Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(55,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.b (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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 358 x^{14} - 2828 x^{13} + 52557 x^{12} - 549972 x^{11} + 4434734 x^{10} + \cdots + 52705588025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{26} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.9 | ||
Root | \(0.467111 - 0.600106i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.55 |
Dual form | 252.4.b.g.55.12 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.79845 | − | 2.18302i | 0.635849 | − | 0.771813i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.53113 | − | 7.85211i | −0.191391 | − | 0.981514i | ||||
\(5\) | − | 17.7710i | − | 1.58949i | −0.606944 | − | 0.794744i | \(-0.707605\pi\) | ||
0.606944 | − | 0.794744i | \(-0.292395\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.15121 | − | 17.7895i | 0.278139 | − | 0.960541i | ||||
\(8\) | −19.8950 | − | 10.7792i | −0.879241 | − | 0.476377i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −38.7945 | − | 31.9604i | −1.22679 | − | 1.01068i | ||||
\(11\) | − | 10.7792i | − | 0.295459i | −0.989028 | − | 0.147729i | \(-0.952804\pi\) | ||
0.989028 | − | 0.147729i | \(-0.0471964\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 72.4083i | 1.54480i | 0.635135 | + | 0.772402i | \(0.280945\pi\) | ||||
−0.635135 | + | 0.772402i | \(0.719055\pi\) | |||||||
\(14\) | −29.5705 | − | 43.2387i | −0.564503 | − | 0.825431i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −59.3113 | + | 24.0452i | −0.926739 | + | 0.375706i | ||||
\(17\) | 62.7518i | 0.895267i | 0.894217 | + | 0.447634i | \(0.147733\pi\) | ||||
−0.894217 | + | 0.447634i | \(0.852267\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 98.1938 | 1.18564 | 0.592821 | − | 0.805334i | \(-0.298014\pi\) | ||||
0.592821 | + | 0.805334i | \(0.298014\pi\) | |||||||
\(20\) | −139.540 | + | 27.2097i | −1.56011 | + | 0.304214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −23.5311 | − | 19.3858i | −0.228039 | − | 0.187867i | ||||
\(23\) | − | 160.312i | − | 1.45336i | −0.686976 | − | 0.726680i | \(-0.741062\pi\) | ||
0.686976 | − | 0.726680i | \(-0.258938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −190.809 | −1.52647 | ||||||||
\(26\) | 158.069 | + | 130.223i | 1.19230 | + | 0.982262i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −147.572 | − | 13.2099i | −0.996017 | − | 0.0891587i | ||||
\(29\) | 90.1466 | 0.577235 | 0.288617 | − | 0.957445i | \(-0.406804\pi\) | ||||
0.288617 | + | 0.957445i | \(0.406804\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −201.859 | −1.16952 | −0.584759 | − | 0.811207i | \(-0.698811\pi\) | ||||
−0.584759 | + | 0.811207i | \(0.698811\pi\) | |||||||
\(32\) | −54.1775 | + | 172.722i | −0.299291 | + | 0.954162i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 136.988 | + | 112.856i | 0.690979 | + | 0.569255i | ||||
\(35\) | −316.137 | − | 91.5424i | −1.52677 | − | 0.442099i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −139.685 | −0.620650 | −0.310325 | − | 0.950631i | \(-0.600438\pi\) | ||||
−0.310325 | + | 0.950631i | \(0.600438\pi\) | |||||||
\(38\) | 176.597 | − | 214.359i | 0.753890 | − | 0.915094i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −191.557 | + | 353.554i | −0.757196 | + | 1.39754i | ||||
\(41\) | − | 297.094i | − | 1.13167i | −0.824520 | − | 0.565833i | \(-0.808555\pi\) | ||
0.824520 | − | 0.565833i | \(-0.191445\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.8078i | 0.0808875i | 0.999182 | + | 0.0404437i | \(0.0128772\pi\) | ||||
−0.999182 | + | 0.0404437i | \(0.987123\pi\) | |||||||
\(44\) | −84.6393 | + | 16.5043i | −0.289997 | + | 0.0565481i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −349.963 | − | 288.313i | −1.12172 | − | 0.924118i | ||||
\(47\) | 484.046 | 1.50224 | 0.751122 | − | 0.660164i | \(-0.229513\pi\) | ||||
0.751122 | + | 0.660164i | \(0.229513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −289.930 | − | 183.275i | −0.845277 | − | 0.534328i | ||||
\(50\) | −343.162 | + | 416.540i | −0.970608 | + | 1.17815i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 568.558 | − | 110.866i | 1.51625 | − | 0.295662i | ||||
\(53\) | 502.433 | 1.30216 | 0.651081 | − | 0.759009i | \(-0.274316\pi\) | ||||
0.651081 | + | 0.759009i | \(0.274316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −191.557 | −0.469628 | ||||||||
\(56\) | −294.239 | + | 298.395i | −0.702131 | + | 0.712048i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 162.125 | − | 196.792i | 0.367034 | − | 0.445517i | ||||
\(59\) | −148.228 | −0.327078 | −0.163539 | − | 0.986537i | \(-0.552291\pi\) | ||||
−0.163539 | + | 0.986537i | \(0.552291\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 438.958i | − | 0.921357i | −0.887567 | − | 0.460678i | \(-0.847606\pi\) | ||
0.887567 | − | 0.460678i | \(-0.152394\pi\) | |||||||
\(62\) | −363.035 | + | 440.663i | −0.743637 | + | 0.902649i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 279.619 | + | 428.903i | 0.546130 | + | 0.837700i | ||||
\(65\) | 1286.77 | 2.45545 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 667.659i | − | 1.21743i | −0.793391 | − | 0.608713i | \(-0.791686\pi\) | ||
0.793391 | − | 0.608713i | \(-0.208314\pi\) | |||||||
\(68\) | 492.734 | − | 96.0811i | 0.878717 | − | 0.171346i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −768.396 | + | 525.498i | −1.31201 | + | 0.897272i | ||||
\(71\) | − | 174.191i | − | 0.291165i | −0.989346 | − | 0.145582i | \(-0.953494\pi\) | ||
0.989346 | − | 0.145582i | \(-0.0465056\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1167.55i | 1.87193i | 0.352088 | + | 0.935967i | \(0.385472\pi\) | ||||
−0.352088 | + | 0.935967i | \(0.614528\pi\) | |||||||
\(74\) | −251.217 | + | 304.934i | −0.394640 | + | 0.479026i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −150.347 | − | 771.028i | −0.226921 | − | 1.16372i | ||||
\(77\) | −191.756 | − | 55.5258i | −0.283800 | − | 0.0821787i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 680.430i | 0.969042i | 0.874780 | + | 0.484521i | \(0.161006\pi\) | ||||
−0.874780 | + | 0.484521i | \(0.838994\pi\) | |||||||
\(80\) | 427.308 | + | 1054.02i | 0.597181 | + | 1.47304i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −648.562 | − | 534.310i | −0.873435 | − | 0.719569i | ||||
\(83\) | −780.502 | −1.03218 | −0.516091 | − | 0.856534i | \(-0.672614\pi\) | ||||
−0.516091 | + | 0.856534i | \(0.672614\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1115.16 | 1.42302 | ||||||||
\(86\) | 49.7899 | + | 41.0188i | 0.0624300 | + | 0.0514323i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −116.191 | + | 214.451i | −0.140750 | + | 0.259779i | ||||
\(89\) | 27.2097i | 0.0324070i | 0.999869 | + | 0.0162035i | \(0.00515796\pi\) | ||||
−0.999869 | + | 0.0162035i | \(0.994842\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1288.10 | + | 372.990i | 1.48385 | + | 0.429671i | ||||
\(92\) | −1258.78 | + | 245.458i | −1.42649 | + | 0.278160i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 870.535 | − | 1056.68i | 0.955201 | − | 1.15945i | ||||
\(95\) | − | 1745.00i | − | 1.88456i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 212.717i | − | 0.222661i | −0.993783 | − | 0.111331i | \(-0.964489\pi\) | ||
0.993783 | − | 0.111331i | \(-0.0355112\pi\) | |||||||
\(98\) | −921.517 | + | 303.311i | −0.949871 | + | 0.312643i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 292.154 | + | 1498.26i | 0.292154 | + | 1.49826i | ||||
\(101\) | − | 896.296i | − | 0.883018i | −0.897257 | − | 0.441509i | \(-0.854443\pi\) | ||
0.897257 | − | 0.441509i | \(-0.145557\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1319.65 | 1.26242 | 0.631210 | − | 0.775612i | \(-0.282559\pi\) | ||||
0.631210 | + | 0.775612i | \(0.282559\pi\) | |||||||
\(104\) | 780.502 | − | 1440.56i | 0.735908 | − | 1.35825i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 903.603 | − | 1096.82i | 0.827978 | − | 1.00503i | ||||
\(107\) | − | 1490.63i | − | 1.34677i | −0.739292 | − | 0.673385i | \(-0.764840\pi\) | ||
0.739292 | − | 0.673385i | \(-0.235160\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 555.346 | 0.488005 | 0.244002 | − | 0.969775i | \(-0.421539\pi\) | ||||
0.244002 | + | 0.969775i | \(0.421539\pi\) | |||||||
\(110\) | −344.506 | + | 418.172i | −0.298613 | + | 0.362465i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 122.226 | + | 1178.98i | 0.103118 | + | 0.994669i | ||||
\(113\) | 75.1011 | 0.0625214 | 0.0312607 | − | 0.999511i | \(-0.490048\pi\) | ||||
0.0312607 | + | 0.999511i | \(0.490048\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2848.90 | −2.31010 | ||||||||
\(116\) | −138.026 | − | 707.841i | −0.110478 | − | 0.566564i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −266.580 | + | 323.583i | −0.207972 | + | 0.252443i | ||||
\(119\) | 1116.32 | + | 323.248i | 0.859941 | + | 0.249009i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1214.81 | 0.912704 | ||||||||
\(122\) | −958.252 | − | 789.445i | −0.711115 | − | 0.585844i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 309.073 | + | 1585.02i | 0.223835 | + | 1.14790i | ||||
\(125\) | 1169.50i | 0.836826i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.4669i | − | 0.0101081i | −0.999987 | − | 0.00505404i | \(-0.998391\pi\) | ||
0.999987 | − | 0.00505404i | \(-0.00160876\pi\) | |||||||
\(128\) | 1439.18 | + | 160.949i | 0.993805 | + | 0.111141i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2314.19 | − | 2809.04i | 1.56129 | − | 1.89515i | ||||
\(131\) | −2380.87 | −1.58792 | −0.793960 | − | 0.607970i | \(-0.791984\pi\) | ||||
−0.793960 | + | 0.607970i | \(0.791984\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 505.817 | − | 1746.81i | 0.329774 | − | 1.13886i | ||||
\(134\) | −1457.51 | − | 1200.75i | −0.939625 | − | 0.774099i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 676.413 | − | 1248.44i | 0.426485 | − | 0.787156i | ||||
\(137\) | −176.710 | −0.110200 | −0.0550999 | − | 0.998481i | \(-0.517548\pi\) | ||||
−0.0550999 | + | 0.998481i | \(0.517548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −370.887 | −0.226318 | −0.113159 | − | 0.993577i | \(-0.536097\pi\) | ||||
−0.113159 | + | 0.993577i | \(0.536097\pi\) | |||||||
\(140\) | −234.754 | + | 2622.51i | −0.141717 | + | 1.58316i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −380.263 | − | 313.275i | −0.224725 | − | 0.185137i | ||||
\(143\) | 780.502 | 0.456425 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1602.00i | − | 0.917508i | ||||||
\(146\) | 2548.78 | + | 2099.78i | 1.44478 | + | 1.19027i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 213.875 | + | 1096.82i | 0.118787 | + | 0.609176i | ||||
\(149\) | 2274.32 | 1.25047 | 0.625234 | − | 0.780437i | \(-0.285003\pi\) | ||||
0.625234 | + | 0.780437i | \(0.285003\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2222.44i | − | 1.19774i | −0.800845 | − | 0.598872i | \(-0.795616\pi\) | ||
0.800845 | − | 0.598872i | \(-0.204384\pi\) | |||||||
\(152\) | −1953.56 | − | 1058.45i | −1.04247 | − | 0.564812i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −466.078 | + | 318.745i | −0.243881 | + | 0.166787i | ||||
\(155\) | 3587.25i | 1.85893i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 158.340i | 0.0804901i | 0.999190 | + | 0.0402450i | \(0.0128139\pi\) | ||||
−0.999190 | + | 0.0402450i | \(0.987186\pi\) | |||||||
\(158\) | 1485.39 | + | 1223.72i | 0.747919 | + | 0.616165i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3069.44 | + | 962.791i | 1.51663 | + | 0.475720i | ||||
\(161\) | −2851.86 | − | 825.799i | −1.39601 | − | 0.404237i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1468.12i | 0.705470i | 0.935723 | + | 0.352735i | \(0.114748\pi\) | ||||
−0.935723 | + | 0.352735i | \(0.885252\pi\) | |||||||
\(164\) | −2332.82 | + | 454.890i | −1.11075 | + | 0.216591i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1403.70 | + | 1703.85i | −0.656313 | + | 0.796652i | ||||
\(167\) | 2529.10 | 1.17190 | 0.585950 | − | 0.810347i | \(-0.300721\pi\) | ||||
0.585950 | + | 0.810347i | \(0.300721\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3045.96 | −1.38642 | ||||||||
\(170\) | 2005.57 | − | 2434.42i | 0.904825 | − | 1.09830i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 179.090 | − | 34.9217i | 0.0793922 | − | 0.0154811i | ||||
\(173\) | − | 834.063i | − | 0.366547i | −0.983062 | − | 0.183273i | \(-0.941331\pi\) | ||
0.983062 | − | 0.183273i | \(-0.0586694\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −982.900 | + | 3394.40i | −0.424573 | + | 1.46624i | ||||
\(176\) | 259.187 | + | 639.327i | 0.111006 | + | 0.273813i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 59.3993 | + | 48.9354i | 0.0250122 | + | 0.0206060i | ||||
\(179\) | 2094.57i | 0.874611i | 0.899313 | + | 0.437305i | \(0.144067\pi\) | ||||
−0.899313 | + | 0.437305i | \(0.855933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2968.74i | 1.21914i | 0.792732 | + | 0.609571i | \(0.208658\pi\) | ||||
−0.792732 | + | 0.609571i | \(0.791342\pi\) | |||||||
\(182\) | 3130.84 | − | 2141.15i | 1.27513 | − | 0.872046i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1728.03 | + | 3189.39i | −0.692347 | + | 1.27785i | ||||
\(185\) | 2482.34i | 0.986516i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 676.413 | 0.264514 | ||||||||
\(188\) | −741.138 | − | 3800.79i | −0.287516 | − | 1.47447i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3809.37 | − | 3138.31i | −1.45453 | − | 1.19830i | ||||
\(191\) | 2411.20i | 0.913446i | 0.889609 | + | 0.456723i | \(0.150977\pi\) | ||||
−0.889609 | + | 0.456723i | \(0.849023\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2435.71 | 0.908426 | 0.454213 | − | 0.890893i | \(-0.349921\pi\) | ||||
0.454213 | + | 0.890893i | \(0.349921\pi\) | |||||||
\(194\) | −464.365 | − | 382.561i | −0.171853 | − | 0.141579i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −995.173 | + | 2557.18i | −0.362672 | + | 0.931917i | ||||
\(197\) | −2087.70 | −0.755039 | −0.377520 | − | 0.926002i | \(-0.623223\pi\) | ||||
−0.377520 | + | 0.926002i | \(0.623223\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3388.82 | 1.20717 | 0.603585 | − | 0.797299i | \(-0.293738\pi\) | ||||
0.603585 | + | 0.797299i | \(0.293738\pi\) | |||||||
\(200\) | 3796.14 | + | 2056.77i | 1.34214 | + | 0.727177i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1956.63 | − | 1611.95i | −0.681525 | − | 0.561466i | ||||
\(203\) | 464.365 | − | 1603.66i | 0.160552 | − | 0.554457i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5279.67 | −1.79877 | ||||||||
\(206\) | 2373.33 | − | 2880.83i | 0.802709 | − | 0.974352i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1741.07 | − | 4294.63i | −0.580392 | − | 1.43163i | ||||
\(209\) | − | 1058.45i | − | 0.350308i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4614.70i | − | 1.50564i | −0.658228 | − | 0.752818i | \(-0.728694\pi\) | ||
0.658228 | − | 0.752818i | \(-0.271306\pi\) | |||||||
\(212\) | −769.290 | − | 3945.16i | −0.249222 | − | 1.27809i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3254.06 | − | 2680.82i | −1.03945 | − | 0.856343i | ||||
\(215\) | 405.319 | 0.128570 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1039.82 | + | 3590.97i | −0.325289 | + | 1.12337i | ||||
\(218\) | 998.765 | − | 1212.33i | 0.310298 | − | 0.376649i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 293.298 | + | 1504.13i | 0.0898826 | + | 0.460946i | ||||
\(221\) | −4543.75 | −1.38301 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 294.922 | 0.0885625 | 0.0442812 | − | 0.999019i | \(-0.485900\pi\) | ||||
0.0442812 | + | 0.999019i | \(0.485900\pi\) | |||||||
\(224\) | 2793.55 | + | 1853.52i | 0.833266 | + | 0.552872i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 135.066 | − | 163.947i | 0.0397542 | − | 0.0482548i | ||||
\(227\) | −2272.00 | −0.664310 | −0.332155 | − | 0.943225i | \(-0.607776\pi\) | ||||
−0.332155 | + | 0.943225i | \(0.607776\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3054.67i | 0.881478i | 0.897635 | + | 0.440739i | \(0.145283\pi\) | ||||
−0.897635 | + | 0.440739i | \(0.854717\pi\) | |||||||
\(230\) | −5123.62 | + | 6219.20i | −1.46888 | + | 1.78297i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1793.46 | − | 971.706i | −0.507529 | − | 0.274981i | ||||
\(233\) | −3277.16 | −0.921433 | −0.460717 | − | 0.887547i | \(-0.652408\pi\) | ||||
−0.460717 | + | 0.887547i | \(0.652408\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 8602.00i | − | 2.38780i | ||||||
\(236\) | 226.955 | + | 1163.90i | 0.0625997 | + | 0.321031i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2713.31 | − | 1855.60i | 0.738981 | − | 0.505381i | ||||
\(239\) | 5776.27i | 1.56333i | 0.623698 | + | 0.781665i | \(0.285629\pi\) | ||||
−0.623698 | + | 0.781665i | \(0.714371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 321.470i | 0.0859240i | 0.999077 | + | 0.0429620i | \(0.0136794\pi\) | ||||
−0.999077 | + | 0.0429620i | \(0.986321\pi\) | |||||||
\(242\) | 2184.78 | − | 2651.95i | 0.580342 | − | 0.704437i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3446.74 | + | 672.101i | −0.904324 | + | 0.176339i | ||||
\(245\) | −3256.98 | + | 5152.35i | −0.849309 | + | 1.34356i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7110.04i | 1.83158i | ||||||||
\(248\) | 4015.99 | + | 2175.88i | 1.02829 | + | 0.557131i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2553.04 | + | 2103.29i | 0.645873 | + | 0.532095i | ||||
\(251\) | 1818.09 | 0.457200 | 0.228600 | − | 0.973520i | \(-0.426585\pi\) | ||||
0.228600 | + | 0.973520i | \(0.426585\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1728.03 | −0.429408 | ||||||||
\(254\) | −31.5814 | − | 26.0180i | −0.00780155 | − | 0.00642722i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2939.66 | − | 2852.30i | 0.717690 | − | 0.696363i | ||||
\(257\) | 2438.33i | 0.591824i | 0.955215 | + | 0.295912i | \(0.0956236\pi\) | ||||
−0.955215 | + | 0.295912i | \(0.904376\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −719.546 | + | 2484.92i | −0.172627 | + | 0.596159i | ||||
\(260\) | −1970.21 | − | 10103.9i | −0.469951 | − | 2.41006i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4281.88 | + | 5197.48i | −1.00968 | + | 1.22558i | ||||
\(263\) | − | 4083.47i | − | 0.957406i | −0.877977 | − | 0.478703i | \(-0.841107\pi\) | ||
0.877977 | − | 0.478703i | \(-0.158893\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8928.76i | − | 2.06977i | ||||||
\(266\) | −2903.64 | − | 4245.77i | −0.669299 | − | 0.978665i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5242.53 | + | 1022.27i | −1.19492 | + | 0.233004i | ||||
\(269\) | − | 2121.53i | − | 0.480862i | −0.970666 | − | 0.240431i | \(-0.922711\pi\) | ||
0.970666 | − | 0.240431i | \(-0.0772888\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6897.68 | −1.54614 | −0.773070 | − | 0.634321i | \(-0.781280\pi\) | ||||
−0.773070 | + | 0.634321i | \(0.781280\pi\) | |||||||
\(272\) | −1508.88 | − | 3721.89i | −0.336357 | − | 0.829679i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −317.805 | + | 385.762i | −0.0700705 | + | 0.0850537i | ||||
\(275\) | 2056.77i | 0.451010i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1456.63 | −0.315957 | −0.157979 | − | 0.987443i | \(-0.550498\pi\) | ||||
−0.157979 | + | 0.987443i | \(0.550498\pi\) | |||||||
\(278\) | −667.024 | + | 809.654i | −0.143904 | + | 0.174676i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5302.78 | + | 5228.93i | 1.13179 | + | 1.11603i | ||||
\(281\) | 6013.55 | 1.27665 | 0.638325 | − | 0.769767i | \(-0.279628\pi\) | ||||
0.638325 | + | 0.769767i | \(0.279628\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2485.71 | 0.522121 | 0.261060 | − | 0.965322i | \(-0.415928\pi\) | ||||
0.261060 | + | 0.965322i | \(0.415928\pi\) | |||||||
\(284\) | −1367.77 | + | 266.709i | −0.285782 | + | 0.0557264i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1403.70 | − | 1703.85i | 0.290218 | − | 0.352275i | ||||
\(287\) | −5285.15 | − | 1530.40i | −1.08701 | − | 0.314761i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 975.214 | 0.198497 | ||||||||
\(290\) | −3497.19 | − | 2881.12i | −0.708145 | − | 0.583397i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9167.72 | − | 1787.67i | 1.83733 | − | 0.358272i | ||||
\(293\) | − | 2245.72i | − | 0.447769i | −0.974616 | − | 0.223884i | \(-0.928126\pi\) | ||
0.974616 | − | 0.223884i | \(-0.0718738\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2634.15i | 0.519886i | ||||||||
\(296\) | 2779.02 | + | 1505.69i | 0.545701 | + | 0.295663i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4090.27 | − | 4964.89i | 0.795110 | − | 0.965128i | ||||
\(299\) | 11607.9 | 2.24516 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 405.739 | + | 117.488i | 0.0776957 | + | 0.0224980i | ||||
\(302\) | −4851.62 | − | 3996.95i | −0.924435 | − | 0.761585i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5824.00 | + | 2361.09i | −1.09878 | + | 0.445453i | ||||
\(305\) | −7800.73 | −1.46449 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 839.287 | 0.156028 | 0.0780141 | − | 0.996952i | \(-0.475142\pi\) | ||||
0.0780141 | + | 0.996952i | \(0.475142\pi\) | |||||||
\(308\) | −142.392 | + | 1590.70i | −0.0263427 | + | 0.294282i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7831.03 | + | 6451.50i | 1.43475 | + | 1.18200i | ||||
\(311\) | 1155.68 | 0.210717 | 0.105358 | − | 0.994434i | \(-0.466401\pi\) | ||||
0.105358 | + | 0.994434i | \(0.466401\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4244.76i | 0.766543i | 0.923636 | + | 0.383272i | \(0.125203\pi\) | ||||
−0.923636 | + | 0.383272i | \(0.874797\pi\) | |||||||
\(314\) | 345.660 | + | 284.768i | 0.0621233 | + | 0.0511796i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5342.81 | − | 1041.83i | 0.951128 | − | 0.185466i | ||||
\(317\) | −3876.67 | −0.686863 | −0.343431 | − | 0.939178i | \(-0.611589\pi\) | ||||
−0.343431 | + | 0.939178i | \(0.611589\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 971.706i | − | 0.170549i | ||||||
\(320\) | 7622.04 | − | 4969.11i | 1.33152 | − | 0.868068i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6931.67 | + | 4740.49i | −1.19965 | + | 0.820426i | ||||
\(323\) | 6161.83i | 1.06147i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 13816.2i | − | 2.35810i | ||||||
\(326\) | 3204.92 | + | 2640.34i | 0.544491 | + | 0.448573i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3202.43 | + | 5910.68i | −0.539100 | + | 0.995008i | ||||
\(329\) | 2493.43 | − | 8610.93i | 0.417833 | − | 1.44297i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 475.573i | − | 0.0789724i | −0.999220 | − | 0.0394862i | \(-0.987428\pi\) | ||
0.999220 | − | 0.0394862i | \(-0.0125721\pi\) | |||||||
\(332\) | 1195.05 | + | 6128.58i | 0.197551 | + | 1.01310i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4548.46 | − | 5521.06i | 0.745152 | − | 0.904488i | ||||
\(335\) | −11865.0 | −1.93508 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10012.6 | 1.61847 | 0.809233 | − | 0.587488i | \(-0.199883\pi\) | ||||
0.809233 | + | 0.587488i | \(0.199883\pi\) | |||||||
\(338\) | −5478.01 | + | 6649.38i | −0.881552 | + | 1.07005i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1707.46 | − | 8756.39i | −0.272353 | − | 1.39671i | ||||
\(341\) | 2175.88i | 0.345544i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4753.85 | + | 4213.61i | −0.748349 | + | 0.663305i | ||||
\(344\) | 245.850 | − | 453.761i | 0.0385329 | − | 0.0711196i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1820.77 | − | 1500.02i | −0.282906 | − | 0.233069i | ||||
\(347\) | − | 10771.5i | − | 1.66642i | −0.552959 | − | 0.833209i | \(-0.686501\pi\) | ||
0.552959 | − | 0.833209i | \(-0.313499\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9281.78i | 1.42362i | 0.702373 | + | 0.711809i | \(0.252124\pi\) | ||||
−0.702373 | + | 0.711809i | \(0.747876\pi\) | |||||||
\(350\) | 5642.33 | + | 8250.35i | 0.861700 | + | 1.26000i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1861.80 | + | 583.989i | 0.281915 | + | 0.0884282i | ||||
\(353\) | 4527.91i | 0.682709i | 0.939935 | + | 0.341355i | \(0.110886\pi\) | ||||
−0.939935 | + | 0.341355i | \(0.889114\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3095.56 | −0.462803 | ||||||||
\(356\) | 213.654 | − | 41.6616i | 0.0318079 | − | 0.00620242i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4572.48 | + | 3766.98i | 0.675036 | + | 0.556121i | ||||
\(359\) | 9834.05i | 1.44574i | 0.690983 | + | 0.722871i | \(0.257178\pi\) | ||||
−0.690983 | + | 0.722871i | \(0.742822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2783.02 | 0.405747 | ||||||||
\(362\) | 6480.81 | + | 5339.14i | 0.940950 | + | 0.775190i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 956.509 | − | 10685.4i | 0.137733 | − | 1.53865i | ||||
\(365\) | 20748.5 | 2.97542 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11847.0 | 1.68504 | 0.842518 | − | 0.538669i | \(-0.181073\pi\) | ||||
0.842518 | + | 0.538669i | \(0.181073\pi\) | |||||||
\(368\) | 3854.72 | + | 9508.29i | 0.546036 | + | 1.34689i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5419.00 | + | 4464.38i | 0.761406 | + | 0.627276i | ||||
\(371\) | 2588.14 | − | 8938.02i | 0.362182 | − | 1.25078i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10310.6 | 1.43127 | 0.715634 | − | 0.698475i | \(-0.246138\pi\) | ||||
0.715634 | + | 0.698475i | \(0.246138\pi\) | |||||||
\(374\) | 1216.50 | − | 1476.62i | 0.168191 | − | 0.204156i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9630.08 | − | 5217.62i | −1.32083 | − | 0.715634i | ||||
\(377\) | 6527.36i | 0.891714i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3861.94i | − | 0.523416i | −0.965147 | − | 0.261708i | \(-0.915714\pi\) | ||
0.965147 | − | 0.261708i | \(-0.0842857\pi\) | |||||||
\(380\) | −13702.0 | + | 2671.83i | −1.84973 | + | 0.360689i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5263.69 | + | 4336.43i | 0.705010 | + | 0.580814i | ||||
\(383\) | −9178.43 | −1.22453 | −0.612266 | − | 0.790652i | \(-0.709742\pi\) | ||||
−0.612266 | + | 0.790652i | \(0.709742\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −986.751 | + | 3407.70i | −0.130622 | + | 0.451097i | ||||
\(386\) | 4380.51 | − | 5317.19i | 0.577622 | − | 0.701135i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1670.28 | + | 325.697i | −0.218545 | + | 0.0426153i | ||||
\(389\) | 314.387 | 0.0409770 | 0.0204885 | − | 0.999790i | \(-0.493478\pi\) | ||||
0.0204885 | + | 0.999790i | \(0.493478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10059.8 | 1.30115 | ||||||||
\(392\) | 3792.60 | + | 6771.45i | 0.488661 | + | 0.872474i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3754.64 | + | 4557.49i | −0.480091 | + | 0.582749i | ||||
\(395\) | 12091.9 | 1.54028 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2126.89i | 0.268880i | 0.990922 | + | 0.134440i | \(0.0429236\pi\) | ||||
−0.990922 | + | 0.134440i | \(0.957076\pi\) | |||||||
\(398\) | 6094.63 | − | 7397.85i | 0.767579 | − | 0.931710i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11317.1 | − | 4588.05i | 1.41464 | − | 0.573506i | ||||
\(401\) | 6506.32 | 0.810249 | 0.405125 | − | 0.914261i | \(-0.367228\pi\) | ||||
0.405125 | + | 0.914261i | \(0.367228\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 14616.3i | − | 1.80667i | ||||||
\(404\) | −7037.82 | + | 1372.34i | −0.866694 | + | 0.169002i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2665.68 | − | 3897.82i | −0.325851 | − | 0.476467i | ||||
\(407\) | 1505.69i | 0.183376i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3280.91i | 0.396652i | 0.980136 | + | 0.198326i | \(0.0635505\pi\) | ||||
−0.980136 | + | 0.198326i | \(0.936450\pi\) | |||||||
\(410\) | −9495.24 | + | 11525.6i | −1.14375 | + | 1.38832i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2020.56 | − | 10362.1i | −0.241616 | − | 1.23908i | ||||
\(413\) | −763.552 | + | 2636.89i | −0.0909732 | + | 0.314171i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13870.3i | 1.64064i | ||||||||
\(416\) | −12506.5 | − | 3922.90i | −1.47399 | − | 0.462346i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2310.61 | − | 1903.57i | −0.270372 | − | 0.222743i | ||||
\(419\) | 1313.14 | 0.153105 | 0.0765526 | − | 0.997066i | \(-0.475609\pi\) | ||||
0.0765526 | + | 0.997066i | \(0.475609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7669.52 | 0.887861 | 0.443931 | − | 0.896061i | \(-0.353584\pi\) | ||||
0.443931 | + | 0.896061i | \(0.353584\pi\) | |||||||
\(422\) | −10074.0 | − | 8299.33i | −1.16207 | − | 0.957358i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9995.89 | − | 5415.82i | −1.14491 | − | 0.620319i | ||||
\(425\) | − | 11973.6i | − | 1.36660i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7808.82 | − | 2261.16i | −0.885001 | − | 0.256266i | ||||
\(428\) | −11704.6 | + | 2282.34i | −1.32187 | + | 0.257760i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 728.947 | − | 884.817i | 0.0817510 | − | 0.0992318i | ||||
\(431\) | − | 2360.49i | − | 0.263807i | −0.991263 | − | 0.131903i | \(-0.957891\pi\) | ||
0.991263 | − | 0.131903i | \(-0.0421088\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4914.75i | − | 0.545468i | −0.962089 | − | 0.272734i | \(-0.912072\pi\) | ||
0.962089 | − | 0.272734i | \(-0.0879279\pi\) | |||||||
\(434\) | 5969.08 | + | 8728.14i | 0.660196 | + | 0.965355i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −850.307 | − | 4360.64i | −0.0933998 | − | 0.478984i | ||||
\(437\) | − | 15741.6i | − | 1.72316i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3334.78 | 0.362552 | 0.181276 | − | 0.983432i | \(-0.441977\pi\) | ||||
0.181276 | + | 0.983432i | \(0.441977\pi\) | |||||||
\(440\) | 3811.02 | + | 2064.83i | 0.412916 | + | 0.223720i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8171.72 | + | 9919.08i | −0.879387 | + | 1.06743i | ||||
\(443\) | − | 3590.57i | − | 0.385086i | −0.981288 | − | 0.192543i | \(-0.938326\pi\) | ||
0.981288 | − | 0.192543i | \(-0.0616736\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 483.545 | 0.0515106 | ||||||||
\(446\) | 530.403 | − | 643.820i | 0.0563124 | − | 0.0683537i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9070.32 | − | 2764.90i | 0.956546 | − | 0.291583i | ||||
\(449\) | 15166.2 | 1.59407 | 0.797037 | − | 0.603931i | \(-0.206400\pi\) | ||||
0.797037 | + | 0.603931i | \(0.206400\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3202.43 | −0.334361 | ||||||||
\(452\) | −114.990 | − | 589.702i | −0.0119660 | − | 0.0613656i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4086.10 | + | 4959.83i | −0.422401 | + | 0.512723i | ||||
\(455\) | 6628.42 | − | 22890.9i | 0.682957 | − | 2.35856i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15092.8 | −1.54489 | −0.772443 | − | 0.635084i | \(-0.780965\pi\) | ||||
−0.772443 | + | 0.635084i | \(0.780965\pi\) | |||||||
\(458\) | 6668.40 | + | 5493.68i | 0.680336 | + | 0.560487i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4362.04 | + | 22369.9i | 0.442133 | + | 2.26740i | ||||
\(461\) | − | 1332.96i | − | 0.134669i | −0.997730 | − | 0.0673344i | \(-0.978551\pi\) | ||
0.997730 | − | 0.0673344i | \(-0.0214494\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10483.5i | 1.05229i | 0.850394 | + | 0.526146i | \(0.176363\pi\) | ||||
−0.850394 | + | 0.526146i | \(0.823637\pi\) | |||||||
\(464\) | −5346.71 | + | 2167.59i | −0.534946 | + | 0.216871i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5893.82 | + | 7154.10i | −0.585893 | + | 0.711174i | ||||
\(467\) | −15964.3 | −1.58188 | −0.790942 | − | 0.611891i | \(-0.790409\pi\) | ||||
−0.790942 | + | 0.611891i | \(0.790409\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11877.3 | − | 3439.25i | −1.16939 | − | 0.338614i | ||||
\(470\) | −18778.3 | − | 15470.3i | −1.84293 | − | 1.51828i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2948.98 | + | 1597.77i | 0.287580 | + | 0.155812i | ||||
\(473\) | 245.850 | 0.0238989 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18736.3 | −1.80985 | ||||||||
\(476\) | 828.947 | − | 9260.41i | 0.0798209 | − | 0.891702i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12609.7 | + | 10388.4i | 1.20660 | + | 0.994043i | ||||
\(479\) | −19452.3 | −1.85553 | −0.927763 | − | 0.373170i | \(-0.878271\pi\) | ||||
−0.927763 | + | 0.373170i | \(0.878271\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 10114.3i | − | 0.958782i | ||||||
\(482\) | 701.774 | + | 578.148i | 0.0663172 | + | 0.0546347i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1860.03 | − | 9538.82i | −0.174683 | − | 0.895832i | ||||
\(485\) | −3780.20 | −0.353917 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8465.85i | 0.787729i | 0.919168 | + | 0.393865i | \(0.128862\pi\) | ||||
−0.919168 | + | 0.393865i | \(0.871138\pi\) | |||||||
\(488\) | −4731.60 | + | 8733.04i | −0.438913 | + | 0.810095i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5390.15 | + | 16376.3i | 0.496943 | + | 1.50981i | ||||
\(491\) | 7175.25i | 0.659500i | 0.944068 | + | 0.329750i | \(0.106965\pi\) | ||||
−0.944068 | + | 0.329750i | \(0.893035\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5656.86i | 0.516779i | ||||||||
\(494\) | 15521.3 | + | 12787.1i | 1.41364 | + | 1.16461i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11972.5 | − | 4853.75i | 1.08384 | − | 0.439395i | ||||
\(497\) | −3098.77 | − | 897.297i | −0.279676 | − | 0.0809844i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17503.9i | − | 1.57030i | −0.619303 | − | 0.785152i | \(-0.712585\pi\) | ||
0.619303 | − | 0.785152i | \(-0.287415\pi\) | |||||||
\(500\) | 9183.04 | − | 1790.65i | 0.821356 | − | 0.160161i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3269.76 | − | 3968.93i | 0.290710 | − | 0.352873i | ||||
\(503\) | 16033.8 | 1.42130 | 0.710648 | − | 0.703548i | \(-0.248402\pi\) | ||||
0.710648 | + | 0.703548i | \(0.248402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15928.1 | −1.40355 | ||||||||
\(506\) | −3107.78 | + | 3772.31i | −0.273039 | + | 0.331423i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −113.595 | + | 22.1506i | −0.00992123 | + | 0.00193460i | ||||
\(509\) | 12929.7i | 1.12593i | 0.826480 | + | 0.562965i | \(0.190340\pi\) | ||||
−0.826480 | + | 0.562965i | \(0.809660\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20770.1 | + | 6014.29i | 1.79807 | + | 0.520659i | ||||
\(512\) | −939.786 | − | 11547.1i | −0.0811193 | − | 0.996704i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5322.92 | + | 4385.22i | 0.456778 | + | 0.376311i | ||||
\(515\) | − | 23451.6i | − | 2.00660i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 5217.62i | − | 0.443851i | ||||||
\(518\) | 4130.55 | + | 6039.79i | 0.350359 | + | 0.512304i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −25600.2 | − | 13870.3i | −2.15893 | − | 1.16972i | ||||
\(521\) | 19765.0i | 1.66204i | 0.556245 | + | 0.831018i | \(0.312241\pi\) | ||||
−0.556245 | + | 0.831018i | \(0.687759\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5646.25 | 0.472071 | 0.236036 | − | 0.971744i | \(-0.424152\pi\) | ||||
0.236036 | + | 0.971744i | \(0.424152\pi\) | |||||||
\(524\) | 3645.42 | + | 18694.8i | 0.303914 | + | 1.55856i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8914.29 | − | 7343.94i | −0.738939 | − | 0.608766i | ||||
\(527\) | − | 12667.0i | − | 1.04703i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13532.8 | −1.11226 | ||||||||
\(530\) | −19491.6 | − | 16058.0i | −1.59748 | − | 1.31606i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14490.7 | − | 1297.13i | −1.18092 | − | 0.105710i | ||||
\(533\) | 21512.1 | 1.74820 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26490.0 | −2.14068 | ||||||||
\(536\) | −7196.81 | + | 13283.0i | −0.579953 | + | 1.07041i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4631.33 | − | 3815.47i | −0.371136 | − | 0.305756i | ||||
\(539\) | −1975.55 | + | 3125.21i | −0.157872 | + | 0.249744i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6642.27 | 0.527862 | 0.263931 | − | 0.964542i | \(-0.414981\pi\) | ||||
0.263931 | + | 0.964542i | \(0.414981\pi\) | |||||||
\(542\) | −12405.2 | + | 15057.7i | −0.983112 | + | 1.19333i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10838.6 | − | 3399.74i | −0.854230 | − | 0.267946i | ||||
\(545\) | − | 9869.08i | − | 0.775678i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 15445.0i | − | 1.20728i | −0.797257 | − | 0.603640i | \(-0.793717\pi\) | ||
0.797257 | − | 0.603640i | \(-0.206283\pi\) | |||||||
\(548\) | 270.566 | + | 1387.55i | 0.0210913 | + | 0.108163i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4489.96 | + | 3699.00i | 0.348095 | + | 0.286774i | ||||
\(551\) | 8851.84 | 0.684394 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12104.5 | + | 3505.04i | 0.930804 | + | 0.269529i | ||||
\(554\) | −2619.67 | + | 3179.84i | −0.200901 | + | 0.243860i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 567.876 | + | 2912.25i | 0.0433153 | + | 0.222135i | ||||
\(557\) | −20224.1 | −1.53846 | −0.769231 | − | 0.638971i | \(-0.779361\pi\) | ||||
−0.769231 | + | 0.638971i | \(0.779361\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1651.48 | −0.124955 | ||||||||
\(560\) | 20951.6 | − | 2172.08i | 1.58102 | − | 0.163905i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10815.1 | − | 13127.7i | 0.811757 | − | 0.985335i | ||||
\(563\) | −12972.1 | −0.971061 | −0.485531 | − | 0.874220i | \(-0.661374\pi\) | ||||
−0.485531 | + | 0.874220i | \(0.661374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1334.62i | − | 0.0993771i | ||||||
\(566\) | 4470.44 | − | 5426.35i | 0.331990 | − | 0.402980i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1877.64 | + | 3465.53i | −0.138704 | + | 0.256004i | ||||
\(569\) | −1451.30 | −0.106928 | −0.0534638 | − | 0.998570i | \(-0.517026\pi\) | ||||
−0.0534638 | + | 0.998570i | \(0.517026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8530.19i | 0.625179i | 0.949888 | + | 0.312590i | \(0.101196\pi\) | ||||
−0.949888 | + | 0.312590i | \(0.898804\pi\) | |||||||
\(572\) | −1195.05 | − | 6128.58i | −0.0873557 | − | 0.447988i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12846.0 | + | 8785.22i | −0.934113 | + | 0.638829i | ||||
\(575\) | 30589.0i | 2.21852i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21396.2i | 1.54374i | 0.635782 | + | 0.771869i | \(0.280678\pi\) | ||||
−0.635782 | + | 0.771869i | \(0.719322\pi\) | |||||||
\(578\) | 1753.88 | − | 2128.91i | 0.126214 | − | 0.153202i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12579.1 | + | 2452.87i | −0.900547 | + | 0.175603i | ||||
\(581\) | −4020.53 | + | 13884.7i | −0.287091 | + | 0.991454i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5415.82i | − | 0.384735i | ||||||
\(584\) | 12585.2 | − | 23228.3i | 0.891746 | − | 1.64588i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4902.44 | − | 4038.82i | −0.345594 | − | 0.284714i | ||||
\(587\) | 7212.11 | 0.507113 | 0.253557 | − | 0.967321i | \(-0.418400\pi\) | ||||
0.253557 | + | 0.967321i | \(0.418400\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19821.3 | −1.38663 | ||||||||
\(590\) | 5750.41 | + | 4737.41i | 0.401255 | + | 0.330569i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8284.89 | − | 3358.75i | 0.575180 | − | 0.233182i | ||||
\(593\) | − | 18362.2i | − | 1.27158i | −0.771863 | − | 0.635789i | \(-0.780675\pi\) | ||
0.771863 | − | 0.635789i | \(-0.219325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5744.45 | − | 19838.2i | 0.395797 | − | 1.36687i | ||||
\(596\) | −3482.28 | − | 17858.2i | −0.239329 | − | 1.22735i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20876.2 | − | 25340.2i | 1.42758 | − | 1.73284i | ||||
\(599\) | − | 2402.54i | − | 0.163881i | −0.996637 | − | 0.0819407i | \(-0.973888\pi\) | ||
0.996637 | − | 0.0819407i | \(-0.0261118\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15264.1i | 1.03600i | 0.855382 | + | 0.517998i | \(0.173323\pi\) | ||||
−0.855382 | + | 0.517998i | \(0.826677\pi\) | |||||||
\(602\) | 986.181 | − | 674.439i | 0.0667670 | − | 0.0456612i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17450.8 | + | 3402.84i | −1.17560 | + | 0.229238i | ||||
\(605\) | − | 21588.4i | − | 1.45073i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18675.5 | 1.24879 | 0.624395 | − | 0.781109i | \(-0.285346\pi\) | ||||
0.624395 | + | 0.781109i | \(0.285346\pi\) | |||||||
\(608\) | −5319.90 | + | 16960.2i | −0.354853 | + | 1.13129i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14029.2 | + | 17029.1i | −0.931193 | + | 1.13031i | ||||
\(611\) | 35049.0i | 2.32067i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6537.07 | 0.430718 | 0.215359 | − | 0.976535i | \(-0.430908\pi\) | ||||
0.215359 | + | 0.976535i | \(0.430908\pi\) | |||||||
\(614\) | 1509.42 | − | 1832.18i | 0.0992104 | − | 0.120425i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3216.45 | + | 3171.65i | 0.210381 | + | 0.207451i | ||||
\(617\) | 3529.67 | 0.230307 | 0.115153 | − | 0.993348i | \(-0.463264\pi\) | ||||
0.115153 | + | 0.993348i | \(0.463264\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −557.614 | −0.0362074 | −0.0181037 | − | 0.999836i | \(-0.505763\pi\) | ||||
−0.0181037 | + | 0.999836i | \(0.505763\pi\) | |||||||
\(620\) | 28167.5 | − | 5492.54i | 1.82457 | − | 0.355783i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2078.44 | − | 2522.88i | 0.133984 | − | 0.162634i | ||||
\(623\) | 484.046 | + | 140.163i | 0.0311283 | + | 0.00901367i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3067.96 | −0.196349 | ||||||||
\(626\) | 9266.38 | + | 7634.00i | 0.591628 | + | 0.487406i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1243.31 | − | 242.440i | 0.0790021 | − | 0.0154051i | ||||
\(629\) | − | 8765.47i | − | 0.555647i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14053.9i | 0.886650i | 0.896361 | + | 0.443325i | \(0.146201\pi\) | ||||
−0.896361 | + | 0.443325i | \(0.853799\pi\) | |||||||
\(632\) | 7334.47 | − | 13537.1i | 0.461629 | − | 0.852022i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6972.01 | + | 8462.83i | −0.436741 | + | 0.530130i | ||||
\(635\) | −257.091 | −0.0160667 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13270.6 | − | 20993.3i | 0.825432 | − | 1.30579i | ||||
\(638\) | −2121.25 | − | 1747.57i | −0.131632 | − | 0.108443i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2860.23 | − | 25575.8i | 0.176657 | − | 1.57964i | ||||
\(641\) | −8223.99 | −0.506752 | −0.253376 | − | 0.967368i | \(-0.581541\pi\) | ||||
−0.253376 | + | 0.967368i | \(0.581541\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26162.2 | 1.60457 | 0.802283 | − | 0.596944i | \(-0.203619\pi\) | ||||
0.802283 | + | 0.596944i | \(0.203619\pi\) | |||||||
\(644\) | −2117.71 | + | 23657.5i | −0.129580 | + | 1.44757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13451.4 | + | 11081.8i | 0.819254 | + | 0.674933i | ||||
\(647\) | 28473.2 | 1.73014 | 0.865068 | − | 0.501654i | \(-0.167275\pi\) | ||||
0.865068 | + | 0.501654i | \(0.167275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1597.77i | 0.0966379i | ||||||||
\(650\) | −30160.9 | − | 24847.7i | −1.82001 | − | 1.49940i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11527.8 | − | 2247.87i | 0.692429 | − | 0.135021i | ||||
\(653\) | 30403.4 | 1.82202 | 0.911009 | − | 0.412386i | \(-0.135304\pi\) | ||||
0.911009 | + | 0.412386i | \(0.135304\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 42310.5i | 2.52398i | ||||||||
\(656\) | 7143.69 | + | 17621.0i | 0.425174 | + | 1.04876i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14313.5 | − | 20929.5i | −0.848021 | − | 1.24000i | ||||
\(659\) | 24719.1i | 1.46118i | 0.682814 | + | 0.730592i | \(0.260756\pi\) | ||||
−0.682814 | + | 0.730592i | \(0.739244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16458.4i | 0.968467i | 0.874939 | + | 0.484233i | \(0.160901\pi\) | ||||
−0.874939 | + | 0.484233i | \(0.839099\pi\) | |||||||
\(662\) | −1038.18 | − | 855.296i | −0.0609519 | − | 0.0502145i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15528.0 | + | 8413.16i | 0.907538 | + | 0.491708i | ||||
\(665\) | −31042.7 | − | 8988.89i | −1.81020 | − | 0.524172i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 14451.6i | − | 0.838930i | ||||||
\(668\) | −3872.37 | − | 19858.7i | −0.224291 | − | 1.15024i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21338.6 | + | 25901.5i | −1.23042 | + | 1.49352i | ||||
\(671\) | −4731.60 | −0.272223 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13350.6 | 0.764676 | 0.382338 | − | 0.924023i | \(-0.375119\pi\) | ||||
0.382338 | + | 0.924023i | \(0.375119\pi\) | |||||||
\(674\) | 18007.3 | − | 21857.8i | 1.02910 | − | 1.24915i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4663.75 | + | 23917.2i | 0.265348 | + | 1.36079i | ||||
\(677\) | 28935.9i | 1.64269i | 0.570435 | + | 0.821343i | \(0.306775\pi\) | ||||
−0.570435 | + | 0.821343i | \(0.693225\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3784.12 | − | 1095.75i | −0.213875 | − | 0.0619308i | ||||
\(680\) | −22186.1 | − | 12020.5i | −1.25118 | − | 0.677892i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4749.98 | + | 3913.22i | 0.266695 | + | 0.219714i | ||||
\(683\) | − | 5796.62i | − | 0.324746i | −0.986729 | − | 0.162373i | \(-0.948085\pi\) | ||
0.986729 | − | 0.162373i | \(-0.0519148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3140.32i | 0.175161i | ||||||||
\(686\) | 648.810 | + | 17955.7i | 0.0361103 | + | 0.999348i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −548.419 | − | 1352.76i | −0.0303899 | − | 0.0749616i | ||||
\(689\) | 36380.3i | 2.01158i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19975.6 | −1.09972 | −0.549861 | − | 0.835256i | \(-0.685319\pi\) | ||||
−0.549861 | + | 0.835256i | \(0.685319\pi\) | |||||||
\(692\) | −6549.15 | + | 1277.06i | −0.359771 | + | 0.0701538i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23514.5 | − | 19372.1i | −1.28616 | − | 1.05959i | ||||
\(695\) | 6591.05i | 0.359731i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18643.2 | 1.01314 | ||||||||
\(698\) | 20262.3 | + | 16692.9i | 1.09877 | + | 0.905206i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 28158.1 | + | 2520.58i | 1.52040 | + | 0.136099i | ||||
\(701\) | −35866.0 | −1.93244 | −0.966219 | − | 0.257723i | \(-0.917028\pi\) | ||||
−0.966219 | + | 0.257723i | \(0.917028\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13716.2 | −0.735868 | ||||||||
\(704\) | 4623.22 | − | 3014.06i | 0.247506 | − | 0.161359i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9884.51 | + | 8143.24i | 0.526924 | + | 0.434100i | ||||
\(707\) | −15944.6 | − | 4617.01i | −0.848174 | − | 0.245602i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1806.89 | −0.0957109 | −0.0478555 | − | 0.998854i | \(-0.515239\pi\) | ||||
−0.0478555 | + | 0.998854i | \(0.515239\pi\) | |||||||
\(710\) | −5567.22 | + | 6757.66i | −0.294273 | + | 0.357198i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 293.298 | − | 541.336i | 0.0154380 | − | 0.0284936i | ||||
\(713\) | 32360.4i | 1.69973i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 13870.3i | − | 0.725483i | ||||||
\(716\) | 16446.8 | − | 3207.05i | 0.858443 | − | 0.167393i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21467.9 | + | 17686.1i | 1.11584 | + | 0.919274i | ||||
\(719\) | 23227.5 | 1.20478 | 0.602391 | − | 0.798201i | \(-0.294215\pi\) | ||||
0.602391 | + | 0.798201i | \(0.294215\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6797.81 | − | 23475.9i | 0.351129 | − | 1.21261i | ||||
\(722\) | 5005.13 | − | 6075.37i | 0.257994 | − | 0.313161i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23310.9 | − | 4545.52i | 1.19660 | − | 0.233333i | ||||
\(725\) | −17200.8 | −0.881134 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27835.1 | −1.42001 | −0.710006 | − | 0.704196i | \(-0.751308\pi\) | ||||
−0.710006 | + | 0.704196i | \(0.751308\pi\) | |||||||
\(728\) | −21606.2 | − | 21305.3i | −1.09997 | − | 1.08465i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 37315.3 | − | 45294.4i | 1.89192 | − | 2.29647i | ||||
\(731\) | −1431.23 | −0.0724159 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 26967.4i | − | 1.35889i | −0.733727 | − | 0.679444i | \(-0.762221\pi\) | ||
0.733727 | − | 0.679444i | \(-0.237779\pi\) | |||||||
\(734\) | 21306.3 | − | 25862.2i | 1.07143 | − | 1.30053i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27689.3 | + | 8685.29i | 1.38674 | + | 0.434978i | ||||
\(737\) | −7196.81 | −0.359699 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4459.65i | − | 0.221990i | −0.993821 | − | 0.110995i | \(-0.964596\pi\) | ||
0.993821 | − | 0.110995i | \(-0.0354038\pi\) | |||||||
\(740\) | 19491.6 | − | 3800.79i | 0.968279 | − | 0.188810i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14857.2 | − | 21724.6i | −0.735074 | − | 1.07484i | ||||
\(743\) | 9276.26i | 0.458026i | 0.973423 | + | 0.229013i | \(0.0735498\pi\) | ||||
−0.973423 | + | 0.229013i | \(0.926450\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 40417.1i | − | 1.98761i | ||||||
\(746\) | 18543.1 | − | 22508.2i | 0.910071 | − | 1.10467i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1035.67 | − | 5311.27i | −0.0506257 | − | 0.259625i | ||||
\(749\) | −26517.5 | − | 7678.54i | −1.29363 | − | 0.374590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6411.40i | 0.311525i | 0.987795 | + | 0.155763i | \(0.0497835\pi\) | ||||
−0.987795 | + | 0.155763i | \(0.950217\pi\) | |||||||
\(752\) | −28709.4 | + | 11639.0i | −1.39219 | + | 0.564402i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14249.3 | + | 11739.2i | 0.688237 | + | 0.566996i | ||||
\(755\) | −39495.0 | −1.90380 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18447.3 | 0.885705 | 0.442853 | − | 0.896594i | \(-0.353967\pi\) | ||||
0.442853 | + | 0.896594i | \(0.353967\pi\) | |||||||
\(758\) | −8430.68 | − | 6945.52i | −0.403979 | − | 0.332814i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18809.7 | + | 34716.8i | −0.897763 | + | 1.65699i | ||||
\(761\) | − | 31940.7i | − | 1.52149i | −0.649054 | − | 0.760743i | \(-0.724835\pi\) | ||
0.649054 | − | 0.760743i | \(-0.275165\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2860.71 | − | 9879.31i | 0.135733 | − | 0.468749i | ||||
\(764\) | 18933.0 | − | 3691.86i | 0.896560 | − | 0.174825i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16507.0 | + | 20036.7i | −0.778618 | + | 0.945110i | ||||
\(767\) | − | 10732.9i | − | 0.505270i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4067.55i | − | 0.190740i | −0.995442 | − | 0.0953702i | \(-0.969597\pi\) | ||
0.995442 | − | 0.0953702i | \(-0.0304035\pi\) | |||||||
\(770\) | 5664.43 | + | 8282.68i | 0.265107 | + | 0.387646i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3729.38 | − | 19125.5i | −0.173865 | − | 0.891632i | ||||
\(773\) | − | 21053.6i | − | 0.979620i | −0.871829 | − | 0.489810i | \(-0.837066\pi\) | ||
0.871829 | − | 0.489810i | \(-0.162934\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38516.7 | 1.78524 | ||||||||
\(776\) | −2292.91 | + | 4231.99i | −0.106071 | + | 0.195773i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 565.410 | − | 686.312i | 0.0260552 | − | 0.0316266i | ||||
\(779\) | − | 29172.8i | − | 1.34175i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1877.64 | −0.0860272 | ||||||||
\(782\) | 18092.2 | − | 21960.8i | 0.827333 | − | 1.00424i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21603.0 | + | 3898.84i | 0.984101 | + | 0.177607i | ||||
\(785\) | 2813.87 | 0.127938 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15197.8 | −0.688367 | −0.344183 | − | 0.938902i | \(-0.611844\pi\) | ||||
−0.344183 | + | 0.938902i | \(0.611844\pi\) | |||||||
\(788\) | 3196.54 | + | 16392.9i | 0.144508 | + | 0.741082i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21746.8 | − | 26396.9i | 0.979387 | − | 1.18881i | ||||
\(791\) | 386.862 | − | 1336.01i | 0.0173897 | − | 0.0600544i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31784.2 | 1.42331 | ||||||||
\(794\) | 4643.03 | + | 3825.11i | 0.207525 | + | 0.170967i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5188.72 | − | 26609.4i | −0.231042 | − | 1.18485i | ||||
\(797\) | − | 3899.94i | − | 0.173329i | −0.996238 | − | 0.0866644i | \(-0.972379\pi\) | ||
0.996238 | − | 0.0866644i | \(-0.0276208\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30374.8i | 1.34491i | ||||||||
\(800\) | 10337.6 | − | 32956.9i | 0.456861 | − | 1.45650i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11701.3 | − | 14203.4i | 0.515196 | − | 0.625361i | ||||
\(803\) | 12585.2 | 0.553079 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14675.3 | + | 50680.4i | −0.642530 | + | 2.21895i | ||||
\(806\) | −31907.6 | − | 26286.7i | −1.39441 | − | 1.14877i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9661.33 | + | 17831.8i | −0.420649 | + | 0.776386i | ||||
\(809\) | −21045.2 | −0.914600 | −0.457300 | − | 0.889313i | \(-0.651183\pi\) | ||||
−0.457300 | + | 0.889313i | \(0.651183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16381.3 | −0.709279 | −0.354640 | − | 0.935003i | \(-0.615396\pi\) | ||||
−0.354640 | + | 0.935003i | \(0.615396\pi\) | |||||||
\(812\) | −13303.1 | − | 1190.83i | −0.574936 | − | 0.0514655i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3286.94 | + | 2707.91i | 0.141532 | + | 0.116600i | ||||
\(815\) | 26089.9 | 1.12134 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2239.59i | 0.0959036i | ||||||||
\(818\) | 7162.29 | + | 5900.57i | 0.306141 | + | 0.252211i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8083.85 | + | 41456.6i | 0.344269 | + | 1.76552i | ||||
\(821\) | −11681.1 | −0.496556 | −0.248278 | − | 0.968689i | \(-0.579865\pi\) | ||||
−0.248278 | + | 0.968689i | \(0.579865\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33978.6i | 1.43915i | 0.694416 | + | 0.719574i | \(0.255663\pi\) | ||||
−0.694416 | + | 0.719574i | \(0.744337\pi\) | |||||||
\(824\) | −26254.4 | − | 14224.8i | −1.10997 | − | 0.601388i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4383.16 | + | 6409.17i | 0.184636 | + | 0.269980i | ||||
\(827\) | 40342.5i | 1.69631i | 0.529750 | + | 0.848154i | \(0.322286\pi\) | ||||
−0.529750 | + | 0.848154i | \(0.677714\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23175.7i | 0.970960i | 0.874248 | + | 0.485480i | \(0.161355\pi\) | ||||
−0.874248 | + | 0.485480i | \(0.838645\pi\) | |||||||
\(830\) | 30279.1 | + | 24945.1i | 1.26627 | + | 1.04320i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −31056.1 | + | 20246.7i | −1.29408 | + | 0.843664i | ||||
\(833\) | 11500.8 | − | 18193.6i | 0.478367 | − | 0.756749i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 44944.6i | − | 1.86272i | ||||||
\(836\) | −8311.05 | + | 1620.62i | −0.343832 | + | 0.0670458i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2361.62 | − | 2866.61i | 0.0973519 | − | 0.118169i | ||||
\(839\) | −3793.64 | −0.156104 | −0.0780519 | − | 0.996949i | \(-0.524870\pi\) | ||||
−0.0780519 | + | 0.996949i | \(0.524870\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16262.6 | −0.666800 | ||||||||
\(842\) | 13793.3 | − | 16742.7i | 0.564546 | − | 0.685263i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −36235.2 | + | 7065.71i | −1.47780 | + | 0.288165i | ||||
\(845\) | 54129.8i | 2.20369i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6257.74 | − | 21610.8i | 0.253859 | − | 0.876690i | ||||
\(848\) | −29800.0 | + | 12081.1i | −1.20676 | + | 0.489230i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −26138.6 | − | 21534.0i | −1.05476 | − | 0.868954i | ||||
\(851\) | 22393.1i | 0.902028i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 18804.2i | − | 0.754798i | −0.926051 | − | 0.377399i | \(-0.876819\pi\) | ||
0.926051 | − | 0.377399i | \(-0.123181\pi\) | |||||||
\(854\) | −18980.0 | + | 12980.2i | −0.760516 | + | 0.520109i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16067.7 | + | 29656.0i | −0.641570 | + | 1.18414i | ||||
\(857\) | 950.192i | 0.0378739i | 0.999821 | + | 0.0189370i | \(0.00602818\pi\) | ||||
−0.999821 | + | 0.0189370i | \(0.993972\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12509.1 | −0.496862 | −0.248431 | − | 0.968650i | \(-0.579915\pi\) | ||||
−0.248431 | + | 0.968650i | \(0.579915\pi\) | |||||||
\(860\) | −620.595 | − | 3182.61i | −0.0246071 | − | 0.126193i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5152.98 | − | 4245.23i | −0.203609 | − | 0.167741i | ||||
\(863\) | − | 7301.04i | − | 0.287984i | −0.989579 | − | 0.143992i | \(-0.954006\pi\) | ||
0.989579 | − | 0.143992i | \(-0.0459940\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14822.2 | −0.582622 | ||||||||
\(866\) | −10729.0 | − | 8838.94i | −0.420999 | − | 0.346835i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 29788.8 | + | 2666.55i | 1.16486 | + | 0.104273i | ||||
\(869\) | 7334.47 | 0.286312 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48344.0 | 1.88068 | ||||||||
\(872\) | −11048.6 | − | 5986.18i | −0.429074 | − | 0.232474i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −34364.2 | − | 28310.5i | −1.32996 | − | 1.09567i | ||||
\(875\) | 20804.8 | + | 6024.34i | 0.803805 | + | 0.232754i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15791.2 | −0.608017 | −0.304009 | − | 0.952669i | \(-0.598325\pi\) | ||||
−0.304009 | + | 0.952669i | \(0.598325\pi\) | |||||||
\(878\) | 5997.45 | − | 7279.88i | 0.230528 | − | 0.279822i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11361.5 | − | 4606.02i | 0.435223 | − | 0.176442i | ||||
\(881\) | 5782.40i | 0.221128i | 0.993869 | + | 0.110564i | \(0.0352657\pi\) | ||||
−0.993869 | + | 0.110564i | \(0.964734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16075.8i | 0.612675i | 0.951923 | + | 0.306338i | \(0.0991037\pi\) | ||||
−0.951923 | + | 0.306338i | \(0.900896\pi\) | |||||||
\(884\) | 6957.06 | + | 35678.0i | 0.264696 | + | 1.35745i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7838.28 | − | 6457.48i | −0.297215 | − | 0.244857i | ||||
\(887\) | −6165.28 | −0.233382 | −0.116691 | − | 0.993168i | \(-0.537229\pi\) | ||||
−0.116691 | + | 0.993168i | \(0.537229\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −257.358 | − | 74.5219i | −0.00970923 | − | 0.00281146i | ||||
\(890\) | 869.633 | − | 1055.59i | 0.0327530 | − | 0.0397566i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −451.564 | − | 2315.76i | −0.0169501 | − | 0.0869253i | ||||
\(893\) | 47530.3 | 1.78112 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37222.6 | 1.39018 | ||||||||
\(896\) | 10276.7 | − | 24773.2i | 0.383171 | − | 0.923677i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 27275.8 | − | 33108.2i | 1.01359 | − | 1.23033i | ||||
\(899\) | −18196.9 | −0.675086 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31528.6i | 1.16578i | ||||||||
\(902\) | −5759.42 | + | 6990.96i | −0.212603 | + | 0.258064i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1494.13 | − | 809.528i | −0.0549714 | − | 0.0297838i | ||||
\(905\) | 52757.5 | 1.93781 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24380.1i | 0.892534i | 0.894900 | + | 0.446267i | \(0.147247\pi\) | ||||
−0.894900 | + | 0.446267i | \(0.852753\pi\) | |||||||
\(908\) | 3478.73 | + | 17840.0i | 0.127143 | + | 0.652029i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −38050.4 | − | 55638.2i | −1.38611 | − | 2.02680i | ||||
\(911\) | 9713.23i | 0.353253i | 0.984278 | + | 0.176627i | \(0.0565185\pi\) | ||||
−0.984278 | + | 0.176627i | \(0.943482\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8413.16i | 0.304967i | ||||||||
\(914\) | −27143.7 | + | 32947.9i | −0.982314 | + | 1.19236i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23985.6 | − | 4677.10i | 0.865182 | − | 0.168707i | ||||
\(917\) | −12264.4 | + | 42354.4i | −0.441663 | + | 1.52526i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 12841.3i | − | 0.460931i | −0.973081 | − | 0.230465i | \(-0.925975\pi\) | ||
0.973081 | − | 0.230465i | \(-0.0740248\pi\) | |||||||
\(920\) | 56678.8 | + | 30708.8i | 2.03114 | + | 1.10048i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2909.88 | − | 2397.28i | −0.103939 | − | 0.0856291i | ||||
\(923\) | 12612.9 | 0.449792 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26653.2 | 0.947406 | ||||||||
\(926\) | 22885.7 | + | 18854.1i | 0.812173 | + | 0.669099i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4883.92 | + | 15570.3i | −0.172761 | + | 0.550775i | ||||
\(929\) | − | 21623.8i | − | 0.763677i | −0.924229 | − | 0.381838i | \(-0.875291\pi\) | ||
0.924229 | − | 0.381838i | \(-0.124709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28469.3 | − | 17996.4i | −1.00220 | − | 0.633522i | ||||
\(932\) | 5017.76 | + | 25732.6i | 0.176354 | + | 0.904399i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28711.1 | + | 34850.4i | −1.00584 | + | 1.22092i | ||||
\(935\) | − | 12020.5i | − | 0.420443i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18396.5i | 0.641395i | 0.947182 | + | 0.320697i | \(0.103917\pi\) | ||||
−0.947182 | + | 0.320697i | \(0.896083\pi\) | |||||||
\(938\) | −28868.7 | + | 19743.0i | −1.00490 | + | 0.687240i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −67543.9 | + | 13170.8i | −2.34366 | + | 0.457004i | ||||
\(941\) | − | 43692.9i | − | 1.51365i | −0.653615 | − | 0.756827i | \(-0.726748\pi\) | ||
0.653615 | − | 0.756827i | \(-0.273252\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47627.7 | −1.64472 | ||||||||
\(944\) | 8791.56 | − | 3564.16i | 0.303116 | − | 0.122885i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 442.149 | − | 536.694i | 0.0151961 | − | 0.0184455i | ||||
\(947\) | − | 6009.34i | − | 0.206206i | −0.994671 | − | 0.103103i | \(-0.967123\pi\) | ||
0.994671 | − | 0.103103i | \(-0.0328772\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −84540.1 | −2.89177 | ||||||||
\(950\) | −33696.3 | + | 40901.6i | −1.15079 | + | 1.39687i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18724.8 | − | 18464.0i | −0.637473 | − | 0.628595i | ||||
\(953\) | 7869.39 | 0.267486 | 0.133743 | − | 0.991016i | \(-0.457300\pi\) | ||||
0.133743 | + | 0.991016i | \(0.457300\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42849.5 | 1.45191 | ||||||||
\(956\) | 45355.9 | − | 8844.22i | 1.53443 | − | 0.299208i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34984.0 | + | 42464.6i | −1.17983 | + | 1.43212i | ||||
\(959\) | −910.272 | + | 3143.58i | −0.0306509 | + | 0.105851i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10956.2 | 0.367770 | ||||||||
\(962\) | −22079.8 | − | 18190.2i | −0.740000 | − | 0.609641i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2524.21 | − | 492.211i | 0.0843356 | − | 0.0164451i | ||||
\(965\) | − | 43285.0i | − | 1.44393i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22172.9i | − | 0.737365i | −0.929555 | − | 0.368682i | \(-0.879809\pi\) | ||
0.929555 | − | 0.368682i | \(-0.120191\pi\) | |||||||
\(968\) | −24168.6 | − | 13094.6i | −0.802487 | − | 0.434791i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6798.51 | + | 8252.23i | −0.225038 | + | 0.273158i | ||||
\(971\) | −23116.1 | −0.763988 | −0.381994 | − | 0.924165i | \(-0.624762\pi\) | ||||
−0.381994 | + | 0.924165i | \(0.624762\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1910.52 | + | 6597.89i | −0.0629481 | + | 0.217388i | ||||
\(974\) | 18481.1 | + | 15225.4i | 0.607980 | + | 0.500877i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10554.8 | + | 26035.1i | 0.346159 | + | 0.853857i | ||||
\(977\) | −6112.67 | −0.200166 | −0.100083 | − | 0.994979i | \(-0.531911\pi\) | ||||
−0.100083 | + | 0.994979i | \(0.531911\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 293.298 | 0.00957493 | ||||||||
\(980\) | 45443.7 | + | 17685.2i | 1.48127 | + | 0.576464i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15663.7 | + | 12904.4i | 0.509011 | + | 0.419343i | ||||
\(983\) | −42147.1 | −1.36753 | −0.683766 | − | 0.729702i | \(-0.739659\pi\) | ||||
−0.683766 | + | 0.729702i | \(0.739659\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37100.6i | 1.20013i | ||||||||
\(986\) | 12349.0 | + | 10173.6i | 0.398857 | + | 0.328594i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 55828.8 | − | 10886.4i | 1.79772 | − | 0.350549i | ||||
\(989\) | 3656.36 | 0.117559 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3294.51i | 0.105604i | 0.998605 | + | 0.0528020i | \(0.0168152\pi\) | ||||
−0.998605 | + | 0.0528020i | \(0.983185\pi\) | |||||||
\(992\) | 10936.2 | − | 34865.5i | 0.350026 | − | 1.11591i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7531.81 | + | 5150.92i | −0.240337 | + | 0.164364i | ||||
\(995\) | − | 60222.8i | − | 1.91878i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 54852.2i | − | 1.74241i | −0.490915 | − | 0.871207i | \(-0.663338\pi\) | ||
0.490915 | − | 0.871207i | \(-0.336662\pi\) | |||||||
\(998\) | −38211.3 | − | 31480.0i | −1.21198 | − | 0.998477i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.4.b.g.55.9 | yes | 16 | |
3.2 | odd | 2 | inner | 252.4.b.g.55.8 | yes | 16 | |
4.3 | odd | 2 | inner | 252.4.b.g.55.11 | yes | 16 | |
7.6 | odd | 2 | inner | 252.4.b.g.55.10 | yes | 16 | |
12.11 | even | 2 | inner | 252.4.b.g.55.6 | yes | 16 | |
21.20 | even | 2 | inner | 252.4.b.g.55.7 | yes | 16 | |
28.27 | even | 2 | inner | 252.4.b.g.55.12 | yes | 16 | |
84.83 | odd | 2 | inner | 252.4.b.g.55.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.b.g.55.5 | ✓ | 16 | 84.83 | odd | 2 | inner | |
252.4.b.g.55.6 | yes | 16 | 12.11 | even | 2 | inner | |
252.4.b.g.55.7 | yes | 16 | 21.20 | even | 2 | inner | |
252.4.b.g.55.8 | yes | 16 | 3.2 | odd | 2 | inner | |
252.4.b.g.55.9 | yes | 16 | 1.1 | even | 1 | trivial | |
252.4.b.g.55.10 | yes | 16 | 7.6 | odd | 2 | inner | |
252.4.b.g.55.11 | yes | 16 | 4.3 | odd | 2 | inner | |
252.4.b.g.55.12 | yes | 16 | 28.27 | even | 2 | inner |