Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(199,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.f (of order \(2\), degree \(1\), not 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.6 | ||
Root | \(-0.587785 - 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.199 |
Dual form | 900.3.f.e.199.5 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.17557 | + | 1.61803i | 0.587785 | + | 0.809017i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.23607 | + | 3.80423i | −0.309017 | + | 0.951057i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.50651 | 1.21522 | 0.607608 | − | 0.794237i | \(-0.292129\pi\) | ||||
0.607608 | + | 0.794237i | \(0.292129\pi\) | |||||||
\(8\) | −7.60845 | + | 2.47214i | −0.951057 | + | 0.309017i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.79611i | − | 0.163283i | −0.996662 | − | 0.0816415i | \(-0.973984\pi\) | ||
0.996662 | − | 0.0816415i | \(-0.0260162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.472136i | − | 0.0363182i | −0.999835 | − | 0.0181591i | \(-0.994219\pi\) | ||
0.999835 | − | 0.0181591i | \(-0.00578053\pi\) | |||||||
\(14\) | 10.0000 | + | 13.7638i | 0.714286 | + | 0.983130i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.9443 | − | 9.40456i | −0.809017 | − | 0.587785i | ||||
\(17\) | 23.8885i | 1.40521i | 0.711581 | + | 0.702604i | \(0.247980\pi\) | ||||
−0.711581 | + | 0.702604i | \(0.752020\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.40456i | 0.494977i | 0.968891 | + | 0.247489i | \(0.0796053\pi\) | ||||
−0.968891 | + | 0.247489i | \(0.920395\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.90617 | − | 2.11146i | 0.132099 | − | 0.0959753i | ||||
\(23\) | 16.1150 | 0.700650 | 0.350325 | − | 0.936628i | \(-0.386071\pi\) | ||||
0.350325 | + | 0.936628i | \(0.386071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.763932 | − | 0.555029i | 0.0293820 | − | 0.0213473i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.5146 | + | 32.3607i | −0.375522 | + | 1.15574i | ||||
\(29\) | 6.94427 | 0.239458 | 0.119729 | − | 0.992807i | \(-0.461797\pi\) | ||||
0.119729 | + | 0.992807i | \(0.461797\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 47.4468i | 1.53054i | 0.643708 | + | 0.765271i | \(0.277395\pi\) | ||||
−0.643708 | + | 0.765271i | \(0.722605\pi\) | |||||||
\(32\) | − | 32.0000i | − | 1.00000i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −38.6525 | + | 28.0827i | −1.13684 | + | 0.825961i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26.3607i | 0.712451i | 0.934400 | + | 0.356225i | \(0.115936\pi\) | ||||
−0.934400 | + | 0.356225i | \(0.884064\pi\) | |||||||
\(38\) | −15.2169 | + | 11.0557i | −0.400445 | + | 0.290940i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 41.4164 | 1.01016 | 0.505078 | − | 0.863074i | \(-0.331464\pi\) | ||||
0.505078 | + | 0.863074i | \(0.331464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00811 | −0.0467003 | −0.0233502 | − | 0.999727i | \(-0.507433\pi\) | ||||
−0.0233502 | + | 0.999727i | \(0.507433\pi\) | |||||||
\(44\) | 6.83282 | + | 2.22012i | 0.155291 | + | 0.0504572i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.9443 | + | 26.0746i | 0.411832 | + | 0.566838i | ||||
\(47\) | −35.3481 | −0.752087 | −0.376044 | − | 0.926602i | \(-0.622716\pi\) | ||||
−0.376044 | + | 0.926602i | \(0.622716\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.3607 | 0.476749 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.79611 | + | 0.583592i | 0.0345406 | + | 0.0112229i | ||||
\(53\) | − | 21.6393i | − | 0.408289i | −0.978941 | − | 0.204145i | \(-0.934559\pi\) | ||
0.978941 | − | 0.204145i | \(-0.0654413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −64.7214 | + | 21.0292i | −1.15574 | + | 0.375522i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.16348 | + | 11.2361i | 0.140750 | + | 0.193725i | ||||
\(59\) | 73.8644i | 1.25194i | 0.779848 | + | 0.625970i | \(0.215297\pi\) | ||||
−0.779848 | + | 0.625970i | \(0.784703\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −26.1378 | −0.428488 | −0.214244 | − | 0.976780i | \(-0.568729\pi\) | ||||
−0.214244 | + | 0.976780i | \(0.568729\pi\) | |||||||
\(62\) | −76.7706 | + | 55.7771i | −1.23824 | + | 0.899630i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 51.7771 | − | 37.6183i | 0.809017 | − | 0.587785i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −88.8693 | −1.32641 | −0.663204 | − | 0.748439i | \(-0.730804\pi\) | ||||
−0.663204 | + | 0.748439i | \(0.730804\pi\) | |||||||
\(68\) | −90.8774 | − | 29.5279i | −1.33643 | − | 0.434233i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 39.4144i | 0.555132i | 0.960707 | + | 0.277566i | \(0.0895277\pi\) | ||||
−0.960707 | + | 0.277566i | \(0.910472\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 137.554i | − | 1.88430i | −0.335186 | − | 0.942152i | \(-0.608799\pi\) | ||
0.335186 | − | 0.942152i | \(-0.391201\pi\) | |||||||
\(74\) | −42.6525 | + | 30.9888i | −0.576385 | + | 0.418768i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −35.7771 | − | 11.6247i | −0.470751 | − | 0.152956i | ||||
\(77\) | − | 15.2786i | − | 0.198424i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 113.703i | 1.43928i | 0.694350 | + | 0.719638i | \(0.255692\pi\) | ||||
−0.694350 | + | 0.719638i | \(0.744308\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 48.6879 | + | 67.0132i | 0.593755 | + | 0.817234i | ||||
\(83\) | −21.2412 | −0.255919 | −0.127959 | − | 0.991779i | \(-0.540843\pi\) | ||||
−0.127959 | + | 0.991779i | \(0.540843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.36068 | − | 3.24920i | −0.0274498 | − | 0.0377814i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.44023 | + | 13.6656i | 0.0504572 | + | 0.155291i | ||||
\(89\) | 67.4427 | 0.757783 | 0.378892 | − | 0.925441i | \(-0.376305\pi\) | ||||
0.378892 | + | 0.925441i | \(0.376305\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.01623i | − | 0.0441344i | ||||||
\(92\) | −19.9192 | + | 61.3050i | −0.216513 | + | 0.666358i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −41.5542 | − | 57.1944i | −0.442066 | − | 0.608451i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 39.1672i | − | 0.403785i | −0.979408 | − | 0.201893i | \(-0.935291\pi\) | ||
0.979408 | − | 0.201893i | \(-0.0647092\pi\) | |||||||
\(98\) | 27.4621 | + | 37.7984i | 0.280226 | + | 0.385698i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −99.8885 | −0.988995 | −0.494498 | − | 0.869179i | \(-0.664648\pi\) | ||||
−0.494498 | + | 0.869179i | \(0.664648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −35.7721 | −0.347302 | −0.173651 | − | 0.984807i | \(-0.555556\pi\) | ||||
−0.173651 | + | 0.984807i | \(0.555556\pi\) | |||||||
\(104\) | 1.16718 | + | 3.59222i | 0.0112229 | + | 0.0345406i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 35.0132 | − | 25.4385i | 0.330313 | − | 0.239986i | ||||
\(107\) | −121.099 | −1.13177 | −0.565884 | − | 0.824485i | \(-0.691465\pi\) | ||||
−0.565884 | + | 0.824485i | \(0.691465\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 197.469 | 1.81164 | 0.905821 | − | 0.423660i | \(-0.139255\pi\) | ||||
0.905821 | + | 0.423660i | \(0.139255\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −110.111 | − | 80.0000i | −0.983130 | − | 0.714286i | ||||
\(113\) | 81.2786i | 0.719280i | 0.933091 | + | 0.359640i | \(0.117100\pi\) | ||||
−0.933091 | + | 0.359640i | \(0.882900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.58359 | + | 26.4176i | −0.0739965 | + | 0.227738i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −119.515 | + | 86.8328i | −1.01284 | + | 0.735871i | ||||
\(119\) | 203.208i | 1.70763i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 117.774 | 0.973339 | ||||||||
\(122\) | −30.7268 | − | 42.2918i | −0.251859 | − | 0.346654i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −180.498 | − | 58.6475i | −1.45563 | − | 0.472964i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.84616 | 0.0145367 | 0.00726834 | − | 0.999974i | \(-0.497686\pi\) | ||||
0.00726834 | + | 0.999974i | \(0.497686\pi\) | |||||||
\(128\) | 121.735 | + | 39.5542i | 0.951057 | + | 0.309017i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 225.609i | − | 1.72221i | −0.508428 | − | 0.861105i | \(-0.669773\pi\) | ||
0.508428 | − | 0.861105i | \(-0.330227\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 80.0000i | 0.601504i | ||||||||
\(134\) | −104.472 | − | 143.794i | −0.779643 | − | 1.07309i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −59.0557 | − | 181.755i | −0.434233 | − | 1.33643i | ||||
\(137\) | 52.8328i | 0.385641i | 0.981234 | + | 0.192820i | \(0.0617635\pi\) | ||||
−0.981234 | + | 0.192820i | \(0.938236\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 125.852i | 0.905407i | 0.891661 | + | 0.452703i | \(0.149540\pi\) | ||||
−0.891661 | + | 0.452703i | \(0.850460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −63.7738 | + | 46.3344i | −0.449111 | + | 0.326298i | ||||
\(143\) | −0.848009 | −0.00593013 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 222.567 | − | 161.705i | 1.52443 | − | 1.10757i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −100.282 | − | 32.5836i | −0.677581 | − | 0.220159i | ||||
\(149\) | 132.971 | 0.892420 | 0.446210 | − | 0.894928i | \(-0.352773\pi\) | ||||
0.446210 | + | 0.894928i | \(0.352773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 151.221i | − | 1.00146i | −0.865603 | − | 0.500732i | \(-0.833064\pi\) | ||
0.865603 | − | 0.500732i | \(-0.166936\pi\) | |||||||
\(152\) | −23.2494 | − | 71.5542i | −0.152956 | − | 0.470751i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 24.7214 | − | 17.9611i | 0.160528 | − | 0.116631i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 36.7477i | − | 0.234062i | −0.993128 | − | 0.117031i | \(-0.962662\pi\) | ||
0.993128 | − | 0.117031i | \(-0.0373376\pi\) | |||||||
\(158\) | −183.975 | + | 133.666i | −1.16440 | + | 0.845985i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 137.082 | 0.851441 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 302.854 | 1.85800 | 0.929000 | − | 0.370079i | \(-0.120669\pi\) | ||||
0.929000 | + | 0.370079i | \(0.120669\pi\) | |||||||
\(164\) | −51.1935 | + | 157.557i | −0.312155 | + | 0.960716i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −24.9706 | − | 34.3691i | −0.150425 | − | 0.207043i | ||||
\(167\) | 99.3839 | 0.595113 | 0.297557 | − | 0.954704i | \(-0.403828\pi\) | ||||
0.297557 | + | 0.954704i | \(0.403828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168.777 | 0.998681 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.48217 | − | 7.63932i | 0.0144312 | − | 0.0444147i | ||||
\(173\) | − | 181.639i | − | 1.04994i | −0.851121 | − | 0.524969i | \(-0.824077\pi\) | ||
0.851121 | − | 0.524969i | \(-0.175923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.8916 | + | 23.2494i | −0.0959753 | + | 0.132099i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 79.2837 | + | 109.125i | 0.445414 | + | 0.613060i | ||||
\(179\) | − | 260.907i | − | 1.45758i | −0.684735 | − | 0.728792i | \(-0.740082\pi\) | ||
0.684735 | − | 0.728792i | \(-0.259918\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 157.777 | 0.871697 | 0.435848 | − | 0.900020i | \(-0.356448\pi\) | ||||
0.435848 | + | 0.900020i | \(0.356448\pi\) | |||||||
\(182\) | 6.49839 | − | 4.72136i | 0.0357055 | − | 0.0259415i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −122.610 | + | 39.8384i | −0.666358 | + | 0.216513i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 42.9065 | 0.229447 | ||||||||
\(188\) | 43.6926 | − | 134.472i | 0.232408 | − | 0.715277i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 324.095i | 1.69683i | 0.529328 | + | 0.848417i | \(0.322444\pi\) | ||||
−0.529328 | + | 0.848417i | \(0.677556\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 181.777i | − | 0.941850i | −0.882173 | − | 0.470925i | \(-0.843920\pi\) | ||
0.882173 | − | 0.470925i | \(-0.156080\pi\) | |||||||
\(194\) | 63.3738 | − | 46.0438i | 0.326669 | − | 0.237339i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −28.8754 | + | 88.8693i | −0.147323 | + | 0.453415i | ||||
\(197\) | − | 140.525i | − | 0.713324i | −0.934234 | − | 0.356662i | \(-0.883915\pi\) | ||
0.934234 | − | 0.356662i | \(-0.116085\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 168.234i | − | 0.845397i | −0.906270 | − | 0.422698i | \(-0.861083\pi\) | ||
0.906270 | − | 0.422698i | \(-0.138917\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −117.426 | − | 161.623i | −0.581317 | − | 0.800114i | ||||
\(203\) | 59.0715 | 0.290993 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −42.0526 | − | 57.8805i | −0.204139 | − | 0.280973i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.44023 | + | 6.11146i | −0.0213473 | + | 0.0293820i | ||||
\(209\) | 16.8916 | 0.0808213 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 93.9455i | 0.445240i | 0.974905 | + | 0.222620i | \(0.0714608\pi\) | ||||
−0.974905 | + | 0.222620i | \(0.928539\pi\) | |||||||
\(212\) | 82.3209 | + | 26.7477i | 0.388306 | + | 0.126168i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −142.361 | − | 195.943i | −0.665237 | − | 0.915620i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 403.607i | 1.85994i | ||||||||
\(218\) | 232.139 | + | 319.512i | 1.06486 | + | 1.46565i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.2786 | 0.0510346 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 214.035 | 0.959797 | 0.479899 | − | 0.877324i | \(-0.340673\pi\) | ||||
0.479899 | + | 0.877324i | \(0.340673\pi\) | |||||||
\(224\) | − | 272.208i | − | 1.21522i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −131.512 | + | 95.5488i | −0.581910 | + | 0.422782i | ||||
\(227\) | −41.4225 | −0.182478 | −0.0912389 | − | 0.995829i | \(-0.529083\pi\) | ||||
−0.0912389 | + | 0.995829i | \(0.529083\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −73.2786 | −0.319994 | −0.159997 | − | 0.987117i | \(-0.551148\pi\) | ||||
−0.159997 | + | 0.987117i | \(0.551148\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −52.8352 | + | 17.1672i | −0.227738 | + | 0.0739965i | ||||
\(233\) | − | 307.050i | − | 1.31781i | −0.752227 | − | 0.658905i | \(-0.771020\pi\) | ||
0.752227 | − | 0.658905i | \(-0.228980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −280.997 | − | 91.3014i | −1.19066 | − | 0.386870i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −328.798 | + | 238.885i | −1.38150 | + | 1.00372i | ||||
\(239\) | − | 42.9065i | − | 0.179525i | −0.995963 | − | 0.0897625i | \(-0.971389\pi\) | ||
0.995963 | − | 0.0897625i | \(-0.0286108\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −135.082 | −0.560506 | −0.280253 | − | 0.959926i | \(-0.590418\pi\) | ||||
−0.280253 | + | 0.959926i | \(0.590418\pi\) | |||||||
\(242\) | 138.452 | + | 190.562i | 0.572114 | + | 0.787448i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 32.3081 | − | 99.4340i | 0.132410 | − | 0.407516i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.44023 | 0.0179767 | ||||||||
\(248\) | −117.295 | − | 360.997i | −0.472964 | − | 1.45563i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 221.169i | 0.881152i | 0.897715 | + | 0.440576i | \(0.145226\pi\) | ||||
−0.897715 | + | 0.440576i | \(0.854774\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 28.9443i | − | 0.114404i | ||||||
\(254\) | 2.17029 | + | 2.98715i | 0.00854445 | + | 0.0117604i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 79.1084 | + | 243.470i | 0.309017 | + | 0.951057i | ||||
\(257\) | 257.056i | 1.00022i | 0.865963 | + | 0.500108i | \(0.166707\pi\) | ||||
−0.865963 | + | 0.500108i | \(0.833293\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 224.237i | 0.865781i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 365.044 | − | 265.220i | 1.39330 | − | 1.01229i | ||||
\(263\) | 164.168 | 0.624212 | 0.312106 | − | 0.950047i | \(-0.398966\pi\) | ||||
0.312106 | + | 0.950047i | \(0.398966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −129.443 | + | 94.0456i | −0.486627 | + | 0.353555i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 109.849 | − | 338.079i | 0.409882 | − | 1.26149i | ||||
\(269\) | −35.4752 | −0.131878 | −0.0659391 | − | 0.997824i | \(-0.521004\pi\) | ||||
−0.0659391 | + | 0.997824i | \(0.521004\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 298.950i | 1.10314i | 0.834130 | + | 0.551568i | \(0.185970\pi\) | ||||
−0.834130 | + | 0.551568i | \(0.814030\pi\) | |||||||
\(272\) | 224.661 | − | 309.220i | 0.825961 | − | 1.13684i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −85.4853 | + | 62.1087i | −0.311990 | + | 0.226674i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 457.246i | − | 1.65071i | −0.564616 | − | 0.825354i | \(-0.690976\pi\) | ||
0.564616 | − | 0.825354i | \(-0.309024\pi\) | |||||||
\(278\) | −203.632 | + | 147.947i | −0.732490 | + | 0.532185i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.63932 | 0.0200688 | 0.0100344 | − | 0.999950i | \(-0.496806\pi\) | ||||
0.0100344 | + | 0.999950i | \(0.496806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −169.918 | −0.600418 | −0.300209 | − | 0.953874i | \(-0.597056\pi\) | ||||
−0.300209 | + | 0.953874i | \(0.597056\pi\) | |||||||
\(284\) | −149.941 | − | 48.7188i | −0.527962 | − | 0.171545i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.996894 | − | 1.37211i | −0.00348564 | − | 0.00479758i | ||||
\(287\) | 352.309 | 1.22756 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −281.663 | −0.974611 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 523.287 | + | 170.026i | 1.79208 | + | 0.582282i | ||||
\(293\) | − | 26.8591i | − | 0.0916694i | −0.998949 | − | 0.0458347i | \(-0.985405\pi\) | ||
0.998949 | − | 0.0458347i | \(-0.0145947\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −65.1672 | − | 200.564i | −0.220159 | − | 0.677581i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 156.316 | + | 215.151i | 0.524551 | + | 0.721983i | ||||
\(299\) | − | 7.60845i | − | 0.0254463i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.0820 | −0.0567510 | ||||||||
\(302\) | 244.681 | − | 177.771i | 0.810201 | − | 0.588645i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 88.4458 | − | 121.735i | 0.290940 | − | 0.400445i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 118.031 | 0.384466 | 0.192233 | − | 0.981349i | \(-0.438427\pi\) | ||||
0.192233 | + | 0.981349i | \(0.438427\pi\) | |||||||
\(308\) | 58.1234 | + | 18.8854i | 0.188712 | + | 0.0613164i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 121.835i | − | 0.391753i | −0.980629 | − | 0.195877i | \(-0.937245\pi\) | ||
0.980629 | − | 0.195877i | \(-0.0627552\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 219.548i | − | 0.701431i | −0.936482 | − | 0.350716i | \(-0.885938\pi\) | ||
0.936482 | − | 0.350716i | \(-0.114062\pi\) | |||||||
\(314\) | 59.4590 | − | 43.1995i | 0.189360 | − | 0.137578i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −432.551 | − | 140.544i | −1.36883 | − | 0.444761i | ||||
\(317\) | − | 366.859i | − | 1.15728i | −0.815582 | − | 0.578642i | \(-0.803583\pi\) | ||
0.815582 | − | 0.578642i | \(-0.196417\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 12.4727i | − | 0.0390993i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 161.150 | + | 221.803i | 0.500465 | + | 0.688830i | ||||
\(323\) | −224.661 | −0.695546 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 356.026 | + | 490.028i | 1.09211 | + | 1.50315i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −315.115 | + | 102.387i | −0.960716 | + | 0.312155i | ||||
\(329\) | −300.689 | −0.913948 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 162.846i | − | 0.491981i | −0.969272 | − | 0.245990i | \(-0.920887\pi\) | ||
0.969272 | − | 0.245990i | \(-0.0791132\pi\) | |||||||
\(332\) | 26.2556 | − | 80.8065i | 0.0790832 | − | 0.243393i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 116.833 | + | 160.807i | 0.349799 | + | 0.481457i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1084i | 0.0507666i | 0.999678 | + | 0.0253833i | \(0.00808063\pi\) | ||||
−0.999678 | + | 0.0253833i | \(0.991919\pi\) | |||||||
\(338\) | 198.409 | + | 273.087i | 0.587010 | + | 0.807950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 85.2198 | 0.249911 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −218.101 | −0.635863 | ||||||||
\(344\) | 15.2786 | − | 4.96433i | 0.0444147 | − | 0.0144312i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 293.899 | − | 213.530i | 0.849418 | − | 0.617138i | ||||
\(347\) | 167.498 | 0.482703 | 0.241351 | − | 0.970438i | \(-0.422409\pi\) | ||||
0.241351 | + | 0.970438i | \(0.422409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 483.495 | 1.38537 | 0.692687 | − | 0.721239i | \(-0.256427\pi\) | ||||
0.692687 | + | 0.721239i | \(0.256427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −57.4756 | −0.163283 | ||||||||
\(353\) | 307.994i | 0.872504i | 0.899825 | + | 0.436252i | \(0.143694\pi\) | ||||
−0.899825 | + | 0.436252i | \(0.856306\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −83.3638 | + | 256.567i | −0.234168 | + | 0.720695i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 422.157 | − | 306.715i | 1.17921 | − | 0.856746i | ||||
\(359\) | − | 23.2494i | − | 0.0647615i | −0.999476 | − | 0.0323807i | \(-0.989691\pi\) | ||
0.999476 | − | 0.0323807i | \(-0.0103089\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 272.554 | 0.754998 | ||||||||
\(362\) | 185.478 | + | 255.289i | 0.512370 | + | 0.705217i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15.2786 | + | 4.96433i | 0.0419743 | + | 0.0136383i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 517.325 | 1.40960 | 0.704802 | − | 0.709404i | \(-0.251036\pi\) | ||||
0.704802 | + | 0.709404i | \(0.251036\pi\) | |||||||
\(368\) | −208.596 | − | 151.554i | −0.566838 | − | 0.411832i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 184.075i | − | 0.496159i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 88.3545i | 0.236875i | 0.992961 | + | 0.118438i | \(0.0377886\pi\) | ||||
−0.992961 | + | 0.118438i | \(0.962211\pi\) | |||||||
\(374\) | 50.4396 | + | 69.4242i | 0.134865 | + | 0.185626i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 268.944 | − | 87.3853i | 0.715277 | − | 0.232408i | ||||
\(377\) | − | 3.27864i | − | 0.00869666i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 19.3332i | − | 0.0510112i | −0.999675 | − | 0.0255056i | \(-0.991880\pi\) | ||
0.999675 | − | 0.0255056i | \(-0.00811956\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −524.397 | + | 380.997i | −1.37277 | + | 0.997374i | ||||
\(383\) | 431.612 | 1.12692 | 0.563462 | − | 0.826142i | \(-0.309469\pi\) | ||||
0.563462 | + | 0.826142i | \(0.309469\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 294.122 | − | 213.692i | 0.761973 | − | 0.553606i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 149.001 | + | 48.4133i | 0.384023 | + | 0.124777i | ||||
\(389\) | −296.354 | −0.761837 | −0.380918 | − | 0.924609i | \(-0.624392\pi\) | ||||
−0.380918 | + | 0.924609i | \(0.624392\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 384.963i | 0.984560i | ||||||||
\(392\) | −177.739 | + | 57.7508i | −0.453415 | + | 0.147323i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 227.374 | − | 165.197i | 0.577091 | − | 0.419281i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 86.1904i | − | 0.217104i | −0.994091 | − | 0.108552i | \(-0.965379\pi\) | ||
0.994091 | − | 0.108552i | \(-0.0346214\pi\) | |||||||
\(398\) | 272.208 | − | 197.771i | 0.683940 | − | 0.496912i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −442.997 | −1.10473 | −0.552365 | − | 0.833602i | \(-0.686275\pi\) | ||||
−0.552365 | + | 0.833602i | \(0.686275\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.4014 | 0.0555865 | ||||||||
\(404\) | 123.469 | − | 379.999i | 0.305616 | − | 0.940591i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 69.4427 | + | 95.5797i | 0.171041 | + | 0.235418i | ||||
\(407\) | 47.3467 | 0.116331 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −63.4102 | −0.155037 | −0.0775186 | − | 0.996991i | \(-0.524700\pi\) | ||||
−0.0775186 | + | 0.996991i | \(0.524700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 44.2167 | − | 136.085i | 0.107322 | − | 0.330304i | ||||
\(413\) | 628.328i | 1.52138i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −15.1084 | −0.0363182 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 19.8573 | + | 27.3313i | 0.0475056 | + | 0.0653858i | ||||
\(419\) | − | 435.678i | − | 1.03980i | −0.854226 | − | 0.519902i | \(-0.825968\pi\) | ||
0.854226 | − | 0.519902i | \(-0.174032\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −582.912 | −1.38459 | −0.692294 | − | 0.721615i | \(-0.743400\pi\) | ||||
−0.692294 | + | 0.721615i | \(0.743400\pi\) | |||||||
\(422\) | −152.007 | + | 110.440i | −0.360206 | + | 0.261705i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 53.4953 | + | 164.642i | 0.126168 | + | 0.388306i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −222.341 | −0.520705 | ||||||||
\(428\) | 149.687 | − | 460.689i | 0.349736 | − | 1.07638i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 375.882i | − | 0.872117i | −0.899918 | − | 0.436058i | \(-0.856374\pi\) | ||
0.899918 | − | 0.436058i | \(-0.143626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 368.164i | 0.850263i | 0.905131 | + | 0.425132i | \(0.139772\pi\) | ||||
−0.905131 | + | 0.425132i | \(0.860228\pi\) | |||||||
\(434\) | −653.050 | + | 474.468i | −1.50472 | + | 1.09324i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −244.085 | + | 751.217i | −0.559828 | + | 1.72297i | ||||
\(437\) | 151.554i | 0.346806i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 483.549i | − | 1.10148i | −0.834677 | − | 0.550739i | \(-0.814346\pi\) | ||
0.834677 | − | 0.550739i | \(-0.185654\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.2588 | + | 18.2492i | 0.0299974 | + | 0.0412878i | ||||
\(443\) | 279.181 | 0.630205 | 0.315102 | − | 0.949058i | \(-0.397961\pi\) | ||||
0.315102 | + | 0.949058i | \(0.397961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 251.613 | + | 346.316i | 0.564155 | + | 0.776492i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 440.442 | − | 320.000i | 0.983130 | − | 0.714286i | ||||
\(449\) | 756.079 | 1.68392 | 0.841959 | − | 0.539542i | \(-0.181403\pi\) | ||||
0.841959 | + | 0.539542i | \(0.181403\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 74.3885i | − | 0.164941i | ||||||
\(452\) | −309.202 | − | 100.466i | −0.684076 | − | 0.222270i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −48.6950 | − | 67.0230i | −0.107258 | − | 0.147628i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 285.672i | 0.625103i | 0.949901 | + | 0.312551i | \(0.101184\pi\) | ||||
−0.949901 | + | 0.312551i | \(0.898816\pi\) | |||||||
\(458\) | −86.1442 | − | 118.567i | −0.188088 | − | 0.258881i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 99.1146 | 0.214999 | 0.107500 | − | 0.994205i | \(-0.465716\pi\) | ||||
0.107500 | + | 0.994205i | \(0.465716\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −630.603 | −1.36199 | −0.680997 | − | 0.732286i | \(-0.738453\pi\) | ||||
−0.680997 | + | 0.732286i | \(0.738453\pi\) | |||||||
\(464\) | −89.8885 | − | 65.3078i | −0.193725 | − | 0.140750i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 496.817 | − | 360.958i | 1.06613 | − | 0.774589i | ||||
\(467\) | 496.010 | 1.06212 | 0.531060 | − | 0.847334i | \(-0.321794\pi\) | ||||
0.531060 | + | 0.847334i | \(0.321794\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −755.967 | −1.61187 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −182.603 | − | 561.994i | −0.386870 | − | 1.19066i | ||||
\(473\) | 3.60680i | 0.00762537i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −773.050 | − | 251.179i | −1.62405 | − | 0.527687i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 69.4242 | − | 50.4396i | 0.145239 | − | 0.105522i | ||||
\(479\) | 579.090i | 1.20896i | 0.796621 | + | 0.604478i | \(0.206618\pi\) | ||||
−0.796621 | + | 0.604478i | \(0.793382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.4458 | 0.0258749 | ||||||||
\(482\) | −158.798 | − | 218.567i | −0.329457 | − | 0.453459i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −145.577 | + | 448.039i | −0.300778 | + | 0.925700i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −626.363 | −1.28617 | −0.643084 | − | 0.765796i | \(-0.722345\pi\) | ||||
−0.643084 | + | 0.765796i | \(0.722345\pi\) | |||||||
\(488\) | 198.868 | − | 64.6161i | 0.407516 | − | 0.132410i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.3013i | − | 0.0454201i | −0.999742 | − | 0.0227100i | \(-0.992771\pi\) | ||
0.999742 | − | 0.0227100i | \(-0.00722945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 165.889i | 0.336488i | ||||||||
\(494\) | 5.21981 | + | 7.18445i | 0.0105664 | + | 0.0145434i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 446.217 | − | 614.165i | 0.899630 | − | 1.23824i | ||||
\(497\) | 335.279i | 0.674605i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 627.362i | − | 1.25724i | −0.777714 | − | 0.628619i | \(-0.783621\pi\) | ||
0.777714 | − | 0.628619i | \(-0.216379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −357.859 | + | 260.000i | −0.712867 | + | 0.517928i | ||||
\(503\) | −780.853 | −1.55239 | −0.776196 | − | 0.630492i | \(-0.782853\pi\) | ||||
−0.776196 | + | 0.630492i | \(0.782853\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 46.8328 | − | 34.0260i | 0.0925550 | − | 0.0672451i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.28198 | + | 7.02321i | −0.00449208 | + | 0.0138252i | ||||
\(509\) | −288.950 | −0.567683 | −0.283841 | − | 0.958871i | \(-0.591609\pi\) | ||||
−0.283841 | + | 0.958871i | \(0.591609\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1170.11i | − | 2.28984i | ||||||
\(512\) | −300.946 | + | 414.217i | −0.587785 | + | 0.809017i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −415.925 | + | 302.187i | −0.809192 | + | 0.587913i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 63.4891i | 0.122803i | ||||||||
\(518\) | −362.824 | + | 263.607i | −0.700432 | + | 0.508893i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 602.984 | 1.15736 | 0.578680 | − | 0.815555i | \(-0.303568\pi\) | ||||
0.578680 | + | 0.815555i | \(0.303568\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 367.962 | 0.703560 | 0.351780 | − | 0.936083i | \(-0.385577\pi\) | ||||
0.351780 | + | 0.936083i | \(0.385577\pi\) | |||||||
\(524\) | 858.269 | + | 278.869i | 1.63792 | + | 0.532192i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 192.991 | + | 265.629i | 0.366902 | + | 0.504998i | ||||
\(527\) | −1133.44 | −2.15073 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −269.308 | −0.509089 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −304.338 | − | 98.8854i | −0.572064 | − | 0.185875i | ||||
\(533\) | − | 19.5542i | − | 0.0366870i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 676.158 | − | 219.697i | 1.26149 | − | 0.409882i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −41.7036 | − | 57.4001i | −0.0775161 | − | 0.106692i | ||||
\(539\) | − | 41.9584i | − | 0.0778449i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −616.885 | −1.14027 | −0.570134 | − | 0.821551i | \(-0.693109\pi\) | ||||
−0.570134 | + | 0.821551i | \(0.693109\pi\) | |||||||
\(542\) | −483.711 | + | 351.437i | −0.892455 | + | 0.648407i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 764.433 | 1.40521 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 97.8499 | 0.178885 | 0.0894423 | − | 0.995992i | \(-0.471492\pi\) | ||||
0.0894423 | + | 0.995992i | \(0.471492\pi\) | |||||||
\(548\) | −200.988 | − | 65.3050i | −0.366766 | − | 0.119170i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 65.3078i | 0.118526i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 967.214i | 1.74903i | ||||||||
\(554\) | 739.840 | − | 537.525i | 1.33545 | − | 0.970262i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −478.768 | − | 155.561i | −0.861093 | − | 0.279786i | ||||
\(557\) | − | 896.302i | − | 1.60916i | −0.593845 | − | 0.804580i | \(-0.702391\pi\) | ||
0.593845 | − | 0.804580i | \(-0.297609\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.948103i | 0.00169607i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.62942 | + | 9.12461i | 0.0117961 | + | 0.0162360i | ||||
\(563\) | −771.186 | −1.36978 | −0.684890 | − | 0.728647i | \(-0.740150\pi\) | ||||
−0.684890 | + | 0.728647i | \(0.740150\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −199.751 | − | 274.933i | −0.352917 | − | 0.485748i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −97.4377 | − | 299.882i | −0.171545 | − | 0.527962i | ||||
\(569\) | 8.74767 | 0.0153738 | 0.00768688 | − | 0.999970i | \(-0.497553\pi\) | ||||
0.00768688 | + | 0.999970i | \(0.497553\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 511.138i | 0.895164i | 0.894243 | + | 0.447582i | \(0.147715\pi\) | ||||
−0.894243 | + | 0.447582i | \(0.852285\pi\) | |||||||
\(572\) | 1.04820 | − | 3.22602i | 0.00183251 | − | 0.00563989i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 414.164 | + | 570.048i | 0.721540 | + | 0.993115i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 713.712i | − | 1.23694i | −0.785810 | − | 0.618468i | \(-0.787754\pi\) | ||
0.785810 | − | 0.618468i | \(-0.212246\pi\) | |||||||
\(578\) | −331.114 | − | 455.740i | −0.572862 | − | 0.788477i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −180.689 | −0.310996 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −38.8666 | −0.0666666 | ||||||||
\(584\) | 340.053 | + | 1046.57i | 0.582282 | + | 1.79208i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.4590 | − | 31.5748i | 0.0741621 | − | 0.0538819i | ||||
\(587\) | −422.169 | −0.719198 | −0.359599 | − | 0.933107i | \(-0.617086\pi\) | ||||
−0.359599 | + | 0.933107i | \(0.617086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −446.217 | −0.757584 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 247.911 | − | 341.220i | 0.418768 | − | 0.576385i | ||||
\(593\) | − | 308.663i | − | 0.520510i | −0.965540 | − | 0.260255i | \(-0.916193\pi\) | ||
0.965540 | − | 0.260255i | \(-0.0838067\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −164.361 | + | 505.850i | −0.275773 | + | 0.848742i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.3107 | − | 8.94427i | 0.0205865 | − | 0.0149570i | ||||
\(599\) | − | 462.196i | − | 0.771612i | −0.922580 | − | 0.385806i | \(-0.873923\pi\) | ||
0.922580 | − | 0.385806i | \(-0.126077\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 355.358 | 0.591277 | 0.295639 | − | 0.955300i | \(-0.404468\pi\) | ||||
0.295639 | + | 0.955300i | \(0.404468\pi\) | |||||||
\(602\) | −20.0811 | − | 27.6393i | −0.0333574 | − | 0.0459125i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 575.279 | + | 186.919i | 0.952448 | + | 0.309469i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −630.403 | −1.03856 | −0.519278 | − | 0.854605i | \(-0.673799\pi\) | ||||
−0.519278 | + | 0.854605i | \(0.673799\pi\) | |||||||
\(608\) | 300.946 | 0.494977 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.6891i | 0.0273144i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 812.525i | − | 1.32549i | −0.748846 | − | 0.662745i | \(-0.769392\pi\) | ||
0.748846 | − | 0.662745i | \(-0.230608\pi\) | |||||||
\(614\) | 138.754 | + | 190.978i | 0.225984 | + | 0.311040i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 37.7709 | + | 116.247i | 0.0613164 | + | 0.188712i | ||||
\(617\) | 437.935i | 0.709781i | 0.934908 | + | 0.354891i | \(0.115482\pi\) | ||||
−0.934908 | + | 0.354891i | \(0.884518\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 770.250i | 1.24435i | 0.782880 | + | 0.622173i | \(0.213750\pi\) | ||||
−0.782880 | + | 0.622173i | \(0.786250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 197.134 | − | 143.226i | 0.316935 | − | 0.230267i | ||||
\(623\) | 573.702 | 0.920870 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 355.236 | − | 258.094i | 0.567470 | − | 0.412291i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 139.796 | + | 45.4226i | 0.222606 | + | 0.0723290i | ||||
\(629\) | −629.718 | −1.00114 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 875.496i | − | 1.38747i | −0.720228 | − | 0.693737i | \(-0.755963\pi\) | ||
0.720228 | − | 0.693737i | \(-0.244037\pi\) | |||||||
\(632\) | −281.089 | − | 865.102i | −0.444761 | − | 1.36883i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 593.591 | − | 431.269i | 0.936263 | − | 0.680235i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 11.0294i | − | 0.0173146i | ||||||
\(638\) | 20.1812 | − | 14.6625i | 0.0316320 | − | 0.0229820i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −842.571 | −1.31446 | −0.657232 | − | 0.753689i | \(-0.728273\pi\) | ||||
−0.657232 | + | 0.753689i | \(0.728273\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1153.20 | −1.79348 | −0.896738 | − | 0.442563i | \(-0.854069\pi\) | ||||
−0.896738 | + | 0.442563i | \(0.854069\pi\) | |||||||
\(644\) | −169.443 | + | 521.491i | −0.263110 | + | 0.809769i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −264.105 | − | 363.510i | −0.408832 | − | 0.562708i | ||||
\(647\) | −355.751 | −0.549847 | −0.274924 | − | 0.961466i | \(-0.588653\pi\) | ||||
−0.274924 | + | 0.961466i | \(0.588653\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 132.669 | 0.204420 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −374.348 | + | 1152.13i | −0.574154 | + | 1.76706i | ||||
\(653\) | − | 557.915i | − | 0.854387i | −0.904160 | − | 0.427194i | \(-0.859502\pi\) | ||
0.904160 | − | 0.427194i | \(-0.140498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −536.105 | − | 389.503i | −0.817234 | − | 0.593755i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −353.481 | − | 486.525i | −0.537205 | − | 0.739399i | ||||
\(659\) | 284.157i | 0.431194i | 0.976482 | + | 0.215597i | \(0.0691697\pi\) | ||||
−0.976482 | + | 0.215597i | \(0.930830\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 716.735 | 1.08432 | 0.542160 | − | 0.840275i | \(-0.317607\pi\) | ||||
0.542160 | + | 0.840275i | \(0.317607\pi\) | |||||||
\(662\) | 263.490 | − | 191.437i | 0.398021 | − | 0.289179i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 161.613 | − | 52.5112i | 0.243393 | − | 0.0790832i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 111.907 | 0.167776 | ||||||||
\(668\) | −122.845 | + | 378.079i | −0.183900 | + | 0.565986i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 46.9464i | 0.0699648i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 695.378i | 1.03325i | 0.856212 | + | 0.516625i | \(0.172812\pi\) | ||||
−0.856212 | + | 0.516625i | \(0.827188\pi\) | |||||||
\(674\) | −27.6819 | + | 20.1121i | −0.0410711 | + | 0.0298399i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −208.620 | + | 642.066i | −0.308609 | + | 0.949802i | ||||
\(677\) | 820.237i | 1.21158i | 0.795626 | + | 0.605788i | \(0.207142\pi\) | ||||
−0.795626 | + | 0.605788i | \(0.792858\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 333.176i | − | 0.490686i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 100.182 | + | 137.889i | 0.146894 | + | 0.202183i | ||||
\(683\) | −335.508 | −0.491227 | −0.245613 | − | 0.969368i | \(-0.578989\pi\) | ||||
−0.245613 | + | 0.969368i | \(0.578989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −256.393 | − | 352.895i | −0.373751 | − | 0.514424i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 25.9936 | + | 18.8854i | 0.0377814 | + | 0.0274498i | ||||
\(689\) | −10.2167 | −0.0148283 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 336.568i | 0.487074i | 0.969892 | + | 0.243537i | \(0.0783077\pi\) | ||||
−0.969892 | + | 0.243537i | \(0.921692\pi\) | |||||||
\(692\) | 690.997 | + | 224.519i | 0.998551 | + | 0.324449i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 196.906 | + | 271.017i | 0.283726 | + | 0.390515i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 989.378i | 1.41948i | ||||||||
\(698\) | 568.383 | + | 782.312i | 0.814302 | + | 1.12079i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 429.364 | 0.612502 | 0.306251 | − | 0.951951i | \(-0.400925\pi\) | ||||
0.306251 | + | 0.951951i | \(0.400925\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −247.911 | −0.352647 | ||||||||
\(704\) | −67.5666 | − | 92.9974i | −0.0959753 | − | 0.132099i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −498.344 | + | 362.068i | −0.705870 | + | 0.512845i | ||||
\(707\) | −849.703 | −1.20184 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1224.60 | −1.72722 | −0.863609 | − | 0.504162i | \(-0.831801\pi\) | ||||
−0.863609 | + | 0.504162i | \(0.831801\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −513.135 | + | 166.728i | −0.720695 | + | 0.234168i | ||||
\(713\) | 764.604i | 1.07238i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 992.551 | + | 322.499i | 1.38624 | + | 0.450418i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 37.6183 | − | 27.3313i | 0.0523931 | − | 0.0380658i | ||||
\(719\) | 496.022i | 0.689877i | 0.938625 | + | 0.344939i | \(0.112100\pi\) | ||||
−0.938625 | + | 0.344939i | \(0.887900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −304.296 | −0.422047 | ||||||||
\(722\) | 320.407 | + | 441.002i | 0.443777 | + | 0.610806i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −195.023 | + | 600.220i | −0.269369 | + | 0.829033i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 152.843 | 0.210238 | 0.105119 | − | 0.994460i | \(-0.466478\pi\) | ||||
0.105119 | + | 0.994460i | \(0.466478\pi\) | |||||||
\(728\) | 9.92866 | + | 30.5573i | 0.0136383 | + | 0.0419743i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 47.9709i | − | 0.0656237i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 761.286i | 1.03859i | 0.854595 | + | 0.519295i | \(0.173805\pi\) | ||||
−0.854595 | + | 0.519295i | \(0.826195\pi\) | |||||||
\(734\) | 608.152 | + | 837.049i | 0.828544 | + | 1.14039i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 515.679i | − | 0.700650i | ||||||
\(737\) | 159.619i | 0.216580i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 183.975i | 0.248951i | 0.992223 | + | 0.124476i | \(0.0397249\pi\) | ||||
−0.992223 | + | 0.124476i | \(0.960275\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 297.840 | − | 216.393i | 0.401401 | − | 0.291635i | ||||
\(743\) | −495.247 | −0.666551 | −0.333275 | − | 0.942830i | \(-0.608154\pi\) | ||||
−0.333275 | + | 0.942830i | \(0.608154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −142.961 | + | 103.867i | −0.191636 | + | 0.139232i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −53.0353 | + | 163.226i | −0.0709029 | + | 0.218217i | ||||
\(749\) | −1030.13 | −1.37534 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 800.059i | 1.06533i | 0.846328 | + | 0.532663i | \(0.178809\pi\) | ||||
−0.846328 | + | 0.532663i | \(0.821191\pi\) | |||||||
\(752\) | 457.555 | + | 332.433i | 0.608451 | + | 0.442066i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.30495 | − | 3.85427i | 0.00703574 | − | 0.00511177i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 276.367i | − | 0.365082i | −0.983198 | − | 0.182541i | \(-0.941568\pi\) | ||
0.983198 | − | 0.182541i | \(-0.0584322\pi\) | |||||||
\(758\) | 31.2818 | − | 22.7276i | 0.0412689 | − | 0.0299836i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −891.207 | −1.17110 | −0.585550 | − | 0.810636i | \(-0.699121\pi\) | ||||
−0.585550 | + | 0.810636i | \(0.699121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1679.77 | 2.20154 | ||||||||
\(764\) | −1232.93 | − | 400.604i | −1.61379 | − | 0.524351i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 507.390 | + | 698.363i | 0.662389 | + | 0.911700i | ||||
\(767\) | 34.8740 | 0.0454681 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 835.430 | 1.08639 | 0.543193 | − | 0.839608i | \(-0.317215\pi\) | ||||
0.543193 | + | 0.839608i | \(0.317215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 691.521 | + | 224.689i | 0.895753 | + | 0.291048i | ||||
\(773\) | 213.522i | 0.276225i | 0.990417 | + | 0.138112i | \(0.0441035\pi\) | ||||
−0.990417 | + | 0.138112i | \(0.955897\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 96.8266 | + | 298.002i | 0.124777 | + | 0.384023i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −348.386 | − | 479.512i | −0.447796 | − | 0.616339i | ||||
\(779\) | 389.503i | 0.500004i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 70.7926 | 0.0906436 | ||||||||
\(782\) | −622.883 | + | 452.551i | −0.796526 | + | 0.578710i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −302.387 | − | 219.697i | −0.385698 | − | 0.280226i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 370.182 | 0.470371 | 0.235185 | − | 0.971951i | \(-0.424430\pi\) | ||||
0.235185 | + | 0.971951i | \(0.424430\pi\) | |||||||
\(788\) | 534.588 | + | 173.698i | 0.678411 | + | 0.220429i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 691.397i | 0.874080i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.3406i | 0.0155619i | ||||||||
\(794\) | 139.459 | − | 101.323i | 0.175641 | − | 0.127611i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 640.000 | + | 207.949i | 0.804020 | + | 0.261242i | ||||
\(797\) | − | 274.426i | − | 0.344323i | −0.985069 | − | 0.172162i | \(-0.944925\pi\) | ||
0.985069 | − | 0.172162i | \(-0.0550752\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 844.414i | − | 1.05684i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −520.774 | − | 716.784i | −0.649344 | − | 0.893746i | ||||
\(803\) | −247.063 | −0.307675 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.3344 | + | 36.2461i | 0.0326729 | + | 0.0449704i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 759.997 | − | 246.938i | 0.940591 | − | 0.305616i | ||||
\(809\) | 665.214 | 0.822266 | 0.411133 | − | 0.911575i | \(-0.365133\pi\) | ||||
0.411133 | + | 0.911575i | \(0.365133\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 360.665i | − | 0.444717i | −0.974965 | − | 0.222358i | \(-0.928624\pi\) | ||
0.974965 | − | 0.222358i | \(-0.0713755\pi\) | |||||||
\(812\) | −73.0164 | + | 224.721i | −0.0899217 | + | 0.276750i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 55.6594 | + | 76.6086i | 0.0683777 | + | 0.0941138i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 18.8854i | − | 0.0231156i | ||||||
\(818\) | −74.5432 | − | 102.600i | −0.0911286 | − | 0.125428i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 666.899 | 0.812301 | 0.406151 | − | 0.913806i | \(-0.366871\pi\) | ||||
0.406151 | + | 0.913806i | \(0.366871\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −122.433 | −0.148764 | −0.0743822 | − | 0.997230i | \(-0.523698\pi\) | ||||
−0.0743822 | + | 0.997230i | \(0.523698\pi\) | |||||||
\(824\) | 272.170 | − | 88.4335i | 0.330304 | − | 0.107322i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1016.66 | + | 738.644i | −1.23082 | + | 0.894242i | ||||
\(827\) | 1532.98 | 1.85366 | 0.926832 | − | 0.375477i | \(-0.122521\pi\) | ||||
0.926832 | + | 0.375477i | \(0.122521\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 195.475 | 0.235796 | 0.117898 | − | 0.993026i | \(-0.462384\pi\) | ||||
0.117898 | + | 0.993026i | \(0.462384\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17.7609 | − | 24.4458i | −0.0213473 | − | 0.0293820i | ||||
\(833\) | 558.053i | 0.669931i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −20.8792 | + | 64.2597i | −0.0249752 | + | 0.0768656i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 704.942 | − | 512.170i | 0.841219 | − | 0.611182i | ||||
\(839\) | − | 1325.97i | − | 1.58041i | −0.612840 | − | 0.790207i | \(-0.709973\pi\) | ||
0.612840 | − | 0.790207i | \(-0.290027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −792.777 | −0.942660 | ||||||||
\(842\) | −685.254 | − | 943.171i | −0.813841 | − | 1.12016i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −357.390 | − | 116.123i | −0.423448 | − | 0.137587i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1001.85 | 1.18282 | ||||||||
\(848\) | −203.508 | + | 280.105i | −0.239986 | + | 0.330313i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 424.801i | 0.499179i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1055.28i | − | 1.23714i | −0.785730 | − | 0.618570i | \(-0.787712\pi\) | ||
0.785730 | − | 0.618570i | \(-0.212288\pi\) | |||||||
\(854\) | −261.378 | − | 359.756i | −0.306063 | − | 0.421259i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 921.378 | − | 299.374i | 1.07638 | − | 0.349736i | ||||
\(857\) | − | 155.378i | − | 0.181304i | −0.995883 | − | 0.0906521i | \(-0.971105\pi\) | ||
0.995883 | − | 0.0906521i | \(-0.0288951\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 226.033i | − | 0.263136i | −0.991307 | − | 0.131568i | \(-0.957999\pi\) | ||
0.991307 | − | 0.131568i | \(-0.0420011\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 608.190 | − | 441.876i | 0.705557 | − | 0.512617i | ||||
\(863\) | 930.702 | 1.07845 | 0.539225 | − | 0.842162i | \(-0.318717\pi\) | ||||
0.539225 | + | 0.842162i | \(0.318717\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −595.702 | + | 432.803i | −0.687878 | + | 0.499772i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1535.41 | − | 498.885i | −1.76891 | − | 0.574753i | ||||
\(869\) | 204.223 | 0.235009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.9584i | 0.0481727i | ||||||||
\(872\) | −1502.43 | + | 488.170i | −1.72297 | + | 0.559828i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −245.220 | + | 178.163i | −0.280572 | + | 0.203847i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 33.5217i | − | 0.0382231i | −0.999817 | − | 0.0191115i | \(-0.993916\pi\) | ||
0.999817 | − | 0.0191115i | \(-0.00608376\pi\) | |||||||
\(878\) | 782.399 | − | 568.446i | 0.891115 | − | 0.647433i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 933.850 | 1.05999 | 0.529994 | − | 0.848001i | \(-0.322194\pi\) | ||||
0.529994 | + | 0.848001i | \(0.322194\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −542.308 | −0.614166 | −0.307083 | − | 0.951683i | \(-0.599353\pi\) | ||||
−0.307083 | + | 0.951683i | \(0.599353\pi\) | |||||||
\(884\) | −13.9412 | + | 42.9065i | −0.0157706 | + | 0.0485368i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 328.197 | + | 451.724i | 0.370425 | + | 0.509846i | ||||
\(887\) | 714.720 | 0.805773 | 0.402886 | − | 0.915250i | \(-0.368007\pi\) | ||||
0.402886 | + | 0.915250i | \(0.368007\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.7044 | 0.0176652 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −264.562 | + | 814.237i | −0.296594 | + | 0.912822i | ||||
\(893\) | − | 332.433i | − | 0.372266i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1035.54 | + | 336.468i | 1.15574 | + | 0.375522i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 888.824 | + | 1223.36i | 0.989782 | + | 1.36232i | ||||
\(899\) | 329.484i | 0.366500i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 516.932 | 0.573731 | ||||||||
\(902\) | 120.363 | − | 87.4489i | 0.133440 | − | 0.0969500i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −200.932 | − | 618.405i | −0.222270 | − | 0.684076i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −347.233 | −0.382837 | −0.191418 | − | 0.981509i | \(-0.561309\pi\) | ||||
−0.191418 | + | 0.981509i | \(0.561309\pi\) | |||||||
\(908\) | 51.2010 | − | 157.580i | 0.0563888 | − | 0.173547i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1427.54i | − | 1.56701i | −0.621386 | − | 0.783504i | \(-0.713430\pi\) | ||
0.621386 | − | 0.783504i | \(-0.286570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.1517i | 0.0417871i | ||||||||
\(914\) | −462.227 | + | 335.827i | −0.505719 | + | 0.367426i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 90.5774 | − | 278.769i | 0.0988836 | − | 0.304332i | ||||
\(917\) | − | 1919.15i | − | 2.09286i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 569.162i | 0.619327i | 0.950846 | + | 0.309664i | \(0.100216\pi\) | ||||
−0.950846 | + | 0.309664i | \(0.899784\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 116.516 | + | 160.371i | 0.126373 | + | 0.173938i | ||||
\(923\) | 18.6089 | 0.0201614 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −741.319 | − | 1020.34i | −0.800560 | − | 1.10188i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 222.217i | − | 0.239458i | ||||||
\(929\) | 1535.96 | 1.65335 | 0.826675 | − | 0.562680i | \(-0.190230\pi\) | ||||
0.826675 | + | 0.562680i | \(0.190230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 219.697i | 0.235980i | ||||||||
\(932\) | 1168.09 | + | 379.534i | 1.25331 | + | 0.407225i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 583.094 | + | 802.561i | 0.624298 | + | 0.859273i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 338.721i | 0.361496i | 0.983529 | + | 0.180748i | \(0.0578518\pi\) | ||||
−0.983529 | + | 0.180748i | \(0.942148\pi\) | |||||||
\(938\) | −888.693 | − | 1223.18i | −0.947434 | − | 1.30403i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1439.77 | −1.53004 | −0.765022 | − | 0.644004i | \(-0.777272\pi\) | ||||
−0.765022 | + | 0.644004i | \(0.777272\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 667.424 | 0.707766 | ||||||||
\(944\) | 694.663 | − | 956.121i | 0.735871 | − | 1.01284i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.83592 | + | 4.24005i | −0.00616905 | + | 0.00448208i | ||||
\(947\) | 656.135 | 0.692856 | 0.346428 | − | 0.938077i | \(-0.387394\pi\) | ||||
0.346428 | + | 0.938077i | \(0.387394\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −64.9443 | −0.0684344 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −502.358 | − | 1546.10i | −0.527687 | − | 1.62405i | ||||
\(953\) | 436.675i | 0.458211i | 0.973402 | + | 0.229105i | \(0.0735801\pi\) | ||||
−0.973402 | + | 0.229105i | \(0.926420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 163.226 | + | 53.0353i | 0.170739 | + | 0.0554763i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −936.988 | + | 680.762i | −0.978067 | + | 0.710607i | ||||
\(959\) | 449.423i | 0.468637i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1290.20 | −1.34256 | ||||||||
\(962\) | 14.6309 | + | 20.1378i | 0.0152089 | + | 0.0209332i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 166.971 | − | 513.883i | 0.173206 | − | 0.533073i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 903.436 | 0.934267 | 0.467133 | − | 0.884187i | \(-0.345287\pi\) | ||||
0.467133 | + | 0.884187i | \(0.345287\pi\) | |||||||
\(968\) | −896.078 | + | 291.153i | −0.925700 | + | 0.300778i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1866.89i | 1.92265i | 0.275420 | + | 0.961324i | \(0.411183\pi\) | ||||
−0.275420 | + | 0.961324i | \(0.588817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1070.56i | 1.10026i | ||||||||
\(974\) | −736.334 | − | 1013.48i | −0.755990 | − | 1.04053i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 338.334 | + | 245.814i | 0.346654 | + | 0.251859i | ||||
\(977\) | 1073.95i | 1.09923i | 0.835418 | + | 0.549615i | \(0.185226\pi\) | ||||
−0.835418 | + | 0.549615i | \(0.814774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 121.135i | − | 0.123733i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.0842 | − | 26.2167i | 0.0367456 | − | 0.0266973i | ||||
\(983\) | −534.114 | −0.543351 | −0.271675 | − | 0.962389i | \(-0.587578\pi\) | ||||
−0.271675 | + | 0.962389i | \(0.587578\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −268.413 | + | 195.014i | −0.272224 | + | 0.197783i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.48843 | + | 16.8916i | −0.00555509 | + | 0.0170968i | ||||
\(989\) | −32.3607 | −0.0327206 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 520.419i | 0.525146i | 0.964912 | + | 0.262573i | \(0.0845710\pi\) | ||||
−0.964912 | + | 0.262573i | \(0.915429\pi\) | |||||||
\(992\) | 1518.30 | 1.53054 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −542.492 | + | 394.144i | −0.545767 | + | 0.396523i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 457.680i | 0.459057i | 0.973302 | + | 0.229528i | \(0.0737184\pi\) | ||||
−0.973302 | + | 0.229528i | \(0.926282\pi\) | |||||||
\(998\) | 1015.09 | − | 737.508i | 1.01713 | − | 0.738986i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))