078.70 | + | 7353.35i | −0.317945 | + | 0.573210i | ||||
\(549\) | − | 5953.38i | − | 0.462813i | ||||||
\(550\) | −2955.40 | − | 764.758i | −0.229125 | − | 0.0592898i | ||||
\(551\) | 28293.7 | 2.18757 | ||||||||
\(552\) | 11782.8 | + | 11190.8i | 0.908531 | + | 0.862886i | ||||
\(553\) | − | 8679.93i | − | 0.667465i | ||||||
\(554\) | 764.010 | − | 2952.51i | 0.0585914 | − | 0.226426i | ||||
\(555\) | 629.815i | 0.0481697i | ||||||||
\(556\) | −12577.9 | − | 6976.62i | −0.959392 | − | 0.532149i | ||||
\(557\) | − | 5127.94i | − | 0.390086i | −0.980795 | − | 0.195043i | \(-0.937515\pi\) | ||
0.980795 | − | 0.195043i | \(-0.0624846\pi\) | |||||||
\(558\) | −5966.59 | + | 1053.52i | −0.452663 | + | 0.0799267i | ||||
\(559\) | − | 14673.5i | − | 1.11024i | ||||||
\(560\) | 4760.98 | − | 2971.31i | 0.359265 | − | 0.224215i | ||||
\(561\) | − | 12682.2i | − | 0.954443i | ||||||
\(562\) | 8627.56 | + | 2232.52i | 0.647565 | + | 0.167568i | ||||
\(563\) | − | 8497.74i | − | 0.636123i | −0.948070 | − | 0.318061i | \(-0.896968\pi\) | ||
0.948070 | − | 0.318061i | \(-0.103032\pi\) | |||||||
\(564\) | −62.0770 | + | 111.916i | −0.00463460 | + | 0.00835555i | ||||
\(565\) | 761.359 | 0.0566913 | ||||||||
\(566\) | −4664.41 | + | 18025.6i | −0.346396 | + | 1.33864i | ||||
\(567\) | − | 2222.88i | − | 0.164642i | ||||||
\(568\) | −17532.4 | + | 18459.8i | −1.29514 | + | 1.36366i | ||||
\(569\) | 19751.4i | 1.45522i | 0.685989 | + | 0.727612i | \(0.259370\pi\) | ||||
−0.685989 | + | 0.727612i | \(0.740630\pi\) | |||||||
\(570\) | 3888.76 | − | 15028.1i | 0.285758 | − | 1.10431i | ||||
\(571\) | 4844.86 | 0.355081 | 0.177540 | − | 0.984113i | \(-0.443186\pi\) | ||||
0.177540 | + | 0.984113i | \(0.443186\pi\) | |||||||
\(572\) | −7625.11 | + | 13747.0i | −0.557381 | + | 1.00488i | ||||
\(573\) | − | 16487.8i | − | 1.20208i | ||||||
\(574\) | 854.499 | − | 3302.20i | 0.0621360 | − | 0.240124i | ||||
\(575\) | 6667.23 | 0.483552 | ||||||||
\(576\) | −327.260 | − | 6345.98i | −0.0236733 | − | 0.459055i | ||||
\(577\) | 13906.9 | 1.00339 | 0.501693 | − | 0.865046i | \(-0.332711\pi\) | ||||
0.501693 | + | 0.865046i | \(0.332711\pi\) | |||||||
\(578\) | 19131.6 | + | 4950.61i | 1.37676 | + | 0.356260i | ||||
\(579\) | 4727.67 | 0.339336 | ||||||||
\(580\) | 6841.76 | − | 12334.8i | 0.489808 | − | 0.883057i | ||||
\(581\) | 5893.67i | 0.420845i | ||||||||
\(582\) | −18667.8 | − | 4830.59i | −1.32956 | − | 0.344045i | ||||
\(583\) | 17519.4i | 1.24456i | ||||||||
\(584\) | 2416.74 | − | 2544.58i | 0.171242 | − | 0.180300i | ||||
\(585\) | − | 7581.77i | − | 0.535842i | ||||||
\(586\) | 14093.9 | + | 3647.02i | 0.993537 | + | 0.257094i | ||||
\(587\) | −115.159 | −0.00809731 | −0.00404865 | − | 0.999992i | \(-0.501289\pi\) | ||||
−0.00404865 | + | 0.999992i | \(0.501289\pi\) | |||||||
\(588\) | 6870.66 | + | 3810.97i | 0.481873 | + | 0.267282i | ||||
\(589\) | 10877.7 | + | 23845.2i | 0.760963 | + | 1.66812i | ||||
\(590\) | −872.637 | + | 3372.30i | −0.0608914 | + | 0.235314i | ||||
\(591\) | − | 1270.88i | − | 0.0884549i | ||||||
\(592\) | 946.111 | − | 590.463i | 0.0656840 | − | 0.0409930i | ||||
\(593\) | 17027.7 | 1.17916 | 0.589581 | − | 0.807710i | \(-0.299293\pi\) | ||||
0.589581 | + | 0.807710i | \(0.299293\pi\) | |||||||
\(594\) | −12546.2 | − | 3246.53i | −0.866627 | − | 0.224254i | ||||
\(595\) | 9565.67 | 0.659083 | ||||||||
\(596\) | −16963.5 | − | 9409.20i | −1.16586 | − | 0.646671i | ||||
\(597\) | −10308.8 | −0.706718 | ||||||||
\(598\) | 8600.91 | − | 33238.2i | 0.588156 | − | 2.27293i | ||||
\(599\) | 10657.5i | 0.726965i | 0.931601 | + | 0.363483i | \(0.118412\pi\) | ||||
−0.931601 | + | 0.363483i | \(0.881588\pi\) | |||||||
\(600\) | 2222.15 | + | 2110.51i | 0.151198 | + | 0.143602i | ||||
\(601\) | 15474.3i | 1.05027i | 0.851020 | + | 0.525134i | \(0.175985\pi\) | ||||
−0.851020 | + | 0.525134i | \(0.824015\pi\) | |||||||
\(602\) | 1492.43 | − | 5767.48i | 0.101041 | − | 0.390473i | ||||
\(603\) | − | 6311.69i | − | 0.426255i | ||||||
\(604\) | 3267.19 | + | 1812.22i | 0.220099 | + | 0.122083i | ||||
\(605\) | 3828.10 | 0.257247 | ||||||||
\(606\) | 1772.18 | + | 458.580i | 0.118795 | + | 0.0307402i | ||||
\(607\) | − | 9398.38i | − | 0.628449i | −0.949349 | − | 0.314224i | \(-0.898256\pi\) | ||
0.949349 | − | 0.314224i | \(-0.101744\pi\) | |||||||
\(608\) | −26221.0 | + | 8247.38i | −1.74902 | + | 0.550124i | ||||
\(609\) | −6595.21 | −0.438836 | ||||||||
\(610\) | −3216.22 | + | 12429.1i | −0.213477 | + | 0.824981i | ||||
\(611\) | 270.392 | 0.0179033 | ||||||||
\(612\) | 5253.58 | − | 9471.48i | 0.346999 | − | 0.625591i | ||||
\(613\) | − | 7795.68i | − | 0.513645i | −0.966459 | − | 0.256823i | \(-0.917324\pi\) | ||
0.966459 | − | 0.256823i | \(-0.0826756\pi\) | |||||||
\(614\) | −1518.83 | + | 5869.52i | −0.0998293 | + | 0.385789i | ||||
\(615\) | −4703.48 | −0.308395 | ||||||||
\(616\) | −4395.26 | + | 4627.77i | −0.287484 | + | 0.302692i | ||||
\(617\) | −26366.1 | −1.72035 | −0.860177 | − | 0.509996i | \(-0.829647\pi\) | ||||
−0.860177 | + | 0.509996i | \(0.829647\pi\) | |||||||
\(618\) | −2534.88 | + | 9796.02i | −0.164996 | + | 0.637627i | ||||
\(619\) | 3059.01 | 0.198630 | 0.0993151 | − | 0.995056i | \(-0.468335\pi\) | ||||
0.0993151 | + | 0.995056i | \(0.468335\pi\) | |||||||
\(620\) | 13025.8 | + | 1023.89i | 0.843756 | + | 0.0663233i | ||||
\(621\) | 28303.5 | 1.82896 | ||||||||
\(622\) | 2732.05 | − | 10558.0i | 0.176118 | − | 0.680605i | ||||
\(623\) | −7023.17 | −0.451649 | ||||||||
\(624\) | 13388.2 | − | 8355.48i | 0.858903 | − | 0.536037i | ||||
\(625\) | −9935.15 | −0.635849 | ||||||||
\(626\) | −5837.61 | + | 22559.4i | −0.372712 | + | 1.44034i | ||||
\(627\) | 17653.6i | 1.12443i | ||||||||
\(628\) | −9607.82 | − | 5329.20i | −0.610500 | − | 0.338628i | ||||
\(629\) | 1900.91 | 0.120499 | ||||||||
\(630\) | 771.132 | − | 2980.03i | 0.0487661 | − | 0.188456i | ||||
\(631\) | 19286.1 | 1.21675 | 0.608374 | − | 0.793651i | \(-0.291822\pi\) | ||||
0.608374 | + | 0.793651i | \(0.291822\pi\) | |||||||
\(632\) | 15367.6 | + | 14595.5i | 0.967230 | + | 0.918635i | ||||
\(633\) | 4928.72i | 0.309477i | ||||||||
\(634\) | −6739.99 | − | 1744.08i | −0.422207 | − | 0.109253i | ||||
\(635\) | 405.723 | 0.0253553 | ||||||||
\(636\) | 8531.02 | − | 15380.3i | 0.531882 | − | 0.958910i | ||||
\(637\) | − | 16599.6i | − | 1.03250i | ||||||
\(638\) | −4018.54 | + | 15529.6i | −0.249366 | + | 0.963673i | ||||
\(639\) | 13963.9i | 0.864483i | ||||||||
\(640\) | −2745.09 | + | 13425.5i | −0.169545 | + | 0.829202i | ||||
\(641\) | − | 12489.2i | − | 0.769572i | −0.923006 | − | 0.384786i | \(-0.874275\pi\) | ||
0.923006 | − | 0.384786i | \(-0.125725\pi\) | |||||||
\(642\) | −1732.66 | + | 6695.85i | −0.106515 | + | 0.411626i | ||||
\(643\) | −11132.3 | −0.682763 | −0.341381 | − | 0.939925i | \(-0.610895\pi\) | ||||
−0.341381 | + | 0.939925i | \(0.610895\pi\) | |||||||
\(644\) | 6761.22 | − | 12189.6i | 0.413711 | − | 0.745863i | ||||
\(645\) | −8214.89 | −0.501490 | ||||||||
\(646\) | −45357.7 | − | 11737.0i | −2.76250 | − | 0.714842i | ||||
\(647\) | −9983.67 | −0.606644 | −0.303322 | − | 0.952888i | \(-0.598096\pi\) | ||||
−0.303322 | + | 0.952888i | \(0.598096\pi\) | |||||||
\(648\) | 3935.55 | + | 3737.82i | 0.238585 | + | 0.226598i | ||||
\(649\) | − | 3961.47i | − | 0.239601i | ||||||
\(650\) | 1622.07 | − | 6268.48i | 0.0978812 | − | 0.378261i | ||||
\(651\) | −2535.57 | − | 5558.28i | −0.152653 | − | 0.334633i | ||||
\(652\) | −7837.76 | + | 14130.4i | −0.470783 | + | 0.848757i | ||||
\(653\) | 24074.4 | 1.44273 | 0.721367 | − | 0.692553i | \(-0.243514\pi\) | ||||
0.721367 | + | 0.692553i | \(0.243514\pi\) | |||||||
\(654\) | 8310.02 | + | 2150.35i | 0.496861 | + | 0.128571i | ||||
\(655\) | − | 2781.79i | − | 0.165944i | ||||||
\(656\) | 4409.60 | + | 7065.59i | 0.262448 | + | 0.420526i | ||||
\(657\) | − | 1924.85i | − | 0.114301i | ||||||
\(658\) | 106.278 | + | 27.5012i | 0.00629660 | + | 0.00162935i | ||||
\(659\) | 16509.4i | 0.975894i | 0.872873 | + | 0.487947i | \(0.162254\pi\) | ||||
−0.872873 | + | 0.487947i | \(0.837746\pi\) | |||||||
\(660\) | 7696.18 | + | 4268.87i | 0.453899 | + | 0.251766i | ||||
\(661\) | −7485.67 | −0.440483 | −0.220241 | − | 0.975445i | \(-0.570684\pi\) | ||||
−0.220241 | + | 0.975445i | \(0.570684\pi\) | |||||||
\(662\) | −11584.9 | − | 2997.78i | −0.680150 | − | 0.176000i | ||||
\(663\) | 26899.2 | 1.57568 | ||||||||
\(664\) | −10434.6 | − | 9910.34i | −0.609850 | − | 0.579210i | ||||
\(665\) | −13315.4 | −0.776466 | ||||||||
\(666\) | 153.241 | − | 592.198i | 0.00891586 | − | 0.0344553i | ||||
\(667\) | − | 35034.0i | − | 2.03376i | ||||||
\(668\) | −9294.37 | − | 5155.34i | −0.538338 | − | 0.298602i | ||||
\(669\) | 3462.74 | 0.200115 | ||||||||
\(670\) | −3409.79 | + | 13177.1i | −0.196615 | + | 0.759815i | ||||
\(671\) | − | 14600.5i | − | 0.840011i | ||||||
\(672\) | 6112.08 | − | 1922.45i | 0.350861 | − | 0.110357i | ||||
\(673\) | 16211.6i | 0.928548i | 0.885692 | + | 0.464274i | \(0.153685\pi\) | ||||
−0.885692 | + | 0.464274i | \(0.846315\pi\) | |||||||
\(674\) | 5264.92 | − | 20346.2i | 0.300886 | − | 1.16277i | ||||
\(675\) | 5337.84 | 0.304376 | ||||||||
\(676\) | −13787.8 | − | 7647.73i | −0.784468 | − | 0.435124i | ||||
\(677\) | 20444.8i | 1.16065i | 0.814386 | + | 0.580324i | \(0.197074\pi\) | ||||
−0.814386 | + | 0.580324i | \(0.802926\pi\) | |||||||
\(678\) | 841.520 | + | 217.757i | 0.0476672 | + | 0.0123347i | ||||
\(679\) | 16540.3i | 0.934844i | ||||||||
\(680\) | −16084.9 | + | 16935.7i | −0.907099 | + | 0.955083i | ||||
\(681\) | − | 14144.2i | − | 0.795897i | ||||||
\(682\) | −14632.9 | + | 2583.74i | −0.821590 | + | 0.145068i | ||||
\(683\) | − | 3374.87i | − | 0.189072i | −0.995521 | − | 0.0945358i | \(-0.969863\pi\) | ||
0.995521 | − | 0.0945358i | \(-0.0301367\pi\) | |||||||
\(684\) | −7312.99 | + | 13184.3i | −0.408800 | + | 0.737010i | ||||
\(685\) | − | 9946.08i | − | 0.554774i | ||||||
\(686\) | 3940.54 | − | 15228.2i | 0.219315 | − | 0.847543i | ||||
\(687\) | 9358.38i | 0.519715i | ||||||||
\(688\) | 7701.60 | + | 12340.4i | 0.426775 | + | 0.683830i | ||||
\(689\) | −37159.0 | −2.05464 | ||||||||
\(690\) | −18608.2 | − | 4815.17i | −1.02667 | − | 0.265667i | ||||
\(691\) | 13420.2i | 0.738825i | 0.929266 | + | 0.369412i | \(0.120441\pi\) | ||||
−0.929266 | + | 0.369412i | \(0.879559\pi\) | |||||||
\(692\) | 999.680 | + | 554.496i | 0.0549163 | + | 0.0304606i | ||||
\(693\) | 3500.67i | 0.191890i | ||||||||
\(694\) | −23278.8 | − | 6023.76i | −1.27327 | − | 0.329479i | ||||
\(695\) | 17012.8 | 0.928534 | ||||||||
\(696\) | 11090.0 | − | 11676.6i | 0.603972 | − | 0.635922i | ||||
\(697\) | 14196.0i | 0.771468i | ||||||||
\(698\) | 7411.95 | + | 1917.96i | 0.401929 | + | 0.104006i | ||||
\(699\) | −17772.9 | −0.961708 | ||||||||
\(700\) | 1275.12 | − | 2298.86i | 0.0688499 | − | 0.124127i | ||||
\(701\) | 14116.8 | 0.760607 | 0.380303 | − | 0.924862i | \(-0.375820\pi\) | ||||
0.380303 | + | 0.924862i | \(0.375820\pi\) | |||||||
\(702\) | 6885.97 | − | 26610.8i | 0.370219 | − | 1.43071i | ||||
\(703\) | −2646.07 | −0.141961 | ||||||||
\(704\) | −802.598 | − | 15563.4i | −0.0429674 | − | 0.833192i | ||||
\(705\) | − | 151.377i | − | 0.00808680i | ||||||
\(706\) | −6841.46 | + | 26438.8i | −0.364705 | + | 1.40940i | ||||
\(707\) | − | 1570.22i | − | 0.0835276i | ||||||
\(708\) | −1929.03 | + | 3477.77i | −0.102397 | + | 0.184608i | ||||
\(709\) | − | 3483.75i | − | 0.184535i | −0.995734 | − | 0.0922673i | \(-0.970589\pi\) | ||
0.995734 | − | 0.0922673i | \(-0.0294114\pi\) | |||||||
\(710\) | 7543.80 | − | 29153.0i | 0.398752 | − | 1.54097i | ||||
\(711\) | 11624.8 | 0.613171 | ||||||||
\(712\) | 11809.6 | − | 12434.3i | 0.621606 | − | 0.654488i | ||||
\(713\) | 29525.8 | − | 13469.0i | 1.55084 | − | 0.707461i | ||||
\(714\) | 10572.8 | + | 2735.89i | 0.554170 | + | 0.143401i | ||||
\(715\) | − | 18594.1i | − | 0.972561i | ||||||
\(716\) | −7487.82 | − | 4153.29i | −0.390828 | − | 0.216782i | ||||
\(717\) | −9191.32 | −0.478739 | ||||||||
\(718\) | 337.934 | − | 1305.94i | 0.0175649 | − | 0.0678793i | ||||
\(719\) | −10584.3 | −0.548996 | −0.274498 | − | 0.961588i | \(-0.588512\pi\) | ||||
−0.274498 | + | 0.961588i | \(0.588512\pi\) | |||||||
\(720\) | 3979.39 | + | 6376.26i | 0.205977 | + | 0.330041i | ||||
\(721\) | 8679.62 | 0.448330 | ||||||||
\(722\) | 44356.4 | + | 11477.9i | 2.28639 | + | 0.591641i | ||||
\(723\) | − | 5405.29i | − | 0.278043i | ||||||
\(724\) | −10668.6 | + | 19234.1i | −0.547647 | + | 0.987333i | ||||
\(725\) | − | 6607.15i | − | 0.338460i | ||||||
\(726\) | 4231.15 | + | 1094.88i | 0.216298 | + | 0.0559707i | ||||
\(727\) | 27393.4i | 1.39748i | 0.715377 | + | 0.698739i | \(0.246255\pi\) | ||||
−0.715377 | + | 0.698739i | \(0.753745\pi\) | |||||||
\(728\) | −9815.60 | − | 9322.45i | −0.499712 | − | 0.474606i | ||||
\(729\) | 18501.2 | 0.939958 | ||||||||
\(730\) | −1039.87 | + | 4018.57i | −0.0527223 | + | 0.203745i | ||||
\(731\) | 24794.2i | 1.25451i | ||||||||
\(732\) | −7109.70 | + | 12817.8i | −0.358992 | + | 0.647213i | ||||
\(733\) | −23289.0 | −1.17353 | −0.586766 | − | 0.809756i | \(-0.699599\pi\) | ||||
−0.586766 | + | 0.809756i | \(0.699599\pi\) | |||||||
\(734\) | 24009.8 | + | 6212.92i | 1.20738 | + | 0.312429i | ||||
\(735\) | −9293.20 | −0.466374 | ||||||||
\(736\) | 10212.1 | + | 32467.6i | 0.511446 | + | 1.62605i | ||||
\(737\) | − | 15479.3i | − | 0.773659i | ||||||
\(738\) | 4422.56 | + | 1144.41i | 0.220591 | + | 0.0570816i | ||||
\(739\) | 39175.7 | 1.95007 | 0.975034 | − | 0.222054i | \(-0.0712760\pi\) | ||||
0.975034 | + | 0.222054i | \(0.0712760\pi\) | |||||||
\(740\) | −639.852 | + | 1153.56i | −0.0317857 | + | 0.0573053i | ||||
\(741\) | −37443.8 | −1.85632 | ||||||||
\(742\) | −14605.4 | − | 3779.40i | −0.722618 | − | 0.186989i | ||||
\(743\) | 8911.68 | 0.440024 | 0.220012 | − | 0.975497i | \(-0.429390\pi\) | ||||
0.220012 | + | 0.975497i | \(0.429390\pi\) | |||||||
\(744\) | 14104.4 | + | 4857.21i | 0.695017 | + | 0.239347i | ||||
\(745\) | 22944.7 | 1.12836 | ||||||||
\(746\) | −20598.8 | − | 5330.26i | −1.01096 | − | 0.261602i | ||||
\(747\) | −7893.24 | −0.386611 | ||||||||
\(748\) | 12884.3 | − | 23228.6i | 0.629808 | − | 1.13546i | ||||
\(749\) | 5932.76 | 0.289424 | ||||||||
\(750\) | −15880.3 | − | 4109.29i | −0.773157 | − | 0.200067i | ||||
\(751\) | 9463.00i | 0.459800i | 0.973214 | + | 0.229900i | \(0.0738399\pi\) | ||||
−0.973214 | + | 0.229900i | \(0.926160\pi\) | |||||||
\(752\) | −227.399 | + | 141.919i | −0.0110271 | + | 0.00688198i | ||||
\(753\) | −9690.24 | −0.468967 | ||||||||
\(754\) | −32938.7 | − | 8523.42i | −1.59092 | − | 0.411677i | ||||
\(755\) | −4419.18 | −0.213020 | ||||||||
\(756\) | 5413.10 | − | 9759.07i | 0.260413 | − | 0.469489i | ||||
\(757\) | − | 18574.5i | − | 0.891811i | −0.895080 | − | 0.445905i | \(-0.852882\pi\) | ||
0.895080 | − | 0.445905i | \(-0.147118\pi\) | |||||||
\(758\) | −1231.56 | + | 4759.36i | −0.0590136 | + | 0.228057i | ||||
\(759\) | 21859.2 | 1.04537 | ||||||||
\(760\) | 22390.2 | − | 23574.6i | 1.06865 | − | 1.12518i | ||||
\(761\) | 11022.0i | 0.525030i | 0.964928 | + | 0.262515i | \(0.0845519\pi\) | ||||
−0.964928 | + | 0.262515i | \(0.915448\pi\) | |||||||
\(762\) | 448.440 | + | 116.041i | 0.0213192 | + | 0.00551670i | ||||
\(763\) | − | 7362.98i | − | 0.349355i | ||||||
\(764\) | 16750.6 | − | 30199.0i | 0.793213 | − | 1.43005i | ||||
\(765\) | 12811.1i | 0.605470i | ||||||||
\(766\) | −25646.6 | − | 6636.46i | −1.20972 | − | 0.313035i | ||||
\(767\) | 8402.37 | 0.395557 | ||||||||
\(768\) | −6873.95 | + | 14053.9i | −0.322972 | + | 0.660321i | ||||
\(769\) | −23335.5 | −1.09428 | −0.547139 | − | 0.837041i | \(-0.684283\pi\) | ||||
−0.547139 | + | 0.837041i | \(0.684283\pi\) | |||||||
\(770\) | 1891.19 | − | 7308.47i | 0.0885112 | − | 0.342051i | ||||
\(771\) | 682.209 | 0.0318666 | ||||||||
\(772\) | 8659.17 | + | 4803.01i | 0.403692 | + | 0.223917i | ||||
\(773\) | − | 19348.4i | − | 0.900275i | −0.892959 | − | 0.450137i | \(-0.851375\pi\) | ||
0.892959 | − | 0.450137i | \(-0.148625\pi\) | |||||||
\(774\) | 7724.23 | + | 1998.77i | 0.358710 | + | 0.0928221i | ||||
\(775\) | 5568.35 | − | 2540.16i | 0.258091 | − | 0.117736i | ||||
\(776\) | −29284.2 | − | 27812.9i | −1.35469 | − | 1.28663i | ||||
\(777\) | 616.794 | 0.0284779 | ||||||||
\(778\) | −10648.4 | + | 41150.8i | −0.490701 | + | 1.89631i | ||||
\(779\) | − | 19760.9i | − | 0.908868i | ||||||
\(780\) | −9054.37 | + | 16323.8i | −0.415639 | + | 0.749340i | ||||
\(781\) | 34246.3i | 1.56905i | ||||||||
\(782\) | −14533.1 | + | 56163.1i | −0.664582 | + | 2.56827i | ||||
\(783\) | − | 28048.5i | − | 1.28017i | ||||||
\(784\) | 8712.54 | + | 13960.3i | 0.396890 | + | 0.635946i | ||||
\(785\) | 12995.5 | 0.590864 | ||||||||
\(786\) | 795.621 | − | 3074.67i | 0.0361054 | − | 0.139529i | ||||
\(787\) | −31328.1 | −1.41896 | −0.709482 | − | 0.704723i | \(-0.751071\pi\) | ||||
−0.709482 | + | 0.704723i | \(0.751071\pi\) | |||||||
\(788\) | 1291.13 | − | 2327.73i | 0.0583687 | − | 0.105231i | ||||
\(789\) | 1252.37 | 0.0565091 | ||||||||
\(790\) | −24269.5 | − | 6280.12i | −1.09300 | − | 0.282831i | ||||
\(791\) | − | 745.617i | − | 0.0335159i | ||||||
\(792\) | −6197.85 | − | 5886.46i | −0.278069 | − | 0.264099i | ||||
\(793\) | 30968.1 | 1.38677 | ||||||||
\(794\) | −25080.2 | − | 6489.92i | −1.12099 | − | 0.290074i | ||||
\(795\) | 20803.2i | 0.928069i | ||||||||
\(796\) | −18881.5 | − | 10473.1i | −0.840750 | − | 0.466341i | ||||
\(797\) | 12772.5i | 0.567659i | 0.958875 | + | 0.283830i | \(0.0916051\pi\) | ||||
−0.958875 | + | 0.283830i | \(0.908395\pi\) | |||||||
\(798\) | −14717.4 | − | 3808.36i | −0.652869 | − | 0.168940i | ||||
\(799\) | −456.886 | −0.0202296 | ||||||||
\(800\) | 1925.93 | + | 6123.15i | 0.0851150 | + | 0.270607i | ||||
\(801\) | − | 9405.94i | − | 0.414910i | ||||||
\(802\) | 3931.26 | − | 15192.3i | 0.173089 | − | 0.668903i | ||||
\(803\) | − | 4720.65i | − | 0.207457i | ||||||
\(804\) | −7537.60 | + | 13589.3i | −0.330635 | + | 0.596090i | ||||
\(805\) | 16487.5i | 0.721874i | ||||||||
\(806\) | −5480.17 | − | 31036.8i | −0.239492 | − | 1.35636i | ||||
\(807\) | 5300.64i | 0.231216i | ||||||||
\(808\) | 2780.02 | + | 2640.35i | 0.121041 | + | 0.114959i | ||||
\(809\) | − | 5227.08i | − | 0.227162i | −0.993529 | − | 0.113581i | \(-0.963768\pi\) | ||
0.993529 | − | 0.113581i | \(-0.0362322\pi\) | |||||||
\(810\) | −6215.27 | − | 1608.30i | −0.269608 | − | 0.0697654i | ||||
\(811\) | 37006.1i | 1.60229i | 0.598467 | + | 0.801147i | \(0.295777\pi\) | ||||
−0.598467 | + | 0.801147i | \(0.704223\pi\) | |||||||
\(812\) | −12079.7 | − | 6700.30i | −0.522063 | − | 0.289575i | ||||
\(813\) | −28520.1 | −1.23031 | ||||||||
\(814\) | 375.820 | − | 1452.35i | 0.0161824 | − | 0.0625368i | ||||
\(815\) | − | 19112.7i | − | 0.821458i | ||||||
\(816\) | −22622.2 | + | 14118.4i | −0.970510 | + | 0.605690i | ||||
\(817\) | − | 34513.5i | − | 1.47794i | ||||||
\(818\) | −4198.82 | + | 16226.3i | −0.179472 | + | 0.693569i | ||||
\(819\) | −7425.01 | −0.316790 | ||||||||
\(820\) | −8614.87 | − | 4778.44i | −0.366883 | − | 0.203500i | ||||
\(821\) | − | 2790.80i | − | 0.118635i | −0.998239 | − | 0.0593177i | \(-0.981107\pi\) | ||
0.998239 | − | 0.0593177i | \(-0.0188925\pi\) | |||||||
\(822\) | 2844.69 | − | 10993.3i | 0.120705 | − | 0.466465i | ||||
\(823\) | 9068.64 | 0.384098 | 0.192049 | − | 0.981385i | \(-0.438487\pi\) | ||||
0.192049 | + | 0.981385i | \(0.438487\pi\) | |||||||
\(824\) | −14595.0 | + | 15367.0i | −0.617039 | + | 0.649680i | ||||
\(825\) | 4122.48 | 0.173972 | ||||||||
\(826\) | 3302.57 | + | 854.595i | 0.139118 | + | 0.0359990i | ||||
\(827\) | −14541.0 | −0.611415 | −0.305708 | − | 0.952125i | \(-0.598893\pi\) | ||||
−0.305708 | + | 0.952125i | \(0.598893\pi\) | |||||||
\(828\) | 16325.2 | + | 9055.13i | 0.685192 | + | 0.380058i | ||||
\(829\) | 10893.8i | 0.456401i | 0.973614 | + | 0.228200i | \(0.0732841\pi\) | ||||
−0.973614 | + | 0.228200i | \(0.926716\pi\) | |||||||
\(830\) | 16479.0 | + | 4264.20i | 0.689149 | + | 0.178329i | ||||
\(831\) | 4118.45i | 0.171922i | ||||||||
\(832\) | 33010.3 | − | 1702.33i | 1.37551 | − | 0.0709346i | ||||
\(833\) | 28048.7i | 1.16666i | ||||||||
\(834\) | 18804.0 | + | 4865.84i | 0.780731 | + | 0.202027i | ||||
\(835\) | 12571.5 | 0.521024 | ||||||||
\(836\) | −17934.9 | + | 32334.2i | −0.741977 | + | 1.33768i | ||||
\(837\) | 23638.6 | − | 10783.4i | 0.976188 | − | 0.445317i | ||||
\(838\) | 3609.45 | − | 13948.7i | 0.148790 | − | 0.574999i | ||||
\(839\) | − | 3041.54i | − | 0.125156i | −0.998040 | − | 0.0625779i | \(-0.980068\pi\) | ||
0.998040 | − | 0.0625779i | \(-0.0199322\pi\) | |||||||
\(840\) | −5219.12 | + | 5495.20i | −0.214377 | + | 0.225717i | ||||
\(841\) | −10329.3 | −0.423523 | ||||||||
\(842\) | −17380.1 | − | 4497.39i | −0.711352 | − | 0.184074i | ||||
\(843\) | −12034.6 | −0.491687 | ||||||||
\(844\) | −5007.26 | + | 9027.41i | −0.204215 | + | 0.368171i | ||||
\(845\) | 18649.3 | 0.759237 | ||||||||
\(846\) | −36.8317 | + | 142.336i | −0.00149681 | + | 0.00578440i | ||||
\(847\) | − | 3748.95i | − | 0.152084i | ||||||
\(848\) | 31250.7 | − | 19503.4i | 1.26551 | − | 0.789799i | ||||
\(849\) | − | 25143.9i | − | 1.01641i | ||||||
\(850\) | −2740.84 | + | 10592.0i | −0.110600 | + | 0.427413i | ||||
\(851\) | 3276.43i | 0.131979i | ||||||||
\(852\) | 16676.1 | − | 30064.8i | 0.670557 | − | 1.20892i | ||||
\(853\) | 2781.25 | 0.111639 | 0.0558196 | − | 0.998441i | \(-0.482223\pi\) | ||||
0.0558196 | + | 0.998441i | \(0.482223\pi\) | |||||||
\(854\) | 12172.1 | + | 3149.73i | 0.487729 | + | 0.126208i | ||||
\(855\) | − | 17833.0i | − | 0.713305i | ||||||
\(856\) | −9976.07 | + | 10503.8i | −0.398335 | + | 0.419407i | ||||
\(857\) | −22771.0 | −0.907635 | −0.453817 | − | 0.891095i | \(-0.649938\pi\) | ||||
−0.453817 | + | 0.891095i | \(0.649938\pi\) | |||||||
\(858\) | 5318.12 | − | 20551.9i | 0.211606 | − | 0.817749i | ||||
\(859\) | −11358.4 | −0.451157 | −0.225579 | − | 0.974225i | \(-0.572427\pi\) | ||||
−0.225579 | + | 0.974225i | \(0.572427\pi\) | |||||||
\(860\) | −15046.3 | − | 8345.80i | −0.596599 | − | 0.330918i | ||||
\(861\) | 4606.24i | 0.182323i | ||||||||
\(862\) | 8887.20 | − | 34344.5i | 0.351159 | − | 1.35705i | ||||
\(863\) | −10371.7 | −0.409106 | −0.204553 | − | 0.978856i | \(-0.565574\pi\) | ||||
−0.204553 | + | 0.978856i | \(0.565574\pi\) | |||||||
\(864\) | 8175.92 | + | 25993.8i | 0.321933 | + | 1.02353i | ||||
\(865\) | −1352.16 | −0.0531501 | ||||||||
\(866\) | 9212.07 | − | 35600.0i | 0.361477 | − | 1.39692i | ||||
\(867\) | −26686.6 | −1.04536 | ||||||||
\(868\) | 1002.72 | − | 12756.5i | 0.0392103 | − | 0.498828i | ||||
\(869\) | 28509.6 | 1.11291 | ||||||||
\(870\) | −4771.78 | + | 18440.5i | −0.185952 | + | 0.718611i | ||||
\(871\) | 32831.9 | 1.27723 | ||||||||
\(872\) | 13035.9 | + | 12381.0i | 0.506253 | + | 0.480818i | ||||
\(873\) | −22152.0 | −0.858800 | ||||||||
\(874\) | 20230.1 | − | 78179.2i | 0.782945 | − | 3.02569i | ||||
\(875\) | 14070.6i | 0.543624i | ||||||||
\(876\) | −2298.71 | + | 4144.26i | −0.0886600 | + | 0.159842i | ||||
\(877\) | −21745.3 | −0.837270 | −0.418635 | − | 0.908155i | \(-0.637491\pi\) | ||||
−0.418635 | + | 0.908155i | \(0.637491\pi\) | |||||||
\(878\) | −7135.58 | + | 27575.4i | −0.274276 | + | 1.05994i | ||||
\(879\) | −19659.5 | −0.754379 | ||||||||
\(880\) | 9759.38 | + | 15637.7i | 0.373851 | + | 0.599029i | ||||
\(881\) | 49333.2i | 1.88658i | 0.331967 | + | 0.943291i | \(0.392288\pi\) | ||||
−0.331967 | + | 0.943291i | \(0.607712\pi\) | |||||||
\(882\) | 8738.14 | + | 2261.13i | 0.333592 | + | 0.0863224i | ||||
\(883\) | 18511.0 | 0.705488 | 0.352744 | − | 0.935720i | \(-0.385249\pi\) | ||||
0.352744 | + | 0.935720i | \(0.385249\pi\) | |||||||
\(884\) | 49268.4 | + | 27327.9i | 1.87452 | + | 1.03975i | ||||
\(885\) | − | 4704.01i | − | 0.178671i | ||||||
\(886\) | 1921.81 | − | 7426.81i | 0.0728718 | − | 0.281612i | ||||
\(887\) | − | 9356.28i | − | 0.354175i | −0.984195 | − | 0.177087i | \(-0.943332\pi\) | ||
0.984195 | − | 0.177087i | \(-0.0566675\pi\) | |||||||
\(888\) | −1037.15 | + | 1092.02i | −0.0391943 | + | 0.0412676i | ||||
\(889\) | − | 397.334i | − | 0.0149900i | ||||||
\(890\) | −5081.42 | + | 19637.1i | −0.191381 | + | 0.739592i | ||||
\(891\) | 7301.14 | 0.274520 | ||||||||
\(892\) | 6342.32 | + | 3517.92i | 0.238068 | + | 0.132050i | ||||
\(893\) | 635.986 | 0.0238326 | ||||||||
\(894\) | 25360.5 | + | 6562.44i | 0.948749 | + | 0.245504i | ||||
\(895\) | 10128.0 | 0.378258 | ||||||||
\(896\) | 13147.9 | + | 2688.33i | 0.490225 | + | 0.100235i | ||||
\(897\) | 46363.8i | 1.72580i | ||||||||
\(898\) | −1551.04 | + | 5993.97i | −0.0576378 | + | 0.222741i | ||||
\(899\) | −13347.7 | − | 29259.7i | −0.495184 | − | 1.08550i | ||||
\(900\) | 3078.81 | + | 1707.73i | 0.114030 | + | 0.0632493i | ||||
\(901\) | 62788.2 | 2.32162 | ||||||||
\(902\) | 10846.2 | + | 2806.64i | 0.400377 | + | 0.103604i | ||||
\(903\) | 8045.04i | 0.296481i | ||||||||
\(904\) | 1320.09 | + | 1253.77i | 0.0485682 | + | 0.0461281i | ||||
\(905\) | − | 26015.9i | − | 0.955577i | ||||||
\(906\) | −4884.46 | − | 1263.93i | −0.179112 | − | 0.0463481i | ||||
\(907\) | − | 40031.7i | − | 1.46552i | −0.680486 | − | 0.732761i | \(-0.738231\pi\) | ||
0.680486 | − | 0.732761i | \(-0.261769\pi\) | |||||||
\(908\) | 14369.6 | − | 25906.4i | 0.525188 | − | 0.946842i | ||||
\(909\) | 2102.95 | 0.0767331 | ||||||||
\(910\) | 15501.4 | + | 4011.25i | 0.564690 | + | 0.146123i | ||||
\(911\) | 89.8672 | 0.00326831 | 0.00163416 | − | 0.999999i | \(-0.499480\pi\) | ||||
0.00163416 | + | 0.999999i | \(0.499480\pi\) | |||||||
\(912\) | 31490.2 | − | 19652.8i | 1.14336 | − | 0.713565i | ||||
\(913\) | −19358.0 | −0.701705 | ||||||||
\(914\) | −9131.24 | + | 35287.6i | −0.330454 | + | 1.27704i | ||||
\(915\) | − | 17337.3i | − | 0.626397i | ||||||
\(916\) | −9507.50 | + | 17140.7i | −0.342944 | + | 0.618281i | ||||
\(917\) | −2724.27 | −0.0981062 | ||||||||
\(918\) | −11635.3 | + | 44964.7i | −0.418326 | + | 1.61662i | ||||
\(919\) | 49107.0i | 1.76267i | 0.472496 | + | 0.881333i | \(0.343353\pi\) | ||||
−0.472496 | + | 0.881333i | \(0.656647\pi\) | |||||||
\(920\) | −29190.7 | − | 27724.1i | −1.04607 | − | 0.993519i | ||||
\(921\) | − | 8187.39i | − | 0.292925i | ||||||
\(922\) | −2752.12 | + | 10635.5i | −0.0983039 | + | 0.379895i | ||||
\(923\) | −72637.1 | −2.59033 | ||||||||
\(924\) | 4180.61 | − | 7537.06i | 0.148844 | − | 0.268345i | ||||
\(925\) | 617.911i | 0.0219641i | ||||||||
\(926\) | 29129.0 | + | 7537.61i | 1.03374 | + | 0.267496i | ||||
\(927\) | 11624.4i | 0.411861i | ||||||||
\(928\) | 32175.0 | − | 10120.1i | 1.13814 | − | 0.357984i | ||||
\(929\) | − | 32104.1i | − | 1.13380i | −0.823786 | − | 0.566901i | \(-0.808142\pi\) | ||
0.823786 | − | 0.566901i | \(-0.191858\pi\) | |||||||
\(930\) | −17375.8 | + | 3068.04i | −0.612660 | + | 0.108177i | ||||
\(931\) | − | 39043.8i | − | 1.37445i | ||||||
\(932\) | −32552.7 | − | 18056.1i | −1.14410 | − | 0.634601i | ||||
\(933\) | 14727.3i | 0.516774i | ||||||||
\(934\) | −9065.66 | + | 35034.2i | −0.317599 | + | 1.22736i | ||||
\(935\) | 31418.8i | 1.09894i | ||||||||
\(936\) | 12485.3 | − | 13145.8i | 0.435999 | − | 0.459063i | ||||
\(937\) | −32113.0 | −1.11962 | −0.559811 | − | 0.828620i | \(-0.689126\pi\) | ||||
−0.559811 | + | 0.828620i | \(0.689126\pi\) | |||||||
\(938\) | 12904.7 | + | 3339.29i | 0.449203 | + | 0.116239i | ||||
\(939\) | − | 31468.1i | − | 1.09363i | ||||||
\(940\) | 153.789 | − | 277.261i | 0.00533623 | − | 0.00962050i | ||||
\(941\) | − | 12035.2i | − | 0.416936i | −0.978029 | − | 0.208468i | \(-0.933152\pi\) | ||
0.978029 | − | 0.208468i | \(-0.0668476\pi\) | |||||||
\(942\) | 14363.7 | + | 3716.85i | 0.496810 | + | 0.128558i | ||||
\(943\) | −24468.5 | −0.844967 | ||||||||
\(944\) | −7066.39 | + | 4410.10i | −0.243635 | + | 0.152051i | ||||
\(945\) | 13200.0i | 0.454389i | ||||||||
\(946\) | 18943.5 | + | 4901.94i | 0.651064 | + | 0.168473i | ||||
\(947\) | 39152.4 | 1.34349 | 0.671744 | − | 0.740783i | \(-0.265546\pi\) | ||||
0.671744 | + | 0.740783i | \(0.265546\pi\) | |||||||
\(948\) | −25028.6 | − | 13882.7i | −0.857479 | − | 0.475621i | ||||
\(949\) | 10012.6 | 0.342490 | ||||||||
\(950\) | 3815.25 | − | 14744.0i | 0.130298 | − | 0.503536i | ||||
\(951\) | 9401.60 | 0.320576 | ||||||||
\(952\) | 16585.6 | + | 15752.3i | 0.564645 | + | 0.536277i | ||||
\(953\) | 12593.2i | 0.428053i | 0.976828 | + | 0.214027i | \(0.0686579\pi\) | ||||
−0.976828 | + | 0.214027i | \(0.931342\pi\) | |||||||
\(954\) | 5061.65 | − | 19560.7i | 0.171779 | − | 0.663837i | ||||
\(955\) | 40846.9i | 1.38406i | ||||||||
\(956\) | −16834.7 | − | 9337.78i | −0.569534 | − | 0.315905i | ||||
\(957\) | − | 21662.2i | − | 0.731704i | ||||||
\(958\) | −57.6473 | + | 222.778i | −0.00194416 | + | 0.00751317i | ||||
\(959\) | −9740.44 | −0.327983 | ||||||||
\(960\) | −953.037 | − | 18480.6i | −0.0320408 | − | 0.621311i | ||||
\(961\) | 19527.8 | − | 22498.2i | 0.655493 | − | 0.755201i | ||||
\(962\) | 3080.47 | + | 797.123i | 0.103242 | + | 0.0267155i | ||||
\(963\) | 7945.60i | 0.265881i | ||||||||
\(964\) | 5491.43 | − | 9900.29i | 0.183472 | − | 0.330775i | ||||
\(965\) | −11712.3 | −0.390708 | ||||||||
\(966\) | −4715.61 | + | 18223.4i | −0.157062 | + | 0.606966i | ||||
\(967\) | 2721.79 | 0.0905139 | 0.0452570 | − | 0.998975i | \(-0.485589\pi\) | ||||
0.0452570 | + | 0.998975i | \(0.485589\pi\) | |||||||
\(968\) | 6637.41 | + | 6303.94i | 0.220387 | + | 0.209314i | ||||
\(969\) | 63269.4 | 2.09753 | ||||||||
\(970\) | 46247.5 | + | 11967.3i | 1.53084 | + | 0.396130i | ||||
\(971\) | − | 17284.8i | − | 0.571263i | −0.958339 | − | 0.285632i | \(-0.907797\pi\) | ||
0.958339 | − | 0.285632i | \(-0.0922034\pi\) | |||||||
\(972\) | 22024.2 | + | 12216.2i | 0.726777 | + | 0.403124i | ||||
\(973\) | − | 16661.0i | − | 0.548950i | ||||||
\(974\) | −7554.13 | − | 1954.75i | −0.248511 | − | 0.0643063i | ||||
\(975\) | 8743.88i | 0.287209i | ||||||||
\(976\) | −26044.1 | + | 16254.0i | −0.854152 | + | 0.533072i | ||||
\(977\) | −60227.2 | −1.97220 | −0.986099 | − | 0.166158i | \(-0.946864\pi\) | ||||
−0.986099 | + | 0.166158i | \(0.946864\pi\) | |||||||
\(978\) | 5466.44 | − | 21125.0i | 0.178730 | − | 0.690699i | ||||
\(979\) | − | 23067.9i | − | 0.753067i | ||||||
\(980\) | −17021.4 | − | 9441.29i | −0.554824 | − | 0.307746i | ||||
\(981\) | 9861.04 | 0.320937 | ||||||||
\(982\) | 45475.2 | + | 11767.5i | 1.47777 | + | 0.382398i | ||||
\(983\) | 29092.5 | 0.943953 | 0.471977 | − | 0.881611i | \(-0.343541\pi\) | ||||
0.471977 | + | 0.881611i | \(0.343541\pi\) | |||||||
\(984\) | −8155.21 | − | 7745.49i | −0.264206 | − | 0.250932i | ||||
\(985\) | 3148.47i | 0.101846i | ||||||||
\(986\) | 55657.1 | + | 14402.2i | 1.79765 | + | 0.465171i | ||||
\(987\) | −148.247 | −0.00478092 | ||||||||
\(988\) | −68581.7 | − | 38040.4i | −2.20837 | − | 1.22493i | ||||
\(989\) | −42735.5 | −1.37403 | ||||||||
\(990\) | 9788.05 | + | 2532.82i | 0.314227 | + | 0.0813113i | ||||
\(991\) | 48237.2 | 1.54622 | 0.773110 | − | 0.634271i | \(-0.218700\pi\) | ||||
0.773110 | + | 0.634271i | \(0.218700\pi\) | |||||||
\(992\) | 20898.9 | + | 23225.6i | 0.668892 | + | 0.743360i | ||||
\(993\) | 16159.7 | 0.516429 | ||||||||
\(994\) | −28550.2 | − | 7387.83i | −0.911024 | − | 0.235742i | ||||
\(995\) | 25539.0 | 0.813708 | ||||||||
\(996\) | 16994.4 | + | 9426.34i | 0.540651 | + | 0.299884i | ||||
\(997\) | 5979.31 | 0.189937 | 0.0949683 | − | 0.995480i | \(-0.469725\pi\) | ||||
0.0949683 | + | 0.995480i | \(0.469725\pi\) | |||||||
\(998\) | 51303.8 | + | 13275.7i | 1.62725 | + | 0.421077i | ||||
\(999\) | 2623.14i | 0.0830755i |
(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 | 124.4.d.c.123.2 | yes | 40 | |
4.3 | odd | 2 | inner | 124.4.d.c.123.3 | yes | 40 | |
31.30 | odd | 2 | inner | 124.4.d.c.123.1 | ✓ | 40 | |
124.123 | even | 2 | inner | 124.4.d.c.123.4 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.4.d.c.123.1 | ✓ | 40 | 31.30 | odd | 2 | inner | |
124.4.d.c.123.2 | yes | 40 | 1.1 | even | 1 | trivial | |
124.4.d.c.123.3 | yes | 40 | 4.3 | odd | 2 | inner | |
124.4.d.c.123.4 | yes | 40 | 124.123 | even | 2 | inner |