Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(451,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("1050.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.p (of order \(6\), degree \(2\), 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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.151613669376.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 12x^{6} + 95x^{4} - 588x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 451.4 | ||
Root | \(-2.56149 + 0.662382i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.451 |
Dual form | 1050.3.p.c.901.4 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 1.22474i | 0.353553 | + | 0.612372i | ||||
\(3\) | −1.50000 | − | 0.866025i | −0.500000 | − | 0.288675i | ||||
\(4\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | 0.440173 | + | 6.98615i | 0.0628819 | + | 0.998021i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.76860 | − | 4.79536i | 0.251691 | − | 0.435942i | −0.712301 | − | 0.701875i | \(-0.752347\pi\) |
0.963991 | + | 0.265933i | \(0.0856800\pi\) | |||||||
\(12\) | 3.00000 | − | 1.73205i | 0.250000 | − | 0.144338i | ||||
\(13\) | 3.50434i | 0.269564i | 0.990875 | + | 0.134782i | \(0.0430335\pi\) | ||||
−0.990875 | + | 0.134782i | \(0.956967\pi\) | |||||||
\(14\) | −8.24500 | + | 5.47905i | −0.588928 | + | 0.391361i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 7.04933 | + | 4.06994i | 0.414667 | + | 0.239408i | 0.692793 | − | 0.721137i | \(-0.256380\pi\) |
−0.278126 | + | 0.960545i | \(0.589713\pi\) | |||||||
\(18\) | −2.12132 | + | 3.67423i | −0.117851 | + | 0.204124i | ||||
\(19\) | −15.3628 | + | 8.86974i | −0.808571 | + | 0.466828i | −0.846459 | − | 0.532454i | \(-0.821270\pi\) |
0.0378887 | + | 0.999282i | \(0.487937\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.38992 | − | 10.8604i | 0.256663 | − | 0.517163i | ||||
\(22\) | 7.83078 | 0.355945 | ||||||||
\(23\) | 5.96495 | + | 10.3316i | 0.259346 | + | 0.449200i | 0.966067 | − | 0.258292i | \(-0.0831597\pi\) |
−0.706721 | + | 0.707492i | \(0.749826\pi\) | |||||||
\(24\) | 4.24264 | + | 2.44949i | 0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.29192 | + | 2.47794i | −0.165074 | + | 0.0953054i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −12.5405 | − | 6.22374i | −0.447876 | − | 0.222277i | ||||
\(29\) | −8.52374 | −0.293922 | −0.146961 | − | 0.989142i | \(-0.546949\pi\) | ||||
−0.146961 | + | 0.989142i | \(0.546949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.68072 | − | 3.85711i | −0.215507 | − | 0.124423i | 0.388361 | − | 0.921507i | \(-0.373041\pi\) |
−0.603868 | + | 0.797084i | \(0.706375\pi\) | |||||||
\(32\) | 2.82843 | − | 4.89898i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −8.30580 | + | 4.79536i | −0.251691 | + | 0.145314i | ||||
\(34\) | 11.5115i | 0.338574i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 14.0267 | + | 24.2950i | 0.379100 | + | 0.656621i | 0.990932 | − | 0.134367i | \(-0.0429002\pi\) |
−0.611831 | + | 0.790988i | \(0.709567\pi\) | |||||||
\(38\) | −21.7263 | − | 12.5437i | −0.571746 | − | 0.330098i | ||||
\(39\) | 3.03484 | − | 5.25650i | 0.0778165 | − | 0.134782i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.14207i | − | 0.0766358i | −0.999266 | − | 0.0383179i | \(-0.987800\pi\) | ||
0.999266 | − | 0.0383179i | \(-0.0121999\pi\) | |||||||
\(42\) | 17.1125 | − | 1.07820i | 0.407440 | − | 0.0256714i | ||||
\(43\) | −43.1943 | −1.00452 | −0.502260 | − | 0.864717i | \(-0.667498\pi\) | ||||
−0.502260 | + | 0.864717i | \(0.667498\pi\) | |||||||
\(44\) | 5.53720 | + | 9.59071i | 0.125845 | + | 0.217971i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.43572 | + | 14.6111i | −0.183385 | + | 0.317632i | ||||
\(47\) | 16.2037 | − | 9.35524i | 0.344761 | − | 0.199048i | −0.317615 | − | 0.948220i | \(-0.602882\pi\) |
0.662375 | + | 0.749172i | \(0.269548\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −48.6125 | + | 6.15023i | −0.992092 | + | 0.125515i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.04933 | − | 12.2098i | −0.138222 | − | 0.239408i | ||||
\(52\) | −6.06969 | − | 3.50434i | −0.116725 | − | 0.0673911i | ||||
\(53\) | −1.40895 | + | 2.44037i | −0.0265840 | + | 0.0460448i | −0.879011 | − | 0.476801i | \(-0.841796\pi\) |
0.852427 | + | 0.522846i | \(0.175130\pi\) | |||||||
\(54\) | 6.36396 | − | 3.67423i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.24500 | − | 19.7598i | −0.0222321 | − | 0.352854i | ||||
\(57\) | 30.7257 | 0.539047 | ||||||||
\(58\) | −6.02720 | − | 10.4394i | −0.103917 | − | 0.179990i | ||||
\(59\) | −26.1612 | − | 15.1042i | −0.443411 | − | 0.256003i | 0.261633 | − | 0.965168i | \(-0.415739\pi\) |
−0.705043 | + | 0.709164i | \(0.749072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −41.0095 | + | 23.6769i | −0.672288 | + | 0.388145i | −0.796943 | − | 0.604055i | \(-0.793551\pi\) |
0.124655 | + | 0.992200i | \(0.460218\pi\) | |||||||
\(62\) | − | 10.9096i | − | 0.175961i | ||||||
\(63\) | −17.4903 | + | 11.6228i | −0.277624 | + | 0.184489i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11.7462 | − | 6.78166i | −0.177972 | − | 0.102752i | ||||
\(67\) | −3.29108 | + | 5.70032i | −0.0491206 | + | 0.0850794i | −0.889540 | − | 0.456857i | \(-0.848975\pi\) |
0.840420 | + | 0.541936i | \(0.182309\pi\) | |||||||
\(68\) | −14.0987 | + | 8.13987i | −0.207333 | + | 0.119704i | ||||
\(69\) | − | 20.6632i | − | 0.299467i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −97.7751 | −1.37711 | −0.688557 | − | 0.725182i | \(-0.741755\pi\) | ||||
−0.688557 | + | 0.725182i | \(0.741755\pi\) | |||||||
\(72\) | −4.24264 | − | 7.34847i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −52.9672 | − | 30.5806i | −0.725578 | − | 0.418913i | 0.0912244 | − | 0.995830i | \(-0.470922\pi\) |
−0.816802 | + | 0.576918i | \(0.804255\pi\) | |||||||
\(74\) | −19.8368 | + | 34.3583i | −0.268064 | + | 0.464301i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 35.4790i | − | 0.466828i | ||||||
\(77\) | 34.7197 | + | 17.2311i | 0.450906 | + | 0.223780i | ||||
\(78\) | 8.58383 | 0.110049 | ||||||||
\(79\) | −61.5670 | − | 106.637i | −0.779329 | − | 1.34984i | −0.932329 | − | 0.361612i | \(-0.882227\pi\) |
0.152999 | − | 0.988226i | \(-0.451107\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 3.84823 | − | 2.22178i | 0.0469296 | − | 0.0270948i | ||||
\(83\) | 89.5815i | 1.07930i | 0.841891 | + | 0.539648i | \(0.181443\pi\) | ||||
−0.841891 | + | 0.539648i | \(0.818557\pi\) | |||||||
\(84\) | 13.4209 | + | 20.1960i | 0.159772 | + | 0.240429i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −30.5430 | − | 52.9020i | −0.355151 | − | 0.615140i | ||||
\(87\) | 12.7856 | + | 7.38178i | 0.146961 | + | 0.0848480i | ||||
\(88\) | −7.83078 | + | 13.5633i | −0.0889862 | + | 0.154129i | ||||
\(89\) | −102.290 | + | 59.0573i | −1.14933 | + | 0.663566i | −0.948724 | − | 0.316107i | \(-0.897624\pi\) |
−0.200606 | + | 0.979672i | \(0.564291\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −24.4818 | + | 1.54251i | −0.269031 | + | 0.0169507i | ||||
\(92\) | −23.8598 | −0.259346 | ||||||||
\(93\) | 6.68072 | + | 11.5713i | 0.0718357 | + | 0.124423i | ||||
\(94\) | 22.9156 | + | 13.2303i | 0.243783 | + | 0.140748i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.48528 | + | 4.89898i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | 65.1965i | 0.672128i | 0.941839 | + | 0.336064i | \(0.109096\pi\) | ||||
−0.941839 | + | 0.336064i | \(0.890904\pi\) | |||||||
\(98\) | −41.9067 | − | 55.1890i | −0.427619 | − | 0.563153i | ||||
\(99\) | 16.6116 | 0.167794 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −120.895 | − | 69.7987i | −1.19698 | − | 0.691076i | −0.237099 | − | 0.971486i | \(-0.576196\pi\) |
−0.959881 | + | 0.280409i | \(0.909530\pi\) | |||||||
\(102\) | 9.96926 | − | 17.2673i | 0.0977379 | − | 0.169287i | ||||
\(103\) | −151.108 | + | 87.2421i | −1.46707 | + | 0.847011i | −0.999321 | − | 0.0368520i | \(-0.988267\pi\) |
−0.467746 | + | 0.883863i | \(0.654934\pi\) | |||||||
\(104\) | − | 9.91176i | − | 0.0953054i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.98511 | −0.0375954 | ||||||||
\(107\) | 30.2382 | + | 52.3741i | 0.282600 | + | 0.489477i | 0.972024 | − | 0.234880i | \(-0.0754698\pi\) |
−0.689424 | + | 0.724358i | \(0.742136\pi\) | |||||||
\(108\) | 9.00000 | + | 5.19615i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | 50.4057 | − | 87.3052i | 0.462437 | − | 0.800965i | −0.536644 | − | 0.843808i | \(-0.680308\pi\) |
0.999082 | + | 0.0428435i | \(0.0136417\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 48.5899i | − | 0.437747i | ||||||
\(112\) | 23.3204 | − | 15.4971i | 0.208218 | − | 0.138367i | ||||
\(113\) | 74.1876 | 0.656527 | 0.328264 | − | 0.944586i | \(-0.393537\pi\) | ||||
0.328264 | + | 0.944586i | \(0.393537\pi\) | |||||||
\(114\) | 21.7263 | + | 37.6311i | 0.190582 | + | 0.330098i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.52374 | − | 14.7636i | 0.0734805 | − | 0.127272i | ||||
\(117\) | −9.10453 | + | 5.25650i | −0.0778165 | + | 0.0449274i | ||||
\(118\) | − | 42.7211i | − | 0.362043i | ||||||
\(119\) | −25.3302 | + | 51.0392i | −0.212859 | + | 0.428901i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 45.1697 | + | 78.2362i | 0.373303 | + | 0.646580i | ||||
\(122\) | −57.9963 | − | 33.4842i | −0.475379 | − | 0.274460i | ||||
\(123\) | −2.72111 | + | 4.71310i | −0.0221228 | + | 0.0383179i | ||||
\(124\) | 13.3614 | − | 7.71423i | 0.107754 | − | 0.0622115i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −26.6025 | − | 13.2026i | −0.211131 | − | 0.104782i | ||||
\(127\) | 151.093 | 1.18971 | 0.594855 | − | 0.803833i | \(-0.297209\pi\) | ||||
0.594855 | + | 0.803833i | \(0.297209\pi\) | |||||||
\(128\) | 5.65685 | + | 9.79796i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 64.7915 | + | 37.4074i | 0.502260 | + | 0.289980i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −186.820 | + | 107.861i | −1.42611 | + | 0.823363i | −0.996811 | − | 0.0798009i | \(-0.974572\pi\) |
−0.429296 | + | 0.903164i | \(0.641238\pi\) | |||||||
\(132\) | − | 19.1814i | − | 0.145314i | ||||||
\(133\) | −68.7276 | − | 103.423i | −0.516749 | − | 0.777615i | ||||
\(134\) | −9.30859 | −0.0694671 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −19.9385 | − | 11.5115i | −0.146607 | − | 0.0846435i | ||||
\(137\) | −66.8203 | + | 115.736i | −0.487739 | + | 0.844789i | −0.999901 | − | 0.0141000i | \(-0.995512\pi\) |
0.512161 | + | 0.858889i | \(0.328845\pi\) | |||||||
\(138\) | 25.3072 | − | 14.6111i | 0.183385 | − | 0.105877i | ||||
\(139\) | − | 193.762i | − | 1.39397i | −0.717085 | − | 0.696986i | \(-0.754524\pi\) | ||
0.717085 | − | 0.696986i | \(-0.245476\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −32.4075 | −0.229840 | ||||||||
\(142\) | −69.1374 | − | 119.750i | −0.486883 | − | 0.843306i | ||||
\(143\) | 16.8045 | + | 9.70210i | 0.117514 | + | 0.0678469i | ||||
\(144\) | 6.00000 | − | 10.3923i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 86.4950i | − | 0.592432i | ||||||
\(147\) | 78.2450 | + | 32.8743i | 0.532279 | + | 0.223635i | ||||
\(148\) | −56.1068 | −0.379100 | ||||||||
\(149\) | −33.0032 | − | 57.1632i | −0.221498 | − | 0.383646i | 0.733765 | − | 0.679403i | \(-0.237761\pi\) |
−0.955263 | + | 0.295758i | \(0.904428\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.4410 | + | 30.2087i | −0.115503 | + | 0.200057i | −0.917981 | − | 0.396625i | \(-0.870181\pi\) |
0.802478 | + | 0.596682i | \(0.203515\pi\) | |||||||
\(152\) | 43.4527 | − | 25.0874i | 0.285873 | − | 0.165049i | ||||
\(153\) | 24.4196i | 0.159605i | ||||||||
\(154\) | 3.44690 | + | 54.7070i | 0.0223825 | + | 0.355240i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.06969 | + | 10.5130i | 0.0389082 | + | 0.0673911i | ||||
\(157\) | −46.3329 | − | 26.7503i | −0.295114 | − | 0.170384i | 0.345132 | − | 0.938554i | \(-0.387834\pi\) |
−0.640246 | + | 0.768170i | \(0.721168\pi\) | |||||||
\(158\) | 87.0689 | − | 150.808i | 0.551069 | − | 0.954480i | ||||
\(159\) | 4.22685 | − | 2.44037i | 0.0265840 | − | 0.0153483i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −69.5525 | + | 46.2197i | −0.432003 | + | 0.287079i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | −102.992 | − | 178.387i | −0.631852 | − | 1.09440i | −0.987173 | − | 0.159655i | \(-0.948962\pi\) |
0.355321 | − | 0.934744i | \(-0.384372\pi\) | |||||||
\(164\) | 5.44222 | + | 3.14207i | 0.0331843 | + | 0.0191589i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −109.714 | + | 63.3437i | −0.660931 | + | 0.381589i | ||||
\(167\) | 137.945i | 0.826020i | 0.910727 | + | 0.413010i | \(0.135523\pi\) | ||||
−0.910727 | + | 0.413010i | \(0.864477\pi\) | |||||||
\(168\) | −15.2450 | + | 30.7179i | −0.0907440 | + | 0.182845i | ||||
\(169\) | 156.720 | 0.927335 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −46.0885 | − | 26.6092i | −0.269524 | − | 0.155609i | ||||
\(172\) | 43.1943 | − | 74.8148i | 0.251130 | − | 0.434970i | ||||
\(173\) | 191.016 | − | 110.283i | 1.10414 | − | 0.637475i | 0.166834 | − | 0.985985i | \(-0.446646\pi\) |
0.937305 | + | 0.348510i | \(0.113312\pi\) | |||||||
\(174\) | 20.8788i | 0.119993i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −22.1488 | −0.125845 | ||||||||
\(177\) | 26.1612 | + | 45.3126i | 0.147804 | + | 0.256003i | ||||
\(178\) | −144.660 | − | 83.5197i | −0.812699 | − | 0.469212i | ||||
\(179\) | 36.6501 | − | 63.4798i | 0.204749 | − | 0.354636i | −0.745304 | − | 0.666725i | \(-0.767695\pi\) |
0.950053 | + | 0.312089i | \(0.101029\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 61.4619i | 0.339568i | 0.985481 | + | 0.169784i | \(0.0543071\pi\) | ||||
−0.985481 | + | 0.169784i | \(0.945693\pi\) | |||||||
\(182\) | −19.2004 | − | 28.8932i | −0.105497 | − | 0.158754i | ||||
\(183\) | 82.0191 | 0.448192 | ||||||||
\(184\) | −16.8714 | − | 29.2222i | −0.0916926 | − | 0.158816i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.44796 | + | 16.3643i | −0.0507955 | + | 0.0879804i | ||||
\(187\) | 39.0336 | − | 22.5360i | 0.208736 | − | 0.120514i | ||||
\(188\) | 37.4210i | 0.199048i | ||||||||
\(189\) | 36.3011 | − | 2.28721i | 0.192069 | − | 0.0121016i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 179.931 | + | 311.650i | 0.942048 | + | 1.63168i | 0.761556 | + | 0.648099i | \(0.224436\pi\) |
0.180492 | + | 0.983577i | \(0.442231\pi\) | |||||||
\(192\) | −12.0000 | − | 6.92820i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 69.8724 | − | 121.023i | 0.362033 | − | 0.627060i | −0.626262 | − | 0.779613i | \(-0.715416\pi\) |
0.988295 | + | 0.152552i | \(0.0487493\pi\) | |||||||
\(194\) | −79.8490 | + | 46.1009i | −0.411593 | + | 0.237633i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 37.9600 | − | 90.3495i | 0.193673 | − | 0.460967i | ||||
\(197\) | 248.343 | 1.26062 | 0.630311 | − | 0.776342i | \(-0.282927\pi\) | ||||
0.630311 | + | 0.776342i | \(0.282927\pi\) | |||||||
\(198\) | 11.7462 | + | 20.3450i | 0.0593241 | + | 0.102752i | ||||
\(199\) | −106.170 | − | 61.2973i | −0.533518 | − | 0.308026i | 0.208930 | − | 0.977931i | \(-0.433002\pi\) |
−0.742448 | + | 0.669904i | \(0.766335\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.87325 | − | 5.70032i | 0.0491206 | − | 0.0283598i | ||||
\(202\) | − | 197.421i | − | 0.977329i | ||||||
\(203\) | −3.75192 | − | 59.5481i | −0.0184824 | − | 0.293341i | ||||
\(204\) | 28.1973 | 0.138222 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −213.699 | − | 123.379i | −1.03737 | − | 0.598927i | ||||
\(207\) | −17.8949 | + | 30.9948i | −0.0864486 | + | 0.149733i | ||||
\(208\) | 12.1394 | − | 7.00867i | 0.0583624 | − | 0.0336955i | ||||
\(209\) | 98.2271i | 0.469986i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 352.829 | 1.67218 | 0.836088 | − | 0.548596i | \(-0.184837\pi\) | ||||
0.836088 | + | 0.548596i | \(0.184837\pi\) | |||||||
\(212\) | −2.81790 | − | 4.88074i | −0.0132920 | − | 0.0230224i | ||||
\(213\) | 146.663 | + | 84.6757i | 0.688557 | + | 0.397538i | ||||
\(214\) | −42.7632 | + | 74.0681i | −0.199828 | + | 0.346113i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 24.0057 | − | 48.3703i | 0.110625 | − | 0.222904i | ||||
\(218\) | 142.569 | 0.653985 | ||||||||
\(219\) | 52.9672 | + | 91.7418i | 0.241859 | + | 0.418913i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.2624 | + | 24.7032i | −0.0645358 | + | 0.111779i | ||||
\(222\) | 59.5103 | − | 34.3583i | 0.268064 | − | 0.154767i | ||||
\(223\) | − | 61.7420i | − | 0.276870i | −0.990372 | − | 0.138435i | \(-0.955793\pi\) | ||
0.990372 | − | 0.138435i | \(-0.0442072\pi\) | |||||||
\(224\) | 35.4700 | + | 17.6034i | 0.158348 | + | 0.0785866i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 52.4586 | + | 90.8609i | 0.232118 | + | 0.402039i | ||||
\(227\) | −181.452 | − | 104.762i | −0.799350 | − | 0.461505i | 0.0438940 | − | 0.999036i | \(-0.486024\pi\) |
−0.843244 | + | 0.537531i | \(0.819357\pi\) | |||||||
\(228\) | −30.7257 | + | 53.2184i | −0.134762 | + | 0.233414i | ||||
\(229\) | −93.3568 | + | 53.8996i | −0.407671 | + | 0.235369i | −0.689789 | − | 0.724011i | \(-0.742297\pi\) |
0.282117 | + | 0.959380i | \(0.408963\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −37.1571 | − | 55.9148i | −0.160853 | − | 0.242055i | ||||
\(232\) | 24.1088 | 0.103917 | ||||||||
\(233\) | 163.423 | + | 283.057i | 0.701387 | + | 1.21484i | 0.967980 | + | 0.251029i | \(0.0807689\pi\) |
−0.266592 | + | 0.963809i | \(0.585898\pi\) | |||||||
\(234\) | −12.8758 | − | 7.43382i | −0.0550246 | − | 0.0317685i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 52.3224 | − | 30.2084i | 0.221705 | − | 0.128002i | ||||
\(237\) | 213.274i | 0.899892i | ||||||||
\(238\) | −80.4211 | + | 5.06706i | −0.337904 | + | 0.0212902i | ||||
\(239\) | −9.20117 | −0.0384986 | −0.0192493 | − | 0.999815i | \(-0.506128\pi\) | ||||
−0.0192493 | + | 0.999815i | \(0.506128\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 278.156 | + | 160.593i | 1.15417 | + | 0.666362i | 0.949900 | − | 0.312553i | \(-0.101184\pi\) |
0.204272 | + | 0.978914i | \(0.434517\pi\) | |||||||
\(242\) | −63.8796 | + | 110.643i | −0.263965 | + | 0.457201i | ||||
\(243\) | 13.5000 | − | 7.79423i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | − | 94.7075i | − | 0.388145i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.69646 | −0.0312864 | ||||||||
\(247\) | −31.0825 | − | 53.8365i | −0.125840 | − | 0.217962i | ||||
\(248\) | 18.8959 | + | 10.9096i | 0.0761932 | + | 0.0439902i | ||||
\(249\) | 77.5799 | − | 134.372i | 0.311566 | − | 0.539648i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 19.2394i | − | 0.0766511i | −0.999265 | − | 0.0383255i | \(-0.987798\pi\) | ||
0.999265 | − | 0.0383255i | \(-0.0122024\pi\) | |||||||
\(252\) | −2.64104 | − | 41.9169i | −0.0104803 | − | 0.166337i | ||||
\(253\) | 66.0583 | 0.261100 | ||||||||
\(254\) | 106.839 | + | 185.051i | 0.420626 | + | 0.728546i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 112.083 | − | 64.7109i | 0.436119 | − | 0.251793i | −0.265831 | − | 0.964020i | \(-0.585646\pi\) |
0.701950 | + | 0.712226i | \(0.252313\pi\) | |||||||
\(258\) | 105.804i | 0.410093i | ||||||||
\(259\) | −163.554 | + | 108.687i | −0.631483 | + | 0.419640i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.7856 | − | 22.1453i | −0.0489870 | − | 0.0848480i | ||||
\(262\) | −264.203 | − | 152.538i | −1.00841 | − | 0.582206i | ||||
\(263\) | −83.4625 | + | 144.561i | −0.317348 | + | 0.549663i | −0.979934 | − | 0.199323i | \(-0.936126\pi\) |
0.662586 | + | 0.748986i | \(0.269459\pi\) | |||||||
\(264\) | 23.4924 | − | 13.5633i | 0.0889862 | − | 0.0513762i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 78.0688 | − | 157.305i | 0.293492 | − | 0.591371i | ||||
\(267\) | 204.581 | 0.766220 | ||||||||
\(268\) | −6.58217 | − | 11.4006i | −0.0245603 | − | 0.0425397i | ||||
\(269\) | 181.081 | + | 104.547i | 0.673162 | + | 0.388650i | 0.797274 | − | 0.603618i | \(-0.206275\pi\) |
−0.124112 | + | 0.992268i | \(0.539608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 123.029 | − | 71.0308i | 0.453981 | − | 0.262106i | −0.255529 | − | 0.966801i | \(-0.582250\pi\) |
0.709510 | + | 0.704695i | \(0.248916\pi\) | |||||||
\(272\) | − | 32.5595i | − | 0.119704i | ||||||
\(273\) | 38.0586 | + | 18.8881i | 0.139409 | + | 0.0691871i | ||||
\(274\) | −188.996 | −0.689768 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 35.7897 | + | 20.6632i | 0.129673 | + | 0.0748667i | ||||
\(277\) | −222.961 | + | 386.179i | −0.804912 | + | 1.39415i | 0.111438 | + | 0.993771i | \(0.464454\pi\) |
−0.916350 | + | 0.400377i | \(0.868879\pi\) | |||||||
\(278\) | 237.309 | − | 137.010i | 0.853630 | − | 0.492843i | ||||
\(279\) | − | 23.1427i | − | 0.0829487i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 482.012 | 1.71534 | 0.857672 | − | 0.514196i | \(-0.171910\pi\) | ||||
0.857672 | + | 0.514196i | \(0.171910\pi\) | |||||||
\(282\) | −22.9156 | − | 39.6909i | −0.0812609 | − | 0.140748i | ||||
\(283\) | −187.506 | − | 108.257i | −0.662566 | − | 0.382533i | 0.130688 | − | 0.991424i | \(-0.458281\pi\) |
−0.793254 | + | 0.608891i | \(0.791615\pi\) | |||||||
\(284\) | 97.7751 | − | 169.351i | 0.344278 | − | 0.596308i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 27.4417i | 0.0959500i | ||||||||
\(287\) | 21.9509 | − | 1.38305i | 0.0764841 | − | 0.00481900i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | −111.371 | − | 192.901i | −0.385368 | − | 0.667476i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 56.4618 | − | 97.7947i | 0.194027 | − | 0.336064i | ||||
\(292\) | 105.934 | − | 61.1612i | 0.362789 | − | 0.209456i | ||||
\(293\) | 383.704i | 1.30957i | 0.755815 | + | 0.654786i | \(0.227241\pi\) | ||||
−0.755815 | + | 0.654786i | \(0.772759\pi\) | |||||||
\(294\) | 15.0649 | + | 119.076i | 0.0512412 | + | 0.405020i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −39.6735 | − | 68.7166i | −0.134032 | − | 0.232151i | ||||
\(297\) | −24.9174 | − | 14.3861i | −0.0838970 | − | 0.0484379i | ||||
\(298\) | 46.6736 | − | 80.8410i | 0.156623 | − | 0.271278i | ||||
\(299\) | −36.2054 | + | 20.9032i | −0.121088 | + | 0.0699104i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.0130 | − | 301.762i | −0.0631661 | − | 1.00253i | ||||
\(302\) | −49.3305 | −0.163346 | ||||||||
\(303\) | 120.895 | + | 209.396i | 0.398993 | + | 0.691076i | ||||
\(304\) | 61.4514 | + | 35.4790i | 0.202143 | + | 0.116707i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −29.9078 | + | 17.2673i | −0.0977379 | + | 0.0564290i | ||||
\(307\) | 21.1264i | 0.0688155i | 0.999408 | + | 0.0344078i | \(0.0109545\pi\) | ||||
−0.999408 | + | 0.0344078i | \(0.989046\pi\) | |||||||
\(308\) | −64.5648 | + | 42.9053i | −0.209626 | + | 0.139303i | ||||
\(309\) | 302.216 | 0.978044 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 75.0288 | + | 43.3179i | 0.241250 | + | 0.139286i | 0.615751 | − | 0.787941i | \(-0.288853\pi\) |
−0.374501 | + | 0.927226i | \(0.622186\pi\) | |||||||
\(312\) | −8.58383 | + | 14.8676i | −0.0275123 | + | 0.0476527i | ||||
\(313\) | −2.45782 | + | 1.41903i | −0.00785247 | + | 0.00453363i | −0.503921 | − | 0.863750i | \(-0.668110\pi\) |
0.496069 | + | 0.868283i | \(0.334776\pi\) | |||||||
\(314\) | − | 75.6613i | − | 0.240960i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 246.268 | 0.779329 | ||||||||
\(317\) | −154.925 | − | 268.338i | −0.488723 | − | 0.846493i | 0.511193 | − | 0.859466i | \(-0.329204\pi\) |
−0.999916 | + | 0.0129730i | \(0.995870\pi\) | |||||||
\(318\) | 5.97767 | + | 3.45121i | 0.0187977 | + | 0.0108529i | ||||
\(319\) | −23.5988 | + | 40.8744i | −0.0739776 | + | 0.128133i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 104.748i | − | 0.326318i | ||||||
\(322\) | −105.788 | − | 52.5018i | −0.328535 | − | 0.163049i | ||||
\(323\) | −144.397 | −0.447050 | ||||||||
\(324\) | −9.00000 | − | 15.5885i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 145.652 | − | 252.278i | 0.446787 | − | 0.773857i | ||||
\(327\) | −151.217 | + | 87.3052i | −0.462437 | + | 0.266988i | ||||
\(328\) | 8.88711i | 0.0270948i | ||||||||
\(329\) | 72.4895 | + | 109.084i | 0.220333 | + | 0.331562i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 208.295 | + | 360.777i | 0.629289 | + | 1.08996i | 0.987695 | + | 0.156394i | \(0.0499871\pi\) |
−0.358406 | + | 0.933566i | \(0.616680\pi\) | |||||||
\(332\) | −155.160 | − | 89.5815i | −0.467349 | − | 0.269824i | ||||
\(333\) | −42.0801 | + | 72.8849i | −0.126367 | + | 0.218874i | ||||
\(334\) | −168.948 | + | 97.5421i | −0.505832 | + | 0.292042i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −48.4014 | + | 3.04961i | −0.144052 | + | 0.00907622i | ||||
\(337\) | −155.491 | −0.461399 | −0.230699 | − | 0.973025i | \(-0.574101\pi\) | ||||
−0.230699 | + | 0.973025i | \(0.574101\pi\) | |||||||
\(338\) | 110.818 | + | 191.942i | 0.327862 | + | 0.567874i | ||||
\(339\) | −111.281 | − | 64.2483i | −0.328264 | − | 0.189523i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.9925 | + | 21.3576i | −0.108482 | + | 0.0626323i | ||||
\(342\) | − | 75.2622i | − | 0.220065i | ||||||
\(343\) | −64.3643 | − | 336.907i | −0.187651 | − | 0.982236i | ||||
\(344\) | 122.172 | 0.355151 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 270.138 | + | 155.964i | 0.780744 | + | 0.450763i | ||||
\(347\) | −256.253 | + | 443.844i | −0.738482 | + | 1.27909i | 0.214697 | + | 0.976681i | \(0.431124\pi\) |
−0.953179 | + | 0.302408i | \(0.902210\pi\) | |||||||
\(348\) | −25.5712 | + | 14.7636i | −0.0734805 | + | 0.0424240i | ||||
\(349\) | − | 269.185i | − | 0.771305i | −0.922644 | − | 0.385652i | \(-0.873976\pi\) | ||
0.922644 | − | 0.385652i | \(-0.126024\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.2091 | 0.0518777 | ||||||||
\(352\) | −15.6616 | − | 27.1266i | −0.0444931 | − | 0.0770643i | ||||
\(353\) | 507.890 | + | 293.231i | 1.43878 | + | 0.830682i | 0.997765 | − | 0.0668166i | \(-0.0212843\pi\) |
0.441018 | + | 0.897498i | \(0.354618\pi\) | |||||||
\(354\) | −36.9976 | + | 64.0816i | −0.104513 | + | 0.181022i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 236.229i | − | 0.663566i | ||||||
\(357\) | 82.1966 | − | 54.6221i | 0.230242 | − | 0.153003i | ||||
\(358\) | 103.662 | 0.289559 | ||||||||
\(359\) | −44.4221 | − | 76.9413i | −0.123738 | − | 0.214321i | 0.797501 | − | 0.603318i | \(-0.206155\pi\) |
−0.921239 | + | 0.388997i | \(0.872822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −23.1554 | + | 40.1064i | −0.0641424 | + | 0.111098i | ||||
\(362\) | −75.2751 | + | 43.4601i | −0.207942 | + | 0.120056i | ||||
\(363\) | − | 156.472i | − | 0.431054i | ||||||
\(364\) | 21.8101 | − | 43.9462i | 0.0599178 | − | 0.120731i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 57.9963 | + | 100.452i | 0.158460 | + | 0.274460i | ||||
\(367\) | −611.446 | − | 353.019i | −1.66607 | − | 0.961904i | −0.969727 | − | 0.244191i | \(-0.921478\pi\) |
−0.696339 | − | 0.717713i | \(-0.745189\pi\) | |||||||
\(368\) | 23.8598 | − | 41.3264i | 0.0648365 | − | 0.112300i | ||||
\(369\) | 8.16333 | − | 4.71310i | 0.0221228 | − | 0.0127726i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.6690 | − | 8.76894i | −0.0476253 | − | 0.0236360i | ||||
\(372\) | −26.7229 | −0.0718357 | ||||||||
\(373\) | −25.6211 | − | 44.3770i | −0.0686892 | − | 0.118973i | 0.829635 | − | 0.558306i | \(-0.188548\pi\) |
−0.898325 | + | 0.439332i | \(0.855215\pi\) | |||||||
\(374\) | 55.2018 | + | 31.8708i | 0.147598 | + | 0.0852160i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −45.8311 | + | 26.4606i | −0.121891 | + | 0.0703740i | ||||
\(377\) | − | 29.8701i | − | 0.0792309i | ||||||
\(378\) | 28.4700 | + | 42.8423i | 0.0753174 | + | 0.113339i | ||||
\(379\) | −194.724 | −0.513784 | −0.256892 | − | 0.966440i | \(-0.582698\pi\) | ||||
−0.256892 | + | 0.966440i | \(0.582698\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −226.640 | − | 130.851i | −0.594855 | − | 0.343440i | ||||
\(382\) | −254.461 | + | 440.740i | −0.666129 | + | 1.15377i | ||||
\(383\) | −454.732 | + | 262.540i | −1.18729 | + | 0.685482i | −0.957690 | − | 0.287803i | \(-0.907075\pi\) |
−0.229600 | + | 0.973285i | \(0.573742\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 197.629 | 0.511993 | ||||||||
\(387\) | −64.7915 | − | 112.222i | −0.167420 | − | 0.289980i | ||||
\(388\) | −112.924 | − | 65.1965i | −0.291040 | − | 0.168032i | ||||
\(389\) | 201.765 | − | 349.467i | 0.518675 | − | 0.898372i | −0.481089 | − | 0.876672i | \(-0.659759\pi\) |
0.999765 | − | 0.0217005i | \(-0.00690803\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 97.1079i | 0.248358i | ||||||||
\(392\) | 137.497 | − | 17.3955i | 0.350757 | − | 0.0443762i | ||||
\(393\) | 373.640 | 0.950738 | ||||||||
\(394\) | 175.605 | + | 304.156i | 0.445697 | + | 0.771971i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −16.6116 | + | 28.7721i | −0.0419485 | + | 0.0726569i | ||||
\(397\) | 139.596 | − | 80.5960i | 0.351628 | − | 0.203013i | −0.313774 | − | 0.949498i | \(-0.601593\pi\) |
0.665402 | + | 0.746485i | \(0.268260\pi\) | |||||||
\(398\) | − | 173.375i | − | 0.435615i | ||||||
\(399\) | 13.5246 | + | 214.654i | 0.0338963 | + | 0.537980i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 212.506 | + | 368.071i | 0.529940 | + | 0.917883i | 0.999390 | + | 0.0349237i | \(0.0111188\pi\) |
−0.469450 | + | 0.882959i | \(0.655548\pi\) | |||||||
\(402\) | 13.9629 | + | 8.06147i | 0.0347335 | + | 0.0200534i | ||||
\(403\) | 13.5166 | − | 23.4115i | 0.0335400 | − | 0.0580930i | ||||
\(404\) | 241.790 | − | 139.597i | 0.598490 | − | 0.345538i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 70.2782 | − | 46.7020i | 0.173099 | − | 0.115030i | ||||
\(407\) | 155.337 | 0.381664 | ||||||||
\(408\) | 19.9385 | + | 34.5345i | 0.0488689 | + | 0.0846435i | ||||
\(409\) | 373.605 | + | 215.701i | 0.913460 | + | 0.527386i | 0.881543 | − | 0.472104i | \(-0.156505\pi\) |
0.0319171 | + | 0.999491i | \(0.489839\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 200.461 | − | 115.736i | 0.487739 | − | 0.281596i | ||||
\(412\) | − | 348.969i | − | 0.847011i | ||||||
\(413\) | 94.0046 | − | 189.415i | 0.227614 | − | 0.458631i | ||||
\(414\) | −50.6143 | −0.122257 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 17.1677 | + | 9.91176i | 0.0412684 | + | 0.0238263i | ||||
\(417\) | −167.803 | + | 290.643i | −0.402405 | + | 0.696986i | ||||
\(418\) | −120.303 | + | 69.4570i | −0.287806 | + | 0.166165i | ||||
\(419\) | 585.412i | 1.39716i | 0.715530 | + | 0.698582i | \(0.246185\pi\) | ||||
−0.715530 | + | 0.698582i | \(0.753815\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 400.267 | 0.950754 | 0.475377 | − | 0.879782i | \(-0.342312\pi\) | ||||
0.475377 | + | 0.879782i | \(0.342312\pi\) | |||||||
\(422\) | 249.488 | + | 432.126i | 0.591203 | + | 1.02399i | ||||
\(423\) | 48.6112 | + | 28.0657i | 0.114920 | + | 0.0663492i | ||||
\(424\) | 3.98511 | − | 6.90241i | 0.00939885 | − | 0.0162793i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 239.499i | 0.562204i | ||||||||
\(427\) | −183.461 | − | 276.077i | −0.429652 | − | 0.646550i | ||||
\(428\) | −120.953 | −0.282600 | ||||||||
\(429\) | −16.8045 | − | 29.1063i | −0.0391714 | − | 0.0678469i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −197.631 | + | 342.307i | −0.458541 | + | 0.794216i | −0.998884 | − | 0.0472289i | \(-0.984961\pi\) |
0.540344 | + | 0.841445i | \(0.318294\pi\) | |||||||
\(432\) | −18.0000 | + | 10.3923i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 2.39222i | 0.00552477i | 0.999996 | + | 0.00276238i | \(0.000879295\pi\) | ||||
−0.999996 | + | 0.00276238i | \(0.999121\pi\) | |||||||
\(434\) | 76.2158 | − | 4.80210i | 0.175613 | − | 0.0110647i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 100.811 | + | 174.610i | 0.231219 | + | 0.400482i | ||||
\(437\) | −183.277 | − | 105.815i | −0.419399 | − | 0.242140i | ||||
\(438\) | −74.9069 | + | 129.743i | −0.171020 | + | 0.296216i | ||||
\(439\) | −350.264 | + | 202.225i | −0.797867 | + | 0.460649i | −0.842725 | − | 0.538345i | \(-0.819050\pi\) |
0.0448578 | + | 0.998993i | \(0.485717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −88.8975 | − | 117.074i | −0.201582 | − | 0.265473i | ||||
\(442\) | −40.3402 | −0.0912674 | ||||||||
\(443\) | 146.005 | + | 252.889i | 0.329583 | + | 0.570855i | 0.982429 | − | 0.186636i | \(-0.0597584\pi\) |
−0.652846 | + | 0.757491i | \(0.726425\pi\) | |||||||
\(444\) | 84.1603 | + | 48.5899i | 0.189550 | + | 0.109437i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 75.6182 | − | 43.6582i | 0.169547 | − | 0.0978883i | ||||
\(447\) | 114.326i | 0.255764i | ||||||||
\(448\) | 3.52139 | + | 55.8892i | 0.00786024 | + | 0.124753i | ||||
\(449\) | 125.680 | 0.279911 | 0.139956 | − | 0.990158i | \(-0.455304\pi\) | ||||
0.139956 | + | 0.990158i | \(0.455304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.0673 | − | 8.69913i | −0.0334087 | − | 0.0192885i | ||||
\(452\) | −74.1876 | + | 128.497i | −0.164132 | + | 0.284285i | ||||
\(453\) | 52.3229 | − | 30.2087i | 0.115503 | − | 0.0666858i | ||||
\(454\) | − | 296.310i | − | 0.652666i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −86.9054 | −0.190582 | ||||||||
\(457\) | 43.0015 | + | 74.4808i | 0.0940952 | + | 0.162978i | 0.909231 | − | 0.416293i | \(-0.136671\pi\) |
−0.815135 | + | 0.579270i | \(0.803338\pi\) | |||||||
\(458\) | −132.026 | − | 76.2255i | −0.288267 | − | 0.166431i | ||||
\(459\) | 21.1480 | − | 36.6294i | 0.0460741 | − | 0.0798027i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 131.449i | − | 0.285138i | −0.989785 | − | 0.142569i | \(-0.954464\pi\) | ||
0.989785 | − | 0.142569i | \(-0.0455362\pi\) | |||||||
\(462\) | 42.2073 | − | 85.0456i | 0.0913578 | − | 0.184081i | ||||
\(463\) | −73.9873 | −0.159800 | −0.0798999 | − | 0.996803i | \(-0.525460\pi\) | ||||
−0.0798999 | + | 0.996803i | \(0.525460\pi\) | |||||||
\(464\) | 17.0475 | + | 29.5271i | 0.0367403 | + | 0.0636360i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −231.115 | + | 400.303i | −0.495956 | + | 0.859020i | ||||
\(467\) | 387.032 | − | 223.453i | 0.828762 | − | 0.478486i | −0.0246667 | − | 0.999696i | \(-0.507852\pi\) |
0.853429 | + | 0.521210i | \(0.174519\pi\) | |||||||
\(468\) | − | 21.0260i | − | 0.0449274i | ||||||
\(469\) | −41.2719 | − | 20.4829i | −0.0879999 | − | 0.0436735i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 46.3329 | + | 80.2509i | 0.0983713 | + | 0.170384i | ||||
\(472\) | 73.9951 | + | 42.7211i | 0.156769 | + | 0.0905108i | ||||
\(473\) | −119.588 | + | 207.132i | −0.252828 | + | 0.437912i | ||||
\(474\) | −261.207 | + | 150.808i | −0.551069 | + | 0.318160i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −63.0722 | − | 94.9124i | −0.132505 | − | 0.199396i | ||||
\(477\) | −8.45370 | −0.0177226 | ||||||||
\(478\) | −6.50621 | − | 11.2691i | −0.0136113 | − | 0.0235755i | ||||
\(479\) | 513.818 | + | 296.653i | 1.07269 | + | 0.619318i | 0.928915 | − | 0.370293i | \(-0.120743\pi\) |
0.143775 | + | 0.989610i | \(0.454076\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −85.1377 | + | 49.1543i | −0.177002 | + | 0.102192i | ||||
\(482\) | 454.226i | 0.942378i | ||||||||
\(483\) | 144.356 | − | 9.09539i | 0.298874 | − | 0.0188310i | ||||
\(484\) | −180.679 | −0.373303 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.0919 | + | 11.0227i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | −409.771 | + | 709.744i | −0.841418 | + | 1.45738i | 0.0472773 | + | 0.998882i | \(0.484946\pi\) |
−0.888696 | + | 0.458498i | \(0.848388\pi\) | |||||||
\(488\) | 115.993 | − | 66.9683i | 0.237690 | − | 0.137230i | ||||
\(489\) | 356.774i | 0.729600i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 554.724 | 1.12978 | 0.564892 | − | 0.825165i | \(-0.308918\pi\) | ||||
0.564892 | + | 0.825165i | \(0.308918\pi\) | |||||||
\(492\) | −5.44222 | − | 9.42620i | −0.0110614 | − | 0.0191589i | ||||
\(493\) | −60.0867 | − | 34.6911i | −0.121880 | − | 0.0703673i | ||||
\(494\) | 43.9574 | − | 76.1364i | 0.0889825 | − | 0.154122i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.8569i | 0.0622115i | ||||||||
\(497\) | −43.0380 | − | 683.071i | −0.0865955 | − | 1.37439i | ||||
\(498\) | 219.429 | 0.440620 | ||||||||
\(499\) | −317.394 | − | 549.742i | −0.636060 | − | 1.10169i | −0.986290 | − | 0.165024i | \(-0.947230\pi\) |
0.350230 | − | 0.936664i | \(-0.386103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 119.464 | − | 206.918i | 0.238451 | − | 0.413010i | ||||
\(502\) | 23.5634 | − | 13.6043i | 0.0469390 | − | 0.0271003i | ||||
\(503\) | − | 120.116i | − | 0.238800i | −0.992846 | − | 0.119400i | \(-0.961903\pi\) | ||
0.992846 | − | 0.119400i | \(-0.0380970\pi\) | |||||||
\(504\) | 49.4700 | − | 32.8743i | 0.0981547 | − | 0.0652268i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 46.7103 | + | 80.9046i | 0.0923128 | + | 0.159890i | ||||
\(507\) | −235.079 | − | 135.723i | −0.463668 | − | 0.267699i | ||||
\(508\) | −151.093 | + | 261.701i | −0.297428 | + | 0.515160i | ||||
\(509\) | 51.1082 | − | 29.5073i | 0.100409 | − | 0.0579712i | −0.448955 | − | 0.893555i | \(-0.648204\pi\) |
0.549364 | + | 0.835583i | \(0.314870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 190.326 | − | 383.497i | 0.372458 | − | 0.750484i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 46.0885 | + | 79.8277i | 0.0898412 | + | 0.155609i | ||||
\(514\) | 158.509 | + | 91.5150i | 0.308383 | + | 0.178045i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −129.583 | + | 74.8148i | −0.251130 | + | 0.144990i | ||||
\(517\) | − | 103.604i | − | 0.200394i | ||||||
\(518\) | −248.764 | − | 123.459i | −0.480239 | − | 0.238338i | ||||
\(519\) | −382.032 | −0.736093 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −841.241 | − | 485.691i | −1.61467 | − | 0.932228i | −0.988269 | − | 0.152725i | \(-0.951195\pi\) |
−0.626398 | − | 0.779504i | \(-0.715471\pi\) | |||||||
\(522\) | 18.0816 | − | 31.3182i | 0.0346391 | − | 0.0599966i | ||||
\(523\) | −598.739 | + | 345.682i | −1.14482 | + | 0.660960i | −0.947619 | − | 0.319404i | \(-0.896517\pi\) |
−0.197197 | + | 0.980364i | \(0.563184\pi\) | |||||||
\(524\) | − | 431.442i | − | 0.823363i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −236.068 | −0.448798 | ||||||||
\(527\) | −31.3964 | − | 54.3802i | −0.0595757 | − | 0.103188i | ||||
\(528\) | 33.2232 | + | 19.1814i | 0.0629227 | + | 0.0363285i | ||||
\(529\) | 193.339 | − | 334.872i | 0.365479 | − | 0.633029i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 90.6251i | − | 0.170669i | ||||||
\(532\) | 247.861 | − | 15.6169i | 0.465905 | − | 0.0293551i | ||||
\(533\) | 11.0109 | 0.0206583 | ||||||||
\(534\) | 144.660 | + | 250.559i | 0.270900 | + | 0.469212i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.30859 | − | 16.1229i | 0.0173668 | − | 0.0300801i | ||||
\(537\) | −109.950 | + | 63.4798i | −0.204749 | + | 0.118212i | ||||
\(538\) | 295.703i | 0.549635i | ||||||||
\(539\) | −105.096 | + | 250.142i | −0.194983 | + | 0.464085i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −270.888 | − | 469.192i | −0.500717 | − | 0.867267i | −1.00000 | 0.000828025i | \(-0.999736\pi\) | |
0.499283 | − | 0.866439i | \(-0.333597\pi\) | |||||||
\(542\) | 173.989 | + | 100.453i | 0.321013 | + | 0.185337i | ||||
\(543\) | 53.2275 | − | 92.1928i | 0.0980249 | − | 0.169784i | ||||
\(544\) | 39.8771 | − | 23.0230i | 0.0733034 | − | 0.0423217i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.77837 | + | 59.9679i | 0.00692010 | + | 0.109831i | ||||
\(547\) | 318.491 | 0.582251 | 0.291126 | − | 0.956685i | \(-0.405970\pi\) | ||||
0.291126 | + | 0.956685i | \(0.405970\pi\) | |||||||
\(548\) | −133.641 | − | 231.472i | −0.243870 | − | 0.422395i | ||||
\(549\) | −123.029 | − | 71.0306i | −0.224096 | − | 0.129382i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 130.949 | − | 75.6034i | 0.237657 | − | 0.137211i | ||||
\(552\) | 58.4444i | 0.105877i | ||||||||
\(553\) | 717.883 | − | 477.055i | 1.29816 | − | 0.862667i | ||||
\(554\) | −630.628 | −1.13832 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 335.606 | + | 193.762i | 0.603607 | + | 0.348493i | ||||
\(557\) | 288.479 | − | 499.660i | 0.517915 | − | 0.897055i | −0.481869 | − | 0.876244i | \(-0.660042\pi\) |
0.999783 | − | 0.0208114i | \(-0.00662495\pi\) | |||||||
\(558\) | 28.3439 | − | 16.3643i | 0.0507955 | − | 0.0293268i | ||||
\(559\) | − | 151.367i | − | 0.270783i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −78.0672 | −0.139157 | ||||||||
\(562\) | 340.834 | + | 590.342i | 0.606466 | + | 1.05043i | ||||
\(563\) | −308.279 | − | 177.985i | −0.547565 | − | 0.316137i | 0.200574 | − | 0.979678i | \(-0.435719\pi\) |
−0.748139 | + | 0.663542i | \(0.769053\pi\) | |||||||
\(564\) | 32.4075 | − | 56.1314i | 0.0574601 | − | 0.0995238i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 306.196i | − | 0.540983i | ||||||
\(567\) | −56.4324 | − | 28.0068i | −0.0995281 | − | 0.0493948i | ||||
\(568\) | 276.550 | 0.486883 | ||||||||
\(569\) | 186.085 | + | 322.308i | 0.327038 | + | 0.566447i | 0.981923 | − | 0.189282i | \(-0.0606161\pi\) |
−0.654885 | + | 0.755729i | \(0.727283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 82.9355 | − | 143.649i | 0.145246 | − | 0.251574i | −0.784219 | − | 0.620485i | \(-0.786936\pi\) |
0.929465 | + | 0.368911i | \(0.120269\pi\) | |||||||
\(572\) | −33.6091 | + | 19.4042i | −0.0587571 | + | 0.0339234i | ||||
\(573\) | − | 623.300i | − | 1.08778i | ||||||
\(574\) | 17.2155 | + | 25.9063i | 0.0299922 | + | 0.0451330i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −13.9714 | − | 8.06639i | −0.0242139 | − | 0.0139799i | 0.487844 | − | 0.872931i | \(-0.337783\pi\) |
−0.512058 | + | 0.858951i | \(0.671117\pi\) | |||||||
\(578\) | 157.503 | − | 272.803i | 0.272496 | − | 0.471977i | ||||
\(579\) | −209.617 | + | 121.023i | −0.362033 | + | 0.209020i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −625.830 | + | 39.4314i | −1.07716 | + | 0.0678681i | ||||
\(582\) | 159.698 | 0.274395 | ||||||||
\(583\) | 7.80164 | + | 13.5128i | 0.0133819 | + | 0.0231781i | ||||
\(584\) | 149.814 | + | 86.4950i | 0.256530 | + | 0.148108i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −469.940 | + | 271.320i | −0.801945 | + | 0.463003i | ||||
\(587\) | − | 204.516i | − | 0.348409i | −0.984709 | − | 0.174205i | \(-0.944265\pi\) | ||
0.984709 | − | 0.174205i | \(-0.0557354\pi\) | |||||||
\(588\) | −135.185 | + | 102.650i | −0.229906 | + | 0.174575i | ||||
\(589\) | 136.846 | 0.232337 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −372.514 | − | 215.071i | −0.630311 | − | 0.363910i | ||||
\(592\) | 56.1068 | − | 97.1799i | 0.0947751 | − | 0.164155i | ||||
\(593\) | 597.577 | − | 345.011i | 1.00772 | − | 0.581806i | 0.0971952 | − | 0.995265i | \(-0.469013\pi\) |
0.910523 | + | 0.413459i | \(0.135680\pi\) | |||||||
\(594\) | − | 40.6899i | − | 0.0685016i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 132.013 | 0.221498 | ||||||||
\(597\) | 106.170 | + | 183.892i | 0.177839 | + | 0.308026i | ||||
\(598\) | −51.2022 | − | 29.5616i | −0.0856224 | − | 0.0494341i | ||||
\(599\) | 477.775 | − | 827.531i | 0.797622 | − | 1.38152i | −0.123539 | − | 0.992340i | \(-0.539425\pi\) |
0.921161 | − | 0.389182i | \(-0.127242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 587.954i | 0.978293i | 0.872202 | + | 0.489146i | \(0.162692\pi\) | ||||
−0.872202 | + | 0.489146i | \(0.837308\pi\) | |||||||
\(602\) | 356.137 | − | 236.664i | 0.591590 | − | 0.393130i | ||||
\(603\) | −19.7465 | −0.0327471 | ||||||||
\(604\) | −34.8820 | − | 60.4173i | −0.0577516 | − | 0.100029i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −170.971 | + | 296.131i | −0.282131 | + | 0.488665i | ||||
\(607\) | 449.438 | − | 259.483i | 0.740425 | − | 0.427485i | −0.0817986 | − | 0.996649i | \(-0.526066\pi\) |
0.822224 | + | 0.569164i | \(0.192733\pi\) | |||||||
\(608\) | 100.350i | 0.165049i | ||||||||
\(609\) | −45.9423 | + | 92.5714i | −0.0754389 | + | 0.152006i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.7839 | + | 56.7834i | 0.0536561 | + | 0.0929351i | ||||
\(612\) | −42.2960 | − | 24.4196i | −0.0691111 | − | 0.0399013i | ||||
\(613\) | −63.7771 | + | 110.465i | −0.104041 | + | 0.180204i | −0.913346 | − | 0.407184i | \(-0.866511\pi\) |
0.809305 | + | 0.587389i | \(0.199844\pi\) | |||||||
\(614\) | −25.8744 | + | 14.9386i | −0.0421407 | + | 0.0243300i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −98.2022 | − | 48.7368i | −0.159419 | − | 0.0791182i | ||||
\(617\) | 486.581 | 0.788624 | 0.394312 | − | 0.918977i | \(-0.370983\pi\) | ||||
0.394312 | + | 0.918977i | \(0.370983\pi\) | |||||||
\(618\) | 213.699 | + | 370.137i | 0.345791 | + | 0.598927i | ||||
\(619\) | 370.662 | + | 214.002i | 0.598808 | + | 0.345722i | 0.768572 | − | 0.639763i | \(-0.220967\pi\) |
−0.169765 | + | 0.985485i | \(0.554301\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 53.6846 | − | 30.9948i | 0.0864486 | − | 0.0499111i | ||||
\(622\) | 122.522i | 0.196980i | ||||||||
\(623\) | −457.609 | − | 688.620i | −0.734524 | − | 1.10533i | ||||
\(624\) | −24.2787 | −0.0389082 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.47589 | − | 2.00680i | −0.00555254 | − | 0.00320576i | ||||
\(627\) | 85.0671 | − | 147.341i | 0.135673 | − | 0.234993i | ||||
\(628\) | 92.6658 | − | 53.5006i | 0.147557 | − | 0.0851921i | ||||
\(629\) | 228.351i | 0.363038i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −64.4987 | −0.102217 | −0.0511083 | − | 0.998693i | \(-0.516275\pi\) | ||||
−0.0511083 | + | 0.998693i | \(0.516275\pi\) | |||||||
\(632\) | 174.138 | + | 301.616i | 0.275535 | + | 0.477240i | ||||
\(633\) | −529.244 | − | 305.559i | −0.836088 | − | 0.482716i | ||||
\(634\) | 219.097 | − | 379.488i | 0.345579 | − | 0.598561i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.76149i | 0.0153483i | ||||||||
\(637\) | −21.5525 | − | 170.354i | −0.0338343 | − | 0.267432i | ||||
\(638\) | −66.7476 | −0.104620 | ||||||||
\(639\) | −146.663 | − | 254.027i | −0.229519 | − | 0.397538i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −352.662 | + | 610.829i | −0.550175 | + | 0.952932i | 0.448086 | + | 0.893990i | \(0.352106\pi\) |
−0.998261 | + | 0.0589413i | \(0.981228\pi\) | |||||||
\(642\) | 128.290 | − | 74.0681i | 0.199828 | − | 0.115371i | ||||
\(643\) | − | 1092.83i | − | 1.69958i | −0.527124 | − | 0.849788i | \(-0.676730\pi\) | ||
0.527124 | − | 0.849788i | \(-0.323270\pi\) | |||||||
\(644\) | −10.5025 | − | 166.688i | −0.0163082 | − | 0.258833i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −102.104 | − | 176.850i | −0.158056 | − | 0.273761i | ||||
\(647\) | −446.083 | − | 257.546i | −0.689463 | − | 0.398062i | 0.113948 | − | 0.993487i | \(-0.463650\pi\) |
−0.803411 | + | 0.595425i | \(0.796984\pi\) | |||||||
\(648\) | 12.7279 | − | 22.0454i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −144.860 | + | 83.6349i | −0.223205 | + | 0.128867i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −77.8984 | + | 51.7659i | −0.119660 | + | 0.0795175i | ||||
\(652\) | 411.967 | 0.631852 | ||||||||
\(653\) | 393.317 | + | 681.245i | 0.602323 | + | 1.04325i | 0.992468 | + | 0.122501i | \(0.0390915\pi\) |
−0.390145 | + | 0.920753i | \(0.627575\pi\) | |||||||
\(654\) | −213.853 | − | 123.468i | −0.326993 | − | 0.188789i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.8844 | + | 6.28413i | −0.0165921 | + | 0.00957947i | ||||
\(657\) | − | 183.484i | − | 0.279275i | ||||||
\(658\) | −82.3420 | + | 165.915i | −0.125140 | + | 0.252151i | ||||
\(659\) | −819.425 | −1.24344 | −0.621719 | − | 0.783241i | \(-0.713565\pi\) | ||||
−0.621719 | + | 0.783241i | \(0.713565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −889.453 | − | 513.526i | −1.34562 | − | 0.776892i | −0.357991 | − | 0.933725i | \(-0.616538\pi\) |
−0.987625 | + | 0.156833i | \(0.949872\pi\) | |||||||
\(662\) | −294.573 | + | 510.216i | −0.444974 | + | 0.770718i | ||||
\(663\) | 42.7873 | − | 24.7032i | 0.0645358 | − | 0.0372598i | ||||
\(664\) | − | 253.375i | − | 0.381589i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −119.021 | −0.178710 | ||||||||
\(667\) | −50.8437 | − | 88.0639i | −0.0762275 | − | 0.132030i | ||||
\(668\) | −238.928 | − | 137.945i | −0.357677 | − | 0.206505i | ||||
\(669\) | −53.4701 | + | 92.6130i | −0.0799254 | + | 0.138435i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 262.207i | 0.390771i | ||||||||
\(672\) | −37.9600 | − | 57.1230i | −0.0564881 | − | 0.0850045i | ||||
\(673\) | 669.779 | 0.995213 | 0.497607 | − | 0.867403i | \(-0.334212\pi\) | ||||
0.497607 | + | 0.867403i | \(0.334212\pi\) | |||||||
\(674\) | −109.949 | − | 190.437i | −0.163129 | − | 0.282548i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −156.720 | + | 271.446i | −0.231834 | + | 0.401548i | ||||
\(677\) | 786.522 | − | 454.099i | 1.16178 | − | 0.670751i | 0.210047 | − | 0.977691i | \(-0.432638\pi\) |
0.951729 | + | 0.306940i | \(0.0993051\pi\) | |||||||
\(678\) | − | 181.722i | − | 0.268026i | ||||||
\(679\) | −455.472 | + | 28.6977i | −0.670798 | + | 0.0422647i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 181.452 | + | 314.285i | 0.266450 | + | 0.461505i | ||||
\(682\) | −52.3153 | − | 30.2042i | −0.0767086 | − | 0.0442877i | ||||
\(683\) | −330.668 | + | 572.733i | −0.484140 | + | 0.838555i | −0.999834 | − | 0.0182177i | \(-0.994201\pi\) |
0.515694 | + | 0.856773i | \(0.327534\pi\) | |||||||
\(684\) | 92.1770 | − | 53.2184i | 0.134762 | − | 0.0778047i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 367.112 | − | 317.059i | 0.535149 | − | 0.462185i | ||||
\(687\) | 186.714 | 0.271781 | ||||||||
\(688\) | 86.3887 | + | 149.630i | 0.125565 | + | 0.217485i | ||||
\(689\) | −8.55188 | − | 4.93743i | −0.0124120 | − | 0.00716608i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −239.610 | + | 138.339i | −0.346759 | + | 0.200201i | −0.663257 | − | 0.748392i | \(-0.730826\pi\) |
0.316498 | + | 0.948593i | \(0.397493\pi\) | |||||||
\(692\) | 441.133i | 0.637475i | ||||||||
\(693\) | 7.31198 | + | 116.051i | 0.0105512 | + | 0.167462i | ||||
\(694\) | −724.794 | −1.04437 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −36.1632 | − | 20.8788i | −0.0519586 | − | 0.0299983i | ||||
\(697\) | 12.7880 | − | 22.1495i | 0.0183472 | − | 0.0317783i | ||||
\(698\) | 329.683 | − | 190.343i | 0.472326 | − | 0.272697i | ||||
\(699\) | − | 566.115i | − | 0.809892i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −415.967 | −0.593391 | −0.296696 | − | 0.954972i | \(-0.595885\pi\) | ||||
−0.296696 | + | 0.954972i | \(0.595885\pi\) | |||||||
\(702\) | 12.8758 | + | 22.3015i | 0.0183415 | + | 0.0317685i | ||||
\(703\) | −430.980 | − | 248.827i | −0.613059 | − | 0.353950i | ||||
\(704\) | 22.1488 | − | 38.3629i | 0.0314614 | − | 0.0544927i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 829.382i | 1.17476i | ||||||||
\(707\) | 434.409 | − | 875.313i | 0.614440 | − | 1.23807i | ||||
\(708\) | −104.645 | −0.147804 | ||||||||
\(709\) | −136.620 | − | 236.632i | −0.192693 | − | 0.333755i | 0.753449 | − | 0.657507i | \(-0.228389\pi\) |
−0.946142 | + | 0.323752i | \(0.895056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 184.701 | − | 319.912i | 0.259776 | − | 0.449946i | ||||
\(712\) | 289.321 | − | 167.039i | 0.406349 | − | 0.234606i | ||||
\(713\) | − | 92.0300i | − | 0.129074i | ||||||
\(714\) | 125.020 | + | 62.0462i | 0.175098 | + | 0.0868994i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 73.3002 | + | 126.960i | 0.102375 | + | 0.177318i | ||||
\(717\) | 13.8018 | + | 7.96845i | 0.0192493 | + | 0.0111136i | ||||
\(718\) | 62.8223 | − | 108.811i | 0.0874962 | − | 0.151548i | ||||
\(719\) | 361.463 | − | 208.691i | 0.502731 | − | 0.290252i | −0.227110 | − | 0.973869i | \(-0.572928\pi\) |
0.729840 | + | 0.683617i | \(0.239594\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −676.000 | − | 1017.26i | −0.937587 | − | 1.41090i | ||||
\(722\) | −65.4934 | −0.0907111 | ||||||||
\(723\) | −278.156 | − | 481.779i | −0.384724 | − | 0.666362i | ||||
\(724\) | −106.455 | − | 61.4619i | −0.147037 | − | 0.0848921i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 191.639 | − | 110.643i | 0.263965 | − | 0.152400i | ||||
\(727\) | 357.267i | 0.491426i | 0.969343 | + | 0.245713i | \(0.0790221\pi\) | ||||
−0.969343 | + | 0.245713i | \(0.920978\pi\) | |||||||
\(728\) | 69.2450 | − | 4.36289i | 0.0951167 | − | 0.00599298i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −304.491 | − | 175.798i | −0.416541 | − | 0.240490i | ||||
\(732\) | −82.0191 | + | 142.061i | −0.112048 | + | 0.194073i | ||||
\(733\) | −373.293 | + | 215.521i | −0.509267 | + | 0.294026i | −0.732532 | − | 0.680732i | \(-0.761662\pi\) |
0.223265 | + | 0.974758i | \(0.428328\pi\) | |||||||
\(734\) | − | 998.488i | − | 1.36034i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 67.4858 | 0.0916926 | ||||||||
\(737\) | 18.2234 | + | 31.5638i | 0.0247264 | + | 0.0428274i | ||||
\(738\) | 11.5447 | + | 6.66533i | 0.0156432 | + | 0.00903161i | ||||
\(739\) | −159.512 | + | 276.282i | −0.215848 | + | 0.373860i | −0.953535 | − | 0.301284i | \(-0.902585\pi\) |
0.737687 | + | 0.675143i | \(0.235918\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 107.673i | 0.145308i | ||||||||
\(742\) | −1.75414 | − | 27.8406i | −0.00236407 | − | 0.0375210i | ||||
\(743\) | −1303.33 | −1.75414 | −0.877072 | − | 0.480360i | \(-0.840506\pi\) | ||||
−0.877072 | + | 0.480360i | \(0.840506\pi\) | |||||||
\(744\) | −18.8959 | − | 32.7287i | −0.0253977 | − | 0.0439902i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 36.2337 | − | 62.7585i | 0.0485706 | − | 0.0841267i | ||||
\(747\) | −232.740 | + | 134.372i | −0.311566 | + | 0.179883i | ||||
\(748\) | 90.1442i | 0.120514i | ||||||||
\(749\) | −352.583 | + | 234.302i | −0.470738 | + | 0.312820i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −614.473 | − | 1064.30i | −0.818206 | − | 1.41717i | −0.907003 | − | 0.421124i | \(-0.861636\pi\) |
0.0887971 | − | 0.996050i | \(-0.471698\pi\) | |||||||
\(752\) | −64.8150 | − | 37.4210i | −0.0861901 | − | 0.0497619i | ||||
\(753\) | −16.6618 | + | 28.8591i | −0.0221273 | + | 0.0383255i | ||||
\(754\) | 36.5832 | − | 21.1213i | 0.0485188 | − | 0.0280124i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −32.3395 | + | 65.1625i | −0.0427771 | + | 0.0861938i | ||||
\(757\) | 1206.22 | 1.59342 | 0.796712 | − | 0.604359i | \(-0.206571\pi\) | ||||
0.796712 | + | 0.604359i | \(0.206571\pi\) | |||||||
\(758\) | −137.691 | − | 238.487i | −0.181650 | − | 0.314627i | ||||
\(759\) | −99.0874 | − | 57.2082i | −0.130550 | − | 0.0753731i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −204.456 | + | 118.043i | −0.268667 | + | 0.155115i | −0.628282 | − | 0.777986i | \(-0.716242\pi\) |
0.359614 | + | 0.933101i | \(0.382908\pi\) | |||||||
\(762\) | − | 370.101i | − | 0.485697i | ||||||
\(763\) | 632.114 | + | 313.712i | 0.828459 | + | 0.411156i | ||||
\(764\) | −719.725 | −0.942048 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −643.088 | − | 371.287i | −0.839540 | − | 0.484709i | ||||
\(767\) | 52.9301 | − | 91.6777i | 0.0690093 | − | 0.119528i | ||||
\(768\) | 24.0000 | − | 13.8564i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | 1341.44i | 1.74440i | 0.489149 | + | 0.872200i | \(0.337307\pi\) | ||||
−0.489149 | + | 0.872200i | \(0.662693\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −224.165 | −0.290746 | ||||||||
\(772\) | 139.745 | + | 242.045i | 0.181017 | + | 0.313530i | ||||
\(773\) | −155.933 | − | 90.0279i | −0.201724 | − | 0.116466i | 0.395735 | − | 0.918365i | \(-0.370490\pi\) |
−0.597460 | + | 0.801899i | \(0.703823\pi\) | |||||||
\(774\) | 91.6290 | − | 158.706i | 0.118384 | − | 0.205047i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 184.403i | − | 0.237633i | ||||||
\(777\) | 339.456 | − | 21.3880i | 0.436881 | − | 0.0275264i | ||||
\(778\) | 570.677 | 0.733518 | ||||||||
\(779\) | 27.8693 | + | 48.2711i | 0.0357758 | + | 0.0619654i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −270.700 | + | 468.866i | −0.346607 | + | 0.600341i | ||||
\(782\) | −118.932 | + | 68.6657i | −0.152087 | + | 0.0878078i | ||||
\(783\) | 44.2907i | 0.0565654i | ||||||||
\(784\) | 118.530 | + | 156.098i | 0.151186 | + | 0.199105i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 264.203 | + | 457.614i | 0.336137 | + | 0.582206i | ||||
\(787\) | −1012.19 | − | 584.386i | −1.28613 | − | 0.742549i | −0.308170 | − | 0.951331i | \(-0.599717\pi\) |
−0.977962 | + | 0.208783i | \(0.933050\pi\) | |||||||
\(788\) | −248.343 | + | 430.142i | −0.315156 | + | 0.545866i | ||||
\(789\) | 250.387 | − | 144.561i | 0.317348 | − | 0.183221i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.6554 | + | 518.285i | 0.0412837 | + | 0.655228i | ||||
\(792\) | −46.9847 | −0.0593241 | ||||||||
\(793\) | −82.9717 | − | 143.711i | −0.104630 | − | 0.181225i | ||||
\(794\) | 197.419 | + | 113.980i | 0.248639 | + | 0.143552i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 212.340 | − | 122.595i | 0.266759 | − | 0.154013i | ||||
\(797\) | 1242.38i | 1.55883i | 0.626510 | + | 0.779413i | \(0.284483\pi\) | ||||
−0.626510 | + | 0.779413i | \(0.715517\pi\) | |||||||
\(798\) | −253.333 | + | 168.348i | −0.317460 | + | 0.210962i | ||||
\(799\) | 152.301 | 0.190614 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −306.871 | − | 177.172i | −0.383110 | − | 0.221189i | ||||
\(802\) | −300.529 | + | 520.531i | −0.374724 | + | 0.649041i | ||||
\(803\) | −293.290 | + | 169.331i | −0.365243 | + | 0.210873i | ||||
\(804\) | 22.8013i | 0.0283598i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 38.2308 | 0.0474327 | ||||||||
\(807\) | −181.081 | − | 313.641i | −0.224387 | − | 0.388650i | ||||
\(808\) | 341.942 | + | 197.421i | 0.423196 | + | 0.244332i | ||||
\(809\) | 44.8275 | − | 77.6435i | 0.0554110 | − | 0.0959747i | −0.836989 | − | 0.547219i | \(-0.815686\pi\) |
0.892400 | + | 0.451244i | \(0.149020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 234.127i | − | 0.288689i | −0.989527 | − | 0.144345i | \(-0.953893\pi\) | ||
0.989527 | − | 0.144345i | \(-0.0461074\pi\) | |||||||
\(812\) | 106.892 | + | 53.0496i | 0.131641 | + | 0.0653320i | ||||
\(813\) | −246.058 | −0.302654 | ||||||||
\(814\) | 109.840 | + | 190.249i | 0.134939 | + | 0.233721i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −28.1973 | + | 48.8392i | −0.0345556 | + | 0.0598520i | ||||
\(817\) | 663.588 | − | 383.123i | 0.812225 | − | 0.468938i | ||||
\(818\) | 610.095i | 0.745837i | ||||||||
\(819\) | −40.7303 | − | 61.2918i | −0.0497317 | − | 0.0748374i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −331.873 | − | 574.821i | −0.404231 | − | 0.700148i | 0.590001 | − | 0.807403i | \(-0.299127\pi\) |
−0.994232 | + | 0.107255i | \(0.965794\pi\) | |||||||
\(822\) | 283.494 | + | 163.676i | 0.344884 | + | 0.199119i | ||||
\(823\) | −430.147 | + | 745.037i | −0.522657 | + | 0.905269i | 0.476995 | + | 0.878906i | \(0.341726\pi\) |
−0.999652 | + | 0.0263632i | \(0.991607\pi\) | |||||||
\(824\) | 427.398 | − | 246.758i | 0.518686 | − | 0.299464i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 298.456 | − | 18.8047i | 0.361327 | − | 0.0227660i | ||||
\(827\) | 703.661 | 0.850860 | 0.425430 | − | 0.904991i | \(-0.360123\pi\) | ||||
0.425430 | + | 0.904991i | \(0.360123\pi\) | |||||||
\(828\) | −35.7897 | − | 61.9896i | −0.0432243 | − | 0.0748667i | ||||
\(829\) | 1282.06 | + | 740.196i | 1.54651 | + | 0.892878i | 0.998404 | + | 0.0564693i | \(0.0179843\pi\) |
0.548106 | + | 0.836409i | \(0.315349\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 668.882 | − | 386.179i | 0.804912 | − | 0.464716i | ||||
\(832\) | 28.0347i | 0.0336955i | ||||||||
\(833\) | −367.717 | − | 154.495i | −0.441437 | − | 0.185468i | ||||
\(834\) | −474.618 | −0.569086 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −170.134 | − | 98.2271i | −0.203510 | − | 0.117496i | ||||
\(837\) | −20.0422 | + | 34.7140i | −0.0239452 | + | 0.0414743i | ||||
\(838\) | −716.980 | + | 413.949i | −0.855585 | + | 0.493972i | ||||
\(839\) | 1377.82i | 1.64222i | 0.570769 | + | 0.821111i | \(0.306645\pi\) | ||||
−0.570769 | + | 0.821111i | \(0.693355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −768.346 | −0.913610 | ||||||||
\(842\) | 283.032 | + | 490.225i | 0.336142 | + | 0.582215i | ||||
\(843\) | −723.018 | − | 417.435i | −0.857672 | − | 0.495177i | ||||
\(844\) | −352.829 | + | 611.118i | −0.418044 | + | 0.724073i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 79.3818i | 0.0938319i | ||||||||
\(847\) | −526.687 | + | 350.000i | −0.621827 | + | 0.413223i | ||||
\(848\) | 11.2716 | 0.0132920 | ||||||||
\(849\) | 187.506 | + | 324.770i | 0.220855 | + | 0.382533i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −167.337 | + | 289.837i | −0.196636 | + | 0.340584i | ||||
\(852\) | −293.325 | + | 169.351i | −0.344278 | + | 0.198769i | ||||
\(853\) | 383.511i | 0.449602i | 0.974405 | + | 0.224801i | \(0.0721733\pi\) | ||||
−0.974405 | + | 0.224801i | \(0.927827\pi\) | |||||||
\(854\) | 208.397 | − | 419.909i | 0.244024 | − | 0.491697i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −85.5265 | − | 148.136i | −0.0999141 | − | 0.173056i | ||||
\(857\) | −284.273 | − | 164.125i | −0.331708 | − | 0.191512i | 0.324891 | − | 0.945751i | \(-0.394672\pi\) |
−0.656599 | + | 0.754240i | \(0.728006\pi\) | |||||||
\(858\) | 23.7652 | − | 41.1625i | 0.0276984 | − | 0.0479750i | ||||
\(859\) | −168.842 | + | 97.4811i | −0.196557 | + | 0.113482i | −0.595048 | − | 0.803690i | \(-0.702867\pi\) |
0.398492 | + | 0.917172i | \(0.369534\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34.1242 | − | 16.9355i | −0.0396332 | − | 0.0196696i | ||||
\(862\) | −558.985 | −0.648474 | ||||||||
\(863\) | −267.881 | − | 463.984i | −0.310407 | − | 0.537641i | 0.668043 | − | 0.744122i | \(-0.267132\pi\) |
−0.978451 | + | 0.206481i | \(0.933799\pi\) | |||||||
\(864\) | −25.4558 | − | 14.6969i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.92986 | + | 1.69156i | −0.00338321 | + | 0.00195330i | ||||
\(867\) | 385.801i | 0.444984i | ||||||||
\(868\) | 59.7741 | + | 89.9493i | 0.0688641 | + | 0.103628i | ||||
\(869\) | −681.818 | −0.784601 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.9758 | − | 11.5331i | −0.0229344 | − | 0.0132412i | ||||
\(872\) | −142.569 | + | 246.936i | −0.163496 | + | 0.283184i | ||||
\(873\) | −169.385 | + | 97.7947i | −0.194027 | + | 0.112021i | ||||
\(874\) | − | 299.291i | − | 0.342438i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −211.869 | −0.241859 | ||||||||
\(877\) | 603.606 | + | 1045.48i | 0.688262 | + | 1.19210i | 0.972400 | + | 0.233321i | \(0.0749594\pi\) |
−0.284138 | + | 0.958784i | \(0.591707\pi\) | |||||||
\(878\) | −495.348 | − | 285.989i | −0.564177 | − | 0.325728i | ||||
\(879\) | 332.298 | − | 575.557i | 0.378041 | − | 0.654786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 629.491i | 0.714519i | 0.934005 | + | 0.357259i | \(0.116289\pi\) | ||||
−0.934005 | + | 0.357259i | \(0.883711\pi\) | |||||||
\(882\) | 80.5253 | − | 191.660i | 0.0912985 | − | 0.217302i | ||||
\(883\) | −177.196 | −0.200675 | −0.100337 | − | 0.994953i | \(-0.531992\pi\) | ||||
−0.100337 | + | 0.994953i | \(0.531992\pi\) | |||||||
\(884\) | −28.5248 | − | 49.4065i | −0.0322679 | − | 0.0558897i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −206.483 | + | 357.639i | −0.233051 | + | 0.403655i | ||||
\(887\) | −1101.94 | + | 636.205i | −1.24232 | + | 0.717255i | −0.969566 | − | 0.244829i | \(-0.921268\pi\) |
−0.272755 | + | 0.962083i | \(0.587935\pi\) | |||||||
\(888\) | 137.433i | 0.154767i | ||||||||
\(889\) | 66.5072 | + | 1055.56i | 0.0748112 | + | 1.18736i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.9174 | + | 43.1582i | 0.0279657 | + | 0.0484379i | ||||
\(892\) | 106.940 | + | 61.7420i | 0.119888 | + | 0.0692175i | ||||
\(893\) | −165.957 | + | 287.446i | −0.185842 | + | 0.321888i | ||||
\(894\) | −140.021 | + | 80.8410i | −0.156623 | + | 0.0904261i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −65.9600 | + | 43.8324i | −0.0736161 | + | 0.0489201i | ||||
\(897\) | 72.4108 | 0.0807255 | ||||||||
\(898\) | 88.8693 | + | 153.926i | 0.0989636 | + | 0.171410i | ||||
\(899\) | 56.9447 | + | 32.8770i | 0.0633423 | + | 0.0365707i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.8643 | + | 11.4687i | −0.0220470 | + | 0.0127288i | ||||
\(902\) | − | 24.6048i | − | 0.0272781i | ||||||
\(903\) | −232.814 | + | 469.109i | −0.257823 | + | 0.519500i | ||||
\(904\) | −209.834 | −0.232118 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 73.9958 | + | 42.7215i | 0.0816731 | + | 0.0471540i | ||||
\(907\) | 89.6364 | − | 155.255i | 0.0988273 | − | 0.171174i | −0.812372 | − | 0.583139i | \(-0.801824\pi\) |
0.911200 | + | 0.411965i | \(0.135158\pi\) | |||||||
\(908\) | 362.905 | − | 209.523i | 0.399675 | − | 0.230752i | ||||
\(909\) | − | 418.792i | − | 0.460718i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 684.893 | 0.751803 | 0.375902 | − | 0.926660i | \(-0.377333\pi\) | ||||
0.375902 | + | 0.926660i | \(0.377333\pi\) | |||||||
\(912\) | −61.4514 | − | 106.437i | −0.0673809 | − | 0.116707i | ||||
\(913\) | 429.575 | + | 248.015i | 0.470510 | + | 0.271649i | ||||
\(914\) | −60.8133 | + | 105.332i | −0.0665353 | + | 0.115243i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 215.598i | − | 0.235369i | ||||||
\(917\) | −835.763 | − | 1257.67i | −0.911410 | − | 1.37151i | ||||
\(918\) | 59.8156 | 0.0651586 | ||||||||
\(919\) | −470.376 | − | 814.715i | −0.511835 | − | 0.886523i | −0.999906 | − | 0.0137197i | \(-0.995633\pi\) |
0.488071 | − | 0.872804i | \(-0.337701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.2960 | − | 31.6896i | 0.0198653 | − | 0.0344078i | ||||
\(922\) | 160.991 | − | 92.9481i | 0.174611 | − | 0.100811i | ||||
\(923\) | − | 342.637i | − | 0.371221i | ||||||
\(924\) | 134.004 | − | 8.44315i | 0.145026 | − | 0.00913761i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −52.3169 | − | 90.6156i | −0.0564978 | − | 0.0978570i | ||||
\(927\) | −453.324 | − | 261.726i | −0.489022 | − | 0.282337i | ||||
\(928\) | −24.1088 | + | 41.7576i | −0.0259793 | + | 0.0449975i | ||||
\(929\) | 5.55322 | − | 3.20616i | 0.00597764 | − | 0.00345119i | −0.497008 | − | 0.867746i | \(-0.665568\pi\) |
0.502986 | + | 0.864295i | \(0.332235\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 692.275 | − | 525.665i | 0.743582 | − | 0.564624i | ||||
\(932\) | −653.693 | −0.701387 | ||||||||
\(933\) | −75.0288 | − | 129.954i | −0.0804167 | − | 0.139286i | ||||
\(934\) | 547.346 | + | 316.010i | 0.586023 | + | 0.338341i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 25.7515 | − | 14.8676i | 0.0275123 | − | 0.0158842i | ||||
\(937\) | 867.253i | 0.925564i | 0.886472 | + | 0.462782i | \(0.153149\pi\) | ||||
−0.886472 | + | 0.462782i | \(0.846851\pi\) | |||||||
\(938\) | −4.09739 | − | 65.0312i | −0.00436822 | − | 0.0693296i | ||||
\(939\) | 4.91565 | 0.00523498 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −500.609 | − | 289.026i | −0.531996 | − | 0.307148i | 0.209833 | − | 0.977737i | \(-0.432708\pi\) |
−0.741829 | + | 0.670589i | \(0.766041\pi\) | |||||||
\(942\) | −65.5246 | + | 113.492i | −0.0695590 | + | 0.120480i | ||||
\(943\) | 32.4626 | − | 18.7423i | 0.0344248 | − | 0.0198752i | ||||
\(944\) | 120.833i | 0.128002i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −338.246 | −0.357553 | ||||||||
\(947\) | −374.280 | − | 648.272i | −0.395227 | − | 0.684553i | 0.597903 | − | 0.801568i | \(-0.296001\pi\) |
−0.993130 | + | 0.117015i | \(0.962667\pi\) | |||||||
\(948\) | −369.402 | − | 213.274i | −0.389665 | − | 0.224973i | ||||
\(949\) | 107.165 | − | 185.615i | 0.112924 | − | 0.195590i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 536.677i | 0.564329i | ||||||||
\(952\) | 71.6447 | − | 144.361i | 0.0752571 | − | 0.151639i | ||||
\(953\) | 21.6304 | 0.0226972 | 0.0113486 | − | 0.999936i | \(-0.496388\pi\) | ||||
0.0113486 | + | 0.999936i | \(0.496388\pi\) | |||||||
\(954\) | −5.97767 | − | 10.3536i | −0.00626590 | − | 0.0108529i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.20117 | − | 15.9369i | 0.00962466 | − | 0.0166704i | ||||
\(957\) | 70.7965 | − | 40.8744i | 0.0739776 | − | 0.0427110i | ||||
\(958\) | 839.062i | 0.875847i | ||||||||
\(959\) | −837.962 | − | 415.872i | −0.873787 | − | 0.433652i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −450.745 | − | 780.714i | −0.469038 | − | 0.812397i | ||||
\(962\) | −120.403 | − | 69.5147i | −0.125159 | − | 0.0722606i | ||||
\(963\) | −90.7146 | + | 157.122i | −0.0941999 | + | 0.163159i | ||||
\(964\) | −556.311 | + | 321.186i | −0.577086 | + | 0.333181i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 113.215 | + | 170.368i | 0.117200 | + | 0.176365i | ||||
\(967\) | 452.988 | 0.468447 | 0.234224 | − | 0.972183i | \(-0.424745\pi\) | ||||
0.234224 | + | 0.972183i | \(0.424745\pi\) | |||||||
\(968\) | −127.759 | − | 221.285i | −0.131983 | − | 0.228601i | ||||
\(969\) | 216.596 | + | 125.052i | 0.223525 | + | 0.129052i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1137.95 | − | 656.994i | 1.17193 | − | 0.676616i | 0.217798 | − | 0.975994i | \(-0.430112\pi\) |
0.954135 | + | 0.299378i | \(0.0967791\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 1353.65 | − | 85.2889i | 1.39121 | − | 0.0876556i | ||||
\(974\) | −1159.01 | −1.18995 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 164.038 | + | 94.7075i | 0.168072 | + | 0.0970364i | ||||
\(977\) | −588.653 | + | 1019.58i | −0.602511 | + | 1.04358i | 0.389929 | + | 0.920845i | \(0.372500\pi\) |
−0.992440 | + | 0.122734i | \(0.960834\pi\) | |||||||
\(978\) | −436.957 | + | 252.278i | −0.446787 | + | 0.257952i | ||||
\(979\) | 654.025i | 0.668054i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 302.434 | 0.308292 | ||||||||
\(982\) | 392.249 | + | 679.395i | 0.399439 | + | 0.691848i | ||||
\(983\) | −695.029 | − | 401.275i | −0.707049 | − | 0.408215i | 0.102918 | − | 0.994690i | \(-0.467182\pi\) |
−0.809967 | + | 0.586475i | \(0.800515\pi\) | |||||||
\(984\) | 7.69646 | − | 13.3307i | 0.00782161 | − | 0.0135474i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 98.1212i | − | 0.0995144i | ||||||
\(987\) | −14.2649 | − | 226.404i | −0.0144528 | − | 0.229386i | ||||
\(988\) | 124.330 | 0.125840 | ||||||||
\(989\) | −257.652 | − | 446.267i | −0.260518 | − | 0.451230i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 91.7946 | − | 158.993i | 0.0926283 | − | 0.160437i | −0.815988 | − | 0.578069i | \(-0.803807\pi\) |
0.908616 | + | 0.417632i | \(0.137140\pi\) | |||||||
\(992\) | −37.7918 | + | 21.8191i | −0.0380966 | + | 0.0219951i | ||||
\(993\) | − | 721.554i | − | 0.726640i | ||||||
\(994\) | 806.155 | − | 535.715i | 0.811021 | − | 0.538948i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 155.160 | + | 268.745i | 0.155783 | + | 0.269824i | ||||
\(997\) | −808.088 | − | 466.550i | −0.810519 | − | 0.467953i | 0.0366170 | − | 0.999329i | \(-0.488342\pi\) |
−0.847136 | + | 0.531376i | \(0.821675\pi\) | |||||||
\(998\) | 448.862 | − | 777.453i | 0.449762 | − | 0.779011i | ||||
\(999\) | 126.240 | − | 72.8849i | 0.126367 | − | 0.0729579i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1050.3.p.c.451.4 | ✓ | 8 | |
5.2 | odd | 4 | 1050.3.q.b.199.1 | 16 | |||
5.3 | odd | 4 | 1050.3.q.b.199.8 | 16 | |||
5.4 | even | 2 | 1050.3.p.d.451.1 | yes | 8 | ||
7.5 | odd | 6 | inner | 1050.3.p.c.901.4 | yes | 8 | |
35.12 | even | 12 | 1050.3.q.b.649.8 | 16 | |||
35.19 | odd | 6 | 1050.3.p.d.901.1 | yes | 8 | ||
35.33 | even | 12 | 1050.3.q.b.649.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.p.c.451.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1050.3.p.c.901.4 | yes | 8 | 7.5 | odd | 6 | inner | |
1050.3.p.d.451.1 | yes | 8 | 5.4 | even | 2 | ||
1050.3.p.d.901.1 | yes | 8 | 35.19 | odd | 6 | ||
1050.3.q.b.199.1 | 16 | 5.2 | odd | 4 | |||
1050.3.q.b.199.8 | 16 | 5.3 | odd | 4 | |||
1050.3.q.b.649.1 | 16 | 35.33 | even | 12 | |||
1050.3.q.b.649.8 | 16 | 35.12 | even | 12 |