Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(104,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("105.104");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.g (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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 104.2 | ||
Character | \(\chi\) | \(=\) | 105.104 |
Dual form | 105.4.g.b.104.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.11138 | −1.80715 | −0.903573 | − | 0.428435i | \(-0.859065\pi\) | ||||
−0.903573 | + | 0.428435i | \(0.859065\pi\) | |||||||
\(3\) | −1.51783 | + | 4.96953i | −0.292107 | + | 0.956386i | ||||
\(4\) | 18.1262 | 2.26578 | ||||||||
\(5\) | −10.9509 | − | 2.25323i | −0.979481 | − | 0.201535i | ||||
\(6\) | 7.75821 | − | 25.4011i | 0.527879 | − | 1.72833i | ||||
\(7\) | −11.4695 | + | 14.5413i | −0.619295 | + | 0.785158i | ||||
\(8\) | −51.7589 | −2.28744 | ||||||||
\(9\) | −22.3924 | − | 15.0858i | −0.829347 | − | 0.558733i | ||||
\(10\) | 55.9744 | + | 11.5171i | 1.77007 | + | 0.364204i | ||||
\(11\) | 55.4308i | 1.51936i | 0.650294 | + | 0.759682i | \(0.274646\pi\) | ||||
−0.650294 | + | 0.759682i | \(0.725354\pi\) | |||||||
\(12\) | −27.5125 | + | 90.0786i | −0.661848 | + | 2.16695i | ||||
\(13\) | −20.9550 | −0.447066 | −0.223533 | − | 0.974696i | \(-0.571759\pi\) | ||||
−0.223533 | + | 0.974696i | \(0.571759\pi\) | |||||||
\(14\) | 58.6250 | − | 74.3263i | 1.11916 | − | 1.41890i | ||||
\(15\) | 27.8192 | − | 51.0009i | 0.478859 | − | 0.877892i | ||||
\(16\) | 119.550 | 1.86796 | ||||||||
\(17\) | − | 96.8237i | − | 1.38136i | −0.723158 | − | 0.690682i | \(-0.757310\pi\) | ||
0.723158 | − | 0.690682i | \(-0.242690\pi\) | |||||||
\(18\) | 114.456 | + | 77.1093i | 1.49875 | + | 1.00971i | ||||
\(19\) | − | 33.1970i | − | 0.400838i | −0.979710 | − | 0.200419i | \(-0.935770\pi\) | ||
0.979710 | − | 0.200419i | \(-0.0642303\pi\) | |||||||
\(20\) | −198.499 | − | 40.8425i | −2.21928 | − | 0.456634i | ||||
\(21\) | −54.8548 | − | 79.0693i | −0.570014 | − | 0.821635i | ||||
\(22\) | − | 283.328i | − | 2.74571i | ||||||
\(23\) | 111.288 | 1.00892 | 0.504460 | − | 0.863435i | \(-0.331692\pi\) | ||||
0.504460 | + | 0.863435i | \(0.331692\pi\) | |||||||
\(24\) | 78.5612 | − | 257.217i | 0.668177 | − | 2.18767i | ||||
\(25\) | 114.846 | + | 49.3500i | 0.918767 | + | 0.394800i | ||||
\(26\) | 107.109 | 0.807914 | ||||||||
\(27\) | 108.957 | − | 88.3818i | 0.776623 | − | 0.629966i | ||||
\(28\) | −207.899 | + | 263.579i | −1.40318 | + | 1.77899i | ||||
\(29\) | − | 156.784i | − | 1.00393i | −0.864888 | − | 0.501965i | \(-0.832611\pi\) | ||
0.864888 | − | 0.501965i | \(-0.167389\pi\) | |||||||
\(30\) | −142.194 | + | 260.685i | −0.865367 | + | 1.58648i | ||||
\(31\) | 80.4962i | 0.466372i | 0.972432 | + | 0.233186i | \(0.0749152\pi\) | ||||
−0.972432 | + | 0.233186i | \(0.925085\pi\) | |||||||
\(32\) | −196.992 | −1.08824 | ||||||||
\(33\) | −275.465 | − | 84.1346i | −1.45310 | − | 0.443817i | ||||
\(34\) | 494.903i | 2.49633i | ||||||||
\(35\) | 158.367 | − | 133.398i | 0.764825 | − | 0.644238i | ||||
\(36\) | −405.889 | − | 273.448i | −1.87911 | − | 1.26596i | ||||
\(37\) | − | 180.365i | − | 0.801402i | −0.916209 | − | 0.400701i | \(-0.868767\pi\) | ||
0.916209 | − | 0.400701i | \(-0.131233\pi\) | |||||||
\(38\) | 169.683i | 0.724372i | ||||||||
\(39\) | 31.8061 | − | 104.136i | 0.130591 | − | 0.427568i | ||||
\(40\) | 566.808 | + | 116.625i | 2.24050 | + | 0.461000i | ||||
\(41\) | 36.5837 | 0.139351 | 0.0696757 | − | 0.997570i | \(-0.477804\pi\) | ||||
0.0696757 | + | 0.997570i | \(0.477804\pi\) | |||||||
\(42\) | 280.384 | + | 404.153i | 1.03010 | + | 1.48481i | ||||
\(43\) | 52.5826i | 0.186483i | 0.995644 | + | 0.0932416i | \(0.0297229\pi\) | ||||
−0.995644 | + | 0.0932416i | \(0.970277\pi\) | |||||||
\(44\) | 1004.75i | 3.44254i | ||||||||
\(45\) | 211.226 | + | 215.659i | 0.699726 | + | 0.714412i | ||||
\(46\) | −568.835 | −1.82326 | ||||||||
\(47\) | 259.660i | 0.805858i | 0.915231 | + | 0.402929i | \(0.132008\pi\) | ||||
−0.915231 | + | 0.402929i | \(0.867992\pi\) | |||||||
\(48\) | −181.456 | + | 594.105i | −0.545644 | + | 1.78649i | ||||
\(49\) | −79.9009 | − | 333.564i | −0.232947 | − | 0.972489i | ||||
\(50\) | −587.021 | − | 252.247i | −1.66035 | − | 0.713461i | ||||
\(51\) | 481.168 | + | 146.962i | 1.32112 | + | 0.403506i | ||||
\(52\) | −379.834 | −1.01295 | ||||||||
\(53\) | −191.690 | −0.496804 | −0.248402 | − | 0.968657i | \(-0.579905\pi\) | ||||
−0.248402 | + | 0.968657i | \(0.579905\pi\) | |||||||
\(54\) | −556.921 | + | 451.753i | −1.40347 | + | 1.13844i | ||||
\(55\) | 124.898 | − | 607.019i | 0.306206 | − | 1.48819i | ||||
\(56\) | 593.648 | − | 752.643i | 1.41660 | − | 1.79600i | ||||
\(57\) | 164.973 | + | 50.3875i | 0.383356 | + | 0.117087i | ||||
\(58\) | 801.380i | 1.81425i | ||||||||
\(59\) | −705.237 | −1.55617 | −0.778085 | − | 0.628159i | \(-0.783809\pi\) | ||||
−0.778085 | + | 0.628159i | \(0.783809\pi\) | |||||||
\(60\) | 504.256 | − | 924.453i | 1.08499 | − | 1.98911i | ||||
\(61\) | − | 427.079i | − | 0.896423i | −0.893928 | − | 0.448212i | \(-0.852061\pi\) | ||
0.893928 | − | 0.448212i | \(-0.147939\pi\) | |||||||
\(62\) | − | 411.447i | − | 0.842803i | ||||||
\(63\) | 476.197 | − | 152.588i | 0.952305 | − | 0.305148i | ||||
\(64\) | 50.5057 | 0.0986440 | ||||||||
\(65\) | 229.476 | + | 47.2164i | 0.437893 | + | 0.0900996i | ||||
\(66\) | 1408.00 | + | 430.044i | 2.62596 | + | 0.802041i | ||||
\(67\) | − | 306.444i | − | 0.558777i | −0.960178 | − | 0.279388i | \(-0.909868\pi\) | ||
0.960178 | − | 0.279388i | \(-0.0901317\pi\) | |||||||
\(68\) | − | 1755.05i | − | 3.12986i | ||||||
\(69\) | −168.916 | + | 553.048i | −0.294712 | + | 0.964916i | ||||
\(70\) | −809.473 | + | 681.846i | −1.38215 | + | 1.16423i | ||||
\(71\) | − | 513.791i | − | 0.858814i | −0.903111 | − | 0.429407i | \(-0.858723\pi\) | ||
0.903111 | − | 0.429407i | \(-0.141277\pi\) | |||||||
\(72\) | 1159.00 | + | 780.824i | 1.89708 | + | 1.27807i | ||||
\(73\) | −360.633 | −0.578204 | −0.289102 | − | 0.957298i | \(-0.593357\pi\) | ||||
−0.289102 | + | 0.957298i | \(0.593357\pi\) | |||||||
\(74\) | 921.916i | 1.44825i | ||||||||
\(75\) | −419.563 | + | 495.825i | −0.645959 | + | 0.763372i | ||||
\(76\) | − | 601.736i | − | 0.908208i | ||||||
\(77\) | −806.038 | − | 635.764i | −1.19294 | − | 0.940935i | ||||
\(78\) | −162.573 | + | 532.280i | −0.235997 | + | 0.772677i | ||||
\(79\) | 85.9838 | 0.122455 | 0.0612274 | − | 0.998124i | \(-0.480499\pi\) | ||||
0.0612274 | + | 0.998124i | \(0.480499\pi\) | |||||||
\(80\) | −1309.18 | − | 269.373i | −1.82963 | − | 0.376460i | ||||
\(81\) | 273.837 | + | 675.614i | 0.375634 | + | 0.926768i | ||||
\(82\) | −186.993 | −0.251828 | ||||||||
\(83\) | 886.893i | 1.17288i | 0.809992 | + | 0.586440i | \(0.199471\pi\) | ||||
−0.809992 | + | 0.586440i | \(0.800529\pi\) | |||||||
\(84\) | −994.309 | − | 1433.23i | −1.29152 | − | 1.86164i | ||||
\(85\) | −218.166 | + | 1060.31i | −0.278394 | + | 1.35302i | ||||
\(86\) | − | 268.770i | − | 0.337002i | ||||||
\(87\) | 779.140 | + | 237.971i | 0.960145 | + | 0.293255i | ||||
\(88\) | − | 2869.03i | − | 3.47545i | ||||||
\(89\) | 1417.80 | 1.68861 | 0.844305 | − | 0.535863i | \(-0.180014\pi\) | ||||
0.844305 | + | 0.535863i | \(0.180014\pi\) | |||||||
\(90\) | −1079.65 | − | 1102.31i | −1.26451 | − | 1.29105i | ||||
\(91\) | 240.343 | − | 304.713i | 0.276866 | − | 0.351018i | ||||
\(92\) | 2017.23 | 2.28598 | ||||||||
\(93\) | −400.028 | − | 122.180i | −0.446032 | − | 0.136231i | ||||
\(94\) | − | 1327.22i | − | 1.45630i | ||||||
\(95\) | −74.8006 | + | 363.538i | −0.0807830 | + | 0.392613i | ||||
\(96\) | 299.001 | − | 978.958i | 0.317882 | − | 1.04078i | ||||
\(97\) | 1055.44 | 1.10478 | 0.552392 | − | 0.833584i | \(-0.313715\pi\) | ||||
0.552392 | + | 0.833584i | \(0.313715\pi\) | |||||||
\(98\) | 408.404 | + | 1704.97i | 0.420970 | + | 1.75743i | ||||
\(99\) | 836.218 | − | 1241.23i | 0.848920 | − | 1.26008i | ||||
\(100\) | 2081.72 | + | 894.528i | 2.08172 | + | 0.894528i | ||||
\(101\) | −740.746 | −0.729772 | −0.364886 | − | 0.931052i | \(-0.618892\pi\) | ||||
−0.364886 | + | 0.931052i | \(0.618892\pi\) | |||||||
\(102\) | −2459.43 | − | 751.179i | −2.38745 | − | 0.729194i | ||||
\(103\) | −935.584 | −0.895008 | −0.447504 | − | 0.894282i | \(-0.647687\pi\) | ||||
−0.447504 | + | 0.894282i | \(0.647687\pi\) | |||||||
\(104\) | 1084.61 | 1.02264 | ||||||||
\(105\) | 422.549 | + | 989.483i | 0.392730 | + | 0.919654i | ||||
\(106\) | 979.799 | 0.897797 | ||||||||
\(107\) | −794.752 | −0.718052 | −0.359026 | − | 0.933328i | \(-0.616891\pi\) | ||||
−0.359026 | + | 0.933328i | \(0.616891\pi\) | |||||||
\(108\) | 1974.98 | − | 1602.03i | 1.75965 | − | 1.42736i | ||||
\(109\) | −202.134 | −0.177623 | −0.0888117 | − | 0.996048i | \(-0.528307\pi\) | ||||
−0.0888117 | + | 0.996048i | \(0.528307\pi\) | |||||||
\(110\) | −638.403 | + | 3102.70i | −0.553358 | + | 2.68937i | ||||
\(111\) | 896.330 | + | 273.764i | 0.766449 | + | 0.234095i | ||||
\(112\) | −1371.17 | + | 1738.41i | −1.15682 | + | 1.46665i | ||||
\(113\) | −1457.83 | −1.21364 | −0.606818 | − | 0.794841i | \(-0.707554\pi\) | ||||
−0.606818 | + | 0.794841i | \(0.707554\pi\) | |||||||
\(114\) | −843.242 | − | 257.550i | −0.692779 | − | 0.211594i | ||||
\(115\) | −1218.71 | − | 250.758i | −0.988218 | − | 0.203333i | ||||
\(116\) | − | 2841.89i | − | 2.27468i | ||||||
\(117\) | 469.232 | + | 316.123i | 0.370773 | + | 0.249791i | ||||
\(118\) | 3604.73 | 2.81223 | ||||||||
\(119\) | 1407.95 | + | 1110.52i | 1.08459 | + | 0.855472i | ||||
\(120\) | −1439.89 | + | 2639.75i | −1.09536 | + | 2.00813i | ||||
\(121\) | −1741.57 | −1.30847 | ||||||||
\(122\) | 2182.96i | 1.61997i | ||||||||
\(123\) | −55.5278 | + | 181.803i | −0.0407055 | + | 0.133274i | ||||
\(124\) | 1459.09i | 1.05669i | ||||||||
\(125\) | −1146.47 | − | 799.203i | −0.820349 | − | 0.571863i | ||||
\(126\) | −2434.02 | + | 779.937i | −1.72095 | + | 0.551447i | ||||
\(127\) | − | 1189.69i | − | 0.831242i | −0.909538 | − | 0.415621i | \(-0.863564\pi\) | ||
0.909538 | − | 0.415621i | \(-0.136436\pi\) | |||||||
\(128\) | 1317.78 | 0.909975 | ||||||||
\(129\) | −261.311 | − | 79.8116i | −0.178350 | − | 0.0544730i | ||||
\(130\) | −1172.94 | − | 241.341i | −0.791337 | − | 0.162823i | ||||
\(131\) | −531.346 | −0.354381 | −0.177190 | − | 0.984177i | \(-0.556701\pi\) | ||||
−0.177190 | + | 0.984177i | \(0.556701\pi\) | |||||||
\(132\) | −4993.13 | − | 1525.04i | −3.29239 | − | 1.00559i | ||||
\(133\) | 482.729 | + | 380.753i | 0.314721 | + | 0.248237i | ||||
\(134\) | 1566.35i | 1.00979i | ||||||||
\(135\) | −1392.33 | + | 722.357i | −0.887648 | + | 0.460523i | ||||
\(136\) | 5011.48i | 3.15979i | ||||||||
\(137\) | 1269.32 | 0.791572 | 0.395786 | − | 0.918343i | \(-0.370472\pi\) | ||||
0.395786 | + | 0.918343i | \(0.370472\pi\) | |||||||
\(138\) | 863.396 | − | 2826.84i | 0.532588 | − | 1.74374i | ||||
\(139\) | − | 1566.53i | − | 0.955910i | −0.878384 | − | 0.477955i | \(-0.841378\pi\) | ||
0.878384 | − | 0.477955i | \(-0.158622\pi\) | |||||||
\(140\) | 2870.59 | − | 2417.99i | 1.73292 | − | 1.45970i | ||||
\(141\) | −1290.39 | − | 394.120i | −0.770711 | − | 0.235397i | ||||
\(142\) | 2626.18i | 1.55200i | ||||||||
\(143\) | − | 1161.55i | − | 0.679257i | ||||||
\(144\) | −2677.00 | − | 1803.50i | −1.54919 | − | 1.04369i | ||||
\(145\) | −353.270 | + | 1716.93i | −0.202327 | + | 0.983331i | ||||
\(146\) | 1843.33 | 1.04490 | ||||||||
\(147\) | 1778.93 | + | 109.224i | 0.998120 | + | 0.0612833i | ||||
\(148\) | − | 3269.34i | − | 1.81580i | ||||||
\(149\) | − | 1112.59i | − | 0.611723i | −0.952076 | − | 0.305862i | \(-0.901055\pi\) | ||
0.952076 | − | 0.305862i | \(-0.0989445\pi\) | |||||||
\(150\) | 2144.54 | − | 2534.35i | 1.16734 | − | 1.37952i | ||||
\(151\) | 1252.15 | 0.674822 | 0.337411 | − | 0.941357i | \(-0.390449\pi\) | ||||
0.337411 | + | 0.941357i | \(0.390449\pi\) | |||||||
\(152\) | 1718.24i | 0.916892i | ||||||||
\(153\) | −1460.66 | + | 2168.11i | −0.771815 | + | 1.14563i | ||||
\(154\) | 4119.96 | + | 3249.63i | 2.15582 | + | 1.70041i | ||||
\(155\) | 181.377 | − | 881.509i | 0.0939905 | − | 0.456803i | ||||
\(156\) | 576.524 | − | 1887.59i | 0.295890 | − | 0.968773i | ||||
\(157\) | 226.625 | 0.115202 | 0.0576009 | − | 0.998340i | \(-0.481655\pi\) | ||||
0.0576009 | + | 0.998340i | \(0.481655\pi\) | |||||||
\(158\) | −439.496 | −0.221294 | ||||||||
\(159\) | 290.953 | − | 952.607i | 0.145120 | − | 0.475136i | ||||
\(160\) | 2157.25 | + | 443.869i | 1.06591 | + | 0.219318i | ||||
\(161\) | −1276.42 | + | 1618.28i | −0.624819 | + | 0.792161i | ||||
\(162\) | −1399.69 | − | 3453.32i | −0.678825 | − | 1.67480i | ||||
\(163\) | − | 1843.89i | − | 0.886042i | −0.896511 | − | 0.443021i | \(-0.853907\pi\) | ||
0.896511 | − | 0.443021i | \(-0.146093\pi\) | |||||||
\(164\) | 663.123 | 0.315739 | ||||||||
\(165\) | 2827.02 | + | 1542.04i | 1.33384 | + | 0.727561i | ||||
\(166\) | − | 4533.24i | − | 2.11957i | ||||||
\(167\) | − | 2144.68i | − | 0.993774i | −0.867815 | − | 0.496887i | \(-0.834476\pi\) | ||
0.867815 | − | 0.496887i | \(-0.165524\pi\) | |||||||
\(168\) | 2839.22 | + | 4092.54i | 1.30387 | + | 1.87944i | ||||
\(169\) | −1757.89 | −0.800132 | ||||||||
\(170\) | 1115.13 | − | 5419.65i | 0.503098 | − | 2.44511i | ||||
\(171\) | −500.804 | + | 743.360i | −0.223962 | + | 0.332434i | ||||
\(172\) | 953.123i | 0.422529i | ||||||||
\(173\) | − | 3462.67i | − | 1.52175i | −0.648901 | − | 0.760873i | \(-0.724771\pi\) | ||
0.648901 | − | 0.760873i | \(-0.275229\pi\) | |||||||
\(174\) | −3982.48 | − | 1216.36i | −1.73512 | − | 0.529954i | ||||
\(175\) | −2034.84 | + | 1103.99i | −0.878968 | + | 0.476880i | ||||
\(176\) | 6626.72i | 2.83811i | ||||||||
\(177\) | 1070.43 | − | 3504.69i | 0.454568 | − | 1.48830i | ||||
\(178\) | −7246.90 | −3.05156 | ||||||||
\(179\) | 3089.42i | 1.29002i | 0.764173 | + | 0.645011i | \(0.223147\pi\) | ||||
−0.764173 | + | 0.645011i | \(0.776853\pi\) | |||||||
\(180\) | 3828.72 | + | 3909.08i | 1.58542 | + | 1.61870i | ||||
\(181\) | 2791.07i | 1.14618i | 0.819493 | + | 0.573090i | \(0.194255\pi\) | ||||
−0.819493 | + | 0.573090i | \(0.805745\pi\) | |||||||
\(182\) | −1228.48 | + | 1557.51i | −0.500337 | + | 0.634340i | ||||
\(183\) | 2122.38 | + | 648.233i | 0.857326 | + | 0.261851i | ||||
\(184\) | −5760.14 | −2.30784 | ||||||||
\(185\) | −406.405 | + | 1975.17i | −0.161511 | + | 0.784958i | ||||
\(186\) | 2044.69 | + | 624.507i | 0.806045 | + | 0.246188i | ||||
\(187\) | 5367.01 | 2.09880 | ||||||||
\(188\) | 4706.65i | 1.82589i | ||||||||
\(189\) | 35.5048 | + | 2598.08i | 0.0136645 | + | 0.999907i | ||||
\(190\) | 382.334 | − | 1858.18i | 0.145987 | − | 0.709509i | ||||
\(191\) | − | 3188.41i | − | 1.20788i | −0.797029 | − | 0.603941i | \(-0.793596\pi\) | ||
0.797029 | − | 0.603941i | \(-0.206404\pi\) | |||||||
\(192\) | −76.6591 | + | 250.989i | −0.0288146 | + | 0.0943417i | ||||
\(193\) | 1762.45i | 0.657327i | 0.944447 | + | 0.328664i | \(0.106598\pi\) | ||||
−0.944447 | + | 0.328664i | \(0.893402\pi\) | |||||||
\(194\) | −5394.77 | −1.99651 | ||||||||
\(195\) | −582.950 | + | 1068.72i | −0.214082 | + | 0.392476i | ||||
\(196\) | −1448.30 | − | 6046.25i | −0.527806 | − | 2.20344i | ||||
\(197\) | −1135.69 | −0.410735 | −0.205367 | − | 0.978685i | \(-0.565839\pi\) | ||||
−0.205367 | + | 0.978685i | \(0.565839\pi\) | |||||||
\(198\) | −4274.23 | + | 6344.38i | −1.53412 | + | 2.27715i | ||||
\(199\) | 1200.54i | 0.427658i | 0.976871 | + | 0.213829i | \(0.0685935\pi\) | ||||
−0.976871 | + | 0.213829i | \(0.931407\pi\) | |||||||
\(200\) | −5944.29 | − | 2554.30i | −2.10162 | − | 0.903081i | ||||
\(201\) | 1522.88 | + | 465.130i | 0.534406 | + | 0.163223i | ||||
\(202\) | 3786.23 | 1.31880 | ||||||||
\(203\) | 2279.84 | + | 1798.23i | 0.788244 | + | 0.621729i | ||||
\(204\) | 8721.75 | + | 2663.86i | 2.99336 | + | 0.914254i | ||||
\(205\) | −400.625 | − | 82.4315i | −0.136492 | − | 0.0280842i | ||||
\(206\) | 4782.13 | 1.61741 | ||||||||
\(207\) | −2492.00 | − | 1678.87i | −0.836744 | − | 0.563717i | ||||
\(208\) | −2505.16 | −0.835103 | ||||||||
\(209\) | 1840.14 | 0.609019 | ||||||||
\(210\) | −2159.81 | − | 5057.62i | −0.709719 | − | 1.66195i | ||||
\(211\) | −835.608 | −0.272633 | −0.136317 | − | 0.990665i | \(-0.543526\pi\) | ||||
−0.136317 | + | 0.990665i | \(0.543526\pi\) | |||||||
\(212\) | −3474.61 | −1.12565 | ||||||||
\(213\) | 2553.30 | + | 779.848i | 0.821357 | + | 0.250865i | ||||
\(214\) | 4062.28 | 1.29762 | ||||||||
\(215\) | 118.481 | − | 575.829i | 0.0375829 | − | 0.182657i | ||||
\(216\) | −5639.50 | + | 4574.54i | −1.77648 | + | 1.44101i | ||||
\(217\) | −1170.52 | − | 923.252i | −0.366176 | − | 0.288822i | ||||
\(218\) | 1033.19 | 0.320991 | ||||||||
\(219\) | 547.380 | − | 1792.17i | 0.168897 | − | 0.552986i | ||||
\(220\) | 2263.93 | − | 11002.9i | 0.693793 | − | 3.37190i | ||||
\(221\) | 2028.94i | 0.617562i | ||||||||
\(222\) | −4581.48 | − | 1399.31i | −1.38509 | − | 0.423044i | ||||
\(223\) | −2734.39 | −0.821115 | −0.410557 | − | 0.911835i | \(-0.634666\pi\) | ||||
−0.410557 | + | 0.911835i | \(0.634666\pi\) | |||||||
\(224\) | 2259.40 | − | 2864.53i | 0.673941 | − | 0.854440i | ||||
\(225\) | −1827.19 | − | 2837.61i | −0.541389 | − | 0.840772i | ||||
\(226\) | 7451.50 | 2.19322 | ||||||||
\(227\) | − | 2207.95i | − | 0.645579i | −0.946471 | − | 0.322790i | \(-0.895379\pi\) | ||
0.946471 | − | 0.322790i | \(-0.104621\pi\) | |||||||
\(228\) | 2990.34 | + | 913.333i | 0.868597 | + | 0.265294i | ||||
\(229\) | − | 1720.95i | − | 0.496610i | −0.968682 | − | 0.248305i | \(-0.920126\pi\) | ||
0.968682 | − | 0.248305i | \(-0.0798735\pi\) | |||||||
\(230\) | 6229.27 | + | 1281.72i | 1.78585 | + | 0.367452i | ||||
\(231\) | 4382.87 | − | 3040.64i | 1.24836 | − | 0.866059i | ||||
\(232\) | 8114.94i | 2.29643i | ||||||||
\(233\) | 2915.58 | 0.819767 | 0.409884 | − | 0.912138i | \(-0.365569\pi\) | ||||
0.409884 | + | 0.912138i | \(0.365569\pi\) | |||||||
\(234\) | −2398.42 | − | 1615.82i | −0.670041 | − | 0.451409i | ||||
\(235\) | 585.075 | − | 2843.52i | 0.162409 | − | 0.789323i | ||||
\(236\) | −12783.3 | −3.52593 | ||||||||
\(237\) | −130.509 | + | 427.299i | −0.0357699 | + | 0.117114i | ||||
\(238\) | −7196.55 | − | 5676.29i | −1.96001 | − | 1.54596i | ||||
\(239\) | − | 6597.22i | − | 1.78552i | −0.450536 | − | 0.892758i | \(-0.648767\pi\) | ||
0.450536 | − | 0.892758i | \(-0.351233\pi\) | |||||||
\(240\) | 3325.77 | − | 6097.14i | 0.894489 | − | 1.63987i | ||||
\(241\) | 5492.27i | 1.46800i | 0.679149 | + | 0.734000i | \(0.262349\pi\) | ||||
−0.679149 | + | 0.734000i | \(0.737651\pi\) | |||||||
\(242\) | 8901.83 | 2.36459 | ||||||||
\(243\) | −3773.12 | + | 335.372i | −0.996073 | + | 0.0885356i | ||||
\(244\) | − | 7741.31i | − | 2.03109i | ||||||
\(245\) | 123.392 | + | 3832.87i | 0.0321765 | + | 0.999482i | ||||
\(246\) | 283.824 | − | 929.266i | 0.0735607 | − | 0.240845i | ||||
\(247\) | 695.643i | 0.179201i | ||||||||
\(248\) | − | 4166.39i | − | 1.06680i | ||||||
\(249\) | −4407.44 | − | 1346.15i | −1.12173 | − | 0.342606i | ||||
\(250\) | 5860.06 | + | 4085.03i | 1.48249 | + | 1.03344i | ||||
\(251\) | −3852.51 | −0.968798 | −0.484399 | − | 0.874847i | \(-0.660962\pi\) | ||||
−0.484399 | + | 0.874847i | \(0.660962\pi\) | |||||||
\(252\) | 8631.65 | − | 2765.85i | 2.15771 | − | 0.691397i | ||||
\(253\) | 6168.78i | 1.53292i | ||||||||
\(254\) | 6080.95i | 1.50218i | ||||||||
\(255\) | −4938.10 | − | 2693.56i | −1.21269 | − | 0.661478i | ||||
\(256\) | −7139.74 | −1.74310 | ||||||||
\(257\) | 445.140i | 0.108043i | 0.998540 | + | 0.0540215i | \(0.0172040\pi\) | ||||
−0.998540 | + | 0.0540215i | \(0.982796\pi\) | |||||||
\(258\) | 1335.66 | + | 407.947i | 0.322304 | + | 0.0984406i | ||||
\(259\) | 2622.75 | + | 2068.70i | 0.629227 | + | 0.496304i | ||||
\(260\) | 4159.54 | + | 855.854i | 0.992167 | + | 0.204146i | ||||
\(261\) | −2365.21 | + | 3510.76i | −0.560929 | + | 0.832607i | ||||
\(262\) | 2715.91 | 0.640418 | ||||||||
\(263\) | −5539.14 | −1.29870 | −0.649350 | − | 0.760490i | \(-0.724959\pi\) | ||||
−0.649350 | + | 0.760490i | \(0.724959\pi\) | |||||||
\(264\) | 14257.7 | + | 4354.71i | 3.32388 | + | 1.01520i | ||||
\(265\) | 2099.18 | + | 431.922i | 0.486610 | + | 0.100124i | ||||
\(266\) | −2467.41 | − | 1946.18i | −0.568747 | − | 0.448600i | ||||
\(267\) | −2151.98 | + | 7045.78i | −0.493254 | + | 1.61496i | ||||
\(268\) | − | 5554.66i | − | 1.26606i | ||||||
\(269\) | 6822.25 | 1.54632 | 0.773160 | − | 0.634211i | \(-0.218675\pi\) | ||||
0.773160 | + | 0.634211i | \(0.218675\pi\) | |||||||
\(270\) | 7116.71 | − | 3692.24i | 1.60411 | − | 0.832232i | ||||
\(271\) | − | 3566.70i | − | 0.799490i | −0.916626 | − | 0.399745i | \(-0.869099\pi\) | ||
0.916626 | − | 0.399745i | \(-0.130901\pi\) | |||||||
\(272\) | − | 11575.2i | − | 2.58034i | ||||||
\(273\) | 1149.48 | + | 1656.89i | 0.254834 | + | 0.367325i | ||||
\(274\) | −6487.98 | −1.43049 | ||||||||
\(275\) | −2735.51 | + | 6366.00i | −0.599845 | + | 1.39594i | ||||
\(276\) | −3061.81 | + | 10024.7i | −0.667751 | + | 2.18628i | ||||
\(277\) | − | 4554.17i | − | 0.987847i | −0.869505 | − | 0.493923i | \(-0.835562\pi\) | ||
0.869505 | − | 0.493923i | \(-0.164438\pi\) | |||||||
\(278\) | 8007.14i | 1.72747i | ||||||||
\(279\) | 1214.35 | − | 1802.50i | 0.260578 | − | 0.386785i | ||||
\(280\) | −8196.88 | + | 6904.51i | −1.74949 | + | 1.47366i | ||||
\(281\) | − | 4934.61i | − | 1.04759i | −0.851843 | − | 0.523797i | \(-0.824515\pi\) | ||
0.851843 | − | 0.523797i | \(-0.175485\pi\) | |||||||
\(282\) | 6595.67 | + | 2014.50i | 1.39279 | + | 0.425396i | ||||
\(283\) | 456.724 | 0.0959344 | 0.0479672 | − | 0.998849i | \(-0.484726\pi\) | ||||
0.0479672 | + | 0.998849i | \(0.484726\pi\) | |||||||
\(284\) | − | 9313.08i | − | 1.94588i | ||||||
\(285\) | −1693.08 | − | 923.513i | −0.351892 | − | 0.191945i | ||||
\(286\) | 5937.12i | 1.22752i | ||||||||
\(287\) | −419.596 | + | 531.975i | −0.0862996 | + | 0.109413i | ||||
\(288\) | 4411.12 | + | 2971.79i | 0.902528 | + | 0.608035i | ||||
\(289\) | −4461.83 | −0.908168 | ||||||||
\(290\) | 1805.70 | − | 8775.86i | 0.365635 | − | 1.77702i | ||||
\(291\) | −1601.99 | + | 5245.05i | −0.322715 | + | 1.05660i | ||||
\(292\) | −6536.90 | −1.31008 | ||||||||
\(293\) | − | 2102.29i | − | 0.419171i | −0.977790 | − | 0.209585i | \(-0.932789\pi\) | ||
0.977790 | − | 0.209585i | \(-0.0672114\pi\) | |||||||
\(294\) | −9092.79 | − | 558.286i | −1.80375 | − | 0.110748i | ||||
\(295\) | 7723.00 | + | 1589.06i | 1.52424 | + | 0.313623i | ||||
\(296\) | 9335.50i | 1.83316i | ||||||||
\(297\) | 4899.07 | + | 6039.58i | 0.957148 | + | 1.17997i | ||||
\(298\) | 5686.86i | 1.10547i | ||||||||
\(299\) | −2332.04 | −0.451054 | ||||||||
\(300\) | −7605.08 | + | 8987.42i | −1.46360 | + | 1.72963i | ||||
\(301\) | −764.622 | − | 603.097i | −0.146419 | − | 0.115488i | ||||
\(302\) | −6400.19 | −1.21950 | ||||||||
\(303\) | 1124.33 | − | 3681.16i | 0.213171 | − | 0.697944i | ||||
\(304\) | − | 3968.69i | − | 0.748750i | ||||||
\(305\) | −962.308 | + | 4676.91i | −0.180661 | + | 0.878030i | ||||
\(306\) | 7466.01 | − | 11082.0i | 1.39478 | − | 2.07032i | ||||
\(307\) | −2780.68 | −0.516944 | −0.258472 | − | 0.966019i | \(-0.583219\pi\) | ||||
−0.258472 | + | 0.966019i | \(0.583219\pi\) | |||||||
\(308\) | −14610.4 | − | 11524.0i | −2.70294 | − | 2.13195i | ||||
\(309\) | 1420.06 | − | 4649.41i | 0.261438 | − | 0.855973i | ||||
\(310\) | −927.085 | + | 4505.72i | −0.169854 | + | 0.825510i | ||||
\(311\) | 440.562 | 0.0803280 | 0.0401640 | − | 0.999193i | \(-0.487212\pi\) | ||||
0.0401640 | + | 0.999193i | \(0.487212\pi\) | |||||||
\(312\) | −1646.25 | + | 5389.97i | −0.298719 | + | 0.978036i | ||||
\(313\) | 6998.87 | 1.26390 | 0.631948 | − | 0.775010i | \(-0.282255\pi\) | ||||
0.631948 | + | 0.775010i | \(0.282255\pi\) | |||||||
\(314\) | −1158.37 | −0.208186 | ||||||||
\(315\) | −5558.62 | + | 598.002i | −0.994263 | + | 0.106964i | ||||
\(316\) | 1558.56 | 0.277455 | ||||||||
\(317\) | −10112.3 | −1.79168 | −0.895839 | − | 0.444379i | \(-0.853424\pi\) | ||||
−0.895839 | + | 0.444379i | \(0.853424\pi\) | |||||||
\(318\) | −1487.17 | + | 4869.14i | −0.262253 | + | 0.858640i | ||||
\(319\) | 8690.64 | 1.52534 | ||||||||
\(320\) | −553.085 | − | 113.801i | −0.0966199 | − | 0.0198802i | ||||
\(321\) | 1206.30 | − | 3949.54i | 0.209748 | − | 0.686735i | ||||
\(322\) | 6524.26 | − | 8271.62i | 1.12914 | − | 1.43155i | ||||
\(323\) | −3214.26 | −0.553703 | ||||||||
\(324\) | 4963.63 | + | 12246.3i | 0.851102 | + | 2.09985i | ||||
\(325\) | −2406.59 | − | 1034.13i | −0.410750 | − | 0.176502i | ||||
\(326\) | 9424.84i | 1.60121i | ||||||||
\(327\) | 306.806 | − | 1004.51i | 0.0518850 | − | 0.169877i | ||||
\(328\) | −1893.53 | −0.318758 | ||||||||
\(329\) | −3775.81 | − | 2978.17i | −0.632726 | − | 0.499064i | ||||
\(330\) | −14450.0 | − | 7881.94i | −2.41044 | − | 1.31481i | ||||
\(331\) | 5030.87 | 0.835413 | 0.417706 | − | 0.908582i | \(-0.362834\pi\) | ||||
0.417706 | + | 0.908582i | \(0.362834\pi\) | |||||||
\(332\) | 16076.0i | 2.65748i | ||||||||
\(333\) | −2720.96 | + | 4038.81i | −0.447770 | + | 0.664641i | ||||
\(334\) | 10962.3i | 1.79589i | ||||||||
\(335\) | −690.489 | + | 3355.84i | −0.112613 | + | 0.547311i | ||||
\(336\) | −6557.86 | − | 9452.70i | −1.06476 | − | 1.53478i | ||||
\(337\) | − | 3231.43i | − | 0.522335i | −0.965293 | − | 0.261168i | \(-0.915892\pi\) | ||
0.965293 | − | 0.261168i | \(-0.0841075\pi\) | |||||||
\(338\) | 8985.24 | 1.44595 | ||||||||
\(339\) | 2212.73 | − | 7244.71i | 0.354511 | − | 1.16070i | ||||
\(340\) | −3954.53 | + | 19219.4i | −0.630778 | + | 3.06564i | ||||
\(341\) | −4461.97 | −0.708590 | ||||||||
\(342\) | 2559.80 | − | 3799.60i | 0.404731 | − | 0.600756i | ||||
\(343\) | 5766.89 | + | 2663.95i | 0.907821 | + | 0.419357i | ||||
\(344\) | − | 2721.62i | − | 0.426569i | ||||||
\(345\) | 3095.94 | − | 5675.79i | 0.483130 | − | 0.885722i | ||||
\(346\) | 17699.0i | 2.75002i | ||||||||
\(347\) | 8184.28 | 1.26615 | 0.633077 | − | 0.774089i | \(-0.281792\pi\) | ||||
0.633077 | + | 0.774089i | \(0.281792\pi\) | |||||||
\(348\) | 14122.8 | + | 4313.51i | 2.17547 | + | 0.664449i | ||||
\(349\) | 11214.5i | 1.72005i | 0.510248 | + | 0.860027i | \(0.329554\pi\) | ||||
−0.510248 | + | 0.860027i | \(0.670446\pi\) | |||||||
\(350\) | 10400.8 | − | 5642.92i | 1.58842 | − | 0.861791i | ||||
\(351\) | −2283.19 | + | 1852.04i | −0.347202 | + | 0.281637i | ||||
\(352\) | − | 10919.4i | − | 1.65343i | ||||||
\(353\) | 804.207i | 0.121257i | 0.998160 | + | 0.0606284i | \(0.0193105\pi\) | ||||
−0.998160 | + | 0.0606284i | \(0.980690\pi\) | |||||||
\(354\) | −5471.38 | + | 17913.8i | −0.821470 | + | 2.68957i | ||||
\(355\) | −1157.69 | + | 5626.49i | −0.173081 | + | 0.841192i | ||||
\(356\) | 25699.3 | 3.82601 | ||||||||
\(357\) | −7655.78 | + | 5311.24i | −1.13498 | + | 0.787397i | ||||
\(358\) | − | 15791.2i | − | 2.33126i | ||||||
\(359\) | − | 4210.90i | − | 0.619060i | −0.950890 | − | 0.309530i | \(-0.899828\pi\) | ||
0.950890 | − | 0.309530i | \(-0.100172\pi\) | |||||||
\(360\) | −10932.8 | − | 11162.3i | −1.60058 | − | 1.63417i | ||||
\(361\) | 5756.96 | 0.839329 | ||||||||
\(362\) | − | 14266.2i | − | 2.07131i | ||||||
\(363\) | 2643.41 | − | 8654.79i | 0.382213 | − | 1.25140i | ||||
\(364\) | 4356.51 | − | 5523.29i | 0.627316 | − | 0.795328i | ||||
\(365\) | 3949.27 | + | 812.590i | 0.566340 | + | 0.116528i | ||||
\(366\) | −10848.3 | − | 3313.37i | −1.54931 | − | 0.473203i | ||||
\(367\) | −12710.6 | −1.80787 | −0.903935 | − | 0.427670i | \(-0.859334\pi\) | ||||
−0.903935 | + | 0.427670i | \(0.859334\pi\) | |||||||
\(368\) | 13304.4 | 1.88462 | ||||||||
\(369\) | −819.195 | − | 551.894i | −0.115571 | − | 0.0778603i | ||||
\(370\) | 2077.29 | − | 10095.8i | 0.291873 | − | 1.41853i | ||||
\(371\) | 2198.59 | − | 2787.43i | 0.307668 | − | 0.390070i | ||||
\(372\) | −7250.99 | − | 2214.65i | −1.01061 | − | 0.308668i | ||||
\(373\) | − | 10529.6i | − | 1.46167i | −0.682555 | − | 0.730835i | \(-0.739131\pi\) | ||
0.682555 | − | 0.730835i | \(-0.260869\pi\) | |||||||
\(374\) | −27432.8 | −3.79283 | ||||||||
\(375\) | 5711.81 | − | 4484.37i | 0.786551 | − | 0.617525i | ||||
\(376\) | − | 13439.7i | − | 1.84335i | ||||||
\(377\) | 3285.39i | 0.448823i | ||||||||
\(378\) | −181.478 | − | 13279.8i | −0.0246938 | − | 1.80698i | ||||
\(379\) | −7340.38 | −0.994855 | −0.497428 | − | 0.867505i | \(-0.665722\pi\) | ||||
−0.497428 | + | 0.867505i | \(0.665722\pi\) | |||||||
\(380\) | −1355.85 | + | 6589.57i | −0.183036 | + | 0.889573i | ||||
\(381\) | 5912.19 | + | 1805.75i | 0.794988 | + | 0.242811i | ||||
\(382\) | 16297.2i | 2.18282i | ||||||||
\(383\) | 12222.6i | 1.63067i | 0.578991 | + | 0.815334i | \(0.303447\pi\) | ||||
−0.578991 | + | 0.815334i | \(0.696553\pi\) | |||||||
\(384\) | −2000.17 | + | 6548.76i | −0.265810 | + | 0.870287i | ||||
\(385\) | 7394.34 | + | 8778.40i | 0.978832 | + | 1.16205i | ||||
\(386\) | − | 9008.57i | − | 1.18789i | ||||||
\(387\) | 793.251 | − | 1177.45i | 0.104194 | − | 0.154659i | ||||
\(388\) | 19131.2 | 2.50319 | ||||||||
\(389\) | 1069.72i | 0.139426i | 0.997567 | + | 0.0697131i | \(0.0222084\pi\) | ||||
−0.997567 | + | 0.0697131i | \(0.977792\pi\) | |||||||
\(390\) | 2979.68 | − | 5462.65i | 0.386877 | − | 0.709261i | ||||
\(391\) | − | 10775.3i | − | 1.39369i | ||||||
\(392\) | 4135.58 | + | 17264.9i | 0.532853 | + | 2.22451i | ||||
\(393\) | 806.493 | − | 2640.54i | 0.103517 | − | 0.338925i | ||||
\(394\) | 5804.95 | 0.742257 | ||||||||
\(395\) | −941.603 | − | 193.742i | −0.119942 | − | 0.0246790i | ||||
\(396\) | 15157.5 | − | 22498.7i | 1.92346 | − | 2.85506i | ||||
\(397\) | −11929.8 | −1.50816 | −0.754082 | − | 0.656780i | \(-0.771918\pi\) | ||||
−0.754082 | + | 0.656780i | \(0.771918\pi\) | |||||||
\(398\) | − | 6136.40i | − | 0.772839i | ||||||
\(399\) | −2624.87 | + | 1821.01i | −0.329342 | + | 0.228483i | ||||
\(400\) | 13729.8 | + | 5899.77i | 1.71622 | + | 0.737471i | ||||
\(401\) | 5198.65i | 0.647402i | 0.946159 | + | 0.323701i | \(0.104927\pi\) | ||||
−0.946159 | + | 0.323701i | \(0.895073\pi\) | |||||||
\(402\) | −7784.02 | − | 2377.45i | −0.965750 | − | 0.294967i | ||||
\(403\) | − | 1686.80i | − | 0.208499i | ||||||
\(404\) | −13426.9 | −1.65350 | ||||||||
\(405\) | −1476.46 | − | 8015.62i | −0.181150 | − | 0.983456i | ||||
\(406\) | −11653.1 | − | 9191.44i | −1.42447 | − | 1.12355i | ||||
\(407\) | 9997.79 | 1.21762 | ||||||||
\(408\) | −24904.7 | − | 7606.59i | −3.02198 | − | 0.922996i | ||||
\(409\) | − | 16413.0i | − | 1.98428i | −0.125136 | − | 0.992140i | \(-0.539937\pi\) | ||
0.125136 | − | 0.992140i | \(-0.460063\pi\) | |||||||
\(410\) | 2047.75 | + | 421.339i | 0.246661 | + | 0.0507523i | ||||
\(411\) | −1926.61 | + | 6307.92i | −0.231223 | + | 0.757048i | ||||
\(412\) | −16958.6 | −2.02789 | ||||||||
\(413\) | 8088.72 | − | 10255.1i | 0.963729 | − | 1.22184i | ||||
\(414\) | 12737.6 | + | 8581.33i | 1.51212 | + | 1.01872i | ||||
\(415\) | 1998.38 | − | 9712.30i | 0.236377 | − | 1.14881i | ||||
\(416\) | 4127.97 | 0.486515 | ||||||||
\(417\) | 7784.92 | + | 2377.73i | 0.914219 | + | 0.279228i | ||||
\(418\) | −9405.64 | −1.10059 | ||||||||
\(419\) | 8997.49 | 1.04906 | 0.524530 | − | 0.851392i | \(-0.324241\pi\) | ||||
0.524530 | + | 0.851392i | \(0.324241\pi\) | |||||||
\(420\) | 7659.22 | + | 17935.6i | 0.889837 | + | 2.08373i | ||||
\(421\) | 2279.63 | 0.263901 | 0.131950 | − | 0.991256i | \(-0.457876\pi\) | ||||
0.131950 | + | 0.991256i | \(0.457876\pi\) | |||||||
\(422\) | 4271.11 | 0.492688 | ||||||||
\(423\) | 3917.18 | − | 5814.41i | 0.450260 | − | 0.668336i | ||||
\(424\) | 9921.64 | 1.13641 | ||||||||
\(425\) | 4778.25 | − | 11119.8i | 0.545363 | − | 1.26915i | ||||
\(426\) | −13050.9 | − | 3986.10i | −1.48431 | − | 0.453350i | ||||
\(427\) | 6210.29 | + | 4898.38i | 0.703834 | + | 0.555150i | ||||
\(428\) | −14405.8 | −1.62694 | ||||||||
\(429\) | 5772.35 | + | 1763.04i | 0.649631 | + | 0.198416i | ||||
\(430\) | −605.601 | + | 2943.28i | −0.0679178 | + | 0.330087i | ||||
\(431\) | − | 14695.9i | − | 1.64240i | −0.570638 | − | 0.821202i | \(-0.693304\pi\) | ||
0.570638 | − | 0.821202i | \(-0.306696\pi\) | |||||||
\(432\) | 13025.8 | − | 10566.0i | 1.45070 | − | 1.17675i | ||||
\(433\) | 3577.42 | 0.397043 | 0.198522 | − | 0.980097i | \(-0.436386\pi\) | ||||
0.198522 | + | 0.980097i | \(0.436386\pi\) | |||||||
\(434\) | 5982.98 | + | 4719.09i | 0.661734 | + | 0.521944i | ||||
\(435\) | −7996.11 | − | 4361.59i | −0.881342 | − | 0.480741i | ||||
\(436\) | −3663.93 | −0.402455 | ||||||||
\(437\) | − | 3694.43i | − | 0.404413i | ||||||
\(438\) | −2797.87 | + | 9160.48i | −0.305222 | + | 0.999326i | ||||
\(439\) | − | 7413.92i | − | 0.806030i | −0.915193 | − | 0.403015i | \(-0.867962\pi\) | ||
0.915193 | − | 0.403015i | \(-0.132038\pi\) | |||||||
\(440\) | −6464.60 | + | 31418.6i | −0.700427 | + | 3.40414i | ||||
\(441\) | −3242.91 | + | 8674.66i | −0.350168 | + | 0.936687i | ||||
\(442\) | − | 10370.7i | − | 1.11602i | ||||||
\(443\) | 5151.58 | 0.552503 | 0.276252 | − | 0.961085i | \(-0.410908\pi\) | ||||
0.276252 | + | 0.961085i | \(0.410908\pi\) | |||||||
\(444\) | 16247.1 | + | 4962.30i | 1.73660 | + | 0.530406i | ||||
\(445\) | −15526.2 | − | 3194.63i | −1.65396 | − | 0.340314i | ||||
\(446\) | 13976.5 | 1.48387 | ||||||||
\(447\) | 5529.04 | + | 1688.72i | 0.585043 | + | 0.178689i | ||||
\(448\) | −579.276 | + | 734.421i | −0.0610897 | + | 0.0774511i | ||||
\(449\) | 5031.60i | 0.528855i | 0.964406 | + | 0.264427i | \(0.0851830\pi\) | ||||
−0.964406 | + | 0.264427i | \(0.914817\pi\) | |||||||
\(450\) | 9339.45 | + | 14504.1i | 0.978369 | + | 1.51940i | ||||
\(451\) | 2027.86i | 0.211726i | ||||||||
\(452\) | −26424.9 | −2.74982 | ||||||||
\(453\) | −1900.55 | + | 6222.57i | −0.197120 | + | 0.645391i | ||||
\(454\) | 11285.7i | 1.16666i | ||||||||
\(455\) | −3318.57 | + | 2795.35i | −0.341928 | + | 0.288017i | ||||
\(456\) | −8538.84 | − | 2608.00i | −0.876903 | − | 0.267830i | ||||
\(457\) | − | 1781.33i | − | 0.182335i | −0.995836 | − | 0.0911673i | \(-0.970940\pi\) | ||
0.995836 | − | 0.0911673i | \(-0.0290598\pi\) | |||||||
\(458\) | 8796.44i | 0.897447i | ||||||||
\(459\) | −8557.45 | − | 10549.6i | −0.870213 | − | 1.07280i | ||||
\(460\) | −22090.5 | − | 4545.28i | −2.23908 | − | 0.460706i | ||||
\(461\) | −17966.1 | −1.81511 | −0.907556 | − | 0.419931i | \(-0.862054\pi\) | ||||
−0.907556 | + | 0.419931i | \(0.862054\pi\) | |||||||
\(462\) | −22402.5 | + | 15541.9i | −2.25597 | + | 1.56509i | ||||
\(463\) | 7730.37i | 0.775941i | 0.921672 | + | 0.387971i | \(0.126824\pi\) | ||||
−0.921672 | + | 0.387971i | \(0.873176\pi\) | |||||||
\(464\) | − | 18743.4i | − | 1.87530i | ||||||
\(465\) | 4105.38 | + | 2239.34i | 0.409425 | + | 0.223326i | ||||
\(466\) | −14902.6 | −1.48144 | ||||||||
\(467\) | 7613.81i | 0.754443i | 0.926123 | + | 0.377222i | \(0.123121\pi\) | ||||
−0.926123 | + | 0.377222i | \(0.876879\pi\) | |||||||
\(468\) | 8505.39 | + | 5730.10i | 0.840089 | + | 0.565970i | ||||
\(469\) | 4456.10 | + | 3514.76i | 0.438728 | + | 0.346048i | ||||
\(470\) | −2990.54 | + | 14534.3i | −0.293497 | + | 1.42642i | ||||
\(471\) | −343.979 | + | 1126.22i | −0.0336512 | + | 0.110177i | ||||
\(472\) | 36502.3 | 3.55965 | ||||||||
\(473\) | −2914.70 | −0.283336 | ||||||||
\(474\) | 667.081 | − | 2184.09i | 0.0646414 | − | 0.211642i | ||||
\(475\) | 1638.27 | − | 3812.54i | 0.158251 | − | 0.368277i | ||||
\(476\) | 25520.7 | + | 20129.5i | 2.45744 | + | 1.93831i | ||||
\(477\) | 4292.39 | + | 2891.79i | 0.412023 | + | 0.277581i | ||||
\(478\) | 33720.9i | 3.22669i | ||||||||
\(479\) | −1660.45 | −0.158388 | −0.0791939 | − | 0.996859i | \(-0.525235\pi\) | ||||
−0.0791939 | + | 0.996859i | \(0.525235\pi\) | |||||||
\(480\) | −5480.16 | + | 10046.8i | −0.521112 | + | 0.955356i | ||||
\(481\) | 3779.55i | 0.358280i | ||||||||
\(482\) | − | 28073.1i | − | 2.65289i | ||||||
\(483\) | −6104.68 | − | 8799.46i | −0.575098 | − | 0.828963i | ||||
\(484\) | −31568.1 | −2.96470 | ||||||||
\(485\) | −11558.1 | − | 2378.16i | −1.08212 | − | 0.222653i | ||||
\(486\) | 19285.8 | − | 1714.21i | 1.80005 | − | 0.159997i | ||||
\(487\) | 1783.16i | 0.165920i | 0.996553 | + | 0.0829599i | \(0.0264373\pi\) | ||||
−0.996553 | + | 0.0829599i | \(0.973563\pi\) | |||||||
\(488\) | 22105.1i | 2.05051i | ||||||||
\(489\) | 9163.28 | + | 2798.72i | 0.847398 | + | 0.258819i | ||||
\(490\) | −630.705 | − | 19591.3i | −0.0581477 | − | 1.80621i | ||||
\(491\) | 4975.18i | 0.457284i | 0.973511 | + | 0.228642i | \(0.0734286\pi\) | ||||
−0.973511 | + | 0.228642i | \(0.926571\pi\) | |||||||
\(492\) | −1006.51 | + | 3295.41i | −0.0922295 | + | 0.301968i | ||||
\(493\) | −15180.4 | −1.38679 | ||||||||
\(494\) | − | 3555.69i | − | 0.323842i | ||||||
\(495\) | −11954.1 | + | 11708.4i | −1.08545 | + | 1.06314i | ||||
\(496\) | 9623.28i | 0.871166i | ||||||||
\(497\) | 7471.21 | + | 5892.93i | 0.674305 | + | 0.531859i | ||||
\(498\) | 22528.1 | + | 6880.70i | 2.02712 | + | 0.619140i | ||||
\(499\) | −7878.69 | −0.706811 | −0.353406 | − | 0.935470i | \(-0.614976\pi\) | ||||
−0.353406 | + | 0.935470i | \(0.614976\pi\) | |||||||
\(500\) | −20781.2 | − | 14486.5i | −1.85873 | − | 1.29571i | ||||
\(501\) | 10658.0 | + | 3255.26i | 0.950431 | + | 0.290288i | ||||
\(502\) | 19691.6 | 1.75076 | ||||||||
\(503\) | − | 3798.11i | − | 0.336678i | −0.985729 | − | 0.168339i | \(-0.946160\pi\) | ||
0.985729 | − | 0.168339i | \(-0.0538404\pi\) | |||||||
\(504\) | −24647.4 | + | 7897.80i | −2.17834 | + | 0.698008i | ||||
\(505\) | 8111.86 | + | 1669.07i | 0.714798 | + | 0.147075i | ||||
\(506\) | − | 31531.0i | − | 2.77020i | ||||||
\(507\) | 2668.18 | − | 8735.88i | 0.233724 | − | 0.765234i | ||||
\(508\) | − | 21564.5i | − | 1.88341i | ||||||
\(509\) | 12066.4 | 1.05075 | 0.525377 | − | 0.850870i | \(-0.323924\pi\) | ||||
0.525377 | + | 0.850870i | \(0.323924\pi\) | |||||||
\(510\) | 25240.5 | + | 13767.8i | 2.19151 | + | 1.19539i | ||||
\(511\) | 4136.28 | − | 5244.08i | 0.358079 | − | 0.453982i | ||||
\(512\) | 25951.6 | 2.24006 | ||||||||
\(513\) | −2934.01 | − | 3617.05i | −0.252514 | − | 0.311300i | ||||
\(514\) | − | 2275.28i | − | 0.195249i | ||||||
\(515\) | 10245.5 | + | 2108.09i | 0.876644 | + | 0.180376i | ||||
\(516\) | −4736.57 | − | 1446.68i | −0.404101 | − | 0.123424i | ||||
\(517\) | −14393.2 | −1.22439 | ||||||||
\(518\) | −13405.9 | − | 10573.9i | −1.13711 | − | 0.896894i | ||||
\(519\) | 17207.8 | + | 5255.75i | 1.45538 | + | 0.444512i | ||||
\(520\) | −11877.4 | − | 2443.87i | −1.00165 | − | 0.206098i | ||||
\(521\) | −671.033 | −0.0564270 | −0.0282135 | − | 0.999602i | \(-0.508982\pi\) | ||||
−0.0282135 | + | 0.999602i | \(0.508982\pi\) | |||||||
\(522\) | 12089.5 | − | 17944.8i | 1.01368 | − | 1.50464i | ||||
\(523\) | 8833.34 | 0.738538 | 0.369269 | − | 0.929323i | \(-0.379608\pi\) | ||||
0.369269 | + | 0.929323i | \(0.379608\pi\) | |||||||
\(524\) | −9631.28 | −0.802947 | ||||||||
\(525\) | −2397.77 | − | 11787.9i | −0.199328 | − | 0.979933i | ||||
\(526\) | 28312.6 | 2.34694 | ||||||||
\(527\) | 7793.94 | 0.644230 | ||||||||
\(528\) | −32931.7 | − | 10058.2i | −2.71433 | − | 0.829032i | ||||
\(529\) | 218.010 | 0.0179181 | ||||||||
\(530\) | −10729.7 | − | 2207.72i | −0.879376 | − | 0.180938i | ||||
\(531\) | 15791.9 | + | 10639.1i | 1.29061 | + | 0.869484i | ||||
\(532\) | 8750.04 | + | 6901.61i | 0.713087 | + | 0.562449i | ||||
\(533\) | −766.609 | −0.0622993 | ||||||||
\(534\) | 10999.6 | − | 36013.7i | 0.891382 | − | 2.91847i | ||||
\(535\) | 8703.27 | + | 1790.76i | 0.703318 | + | 0.144713i | ||||
\(536\) | 15861.2i | 1.27817i | ||||||||
\(537\) | −15352.9 | − | 4689.22i | −1.23376 | − | 0.376824i | ||||
\(538\) | −34871.1 | −2.79443 | ||||||||
\(539\) | 18489.7 | − | 4428.97i | 1.47757 | − | 0.353932i | ||||
\(540\) | −25237.6 | + | 13093.6i | −2.01121 | + | 1.04344i | ||||
\(541\) | −16688.3 | −1.32623 | −0.663113 | − | 0.748519i | \(-0.730765\pi\) | ||||
−0.663113 | + | 0.748519i | \(0.730765\pi\) | |||||||
\(542\) | 18230.8i | 1.44480i | ||||||||
\(543\) | −13870.3 | − | 4236.37i | −1.09619 | − | 0.334807i | ||||
\(544\) | 19073.5i | 1.50325i | ||||||||
\(545\) | 2213.56 | + | 455.456i | 0.173979 | + | 0.0357974i | ||||
\(546\) | −5875.43 | − | 8469.02i | −0.460522 | − | 0.663810i | ||||
\(547\) | 19572.5i | 1.52991i | 0.644086 | + | 0.764953i | \(0.277238\pi\) | ||||
−0.644086 | + | 0.764953i | \(0.722762\pi\) | |||||||
\(548\) | 23008.0 | 1.79352 | ||||||||
\(549\) | −6442.82 | + | 9563.30i | −0.500862 | + | 0.743446i | ||||
\(550\) | 13982.2 | − | 32539.0i | 1.08401 | − | 2.52267i | ||||
\(551\) | −5204.75 | −0.402413 | ||||||||
\(552\) | 8742.92 | − | 28625.2i | 0.674136 | − | 2.20719i | ||||
\(553\) | −986.192 | + | 1250.32i | −0.0758357 | + | 0.0961464i | ||||
\(554\) | 23278.1i | 1.78518i | ||||||||
\(555\) | −9198.80 | − | 5017.61i | −0.703544 | − | 0.383758i | ||||
\(556\) | − | 28395.3i | − | 2.16588i | ||||||
\(557\) | −23150.1 | −1.76104 | −0.880521 | − | 0.474008i | \(-0.842807\pi\) | ||||
−0.880521 | + | 0.474008i | \(0.842807\pi\) | |||||||
\(558\) | −6207.00 | + | 9213.27i | −0.470902 | + | 0.698976i | ||||
\(559\) | − | 1101.87i | − | 0.0833704i | ||||||
\(560\) | 18932.7 | − | 15947.6i | 1.42866 | − | 1.20341i | ||||
\(561\) | −8146.22 | + | 26671.5i | −0.613073 | + | 2.00726i | ||||
\(562\) | 25222.7i | 1.89316i | ||||||||
\(563\) | 5111.84i | 0.382661i | 0.981526 | + | 0.191331i | \(0.0612803\pi\) | ||||
−0.981526 | + | 0.191331i | \(0.938720\pi\) | |||||||
\(564\) | −23389.8 | − | 7143.91i | −1.74626 | − | 0.533356i | ||||
\(565\) | 15964.6 | + | 3284.82i | 1.18873 | + | 0.244590i | ||||
\(566\) | −2334.49 | −0.173367 | ||||||||
\(567\) | −12965.1 | − | 3767.00i | −0.960288 | − | 0.279011i | ||||
\(568\) | 26593.2i | 1.96448i | ||||||||
\(569\) | 1896.42i | 0.139723i | 0.997557 | + | 0.0698613i | \(0.0222557\pi\) | ||||
−0.997557 | + | 0.0698613i | \(0.977744\pi\) | |||||||
\(570\) | 8653.97 | + | 4720.43i | 0.635921 | + | 0.346872i | ||||
\(571\) | −17070.6 | −1.25111 | −0.625554 | − | 0.780181i | \(-0.715127\pi\) | ||||
−0.625554 | + | 0.780181i | \(0.715127\pi\) | |||||||
\(572\) | − | 21054.5i | − | 1.53904i | ||||||
\(573\) | 15844.9 | + | 4839.47i | 1.15520 | + | 0.352831i | ||||
\(574\) | 2144.72 | − | 2719.13i | 0.155956 | − | 0.197725i | ||||
\(575\) | 12781.0 | + | 5492.06i | 0.926962 | + | 0.398321i | ||||
\(576\) | −1130.94 | − | 761.919i | −0.0818101 | − | 0.0551157i | ||||
\(577\) | −4537.92 | −0.327411 | −0.163705 | − | 0.986509i | \(-0.552345\pi\) | ||||
−0.163705 | + | 0.986509i | \(0.552345\pi\) | |||||||
\(578\) | 22806.1 | 1.64119 | ||||||||
\(579\) | −8758.56 | − | 2675.11i | −0.628658 | − | 0.192010i | ||||
\(580\) | −6403.44 | + | 31121.4i | −0.458428 | + | 2.22801i | ||||
\(581\) | −12896.6 | − | 10172.2i | −0.920897 | − | 0.726359i | ||||
\(582\) | 8188.35 | − | 26809.5i | 0.583193 | − | 1.90943i | ||||
\(583\) | − | 10625.5i | − | 0.754826i | ||||||
\(584\) | 18665.9 | 1.32261 | ||||||||
\(585\) | −4426.23 | − | 4519.13i | −0.312824 | − | 0.319389i | ||||
\(586\) | 10745.6i | 0.757503i | ||||||||
\(587\) | 15763.7i | 1.10841i | 0.832380 | + | 0.554205i | \(0.186978\pi\) | ||||
−0.832380 | + | 0.554205i | \(0.813022\pi\) | |||||||
\(588\) | 32245.2 | + | 1979.82i | 2.26152 | + | 0.138854i | ||||
\(589\) | 2672.23 | 0.186940 | ||||||||
\(590\) | −39475.2 | − | 8122.31i | −2.75452 | − | 0.566763i | ||||
\(591\) | 1723.79 | − | 5643.85i | 0.119978 | − | 0.392821i | ||||
\(592\) | − | 21562.6i | − | 1.49699i | ||||||
\(593\) | − | 2405.31i | − | 0.166567i | −0.996526 | − | 0.0832834i | \(-0.973459\pi\) | ||
0.996526 | − | 0.0832834i | \(-0.0265407\pi\) | |||||||
\(594\) | −25041.0 | − | 30870.6i | −1.72971 | − | 2.13238i | ||||
\(595\) | −12916.1 | − | 15333.7i | −0.889928 | − | 1.05650i | ||||
\(596\) | − | 20167.0i | − | 1.38603i | ||||||
\(597\) | −5966.10 | − | 1822.21i | −0.409006 | − | 0.124922i | ||||
\(598\) | 11919.9 | 0.815120 | ||||||||
\(599\) | 8892.20i | 0.606553i | 0.952903 | + | 0.303277i | \(0.0980806\pi\) | ||||
−0.952903 | + | 0.303277i | \(0.901919\pi\) | |||||||
\(600\) | 21716.1 | − | 25663.3i | 1.47759 | − | 1.74617i | ||||
\(601\) | 2916.97i | 0.197980i | 0.995088 | + | 0.0989898i | \(0.0315611\pi\) | ||||
−0.995088 | + | 0.0989898i | \(0.968439\pi\) | |||||||
\(602\) | 3908.27 | + | 3082.66i | 0.264600 | + | 0.208704i | ||||
\(603\) | −4622.95 | + | 6862.00i | −0.312207 | + | 0.463420i | ||||
\(604\) | 22696.6 | 1.52900 | ||||||||
\(605\) | 19071.8 | + | 3924.17i | 1.28162 | + | 0.263703i | ||||
\(606\) | −5746.86 | + | 18815.8i | −0.385232 | + | 1.26129i | ||||
\(607\) | 12105.3 | 0.809458 | 0.404729 | − | 0.914437i | \(-0.367366\pi\) | ||||
0.404729 | + | 0.914437i | \(0.367366\pi\) | |||||||
\(608\) | 6539.55i | 0.436207i | ||||||||
\(609\) | −12396.8 | + | 8600.33i | −0.824864 | + | 0.572254i | ||||
\(610\) | 4918.72 | − | 23905.5i | 0.326481 | − | 1.58673i | ||||
\(611\) | − | 5441.17i | − | 0.360272i | ||||||
\(612\) | −26476.3 | + | 39299.7i | −1.74876 | + | 2.59574i | ||||
\(613\) | 11262.7i | 0.742083i | 0.928616 | + | 0.371041i | \(0.120999\pi\) | ||||
−0.928616 | + | 0.371041i | \(0.879001\pi\) | |||||||
\(614\) | 14213.1 | 0.934194 | ||||||||
\(615\) | 1017.73 | − | 1865.80i | 0.0667296 | − | 0.122335i | ||||
\(616\) | 41719.6 | + | 32906.4i | 2.72878 | + | 2.15233i | ||||
\(617\) | −5183.80 | −0.338236 | −0.169118 | − | 0.985596i | \(-0.554092\pi\) | ||||
−0.169118 | + | 0.985596i | \(0.554092\pi\) | |||||||
\(618\) | −7258.46 | + | 23764.9i | −0.472456 | + | 1.54687i | ||||
\(619\) | 26124.4i | 1.69633i | 0.529734 | + | 0.848164i | \(0.322292\pi\) | ||||
−0.529734 | + | 0.848164i | \(0.677708\pi\) | |||||||
\(620\) | 3287.67 | − | 15978.4i | 0.212961 | − | 1.03501i | ||||
\(621\) | 12125.6 | − | 9835.83i | 0.783550 | − | 0.635585i | ||||
\(622\) | −2251.88 | −0.145164 | ||||||||
\(623\) | −16261.4 | + | 20616.7i | −1.04575 | + | 1.32583i | ||||
\(624\) | 3802.41 | − | 12449.4i | 0.243939 | − | 0.798680i | ||||
\(625\) | 10754.2 | + | 11335.3i | 0.688266 | + | 0.725459i | ||||
\(626\) | −35773.9 | −2.28405 | ||||||||
\(627\) | −2793.02 | + | 9144.61i | −0.177899 | + | 0.582457i | ||||
\(628\) | 4107.86 | 0.261021 | ||||||||
\(629\) | −17463.6 | −1.10703 | ||||||||
\(630\) | 28412.2 | − | 3056.61i | 1.79678 | − | 0.193299i | ||||
\(631\) | −10304.6 | −0.650110 | −0.325055 | − | 0.945695i | \(-0.605383\pi\) | ||||
−0.325055 | + | 0.945695i | \(0.605383\pi\) | |||||||
\(632\) | −4450.42 | −0.280108 | ||||||||
\(633\) | 1268.31 | − | 4152.58i | 0.0796380 | − | 0.260743i | ||||
\(634\) | 51687.7 | 3.23782 | ||||||||
\(635\) | −2680.64 | + | 13028.2i | −0.167525 | + | 0.814186i | ||||
\(636\) | 5273.87 | − | 17267.2i | 0.328809 | − | 1.07655i | ||||
\(637\) | 1674.32 | + | 6989.82i | 0.104143 | + | 0.434767i | ||||
\(638\) | −44421.1 | −2.75650 | ||||||||
\(639\) | −7750.95 | + | 11505.0i | −0.479848 | + | 0.712255i | ||||
\(640\) | −14431.0 | − | 2969.27i | −0.891303 | − | 0.183392i | ||||
\(641\) | − | 23841.8i | − | 1.46910i | −0.678552 | − | 0.734552i | \(-0.737392\pi\) | ||
0.678552 | − | 0.734552i | \(-0.262608\pi\) | |||||||
\(642\) | −6165.85 | + | 20187.6i | −0.379045 | + | 1.24103i | ||||
\(643\) | −8773.65 | −0.538101 | −0.269050 | − | 0.963126i | \(-0.586710\pi\) | ||||
−0.269050 | + | 0.963126i | \(0.586710\pi\) | |||||||
\(644\) | −23136.6 | + | 29333.2i | −1.41570 | + | 1.79486i | ||||
\(645\) | 2681.76 | + | 1462.81i | 0.163712 | + | 0.0892991i | ||||
\(646\) | 16429.3 | 1.00062 | ||||||||
\(647\) | 8008.70i | 0.486638i | 0.969946 | + | 0.243319i | \(0.0782362\pi\) | ||||
−0.969946 | + | 0.243319i | \(0.921764\pi\) | |||||||
\(648\) | −14173.5 | − | 34969.0i | −0.859240 | − | 2.11993i | ||||
\(649\) | − | 39091.8i | − | 2.36439i | ||||||
\(650\) | 12301.0 | + | 5285.82i | 0.742285 | + | 0.318964i | ||||
\(651\) | 6364.78 | − | 4415.60i | 0.383188 | − | 0.265839i | ||||
\(652\) | − | 33422.8i | − | 2.00757i | ||||||
\(653\) | 4305.61 | 0.258027 | 0.129014 | − | 0.991643i | \(-0.458819\pi\) | ||||
0.129014 | + | 0.991643i | \(0.458819\pi\) | |||||||
\(654\) | −1568.20 | + | 5134.44i | −0.0937638 | + | 0.306992i | ||||
\(655\) | 5818.73 | + | 1197.25i | 0.347109 | + | 0.0714202i | ||||
\(656\) | 4373.56 | 0.260303 | ||||||||
\(657\) | 8075.43 | + | 5440.44i | 0.479532 | + | 0.323062i | ||||
\(658\) | 19299.6 | + | 15222.6i | 1.14343 | + | 0.901882i | ||||
\(659\) | 24759.2i | 1.46355i | 0.681545 | + | 0.731777i | \(0.261309\pi\) | ||||
−0.681545 | + | 0.731777i | \(0.738691\pi\) | |||||||
\(660\) | 51243.1 | + | 27951.3i | 3.02218 | + | 1.64849i | ||||
\(661\) | − | 10995.7i | − | 0.647022i | −0.946224 | − | 0.323511i | \(-0.895137\pi\) | ||
0.946224 | − | 0.323511i | \(-0.104863\pi\) | |||||||
\(662\) | −25714.7 | −1.50971 | ||||||||
\(663\) | −10082.9 | − | 3079.59i | −0.590627 | − | 0.180394i | ||||
\(664\) | − | 45904.5i | − | 2.68289i | ||||||
\(665\) | −4428.41 | − | 5257.31i | −0.258235 | − | 0.306571i | ||||
\(666\) | 13907.8 | − | 20643.9i | 0.809186 | − | 1.20110i | ||||
\(667\) | − | 17448.1i | − | 1.01288i | ||||||
\(668\) | − | 38874.9i | − | 2.25167i | ||||||
\(669\) | 4150.35 | − | 13588.6i | 0.239853 | − | 0.785302i | ||||
\(670\) | 3529.35 | − | 17153.0i | 0.203509 | − | 0.989071i | ||||
\(671\) | 23673.3 | 1.36199 | ||||||||
\(672\) | 10806.0 | + | 15576.0i | 0.620311 | + | 0.894135i | ||||
\(673\) | − | 18477.5i | − | 1.05833i | −0.848520 | − | 0.529163i | \(-0.822506\pi\) | ||
0.848520 | − | 0.529163i | \(-0.177494\pi\) | |||||||
\(674\) | 16517.0i | 0.943936i | ||||||||
\(675\) | 16874.9 | − | 4773.25i | 0.962246 | − | 0.272181i | ||||
\(676\) | −31863.9 | −1.81292 | ||||||||
\(677\) | − | 6639.83i | − | 0.376942i | −0.982079 | − | 0.188471i | \(-0.939647\pi\) | ||
0.982079 | − | 0.188471i | \(-0.0603531\pi\) | |||||||
\(678\) | −11310.1 | + | 37030.4i | −0.640653 | + | 2.09756i | ||||
\(679\) | −12105.4 | + | 15347.6i | −0.684187 | + | 0.867430i | ||||
\(680\) | 11292.0 | − | 54880.4i | 0.636809 | − | 3.09495i | ||||
\(681\) | 10972.4 | + | 3351.29i | 0.617423 | + | 0.188578i | ||||
\(682\) | 22806.8 | 1.28052 | ||||||||
\(683\) | 6422.87 | 0.359830 | 0.179915 | − | 0.983682i | \(-0.442418\pi\) | ||||
0.179915 | + | 0.983682i | \(0.442418\pi\) | |||||||
\(684\) | −9077.67 | + | 13474.3i | −0.507446 | + | 0.753220i | ||||
\(685\) | −13900.2 | − | 2860.07i | −0.775330 | − | 0.159530i | ||||
\(686\) | −29476.8 | − | 13616.4i | −1.64057 | − | 0.757840i | ||||
\(687\) | 8552.32 | + | 2612.11i | 0.474951 | + | 0.145063i | ||||
\(688\) | 6286.23i | 0.348343i | ||||||||
\(689\) | 4016.85 | 0.222104 | ||||||||
\(690\) | −15824.5 | + | 29011.1i | −0.873086 | + | 1.60063i | ||||
\(691\) | 33292.1i | 1.83284i | 0.400221 | + | 0.916419i | \(0.368933\pi\) | ||||
−0.400221 | + | 0.916419i | \(0.631067\pi\) | |||||||
\(692\) | − | 62765.1i | − | 3.44793i | ||||||
\(693\) | 8458.09 | + | 26396.0i | 0.463631 | + | 1.44690i | ||||
\(694\) | −41833.0 | −2.28812 | ||||||||
\(695\) | −3529.76 | + | 17155.0i | −0.192650 | + | 0.936296i | ||||
\(696\) | −40327.4 | − | 12317.1i | −2.19627 | − | 0.670803i | ||||
\(697\) | − | 3542.17i | − | 0.192495i | ||||||
\(698\) | − | 57321.6i | − | 3.10839i | ||||||
\(699\) | −4425.35 | + | 14489.0i | −0.239460 | + | 0.784014i | ||||
\(700\) | −36883.9 | + | 20011.2i | −1.99154 | + | 1.08050i | ||||
\(701\) | 21719.6i | 1.17024i | 0.810946 | + | 0.585121i | \(0.198953\pi\) | ||||
−0.810946 | + | 0.585121i | \(0.801047\pi\) | |||||||
\(702\) | 11670.3 | − | 9466.47i | 0.627444 | − | 0.508958i | ||||
\(703\) | −5987.59 | −0.321232 | ||||||||
\(704\) | 2799.57i | 0.149876i | ||||||||
\(705\) | 13242.9 | + | 7223.53i | 0.707457 | + | 0.385892i | ||||
\(706\) | − | 4110.61i | − | 0.219129i | ||||||
\(707\) | 8495.99 | − | 10771.4i | 0.451944 | − | 0.572987i | ||||
\(708\) | 19402.8 | − | 63526.8i | 1.02995 | − | 3.37215i | ||||
\(709\) | 9450.02 | 0.500568 | 0.250284 | − | 0.968172i | \(-0.419476\pi\) | ||||
0.250284 | + | 0.968172i | \(0.419476\pi\) | |||||||
\(710\) | 5917.40 | − | 28759.1i | 0.312783 | − | 1.52016i | ||||
\(711\) | −1925.38 | − | 1297.13i | −0.101558 | − | 0.0684196i | ||||
\(712\) | −73383.6 | −3.86259 | ||||||||
\(713\) | 8958.26i | 0.470532i | ||||||||
\(714\) | 39131.6 | − | 27147.8i | 2.05107 | − | 1.42294i | ||||
\(715\) | −2617.24 | + | 12720.1i | −0.136894 | + | 0.665319i | ||||
\(716\) | 55999.4i | 2.92290i | ||||||||
\(717\) | 32785.0 | + | 10013.5i | 1.70764 | + | 0.521562i | ||||
\(718\) | 21523.5i | 1.11873i | ||||||||
\(719\) | −29056.2 | −1.50711 | −0.753555 | − | 0.657385i | \(-0.771662\pi\) | ||||
−0.753555 | + | 0.657385i | \(0.771662\pi\) | |||||||
\(720\) | 25251.9 | + | 25781.9i | 1.30706 | + | 1.33449i | ||||
\(721\) | 10730.7 | − | 13604.6i | 0.554274 | − | 0.702723i | ||||
\(722\) | −29426.0 | −1.51679 | ||||||||
\(723\) | −27294.0 | − | 8336.34i | −1.40398 | − | 0.428813i | ||||
\(724\) | 50591.4i | 2.59698i | ||||||||
\(725\) | 7737.27 | − | 18005.9i | 0.396352 | − | 0.922378i | ||||
\(726\) | −13511.5 | + | 44237.9i | −0.690714 | + | 2.26146i | ||||
\(727\) | −3457.74 | −0.176397 | −0.0881983 | − | 0.996103i | \(-0.528111\pi\) | ||||
−0.0881983 | + | 0.996103i | \(0.528111\pi\) | |||||||
\(728\) | −12439.9 | + | 15771.6i | −0.633314 | + | 0.802932i | ||||
\(729\) | 4060.32 | − | 19259.7i | 0.206286 | − | 0.978492i | ||||
\(730\) | −20186.2 | − | 4153.45i | −1.02346 | − | 0.210584i | ||||
\(731\) | 5091.25 | 0.257601 | ||||||||
\(732\) | 38470.7 | + | 11750.0i | 1.94251 | + | 0.593296i | ||||
\(733\) | 22212.1 | 1.11927 | 0.559634 | − | 0.828740i | \(-0.310942\pi\) | ||||
0.559634 | + | 0.828740i | \(0.310942\pi\) | |||||||
\(734\) | 64968.7 | 3.26708 | ||||||||
\(735\) | −19234.8 | − | 5204.45i | −0.965289 | − | 0.261182i | ||||
\(736\) | −21922.9 | −1.09794 | ||||||||
\(737\) | 16986.4 | 0.848986 | ||||||||
\(738\) | 4187.22 | + | 2820.94i | 0.208853 | + | 0.140705i | ||||
\(739\) | −35565.7 | −1.77037 | −0.885186 | − | 0.465237i | \(-0.845969\pi\) | ||||
−0.885186 | + | 0.465237i | \(0.845969\pi\) | |||||||
\(740\) | −7366.58 | + | 35802.3i | −0.365947 | + | 1.77854i | ||||
\(741\) | −3457.01 | − | 1055.87i | −0.171385 | − | 0.0523459i | ||||
\(742\) | −11237.8 | + | 14247.6i | −0.556001 | + | 0.704913i | ||||
\(743\) | 20992.4 | 1.03652 | 0.518262 | − | 0.855222i | \(-0.326579\pi\) | ||||
0.518262 | + | 0.855222i | \(0.326579\pi\) | |||||||
\(744\) | 20705.0 | + | 6323.88i | 1.02027 | + | 0.311619i | ||||
\(745\) | −2506.92 | + | 12183.9i | −0.123284 | + | 0.599172i | ||||
\(746\) | 53820.8i | 2.64145i | ||||||||
\(747\) | 13379.5 | − | 19859.6i | 0.655328 | − | 0.972725i | ||||
\(748\) | 97283.6 | 4.75540 | ||||||||
\(749\) | 9115.41 | − | 11556.8i | 0.444686 | − | 0.563785i | ||||
\(750\) | −29195.2 | + | 22921.3i | −1.42141 | + | 1.11596i | ||||
\(751\) | 5971.01 | 0.290127 | 0.145063 | − | 0.989422i | \(-0.453661\pi\) | ||||
0.145063 | + | 0.989422i | \(0.453661\pi\) | |||||||
\(752\) | 31042.3i | 1.50531i | ||||||||
\(753\) | 5847.46 | − | 19145.1i | 0.282992 | − | 0.926545i | ||||
\(754\) | − | 16792.9i | − | 0.811089i | ||||||
\(755\) | −13712.2 | − | 2821.38i | −0.660976 | − | 0.136001i | ||||
\(756\) | 643.567 | + | 47093.3i | 0.0309607 | + | 2.26556i | ||||
\(757\) | − | 23358.2i | − | 1.12149i | −0.827988 | − | 0.560745i | \(-0.810515\pi\) | ||
0.827988 | − | 0.560745i | \(-0.189485\pi\) | |||||||
\(758\) | 37519.5 | 1.79785 | ||||||||
\(759\) | −30655.9 | − | 9363.17i | −1.46606 | − | 0.447775i | ||||
\(760\) | 3871.59 | − | 18816.3i | 0.184786 | − | 0.898079i | ||||
\(761\) | 428.292 | 0.0204015 | 0.0102008 | − | 0.999948i | \(-0.496753\pi\) | ||||
0.0102008 | + | 0.999948i | \(0.496753\pi\) | |||||||
\(762\) | −30219.4 | − | 9229.85i | −1.43666 | − | 0.438796i | ||||
\(763\) | 2318.38 | − | 2939.30i | 0.110001 | − | 0.139463i | ||||
\(764\) | − | 57793.8i | − | 2.73679i | ||||||
\(765\) | 20880.9 | − | 20451.6i | 0.986863 | − | 0.966576i | ||||
\(766\) | − | 62474.4i | − | 2.94686i | ||||||
\(767\) | 14778.2 | 0.695711 | ||||||||
\(768\) | 10836.9 | − | 35481.1i | 0.509171 | − | 1.66708i | ||||
\(769\) | 16393.0i | 0.768720i | 0.923183 | + | 0.384360i | \(0.125578\pi\) | ||||
−0.923183 | + | 0.384360i | \(0.874422\pi\) | |||||||
\(770\) | −37795.3 | − | 44869.7i | −1.76889 | − | 2.09999i | ||||
\(771\) | −2212.13 | − | 675.647i | −0.103331 | − | 0.0315601i | ||||
\(772\) | 31946.6i | 1.48936i | ||||||||
\(773\) | − | 22894.4i | − | 1.06527i | −0.846344 | − | 0.532636i | \(-0.821201\pi\) | ||
0.846344 | − | 0.532636i | \(-0.178799\pi\) | |||||||
\(774\) | −4054.61 | + | 6018.39i | −0.188294 | + | 0.279492i | ||||
\(775\) | −3972.49 | + | 9244.66i | −0.184124 | + | 0.428488i | ||||
\(776\) | −54628.5 | −2.52713 | ||||||||
\(777\) | −14261.4 | + | 9893.90i | −0.658460 | + | 0.456810i | ||||
\(778\) | − | 5467.73i | − | 0.251963i | ||||||
\(779\) | − | 1214.47i | − | 0.0558573i | ||||||
\(780\) | −10566.7 | + | 19371.9i | −0.485061 | + | 0.889262i | ||||
\(781\) | 28479.8 | 1.30485 | ||||||||
\(782\) | 55076.7i | 2.51859i | ||||||||
\(783\) | −13856.8 | − | 17082.7i | −0.632442 | − | 0.779675i | ||||
\(784\) | −9552.12 | − | 39877.4i | −0.435136 | − | 1.81657i | ||||
\(785\) | −2481.76 | − | 510.640i | −0.112838 | − | 0.0232172i | ||||
\(786\) | −4122.29 | + | 13496.8i | −0.187070 | + | 0.612486i | ||||
\(787\) | −37222.3 | −1.68594 | −0.842969 | − | 0.537963i | \(-0.819194\pi\) | ||||
−0.842969 | + | 0.537963i | \(0.819194\pi\) | |||||||
\(788\) | −20585.8 | −0.930632 | ||||||||
\(789\) | 8407.48 | − | 27526.9i | 0.379359 | − | 1.24206i | ||||
\(790\) | 4812.89 | + | 990.286i | 0.216753 | + | 0.0445985i | ||||
\(791\) | 16720.5 | − | 21198.7i | 0.751598 | − | 0.952896i | ||||
\(792\) | −43281.7 | + | 64244.5i | −1.94185 | + | 2.88236i | ||||
\(793\) | 8949.42i | 0.400761i | ||||||||
\(794\) | 60977.9 | 2.72547 | ||||||||
\(795\) | −5332.65 | + | 9776.35i | −0.237899 | + | 0.436140i | ||||
\(796\) | 21761.2i | 0.968976i | ||||||||
\(797\) | − | 10475.1i | − | 0.465554i | −0.972530 | − | 0.232777i | \(-0.925219\pi\) | ||
0.972530 | − | 0.232777i | \(-0.0747812\pi\) | |||||||
\(798\) | 13416.7 | − | 9307.90i | 0.595170 | − | 0.412902i | ||||
\(799\) | 25141.3 | 1.11318 | ||||||||
\(800\) | −22623.7 | − | 9721.57i | −0.999838 | − | 0.429637i | ||||
\(801\) | −31747.9 | − | 21388.6i | −1.40044 | − | 0.943483i | ||||
\(802\) | − | 26572.3i | − | 1.16995i | ||||||
\(803\) | − | 19990.2i | − | 0.878502i | ||||||
\(804\) | 27604.0 | + | 8431.04i | 1.21084 | + | 0.369825i | ||||
\(805\) | 17624.3 | − | 14845.6i | 0.771647 | − | 0.649984i | ||||
\(806\) | 8621.85i | 0.376789i | ||||||||
\(807\) | −10355.0 | + | 33903.4i | −0.451691 | + | 1.47888i | ||||
\(808\) | 38340.2 | 1.66931 | ||||||||
\(809\) | 8052.55i | 0.349954i | 0.984573 | + | 0.174977i | \(0.0559850\pi\) | ||||
−0.984573 | + | 0.174977i | \(0.944015\pi\) | |||||||
\(810\) | 7546.72 | + | 40970.9i | 0.327364 | + | 1.77725i | ||||
\(811\) | − | 11903.9i | − | 0.515416i | −0.966223 | − | 0.257708i | \(-0.917033\pi\) | ||
0.966223 | − | 0.257708i | \(-0.0829672\pi\) | |||||||
\(812\) | 41324.9 | + | 32595.1i | 1.78598 | + | 1.40870i | ||||
\(813\) | 17724.8 | + | 5413.66i | 0.764621 | + | 0.233537i | ||||
\(814\) | −51102.5 | −2.20042 | ||||||||
\(815\) | −4154.72 | + | 20192.4i | −0.178569 | + | 0.867862i | ||||
\(816\) | 57523.4 | + | 17569.2i | 2.46780 | + | 0.753734i | ||||
\(817\) | 1745.59 | 0.0747495 | ||||||||
\(818\) | 83893.0i | 3.58588i | ||||||||
\(819\) | −9978.70 | + | 3197.48i | −0.425744 | + | 0.136421i | ||||
\(820\) | −7261.81 | − | 1494.17i | −0.309260 | − | 0.0636325i | ||||
\(821\) | 16286.9i | 0.692346i | 0.938171 | + | 0.346173i | \(0.112519\pi\) | ||||
−0.938171 | + | 0.346173i | \(0.887481\pi\) | |||||||
\(822\) | 9847.65 | − | 32242.2i | 0.417855 | − | 1.36810i | ||||
\(823\) | − | 6282.68i | − | 0.266100i | −0.991109 | − | 0.133050i | \(-0.957523\pi\) | ||
0.991109 | − | 0.133050i | \(-0.0424771\pi\) | |||||||
\(824\) | 48424.8 | 2.04728 | ||||||||
\(825\) | −27483.9 | − | 23256.7i | −1.15984 | − | 0.981447i | ||||
\(826\) | −41344.5 | + | 52417.7i | −1.74160 | + | 2.20804i | ||||
\(827\) | −11366.9 | −0.477953 | −0.238977 | − | 0.971025i | \(-0.576812\pi\) | ||||
−0.238977 | + | 0.971025i | \(0.576812\pi\) | |||||||
\(828\) | −45170.5 | − | 30431.5i | −1.89587 | − | 1.27726i | ||||
\(829\) | − | 9728.24i | − | 0.407570i | −0.979016 | − | 0.203785i | \(-0.934676\pi\) | ||
0.979016 | − | 0.203785i | \(-0.0653244\pi\) | |||||||
\(830\) | −10214.5 | + | 49643.3i | −0.427167 | + | 2.07608i | ||||
\(831\) | 22632.1 | + | 6912.46i | 0.944762 | + | 0.288557i | ||||
\(832\) | −1058.35 | −0.0441004 | ||||||||
\(833\) | −32296.9 | + | 7736.30i | −1.34336 | + | 0.321785i | ||||
\(834\) | −39791.7 | − | 12153.5i | −1.65213 | − | 0.504605i | ||||
\(835\) | −4832.46 | + | 23486.2i | −0.200280 | + | 0.973383i | ||||
\(836\) | 33354.7 | 1.37990 | ||||||||
\(837\) | 7114.40 | + | 8770.64i | 0.293799 | + | 0.362195i | ||||
\(838\) | −45989.6 | −1.89580 | ||||||||
\(839\) | −12992.1 | −0.534610 | −0.267305 | − | 0.963612i | \(-0.586133\pi\) | ||||
−0.267305 | + | 0.963612i | \(0.586133\pi\) | |||||||
\(840\) | −21870.7 | − | 51214.5i | −0.898345 | − | 2.10365i | ||||
\(841\) | −192.087 | −0.00787596 | ||||||||
\(842\) | −11652.0 | −0.476907 | ||||||||
\(843\) | 24522.7 | + | 7489.91i | 1.00190 | + | 0.306010i | ||||
\(844\) | −15146.4 | −0.617726 | ||||||||
\(845\) | 19250.5 | + | 3960.93i | 0.783714 | + | 0.161255i | ||||
\(846\) | −20022.2 | + | 29719.7i | −0.813685 | + | 1.20778i | ||||
\(847\) | 19975.0 | − | 25324.8i | 0.810328 | − | 1.02736i | ||||
\(848\) | −22916.4 | −0.928011 | ||||||||
\(849\) | −693.230 | + | 2269.70i | −0.0280231 | + | 0.0917503i | ||||
\(850\) | −24423.5 | + | 56837.5i | −0.985550 | + | 2.29354i | ||||
\(851\) | − | 20072.5i | − | 0.808550i | ||||||
\(852\) | 46281.6 | + | 14135.7i | 1.86101 | + | 0.568404i | ||||
\(853\) | 10335.1 | 0.414849 | 0.207424 | − | 0.978251i | \(-0.433492\pi\) | ||||
0.207424 | + | 0.978251i | \(0.433492\pi\) | |||||||
\(854\) | −31743.2 | − | 25037.5i | −1.27193 | − | 1.00324i | ||||
\(855\) | 7159.23 | − | 7012.06i | 0.286363 | − | 0.280476i | ||||
\(856\) | 41135.4 | 1.64250 | ||||||||
\(857\) | − | 21299.4i | − | 0.848977i | −0.905433 | − | 0.424489i | \(-0.860454\pi\) | ||
0.905433 | − | 0.424489i | \(-0.139546\pi\) | |||||||
\(858\) | −29504.7 | − | 9011.55i | −1.17398 | − | 0.358566i | ||||
\(859\) | − | 12245.3i | − | 0.486386i | −0.969978 | − | 0.243193i | \(-0.921805\pi\) | ||
0.969978 | − | 0.243193i | \(-0.0781948\pi\) | |||||||
\(860\) | 2147.61 | − | 10437.6i | 0.0851545 | − | 0.413859i | ||||
\(861\) | −2006.79 | − | 2892.64i | −0.0794322 | − | 0.114496i | ||||
\(862\) | 75116.3i | 2.96806i | ||||||||
\(863\) | 24644.7 | 0.972092 | 0.486046 | − | 0.873933i | \(-0.338439\pi\) | ||||
0.486046 | + | 0.873933i | \(0.338439\pi\) | |||||||
\(864\) | −21463.7 | + | 17410.5i | −0.845151 | + | 0.685553i | ||||
\(865\) | −7802.21 | + | 37919.5i | −0.306685 | + | 1.49052i | ||||
\(866\) | −18285.5 | −0.717515 | ||||||||
\(867\) | 6772.31 | − | 22173.2i | 0.265282 | − | 0.868559i | ||||
\(868\) | −21217.1 | − | 16735.0i | −0.829673 | − | 0.654406i | ||||
\(869\) | 4766.15i | 0.186054i | ||||||||
\(870\) | 40871.1 | + | 22293.7i | 1.59271 | + | 0.868768i | ||||
\(871\) | 6421.52i | 0.249810i | ||||||||
\(872\) | 10462.2 | 0.406303 | ||||||||
\(873\) | −23633.9 | − | 15922.2i | −0.916250 | − | 0.617280i | ||||
\(874\) | 18883.6i | 0.730833i | ||||||||
\(875\) | 24771.0 | − | 7504.78i | 0.957041 | − | 0.289952i | ||||
\(876\) | 9921.91 | − | 32485.3i | 0.382683 | − | 1.25294i | ||||
\(877\) | − | 41124.6i | − | 1.58344i | −0.610883 | − | 0.791721i | \(-0.709185\pi\) | ||
0.610883 | − | 0.791721i | \(-0.290815\pi\) | |||||||
\(878\) | 37895.4i | 1.45661i | ||||||||
\(879\) | 10447.4 | + | 3190.92i | 0.400889 | + | 0.122443i | ||||
\(880\) | 14931.6 | − | 72568.8i | 0.571980 | − | 2.77988i | ||||
\(881\) | −40650.0 | −1.55452 | −0.777261 | − | 0.629179i | \(-0.783391\pi\) | ||||
−0.777261 | + | 0.629179i | \(0.783391\pi\) | |||||||
\(882\) | 16575.7 | − | 44339.5i | 0.632805 | − | 1.69273i | ||||
\(883\) | 31725.7i | 1.20912i | 0.796559 | + | 0.604561i | \(0.206651\pi\) | ||||
−0.796559 | + | 0.604561i | \(0.793349\pi\) | |||||||
\(884\) | 36776.9i | 1.39926i | ||||||||
\(885\) | −19619.1 | + | 35967.7i | −0.745186 | + | 1.36615i | ||||
\(886\) | −26331.7 | −0.998454 | ||||||||
\(887\) | − | 6747.77i | − | 0.255432i | −0.991811 | − | 0.127716i | \(-0.959235\pi\) | ||
0.991811 | − | 0.127716i | \(-0.0407646\pi\) | |||||||
\(888\) | −46393.0 | − | 14169.7i | −1.75321 | − | 0.535478i | ||||
\(889\) | 17299.7 | + | 13645.1i | 0.652657 | + | 0.514784i | ||||
\(890\) | 79360.3 | + | 16329.0i | 2.98895 | + | 0.614998i | ||||
\(891\) | −37449.8 | + | 15179.0i | −1.40810 | + | 0.570725i | ||||
\(892\) | −49564.2 | −1.86046 | ||||||||
\(893\) | 8619.95 | 0.323019 | ||||||||
\(894\) | −28261.0 | − | 8631.70i | −1.05726 | − | 0.322916i | ||||
\(895\) | 6961.18 | − | 33832.0i | 0.259985 | − | 1.26355i | ||||
\(896\) | −15114.3 | + | 19162.3i | −0.563543 | + | 0.714474i | ||||
\(897\) | 3539.64 | − | 11589.1i | 0.131756 | − | 0.431381i | ||||
\(898\) | − | 25718.4i | − | 0.955718i | ||||||
\(899\) | 12620.5 | 0.468205 | ||||||||
\(900\) | −33120.0 | − | 51435.0i | −1.22667 | − | 1.90500i | ||||
\(901\) | 18560.1i | 0.686268i | ||||||||
\(902\) | − | 10365.2i | − | 0.382619i | ||||||
\(903\) | 4157.67 | − | 2884.41i | 0.153221 | − | 0.106298i | ||||
\(904\) | 75455.4 | 2.77612 | ||||||||
\(905\) | 6288.92 | − | 30564.8i | 0.230996 | − | 1.12266i | ||||
\(906\) | 9714.41 | − | 31805.9i | 0.356225 | − | 1.16631i | ||||
\(907\) | − | 49852.4i | − | 1.82505i | −0.409020 | − | 0.912525i | \(-0.634129\pi\) | ||
0.409020 | − | 0.912525i | \(-0.365871\pi\) | |||||||
\(908\) | − | 40021.7i | − | 1.46274i | ||||||
\(909\) | 16587.1 | + | 11174.7i | 0.605234 | + | 0.407748i | ||||
\(910\) | 16962.5 | − | 14288.1i | 0.617913 | − | 0.520489i | ||||
\(911\) | − | 14687.9i | − | 0.534175i | −0.963672 | − | 0.267087i | \(-0.913939\pi\) | ||
0.963672 | − | 0.267087i | \(-0.0860612\pi\) | |||||||
\(912\) | 19722.5 | + | 6023.80i | 0.716093 | + | 0.218715i | ||||
\(913\) | −49161.1 | −1.78203 | ||||||||
\(914\) | 9105.03i | 0.329505i | ||||||||
\(915\) | −21781.4 | − | 11881.0i | −0.786963 | − | 0.429260i | ||||
\(916\) | − | 31194.3i | − | 1.12521i | ||||||
\(917\) | 6094.27 | − | 7726.47i | 0.219466 | − | 0.278245i | ||||
\(918\) | 43740.4 | + | 53923.2i | 1.57260 | + | 1.93870i | ||||
\(919\) | 48920.4 | 1.75597 | 0.877984 | − | 0.478689i | \(-0.158888\pi\) | ||||
0.877984 | + | 0.478689i | \(0.158888\pi\) | |||||||
\(920\) | 63078.9 | + | 12978.9i | 2.26049 | + | 0.465112i | ||||
\(921\) | 4220.61 | − | 13818.7i | 0.151003 | − | 0.494398i | ||||
\(922\) | 91831.7 | 3.28017 | ||||||||
\(923\) | 10766.5i | 0.383947i | ||||||||
\(924\) | 79444.8 | − | 55115.3i | 2.82851 | − | 1.96229i | ||||
\(925\) | 8901.03 | − | 20714.2i | 0.316394 | − | 0.736302i | ||||
\(926\) | − | 39512.8i | − | 1.40224i | ||||||
\(927\) | 20950.0 | + | 14114.0i | 0.742273 | + | 0.500071i | ||||
\(928\) | 30885.1i | 1.09252i | ||||||||
\(929\) | −34688.5 | −1.22507 | −0.612537 | − | 0.790442i | \(-0.709851\pi\) | ||||
−0.612537 | + | 0.790442i | \(0.709851\pi\) | |||||||
\(930\) | −20984.2 | − | 11446.1i | −0.739890 | − | 0.403583i | ||||
\(931\) | −11073.3 | + | 2652.47i | −0.389811 | + | 0.0933741i | ||||
\(932\) | 52848.3 | 1.85741 | ||||||||
\(933\) | −668.699 | + | 2189.39i | −0.0234643 | + | 0.0768245i | ||||
\(934\) | − | 38917.1i | − | 1.36339i | ||||||
\(935\) | −58773.8 | − | 12093.1i | −2.05573 | − | 0.422982i | ||||
\(936\) | −24286.9 | − | 16362.1i | −0.848122 | − | 0.571382i | ||||
\(937\) | 29779.4 | 1.03826 | 0.519130 | − | 0.854695i | \(-0.326256\pi\) | ||||
0.519130 | + | 0.854695i | \(0.326256\pi\) | |||||||
\(938\) | −22776.8 | − | 17965.3i | −0.792846 | − | 0.625359i | ||||
\(939\) | −10623.1 | + | 34781.1i | −0.369193 | + | 1.20877i | ||||
\(940\) | 10605.2 | − | 51542.3i | 0.367982 | − | 1.78843i | ||||
\(941\) | −18023.5 | −0.624389 | −0.312195 | − | 0.950018i | \(-0.601064\pi\) | ||||
−0.312195 | + | 0.950018i | \(0.601064\pi\) | |||||||
\(942\) | 1758.21 | − | 5756.54i | 0.0608127 | − | 0.199107i | ||||
\(943\) | 4071.32 | 0.140594 | ||||||||
\(944\) | −84310.8 | −2.90687 | ||||||||
\(945\) | 5465.26 | − | 28531.4i | 0.188132 | − | 0.982144i | ||||
\(946\) | 14898.1 | 0.512029 | ||||||||
\(947\) | −34592.1 | −1.18700 | −0.593501 | − | 0.804833i | \(-0.702255\pi\) | ||||
−0.593501 | + | 0.804833i | \(0.702255\pi\) | |||||||
\(948\) | −2365.63 | + | 7745.30i | −0.0810465 | + | 0.265354i | ||||
\(949\) | 7557.05 | 0.258495 | ||||||||
\(950\) | −8373.84 | + | 19487.3i | −0.285982 | + | 0.665529i | ||||
\(951\) | 15348.7 | − | 50253.2i | 0.523361 | − | 1.71354i | ||||
\(952\) | −72873.7 | − | 57479.2i | −2.48093 | − | 1.95684i | ||||
\(953\) | −41901.5 | −1.42426 | −0.712132 | − | 0.702046i | \(-0.752270\pi\) | ||||
−0.712132 | + | 0.702046i | \(0.752270\pi\) | |||||||
\(954\) | −21940.0 | − | 14781.1i | −0.744586 | − | 0.501629i | ||||
\(955\) | −7184.24 | + | 34916.1i | −0.243431 | + | 1.18310i | ||||
\(956\) | − | 119582.i | − | 4.04558i | ||||||
\(957\) | −13190.9 | + | 43188.3i | −0.445561 | + | 1.45881i | ||||
\(958\) | 8487.17 | 0.286230 | ||||||||
\(959\) | −14558.5 | + | 18457.6i | −0.490217 | + | 0.621509i | ||||
\(960\) | 1405.03 | − | 2575.84i | 0.0472365 | − | 0.0865988i | ||||
\(961\) | 23311.4 | 0.782497 | ||||||||
\(962\) | − | 19318.7i | − | 0.647464i | ||||||
\(963\) | 17796.4 | + | 11989.5i | 0.595514 | + | 0.401200i | ||||
\(964\) | 99554.0i | 3.32616i | ||||||||
\(965\) | 3971.22 | − | 19300.5i | 0.132475 | − | 0.643840i | ||||
\(966\) | 31203.3 | + | 44977.4i | 1.03929 | + | 1.49806i | ||||
\(967\) | 1876.37i | 0.0623993i | 0.999513 | + | 0.0311996i | \(0.00993277\pi\) | ||||
−0.999513 | + | 0.0311996i | \(0.990067\pi\) | |||||||
\(968\) | 90141.8 | 2.99304 | ||||||||
\(969\) | 4878.70 | − | 15973.3i | 0.161740 | − | 0.529554i | ||||
\(970\) | 59077.8 | + | 12155.7i | 1.95554 | + | 0.402366i | ||||
\(971\) | 42968.7 | 1.42011 | 0.710057 | − | 0.704144i | \(-0.248669\pi\) | ||||
0.710057 | + | 0.704144i | \(0.248669\pi\) | |||||||
\(972\) | −68392.3 | + | 6079.02i | −2.25688 | + | 0.200602i | ||||
\(973\) | 22779.5 | + | 17967.4i | 0.750541 | + | 0.591991i | ||||
\(974\) | − | 9114.43i | − | 0.299841i | ||||||
\(975\) | 8791.93 | − | 10390.0i | 0.288787 | − | 0.341278i | ||||
\(976\) | − | 51057.0i | − | 1.67448i | ||||||
\(977\) | 18443.6 | 0.603954 | 0.301977 | − | 0.953315i | \(-0.402353\pi\) | ||||
0.301977 | + | 0.953315i | \(0.402353\pi\) | |||||||
\(978\) | −46837.0 | − | 14305.3i | −1.53137 | − | 0.467723i | ||||
\(979\) | 78589.6i | 2.56561i | ||||||||
\(980\) | 2236.63 | + | 69475.4i | 0.0729048 | + | 2.26460i | ||||
\(981\) | 4526.27 | + | 3049.36i | 0.147312 | + | 0.0992442i | ||||
\(982\) | − | 25430.0i | − | 0.826379i | ||||||
\(983\) | − | 17892.5i | − | 0.580550i | −0.956943 | − | 0.290275i | \(-0.906253\pi\) | ||
0.956943 | − | 0.290275i | \(-0.0937468\pi\) | |||||||
\(984\) | 2874.06 | − | 9409.94i | 0.0931113 | − | 0.304855i | ||||
\(985\) | 12436.9 | + | 2558.98i | 0.402307 | + | 0.0827775i | ||||
\(986\) | 77592.6 | 2.50614 | ||||||||
\(987\) | 20531.2 | − | 14243.6i | 0.662121 | − | 0.459351i | ||||
\(988\) | 12609.4i | 0.406029i | ||||||||
\(989\) | 5851.81i | 0.188146i | ||||||||
\(990\) | 61102.1 | − | 59846.1i | 1.96157 | − | 1.92125i | ||||
\(991\) | 26347.5 | 0.844557 | 0.422278 | − | 0.906466i | \(-0.361230\pi\) | ||||
0.422278 | + | 0.906466i | \(0.361230\pi\) | |||||||
\(992\) | − | 15857.1i | − | 0.507524i | ||||||
\(993\) | −7636.01 | + | 25001.0i | −0.244030 | + | 0.798977i | ||||
\(994\) | −38188.2 | − | 30121.0i | −1.21857 | − | 0.961147i | ||||
\(995\) | 2705.09 | − | 13147.0i | 0.0861881 | − | 0.418883i | ||||
\(996\) | −79890.1 | − | 24400.6i | −2.54158 | − | 0.776269i | ||||
\(997\) | 37680.0 | 1.19693 | 0.598463 | − | 0.801150i | \(-0.295778\pi\) | ||||
0.598463 | + | 0.801150i | \(0.295778\pi\) | |||||||
\(998\) | 40271.0 | 1.27731 | ||||||||
\(999\) | −15941.0 | − | 19652.1i | −0.504856 | − | 0.622387i |
(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 | 105.4.g.b.104.2 | yes | 40 | |
3.2 | odd | 2 | inner | 105.4.g.b.104.37 | yes | 40 | |
5.4 | even | 2 | inner | 105.4.g.b.104.39 | yes | 40 | |
7.6 | odd | 2 | inner | 105.4.g.b.104.3 | yes | 40 | |
15.14 | odd | 2 | inner | 105.4.g.b.104.4 | yes | 40 | |
21.20 | even | 2 | inner | 105.4.g.b.104.40 | yes | 40 | |
35.34 | odd | 2 | inner | 105.4.g.b.104.38 | yes | 40 | |
105.104 | even | 2 | inner | 105.4.g.b.104.1 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.g.b.104.1 | ✓ | 40 | 105.104 | even | 2 | inner | |
105.4.g.b.104.2 | yes | 40 | 1.1 | even | 1 | trivial | |
105.4.g.b.104.3 | yes | 40 | 7.6 | odd | 2 | inner | |
105.4.g.b.104.4 | yes | 40 | 15.14 | odd | 2 | inner | |
105.4.g.b.104.37 | yes | 40 | 3.2 | odd | 2 | inner | |
105.4.g.b.104.38 | yes | 40 | 35.34 | odd | 2 | inner | |
105.4.g.b.104.39 | yes | 40 | 5.4 | even | 2 | inner | |
105.4.g.b.104.40 | yes | 40 | 21.20 | even | 2 | inner |