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 | 55.10 | ||
Root | \(0.467111 + 1.75957i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.55 |
Dual form | 252.4.b.g.55.11 |
$q$-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 | \(-0.952804\pi\) | ||
0.989028 | − | 0.147729i | \(-0.0471964\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 72.4083i | − | 1.54480i | −0.635135 | − | 0.772402i | \(-0.719055\pi\) | ||
0.635135 | − | 0.772402i | \(-0.280945\pi\) | |||||||
\(14\) | −48.0989 | − | 20.7483i | −0.918213 | − | 0.396088i | ||||
\(15\) | 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 | \(-0.701986\pi\) | ||||
−0.592821 | + | 0.805334i | \(0.701986\pi\) | |||||||
\(20\) | 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 | ||||||||
\(28\) | −131.798 | + | 67.6859i | −0.889551 | + | 0.456837i | ||||
\(29\) | 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 | \(-0.301189\pi\) | ||||
0.584759 | + | 0.811207i | \(0.301189\pi\) | |||||||
\(32\) | −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 | \(-0.274316\pi\) | ||||
0.651081 | + | 0.759009i | \(0.274316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 191.557 | 0.469628 | ||||||||
\(56\) | −89.2726 | + | 409.446i | −0.213028 | + | 0.977046i | ||||
\(57\) | 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 | \(0.152394\pi\) | ||||
−0.887567 | + | 0.460678i | \(0.847606\pi\) | |||||||
\(62\) | 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 | ||||||||
\(70\) | 368.719 | − | 854.767i | 0.629577 | − | 1.45949i | ||||
\(71\) | − | 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 | \(-0.614528\pi\) | ||
0.352088 | − | 0.935967i | \(-0.385472\pi\) | |||||||
\(74\) | −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 | \(0.0355112\pi\) | ||||
−0.993783 | + | 0.111331i | \(0.964489\pi\) | |||||||
\(98\) | −121.334 | + | 962.533i | −0.125067 | + | 0.992148i | ||||
\(99\) | 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 | \(-0.717441\pi\) | ||||
−0.631210 | + | 0.775612i | \(0.717441\pi\) | |||||||
\(104\) | −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 | ||||||||
\(112\) | 733.276 | + | 931.254i | 0.618644 | + | 0.785672i | ||||
\(113\) | 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 | \(-0.208016\pi\) | ||||
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 | \(-0.517548\pi\) | ||||
−0.0550999 | + | 0.998481i | \(0.517548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 370.887 | 0.226318 | 0.113159 | − | 0.993577i | \(-0.463903\pi\) | ||||
0.113159 | + | 0.993577i | \(0.463903\pi\) | |||||||
\(140\) | −1202.85 | − | 2342.18i | −0.726137 | − | 1.41393i | ||||
\(141\) | 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 | ||||||||
\(154\) | −223.650 | + | 518.467i | −0.117027 | + | 0.271294i | ||||
\(155\) | 3587.25i | 1.85893i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 158.340i | − | 0.0804901i | −0.999190 | − | 0.0402450i | \(-0.987186\pi\) | ||
0.999190 | − | 0.0402450i | \(-0.0128139\pi\) | |||||||
\(158\) | 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 | \(0.144067\pi\) | ||||
−0.899313 | + | 0.437305i | \(0.855933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2968.74i | − | 1.21914i | −0.792732 | − | 0.609571i | \(-0.791342\pi\) | ||
0.792732 | − | 0.609571i | \(-0.208658\pi\) | |||||||
\(182\) | −1502.35 | + | 3482.76i | −0.611877 | + | 1.41846i | ||||
\(183\) | 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 | ||||||||
\(196\) | 1883.01 | + | 1995.95i | 0.686229 | + | 0.727385i | ||||
\(197\) | −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 | \(-0.706262\pi\) | ||||
−0.603585 | + | 0.797299i | \(0.706262\pi\) | |||||||
\(200\) | 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 | \(-0.514100\pi\) | ||||
−0.0442812 | + | 0.999019i | \(0.514100\pi\) | |||||||
\(224\) | 3351.71 | + | 74.0629i | 0.999756 | + | 0.0220917i | ||||
\(225\) | 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 | \(-0.854717\pi\) | ||
0.897635 | − | 0.440739i | \(-0.145283\pi\) | |||||||
\(230\) | 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 | ||||||||
\(238\) | −1302.00 | + | 3018.29i | −0.354604 | + | 0.822046i | ||||
\(239\) | 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 | \(-0.986321\pi\) | ||
0.999077 | − | 0.0429620i | \(-0.0136794\pi\) | |||||||
\(242\) | 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 | \(-0.841107\pi\) | ||
0.877977 | − | 0.478703i | \(-0.158893\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8928.76i | 2.06977i | ||||||||
\(266\) | 4723.01 | + | 2037.36i | 1.08867 | + | 0.469618i | ||||
\(267\) | 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 | \(-0.218720\pi\) | ||||
0.773070 | + | 0.634321i | \(0.218720\pi\) | |||||||
\(272\) | 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 | ||||||||
\(280\) | −7276.28 | − | 1586.47i | −1.55300 | − | 0.338605i | ||||
\(281\) | 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 | \(-0.584072\pi\) | ||||
−0.261060 | + | 0.965322i | \(0.584072\pi\) | |||||||
\(284\) | −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 | \(-0.524858\pi\) | ||||
−0.0780141 | + | 0.996952i | \(0.524858\pi\) | |||||||
\(308\) | 729.598 | + | 1420.67i | 0.134976 | + | 0.262825i | ||||
\(309\) | 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 | \(-0.874797\pi\) | ||
0.923636 | − | 0.383272i | \(-0.125203\pi\) | |||||||
\(314\) | −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 | ||||||||
\(322\) | −3326.20 | + | 7710.82i | −0.575658 | + | 1.33449i | ||||
\(323\) | 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 | \(-0.747876\pi\) | ||
0.702373 | − | 0.711809i | \(-0.252124\pi\) | |||||||
\(350\) | 9177.72 | + | 3958.98i | 1.40163 | + | 0.604618i | ||||
\(351\) | 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 | \(0.257178\pi\) | ||||
−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 | ||||||||
\(364\) | 4901.02 | + | 9543.24i | 0.705723 | + | 1.37418i | ||||
\(365\) | 20748.5 | 2.97542 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11847.0 | −1.68504 | −0.842518 | − | 0.538669i | \(-0.818927\pi\) | ||||
−0.842518 | + | 0.538669i | \(0.818927\pi\) | |||||||
\(368\) | 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 | \(-0.493478\pi\) | ||||
0.0204885 | + | 0.999790i | \(0.493478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10059.8 | −1.30115 | ||||||||
\(392\) | 7743.69 | − | 521.035i | 0.997744 | − | 0.0671333i | ||||
\(393\) | 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 | \(-0.957076\pi\) | ||
0.990922 | − | 0.134440i | \(-0.0429236\pi\) | |||||||
\(398\) | −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 | ||||||||
\(406\) | −4335.96 | − | 1870.39i | −0.530024 | − | 0.228635i | ||||
\(407\) | 1505.69i | 0.183376i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3280.91i | − | 0.396652i | −0.980136 | − | 0.198326i | \(-0.936450\pi\) | ||
0.980136 | − | 0.198326i | \(-0.0635505\pi\) | |||||||
\(410\) | −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 | \(-0.957891\pi\) | ||
0.991263 | − | 0.131903i | \(-0.0421088\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4914.75i | 0.545468i | 0.962089 | + | 0.272734i | \(0.0879279\pi\) | ||||
−0.962089 | + | 0.272734i | \(0.912072\pi\) | |||||||
\(434\) | −9709.22 | − | 4188.25i | −1.07387 | − | 0.463231i | ||||
\(435\) | 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 | \(-0.558023\pi\) | ||||
−0.181276 | + | 0.983432i | \(0.558023\pi\) | |||||||
\(440\) | −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 | ||||||||
\(448\) | 6189.57 | − | 7183.64i | 0.652745 | − | 0.757578i | ||||
\(449\) | 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 | \(0.0214494\pi\) | ||||
−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 | ||||||||
\(476\) | 4247.41 | + | 8270.54i | 0.408991 | + | 0.796385i | ||||
\(477\) | 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 | ||||||||
\(490\) | −17105.2 | − | 2156.23i | −1.57701 | − | 0.198793i | ||||
\(491\) | 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 | \(-0.751598\pi\) | ||||
−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 | ||||||||
\(518\) | 6718.69 | + | 2898.23i | 0.569889 | + | 0.245832i | ||||
\(519\) | 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 | \(-0.575848\pi\) | ||||
−0.236036 | + | 0.971744i | \(0.575848\pi\) | |||||||
\(524\) | −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 | ||||||||
\(532\) | 12941.7 | − | 6646.33i | 1.05469 | − | 0.541645i | ||||
\(533\) | 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 | ||||||||
\(560\) | −16549.3 | + | 13031.1i | −1.24882 | + | 0.983327i | ||||
\(561\) | 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 | \(-0.517026\pi\) | ||||
−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 | ||||||||
\(574\) | 6164.21 | − | 14289.9i | 0.448239 | − | 1.03911i | ||||
\(575\) | 30589.0i | 2.21852i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21396.2i | − | 1.54374i | −0.635782 | − | 0.771869i | \(-0.719322\pi\) | ||
0.635782 | − | 0.771869i | \(-0.280678\pi\) | |||||||
\(578\) | 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 | \(-0.973888\pi\) | ||
0.996637 | − | 0.0819407i | \(-0.0261118\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15264.1i | − | 1.03600i | −0.855382 | − | 0.517998i | \(-0.826677\pi\) | ||
0.855382 | − | 0.517998i | \(-0.173323\pi\) | |||||||
\(602\) | 473.225 | − | 1097.03i | 0.0320385 | − | 0.0742719i | ||||
\(603\) | 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 | \(-0.714654\pi\) | ||||
−0.624395 | + | 0.781109i | \(0.714654\pi\) | |||||||
\(608\) | 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 | ||||||||
\(616\) | 4413.50 | + | 962.285i | 0.288677 | + | 0.0629409i | ||||
\(617\) | 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 | \(-0.494237\pi\) | ||||
0.0181037 | + | 0.999836i | \(0.494237\pi\) | |||||||
\(620\) | 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 | \(-0.796381\pi\) | ||||
−0.802283 | + | 0.596944i | \(0.796381\pi\) | |||||||
\(644\) | 10850.8 | + | 21128.7i | 0.663948 | + | 1.29284i | ||||
\(645\) | 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 | \(-0.135304\pi\) | ||||
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 | ||||||||
\(658\) | 23282.1 | + | 10043.2i | 1.37938 | + | 0.595020i | ||||
\(659\) | 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 | \(-0.839099\pi\) | ||
0.874939 | − | 0.484233i | \(-0.160901\pi\) | |||||||
\(662\) | −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 | \(-0.948085\pi\) | ||
0.986729 | − | 0.162373i | \(-0.0519148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3140.32i | − | 0.175161i | ||||||
\(686\) | 17748.0 | − | 2799.75i | 0.987785 | − | 0.155824i | ||||
\(687\) | 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 | \(-0.314681\pi\) | ||||
0.549861 | + | 0.835256i | \(0.314681\pi\) | |||||||
\(692\) | 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 | ||||||||
\(700\) | 25148.2 | − | 12915.1i | 1.35788 | − | 0.697350i | ||||
\(701\) | −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 | \(-0.705785\pi\) | ||||
−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 | \(-0.248692\pi\) | ||||
0.710006 | + | 0.704196i | \(0.248692\pi\) | |||||||
\(728\) | 29647.3 | + | 6464.07i | 1.50934 | + | 0.329086i | ||||
\(729\) | 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 | \(0.237779\pi\) | ||||
−0.733727 | + | 0.679444i | \(0.762221\pi\) | |||||||
\(734\) | −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 | ||||||||
\(742\) | −24166.5 | − | 10424.7i | −1.19566 | − | 0.515770i | ||||
\(743\) | 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 | \(0.275165\pi\) | ||||
−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 | \(0.0304035\pi\) | ||||
−0.995442 | + | 0.0953702i | \(0.969597\pi\) | |||||||
\(770\) | −9213.69 | − | 3974.49i | −0.431218 | − | 0.186014i | ||||
\(771\) | 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 | ||||||||
\(784\) | 12789.2 | − | 17841.7i | 0.582601 | − | 0.812759i | ||||
\(785\) | 2813.87 | 0.127938 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15197.8 | 0.688367 | 0.344183 | − | 0.938902i | \(-0.388156\pi\) | ||||
0.344183 | + | 0.938902i | \(0.388156\pi\) | |||||||
\(788\) | 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 | \(-0.651183\pi\) | ||||
−0.457300 | + | 0.889313i | \(0.651183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16381.3 | 0.709279 | 0.354640 | − | 0.935003i | \(-0.384604\pi\) | ||||
0.354640 | + | 0.935003i | \(0.384604\pi\) | |||||||
\(812\) | −11881.1 | + | 6101.65i | −0.513479 | + | 0.263702i | ||||
\(813\) | 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 | ||||||||
\(826\) | −7129.58 | − | 3075.47i | −0.300327 | − | 0.129551i | ||||
\(827\) | 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 | \(-0.838645\pi\) | ||
0.874248 | − | 0.485480i | \(-0.161355\pi\) | |||||||
\(830\) | 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 | \(0.123181\pi\) | ||||
−0.926051 | + | 0.377399i | \(0.876819\pi\) | |||||||
\(854\) | 9107.64 | − | 21113.4i | 0.364938 | − | 0.846001i | ||||
\(855\) | 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 | \(-0.420085\pi\) | ||||
0.248431 | + | 0.968650i | \(0.420085\pi\) | |||||||
\(860\) | 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 | ||||||||
\(868\) | −26604.6 | + | 13663.0i | −1.04034 | + | 0.534278i | ||||
\(869\) | 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 | ||||||||
\(896\) | −4550.35 | − | 26431.4i | −0.169661 | − | 0.985502i | ||||
\(897\) | 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 | ||||||||
\(910\) | −61892.2 | − | 26698.3i | −2.25462 | − | 0.972572i | ||||
\(911\) | 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 | \(0.124709\pi\) | ||||
−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 | \(-0.896083\pi\) | ||
0.947182 | − | 0.320697i | \(-0.103917\pi\) | |||||||
\(938\) | −13852.8 | + | 32113.7i | −0.482207 | + | 1.11786i | ||||
\(939\) | 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 | \(-0.967123\pi\) | ||
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 | ||||||||
\(952\) | 25693.5 | + | 5602.01i | 0.874717 | + | 0.190717i | ||||
\(953\) | 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 | \(-0.375238\pi\) | ||||
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 | \(-0.531911\pi\) | ||||
−0.100083 | + | 0.994979i | \(0.531911\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −293.298 | −0.00957493 | ||||||||
\(980\) | −35470.0 | + | 33463.1i | −1.15617 | + | 1.09075i | ||||
\(981\) | 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 | ||||||||
\(994\) | −3614.18 | + | 8378.42i | −0.115327 | + | 0.267351i | ||||
\(995\) | − | 60222.8i | − | 1.91878i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54852.2i | 1.74241i | 0.490915 | + | 0.871207i | \(0.336662\pi\) | ||||
−0.490915 | + | 0.871207i | \(0.663338\pi\) | |||||||
\(998\) | −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.55.10 | yes | 16 | |
3.2 | odd | 2 | inner | 252.4.b.g.55.7 | yes | 16 | |
4.3 | odd | 2 | inner | 252.4.b.g.55.12 | yes | 16 | |
7.6 | odd | 2 | inner | 252.4.b.g.55.9 | yes | 16 | |
12.11 | even | 2 | inner | 252.4.b.g.55.5 | ✓ | 16 | |
21.20 | even | 2 | inner | 252.4.b.g.55.8 | yes | 16 | |
28.27 | even | 2 | inner | 252.4.b.g.55.11 | yes | 16 | |
84.83 | odd | 2 | inner | 252.4.b.g.55.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.b.g.55.5 | ✓ | 16 | 12.11 | even | 2 | inner | |
252.4.b.g.55.6 | yes | 16 | 84.83 | odd | 2 | inner | |
252.4.b.g.55.7 | yes | 16 | 3.2 | odd | 2 | inner | |
252.4.b.g.55.8 | yes | 16 | 21.20 | even | 2 | inner | |
252.4.b.g.55.9 | yes | 16 | 7.6 | odd | 2 | inner | |
252.4.b.g.55.10 | yes | 16 | 1.1 | even | 1 | trivial | |
252.4.b.g.55.11 | yes | 16 | 28.27 | even | 2 | inner | |
252.4.b.g.55.12 | yes | 16 | 4.3 | odd | 2 | inner |