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 | 55.8 | ||
Root | \(4.06402 + 0.600106i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.55 |
Dual form | 252.4.b.g.55.5 |
$q$-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 | \(0.292395\pi\) | ||||
−0.606944 | + | 0.794744i | \(0.707605\pi\) | |||||||
\(6\) | 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 | \(0.0471964\pi\) | ||||
−0.989028 | + | 0.147729i | \(0.952804\pi\) | |||||||
\(12\) | 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 | \(-0.852267\pi\) | ||
0.894217 | − | 0.447634i | \(-0.147733\pi\) | |||||||
\(18\) | 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 | \(0.258938\pi\) | ||||
−0.686976 | + | 0.726680i | \(0.741062\pi\) | |||||||
\(24\) | 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 | \(-0.593196\pi\) | ||||
−0.288617 | + | 0.957445i | \(0.593196\pi\) | |||||||
\(30\) | 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 | \(0.191445\pi\) | ||||
−0.824520 | + | 0.565833i | \(0.808555\pi\) | |||||||
\(42\) | 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 | \(-0.770487\pi\) | ||||
−0.751122 | + | 0.660164i | \(0.770487\pi\) | |||||||
\(48\) | 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 | \(-0.725684\pi\) | ||||
−0.651081 | + | 0.759009i | \(0.725684\pi\) | |||||||
\(54\) | 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 | \(-0.447709\pi\) | ||||
0.163539 | + | 0.986537i | \(0.447709\pi\) | |||||||
\(60\) | 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 | \(0.0465056\pi\) | ||||
−0.989346 | + | 0.145582i | \(0.953494\pi\) | |||||||
\(72\) | 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 | \(-0.327386\pi\) | ||||
0.516091 | + | 0.856534i | \(0.327386\pi\) | |||||||
\(84\) | 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 | \(-0.994842\pi\) | ||
0.999869 | − | 0.0162035i | \(-0.00515796\pi\) | |||||||
\(90\) | 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 | \(0.145557\pi\) | ||||
−0.897257 | + | 0.441509i | \(0.854443\pi\) | |||||||
\(102\) | 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 | \(0.235160\pi\) | ||||
−0.739292 | + | 0.673385i | \(0.764840\pi\) | |||||||
\(108\) | 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 | \(-0.509952\pi\) | ||||
−0.0312607 | + | 0.999511i | \(0.509952\pi\) | |||||||
\(114\) | 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 | \(-0.208016\pi\) | ||||
0.793960 | + | 0.607970i | \(0.208016\pi\) | |||||||
\(132\) | 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 | \(-0.482452\pi\) | ||||
0.0550999 | + | 0.998481i | \(0.482452\pi\) | |||||||
\(138\) | 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 | \(-0.714997\pi\) | ||||
−0.625234 | + | 0.780437i | \(0.714997\pi\) | |||||||
\(150\) | 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 | \(-0.699279\pi\) | ||||
−0.585950 | + | 0.810347i | \(0.699279\pi\) | |||||||
\(168\) | 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 | \(0.0586694\pi\) | ||||
−0.983062 | + | 0.183273i | \(0.941331\pi\) | |||||||
\(174\) | 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 | \(-0.855933\pi\) | ||
0.899313 | − | 0.437305i | \(-0.144067\pi\) | |||||||
\(180\) | 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 | \(-0.849023\pi\) | ||
0.889609 | − | 0.456723i | \(-0.150977\pi\) | |||||||
\(192\) | 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 | \(-0.376777\pi\) | ||||
0.377520 | + | 0.926002i | \(0.376777\pi\) | |||||||
\(198\) | 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 | \(-0.392224\pi\) | ||||
0.332155 | + | 0.943225i | \(0.392224\pi\) | |||||||
\(228\) | 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 | \(-0.347592\pi\) | ||||
0.460717 | + | 0.887547i | \(0.347592\pi\) | |||||||
\(234\) | 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 | \(-0.714371\pi\) | ||
0.623698 | − | 0.781665i | \(-0.285629\pi\) | |||||||
\(240\) | 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 | \(-0.573415\pi\) | ||||
−0.228600 | + | 0.973520i | \(0.573415\pi\) | |||||||
\(252\) | 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 | \(-0.904376\pi\) | ||
0.955215 | − | 0.295912i | \(-0.0956236\pi\) | |||||||
\(258\) | 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 | \(0.158893\pi\) | ||||
−0.877977 | + | 0.478703i | \(0.841107\pi\) | |||||||
\(264\) | 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 | \(0.0772888\pi\) | ||||
−0.970666 | + | 0.240431i | \(0.922711\pi\) | |||||||
\(270\) | 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 | \(-0.720372\pi\) | ||||
−0.638325 | + | 0.769767i | \(0.720372\pi\) | |||||||
\(282\) | 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 | \(0.0718738\pi\) | ||||
−0.974616 | + | 0.223884i | \(0.928126\pi\) | |||||||
\(294\) | 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 | \(-0.533599\pi\) | ||||
−0.105358 | + | 0.994434i | \(0.533599\pi\) | |||||||
\(312\) | 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 | \(-0.388411\pi\) | ||||
0.343431 | + | 0.939178i | \(0.388411\pi\) | |||||||
\(318\) | 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 | \(0.313499\pi\) | ||||
−0.552959 | + | 0.833209i | \(0.686501\pi\) | |||||||
\(348\) | 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 | \(-0.889114\pi\) | ||
0.939935 | − | 0.341355i | \(-0.110886\pi\) | |||||||
\(354\) | 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 | \(-0.742822\pi\) | ||
0.690983 | − | 0.722871i | \(-0.257178\pi\) | |||||||
\(360\) | 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 | \(-0.290258\pi\) | ||||
0.612266 | + | 0.790652i | \(0.290258\pi\) | |||||||
\(384\) | 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 | \(-0.506522\pi\) | ||||
−0.0204885 | + | 0.999790i | \(0.506522\pi\) | |||||||
\(390\) | 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 | \(-0.632772\pi\) | ||||
−0.405125 | + | 0.914261i | \(0.632772\pi\) | |||||||
\(402\) | 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 | \(-0.524391\pi\) | ||||
−0.0765526 | + | 0.997066i | \(0.524391\pi\) | |||||||
\(420\) | 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 | \(0.0421088\pi\) | ||||
−0.991263 | + | 0.131903i | \(0.957891\pi\) | |||||||
\(432\) | 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 | \(0.0616736\pi\) | ||||
−0.981288 | + | 0.192543i | \(0.938326\pi\) | |||||||
\(444\) | 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 | \(-0.793600\pi\) | ||||
−0.797037 | + | 0.603931i | \(0.793600\pi\) | |||||||
\(450\) | 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 | \(0.0214494\pi\) | ||||
−0.997730 | + | 0.0673344i | \(0.978551\pi\) | |||||||
\(462\) | 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 | \(-0.209591\pi\) | ||||
0.790942 | + | 0.611891i | \(0.209591\pi\) | |||||||
\(468\) | 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 | \(-0.121729\pi\) | ||||
0.927763 | + | 0.373170i | \(0.121729\pi\) | |||||||
\(480\) | 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 | \(-0.893035\pi\) | ||
0.944068 | − | 0.329750i | \(-0.106965\pi\) | |||||||
\(492\) | 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 | \(-0.751598\pi\) | ||||
−0.710648 | + | 0.703548i | \(0.751598\pi\) | |||||||
\(504\) | 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 | \(-0.809660\pi\) | ||
0.826480 | − | 0.562965i | \(-0.190340\pi\) | |||||||
\(510\) | 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 | \(-0.687759\pi\) | ||
0.556245 | − | 0.831018i | \(-0.312241\pi\) | |||||||
\(522\) | 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 | \(-0.220639\pi\) | ||||
0.769231 | + | 0.638971i | \(0.220639\pi\) | |||||||
\(558\) | 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 | \(-0.338626\pi\) | ||||
0.485531 | + | 0.874220i | \(0.338626\pi\) | |||||||
\(564\) | 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 | \(-0.482974\pi\) | ||||
0.0534638 | + | 0.998570i | \(0.482974\pi\) | |||||||
\(570\) | 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 | \(-0.581600\pi\) | ||||
−0.253557 | + | 0.967321i | \(0.581600\pi\) | |||||||
\(588\) | 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 | \(0.219325\pi\) | ||||
−0.771863 | + | 0.635789i | \(0.780675\pi\) | |||||||
\(594\) | 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 | \(0.0261118\pi\) | ||||
−0.996637 | + | 0.0819407i | \(0.973888\pi\) | |||||||
\(600\) | 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 | \(-0.536736\pi\) | ||||
−0.115153 | + | 0.993348i | \(0.536736\pi\) | |||||||
\(618\) | 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 | \(-0.418459\pi\) | ||||
0.253376 | + | 0.967368i | \(0.418459\pi\) | |||||||
\(642\) | 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 | \(-0.832725\pi\) | ||||
−0.865068 | + | 0.501654i | \(0.832725\pi\) | |||||||
\(648\) | 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 | \(-0.864696\pi\) | ||||
−0.911009 | + | 0.412386i | \(0.864696\pi\) | |||||||
\(654\) | 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 | \(-0.739244\pi\) | ||
0.682814 | − | 0.730592i | \(-0.260756\pi\) | |||||||
\(660\) | 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 | \(-0.693225\pi\) | ||
0.570435 | − | 0.821343i | \(-0.306775\pi\) | |||||||
\(678\) | 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 | \(0.0519148\pi\) | ||||
−0.986729 | + | 0.162373i | \(0.948085\pi\) | |||||||
\(684\) | 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 | \(-0.0829721\pi\) | ||||
0.966219 | + | 0.257723i | \(0.0829721\pi\) | |||||||
\(702\) | 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 | \(-0.705785\pi\) | ||||
−0.602391 | + | 0.798201i | \(0.705785\pi\) | |||||||
\(720\) | 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 | \(-0.926450\pi\) | ||
0.973423 | − | 0.229013i | \(-0.0735498\pi\) | |||||||
\(744\) | 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 | \(0.275165\pi\) | ||||
−0.649054 | + | 0.760743i | \(0.724835\pi\) | |||||||
\(762\) | 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 | \(0.162934\pi\) | ||||
−0.871829 | + | 0.489810i | \(0.837066\pi\) | |||||||
\(774\) | 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 | \(0.0276208\pi\) | ||||
−0.996238 | + | 0.0866644i | \(0.972379\pi\) | |||||||
\(798\) | 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 | \(-0.348817\pi\) | ||||
0.457300 | + | 0.889313i | \(0.348817\pi\) | |||||||
\(810\) | 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 | \(-0.420135\pi\) | ||||
0.248278 | + | 0.968689i | \(0.420135\pi\) | |||||||
\(822\) | 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 | \(-0.677714\pi\) | ||
0.529750 | − | 0.848154i | \(-0.322286\pi\) | |||||||
\(828\) | 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 | \(-0.475130\pi\) | ||||
0.0780519 | + | 0.996949i | \(0.475130\pi\) | |||||||
\(840\) | 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 | \(-0.993972\pi\) | ||
0.999821 | − | 0.0189370i | \(-0.00602818\pi\) | |||||||
\(858\) | 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 | \(0.0459940\pi\) | ||||
−0.989579 | + | 0.143992i | \(0.954006\pi\) | |||||||
\(864\) | 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 | \(-0.964734\pi\) | ||
0.993869 | − | 0.110564i | \(-0.0352657\pi\) | |||||||
\(882\) | 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 | \(-0.462771\pi\) | ||||
0.116691 | + | 0.993168i | \(0.462771\pi\) | |||||||
\(888\) | 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 | \(-0.943482\pi\) | ||
0.984278 | − | 0.176627i | \(-0.0565185\pi\) | |||||||
\(912\) | 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 | \(0.124709\pi\) | ||||
−0.924229 | + | 0.381838i | \(0.875291\pi\) | |||||||
\(930\) | 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 | \(0.273252\pi\) | ||||
−0.653615 | + | 0.756827i | \(0.726748\pi\) | |||||||
\(942\) | 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 | \(0.0328772\pi\) | ||||
−0.994671 | + | 0.103103i | \(0.967123\pi\) | |||||||
\(948\) | 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 | \(-0.542700\pi\) | ||||
−0.133743 | + | 0.991016i | \(0.542700\pi\) | |||||||
\(954\) | 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 | \(-0.375238\pi\) | ||||
0.381994 | + | 0.924165i | \(0.375238\pi\) | |||||||
\(972\) | 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 | \(-0.468089\pi\) | ||||
0.100083 | + | 0.994979i | \(0.468089\pi\) | |||||||
\(978\) | 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 | \(-0.260341\pi\) | ||||
0.683766 | + | 0.729702i | \(0.260341\pi\) | |||||||
\(984\) | 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.55.8 | yes | 16 | |
3.2 | odd | 2 | inner | 252.4.b.g.55.9 | yes | 16 | |
4.3 | odd | 2 | inner | 252.4.b.g.55.6 | yes | 16 | |
7.6 | odd | 2 | inner | 252.4.b.g.55.7 | yes | 16 | |
12.11 | even | 2 | inner | 252.4.b.g.55.11 | yes | 16 | |
21.20 | even | 2 | inner | 252.4.b.g.55.10 | yes | 16 | |
28.27 | even | 2 | inner | 252.4.b.g.55.5 | ✓ | 16 | |
84.83 | odd | 2 | inner | 252.4.b.g.55.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.b.g.55.5 | ✓ | 16 | 28.27 | even | 2 | inner | |
252.4.b.g.55.6 | yes | 16 | 4.3 | odd | 2 | inner | |
252.4.b.g.55.7 | yes | 16 | 7.6 | odd | 2 | inner | |
252.4.b.g.55.8 | yes | 16 | 1.1 | even | 1 | trivial | |
252.4.b.g.55.9 | yes | 16 | 3.2 | odd | 2 | inner | |
252.4.b.g.55.10 | yes | 16 | 21.20 | even | 2 | inner | |
252.4.b.g.55.11 | yes | 16 | 12.11 | even | 2 | inner | |
252.4.b.g.55.12 | yes | 16 | 84.83 | odd | 2 | inner |