Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(451,900)]
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, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.451");
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.c (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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 451.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.451 |
Dual form | 900.3.c.k.451.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | − | 1.17557i | −0.809017 | − | 0.587785i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.23607 | + | 3.80423i | 0.309017 | + | 0.951057i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 8.50651i | − | 1.21522i | −0.794237 | − | 0.607608i | \(-0.792129\pi\) | ||
0.794237 | − | 0.607608i | \(-0.207871\pi\) | |||||||
\(8\) | 2.47214 | − | 7.60845i | 0.309017 | − | 0.951057i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.79611i | 0.163283i | 0.996662 | + | 0.0816415i | \(0.0260162\pi\) | ||||
−0.996662 | + | 0.0816415i | \(0.973984\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.472136 | −0.0363182 | −0.0181591 | − | 0.999835i | \(-0.505781\pi\) | ||||
−0.0181591 | + | 0.999835i | \(0.505781\pi\) | |||||||
\(14\) | −10.0000 | + | 13.7638i | −0.714286 | + | 0.983130i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.9443 | + | 9.40456i | −0.809017 | + | 0.587785i | ||||
\(17\) | −23.8885 | −1.40521 | −0.702604 | − | 0.711581i | \(-0.747980\pi\) | ||||
−0.702604 | + | 0.711581i | \(0.747980\pi\) | |||||||
\(18\) | 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 | ||||||||
\(22\) | 2.11146 | − | 2.90617i | 0.0959753 | − | 0.132099i | ||||
\(23\) | 16.1150i | 0.700650i | 0.936628 | + | 0.350325i | \(0.113929\pi\) | ||||
−0.936628 | + | 0.350325i | \(0.886071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.763932 | + | 0.555029i | 0.0293820 | + | 0.0213473i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 32.3607 | − | 10.5146i | 1.15574 | − | 0.375522i | ||||
\(29\) | −6.94427 | −0.239458 | −0.119729 | − | 0.992807i | \(-0.538203\pi\) | ||||
−0.119729 | + | 0.992807i | \(0.538203\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 47.4468i | − | 1.53054i | −0.643708 | − | 0.765271i | \(-0.722605\pi\) | ||
0.643708 | − | 0.765271i | \(-0.277395\pi\) | |||||||
\(32\) | 32.0000 | 1.00000 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 38.6525 | + | 28.0827i | 1.13684 | + | 0.825961i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −26.3607 | −0.712451 | −0.356225 | − | 0.934400i | \(-0.615936\pi\) | ||||
−0.356225 | + | 0.934400i | \(0.615936\pi\) | |||||||
\(38\) | 11.0557 | − | 15.2169i | 0.290940 | − | 0.400445i | ||||
\(39\) | 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 | ||||||||
\(43\) | − | 2.00811i | − | 0.0467003i | −0.999727 | − | 0.0233502i | \(-0.992567\pi\) | ||
0.999727 | − | 0.0233502i | \(-0.00743326\pi\) | |||||||
\(44\) | −6.83282 | + | 2.22012i | −0.155291 | + | 0.0504572i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.9443 | − | 26.0746i | 0.411832 | − | 0.566838i | ||||
\(47\) | 35.3481i | 0.752087i | 0.926602 | + | 0.376044i | \(0.122716\pi\) | ||||
−0.926602 | + | 0.376044i | \(0.877284\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −23.3607 | −0.476749 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.583592 | − | 1.79611i | −0.0112229 | − | 0.0345406i | ||||
\(53\) | −21.6393 | −0.408289 | −0.204145 | − | 0.978941i | \(-0.565441\pi\) | ||||
−0.204145 | + | 0.978941i | \(0.565441\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −64.7214 | − | 21.0292i | −1.15574 | − | 0.375522i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.2361 | + | 8.16348i | 0.193725 | + | 0.140750i | ||||
\(59\) | 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 | \(0.568729\pi\) | |||||||
\(62\) | −55.7771 | + | 76.7706i | −0.899630 | + | 1.23824i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −51.7771 | − | 37.6183i | −0.809017 | − | 0.587785i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 88.8693i | 1.32641i | 0.748439 | + | 0.663204i | \(0.230804\pi\) | ||||
−0.748439 | + | 0.663204i | \(0.769196\pi\) | |||||||
\(68\) | −29.5279 | − | 90.8774i | −0.434233 | − | 1.33643i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 39.4144i | − | 0.555132i | −0.960707 | − | 0.277566i | \(-0.910472\pi\) | ||
0.960707 | − | 0.277566i | \(-0.0895277\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −137.554 | −1.88430 | −0.942152 | − | 0.335186i | \(-0.891201\pi\) | ||||
−0.942152 | + | 0.335186i | \(0.891201\pi\) | |||||||
\(74\) | 42.6525 | + | 30.9888i | 0.576385 | + | 0.418768i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −35.7771 | + | 11.6247i | −0.470751 | + | 0.152956i | ||||
\(77\) | 15.2786 | 0.198424 | ||||||||
\(78\) | 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 | ||||||||
\(82\) | −67.0132 | − | 48.6879i | −0.817234 | − | 0.593755i | ||||
\(83\) | − | 21.2412i | − | 0.255919i | −0.991779 | − | 0.127959i | \(-0.959157\pi\) | ||
0.991779 | − | 0.127959i | \(-0.0408427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.36068 | + | 3.24920i | −0.0274498 | + | 0.0377814i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.6656 | + | 4.44023i | 0.155291 | + | 0.0504572i | ||||
\(89\) | −67.4427 | −0.757783 | −0.378892 | − | 0.925441i | \(-0.623695\pi\) | ||||
−0.378892 | + | 0.925441i | \(0.623695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.01623i | 0.0441344i | ||||||||
\(92\) | −61.3050 | + | 19.9192i | −0.666358 | + | 0.216513i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 41.5542 | − | 57.1944i | 0.442066 | − | 0.608451i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 39.1672 | 0.403785 | 0.201893 | − | 0.979408i | \(-0.435291\pi\) | ||||
0.201893 | + | 0.979408i | \(0.435291\pi\) | |||||||
\(98\) | 37.7984 | + | 27.4621i | 0.385698 | + | 0.280226i | ||||
\(99\) | 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 | ||||||||
\(103\) | − | 35.7721i | − | 0.347302i | −0.984807 | − | 0.173651i | \(-0.944444\pi\) | ||
0.984807 | − | 0.173651i | \(-0.0555565\pi\) | |||||||
\(104\) | −1.16718 | + | 3.59222i | −0.0112229 | + | 0.0345406i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 35.0132 | + | 25.4385i | 0.330313 | + | 0.239986i | ||||
\(107\) | 121.099i | 1.13177i | 0.824485 | + | 0.565884i | \(0.191465\pi\) | ||||
−0.824485 | + | 0.565884i | \(0.808535\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −197.469 | −1.81164 | −0.905821 | − | 0.423660i | \(-0.860745\pi\) | ||||
−0.905821 | + | 0.423660i | \(0.860745\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 80.0000 | + | 110.111i | 0.714286 | + | 0.983130i | ||||
\(113\) | 81.2786 | 0.719280 | 0.359640 | − | 0.933091i | \(-0.382900\pi\) | ||||
0.359640 | + | 0.933091i | \(0.382900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.58359 | − | 26.4176i | −0.0739965 | − | 0.227738i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 86.8328 | − | 119.515i | 0.735871 | − | 1.01284i | ||||
\(119\) | 203.208i | 1.70763i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 117.774 | 0.973339 | ||||||||
\(122\) | 42.2918 | + | 30.7268i | 0.346654 | + | 0.251859i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 180.498 | − | 58.6475i | 1.45563 | − | 0.472964i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.84616i | − | 0.0145367i | −0.999974 | − | 0.00726834i | \(-0.997686\pi\) | ||
0.999974 | − | 0.00726834i | \(-0.00231361\pi\) | |||||||
\(128\) | 39.5542 | + | 121.735i | 0.309017 | + | 0.951057i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 225.609i | 1.72221i | 0.508428 | + | 0.861105i | \(0.330227\pi\) | ||||
−0.508428 | + | 0.861105i | \(0.669773\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 80.0000 | 0.601504 | ||||||||
\(134\) | 104.472 | − | 143.794i | 0.779643 | − | 1.07309i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −59.0557 | + | 181.755i | −0.434233 | + | 1.33643i | ||||
\(137\) | −52.8328 | −0.385641 | −0.192820 | − | 0.981234i | \(-0.561764\pi\) | ||||
−0.192820 | + | 0.981234i | \(0.561764\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | −46.3344 | + | 63.7738i | −0.326298 | + | 0.449111i | ||||
\(143\) | − | 0.848009i | − | 0.00593013i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 222.567 | + | 161.705i | 1.52443 | + | 1.10757i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −32.5836 | − | 100.282i | −0.220159 | − | 0.677581i | ||||
\(149\) | −132.971 | −0.892420 | −0.446210 | − | 0.894928i | \(-0.647227\pi\) | ||||
−0.446210 | + | 0.894928i | \(0.647227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 151.221i | 1.00146i | 0.865603 | + | 0.500732i | \(0.166936\pi\) | ||||
−0.865603 | + | 0.500732i | \(0.833064\pi\) | |||||||
\(152\) | 71.5542 | + | 23.2494i | 0.470751 | + | 0.152956i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −24.7214 | − | 17.9611i | −0.160528 | − | 0.116631i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.7477 | 0.234062 | 0.117031 | − | 0.993128i | \(-0.462662\pi\) | ||||
0.117031 | + | 0.993128i | \(0.462662\pi\) | |||||||
\(158\) | 133.666 | − | 183.975i | 0.845985 | − | 1.16440i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 137.082 | 0.851441 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 302.854i | 1.85800i | 0.370079 | + | 0.929000i | \(0.379331\pi\) | ||||
−0.370079 | + | 0.929000i | \(0.620669\pi\) | |||||||
\(164\) | 51.1935 | + | 157.557i | 0.312155 | + | 0.960716i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −24.9706 | + | 34.3691i | −0.150425 | + | 0.207043i | ||||
\(167\) | − | 99.3839i | − | 0.595113i | −0.954704 | − | 0.297557i | \(-0.903828\pi\) | ||
0.954704 | − | 0.297557i | \(-0.0961717\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −168.777 | −0.998681 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.63932 | − | 2.48217i | 0.0444147 | − | 0.0144312i | ||||
\(173\) | −181.639 | −1.04994 | −0.524969 | − | 0.851121i | \(-0.675923\pi\) | ||||
−0.524969 | + | 0.851121i | \(0.675923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.8916 | − | 23.2494i | −0.0959753 | − | 0.132099i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 109.125 | + | 79.2837i | 0.613060 | + | 0.445414i | ||||
\(179\) | − | 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 | \(0.356448\pi\) | |||||||
\(182\) | 4.72136 | − | 6.49839i | 0.0259415 | − | 0.0357055i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 122.610 | + | 39.8384i | 0.666358 | + | 0.216513i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 42.9065i | − | 0.229447i | ||||||
\(188\) | −134.472 | + | 43.6926i | −0.715277 | + | 0.232408i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 324.095i | − | 1.69683i | −0.529328 | − | 0.848417i | \(-0.677556\pi\) | ||
0.529328 | − | 0.848417i | \(-0.322444\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −181.777 | −0.941850 | −0.470925 | − | 0.882173i | \(-0.656080\pi\) | ||||
−0.470925 | + | 0.882173i | \(0.656080\pi\) | |||||||
\(194\) | −63.3738 | − | 46.0438i | −0.326669 | − | 0.237339i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −28.8754 | − | 88.8693i | −0.147323 | − | 0.453415i | ||||
\(197\) | 140.525 | 0.713324 | 0.356662 | − | 0.934234i | \(-0.383915\pi\) | ||||
0.356662 | + | 0.934234i | \(0.383915\pi\) | |||||||
\(198\) | 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 | ||||||||
\(202\) | 161.623 | + | 117.426i | 0.800114 | + | 0.581317i | ||||
\(203\) | 59.0715i | 0.290993i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −42.0526 | + | 57.8805i | −0.204139 | + | 0.280973i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.11146 | − | 4.44023i | 0.0293820 | − | 0.0213473i | ||||
\(209\) | −16.8916 | −0.0808213 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 93.9455i | − | 0.445240i | −0.974905 | − | 0.222620i | \(-0.928539\pi\) | ||
0.974905 | − | 0.222620i | \(-0.0714608\pi\) | |||||||
\(212\) | −26.7477 | − | 82.3209i | −0.126168 | − | 0.388306i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 142.361 | − | 195.943i | 0.665237 | − | 0.915620i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −403.607 | −1.85994 | ||||||||
\(218\) | 319.512 | + | 232.139i | 1.46565 | + | 1.06486i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.2786 | 0.0510346 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 214.035i | 0.959797i | 0.877324 | + | 0.479899i | \(0.159327\pi\) | ||||
−0.877324 | + | 0.479899i | \(0.840673\pi\) | |||||||
\(224\) | − | 272.208i | − | 1.21522i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −131.512 | − | 95.5488i | −0.581910 | − | 0.422782i | ||||
\(227\) | 41.4225i | 0.182478i | 0.995829 | + | 0.0912389i | \(0.0290827\pi\) | ||||
−0.995829 | + | 0.0912389i | \(0.970917\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 73.2786 | 0.319994 | 0.159997 | − | 0.987117i | \(-0.448852\pi\) | ||||
0.159997 | + | 0.987117i | \(0.448852\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.1672 | + | 52.8352i | −0.0739965 | + | 0.227738i | ||||
\(233\) | −307.050 | −1.31781 | −0.658905 | − | 0.752227i | \(-0.728980\pi\) | ||||
−0.658905 | + | 0.752227i | \(0.728980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −280.997 | + | 91.3014i | −1.19066 | + | 0.386870i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 238.885 | − | 328.798i | 1.00372 | − | 1.38150i | ||||
\(239\) | − | 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 | \(0.590418\pi\) | |||||||
\(242\) | −190.562 | − | 138.452i | −0.787448 | − | 0.572114i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −32.3081 | − | 99.4340i | −0.132410 | − | 0.407516i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.44023i | − | 0.0179767i | ||||||
\(248\) | −360.997 | − | 117.295i | −1.45563 | − | 0.472964i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 221.169i | − | 0.881152i | −0.897715 | − | 0.440576i | \(-0.854774\pi\) | ||
0.897715 | − | 0.440576i | \(-0.145226\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.9443 | −0.114404 | ||||||||
\(254\) | −2.17029 | + | 2.98715i | −0.00854445 | + | 0.0117604i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 79.1084 | − | 243.470i | 0.309017 | − | 0.951057i | ||||
\(257\) | −257.056 | −1.00022 | −0.500108 | − | 0.865963i | \(-0.666707\pi\) | ||||
−0.500108 | + | 0.865963i | \(0.666707\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 224.237i | 0.865781i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 265.220 | − | 365.044i | 1.01229 | − | 1.39330i | ||||
\(263\) | 164.168i | 0.624212i | 0.950047 | + | 0.312106i | \(0.101034\pi\) | ||||
−0.950047 | + | 0.312106i | \(0.898966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −129.443 | − | 94.0456i | −0.486627 | − | 0.353555i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −338.079 | + | 109.849i | −1.26149 | + | 0.409882i | ||||
\(269\) | 35.4752 | 0.131878 | 0.0659391 | − | 0.997824i | \(-0.478996\pi\) | ||||
0.0659391 | + | 0.997824i | \(0.478996\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 298.950i | − | 1.10314i | −0.834130 | − | 0.551568i | \(-0.814030\pi\) | ||
0.834130 | − | 0.551568i | \(-0.185970\pi\) | |||||||
\(272\) | 309.220 | − | 224.661i | 1.13684 | − | 0.825961i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 85.4853 | + | 62.1087i | 0.311990 | + | 0.226674i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 457.246 | 1.65071 | 0.825354 | − | 0.564616i | \(-0.190976\pi\) | ||||
0.825354 | + | 0.564616i | \(0.190976\pi\) | |||||||
\(278\) | 147.947 | − | 203.632i | 0.532185 | − | 0.732490i | ||||
\(279\) | 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 | ||||||||
\(283\) | − | 169.918i | − | 0.600418i | −0.953874 | − | 0.300209i | \(-0.902944\pi\) | ||
0.953874 | − | 0.300209i | \(-0.0970563\pi\) | |||||||
\(284\) | 149.941 | − | 48.7188i | 0.527962 | − | 0.171545i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.996894 | + | 1.37211i | −0.00348564 | + | 0.00479758i | ||||
\(287\) | − | 352.309i | − | 1.22756i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 281.663 | 0.974611 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −170.026 | − | 523.287i | −0.582282 | − | 1.79208i | ||||
\(293\) | −26.8591 | −0.0916694 | −0.0458347 | − | 0.998949i | \(-0.514595\pi\) | ||||
−0.0458347 | + | 0.998949i | \(0.514595\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −65.1672 | + | 200.564i | −0.220159 | + | 0.677581i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 215.151 | + | 156.316i | 0.721983 | + | 0.524551i | ||||
\(299\) | − | 7.60845i | − | 0.0254463i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.0820 | −0.0567510 | ||||||||
\(302\) | 177.771 | − | 244.681i | 0.588645 | − | 0.810201i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −88.4458 | − | 121.735i | −0.290940 | − | 0.400445i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 118.031i | − | 0.384466i | −0.981349 | − | 0.192233i | \(-0.938427\pi\) | ||
0.981349 | − | 0.192233i | \(-0.0615730\pi\) | |||||||
\(308\) | 18.8854 | + | 58.1234i | 0.0613164 | + | 0.188712i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 121.835i | 0.391753i | 0.980629 | + | 0.195877i | \(0.0627552\pi\) | ||||
−0.980629 | + | 0.195877i | \(0.937245\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −219.548 | −0.701431 | −0.350716 | − | 0.936482i | \(-0.614062\pi\) | ||||
−0.350716 | + | 0.936482i | \(0.614062\pi\) | |||||||
\(314\) | −59.4590 | − | 43.1995i | −0.189360 | − | 0.137578i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −432.551 | + | 140.544i | −1.36883 | + | 0.444761i | ||||
\(317\) | 366.859 | 1.15728 | 0.578642 | − | 0.815582i | \(-0.303583\pi\) | ||||
0.578642 | + | 0.815582i | \(0.303583\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 12.4727i | − | 0.0390993i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −221.803 | − | 161.150i | −0.688830 | − | 0.500465i | ||||
\(323\) | − | 224.661i | − | 0.695546i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 356.026 | − | 490.028i | 1.09211 | − | 1.50315i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 102.387 | − | 315.115i | 0.312155 | − | 0.960716i | ||||
\(329\) | 300.689 | 0.913948 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 162.846i | 0.491981i | 0.969272 | + | 0.245990i | \(0.0791132\pi\) | ||||
−0.969272 | + | 0.245990i | \(0.920887\pi\) | |||||||
\(332\) | 80.8065 | − | 26.2556i | 0.243393 | − | 0.0790832i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −116.833 | + | 160.807i | −0.349799 | + | 0.481457i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1084 | −0.0507666 | −0.0253833 | − | 0.999678i | \(-0.508081\pi\) | ||||
−0.0253833 | + | 0.999678i | \(0.508081\pi\) | |||||||
\(338\) | 273.087 | + | 198.409i | 0.807950 | + | 0.587010i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 85.2198 | 0.249911 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 218.101i | − | 0.635863i | ||||||
\(344\) | −15.2786 | − | 4.96433i | −0.0444147 | − | 0.0144312i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 293.899 | + | 213.530i | 0.849418 | + | 0.617138i | ||||
\(347\) | − | 167.498i | − | 0.482703i | −0.970438 | − | 0.241351i | \(-0.922409\pi\) | ||
0.970438 | − | 0.241351i | \(-0.0775906\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −483.495 | −1.38537 | −0.692687 | − | 0.721239i | \(-0.743573\pi\) | ||||
−0.692687 | + | 0.721239i | \(0.743573\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 57.4756i | 0.163283i | ||||||||
\(353\) | 307.994 | 0.872504 | 0.436252 | − | 0.899825i | \(-0.356306\pi\) | ||||
0.436252 | + | 0.899825i | \(0.356306\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −83.3638 | − | 256.567i | −0.234168 | − | 0.720695i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −306.715 | + | 422.157i | −0.856746 | + | 1.17921i | ||||
\(359\) | − | 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 | ||||||||
\(362\) | −255.289 | − | 185.478i | −0.705217 | − | 0.512370i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.2786 | + | 4.96433i | −0.0419743 | + | 0.0136383i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 517.325i | − | 1.40960i | −0.709404 | − | 0.704802i | \(-0.751036\pi\) | ||
0.709404 | − | 0.704802i | \(-0.248964\pi\) | |||||||
\(368\) | −151.554 | − | 208.596i | −0.411832 | − | 0.566838i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 184.075i | 0.496159i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 88.3545 | 0.236875 | 0.118438 | − | 0.992961i | \(-0.462211\pi\) | ||||
0.118438 | + | 0.992961i | \(0.462211\pi\) | |||||||
\(374\) | −50.4396 | + | 69.4242i | −0.134865 | + | 0.185626i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 268.944 | + | 87.3853i | 0.715277 | + | 0.232408i | ||||
\(377\) | 3.27864 | 0.00869666 | ||||||||
\(378\) | 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 | ||||||||
\(382\) | −380.997 | + | 524.397i | −0.997374 | + | 1.37277i | ||||
\(383\) | 431.612i | 1.12692i | 0.826142 | + | 0.563462i | \(0.190531\pi\) | ||||
−0.826142 | + | 0.563462i | \(0.809469\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 294.122 | + | 213.692i | 0.761973 | + | 0.553606i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 48.4133 | + | 149.001i | 0.124777 | + | 0.384023i | ||||
\(389\) | 296.354 | 0.761837 | 0.380918 | − | 0.924609i | \(-0.375608\pi\) | ||||
0.380918 | + | 0.924609i | \(0.375608\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 384.963i | − | 0.984560i | ||||||
\(392\) | −57.7508 | + | 177.739i | −0.147323 | + | 0.453415i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −227.374 | − | 165.197i | −0.577091 | − | 0.419281i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 86.1904 | 0.217104 | 0.108552 | − | 0.994091i | \(-0.465379\pi\) | ||||
0.108552 | + | 0.994091i | \(0.465379\pi\) | |||||||
\(398\) | −197.771 | + | 272.208i | −0.496912 | + | 0.683940i | ||||
\(399\) | 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 | ||||||||
\(403\) | 22.4014i | 0.0555865i | ||||||||
\(404\) | −123.469 | − | 379.999i | −0.305616 | − | 0.940591i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 69.4427 | − | 95.5797i | 0.171041 | − | 0.235418i | ||||
\(407\) | − | 47.3467i | − | 0.116331i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 63.4102 | 0.155037 | 0.0775186 | − | 0.996991i | \(-0.475300\pi\) | ||||
0.0775186 | + | 0.996991i | \(0.475300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 136.085 | − | 44.2167i | 0.330304 | − | 0.107322i | ||||
\(413\) | 628.328 | 1.52138 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −15.1084 | −0.0363182 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 27.3313 | + | 19.8573i | 0.0653858 | + | 0.0475056i | ||||
\(419\) | − | 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 | \(0.743400\pi\) | |||||||
\(422\) | −110.440 | + | 152.007i | −0.261705 | + | 0.360206i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −53.4953 | + | 164.642i | −0.126168 | + | 0.388306i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 222.341i | 0.520705i | ||||||||
\(428\) | −460.689 | + | 149.687i | −1.07638 | + | 0.349736i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 375.882i | 0.872117i | 0.899918 | + | 0.436058i | \(0.143626\pi\) | ||||
−0.899918 | + | 0.436058i | \(0.856374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 368.164 | 0.850263 | 0.425132 | − | 0.905131i | \(-0.360228\pi\) | ||||
0.425132 | + | 0.905131i | \(0.360228\pi\) | |||||||
\(434\) | 653.050 | + | 474.468i | 1.50472 | + | 1.09324i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −244.085 | − | 751.217i | −0.559828 | − | 1.72297i | ||||
\(437\) | −151.554 | −0.346806 | ||||||||
\(438\) | 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 | ||||||||
\(442\) | −18.2492 | − | 13.2588i | −0.0412878 | − | 0.0299974i | ||||
\(443\) | 279.181i | 0.630205i | 0.949058 | + | 0.315102i | \(0.102039\pi\) | ||||
−0.949058 | + | 0.315102i | \(0.897961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 251.613 | − | 346.316i | 0.564155 | − | 0.776492i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −320.000 | + | 440.442i | −0.714286 | + | 0.983130i | ||||
\(449\) | −756.079 | −1.68392 | −0.841959 | − | 0.539542i | \(-0.818597\pi\) | ||||
−0.841959 | + | 0.539542i | \(0.818597\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 74.3885i | 0.164941i | ||||||||
\(452\) | 100.466 | + | 309.202i | 0.222270 | + | 0.684076i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 48.6950 | − | 67.0230i | 0.107258 | − | 0.147628i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −285.672 | −0.625103 | −0.312551 | − | 0.949901i | \(-0.601184\pi\) | ||||
−0.312551 | + | 0.949901i | \(0.601184\pi\) | |||||||
\(458\) | −118.567 | − | 86.1442i | −0.258881 | − | 0.188088i | ||||
\(459\) | 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 | ||||||||
\(463\) | − | 630.603i | − | 1.36199i | −0.732286 | − | 0.680997i | \(-0.761547\pi\) | ||
0.732286 | − | 0.680997i | \(-0.238453\pi\) | |||||||
\(464\) | 89.8885 | − | 65.3078i | 0.193725 | − | 0.140750i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 496.817 | + | 360.958i | 1.06613 | + | 0.774589i | ||||
\(467\) | − | 496.010i | − | 1.06212i | −0.847334 | − | 0.531060i | \(-0.821794\pi\) | ||
0.847334 | − | 0.531060i | \(-0.178206\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 755.967 | 1.61187 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 561.994 | + | 182.603i | 1.19066 | + | 0.386870i | ||||
\(473\) | 3.60680 | 0.00762537 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −773.050 | + | 251.179i | −1.62405 | + | 0.527687i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −50.4396 | + | 69.4242i | −0.105522 | + | 0.145239i | ||||
\(479\) | 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 | ||||||||
\(482\) | 218.567 | + | 158.798i | 0.453459 | + | 0.329457i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 145.577 | + | 448.039i | 0.300778 | + | 0.925700i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 626.363i | 1.28617i | 0.765796 | + | 0.643084i | \(0.222345\pi\) | ||||
−0.765796 | + | 0.643084i | \(0.777655\pi\) | |||||||
\(488\) | −64.6161 | + | 198.868i | −0.132410 | + | 0.407516i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.3013i | 0.0454201i | 0.999742 | + | 0.0227100i | \(0.00722945\pi\) | ||||
−0.999742 | + | 0.0227100i | \(0.992771\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 165.889 | 0.336488 | ||||||||
\(494\) | −5.21981 | + | 7.18445i | −0.0105664 | + | 0.0145434i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 446.217 | + | 614.165i | 0.899630 | + | 1.23824i | ||||
\(497\) | −335.279 | −0.674605 | ||||||||
\(498\) | 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 | ||||||||
\(502\) | −260.000 | + | 357.859i | −0.517928 | + | 0.712867i | ||||
\(503\) | − | 780.853i | − | 1.55239i | −0.630492 | − | 0.776196i | \(-0.717147\pi\) | ||
0.630492 | − | 0.776196i | \(-0.282853\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 46.8328 | + | 34.0260i | 0.0925550 | + | 0.0672451i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.02321 | − | 2.28198i | 0.0138252 | − | 0.00449208i | ||||
\(509\) | 288.950 | 0.567683 | 0.283841 | − | 0.958871i | \(-0.408391\pi\) | ||||
0.283841 | + | 0.958871i | \(0.408391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1170.11i | 2.28984i | ||||||||
\(512\) | −414.217 | + | 300.946i | −0.809017 | + | 0.587785i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 415.925 | + | 302.187i | 0.809192 | + | 0.587913i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −63.4891 | −0.122803 | ||||||||
\(518\) | 263.607 | − | 362.824i | 0.508893 | − | 0.700432i | ||||
\(519\) | 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 | ||||||||
\(523\) | 367.962i | 0.703560i | 0.936083 | + | 0.351780i | \(0.114423\pi\) | ||||
−0.936083 | + | 0.351780i | \(0.885577\pi\) | |||||||
\(524\) | −858.269 | + | 278.869i | −1.63792 | + | 0.532192i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 192.991 | − | 265.629i | 0.366902 | − | 0.504998i | ||||
\(527\) | 1133.44i | 2.15073i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 269.308 | 0.509089 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 98.8854 | + | 304.338i | 0.185875 | + | 0.572064i | ||||
\(533\) | −19.5542 | −0.0366870 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 676.158 | + | 219.697i | 1.26149 | + | 0.409882i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −57.4001 | − | 41.7036i | −0.106692 | − | 0.0775161i | ||||
\(539\) | − | 41.9584i | − | 0.0778449i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −616.885 | −1.14027 | −0.570134 | − | 0.821551i | \(-0.693109\pi\) | ||||
−0.570134 | + | 0.821551i | \(0.693109\pi\) | |||||||
\(542\) | −351.437 | + | 483.711i | −0.648407 | + | 0.892455i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −764.433 | −1.40521 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 97.8499i | − | 0.178885i | −0.995992 | − | 0.0894423i | \(-0.971492\pi\) | ||
0.995992 | − | 0.0894423i | \(-0.0285085\pi\) | |||||||
\(548\) | −65.3050 | − | 200.988i | −0.119170 | − | 0.366766i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 65.3078i | − | 0.118526i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 967.214 | 1.74903 | ||||||||
\(554\) | −739.840 | − | 537.525i | −1.33545 | − | 0.970262i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −478.768 | + | 155.561i | −0.861093 | + | 0.279786i | ||||
\(557\) | 896.302 | 1.60916 | 0.804580 | − | 0.593845i | \(-0.202391\pi\) | ||||
0.804580 | + | 0.593845i | \(0.202391\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.948103i | 0.00169607i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.12461 | − | 6.62942i | −0.0162360 | − | 0.0117961i | ||||
\(563\) | − | 771.186i | − | 1.36978i | −0.728647 | − | 0.684890i | \(-0.759850\pi\) | ||
0.728647 | − | 0.684890i | \(-0.240150\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −199.751 | + | 274.933i | −0.352917 | + | 0.485748i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −299.882 | − | 97.4377i | −0.527962 | − | 0.171545i | ||||
\(569\) | −8.74767 | −0.0153738 | −0.00768688 | − | 0.999970i | \(-0.502447\pi\) | ||||
−0.00768688 | + | 0.999970i | \(0.502447\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 511.138i | − | 0.895164i | −0.894243 | − | 0.447582i | \(-0.852285\pi\) | ||
0.894243 | − | 0.447582i | \(-0.147715\pi\) | |||||||
\(572\) | 3.22602 | − | 1.04820i | 0.00563989 | − | 0.00183251i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −414.164 | + | 570.048i | −0.721540 | + | 0.993115i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 713.712 | 1.23694 | 0.618468 | − | 0.785810i | \(-0.287754\pi\) | ||||
0.618468 | + | 0.785810i | \(0.287754\pi\) | |||||||
\(578\) | −455.740 | − | 331.114i | −0.788477 | − | 0.572862i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −180.689 | −0.310996 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 38.8666i | − | 0.0666666i | ||||||
\(584\) | −340.053 | + | 1046.57i | −0.582282 | + | 1.79208i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.4590 | + | 31.5748i | 0.0741621 | + | 0.0538819i | ||||
\(587\) | 422.169i | 0.719198i | 0.933107 | + | 0.359599i | \(0.117086\pi\) | ||||
−0.933107 | + | 0.359599i | \(0.882914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 446.217 | 0.757584 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 341.220 | − | 247.911i | 0.576385 | − | 0.418768i | ||||
\(593\) | −308.663 | −0.520510 | −0.260255 | − | 0.965540i | \(-0.583807\pi\) | ||||
−0.260255 | + | 0.965540i | \(0.583807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −164.361 | − | 505.850i | −0.275773 | − | 0.848742i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.94427 | + | 12.3107i | −0.0149570 | + | 0.0205865i | ||||
\(599\) | − | 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 | \(0.404468\pi\) | |||||||
\(602\) | 27.6393 | + | 20.0811i | 0.0459125 | + | 0.0333574i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −575.279 | + | 186.919i | −0.952448 | + | 0.309469i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 630.403i | 1.03856i | 0.854605 | + | 0.519278i | \(0.173799\pi\) | ||||
−0.854605 | + | 0.519278i | \(0.826201\pi\) | |||||||
\(608\) | 300.946i | 0.494977i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 16.6891i | − | 0.0273144i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −812.525 | −1.32549 | −0.662745 | − | 0.748846i | \(-0.730608\pi\) | ||||
−0.662745 | + | 0.748846i | \(0.730608\pi\) | |||||||
\(614\) | −138.754 | + | 190.978i | −0.225984 | + | 0.311040i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 37.7709 | − | 116.247i | 0.0613164 | − | 0.188712i | ||||
\(617\) | −437.935 | −0.709781 | −0.354891 | − | 0.934908i | \(-0.615482\pi\) | ||||
−0.354891 | + | 0.934908i | \(0.615482\pi\) | |||||||
\(618\) | 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 | ||||||||
\(622\) | 143.226 | − | 197.134i | 0.230267 | − | 0.316935i | ||||
\(623\) | 573.702i | 0.920870i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 355.236 | + | 258.094i | 0.567470 | + | 0.412291i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 45.4226 | + | 139.796i | 0.0723290 | + | 0.222606i | ||||
\(629\) | 629.718 | 1.00114 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 875.496i | 1.38747i | 0.720228 | + | 0.693737i | \(0.244037\pi\) | ||||
−0.720228 | + | 0.693737i | \(0.755963\pi\) | |||||||
\(632\) | 865.102 | + | 281.089i | 1.36883 | + | 0.444761i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −593.591 | − | 431.269i | −0.936263 | − | 0.680235i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.0294 | 0.0173146 | ||||||||
\(638\) | −14.6625 | + | 20.1812i | −0.0229820 | + | 0.0316320i | ||||
\(639\) | 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 | ||||||||
\(643\) | − | 1153.20i | − | 1.79348i | −0.442563 | − | 0.896738i | \(-0.645931\pi\) | ||
0.442563 | − | 0.896738i | \(-0.354069\pi\) | |||||||
\(644\) | 169.443 | + | 521.491i | 0.263110 | + | 0.809769i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −264.105 | + | 363.510i | −0.408832 | + | 0.562708i | ||||
\(647\) | 355.751i | 0.549847i | 0.961466 | + | 0.274924i | \(0.0886526\pi\) | ||||
−0.961466 | + | 0.274924i | \(0.911347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −132.669 | −0.204420 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1152.13 | + | 374.348i | −1.76706 | + | 0.574154i | ||||
\(653\) | −557.915 | −0.854387 | −0.427194 | − | 0.904160i | \(-0.640498\pi\) | ||||
−0.427194 | + | 0.904160i | \(0.640498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −536.105 | + | 389.503i | −0.817234 | + | 0.593755i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −486.525 | − | 353.481i | −0.739399 | − | 0.537205i | ||||
\(659\) | 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 | \(0.317607\pi\) | |||||||
\(662\) | 191.437 | − | 263.490i | 0.289179 | − | 0.398021i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −161.613 | − | 52.5112i | −0.243393 | − | 0.0790832i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 111.907i | − | 0.167776i | ||||||
\(668\) | 378.079 | − | 122.845i | 0.565986 | − | 0.183900i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 46.9464i | − | 0.0699648i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 695.378 | 1.03325 | 0.516625 | − | 0.856212i | \(-0.327188\pi\) | ||||
0.516625 | + | 0.856212i | \(0.327188\pi\) | |||||||
\(674\) | 27.6819 | + | 20.1121i | 0.0410711 | + | 0.0298399i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −208.620 | − | 642.066i | −0.308609 | − | 0.949802i | ||||
\(677\) | −820.237 | −1.21158 | −0.605788 | − | 0.795626i | \(-0.707142\pi\) | ||||
−0.605788 | + | 0.795626i | \(0.707142\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 333.176i | − | 0.490686i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −137.889 | − | 100.182i | −0.202183 | − | 0.146894i | ||||
\(683\) | − | 335.508i | − | 0.491227i | −0.969368 | − | 0.245613i | \(-0.921011\pi\) | ||
0.969368 | − | 0.245613i | \(-0.0789894\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −256.393 | + | 352.895i | −0.373751 | + | 0.514424i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18.8854 | + | 25.9936i | 0.0274498 | + | 0.0377814i | ||||
\(689\) | 10.2167 | 0.0148283 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 336.568i | − | 0.487074i | −0.969892 | − | 0.243537i | \(-0.921692\pi\) | ||
0.969892 | − | 0.243537i | \(-0.0783077\pi\) | |||||||
\(692\) | −224.519 | − | 690.997i | −0.324449 | − | 0.998551i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −196.906 | + | 271.017i | −0.283726 | + | 0.390515i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −989.378 | −1.41948 | ||||||||
\(698\) | 782.312 | + | 568.383i | 1.12079 | + | 0.814302i | ||||
\(699\) | 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 | ||||||||
\(703\) | − | 247.911i | − | 0.352647i | ||||||
\(704\) | 67.5666 | − | 92.9974i | 0.0959753 | − | 0.132099i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −498.344 | − | 362.068i | −0.705870 | − | 0.512845i | ||||
\(707\) | 849.703i | 1.20184i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1224.60 | 1.72722 | 0.863609 | − | 0.504162i | \(-0.168199\pi\) | ||||
0.863609 | + | 0.504162i | \(0.168199\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −166.728 | + | 513.135i | −0.234168 | + | 0.720695i | ||||
\(713\) | 764.604 | 1.07238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 992.551 | − | 322.499i | 1.38624 | − | 0.450418i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −27.3313 | + | 37.6183i | −0.0380658 | + | 0.0523931i | ||||
\(719\) | 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 | ||||||||
\(722\) | −441.002 | − | 320.407i | −0.610806 | − | 0.443777i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 195.023 | + | 600.220i | 0.269369 | + | 0.829033i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 152.843i | − | 0.210238i | −0.994460 | − | 0.105119i | \(-0.966478\pi\) | ||
0.994460 | − | 0.105119i | \(-0.0335224\pi\) | |||||||
\(728\) | 30.5573 | + | 9.92866i | 0.0419743 | + | 0.0136383i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.9709i | 0.0656237i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 761.286 | 1.03859 | 0.519295 | − | 0.854595i | \(-0.326195\pi\) | ||||
0.519295 | + | 0.854595i | \(0.326195\pi\) | |||||||
\(734\) | −608.152 | + | 837.049i | −0.828544 | + | 1.14039i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 515.679i | 0.700650i | ||||||||
\(737\) | −159.619 | −0.216580 | ||||||||
\(738\) | 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 | ||||||||
\(742\) | 216.393 | − | 297.840i | 0.291635 | − | 0.401401i | ||||
\(743\) | − | 495.247i | − | 0.666551i | −0.942830 | − | 0.333275i | \(-0.891846\pi\) | ||
0.942830 | − | 0.333275i | \(-0.108154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −142.961 | − | 103.867i | −0.191636 | − | 0.139232i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 163.226 | − | 53.0353i | 0.218217 | − | 0.0709029i | ||||
\(749\) | 1030.13 | 1.37534 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 800.059i | − | 1.06533i | −0.846328 | − | 0.532663i | \(-0.821191\pi\) | ||
0.846328 | − | 0.532663i | \(-0.178809\pi\) | |||||||
\(752\) | −332.433 | − | 457.555i | −0.442066 | − | 0.608451i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.30495 | − | 3.85427i | −0.00703574 | − | 0.00511177i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 276.367 | 0.365082 | 0.182541 | − | 0.983198i | \(-0.441568\pi\) | ||||
0.182541 | + | 0.983198i | \(0.441568\pi\) | |||||||
\(758\) | −22.7276 | + | 31.2818i | −0.0299836 | + | 0.0412689i | ||||
\(759\) | 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 | ||||||||
\(763\) | 1679.77i | 2.20154i | ||||||||
\(764\) | 1232.93 | − | 400.604i | 1.61379 | − | 0.524351i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 507.390 | − | 698.363i | 0.662389 | − | 0.911700i | ||||
\(767\) | − | 34.8740i | − | 0.0454681i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −835.430 | −1.08639 | −0.543193 | − | 0.839608i | \(-0.682785\pi\) | ||||
−0.543193 | + | 0.839608i | \(0.682785\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −224.689 | − | 691.521i | −0.291048 | − | 0.895753i | ||||
\(773\) | 213.522 | 0.276225 | 0.138112 | − | 0.990417i | \(-0.455897\pi\) | ||||
0.138112 | + | 0.990417i | \(0.455897\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 96.8266 | − | 298.002i | 0.124777 | − | 0.384023i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −479.512 | − | 348.386i | −0.616339 | − | 0.447796i | ||||
\(779\) | 389.503i | 0.500004i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 70.7926 | 0.0906436 | ||||||||
\(782\) | −452.551 | + | 622.883i | −0.578710 | + | 0.796526i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 302.387 | − | 219.697i | 0.385698 | − | 0.280226i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 370.182i | − | 0.470371i | −0.971951 | − | 0.235185i | \(-0.924430\pi\) | ||
0.971951 | − | 0.235185i | \(-0.0755697\pi\) | |||||||
\(788\) | 173.698 | + | 534.588i | 0.220429 | + | 0.678411i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 691.397i | − | 0.874080i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.3406 | 0.0155619 | ||||||||
\(794\) | −139.459 | − | 101.323i | −0.175641 | − | 0.127611i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 640.000 | − | 207.949i | 0.804020 | − | 0.261242i | ||||
\(797\) | 274.426 | 0.344323 | 0.172162 | − | 0.985069i | \(-0.444925\pi\) | ||||
0.172162 | + | 0.985069i | \(0.444925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 844.414i | − | 1.05684i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 716.784 | + | 520.774i | 0.893746 | + | 0.649344i | ||||
\(803\) | − | 247.063i | − | 0.307675i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.3344 | − | 36.2461i | 0.0326729 | − | 0.0449704i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −246.938 | + | 759.997i | −0.305616 | + | 0.940591i | ||||
\(809\) | −665.214 | −0.822266 | −0.411133 | − | 0.911575i | \(-0.634867\pi\) | ||||
−0.411133 | + | 0.911575i | \(0.634867\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 360.665i | 0.444717i | 0.974965 | + | 0.222358i | \(0.0713755\pi\) | ||||
−0.974965 | + | 0.222358i | \(0.928624\pi\) | |||||||
\(812\) | −224.721 | + | 73.0164i | −0.276750 | + | 0.0899217i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −55.6594 | + | 76.6086i | −0.0683777 | + | 0.0941138i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.8854 | 0.0231156 | ||||||||
\(818\) | −102.600 | − | 74.5432i | −0.125428 | − | 0.0911286i | ||||
\(819\) | 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 | ||||||||
\(823\) | − | 122.433i | − | 0.148764i | −0.997230 | − | 0.0743822i | \(-0.976302\pi\) | ||
0.997230 | − | 0.0743822i | \(-0.0236985\pi\) | |||||||
\(824\) | −272.170 | − | 88.4335i | −0.330304 | − | 0.107322i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1016.66 | − | 738.644i | −1.23082 | − | 0.894242i | ||||
\(827\) | − | 1532.98i | − | 1.85366i | −0.375477 | − | 0.926832i | \(-0.622521\pi\) | ||
0.375477 | − | 0.926832i | \(-0.377479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −195.475 | −0.235796 | −0.117898 | − | 0.993026i | \(-0.537616\pi\) | ||||
−0.117898 | + | 0.993026i | \(0.537616\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.4458 | + | 17.7609i | 0.0293820 | + | 0.0213473i | ||||
\(833\) | 558.053 | 0.669931 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −20.8792 | − | 64.2597i | −0.0249752 | − | 0.0768656i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −512.170 | + | 704.942i | −0.611182 | + | 0.841219i | ||||
\(839\) | − | 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 | ||||||||
\(842\) | 943.171 | + | 685.254i | 1.12016 | + | 0.813841i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 357.390 | − | 116.123i | 0.423448 | − | 0.137587i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1001.85i | − | 1.18282i | ||||||
\(848\) | 280.105 | − | 203.508i | 0.330313 | − | 0.239986i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 424.801i | − | 0.499179i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1055.28 | −1.23714 | −0.618570 | − | 0.785730i | \(-0.712288\pi\) | ||||
−0.618570 | + | 0.785730i | \(0.712288\pi\) | |||||||
\(854\) | 261.378 | − | 359.756i | 0.306063 | − | 0.421259i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 921.378 | + | 299.374i | 1.07638 | + | 0.349736i | ||||
\(857\) | 155.378 | 0.181304 | 0.0906521 | − | 0.995883i | \(-0.471105\pi\) | ||||
0.0906521 | + | 0.995883i | \(0.471105\pi\) | |||||||
\(858\) | 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 | ||||||||
\(862\) | 441.876 | − | 608.190i | 0.512617 | − | 0.705557i | ||||
\(863\) | 930.702i | 1.07845i | 0.842162 | + | 0.539225i | \(0.181283\pi\) | ||||
−0.842162 | + | 0.539225i | \(0.818717\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −595.702 | − | 432.803i | −0.687878 | − | 0.499772i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −498.885 | − | 1535.41i | −0.574753 | − | 1.76891i | ||||
\(869\) | −204.223 | −0.235009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 41.9584i | − | 0.0481727i | ||||||
\(872\) | −488.170 | + | 1502.43i | −0.559828 | + | 1.72297i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 245.220 | + | 178.163i | 0.280572 | + | 0.203847i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.5217 | 0.0382231 | 0.0191115 | − | 0.999817i | \(-0.493916\pi\) | ||||
0.0191115 | + | 0.999817i | \(0.493916\pi\) | |||||||
\(878\) | −568.446 | + | 782.399i | −0.647433 | + | 0.891115i | ||||
\(879\) | 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 | ||||||||
\(883\) | − | 542.308i | − | 0.614166i | −0.951683 | − | 0.307083i | \(-0.900647\pi\) | ||
0.951683 | − | 0.307083i | \(-0.0993529\pi\) | |||||||
\(884\) | 13.9412 | + | 42.9065i | 0.0157706 | + | 0.0485368i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 328.197 | − | 451.724i | 0.370425 | − | 0.509846i | ||||
\(887\) | − | 714.720i | − | 0.805773i | −0.915250 | − | 0.402886i | \(-0.868007\pi\) | ||
0.915250 | − | 0.402886i | \(-0.131993\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.7044 | −0.0176652 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −814.237 | + | 264.562i | −0.912822 | + | 0.296594i | ||||
\(893\) | −332.433 | −0.372266 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1035.54 | − | 336.468i | 1.15574 | − | 0.375522i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1223.36 | + | 888.824i | 1.36232 | + | 0.989782i | ||||
\(899\) | 329.484i | 0.366500i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 516.932 | 0.573731 | ||||||||
\(902\) | 87.4489 | − | 120.363i | 0.0969500 | − | 0.133440i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 200.932 | − | 618.405i | 0.222270 | − | 0.684076i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 347.233i | 0.382837i | 0.981509 | + | 0.191418i | \(0.0613087\pi\) | ||||
−0.981509 | + | 0.191418i | \(0.938691\pi\) | |||||||
\(908\) | −157.580 | + | 51.2010i | −0.173547 | + | 0.0563888i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1427.54i | 1.56701i | 0.621386 | + | 0.783504i | \(0.286570\pi\) | ||||
−0.621386 | + | 0.783504i | \(0.713430\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.1517 | 0.0417871 | ||||||||
\(914\) | 462.227 | + | 335.827i | 0.505719 | + | 0.367426i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 90.5774 | + | 278.769i | 0.0988836 | + | 0.304332i | ||||
\(917\) | 1919.15 | 2.09286 | ||||||||
\(918\) | 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 | ||||||||
\(922\) | −160.371 | − | 116.516i | −0.173938 | − | 0.126373i | ||||
\(923\) | 18.6089i | 0.0201614i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −741.319 | + | 1020.34i | −0.800560 | + | 1.10188i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −222.217 | −0.239458 | ||||||||
\(929\) | −1535.96 | −1.65335 | −0.826675 | − | 0.562680i | \(-0.809770\pi\) | ||||
−0.826675 | + | 0.562680i | \(0.809770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 219.697i | − | 0.235980i | ||||||
\(932\) | −379.534 | − | 1168.09i | −0.407225 | − | 1.25331i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −583.094 | + | 802.561i | −0.624298 | + | 0.859273i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −338.721 | −0.361496 | −0.180748 | − | 0.983529i | \(-0.557852\pi\) | ||||
−0.180748 | + | 0.983529i | \(0.557852\pi\) | |||||||
\(938\) | −1223.18 | − | 888.693i | −1.30403 | − | 0.947434i | ||||
\(939\) | 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 | ||||||||
\(943\) | 667.424i | 0.707766i | ||||||||
\(944\) | −694.663 | − | 956.121i | −0.735871 | − | 1.01284i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.83592 | − | 4.24005i | −0.00616905 | − | 0.00448208i | ||||
\(947\) | − | 656.135i | − | 0.692856i | −0.938077 | − | 0.346428i | \(-0.887394\pi\) | ||
0.938077 | − | 0.346428i | \(-0.112606\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 64.9443 | 0.0684344 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1546.10 | + | 502.358i | 1.62405 | + | 0.527687i | ||||
\(953\) | 436.675 | 0.458211 | 0.229105 | − | 0.973402i | \(-0.426420\pi\) | ||||
0.229105 | + | 0.973402i | \(0.426420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 163.226 | − | 53.0353i | 0.170739 | − | 0.0554763i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 680.762 | − | 936.988i | 0.710607 | − | 0.978067i | ||||
\(959\) | 449.423i | 0.468637i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1290.20 | −1.34256 | ||||||||
\(962\) | −20.1378 | − | 14.6309i | −0.0209332 | − | 0.0152089i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −166.971 | − | 513.883i | −0.173206 | − | 0.533073i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 903.436i | − | 0.934267i | −0.884187 | − | 0.467133i | \(-0.845287\pi\) | ||
0.884187 | − | 0.467133i | \(-0.154713\pi\) | |||||||
\(968\) | 291.153 | − | 896.078i | 0.300778 | − | 0.925700i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1866.89i | − | 1.92265i | −0.275420 | − | 0.961324i | \(-0.588817\pi\) | ||
0.275420 | − | 0.961324i | \(-0.411183\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1070.56 | 1.10026 | ||||||||
\(974\) | 736.334 | − | 1013.48i | 0.755990 | − | 1.04053i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 338.334 | − | 245.814i | 0.346654 | − | 0.251859i | ||||
\(977\) | −1073.95 | −1.09923 | −0.549615 | − | 0.835418i | \(-0.685226\pi\) | ||||
−0.549615 | + | 0.835418i | \(0.685226\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 121.135i | − | 0.123733i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 26.2167 | − | 36.0842i | 0.0266973 | − | 0.0367456i | ||||
\(983\) | − | 534.114i | − | 0.543351i | −0.962389 | − | 0.271675i | \(-0.912422\pi\) | ||
0.962389 | − | 0.271675i | \(-0.0875777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −268.413 | − | 195.014i | −0.272224 | − | 0.197783i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.8916 | − | 5.48843i | 0.0170968 | − | 0.00555509i | ||||
\(989\) | 32.3607 | 0.0327206 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 520.419i | − | 0.525146i | −0.964912 | − | 0.262573i | \(-0.915429\pi\) | ||
0.964912 | − | 0.262573i | \(-0.0845710\pi\) | |||||||
\(992\) | − | 1518.30i | − | 1.53054i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 542.492 | + | 394.144i | 0.545767 | + | 0.396523i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −457.680 | −0.459057 | −0.229528 | − | 0.973302i | \(-0.573718\pi\) | ||||
−0.229528 | + | 0.973302i | \(0.573718\pi\) | |||||||
\(998\) | −737.508 | + | 1015.09i | −0.738986 | + | 1.01713i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))